LMFDB - Embedded newform 69.7.f.a.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(7,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.f (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	69.7
Dual form			69.7.f.a.10.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.37873 + 8.51551i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(-8.96008 - 62.3187i) q^{4} +(186.661 - 85.2451i) q^{5} +(24.9969 - 173.857i) q^{6} +(65.3761 + 222.650i) q^{7} +(-9.86246 - 6.33822i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})$	\(q+(-7.37873 + 8.51551i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(-8.96008 - 62.3187i) q^{4} +(186.661 - 85.2451i) q^{5} +(24.9969 - 173.857i) q^{6} +(65.3761 + 222.650i) q^{7} +(-9.86246 - 6.33822i) q^{8} +(100.946 - 221.041i) q^{9} +(-651.414 + 2218.51i) q^{10} +(-1470.73 + 1274.40i) q^{11} +(642.708 + 741.724i) q^{12} +(-1703.94 - 500.321i) q^{13} +(-2378.37 - 1086.17i) q^{14} +(-1729.41 + 2691.02i) q^{15} +(3992.94 - 1172.43i) q^{16} +(-235.748 - 33.8954i) q^{17} +(1137.42 + 2490.60i) q^{18} +(-3800.51 + 546.430i) q^{19} +(-6984.86 - 10868.7i) q^{20} +(-2733.78 - 2368.83i) q^{21} -21927.5i q^{22} +(-5306.25 + 10949.0i) q^{23} +182.752 q^{24} +(17343.3 - 20015.2i) q^{25} +(16833.4 - 10818.2i) q^{26} +(539.088 + 3749.44i) q^{27} +(13289.5 - 6069.12i) q^{28} +(496.323 - 3452.00i) q^{29} +(-10154.5 - 34583.2i) q^{30} +(-27080.9 - 17403.9i) q^{31} +(-19167.3 + 41970.4i) q^{32} +(8546.66 - 29107.2i) q^{33} +(2028.16 - 1757.41i) q^{34} +(31183.0 + 35987.1i) q^{35} +(-14679.4 - 4310.27i) q^{36} +(-59518.2 - 27181.1i) q^{37} +(23389.8 - 36395.2i) q^{38} +(26561.7 - 7799.23i) q^{39} +(-2381.24 - 342.370i) q^{40} +(585.616 + 1282.32i) q^{41} +(40343.6 - 5800.53i) q^{42} +(-53958.4 - 83960.9i) q^{43} +(92596.7 + 80235.5i) q^{44} -49864.7i q^{45} +(-54082.6 - 125975. i) q^{46} -131918. q^{47} +(-42481.8 + 49026.6i) q^{48} +(53673.4 - 34493.8i) q^{49} +(42468.4 + 295374. i) q^{50} +(3377.22 - 1542.33i) q^{51} +(-15911.9 + 110670. i) q^{52} +(26247.8 + 89391.8i) q^{53} +(-35906.2 - 23075.5i) q^{54} +(-165892. + 363253. i) q^{55} +(766.439 - 2610.25i) q^{56} +(45234.1 - 39195.6i) q^{57} +(25733.3 + 29697.8i) q^{58} +(80114.4 + 23523.7i) q^{59} +(183197. + 83663.1i) q^{60} +(30952.6 - 48163.1i) q^{61} +(348026. - 102190. i) q^{62} +(55814.2 + 8024.88i) q^{63} +(-105329. - 230639. i) q^{64} +(-360708. + 51862.0i) q^{65} +(184800. + 287554. i) q^{66} +(329120. + 285184. i) q^{67} +14995.2i q^{68} +(-22689.8 - 188303. i) q^{69} -536540. q^{70} +(-447235. + 516137. i) q^{71} +(-2396.58 + 1540.19i) q^{72} +(-58498.6 - 406866. i) q^{73} +(670629. - 306266. i) q^{74} +(-58753.8 + 408642. i) q^{75} +(68105.7 + 231947. i) q^{76} +(-379896. - 244144. i) q^{77} +(-129577. + 283735. i) q^{78} +(219982. - 749190. i) q^{79} +(645380. - 559225. i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(-15240.7 - 4475.08i) q^{82} +(-652242. - 297869. i) q^{83} +(-123128. + 191590. i) q^{84} +(-46894.2 + 13769.4i) q^{85} +(1.11311e6 + 160042. i) q^{86} +(22583.9 + 49451.9i) q^{87} +(22582.5 - 3246.87i) q^{88} +(-84710.6 - 131812. i) q^{89} +(424624. + 367938. i) q^{90} -412091. i q^{91} +(729869. + 232575. i) q^{92} +501811. q^{93} +(973386. - 1.12335e6i) q^{94} +(-662825. + 425972. i) q^{95} +(-102360. - 711931. i) q^{96} +(-995439. + 454602. i) q^{97} +(-102309. + 711577. i) q^{98} +(133229. + 453737. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{19}{22}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−7.37873	+	8.51551i	−0.922341	+	1.06444i	0.0753926	+	0.997154i	$0.475979\pi$
$2$	−7.37873	+	8.51551i	−0.922341	+	1.06444i	−0.997734	+	0.0672846i	$0.978566\pi$
$3$	−13.1138	+	8.42776i	−0.485698	+	0.312139i
$3$	−13.1138	+	8.42776i	−0.485698	+	0.312139i
$4$	−8.96008	−	62.3187i	−0.140001	−	0.973730i
$5$	186.661	−	85.2451i	1.49329	−	0.681961i	0.509362	−	0.860552i	$-0.329881\pi$
$5$	186.661	−	85.2451i	1.49329	−	0.681961i	0.983923	+	0.178591i	$0.0571540\pi$
$6$	24.9969	−	173.857i	0.115726	−	0.804894i
$7$	65.3761	+	222.650i	0.190601	+	0.649127i	0.998232	+	0.0594388i	$0.0189311\pi$
$7$	65.3761	+	222.650i	0.190601	+	0.649127i	−0.807631	+	0.589688i	$0.799251\pi$
$8$	−9.86246	−	6.33822i	−0.0192626	−	0.0123793i
$9$	100.946	−	221.041i	0.138472	−	0.303211i
$10$	−651.414	+	2218.51i	−0.651414	+	2.21851i
$11$	−1470.73	+	1274.40i	−1.10498	+	0.957474i	−0.999318	−	0.0369274i	$-0.988243\pi$
$11$	−1470.73	+	1274.40i	−1.10498	+	0.957474i	−0.105666	+	0.994402i	$0.533698\pi$
$12$	642.708	+	741.724i	0.371937	+	0.429239i
$13$	−1703.94	−	500.321i	−0.775574	−	0.227729i	−0.130089	−	0.991502i	$-0.541526\pi$
$13$	−1703.94	−	500.321i	−0.775574	−	0.227729i	−0.645485	+	0.763773i	$0.723345\pi$
$14$	−2378.37	−	1086.17i	−0.866755	−	0.395834i
$15$	−1729.41	+	2691.02i	−0.512419	+	0.797340i
$16$	3992.94	−	1172.43i	0.974838	−	0.286238i
$17$	−235.748	−	33.8954i	−0.0479845	−	0.00689912i	0.118281	−	0.992980i	$-0.462262\pi$
$17$	−235.748	−	33.8954i	−0.0479845	−	0.00689912i	−0.166265	+	0.986081i	$0.553171\pi$
$18$	1137.42	+	2490.60i	0.195031	+	0.427058i
$19$	−3800.51	+	546.430i	−0.554091	+	0.0796662i	−0.413672	−	0.910426i	$-0.635754\pi$
$19$	−3800.51	+	546.430i	−0.554091	+	0.0796662i	−0.140419	+	0.990092i	$0.544845\pi$
$20$	−6984.86	−	10868.7i	−0.873107	−	1.35858i
$21$	−2733.78	−	2368.83i	−0.295192	−	0.255786i
$22$		−	21927.5i		−	2.05931i
$23$	−5306.25	+	10949.0i	−0.436118	+	0.899890i
$23$	−5306.25	+	10949.0i	−0.436118	+	0.899890i
$24$	182.752			0.0132199
$25$	17343.3	−	20015.2i	1.10997	−	1.28097i
$26$	16833.4	−	10818.2i	0.957748	−	0.615507i
$27$	539.088	+	3749.44i	0.0273885	+	0.190491i
$28$	13289.5	−	6069.12i	0.605390	−	0.276472i
$29$	496.323	−	3452.00i	0.0203503	−	0.141539i	−0.977113	−	0.212720i	$-0.931768\pi$
$29$	496.323	−	3452.00i	0.0203503	−	0.141539i	0.997463	+	0.0711810i	$0.0226768\pi$
$30$	−10154.5	−	34583.2i	−0.376094	−	1.28086i
$31$	−27080.9	−	17403.9i	−0.909031	−	0.584199i	0.000424692	−	1.00000i	$-0.499865\pi$
$31$	−27080.9	−	17403.9i	−0.909031	−	0.584199i	−0.909455	+	0.415801i	$0.863501\pi$
$32$	−19167.3	+	41970.4i	−0.584938	+	1.28084i
$33$	8546.66	−	29107.2i	0.237823	−	0.809952i
$34$	2028.16	−	1757.41i	0.0516017	−	0.0447132i
$35$	31183.0	+	35987.1i	0.727300	+	0.839349i
$36$	−14679.4	−	4310.27i	−0.314631	−	0.0923841i
$37$	−59518.2	−	27181.1i	−1.17502	−	0.536613i	−0.270364	−	0.962758i	$-0.587144\pi$
$37$	−59518.2	−	27181.1i	−1.17502	−	0.536613i	−0.904655	+	0.426145i	$0.859871\pi$
$38$	23389.8	−	36395.2i	0.426261	−	0.663275i
$39$	26561.7	−	7799.23i	0.447778	−	0.131479i
$40$	−2381.24	−	342.370i	−0.0372068	−	0.00534953i
$41$	585.616	+	1282.32i	0.00849691	+	0.0186056i	0.913833	−	0.406090i	$-0.133108\pi$
$41$	585.616	+	1282.32i	0.00849691	+	0.0186056i	−0.905336	+	0.424696i	$0.860381\pi$
$42$	40343.6	−	5800.53i	0.544536	−	0.0782925i
$43$	−53958.4	−	83960.9i	−0.678662	−	1.05602i	−0.994246	−	0.107121i	$-0.965837\pi$
$43$	−53958.4	−	83960.9i	−0.678662	−	1.05602i	0.315584	−	0.948898i	$-0.397800\pi$
$44$	92596.7	+	80235.5i	1.08702	+	0.941908i
$45$		−	49864.7i		−	0.547212i
$46$	−54082.6	−	125975.i	−0.555628	−	1.29423i
$47$	−131918.			−1.27060			−0.635302	−	0.772264i	$-0.719124\pi$
$47$	−131918.			−1.27060			−0.635302	+	0.772264i	$0.719124\pi$
$48$	−42481.8	+	49026.6i	−0.384131	+	0.443310i
$49$	53673.4	−	34493.8i	0.456217	−	0.293193i
$50$	42468.4	+	295374.i	0.339747	+	2.36299i
$51$	3377.22	−	1542.33i	0.0254594	−	0.0116269i
$52$	−15911.9	+	110670.i	−0.113165	+	0.787082i
$53$	26247.8	+	89391.8i	0.176305	+	0.600441i	0.999467	+	0.0326342i	$0.0103896\pi$
$53$	26247.8	+	89391.8i	0.176305	+	0.600441i	−0.823162	+	0.567807i	$0.807792\pi$
$54$	−35906.2	−	23075.5i	−0.228028	−	0.146545i
$55$	−165892.	+	363253.i	−0.997097	+	2.18334i
$56$	766.439	−	2610.25i	0.00436429	−	0.0148634i
$57$	45234.1	−	39195.6i	0.244254	−	0.211647i
$58$	25733.3	+	29697.8i	0.131890	+	0.152209i
$59$	80114.4	+	23523.7i	0.390081	+	0.114538i	0.470891	−	0.882191i	$-0.343933\pi$
$59$	80114.4	+	23523.7i	0.390081	+	0.114538i	−0.0808101	+	0.996730i	$0.525751\pi$
$60$	183197.	+	83663.1i	0.848133	+	0.387329i
$61$	30952.6	−	48163.1i	0.136366	−	0.212190i	−0.766353	−	0.642419i	$-0.777931\pi$
$61$	30952.6	−	48163.1i	0.136366	−	0.212190i	0.902720	+	0.430229i	$0.141567\pi$
$62$	348026.	−	102190.i	1.46028	−	0.428777i
$63$	55814.2	+	8024.88i	0.223215	+	0.0320935i
$64$	−105329.	−	230639.i	−0.401800	−	0.879819i
$65$	−360708.	+	51862.0i	−1.31346	+	0.188846i
$66$	184800.	+	287554.i	0.642790	+	1.00020i
$67$	329120.	+	285184.i	1.09428	+	0.948202i	0.998884	−	0.0472369i	$-0.0150416\pi$
$67$	329120.	+	285184.i	1.09428	+	0.948202i	0.0953999	+	0.995439i	$0.469587\pi$
$68$			14995.2i			0.0476898i
$69$	−22689.8	−	188303.i	−0.0690692	−	0.573204i
$70$	−536540.			−1.56426
$71$	−447235.	+	516137.i	−1.24957	+	1.44208i	−0.398385	+	0.917218i	$0.630429\pi$
$71$	−447235.	+	516137.i	−1.24957	+	1.44208i	−0.851186	+	0.524864i	$0.824116\pi$
$72$	−2396.58	+	1540.19i	−0.00642087	+	0.00412644i
$73$	−58498.6	−	406866.i	−0.150375	−	1.04588i	−0.915591	−	0.402110i	$-0.868277\pi$
$73$	−58498.6	−	406866.i	−0.150375	−	1.04588i	0.765216	−	0.643774i	$-0.222632\pi$
$74$	670629.	−	306266.i	1.65496	−	0.755795i
$75$	−58753.8	+	408642.i	−0.139268	+	0.968632i
$76$	68105.7	+	231947.i	0.155147	+	0.528381i
$77$	−379896.	−	244144.i	−0.832133	−	0.534779i
$78$	−129577.	+	283735.i	−0.273052	+	0.597901i
$79$	219982.	−	749190.i	0.446176	−	1.51953i	−0.362899	−	0.931829i	$-0.618213\pi$
$79$	219982.	−	749190.i	0.446176	−	1.51953i	0.809074	−	0.587706i	$-0.199969\pi$
$80$	645380.	−	559225.i	1.26051	−	1.09224i
$81$	−38668.9	−	44626.3i	−0.0727623	−	0.0839722i
$82$	−15240.7	−	4475.08i	−0.0276416	−	0.00811631i
$83$	−652242.	−	297869.i	−1.14071	−	0.520944i	−0.246744	−	0.969081i	$-0.579361\pi$
$83$	−652242.	−	297869.i	−1.14071	−	0.520944i	−0.893965	+	0.448136i	$0.852088\pi$
$84$	−123128.	+	191590.i	−0.207739	+	0.323248i
$85$	−46894.2	+	13769.4i	−0.0763595	+	0.0224212i
$86$	1.11311e6	+	160042.i	1.75003	+	0.251616i
$87$	22583.9	+	49451.9i	0.0342958	+	0.0750974i
$88$	22582.5	−	3246.87i	0.0331378	−	0.00476449i
$89$	−84710.6	−	131812.i	−0.120162	−	0.186976i	0.775962	−	0.630780i	$-0.217265\pi$
$89$	−84710.6	−	131812.i	−0.120162	−	0.186976i	−0.896124	+	0.443804i	$0.853629\pi$
$90$	424624.	+	367938.i	0.582474	+	0.504717i
$91$		−	412091.i		−	0.546851i
$92$	729869.	+	232575.i	0.937306	+	0.298675i
$93$	501811.			0.623866
$94$	973386.	−	1.12335e6i	1.17193	−	1.35248i
$95$	−662825.	+	425972.i	−0.773086	+	0.496832i
$96$	−102360.	−	711931.i	−0.115696	−	0.804682i
$97$	−995439.	+	454602.i	−1.09068	+	0.498099i	−0.877824	−	0.478983i	$-0.841005\pi$
$97$	−995439.	+	454602.i	−1.09068	+	0.498099i	−0.212861	+	0.977083i	$0.568278\pi$
$98$	−102309.	+	711577.i	−0.108702	+	0.756038i
$99$	133229.	+	453737.i	0.137307	+	0.467626i
$100$	−1.40272e6	−	901474.i	−1.40272	−	0.901474i
$101$	107051.	−	234409.i	0.103903	−	0.227515i	−0.850539	−	0.525911i	$-0.823724\pi$
$101$	107051.	−	234409.i	0.103903	−	0.227515i	0.954442	+	0.298396i	$0.0964517\pi$
$102$	−11785.9	+	40139.2i	−0.0111061	+	0.0378240i
$103$	−899051.	+	779032.i	−0.822759	+	0.712925i	−0.960722	−	0.277512i	$-0.910490\pi$
$103$	−899051.	+	779032.i	−0.822759	+	0.712925i	0.137963	+	0.990437i	$0.455945\pi$
$104$	13633.9	+	15734.3i	0.0121205	+	0.0139877i
$105$	−712220.	−	209127.i	−0.615242	−	0.180651i
$106$	−954892.	−	436085.i	−0.801746	−	0.366145i
$107$	355327.	−	552899.i	0.290052	−	0.451330i	−0.665395	−	0.746491i	$-0.731737\pi$
$107$	355327.	−	552899.i	0.290052	−	0.451330i	0.955448	+	0.295161i	$0.0953733\pi$
$108$	228830.	−	67190.5i	0.181653	−	0.0533380i
$109$	−1.85533e6	−	266756.i	−1.43266	−	0.205985i	−0.618113	−	0.786089i	$-0.712103\pi$
$109$	−1.85533e6	−	266756.i	−1.43266	−	0.205985i	−0.814542	+	0.580104i	$0.803012\pi$
$110$	−1.86921e6	−	4.09300e6i	−1.40437	−	3.07513i
$111$	1.00959e6	−	145157.i	0.738202	−	0.106137i
$112$	522085.	+	812380.i	0.371610	+	0.578236i
$113$	1.38209e6	+	1.19759e6i	0.957858	+	0.829989i	0.985508	−	0.169629i	$-0.0542568\pi$
$113$	1.38209e6	+	1.19759e6i	0.957858	+	0.829989i	−0.0276496	+	0.999618i	$0.508802\pi$
$114$			674405.i			0.455204i
$115$	−57122.9	+	2.49607e6i	−0.0375592	+	1.64121i
$116$	−219571.			−0.140670
$117$	−282596.	+	326134.i	−0.176445	+	0.203628i
$118$	−791459.	+	508640.i	−0.481706	+	0.309574i
$119$	−7865.43	−	54705.3i	−0.00466747	−	0.0324630i
$120$	34112.6	−	15578.7i	0.0197411	−	0.00901545i
$121$	286848.	−	1.99507e6i	0.161918	−	1.12617i
$122$	181743.	+	618960.i	0.100087	+	0.340865i
$123$	−18486.8	−	11880.7i	−0.00993448	−	0.00638451i
$124$	−841939.	+	1.84359e6i	−0.441586	+	0.966939i
$125$	627786.	−	2.13804e6i	0.321427	−	1.09468i
$126$	−480174.	+	416073.i	−0.240042	+	0.207998i
$127$	2.43726e6	+	2.81275e6i	1.18985	+	1.37316i	0.910784	+	0.412882i	$0.135478\pi$
$127$	2.43726e6	+	2.81275e6i	1.18985	+	1.37316i	0.279062	+	0.960273i	$0.409977\pi$
$128$	−92136.7	−	27053.8i	−0.0439342	−	0.0129002i
$129$	1.41520e6	+	646302.i	0.659250	+	0.301069i
$130$	2.21993e6	−	3.45429e6i	1.01044	−	1.57227i
$131$	−786338.	+	230890.i	−0.349780	+	0.102705i	−0.451903	−	0.892067i	$-0.649255\pi$
$131$	−786338.	+	230890.i	−0.349780	+	0.102705i	0.102123	+	0.994772i	$0.467437\pi$
$132$	−1.89050e6	−	271814.i	−0.821970	−	0.118181i
$133$	−370125.	−	810461.i	−0.157324	−	0.344491i
$134$	−4.85698e6	+	698328.i	−2.01861	+	0.290232i
$135$	420248.	+	653918.i	0.170806	+	0.265780i
$136$	2110.22	+	1828.51i	0.000838900	+	0.000726911i
$137$			4.26794e6i			1.65980i	0.557910	+	0.829901i	$0.311603\pi$
$137$			4.26794e6i			1.65980i	−0.557910	+	0.829901i	$0.688397\pi$
$138$	1.77092e6	+	1.19622e6i	0.673846	+	0.455170i
$139$	4.46179e6			1.66136			0.830682	−	0.556747i	$-0.187951\pi$
$139$	4.46179e6			1.66136			0.830682	+	0.556747i	$0.187951\pi$
$140$	1.96327e6	−	2.26573e6i	0.715477	−	0.825704i
$141$	1.72995e6	−	1.11177e6i	0.617130	−	0.396605i
$142$	−1.09514e6	−	7.61687e6i	−0.382477	−	2.66018i
$143$	3.14364e6	−	1.43565e6i	1.07504	−	0.490955i
$144$	143915.	−	1.00095e6i	0.0481970	−	0.335217i
$145$	−201622.	−	686662.i	−0.0661354	−	0.225237i
$146$	3.89632e6	+	2.50401e6i	1.25198	+	0.804596i
$147$	−413159.	+	904693.i	−0.130067	+	0.284806i
$148$	−1.16060e6	+	3.95264e6i	−0.358012	+	1.21928i
$149$	1.42467e6	−	1.23448e6i	0.430681	−	0.373187i	−0.412374	−	0.911015i	$-0.635300\pi$
$149$	1.42467e6	−	1.23448e6i	0.430681	−	0.373187i	0.843055	+	0.537828i	$0.180755\pi$
$150$	−3.04626e6	−	3.51558e6i	−0.902597	−	1.04165i
$151$	−3.91386e6	−	1.14921e6i	−1.13677	−	0.333787i	−0.341408	−	0.939915i	$-0.610904\pi$
$151$	−3.91386e6	−	1.14921e6i	−1.13677	−	0.333787i	−0.795367	+	0.606128i	$0.792722\pi$
$152$	40945.8	+	18699.3i	0.0116595	+	0.00532469i
$153$	−31290.0	+	48688.2i	−0.00873638	+	0.0135941i
$154$	4.88217e6	−	1.43353e6i	1.33675	−	0.392505i
$155$	−6.53854e6	−	940100.i	−1.75584	−	0.252452i
$156$	−724033.	−	1.58541e6i	−0.190715	−	0.417607i
$157$	−1.31116e6	+	188517.i	−0.338811	+	0.0487137i	−0.309621	−	0.950860i	$-0.600202\pi$
$157$	−1.31116e6	+	188517.i	−0.338811	+	0.0487137i	−0.0291905	+	0.999574i	$0.509293\pi$
$158$	4.75654e6	+	7.40133e6i	1.20593	+	1.87646i
$159$	−1.09758e6	−	951060.i	−0.273052	−	0.236601i
$160$			9.46815e6i			2.31156i
$161$	−2.78469e6	−	465638.i	−0.667267	−	0.111576i
$162$	665342.			0.156495
$163$	−905428.	+	1.04492e6i	−0.209070	+	0.241279i	−0.850593	−	0.525824i	$-0.823757\pi$
$163$	−905428.	+	1.04492e6i	−0.209070	+	0.241279i	0.641524	+	0.767103i	$0.278303\pi$
$164$	74665.3	−	47984.5i	0.0169273	−	0.0108785i
$165$	−885925.	−	6.16174e6i	−0.197217	−	1.37168i
$166$	7.34923e6	−	3.35628e6i	1.60664	−	0.733726i
$167$	−1.14097e6	+	7.93559e6i	−0.244976	+	1.70384i	0.381472	+	0.924380i	$0.375417\pi$
$167$	−1.14097e6	+	7.93559e6i	−0.244976	+	1.70384i	−0.626448	+	0.779464i	$0.715492\pi$
$168$	11947.6	+	40689.8i	0.00251972	+	0.00858139i
$169$	−1.40749e6	−	904541.i	−0.291599	−	0.187399i
$170$	228767.	−	500929.i	0.0465635	−	0.101960i
$171$	−262862.	+	895226.i	−0.0525702	+	0.179038i
$172$	−4.74886e6	+	4.11491e6i	−0.933263	+	0.808677i
$173$	4.55385e6	+	5.25542e6i	0.879509	+	1.01501i	0.999752	+	0.0222634i	$0.00708724\pi$
$173$	4.55385e6	+	5.25542e6i	0.879509	+	1.01501i	−0.120243	+	0.992745i	$0.538367\pi$
$174$	−587748.	−	172579.i	−0.111569	−	0.0327596i
$175$	5.59024e6	+	2.55298e6i	1.04308	+	0.476357i
$176$	−4.37840e6	+	6.81293e6i	−0.803115	+	1.24967i
$177$	−1.24886e6	+	366698.i	−0.225213	+	0.0661286i
$178$	1.74750e6	+	251253.i	0.309855	+	0.0445504i
$179$	−1.08657e6	−	2.37926e6i	−0.189452	−	0.414841i	0.790942	−	0.611891i	$-0.209591\pi$
$179$	−1.08657e6	−	2.37926e6i	−0.189452	−	0.414841i	−0.980393	+	0.197050i	$0.936864\pi$
$180$	−3.10751e6	+	446792.i	−0.532837	+	0.0766104i
$181$	4.23003e6	+	6.58206e6i	0.713359	+	1.11001i	0.988880	+	0.148713i	$0.0475131\pi$
$181$	4.23003e6	+	6.58206e6i	0.713359	+	1.11001i	−0.275522	+	0.961295i	$0.588851\pi$
$182$	3.50917e6	+	3.04071e6i	0.582090	+	0.504383i
$183$			892465.i			0.145626i
$184$	121730.	−	74351.5i	0.0195408	−	0.0119354i
$185$	−1.34268e7			−2.12059
$186$	−3.70273e6	+	4.27317e6i	−0.575417	+	0.664067i
$187$	389918.	−	250585.i	0.0596278	−	0.0383205i
$188$	1.18199e6	+	8.22095e6i	0.177886	+	1.23722i
$189$	−799571.	+	365152.i	−0.118433	+	0.0540864i
$190$	1.26344e6	−	8.78742e6i	0.184202	−	1.28115i
$191$	−811561.	−	2.76392e6i	−0.116472	−	0.396667i	0.880535	−	0.473981i	$-0.157184\pi$
$191$	−811561.	−	2.76392e6i	−0.116472	−	0.396667i	−0.997007	+	0.0773146i	$0.975365\pi$
$192$	3.32505e6	+	2.13688e6i	0.469779	+	0.301909i
$193$	−1.95404e6	+	4.27876e6i	−0.271808	+	0.595177i	−0.995480	−	0.0949670i	$-0.969725\pi$
$193$	−1.95404e6	+	4.27876e6i	−0.271808	+	0.595177i	0.723672	+	0.690144i	$0.242453\pi$
$194$	3.47391e6	−	1.18310e7i	0.475788	−	1.62038i
$195$	4.29319e6	−	3.72007e6i	0.578996	−	0.501703i
$196$	−2.63053e6	−	3.03579e6i	−0.349361	−	0.403184i
$197$	−3.47467e6	−	1.02025e6i	−0.454480	−	0.133447i	0.0464774	−	0.998919i	$-0.485200\pi$
$197$	−3.47467e6	−	1.02025e6i	−0.454480	−	0.133447i	−0.500957	+	0.865472i	$0.667019\pi$
$198$	−4.84686e6	−	2.21349e6i	−0.624403	−	0.285156i
$199$	5.24302e6	−	8.15830e6i	0.665307	−	1.03524i	−0.330504	−	0.943805i	$-0.607219\pi$
$199$	5.24302e6	−	8.15830e6i	0.665307	−	1.03524i	0.995811	−	0.0914339i	$-0.0291450\pi$
$200$	−297909.	+	87473.8i	−0.0372386	+	0.0109342i
$201$	−6.71949e6	−	966117.i	−0.827462	−	0.118971i
$202$	1.20621e6	+	2.64124e6i	0.146342	+	0.320445i
$203$	801037.	−	115172.i	0.0957557	−	0.0137676i
$204$	−126376.	−	196645.i	−0.0148858	−	0.0231628i
$205$	218623.	+	189438.i	0.0253766	+	0.0219890i
$206$		−	1.34041e7i		−	1.53334i
$207$	1.88452e6	+	2.27815e6i	0.212466	+	0.256845i
$208$	−7.39030e6			−0.821244
$209$	4.89317e6	−	5.64701e6i	0.535983	−	0.618557i
$210$	7.03610e6	−	4.52182e6i	0.759756	−	0.488265i
$211$	104394.	+	726076.i	0.0111129	+	0.0772920i	0.994623	−	0.103560i	$-0.0330235\pi$
$211$	104394.	+	726076.i	0.0111129	+	0.0772920i	−0.983510	+	0.180852i	$0.942114\pi$
$212$	5.33560e6	−	2.43669e6i	0.559984	−	0.255736i
$213$	1.51510e6	−	1.05377e7i	0.156784	−	1.09046i
$214$	2.08636e6	+	7.10548e6i	0.212886	+	0.725024i
$215$	−1.72292e7	−	1.10725e7i	−1.73360	−	1.11412i
$216$	18448.0	−	40395.6i	0.00183058	−	0.00400841i
$217$	2.10453e6	−	7.16738e6i	0.205957	−	0.701425i
$218$	1.59615e7	−	1.38308e7i	1.54066	−	1.33499i
$219$	4.19611e6	+	4.84257e6i	0.399498	+	0.461045i
$220$	2.41239e7	+	7.08340e6i	2.26558	+	0.665233i
$221$	384740.	+	175705.i	0.0356444	+	0.0162782i
$222$	−6.21339e6	+	9.66823e6i	−0.567897	+	0.883666i
$223$	4.97232e6	−	1.46000e6i	0.448378	−	0.131656i	−0.0497451	−	0.998762i	$-0.515841\pi$
$223$	4.97232e6	−	1.46000e6i	0.448378	−	0.131656i	0.498123	+	0.867106i	$0.334023\pi$
$224$	−1.05978e7	−	1.52374e6i	−0.942915	−	0.135571i
$225$	−2.67344e6	−	5.85403e6i	−0.234706	−	0.513934i
$226$	−2.03962e7	+	2.93252e6i	−1.76694	+	0.254048i
$227$	−9.72692e6	−	1.51354e7i	−0.831568	−	1.29395i	−0.953496	−	0.301406i	$-0.902544\pi$
$227$	−9.72692e6	−	1.51354e7i	−0.831568	−	1.29395i	0.121928	−	0.992539i	$-0.461092\pi$
$228$	−2.84792e6	−	2.46773e6i	−0.240283	−	0.208206i
$229$			1.86165e7i			1.55021i	0.631831	+	0.775106i	$0.282304\pi$
$229$			1.86165e7i			1.55021i	−0.631831	+	0.775106i	$0.717696\pi$
$230$	−2.08338e7	−	1.89043e7i	−1.71232	−	1.55373i
$231$	7.03949e6			0.571091
$232$	−26774.5	+	30899.4i	−0.00214416	+	0.00247449i
$233$	1.38298e7	−	8.88785e6i	1.09332	−	0.702634i	0.135723	−	0.990747i	$-0.456664\pi$
$233$	1.38298e7	−	8.88785e6i	1.09332	−	0.702634i	0.957596	+	0.288113i	$0.0930279\pi$
$234$	−691991.	−	4.81291e6i	−0.0540074	−	0.375630i
$235$	−2.46239e7	+	1.12454e7i	−1.89737	+	0.866502i
$236$	748136.	−	5.20340e6i	0.0569173	−	0.395869i
$237$	3.42918e6	+	1.16787e7i	0.257600	+	0.877304i
$238$	523880.	+	336677.i	0.0388599	+	0.0249737i
$239$	5.60696e6	−	1.22775e7i	0.410709	−	0.899327i	−0.585362	−	0.810772i	$-0.699048\pi$
$239$	5.60696e6	−	1.22775e7i	0.410709	−	0.899327i	0.996071	−	0.0885553i	$-0.0282250\pi$
$240$	−3.75040e6	+	1.27727e7i	−0.271297	+	0.923951i
$241$	2.38491e6	−	2.06654e6i	0.170381	−	0.147636i	−0.565497	−	0.824751i	$-0.691315\pi$
$241$	2.38491e6	−	2.06654e6i	0.170381	−	0.147636i	0.735877	+	0.677115i	$0.236770\pi$
$242$	1.48725e7	+	1.71638e7i	1.04939	+	1.21106i
$243$	883197.	+	259330.i	0.0615515	+	0.0180732i
$244$	−3.27880e6	−	1.49738e6i	−0.225707	−	0.103077i
$245$	7.07829e6	−	1.10140e7i	0.481316	−	0.748942i
$246$	237579.	−	69759.5i	0.0159589	−	0.00468596i
$247$	6.74921e6	+	970390.i	0.447881	+	0.0643955i
$248$	156775.	+	343290.i	0.0102783	+	0.0225064i
$249$	1.10638e7	−	1.59073e6i	0.716647	−	0.103038i
$250$	1.35743e7	+	2.11220e7i	0.868753	+	1.35181i
$251$	1.30887e7	+	1.13414e7i	0.827705	+	0.717210i	0.961799	−	0.273758i	$-0.0882668\pi$
$251$	1.30887e7	+	1.13414e7i	0.827705	+	0.717210i	−0.134094	+	0.990969i	$0.542812\pi$
$252$		−	3.55017e6i		−	0.221844i
$253$	−6.14925e6	−	2.28653e7i	−0.379718	−	1.41194i
$254$	−4.19359e7			−2.55908
$255$	498919.	−	575783.i	0.0300891	−	0.0347247i
$256$	1.45615e7	−	9.35814e6i	0.867936	−	0.557788i
$257$	3.67029e6	+	2.55274e7i	0.216223	+	1.50386i	0.751809	+	0.659381i	$0.229182\pi$
$257$	3.67029e6	+	2.55274e7i	0.216223	+	1.50386i	−0.535586	+	0.844481i	$0.679909\pi$
$258$	−1.59460e7	+	7.28229e6i	−0.928523	+	0.424042i
$259$	2.16081e6	−	1.50288e7i	0.124370	−	0.865015i
$260$	6.46394e6	+	2.20142e7i	0.367771	+	1.25251i
$261$	−712930.	−	458172.i	−0.0400983	−	0.0257696i
$262$	3.83603e6	−	8.39974e6i	0.213294	−	0.467049i
$263$	5.11883e6	−	1.74331e7i	0.281387	−	0.958315i	−0.690592	−	0.723245i	$-0.742650\pi$
$263$	5.11883e6	−	1.74331e7i	0.281387	−	0.958315i	0.971978	−	0.235070i	$-0.0755319\pi$
$264$	−268779.	+	232899.i	−0.0146078	+	0.0126577i
$265$	1.25196e7	+	1.44484e7i	0.672751	+	0.776396i
$266$	9.63255e6	+	2.82837e6i	0.511795	+	0.150277i
$267$	2.22176e6	+	1.01465e6i	0.116725	+	0.0533065i
$268$	1.48234e7	−	2.30656e7i	0.770092	−	1.19829i
$269$	9.59407e6	−	2.81707e6i	0.492885	−	0.144724i	−0.0258384	−	0.999666i	$-0.508226\pi$
$269$	9.59407e6	−	2.81707e6i	0.492885	−	0.144724i	0.518724	+	0.854942i	$0.326407\pi$
$270$	−8.66934e6	−	1.24646e6i	−0.440448	−	0.0633269i
$271$	7.44509e6	+	1.63025e7i	0.374078	+	0.819116i	0.999253	+	0.0386323i	$0.0123001\pi$
$271$	7.44509e6	+	1.63025e7i	0.374078	+	0.819116i	−0.625176	+	0.780484i	$0.714973\pi$
$272$	−981066.	+	141056.i	−0.0487519	+	0.00700946i
$273$	3.47300e6	+	5.40410e6i	0.170694	+	0.265605i
$274$	−3.63437e7	−	3.14920e7i	−1.76676	−	1.53090i
$275$			5.15393e7i			2.47823i
$276$	−1.15315e7	+	3.10121e6i	−0.548476	+	0.147504i
$277$	−2.27641e7			−1.07105			−0.535527	−	0.844518i	$-0.679887\pi$
$277$	−2.27641e7			−1.07105			−0.535527	+	0.844518i	$0.679887\pi$
$278$	−3.29224e7	+	3.79944e7i	−1.53235	+	1.76842i
$279$	−6.58067e6	+	4.22914e6i	−0.303010	+	0.194733i
$280$	−79447.0	−	552566.i	−0.00361912	−	0.0251716i
$281$	−2.49007e7	+	1.13717e7i	−1.12226	+	0.512517i	−0.888085	−	0.459679i	$-0.847965\pi$
$281$	−2.49007e7	+	1.13717e7i	−1.12226	+	0.512517i	−0.234170	+	0.972196i	$0.575237\pi$
$282$	−3.29754e6	+	2.29349e7i	−0.147042	+	1.02270i
$283$	5.98753e6	+	2.03917e7i	0.264173	+	0.899691i	0.979592	+	0.200996i	$0.0644177\pi$
$283$	5.98753e6	+	2.03917e7i	0.264173	+	0.899691i	−0.715419	+	0.698696i	$0.753764\pi$
$284$	3.61723e7	+	2.32465e7i	1.57914	+	1.01485i
$285$	5.10220e6	−	1.11723e7i	0.220406	−	0.482621i
$286$	−1.09708e7	+	3.73630e7i	−0.468964	+	1.59714i
$287$	−247224.	+	214221.i	−0.0104579	+	0.00906183i
$288$	7.34232e6	+	8.47348e6i	0.307366	+	0.354719i
$289$	−2.31054e7	−	6.78436e6i	−0.957238	−	0.281070i
$290$	7.33499e6	+	3.34978e6i	0.300750	+	0.137348i
$291$	9.22276e6	−	1.43509e7i	0.374267	−	0.582371i
$292$	−2.48312e7	+	7.29111e6i	−0.997355	+	0.292850i
$293$	3.32659e6	+	478291.i	0.132250	+	0.0190147i	0.208122	−	0.978103i	$-0.433265\pi$
$293$	3.32659e6	+	478291.i	0.132250	+	0.0190147i	−0.0758719	+	0.997118i	$0.524174\pi$
$294$	−4.65533e6	−	1.01937e7i	−0.183193	−	0.401136i
$295$	1.69595e7	−	2.43841e6i	0.660613	−	0.0949817i
$296$	414717.	+	645312.i	0.0159910	+	0.0248825i
$297$	−5.57113e6	−	4.82741e6i	−0.212654	−	0.184266i
$298$			2.12407e7i			0.802639i
$299$	1.45195e7	−	1.60015e7i	0.543173	−	0.598614i
$300$	2.59925e7			0.962684
$301$	1.51663e7	−	1.75029e7i	0.556137	−	0.641816i
$302$	3.86655e7	−	2.48488e7i	1.40379	−	0.902161i
$303$	571692.	+	3.97620e6i	0.0205511	+	0.142936i
$304$	−1.45345e7	+	6.63770e6i	−0.517345	+	0.236264i
$305$	1.67196e6	−	1.16287e7i	0.0589285	−	0.409857i
$306$	−183724.	−	625707.i	−0.00641213	−	0.0218377i
$307$	−1.23726e7	−	7.95137e6i	−0.427607	−	0.274807i	0.309085	−	0.951034i	$-0.399977\pi$
$307$	−1.23726e7	−	7.95137e6i	−0.427607	−	0.274807i	−0.736693	+	0.676228i	$0.763614\pi$
$308$	−1.18109e7	+	2.58622e7i	−0.404231	+	0.885143i
$309$	5.22452e6	−	1.77931e7i	0.177081	−	0.603082i
$310$	5.62516e7	−	4.87423e7i	1.88821	−	1.63614i
$311$	2.19522e6	+	2.53342e6i	0.0729789	+	0.0842221i	0.791065	−	0.611732i	$-0.209527\pi$
$311$	2.19522e6	+	2.53342e6i	0.0729789	+	0.0842221i	−0.718086	+	0.695954i	$0.754982\pi$
$312$	−311397.	−	91434.5i	−0.0102530	−	0.00301055i
$313$	2.18339e7	+	9.97120e6i	0.712029	+	0.325173i	0.738291	−	0.674482i	$-0.235633\pi$
$313$	2.18339e7	+	9.97120e6i	0.712029	+	0.325173i	−0.0262619	+	0.999655i	$0.508360\pi$
$314$	8.06940e6	−	1.25562e7i	0.260647	−	0.405574i
$315$	1.11024e7	−	3.25996e6i	0.355210	−	0.104299i
$316$	−4.86596e7	−	6.99619e6i	−1.54208	−	0.221718i
$317$	−7.12528e6	−	1.56022e7i	−0.223678	−	0.489787i	0.764207	−	0.644971i	$-0.223130\pi$
$317$	−7.12528e6	−	1.56022e7i	−0.223678	−	0.489787i	−0.987886	+	0.155183i	$0.950403\pi$
$318$	1.61975e7	−	2.32885e6i	0.503695	−	0.0724203i
$319$	3.66926e6	+	5.70949e6i	0.113033	+	0.175883i
$320$	−3.93217e7	−	3.40725e7i	−1.20000	−	1.03981i
$321$			1.02452e7i			0.309747i
$322$	2.45126e7	−	2.02772e7i	0.734214	−	0.607353i
$323$	914482.			0.0271374
$324$	−2.43457e6	+	2.80965e6i	−0.0715794	+	0.0826070i
$325$	−3.95659e7	+	2.54275e7i	−1.15258	+	0.740718i
$326$	−2.21711e6	−	1.54204e7i	−0.0639934	−	0.445084i
$327$	2.65787e7	−	1.21381e7i	0.760134	−	0.347141i
$328$	2352.01	−	16358.6i	6.66527e−5	−	0.000463580i
$329$	−8.62427e6	−	2.93716e7i	−0.242178	−	0.824783i
$330$	5.90074e7	+	3.79217e7i	1.64197	+	1.05523i
$331$	9.99532e6	−	2.18867e7i	0.275621	−	0.603526i	−0.720309	−	0.693653i	$-0.756000\pi$
$331$	9.99532e6	−	2.18867e7i	0.275621	−	0.603526i	0.995930	+	0.0901269i	$0.0287273\pi$
$332$	−1.27187e7	+	4.33158e7i	−0.347558	+	1.18367i
$333$	−1.20162e7	+	1.04121e7i	−0.325414	+	0.281972i
$334$	−5.91567e7	−	6.82705e7i	−1.58769	−	1.83229i
$335$	8.57443e7	+	2.51768e7i	2.28071	+	0.669678i
$336$	−1.36931e7	−	6.25342e6i	−0.360980	−	0.164854i
$337$	2.22855e7	−	3.46769e7i	0.582281	−	0.906047i	−0.417716	−	0.908578i	$-0.637169\pi$
$337$	2.22855e7	−	3.46769e7i	0.582281	−	0.906047i	0.999997	+	0.00253052i	$0.000805492\pi$
$338$	1.80881e7	−	5.31115e6i	0.468429	−	0.137543i
$339$	−2.82175e7	−	4.05707e6i	−0.724302	−	0.104139i
$340$	1.27827e6	+	2.79901e6i	0.0325226	+	0.0712145i
$341$	6.20083e7	−	8.91545e6i	1.56382	−	0.224843i
$342$	−5.68372e6	−	8.84404e6i	−0.142087	−	0.221092i
$343$	3.18213e7	+	2.75733e7i	0.788563	+	0.683293i
$344$			1.17006e6i			0.0287431i
$345$	−2.02872e7	−	3.32145e7i	−0.494043	−	0.808855i
$346$	−7.83542e7			−1.89162
$347$	−4.34651e7	+	5.01613e7i	−1.04028	+	1.20055i	−0.0609833	+	0.998139i	$0.519424\pi$
$347$	−4.34651e7	+	5.01613e7i	−1.04028	+	1.20055i	−0.979300	+	0.202413i	$0.935122\pi$
$348$	2.87942e6	−	1.85049e6i	0.0683231	−	0.0439086i
$349$	−9.24022e6	−	6.42672e7i	−0.217373	−	1.51186i	−0.747680	−	0.664059i	$-0.768832\pi$
$349$	−9.24022e6	−	6.42672e7i	−0.217373	−	1.51186i	0.530307	−	0.847806i	$-0.322077\pi$
$350$	−6.29887e7	+	2.87660e7i	−1.46913	+	0.670927i
$351$	957351.	−	6.65852e6i	0.0221386	−	0.153977i
$352$	−2.52971e7	−	8.61541e7i	−0.580020	−	1.97537i
$353$	6.22076e7	+	3.99784e7i	1.41423	+	0.908869i	0.999999	−	0.00130420i	$-0.000415139\pi$
$353$	6.22076e7	+	3.99784e7i	1.41423	+	0.908869i	0.414228	+	0.910173i	$0.364052\pi$
$354$	6.09238e6	−	1.33404e7i	0.137334	−	0.300719i
$355$	−3.94831e7	+	1.34467e8i	−0.882523	+	3.00560i
$356$	−7.45535e6	+	6.46010e6i	−0.165241	+	0.143182i
$357$	564189.	+	651109.i	0.0123999	+	0.0143103i
$358$	2.82781e7	+	8.30319e6i	0.616312	+	0.180966i
$359$	3.39707e7	+	1.55139e7i	0.734212	+	0.335304i	0.747188	−	0.664612i	$-0.231403\pi$
$359$	3.39707e7	+	1.55139e7i	0.734212	+	0.335304i	−0.0129760	+	0.999916i	$0.504131\pi$
$360$	−316054.	+	491789.i	−0.00677413	+	0.0105407i
$361$	−3.09949e7	+	9.10093e6i	−0.658823	+	0.193448i
$362$	−8.72619e7	−	1.25464e7i	−1.83950	−	0.264480i
$363$	1.30523e7	+	2.85806e7i	0.272877	+	0.597518i
$364$	−2.56810e7	+	3.69237e6i	−0.532485	+	0.0765598i
$365$	−4.56028e7	−	7.09593e7i	−0.937805	−	1.45925i
$366$	−7.59979e6	−	6.58525e6i	−0.155009	−	0.134316i
$367$			1.70815e7i			0.345564i	0.984960	+	0.172782i	$0.0552757\pi$
$367$			1.70815e7i			0.345564i	−0.984960	+	0.172782i	$0.944724\pi$
$368$	−8.35060e6	+	4.99397e7i	−0.167561	+	1.00208i
$369$	342560.			0.00681801
$370$	9.90725e7	−	1.14336e8i	1.95591	−	2.25723i
$371$	−1.81872e7	+	1.16882e7i	−0.356158	+	0.228889i
$372$	−4.49626e6	−	3.12722e7i	−0.0873419	−	0.607477i
$373$	−4.04664e7	+	1.84804e7i	−0.779773	+	0.356110i	−0.765208	−	0.643784i	$-0.777364\pi$
$373$	−4.04664e7	+	1.84804e7i	−0.779773	+	0.356110i	−0.0145652	+	0.999894i	$0.504636\pi$
$374$	−743241.	+	5.16935e6i	−0.0142074	+	0.0988147i
$375$	9.78622e6	+	3.33288e7i	0.185576	+	0.632013i
$376$	1.30104e6	+	836125.i	0.0244752	+	0.0157292i
$377$	−2.57281e6	+	5.63367e6i	−0.0480157	+	0.105140i
$378$	2.79036e6	−	9.50311e6i	0.0516637	−	0.175950i
$379$	−3.85178e6	+	3.33759e6i	−0.0707529	+	0.0613077i	−0.689519	−	0.724267i	$-0.742178\pi$
$379$	−3.85178e6	+	3.33759e6i	−0.0707529	+	0.0613077i	0.618766	+	0.785575i	$0.287633\pi$
$380$	3.24850e7	+	3.74896e7i	0.592013	+	0.683220i
$381$	−5.56670e7	−	1.63453e7i	−1.00652	−	0.295541i
$382$	2.95245e7	+	1.34834e7i	0.529654	+	0.241885i
$383$	2.52306e7	−	3.92596e7i	0.449088	−	0.698794i	−0.540720	−	0.841202i	$-0.681848\pi$
$383$	2.52306e7	−	3.92596e7i	0.449088	−	0.698794i	0.989808	+	0.142408i	$0.0454846\pi$
$384$	1.43627e6	−	421727.i	0.0253654	−	0.00744796i
$385$	−9.17238e7	−	1.31879e7i	−1.60731	−	0.231096i
$386$	−2.20174e7	−	4.82115e7i	−0.382829	−	0.838279i
$387$	−2.40056e7	+	3.45149e6i	−0.414172	+	0.0595489i
$388$	3.72494e7	+	5.79612e7i	0.637711	+	0.992298i
$389$	−1.35164e7	−	1.17121e7i	−0.229622	−	0.198969i	0.532449	−	0.846462i	$-0.321272\pi$
$389$	−1.35164e7	−	1.17121e7i	−0.229622	−	0.198969i	−0.762071	+	0.647494i	$0.775817\pi$
$390$			6.40080e7i			1.07905i
$391$	1.62205e6	−	2.40133e6i	0.0271353	−	0.0401719i
$392$	−747981.			−0.0124175
$393$	8.36603e6	−	9.65492e6i	0.137829	−	0.159064i
$394$	3.43266e7	−	2.20604e7i	0.561232	−	0.360682i
$395$	−2.28028e7	−	1.58597e8i	−0.369995	−	2.57337i
$396$	2.70826e7	−	1.23682e7i	0.436118	−	0.199169i
$397$	−187878.	+	1.30672e6i	−0.00300264	+	0.0208838i	−0.991268	−	0.131865i	$-0.957903\pi$
$397$	−187878.	+	1.30672e6i	−0.00300264	+	0.0208838i	0.988265	+	0.152749i	$0.0488126\pi$
$398$	3.07852e7	+	1.04845e8i	0.488307	+	1.66302i
$399$	1.16841e7	+	7.50894e6i	0.183941	+	0.118212i
$400$	4.57842e7	−	1.00253e8i	0.715378	−	1.56646i
$401$	2.09783e6	−	7.14454e6i	0.0325339	−	0.110800i	−0.941625	−	0.336663i	$-0.890702\pi$
$401$	2.09783e6	−	7.14454e6i	0.0325339	−	0.110800i	0.974159	+	0.225862i	$0.0725200\pi$
$402$	5.78083e7	−	5.00912e7i	0.889840	−	0.771051i
$403$	3.74367e7	+	4.32042e7i	0.571982	+	0.660102i
$404$	−1.55673e7	−	4.57096e6i	−0.236085	−	0.0693207i
$405$	−1.10221e7	−	5.03364e6i	−0.165921	−	0.0757734i
$406$	−4.92989e6	+	7.67106e6i	−0.0736647	+	0.114624i
$407$	1.22175e8	−	3.58738e7i	1.81217	−	0.532101i
$408$	−43083.3	−	6194.44i	−0.000634349	−	9.12057e-5i
$409$	−5.25971e6	−	1.15172e7i	−0.0768762	−	0.168335i	0.867292	−	0.497801i	$-0.165859\pi$
$409$	−5.25971e6	−	1.15172e7i	−0.0768762	−	0.168335i	−0.944168	+	0.329465i	$0.893132\pi$
$410$	−3.22632e6	+	463875.i	−0.0468118	+	0.00673053i
$411$	−3.59691e7	−	5.59691e7i	−0.518089	−	0.806163i
$412$	5.66039e7	+	4.90475e7i	0.809384	+	0.701335i
$413$			1.93754e7i			0.275043i
$414$	−3.33049e7	−	762187.i	−0.469362	−	0.0107414i
$415$	−1.47140e8			−2.05867
$416$	5.36585e7	−	6.19252e7i	0.745347	−	0.860176i
$417$	−5.85113e7	+	3.76029e7i	−0.806921	+	0.518577i
$418$	1.19818e7	+	8.33356e7i	0.164057	+	1.14104i
$419$	−7.52073e7	+	3.43460e7i	−1.02239	+	0.466912i	−0.854807	−	0.518946i	$-0.826325\pi$
$419$	−7.52073e7	+	3.43460e7i	−1.02239	+	0.466912i	−0.167587	+	0.985857i	$0.553597\pi$
$420$	−6.65095e6	+	4.62584e7i	−0.0897710	+	0.624371i
$421$	2.99294e7	+	1.01930e8i	0.401099	+	1.36602i	0.874438	+	0.485137i	$0.161230\pi$
$421$	2.99294e7	+	1.01930e8i	0.401099	+	1.36602i	−0.473339	+	0.880880i	$0.656951\pi$
$422$	−6.95320e6	−	4.46855e6i	−0.0925225	−	0.0594606i
$423$	−1.33166e7	+	2.91592e7i	−0.175943	+	0.385261i
$424$	307717.	−	1.04799e6i	0.00403695	−	0.0137486i
$425$	−4.76707e6	+	4.13069e6i	−0.0620990	+	0.0538091i
$426$	7.85546e7	+	9.06569e7i	1.01612	+	1.17266i
$427$	1.27471e7	+	3.74289e6i	0.163730	+	0.0480754i
$428$	−3.76397e7	−	1.71895e7i	−0.480082	−	0.219246i
$429$	−2.91259e7	+	4.53208e7i	−0.368899	+	0.574019i
$430$	2.21417e8	−	6.50140e7i	2.78488	−	0.817714i
$431$	−5.52300e7	−	7.94087e6i	−0.689832	−	0.0991828i	−0.211521	−	0.977373i	$-0.567842\pi$
$431$	−5.52300e7	−	7.94087e6i	−0.689832	−	0.0991828i	−0.478311	+	0.878191i	$0.658751\pi$
$432$	6.54851e6	+	1.43392e7i	0.0812252	+	0.177858i
$433$	−8.77449e7	+	1.26158e7i	−1.08083	+	0.155400i	−0.659648	−	0.751575i	$-0.729294\pi$
$433$	−8.77449e7	+	1.26158e7i	−1.08083	+	0.155400i	−0.421184	+	0.906975i	$0.638385\pi$
$434$	4.55051e7	+	7.08073e7i	0.556661	+	0.866182i
$435$	8.43106e6	+	7.30555e6i	0.102427	+	0.0887535i
$436$			1.18012e8i			1.42386i
$437$	1.41836e7	−	4.45111e7i	0.169958	−	0.533364i
$438$	−7.21989e7			−0.859228
$439$	2.85888e7	−	3.29932e7i	0.337911	−	0.389970i	−0.561208	−	0.827675i	$-0.689663\pi$
$439$	2.85888e7	−	3.29932e7i	0.337911	−	0.389970i	0.899119	+	0.437705i	$0.144209\pi$
$440$	3.93848e6	−	2.53111e6i	0.0462350	−	0.0297134i
$441$	−2.20642e6	−	1.53460e7i	−0.0257260	−	0.178929i
$442$	−4.33511e6	+	1.97978e6i	−0.0502035	+	0.0229272i
$443$	−1.78636e7	+	1.24244e8i	−0.205475	+	1.42911i	0.582214	+	0.813036i	$0.302187\pi$
$443$	−1.78636e7	+	1.24244e8i	−0.205475	+	1.42911i	−0.787689	+	0.616074i	$0.788722\pi$
$444$	−1.80920e7	−	6.16156e7i	−0.206698	−	0.703950i
$445$	−2.70485e7	−	1.73830e7i	−0.306947	−	0.197263i
$446$	−2.42567e7	+	5.31148e7i	−0.273418	+	0.598702i
$447$	−8.27897e6	+	2.81956e7i	−0.0926945	+	0.315688i
$448$	4.44659e7	−	3.85300e7i	0.494531	−	0.428513i
$449$	−5.35915e7	−	6.18479e7i	−0.592048	−	0.683260i	0.378102	−	0.925764i	$-0.376577\pi$
$449$	−5.35915e7	−	6.18479e7i	−0.592048	−	0.683260i	−0.970150	+	0.242504i	$0.922031\pi$
$450$	6.95766e7	+	2.04295e7i	0.763530	+	0.224193i
$451$	−2.49547e6	−	1.13964e6i	−0.0272034	−	0.0124234i
$452$	6.22485e7	−	9.68606e7i	0.674084	−	1.04889i
$453$	6.10110e7	−	1.79145e7i	0.656317	−	0.192712i
$454$	2.00658e8	+	2.88502e7i	2.14431	+	0.308306i
$455$	−3.51288e7	−	7.69212e7i	−0.372931	−	0.816605i
$456$	−694549.	+	99861.1i	−0.00732502	+	0.00105318i
$457$	−4.91103e7	−	7.64172e7i	−0.514546	−	0.800649i	0.482624	−	0.875828i	$-0.339684\pi$
$457$	−4.91103e7	−	7.64172e7i	−0.514546	−	0.800649i	−0.997170	+	0.0751784i	$0.976047\pi$
$458$	−1.58529e8	−	1.37366e8i	−1.65011	−	1.42982i
$459$		−	902194.i		−	0.00932958i
$460$	1.56064e8	−	1.88052e7i	1.60335	−	0.193198i
$461$	−6.03203e7			−0.615688			−0.307844	−	0.951437i	$-0.599607\pi$
$461$	−6.03203e7			−0.615688			−0.307844	+	0.951437i	$0.599607\pi$
$462$	−5.19425e7	+	5.99448e7i	−0.526741	+	0.607891i
$463$	−6.83343e7	+	4.39158e7i	−0.688487	+	0.442464i	−0.837548	−	0.546364i	$-0.816011\pi$
$463$	−6.83343e7	+	4.39158e7i	−0.688487	+	0.442464i	0.149061	+	0.988828i	$0.452375\pi$
$464$	−2.06545e6	−	1.43655e7i	−0.0206757	−	0.143803i
$465$	9.36683e7	−	4.27769e7i	0.931610	−	0.425452i
$466$	−2.63615e7	+	1.83349e8i	−0.260503	+	1.81184i
$467$	−2.59497e7	−	8.83765e7i	−0.254790	−	0.867733i	−0.983191	−	0.182582i	$-0.941554\pi$
$467$	−2.59497e7	−	8.83765e7i	−0.254790	−	0.867733i	0.728401	−	0.685151i	$-0.240264\pi$
$468$	2.28563e7	+	1.46889e7i	0.222981	+	0.143301i
$469$	−4.19798e7	+	9.19230e7i	−0.406932	+	0.891057i
$470$	8.59331e7	−	2.92661e8i	0.827689	−	2.81885i
$471$	1.56056e7	−	1.35223e7i	0.149354	−	0.129416i
$472$	−641027.	−	739784.i	−0.00609607	−	0.00703524i
$473$	1.86358e8	+	5.47197e7i	1.76102	+	0.517083i
$474$	−1.24753e8	−	5.69729e7i	−1.17143	−	0.534974i
$475$	−5.49764e7	+	8.55449e7i	−0.512974	+	0.798203i
$476$	−3.33869e6	+	980327.i	−0.0309567	+	0.00908971i
$477$	2.24088e7	+	3.22190e6i	0.206473	+	0.0296864i
$478$	6.31772e7	+	1.38339e8i	0.578465	+	1.26666i
$479$	2.06067e8	−	2.96279e7i	1.87500	−	0.269585i	0.891844	−	0.452343i	$-0.149412\pi$
$479$	2.06067e8	−	2.96279e7i	1.87500	−	0.269585i	0.983158	+	0.182759i	$0.0585028\pi$
$480$	−7.97952e7	−	1.24164e8i	−0.721528	−	1.12272i
$481$	8.78160e7	+	7.60930e7i	0.789111	+	0.683769i
$482$			3.55571e7i			0.317531i
$483$	4.04423e7	−	1.73624e7i	0.358917	−	0.154088i
$484$	−1.26901e8			−1.11925
$485$	−1.47057e8	+	1.69713e8i	−1.28902	+	1.48761i
$486$	−8.72520e6	+	5.60734e6i	−0.0760092	+	0.0488482i
$487$	1.13982e7	+	7.92763e7i	0.0986847	+	0.686367i	0.977767	+	0.209696i	$0.0672476\pi$
$487$	1.13982e7	+	7.92763e7i	0.0986847	+	0.686367i	−0.879082	+	0.476671i	$0.841843\pi$
$488$	−610537.	+	278823.i	−0.00525355	+	0.00239921i
$489$	3.06731e6	−	2.13336e7i	0.0262320	−	0.182448i
$490$	4.15613e7	+	1.41545e8i	0.353265	+	1.20311i
$491$	−7.32270e7	−	4.70602e7i	−0.618624	−	0.397566i	0.193458	−	0.981109i	$-0.438030\pi$
$491$	−7.32270e7	−	4.70602e7i	−0.618624	−	0.397566i	−0.812082	+	0.583543i	$0.801666\pi$
$492$	−574748.	+	1.25852e6i	−0.00482594	+	0.0105673i
$493$	−234014.	+	796978.i	−0.00195299	+	0.00665128i
$494$	−5.80640e7	+	5.03127e7i	−0.481644	+	0.417347i
$495$	6.35475e7	+	7.33378e7i	0.523942	+	0.604661i
$496$	−1.28537e8	−	3.77420e7i	−1.05338	−	0.309300i
$497$	−1.44157e8	−	6.58341e7i	−1.17426	−	0.536268i
$498$	−6.80907e7	+	1.05951e8i	−0.551315	+	0.857863i
$499$	9.31153e7	−	2.73411e7i	0.749410	−	0.220047i	0.115344	−	0.993326i	$-0.463203\pi$
$499$	9.31153e7	−	2.73411e7i	0.749410	−	0.220047i	0.634066	+	0.773279i	$0.281385\pi$
$500$	−1.38865e8	−	1.99658e7i	−1.11092	−	0.159726i
$501$	−5.19168e7	−	1.13682e8i	−0.412852	−	0.904020i
$502$	−1.93156e8	+	2.77716e7i	−1.52685	+	0.219528i
$503$	8.60982e7	+	1.33971e8i	0.676535	+	1.05271i	0.994513	+	0.104611i	$0.0333598\pi$
$503$	8.60982e7	+	1.33971e8i	0.676535	+	1.05271i	−0.317978	+	0.948098i	$0.603004\pi$
$504$	−499602.	−	432908.i	−0.00390241	−	0.00338146i
$505$		−	5.28805e7i		−	0.410603i
$506$	2.40083e8	+	1.16353e8i	1.85315	+	0.898100i
$507$	2.60809e7			0.200124
$508$	1.53449e8	−	1.77089e8i	1.17050	−	1.35083i
$509$	6.43364e7	−	4.13465e7i	0.487869	−	0.313535i	−0.273479	−	0.961878i	$-0.588174\pi$
$509$	6.43364e7	−	4.13465e7i	0.487869	−	0.313535i	0.761348	+	0.648343i	$0.224538\pi$
$510$	1.22170e6	+	8.49709e6i	0.00920986	+	0.0640560i
$511$	8.67646e7	−	3.96241e7i	0.650249	−	0.296959i
$512$	−2.68818e7	+	1.86967e8i	−0.200285	+	1.39301i
$513$	−4.09762e6	−	1.39552e7i	−0.0303514	−	0.103367i
$514$	−2.44461e8	−	1.57106e8i	−1.80020	−	1.15692i
$515$	−1.01409e8	+	2.22054e8i	−0.742428	+	1.62569i
$516$	2.75964e7	−	9.39846e7i	0.200864	−	0.684081i
$517$	1.94016e8	−	1.68116e8i	1.40400	−	1.21657i
$518$	1.12033e8	+	1.29293e8i	0.806043	+	0.930223i
$519$	−1.04010e8	−	3.05401e7i	−0.744000	−	0.218458i
$520$	3.88618e6	+	1.77476e6i	0.0276384	+	0.0126220i
$521$	−1.06236e7	+	1.65307e7i	−0.0751206	+	0.116890i	−0.876781	−	0.480890i	$-0.840314\pi$
$521$	−1.06236e7	+	1.65307e7i	−0.0751206	+	0.116890i	0.801661	+	0.597780i	$0.203950\pi$
$522$	9.16209e6	−	2.69023e6i	0.0644144	−	0.0189138i
$523$	1.63449e7	+	2.35004e6i	0.114255	+	0.0164274i	0.199205	−	0.979958i	$-0.436164\pi$
$523$	1.63449e7	+	2.35004e6i	0.114255	+	0.0164274i	−0.0849500	+	0.996385i	$0.527073\pi$
$524$	2.14344e7	+	4.69348e7i	0.148976	+	0.326213i
$525$	−9.48254e7	+	1.36338e7i	−0.655310	+	0.0942193i
$526$	1.10682e8	+	1.72224e8i	0.760533	+	1.18341i
$527$	5.79436e6	+	5.02084e6i	0.0395889	+	0.0343040i
$528$		−	1.26244e8i		−	0.857646i
$529$	−9.17234e7	−	1.16196e8i	−0.619602	−	0.784916i
$530$	−2.15415e8			−1.44693
$531$	1.32869e7	−	1.53339e7i	0.0887443	−	0.102416i
$532$	−4.71905e7	+	3.03275e7i	−0.313415	+	0.201420i
$533$	−356281.	−	2.47799e6i	−0.00235294	−	0.0163651i
$534$	−2.50340e7	+	1.14326e7i	−0.164402	+	0.0750798i
$535$	1.91936e7	−	1.33494e8i	0.125342	−	0.871770i
$536$	−1.43837e6	−	4.89865e6i	−0.00934066	−	0.0318114i
$537$	3.43009e7	+	2.20438e7i	0.221505	+	0.142352i
$538$	−4.68032e7	+	1.02485e8i	−0.300558	+	0.658131i
$539$	−3.49805e7	+	1.19133e8i	−0.223388	+	0.760789i
$540$	3.69859e7	−	3.20485e7i	0.234885	−	0.203529i
$541$	−5.06728e7	−	5.84795e7i	−0.320024	−	0.369328i	0.572829	−	0.819675i	$-0.305846\pi$
$541$	−5.06728e7	−	5.84795e7i	−0.320024	−	0.369328i	−0.892854	+	0.450347i	$0.851300\pi$
$542$	−1.93759e8	−	5.68928e7i	−1.21693	−	0.357322i
$543$	−1.10944e8	−	5.06664e7i	−0.692954	−	0.316461i
$544$	5.94124e6	−	9.24475e6i	0.0369046	−	0.0574247i
$545$	−3.69057e8	+	1.08365e8i	−2.27984	+	0.669421i
$546$	−7.16450e7	−	1.03010e7i	−0.440158	−	0.0632851i
$547$	1.23420e7	+	2.70252e7i	0.0754091	+	0.165123i	0.943582	−	0.331139i	$-0.107433\pi$
$547$	1.23420e7	+	2.70252e7i	0.0754091	+	0.165123i	−0.868173	+	0.496262i	$0.834706\pi$
$548$	2.65972e8	−	3.82411e7i	1.61620	−	0.232374i
$549$	−7.52147e6	−	1.17036e7i	−0.0454554	−	0.0707301i
$550$	−4.38884e8	−	3.80295e8i	−2.63792	−	2.28577i
$551$			1.33906e7i			0.0800468i
$552$	−969726.	+	2.00094e6i	−0.00576543	+	0.0118964i
$553$	1.81189e8			1.07141
$554$	1.67970e8	−	1.93848e8i	0.987877	−	1.14007i
$555$	1.76076e8	−	1.13157e8i	1.02996	−	0.661918i
$556$	−3.99780e7	−	2.78053e8i	−0.232593	−	1.61772i
$557$	2.57512e8	−	1.17602e8i	1.49016	−	0.680531i	0.506774	−	0.862079i	$-0.330838\pi$
$557$	2.57512e8	−	1.17602e8i	1.49016	−	0.680531i	0.983382	+	0.181548i	$0.0581106\pi$
$558$	1.25437e7	−	8.72434e7i	0.0721977	−	0.502146i
$559$	4.99343e7	+	1.70061e8i	0.285867	+	0.973572i
$560$	1.66704e8	+	1.07134e8i	0.949254	+	0.610049i
$561$	−3.00146e6	+	6.57227e6i	−0.0169998	+	0.0372243i
$562$	8.68990e7	−	2.95951e8i	0.489560	−	1.66729i
$563$	1.21378e8	−	1.05174e8i	0.680163	−	0.589365i	−0.244730	−	0.969591i	$-0.578699\pi$
$563$	1.21378e8	−	1.05174e8i	0.680163	−	0.589365i	0.924893	+	0.380227i	$0.124154\pi$
$564$	−8.47847e7	−	9.78467e7i	−0.472585	−	0.545392i
$565$	3.60071e8	+	1.05726e8i	1.99638	+	0.586189i
$566$	−2.17826e8	−	9.94777e7i	−1.20132	−	0.548626i
$567$	7.40804e6	−	1.15271e7i	0.0406400	−	0.0632371i
$568$	7.68223e6	−	2.25571e6i	0.0419220	−	0.0123094i
$569$	−1.09384e8	−	1.57271e7i	−0.593770	−	0.0853713i	−0.161123	−	0.986934i	$-0.551511\pi$
$569$	−1.09384e8	−	1.57271e7i	−0.593770	−	0.0853713i	−0.432648	+	0.901563i	$0.642421\pi$
$570$	5.74897e7	+	1.25885e8i	0.310431	+	0.679749i
$571$	1.05483e8	−	1.51662e7i	0.566598	−	0.0814645i	0.146938	−	0.989146i	$-0.453058\pi$
$571$	1.05483e8	−	1.51662e7i	0.566598	−	0.0814645i	0.419660	+	0.907681i	$0.362149\pi$
$572$	−1.17635e8	−	1.83044e8i	−0.628565	−	0.978066i
$573$	3.39363e7	+	2.94060e7i	0.180385	+	0.156305i
$574$		−	3.68591e6i		−	0.0194899i
$575$	1.27118e8	+	2.96097e8i	0.668658	+	1.55751i
$576$	−6.16132e7			−0.322409
$577$	1.80182e8	−	2.07941e8i	0.937959	−	1.08246i	−0.0584918	−	0.998288i	$-0.518629\pi$
$577$	1.80182e8	−	2.07941e8i	0.937959	−	1.08246i	0.996451	−	0.0841748i	$-0.0268254\pi$
$578$	2.28261e8	−	1.46694e8i	1.18208	−	0.759678i
$579$	−1.04353e7	−	7.25792e7i	−0.0537613	−	0.373918i
$580$	−4.09853e7	+	1.87174e7i	−0.210060	+	0.0959314i
$581$	2.36797e7	−	1.64696e8i	0.120739	−	0.839757i
$582$	5.41529e7	+	1.84428e8i	0.274696	+	0.935529i
$583$	−1.52524e8	−	9.80214e7i	−0.769721	−	0.494670i
$584$	−2.00187e6	+	4.38348e6i	−0.0100507	+	0.0220080i
$585$	−2.49484e7	+	8.49663e7i	−0.124616	+	0.424404i
$586$	−2.86189e7	+	2.47984e7i	−0.142220	+	0.123234i
$587$	−5.24661e7	−	6.05491e7i	−0.259397	−	0.299360i	0.611081	−	0.791568i	$-0.290735\pi$
$587$	−5.24661e7	−	6.05491e7i	−0.259397	−	0.299360i	−0.870477	+	0.492209i	$0.836190\pi$
$588$	6.00812e7	+	1.76414e7i	0.295534	+	0.0867765i
$589$	1.12431e8	+	5.13457e7i	0.550226	+	0.251280i
$590$	−1.04375e8	+	1.62411e8i	−0.508208	+	0.790787i
$591$	5.41647e7	−	1.59042e7i	0.262394	−	0.0770459i
$592$	−2.69520e8	−	3.87512e7i	−1.29905	−	0.186775i
$593$	−1.32343e7	−	2.89791e7i	−0.0634655	−	0.138970i	0.875241	−	0.483686i	$-0.160702\pi$
$593$	−1.32343e7	−	2.89791e7i	−0.0634655	−	0.138970i	−0.938707	+	0.344716i	$0.887975\pi$
$594$	8.22158e7	−	1.18208e7i	0.392280	−	0.0564013i
$595$	−6.13152e6	−	9.54084e6i	−0.0291083	−	0.0452935i
$596$	−8.96965e7	−	7.77225e7i	−0.423679	−	0.367120i
$597$			1.51174e8i			0.710482i
$598$	2.91255e7	+	2.41712e8i	0.136197	+	1.13030i
$599$	3.33888e7			0.155353			0.0776767	−	0.996979i	$-0.475250\pi$
$599$	3.33888e7			0.155353			0.0776767	+	0.996979i	$0.475250\pi$
$600$	3.16952e6	−	3.65782e6i	0.0146737	−	0.0169343i
$601$	−1.82832e8	+	1.17499e8i	−0.842226	+	0.541266i	−0.889141	−	0.457633i	$-0.848697\pi$
$601$	−1.82832e8	+	1.17499e8i	−0.842226	+	0.541266i	0.0469152	+	0.998899i	$0.485061\pi$
$602$	3.71377e7	+	2.58298e8i	0.170226	+	1.18395i
$603$	9.62606e7	−	4.39607e7i	0.439032	−	0.200499i
$604$	−3.65490e7	+	2.54204e8i	−0.165869	+	1.15364i
$605$	−1.16527e8	−	3.96854e8i	−0.526211	−	1.79211i
$606$	−3.80778e7	−	2.44711e7i	−0.171101	−	0.109960i
$607$	−1.40254e8	+	3.07113e8i	−0.627118	+	1.37320i	0.283110	+	0.959087i	$0.408634\pi$
$607$	−1.40254e8	+	3.07113e8i	−0.627118	+	1.37320i	−0.910228	+	0.414108i	$0.864093\pi$
$608$	4.99114e7	−	1.69983e8i	0.222069	−	0.756299i
$609$	−9.53404e6	+	8.26129e6i	−0.0422109	+	0.0365760i
$610$	8.66875e7	+	1.00043e8i	0.381915	+	0.440754i
$611$	2.24780e8	+	6.60013e7i	0.985447	+	0.289353i
$612$	3.31455e6	+	1.51370e6i	0.0144601	+	0.00660368i
$613$	9.03812e7	−	1.40636e8i	0.392371	−	0.610541i	−0.587726	−	0.809060i	$-0.699977\pi$
$613$	9.03812e7	−	1.40636e8i	0.392371	−	0.610541i	0.980097	+	0.198519i	$0.0636132\pi$
$614$	1.59004e8	−	4.66878e7i	0.686914	−	0.201696i
$615$	−4.46352e6	−	641758.i	−0.0191890	−	0.00275896i
$616$	2.19927e6	+	4.81573e6i	0.00940885	+	0.0206025i
$617$	−3.17018e8	+	4.55803e7i	−1.34967	+	0.194053i	−0.778948	−	0.627089i	$-0.784246\pi$
$617$	−3.17018e8	+	4.55803e7i	−1.34967	+	0.194053i	−0.570724	+	0.821142i	$0.693337\pi$
$618$	1.12967e8	+	1.75780e8i	0.478614	+	0.744739i
$619$	−1.95481e8	−	1.69385e8i	−0.824201	−	0.714174i	0.136836	−	0.990594i	$-0.456307\pi$
$619$	−1.95481e8	−	1.69385e8i	−0.824201	−	0.714174i	−0.961037	+	0.276419i	$0.910852\pi$
$620$			4.15897e8i			1.74506i
$621$	−4.39130e7	−	1.39930e7i	−0.183366	−	0.0584300i
$622$	−3.77713e7			−0.156961
$623$	2.38100e7	−	2.74782e7i	0.0984681	−	0.113638i
$624$	9.69153e7	−	6.22837e7i	0.398876	−	0.256342i
$625$	−6.18317e6	−	4.30049e7i	−0.0253263	−	0.176148i
$626$	−2.46016e8	+	1.12352e8i	−1.00286	+	0.457991i
$627$	−1.65766e7	+	1.15292e8i	−0.0672499	+	0.467733i
$628$	2.34962e7	+	8.00208e7i	0.0948679	+	0.323090i
$629$	1.31100e7	+	8.42526e6i	0.0526805	+	0.0338557i
$630$	−5.41614e7	+	1.18597e8i	−0.216605	+	0.474299i
$631$	1.74293e7	−	5.93586e7i	0.0693730	−	0.236263i	−0.917507	−	0.397721i	$-0.869801\pi$
$631$	1.74293e7	−	5.93586e7i	0.0693730	−	0.236263i	0.986880	+	0.161458i	$0.0516195\pi$
$632$	−6.91809e6	+	5.99456e6i	−0.0274053	+	0.0237469i
$633$	−7.48819e6	−	8.64184e6i	−0.0295234	−	0.0340718i
$634$	1.85436e8	+	5.44489e7i	0.727656	+	0.213659i
$635$	6.94714e8	+	3.17265e8i	2.71322	+	1.23909i
$636$	−4.94344e7	+	7.69215e7i	−0.192158	+	0.299003i
$637$	−1.08714e8	+	3.19213e7i	−0.420598	+	0.123499i
$638$	−7.56937e7	−	1.08831e7i	−0.291472	−	0.0419074i
$639$	6.89407e7	+	1.50959e8i	0.264224	+	0.578571i
$640$	−1.95045e7	+	2.80433e6i	−0.0744038	+	0.0106977i
$641$	−1.28385e8	−	1.99770e8i	−0.487459	−	0.758502i	0.507187	−	0.861836i	$-0.330685\pi$
$641$	−1.28385e8	−	1.99770e8i	−0.487459	−	0.758502i	−0.994647	+	0.103334i	$0.967049\pi$
$642$	−8.72434e7	−	7.55969e7i	−0.329707	−	0.285692i
$643$		−	4.24391e8i		−	1.59637i	−0.602412	−	0.798185i	$-0.705794\pi$
$643$		−	4.24391e8i		−	1.59637i	0.602412	−	0.798185i	$-0.294206\pi$
$644$	−4.06693e6	+	1.77711e8i	−0.0152268	+	0.665358i
$645$	3.19257e8			1.18977
$646$	−6.74772e6	+	7.78728e6i	−0.0250299	+	0.0288861i
$647$	−3.85687e8	+	2.47866e8i	−1.42404	+	0.915176i	−0.424087	+	0.905621i	$0.639405\pi$
$647$	−3.85687e8	+	2.47866e8i	−1.42404	+	0.915176i	−0.999954	+	0.00955461i	$0.996959\pi$
$648$	98519.3	+	685217.i	0.000362073	+	0.00251827i
$649$	−1.47806e8	+	6.75005e7i	−0.540700	+	0.246930i
$650$	7.54184e7	−	5.24546e8i	0.274623	−	1.91005i
$651$	3.28064e7	+	1.11728e8i	0.118909	+	0.404968i
$652$	7.32307e7	+	4.70625e7i	0.264211	+	0.169798i
$653$	−8.51007e7	+	1.86344e8i	−0.305628	+	0.669232i	−0.998664	−	0.0516707i	$-0.983545\pi$
$653$	−8.51007e7	+	1.86344e8i	−0.305628	+	0.669232i	0.693036	+	0.720903i	$0.256273\pi$
$654$	−9.27550e7	+	3.15894e8i	−0.331592	+	1.12930i
$655$	−1.27096e8	+	1.10129e8i	−0.452281	+	0.391904i
$656$	3.84176e6	+	4.43363e6i	0.0136088	+	0.0157054i
$657$	−9.58392e7	−	2.81409e7i	−0.337946	−	0.0992298i
$658$	3.13750e8	+	1.43285e8i	1.10130	+	0.502948i
$659$	−1.03392e8	+	1.60881e8i	−0.361268	+	0.562144i	−0.973544	−	0.228500i	$-0.926618\pi$
$659$	−1.03392e8	+	1.60881e8i	−0.361268	+	0.562144i	0.612276	+	0.790644i	$0.290254\pi$
$660$	−3.76054e8	+	1.10419e8i	−1.30803	+	0.384073i
$661$	−2.75222e8	−	3.95709e7i	−0.952967	−	0.137016i	−0.351743	−	0.936097i	$-0.614411\pi$
$661$	−2.75222e8	−	3.95709e7i	−0.952967	−	0.137016i	−0.601224	+	0.799080i	$0.705320\pi$
$662$	1.12624e8	+	2.46611e8i	0.388200	+	0.850039i
$663$	−6.52623e6	+	938330.i	−0.0223935	+	0.00321970i
$664$	4.54476e6	+	7.07178e6i	0.0155241	+	0.0241560i
$665$	−1.38176e8	−	1.19730e8i	−0.469858	−	0.407134i
$666$		−	1.79153e8i		−	0.606458i
$667$	3.51622e7	+	2.37514e7i	0.118495	+	0.0800408i
$668$	5.04759e8			1.69338
$669$	−5.29017e7	+	6.10518e7i	−0.176681	+	0.203901i
$670$	−8.47077e8	+	5.44384e8i	−2.81643	+	1.81001i
$671$	1.58560e7	+	1.10281e8i	0.0524840	+	0.365034i
$672$	1.51820e8	−	6.93338e7i	0.500289	−	0.228474i
$673$	1.04790e7	−	7.28830e7i	0.0343775	−	0.239101i	−0.965387	−	0.260823i	$-0.916006\pi$
$673$	1.04790e7	−	7.28830e7i	0.0343775	−	0.239101i	0.999764	+	0.0217226i	$0.00691506\pi$
$674$	1.30853e8	+	4.45644e8i	0.427370	+	1.45549i
$675$	8.43954e7	+	5.42377e7i	0.274415	+	0.176356i
$676$	−4.37586e7	+	9.58179e7i	−0.141652	+	0.310175i
$677$	1.11934e8	−	3.81211e8i	0.360740	−	1.22857i	−0.556707	−	0.830709i	$-0.687935\pi$
$677$	1.11934e8	−	3.81211e8i	0.360740	−	1.22857i	0.917447	−	0.397858i	$-0.130246\pi$
$678$	2.42757e8	−	2.10350e8i	0.778903	−	0.674923i
$679$	−1.66295e8	−	1.91915e8i	−0.531215	−	0.613055i
$680$	549766.	+	161426.i	0.00174844	+	0.000513389i
$681$	2.55115e8	+	1.16507e8i	0.807782	+	0.368902i
$682$	−3.81623e8	+	5.93817e8i	−1.20304	+	1.87197i
$683$	−4.07859e8	+	1.19758e8i	−1.28011	+	0.375875i	−0.849944	−	0.526874i	$-0.823364\pi$
$683$	−4.07859e8	+	1.19758e8i	−1.28011	+	0.375875i	−0.430169	+	0.902748i	$0.641546\pi$
$684$	5.81446e7	+	8.35993e6i	0.181694	+	0.0261237i
$685$	3.63821e8	+	7.96656e8i	1.13192	+	2.47856i
$686$	−4.69602e8	+	6.75186e7i	−1.45465	+	0.209147i
$687$	−1.56895e8	−	2.44134e8i	−0.483882	−	0.752935i
$688$	−3.13891e8	−	2.71988e8i	−0.963859	−	0.835188i
$689$		−	1.65450e8i		−	0.505836i
$690$	4.32532e8	+	7.23252e7i	1.31665	+	0.220162i
$691$	5.37861e8			1.63018			0.815091	−	0.579333i	$-0.196687\pi$
$691$	5.37861e8			1.63018			0.815091	+	0.579333i	$0.196687\pi$
$692$	2.86708e8	−	3.30879e8i	0.865211	−	0.998507i
$693$	−9.23148e7	+	5.93271e7i	−0.277378	+	0.178260i
$694$	−1.06432e8	−	7.40254e8i	−0.318417	−	2.21464i
$695$	8.32841e8	−	3.80346e8i	2.48089	−	1.13299i
$696$	90703.8	−	630859.i	0.000269028	−	0.00187113i
$697$	−94592.8	−	322154.i	−0.000279357	−	0.000951403i
$698$	6.15449e8	+	3.95525e8i	1.80978	+	1.16307i
$699$	−1.06457e8	+	2.33108e8i	−0.311704	+	0.682535i
$700$	1.09009e8	−	3.71251e8i	0.317811	−	1.08237i
$701$	3.03913e8	−	2.63343e8i	0.882259	−	0.764481i	−0.0905986	−	0.995887i	$-0.528878\pi$
$701$	3.03913e8	−	2.63343e8i	0.882259	−	0.764481i	0.972857	+	0.231406i	$0.0743326\pi$
$702$	4.96367e7	+	5.72838e7i	0.143480	+	0.165585i
$703$	2.41052e8	+	7.07792e7i	0.693817	+	0.203723i
$704$	4.48838e8	+	2.04977e8i	1.28639	+	0.587473i
$705$	2.28141e8	−	3.54994e8i	0.651082	−	1.01310i
$706$	−7.99449e8	+	2.34740e8i	−2.27184	+	0.667071i
$707$	5.91899e7	+	8.51022e6i	0.167490	+	0.0240814i
$708$	3.40420e7	+	7.45417e7i	0.0959215	+	0.210039i
$709$	2.33352e8	−	3.35510e7i	0.654747	−	0.0941385i	0.193068	−	0.981185i	$-0.438156\pi$
$709$	2.33352e8	−	3.35510e7i	0.654747	−	0.0941385i	0.461679	+	0.887047i	$0.347247\pi$
$710$	−8.53721e8	−	1.32842e9i	−2.38529	−	3.71158i
$711$	−1.43395e8	−	1.24253e8i	−0.398956	−	0.345698i
$712$			1.83691e6i			0.00508917i
$713$	3.34252e8	−	2.04159e8i	0.922159	−	0.563248i
$714$	−9.70752e6			−0.0266694
$715$	4.64412e8	−	5.35961e8i	1.27053	−	1.46627i
$716$	−1.38536e8	+	8.90319e7i	−0.377420	+	0.242553i
$717$	2.99433e7	+	2.08260e8i	0.0812347	+	0.565000i
$718$	−3.82770e8	+	1.74805e8i	−1.03410	+	0.472260i
$719$	−4.71800e7	+	3.28144e8i	−0.126932	+	0.882832i	0.822479	+	0.568796i	$0.192590\pi$
$719$	−4.71800e7	+	3.28144e8i	−0.126932	+	0.882832i	−0.949411	+	0.314036i	$0.898319\pi$
$720$	−5.84630e7	−	1.99107e8i	−0.156633	−	0.533443i
$721$	−2.32228e8	−	1.49244e8i	−0.619597	−	0.398191i
$722$	1.51204e8	−	3.31091e8i	0.401746	−	0.879702i
$723$	−1.38591e7	+	4.71997e7i	−0.0366707	+	0.124889i
$724$	3.72284e8	−	3.22586e8i	0.980977	−	0.850021i
$725$	−6.04847e7	−	6.98031e7i	−0.158720	−	0.183173i
$726$	−3.39687e8	−	9.97412e7i	−0.887707	−	0.260654i
$727$	−4.69212e8	−	2.14282e8i	−1.22114	−	0.557676i	−0.302643	−	0.953104i	$-0.597869\pi$
$727$	−4.69212e8	−	2.14282e8i	−1.22114	−	0.557676i	−0.918497	+	0.395428i	$0.870596\pi$
$728$	−2.61192e6	+	4.06423e6i	−0.00676965	+	0.0105338i
$729$	−1.37677e7	+	4.04255e6i	−0.0355368	+	0.0104345i
$730$	9.40745e8	+	1.35259e8i	2.41826	+	0.347693i
$731$	9.87468e6	+	2.16225e7i	0.0252796	+	0.0553547i
$732$	5.56172e7	−	7.99655e6i	0.141800	−	0.0203878i
$733$	−6.38266e7	−	9.93162e7i	−0.162065	−	0.252179i	0.750718	−	0.660623i	$-0.229708\pi$
$733$	−6.38266e7	−	9.93162e7i	−0.162065	−	0.252179i	−0.912783	+	0.408444i	$0.866071\pi$
$734$	−1.45458e8	−	1.26040e8i	−0.367832	−	0.318728i
$735$			2.04090e8i			0.513997i
$736$	−3.57826e8	−	4.32567e8i	−0.897509	−	1.08498i
$737$	−8.47486e8			−2.11705
$738$	−2.52766e6	+	2.91707e6i	−0.00628853	+	0.00725736i
$739$	4.74662e8	−	3.05046e8i	1.17612	−	0.755845i	0.201449	−	0.979499i	$-0.435435\pi$
$739$	4.74662e8	−	3.05046e8i	1.17612	−	0.755845i	0.974669	+	0.223654i	$0.0717986\pi$
$740$	1.20305e8	+	8.36738e8i	0.296885	+	2.06488i
$741$	−9.66863e7	+	4.41552e7i	−0.237635	+	0.108524i
$742$	3.46674e7	−	2.41117e8i	0.0848612	−	0.590222i
$743$	−1.02806e8	−	3.50124e8i	−0.250640	−	0.853602i	−0.984661	−	0.174476i	$-0.944177\pi$
$743$	−1.02806e8	−	3.50124e8i	−0.250640	−	0.853602i	0.734021	−	0.679126i	$-0.237641\pi$
$744$	−4.94909e6	−	3.18059e6i	−0.0120173	−	0.00772304i
$745$	1.60696e8	−	3.51876e8i	0.388630	−	0.850982i
$746$	1.41221e8	−	4.80954e8i	0.340159	−	1.15848i
$747$	−1.31682e8	+	1.14103e8i	−0.315912	+	0.273739i
$748$	−1.91099e7	−	2.20539e7i	−0.0456617	−	0.0526965i
$749$	1.46333e8	+	4.29673e7i	0.348255	+	0.102257i
$750$	−3.56022e8	−	1.62590e8i	−0.843903	−	0.385398i
$751$	−8.47727e7	+	1.31909e8i	−0.200141	+	0.311426i	−0.926788	−	0.375586i	$-0.877441\pi$
$751$	−8.47727e7	+	1.31909e8i	−0.200141	+	0.311426i	0.726646	+	0.687012i	$0.241078\pi$
$752$	−5.26740e8	+	1.54665e8i	−1.23863	+	0.363695i
$753$	−2.67226e8	−	3.84213e7i	−0.625884	−	0.0899885i
$754$	−2.89895e7	−	6.34781e7i	−0.0676279	−	0.148085i
$755$	−8.28529e8	+	1.19124e8i	−1.92516	+	0.276796i
$756$	2.99200e7	+	4.65564e7i	0.0692463	+	0.107749i
$757$	4.08608e8	+	3.54061e8i	0.941931	+	0.816188i	0.983120	−	0.182964i	$-0.0585690\pi$
$757$	4.08608e8	+	3.54061e8i	0.941931	+	0.816188i	−0.0411887	+	0.999151i	$0.513114\pi$
$758$		−	5.74270e7i		−	0.131859i
$759$	2.73343e8	+	2.48027e8i	0.625148	+	0.567249i
$760$	9.23699e6			0.0210421
$761$	−3.95173e8	+	4.56054e8i	−0.896672	+	1.03481i	0.102525	+	0.994730i	$0.467308\pi$
$761$	−3.95173e8	+	4.56054e8i	−0.896672	+	1.03481i	−0.999196	+	0.0400839i	$0.987237\pi$
$762$	5.49940e8	−	3.53425e8i	1.24294	−	0.798790i
$763$	−6.19008e7	−	4.30530e8i	−0.139355	−	0.969236i
$764$	−1.64972e8	+	7.53404e7i	−0.369940	+	0.168946i
$765$	−1.69018e6	+	1.17555e7i	−0.00377529	+	0.0262577i
$766$	1.48145e8	+	5.04537e8i	0.329611	+	1.12255i
$767$	−1.24740e8	−	8.01658e7i	−0.276453	−	0.177665i
$768$	−1.12090e8	+	2.45442e8i	−0.247447	+	0.541833i
$769$	2.18897e7	−	7.45494e7i	0.0481349	−	0.163932i	−0.931918	−	0.362669i	$-0.881866\pi$
$769$	2.18897e7	−	7.45494e7i	0.0481349	−	0.163932i	0.980053	+	0.198736i	$0.0636838\pi$
$770$	7.89107e8	−	6.83765e8i	1.72848	−	1.49773i
$771$	−2.63271e8	−	3.03831e8i	−0.574433	−	0.662931i
$772$	2.84155e8	+	8.34355e7i	0.617595	+	0.181342i
$773$	−1.93855e8	−	8.85305e7i	−0.419699	−	0.191670i	0.194360	−	0.980930i	$-0.437737\pi$
$773$	−1.93855e8	−	8.85305e7i	−0.419699	−	0.191670i	−0.614059	+	0.789260i	$0.710464\pi$
$774$	1.47740e8	−	2.29888e8i	0.318621	−	0.495785i
$775$	−8.18015e8	+	2.40191e8i	−1.75734	+	0.516002i
$776$	1.26988e7	+	1.82582e6i	0.0271756	+	0.00390726i
$777$	9.83221e7	+	2.15295e8i	0.209599	+	0.458957i
$778$	1.99468e8	−	2.86792e7i	0.423579	−	0.0609015i
$779$	−2.92634e6	−	4.55347e6i	−0.00619030	−	0.00963230i
$780$	−2.70297e8	−	2.34214e8i	−0.569584	−	0.493547i
$781$		−	1.32906e9i		−	2.78991i
$782$	8.47988e6	+	3.15314e7i	0.0177325	+	0.0659361i
$783$	1.32106e7			0.0275193
$784$	1.73873e8	−	2.00660e8i	0.360814	−	0.416402i
$785$	−2.28672e8	+	1.46959e8i	−0.472721	+	0.303799i
$786$	2.04858e7	+	1.42482e8i	0.0421877	+	0.293422i
$787$	−3.62093e8	+	1.65362e8i	−0.742841	+	0.339244i	−0.750628	−	0.660726i	$-0.770249\pi$
$787$	−3.62093e8	+	1.65362e8i	−0.742841	+	0.339244i	0.00778658	+	0.999970i	$0.497521\pi$
$788$	−3.24477e7	+	2.25678e8i	−0.0663139	+	0.461223i
$789$	7.97946e7	+	2.71756e8i	0.162459	+	0.553283i
$790$	1.51879e9	+	9.76065e8i	3.08046	+	1.97969i
$791$	−1.76288e8	+	3.86017e8i	−0.356200	+	0.779968i
$792$	1.56192e6	−	5.31940e6i	0.00314400	−	0.0107075i
$793$	−7.68382e7	+	6.65807e7i	−0.154084	+	0.133515i
$794$	−9.74107e6	−	1.12418e7i	−0.0194601	−	0.0224581i
$795$	−2.85949e8	−	8.39621e7i	−0.569098	−	0.167102i
$796$	−5.55393e8	−	2.53639e8i	−1.10119	−	0.502895i
$797$	−5.01297e7	+	7.80033e7i	−0.0990193	+	0.154077i	−0.887228	−	0.461331i	$-0.847372\pi$
$797$	−5.01297e7	+	7.80033e7i	−0.0990193	+	0.154077i	0.788209	+	0.615408i	$0.211009\pi$
$798$	−1.50157e8	+	4.40899e7i	−0.295485	+	0.0867622i
$799$	3.10993e7	+	4.47141e6i	0.0609692	+	0.00876605i
$800$	5.07625e8	+	1.11154e9i	0.991454	+	2.17098i
$801$	−3.76870e7	+	5.41858e6i	−0.0733321	+	0.0105436i
$802$	4.53601e7	+	7.05817e7i	0.0879327	+	0.136826i
$803$	6.04546e8	+	5.23842e8i	1.16757	+	1.01170i
$804$			4.27406e8i			0.822381i
$805$	−5.59486e8	+	1.50465e8i	−1.07251	+	0.288435i
$806$	−6.44141e8			−1.23020
$807$	−1.02073e8	+	1.17799e8i	−0.194219	+	0.224141i
$808$	−2.54152e6	+	1.63334e6i	−0.00481792	+	0.00309629i
$809$	5.74450e7	+	3.99539e8i	0.108494	+	0.754595i	0.969339	+	0.245727i	$0.0790267\pi$
$809$	5.74450e7	+	3.99539e8i	0.108494	+	0.754595i	−0.860845	+	0.508868i	$0.830064\pi$
$810$	1.24193e8	−	5.67172e7i	0.233692	−	0.106723i
$811$	−7.25319e7	+	5.04471e8i	−0.135977	+	0.945743i	0.801574	+	0.597896i	$0.203996\pi$
$811$	−7.25319e7	+	5.04471e8i	−0.135977	+	0.945743i	−0.937551	+	0.347847i	$0.886913\pi$
$812$	−1.43547e7	−	4.88876e7i	−0.0268118	−	0.0913127i
$813$	−2.35027e8	−	1.51043e8i	−0.437367	−	0.281079i
$814$	−5.96012e8	+	1.30508e9i	−1.10505	+	2.41972i
$815$	−7.99336e7	+	2.72229e8i	−0.147658	+	0.502876i
$816$	1.16768e7	−	1.01180e7i	0.0214908	−	0.0186219i
$817$	2.50948e8	+	2.89609e8i	0.460169	+	0.531064i
$818$	1.36884e8	+	4.01929e7i	0.250089	+	0.0734327i
$819$	−9.10889e7	−	4.15989e7i	−0.165811	−	0.0757234i
$820$	9.84664e6	−	1.53217e7i	0.0178586	−	0.0277885i
$821$	5.43492e8	−	1.59584e8i	0.982119	−	0.288376i	0.249020	−	0.968498i	$-0.419891\pi$
$821$	5.43492e8	−	1.59584e8i	0.982119	−	0.288376i	0.733099	+	0.680122i	$0.238073\pi$
$822$	7.42012e8	+	1.06685e8i	1.33597	+	0.192083i
$823$	−3.33386e8	−	7.30013e8i	−0.598064	−	1.30958i	−0.930445	−	0.366432i	$-0.880579\pi$
$823$	−3.33386e8	−	7.30013e8i	−0.598064	−	1.30958i	0.332381	−	0.943145i	$-0.392148\pi$
$824$	1.38045e7	−	1.98479e6i	0.0246740	−	0.00354759i
$825$	−4.34361e8	−	6.75879e8i	−0.773551	−	1.20367i
$826$	−1.64991e8	−	1.42966e8i	−0.292766	−	0.253683i
$827$		−	8.02001e8i		−	1.41794i	−0.705237	−	0.708971i	$-0.749160\pi$
$827$		−	8.02001e8i		−	1.41794i	0.705237	−	0.708971i	$-0.250840\pi$
$828$	1.25086e8	−	1.37853e8i	0.220352	−	0.242843i
$829$	1.09372e8			0.191973			0.0959866	−	0.995383i	$-0.469399\pi$
$829$	1.09372e8			0.191973			0.0959866	+	0.995383i	$0.469399\pi$
$830$	1.08571e9	−	1.25297e9i	1.89879	−	2.19133i
$831$	2.98525e8	−	1.91850e8i	0.520209	−	0.334318i
$832$	6.40810e7	+	4.45693e8i	0.111265	+	0.773867i
$833$	−1.38226e7	+	6.31256e6i	−0.0239141	+	0.0109212i
$834$	1.11531e8	−	7.75715e8i	0.192264	−	1.33722i
$835$	4.63497e8	+	1.57852e9i	0.796136	+	2.71139i
$836$	−3.95758e8	−	2.54338e8i	−0.677346	−	0.435304i
$837$	5.06557e7	−	1.10921e8i	0.0863877	−	0.189163i
$838$	2.62461e8	−	8.93859e8i	0.445997	−	1.51893i
$839$	−6.83882e8	+	5.92587e8i	−1.15796	+	1.00338i	−0.158092	+	0.987424i	$0.550534\pi$
$839$	−6.83882e8	+	5.92587e8i	−1.15796	+	1.00338i	−0.999873	+	0.0159576i	$0.994920\pi$
$840$	5.69875e6	+	6.57671e6i	0.00961483	+	0.0110961i
$841$	5.59059e8	+	1.64154e8i	0.939874	+	0.275972i
$842$	−1.08883e9	−	4.97251e8i	−1.82399	−	0.832989i
$843$	2.30705e8	−	3.58984e8i	0.385101	−	0.599228i
$844$	4.43127e7	−	1.30114e7i	0.0737057	−	0.0216419i
$845$	−3.39831e8	−	4.88604e7i	−0.563240	−	0.0809816i
$846$	−1.50046e8	−	3.28555e8i	−0.247807	−	0.542622i
$847$	4.62957e8	−	6.65632e7i	0.761887	−	0.109543i
$848$	2.09612e8	+	3.26162e8i	0.343738	+	0.534867i
$849$	−2.50376e8	−	2.16952e8i	−0.409137	−	0.354519i
$850$		−	7.10732e7i		−	0.115731i
$851$	6.13422e8	−	5.07433e8i	0.995339	−	0.823360i
$852$	−6.70273e8			−1.08376
$853$	−3.36771e8	+	3.88654e8i	−0.542609	+	0.626204i	−0.959145	−	0.282915i	$-0.908699\pi$
$853$	−3.36771e8	+	3.88654e8i	−0.542609	+	0.626204i	0.416536	+	0.909119i	$0.363244\pi$
$854$	−1.25930e8	+	8.09303e7i	−0.202188	+	0.129938i
$855$	2.72476e7	+	1.89511e8i	0.0435943	+	0.303205i
$856$	−7.00879e6	+	3.20081e6i	−0.0111743	+	0.00510315i
$857$	−9.63166e7	+	6.69897e8i	−0.153024	+	1.06430i	0.758090	+	0.652149i	$0.226133\pi$
$857$	−9.63166e7	+	6.69897e8i	−0.153024	+	1.06430i	−0.911114	+	0.412154i	$0.864777\pi$
$858$	−1.71018e8	−	5.82432e8i	−0.270756	−	0.922112i
$859$	−7.40426e8	−	4.75843e8i	−1.16816	−	0.750730i	−0.194986	−	0.980806i	$-0.562466\pi$
$859$	−7.40426e8	−	4.75843e8i	−1.16816	−	0.750730i	−0.973173	+	0.230076i	$0.926103\pi$
$860$	−5.35650e8	+	1.17291e9i	−0.842143	+	1.84404i
$861$	1.43666e6	−	4.89280e6i	0.00225083	−	0.00766563i
$862$	4.75148e8	−	4.11718e8i	0.741834	−	0.642803i
$863$	−3.02478e8	−	3.49078e8i	−0.470610	−	0.543112i	0.469972	−	0.882682i	$-0.344264\pi$
$863$	−3.02478e8	−	3.49078e8i	−0.470610	−	0.543112i	−0.940581	+	0.339569i	$0.889719\pi$
$864$	−1.67698e8	−	4.92407e7i	−0.260009	−	0.0763454i
$865$	1.29802e9	+	5.92788e8i	2.00555	+	0.915906i
$866$	5.40016e8	−	8.40281e8i	0.831482	−	1.29381i
$867$	3.60178e8	−	1.05758e8i	0.552662	−	0.162276i
$868$	−4.65519e8	−	6.69315e7i	−0.711833	−	0.102346i
$869$	6.31231e8	+	1.38220e9i	0.961898	+	2.10626i
$870$	−1.24421e8	+	1.78890e7i	−0.188945	+	0.0271662i
$871$	−4.18116e8	−	6.50601e8i	−0.632765	−	0.984601i
$872$	1.66074e7	+	1.43904e7i	0.0250467	+	0.0217031i
$873$			2.65922e8i			0.399680i
$874$	2.74378e8	+	4.49216e8i	0.410974	+	0.672854i
$875$	5.17079e8			0.771849
$876$	2.64185e8	−	3.04886e8i	0.393003	−	0.453550i
$877$	5.69941e7	−	3.66279e7i	0.0844949	−	0.0543016i	−0.497711	−	0.867343i	$-0.665826\pi$
$877$	5.69941e7	−	3.66279e7i	0.0844949	−	0.0543016i	0.582206	+	0.813041i	$0.302190\pi$
$878$	7.00051e7	+	4.86896e8i	0.103430	+	0.719371i
$879$	−4.76552e7	+	2.17634e7i	−0.0701688	+	0.0320450i
$880$	−2.36507e8	+	1.64494e9i	−0.347053	+	2.41381i
$881$	2.04450e8	+	6.96292e8i	0.298992	+	1.01827i	0.962765	+	0.270339i	$0.0871357\pi$
$881$	2.04450e8	+	6.96292e8i	0.298992	+	1.01827i	−0.663774	+	0.747934i	$0.731046\pi$
$882$	1.46960e8	+	9.44453e7i	0.214187	+	0.137649i
$883$	3.13691e8	−	6.86889e8i	0.455639	−	0.997710i	−0.532821	−	0.846228i	$-0.678868\pi$
$883$	3.13691e8	−	6.86889e8i	0.455639	−	0.997710i	0.988460	−	0.151482i	$-0.0484045\pi$
$884$	7.50241e6	−	2.55509e7i	0.0108604	−	0.0369870i
$885$	−2.01854e8	+	1.74907e8i	−0.291211	+	0.252335i
$886$	−9.26193e8	−	1.06888e9i	−1.33168	−	1.53684i
$887$	−6.52041e8	−	1.91457e8i	−0.934338	−	0.274346i	−0.221086	−	0.975254i	$-0.570960\pi$
$887$	−6.52041e8	−	1.91457e8i	−0.934338	−	0.274346i	−0.713252	+	0.700908i	$0.752778\pi$
$888$	−1.08771e7	−	4.96739e6i	−0.0155336	−	0.00709396i
$889$	−4.66921e8	+	7.26544e8i	−0.664566	+	1.03409i
$890$	3.47609e8	−	1.02067e8i	0.493083	−	0.144782i
$891$	1.13743e8	+	1.63538e7i	0.160802	+	0.0231199i
$892$	−1.35538e8	−	2.96787e8i	−0.190971	−	0.418167i
$893$	5.01355e8	−	7.20840e7i	0.704030	−	0.101224i
$894$	−1.79011e8	−	2.78547e8i	−0.250535	−	0.389840i
$895$	−4.05640e8	−	3.51489e8i	−0.565811	−	0.490278i
$896$		−	2.22830e7i		−	0.0309777i
$897$	−5.55497e7	+	3.32208e8i	−0.0769669	+	0.460291i
$898$	9.22103e8			1.27336
$899$	−7.35190e7	+	8.48455e7i	−0.101186	+	0.116775i
$900$	−3.40861e8	+	2.19058e8i	−0.467573	+	0.300491i
$901$	−3.15789e6	−	2.19636e7i	−0.00431740	−	0.0300282i
$902$	2.81181e7	−	1.28411e7i	0.0383147	−	0.0174977i
$903$	−5.13790e7	+	3.57349e8i	−0.0697786	+	0.485321i
$904$	−6.04024e6	−	2.05712e7i	−0.00817615	−	0.0278454i
$905$	1.35067e9	+	8.68022e8i	1.82223	+	1.17108i
$906$	−2.97633e8	+	6.51726e8i	−0.400218	+	0.876356i
$907$	3.40632e8	−	1.16009e9i	0.456524	−	1.55478i	−0.334138	−	0.942524i	$-0.608445\pi$
$907$	3.40632e8	−	1.16009e9i	0.456524	−	1.55478i	0.790662	−	0.612253i	$-0.209737\pi$
$908$	−8.56064e8	+	7.41783e8i	−1.14353	+	0.990877i
$909$	−4.10076e7	−	4.73252e7i	−0.0545974	−	0.0630088i
$910$	9.14229e8	+	2.68442e8i	1.21320	+	0.356226i
$911$	−1.07617e9	−	4.91471e8i	−1.42340	−	0.650044i	−0.452990	−	0.891516i	$-0.649643\pi$
$911$	−1.07617e9	−	4.91471e8i	−1.42340	−	0.650044i	−0.970408	+	0.241472i	$0.922370\pi$
$912$	1.34663e8	−	2.09539e8i	0.177526	−	0.276236i
$913$	1.33888e9	−	3.93130e8i	1.75926	−	0.516564i
$914$	1.01310e9	+	1.45662e8i	1.32683	+	0.190769i
$915$	7.60782e7	+	1.66588e8i	0.0993109	+	0.217461i
$916$	1.16015e9	−	1.66805e8i	1.50949	−	0.217031i
$917$	−1.02815e8	−	1.59984e8i	−0.133337	−	0.207476i
$918$	7.68264e6	+	6.65705e6i	0.00993076	+	0.00860505i
$919$			3.12207e8i			0.402250i	0.979566	+	0.201125i	$0.0644598\pi$
$919$			3.12207e8i			0.402250i	−0.979566	+	0.201125i	$0.935540\pi$
$920$	1.63840e7	−	2.42554e7i	0.0210405	−	0.0311490i
$921$	2.29264e8			0.293466
$922$	4.45087e8	−	5.13658e8i	0.567874	−	0.655362i
$923$	1.02029e9	−	6.55703e8i	1.29754	−	0.833878i
$924$	−6.30744e7	−	4.38692e8i	−0.0799534	−	0.556088i
$925$	−1.57628e9	+	7.19862e8i	−1.99162	+	0.909544i
$926$	1.30255e8	−	9.05944e8i	0.164045	−	1.14095i
$927$	8.14423e7	+	2.77367e8i	0.102238	+	0.348189i
$928$	1.35369e8	+	8.69962e7i	0.169385	+	0.108857i
$929$	7.06316e7	−	1.54662e8i	0.0880952	−	0.192902i	−0.860456	−	0.509524i	$-0.829822\pi$
$929$	7.06316e7	−	1.54662e8i	0.0880952	−	0.192902i	0.948552	+	0.316622i	$0.102549\pi$
$930$	−3.26886e8	+	1.11327e9i	−0.406395	+	1.38405i
$931$	−1.85138e8	+	1.60423e8i	−0.229428	+	0.198800i
$932$	−6.77795e8	−	7.82217e8i	−0.837241	−	0.966228i
$933$	−5.01389e7	−	1.47221e7i	−0.0617347	−	0.0181270i
$934$	9.44047e8	+	4.31132e8i	1.15865	+	0.529139i
$935$	5.14213e7	−	8.00131e7i	0.0629083	−	0.0978872i
$936$	4.85420e6	−	1.42532e6i	0.00591957	−	0.00173814i
$937$	1.13512e9	+	1.63206e8i	1.37983	+	0.198389i	0.791962	−	0.610571i	$-0.209060\pi$
$937$	1.13512e9	+	1.63206e8i	1.37983	+	0.198389i	0.587864	+	0.808960i	$0.299969\pi$
$938$	−4.73013e8	−	1.03575e9i	−0.573145	−	1.25501i
$939$	−3.70361e8	+	5.32498e7i	−0.447330	+	0.0643164i
$940$	9.21428e8	+	1.43377e9i	1.10937	+	1.72622i
$941$	−8.97032e8	−	7.77283e8i	−1.07656	−	0.932846i	−0.0786161	−	0.996905i	$-0.525050\pi$
$941$	−8.97032e8	−	7.77283e8i	−1.07656	−	0.932846i	−0.997946	+	0.0640585i	$0.979596\pi$
$942$			2.32667e8i			0.278345i
$943$	−1.71475e7	−	392422.i	−0.0204487	−	0.000467970i
$944$	3.47472e8			0.413051
$945$	−1.18121e8	+	1.36319e8i	−0.139969	+	0.161533i
$946$	−1.84105e9	+	1.18317e9i	−2.17467	+	1.39757i
$947$	−2.10211e8	−	1.46205e9i	−0.247517	−	1.72152i	−0.612473	−	0.790492i	$-0.709825\pi$
$947$	−2.10211e8	−	1.46205e9i	−0.247517	−	1.72152i	0.364956	−	0.931025i	$-0.381084\pi$
$948$	6.97077e8	−	3.18344e8i	0.818193	−	0.373656i
$949$	−1.03886e8	+	7.22543e8i	−0.121551	+	0.845405i
$950$	−3.22803e8	−	1.09936e9i	−0.376501	−	1.28225i
$951$	2.24931e8	+	1.44554e8i	0.261522	+	0.168070i
$952$	−269162.	+	589382.i	−0.000311962	+	0.000683102i
$953$	−7.06753e7	+	2.40698e8i	−0.0816562	+	0.278095i	−0.990192	−	0.139711i	$-0.955383\pi$
$953$	−7.06753e7	+	2.40698e8i	−0.0816562	+	0.278095i	0.908536	+	0.417806i	$0.137201\pi$
$954$	−1.92785e8	+	1.67049e8i	−0.222038	+	0.192397i
$955$	−3.87097e8	−	4.46734e8i	−0.444437	−	0.512907i
$956$	−8.15359e8	−	2.39411e8i	−0.933201	−	0.274013i
$957$	−9.62363e7	−	4.39496e7i	−0.109800	−	0.0501441i
$958$	−1.26821e9	+	1.97338e9i	−1.44244	+	2.24447i
$959$	−9.50259e8	+	2.79021e8i	−1.07742	+	0.316360i
$960$	8.02814e8	+	1.15427e8i	0.907405	+	0.130465i
$961$	6.18004e7	+	1.35324e8i	0.0696340	+	0.152477i
$962$	−1.29594e9	+	1.86328e8i	−1.45566	+	0.209292i
$963$	−8.63444e7	−	1.34354e8i	−0.0966841	−	0.150443i
$964$	−1.50153e8	−	1.30108e8i	−0.167611	−	0.145236i
$965$			9.65249e8i			1.07413i
$966$	−1.50563e8	+	4.72499e8i	−0.167027	+	0.524167i
$967$	−1.20170e9			−1.32897			−0.664485	−	0.747302i	$-0.731349\pi$
$967$	−1.20170e9			−1.32897			−0.664485	+	0.747302i	$0.731349\pi$
$968$	−1.54742e7	+	1.78582e7i	−0.0170602	+	0.0196885i
$969$	−1.19924e7	+	7.70703e6i	−0.0131806	+	0.00847063i
$970$	−3.60096e8	−	2.50453e9i	−0.394551	−	2.74417i
$971$	7.83786e8	−	3.57943e8i	0.856131	−	0.390982i	0.0615234	−	0.998106i	$-0.480404\pi$
$971$	7.83786e8	−	3.57943e8i	0.856131	−	0.390982i	0.794607	+	0.607124i	$0.207677\pi$
$972$	8.24760e6	−	5.73633e7i	0.00898108	−	0.0624648i
$973$	2.91695e8	+	9.93420e8i	0.316657	+	1.07844i
$974$	−7.59183e8	−	4.87897e8i	−0.821617	−	0.528021i
$975$	3.04565e8	−	6.66904e8i	0.328599	−	0.719531i
$976$	6.71236e7	−	2.28602e8i	0.0721981	−	0.245884i
$977$	−4.18825e8	+	3.62914e8i	−0.449106	+	0.389153i	−0.849839	−	0.527042i	$-0.823301\pi$
$977$	−4.18825e8	+	3.62914e8i	−0.449106	+	0.389153i	0.400733	+	0.916195i	$0.368756\pi$
$978$	1.59034e8	+	1.83535e8i	0.170009	+	0.196201i
$979$	2.92568e8	+	8.59057e7i	0.311802	+	0.0915533i
$980$	−7.49802e8	−	3.42423e8i	−0.796652	−	0.363819i
$981$	−2.46252e8	+	3.83175e8i	−0.260839	+	0.405873i
$982$	9.41064e8	−	2.76321e8i	0.993767	−	0.291796i
$983$	−8.76273e8	−	1.25989e8i	−0.922527	−	0.132639i	−0.335346	−	0.942095i	$-0.608853\pi$
$983$	−8.76273e8	−	1.25989e8i	−0.922527	−	0.132639i	−0.587181	+	0.809456i	$0.699762\pi$
$984$	107022.	+	234346.i	0.000112328	+	0.000245965i
$985$	−7.35556e8	+	1.05757e8i	−0.769674	+	0.110662i
$986$	−5.05995e6	−	7.87343e6i	−0.00527856	−	0.00821360i
$987$	3.60634e8	+	3.12491e8i	0.375072	+	0.325002i
$988$		−	4.29297e8i		−	0.445130i
$989$	1.20560e9	−	1.45271e8i	1.24628	−	0.150172i
$990$	−1.09341e9			−1.12688
$991$	4.61052e8	−	5.32082e8i	0.473728	−	0.546711i	−0.467717	−	0.883878i	$-0.654923\pi$
$991$	4.61052e8	−	5.32082e8i	0.473728	−	0.546711i	0.941445	+	0.337167i	$0.109469\pi$
$992$	1.24952e9	−	8.03015e8i	1.27999	−	0.822599i
$993$	5.33787e7	+	3.71257e8i	0.0545155	+	0.379164i
$994$	1.62430e9	−	7.41795e8i	1.65390	−	0.755309i
$995$	2.83211e8	−	1.96978e9i	0.287502	−	1.99962i
$996$	−1.98265e8	−	6.75227e8i	−0.200663	−	0.683395i
$997$	−3.39980e7	−	2.18492e7i	−0.0343059	−	0.0220470i	0.523375	−	0.852102i	$-0.324673\pi$
$997$	−3.39980e7	−	2.18492e7i	−0.0343059	−	0.0220470i	−0.557681	+	0.830055i	$0.688309\pi$
$998$	−4.54249e8	+	9.94667e8i	−0.456985	+	1.00066i
$999$	6.98282e7	−	2.37813e8i	0.0700381	−	0.238528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.7.5	✓	240
23.10	odd	22	inner	69.7.f.a.10.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.7.5	✓	240	1.1	even	1	trivial
69.7.f.a.10.5	yes	240	23.10	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.37873 + 8.51551i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(-8.96008 - 62.3187i) q^{4} +(186.661 - 85.2451i) q^{5} +(24.9969 - 173.857i) q^{6} +(65.3761 + 222.650i) q^{7} +(-9.86246 - 6.33822i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})\)	\(q+(-7.37873 + 8.51551i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(-8.96008 - 62.3187i) q^{4} +(186.661 - 85.2451i) q^{5} +(24.9969 - 173.857i) q^{6} +(65.3761 + 222.650i) q^{7} +(-9.86246 - 6.33822i) q^{8} +(100.946 - 221.041i) q^{9} +(-651.414 + 2218.51i) q^{10} +(-1470.73 + 1274.40i) q^{11} +(642.708 + 741.724i) q^{12} +(-1703.94 - 500.321i) q^{13} +(-2378.37 - 1086.17i) q^{14} +(-1729.41 + 2691.02i) q^{15} +(3992.94 - 1172.43i) q^{16} +(-235.748 - 33.8954i) q^{17} +(1137.42 + 2490.60i) q^{18} +(-3800.51 + 546.430i) q^{19} +(-6984.86 - 10868.7i) q^{20} +(-2733.78 - 2368.83i) q^{21} -21927.5i q^{22} +(-5306.25 + 10949.0i) q^{23} +182.752 q^{24} +(17343.3 - 20015.2i) q^{25} +(16833.4 - 10818.2i) q^{26} +(539.088 + 3749.44i) q^{27} +(13289.5 - 6069.12i) q^{28} +(496.323 - 3452.00i) q^{29} +(-10154.5 - 34583.2i) q^{30} +(-27080.9 - 17403.9i) q^{31} +(-19167.3 + 41970.4i) q^{32} +(8546.66 - 29107.2i) q^{33} +(2028.16 - 1757.41i) q^{34} +(31183.0 + 35987.1i) q^{35} +(-14679.4 - 4310.27i) q^{36} +(-59518.2 - 27181.1i) q^{37} +(23389.8 - 36395.2i) q^{38} +(26561.7 - 7799.23i) q^{39} +(-2381.24 - 342.370i) q^{40} +(585.616 + 1282.32i) q^{41} +(40343.6 - 5800.53i) q^{42} +(-53958.4 - 83960.9i) q^{43} +(92596.7 + 80235.5i) q^{44} -49864.7i q^{45} +(-54082.6 - 125975. i) q^{46} -131918. q^{47} +(-42481.8 + 49026.6i) q^{48} +(53673.4 - 34493.8i) q^{49} +(42468.4 + 295374. i) q^{50} +(3377.22 - 1542.33i) q^{51} +(-15911.9 + 110670. i) q^{52} +(26247.8 + 89391.8i) q^{53} +(-35906.2 - 23075.5i) q^{54} +(-165892. + 363253. i) q^{55} +(766.439 - 2610.25i) q^{56} +(45234.1 - 39195.6i) q^{57} +(25733.3 + 29697.8i) q^{58} +(80114.4 + 23523.7i) q^{59} +(183197. + 83663.1i) q^{60} +(30952.6 - 48163.1i) q^{61} +(348026. - 102190. i) q^{62} +(55814.2 + 8024.88i) q^{63} +(-105329. - 230639. i) q^{64} +(-360708. + 51862.0i) q^{65} +(184800. + 287554. i) q^{66} +(329120. + 285184. i) q^{67} +14995.2i q^{68} +(-22689.8 - 188303. i) q^{69} -536540. q^{70} +(-447235. + 516137. i) q^{71} +(-2396.58 + 1540.19i) q^{72} +(-58498.6 - 406866. i) q^{73} +(670629. - 306266. i) q^{74} +(-58753.8 + 408642. i) q^{75} +(68105.7 + 231947. i) q^{76} +(-379896. - 244144. i) q^{77} +(-129577. + 283735. i) q^{78} +(219982. - 749190. i) q^{79} +(645380. - 559225. i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(-15240.7 - 4475.08i) q^{82} +(-652242. - 297869. i) q^{83} +(-123128. + 191590. i) q^{84} +(-46894.2 + 13769.4i) q^{85} +(1.11311e6 + 160042. i) q^{86} +(22583.9 + 49451.9i) q^{87} +(22582.5 - 3246.87i) q^{88} +(-84710.6 - 131812. i) q^{89} +(424624. + 367938. i) q^{90} -412091. i q^{91} +(729869. + 232575. i) q^{92} +501811. q^{93} +(973386. - 1.12335e6i) q^{94} +(-662825. + 425972. i) q^{95} +(-102360. - 711931. i) q^{96} +(-995439. + 454602. i) q^{97} +(-102309. + 711577. i) q^{98} +(133229. + 453737. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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