LMFDB - Embedded newform 29.7.c.a.12.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,7,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, 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:	$6.67156842498$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.8
Character	$\chi$	$=$	29.12
Dual form			29.7.c.a.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.260765 + 0.260765i) q^{2} +(29.0542 + 29.0542i) q^{3} -63.8640i q^{4} -194.251i q^{5} +15.1526i q^{6} +282.863 q^{7} +(33.3424 - 33.3424i) q^{8} +959.292i q^{9} +O(q^{10})$	\(q+(0.260765 + 0.260765i) q^{2} +(29.0542 + 29.0542i) q^{3} -63.8640i q^{4} -194.251i q^{5} +15.1526i q^{6} +282.863 q^{7} +(33.3424 - 33.3424i) q^{8} +959.292i q^{9} +(50.6540 - 50.6540i) q^{10} +(664.299 + 664.299i) q^{11} +(1855.52 - 1855.52i) q^{12} -386.631i q^{13} +(73.7609 + 73.7609i) q^{14} +(5643.82 - 5643.82i) q^{15} -4069.91 q^{16} +(-1667.75 - 1667.75i) q^{17} +(-250.150 + 250.150i) q^{18} +(8741.21 + 8741.21i) q^{19} -12405.7 q^{20} +(8218.37 + 8218.37i) q^{21} +346.452i q^{22} -14067.5 q^{23} +1937.48 q^{24} -22108.6 q^{25} +(100.820 - 100.820i) q^{26} +(-6690.94 + 6690.94i) q^{27} -18064.8i q^{28} +(20921.6 + 12534.4i) q^{29} +2943.42 q^{30} +(-25934.6 - 25934.6i) q^{31} +(-3195.21 - 3195.21i) q^{32} +38601.3i q^{33} -869.783i q^{34} -54946.6i q^{35} +61264.2 q^{36} +(-43954.6 + 43954.6i) q^{37} +4558.80i q^{38} +(11233.3 - 11233.3i) q^{39} +(-6476.82 - 6476.82i) q^{40} +(-63016.8 + 63016.8i) q^{41} +4286.12i q^{42} +(55909.5 + 55909.5i) q^{43} +(42424.8 - 42424.8i) q^{44} +186344. q^{45} +(-3668.31 - 3668.31i) q^{46} +(83994.4 - 83994.4i) q^{47} +(-118248. - 118248. i) q^{48} -37637.2 q^{49} +(-5765.15 - 5765.15i) q^{50} -96910.4i q^{51} -24691.8 q^{52} +80337.4 q^{53} -3489.52 q^{54} +(129041. - 129041. i) q^{55} +(9431.36 - 9431.36i) q^{56} +507938. i q^{57} +(2187.08 + 8724.14i) q^{58} -199137. q^{59} +(-360437. - 360437. i) q^{60} +(111148. + 111148. i) q^{61} -13525.7i q^{62} +271349. i q^{63} +258808. i q^{64} -75103.7 q^{65} +(-10065.9 + 10065.9i) q^{66} +460175. i q^{67} +(-106509. + 106509. i) q^{68} +(-408720. - 408720. i) q^{69} +(14328.2 - 14328.2i) q^{70} -509411. i q^{71} +(31985.1 + 31985.1i) q^{72} +(58913.5 - 58913.5i) q^{73} -22923.6 q^{74} +(-642348. - 642348. i) q^{75} +(558249. - 558249. i) q^{76} +(187906. + 187906. i) q^{77} +5858.48 q^{78} +(502900. + 502900. i) q^{79} +790585. i q^{80} +310524. q^{81} -32865.1 q^{82} -184758. q^{83} +(524858. - 524858. i) q^{84} +(-323963. + 323963. i) q^{85} +29158.5i q^{86} +(243682. + 972036. i) q^{87} +44298.7 q^{88} +(-575875. - 575875. i) q^{89} +(48591.9 + 48591.9i) q^{90} -109364. i q^{91} +898408. i q^{92} -1.50702e6i q^{93} +43805.6 q^{94} +(1.69799e6 - 1.69799e6i) q^{95} -185668. i q^{96} +(-494744. + 494744. i) q^{97} +(-9814.47 - 9814.47i) q^{98} +(-637256. + 637256. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) $ 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.260765	+	0.260765i	0.0325956	+	0.0325956i	0.723217	−	0.690621i	$-0.242663\pi$
$2$	0.260765	+	0.260765i	0.0325956	+	0.0325956i	−0.690621	+	0.723217i	$0.742663\pi$
$3$	29.0542	+	29.0542i	1.07608	+	1.07608i	0.996857	+	0.0792242i	$0.0252443\pi$
$3$	29.0542	+	29.0542i	1.07608	+	1.07608i	0.0792242	+	0.996857i	$0.474756\pi$
$4$		−	63.8640i		−	0.997875i
$5$		−	194.251i		−	1.55401i	−0.629493	−	0.777006i	$-0.716738\pi$
$5$		−	194.251i		−	1.55401i	0.629493	−	0.777006i	$-0.283262\pi$
$6$			15.1526i			0.0701510i
$7$	282.863			0.824675			0.412337	−	0.911031i	$-0.364712\pi$
$7$	282.863			0.824675			0.412337	+	0.911031i	$0.364712\pi$
$8$	33.3424	−	33.3424i	0.0651220	−	0.0651220i
$9$			959.292i			1.31590i
$10$	50.6540	−	50.6540i	0.0506540	−	0.0506540i
$11$	664.299	+	664.299i	0.499098	+	0.499098i	0.911157	−	0.412059i	$-0.135190\pi$
$11$	664.299	+	664.299i	0.499098	+	0.499098i	−0.412059	+	0.911157i	$0.635190\pi$
$12$	1855.52	−	1855.52i	1.07379	−	1.07379i
$13$		−	386.631i		−	0.175981i	−0.996121	−	0.0879907i	$-0.971955\pi$
$13$		−	386.631i		−	0.175981i	0.996121	−	0.0879907i	$-0.0280446\pi$
$14$	73.7609	+	73.7609i	0.0268808	+	0.0268808i
$15$	5643.82	−	5643.82i	1.67224	−	1.67224i
$16$	−4069.91			−0.993630
$17$	−1667.75	−	1667.75i	−0.339457	−	0.339457i	0.516706	−	0.856163i	$-0.327158\pi$
$17$	−1667.75	−	1667.75i	−0.339457	−	0.339457i	−0.856163	+	0.516706i	$0.827158\pi$
$18$	−250.150	+	250.150i	−0.0428926	+	0.0428926i
$19$	8741.21	+	8741.21i	1.27441	+	1.27441i	0.943747	+	0.330667i	$0.107274\pi$
$19$	8741.21	+	8741.21i	1.27441	+	1.27441i	0.330667	+	0.943747i	$0.392726\pi$
$20$	−12405.7			−1.55071
$21$	8218.37	+	8218.37i	0.887417	+	0.887417i
$22$			346.452i			0.0325368i
$23$	−14067.5			−1.15620			−0.578101	−	0.815965i	$-0.696206\pi$
$23$	−14067.5			−1.15620			−0.578101	+	0.815965i	$0.696206\pi$
$24$	1937.48			0.140153
$25$	−22108.6			−1.41495
$26$	100.820	−	100.820i	0.00573622	−	0.00573622i
$27$	−6690.94	+	6690.94i	−0.339935	+	0.339935i
$28$		−	18064.8i		−	0.822923i
$29$	20921.6	+	12534.4i	0.857828	+	0.513937i
$29$	20921.6	+	12534.4i	0.857828	+	0.513937i
$30$	2943.42			0.109016
$31$	−25934.6	−	25934.6i	−0.870552	−	0.870552i	0.121980	−	0.992533i	$-0.461076\pi$
$31$	−25934.6	−	25934.6i	−0.870552	−	0.870552i	−0.992533	+	0.121980i	$0.961076\pi$
$32$	−3195.21	−	3195.21i	−0.0975099	−	0.0975099i
$33$			38601.3i			1.07414i
$34$		−	869.783i		−	0.0221296i
$35$		−	54946.6i		−	1.28155i
$36$	61264.2			1.31310
$37$	−43954.6	+	43954.6i	−0.867759	+	0.867759i	−0.992224	−	0.124465i	$-0.960279\pi$
$37$	−43954.6	+	43954.6i	−0.867759	+	0.867759i	0.124465	+	0.992224i	$0.460279\pi$
$38$			4558.80i			0.0830807i
$39$	11233.3	−	11233.3i	0.189370	−	0.189370i
$40$	−6476.82	−	6476.82i	−0.101200	−	0.101200i
$41$	−63016.8	+	63016.8i	−0.914334	+	0.914334i	−0.996610	−	0.0822757i	$-0.973781\pi$
$41$	−63016.8	+	63016.8i	−0.914334	+	0.914334i	0.0822757	+	0.996610i	$0.473781\pi$
$42$			4286.12i			0.0578518i
$43$	55909.5	+	55909.5i	0.703202	+	0.703202i	0.965097	−	0.261894i	$-0.0843472\pi$
$43$	55909.5	+	55909.5i	0.703202	+	0.703202i	−0.261894	+	0.965097i	$0.584347\pi$
$44$	42424.8	−	42424.8i	0.498037	−	0.498037i
$45$	186344.			2.04493
$46$	−3668.31	−	3668.31i	−0.0376871	−	0.0376871i
$47$	83994.4	−	83994.4i	0.809015	−	0.809015i	−0.175469	−	0.984485i	$-0.556144\pi$
$47$	83994.4	−	83994.4i	0.809015	−	0.809015i	0.984485	+	0.175469i	$0.0561443\pi$
$48$	−118248.	−	118248.i	−1.06923	−	1.06923i
$49$	−37637.2			−0.319911
$50$	−5765.15	−	5765.15i	−0.0461212	−	0.0461212i
$51$		−	96910.4i		−	0.730567i
$52$	−24691.8			−0.175607
$53$	80337.4			0.539622			0.269811	−	0.962913i	$-0.413039\pi$
$53$	80337.4			0.539622			0.269811	+	0.962913i	$0.413039\pi$
$54$	−3489.52			−0.0221608
$55$	129041.	−	129041.i	0.775603	−	0.775603i
$56$	9431.36	−	9431.36i	0.0537044	−	0.0537044i
$57$			507938.i			2.74275i
$58$	2187.08	+	8724.14i	0.0112093	+	0.0447135i
$59$	−199137.			−0.969608			−0.484804	−	0.874623i	$-0.661109\pi$
$59$	−199137.			−0.969608			−0.484804	+	0.874623i	$0.661109\pi$
$60$	−360437.	−	360437.i	−1.66869	−	1.66869i
$61$	111148.	+	111148.i	0.489678	+	0.489678i	0.908205	−	0.418526i	$-0.137453\pi$
$61$	111148.	+	111148.i	0.489678	+	0.489678i	−0.418526	+	0.908205i	$0.637453\pi$
$62$		−	13525.7i		−	0.0567524i
$63$			271349.i			1.08519i
$64$			258808.i			0.987273i
$65$	−75103.7			−0.273477
$66$	−10065.9	+	10065.9i	−0.0350122	+	0.0350122i
$67$			460175.i			1.53002i	0.644016	+	0.765012i	$0.277267\pi$
$67$			460175.i			1.53002i	−0.644016	+	0.765012i	$0.722733\pi$
$68$	−106509.	+	106509.i	−0.338736	+	0.338736i
$69$	−408720.	−	408720.i	−1.24417	−	1.24417i
$70$	14328.2	−	14328.2i	0.0417730	−	0.0417730i
$71$		−	509411.i		−	1.42329i	−0.702540	−	0.711644i	$-0.747951\pi$
$71$		−	509411.i		−	1.42329i	0.702540	−	0.711644i	$-0.252049\pi$
$72$	31985.1	+	31985.1i	0.0856940	+	0.0856940i
$73$	58913.5	−	58913.5i	0.151442	−	0.151442i	−0.627320	−	0.778762i	$-0.715848\pi$
$73$	58913.5	−	58913.5i	0.151442	−	0.151442i	0.778762	+	0.627320i	$0.215848\pi$
$74$	−22923.6			−0.0565703
$75$	−642348.	−	642348.i	−1.52260	−	1.52260i
$76$	558249.	−	558249.i	1.27171	−	1.27171i
$77$	187906.	+	187906.i	0.411593	+	0.411593i
$78$	5858.48			0.0123453
$79$	502900.	+	502900.i	1.02000	+	1.02000i	0.999796	+	0.0202050i	$0.00643188\pi$
$79$	502900.	+	502900.i	1.02000	+	1.02000i	0.0202050	+	0.999796i	$0.493568\pi$
$80$			790585.i			1.54411i
$81$	310524.			0.584306
$82$	−32865.1			−0.0596066
$83$	−184758.			−0.323124			−0.161562	−	0.986863i	$-0.551653\pi$
$83$	−184758.			−0.323124			−0.161562	+	0.986863i	$0.551653\pi$
$84$	524858.	−	524858.i	0.885531	−	0.885531i
$85$	−323963.	+	323963.i	−0.527520	+	0.527520i
$86$			29158.5i			0.0458426i
$87$	243682.	+	972036.i	0.370055	+	1.47613i
$88$	44298.7			0.0650044
$89$	−575875.	−	575875.i	−0.816880	−	0.816880i	0.168774	−	0.985655i	$-0.446019\pi$
$89$	−575875.	−	575875.i	−0.816880	−	0.816880i	−0.985655	+	0.168774i	$0.946019\pi$
$90$	48591.9	+	48591.9i	0.0666556	+	0.0666556i
$91$		−	109364.i		−	0.145127i
$92$			898408.i			1.15375i
$93$		−	1.50702e6i		−	1.87357i
$94$	43805.6			0.0527407
$95$	1.69799e6	−	1.69799e6i	1.98046	−	1.98046i
$96$		−	185668.i		−	0.209857i
$97$	−494744.	+	494744.i	−0.542082	+	0.542082i	−0.924139	−	0.382057i	$-0.875216\pi$
$97$	−494744.	+	494744.i	−0.542082	+	0.542082i	0.382057	+	0.924139i	$0.375216\pi$
$98$	−9814.47	−	9814.47i	−0.0104277	−	0.0104277i
$99$	−637256.	+	637256.i	−0.656763	+	0.656763i
$100$			1.41195e6i			1.41195i
$101$	−368796.	−	368796.i	−0.357950	−	0.357950i	0.505107	−	0.863057i	$-0.331453\pi$
$101$	−368796.	−	368796.i	−0.357950	−	0.357950i	−0.863057	+	0.505107i	$0.831453\pi$
$102$	25270.8	−	25270.8i	0.0238133	−	0.0238133i
$103$	1.42779e6			1.30663			0.653317	−	0.757085i	$-0.273377\pi$
$103$	1.42779e6			1.30663			0.653317	+	0.757085i	$0.273377\pi$
$104$	−12891.2	−	12891.2i	−0.0114603	−	0.0114603i
$105$	1.59643e6	−	1.59643e6i	1.37906	−	1.37906i
$106$	20949.2	+	20949.2i	0.0175893	+	0.0175893i
$107$	−1.09878e6			−0.896930			−0.448465	−	0.893800i	$-0.648029\pi$
$107$	−1.09878e6			−0.896930			−0.448465	+	0.893800i	$0.648029\pi$
$108$	427310.	+	427310.i	0.339213	+	0.339213i
$109$			697035.i			0.538239i	0.963107	+	0.269119i	$0.0867326\pi$
$109$			697035.i			0.538239i	−0.963107	+	0.269119i	$0.913267\pi$
$110$	67298.7			0.0505625
$111$	−2.55413e6			−1.86756
$112$	−1.15123e6			−0.819421
$113$	485843.	−	485843.i	0.336713	−	0.336713i	−0.518416	−	0.855129i	$-0.673478\pi$
$113$	485843.	−	485843.i	0.336713	−	0.336713i	0.855129	+	0.518416i	$0.173478\pi$
$114$	−132452.	+	132452.i	−0.0894015	+	0.0894015i
$115$			2.73263e6i			1.79675i
$116$	800497.	−	1.33614e6i	0.512845	−	0.856005i
$117$	370892.			0.231574
$118$	−51928.0	−	51928.0i	−0.0316050	−	0.0316050i
$119$	−471747.	−	471747.i	−0.279942	−	0.279942i
$120$		−	376357.i		−	0.217799i
$121$		−	888975.i		−	0.501803i
$122$			57966.8i			0.0319227i
$123$	−3.66180e6			−1.96779
$124$	−1.65629e6	+	1.65629e6i	−0.868702	+	0.868702i
$125$			1.25945e6i			0.644840i
$126$	−70758.2	+	70758.2i	−0.0353724	+	0.0353724i
$127$	−2.52784e6	−	2.52784e6i	−1.23407	−	1.23407i	−0.962388	−	0.271679i	$-0.912421\pi$
$127$	−2.52784e6	−	2.52784e6i	−1.23407	−	1.23407i	−0.271679	−	0.962388i	$-0.587579\pi$
$128$	−271981.	+	271981.i	−0.129691	+	0.129691i
$129$			3.24881e6i			1.51341i
$130$	−19584.4	−	19584.4i	−0.00891416	−	0.00891416i
$131$	1.65675e6	−	1.65675e6i	0.736957	−	0.736957i	−0.235031	−	0.971988i	$-0.575519\pi$
$131$	1.65675e6	−	1.65675e6i	0.736957	−	0.736957i	0.971988	+	0.235031i	$0.0755193\pi$
$132$	2.46524e6			1.07186
$133$	2.47257e6	+	2.47257e6i	1.05098	+	1.05098i
$134$	−119997.	+	119997.i	−0.0498721	+	0.0498721i
$135$	1.29972e6	+	1.29972e6i	0.528263	+	0.528263i
$136$	−111214.			−0.0442122
$137$	−1.03087e6	−	1.03087e6i	−0.400907	−	0.400907i	0.477645	−	0.878553i	$-0.341490\pi$
$137$	−1.03087e6	−	1.03087e6i	−0.400907	−	0.400907i	−0.878553	+	0.477645i	$0.841490\pi$
$138$		−	213160.i		−	0.0811088i
$139$	249130.			0.0927643			0.0463821	−	0.998924i	$-0.485231\pi$
$139$	249130.			0.0927643			0.0463821	+	0.998924i	$0.485231\pi$
$140$	−3.50911e6			−1.27883
$141$	4.88078e6			1.74113
$142$	132836.	−	132836.i	0.0463930	−	0.0463930i
$143$	256839.	−	256839.i	0.0878319	−	0.0878319i
$144$		−	3.90423e6i		−	1.30752i
$145$	2.43483e6	−	4.06405e6i	0.798664	−	1.33307i
$146$	30725.2			0.00987269
$147$	−1.09352e6	−	1.09352e6i	−0.344250	−	0.344250i
$148$	2.80712e6	+	2.80712e6i	0.865915	+	0.865915i
$149$		−	5.00318e6i		−	1.51247i	−0.654300	−	0.756236i	$-0.727036\pi$
$149$		−	5.00318e6i		−	1.51247i	0.654300	−	0.756236i	$-0.272964\pi$
$150$		−	335004.i		−	0.0992603i
$151$			280311.i			0.0814160i	0.999171	+	0.0407080i	$0.0129613\pi$
$151$			280311.i			0.0814160i	−0.999171	+	0.0407080i	$0.987039\pi$
$152$	582907.			0.165985
$153$	1.59986e6	−	1.59986e6i	0.446692	−	0.446692i
$154$			97998.5i			0.0268323i
$155$	−5.03784e6	+	5.03784e6i	−1.35285	+	1.35285i
$156$	−717401.	−	717401.i	−0.188968	−	0.188968i
$157$	−426089.	+	426089.i	−0.110104	+	0.110104i	−0.760012	−	0.649909i	$-0.774807\pi$
$157$	−426089.	+	426089.i	−0.110104	+	0.110104i	0.649909	+	0.760012i	$0.274807\pi$
$158$			262277.i			0.0664951i
$159$	2.33414e6	+	2.33414e6i	0.580678	+	0.580678i
$160$	−620673.	+	620673.i	−0.151532	+	0.151532i
$161$	−3.97919e6			−0.953491
$162$	80973.8	+	80973.8i	0.0190458	+	0.0190458i
$163$	1.48894e6	−	1.48894e6i	0.343806	−	0.343806i	−0.513990	−	0.857796i	$-0.671833\pi$
$163$	1.48894e6	−	1.48894e6i	0.343806	−	0.343806i	0.857796	+	0.513990i	$0.171833\pi$
$164$	4.02451e6	+	4.02451e6i	0.912391	+	0.912391i
$165$	7.49836e6			1.66922
$166$	−48178.5	−	48178.5i	−0.0105324	−	0.0105324i
$167$			6.60318e6i			1.41776i	0.705327	+	0.708882i	$0.250800\pi$
$167$			6.60318e6i			1.41776i	−0.705327	+	0.708882i	$0.749200\pi$
$168$	548041.			0.115581
$169$	4.67733e6			0.969031
$170$	−168957.			−0.0343897
$171$	−8.38537e6	+	8.38537e6i	−1.67700	+	1.67700i
$172$	3.57060e6	−	3.57060e6i	0.701708	−	0.701708i
$173$		−	5.01025e6i		−	0.967657i	−0.875163	−	0.483828i	$-0.839246\pi$
$173$		−	5.01025e6i		−	0.967657i	0.875163	−	0.483828i	$-0.160754\pi$
$174$	−189929.	+	317017.i	−0.0360532	+	0.0601775i
$175$	−6.25372e6			−1.16688
$176$	−2.70363e6	−	2.70363e6i	−0.495918	−	0.495918i
$177$	−5.78577e6	−	5.78577e6i	−1.04338	−	1.04338i
$178$		−	300336.i		−	0.0532534i
$179$		−	5.61449e6i		−	0.978930i	−0.872023	−	0.489465i	$-0.837192\pi$
$179$		−	5.61449e6i		−	0.978930i	0.872023	−	0.489465i	$-0.162808\pi$
$180$		−	1.19007e7i		−	2.04058i
$181$	−3.35111e6			−0.565137			−0.282568	−	0.959247i	$-0.591186\pi$
$181$	−3.35111e6			−0.565137			−0.282568	+	0.959247i	$0.591186\pi$
$182$	28518.3	−	28518.3i	0.00473052	−	0.00473052i
$183$			6.45861e6i			1.05387i
$184$	−469045.	+	469045.i	−0.0752941	+	0.0752941i
$185$	8.53825e6	+	8.53825e6i	1.34851	+	1.34851i
$186$	392978.	−	392978.i	0.0610701	−	0.0610701i
$187$		−	2.21577e6i		−	0.338845i
$188$	−5.36422e6	−	5.36422e6i	−0.807296	−	0.807296i
$189$	−1.89262e6	+	1.89262e6i	−0.280336	+	0.280336i
$190$	885554.			0.129108
$191$	3.51894e6	+	3.51894e6i	0.505023	+	0.505023i	0.912995	−	0.407972i	$-0.133764\pi$
$191$	3.51894e6	+	3.51894e6i	0.505023	+	0.505023i	−0.407972	+	0.912995i	$0.633764\pi$
$192$	−7.51945e6	+	7.51945e6i	−1.06239	+	1.06239i
$193$	−2.61321e6	−	2.61321e6i	−0.363499	−	0.363499i	0.501601	−	0.865099i	$-0.332745\pi$
$193$	−2.61321e6	−	2.61321e6i	−0.363499	−	0.363499i	−0.865099	+	0.501601i	$0.832745\pi$
$194$	−258024.			−0.0353390
$195$	−2.18208e6	−	2.18208e6i	−0.294284	−	0.294284i
$196$			2.40366e6i			0.319231i
$197$	6.00204e6			0.785056			0.392528	−	0.919740i	$-0.371601\pi$
$197$	6.00204e6			0.785056			0.392528	+	0.919740i	$0.371601\pi$
$198$	−332348.			−0.0428152
$199$	−4.12509e6			−0.523448			−0.261724	−	0.965143i	$-0.584291\pi$
$199$	−4.12509e6			−0.523448			−0.261724	+	0.965143i	$0.584291\pi$
$200$	−737156.	+	737156.i	−0.0921444	+	0.0921444i
$201$	−1.33700e7	+	1.33700e7i	−1.64643	+	1.64643i
$202$		−	192338.i		−	0.0233352i
$203$	5.91795e6	+	3.54553e6i	0.707429	+	0.423831i
$204$	−6.18909e6			−0.729015
$205$	1.22411e7	+	1.22411e7i	1.42089	+	1.42089i
$206$	372319.	+	372319.i	0.0425905	+	0.0425905i
$207$		−	1.34948e7i		−	1.52145i
$208$			1.57355e6i			0.174860i
$209$			1.16136e7i			1.27211i
$210$	832586.			0.0899024
$211$	−8.00450e6	+	8.00450e6i	−0.852093	+	0.852093i	−0.990391	−	0.138298i	$-0.955837\pi$
$211$	−8.00450e6	+	8.00450e6i	−0.852093	+	0.852093i	0.138298	+	0.990391i	$0.455837\pi$
$212$		−	5.13067e6i		−	0.538476i
$213$	1.48005e7	−	1.48005e7i	1.53157	−	1.53157i
$214$	−286523.	−	286523.i	−0.0292360	−	0.0292360i
$215$	1.08605e7	−	1.08605e7i	1.09278	−	1.09278i
$216$			446185.i			0.0442745i
$217$	−7.33596e6	−	7.33596e6i	−0.717923	−	0.717923i
$218$	−181762.	+	181762.i	−0.0175442	+	0.0175442i
$219$	3.42337e6			0.325928
$220$	−8.24108e6	−	8.24108e6i	−0.773955	−	0.773955i
$221$	−644805.	+	644805.i	−0.0597382	+	0.0597382i
$222$	−666028.	−	666028.i	−0.0608742	−	0.0608742i
$223$	−3.61255e6			−0.325761			−0.162881	−	0.986646i	$-0.552079\pi$
$223$	−3.61255e6			−0.325761			−0.162881	+	0.986646i	$0.552079\pi$
$224$	−903807.	−	903807.i	−0.0804140	−	0.0804140i
$225$		−	2.12086e7i		−	1.86194i
$226$	253381.			0.0219508
$227$	1.61332e7			1.37925			0.689627	−	0.724165i	$-0.257775\pi$
$227$	1.61332e7			1.37925			0.689627	+	0.724165i	$0.257775\pi$
$228$	3.24389e7			2.73692
$229$	1.06939e7	−	1.06939e7i	0.890488	−	0.890488i	−0.104081	−	0.994569i	$-0.533190\pi$
$229$	1.06939e7	−	1.06939e7i	0.890488	−	0.890488i	0.994569	+	0.104081i	$0.0331901\pi$
$230$	−712575.	+	712575.i	−0.0585662	+	0.0585662i
$231$			1.09189e7i			0.885815i
$232$	1.11550e6	−	279649.i	0.0893320	−	0.0223949i
$233$	3.00651e6			0.237681			0.118841	−	0.992913i	$-0.462082\pi$
$233$	3.00651e6			0.237681			0.118841	+	0.992913i	$0.462082\pi$
$234$	96715.6	+	96715.6i	0.00754830	+	0.00754830i
$235$	−1.63160e7	−	1.63160e7i	−1.25722	−	1.25722i
$236$			1.27177e7i			0.967548i
$237$			2.92227e7i			2.19521i
$238$		−	246030.i		−	0.0182498i
$239$	−4.72805e6			−0.346329			−0.173164	−	0.984893i	$-0.555399\pi$
$239$	−4.72805e6			−0.346329			−0.173164	+	0.984893i	$0.555399\pi$
$240$	−2.29698e7	+	2.29698e7i	−1.66159	+	1.66159i
$241$		−	1.49463e7i		−	1.06778i	−0.845553	−	0.533892i	$-0.820729\pi$
$241$		−	1.49463e7i		−	1.06778i	0.845553	−	0.533892i	$-0.179271\pi$
$242$	231814.	−	231814.i	0.0163566	−	0.0163566i
$243$	1.38997e7	+	1.38997e7i	0.968695	+	0.968695i
$244$	7.09833e6	−	7.09833e6i	0.488638	−	0.488638i
$245$			7.31109e6i			0.497146i
$246$	−954870.	−	954870.i	−0.0641415	−	0.0641415i
$247$	3.37962e6	−	3.37962e6i	0.224273	−	0.224273i
$248$	−1.72945e6			−0.113384
$249$	−5.36800e6	−	5.36800e6i	−0.347708	−	0.347708i
$250$	−328421.	+	328421.i	−0.0210190	+	0.0210190i
$251$	−6.38751e6	−	6.38751e6i	−0.403934	−	0.403934i	0.475683	−	0.879617i	$-0.342201\pi$
$251$	−6.38751e6	−	6.38751e6i	−0.403934	−	0.403934i	−0.879617	+	0.475683i	$0.842201\pi$
$252$	1.73294e7			1.08288
$253$	−9.34503e6	−	9.34503e6i	−0.577058	−	0.577058i
$254$		−	1.31834e6i		−	0.0804503i
$255$	−1.88250e7			−1.13531
$256$	1.64218e7			0.978818
$257$	−1.69768e7			−1.00013			−0.500066	−	0.865988i	$-0.666691\pi$
$257$	−1.69768e7			−1.00013			−0.500066	+	0.865988i	$0.666691\pi$
$258$	−847176.	+	847176.i	−0.0493304	+	0.0493304i
$259$	−1.24332e7	+	1.24332e7i	−0.715619	+	0.715619i
$260$			4.79642e6i			0.272896i
$261$	−1.20241e7	+	2.00699e7i	−0.676290	+	1.12882i
$262$	864042.			0.0480431
$263$	488269.	+	488269.i	0.0268406	+	0.0268406i	0.720400	−	0.693559i	$-0.243958\pi$
$263$	488269.	+	488269.i	0.0268406	+	0.0268406i	−0.693559	+	0.720400i	$0.743958\pi$
$264$	1.28706e6	+	1.28706e6i	0.0699500	+	0.0699500i
$265$		−	1.56057e7i		−	0.838580i
$266$			1.28952e6i			0.0685145i
$267$		−	3.34632e7i		−	1.75806i
$268$	2.93886e7			1.52677
$269$	−1.48115e7	+	1.48115e7i	−0.760927	+	0.760927i	−0.976490	−	0.215563i	$-0.930841\pi$
$269$	−1.48115e7	+	1.48115e7i	−0.760927	+	0.760927i	0.215563	+	0.976490i	$0.430841\pi$
$270$			677845.i			0.0344381i
$271$	−6.94603e6	+	6.94603e6i	−0.349003	+	0.349003i	−0.859738	−	0.510735i	$-0.829373\pi$
$271$	−6.94603e6	+	6.94603e6i	−0.349003	+	0.349003i	0.510735	+	0.859738i	$0.329373\pi$
$272$	6.78760e6	+	6.78760e6i	0.337295	+	0.337295i
$273$	3.17748e6	−	3.17748e6i	0.156169	−	0.156169i
$274$		−	537632.i		−	0.0261357i
$275$	−1.46867e7	−	1.46867e7i	−0.706199	−	0.706199i
$276$	−2.61025e7	+	2.61025e7i	−1.24152	+	1.24152i
$277$	−2.76779e7			−1.30225			−0.651124	−	0.758971i	$-0.725702\pi$
$277$	−2.76779e7			−1.30225			−0.651124	+	0.758971i	$0.725702\pi$
$278$	64964.2	+	64964.2i	0.00302371	+	0.00302371i
$279$	2.48789e7	−	2.48789e7i	1.14556	−	1.14556i
$280$	−1.83206e6	−	1.83206e6i	−0.0834573	−	0.0834573i
$281$	−1.32622e7			−0.597720			−0.298860	−	0.954297i	$-0.596606\pi$
$281$	−1.32622e7			−0.597720			−0.298860	+	0.954297i	$0.596606\pi$
$282$	1.27274e6	+	1.27274e6i	0.0567533	+	0.0567533i
$283$		−	1.98545e7i		−	0.875992i	−0.898977	−	0.437996i	$-0.855688\pi$
$283$		−	1.98545e7i		−	0.875992i	0.898977	−	0.437996i	$-0.144312\pi$
$284$	−3.25330e7			−1.42026
$285$	9.86676e7			4.26226
$286$	133949.			0.00572587
$287$	−1.78252e7	+	1.78252e7i	−0.754028	+	0.754028i
$288$	3.06513e6	−	3.06513e6i	0.128313	−	0.128313i
$289$		−	1.85748e7i		−	0.769538i
$290$	1.69468e6	−	424843.i	0.0694853	−	0.0174195i
$291$	−2.87488e7			−1.16665
$292$	−3.76245e6	−	3.76245e6i	−0.151120	−	0.151120i
$293$	1.94582e7	+	1.94582e7i	0.773570	+	0.773570i	0.978729	−	0.205159i	$-0.0657711\pi$
$293$	1.94582e7	+	1.94582e7i	0.773570	+	0.773570i	−0.205159	+	0.978729i	$0.565771\pi$
$294$		−	570303.i		−	0.0224421i
$295$			3.86827e7i			1.50678i
$296$			2.93111e6i			0.113020i
$297$	−8.88957e6			−0.339321
$298$	1.30465e6	−	1.30465e6i	0.0492999	−	0.0492999i
$299$			5.43894e6i			0.203470i
$300$	−4.10229e7	+	4.10229e7i	−1.51937	+	1.51937i
$301$	1.58148e7	+	1.58148e7i	0.579913	+	0.579913i
$302$	−73095.3	+	73095.3i	−0.00265380	+	0.00265380i
$303$		−	2.14302e7i		−	0.770367i
$304$	−3.55759e7	−	3.55759e7i	−1.26630	−	1.26630i
$305$	2.15906e7	−	2.15906e7i	0.760966	−	0.760966i
$306$	834376.			0.0291204
$307$	2.51157e7	+	2.51157e7i	0.868022	+	0.868022i	0.992253	−	0.124231i	$-0.0396465\pi$
$307$	2.51157e7	+	2.51157e7i	0.868022	+	0.868022i	−0.124231	+	0.992253i	$0.539646\pi$
$308$	1.20004e7	−	1.20004e7i	0.410719	−	0.410719i
$309$	4.14834e7	+	4.14834e7i	1.40604	+	1.40604i
$310$	−2.62738e6			−0.0881938
$311$	−3.41329e7	−	3.41329e7i	−1.13473	−	1.13473i	−0.989381	−	0.145346i	$-0.953570\pi$
$311$	−3.41329e7	−	3.41329e7i	−1.13473	−	1.13473i	−0.145346	−	0.989381i	$-0.546430\pi$
$312$		−	749088.i		−	0.0246643i
$313$	−1.05217e7			−0.343126			−0.171563	−	0.985173i	$-0.554882\pi$
$313$	−1.05217e7			−0.343126			−0.171563	+	0.985173i	$0.554882\pi$
$314$	−222218.			−0.00717779
$315$	5.27099e7			1.68640
$316$	3.21172e7	−	3.21172e7i	1.01783	−	1.01783i
$317$	−5.85216e6	+	5.85216e6i	−0.183712	+	0.183712i	−0.792971	−	0.609259i	$-0.791467\pi$
$317$	−5.85216e6	+	5.85216e6i	−0.183712	+	0.183712i	0.609259	+	0.792971i	$0.291467\pi$
$318$			1.21732e6i			0.0378551i
$319$	5.57159e6	+	2.22248e7i	0.171635	+	0.684644i
$320$	5.02738e7			1.53423
$321$	−3.19241e7	−	3.19241e7i	−0.965169	−	0.965169i
$322$	−1.03763e6	−	1.03763e6i	−0.0310796	−	0.0310796i
$323$		−	2.91564e7i		−	0.865219i
$324$		−	1.98313e7i		−	0.583064i
$325$			8.54788e6i			0.249005i
$326$	776525.			0.0224131
$327$	−2.02518e7	+	2.02518e7i	−0.579188	+	0.579188i
$328$			4.20227e6i			0.119086i
$329$	2.37590e7	−	2.37590e7i	0.667175	−	0.667175i
$330$	1.95531e6	+	1.95531e6i	0.0544094	+	0.0544094i
$331$	1.47017e7	−	1.47017e7i	0.405400	−	0.405400i	−0.474731	−	0.880131i	$-0.657455\pi$
$331$	1.47017e7	−	1.47017e7i	0.405400	−	0.405400i	0.880131	+	0.474731i	$0.157455\pi$
$332$			1.17994e7i			0.322438i
$333$	−4.21653e7	−	4.21653e7i	−1.14189	−	1.14189i
$334$	−1.72188e6	+	1.72188e6i	−0.0462129	+	0.0462129i
$335$	8.93896e7			2.37768
$336$	−3.34480e7	−	3.34480e7i	−0.881764	−	0.881764i
$337$	−4.74607e6	+	4.74607e6i	−0.124006	+	0.124006i	−0.766386	−	0.642380i	$-0.777947\pi$
$337$	−4.74607e6	+	4.74607e6i	−0.124006	+	0.124006i	0.642380	+	0.766386i	$0.277947\pi$
$338$	1.21968e6	+	1.21968e6i	0.0315861	+	0.0315861i
$339$	2.82315e7			0.724662
$340$	2.06896e7	+	2.06896e7i	0.526399	+	0.526399i
$341$		−	3.44567e7i		−	0.868981i
$342$	−4.37322e6			−0.109326
$343$	−4.39248e7			−1.08850
$344$	3.72832e6			0.0915878
$345$	−7.93945e7	+	7.93945e7i	−1.93345	+	1.93345i
$346$	1.30650e6	−	1.30650e6i	0.0315414	−	0.0315414i
$347$			6.80134e7i			1.62782i	0.580991	+	0.813910i	$0.302665\pi$
$347$			6.80134e7i			1.62782i	−0.580991	+	0.813910i	$0.697335\pi$
$348$	6.20781e7	−	1.55625e7i	1.47299	−	0.369269i
$349$	−1.84989e7			−0.435180			−0.217590	−	0.976040i	$-0.569820\pi$
$349$	−1.84989e7			−0.435180			−0.217590	+	0.976040i	$0.569820\pi$
$350$	−1.63075e6	−	1.63075e6i	−0.0380350	−	0.0380350i
$351$	2.58693e6	+	2.58693e6i	0.0598222	+	0.0598222i
$352$		−	4.24514e6i		−	0.0973339i
$353$			3.47933e7i			0.790991i	0.918468	+	0.395495i	$0.129427\pi$
$353$			3.47933e7i			0.790991i	−0.918468	+	0.395495i	$0.870573\pi$
$354$		−	3.01745e6i		−	0.0680190i
$355$	−9.89537e7			−2.21181
$356$	−3.67777e7	+	3.67777e7i	−0.815144	+	0.815144i
$357$		−	2.74124e7i		−	0.602480i
$358$	1.46406e6	−	1.46406e6i	0.0319088	−	0.0319088i
$359$	−2.10355e6	−	2.10355e6i	−0.0454643	−	0.0454643i	0.684009	−	0.729473i	$-0.260235\pi$
$359$	−2.10355e6	−	2.10355e6i	−0.0454643	−	0.0454643i	−0.729473	+	0.684009i	$0.760235\pi$
$360$	6.21316e6	−	6.21316e6i	0.133170	−	0.133170i
$361$			1.05772e8i			2.24827i
$362$	−873853.	−	873853.i	−0.0184210	−	0.0184210i
$363$	2.58284e7	−	2.58284e7i	0.539981	−	0.539981i
$364$	−6.98441e6			−0.144819
$365$	−1.14440e7	−	1.14440e7i	−0.235343	−	0.235343i
$366$	−1.68418e6	+	1.68418e6i	−0.0343514	+	0.0343514i
$367$	3.07961e7	+	3.07961e7i	0.623013	+	0.623013i	0.946301	−	0.323288i	$-0.104788\pi$
$367$	3.07961e7	+	3.07961e7i	0.623013	+	0.623013i	−0.323288	+	0.946301i	$0.604788\pi$
$368$	5.72535e7			1.14884
$369$	−6.04515e7	−	6.04515e7i	−1.20317	−	1.20317i
$370$			4.45295e6i			0.0879109i
$371$	2.27245e7			0.445013
$372$	−9.62443e7			−1.86959
$373$	2.39821e7			0.462127			0.231064	−	0.972939i	$-0.425779\pi$
$373$	2.39821e7			0.462127			0.231064	+	0.972939i	$0.425779\pi$
$374$	577796.	−	577796.i	0.0110448	−	0.0110448i
$375$	−3.65924e7	+	3.65924e7i	−0.693900	+	0.693900i
$376$		−	5.60116e6i		−	0.105369i
$377$	4.84619e6	−	8.08893e6i	0.0904433	−	0.150962i
$378$	−987059.			−0.0182754
$379$	3.46386e7	+	3.46386e7i	0.636271	+	0.636271i	0.949634	−	0.313362i	$-0.101455\pi$
$379$	3.46386e7	+	3.46386e7i	0.636271	+	0.636271i	−0.313362	+	0.949634i	$0.601455\pi$
$380$	−1.08441e8	−	1.08441e8i	−1.97625	−	1.97625i
$381$		−	1.46889e8i		−	2.65591i
$382$			1.83523e6i			0.0329231i
$383$		−	6.99080e6i		−	0.124432i	−0.998063	−	0.0622158i	$-0.980183\pi$
$383$		−	6.99080e6i		−	0.124432i	0.998063	−	0.0622158i	$-0.0198167\pi$
$384$	−1.58044e7			−0.279115
$385$	3.65010e7	−	3.65010e7i	0.639621	−	0.639621i
$386$		−	1.36287e6i		−	0.0236969i
$387$	−5.36335e7	+	5.36335e7i	−0.925345	+	0.925345i
$388$	3.15963e7	+	3.15963e7i	0.540930	+	0.540930i
$389$	−7.18004e7	+	7.18004e7i	−1.21977	+	1.21977i	−0.252058	+	0.967712i	$0.581107\pi$
$389$	−7.18004e7	+	7.18004e7i	−1.21977	+	1.21977i	−0.967712	+	0.252058i	$0.918893\pi$
$390$		−	1.13802e6i		−	0.0191847i
$391$	2.34611e7	+	2.34611e7i	0.392481	+	0.392481i
$392$	−1.25492e6	+	1.25492e6i	−0.0208332	+	0.0208332i
$393$	9.62708e7			1.58605
$394$	1.56512e6	+	1.56512e6i	0.0255894	+	0.0255894i
$395$	9.76891e7	−	9.76891e7i	1.58509	−	1.58509i
$396$	4.06977e7	+	4.06977e7i	0.655367	+	0.655367i
$397$	3.17022e7			0.506661			0.253330	−	0.967380i	$-0.418474\pi$
$397$	3.17022e7			0.506661			0.253330	+	0.967380i	$0.418474\pi$
$398$	−1.07568e6	−	1.07568e6i	−0.0170621	−	0.0170621i
$399$			1.43677e8i			2.26187i
$400$	8.99800e7			1.40594
$401$	181232.			0.00281062			0.00140531	−	0.999999i	$-0.499553\pi$
$401$	181232.			0.00281062			0.00140531	+	0.999999i	$0.499553\pi$
$402$	−6.97285e6			−0.107333
$403$	−1.00271e7	+	1.00271e7i	−0.153201	+	0.153201i
$404$	−2.35528e7	+	2.35528e7i	−0.357189	+	0.357189i
$405$		−	6.03197e7i		−	0.908018i
$406$	618645.	+	2.46774e6i	0.00924407	+	0.0368741i
$407$	−5.83980e7			−0.866193
$408$	−3.23123e6	−	3.23123e6i	−0.0475760	−	0.0475760i
$409$	2.87251e7	+	2.87251e7i	0.419847	+	0.419847i	0.885151	−	0.465304i	$-0.154055\pi$
$409$	2.87251e7	+	2.87251e7i	0.419847	+	0.419847i	−0.465304	+	0.885151i	$0.654055\pi$
$410$			6.38410e6i			0.0926293i
$411$		−	5.99025e7i		−	0.862818i
$412$		−	9.11846e7i		−	1.30386i
$413$	−5.63286e7			−0.799612
$414$	3.51898e6	−	3.51898e6i	0.0495925	−	0.0495925i
$415$			3.58895e7i			0.502139i
$416$	−1.23537e6	+	1.23537e6i	−0.0171599	+	0.0171599i
$417$	7.23826e6	+	7.23826e6i	0.0998219	+	0.0998219i
$418$	−3.02841e6	+	3.02841e6i	−0.0414654	+	0.0414654i
$419$		−	3.33676e7i		−	0.453611i	−0.973940	−	0.226805i	$-0.927172\pi$
$419$		−	3.33676e7i		−	0.453611i	0.973940	−	0.226805i	$-0.0728281\pi$
$420$	−1.01954e8	−	1.01954e8i	−1.37613	−	1.37613i
$421$	2.66557e6	−	2.66557e6i	0.0357227	−	0.0357227i	−0.689020	−	0.724743i	$-0.741959\pi$
$421$	2.66557e6	−	2.66557e6i	0.0357227	−	0.0357227i	0.724743	+	0.689020i	$0.241959\pi$
$422$	−4.17459e6			−0.0555490
$423$	8.05751e7	+	8.05751e7i	1.06458	+	1.06458i
$424$	2.67864e6	−	2.67864e6i	0.0351413	−	0.0351413i
$425$	3.68717e7	+	3.68717e7i	0.480316	+	0.480316i
$426$	7.71891e6			0.0998452
$427$	3.14396e7	+	3.14396e7i	0.403825	+	0.403825i
$428$			7.01723e7i			0.895024i
$429$	1.49245e7			0.189028
$430$	5.66408e6			0.0712400
$431$	−2.38753e7			−0.298206			−0.149103	−	0.988822i	$-0.547639\pi$
$431$	−2.38753e7			−0.298206			−0.149103	+	0.988822i	$0.547639\pi$
$432$	2.72315e7	−	2.72315e7i	0.337769	−	0.337769i
$433$	−1.99868e7	+	1.99868e7i	−0.246195	+	0.246195i	−0.819407	−	0.573212i	$-0.805697\pi$
$433$	−1.99868e7	+	1.99868e7i	−0.246195	+	0.246195i	0.573212	+	0.819407i	$0.305697\pi$
$434$		−	3.82592e6i		−	0.0468023i
$435$	1.88819e8	−	4.73356e7i	2.29392	−	0.575070i
$436$	4.45154e7			0.537095
$437$	−1.22967e8	−	1.22967e8i	−1.47348	−	1.47348i
$438$	892694.	+	892694.i	0.0106238	+	0.0106238i
$439$		−	8.17017e7i		−	0.965690i	−0.875706	−	0.482845i	$-0.839604\pi$
$439$		−	8.17017e7i		−	0.965690i	0.875706	−	0.482845i	$-0.160396\pi$
$440$		−	8.60509e6i		−	0.101018i
$441$		−	3.61051e7i		−	0.420972i
$442$	−336285.			−0.00389440
$443$	4.03279e7	−	4.03279e7i	0.463868	−	0.463868i	−0.436053	−	0.899921i	$-0.643624\pi$
$443$	4.03279e7	−	4.03279e7i	0.463868	−	0.463868i	0.899921	+	0.436053i	$0.143624\pi$
$444$			1.63117e8i			1.86359i
$445$	−1.11865e8	+	1.11865e8i	−1.26944	+	1.26944i
$446$	−942026.	−	942026.i	−0.0106184	−	0.0106184i
$447$	1.45363e8	−	1.45363e8i	1.62754	−	1.62754i
$448$			7.32072e7i			0.814179i
$449$	5.13844e7	+	5.13844e7i	0.567666	+	0.567666i	0.931474	−	0.363808i	$-0.118524\pi$
$449$	5.13844e7	+	5.13844e7i	0.567666	+	0.567666i	−0.363808	+	0.931474i	$0.618524\pi$
$450$	5.53046e6	−	5.53046e6i	0.0606910	−	0.0606910i
$451$	−8.37240e7			−0.912684
$452$	−3.10279e7	−	3.10279e7i	−0.335998	−	0.335998i
$453$	−8.14422e6	+	8.14422e6i	−0.0876102	+	0.0876102i
$454$	4.20698e6	+	4.20698e6i	0.0449576	+	0.0449576i
$455$	−2.12441e7			−0.225530
$456$	1.69359e7	+	1.69359e7i	0.178613	+	0.178613i
$457$			5.76090e7i			0.603590i	0.953373	+	0.301795i	$0.0975857\pi$
$457$			5.76090e7i			0.603590i	−0.953373	+	0.301795i	$0.902414\pi$
$458$	5.57717e6			0.0580520
$459$	2.23177e7			0.230787
$460$	1.74517e8			1.79293
$461$	4.92117e6	−	4.92117e6i	0.0502302	−	0.0502302i	−0.681546	−	0.731776i	$-0.738692\pi$
$461$	4.92117e6	−	4.92117e6i	0.0502302	−	0.0502302i	0.731776	+	0.681546i	$0.238692\pi$
$462$	−2.84727e6	+	2.84727e6i	−0.0288737	+	0.0288737i
$463$		−	1.32177e8i		−	1.33172i	−0.746077	−	0.665859i	$-0.768065\pi$
$463$		−	1.32177e8i		−	1.33172i	0.746077	−	0.665859i	$-0.231935\pi$
$464$	−8.51488e7	−	5.10139e7i	−0.852363	−	0.510663i
$465$	−2.92741e8			−2.91155
$466$	783992.	+	783992.i	0.00774736	+	0.00774736i
$467$	4.46349e7	+	4.46349e7i	0.438252	+	0.438252i	0.891423	−	0.453172i	$-0.149708\pi$
$467$	4.46349e7	+	4.46349e7i	0.438252	+	0.438252i	−0.453172	+	0.891423i	$0.649708\pi$
$468$		−	2.36867e7i		−	0.231082i
$469$			1.30167e8i			1.26177i
$470$		−	8.50930e6i		−	0.0819597i
$471$	−2.47593e7			−0.236961
$472$	−6.63972e6	+	6.63972e6i	−0.0631428	+	0.0631428i
$473$			7.42812e7i			0.701933i
$474$	−7.62026e6	+	7.62026e6i	−0.0715541	+	0.0715541i
$475$	−1.93256e8	−	1.93256e8i	−1.80324	−	1.80324i
$476$	−3.01276e7	+	3.01276e7i	−0.279347	+	0.279347i
$477$			7.70670e7i			0.710090i
$478$	−1.23291e6	−	1.23291e6i	−0.0112888	−	0.0112888i
$479$	4.83305e7	−	4.83305e7i	0.439759	−	0.439759i	−0.452172	−	0.891931i	$-0.649351\pi$
$479$	4.83305e7	−	4.83305e7i	0.439759	−	0.439759i	0.891931	+	0.452172i	$0.149351\pi$
$480$	−3.60663e7			−0.326120
$481$	1.69942e7	+	1.69942e7i	0.152710	+	0.152710i
$482$	3.89748e6	−	3.89748e6i	0.0348051	−	0.0348051i
$483$	−1.15612e8	−	1.15612e8i	−1.02603	−	1.02603i
$484$	−5.67735e7			−0.500737
$485$	9.61047e7	+	9.61047e7i	0.842402	+	0.842402i
$486$			7.24912e6i			0.0631504i
$487$	−2.27370e8			−1.96855			−0.984275	−	0.176645i	$-0.943475\pi$
$487$	−2.27370e8			−1.96855			−0.984275	+	0.176645i	$0.943475\pi$
$488$	7.41187e6			0.0637776
$489$	8.65197e7			0.739926
$490$	−1.90648e6	+	1.90648e6i	−0.0162048	+	0.0162048i
$491$	−4.29493e7	+	4.29493e7i	−0.362837	+	0.362837i	−0.864857	−	0.502019i	$-0.832591\pi$
$491$	−4.29493e7	+	4.29493e7i	−0.362837	+	0.362837i	0.502019	+	0.864857i	$0.332591\pi$
$492$			2.33857e8i			1.96361i
$493$	−1.39877e7	−	5.57963e7i	−0.116736	−	0.465655i
$494$	1.76257e6			0.0146207
$495$	1.23788e8	+	1.23788e8i	1.02062	+	1.02062i
$496$	1.05552e8	+	1.05552e8i	0.865007	+	0.865007i
$497$		−	1.44094e8i		−	1.17375i
$498$		−	2.79957e6i		−	0.0226675i
$499$		−	2.38879e8i		−	1.92254i	−0.275608	−	0.961270i	$-0.588879\pi$
$499$		−	2.38879e8i		−	1.92254i	0.275608	−	0.961270i	$-0.411121\pi$
$500$	8.04337e7			0.643470
$501$	−1.91850e8	+	1.91850e8i	−1.52563	+	1.52563i
$502$		−	3.33128e6i		−	0.0263330i
$503$	4.97856e7	−	4.97856e7i	0.391201	−	0.391201i	−0.483915	−	0.875115i	$-0.660785\pi$
$503$	4.97856e7	−	4.97856e7i	0.391201	−	0.391201i	0.875115	+	0.483915i	$0.160785\pi$
$504$	9.04743e6	+	9.04743e6i	0.0706697	+	0.0706697i
$505$	−7.16392e7	+	7.16392e7i	−0.556258	+	0.556258i
$506$		−	4.87371e6i		−	0.0376191i
$507$	1.35896e8	+	1.35896e8i	1.04276	+	1.04276i
$508$	−1.61438e8	+	1.61438e8i	−1.23144	+	1.23144i
$509$	1.11012e8			0.841812			0.420906	−	0.907104i	$-0.361712\pi$
$509$	1.11012e8			0.841812			0.420906	+	0.907104i	$0.361712\pi$
$510$	−4.90890e6	−	4.90890e6i	−0.0370061	−	0.0370061i
$511$	1.66645e7	−	1.66645e7i	0.124890	−	0.124890i
$512$	2.16890e7	+	2.16890e7i	0.161596	+	0.161596i
$513$	−1.16974e8			−0.866436
$514$	−4.42696e6	−	4.42696e6i	−0.0325999	−	0.0325999i
$515$		−	2.77351e8i		−	2.03052i
$516$	2.07482e8			1.51019
$517$	1.11595e8			0.807555
$518$	−6.48426e6			−0.0466521
$519$	1.45569e8	−	1.45569e8i	1.04128	−	1.04128i
$520$	−2.50414e6	+	2.50414e6i	−0.0178094	+	0.0178094i
$521$			7.69489e7i			0.544113i	0.962281	+	0.272057i	$0.0877038\pi$
$521$			7.69489e7i			0.544113i	−0.962281	+	0.272057i	$0.912296\pi$
$522$	−8.36900e6	+	2.09805e6i	−0.0588386	+	0.0147504i
$523$	8.79528e7			0.614815			0.307408	−	0.951578i	$-0.400538\pi$
$523$	8.79528e7			0.614815			0.307408	+	0.951578i	$0.400538\pi$
$524$	−1.05806e8	−	1.05806e8i	−0.735391	−	0.735391i
$525$	−1.81697e8	−	1.81697e8i	−1.25565	−	1.25565i
$526$			254647.i			0.00174977i
$527$			8.65051e7i			0.591030i
$528$		−	1.57104e8i		−	1.06730i
$529$	4.98590e7			0.336803
$530$	4.06941e6	−	4.06941e6i	0.0273340	−	0.0273340i
$531$		−	1.91031e8i		−	1.27591i
$532$	1.57908e8	−	1.57908e8i	1.04874	−	1.04874i
$533$	2.43643e7	+	2.43643e7i	0.160906	+	0.160906i
$534$	8.72602e6	−	8.72602e6i	0.0573050	−	0.0573050i
$535$			2.13439e8i			1.39384i
$536$	1.53433e7	+	1.53433e7i	0.0996382	+	0.0996382i
$537$	1.63125e8	−	1.63125e8i	1.05341	−	1.05341i
$538$	−7.72466e6			−0.0496058
$539$	−2.50024e7	−	2.50024e7i	−0.159667	−	0.159667i
$540$	8.30056e7	−	8.30056e7i	0.527140	−	0.527140i
$541$	−1.07586e8	−	1.07586e8i	−0.679458	−	0.679458i	0.280419	−	0.959878i	$-0.409527\pi$
$541$	−1.07586e8	−	1.07586e8i	−0.679458	−	0.679458i	−0.959878	+	0.280419i	$0.909527\pi$
$542$	−3.62256e6			−0.0227519
$543$	−9.73639e7	−	9.73639e7i	−0.608133	−	0.608133i
$544$			1.06576e7i			0.0662009i
$545$	1.35400e8			0.836429
$546$	1.65715e6			0.0101808
$547$	−9.00694e6			−0.0550320			−0.0275160	−	0.999621i	$-0.508760\pi$
$547$	−9.00694e6			−0.0550320			−0.0275160	+	0.999621i	$0.508760\pi$
$548$	−6.58358e7	+	6.58358e7i	−0.400056	+	0.400056i
$549$	−1.06623e8	+	1.06623e8i	−0.644368	+	0.644368i
$550$		−	7.65957e6i		−	0.0460380i
$551$	7.33140e7	+	2.92446e8i	0.438260	+	1.74820i
$552$	−2.72555e7			−0.162045
$553$	1.42252e8	+	1.42252e8i	0.841169	+	0.841169i
$554$	−7.21742e6	−	7.21742e6i	−0.0424476	−	0.0424476i
$555$			4.96144e8i			2.90221i
$556$		−	1.59104e7i		−	0.0925672i
$557$			1.12103e8i			0.648713i	0.945935	+	0.324357i	$0.105148\pi$
$557$			1.12103e8i			0.648713i	−0.945935	+	0.324357i	$0.894852\pi$
$558$	1.29751e7			0.0746805
$559$	2.16164e7	−	2.16164e7i	0.123751	−	0.123751i
$560$			2.23628e8i			1.27339i
$561$	6.43775e7	−	6.43775e7i	0.364624	−	0.364624i
$562$	−3.45832e6	−	3.45832e6i	−0.0194830	−	0.0194830i
$563$	−4.43653e7	+	4.43653e7i	−0.248610	+	0.248610i	−0.820400	−	0.571790i	$-0.806249\pi$
$563$	−4.43653e7	+	4.43653e7i	−0.248610	+	0.248610i	0.571790	+	0.820400i	$0.306249\pi$
$564$		−	3.11706e8i		−	1.73743i
$565$	−9.43756e7	−	9.43756e7i	−0.523256	−	0.523256i
$566$	5.17736e6	−	5.17736e6i	0.0285535	−	0.0285535i
$567$	8.78359e7			0.481862
$568$	−1.69850e7	−	1.69850e7i	−0.0926873	−	0.0926873i
$569$	−1.40887e8	+	1.40887e8i	−0.764773	+	0.764773i	−0.977181	−	0.212408i	$-0.931869\pi$
$569$	−1.40887e8	+	1.40887e8i	−0.764773	+	0.764773i	0.212408	+	0.977181i	$0.431869\pi$
$570$	2.57290e7	+	2.57290e7i	0.138931	+	0.138931i
$571$	6.81919e7			0.366290			0.183145	−	0.983086i	$-0.441372\pi$
$571$	6.81919e7			0.366290			0.183145	+	0.983086i	$0.441372\pi$
$572$	−1.64027e7	−	1.64027e7i	−0.0876453	−	0.0876453i
$573$			2.04480e8i			1.08689i
$574$	−9.29635e6			−0.0491560
$575$	3.11013e8			1.63597
$576$	−2.48272e8			−1.29915
$577$	1.86052e8	−	1.86052e8i	0.968515	−	0.968515i	−0.0310047	−	0.999519i	$-0.509871\pi$
$577$	1.86052e8	−	1.86052e8i	0.968515	−	0.968515i	0.999519	+	0.0310047i	$0.00987068\pi$
$578$	4.84365e6	−	4.84365e6i	0.0250835	−	0.0250835i
$579$		−	1.51850e8i		−	0.782308i
$580$	−2.59546e8	−	1.55498e8i	−1.33024	−	0.796966i
$581$	−5.22613e7			−0.266472
$582$	−7.49667e6	−	7.49667e6i	−0.0380276	−	0.0380276i
$583$	5.33680e7	+	5.33680e7i	0.269324	+	0.269324i
$584$		−	3.92864e6i		−	0.0197244i
$585$		−	7.20463e7i		−	0.359869i
$586$			1.01480e7i			0.0504300i
$587$	−7.34302e7			−0.363045			−0.181522	−	0.983387i	$-0.558102\pi$
$587$	−7.34302e7			−0.363045			−0.181522	+	0.983387i	$0.558102\pi$
$588$	−6.98365e7	+	6.98365e7i	−0.343519	+	0.343519i
$589$		−	4.53400e8i		−	2.21889i
$590$	−1.00871e7	+	1.00871e7i	−0.0491145	+	0.0491145i
$591$	1.74385e8	+	1.74385e8i	0.844784	+	0.844784i
$592$	1.78891e8	−	1.78891e8i	0.862231	−	0.862231i
$593$		−	2.37008e8i		−	1.13658i	−0.822829	−	0.568289i	$-0.807605\pi$
$593$		−	2.37008e8i		−	1.13658i	0.822829	−	0.568289i	$-0.192395\pi$
$594$	−2.31809e6	−	2.31809e6i	−0.0110604	−	0.0110604i
$595$	−9.16374e7	+	9.16374e7i	−0.435033	+	0.435033i
$596$	−3.19523e8			−1.50926
$597$	−1.19851e8	−	1.19851e8i	−0.563273	−	0.563273i
$598$	−1.41828e6	+	1.41828e6i	−0.00663223	+	0.00663223i
$599$	−3.35676e7	−	3.35676e7i	−0.156185	−	0.156185i	0.624689	−	0.780874i	$-0.285226\pi$
$599$	−3.35676e7	−	3.35676e7i	−0.156185	−	0.156185i	−0.780874	+	0.624689i	$0.785226\pi$
$600$	−4.28349e7			−0.198310
$601$	1.83099e8	+	1.83099e8i	0.843458	+	0.843458i	0.989307	−	0.145849i	$-0.0465914\pi$
$601$	1.83099e8	+	1.83099e8i	0.843458	+	0.843458i	−0.145849	+	0.989307i	$0.546591\pi$
$602$			8.24787e6i			0.0378053i
$603$	−4.41442e8			−2.01336
$604$	1.79018e7			0.0812430
$605$	−1.72685e8			−0.779808
$606$	5.58823e6	−	5.58823e6i	0.0251106	−	0.0251106i
$607$	3.30745e7	−	3.30745e7i	0.147886	−	0.147886i	−0.629287	−	0.777173i	$-0.716653\pi$
$607$	3.30745e7	−	3.30745e7i	0.147886	−	0.147886i	0.777173	+	0.629287i	$0.216653\pi$
$608$		−	5.58599e7i		−	0.248536i
$609$	6.89288e7	+	2.74954e8i	0.305175	+	1.21733i
$610$	1.12601e7			0.0496083
$611$	−3.24749e7	−	3.24749e7i	−0.142372	−	0.142372i
$612$	−1.02174e8	−	1.02174e8i	−0.445743	−	0.445743i
$613$		−	9.38622e7i		−	0.407483i	−0.979025	−	0.203741i	$-0.934690\pi$
$613$		−	9.38622e7i		−	0.407483i	0.979025	−	0.203741i	$-0.0653102\pi$
$614$			1.30986e7i			0.0565874i
$615$			7.11311e8i			3.05798i
$616$	1.25305e7			0.0536075
$617$	2.32812e8	−	2.32812e8i	0.991176	−	0.991176i	−0.00878590	−	0.999961i	$-0.502797\pi$
$617$	2.32812e8	−	2.32812e8i	0.991176	−	0.991176i	0.999961	+	0.00878590i	$0.00279667\pi$
$618$			2.16348e7i			0.0916617i
$619$	−9.29470e7	+	9.29470e7i	−0.391889	+	0.391889i	−0.875360	−	0.483471i	$-0.839376\pi$
$619$	−9.29470e7	+	9.29470e7i	−0.391889	+	0.391889i	0.483471	+	0.875360i	$0.339376\pi$
$620$	3.21736e8	+	3.21736e8i	1.34997	+	1.34997i
$621$	9.41249e7	−	9.41249e7i	0.393033	−	0.393033i
$622$		−	1.78013e7i		−	0.0739743i
$623$	−1.62894e8	−	1.62894e8i	−0.673661	−	0.673661i
$624$	−4.57183e7	+	4.57183e7i	−0.188164	+	0.188164i
$625$	−1.00797e8			−0.412863
$626$	−2.74370e6	−	2.74370e6i	−0.0111844	−	0.0111844i
$627$	−3.37422e8	+	3.37422e8i	−1.36890	+	1.36890i
$628$	2.72118e7	+	2.72118e7i	0.109870	+	0.109870i
$629$	1.46611e8			0.589134
$630$	1.37449e7	+	1.37449e7i	0.0549692	+	0.0549692i
$631$		−	2.25709e8i		−	0.898382i	−0.893436	−	0.449191i	$-0.851712\pi$
$631$		−	2.25709e8i		−	0.898382i	0.893436	−	0.449191i	$-0.148288\pi$
$632$	3.35358e7			0.132849
$633$	−4.65128e8			−1.83384
$634$	−3.05207e6			−0.0119764
$635$	−4.91037e8	+	4.91037e8i	−1.91775	+	1.91775i
$636$	1.49067e8	−	1.49067e8i	0.579444	−	0.579444i
$637$			1.45517e7i			0.0562984i
$638$	−4.34256e6	+	7.24831e6i	−0.0167218	+	0.0279110i
$639$	4.88673e8			1.87291
$640$	5.28327e7	+	5.28327e7i	0.201541	+	0.201541i
$641$	1.39587e8	+	1.39587e8i	0.529992	+	0.529992i	0.920570	−	0.390578i	$-0.127725\pi$
$641$	1.39587e8	+	1.39587e8i	0.529992	+	0.529992i	−0.390578	+	0.920570i	$0.627725\pi$
$642$		−	1.66494e7i		−	0.0629206i
$643$			1.39219e7i			0.0523679i	0.999657	+	0.0261839i	$0.00833556\pi$
$643$			1.39219e7i			0.0523679i	−0.999657	+	0.0261839i	$0.991664\pi$
$644$			2.54127e8i			0.951465i
$645$	6.31086e8			2.35185
$646$	7.60296e6	−	7.60296e6i	0.0282023	−	0.0282023i
$647$			3.61756e8i			1.33568i	0.744304	+	0.667841i	$0.232781\pi$
$647$			3.61756e8i			1.33568i	−0.744304	+	0.667841i	$0.767219\pi$
$648$	1.03536e7	−	1.03536e7i	0.0380511	−	0.0380511i
$649$	−1.32287e8	−	1.32287e8i	−0.483929	−	0.483929i
$650$	−2.22899e6	+	2.22899e6i	−0.00811648	+	0.00811648i
$651$		−	4.26281e8i		−	1.54509i
$652$	−9.50895e7	−	9.50895e7i	−0.343075	−	0.343075i
$653$	−1.10644e7	+	1.10644e7i	−0.0397364	+	0.0397364i	−0.726696	−	0.686959i	$-0.758945\pi$
$653$	−1.10644e7	+	1.10644e7i	−0.0397364	+	0.0397364i	0.686959	+	0.726696i	$0.258945\pi$
$654$	−1.05619e7			−0.0377580
$655$	−3.21825e8	−	3.21825e8i	−1.14524	−	1.14524i
$656$	2.56473e8	−	2.56473e8i	0.908509	−	0.908509i
$657$	5.65152e7	+	5.65152e7i	0.199283	+	0.199283i
$658$	1.23910e7			0.0434939
$659$	−3.30437e8	−	3.30437e8i	−1.15460	−	1.15460i	−0.985619	−	0.168985i	$-0.945951\pi$
$659$	−3.30437e8	−	3.30437e8i	−1.15460	−	1.15460i	−0.168985	−	0.985619i	$-0.554049\pi$
$660$		−	4.78876e8i		−	1.66568i
$661$	2.69272e7			0.0932367			0.0466184	−	0.998913i	$-0.485156\pi$
$661$	2.69272e7			0.0932367			0.0466184	+	0.998913i	$0.485156\pi$
$662$	7.66738e6			0.0264285
$663$	−3.74686e7			−0.128566
$664$	−6.16029e6	+	6.16029e6i	−0.0210425	+	0.0210425i
$665$	4.80300e8	−	4.80300e8i	1.63323	−	1.63323i
$666$		−	2.19905e7i		−	0.0744409i
$667$	−2.94314e8	−	1.76328e8i	−0.991823	−	0.594215i
$668$	4.21706e8			1.41475
$669$	−1.04960e8	−	1.04960e8i	−0.350545	−	0.350545i
$670$	2.33097e7	+	2.33097e7i	0.0775018	+	0.0775018i
$671$			1.47671e8i			0.488794i
$672$		−	5.25188e7i		−	0.173064i
$673$			4.54100e8i			1.48973i	0.667217	+	0.744863i	$0.267485\pi$
$673$			4.54100e8i			1.48973i	−0.667217	+	0.744863i	$0.732515\pi$
$674$	−2.47522e6			−0.00808413
$675$	1.47927e8	−	1.47927e8i	0.480992	−	0.480992i
$676$		−	2.98713e8i		−	0.966971i
$677$	2.15265e8	−	2.15265e8i	0.693755	−	0.693755i	−0.269301	−	0.963056i	$-0.586793\pi$
$677$	2.15265e8	−	2.15265e8i	0.693755	−	0.693755i	0.963056	+	0.269301i	$0.0867925\pi$
$678$	7.36179e6	+	7.36179e6i	0.0236208	+	0.0236208i
$679$	−1.39945e8	+	1.39945e8i	−0.447042	+	0.447042i
$680$			2.16035e7i			0.0687063i
$681$	4.68738e8	+	4.68738e8i	1.48419	+	1.48419i
$682$	8.98509e6	−	8.98509e6i	0.0283250	−	0.0283250i
$683$	1.89028e7			0.0593285			0.0296642	−	0.999560i	$-0.490556\pi$
$683$	1.89028e7			0.0593285			0.0296642	+	0.999560i	$0.490556\pi$
$684$	5.35523e8	+	5.35523e8i	1.67344	+	1.67344i
$685$	−2.00249e8	+	2.00249e8i	−0.623015	+	0.623015i
$686$	−1.14540e7	−	1.14540e7i	−0.0354803	−	0.0354803i
$687$	6.21403e8			1.91647
$688$	−2.27547e8	−	2.27547e8i	−0.698723	−	0.698723i
$689$		−	3.10609e7i		−	0.0949635i
$690$	−4.14066e7			−0.126044
$691$	5.82001e8			1.76396			0.881981	−	0.471285i	$-0.156210\pi$
$691$	5.82001e8			1.76396			0.881981	+	0.471285i	$0.156210\pi$
$692$	−3.19975e8			−0.965601
$693$	−1.80257e8	+	1.80257e8i	−0.541616	+	0.541616i
$694$	−1.77355e7	+	1.77355e7i	−0.0530598	+	0.0530598i
$695$		−	4.83938e7i		−	0.144157i
$696$	4.05350e7	+	2.42851e7i	0.120227	+	0.0720298i
$697$	2.10193e8			0.620755
$698$	−4.82386e6	−	4.82386e6i	−0.0141850	−	0.0141850i
$699$	8.73517e7	+	8.73517e7i	0.255764	+	0.255764i
$700$			3.99388e8i			1.16440i
$701$		−	5.54167e8i		−	1.60874i	−0.594126	−	0.804372i	$-0.702502\pi$
$701$		−	5.54167e8i		−	1.60874i	0.594126	−	0.804372i	$-0.297498\pi$
$702$			1.34916e6i			0.00389988i
$703$	−7.68433e8			−2.21177
$704$	−1.71926e8	+	1.71926e8i	−0.492745	+	0.492745i
$705$		−	9.48098e8i		−	2.70574i
$706$	−9.07287e6	+	9.07287e6i	−0.0257828	+	0.0257828i
$707$	−1.04319e8	−	1.04319e8i	−0.295192	−	0.295192i
$708$	−3.69502e8	+	3.69502e8i	−1.04116	+	1.04116i
$709$			2.96613e8i			0.832245i	0.909308	+	0.416123i	$0.136611\pi$
$709$			2.96613e8i			0.832245i	−0.909308	+	0.416123i	$0.863389\pi$
$710$	−2.58037e7	−	2.58037e7i	−0.0720952	−	0.0720952i
$711$	−4.82428e8	+	4.82428e8i	−1.34222	+	1.34222i
$712$	−3.84022e7			−0.106394
$713$	3.64836e8	+	3.64836e8i	1.00653	+	1.00653i
$714$	7.14820e6	−	7.14820e6i	0.0196382	−	0.0196382i
$715$	−4.98913e7	−	4.98913e7i	−0.136492	−	0.136492i
$716$	−3.58564e8			−0.976849
$717$	−1.37370e8	−	1.37370e8i	−0.372678	−	0.372678i
$718$		−	1.09707e6i		−	0.00296387i
$719$	3.10707e8			0.835919			0.417960	−	0.908466i	$-0.362745\pi$
$719$	3.10707e8			0.835919			0.417960	+	0.908466i	$0.362745\pi$
$720$	−7.58402e8			−2.03190
$721$	4.03871e8			1.07755
$722$	−2.75815e7	+	2.75815e7i	−0.0732836	+	0.0732836i
$723$	4.34253e8	−	4.34253e8i	1.14902	−	1.14902i
$724$			2.14016e8i			0.563936i
$725$	−4.62547e8	−	2.77118e8i	−1.21379	−	0.727196i
$726$	1.34703e7			0.0352020
$727$	3.32173e8	+	3.32173e8i	0.864492	+	0.864492i	0.991856	−	0.127364i	$-0.0406517\pi$
$727$	3.32173e8	+	3.32173e8i	0.864492	+	0.864492i	−0.127364	+	0.991856i	$0.540652\pi$
$728$	−3.64646e6	−	3.64646e6i	−0.00945099	−	0.00945099i
$729$			5.81318e8i			1.50048i
$730$		−	5.96841e6i		−	0.0153423i
$731$		−	1.86487e8i		−	0.477414i
$732$	4.12473e8			1.05163
$733$	2.47422e8	−	2.47422e8i	0.628242	−	0.628242i	−0.319383	−	0.947626i	$-0.603476\pi$
$733$	2.47422e8	−	2.47422e8i	0.628242	−	0.628242i	0.947626	+	0.319383i	$0.103476\pi$
$734$			1.60611e7i			0.0406150i
$735$	−2.12418e8	+	2.12418e8i	−0.534969	+	0.534969i
$736$	4.49486e7	+	4.49486e7i	0.112741	+	0.112741i
$737$	−3.05693e8	+	3.05693e8i	−0.763631	+	0.763631i
$738$		−	3.15273e7i		−	0.0784363i
$739$	−2.91256e8	−	2.91256e8i	−0.721674	−	0.721674i	0.247272	−	0.968946i	$-0.420466\pi$
$739$	−2.91256e8	−	2.91256e8i	−0.721674	−	0.721674i	−0.968946	+	0.247272i	$0.920466\pi$
$740$	5.45287e8	−	5.45287e8i	1.34564	−	1.34564i
$741$	1.96384e8			0.482673
$742$	5.92576e6	+	5.92576e6i	0.0145055	+	0.0145055i
$743$	−5.47071e8	+	5.47071e8i	−1.33376	+	1.33376i	−0.431779	+	0.901979i	$0.642114\pi$
$743$	−5.47071e8	+	5.47071e8i	−1.33376	+	1.33376i	−0.901979	+	0.431779i	$0.857886\pi$
$744$	−5.02477e7	−	5.02477e7i	−0.122011	−	0.122011i
$745$	−9.71874e8			−2.35040
$746$	6.25370e6	+	6.25370e6i	0.0150633	+	0.0150633i
$747$		−	1.77237e8i		−	0.425199i
$748$	−1.41508e8			−0.338124
$749$	−3.10804e8			−0.739676
$750$	−1.90840e7			−0.0452362
$751$	5.17766e8	−	5.17766e8i	1.22240	−	1.22240i	0.255625	−	0.966776i	$-0.417719\pi$
$751$	5.17766e8	−	5.17766e8i	1.22240	−	1.22240i	0.966776	−	0.255625i	$-0.0822813\pi$
$752$	−3.41849e8	+	3.41849e8i	−0.803862	+	0.803862i
$753$		−	3.71168e8i		−	0.869332i
$754$	3.37303e6	−	845593.i	0.00786875	−	0.00197264i
$755$	5.44509e7			0.126521
$756$	1.20870e8	+	1.20870e8i	0.279740	+	0.279740i
$757$	3.94402e8	+	3.94402e8i	0.909184	+	0.909184i	0.996206	−	0.0870221i	$-0.0277351\pi$
$757$	3.94402e8	+	3.94402e8i	0.909184	+	0.909184i	−0.0870221	+	0.996206i	$0.527735\pi$
$758$			1.80651e7i			0.0414793i
$759$		−	5.43025e8i		−	1.24192i
$760$		−	1.13230e8i		−	0.257942i
$761$	8.32615e7			0.188925			0.0944627	−	0.995528i	$-0.469887\pi$
$761$	8.32615e7			0.188925			0.0944627	+	0.995528i	$0.469887\pi$
$762$	3.83034e7	−	3.83034e7i	0.0865711	−	0.0865711i
$763$			1.97166e8i			0.443872i
$764$	2.24733e8	−	2.24733e8i	0.503950	−	0.503950i
$765$	−3.10775e8	−	3.10775e8i	−0.694165	−	0.694165i
$766$	1.82295e6	−	1.82295e6i	0.00405592	−	0.00405592i
$767$			7.69927e7i			0.170633i
$768$	4.77123e8	+	4.77123e8i	1.05329	+	1.05329i
$769$	5.51450e7	−	5.51450e7i	0.121263	−	0.121263i	−0.643871	−	0.765134i	$-0.722673\pi$
$769$	5.51450e7	−	5.51450e7i	0.121263	−	0.121263i	0.765134	+	0.643871i	$0.222673\pi$
$770$	1.90364e7			0.0416977
$771$	−4.93248e8	−	4.93248e8i	−1.07622	−	1.07622i
$772$	−1.66890e8	+	1.66890e8i	−0.362726	+	0.362726i
$773$	4.63782e8	+	4.63782e8i	1.00410	+	1.00410i	0.999992	+	0.00410576i	$0.00130691\pi$
$773$	4.63782e8	+	4.63782e8i	1.00410	+	1.00410i	0.00410576	+	0.999992i	$0.498693\pi$
$774$	−2.79715e7			−0.0603243
$775$	5.73379e8	+	5.73379e8i	1.23179	+	1.23179i
$776$			3.29919e7i			0.0706029i
$777$	−7.22471e8			−1.54013
$778$	−3.74460e7			−0.0795183
$779$	−1.10169e9			−2.33048
$780$	−1.39356e8	+	1.39356e8i	−0.293658	+	0.293658i
$781$	3.38401e8	−	3.38401e8i	0.710360	−	0.710360i
$782$			1.22357e7i			0.0255863i
$783$	−2.23852e8	+	5.61180e7i	−0.466311	+	0.116901i
$784$	1.53180e8			0.317873
$785$	8.27684e7	+	8.27684e7i	0.171102	+	0.171102i
$786$	2.51040e7	+	2.51040e7i	0.0516983	+	0.0516983i
$787$			1.75040e8i			0.359098i	0.983749	+	0.179549i	$0.0574639\pi$
$787$			1.75040e8i			0.359098i	−0.983749	+	0.179549i	$0.942536\pi$
$788$		−	3.83315e8i		−	0.783388i
$789$			2.83725e7i			0.0577653i
$790$	5.09478e7			0.103334
$791$	1.37427e8	−	1.37427e8i	0.277679	−	0.277679i
$792$			4.24954e7i			0.0855394i
$793$	4.29731e7	−	4.29731e7i	0.0861743	−	0.0861743i
$794$	8.26681e6	+	8.26681e6i	0.0165149	+	0.0165149i
$795$	4.53410e8	−	4.53410e8i	0.902380	−	0.902380i
$796$			2.63445e8i			0.522336i
$797$	1.86950e8	+	1.86950e8i	0.369275	+	0.369275i	0.867213	−	0.497938i	$-0.165909\pi$
$797$	1.86950e8	+	1.86950e8i	0.369275	+	0.369275i	−0.497938	+	0.867213i	$0.665909\pi$
$798$	−3.74659e7	+	3.74659e7i	−0.0737272	+	0.0737272i
$799$	−2.80164e8			−0.549252
$800$	7.06416e7	+	7.06416e7i	0.137972	+	0.137972i
$801$	5.52432e8	−	5.52432e8i	1.07493	−	1.07493i
$802$	47258.9	+	47258.9i	9.16138e−5	+	9.16138e-5i
$803$	7.82724e7			0.151169
$804$	8.53862e8	+	8.53862e8i	1.64293	+	1.64293i
$805$			7.72962e8i			1.48174i
$806$	−5.22945e6			−0.00998736
$807$	−8.60674e8			−1.63764
$808$	−2.45931e7			−0.0466208
$809$	4.10866e8	−	4.10866e8i	0.775988	−	0.775988i	−0.203158	−	0.979146i	$-0.565121\pi$
$809$	4.10866e8	−	4.10866e8i	0.775988	−	0.775988i	0.979146	+	0.203158i	$0.0651205\pi$
$810$	1.57293e7	−	1.57293e7i	0.0295974	−	0.0295974i
$811$		−	4.44358e8i		−	0.833049i	−0.909124	−	0.416525i	$-0.863248\pi$
$811$		−	4.44358e8i		−	0.833049i	0.909124	−	0.416525i	$-0.136752\pi$
$812$	2.26431e8	−	3.77944e8i	0.422930	−	0.705926i
$813$	−4.03622e8			−0.751110
$814$	−1.52281e7	−	1.52281e7i	−0.0282341	−	0.0282341i
$815$	−2.89228e8	−	2.89228e8i	−0.534279	−	0.534279i
$816$			3.94416e8i			0.725913i
$817$			9.77434e8i			1.79234i
$818$			1.49810e7i			0.0273704i
$819$	1.04912e8			0.190973
$820$	7.81766e8	−	7.81766e8i	1.41787	−	1.41787i
$821$			9.36838e8i			1.69291i	0.532457	+	0.846457i	$0.321269\pi$
$821$			9.36838e8i			1.69291i	−0.532457	+	0.846457i	$0.678731\pi$
$822$	1.56205e7	−	1.56205e7i	0.0281241	−	0.0281241i
$823$	−8.02259e7	−	8.02259e7i	−0.143918	−	0.143918i	0.631477	−	0.775395i	$-0.282449\pi$
$823$	−8.02259e7	−	8.02259e7i	−0.143918	−	0.143918i	−0.775395	+	0.631477i	$0.782449\pi$
$824$	4.76061e7	−	4.76061e7i	0.0850906	−	0.0850906i
$825$		−	8.53422e8i		−	1.51985i
$826$	−1.46885e7	−	1.46885e7i	−0.0260638	−	0.0260638i
$827$	3.12636e8	−	3.12636e8i	0.552742	−	0.552742i	−0.374489	−	0.927231i	$-0.622182\pi$
$827$	3.12636e8	−	3.12636e8i	0.552742	−	0.552742i	0.927231	+	0.374489i	$0.122182\pi$
$828$	−8.61835e8			−1.51821
$829$	7.79282e7	+	7.79282e7i	0.136783	+	0.136783i	0.772183	−	0.635400i	$-0.219165\pi$
$829$	7.79282e7	+	7.79282e7i	0.136783	+	0.136783i	−0.635400	+	0.772183i	$0.719165\pi$
$830$	−9.35873e6	+	9.35873e6i	−0.0163675	+	0.0163675i
$831$	−8.04159e8	−	8.04159e8i	−1.40132	−	1.40132i
$832$	1.00063e8			0.173742
$833$	6.27696e7	+	6.27696e7i	0.108596	+	0.108596i
$834$			3.77497e6i			0.00650751i
$835$	1.28268e9			2.20322
$836$	7.41688e8			1.26941
$837$	3.47054e8			0.591862
$838$	8.70111e6	−	8.70111e6i	0.0147857	−	0.0147857i
$839$	−1.64833e8	+	1.64833e8i	−0.279099	+	0.279099i	−0.832749	−	0.553650i	$-0.813235\pi$
$839$	−1.64833e8	+	1.64833e8i	−0.279099	+	0.279099i	0.553650	+	0.832749i	$0.313235\pi$
$840$		−	1.06458e8i		−	0.179614i
$841$	2.80601e8	+	5.24479e8i	0.471738	+	0.881739i
$842$	1.39018e6			0.00232881
$843$	−3.85323e8	−	3.85323e8i	−0.643195	−	0.643195i
$844$	5.11199e8	+	5.11199e8i	0.850282	+	0.850282i
$845$		−	9.08577e8i		−	1.50588i
$846$			4.20223e7i			0.0694015i
$847$		−	2.51459e8i		−	0.413825i
$848$	−3.26966e8			−0.536185
$849$	5.76857e8	−	5.76857e8i	0.942639	−	0.942639i
$850$			1.92297e7i			0.0313124i
$851$	6.18332e8	−	6.18332e8i	1.00331	−	1.00331i
$852$	−9.45220e8	−	9.45220e8i	−1.52832	−	1.52832i
$853$	8.29818e7	−	8.29818e7i	0.133701	−	0.133701i	−0.637089	−	0.770790i	$-0.719862\pi$
$853$	8.29818e7	−	8.29818e7i	0.133701	−	0.133701i	0.770790	+	0.637089i	$0.219862\pi$
$854$			1.63967e7i			0.0263259i
$855$	1.62887e9	+	1.62887e9i	2.60608	+	2.60608i
$856$	−3.66359e7	+	3.66359e7i	−0.0584098	+	0.0584098i
$857$	−2.49764e8			−0.396815			−0.198407	−	0.980120i	$-0.563577\pi$
$857$	−2.49764e8			−0.396815			−0.198407	+	0.980120i	$0.563577\pi$
$858$	3.89178e6	+	3.89178e6i	0.00616150	+	0.00616150i
$859$	−1.52019e8	+	1.52019e8i	−0.239838	+	0.239838i	−0.816783	−	0.576945i	$-0.804245\pi$
$859$	−1.52019e8	+	1.52019e8i	−0.239838	+	0.239838i	0.576945	+	0.816783i	$0.304245\pi$
$860$	−6.93595e8	−	6.93595e8i	−1.09046	−	1.09046i
$861$	−1.03579e9			−1.62279
$862$	−6.22583e6	−	6.22583e6i	−0.00972020	−	0.00972020i
$863$			5.51335e8i			0.857794i	0.903353	+	0.428897i	$0.141098\pi$
$863$			5.51335e8i			0.857794i	−0.903353	+	0.428897i	$0.858902\pi$
$864$	4.27578e7			0.0662941
$865$	−9.73249e8			−1.50375
$866$	−1.04237e7			−0.0160497
$867$	5.39675e8	−	5.39675e8i	0.828085	−	0.828085i
$868$	−4.68504e8	+	4.68504e8i	−0.716397	+	0.716397i
$869$			6.68152e8i			1.01816i
$870$	6.15810e7	+	3.68940e7i	0.0935166	+	0.0560271i
$871$	1.77918e8			0.269256
$872$	2.32408e7	+	2.32408e7i	0.0350512	+	0.0350512i
$873$	−4.74604e8	−	4.74604e8i	−0.713327	−	0.713327i
$874$		−	6.41310e7i		−	0.0960580i
$875$			3.56253e8i			0.531783i
$876$		−	2.18630e8i		−	0.325235i
$877$	1.29540e9			1.92046			0.960228	−	0.279217i	$-0.0900747\pi$
$877$	1.29540e9			1.92046			0.960228	+	0.279217i	$0.0900747\pi$
$878$	2.13049e7	−	2.13049e7i	0.0314772	−	0.0314772i
$879$			1.13068e9i			1.66485i
$880$	−5.25185e8	+	5.25185e8i	−0.770663	+	0.770663i
$881$	−3.85518e8	−	3.85518e8i	−0.563789	−	0.563789i	0.366592	−	0.930382i	$-0.380524\pi$
$881$	−3.85518e8	−	3.85518e8i	−0.563789	−	0.563789i	−0.930382	+	0.366592i	$0.880524\pi$
$882$	9.41494e6	−	9.41494e6i	0.0137218	−	0.0137218i
$883$			1.07378e9i			1.55967i	0.625984	+	0.779836i	$0.284698\pi$
$883$			1.07378e9i			1.55967i	−0.625984	+	0.779836i	$0.715302\pi$
$884$	4.11799e7	+	4.11799e7i	0.0596112	+	0.0596112i
$885$	−1.12389e9	+	1.12389e9i	−1.62142	+	1.62142i
$886$	2.10322e7			0.0302401
$887$	−7.19042e7	−	7.19042e7i	−0.103035	−	0.103035i	0.653710	−	0.756745i	$-0.273212\pi$
$887$	−7.19042e7	−	7.19042e7i	−0.103035	−	0.103035i	−0.756745	+	0.653710i	$0.773212\pi$
$888$	−8.51610e7	+	8.51610e7i	−0.121619	+	0.121619i
$889$	−7.15034e8	−	7.15034e8i	−1.01770	−	1.01770i
$890$	−5.83407e7			−0.0827564
$891$	2.06281e8	+	2.06281e8i	0.291626	+	0.291626i
$892$			2.30712e8i			0.325069i
$893$	1.46843e9			2.06204
$894$	7.58113e7			0.106101
$895$	−1.09062e9			−1.52127
$896$	−7.69335e7	+	7.69335e7i	−0.106953	+	0.106953i
$897$	−1.58024e8	+	1.58024e8i	−0.218950	+	0.218950i
$898$			2.67985e7i			0.0370068i
$899$	−2.17518e8	−	8.67668e8i	−0.299375	−	1.19419i
$900$	−1.35447e9			−1.85798
$901$	−1.33983e8	−	1.33983e8i	−0.183179	−	0.183179i
$902$	−2.18323e7	−	2.18323e7i	−0.0297495	−	0.0297495i
$903$			9.18970e8i			1.24807i
$904$		−	3.23984e7i		−	0.0438549i
$905$			6.50959e8i			0.878229i
$906$	−4.24745e6			−0.00571142
$907$	−4.65895e8	+	4.65895e8i	−0.624405	+	0.624405i	−0.946655	−	0.322250i	$-0.895561\pi$
$907$	−4.65895e8	+	4.65895e8i	−0.624405	+	0.624405i	0.322250	+	0.946655i	$0.395561\pi$
$908$		−	1.03033e9i		−	1.37632i
$909$	3.53783e8	−	3.53783e8i	0.471027	−	0.471027i
$910$	−5.53971e6	−	5.53971e6i	−0.00735128	−	0.00735128i
$911$	−5.61794e8	+	5.61794e8i	−0.743057	+	0.743057i	−0.973165	−	0.230108i	$-0.926092\pi$
$911$	−5.61794e8	+	5.61794e8i	−0.743057	+	0.743057i	0.230108	+	0.973165i	$0.426092\pi$
$912$		−	2.06726e9i		−	2.72527i
$913$	−1.22735e8	−	1.22735e8i	−0.161270	−	0.161270i
$914$	−1.50224e7	+	1.50224e7i	−0.0196744	+	0.0196744i
$915$	1.25459e9			1.63772
$916$	−6.82953e8	−	6.82953e8i	−0.888595	−	0.888595i
$917$	4.68633e8	−	4.68633e8i	0.607750	−	0.607750i
$918$	5.81967e6	+	5.81967e6i	0.00752263	+	0.00752263i
$919$	3.97033e8			0.511541			0.255770	−	0.966738i	$-0.417671\pi$
$919$	3.97033e8			0.511541			0.255770	+	0.966738i	$0.417671\pi$
$920$	9.11127e7	+	9.11127e7i	0.117008	+	0.117008i
$921$			1.45943e9i			1.86812i
$922$	2.56653e6			0.00327457
$923$	−1.96954e8			−0.250472
$924$	6.97325e8			0.883933
$925$	9.71776e8	−	9.71776e8i	1.22784	−	1.22784i
$926$	3.44671e7	−	3.44671e7i	0.0434082	−	0.0434082i
$927$			1.36967e9i			1.71940i
$928$	−2.67987e7	−	1.06899e8i	−0.0335328	−	0.133761i
$929$	−1.42618e9			−1.77880			−0.889400	−	0.457129i	$-0.848878\pi$
$929$	−1.42618e9			−1.77880			−0.889400	+	0.457129i	$0.848878\pi$
$930$	−7.63365e7	−	7.63365e7i	−0.0949037	−	0.0949037i
$931$	−3.28995e8	−	3.28995e8i	−0.407700	−	0.407700i
$932$		−	1.92008e8i		−	0.237176i
$933$		−	1.98340e9i		−	2.44212i
$934$			2.32784e7i			0.0285702i
$935$	−4.30417e8			−0.526568
$936$	1.23664e7	−	1.23664e7i	0.0150806	−	0.0150806i
$937$			9.54523e8i			1.16029i	0.814512	+	0.580147i	$0.197005\pi$
$937$			9.54523e8i			1.16029i	−0.814512	+	0.580147i	$0.802995\pi$
$938$	−3.39429e7	+	3.39429e7i	−0.0411282	+	0.0411282i
$939$	−3.05700e8	−	3.05700e8i	−0.369231	−	0.369231i
$940$	−1.04201e9	+	1.04201e9i	−1.25455	+	1.25455i
$941$			8.41983e8i			1.01050i	0.862974	+	0.505248i	$0.168599\pi$
$941$			8.41983e8i			1.01050i	−0.862974	+	0.505248i	$0.831401\pi$
$942$	−6.45637e6	−	6.45637e6i	−0.00772388	−	0.00772388i
$943$	8.86490e8	−	8.86490e8i	1.05715	−	1.05715i
$944$	8.10470e8			0.963432
$945$	3.67645e8	+	3.67645e8i	0.435645	+	0.435645i
$946$	−1.93699e7	+	1.93699e7i	−0.0228799	+	0.0228799i
$947$	−2.91866e8	−	2.91866e8i	−0.343664	−	0.343664i	0.514079	−	0.857743i	$-0.328134\pi$
$947$	−2.91866e8	−	2.91866e8i	−0.343664	−	0.343664i	−0.857743	+	0.514079i	$0.828134\pi$
$948$	1.86628e9			2.19054
$949$	−2.27778e7	−	2.27778e7i	−0.0266510	−	0.0266510i
$950$		−	1.00789e8i		−	0.117555i
$951$	−3.40059e8			−0.395379
$952$	−3.14584e7			−0.0364607
$953$	3.18787e8			0.368318			0.184159	−	0.982896i	$-0.441044\pi$
$953$	3.18787e8			0.368318			0.184159	+	0.982896i	$0.441044\pi$
$954$	−2.00964e7	+	2.00964e7i	−0.0231458	+	0.0231458i
$955$	6.83558e8	−	6.83558e8i	0.784812	−	0.784812i
$956$			3.01952e8i			0.345593i
$957$	−4.83845e8	+	8.07600e8i	−0.552039	+	0.921426i
$958$	2.52058e7			0.0286684
$959$	−2.91597e8	−	2.91597e8i	−0.330618	−	0.330618i
$960$	1.46066e9	+	1.46066e9i	1.65096	+	1.65096i
$961$			4.57705e8i			0.515722i
$962$			8.86299e6i			0.00995532i
$963$		−	1.05405e9i		−	1.18027i
$964$	−9.54532e8			−1.06552
$965$	−5.07620e8	+	5.07620e8i	−0.564881	+	0.564881i
$966$		−	6.02951e7i		−	0.0668884i
$967$	−5.47308e7	+	5.47308e7i	−0.0605274	+	0.0605274i	−0.736723	−	0.676195i	$-0.763628\pi$
$967$	−5.47308e7	+	5.47308e7i	−0.0605274	+	0.0605274i	0.676195	+	0.736723i	$0.263628\pi$
$968$	−2.96406e7	−	2.96406e7i	−0.0326784	−	0.0326784i
$969$	8.47115e8	−	8.47115e8i	0.931045	−	0.931045i
$970$			5.01215e7i			0.0549172i
$971$	9.25654e8	+	9.25654e8i	1.01109	+	1.01109i	0.999938	+	0.0111547i	$0.00355072\pi$
$971$	9.25654e8	+	9.25654e8i	1.01109	+	1.01109i	0.0111547	+	0.999938i	$0.496449\pi$
$972$	8.87692e8	−	8.87692e8i	0.966637	−	0.966637i
$973$	7.04697e7			0.0765004
$974$	−5.92901e7	−	5.92901e7i	−0.0641661	−	0.0641661i
$975$	−2.48352e8	+	2.48352e8i	−0.267950	+	0.267950i
$976$	−4.52361e8	−	4.52361e8i	−0.486559	−	0.486559i
$977$	−1.30084e9			−1.39489			−0.697444	−	0.716639i	$-0.745679\pi$
$977$	−1.30084e9			−1.39489			−0.697444	+	0.716639i	$0.745679\pi$
$978$	2.25613e7	+	2.25613e7i	0.0241184	+	0.0241184i
$979$		−	7.65107e8i		−	0.815406i
$980$	4.66915e8			0.496089
$981$	−6.68659e8			−0.708269
$982$	−2.23994e7			−0.0236538
$983$	2.67634e7	−	2.67634e7i	0.0281761	−	0.0281761i	−0.692878	−	0.721054i	$-0.743658\pi$
$983$	2.67634e7	−	2.67634e7i	0.0281761	−	0.0281761i	0.721054	+	0.692878i	$0.243658\pi$
$984$	−1.22094e8	+	1.22094e8i	−0.128147	+	0.128147i
$985$		−	1.16591e9i		−	1.21999i
$986$	1.09022e7	−	1.81972e7i	0.0113732	−	0.0189834i
$987$	1.38059e9			1.43587
$988$	−2.15836e8	−	2.15836e8i	−0.223797	−	0.223797i
$989$	−7.86508e8	−	7.86508e8i	−0.813044	−	0.813044i
$990$			6.45591e7i			0.0665353i
$991$			1.40170e8i			0.144024i	0.997404	+	0.0720118i	$0.0229419\pi$
$991$			1.40170e8i			0.144024i	−0.997404	+	0.0720118i	$0.977058\pi$
$992$			1.65733e8i			0.169775i
$993$	8.54292e8			0.872486
$994$	3.75746e7	−	3.75746e7i	0.0382591	−	0.0382591i
$995$			8.01304e8i			0.813445i
$996$	−3.42822e8	+	3.42822e8i	−0.346969	+	0.346969i
$997$	−1.62157e8	−	1.62157e8i	−0.163625	−	0.163625i	0.620545	−	0.784171i	$-0.286911\pi$
$997$	−1.62157e8	−	1.62157e8i	−0.163625	−	0.163625i	−0.784171	+	0.620545i	$0.786911\pi$
$998$	6.22911e7	−	6.22911e7i	0.0626664	−	0.0626664i
$999$		−	5.88195e8i		−	0.589963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.7.c.a.12.8	✓	28
29.17	odd	4	inner	29.7.c.a.17.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.7.c.a.12.8	✓	28	1.1	even	1	trivial
29.7.c.a.17.8	yes	28	29.17	odd	4	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.260765 + 0.260765i) q^{2} +(29.0542 + 29.0542i) q^{3} -63.8640i q^{4} -194.251i q^{5} +15.1526i q^{6} +282.863 q^{7} +(33.3424 - 33.3424i) q^{8} +959.292i q^{9} +O(q^{10})\)	\(q+(0.260765 + 0.260765i) q^{2} +(29.0542 + 29.0542i) q^{3} -63.8640i q^{4} -194.251i q^{5} +15.1526i q^{6} +282.863 q^{7} +(33.3424 - 33.3424i) q^{8} +959.292i q^{9} +(50.6540 - 50.6540i) q^{10} +(664.299 + 664.299i) q^{11} +(1855.52 - 1855.52i) q^{12} -386.631i q^{13} +(73.7609 + 73.7609i) q^{14} +(5643.82 - 5643.82i) q^{15} -4069.91 q^{16} +(-1667.75 - 1667.75i) q^{17} +(-250.150 + 250.150i) q^{18} +(8741.21 + 8741.21i) q^{19} -12405.7 q^{20} +(8218.37 + 8218.37i) q^{21} +346.452i q^{22} -14067.5 q^{23} +1937.48 q^{24} -22108.6 q^{25} +(100.820 - 100.820i) q^{26} +(-6690.94 + 6690.94i) q^{27} -18064.8i q^{28} +(20921.6 + 12534.4i) q^{29} +2943.42 q^{30} +(-25934.6 - 25934.6i) q^{31} +(-3195.21 - 3195.21i) q^{32} +38601.3i q^{33} -869.783i q^{34} -54946.6i q^{35} +61264.2 q^{36} +(-43954.6 + 43954.6i) q^{37} +4558.80i q^{38} +(11233.3 - 11233.3i) q^{39} +(-6476.82 - 6476.82i) q^{40} +(-63016.8 + 63016.8i) q^{41} +4286.12i q^{42} +(55909.5 + 55909.5i) q^{43} +(42424.8 - 42424.8i) q^{44} +186344. q^{45} +(-3668.31 - 3668.31i) q^{46} +(83994.4 - 83994.4i) q^{47} +(-118248. - 118248. i) q^{48} -37637.2 q^{49} +(-5765.15 - 5765.15i) q^{50} -96910.4i q^{51} -24691.8 q^{52} +80337.4 q^{53} -3489.52 q^{54} +(129041. - 129041. i) q^{55} +(9431.36 - 9431.36i) q^{56} +507938. i q^{57} +(2187.08 + 8724.14i) q^{58} -199137. q^{59} +(-360437. - 360437. i) q^{60} +(111148. + 111148. i) q^{61} -13525.7i q^{62} +271349. i q^{63} +258808. i q^{64} -75103.7 q^{65} +(-10065.9 + 10065.9i) q^{66} +460175. i q^{67} +(-106509. + 106509. i) q^{68} +(-408720. - 408720. i) q^{69} +(14328.2 - 14328.2i) q^{70} -509411. i q^{71} +(31985.1 + 31985.1i) q^{72} +(58913.5 - 58913.5i) q^{73} -22923.6 q^{74} +(-642348. - 642348. i) q^{75} +(558249. - 558249. i) q^{76} +(187906. + 187906. i) q^{77} +5858.48 q^{78} +(502900. + 502900. i) q^{79} +790585. i q^{80} +310524. q^{81} -32865.1 q^{82} -184758. q^{83} +(524858. - 524858. i) q^{84} +(-323963. + 323963. i) q^{85} +29158.5i q^{86} +(243682. + 972036. i) q^{87} +44298.7 q^{88} +(-575875. - 575875. i) q^{89} +(48591.9 + 48591.9i) q^{90} -109364. i q^{91} +898408. i q^{92} -1.50702e6i q^{93} +43805.6 q^{94} +(1.69799e6 - 1.69799e6i) q^{95} -185668. i q^{96} +(-494744. + 494744. i) q^{97} +(-9814.47 - 9814.47i) q^{98} +(-637256. + 637256. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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