LMFDB - Embedded newform 31.8.g.a.9.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,8,Mod(7,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.7"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.68393579001$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.16
Character	$\chi$	$=$	31.9
Dual form			31.8.g.a.7.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.12040 - 15.7590i) q^{2} +(-83.6064 - 17.7711i) q^{3} +(-118.572 - 86.1478i) q^{4} +(-218.479 - 378.417i) q^{5} +(-708.152 + 1226.56i) q^{6} +(384.830 - 171.337i) q^{7} +(-248.849 + 180.799i) q^{8} +(4676.30 + 2082.02i) q^{9} +(-7082.16 + 1505.36i) q^{10} +(54.5220 - 518.743i) q^{11} +(8382.46 + 9309.67i) q^{12} +(-5051.12 + 5609.84i) q^{13} +(-729.617 - 6941.84i) q^{14} +(11541.4 + 35520.7i) q^{15} +(-4222.19 - 12994.6i) q^{16} +(-3501.49 - 33314.4i) q^{17} +(56755.0 - 63032.8i) q^{18} +(17764.1 + 19729.0i) q^{19} +(-6694.22 + 63691.3i) q^{20} +(-35219.1 + 7486.05i) q^{21} +(-7895.67 - 3515.38i) q^{22} +(-22269.7 + 16179.9i) q^{23} +(24018.4 - 10693.7i) q^{24} +(-56403.9 + 97694.4i) q^{25} +(62541.5 + 108325. i) q^{26} +(-202737. - 147297. i) q^{27} +(-60390.5 - 12836.4i) q^{28} +(-34221.5 + 105323. i) q^{29} +618866. q^{30} +(65077.6 - 152570. i) q^{31} -265772. q^{32} +(-13777.0 + 42401.3i) q^{33} +(-542930. - 115403. i) q^{34} +(-148914. - 108193. i) q^{35} +(-375117. - 649722. i) q^{36} +(-189779. + 328707. i) q^{37} +(401869. - 178923. i) q^{38} +(521999. - 379255. i) q^{39} +(122786. + 54667.8i) q^{40} +(496059. - 105441. i) q^{41} +(-62363.4 + 593348. i) q^{42} +(341916. + 379736. i) q^{43} +(-51153.3 + 56811.5i) q^{44} +(-233801. - 2.22447e6i) q^{45} +(140948. + 433795. i) q^{46} +(-398223. - 1.22560e6i) q^{47} +(122074. + 1.16146e6i) q^{48} +(-432320. + 480140. i) q^{49} +(1.25075e6 + 1.38910e6i) q^{50} +(-299287. + 2.84752e6i) q^{51} +(1.08220e6 - 230028. i) q^{52} +(-201868. - 89877.5i) q^{53} +(-3.35935e6 + 2.44071e6i) q^{54} +(-208213. + 92702.4i) q^{55} +(-64786.9 + 112214. i) q^{56} +(-1.13459e6 - 1.96516e6i) q^{57} +(1.48455e6 + 1.07859e6i) q^{58} +(1.97631e6 + 420079. i) q^{59} +(1.69154e6 - 5.20604e6i) q^{60} -2.07604e6 q^{61} +(-2.07112e6 - 1.80677e6i) q^{62} +2.15631e6 q^{63} +(-820419. + 2.52499e6i) q^{64} +(3.22643e6 + 685798. i) q^{65} +(597657. + 434223. i) q^{66} +(-862318. - 1.49358e6i) q^{67} +(-2.45479e6 + 4.25181e6i) q^{68} +(2.14942e6 - 956985. i) q^{69} +(-2.46750e6 + 1.79275e6i) q^{70} +(-938747. - 417957. i) q^{71} +(-1.54012e6 + 327363. i) q^{72} +(154396. - 1.46898e6i) q^{73} +(4.20834e6 + 4.67384e6i) q^{74} +(6.45186e6 - 7.16552e6i) q^{75} +(-406717. - 3.86966e6i) q^{76} +(-67898.3 - 208969. i) q^{77} +(-3.30382e6 - 1.01681e7i) q^{78} +(-1327.80 - 12633.2i) q^{79} +(-3.99490e6 + 4.43679e6i) q^{80} +(6.84164e6 + 7.59841e6i) q^{81} +(878385. - 8.35728e6i) q^{82} +(-3.63995e6 + 773695. i) q^{83} +(4.82092e6 + 2.14641e6i) q^{84} +(-1.18417e7 + 8.60353e6i) q^{85} +(7.73498e6 - 3.44384e6i) q^{86} +(4.73284e6 - 8.19751e6i) q^{87} +(80220.6 + 138946. i) q^{88} +(895312. + 650482. i) q^{89} +(-3.62525e7 - 7.70570e6i) q^{90} +(-982649. + 3.02428e6i) q^{91} +4.03443e6 q^{92} +(-8.15223e6 + 1.15993e7i) q^{93} -2.13533e7 q^{94} +(3.58472e6 - 1.10326e7i) q^{95} +(2.22203e7 + 4.72306e6i) q^{96} +(-9.76134e6 - 7.09203e6i) q^{97} +(5.35286e6 + 9.27143e6i) q^{98} +(1.33499e6 - 2.31228e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{2} - 8 q^{3} - 2362 q^{4} - 75 q^{5} - 1637 q^{6} + 5518 q^{7} + 3401 q^{8} + 14542 q^{9} - 5312 q^{10} + 1361 q^{11} - 18281 q^{12} + 22457 q^{13} + 28470 q^{14} - 86918 q^{15} - 155730 q^{16}+ \cdots - 102755966 q^{99}+O(q^{100}) $ 144 * q - 6 * q^2 - 8 * q^3 - 2362 * q^4 - 75 * q^5 - 1637 * q^6 + 5518 * q^7 + 3401 * q^8 + 14542 * q^9 - 5312 * q^10 + 1361 * q^11 - 18281 * q^12 + 22457 * q^13 + 28470 * q^14 - 86918 * q^15 - 155730 * q^16 + 51582 * q^17 - 24915 * q^18 + 206748 * q^19 + 53815 * q^20 - 28547 * q^21 + 471441 * q^22 - 10235 * q^23 + 69278 * q^24 - 974301 * q^25 - 279651 * q^26 - 948323 * q^27 + 550632 * q^28 - 32990 * q^29 + 2457990 * q^30 + 899715 * q^31 - 1048518 * q^32 + 780887 * q^33 - 1741528 * q^34 + 40023 * q^35 - 2118881 * q^36 - 787972 * q^37 + 580274 * q^38 + 2541281 * q^39 + 2341817 * q^40 + 1129504 * q^41 - 4390379 * q^42 + 481927 * q^43 - 3123681 * q^44 - 1715971 * q^45 + 2065430 * q^46 - 3123106 * q^47 + 1041890 * q^48 + 76766 * q^49 + 7537425 * q^50 + 6145978 * q^51 + 3260257 * q^52 + 141486 * q^53 - 8979668 * q^54 - 8182779 * q^55 - 5240874 * q^56 - 5487037 * q^57 + 5315215 * q^58 + 7471552 * q^59 + 8590679 * q^60 + 10667852 * q^61 + 27020951 * q^62 - 23783686 * q^63 - 3962521 * q^64 + 935148 * q^65 + 3015728 * q^66 - 17382495 * q^67 - 29462568 * q^68 - 26986306 * q^69 - 31811186 * q^70 - 6186650 * q^71 + 35811589 * q^72 + 6470154 * q^73 + 55339663 * q^74 + 17367737 * q^75 + 2919592 * q^76 + 31865334 * q^77 - 7291717 * q^78 + 4223078 * q^79 + 77431338 * q^80 - 5164601 * q^81 - 19477394 * q^82 - 28867780 * q^83 - 76561164 * q^84 - 45198987 * q^85 - 60993764 * q^86 + 18253055 * q^87 - 45197061 * q^88 - 8429459 * q^89 + 83458809 * q^90 - 53128088 * q^91 + 77469728 * q^92 + 41662009 * q^93 - 16867972 * q^94 - 12744274 * q^95 + 119555444 * q^96 + 20643027 * q^97 + 49624796 * q^98 - 102755966 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	5.12040	−	15.7590i	0.452583	−	1.39291i	−0.421365	−	0.906891i	$-0.638449\pi$
$2$	5.12040	−	15.7590i	0.452583	−	1.39291i	0.873949	−	0.486018i	$-0.161551\pi$
$3$	−83.6064	−	17.7711i	−1.78778	−	0.380005i	−0.809475	−	0.587154i	$-0.800248\pi$
$3$	−83.6064	−	17.7711i	−1.78778	−	0.380005i	−0.978309	+	0.207149i	$0.933582\pi$
$4$	−118.572	−	86.1478i	−0.926346	−	0.673030i
$5$	−218.479	−	378.417i	−0.781655	−	1.35387i	−0.930977	−	0.365078i	$-0.881042\pi$
$5$	−218.479	−	378.417i	−0.781655	−	1.35387i	0.149322	−	0.988789i	$-0.452291\pi$
$6$	−708.152	+	1226.56i	−1.33843	+	2.31824i
$7$	384.830	−	171.337i	0.424059	−	0.188803i	−0.183601	−	0.983001i	$-0.558775\pi$
$7$	384.830	−	171.337i	0.424059	−	0.188803i	0.607659	+	0.794198i	$0.292109\pi$
$8$	−248.849	+	180.799i	−0.171839	+	0.124848i
$9$	4676.30	+	2082.02i	2.13822	+	0.951999i
$10$	−7082.16	+	1505.36i	−2.23958	+	0.476037i
$11$	54.5220	−	518.743i	0.0123509	−	0.117511i	−0.986609	−	0.163101i	$-0.947850\pi$
$11$	54.5220	−	518.743i	0.0123509	−	0.117511i	0.998960	+	0.0455905i	$0.0145169\pi$
$12$	8382.46	+	9309.67i	1.40035	+	1.55525i
$13$	−5051.12	+	5609.84i	−0.637656	+	0.708189i	−0.972190	−	0.234195i	$-0.924755\pi$
$13$	−5051.12	+	5609.84i	−0.637656	+	0.708189i	0.334534	+	0.942384i	$0.391421\pi$
$14$	−729.617	−	6941.84i	−0.0710635	−	0.676124i
$15$	11541.4	+	35520.7i	0.882954	+	2.71745i
$16$	−4222.19	−	12994.6i	−0.257702	−	0.793125i
$17$	−3501.49	−	33314.4i	−0.172855	−	1.64460i	−0.645797	−	0.763510i	$-0.723475\pi$
$17$	−3501.49	−	33314.4i	−0.172855	−	1.64460i	0.472942	−	0.881094i	$-0.343192\pi$
$18$	56755.0	−	63032.8i	2.29377	−	2.54749i
$19$	17764.1	+	19729.0i	0.594163	+	0.659885i	0.962966	−	0.269622i	$-0.0868989\pi$
$19$	17764.1	+	19729.0i	0.594163	+	0.659885i	−0.368803	+	0.929508i	$0.620232\pi$
$20$	−6694.22	+	63691.3i	−0.187109	+	1.78023i
$21$	−35219.1	+	7486.05i	−0.829871	+	0.176395i
$22$	−7895.67	−	3515.38i	−0.158092	−	0.0703871i
$23$	−22269.7	+	16179.9i	−0.381651	+	0.277286i	−0.762026	−	0.647547i	$-0.775795\pi$
$23$	−22269.7	+	16179.9i	−0.381651	+	0.277286i	0.380375	+	0.924833i	$0.375795\pi$
$24$	24018.4	−	10693.7i	0.354654	−	0.157902i
$25$	−56403.9	+	97694.4i	−0.721969	+	1.25049i
$26$	62541.5	+	108325.i	0.697849	+	1.20871i
$27$	−202737.	−	147297.i	−1.98226	−	1.44020i
$28$	−60390.5	−	12836.4i	−0.519895	−	0.110507i
$29$	−34221.5	+	105323.i	−0.260559	+	0.801918i	0.732125	+	0.681171i	$0.238529\pi$
$29$	−34221.5	+	105323.i	−0.260559	+	0.801918i	−0.992683	+	0.120747i	$0.961471\pi$
$30$	618866.			4.18478
$31$	65077.6	−	152570.i	0.392343	−	0.919819i
$31$	65077.6	−	152570.i	0.392343	−	0.919819i
$32$	−265772.			−1.43379
$33$	−13777.0	+	42401.3i	−0.0667354	+	0.205390i
$34$	−542930.	−	115403.i	−2.36901	−	0.503549i
$35$	−148914.	−	108193.i	−0.587082	−	0.426540i
$36$	−375117.	−	649722.i	−1.34001	−	2.32097i
$37$	−189779.	+	328707.i	−0.615946	+	1.06685i	0.374271	+	0.927319i	$0.377893\pi$
$37$	−189779.	+	328707.i	−0.615946	+	1.06685i	−0.990218	+	0.139531i	$0.955440\pi$
$38$	401869.	−	178923.i	1.18807	−	0.528962i
$39$	521999.	−	379255.i	1.40911	−	1.02378i
$40$	122786.	+	54667.8i	0.303346	+	0.135059i
$41$	496059.	−	105441.i	1.12406	−	0.238927i	0.391867	−	0.920022i	$-0.371829\pi$
$41$	496059.	−	105441.i	1.12406	−	0.238927i	0.732195	+	0.681095i	$0.238496\pi$
$42$	−62363.4	+	593348.i	−0.129884	+	1.23577i
$43$	341916.	+	379736.i	0.655812	+	0.728353i	0.975702	−	0.219102i	$-0.0703127\pi$
$43$	341916.	+	379736.i	0.655812	+	0.728353i	−0.319890	+	0.947455i	$0.603646\pi$
$44$	−51153.3	+	56811.5i	−0.0905294	+	0.100543i
$45$	−233801.	−	2.22447e6i	−0.382475	−	3.63900i
$46$	140948.	+	433795.i	0.213505	+	0.657100i
$47$	−398223.	−	1.22560e6i	−0.559479	−	1.72190i	−0.683811	−	0.729659i	$-0.739679\pi$
$47$	−398223.	−	1.22560e6i	−0.559479	−	1.72190i	0.124331	−	0.992241i	$-0.460321\pi$
$48$	122074.	+	1.16146e6i	0.159324	+	1.51586i
$49$	−432320.	+	480140.i	−0.524952	+	0.583018i
$50$	1.25075e6	+	1.38910e6i	1.41506	+	1.57159i
$51$	−299287.	+	2.84752e6i	−0.315931	+	3.00588i
$52$	1.08220e6	−	230028.i	1.06732	−	0.226866i
$53$	−201868.	−	89877.5i	−0.186253	−	0.0829250i	0.311492	−	0.950249i	$-0.399171\pi$
$53$	−201868.	−	89877.5i	−0.186253	−	0.0829250i	−0.497744	+	0.867324i	$0.665838\pi$
$54$	−3.35935e6	+	2.44071e6i	−2.90320	+	2.10930i
$55$	−208213.	+	92702.4i	−0.168748	+	0.0751314i
$56$	−64786.9	+	112214.i	−0.0492980	+	0.0853866i
$57$	−1.13459e6	−	1.96516e6i	−0.811476	−	1.40552i
$58$	1.48455e6	+	1.07859e6i	0.999073	+	0.725869i
$59$	1.97631e6	+	420079.i	1.25278	+	0.266286i	0.786077	−	0.618129i	$-0.212109\pi$
$59$	1.97631e6	+	420079.i	1.25278	+	0.266286i	0.466701	+	0.884415i	$0.345442\pi$
$60$	1.69154e6	−	5.20604e6i	1.01101	−	3.11156i
$61$	−2.07604e6			−1.17107			−0.585534	−	0.810648i	$-0.699115\pi$
$61$	−2.07604e6			−1.17107			−0.585534	+	0.810648i	$0.699115\pi$
$62$	−2.07112e6	−	1.80677e6i	−1.10366	−	0.962792i
$63$	2.15631e6			1.08647
$64$	−820419.	+	2.52499e6i	−0.391206	+	1.20401i
$65$	3.22643e6	+	685798.i	1.45722	+	0.309742i
$66$	597657.	+	434223.i	0.255887	+	0.185913i
$67$	−862318.	−	1.49358e6i	−0.350272	−	0.606689i	0.636025	−	0.771668i	$-0.280578\pi$
$67$	−862318.	−	1.49358e6i	−0.350272	−	0.606689i	−0.986297	+	0.164980i	$0.947244\pi$
$68$	−2.45479e6	+	4.25181e6i	−0.946743	+	1.63981i
$69$	2.14942e6	−	956985.i	0.787680	−	0.350698i
$70$	−2.46750e6	+	1.79275e6i	−0.859834	+	0.624706i
$71$	−938747.	−	417957.i	−0.311275	−	0.138589i	0.245153	−	0.969484i	$-0.421162\pi$
$71$	−938747.	−	417957.i	−0.311275	−	0.138589i	−0.556428	+	0.830896i	$0.687828\pi$
$72$	−1.54012e6	+	327363.i	−0.486285	+	0.103363i
$73$	154396.	−	1.46898e6i	0.0464522	−	0.441963i	−0.946434	−	0.322897i	$-0.895343\pi$
$73$	154396.	−	1.46898e6i	0.0464522	−	0.441963i	0.992886	−	0.119066i	$-0.0379900\pi$
$74$	4.20834e6	+	4.67384e6i	1.20726	+	1.34080i
$75$	6.45186e6	−	7.16552e6i	1.76592	−	1.96125i
$76$	−406717.	−	3.86966e6i	−0.106278	−	1.01117i
$77$	−67898.3	−	208969.i	−0.0169489	−	0.0521633i
$78$	−3.30382e6	−	1.01681e7i	−0.788288	−	2.42610i
$79$	−1327.80	−	12633.2i	−0.000302997	−	0.00288282i	0.994369	−	0.105970i	$-0.0337947\pi$
$79$	−1327.80	−	12633.2i	−0.000302997	−	0.00288282i	−0.994672	+	0.103087i	$0.967128\pi$
$80$	−3.99490e6	+	4.43679e6i	−0.872351	+	0.968844i
$81$	6.84164e6	+	7.59841e6i	1.43042	+	1.58864i
$82$	878385.	−	8.35728e6i	0.175929	−	1.67385i
$83$	−3.63995e6	+	773695.i	−0.698750	+	0.148524i	−0.543572	−	0.839363i	$-0.682929\pi$
$83$	−3.63995e6	+	773695.i	−0.698750	+	0.148524i	−0.155178	+	0.987886i	$0.549595\pi$
$84$	4.82092e6	+	2.14641e6i	0.887467	+	0.395126i
$85$	−1.18417e7	+	8.60353e6i	−2.09146	+	1.51953i
$86$	7.73498e6	−	3.44384e6i	1.31134	−	0.583846i
$87$	4.73284e6	−	8.19751e6i	0.770556	−	1.33464i
$88$	80220.6	+	138946.i	0.0125486	+	0.0217349i
$89$	895312.	+	650482.i	0.134620	+	0.0978071i	0.653057	−	0.757309i	$-0.273486\pi$
$89$	895312.	+	650482.i	0.134620	+	0.0978071i	−0.518437	+	0.855116i	$0.673486\pi$
$90$	−3.62525e7	−	7.70570e6i	−5.24190	−	1.11420i
$91$	−982649.	+	3.02428e6i	−0.136695	+	0.420705i
$92$	4.03443e6			0.540163
$93$	−8.15223e6	+	1.15993e7i	−1.05096	+	1.49535i
$94$	−2.13533e7			−2.65166
$95$	3.58472e6	−	1.10326e7i	0.428966	−	1.32022i
$96$	2.22203e7	+	4.72306e6i	2.56330	+	0.544847i
$97$	−9.76134e6	−	7.09203e6i	−1.08595	−	0.788986i	−0.107236	−	0.994234i	$-0.534200\pi$
$97$	−9.76134e6	−	7.09203e6i	−1.08595	−	0.788986i	−0.978710	+	0.205247i	$0.934200\pi$
$98$	5.35286e6	+	9.27143e6i	0.574506	+	0.995074i
$99$	1.33499e6	−	2.31228e6i	0.138279	−	0.239506i
$100$	1.51041e7	−	6.72477e6i	1.51041	−	0.672477i
$101$	−9.33572e6	+	6.78280e6i	−0.901619	+	0.655065i	−0.938881	−	0.344241i	$-0.888136\pi$
$101$	−9.33572e6	+	6.78280e6i	−0.901619	+	0.655065i	0.0372624	+	0.999306i	$0.488136\pi$
$102$	4.33416e7	+	1.92969e7i	4.04393	+	1.80048i
$103$	1.66704e6	−	354339.i	0.150319	−	0.0319513i	−0.132137	−	0.991231i	$-0.542184\pi$
$103$	1.66704e6	−	354339.i	0.150319	−	0.0319513i	0.282457	+	0.959280i	$0.408851\pi$
$104$	242711.	−	2.30924e6i	0.0211579	−	0.201304i
$105$	1.05275e7	+	1.16920e7i	0.887488	+	0.985655i
$106$	−2.45002e6	+	2.72102e6i	−0.199802	+	0.221902i
$107$	−1.52871e6	−	1.45447e7i	−0.120638	−	1.14779i	−0.872549	−	0.488526i	$-0.837535\pi$
$107$	−1.52871e6	−	1.45447e7i	−0.120638	−	1.14779i	0.751912	−	0.659264i	$-0.229132\pi$
$108$	1.13497e7	+	3.49307e7i	0.866963	+	2.66824i
$109$	−3.25218e6	−	1.00092e7i	−0.240537	−	0.740297i	−0.996339	−	0.0854961i	$-0.972752\pi$
$109$	−3.25218e6	−	1.00092e7i	−0.240537	−	0.740297i	0.755801	−	0.654801i	$-0.227248\pi$
$110$	394760.	+	3.75589e6i	0.0282787	+	0.269054i
$111$	2.17083e7	−	2.41095e7i	1.50659	−	1.67324i
$112$	−3.85128e6	−	4.27728e6i	−0.259025	−	0.287676i
$113$	−853708.	+	8.12249e6i	−0.0556589	+	0.529559i	0.930797	+	0.365535i	$0.119114\pi$
$113$	−853708.	+	8.12249e6i	−0.0556589	+	0.529559i	−0.986456	+	0.164024i	$0.947553\pi$
$114$	−3.67785e7	+	7.81750e6i	−2.32502	+	0.494198i
$115$	1.09882e7	+	4.89227e6i	0.673728	+	0.299963i
$116$	1.31311e7	−	9.54027e6i	0.781082	−	0.567489i
$117$	−3.53004e7	+	1.57167e7i	−2.03765	+	0.907218i
$118$	1.67395e7	−	2.89937e7i	0.937899	−	1.62449i
$119$	−7.05548e6	−	1.22205e7i	−0.383807	−	0.664773i
$120$	−9.29419e6	−	6.75262e6i	−0.490995	−	0.356729i
$121$	1.87952e7	+	3.99504e6i	0.964491	+	0.205009i
$122$	−1.06302e7	+	3.27163e7i	−0.530006	+	1.63119i
$123$	−4.33475e7			−2.10037
$124$	−2.08599e7	+	1.24843e7i	−0.982510	+	0.588013i
$125$	1.51549e7			0.694014
$126$	1.10411e7	−	3.39812e7i	0.491719	−	1.51336i
$127$	1.27702e7	+	2.71438e6i	0.553202	+	0.117587i	0.476027	−	0.879431i	$-0.342077\pi$
$127$	1.27702e7	+	2.71438e6i	0.553202	+	0.117587i	0.0771751	+	0.997018i	$0.475410\pi$
$128$	8.06853e6	+	5.86213e6i	0.340063	+	0.247070i
$129$	−2.18380e7	−	3.78245e7i	−0.895672	−	1.55135i
$130$	2.73281e7	−	4.73336e7i	1.09096	−	1.88959i
$131$	−1.22303e7	+	5.44528e6i	−0.475321	+	0.211627i	−0.630392	−	0.776277i	$-0.717106\pi$
$131$	−1.22303e7	+	5.44528e6i	−0.475321	+	0.211627i	0.155071	+	0.987903i	$0.450439\pi$
$132$	5.28635e6	−	3.84076e6i	0.200054	−	0.145348i
$133$	1.02165e7	+	4.54867e6i	0.376548	+	0.167650i
$134$	−2.79526e7	+	5.94152e6i	−1.00359	+	0.213320i
$135$	−1.14459e7	+	1.08901e8i	−0.400389	+	3.80945i
$136$	6.89457e6	+	7.65720e6i	0.235029	+	0.261026i
$137$	−4.83944e6	+	5.37474e6i	−0.160795	+	0.178581i	−0.818159	−	0.574992i	$-0.805005\pi$
$137$	−4.83944e6	+	5.37474e6i	−0.160795	+	0.178581i	0.657363	+	0.753574i	$0.271672\pi$
$138$	−4.07519e6	−	3.87728e7i	−0.131999	−	1.25589i
$139$	−1.16914e6	−	3.59825e6i	−0.0369246	−	0.113642i	0.930895	−	0.365286i	$-0.119029\pi$
$139$	−1.16914e6	−	3.59825e6i	−0.0369246	−	0.113642i	−0.967820	+	0.251644i	$0.919029\pi$
$140$	8.33656e6	+	2.56573e7i	0.256767	+	0.790247i
$141$	1.15137e7	+	1.09545e8i	0.345897	+	3.29099i
$142$	−1.13933e7	+	1.26536e7i	−0.333919	+	0.370855i
$143$	2.63467e6	+	2.92609e6i	0.0753441	+	0.0836781i
$144$	7.31074e6	−	6.95571e7i	0.204029	−	1.94121i
$145$	4.73327e7	−	1.00609e7i	1.28936	−	0.274061i
$146$	−2.23590e7	−	9.95488e6i	−0.594590	−	0.264729i
$147$	4.46773e7	−	3.24600e7i	1.16005	−	0.842826i
$148$	5.08200e7	−	2.26265e7i	1.28860	−	0.573722i
$149$	−2.52183e7	+	4.36794e7i	−0.624546	+	1.08174i	0.364083	+	0.931367i	$0.381383\pi$
$149$	−2.52183e7	+	4.36794e7i	−0.624546	+	1.08174i	−0.988629	+	0.150378i	$0.951951\pi$
$150$	−7.98850e7	−	1.38365e8i	−1.93262	−	3.34739i
$151$	−3.27443e7	−	2.37901e7i	−0.773956	−	0.562312i	0.129203	−	0.991618i	$-0.458758\pi$
$151$	−3.27443e7	−	2.37901e7i	−0.773956	−	0.562312i	−0.903159	+	0.429306i	$0.858758\pi$
$152$	−7.98758e6	−	1.69781e6i	−0.184486	−	0.0392137i
$153$	5.29873e7	−	1.63078e8i	1.19606	−	3.68109i
$154$	−3.64081e6			−0.0803295
$155$	−7.19531e7	+	8.70685e6i	−1.55199	+	0.187802i
$156$	−9.45666e7			−1.99435
$157$	−1.09576e7	+	3.37241e7i	−0.225979	+	0.695492i	0.772212	+	0.635365i	$0.219150\pi$
$157$	−1.09576e7	+	3.37241e7i	−0.225979	+	0.695492i	−0.998191	+	0.0601266i	$0.980850\pi$
$158$	−205885.	−	43762.2i	−0.00415264	−	0.000882671i
$159$	1.52802e7	+	1.11017e7i	0.301467	+	0.219029i
$160$	5.80657e7	+	1.00573e8i	1.12073	+	1.94116i
$161$	−5.79783e6	+	1.00421e7i	−0.109490	+	0.189642i
$162$	1.54775e8	−	6.89103e7i	2.86021	−	1.27345i
$163$	4.34980e7	−	3.16032e7i	0.786707	−	0.571576i	−0.120278	−	0.992740i	$-0.538378\pi$
$163$	4.34980e7	−	3.16032e7i	0.786707	−	0.571576i	0.906984	+	0.421164i	$0.138378\pi$
$164$	−6.79023e7	−	3.02321e7i	−1.20207	−	0.535198i
$165$	1.90554e7	−	4.05034e6i	0.330235	−	0.0701937i
$166$	−6.44536e6	+	6.13235e7i	−0.109363	+	1.04051i
$167$	1.97249e7	+	2.19068e7i	0.327724	+	0.363974i	0.884379	−	0.466769i	$-0.154582\pi$
$167$	1.97249e7	+	2.19068e7i	0.327724	+	0.363974i	−0.556655	+	0.830744i	$0.687916\pi$
$168$	7.41077e6	−	8.23049e6i	0.120582	−	0.133919i
$169$	602537.	+	5.73276e6i	0.00960241	+	0.0913608i
$170$	7.49483e7	+	2.30667e8i	1.17001	+	3.60093i
$171$	4.19940e7	+	1.29244e8i	0.642244	+	1.97663i
$172$	−7.82831e6	−	7.44814e7i	−0.117306	−	1.11609i
$173$	1.86173e6	−	2.06766e6i	0.0273373	−	0.0303611i	−0.729321	−	0.684172i	$-0.760164\pi$
$173$	1.86173e6	−	2.06766e6i	0.0273373	−	0.0303611i	0.756658	+	0.653810i	$0.226831\pi$
$174$	−1.04950e8	−	1.16559e8i	−1.51029	−	1.67735i
$175$	−4.96721e6	+	4.72598e7i	−0.0700614	+	0.666590i
$176$	−6.97103e6	+	1.48174e6i	−0.0963835	+	0.0204870i
$177$	−1.57767e8	−	7.02425e7i	−2.13851	−	0.952124i
$178$	1.48353e7	−	1.07785e7i	0.197163	−	0.143247i
$179$	9.03511e7	−	4.02269e7i	1.17746	−	0.524241i	0.277722	−	0.960662i	$-0.410421\pi$
$179$	9.03511e7	−	4.02269e7i	1.17746	−	0.524241i	0.899743	+	0.436421i	$0.143754\pi$
$180$	−1.63911e8	+	2.83902e8i	−2.09485	+	3.62839i
$181$	−5.36356e7	−	9.28996e7i	−0.672323	−	1.16450i	−0.977244	−	0.212120i	$-0.931963\pi$
$181$	−5.36356e7	−	9.28996e7i	−0.672323	−	1.16450i	0.304920	−	0.952378i	$-0.401370\pi$
$182$	4.26280e7	+	3.09711e7i	0.524137	+	0.380808i
$183$	1.73570e8	+	3.68935e7i	2.09362	+	0.445012i
$184$	2.61648e6	−	8.05270e6i	0.0309639	−	0.0952969i
$185$	1.65851e8			1.92583
$186$	1.41050e8	+	1.87864e8i	1.60723	+	2.14066i
$187$	−1.74725e7			−0.195393
$188$	−5.83649e7	+	1.79629e8i	−0.640619	+	1.97162i
$189$	−1.03257e8	−	2.19479e7i	−1.11251	−	0.236471i
$190$	−1.55508e8	−	1.12983e8i	−1.64480	−	1.19502i
$191$	4.60083e6	+	7.96888e6i	0.0477771	+	0.0827524i	0.888925	−	0.458053i	$-0.151453\pi$
$191$	4.60083e6	+	7.96888e6i	0.0477771	+	0.0827524i	−0.841148	+	0.540805i	$0.818120\pi$
$192$	1.13464e8	−	1.96526e8i	1.15692	−	2.00385i
$193$	766294.	−	341176.i	0.00767264	−	0.00341608i	−0.402897	−	0.915245i	$-0.631997\pi$
$193$	766294.	−	341176.i	0.00767264	−	0.00341608i	0.410569	+	0.911829i	$0.365330\pi$
$194$	−1.61745e8	+	1.17515e8i	−1.59047	+	1.15554i
$195$	−2.57563e8	−	1.14674e8i	−2.48749	−	1.10750i
$196$	9.26242e7	−	1.96879e7i	0.878675	−	0.186768i
$197$	7.74077e6	−	7.36485e7i	0.0721360	−	0.686328i	−0.897373	−	0.441273i	$-0.854527\pi$
$197$	7.74077e6	−	7.36485e7i	0.0721360	−	0.686328i	0.969509	−	0.245056i	$-0.0788062\pi$
$198$	−2.96034e7	−	3.28779e7i	−0.271028	−	0.301007i
$199$	3.49629e7	−	3.88302e7i	0.314501	−	0.349289i	−0.565082	−	0.825035i	$-0.691155\pi$
$199$	3.49629e7	−	3.88302e7i	0.314501	−	0.349289i	0.879582	+	0.475746i	$0.157822\pi$
$200$	−3.62704e6	−	3.45089e7i	−0.0320588	−	0.305019i
$201$	4.55528e7	+	1.40197e8i	0.395666	+	1.21773i
$202$	5.90873e7	+	1.81852e8i	0.504387	+	1.55234i
$203$	4.87629e6	+	4.63948e7i	0.0409123	+	0.389254i
$204$	2.80795e8	−	3.11855e8i	2.31571	−	2.57186i
$205$	−1.48279e8	−	1.64681e8i	−1.20210	−	1.33507i
$206$	2.95186e6	−	2.80851e7i	0.0235267	−	0.223842i
$207$	−1.37826e8	+	2.92959e7i	−1.08003	+	0.229568i
$208$	9.42242e7	+	4.19513e7i	0.726007	+	0.323239i
$209$	1.12028e7	−	8.13933e6i	0.0848820	−	0.0616704i
$210$	2.38158e8	−	1.06035e8i	1.77459	−	0.790098i
$211$	7.61861e7	−	1.31958e8i	0.558325	−	0.967047i	−0.439311	−	0.898335i	$-0.644778\pi$
$211$	7.61861e7	−	1.31958e8i	0.558325	−	0.967047i	0.997636	−	0.0687126i	$-0.0218892\pi$
$212$	1.61932e7	+	2.80475e7i	0.116723	+	0.202171i
$213$	7.10577e7	+	5.16264e7i	0.503828	+	0.366053i
$214$	−2.37037e8	−	5.03838e7i	−1.65336	−	0.351433i
$215$	6.89970e7	−	2.12351e8i	0.473474	−	1.45720i
$216$	7.70822e7			0.520435
$217$	−1.09710e6	−	6.98636e7i	−0.00728846	−	0.464133i
$218$	−1.74387e8			−1.14003
$219$	−3.90139e7	+	1.20072e8i	−0.250995	+	0.772482i
$220$	3.26744e7	+	6.94516e6i	0.206885	+	0.0439747i
$221$	2.04575e8	+	1.48633e8i	1.27491	+	0.926277i
$222$	−2.68785e8	−	4.65550e8i	−1.64881	−	2.85582i
$223$	1.31564e8	−	2.27875e8i	0.794455	−	1.37604i	−0.128730	−	0.991680i	$-0.541090\pi$
$223$	1.31564e8	−	2.27875e8i	0.794455	−	1.37604i	0.923185	−	0.384356i	$-0.125577\pi$
$224$	−1.02277e8	+	4.55367e7i	−0.608009	+	0.270703i
$225$	−4.67163e8	+	3.39414e8i	−2.73419	+	1.98651i
$226$	1.23631e8	+	5.50439e7i	0.712437	+	0.317197i
$227$	1.74372e8	−	3.70639e7i	0.989432	−	0.210310i	0.315357	−	0.948973i	$-0.397876\pi$
$227$	1.74372e8	−	3.70639e7i	0.989432	−	0.210310i	0.674075	+	0.738663i	$0.264542\pi$
$228$	−3.47638e7	+	3.30756e8i	−0.194248	+	1.84814i
$229$	9.24906e7	+	1.02721e8i	0.508948	+	0.565244i	0.941780	−	0.336231i	$-0.109152\pi$
$229$	9.24906e7	+	1.02721e8i	0.508948	+	0.565244i	−0.432832	+	0.901475i	$0.642486\pi$
$230$	1.33361e8	−	1.48112e8i	0.722739	−	0.802683i
$231$	1.96312e6	+	1.86778e7i	0.0104786	+	0.0996974i
$232$	−1.05263e7	−	3.23967e7i	−0.0553438	−	0.170331i
$233$	−8.92517e7	−	2.74688e8i	−0.462243	−	1.42264i	−0.862417	−	0.506199i	$-0.831050\pi$
$233$	−8.92517e7	−	2.74688e8i	−0.462243	−	1.42264i	0.400173	−	0.916439i	$-0.368950\pi$
$234$	6.69275e7	+	6.36773e8i	0.341467	+	3.24885i
$235$	−3.76786e8	+	4.18464e8i	−1.89390	+	2.10339i
$236$	−1.98147e8	−	2.20065e8i	−0.981287	−	1.08983i
$237$	−113493.	+	1.07981e6i	−0.000553795	+	0.00526901i
$238$	−2.28709e8	+	4.86135e7i	−1.09967	+	0.233742i
$239$	−3.42432e7	−	1.52461e7i	−0.162249	−	0.0722379i	0.324005	−	0.946055i	$-0.394970\pi$
$239$	−3.42432e7	−	1.52461e7i	−0.162249	−	0.0722379i	−0.486254	+	0.873817i	$0.661637\pi$
$240$	4.12846e8	−	2.99950e8i	1.92774	−	1.40059i
$241$	−1.26176e8	+	5.61770e7i	−0.580652	+	0.258523i	−0.675976	−	0.736923i	$-0.736278\pi$
$241$	−1.26176e8	+	5.61770e7i	−0.580652	+	0.258523i	0.0953242	+	0.995446i	$0.469611\pi$
$242$	1.59197e8	−	2.75737e8i	0.722072	−	1.25066i
$243$	−1.62945e8	−	2.82229e8i	−0.728483	−	1.26177i
$244$	2.46161e8	+	1.78846e8i	1.08481	+	0.788163i
$245$	2.76146e8	+	5.86967e7i	1.19966	+	0.254995i
$246$	−2.21957e8	+	6.83112e8i	−0.950594	+	2.92563i
$247$	−2.00406e8			−0.846195
$248$	1.13900e7	+	4.97328e7i	0.0474181	+	0.207044i
$249$	3.18072e8			1.30565
$250$	7.75992e7	−	2.38826e8i	0.314099	−	0.966698i
$251$	−1.15086e8	−	2.44622e7i	−0.459370	−	0.0976422i	−0.0275867	−	0.999619i	$-0.508782\pi$
$251$	−1.15086e8	−	2.44622e7i	−0.459370	−	0.0976422i	−0.431784	+	0.901977i	$0.642116\pi$
$252$	−2.55678e8	−	1.85761e8i	−1.00645	−	0.731228i
$253$	7.17900e6	+	1.24344e7i	0.0278703	+	0.0482728i
$254$	1.08164e8	−	1.87346e8i	0.414157	−	0.717342i
$255$	1.14294e9	−	5.08870e8i	4.31651	−	1.92183i
$256$	−1.41234e8	+	1.02612e8i	−0.526138	+	0.382261i
$257$	−8.75438e7	−	3.89770e7i	−0.321706	−	0.143233i	0.239529	−	0.970889i	$-0.423007\pi$
$257$	−8.75438e7	−	3.89770e7i	−0.321706	−	0.143233i	−0.561235	+	0.827656i	$0.689674\pi$
$258$	−7.07895e8	+	1.50468e8i	−2.56626	+	0.545474i
$259$	−1.67129e7	+	1.59013e8i	−0.0597727	+	0.568700i
$260$	−3.23485e8	−	3.59266e8i	−1.14142	−	1.26768i
$261$	−3.79314e8	+	4.21271e8i	−1.32056	+	1.46663i
$262$	2.31880e7	+	2.20619e8i	0.0796541	+	0.757858i
$263$	6.54126e6	+	2.01319e7i	0.0221726	+	0.0682402i	0.961531	−	0.274698i	$-0.0885779\pi$
$263$	6.54126e6	+	2.01319e7i	0.0221726	+	0.0682402i	−0.939358	+	0.342938i	$0.888578\pi$
$264$	−4.23773e6	−	1.30424e7i	−0.0141749	−	0.0436258i
$265$	1.00928e7	+	9.60267e7i	0.0333159	+	0.316980i
$266$	1.23995e8	−	1.37710e8i	0.403941	−	0.448622i
$267$	−6.32940e7	−	7.02951e7i	−0.203504	−	0.226014i
$268$	−2.64215e7	+	2.51384e8i	−0.0838466	+	0.797747i
$269$	−3.29222e8	+	6.99782e7i	−1.03123	+	0.219195i	−0.692294	−	0.721615i	$-0.743400\pi$
$269$	−3.29222e8	+	6.99782e7i	−1.03123	+	0.219195i	−0.338935	+	0.940810i	$0.610067\pi$
$270$	1.65755e9	+	7.37990e8i	5.12500	+	2.28180i
$271$	−1.15530e8	+	8.39375e7i	−0.352616	+	0.256191i	−0.749966	−	0.661477i	$-0.769930\pi$
$271$	−1.15530e8	+	8.39375e7i	−0.352616	+	0.256191i	0.397350	+	0.917667i	$0.369930\pi$
$272$	−4.18122e8	+	1.86160e8i	−1.25983	+	0.560913i
$273$	1.35901e8	−	2.35387e8i	0.404252	−	0.700184i
$274$	5.99205e7	+	1.03785e8i	0.175974	+	0.304796i
$275$	4.76030e7	+	3.45856e7i	0.138029	+	0.100284i
$276$	−3.37304e8	−	7.16962e7i	−0.965695	−	0.205265i
$277$	1.86450e8	−	5.73835e8i	0.527089	−	1.62221i	−0.233060	−	0.972462i	$-0.574874\pi$
$277$	1.86450e8	−	5.73835e8i	0.527089	−	1.62221i	0.760148	−	0.649750i	$-0.225126\pi$
$278$	−6.26911e7			−0.175004
$279$	6.21975e8	−	5.77968e8i	1.71458	−	1.59327i
$280$	5.66184e7			0.154136
$281$	2.18011e6	−	6.70967e6i	0.00586145	−	0.0180397i	−0.948083	−	0.318023i	$-0.896981\pi$
$281$	2.18011e6	−	6.70967e6i	0.00586145	−	0.0180397i	0.953944	+	0.299983i	$0.0969811\pi$
$282$	1.78527e9	+	3.79472e8i	4.74060	+	1.00765i
$283$	−9.84363e7	−	7.15181e7i	−0.258168	−	0.187570i	0.451171	−	0.892438i	$-0.351006\pi$
$283$	−9.84363e7	−	7.15181e7i	−0.258168	−	0.187570i	−0.709339	+	0.704867i	$0.751006\pi$
$284$	7.53033e7	+	1.30429e8i	0.195074	+	0.337878i
$285$	−4.95767e8	+	8.58694e8i	−1.26859	+	2.19726i
$286$	5.96027e7	−	2.65368e7i	0.150656	−	0.0670762i
$287$	1.72833e8	−	1.25570e8i	0.431558	−	0.313545i
$288$	−1.24283e9	−	5.53343e8i	−3.06576	−	1.36496i
$289$	−6.96219e8	+	1.47986e8i	−1.69669	+	0.360643i
$290$	8.38132e7	−	7.97429e8i	0.201799	−	1.91999i
$291$	6.90077e8	+	7.66409e8i	1.64162	+	1.82320i
$292$	−1.44856e8	+	1.60879e8i	−0.340485	+	0.378147i
$293$	5.05993e7	+	4.81420e8i	0.117519	+	1.11812i	0.881272	+	0.472609i	$0.156688\pi$
$293$	5.05993e7	+	4.81420e8i	0.117519	+	1.11812i	−0.763753	+	0.645509i	$0.776645\pi$
$294$	−2.82770e8	−	8.70277e8i	−0.648960	−	1.99729i
$295$	−2.72819e8	−	8.39650e8i	−0.618724	−	1.90424i
$296$	−1.22037e7	−	1.16111e8i	−0.0273509	−	0.260226i
$297$	−8.74630e7	+	9.71375e7i	−0.193721	+	0.215149i
$298$	5.59214e8	+	6.21071e8i	1.22411	+	1.35951i
$299$	2.17204e7	−	2.06656e8i	0.0469915	−	0.447094i
$300$	−1.38230e9	+	2.93818e8i	−2.95583	+	0.628281i
$301$	1.96642e8	+	8.75508e7i	0.415618	+	0.185045i
$302$	−5.42572e8	+	3.94201e8i	−1.13353	+	0.823557i
$303$	9.01064e8	−	4.01179e8i	1.86083	−	0.828494i
$304$	1.81367e8	−	3.14137e8i	0.370254	−	0.641299i
$305$	4.53572e8	+	7.85610e8i	0.915371	+	1.58547i
$306$	−2.29863e9	−	1.67005e9i	−4.58610	−	3.33200i
$307$	−5.01520e8	−	1.06601e8i	−0.989246	−	0.210271i	−0.315252	−	0.949008i	$-0.602089\pi$
$307$	−5.01520e8	−	1.06601e8i	−0.989246	−	0.210271i	−0.673994	+	0.738737i	$0.735422\pi$
$308$	−9.95140e6	+	3.06273e7i	−0.0194069	+	0.0597284i
$309$	−1.45672e8			−0.280880
$310$	−2.31217e8	+	1.17849e9i	−0.440813	+	2.24677i
$311$	−7.16991e7			−0.135161			−0.0675806	−	0.997714i	$-0.521528\pi$
$311$	−7.16991e7			−0.135161			−0.0675806	+	0.997714i	$0.521528\pi$
$312$	−6.13300e7	+	1.88754e8i	−0.114323	+	0.351849i
$313$	−2.64970e8	−	5.63210e7i	−0.488417	−	0.103816i	−0.0428809	−	0.999080i	$-0.513654\pi$
$313$	−2.64970e8	−	5.63210e7i	−0.488417	−	0.103816i	−0.445536	+	0.895264i	$0.646987\pi$
$314$	4.75350e8	+	3.45362e8i	0.866482	+	0.629536i
$315$	−4.71108e8	−	8.15983e8i	−0.849247	−	1.47094i
$316$	−930881.	+	1.61233e6i	−0.00165955	+	0.00287442i
$317$	7.06517e8	−	3.14562e8i	1.24571	−	0.554624i	0.325308	−	0.945608i	$-0.394532\pi$
$317$	7.06517e8	−	3.14562e8i	1.24571	−	0.554624i	0.920397	+	0.390985i	$0.127865\pi$
$318$	2.53193e8	−	1.83955e8i	0.441527	−	0.320788i
$319$	5.27696e7	+	2.34946e7i	0.0910158	+	0.0405228i
$320$	1.13474e9	−	2.41197e8i	1.93586	−	0.411479i
$321$	−1.30665e8	+	1.24320e9i	−0.220492	+	2.09784i
$322$	1.28566e8	+	1.42787e8i	0.214601	+	0.238339i
$323$	5.95061e8	−	6.60882e8i	0.982545	−	1.09123i
$324$	−1.56642e8	−	1.49035e9i	−0.255860	−	2.43434i
$325$	−2.63147e8	−	8.09883e8i	−0.425213	−	1.30867i
$326$	−2.75306e8	−	8.47305e8i	−0.440103	−	1.35450i
$327$	9.40291e7	+	8.94627e8i	0.148712	+	1.41490i
$328$	−1.04380e8	+	1.15926e8i	−0.163328	+	0.181394i
$329$	−3.63240e8	−	4.03419e8i	−0.562352	−	0.624555i
$330$	3.37418e7	−	3.21032e8i	0.0516856	−	0.491756i
$331$	3.25895e8	−	6.92711e7i	0.493946	−	0.104992i	0.0457979	−	0.998951i	$-0.485417\pi$
$331$	3.25895e8	−	6.92711e7i	0.493946	−	0.104992i	0.448148	+	0.893959i	$0.352084\pi$
$332$	4.98249e8	+	2.21835e8i	0.747246	+	0.332695i
$333$	−1.57184e9	+	1.14201e9i	−2.33267	+	1.69478i
$334$	4.46227e8	−	1.98673e8i	0.655305	−	0.291761i
$335$	−3.76797e8	+	6.52632e8i	−0.547584	+	0.948443i
$336$	2.45980e8	+	4.26049e8i	0.353762	+	0.612734i
$337$	5.98510e8	+	4.34843e8i	0.851857	+	0.618910i	0.925657	−	0.378363i	$-0.123513\pi$
$337$	5.98510e8	+	4.34843e8i	0.851857	+	0.618910i	−0.0738005	+	0.997273i	$0.523513\pi$
$338$	9.34275e7	+	1.98586e7i	0.131603	+	0.0279731i
$339$	2.15721e8	−	6.63921e8i	0.300741	−	0.925587i
$340$	2.14528e9			2.96011
$341$	−7.55963e7	−	4.20769e7i	−0.103243	−	0.0574650i
$342$	2.25178e9			3.04393
$343$	−1.91307e8	+	5.88782e8i	−0.255977	+	0.787817i
$344$	−1.53741e8	−	3.26787e7i	−0.203627	−	0.0432823i
$345$	−8.31744e8	−	6.04297e8i	−1.09049	−	0.792289i
$346$	−2.30514e7	−	3.99262e7i	−0.0299179	−	0.0518193i
$347$	−3.92136e7	+	6.79200e7i	−0.0503830	+	0.0872658i	−0.890117	−	0.455732i	$-0.849378\pi$
$347$	−3.92136e7	+	6.79200e7i	−0.0503830	+	0.0872658i	0.839734	+	0.542998i	$0.182711\pi$
$348$	−1.26738e9	+	5.64274e8i	−1.61206	+	0.717733i
$349$	−7.40432e8	+	5.37956e8i	−0.932387	+	0.677419i	−0.946576	−	0.322480i	$-0.895483\pi$
$349$	−7.40432e8	+	5.37956e8i	−0.932387	+	0.677419i	0.0141888	+	0.999899i	$0.495483\pi$
$350$	7.19332e8	+	3.20267e8i	0.896790	+	0.399277i
$351$	1.85036e9	−	3.93307e8i	2.28393	−	0.485464i
$352$	−1.44904e7	+	1.37867e8i	−0.0177085	+	0.168485i
$353$	−8.54249e8	−	9.48740e8i	−1.03365	−	1.14798i	−0.988839	−	0.148988i	$-0.952399\pi$
$353$	−8.54249e8	−	9.48740e8i	−1.03365	−	1.14798i	−0.0448098	−	0.998996i	$-0.514268\pi$
$354$	−1.91478e9	+	2.12658e9i	−2.29407	+	2.54783i
$355$	4.69346e7	+	4.46553e8i	0.0556793	+	0.529753i
$356$	−5.01216e7	−	1.54258e8i	−0.0588775	−	0.181206i
$357$	3.72713e8	+	1.14709e9i	0.433546	+	1.33432i
$358$	−1.71301e8	−	1.62982e9i	−0.197319	−	1.87736i
$359$	−4.85247e8	+	5.38921e8i	−0.553519	+	0.614745i	−0.953358	−	0.301840i	$-0.902399\pi$
$359$	−4.85247e8	+	5.38921e8i	−0.553519	+	0.614745i	0.399840	+	0.916585i	$0.369066\pi$
$360$	4.60364e8	+	5.11286e8i	0.520047	+	0.577571i
$361$	1.97635e7	−	1.88037e8i	0.0221100	−	0.210363i
$362$	−1.73864e9	+	3.69559e8i	−1.92632	+	0.409452i
$363$	−1.50040e9	−	6.68023e8i	−1.64640	−	0.733024i
$364$	3.77050e8	−	2.73943e8i	0.409774	−	0.297718i
$365$	−5.89619e8	+	2.62515e8i	−0.634668	+	0.282572i
$366$	1.47015e9	−	2.54638e9i	1.56740	−	2.71481i
$367$	7.59287e8	+	1.31512e9i	0.801816	+	1.38879i	0.918420	+	0.395608i	$0.129466\pi$
$367$	7.59287e8	+	1.31512e9i	0.801816	+	1.38879i	−0.116603	+	0.993179i	$0.537201\pi$
$368$	3.04277e8	+	2.21070e8i	0.318275	+	0.231240i
$369$	2.53925e9	+	5.39734e8i	2.63095	+	0.559226i
$370$	8.49225e8	−	2.61365e9i	0.871599	−	2.68251i
$371$	−9.30843e7			−0.0946385
$372$	1.96588e9	−	6.73059e8i	1.97996	−	0.677881i
$373$	−4.73661e7			−0.0472593			−0.0236296	−	0.999721i	$-0.507522\pi$
$373$	−4.73661e7			−0.0472593			−0.0236296	+	0.999721i	$0.507522\pi$
$374$	−8.94662e7	+	2.75349e8i	−0.0884318	+	0.272165i
$375$	−1.26705e9	−	2.69319e8i	−1.24075	−	0.263729i
$376$	3.20686e8	+	2.32992e8i	0.311116	+	0.226039i
$377$	−4.17988e8	−	7.23976e8i	−0.401762	−	0.695872i
$378$	−8.74593e8	+	1.51484e9i	−0.832884	+	1.44260i
$379$	−1.91758e9	+	8.53760e8i	−1.80932	+	0.805561i	−0.848069	+	0.529886i	$0.822235\pi$
$379$	−1.91758e9	+	8.53760e8i	−1.80932	+	0.805561i	−0.961251	+	0.275675i	$0.911099\pi$
$380$	−1.37549e9	+	9.99348e8i	−1.28592	+	0.934274i
$381$	−1.01943e9	−	4.53879e8i	−0.944322	−	0.420439i
$382$	1.49139e8	−	3.17005e7i	0.136890	−	0.0290968i
$383$	−8.63007e7	+	8.21096e8i	−0.0784908	+	0.746790i	0.882519	+	0.470276i	$0.155846\pi$
$383$	−8.63007e7	+	8.21096e8i	−0.0784908	+	0.746790i	−0.961010	+	0.276514i	$0.910821\pi$
$384$	−5.70405e8	−	6.33499e8i	−0.514072	−	0.570935i
$385$	−6.42432e7	+	7.13493e7i	−0.0573740	+	0.0637202i
$386$	−1.45285e6	−	1.38229e7i	−0.00128578	−	0.0122333i
$387$	8.08280e8	+	2.48763e9i	0.708882	+	2.18171i
$388$	5.46462e8	+	1.68184e9i	0.474951	+	1.46175i
$389$	−1.19593e8	−	1.13785e9i	−0.103011	−	0.980083i	−0.916915	−	0.399083i	$-0.869328\pi$
$389$	−1.19593e8	−	1.13785e9i	−0.103011	−	0.980083i	0.813904	−	0.581000i	$-0.197338\pi$
$390$	−3.12597e9	+	3.47174e9i	−2.66845	+	2.96361i
$391$	6.17000e8	+	6.85248e8i	0.521996	+	0.579735i
$392$	2.07734e7	−	1.97646e8i	0.0174183	−	0.165724i
$393$	1.11930e9	−	2.37914e8i	0.930191	−	0.197718i
$394$	−1.12099e9	−	4.99096e8i	−0.923345	−	0.411100i
$395$	−4.49052e6	+	3.26255e6i	−0.00366612	+	0.00266359i
$396$	−3.57491e8	+	1.59165e8i	−0.289289	+	0.128800i
$397$	3.63146e8	−	6.28987e8i	0.291282	−	0.504516i	−0.682831	−	0.730576i	$-0.739251\pi$
$397$	3.63146e8	−	6.28987e8i	0.291282	−	0.504516i	0.974113	+	0.226061i	$0.0725848\pi$
$398$	−4.32900e8	−	7.49805e8i	−0.344189	−	0.596153i
$399$	−7.73329e8	−	5.61856e8i	−0.609479	−	0.442813i
$400$	1.50764e9	+	3.20459e8i	1.17785	+	0.250359i
$401$	4.93845e8	−	1.51990e9i	0.382459	−	1.17709i	−0.555847	−	0.831284i	$-0.687606\pi$
$401$	4.93845e8	−	1.51990e9i	0.382459	−	1.17709i	0.938307	−	0.345804i	$-0.112394\pi$
$402$	2.44261e9			1.87526
$403$	5.27177e8	+	1.13572e9i	0.401226	+	0.864381i
$404$	1.69128e9			1.27609
$405$	1.38061e9	−	4.24909e9i	1.03271	−	3.17836i
$406$	7.56103e8	+	1.60715e8i	0.560712	+	0.119183i
$407$	1.60167e8	+	1.16368e8i	0.117759	+	0.0855568i
$408$	−4.40354e8	−	7.62715e8i	−0.320990	−	0.555970i
$409$	2.06395e8	−	3.57487e8i	0.149166	−	0.258362i	−0.781754	−	0.623587i	$-0.785675\pi$
$409$	2.06395e8	−	3.57487e8i	0.149166	−	0.258362i	0.930919	+	0.365225i	$0.119008\pi$
$410$	−3.35445e9	+	1.49350e9i	−2.40368	+	1.07019i
$411$	5.00123e8	−	3.63361e8i	0.355329	−	0.258162i
$412$	−2.28190e8	−	1.01597e8i	−0.160752	−	0.0715713i
$413$	8.32520e8	−	1.76958e8i	0.581527	−	0.123607i
$414$	−2.44053e8	+	2.32201e9i	−0.169037	+	1.60828i
$415$	1.08803e9	+	1.20838e9i	0.747263	+	0.829920i
$416$	1.34245e9	−	1.49094e9i	0.914262	−	1.01539i
$417$	3.38029e7	+	3.21613e8i	0.0228285	+	0.217199i
$418$	−7.09045e7	−	2.18222e8i	−0.0474850	−	0.146144i
$419$	−6.39297e8	−	1.96755e9i	−0.424574	−	1.30670i	−0.903402	−	0.428796i	$-0.858938\pi$
$419$	−6.39297e8	−	1.96755e9i	−0.424574	−	1.30670i	0.478827	−	0.877909i	$-0.341062\pi$
$420$	−2.41032e8	−	2.29326e9i	−0.158746	−	1.51036i
$421$	1.42783e9	−	1.58576e9i	0.932584	−	1.03574i	−0.0666950	−	0.997773i	$-0.521245\pi$
$421$	1.42783e9	−	1.58576e9i	0.932584	−	1.03574i	0.999279	−	0.0379661i	$-0.0120879\pi$
$422$	−1.68942e9	−	1.87629e9i	−1.09432	−	1.21537i
$423$	6.89526e8	−	6.56040e9i	0.442955	−	4.21443i
$424$	6.64845e7	−	1.41317e7i	0.0423584	−	0.00900356i
$425$	3.45213e9	+	1.53699e9i	2.18135	+	0.971200i
$426$	1.17742e9	−	8.55448e8i	0.737902	−	0.536117i
$427$	−7.98923e8	+	3.55704e8i	−0.496601	+	0.221101i
$428$	−1.07173e9	+	1.85630e9i	−0.660744	+	1.14444i
$429$	−1.68275e8	−	2.91461e8i	−0.102901	−	0.178230i
$430$	−2.99314e9	−	2.17464e9i	−1.81546	−	1.31901i
$431$	7.78835e8	+	1.65546e8i	0.468570	+	0.0995977i	0.436145	−	0.899876i	$-0.356343\pi$
$431$	7.78835e8	+	1.65546e8i	0.468570	+	0.0995977i	0.0324255	+	0.999474i	$0.489677\pi$
$432$	−1.05807e9	+	3.25640e9i	−0.631423	+	1.94332i
$433$	−2.28862e9			−1.35477			−0.677385	−	0.735629i	$-0.736887\pi$
$433$	−2.28862e9			−1.35477			−0.677385	+	0.735629i	$0.736887\pi$
$434$	−1.10660e9	−	3.40440e8i	−0.649793	−	0.199907i
$435$	−4.13611e9			−2.40924
$436$	−4.76651e8	+	1.46698e9i	−0.275421	+	0.847660i
$437$	−7.14815e8	−	1.51939e8i	−0.409740	−	0.0870930i
$438$	1.69245e9	+	1.22964e9i	0.962401	+	0.699225i
$439$	−1.01996e8	−	1.76663e8i	−0.0575386	−	0.0996597i	0.835821	−	0.549002i	$-0.184992\pi$
$439$	−1.01996e8	−	1.76663e8i	−0.0575386	−	0.0996597i	−0.893360	+	0.449342i	$0.851659\pi$
$440$	3.50531e7	−	6.07137e7i	0.0196174	−	0.0339784i
$441$	−3.02132e9	+	1.34518e9i	−1.67750	+	0.746869i
$442$	3.38980e9	−	2.46283e9i	1.86722	−	1.35662i
$443$	−1.09663e9	−	4.88250e8i	−0.599302	−	0.266827i	0.0845826	−	0.996416i	$-0.473044\pi$
$443$	−1.09663e9	−	4.88250e8i	−0.599302	−	0.266827i	−0.683885	+	0.729590i	$0.739711\pi$
$444$	−4.65097e9	+	9.88595e8i	−2.52176	+	0.536016i
$445$	5.05465e7	−	4.80918e8i	0.0271914	−	0.258709i
$446$	−2.91742e9	−	3.24012e9i	−1.55714	−	1.72937i
$447$	2.88464e9	−	3.20372e9i	1.52762	−	1.69660i
$448$	1.16903e8	+	1.11226e9i	0.0614262	+	0.584431i
$449$	5.85402e8	+	1.80168e9i	0.305205	+	0.939326i	0.979601	+	0.200955i	$0.0644045\pi$
$449$	5.85402e8	+	1.80168e9i	0.305205	+	0.939326i	−0.674395	+	0.738371i	$0.735596\pi$
$450$	2.95675e9	+	9.09993e9i	1.52957	+	4.70754i
$451$	−2.76504e7	−	2.63076e8i	−0.0141933	−	0.135040i
$452$	8.00960e8	−	8.89557e8i	0.407968	−	0.453095i
$453$	2.31486e9	+	2.57091e9i	1.16999	+	1.29940i
$454$	3.08765e8	−	2.93770e9i	0.154858	−	1.47337i
$455$	1.35913e9	−	2.88892e8i	0.676427	−	0.143779i
$456$	6.37641e8	+	2.83896e8i	0.314919	+	0.140211i
$457$	3.92679e8	−	2.85298e8i	0.192456	−	0.139827i	−0.487385	−	0.873187i	$-0.662049\pi$
$457$	3.92679e8	−	2.85298e8i	0.192456	−	0.139827i	0.679841	+	0.733360i	$0.262049\pi$
$458$	2.09237e9	−	9.31582e8i	1.01767	−	0.453098i
$459$	−4.19724e9	+	7.26983e9i	−2.02591	+	3.50897i
$460$	−8.81439e8	−	1.52670e9i	−0.422221	−	0.731308i
$461$	−2.63330e8	−	1.91320e8i	−0.125183	−	0.0909511i	0.523432	−	0.852068i	$-0.324652\pi$
$461$	−2.63330e8	−	1.91320e8i	−0.125183	−	0.0909511i	−0.648615	+	0.761117i	$0.724652\pi$
$462$	3.04395e8	+	6.47011e7i	0.143612	+	0.0305256i
$463$	−1.00689e9	+	3.09888e9i	−0.471462	+	1.45101i	0.379208	+	0.925312i	$0.376197\pi$
$463$	−1.00689e9	+	3.09888e9i	−0.471462	+	1.45101i	−0.850670	+	0.525700i	$0.823803\pi$
$464$	1.51311e9			0.703167
$465$	6.17047e9	+	5.50736e8i	2.84599	+	0.254014i
$466$	−4.78581e9			−2.19081
$467$	9.74160e8	−	2.99816e9i	0.442610	−	1.36221i	−0.442473	−	0.896782i	$-0.645899\pi$
$467$	9.74160e8	−	2.99816e9i	0.442610	−	1.36221i	0.885083	−	0.465432i	$-0.154101\pi$
$468$	5.53961e9	+	1.17748e9i	2.49815	+	0.530998i
$469$	−5.87751e8	−	4.27026e8i	−0.263081	−	0.191139i
$470$	4.66526e9	+	8.08046e9i	2.07268	+	3.58999i
$471$	1.51544e9	−	2.62482e9i	0.668292	−	1.15752i
$472$	−5.67754e8	+	2.52780e8i	−0.248521	+	0.110649i
$473$	2.15627e8	−	1.56662e8i	0.0936891	−	0.0680691i
$474$	1.64356e7	+	7.31760e6i	0.00708861	+	0.00315605i
$475$	−2.92938e9	+	6.22659e8i	−1.25415	+	0.266577i
$476$	−2.16181e8	+	2.05682e9i	−0.0918740	+	0.874122i
$477$	−7.56868e8	−	8.40587e8i	−0.319305	−	0.354624i
$478$	−4.15601e8	+	4.61572e8i	−0.174052	+	0.193304i
$479$	2.95562e8	+	2.81209e9i	0.122878	+	1.16911i	0.866033	+	0.499988i	$0.166662\pi$
$479$	2.95562e8	+	2.81209e9i	0.122878	+	1.16911i	−0.743154	+	0.669120i	$0.766671\pi$
$480$	−3.06738e9	−	9.44042e9i	−1.26597	−	3.89625i
$481$	−8.85398e8	−	2.72497e9i	−0.362769	−	1.11649i
$482$	2.39222e8	+	2.27605e9i	0.0973054	+	0.925799i
$483$	6.63195e8	−	7.36553e8i	0.267810	−	0.297433i
$484$	−1.88443e9	−	2.09287e9i	−0.755475	−	0.839041i
$485$	−5.51095e8	+	5.24332e9i	−0.219346	+	2.08694i
$486$	−5.28198e9	+	1.12272e9i	−2.08723	+	0.443654i
$487$	−2.81114e9	−	1.25160e9i	−1.10289	−	0.491036i	−0.227166	−	0.973856i	$-0.572946\pi$
$487$	−2.81114e9	−	1.25160e9i	−1.10289	−	0.491036i	−0.875720	+	0.482820i	$0.839613\pi$
$488$	5.16621e8	−	3.75347e8i	0.201235	−	0.146206i
$489$	−4.19834e9	+	1.86922e9i	−1.62366	+	0.722902i
$490$	2.33898e9	−	4.05123e9i	0.898131	−	1.55561i
$491$	1.23205e9	+	2.13397e9i	0.469725	+	0.813587i	0.999401	−	0.0346129i	$-0.0110198\pi$
$491$	1.23205e9	+	2.13397e9i	0.469725	+	0.813587i	−0.529676	+	0.848200i	$0.677686\pi$
$492$	5.13981e9	+	3.73429e9i	1.94567	+	1.41361i
$493$	3.62860e9	+	7.71282e8i	1.36388	+	0.289901i
$494$	−1.02616e9	+	3.15818e9i	−0.382974	+	1.17867i
$495$	−1.16667e9			−0.432346
$496$	−2.25735e9	−	2.01476e8i	−0.830639	−	0.0741375i
$497$	−4.32870e8			−0.158165
$498$	1.62866e9	−	5.01249e9i	0.590918	−	1.81866i
$499$	2.49404e9	+	5.30126e8i	0.898571	+	0.190997i	0.633967	−	0.773360i	$-0.281425\pi$
$499$	2.49404e9	+	5.30126e8i	0.898571	+	0.190997i	0.264604	+	0.964357i	$0.414759\pi$
$500$	−1.79695e9	−	1.30556e9i	−0.642897	−	0.467092i
$501$	−1.25982e9	−	2.18208e9i	−0.447588	−	0.775244i
$502$	−9.74783e8	+	1.68837e9i	−0.343910	+	0.595670i
$503$	3.17068e9	−	1.41168e9i	1.11087	−	0.494593i	0.232514	−	0.972593i	$-0.425305\pi$
$503$	3.17068e9	−	1.41168e9i	1.11087	−	0.494593i	0.878360	+	0.478000i	$0.158638\pi$
$504$	−5.36595e8	+	3.89859e8i	−0.186698	+	0.135644i
$505$	4.60639e9	+	2.05090e9i	1.59162	+	0.708637i
$506$	2.32713e8	−	4.94646e7i	0.0798533	−	0.0169733i
$507$	5.15014e7	−	4.90003e8i	0.0175506	−	0.166982i
$508$	−1.28035e9	−	1.42197e9i	−0.433317	−	0.481247i
$509$	1.23368e9	−	1.37014e9i	0.414659	−	0.460526i	−0.499242	−	0.866463i	$-0.666388\pi$
$509$	1.23368e9	−	1.37014e9i	0.414659	−	0.460526i	0.913901	+	0.405937i	$0.133055\pi$
$510$	−2.16695e9	−	2.06172e10i	−0.723359	−	6.88230i
$511$	−1.92275e8	−	5.91761e8i	−0.0637455	−	0.196188i
$512$	1.28838e9	+	3.96521e9i	0.424227	+	1.30564i
$513$	−6.95413e8	−	6.61642e9i	−0.227422	−	2.16377i
$514$	−1.06250e9	+	1.18002e9i	−0.345109	+	0.383283i
$515$	−4.98301e8	−	5.53419e8i	−0.160756	−	0.178537i
$516$	−6.69119e8	+	6.36624e9i	−0.214402	+	2.03990i
$517$	−6.57485e8	+	1.39753e8i	−0.209252	+	0.0444778i
$518$	2.42030e9	+	1.07759e9i	0.765094	+	0.340642i
$519$	−1.92397e8	+	1.39785e8i	−0.0604106	+	0.0438909i
$520$	−9.26885e8	+	4.12676e8i	−0.289077	+	0.128706i
$521$	1.85076e9	−	3.20562e9i	0.573349	−	0.993070i	−0.422870	−	0.906190i	$-0.638977\pi$
$521$	1.85076e9	−	3.20562e9i	0.573349	−	0.993070i	0.996219	−	0.0868793i	$-0.0276895\pi$
$522$	4.69656e9	+	8.13467e9i	1.44522	+	2.50319i
$523$	1.12128e9	+	8.14660e8i	0.342736	+	0.249012i	0.745815	−	0.666153i	$-0.232060\pi$
$523$	1.12128e9	+	8.14660e8i	0.342736	+	0.249012i	−0.403080	+	0.915165i	$0.632060\pi$
$524$	1.91927e9	+	4.07954e8i	0.582743	+	0.123866i
$525$	1.25515e9	−	3.86295e9i	0.378562	−	1.16510i
$526$	3.50752e8			0.105087
$527$	−5.31064e9	−	1.63380e9i	−1.58056	−	0.486253i
$528$	6.09155e8			0.180098
$529$	−8.17998e8	+	2.51754e9i	−0.240247	+	0.739403i
$530$	1.56496e9	+	3.32643e8i	0.456602	+	0.0970538i
$531$	8.36722e9	+	6.07914e9i	2.42521	+	1.76202i
$532$	−8.19534e8	−	1.41947e9i	−0.235981	−	0.408730i
$533$	−1.91415e9	+	3.31541e9i	−0.547559	+	0.948400i
$534$	−1.43187e9	+	6.37509e8i	−0.406920	+	0.181172i
$535$	−5.16998e9	+	3.75621e9i	−1.45966	+	1.06050i
$536$	4.84625e8	+	2.15769e8i	0.135934	+	0.0605219i
$537$	−8.26880e9	+	1.75759e9i	−2.30427	+	0.489787i
$538$	−5.82961e8	+	5.54651e9i	−0.161399	+	1.53561i
$539$	2.25498e8	+	2.50441e8i	0.0620272	+	0.0688882i
$540$	1.07387e10	−	1.19266e10i	2.93477	−	3.25939i
$541$	−4.14632e8	−	3.94496e9i	−0.112583	−	1.07116i	−0.894283	−	0.447501i	$-0.852314\pi$
$541$	−4.14632e8	−	3.94496e9i	−0.112583	−	1.07116i	0.781700	−	0.623654i	$-0.214353\pi$
$542$	7.31208e8	+	2.25043e9i	0.197262	+	0.607110i
$543$	2.83335e9	+	8.72016e9i	0.759453	+	2.33736i
$544$	9.30598e8	+	8.85405e9i	0.247837	+	2.35801i
$545$	−3.07711e9	+	3.41748e9i	−0.814246	+	0.904312i
$546$	−3.01358e9	−	3.34692e9i	−0.792335	−	0.879978i
$547$	−5.48848e7	+	5.22194e8i	−0.0143382	+	0.136419i	−0.999349	−	0.0360727i	$-0.988515\pi$
$547$	−5.48848e7	+	5.22194e8i	−0.0143382	+	0.136419i	0.985011	+	0.172492i	$0.0551819\pi$
$548$	1.03685e9	−	2.20388e8i	0.269142	−	0.0572080i
$549$	−9.70819e9	−	4.32236e9i	−2.50400	−	1.11485i
$550$	7.88779e8	−	5.73081e8i	0.202156	−	0.146875i
$551$	−2.68583e9	+	1.19581e9i	−0.683988	+	0.304531i
$552$	−3.61860e8	+	6.26759e8i	−0.0915700	+	0.158604i
$553$	−2.67552e6	−	4.63413e6i	−0.000672774	−	0.00116528i
$554$	−8.08834e9	−	5.87652e9i	−2.02104	−	1.46837i
$555$	−1.38662e10	−	2.94736e9i	−3.44297	−	0.731826i
$556$	−1.71353e8	+	5.27371e8i	−0.0422796	+	0.130123i
$557$	4.59880e9			1.12759			0.563795	−	0.825915i	$-0.309341\pi$
$557$	4.59880e9			1.12759			0.563795	+	0.825915i	$0.309341\pi$
$558$	−5.92342e9	−	1.27611e10i	−1.44329	−	3.10934i
$559$	−3.85732e9			−0.933993
$560$	−7.77171e8	+	2.39189e9i	−0.187007	+	0.575549i
$561$	1.46081e9	+	3.10506e8i	0.349321	+	0.0742505i
$562$	−9.45745e7	−	6.87124e7i	−0.0224749	−	0.0163289i
$563$	−3.46978e9	−	6.00984e9i	−0.819450	−	1.41933i	−0.906088	−	0.423090i	$-0.860946\pi$
$563$	−3.46978e9	−	6.00984e9i	−0.819450	−	1.41933i	0.0866374	−	0.996240i	$-0.472388\pi$
$564$	8.07188e9	−	1.39809e10i	1.89451	−	3.28140i
$565$	3.26021e9	−	1.45154e9i	0.760458	−	0.338578i
$566$	−1.63108e9	+	1.18505e9i	−0.378111	+	0.274713i
$567$	3.93476e9	+	1.75187e9i	0.906520	+	0.403609i
$568$	3.09173e8	−	6.57167e7i	0.0707917	−	0.0150472i
$569$	7.56400e8	−	7.19666e9i	0.172131	−	1.63771i	−0.478334	−	0.878178i	$-0.658759\pi$
$569$	7.56400e8	−	7.19666e9i	0.172131	−	1.63771i	0.650465	−	0.759536i	$-0.274574\pi$
$570$	1.09936e10	+	1.22096e10i	2.48644	+	2.76147i
$571$	5.25252e9	−	5.83351e9i	1.18070	−	1.31130i	0.240517	−	0.970645i	$-0.422683\pi$
$571$	5.25252e9	−	5.83351e9i	1.18070	−	1.31130i	0.940187	−	0.340659i	$-0.110650\pi$
$572$	−6.03219e7	−	5.73924e8i	−0.0134769	−	0.128224i
$573$	−2.43044e8	−	7.48011e8i	−0.0539688	−	0.166099i
$574$	−1.09388e9	−	3.36663e9i	−0.241424	−	0.743026i
$575$	−3.24586e8	−	3.08823e9i	−0.0712020	−	0.677442i
$576$	−9.09360e9	+	1.00995e10i	−1.98270	+	2.20201i
$577$	2.61779e9	+	2.90735e9i	0.567309	+	0.630060i	0.956722	−	0.291003i	$-0.0939889\pi$
$577$	2.61779e9	+	2.90735e9i	0.567309	+	0.630060i	−0.389413	+	0.921063i	$0.627322\pi$
$578$	−1.23281e9	+	1.17294e10i	−0.265552	+	2.52656i
$579$	−7.01301e7	+	1.49066e7i	−0.0150151	+	0.00319157i
$580$	−6.47906e9	−	2.88467e9i	−1.37884	−	0.613900i
$581$	−1.26820e9	+	9.21400e8i	−0.268269	+	0.194909i
$582$	1.56113e10	−	6.95059e9i	3.28252	−	1.46147i
$583$	−5.76295e7	+	9.98173e7i	−0.0120450	+	0.0208625i
$584$	2.27169e8	+	3.93469e8i	0.0471960	+	0.0817458i
$585$	1.36599e10	+	9.92448e9i	2.82099	+	2.04957i
$586$	7.84577e9	+	1.66767e9i	1.61062	+	0.342349i
$587$	−6.86544e7	+	2.11297e8i	−0.0140099	+	0.0431181i	−0.957817	−	0.287379i	$-0.907216\pi$
$587$	−6.86544e7	+	2.11297e8i	−0.0140099	+	0.0431181i	0.943807	+	0.330497i	$0.107216\pi$
$588$	−8.09385e9			−1.64185
$589$	4.16610e9	−	1.42635e9i	0.840091	−	0.287622i
$590$	−1.46289e10			−2.93245
$591$	−1.95599e9	+	6.01992e9i	−0.389772	+	1.19960i
$592$	5.07269e9	+	1.07823e9i	1.00488	+	0.213593i
$593$	6.49939e9	+	4.72208e9i	1.27992	+	0.929913i	0.999550	−	0.0299804i	$-0.00954449\pi$
$593$	6.49939e9	+	4.72208e9i	1.27992	+	0.929913i	0.280365	+	0.959893i	$0.409544\pi$
$594$	1.08294e9	+	1.87571e9i	0.212008	+	0.367209i
$595$	−3.08295e9	+	5.33983e9i	−0.600009	+	1.03925i
$596$	6.75308e9	−	3.00666e9i	1.30659	−	0.581732i
$597$	−3.61318e9	+	2.62513e9i	−0.694991	+	0.504941i
$598$	−3.14547e9	−	1.40045e9i	−0.601494	−	0.267802i
$599$	6.49280e8	−	1.38009e8i	0.123435	−	0.0262369i	−0.145780	−	0.989317i	$-0.546569\pi$
$599$	6.49280e8	−	1.38009e8i	0.123435	−	0.0262369i	0.269215	+	0.963080i	$0.413236\pi$
$600$	−3.10018e8	+	2.94962e9i	−0.0585946	+	0.557490i
$601$	−3.09207e9	−	3.43409e9i	−0.581017	−	0.645285i	0.378943	−	0.925420i	$-0.376287\pi$
$601$	−3.09207e9	−	3.43409e9i	−0.581017	−	0.645285i	−0.959961	+	0.280135i	$0.909621\pi$
$602$	2.38660e9	−	2.65058e9i	0.445853	−	0.495169i
$603$	−9.22791e8	−	8.77977e9i	−0.171393	−	1.63070i
$604$	1.83310e9	+	5.64170e9i	0.338498	+	1.04179i
$605$	−2.59457e9	−	7.98526e9i	−0.476345	−	1.46604i
$606$	−1.70837e9	−	1.62540e10i	−0.311837	−	2.96693i
$607$	3.74950e9	−	4.16424e9i	0.680475	−	0.755745i	−0.299666	−	0.954044i	$-0.596875\pi$
$607$	3.74950e9	−	4.16424e9i	0.680475	−	0.755745i	0.980141	+	0.198300i	$0.0635419\pi$
$608$	−4.72121e9	−	5.24343e9i	−0.851904	−	0.946135i
$609$	4.16797e8	−	3.96556e9i	0.0747764	−	0.711450i
$610$	1.47029e10	−	3.12519e9i	2.62269	−	0.557471i
$611$	8.88692e9	+	3.95671e9i	1.57619	+	0.701763i
$612$	−2.03317e10	+	1.47718e10i	−3.58544	+	2.60498i
$613$	−4.08457e9	+	1.81857e9i	−0.716200	+	0.318873i	−0.732285	−	0.680998i	$-0.761546\pi$
$613$	−4.08457e9	+	1.81857e9i	−0.716200	+	0.318873i	0.0160853	+	0.999871i	$0.494880\pi$
$614$	−4.24791e9	+	7.35760e9i	−0.740604	+	1.28276i
$615$	9.47053e9	+	1.64034e10i	1.64177	+	2.84362i
$616$	5.46780e7	+	3.97259e7i	0.00942497	+	0.00684764i
$617$	−2.66415e9	−	5.66283e8i	−0.456627	−	0.0970590i	−0.0261447	−	0.999658i	$-0.508323\pi$
$617$	−2.66415e9	−	5.66283e8i	−0.456627	−	0.0970590i	−0.430482	+	0.902599i	$0.641656\pi$
$618$	−7.45898e8	+	2.29564e9i	−0.127122	+	0.391240i
$619$	9.16754e9			1.55359			0.776793	−	0.629756i	$-0.216845\pi$
$619$	9.16754e9			1.55359			0.776793	+	0.629756i	$0.216845\pi$
$620$	9.28172e9	+	5.16621e9i	1.56407	+	0.870565i
$621$	6.89815e9			1.15588
$622$	−3.67128e8	+	1.12990e9i	−0.0611718	+	0.188267i
$623$	4.55995e8	+	9.69247e7i	0.0755530	+	0.0160593i
$624$	−7.13223e9	−	5.18187e9i	−1.17511	−	0.853769i
$625$	1.09552e9	+	1.89749e9i	0.179490	+	0.310885i
$626$	−2.24431e9	+	3.88726e9i	−0.365656	+	0.633335i
$627$	−1.08127e9	+	4.81414e8i	−0.175186	+	0.0779978i
$628$	4.20453e9	−	3.05477e9i	0.677421	−	0.492175i
$629$	1.16152e10	+	5.17142e9i	1.86101	+	0.828577i
$630$	−1.52713e10	+	3.24602e9i	−2.43324	+	0.517201i
$631$	−7.63100e8	+	7.26042e9i	−0.120915	+	1.15043i	0.750840	+	0.660484i	$0.229649\pi$
$631$	−7.63100e8	+	7.26042e9i	−0.120915	+	1.15043i	−0.871755	+	0.489942i	$0.837018\pi$
$632$	2.61450e6	+	2.90369e6i	0.000411982	+	0.000457552i
$633$	−8.71469e9	+	9.67864e9i	−1.36565	+	1.51671i
$634$	−1.33952e9	−	1.27447e10i	−0.208755	−	1.98617i
$635$	−1.76285e9	−	5.42549e9i	−0.273216	−	0.840873i
$636$	−8.55422e8	−	2.63272e9i	−0.131850	−	0.405793i
$637$	−5.09808e8	−	4.85050e9i	−0.0781481	−	0.743529i
$638$	6.40451e8	−	7.11293e8i	0.0976369	−	0.108437i
$639$	−3.51966e9	−	3.90898e9i	−0.533640	−	0.592667i
$640$	4.55525e8	−	4.33403e9i	0.0686882	−	0.653524i
$641$	−2.38715e9	+	5.07404e8i	−0.357994	+	0.0760940i	−0.383398	−	0.923583i	$-0.625246\pi$
$641$	−2.38715e9	+	5.07404e8i	−0.357994	+	0.0760940i	0.0254037	+	0.999677i	$0.491913\pi$
$642$	1.89225e10	+	8.42482e9i	2.82231	+	1.25657i
$643$	−2.95452e9	+	2.14658e9i	−0.438277	+	0.318427i	−0.784950	−	0.619559i	$-0.787311\pi$
$643$	−2.95452e9	+	2.14658e9i	−0.438277	+	0.318427i	0.346673	+	0.937986i	$0.387311\pi$
$644$	1.55257e9	−	6.91248e8i	0.229061	−	0.101984i
$645$	−9.54230e9	+	1.65278e10i	−1.40021	+	2.42524i
$646$	−7.36787e9	−	1.27615e10i	−1.07530	−	1.86247i
$647$	−9.27369e9	−	6.73773e9i	−1.34613	−	0.978022i	−0.999194	−	0.0401330i	$-0.987222\pi$
$647$	−9.27369e9	−	6.73773e9i	−1.34613	−	0.978022i	−0.346937	−	0.937889i	$-0.612778\pi$
$648$	−3.07633e9	−	6.53893e8i	−0.444140	−	0.0944048i
$649$	3.25665e8	−	1.00229e9i	0.0467644	−	0.143926i
$650$	−1.41103e10			−2.01530
$651$	−1.14983e9	+	5.86054e9i	−0.163343	+	0.832539i
$652$	−7.88020e9			−1.11345
$653$	−2.11281e8	+	6.50255e8i	−0.0296936	+	0.0913876i	−0.964805	−	0.262966i	$-0.915299\pi$
$653$	−2.11281e8	+	6.50255e8i	−0.0296936	+	0.0913876i	0.935111	+	0.354354i	$0.115299\pi$
$654$	1.45799e10	+	3.09904e9i	2.03813	+	0.433217i
$655$	4.73265e9	+	3.43847e9i	0.658052	+	0.478103i
$656$	−3.46461e9	−	6.00088e9i	−0.479171	−	0.829949i
$657$	3.78045e9	−	6.54793e9i	0.520073	−	0.900793i
$658$	−8.21740e9	+	3.65862e9i	−1.12446	+	0.500642i
$659$	9.72874e9	−	7.06834e9i	1.32421	−	0.962096i	0.324342	−	0.945940i	$-0.394857\pi$
$659$	9.72874e9	−	7.06834e9i	1.32421	−	0.962096i	0.999869	−	0.0161564i	$-0.00514297\pi$
$660$	−2.60837e9	−	1.16132e9i	−0.353155	−	0.157235i
$661$	7.74501e9	−	1.64625e9i	1.04308	−	0.221713i	0.345647	−	0.938365i	$-0.387659\pi$
$661$	7.74501e9	−	1.64625e9i	1.04308	−	0.221713i	0.697432	+	0.716651i	$0.254326\pi$
$662$	5.77071e8	−	5.49046e9i	0.0773083	−	0.735539i
$663$	−1.44624e10	−	1.60622e10i	−1.92728	−	2.14046i
$664$	7.65915e8	−	8.50634e8i	0.101529	−	0.112760i
$665$	−5.10794e8	−	4.85988e9i	−0.0673551	−	0.640841i
$666$	9.94843e9	+	3.06181e10i	1.30495	+	4.01623i
$667$	−9.42010e8	−	2.89921e9i	−0.122918	−	0.378302i
$668$	−4.51611e8	−	4.29680e9i	−0.0586202	−	0.557734i
$669$	−1.50492e10	+	1.67138e10i	−1.94321	+	2.15816i
$670$	8.35545e9	+	9.27966e9i	1.07327	+	1.19198i
$671$	−1.13190e8	+	1.07693e9i	−0.0144637	+	0.137613i
$672$	9.36026e9	−	1.98958e9i	1.18986	−	0.252912i
$673$	2.75536e8	+	1.22677e8i	0.0348438	+	0.0155135i	0.424085	−	0.905623i	$-0.360596\pi$
$673$	2.75536e8	+	1.22677e8i	0.0348438	+	0.0155135i	−0.389241	+	0.921136i	$0.627263\pi$
$674$	9.91728e9	−	7.20533e9i	1.24762	−	0.906450i
$675$	2.58253e10	−	1.14981e10i	3.23208	−	1.43901i
$676$	4.22420e8	−	7.31653e8i	0.0525934	−	0.0910944i
$677$	−7.02430e9	−	1.21664e10i	−0.870047	−	1.50697i	−0.861947	−	0.506998i	$-0.830755\pi$
$677$	−7.02430e9	−	1.21664e10i	−0.870047	−	1.50697i	−0.00809964	−	0.999967i	$-0.502578\pi$
$678$	−9.35812e9	−	6.79907e9i	−1.15315	−	0.837811i
$679$	−4.97159e9	−	1.05674e9i	−0.609468	−	0.129546i
$680$	1.39129e9	−	4.28196e9i	0.169683	−	0.522230i
$681$	−1.52373e10			−1.84881
$682$	−1.05017e9	+	9.75868e8i	−0.126770	+	0.117800i
$683$	−1.15569e10			−1.38794			−0.693968	−	0.720006i	$-0.744139\pi$
$683$	−1.15569e10			−1.38794			−0.693968	+	0.720006i	$0.744139\pi$
$684$	6.15478e9	−	1.89425e10i	0.735387	−	2.26329i
$685$	3.09121e9	+	6.57058e8i	0.367462	+	0.0781064i
$686$	8.29903e9	+	6.02960e9i	0.981506	+	0.713106i
$687$	−5.90734e9	−	1.02318e10i	−0.695093	−	1.20394i
$688$	3.49087e9	−	6.04636e9i	0.408671	−	0.707839i
$689$	1.52386e9	−	6.78466e8i	0.177492	−	0.0790243i
$690$	−1.37820e10	+	1.00132e10i	−1.59713	+	1.16038i
$691$	−1.87757e9	−	8.35950e8i	−0.216483	−	0.0963844i	0.295630	−	0.955303i	$-0.404470\pi$
$691$	−1.87757e9	−	8.35950e8i	−0.216483	−	0.0963844i	−0.512113	+	0.858918i	$0.671137\pi$
$692$	−3.98874e8	+	8.47833e7i	−0.0457577	+	0.00972611i
$693$	1.17566e8	−	1.11857e9i	0.0134189	−	0.127672i
$694$	8.69559e8	+	9.65743e8i	0.0987509	+	0.109674i
$695$	−1.10621e9	+	1.22857e9i	−0.124994	+	0.138820i
$696$	3.04344e8	+	2.89564e9i	0.0342162	+	0.325546i
$697$	−5.24964e9	−	1.61567e10i	−0.587239	−	1.80734i
$698$	4.68631e9	+	1.44230e10i	0.521600	+	1.60532i
$699$	2.58050e9	+	2.45518e10i	0.285781	+	2.71903i
$700$	4.66030e9	−	5.17579e9i	0.513536	−	0.570339i
$701$	5.96546e9	+	6.62531e9i	0.654080	+	0.726429i	0.975376	−	0.220550i	$-0.0707852\pi$
$701$	5.96546e9	+	6.62531e9i	0.654080	+	0.726429i	−0.321296	+	0.946979i	$0.604119\pi$
$702$	3.27649e9	−	3.11737e10i	0.357461	−	3.40102i
$703$	−9.85635e9	+	2.09503e9i	−1.06997	+	0.227429i
$704$	1.26509e9	+	5.63254e8i	0.136652	+	0.0608415i
$705$	3.89383e10	−	2.82903e10i	4.18519	−	3.04072i
$706$	−1.93252e10	+	8.60415e9i	−2.06685	+	0.920220i
$707$	−2.43052e9	+	4.20978e9i	−0.258661	+	0.448014i
$708$	1.26556e10	+	2.19201e10i	1.34019	+	2.32127i
$709$	9.32879e8	+	6.77776e8i	0.0983022	+	0.0714208i	0.635851	−	0.771812i	$-0.280649\pi$
$709$	9.32879e8	+	6.77776e8i	0.0983022	+	0.0714208i	−0.537548	+	0.843233i	$0.680649\pi$
$710$	7.27753e9	+	1.54689e9i	0.763097	+	0.162201i
$711$	2.00934e7	−	6.18410e7i	0.00209657	−	0.00645258i
$712$	−3.40404e8			−0.0353440
$713$	1.01930e9	+	4.45063e9i	0.105315	+	0.459841i
$714$	1.99854e10			2.05480
$715$	5.31664e8	−	1.63629e9i	0.0543959	−	0.167413i
$716$	−1.41786e10	−	3.01375e9i	−1.44357	−	0.306840i
$717$	2.59201e9	+	1.88321e9i	0.262615	+	0.190801i
$718$	6.00818e9	+	1.04065e10i	0.605770	+	1.04922i
$719$	1.86941e8	−	3.23791e8i	0.0187565	−	0.0324873i	−0.856495	−	0.516156i	$-0.827363\pi$
$719$	1.86941e8	−	3.23791e8i	0.0187565	−	0.0324873i	0.875251	+	0.483668i	$0.160696\pi$
$720$	−2.79188e10	+	1.24303e10i	−2.78762	+	1.24113i
$721$	5.80814e8	−	4.21986e8i	0.0577116	−	0.0419300i
$722$	−2.86207e9	−	1.27428e9i	−0.283009	−	0.126004i
$723$	1.15474e10	−	2.45448e9i	1.13632	−	0.241532i
$724$	−1.64340e9	+	1.56359e10i	−0.160938	+	1.53122i
$725$	−8.35923e9	−	9.28386e9i	−0.814673	−	0.904786i
$726$	−1.82100e10	+	2.02243e10i	−1.76617	+	1.96153i
$727$	8.49400e8	+	8.08150e9i	0.0819864	+	0.780048i	0.955846	+	0.293869i	$0.0949430\pi$
$727$	8.49400e8	+	8.08150e9i	0.0819864	+	0.780048i	−0.873859	+	0.486179i	$0.838390\pi$
$728$	−3.02257e8	−	9.30252e8i	−0.0290347	−	0.0893595i
$729$	1.69770e9	+	5.22497e9i	0.162298	+	0.499503i
$730$	1.11789e9	+	1.06360e10i	0.106357	+	1.01192i
$731$	1.14535e10	−	1.27204e10i	1.08449	−	1.20445i
$732$	−1.74023e10	−	1.93273e10i	−1.63991	−	1.82130i
$733$	−1.73359e9	+	1.64940e10i	−0.162586	+	1.54690i	0.543888	+	0.839158i	$0.316952\pi$
$733$	−1.73359e9	+	1.64940e10i	−0.162586	+	1.54690i	−0.706473	+	0.707740i	$0.749715\pi$
$734$	2.46128e10	−	5.23162e9i	2.29734	−	0.488315i
$735$	−2.20445e10	−	9.81484e9i	−2.04783	−	0.911754i
$736$	5.91866e9	−	4.30016e9i	0.547207	−	0.397569i
$737$	−8.21798e8	+	3.65888e8i	−0.0756186	+	0.0336676i
$738$	2.15076e10	−	3.72523e10i	1.96968	−	3.41158i
$739$	−7.53336e9	−	1.30482e10i	−0.686646	−	1.18931i	−0.972916	−	0.231157i	$-0.925749\pi$
$739$	−7.53336e9	−	1.30482e10i	−0.686646	−	1.18931i	0.286270	−	0.958149i	$-0.407585\pi$
$740$	−1.96654e10	−	1.42877e10i	−1.78399	−	1.29614i
$741$	1.67552e10	+	3.56143e9i	1.51281	+	0.321559i
$742$	−4.76629e8	+	1.46691e9i	−0.0428318	+	0.131823i
$743$	−4.10906e9			−0.367521			−0.183760	−	0.982971i	$-0.558827\pi$
$743$	−4.10906e9			−0.367521			−0.183760	+	0.982971i	$0.558827\pi$
$744$	−6.84730e7	−	4.36040e9i	−0.00609557	−	0.388169i
$745$	2.20387e10			1.95272
$746$	−2.42534e8	+	7.46441e8i	−0.0213888	+	0.0658279i
$747$	−1.86323e10	−	3.96042e9i	−1.63548	−	0.347632i
$748$	2.07176e9	+	1.50522e9i	0.181002	+	0.131506i
$749$	−3.08035e9	−	5.33532e9i	−0.267863	−	0.463953i
$750$	−1.07320e10	+	1.85883e10i	−0.928892	+	1.60889i
$751$	2.57051e9	−	1.14446e9i	0.221452	−	0.0985967i	−0.293012	−	0.956109i	$-0.594658\pi$
$751$	2.57051e9	−	1.14446e9i	0.221452	−	0.0985967i	0.514464	+	0.857512i	$0.327991\pi$
$752$	−1.42448e10	+	1.03495e10i	−1.22150	+	0.887474i
$753$	9.18717e9	+	4.09039e9i	0.784151	+	0.349126i
$754$	−1.35494e10	+	2.88001e9i	−1.15112	+	0.244678i
$755$	−1.84864e9	+	1.75887e10i	−0.156329	+	1.48737i
$756$	1.03526e10	+	1.14978e10i	0.871414	+	0.967804i
$757$	−3.10254e9	+	3.44572e9i	−0.259945	+	0.288698i	−0.858963	−	0.512037i	$-0.828891\pi$
$757$	−3.10254e9	+	3.44572e9i	−0.259945	+	0.288698i	0.599018	+	0.800735i	$0.295558\pi$
$758$	3.63562e9	+	3.45906e10i	0.303205	+	2.88480i
$759$	−3.79238e8	−	1.16717e9i	−0.0314822	−	0.0968923i
$760$	1.10264e9	+	3.39358e9i	0.0911142	+	0.280421i
$761$	−1.78786e9	−	1.70104e10i	−0.147058	−	1.39916i	−0.780395	−	0.625287i	$-0.784982\pi$
$761$	−1.78786e9	−	1.70104e10i	−0.147058	−	1.39916i	0.633337	−	0.773876i	$-0.281685\pi$
$762$	−1.23726e10	+	1.37411e10i	−1.01302	+	1.12507i
$763$	−2.96648e9	−	3.29461e9i	−0.241772	−	0.268515i
$764$	1.40970e8	−	1.34124e9i	0.0114367	−	0.108813i
$765$	−7.32882e10	+	1.55779e10i	−5.91860	+	1.25804i
$766$	1.24977e10	+	5.56435e9i	1.00469	+	0.447315i
$767$	−1.23392e10	+	8.96494e9i	−0.987422	+	0.717404i
$768$	1.36316e10	−	6.06918e9i	1.08588	−	0.483466i
$769$	6.89692e8	−	1.19458e9i	0.0546907	−	0.0947270i	−0.837384	−	0.546615i	$-0.815916\pi$
$769$	6.89692e8	−	1.19458e9i	0.0546907	−	0.0947270i	0.892075	+	0.451888i	$0.149249\pi$
$770$	7.95441e8	+	1.37774e9i	0.0627900	+	0.108755i
$771$	6.62656e9	+	4.81448e9i	0.520712	+	0.378320i
$772$	−1.20253e8	−	2.55605e7i	−0.00940664	−	0.00199944i
$773$	4.75279e9	−	1.46276e10i	0.370101	−	1.13905i	−0.576624	−	0.817010i	$-0.695630\pi$
$773$	4.75279e9	−	1.46276e10i	0.370101	−	1.13905i	0.946725	−	0.322044i	$-0.104370\pi$
$774$	4.33412e10			3.35976
$775$	1.12346e10	+	1.49632e10i	0.866963	+	1.15470i
$776$	3.71134e9			0.285111
$777$	4.22314e9	−	1.29975e10i	0.322970	−	0.993998i
$778$	−1.85438e10	−	3.94160e9i	−1.41179	−	0.300085i
$779$	1.08923e10	+	7.91371e9i	0.825540	+	0.599790i
$780$	2.06608e10	+	3.57856e10i	1.55890	+	2.70009i
$781$	−2.67995e8	+	4.64180e8i	−0.0201302	+	0.0348665i
$782$	1.39581e10	−	6.21454e9i	1.04376	−	0.464714i
$783$	2.24517e10	−	1.63121e10i	1.67141	−	1.21435i
$784$	8.06455e9	+	3.59057e9i	0.597687	+	0.266107i
$785$	1.51558e10	−	3.22147e9i	1.11824	−	0.237689i
$786$	1.98197e9	−	1.88572e10i	0.145586	−	1.38516i
$787$	1.25099e10	+	1.38936e10i	0.914831	+	1.01602i	0.999807	+	0.0196394i	$0.00625183\pi$
$787$	1.25099e10	+	1.38936e10i	0.914831	+	1.01602i	−0.0849764	+	0.996383i	$0.527082\pi$
$788$	−7.26249e9	+	8.06582e9i	−0.528742	+	0.587228i
$789$	−1.89125e8	−	1.79940e9i	−0.0137082	−	0.130424i
$790$	2.84212e7	+	8.74715e7i	0.00205091	+	0.00631207i
$791$	1.06315e9	+	3.27205e9i	0.0763797	+	0.235073i
$792$	8.58465e7	+	8.16774e8i	0.00614022	+	0.0584203i
$793$	1.04863e10	−	1.16463e10i	0.746738	−	0.829336i
$794$	−8.05273e9	−	8.94346e9i	−0.570915	−	0.634065i
$795$	8.62676e8	−	8.20781e9i	0.0608923	−	0.579352i
$796$	−7.49077e9	+	1.59221e9i	−0.526418	+	0.111894i
$797$	−1.34725e10	−	5.99833e9i	−0.942634	−	0.419688i	−0.122892	−	0.992420i	$-0.539217\pi$
$797$	−1.34725e10	−	5.99833e9i	−0.942634	−	0.419688i	−0.819742	+	0.572732i	$0.805883\pi$
$798$	−1.28140e10	+	9.30993e9i	−0.892638	+	0.648539i
$799$	−3.94359e10	+	1.75580e10i	−2.73513	+	1.21776i
$800$	1.49906e10	−	2.59644e10i	1.03515	−	1.79293i
$801$	2.83243e9	+	4.90590e9i	0.194735	+	0.337291i
$802$	−2.14233e10	−	1.55650e10i	−1.46648	−	1.06546i
$803$	−7.53604e8	−	1.60184e8i	−0.0513616	−	0.0109173i
$804$	6.67637e9	−	2.05477e10i	0.453048	−	1.39434i
$805$	5.06682e9			0.342334
$806$	2.05972e10	−	2.49241e9i	1.38559	−	0.167667i
$807$	2.87686e10			1.92691
$808$	1.09686e9	−	3.37579e9i	0.0731495	−	0.225131i
$809$	1.85064e10	+	3.93365e9i	1.22886	+	0.261202i	0.776202	−	0.630484i	$-0.217144\pi$
$809$	1.85064e10	+	3.93365e9i	1.22886	+	0.261202i	0.452655	+	0.891686i	$0.350477\pi$
$810$	−5.98920e10	−	4.35141e10i	−3.95978	−	2.87695i
$811$	1.03513e10	+	1.79290e10i	0.681431	+	1.18027i	0.974544	+	0.224195i	$0.0719753\pi$
$811$	1.03513e10	+	1.79290e10i	0.681431	+	1.18027i	−0.293113	+	0.956078i	$0.594691\pi$
$812$	3.41862e9	−	5.92122e9i	0.224081	−	0.388119i
$813$	1.11507e10	−	4.96462e9i	0.727756	−	0.324018i
$814$	2.65397e9	−	1.92822e9i	0.172469	−	0.125306i
$815$	−2.14626e10	−	9.55576e9i	−1.38877	−	0.618321i
$816$	3.82660e10	−	8.13368e9i	2.46546	−	0.524049i
$817$	−1.41800e9	+	1.34913e10i	−0.0909699	+	0.865521i
$818$	−4.57680e9	−	5.08305e9i	−0.292365	−	0.324704i
$819$	−1.08918e10	+	1.20965e10i	−0.692795	+	0.769427i
$820$	3.39492e9	+	3.23005e10i	0.215021	+	2.04579i
$821$	−7.77486e9	−	2.39285e10i	−0.490333	−	1.50909i	−0.824105	−	0.566437i	$-0.808322\pi$
$821$	−7.77486e9	−	2.39285e10i	−0.490333	−	1.50909i	0.333772	−	0.942654i	$-0.391678\pi$
$822$	−3.16536e9	−	9.74198e9i	−0.198780	−	0.611781i
$823$	−1.92671e9	−	1.83314e10i	−0.120480	−	1.14630i	−0.872998	−	0.487723i	$-0.837827\pi$
$823$	−1.92671e9	−	1.83314e10i	−0.120480	−	1.14630i	0.752518	−	0.658572i	$-0.228839\pi$
$824$	−3.50776e8	+	3.89576e8i	−0.0218416	+	0.0242576i
$825$	−3.36529e9	−	3.73753e9i	−0.208657	−	0.231737i
$826$	1.47417e9	−	1.40257e10i	0.0910157	−	0.865956i
$827$	6.49103e9	−	1.37971e9i	0.399065	−	0.0848240i	−0.00400721	−	0.999992i	$-0.501276\pi$
$827$	6.49103e9	−	1.37971e9i	0.399065	−	0.0848240i	0.403073	+	0.915168i	$0.367942\pi$
$828$	1.88662e10	+	8.39976e9i	1.15499	+	0.514234i
$829$	−1.65269e10	+	1.20075e10i	−1.00751	+	0.732000i	−0.963686	−	0.267040i	$-0.913955\pi$
$829$	−1.65269e10	+	1.20075e10i	−1.00751	+	0.732000i	−0.0438255	+	0.999039i	$0.513955\pi$
$830$	2.46140e10	−	1.09589e10i	1.49420	−	0.665262i
$831$	−2.57861e10	+	4.46628e10i	−1.55877	+	2.69987i
$832$	−1.00208e10	−	1.73565e10i	−0.603210	−	1.04479i
$833$	1.75094e10	+	1.27213e10i	1.04957	+	0.762560i
$834$	5.24138e9	+	1.11409e9i	0.312870	+	0.0665026i
$835$	3.98041e9	−	1.22504e10i	0.236605	−	0.728197i
$836$	−2.02953e9			−0.120136
$837$	−3.56667e10	+	2.13458e10i	−2.10244	+	1.25827i
$838$	−3.42801e10			−2.01228
$839$	−1.35346e9	+	4.16552e9i	−0.0791186	+	0.243502i	−0.982791	−	0.184723i	$-0.940861\pi$
$839$	−1.35346e9	+	4.16552e9i	−0.0791186	+	0.243502i	0.903672	+	0.428225i	$0.140861\pi$
$840$	−4.73366e9	−	1.00617e9i	−0.275562	−	0.0585725i
$841$	4.03364e9	+	2.93061e9i	0.233836	+	0.169892i
$842$	−1.76789e10	−	3.06208e10i	−1.02062	−	1.76776i
$843$	−3.01509e8	+	5.22229e8i	−0.0173342	+	0.0300237i
$844$	−2.04015e10	+	9.08332e9i	−1.16805	+	0.520051i
$845$	2.03773e9	−	1.48050e9i	0.116185	−	0.0844130i
$846$	−9.98544e10	−	4.44581e10i	−5.66984	−	2.52438i
$847$	7.91746e9	−	1.68291e9i	0.447707	−	0.0951631i
$848$	−3.15593e8	+	3.00267e9i	−0.0177722	+	0.169091i
$849$	6.95895e9	+	7.72869e9i	0.390271	+	0.433440i
$850$	4.18976e10	−	4.65320e10i	2.34004	−	2.59887i
$851$	−1.09212e9	−	1.03908e10i	−0.0607458	−	0.577958i
$852$	−3.97797e9	−	1.22429e10i	−0.220355	−	0.678183i
$853$	5.71845e9	+	1.75996e10i	0.315469	+	0.970915i	0.975561	+	0.219729i	$0.0705175\pi$
$853$	5.71845e9	+	1.75996e10i	0.315469	+	0.970915i	−0.660092	+	0.751185i	$0.729483\pi$
$854$	1.51471e9	+	1.44115e10i	0.0832201	+	0.791787i
$855$	3.97334e10	−	4.41284e10i	2.17407	−	2.41455i
$856$	3.01010e9	+	3.34305e9i	0.164030	+	0.182173i
$857$	7.10999e7	−	6.76470e8i	0.00385866	−	0.0367127i	−0.992423	−	0.122867i	$-0.960791\pi$
$857$	7.10999e7	−	6.76470e8i	0.00385866	−	0.0367127i	0.996282	+	0.0861543i	$0.0274578\pi$
$858$	−5.45476e9	+	1.15944e9i	−0.294829	+	0.0626678i
$859$	1.88543e9	+	8.39449e8i	0.101493	+	0.0451875i	0.456855	−	0.889541i	$-0.348976\pi$
$859$	1.88543e9	+	8.39449e8i	0.101493	+	0.0451875i	−0.355362	+	0.934729i	$0.615642\pi$
$860$	−2.64747e10	+	1.92350e10i	−1.41934	+	1.03121i
$861$	−1.66814e10	+	7.42705e9i	−0.890681	+	0.396557i
$862$	6.59678e9	−	1.14260e10i	0.350798	−	0.607600i
$863$	1.41009e10	+	2.44235e10i	0.746809	+	1.29351i	0.949345	+	0.314237i	$0.101749\pi$
$863$	1.41009e10	+	2.44235e10i	0.746809	+	1.29351i	−0.202535	+	0.979275i	$0.564918\pi$
$864$	5.38819e10	+	3.91475e10i	2.84214	+	2.06493i
$865$	−1.18919e9	−	2.52770e8i	−0.0624733	−	0.0132791i
$866$	−1.17186e10	+	3.60662e10i	−0.613146	+	1.88707i
$867$	6.08382e10			3.17037
$868$	−5.88851e9	+	8.37840e9i	−0.305623	+	0.434853i
$869$	−6.62577e6			−0.000342505
$870$	−2.11785e10	+	6.51808e10i	−1.09038	+	3.35585i
$871$	1.27344e10	+	2.70678e9i	0.653003	+	0.138800i
$872$	2.61896e9	+	1.90278e9i	0.133758	+	0.0971811i
$873$	−3.08812e10	−	5.34877e10i	−1.57088	−	2.72085i
$874$	−6.05453e9	+	1.04868e10i	−0.306754	+	0.531314i
$875$	5.83206e9	−	2.59660e9i	0.294303	−	0.131032i
$876$	1.49699e10	−	1.08763e10i	0.752411	−	0.546659i
$877$	7.53248e9	+	3.35368e9i	0.377085	+	0.167889i	0.586522	−	0.809933i	$-0.300497\pi$
$877$	7.53248e9	+	3.35368e9i	0.377085	+	0.167889i	−0.209437	+	0.977822i	$0.567163\pi$
$878$	−3.30629e9	+	7.02773e8i	−0.164858	+	0.0350416i
$879$	4.32494e9	−	4.11490e10i	0.214792	−	2.04361i
$880$	2.08374e9	+	2.31423e9i	0.103075	+	0.114477i
$881$	−2.08925e9	+	2.32034e9i	−0.102938	+	0.114324i	−0.792412	−	0.609986i	$-0.791175\pi$
$881$	−2.08925e9	+	2.32034e9i	−0.102938	+	0.114324i	0.689474	+	0.724310i	$0.257842\pi$
$882$	5.72825e9	+	5.45007e10i	0.281114	+	2.67462i
$883$	−5.64995e9	−	1.73887e10i	−0.276173	−	0.849974i	−0.988907	−	0.148539i	$-0.952543\pi$
$883$	−5.64995e9	−	1.73887e10i	−0.276173	−	0.849974i	0.712733	−	0.701435i	$-0.247457\pi$
$884$	−1.14526e10	−	3.52474e10i	−0.557597	−	1.71611i
$885$	7.88790e9	+	7.50484e10i	0.382525	+	3.63948i
$886$	−1.33095e10	+	1.47817e10i	−0.642899	+	0.714012i
$887$	2.38214e10	+	2.64564e10i	1.14613	+	1.27291i	0.956720	+	0.291011i	$0.0939918\pi$
$887$	2.38214e10	+	2.64564e10i	1.14613	+	1.27291i	0.189413	+	0.981898i	$0.439342\pi$
$888$	−1.04310e9	+	9.92446e9i	−0.0499898	+	0.475622i
$889$	5.37942e9	−	1.14343e9i	0.256791	−	0.0545825i
$890$	−7.31995e9	−	3.25905e9i	−0.348051	−	0.154962i
$891$	4.31464e9	−	3.13477e9i	0.204349	−	0.148468i
$892$	−3.52307e10	+	1.56857e10i	−1.66205	+	0.739994i
$893$	1.71059e10	−	2.96283e10i	0.803834	−	1.39228i
$894$	−3.57168e10	−	6.18633e10i	−1.67183	−	2.89569i
$895$	−3.49624e10	−	2.54017e10i	−1.63012	−	1.18435i
$896$	4.10942e9	+	8.73484e8i	0.190854	+	0.0405674i
$897$	−5.48847e9	+	1.68918e10i	−0.253909	+	0.781451i
$898$	3.13901e10			1.44653
$899$	1.38420e10	+	1.20753e10i	0.635391	+	0.554293i
$900$	8.46323e10			3.86979
$901$	−2.28738e9	+	7.03983e9i	−0.104184	+	0.320645i
$902$	−4.28738e9	−	9.11312e8i	−0.194522	−	0.0413470i
$903$	−1.48847e10	−	1.08144e10i	−0.672717	−	0.488758i
$904$	−1.25610e9	−	2.17562e9i	−0.0565501	−	0.0979477i
$905$	−2.34365e10	+	4.05933e10i	−1.05105	+	1.82047i
$906$	5.23678e10	−	2.33157e10i	2.33946	−	1.04160i
$907$	−2.51347e10	+	1.82615e10i	−1.11853	+	0.812662i	−0.983986	−	0.178245i	$-0.942958\pi$
$907$	−2.51347e10	+	1.82615e10i	−1.11853	+	0.812662i	−0.134547	+	0.990907i	$0.542958\pi$
$908$	−2.38687e10	−	1.06270e10i	−1.05810	−	0.471097i
$909$	−5.77785e10	+	1.22812e10i	−2.55148	+	0.542335i
$910$	2.40664e9	−	2.28977e10i	0.105869	−	1.00727i
$911$	9.94345e9	+	1.10433e10i	0.435735	+	0.483933i	0.920517	−	0.390702i	$-0.127768\pi$
$911$	9.94345e9	+	1.10433e10i	0.435735	+	0.483933i	−0.484782	+	0.874635i	$0.661101\pi$
$912$	−2.07460e10	+	2.30407e10i	−0.905632	+	1.00581i
$913$	2.02891e8	+	1.93038e9i	0.00882298	+	0.0839451i
$914$	−2.48533e9	−	7.64906e9i	−0.107665	−	0.331357i
$915$	−2.39604e10	−	7.37425e10i	−1.03400	−	3.18232i
$916$	−2.11761e9	−	2.01477e10i	−0.0910359	−	0.866148i
$917$	−3.77360e9	+	4.19101e9i	−0.161608	+	0.179484i
$918$	9.30735e10	+	1.03369e11i	3.97079	+	4.41001i
$919$	6.03643e8	−	5.74328e9i	0.0256552	−	0.244093i	−0.974177	−	0.225785i	$-0.927505\pi$
$919$	6.03643e8	−	5.74328e9i	0.0256552	−	0.244093i	0.999832	−	0.0183082i	$-0.00582800\pi$
$920$	−3.61893e9	+	7.69226e8i	−0.153222	+	0.0325684i
$921$	4.00359e10	+	1.78251e10i	1.68865	+	0.751837i
$922$	−4.36337e9	+	3.17017e9i	−0.183343	+	0.133206i
$923$	7.08640e9	−	3.15507e9i	0.296633	−	0.132070i
$924$	1.37628e9	−	2.38379e9i	0.0573925	−	0.0994067i
$925$	−2.14086e10	−	3.70807e10i	−0.889389	−	1.54047i
$926$	4.36794e10	+	3.17350e10i	1.80775	+	1.31341i
$927$	8.53329e9	+	1.81381e9i	0.351834	+	0.0747846i
$928$	9.09512e9	−	2.79919e10i	0.373586	−	1.14978i
$929$	−2.49221e10			−1.01984			−0.509918	−	0.860223i	$-0.670324\pi$
$929$	−2.49221e10			−1.01984			−0.509918	+	0.860223i	$0.670324\pi$
$930$	4.02743e10	−	9.44202e10i	1.64187	−	3.84924i
$931$	−1.71525e10			−0.696632
$932$	−1.30810e10	+	4.02593e10i	−0.529281	+	1.62896i
$933$	5.99450e9	+	1.27417e9i	0.241639	+	0.0513620i
$934$	−4.22598e10	−	3.07035e10i	−1.69712	−	1.23303i
$935$	3.81738e9	+	6.61190e9i	0.152730	+	0.264537i
$936$	5.94289e9	−	1.02934e10i	0.236882	−	0.410292i
$937$	1.70379e10	−	7.58578e9i	0.676595	−	0.301239i	−0.0395234	−	0.999219i	$-0.512584\pi$
$937$	1.70379e10	−	7.58578e9i	0.676595	−	0.301239i	0.716118	+	0.697979i	$0.245917\pi$
$938$	−9.73901e9	+	7.07581e9i	−0.385305	+	0.279941i
$939$	2.11523e10	+	9.41760e9i	0.833734	+	0.371202i
$940$	8.07261e10	−	1.71589e10i	3.17005	−	0.673816i
$941$	3.09598e8	−	2.94563e9i	0.0121125	−	0.115243i	−0.986795	−	0.161974i	$-0.948214\pi$
$941$	3.09598e8	−	2.94563e9i	0.0121125	−	0.115243i	0.998907	+	0.0467314i	$0.0148805\pi$
$942$	−3.36048e10	−	3.73220e10i	−1.30986	−	1.45474i
$943$	−9.34107e9	+	1.03743e10i	−0.362748	+	0.402873i
$944$	−2.88563e9	−	2.74550e10i	−0.111645	−	1.06223i
$945$	1.42540e10	+	4.38693e10i	0.549447	+	1.69102i
$946$	−1.36474e9	−	4.20023e9i	−0.0524119	−	0.161307i
$947$	−1.40565e9	−	1.33738e10i	−0.0537837	−	0.511718i	−0.987938	−	0.154849i	$-0.950511\pi$
$947$	−1.40565e9	−	1.33738e10i	−0.0537837	−	0.511718i	0.934154	−	0.356869i	$-0.116156\pi$
$948$	1.06481e8	−	1.18259e8i	0.00405920	−	0.00450820i
$949$	7.46087e9	+	8.28613e9i	0.283372	+	0.314717i
$950$	−5.18713e9	+	4.93523e10i	−0.196288	+	1.86756i
$951$	−6.46595e10	+	1.37438e10i	−2.43781	+	0.518173i
$952$	3.96520e9	+	1.76542e9i	0.148948	+	0.0663161i
$953$	1.21909e10	−	8.85718e9i	0.456257	−	0.331490i	−0.335804	−	0.941932i	$-0.609008\pi$
$953$	1.21909e10	−	8.85718e9i	0.456257	−	0.331490i	0.792061	+	0.610442i	$0.209008\pi$
$954$	−1.71223e10	+	7.62332e9i	−0.638472	+	0.284266i
$955$	2.01037e9	−	3.48207e9i	0.0746904	−	0.129368i
$956$	2.74688e9	+	4.75774e9i	0.101680	+	0.176116i
$957$	−3.99436e9	−	2.90207e9i	−0.147318	−	0.107033i
$958$	4.58290e10	+	9.74125e9i	1.68407	+	0.357961i
$959$	−9.41468e8	+	2.89754e9i	−0.0344699	+	0.106088i
$960$	−9.91582e10			−3.61726
$961$	−1.90424e10	−	1.98577e10i	−0.692135	−	0.721768i
$962$	−4.74764e10			−1.71935
$963$	2.31337e10	−	7.11982e10i	0.834744	−	2.56908i
$964$	1.98005e10	+	4.20872e9i	0.711878	+	0.151314i
$965$	−2.96526e8	−	2.15439e8i	−0.0106223	−	0.00771753i
$966$	−8.21149e9	−	1.42227e10i	−0.293091	−	0.507648i
$967$	−9.27558e9	+	1.60658e10i	−0.329874	+	0.571359i	−0.982487	−	0.186333i	$-0.940340\pi$
$967$	−9.27558e9	+	1.60658e10i	−0.329874	+	0.571359i	0.652612	+	0.757692i	$0.273673\pi$
$968$	−5.39947e9	+	2.40400e9i	−0.191332	+	0.0851865i
$969$	−6.14955e10	+	4.46791e10i	−2.17125	+	1.57751i
$970$	7.98074e10	+	3.55326e10i	2.80765	+	1.25004i
$971$	−1.76246e9	+	3.74623e8i	−0.0617807	+	0.0131319i	−0.238698	−	0.971094i	$-0.576721\pi$
$971$	−1.76246e9	+	3.74623e8i	−0.0617807	+	0.0131319i	0.176918	+	0.984226i	$0.443387\pi$
$972$	−4.99265e9	+	4.75019e10i	−0.174381	+	1.65913i
$973$	−1.06643e9	−	1.18440e9i	−0.0371141	−	0.0412194i
$974$	−3.41180e10	+	3.78919e10i	−1.18312	+	1.31398i
$975$	7.60827e9	+	7.23878e10i	0.262887	+	2.50121i
$976$	8.76544e9	+	2.69773e10i	0.301786	+	0.928803i
$977$	6.64229e9	+	2.04429e10i	0.227870	+	0.701312i	0.997988	+	0.0634098i	$0.0201975\pi$
$977$	6.64229e9	+	2.04429e10i	0.227870	+	0.701312i	−0.770118	+	0.637902i	$0.779802\pi$
$978$	7.95981e9	+	7.57326e10i	0.272093	+	2.58879i
$979$	3.86247e8	−	4.28971e8i	0.0131561	−	0.0146113i
$980$	−2.76867e10	−	3.07492e10i	−0.939680	−	1.04362i
$981$	5.63117e9	−	5.35770e10i	0.190440	−	1.81191i
$982$	3.99378e10	−	8.48905e9i	1.34584	−	0.286068i
$983$	−5.30091e9	−	2.36012e9i	−0.177997	−	0.0792495i	0.315803	−	0.948825i	$-0.397726\pi$
$983$	−5.30091e9	−	2.36012e9i	−0.177997	−	0.0792495i	−0.493801	+	0.869575i	$0.664393\pi$
$984$	1.07870e10	−	7.83721e9i	0.360925	−	0.262228i
$985$	−2.95610e10	+	1.31614e10i	−0.985582	+	0.438810i
$986$	3.07345e10	−	5.32337e10i	1.02107	−	1.76855i
$987$	2.32000e10	+	4.01836e10i	0.768030	+	1.33027i
$988$	2.37625e10	+	1.72645e10i	0.783869	+	0.569514i
$989$	−1.37584e10	−	2.92444e9i	−0.452253	−	0.0961294i
$990$	−5.97383e9	+	1.83856e10i	−0.195673	+	0.602218i
$991$	4.15732e10			1.35693			0.678463	−	0.734635i	$-0.262646\pi$
$991$	4.15732e10			1.35693			0.678463	+	0.734635i	$0.262646\pi$
$992$	−1.72958e10	+	4.05488e10i	−0.562535	+	1.31882i
$993$	−2.84779e10			−0.922967
$994$	−2.21646e9	+	6.82158e9i	−0.0715828	+	0.220309i
$995$	−2.23327e10	−	4.74696e9i	−0.718721	−	0.152769i
$996$	−3.77146e10	−	2.74012e10i	−1.20949	−	0.878744i
$997$	−2.25028e10	−	3.89759e10i	−0.719122	−	1.24556i	−0.961348	−	0.275336i	$-0.911211\pi$
$997$	−2.25028e10	−	3.89759e10i	−0.719122	−	1.24556i	0.242226	−	0.970220i	$-0.422122\pi$
$998$	2.11247e10	−	3.65891e10i	0.672720	−	1.16519i
$999$	8.68930e10	−	3.86873e10i	2.75744	−	1.22769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.8.g.a.9.16	yes	144
31.7	even	15	inner	31.8.g.a.7.16	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.8.g.a.7.16	✓	144	31.7	even	15	inner
31.8.g.a.9.16	yes	144	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(5.12040 - 15.7590i) q^{2} +(-83.6064 - 17.7711i) q^{3} +(-118.572 - 86.1478i) q^{4} +(-218.479 - 378.417i) q^{5} +(-708.152 + 1226.56i) q^{6} +(384.830 - 171.337i) q^{7} +(-248.849 + 180.799i) q^{8} +(4676.30 + 2082.02i) q^{9} +(-7082.16 + 1505.36i) q^{10} +(54.5220 - 518.743i) q^{11} +(8382.46 + 9309.67i) q^{12} +(-5051.12 + 5609.84i) q^{13} +(-729.617 - 6941.84i) q^{14} +(11541.4 + 35520.7i) q^{15} +(-4222.19 - 12994.6i) q^{16} +(-3501.49 - 33314.4i) q^{17} +(56755.0 - 63032.8i) q^{18} +(17764.1 + 19729.0i) q^{19} +(-6694.22 + 63691.3i) q^{20} +(-35219.1 + 7486.05i) q^{21} +(-7895.67 - 3515.38i) q^{22} +(-22269.7 + 16179.9i) q^{23} +(24018.4 - 10693.7i) q^{24} +(-56403.9 + 97694.4i) q^{25} +(62541.5 + 108325. i) q^{26} +(-202737. - 147297. i) q^{27} +(-60390.5 - 12836.4i) q^{28} +(-34221.5 + 105323. i) q^{29} +618866. q^{30} +(65077.6 - 152570. i) q^{31} -265772. q^{32} +(-13777.0 + 42401.3i) q^{33} +(-542930. - 115403. i) q^{34} +(-148914. - 108193. i) q^{35} +(-375117. - 649722. i) q^{36} +(-189779. + 328707. i) q^{37} +(401869. - 178923. i) q^{38} +(521999. - 379255. i) q^{39} +(122786. + 54667.8i) q^{40} +(496059. - 105441. i) q^{41} +(-62363.4 + 593348. i) q^{42} +(341916. + 379736. i) q^{43} +(-51153.3 + 56811.5i) q^{44} +(-233801. - 2.22447e6i) q^{45} +(140948. + 433795. i) q^{46} +(-398223. - 1.22560e6i) q^{47} +(122074. + 1.16146e6i) q^{48} +(-432320. + 480140. i) q^{49} +(1.25075e6 + 1.38910e6i) q^{50} +(-299287. + 2.84752e6i) q^{51} +(1.08220e6 - 230028. i) q^{52} +(-201868. - 89877.5i) q^{53} +(-3.35935e6 + 2.44071e6i) q^{54} +(-208213. + 92702.4i) q^{55} +(-64786.9 + 112214. i) q^{56} +(-1.13459e6 - 1.96516e6i) q^{57} +(1.48455e6 + 1.07859e6i) q^{58} +(1.97631e6 + 420079. i) q^{59} +(1.69154e6 - 5.20604e6i) q^{60} -2.07604e6 q^{61} +(-2.07112e6 - 1.80677e6i) q^{62} +2.15631e6 q^{63} +(-820419. + 2.52499e6i) q^{64} +(3.22643e6 + 685798. i) q^{65} +(597657. + 434223. i) q^{66} +(-862318. - 1.49358e6i) q^{67} +(-2.45479e6 + 4.25181e6i) q^{68} +(2.14942e6 - 956985. i) q^{69} +(-2.46750e6 + 1.79275e6i) q^{70} +(-938747. - 417957. i) q^{71} +(-1.54012e6 + 327363. i) q^{72} +(154396. - 1.46898e6i) q^{73} +(4.20834e6 + 4.67384e6i) q^{74} +(6.45186e6 - 7.16552e6i) q^{75} +(-406717. - 3.86966e6i) q^{76} +(-67898.3 - 208969. i) q^{77} +(-3.30382e6 - 1.01681e7i) q^{78} +(-1327.80 - 12633.2i) q^{79} +(-3.99490e6 + 4.43679e6i) q^{80} +(6.84164e6 + 7.59841e6i) q^{81} +(878385. - 8.35728e6i) q^{82} +(-3.63995e6 + 773695. i) q^{83} +(4.82092e6 + 2.14641e6i) q^{84} +(-1.18417e7 + 8.60353e6i) q^{85} +(7.73498e6 - 3.44384e6i) q^{86} +(4.73284e6 - 8.19751e6i) q^{87} +(80220.6 + 138946. i) q^{88} +(895312. + 650482. i) q^{89} +(-3.62525e7 - 7.70570e6i) q^{90} +(-982649. + 3.02428e6i) q^{91} +4.03443e6 q^{92} +(-8.15223e6 + 1.15993e7i) q^{93} -2.13533e7 q^{94} +(3.58472e6 - 1.10326e7i) q^{95} +(2.22203e7 + 4.72306e6i) q^{96} +(-9.76134e6 - 7.09203e6i) q^{97} +(5.35286e6 + 9.27143e6i) q^{98} +(1.33499e6 - 2.31228e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{2} - 8 q^{3} - 2362 q^{4} - 75 q^{5} - 1637 q^{6} + 5518 q^{7} + 3401 q^{8} + 14542 q^{9} - 5312 q^{10} + 1361 q^{11} - 18281 q^{12} + 22457 q^{13} + 28470 q^{14} - 86918 q^{15} - 155730 q^{16}+ \cdots - 102755966 q^{99}+O(q^{100}) \) 144 * q - 6 * q^2 - 8 * q^3 - 2362 * q^4 - 75 * q^5 - 1637 * q^6 + 5518 * q^7 + 3401 * q^8 + 14542 * q^9 - 5312 * q^10 + 1361 * q^11 - 18281 * q^12 + 22457 * q^13 + 28470 * q^14 - 86918 * q^15 - 155730 * q^16 + 51582 * q^17 - 24915 * q^18 + 206748 * q^19 + 53815 * q^20 - 28547 * q^21 + 471441 * q^22 - 10235 * q^23 + 69278 * q^24 - 974301 * q^25 - 279651 * q^26 - 948323 * q^27 + 550632 * q^28 - 32990 * q^29 + 2457990 * q^30 + 899715 * q^31 - 1048518 * q^32 + 780887 * q^33 - 1741528 * q^34 + 40023 * q^35 - 2118881 * q^36 - 787972 * q^37 + 580274 * q^38 + 2541281 * q^39 + 2341817 * q^40 + 1129504 * q^41 - 4390379 * q^42 + 481927 * q^43 - 3123681 * q^44 - 1715971 * q^45 + 2065430 * q^46 - 3123106 * q^47 + 1041890 * q^48 + 76766 * q^49 + 7537425 * q^50 + 6145978 * q^51 + 3260257 * q^52 + 141486 * q^53 - 8979668 * q^54 - 8182779 * q^55 - 5240874 * q^56 - 5487037 * q^57 + 5315215 * q^58 + 7471552 * q^59 + 8590679 * q^60 + 10667852 * q^61 + 27020951 * q^62 - 23783686 * q^63 - 3962521 * q^64 + 935148 * q^65 + 3015728 * q^66 - 17382495 * q^67 - 29462568 * q^68 - 26986306 * q^69 - 31811186 * q^70 - 6186650 * q^71 + 35811589 * q^72 + 6470154 * q^73 + 55339663 * q^74 + 17367737 * q^75 + 2919592 * q^76 + 31865334 * q^77 - 7291717 * q^78 + 4223078 * q^79 + 77431338 * q^80 - 5164601 * q^81 - 19477394 * q^82 - 28867780 * q^83 - 76561164 * q^84 - 45198987 * q^85 - 60993764 * q^86 + 18253055 * q^87 - 45197061 * q^88 - 8429459 * q^89 + 83458809 * q^90 - 53128088 * q^91 + 77469728 * q^92 + 41662009 * q^93 - 16867972 * q^94 - 12744274 * q^95 + 119555444 * q^96 + 20643027 * q^97 + 49624796 * q^98 - 102755966 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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