LMFDB - Embedded newform 31.7.h.a.3.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,7,Mod(3,31)] 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([1])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.3"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	31.h (of order $30$, 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:	$7.13167659222$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$15$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			3.11
Character	$\chi$	$=$	31.3
Dual form			31.7.h.a.21.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.47146 - 3.97525i) q^{2} +(20.3573 + 2.13963i) q^{3} +(-5.64283 + 17.3668i) q^{4} +(21.9247 - 37.9746i) q^{5} +(119.889 - 69.2182i) q^{6} +(611.595 - 129.999i) q^{7} +(171.917 + 529.107i) q^{8} +(-303.230 - 64.4535i) q^{9} +(-30.9987 - 294.932i) q^{10} +(385.703 - 347.289i) q^{11} +(-152.031 + 341.467i) q^{12} +(-426.196 - 957.253i) q^{13} +(2829.54 - 3142.52i) q^{14} +(527.578 - 726.148i) q^{15} +(2098.49 + 1524.64i) q^{16} +(3577.74 + 3221.42i) q^{17} +(-1915.33 + 852.759i) q^{18} +(-10237.7 - 4558.11i) q^{19} +(535.782 + 595.046i) q^{20} +(12728.5 - 1337.82i) q^{21} +(729.800 - 3433.44i) q^{22} +(-10780.4 + 3502.77i) q^{23} +(2367.67 + 11139.0i) q^{24} +(6851.12 + 11866.5i) q^{25} +(-6137.23 - 3543.33i) q^{26} +(-20226.9 - 6572.11i) q^{27} +(-1193.46 + 11355.0i) q^{28} +(-13456.6 - 18521.4i) q^{29} -6070.34i q^{30} +(-7452.40 + 28843.8i) q^{31} -18062.9 q^{32} +(8594.93 - 6244.58i) q^{33} +(32381.4 + 3403.42i) q^{34} +(8472.37 - 26075.3i) q^{35} +(2830.43 - 4902.44i) q^{36} +(-41160.7 + 23764.2i) q^{37} +(-74134.6 + 15757.8i) q^{38} +(-6628.02 - 20398.9i) q^{39} +(23861.9 + 5071.99i) q^{40} +(2649.43 + 25207.7i) q^{41} +(64325.5 - 57918.9i) q^{42} +(25561.7 - 57412.5i) q^{43} +(3854.85 + 8658.13i) q^{44} +(-9095.81 + 10101.9i) q^{45} +(-45060.2 + 62020.1i) q^{46} +(26365.8 + 19155.9i) q^{47} +(39457.3 + 35527.5i) q^{48} +(249671. - 111161. i) q^{49} +(84657.8 + 37692.1i) q^{50} +(65940.4 + 73234.2i) q^{51} +(19029.4 - 2000.07i) q^{52} +(48975.7 - 230413. i) q^{53} +(-136796. + 44447.8i) q^{54} +(-4731.74 - 22261.1i) q^{55} +(173927. + 301250. i) q^{56} +(-198658. - 114695. i) q^{57} +(-147254. - 47845.7i) q^{58} +(39317.6 - 374082. i) q^{59} +(9633.87 + 13259.9i) q^{60} +71016.7i q^{61} +(73885.8 + 187443. i) q^{62} -193833. q^{63} +(-233134. + 169381. i) q^{64} +(-45695.5 - 4802.79i) q^{65} +(22203.0 - 68333.9i) q^{66} +(-108847. + 188529. i) q^{67} +(-76134.4 + 43956.2i) q^{68} +(-226954. + 48240.6i) q^{69} +(-57299.4 - 176349. i) q^{70} +(-201658. - 42863.8i) q^{71} +(-18027.7 - 171522. i) q^{72} +(-160986. + 144952. i) q^{73} +(-130741. + 293649. i) q^{74} +(114080. + 256228. i) q^{75} +(136929. - 152075. i) q^{76} +(190747. - 262541. i) q^{77} +(-117356. - 85264.0i) q^{78} +(391206. + 352243. i) q^{79} +(103906. - 46262.1i) q^{80} +(-191247. - 85148.5i) q^{81} +(114703. + 127390. i) q^{82} +(625938. - 65788.8i) q^{83} +(-48591.2 + 228604. i) q^{84} +(200773. - 65235.1i) q^{85} +(-88369.2 - 415744. i) q^{86} +(-234310. - 405836. i) q^{87} +(250062. + 144373. i) q^{88} +(562400. + 182735. i) q^{89} +(-9609.71 + 91430.3i) q^{90} +(-385101. - 530046. i) q^{91} -206987. i q^{92} +(-213426. + 571235. i) q^{93} +220409. q^{94} +(-397550. + 288837. i) q^{95} +(-367711. - 38647.9i) q^{96} +(-156612. + 482003. i) q^{97} +(924173. - 1.60072e6i) q^{98} +(-139341. + 80448.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 6 q^{2} - 7 q^{3} - 1034 q^{4} + 68 q^{5} + 1431 q^{6} - 1753 q^{7} + 811 q^{8} - 3488 q^{9} + 1158 q^{10} + 633 q^{11} + 12777 q^{12} - 10627 q^{13} + 16244 q^{14} + 8395 q^{15} - 4178 q^{16} + 1713 q^{17}+ \cdots - 3201573 q^{99}+O(q^{100}) $ 120 * q - 6 * q^2 - 7 * q^3 - 1034 * q^4 + 68 * q^5 + 1431 * q^6 - 1753 * q^7 + 811 * q^8 - 3488 * q^9 + 1158 * q^10 + 633 * q^11 + 12777 * q^12 - 10627 * q^13 + 16244 * q^14 + 8395 * q^15 - 4178 * q^16 + 1713 * q^17 - 10077 * q^18 - 8345 * q^19 + 60861 * q^20 - 31195 * q^21 - 43117 * q^22 - 67730 * q^23 - 29436 * q^24 - 85880 * q^25 + 25485 * q^26 + 18770 * q^27 + 322940 * q^28 + 48150 * q^29 + 49476 * q^31 - 395322 * q^32 - 92548 * q^33 - 457978 * q^34 + 157789 * q^35 + 129427 * q^36 + 238344 * q^37 + 185830 * q^38 + 309716 * q^39 + 606677 * q^40 + 35959 * q^41 - 164607 * q^42 - 311135 * q^43 - 702621 * q^44 + 772689 * q^45 - 287890 * q^46 + 150530 * q^47 - 523632 * q^48 + 784094 * q^49 - 1034303 * q^50 - 1566491 * q^51 - 1080753 * q^52 - 1164247 * q^53 + 989080 * q^54 + 1197682 * q^55 + 1178042 * q^56 + 2398464 * q^57 + 2436965 * q^58 - 1106237 * q^59 + 1934095 * q^60 - 520303 * q^62 - 3411888 * q^63 + 235127 * q^64 - 583738 * q^65 - 4572168 * q^66 + 111900 * q^67 - 1524354 * q^68 - 2029246 * q^69 + 3662018 * q^70 + 1528315 * q^71 + 6241105 * q^72 + 2588381 * q^73 - 1260273 * q^74 + 707440 * q^75 + 1167086 * q^76 - 597130 * q^77 - 3405041 * q^78 - 1879167 * q^79 - 4997402 * q^80 - 6030051 * q^81 - 1060742 * q^82 + 2947757 * q^83 - 10179536 * q^84 + 2714035 * q^85 + 4916650 * q^86 + 3744039 * q^87 + 11144193 * q^88 + 2916290 * q^89 - 993633 * q^90 + 3702510 * q^91 - 975871 * q^93 - 7349352 * q^94 + 574613 * q^95 + 9276322 * q^96 - 9366930 * q^97 - 3320822 * q^98 - 3201573 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{30}\right)$

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 $

$2$	5.47146	−	3.97525i	0.683932	−	0.496906i	−0.190728	−	0.981643i	$-0.561085\pi$
$2$	5.47146	−	3.97525i	0.683932	−	0.496906i	0.874660	+	0.484737i	$0.161085\pi$
$3$	20.3573	+	2.13963i	0.753972	+	0.0792457i	0.473714	−	0.880679i	$-0.342913\pi$
$3$	20.3573	+	2.13963i	0.753972	+	0.0792457i	0.280259	+	0.959925i	$0.409580\pi$
$4$	−5.64283	+	17.3668i	−0.0881691	+	0.271357i
$5$	21.9247	−	37.9746i	0.175397	−	0.303797i	−0.764901	−	0.644147i	$-0.777212\pi$
$5$	21.9247	−	37.9746i	0.175397	−	0.303797i	0.940299	+	0.340350i	$0.110546\pi$
$6$	119.889	−	69.2182i	0.555044	−	0.320455i
$7$	611.595	−	129.999i	1.78308	−	0.379004i	0.806003	−	0.591911i	$-0.201626\pi$
$7$	611.595	−	129.999i	1.78308	−	0.379004i	0.977073	+	0.212907i	$0.0682931\pi$
$8$	171.917	+	529.107i	0.335776	+	1.03341i
$9$	−303.230	−	64.4535i	−0.415953	−	0.0884136i
$10$	−30.9987	−	294.932i	−0.0309987	−	0.294932i
$11$	385.703	−	347.289i	0.289784	−	0.260923i	−0.511397	−	0.859345i	$-0.670872\pi$
$11$	385.703	−	347.289i	0.289784	−	0.260923i	0.801181	+	0.598422i	$0.204205\pi$
$12$	−152.031	+	341.467i	−0.0879810	+	0.197608i
$13$	−426.196	−	957.253i	−0.193990	−	0.435709i	0.790194	−	0.612857i	$-0.209980\pi$
$13$	−426.196	−	957.253i	−0.193990	−	0.435709i	−0.984184	+	0.177148i	$0.943313\pi$
$14$	2829.54	−	3142.52i	1.03117	−	1.14523i
$15$	527.578	−	726.148i	0.156319	−	0.215155i
$16$	2098.49	+	1524.64i	0.512327	+	0.372227i
$17$	3577.74	+	3221.42i	0.728220	+	0.655692i	0.947422	−	0.319987i	$-0.103679\pi$
$17$	3577.74	+	3221.42i	0.728220	+	0.655692i	−0.219202	+	0.975680i	$0.570345\pi$
$18$	−1915.33	+	852.759i	−0.328417	+	0.146221i
$19$	−10237.7	−	4558.11i	−1.49259	−	0.664544i	−0.511710	−	0.859158i	$-0.670988\pi$
$19$	−10237.7	−	4558.11i	−1.49259	−	0.664544i	−0.980880	+	0.194615i	$0.937654\pi$
$20$	535.782	+	595.046i	0.0669727	+	0.0743807i
$21$	12728.5	−	1337.82i	1.37442	−	0.144458i
$22$	729.800	−	3433.44i	0.0685387	−	0.322449i
$23$	−10780.4	+	3502.77i	−0.886037	+	0.287891i	−0.716462	−	0.697626i	$-0.754240\pi$
$23$	−10780.4	+	3502.77i	−0.886037	+	0.287891i	−0.169575	+	0.985517i	$0.554240\pi$
$24$	2367.67	+	11139.0i	0.171272	+	0.805773i
$25$	6851.12	+	11866.5i	0.438472	+	0.759455i
$26$	−6137.23	−	3543.33i	−0.349183	−	0.201601i
$27$	−20226.9	−	6572.11i	−1.02763	−	0.333898i
$28$	−1193.46	+	11355.0i	−0.0543669	+	0.517266i
$29$	−13456.6	−	18521.4i	−0.551747	−	0.759415i	0.438501	−	0.898731i	$-0.355510\pi$
$29$	−13456.6	−	18521.4i	−0.551747	−	0.759415i	−0.990248	+	0.139316i	$0.955510\pi$
$30$		−	6070.34i		−	0.224827i
$31$	−7452.40	+	28843.8i	−0.250156	+	0.968205i
$31$	−7452.40	+	28843.8i	−0.250156	+	0.968205i
$32$	−18062.9			−0.551235
$33$	8594.93	−	6244.58i	0.239166	−	0.173765i
$34$	32381.4	+	3403.42i	0.823870	+	0.0865923i
$35$	8472.37	−	26075.3i	0.197606	−	0.608169i
$36$	2830.43	−	4902.44i	0.0606658	−	0.105076i
$37$	−41160.7	+	23764.2i	−0.812602	+	0.469156i	−0.847859	−	0.530222i	$-0.822108\pi$
$37$	−41160.7	+	23764.2i	−0.812602	+	0.469156i	0.0352566	+	0.999378i	$0.488775\pi$
$38$	−74134.6	+	15757.8i	−1.35105	+	0.287174i
$39$	−6628.02	−	20398.9i	−0.111735	−	0.343886i
$40$	23861.9	+	5071.99i	0.372842	+	0.0792499i
$41$	2649.43	+	25207.7i	0.0384416	+	0.365747i	0.996785	+	0.0801275i	$0.0255327\pi$
$41$	2649.43	+	25207.7i	0.0384416	+	0.365747i	−0.958343	+	0.285620i	$0.907801\pi$
$42$	64325.5	−	57918.9i	0.868231	−	0.781759i
$43$	25561.7	−	57412.5i	0.321503	−	0.722107i	−0.678418	−	0.734676i	$-0.737334\pi$
$43$	25561.7	−	57412.5i	0.321503	−	0.722107i	0.999921	+	0.0125691i	$0.00400097\pi$
$44$	3854.85	+	8658.13i	0.0452532	+	0.101640i
$45$	−9095.81	+	10101.9i	−0.0998168	+	0.110858i
$46$	−45060.2	+	62020.1i	−0.462935	+	0.637175i
$47$	26365.8	+	19155.9i	0.253950	+	0.184505i	0.707475	−	0.706738i	$-0.249834\pi$
$47$	26365.8	+	19155.9i	0.253950	+	0.184505i	−0.453526	+	0.891243i	$0.649834\pi$
$48$	39457.3	+	35527.5i	0.356783	+	0.321249i
$49$	249671.	−	111161.i	2.12217	−	0.944850i
$50$	84657.8	+	37692.1i	0.677263	+	0.301537i
$51$	65940.4	+	73234.2i	0.497097	+	0.552082i
$52$	19029.4	−	2000.07i	0.135337	−	0.0142244i
$53$	48975.7	−	230413.i	0.328968	−	1.54767i	−0.433807	−	0.901006i	$-0.642830\pi$
$53$	48975.7	−	230413.i	0.328968	−	1.54767i	0.762774	−	0.646665i	$-0.223837\pi$
$54$	−136796.	+	44447.8i	−0.868746	+	0.282273i
$55$	−4731.74	−	22261.1i	−0.0284402	−	0.133801i
$56$	173927.	+	301250.i	0.990381	+	1.71539i
$57$	−198658.	−	114695.i	−1.07271	−	0.619329i
$58$	−147254.	−	47845.7i	−0.754715	−	0.245222i
$59$	39317.6	−	374082.i	0.191439	−	1.82142i	−0.303880	−	0.952710i	$-0.598282\pi$
$59$	39317.6	−	374082.i	0.191439	−	1.82142i	0.495319	−	0.868711i	$-0.335051\pi$
$60$	9633.87	+	13259.9i	0.0446012	+	0.0613883i
$61$			71016.7i			0.312875i	0.987688	+	0.156437i	$0.0500010\pi$
$61$			71016.7i			0.312875i	−0.987688	+	0.156437i	$0.949999\pi$
$62$	73885.8	+	187443.i	0.310017	+	0.786491i
$63$	−193833.			−0.775185
$64$	−233134.	+	169381.i	−0.889334	+	0.646139i
$65$	−45695.5	−	4802.79i	−0.166392	−	0.0174886i
$66$	22203.0	−	68333.9i	0.0772290	−	0.237686i
$67$	−108847.	+	188529.i	−0.361904	+	0.626837i	−0.988274	−	0.152689i	$-0.951207\pi$
$67$	−108847.	+	188529.i	−0.361904	+	0.626837i	0.626370	+	0.779526i	$0.284540\pi$
$68$	−76134.4	+	43956.2i	−0.242133	+	0.139796i
$69$	−226954.	+	48240.6i	−0.690862	+	0.146847i
$70$	−57299.4	−	176349.i	−0.167054	−	0.514138i
$71$	−201658.	−	42863.8i	−0.563431	−	0.119761i	−0.0826136	−	0.996582i	$-0.526327\pi$
$71$	−201658.	−	42863.8i	−0.563431	−	0.119761i	−0.480818	+	0.876821i	$0.659660\pi$
$72$	−18027.7	−	171522.i	−0.0482994	−	0.459538i
$73$	−160986.	+	144952.i	−0.413827	+	0.372612i	−0.849585	−	0.527452i	$-0.823147\pi$
$73$	−160986.	+	144952.i	−0.413827	+	0.372612i	0.435757	+	0.900064i	$0.356481\pi$
$74$	−130741.	+	293649.i	−0.322638	+	0.724658i
$75$	114080.	+	256228.i	0.270412	+	0.607355i
$76$	136929.	−	152075.i	0.311929	−	0.346432i
$77$	190747.	−	262541.i	0.417816	−	0.575075i
$78$	−117356.	−	85264.0i	−0.247298	−	0.179673i
$79$	391206.	+	352243.i	0.793458	+	0.714433i	0.962531	−	0.271170i	$-0.0874107\pi$
$79$	391206.	+	352243.i	0.793458	+	0.714433i	−0.169073	+	0.985604i	$0.554077\pi$
$80$	103906.	−	46262.1i	0.202942	−	0.0903556i
$81$	−191247.	−	85148.5i	−0.359864	−	0.160222i
$82$	114703.	+	127390.i	0.208033	+	0.231044i
$83$	625938.	−	65788.8i	1.09471	−	0.115058i	0.460080	−	0.887878i	$-0.347821\pi$
$83$	625938.	−	65788.8i	1.09471	−	0.115058i	0.634626	+	0.772820i	$0.281154\pi$
$84$	−48591.2	+	228604.i	−0.0819822	+	0.385696i
$85$	200773.	−	65235.1i	0.326925	−	0.106224i
$86$	−88369.2	−	415744.i	−0.138933	−	0.653629i
$87$	−234310.	−	405836.i	−0.355822	−	0.616301i
$88$	250062.	+	144373.i	0.366944	+	0.211855i
$89$	562400.	+	182735.i	0.797765	+	0.259210i	0.679407	−	0.733761i	$-0.262237\pi$
$89$	562400.	+	182735.i	0.797765	+	0.259210i	0.118358	+	0.992971i	$0.462237\pi$
$90$	−9609.71	+	91430.3i	−0.0131820	+	0.125419i
$91$	−385101.	−	530046.i	−0.511035	−	0.703379i
$92$		−	206987.i		−	0.265815i
$93$	−213426.	+	571235.i	−0.265337	+	0.710176i
$94$	220409.			0.265366
$95$	−397550.	+	288837.i	−0.463683	+	0.336885i
$96$	−367711.	−	38647.9i	−0.415616	−	0.0436830i
$97$	−156612.	+	482003.i	−0.171598	+	0.528123i	−0.999462	−	0.0328057i	$-0.989556\pi$
$97$	−156612.	+	482003.i	−0.171598	+	0.528123i	0.827864	+	0.560929i	$0.189556\pi$
$98$	924173.	−	1.60072e6i	0.981918	−	1.70073i
$99$	−139341.	+	80448.3i	−0.143606	+	0.0829109i
$100$	−244743.	+	52021.7i	−0.244743	+	0.0520217i
$101$	403554.	+	1.24201e6i	0.391686	+	1.20549i	0.931513	+	0.363709i	$0.118490\pi$
$101$	403554.	+	1.24201e6i	0.391686	+	1.20549i	−0.539827	+	0.841776i	$0.681510\pi$
$102$	651914.	+	138569.i	0.614313	+	0.130576i
$103$	34672.8	+	329890.i	0.0317305	+	0.301896i	0.998865	+	0.0476305i	$0.0151670\pi$
$103$	34672.8	+	329890.i	0.0317305	+	0.301896i	−0.967134	+	0.254265i	$0.918166\pi$
$104$	433219.	−	390072.i	0.385130	−	0.346772i
$105$	228266.	−	512693.i	0.197184	−	0.442883i
$106$	−647978.	−	1.45538e6i	−0.544055	−	1.22197i
$107$	128407.	−	142610.i	0.104818	−	0.116412i	−0.688453	−	0.725281i	$-0.741710\pi$
$107$	128407.	−	142610.i	0.104818	−	0.116412i	0.793271	+	0.608869i	$0.208376\pi$
$108$	228273.	−	314191.i	0.181211	−	0.249415i
$109$	−529516.	−	384716.i	−0.408883	−	0.297071i	0.364266	−	0.931295i	$-0.381320\pi$
$109$	−529516.	−	384716.i	−0.408883	−	0.297071i	−0.773150	+	0.634224i	$0.781320\pi$
$110$	−114383.	−	102991.i	−0.0859376	−	0.0773786i
$111$	−888766.	+	395704.i	−0.649858	+	0.289335i
$112$	1.48163e6	+	659663.i	1.05459	+	0.469535i
$113$	150868.	+	167556.i	0.104559	+	0.116125i	0.793153	−	0.609023i	$-0.208438\pi$
$113$	150868.	+	167556.i	0.104559	+	0.116125i	−0.688594	+	0.725147i	$0.741772\pi$
$114$	−1.54289e6	+	162165.i	−1.04141	+	0.109456i
$115$	−103341.	+	486179.i	−0.0679481	+	0.319671i
$116$	397590.	−	129185.i	0.254719	−	0.0827633i
$117$	67537.2	+	317737.i	0.0421682	+	0.198386i
$118$	−1.27194e6	−	2.20307e6i	−0.774144	−	1.34086i
$119$	2.60691e6	+	1.50510e6i	1.54698	+	0.893150i
$120$	474910.	+	154308.i	0.274832	+	0.0892983i
$121$	−157021.	+	1.49396e6i	−0.0886343	+	0.843299i
$122$	282309.	+	388565.i	0.155469	+	0.213985i
$123$			518828.i			0.278810i
$124$	−458873.	−	292185.i	−0.240673	−	0.153247i
$125$	1.28598e6			0.658421
$126$	−1.06055e6	+	770533.i	−0.530174	+	0.385194i
$127$	−2.56898e6	−	270011.i	−1.25415	−	0.131816i	−0.545944	−	0.837822i	$-0.683829\pi$
$127$	−2.56898e6	−	270011.i	−1.25415	−	0.131816i	−0.708206	+	0.706005i	$0.750495\pi$
$128$	−245016.	+	754083.i	−0.116833	+	0.359575i
$129$	643208.	−	1.11407e6i	0.299628	−	0.518971i
$130$	−269113.	+	155373.i	−0.122491	+	0.0707204i
$131$	2.78376e6	−	591707.i	1.23828	−	0.263204i	0.458179	−	0.888860i	$-0.348502\pi$
$131$	2.78376e6	−	591707.i	1.23828	−	0.263204i	0.780100	+	0.625655i	$0.215168\pi$
$132$	59948.9	+	184504.i	0.0260651	+	0.0802201i
$133$	−6.85386e6	−	1.45683e6i	−2.91327	−	0.619234i
$134$	153896.	+	1.46423e6i	0.0639608	+	0.608546i
$135$	−693040.	+	624016.i	−0.281681	+	0.253626i
$136$	−1.08940e6	+	2.44683e6i	−0.433081	+	0.972717i
$137$	−1.36677e6	−	3.06981e6i	−0.531535	−	1.19385i	−0.957322	−	0.289024i	$-0.906669\pi$
$137$	−1.36677e6	−	3.06981e6i	−0.531535	−	1.19385i	0.425786	−	0.904824i	$-0.359998\pi$
$138$	−1.05000e6	+	1.16615e6i	−0.399533	+	0.443727i
$139$	462031.	−	635931.i	0.172039	−	0.236791i	−0.714287	−	0.699853i	$-0.753249\pi$
$139$	462031.	−	635931.i	0.172039	−	0.236791i	0.886326	+	0.463061i	$0.153249\pi$
$140$	405037.	+	294276.i	0.147608	+	0.107244i
$141$	495749.	+	446374.i	0.176850	+	0.159236i
$142$	−1.27376e6	+	567114.i	−0.444859	+	0.198064i
$143$	−496828.	−	221202.i	−0.169902	−	0.0756452i
$144$	−538056.	−	597572.i	−0.180194	−	0.200126i
$145$	−998372.	+	104933.i	−0.327483	+	0.0344198i
$146$	−304606.	+	1.43306e6i	−0.0978768	+	0.460474i
$147$	5.32046e6	−	1.72872e6i	1.67493	−	0.544218i
$148$	−180445.	−	848928.i	−0.0556622	−	0.261870i
$149$	190804.	+	330482.i	0.0576804	+	0.0999055i	0.893424	−	0.449215i	$-0.148296\pi$
$149$	190804.	+	330482.i	0.0576804	+	0.0999055i	−0.835743	+	0.549120i	$0.814963\pi$
$150$	1.64275e6	+	948444.i	0.486742	+	0.281020i
$151$	5.82798e6	+	1.89363e6i	1.69273	+	0.550001i	0.987312	−	0.158793i	$-0.0507602\pi$
$151$	5.82798e6	+	1.89363e6i	1.69273	+	0.550001i	0.705416	+	0.708793i	$0.250760\pi$
$152$	651693.	−	6.20044e6i	0.185572	−	1.76560i
$153$	−877247.	−	1.20743e6i	−0.244933	−	0.337122i
$154$		−	2.19475e6i		−	0.600928i
$155$	931941.	+	915393.i	0.250261	+	0.245817i
$156$	391666.			0.103167
$157$	−1.75961e6	+	1.27843e6i	−0.454693	+	0.330354i	−0.791446	−	0.611239i	$-0.790671\pi$
$157$	−1.75961e6	+	1.27843e6i	−0.454693	+	0.330354i	0.336753	+	0.941593i	$0.390671\pi$
$158$	3.54072e6	+	372145.i	0.897678	+	0.0943497i
$159$	1.49001e6	−	4.58578e6i	0.370679	−	1.14083i
$160$	−396022.	+	685931.i	−0.0966851	+	0.167464i
$161$	−6.13789e6	+	3.54371e6i	−1.47076	+	0.849143i
$162$	−1.38488e6	+	294366.i	−0.325738	+	0.0692377i
$163$	156866.	+	482785.i	0.0362216	+	0.111478i	0.967533	−	0.252747i	$-0.0813339\pi$
$163$	156866.	+	482785.i	0.0362216	+	0.111478i	−0.931311	+	0.364225i	$0.881334\pi$
$164$	−452727.	−	96230.2i	−0.102637	−	0.0218162i
$165$	−48694.7	−	463299.i	−0.0108400	−	0.103136i
$166$	3.16327e6	−	2.84822e6i	0.691531	−	0.622657i
$167$	−1.34690e6	+	3.02519e6i	−0.289192	+	0.649536i	−0.998464	−	0.0553989i	$-0.982357\pi$
$167$	−1.34690e6	+	3.02519e6i	−0.289192	+	0.649536i	0.709272	+	0.704934i	$0.249024\pi$
$168$	2.89611e6	+	6.50477e6i	0.610783	+	1.37184i
$169$	2.49508e6	−	2.77106e6i	0.516920	−	0.574098i
$170$	839195.	−	1.15505e6i	0.170811	−	0.235101i
$171$	2.81058e6	+	2.04201e6i	0.562093	+	0.408384i
$172$	852833.	+	767895.i	0.167602	+	0.150909i
$173$	3.28290e6	−	1.46164e6i	0.634045	−	0.282295i	−0.0644382	−	0.997922i	$-0.520526\pi$
$173$	3.28290e6	−	1.46164e6i	0.634045	−	0.282295i	0.698483	+	0.715627i	$0.253859\pi$
$174$	−2.89531e6	−	1.28908e6i	−0.549602	−	0.244698i
$175$	5.73274e6	+	6.36685e6i	1.06966	+	1.18798i
$176$	1.33888e6	−	140722.i	0.245587	−	0.0258122i
$177$	1.60080e6	−	7.53115e6i	0.288680	−	1.35813i
$178$	3.80356e6	−	1.23585e6i	0.674420	−	0.219132i
$179$	321525.	+	1.51266e6i	0.0560603	+	0.263743i	0.997248	−	0.0741420i	$-0.0236218\pi$
$179$	321525.	+	1.51266e6i	0.0560603	+	0.263743i	−0.941187	+	0.337885i	$0.890288\pi$
$180$	−124112.	−	214969.i	−0.0212812	−	0.0368602i
$181$	−5.69158e6	−	3.28604e6i	−0.959836	−	0.554162i	−0.0637135	−	0.997968i	$-0.520294\pi$
$181$	−5.69158e6	−	3.28604e6i	−0.959836	−	0.554162i	−0.896123	+	0.443807i	$0.853628\pi$
$182$	−4.21413e6	−	1.36925e6i	−0.699026	−	0.227127i
$183$	−151950.	+	1.44570e6i	−0.0247940	+	0.235899i
$184$	−3.70668e6	−	5.10180e6i	−0.595020	−	0.818974i
$185$			2.08408e6i			0.329155i
$186$	1.10305e6	+	3.97391e6i	0.171418	+	0.617560i
$187$	2.49871e6			0.382112
$188$	−481455.	+	349797.i	−0.0724572	+	0.0526433i
$189$	−1.32250e7	−	1.39000e6i	−1.95889	−	0.205888i
$190$	−1.02698e6	+	3.16072e6i	−0.149727	+	0.460813i
$191$	942469.	−	1.63240e6i	0.135259	−	0.234276i	−0.790437	−	0.612543i	$-0.790147\pi$
$191$	942469.	−	1.63240e6i	0.135259	−	0.234276i	0.925696	+	0.378267i	$0.123480\pi$
$192$	−5.10837e6	+	2.94932e6i	−0.721737	+	0.416695i
$193$	−5.25952e6	+	1.11795e6i	−0.731601	+	0.155507i	−0.558626	−	0.829420i	$-0.688671\pi$
$193$	−5.25952e6	+	1.11795e6i	−0.731601	+	0.155507i	−0.172975	+	0.984926i	$0.555338\pi$
$194$	1.05918e6	+	3.25983e6i	0.145066	+	0.446468i
$195$	−919959.	−	195543.i	−0.124069	−	0.0263718i
$196$	521659.	+	4.96326e6i	0.0692817	+	0.659171i
$197$	7.64769e6	−	6.88601e6i	1.00030	−	0.900677i	0.00524607	−	0.999986i	$-0.498330\pi$
$197$	7.64769e6	−	6.88601e6i	1.00030	−	0.900677i	0.995057	+	0.0993097i	$0.0316635\pi$
$198$	−442594.	+	994083.i	−0.0570178	+	0.128064i
$199$	−4.80772e6	−	1.07983e7i	−0.610070	−	1.37024i	−0.909333	−	0.416070i	$-0.863407\pi$
$199$	−4.80772e6	−	1.07983e7i	−0.610070	−	1.37024i	0.299262	−	0.954171i	$-0.403259\pi$
$200$	−5.10081e6	+	5.66503e6i	−0.637602	+	0.708128i
$201$	−2.61922e6	+	3.60504e6i	−0.322540	+	0.443938i
$202$	7.14534e6	+	5.19139e6i	0.866899	+	0.629839i
$203$	−1.06377e7	−	9.57824e6i	−1.27163	−	1.14498i
$204$	−1.64394e6	+	731928.i	−0.193640	+	0.0862140i
$205$	1.01534e6	+	452058.i	0.117855	+	0.0524726i
$206$	1.50110e6	+	1.66714e6i	0.171715	+	0.190709i
$207$	3.49471e6	−	367309.i	0.394003	−	0.0414114i
$208$	565099.	−	2.65858e6i	0.0627964	−	0.295434i
$209$	−5.53168e6	+	1.79735e6i	−0.605924	+	0.196877i
$210$	−789135.	−	3.71259e6i	−0.0852106	−	0.400884i
$211$	7.41453e6	+	1.28423e7i	0.789289	+	1.36709i	0.926403	+	0.376534i	$0.122884\pi$
$211$	7.41453e6	+	1.28423e7i	0.789289	+	1.36709i	−0.137113	+	0.990555i	$0.543782\pi$
$212$	3.72517e6	+	2.15073e6i	0.390966	+	0.225724i
$213$	−4.01349e6	−	1.30406e6i	−0.415321	−	0.134946i
$214$	135662.	−	1.29074e6i	0.0138426	−	0.131703i
$215$	−1.61979e6	−	2.22945e6i	−0.162983	−	0.224327i
$216$		−	1.18320e7i		−	1.17408i
$217$	−808200.	+	1.86095e7i	−0.0790932	+	1.82119i
$218$	−4.42656e6			−0.427265
$219$	−3.58737e6	+	2.60638e6i	−0.341542	+	0.248145i
$220$	413305.	+	43440.1i	0.0388153	+	0.00407965i
$221$	1.55889e6	−	4.79776e6i	0.144424	−	0.444490i
$222$	−3.28982e6	+	5.69814e6i	−0.300686	+	0.520804i
$223$	5.64047e6	−	3.25653e6i	0.508629	−	0.293657i	−0.223641	−	0.974672i	$-0.571794\pi$
$223$	5.64047e6	−	3.25653e6i	0.508629	−	0.293657i	0.732270	+	0.681015i	$0.238461\pi$
$224$	−1.10472e7	+	2.34815e6i	−0.982894	+	0.208921i
$225$	−1.31263e6	−	4.03985e6i	−0.115237	−	0.354665i
$226$	1.49154e6	+	317037.i	0.129214	+	0.0274654i
$227$	656293.	+	6.24421e6i	0.0561074	+	0.533827i	0.986089	+	0.166220i	$0.0531561\pi$
$227$	656293.	+	6.24421e6i	0.0561074	+	0.533827i	−0.929981	+	0.367607i	$0.880177\pi$
$228$	3.11289e6	−	2.80286e6i	0.262639	−	0.236481i
$229$	3.57493e6	−	8.02942e6i	0.297688	−	0.668617i	−0.701334	−	0.712832i	$-0.747412\pi$
$229$	3.57493e6	−	8.02942e6i	0.297688	−	0.668617i	0.999022	+	0.0442151i	$0.0140787\pi$
$230$	1.36726e6	+	3.07091e6i	0.112374	+	0.252397i
$231$	4.44483e6	−	4.93648e6i	0.360594	−	0.400481i
$232$	7.48637e6	−	1.03041e7i	0.599525	−	0.825175i
$233$	8.57855e6	+	6.23268e6i	0.678182	+	0.492728i	0.872754	−	0.488160i	$-0.162332\pi$
$233$	8.57855e6	+	6.23268e6i	0.678182	+	0.492728i	−0.194572	+	0.980888i	$0.562332\pi$
$234$	1.63261e6	+	1.47001e6i	0.127419	+	0.114729i
$235$	1.30550e6	−	581246.i	0.100594	−	0.0447874i
$236$	6.27475e6	+	2.79370e6i	0.477376	+	0.212541i
$237$	7.21021e6	+	8.00774e6i	0.541630	+	0.601541i
$238$	2.02467e7	−	2.12802e6i	1.50184	−	0.157850i
$239$	5.28560e6	−	2.48668e7i	0.387169	−	1.82149i	−0.163235	−	0.986587i	$-0.552193\pi$
$239$	5.28560e6	−	2.48668e7i	0.387169	−	1.82149i	0.550404	−	0.834899i	$-0.314474\pi$
$240$	2.21423e6	−	719448.i	0.160173	−	0.0520434i
$241$	−1.29458e6	−	6.09050e6i	−0.0924860	−	0.435113i	−0.999890	−	0.0148524i	$-0.995272\pi$
$241$	−1.29458e6	−	6.09050e6i	−0.0924860	−	0.435113i	0.907404	−	0.420260i	$-0.138061\pi$
$242$	5.07971e6	+	8.79831e6i	0.358420	+	0.620802i
$243$	9.71597e6	+	5.60952e6i	0.677123	+	0.390937i
$244$	−1.23333e6	−	400735.i	−0.0849007	−	0.0275859i
$245$	1.25267e6	−	1.19183e7i	0.0851799	−	0.810433i
$246$	2.06247e6	+	2.83874e6i	0.138542	+	0.190687i
$247$			1.17427e7i			0.779250i
$248$	−1.65427e7	+	1.01563e6i	−1.08455	+	0.0665857i
$249$	1.28831e7			0.834496
$250$	7.03618e6	−	5.11208e6i	0.450316	−	0.327173i
$251$	−2.61216e7	−	2.74549e6i	−1.65188	−	0.173620i	−0.767715	−	0.640792i	$-0.778606\pi$
$251$	−2.61216e7	−	2.74549e6i	−1.65188	−	0.173620i	−0.884166	+	0.467172i	$0.845273\pi$
$252$	1.09376e6	−	3.36626e6i	0.0683474	−	0.210352i
$253$	−2.94157e6	+	5.09494e6i	−0.181642	+	0.314614i
$254$	−1.51294e7	+	8.73498e6i	−0.923254	+	0.533041i
$255$	4.22676e6	−	898426.i	0.254910	−	0.0541829i
$256$	−4.04207e6	−	1.24402e7i	−0.240926	−	0.741495i
$257$	−851464.	−	180984.i	−0.0501611	−	0.0106621i	0.182763	−	0.983157i	$-0.441496\pi$
$257$	−851464.	−	180984.i	−0.0501611	−	0.0106621i	−0.232924	+	0.972495i	$0.574829\pi$
$258$	−909413.	−	8.65249e6i	−0.0529544	−	0.503828i
$259$	−2.20844e7	+	1.98849e7i	−1.27112	+	1.14452i
$260$	341261.	−	766485.i	0.0194163	−	0.0436098i
$261$	2.88666e6	+	6.48355e6i	0.162358	+	0.364663i
$262$	1.28791e7	−	1.43036e7i	0.716111	−	0.795322i
$263$	1.25107e7	−	1.72195e7i	0.687725	−	0.946572i	−0.312269	−	0.949994i	$-0.601089\pi$
$263$	1.25107e7	−	1.72195e7i	0.687725	−	0.946572i	0.999994	+	0.00342155i	$0.00108911\pi$
$264$	4.78167e6	+	3.47408e6i	0.259877	+	0.188812i
$265$	−7.67606e6	−	6.91155e6i	−0.412478	−	0.371397i
$266$	−4.32918e7	+	1.92748e7i	−2.30018	+	1.02410i
$267$	1.10579e7	+	4.92331e6i	0.580952	+	0.258656i
$268$	−2.65995e6	−	2.95417e6i	−0.138188	−	0.153473i
$269$	−2.06027e7	+	2.16543e6i	−1.05844	+	0.111247i	−0.617721	−	0.786397i	$-0.711944\pi$
$269$	−2.06027e7	+	2.16543e6i	−1.05844	+	0.111247i	−0.440721	+	0.897644i	$0.645277\pi$
$270$	−1.31132e6	+	6.16928e6i	−0.0666220	+	0.313432i
$271$	3.51303e7	−	1.14145e7i	1.76512	−	0.573523i	0.767411	−	0.641156i	$-0.221545\pi$
$271$	3.51303e7	−	1.14145e7i	1.76512	−	0.573523i	0.997710	+	0.0676334i	$0.0215448\pi$
$272$	2.59635e6	+	1.22149e7i	0.129020	+	0.606992i
$273$	−6.70550e6	−	1.16143e7i	−0.329566	−	0.570826i
$274$	−1.96814e7	−	1.13631e7i	−0.956764	−	0.552388i
$275$	6.76359e6	+	2.19762e6i	0.325222	+	0.105671i
$276$	442877.	−	4.21369e6i	0.0210647	−	0.200417i
$277$	1.17326e7	+	1.61485e7i	0.552019	+	0.759789i	0.990284	−	0.139056i	$-0.0444069\pi$
$277$	1.17326e7	+	1.61485e7i	0.552019	+	0.759789i	−0.438265	+	0.898846i	$0.644407\pi$
$278$		−	5.31616e6i		−	0.247436i
$279$	4.11887e6	−	8.26597e6i	0.189656	−	0.380611i
$280$	1.52531e7			0.694841
$281$	1.93115e6	−	1.40306e6i	0.0870357	−	0.0632352i	−0.543416	−	0.839463i	$-0.682870\pi$
$281$	1.93115e6	−	1.40306e6i	0.0870357	−	0.0632352i	0.630452	+	0.776228i	$0.282870\pi$
$282$	4.48692e6	+	471594.i	0.200079	+	0.0210291i
$283$	−1.39519e7	+	4.29394e7i	−0.615563	+	1.89451i	−0.222824	+	0.974859i	$0.571528\pi$
$283$	−1.39519e7	+	4.29394e7i	−0.615563	+	1.89451i	−0.392739	+	0.919650i	$0.628472\pi$
$284$	1.88233e6	−	3.26029e6i	0.0821752	−	0.142332i
$285$	−8.71103e6	+	5.02931e6i	−0.376301	+	0.217257i
$286$	−3.59771e6	+	764716.i	−0.153790	+	0.0326890i
$287$	4.89734e6	+	1.50725e7i	0.207164	+	0.637585i
$288$	5.47720e6	+	1.16422e6i	0.229288	+	0.0487367i
$289$	−100326.	−	954538.i	−0.00415642	−	0.0395457i
$290$	−5.04542e6	+	4.54291e6i	−0.206873	+	0.186269i
$291$	−4.21951e6	+	9.47717e6i	−0.171231	+	0.384592i
$292$	−1.60895e6	−	3.61375e6i	−0.0646239	−	0.145148i
$293$	−2.91386e7	+	3.23616e7i	−1.15842	+	1.28655i	−0.207107	+	0.978318i	$0.566405\pi$
$293$	−2.91386e7	+	3.23616e7i	−1.15842	+	1.28655i	−0.951310	+	0.308235i	$0.900262\pi$
$294$	2.22386e7	−	3.06088e7i	0.875115	−	1.20449i
$295$	−1.33436e7	−	9.69468e6i	−0.519764	−	0.377631i
$296$	−1.96500e7	−	1.76930e7i	−0.757684	−	0.682221i
$297$	−1.00840e7	+	4.48968e6i	−0.384913	+	0.171374i
$298$	2.35772e6	+	1.04973e6i	0.0890931	+	0.0396668i
$299$	7.94761e6	+	8.82671e6i	0.297319	+	0.330206i
$300$	−5.09360e6	+	535359.i	−0.188652	+	0.0198281i
$301$	8.16987e6	−	3.84362e7i	0.299582	−	1.40942i
$302$	3.94152e7	−	1.28068e7i	1.43101	−	0.464963i
$303$	5.55781e6	+	2.61474e7i	0.199791	+	0.939942i
$304$	−1.45342e7	−	2.51739e7i	−0.517332	−	0.896046i
$305$	2.69683e6	+	1.55702e6i	0.0950505	+	0.0548774i
$306$	−9.59964e6	−	3.11911e6i	−0.335035	−	0.108860i
$307$	−2.73377e6	+	2.60101e7i	−0.0944815	+	0.898931i	0.839920	+	0.542710i	$0.182602\pi$
$307$	−2.73377e6	+	2.60101e7i	−0.0944815	+	0.898931i	−0.934402	+	0.356221i	$0.884065\pi$
$308$	3.48315e6	+	4.79414e6i	0.119212	+	0.164081i
$309$			6.78984e6i			0.230136i
$310$	8.73799e6	+	1.30384e6i	0.293310	+	0.0437661i
$311$	9.07310e6			0.301630			0.150815	−	0.988562i	$-0.451810\pi$
$311$	9.07310e6			0.301630			0.150815	+	0.988562i	$0.451810\pi$
$312$	9.65375e6	−	7.01386e6i	0.317857	−	0.230937i
$313$	−3.60432e7	−	3.78829e6i	−1.17541	−	0.123541i	−0.503381	−	0.864064i	$-0.667911\pi$
$313$	−3.60432e7	−	3.78829e6i	−1.17541	−	0.123541i	−0.672030	+	0.740524i	$0.734577\pi$
$314$	−4.54556e6	+	1.39898e7i	−0.146825	+	0.451880i
$315$	−4.24971e6	+	7.36072e6i	−0.135965	+	0.235499i
$316$	−8.32486e6	+	4.80636e6i	−0.263825	+	0.152319i
$317$	2.38758e7	−	5.07497e6i	0.749516	−	0.159315i	0.182711	−	0.983167i	$-0.441513\pi$
$317$	2.38758e7	−	5.07497e6i	0.749516	−	0.159315i	0.566805	+	0.823852i	$0.308179\pi$
$318$	−1.00771e7	−	3.10140e7i	−0.313367	−	0.964444i
$319$	−1.16225e7	−	2.47044e6i	−0.358037	−	0.0761030i
$320$	1.32082e6	+	1.25668e7i	0.0403083	+	0.383508i
$321$	2.91915e6	−	2.62841e6i	0.0882553	−	0.0794654i
$322$	−1.94961e7	+	4.37889e7i	−0.583955	+	1.31159i
$323$	−2.19442e7	−	4.92875e7i	−0.651197	−	1.46261i
$324$	2.55793e6	−	2.84087e6i	0.0752062	−	0.0835249i
$325$	8.43930e6	−	1.16157e7i	0.245842	−	0.338373i
$326$	2.77748e6	+	2.01796e6i	0.0801674	+	0.0582450i
$327$	−9.95634e6	−	8.96473e6i	−0.284745	−	0.256386i
$328$	−1.28821e7	+	5.73546e6i	−0.365060	+	0.162535i
$329$	1.86154e7	+	8.28813e6i	0.522740	+	0.232739i
$330$	−2.10816e6	−	2.34135e6i	−0.0586627	−	0.0651515i
$331$	−6.29726e6	+	661869.i	−0.173647	+	0.0182511i	−0.190953	−	0.981599i	$-0.561158\pi$
$331$	−6.29726e6	+	661869.i	−0.173647	+	0.0182511i	0.0173057	+	0.999850i	$0.494491\pi$
$332$	−2.38952e6	+	1.12418e7i	−0.0652974	+	0.307200i
$333$	1.40128e7	−	4.55305e6i	0.379484	−	0.123302i
$334$	4.65636e6	+	2.19064e7i	0.124970	+	0.587939i
$335$	4.77288e6	+	8.26688e6i	0.126954	+	0.219891i
$336$	2.87504e7	+	1.65991e7i	0.757925	+	0.437588i
$337$	−5.06183e7	−	1.64469e7i	−1.32257	−	0.429728i	−0.439192	−	0.898393i	$-0.644735\pi$
$337$	−5.06183e7	−	1.64469e7i	−1.32257	−	0.429728i	−0.883376	+	0.468665i	$0.844735\pi$
$338$	2.63605e6	−	2.50803e7i	0.0682657	−	0.649505i
$339$	2.71275e6	+	3.73378e6i	0.0696323	+	0.0958406i
$340$			3.85490e6i			0.0980790i
$341$	7.14271e6	+	1.37133e7i	0.180136	+	0.345842i
$342$	2.34955e7			0.587362
$343$	7.87347e7	−	5.72041e7i	1.95112	−	1.41757i
$344$	3.47719e7	+	3.65467e6i	0.854186	+	0.0897786i
$345$	−3.14398e6	+	9.67616e6i	−0.0765635	+	0.235638i
$346$	1.21519e7	−	2.10477e7i	0.293370	−	0.508131i
$347$	4.01245e7	−	2.31659e7i	0.960331	−	0.554448i	0.0640564	−	0.997946i	$-0.479596\pi$
$347$	4.01245e7	−	2.31659e7i	0.960331	−	0.554448i	0.896275	+	0.443499i	$0.146263\pi$
$348$	8.37026e6	−	1.77915e6i	0.198610	−	0.0422159i
$349$	−1.54318e7	−	4.74943e7i	−0.363029	−	1.11729i	−0.951206	−	0.308556i	$-0.900154\pi$
$349$	−1.54318e7	−	4.74943e7i	−0.363029	−	1.11729i	0.588177	−	0.808732i	$-0.299846\pi$
$350$	5.66762e7	+	1.20469e7i	1.32189	+	0.280977i
$351$	2.32945e6	+	2.21632e7i	0.0538681	+	0.512521i
$352$	−6.96691e6	+	6.27303e6i	−0.159739	+	0.143830i
$353$	9.23092e6	−	2.07330e7i	0.209856	−	0.471344i	−0.777695	−	0.628641i	$-0.783611\pi$
$353$	9.23092e6	−	2.07330e7i	0.209856	−	0.471344i	0.987551	+	0.157297i	$0.0502781\pi$
$354$	−2.11795e7	−	4.75699e7i	−0.477426	−	1.07232i
$355$	−6.04902e6	+	6.71812e6i	−0.135207	+	0.150163i
$356$	−6.34705e6	+	8.73596e6i	−0.140677	+	0.193625i
$357$	4.98492e7	+	3.62175e7i	1.09560	+	0.796002i
$358$	7.77239e6	+	6.99829e6i	0.169397	+	0.152526i
$359$	−8.08175e7	+	3.59822e7i	−1.74671	+	0.777687i	−0.754045	+	0.656823i	$0.771900\pi$
$359$	−8.08175e7	+	3.59822e7i	−1.74671	+	0.777687i	−0.992669	+	0.120864i	$0.961433\pi$
$360$	−6.90872e6	−	3.07596e6i	−0.148078	−	0.0659285i
$361$	5.25538e7	+	5.83669e7i	1.11707	+	1.24064i
$362$	−4.42040e7	+	4.64603e6i	−0.931829	+	0.0979392i
$363$	−6.39304e6	+	3.00769e7i	−0.133656	+	0.628800i
$364$	1.13783e7	−	3.69703e6i	0.235924	−	0.0766564i
$365$	1.97495e6	+	9.29141e6i	0.0406141	+	0.191075i
$366$	4.91565e6	+	8.51415e6i	0.100262	+	0.173659i
$367$	1.44383e7	+	8.33594e6i	0.292090	+	0.168638i	0.638884	−	0.769303i	$-0.279396\pi$
$367$	1.44383e7	+	8.33594e6i	0.292090	+	0.168638i	−0.346794	+	0.937941i	$0.612730\pi$
$368$	−2.79631e7	−	9.08575e6i	−0.561101	−	0.182313i
$369$	821335.	−	7.81448e6i	0.0163471	−	0.155532i
$370$	8.28475e6	+	1.14030e7i	0.163559	+	0.225120i
$371$		−	1.47286e8i		−	2.88429i
$372$	−8.71622e6	−	6.92991e6i	−0.169317	−	0.134617i
$373$	8.17916e6			0.157609			0.0788047	−	0.996890i	$-0.474890\pi$
$373$	8.17916e6			0.157609			0.0788047	+	0.996890i	$0.474890\pi$
$374$	1.36716e7	−	9.93298e6i	0.261339	−	0.189874i
$375$	2.61790e7	+	2.75152e6i	0.496432	+	0.0521771i
$376$	−5.60277e6	+	1.72436e7i	−0.105400	+	0.324387i
$377$	−1.19945e7	+	2.07751e7i	−0.223850	+	0.387720i
$378$	−7.78857e7	+	4.49673e7i	−1.44206	+	0.832572i
$379$	−3.82906e7	+	8.13893e6i	−0.703356	+	0.149503i	−0.545687	−	0.837989i	$-0.683731\pi$
$379$	−3.82906e7	+	8.13893e6i	−0.703356	+	0.149503i	−0.157669	+	0.987492i	$0.550398\pi$
$380$	−2.77288e6	−	8.53404e6i	−0.0505335	−	0.155526i
$381$	−5.17197e7	−	1.09934e7i	−0.935149	−	0.198772i
$382$	−1.33253e6	−	1.26782e7i	−0.0239049	−	0.227440i
$383$	−3.71762e7	+	3.34736e7i	−0.661712	+	0.595808i	−0.930013	−	0.367527i	$-0.880205\pi$
$383$	−3.71762e7	+	3.34736e7i	−0.661712	+	0.595808i	0.268301	+	0.963335i	$0.413538\pi$
$384$	−6.60132e6	+	1.48268e7i	−0.116584	+	0.261851i
$385$	−5.78782e6	−	1.29997e7i	−0.101422	−	0.227798i
$386$	−2.43331e7	+	2.70247e7i	−0.423093	+	0.469893i
$387$	−1.14515e7	+	1.57616e7i	−0.197574	+	0.271937i
$388$	−7.48714e6	−	5.43972e6i	−0.128180	−	0.0931283i
$389$	2.06481e7	+	1.85916e7i	0.350777	+	0.315841i	0.825617	−	0.564231i	$-0.190827\pi$
$389$	2.06481e7	+	1.85916e7i	0.350777	+	0.315841i	−0.474840	+	0.880072i	$0.657494\pi$
$390$	−5.81085e6	+	2.58716e6i	−0.0979594	+	0.0436143i
$391$	−4.98534e7	−	2.21962e7i	−0.833998	−	0.371320i
$392$	1.01739e8	+	1.12992e8i	1.68899	+	1.87582i
$393$	5.79358e7	−	6.08930e6i	0.954486	−	0.100321i
$394$	1.44704e7	−	6.80779e7i	0.236588	−	1.11306i
$395$	2.19534e7	−	7.13308e6i	0.356213	−	0.115741i
$396$	−610858.	−	2.87386e6i	−0.00983682	−	0.0462786i
$397$	1.35638e7	+	2.34932e7i	0.216776	+	0.375467i	0.953820	−	0.300377i	$-0.0971126\pi$
$397$	1.35638e7	+	2.34932e7i	0.216776	+	0.375467i	−0.737045	+	0.675844i	$0.763779\pi$
$398$	−6.92312e7	−	3.99707e7i	−1.09813	−	0.634004i
$399$	−1.36409e8	−	4.43218e7i	−2.14745	−	0.697749i
$400$	−3.71514e6	+	3.53472e7i	−0.0580491	+	0.552300i
$401$	1.42114e7	+	1.95604e7i	0.220396	+	0.303350i	0.904870	−	0.425688i	$-0.139968\pi$
$401$	1.42114e7	+	1.95604e7i	0.220396	+	0.303350i	−0.684474	+	0.729038i	$0.739968\pi$
$402$			3.01369e7i			0.463896i
$403$	3.07870e7	−	5.15929e6i	0.470384	−	0.0788270i
$404$	−2.38470e7			−0.361651
$405$	−7.42650e6	+	5.39567e6i	−0.111794	+	0.0812232i
$406$	−9.62797e7	−	1.01194e7i	−1.43865	−	0.151209i
$407$	−7.62280e6	+	2.34606e7i	−0.113066	+	0.347981i
$408$	−2.74124e7	+	4.74798e7i	−0.403615	+	0.699082i
$409$	−8.81218e7	+	5.08772e7i	−1.28799	+	0.743623i	−0.978296	−	0.207212i	$-0.933561\pi$
$409$	−8.81218e7	+	5.08772e7i	−1.28799	+	0.743623i	−0.309697	+	0.950835i	$0.600228\pi$
$410$	7.35243e6	−	1.56281e6i	0.106679	−	0.0226753i
$411$	−2.12553e7	−	6.54172e7i	−0.306156	−	0.942251i
$412$	−5.92479e6	−	1.25935e6i	−0.0847191	−	0.0180076i
$413$	−2.45836e7	−	2.33898e8i	−0.348976	−	3.32029i
$414$	1.76610e7	−	1.59020e7i	0.248894	−	0.224105i
$415$	1.12252e7	−	2.52122e7i	0.157054	−	0.352749i
$416$	7.69833e6	+	1.72907e7i	0.106934	+	0.240178i
$417$	1.07663e7	−	1.19572e7i	0.148477	−	0.164901i
$418$	−2.31214e7	+	3.18239e7i	−0.316582	+	0.435737i
$419$	1.00670e8	+	7.31409e7i	1.36854	+	0.994302i	0.997850	+	0.0655459i	$0.0208789\pi$
$419$	1.00670e8	+	7.31409e7i	1.36854	+	0.994302i	0.370690	+	0.928757i	$0.379121\pi$
$420$	7.61579e6	+	6.85729e6i	0.102794	+	0.0925560i
$421$	9.05668e7	−	4.03229e7i	1.21373	−	0.540388i	0.302843	−	0.953040i	$-0.402064\pi$
$421$	9.05668e7	−	4.03229e7i	1.21373	−	0.540388i	0.910889	+	0.412652i	$0.135398\pi$
$422$	9.16198e7	+	4.07918e7i	1.21914	+	0.542794i
$423$	−6.76024e6	−	7.50800e6i	−0.0893184	−	0.0991981i
$424$	1.30333e8	−	1.36985e7i	1.70984	−	0.179712i
$425$	−1.37153e7	+	6.45256e7i	−0.178665	+	0.840553i
$426$	−2.71436e7	+	8.81950e6i	−0.351107	+	0.114082i
$427$	9.23206e6	+	4.34334e7i	0.118581	+	0.557880i
$428$	1.75211e6	+	3.03475e6i	0.0223476	+	0.0387071i
$429$	−9.64077e6	−	5.56610e6i	−0.122107	−	0.0704984i
$430$	−1.77252e7	−	5.75927e6i	−0.222939	−	0.0724372i
$431$	1.52073e7	−	1.44688e8i	0.189942	−	1.80717i	−0.320487	−	0.947253i	$-0.603846\pi$
$431$	1.52073e7	−	1.44688e8i	0.189942	−	1.80717i	0.510428	−	0.859920i	$-0.329487\pi$
$432$	−3.24257e7	−	4.46302e7i	−0.402197	−	0.553577i
$433$			2.82949e7i			0.348534i	0.984698	+	0.174267i	$0.0557555\pi$
$433$			2.82949e7i			0.348534i	−0.984698	+	0.174267i	$0.944244\pi$
$434$	6.95554e7	+	1.05034e8i	0.850867	+	1.28488i
$435$	−2.05486e7			−0.249641
$436$	9.66926e6	−	7.02513e6i	0.116663	−	0.0847607i
$437$	1.26332e8	+	1.32781e7i	1.51381	+	0.159107i
$438$	−9.26716e6	+	2.85214e7i	−0.110287	+	0.339429i
$439$	−2.93524e7	+	5.08399e7i	−0.346937	+	0.600912i	−0.985704	−	0.168488i	$-0.946112\pi$
$439$	−2.93524e7	+	5.08399e7i	−0.346937	+	0.600912i	0.638767	+	0.769400i	$0.279445\pi$
$440$	1.09650e7	−	6.33067e6i	0.128722	−	0.0743176i
$441$	−8.28724e7	+	1.76151e7i	−0.966260	+	0.205385i
$442$	−1.05429e7	−	3.24477e7i	−0.122094	−	0.375766i
$443$	9.69891e7	+	2.06157e7i	1.11561	+	0.237130i	0.728596	−	0.684944i	$-0.240173\pi$
$443$	9.69891e7	+	2.06157e7i	1.11561	+	0.237130i	0.387013	+	0.922074i	$0.373507\pi$
$444$	−1.85698e6	−	1.76679e7i	−0.0212157	−	0.201854i
$445$	1.92697e7	−	1.73505e7i	0.218673	−	0.196894i
$446$	1.79161e7	−	4.02402e7i	0.201948	−	0.453582i
$447$	3.17713e6	+	7.13596e6i	0.0355724	+	0.0798969i
$448$	−1.20564e8	+	1.33900e8i	−1.34086	+	1.48918i
$449$	6.75463e7	−	9.29695e7i	0.746213	−	1.02707i	−0.252024	−	0.967721i	$-0.581096\pi$
$449$	6.75463e7	−	9.29695e7i	0.746213	−	1.02707i	0.998237	−	0.0593528i	$-0.0189037\pi$
$450$	−2.32414e7	−	1.68859e7i	−0.255049	−	0.185304i
$451$	9.77623e6	+	8.80255e6i	0.106572	+	0.0959575i
$452$	−3.76124e6	+	1.67461e6i	−0.0407301	+	0.0181342i
$453$	1.14590e8	+	5.10188e7i	1.23269	+	0.548827i
$454$	2.84132e7	+	3.15560e7i	0.303635	+	0.337221i
$455$	−2.85715e7	+	3.00299e6i	−0.303319	+	0.0318801i
$456$	2.65333e7	−	1.24830e8i	0.279832	−	1.31651i
$457$	−2.84853e6	+	925543.i	−0.0298450	+	0.00969723i	−0.323901	−	0.946091i	$-0.604995\pi$
$457$	−2.84853e6	+	925543.i	−0.0298450	+	0.00969723i	0.294056	+	0.955788i	$0.404995\pi$
$458$	−1.23589e7	−	5.81438e7i	−0.128642	−	0.605212i
$459$	−5.11951e7	−	8.86724e7i	−0.529407	−	0.916960i
$460$	−7.86026e6	−	4.53812e6i	−0.0807539	−	0.0466233i
$461$	−4.29523e7	−	1.39560e7i	−0.438413	−	0.142449i	0.0814903	−	0.996674i	$-0.474032\pi$
$461$	−4.29523e7	−	1.39560e7i	−0.438413	−	0.142449i	−0.519903	+	0.854225i	$0.674032\pi$
$462$	4.69595e6	−	4.46790e7i	0.0476209	−	0.453083i
$463$	6.96255e7	+	9.58312e7i	0.701496	+	0.965526i	0.999938	+	0.0110986i	$0.00353287\pi$
$463$	6.96255e7	+	9.58312e7i	0.701496	+	0.965526i	−0.298443	+	0.954428i	$0.596467\pi$
$464$		−	5.93833e7i		−	0.594443i
$465$	1.70132e7	+	2.06289e7i	0.169210	+	0.205172i
$466$	7.17137e7			0.708670
$467$	−5.73594e7	+	4.16740e7i	−0.563188	+	0.409180i	−0.832624	−	0.553838i	$-0.813163\pi$
$467$	−5.73594e7	+	4.16740e7i	−0.563188	+	0.409180i	0.269436	+	0.963018i	$0.413163\pi$
$468$	−5.89919e6	−	620030.i	−0.0575513	−	0.00604888i
$469$	−4.20620e7	+	1.29454e8i	−0.407729	+	1.25486i
$470$	4.83239e6	−	8.36994e6i	0.0465445	−	0.0806174i
$471$	−3.85563e7	+	2.22605e7i	−0.369005	+	0.213045i
$472$	2.04689e8	−	4.35079e7i	1.94656	−	0.413754i
$473$	−1.00795e7	−	3.10215e7i	−0.0952478	−	0.293143i
$474$	7.12831e7	+	1.51517e7i	0.669347	+	0.142274i
$475$	−1.60508e7	−	1.52713e8i	−0.149767	−	1.42494i
$476$	−4.08492e7	+	3.67807e7i	−0.378758	+	0.341036i
$477$	−2.97018e7	+	6.67113e7i	−0.273670	+	0.614673i
$478$	−6.99316e7	−	1.57069e8i	−0.640310	−	1.43816i
$479$	−2.57169e7	+	2.85615e7i	−0.233998	+	0.259881i	−0.848695	−	0.528882i	$-0.822611\pi$
$479$	−2.57169e7	+	2.85615e7i	−0.233998	+	0.259881i	0.614698	+	0.788763i	$0.289278\pi$
$480$	−9.52957e6	+	1.31163e7i	−0.0861687	+	0.118601i
$481$	4.02909e7	+	2.92730e7i	0.362052	+	0.263046i
$482$	−3.12944e7	−	2.81776e7i	−0.279464	−	0.251631i
$483$	−1.32533e8	+	5.90074e7i	−1.17620	+	0.523679i
$484$	−2.50592e7	−	1.11571e7i	−0.221020	−	0.0984045i
$485$	1.48702e7	+	1.65151e7i	0.130344	+	0.144762i
$486$	7.54598e7	−	7.93114e6i	0.657365	−	0.0690918i
$487$	−1.16543e7	+	5.48293e7i	−0.100902	+	0.474707i	0.898462	+	0.439051i	$0.144685\pi$
$487$	−1.16543e7	+	5.48293e7i	−0.100902	+	0.474707i	−0.999364	+	0.0356559i	$0.988648\pi$
$488$	−3.75754e7	+	1.22090e7i	−0.323329	+	0.105056i
$489$	2.16039e6	+	1.01638e7i	0.0184759	+	0.0869221i
$490$	−4.05244e7	−	7.01903e7i	−0.344451	−	0.596607i
$491$	5.90561e7	+	3.40960e7i	0.498908	+	0.288044i	0.728262	−	0.685298i	$-0.240328\pi$
$491$	5.90561e7	+	3.40960e7i	0.498908	+	0.288044i	−0.229355	+	0.973343i	$0.573662\pi$
$492$	−9.01039e6	−	2.92765e6i	−0.0756569	−	0.0245824i
$493$	1.15209e7	−	1.09614e8i	0.0961491	−	0.914797i
$494$	4.66801e7	+	6.42496e7i	0.387214	+	0.532954i
$495$			7.05521e6i			0.0581694i
$496$	−5.96153e7	+	4.91662e7i	−0.488554	+	0.402922i
$497$	−1.28905e8			−1.05003
$498$	7.04896e7	−	5.12137e7i	0.570738	−	0.414666i
$499$	−1.31878e8	−	1.38610e7i	−1.06138	−	0.111556i	−0.442289	−	0.896873i	$-0.645833\pi$
$499$	−1.31878e8	−	1.38610e7i	−1.06138	−	0.111556i	−0.619094	+	0.785317i	$0.712500\pi$
$500$	−7.25656e6	+	2.23334e7i	−0.0580524	+	0.178667i
$501$	−3.38920e7	+	5.87026e7i	−0.269516	+	0.466815i
$502$	−1.53837e8	+	8.88180e7i	−1.21605	+	0.702085i
$503$	−4.67509e7	+	9.93722e6i	−0.367355	+	0.0780838i	−0.387891	−	0.921705i	$-0.626796\pi$
$503$	−4.67509e7	+	9.93722e6i	−0.367355	+	0.0780838i	0.0205354	+	0.999789i	$0.493463\pi$
$504$	−3.33232e7	−	1.02558e8i	−0.260288	−	0.801085i
$505$	5.60128e7	+	1.19059e7i	0.434923	+	0.0924458i
$506$	4.15900e6	+	3.95702e7i	0.0321024	+	0.305434i
$507$	5.67220e7	−	5.10727e7i	0.435239	−	0.391891i
$508$	1.91855e7	−	4.30914e7i	0.146347	−	0.328700i
$509$	−2.25430e7	−	5.06324e7i	−0.170946	−	0.383950i	0.807674	−	0.589630i	$-0.200726\pi$
$509$	−2.25430e7	−	5.06324e7i	−0.170946	−	0.383950i	−0.978619	+	0.205679i	$0.934060\pi$
$510$	1.95551e7	−	2.17181e7i	0.147418	−	0.163724i
$511$	−7.96145e7	+	1.09580e8i	−0.596664	+	0.821237i
$512$	−1.12623e8	−	8.18250e7i	−0.839103	−	0.609644i
$513$	1.77120e8	+	1.59479e8i	1.31194	+	1.18128i
$514$	−5.37821e6	+	2.39453e6i	−0.0396048	+	0.0176332i
$515$	1.32876e7	+	5.91603e6i	0.0972805	+	0.0433121i
$516$	1.57183e7	+	1.74570e7i	0.114408	+	0.127063i
$517$	1.68220e7	−	1.76806e6i	0.121732	−	0.0127946i
$518$	−4.17865e7	+	1.96590e8i	−0.300640	+	1.41440i
$519$	6.99583e7	−	2.27308e7i	0.500423	−	0.162597i
$520$	−5.31466e6	−	2.50035e7i	−0.0377977	−	0.177824i
$521$	1.00461e7	+	1.74004e7i	0.0710371	+	0.123040i	0.899356	−	0.437217i	$-0.144036\pi$
$521$	1.00461e7	+	1.74004e7i	0.0710371	+	0.123040i	−0.828319	+	0.560257i	$0.810702\pi$
$522$	4.15680e7	+	2.39993e7i	0.292245	+	0.168728i
$523$	−1.24085e8	−	4.03177e7i	−0.867390	−	0.281832i	−0.158678	−	0.987330i	$-0.550723\pi$
$523$	−1.24085e8	−	4.03177e7i	−0.867390	−	0.281832i	−0.708712	+	0.705498i	$0.750723\pi$
$524$	−5.43221e6	+	5.16841e7i	−0.0377557	+	0.359222i
$525$	1.03080e8	+	1.41877e8i	0.712355	+	0.980473i
$526$		−	1.43949e8i		−	0.989126i
$527$	−1.19581e8	+	7.91885e7i	−0.817013	+	0.541041i
$528$	2.75571e7			0.187211
$529$	−1.58156e7	+	1.14907e7i	−0.106836	+	0.0776212i
$530$	−6.94743e7	−	7.30205e6i	−0.466656	−	0.0490475i
$531$	−3.60331e7	+	1.10899e8i	−0.240668	+	0.740700i
$532$	6.39757e7	−	1.10809e8i	0.424893	−	0.735937i
$533$	2.30009e7	−	1.32796e7i	0.151902	−	0.0877007i
$534$	8.00744e7	−	1.70203e7i	0.525859	−	0.111775i
$535$	−2.60030e6	−	8.00289e6i	−0.0169809	−	0.0522619i
$536$	−1.18465e8	−	2.51805e7i	−0.769299	−	0.163520i
$537$	3.30884e6	+	3.14815e7i	0.0213674	+	0.203298i
$538$	−1.04119e8	+	9.37489e7i	−0.668624	+	0.602032i
$539$	5.76940e7	−	1.29583e8i	0.368438	−	0.827526i
$540$	−6.92648e6	−	1.55571e7i	−0.0439877	−	0.0987980i
$541$	5.75057e6	−	6.38666e6i	0.0363178	−	0.0403350i	−0.724712	−	0.689052i	$-0.758027\pi$
$541$	5.75057e6	−	6.38666e6i	0.0363178	−	0.0403350i	0.761030	+	0.648717i	$0.224694\pi$
$542$	1.46839e8	−	2.02106e8i	0.922236	−	1.26935i
$543$	−1.08834e8	−	7.90726e7i	−0.679775	−	0.493885i
$544$	−6.46243e7	−	5.81880e7i	−0.401420	−	0.361441i
$545$	−2.62189e7	+	1.16734e7i	−0.161966	+	0.0721121i
$546$	−8.28584e7	−	3.68909e7i	−0.509048	−	0.226643i
$547$	7.73233e7	+	8.58762e7i	0.472442	+	0.524700i	0.931517	−	0.363697i	$-0.118486\pi$
$547$	7.73233e7	+	8.58762e7i	0.472442	+	0.524700i	−0.459075	+	0.888397i	$0.651819\pi$
$548$	6.10252e7	−	6.41401e6i	0.370824	−	0.0389751i
$549$	4.57727e6	−	2.15344e7i	0.0276624	−	0.130141i
$550$	4.57428e7	−	1.48627e7i	0.274938	−	0.0893328i
$551$	5.33415e7	+	2.50952e8i	0.318868	+	1.50015i
$552$	−6.45418e7	−	1.11790e8i	−0.383728	−	0.664637i
$553$	2.85051e8	+	1.64574e8i	1.68557	+	0.973164i
$554$	1.28389e8	+	4.17160e7i	0.755088	+	0.245343i
$555$	−4.45918e6	+	4.24262e7i	−0.0260841	+	0.248174i
$556$	8.43694e6	+	1.16125e7i	0.0490864	+	0.0675616i
$557$		−	1.77342e8i		−	1.02623i	−0.858319	−	0.513116i	$-0.828491\pi$
$557$		−	1.77342e8i		−	1.02623i	0.858319	−	0.513116i	$-0.171509\pi$
$558$	−1.03230e7	−	6.16004e7i	−0.0594161	−	0.354553i
$559$	−6.58526e7			−0.376997
$560$	5.75346e7	−	4.18013e7i	0.327616	−	0.238027i
$561$	5.08668e7	+	5.34632e6i	0.288102	+	0.0302807i
$562$	4.98869e6	−	1.53536e7i	0.0281046	−	0.0864971i
$563$	1.23585e8	−	2.14055e8i	0.692531	−	1.19950i	−0.278476	−	0.960443i	$-0.589829\pi$
$563$	1.23585e8	−	2.14055e8i	0.692531	−	1.19950i	0.971006	−	0.239055i	$-0.0768376\pi$
$564$	−1.05495e7	+	6.09078e6i	−0.0588025	+	0.0339496i
$565$	9.67060e6	−	2.05555e6i	0.0536177	−	0.0113968i
$566$	9.43577e7	+	2.90403e8i	0.520389	+	1.60159i
$567$	−1.28035e8	−	2.72146e7i	−0.702390	−	0.149298i
$568$	−1.19890e7	−	1.14068e8i	−0.0654242	−	0.622469i
$569$	−4.67877e7	+	4.21279e7i	−0.253977	+	0.228682i	−0.786278	−	0.617873i	$-0.787994\pi$
$569$	−4.67877e7	+	4.21279e7i	−0.253977	+	0.228682i	0.532300	+	0.846556i	$0.321328\pi$
$570$	−2.76693e7	+	6.21462e7i	−0.149408	+	0.335575i
$571$	−2.50477e7	−	5.62580e7i	−0.134542	−	0.302187i	0.833693	−	0.552229i	$-0.186222\pi$
$571$	−2.50477e7	−	5.62580e7i	−0.134542	−	0.302187i	−0.968235	+	0.250041i	$0.919556\pi$
$572$	6.64510e6	−	7.38013e6i	0.0355069	−	0.0394344i
$573$	2.26788e7	−	3.12147e7i	0.120547	−	0.165919i
$574$	8.67123e7	+	6.30002e7i	0.458506	+	0.333124i
$575$	−1.15423e8	−	1.03928e8i	−0.607142	−	0.546673i
$576$	8.16103e7	−	3.63352e7i	0.427049	−	0.190134i
$577$	−9.99929e7	−	4.45197e7i	−0.520525	−	0.231753i	0.129619	−	0.991564i	$-0.458625\pi$
$577$	−9.99929e7	−	4.45197e7i	−0.520525	−	0.231753i	−0.650144	+	0.759811i	$0.725291\pi$
$578$	−4.34345e6	−	4.82389e6i	−0.0224932	−	0.0249813i
$579$	−1.09461e8	+	1.15049e7i	−0.563930	+	0.0592715i
$580$	3.81128e6	−	1.79307e7i	0.0195338	−	0.0918994i
$581$	3.74268e8	−	1.21607e8i	1.90833	−	0.620056i
$582$	1.45872e7	+	6.86276e7i	0.0739953	+	0.348120i
$583$	−6.11296e7	−	1.05880e8i	−0.308493	−	0.534326i
$584$	−1.04371e8	−	6.02589e7i	−0.524015	−	0.302540i
$585$	1.35467e7	+	4.40159e6i	0.0676652	+	0.0219858i
$586$	−3.07849e7	+	2.92898e8i	−0.152983	+	1.45554i
$587$	−1.15549e8	−	1.59040e8i	−0.571284	−	0.786305i	0.421422	−	0.906865i	$-0.361531\pi$
$587$	−1.15549e8	−	1.59040e8i	−0.571284	−	0.786305i	−0.992706	+	0.120560i	$0.961531\pi$
$588$			1.02154e8i			0.502487i
$589$	2.07768e8	−	2.61325e8i	1.01680	−	1.27889i
$590$	−1.11548e8			−0.543131
$591$	1.70419e8	−	1.23817e8i	0.825575	−	0.599816i
$592$	−1.22607e8	−	1.28865e7i	−0.590950	−	0.0621114i
$593$	−8.87253e7	+	2.73068e8i	−0.425484	+	1.30951i	0.477046	+	0.878878i	$0.341708\pi$
$593$	−8.87253e7	+	2.73068e8i	−0.425484	+	1.30951i	−0.902530	+	0.430627i	$0.858292\pi$
$594$	−3.73265e7	+	6.46514e7i	−0.178097	+	0.308474i
$595$	1.14311e8	−	6.59976e7i	0.542673	−	0.313312i
$596$	−6.81610e6	+	1.44881e6i	−0.0321957	+	0.00684340i
$597$	−7.47675e7	−	2.30111e8i	−0.351391	−	1.08147i
$598$	7.85734e7	+	1.67013e7i	0.367428	+	0.0780992i
$599$	2.48475e7	+	2.36408e8i	0.115612	+	1.09997i	0.886413	+	0.462895i	$0.153189\pi$
$599$	2.48475e7	+	2.36408e8i	0.115612	+	1.09997i	−0.770801	+	0.637076i	$0.780144\pi$
$600$	−1.15960e8	+	1.04411e8i	−0.536850	+	0.483382i
$601$	−1.28330e8	+	2.88235e8i	−0.591162	+	1.32777i	0.331971	+	0.943290i	$0.392286\pi$
$601$	−1.28330e8	+	2.88235e8i	−0.591162	+	1.32777i	−0.923133	+	0.384481i	$0.874380\pi$
$602$	−1.08092e8	−	2.42779e8i	−0.495456	−	1.11281i
$603$	4.51571e7	−	5.01521e7i	0.205956	−	0.228737i
$604$	−6.57725e7	+	9.05281e7i	−0.298493	+	0.410840i
$605$	5.32898e7	+	3.87173e7i	0.240645	+	0.174839i
$606$	1.34352e8	+	1.20971e8i	0.603706	+	0.543580i
$607$	1.20260e7	−	5.35434e6i	0.0537720	−	0.0239408i	−0.379674	−	0.925120i	$-0.623964\pi$
$607$	1.20260e7	−	5.35434e6i	0.0537720	−	0.0239408i	0.433446	+	0.901179i	$0.357297\pi$
$608$	1.84922e8	+	8.23325e7i	0.822768	+	0.366320i
$609$	−1.96061e8	−	2.17748e8i	−0.868038	−	0.964054i
$610$	2.09451e7	−	2.20142e6i	0.0922770	−	0.00969870i
$611$	7.10001e6	−	3.34029e7i	0.0311269	−	0.146440i
$612$	2.59193e7	−	8.42170e6i	0.113076	−	0.0367405i
$613$	−1.57495e7	−	7.40955e7i	−0.0683730	−	0.321670i	0.930648	−	0.365917i	$-0.119244\pi$
$613$	−1.57495e7	−	7.40955e7i	−0.0683730	−	0.321670i	−0.999021	+	0.0442469i	$0.985911\pi$
$614$	8.84388e7	+	1.53180e8i	0.382065	+	0.661756i
$615$	1.97023e7	+	1.13751e7i	0.0847015	+	0.0489024i
$616$	1.71705e8	+	5.57903e7i	0.734582	+	0.238680i
$617$	3.13070e7	−	2.97866e8i	0.133287	−	1.26814i	−0.699536	−	0.714597i	$-0.746610\pi$
$617$	3.13070e7	−	2.97866e8i	0.133287	−	1.26814i	0.832823	−	0.553540i	$-0.186723\pi$
$618$	2.69913e7	+	3.71503e7i	0.114356	+	0.157397i
$619$			2.12898e7i			0.0897635i	0.998992	+	0.0448817i	$0.0142911\pi$
$619$			2.12898e7i			0.0897635i	−0.998992	+	0.0448817i	$0.985709\pi$
$620$	−2.11563e7	+	1.10195e7i	−0.0887695	+	0.0462366i
$621$	2.41074e8			1.00665
$622$	4.96431e7	−	3.60678e7i	0.206295	−	0.149882i
$623$	3.67716e8	+	3.86485e7i	1.52072	+	0.159834i
$624$	1.71923e7	−	5.29123e7i	0.0707586	−	0.217773i
$625$	−7.88541e7	+	1.36579e8i	−0.322986	+	0.559429i
$626$	−2.12268e8	+	1.22553e8i	−0.865290	+	0.499575i
$627$	−1.16455e8	+	2.47534e7i	−0.472452	+	0.100423i
$628$	−1.22732e7	−	3.77729e7i	−0.0495539	−	0.152511i
$629$	−2.23817e8	−	4.75737e7i	−0.899375	−	0.191168i
$630$	6.00855e6	+	5.71675e7i	0.0240297	+	0.228627i
$631$	3.51743e8	−	3.16711e8i	1.40003	−	1.26059i	0.475377	−	0.879782i	$-0.342312\pi$
$631$	3.51743e8	−	3.16711e8i	1.40003	−	1.26059i	0.924653	−	0.380811i	$-0.124355\pi$
$632$	−1.19119e8	+	2.67546e8i	−0.471879	+	1.05986i
$633$	1.23462e8	+	2.77299e8i	0.486767	+	1.09330i
$634$	1.10461e8	−	1.22680e8i	0.433454	−	0.481399i
$635$	−6.65776e7	+	9.16361e7i	−0.260020	+	0.357887i
$636$	7.12326e7	+	5.17535e7i	0.276890	+	0.201172i
$637$	−2.12818e8	−	1.91622e8i	−0.823360	−	0.741357i
$638$	−7.34126e7	+	3.26854e7i	−0.282689	+	0.125861i
$639$	5.83860e7	+	2.59951e7i	0.223772	+	0.0996299i
$640$	2.32641e7	+	2.58374e7i	0.0887455	+	0.0985619i
$641$	−4.36152e8	+	4.58414e7i	−1.65601	+	0.174054i	−0.885907	−	0.463863i	$-0.846463\pi$
$641$	−4.36152e8	+	4.58414e7i	−1.65601	+	0.174054i	−0.770105	+	0.637917i	$0.779796\pi$
$642$	5.52340e6	−	2.59856e7i	0.0208738	−	0.0982035i
$643$	−1.15270e8	+	3.74536e7i	−0.433595	+	0.140884i	−0.517679	−	0.855575i	$-0.673204\pi$
$643$	−1.15270e8	+	3.74536e7i	−0.433595	+	0.140884i	0.0840836	+	0.996459i	$0.473204\pi$
$644$	−2.69080e7	−	1.26592e8i	−0.100745	−	0.473969i
$645$	−2.82042e7	−	4.88512e7i	−0.105108	−	0.182052i
$646$	−3.15997e8	−	1.82441e8i	−1.17216	−	0.676745i
$647$	−1.79383e8	−	5.82850e7i	−0.662320	−	0.215201i	−0.0414817	−	0.999139i	$-0.513208\pi$
$647$	−1.79383e8	−	5.82850e7i	−0.662320	−	0.215201i	−0.620839	+	0.783938i	$0.713208\pi$
$648$	1.21741e7	−	1.15828e8i	0.0447415	−	0.425687i
$649$	−1.14749e8	−	1.57939e8i	−0.419775	−	0.577770i
$650$		−	9.71032e7i		−	0.353585i
$651$	−5.62703e7	+	3.77110e8i	−0.203956	+	1.36686i
$652$	−9.26962e6			−0.0334441
$653$	−2.76055e8	+	2.00565e8i	−0.991415	+	0.720305i	−0.960230	−	0.279209i	$-0.909928\pi$
$653$	−2.76055e8	+	2.00565e8i	−0.991415	+	0.720305i	−0.0311842	+	0.999514i	$0.509928\pi$
$654$	−9.01127e7	−	9.47122e6i	−0.322146	−	0.0338589i
$655$	3.85632e7	−	1.18685e8i	0.137230	−	0.422351i
$656$	−3.28728e7	+	5.69374e7i	−0.116446	+	0.201691i
$657$	5.81584e7	−	3.35778e7i	0.205077	−	0.118401i
$658$	1.34801e8	−	2.86528e7i	0.473168	−	0.100575i
$659$	3.20880e7	+	9.87566e7i	0.112121	+	0.345072i	0.991336	−	0.131353i	$-0.0419322\pi$
$659$	3.20880e7	+	9.87566e7i	0.112121	+	0.345072i	−0.879215	+	0.476425i	$0.841932\pi$
$660$	8.32082e6	+	1.76864e6i	0.0289424	+	0.00615189i
$661$	3.30054e7	+	3.14025e8i	0.114283	+	1.08733i	0.889910	+	0.456136i	$0.150767\pi$
$661$	3.30054e7	+	3.14025e8i	0.114283	+	1.08733i	−0.775627	+	0.631191i	$0.782566\pi$
$662$	−3.18241e7	+	2.86546e7i	−0.109694	+	0.0987688i
$663$	4.20001e7	−	9.43338e7i	0.144115	−	0.323688i
$664$	1.42419e8	+	3.19878e8i	0.486478	+	1.09265i
$665$	−2.05591e8	+	2.28332e8i	−0.699100	+	0.776429i
$666$	5.85712e7	−	8.06163e7i	0.198272	−	0.272898i
$667$	2.09943e8	+	1.52533e8i	0.707497	+	0.514027i
$668$	−4.49376e7	−	4.04620e7i	−0.150758	−	0.135743i
$669$	1.21792e8	−	5.42254e7i	0.406763	−	0.181103i
$670$	5.89775e7	+	2.62585e7i	0.196093	+	0.0873062i
$671$	2.46633e7	+	2.73913e7i	0.0816363	+	0.0906663i
$672$	−2.29914e8	+	2.41649e7i	−0.757631	+	0.0796302i
$673$	9.29716e7	−	4.37397e8i	0.305004	−	1.43493i	−0.512342	−	0.858782i	$-0.671222\pi$
$673$	9.29716e7	−	4.37397e8i	0.305004	−	1.43493i	0.817346	−	0.576148i	$-0.195445\pi$
$674$	−3.42336e8	+	1.11232e8i	−1.11808	+	0.363287i
$675$	−6.05888e7	−	2.85048e8i	−0.197007	−	0.926844i
$676$	3.40453e7	+	5.89682e7i	0.110209	+	0.190888i
$677$	−4.47815e8	−	2.58546e8i	−1.44322	−	0.833243i	−0.445156	−	0.895453i	$-0.646852\pi$
$677$	−4.47815e8	−	2.58546e8i	−1.44322	−	0.833243i	−0.998063	+	0.0622101i	$0.980185\pi$
$678$	2.96854e7	+	9.64537e6i	0.0952476	+	0.0309478i
$679$	−3.31236e7	+	3.15150e8i	−0.105810	+	1.00672i
$680$	6.90326e7	+	9.50153e7i	0.219547	+	0.302181i
$681$			1.28519e8i			0.406937i
$682$	9.35947e7	+	4.66376e7i	0.295052	+	0.147022i
$683$	6.01927e7			0.188922			0.0944608	−	0.995529i	$-0.469887\pi$
$683$	6.01927e7			0.188922			0.0944608	+	0.995529i	$0.469887\pi$
$684$	−5.13228e7	+	3.72882e7i	−0.160377	+	0.116521i
$685$	−1.46541e8	−	1.54020e7i	−0.455917	−	0.0479188i
$686$	2.03393e8	−	6.25980e8i	0.630034	−	1.93905i
$687$	8.99557e7	−	1.55808e8i	0.277433	−	0.480529i
$688$	1.41175e8	−	8.15071e7i	0.433502	−	0.250282i
$689$	−2.41436e8	+	5.13189e7i	−0.738151	+	0.156899i
$690$	2.12630e7	+	6.54408e7i	0.0647258	+	0.199205i
$691$	−2.11083e8	−	4.48670e7i	−0.639762	−	0.135986i	−0.123401	−	0.992357i	$-0.539380\pi$
$691$	−2.11083e8	−	4.48670e7i	−0.639762	−	0.135986i	−0.516361	+	0.856371i	$0.672714\pi$
$692$	6.85925e6	+	6.52614e7i	0.0206994	+	0.196942i
$693$	−7.47618e7	+	6.73159e7i	−0.224636	+	0.202264i
$694$	1.27449e8	−	2.86256e8i	0.381293	−	0.856399i
$695$	−1.40194e7	−	3.14880e7i	−0.0417613	−	0.0937974i
$696$	1.74449e8	−	1.93745e8i	0.517417	−	0.574650i
$697$	−7.17254e7	+	9.87215e7i	−0.211824	+	0.291550i
$698$	−2.73236e8	−	1.98518e8i	−0.803475	−	0.583758i
$699$	1.61300e8	+	1.45235e8i	0.472284	+	0.425246i
$700$	−1.42921e8	+	6.36324e7i	−0.416679	+	0.185517i
$701$	−3.28877e8	−	1.46426e8i	−0.954728	−	0.425072i	−0.130574	−	0.991439i	$-0.541682\pi$
$701$	−3.28877e8	−	1.46426e8i	−0.954728	−	0.425072i	−0.824154	+	0.566366i	$0.808349\pi$
$702$	1.00850e8	+	1.12005e8i	0.291517	+	0.323762i
$703$	5.29710e8	−	5.56747e7i	1.52466	−	0.160248i
$704$	−3.10961e7	+	1.46296e8i	−0.0891226	+	0.419289i
$705$	2.78200e7	−	9.03927e6i	0.0793945	−	0.0257968i
$706$	−3.19122e7	−	1.50135e8i	−0.0906864	−	0.426646i
$707$	4.08272e8	+	7.07147e8i	1.15529	+	2.00102i
$708$	1.21759e8	+	7.02977e7i	0.343085	+	0.198080i
$709$	3.35629e8	+	1.09053e8i	0.941719	+	0.305983i	0.739346	−	0.673326i	$-0.235135\pi$
$709$	3.35629e8	+	1.09053e8i	0.941719	+	0.305983i	0.202373	+	0.979309i	$0.435135\pi$
$710$	−6.39079e6	+	6.08043e7i	−0.0178558	+	0.169887i
$711$	−9.59220e7	−	1.32025e8i	−0.266876	−	0.367323i
$712$			3.28985e8i			0.911456i
$713$	−2.06932e7	−	3.37052e8i	−0.0570899	−	0.929884i
$714$	4.16721e8			1.14486
$715$	−1.92929e7	+	1.40171e7i	−0.0527811	+	0.0383477i
$716$	−2.80844e7	−	2.95178e6i	−0.0765113	−	0.00804166i
$717$	1.60806e8	−	4.94910e8i	0.436259	−	1.34267i
$718$	−2.99151e8	+	5.18145e8i	−0.808197	+	1.39984i
$719$	4.90855e8	−	2.83395e8i	1.32059	−	0.762441i	0.336764	−	0.941589i	$-0.390668\pi$
$719$	4.90855e8	−	2.83395e8i	1.32059	−	0.762441i	0.983822	+	0.179149i	$0.0573343\pi$
$720$	−3.44893e7	+	7.33092e6i	−0.0924031	+	0.0196409i
$721$	6.40909e7	+	1.97251e8i	0.170998	+	0.526277i
$722$	5.19569e8	+	1.10438e8i	1.38048	+	0.293431i
$723$	−1.33226e7	−	1.26756e8i	−0.0352511	−	0.335392i
$724$	8.91846e7	−	8.03022e7i	0.235003	−	0.211598i
$725$	1.27591e8	−	2.86574e8i	0.334816	−	0.752009i
$726$	8.45838e7	+	1.89978e8i	0.221043	+	0.496471i
$727$	2.32711e8	−	2.58451e8i	0.605638	−	0.672629i	−0.359870	−	0.933002i	$-0.617179\pi$
$727$	2.32711e8	−	2.58451e8i	0.605638	−	0.672629i	0.965508	+	0.260373i	$0.0838456\pi$
$728$	2.14246e8	−	2.94884e8i	0.555287	−	0.764287i
$729$	3.09255e8	+	2.24687e8i	0.798240	+	0.579955i
$730$	4.77415e7	+	4.29866e7i	0.122723	+	0.110501i
$731$	2.76403e8	−	1.23062e8i	0.707604	−	0.315046i
$732$	−2.42499e7	−	1.07967e7i	−0.0618267	−	0.0275270i
$733$	−2.93141e7	−	3.25566e7i	−0.0744329	−	0.0826661i	0.704778	−	0.709428i	$-0.251047\pi$
$733$	−2.93141e7	−	3.25566e7i	−0.0744329	−	0.0826661i	−0.779211	+	0.626762i	$0.784380\pi$
$734$	1.12136e8	−	1.17860e7i	0.283567	−	0.0298041i
$735$	5.10017e7	−	2.39944e8i	0.128447	−	0.604294i
$736$	1.94725e8	−	6.32701e7i	0.488415	−	0.158696i
$737$	2.34913e7	+	1.10518e8i	0.0586819	+	0.276077i
$738$	−2.65706e7	−	4.60216e7i	−0.0661046	−	0.114497i
$739$	4.27884e8	+	2.47039e8i	1.06021	+	0.612114i	0.925491	−	0.378769i	$-0.123653\pi$
$739$	4.27884e8	+	2.47039e8i	1.06021	+	0.612114i	0.134722	+	0.990883i	$0.456986\pi$
$740$	−3.61939e7	−	1.17601e7i	−0.0893183	−	0.0290213i
$741$	−2.51251e7	+	2.39049e8i	−0.0617522	+	0.587533i
$742$	−5.85498e8	−	8.05869e8i	−1.43322	−	1.97266i
$743$			7.23526e8i			1.76395i	0.471292	+	0.881977i	$0.343788\pi$
$743$			7.23526e8i			1.76395i	−0.471292	+	0.881977i	$0.656212\pi$
$744$	−3.38936e8	−	1.47198e7i	−0.822999	−	0.0357423i
$745$	1.67332e7			0.0404680
$746$	4.47519e7	−	3.25142e7i	0.107794	−	0.0783170i
$747$	−1.94043e8	−	2.03948e7i	−0.465519	−	0.0489280i
$748$	−1.40998e7	+	4.33946e7i	−0.0336905	+	0.103689i
$749$	5.99939e7	−	1.03912e8i	0.142778	−	0.247299i
$750$	1.54175e8	−	8.90132e7i	0.365453	−	0.210994i
$751$	−5.94847e8	+	1.26439e8i	−1.40438	+	0.298511i	−0.846933	−	0.531700i	$-0.821553\pi$
$751$	−5.94847e8	+	1.26439e8i	−1.40438	+	0.298511i	−0.557449	+	0.830211i	$0.688220\pi$
$752$	2.61225e7	+	8.03968e7i	0.0614273	+	0.189054i
$753$	−5.25890e8	−	1.11781e8i	−1.23171	−	0.261809i
$754$	1.69587e7	+	1.61351e8i	0.0395620	+	0.376407i
$755$	1.99686e8	−	1.79798e8i	0.463988	−	0.417777i
$756$	9.87664e7	−	2.21833e8i	0.228583	−	0.513406i
$757$	6.26683e7	+	1.40755e8i	0.144464	+	0.324472i	0.971256	−	0.238035i	$-0.0765034\pi$
$757$	6.26683e7	+	1.40755e8i	0.144464	+	0.324472i	−0.826792	+	0.562507i	$0.809837\pi$
$758$	−1.77151e8	+	1.96747e8i	−0.406759	+	0.451751i
$759$	−7.07835e7	+	9.74252e7i	−0.161885	+	0.222816i
$760$	−2.21171e8	−	1.60690e8i	−0.503834	−	0.366057i
$761$	−4.78883e8	−	4.31188e8i	−1.08661	−	0.978392i	−0.0867730	−	0.996228i	$-0.527655\pi$
$761$	−4.78883e8	−	4.31188e8i	−1.08661	−	0.978392i	−0.999841	+	0.0178366i	$0.994322\pi$
$762$	−3.26683e8	+	1.45449e8i	−0.738349	+	0.328734i
$763$	−3.73862e8	−	1.66454e8i	−0.841661	−	0.374732i
$764$	2.30315e7	+	2.55791e7i	0.0516466	+	0.0573594i
$765$	−6.50849e7	+	6.84070e6i	−0.145377	+	0.0152798i
$766$	−7.03422e7	+	3.30934e8i	−0.156506	+	0.736301i
$767$	−3.74848e8	+	1.21795e8i	−0.830747	+	0.269926i
$768$	−5.56680e7	−	2.61897e8i	−0.122892	−	0.578159i
$769$	2.26337e8	+	3.92027e8i	0.497710	+	0.862060i	0.999997	−	0.00264186i	$-0.000840932\pi$
$769$	2.26337e8	+	3.92027e8i	0.497710	+	0.862060i	−0.502286	+	0.864701i	$0.667508\pi$
$770$	−8.33447e7	−	4.81191e7i	−0.182560	−	0.105401i
$771$	−1.69462e7	−	5.50616e6i	−0.0369751	−	0.0120140i
$772$	1.02634e7	−	9.76496e7i	0.0223069	−	0.212236i
$773$	1.43364e8	+	1.97324e8i	0.310386	+	0.427210i	0.935502	−	0.353323i	$-0.114948\pi$
$773$	1.43364e8	+	1.97324e8i	0.310386	+	0.427210i	−0.625116	+	0.780532i	$0.714948\pi$
$774$			1.31762e8i			0.284162i
$775$	−3.93332e8	+	1.09179e8i	−0.844995	+	0.234548i
$776$	−2.81956e8			−0.603387
$777$	−4.92124e8	+	3.57549e8i	−1.04909	+	0.762206i
$778$	1.86881e8	+	1.96420e7i	0.396851	+	0.0417107i
$779$	8.77752e7	−	2.70144e8i	0.185677	−	0.571457i
$780$	8.58714e6	−	1.48734e7i	0.0180953	−	0.0313419i
$781$	−9.26663e7	+	5.35009e7i	−0.194522	+	0.112307i
$782$	−3.61006e8	+	7.67343e7i	−0.754909	+	0.160461i
$783$	1.50460e8	+	4.63067e8i	0.313426	+	0.964625i
$784$	6.93412e8	+	1.47389e8i	1.43894	+	0.305857i
$785$	9.96913e6	+	9.48499e7i	0.0206086	+	0.196078i
$786$	2.92787e8	−	2.63627e8i	0.602954	−	0.542902i
$787$	2.02085e8	−	4.53890e8i	0.414581	−	0.931164i	−0.578711	−	0.815533i	$-0.696444\pi$
$787$	2.02085e8	−	4.53890e8i	0.414581	−	0.931164i	0.993292	−	0.115632i	$-0.0368892\pi$
$788$	7.64336e7	+	1.71673e8i	0.156209	+	0.350851i
$789$	2.91527e8	−	3.23774e8i	0.593537	−	0.659190i
$790$	9.17611e7	−	1.26298e8i	0.186113	−	0.256163i
$791$	1.14052e8	+	8.28637e7i	0.230449	+	0.167431i
$792$	−6.65208e7	−	5.98956e7i	−0.133900	−	0.120565i
$793$	6.79809e7	−	3.02671e7i	0.136322	−	0.0606947i
$794$	1.67605e8	+	7.46227e7i	0.334832	+	0.149077i
$795$	−1.41475e8	−	1.57124e8i	−0.281565	−	0.312710i
$796$	2.14662e8	−	2.25618e7i	0.425613	−	0.0447338i
$797$	1.09488e8	−	5.15101e8i	0.216268	−	1.01746i	−0.727310	−	0.686309i	$-0.759230\pi$
$797$	1.09488e8	−	5.15101e8i	0.216268	−	1.01746i	0.943578	−	0.331151i	$-0.107437\pi$
$798$	−9.22544e8	+	2.99753e8i	−1.81543	+	0.589868i
$799$	3.26211e7	+	1.53470e8i	0.0639526	+	0.300873i
$800$	−1.23751e8	−	2.14343e8i	−0.241701	−	0.418638i
$801$	−1.58758e8	−	9.16592e7i	−0.308915	−	0.178352i
$802$	1.55514e8	+	5.05297e7i	0.301473	+	0.0979544i
$803$	−1.17524e7	+	1.11817e8i	−0.0226977	+	0.215954i
$804$	−4.78284e7	−	6.58302e7i	−0.0920275	−	0.126665i
$805$			3.10779e8i			0.595750i
$806$	1.47940e8	−	1.50615e8i	0.282541	−	0.287649i
$807$	−4.24048e8			−0.806852
$808$	−5.87780e8	+	4.27047e8i	−1.11424	+	0.809546i
$809$	−3.78038e8	−	3.97334e7i	−0.713986	−	0.0750429i	−0.259431	−	0.965762i	$-0.583535\pi$
$809$	−3.78038e8	−	3.97334e7i	−0.713986	−	0.0750429i	−0.454555	+	0.890719i	$0.650202\pi$
$810$	−1.91847e7	+	5.90443e7i	−0.0360993	+	0.111102i
$811$	3.11968e8	−	5.40344e8i	0.584854	−	1.01300i	−0.410040	−	0.912068i	$-0.634485\pi$
$811$	3.11968e8	−	5.40344e8i	0.584854	−	1.01300i	0.994894	−	0.100929i	$-0.0321815\pi$
$812$	2.26370e8	−	1.30695e8i	0.422816	−	0.244113i
$813$	7.39580e8	−	1.57203e8i	1.37630	−	0.292542i
$814$	5.15537e7	+	1.58666e8i	0.0955843	+	0.294178i
$815$	2.17728e7	+	4.62796e6i	0.0402200	+	0.00854902i
$816$	2.67193e7	+	2.54217e8i	0.0491761	+	0.467879i
$817$	−5.23385e8	+	4.71258e8i	−0.959743	+	0.864156i
$818$	−2.79906e8	+	6.28678e8i	−0.511389	+	1.14860i
$819$	8.26108e7	+	1.85547e8i	0.150378	+	0.337755i
$820$	−1.35802e7	+	1.50823e7i	−0.0246300	+	0.0273544i
$821$	−3.98970e8	+	5.49135e8i	−0.720959	+	0.992315i	0.278533	+	0.960427i	$0.410152\pi$
$821$	−3.98970e8	+	5.49135e8i	−0.720959	+	0.992315i	−0.999491	+	0.0318879i	$0.989848\pi$
$822$	−3.76347e8	−	2.73432e8i	−0.677600	−	0.492305i
$823$	−1.17736e8	−	1.06010e8i	−0.211208	−	0.190173i	0.556736	−	0.830690i	$-0.312054\pi$
$823$	−1.17736e8	−	1.06010e8i	−0.211208	−	0.190173i	−0.767944	+	0.640517i	$0.778720\pi$
$824$	−1.68586e8	+	7.50594e7i	−0.301328	+	0.134160i
$825$	1.32986e8	+	5.92092e7i	0.236834	+	0.105445i
$826$	−1.06431e9	−	1.18204e9i	−1.88855	−	2.09744i
$827$	−1.68766e8	+	1.77380e7i	−0.298378	+	0.0313608i	−0.252535	−	0.967588i	$-0.581264\pi$
$827$	−1.68766e8	+	1.77380e7i	−0.298378	+	0.0313608i	−0.0458436	+	0.998949i	$0.514598\pi$
$828$	−1.33410e7	+	6.27647e7i	−0.0235017	+	0.110567i
$829$	2.89282e8	−	9.39935e7i	0.507759	−	0.164981i	−0.0439236	−	0.999035i	$-0.513986\pi$
$829$	2.89282e8	−	9.39935e7i	0.507759	−	0.164981i	0.551683	+	0.834054i	$0.313986\pi$
$830$	−3.88065e7	−	1.82570e8i	−0.0678688	−	0.319297i
$831$	2.04291e8	+	3.53843e8i	0.355997	+	0.616605i
$832$	2.61502e8	+	1.50978e8i	0.454051	+	0.262146i
$833$	1.25135e9	+	4.06590e8i	2.16494	+	0.703431i
$834$	1.13746e7	−	1.08222e8i	0.0196083	−	0.186560i
$835$	8.53500e7	+	1.17474e8i	0.146603	+	0.201782i
$836$		−	1.06210e8i		−	0.181780i
$837$	3.40303e8	−	5.34442e8i	0.580350	−	0.911431i
$838$	8.41564e8			1.43006
$839$	1.09352e7	−	7.94486e6i	0.0185157	−	0.0134524i	−0.578489	−	0.815690i	$-0.696357\pi$
$839$	1.09352e7	−	7.94486e6i	0.0185157	−	0.0134524i	0.597005	+	0.802238i	$0.296357\pi$
$840$	3.10512e8	+	3.26361e7i	0.523891	+	0.0550631i
$841$	2.18485e7	−	6.72428e7i	0.0367311	−	0.113047i
$842$	3.35239e8	−	5.80650e8i	0.561588	−	0.972699i
$843$	4.23150e7	−	2.44306e7i	0.0706337	−	0.0407804i
$844$	−2.64870e8	+	5.62998e7i	−0.440560	+	0.0936439i
$845$	−5.05264e7	−	1.55504e8i	−0.0837429	−	0.257734i
$846$	−6.68345e7	−	1.42061e7i	−0.110380	−	0.0234620i
$847$	9.81787e7	+	9.34108e8i	0.161572	+	1.53726i
$848$	4.54072e8	−	4.08848e8i	0.744624	−	0.670462i
$849$	−3.75896e8	+	8.44276e8i	−0.614249	+	1.37963i
$850$	1.81462e8	+	4.07571e8i	0.295481	+	0.663661i
$851$	3.60489e8	−	4.00364e8i	0.584930	−	0.649630i
$852$	4.52949e7	−	6.23431e7i	0.0732370	−	0.100802i
$853$	−8.87820e8	−	6.45039e8i	−1.43047	−	1.03930i	−0.989929	−	0.141562i	$-0.954788\pi$
$853$	−8.87820e8	−	6.45039e8i	−1.43047	−	1.03930i	−0.440538	−	0.897734i	$-0.645212\pi$
$854$	2.23171e8	+	2.00944e8i	0.358315	+	0.322628i
$855$	1.39165e8	−	6.19605e7i	0.222655	−	0.0991326i
$856$	9.75315e7	+	4.34238e7i	0.155498	+	0.0692320i
$857$	−2.59968e8	−	2.88723e8i	−0.413025	−	0.458711i	0.500354	−	0.865821i	$-0.333203\pi$
$857$	−2.59968e8	−	2.88723e8i	−0.413025	−	0.458711i	−0.913379	+	0.407110i	$0.866537\pi$
$858$	−7.48757e7	+	7.86975e6i	−0.118544	+	0.0124595i
$859$	−8.10813e7	+	3.81457e8i	−0.127921	+	0.601820i	0.866752	+	0.498739i	$0.166203\pi$
$859$	−8.10813e7	+	3.81457e8i	−0.127921	+	0.601820i	−0.994673	+	0.103081i	$0.967130\pi$
$860$	4.78586e7	−	1.55502e7i	0.0752427	−	0.0244478i
$861$	6.74468e7	+	3.17312e8i	0.105670	+	0.497139i
$862$	−4.91963e8	−	8.52105e8i	−0.768088	−	1.33037i
$863$	2.47754e8	+	1.43041e8i	0.385468	+	0.222550i	0.680195	−	0.733032i	$-0.261895\pi$
$863$	2.47754e8	+	1.43041e8i	0.385468	+	0.222550i	−0.294727	+	0.955582i	$0.595229\pi$
$864$	3.65355e8	+	1.18711e8i	0.566466	+	0.184056i
$865$	1.64712e7	−	1.56713e8i	0.0254494	−	0.242135i
$866$	1.12479e8	+	1.54814e8i	0.173188	+	0.238373i
$867$		−	1.96464e7i		−	0.0301458i
$868$	−3.18628e8	−	1.19046e8i	−0.487220	−	0.182036i
$869$	2.73219e8			0.416344
$870$	−1.12431e8	+	8.16859e7i	−0.170737	+	0.124048i
$871$	2.26861e8	+	2.38440e7i	0.343324	+	0.0360848i
$872$	1.12523e8	−	3.46310e8i	0.169704	−	0.522294i
$873$	7.85564e7	−	1.36064e8i	0.118070	−	0.204503i
$874$	7.44006e8	−	4.29552e8i	1.11440	−	0.643400i
$875$	7.86498e8	−	1.67175e8i	1.17402	−	0.249545i
$876$	−2.50216e7	−	7.70087e7i	−0.0372223	−	0.114558i
$877$	−5.66119e8	−	1.20332e8i	−0.839284	−	0.178395i	−0.231836	−	0.972755i	$-0.574473\pi$
$877$	−5.66119e8	−	1.20332e8i	−0.839284	−	0.178395i	−0.607448	+	0.794360i	$0.707807\pi$
$878$	4.15006e7	+	3.94852e8i	0.0613155	+	0.583378i
$879$	−6.62423e8	+	5.96448e8i	−0.975369	+	0.878226i
$880$	2.40107e7	−	5.39289e7i	0.0352336	−	0.0791359i
$881$	3.93148e8	+	8.83024e8i	0.574947	+	1.29135i	0.933745	+	0.357938i	$0.116520\pi$
$881$	3.93148e8	+	8.83024e8i	0.574947	+	1.29135i	−0.358798	+	0.933415i	$0.616813\pi$
$882$	−3.83409e8	+	4.25818e8i	−0.558800	+	0.620610i
$883$	1.00987e8	−	1.38996e8i	0.146684	−	0.201893i	−0.729353	−	0.684138i	$-0.760179\pi$
$883$	1.00987e8	−	1.38996e8i	0.146684	−	0.201893i	0.876036	+	0.482245i	$0.160179\pi$
$884$	7.45254e7	+	5.41459e7i	0.107882	+	0.0783806i
$885$	−2.50896e8	−	2.25908e8i	−0.361962	−	0.325912i
$886$	6.12624e8	−	2.72758e8i	0.880832	−	0.392172i
$887$	−3.92663e8	−	1.74825e8i	−0.562664	−	0.250514i	0.105638	−	0.994405i	$-0.466312\pi$
$887$	−3.92663e8	−	1.74825e8i	−0.562664	−	0.250514i	−0.668301	+	0.743891i	$0.732978\pi$
$888$	−3.62164e8	−	4.02224e8i	−0.517209	−	0.574419i
$889$	−1.60628e9	+	1.68826e8i	−2.28620	+	0.240290i
$890$	3.64608e7	−	1.71534e8i	0.0517197	−	0.243322i
$891$	−1.03335e8	+	3.35757e7i	−0.146089	+	0.0474671i
$892$	2.47274e7	+	1.16333e8i	0.0348404	+	0.163911i
$893$	−1.82610e8	−	3.16290e8i	−0.256431	−	0.444151i
$894$	4.57508e7	+	2.64142e7i	0.0640303	+	0.0369679i
$895$	6.44919e7	+	2.09547e7i	0.0899572	+	0.0292289i
$896$	−5.18211e7	+	4.93045e8i	−0.0720415	+	0.685429i
$897$	1.42906e8	+	1.96693e8i	0.198003	+	0.272528i
$898$		−	7.77192e8i		−	1.07325i
$899$	6.34510e8	−	2.50110e8i	0.873292	−	0.344232i
$900$	7.75663e7			0.106401
$901$	9.17477e8	−	6.66586e8i	1.25436	−	0.911343i
$902$	8.84825e7	+	9.29989e6i	0.120570	+	0.0126724i
$903$	2.48555e8	−	7.64975e8i	0.337567	−	1.03892i
$904$	−6.27182e7	+	1.08631e8i	−0.0848962	+	0.147044i
$905$	−2.49572e8	+	1.44090e8i	−0.336705	+	0.194397i
$906$	8.29786e8	−	1.76377e8i	1.11579	−	0.237168i
$907$	3.03076e8	+	9.32773e8i	0.406191	+	1.25013i	0.919897	+	0.392161i	$0.128272\pi$
$907$	3.03076e8	+	9.32773e8i	0.406191	+	1.25013i	−0.513706	+	0.857967i	$0.671728\pi$
$908$	−1.12146e8	−	2.38373e7i	−0.149804	−	0.0318419i
$909$	−4.23177e7	−	4.02626e8i	−0.0563417	−	0.536056i
$910$	−1.44390e8	+	1.30010e8i	−0.191608	+	0.172525i
$911$	2.94015e8	−	6.60368e8i	0.388879	−	0.873436i	−0.607959	−	0.793969i	$-0.708011\pi$
$911$	2.94015e8	−	6.60368e8i	0.388879	−	0.873436i	0.996837	−	0.0794673i	$-0.0253219\pi$
$912$	−2.42013e8	−	5.43570e8i	−0.319046	−	0.716590i
$913$	2.18579e8	−	2.42756e8i	0.287207	−	0.318976i
$914$	−1.19063e7	+	1.63877e7i	−0.0155934	+	0.0214624i
$915$	5.15686e7	+	3.74668e7i	0.0673166	+	0.0489084i
$916$	1.19273e8	+	1.07394e8i	0.155187	+	0.139731i
$917$	1.62561e9	−	7.23770e8i	2.10819	−	0.938626i
$918$	−6.32606e8	−	2.81655e8i	−0.817722	−	0.364073i
$919$	3.27037e8	+	3.63211e8i	0.421357	+	0.467964i	0.916027	−	0.401116i	$-0.131378\pi$
$919$	3.27037e8	+	3.63211e8i	0.421357	+	0.467964i	−0.494670	+	0.869081i	$0.664711\pi$
$920$	−2.75007e8	+	2.89044e7i	−0.353167	+	0.0371193i
$921$	−1.11304e8	+	5.23644e8i	−0.142473	+	0.670282i
$922$	−2.90490e8	+	9.43860e7i	−0.370628	+	0.120424i
$923$	4.49145e7	+	2.11306e8i	0.0571192	+	0.268724i
$924$	6.06496e7	+	1.05048e8i	0.0768798	+	0.133160i
$925$	−5.63994e8	−	3.25622e8i	−0.712606	−	0.411423i
$926$	7.61906e8	+	2.47558e8i	0.959551	+	0.311777i
$927$	1.07487e7	−	1.02267e8i	0.0134933	−	0.128380i
$928$	2.43064e8	+	3.34549e8i	0.304142	+	0.418616i
$929$			9.21229e8i			1.14900i	0.818504	+	0.574501i	$0.194804\pi$
$929$			9.21229e8i			1.14900i	−0.818504	+	0.574501i	$0.805196\pi$
$930$	1.75092e8	+	4.52386e7i	0.217679	+	0.0562420i
$931$	−3.06273e9			−3.79542
$932$	−1.56649e8	+	1.13812e8i	−0.193500	+	0.140586i
$933$	1.84703e8	+	1.94131e7i	0.227421	+	0.0239029i
$934$	−1.48175e8	+	4.56035e8i	−0.181859	+	0.559703i
$935$	5.47833e7	−	9.48875e7i	0.0670214	−	0.116084i
$936$	−1.56506e8	+	9.03589e7i	−0.190855	+	0.110190i
$937$	−7.80373e8	+	1.65873e8i	−0.948601	+	0.201631i	−0.656134	−	0.754644i	$-0.727809\pi$
$937$	−7.80373e8	+	1.65873e8i	−0.948601	+	0.201631i	−0.292467	+	0.956276i	$0.594476\pi$
$938$	2.84469e8	+	8.75506e8i	0.344689	+	1.06084i
$939$	−7.25634e8	−	1.54238e8i	−0.876438	−	0.186293i
$940$	2.72769e6	+	2.59522e7i	0.00328406	+	0.0312458i
$941$	2.17279e8	−	1.95639e8i	0.260765	−	0.234794i	−0.528369	−	0.849015i	$-0.677196\pi$
$941$	2.17279e8	−	1.95639e8i	0.260765	−	0.234794i	0.789134	+	0.614221i	$0.210530\pi$
$942$	−1.22468e8	+	2.75068e8i	−0.146511	+	0.329069i
$943$	−1.16859e8	−	2.62469e8i	−0.139356	−	0.312999i
$944$	6.52848e8	−	7.25061e8i	0.776062	−	0.861904i
$945$	−3.42739e8	+	4.71739e8i	−0.406132	+	0.558993i
$946$	−1.78468e8	−	1.29664e8i	−0.210807	−	0.153161i
$947$	1.25490e9	+	1.12992e9i	1.47761	+	1.33045i	0.811002	+	0.585043i	$0.198923\pi$
$947$	1.25490e9	+	1.12992e9i	1.47761	+	1.33045i	0.666611	+	0.745406i	$0.267744\pi$
$948$	−1.79755e8	+	8.00321e7i	−0.210987	+	0.0939376i
$949$	2.07368e8	+	9.23260e7i	0.242629	+	0.108025i
$950$	−6.94894e8	−	7.71759e8i	−0.810491	−	0.900141i
$951$	4.96905e8	−	5.22268e7i	0.577739	−	0.0607228i
$952$	−3.48186e8	+	1.63809e9i	−0.403553	+	1.89857i
$953$	3.43780e8	−	1.11701e8i	0.397193	−	0.129056i	−0.103608	−	0.994618i	$-0.533039\pi$
$953$	3.43780e8	−	1.11701e8i	0.397193	−	0.129056i	0.500801	+	0.865562i	$0.333039\pi$
$954$	1.02682e8	+	4.83080e8i	0.118263	+	0.556383i
$955$	−4.13266e7	−	7.15798e7i	−0.0474482	−	0.0821827i
$956$	4.02031e8	+	2.32113e8i	0.460136	+	0.265660i
$957$	−2.31316e8	−	7.51592e7i	−0.263919	−	0.0857524i
$958$	−2.71698e7	+	2.58504e8i	−0.0309023	+	0.294016i
$959$	−1.23498e9	−	1.69980e9i	−1.40024	−	1.92727i
$960$			2.58651e8i			0.292349i
$961$	−7.76427e8	−	4.29911e8i	−0.874844	−	0.484405i
$962$	3.36817e8			0.378329
$963$	−4.81285e7	+	3.49674e7i	−0.0538919	+	0.0391548i
$964$	1.13078e8	+	1.18849e7i	0.126225	+	0.0132668i
$965$	−7.28596e7	+	2.24239e8i	−0.0810784	+	0.249534i
$966$	−4.90579e8	+	8.49708e8i	−0.544224	+	0.942623i
$967$	8.31021e8	−	4.79790e8i	0.919037	−	0.530606i	0.0357091	−	0.999362i	$-0.488631\pi$
$967$	8.31021e8	−	4.79790e8i	0.919037	−	0.530606i	0.883328	+	0.468756i	$0.155298\pi$
$968$	−8.17457e8	+	1.73756e8i	−0.901237	+	0.191564i
$969$	−3.41267e8	−	1.05031e9i	−0.375079	−	1.15437i
$970$	1.47013e8	+	3.12486e7i	0.161080	+	0.0342386i
$971$	7.87556e6	+	7.49309e7i	0.00860248	+	0.0818471i	0.997981	−	0.0635164i	$-0.0202315\pi$
$971$	7.87556e6	+	7.49309e7i	0.00860248	+	0.0818471i	−0.989378	+	0.145363i	$0.953565\pi$
$972$	−1.52245e8	+	1.37082e8i	−0.165785	+	0.149273i
$973$	1.99906e8	−	4.48995e8i	0.217013	−	0.487420i
$974$	1.54194e8	+	3.46325e8i	0.166875	+	0.374806i
$975$	1.96654e8	−	2.18407e8i	0.212173	−	0.235642i
$976$	−1.08275e8	+	1.49028e8i	−0.116461	+	0.160294i
$977$	2.10018e8	+	1.52587e8i	0.225202	+	0.163619i	0.694665	−	0.719333i	$-0.255552\pi$
$977$	2.10018e8	+	1.52587e8i	0.225202	+	0.163619i	−0.469463	+	0.882952i	$0.655552\pi$
$978$	5.22241e7	+	4.70228e7i	0.0558283	+	0.0502681i
$979$	2.80381e8	−	1.24834e8i	0.298814	−	0.133040i
$980$	1.99915e8	+	8.90079e7i	0.212406	+	0.0945693i
$981$	1.35769e8	+	1.50786e8i	0.143811	+	0.159718i
$982$	4.58663e8	−	4.82074e7i	0.484350	−	0.0509072i
$983$	−2.28550e8	+	1.07525e9i	−0.240614	+	1.13200i	0.677450	+	0.735569i	$0.263085\pi$
$983$	−2.28550e8	+	1.07525e9i	−0.240614	+	1.13200i	−0.918064	+	0.396432i	$0.870248\pi$
$984$	−2.74515e8	+	8.91954e7i	−0.288125	+	0.0936175i
$985$	−9.38206e7	−	4.41391e8i	−0.0981725	−	0.461865i
$986$	−3.72706e8	−	6.45546e8i	−0.388809	−	0.673436i
$987$	3.61226e8	+	2.08554e8i	0.375688	+	0.216903i
$988$	−2.03933e8	−	6.62619e7i	−0.211455	−	0.0687058i
$989$	−7.44629e7	+	7.08468e8i	−0.0769753	+	0.732371i
$990$	2.80462e7	+	3.86023e7i	0.0289047	+	0.0397839i
$991$		−	1.78887e9i		−	1.83805i	−0.394200	−	0.919025i	$-0.628978\pi$
$991$		−	1.78887e9i		−	1.83805i	0.394200	−	0.919025i	$-0.371022\pi$
$992$	1.34612e8	−	5.21002e8i	0.137895	−	0.533709i
$993$	−1.29611e8			−0.132372
$994$	−7.05300e8	+	5.12431e8i	−0.718149	+	0.521766i
$995$	−5.15470e8	−	5.41780e7i	−0.523280	−	0.0549989i
$996$	−7.26974e7	+	2.23739e8i	−0.0735768	+	0.226446i
$997$	4.25632e8	−	7.37215e8i	0.429485	−	0.743890i	−0.567342	−	0.823482i	$-0.692028\pi$
$997$	4.25632e8	−	7.37215e8i	0.429485	−	0.743890i	0.996828	+	0.0795917i	$0.0253617\pi$
$998$	−7.76668e8	+	4.48409e8i	−0.781346	+	0.451111i
$999$	9.88733e8	−	2.10162e8i	0.991705	−	0.210793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.7.h.a.3.11	✓	120
31.21	odd	30	inner	31.7.h.a.21.11	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.7.h.a.3.11	✓	120	1.1	even	1	trivial
31.7.h.a.21.11	yes	120	31.21	odd	30	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	31.h (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(5.47146 - 3.97525i) q^{2} +(20.3573 + 2.13963i) q^{3} +(-5.64283 + 17.3668i) q^{4} +(21.9247 - 37.9746i) q^{5} +(119.889 - 69.2182i) q^{6} +(611.595 - 129.999i) q^{7} +(171.917 + 529.107i) q^{8} +(-303.230 - 64.4535i) q^{9} +(-30.9987 - 294.932i) q^{10} +(385.703 - 347.289i) q^{11} +(-152.031 + 341.467i) q^{12} +(-426.196 - 957.253i) q^{13} +(2829.54 - 3142.52i) q^{14} +(527.578 - 726.148i) q^{15} +(2098.49 + 1524.64i) q^{16} +(3577.74 + 3221.42i) q^{17} +(-1915.33 + 852.759i) q^{18} +(-10237.7 - 4558.11i) q^{19} +(535.782 + 595.046i) q^{20} +(12728.5 - 1337.82i) q^{21} +(729.800 - 3433.44i) q^{22} +(-10780.4 + 3502.77i) q^{23} +(2367.67 + 11139.0i) q^{24} +(6851.12 + 11866.5i) q^{25} +(-6137.23 - 3543.33i) q^{26} +(-20226.9 - 6572.11i) q^{27} +(-1193.46 + 11355.0i) q^{28} +(-13456.6 - 18521.4i) q^{29} -6070.34i q^{30} +(-7452.40 + 28843.8i) q^{31} -18062.9 q^{32} +(8594.93 - 6244.58i) q^{33} +(32381.4 + 3403.42i) q^{34} +(8472.37 - 26075.3i) q^{35} +(2830.43 - 4902.44i) q^{36} +(-41160.7 + 23764.2i) q^{37} +(-74134.6 + 15757.8i) q^{38} +(-6628.02 - 20398.9i) q^{39} +(23861.9 + 5071.99i) q^{40} +(2649.43 + 25207.7i) q^{41} +(64325.5 - 57918.9i) q^{42} +(25561.7 - 57412.5i) q^{43} +(3854.85 + 8658.13i) q^{44} +(-9095.81 + 10101.9i) q^{45} +(-45060.2 + 62020.1i) q^{46} +(26365.8 + 19155.9i) q^{47} +(39457.3 + 35527.5i) q^{48} +(249671. - 111161. i) q^{49} +(84657.8 + 37692.1i) q^{50} +(65940.4 + 73234.2i) q^{51} +(19029.4 - 2000.07i) q^{52} +(48975.7 - 230413. i) q^{53} +(-136796. + 44447.8i) q^{54} +(-4731.74 - 22261.1i) q^{55} +(173927. + 301250. i) q^{56} +(-198658. - 114695. i) q^{57} +(-147254. - 47845.7i) q^{58} +(39317.6 - 374082. i) q^{59} +(9633.87 + 13259.9i) q^{60} +71016.7i q^{61} +(73885.8 + 187443. i) q^{62} -193833. q^{63} +(-233134. + 169381. i) q^{64} +(-45695.5 - 4802.79i) q^{65} +(22203.0 - 68333.9i) q^{66} +(-108847. + 188529. i) q^{67} +(-76134.4 + 43956.2i) q^{68} +(-226954. + 48240.6i) q^{69} +(-57299.4 - 176349. i) q^{70} +(-201658. - 42863.8i) q^{71} +(-18027.7 - 171522. i) q^{72} +(-160986. + 144952. i) q^{73} +(-130741. + 293649. i) q^{74} +(114080. + 256228. i) q^{75} +(136929. - 152075. i) q^{76} +(190747. - 262541. i) q^{77} +(-117356. - 85264.0i) q^{78} +(391206. + 352243. i) q^{79} +(103906. - 46262.1i) q^{80} +(-191247. - 85148.5i) q^{81} +(114703. + 127390. i) q^{82} +(625938. - 65788.8i) q^{83} +(-48591.2 + 228604. i) q^{84} +(200773. - 65235.1i) q^{85} +(-88369.2 - 415744. i) q^{86} +(-234310. - 405836. i) q^{87} +(250062. + 144373. i) q^{88} +(562400. + 182735. i) q^{89} +(-9609.71 + 91430.3i) q^{90} +(-385101. - 530046. i) q^{91} -206987. i q^{92} +(-213426. + 571235. i) q^{93} +220409. q^{94} +(-397550. + 288837. i) q^{95} +(-367711. - 38647.9i) q^{96} +(-156612. + 482003. i) q^{97} +(924173. - 1.60072e6i) q^{98} +(-139341. + 80448.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 6 q^{2} - 7 q^{3} - 1034 q^{4} + 68 q^{5} + 1431 q^{6} - 1753 q^{7} + 811 q^{8} - 3488 q^{9} + 1158 q^{10} + 633 q^{11} + 12777 q^{12} - 10627 q^{13} + 16244 q^{14} + 8395 q^{15} - 4178 q^{16} + 1713 q^{17}+ \cdots - 3201573 q^{99}+O(q^{100}) \) 120 * q - 6 * q^2 - 7 * q^3 - 1034 * q^4 + 68 * q^5 + 1431 * q^6 - 1753 * q^7 + 811 * q^8 - 3488 * q^9 + 1158 * q^10 + 633 * q^11 + 12777 * q^12 - 10627 * q^13 + 16244 * q^14 + 8395 * q^15 - 4178 * q^16 + 1713 * q^17 - 10077 * q^18 - 8345 * q^19 + 60861 * q^20 - 31195 * q^21 - 43117 * q^22 - 67730 * q^23 - 29436 * q^24 - 85880 * q^25 + 25485 * q^26 + 18770 * q^27 + 322940 * q^28 + 48150 * q^29 + 49476 * q^31 - 395322 * q^32 - 92548 * q^33 - 457978 * q^34 + 157789 * q^35 + 129427 * q^36 + 238344 * q^37 + 185830 * q^38 + 309716 * q^39 + 606677 * q^40 + 35959 * q^41 - 164607 * q^42 - 311135 * q^43 - 702621 * q^44 + 772689 * q^45 - 287890 * q^46 + 150530 * q^47 - 523632 * q^48 + 784094 * q^49 - 1034303 * q^50 - 1566491 * q^51 - 1080753 * q^52 - 1164247 * q^53 + 989080 * q^54 + 1197682 * q^55 + 1178042 * q^56 + 2398464 * q^57 + 2436965 * q^58 - 1106237 * q^59 + 1934095 * q^60 - 520303 * q^62 - 3411888 * q^63 + 235127 * q^64 - 583738 * q^65 - 4572168 * q^66 + 111900 * q^67 - 1524354 * q^68 - 2029246 * q^69 + 3662018 * q^70 + 1528315 * q^71 + 6241105 * q^72 + 2588381 * q^73 - 1260273 * q^74 + 707440 * q^75 + 1167086 * q^76 - 597130 * q^77 - 3405041 * q^78 - 1879167 * q^79 - 4997402 * q^80 - 6030051 * q^81 - 1060742 * q^82 + 2947757 * q^83 - 10179536 * q^84 + 2714035 * q^85 + 4916650 * q^86 + 3744039 * q^87 + 11144193 * q^88 + 2916290 * q^89 - 993633 * q^90 + 3702510 * q^91 - 975871 * q^93 - 7349352 * q^94 + 574613 * q^95 + 9276322 * q^96 - 9366930 * q^97 - 3320822 * q^98 - 3201573 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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