LMFDB - Embedded newform 31.7.h.a.21.12

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			21.12
Character	$\chi$	$=$	31.21
Dual form			31.7.h.a.3.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(7.18633 + 5.22117i) q^{2} +(49.0045 - 5.15058i) q^{3} +(4.60558 + 14.1745i) q^{4} +(67.5410 + 116.984i) q^{5} +(379.054 + 218.847i) q^{6} +(-500.379 - 106.359i) q^{7} +(134.765 - 414.765i) q^{8} +(1661.84 - 353.235i) q^{9} +(-125.424 + 1193.33i) q^{10} +(-942.897 - 848.989i) q^{11} +(298.701 + 670.893i) q^{12} +(-1177.35 + 2644.38i) q^{13} +(-3040.57 - 3376.90i) q^{14} +(3912.34 + 5384.88i) q^{15} +(3905.71 - 2837.67i) q^{16} +(-4400.77 + 3962.47i) q^{17} +(13786.8 + 6138.29i) q^{18} +(6758.09 - 3008.90i) q^{19} +(-1347.13 + 1496.14i) q^{20} +(-25068.6 - 2634.82i) q^{21} +(-2343.25 - 11024.1i) q^{22} +(-3805.50 - 1236.48i) q^{23} +(4467.82 - 21019.5i) q^{24} +(-1311.06 + 2270.82i) q^{25} +(-22267.6 + 12856.2i) q^{26} +(45455.3 - 14769.3i) q^{27} +(-796.951 - 7582.48i) q^{28} +(-5282.88 + 7271.26i) q^{29} +59124.6i q^{30} +(-15030.2 - 25721.5i) q^{31} +14972.7 q^{32} +(-50579.0 - 36747.8i) q^{33} +(-52314.1 + 5498.43i) q^{34} +(-21353.8 - 65720.1i) q^{35} +(12660.7 + 21928.9i) q^{36} +(39707.6 + 22925.2i) q^{37} +(64275.8 + 13662.2i) q^{38} +(-44075.5 + 135650. i) q^{39} +(57623.2 - 12248.2i) q^{40} +(2297.33 - 21857.6i) q^{41} +(-166395. - 149822. i) q^{42} +(-10850.1 - 24369.8i) q^{43} +(7691.42 - 17275.2i) q^{44} +(153565. + 170551. i) q^{45} +(-20891.7 - 28755.0i) q^{46} +(17282.2 - 12556.2i) q^{47} +(176782. - 159175. i) q^{48} +(131589. + 58587.4i) q^{49} +(-21278.1 + 9473.61i) q^{50} +(-195248. + 216845. i) q^{51} +(-42905.2 - 4509.52i) q^{52} +(33235.5 + 156361. i) q^{53} +(403770. + 131193. i) q^{54} +(35634.2 - 167646. i) q^{55} +(-111548. + 193206. i) q^{56} +(315679. - 182257. i) q^{57} +(-75929.0 + 24670.8i) q^{58} +(-17134.4 - 163023. i) q^{59} +(-58309.5 + 80256.1i) q^{60} +203975. i q^{61} +(26284.4 - 263319. i) q^{62} -869119. q^{63} +(-142367. - 103436. i) q^{64} +(-388870. + 40871.9i) q^{65} +(-171611. - 528163. i) q^{66} +(258871. + 448378. i) q^{67} +(-76434.2 - 44129.3i) q^{68} +(-192855. - 40992.7i) q^{69} +(189681. - 583778. i) q^{70} +(-144251. + 30661.4i) q^{71} +(77448.9 - 736877. i) q^{72} +(103577. + 93261.5i) q^{73} +(165655. + 372068. i) q^{74} +(-52551.8 + 118033. i) q^{75} +(73774.6 + 81935.0i) q^{76} +(381509. + 525102. i) q^{77} +(-1.02500e6 + 744703. i) q^{78} +(219071. - 197252. i) q^{79} +(595758. + 265249. i) q^{80} +(1.01997e6 - 454121. i) q^{81} +(130632. - 145081. i) q^{82} +(155483. + 16341.9i) q^{83} +(-78108.3 - 367471. i) q^{84} +(-760779. - 247192. i) q^{85} +(49266.4 - 231780. i) q^{86} +(-221433. + 383534. i) q^{87} +(-479201. + 276667. i) q^{88} +(575134. - 186872. i) q^{89} +(213091. + 2.02743e6i) q^{90} +(870376. - 1.19797e6i) q^{91} -59635.9i q^{92} +(-869028. - 1.18305e6i) q^{93} +189753. q^{94} +(808441. + 587367. i) q^{95} +(733727. - 77117.8i) q^{96} +(166227. + 511594. i) q^{97} +(639750. + 1.10808e6i) q^{98} +(-1.86684e6 - 1.07782e6i) 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 $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{29}{30}\right)$

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 $

$2$	7.18633	+	5.22117i	0.898291	+	0.652647i	0.938026	−	0.346564i	$-0.112652\pi$
$2$	7.18633	+	5.22117i	0.898291	+	0.652647i	−0.0397354	+	0.999210i	$0.512652\pi$
$3$	49.0045	−	5.15058i	1.81498	−	0.190762i	0.864727	−	0.502242i	$-0.167491\pi$
$3$	49.0045	−	5.15058i	1.81498	−	0.190762i	0.950253	+	0.311480i	$0.100825\pi$
$4$	4.60558	+	14.1745i	0.0719622	+	0.221477i
$5$	67.5410	+	116.984i	0.540328	+	0.935875i	0.998885	+	0.0472101i	$0.0150330\pi$
$5$	67.5410	+	116.984i	0.540328	+	0.935875i	−0.458557	+	0.888665i	$0.651634\pi$
$6$	379.054	+	218.847i	1.75488	+	1.01318i
$7$	−500.379	−	106.359i	−1.45883	−	0.310084i	−0.590890	−	0.806752i	$-0.701223\pi$
$7$	−500.379	−	106.359i	−1.45883	−	0.310084i	−0.867941	+	0.496668i	$0.834557\pi$
$8$	134.765	−	414.765i	0.263214	−	0.810088i
$9$	1661.84	−	353.235i	2.27962	−	0.484547i
$10$	−125.424	+	1193.33i	−0.125424	+	1.19333i
$11$	−942.897	−	848.989i	−0.708413	−	0.637858i	0.234028	−	0.972230i	$-0.424809\pi$
$11$	−942.897	−	848.989i	−0.708413	−	0.637858i	−0.942441	+	0.334372i	$0.891476\pi$
$12$	298.701	+	670.893i	0.172859	+	0.388248i
$13$	−1177.35	+	2644.38i	−0.535891	+	1.20363i	0.419356	+	0.907822i	$0.362256\pi$
$13$	−1177.35	+	2644.38i	−0.535891	+	1.20363i	−0.955247	+	0.295810i	$0.904411\pi$
$14$	−3040.57	−	3376.90i	−1.10808	−	1.23065i
$15$	3912.34	+	5384.88i	1.15921	+	1.59552i
$16$	3905.71	−	2837.67i	0.953543	−	0.692790i
$17$	−4400.77	+	3962.47i	−0.895740	+	0.806528i	−0.981831	−	0.189760i	$-0.939229\pi$
$17$	−4400.77	+	3962.47i	−0.895740	+	0.806528i	0.0860909	+	0.996287i	$0.472562\pi$
$18$	13786.8	+	6138.29i	2.36400	+	1.05252i
$19$	6758.09	−	3008.90i	0.985288	−	0.438678i	0.150117	−	0.988668i	$-0.452035\pi$
$19$	6758.09	−	3008.90i	0.985288	−	0.438678i	0.835171	+	0.549990i	$0.185368\pi$
$20$	−1347.13	+	1496.14i	−0.168391	+	0.187018i
$21$	−25068.6	−	2634.82i	−2.70690	−	0.284507i
$22$	−2343.25	−	11024.1i	−0.220065	−	1.03533i
$23$	−3805.50	−	1236.48i	−0.312773	−	0.101626i	0.148424	−	0.988924i	$-0.452580\pi$
$23$	−3805.50	−	1236.48i	−0.312773	−	0.101626i	−0.461197	+	0.887298i	$0.652580\pi$
$24$	4467.82	−	21019.5i	0.323193	−	1.52050i
$25$	−1311.06	+	2270.82i	−0.0839078	+	0.145333i
$26$	−22267.6	+	12856.2i	−1.26693	+	0.731464i
$27$	45455.3	−	14769.3i	2.30937	−	0.750359i
$28$	−796.951	−	7582.48i	−0.0363042	−	0.345412i
$29$	−5282.88	+	7271.26i	−0.216609	+	0.298137i	−0.903469	−	0.428653i	$-0.858988\pi$
$29$	−5282.88	+	7271.26i	−0.216609	+	0.298137i	0.686860	+	0.726789i	$0.258988\pi$
$30$			59124.6i			2.18980i
$31$	−15030.2	−	25721.5i	−0.504522	−	0.863399i
$31$	−15030.2	−	25721.5i	−0.504522	−	0.863399i
$32$	14972.7			0.456929
$33$	−50579.0	−	36747.8i	−1.40743	−	1.02256i
$34$	−52314.1	+	5498.43i	−1.33101	+	0.139895i
$35$	−21353.8	−	65720.1i	−0.498047	−	1.53283i
$36$	12660.7	+	21928.9i	0.271362	+	0.470013i
$37$	39707.6	+	22925.2i	0.783914	+	0.452593i	0.837816	−	0.545953i	$-0.183832\pi$
$37$	39707.6	+	22925.2i	0.783914	+	0.452593i	−0.0539018	+	0.998546i	$0.517166\pi$
$38$	64275.8	+	13662.2i	1.17138	+	0.248984i
$39$	−44075.5	+	135650.i	−0.743025	+	2.28680i
$40$	57623.2	−	12248.2i	0.900362	−	0.191378i
$41$	2297.33	−	21857.6i	0.0333327	−	0.317140i	−0.965133	−	0.261761i	$-0.915697\pi$
$41$	2297.33	−	21857.6i	0.0333327	−	0.317140i	0.998465	−	0.0553787i	$-0.0176366\pi$
$42$	−166395.	−	149822.i	−2.24590	−	2.02222i
$43$	−10850.1	−	24369.8i	−0.136468	−	0.306512i	0.832365	−	0.554228i	$-0.186987\pi$
$43$	−10850.1	−	24369.8i	−0.136468	−	0.306512i	−0.968833	+	0.247717i	$0.920320\pi$
$44$	7691.42	−	17275.2i	0.0902918	−	0.202799i
$45$	153565.	+	170551.i	1.68521	+	1.87162i
$46$	−20891.7	−	28755.0i	−0.214635	−	0.295420i
$47$	17282.2	−	12556.2i	0.166458	−	0.120939i	−0.501438	−	0.865194i	$-0.667195\pi$
$47$	17282.2	−	12556.2i	0.166458	−	0.120939i	0.667895	+	0.744255i	$0.267195\pi$
$48$	176782.	−	159175.i	1.59850	−	1.43930i
$49$	131589.	+	58587.4i	1.11849	+	0.497984i
$50$	−21278.1	+	9473.61i	−0.170225	+	0.0757889i
$51$	−195248.	+	216845.i	−1.47189	+	1.63470i
$52$	−42905.2	−	4509.52i	−0.305140	−	0.0320716i
$53$	33235.5	+	156361.i	0.223242	+	1.05027i	0.936852	+	0.349726i	$0.113725\pi$
$53$	33235.5	+	156361.i	0.223242	+	1.05027i	−0.713610	+	0.700543i	$0.752941\pi$
$54$	403770.	+	131193.i	2.56420	+	0.833160i
$55$	35634.2	−	167646.i	0.214180	−	1.00764i
$56$	−111548.	+	193206.i	−0.635180	+	1.10016i
$57$	315679.	−	182257.i	1.70459	−	0.984148i
$58$	−75929.0	+	24670.8i	−0.389156	+	0.126444i
$59$	−17134.4	−	163023.i	−0.0834283	−	0.793767i	−0.953612	−	0.301039i	$-0.902666\pi$
$59$	−17134.4	−	163023.i	−0.0834283	−	0.793767i	0.870183	−	0.492728i	$-0.164000\pi$
$60$	−58309.5	+	80256.1i	−0.269951	+	0.371556i
$61$			203975.i			0.898645i	0.893370	+	0.449323i	$0.148335\pi$
$61$			203975.i			0.898645i	−0.893370	+	0.449323i	$0.851665\pi$
$62$	26284.4	−	263319.i	0.110287	−	1.10486i
$63$	−869119.			−3.47582
$64$	−142367.	−	103436.i	−0.543088	−	0.394576i
$65$	−388870.	+	40871.9i	−1.41601	+	0.148828i
$66$	−171611.	−	528163.i	−0.596915	−	1.83711i
$67$	258871.	+	448378.i	0.860715	+	1.49080i	0.871240	+	0.490858i	$0.163317\pi$
$67$	258871.	+	448378.i	0.860715	+	1.49080i	−0.0105245	+	0.999945i	$0.503350\pi$
$68$	−76434.2	−	44129.3i	−0.243087	−	0.140346i
$69$	−192855.	−	40992.7i	−0.587062	−	0.124784i
$70$	189681.	−	583778.i	0.553006	−	1.70198i
$71$	−144251.	+	30661.4i	−0.403035	+	0.0856677i	−0.404969	−	0.914330i	$-0.632718\pi$
$71$	−144251.	+	30661.4i	−0.403035	+	0.0856677i	0.00193403	+	0.999998i	$0.499384\pi$
$72$	77448.9	−	736877.i	0.207500	−	1.97423i
$73$	103577.	+	93261.5i	0.266254	+	0.239736i	0.791433	−	0.611255i	$-0.209335\pi$
$73$	103577.	+	93261.5i	0.266254	+	0.239736i	−0.525179	+	0.850992i	$0.676002\pi$
$74$	165655.	+	372068.i	0.408800	+	0.918179i
$75$	−52551.8	+	118033.i	−0.124567	+	0.279782i
$76$	73774.6	+	81935.0i	0.168061	+	0.186650i
$77$	381509.	+	525102.i	0.835665	+	1.15019i
$78$	−1.02500e6	+	744703.i	−2.15992	+	1.56928i
$79$	219071.	−	197252.i	0.444328	−	0.400074i	−0.416367	−	0.909197i	$-0.636697\pi$
$79$	219071.	−	197252.i	0.444328	−	0.400074i	0.860694	+	0.509123i	$0.170030\pi$
$80$	595758.	+	265249.i	1.16359	+	0.518064i
$81$	1.01997e6	−	454121.i	1.91926	−	0.854508i
$82$	130632.	−	145081.i	0.236923	−	0.263129i
$83$	155483.	+	16341.9i	0.271924	+	0.0285804i	0.239509	−	0.970894i	$-0.423014\pi$
$83$	155483.	+	16341.9i	0.271924	+	0.0285804i	0.0324150	+	0.999474i	$0.489680\pi$
$84$	−78108.3	−	367471.i	−0.131783	−	0.619990i
$85$	−760779.	−	247192.i	−1.23880	−	0.402511i
$86$	49266.4	−	231780.i	0.0774560	−	0.364402i
$87$	−221433.	+	383534.i	−0.336268	+	0.582433i
$88$	−479201.	+	276667.i	−0.703185	+	0.405984i
$89$	575134.	−	186872.i	0.815829	−	0.265079i	0.128764	−	0.991675i	$-0.458899\pi$
$89$	575134.	−	186872.i	0.815829	−	0.265079i	0.687064	+	0.726596i	$0.258899\pi$
$90$	213091.	+	2.02743e6i	0.292306	+	2.78111i
$91$	870376.	−	1.19797e6i	1.15500	−	1.58972i
$92$		−	59635.9i		−	0.0765851i
$93$	−869028.	−	1.18305e6i	−1.08040	−	1.47081i
$94$	189753.			0.228458
$95$	808441.	+	587367.i	0.942926	+	0.685076i
$96$	733727.	−	77117.8i	0.829317	−	0.0871648i
$97$	166227.	+	511594.i	0.182132	+	0.560545i	0.999887	−	0.0150215i	$-0.00478168\pi$
$97$	166227.	+	511594.i	0.182132	+	0.560545i	−0.817755	+	0.575566i	$0.804782\pi$
$98$	639750.	+	1.10808e6i	0.679723	+	1.17731i
$99$	−1.86684e6	−	1.07782e6i	−1.92398	−	1.11081i
$100$	−38226.0	−	8125.19i	−0.0382260	−	0.00812519i
$101$	165610.	−	509695.i	0.160740	−	0.494705i	−0.837958	−	0.545735i	$-0.816250\pi$
$101$	165610.	−	509695.i	0.160740	−	0.494705i	0.998697	+	0.0510300i	$0.0162504\pi$
$102$	−2.53530e6	+	538896.i	−2.38907	+	0.507813i
$103$	−101775.	+	968325.i	−0.0931386	+	0.886155i	0.843799	+	0.536659i	$0.180314\pi$
$103$	−101775.	+	968325.i	−0.0931386	+	0.886155i	−0.936938	+	0.349496i	$0.886353\pi$
$104$	938129.	+	844695.i	0.833994	+	0.750931i
$105$	−1.38493e6	−	3.11059e6i	−1.19635	−	2.68705i
$106$	−577546.	+	1.29719e6i	−0.484919	+	1.08915i
$107$	3648.29	+	4051.84i	0.00297809	+	0.00330751i	0.744632	−	0.667475i	$-0.232625\pi$
$107$	3648.29	+	4051.84i	0.00297809	+	0.00330751i	−0.741654	+	0.670783i	$0.765958\pi$
$108$	418696.	+	576285.i	0.332374	+	0.457474i
$109$	429761.	−	312240.i	0.331855	−	0.241107i	−0.409363	−	0.912372i	$-0.634249\pi$
$109$	429761.	−	312240.i	0.331855	−	0.241107i	0.741217	+	0.671265i	$0.234249\pi$
$110$	1.13139e6	−	1.01871e6i	0.850027	−	0.765368i
$111$	2.06393e6	+	918919.i	1.50913	+	0.671906i
$112$	−2.25615e6	+	1.00450e6i	−1.60588	+	0.714984i
$113$	253329.	−	281350.i	0.175570	−	0.194990i	−0.648937	−	0.760842i	$-0.724786\pi$
$113$	253329.	−	281350.i	0.175570	−	0.194990i	0.824507	+	0.565852i	$0.191453\pi$
$114$	3.22017e6	+	338454.i	2.17352	+	0.228446i
$115$	−112378.	−	528698.i	−0.0738905	−	0.347627i
$116$	−127397.	−	41393.9i	−0.0816181	−	0.0265193i
$117$	−1.02249e6	+	4.81041e6i	−0.638410	+	3.00348i
$118$	728038.	−	1.26100e6i	0.443107	−	0.767483i
$119$	2.62350e6	−	1.51468e6i	1.55682	−	0.898833i
$120$	2.76071e6	−	897009.i	1.59763	−	0.519102i
$121$	−16904.8	−	160838.i	−0.00954230	−	0.0907889i
$122$	−1.06499e6	+	1.46583e6i	−0.586498	+	0.807245i
$123$		−	1.08295e6i		−	0.581961i
$124$	295367.	−	331509.i	0.154916	−	0.173872i
$125$	1.75645e6			0.899304
$126$	−6.24578e6	−	4.53782e6i	−3.12230	−	2.26849i
$127$	−1.66669e6	+	175176.i	−0.813660	+	0.0855192i	−0.502213	−	0.864744i	$-0.667481\pi$
$127$	−1.66669e6	+	175176.i	−0.813660	+	0.0855192i	−0.311448	+	0.950263i	$0.600814\pi$
$128$	−779156.	−	2.39800e6i	−0.371531	−	1.14345i
$129$	−657224.	−	1.13835e6i	−0.306157	−	0.530280i
$130$	−3.00795e6	−	1.73664e6i	−1.36912	−	0.790460i
$131$	−3.47736e6	−	739135.i	−1.54680	−	0.328783i	−0.646113	−	0.763242i	$-0.723606\pi$
$131$	−3.47736e6	−	739135.i	−1.54680	−	0.328783i	−0.900692	+	0.434458i	$0.856940\pi$
$132$	287936.	−	886177.i	0.125191	−	0.385300i
$133$	−3.70163e6	+	786806.i	−1.57340	+	0.334436i
$134$	−480726.	+	4.57381e6i	−0.199794	+	1.90092i
$135$	4.79787e6	+	4.32002e6i	1.95006	+	1.75584i
$136$	1.05042e6	+	2.35929e6i	0.417587	+	0.937917i
$137$	−529358.	+	1.18896e6i	−0.205867	+	0.462386i	−0.986741	−	0.162303i	$-0.948108\pi$
$137$	−529358.	+	1.18896e6i	−0.205867	+	0.462386i	0.780873	+	0.624689i	$0.214774\pi$
$138$	−1.17189e6	−	1.30152e6i	−0.445913	−	0.495237i
$139$	−2.61177e6	−	3.59480e6i	−0.972504	−	1.33854i	−0.940772	−	0.339040i	$-0.889898\pi$
$139$	−2.61177e6	−	3.59480e6i	−0.972504	−	1.33854i	−0.0317317	−	0.999496i	$-0.510102\pi$
$140$	833205.	−	605359.i	0.303646	−	0.220612i
$141$	782231.	−	704324.i	0.279047	−	0.251255i
$142$	−1.19672e6	−	532815.i	−0.417954	−	0.186085i
$143$	3.35517e6	−	1.49382e6i	1.14738	−	0.510846i
$144$	5.48830e6	−	6.09538e6i	1.83802	−	2.04133i
$145$	−1.20743e6	−	126906.i	−0.396059	−	0.0416274i
$146$	257407.	+	1.21100e6i	0.0827106	+	0.389123i
$147$	6.75022e6	+	2.19328e6i	2.12504	+	0.690466i
$148$	−142077.	+	668420.i	−0.0438267	+	0.206188i
$149$	−1.97911e6	+	3.42793e6i	−0.598290	+	1.03627i	0.394783	+	0.918774i	$0.370820\pi$
$149$	−1.97911e6	+	3.42793e6i	−0.598290	+	1.03627i	−0.993073	+	0.117495i	$0.962514\pi$
$150$	−993926.	+	573843.i	−0.294497	+	0.170028i
$151$	−1.39168e6	+	452184.i	−0.404211	+	0.131336i	−0.504065	−	0.863666i	$-0.668163\pi$
$151$	−1.39168e6	+	452184.i	−0.404211	+	0.131336i	0.0998534	+	0.995002i	$0.468163\pi$
$152$	−337228.	−	3.20851e6i	−0.0960270	−	0.913636i
$153$	−5.91369e6	+	8.13949e6i	−1.65114	+	2.27260i
$154$			5.76548e6i			1.57860i
$155$	1.99386e6	−	3.49556e6i	0.535426	−	0.938688i
$156$	−2.12577e6			−0.559942
$157$	−4.82490e6	−	3.50549e6i	−1.24678	−	0.905838i	−0.248748	−	0.968568i	$-0.580019\pi$
$157$	−4.82490e6	−	3.50549e6i	−1.24678	−	0.905838i	−0.998031	+	0.0627305i	$0.980019\pi$
$158$	2.60420e6	−	273713.i	0.660243	−	0.0693943i
$159$	2.43404e6	+	7.49120e6i	0.605530	+	1.86363i
$160$	1.01127e6	+	1.75157e6i	0.246891	+	0.427629i
$161$	1.77268e6	+	1.02346e6i	0.424770	+	0.245241i
$162$	9.70089e6	+	2.06199e6i	2.28174	+	0.484999i
$163$	1.91256e6	−	5.88626e6i	0.441624	−	1.35918i	−0.444520	−	0.895769i	$-0.646626\pi$
$163$	1.91256e6	−	5.88626e6i	0.441624	−	1.35918i	0.886144	−	0.463410i	$-0.153374\pi$
$164$	320401.	−	68103.4i	0.0726378	−	0.0154396i
$165$	882763.	−	8.39893e6i	0.196513	−	1.86970i
$166$	1.03203e6	+	929240.i	0.225614	+	0.203144i
$167$	1.77443e6	+	3.98543e6i	0.380986	+	0.855708i	0.997652	+	0.0684837i	$0.0218161\pi$
$167$	1.77443e6	+	3.98543e6i	0.380986	+	0.855708i	−0.616666	+	0.787225i	$0.711517\pi$
$168$	−4.47121e6	+	1.00425e7i	−0.942969	+	2.11794i
$169$	−2.37681e6	−	2.63972e6i	−0.492419	−	0.546887i
$170$	−4.17658e6	−	5.74856e6i	−0.850107	−	1.17007i
$171$	1.01680e7	−	7.38749e6i	2.03352	−	1.47744i
$172$	295459.	−	266033.i	0.0580647	−	0.0522817i
$173$	−2.07861e6	−	925459.i	−0.401454	−	0.178739i	0.196070	−	0.980590i	$-0.437182\pi$
$173$	−2.07861e6	−	925459.i	−0.401454	−	0.178739i	−0.597524	+	0.801851i	$0.703849\pi$
$174$	−3.59379e6	+	1.60006e6i	−0.682190	+	0.303730i
$175$	897549.	−	996829.i	0.167473	−	0.185997i
$176$	−6.09183e6	−	640277.i	−1.11740	−	0.117444i
$177$	−1.67933e6	−	7.90061e6i	−0.302841	−	1.42476i
$178$	5.10879e6	+	1.65995e6i	0.905854	+	0.294330i
$179$	−1.98560e6	+	9.34152e6i	−0.346205	+	1.62877i	0.368703	+	0.929547i	$0.379802\pi$
$179$	−1.98560e6	+	9.34152e6i	−0.346205	+	1.62877i	−0.714908	+	0.699218i	$0.753531\pi$
$180$	−1.71023e6	+	2.96220e6i	−0.293249	+	0.507922i
$181$	8.00281e6	−	4.62043e6i	1.34961	−	0.779195i	0.361412	−	0.932406i	$-0.382295\pi$
$181$	8.00281e6	−	4.62043e6i	1.34961	−	0.779195i	0.988194	+	0.153211i	$0.0489614\pi$
$182$	1.25096e7	−	4.06462e6i	2.07506	−	0.674227i
$183$	1.05059e6	+	9.99571e6i	0.171427	+	1.63102i
$184$	−1.02570e6	+	1.41175e6i	−0.164652	+	0.226624i
$185$			6.19355e6i			0.978194i
$186$	−68190.6	−	1.30392e7i	−0.0105971	−	2.02633i
$187$	7.51356e6			1.14900
$188$	257573.	+	187138.i	0.0387638	+	0.0281635i
$189$	−2.43157e7	+	2.55568e6i	−3.60165	+	0.378549i
$190$	2.74298e6	+	8.44203e6i	0.399910	+	1.23080i
$191$	−402386.	−	696952.i	−0.0577487	−	0.100024i	0.835706	−	0.549177i	$-0.185059\pi$
$191$	−402386.	−	696952.i	−0.0577487	−	0.100024i	−0.893454	+	0.449154i	$0.851726\pi$
$192$	−7.50938e6	−	4.33554e6i	−1.06096	−	0.612548i
$193$	−517886.	−	110080.i	−0.0720381	−	0.0153122i	0.171752	−	0.985140i	$-0.445057\pi$
$193$	−517886.	−	110080.i	−0.0720381	−	0.0153122i	−0.243790	+	0.969828i	$0.578391\pi$
$194$	−1.47656e6	+	4.54438e6i	−0.202230	+	0.622400i
$195$	−1.88459e7	+	4.00581e6i	−2.54163	+	0.540240i
$196$	−224402.	+	2.13504e6i	−0.0298029	+	0.283556i
$197$	−3.00115e6	−	2.70224e6i	−0.392544	−	0.353448i	0.449099	−	0.893482i	$-0.351745\pi$
$197$	−3.00115e6	−	2.70224e6i	−0.392544	−	0.353448i	−0.841643	+	0.540034i	$0.818412\pi$
$198$	−7.78822e6	−	1.74926e7i	−1.00333	−	2.25351i
$199$	6.00517e6	−	1.34878e7i	0.762020	−	1.71152i	0.0612666	−	0.998121i	$-0.480486\pi$
$199$	6.00517e6	−	1.34878e7i	0.762020	−	1.71152i	0.700753	−	0.713404i	$-0.252847\pi$
$200$	765172.	+	849810.i	0.0956465	+	0.106226i
$201$	1.49953e7	+	2.06392e7i	1.84657	+	2.54158i
$202$	3.85134e6	−	2.79816e6i	0.467259	−	0.339483i
$203$	3.41681e6	−	3.07651e6i	0.408444	−	0.367764i
$204$	−3.97291e6	−	1.76885e6i	−0.467970	−	0.208354i
$205$	2.71216e6	−	1.20753e6i	0.314814	−	0.140164i
$206$	−5.78718e6	+	6.42732e6i	−0.662011	+	0.735238i
$207$	−6.76091e6	−	710600.i	−0.762244	−	0.0801150i
$208$	2.90546e6	+	1.36691e7i	0.322868	+	1.51897i
$209$	−8.92670e6	−	2.90046e6i	−0.977805	−	0.317708i
$210$	6.28842e6	−	2.95847e7i	0.679022	−	3.19455i
$211$	−2.40508e6	+	4.16572e6i	−0.256025	+	0.443448i	−0.965173	−	0.261611i	$-0.915746\pi$
$211$	−2.40508e6	+	4.16572e6i	−0.256025	+	0.443448i	0.709149	+	0.705059i	$0.249079\pi$
$212$	−2.06327e6	+	1.19123e6i	−0.216545	+	0.125023i
$213$	−6.91100e6	+	2.24552e6i	−0.715158	+	0.232369i
$214$	5062.47	+	48166.2i	0.000516560	+	0.00491474i
$215$	2.11806e6	−	2.91526e6i	0.213119	−	0.293334i
$216$		−	2.08436e7i		−	2.06829i
$217$	4.78510e6	+	1.44691e7i	0.468286	+	1.41600i
$218$	4.71867e6			0.455459
$219$	5.55610e6	+	4.03674e6i	0.528978	+	0.384325i
$220$	2.54041e6	−	267008.i	0.238581	−	0.0250759i
$221$	−5.29701e6	−	1.63025e7i	−0.490743	−	1.51035i
$222$	1.00342e7	+	1.73798e7i	0.917117	+	1.58849i
$223$	−1.29374e7	−	7.46943e6i	−1.16663	−	0.673555i	−0.213747	−	0.976889i	$-0.568567\pi$
$223$	−1.29374e7	−	7.46943e6i	−1.16663	−	0.673555i	−0.952884	+	0.303334i	$0.901900\pi$
$224$	−7.49200e6	−	1.59247e6i	−0.666583	−	0.141686i
$225$	−1.37664e6	+	4.23685e6i	−0.120857	+	0.371960i
$226$	3.28948e6	−	699201.i	0.284972	−	0.0605727i
$227$	1.97122e6	−	1.87549e7i	0.168522	−	1.60338i	−0.504266	−	0.863548i	$-0.668237\pi$
$227$	1.97122e6	−	1.87549e7i	0.168522	−	1.60338i	0.672789	−	0.739835i	$-0.265096\pi$
$228$	4.03730e6	+	3.63520e6i	0.340632	+	0.306707i
$229$	−1.00932e6	−	2.26698e6i	−0.0840473	−	0.188773i	0.866633	−	0.498947i	$-0.166280\pi$
$229$	−1.00932e6	−	2.26698e6i	−0.0840473	−	0.188773i	−0.950680	+	0.310173i	$0.899613\pi$
$230$	1.95284e6	−	4.38614e6i	0.160503	−	0.360495i
$231$	2.14002e7	+	2.37673e7i	1.73613	+	1.92817i
$232$	2.30392e6	+	3.17107e6i	0.184503	+	0.253946i
$233$	−7.91075e6	+	5.74750e6i	−0.625389	+	0.454372i	−0.854800	−	0.518958i	$-0.826320\pi$
$233$	−7.91075e6	+	5.74750e6i	−0.625389	+	0.454372i	0.229411	+	0.973330i	$0.426320\pi$
$234$	−3.24639e7	+	2.92306e7i	−2.53369	+	2.28134i
$235$	2.63613e6	+	1.17368e6i	0.203125	+	0.0904372i
$236$	2.23186e6	−	993688.i	0.169797	−	0.0755987i
$237$	9.71948e6	−	1.07946e7i	0.730127	−	0.810888i
$238$	2.67617e7	+	2.81277e6i	1.98510	+	0.208643i
$239$	3.55326e6	+	1.67168e7i	0.260276	+	1.22450i	0.892976	+	0.450104i	$0.148613\pi$
$239$	3.55326e6	+	1.67168e7i	0.260276	+	1.22450i	−0.632701	+	0.774396i	$0.718054\pi$
$240$	3.05610e7	+	9.92987e6i	2.21072	+	0.718306i
$241$	4.03662e6	−	1.89908e7i	0.288381	−	1.35672i	−0.560506	−	0.828150i	$-0.689393\pi$
$241$	4.03662e6	−	1.89908e7i	0.288381	−	1.35672i	0.848887	−	0.528575i	$-0.177273\pi$
$242$	718281.	−	1.24410e6i	0.0506813	−	0.0877826i
$243$	1.74700e7	−	1.00863e7i	1.21751	−	0.702931i
$244$	−2.89125e6	+	939425.i	−0.199029	+	0.0646685i
$245$	2.03387e6	+	1.93509e7i	0.138301	+	1.31584i
$246$	5.65428e6	−	7.78245e6i	0.379815	−	0.522770i
$247$			2.14135e7i			1.42101i
$248$	−1.26939e7	+	2.76764e6i	−0.832226	+	0.181449i
$249$	7.70352e6			0.498989
$250$	1.26225e7	+	9.17075e6i	0.807837	+	0.586928i
$251$	−1.90374e7	+	2.00091e6i	−1.20389	+	0.126534i	−0.685153	−	0.728399i	$-0.740265\pi$
$251$	−1.90374e7	+	2.00091e6i	−1.20389	+	0.126534i	−0.518738	+	0.854933i	$0.673598\pi$
$252$	−4.00280e6	−	1.23194e7i	−0.250128	−	0.769815i
$253$	2.53844e6	+	4.39671e6i	0.156749	+	0.271498i
$254$	−1.28920e7	−	7.44320e6i	−0.786718	−	0.454212i
$255$	−3.85548e7	−	8.19507e6i	−2.32518	−	0.494233i
$256$	3.44080e6	−	1.05897e7i	0.205088	−	0.631195i
$257$	2.74934e7	−	5.84390e6i	1.61968	−	0.344273i	0.693236	−	0.720710i	$-0.256184\pi$
$257$	2.74934e7	−	5.84390e6i	1.61968	−	0.344273i	0.926442	+	0.376437i	$0.122851\pi$
$258$	1.22047e6	−	1.16120e7i	0.0710671	−	0.676158i
$259$	−1.74305e7	−	1.56945e7i	−1.00326	−	0.903336i
$260$	−2.37031e6	−	5.32381e6i	−0.134861	−	0.302902i
$261$	−6.21083e6	+	1.39498e7i	−0.349324	+	0.784595i
$262$	−2.11303e7	−	2.34676e7i	−1.17490	−	1.30486i
$263$	9.35802e6	+	1.28802e7i	0.514418	+	0.708036i	0.984657	−	0.174503i	$-0.0558320\pi$
$263$	9.35802e6	+	1.28802e7i	0.514418	+	0.708036i	−0.470238	+	0.882540i	$0.655832\pi$
$264$	−2.20580e7	+	1.60261e7i	−1.19882	+	0.870994i
$265$	−1.60470e7	+	1.44488e7i	−0.862297	+	0.776415i
$266$	−3.07092e7	−	1.36726e7i	−1.63164	−	0.726451i
$267$	2.72216e7	−	1.21198e7i	1.43015	−	0.636742i
$268$	−5.16329e6	+	5.73442e6i	−0.268239	+	0.297910i
$269$	−8.07468e6	−	848683.i	−0.414828	−	0.0436002i	−0.105184	−	0.994453i	$-0.533543\pi$
$269$	−8.07468e6	−	848683.i	−0.414828	−	0.0436002i	−0.309644	+	0.950853i	$0.600210\pi$
$270$	1.19235e7	+	5.60956e7i	0.605776	+	2.84995i
$271$	6.53688e6	+	2.12396e6i	0.328445	+	0.106718i	0.468598	−	0.883412i	$-0.344759\pi$
$271$	6.53688e6	+	2.12396e6i	0.328445	+	0.106718i	−0.140153	+	0.990130i	$0.544759\pi$
$272$	−5.94397e6	+	2.79642e7i	−0.295372	+	1.38962i
$273$	3.64821e7	−	6.31888e7i	1.79305	−	3.10565i
$274$	−1.00119e7	+	5.78037e6i	−0.486704	+	0.280998i
$275$	3.16410e6	−	1.02808e6i	0.152143	−	0.0494342i
$276$	−307159.	−	2.92243e6i	−0.0146095	−	0.139000i
$277$	7.32812e6	−	1.00863e7i	0.344789	−	0.474561i	−0.601044	−	0.799216i	$-0.705248\pi$
$277$	7.32812e6	−	1.00863e7i	0.344789	−	0.474561i	0.945832	+	0.324655i	$0.105248\pi$
$278$		−	3.94699e7i		−	1.83710i
$279$	−3.40635e7	−	3.74358e7i	−1.56847	−	1.72375i
$280$	−3.01361e7			−1.37282
$281$	−9.14907e6	−	6.64719e6i	−0.412342	−	0.299584i	0.362207	−	0.932098i	$-0.382023\pi$
$281$	−9.14907e6	−	6.64719e6i	−0.412342	−	0.299584i	−0.774549	+	0.632513i	$0.782023\pi$
$282$	9.29876e6	−	977339.i	0.414646	−	0.0435811i
$283$	8.33401e6	+	2.56495e7i	0.367701	+	1.13167i	0.948272	+	0.317458i	$0.102829\pi$
$283$	8.33401e6	+	2.56495e7i	0.367701	+	1.13167i	−0.580571	+	0.814210i	$0.697171\pi$
$284$	−1.09897e6	−	1.90347e6i	−0.0479767	−	0.0830981i
$285$	4.26425e7	+	2.46197e7i	1.84208	+	1.06352i
$286$	3.19108e7	+	6.78286e6i	1.36408	+	0.289944i
$287$	−3.47428e6	+	1.06927e7i	−0.146967	+	0.452318i
$288$	2.48821e7	−	5.28886e6i	1.04162	−	0.221404i
$289$	1.14253e6	−	1.08705e7i	0.0473343	−	0.450356i
$290$	−8.01442e6	−	7.21622e6i	−0.328608	−	0.295880i
$291$	1.07809e7	+	2.42142e7i	0.437497	+	0.982634i
$292$	−844903.	+	1.89768e6i	−0.0339358	+	0.0762211i
$293$	−4.14119e6	−	4.59926e6i	−0.164635	−	0.182846i	0.655182	−	0.755471i	$-0.272592\pi$
$293$	−4.14119e6	−	4.59926e6i	−0.164635	−	0.182846i	−0.819817	+	0.572625i	$0.805925\pi$
$294$	3.70578e7	+	5.10057e7i	1.45827	+	2.00714i
$295$	1.79139e7	−	1.30152e7i	0.697788	−	0.506973i
$296$	1.48598e7	−	1.33798e7i	0.572977	−	0.515911i
$297$	−5.53986e7	−	2.46650e7i	−2.11461	−	0.941483i
$298$	−3.21204e7	+	1.43009e7i	−1.21376	+	0.540399i
$299$	7.75015e6	−	8.60742e6i	0.289932	−	0.322002i
$300$	−1.91509e6	−	201285.i	−0.0709294	−	0.00745498i
$301$	2.83724e6	+	1.33482e7i	0.104039	+	0.489465i
$302$	−1.23620e7	−	4.01666e6i	−0.448815	−	0.145829i
$303$	5.49041e6	−	2.58303e7i	0.197368	−	0.928543i
$304$	1.78569e7	−	3.09291e7i	0.635603	−	1.10090i
$305$	−2.38619e7	+	1.37767e7i	−0.841020	+	0.485563i
$306$	−8.49954e7	+	2.76167e7i	−2.96641	+	0.963845i
$307$	−2.05998e6	−	1.95994e7i	−0.0711947	−	0.677372i	−0.970672	−	0.240406i	$-0.922720\pi$
$307$	−2.05998e6	−	1.95994e7i	−0.0711947	−	0.677372i	0.899478	−	0.436966i	$-0.143947\pi$
$308$	−5.68599e6	+	7.82610e6i	−0.194605	+	0.267851i
$309$			4.79764e7i			1.62612i
$310$	3.25794e7	−	1.47099e7i	1.09360	−	0.493771i
$311$	5.92975e7			1.97131			0.985656	−	0.168769i	$-0.0539793\pi$
$311$	5.92975e7			1.97131			0.985656	+	0.168769i	$0.0539793\pi$
$312$	5.03232e7	+	3.65619e7i	1.65693	+	1.20383i
$313$	−3.66067e7	+	3.84751e6i	−1.19379	+	0.125472i	−0.680502	−	0.732746i	$-0.738238\pi$
$313$	−3.66067e7	+	3.84751e6i	−1.19379	+	0.125472i	−0.513285	+	0.858218i	$0.671572\pi$
$314$	−1.63705e7	−	5.03833e7i	−0.528778	−	1.62741i
$315$	−5.87012e7	−	1.01673e8i	−1.87808	−	3.25294i
$316$	3.80490e6	+	2.19676e6i	0.120582	+	0.0696180i
$317$	−4.08785e7	−	8.68900e6i	−1.28327	−	0.272767i	−0.484705	−	0.874678i	$-0.661073\pi$
$317$	−4.08785e7	−	8.68900e6i	−1.28327	−	0.272767i	−0.798563	+	0.601911i	$0.794406\pi$
$318$	−2.16211e7	+	6.65428e7i	−0.672350	+	2.06928i
$319$	1.11544e7	−	2.37095e6i	0.343618	−	0.0730382i
$320$	2.48476e6	−	2.36409e7i	0.0758288	−	0.721463i
$321$	199652.	+	179767.i	0.00603612	+	0.00543495i
$322$	7.39543e6	+	1.66104e7i	0.221511	+	0.497522i
$323$	−1.78181e7	+	4.00202e7i	−0.528755	+	1.18760i
$324$	1.11345e7	+	1.23661e7i	0.327368	+	0.363579i
$325$	−4.46133e6	−	6.14050e6i	−0.129961	−	0.178877i
$326$	4.44775e7	−	3.23148e7i	1.28377	−	0.932714i
$327$	1.94520e7	−	1.75147e7i	0.556316	−	0.500909i
$328$	−8.75617e6	−	3.89850e6i	−0.248138	−	0.110478i
$329$	−9.98309e6	+	4.44476e6i	−0.280335	+	0.124813i
$330$	5.01961e7	−	5.57484e7i	1.39678	−	1.55128i
$331$	−2.70445e7	−	2.84249e6i	−0.745752	−	0.0783817i	−0.275973	−	0.961166i	$-0.589000\pi$
$331$	−2.70445e7	−	2.84249e6i	−0.745752	−	0.0783817i	−0.469779	+	0.882784i	$0.655667\pi$
$332$	484450.	+	2.27916e6i	0.0132384	+	0.0622816i
$333$	7.40856e7	+	2.40719e7i	2.00632	+	0.651894i
$334$	−8.05700e6	+	3.79052e7i	−0.216239	+	1.01732i
$335$	−3.49688e7	+	6.05678e7i	−0.930136	+	1.61104i
$336$	−1.05388e8	+	6.08455e7i	−2.77825	+	1.60402i
$337$	2.42640e7	−	7.88384e6i	0.633975	−	0.205991i	0.0256396	−	0.999671i	$-0.491838\pi$
$337$	2.42640e7	−	7.88384e6i	0.633975	−	0.205991i	0.608335	+	0.793680i	$0.291838\pi$
$338$	−3.29813e6	−	3.13796e7i	−0.0854118	−	0.812639i
$339$	1.09651e7	−	1.50922e7i	0.281459	−	0.387395i
$340$		−	1.19221e7i		−	0.303332i
$341$	−7.66532e6	+	3.70132e7i	−0.193316	+	0.933456i
$342$	1.11642e8			2.79093
$343$	−1.09232e7	−	7.93615e6i	−0.270687	−	0.196665i
$344$	−1.15700e7	+	1.21605e6i	−0.284222	+	0.0298729i
$345$	−8.23013e6	−	2.53297e7i	−0.200424	−	0.616841i
$346$	−1.01056e7	−	1.75035e7i	−0.243969	−	0.422567i
$347$	3.31932e7	+	1.91641e7i	0.794439	+	0.458670i	0.841523	−	0.540221i	$-0.181659\pi$
$347$	3.31932e7	+	1.91641e7i	0.794439	+	0.458670i	−0.0470839	+	0.998891i	$0.514993\pi$
$348$	−6.45624e6	−	1.37232e6i	−0.153194	−	0.0325624i
$349$	−9.11353e6	+	2.80486e7i	−0.214393	+	0.659833i	0.784803	+	0.619745i	$0.212764\pi$
$349$	−9.11353e6	+	2.80486e7i	−0.214393	+	0.659833i	−0.999196	+	0.0400885i	$0.987236\pi$
$350$	1.16547e7	−	2.47728e6i	0.271830	−	0.0577792i
$351$	−1.44612e7	+	1.37590e8i	−0.334414	+	3.18174i
$352$	−1.41177e7	−	1.27116e7i	−0.323694	−	0.291456i
$353$	7.51585e6	+	1.68809e7i	0.170865	+	0.383770i	0.978599	−	0.205778i	$-0.0659725\pi$
$353$	7.51585e6	+	1.68809e7i	0.170865	+	0.383770i	−0.807733	+	0.589548i	$0.799306\pi$
$354$	2.91823e7	−	6.55444e7i	0.657823	−	1.47749i
$355$	−1.33297e7	−	1.48042e7i	−0.297945	−	0.330902i
$356$	5.29765e6	+	7.29159e6i	0.117418	+	0.161612i
$357$	1.20762e8	−	8.77384e7i	2.65414	−	1.92835i
$358$	−6.30429e7	+	5.67641e7i	−1.37400	+	1.23716i
$359$	4.94579e7	+	2.20201e7i	1.06894	+	0.475921i	0.864331	−	0.502923i	$-0.167742\pi$
$359$	4.94579e7	+	2.20201e7i	1.06894	+	0.475921i	0.204606	+	0.978844i	$0.434409\pi$
$360$	9.14340e7	−	4.07090e7i	1.95975	−	0.872536i
$361$	5.13848e6	−	5.70686e6i	0.109223	−	0.121304i
$362$	8.16349e7	+	8.58017e6i	1.72088	+	0.180872i
$363$	−1.65682e6	−	7.79472e6i	−0.0346382	−	0.162960i
$364$	2.09892e7	+	6.81982e6i	0.435204	+	0.141406i
$365$	−3.91442e6	+	1.84159e7i	−0.0804987	+	0.378717i
$366$	−4.46394e7	+	7.73177e7i	−0.910490	+	1.57702i
$367$	−1.30682e7	+	7.54495e6i	−0.264374	+	0.152636i	−0.626328	−	0.779560i	$-0.715443\pi$
$367$	−1.30682e7	+	7.54495e6i	−0.264374	+	0.152636i	0.361954	+	0.932196i	$0.382110\pi$
$368$	−1.83719e7	+	5.96940e6i	−0.368648	+	0.119781i
$369$	−3.90308e6	−	3.71353e7i	−0.0776834	−	0.739108i
$370$	−3.23376e7	+	4.45089e7i	−0.638415	+	0.878703i
$371$		−	8.17746e7i		−	1.60139i
$372$	1.27669e7	−	1.77667e7i	0.248002	−	0.345126i
$373$	−8.93153e7			−1.72107			−0.860537	−	0.509388i	$-0.829872\pi$
$373$	−8.93153e7			−1.72107			−0.860537	+	0.509388i	$0.829872\pi$
$374$	5.39949e7	+	3.92296e7i	1.03214	+	0.749893i
$375$	8.60741e7	−	9.04675e6i	1.63222	−	0.171553i
$376$	−2.87885e6	−	8.86017e6i	−0.0541570	−	0.166678i
$377$	−1.30081e7	−	2.25308e7i	−0.242768	−	0.420486i
$378$	−1.88084e8	−	1.08591e8i	−3.48239	−	2.01056i
$379$	3.32160e7	+	7.06028e6i	0.610141	+	0.129689i	0.502611	−	0.864512i	$-0.332373\pi$
$379$	3.32160e7	+	7.06028e6i	0.610141	+	0.129689i	0.107529	+	0.994202i	$0.465706\pi$
$380$	−4.60230e6	+	1.41644e7i	−0.0838735	+	0.258136i
$381$	−8.07729e7	+	1.71688e7i	−1.46046	+	0.310431i
$382$	747234.	−	7.10945e6i	0.0134050	−	0.127540i
$383$	1.41759e7	+	1.27641e7i	0.252322	+	0.227192i	0.785579	−	0.618762i	$-0.212365\pi$
$383$	1.41759e7	+	1.27641e7i	0.252322	+	0.227192i	−0.533257	+	0.845953i	$0.679032\pi$
$384$	−5.05332e7	−	1.13499e8i	−0.892449	−	2.00447i
$385$	−3.56612e7	+	8.00964e7i	−0.624905	+	1.40356i
$386$	−3.14695e6	−	3.49504e6i	−0.0547177	−	0.0607702i
$387$	−2.66395e7	−	3.66661e7i	−0.459613	−	0.632604i
$388$	−6.48603e6	+	4.71238e6i	−0.111041	+	0.0806761i
$389$	−2.67473e7	+	2.40834e7i	−0.454392	+	0.409137i	−0.864289	−	0.502995i	$-0.832231\pi$
$389$	−2.67473e7	+	2.40834e7i	−0.454392	+	0.409137i	0.409897	+	0.912132i	$0.365565\pi$
$390$	−1.56348e8	−	6.96105e7i	−2.63571	−	1.17349i
$391$	2.16467e7	−	9.63772e6i	0.362127	−	0.161229i
$392$	4.20337e7	−	4.66831e7i	0.697813	−	0.775000i
$393$	−1.74213e8	−	1.83105e7i	−2.87014	−	0.301664i
$394$	−7.45834e6	−	3.50887e7i	−0.121942	−	0.573692i
$395$	3.78717e7	+	1.23053e7i	0.614502	+	0.199664i
$396$	6.67969e6	−	3.14255e7i	0.107565	−	0.506054i
$397$	5.68870e7	−	9.85311e7i	0.909162	−	1.57471i	0.0939309	−	0.995579i	$-0.470057\pi$
$397$	5.68870e7	−	9.85311e7i	0.909162	−	1.57471i	0.815231	−	0.579136i	$-0.196610\pi$
$398$	1.13578e8	−	6.55740e7i	1.80154	−	1.04012i
$399$	−1.77344e8	+	5.76225e7i	−2.79188	+	0.907138i
$400$	1.32321e6	+	1.25895e7i	0.0206752	+	0.196711i
$401$	2.41180e7	−	3.31955e7i	0.374031	−	0.514810i	−0.579960	−	0.814645i	$-0.696932\pi$
$401$	2.41180e7	−	3.31955e7i	0.374031	−	0.514810i	0.953991	+	0.299835i	$0.0969318\pi$
$402$			2.26613e8i			3.48824i
$403$	8.57133e7	−	9.46228e6i	1.30958	−	0.144571i
$404$	7.98742e6			0.121133
$405$	1.22015e8	+	8.86490e7i	1.83674	+	1.33447i
$406$	4.06173e7	−	4.26905e6i	0.606921	−	0.0637900i
$407$	−1.79770e7	−	5.53274e7i	−0.266645	−	0.820648i
$408$	6.36271e7	+	1.10205e8i	0.936832	+	1.62264i
$409$	9.88060e7	+	5.70457e7i	1.44415	+	0.833783i	0.998123	−	0.0612349i	$-0.0195039\pi$
$409$	9.88060e7	+	5.70457e7i	1.44415	+	0.833783i	0.446031	+	0.895018i	$0.352837\pi$
$410$	2.57952e7	+	5.48294e6i	0.374272	+	0.0795540i
$411$	−1.98171e7	+	6.09907e7i	−0.285440	+	0.878493i
$412$	−1.41943e7	+	3.01709e6i	−0.202965	+	0.0431416i
$413$	−8.76525e6	+	8.33957e7i	−0.124427	+	1.18384i
$414$	−4.48759e7	−	4.04065e7i	−0.632430	−	0.569442i
$415$	8.58970e6	+	1.92928e7i	0.120180	+	0.269930i
$416$	−1.76281e7	+	3.95934e7i	−0.244864	+	0.549974i
$417$	−1.46504e8	−	1.62709e8i	−2.02042	−	2.24390i
$418$	−4.90064e7	−	6.74515e7i	−0.671002	−	0.923555i
$419$	−8.68158e7	+	6.30754e7i	−1.18020	+	0.857468i	−0.992195	−	0.124700i	$-0.960203\pi$
$419$	−8.68158e7	+	6.30754e7i	−1.18020	+	0.857468i	−0.188008	+	0.982167i	$0.560203\pi$
$420$	3.77128e7	−	3.39568e7i	0.509027	−	0.458330i
$421$	−1.70182e7	−	7.57699e6i	−0.228070	−	0.101543i	0.289521	−	0.957172i	$-0.406504\pi$
$421$	−1.70182e7	−	7.57699e6i	−0.228070	−	0.101543i	−0.517590	+	0.855629i	$0.673171\pi$
$422$	−3.90336e7	+	1.73789e7i	−0.519399	+	0.231251i
$423$	2.42849e7	−	2.69711e7i	0.320859	−	0.356350i
$424$	6.93320e7	+	7.28709e6i	0.909570	+	0.0955997i
$425$	−3.22839e6	−	1.51884e7i	−0.0420552	−	0.197854i
$426$	−6.13890e7	−	1.99465e7i	−0.794075	−	0.258011i
$427$	2.16946e7	−	1.02065e8i	0.278656	−	1.31097i
$428$	−40630.3	+	70373.8i	−0.000518226	+	0.000897594i
$429$	1.56724e8	−	9.04848e7i	1.98502	−	1.14605i
$430$	3.04421e7	−	9.89125e6i	0.382886	−	0.124407i
$431$	1.24666e7	+	1.18611e8i	0.155709	+	1.48148i	0.741467	+	0.670989i	$0.234130\pi$
$431$	1.24666e7	+	1.18611e8i	0.155709	+	1.48148i	−0.585758	+	0.810486i	$0.699203\pi$
$432$	1.35625e8	−	1.86671e8i	1.68224	−	2.31540i
$433$			1.51913e8i			1.87124i	0.353002	+	0.935622i	$0.385161\pi$
$433$			1.51913e8i			1.87124i	−0.353002	+	0.935622i	$0.614839\pi$
$434$	−4.11584e7	+	1.28964e8i	−0.503489	+	1.57760i
$435$	−5.98233e7			−0.726780
$436$	6.40515e6	+	4.65362e6i	0.0772805	+	0.0561476i
$437$	−2.94384e7	+	3.09410e6i	−0.352752	+	0.0370757i
$438$	1.88514e7	+	5.80188e7i	0.224348	+	0.690472i
$439$	−3.53247e7	−	6.11843e7i	−0.417528	−	0.723180i	0.578162	−	0.815922i	$-0.303770\pi$
$439$	−3.53247e7	−	6.11843e7i	−0.417528	−	0.723180i	−0.995690	+	0.0927423i	$0.970437\pi$
$440$	−6.47313e7	−	3.73727e7i	−0.759900	−	0.438729i
$441$	2.39375e8	+	5.08808e7i	2.79103	+	0.593251i
$442$	4.70522e7	−	1.44812e8i	0.544896	−	1.67702i
$443$	4.28030e7	−	9.09806e6i	0.492338	−	0.104650i	0.0449491	−	0.998989i	$-0.485687\pi$
$443$	4.28030e7	−	9.09806e6i	0.492338	−	0.104650i	0.447389	+	0.894340i	$0.352354\pi$
$444$	−3.51966e6	+	3.34873e7i	−0.0402116	+	0.382588i
$445$	6.07062e7	+	5.46601e7i	0.688895	+	0.620284i
$446$	−5.39735e7	−	1.21226e8i	−0.608381	−	1.36645i
$447$	−7.93296e7	+	1.78177e8i	−0.888204	+	1.99494i
$448$	6.02362e7	+	6.68991e7i	0.669921	+	0.744023i
$449$	2.85413e7	+	3.92838e7i	0.315308	+	0.433984i	0.937027	−	0.349256i	$-0.113566\pi$
$449$	2.85413e7	+	3.92838e7i	0.315308	+	0.433984i	−0.621719	+	0.783240i	$0.713566\pi$
$450$	−3.20143e7	+	2.32598e7i	−0.351323	+	0.255251i
$451$	−2.07230e7	+	1.86591e7i	−0.225903	+	0.203404i
$452$	5.15473e6	+	2.29503e6i	0.0558201	+	0.0248527i
$453$	−6.58695e7	+	2.93270e7i	−0.708581	+	0.315481i
$454$	1.12088e8	−	1.24487e8i	1.19782	−	1.33032i
$455$	1.98930e8	+	2.09084e7i	2.11186	+	0.221966i
$456$	−3.30514e7	−	1.55495e8i	−0.348574	−	1.63991i
$457$	2.69692e7	+	8.76281e6i	0.282565	+	0.0918110i	0.446871	−	0.894598i	$-0.352538\pi$
$457$	2.69692e7	+	8.76281e6i	0.282565	+	0.0918110i	−0.164306	+	0.986409i	$0.552538\pi$
$458$	4.58295e6	−	2.15611e7i	0.0477033	−	0.224427i
$459$	−1.41515e8	+	2.45111e8i	−1.46341	+	2.53469i
$460$	6.97647e6	−	4.02787e6i	0.0716741	−	0.0413811i
$461$	−4.84297e7	+	1.57358e7i	−0.494321	+	0.160615i	−0.545560	−	0.838072i	$-0.683683\pi$
$461$	−4.84297e7	+	1.57358e7i	−0.494321	+	0.160615i	0.0512390	+	0.998686i	$0.483683\pi$
$462$	2.96955e7	+	2.82534e8i	0.301138	+	2.86513i
$463$	6.59797e7	−	9.08133e7i	0.664764	−	0.914969i	−0.334863	−	0.942267i	$-0.608690\pi$
$463$	6.59797e7	−	9.08133e7i	0.664764	−	0.914969i	0.999627	+	0.0272973i	$0.00869008\pi$
$464$			4.33905e7i			0.434351i
$465$	7.97039e7	−	1.81567e8i	0.792721	−	1.80584i
$466$	−8.68580e7			−0.858325
$467$	−1.24635e8	−	9.05525e7i	−1.22374	−	0.889098i	−0.227333	−	0.973817i	$-0.573001\pi$
$467$	−1.24635e8	−	9.05525e7i	−1.22374	−	0.889098i	−0.996405	+	0.0847191i	$0.973001\pi$
$468$	−7.28945e7	+	7.66152e6i	−0.711143	+	0.0747441i
$469$	−8.18448e7	−	2.51892e8i	−0.793364	−	2.44172i
$470$	1.28161e7	+	2.21982e7i	0.123442	+	0.213808i
$471$	−2.54497e8	−	1.46934e8i	−2.43568	−	1.40624i
$472$	−6.99254e7	−	1.48631e7i	−0.664981	−	0.141346i
$473$	−1.04591e7	+	3.21899e7i	−0.0988353	+	0.304184i
$474$	1.26208e8	−	2.68263e7i	1.18509	−	0.251899i
$475$	−2.02759e6	+	1.92913e7i	−0.0189191	+	0.180003i
$476$	3.35525e7	+	3.02108e7i	0.311103	+	0.280119i
$477$	1.10464e8	+	2.48107e8i	1.01781	+	2.28604i
$478$	−6.17463e7	+	1.38684e8i	−0.565363	+	1.26983i
$479$	−1.93838e6	−	2.15279e6i	−0.0176373	−	0.0195882i	0.734262	−	0.678867i	$-0.237529\pi$
$479$	−1.93838e6	−	2.15279e6i	−0.0176373	−	0.0195882i	−0.751899	+	0.659278i	$0.770862\pi$
$480$	5.85782e7	+	8.06260e7i	0.529678	+	0.729040i
$481$	−1.07373e8	+	7.80108e7i	−0.964848	+	0.701003i
$482$	1.28163e8	−	1.15398e8i	1.14451	−	1.03052i
$483$	9.21408e7	+	4.10237e7i	0.817731	+	0.364077i
$484$	2.20195e6	−	980370.i	0.0194210	−	0.00864677i
$485$	−4.86214e7	+	5.39995e7i	−0.426189	+	0.473331i
$486$	1.78207e8	+	1.87303e7i	1.55245	+	0.163169i
$487$	1.39119e7	+	6.54502e7i	0.120448	+	0.566662i	0.996438	+	0.0843327i	$0.0268759\pi$
$487$	1.39119e7	+	6.54502e7i	0.120448	+	0.566662i	−0.875990	+	0.482329i	$0.839791\pi$
$488$	8.46019e7	+	2.74888e7i	0.727982	+	0.236536i
$489$	6.34064e7	−	2.98304e8i	0.542259	−	2.55113i
$490$	−8.64186e7	+	1.49681e8i	−0.734546	+	1.27227i
$491$	1.03874e8	−	5.99718e7i	0.877533	−	0.506644i	0.00768893	−	0.999970i	$-0.497553\pi$
$491$	1.03874e8	−	5.99718e7i	0.877533	−	0.506644i	0.869844	+	0.493326i	$0.164219\pi$
$492$	1.53503e7	−	4.98762e6i	0.128891	−	0.0418792i
$493$	−5.56342e6	−	5.29324e7i	−0.0464302	−	0.441754i
$494$	−1.11803e8	+	1.53884e8i	−0.927416	+	1.27648i
$495$		−	2.91188e8i		−	2.40081i
$496$	−1.31693e8	−	5.78101e7i	−1.07924	−	0.473760i
$497$	7.54411e7			0.614524
$498$	5.53600e7	+	4.02214e7i	0.448237	+	0.325663i
$499$	−1.33593e8	+	1.40412e7i	−1.07519	+	0.113007i	−0.625534	−	0.780197i	$-0.715119\pi$
$499$	−1.33593e8	+	1.40412e7i	−1.07519	+	0.113007i	−0.449652	+	0.893204i	$0.648452\pi$
$500$	8.08949e6	+	2.48969e7i	0.0647159	+	0.199175i
$501$	1.07482e8	+	1.86165e8i	0.854719	+	1.48042i
$502$	−1.47256e8	−	8.50185e7i	−1.16403	−	0.672051i
$503$	−2.38200e8	−	5.06309e7i	−1.87171	−	0.397843i	−0.875376	−	0.483443i	$-0.839386\pi$
$503$	−2.38200e8	−	5.06309e7i	−1.87171	−	0.397843i	−0.996330	+	0.0856000i	$0.972719\pi$
$504$	−1.17127e8	+	3.60480e8i	−0.914884	+	2.81572i
$505$	7.08119e7	−	1.50515e7i	0.549834	−	0.116871i
$506$	−4.71390e6	+	4.48498e7i	−0.0363856	+	0.346186i
$507$	−1.30070e8	−	1.17116e8i	−0.998056	−	0.898653i
$508$	−1.01591e7	−	2.28177e7i	−0.0774933	−	0.174053i
$509$	9.86297e7	−	2.21526e8i	0.747918	−	1.67985i	0.0146687	−	0.999892i	$-0.495331\pi$
$509$	9.86297e7	−	2.21526e8i	0.747918	−	1.67985i	0.733250	−	0.679960i	$-0.238003\pi$
$510$	−2.34279e8	−	2.60193e8i	−1.76613	−	1.96149i
$511$	−4.19088e7	−	5.76825e7i	−0.314081	−	0.432296i
$512$	−5.05335e7	+	3.67148e7i	−0.376504	+	0.273546i
$513$	2.62751e8	−	2.36582e8i	1.94622	−	1.75239i
$514$	2.28089e8	+	1.01552e8i	1.67963	+	0.747820i
$515$	−1.20153e8	+	5.34955e7i	−0.879655	+	0.391648i
$516$	1.31086e7	−	1.45586e7i	0.0954130	−	0.105967i
$517$	−2.69554e7	−	2.83312e6i	−0.195063	−	0.0205019i
$518$	−4.33178e7	−	2.03794e8i	−0.311657	−	1.46623i
$519$	−1.06628e8	−	3.46456e7i	−0.762728	−	0.247825i
$520$	−3.54540e7	+	1.66798e8i	−0.252148	+	1.18626i
$521$	4.06505e7	−	7.04087e7i	0.287444	−	0.497867i	−0.685755	−	0.727832i	$-0.740528\pi$
$521$	4.06505e7	−	7.04087e7i	0.287444	−	0.497867i	0.973199	+	0.229965i	$0.0738613\pi$
$522$	−1.17467e8	+	6.78197e7i	−0.825858	+	0.476809i
$523$	2.90020e7	−	9.42331e6i	0.202732	−	0.0658716i	−0.205891	−	0.978575i	$-0.566009\pi$
$523$	2.90020e7	−	9.42331e6i	0.202732	−	0.0658716i	0.408623	+	0.912703i	$0.366009\pi$
$524$	−5.53836e6	−	5.26940e7i	−0.0384935	−	0.366241i
$525$	3.88497e7	−	5.34720e7i	0.268478	−	0.369529i
$526$			1.41421e8i			0.971756i
$527$	1.68065e8	+	5.36376e7i	1.14828	+	0.366469i
$528$	−3.01825e8			−2.05047
$529$	−1.06811e8	−	7.76024e7i	−0.721518	−	0.524214i
$530$	−1.90759e8	+	2.00496e7i	−1.28132	+	0.134672i
$531$	−8.60601e7	−	2.64866e8i	−0.574802	−	1.76906i
$532$	−2.82007e7	−	4.88451e7i	−0.187295	−	0.324404i
$533$	5.50950e7	+	3.18091e7i	0.363857	+	0.210073i
$534$	2.58903e8	+	5.50316e7i	1.70025	+	0.361400i
$535$	−227593.	+	700458.i	−0.00148627	+	0.00457426i
$536$	2.20858e8	−	4.69449e7i	1.43423	−	0.304856i
$537$	−4.91891e7	+	4.68003e8i	−0.317648	+	3.02222i
$538$	−5.35962e7	−	4.82582e7i	−0.344181	−	0.309902i
$539$	−7.43353e7	−	1.66960e8i	−0.474710	−	1.06622i
$540$	−3.91372e7	+	8.79037e7i	−0.248547	+	0.558246i
$541$	5.09074e7	+	5.65384e7i	0.321506	+	0.357068i	0.882133	−	0.471000i	$-0.156107\pi$
$541$	5.09074e7	+	5.65384e7i	0.321506	+	0.357068i	−0.560628	+	0.828068i	$0.689440\pi$
$542$	3.58866e7	+	4.93937e7i	0.225390	+	0.310223i
$543$	3.68376e8	−	2.67641e8i	2.30087	−	1.67168i
$544$	−6.58912e7	+	5.93287e7i	−0.409290	+	0.368526i
$545$	6.55537e7	+	2.91864e7i	0.404956	+	0.180298i
$546$	5.92092e8	−	2.63616e8i	3.63757	−	1.61955i
$547$	−5.54963e7	+	6.16349e7i	−0.339080	+	0.376586i	−0.888435	−	0.459003i	$-0.848207\pi$
$547$	−5.54963e7	+	6.16349e7i	−0.339080	+	0.376586i	0.549355	+	0.835589i	$0.314873\pi$
$548$	−1.92909e7	−	2.02756e6i	−0.117222	−	0.0123206i
$549$	7.20512e7	+	3.38974e8i	0.435436	+	2.04857i
$550$	2.81060e7	+	9.13220e6i	0.168932	+	0.0548892i
$551$	−1.38237e7	+	6.50354e7i	−0.0826361	+	0.388772i
$552$	−4.29925e7	+	7.44652e7i	−0.255609	+	0.442727i
$553$	−1.30598e8	+	7.54008e7i	−0.772256	+	0.445862i
$554$	1.05325e8	−	3.42220e7i	0.619442	−	0.201269i
$555$	3.19004e7	+	3.03512e8i	0.186602	+	1.77540i
$556$	3.89258e7	−	5.35768e7i	0.226471	−	0.311711i
$557$			1.99352e8i			1.15360i	0.816886	+	0.576800i	$0.195699\pi$
$557$			1.99352e8i			1.15360i	−0.816886	+	0.576800i	$0.804301\pi$
$558$	−4.93329e7	−	4.46878e8i	−0.283945	−	2.57209i
$559$	7.72175e7			0.442059
$560$	−2.69893e8	−	1.96089e8i	−1.53684	−	1.11658i
$561$	3.68198e8	−	3.86992e7i	2.08542	−	0.219186i
$562$	−3.10421e7	−	9.55378e7i	−0.174881	−	0.538228i
$563$	5.79796e7	+	1.00424e8i	0.324900	+	0.562744i	0.981492	−	0.191502i	$-0.0613360\pi$
$563$	5.79796e7	+	1.00424e8i	0.324900	+	0.562744i	−0.656592	+	0.754246i	$0.728003\pi$
$564$	1.35861e7	+	7.84393e6i	0.0757281	+	0.0437216i
$565$	5.00236e7	+	1.06329e7i	0.277351	+	0.0589528i
$566$	−7.40293e7	+	2.27839e8i	−0.408277	+	1.25655i
$567$	−5.58672e8	+	1.18749e8i	−3.06484	+	0.651452i
$568$	−6.72270e6	+	6.39622e7i	−0.0366859	+	0.349043i
$569$	−4.93554e7	−	4.44398e7i	−0.267915	−	0.241232i	0.524212	−	0.851588i	$-0.324360\pi$
$569$	−4.93554e7	−	4.44398e7i	−0.267915	−	0.241232i	−0.792127	+	0.610356i	$0.791027\pi$
$570$	1.77900e8	+	3.99569e8i	0.960617	+	2.15758i
$571$	9.53381e6	−	2.14133e7i	0.0512104	−	0.115020i	−0.886128	−	0.463440i	$-0.846615\pi$
$571$	9.53381e6	−	2.14133e7i	0.0512104	−	0.115020i	0.937339	+	0.348420i	$0.113282\pi$
$572$	3.66267e7	+	4.06780e7i	0.195708	+	0.217356i
$573$	−2.33084e7	−	3.20813e7i	−0.123893	−	0.170525i
$574$	−8.07960e7	+	5.87017e7i	−0.427223	+	0.310395i
$575$	7.79708e6	−	7.02052e6i	0.0410136	−	0.0369289i
$576$	−2.73128e8	−	1.21605e8i	−1.42922	−	0.636330i
$577$	4.23540e7	−	1.88572e7i	0.220479	−	0.0981636i	−0.293525	−	0.955951i	$-0.594828\pi$
$577$	4.23540e7	−	1.88572e7i	0.220479	−	0.0981636i	0.514004	+	0.857788i	$0.328162\pi$
$578$	6.49673e7	−	7.21535e7i	0.336443	−	0.373658i
$579$	−2.59457e7	−	2.72700e6i	−0.133669	−	0.0140491i
$580$	−3.76210e6	−	1.76993e7i	−0.0192817	−	0.0907134i
$581$	−7.60622e7	−	2.47141e7i	−0.387829	−	0.126013i
$582$	−4.89518e7	+	2.30300e8i	−0.248313	+	1.16822i
$583$	1.01411e8	−	1.75649e8i	0.511775	−	0.886420i
$584$	5.26402e7	−	3.03918e7i	0.264289	−	0.152587i
$585$	−6.31803e8	+	2.05285e8i	−3.15583	+	1.02539i
$586$	−5.74643e6	−	5.46736e7i	−0.0285565	−	0.271697i
$587$	6.58846e7	−	9.06824e7i	0.325739	−	0.448341i	−0.614470	−	0.788940i	$-0.710630\pi$
$587$	6.58846e7	−	9.06824e7i	0.325739	−	0.448341i	0.940209	+	0.340599i	$0.110630\pi$
$588$			1.05783e8i			0.520334i
$589$	−1.78969e8	−	1.28604e8i	−0.875854	−	0.629373i
$590$	1.96690e8			0.957691
$591$	−1.60988e8	−	1.16964e8i	−0.779884	−	0.566619i
$592$	2.20140e8	−	2.31377e7i	1.06105	−	0.111521i
$593$	4.08222e7	+	1.25638e8i	0.195764	+	0.602498i	0.999967	+	0.00814392i	$0.00259232\pi$
$593$	4.08222e7	+	1.25638e8i	0.195764	+	0.602498i	−0.804203	+	0.594354i	$0.797408\pi$
$594$	−2.69332e8	−	4.66497e8i	−1.28508	−	2.22582i
$595$	3.54387e8	+	2.04605e8i	1.68239	+	0.971329i
$596$	−5.77042e7	−	1.22654e7i	−0.272564	−	0.0579353i
$597$	2.24810e8	−	6.91895e8i	1.05656	−	3.25175i
$598$	1.00636e8	−	2.13908e7i	0.470597	−	0.100029i
$599$	−1.73117e7	+	1.64710e8i	−0.0805490	+	0.766372i	0.877463	+	0.479644i	$0.159234\pi$
$599$	−1.73117e7	+	1.64710e8i	−0.0805490	+	0.766372i	−0.958012	+	0.286728i	$0.907432\pi$
$600$	4.18739e7	+	3.77034e7i	0.193861	+	0.174553i
$601$	−5.40148e7	−	1.21319e8i	−0.248823	−	0.558865i	0.745349	−	0.666675i	$-0.232283\pi$
$601$	−5.40148e7	−	1.21319e8i	−0.248823	−	0.558865i	−0.994172	+	0.107810i	$0.965616\pi$
$602$	−4.93037e7	+	1.10738e8i	−0.225991	+	0.507583i
$603$	5.88585e8	+	6.53690e8i	2.68446	+	2.98140i
$604$	−1.28190e7	−	1.76438e7i	−0.0581758	−	0.0800722i
$605$	1.76738e7	−	1.28408e7i	0.0798111	−	0.0579862i
$606$	1.74321e8	−	1.56959e8i	0.783305	−	0.705291i
$607$	1.95874e8	+	8.72085e7i	0.875810	+	0.389936i	0.794867	−	0.606783i	$-0.207540\pi$
$607$	1.95874e8	+	8.72085e7i	0.875810	+	0.389936i	0.0809422	+	0.996719i	$0.474207\pi$
$608$	1.01187e8	−	4.50511e7i	0.450207	−	0.200445i
$609$	1.51593e8	−	1.68361e8i	0.671162	−	0.745400i
$610$	−2.43410e8	−	2.55834e7i	−1.07238	−	0.112712i
$611$	1.28562e7	+	6.04837e7i	0.0563623	+	0.265164i
$612$	−1.42609e8	−	4.63366e7i	−0.622148	−	0.202148i
$613$	−3.43573e7	+	1.61638e8i	−0.149155	+	0.701718i	0.838478	+	0.544935i	$0.183446\pi$
$613$	−3.43573e7	+	1.61638e8i	−0.149155	+	0.701718i	−0.987633	+	0.156783i	$0.949888\pi$
$614$	8.75281e7	−	1.51603e8i	0.378131	−	0.654942i
$615$	1.26688e8	−	7.31436e7i	0.544643	−	0.314450i
$616$	2.69208e8	−	8.74710e7i	1.15172	−	0.374215i
$617$	−3.00976e7	−	2.86359e8i	−0.128137	−	1.21915i	−0.849877	−	0.526981i	$-0.823324\pi$
$617$	−3.00976e7	−	2.86359e8i	−0.128137	−	1.21915i	0.721739	−	0.692165i	$-0.243343\pi$
$618$	−2.50493e8	+	3.44775e8i	−1.06128	+	1.46073i
$619$			1.00659e8i			0.424407i	0.977226	+	0.212203i	$0.0680639\pi$
$619$			1.00659e8i			0.424407i	−0.977226	+	0.212203i	$0.931936\pi$
$620$	5.87307e7	+	1.21629e7i	0.246428	+	0.0510344i
$621$	−1.91242e8			−0.798562
$622$	4.26131e8	+	3.09603e8i	1.77081	+	1.28657i
$623$	−3.07660e8	+	3.23364e7i	−1.27235	+	0.133730i
$624$	2.12784e8	+	6.54883e8i	0.875762	+	2.69532i
$625$	1.39118e8	+	2.40959e8i	0.569827	+	0.986969i
$626$	−2.83156e8	−	1.63480e8i	−1.15426	−	0.666411i
$627$	−4.52387e8	−	9.61579e7i	−1.83530	−	0.390106i
$628$	2.74672e7	−	8.45355e7i	0.110901	−	0.341319i
$629$	−2.65584e8	+	5.64517e7i	−1.06721	+	0.226843i
$630$	1.09009e8	−	1.03715e9i	0.435952	−	4.14781i
$631$	1.10171e8	+	9.91982e7i	0.438509	+	0.394835i	0.858599	−	0.512647i	$-0.171335\pi$
$631$	1.10171e8	+	9.91982e7i	0.438509	+	0.394835i	−0.420091	+	0.907482i	$0.638002\pi$
$632$	−5.22902e7	−	1.17446e8i	−0.207142	−	0.465249i
$633$	−9.64037e7	+	2.16526e8i	−0.380087	+	0.853688i
$634$	−2.48400e8	−	2.75876e8i	−0.974728	−	1.08254i
$635$	−1.33063e8	−	1.83145e8i	−0.519678	−	0.715276i
$636$	−9.49740e7	+	6.90026e7i	−0.369176	+	0.268222i
$637$	−3.09854e8	+	2.78994e8i	−1.19878	+	1.07939i
$638$	9.25385e7	+	4.12008e7i	0.356337	+	0.158651i
$639$	−2.28891e8	+	1.01909e8i	−0.877255	+	0.390579i
$640$	2.27903e8	−	2.53112e8i	0.869382	−	0.965546i
$641$	1.39172e8	+	1.46275e7i	0.528417	+	0.0555389i	0.364981	−	0.931015i	$-0.381076\pi$
$641$	1.39172e8	+	1.46275e7i	0.528417	+	0.0555389i	0.163436	+	0.986554i	$0.447742\pi$
$642$	496167.	+	2.33428e6i	0.00187509	+	0.00882162i
$643$	4.31497e8	+	1.40202e8i	1.62310	+	0.527377i	0.972670	−	0.232191i	$-0.0745893\pi$
$643$	4.31497e8	+	1.40202e8i	1.62310	+	0.527377i	0.650429	+	0.759567i	$0.274589\pi$
$644$	−6.34281e6	+	2.98406e7i	−0.0237478	+	0.111725i
$645$	8.87791e7	−	1.53770e8i	0.330850	−	0.573050i
$646$	−3.36999e8	+	1.94567e8i	−1.25006	+	0.721723i
$647$	3.04328e7	−	9.88821e6i	0.112364	−	0.0365094i	−0.252295	−	0.967650i	$-0.581185\pi$
$647$	3.04328e7	−	9.88821e6i	0.112364	−	0.0365094i	0.364660	+	0.931141i	$0.381185\pi$
$648$	−5.08965e7	−	4.84248e8i	−0.187052	−	1.77968i
$649$	−1.22249e8	+	1.68261e8i	−0.447209	+	0.615530i
$650$		−	6.74210e7i		−	0.245502i
$651$	3.09015e8	+	6.84405e8i	1.12005	+	2.48068i
$652$	9.22434e7			0.332807
$653$	4.02590e8	+	2.92499e8i	1.44585	+	1.05047i	0.986779	+	0.162073i	$0.0518179\pi$
$653$	4.02590e8	+	2.92499e8i	1.44585	+	1.05047i	0.459072	+	0.888399i	$0.348182\pi$
$654$	2.31236e8	−	2.43038e7i	0.826650	−	0.0868844i
$655$	−1.48397e8	−	4.56718e8i	−0.528081	−	1.62527i
$656$	−5.30519e7	−	9.18885e7i	−0.187927	−	0.325499i
$657$	2.05072e8	+	1.18398e8i	0.723120	+	0.417494i
$658$	−9.49486e7	−	2.01820e7i	−0.333281	−	0.0708412i
$659$	−1.57802e8	+	4.85665e8i	−0.551387	+	1.69700i	0.153911	+	0.988085i	$0.450813\pi$
$659$	−1.57802e8	+	4.85665e8i	−0.551387	+	1.69700i	−0.705298	+	0.708911i	$0.749187\pi$
$660$	1.23116e8	−	2.61692e7i	0.428237	−	0.0910245i
$661$	232867.	−	2.21558e6i	0.000806314	−	0.00767156i	−0.994111	−	0.108363i	$-0.965439\pi$
$661$	232867.	−	2.21558e6i	0.000806314	−	0.00767156i	0.994918	+	0.100692i	$0.0321056\pi$
$662$	−1.79509e8	−	1.61631e8i	−0.618747	−	0.557122i
$663$	−3.43545e8	−	7.71614e8i	−1.17881	−	2.64764i
$664$	2.77317e7	−	6.22865e7i	0.0947267	−	0.212760i
$665$	−3.42056e8	−	3.79891e8i	−1.16314	−	1.29180i
$666$	4.06720e8	+	5.59802e8i	1.37681	+	1.89501i
$667$	2.90948e7	−	2.11386e7i	0.0980478	−	0.0712359i
$668$	−4.83193e7	+	4.35069e7i	−0.162103	+	0.145958i
$669$	−6.72464e8	−	2.99400e8i	−2.24590	−	0.999940i
$670$	−5.67532e8	+	2.52682e8i	−1.88698	+	0.840136i
$671$	1.73173e8	−	1.92328e8i	0.573208	−	0.636612i
$672$	−3.75344e8	−	3.94502e7i	−1.23686	−	0.129999i
$673$	−9.39487e7	−	4.41994e8i	−0.308209	−	1.45001i	−0.810717	−	0.585438i	$-0.800923\pi$
$673$	−9.39487e7	−	4.41994e8i	−0.308209	−	1.45001i	0.502508	−	0.864573i	$-0.332411\pi$
$674$	2.15532e8	+	7.00305e7i	0.703933	+	0.228722i
$675$	−2.60561e7	+	1.22584e8i	−0.0847223	+	0.398587i
$676$	2.64701e7	−	4.58476e7i	0.0856872	−	0.148415i
$677$	−1.73325e8	+	1.00069e8i	−0.558592	+	0.322503i	−0.752580	−	0.658501i	$-0.771191\pi$
$677$	−1.73325e8	+	1.00069e8i	−0.558592	+	0.322503i	0.193988	+	0.981004i	$0.437858\pi$
$678$	1.57598e8	−	5.12067e7i	0.505663	−	0.164300i
$679$	−2.87639e7	−	2.73671e8i	−0.0918839	−	0.874216i
$680$	−2.05053e8	+	2.82232e8i	−0.652139	+	0.897592i
$681$		−	9.29227e8i		−	2.94226i
$682$	−2.48338e8	+	2.25967e8i	−0.782871	+	0.712348i
$683$	2.32434e8			0.729519			0.364760	−	0.931102i	$-0.381151\pi$
$683$	2.32434e8			0.729519			0.364760	+	0.931102i	$0.381151\pi$
$684$	1.51544e8	+	1.10103e8i	0.473554	+	0.344057i
$685$	−1.74843e8	+	1.83767e7i	−0.543971	+	0.0571737i
$686$	−3.70615e7	−	1.14064e8i	−0.114802	−	0.353325i
$687$	−6.11376e7	−	1.05893e8i	−0.188555	−	0.326587i
$688$	−1.11531e8	−	6.43924e7i	−0.342476	−	0.197729i
$689$	−4.52607e8	−	9.62047e7i	−1.38377	−	0.294129i
$690$	7.31065e7	−	2.24999e8i	0.222540	−	0.684909i
$691$	659101.	−	140096.i	0.00199764	−	0.000424612i	−0.206913	−	0.978359i	$-0.566342\pi$
$691$	659101.	−	140096.i	0.00199764	−	0.000424612i	0.208910	+	0.977935i	$0.433008\pi$
$692$	3.54471e6	−	3.37256e7i	0.0106970	−	0.101775i
$693$	8.19490e8	+	7.37872e8i	2.46232	+	2.21708i
$694$	1.38478e8	+	3.11027e8i	0.414288	+	0.930507i
$695$	2.44134e8	−	5.48333e8i	0.727232	−	1.63339i
$696$	1.29235e8	+	1.43530e8i	0.383312	+	0.425711i
$697$	7.65001e7	+	1.05293e8i	0.225925	+	0.310958i
$698$	−2.11939e8	+	1.53983e8i	−0.623225	+	0.452800i
$699$	−3.58059e8	+	3.22398e8i	−1.04839	+	0.943976i
$700$	1.82633e7	+	8.13135e6i	0.0532458	+	0.0237066i
$701$	−3.36857e8	+	1.49979e8i	−0.977894	+	0.435387i	−0.832523	−	0.553991i	$-0.813104\pi$
$701$	−3.36857e8	+	1.49979e8i	−0.977894	+	0.435387i	−0.145371	+	0.989377i	$0.546438\pi$
$702$	−8.22302e8	+	9.13259e8i	−2.37695	+	2.63987i
$703$	3.37327e8	+	3.54545e7i	0.970923	+	0.102048i
$704$	4.64218e7	+	2.18397e8i	0.133047	+	0.625935i
$705$	1.35227e8	+	4.39381e7i	0.385920	+	0.125393i
$706$	−3.41266e7	+	1.60553e8i	−0.0969793	+	0.456252i
$707$	−1.37078e8	+	2.37427e8i	−0.387892	+	0.671849i
$708$	1.04253e8	−	6.01905e7i	0.293757	−	0.169601i
$709$	4.27071e8	−	1.38764e8i	1.19829	−	0.389348i	0.359158	−	0.933277i	$-0.383064\pi$
$709$	4.27071e8	−	1.38764e8i	1.19829	−	0.389348i	0.839131	+	0.543929i	$0.183064\pi$
$710$	−1.84967e7	−	1.75984e8i	−0.0516796	−	0.491699i
$711$	2.94384e8	−	4.05185e8i	0.819041	−	1.12731i
$712$		−	2.63729e8i		−	0.730665i
$713$	2.53933e7	+	1.16468e8i	0.0700569	+	0.321320i
$714$	1.32593e9			3.64272
$715$	4.01365e8	+	2.91609e8i	1.09805	+	0.797778i
$716$	−1.41556e8	+	1.48782e7i	−0.385648	+	0.0405332i
$717$	2.60227e8	+	8.00895e8i	0.705983	+	2.17279i
$718$	2.40450e8	+	4.16472e8i	0.649608	+	1.12515i
$719$	3.29722e8	+	1.90365e8i	0.887078	+	0.512155i	0.872986	−	0.487746i	$-0.162181\pi$
$719$	3.29722e8	+	1.90365e8i	0.887078	+	0.512155i	0.0140925	+	0.999901i	$0.495514\pi$
$720$	1.08375e9	+	2.30358e8i	2.90356	+	0.617171i
$721$	1.53916e8	−	4.73705e8i	0.410656	−	1.26387i
$722$	6.67233e7	−	1.41825e7i	0.177283	−	0.0376826i
$723$	9.99987e7	−	9.51424e8i	0.264594	−	2.51744i
$724$	1.02350e8	+	9.21563e7i	0.269694	+	0.242834i
$725$	−9.58557e6	−	2.15295e7i	−0.0251538	−	0.0564964i
$726$	2.87911e7	−	6.46659e7i	0.0752400	−	0.168992i
$727$	−1.21929e8	−	1.35415e8i	−0.317324	−	0.352424i	0.563289	−	0.826260i	$-0.309536\pi$
$727$	−1.21929e8	−	1.35415e8i	−0.317324	−	0.352424i	−0.880613	+	0.473836i	$0.842869\pi$
$728$	−3.79579e8	−	5.22446e8i	−0.983804	−	1.35409i
$729$	1.45676e8	−	1.05839e8i	0.376014	−	0.273190i
$730$	−1.24283e8	+	1.11905e8i	−0.319479	+	0.287661i
$731$	1.44314e8	+	6.42526e7i	0.369450	+	0.164490i
$732$	−1.36846e8	+	6.09277e7i	−0.348898	+	0.155339i
$733$	−1.27877e8	+	1.42022e8i	−0.324700	+	0.360615i	−0.883289	−	0.468829i	$-0.844676\pi$
$733$	−1.27877e8	+	1.42022e8i	−0.324700	+	0.360615i	0.558589	+	0.829444i	$0.311343\pi$
$734$	−1.33306e8	−	1.40110e7i	−0.337102	−	0.0354309i
$735$	1.99337e8	+	9.37807e8i	0.502026	+	2.36185i
$736$	−5.69785e7	−	1.85134e7i	−0.142915	−	0.0464359i
$737$	1.36579e8	−	6.42553e8i	0.341178	−	1.60512i
$738$	1.65841e8	−	2.87245e8i	0.412594	−	0.714634i
$739$	1.35806e8	−	7.84078e7i	0.336501	−	0.194279i	−0.322223	−	0.946664i	$-0.604430\pi$
$739$	1.35806e8	−	7.84078e7i	0.336501	−	0.194279i	0.658724	+	0.752385i	$0.271097\pi$
$740$	−8.77907e7	+	2.85249e7i	−0.216647	+	0.0703930i
$741$	1.10292e8	+	1.04936e9i	0.271074	+	2.57910i
$742$	4.26959e8	−	5.87659e8i	1.04514	−	1.43851i
$743$			1.62338e8i			0.395780i	0.980224	+	0.197890i	$0.0634089\pi$
$743$			1.62338e8i			0.395780i	−0.980224	+	0.197890i	$0.936591\pi$
$744$	−6.07805e8	+	2.01008e8i	−1.47586	+	0.488084i
$745$	−5.34685e8			−1.29309
$746$	−6.41849e8	−	4.66331e8i	−1.54603	−	1.12325i
$747$	2.64160e8	−	2.77643e7i	0.633731	−	0.0666078i
$748$	3.46043e7	+	1.06501e8i	0.0826848	+	0.254478i
$749$	−1.39458e6	−	2.41548e6i	−0.00331893	−	0.00574855i
$750$	6.65791e8	+	3.84395e8i	1.57817	+	0.911158i
$751$	−4.62275e8	−	9.82596e7i	−1.09139	−	0.231983i	−0.373147	−	0.927772i	$-0.621721\pi$
$751$	−4.62275e8	−	9.82596e7i	−1.09139	−	0.231983i	−0.718245	+	0.695790i	$0.755054\pi$
$752$	3.18688e7	−	9.80819e7i	0.0749396	−	0.230640i
$753$	−9.22613e8	+	1.96107e8i	−2.16090	+	0.459313i
$754$	2.41562e7	−	2.29831e8i	0.0563528	−	0.536161i
$755$	−1.46894e8	−	1.32264e8i	−0.341321	−	0.307326i
$756$	−1.48214e8	−	3.32893e8i	−0.343022	−	0.770441i
$757$	−5.78488e7	+	1.29931e8i	−0.133354	+	0.299519i	−0.967864	−	0.251475i	$-0.919084\pi$
$757$	−5.78488e7	+	1.29931e8i	−0.133354	+	0.299519i	0.834510	+	0.550993i	$0.185751\pi$
$758$	2.01838e8	+	2.24164e8i	0.463443	+	0.514705i
$759$	1.47040e8	+	2.02384e8i	0.336288	+	0.462861i
$760$	3.52569e8	−	2.56157e8i	0.803163	−	0.583532i
$761$	−5.32384e8	+	4.79361e8i	−1.20801	+	1.08770i	−0.214180	+	0.976794i	$0.568708\pi$
$761$	−5.32384e8	+	4.79361e8i	−1.20801	+	1.08770i	−0.993831	+	0.110904i	$0.964625\pi$
$762$	−6.70102e8	−	2.98349e8i	−1.51452	−	0.674309i
$763$	−2.48253e8	+	1.10529e8i	−0.558883	+	0.248831i
$764$	8.02574e6	−	8.91349e6i	0.0179972	−	0.0199879i
$765$	−1.35161e9	−	1.42060e8i	−3.01903	−	0.317313i
$766$	3.52295e7	+	1.65742e8i	0.0783827	+	0.368762i
$767$	4.51268e8	+	1.46626e8i	1.00011	+	0.324956i
$768$	1.14072e8	−	5.36665e8i	0.251822	−	1.18473i
$769$	3.72873e8	−	6.45835e8i	0.819939	−	1.42018i	−0.0857872	−	0.996313i	$-0.527341\pi$
$769$	3.72873e8	−	6.45835e8i	0.819939	−	1.42018i	0.905726	−	0.423863i	$-0.139326\pi$
$770$	−6.74471e8	+	3.89406e8i	−1.47738	+	0.852963i
$771$	1.31720e9	−	4.27984e8i	2.87401	−	0.933822i
$772$	−824834.	−	7.84777e6i	−0.00179273	−	0.0170567i
$773$	−3.48787e8	+	4.80064e8i	−0.755129	+	1.03935i	0.242474	+	0.970158i	$0.422041\pi$
$773$	−3.48787e8	+	4.80064e8i	−0.755129	+	1.03935i	−0.997604	+	0.0691885i	$0.977959\pi$
$774$		−	4.02584e8i		−	0.868227i
$775$	7.81145e7	−	408514.i	0.167813	−	0.000877610i
$776$	2.34593e8			0.502030
$777$	−9.35011e8	−	6.79325e8i	−1.99321	−	1.44815i
$778$	−3.17958e8	+	3.34187e7i	−0.675198	+	0.0709662i
$779$	−5.02417e7	−	1.54628e8i	−0.106280	−	0.327096i
$780$	−1.43577e8	−	2.48682e8i	−0.302552	−	0.524036i
$781$	1.62045e8	+	9.35566e7i	0.340159	+	0.196391i
$782$	2.05880e8	+	4.37612e7i	0.430521	+	0.0915101i
$783$	−1.32743e8	+	4.08541e8i	−0.276520	+	0.851042i
$784$	6.80201e8	−	1.44581e8i	1.41153	−	0.300029i
$785$	8.42098e7	−	8.01202e8i	0.174082	−	1.65628i
$786$	−1.15635e9	−	1.04118e9i	−2.38134	−	2.14417i
$787$	2.95079e8	+	6.62758e8i	0.605360	+	1.35966i	0.912922	+	0.408134i	$0.133820\pi$
$787$	2.95079e8	+	6.62758e8i	0.605360	+	1.35966i	−0.307562	+	0.951528i	$0.599513\pi$
$788$	2.44810e7	−	5.49852e7i	0.0500323	−	0.112374i
$789$	5.24925e8	+	5.82988e8i	1.06873	+	1.18694i
$790$	2.07910e8	+	2.86164e8i	0.421692	+	0.580409i
$791$	−1.56685e8	+	1.13838e8i	−0.316590	+	0.230016i
$792$	−6.98626e8	+	6.29046e8i	−1.40627	+	1.26621i
$793$	−5.39388e8	−	2.40151e8i	−1.08164	−	0.481576i
$794$	9.23256e8	−	4.11060e8i	1.84442	−	0.821191i
$795$	−7.11956e8	+	7.90707e8i	−1.41694	+	1.57367i
$796$	2.18841e8	+	2.30011e7i	0.433900	+	0.0456047i
$797$	1.75276e7	+	8.24609e7i	0.0346216	+	0.162882i	0.992062	−	0.125749i	$-0.0401333\pi$
$797$	1.75276e7	+	8.24609e7i	0.0346216	+	0.162882i	−0.957440	+	0.288631i	$0.906800\pi$
$798$	−1.57531e9	−	5.11849e8i	−3.09997	−	1.00724i
$799$	−2.63011e7	+	1.23737e8i	−0.0515625	+	0.242582i
$800$	−1.96301e7	+	3.40002e7i	−0.0383399	+	0.0664067i
$801$	8.89770e8	−	5.13709e8i	1.73133	−	0.999585i
$802$	3.46639e8	−	1.12630e8i	0.671977	−	0.218339i
$803$	−1.84849e7	−	1.75872e8i	−0.0357002	−	0.339664i
$804$	−2.23489e8	+	3.07606e8i	−0.430019	+	0.591870i
$805$			2.76502e8i			0.530042i
$806$	6.65368e8	+	3.79525e8i	1.27074	+	0.724828i
$807$	−4.00066e8			−0.761222
$808$	−1.89085e8	−	1.37379e8i	−0.358446	−	0.260426i
$809$	5.78627e8	−	6.08162e7i	1.09283	−	0.114861i	0.459078	−	0.888396i	$-0.348180\pi$
$809$	5.78627e8	−	6.08162e7i	1.09283	−	0.114861i	0.633754	+	0.773535i	$0.281513\pi$
$810$	4.13987e8	+	1.27412e9i	0.778990	+	2.39748i
$811$	−2.63936e8	−	4.57151e8i	−0.494808	−	0.857032i	0.505174	−	0.863017i	$-0.331428\pi$
$811$	−2.63936e8	−	4.57151e8i	−0.494808	−	0.857032i	−0.999982	+	0.00598522i	$0.998095\pi$
$812$	5.93444e7	+	3.42625e7i	0.110844	+	0.0639957i
$813$	3.31276e8	+	7.04149e7i	0.616479	+	0.131037i
$814$	1.59686e8	−	4.91462e8i	0.296069	−	0.911205i
$815$	8.17777e8	−	1.73824e8i	1.51064	−	0.321097i
$816$	−1.47249e8	+	1.40098e9i	−0.271009	+	2.57847i
$817$	−1.46653e8	−	1.32047e8i	−0.268920	−	0.242137i
$818$	4.12207e8	+	9.25833e8i	0.753105	+	1.69150i
$819$	1.02326e9	−	2.29828e9i	1.86266	−	4.18361i
$820$	2.96073e7	+	3.28822e7i	0.0536978	+	0.0596375i
$821$	−4.68457e6	−	6.44776e6i	−0.00846526	−	0.0116514i	0.804763	−	0.593596i	$-0.202292\pi$
$821$	−4.68457e6	−	6.44776e6i	−0.00846526	−	0.0116514i	−0.813229	+	0.581944i	$0.802292\pi$
$822$	−4.60855e8	+	3.34831e8i	−0.829753	+	0.602851i
$823$	−7.52603e7	+	6.77647e7i	−0.135010	+	0.121564i	−0.733869	−	0.679291i	$-0.762288\pi$
$823$	−7.52603e7	+	6.77647e7i	−0.135010	+	0.121564i	0.598859	+	0.800854i	$0.295621\pi$
$824$	3.87912e8	+	1.72709e8i	0.693348	+	0.308698i
$825$	1.49760e8	−	6.66773e7i	0.266706	−	0.118745i
$826$	−4.98414e8	+	5.53544e8i	−0.884402	+	0.982228i
$827$	−1.43377e8	−	1.50696e7i	−0.253492	−	0.0266431i	−0.0230698	−	0.999734i	$-0.507344\pi$
$827$	−1.43377e8	−	1.50696e7i	−0.253492	−	0.0266431i	−0.230422	+	0.973091i	$0.574011\pi$
$828$	−2.10655e7	−	9.91053e7i	−0.0371091	−	0.174585i
$829$	1.35169e8	+	4.39192e7i	0.237254	+	0.0770886i	0.425231	−	0.905085i	$-0.360193\pi$
$829$	1.35169e8	+	4.39192e7i	0.237254	+	0.0770886i	−0.187976	+	0.982174i	$0.560193\pi$
$830$	−3.90026e7	+	1.83493e8i	−0.0682117	+	0.320911i
$831$	3.07160e8	−	5.32017e8i	0.535257	−	0.927092i
$832$	4.41140e8	−	2.54692e8i	0.765960	−	0.442227i
$833$	−8.11245e8	+	2.63589e8i	−1.40351	+	0.456030i
$834$	−2.03293e8	−	1.93420e9i	−0.350448	−	3.33429i
$835$	−3.46386e8	+	4.76760e8i	−0.594979	+	0.818918i
$836$		−	1.39890e8i		−	0.239424i
$837$	−1.06309e9	−	9.47192e8i	−1.81298	−	1.61533i
$838$	−9.53214e8			−1.61979
$839$	5.29451e8	+	3.84669e8i	0.896479	+	0.651330i	0.937559	−	0.347826i	$-0.113080\pi$
$839$	5.29451e8	+	3.84669e8i	0.896479	+	0.651330i	−0.0410802	+	0.999156i	$0.513080\pi$
$840$	−1.47681e9	+	1.55219e8i	−2.49164	+	0.261882i
$841$	1.58848e8	+	4.88884e8i	0.267051	+	0.821898i
$842$	−8.27376e7	−	1.43306e8i	−0.138601	−	0.240064i
$843$	−4.82582e8	−	2.78619e8i	−0.805543	−	0.465080i
$844$	−7.01238e7	−	1.49053e7i	−0.116637	−	0.0247921i
$845$	1.48273e8	−	4.56339e8i	0.245750	−	0.756340i
$846$	3.15340e8	−	6.70275e7i	0.520796	−	0.110699i
$847$	−8.64777e6	+	8.22780e7i	−0.0142316	+	0.135405i
$848$	5.73508e8	+	5.16389e8i	0.940486	+	0.846817i
$849$	5.40513e8	+	1.21401e9i	0.883250	+	1.98381i
$850$	5.61010e7	−	1.26005e8i	0.0913511	−	0.205178i
$851$	−1.22761e8	−	1.36340e8i	−0.199192	−	0.221225i
$852$	−6.36584e7	−	8.76182e7i	−0.102929	−	0.141669i
$853$	6.43403e8	−	4.67459e8i	1.03666	−	0.753176i	0.0670279	−	0.997751i	$-0.478648\pi$
$853$	6.43403e8	−	4.67459e8i	1.03666	−	0.753176i	0.969630	+	0.244575i	$0.0786483\pi$
$854$	6.88804e8	−	6.20202e8i	1.10592	−	0.995771i
$855$	1.55098e9	+	6.90540e8i	2.48146	+	1.10482i
$856$	2.17222e6	−	967136.i	0.00346324	−	0.00154194i
$857$	−1.41679e8	+	1.57351e8i	−0.225094	+	0.249993i	−0.845104	−	0.534601i	$-0.820462\pi$
$857$	−1.41679e8	+	1.57351e8i	−0.225094	+	0.249993i	0.620010	+	0.784594i	$0.287128\pi$
$858$	1.59871e9	+	1.68031e8i	2.53109	+	0.266028i
$859$	−9.40204e7	−	4.42331e8i	−0.148335	−	0.697860i	−0.987962	−	0.154697i	$-0.950560\pi$
$859$	−9.40204e7	−	4.42331e8i	−0.148335	−	0.697860i	0.839627	−	0.543163i	$-0.182773\pi$
$860$	5.10773e7	+	1.65960e7i	0.0803031	+	0.0260921i
$861$	−1.15182e8	+	5.41887e8i	−0.180457	+	0.848983i
$862$	−5.29702e8	+	9.17470e8i	−0.827007	+	1.43242i
$863$	5.18734e8	−	2.99491e8i	0.807072	−	0.465963i	−0.0388659	−	0.999244i	$-0.512375\pi$
$863$	5.18734e8	−	2.99491e8i	0.807072	−	0.465963i	0.845938	+	0.533281i	$0.179041\pi$
$864$	6.80586e8	−	2.21136e8i	1.05522	−	0.342861i
$865$	−3.21274e7	−	3.05672e8i	−0.0496395	−	0.472288i
$866$	−7.93163e8	+	1.09170e9i	−1.22126	+	1.68092i
$867$		−	5.38587e8i		−	0.826416i
$868$	−1.83054e8	+	1.34465e8i	−0.279912	+	0.205613i
$869$	−3.74026e8			−0.569958
$870$	−4.29910e8	−	3.12348e8i	−0.652860	−	0.474330i
$871$	−1.49046e9	+	1.56654e8i	−2.25563	+	0.237076i
$872$	−7.15893e7	−	2.20329e8i	−0.107969	−	0.332294i
$873$	4.56955e8	+	7.91470e8i	0.686801	+	1.18957i
$874$	−2.27709e8	−	1.31468e8i	−0.341071	−	0.196918i
$875$	−8.78893e8	−	1.86814e8i	−1.31193	−	0.278860i
$876$	−3.16298e7	+	9.73466e7i	−0.0470527	+	0.144813i
$877$	7.07763e8	−	1.50440e8i	1.04928	−	0.223030i	0.349162	−	0.937062i	$-0.386466\pi$
$877$	7.07763e8	−	1.50440e8i	1.04928	−	0.223030i	0.700113	+	0.714032i	$0.253133\pi$
$878$	6.55984e7	−	6.24127e8i	0.0969191	−	0.922124i
$879$	−2.26626e8	−	2.04055e8i	−0.333689	−	0.300455i
$880$	−3.36546e8	−	7.55894e8i	−0.493851	−	1.10921i
$881$	−4.74815e8	+	1.06645e9i	−0.694379	+	1.55960i	0.128707	+	0.991683i	$0.458917\pi$
$881$	−4.74815e8	+	1.06645e9i	−0.694379	+	1.55960i	−0.823085	+	0.567918i	$0.807749\pi$
$882$	1.45457e9	+	1.61547e9i	2.11997	+	2.35447i
$883$	−3.05936e8	−	4.21084e8i	−0.444373	−	0.611627i	0.526804	−	0.849987i	$-0.323390\pi$
$883$	−3.05936e8	−	4.21084e8i	−0.444373	−	0.611627i	−0.971177	+	0.238360i	$0.923390\pi$
$884$	2.06685e8	−	1.50165e8i	0.299193	−	0.217376i
$885$	8.10824e8	−	7.30069e8i	1.16976	−	1.05326i
$886$	3.55099e8	+	1.58100e8i	0.510562	+	0.227317i
$887$	6.86048e8	−	3.05448e8i	0.983068	−	0.437690i	0.148690	−	0.988884i	$-0.452494\pi$
$887$	6.86048e8	−	3.05448e8i	0.983068	−	0.437690i	0.834377	+	0.551194i	$0.185828\pi$
$888$	6.59281e8	−	7.32206e8i	0.941525	−	1.04567i
$889$	8.52608e8	+	8.96127e7i	1.21351	+	0.127545i
$890$	1.50865e8	+	7.09763e8i	0.214002	+	1.00680i
$891$	−1.34727e9	−	4.37755e8i	−1.90468	−	0.618868i
$892$	4.62912e7	−	2.17783e8i	0.0652235	−	0.306852i
$893$	7.90140e7	−	1.36856e8i	0.110956	−	0.192181i
$894$	−1.50038e9	+	8.66247e8i	−2.09986	+	1.21235i
$895$	−1.22692e9	+	3.98651e8i	−1.71138	+	0.556063i
$896$	1.34825e8	+	1.28278e9i	0.187434	+	1.78331i
$897$	3.35459e8	−	4.61720e8i	0.464796	−	0.639736i
$898$			4.31325e8i			0.595629i
$899$	2.66431e8	+	2.65950e7i	0.366695	+	0.0366034i
$900$	−6.63956e7			−0.0910776
$901$	−7.65837e8	−	5.56413e8i	−1.04704	−	0.760717i
$902$	−2.46344e8	+	2.58918e7i	−0.335678	+	0.0352812i
$903$	2.07788e8	+	6.39506e8i	0.282200	+	0.868523i
$904$	−8.25542e7	−	1.42988e8i	−0.111747	−	0.193551i
$905$	1.08104e9	+	6.24136e8i	1.45846	+	0.842041i
$906$	−6.26481e8	−	1.33163e8i	−0.842410	−	0.179060i
$907$	−1.41710e8	+	4.36140e8i	−0.189924	+	0.584526i	−0.999998	−	0.00180106i	$-0.999427\pi$
$907$	−1.41710e8	+	4.36140e8i	−0.189924	+	0.584526i	0.810074	+	0.586327i	$0.199427\pi$
$908$	2.74920e8	−	5.84361e7i	0.367239	−	0.0780592i
$909$	9.51752e7	−	9.05531e8i	0.126716	−	1.20562i
$910$	1.32041e9	+	1.18890e9i	1.75220	+	1.57769i
$911$	−2.41673e8	−	5.42806e8i	−0.319649	−	0.717943i	0.680238	−	0.732991i	$-0.261876\pi$
$911$	−2.41673e8	−	5.42806e8i	−0.319649	−	0.717943i	−0.999887	+	0.0150484i	$0.995210\pi$
$912$	7.15766e8	−	1.60764e9i	0.943597	−	2.11935i
$913$	−1.32730e8	−	1.47412e8i	−0.174404	−	0.193696i
$914$	1.48057e8	+	2.03783e8i	0.193906	+	0.266888i
$915$	−1.09838e9	+	7.98022e8i	−1.43381	+	1.04172i
$916$	2.74848e7	−	2.47474e7i	0.0357607	−	0.0321991i
$917$	1.66138e9	+	7.39696e8i	2.15458	+	0.959279i
$918$	−2.29674e9	+	1.02258e9i	−2.96882	+	1.32181i
$919$	−6.88842e8	+	7.65037e8i	−0.887510	+	0.985679i	−0.999968	−	0.00797713i	$-0.997461\pi$
$919$	−6.88842e8	+	7.65037e8i	−0.887510	+	0.985679i	0.112459	+	0.993656i	$0.464127\pi$
$920$	−2.34430e8	−	2.46396e7i	−0.301058	−	0.0316424i
$921$	−2.01896e8	−	9.49847e8i	−0.258434	−	1.21584i
$922$	−4.30191e8	−	1.39778e8i	−0.548869	−	0.178338i
$923$	8.87536e7	−	4.17553e8i	0.112871	−	0.531014i
$924$	−2.38330e8	+	4.12800e8i	−0.302109	+	0.523268i
$925$	−1.04118e8	+	6.01126e7i	−0.131553	+	0.0759522i
$926$	9.48304e8	−	3.08123e8i	1.19430	−	0.388053i
$927$	1.72912e8	+	1.64515e9i	0.217064	+	2.06522i
$928$	−7.90987e7	+	1.08870e8i	−0.0989750	+	0.136227i
$929$			1.84639e8i			0.230290i	0.993349	+	0.115145i	$0.0367333\pi$
$929$			1.84639e8i			0.230290i	−0.993349	+	0.115145i	$0.963267\pi$
$930$	1.52077e9	−	8.88655e8i	1.89067	−	1.10480i
$931$	1.06558e9			1.32049
$932$	−1.17902e8	−	8.56606e7i	−0.145637	−	0.105812i
$933$	2.90584e9	−	3.05416e8i	3.57789	−	0.376051i
$934$	−4.22876e8	−	1.30148e9i	−0.519006	−	1.59734i
$935$	5.07473e8	+	8.78970e8i	0.620838	+	1.07532i
$936$	1.85740e9	+	1.07237e9i	2.26505	+	1.30772i
$937$	3.97467e7	+	8.44841e6i	0.0483150	+	0.0102697i	0.232006	−	0.972714i	$-0.425471\pi$
$937$	3.97467e7	+	8.44841e6i	0.0483150	+	0.0102697i	−0.183691	+	0.982984i	$0.558805\pi$
$938$	7.27010e8	−	2.23751e9i	0.880911	−	2.71116i
$939$	−1.77407e9	+	3.77091e8i	−2.14277	+	0.455459i
$940$	−4.49546e6	+	4.27714e7i	−0.00541241	+	0.0514956i
$941$	−3.33220e8	−	3.00033e8i	−0.399910	−	0.360081i	0.444499	−	0.895779i	$-0.353382\pi$
$941$	−3.33220e8	−	3.00033e8i	−0.399910	−	0.360081i	−0.844409	+	0.535699i	$0.820048\pi$
$942$	−1.06173e9	−	2.38469e9i	−1.27017	−	2.85285i
$943$	−3.57690e7	+	8.03385e7i	−0.0426552	+	0.0958052i
$944$	−5.29527e8	−	5.88099e8i	−0.629466	−	0.699093i
$945$	−1.94128e9	−	2.67194e9i	−2.30034	−	3.16615i
$946$	−2.43232e8	+	1.76718e8i	−0.287307	+	0.208741i
$947$	−2.54482e7	+	2.29137e7i	−0.0299645	+	0.0269802i	−0.683977	−	0.729504i	$-0.739751\pi$
$947$	−2.54482e7	+	2.29137e7i	−0.0299645	+	0.0269802i	0.654012	+	0.756484i	$0.273084\pi$
$948$	1.97772e8	+	8.80537e7i	0.232134	+	0.103353i
$949$	−3.68566e8	+	1.64096e8i	−0.431237	+	0.191999i
$950$	−1.15294e8	+	1.28047e8i	−0.134473	+	0.149348i
$951$	−2.04798e9	−	2.15252e8i	−2.38114	−	0.250268i
$952$	−2.74678e8	−	1.29226e9i	−0.318357	−	1.49775i
$953$	−5.94091e8	−	1.93032e8i	−0.686396	−	0.223024i	−0.0550024	−	0.998486i	$-0.517517\pi$
$953$	−5.94091e8	−	1.93032e8i	−0.686396	−	0.223024i	−0.631393	+	0.775463i	$0.717517\pi$
$954$	−5.01576e8	+	2.35973e9i	−0.577686	+	2.71780i
$955$	5.43550e7	−	9.41456e7i	0.0624064	−	0.108091i
$956$	−2.20587e8	+	1.27356e8i	−0.252468	+	0.145763i
$957$	5.34405e8	−	1.73639e8i	0.609726	−	0.198112i
$958$	−2.68975e6	−	2.55913e7i	−0.00305926	−	0.0291069i
$959$	3.91336e8	−	5.38628e8i	0.443704	−	0.610707i
$960$		−	1.17131e9i		−	1.32391i
$961$	−4.35689e8	+	7.73200e8i	−0.490915	+	0.871208i
$962$	−1.17892e9			−1.32422
$963$	7.49412e6	+	5.44480e6i	0.00839154	+	0.00609681i
$964$	2.87776e8	−	3.02465e7i	0.321236	−	0.0337632i
$965$	−2.21009e7	−	6.80195e7i	−0.0245939	−	0.0756922i
$966$	4.47962e8	+	7.75893e8i	0.496947	+	0.860737i
$967$	−1.07082e9	−	6.18240e8i	−1.18424	−	0.683719i	−0.227245	−	0.973838i	$-0.572972\pi$
$967$	−1.07082e9	−	6.18240e8i	−1.18424	−	0.683719i	−0.956991	+	0.290118i	$0.906305\pi$
$968$	−6.89882e7	−	1.46639e7i	−0.0760587	−	0.0161668i
$969$	−6.67041e8	+	2.05294e9i	−0.733130	+	2.25634i
$970$	−6.31350e8	+	1.34198e8i	−0.691759	+	0.147038i
$971$	−4.80721e7	+	4.57375e8i	−0.0525092	+	0.499591i	0.936386	+	0.350973i	$0.114149\pi$
$971$	−4.80721e7	+	4.57375e8i	−0.0525092	+	0.499591i	−0.988895	+	0.148618i	$0.952518\pi$
$972$	2.23428e8	+	2.01175e8i	0.243298	+	0.219066i
$973$	9.24539e8	+	2.07655e9i	1.00366	+	2.25426i
$974$	−2.41752e8	+	5.42983e8i	−0.261633	+	0.587637i
$975$	−2.50252e8	−	2.77933e8i	−0.270000	−	0.299866i
$976$	5.78814e8	+	7.96669e8i	0.622572	+	0.856897i
$977$	6.22732e8	−	4.52441e8i	0.667755	−	0.485153i	−0.201518	−	0.979485i	$-0.564587\pi$
$977$	6.22732e8	−	4.52441e8i	0.667755	−	0.485153i	0.869273	+	0.494332i	$0.164587\pi$
$978$	2.01316e9	−	1.81265e9i	2.15209	−	1.93775i
$979$	−7.00945e8	−	3.12081e8i	−0.747026	−	0.332597i
$980$	−2.64923e8	+	1.17951e8i	−0.281476	+	0.125321i
$981$	6.03900e8	−	6.70699e8i	0.639673	−	0.710429i
$982$	1.05960e9	+	1.11368e8i	1.11894	+	0.117605i
$983$	−1.35612e7	−	6.38005e7i	−0.0142770	−	0.0671681i	0.970432	−	0.241373i	$-0.0775978\pi$
$983$	−1.35612e7	−	6.38005e7i	−0.0142770	−	0.0671681i	−0.984709	+	0.174205i	$0.944264\pi$
$984$	−4.49171e8	−	1.45944e8i	−0.471440	−	0.153180i
$985$	1.13420e8	−	5.33599e8i	0.118681	−	0.558350i
$986$	2.36389e8	−	4.09437e8i	0.246602	−	0.427126i
$987$	−4.66323e8	+	2.69232e8i	−0.484993	+	0.280011i
$988$	−3.03526e8	+	9.86215e7i	−0.314720	+	0.102259i
$989$	1.11574e7	+	1.06155e8i	0.0115338	+	0.109737i
$990$	1.52034e9	−	2.09257e9i	1.56688	−	2.15662i
$991$			2.21818e8i			0.227916i	0.993486	+	0.113958i	$0.0363529\pi$
$991$			2.21818e8i			0.227916i	−0.993486	+	0.113958i	$0.963647\pi$
$992$	−2.25042e8	−	3.85119e8i	−0.230531	−	0.394512i
$993$	−1.33994e9			−1.36848
$994$	5.42145e8	+	3.93891e8i	0.552022	+	0.401067i
$995$	1.98346e9	−	2.08470e8i	2.01351	−	0.211629i
$996$	3.54792e7	+	1.09194e8i	0.0359083	+	0.110515i
$997$	−4.62206e8	−	8.00564e8i	−0.466391	−	0.807812i	0.532873	−	0.846196i	$-0.321113\pi$
$997$	−4.62206e8	−	8.00564e8i	−0.466391	−	0.807812i	−0.999263	+	0.0383834i	$0.987779\pi$
$998$	−1.03336e9	−	5.96610e8i	−1.03958	−	0.600204i
$999$	2.14351e9	+	4.55617e8i	2.14995	+	0.456986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.7.h.a.21.12	yes	120
31.3	odd	30	inner	31.7.h.a.3.12	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.7.h.a.3.12	✓	120	31.3	odd	30	inner
31.7.h.a.21.12	yes	120	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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	31.h (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(7.18633 + 5.22117i) q^{2} +(49.0045 - 5.15058i) q^{3} +(4.60558 + 14.1745i) q^{4} +(67.5410 + 116.984i) q^{5} +(379.054 + 218.847i) q^{6} +(-500.379 - 106.359i) q^{7} +(134.765 - 414.765i) q^{8} +(1661.84 - 353.235i) q^{9} +(-125.424 + 1193.33i) q^{10} +(-942.897 - 848.989i) q^{11} +(298.701 + 670.893i) q^{12} +(-1177.35 + 2644.38i) q^{13} +(-3040.57 - 3376.90i) q^{14} +(3912.34 + 5384.88i) q^{15} +(3905.71 - 2837.67i) q^{16} +(-4400.77 + 3962.47i) q^{17} +(13786.8 + 6138.29i) q^{18} +(6758.09 - 3008.90i) q^{19} +(-1347.13 + 1496.14i) q^{20} +(-25068.6 - 2634.82i) q^{21} +(-2343.25 - 11024.1i) q^{22} +(-3805.50 - 1236.48i) q^{23} +(4467.82 - 21019.5i) q^{24} +(-1311.06 + 2270.82i) q^{25} +(-22267.6 + 12856.2i) q^{26} +(45455.3 - 14769.3i) q^{27} +(-796.951 - 7582.48i) q^{28} +(-5282.88 + 7271.26i) q^{29} +59124.6i q^{30} +(-15030.2 - 25721.5i) q^{31} +14972.7 q^{32} +(-50579.0 - 36747.8i) q^{33} +(-52314.1 + 5498.43i) q^{34} +(-21353.8 - 65720.1i) q^{35} +(12660.7 + 21928.9i) q^{36} +(39707.6 + 22925.2i) q^{37} +(64275.8 + 13662.2i) q^{38} +(-44075.5 + 135650. i) q^{39} +(57623.2 - 12248.2i) q^{40} +(2297.33 - 21857.6i) q^{41} +(-166395. - 149822. i) q^{42} +(-10850.1 - 24369.8i) q^{43} +(7691.42 - 17275.2i) q^{44} +(153565. + 170551. i) q^{45} +(-20891.7 - 28755.0i) q^{46} +(17282.2 - 12556.2i) q^{47} +(176782. - 159175. i) q^{48} +(131589. + 58587.4i) q^{49} +(-21278.1 + 9473.61i) q^{50} +(-195248. + 216845. i) q^{51} +(-42905.2 - 4509.52i) q^{52} +(33235.5 + 156361. i) q^{53} +(403770. + 131193. i) q^{54} +(35634.2 - 167646. i) q^{55} +(-111548. + 193206. i) q^{56} +(315679. - 182257. i) q^{57} +(-75929.0 + 24670.8i) q^{58} +(-17134.4 - 163023. i) q^{59} +(-58309.5 + 80256.1i) q^{60} +203975. i q^{61} +(26284.4 - 263319. i) q^{62} -869119. q^{63} +(-142367. - 103436. i) q^{64} +(-388870. + 40871.9i) q^{65} +(-171611. - 528163. i) q^{66} +(258871. + 448378. i) q^{67} +(-76434.2 - 44129.3i) q^{68} +(-192855. - 40992.7i) q^{69} +(189681. - 583778. i) q^{70} +(-144251. + 30661.4i) q^{71} +(77448.9 - 736877. i) q^{72} +(103577. + 93261.5i) q^{73} +(165655. + 372068. i) q^{74} +(-52551.8 + 118033. i) q^{75} +(73774.6 + 81935.0i) q^{76} +(381509. + 525102. i) q^{77} +(-1.02500e6 + 744703. i) q^{78} +(219071. - 197252. i) q^{79} +(595758. + 265249. i) q^{80} +(1.01997e6 - 454121. i) q^{81} +(130632. - 145081. i) q^{82} +(155483. + 16341.9i) q^{83} +(-78108.3 - 367471. i) q^{84} +(-760779. - 247192. i) q^{85} +(49266.4 - 231780. i) q^{86} +(-221433. + 383534. i) q^{87} +(-479201. + 276667. i) q^{88} +(575134. - 186872. i) q^{89} +(213091. + 2.02743e6i) q^{90} +(870376. - 1.19797e6i) q^{91} -59635.9i q^{92} +(-869028. - 1.18305e6i) q^{93} +189753. q^{94} +(808441. + 587367. i) q^{95} +(733727. - 77117.8i) q^{96} +(166227. + 511594. i) q^{97} +(639750. + 1.10808e6i) q^{98} +(-1.86684e6 - 1.07782e6i) 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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