LMFDB - Embedded newform 770.2.bv.a.537.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			537.6
Character	$\chi$	$=$	770.537
Dual form			770.2.bv.a.423.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0523360 + 0.998630i) q^{2} +(-0.571941 - 1.48996i) q^{3} +(-0.994522 - 0.104528i) q^{4} +(-0.530105 - 2.17232i) q^{5} +(1.51785 - 0.493179i) q^{6} +(2.02695 - 1.70043i) q^{7} +(0.156434 - 0.987688i) q^{8} +(0.336578 - 0.303057i) q^{9} +O(q^{10})$	\(q+(-0.0523360 + 0.998630i) q^{2} +(-0.571941 - 1.48996i) q^{3} +(-0.994522 - 0.104528i) q^{4} +(-0.530105 - 2.17232i) q^{5} +(1.51785 - 0.493179i) q^{6} +(2.02695 - 1.70043i) q^{7} +(0.156434 - 0.987688i) q^{8} +(0.336578 - 0.303057i) q^{9} +(2.19709 - 0.415688i) q^{10} +(-2.46604 - 2.21780i) q^{11} +(0.413065 + 1.54158i) q^{12} +(-0.930007 + 0.473862i) q^{13} +(1.59202 + 2.11317i) q^{14} +(-2.93348 + 2.03227i) q^{15} +(0.978148 + 0.207912i) q^{16} +(0.257201 + 4.90769i) q^{17} +(0.285026 + 0.351978i) q^{18} +(-0.153055 - 1.45622i) q^{19} +(0.300131 + 2.21583i) q^{20} +(-3.69286 - 2.04753i) q^{21} +(2.34382 - 2.34659i) q^{22} +(-1.39055 - 5.18961i) q^{23} +(-1.56108 + 0.331819i) q^{24} +(-4.43798 + 2.30312i) q^{25} +(-0.424540 - 0.953533i) q^{26} +(-4.91008 - 2.50181i) q^{27} +(-2.19359 + 1.47924i) q^{28} +(-0.541665 + 0.745537i) q^{29} +(-1.87596 - 3.03582i) q^{30} +(2.13601 + 10.0491i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-1.89399 + 4.94275i) q^{33} -4.91442 q^{34} +(-4.76838 - 3.50179i) q^{35} +(-0.366413 + 0.266214i) q^{36} +(-1.77787 - 0.682459i) q^{37} +(1.46224 - 0.0766325i) q^{38} +(1.23794 + 1.11465i) q^{39} +(-2.22851 + 0.183752i) q^{40} +(-2.93074 - 4.03382i) q^{41} +(2.23799 - 3.58064i) q^{42} +(5.11915 - 5.11915i) q^{43} +(2.22071 + 2.46342i) q^{44} +(-0.836759 - 0.570506i) q^{45} +(5.25528 - 1.11704i) q^{46} +(-8.64564 - 7.00110i) q^{47} +(-0.249663 - 1.57631i) q^{48} +(1.21708 - 6.89338i) q^{49} +(-2.06770 - 4.55243i) q^{50} +(7.16514 - 3.19012i) q^{51} +(0.974445 - 0.374054i) q^{52} +(2.46430 - 3.79470i) q^{53} +(2.75535 - 4.77241i) q^{54} +(-3.51051 + 6.53271i) q^{55} +(-1.36241 - 2.26800i) q^{56} +(-2.08217 + 1.06092i) q^{57} +(-0.716167 - 0.579941i) q^{58} +(-0.358727 + 3.41306i) q^{59} +(3.12984 - 1.71451i) q^{60} +(1.60053 - 7.52991i) q^{61} +(-10.1471 + 1.60715i) q^{62} +(0.166902 - 1.18661i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(1.52238 + 1.76908i) q^{65} +(-4.83685 - 2.15008i) q^{66} +(-0.648703 + 2.42099i) q^{67} +(0.257201 - 4.90769i) q^{68} +(-6.93699 + 5.04002i) q^{69} +(3.74655 - 4.57858i) q^{70} +(1.76211 + 5.42322i) q^{71} +(-0.246673 - 0.379843i) q^{72} +(-6.83407 + 5.53412i) q^{73} +(0.774570 - 1.73971i) q^{74} +(5.96981 + 5.29515i) q^{75} +1.46424i q^{76} +(-8.76976 - 0.302042i) q^{77} +(-1.17791 + 1.17791i) q^{78} +(1.80606 - 1.62619i) q^{79} +(-0.0668694 - 2.23507i) q^{80} +(-0.777288 + 7.39540i) q^{81} +(4.18168 - 2.71561i) q^{82} +(4.13319 - 8.11183i) q^{83} +(3.45861 + 2.42232i) q^{84} +(10.5247 - 3.16031i) q^{85} +(4.84422 + 5.38005i) q^{86} +(1.42062 + 0.380654i) q^{87} +(-2.57627 + 2.08874i) q^{88} +(-4.16476 + 7.21357i) q^{89} +(0.613516 - 0.805754i) q^{90} +(-1.07931 + 2.54191i) q^{91} +(0.840473 + 5.30654i) q^{92} +(13.7511 - 8.93006i) q^{93} +(7.44398 - 8.26738i) q^{94} +(-3.08225 + 1.10443i) q^{95} +(1.58722 - 0.166823i) q^{96} +(-0.592364 - 1.16258i) q^{97} +(6.82024 + 1.57618i) q^{98} +(-1.50214 + 0.000887499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.0523360	+	0.998630i	−0.0370071	+	0.706138i
$2$	−0.0523360	+	0.998630i	−0.0370071	+	0.706138i
$3$	−0.571941	−	1.48996i	−0.330210	−	0.860227i	−0.993703	−	0.112045i	$-0.964260\pi$
$3$	−0.571941	−	1.48996i	−0.330210	−	0.860227i	0.663493	−	0.748183i	$-0.269073\pi$
$4$	−0.994522	−	0.104528i	−0.497261	−	0.0522642i
$5$	−0.530105	−	2.17232i	−0.237070	−	0.971493i
$5$	−0.530105	−	2.17232i	−0.237070	−	0.971493i
$6$	1.51785	−	0.493179i	0.619659	−	0.201339i
$7$	2.02695	−	1.70043i	0.766116	−	0.642702i
$7$	2.02695	−	1.70043i	0.766116	−	0.642702i
$8$	0.156434	−	0.987688i	0.0553079	−	0.349201i
$9$	0.336578	−	0.303057i	0.112193	−	0.101019i
$10$	2.19709	−	0.415688i	0.694781	−	0.131452i
$11$	−2.46604	−	2.21780i	−0.743540	−	0.668691i
$11$	−2.46604	−	2.21780i	−0.743540	−	0.668691i
$12$	0.413065	+	1.54158i	0.119242	+	0.445016i
$13$	−0.930007	+	0.473862i	−0.257938	+	0.131426i	−0.578178	−	0.815910i	$-0.696236\pi$
$13$	−0.930007	+	0.473862i	−0.257938	+	0.131426i	0.320241	+	0.947336i	$0.396236\pi$
$14$	1.59202	+	2.11317i	0.425484	+	0.564768i
$15$	−2.93348	+	2.03227i	−0.757421	+	0.524731i
$16$	0.978148	+	0.207912i	0.244537	+	0.0519779i
$17$	0.257201	+	4.90769i	0.0623804	+	1.19029i	0.833103	+	0.553118i	$0.186562\pi$
$17$	0.257201	+	4.90769i	0.0623804	+	1.19029i	−0.770723	+	0.637171i	$0.780105\pi$
$18$	0.285026	+	0.351978i	0.0671813	+	0.0829620i
$19$	−0.153055	−	1.45622i	−0.0351132	−	0.334080i	−0.997950	−	0.0639965i	$-0.979615\pi$
$19$	−0.153055	−	1.45622i	−0.0351132	−	0.334080i	0.962837	−	0.270084i	$-0.0870513\pi$
$20$	0.300131	+	2.21583i	0.0671114	+	0.495476i
$21$	−3.69286	−	2.04753i	−0.805849	−	0.446807i
$22$	2.34382	−	2.34659i	0.499705	−	0.500295i
$23$	−1.39055	−	5.18961i	−0.289950	−	1.08211i	−0.945145	−	0.326650i	$-0.894080\pi$
$23$	−1.39055	−	5.18961i	−0.289950	−	1.08211i	0.655195	−	0.755460i	$-0.272586\pi$
$24$	−1.56108	+	0.331819i	−0.318655	+	0.0677322i
$25$	−4.43798	+	2.30312i	−0.887596	+	0.460624i
$26$	−0.424540	−	0.953533i	−0.0832592	−	0.187003i
$27$	−4.91008	−	2.50181i	−0.944945	−	0.481473i
$28$	−2.19359	+	1.47924i	−0.414550	+	0.279550i
$29$	−0.541665	+	0.745537i	−0.100585	+	0.138443i	−0.856342	−	0.516408i	$-0.827269\pi$
$29$	−0.541665	+	0.745537i	−0.100585	+	0.138443i	0.755758	+	0.654851i	$0.227269\pi$
$30$	−1.87596	−	3.03582i	−0.342502	−	0.554263i
$31$	2.13601	+	10.0491i	0.383638	+	1.80488i	0.569151	+	0.822233i	$0.307272\pi$
$31$	2.13601	+	10.0491i	0.383638	+	1.80488i	−0.185512	+	0.982642i	$0.559394\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−1.89399	+	4.94275i	−0.329702	+	0.860422i
$34$	−4.91442			−0.842816
$35$	−4.76838	−	3.50179i	−0.806003	−	0.591911i
$36$	−0.366413	+	0.266214i	−0.0610688	+	0.0443691i
$37$	−1.77787	−	0.682459i	−0.292279	−	0.112196i	0.207810	−	0.978169i	$-0.433366\pi$
$37$	−1.77787	−	0.682459i	−0.292279	−	0.112196i	−0.500090	+	0.865974i	$0.666700\pi$
$38$	1.46224	−	0.0766325i	0.237206	−	0.0124314i
$39$	1.23794	+	1.11465i	0.198230	+	0.178487i
$40$	−2.22851	+	0.183752i	−0.352358	+	0.0290538i
$41$	−2.93074	−	4.03382i	−0.457705	−	0.629977i	0.516326	−	0.856392i	$-0.327299\pi$
$41$	−2.93074	−	4.03382i	−0.457705	−	0.629977i	−0.974031	+	0.226415i	$0.927299\pi$
$42$	2.23799	−	3.58064i	0.345330	−	0.552505i
$43$	5.11915	−	5.11915i	0.780664	−	0.780664i	−0.199279	−	0.979943i	$-0.563860\pi$
$43$	5.11915	−	5.11915i	0.780664	−	0.780664i	0.979943	+	0.199279i	$0.0638601\pi$
$44$	2.22071	+	2.46342i	0.334785	+	0.371375i
$45$	−0.836759	−	0.570506i	−0.124737	−	0.0850459i
$46$	5.25528	−	1.11704i	0.774848	−	0.164699i
$47$	−8.64564	−	7.00110i	−1.26110	−	1.02121i	−0.998412	−	0.0563329i	$-0.982059\pi$
$47$	−8.64564	−	7.00110i	−1.26110	−	1.02121i	−0.262683	−	0.964882i	$-0.584607\pi$
$48$	−0.249663	−	1.57631i	−0.0360358	−	0.227521i
$49$	1.21708	−	6.89338i	0.173869	−	0.984769i
$50$	−2.06770	−	4.55243i	−0.292416	−	0.643811i
$51$	7.16514	−	3.19012i	1.00332	−	0.446707i
$52$	0.974445	−	0.374054i	0.135131	−	0.0518720i
$53$	2.46430	−	3.79470i	0.338498	−	0.521242i	−0.627899	−	0.778295i	$-0.716085\pi$
$53$	2.46430	−	3.79470i	0.338498	−	0.521242i	0.966397	+	0.257053i	$0.0827516\pi$
$54$	2.75535	−	4.77241i	0.374956	−	0.649443i
$55$	−3.51051	+	6.53271i	−0.473358	+	0.880870i
$56$	−1.36241	−	2.26800i	−0.182060	−	0.303075i
$57$	−2.08217	+	1.06092i	−0.275790	+	0.140522i
$58$	−0.716167	−	0.579941i	−0.0940374	−	0.0761500i
$59$	−0.358727	+	3.41306i	−0.0467023	+	0.444343i	0.946037	+	0.324058i	$0.105047\pi$
$59$	−0.358727	+	3.41306i	−0.0467023	+	0.444343i	−0.992739	+	0.120285i	$0.961619\pi$
$60$	3.12984	−	1.71451i	0.404061	−	0.221342i
$61$	1.60053	−	7.52991i	0.204927	−	0.964106i	−0.748652	−	0.662963i	$-0.769299\pi$
$61$	1.60053	−	7.52991i	0.204927	−	0.964106i	0.953579	−	0.301143i	$-0.0973681\pi$
$62$	−10.1471	+	1.60715i	−1.28869	+	0.204108i
$63$	0.166902	−	1.18661i	0.0210277	−	0.149499i
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$	1.52238	+	1.76908i	0.188828	+	0.219427i
$66$	−4.83685	−	2.15008i	−0.595375	−	0.264657i
$67$	−0.648703	+	2.42099i	−0.0792517	+	0.295771i	−0.994164	−	0.107882i	$-0.965593\pi$
$67$	−0.648703	+	2.42099i	−0.0792517	+	0.295771i	0.914912	+	0.403653i	$0.132260\pi$
$68$	0.257201	−	4.90769i	0.0311902	−	0.595144i
$69$	−6.93699	+	5.04002i	−0.835115	+	0.606747i
$70$	3.74655	−	4.57858i	0.447798	−	0.547244i
$71$	1.76211	+	5.42322i	0.209124	+	0.643618i	0.999519	+	0.0310197i	$0.00987546\pi$
$71$	1.76211	+	5.42322i	0.209124	+	0.643618i	−0.790395	+	0.612598i	$0.790125\pi$
$72$	−0.246673	−	0.379843i	−0.0290707	−	0.0447649i
$73$	−6.83407	+	5.53412i	−0.799867	+	0.647720i	−0.939525	−	0.342480i	$-0.888733\pi$
$73$	−6.83407	+	5.53412i	−0.799867	+	0.647720i	0.139658	+	0.990200i	$0.455400\pi$
$74$	0.774570	−	1.73971i	0.0900419	−	0.202237i
$75$	5.96981	+	5.29515i	0.689334	+	0.611431i
$76$			1.46424i			0.167960i
$77$	−8.76976	−	0.302042i	−0.999407	−	0.0344208i
$78$	−1.17791	+	1.17791i	−0.133372	+	0.133372i
$79$	1.80606	−	1.62619i	0.203198	−	0.182960i	−0.561249	−	0.827647i	$-0.689679\pi$
$79$	1.80606	−	1.62619i	0.203198	−	0.182960i	0.764447	+	0.644687i	$0.223012\pi$
$80$	−0.0668694	−	2.23507i	−0.00747622	−	0.249888i
$81$	−0.777288	+	7.39540i	−0.0863653	+	0.821711i
$82$	4.18168	−	2.71561i	0.461789	−	0.299889i
$83$	4.13319	−	8.11183i	0.453676	−	0.890389i	−0.544974	−	0.838453i	$-0.683461\pi$
$83$	4.13319	−	8.11183i	0.453676	−	0.890389i	0.998650	−	0.0519367i	$-0.0165394\pi$
$84$	3.45861	+	2.42232i	0.377365	+	0.264297i
$85$	10.5247	−	3.16031i	1.14157	−	0.342784i
$86$	4.84422	+	5.38005i	0.522366	+	0.580146i
$87$	1.42062	+	0.380654i	0.152306	+	0.0408104i
$88$	−2.57627	+	2.08874i	−0.274631	+	0.222661i
$89$	−4.16476	+	7.21357i	−0.441463	+	0.764637i	−0.997798	−	0.0663211i	$-0.978874\pi$
$89$	−4.16476	+	7.21357i	−0.441463	+	0.764637i	0.556335	+	0.830958i	$0.312207\pi$
$90$	0.613516	−	0.805754i	0.0646703	−	0.0849339i
$91$	−1.07931	+	2.54191i	−0.113143	+	0.266464i
$92$	0.840473	+	5.30654i	0.0876254	+	0.553245i
$93$	13.7511	−	8.93006i	1.42592	−	0.926004i
$94$	7.44398	−	8.26738i	0.767788	−	0.852715i
$95$	−3.08225	+	1.10443i	−0.316232	+	0.113313i
$96$	1.58722	−	0.166823i	0.161995	−	0.0170263i
$97$	−0.592364	−	1.16258i	−0.0601454	−	0.118042i	0.858977	−	0.512014i	$-0.171101\pi$
$97$	−0.592364	−	1.16258i	−0.0601454	−	0.118042i	−0.919122	+	0.393972i	$0.871101\pi$
$98$	6.82024	+	1.57618i	0.688948	+	0.159219i
$99$	−1.50214		0.000887499i	−0.150970		8.91970e-5i
$100$	4.65441	−	1.82661i	0.465441	−	0.182661i
$101$	2.00156	+	9.41662i	0.199163	+	0.936989i	0.958235	+	0.285982i	$0.0923198\pi$
$101$	2.00156	+	9.41662i	0.199163	+	0.936989i	−0.759072	+	0.651007i	$0.774347\pi$
$102$	2.81076	+	7.32228i	0.278307	+	0.725013i
$103$	0.995018	+	0.381952i	0.0980420	+	0.0376348i	0.406895	−	0.913475i	$-0.366612\pi$
$103$	0.995018	+	0.381952i	0.0980420	+	0.0376348i	−0.308853	+	0.951110i	$0.599945\pi$
$104$	0.322543	+	0.992686i	0.0316280	+	0.0973408i
$105$	−2.49029	+	9.10750i	−0.243027	+	0.888801i
$106$	3.66052	+	2.65953i	0.355542	+	0.258316i
$107$	11.5847	−	14.3060i	1.11994	−	1.38301i	0.205319	−	0.978695i	$-0.434177\pi$
$107$	11.5847	−	14.3060i	1.11994	−	1.38301i	0.914620	−	0.404314i	$-0.132490\pi$
$108$	4.62167	+	3.00135i	0.444720	+	0.288805i
$109$	3.94873	−	2.27980i	0.378220	−	0.218365i	−0.298824	−	0.954308i	$-0.596594\pi$
$109$	3.94873	−	2.27980i	0.378220	−	0.218365i	0.677043	+	0.735943i	$0.263261\pi$
$110$	−6.34003	−	3.84760i	−0.604498	−	0.366854i
$111$			3.03927i			0.288475i
$112$	2.33620	−	1.24184i	0.220750	−	0.117343i
$113$	1.18961	−	7.51093i	0.111910	−	0.706569i	−0.866389	−	0.499369i	$-0.833565\pi$
$113$	1.18961	−	7.51093i	0.111910	−	0.706569i	0.978299	−	0.207199i	$-0.0664349\pi$
$114$	−0.950492	−	2.13484i	−0.0890217	−	0.199946i
$115$	−10.5364	+	5.77177i	−0.982523	+	0.538220i
$116$	0.616627	−	0.684834i	0.0572524	−	0.0635852i
$117$	−0.169413	+	0.441337i	−0.0156623	+	0.0408016i
$118$	−3.38961	−	0.536862i	−0.312039	−	0.0494221i
$119$	8.86651	+	9.51030i	0.812791	+	0.871807i
$120$	1.54836	+	3.21528i	0.141345	+	0.293514i
$121$	1.16274	+	10.9384i	0.105704	+	0.994398i
$122$	7.43582	+	1.99242i	0.673208	+	0.180385i
$123$	−4.33401	+	6.67379i	−0.390785	+	0.601755i
$124$	−1.07389	−	10.2173i	−0.0964378	−	0.917545i
$125$	7.35571	+	8.41983i	0.657915	+	0.753092i
$126$	1.17625	+	0.228776i	0.104789	+	0.0203810i
$127$	4.24414	−	8.32959i	0.376606	−	0.739131i	−0.622446	−	0.782663i	$-0.713861\pi$
$127$	4.24414	−	8.32959i	0.376606	−	0.739131i	0.999052	+	0.0435316i	$0.0138609\pi$
$128$	0.358368	−	0.933580i	0.0316756	−	0.0825176i
$129$	−10.5552	−	4.69947i	−0.929331	−	0.413765i
$130$	−1.84633	+	1.42771i	−0.161934	+	0.125219i
$131$	−9.63453	−	5.56250i	−0.841773	−	0.485998i	0.0160937	−	0.999870i	$-0.494877\pi$
$131$	−9.63453	−	5.56250i	−0.841773	−	0.485998i	−0.857866	+	0.513873i	$0.828210\pi$
$132$	2.40028	−	4.71770i	0.208917	−	0.410623i
$133$	−2.78644	−	2.69143i	−0.241615	−	0.233377i
$134$	−2.38373	−	0.774519i	−0.205922	−	0.0669083i
$135$	−2.83188	+	11.9925i	−0.243730	+	1.03215i
$136$	4.88750	+	0.513697i	0.419100	+	0.0440491i
$137$	0.722472	−	0.0378632i	0.0617250	−	0.00323487i	−0.0214485	−	0.999770i	$-0.506828\pi$
$137$	0.722472	−	0.0378632i	0.0617250	−	0.00323487i	0.0831734	+	0.996535i	$0.473494\pi$
$138$	−4.67006	−	7.19126i	−0.397542	−	0.612160i
$139$	9.38916	+	6.82162i	0.796378	+	0.578603i	0.909849	−	0.414939i	$-0.136197\pi$
$139$	9.38916	+	6.82162i	0.796378	+	0.578603i	−0.113471	+	0.993541i	$0.536197\pi$
$140$	4.37622	+	3.98104i	0.369858	+	0.336459i
$141$	−5.48654	+	16.8858i	−0.462050	+	1.42204i
$142$	−5.50801	+	1.47587i	−0.462222	+	0.123852i
$143$	3.34437	+	0.894004i	0.279670	+	0.0747603i
$144$	0.392232	−	0.226456i	0.0326860	−	0.0188713i
$145$	1.90669	+	0.781458i	0.158342	+	0.0648965i
$146$	−5.16887	−	7.11434i	−0.427779	−	0.588787i
$147$	−10.9669	+	2.12921i	−0.904538	+	0.175614i
$148$	1.69679	+	0.864558i	0.139475	+	0.0710662i
$149$	−2.20279	+	10.3633i	−0.180460	+	0.848996i	0.791005	+	0.611810i	$0.209558\pi$
$149$	−2.20279	+	10.3633i	−0.180460	+	0.848996i	−0.971464	+	0.237186i	$0.923775\pi$
$150$	−5.60033	+	5.68450i	−0.457265	+	0.464138i
$151$	10.3993	+	4.63005i	0.846281	+	0.376788i	0.783616	−	0.621246i	$-0.213373\pi$
$151$	10.3993	+	4.63005i	0.846281	+	0.376788i	0.0626653	+	0.998035i	$0.480040\pi$
$152$	−1.46224	−	0.0766325i	−0.118603	−	0.00621572i
$153$	1.57387	+	1.57387i	0.127240	+	0.127240i
$154$	0.760602	−	8.74194i	0.0612910	−	0.704445i
$155$	20.6976	−	9.96718i	1.66247	−	0.800583i
$156$	−1.11465	−	1.23794i	−0.0892434	−	0.0991148i
$157$	4.52135	−	1.73559i	0.360843	−	0.138515i	−0.171190	−	0.985238i	$-0.554761\pi$
$157$	4.52135	−	1.73559i	0.360843	−	0.138515i	0.532034	+	0.846723i	$0.321428\pi$
$158$	1.52943	+	1.88869i	0.121675	+	0.150256i
$159$	−7.06337	−	1.50137i	−0.560162	−	0.119066i
$160$	2.23550	+	0.0501967i	0.176732	+	0.00396840i
$161$	−11.6432	−	8.15457i	−0.917609	−	0.642670i
$162$	−7.34459	−	1.16327i	−0.577045	−	0.0913950i
$163$	12.3888	+	0.649270i	0.970367	+	0.0508548i	0.530927	−	0.847417i	$-0.321844\pi$
$163$	12.3888	+	0.649270i	0.970367	+	0.0508548i	0.439439	+	0.898272i	$0.355177\pi$
$164$	2.49304	+	4.31807i	0.194674	+	0.337185i
$165$	11.7413	+	1.49419i	0.914056	+	0.116323i
$166$	7.88440	+	4.55206i	0.611948	+	0.353309i
$167$	−4.26522	−	8.37096i	−0.330052	−	0.647764i	0.665030	−	0.746817i	$-0.268419\pi$
$167$	−4.26522	−	8.37096i	−0.330052	−	0.647764i	−0.995082	+	0.0990525i	$0.968419\pi$
$168$	−2.60001	+	3.32710i	−0.200595	+	0.256691i
$169$	−7.00084	+	9.63583i	−0.538526	+	0.741218i
$170$	2.60516	+	10.6757i	0.199807	+	0.818790i
$171$	−0.492832	−	0.443748i	−0.0376878	−	0.0339343i
$172$	−5.62621	+	4.55601i	−0.428994	+	0.347393i
$173$	7.17958	−	8.86605i	0.545854	−	0.674073i	−0.427332	−	0.904095i	$-0.640546\pi$
$173$	7.17958	−	8.86605i	0.545854	−	0.674073i	0.973185	+	0.230022i	$0.0738797\pi$
$174$	−0.454482	+	1.39875i	−0.0344542	+	0.106039i
$175$	−5.07928	+	12.2148i	−0.383958	+	0.923351i
$176$	−1.95105	−	2.68205i	−0.147066	−	0.202167i
$177$	5.29049	−	1.41758i	0.397657	−	0.106552i
$178$	−6.98572	−	4.53658i	−0.523602	−	0.340031i
$179$	7.80432	−	17.5288i	0.583322	−	1.31016i	−0.345075	−	0.938575i	$-0.612147\pi$
$179$	7.80432	−	17.5288i	0.583322	−	1.31016i	0.928398	−	0.371589i	$-0.121187\pi$
$180$	0.772541	+	0.654845i	0.0575818	+	0.0488093i
$181$	−22.9915	+	7.47038i	−1.70894	+	0.555269i	−0.990157	−	0.139962i	$-0.955302\pi$
$181$	−22.9915	+	7.47038i	−1.70894	+	0.555269i	−0.718786	+	0.695232i	$0.755302\pi$
$182$	−2.48194	−	1.21087i	−0.183973	−	0.0897553i
$183$	−12.1347	+	1.92194i	−0.897019	+	0.142074i
$184$	−5.34325	+	0.561598i	−0.393910	+	0.0414016i
$185$	−0.540066	+	4.22387i	−0.0397064	+	0.310545i
$186$	8.19815	+	14.1996i	0.601117	+	1.04117i
$187$	10.2500	−	12.6730i	0.749553	−	0.926740i
$188$	7.86646	+	7.86646i	0.573721	+	0.573721i
$189$	−14.2066	+	3.27819i	−1.03338	+	0.238453i
$190$	−0.941609	−	3.13583i	−0.0683115	−	0.227497i
$191$	18.7359	−	8.34176i	1.35568	−	0.603588i	0.405160	−	0.914246i	$-0.367216\pi$
$191$	18.7359	−	8.34176i	1.35568	−	0.603588i	0.950522	+	0.310658i	$0.100549\pi$
$192$	0.0835261	+	1.59377i	0.00602798	+	0.115021i
$193$	−0.0673314	−	1.28476i	−0.00484662	−	0.0924790i	0.995135	−	0.0985193i	$-0.0314106\pi$
$193$	−0.0673314	−	1.28476i	−0.00484662	−	0.0924790i	−0.999982	+	0.00604034i	$0.998077\pi$
$194$	1.19199	−	0.530707i	0.0855797	−	0.0381025i
$195$	1.76514	−	3.28010i	0.126404	−	0.234893i
$196$	−1.93097	+	6.72840i	−0.137926	+	0.480600i
$197$	−11.7303	−	11.7303i	−0.835749	−	0.835749i	0.152548	−	0.988296i	$-0.451252\pi$
$197$	−11.7303	−	11.7303i	−0.835749	−	0.835749i	−0.988296	+	0.152548i	$0.951252\pi$
$198$	0.0777294	−	1.50012i	0.00552399	−	0.106609i
$199$	−0.327870	−	0.567887i	−0.0232421	−	0.0402564i	0.854170	−	0.519993i	$-0.174066\pi$
$199$	−0.327870	−	0.567887i	−0.0232421	−	0.0402564i	−0.877412	+	0.479737i	$0.840732\pi$
$200$	1.58051	+	4.74363i	0.111759	+	0.335425i
$201$	3.97820	−	0.418125i	0.280600	−	0.0294923i
$202$	−9.50847	+	1.50599i	−0.669014	+	0.105961i
$203$	0.169805	+	2.43223i	0.0119180	+	0.170709i
$204$	−7.45934	+	2.42369i	−0.522259	+	0.169692i
$205$	−7.20917	+	8.50487i	−0.503510	+	0.594006i
$206$	−0.433503	+	0.973664i	−0.0302036	+	0.0678384i
$207$	−2.04078	−	1.32530i	−0.141844	−	0.0921144i
$208$	−1.00821	+	0.270148i	−0.0699065	+	0.0187314i
$209$	−2.85216	+	3.93055i	−0.197288	+	0.271882i
$210$	−8.96469	−	2.96353i	−0.618622	−	0.204503i
$211$	5.63475	−	17.3420i	0.387912	−	1.19387i	−0.546434	−	0.837502i	$-0.684015\pi$
$211$	5.63475	−	17.3420i	0.387912	−	1.19387i	0.934346	−	0.356368i	$-0.115985\pi$
$212$	−2.84746	+	3.51632i	−0.195564	+	0.241502i
$213$	7.07254	−	5.72723i	0.484602	−	0.392423i
$214$	13.6801	+	12.3176i	0.935149	+	0.842012i
$215$	−13.8341	−	8.40677i	−0.943481	−	0.573337i
$216$	−3.23911	+	4.45826i	−0.220394	+	0.303346i
$217$	21.4174	+	16.7370i	1.45391	+	1.13618i
$218$	2.07002	+	4.06263i	0.140199	+	0.275156i
$219$	12.1543	+	7.01728i	0.821311	+	0.474184i
$220$	4.17414	−	6.12997i	0.281420	−	0.413283i
$221$	−2.56477	−	4.44230i	−0.172525	−	0.298822i
$222$	−3.03510	−	0.159063i	−0.203703	−	0.0106756i
$223$	16.8094	+	2.66235i	1.12564	+	0.178284i	0.691371	−	0.722500i	$-0.257007\pi$
$223$	16.8094	+	2.66235i	1.12564	+	0.178284i	0.434269	+	0.900783i	$0.357007\pi$
$224$	1.11787	+	2.39799i	0.0746911	+	0.160222i
$225$	−0.795752	+	2.12014i	−0.0530502	+	0.141343i
$226$	7.43838	+	1.58108i	0.494793	+	0.105172i
$227$	−5.09688	−	6.29412i	−0.338292	−	0.417756i	0.579403	−	0.815041i	$-0.303286\pi$
$227$	−5.09688	−	6.29412i	−0.338292	−	0.417756i	−0.917695	+	0.397285i	$0.869952\pi$
$228$	2.18166	−	0.837460i	0.144484	−	0.0554622i
$229$	17.8207	+	19.7919i	1.17762	+	1.30788i	0.941833	+	0.336080i	$0.109101\pi$
$229$	17.8207	+	19.7919i	1.17762	+	1.30788i	0.235791	+	0.971804i	$0.424232\pi$
$230$	−5.21243	−	10.8240i	−0.343697	−	0.713714i
$231$	4.56576	+	13.2393i	0.300405	+	0.871084i
$232$	0.651624	+	0.651624i	0.0427812	+	0.0427812i
$233$	−18.2937	−	0.958733i	−1.19846	−	0.0628087i	−0.557364	−	0.830269i	$-0.688187\pi$
$233$	−18.2937	−	0.958733i	−1.19846	−	0.0628087i	−0.641097	+	0.767460i	$0.721520\pi$
$234$	−0.431865	−	0.192279i	−0.0282319	−	0.0125697i
$235$	−10.6256	+	22.4924i	−0.693135	+	1.46724i
$236$	0.713524	−	3.35687i	0.0464465	−	0.218514i
$237$	−3.45591	−	1.76087i	−0.224485	−	0.114381i
$238$	−9.96130	+	8.35662i	−0.645695	+	0.541680i
$239$	−9.14792	−	12.5910i	−0.591730	−	0.814446i	0.403190	−	0.915116i	$-0.367901\pi$
$239$	−9.14792	−	12.5910i	−0.591730	−	0.814446i	−0.994920	+	0.100670i	$0.967901\pi$
$240$	−3.29191	+	1.37796i	−0.212492	+	0.0889469i
$241$	16.8410	−	9.72316i	1.08482	−	0.626324i	0.152631	−	0.988283i	$-0.451225\pi$
$241$	16.8410	−	9.72316i	1.08482	−	0.626324i	0.932194	+	0.361960i	$0.117892\pi$
$242$	−10.9842	+	0.588675i	−0.706093	+	0.0378415i
$243$	−4.50541	+	1.20722i	−0.289022	+	0.0774433i
$244$	−2.37885	+	7.32136i	−0.152290	+	0.468702i
$245$	−15.6198	+	1.01032i	−0.997915	+	0.0645473i
$246$	−6.43782	−	4.67735i	−0.410460	−	0.298217i
$247$	0.832391	+	1.28177i	0.0529637	+	0.0815570i
$248$	10.2595	−	0.537680i	0.651482	−	0.0341427i
$249$	−14.4502	−	1.51878i	−0.915746	−	0.0962488i
$250$	−8.79326	+	6.90497i	−0.556134	+	0.436709i
$251$	9.44419	+	3.06860i	0.596112	+	0.193688i	0.591505	−	0.806301i	$-0.298534\pi$
$251$	9.44419	+	3.06860i	0.596112	+	0.193688i	0.00460618	+	0.999989i	$0.498534\pi$
$252$	−0.290023	+	1.16266i	−0.0182697	+	0.0732409i
$253$	−8.08035	+	15.8818i	−0.508008	+	0.998479i
$254$	8.09605	+	4.67426i	0.507991	+	0.293289i
$255$	−10.7283	−	13.8739i	−0.671829	−	0.868817i
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	2.02994	−	5.28817i	0.126624	−	0.329867i	−0.855584	−	0.517664i	$-0.826802\pi$
$257$	2.02994	−	5.28817i	0.126624	−	0.329867i	0.982208	+	0.187798i	$0.0601349\pi$
$258$	5.24544	−	10.2948i	0.326567	−	0.640924i
$259$	−4.76412	+	1.63982i	−0.296028	+	0.101894i
$260$	−1.32912	−	1.91852i	−0.0824288	−	0.118982i
$261$	0.0436274	+	0.415087i	0.00270047	+	0.0256932i
$262$	6.05911	−	9.33021i	0.374333	−	0.576422i
$263$	17.0776	+	4.57593i	1.05305	+	0.282164i	0.743512	−	0.668723i	$-0.233159\pi$
$263$	17.0776	+	4.57593i	1.05305	+	0.282164i	0.309539	+	0.950887i	$0.399825\pi$
$264$	4.58561	+	2.64389i	0.282225	+	0.162720i
$265$	−9.54965	−	3.34168i	−0.586630	−	0.205278i
$266$	2.83358	−	2.64176i	0.173738	−	0.161977i
$267$	13.1299	+	2.07957i	0.803537	+	0.127268i
$268$	0.898212	−	2.33992i	0.0548671	−	0.142934i
$269$	8.39865	−	9.32764i	0.512075	−	0.568717i	−0.430552	−	0.902566i	$-0.641681\pi$
$269$	8.39865	−	9.32764i	0.512075	−	0.568717i	0.942626	+	0.333849i	$0.108348\pi$
$270$	−11.8279	−	3.45564i	−0.719820	−	0.210304i
$271$	−8.41953	−	18.9106i	−0.511450	−	1.14874i	−0.966124	−	0.258078i	$-0.916911\pi$
$271$	−8.41953	−	18.9106i	−0.511450	−	1.14874i	0.454674	−	0.890658i	$-0.349756\pi$
$272$	−0.768785	+	4.85392i	−0.0466144	+	0.294312i
$273$	4.40464	+	0.154307i	0.266581	+	0.00933907i
$274$			0.723464i			0.0437060i
$275$	16.0521	+	4.16295i	0.967978	+	0.251035i
$276$	7.42581	−	4.28729i	0.446981	−	0.258065i
$277$	−3.67746	−	2.38817i	−0.220957	−	0.143491i	0.429414	−	0.903108i	$-0.358720\pi$
$277$	−3.67746	−	2.38817i	−0.220957	−	0.143491i	−0.650371	+	0.759616i	$0.725387\pi$
$278$	−7.30367	+	9.01928i	−0.438045	+	0.540940i
$279$	3.76439	+	2.73499i	0.225368	+	0.163739i
$280$	−4.20462	+	4.16187i	−0.251274	+	0.248719i
$281$	3.12517	+	9.61829i	0.186432	+	0.573779i	0.999970	−	0.00773263i	$-0.00246140\pi$
$281$	3.12517	+	9.61829i	0.186432	+	0.573779i	−0.813538	+	0.581512i	$0.802461\pi$
$282$	−16.5756	−	6.36276i	−0.987060	−	0.378897i
$283$	8.00135	+	20.8442i	0.475631	+	1.23906i	0.936210	+	0.351442i	$0.114309\pi$
$283$	8.00135	+	20.8442i	0.475631	+	1.23906i	−0.460579	+	0.887619i	$0.652358\pi$
$284$	−1.18558	−	5.57770i	−0.0703510	−	0.330976i
$285$	3.40842	+	3.96075i	0.201898	+	0.234614i
$286$	−1.06781	+	3.29300i	−0.0631409	+	0.194719i
$287$	−12.7997	−	3.19285i	−0.755543	−	0.188468i
$288$	0.205617	+	0.403547i	0.0121161	+	0.0237792i
$289$	−7.11235	+	0.747538i	−0.418373	+	0.0439728i
$290$	−0.880175	+	1.86318i	−0.0516857	+	0.109409i
$291$	−1.39340	+	1.54752i	−0.0816823	+	0.0907174i
$292$	7.37510	−	4.78945i	0.431595	−	0.280281i
$293$	0.956585	+	6.03964i	0.0558843	+	0.352840i	0.999747	+	0.0225011i	$0.00716293\pi$
$293$	0.956585	+	6.03964i	0.0558843	+	0.352840i	−0.943863	+	0.330339i	$0.892837\pi$
$294$	−1.55233	−	11.0633i	−0.0905336	−	0.645227i
$295$	7.60444	−	1.03001i	0.442748	−	0.0599695i
$296$	−0.952176	+	1.64922i	−0.0553441	+	0.0958588i
$297$	6.55995	+	17.0591i	0.380647	+	0.989871i
$298$	−10.2338	−	2.74215i	−0.592830	−	0.158848i
$299$	3.75239	+	4.16745i	0.217006	+	0.241010i
$300$	−5.38361	−	5.89016i	−0.310823	−	0.340068i
$301$	1.67153	−	19.0810i	0.0963452	−	1.09981i
$302$	−5.16796	+	10.1427i	−0.297383	+	0.583647i
$303$	12.8856	−	8.36800i	0.740258	−	0.480729i
$304$	0.153055	−	1.45622i	0.00877831	−	0.0835200i
$305$	−17.2058	+	0.514769i	−0.985204	+	0.0294756i
$306$	−1.65409	+	1.48935i	−0.0945579	+	0.0851403i
$307$	18.1202	−	18.1202i	1.03418	−	1.03418i	0.0347821	−	0.999395i	$-0.488926\pi$
$307$	18.1202	−	18.1202i	1.03418	−	1.03418i	0.999395	−	0.0347821i	$-0.0110737\pi$
$308$	8.69015	+	1.21708i	0.495167	+	0.0693494i
$309$		−	1.70099i		−	0.0967658i
$310$	8.87029	+	21.1909i	0.503799	+	1.20356i
$311$	−2.46196	+	5.52966i	−0.139605	+	0.313558i	−0.969795	−	0.243923i	$-0.921566\pi$
$311$	−2.46196	+	5.52966i	−0.139605	+	0.313558i	0.830189	+	0.557481i	$0.188232\pi$
$312$	1.29458	−	1.04833i	0.0732914	−	0.0593502i
$313$	3.17585	+	4.89039i	0.179510	+	0.276421i	0.916959	−	0.398982i	$-0.130636\pi$
$313$	3.17585	+	4.89039i	0.179510	+	0.276421i	−0.737449	+	0.675403i	$0.763970\pi$
$314$	1.49658	+	4.60599i	0.0844568	+	0.259931i
$315$	−2.66618	+	0.266461i	−0.150222	+	0.0150134i
$316$	−1.96615	+	1.42849i	−0.110605	+	0.0803590i
$317$	0.806725	−	15.3932i	0.0453102	−	0.864570i	−0.877562	−	0.479463i	$-0.840831\pi$
$317$	0.806725	−	15.3932i	0.0453102	−	0.864570i	0.922872	−	0.385107i	$-0.125835\pi$
$318$	1.86898	−	6.97512i	0.104807	−	0.391145i
$319$	2.98922	−	0.637225i	0.167364	−	0.0356777i
$320$	−0.167125	+	2.22981i	−0.00934258	+	0.124650i
$321$	−27.9411	−	9.07860i	−1.55952	−	0.506718i
$322$	8.75275	−	11.2004i	0.487772	−	0.624175i
$323$	7.10731	−	1.12569i	0.395461	−	0.0626349i
$324$	1.54606	−	7.27364i	0.0858922	−	0.404091i
$325$	3.03599	−	4.24491i	0.168406	−	0.235465i
$326$	−1.29676	+	12.3379i	−0.0718209	+	0.683330i
$327$	−5.65525	−	4.57953i	−0.312736	−	0.253248i
$328$	−4.44263	+	2.26363i	−0.245303	+	0.124988i
$329$	−29.4292	+	0.510394i	−1.62248	+	0.0281390i
$330$	−2.10663	+	11.6470i	−0.115966	+	0.641145i
$331$	17.2739	−	29.9192i	0.949458	−	1.64451i	0.202889	−	0.979202i	$-0.434967\pi$
$331$	17.2739	−	29.9192i	0.949458	−	1.64451i	0.746569	−	0.665308i	$-0.231700\pi$
$332$	−4.95846	+	7.63536i	−0.272131	+	0.419045i
$333$	−0.805215	+	0.309093i	−0.0441255	+	0.0169382i
$334$	8.58271	−	3.82127i	0.469625	−	0.209091i
$335$	5.60306	+	0.125813i	0.306128	+	0.00687389i
$336$	−3.18646	−	2.77057i	−0.173836	−	0.151147i
$337$	1.46158	+	9.22805i	0.0796173	+	0.502684i	0.994982	+	0.100057i	$0.0319026\pi$
$337$	1.46158	+	9.22805i	0.0796173	+	0.502684i	−0.915364	+	0.402626i	$0.868097\pi$
$338$	−9.25623	−	7.49555i	−0.503472	−	0.407704i
$339$	−11.8714	+	2.52333i	−0.644763	+	0.137049i
$340$	−10.7974	+	2.04286i	−0.585572	+	0.110790i
$341$	17.0194	−	29.5188i	0.921654	−	1.59853i
$342$	0.468933	−	0.468933i	0.0253570	−	0.0253570i
$343$	−9.25475	−	16.0421i	−0.499709	−	0.866193i
$344$	−4.25532	−	5.85694i	−0.229431	−	0.315785i
$345$	14.6259	+	12.3976i	0.787431	+	0.667467i
$346$	8.47815	+	7.63376i	0.455788	+	0.410393i
$347$	−33.0449	+	1.73181i	−1.77394	+	0.0929685i	−0.911020	−	0.412363i	$-0.864704\pi$
$347$	−33.0449	+	1.73181i	−1.77394	+	0.0929685i	−0.862925	+	0.505332i	$0.831370\pi$
$348$	−1.37305	−	0.527064i	−0.0736031	−	0.0282536i
$349$	−17.0080	+	12.3571i	−0.910419	+	0.661458i	−0.941121	−	0.338071i	$-0.890226\pi$
$349$	−17.0080	+	12.3571i	−0.910419	+	0.661458i	0.0307021	+	0.999529i	$0.490226\pi$
$350$	−11.9322	−	5.71159i	−0.637804	−	0.305298i
$351$	5.75192			0.307015
$352$	2.78049	−	1.80801i	0.148201	−	0.0963671i
$353$	7.65553	−	28.5708i	0.407463	−	1.52067i	−0.392005	−	0.919963i	$-0.628218\pi$
$353$	7.65553	−	28.5708i	0.407463	−	1.52067i	0.799468	−	0.600709i	$-0.205115\pi$
$354$	1.13876	+	5.35743i	0.0605242	+	0.284744i
$355$	10.8469	−	6.70275i	0.575693	−	0.355745i
$356$	4.89597	−	6.73872i	0.259486	−	0.357151i
$357$	9.09882	−	18.6500i	0.481560	−	0.987065i
$358$	17.0963	+	8.71101i	0.903569	+	0.460391i
$359$	14.8527	+	33.3598i	0.783898	+	1.76066i	0.636041	+	0.771655i	$0.280571\pi$
$359$	14.8527	+	33.3598i	0.783898	+	1.76066i	0.147857	+	0.989009i	$0.452762\pi$
$360$	−0.694380	+	0.737210i	−0.0365970	+	0.0388544i
$361$	16.4877	−	3.50456i	0.867771	−	0.184450i
$362$	−6.25686	−	23.3509i	−0.328853	−	1.22730i
$363$	15.6327	−	7.98854i	0.820504	−	0.419289i
$364$	1.33910	−	2.41516i	0.0701880	−	0.126589i
$365$	15.6447	+	11.9121i	0.818879	+	0.623510i
$366$	−1.28423	−	12.2186i	−0.0671276	−	0.638677i
$367$	−20.7135	−	25.5790i	−1.08123	−	1.33521i	−0.938433	−	0.345463i	$-0.887722\pi$
$367$	−20.7135	−	25.5790i	−1.08123	−	1.33521i	−0.142802	−	0.989751i	$-0.545611\pi$
$368$	−0.281185	−	5.36532i	−0.0146578	−	0.279687i
$369$	−2.20890	−	0.469517i	−0.114991	−	0.0244421i
$370$	−4.18982	−	0.760386i	−0.217818	−	0.0395306i
$371$	−1.45758	−	11.8820i	−0.0756739	−	0.616885i
$372$	−14.6092	+	7.44376i	−0.757452	+	0.385941i
$373$	−8.23479	−	30.7326i	−0.426381	−	1.59128i	−0.760888	−	0.648883i	$-0.775236\pi$
$373$	−8.23479	−	30.7326i	−0.426381	−	1.59128i	0.334507	−	0.942393i	$-0.391430\pi$
$374$	12.1192	+	10.8992i	0.626668	+	0.563584i
$375$	8.33815	−	15.7753i	0.430580	−	0.814635i
$376$	−8.26738	+	7.44398i	−0.426357	+	0.383894i
$377$	0.150470	−	0.950030i	0.00774960	−	0.0489290i
$378$	−2.53018	−	14.3587i	−0.130138	−	0.738534i
$379$	4.29129	−	1.39433i	0.220429	−	0.0716217i	−0.196721	−	0.980460i	$-0.563029\pi$
$379$	4.29129	−	1.39433i	0.220429	−	0.0716217i	0.417149	+	0.908838i	$0.363029\pi$
$380$	3.18081	−	0.776202i	0.163172	−	0.0398183i
$381$	−14.8381	−	1.55955i	−0.760180	−	0.0798981i
$382$	7.34976	+	19.1468i	0.376047	+	0.979635i
$383$	−0.474731	+	9.05842i	−0.0242576	+	0.462863i	0.959314	+	0.282343i	$0.0911116\pi$
$383$	−0.474731	+	9.05842i	−0.0242576	+	0.462863i	−0.983571	+	0.180521i	$0.942222\pi$
$384$	−1.59596			−0.0814435
$385$	3.99276	+	19.2109i	0.203490	+	0.979077i
$386$	1.28652			0.0654822
$387$	0.171604	−	3.27439i	0.00872310	−	0.166447i
$388$	0.467596	+	1.21813i	0.0237386	+	0.0618411i
$389$	−28.1838	−	2.96224i	−1.42898	−	0.150191i	−0.641777	−	0.766891i	$-0.721803\pi$
$389$	−28.1838	−	2.96224i	−1.42898	−	0.150191i	−0.787198	+	0.616700i	$0.788469\pi$
$390$	3.18322	+	1.93439i	0.161189	+	0.0979515i
$391$	25.1113	−	8.15917i	1.26994	−	0.412627i
$392$	−6.61812	−	2.28046i	−0.334266	−	0.115181i
$393$	−2.77750	+	17.5365i	−0.140106	+	0.884597i
$394$	12.3281	−	11.1003i	0.621082	−	0.559225i
$395$	−4.49000	−	3.06130i	−0.225917	−	0.154031i
$396$	1.49400	+	0.156133i	0.0750763	+	0.00784599i
$397$	−0.236563	−	0.882864i	−0.0118727	−	0.0443097i	0.959735	−	0.280906i	$-0.0906349\pi$
$397$	−0.236563	−	0.882864i	−0.0118727	−	0.0443097i	−0.971608	+	0.236596i	$0.923968\pi$
$398$	0.584268	−	0.297699i	0.0292867	−	0.0149223i
$399$	−2.41644	+	5.69101i	−0.120973	+	0.284907i
$400$	−4.81984	+	1.33008i	−0.240992	+	0.0665041i
$401$	9.33943	+	1.98516i	0.466389	+	0.0991340i	0.435111	−	0.900377i	$-0.356709\pi$
$401$	9.33943	+	1.98516i	0.466389	+	0.0991340i	0.0312777	+	0.999511i	$0.490042\pi$
$402$	0.209350	+	3.99463i	0.0104414	+	0.199234i
$403$	−6.74840	−	8.33358i	−0.336162	−	0.415125i
$404$	−1.00630	−	9.57426i	−0.0500650	−	0.476337i
$405$	16.4773	−	2.23182i	0.818761	−	0.110900i
$406$	−2.43779	+	0.0422789i	−0.120985	+	0.00209827i
$407$	2.87074	+	5.62592i	0.142297	+	0.278867i
$408$	−2.02997	−	7.57597i	−0.100499	−	0.375066i
$409$	27.8232	−	5.91400i	1.37577	−	0.292429i	0.540071	−	0.841619i	$-0.318397\pi$
$409$	27.8232	−	5.91400i	1.37577	−	0.292429i	0.835697	+	0.549191i	$0.185064\pi$
$410$	−8.11592	−	7.64440i	−0.400817	−	0.377530i
$411$	−0.469626	−	1.05480i	−0.0231649	−	0.0520293i
$412$	−0.949642	−	0.483867i	−0.0467855	−	0.0238384i
$413$	5.07655	+	7.52811i	0.249801	+	0.370434i
$414$	1.43029	−	1.96862i	0.0702947	−	0.0967524i
$415$	−19.8125	−	4.67849i	−0.972560	−	0.229658i
$416$	−0.217012	−	1.02096i	−0.0106399	−	0.0500568i
$417$	4.79388	−	17.8910i	0.234757	−	0.876127i
$418$	−3.77589	−	3.05396i	−0.184685	−	0.149374i
$419$	−38.3664			−1.87432			−0.937162	−	0.348896i	$-0.886557\pi$
$419$	−38.3664			−1.87432			−0.937162	+	0.348896i	$0.886557\pi$
$420$	3.42864	−	8.79730i	0.167300	−	0.429264i
$421$	30.6310	−	22.2547i	1.49286	−	1.08463i	0.519744	−	0.854322i	$-0.326027\pi$
$421$	30.6310	−	22.2547i	1.49286	−	1.08463i	0.973118	−	0.230306i	$-0.0739727\pi$
$422$	17.0233	+	6.53463i	0.828681	+	0.318101i
$423$	−5.03166	+	0.263698i	−0.244648	+	0.0128215i
$424$	−3.36248	−	3.02759i	−0.163296	−	0.147033i
$425$	−12.4444	−	21.1878i	−0.603644	−	1.02776i
$426$	5.34923	+	7.36259i	0.259171	+	0.356719i
$427$	−9.55987	−	17.9844i	−0.462635	−	0.870324i
$428$	−13.0167	+	13.0167i	−0.629184	+	0.629184i
$429$	−0.580755	−	5.49428i	−0.0280391	−	0.265267i
$430$	9.11927	−	13.3752i	0.439770	−	0.645010i
$431$	−11.8171	+	2.51179i	−0.569208	+	0.120989i	−0.483520	−	0.875333i	$-0.660642\pi$
$431$	−11.8171	+	2.51179i	−0.569208	+	0.120989i	−0.0856875	+	0.996322i	$0.527309\pi$
$432$	−4.28262	−	3.46800i	−0.206048	−	0.166854i
$433$	2.06873	+	13.0614i	0.0994168	+	0.627693i	0.986206	+	0.165520i	$0.0529301\pi$
$433$	2.06873	+	13.0614i	0.0994168	+	0.627693i	−0.886790	+	0.462173i	$0.847070\pi$
$434$	−17.8349	+	20.5121i	−0.856104	+	0.984613i
$435$	0.0738259	−	3.28783i	0.00353968	−	0.157639i
$436$	−4.16540	+	1.85456i	−0.199487	+	0.0888172i
$437$	−7.34439	+	2.81925i	−0.351330	+	0.134863i
$438$	−7.64377	+	11.7704i	−0.365233	+	0.562410i
$439$	−16.4031	+	28.4110i	−0.782878	+	1.35598i	0.147380	+	0.989080i	$0.452916\pi$
$439$	−16.4031	+	28.4110i	−0.782878	+	1.35598i	−0.930258	+	0.366905i	$0.880417\pi$
$440$	5.90312	+	4.48923i	0.281420	+	0.214016i
$441$	−1.67944	−	2.68901i	−0.0799734	−	0.128048i
$442$	4.57045	−	2.32876i	0.217394	−	0.110768i
$443$	−9.11073	−	7.37772i	−0.432864	−	0.350526i	0.387991	−	0.921663i	$-0.373169\pi$
$443$	−9.11073	−	7.37772i	−0.432864	−	0.350526i	−0.820855	+	0.571137i	$0.806503\pi$
$444$	0.317690	−	3.02262i	0.0150769	−	0.143447i
$445$	17.8780	+	5.22325i	0.847497	+	0.247606i
$446$	−3.53843	+	16.6470i	−0.167550	+	0.788259i
$447$	16.7008	−	2.64514i	0.789919	−	0.125111i
$448$	−2.45321	+	0.990841i	−0.115903	+	0.0468129i
$449$	17.5176	+	5.69182i	0.826708	+	0.268614i	0.691658	−	0.722225i	$-0.256881\pi$
$449$	17.5176	+	5.69182i	0.826708	+	0.268614i	0.135050	+	0.990839i	$0.456881\pi$
$450$	−2.07559	−	0.905621i	−0.0978441	−	0.0426914i
$451$	−1.71886	+	16.4474i	−0.0809382	+	0.774477i
$452$	−1.96820	+	7.34544i	−0.0925765	+	0.345500i
$453$	0.950813	−	18.1426i	0.0446731	−	0.852413i
$454$	6.55225	−	4.76048i	0.307512	−	0.223421i
$455$	6.09400	+	0.997136i	0.285691	+	0.0467465i
$456$	0.722133	+	2.22250i	0.0338170	+	0.104078i
$457$	16.1614	+	24.8864i	0.755999	+	1.16414i	0.981792	+	0.189961i	$0.0608361\pi$
$457$	16.1614	+	24.8864i	0.755999	+	1.16414i	−0.225793	+	0.974175i	$0.572497\pi$
$458$	−20.6974	+	16.7604i	−0.967127	+	0.783164i
$459$	11.0152	−	24.7406i	0.514146	−	1.15479i
$460$	11.0820	−	4.63880i	0.516700	−	0.216285i
$461$		−	8.81091i		−	0.410365i	−0.978724	−	0.205182i	$-0.934221\pi$
$461$		−	8.81091i		−	0.410365i	0.978724	−	0.205182i	$-0.0657788\pi$
$462$	−13.4601	+	3.86661i	−0.626222	+	0.179891i
$463$	−24.8683	+	24.8683i	−1.15573	+	1.15573i	−0.170346	+	0.985384i	$0.554488\pi$
$463$	−24.8683	+	24.8683i	−1.15573	+	1.15573i	−0.985384	+	0.170346i	$0.945512\pi$
$464$	−0.684834	+	0.616627i	−0.0317926	+	0.0286262i
$465$	−26.6885	−	25.1379i	−1.23765	−	1.16574i
$466$	1.91484	−	18.2185i	0.0887031	−	0.843954i
$467$	24.4740	−	15.8936i	1.13252	−	0.735468i	0.164511	−	0.986375i	$-0.447396\pi$
$467$	24.4740	−	15.8936i	1.13252	−	0.735468i	0.968011	+	0.250907i	$0.0807288\pi$
$468$	0.214617	−	0.421210i	0.00992070	−	0.0194705i
$469$	2.80184	+	6.01032i	0.129377	+	0.277531i
$470$	−21.9055	−	11.7882i	−1.01043	−	0.543747i
$471$	−5.17190	−	5.74397i	−0.238308	−	0.264668i
$472$	3.31493	+	0.888231i	0.152582	+	0.0408842i
$473$	−23.9773	+	1.27080i	−1.10248	+	0.0584316i
$474$	1.93933	−	3.35901i	0.0890763	−	0.154285i
$475$	4.03310	+	6.11017i	0.185052	+	0.280354i
$476$	−7.82384	−	10.3850i	−0.358605	−	0.475996i
$477$	−0.320576	−	2.02404i	−0.0146782	−	0.0926743i
$478$	13.0525	−	8.47642i	0.597010	−	0.387703i
$479$	27.5278	−	30.5728i	1.25778	−	1.39691i	0.375063	−	0.926999i	$-0.377621\pi$
$479$	27.5278	−	30.5728i	1.25778	−	1.39691i	0.882716	−	0.469906i	$-0.155712\pi$
$480$	−1.20379	−	3.35952i	−0.0549450	−	0.153340i
$481$	1.97682	−	0.207772i	0.0901352	−	0.00947359i
$482$	8.82844	+	17.3268i	0.402125	+	0.789214i
$483$	−5.49076	+	22.0117i	−0.249838	+	1.00157i
$484$	−0.0129981	−	11.0000i	−0.000590825	−	0.500000i
$485$	−2.21148	+	1.90309i	−0.100418	+	0.0864150i
$486$	−0.969772	−	4.56242i	−0.0439897	−	0.206955i
$487$	1.86017	+	4.84591i	0.0842924	+	0.219589i	0.969248	−	0.246086i	$-0.0791447\pi$
$487$	1.86017	+	4.84591i	0.0842924	+	0.219589i	−0.884955	+	0.465676i	$0.845811\pi$
$488$	−7.18682	−	2.75876i	−0.325332	−	0.124883i
$489$	−6.11828	−	18.8301i	−0.276678	−	0.851528i
$490$	−0.191461	−	15.6513i	−0.00864932	−	0.707054i
$491$	28.0351	+	20.3687i	1.26521	+	0.919227i	0.999001	−	0.0446892i	$-0.0142297\pi$
$491$	28.0351	+	20.3687i	1.26521	+	0.919227i	0.266206	+	0.963916i	$0.414230\pi$
$492$	5.00787	−	6.18420i	0.225772	−	0.278805i
$493$	−3.79818	−	2.46657i	−0.171061	−	0.111089i
$494$	−1.32358	+	0.764167i	−0.0595505	+	0.0343815i
$495$	0.798217	+	3.26265i	0.0358772	+	0.146645i
$496$			10.2736i			0.461299i
$497$	12.7935	+	7.99627i	0.573868	+	0.358682i
$498$	2.27296	−	14.3509i	0.101854	−	0.643081i
$499$	2.75035	+	6.17738i	0.123122	+	0.276537i	0.964582	−	0.263782i	$-0.0849700\pi$
$499$	2.75035	+	6.17738i	0.123122	+	0.276537i	−0.841460	+	0.540320i	$0.818303\pi$
$500$	−6.43530	−	9.14258i	−0.287796	−	0.408869i
$501$	−10.0329	+	11.1427i	−0.448238	+	0.497818i
$502$	−3.55867	+	9.27064i	−0.158831	+	0.413769i
$503$	41.9732	+	6.64790i	1.87149	+	0.296415i	0.985809	−	0.167873i	$-0.0536900\pi$
$503$	41.9732	+	6.64790i	1.87149	+	0.296415i	0.885684	+	0.464289i	$0.153690\pi$
$504$	−1.14589	−	0.350474i	−0.0510420	−	0.0156114i
$505$	19.3949	−	9.33984i	0.863062	−	0.415618i
$506$	−15.4371	−	8.90047i	−0.686264	−	0.395674i
$507$	18.3610	+	4.91983i	0.815443	+	0.218497i
$508$	−5.09157	+	7.84032i	−0.225902	+	0.347858i
$509$	1.04960	+	9.98628i	0.0465227	+	0.442634i	0.992845	+	0.119410i	$0.0381002\pi$
$509$	1.04960	+	9.98628i	0.0465227	+	0.442634i	−0.946322	+	0.323224i	$0.895233\pi$
$510$	14.4164	−	9.98745i	0.638367	−	0.442252i
$511$	−4.44196	+	22.8383i	−0.196501	+	1.01030i
$512$	−0.453990	+	0.891007i	−0.0200637	+	0.0393773i
$513$	−2.89168	+	7.53307i	−0.127671	+	0.332593i
$514$	5.17468	+	2.30392i	0.228245	+	0.101621i
$515$	0.302259	−	2.36398i	0.0133191	−	0.104169i
$516$	10.0061	+	5.77704i	0.440495	+	0.254320i
$517$	5.79349	+	36.4393i	0.254797	+	1.60260i
$518$	−1.38824	−	4.84342i	−0.0609958	−	0.212807i
$519$	−17.3163	−	5.62642i	−0.760103	−	0.246972i
$520$	1.98545	−	1.22690i	0.0870679	−	0.0538029i
$521$	−30.5283	−	3.20866i	−1.33747	−	0.140574i	−0.591366	−	0.806403i	$-0.701411\pi$
$521$	−30.5283	−	3.20866i	−1.33747	−	0.140574i	−0.746104	+	0.665829i	$0.768078\pi$
$522$	−0.416801	+	0.0218436i	−0.0182429	+	0.000956070i
$523$	13.0040	+	20.0245i	0.568627	+	0.875608i	0.999643	−	0.0267361i	$-0.00851139\pi$
$523$	13.0040	+	20.0245i	0.568627	+	0.875608i	−0.431016	+	0.902344i	$0.641845\pi$
$524$	9.00031	+	6.53911i	0.393180	+	0.285662i
$525$	21.1046	+	0.581781i	0.921078	+	0.0253910i
$526$	−5.46344	+	16.8147i	−0.238217	+	0.733157i
$527$	−48.7685	+	13.0675i	−2.12439	+	0.569229i
$528$	−2.88026	+	4.44095i	−0.125347	+	0.193268i
$529$	−5.07987	+	2.93286i	−0.220864	+	0.127516i
$530$	3.83689	−	9.36167i	0.166664	−	0.406645i
$531$	0.913611	+	1.25748i	0.0396474	+	0.0545699i
$532$	2.48984	+	2.96795i	0.107948	+	0.128677i
$533$	4.63709	+	2.36271i	0.200855	+	0.102341i
$534$	−2.76389	+	13.0031i	−0.119605	+	0.562698i
$535$	−37.2183	−	17.5821i	−1.60909	−	0.760142i
$536$	2.28971	+	1.01944i	0.0989003	+	0.0440333i
$537$	−30.5808	−	1.60267i	−1.31966	−	0.0691603i
$538$	8.87531	+	8.87531i	0.382642	+	0.382642i
$539$	−18.2895	+	14.3001i	−0.787785	+	0.615951i
$540$	4.06993	−	11.6308i	0.175142	−	0.500509i
$541$	−19.7752	−	21.9626i	−0.850202	−	0.944245i	0.148802	−	0.988867i	$-0.452458\pi$
$541$	−19.7752	−	21.9626i	−0.850202	−	0.944245i	−0.999004	+	0.0446216i	$0.985792\pi$
$542$	19.3253	−	7.41829i	0.830093	−	0.318643i
$543$	24.2803	+	29.9837i	1.04197	+	1.28672i
$544$	−4.80703	−	1.02177i	−0.206100	−	0.0438078i
$545$	−7.04571	−	7.36939i	−0.301805	−	0.315670i
$546$	−0.384616	+	4.39053i	−0.0164601	+	0.187897i
$547$	8.11698	+	1.28560i	0.347057	+	0.0549684i	0.327530	−	0.944841i	$-0.393784\pi$
$547$	8.11698	+	1.28560i	0.347057	+	0.0549684i	0.0195274	+	0.999809i	$0.493784\pi$
$548$	−0.722472	−	0.0378632i	−0.0308625	−	0.00161743i
$549$	−1.74328	−	3.01946i	−0.0744016	−	0.128867i
$550$	−4.99735	+	15.8122i	−0.213088	+	0.674236i
$551$	1.16857	+	0.674675i	0.0497828	+	0.0287421i
$552$	3.89278	+	7.64001i	0.165688	+	0.325181i
$553$	0.895590	−	6.36728i	0.0380843	−	0.270764i
$554$	2.57736	−	3.54743i	0.109502	−	0.150716i
$555$	6.60228	−	1.61113i	0.280251	−	0.0683887i
$556$	−8.62467	−	7.76569i	−0.365768	−	0.329339i
$557$	5.96667	−	4.83171i	0.252816	−	0.204726i	−0.494532	−	0.869160i	$-0.664660\pi$
$557$	5.96667	−	4.83171i	0.252816	−	0.204726i	0.747347	+	0.664433i	$0.231327\pi$
$558$	−2.92825	+	3.61609i	−0.123963	+	0.153081i
$559$	−2.33508	+	7.18662i	−0.0987632	+	0.303962i
$560$	−3.93612	−	4.41667i	−0.166331	−	0.186638i
$561$	−24.7446	−	8.02385i	−1.04472	−	0.338767i
$562$	−9.76867	+	2.61751i	−0.412066	+	0.110413i
$563$	−35.9259	−	23.3305i	−1.51409	−	0.983264i	−0.991418	−	0.130734i	$-0.958267\pi$
$563$	−35.9259	−	23.3305i	−1.51409	−	0.983264i	−0.522677	−	0.852531i	$-0.675067\pi$
$564$	7.22154	−	16.2198i	0.304082	−	0.682978i
$565$	−16.9468	+	1.39735i	−0.712957	+	0.0587871i
$566$	−21.2344	+	6.89948i	−0.892550	+	0.290007i
$567$	10.9998	+	16.3119i	0.461950	+	0.685034i
$568$	5.63210	−	0.892038i	0.236318	−	0.0374291i
$569$	0.393237	−	0.0413309i	0.0164853	−	0.00173268i	−0.0962822	−	0.995354i	$-0.530695\pi$
$569$	0.393237	−	0.0413309i	0.0164853	−	0.00173268i	0.112768	+	0.993621i	$0.464028\pi$
$570$	−4.13370	+	3.19646i	−0.173142	+	0.133885i
$571$	0.0383424	+	0.0664110i	0.00160458	+	0.00277921i	0.866827	−	0.498610i	$-0.166156\pi$
$571$	0.0383424	+	0.0664110i	0.00160458	+	0.00277921i	−0.865222	+	0.501389i	$0.832823\pi$
$572$	−3.23260	−	1.23869i	−0.135162	−	0.0517921i
$573$	−23.1447	−	23.1447i	−0.966883	−	0.966883i
$574$	3.85836	−	12.6151i	0.161045	−	0.526543i
$575$	18.1235	+	19.8288i	0.755804	+	0.826917i
$576$	−0.413755	+	0.184216i	−0.0172398	+	0.00767565i
$577$	2.36555	+	45.1374i	0.0984792	+	1.87909i	0.387636	+	0.921813i	$0.373292\pi$
$577$	2.36555	+	45.1374i	0.0984792	+	1.87909i	−0.289157	+	0.957282i	$0.593375\pi$
$578$	−0.374282	−	7.14173i	−0.0155681	−	0.297057i
$579$	−1.87573	+	0.835127i	−0.0779525	+	0.0347067i
$580$	−1.81456	−	0.976480i	−0.0753454	−	0.0405461i
$581$	−5.41583	−	23.4705i	−0.224686	−	0.973720i
$582$	−1.47248	−	1.47248i	−0.0610361	−	0.0610361i
$583$	−14.4930	+	3.89255i	−0.600237	+	0.161213i
$584$	4.39690	+	7.61566i	0.181945	+	0.315138i
$585$	1.04853	+	0.134066i	0.0433515	+	0.00554293i
$586$	−6.08143	+	0.639184i	−0.251222	+	0.0264044i
$587$	−14.0039	+	2.21800i	−0.578002	+	0.0915466i	−0.438589	−	0.898688i	$-0.644522\pi$
$587$	−14.0039	+	2.21800i	−0.578002	+	0.0915466i	−0.139413	+	0.990234i	$0.544522\pi$
$588$	11.1294	−	0.971189i	0.458970	−	0.0400512i
$589$	14.3068	−	4.64857i	0.589502	−	0.191541i
$590$	0.630612	+	7.64792i	0.0259619	+	0.314860i
$591$	−10.7686	+	24.1867i	−0.442961	+	0.994906i
$592$	−1.59712	−	1.03718i	−0.0656414	−	0.0426280i
$593$	19.4635	−	5.21522i	0.799269	−	0.214163i	0.164006	−	0.986459i	$-0.447558\pi$
$593$	19.4635	−	5.21522i	0.799269	−	0.214163i	0.635263	+	0.772296i	$0.280892\pi$
$594$	−17.3791	+	5.65816i	−0.713072	+	0.232157i
$595$	15.9593	−	24.3024i	0.654266	−	0.996300i
$596$	3.27398	−	10.0763i	0.134108	−	0.412741i
$597$	−0.658605	+	0.813310i	−0.0269549	+	0.0332865i
$598$	−4.35812	+	3.52914i	−0.178217	+	0.144317i
$599$	−23.4196	−	21.0871i	−0.956899	−	0.861596i	0.0335551	−	0.999437i	$-0.489317\pi$
$599$	−23.4196	−	21.0871i	−0.956899	−	0.861596i	−0.990454	+	0.137841i	$0.955984\pi$
$600$	6.16384	−	5.06797i	0.251638	−	0.206899i
$601$	−0.442779	+	0.609433i	−0.0180613	+	0.0248593i	−0.817952	−	0.575286i	$-0.804891\pi$
$601$	−0.442779	+	0.609433i	−0.0180613	+	0.0248593i	0.799891	+	0.600146i	$0.204891\pi$
$602$	18.9674	+	2.66786i	0.773054	+	0.108734i
$603$	0.515359	+	1.01145i	0.0209870	+	0.0411894i
$604$	−9.85833	−	5.69171i	−0.401130	−	0.231592i
$605$	23.1453	−	8.32433i	0.940991	−	0.338432i
$606$	7.68215	+	13.3059i	0.312066	+	0.540514i
$607$	−24.5245	−	1.28528i	−0.995419	−	0.0521677i	−0.452337	−	0.891847i	$-0.649410\pi$
$607$	−24.5245	−	1.28528i	−0.995419	−	0.0521677i	−0.543082	+	0.839679i	$0.682743\pi$
$608$	1.44622	+	0.229058i	0.0586518	+	0.00928953i
$609$	3.52680	−	1.64410i	0.142913	−	0.0666221i
$610$	0.386421	−	17.2092i	0.0156457	−	0.696780i
$611$	11.3581	+	2.41423i	0.459498	+	0.0976693i
$612$	−1.40074	−	1.72977i	−0.0566215	−	0.0699217i
$613$	−30.6200	+	11.7539i	−1.23673	+	0.474736i	−0.886849	−	0.462059i	$-0.847111\pi$
$613$	−30.6200	+	11.7539i	−1.23673	+	0.474736i	−0.349880	+	0.936795i	$0.613778\pi$
$614$	17.1471	+	19.0438i	0.692000	+	0.768543i
$615$	16.7951	+	5.87706i	0.677244	+	0.236986i
$616$	−1.67022	+	8.61454i	−0.0672949	+	0.347090i
$617$	6.63131	+	6.63131i	0.266966	+	0.266966i	0.827877	−	0.560910i	$-0.189549\pi$
$617$	6.63131	+	6.63131i	0.266966	+	0.266966i	−0.560910	+	0.827877i	$0.689549\pi$
$618$	1.69866	+	0.0890228i	0.0683300	+	0.00358102i
$619$	17.3231	+	7.71273i	0.696273	+	0.310001i	0.724181	−	0.689610i	$-0.242218\pi$
$619$	17.3231	+	7.71273i	0.696273	+	0.310001i	−0.0279083	+	0.999610i	$0.508885\pi$
$620$	−21.6261	+	7.74909i	−0.868525	+	0.311211i
$621$	−6.15570	+	28.9603i	−0.247020	+	1.16214i
$622$	−5.39324	−	2.74799i	−0.216249	−	0.110184i
$623$	3.82440	+	21.7034i	0.153221	+	0.869530i
$624$	0.979143	+	1.34767i	0.0391971	+	0.0539502i
$625$	14.3913	−	20.4424i	0.575652	−	0.817695i
$626$	−5.04989	+	2.91556i	−0.201834	+	0.116529i
$627$	7.48762	+	2.00156i	0.299027	+	0.0799346i
$628$	−4.67800	+	1.25347i	−0.186673	+	0.0500188i
$629$	2.89202	−	8.90073i	0.115313	−	0.354895i
$630$	−0.126559	−	2.67647i	−0.00504224	−	0.106633i
$631$	−10.3967	−	7.55364i	−0.413886	−	0.300705i	0.361287	−	0.932455i	$-0.382337\pi$
$631$	−10.3967	−	7.55364i	−0.413886	−	0.300705i	−0.775173	+	0.631749i	$0.782337\pi$
$632$	−1.32363	−	2.03822i	−0.0526513	−	0.0810759i
$633$	−29.0615	+	1.52305i	−1.15509	+	0.0605358i
$634$	15.3299	+	1.61124i	0.608829	+	0.0639905i
$635$	−20.3444	−	4.80408i	−0.807343	−	0.190644i
$636$	6.86774	+	2.23146i	0.272324	+	0.0884833i
$637$	2.13462	+	6.98762i	0.0845768	+	0.276860i
$638$	0.479908	+	3.01847i	0.0189997	+	0.119503i
$639$	2.23663	+	1.29132i	0.0884797	+	0.0510838i
$640$	−2.21801	−	0.283596i	−0.0876746	−	0.0112101i
$641$	9.02923	+	4.02007i	0.356633	+	0.158783i	0.577230	−	0.816582i	$-0.304134\pi$
$641$	9.02923	+	4.02007i	0.356633	+	0.158783i	−0.220597	+	0.975365i	$0.570800\pi$
$642$	10.5285	−	27.4276i	0.415526	−	1.08248i
$643$	−9.33470	+	18.3204i	−0.368124	+	0.722485i	−0.998554	−	0.0537617i	$-0.982879\pi$
$643$	−9.33470	+	18.3204i	−0.368124	+	0.722485i	0.630429	+	0.776247i	$0.282879\pi$
$644$	10.7270	+	9.32694i	0.422703	+	0.367533i
$645$	−4.61341	+	25.4205i	−0.181653	+	1.00093i
$646$	0.752177	+	7.15648i	0.0295940	+	0.281568i
$647$	−21.7040	+	33.4212i	−0.853270	+	1.31392i	0.0946816	+	0.995508i	$0.469817\pi$
$647$	−21.7040	+	33.4212i	−0.853270	+	1.31392i	−0.947952	+	0.318414i	$0.896850\pi$
$648$	7.18276	+	1.92461i	0.282165	+	0.0756060i
$649$	8.45412	−	7.62118i	0.331853	−	0.299157i
$650$	4.08020	+	3.25399i	0.160039	+	0.127632i
$651$	12.6879	−	41.4836i	0.497277	−	1.62587i
$652$	−12.2531	−	1.94070i	−0.479868	−	0.0760035i
$653$	−15.1897	+	39.5705i	−0.594418	+	1.54851i	0.224423	+	0.974492i	$0.427950\pi$
$653$	−15.1897	+	39.5705i	−0.594418	+	1.54851i	−0.818841	+	0.574021i	$0.805383\pi$
$654$	4.86923	−	5.40782i	0.190402	−	0.211463i
$655$	−6.97623	+	23.8780i	−0.272584	+	0.932991i
$656$	−2.02802	−	4.55501i	−0.0791809	−	0.177843i
$657$	−0.623049	+	3.93378i	−0.0243074	+	0.153471i
$658$	1.03051	−	29.4156i	0.0401734	−	1.14674i
$659$			41.3001i			1.60882i	0.594073	+	0.804411i	$0.297519\pi$
$659$			41.3001i			1.60882i	−0.594073	+	0.804411i	$0.702481\pi$
$660$	−11.5208	−	2.71330i	−0.448445	−	0.105615i
$661$	−18.2894	+	10.5594i	−0.711375	+	0.410712i	−0.811570	−	0.584255i	$-0.801387\pi$
$661$	−18.2894	+	10.5594i	−0.711375	+	0.410712i	0.100195	+	0.994968i	$0.468053\pi$
$662$	28.9742	+	18.8161i	1.12611	+	0.731307i
$663$	−5.15195	+	6.36213i	−0.200085	+	0.247085i
$664$	−7.36539	−	5.35127i	−0.285833	−	0.207670i
$665$	−4.36956	+	7.47978i	−0.169444	+	0.290054i
$666$	−0.266528	−	0.820288i	−0.0103277	−	0.0317855i
$667$	4.62226	+	1.77432i	0.178975	+	0.0687020i
$668$	3.36685	+	8.77094i	0.130267	+	0.339358i
$669$	−5.64720	−	26.5680i	−0.218333	−	1.02718i
$670$	−0.418882	+	5.58880i	−0.0161828	+	0.215914i
$671$	−20.6468	+	15.0194i	−0.797061	+	0.579818i
$672$	2.93354	−	3.03709i	0.113164	−	0.117158i
$673$	−7.84874	−	15.4040i	−0.302547	−	0.593782i	0.688815	−	0.724937i	$-0.258131\pi$
$673$	−7.84874	−	15.4040i	−0.302547	−	0.593782i	−0.991362	+	0.131156i	$0.958131\pi$
$674$	−9.29189	+	0.976617i	−0.357910	+	0.0376179i
$675$	27.5528	−	0.205515i	1.06051	−	0.00791028i
$676$	7.96971	−	8.85126i	0.306527	−	0.340433i
$677$	−33.6789	+	21.8714i	−1.29439	+	0.840585i	−0.993583	−	0.113102i	$-0.963921\pi$
$677$	−33.6789	+	21.8714i	−1.29439	+	0.840585i	−0.300803	+	0.953686i	$0.597255\pi$
$678$	−1.89858	−	11.9871i	−0.0729144	−	0.460364i
$679$	−3.17758	−	1.34922i	−0.121944	−	0.0517783i
$680$	−1.47497	−	10.8895i	−0.0565626	−	0.417595i
$681$	−6.46286	+	11.1940i	−0.247657	+	0.428955i
$682$	28.5876	+	18.5410i	1.09468	+	0.709972i
$683$	32.4993	+	8.70817i	1.24355	+	0.333209i	0.819842	−	0.572589i	$-0.194061\pi$
$683$	32.4993	+	8.70817i	1.24355	+	0.333209i	0.423709	+	0.905798i	$0.360728\pi$
$684$	0.443748	+	0.492832i	0.0169671	+	0.0188439i
$685$	−0.465237	−	1.54937i	−0.0177758	−	0.0591984i
$686$	16.5045	−	8.40248i	0.630144	−	0.320808i
$687$	19.2967	−	37.8718i	0.736214	−	1.44490i
$688$	6.07162	−	3.94296i	0.231478	−	0.150324i
$689$	−0.493657	+	4.69684i	−0.0188068	+	0.178935i
$690$	−13.1461	+	13.9570i	−0.500464	+	0.531334i
$691$	−10.1584	+	9.14666i	−0.386444	+	0.347955i	−0.839339	−	0.543608i	$-0.817058\pi$
$691$	−10.1584	+	9.14666i	−0.386444	+	0.347955i	0.452895	+	0.891564i	$0.350391\pi$
$692$	−8.06701	+	8.06701i	−0.306662	+	0.306662i
$693$	−3.04325	+	2.55607i	−0.115603	+	0.0970972i
$694$		−	33.0903i		−	1.25609i
$695$	9.84153	−	24.0125i	0.373311	−	0.910845i
$696$	0.598201	−	1.34358i	0.0226748	−	0.0509283i
$697$	19.0429	−	15.4207i	0.721303	−	0.584099i
$698$	−11.4500	−	17.6314i	−0.433388	−	0.667360i
$699$	9.03445	+	27.8052i	0.341714	+	1.05169i
$700$	6.32825	−	11.6169i	0.239185	−	0.439079i
$701$	−24.0897	+	17.5022i	−0.909854	+	0.661048i	−0.940978	−	0.338468i	$-0.890091\pi$
$701$	−24.0897	+	17.5022i	−0.909854	+	0.661048i	0.0311237	+	0.999516i	$0.490091\pi$
$702$	−0.301032	+	5.74404i	−0.0113617	+	0.216795i
$703$	−0.721699	+	2.69342i	−0.0272194	+	0.101584i
$704$	1.66001	+	2.87130i	0.0625639	+	0.108216i
$705$	39.5899	+	2.96728i	1.49104	+	0.111754i
$706$	28.1310	+	9.14032i	1.05873	+	0.344001i
$707$	20.0694	+	15.6835i	0.754787	+	0.589840i
$708$	−5.40968	+	0.856810i	−0.203308	+	0.0322009i
$709$	3.61208	−	16.9935i	0.135655	−	0.638205i	−0.856806	−	0.515639i	$-0.827554\pi$
$709$	3.61208	−	16.9935i	0.135655	−	0.638205i	0.992460	−	0.122566i	$-0.0391122\pi$
$710$	6.12588	+	11.1828i	0.229900	+	0.419683i
$711$	0.115055	−	1.09468i	0.00431491	−	0.0410536i
$712$	6.47325	+	5.24193i	0.242595	+	0.196450i
$713$	49.1808	−	25.0589i	1.84184	−	0.938462i
$714$	18.1483	+	10.0624i	0.679183	+	0.376576i
$715$	0.169198	−	7.73897i	0.00632766	−	0.289421i
$716$	−9.59383	+	16.6170i	−0.358538	+	0.621006i
$717$	−13.5280	+	20.8313i	−0.505214	+	0.777961i
$718$	−34.0914	+	13.0865i	−1.27228	+	0.488383i
$719$	12.7489	−	5.67618i	0.475454	−	0.211686i	−0.154997	−	0.987915i	$-0.549537\pi$
$719$	12.7489	−	5.67618i	0.475454	−	0.211686i	0.630451	+	0.776229i	$0.282870\pi$
$720$	−0.699859	−	0.732011i	−0.0260822	−	0.0272804i
$721$	2.66634	−	0.917760i	0.0992996	−	0.0341792i
$722$	2.63686	+	16.6485i	0.0981337	+	0.619592i
$723$	−24.1192	−	19.5313i	−0.897001	−	0.726377i
$724$	23.6464	−	5.02620i	0.878811	−	0.186797i
$725$	0.686835	−	4.55620i	0.0255084	−	0.169213i
$726$	7.15944	+	16.0294i	0.265712	+	0.594905i
$727$	8.56078	−	8.56078i	0.317502	−	0.317502i	−0.530305	−	0.847807i	$-0.677923\pi$
$727$	8.56078	−	8.56078i	0.317502	−	0.317502i	0.847807	+	0.530305i	$0.177923\pi$
$728$	2.34177	+	1.46367i	0.0867918	+	0.0542471i
$729$	17.4881	+	24.0703i	0.647707	+	0.891492i
$730$	−12.7146	+	14.9998i	−0.470588	+	0.555167i
$731$	26.4398	+	23.8065i	0.977913	+	0.880517i
$732$	12.2691	−	0.642995i	0.453478	−	0.0237658i
$733$	42.9906	+	16.5025i	1.58789	+	0.609535i	0.982479	−	0.186374i	$-0.0596737\pi$
$733$	42.9906	+	16.5025i	1.58789	+	0.609535i	0.605415	+	0.795910i	$0.293007\pi$
$734$	26.6280	−	19.3464i	0.982858	−	0.714088i
$735$	10.4390	+	22.6950i	0.385047	+	0.837119i
$736$	5.37268			0.198040
$737$	6.96901	−	4.53158i	0.256707	−	0.166923i
$738$	0.584478	−	2.18130i	0.0215149	−	0.0802948i
$739$	−3.91406	−	18.4142i	−0.143981	−	0.677377i	−0.989630	−	0.143638i	$-0.954120\pi$
$739$	−3.91406	−	18.4142i	−0.143981	−	0.677377i	0.845649	−	0.533739i	$-0.179214\pi$
$740$	0.978622	−	4.14428i	0.0359749	−	0.152347i
$741$	1.43370	−	1.97332i	0.0526684	−	0.0724918i
$742$	11.9420	−	0.833727i	0.438406	−	0.0306071i
$743$	18.8182	+	9.58836i	0.690374	+	0.351763i	0.763724	−	0.645543i	$-0.223369\pi$
$743$	18.8182	+	9.58836i	0.690374	+	0.351763i	−0.0733500	+	0.997306i	$0.523369\pi$
$744$	−6.66897	−	14.9788i	−0.244496	−	0.549148i
$745$	23.6802	−	0.708470i	0.867575	−	0.0259563i
$746$	31.1215	−	6.61508i	1.13944	−	0.242195i
$747$	−1.06720	−	3.98286i	−0.0390469	−	0.145725i
$748$	−11.5185	+	11.5321i	−0.421159	+	0.421657i
$749$	−0.844551	−	48.6965i	−0.0308592	−	1.77933i
$750$	15.3173	+	9.15234i	0.559310	+	0.334196i
$751$	2.61102	+	24.8422i	0.0952774	+	0.906504i	0.932871	+	0.360210i	$0.117295\pi$
$751$	2.61102	+	24.8422i	0.0952774	+	0.906504i	−0.837594	+	0.546294i	$0.816038\pi$
$752$	−7.00110	−	8.64564i	−0.255304	−	0.315274i
$753$	−0.829431	−	15.8265i	−0.0302262	−	0.576749i
$754$	0.940853	+	0.199984i	0.0342638	+	0.00728300i
$755$	4.54527	−	25.0450i	0.165419	−	0.911481i
$756$	14.4715	−	1.77523i	0.526323	−	0.0645645i
$757$	−29.4112	+	14.9857i	−1.06897	+	0.544666i	−0.897722	−	0.440562i	$-0.854779\pi$
$757$	−29.4112	+	14.9857i	−1.06897	+	0.544666i	−0.171245	+	0.985228i	$0.554779\pi$
$758$	1.16783	+	4.35838i	0.0424173	+	0.158304i
$759$	28.2847	+	2.95594i	1.02667	+	0.107294i
$760$	0.608668	+	3.21707i	0.0220787	+	0.116695i
$761$	1.70826	−	1.53812i	0.0619243	−	0.0557569i	−0.637587	−	0.770378i	$-0.720068\pi$
$761$	1.70826	−	1.53812i	0.0619243	−	0.0557569i	0.699512	+	0.714621i	$0.253401\pi$
$762$	2.33398	−	14.7362i	0.0845512	−	0.533835i
$763$	4.12725	−	11.3356i	0.149417	−	0.410376i
$764$	−19.5052	+	6.33763i	−0.705674	+	0.229287i
$765$	2.58465	−	4.25328i	0.0934481	−	0.153778i
$766$	−9.02116	−	0.948162i	−0.325948	−	0.0342585i
$767$	−1.28370	−	3.34416i	−0.0463518	−	0.120751i
$768$	0.0835261	−	1.59377i	0.00301399	−	0.0575103i
$769$	17.3647			0.626188			0.313094	−	0.949722i	$-0.398635\pi$
$769$	17.3647			0.626188			0.313094	+	0.949722i	$0.398635\pi$
$770$	−19.3935	+	2.98187i	−0.698894	+	0.107459i
$771$	−9.04015			−0.325573
$772$	−0.0673314	+	1.28476i	−0.00242331	+	0.0462395i
$773$	1.67484	+	4.36310i	0.0602397	+	0.156930i	0.960397	−	0.278635i	$-0.0898820\pi$
$773$	1.67484	+	4.36310i	0.0602397	+	0.156930i	−0.900157	+	0.435565i	$0.856549\pi$
$774$	3.26092	+	0.342737i	0.117211	+	0.0123194i
$775$	−32.6239	−	39.6783i	−1.17188	−	1.42529i
$776$	−1.24093	+	0.403203i	−0.0445469	+	0.0144741i
$777$	5.16806	+	6.16046i	0.185403	+	0.221005i
$778$	4.43320	−	27.9901i	0.158938	−	1.00350i
$779$	−5.42557	+	4.88521i	−0.194391	+	0.175031i
$780$	−2.09833	+	3.07762i	−0.0751324	+	0.110196i
$781$	7.68216	−	17.2819i	0.274889	−	0.618395i
$782$	6.83376	+	25.5039i	0.244375	+	0.912019i
$783$	4.52481	−	2.30550i	0.161703	−	0.0823920i
$784$	2.62370	−	6.48970i	0.0937035	−	0.231775i
$785$	−6.16704	−	8.90180i	−0.220111	−	0.317719i
$786$	−17.3671	−	3.69148i	−0.619463	−	0.131671i
$787$	0.384567	+	7.33797i	0.0137083	+	0.261570i	0.996883	+	0.0789000i	$0.0251408\pi$
$787$	0.384567	+	7.33797i	0.0137083	+	0.261570i	−0.983174	+	0.182670i	$0.941526\pi$
$788$	10.4399	+	12.8922i	0.371905	+	0.459265i
$789$	−2.94944	−	28.0621i	−0.105003	−	0.999037i
$790$	3.29209	−	4.32363i	0.117127	−	0.153828i
$791$	−10.3605	−	17.2472i	−0.368377	−	0.613238i
$792$	−0.234109	+	1.48378i	−0.00831871	+	0.0527239i
$793$	2.07963	+	7.76130i	0.0738500	+	0.275612i
$794$	0.894035	−	0.190033i	0.0317281	−	0.00674402i
$795$	0.482875	+	16.1398i	0.0171258	+	0.572420i
$796$	0.266713	+	0.599048i	0.00945340	+	0.0212327i
$797$	−15.3960	−	7.84464i	−0.545353	−	0.277871i	0.159532	−	0.987193i	$-0.449002\pi$
$797$	−15.3960	−	7.84464i	−0.545353	−	0.277871i	−0.704885	+	0.709321i	$0.749002\pi$
$798$	−5.55675	−	2.71098i	−0.196707	−	0.0959675i
$799$	32.1355	−	44.2307i	1.13687	−	1.56477i
$800$	−1.07601	−	4.88285i	−0.0380426	−	0.172635i
$801$	0.784353	+	3.69009i	0.0277137	+	0.130383i
$802$	−2.47123	+	9.22274i	−0.0872620	+	0.325666i
$803$	29.1267	+	1.50921i	1.02786	+	0.0532588i
$804$	−4.00011			−0.141073
$805$	−11.5423	+	29.6155i	−0.406811	+	1.04381i
$806$	8.67534	−	6.30301i	0.305576	−	0.222014i
$807$	−18.7013	−	7.17877i	−0.658318	−	0.252704i
$808$	9.61380	−	0.503838i	0.338212	−	0.0177250i
$809$	9.61775	+	8.65986i	0.338142	+	0.304464i	0.820655	−	0.571425i	$-0.193609\pi$
$809$	9.61775	+	8.65986i	0.338142	+	0.304464i	−0.482513	+	0.875889i	$0.660276\pi$
$810$	1.36641	+	16.5715i	0.0480106	+	0.582262i
$811$	−17.7360	−	24.4115i	−0.622795	−	0.857204i	0.374757	−	0.927123i	$-0.377726\pi$
$811$	−17.7360	−	24.4115i	−0.622795	−	0.857204i	−0.997553	+	0.0699188i	$0.977726\pi$
$812$	0.0853629	−	2.43666i	0.00299565	−	0.0855099i
$813$	−23.3605	+	23.3605i	−0.819288	+	0.819288i
$814$	−5.76845	+	2.57237i	−0.202184	+	0.0901614i
$815$	−5.15694	−	27.2567i	−0.180640	−	0.954760i
$816$	7.67183	−	1.63070i	0.268568	−	0.0570858i
$817$	−8.23813	−	6.67111i	−0.288216	−	0.233392i
$818$	4.44974	+	28.0946i	0.155582	+	0.982304i
$819$	0.407069	+	1.18264i	0.0142241	+	0.0413249i
$820$	8.05867	−	7.70472i	0.281421	−	0.269060i
$821$	−1.07726	+	0.479626i	−0.0375966	+	0.0167391i	−0.425449	−	0.904982i	$-0.639884\pi$
$821$	−1.07726	+	0.479626i	−0.0375966	+	0.0167391i	0.387852	+	0.921722i	$0.373217\pi$
$822$	1.07793	−	0.413778i	0.0375971	−	0.0144322i
$823$	−9.12628	+	14.0532i	−0.318122	+	0.489865i	−0.961169	−	0.275962i	$-0.911004\pi$
$823$	−9.12628	+	14.0532i	−0.318122	+	0.489865i	0.643046	+	0.765827i	$0.277670\pi$
$824$	0.532904	−	0.923017i	0.0185646	−	0.0321548i
$825$	−2.97823	−	26.2979i	−0.103689	−	0.915575i
$826$	−7.78348	+	4.67560i	−0.270822	+	0.162685i
$827$	−38.0637	+	19.3944i	−1.32361	+	0.674411i	−0.965776	−	0.259376i	$-0.916483\pi$
$827$	−38.0637	+	19.3944i	−1.32361	+	0.674411i	−0.357830	+	0.933787i	$0.616483\pi$
$828$	1.89107	+	1.53136i	0.0657191	+	0.0532183i
$829$	−2.10073	+	19.9872i	−0.0729615	+	0.694182i	0.895507	+	0.445047i	$0.146813\pi$
$829$	−2.10073	+	19.9872i	−0.0729615	+	0.694182i	−0.968469	+	0.249135i	$0.919854\pi$
$830$	5.70899	−	19.5405i	0.198162	−	0.678262i
$831$	−1.45498	+	6.84515i	−0.0504727	+	0.237456i
$832$	1.03092	−	0.163282i	0.0357408	−	0.00566078i
$833$	34.1436	+	4.20006i	1.18301	+	0.145523i
$834$	17.6156	+	5.72366i	0.609978	+	0.198194i
$835$	−15.9234	+	13.7029i	−0.551053	+	0.474209i
$836$	3.24739	−	3.61089i	0.112313	−	0.124885i
$837$	14.6530	−	54.6858i	0.506483	−	1.89022i
$838$	2.00794	−	38.3139i	0.0693633	−	1.32353i
$839$	−13.0700	+	9.49588i	−0.451225	+	0.327834i	−0.790079	−	0.613005i	$-0.789961\pi$
$839$	−13.0700	+	9.49588i	−0.451225	+	0.327834i	0.338854	+	0.940839i	$0.389961\pi$
$840$	8.60581	+	3.88436i	0.296929	+	0.134023i
$841$	8.69907	+	26.7730i	0.299968	+	0.923206i
$842$	20.6211	+	31.7537i	0.710650	+	1.09431i
$843$	12.5434	−	10.1575i	0.432019	−	0.349842i
$844$	−7.41661	+	16.6580i	−0.255290	+	0.573391i
$845$	24.6433	+	10.1001i	0.847756	+	0.347454i
$846$		−	5.03857i		−	0.173230i
$847$	20.9568	+	20.1944i	0.720083	+	0.693888i
$848$	3.19942	−	3.19942i	0.109868	−	0.109868i
$849$	26.4807	−	23.8433i	0.908816	−	0.818301i
$850$	21.8101	−	11.3185i	0.748080	−	0.388221i
$851$	−1.06948	+	10.1754i	−0.0366613	+	0.348809i
$852$	−7.63245	+	4.95657i	−0.261484	+	0.169809i
$853$	−0.279089	+	0.547743i	−0.00955583	+	0.0187544i	−0.895735	−	0.444588i	$-0.853350\pi$
$853$	−0.279089	+	0.547743i	−0.00955583	+	0.0187544i	0.886179	+	0.463343i	$0.153350\pi$
$854$	18.4600	−	8.60554i	0.631690	−	0.294476i
$855$	−0.702712	+	1.30582i	−0.0240322	+	0.0446583i
$856$	−12.3176	−	13.6801i	−0.421006	−	0.467575i
$857$	3.71134	+	0.994450i	0.126777	+	0.0339698i	0.321650	−	0.946859i	$-0.395763\pi$
$857$	3.71134	+	0.994450i	0.126777	+	0.0339698i	−0.194873	+	0.980829i	$0.562429\pi$
$858$	5.51715	−	0.292410i	0.188352	−	0.00998272i
$859$	−13.1158	+	22.7173i	−0.447506	+	0.775104i	−0.998223	−	0.0595884i	$-0.981021\pi$
$859$	−13.1158	+	22.7173i	−0.447506	+	0.775104i	0.550717	+	0.834692i	$0.314355\pi$
$860$	12.8796	+	9.80678i	0.439191	+	0.334408i
$861$	2.56347	+	20.8971i	0.0873629	+	0.712173i
$862$	−1.88989	−	11.9323i	−0.0643700	−	0.406416i
$863$	−35.9169	+	23.3247i	−1.22263	+	0.793982i	−0.984180	−	0.177173i	$-0.943305\pi$
$863$	−35.9169	+	23.3247i	−1.22263	+	0.793982i	−0.238446	+	0.971156i	$0.576638\pi$
$864$	3.68738	−	4.09525i	0.125447	−	0.139323i
$865$	−23.0659	−	10.8964i	−0.784263	−	0.370490i
$866$	−13.1518	+	1.38231i	−0.446917	+	0.0469728i
$867$	5.18164	+	10.1695i	0.175978	+	0.345376i
$868$	−19.5506	−	18.8840i	−0.663590	−	0.640965i
$869$	−8.06038	+	0.00476227i	−0.273430	+	0.000161549i
$870$	3.27946	+	0.245797i	0.111184	+	0.00833328i
$871$	−0.543919	−	2.55894i	−0.0184300	−	0.0867063i
$872$	−1.63402	−	4.25675i	−0.0553347	−	0.144152i
$873$	−0.551704	−	0.211779i	−0.0186724	−	0.00716764i
$874$	−2.43101	−	7.48188i	−0.0822301	−	0.253078i
$875$	29.2270	+	4.55873i	0.988053	+	0.154113i
$876$	−11.3542	−	8.24931i	−0.383623	−	0.278718i
$877$	−3.18013	+	3.92714i	−0.107386	+	0.132610i	−0.828005	−	0.560721i	$-0.810524\pi$
$877$	−3.18013	+	3.92714i	−0.107386	+	0.132610i	0.720620	+	0.693331i	$0.243857\pi$
$878$	−27.5136	−	17.8676i	−0.928540	−	0.603001i
$879$	8.45170	−	4.87959i	0.285069	−	0.164585i
$880$	−4.79203	+	5.66008i	−0.161539	+	0.190801i
$881$			25.6088i			0.862781i	0.902165	+	0.431390i	$0.141977\pi$
$881$			25.6088i			0.862781i	−0.902165	+	0.431390i	$0.858023\pi$
$882$	2.77322	−	1.53641i	0.0933791	−	0.0517336i
$883$	5.29862	−	33.4542i	0.178313	−	1.12582i	−0.722421	−	0.691453i	$-0.756971\pi$
$883$	5.29862	−	33.4542i	0.178313	−	1.12582i	0.900734	−	0.434370i	$-0.143029\pi$
$884$	2.08637	+	4.68606i	0.0701722	+	0.157609i
$885$	−5.88396	−	10.7412i	−0.197787	−	0.361061i
$886$	7.84443	−	8.71212i	0.263539	−	0.292689i
$887$	−2.20709	+	5.74967i	−0.0741069	+	0.193055i	−0.965630	−	0.259920i	$-0.916304\pi$
$887$	−2.20709	+	5.74967i	−0.0741069	+	0.193055i	0.891523	+	0.452975i	$0.149637\pi$
$888$	3.00185	+	0.475447i	0.100736	+	0.0159549i
$889$	−5.56121	−	24.1005i	−0.186517	−	0.808306i
$890$	−6.15175	+	17.5801i	−0.206207	+	0.589286i
$891$	18.3183	−	16.5135i	0.613687	−	0.553224i
$892$	−16.4390	−	4.40482i	−0.550419	−	0.147484i
$893$	−8.87189	+	13.6615i	−0.296886	+	0.457165i
$894$	1.76747	+	16.8163i	0.0591129	+	0.562422i
$895$	−42.2153	−	7.66141i	−1.41110	−	0.256093i
$896$	−0.861092	−	2.50170i	−0.0287671	−	0.0835760i
$897$	4.06317	−	7.97443i	0.135665	−	0.266258i
$898$	−6.60082	+	17.1957i	−0.220272	+	0.573829i
$899$	−8.64899	−	3.85078i	−0.288460	−	0.128431i
$900$	1.01301	−	2.02535i	0.0337669	−	0.0675115i
$901$	19.2570	+	11.1180i	0.641544	+	0.370395i
$902$	−16.3349	−	2.57730i	−0.543892	−	0.0858147i
$903$	−29.3860	+	8.42273i	−0.977903	+	0.280291i
$904$	−7.23236	−	2.34994i	−0.240545	−	0.0781577i
$905$	28.4160	+	45.9848i	0.944579	+	1.52859i
$906$	18.0680	+	1.89902i	0.600268	+	0.0630907i
$907$	58.2292	−	3.05166i	1.93347	−	0.101329i	0.953613	−	0.301036i	$-0.0973323\pi$
$907$	58.2292	−	3.05166i	1.93347	−	0.101329i	0.979856	+	0.199707i	$0.0639990\pi$
$908$	4.41104	+	6.79241i	0.146386	+	0.225414i
$909$	3.52745	+	2.56284i	0.116998	+	0.0850042i
$910$	−1.31470	+	6.03346i	−0.0435820	+	0.200007i
$911$	−10.2433	+	31.5257i	−0.339376	+	1.04449i	0.625150	+	0.780504i	$0.285038\pi$
$911$	−10.2433	+	31.5257i	−0.339376	+	1.04449i	−0.964526	+	0.263987i	$0.914962\pi$
$912$	−2.25725	+	0.604827i	−0.0747449	+	0.0200278i
$913$	−28.1830	+	10.8376i	−0.932722	+	0.358671i
$914$	−25.6981	+	14.8368i	−0.850018	+	0.490758i
$915$	10.6077	+	25.3416i	0.350680	+	0.837766i
$916$	−15.6542	−	21.5462i	−0.517231	−	0.711907i
$917$	−28.9874	+	5.10791i	−0.957247	+	0.168678i
$918$	24.1302	+	12.2949i	0.796415	+	0.405794i
$919$	6.34923	−	29.8708i	0.209442	−	0.985346i	−0.740292	−	0.672286i	$-0.765313\pi$
$919$	6.34923	−	29.8708i	0.209442	−	0.985346i	0.949733	−	0.313060i	$-0.101354\pi$
$920$	4.05246	+	11.3096i	0.133606	+	0.372865i
$921$	−37.3621	−	16.6347i	−1.23112	−	0.548131i
$922$	8.79883	+	0.461127i	0.289774	+	0.0151864i
$923$	−4.20863	−	4.20863i	−0.138529	−	0.138529i
$924$	−3.15686	−	13.6440i	−0.103853	−	0.448856i
$925$	9.46191	−	1.06590i	0.311106	−	0.0350465i
$926$	−23.5328	−	26.1358i	−0.773334	−	0.858875i
$927$	0.450655	−	0.172990i	0.0148014	−	0.00568174i
$928$	−0.579941	−	0.716167i	−0.0190375	−	0.0235093i
$929$	26.9232	+	5.72269i	0.883320	+	0.187756i	0.627171	−	0.778882i	$-0.284213\pi$
$929$	26.9232	+	5.72269i	0.883320	+	0.187756i	0.256149	+	0.966637i	$0.417546\pi$
$930$	26.5003	−	25.3363i	0.868978	−	0.830810i
$931$	−10.2246	−	0.717271i	−0.335097	−	0.0235076i
$932$	18.0933	+	2.86569i	0.592665	+	0.0938689i
$933$	9.64706	+	0.505581i	0.315831	+	0.0165520i
$934$	14.5910	+	25.2723i	0.477431	+	0.826934i
$935$	−32.9634	−	15.5483i	−1.07802	−	0.508483i
$936$	0.409401	+	0.236368i	0.0133817	+	0.00772592i
$937$	−5.82793	−	11.4380i	−0.190390	−	0.373662i	0.776003	−	0.630729i	$-0.217244\pi$
$937$	−5.82793	−	11.4380i	−0.190390	−	0.373662i	−0.966394	+	0.257067i	$0.917244\pi$
$938$	−6.14872	+	2.48344i	−0.200763	+	0.0810873i
$939$	5.47006	−	7.52890i	0.178509	−	0.245696i
$940$	12.9184	−	21.2585i	0.421353	−	0.693377i
$941$	−19.3744	−	17.4448i	−0.631588	−	0.568684i	0.289917	−	0.957052i	$-0.406372\pi$
$941$	−19.3744	−	17.4448i	−0.631588	−	0.568684i	−0.921504	+	0.388368i	$0.873039\pi$
$942$	6.00678	−	4.86419i	0.195711	−	0.158484i
$943$	−16.8586	+	20.8187i	−0.548992	+	0.677949i
$944$	−1.06050	+	3.26390i	−0.0345165	+	0.106231i
$945$	14.6523	+	29.1236i	0.476639	+	0.947392i
$946$	−0.0141863	−	24.0110i	−0.000461235	−	0.780663i
$947$	30.4007	−	8.14584i	0.987890	−	0.264704i	0.271526	−	0.962431i	$-0.412472\pi$
$947$	30.4007	−	8.14584i	0.987890	−	0.264704i	0.716364	+	0.697727i	$0.245805\pi$
$948$	3.25291	+	2.11247i	0.105650	+	0.0686097i
$949$	3.73332	−	8.38518i	0.121189	−	0.272194i
$950$	−6.31288	+	3.70780i	−0.204817	+	0.120297i
$951$	−23.3966	+	7.60203i	−0.758688	+	0.246513i
$952$	10.7802	−	7.26961i	0.349389	−	0.235609i
$953$	−3.46020	+	0.548042i	−0.112087	+	0.0177528i	−0.212226	−	0.977221i	$-0.568071\pi$
$953$	−3.46020	+	0.548042i	−0.112087	+	0.0177528i	0.100139	+	0.994973i	$0.468071\pi$
$954$	2.03804	−	0.214207i	0.0659840	−	0.00693520i
$955$	−28.0530	−	36.2784i	−0.907773	−	1.17394i
$956$	7.78169	+	13.4783i	0.251678	+	0.435919i
$957$	−2.65910	−	4.08936i	−0.0859563	−	0.132190i
$958$	29.0902	+	29.0902i	0.939861	+	0.939861i
$959$	1.40003	−	1.30526i	0.0452094	−	0.0421490i
$960$	3.41791	−	1.02631i	0.110313	−	0.0331241i
$961$	−68.1024	+	30.3211i	−2.19685	+	0.978101i
$962$	0.104029	+	1.98498i	0.00335402	+	0.0639985i
$963$	−0.436342	−	8.32591i	−0.0140609	−	0.268299i
$964$	−17.7651	+	7.90953i	−0.572175	+	0.254749i
$965$	−2.75522	+	0.827322i	−0.0886936	+	0.0266325i
$966$	−21.6942	−	6.63524i	−0.698000	−	0.213485i
$967$	−14.4218	−	14.4218i	−0.463773	−	0.463773i	0.436117	−	0.899890i	$-0.356353\pi$
$967$	−14.4218	−	14.4218i	−0.463773	−	0.463773i	−0.899890	+	0.436117i	$0.856353\pi$
$968$	10.9856	+	0.562715i	0.353090	+	0.0180863i
$969$	−5.74219	−	9.94576i	−0.184466	−	0.319504i
$970$	−1.78475	−	2.30805i	−0.0573047	−	0.0741071i
$971$	−14.7559	+	1.55091i	−0.473539	+	0.0497709i	−0.338292	−	0.941041i	$-0.609849\pi$
$971$	−14.7559	+	1.55091i	−0.473539	+	0.0497709i	−0.135246	+	0.990812i	$0.543183\pi$
$972$	4.60692	−	0.729664i	0.147767	−	0.0234040i
$973$	30.6311	−	2.13849i	0.981987	−	0.0685568i
$974$	−4.93663	+	1.60401i	−0.158180	+	0.0513957i
$975$	−8.06114	−	2.09566i	−0.258163	−	0.0671148i
$976$	3.13111	−	7.03259i	0.100224	−	0.225108i
$977$	40.9676	+	26.6046i	1.31067	+	0.851158i	0.995208	−	0.0977806i	$-0.0311743\pi$
$977$	40.9676	+	26.6046i	1.31067	+	0.851158i	0.315461	+	0.948939i	$0.397841\pi$
$978$	19.1245	−	5.12441i	0.611535	−	0.163860i
$979$	26.2687	−	8.55239i	0.839552	−	0.273335i
$980$	15.6399	+	0.627928i	0.499597	+	0.0200584i
$981$	0.638149	−	1.96402i	0.0203745	−	0.0627064i
$982$	−21.8080	+	26.9307i	−0.695922	+	0.859393i
$983$	26.0986	−	21.1342i	0.832416	−	0.674077i	−0.115252	−	0.993336i	$-0.536767\pi$
$983$	26.0986	−	21.1342i	0.832416	−	0.674077i	0.947667	+	0.319259i	$0.103434\pi$
$984$	5.91364	+	5.32466i	0.188520	+	0.169744i
$985$	−19.2637	+	31.7003i	−0.613793	+	1.01005i
$986$	2.66197	−	3.66388i	0.0847743	−	0.116682i
$987$	17.5922	+	43.5563i	0.559966	+	1.38641i
$988$	−0.693849	−	1.36176i	−0.0220743	−	0.0433232i
$989$	−33.6849	−	19.4480i	−1.07112	−	0.618410i
$990$	−3.29996	+	0.626369i	−0.104880	+	0.0199073i
$991$	−0.607212	−	1.05172i	−0.0192887	−	0.0334090i	0.856220	−	0.516611i	$-0.172807\pi$
$991$	−0.607212	−	1.05172i	−0.0192887	−	0.0334090i	−0.875509	+	0.483202i	$0.839474\pi$
$992$	−10.2595	−	0.537680i	−0.325741	−	0.0170714i
$993$	−54.4580	−	8.62530i	−1.72817	−	0.273716i
$994$	−8.65487	+	12.3575i	−0.274516	+	0.391956i
$995$	−1.05983	+	1.01328i	−0.0335988	+	0.0321231i
$996$	14.2123	+	3.02092i	0.450334	+	0.0957215i
$997$	2.93974	+	3.63028i	0.0931026	+	0.114972i	0.821568	−	0.570110i	$-0.193100\pi$
$997$	2.93974	+	3.63028i	0.0931026	+	0.114972i	−0.728466	+	0.685082i	$0.759766\pi$
$998$	−6.31285	+	2.42328i	−0.199830	+	0.0767075i
$999$	7.02208	+	7.79881i	0.222169	+	0.246743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.537.6	yes	768
5.3	odd	4	inner	770.2.bv.a.383.43	yes	768
7.3	odd	6	inner	770.2.bv.a.647.19	yes	768
11.5	even	5	inner	770.2.bv.a.467.19	yes	768
35.3	even	12	inner	770.2.bv.a.493.19	yes	768
55.38	odd	20	inner	770.2.bv.a.313.19	✓	768
77.38	odd	30	inner	770.2.bv.a.577.43	yes	768
385.38	even	60	inner	770.2.bv.a.423.6	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.313.19	✓	768	55.38	odd	20	inner
770.2.bv.a.383.43	yes	768	5.3	odd	4	inner
770.2.bv.a.423.6	yes	768	385.38	even	60	inner
770.2.bv.a.467.19	yes	768	11.5	even	5	inner
770.2.bv.a.493.19	yes	768	35.3	even	12	inner
770.2.bv.a.537.6	yes	768	1.1	even	1	trivial
770.2.bv.a.577.43	yes	768	77.38	odd	30	inner
770.2.bv.a.647.19	yes	768	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0523360 + 0.998630i) q^{2} +(-0.571941 - 1.48996i) q^{3} +(-0.994522 - 0.104528i) q^{4} +(-0.530105 - 2.17232i) q^{5} +(1.51785 - 0.493179i) q^{6} +(2.02695 - 1.70043i) q^{7} +(0.156434 - 0.987688i) q^{8} +(0.336578 - 0.303057i) q^{9} +O(q^{10})\)	\(q+(-0.0523360 + 0.998630i) q^{2} +(-0.571941 - 1.48996i) q^{3} +(-0.994522 - 0.104528i) q^{4} +(-0.530105 - 2.17232i) q^{5} +(1.51785 - 0.493179i) q^{6} +(2.02695 - 1.70043i) q^{7} +(0.156434 - 0.987688i) q^{8} +(0.336578 - 0.303057i) q^{9} +(2.19709 - 0.415688i) q^{10} +(-2.46604 - 2.21780i) q^{11} +(0.413065 + 1.54158i) q^{12} +(-0.930007 + 0.473862i) q^{13} +(1.59202 + 2.11317i) q^{14} +(-2.93348 + 2.03227i) q^{15} +(0.978148 + 0.207912i) q^{16} +(0.257201 + 4.90769i) q^{17} +(0.285026 + 0.351978i) q^{18} +(-0.153055 - 1.45622i) q^{19} +(0.300131 + 2.21583i) q^{20} +(-3.69286 - 2.04753i) q^{21} +(2.34382 - 2.34659i) q^{22} +(-1.39055 - 5.18961i) q^{23} +(-1.56108 + 0.331819i) q^{24} +(-4.43798 + 2.30312i) q^{25} +(-0.424540 - 0.953533i) q^{26} +(-4.91008 - 2.50181i) q^{27} +(-2.19359 + 1.47924i) q^{28} +(-0.541665 + 0.745537i) q^{29} +(-1.87596 - 3.03582i) q^{30} +(2.13601 + 10.0491i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-1.89399 + 4.94275i) q^{33} -4.91442 q^{34} +(-4.76838 - 3.50179i) q^{35} +(-0.366413 + 0.266214i) q^{36} +(-1.77787 - 0.682459i) q^{37} +(1.46224 - 0.0766325i) q^{38} +(1.23794 + 1.11465i) q^{39} +(-2.22851 + 0.183752i) q^{40} +(-2.93074 - 4.03382i) q^{41} +(2.23799 - 3.58064i) q^{42} +(5.11915 - 5.11915i) q^{43} +(2.22071 + 2.46342i) q^{44} +(-0.836759 - 0.570506i) q^{45} +(5.25528 - 1.11704i) q^{46} +(-8.64564 - 7.00110i) q^{47} +(-0.249663 - 1.57631i) q^{48} +(1.21708 - 6.89338i) q^{49} +(-2.06770 - 4.55243i) q^{50} +(7.16514 - 3.19012i) q^{51} +(0.974445 - 0.374054i) q^{52} +(2.46430 - 3.79470i) q^{53} +(2.75535 - 4.77241i) q^{54} +(-3.51051 + 6.53271i) q^{55} +(-1.36241 - 2.26800i) q^{56} +(-2.08217 + 1.06092i) q^{57} +(-0.716167 - 0.579941i) q^{58} +(-0.358727 + 3.41306i) q^{59} +(3.12984 - 1.71451i) q^{60} +(1.60053 - 7.52991i) q^{61} +(-10.1471 + 1.60715i) q^{62} +(0.166902 - 1.18661i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(1.52238 + 1.76908i) q^{65} +(-4.83685 - 2.15008i) q^{66} +(-0.648703 + 2.42099i) q^{67} +(0.257201 - 4.90769i) q^{68} +(-6.93699 + 5.04002i) q^{69} +(3.74655 - 4.57858i) q^{70} +(1.76211 + 5.42322i) q^{71} +(-0.246673 - 0.379843i) q^{72} +(-6.83407 + 5.53412i) q^{73} +(0.774570 - 1.73971i) q^{74} +(5.96981 + 5.29515i) q^{75} +1.46424i q^{76} +(-8.76976 - 0.302042i) q^{77} +(-1.17791 + 1.17791i) q^{78} +(1.80606 - 1.62619i) q^{79} +(-0.0668694 - 2.23507i) q^{80} +(-0.777288 + 7.39540i) q^{81} +(4.18168 - 2.71561i) q^{82} +(4.13319 - 8.11183i) q^{83} +(3.45861 + 2.42232i) q^{84} +(10.5247 - 3.16031i) q^{85} +(4.84422 + 5.38005i) q^{86} +(1.42062 + 0.380654i) q^{87} +(-2.57627 + 2.08874i) q^{88} +(-4.16476 + 7.21357i) q^{89} +(0.613516 - 0.805754i) q^{90} +(-1.07931 + 2.54191i) q^{91} +(0.840473 + 5.30654i) q^{92} +(13.7511 - 8.93006i) q^{93} +(7.44398 - 8.26738i) q^{94} +(-3.08225 + 1.10443i) q^{95} +(1.58722 - 0.166823i) q^{96} +(-0.592364 - 1.16258i) q^{97} +(6.82024 + 1.57618i) q^{98} +(-1.50214 + 0.000887499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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