LMFDB - Embedded newform 770.2.bd.a.527.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(263,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 8, 6]))

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

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

chi := DirichletCharacter("770.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bd (of order $12$, degree $4$, 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:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.31
Character	$\chi$	$=$	770.527
Dual form			770.2.bd.a.263.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-1.66804 - 0.446949i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.10823 - 0.745241i) q^{5} -1.72688i q^{6} +(1.49658 + 2.18180i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.0154982 - 0.00894790i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-1.66804 - 0.446949i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.10823 - 0.745241i) q^{5} -1.72688i q^{6} +(1.49658 + 2.18180i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.0154982 - 0.00894790i) q^{9} +(0.174199 - 2.22927i) q^{10} +(-1.04087 - 3.14906i) q^{11} +(1.66804 - 0.446949i) q^{12} +(2.15820 + 2.15820i) q^{13} +(-1.72011 + 2.01028i) q^{14} +(3.18351 + 2.18536i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.94259 - 0.788464i) q^{17} +(0.00463178 - 0.0172860i) q^{18} +(0.776257 - 1.34452i) q^{19} +(2.19840 - 0.408715i) q^{20} +(-1.52120 - 4.30821i) q^{21} +(2.77236 - 1.82044i) q^{22} +(-0.955268 - 3.56511i) q^{23} +(0.863439 + 1.49552i) q^{24} +(3.88923 + 3.14227i) q^{25} +(-1.52608 + 2.64324i) q^{26} +(3.68511 + 3.68511i) q^{27} +(-2.38698 - 1.14120i) q^{28} +8.75642 q^{29} +(-1.28694 + 3.64065i) q^{30} +(3.11504 + 5.39541i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.328745 + 5.71796i) q^{33} -3.04639i q^{34} +(-1.52916 - 5.71504i) q^{35} +0.0178958 q^{36} +(7.25971 - 1.94523i) q^{37} +(1.49961 + 0.401820i) q^{38} +(-2.63535 - 4.56456i) q^{39} +(0.963776 + 2.01771i) q^{40} -6.18993i q^{41} +(3.76770 - 2.58441i) q^{42} +(6.93669 + 6.93669i) q^{43} +(2.47595 + 2.20673i) q^{44} +(0.0260054 + 0.0304141i) q^{45} +(3.19639 - 1.84544i) q^{46} +(1.73493 - 0.464873i) q^{47} +(-1.22109 + 1.22109i) q^{48} +(-2.52050 + 6.53048i) q^{49} +(-2.02860 + 4.56999i) q^{50} +(4.55593 + 2.63037i) q^{51} +(-2.94816 - 0.789956i) q^{52} +(8.78311 + 2.35343i) q^{53} +(-2.60577 + 4.51332i) q^{54} +(-0.152413 + 7.41463i) q^{55} +(0.484523 - 2.60101i) q^{56} +(-1.89575 + 1.89575i) q^{57} +(2.26633 + 8.45805i) q^{58} +(-4.01387 + 2.31741i) q^{59} +(-3.84968 - 0.300820i) q^{60} +(-7.39576 - 4.26995i) q^{61} +(-4.40534 + 4.40534i) q^{62} +(-0.00367181 - 0.0472053i) q^{63} +1.00000i q^{64} +(-2.94159 - 6.15835i) q^{65} +(-5.43804 + 1.79746i) q^{66} +(4.01993 - 15.0026i) q^{67} +(2.94259 - 0.788464i) q^{68} +6.37368i q^{69} +(5.12453 - 2.95622i) q^{70} +4.05504 q^{71} +(0.00463178 + 0.0172860i) q^{72} +(2.81204 - 10.4947i) q^{73} +(3.75790 + 6.50888i) q^{74} +(-5.08294 - 6.97971i) q^{75} +1.55251i q^{76} +(5.31287 - 6.98380i) q^{77} +(3.72695 - 3.72695i) q^{78} +(-0.693914 + 1.20189i) q^{79} +(-1.69951 + 1.45316i) q^{80} +(-4.47300 - 7.74746i) q^{81} +(5.97901 - 1.60207i) q^{82} +(6.01057 + 6.01057i) q^{83} +(3.47150 + 2.97042i) q^{84} +(5.61604 + 3.85520i) q^{85} +(-4.90498 + 8.49568i) q^{86} +(-14.6060 - 3.91367i) q^{87} +(-1.49071 + 2.96273i) q^{88} +(-12.4567 - 7.19191i) q^{89} +(-0.0226471 + 0.0329910i) q^{90} +(-1.47884 + 7.93868i) q^{91} +(2.60984 + 2.60984i) q^{92} +(-2.78453 - 10.3920i) q^{93} +(0.898066 + 1.55550i) q^{94} +(-2.63851 + 2.25605i) q^{95} +(-1.49552 - 0.863439i) q^{96} +(-6.27407 - 6.27407i) q^{97} +(-6.96031 - 0.744400i) q^{98} +(-0.0120458 + 0.0581185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{5}+O(q^{10}) $ 192 * q + 8 * q^5	$ 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) $ 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−1.66804	−	0.446949i	−0.963041	−	0.258046i	−0.257154	−	0.966371i	$-0.582785\pi$
$3$	−1.66804	−	0.446949i	−0.963041	−	0.258046i	−0.705887	+	0.708325i	$0.749451\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−2.10823	−	0.745241i	−0.942827	−	0.333282i
$5$	−2.10823	−	0.745241i	−0.942827	−	0.333282i
$6$		−	1.72688i		−	0.704995i
$7$	1.49658	+	2.18180i	0.565654	+	0.824643i
$7$	1.49658	+	2.18180i	0.565654	+	0.824643i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.0154982	−	0.00894790i	−0.00516607	−	0.00298263i
$10$	0.174199	−	2.22927i	0.0550864	−	0.704958i
$11$	−1.04087	−	3.14906i	−0.313835	−	0.949477i
$11$	−1.04087	−	3.14906i	−0.313835	−	0.949477i
$12$	1.66804	−	0.446949i	0.481520	−	0.129023i
$13$	2.15820	+	2.15820i	0.598577	+	0.598577i	0.939934	−	0.341357i	$-0.110886\pi$
$13$	2.15820	+	2.15820i	0.598577	+	0.598577i	−0.341357	+	0.939934i	$0.610886\pi$
$14$	−1.72011	+	2.01028i	−0.459719	+	0.537269i
$15$	3.18351	+	2.18536i	0.821979	+	0.564257i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.94259	−	0.788464i	−0.713682	−	0.191231i	−0.116331	−	0.993210i	$-0.537113\pi$
$17$	−2.94259	−	0.788464i	−0.713682	−	0.191231i	−0.597351	+	0.801980i	$0.703780\pi$
$18$	0.00463178	−	0.0172860i	0.00109172	−	0.00407435i
$19$	0.776257	−	1.34452i	0.178086	−	0.308453i	−0.763139	−	0.646234i	$-0.776343\pi$
$19$	0.776257	−	1.34452i	0.178086	−	0.308453i	0.941225	+	0.337781i	$0.109676\pi$
$20$	2.19840	−	0.408715i	0.491577	−	0.0913915i
$21$	−1.52120	−	4.30821i	−0.331952	−	0.940129i
$22$	2.77236	−	1.82044i	0.591069	−	0.388120i
$23$	−0.955268	−	3.56511i	−0.199187	−	0.743376i	−0.991143	−	0.132798i	$-0.957604\pi$
$23$	−0.955268	−	3.56511i	−0.199187	−	0.743376i	0.791956	−	0.610578i	$-0.209063\pi$
$24$	0.863439	+	1.49552i	0.176249	+	0.305272i
$25$	3.88923	+	3.14227i	0.777846	+	0.628455i
$26$	−1.52608	+	2.64324i	−0.299289	+	0.518383i
$27$	3.68511	+	3.68511i	0.709200	+	0.709200i
$28$	−2.38698	−	1.14120i	−0.451096	−	0.215667i
$29$	8.75642			1.62603			0.813013	−	0.582246i	$-0.197826\pi$
$29$	8.75642			1.62603			0.813013	+	0.582246i	$0.197826\pi$
$30$	−1.28694	+	3.64065i	−0.234962	+	0.664688i
$31$	3.11504	+	5.39541i	0.559478	+	0.969045i	0.997540	+	0.0701000i	$0.0223318\pi$
$31$	3.11504	+	5.39541i	0.559478	+	0.969045i	−0.438062	+	0.898945i	$0.644335\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	0.328745	+	5.71796i	0.0572272	+	0.995369i
$34$		−	3.04639i		−	0.522452i
$35$	−1.52916	−	5.71504i	−0.258476	−	0.966018i
$36$	0.0178958			0.00298263
$37$	7.25971	−	1.94523i	1.19349	−	0.319795i	0.393225	−	0.919442i	$-0.371359\pi$
$37$	7.25971	−	1.94523i	1.19349	−	0.319795i	0.800264	+	0.599647i	$0.204693\pi$
$38$	1.49961	+	0.401820i	0.243269	+	0.0651839i
$39$	−2.63535	−	4.56456i	−0.421994	−	0.730914i
$40$	0.963776	+	2.01771i	0.152386	+	0.319027i
$41$		−	6.18993i		−	0.966704i	−0.875426	−	0.483352i	$-0.839419\pi$
$41$		−	6.18993i		−	0.966704i	0.875426	−	0.483352i	$-0.160581\pi$
$42$	3.76770	−	2.58441i	0.581369	−	0.398783i
$43$	6.93669	+	6.93669i	1.05784	+	1.05784i	0.998221	+	0.0596141i	$0.0189870\pi$
$43$	6.93669	+	6.93669i	1.05784	+	1.05784i	0.0596141	+	0.998221i	$0.481013\pi$
$44$	2.47595	+	2.20673i	0.373264	+	0.332677i
$45$	0.0260054	+	0.0304141i	0.00387666	+	0.00453387i
$46$	3.19639	−	1.84544i	0.471282	−	0.272095i
$47$	1.73493	−	0.464873i	0.253066	−	0.0678087i	−0.130056	−	0.991507i	$-0.541516\pi$
$47$	1.73493	−	0.464873i	0.253066	−	0.0678087i	0.383122	+	0.923698i	$0.374849\pi$
$48$	−1.22109	+	1.22109i	−0.176249	+	0.176249i
$49$	−2.52050	+	6.53048i	−0.360071	+	0.932925i
$50$	−2.02860	+	4.56999i	−0.286887	+	0.646294i
$51$	4.55593	+	2.63037i	0.637958	+	0.368325i
$52$	−2.94816	−	0.789956i	−0.408836	−	0.109547i
$53$	8.78311	+	2.35343i	1.20645	+	0.323268i	0.805369	−	0.592774i	$-0.201967\pi$
$53$	8.78311	+	2.35343i	1.20645	+	0.323268i	0.401083	+	0.916042i	$0.368634\pi$
$54$	−2.60577	+	4.51332i	−0.354600	+	0.614185i
$55$	−0.152413	+	7.41463i	−0.0205513	+	0.999789i
$56$	0.484523	−	2.60101i	0.0647471	−	0.347574i
$57$	−1.89575	+	1.89575i	−0.251099	+	0.251099i
$58$	2.26633	+	8.45805i	0.297583	+	1.11060i
$59$	−4.01387	+	2.31741i	−0.522561	+	0.301701i	−0.737982	−	0.674821i	$-0.764221\pi$
$59$	−4.01387	+	2.31741i	−0.522561	+	0.301701i	0.215421	+	0.976521i	$0.430888\pi$
$60$	−3.84968	−	0.300820i	−0.496991	−	0.0388356i
$61$	−7.39576	−	4.26995i	−0.946931	−	0.546711i	−0.0548045	−	0.998497i	$-0.517454\pi$
$61$	−7.39576	−	4.26995i	−0.946931	−	0.546711i	−0.892126	+	0.451786i	$0.850787\pi$
$62$	−4.40534	+	4.40534i	−0.559478	+	0.559478i
$63$	−0.00367181	−	0.0472053i	−0.000462604	−	0.00594730i
$64$			1.00000i			0.125000i
$65$	−2.94159	−	6.15835i	−0.364860	−	0.763850i
$66$	−5.43804	+	1.79746i	−0.669376	+	0.221252i
$67$	4.01993	−	15.0026i	0.491113	−	1.83286i	−0.0596825	−	0.998217i	$-0.519009\pi$
$67$	4.01993	−	15.0026i	0.491113	−	1.83286i	0.550795	−	0.834640i	$-0.314325\pi$
$68$	2.94259	−	0.788464i	0.356841	−	0.0956153i
$69$			6.37368i			0.767301i
$70$	5.12453	−	2.95622i	0.612498	−	0.353336i
$71$	4.05504			0.481244			0.240622	−	0.970619i	$-0.422649\pi$
$71$	4.05504			0.481244			0.240622	+	0.970619i	$0.422649\pi$
$72$	0.00463178	+	0.0172860i	0.000545860	+	0.00203718i
$73$	2.81204	−	10.4947i	0.329125	−	1.22831i	−0.580975	−	0.813921i	$-0.697329\pi$
$73$	2.81204	−	10.4947i	0.329125	−	1.22831i	0.910100	−	0.414389i	$-0.136005\pi$
$74$	3.75790	+	6.50888i	0.436848	+	0.756642i
$75$	−5.08294	−	6.97971i	−0.586927	−	0.805947i
$76$			1.55251i			0.178086i
$77$	5.31287	−	6.98380i	0.605457	−	0.795878i
$78$	3.72695	−	3.72695i	0.421994	−	0.421994i
$79$	−0.693914	+	1.20189i	−0.0780714	+	0.135224i	−0.902418	−	0.430862i	$-0.858210\pi$
$79$	−0.693914	+	1.20189i	−0.0780714	+	0.135224i	0.824346	+	0.566086i	$0.191543\pi$
$80$	−1.69951	+	1.45316i	−0.190011	+	0.162468i
$81$	−4.47300	−	7.74746i	−0.497000	−	0.860829i
$82$	5.97901	−	1.60207i	0.660271	−	0.176919i
$83$	6.01057	+	6.01057i	0.659746	+	0.659746i	0.955320	−	0.295574i	$-0.0955109\pi$
$83$	6.01057	+	6.01057i	0.659746	+	0.659746i	−0.295574	+	0.955320i	$0.595511\pi$
$84$	3.47150	+	2.97042i	0.378772	+	0.324100i
$85$	5.61604	+	3.85520i	0.609145	+	0.418155i
$86$	−4.90498	+	8.49568i	−0.528918	+	0.916113i
$87$	−14.6060	−	3.91367i	−1.56593	−	0.419589i
$88$	−1.49071	+	2.96273i	−0.158911	+	0.315828i
$89$	−12.4567	−	7.19191i	−1.32041	−	0.762340i	−0.336618	−	0.941641i	$-0.609283\pi$
$89$	−12.4567	−	7.19191i	−1.32041	−	0.762340i	−0.983794	+	0.179301i	$0.942616\pi$
$90$	−0.0226471	+	0.0329910i	−0.00238721	+	0.00347756i
$91$	−1.47884	+	7.93868i	−0.155025	+	0.832200i
$92$	2.60984	+	2.60984i	0.272095	+	0.272095i
$93$	−2.78453	−	10.3920i	−0.288742	−	1.07760i
$94$	0.898066	+	1.55550i	0.0926284	+	0.160437i
$95$	−2.63851	+	2.25605i	−0.270706	+	0.231465i
$96$	−1.49552	−	0.863439i	−0.152636	−	0.0881243i
$97$	−6.27407	−	6.27407i	−0.637035	−	0.637035i	0.312788	−	0.949823i	$-0.398737\pi$
$97$	−6.27407	−	6.27407i	−0.637035	−	0.637035i	−0.949823	+	0.312788i	$0.898737\pi$
$98$	−6.96031	−	0.744400i	−0.703097	−	0.0751958i
$99$	−0.0120458	+	0.0581185i	−0.00121065	+	0.00584113i
$100$	−4.93931	−	0.776672i	−0.493931	−	0.0776672i
$101$	0.821255	−	0.474152i	0.0817180	−	0.0471799i	−0.458584	−	0.888651i	$-0.651643\pi$
$101$	0.821255	−	0.474152i	0.0817180	−	0.0471799i	0.540302	+	0.841471i	$0.318310\pi$
$102$	−1.36158	+	5.08148i	−0.134816	+	0.503142i
$103$	3.08716	+	11.5214i	0.304187	+	1.13524i	0.933643	+	0.358204i	$0.116611\pi$
$103$	3.08716	+	11.5214i	0.304187	+	1.13524i	−0.629457	+	0.777036i	$0.716722\pi$
$104$		−	3.05216i		−	0.299289i
$105$	−0.00363158	+	10.2163i	−0.000354406	+	0.997013i
$106$			9.09294i			0.883184i
$107$	2.07577	+	7.74689i	0.200673	+	0.748920i	0.990725	+	0.135881i	$0.0433865\pi$
$107$	2.07577	+	7.74689i	0.200673	+	0.748920i	−0.790053	+	0.613039i	$0.789947\pi$
$108$	−5.03396	−	1.34884i	−0.484393	−	0.129793i
$109$	−4.25423	−	7.36854i	−0.407481	−	0.705778i	0.587126	−	0.809496i	$-0.300259\pi$
$109$	−4.25423	−	7.36854i	−0.407481	−	0.705778i	−0.994607	+	0.103718i	$0.966926\pi$
$110$	−7.20143	+	1.77183i	−0.686630	+	0.168937i
$111$	−12.9789			−1.23190
$112$	2.63778	−	0.205177i	0.249247	−	0.0193874i
$113$	0.199487	−	0.199487i	0.0187662	−	0.0187662i	−0.697661	−	0.716428i	$-0.745776\pi$
$113$	0.199487	−	0.199487i	0.0187662	−	0.0187662i	0.716428	+	0.697661i	$0.245776\pi$
$114$	−2.32182	−	1.34050i	−0.217458	−	0.125549i
$115$	−0.642945	+	8.22796i	−0.0599549	+	0.767261i
$116$	−7.58328	+	4.37821i	−0.704090	+	0.406506i
$117$	−0.0141369	−	0.0527596i	−0.00130696	−	0.00487763i
$118$	−3.27731	−	3.27731i	−0.301701	−	0.301701i
$119$	−2.68355	−	7.60013i	−0.246000	−	0.696703i
$120$	−0.705801	−	3.79636i	−0.0644305	−	0.346559i
$121$	−8.83316	+	6.55555i	−0.803015	+	0.595959i
$122$	2.21029	−	8.24890i	0.200110	−	0.746821i
$123$	−2.76658	+	10.3250i	−0.249454	+	0.930975i
$124$	−5.39541	−	3.11504i	−0.484522	−	0.279739i
$125$	−5.85763	−	9.52304i	−0.523922	−	0.851766i
$126$	0.0446464	−	0.0157643i	0.00397742	−	0.00140440i
$127$	7.38236	−	7.38236i	0.655078	−	0.655078i	−0.299133	−	0.954211i	$-0.596697\pi$
$127$	7.38236	−	7.38236i	0.655078	−	0.655078i	0.954211	+	0.299133i	$0.0966975\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−8.47030	−	14.6710i	−0.745768	−	1.29171i
$130$	5.18717	−	4.43526i	0.454945	−	0.388998i
$131$	14.9227	+	8.61561i	1.30380	+	0.752749i	0.981054	−	0.193736i	$-0.0620606\pi$
$131$	14.9227	+	8.61561i	1.30380	+	0.752749i	0.322746	+	0.946485i	$0.395394\pi$
$132$	−3.14368	−	4.78753i	−0.273622	−	0.416701i
$133$	4.09520	−	0.318540i	0.355099	−	0.0276209i
$134$	15.5318			1.34175
$135$	−5.02275	−	10.5153i	−0.432290	−	0.905017i
$136$	1.52319	+	2.63825i	0.130613	+	0.226228i
$137$	−1.35879	+	5.07109i	−0.116090	+	0.433252i	−0.999366	−	0.0356002i	$-0.988666\pi$
$137$	−1.35879	+	5.07109i	−0.116090	+	0.433252i	0.883277	+	0.468852i	$0.155332\pi$
$138$	−6.15650	+	1.64963i	−0.524076	+	0.140426i
$139$	−13.9277			−1.18133			−0.590666	−	0.806916i	$-0.701135\pi$
$139$	−13.9277			−1.18133			−0.590666	+	0.806916i	$0.701135\pi$
$140$	4.18181	+	4.18479i	0.353428	+	0.353679i
$141$	−3.10170			−0.261210
$142$	1.04952	+	3.91686i	0.0880738	+	0.328696i
$143$	4.54989	−	9.04272i	0.380481	−	0.756190i
$144$	−0.0154982	+	0.00894790i	−0.00129152	+	0.000745659i
$145$	−18.4605	−	6.52564i	−1.53306	−	0.541925i
$146$	10.8649			0.899186
$147$	7.12306	−	9.76653i	0.587500	−	0.805530i
$148$	−5.31448	+	5.31448i	−0.436848	+	0.436848i
$149$	2.39807	−	4.15358i	0.196457	−	0.340274i	−0.750920	−	0.660393i	$-0.770390\pi$
$149$	2.39807	−	4.15358i	0.196457	−	0.340274i	0.947377	+	0.320119i	$0.103723\pi$
$150$	5.42632	−	6.71622i	0.443057	−	0.548377i
$151$	8.13638	−	4.69754i	0.662129	−	0.382281i	−0.130958	−	0.991388i	$-0.541805\pi$
$151$	8.13638	−	4.69754i	0.662129	−	0.382281i	0.793088	+	0.609107i	$0.208472\pi$
$152$	−1.49961	+	0.401820i	−0.121635	+	0.0325919i
$153$	0.0385498	+	0.0385498i	0.00311656	+	0.00311656i
$154$	8.12090	+	3.32430i	0.654401	+	0.267879i
$155$	−2.54633	−	13.6962i	−0.204526	−	1.10011i
$156$	4.56456	+	2.63535i	0.365457	+	0.210997i
$157$	−2.15787	+	8.05326i	−0.172216	+	0.642720i	0.824793	+	0.565435i	$0.191292\pi$
$157$	−2.15787	+	8.05326i	−0.172216	+	0.642720i	−0.997009	+	0.0772850i	$0.975375\pi$
$158$	−1.34054	−	0.359196i	−0.106648	−	0.0285761i
$159$	−13.5987	−	7.85119i	−1.07844	−	0.622640i
$160$	−1.84351	−	1.26550i	−0.145742	−	0.100046i
$161$	6.34871	−	7.41967i	0.500349	−	0.584752i
$162$	6.32577	−	6.32577i	0.497000	−	0.497000i
$163$	1.16013	+	4.32967i	0.0908686	+	0.339126i	0.996361	−	0.0852369i	$-0.0271647\pi$
$163$	1.16013	+	4.32967i	0.0908686	+	0.339126i	−0.905492	+	0.424363i	$0.860498\pi$
$164$	3.09496	+	5.36063i	0.241676	+	0.418595i
$165$	3.56819	−	12.2997i	0.277783	−	0.957534i
$166$	−4.25011	+	7.36141i	−0.329873	+	0.571357i
$167$	−7.29704	+	7.29704i	−0.564662	+	0.564662i	−0.930628	−	0.365966i	$-0.880739\pi$
$167$	−7.29704	+	7.29704i	−0.564662	+	0.564662i	0.365966	+	0.930628i	$0.380739\pi$
$168$	−1.97072	+	4.12201i	−0.152044	+	0.318020i
$169$		−	3.68434i		−	0.283411i
$170$	−2.27029	+	6.42248i	−0.174124	+	0.492581i
$171$	−0.0240612	+	0.0138917i	−0.00184001	+	0.00106233i
$172$	−9.47570	−	2.53901i	−0.722515	−	0.193597i
$173$	21.9767	−	5.88864i	1.67086	−	0.447705i	0.705516	−	0.708694i	$-0.250715\pi$
$173$	21.9767	−	5.88864i	1.67086	−	0.447705i	0.965342	+	0.260989i	$0.0840487\pi$
$174$		−	15.1213i		−	1.14634i
$175$	−1.03526	+	13.1882i	−0.0782584	+	0.996933i
$176$	−3.24760	−	0.673107i	−0.244797	−	0.0507374i
$177$	7.73103	−	2.07152i	0.581100	−	0.155705i
$178$	3.72280	−	13.8937i	0.279036	−	1.04138i
$179$	−5.54106	+	3.19913i	−0.414158	+	0.239114i	−0.692575	−	0.721346i	$-0.743524\pi$
$179$	−5.54106	+	3.19913i	−0.414158	+	0.239114i	0.278417	+	0.960460i	$0.410190\pi$
$180$	−0.0377284	−	0.0133367i	−0.00281211	−	0.000994058i
$181$	−1.74418			−0.129644			−0.0648218	−	0.997897i	$-0.520648\pi$
$181$	−1.74418			−0.129644			−0.0648218	+	0.997897i	$0.520648\pi$
$182$	−8.05093	+	0.626232i	−0.596774	+	0.0464194i
$183$	10.4279	+	10.4279i	0.770856	+	0.770856i
$184$	−1.84544	+	3.19639i	−0.136047	+	0.235641i
$185$	−16.7548	−	1.30924i	−1.23184	−	0.0962575i
$186$	9.31722	−	5.37930i	0.683171	−	0.394429i
$187$	0.579940	+	10.0871i	0.0424094	+	0.737640i
$188$	−1.27006	+	1.27006i	−0.0926284	+	0.0926284i
$189$	−2.52511	+	13.5552i	−0.183675	+	0.985999i
$190$	−2.86207	−	1.96470i	−0.207636	−	0.142534i
$191$	0.510567	−	0.884328i	0.0369433	−	0.0639877i	−0.846963	−	0.531653i	$-0.821571\pi$
$191$	0.510567	−	0.884328i	0.0369433	−	0.0639877i	0.883906	+	0.467665i	$0.154905\pi$
$192$	0.446949	−	1.66804i	0.0322557	−	0.120380i
$193$	0.788030	−	2.94097i	0.0567237	−	0.211696i	−0.931747	−	0.363108i	$-0.881716\pi$
$193$	0.788030	−	2.94097i	0.0567237	−	0.211696i	0.988471	+	0.151413i	$0.0483822\pi$
$194$	4.43644	−	7.68413i	0.318518	−	0.551689i
$195$	2.15421	+	11.5871i	0.154267	+	0.829769i
$196$	−1.08242	−	6.91580i	−0.0773160	−	0.493986i
$197$	19.7134	−	19.7134i	1.40452	−	1.40452i	0.619603	−	0.784916i	$-0.287294\pi$
$197$	19.7134	−	19.7134i	1.40452	−	1.40452i	0.784916	−	0.619603i	$-0.212706\pi$
$198$	−0.0592558	+	0.00340682i	−0.00421113	+	0.000242112i
$199$	20.9597	−	12.1011i	1.48580	−	0.857825i	0.485928	−	0.873999i	$-0.338482\pi$
$199$	20.9597	−	12.1011i	1.48580	−	0.857825i	0.999869	+	0.0161734i	$0.00514837\pi$
$200$	−0.528180	−	4.97202i	−0.0373479	−	0.351575i
$201$	−13.4108	+	23.2281i	−0.945923	+	1.63839i
$202$	0.670552	+	0.670552i	0.0471799	+	0.0471799i
$203$	13.1047	+	19.1047i	0.919768	+	1.34089i
$204$	−5.26074			−0.368325
$205$	−4.61299	+	13.0498i	−0.322185	+	0.911435i
$206$	−10.3298	+	5.96393i	−0.719713	+	0.415527i
$207$	−0.0170953	+	0.0638005i	−0.00118820	+	0.00443444i
$208$	2.94816	−	0.789956i	0.204418	−	0.0547736i
$209$	−5.04195	−	1.04501i	−0.348759	−	0.0722848i
$210$	−9.86917	+	2.64068i	−0.681037	+	0.182224i
$211$		−	4.12319i		−	0.283852i	−0.989877	−	0.141926i	$-0.954671\pi$
$211$		−	4.12319i		−	0.283852i	0.989877	−	0.141926i	$-0.0453295\pi$
$212$	−8.78311	+	2.35343i	−0.603226	+	0.161634i
$213$	−6.76394	−	1.81239i	−0.463458	−	0.124183i
$214$	−6.94567	+	4.01009i	−0.474796	+	0.274124i
$215$	−9.45461	−	19.7936i	−0.644799	−	1.34991i
$216$		−	5.21153i		−	0.354600i
$217$	−7.10980	+	14.8711i	−0.482644	+	1.00951i
$218$	6.01639	−	6.01639i	0.407481	−	0.407481i
$219$	−9.38117	+	16.2487i	−0.633921	+	1.09798i
$220$	−3.57532	−	6.49747i	−0.241048	−	0.438059i
$221$	−4.64903	−	8.05235i	−0.312727	−	0.541660i
$222$	−3.35918	−	12.5366i	−0.225453	−	0.841404i
$223$	−5.84761	+	5.84761i	−0.391585	+	0.391585i	−0.875252	−	0.483667i	$-0.839305\pi$
$223$	−5.84761	+	5.84761i	−0.391585	+	0.391585i	0.483667	+	0.875252i	$0.339305\pi$
$224$	0.880894	+	2.49480i	0.0588572	+	0.166691i
$225$	−0.0321594	−	0.0835001i	−0.00214396	−	0.00556667i
$226$	0.244321	+	0.141059i	0.0162520	+	0.00938308i
$227$	20.6574	+	5.53514i	1.37108	+	0.367380i	0.867874	−	0.496785i	$-0.165486\pi$
$227$	20.6574	+	5.53514i	1.37108	+	0.367380i	0.503208	+	0.864165i	$0.332153\pi$
$228$	0.693894	−	2.58965i	0.0459543	−	0.171504i
$229$	17.6162	+	10.1707i	1.16411	+	0.672100i	0.952286	−	0.305207i	$-0.0987258\pi$
$229$	17.6162	+	10.1707i	1.16411	+	0.672100i	0.211826	+	0.977307i	$0.432059\pi$
$230$	−8.11400	+	1.50851i	−0.535021	+	0.0994685i
$231$	−11.9834	+	9.27464i	−0.788453	+	0.610227i
$232$	−6.19172	−	6.19172i	−0.406506	−	0.406506i
$233$	−28.1370	+	7.53929i	−1.84332	+	0.493915i	−0.999113	−	0.0421062i	$-0.986593\pi$
$233$	−28.1370	+	7.53929i	−1.84332	+	0.493915i	−0.844204	+	0.536022i	$0.819927\pi$
$234$	0.0473030	−	0.0273104i	0.00309229	−	0.00178534i
$235$	−4.00407	−	0.312884i	−0.261197	−	0.0204103i
$236$	2.31741	−	4.01387i	0.150850	−	0.261280i
$237$	1.69466	−	1.69466i	0.110080	−	0.110080i
$238$	6.64661	−	4.55917i	0.430836	−	0.295527i
$239$	7.18083			0.464489			0.232245	−	0.972657i	$-0.425393\pi$
$239$	7.18083			0.464489			0.232245	+	0.972657i	$0.425393\pi$
$240$	3.48433	−	1.66432i	0.224913	−	0.107432i
$241$	7.61472	−	4.39636i	0.490507	−	0.283194i	−0.234278	−	0.972170i	$-0.575273\pi$
$241$	7.61472	−	4.39636i	0.490507	−	0.283194i	0.724785	+	0.688975i	$0.241939\pi$
$242$	−8.61836	−	6.83548i	−0.554009	−	0.439401i
$243$	−0.0481342	−	0.179639i	−0.00308781	−	0.0115239i
$244$	8.53989			0.546711
$245$	10.1806	−	11.8893i	0.650412	−	0.759582i
$246$	−10.6892			−0.681521
$247$	4.57706	−	1.22642i	0.291231	−	0.0780351i
$248$	1.61247	−	6.01780i	0.102392	−	0.382131i
$249$	−7.33943	−	12.7123i	−0.465117	−	0.805607i
$250$	7.68248	−	8.12278i	0.485883	−	0.513729i
$251$	4.54374			0.286798			0.143399	−	0.989665i	$-0.454197\pi$
$251$	4.54374			0.286798			0.143399	+	0.989665i	$0.454197\pi$
$252$	0.0267825	+	0.0390451i	0.00168714	+	0.00245961i
$253$	−10.2324	+	6.71902i	−0.643307	+	0.422421i
$254$	9.04150	+	5.22012i	0.567314	+	0.327539i
$255$	−7.64468	−	8.94068i	−0.478728	−	0.559887i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.1428	−	3.78955i	0.882204	−	0.236386i	0.210846	−	0.977519i	$-0.432378\pi$
$257$	14.1428	−	3.78955i	0.882204	−	0.236386i	0.671358	+	0.741133i	$0.265711\pi$
$258$	11.9788	−	11.9788i	0.745768	−	0.745768i
$259$	15.1089	+	12.9280i	0.938819	+	0.803309i
$260$	5.62667	+	3.86249i	0.348951	+	0.239542i
$261$	−0.135709	−	0.0783516i	−0.00840017	−	0.00484984i
$262$	−4.45977	+	16.6441i	−0.275525	+	1.02827i
$263$	−6.34301	+	23.6725i	−0.391127	+	1.45971i	0.437151	+	0.899388i	$0.355988\pi$
$263$	−6.34301	+	23.6725i	−0.391127	+	1.45971i	−0.828278	+	0.560318i	$0.810679\pi$
$264$	3.81075	−	4.27567i	0.234535	−	0.263149i
$265$	−16.7629	−	11.5071i	−1.02974	−	0.706875i
$266$	1.36760	+	3.87321i	0.0838530	+	0.237482i
$267$	17.5639	+	17.5639i	1.07489	+	1.07489i
$268$	4.01993	+	15.0026i	0.245556	+	0.916429i
$269$	−13.9510	+	8.05459i	−0.850605	+	0.491097i	−0.860855	−	0.508850i	$-0.830071\pi$
$269$	−13.9510	+	8.05459i	−0.850605	+	0.491097i	0.0102498	+	0.999947i	$0.496737\pi$
$270$	8.85706	−	7.57318i	0.539023	−	0.460889i
$271$	1.92331	+	1.11042i	0.116832	+	0.0674533i	0.557277	−	0.830326i	$-0.311846\pi$
$271$	1.92331	+	1.11042i	0.116832	+	0.0674533i	−0.440445	+	0.897780i	$0.645179\pi$
$272$	−2.15412	+	2.15412i	−0.130613	+	0.130613i
$273$	6.01494	−	12.5810i	0.364041	−	0.761439i
$274$	−5.24998			−0.317163
$275$	5.84701	−	15.5181i	0.352588	−	0.935779i
$276$	−3.18684	−	5.51977i	−0.191825	−	0.332251i
$277$	−20.6259	−	5.52669i	−1.23929	−	0.332066i	−0.421099	−	0.907015i	$-0.638356\pi$
$277$	−20.6259	−	5.52669i	−1.23929	−	0.332066i	−0.818190	+	0.574948i	$0.805022\pi$
$278$	−3.60475	−	13.4531i	−0.216199	−	0.806865i
$279$		−	0.111492i		−	0.00667488i
$280$	−2.95986	+	5.12242i	−0.176886	+	0.306123i
$281$		−	20.9838i		−	1.25179i	−0.779909	−	0.625893i	$-0.784735\pi$
$281$		−	20.9838i		−	1.25179i	0.779909	−	0.625893i	$-0.215265\pi$
$282$	−0.802779	−	2.99601i	−0.0478048	−	0.178410i
$283$	−1.45504	+	5.43029i	−0.0864933	+	0.322797i	−0.995593	−	0.0937817i	$-0.970104\pi$
$283$	−1.45504	+	5.43029i	−0.0864933	+	0.322797i	0.909099	+	0.416579i	$0.136771\pi$
$284$	−3.51177	+	2.02752i	−0.208385	+	0.120311i
$285$	5.40947	−	2.58388i	0.320429	−	0.153056i
$286$	9.91219	+	2.05443i	0.586120	+	0.121481i
$287$	13.5052	−	9.26372i	0.797185	−	0.546820i
$288$	−0.0126542	−	0.0126542i	−0.000745659	−	0.000745659i
$289$	−6.68529	−	3.85976i	−0.393252	−	0.227044i
$290$	1.52536	−	19.5204i	0.0895720	−	1.14628i
$291$	7.66118	+	13.2696i	0.449106	+	0.777875i
$292$	2.81204	+	10.4947i	0.164562	+	0.614155i
$293$	−5.42475	−	5.42475i	−0.316917	−	0.316917i	0.530665	−	0.847582i	$-0.321942\pi$
$293$	−5.42475	−	5.42475i	−0.316917	−	0.316917i	−0.847582	+	0.530665i	$0.821942\pi$
$294$	11.2773	+	4.35259i	0.657707	+	0.253848i
$295$	10.1892	−	1.89432i	0.593236	−	0.110291i
$296$	−6.50888	−	3.75790i	−0.378321	−	0.218424i
$297$	7.76890	−	15.4404i	0.450798	−	0.895941i
$298$	4.63271	+	1.24133i	0.268366	+	0.0719084i
$299$	5.63256	−	9.75588i	0.325739	−	0.564197i
$300$	7.89181	+	3.50313i	0.455634	+	0.202254i
$301$	−4.75315	+	25.5158i	−0.273967	+	1.47071i
$302$	6.64333	+	6.64333i	0.382281	+	0.382281i
$303$	−1.58180	+	0.423843i	−0.0908723	+	0.0243492i
$304$	−0.776257	−	1.34452i	−0.0445214	−	0.0771133i
$305$	12.4098	+	14.5136i	0.710583	+	0.831049i
$306$	−0.0272588	+	0.0472136i	−0.00155828	+	0.00269902i
$307$	6.63243	−	6.63243i	0.378533	−	0.378533i	−0.492040	−	0.870573i	$-0.663749\pi$
$307$	6.63243	−	6.63243i	0.378533	−	0.378533i	0.870573	+	0.492040i	$0.163749\pi$
$308$	−1.10918	+	8.70458i	−0.0632013	+	0.495990i
$309$		−	20.5979i		−	1.17178i
$310$	12.5705	−	6.00441i	0.713955	−	0.341027i
$311$	6.80279	+	11.7828i	0.385751	+	0.668140i	0.991873	−	0.127232i	$-0.0406092\pi$
$311$	6.80279	+	11.7828i	0.385751	+	0.668140i	−0.606122	+	0.795371i	$0.707276\pi$
$312$	−1.36416	+	5.09110i	−0.0772302	+	0.288227i
$313$	6.41779	+	23.9515i	0.362755	+	1.35382i	0.870439	+	0.492276i	$0.163835\pi$
$313$	6.41779	+	23.9515i	0.362755	+	1.35382i	−0.507684	+	0.861543i	$0.669498\pi$
$314$	−8.33735			−0.470504
$315$	−0.0274383	+	0.102256i	−0.00154597	+	0.00576146i
$316$		−	1.38783i		−	0.0780714i
$317$	−20.2960	+	5.43830i	−1.13994	+	0.305445i	−0.778926	−	0.627116i	$-0.784235\pi$
$317$	−20.2960	+	5.43830i	−1.13994	+	0.305445i	−0.361012	+	0.932561i	$0.617569\pi$
$318$	4.06408	−	15.1673i	0.227902	−	0.850542i
$319$	−9.11432	−	27.5745i	−0.510304	−	1.54387i
$320$	0.745241	−	2.10823i	0.0416602	−	0.117853i
$321$		−	13.8499i		−	0.773023i
$322$	8.81002	+	4.21203i	0.490963	+	0.234727i
$323$	−3.34431	+	3.34431i	−0.186082	+	0.186082i
$324$	7.74746	+	4.47300i	0.430414	+	0.248500i
$325$	1.61209	+	15.1754i	0.0894225	+	0.841779i
$326$	−3.88188	+	2.24120i	−0.214997	+	0.124129i
$327$	3.80284	+	14.1924i	0.210298	+	0.784841i
$328$	−4.37694	+	4.37694i	−0.241676	+	0.241676i
$329$	3.61072	+	3.08955i	0.199066	+	0.170332i
$330$	12.8042	+	0.263198i	0.704846	+	0.0144886i
$331$	5.43730	−	9.41768i	0.298861	−	0.517643i	−0.677015	−	0.735970i	$-0.736727\pi$
$331$	5.43730	−	9.41768i	0.298861	−	0.517643i	0.975876	+	0.218327i	$0.0700600\pi$
$332$	−8.21059	−	2.20002i	−0.450615	−	0.120742i
$333$	−0.129918	−	0.0348115i	−0.00711949	−	0.00190766i
$334$	−8.93701	−	5.15979i	−0.489011	−	0.282331i
$335$	−19.6555	+	28.6330i	−1.07389	+	1.56439i
$336$	−4.49162	−	0.836712i	−0.245038	−	0.0456464i
$337$	6.64080	−	6.64080i	0.361747	−	0.361747i	−0.502709	−	0.864456i	$-0.667663\pi$
$337$	6.64080	−	6.64080i	0.361747	−	0.361747i	0.864456	+	0.502709i	$0.167663\pi$
$338$	3.55880	−	0.953578i	0.193573	−	0.0518678i
$339$	−0.421912	+	0.243591i	−0.0229151	+	0.0132300i
$340$	−6.79123	−	0.530677i	−0.368306	−	0.0287800i
$341$	13.7481	−	15.4254i	0.744502	−	0.835332i
$342$	−0.0196459	−	0.0196459i	−0.00106233	−	0.00106233i
$343$	−18.0203	+	4.27417i	−0.973005	+	0.230783i
$344$		−	9.80996i		−	0.528918i
$345$	4.74993	−	13.4372i	0.255728	−	0.723432i
$346$	11.3760	+	19.7038i	0.611576	+	1.05928i
$347$	5.08406	+	1.36227i	0.272927	+	0.0731305i	0.392687	−	0.919672i	$-0.371546\pi$
$347$	5.08406	+	1.36227i	0.272927	+	0.0731305i	−0.119760	+	0.992803i	$0.538212\pi$
$348$	14.6060	−	3.91367i	0.782964	−	0.209795i
$349$	−15.3310			−0.820652			−0.410326	−	0.911939i	$-0.634585\pi$
$349$	−15.3310			−0.820652			−0.410326	+	0.911939i	$0.634585\pi$
$350$	−13.0068	+	2.41337i	−0.695240	+	0.129000i
$351$			15.9064i			0.849022i
$352$	−0.190370	−	3.31116i	−0.0101467	−	0.176485i
$353$	−0.127441	−	0.0341476i	−0.00678298	−	0.00181749i	0.255426	−	0.966829i	$-0.417784\pi$
$353$	−0.127441	−	0.0341476i	−0.00678298	−	0.00181749i	−0.262209	+	0.965011i	$0.584451\pi$
$354$	4.00188	+	6.93145i	0.212697	+	0.368403i
$355$	−8.54893	−	3.02198i	−0.453730	−	0.160390i
$356$	14.3838			0.762340
$357$	1.07938	+	13.8767i	0.0571270	+	0.734433i
$358$	−4.52425	−	4.52425i	−0.239114	−	0.239114i
$359$	−15.7554	+	27.2891i	−0.831536	+	1.44026i	0.0652836	+	0.997867i	$0.479205\pi$
$359$	−15.7554	+	27.2891i	−0.831536	+	1.44026i	−0.896820	+	0.442396i	$0.854129\pi$
$360$	0.00311742	−	0.0398946i	0.000164303	−	0.00210263i
$361$	8.29485	+	14.3671i	0.436571	+	0.756163i
$362$	−0.451426	−	1.68475i	−0.0237264	−	0.0885482i
$363$	17.6640	−	6.98691i	0.927121	−	0.366718i
$364$	−2.68863	−	7.61452i	−0.140922	−	0.399109i
$365$	−13.7495	+	20.0295i	−0.719681	+	1.04839i
$366$	−7.37367	+	12.7716i	−0.385428	+	0.667581i
$367$	−3.70581	+	13.8303i	−0.193442	+	0.721935i	0.799223	+	0.601035i	$0.205245\pi$
$367$	−3.70581	+	13.8303i	−0.193442	+	0.721935i	−0.992665	+	0.120900i	$0.961422\pi$
$368$	−3.56511	−	0.955268i	−0.185844	−	0.0497968i
$369$	−0.0553869	+	0.0959328i	−0.00288332	+	0.00499406i
$370$	−3.07183	−	16.5227i	−0.159697	−	0.858976i
$371$	8.00992	+	22.6851i	0.415854	+	1.17775i
$372$	7.60748	+	7.60748i	0.394429	+	0.394429i
$373$	12.8496	−	3.44304i	0.665327	−	0.178274i	0.0896779	−	0.995971i	$-0.471416\pi$
$373$	12.8496	−	3.44304i	0.665327	−	0.178274i	0.575649	+	0.817697i	$0.304750\pi$
$374$	−9.59327	+	3.17091i	−0.496056	+	0.163964i
$375$	5.51442	+	18.5028i	0.284763	+	0.955481i
$376$	−1.55550	−	0.898066i	−0.0802186	−	0.0463142i
$377$	18.8981	+	18.8981i	0.973302	+	0.973302i
$378$	−13.7469	+	1.06929i	−0.707064	+	0.0549982i
$379$			3.34431i			0.171786i	0.996304	+	0.0858928i	$0.0273743\pi$
$379$			3.34431i			0.171786i	−0.996304	+	0.0858928i	$0.972626\pi$
$380$	1.15700	−	3.27305i	0.0593527	−	0.167904i
$381$	−15.6136	+	9.01450i	−0.799907	+	0.461827i
$382$	0.986340	+	0.264289i	0.0504655	+	0.0135222i
$383$	−5.32581	−	19.8762i	−0.272136	−	1.01563i	−0.957736	−	0.287647i	$-0.907127\pi$
$383$	−5.32581	−	19.8762i	−0.272136	−	1.01563i	0.685601	−	0.727978i	$-0.259540\pi$
$384$	1.72688			0.0881243
$385$	−16.4053	+	10.7641i	−0.836093	+	0.548587i
$386$	3.04471			0.154972
$387$	−0.0454376	−	0.169575i	−0.00230972	−	0.00861999i
$388$	8.57054	+	2.29647i	0.435103	+	0.116586i
$389$	12.2119	−	7.05055i	0.619168	−	0.357477i	−0.157377	−	0.987539i	$-0.550304\pi$
$389$	12.2119	−	7.05055i	0.619168	−	0.357477i	0.776545	+	0.630062i	$0.216970\pi$
$390$	−10.6347	+	5.07977i	−0.538510	+	0.257224i
$391$			11.2438i			0.568625i
$392$	6.40000	−	2.83548i	0.323249	−	0.143214i
$393$	−21.0408	−	21.0408i	−1.06137	−	1.06137i
$394$	24.1438	+	13.9394i	1.21635	+	0.702259i
$395$	2.35863	−	2.01673i	0.118675	−	0.101473i
$396$	−0.0186273	−	0.0563550i	−0.000936056	−	0.00283194i
$397$	33.4441	−	8.96132i	1.67851	−	0.449756i	0.711127	−	0.703064i	$-0.248185\pi$
$397$	33.4441	−	8.96132i	1.67851	−	0.449756i	0.967386	+	0.253308i	$0.0815186\pi$
$398$	17.1136	+	17.1136i	0.857825	+	0.857825i
$399$	−6.97330	−	1.29901i	−0.349102	−	0.0650317i
$400$	4.66590	−	1.79704i	0.233295	−	0.0898518i
$401$	6.32514	−	10.9555i	0.315862	−	0.547090i	−0.663758	−	0.747947i	$-0.731040\pi$
$401$	6.32514	−	10.9555i	0.315862	−	0.547090i	0.979620	+	0.200858i	$0.0643729\pi$
$402$	−25.9076	−	6.94193i	−1.29215	−	0.346232i
$403$	−4.92150	+	18.3673i	−0.245157	+	0.914939i
$404$	−0.474152	+	0.821255i	−0.0235899	+	0.0408590i
$405$	3.65636	+	19.6668i	0.181686	+	0.977254i
$406$	−15.0620	+	17.6028i	−0.747516	+	0.873613i
$407$	−13.6821	−	20.8365i	−0.678197	−	1.03283i
$408$	−1.36158	−	5.08148i	−0.0674082	−	0.251571i
$409$	2.34735	+	4.06573i	0.116069	+	0.201038i	0.918207	−	0.396102i	$-0.129637\pi$
$409$	2.34735	+	4.06573i	0.116069	+	0.201038i	−0.802138	+	0.597139i	$0.796304\pi$
$410$	−13.7990	−	1.07828i	−0.681485	−	0.0532523i
$411$	4.53303	−	7.85144i	0.223598	−	0.387283i
$412$	−8.43427	−	8.43427i	−0.415527	−	0.415527i
$413$	−11.0632	−	5.28926i	−0.544384	−	0.260268i
$414$	−0.0660511			−0.00324623
$415$	−8.19231	−	17.1510i	−0.402145	−	0.841908i
$416$	1.52608	+	2.64324i	0.0748221	+	0.129596i
$417$	23.2319	+	6.22497i	1.13767	+	0.304838i
$418$	−0.295552	−	5.14062i	−0.0144559	−	0.251436i
$419$			26.6533i			1.30210i	0.759036	+	0.651049i	$0.225671\pi$
$419$			26.6533i			1.30210i	−0.759036	+	0.651049i	$0.774329\pi$
$420$	−5.10503	−	8.84943i	−0.249100	−	0.431808i
$421$	9.06968			0.442029			0.221015	−	0.975270i	$-0.429063\pi$
$421$	9.06968			0.442029			0.221015	+	0.975270i	$0.429063\pi$
$422$	3.98269	−	1.06716i	0.193874	−	0.0519485i
$423$	−0.0310480	−	0.00831928i	−0.00150960	−	0.000404497i
$424$	−4.54647	−	7.87472i	−0.220796	−	0.382430i
$425$	−8.96683	−	12.3129i	−0.434955	−	0.597265i
$426$		−	7.00255i		−	0.339275i
$427$	−1.75219	−	22.5264i	−0.0847944	−	1.09013i
$428$	−5.67112	−	5.67112i	−0.274124	−	0.274124i
$429$	−11.6310	+	13.0500i	−0.561550	+	0.630060i
$430$	16.6721	−	14.2554i	0.804002	−	0.687457i
$431$	16.5720	−	9.56786i	0.798246	−	0.460867i	−0.0446117	−	0.999004i	$-0.514205\pi$
$431$	16.5720	−	9.56786i	0.798246	−	0.460867i	0.842857	+	0.538137i	$0.180872\pi$
$432$	5.03396	−	1.34884i	0.242196	−	0.0648963i
$433$	−2.40966	+	2.40966i	−0.115801	+	0.115801i	−0.762633	−	0.646832i	$-0.776094\pi$
$433$	−2.40966	+	2.40966i	−0.115801	+	0.115801i	0.646832	+	0.762633i	$0.276094\pi$
$434$	−16.2045	−	3.01862i	−0.777841	−	0.144898i
$435$	27.8761	+	19.1359i	1.33656	+	0.917496i
$436$	7.36854	+	4.25423i	0.352889	+	0.203741i
$437$	−5.53488	−	1.48307i	−0.264769	−	0.0709447i
$438$	−18.1230	−	4.85605i	−0.865952	−	0.232031i
$439$	17.0113	−	29.4645i	0.811907	−	1.40626i	−0.0996203	−	0.995026i	$-0.531763\pi$
$439$	17.0113	−	29.4645i	0.811907	−	1.40626i	0.911528	−	0.411239i	$-0.134904\pi$
$440$	5.35071	−	5.13516i	0.255085	−	0.244809i
$441$	0.0974973	−	0.0786576i	0.00464273	−	0.00374560i
$442$	6.57472	−	6.57472i	0.312727	−	0.312727i
$443$	−2.87977	−	10.7474i	−0.136822	−	0.510627i	−0.999984	−	0.00569915i	$-0.998186\pi$
$443$	−2.87977	−	10.7474i	−0.136822	−	0.510627i	0.863162	−	0.504927i	$-0.168481\pi$
$444$	11.2400	−	6.48944i	0.533429	−	0.307975i
$445$	20.9019	+	24.4454i	0.990846	+	1.15882i
$446$	−7.16183	−	4.13488i	−0.339122	−	0.195792i
$447$	−5.85650	+	5.85650i	−0.277003	+	0.277003i
$448$	−2.18180	+	1.49658i	−0.103080	+	0.0707068i
$449$			37.4110i			1.76553i	0.469810	+	0.882767i	$0.344322\pi$
$449$			37.4110i			1.76553i	−0.469810	+	0.882767i	$0.655678\pi$
$450$	0.0723314	−	0.0526750i	0.00340974	−	0.00248313i
$451$	−19.4925	+	6.44293i	−0.917864	+	0.303386i
$452$	−0.0730173	+	0.272504i	−0.00343445	+	0.0128175i
$453$	−15.6713	+	4.19912i	−0.736303	+	0.197292i
$454$			21.3861i			1.00370i
$455$	9.03396	−	15.6344i	0.423518	−	0.732954i
$456$	2.68100			0.125549
$457$	5.26827	+	19.6614i	0.246439	+	0.919723i	0.972655	+	0.232256i	$0.0746108\pi$
$457$	5.26827	+	19.6614i	0.246439	+	0.919723i	−0.726216	+	0.687467i	$0.758723\pi$
$458$	−5.26475	+	19.6483i	−0.246006	+	0.918106i
$459$	−7.93818	−	13.7493i	−0.370523	−	0.641764i
$460$	−3.55717	−	7.44709i	−0.165854	−	0.347222i
$461$		−	7.33590i		−	0.341667i	−0.985300	−	0.170834i	$-0.945354\pi$
$461$		−	7.33590i		−	0.341667i	0.985300	−	0.170834i	$-0.0546460\pi$
$462$	−12.0602	−	9.17467i	−0.561089	−	0.426844i
$463$	−27.0696	+	27.0696i	−1.25803	+	1.25803i	−0.305998	+	0.952032i	$0.598990\pi$
$463$	−27.0696	+	27.0696i	−1.25803	+	1.25803i	−0.952032	+	0.305998i	$0.901010\pi$
$464$	4.37821	−	7.58328i	0.203253	−	0.352045i
$465$	−1.87413	+	23.9838i	−0.0869108	+	1.11222i
$466$	−14.5648	−	25.2270i	−0.674701	−	1.16862i
$467$	−24.2941	+	6.50958i	−1.12420	+	0.301227i	−0.772580	−	0.634917i	$-0.781034\pi$
$467$	−24.2941	+	6.50958i	−1.12420	+	0.301227i	−0.351616	+	0.936145i	$0.614368\pi$
$468$	0.0386227	+	0.0386227i	0.00178534	+	0.00178534i
$469$	38.7488	−	13.6819i	1.78925	−	0.631771i
$470$	−0.734106	−	3.94861i	−0.0338618	−	0.182136i
$471$	7.19879	−	12.4687i	0.331703	−	0.574526i
$472$	4.47689	+	1.19958i	0.206065	+	0.0552150i
$473$	14.6238	−	29.0643i	0.672405	−	1.33638i
$474$	2.07552	+	1.19830i	0.0953320	+	0.0550399i
$475$	7.24388	−	2.78993i	0.332372	−	0.128011i
$476$	6.12409	+	5.24013i	0.280697	+	0.240181i
$477$	−0.115064	−	0.115064i	−0.00526843	−	0.00526843i
$478$	1.85854	+	6.93615i	0.0850074	+	0.317252i
$479$	−10.1662	−	17.6085i	−0.464508	−	0.804551i	0.534671	−	0.845060i	$-0.320435\pi$
$479$	−10.1662	−	17.6085i	−0.464508	−	0.804551i	−0.999179	+	0.0405090i	$0.987102\pi$
$480$	2.50942	+	2.93485i	0.114539	+	0.133957i
$481$	19.8661	+	11.4697i	0.905817	+	0.522974i
$482$	6.21739	+	6.21739i	0.283194	+	0.283194i
$483$	−13.9061	+	9.53872i	−0.632749	+	0.434027i
$484$	4.37197	−	10.0939i	0.198726	−	0.458811i
$485$	8.55146	+	17.9028i	0.388302	+	0.812926i
$486$	0.161060	−	0.0929881i	0.00730583	−	0.00421803i
$487$	−10.7838	+	40.2456i	−0.488660	+	1.82370i	0.0743210	+	0.997234i	$0.476321\pi$
$487$	−10.7838	+	40.2456i	−0.488660	+	1.82370i	−0.562981	+	0.826470i	$0.690346\pi$
$488$	2.21029	+	8.24890i	0.100055	+	0.373410i
$489$		−	7.74057i		−	0.350041i
$490$	14.1191	+	6.75647i	0.637838	+	0.305226i
$491$			13.6711i			0.616969i	0.951229	+	0.308484i	$0.0998217\pi$
$491$			13.6711i			0.616969i	−0.951229	+	0.308484i	$0.900178\pi$
$492$	−2.76658	−	10.3250i	−0.124727	−	0.465488i
$493$	−25.7665	−	6.90412i	−1.16047	−	0.310946i
$494$	2.36926	+	4.10368i	0.106598	+	0.184633i
$495$	0.0687075	−	0.113550i	0.00308817	−	0.00510369i
$496$	6.23009			0.279739
$497$	6.06869	+	8.84728i	0.272218	+	0.396855i
$498$	10.3795	−	10.3795i	0.465117	−	0.465117i
$499$	3.10495	+	1.79265i	0.138997	+	0.0802498i	0.567886	−	0.823107i	$-0.307762\pi$
$499$	3.10495	+	1.79265i	0.138997	+	0.0802498i	−0.428889	+	0.903357i	$0.641095\pi$
$500$	9.83437	+	5.31838i	0.439806	+	0.237845i
$501$	15.4331	−	8.91031i	0.689501	−	0.398083i
$502$	1.17601	+	4.38892i	0.0524878	+	0.195887i
$503$	−20.7003	−	20.7003i	−0.922979	−	0.922979i	0.0742598	−	0.997239i	$-0.476341\pi$
$503$	−20.7003	−	20.7003i	−0.922979	−	0.922979i	−0.997239	+	0.0742598i	$0.976341\pi$
$504$	−0.0307828	+	0.0359755i	−0.00137118	+	0.00160248i
$505$	−2.08475	+	0.387586i	−0.0927701	+	0.0172474i
$506$	−9.13842	−	8.14475i	−0.406252	−	0.362078i
$507$	−1.64671	+	6.14561i	−0.0731330	+	0.272936i
$508$	−2.70213	+	10.0845i	−0.119888	+	0.447427i
$509$	6.48630	+	3.74487i	0.287500	+	0.165988i	0.636814	−	0.771017i	$-0.280252\pi$
$509$	6.48630	+	3.74487i	0.287500	+	0.165988i	−0.349314	+	0.937006i	$0.613585\pi$
$510$	6.65745	−	9.69821i	0.294797	−	0.429444i
$511$	27.1057	−	9.57083i	1.19909	−	0.423389i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	7.81529	−	2.09410i	0.345053	−	0.0924568i
$514$	7.32085	+	12.6801i	0.322909	+	0.559295i
$515$	2.07782	−	26.5904i	0.0915595	−	1.17171i
$516$	14.6710	+	8.47030i	0.645854	+	0.372884i
$517$	−3.26976	−	4.97953i	−0.143804	−	0.218999i
$518$	−8.57707	+	17.9401i	−0.376855	+	0.788241i
$519$	−39.2898			−1.72463
$520$	−2.27459	+	6.43463i	−0.0997475	+	0.282177i
$521$	−12.7223	−	22.0357i	−0.557376	−	0.965403i	−0.997714	−	0.0675712i	$-0.978475\pi$
$521$	−12.7223	−	22.0357i	−0.557376	−	0.965403i	0.440339	−	0.897832i	$-0.354858\pi$
$522$	0.0405578	−	0.151364i	0.00177516	−	0.00662500i
$523$	−5.00656	+	1.34150i	−0.218921	+	0.0586598i	−0.366613	−	0.930374i	$-0.619483\pi$
$523$	−5.00656	+	1.34150i	−0.218921	+	0.0586598i	0.147691	+	0.989034i	$0.452816\pi$
$524$	−17.2312			−0.752749
$525$	7.62129	−	21.5356i	0.332621	−	0.939893i
$526$	−24.5075			−1.06858
$527$	−4.91220	−	18.3326i	−0.213979	−	0.798579i
$528$	5.11627	+	2.57428i	0.222657	+	0.112031i
$529$	8.12113	−	4.68874i	0.353093	−	0.203858i
$530$	6.77643	−	19.1700i	0.294349	−	0.832690i
$531$	0.0829437			0.00359945
$532$	−3.38727	+	2.32346i	−0.146857	+	0.100735i
$533$	13.3591	−	13.3591i	0.578647	−	0.578647i
$534$	−12.4195	+	21.5113i	−0.537446	+	0.930884i
$535$	1.39710	−	17.8791i	0.0604020	−	0.772983i
$536$	−13.4510	+	7.76591i	−0.580993	+	0.335436i
$537$	10.6725	−	2.85969i	0.460553	−	0.123405i
$538$	−11.3909	−	11.3909i	−0.491097	−	0.491097i
$539$	23.1884	+	1.13979i	0.998794	+	0.0490944i
$540$	9.60750	+	6.59518i	0.413441	+	0.283811i
$541$	29.6625	+	17.1257i	1.27529	+	0.736290i	0.975979	−	0.217865i	$-0.0699092\pi$
$541$	29.6625	+	17.1257i	1.27529	+	0.736290i	0.299313	+	0.954155i	$0.403243\pi$
$542$	−0.574796	+	2.14517i	−0.0246896	+	0.0921429i
$543$	2.90935	+	0.779557i	0.124852	+	0.0334540i
$544$	−2.63825	−	1.52319i	−0.113114	−	0.0653064i
$545$	3.47753	+	18.7050i	0.148961	+	0.801233i
$546$	13.7091	+	2.55377i	0.586696	+	0.109291i
$547$	27.6507	−	27.6507i	1.18226	−	1.18226i	0.203101	−	0.979158i	$-0.434898\pi$
$547$	27.6507	−	27.6507i	1.18226	−	1.18226i	0.979158	−	0.203101i	$-0.0651019\pi$
$548$	−1.35879	−	5.07109i	−0.0580448	−	0.216626i
$549$	0.0764141	+	0.132353i	0.00326128	+	0.00564870i
$550$	16.5027	+	1.63139i	0.703677	+	0.0695626i
$551$	6.79723	−	11.7731i	0.289572	−	0.501553i
$552$	4.50687	−	4.50687i	0.191825	−	0.191825i
$553$	−3.66079	+	0.284750i	−0.155673	+	0.0121088i
$554$		−	21.3535i		−	0.907223i
$555$	27.3624	+	9.67239i	1.16147	+	0.410570i
$556$	12.0617	−	6.96385i	0.511532	−	0.295333i
$557$	8.03579	+	2.15318i	0.340487	+	0.0912333i	0.425011	−	0.905188i	$-0.360270\pi$
$557$	8.03579	+	2.15318i	0.340487	+	0.0912333i	−0.0845237	+	0.996421i	$0.526937\pi$
$558$	0.107693	−	0.0288564i	0.00455903	−	0.00122159i
$559$			29.9415i			1.26639i
$560$	−5.71395	−	1.53323i	−0.241458	−	0.0647906i
$561$	3.54104	−	17.0848i	0.149503	−	0.721321i
$562$	20.2688	−	5.43100i	0.854986	−	0.229093i
$563$	4.42137	−	16.5008i	0.186338	−	0.695424i	−0.808002	−	0.589180i	$-0.799451\pi$
$563$	4.42137	−	16.5008i	0.186338	−	0.695424i	0.994340	−	0.106244i	$-0.0338825\pi$
$564$	2.68615	−	1.55085i	0.113107	−	0.0653025i
$565$	−0.569229	+	0.271898i	−0.0239477	+	0.0114388i
$566$	−5.62185			−0.236304
$567$	10.2092	−	21.3539i	0.428746	−	0.896778i
$568$	−2.86734	−	2.86734i	−0.120311	−	0.120311i
$569$	−0.641650	+	1.11137i	−0.0268994	+	0.0465911i	−0.879162	−	0.476524i	$-0.841897\pi$
$569$	−0.641650	+	1.11137i	−0.0268994	+	0.0465911i	0.852262	+	0.523115i	$0.175230\pi$
$570$	3.89591	+	4.55639i	0.163182	+	0.190846i
$571$	7.41728	−	4.28237i	0.310404	−	0.179212i	−0.336703	−	0.941611i	$-0.609312\pi$
$571$	7.41728	−	4.28237i	0.310404	−	0.179212i	0.647107	+	0.762399i	$0.275979\pi$
$572$	0.581038	+	10.1062i	0.0242944	+	0.422560i
$573$	−1.24689	+	1.24689i	−0.0520897	+	0.0520897i
$574$	12.4435	+	10.6474i	0.519380	+	0.444413i
$575$	7.48728	−	16.8672i	0.312241	−	0.703413i
$576$	0.00894790	−	0.0154982i	0.000372829	−	0.000645759i
$577$	9.57305	−	35.7271i	0.398531	−	1.48734i	−0.417150	−	0.908838i	$-0.636971\pi$
$577$	9.57305	−	35.7271i	0.398531	−	1.48734i	0.815681	−	0.578501i	$-0.196362\pi$
$578$	1.99796	−	7.45647i	0.0831040	−	0.310148i
$579$	−2.62892	+	4.55343i	−0.109254	+	0.189234i
$580$	19.2501	−	3.57888i	0.799316	−	0.148605i
$581$	−4.11856	+	22.1092i	−0.170866	+	0.917242i
$582$	−10.8345	+	10.8345i	−0.449106	+	0.449106i
$583$	−1.73102	−	30.1082i	−0.0716916	−	1.24695i
$584$	−9.40928	+	5.43245i	−0.389359	+	0.224796i
$585$	−0.00951487	+	0.121765i	−0.000393391	+	0.00503435i
$586$	3.83588	−	6.64393i	0.158459	−	0.274458i
$587$	−23.3298	−	23.3298i	−0.962925	−	0.962925i	0.0364115	−	0.999337i	$-0.488407\pi$
$587$	−23.3298	−	23.3298i	−0.962925	−	0.962925i	−0.999337	+	0.0364115i	$0.988407\pi$
$588$	−1.28549	+	12.0196i	−0.0530126	+	0.495680i
$589$	9.67230			0.398540
$590$	4.46692	+	9.35169i	0.183900	+	0.385003i
$591$	−41.6934	+	24.0717i	−1.71504	+	0.990178i
$592$	1.94523	−	7.25971i	0.0799487	−	0.298372i
$593$	33.1220	−	8.87501i	1.36016	−	0.364453i	0.496283	−	0.868161i	$-0.334698\pi$
$593$	33.1220	−	8.87501i	1.36016	−	0.364453i	0.863874	+	0.503708i	$0.168031\pi$
$594$	16.9250	+	3.50792i	0.694441	+	0.143932i
$595$	−0.00640649	+	18.0227i	−0.000262640	+	0.738858i
$596$			4.79614i			0.196457i
$597$	−40.3702	+	10.8172i	−1.65224	+	0.442717i
$598$	10.8813	+	2.91563i	0.444968	+	0.119229i
$599$	−32.8575	+	18.9703i	−1.34252	+	0.775106i	−0.987177	−	0.159629i	$-0.948970\pi$
$599$	−32.8575	+	18.9703i	−1.34252	+	0.775106i	−0.355346	+	0.934735i	$0.615637\pi$
$600$	−1.34122	+	8.52958i	−0.0547550	+	0.348219i
$601$		−	18.4286i		−	0.751717i	−0.926677	−	0.375858i	$-0.877348\pi$
$601$		−	18.4286i		−	0.751717i	0.926677	−	0.375858i	$-0.122652\pi$
$602$	−25.8766	+	2.01278i	−1.05465	+	0.0820347i
$603$	−0.196543	+	0.196543i	−0.00800387	+	0.00800387i
$604$	−4.69754	+	8.13638i	−0.191140	+	0.331065i
$605$	23.5078	−	7.23774i	0.955727	−	0.294256i
$606$	−0.818802	−	1.41821i	−0.0332616	−	0.0576107i
$607$	2.29557	+	8.56717i	0.0931742	+	0.347731i	0.996736	−	0.0807263i	$-0.0257240\pi$
$607$	2.29557	+	8.56717i	0.0931742	+	0.347731i	−0.903562	+	0.428457i	$0.859057\pi$
$608$	1.09779	−	1.09779i	0.0445214	−	0.0445214i
$609$	−13.3202	−	37.7245i	−0.539763	−	1.52867i
$610$	−10.8072	+	15.7434i	−0.437571	+	0.637430i
$611$	4.74762	+	2.74104i	0.192068	+	0.110891i
$612$	−0.0526600	−	0.0141102i	−0.00212865	−	0.000570371i
$613$	−7.39891	+	27.6131i	−0.298839	+	1.11528i	0.639281	+	0.768973i	$0.279232\pi$
$613$	−7.39891	+	27.6131i	−0.298839	+	1.11528i	−0.938120	+	0.346310i	$0.887435\pi$
$614$	8.12304	+	4.68984i	0.327819	+	0.189266i
$615$	13.5272	−	19.7057i	0.545469	−	0.794610i
$616$	−8.69506	+	1.18153i	−0.350334	+	0.0476051i
$617$	−13.2472	−	13.2472i	−0.533311	−	0.533311i	0.388245	−	0.921556i	$-0.373081\pi$
$617$	−13.2472	−	13.2472i	−0.533311	−	0.533311i	−0.921556	+	0.388245i	$0.873081\pi$
$618$	19.8961	−	5.33114i	0.800338	−	0.214450i
$619$	11.5612	−	6.67484i	0.464682	−	0.268284i	−0.249329	−	0.968419i	$-0.580210\pi$
$619$	11.5612	−	6.67484i	0.464682	−	0.268284i	0.714011	+	0.700134i	$0.246877\pi$
$620$	9.05329	+	10.5881i	0.363589	+	0.425228i
$621$	9.61755	−	16.6581i	0.385939	−	0.668466i
$622$	−9.62059	+	9.62059i	−0.385751	+	0.385751i
$623$	−2.95123	−	37.9414i	−0.118238	−	1.52009i
$624$	−5.27070			−0.210997
$625$	5.25224	+	24.4421i	0.210090	+	0.977682i
$626$	−21.4743	+	12.3982i	−0.858287	+	0.495532i
$627$	7.94308	+	3.99660i	0.317216	+	0.159609i
$628$	−2.15787	−	8.05326i	−0.0861082	−	0.321360i
$629$	−22.8961			−0.912927
$630$	−0.105873		3.76345e-5i	−0.00421808		1.49939e-6i
$631$	−24.0117			−0.955891			−0.477945	−	0.878390i	$-0.658618\pi$
$631$	−24.0117			−0.955891			−0.477945	+	0.878390i	$0.658618\pi$
$632$	1.34054	−	0.359196i	0.0533238	−	0.0142881i
$633$	−1.84285	+	6.87762i	−0.0732468	+	0.273361i
$634$	−10.5060	−	18.1969i	−0.417246	−	0.722691i
$635$	−21.0653	+	10.0620i	−0.835951	+	0.399300i
$636$	15.7024			0.622640
$637$	−19.5338	+	8.65434i	−0.773958	+	0.342897i
$638$	24.2759	−	15.9406i	0.961094	−	0.631093i
$639$	−0.0628459	−	0.0362841i	−0.00248614	−	0.00143538i
$640$	2.22927	+	0.174199i	0.0881197	+	0.00688580i
$641$	−7.74123	−	13.4082i	−0.305760	−	0.529592i	0.671670	−	0.740850i	$-0.265577\pi$
$641$	−7.74123	−	13.4082i	−0.305760	−	0.529592i	−0.977430	+	0.211258i	$0.932244\pi$
$642$	13.3779	−	3.58460i	0.527985	−	0.141473i
$643$	21.5362	−	21.5362i	0.849306	−	0.849306i	−0.140741	−	0.990047i	$-0.544948\pi$
$643$	21.5362	−	21.5362i	0.849306	−	0.849306i	0.990047	+	0.140741i	$0.0449484\pi$
$644$	−1.78831	+	9.59998i	−0.0704693	+	0.378292i
$645$	6.92388	+	37.2422i	0.272628	+	1.46641i
$646$	−4.09592	−	2.36478i	−0.161152	−	0.0930411i
$647$	−5.68867	+	21.2304i	−0.223645	+	0.834653i	0.759298	+	0.650743i	$0.225542\pi$
$647$	−5.68867	+	21.2304i	−0.223645	+	0.834653i	−0.982943	+	0.183911i	$0.941124\pi$
$648$	−2.31539	+	8.64117i	−0.0909572	+	0.339457i
$649$	11.4756	+	10.2278i	0.450456	+	0.401475i
$650$	−14.2411	+	5.48484i	−0.558581	+	0.215133i
$651$	18.5060	−	21.6278i	0.725307	−	0.847658i
$652$	−3.16954	−	3.16954i	−0.124129	−	0.124129i
$653$	5.48815	+	20.4821i	0.214768	+	0.801525i	0.986248	+	0.165272i	$0.0528501\pi$
$653$	5.48815	+	20.4821i	0.214768	+	0.801525i	−0.771480	+	0.636254i	$0.780483\pi$
$654$	−12.7246	+	7.34653i	−0.497570	+	0.287272i
$655$	−25.0397	−	29.2846i	−0.978380	−	1.14425i
$656$	−5.36063	−	3.09496i	−0.209298	−	0.120838i
$657$	−0.137487	+	0.137487i	−0.00536388	+	0.00536388i
$658$	−2.04975	+	4.28732i	−0.0799077	+	0.167137i
$659$	−38.3028			−1.49207			−0.746033	−	0.665909i	$-0.768044\pi$
$659$	−38.3028			−1.49207			−0.746033	+	0.665909i	$0.768044\pi$
$660$	3.05973	+	12.4360i	0.119100	+	0.484070i
$661$	−18.3949	−	31.8609i	−0.715479	−	1.23925i	−0.962775	−	0.270305i	$-0.912875\pi$
$661$	−18.3949	−	31.8609i	−0.715479	−	1.23925i	0.247296	−	0.968940i	$-0.420458\pi$
$662$	10.5041	+	2.81455i	0.408252	+	0.109391i
$663$	4.15575	+	15.5095i	0.161396	+	0.602339i
$664$		−	8.50023i		−	0.329873i
$665$	−8.87099	−	2.38035i	−0.344002	−	0.0923062i
$666$		−	0.134501i		−	0.00521183i
$667$	−8.36472	−	31.2176i	−0.323883	−	1.20875i
$668$	2.67090	−	9.96794i	0.103340	−	0.385671i
$669$	12.3676	−	7.14044i	0.478159	−	0.276065i
$670$	−32.7446	−	11.5750i	−1.26503	−	0.447179i
$671$	−5.74827	+	27.7342i	−0.221909	+	1.07067i
$672$	−0.354315	−	4.55513i	−0.0136680	−	0.175718i
$673$	20.0131	+	20.0131i	0.771447	+	0.771447i	0.978360	−	0.206912i	$-0.0663415\pi$
$673$	20.0131	+	20.0131i	0.771447	+	0.771447i	−0.206912	+	0.978360i	$0.566341\pi$
$674$	8.13329	+	4.69575i	0.313282	+	0.180874i
$675$	2.75263	+	25.9119i	0.105949	+	0.997349i
$676$	1.84217	+	3.19073i	0.0708527	+	0.122721i
$677$	0.0780567	+	0.291312i	0.00299996	+	0.0111960i	0.967410	−	0.253217i	$-0.0814886\pi$
$677$	0.0780567	+	0.291312i	0.00299996	+	0.0111960i	−0.964410	+	0.264413i	$0.914822\pi$
$678$	−0.344489	−	0.344489i	−0.0132300	−	0.0132300i
$679$	4.29911	−	23.0784i	0.164985	−	0.885668i
$680$	−1.24511	−	6.69718i	−0.0477476	−	0.256825i
$681$	−31.9834	−	18.4656i	−1.22561	−	0.707604i
$682$	18.4581	+	9.28727i	0.706796	+	0.355628i
$683$	2.97640	+	0.797525i	0.113889	+	0.0305164i	0.315313	−	0.948988i	$-0.397890\pi$
$683$	2.97640	+	0.797525i	0.113889	+	0.0305164i	−0.201424	+	0.979504i	$0.564557\pi$
$684$	0.0138917	−	0.0240612i	0.000531164	−	0.000920003i
$685$	6.64383	−	9.67837i	0.253848	−	0.369791i
$686$	−8.79253	−	16.3000i	−0.335700	−	0.622339i
$687$	−24.8387	−	24.8387i	−0.947654	−	0.947654i
$688$	9.47570	−	2.53901i	0.361258	−	0.0967987i
$689$	13.8765	+	24.0349i	0.528654	+	0.915656i
$690$	14.2087	+	1.11029i	0.540915	+	0.0422679i
$691$	−16.0250	+	27.7562i	−0.609621	+	1.05590i	0.381681	+	0.924294i	$0.375345\pi$
$691$	−16.0250	+	27.7562i	−0.609621	+	1.05590i	−0.991303	+	0.131601i	$0.957988\pi$
$692$	−16.0881	+	16.0881i	−0.611576	+	0.611576i
$693$	−0.144830	+	0.0606974i	−0.00550165	+	0.00230571i
$694$			5.26341i			0.199796i
$695$	29.3627	+	10.3795i	1.11379	+	0.393717i
$696$	7.56063	+	13.0954i	0.286585	+	0.496379i
$697$	−4.88053	+	18.2144i	−0.184863	+	0.689919i
$698$	−3.96796	−	14.8086i	−0.150190	−	0.560516i
$699$	50.3032			1.90264
$700$	−5.69753	−	11.9389i	−0.215346	−	0.451249i
$701$		−	19.0530i		−	0.719622i	−0.933025	−	0.359811i	$-0.882841\pi$
$701$		−	19.0530i		−	0.719622i	0.933025	−	0.359811i	$-0.117159\pi$
$702$	−15.3644	+	4.11688i	−0.579893	+	0.155382i
$703$	3.02000	−	11.2708i	0.113902	−	0.425087i
$704$	3.14906	−	1.04087i	0.118685	−	0.0392294i
$705$	6.53908	+	2.31151i	0.246276	+	0.0870566i
$706$		−	0.131936i		−	0.00496548i
$707$	2.26358	+	1.08221i	0.0851307	+	0.0407006i
$708$	−5.65951	+	5.65951i	−0.212697	+	0.212697i
$709$	−40.5341	−	23.4024i	−1.52229	−	0.878894i	−0.999653	−	0.0263376i	$-0.991616\pi$
$709$	−40.5341	−	23.4024i	−1.52229	−	0.878894i	−0.522636	−	0.852556i	$-0.675051\pi$
$710$	0.706382	−	9.03978i	0.0265100	−	0.339257i
$711$	0.0215089	−	0.0124181i	0.000806646	−	0.000465717i
$712$	3.72280	+	13.8937i	0.139518	+	0.520688i
$713$	16.2595	−	16.2595i	0.608924	−	0.608924i
$714$	−13.1245	+	4.63416i	−0.491172	+	0.173429i
$715$	−16.3312	+	15.6733i	−0.610752	+	0.586149i
$716$	3.19913	−	5.54106i	0.119557	−	0.207079i
$717$	−11.9779	−	3.20946i	−0.447322	−	0.119860i
$718$	−30.4370	−	8.15558i	−1.13590	−	0.304363i
$719$	−14.6358	−	8.45001i	−0.545825	−	0.315132i	0.201611	−	0.979466i	$-0.435382\pi$
$719$	−14.6358	−	8.45001i	−0.545825	−	0.315132i	−0.747436	+	0.664333i	$0.768716\pi$
$720$	0.0393421	−	0.00731429i	0.00146619	−	0.000272587i
$721$	−20.5173	+	23.9783i	−0.764103	+	0.892998i
$722$	−11.7307	+	11.7307i	−0.436571	+	0.436571i
$723$	−14.6666	+	3.92989i	−0.545455	+	0.146154i
$724$	1.51050	−	0.872088i	0.0561373	−	0.0324109i
$725$	34.0557	+	27.5150i	1.26480	+	1.02188i
$726$	11.3206	+	15.2538i	0.420148	+	0.566121i
$727$	−14.1045	−	14.1045i	−0.523106	−	0.523106i	0.395402	−	0.918508i	$-0.370605\pi$
$727$	−14.1045	−	14.1045i	−0.523106	−	0.523106i	−0.918508	+	0.395402i	$0.870605\pi$
$728$	6.65919	−	4.56780i	0.246806	−	0.169294i
$729$			27.1591i			1.00589i
$730$	−22.9057	−	8.09697i	−0.847777	−	0.299682i
$731$	−14.9425	−	25.8811i	−0.552668	−	0.957249i
$732$	−14.2448	−	3.81689i	−0.526505	−	0.141076i
$733$	−4.01086	+	1.07471i	−0.148144	+	0.0396952i	−0.332129	−	0.943234i	$-0.607767\pi$
$733$	−4.01086	+	1.07471i	−0.148144	+	0.0396952i	0.183985	+	0.982929i	$0.441100\pi$
$734$	−14.3182			−0.528493
$735$	−22.2954	+	15.2817i	−0.822380	+	0.563672i
$736$		−	3.69087i		−	0.136047i
$737$	−51.4283	+	2.95679i	−1.89439	+	0.108915i
$738$	−0.106999	−	0.0286703i	−0.00393869	−	0.00105537i
$739$	8.71193	+	15.0895i	0.320474	+	0.555076i	0.980586	−	0.196091i	$-0.0628246\pi$
$739$	8.71193	+	15.0895i	0.320474	+	0.555076i	−0.660112	+	0.751167i	$0.729491\pi$
$740$	15.1647	−	7.24356i	0.557465	−	0.266278i
$741$	−8.18283			−0.300604
$742$	−19.8390	+	13.6083i	−0.728311	+	0.499577i
$743$	−3.91434	−	3.91434i	−0.143603	−	0.143603i	0.631650	−	0.775254i	$-0.282378\pi$
$743$	−3.91434	−	3.91434i	−0.143603	−	0.143603i	−0.775254	+	0.631650i	$0.782378\pi$
$744$	−5.37930	+	9.31722i	−0.197215	+	0.341586i
$745$	−8.15108	+	6.96954i	−0.298633	+	0.255344i
$746$	6.65144	+	11.5206i	0.243526	+	0.421800i
$747$	−0.0393712	−	0.146935i	−0.00144052	−	0.00537608i
$748$	−5.54578	−	8.44569i	−0.202774	−	0.308805i
$749$	−13.7956	+	16.1228i	−0.504080	+	0.589113i
$750$	−16.4451	+	10.1154i	−0.600491	+	0.369362i
$751$	9.90854	−	17.1621i	0.361568	−	0.626254i	−0.626651	−	0.779300i	$-0.715575\pi$
$751$	9.90854	−	17.1621i	0.361568	−	0.626254i	0.988219	+	0.153046i	$0.0489083\pi$
$752$	0.464873	−	1.73493i	0.0169522	−	0.0632664i
$753$	−7.57912	−	2.03082i	−0.276199	−	0.0740072i
$754$	−13.3630	+	23.1454i	−0.486651	+	0.842904i
$755$	−20.6541	+	3.83991i	−0.751681	+	0.139749i
$756$	−4.59081	−	13.0017i	−0.166966	−	0.472869i
$757$	−29.2726	−	29.2726i	−1.06393	−	1.06393i	−0.997812	−	0.0661176i	$-0.978939\pi$
$757$	−29.2726	−	29.2726i	−1.06393	−	1.06393i	−0.0661176	−	0.997812i	$-0.521061\pi$
$758$	−3.23035	+	0.865571i	−0.117332	+	0.0314389i
$759$	20.0711	−	6.63419i	0.728535	−	0.240806i
$760$	3.46098	+	0.270446i	0.125543	+	0.00981010i
$761$	−11.0793	−	6.39665i	−0.401625	−	0.231879i	0.285560	−	0.958361i	$-0.407821\pi$
$761$	−11.0793	−	6.39665i	−0.401625	−	0.231879i	−0.687185	+	0.726482i	$0.741154\pi$
$762$	−12.7484	−	12.7484i	−0.461827	−	0.461827i
$763$	9.70988	−	20.3095i	0.351521	−	0.735252i
$764$			1.02113i			0.0369433i
$765$	−0.0525427	−	0.110000i	−0.00189969	−	0.00397708i
$766$	17.8205	−	10.2887i	0.643881	−	0.371745i
$767$	−13.6642	−	3.66130i	−0.493384	−	0.132202i
$768$	0.446949	+	1.66804i	0.0161279	+	0.0601900i
$769$	25.9007			0.934002			0.467001	−	0.884257i	$-0.345334\pi$
$769$	25.9007			0.934002			0.467001	+	0.884257i	$0.345334\pi$
$770$	−14.6433	−	13.0604i	−0.527708	−	0.470664i
$771$	−25.2844			−0.910597
$772$	0.788030	+	2.94097i	0.0283618	+	0.105848i
$773$	−20.5331	−	5.50184i	−0.738526	−	0.197887i	−0.130103	−	0.991500i	$-0.541531\pi$
$773$	−20.5331	−	5.50184i	−0.738526	−	0.197887i	−0.608423	+	0.793613i	$0.708197\pi$
$774$	0.152037	−	0.0877786i	0.00546486	−	0.00315514i
$775$	−4.83874	+	30.7723i	−0.173813	+	1.10537i
$776$			8.87287i			0.318518i
$777$	−19.4239	−	28.3173i	−0.696830	−	1.01588i
$778$	9.97098	+	9.97098i	0.357477	+	0.357477i
$779$	−8.32246	−	4.80497i	−0.298183	−	0.172156i
$780$	−7.65915	−	8.95761i	−0.274242	−	0.320734i
$781$	−4.22078	−	12.7696i	−0.151031	−	0.456931i
$782$	−10.8607	+	2.91012i	−0.388378	+	0.104066i
$783$	32.2684	+	32.2684i	1.15318	+	1.15318i
$784$	4.39531	+	5.44805i	0.156975	+	0.194573i
$785$	10.5509	−	15.3700i	0.376577	−	0.548578i
$786$	14.8781	−	25.7696i	0.530684	−	0.919172i
$787$	30.1814	+	8.08708i	1.07585	+	0.288273i	0.752895	−	0.658141i	$-0.228657\pi$
$787$	30.1814	+	8.08708i	1.07585	+	0.288273i	0.322955	+	0.946414i	$0.395324\pi$
$788$	−7.21559	+	26.9289i	−0.257045	+	0.959304i
$789$	21.1607	−	36.6515i	0.753342	−	1.30483i
$790$	2.55847	+	1.75629i	0.0910263	+	0.0624860i
$791$	0.733789	+	0.136692i	0.0260905	+	0.00486022i
$792$	0.0496136	−	0.0325783i	0.00176294	−	0.00115762i
$793$	−6.74614	−	25.1769i	−0.239563	−	0.894059i
$794$	17.3119	+	29.9852i	0.614378	+	1.06413i
$795$	22.8180	+	26.6864i	0.809272	+	0.946468i
$796$	−12.1011	+	20.9597i	−0.428913	+	0.742899i
$797$	−25.8913	−	25.8913i	−0.917117	−	0.917117i	0.0797018	−	0.996819i	$-0.474603\pi$
$797$	−25.8913	−	25.8913i	−0.917117	−	0.917117i	−0.996819	+	0.0797018i	$0.974603\pi$
$798$	−0.550080	−	7.07190i	−0.0194726	−	0.250343i
$799$	−5.47172			−0.193575
$800$	2.94343	+	4.04181i	0.104066	+	0.142900i
$801$	0.128705	+	0.222923i	0.00454757	+	0.00787661i
$802$	12.2192	+	3.27413i	0.431476	+	0.115614i
$803$	−35.9754	+	2.06835i	−1.26954	+	0.0729904i
$804$		−	26.8215i		−	0.945923i
$805$	−18.9140	+	10.9110i	−0.666630	+	0.384563i
$806$	−19.0152			−0.669782
$807$	26.8707	−	7.19998i	0.945893	−	0.253451i
$808$	−0.915991	−	0.245439i	−0.0322245	−	0.00863452i
$809$	−12.5651	−	21.7634i	−0.441766	−	0.765161i	0.556055	−	0.831146i	$-0.312314\pi$
$809$	−12.5651	−	21.7634i	−0.441766	−	0.765161i	−0.997821	+	0.0659848i	$0.978981\pi$
$810$	−18.0504	+	8.62193i	−0.634226	+	0.302944i
$811$		−	17.5697i		−	0.616955i	−0.951232	−	0.308478i	$-0.900180\pi$
$811$		−	17.5697i		−	0.616955i	0.951232	−	0.308478i	$-0.0998195\pi$
$812$	−20.9014	−	9.99285i	−0.733494	−	0.350680i
$813$	−2.71184	−	2.71184i	−0.0951084	−	0.0951084i
$814$	16.5854	−	18.6088i	0.581317	−	0.652238i
$815$	0.780829	−	9.99251i	0.0273513	−	0.350022i
$816$	4.55593	−	2.63037i	0.159490	−	0.0920814i
$817$	14.7112	−	3.94184i	0.514678	−	0.137908i
$818$	−3.31966	+	3.31966i	−0.116069	+	0.116069i
$819$	0.0939539	−	0.109803i	0.00328302	−	0.00383682i
$820$	−2.52992	−	13.6079i	−0.0883485	−	0.475209i
$821$	−36.5744	−	21.1162i	−1.27645	−	0.736961i	−0.300259	−	0.953858i	$-0.597073\pi$
$821$	−36.5744	−	21.1162i	−1.27645	−	0.736961i	−0.976195	+	0.216897i	$0.930406\pi$
$822$	8.75714	+	2.34647i	0.305440	+	0.0818425i
$823$	7.36520	+	1.97350i	0.256735	+	0.0687919i	0.384891	−	0.922962i	$-0.374239\pi$
$823$	7.36520	+	1.97350i	0.256735	+	0.0687919i	−0.128156	+	0.991754i	$0.540906\pi$
$824$	5.96393	−	10.3298i	0.207763	−	0.359857i
$825$	−16.6888	+	23.2715i	−0.581030	+	0.810209i
$826$	2.24567	−	12.0552i	0.0781370	−	0.419453i
$827$	−5.22768	+	5.22768i	−0.181784	+	0.181784i	−0.792133	−	0.610349i	$-0.791029\pi$
$827$	−5.22768	+	5.22768i	−0.181784	+	0.181784i	0.610349	+	0.792133i	$0.291029\pi$
$828$	−0.0170953	−	0.0638005i	−0.000594102	−	0.00221722i
$829$	−11.5497	+	6.66821i	−0.401137	+	0.231597i	−0.686974	−	0.726682i	$-0.741062\pi$
$829$	−11.5497	+	6.66821i	−0.401137	+	0.231597i	0.285837	+	0.958278i	$0.407728\pi$
$830$	14.4462	−	12.3522i	0.501436	−	0.428750i
$831$	31.9345	+	18.4374i	1.10780	+	0.639587i
$832$	−2.15820	+	2.15820i	−0.0748221	+	0.0748221i
$833$	12.5658	−	17.2292i	0.435380	−	0.596955i
$834$			24.0514i			0.832833i
$835$	20.8219	−	9.94575i	0.720570	−	0.344187i
$836$	4.88896	−	1.61597i	0.169088	−	0.0558895i
$837$	−8.40342	+	31.3620i	−0.290465	+	1.08403i
$838$	−25.7451	+	6.89837i	−0.889349	+	0.238300i
$839$		−	9.53037i		−	0.329025i	−0.986375	−	0.164513i	$-0.947395\pi$
$839$		−	9.53037i		−	0.329025i	0.986375	−	0.164513i	$-0.0526051\pi$
$840$	7.22661	−	7.22148i	0.249342	−	0.249165i
$841$	47.6748			1.64396
$842$	2.34741	+	8.76064i	0.0808970	+	0.301912i
$843$	−9.37866	+	35.0016i	−0.323018	+	1.20552i
$844$	2.06159	+	3.57078i	0.0709629	+	0.122911i
$845$	−2.74572	+	7.76743i	−0.0944557	+	0.267208i
$846$		−	0.0321432i		−	0.00110511i
$847$	−27.5224	−	9.46129i	−0.945682	−	0.325094i
$848$	6.42968	−	6.42968i	0.220796	−	0.220796i
$849$	4.85412	−	8.40759i	0.166593	−	0.288548i
$850$	9.57259	−	11.8481i	0.328337	−	0.406387i
$851$	−13.8699	−	24.0234i	−0.475455	−	0.823513i
$852$	6.76394	−	1.81239i	0.231729	−	0.0620916i
$853$	27.2492	+	27.2492i	0.932996	+	0.932996i	0.997892	−	0.0648958i	$-0.0206715\pi$
$853$	27.2492	+	27.2492i	0.932996	+	0.932996i	−0.0648958	+	0.997892i	$0.520671\pi$
$854$	21.3053	−	7.52274i	0.729053	−	0.257423i
$855$	0.0610792	−	0.0113555i	0.00208886	−	0.000388351i
$856$	4.01009	−	6.94567i	0.137062	−	0.237398i
$857$	−19.5177	−	5.22975i	−0.666712	−	0.178645i	−0.0904388	−	0.995902i	$-0.528827\pi$
$857$	−19.5177	−	5.22975i	−0.666712	−	0.178645i	−0.576273	+	0.817257i	$0.695494\pi$
$858$	−15.6157	−	7.85710i	−0.533110	−	0.268237i
$859$	−9.45623	−	5.45956i	−0.322642	−	0.186278i	0.329927	−	0.944006i	$-0.392976\pi$
$859$	−9.45623	−	5.45956i	−0.322642	−	0.186278i	−0.652570	+	0.757729i	$0.726309\pi$
$860$	18.0847	+	12.4145i	0.616684	+	0.423330i
$861$	−26.6675	+	9.41609i	−0.908826	+	0.320900i
$862$	13.5310	+	13.5310i	0.460867	+	0.460867i
$863$	7.53766	+	28.1309i	0.256585	+	0.957587i	0.967202	+	0.254009i	$0.0817491\pi$
$863$	7.53766	+	28.1309i	0.256585	+	0.957587i	−0.710617	+	0.703579i	$0.751584\pi$
$864$	2.60577	+	4.51332i	0.0886500	+	0.153546i
$865$	−50.7203	−	3.96336i	−1.72454	−	0.134758i
$866$	−2.95122	−	1.70389i	−0.100286	−	0.0579004i
$867$	9.42619	+	9.42619i	0.320130	+	0.320130i
$868$	−1.27827	−	16.4336i	−0.0433873	−	0.557793i
$869$	4.50711	+	0.934157i	0.152893	+	0.0316891i
$870$	−11.2690	+	31.8790i	−0.382054	+	1.08080i
$871$	41.0544	−	23.7028i	1.39108	−	0.803138i
$872$	−2.20215	+	8.21853i	−0.0745742	+	0.278315i
$873$	0.0410972	+	0.153377i	0.00139093	+	0.00519101i
$874$		−	5.73013i		−	0.193825i
$875$	12.0109	−	27.0322i	0.406044	−	0.913854i
$876$		−	18.7623i		−	0.633921i
$877$	9.87536	+	36.8553i	0.333467	+	1.24452i	0.905521	+	0.424301i	$0.139480\pi$
$877$	9.87536	+	36.8553i	0.333467	+	1.24452i	−0.572054	+	0.820216i	$0.693853\pi$
$878$	32.8634	+	8.80572i	1.10909	+	0.297179i
$879$	6.62409	+	11.4733i	0.223425	+	0.386983i
$880$	6.34505	+	3.83931i	0.213892	+	0.129423i
$881$	2.15561			0.0726244			0.0363122	−	0.999340i	$-0.488439\pi$
$881$	2.15561			0.0726244			0.0363122	+	0.999340i	$0.488439\pi$
$882$	0.101212	+	0.0738170i	0.00340797	+	0.00248555i
$883$	−8.11184	+	8.11184i	−0.272985	+	0.272985i	−0.830301	−	0.557316i	$-0.811831\pi$
$883$	−8.11184	+	8.11184i	−0.272985	+	0.272985i	0.557316	+	0.830301i	$0.311831\pi$
$884$	8.05235	+	4.64903i	0.270830	+	0.156364i
$885$	−17.8425	−	1.39424i	−0.599770	−	0.0468669i
$886$	9.63590	−	5.56329i	0.323724	−	0.186902i
$887$	7.88657	+	29.4331i	0.264805	+	0.988266i	0.962370	+	0.271744i	$0.0876004\pi$
$887$	7.88657	+	29.4331i	0.264805	+	0.988266i	−0.697565	+	0.716522i	$0.745733\pi$
$888$	9.17745	+	9.17745i	0.307975	+	0.307975i
$889$	27.1551	+	5.05853i	0.910753	+	0.169658i
$890$	−18.2027	+	26.5167i	−0.610155	+	0.888840i
$891$	−19.7414	+	22.1499i	−0.661361	+	0.742048i
$892$	2.14037	−	7.98798i	0.0716650	−	0.267457i
$893$	0.721722	−	2.69350i	0.0241515	−	0.0901347i
$894$	−7.17271	−	4.14117i	−0.239891	−	0.138501i
$895$	14.0659	−	2.61507i	0.470172	−	0.0874120i
$896$	−2.01028	−	1.72011i	−0.0671586	−	0.0574649i
$897$	−13.7557	+	13.7557i	−0.459289	+	0.459289i
$898$	−36.1363	+	9.68268i	−1.20588	+	0.323115i
$899$	27.2766	+	47.2445i	0.909726	+	1.57569i
$900$	0.0696009	+	0.0562335i	0.00232003	+	0.00187445i
$901$	−23.9895	−	13.8503i	−0.799205	−	0.461421i
$902$	−11.2684	−	17.1607i	−0.375197	−	0.571389i
$903$	19.3327	−	40.4368i	0.643351	−	1.34565i
$904$	−0.282117			−0.00938308
$905$	3.67712	+	1.29983i	0.122232	+	0.0432079i
$906$	−8.11208	−	14.0505i	−0.269506	−	0.466798i
$907$	−6.27854	+	23.4318i	−0.208476	+	0.778041i	0.779886	+	0.625921i	$0.215277\pi$
$907$	−6.27854	+	23.4318i	−0.208476	+	0.778041i	−0.988362	+	0.152120i	$0.951390\pi$
$908$	−20.6574	+	5.53514i	−0.685541	+	0.183690i
$909$	−0.0169707			−0.000562881
$910$	17.4399	+	4.67964i	0.578126	+	0.155129i
$911$	45.8604			1.51942			0.759712	−	0.650260i	$-0.225340\pi$
$911$	45.8604			1.51942			0.759712	+	0.650260i	$0.225340\pi$
$912$	0.693894	+	2.58965i	0.0229771	+	0.0857518i
$913$	12.6714	−	25.1839i	0.419362	−	0.833465i
$914$	−17.6280	+	10.1775i	−0.583081	+	0.336642i
$915$	−14.2131	−	29.7558i	−0.469872	−	0.983697i
$916$	−20.3414			−0.672100
$917$	3.53545	+	45.4522i	0.116751	+	1.50096i
$918$	11.2263	−	11.2263i	0.370523	−	0.370523i
$919$	28.4093	−	49.2063i	0.937135	−	1.62316i	0.166352	−	0.986066i	$-0.446801\pi$
$919$	28.4093	−	49.2063i	0.937135	−	1.62316i	0.770782	−	0.637099i	$-0.219866\pi$
$920$	6.27267	−	5.36341i	0.206804	−	0.176826i
$921$	−14.0275	+	8.09877i	−0.462221	+	0.266864i
$922$	7.08594	−	1.89867i	0.233363	−	0.0625294i
$923$	8.75158	+	8.75158i	0.288062	+	0.288062i
$924$	5.74065	−	14.0238i	0.188853	−	0.461349i
$925$	34.3472	+	15.2465i	1.12933	+	0.501303i
$926$	−33.1533	−	19.1411i	−1.08949	−	0.629015i
$927$	0.0552472	−	0.206185i	0.00181455	−	0.00677201i
$928$	8.45805	+	2.26633i	0.277649	+	0.0743958i
$929$	1.49777	+	0.864739i	0.0491403	+	0.0283712i	0.524369	−	0.851491i	$-0.324301\pi$
$929$	1.49777	+	0.864739i	0.0491403	+	0.0283712i	−0.475229	+	0.879862i	$0.657635\pi$
$930$	−23.6517	+	4.39720i	−0.775569	+	0.144190i
$931$	6.82378	+	8.45818i	0.223640	+	0.277206i
$932$	20.5977	−	20.5977i	0.674701	−	0.674701i
$933$	−6.08099	−	22.6946i	−0.199083	−	0.742987i
$934$	−12.5755	−	21.7815i	−0.411484	−	0.712712i
$935$	6.29466	−	21.6980i	0.205857	−	0.709601i
$936$	−0.0273104	+	0.0473030i	−0.000892668	+	0.00154615i
$937$	−15.8368	+	15.8368i	−0.517366	+	0.517366i	−0.916773	−	0.399408i	$-0.869216\pi$
$937$	−15.8368	+	15.8368i	−0.517366	+	0.517366i	0.399408	+	0.916773i	$0.369216\pi$
$938$	23.2446	+	33.8873i	0.758964	+	1.10646i
$939$		−	42.8204i		−	1.39739i
$940$	3.62407	−	1.73107i	0.118204	−	0.0564612i
$941$	−6.78038	+	3.91465i	−0.221034	+	0.127614i	−0.606429	−	0.795138i	$-0.707399\pi$
$941$	−6.78038	+	3.91465i	−0.221034	+	0.127614i	0.385395	+	0.922752i	$0.374065\pi$
$942$	13.9070	+	3.72637i	0.453114	+	0.121412i
$943$	−22.0677	+	5.91304i	−0.718625	+	0.192555i
$944$			4.63481i			0.150850i
$945$	15.4254	−	26.6957i	0.501789	−	0.868411i
$946$	31.8589	+	6.60316i	1.03582	+	0.214687i
$947$	28.5814	−	7.65837i	0.928772	−	0.248864i	0.237441	−	0.971402i	$-0.423691\pi$
$947$	28.5814	−	7.65837i	0.928772	−	0.248864i	0.691331	+	0.722538i	$0.257025\pi$
$948$	−0.620288	+	2.31495i	−0.0201460	+	0.0751859i
$949$	28.7186	−	16.5807i	0.932245	−	0.538232i
$950$	4.56972	+	6.27497i	0.148261	+	0.203587i
$951$	36.2851			1.17662
$952$	−3.47655	+	7.27166i	−0.112676	+	0.235676i
$953$	26.5887	+	26.5887i	0.861292	+	0.861292i	0.991488	−	0.130196i	$-0.0415607\pi$
$953$	26.5887	+	26.5887i	0.861292	+	0.861292i	−0.130196	+	0.991488i	$0.541561\pi$
$954$	0.0813627	−	0.140924i	0.00263422	−	0.00456260i
$955$	−1.73543	+	1.48387i	−0.0561571	+	0.0480168i
$956$	−6.21878	+	3.59041i	−0.201130	+	0.116122i
$957$	2.87863	+	50.0688i	0.0930529	+	1.61850i
$958$	14.3772	−	14.3772i	0.464508	−	0.464508i
$959$	−13.0976	+	4.62467i	−0.422945	+	0.149339i
$960$	−2.18536	+	3.18351i	−0.0705321	+	0.102747i
$961$	−3.90699	+	6.76711i	−0.126032	+	0.218294i
$962$	−5.93716	+	22.1578i	−0.191422	+	0.714396i
$963$	0.0371476	−	0.138637i	0.00119707	−	0.00446751i
$964$	−4.39636	+	7.61472i	−0.141597	+	0.245253i
$965$	−3.85308	+	5.61295i	−0.124035	+	0.180687i
$966$	−12.8129	−	10.9634i	−0.412247	−	0.352743i
$967$	−29.2744	+	29.2744i	−0.941402	+	0.941402i	−0.998376	−	0.0569738i	$-0.981855\pi$
$967$	−29.2744	+	29.2744i	−0.941402	+	0.941402i	0.0569738	+	0.998376i	$0.481855\pi$
$968$	10.8815	+	1.61052i	0.349743	+	0.0517640i
$969$	7.07315	−	4.08369i	0.227222	−	0.131187i
$970$	−15.0795	+	12.8937i	−0.484175	+	0.413991i
$971$	−1.80209	+	3.12131i	−0.0578319	+	0.100168i	−0.893492	−	0.449079i	$-0.851752\pi$
$971$	−1.80209	+	3.12131i	−0.0578319	+	0.100168i	0.835660	+	0.549247i	$0.185085\pi$
$972$	0.131505	+	0.131505i	0.00421803	+	0.00421803i
$973$	−20.8439	−	30.3875i	−0.668226	−	0.974177i
$974$	−41.6654			−1.33504
$975$	4.09361	−	26.0336i	0.131100	−	0.833743i
$976$	−7.39576	+	4.26995i	−0.236733	+	0.136678i
$977$	−2.02720	+	7.56560i	−0.0648557	+	0.242045i	−0.990742	−	0.135757i	$-0.956653\pi$
$977$	−2.02720	+	7.56560i	−0.0648557	+	0.242045i	0.925886	+	0.377802i	$0.123320\pi$
$978$	7.47681	−	2.00341i	0.239082	−	0.0640619i
$979$	−9.68185	+	46.7129i	−0.309433	+	1.49295i
$980$	−2.87195	+	15.3867i	−0.0917410	+	0.491512i
$981$			0.152266i			0.00486147i
$982$	−13.2053	+	3.53834i	−0.421397	+	0.112913i
$983$	−1.60231	−	0.429337i	−0.0511057	−	0.0136937i	0.233176	−	0.972435i	$-0.425088\pi$
$983$	−1.60231	−	0.429337i	−0.0511057	−	0.0136937i	−0.284281	+	0.958741i	$0.591755\pi$
$984$	9.25715	−	5.34462i	0.295107	−	0.170380i
$985$	−56.2514	+	26.8690i	−1.79232	+	0.856117i
$986$		−	26.6755i		−	0.849520i
$987$	−4.64194	−	6.76728i	−0.147755	−	0.215405i
$988$	−3.35064	+	3.35064i	−0.106598	+	0.106598i
$989$	18.1037	−	31.3565i	0.575663	−	0.997077i
$990$	0.127464	+	0.0369775i	0.00405106	+	0.00117522i
$991$	−0.586202	−	1.01533i	−0.0186213	−	0.0322530i	0.856565	−	0.516040i	$-0.172594\pi$
$991$	−0.586202	−	1.01533i	−0.0186213	−	0.0322530i	−0.875186	+	0.483787i	$0.839261\pi$
$992$	1.61247	+	6.01780i	0.0511958	+	0.191065i
$993$	−13.2788	+	13.2788i	−0.421391	+	0.421391i
$994$	−6.97512	+	8.15175i	−0.221237	+	0.258558i
$995$	−53.2061	+	9.89182i	−1.68675	+	0.313592i
$996$	12.7123	+	7.33943i	0.402803	+	0.232559i
$997$	−25.4975	−	6.83204i	−0.807514	−	0.216373i	−0.168634	−	0.985679i	$-0.553935\pi$
$997$	−25.4975	−	6.83204i	−0.807514	−	0.216373i	−0.638880	+	0.769306i	$0.720602\pi$
$998$	−0.927941	+	3.46312i	−0.0293735	+	0.109623i
$999$	33.9213	+	19.5845i	1.07322	+	0.619625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bd.a.527.31	yes	192
5.3	odd	4	inner	770.2.bd.a.373.42	yes	192
7.4	even	3	inner	770.2.bd.a.417.18	yes	192
11.10	odd	2	inner	770.2.bd.a.527.7	yes	192
35.18	odd	12	inner	770.2.bd.a.263.7	✓	192
55.43	even	4	inner	770.2.bd.a.373.18	yes	192
77.32	odd	6	inner	770.2.bd.a.417.42	yes	192
385.263	even	12	inner	770.2.bd.a.263.31	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bd.a.263.7	✓	192	35.18	odd	12	inner
770.2.bd.a.263.31	yes	192	385.263	even	12	inner
770.2.bd.a.373.18	yes	192	55.43	even	4	inner
770.2.bd.a.373.42	yes	192	5.3	odd	4	inner
770.2.bd.a.417.18	yes	192	7.4	even	3	inner
770.2.bd.a.417.42	yes	192	77.32	odd	6	inner
770.2.bd.a.527.7	yes	192	11.10	odd	2	inner
770.2.bd.a.527.31	yes	192	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.66804 - 0.446949i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.10823 - 0.745241i) q^{5} -1.72688i q^{6} +(1.49658 + 2.18180i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.0154982 - 0.00894790i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.66804 - 0.446949i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.10823 - 0.745241i) q^{5} -1.72688i q^{6} +(1.49658 + 2.18180i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.0154982 - 0.00894790i) q^{9} +(0.174199 - 2.22927i) q^{10} +(-1.04087 - 3.14906i) q^{11} +(1.66804 - 0.446949i) q^{12} +(2.15820 + 2.15820i) q^{13} +(-1.72011 + 2.01028i) q^{14} +(3.18351 + 2.18536i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.94259 - 0.788464i) q^{17} +(0.00463178 - 0.0172860i) q^{18} +(0.776257 - 1.34452i) q^{19} +(2.19840 - 0.408715i) q^{20} +(-1.52120 - 4.30821i) q^{21} +(2.77236 - 1.82044i) q^{22} +(-0.955268 - 3.56511i) q^{23} +(0.863439 + 1.49552i) q^{24} +(3.88923 + 3.14227i) q^{25} +(-1.52608 + 2.64324i) q^{26} +(3.68511 + 3.68511i) q^{27} +(-2.38698 - 1.14120i) q^{28} +8.75642 q^{29} +(-1.28694 + 3.64065i) q^{30} +(3.11504 + 5.39541i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.328745 + 5.71796i) q^{33} -3.04639i q^{34} +(-1.52916 - 5.71504i) q^{35} +0.0178958 q^{36} +(7.25971 - 1.94523i) q^{37} +(1.49961 + 0.401820i) q^{38} +(-2.63535 - 4.56456i) q^{39} +(0.963776 + 2.01771i) q^{40} -6.18993i q^{41} +(3.76770 - 2.58441i) q^{42} +(6.93669 + 6.93669i) q^{43} +(2.47595 + 2.20673i) q^{44} +(0.0260054 + 0.0304141i) q^{45} +(3.19639 - 1.84544i) q^{46} +(1.73493 - 0.464873i) q^{47} +(-1.22109 + 1.22109i) q^{48} +(-2.52050 + 6.53048i) q^{49} +(-2.02860 + 4.56999i) q^{50} +(4.55593 + 2.63037i) q^{51} +(-2.94816 - 0.789956i) q^{52} +(8.78311 + 2.35343i) q^{53} +(-2.60577 + 4.51332i) q^{54} +(-0.152413 + 7.41463i) q^{55} +(0.484523 - 2.60101i) q^{56} +(-1.89575 + 1.89575i) q^{57} +(2.26633 + 8.45805i) q^{58} +(-4.01387 + 2.31741i) q^{59} +(-3.84968 - 0.300820i) q^{60} +(-7.39576 - 4.26995i) q^{61} +(-4.40534 + 4.40534i) q^{62} +(-0.00367181 - 0.0472053i) q^{63} +1.00000i q^{64} +(-2.94159 - 6.15835i) q^{65} +(-5.43804 + 1.79746i) q^{66} +(4.01993 - 15.0026i) q^{67} +(2.94259 - 0.788464i) q^{68} +6.37368i q^{69} +(5.12453 - 2.95622i) q^{70} +4.05504 q^{71} +(0.00463178 + 0.0172860i) q^{72} +(2.81204 - 10.4947i) q^{73} +(3.75790 + 6.50888i) q^{74} +(-5.08294 - 6.97971i) q^{75} +1.55251i q^{76} +(5.31287 - 6.98380i) q^{77} +(3.72695 - 3.72695i) q^{78} +(-0.693914 + 1.20189i) q^{79} +(-1.69951 + 1.45316i) q^{80} +(-4.47300 - 7.74746i) q^{81} +(5.97901 - 1.60207i) q^{82} +(6.01057 + 6.01057i) q^{83} +(3.47150 + 2.97042i) q^{84} +(5.61604 + 3.85520i) q^{85} +(-4.90498 + 8.49568i) q^{86} +(-14.6060 - 3.91367i) q^{87} +(-1.49071 + 2.96273i) q^{88} +(-12.4567 - 7.19191i) q^{89} +(-0.0226471 + 0.0329910i) q^{90} +(-1.47884 + 7.93868i) q^{91} +(2.60984 + 2.60984i) q^{92} +(-2.78453 - 10.3920i) q^{93} +(0.898066 + 1.55550i) q^{94} +(-2.63851 + 2.25605i) q^{95} +(-1.49552 - 0.863439i) q^{96} +(-6.27407 - 6.27407i) q^{97} +(-6.96031 - 0.744400i) q^{98} +(-0.0120458 + 0.0581185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{5}+O(q^{10}) \) 192 * q + 8 * q^5	\( 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) \) 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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