LMFDB - Embedded newform 770.2.bd.a.263.7

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			263.7
Character	$\chi$	$=$	770.263
Dual form			770.2.bd.a.527.7

$q$-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} +(-2.20673 + 2.47595i) 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} +(-1.82044 - 2.77236i) 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} +(2.57428 - 5.11627i) 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} +(3.14906 - 1.04087i) 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} +(2.80710 - 6.86441i) 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} +(4.27567 + 3.81075i) 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} +(-2.09948 - 8.52010i) 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} +(0.190370 + 3.31116i) 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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

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	−0.705887	−	0.708325i	$-0.749451\pi$
$3$	−1.66804	+	0.446949i	−0.963041	+	0.258046i	−0.257154	+	0.966371i	$0.582785\pi$
$4$	−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
$11$	−2.20673	+	2.47595i	−0.665354	+	0.746528i
$11$	−2.20673	+	2.47595i	−0.665354	+	0.746528i
$12$	1.66804	+	0.446949i	0.481520	+	0.129023i
$13$	−2.15820	+	2.15820i	−0.598577	+	0.598577i	−0.939934	−	0.341357i	$-0.889114\pi$
$13$	−2.15820	+	2.15820i	−0.598577	+	0.598577i	0.341357	+	0.939934i	$0.389114\pi$
$14$	−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	$-0.462887\pi$
$17$	2.94259	−	0.788464i	0.713682	−	0.191231i	0.597351	+	0.801980i	$0.296220\pi$
$18$	−0.00463178	−	0.0172860i	−0.00109172	−	0.00407435i
$19$	−0.776257	−	1.34452i	−0.178086	−	0.308453i	0.763139	−	0.646234i	$-0.223657\pi$
$19$	−0.776257	−	1.34452i	−0.178086	−	0.308453i	−0.941225	+	0.337781i	$0.890324\pi$
$20$	2.19840	+	0.408715i	0.491577	+	0.0913915i
$21$	1.52120	−	4.30821i	0.331952	−	0.940129i
$22$	−1.82044	−	2.77236i	−0.388120	−	0.591069i
$23$	−0.955268	+	3.56511i	−0.199187	+	0.743376i	0.791956	+	0.610578i	$0.209063\pi$
$23$	−0.955268	+	3.56511i	−0.199187	+	0.743376i	−0.991143	+	0.132798i	$0.957604\pi$
$24$	−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	$-0.802174\pi$
$29$	−8.75642			−1.62603			−0.813013	+	0.582246i	$0.802174\pi$
$30$	1.28694	+	3.64065i	0.234962	+	0.664688i
$31$	3.11504	−	5.39541i	0.559478	−	0.969045i	−0.438062	−	0.898945i	$-0.644335\pi$
$31$	3.11504	−	5.39541i	0.559478	−	0.969045i	0.997540	−	0.0701000i	$-0.0223318\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	2.57428	−	5.11627i	0.448124	−	0.890629i
$34$			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	0.800264	−	0.599647i	$-0.204693\pi$
$37$	7.25971	+	1.94523i	1.19349	+	0.319795i	0.393225	+	0.919442i	$0.371359\pi$
$38$	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	−0.0596141	+	0.998221i	$0.518987\pi$
$43$	−6.93669	+	6.93669i	−1.05784	+	1.05784i	−0.998221	+	0.0596141i	$0.981013\pi$
$44$	3.14906	−	1.04087i	0.474739	−	0.156918i
$45$	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	0.383122	−	0.923698i	$-0.374849\pi$
$47$	1.73493	+	0.464873i	0.253066	+	0.0678087i	−0.130056	+	0.991507i	$0.541516\pi$
$48$	−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	0.401083	−	0.916042i	$-0.368634\pi$
$53$	8.78311	−	2.35343i	1.20645	−	0.323268i	0.805369	+	0.592774i	$0.201967\pi$
$54$	2.60577	+	4.51332i	0.354600	+	0.614185i
$55$	2.80710	−	6.86441i	0.378510	−	0.925597i
$56$	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	0.215421	−	0.976521i	$-0.430888\pi$
$59$	−4.01387	−	2.31741i	−0.522561	−	0.301701i	−0.737982	+	0.674821i	$0.764221\pi$
$60$	−3.84968	+	0.300820i	−0.496991	+	0.0388356i
$61$	7.39576	−	4.26995i	0.946931	−	0.546711i	0.0548045	−	0.998497i	$-0.482546\pi$
$61$	7.39576	−	4.26995i	0.946931	−	0.546711i	0.892126	+	0.451786i	$0.149213\pi$
$62$	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
$66$	4.27567	+	3.81075i	0.526298	+	0.469071i
$67$	4.01993	+	15.0026i	0.491113	+	1.83286i	0.550795	+	0.834640i	$0.314325\pi$
$67$	4.01993	+	15.0026i	0.491113	+	1.83286i	−0.0596825	+	0.998217i	$0.519009\pi$
$68$	−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	−0.910100	−	0.414389i	$-0.863995\pi$
$73$	−2.81204	−	10.4947i	−0.329125	−	1.22831i	0.580975	−	0.813921i	$-0.302671\pi$
$74$	−3.75790	+	6.50888i	−0.436848	+	0.756642i
$75$	−5.08294	+	6.97971i	−0.586927	+	0.805947i
$76$			1.55251i			0.178086i
$77$	−2.09948	−	8.52010i	−0.239258	−	0.970956i
$78$	3.72695	+	3.72695i	0.421994	+	0.421994i
$79$	0.693914	+	1.20189i	0.0780714	+	0.135224i	0.902418	−	0.430862i	$-0.141790\pi$
$79$	0.693914	+	1.20189i	0.0780714	+	0.135224i	−0.824346	+	0.566086i	$0.808457\pi$
$80$	−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	$-0.904489\pi$
$83$	−6.01057	+	6.01057i	−0.659746	+	0.659746i	0.295574	+	0.955320i	$0.404489\pi$
$84$	−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
$88$	0.190370	+	3.31116i	0.0202935	+	0.352971i
$89$	−12.4567	+	7.19191i	−1.32041	+	0.762340i	−0.983794	−	0.179301i	$-0.942616\pi$
$89$	−12.4567	+	7.19191i	−1.32041	+	0.762340i	−0.336618	+	0.941641i	$0.609283\pi$
$90$	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	−0.949823	−	0.312788i	$-0.898737\pi$
$97$	−6.27407	+	6.27407i	−0.637035	+	0.637035i	0.312788	+	0.949823i	$0.398737\pi$
$98$	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	$-0.348357\pi$
$101$	−0.821255	−	0.474152i	−0.0817180	−	0.0471799i	−0.540302	+	0.841471i	$0.681690\pi$
$102$	−1.36158	−	5.08148i	−0.134816	−	0.503142i
$103$	3.08716	−	11.5214i	0.304187	−	1.13524i	−0.629457	−	0.777036i	$-0.716722\pi$
$103$	3.08716	−	11.5214i	0.304187	−	1.13524i	0.933643	−	0.358204i	$-0.116611\pi$
$104$			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	0.790053	+	0.613039i	$0.210053\pi$
$107$	−2.07577	+	7.74689i	−0.200673	+	0.748920i	−0.990725	+	0.135881i	$0.956613\pi$
$108$	−5.03396	+	1.34884i	−0.484393	+	0.129793i
$109$	4.25423	−	7.36854i	0.407481	−	0.705778i	−0.587126	−	0.809496i	$-0.699741\pi$
$109$	4.25423	−	7.36854i	0.407481	−	0.705778i	0.994607	+	0.103718i	$0.0330739\pi$
$110$	5.90398	+	4.48809i	0.562923	+	0.427923i
$111$	−12.9789			−1.23190
$112$	−2.63778	−	0.205177i	−0.249247	−	0.0193874i
$113$	0.199487	+	0.199487i	0.0187662	+	0.0187662i	0.716428	−	0.697661i	$-0.245776\pi$
$113$	0.199487	+	0.199487i	0.0187662	+	0.0187662i	−0.697661	+	0.716428i	$0.745776\pi$
$114$	−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
$121$	−1.26069	−	10.9275i	−0.114608	−	0.993411i
$122$	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	$-0.403303\pi$
$127$	−7.38236	−	7.38236i	−0.655078	−	0.655078i	−0.954211	+	0.299133i	$0.903303\pi$
$128$	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	$-0.937939\pi$
$131$	−14.9227	+	8.61561i	−1.30380	+	0.752749i	−0.322746	+	0.946485i	$0.604606\pi$
$132$	−4.78753	+	3.14368i	−0.416701	+	0.273622i
$133$	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	0.883277	−	0.468852i	$-0.155332\pi$
$137$	−1.35879	−	5.07109i	−0.116090	−	0.433252i	−0.999366	+	0.0356002i	$0.988666\pi$
$138$	6.15650	+	1.64963i	0.524076	+	0.140426i
$139$	13.9277			1.18133			0.590666	−	0.806916i	$-0.298865\pi$
$139$	13.9277			1.18133			0.590666	+	0.806916i	$0.298865\pi$
$140$	−4.18181	+	4.18479i	−0.353428	+	0.353679i
$141$	−3.10170			−0.261210
$142$	−1.04952	+	3.91686i	−0.0880738	+	0.328696i
$143$	−0.581038	−	10.1062i	−0.0485889	−	0.845120i
$144$	−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	$-0.229610\pi$
$149$	−2.39807	−	4.15358i	−0.196457	−	0.340274i	−0.947377	+	0.320119i	$0.896277\pi$
$150$	−5.42632	−	6.71622i	−0.443057	−	0.548377i
$151$	−8.13638	−	4.69754i	−0.662129	−	0.382281i	0.130958	−	0.991388i	$-0.458195\pi$
$151$	−8.13638	−	4.69754i	−0.662129	−	0.382281i	−0.793088	+	0.609107i	$0.791528\pi$
$152$	−1.49961	−	0.401820i	−0.121635	−	0.0325919i
$153$	−0.0385498	+	0.0385498i	−0.00311656	+	0.00311656i
$154$	8.77317	+	0.177219i	0.706963	+	0.0142807i
$155$	−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	−0.997009	−	0.0772850i	$-0.975375\pi$
$157$	−2.15787	−	8.05326i	−0.172216	−	0.642720i	0.824793	−	0.565435i	$-0.191292\pi$
$158$	−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	−0.905492	−	0.424363i	$-0.860498\pi$
$163$	1.16013	−	4.32967i	0.0908686	−	0.339126i	0.996361	+	0.0852369i	$0.0271647\pi$
$164$	−3.09496	+	5.36063i	−0.241676	+	0.418595i
$165$	−1.61430	+	12.7047i	−0.125673	+	0.989061i
$166$	−4.25011	−	7.36141i	−0.329873	−	0.571357i
$167$	7.29704	+	7.29704i	0.564662	+	0.564662i	0.930628	−	0.365966i	$-0.119261\pi$
$167$	7.29704	+	7.29704i	0.564662	+	0.564662i	−0.365966	+	0.930628i	$0.619261\pi$
$168$	−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	$-0.749285\pi$
$173$	−21.9767	−	5.88864i	−1.67086	−	0.447705i	−0.965342	+	0.260989i	$0.915951\pi$
$174$			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	0.278417	−	0.960460i	$-0.410190\pi$
$179$	−5.54106	−	3.19913i	−0.414158	−	0.239114i	−0.692575	+	0.721346i	$0.743524\pi$
$180$	−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
$187$	−4.54129	+	9.02563i	−0.332092	+	0.660020i
$188$	−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	0.883906	−	0.467665i	$-0.154905\pi$
$191$	0.510567	+	0.884328i	0.0369433	+	0.0639877i	−0.846963	+	0.531653i	$0.821571\pi$
$192$	0.446949	+	1.66804i	0.0322557	+	0.120380i
$193$	−0.788030	−	2.94097i	−0.0567237	−	0.211696i	0.931747	−	0.363108i	$-0.118284\pi$
$193$	−0.788030	−	2.94097i	−0.0567237	−	0.211696i	−0.988471	+	0.151413i	$0.951618\pi$
$194$	−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	−0.784916	−	0.619603i	$-0.787294\pi$
$197$	−19.7134	−	19.7134i	−1.40452	−	1.40452i	−0.619603	−	0.784916i	$-0.712706\pi$
$198$	0.0530205	+	0.0266775i	0.00376800	+	0.00189589i
$199$	20.9597	+	12.1011i	1.48580	+	0.857825i	0.999869	−	0.0161734i	$-0.00514837\pi$
$199$	20.9597	+	12.1011i	1.48580	+	0.857825i	0.485928	+	0.873999i	$0.338482\pi$
$200$	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
$220$	−5.86323	+	4.54121i	−0.395299	+	0.306168i
$221$	−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	0.483667	−	0.875252i	$-0.339305\pi$
$223$	−5.84761	−	5.84761i	−0.391585	−	0.391585i	−0.875252	+	0.483667i	$0.839305\pi$
$224$	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	$-0.834514\pi$
$227$	−20.6574	+	5.53514i	−1.37108	+	0.367380i	−0.503208	+	0.864165i	$0.667847\pi$
$228$	−0.693894	−	2.58965i	−0.0459543	−	0.171504i
$229$	17.6162	−	10.1707i	1.16411	−	0.672100i	0.211826	−	0.977307i	$-0.432059\pi$
$229$	17.6162	−	10.1707i	1.16411	−	0.672100i	0.952286	+	0.305207i	$0.0987258\pi$
$230$	8.11400	+	1.50851i	0.535021	+	0.0994685i
$231$	7.31006	+	13.2735i	0.480967	+	0.873330i
$232$	−6.19172	+	6.19172i	−0.406506	+	0.406506i
$233$	28.1370	+	7.53929i	1.84332	+	0.493915i	0.999113	−	0.0421062i	$-0.0134068\pi$
$233$	28.1370	+	7.53929i	1.84332	+	0.493915i	0.844204	+	0.536022i	$0.180073\pi$
$234$	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	$-0.574607\pi$
$239$	−7.18083			−0.464489			−0.232245	+	0.972657i	$0.574607\pi$
$240$	3.48433	+	1.66432i	0.224913	+	0.107432i
$241$	−7.61472	−	4.39636i	−0.490507	−	0.283194i	0.234278	−	0.972170i	$-0.424727\pi$
$241$	−7.61472	−	4.39636i	−0.490507	−	0.283194i	−0.724785	+	0.688975i	$0.758061\pi$
$242$	10.8815	+	1.61052i	0.699487	+	0.103528i
$243$	−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
$253$	−6.71902	−	10.2324i	−0.422421	−	0.643307i
$254$	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	0.671358	−	0.741133i	$-0.265711\pi$
$257$	14.1428	+	3.78955i	0.882204	+	0.236386i	0.210846	+	0.977519i	$0.432378\pi$
$258$	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	0.828278	+	0.560318i	$0.189321\pi$
$263$	6.34301	+	23.6725i	0.391127	+	1.45971i	−0.437151	+	0.899388i	$0.644012\pi$
$264$	−1.79746	−	5.43804i	−0.110626	−	0.334688i
$265$	−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	0.0102498	−	0.999947i	$-0.496737\pi$
$269$	−13.9510	−	8.05459i	−0.850605	−	0.491097i	−0.860855	+	0.508850i	$0.830071\pi$
$270$	−8.85706	−	7.57318i	−0.539023	−	0.460889i
$271$	−1.92331	+	1.11042i	−0.116832	+	0.0674533i	−0.557277	−	0.830326i	$-0.688154\pi$
$271$	−1.92331	+	1.11042i	−0.116832	+	0.0674533i	0.440445	+	0.897780i	$0.354821\pi$
$272$	2.15412	+	2.15412i	0.130613	+	0.130613i
$273$	6.01494	+	12.5810i	0.364041	+	0.761439i
$274$	5.24998			0.317163
$275$	−0.802363	+	16.5637i	−0.0483843	+	0.998829i
$276$	−3.18684	+	5.51977i	−0.191825	+	0.332251i
$277$	20.6259	−	5.52669i	1.23929	−	0.332066i	0.421099	−	0.907015i	$-0.361644\pi$
$277$	20.6259	−	5.52669i	1.23929	−	0.332066i	0.818190	+	0.574948i	$0.194978\pi$
$278$	−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	$-0.0298956\pi$
$283$	1.45504	+	5.43029i	0.0864933	+	0.322797i	−0.909099	+	0.416579i	$0.863229\pi$
$284$	−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	$-0.678058\pi$
$293$	5.42475	−	5.42475i	0.316917	−	0.316917i	0.847582	+	0.530665i	$0.178058\pi$
$294$	−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
$297$	0.992119	+	17.2562i	0.0575686	+	1.00131i
$298$	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	$-0.336251\pi$
$307$	−6.63243	−	6.63243i	−0.378533	−	0.378533i	−0.870573	+	0.492040i	$0.836251\pi$
$308$	−2.44184	+	8.42837i	−0.139137	+	0.480251i
$309$			20.5979i			1.17178i
$310$	−12.5705	−	6.00441i	−0.713955	−	0.341027i
$311$	6.80279	−	11.7828i	0.385751	−	0.668140i	−0.606122	−	0.795371i	$-0.707276\pi$
$311$	6.80279	−	11.7828i	0.385751	−	0.668140i	0.991873	+	0.127232i	$0.0406092\pi$
$312$	−1.36416	−	5.09110i	−0.0772302	−	0.288227i
$313$	6.41779	−	23.9515i	0.362755	−	1.35382i	−0.507684	−	0.861543i	$-0.669498\pi$
$313$	6.41779	−	23.9515i	0.362755	−	1.35382i	0.870439	−	0.492276i	$-0.163835\pi$
$314$	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	−0.361012	−	0.932561i	$-0.617569\pi$
$317$	−20.2960	−	5.43830i	−1.13994	−	0.305445i	−0.778926	+	0.627116i	$0.784235\pi$
$318$	−4.06408	−	15.1673i	−0.227902	−	0.850542i
$319$	19.3230	−	21.6805i	1.08188	−	1.21387i
$320$	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
$330$	−11.8540	−	4.84752i	−0.652541	−	0.266847i
$331$	5.43730	+	9.41768i	0.298861	+	0.517643i	0.975876	−	0.218327i	$-0.0700600\pi$
$331$	5.43730	+	9.41768i	0.298861	+	0.517643i	−0.677015	+	0.735970i	$0.736727\pi$
$332$	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	$-0.332337\pi$
$337$	−6.64080	−	6.64080i	−0.361747	−	0.361747i	−0.864456	+	0.502709i	$0.832337\pi$
$338$	−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
$341$	6.48473	+	19.6189i	0.351168	+	1.06242i
$342$	−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	$-0.628454\pi$
$347$	−5.08406	+	1.36227i	−0.272927	+	0.0731305i	0.119760	+	0.992803i	$0.461788\pi$
$348$	−14.6060	−	3.91367i	−0.782964	−	0.209795i
$349$	15.3310			0.820652			0.410326	−	0.911939i	$-0.365415\pi$
$349$	15.3310			0.820652			0.410326	+	0.911939i	$0.365415\pi$
$350$	−13.0068	−	2.41337i	−0.695240	−	0.129000i
$351$			15.9064i			0.849022i
$352$	1.49071	−	2.96273i	0.0794553	−	0.157914i
$353$	−0.127441	+	0.0341476i	−0.00678298	+	0.00181749i	−0.262209	−	0.965011i	$-0.584451\pi$
$353$	−0.127441	+	0.0341476i	−0.00678298	+	0.00181749i	0.255426	+	0.966829i	$0.417784\pi$
$354$	−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	0.896820	+	0.442396i	$0.145871\pi$
$359$	15.7554	+	27.2891i	0.831536	+	1.44026i	−0.0652836	+	0.997867i	$0.520795\pi$
$360$	−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
$363$	6.98691	+	17.6640i	0.366718	+	0.927121i
$364$	−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	−0.992665	−	0.120900i	$-0.961422\pi$
$367$	−3.70581	−	13.8303i	−0.193442	−	0.721935i	0.799223	−	0.601035i	$-0.205245\pi$
$368$	−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	$-0.528584\pi$
$373$	−12.8496	−	3.44304i	−0.665327	−	0.178274i	−0.575649	+	0.817697i	$0.695250\pi$
$374$	−7.54272	−	6.72256i	−0.390025	−	0.347615i
$375$	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	$-0.972626\pi$
$379$		−	3.34431i		−	0.171786i	0.996304	−	0.0858928i	$-0.0273743\pi$
$380$	−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	0.685601	+	0.727978i	$0.259540\pi$
$383$	−5.32581	+	19.8762i	−0.272136	+	1.01563i	−0.957736	+	0.287647i	$0.907127\pi$
$384$	−1.72688			−0.0881243
$385$	10.7757	+	16.3977i	0.549181	+	0.835703i
$386$	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	0.776545	−	0.630062i	$-0.216970\pi$
$389$	12.2119	+	7.05055i	0.619168	+	0.357477i	−0.157377	+	0.987539i	$0.550304\pi$
$390$	−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
$396$	−0.0394912	+	0.0443092i	−0.00198451	+	0.00222662i
$397$	33.4441	+	8.96132i	1.67851	+	0.449756i	0.967386	−	0.253308i	$-0.0815186\pi$
$397$	33.4441	+	8.96132i	1.67851	+	0.449756i	0.711127	+	0.703064i	$0.248185\pi$
$398$	−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	0.979620	−	0.200858i	$-0.0643729\pi$
$401$	6.32514	+	10.9555i	0.315862	+	0.547090i	−0.663758	+	0.747947i	$0.731040\pi$
$402$	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
$407$	−20.8365	+	13.6821i	−1.03283	+	0.678197i
$408$	−1.36158	+	5.08148i	−0.0674082	+	0.251571i
$409$	−2.34735	+	4.06573i	−0.116069	+	0.201038i	−0.918207	−	0.396102i	$-0.870363\pi$
$409$	−2.34735	+	4.06573i	−0.116069	+	0.201038i	0.802138	+	0.597139i	$0.203696\pi$
$410$	−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
$418$	−2.31435	+	4.59968i	−0.113199	+	0.224978i
$419$		−	26.6533i		−	1.30210i	−0.759036	−	0.651049i	$-0.774329\pi$
$419$		−	26.6533i		−	1.30210i	0.759036	−	0.651049i	$-0.225671\pi$
$420$	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
$429$	5.48613	+	16.5977i	0.264873	+	0.801347i
$430$	16.6721	+	14.2554i	0.804002	+	0.687457i
$431$	−16.5720	−	9.56786i	−0.798246	−	0.460867i	0.0446117	−	0.999004i	$-0.485795\pi$
$431$	−16.5720	−	9.56786i	−0.798246	−	0.460867i	−0.842857	+	0.538137i	$0.819128\pi$
$432$	5.03396	+	1.34884i	0.242196	+	0.0648963i
$433$	−2.40966	−	2.40966i	−0.115801	−	0.115801i	0.646832	−	0.762633i	$-0.276094\pi$
$433$	−2.40966	−	2.40966i	−0.115801	−	0.115801i	−0.762633	+	0.646832i	$0.776094\pi$
$434$	−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	−0.911528	−	0.411239i	$-0.865096\pi$
$439$	−17.0113	−	29.4645i	−0.811907	−	1.40626i	0.0996203	−	0.995026i	$-0.468237\pi$
$440$	−2.86895	−	6.83879i	−0.136772	−	0.326027i
$441$	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	0.863162	+	0.504927i	$0.168481\pi$
$443$	−2.87977	+	10.7474i	−0.136822	+	0.510627i	−0.999984	+	0.00569915i	$0.998186\pi$
$444$	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	$-0.655678\pi$
$449$		−	37.4110i		−	1.76553i	0.469810	−	0.882767i	$-0.344322\pi$
$450$	−0.0723314	−	0.0526750i	−0.00340974	−	0.00248313i
$451$	15.3260	+	13.6595i	0.721672	+	0.643200i
$452$	−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	0.726216	+	0.687467i	$0.241277\pi$
$457$	−5.26827	+	19.6614i	−0.246439	+	0.919723i	−0.972655	+	0.232256i	$0.925389\pi$
$458$	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	$-0.0546460\pi$
$462$	−14.7132	+	3.62555i	−0.684519	+	0.168676i
$463$	−27.0696	−	27.0696i	−1.25803	−	1.25803i	−0.952032	−	0.305998i	$-0.901010\pi$
$463$	−27.0696	−	27.0696i	−1.25803	−	1.25803i	−0.305998	−	0.952032i	$-0.598990\pi$
$464$	−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	−0.351616	−	0.936145i	$-0.614368\pi$
$467$	−24.2941	−	6.50958i	−1.12420	−	0.301227i	−0.772580	+	0.634917i	$0.781034\pi$
$468$	−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
$473$	−1.86752	−	32.4823i	−0.0858687	−	1.49354i
$474$	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	$-0.679565\pi$
$479$	10.1662	−	17.6085i	0.464508	−	0.804551i	0.999179	+	0.0405090i	$0.0128979\pi$
$480$	−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	−0.562981	−	0.826470i	$-0.690346\pi$
$487$	−10.7838	−	40.2456i	−0.488660	−	1.82370i	0.0743210	−	0.997234i	$-0.476321\pi$
$488$	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
$495$	0.0179170	+	0.131504i	0.000805310	+	0.00591066i
$496$	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	−0.428889	−	0.903357i	$-0.641095\pi$
$499$	3.10495	−	1.79265i	0.138997	−	0.0802498i	0.567886	+	0.823107i	$0.307762\pi$
$500$	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	$-0.523659\pi$
$503$	20.7003	−	20.7003i	0.922979	−	0.922979i	0.997239	+	0.0742598i	$0.0236594\pi$
$504$	−0.0307828	−	0.0359755i	−0.00137118	−	0.00160248i
$505$	2.08475	+	0.387586i	0.0927701	+	0.0172474i
$506$	11.6228	−	3.84173i	0.516695	−	0.170786i
$507$	−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	−0.349314	−	0.937006i	$-0.613585\pi$
$509$	6.48630	−	3.74487i	0.287500	−	0.165988i	0.636814	+	0.771017i	$0.280252\pi$
$510$	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
$517$	−4.97953	+	3.26976i	−0.218999	+	0.143804i
$518$	−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	0.440339	+	0.897832i	$0.354858\pi$
$521$	−12.7223	+	22.0357i	−0.557376	+	0.965403i	−0.997714	+	0.0675712i	$0.978475\pi$
$522$	0.0405578	+	0.151364i	0.00177516	+	0.00662500i
$523$	5.00656	+	1.34150i	0.218921	+	0.0586598i	0.366613	−	0.930374i	$-0.380517\pi$
$523$	5.00656	+	1.34150i	0.218921	+	0.0586598i	−0.147691	+	0.989034i	$0.547184\pi$
$524$	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
$528$	5.71796	−	0.328745i	0.248842	−	0.0143068i
$529$	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
$539$	21.7312	+	8.17037i	0.936029	+	0.351923i
$540$	9.60750	−	6.59518i	0.413441	−	0.283811i
$541$	−29.6625	+	17.1257i	−1.27529	+	0.736290i	−0.975979	−	0.217865i	$-0.930091\pi$
$541$	−29.6625	+	17.1257i	−1.27529	+	0.736290i	−0.299313	+	0.954155i	$0.596757\pi$
$542$	−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	−0.979158	−	0.203101i	$-0.934898\pi$
$547$	−27.6507	−	27.6507i	−1.18226	−	1.18226i	−0.203101	−	0.979158i	$-0.565102\pi$
$548$	−1.35879	+	5.07109i	−0.0580448	+	0.216626i
$549$	−0.0764141	+	0.132353i	−0.00326128	+	0.00564870i
$550$	−15.7916	−	5.06202i	−0.673358	−	0.215845i
$551$	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	$-0.639730\pi$
$557$	−8.03579	+	2.15318i	−0.340487	+	0.0912333i	0.0845237	+	0.996421i	$0.473063\pi$
$558$	−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	−0.994340	−	0.106244i	$-0.966118\pi$
$563$	−4.42137	−	16.5008i	−0.186338	−	0.695424i	0.808002	−	0.589180i	$-0.200549\pi$
$564$	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	$-0.158103\pi$
$569$	0.641650	+	1.11137i	0.0268994	+	0.0465911i	−0.852262	+	0.523115i	$0.824770\pi$
$570$	3.89591	−	4.55639i	0.163182	−	0.190846i
$571$	−7.41728	−	4.28237i	−0.310404	−	0.179212i	0.336703	−	0.941611i	$-0.390688\pi$
$571$	−7.41728	−	4.28237i	−0.310404	−	0.179212i	−0.647107	+	0.762399i	$0.724021\pi$
$572$	−4.54989	+	9.04272i	−0.190240	+	0.378095i
$573$	−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	0.815681	+	0.578501i	$0.196362\pi$
$577$	9.57305	+	35.7271i	0.398531	+	1.48734i	−0.417150	+	0.908838i	$0.636971\pi$
$578$	−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
$583$	−13.5550	+	26.9399i	−0.561389	+	1.11574i
$584$	−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	−0.999337	−	0.0364115i	$-0.988407\pi$
$587$	−23.3298	+	23.3298i	−0.962925	+	0.962925i	0.0364115	+	0.999337i	$0.488407\pi$
$588$	−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	$-0.665302\pi$
$593$	−33.1220	−	8.87501i	−1.36016	−	0.364453i	−0.863874	+	0.503708i	$0.831969\pi$
$594$	−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	−0.355346	−	0.934735i	$-0.615637\pi$
$599$	−32.8575	−	18.9703i	−1.34252	−	0.775106i	−0.987177	+	0.159629i	$0.948970\pi$
$600$	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
$605$	10.8015	+	22.0982i	0.439141	+	0.898418i
$606$	−0.818802	+	1.41821i	−0.0332616	+	0.0576107i
$607$	−2.29557	+	8.56717i	−0.0931742	+	0.347731i	−0.996736	−	0.0807263i	$-0.974276\pi$
$607$	−2.29557	+	8.56717i	−0.0931742	+	0.347731i	0.903562	+	0.428457i	$0.140943\pi$
$608$	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	0.938120	+	0.346310i	$0.112565\pi$
$613$	7.39891	+	27.6131i	0.298839	+	1.11528i	−0.639281	+	0.768973i	$0.720768\pi$
$614$	8.12304	−	4.68984i	0.327819	−	0.189266i
$615$	−13.5272	−	19.7057i	−0.545469	−	0.794610i
$616$	−7.50918	−	4.54006i	−0.302554	−	0.182924i
$617$	−13.2472	+	13.2472i	−0.533311	+	0.533311i	−0.921556	−	0.388245i	$-0.873081\pi$
$617$	−13.2472	+	13.2472i	−0.533311	+	0.533311i	0.388245	+	0.921556i	$0.373081\pi$
$618$	−19.8961	−	5.33114i	−0.800338	−	0.214450i
$619$	11.5612	+	6.67484i	0.464682	+	0.268284i	0.714011	−	0.700134i	$-0.246877\pi$
$619$	11.5612	+	6.67484i	0.464682	+	0.268284i	−0.249329	+	0.968419i	$0.580210\pi$
$620$	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
$627$	−8.87722	+	0.510382i	−0.354522	+	0.0203827i
$628$	−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
$638$	15.9406	+	24.2759i	0.631093	+	0.961094i
$639$	−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	−0.977430	−	0.211258i	$-0.932244\pi$
$641$	−7.74123	+	13.4082i	−0.305760	+	0.529592i	0.671670	+	0.740850i	$0.265577\pi$
$642$	13.3779	+	3.58460i	0.527985	+	0.141473i
$643$	21.5362	+	21.5362i	0.849306	+	0.849306i	0.990047	−	0.140741i	$-0.0449484\pi$
$643$	21.5362	+	21.5362i	0.849306	+	0.849306i	−0.140741	+	0.990047i	$0.544948\pi$
$644$	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	−0.982943	−	0.183911i	$-0.941124\pi$
$647$	−5.68867	−	21.2304i	−0.223645	−	0.834653i	0.759298	−	0.650743i	$-0.225542\pi$
$648$	2.31539	+	8.64117i	0.0909572	+	0.339457i
$649$	14.5953	−	4.82425i	0.572916	−	0.189369i
$650$	−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	−0.771480	−	0.636254i	$-0.780483\pi$
$653$	5.48815	−	20.4821i	0.214768	−	0.801525i	0.986248	−	0.165272i	$-0.0528501\pi$
$654$	−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	$-0.231956\pi$
$659$	38.3028			1.49207			0.746033	+	0.665909i	$0.231956\pi$
$660$	7.75039	−	10.1955i	0.301683	−	0.396857i
$661$	−18.3949	+	31.8609i	−0.715479	+	1.23925i	0.247296	+	0.968940i	$0.420458\pi$
$661$	−18.3949	+	31.8609i	−0.715479	+	1.23925i	−0.962775	+	0.270305i	$0.912875\pi$
$662$	−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	$-0.933659\pi$
$673$	−20.0131	+	20.0131i	−0.771447	+	0.771447i	0.206912	+	0.978360i	$0.433659\pi$
$674$	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	$-0.918511\pi$
$677$	−0.0780567	+	0.291312i	−0.00299996	+	0.0111960i	0.964410	+	0.264413i	$0.0851781\pi$
$678$	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
$682$	−20.6288	+	1.18602i	−0.789917	+	0.0454151i
$683$	2.97640	−	0.797525i	0.113889	−	0.0305164i	−0.201424	−	0.979504i	$-0.564557\pi$
$683$	2.97640	−	0.797525i	0.113889	−	0.0305164i	0.315313	+	0.948988i	$0.397890\pi$
$684$	−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	−0.991303	−	0.131601i	$-0.957988\pi$
$691$	−16.0250	−	27.7562i	−0.609621	−	1.05590i	0.381681	−	0.924294i	$-0.375345\pi$
$692$	16.0881	+	16.0881i	0.611576	+	0.611576i
$693$	0.108775	+	0.113260i	0.00413203	+	0.00430241i
$694$		−	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
$704$	2.47595	+	2.20673i	0.0933160	+	0.0831693i
$705$	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	−0.522636	+	0.852556i	$0.675051\pi$
$709$	−40.5341	+	23.4024i	−1.52229	+	0.878894i	−0.999653	+	0.0263376i	$0.991616\pi$
$710$	−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
$715$	8.75649	+	20.8731i	0.327474	+	0.780609i
$716$	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	−0.747436	−	0.664333i	$-0.768716\pi$
$719$	−14.6358	+	8.45001i	−0.545825	+	0.315132i	0.201611	+	0.979466i	$0.435382\pi$
$720$	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
$726$	−18.8705	+	2.17705i	−0.700349	+	0.0807980i
$727$	−14.1045	+	14.1045i	−0.523106	+	0.523106i	−0.918508	−	0.395402i	$-0.870605\pi$
$727$	−14.1045	+	14.1045i	−0.523106	+	0.523106i	0.395402	+	0.918508i	$0.370605\pi$
$728$	−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	$-0.392233\pi$
$733$	4.01086	+	1.07471i	0.148144	+	0.0396952i	−0.183985	+	0.982929i	$0.558900\pi$
$734$	14.3182			0.528493
$735$	−22.2954	−	15.2817i	−0.822380	−	0.563672i
$736$		−	3.69087i		−	0.136047i
$737$	−46.0166	−	23.1535i	−1.69504	−	0.852870i
$738$	−0.106999	+	0.0286703i	−0.00393869	+	0.00105537i
$739$	−8.71193	+	15.0895i	−0.320474	+	0.555076i	−0.980586	−	0.196091i	$-0.937175\pi$
$739$	−8.71193	+	15.0895i	−0.320474	+	0.555076i	0.660112	+	0.751167i	$0.270509\pi$
$740$	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	$-0.717622\pi$
$743$	3.91434	−	3.91434i	0.143603	−	0.143603i	0.775254	+	0.631650i	$0.217622\pi$
$744$	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
$748$	8.44569	−	5.54578i	0.308805	−	0.202774i
$749$	−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	0.988219	−	0.153046i	$-0.0489083\pi$
$751$	9.90854	+	17.1621i	0.361568	+	0.626254i	−0.626651	+	0.779300i	$0.715575\pi$
$752$	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	−0.0661176	+	0.997812i	$0.521061\pi$
$757$	−29.2726	+	29.2726i	−1.06393	+	1.06393i	−0.997812	+	0.0661176i	$0.978939\pi$
$758$	3.23035	+	0.865571i	0.117332	+	0.0314389i
$759$	15.7809	+	14.0650i	0.572812	+	0.510527i
$760$	3.46098	−	0.270446i	0.125543	−	0.00981010i
$761$	11.0793	−	6.39665i	0.401625	−	0.231879i	−0.285560	−	0.958361i	$-0.592179\pi$
$761$	11.0793	−	6.39665i	0.401625	−	0.231879i	0.687185	+	0.726482i	$0.258846\pi$
$762$	−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	$-0.654666\pi$
$769$	−25.9007			−0.934002			−0.467001	+	0.884257i	$0.654666\pi$
$770$	−18.6279	+	6.16451i	−0.671303	+	0.222154i
$771$	−25.2844			−0.910597
$772$	−0.788030	+	2.94097i	−0.0283618	+	0.105848i
$773$	−20.5331	+	5.50184i	−0.738526	+	0.197887i	−0.608423	−	0.793613i	$-0.708197\pi$
$773$	−20.5331	+	5.50184i	−0.738526	+	0.197887i	−0.130103	+	0.991500i	$0.541531\pi$
$774$	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
$781$	−8.94837	+	10.0401i	−0.320198	+	0.359262i
$782$	−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	$-0.771343\pi$
$787$	−30.1814	+	8.08708i	−1.07585	+	0.288273i	−0.322955	+	0.946414i	$0.604676\pi$
$788$	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
$792$	−0.0325783	−	0.0496136i	−0.00115762	−	0.00176294i
$793$	−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	−0.996819	−	0.0797018i	$-0.974603\pi$
$797$	−25.8913	+	25.8913i	−0.917117	+	0.917117i	0.0797018	+	0.996819i	$0.474603\pi$
$798$	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
$803$	32.1898	+	16.1965i	1.13595	+	0.571560i
$804$			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	$-0.687686\pi$
$809$	12.5651	−	21.7634i	0.441766	−	0.765161i	0.997821	+	0.0659848i	$0.0210189\pi$
$810$	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
$814$	−7.82301	−	23.6677i	−0.274196	−	0.829554i
$815$	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	$-0.402927\pi$
$821$	36.5744	−	21.1162i	1.27645	−	0.736961i	0.976195	+	0.216897i	$0.0695935\pi$
$822$	−8.75714	+	2.34647i	−0.305440	+	0.0818425i
$823$	7.36520	−	1.97350i	0.256735	−	0.0687919i	−0.128156	−	0.991754i	$-0.540906\pi$
$823$	7.36520	−	1.97350i	0.256735	−	0.0687919i	0.384891	+	0.922962i	$0.374239\pi$
$824$	−5.96393	−	10.3298i	−0.207763	−	0.359857i
$825$	−6.06476	−	27.9875i	−0.211148	−	0.974398i
$826$	2.24567	+	12.0552i	0.0781370	+	0.419453i
$827$	5.22768	+	5.22768i	0.181784	+	0.181784i	0.792133	−	0.610349i	$-0.208971\pi$
$827$	5.22768	+	5.22768i	0.181784	+	0.181784i	−0.610349	+	0.792133i	$0.708971\pi$
$828$	−0.0170953	+	0.0638005i	−0.000594102	+	0.00221722i
$829$	−11.5497	−	6.66821i	−0.401137	−	0.231597i	0.285837	−	0.958278i	$-0.407728\pi$
$829$	−11.5497	−	6.66821i	−0.401137	−	0.231597i	−0.686974	+	0.726682i	$0.741062\pi$
$830$	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
$836$	−3.84395	−	3.42598i	−0.132946	−	0.118490i
$837$	−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	$0.0526051\pi$
$839$			9.53037i			0.329025i	−0.986375	+	0.164513i	$0.947395\pi$
$840$	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
$847$	25.7284	+	13.6033i	0.884037	+	0.467416i
$848$	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	$-0.979329\pi$
$853$	−27.2492	+	27.2492i	−0.932996	+	0.932996i	0.0648958	+	0.997892i	$0.479329\pi$
$854$	−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	$-0.471173\pi$
$857$	19.5177	−	5.22975i	0.666712	−	0.178645i	0.576273	+	0.817257i	$0.304506\pi$
$858$	−17.4521	+	1.00338i	−0.595805	+	0.0342549i
$859$	−9.45623	+	5.45956i	−0.322642	+	0.186278i	−0.652570	−	0.757729i	$-0.726309\pi$
$859$	−9.45623	+	5.45956i	−0.322642	+	0.186278i	0.329927	+	0.944006i	$0.392976\pi$
$860$	−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	−0.710617	−	0.703579i	$-0.751584\pi$
$863$	7.53766	−	28.1309i	0.256585	−	0.957587i	0.967202	−	0.254009i	$-0.0817491\pi$
$864$	−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	0.572054	+	0.820216i	$0.306147\pi$
$877$	−9.87536	+	36.8553i	−0.333467	+	1.24452i	−0.905521	+	0.424301i	$0.860520\pi$
$878$	32.8634	−	8.80572i	1.10909	−	0.297179i
$879$	−6.62409	+	11.4733i	−0.223425	+	0.386983i
$880$	7.34831	−	1.00118i	0.247711	−	0.0337499i
$881$	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	0.557316	−	0.830301i	$-0.311831\pi$
$883$	−8.11184	−	8.11184i	−0.272985	−	0.272985i	−0.830301	+	0.557316i	$0.811831\pi$
$884$	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	0.697565	+	0.716522i	$0.254267\pi$
$887$	−7.88657	+	29.4331i	−0.264805	+	0.988266i	−0.962370	+	0.271744i	$0.912400\pi$
$888$	−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
$891$	−9.31165	−	28.1715i	−0.311952	−	0.943780i
$892$	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
$902$	−17.1607	+	11.2684i	−0.571389	+	0.375197i
$903$	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	−0.988362	−	0.152120i	$-0.951390\pi$
$907$	−6.27854	−	23.4318i	−0.208476	−	0.778041i	0.779886	−	0.625921i	$-0.215277\pi$
$908$	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
$913$	−1.61819	−	28.1456i	−0.0535542	−	0.931483i
$914$	−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	−0.770782	−	0.637099i	$-0.780134\pi$
$919$	−28.4093	−	49.2063i	−0.937135	−	1.62316i	−0.166352	−	0.986066i	$-0.553199\pi$
$920$	−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
$924$	0.306035	−	15.1502i	0.0100678	−	0.498405i
$925$	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	−0.475229	−	0.879862i	$-0.657635\pi$
$929$	1.49777	−	0.864739i	0.0491403	−	0.0283712i	0.524369	+	0.851491i	$0.324301\pi$
$930$	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
$935$	2.84780	−	22.4124i	0.0931330	−	0.732965i
$936$	−0.0273104	−	0.0473030i	−0.000892668	−	0.00154615i
$937$	15.8368	+	15.8368i	0.517366	+	0.517366i	0.916773	−	0.399408i	$-0.130784\pi$
$937$	15.8368	+	15.8368i	0.517366	+	0.517366i	−0.399408	+	0.916773i	$0.630784\pi$
$938$	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	$-0.292601\pi$
$941$	6.78038	+	3.91465i	0.221034	+	0.127614i	−0.385395	+	0.922752i	$0.625935\pi$
$942$	−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	0.691331	−	0.722538i	$-0.257025\pi$
$947$	28.5814	+	7.65837i	0.928772	+	0.248864i	0.237441	+	0.971402i	$0.423691\pi$
$948$	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	$-0.958439\pi$
$953$	−26.5887	+	26.5887i	−0.861292	+	0.861292i	0.130196	+	0.991488i	$0.458439\pi$
$954$	−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
$957$	−22.5415	+	44.8002i	−0.728662	+	1.44818i
$958$	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	$-0.0181451\pi$
$967$	29.2744	+	29.2744i	0.941402	+	0.941402i	−0.0569738	+	0.998376i	$0.518145\pi$
$968$	−8.61836	−	6.83548i	−0.277005	−	0.219701i
$969$	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	0.835660	−	0.549247i	$-0.185085\pi$
$971$	−1.80209	−	3.12131i	−0.0578319	−	0.100168i	−0.893492	+	0.449079i	$0.851752\pi$
$972$	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	0.925886	−	0.377802i	$-0.123320\pi$
$977$	−2.02720	−	7.56560i	−0.0648557	−	0.242045i	−0.990742	+	0.135757i	$0.956653\pi$
$978$	−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	−0.284281	−	0.958741i	$-0.591755\pi$
$983$	−1.60231	+	0.429337i	−0.0511057	+	0.0136937i	0.233176	+	0.972435i	$0.425088\pi$
$984$	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
$990$	−0.131660	−	0.0167292i	−0.00418444	−	0.000531689i
$991$	−0.586202	+	1.01533i	−0.0186213	+	0.0322530i	−0.875186	−	0.483787i	$-0.839261\pi$
$991$	−0.586202	+	1.01533i	−0.0186213	+	0.0322530i	0.856565	+	0.516040i	$0.172594\pi$
$992$	−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	$-0.446065\pi$
$997$	25.4975	−	6.83204i	0.807514	−	0.216373i	0.638880	+	0.769306i	$0.279398\pi$
$998$	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.263.7	✓	192
5.2	odd	4	inner	770.2.bd.a.417.18	yes	192
7.2	even	3	inner	770.2.bd.a.373.42	yes	192
11.10	odd	2	inner	770.2.bd.a.263.31	yes	192
35.2	odd	12	inner	770.2.bd.a.527.31	yes	192
55.32	even	4	inner	770.2.bd.a.417.42	yes	192
77.65	odd	6	inner	770.2.bd.a.373.18	yes	192
385.142	even	12	inner	770.2.bd.a.527.7	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bd.a.263.7	✓	192	1.1	even	1	trivial
770.2.bd.a.263.31	yes	192	11.10	odd	2	inner
770.2.bd.a.373.18	yes	192	77.65	odd	6	inner
770.2.bd.a.373.42	yes	192	7.2	even	3	inner
770.2.bd.a.417.18	yes	192	5.2	odd	4	inner
770.2.bd.a.417.42	yes	192	55.32	even	4	inner
770.2.bd.a.527.7	yes	192	385.142	even	12	inner
770.2.bd.a.527.31	yes	192	35.2	odd	12	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.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} +(-2.20673 + 2.47595i) 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} +(-1.82044 - 2.77236i) 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} +(2.57428 - 5.11627i) 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} +(3.14906 - 1.04087i) 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} +(2.80710 - 6.86441i) 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} +(4.27567 + 3.81075i) 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} +(-2.09948 - 8.52010i) 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} +(0.190370 + 3.31116i) 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

Related objects

Downloads

Learn more