LMFDB - Embedded newform 770.2.bd.a.527.9

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			527.9
Character	$\chi$	$=$	770.527
Dual form			770.2.bd.a.263.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.886001 - 0.237403i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.83005 - 1.28488i) q^{5} +0.917256i q^{6} +(2.44857 + 1.00226i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.86944 - 1.07932i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.886001 - 0.237403i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.83005 - 1.28488i) q^{5} +0.917256i q^{6} +(2.44857 + 1.00226i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.86944 - 1.07932i) q^{9} +(-0.767449 + 2.10024i) q^{10} +(1.44099 + 2.98723i) q^{11} +(0.886001 - 0.237403i) q^{12} +(-2.12323 - 2.12323i) q^{13} +(0.334373 - 2.62454i) q^{14} +(1.31639 + 1.57287i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-5.54661 - 1.48621i) q^{17} +(-0.558697 + 2.08509i) q^{18} +(-1.63705 + 2.83546i) q^{19} +(2.22731 + 0.197716i) q^{20} +(-1.93149 - 1.46930i) q^{21} +(2.51249 - 2.16504i) q^{22} +(1.48880 + 5.55626i) q^{23} +(-0.458628 - 0.794367i) q^{24} +(1.69816 + 4.70279i) q^{25} +(-1.50135 + 2.60042i) q^{26} +(3.34588 + 3.34588i) q^{27} +(-2.62165 + 0.356300i) q^{28} -1.08921 q^{29} +(1.17857 - 1.67862i) q^{30} +(0.726592 + 1.25849i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.567539 - 2.98879i) q^{33} +5.74228i q^{34} +(-3.19321 - 4.98030i) q^{35} +2.15864 q^{36} +(5.52706 - 1.48097i) q^{37} +(3.16254 + 0.847401i) q^{38} +(1.37712 + 2.38525i) q^{39} +(-0.385491 - 2.20259i) q^{40} +9.05144i q^{41} +(-0.919329 + 2.24596i) q^{42} +(4.48914 + 4.48914i) q^{43} +(-2.74155 - 1.86652i) q^{44} +(2.03436 + 4.37722i) q^{45} +(4.98161 - 2.87613i) q^{46} +(10.7095 - 2.86959i) q^{47} +(-0.648598 + 0.648598i) q^{48} +(4.99095 + 4.90820i) q^{49} +(4.10303 - 2.85747i) q^{50} +(4.56148 + 2.63357i) q^{51} +(2.90039 + 0.777156i) q^{52} +(-4.26434 - 1.14263i) q^{53} +(2.36590 - 4.09786i) q^{54} +(1.20116 - 7.31828i) q^{55} +(1.02269 + 2.44010i) q^{56} +(2.12358 - 2.12358i) q^{57} +(0.281907 + 1.05209i) q^{58} +(-5.17478 + 2.98766i) q^{59} +(-1.92646 - 0.703948i) q^{60} +(0.666489 + 0.384798i) q^{61} +(1.02756 - 1.02756i) q^{62} +(-3.49568 - 4.51645i) q^{63} +1.00000i q^{64} +(1.15751 + 6.61372i) q^{65} +(-2.74006 + 1.32176i) q^{66} +(-3.31614 + 12.3760i) q^{67} +(5.54661 - 1.48621i) q^{68} -5.27630i q^{69} +(-3.98414 + 4.37340i) q^{70} -8.83561 q^{71} +(-0.558697 - 2.08509i) q^{72} +(1.38004 - 5.15037i) q^{73} +(-2.86102 - 4.95543i) q^{74} +(-0.388110 - 4.56983i) q^{75} -3.27410i q^{76} +(0.534374 + 8.75868i) q^{77} +(1.94755 - 1.94755i) q^{78} +(-4.54539 + 7.87284i) q^{79} +(-2.02776 + 0.942428i) q^{80} +(1.06783 + 1.84953i) q^{81} +(8.74302 - 2.34269i) q^{82} +(-9.94541 - 9.94541i) q^{83} +(2.40737 + 0.306706i) q^{84} +(8.24097 + 9.84658i) q^{85} +(3.17430 - 5.49805i) q^{86} +(0.965039 + 0.258581i) q^{87} +(-1.09336 + 3.13122i) q^{88} +(-1.27069 - 0.733635i) q^{89} +(3.70153 - 3.09795i) q^{90} +(-3.07084 - 7.32690i) q^{91} +(-4.06746 - 4.06746i) q^{92} +(-0.344991 - 1.28752i) q^{93} +(-5.54363 - 9.60185i) q^{94} +(6.63911 - 3.08561i) q^{95} +(0.794367 + 0.458628i) q^{96} +(7.76343 + 7.76343i) q^{97} +(3.44920 - 6.09122i) q^{98} +(0.530341 - 7.13973i) 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
$3$	−0.886001	−	0.237403i	−0.511533	−	0.137065i	−0.00618575	−	0.999981i	$-0.501969\pi$
$3$	−0.886001	−	0.237403i	−0.511533	−	0.137065i	−0.505347	+	0.862916i	$0.668636\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.83005	−	1.28488i	−0.818423	−	0.574617i
$5$	−1.83005	−	1.28488i	−0.818423	−	0.574617i
$6$			0.917256i			0.374468i
$7$	2.44857	+	1.00226i	0.925471	+	0.378819i
$7$	2.44857	+	1.00226i	0.925471	+	0.378819i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.86944	−	1.07932i	−0.623146	−	0.359773i
$10$	−0.767449	+	2.10024i	−0.242689	+	0.664155i
$11$	1.44099	+	2.98723i	0.434474	+	0.900684i
$11$	1.44099	+	2.98723i	0.434474	+	0.900684i
$12$	0.886001	−	0.237403i	0.255767	−	0.0685325i
$13$	−2.12323	−	2.12323i	−0.588878	−	0.588878i	0.348449	−	0.937328i	$-0.386708\pi$
$13$	−2.12323	−	2.12323i	−0.588878	−	0.588878i	−0.937328	+	0.348449i	$0.886708\pi$
$14$	0.334373	−	2.62454i	0.0893650	−	0.701437i
$15$	1.31639	+	1.57287i	0.339891	+	0.406113i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−5.54661	−	1.48621i	−1.34525	−	0.360459i	−0.486872	−	0.873474i	$-0.661862\pi$
$17$	−5.54661	−	1.48621i	−1.34525	−	0.360459i	−0.858380	+	0.513015i	$0.828529\pi$
$18$	−0.558697	+	2.08509i	−0.131686	+	0.491460i
$19$	−1.63705	+	2.83546i	−0.375566	+	0.650499i	−0.990412	−	0.138149i	$-0.955885\pi$
$19$	−1.63705	+	2.83546i	−0.375566	+	0.650499i	0.614846	+	0.788647i	$0.289218\pi$
$20$	2.22731	+	0.197716i	0.498042	+	0.0442107i
$21$	−1.93149	−	1.46930i	−0.421486	−	0.320628i
$22$	2.51249	−	2.16504i	0.535664	−	0.461588i
$23$	1.48880	+	5.55626i	0.310435	+	1.15856i	0.928165	+	0.372170i	$0.121386\pi$
$23$	1.48880	+	5.55626i	0.310435	+	1.15856i	−0.617730	+	0.786391i	$0.711947\pi$
$24$	−0.458628	−	0.794367i	−0.0936171	−	0.162150i
$25$	1.69816	+	4.70279i	0.339631	+	0.940559i
$26$	−1.50135	+	2.60042i	−0.294439	+	0.509983i
$27$	3.34588	+	3.34588i	0.643916	+	0.643916i
$28$	−2.62165	+	0.356300i	−0.495445	+	0.0673344i
$29$	−1.08921			−0.202261			−0.101130	−	0.994873i	$-0.532246\pi$
$29$	−1.08921			−0.202261			−0.101130	+	0.994873i	$0.532246\pi$
$30$	1.17857	−	1.67862i	0.215176	−	0.306473i
$31$	0.726592	+	1.25849i	0.130500	+	0.226032i	0.923869	−	0.382708i	$-0.125008\pi$
$31$	0.726592	+	1.25849i	0.130500	+	0.226032i	−0.793370	+	0.608740i	$0.791675\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−0.567539	−	2.98879i	−0.0987959	−	0.520281i
$34$			5.74228i			0.984792i
$35$	−3.19321	−	4.98030i	−0.539751	−	0.841825i
$36$	2.15864			0.359773
$37$	5.52706	−	1.48097i	0.908643	−	0.243470i	0.225919	−	0.974146i	$-0.427462\pi$
$37$	5.52706	−	1.48097i	0.908643	−	0.243470i	0.682725	+	0.730676i	$0.260795\pi$
$38$	3.16254	+	0.847401i	0.513032	+	0.137467i
$39$	1.37712	+	2.38525i	0.220516	+	0.381945i
$40$	−0.385491	−	2.20259i	−0.0609515	−	0.348260i
$41$			9.05144i			1.41360i	0.707415	+	0.706799i	$0.249861\pi$
$41$			9.05144i			1.41360i	−0.707415	+	0.706799i	$0.750139\pi$
$42$	−0.919329	+	2.24596i	−0.141856	+	0.346560i
$43$	4.48914	+	4.48914i	0.684587	+	0.684587i	0.961030	−	0.276443i	$-0.0891558\pi$
$43$	4.48914	+	4.48914i	0.684587	+	0.684587i	−0.276443	+	0.961030i	$0.589156\pi$
$44$	−2.74155	−	1.86652i	−0.413304	−	0.281389i
$45$	2.03436	+	4.37722i	0.303265	+	0.652517i
$46$	4.98161	−	2.87613i	0.734498	−	0.424062i
$47$	10.7095	−	2.86959i	1.56214	−	0.418573i	0.628798	−	0.777569i	$-0.283547\pi$
$47$	10.7095	−	2.86959i	1.56214	−	0.418573i	0.933339	+	0.358996i	$0.116881\pi$
$48$	−0.648598	+	0.648598i	−0.0936171	+	0.0936171i
$49$	4.99095	+	4.90820i	0.712993	+	0.701171i
$50$	4.10303	−	2.85747i	0.580257	−	0.404107i
$51$	4.56148	+	2.63357i	0.638735	+	0.368774i
$52$	2.90039	+	0.777156i	0.402211	+	0.107772i
$53$	−4.26434	−	1.14263i	−0.585752	−	0.156952i	−0.0462411	−	0.998930i	$-0.514724\pi$
$53$	−4.26434	−	1.14263i	−0.585752	−	0.156952i	−0.539511	+	0.841978i	$0.681391\pi$
$54$	2.36590	−	4.09786i	0.321958	−	0.557647i
$55$	1.20116	−	7.31828i	0.161964	−	0.986797i
$56$	1.02269	+	2.44010i	0.136663	+	0.326072i
$57$	2.12358	−	2.12358i	0.281275	−	0.281275i
$58$	0.281907	+	1.05209i	0.0370163	+	0.138147i
$59$	−5.17478	+	2.98766i	−0.673699	+	0.388960i	−0.797477	−	0.603350i	$-0.793832\pi$
$59$	−5.17478	+	2.98766i	−0.673699	+	0.388960i	0.123778	+	0.992310i	$0.460499\pi$
$60$	−1.92646	−	0.703948i	−0.248705	−	0.0908793i
$61$	0.666489	+	0.384798i	0.0853352	+	0.0492683i	0.542060	−	0.840340i	$-0.317644\pi$
$61$	0.666489	+	0.384798i	0.0853352	+	0.0492683i	−0.456725	+	0.889608i	$0.650978\pi$
$62$	1.02756	−	1.02756i	0.130500	−	0.130500i
$63$	−3.49568	−	4.51645i	−0.440415	−	0.569019i
$64$			1.00000i			0.125000i
$65$	1.15751	+	6.61372i	0.143572	+	0.820330i
$66$	−2.74006	+	1.32176i	−0.337278	+	0.162697i
$67$	−3.31614	+	12.3760i	−0.405131	+	1.51197i	0.398683	+	0.917089i	$0.369467\pi$
$67$	−3.31614	+	12.3760i	−0.405131	+	1.51197i	−0.803814	+	0.594880i	$0.797199\pi$
$68$	5.54661	−	1.48621i	0.672626	−	0.180230i
$69$		−	5.27630i		−	0.635192i
$70$	−3.98414	+	4.37340i	−0.476196	+	0.522721i
$71$	−8.83561			−1.04859			−0.524297	−	0.851536i	$-0.675672\pi$
$71$	−8.83561			−1.04859			−0.524297	+	0.851536i	$0.675672\pi$
$72$	−0.558697	−	2.08509i	−0.0658431	−	0.245730i
$73$	1.38004	−	5.15037i	0.161521	−	0.602806i	−0.836937	−	0.547299i	$-0.815656\pi$
$73$	1.38004	−	5.15037i	0.161521	−	0.602806i	0.998458	−	0.0555064i	$-0.0176773\pi$
$74$	−2.86102	−	4.95543i	−0.332587	−	0.576057i
$75$	−0.388110	−	4.56983i	−0.0448151	−	0.527679i
$76$		−	3.27410i		−	0.375566i
$77$	0.534374	+	8.75868i	0.0608976	+	0.998144i
$78$	1.94755	−	1.94755i	0.220516	−	0.220516i
$79$	−4.54539	+	7.87284i	−0.511396	+	0.885763i	0.488517	+	0.872554i	$0.337538\pi$
$79$	−4.54539	+	7.87284i	−0.511396	+	0.885763i	−0.999913	+	0.0132091i	$0.995795\pi$
$80$	−2.02776	+	0.942428i	−0.226711	+	0.105367i
$81$	1.06783	+	1.84953i	0.118647	+	0.205503i
$82$	8.74302	−	2.34269i	0.965505	−	0.258706i
$83$	−9.94541	−	9.94541i	−1.09165	−	1.09165i	−0.995353	−	0.0962978i	$-0.969300\pi$
$83$	−9.94541	−	9.94541i	−1.09165	−	1.09165i	−0.0962978	−	0.995353i	$-0.530700\pi$
$84$	2.40737	+	0.306706i	0.262666	+	0.0334644i
$85$	8.24097	+	9.84658i	0.893859	+	1.06801i
$86$	3.17430	−	5.49805i	0.342293	−	0.592870i
$87$	0.965039	+	0.258581i	0.103463	+	0.0277228i
$88$	−1.09336	+	3.13122i	−0.116552	+	0.333790i
$89$	−1.27069	−	0.733635i	−0.134693	−	0.0777652i	0.431139	−	0.902285i	$-0.358112\pi$
$89$	−1.27069	−	0.733635i	−0.134693	−	0.0777652i	−0.565832	+	0.824520i	$0.691445\pi$
$90$	3.70153	−	3.09795i	0.390176	−	0.326553i
$91$	−3.07084	−	7.32690i	−0.321912	−	0.768068i
$92$	−4.06746	−	4.06746i	−0.424062	−	0.424062i
$93$	−0.344991	−	1.28752i	−0.0357739	−	0.133510i
$94$	−5.54363	−	9.60185i	−0.571782	−	0.990355i
$95$	6.63911	−	3.08561i	0.681159	−	0.316577i
$96$	0.794367	+	0.458628i	0.0810748	+	0.0468085i
$97$	7.76343	+	7.76343i	0.788256	+	0.788256i	0.981208	−	0.192952i	$-0.0618061\pi$
$97$	7.76343	+	7.76343i	0.788256	+	0.788256i	−0.192952	+	0.981208i	$0.561806\pi$
$98$	3.44920	−	6.09122i	0.348422	−	0.615306i
$99$	0.530341	−	7.13973i	0.0533012	−	0.717570i
$100$	−3.82204	−	3.22366i	−0.382204	−	0.322366i
$101$	−13.6616	+	7.88750i	−1.35938	+	0.784836i	−0.989540	−	0.144261i	$-0.953919\pi$
$101$	−13.6616	+	7.88750i	−1.35938	+	0.784836i	−0.369836	+	0.929097i	$0.620586\pi$
$102$	1.36324	−	5.08767i	0.134980	−	0.503754i
$103$	2.64367	+	9.86630i	0.260488	+	0.972155i	0.964954	+	0.262418i	$0.0845198\pi$
$103$	2.64367	+	9.86630i	0.260488	+	0.972155i	−0.704466	+	0.709737i	$0.748814\pi$
$104$		−	3.00270i		−	0.294439i
$105$	1.64685	+	5.17063i	0.160716	+	0.504602i
$106$			4.41477i			0.428800i
$107$	−0.352342	−	1.31496i	−0.0340622	−	0.127122i	0.946801	−	0.321819i	$-0.104294\pi$
$107$	−0.352342	−	1.31496i	−0.0340622	−	0.127122i	−0.980863	+	0.194697i	$0.937628\pi$
$108$	−4.57056	−	1.22468i	−0.439803	−	0.117845i
$109$	−4.22294	−	7.31434i	−0.404484	−	0.700587i	0.589777	−	0.807566i	$-0.299216\pi$
$109$	−4.22294	−	7.31434i	−0.404484	−	0.700587i	−0.994261	+	0.106979i	$0.965882\pi$
$110$	−7.37980	+	0.733879i	−0.703636	+	0.0699726i
$111$	−5.24857			−0.498173
$112$	2.09227	−	1.61939i	0.197701	−	0.153018i
$113$	0.168619	−	0.168619i	0.0158623	−	0.0158623i	−0.699131	−	0.714993i	$-0.746430\pi$
$113$	0.168619	−	0.168619i	0.0158623	−	0.0158623i	0.714993	+	0.699131i	$0.246430\pi$
$114$	−2.60084	−	1.50160i	−0.243591	−	0.140637i
$115$	4.41457	−	12.0812i	0.411661	−	1.12657i
$116$	0.943281	−	0.544603i	0.0875814	−	0.0505651i
$117$	1.67760	+	6.26089i	0.155094	+	0.578820i
$118$	4.22519	+	4.22519i	0.388960	+	0.388960i
$119$	−12.0917	−	9.19823i	−1.10844	−	0.843201i
$120$	−0.181356	+	2.04301i	−0.0165555	+	0.186501i
$121$	−6.84710	+	8.60913i	−0.622464	+	0.782649i
$122$	0.199186	−	0.743372i	0.0180335	−	0.0673018i
$123$	2.14884	−	8.01959i	0.193755	−	0.723102i
$124$	−1.25849	−	0.726592i	−0.113016	−	0.0652499i
$125$	2.93483	−	10.7883i	0.262499	−	0.964932i
$126$	−3.45781	+	4.54551i	−0.308046	+	0.404946i
$127$	11.6880	−	11.6880i	1.03714	−	1.03714i	0.0378585	−	0.999283i	$-0.487946\pi$
$127$	11.6880	−	11.6880i	1.03714	−	1.03714i	0.999283	−	0.0378585i	$-0.0120536\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−2.91164	−	5.04312i	−0.256356	−	0.444022i
$130$	6.08877	−	2.82983i	0.534021	−	0.248192i
$131$	−13.0225	−	7.51855i	−1.13778	−	0.656899i	−0.191902	−	0.981414i	$-0.561466\pi$
$131$	−13.0225	−	7.51855i	−1.13778	−	0.656899i	−0.945880	+	0.324515i	$0.894799\pi$
$132$	1.98590	+	2.30460i	0.172850	+	0.200589i
$133$	−6.85030	+	5.30205i	−0.593996	+	0.459746i
$134$	12.8126			1.10684
$135$	−1.82406	−	10.4222i	−0.156991	−	0.897000i
$136$	−2.87114	−	4.97296i	−0.246198	−	0.426428i
$137$	1.00788	−	3.76147i	0.0861093	−	0.321364i	−0.909413	−	0.415895i	$-0.863468\pi$
$137$	1.00788	−	3.76147i	0.0861093	−	0.321364i	0.995522	+	0.0945308i	$0.0301351\pi$
$138$	−5.09651	+	1.36561i	−0.433844	+	0.116248i
$139$	−1.18051			−0.100129			−0.0500647	−	0.998746i	$-0.515943\pi$
$139$	−1.18051			−0.100129			−0.0500647	+	0.998746i	$0.515943\pi$
$140$	5.25555	+	2.71646i	0.444175	+	0.229583i
$141$	−10.1699			−0.856457
$142$	2.28682	+	8.53454i	0.191906	+	0.716203i
$143$	3.28303	−	9.40213i	0.274541	−	0.786246i
$144$	−1.86944	+	1.07932i	−0.155786	+	0.0899434i
$145$	1.99330	+	1.39950i	0.165535	+	0.116222i
$146$	−5.33206			−0.441284
$147$	−3.25677	−	5.53354i	−0.268614	−	0.456399i
$148$	−4.04609	+	4.04609i	−0.332587	+	0.332587i
$149$	−8.36237	+	14.4841i	−0.685072	+	1.18658i	0.288342	+	0.957528i	$0.406896\pi$
$149$	−8.36237	+	14.4841i	−0.685072	+	1.18658i	−0.973414	+	0.229052i	$0.926437\pi$
$150$	−4.31367	+	1.55764i	−0.352209	+	0.127181i
$151$	−4.16857	+	2.40672i	−0.339233	+	0.195856i	−0.659933	−	0.751325i	$-0.729415\pi$
$151$	−4.16857	+	2.40672i	−0.339233	+	0.195856i	0.320700	+	0.947181i	$0.396082\pi$
$152$	−3.16254	+	0.847401i	−0.256516	+	0.0687333i
$153$	8.76495	+	8.76495i	0.708604	+	0.708604i
$154$	8.32193	−	2.78308i	0.670600	−	0.224267i
$155$	0.287318	−	3.23669i	0.0230779	−	0.259977i
$156$	−2.38525	−	1.37712i	−0.190973	−	0.110258i
$157$	5.43933	−	20.2999i	0.434106	−	1.62011i	−0.309090	−	0.951033i	$-0.600025\pi$
$157$	5.43933	−	20.2999i	0.434106	−	1.62011i	0.743196	−	0.669073i	$-0.233309\pi$
$158$	8.78101	+	2.35286i	0.698580	+	0.187184i
$159$	3.50695	+	2.02474i	0.278119	+	0.160572i
$160$	1.43514	+	1.71475i	0.113458	+	0.135563i
$161$	−1.92340	+	15.0970i	−0.151585	+	1.18981i
$162$	1.51014	−	1.51014i	0.118647	−	0.118647i
$163$	6.01090	+	22.4330i	0.470810	+	1.75709i	0.636870	+	0.770971i	$0.280229\pi$
$163$	6.01090	+	22.4330i	0.470810	+	1.75709i	−0.166060	+	0.986116i	$0.553105\pi$
$164$	−4.52572	−	7.83878i	−0.353399	−	0.612106i
$165$	−2.80161	+	6.19885i	−0.218105	+	0.482580i
$166$	−7.03247	+	12.1806i	−0.545825	+	0.945397i
$167$	−12.0321	+	12.0321i	−0.931069	+	0.931069i	−0.997773	−	0.0667037i	$-0.978752\pi$
$167$	−12.0321	+	12.0321i	−0.931069	+	0.931069i	0.0667037	+	0.997773i	$0.478752\pi$
$168$	−0.326819	−	2.40473i	−0.0252146	−	0.185529i
$169$		−	3.98379i		−	0.306445i
$170$	7.37815	−	10.5086i	0.565878	−	0.805976i
$171$	6.12074	−	3.53381i	0.468064	−	0.270237i
$172$	−6.13227	−	1.64314i	−0.467581	−	0.125288i
$173$	6.44480	−	1.72688i	0.489989	−	0.131292i	−0.00536095	−	0.999986i	$-0.501706\pi$
$173$	6.44480	−	1.72688i	0.489989	−	0.131292i	0.495350	+	0.868693i	$0.335040\pi$
$174$		−	0.999081i		−	0.0757402i
$175$	−0.555374	+	13.2171i	−0.0419823	+	0.999118i
$176$	3.30751	+	0.245683i	0.249313	+	0.0185190i
$177$	5.29415	−	1.41856i	0.397932	−	0.106626i
$178$	−0.379758	+	1.41727i	−0.0284640	+	0.106229i
$179$	3.42495	−	1.97740i	0.255993	−	0.147797i	−0.366512	−	0.930413i	$-0.619448\pi$
$179$	3.42495	−	1.97740i	0.255993	−	0.147797i	0.622505	+	0.782616i	$0.286115\pi$
$180$	−3.95042	−	2.77360i	−0.294447	−	0.206732i
$181$	−15.5809			−1.15812			−0.579058	−	0.815286i	$-0.696580\pi$
$181$	−15.5809			−1.15812			−0.579058	+	0.815286i	$0.696580\pi$
$182$	−6.28245	+	4.86255i	−0.465686	+	0.360436i
$183$	−0.499158	−	0.499158i	−0.0368988	−	0.0368988i
$184$	−2.87613	+	4.98161i	−0.212031	+	0.367249i
$185$	−12.0177	−	4.39137i	−0.883556	−	0.322860i
$186$	−1.15436	+	0.666471i	−0.0846419	+	0.0488681i
$187$	−3.55295	−	18.7106i	−0.259818	−	1.36826i
$188$	−7.83988	+	7.83988i	−0.571782	+	0.571782i
$189$	4.83917	+	11.5461i	0.351998	+	0.839853i
$190$	−4.69880	−	5.61428i	−0.340887	−	0.407303i
$191$	−1.64684	+	2.85240i	−0.119161	+	0.206393i	−0.919435	−	0.393241i	$-0.871354\pi$
$191$	−1.64684	+	2.85240i	−0.119161	+	0.206393i	0.800275	+	0.599634i	$0.204687\pi$
$192$	0.237403	−	0.886001i	0.0171331	−	0.0639417i
$193$	−3.92901	+	14.6633i	−0.282817	+	1.05549i	0.667604	+	0.744517i	$0.267320\pi$
$193$	−3.92901	+	14.6633i	−0.282817	+	1.05549i	−0.950420	+	0.310969i	$0.899347\pi$
$194$	5.48957	−	9.50822i	0.394128	−	0.682650i
$195$	0.544559	−	6.13456i	0.0389967	−	0.439305i
$196$	−6.77639	−	1.75515i	−0.484028	−	0.125368i
$197$	10.8733	−	10.8733i	0.774691	−	0.774691i	−0.204232	−	0.978923i	$-0.565470\pi$
$197$	10.8733	−	10.8733i	0.774691	−	0.774691i	0.978923	+	0.204232i	$0.0654696\pi$
$198$	−7.03371	+	1.33563i	−0.499864	+	0.0949190i
$199$	−6.06205	+	3.49993i	−0.429728	+	0.248103i	−0.699231	−	0.714896i	$-0.746474\pi$
$199$	−6.06205	+	3.49993i	−0.429728	+	0.248103i	0.269503	+	0.963000i	$0.413141\pi$
$200$	−2.12460	+	4.52615i	−0.150232	+	0.320047i
$201$	5.87621	−	10.1779i	0.414476	−	0.717893i
$202$	11.1546	+	11.1546i	0.784836	+	0.784836i
$203$	−2.66699	−	1.09167i	−0.187186	−	0.0766201i
$204$	−5.26714			−0.368774
$205$	11.6300	−	16.5646i	0.812277	−	1.15692i
$206$	8.84588	−	5.10717i	0.616322	−	0.355833i
$207$	3.21377	−	11.9940i	0.223373	−	0.833638i
$208$	−2.90039	+	0.777156i	−0.201106	+	0.0538861i
$209$	−10.8291	−	0.804391i	−0.749067	−	0.0556409i
$210$	4.56821	−	2.92899i	0.315237	−	0.202120i
$211$		−	18.5581i		−	1.27759i	−0.769376	−	0.638797i	$-0.779433\pi$
$211$		−	18.5581i		−	1.27759i	0.769376	−	0.638797i	$-0.220567\pi$
$212$	4.26434	−	1.14263i	0.292876	−	0.0784759i
$213$	7.82836	+	2.09760i	0.536390	+	0.143725i
$214$	−1.17896	+	0.680673i	−0.0805920	+	0.0465298i
$215$	−2.44733	−	13.9833i	−0.166906	−	0.953656i
$216$			4.73180i			0.321958i
$217$	0.517770	+	3.80974i	0.0351485	+	0.258622i
$218$	−5.97213	+	5.97213i	−0.404484	+	0.404484i
$219$	−2.44543	+	4.23561i	−0.165247	+	0.286216i
$220$	2.61890	+	6.93840i	0.176567	+	0.467787i
$221$	8.62117	+	14.9323i	0.579923	+	1.00446i
$222$	1.35843	+	5.06973i	0.0911719	+	0.340258i
$223$	−1.11122	+	1.11122i	−0.0744127	+	0.0744127i	−0.743334	−	0.668921i	$-0.766756\pi$
$223$	−1.11122	+	1.11122i	−0.0744127	+	0.0744127i	0.668921	+	0.743334i	$0.266756\pi$
$224$	−2.10573	−	1.60184i	−0.140695	−	0.107028i
$225$	1.90122	−	10.6244i	0.126748	−	0.708296i
$226$	−0.206515	−	0.119232i	−0.0137372	−	0.00793117i
$227$	−21.6405	−	5.79857i	−1.43633	−	0.384864i	−0.545085	−	0.838381i	$-0.683503\pi$
$227$	−21.6405	−	5.79857i	−1.43633	−	0.384864i	−0.891248	+	0.453516i	$0.850169\pi$
$228$	−0.777284	+	2.90086i	−0.0514769	+	0.192114i
$229$	−0.304389	−	0.175739i	−0.0201146	−	0.0116132i	0.489909	−	0.871774i	$-0.337030\pi$
$229$	−0.304389	−	0.175739i	−0.0201146	−	0.0116132i	−0.510024	+	0.860160i	$0.670363\pi$
$230$	−12.8121	−	1.13732i	−0.844803	−	0.0749923i
$231$	1.60588	−	7.88706i	0.105659	−	0.518931i
$232$	−0.770185	−	0.770185i	−0.0505651	−	0.0505651i
$233$	−21.4702	+	5.75293i	−1.40656	+	0.376887i	−0.880696	−	0.473681i	$-0.842925\pi$
$233$	−21.4702	+	5.75293i	−1.40656	+	0.376887i	−0.525865	+	0.850568i	$0.676258\pi$
$234$	5.61336	−	3.24088i	0.366957	−	0.211863i
$235$	−23.2859	−	8.50891i	−1.51901	−	0.555060i
$236$	2.98766	−	5.17478i	0.194480	−	0.336850i
$237$	5.89626	−	5.89626i	0.383003	−	0.383003i
$238$	−5.75525	+	14.0603i	−0.373058	+	0.911397i
$239$	17.0499			1.10286			0.551432	−	0.834220i	$-0.314082\pi$
$239$	17.0499			1.10286			0.551432	+	0.834220i	$0.314082\pi$
$240$	2.02034	−	0.353594i	0.130412	−	0.0228244i
$241$	−3.71736	+	2.14622i	−0.239456	+	0.138250i	−0.614927	−	0.788584i	$-0.710814\pi$
$241$	−3.71736	+	2.14622i	−0.239456	+	0.138250i	0.375471	+	0.926834i	$0.377481\pi$
$242$	10.0879	+	4.38558i	0.648478	+	0.281916i
$243$	−4.18105	−	15.6039i	−0.268214	−	1.00099i
$244$	−0.769596			−0.0492683
$245$	−2.82723	−	15.3950i	−0.180625	−	0.983552i
$246$	−8.30249			−0.529348
$247$	9.49617	−	2.54449i	0.604227	−	0.161902i
$248$	−0.376112	+	1.40367i	−0.0238831	+	0.0891330i
$249$	6.45057	+	11.1727i	0.408788	+	0.708042i
$250$	−11.1803	−	0.0426140i	−0.707102	−	0.00269515i
$251$	10.4665			0.660642			0.330321	−	0.943869i	$-0.392843\pi$
$251$	10.4665			0.660642			0.330321	+	0.943869i	$0.392843\pi$
$252$	5.28557	+	2.16352i	0.332960	+	0.136289i
$253$	−14.4525	+	12.4539i	−0.908621	+	0.782969i
$254$	−14.3148	−	8.26466i	−0.898191	−	0.518571i
$255$	−4.96390	−	10.6805i	−0.310851	−	0.668840i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.8573	+	3.17717i	−0.739641	+	0.198186i	−0.608919	−	0.793233i	$-0.708396\pi$
$257$	−11.8573	+	3.17717i	−0.739641	+	0.198186i	−0.130723	+	0.991419i	$0.541730\pi$
$258$	−4.11769	+	4.11769i	−0.256356	+	0.256356i
$259$	15.0177	+	1.91330i	0.933154	+	0.118886i
$260$	−4.30929	−	5.14889i	−0.267251	−	0.319321i
$261$	2.03620	+	1.17560i	0.126038	+	0.0727680i
$262$	−3.89189	+	14.5247i	−0.240442	+	0.897341i
$263$	−1.26749	+	4.73034i	−0.0781569	+	0.291685i	−0.993931	−	0.110009i	$-0.964912\pi$
$263$	−1.26749	+	4.73034i	−0.0781569	+	0.291685i	0.915774	+	0.401695i	$0.131579\pi$
$264$	1.71208	−	2.51470i	0.105371	−	0.154769i
$265$	6.33581	+	7.57024i	0.389206	+	0.465036i
$266$	6.89438	+	5.24461i	0.422721	+	0.321567i
$267$	0.951669	+	0.951669i	0.0582412	+	0.0582412i
$268$	−3.31614	−	12.3760i	−0.202565	−	0.755985i
$269$	9.88871	−	5.70925i	0.602926	−	0.348099i	−0.167266	−	0.985912i	$-0.553494\pi$
$269$	9.88871	−	5.70925i	0.602926	−	0.348099i	0.770192	+	0.637813i	$0.220161\pi$
$270$	−9.59497	+	4.45937i	−0.583931	+	0.271389i
$271$	22.6390	+	13.0707i	1.37522	+	0.793985i	0.991580	−	0.129496i	$-0.0413359\pi$
$271$	22.6390	+	13.0707i	1.37522	+	0.793985i	0.383643	+	0.923481i	$0.374669\pi$
$272$	−4.06040	+	4.06040i	−0.246198	+	0.246198i
$273$	0.981339	+	7.22067i	0.0593933	+	0.437015i
$274$	−3.89416			−0.235255
$275$	−11.6013	+	11.8495i	−0.699585	+	0.714549i
$276$	2.63815	+	4.56941i	0.158798	+	0.275046i
$277$	−25.5213	−	6.83842i	−1.53343	−	0.410881i	−0.609293	−	0.792945i	$-0.708547\pi$
$277$	−25.5213	−	6.83842i	−1.53343	−	0.410881i	−0.924136	+	0.382064i	$0.875213\pi$
$278$	0.305538	+	1.14028i	0.0183249	+	0.0683896i
$279$		−	3.13690i		−	0.187802i
$280$	1.26367	−	5.77955i	0.0755185	−	0.345394i
$281$			10.8568i			0.647664i	0.946115	+	0.323832i	$0.104971\pi$
$281$			10.8568i			0.647664i	−0.946115	+	0.323832i	$0.895029\pi$
$282$	2.63215	+	9.82333i	0.156742	+	0.584971i
$283$	7.26190	−	27.1018i	0.431675	−	1.61103i	−0.317224	−	0.948351i	$-0.602751\pi$
$283$	7.26190	−	27.1018i	0.431675	−	1.61103i	0.748899	−	0.662684i	$-0.230583\pi$
$284$	7.65186	−	4.41780i	0.454054	−	0.262148i
$285$	−6.61480	+	1.15770i	−0.391827	+	0.0685765i
$286$	−9.93147	−	0.737712i	−0.587260	−	0.0436218i
$287$	−9.07190	+	22.1631i	−0.535497	+	1.30824i
$288$	1.52639	+	1.52639i	0.0899434	+	0.0899434i
$289$	13.8337	+	7.98688i	0.813745	+	0.469816i
$290$	0.835911	−	2.28760i	0.0490864	−	0.134332i
$291$	−5.03534	−	8.72147i	−0.295177	−	0.511262i
$292$	1.38004	+	5.15037i	0.0807606	+	0.301403i
$293$	8.54554	+	8.54554i	0.499236	+	0.499236i	0.911200	−	0.411964i	$-0.135157\pi$
$293$	8.54554	+	8.54554i	0.499236	+	0.499236i	−0.411964	+	0.911200i	$0.635157\pi$
$294$	−4.50208	+	4.57798i	−0.262566	+	0.266993i
$295$	13.3089	+	1.18142i	0.774874	+	0.0687848i
$296$	4.95543	+	2.86102i	0.288028	+	0.166293i
$297$	−5.17355	+	14.8163i	−0.300200	+	0.859730i
$298$	16.1549	+	4.32868i	0.935826	+	0.250754i
$299$	8.63616	−	14.9583i	0.499442	−	0.865059i
$300$	2.62103	+	3.76353i	0.151325	+	0.217288i
$301$	6.49266	+	15.4912i	0.374231	+	0.892899i
$302$	3.40362	+	3.40362i	0.195856	+	0.195856i
$303$	13.9767	−	3.74504i	0.802939	−	0.215147i
$304$	1.63705	+	2.83546i	0.0938914	+	0.162625i
$305$	−0.725288	−	1.56056i	−0.0415299	−	0.0893574i
$306$	6.19776	−	10.7348i	0.354302	−	0.613669i
$307$	−2.51961	+	2.51961i	−0.143802	+	0.143802i	−0.775343	−	0.631541i	$-0.782423\pi$
$307$	−2.51961	+	2.51961i	−0.143802	+	0.143802i	0.631541	+	0.775343i	$0.282423\pi$
$308$	−4.84212	−	7.31805i	−0.275905	−	0.416985i
$309$		−	9.36917i		−	0.532993i
$310$	−3.20077	+	0.560190i	−0.181791	+	0.0318166i
$311$	−1.30460	−	2.25964i	−0.0739772	−	0.128132i	0.826664	−	0.562696i	$-0.190236\pi$
$311$	−1.30460	−	2.25964i	−0.0739772	−	0.128132i	−0.900641	+	0.434564i	$0.856903\pi$
$312$	−0.712851	+	2.66040i	−0.0403573	+	0.150615i
$313$	−4.46679	−	16.6703i	−0.252478	−	0.942260i	−0.969476	−	0.245185i	$-0.921151\pi$
$313$	−4.46679	−	16.6703i	−0.252478	−	0.942260i	0.716998	−	0.697075i	$-0.245516\pi$
$314$	−21.0160			−1.18600
$315$	0.594163	+	12.7569i	0.0334773	+	0.718768i
$316$		−	9.09077i		−	0.511396i
$317$	22.8268	−	6.11641i	1.28208	−	0.343532i	0.447432	−	0.894318i	$-0.352339\pi$
$317$	22.8268	−	6.11641i	1.28208	−	0.343532i	0.834647	+	0.550786i	$0.185672\pi$
$318$	1.04808	−	3.91149i	0.0587735	−	0.219346i
$319$	−1.56953	−	3.25371i	−0.0878771	−	0.182173i
$320$	1.28488	−	1.83005i	0.0718271	−	0.102303i
$321$			1.24870i			0.0696958i
$322$	15.0804	−	2.04953i	0.840399	−	0.114216i
$323$	13.2942	−	13.2942i	0.739708	−	0.739708i
$324$	−1.84953	−	1.06783i	−0.102752	−	0.0593237i
$325$	6.37954	−	13.5907i	0.353873	−	0.753876i
$326$	20.1129	−	11.6122i	1.11395	−	0.643138i
$327$	2.00508	+	7.48306i	0.110881	+	0.413814i
$328$	−6.40034	+	6.40034i	−0.353399	+	0.353399i
$329$	29.0989	+	3.70728i	1.60428	+	0.204389i
$330$	6.71274	+	1.10177i	0.369524	+	0.0606505i
$331$	−14.1358	+	24.4839i	−0.776972	+	1.34576i	0.156707	+	0.987645i	$0.449912\pi$
$331$	−14.1358	+	24.4839i	−0.776972	+	1.34576i	−0.933679	+	0.358110i	$0.883421\pi$
$332$	13.5857	+	3.64027i	0.745611	+	0.199786i
$333$	−11.9309	−	3.19689i	−0.653812	−	0.175188i
$334$	14.7362	+	8.50795i	0.806330	+	0.465535i
$335$	21.9704	−	18.3878i	1.20037	−	1.00463i
$336$	−2.23820	+	0.938071i	−0.122104	+	0.0511760i
$337$	17.0261	−	17.0261i	0.927468	−	0.927468i	−0.0700738	−	0.997542i	$-0.522323\pi$
$337$	17.0261	−	17.0261i	0.927468	−	0.927468i	0.997542	+	0.0700738i	$0.0223235\pi$
$338$	−3.84804	+	1.03108i	−0.209306	+	0.0560833i
$339$	−0.189427	+	0.109366i	−0.0102883	+	0.00593995i
$340$	−12.0602	−	4.40691i	−0.654055	−	0.238998i
$341$	−2.71240	+	3.98398i	−0.146885	+	0.215744i
$342$	−4.99756	−	4.99756i	−0.270237	−	0.270237i
$343$	7.30138	+	17.0203i	0.394237	+	0.919009i
$344$			6.34860i			0.342293i
$345$	−6.77942	+	9.65588i	−0.364992	+	0.519855i
$346$	−3.33607	−	5.77825i	−0.179348	−	0.310641i
$347$	−0.852126	−	0.228326i	−0.0457445	−	0.0122572i	0.235874	−	0.971784i	$-0.424205\pi$
$347$	−0.852126	−	0.228326i	−0.0457445	−	0.0122572i	−0.281619	+	0.959526i	$0.590871\pi$
$348$	−0.965039	+	0.258581i	−0.0517315	+	0.0138614i
$349$	0.321048			0.0171853			0.00859265	−	0.999963i	$-0.497265\pi$
$349$	0.321048			0.0171853			0.00859265	+	0.999963i	$0.497265\pi$
$350$	12.9105	−	2.88439i	0.690094	−	0.154177i
$351$		−	14.2082i		−	0.758376i
$352$	−0.618736	−	3.25840i	−0.0329787	−	0.173673i
$353$	26.3703	+	7.06591i	1.40355	+	0.376080i	0.879619	−	0.475680i	$-0.157798\pi$
$353$	26.3703	+	7.06591i	1.40355	+	0.376080i	0.523932	+	0.851760i	$0.324465\pi$
$354$	−2.74045	−	4.74660i	−0.145653	−	0.252279i
$355$	16.1696	+	11.3527i	0.858193	+	0.602539i
$356$	1.46727			0.0777652
$357$	8.52956	+	11.0203i	0.451432	+	0.583254i
$358$	−2.79646	−	2.79646i	−0.147797	−	0.147797i
$359$	−8.49168	+	14.7080i	−0.448174	+	0.776260i	−0.998267	−	0.0588435i	$-0.981259\pi$
$359$	−8.49168	+	14.7080i	−0.448174	+	0.776260i	0.550094	+	0.835103i	$0.314592\pi$
$360$	−1.65665	+	4.53367i	−0.0873130	+	0.238945i
$361$	4.14012	+	7.17090i	0.217901	+	0.377416i
$362$	4.03263	+	15.0500i	0.211950	+	0.791008i
$363$	8.11038	−	6.00218i	0.425685	−	0.315033i
$364$	6.32288	+	4.80986i	0.331409	+	0.252105i
$365$	−9.14316	+	7.65225i	−0.478575	+	0.400537i
$366$	−0.352958	+	0.611342i	−0.0184494	+	0.0319553i
$367$	−2.49149	+	9.29836i	−0.130055	+	0.485370i	−0.999969	−	0.00783187i	$-0.997507\pi$
$367$	−2.49149	+	9.29836i	−0.130055	+	0.485370i	0.869915	+	0.493202i	$0.164174\pi$
$368$	5.55626	+	1.48880i	0.289640	+	0.0776088i
$369$	9.76941	−	16.9211i	0.508575	−	0.880878i
$370$	−1.13134	+	12.7447i	−0.0588155	+	0.662568i
$371$	−9.29631	−	7.07177i	−0.482640	−	0.367148i
$372$	0.942533	+	0.942533i	0.0488681	+	0.0488681i
$373$	24.2923	−	6.50910i	1.25781	−	0.337029i	0.432460	−	0.901653i	$-0.357646\pi$
$373$	24.2923	−	6.50910i	1.25781	−	0.337029i	0.825348	+	0.564624i	$0.190979\pi$
$374$	−17.1535	+	8.27456i	−0.886987	+	0.427867i
$375$	−5.16143	+	8.86169i	−0.266535	+	0.457616i
$376$	9.60185	+	5.54363i	0.495178	+	0.285891i
$377$	2.31264	+	2.31264i	0.119107	+	0.119107i
$378$	9.90017	−	7.66262i	0.509210	−	0.394123i
$379$			12.7848i			0.656710i	0.944554	+	0.328355i	$0.106494\pi$
$379$			12.7848i			0.656710i	−0.944554	+	0.328355i	$0.893506\pi$
$380$	−4.20684	+	5.99177i	−0.215806	+	0.307371i
$381$	−13.1303	+	7.58081i	−0.672688	+	0.388377i
$382$	3.18144	+	0.852465i	0.162777	+	0.0436159i
$383$	1.22771	+	4.58187i	0.0627330	+	0.234123i	0.990173	−	0.139850i	$-0.0446620\pi$
$383$	1.22771	+	4.58187i	0.0627330	+	0.234123i	−0.927440	+	0.373973i	$0.877995\pi$
$384$	−0.917256			−0.0468085
$385$	10.2759	−	16.7154i	0.523710	−	0.851896i
$386$	15.1805			0.772669
$387$	−3.54694	−	13.2374i	−0.180301	−	0.672894i
$388$	−10.6050	−	2.84161i	−0.538389	−	0.144261i
$389$	−23.7499	+	13.7120i	−1.20417	+	0.695226i	−0.961479	−	0.274879i	$-0.911362\pi$
$389$	−23.7499	+	13.7120i	−1.20417	+	0.695226i	−0.242688	+	0.970105i	$0.578029\pi$
$390$	−6.06647	+	1.06174i	−0.307188	+	0.0537632i
$391$		−	33.0311i		−	1.67045i
$392$	0.0585139	+	6.99976i	0.00295540	+	0.353541i
$393$	9.75304	+	9.75304i	0.491976	+	0.491976i
$394$	−13.3170	−	7.68859i	−0.670902	−	0.387345i
$395$	18.4339	−	8.56739i	0.927512	−	0.431072i
$396$	3.11058	+	6.44836i	0.156312	+	0.324042i
$397$	−36.0060	+	9.64778i	−1.80709	+	0.484208i	−0.995048	−	0.0993924i	$-0.968310\pi$
$397$	−36.0060	+	9.64778i	−1.80709	+	0.484208i	−0.812041	+	0.583601i	$0.801643\pi$
$398$	4.94965	+	4.94965i	0.248103	+	0.248103i
$399$	7.32810	−	3.07134i	0.366864	−	0.153760i
$400$	4.92182	+	0.880750i	0.246091	+	0.0440375i
$401$	15.6067	−	27.0316i	0.779363	−	1.34990i	−0.152947	−	0.988234i	$-0.548876\pi$
$401$	15.6067	−	27.0316i	0.779363	−	1.34990i	0.932310	−	0.361661i	$-0.117790\pi$
$402$	−11.3520	−	3.04175i	−0.566184	−	0.151709i
$403$	1.12935	−	4.21480i	0.0562570	−	0.209954i
$404$	7.88750	−	13.6616i	0.392418	−	0.679688i
$405$	0.422253	−	4.75676i	0.0209819	−	0.236365i
$406$	−0.364202	+	2.85866i	−0.0180750	+	0.141873i
$407$	12.3884	+	14.3766i	0.614072	+	0.712619i
$408$	1.36324	+	5.08767i	0.0674902	+	0.251877i
$409$	6.84762	+	11.8604i	0.338593	+	0.586460i	0.984168	−	0.177236i	$-0.0567157\pi$
$409$	6.84762	+	11.8604i	0.338593	+	0.586460i	−0.645575	+	0.763697i	$0.723382\pi$
$410$	−19.0102	−	6.94652i	−0.938848	−	0.343064i
$411$	−1.78597	+	3.09339i	−0.0880955	+	0.152586i
$412$	−7.22263	−	7.22263i	−0.355833	−	0.355833i
$413$	−15.6652	+	2.12901i	−0.770834	+	0.104762i
$414$	−12.4171			−0.610266
$415$	5.42190	+	30.9793i	0.266151	+	1.52071i
$416$	1.50135	+	2.60042i	0.0736098	+	0.127496i
$417$	1.04593	+	0.280257i	0.0512195	+	0.0137242i
$418$	2.02581	+	10.6683i	0.0990854	+	0.521806i
$419$		−	4.14500i		−	0.202496i	−0.994861	−	0.101248i	$-0.967716\pi$
$419$		−	4.14500i		−	0.202496i	0.994861	−	0.101248i	$-0.0322836\pi$
$420$	−4.01153	−	3.65448i	−0.195743	−	0.178320i
$421$	10.8019			0.526452			0.263226	−	0.964734i	$-0.415214\pi$
$421$	10.8019			0.526452			0.263226	+	0.964734i	$0.415214\pi$
$422$	−17.9258	+	4.80319i	−0.872612	+	0.233816i
$423$	−23.1179	−	6.19442i	−1.12403	−	0.301183i
$424$	−2.20739	−	3.82330i	−0.107200	−	0.185676i
$425$	−2.42968	−	28.6084i	−0.117857	−	1.38771i
$426$		−	8.10452i		−	0.392665i
$427$	1.24628	+	1.61020i	0.0603115	+	0.0779230i
$428$	0.962617	+	0.962617i	0.0465298	+	0.0465298i
$429$	−5.14087	+	7.55090i	−0.248203	+	0.364561i
$430$	−12.8735	+	5.98309i	−0.620813	+	0.288530i
$431$	22.2356	−	12.8377i	1.07105	−	0.618372i	0.142583	−	0.989783i	$-0.454459\pi$
$431$	22.2356	−	12.8377i	1.07105	−	0.618372i	0.928469	+	0.371411i	$0.121126\pi$
$432$	4.57056	−	1.22468i	0.219901	−	0.0589224i
$433$	−0.631981	+	0.631981i	−0.0303711	+	0.0303711i	−0.722129	−	0.691758i	$-0.756836\pi$
$433$	−0.631981	+	0.631981i	−0.0303711	+	0.0303711i	0.691758	+	0.722129i	$0.256836\pi$
$434$	3.54592	−	1.48616i	0.170210	−	0.0713380i
$435$	−1.43382	−	1.71318i	−0.0687465	−	0.0821406i
$436$	7.31434	+	4.22294i	0.350293	+	0.202242i
$437$	−18.1918	−	4.87447i	−0.870231	−	0.233178i
$438$	4.72421	+	1.26585i	0.225732	+	0.0604846i
$439$	−5.16978	+	8.95432i	−0.246740	+	0.427366i	−0.962619	−	0.270858i	$-0.912693\pi$
$439$	−5.16978	+	8.95432i	−0.246740	+	0.427366i	0.715879	+	0.698224i	$0.246026\pi$
$440$	6.02415	−	4.32546i	0.287190	−	0.206208i
$441$	−4.03275	−	14.5624i	−0.192036	−	0.693448i
$442$	12.1922	−	12.1922i	0.579923	−	0.579923i
$443$	−0.965786	−	3.60436i	−0.0458859	−	0.171248i	0.939180	−	0.343424i	$-0.111587\pi$
$443$	−0.965786	−	3.60436i	−0.0458859	−	0.171248i	−0.985066	+	0.172176i	$0.944920\pi$
$444$	4.54540	−	2.62429i	0.215715	−	0.124543i
$445$	1.38280	+	2.97528i	0.0655508	+	0.141042i
$446$	1.36096	+	0.785750i	0.0644433	+	0.0372064i
$447$	10.8476	−	10.8476i	0.513076	−	0.513076i
$448$	−1.00226	+	2.44857i	−0.0473523	+	0.115684i
$449$			3.23662i			0.152745i	0.997079	+	0.0763727i	$0.0243339\pi$
$449$			3.23662i			0.152745i	−0.997079	+	0.0763727i	$0.975666\pi$
$450$	−10.7545	+	0.913365i	−0.506971	+	0.0430565i
$451$	−27.0388	+	13.0430i	−1.27321	+	0.614172i
$452$	−0.0617189	+	0.230338i	−0.00290301	+	0.0108342i
$453$	4.26472	−	1.14273i	0.200374	−	0.0536901i
$454$			22.4039i			1.05147i
$455$	−3.79441	+	17.3542i	−0.177885	+	0.813580i
$456$	3.00319			0.140637
$457$	3.98241	+	14.8626i	0.186289	+	0.695242i	0.994351	+	0.106143i	$0.0338503\pi$
$457$	3.98241	+	14.8626i	0.186289	+	0.695242i	−0.808061	+	0.589098i	$0.799483\pi$
$458$	−0.0909692	+	0.339502i	−0.00425071	+	0.0158639i
$459$	−13.5856	−	23.5310i	−0.634123	−	1.09833i
$460$	2.21745	+	12.6699i	0.103389	+	0.590736i
$461$		−	7.32747i		−	0.341274i	−0.985334	−	0.170637i	$-0.945417\pi$
$461$		−	7.32747i		−	0.341274i	0.985334	−	0.170637i	$-0.0545826\pi$
$462$	−8.03395	+	0.490158i	−0.373773	+	0.0228042i
$463$	−13.3123	+	13.3123i	−0.618673	+	0.618673i	−0.945191	−	0.326518i	$-0.894125\pi$
$463$	−13.3123	+	13.3123i	−0.618673	+	0.618673i	0.326518	+	0.945191i	$0.394125\pi$
$464$	−0.544603	+	0.943281i	−0.0252826	+	0.0437907i
$465$	−1.02297	+	2.79950i	−0.0474389	+	0.129824i
$466$	11.1138	+	19.2497i	0.514837	+	0.891724i
$467$	0.285068	−	0.0763838i	0.0131914	−	0.00353462i	−0.252217	−	0.967671i	$-0.581160\pi$
$467$	0.285068	−	0.0763838i	0.0131914	−	0.00353462i	0.265409	+	0.964136i	$0.414493\pi$
$468$	−4.58329	−	4.58329i	−0.211863	−	0.211863i
$469$	−20.5238	+	26.9798i	−0.947699	+	1.24581i
$470$	−2.19213	+	24.6948i	−0.101115	+	1.13908i
$471$	−9.63852	+	16.6944i	−0.444119	+	0.769237i
$472$	−5.77172	−	1.54653i	−0.265665	−	0.0711847i
$473$	−6.94129	+	19.8789i	−0.319161	+	0.914032i
$474$	−7.22141	−	4.16928i	−0.331690	−	0.191502i
$475$	−16.1145	−	2.88367i	−0.739386	−	0.132312i
$476$	15.0708	+	1.92006i	0.690770	+	0.0880060i
$477$	6.73866	+	6.73866i	0.308542	+	0.308542i
$478$	−4.41283	−	16.4689i	−0.201838	−	0.753270i
$479$	18.3212	+	31.7332i	0.837116	+	1.44993i	0.892296	+	0.451452i	$0.149094\pi$
$479$	18.3212	+	31.7332i	0.837116	+	1.44993i	−0.0551791	+	0.998476i	$0.517573\pi$
$480$	−0.864448	−	1.85998i	−0.0394565	−	0.0848961i
$481$	−14.8797	−	8.59078i	−0.678455	−	0.391706i
$482$	3.03521	+	3.03521i	0.138250	+	0.138250i
$483$	5.28822	−	12.9194i	0.240622	−	0.587852i
$484$	1.62520	−	10.8793i	0.0738726	−	0.494513i
$485$	−4.23236	−	24.1825i	−0.192182	−	1.09807i
$486$	−13.9901	+	8.07716i	−0.634602	+	0.366388i
$487$	8.53370	−	31.8482i	0.386699	−	1.44318i	−0.448773	−	0.893646i	$-0.648139\pi$
$487$	8.53370	−	31.8482i	0.386699	−	1.44318i	0.835471	−	0.549534i	$-0.185195\pi$
$488$	0.199186	+	0.743372i	0.00901673	+	0.0336509i
$489$		−	21.3027i		−	0.963340i
$490$	−14.1387	+	6.71542i	−0.638722	+	0.303372i
$491$		−	22.1672i		−	1.00039i	−0.865913	−	0.500195i	$-0.833262\pi$
$491$		−	22.1672i		−	1.00039i	0.865913	−	0.500195i	$-0.166738\pi$
$492$	2.14884	+	8.01959i	0.0968773	+	0.361551i
$493$	6.04141	+	1.61879i	0.272091	+	0.0729067i
$494$	−4.91558	−	8.51403i	−0.221162	−	0.383064i
$495$	−10.1443	+	12.3846i	−0.455951	+	0.556648i
$496$	1.45318			0.0652499
$497$	−21.6346	−	8.85557i	−0.970443	−	0.397227i
$498$	9.12249	−	9.12249i	0.408788	−	0.408788i
$499$	24.7674	+	14.2994i	1.10874	+	0.640131i	0.938503	−	0.345272i	$-0.112213\pi$
$499$	24.7674	+	14.2994i	1.10874	+	0.640131i	0.170237	+	0.985403i	$0.445547\pi$
$500$	2.85250	+	10.8103i	0.127568	+	0.483453i
$501$	13.5169	−	7.80397i	0.603890	−	0.348656i
$502$	−2.70894	−	10.1099i	−0.120906	−	0.451227i
$503$	11.3614	+	11.3614i	0.506581	+	0.506581i	0.913475	−	0.406894i	$-0.133388\pi$
$503$	11.3614	+	11.3614i	0.506581	+	0.506581i	−0.406894	+	0.913475i	$0.633388\pi$
$504$	0.721792	−	5.66543i	0.0321512	−	0.252358i
$505$	35.1358	+	3.11897i	1.56352	+	0.138792i
$506$	15.7701	+	10.7367i	0.701067	+	0.477306i
$507$	−0.945764	+	3.52964i	−0.0420029	+	0.156757i
$508$	−4.27810	+	15.9661i	−0.189810	+	0.708381i
$509$	−4.52235	−	2.61098i	−0.200450	−	0.115730i	0.396415	−	0.918071i	$-0.370254\pi$
$509$	−4.52235	−	2.61098i	−0.200450	−	0.115730i	−0.596865	+	0.802341i	$0.703587\pi$
$510$	−9.03184	+	7.55908i	−0.399937	+	0.334722i
$511$	8.54113	−	11.2279i	0.377837	−	0.496692i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−14.9645	+	4.00973i	−0.660699	+	0.177034i
$514$	6.13782	+	10.6310i	0.270727	+	0.468914i
$515$	7.83899	−	21.4526i	0.345427	−	0.945315i
$516$	5.04312	+	2.91164i	0.222011	+	0.128178i
$517$	24.0044	+	27.8566i	1.05571	+	1.22513i
$518$	−2.03876	−	15.0012i	−0.0895781	−	0.659114i
$519$	−6.12007			−0.268641
$520$	−3.85812	+	5.49509i	−0.169190	+	0.240976i
$521$	17.3616	+	30.0711i	0.760625	+	1.31744i	0.942529	+	0.334125i	$0.108441\pi$
$521$	17.3616	+	30.0711i	0.760625	+	1.31744i	−0.181904	+	0.983316i	$0.558226\pi$
$522$	0.608537	−	2.27109i	0.0266349	−	0.0994029i
$523$	22.2655	−	5.96604i	0.973604	−	0.260877i	0.263255	−	0.964726i	$-0.415204\pi$
$523$	22.2655	−	5.96604i	0.973604	−	0.260877i	0.710349	+	0.703850i	$0.248537\pi$
$524$	15.0371			0.656899
$525$	3.62984	−	11.5785i	0.158419	−	0.505328i
$526$	4.89721			0.213529
$527$	−2.15974	−	8.06025i	−0.0940797	−	0.351110i
$528$	−2.87214	−	1.00289i	−0.124994	−	0.0436452i
$529$	−8.73692	+	5.04427i	−0.379866	+	0.219316i
$530$	5.67246	−	8.07925i	0.246396	−	0.350940i
$531$	12.8986			0.559751
$532$	3.28150	−	8.01686i	0.142271	−	0.347575i
$533$	19.2183	−	19.2183i	0.832437	−	0.832437i
$534$	0.672932	−	1.16555i	0.0291206	−	0.0504384i
$535$	−1.04476	+	2.85916i	−0.0451691	+	0.123612i
$536$	−11.0960	+	6.40629i	−0.479275	+	0.276710i
$537$	−3.50395	+	0.938881i	−0.151207	+	0.0405157i
$538$	−8.07410	−	8.07410i	−0.348099	−	0.348099i
$539$	−7.47002	+	21.9818i	−0.321757	+	0.946822i
$540$	6.79079	+	8.11386i	0.292229	+	0.349165i
$541$	4.95657	+	2.86168i	0.213100	+	0.123033i	0.602751	−	0.797929i	$-0.294071\pi$
$541$	4.95657	+	2.86168i	0.213100	+	0.123033i	−0.389651	+	0.920962i	$0.627405\pi$
$542$	6.76587	−	25.2506i	0.290619	−	1.08460i
$543$	13.8047	+	3.69895i	0.592415	+	0.158737i
$544$	4.97296	+	2.87114i	0.213214	+	0.123099i
$545$	−1.66989	+	18.8116i	−0.0715300	+	0.805799i
$546$	6.72064	−	2.81675i	0.287617	−	0.120546i
$547$	−17.6389	+	17.6389i	−0.754184	+	0.754184i	−0.975257	−	0.221073i	$-0.929044\pi$
$547$	−17.6389	+	17.6389i	−0.754184	+	0.754184i	0.221073	+	0.975257i	$0.429044\pi$
$548$	1.00788	+	3.76147i	0.0430546	+	0.160682i
$549$	−0.830640	−	1.43871i	−0.0354509	−	0.0614027i
$550$	14.4483	+	8.13914i	0.616079	+	0.347054i
$551$	1.78309	−	3.08840i	0.0759621	−	0.131570i
$552$	3.73091	−	3.73091i	0.158798	−	0.158798i
$553$	−19.0203	+	14.7215i	−0.808826	+	0.626022i
$554$			26.4216i			1.12255i
$555$	9.60514	+	6.74380i	0.407716	+	0.286258i
$556$	1.02235	−	0.590254i	0.0433573	−	0.0250323i
$557$	1.24225	+	0.332861i	0.0526360	+	0.0141038i	0.285041	−	0.958515i	$-0.407993\pi$
$557$	1.24225	+	0.332861i	0.0526360	+	0.0141038i	−0.232405	+	0.972619i	$0.574659\pi$
$558$	−3.03002	+	0.811890i	−0.128271	+	0.0343701i
$559$		−	19.0629i		−	0.806276i
$560$	−5.90967	+	0.275249i	−0.249729	+	0.0116314i
$561$	−1.29405	+	17.4211i	−0.0546346	+	0.735521i
$562$	10.4869	−	2.80995i	0.442362	−	0.118531i
$563$	−0.377258	+	1.40795i	−0.0158995	+	0.0593379i	−0.973420	−	0.229028i	$-0.926445\pi$
$563$	−0.377258	+	1.40795i	−0.0158995	+	0.0593379i	0.957520	+	0.288366i	$0.0931119\pi$
$564$	8.80736	−	5.08493i	0.370857	−	0.214114i
$565$	−0.525237	+	0.0919255i	−0.0220969	+	0.00386733i
$566$	−28.0578			−1.17936
$567$	0.760934	+	5.59894i	0.0319562	+	0.235133i
$568$	−6.24772	−	6.24772i	−0.262148	−	0.262148i
$569$	14.6168	−	25.3171i	0.612769	−	1.06135i	−0.378003	−	0.925804i	$-0.623389\pi$
$569$	14.6168	−	25.3171i	0.612769	−	1.06135i	0.990772	−	0.135542i	$-0.0432776\pi$
$570$	2.83029	+	6.08977i	0.118548	+	0.255072i
$571$	−22.8239	+	13.1774i	−0.955150	+	0.551456i	−0.894677	−	0.446714i	$-0.852594\pi$
$571$	−22.8239	+	13.1774i	−0.955150	+	0.551456i	−0.0604732	+	0.998170i	$0.519261\pi$
$572$	1.85788	+	9.78400i	0.0776818	+	0.409090i
$573$	2.13627	−	2.13627i	0.0892439	−	0.0892439i
$574$	23.7558	+	3.02656i	0.991550	+	0.126326i
$575$	−23.6017	+	16.4369i	−0.984260	+	0.685466i
$576$	1.07932	−	1.86944i	0.0449717	−	0.0778932i
$577$	2.05355	−	7.66397i	0.0854906	−	0.319055i	−0.909916	−	0.414792i	$-0.863854\pi$
$577$	2.05355	−	7.66397i	0.0854906	−	0.319055i	0.995407	+	0.0957373i	$0.0305209\pi$
$578$	4.13431	−	15.4295i	0.171965	−	0.641781i
$579$	6.96222	−	12.0589i	0.289340	−	0.501152i
$580$	−2.42600	−	0.215354i	−0.100734	−	0.00894208i
$581$	−14.3841	−	34.3199i	−0.596753	−	1.42383i
$582$	−7.12105	+	7.12105i	−0.295177	+	0.295177i
$583$	−2.73158	−	14.3851i	−0.113130	−	0.595769i
$584$	4.61770	−	2.66603i	0.191082	−	0.110321i
$585$	4.97442	−	13.6133i	0.205667	−	0.562839i
$586$	6.04261	−	10.4661i	0.249618	−	0.432351i
$587$	−26.2081	−	26.2081i	−1.08173	−	1.08173i	−0.996349	−	0.0853768i	$-0.972791\pi$
$587$	−26.2081	−	26.2081i	−1.08173	−	1.08173i	−0.0853768	−	0.996349i	$-0.527209\pi$
$588$	5.58721	+	3.16380i	0.230413	+	0.130473i
$589$	−4.75788			−0.196045
$590$	−2.30343	−	13.1612i	−0.0948309	−	0.541837i
$591$	−12.2151	+	7.05240i	−0.502463	+	0.290097i
$592$	1.48097	−	5.52706i	0.0608676	−	0.227161i
$593$	−24.8337	+	6.65417i	−1.01980	+	0.273254i	−0.729718	−	0.683748i	$-0.760349\pi$
$593$	−24.8337	+	6.65417i	−1.01980	+	0.273254i	−0.290080	+	0.957002i	$0.593682\pi$
$594$	15.6505	+	1.16252i	0.642147	+	0.0476988i
$595$	10.3097	+	32.3696i	0.422657	+	1.32702i
$596$		−	16.7247i		−	0.685072i
$597$	6.20188	−	1.66179i	0.253826	−	0.0680125i
$598$	−16.6838	−	4.47041i	−0.682251	−	0.182809i
$599$	0.700534	−	0.404454i	0.0286231	−	0.0165255i	−0.485620	−	0.874170i	$-0.661406\pi$
$599$	0.700534	−	0.404454i	0.0286231	−	0.0165255i	0.514243	+	0.857644i	$0.328073\pi$
$600$	2.95692	−	3.50579i	0.120716	−	0.143123i
$601$		−	12.1543i		−	0.495782i	−0.968788	−	0.247891i	$-0.920262\pi$
$601$		−	12.1543i		−	0.495782i	0.968788	−	0.247891i	$-0.0797375\pi$
$602$	13.2829	−	10.2809i	0.541373	−	0.419016i
$603$	19.5570	−	19.5570i	0.796422	−	0.796422i
$604$	2.40672	−	4.16857i	0.0979282	−	0.169617i
$605$	23.5923	−	6.95742i	0.959161	−	0.282859i
$606$	−7.23486	−	12.5311i	−0.293896	−	0.509043i
$607$	9.78442	+	36.5159i	0.397137	+	1.48214i	0.818109	+	0.575063i	$0.195022\pi$
$607$	9.78442	+	36.5159i	0.397137	+	1.48214i	−0.420972	+	0.907074i	$0.638311\pi$
$608$	2.31514	−	2.31514i	0.0938914	−	0.0938914i
$609$	2.10379	+	1.60037i	0.0852501	+	0.0648504i
$610$	−1.31967	+	1.10448i	−0.0534317	+	0.0447190i
$611$	−28.8315	−	16.6459i	−1.16640	−	0.673420i
$612$	−11.9731	−	3.20820i	−0.483986	−	0.129684i
$613$	1.95910	−	7.31144i	0.0791271	−	0.295306i	−0.915010	−	0.403431i	$-0.867818\pi$
$613$	1.95910	−	7.31144i	0.0791271	−	0.295306i	0.994137	+	0.108124i	$0.0344844\pi$
$614$	3.08588	+	1.78163i	0.124536	+	0.0719009i
$615$	−14.2367	+	11.9152i	−0.574080	+	0.480469i
$616$	−5.81546	+	6.57118i	−0.234312	+	0.264760i
$617$	−33.2565	−	33.2565i	−1.33885	−	1.33885i	−0.897170	−	0.441685i	$-0.854381\pi$
$617$	−33.2565	−	33.2565i	−1.33885	−	1.33885i	−0.441685	−	0.897170i	$-0.645619\pi$
$618$	−9.04992	+	2.42492i	−0.364041	+	0.0975446i
$619$	−0.784667	+	0.453028i	−0.0315384	+	0.0182087i	−0.515686	−	0.856777i	$-0.672463\pi$
$619$	−0.784667	+	0.453028i	−0.0315384	+	0.0182087i	0.484148	+	0.874986i	$0.339130\pi$
$620$	1.36952	+	2.94672i	0.0550013	+	0.118343i
$621$	−13.6093	+	23.5719i	−0.546121	+	0.945909i
$622$	−1.84499	+	1.84499i	−0.0739772	+	0.0739772i
$623$	−2.37608	−	3.06992i	−0.0951958	−	0.122994i
$624$	2.75425			0.110258
$625$	−19.2325	+	15.9722i	−0.769301	+	0.638886i
$626$	−14.9462	+	8.62918i	−0.597369	+	0.344891i
$627$	9.40367	+	3.28357i	0.375546	+	0.131133i
$628$	5.43933	+	20.2999i	0.217053	+	0.810053i
$629$	−32.8575			−1.31012
$630$	12.1684	−	3.87564i	0.484801	−	0.154409i
$631$	15.1409			0.602750			0.301375	−	0.953506i	$-0.402554\pi$
$631$	15.1409			0.602750			0.301375	+	0.953506i	$0.402554\pi$
$632$	−8.78101	+	2.35286i	−0.349290	+	0.0935919i
$633$	−4.40576	+	16.4425i	−0.175113	+	0.653531i
$634$	−11.8160	−	20.4659i	−0.469273	−	0.812805i
$635$	−36.4073	+	6.37190i	−1.44478	+	0.252861i
$636$	−4.04948			−0.160572
$637$	−0.175700	−	21.0182i	−0.00696148	−	0.832770i
$638$	−2.73662	+	2.35818i	−0.108344	+	0.0933611i
$639$	16.5176	+	9.53645i	0.653427	+	0.377256i
$640$	−2.10024	−	0.767449i	−0.0830194	−	0.0303361i
$641$	−22.3020	−	38.6281i	−0.880875	−	1.52572i	−0.850370	−	0.526185i	$-0.823622\pi$
$641$	−22.3020	−	38.6281i	−0.880875	−	1.52572i	−0.0305051	−	0.999535i	$-0.509712\pi$
$642$	1.20615	−	0.323188i	0.0476031	−	0.0127552i
$643$	−24.5566	+	24.5566i	−0.968416	+	0.968416i	−0.999516	−	0.0311001i	$-0.990099\pi$
$643$	−24.5566	+	24.5566i	−0.968416	+	0.968416i	0.0311001	+	0.999516i	$0.490099\pi$
$644$	−5.88280	−	14.0361i	−0.231815	−	0.553100i
$645$	−1.15136	+	12.9703i	−0.0453347	+	0.510704i
$646$	−16.2820	−	9.40041i	−0.640606	−	0.369854i
$647$	−1.10228	+	4.11378i	−0.0433353	+	0.161730i	−0.984203	−	0.177046i	$-0.943346\pi$
$647$	−1.10228	+	4.11378i	−0.0433353	+	0.161730i	0.940867	+	0.338775i	$0.110013\pi$
$648$	−0.552748	+	2.06288i	−0.0217140	+	0.0810377i
$649$	−16.3816	−	11.1531i	−0.643036	−	0.437797i
$650$	−14.7787	−	2.64463i	−0.579670	−	0.103731i
$651$	0.445700	−	3.49836i	0.0174684	−	0.137111i
$652$	−16.4221	−	16.4221i	−0.643138	−	0.643138i
$653$	0.231283	+	0.863158i	0.00905079	+	0.0337780i	0.970304	−	0.241890i	$-0.0777675\pi$
$653$	0.231283	+	0.863158i	0.00905079	+	0.0337780i	−0.961253	+	0.275668i	$0.911101\pi$
$654$	6.70912	−	3.87351i	0.262348	−	0.151466i
$655$	14.1714	+	30.4917i	0.553722	+	1.19141i
$656$	7.83878	+	4.52572i	0.306053	+	0.176700i
$657$	−8.13880	+	8.13880i	−0.317525	+	0.317525i
$658$	−3.95040	−	29.0669i	−0.154002	−	1.13315i
$659$	8.11199			0.315998			0.157999	−	0.987439i	$-0.449496\pi$
$659$	8.11199			0.315998			0.157999	+	0.987439i	$0.449496\pi$
$660$	−0.673155	−	6.76917i	−0.0262025	−	0.263489i
$661$	9.93281	+	17.2041i	0.386342	+	0.669163i	0.991954	−	0.126596i	$-0.0404053\pi$
$661$	9.93281	+	17.2041i	0.386342	+	0.669163i	−0.605613	+	0.795759i	$0.707072\pi$
$662$	27.3082	+	7.31721i	1.06136	+	0.284391i
$663$	−4.09339	−	15.2767i	−0.158974	−	0.593300i
$664$		−	14.0649i		−	0.545825i
$665$	19.3489	−	0.901193i	0.750318	−	0.0349468i
$666$			12.3518i			0.478623i
$667$	−1.62161	−	6.05191i	−0.0627888	−	0.234331i
$668$	4.40404	−	16.4361i	0.170397	−	0.635932i
$669$	1.24835	−	0.720734i	0.0482639	−	0.0278652i
$670$	−23.4476	−	16.4627i	−0.905861	−	0.636008i
$671$	−0.189076	+	2.54545i	−0.00729921	+	0.0982659i
$672$	1.48540	+	1.91914i	0.0573004	+	0.0740326i
$673$	−14.7056	−	14.7056i	−0.566858	−	0.566858i	0.364389	−	0.931247i	$-0.381278\pi$
$673$	−14.7056	−	14.7056i	−0.566858	−	0.566858i	−0.931247	+	0.364389i	$0.881278\pi$
$674$	−20.8526	−	12.0392i	−0.803211	−	0.463734i
$675$	−10.0532	+	21.4168i	−0.386947	+	0.824335i
$676$	1.99189	+	3.45006i	0.0766113	+	0.132695i
$677$	2.43383	+	9.08316i	0.0935395	+	0.349094i	0.996794	−	0.0800111i	$-0.0254956\pi$
$677$	2.43383	+	9.08316i	0.0935395	+	0.349094i	−0.903254	+	0.429105i	$0.858829\pi$
$678$	0.154667	+	0.154667i	0.00593995	+	0.00593995i
$679$	11.2283	+	26.7902i	0.430902	+	1.02811i
$680$	−1.13534	+	12.7898i	−0.0435383	+	0.490468i
$681$	17.7970	+	10.2751i	0.681981	+	0.393742i
$682$	4.55025	+	1.58885i	0.174238	+	0.0608403i
$683$	−0.598423	−	0.160347i	−0.0228980	−	0.00613551i	0.247352	−	0.968926i	$-0.420440\pi$
$683$	−0.598423	−	0.160347i	−0.0228980	−	0.00613551i	−0.270250	+	0.962790i	$0.587106\pi$
$684$	−3.53381	+	6.12074i	−0.135119	+	0.234032i
$685$	−6.67752	+	5.58866i	−0.255135	+	0.213532i
$686$	14.5506	−	11.4578i	0.555544	−	0.437459i
$687$	0.227968	+	0.227968i	0.00869752	+	0.00869752i
$688$	6.13227	−	1.64314i	0.233791	−	0.0626440i
$689$	6.62812	+	11.4802i	0.252511	+	0.437362i
$690$	11.0815	+	4.04929i	0.421866	+	0.154154i
$691$	18.6737	−	32.3437i	0.710379	−	1.23041i	−0.254335	−	0.967116i	$-0.581857\pi$
$691$	18.6737	−	32.3437i	0.710379	−	1.23041i	0.964715	−	0.263297i	$-0.0848100\pi$
$692$	−4.71792	+	4.71792i	−0.179348	+	0.179348i
$693$	8.45444	−	16.9506i	0.321158	−	0.643899i
$694$			0.882186i			0.0334873i
$695$	2.16039	+	1.51681i	0.0819482	+	0.0575360i
$696$	0.499541	+	0.865230i	0.0189350	+	0.0327965i
$697$	13.4524	−	50.2049i	0.509544	−	1.90164i
$698$	−0.0830933	−	0.310108i	−0.00314513	−	0.0117378i
$699$	20.3884			0.771161
$700$	−6.12758	−	11.7240i	−0.231601	−	0.443127i
$701$			13.7055i			0.517649i	0.965924	+	0.258825i	$0.0833352\pi$
$701$			13.7055i			0.517649i	−0.965924	+	0.258825i	$0.916665\pi$
$702$	−13.7240	+	3.67734i	−0.517980	+	0.138792i
$703$	−4.84886	+	18.0962i	−0.182878	+	0.682510i
$704$	−2.98723	+	1.44099i	−0.112586	+	0.0543093i
$705$	18.6113	+	13.0671i	0.700944	+	0.492134i
$706$		−	27.3006i		−	1.02747i
$707$	−41.3565	+	5.62064i	−1.55537	+	0.211386i
$708$	−3.87558	+	3.87558i	−0.145653	+	0.145653i
$709$	32.7487	+	18.9075i	1.22990	+	0.710086i	0.967010	−	0.254739i	$-0.0819895\pi$
$709$	32.7487	+	18.9075i	1.22990	+	0.710086i	0.262895	+	0.964825i	$0.415323\pi$
$710$	6.78088	−	18.5569i	0.254482	−	0.696429i
$711$	16.9946	−	9.81185i	0.637348	−	0.367973i
$712$	−0.379758	−	1.41727i	−0.0142320	−	0.0531146i
$713$	−5.91078	+	5.91078i	−0.221360	+	0.221360i
$714$	8.43714	−	11.0912i	0.315752	−	0.415077i
$715$	−18.0887	+	12.9881i	−0.676480	+	0.485726i
$716$	−1.97740	+	3.42495i	−0.0738987	+	0.127996i
$717$	−15.1062	−	4.04769i	−0.564151	−	0.151164i
$718$	16.4047	+	4.39562i	0.612217	+	0.164043i
$719$	−16.0392	−	9.26024i	−0.598161	−	0.345349i	0.170157	−	0.985417i	$-0.445573\pi$
$719$	−16.0392	−	9.26024i	−0.598161	−	0.345349i	−0.768318	+	0.640068i	$0.778906\pi$
$720$	4.80796	+	0.426798i	0.179182	+	0.0159058i
$721$	−3.41540	+	26.8079i	−0.127196	+	0.998379i
$722$	5.85501	−	5.85501i	0.217901	−	0.217901i
$723$	3.80310	−	1.01904i	0.141439	−	0.0378985i
$724$	13.4934	−	7.79043i	0.501479	−	0.289529i
$725$	−1.84964	−	5.12231i	−0.0686940	−	0.190238i
$726$	−7.89678	−	6.28055i	−0.293077	−	0.233093i
$727$	−24.5333	−	24.5333i	−0.909888	−	0.909888i	0.0863743	−	0.996263i	$-0.472472\pi$
$727$	−24.5333	−	24.5333i	−0.909888	−	0.909888i	−0.996263	+	0.0863743i	$0.972472\pi$
$728$	3.00949	−	7.35231i	0.111539	−	0.272495i
$729$			8.41070i			0.311507i
$730$	9.75793	+	6.85107i	0.361157	+	0.253569i
$731$	−18.2277	−	31.5713i	−0.674176	−	1.16771i
$732$	0.681863	+	0.182705i	0.0252024	+	0.00675296i
$733$	−28.6944	+	7.68865i	−1.05985	+	0.283987i	−0.746318	−	0.665590i	$-0.768180\pi$
$733$	−28.6944	+	7.68865i	−1.05985	+	0.283987i	−0.313535	+	0.949577i	$0.601513\pi$
$734$	9.62637			0.355316
$735$	−1.14991	+	14.3112i	−0.0424149	+	0.527877i
$736$		−	5.75226i		−	0.212031i
$737$	−41.7485	+	7.92760i	−1.53783	+	0.292017i
$738$	−18.8730	−	5.05702i	−0.694726	−	0.186151i
$739$	−25.2623	−	43.7556i	−0.929289	−	1.60958i	−0.784514	−	0.620111i	$-0.787088\pi$
$739$	−25.2623	−	43.7556i	−0.929289	−	1.60958i	−0.144775	−	0.989465i	$-0.546246\pi$
$740$	12.6033	−	2.20579i	0.463306	−	0.0810866i
$741$	−9.01769			−0.331273
$742$	−4.42475	+	10.8099i	−0.162438	+	0.396842i
$743$	21.7343	+	21.7343i	0.797352	+	0.797352i	0.982677	−	0.185325i	$-0.0593338\pi$
$743$	21.7343	+	21.7343i	0.797352	+	0.797352i	−0.185325	+	0.982677i	$0.559334\pi$
$744$	0.666471	−	1.15436i	0.0244340	−	0.0423210i
$745$	33.9138	−	15.7619i	1.24251	−	0.577470i
$746$	−12.5746	−	21.7799i	−0.460390	−	0.797418i
$747$	7.85804	+	29.3266i	0.287511	+	1.07300i
$748$	12.4323	+	14.4274i	0.454569	+	0.527518i
$749$	0.455198	−	3.57290i	0.0166326	−	0.130551i
$750$	9.89561	+	2.69199i	0.361337	+	0.0982975i
$751$	8.60341	−	14.9015i	0.313943	−	0.543765i	−0.665269	−	0.746604i	$-0.731683\pi$
$751$	8.60341	−	14.9015i	0.313943	−	0.543765i	0.979212	+	0.202838i	$0.0650166\pi$
$752$	2.86959	−	10.7095i	0.104643	−	0.390534i
$753$	−9.27337	−	2.48479i	−0.337940	−	0.0905509i
$754$	1.63528	−	2.83239i	0.0595534	−	0.103150i
$755$	10.7210	+	0.951696i	0.390179	+	0.0346358i
$756$	−9.96388	−	7.57960i	−0.362383	−	0.275667i
$757$	−1.35037	−	1.35037i	−0.0490799	−	0.0490799i	0.682141	−	0.731221i	$-0.261049\pi$
$757$	−1.35037	−	1.35037i	−0.0490799	−	0.0490799i	−0.731221	+	0.682141i	$0.761049\pi$
$758$	12.3491	−	3.30894i	0.448541	−	0.120186i
$759$	15.7615	−	7.60309i	0.572107	−	0.275975i
$760$	6.87642	+	2.51271i	0.249434	+	0.0911455i
$761$	43.5223	+	25.1276i	1.57768	+	0.910876i	0.995182	+	0.0980462i	$0.0312593\pi$
$761$	43.5223	+	25.1276i	1.57768	+	0.910876i	0.582501	+	0.812830i	$0.302074\pi$
$762$	10.7209	+	10.7209i	0.388377	+	0.388377i
$763$	−3.00927	−	22.1421i	−0.108943	−	0.801599i
$764$		−	3.29367i		−	0.119161i
$765$	−4.77836	−	27.3022i	−0.172762	−	0.987114i
$766$	4.10799	−	2.37175i	0.148428	−	0.0856948i
$767$	17.3307	+	4.64376i	0.625777	+	0.167676i
$768$	0.237403	+	0.886001i	0.00856656	+	0.0319708i
$769$	−22.1044			−0.797106			−0.398553	−	0.917145i	$-0.630488\pi$
$769$	−22.1044			−0.797106			−0.398553	+	0.917145i	$0.630488\pi$
$770$	−18.8055	−	5.59953i	−0.677702	−	0.201793i
$771$	11.2599			0.405515
$772$	−3.92901	−	14.6633i	−0.141408	−	0.527743i
$773$	27.2093	+	7.29071i	0.978651	+	0.262229i	0.712476	−	0.701696i	$-0.247574\pi$
$773$	27.2093	+	7.29071i	0.978651	+	0.262229i	0.266174	+	0.963925i	$0.414240\pi$
$774$	−11.8683	+	6.85217i	−0.426597	+	0.246296i
$775$	−4.68457	+	5.55413i	−0.168275	+	0.199510i
$776$			10.9791i			0.394128i
$777$	−12.8515	−	5.26043i	−0.461044	−	0.188717i
$778$	19.3917	+	19.3917i	0.695226	+	0.695226i
$779$	−25.6650	−	14.8177i	−0.919543	−	0.530899i
$780$	2.59568	+	5.58496i	0.0929402	+	0.199974i
$781$	−12.7320	−	26.3940i	−0.455587	−	0.944452i
$782$	−31.9056	+	8.54908i	−1.14094	+	0.305714i
$783$	−3.64436	−	3.64436i	−0.130239	−	0.130239i
$784$	6.74610	−	1.86819i	0.240932	−	0.0667211i
$785$	−36.0372	+	30.1608i	−1.28622	+	1.07649i
$786$	6.89644	−	11.9450i	0.245988	−	0.426063i
$787$	−11.9012	−	3.18893i	−0.424234	−	0.113673i	0.0403845	−	0.999184i	$-0.487142\pi$
$787$	−11.9012	−	3.18893i	−0.424234	−	0.113673i	−0.464618	+	0.885511i	$0.653808\pi$
$788$	−3.97990	+	14.8532i	−0.141778	+	0.529124i
$789$	2.24600	−	3.89018i	0.0799597	−	0.138494i
$790$	−13.0465	−	15.5884i	−0.464174	−	0.554611i
$791$	0.581875	−	0.243875i	0.0206891	−	0.00867119i
$792$	5.42356	−	4.67355i	0.192718	−	0.166067i
$793$	−0.598096	−	2.23213i	−0.0212390	−	0.0792651i
$794$	18.6381	+	32.2821i	0.661441	+	1.14565i
$795$	−3.81634	−	8.21138i	−0.135352	−	0.291228i
$796$	3.49993	−	6.06205i	0.124052	−	0.214864i
$797$	10.8563	+	10.8563i	0.384549	+	0.384549i	0.872738	−	0.488189i	$-0.162342\pi$
$797$	10.8563	+	10.8563i	0.384549	+	0.384549i	−0.488189	+	0.872738i	$0.662342\pi$
$798$	−4.86334	−	6.28348i	−0.172160	−	0.222433i
$799$	−63.6661			−2.25235
$800$	−0.423121	−	4.98206i	−0.0149596	−	0.176143i
$801$	1.58366	+	2.74297i	0.0559557	+	0.0969181i
$802$	−30.1499	−	8.07864i	−1.06463	−	0.285267i
$803$	17.3740	−	3.29914i	0.613114	−	0.116424i
$804$			11.7524i			0.414476i
$805$	22.9178	−	25.1569i	0.807747	−	0.886666i
$806$	−4.36348			−0.153697
$807$	−10.1168	+	2.71079i	−0.356129	+	0.0954244i
$808$	−15.2375	−	4.08287i	−0.536053	−	0.143635i
$809$	15.2557	+	26.4236i	0.536361	+	0.929005i	0.999096	+	0.0425082i	$0.0135349\pi$
$809$	15.2557	+	26.4236i	0.536361	+	0.929005i	−0.462735	+	0.886497i	$0.653132\pi$
$810$	−4.70397	+	0.823275i	−0.165281	+	0.0289269i
$811$			9.76526i			0.342905i	0.985192	+	0.171452i	$0.0548459\pi$
$811$			9.76526i			0.342905i	−0.985192	+	0.171452i	$0.945154\pi$
$812$	2.85552	−	0.388085i	0.100209	−	0.0136191i
$813$	−16.9552	−	16.9552i	−0.594645	−	0.594645i
$814$	10.6803	−	15.6872i	0.374345	−	0.549837i
$815$	17.8235	−	48.7767i	0.624330	−	1.70857i
$816$	4.56148	−	2.63357i	0.159684	−	0.0921934i
$817$	−20.0777	+	5.37980i	−0.702430	+	0.188216i
$818$	9.68399	−	9.68399i	0.338593	−	0.338593i
$819$	−2.16733	+	17.0116i	−0.0757325	+	0.594434i
$820$	−1.78962	+	20.1604i	−0.0624961	+	0.704030i
$821$	−21.5322	−	12.4316i	−0.751480	−	0.433867i	0.0747487	−	0.997202i	$-0.476185\pi$
$821$	−21.5322	−	12.4316i	−0.751480	−	0.433867i	−0.826228	+	0.563336i	$0.809518\pi$
$822$	3.45023	+	0.924487i	0.120341	+	0.0322452i
$823$	−25.1657	−	6.74313i	−0.877222	−	0.235051i	−0.208014	−	0.978126i	$-0.566700\pi$
$823$	−25.1657	−	6.74313i	−0.877222	−	0.235051i	−0.669208	+	0.743075i	$0.733366\pi$
$824$	−5.10717	+	8.84588i	−0.177917	+	0.308161i
$825$	13.0919	−	7.74445i	0.455801	−	0.269627i
$826$	6.11092	+	14.5804i	0.212626	+	0.507317i
$827$	11.7187	−	11.7187i	0.407501	−	0.407501i	−0.473365	−	0.880866i	$-0.656961\pi$
$827$	11.7187	−	11.7187i	0.407501	−	0.407501i	0.880866	+	0.473365i	$0.156961\pi$
$828$	3.21377	+	11.9940i	0.111686	+	0.416819i
$829$	−24.4200	+	14.0989i	−0.848141	+	0.489674i	−0.860023	−	0.510255i	$-0.829551\pi$
$829$	−24.4200	+	14.0989i	−0.848141	+	0.489674i	0.0118823	+	0.999929i	$0.496218\pi$
$830$	28.5204	−	13.2552i	0.989957	−	0.460094i
$831$	20.9885	+	12.1177i	0.728082	+	0.420359i
$832$	2.12323	−	2.12323i	0.0736098	−	0.0736098i
$833$	−20.3883	−	34.6415i	−0.706411	−	1.20026i
$834$		−	1.08283i		−	0.0374953i
$835$	37.4790	−	6.55948i	1.29702	−	0.227000i
$836$	9.78051	−	4.71795i	0.338266	−	0.163174i
$837$	−1.77968	+	6.64187i	−0.0615149	+	0.229577i
$838$	−4.00376	+	1.07280i	−0.138308	+	0.0370594i
$839$		−	9.34234i		−	0.322533i	−0.986911	−	0.161267i	$-0.948442\pi$
$839$		−	9.34234i		−	0.322533i	0.986911	−	0.161267i	$-0.0515579\pi$
$840$	−2.49169	+	4.82069i	−0.0859716	+	0.166330i
$841$	−27.8136			−0.959091
$842$	−2.79573	−	10.4338i	−0.0963473	−	0.359573i
$843$	2.57745	−	9.61916i	0.0887719	−	0.331301i
$844$	9.27906	+	16.0718i	0.319398	+	0.553214i
$845$	−5.11869	+	7.29052i	−0.176088	+	0.250802i
$846$			23.9334i			0.822848i
$847$	−25.3942	+	14.2175i	−0.872554	+	0.488518i
$848$	−3.12171	+	3.12171i	−0.107200	+	0.107200i
$849$	−12.8681	+	22.2882i	−0.441633	+	0.764930i
$850$	−27.0047	+	9.75128i	−0.926255	+	0.334466i
$851$	16.4573	+	28.5049i	0.564150	+	0.977136i
$852$	−7.82836	+	2.09760i	−0.268195	+	0.0718627i
$853$	0.591678	+	0.591678i	0.0202587	+	0.0202587i	0.717164	−	0.696905i	$-0.245440\pi$
$853$	0.591678	+	0.591678i	0.0202587	+	0.0202587i	−0.696905	+	0.717164i	$0.745440\pi$
$854$	1.23277	−	1.62056i	0.0421846	−	0.0554544i
$855$	−15.7418	−	1.39738i	−0.538357	−	0.0477894i
$856$	0.680673	−	1.17896i	0.0232649	−	0.0402960i
$857$	32.4896	+	8.70557i	1.10982	+	0.297377i	0.766759	−	0.641935i	$-0.221868\pi$
$857$	32.4896	+	8.70557i	1.10982	+	0.297377i	0.343065	+	0.939312i	$0.388535\pi$
$858$	8.62416	+	3.01138i	0.294424	+	0.102807i
$859$	−2.41950	−	1.39690i	−0.0825524	−	0.0476616i	0.458156	−	0.888872i	$-0.348510\pi$
$859$	−2.41950	−	1.39690i	−0.0825524	−	0.0476616i	−0.540708	+	0.841210i	$0.681844\pi$
$860$	9.11112	+	10.8863i	0.310687	+	0.371219i
$861$	13.2993	−	17.4828i	0.453239	−	0.595812i
$862$	−18.1553	−	18.1553i	−0.618372	−	0.618372i
$863$	4.42687	+	16.5213i	0.150692	+	0.562392i	0.999436	+	0.0335868i	$0.0106930\pi$
$863$	4.42687	+	16.5213i	0.150692	+	0.562392i	−0.848743	+	0.528805i	$0.822640\pi$
$864$	−2.36590	−	4.09786i	−0.0804895	−	0.139412i
$865$	−14.0131	−	5.12054i	−0.476461	−	0.174103i
$866$	0.774016	+	0.446878i	0.0263021	+	0.0151855i
$867$	−10.3605	−	10.3605i	−0.351863	−	0.351863i
$868$	−2.35327	−	3.04045i	−0.0798753	−	0.103200i
$869$	−30.0678	−	2.23344i	−1.01998	−	0.0757644i
$870$	−1.28370	+	1.82837i	−0.0435216	+	0.0619875i
$871$	33.3180	−	19.2362i	1.12894	−	0.651793i
$872$	2.18595	−	8.15809i	0.0740257	−	0.276268i
$873$	−6.13402	−	22.8925i	−0.207605	−	0.774793i
$874$			18.8335i			0.637053i
$875$	17.9988	−	23.4743i	0.608469	−	0.793577i
$876$		−	4.89086i		−	0.165247i
$877$	−3.20719	−	11.9694i	−0.108299	−	0.404178i	0.890399	−	0.455180i	$-0.150425\pi$
$877$	−3.20719	−	11.9694i	−0.108299	−	0.404178i	−0.998699	+	0.0510022i	$0.983758\pi$
$878$	9.98725	+	2.67607i	0.337053	+	0.0903131i
$879$	−5.54262	−	9.60010i	−0.186948	−	0.323803i
$880$	−5.73724	−	4.69937i	−0.193402	−	0.158416i
$881$	16.3561			0.551051			0.275526	−	0.961294i	$-0.411148\pi$
$881$	16.3561			0.551051			0.275526	+	0.961294i	$0.411148\pi$
$882$	−13.0225	+	7.66437i	−0.438489	+	0.258073i
$883$	37.6056	−	37.6056i	1.26553	−	1.26553i	0.317156	−	0.948373i	$-0.397272\pi$
$883$	37.6056	−	37.6056i	1.26553	−	1.26553i	0.948373	−	0.317156i	$-0.102728\pi$
$884$	−14.9323	−	8.62117i	−0.502228	−	0.289961i
$885$	−11.5112	−	4.20631i	−0.386946	−	0.141394i
$886$	−3.23158	+	1.86576i	−0.108567	+	0.0626813i
$887$	−0.406676	−	1.51774i	−0.0136548	−	0.0509606i	0.958762	−	0.284209i	$-0.0917310\pi$
$887$	−0.406676	−	1.51774i	−0.0136548	−	0.0509606i	−0.972417	+	0.233249i	$0.925064\pi$
$888$	−3.71130	−	3.71130i	−0.124543	−	0.124543i
$889$	40.3332	−	16.9044i	1.35273	−	0.566956i
$890$	2.51601	−	2.10574i	0.0843367	−	0.0705845i
$891$	−3.98625	+	5.85500i	−0.133544	+	0.196150i
$892$	0.406734	−	1.51795i	0.0136185	−	0.0508248i
$893$	−9.39535	+	35.0639i	−0.314403	+	1.17337i
$894$	−13.2856	−	7.67044i	−0.444337	−	0.256538i
$895$	−8.80854	−	0.781926i	−0.294437	−	0.0261369i
$896$	2.62454	+	0.334373i	0.0876796	+	0.0111706i
$897$	−11.2028	+	11.2028i	−0.374051	+	0.374051i
$898$	3.12633	−	0.837698i	0.104327	−	0.0279543i
$899$	−0.791409	−	1.37076i	−0.0263950	−	0.0457174i
$900$	3.66571	+	10.1516i	0.122190	+	0.338388i
$901$	21.9545	+	12.6754i	0.731409	+	0.422279i
$902$	19.5967	+	22.7416i	0.652500	+	0.757214i
$903$	−2.07484	−	15.2666i	−0.0690464	−	0.508042i
$904$	0.238463			0.00793117
$905$	28.5137	+	20.0196i	0.947829	+	0.665473i
$906$	−2.20758	−	3.82365i	−0.0733420	−	0.127032i
$907$	−7.56210	+	28.2221i	−0.251095	+	0.937100i	0.719126	+	0.694880i	$0.244542\pi$
$907$	−7.56210	+	28.2221i	−0.251095	+	0.937100i	−0.970221	+	0.242221i	$0.922124\pi$
$908$	21.6405	−	5.79857i	0.718167	−	0.192432i
$909$	34.0526			1.12945
$910$	17.7450	−	0.826490i	0.588240	−	0.0273979i
$911$	20.2031			0.669360			0.334680	−	0.942332i	$-0.391372\pi$
$911$	20.2031			0.669360			0.334680	+	0.942332i	$0.391372\pi$
$912$	−0.777284	−	2.90086i	−0.0257384	−	0.0960571i
$913$	15.3780	−	44.0405i	0.508938	−	1.45753i
$914$	13.3254	−	7.69343i	0.440766	−	0.254476i
$915$	0.272124	+	1.55484i	0.00899616	+	0.0514015i
$916$	0.351478			0.0116132
$917$	−24.3509	−	31.4616i	−0.804139	−	1.03895i
$918$	−19.2130	+	19.2130i	−0.634123	+	0.634123i
$919$	0.721983	−	1.25051i	0.0238160	−	0.0412506i	−0.853872	−	0.520483i	$-0.825752\pi$
$919$	0.721983	−	1.25051i	0.0238160	−	0.0412506i	0.877688	+	0.479233i	$0.159085\pi$
$920$	11.6642	−	5.42109i	0.384558	−	0.178728i
$921$	2.83054	−	1.63422i	0.0932696	−	0.0538492i
$922$	−7.07779	+	1.89649i	−0.233095	+	0.0624575i
$923$	18.7600	+	18.7600i	0.617494	+	0.617494i
$924$	2.55280	+	7.63334i	0.0839808	+	0.251118i
$925$	16.3505	+	23.4777i	0.537602	+	0.771942i
$926$	16.3041	+	9.41319i	0.535787	+	0.309336i
$927$	5.70673	−	21.2978i	0.187433	−	0.699511i
$928$	1.05209	+	0.281907i	0.0345366	+	0.00925406i
$929$	26.4790	+	15.2876i	0.868747	+	0.501571i	0.866932	−	0.498427i	$-0.166089\pi$
$929$	26.4790	+	15.2876i	0.868747	+	0.501571i	0.00181549	+	0.999998i	$0.499422\pi$
$930$	2.96888	+	0.263544i	0.0973533	+	0.00864196i
$931$	−22.0874	+	6.11665i	−0.723887	+	0.200465i
$932$	15.7173	−	15.7173i	0.514837	−	0.514837i
$933$	0.619434	+	2.31176i	0.0202794	+	0.0756836i
$934$	−0.147562	−	0.255585i	−0.00482838	−	0.00836301i
$935$	−17.5389	+	38.8065i	−0.573583	+	1.26911i
$936$	−3.24088	+	5.61336i	−0.105931	+	0.183479i
$937$	7.66075	−	7.66075i	0.250266	−	0.250266i	−0.570814	−	0.821080i	$-0.693372\pi$
$937$	7.66075	−	7.66075i	0.250266	−	0.250266i	0.821080	+	0.570814i	$0.193372\pi$
$938$	31.3724	+	12.8415i	1.02435	+	0.419291i
$939$			15.8303i			0.516603i
$940$	24.4207	−	4.27404i	0.796515	−	0.139404i
$941$	19.8834	−	11.4797i	0.648180	−	0.374227i	−0.139578	−	0.990211i	$-0.544575\pi$
$941$	19.8834	−	11.4797i	0.648180	−	0.374227i	0.787759	+	0.615984i	$0.211241\pi$
$942$	18.6202	+	4.98926i	0.606678	+	0.162559i
$943$	−50.2922	+	13.4757i	−1.63774	+	0.438831i
$944$			5.97532i			0.194480i
$945$	5.97941	−	27.3476i	0.194510	−	0.889618i
$946$	20.9981	+	1.55974i	0.682706	+	0.0507115i
$947$	42.1697	−	11.2993i	1.37033	−	0.367179i	0.502732	−	0.864442i	$-0.332328\pi$
$947$	42.1697	−	11.2993i	1.37033	−	0.367179i	0.867600	+	0.497263i	$0.165662\pi$
$948$	−2.15818	+	8.05444i	−0.0700944	+	0.261596i
$949$	−13.8656	+	8.00529i	−0.450095	+	0.259863i
$950$	1.38534	+	16.3118i	0.0449464	+	0.529225i
$951$	−21.6766			−0.702912
$952$	−2.04598	−	15.0542i	−0.0663105	−	0.487911i
$953$	−17.7860	−	17.7860i	−0.576144	−	0.576144i	0.357695	−	0.933839i	$-0.383563\pi$
$953$	−17.7860	−	17.7860i	−0.576144	−	0.576144i	−0.933839	+	0.357695i	$0.883563\pi$
$954$	4.76495	−	8.25314i	0.154271	−	0.267205i
$955$	6.67879	−	3.10405i	0.216121	−	0.100445i
$956$	−14.7656	+	8.52493i	−0.477554	+	0.275716i
$957$	0.618168	+	3.25541i	0.0199825	+	0.105232i
$958$	25.9101	−	25.9101i	0.837116	−	0.837116i
$959$	6.23784	−	8.20005i	0.201430	−	0.264793i
$960$	−1.57287	+	1.31639i	−0.0507641	+	0.0424863i
$961$	14.4441	−	25.0180i	0.465940	−	0.807031i
$962$	−4.44692	+	16.5961i	−0.143374	+	0.535080i
$963$	−0.760580	+	2.83852i	−0.0245094	+	0.0914702i
$964$	2.14622	−	3.71736i	0.0691250	−	0.119728i
$965$	26.0309	−	21.7862i	0.837963	−	0.701322i
$966$	−13.8478	−	1.76425i	−0.445547	−	0.0567639i
$967$	22.4281	−	22.4281i	0.721241	−	0.721241i	−0.247617	−	0.968858i	$-0.579648\pi$
$967$	22.4281	−	22.4281i	0.721241	−	0.721241i	0.968858	+	0.247617i	$0.0796476\pi$
$968$	−10.9292	+	1.24594i	−0.351278	+	0.0400462i
$969$	−14.9348	+	8.62258i	−0.479773	+	0.276997i
$970$	−22.2631	+	10.3470i	−0.714826	+	0.332224i
$971$	−1.37739	+	2.38570i	−0.0442024	+	0.0765609i	−0.887280	−	0.461231i	$-0.847408\pi$
$971$	−1.37739	+	2.38570i	−0.0442024	+	0.0765609i	0.843078	+	0.537792i	$0.180741\pi$
$972$	11.4228	+	11.4228i	0.366388	+	0.366388i
$973$	−2.89055	−	1.18318i	−0.0926668	−	0.0379309i
$974$	−32.9717			−1.05648
$975$	−8.87876	+	10.5268i	−0.284348	+	0.337129i
$976$	0.666489	−	0.384798i	0.0213338	−	0.0123171i
$977$	−11.6613	+	43.5207i	−0.373079	+	1.39235i	0.483052	+	0.875592i	$0.339528\pi$
$977$	−11.6613	+	43.5207i	−0.373079	+	1.39235i	−0.856131	+	0.516759i	$0.827138\pi$
$978$	−20.5768	+	5.51354i	−0.657973	+	0.176303i
$979$	0.360483	−	4.85302i	0.0115211	−	0.155103i
$980$	10.1460	+	11.9189i	0.324101	+	0.380734i
$981$			18.2316i			0.582090i
$982$	−21.4118	+	5.73728i	−0.683279	+	0.183084i
$983$	29.1379	+	7.80748i	0.929355	+	0.249020i	0.691580	−	0.722300i	$-0.256915\pi$
$983$	29.1379	+	7.80748i	0.929355	+	0.249020i	0.237775	+	0.971320i	$0.423582\pi$
$984$	7.19017	−	4.15125i	0.229214	−	0.132337i
$985$	−33.8696	+	5.92776i	−1.07917	+	0.188874i
$986$		−	6.25453i		−	0.199185i
$987$	−24.9016	−	10.1928i	−0.792626	−	0.324442i
$988$	−6.95168	+	6.95168i	−0.221162	+	0.221162i
$989$	−18.2594	+	31.6262i	−0.580615	+	1.00565i
$990$	14.5882	+	6.59323i	0.463642	+	0.209547i
$991$	0.349768	+	0.605815i	0.0111107	+	0.0192444i	0.871527	−	0.490347i	$-0.163130\pi$
$991$	0.349768	+	0.605815i	0.0111107	+	0.0192444i	−0.860417	+	0.509591i	$0.829797\pi$
$992$	−0.376112	−	1.40367i	−0.0119416	−	0.0445665i
$993$	18.3369	−	18.3369i	0.581903	−	0.581903i
$994$	−2.95439	+	23.1894i	−0.0937076	+	0.735522i
$995$	15.5908	+	1.38398i	0.494263	+	0.0438753i
$996$	−11.1727	−	6.45057i	−0.354021	−	0.204394i
$997$	23.5625	+	6.31356i	0.746233	+	0.199952i	0.611846	−	0.790977i	$-0.290427\pi$
$997$	23.5625	+	6.31356i	0.746233	+	0.199952i	0.134386	+	0.990929i	$0.457094\pi$
$998$	7.40194	−	27.6244i	0.234304	−	0.874436i
$999$	23.4481	+	13.5378i	0.741864	+	0.428316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bd.a.527.9	yes	192
5.3	odd	4	inner	770.2.bd.a.373.16	yes	192
7.4	even	3	inner	770.2.bd.a.417.40	yes	192
11.10	odd	2	inner	770.2.bd.a.527.33	yes	192
35.18	odd	12	inner	770.2.bd.a.263.33	yes	192
55.43	even	4	inner	770.2.bd.a.373.40	yes	192
77.32	odd	6	inner	770.2.bd.a.417.16	yes	192
385.263	even	12	inner	770.2.bd.a.263.9	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bd.a.263.9	✓	192	385.263	even	12	inner
770.2.bd.a.263.33	yes	192	35.18	odd	12	inner
770.2.bd.a.373.16	yes	192	5.3	odd	4	inner
770.2.bd.a.373.40	yes	192	55.43	even	4	inner
770.2.bd.a.417.16	yes	192	77.32	odd	6	inner
770.2.bd.a.417.40	yes	192	7.4	even	3	inner
770.2.bd.a.527.9	yes	192	1.1	even	1	trivial
770.2.bd.a.527.33	yes	192	11.10	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.886001 - 0.237403i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.83005 - 1.28488i) q^{5} +0.917256i q^{6} +(2.44857 + 1.00226i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.86944 - 1.07932i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.886001 - 0.237403i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.83005 - 1.28488i) q^{5} +0.917256i q^{6} +(2.44857 + 1.00226i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.86944 - 1.07932i) q^{9} +(-0.767449 + 2.10024i) q^{10} +(1.44099 + 2.98723i) q^{11} +(0.886001 - 0.237403i) q^{12} +(-2.12323 - 2.12323i) q^{13} +(0.334373 - 2.62454i) q^{14} +(1.31639 + 1.57287i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-5.54661 - 1.48621i) q^{17} +(-0.558697 + 2.08509i) q^{18} +(-1.63705 + 2.83546i) q^{19} +(2.22731 + 0.197716i) q^{20} +(-1.93149 - 1.46930i) q^{21} +(2.51249 - 2.16504i) q^{22} +(1.48880 + 5.55626i) q^{23} +(-0.458628 - 0.794367i) q^{24} +(1.69816 + 4.70279i) q^{25} +(-1.50135 + 2.60042i) q^{26} +(3.34588 + 3.34588i) q^{27} +(-2.62165 + 0.356300i) q^{28} -1.08921 q^{29} +(1.17857 - 1.67862i) q^{30} +(0.726592 + 1.25849i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.567539 - 2.98879i) q^{33} +5.74228i q^{34} +(-3.19321 - 4.98030i) q^{35} +2.15864 q^{36} +(5.52706 - 1.48097i) q^{37} +(3.16254 + 0.847401i) q^{38} +(1.37712 + 2.38525i) q^{39} +(-0.385491 - 2.20259i) q^{40} +9.05144i q^{41} +(-0.919329 + 2.24596i) q^{42} +(4.48914 + 4.48914i) q^{43} +(-2.74155 - 1.86652i) q^{44} +(2.03436 + 4.37722i) q^{45} +(4.98161 - 2.87613i) q^{46} +(10.7095 - 2.86959i) q^{47} +(-0.648598 + 0.648598i) q^{48} +(4.99095 + 4.90820i) q^{49} +(4.10303 - 2.85747i) q^{50} +(4.56148 + 2.63357i) q^{51} +(2.90039 + 0.777156i) q^{52} +(-4.26434 - 1.14263i) q^{53} +(2.36590 - 4.09786i) q^{54} +(1.20116 - 7.31828i) q^{55} +(1.02269 + 2.44010i) q^{56} +(2.12358 - 2.12358i) q^{57} +(0.281907 + 1.05209i) q^{58} +(-5.17478 + 2.98766i) q^{59} +(-1.92646 - 0.703948i) q^{60} +(0.666489 + 0.384798i) q^{61} +(1.02756 - 1.02756i) q^{62} +(-3.49568 - 4.51645i) q^{63} +1.00000i q^{64} +(1.15751 + 6.61372i) q^{65} +(-2.74006 + 1.32176i) q^{66} +(-3.31614 + 12.3760i) q^{67} +(5.54661 - 1.48621i) q^{68} -5.27630i q^{69} +(-3.98414 + 4.37340i) q^{70} -8.83561 q^{71} +(-0.558697 - 2.08509i) q^{72} +(1.38004 - 5.15037i) q^{73} +(-2.86102 - 4.95543i) q^{74} +(-0.388110 - 4.56983i) q^{75} -3.27410i q^{76} +(0.534374 + 8.75868i) q^{77} +(1.94755 - 1.94755i) q^{78} +(-4.54539 + 7.87284i) q^{79} +(-2.02776 + 0.942428i) q^{80} +(1.06783 + 1.84953i) q^{81} +(8.74302 - 2.34269i) q^{82} +(-9.94541 - 9.94541i) q^{83} +(2.40737 + 0.306706i) q^{84} +(8.24097 + 9.84658i) q^{85} +(3.17430 - 5.49805i) q^{86} +(0.965039 + 0.258581i) q^{87} +(-1.09336 + 3.13122i) q^{88} +(-1.27069 - 0.733635i) q^{89} +(3.70153 - 3.09795i) q^{90} +(-3.07084 - 7.32690i) q^{91} +(-4.06746 - 4.06746i) q^{92} +(-0.344991 - 1.28752i) q^{93} +(-5.54363 - 9.60185i) q^{94} +(6.63911 - 3.08561i) q^{95} +(0.794367 + 0.458628i) q^{96} +(7.76343 + 7.76343i) q^{97} +(3.44920 - 6.09122i) q^{98} +(0.530341 - 7.13973i) 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

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