LMFDB - Embedded newform 640.2.bm.a.101.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("640.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.31
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0538080 - 1.41319i) q^{2} +(0.692518 - 0.370159i) q^{3} +(-1.99421 + 0.152082i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-0.560367 - 0.958742i) q^{6} +(-1.17185 + 0.783003i) q^{7} +(0.322225 + 2.81001i) q^{8} +(-1.32415 + 1.98173i) q^{9} +(1.05827 - 0.938112i) q^{10} +(5.63534 - 1.70946i) q^{11} +(-1.32473 + 0.843493i) q^{12} +(-0.319908 - 0.262542i) q^{13} +(1.16959 + 1.61391i) q^{14} +(0.725465 + 0.300498i) q^{15} +(3.95374 - 0.606566i) q^{16} +(6.62302 - 2.74334i) q^{17} +(2.87180 + 1.76464i) q^{18} +(-0.673901 - 6.84223i) q^{19} +(-1.38267 - 1.44507i) q^{20} +(-0.521690 + 0.976013i) q^{21} +(-2.71902 - 7.87183i) q^{22} +(3.20840 - 0.638190i) q^{23} +(1.26330 + 1.82671i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-0.353808 + 0.466218i) q^{26} +(-0.414343 + 4.20690i) q^{27} +(2.21783 - 1.73969i) q^{28} +(0.162901 - 0.537013i) q^{29} +(0.385624 - 1.04139i) q^{30} +(4.09405 + 4.09405i) q^{31} +(-1.06993 - 5.55475i) q^{32} +(3.26981 - 3.26981i) q^{33} +(-4.23323 - 9.21196i) q^{34} +(-1.34868 - 0.409118i) q^{35} +(2.33924 - 4.15335i) q^{36} +(-3.30381 - 0.325397i) q^{37} +(-9.63311 + 1.32052i) q^{38} +(-0.318725 - 0.0633982i) q^{39} +(-1.96775 + 2.03174i) q^{40} +(-0.0419679 - 0.210987i) q^{41} +(1.40736 + 0.684729i) q^{42} +(1.62271 + 0.867358i) q^{43} +(-10.9781 + 4.26606i) q^{44} +(-2.37192 + 0.233614i) q^{45} +(-1.07452 - 4.49974i) q^{46} +(3.99557 + 9.64615i) q^{47} +(2.51351 - 1.88357i) q^{48} +(-1.91865 + 4.63204i) q^{49} +(1.39653 + 0.222926i) q^{50} +(3.57109 - 4.35138i) q^{51} +(0.677892 + 0.474911i) q^{52} +(1.68871 + 5.56693i) q^{53} +(5.96744 + 0.359181i) q^{54} +(4.89646 + 3.27171i) q^{55} +(-2.57785 - 3.04060i) q^{56} +(-2.99940 - 4.48892i) q^{57} +(-0.767667 - 0.201315i) q^{58} +(2.63336 - 2.16114i) q^{59} +(-1.49243 - 0.488925i) q^{60} +(-5.79540 - 10.8424i) q^{61} +(5.56538 - 6.00596i) q^{62} -3.35909i q^{63} +(-7.79234 + 1.81091i) q^{64} -0.413847i q^{65} +(-4.79680 - 4.44491i) q^{66} +(3.33539 + 6.24008i) q^{67} +(-12.7905 + 6.47804i) q^{68} +(1.98564 - 1.62957i) q^{69} +(-0.505591 + 1.92796i) q^{70} +(-6.18671 - 9.25907i) q^{71} +(-5.99535 - 3.08231i) q^{72} +(0.0908549 + 0.0607073i) q^{73} +(-0.282076 + 4.68642i) q^{74} +(0.227943 + 0.751426i) q^{75} +(2.38448 + 13.5424i) q^{76} +(-5.26525 + 6.41572i) q^{77} +(-0.0724438 + 0.453829i) q^{78} +(0.425661 - 1.02764i) q^{79} +(2.97711 + 2.67148i) q^{80} +(-1.46598 - 3.53920i) q^{81} +(-0.295906 + 0.0706613i) q^{82} +(4.26158 - 0.419729i) q^{83} +(0.891925 - 2.02571i) q^{84} +(6.32223 + 3.37930i) q^{85} +(1.13843 - 2.33987i) q^{86} +(-0.0859681 - 0.432191i) q^{87} +(6.61946 + 15.2846i) q^{88} +(-14.9762 - 2.97895i) q^{89} +(0.457769 + 3.33941i) q^{90} +(0.580455 + 0.0571698i) q^{91} +(-6.30116 + 1.76062i) q^{92} +(4.35065 + 1.31976i) q^{93} +(13.4168 - 6.16553i) q^{94} +(4.86160 - 4.86160i) q^{95} +(-2.79709 - 3.45072i) q^{96} +(1.81852 + 1.81852i) q^{97} +(6.64919 + 2.46218i) q^{98} +(-4.07434 + 13.4313i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	−0.0538080	−	1.41319i	−0.0380480	−	0.999276i
$2$	−0.0538080	−	1.41319i	−0.0380480	−	0.999276i
$3$	0.692518	−	0.370159i	0.399826	−	0.213711i	−0.259213	−	0.965820i	$-0.583463\pi$
$3$	0.692518	−	0.370159i	0.399826	−	0.213711i	0.659039	+	0.752109i	$0.270963\pi$
$4$	−1.99421	+	0.152082i	−0.997105	+	0.0760409i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	−0.560367	−	0.958742i	−0.228769	−	0.391405i
$7$	−1.17185	+	0.783003i	−0.442916	+	0.295947i	−0.756960	−	0.653461i	$-0.773316\pi$
$7$	−1.17185	+	0.783003i	−0.442916	+	0.295947i	0.314043	+	0.949409i	$0.398316\pi$
$8$	0.322225	+	2.81001i	0.113924	+	0.993490i
$9$	−1.32415	+	1.98173i	−0.441382	+	0.660575i
$10$	1.05827	−	0.938112i	0.334656	−	0.296657i
$11$	5.63534	−	1.70946i	1.69912	−	0.515423i	0.715956	−	0.698145i	$-0.245991\pi$
$11$	5.63534	−	1.70946i	1.69912	−	0.515423i	0.983164	+	0.182723i	$0.0584911\pi$
$12$	−1.32473	+	0.843493i	−0.382417	+	0.243496i
$13$	−0.319908	−	0.262542i	−0.0887266	−	0.0728160i	0.588984	−	0.808144i	$-0.299528\pi$
$13$	−0.319908	−	0.262542i	−0.0887266	−	0.0728160i	−0.677711	+	0.735328i	$0.737028\pi$
$14$	1.16959	+	1.61391i	0.312585	+	0.431336i
$15$	0.725465	+	0.300498i	0.187314	+	0.0775882i
$16$	3.95374	−	0.606566i	0.988436	−	0.151641i
$17$	6.62302	−	2.74334i	1.60632	−	0.665358i	0.614026	−	0.789286i	$-0.289549\pi$
$17$	6.62302	−	2.74334i	1.60632	−	0.665358i	0.992291	+	0.123928i	$0.0395490\pi$
$18$	2.87180	+	1.76464i	0.676891	+	0.415929i
$19$	−0.673901	−	6.84223i	−0.154604	−	1.56972i	−0.689177	−	0.724593i	$-0.742028\pi$
$19$	−0.673901	−	6.84223i	−0.154604	−	1.56972i	0.534573	−	0.845122i	$-0.320472\pi$
$20$	−1.38267	−	1.44507i	−0.309175	−	0.323126i
$21$	−0.521690	+	0.976013i	−0.113842	+	0.212984i
$22$	−2.71902	−	7.87183i	−0.579697	−	1.67828i
$23$	3.20840	−	0.638190i	0.668997	−	0.133072i	0.151105	−	0.988518i	$-0.451717\pi$
$23$	3.20840	−	0.638190i	0.668997	−	0.133072i	0.517892	+	0.855446i	$0.326717\pi$
$24$	1.26330	+	1.82671i	0.257869	+	0.372876i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	−0.353808	+	0.466218i	−0.0693874	+	0.0914329i
$27$	−0.414343	+	4.20690i	−0.0797404	+	0.809618i
$28$	2.21783	−	1.73969i	0.419130	−	0.328770i
$29$	0.162901	−	0.537013i	0.0302500	−	0.0997209i	−0.940515	−	0.339751i	$-0.889657\pi$
$29$	0.162901	−	0.537013i	0.0302500	−	0.0997209i	0.970765	+	0.240030i	$0.0771573\pi$
$30$	0.385624	−	1.04139i	0.0704050	−	0.190131i
$31$	4.09405	+	4.09405i	0.735313	+	0.735313i	0.971667	−	0.236354i	$-0.0759525\pi$
$31$	4.09405	+	4.09405i	0.735313	+	0.735313i	−0.236354	+	0.971667i	$0.575952\pi$
$32$	−1.06993	−	5.55475i	−0.189140	−	0.981950i
$33$	3.26981	−	3.26981i	0.569200	−	0.569200i
$34$	−4.23323	−	9.21196i	−0.725994	−	1.57984i
$35$	−1.34868	−	0.409118i	−0.227969	−	0.0691536i
$36$	2.33924	−	4.15335i	0.389874	−	0.692226i
$37$	−3.30381	−	0.325397i	−0.543143	−	0.0534949i	−0.177274	−	0.984161i	$-0.556728\pi$
$37$	−3.30381	−	0.325397i	−0.543143	−	0.0534949i	−0.365869	+	0.930667i	$0.619228\pi$
$38$	−9.63311	+	1.32052i	−1.56270	+	0.214216i
$39$	−0.318725	−	0.0633982i	−0.0510368	−	0.0101518i
$40$	−1.96775	+	2.03174i	−0.311129	+	0.321246i
$41$	−0.0419679	−	0.210987i	−0.00655428	−	0.0329506i	0.977370	−	0.211538i	$-0.0678472\pi$
$41$	−0.0419679	−	0.210987i	−0.00655428	−	0.0329506i	−0.983924	+	0.178587i	$0.942847\pi$
$42$	1.40736	+	0.684729i	0.217161	+	0.105656i
$43$	1.62271	+	0.867358i	0.247461	+	0.132271i	0.590465	−	0.807063i	$-0.298944\pi$
$43$	1.62271	+	0.867358i	0.247461	+	0.132271i	−0.343004	+	0.939334i	$0.611444\pi$
$44$	−10.9781	+	4.26606i	−1.65501	+	0.643133i
$45$	−2.37192	+	0.233614i	−0.353586	+	0.0348251i
$46$	−1.07452	−	4.49974i	−0.158429	−	0.663450i
$47$	3.99557	+	9.64615i	0.582813	+	1.40704i	0.890252	+	0.455468i	$0.150528\pi$
$47$	3.99557	+	9.64615i	0.582813	+	1.40704i	−0.307439	+	0.951568i	$0.599472\pi$
$48$	2.51351	−	1.88357i	0.362794	−	0.271870i
$49$	−1.91865	+	4.63204i	−0.274093	+	0.661720i
$50$	1.39653	+	0.222926i	0.197500	+	0.0315264i
$51$	3.57109	−	4.35138i	0.500052	−	0.609315i
$52$	0.677892	+	0.474911i	0.0940067	+	0.0658584i
$53$	1.68871	+	5.56693i	0.231962	+	0.764676i	0.993222	+	0.116230i	$0.0370809\pi$
$53$	1.68871	+	5.56693i	0.231962	+	0.764676i	−0.761260	+	0.648446i	$0.775419\pi$
$54$	5.96744	+	0.359181i	0.812065	+	0.0488783i
$55$	4.89646	+	3.27171i	0.660238	+	0.441157i
$56$	−2.57785	−	3.04060i	−0.344479	−	0.406317i
$57$	−2.99940	−	4.48892i	−0.397280	−	0.594572i
$58$	−0.767667	−	0.201315i	−0.100800	−	0.0264339i
$59$	2.63336	−	2.16114i	0.342834	−	0.281357i	−0.447182	−	0.894443i	$-0.647572\pi$
$59$	2.63336	−	2.16114i	0.342834	−	0.281357i	0.790016	+	0.613086i	$0.210072\pi$
$60$	−1.49243	−	0.488925i	−0.192672	−	0.0631200i
$61$	−5.79540	−	10.8424i	−0.742025	−	1.38823i	−0.915061	−	0.403315i	$-0.867858\pi$
$61$	−5.79540	−	10.8424i	−0.742025	−	1.38823i	0.173036	−	0.984915i	$-0.444642\pi$
$62$	5.56538	−	6.00596i	0.706804	−	0.762758i
$63$		−	3.35909i		−	0.423205i
$64$	−7.79234	+	1.81091i	−0.974043	+	0.226364i
$65$		−	0.413847i		−	0.0513314i
$66$	−4.79680	−	4.44491i	−0.590445	−	0.547131i
$67$	3.33539	+	6.24008i	0.407483	+	0.762348i	0.999035	−	0.0439194i	$-0.0139845\pi$
$67$	3.33539	+	6.24008i	0.407483	+	0.762348i	−0.591552	+	0.806267i	$0.701484\pi$
$68$	−12.7905	+	6.47804i	−1.55107	+	0.785578i
$69$	1.98564	−	1.62957i	0.239043	−	0.196178i
$70$	−0.505591	+	1.92796i	−0.0604297	+	0.230435i
$71$	−6.18671	−	9.25907i	−0.734227	−	1.09885i	−0.991193	−	0.132428i	$-0.957723\pi$
$71$	−6.18671	−	9.25907i	−0.734227	−	1.09885i	0.256965	−	0.966421i	$-0.417277\pi$
$72$	−5.99535	−	3.08231i	−0.706558	−	0.363253i
$73$	0.0908549	+	0.0607073i	0.0106338	+	0.00710526i	0.560876	−	0.827900i	$-0.310465\pi$
$73$	0.0908549	+	0.0607073i	0.0106338	+	0.00710526i	−0.550242	+	0.835005i	$0.685465\pi$
$74$	−0.282076	+	4.68642i	−0.0327907	+	0.544785i
$75$	0.227943	+	0.751426i	0.0263205	+	0.0867672i
$76$	2.38448	+	13.5424i	0.273518	+	1.55341i
$77$	−5.26525	+	6.41572i	−0.600030	+	0.731139i
$78$	−0.0724438	+	0.453829i	−0.00820265	+	0.0513861i
$79$	0.425661	−	1.02764i	0.0478907	−	0.115618i	−0.898124	−	0.439743i	$-0.855070\pi$
$79$	0.425661	−	1.02764i	0.0478907	−	0.115618i	0.946014	+	0.324124i	$0.105070\pi$
$80$	2.97711	+	2.67148i	0.332851	+	0.298681i
$81$	−1.46598	−	3.53920i	−0.162887	−	0.393245i
$82$	−0.295906	+	0.0706613i	−0.0326774	+	0.00780324i
$83$	4.26158	−	0.419729i	0.467770	−	0.0460713i	0.138613	−	0.990347i	$-0.455736\pi$
$83$	4.26158	−	0.419729i	0.467770	−	0.0460713i	0.329157	+	0.944275i	$0.393236\pi$
$84$	0.891925	−	2.02571i	0.0973170	−	0.221024i
$85$	6.32223	+	3.37930i	0.685742	+	0.366537i
$86$	1.13843	−	2.33987i	0.122760	−	0.252315i
$87$	−0.0859681	−	0.432191i	−0.00921675	−	0.0463357i
$88$	6.61946	+	15.2846i	0.705637	+	1.62934i
$89$	−14.9762	−	2.97895i	−1.58747	−	0.315768i	−0.679137	−	0.734011i	$-0.737646\pi$
$89$	−14.9762	−	2.97895i	−1.58747	−	0.315768i	−0.908335	+	0.418243i	$0.862646\pi$
$90$	0.457769	+	3.33941i	0.0482531	+	0.352005i
$91$	0.580455	+	0.0571698i	0.0608482	+	0.00599302i
$92$	−6.30116	+	1.76062i	−0.656941	+	0.183558i
$93$	4.35065	+	1.31976i	0.451142	+	0.136852i
$94$	13.4168	−	6.16553i	1.38384	−	0.635926i
$95$	4.86160	−	4.86160i	0.498789	−	0.498789i
$96$	−2.79709	−	3.45072i	−0.285477	−	0.352188i
$97$	1.81852	+	1.81852i	0.184643	+	0.184643i	0.793376	−	0.608732i	$-0.208322\pi$
$97$	1.81852	+	1.81852i	0.184643	+	0.184643i	−0.608732	+	0.793376i	$0.708322\pi$
$98$	6.64919	+	2.46218i	0.671669	+	0.248718i
$99$	−4.07434	+	13.4313i	−0.409486	+	1.34990i
$100$	0.239891	−	1.98556i	0.0239891	−	0.198556i
$101$	−0.489066	+	4.96557i	−0.0486638	+	0.494092i	0.939702	+	0.341995i	$0.111103\pi$
$101$	−0.489066	+	4.96557i	−0.0486638	+	0.494092i	−0.988366	+	0.152097i	$0.951397\pi$
$102$	−6.34148	−	4.81248i	−0.627900	−	0.476507i
$103$	−0.747892	+	3.75991i	−0.0736920	+	0.370475i	−0.999980	−	0.00634197i	$-0.997981\pi$
$103$	−0.747892	+	3.75991i	−0.0736920	+	0.370475i	0.926288	+	0.376817i	$0.122981\pi$
$104$	0.634664	−	0.983544i	0.0622339	−	0.0964444i
$105$	−1.08542	+	0.215904i	−0.105927	+	0.0210701i
$106$	7.77626	−	2.68601i	0.755297	−	0.260888i
$107$	0.999427	−	1.86980i	0.0966182	−	0.180760i	−0.828969	−	0.559295i	$-0.811072\pi$
$107$	0.999427	−	1.86980i	0.0966182	−	0.180760i	0.925587	+	0.378535i	$0.123572\pi$
$108$	0.186495	−	8.45245i	0.0179455	−	0.813337i
$109$	−0.0315822	−	0.320659i	−0.00302502	−	0.0307136i	0.993554	−	0.113362i	$-0.0361621\pi$
$109$	−0.0315822	−	0.320659i	−0.00302502	−	0.0307136i	−0.996579	+	0.0826487i	$0.973662\pi$
$110$	4.36008	−	7.09567i	0.415717	−	0.676545i
$111$	−2.40840	+	0.997591i	−0.228595	+	0.0946871i
$112$	−4.15824	+	3.80659i	−0.392916	+	0.359689i
$113$	−16.7402	−	6.93402i	−1.57479	−	0.652297i	−0.587209	−	0.809436i	$-0.699773\pi$
$113$	−16.7402	−	6.93402i	−1.57479	−	0.652297i	−0.987577	+	0.157138i	$0.949773\pi$
$114$	−6.18230	+	4.48026i	−0.579026	+	0.419615i
$115$	2.52871	+	2.07526i	0.235804	+	0.193519i
$116$	−0.243189	+	1.09569i	−0.0225796	+	0.101732i
$117$	0.943892	−	0.286326i	0.0872628	−	0.0264709i
$118$	−3.19580	−	3.60515i	−0.294197	−	0.331881i
$119$	−5.61311	+	8.40062i	−0.514553	+	0.770083i
$120$	−0.610639	+	2.13539i	−0.0557435	+	0.194934i
$121$	19.6887	−	13.1556i	1.78988	−	1.19596i
$122$	−15.0106	+	8.77340i	−1.35899	+	0.794307i
$123$	−0.107162	−	0.130577i	−0.00966248	−	0.0117738i
$124$	−8.78702	−	7.54176i	−0.789098	−	0.677270i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	−4.74703	+	0.180746i	−0.422899	+	0.0161021i
$127$	−19.7370			−1.75138			−0.875690	−	0.482874i	$-0.839593\pi$
$127$	−19.7370			−1.75138			−0.875690	+	0.482874i	$0.839593\pi$
$128$	2.97845	+	10.9146i	0.263260	+	0.964725i
$129$	1.44482			0.127209
$130$	−0.584845	+	0.0222683i	−0.0512943	+	0.00195306i
$131$	11.5115	−	6.15305i	1.00577	−	0.537594i	0.115634	−	0.993292i	$-0.463110\pi$
$131$	11.5115	−	6.15305i	1.00577	−	0.537594i	0.890135	+	0.455697i	$0.150610\pi$
$132$	−6.02340	+	7.01796i	−0.524270	+	0.610835i
$133$	6.14720	+	7.49038i	0.533030	+	0.649498i
$134$	8.63895	−	5.04931i	0.746292	−	0.436194i
$135$	−3.51483	+	2.34854i	−0.302509	+	0.202130i
$136$	9.84293	+	17.7268i	0.844024	+	1.52006i
$137$	−3.49192	+	5.22603i	−0.298335	+	0.446489i	−0.950107	−	0.311926i	$-0.899026\pi$
$137$	−3.49192	+	5.22603i	−0.298335	+	0.446489i	0.651772	+	0.758415i	$0.274026\pi$
$138$	−2.40974	−	2.71841i	−0.205131	−	0.231406i
$139$	14.1609	−	4.29568i	1.20112	−	0.364354i	0.374556	−	0.927204i	$-0.377795\pi$
$139$	14.1609	−	4.29568i	1.20112	−	0.364354i	0.826559	+	0.562850i	$0.190295\pi$
$140$	2.75177	+	0.610757i	0.232567	+	0.0516184i
$141$	6.33761	+	5.20114i	0.533723	+	0.438015i
$142$	−12.7519	+	9.24121i	−1.07012	+	0.775505i
$143$	−2.25160	−	0.932643i	−0.188288	−	0.0779915i
$144$	−4.03329	+	8.63841i	−0.336107	+	0.719868i
$145$	0.518460	−	0.214753i	0.0430558	−	0.0178343i
$146$	0.0809022	−	0.131662i	0.00669552	−	0.0108964i
$147$	0.385887	+	3.91798i	0.0318274	+	0.323149i
$148$	6.63798	+	0.146460i	0.545638	+	0.0120390i
$149$	2.25241	−	4.21396i	0.184525	−	0.345221i	−0.772602	−	0.634890i	$-0.781045\pi$
$149$	2.25241	−	4.21396i	0.184525	−	0.345221i	0.957127	+	0.289669i	$0.0935453\pi$
$150$	1.04964	−	0.362559i	0.0857029	−	0.0296028i
$151$	1.15130	−	0.229008i	0.0936916	−	0.0186364i	−0.148022	−	0.988984i	$-0.547291\pi$
$151$	1.15130	−	0.229008i	0.0936916	−	0.0186364i	0.241713	+	0.970348i	$0.422291\pi$
$152$	19.0096	−	4.09841i	1.54188	−	0.332425i
$153$	−3.33329	+	16.7576i	−0.269481	+	1.35477i
$154$	9.34994	+	7.09557i	0.753440	+	0.571778i
$155$	−0.567506	+	5.76198i	−0.0455831	+	0.462813i
$156$	0.645245	+	0.0779572i	0.0516610	+	0.00624157i
$157$	−0.309094	+	1.01895i	−0.0246684	+	0.0813207i	−0.968410	−	0.249362i	$-0.919779\pi$
$157$	−0.309094	+	1.01895i	−0.0246684	+	0.0813207i	0.943742	+	0.330683i	$0.107279\pi$
$158$	−1.47515	−	0.546245i	−0.117357	−	0.0434569i
$159$	3.23011	+	3.23011i	0.256164	+	0.256164i
$160$	3.61512	−	4.35097i	0.285800	−	0.343974i
$161$	−3.26005	+	3.26005i	−0.256928	+	0.256928i
$162$	−4.92268	+	2.26215i	−0.386762	+	0.177731i
$163$	−3.37990	−	1.02528i	−0.264734	−	0.0803061i	0.155127	−	0.987894i	$-0.450421\pi$
$163$	−3.37990	−	1.02528i	−0.264734	−	0.0803061i	−0.419861	+	0.907588i	$0.637921\pi$
$164$	0.115780	+	0.414369i	0.00904089	+	0.0323568i
$165$	4.60194	+	0.453251i	0.358260	+	0.0352856i
$166$	−0.822465	−	5.99984i	−0.0638356	−	0.465678i
$167$	3.66518	+	0.729050i	0.283620	+	0.0564156i	0.334850	−	0.942271i	$-0.391314\pi$
$167$	3.66518	+	0.729050i	0.283620	+	0.0564156i	−0.0512301	+	0.998687i	$0.516314\pi$
$168$	−2.91071	−	1.15146i	−0.224566	−	0.0888370i
$169$	−2.50276	−	12.5822i	−0.192520	−	0.967864i
$170$	4.43541	−	9.11634i	0.340180	−	0.699191i
$171$	14.4518	+	7.72463i	1.10515	+	0.590717i
$172$	−3.36794	−	1.48291i	−0.256803	−	0.113071i
$173$	−10.3467	+	1.01906i	−0.786642	+	0.0774775i	−0.483358	−	0.875423i	$-0.660583\pi$
$173$	−10.3467	+	1.01906i	−0.786642	+	0.0774775i	−0.303284	+	0.952900i	$0.598083\pi$
$174$	−0.606142	+	0.144745i	−0.0459515	+	0.0109731i
$175$	−0.539342	−	1.30209i	−0.0407704	−	0.0984285i
$176$	21.2438	−	10.1770i	1.60131	−	0.767119i
$177$	1.02368	−	2.47139i	0.0769448	−	0.185761i
$178$	−3.40398	+	21.3245i	−0.255139	+	1.59834i
$179$	−0.185711	+	0.226290i	−0.0138807	+	0.0169137i	−0.779905	−	0.625898i	$-0.784732\pi$
$179$	−0.185711	+	0.226290i	−0.0138807	+	0.0169137i	0.766024	+	0.642812i	$0.222232\pi$
$180$	4.69459	−	0.826602i	0.349914	−	0.0616113i
$181$	3.73581	+	12.3153i	0.277681	+	0.915390i	0.979227	+	0.202766i	$0.0649932\pi$
$181$	3.73581	+	12.3153i	0.277681	+	0.915390i	−0.701547	+	0.712624i	$0.747507\pi$
$182$	0.0495587	−	0.823369i	0.00367353	−	0.0610321i
$183$	−8.02684	−	5.36336i	−0.593361	−	0.396471i
$184$	2.82715	+	8.81000i	0.208420	+	0.649482i
$185$	−1.84438	−	2.76031i	−0.135601	−	0.202942i
$186$	1.63097	−	6.21931i	0.119588	−	0.456022i
$187$	32.6333	−	26.7815i	2.38639	−	1.95846i
$188$	−9.43500	−	18.6288i	−0.688118	−	1.35864i
$189$	−2.80847	−	5.25427i	−0.204286	−	0.382192i
$190$	−7.13195	−	6.60877i	−0.517406	−	0.479450i
$191$			14.5901i			1.05570i	0.849336	+	0.527852i	$0.177003\pi$
$191$			14.5901i			1.05570i	−0.849336	+	0.527852i	$0.822997\pi$
$192$	−4.72602	+	4.13849i	−0.341071	+	0.298670i
$193$			1.16804i			0.0840776i	0.999116	+	0.0420388i	$0.0133853\pi$
$193$			1.16804i			0.0840776i	−0.999116	+	0.0420388i	$0.986615\pi$
$194$	2.47207	−	2.66777i	0.177484	−	0.191535i
$195$	−0.153189	−	0.286597i	−0.0109701	−	0.0205236i
$196$	3.12175	−	9.52905i	0.222982	−	0.680646i
$197$	−21.5629	+	17.6963i	−1.53630	+	1.26081i	−0.697106	+	0.716968i	$0.745529\pi$
$197$	−21.5629	+	17.6963i	−1.53630	+	1.26081i	−0.839190	+	0.543838i	$0.816971\pi$
$198$	19.2002	+	5.03510i	1.36450	+	0.357829i
$199$	13.1703	+	19.7107i	0.933616	+	1.39725i	0.917653	+	0.397382i	$0.130081\pi$
$199$	13.1703	+	19.7107i	0.933616	+	1.39725i	0.0159625	+	0.999873i	$0.494919\pi$
$200$	−2.81888	−	0.232173i	−0.199325	−	0.0164171i
$201$	4.61964	+	3.08675i	0.325845	+	0.217722i
$202$	7.04360	+	0.423955i	0.495586	+	0.0298294i
$203$	0.229588	+	0.756849i	0.0161139	+	0.0531204i
$204$	−6.45973	+	9.22066i	−0.452272	+	0.645576i
$205$	0.136471	−	0.166290i	0.00953153	−	0.0116142i
$206$	5.35370	+	0.854600i	0.373010	+	0.0595428i
$207$	−2.98367	+	7.20322i	−0.207380	+	0.500659i
$208$	−1.42408	−	0.843978i	−0.0987424	−	0.0585193i
$209$	−15.4942	−	37.4063i	−1.07176	−	2.58745i
$210$	0.363518	+	1.52229i	0.0250852	+	0.105048i
$211$	−7.80269	+	0.768498i	−0.537160	+	0.0529056i	−0.362960	−	0.931805i	$-0.618234\pi$
$211$	−7.80269	+	0.768498i	−0.537160	+	0.0529056i	−0.174200	+	0.984710i	$0.555734\pi$
$212$	−4.21427	−	10.8448i	−0.289437	−	0.744824i
$213$	−7.71173	−	4.12201i	−0.528399	−	0.282435i
$214$	−2.69615	−	1.31177i	−0.184305	−	0.0896707i
$215$	0.358961	+	1.80462i	0.0244809	+	0.123074i
$216$	−11.9549	+	0.191256i	−0.813431	+	0.0130133i
$217$	−8.00325	−	1.59195i	−0.543296	−	0.108068i
$218$	−0.451453	+	0.0618856i	−0.0305762	+	0.00419142i
$219$	0.0853901	+	0.00841019i	0.00577013	+	0.000568308i
$220$	−10.2621	−	5.77981i	−0.691873	−	0.389675i
$221$	−2.83900	−	0.861201i	−0.190972	−	0.0579307i
$222$	1.53938	+	3.34984i	0.103316	+	0.224827i
$223$	4.07303	−	4.07303i	0.272750	−	0.272750i	−0.557456	−	0.830206i	$-0.688223\pi$
$223$	4.07303	−	4.07303i	0.272750	−	0.272750i	0.830206	+	0.557456i	$0.188223\pi$
$224$	5.60318	+	5.67155i	0.374379	+	0.378947i
$225$	−1.68532	−	1.68532i	−0.112355	−	0.112355i
$226$	−8.89832	+	24.0302i	−0.591908	+	1.59846i
$227$	−3.36853	+	11.1046i	−0.223577	+	0.737036i	0.771347	+	0.636414i	$0.219583\pi$
$227$	−3.36853	+	11.1046i	−0.223577	+	0.737036i	−0.994925	+	0.100622i	$0.967917\pi$
$228$	6.66412	+	8.49569i	0.441342	+	0.562641i
$229$	−1.05724	+	10.7344i	−0.0698646	+	0.709348i	0.894906	+	0.446255i	$0.147243\pi$
$229$	−1.05724	+	10.7344i	−0.0698646	+	0.709348i	−0.964771	+	0.263093i	$0.915257\pi$
$230$	2.79667	−	3.68522i	0.184407	−	0.242996i
$231$	−1.27144	+	6.39198i	−0.0836549	+	0.420561i
$232$	1.56151	+	0.284716i	0.102518	+	0.0186925i
$233$	−20.2698	+	4.03190i	−1.32792	+	0.264139i	−0.807547	−	0.589803i	$-0.799205\pi$
$233$	−20.2698	+	4.03190i	−1.32792	+	0.264139i	−0.520368	+	0.853942i	$0.674205\pi$
$234$	−0.455422	−	1.31849i	−0.0297719	−	0.0861925i
$235$	−4.92181	+	9.20807i	−0.321064	+	0.600668i
$236$	−4.92280	+	4.71026i	−0.320447	+	0.306612i
$237$	−0.0856107	−	0.869220i	−0.00556101	−	0.0564619i
$238$	12.1737	+	7.48037i	0.789103	+	0.484881i
$239$	−6.40720	+	2.65395i	−0.414448	+	0.171670i	−0.580157	−	0.814505i	$-0.697009\pi$
$239$	−6.40720	+	2.65395i	−0.414448	+	0.171670i	0.165709	+	0.986175i	$0.447009\pi$
$240$	3.05058	+	0.748048i	0.196914	+	0.0482863i
$241$	−26.4315	−	10.9483i	−1.70260	−	0.705240i	−0.702620	−	0.711566i	$-0.747986\pi$
$241$	−26.4315	−	10.9483i	−1.70260	−	0.705240i	−0.999980	+	0.00632586i	$0.997986\pi$
$242$	−19.6507	−	27.1160i	−1.26319	−	1.74308i
$243$	−12.1284	−	9.95353i	−0.778038	−	0.638520i
$244$	13.2062	+	20.7407i	0.845439	+	1.32779i
$245$	−4.79779	+	1.45539i	−0.306520	+	0.0929818i
$246$	−0.178764	+	0.158466i	−0.0113976	+	0.0101035i
$247$	−1.58079	+	2.36581i	−0.100583	+	0.150533i
$248$	−10.1851	+	12.8235i	−0.646756	+	0.814295i
$249$	2.79586	−	1.86813i	0.177180	−	0.118388i
$250$	0.713627	+	1.22096i	0.0451338	+	0.0772201i
$251$	−8.55593	−	10.4254i	−0.540045	−	0.658047i	0.429469	−	0.903082i	$-0.358701\pi$
$251$	−8.55593	−	10.4254i	−0.540045	−	0.658047i	−0.969514	+	0.245034i	$0.921201\pi$
$252$	0.510856	+	6.69873i	0.0321809	+	0.421980i
$253$	16.9895	−	9.08106i	1.06812	−	0.570921i
$254$	1.06201	+	27.8922i	0.0666365	+	1.75011i
$255$	5.62914			0.352510
$256$	15.2642	−	4.79641i	0.954010	−	0.299775i
$257$	−5.83645			−0.364067			−0.182034	−	0.983292i	$-0.558268\pi$
$257$	−5.83645			−0.364067			−0.182034	+	0.983292i	$0.558268\pi$
$258$	−0.0777427	−	2.04180i	−0.00484005	−	0.127117i
$259$	4.12635	−	2.20558i	0.256399	−	0.137048i
$260$	0.0629386	+	0.825298i	0.00390329	+	0.0511828i
$261$	0.848508	+	1.03391i	0.0525213	+	0.0639974i
$262$	−9.31484	−	15.9369i	−0.575473	−	0.984586i
$263$	12.8116	−	8.56044i	0.789998	−	0.527860i	−0.0938768	−	0.995584i	$-0.529926\pi$
$263$	12.8116	−	8.56044i	0.789998	−	0.527860i	0.883874	+	0.467724i	$0.154926\pi$
$264$	10.2418	+	8.13459i	0.630340	+	0.500649i
$265$	−3.23199	+	4.83701i	−0.198539	+	0.297135i
$266$	10.2546	−	9.09020i	0.628747	−	0.557356i
$267$	−11.4740	+	3.48059i	−0.702195	+	0.213009i
$268$	−7.60048	−	11.9368i	−0.464273	−	0.729155i
$269$	−24.8273	−	20.3752i	−1.51375	−	1.24230i	−0.885820	−	0.464028i	$-0.846404\pi$
$269$	−24.8273	−	20.3752i	−1.51375	−	1.24230i	−0.627927	−	0.778272i	$-0.716096\pi$
$270$	3.50805	+	4.84075i	0.213493	+	0.294599i
$271$	−0.354591	−	0.146876i	−0.0215398	−	0.00892210i	0.371888	−	0.928278i	$-0.378711\pi$
$271$	−0.354591	−	0.146876i	−0.0215398	−	0.00892210i	−0.393427	+	0.919356i	$0.628711\pi$
$272$	24.5217	−	14.8638i	1.48685	−	0.901248i
$273$	0.423137	−	0.175269i	0.0256094	−	0.0106078i
$274$	7.57326	+	4.65354i	0.457517	+	0.281131i
$275$	0.577215	+	5.86056i	0.0348074	+	0.353405i
$276$	−3.71196	+	3.55169i	−0.223434	+	0.213787i
$277$	11.1201	−	20.8042i	0.668141	−	1.25000i	−0.288150	−	0.957585i	$-0.593040\pi$
$277$	11.1201	−	20.8042i	0.668141	−	1.25000i	0.956290	−	0.292418i	$-0.0944600\pi$
$278$	−6.83258	−	19.7810i	−0.409791	−	1.18638i
$279$	−13.5344	+	2.69216i	−0.810284	+	0.161175i
$280$	0.715048	−	3.92164i	0.0427323	−	0.234363i
$281$	1.47345	−	7.40756i	0.0878989	−	0.441898i	−0.911624	−	0.411024i	$-0.865171\pi$
$281$	1.47345	−	7.40756i	0.0878989	−	0.441898i	0.999523	−	0.0308734i	$-0.00982888\pi$
$282$	7.00918	−	9.23611i	0.417391	−	0.550002i
$283$	2.85954	−	29.0334i	0.169982	−	1.72586i	−0.410740	−	0.911753i	$-0.634729\pi$
$283$	2.85954	−	29.0334i	0.169982	−	1.72586i	0.580721	−	0.814102i	$-0.302771\pi$
$284$	13.7457	+	17.5236i	0.815659	+	1.03984i
$285$	1.56718	−	5.16631i	0.0928319	−	0.306026i
$286$	−1.19685	+	3.23212i	−0.0707711	+	0.191119i
$287$	0.214383	+	0.214383i	0.0126546	+	0.0126546i
$288$	12.4247	+	5.23499i	0.732135	+	0.308474i
$289$	24.3176	−	24.3176i	1.43045	−	1.43045i
$290$	−0.331384	−	0.721127i	−0.0194596	−	0.0423461i
$291$	1.93250	+	0.586219i	0.113285	+	0.0343648i
$292$	−0.190416	−	0.107246i	−0.0111433	−	0.00627608i
$293$	2.58997	+	0.255090i	0.151308	+	0.0149025i	0.173387	−	0.984854i	$-0.444529\pi$
$293$	2.58997	+	0.255090i	0.151308	+	0.0149025i	−0.0220797	+	0.999756i	$0.507029\pi$
$294$	5.51608	−	0.756150i	0.321704	−	0.0440996i
$295$	3.34117	+	0.664600i	0.194531	+	0.0386945i
$296$	−0.150200	−	9.38860i	−0.00873018	−	0.545701i
$297$	4.85657	+	24.4156i	0.281807	+	1.41674i
$298$	−6.07633	−	2.95634i	−0.351992	−	0.171256i
$299$	−1.19394	−	0.638177i	−0.0690476	−	0.0369067i
$300$	−0.568843	−	1.46384i	−0.0328422	−	0.0845146i
$301$	−2.58071	+	0.254178i	−0.148750	+	0.0146506i
$302$	−0.385581	−	1.61468i	−0.0221877	−	0.0929147i
$303$	1.49936	+	3.61978i	0.0861360	+	0.207951i
$304$	−6.81469	−	26.6437i	−0.390849	−	1.52812i
$305$	4.70475	−	11.3583i	0.269393	−	0.650372i
$306$	23.8610	+	3.80888i	1.36404	+	0.217739i
$307$	−16.7286	+	20.3838i	−0.954751	+	1.16337i	0.0317305	+	0.999496i	$0.489898\pi$
$307$	−16.7286	+	20.3838i	−0.954751	+	1.16337i	−0.986482	+	0.163871i	$0.947602\pi$
$308$	9.52429	−	13.5950i	0.542697	−	0.774649i
$309$	0.873833	+	2.88064i	0.0497106	+	0.163874i
$310$	8.17331	+	0.491953i	0.464213	+	0.0279410i
$311$	−26.5679	−	17.7521i	−1.50653	−	1.00663i	−0.988492	−	0.151270i	$-0.951664\pi$
$311$	−26.5679	−	17.7521i	−1.50653	−	1.00663i	−0.518035	−	0.855359i	$-0.673336\pi$
$312$	0.0754490	−	0.916048i	0.00427146	−	0.0518610i
$313$	14.3829	+	21.5256i	0.812971	+	1.21670i	0.973278	+	0.229630i	$0.0737517\pi$
$313$	14.3829	+	21.5256i	0.812971	+	1.21670i	−0.160307	+	0.987067i	$0.551248\pi$
$314$	1.45659	+	0.381981i	0.0822004	+	0.0215564i
$315$	2.59661	−	2.13098i	0.146302	−	0.120067i
$316$	−0.692573	+	2.11406i	−0.0389603	+	0.118925i
$317$	9.31705	+	17.4310i	0.523298	+	0.979021i	0.995246	+	0.0973948i	$0.0310509\pi$
$317$	9.31705	+	17.4310i	0.523298	+	0.979021i	−0.471948	+	0.881626i	$0.656449\pi$
$318$	4.39095	−	4.73856i	0.246232	−	0.265725i
$319$		−	3.30473i		−	0.185029i
$320$	−6.34326	−	4.87473i	−0.354599	−	0.272506i
$321$		−	1.66481i		−	0.0929209i
$322$	4.78248	+	4.43165i	0.266517	+	0.246966i
$323$	−23.2338	−	43.4675i	−1.29277	−	2.41859i
$324$	3.46173	+	6.83496i	0.192318	+	0.379720i
$325$	0.319908	−	0.262542i	0.0177453	−	0.0145632i
$326$	−1.26705	+	4.83160i	−0.0701754	+	0.267598i
$327$	−0.140566	−	0.210372i	−0.00777332	−	0.0116336i
$328$	0.579352	−	0.185915i	0.0319894	−	0.0102655i
$329$	−12.2352	−	8.17527i	−0.674546	−	0.450717i
$330$	0.392909	−	6.52780i	0.0216289	−	0.359344i
$331$	4.04495	+	13.3344i	0.222330	+	0.732925i	0.995156	+	0.0983067i	$0.0313426\pi$
$331$	4.04495	+	13.3344i	0.222330	+	0.732925i	−0.772826	+	0.634618i	$0.781157\pi$
$332$	−8.43466	+	1.48514i	−0.462912	+	0.0815075i
$333$	5.01958	−	6.11637i	0.275071	−	0.335175i
$334$	0.833070	−	5.21883i	0.0455836	−	0.285561i
$335$	−2.70770	+	6.53696i	−0.147937	+	0.357152i
$336$	−1.47061	+	4.17534i	−0.0802284	+	0.227784i
$337$	8.07024	+	19.4833i	0.439614	+	1.06132i	0.976082	+	0.217402i	$0.0697581\pi$
$337$	8.07024	+	19.4833i	0.439614	+	1.06132i	−0.536468	+	0.843921i	$0.680242\pi$
$338$	−17.6464	+	4.21390i	−0.959838	+	0.229206i
$339$	−14.1596	+	1.39460i	−0.769043	+	0.0757441i
$340$	−13.1218	−	5.77754i	−0.711628	−	0.313331i
$341$	30.0700	+	16.0728i	1.62838	+	0.870389i
$342$	10.1387	−	20.8387i	0.548241	−	1.12683i
$343$	−3.30321	−	16.6064i	−0.178357	−	0.896659i
$344$	−1.91441	+	4.83933i	−0.103218	+	0.260919i
$345$	2.51936	+	0.501131i	0.135638	+	0.0269800i
$346$	1.99685	+	14.5670i	0.107352	+	0.783125i
$347$	24.7956	+	2.44216i	1.33110	+	0.131102i	0.738422	−	0.674339i	$-0.235571\pi$
$347$	24.7956	+	2.44216i	1.33110	+	0.131102i	0.592677	+	0.805440i	$0.298071\pi$
$348$	0.237167	+	0.848805i	0.0127135	+	0.0455007i
$349$	5.44858	+	1.65281i	0.291656	+	0.0884728i	0.432722	−	0.901527i	$-0.357553\pi$
$349$	5.44858	+	1.65281i	0.291656	+	0.0884728i	−0.141067	+	0.990000i	$0.545053\pi$
$350$	−1.81107	+	0.832255i	−0.0968060	+	0.0444859i
$351$	1.23704	−	1.23704i	0.0660282	−	0.0660282i
$352$	−15.5251	−	29.4739i	−0.827490	−	1.57096i
$353$	2.25780	+	2.25780i	0.120171	+	0.120171i	0.764635	−	0.644464i	$-0.222919\pi$
$353$	2.25780	+	2.25780i	0.120171	+	0.120171i	−0.644464	+	0.764635i	$0.722919\pi$
$354$	−3.54763	−	1.31368i	−0.188554	−	0.0698213i
$355$	3.23255	−	10.6563i	0.171566	−	0.565577i
$356$	30.3187	+	3.66304i	1.60689	+	0.194141i
$357$	−0.777622	+	7.89532i	−0.0411561	+	0.417865i
$358$	0.329783	+	0.250269i	0.0174296	+	0.0132271i
$359$	6.64235	−	33.3934i	0.350570	−	1.76243i	−0.255291	−	0.966864i	$-0.582171\pi$
$359$	6.64235	−	33.3934i	0.350570	−	1.76243i	0.605861	−	0.795570i	$-0.292829\pi$
$360$	−1.42075	−	6.58986i	−0.0748802	−	0.347316i
$361$	−27.7271	+	5.51526i	−1.45932	+	0.290277i
$362$	17.2029	−	5.94207i	0.904162	−	0.312308i
$363$	8.76513	−	16.3984i	0.460050	−	0.860693i
$364$	−1.16624	−	0.0257320i	−0.0611277	−	0.00134872i
$365$	0.0107104	+	0.108744i	0.000560606	+	0.00569193i
$366$	−7.14754	+	11.6320i	−0.373608	+	0.608016i
$367$	−32.1833	+	13.3307i	−1.67995	+	0.695859i	−0.999324	−	0.0367699i	$-0.988293\pi$
$367$	−32.1833	+	13.3307i	−1.67995	+	0.695859i	−0.680628	+	0.732629i	$0.738293\pi$
$368$	12.2981	−	4.46934i	0.641082	−	0.232981i
$369$	0.473689	+	0.196209i	0.0246593	+	0.0102142i
$370$	−3.80160	+	2.75498i	−0.197636	+	0.143225i
$371$	−6.33783	−	5.20132i	−0.329044	−	0.270039i
$372$	−8.87682	−	1.97022i	−0.460242	−	0.102151i
$373$	6.64403	−	2.01544i	0.344015	−	0.104356i	−0.113549	−	0.993532i	$-0.536222\pi$
$373$	6.64403	−	2.01544i	0.344015	−	0.104356i	0.457564	+	0.889177i	$0.348722\pi$
$374$	−39.6032	−	44.6760i	−2.04784	−	2.31014i
$375$	−0.436255	+	0.652902i	−0.0225281	+	0.0337157i
$376$	−25.8183	+	14.3358i	−1.33148	+	0.739313i
$377$	−0.193102	+	0.129027i	−0.00994526	+	0.00664521i
$378$	−7.27416	+	4.25162i	−0.374143	+	0.218680i
$379$	−14.0673	−	17.1411i	−0.722590	−	0.880478i	0.274106	−	0.961699i	$-0.411618\pi$
$379$	−14.0673	−	17.1411i	−0.722590	−	0.880478i	−0.996696	+	0.0812212i	$0.974118\pi$
$380$	−8.95569	+	10.4344i	−0.459417	+	0.535274i
$381$	−13.6683	+	7.30584i	−0.700247	+	0.374290i
$382$	20.6186	−	0.785065i	1.05494	−	0.0401674i
$383$	0.866669			0.0442847			0.0221424	−	0.999755i	$-0.492951\pi$
$383$	0.866669			0.0442847			0.0221424	+	0.999755i	$0.492951\pi$
$384$	6.10277	+	6.45607i	0.311431	+	0.329460i
$385$	−8.29966			−0.422990
$386$	1.65067	−	0.0628500i	0.0840167	−	0.00319898i
$387$	−3.86757	+	2.06726i	−0.196600	+	0.105085i
$388$	−3.90308	−	3.34995i	−0.198149	−	0.170068i
$389$	−6.67813	−	8.13733i	−0.338595	−	0.412579i	0.575679	−	0.817676i	$-0.304738\pi$
$389$	−6.67813	−	8.13733i	−0.338595	−	0.412579i	−0.914274	+	0.405097i	$0.867238\pi$
$390$	−0.396773	+	0.231907i	−0.0200914	+	0.0117430i
$391$	19.4985	−	13.0285i	0.986081	−	0.658878i
$392$	−13.6343	−	3.89888i	−0.688637	−	0.196923i
$393$	5.69435	−	8.52220i	0.287242	−	0.429888i
$394$	26.1684	+	29.5203i	1.31835	+	1.48721i
$395$	1.06441	−	0.322886i	0.0535564	−	0.0162461i
$396$	6.08243	−	27.4044i	0.305653	−	1.37712i
$397$	23.6100	+	19.3762i	1.18495	+	0.972466i	0.999947	−	0.0102717i	$-0.00326963\pi$
$397$	23.6100	+	19.3762i	1.18495	+	0.972466i	0.185006	+	0.982737i	$0.440770\pi$
$398$	27.1463	−	19.6727i	1.36072	−	0.986102i
$399$	7.02968	+	2.91179i	0.351924	+	0.145772i
$400$	−0.176426	+	3.99611i	−0.00882131	+	0.199805i
$401$	29.4907	−	12.2155i	1.47270	−	0.610011i	0.505224	−	0.862988i	$-0.331410\pi$
$401$	29.4907	−	12.2155i	1.47270	−	0.610011i	0.967472	+	0.252978i	$0.0814100\pi$
$402$	4.11359	−	6.69452i	0.205167	−	0.333892i
$403$	−0.234861	−	2.38458i	−0.0116992	−	0.118784i
$404$	0.220127	−	9.97676i	0.0109517	−	0.496362i
$405$	1.80583	−	3.37847i	0.0897323	−	0.167877i
$406$	1.05722	−	0.365176i	0.0524689	−	0.0181234i
$407$	−19.1744	+	3.81402i	−0.950438	+	0.189054i
$408$	13.3781	+	8.63268i	0.662316	+	0.427381i
$409$	3.40607	−	17.1235i	0.168419	−	0.846701i	−0.800502	−	0.599330i	$-0.795434\pi$
$409$	3.40607	−	17.1235i	0.168419	−	0.846701i	0.968921	−	0.247370i	$-0.0795664\pi$
$410$	−0.242343	−	0.183911i	−0.0119685	−	0.00908274i
$411$	−0.483758	+	4.91168i	−0.0238620	+	0.242275i
$412$	0.919640	−	7.61178i	0.0453074	−	0.375006i
$413$	−1.39371	+	4.59446i	−0.0685801	+	0.226078i
$414$	10.3401	+	3.82890i	0.508186	+	0.188180i
$415$	3.02798	+	3.02798i	0.148637	+	0.148637i
$416$	−1.11607	+	2.05791i	−0.0547200	+	0.100897i
$417$	8.21663	−	8.21663i	0.402370	−	0.402370i
$418$	−52.0285	+	23.9090i	−2.54480	+	1.16943i
$419$	25.1661	+	7.63407i	1.22945	+	0.372949i	0.837193	−	0.546908i	$-0.184195\pi$
$419$	25.1661	+	7.63407i	1.22945	+	0.372949i	0.392254	+	0.919857i	$0.371695\pi$
$420$	2.13173	−	0.595632i	0.104018	−	0.0290639i
$421$	35.2422	+	3.47105i	1.71760	+	0.169169i	0.908326	−	0.418262i	$-0.137361\pi$
$421$	35.2422	+	3.47105i	1.71760	+	0.169169i	0.809274	+	0.587431i	$0.199861\pi$
$422$	1.50588	+	10.9853i	0.0733051	+	0.534758i
$423$	−24.4067	−	4.85480i	−1.18670	−	0.236049i
$424$	−15.0990	+	6.53909i	−0.733272	+	0.317567i
$425$	1.39854	+	7.03096i	0.0678393	+	0.341051i
$426$	−5.41023	+	11.1199i	−0.262126	+	0.538763i
$427$	15.2810	+	8.16785i	0.739498	+	0.395270i
$428$	−1.70870	+	3.88076i	−0.0825934	+	0.187584i
$429$	−1.90450	+	0.187577i	−0.0919501	+	0.00905629i
$430$	2.53095	−	0.604383i	0.122053	−	0.0291459i
$431$	−10.6420	−	25.6921i	−0.512608	−	1.23754i	−0.942361	−	0.334598i	$-0.891400\pi$
$431$	−10.6420	−	25.6921i	−0.512608	−	1.23754i	0.429753	−	0.902946i	$-0.358600\pi$
$432$	0.913553	+	16.8843i	0.0439533	+	0.812347i
$433$	−5.26618	+	12.7137i	−0.253077	+	0.610981i	−0.998449	−	0.0556668i	$-0.982272\pi$
$433$	−5.26618	+	12.7137i	−0.253077	+	0.610981i	0.745373	+	0.666648i	$0.232272\pi$
$434$	−1.81908	+	11.3958i	−0.0873188	+	0.547015i
$435$	0.279550	−	0.340633i	0.0134034	−	0.0163321i
$436$	0.111748	+	0.634658i	0.00535175	+	0.0303946i
$437$	−6.52879	−	21.5225i	−0.312314	−	1.02956i
$438$	0.00729052	−	0.121125i	0.000348355	−	0.00578757i
$439$	−21.2209	−	14.1794i	−1.01282	−	0.676744i	−0.0657706	−	0.997835i	$-0.520951\pi$
$439$	−21.2209	−	14.1794i	−1.01282	−	0.676744i	−0.947048	+	0.321091i	$0.895951\pi$
$440$	−7.61578	+	14.8133i	−0.363068	+	0.706198i
$441$	−6.63885	−	9.93574i	−0.316136	−	0.473131i
$442$	−1.06428	+	4.05838i	−0.0506226	+	0.193038i
$443$	−1.90665	+	1.56475i	−0.0905878	+	0.0743435i	−0.678597	−	0.734511i	$-0.737412\pi$
$443$	−1.90665	+	1.56475i	−0.0905878	+	0.0743435i	0.588009	+	0.808854i	$0.299912\pi$
$444$	4.65113	−	2.35568i	0.220733	−	0.111796i
$445$	−7.19803	−	13.4666i	−0.341220	−	0.638377i
$446$	−5.97513	−	5.53680i	−0.282930	−	0.262175i
$447$		−	3.75200i		−	0.177463i
$448$	7.71348	−	8.22354i	0.364428	−	0.388526i
$449$			16.1175i			0.760632i	0.924857	+	0.380316i	$0.124185\pi$
$449$			16.1175i			0.760632i	−0.924857	+	0.380316i	$0.875815\pi$
$450$	−2.29099	+	2.47236i	−0.107998	+	0.116548i
$451$	−0.597177	−	1.11724i	−0.0281200	−	0.0526088i
$452$	34.4380	+	11.2820i	1.61983	+	0.530661i
$453$	0.712528	−	0.584757i	0.0334775	−	0.0274743i
$454$	15.8741	+	4.16286i	0.745009	+	0.195373i
$455$	0.324044	+	0.484966i	0.0151914	+	0.0227355i
$456$	11.6474	−	9.87479i	0.545441	−	0.462430i
$457$	−21.4354	−	14.3227i	−1.00271	−	0.669988i	−0.0581416	−	0.998308i	$-0.518517\pi$
$457$	−21.4354	−	14.3227i	−1.00271	−	0.669988i	−0.944566	+	0.328320i	$0.893517\pi$
$458$	15.2266	+	0.916491i	0.711492	+	0.0428248i
$459$	8.79676	+	28.9990i	0.410598	+	1.35356i
$460$	−5.35839	−	3.75394i	−0.249836	−	0.175028i
$461$	−12.4741	+	15.1997i	−0.580975	+	0.707920i	−0.977697	−	0.210019i	$-0.932648\pi$
$461$	−12.4741	+	15.1997i	−0.580975	+	0.707920i	0.396722	+	0.917939i	$0.370148\pi$
$462$	9.10149	+	1.45285i	0.423440	+	0.0675928i
$463$	−11.6047	+	28.0162i	−0.539315	+	1.30202i	0.385886	+	0.922546i	$0.373896\pi$
$463$	−11.6047	+	28.0162i	−0.539315	+	1.30202i	−0.925202	+	0.379476i	$0.876104\pi$
$464$	0.318336	−	2.22202i	0.0147784	−	0.103155i
$465$	1.73984	+	4.20034i	0.0806831	+	0.194786i
$466$	6.78852	+	28.4281i	0.314472	+	1.31690i
$467$	12.6835	−	1.24922i	0.586922	−	0.0578068i	0.199802	−	0.979836i	$-0.435970\pi$
$467$	12.6835	−	1.24922i	0.586922	−	0.0578068i	0.387120	+	0.922029i	$0.373470\pi$
$468$	−1.83877	+	0.714543i	−0.0849973	+	0.0330298i
$469$	−8.79458	−	4.70080i	−0.406096	−	0.217063i
$470$	13.2776	+	6.45999i	0.612449	+	0.297977i
$471$	0.163118	+	0.820052i	0.00751610	+	0.0377860i
$472$	6.92137	+	6.70340i	0.318582	+	0.308549i
$473$	10.6273	+	2.11389i	0.488642	+	0.0971969i
$474$	−1.22377	+	0.167755i	−0.0562094	+	0.00770525i
$475$	6.84223	+	0.673901i	0.313943	+	0.0309207i
$476$	9.91614	−	17.6062i	0.454506	−	0.806981i
$477$	−13.2682	−	4.02487i	−0.607510	−	0.184286i
$478$	4.09529	+	8.91179i	0.187314	+	0.407616i
$479$	−24.4907	+	24.4907i	−1.11901	+	1.11901i	−0.127120	+	0.991887i	$0.540573\pi$
$479$	−24.4907	+	24.4907i	−1.11901	+	1.11901i	−0.991887	+	0.127120i	$0.959427\pi$
$480$	0.892988	−	4.35129i	0.0407591	−	0.198608i
$481$	0.971486	+	0.971486i	0.0442959	+	0.0442959i
$482$	−14.0498	+	37.9418i	−0.639949	+	1.72820i
$483$	−1.05091	+	3.46438i	−0.0478179	+	0.157635i
$484$	−37.2626	+	29.2292i	−1.69376	+	1.32860i
$485$	−0.252079	+	2.55940i	−0.0114463	+	0.116216i
$486$	−13.4136	+	17.6753i	−0.608454	+	0.801769i
$487$	5.88264	−	29.5740i	0.266568	−	1.34013i	−0.582925	−	0.812526i	$-0.698092\pi$
$487$	5.88264	−	29.5740i	0.266568	−	1.34013i	0.849493	−	0.527600i	$-0.176908\pi$
$488$	28.5999	−	19.7788i	1.29466	−	0.895346i
$489$	−2.72016	+	0.541073i	−0.123010	+	0.0244681i
$490$	2.31491	+	6.70188i	0.104577	+	0.302760i
$491$	−10.5992	+	19.8297i	−0.478334	+	0.894901i	0.520815	+	0.853669i	$0.325628\pi$
$491$	−10.5992	+	19.8297i	−0.478334	+	0.894901i	−0.999150	+	0.0412313i	$0.986872\pi$
$492$	0.233562	+	0.244101i	0.0105298	+	0.0110049i
$493$	−0.394314	−	4.00354i	−0.0177590	−	0.180310i
$494$	3.42840	+	2.10665i	0.154251	+	0.0947827i
$495$	−12.9673	+	5.37121i	−0.582835	+	0.241418i
$496$	18.6701	+	13.7035i	0.838314	+	0.615306i
$497$	14.4998	+	6.00599i	0.650403	+	0.269406i
$498$	−2.79047	−	3.85056i	−0.125044	−	0.172548i
$499$	8.19671	+	6.72687i	0.366935	+	0.301136i	0.799734	−	0.600355i	$-0.204974\pi$
$499$	8.19671	+	6.72687i	0.366935	+	0.301136i	−0.432799	+	0.901491i	$0.642474\pi$
$500$	1.68704	−	1.07419i	0.0754469	−	0.0480391i
$501$	2.80807	−	0.851819i	0.125455	−	0.0380565i
$502$	−14.2727	+	12.6521i	−0.637023	+	0.564692i
$503$	5.52142	−	8.26338i	0.246188	−	0.368446i	−0.687710	−	0.725985i	$-0.741384\pi$
$503$	5.52142	−	8.26338i	0.246188	−	0.368446i	0.933898	+	0.357539i	$0.116384\pi$
$504$	9.43908	−	1.08238i	0.420450	−	0.0482131i
$505$	−4.14869	+	2.77207i	−0.184614	+	0.123355i
$506$	−13.7474	−	23.5207i	−0.611148	−	1.04562i
$507$	−6.39063	−	7.78701i	−0.283818	−	0.345833i
$508$	39.3598	−	3.00164i	1.74631	−	0.133176i
$509$	−2.94179	+	1.57242i	−0.130393	+	0.0696964i	−0.535303	−	0.844660i	$-0.679803\pi$
$509$	−2.94179	+	1.57242i	−0.130393	+	0.0696964i	0.404911	+	0.914356i	$0.367303\pi$
$510$	−0.302892	−	7.95504i	−0.0134123	−	0.352255i
$511$	−0.154002			−0.00681265
$512$	−7.59957	−	21.3131i	−0.335857	−	0.941913i
$513$	29.0638			1.28320
$514$	0.314047	+	8.24800i	0.0138520	+	0.363804i
$515$	−3.38090	+	1.80713i	−0.148980	+	0.0796317i
$516$	−2.88127	+	0.219730i	−0.126841	+	0.00967309i
$517$	39.0061	+	47.5291i	1.71549	+	2.09033i
$518$	−3.33893	−	5.71263i	−0.146704	−	0.250999i
$519$	−6.78804	+	4.53562i	−0.297962	+	0.199092i
$520$	1.16292	−	0.133352i	0.0509972	−	0.00584786i
$521$	−10.0179	+	14.9929i	−0.438894	+	0.656851i	−0.983304	−	0.181968i	$-0.941753\pi$
$521$	−10.0179	+	14.9929i	−0.438894	+	0.656851i	0.544411	+	0.838819i	$0.316753\pi$
$522$	1.41545	−	1.25474i	0.0619527	−	0.0549183i
$523$	−5.87163	+	1.78114i	−0.256748	+	0.0778838i	−0.416035	−	0.909349i	$-0.636581\pi$
$523$	−5.87163	+	1.78114i	−0.256748	+	0.0778838i	0.159287	+	0.987232i	$0.449081\pi$
$524$	−22.0207	+	14.0212i	−0.961977	+	0.612517i
$525$	−0.855483	−	0.702076i	−0.0373363	−	0.0306411i
$526$	−12.7869	−	17.6446i	−0.557535	−	0.769342i
$527$	38.3463	+	15.8836i	1.67039	+	0.691899i
$528$	10.9446	−	14.9113i	0.476303	−	0.648932i
$529$	−11.3627	+	4.70658i	−0.494030	+	0.204634i
$530$	7.00952	+	4.30714i	0.304474	+	0.187090i
$531$	0.795837	+	8.08027i	0.0345364	+	0.350654i
$532$	−13.3979	−	14.0025i	−0.580875	−	0.607086i
$533$	−0.0419670	+	0.0785147i	−0.00181779	+	0.00340085i
$534$	5.53612	+	16.0276i	0.239571	+	0.693582i
$535$	2.07940	−	0.413619i	0.0899004	−	0.0178823i
$536$	−16.4600	+	11.3832i	−0.710962	+	0.491680i
$537$	−0.0448452	+	0.225452i	−0.00193521	+	0.00972898i
$538$	−27.4582	+	36.1820i	−1.18381	+	1.55992i
$539$	−2.89397	+	29.3830i	−0.124652	+	1.26562i
$540$	6.65214	−	5.21801i	0.286263	−	0.224548i
$541$	−9.75368	+	32.1536i	−0.419343	+	1.38239i	0.452132	+	0.891951i	$0.350664\pi$
$541$	−9.75368	+	32.1536i	−0.419343	+	1.38239i	−0.871475	+	0.490439i	$0.836836\pi$
$542$	−0.188484	+	0.509007i	−0.00809609	+	0.0218637i
$543$	7.14574	+	7.14574i	0.306653	+	0.306653i
$544$	−22.3248	−	33.8540i	−0.957167	−	1.45148i
$545$	0.227837	−	0.227837i	0.00975948	−	0.00975948i
$546$	−0.270457	−	0.588542i	−0.0115745	−	0.0251873i
$547$	3.27374	+	0.993079i	0.139975	+	0.0424610i	0.359495	−	0.933147i	$-0.382949\pi$
$547$	3.27374	+	0.993079i	0.139975	+	0.0424610i	−0.219520	+	0.975608i	$0.570449\pi$
$548$	6.16883	−	10.9528i	0.263520	−	0.467882i
$549$	29.1607	+	2.87208i	1.24455	+	0.122577i
$550$	8.25103	−	1.13106i	0.351825	−	0.0482285i
$551$	−3.78415	−	0.752714i	−0.161210	−	0.0320667i
$552$	5.21895	+	5.05459i	0.222133	+	0.215138i
$553$	0.305833	+	1.53753i	0.0130054	+	0.0653823i
$554$	−29.9986	−	14.5954i	−1.27452	−	0.620097i
$555$	−2.29902	−	1.22885i	−0.0975879	−	0.0521618i
$556$	−27.5866	+	10.7201i	−1.16993	+	0.454633i
$557$	3.51226	−	0.345927i	0.148819	−	0.0146574i	−0.0233332	−	0.999728i	$-0.507428\pi$
$557$	3.51226	−	0.345927i	0.148819	−	0.0146574i	0.172152	+	0.985070i	$0.444928\pi$
$558$	4.53279	+	18.9818i	0.191888	+	0.803565i
$559$	−0.291401	−	0.703505i	−0.0123250	−	0.0297551i
$560$	−5.58049	−	0.799483i	−0.235819	−	0.0337843i
$561$	12.6858	−	30.6262i	0.535594	−	1.29304i
$562$	−10.5476	−	1.68369i	−0.444922	−	0.0710220i
$563$	−13.8271	+	16.8483i	−0.582741	+	0.710073i	−0.978025	−	0.208487i	$-0.933146\pi$
$563$	−13.8271	+	16.8483i	−0.582741	+	0.710073i	0.395284	+	0.918559i	$0.370646\pi$
$564$	−13.4295	−	9.40833i	−0.565485	−	0.396162i
$565$	−5.25980	−	17.3392i	−0.221281	−	0.729467i
$566$	−41.1835	−	2.47884i	−1.73107	−	0.104194i
$567$	4.48911	+	2.99953i	0.188525	+	0.125968i
$568$	24.0246	−	20.3682i	1.00805	−	0.854632i
$569$	16.8705	+	25.2485i	0.707249	+	1.05847i	0.994913	+	0.100741i	$0.0321214\pi$
$569$	16.8705	+	25.2485i	0.707249	+	1.05847i	−0.287664	+	0.957731i	$0.592879\pi$
$570$	−7.38530	−	1.93674i	−0.309336	−	0.0811210i
$571$	−16.5942	+	13.6185i	−0.694446	+	0.569917i	−0.914015	−	0.405680i	$-0.867035\pi$
$571$	−16.5942	+	13.6185i	−0.694446	+	0.569917i	0.219570	+	0.975597i	$0.429535\pi$
$572$	4.63200	+	1.51746i	0.193674	+	0.0634481i
$573$	5.40066	+	10.1039i	0.225616	+	0.422098i
$574$	0.291428	−	0.314500i	0.0121640	−	0.0131270i
$575$			3.27125i			0.136421i
$576$	6.72948	−	17.8402i	0.280395	−	0.743341i
$577$		−	26.7516i		−	1.11368i	−0.830619	−	0.556841i	$-0.812013\pi$
$577$		−	26.7516i		−	1.11368i	0.830619	−	0.556841i	$-0.187987\pi$
$578$	−35.6738	−	33.0569i	−1.48384	−	1.37498i
$579$	0.432361	+	0.808891i	0.0179683	+	0.0336164i
$580$	−1.00126	+	0.507111i	−0.0415750	+	0.0210567i
$581$	−4.66527	+	3.82869i	−0.193548	+	0.158841i
$582$	0.724454	−	2.76254i	0.0300296	−	0.114511i
$583$	19.0329	+	28.4848i	0.788263	+	1.17972i
$584$	−0.141313	+	0.274865i	−0.00584756	+	0.0113740i
$585$	0.820132	+	0.547995i	0.0339083	+	0.0226568i
$586$	0.221129	−	3.67384i	0.00913476	−	0.151765i
$587$	−3.34417	−	11.0242i	−0.138028	−	0.455019i	0.860488	−	0.509471i	$-0.170159\pi$
$587$	−3.34417	−	11.0242i	−0.138028	−	0.455019i	−0.998516	+	0.0544519i	$0.982659\pi$
$588$	−1.36539	−	7.75458i	−0.0563078	−	0.319793i
$589$	25.2535	−	30.7714i	1.04055	−	1.26791i
$590$	0.759425	−	4.75747i	0.0312650	−	0.195862i
$591$	−8.38231	+	20.2367i	−0.344802	+	0.832426i
$592$	−13.2598	+	0.717442i	−0.544974	+	0.0294867i
$593$	14.8849	+	35.9354i	0.611251	+	1.47569i	0.861627	+	0.507543i	$0.169446\pi$
$593$	14.8849	+	35.9354i	0.611251	+	1.47569i	−0.250375	+	0.968149i	$0.580554\pi$
$594$	34.2426	−	8.17701i	1.40499	−	0.335507i
$595$	−10.0547	+	0.990300i	−0.412202	+	0.0405984i
$596$	−3.85091	+	8.74607i	−0.157739	+	0.358253i
$597$	16.4167	+	8.77493i	0.671893	+	0.359134i
$598$	−0.837621	+	1.72161i	−0.0342529	+	0.0704018i
$599$	−5.92524	−	29.7882i	−0.242099	−	1.21711i	−0.890204	−	0.455562i	$-0.849438\pi$
$599$	−5.92524	−	29.7882i	−0.242099	−	1.21711i	0.648105	−	0.761551i	$-0.275562\pi$
$600$	−2.03807	+	0.882650i	−0.0832038	+	0.0360340i
$601$	1.29688	+	0.257965i	0.0529007	+	0.0105226i	0.221470	−	0.975167i	$-0.428915\pi$
$601$	1.29688	+	0.257965i	0.0529007	+	0.0105226i	−0.168569	+	0.985690i	$0.553915\pi$
$602$	0.498065	+	3.63336i	0.0202996	+	0.148085i
$603$	−16.7827	−	1.65295i	−0.683444	−	0.0673133i
$604$	−2.26111	+	0.631782i	−0.0920032	+	0.0257068i
$605$	22.6597	+	6.87376i	0.921250	+	0.279458i
$606$	5.03475	−	2.31365i	0.204523	−	0.0939858i
$607$	22.3313	−	22.3313i	0.906399	−	0.906399i	−0.0895803	−	0.995980i	$-0.528553\pi$
$607$	22.3313	−	22.3313i	0.906399	−	0.906399i	0.995980	+	0.0895803i	$0.0285526\pi$
$608$	−37.2859	+	11.0641i	−1.51214	+	0.448708i
$609$	0.439148	+	0.439148i	0.0177952	+	0.0177952i
$610$	−16.3045	−	6.03754i	−0.660151	−	0.244453i
$611$	1.25430	−	4.13489i	0.0507437	−	0.167280i
$612$	4.09876	−	33.9251i	0.165682	−	1.37134i
$613$	2.43903	−	24.7639i	0.0985116	−	1.00021i	−0.811145	−	0.584845i	$-0.801155\pi$
$613$	2.43903	−	24.7639i	0.0985116	−	1.00021i	0.909657	−	0.415361i	$-0.136345\pi$
$614$	29.7064	+	22.5439i	1.19885	+	0.909796i
$615$	0.0329548	−	0.165675i	0.00132886	−	0.00668065i
$616$	−19.7248	−	12.7281i	−0.794737	−	0.512830i
$617$	22.8367	−	4.54250i	0.919371	−	0.182874i	0.287350	−	0.957826i	$-0.407226\pi$
$617$	22.8367	−	4.54250i	0.919371	−	0.182874i	0.632021	+	0.774951i	$0.282226\pi$
$618$	4.02387	−	1.38989i	0.161864	−	0.0559097i
$619$	15.2465	−	28.5242i	0.612809	−	1.14649i	−0.363803	−	0.931476i	$-0.618522\pi$
$619$	15.2465	−	28.5242i	0.612809	−	1.14649i	0.976612	−	0.215010i	$-0.0689782\pi$
$620$	0.255433	−	11.5769i	0.0102584	−	0.464940i
$621$	1.35542	+	13.7618i	0.0543912	+	0.552243i
$622$	−23.6575	+	38.5007i	−0.948580	+	1.54374i
$623$	19.8823	−	8.23553i	0.796568	−	0.329949i
$624$	−1.29861	−	0.0573330i	−0.0519860	−	0.00229516i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	29.6458	−	21.4841i	1.18488	−	0.858675i
$627$	−24.5763	−	20.1692i	−0.981483	−	0.805482i
$628$	0.461435	−	2.07900i	0.0184132	−	0.0829611i
$629$	−22.7739	+	6.90837i	−0.908053	+	0.275455i
$630$	−3.15120	−	3.55484i	−0.125547	−	0.141628i
$631$	−1.61940	+	2.42361i	−0.0644674	+	0.0964823i	−0.862303	−	0.506393i	$-0.830978\pi$
$631$	−1.61940	+	2.42361i	−0.0644674	+	0.0964823i	0.797835	+	0.602876i	$0.205978\pi$
$632$	3.02483	+	0.864984i	0.120321	+	0.0344072i
$633$	−5.11904	+	3.42043i	−0.203464	+	0.135950i
$634$	24.1319	−	14.1047i	0.958402	−	0.560169i
$635$	−12.5211	−	15.2569i	−0.496883	−	0.605453i
$636$	−6.93275	−	5.95027i	−0.274902	−	0.235944i
$637$	1.82990	−	0.978100i	0.0725032	−	0.0387537i
$638$	−4.67021	+	0.177821i	−0.184895	+	0.00703999i
$639$	26.5410			1.04995
$640$	−6.54760	+	9.22653i	−0.258817	+	0.364711i
$641$	24.3354			0.961192			0.480596	−	0.876942i	$-0.340420\pi$
$641$	24.3354			0.961192			0.480596	+	0.876942i	$0.340420\pi$
$642$	−2.35270	+	0.0895803i	−0.0928536	+	0.00353545i
$643$	−23.5003	+	12.5612i	−0.926762	+	0.495365i	−0.864465	−	0.502693i	$-0.832343\pi$
$643$	−23.5003	+	12.5612i	−0.926762	+	0.495365i	−0.0622973	+	0.998058i	$0.519843\pi$
$644$	6.00542	−	6.99701i	0.236647	−	0.275721i
$645$	0.916583	+	1.11686i	0.0360904	+	0.0439763i
$646$	−60.1776	+	35.1727i	−2.36766	+	1.38385i
$647$	7.97845	−	5.33103i	0.313665	−	0.209585i	−0.388765	−	0.921337i	$-0.627098\pi$
$647$	7.97845	−	5.33103i	0.313665	−	0.209585i	0.702430	+	0.711752i	$0.252098\pi$
$648$	9.47282	−	5.25985i	0.372128	−	0.206627i
$649$	11.1455	−	16.6804i	0.437499	−	0.654764i
$650$	−0.388235	−	0.437964i	−0.0152278	−	0.0171784i
$651$	−6.13167	+	1.86002i	−0.240319	+	0.0729000i
$652$	6.89614	+	1.53060i	0.270074	+	0.0599430i
$653$	−16.7100	−	13.7135i	−0.653912	−	0.536652i	0.247897	−	0.968786i	$-0.420261\pi$
$653$	−16.7100	−	13.7135i	−0.653912	−	0.536652i	−0.901809	+	0.432134i	$0.857761\pi$
$654$	−0.289732	+	0.209966i	−0.0113294	+	0.00821032i
$655$	12.0592	+	4.99509i	0.471193	+	0.195174i
$656$	−0.293907	−	0.808731i	−0.0114752	−	0.0315756i
$657$	−0.240611	+	0.0996641i	−0.00938711	+	0.00388827i
$658$	−10.8949	+	17.7305i	−0.424726	+	0.691206i
$659$	1.48115	+	15.0384i	0.0576976	+	0.585814i	0.979953	+	0.199231i	$0.0638445\pi$
$659$	1.48115	+	15.0384i	0.0576976	+	0.585814i	−0.922255	+	0.386582i	$0.873656\pi$
$660$	−9.24616	−	0.204007i	−0.359906	−	0.00794098i
$661$	−10.7130	+	20.0425i	−0.416686	+	0.779564i	−0.999453	−	0.0330749i	$-0.989470\pi$
$661$	−10.7130	+	20.0425i	−0.416686	+	0.779564i	0.582767	+	0.812639i	$0.301970\pi$
$662$	18.6264	−	6.43377i	0.723935	−	0.250056i
$663$	−2.28484	+	0.454483i	−0.0887359	+	0.0176507i
$664$	2.55263	+	11.8399i	0.0990614	+	0.459476i
$665$	−1.89040	+	9.50369i	−0.0733067	+	0.368537i
$666$	−8.91368	−	6.76450i	−0.345398	−	0.262119i
$667$	0.179935	−	1.82691i	0.00696713	−	0.0707384i
$668$	−7.42002	−	0.896471i	−0.287089	−	0.0346855i
$669$	1.31298	−	4.32832i	0.0507628	−	0.167342i
$670$	9.38366	+	3.47475i	0.362523	+	0.134241i
$671$	−51.1938	−	51.1938i	−1.97631	−	1.97631i
$672$	5.97968	+	1.85359i	0.230671	+	0.0715036i
$673$	−22.2090	+	22.2090i	−0.856094	+	0.856094i	−0.990875	−	0.134782i	$-0.956967\pi$
$673$	−22.2090	+	22.2090i	−0.856094	+	0.856094i	0.134782	+	0.990875i	$0.456967\pi$
$674$	27.0993	−	12.4531i	1.04383	−	0.479677i
$675$	−4.04523	−	1.22711i	−0.155701	−	0.0472314i
$676$	6.90456	+	24.7110i	0.265560	+	0.950422i
$677$	−42.8182	−	4.21722i	−1.64564	−	0.162081i	−0.767683	−	0.640829i	$-0.778591\pi$
$677$	−42.8182	−	4.21722i	−1.64564	−	0.162081i	−0.877952	+	0.478748i	$0.841091\pi$
$678$	2.73273	+	19.9351i	0.104950	+	0.765604i
$679$	−3.55494	−	0.707122i	−0.136426	−	0.0271369i
$680$	−7.45870	+	18.8544i	−0.286028	+	0.723035i
$681$	1.77768	+	8.93701i	0.0681209	+	0.342467i
$682$	21.0958	−	43.3595i	0.807802	−	1.66032i
$683$	32.1866	+	17.2041i	1.23159	+	0.658296i	0.953249	−	0.302187i	$-0.0977168\pi$
$683$	32.1866	+	17.2041i	1.23159	+	0.658296i	0.278337	+	0.960483i	$0.410217\pi$
$684$	−29.9946	−	13.2067i	−1.14687	−	0.504970i
$685$	−6.25502	+	0.616066i	−0.238992	+	0.0235387i
$686$	−23.2902	+	5.56162i	−0.889224	+	0.212344i
$687$	3.24126	+	7.82510i	0.123662	+	0.298546i
$688$	6.94190	+	2.44503i	0.264657	+	0.0932158i
$689$	0.921320	−	2.22426i	0.0350995	−	0.0847377i
$690$	0.572632	−	3.58729i	0.0217997	−	0.136566i
$691$	15.1080	−	18.4091i	0.574735	−	0.700316i	−0.401788	−	0.915733i	$-0.631611\pi$
$691$	15.1080	−	18.4091i	0.574735	−	0.700316i	0.976522	+	0.215417i	$0.0691110\pi$
$692$	20.4784	−	3.60575i	0.778473	−	0.137070i
$693$	−5.74224	−	18.9296i	−0.218130	−	0.719077i
$694$	2.11703	−	35.1723i	0.0803612	−	1.33512i
$695$	12.3042	+	8.22141i	0.466725	+	0.311856i
$696$	1.18676	−	0.380834i	0.0449840	−	0.0144355i
$697$	−0.856763	−	1.28224i	−0.0324522	−	0.0485682i
$698$	2.04255	−	7.78880i	0.0773118	−	0.294811i
$699$	−12.5447	+	10.2952i	−0.474485	+	0.389400i
$700$	1.27358	+	2.51461i	0.0481370	+	0.0950433i
$701$	9.06298	+	16.9557i	0.342304	+	0.640406i	0.992891	−	0.119026i	$-0.0379771\pi$
$701$	9.06298	+	16.9557i	0.342304	+	0.640406i	−0.650587	+	0.759432i	$0.725477\pi$
$702$	−1.81473	−	1.68161i	−0.0684927	−	0.0634682i
$703$			22.8247i			0.860851i
$704$	−40.8169	+	23.5258i	−1.53834	+	0.886663i
$705$			8.19861i			0.308777i
$706$	3.06921	−	3.31219i	0.115511	−	0.124656i
$707$	−3.31494	−	6.20182i	−0.124671	−	0.233244i
$708$	−1.66559	+	5.08416i	−0.0625966	+	0.191074i
$709$	1.40528	−	1.15328i	0.0527763	−	0.0433124i	−0.607635	−	0.794216i	$-0.707882\pi$
$709$	1.40528	−	1.15328i	0.0527763	−	0.0433124i	0.660412	+	0.750904i	$0.270382\pi$
$710$	−15.2333	−	3.99481i	−0.571695	−	0.149923i
$711$	1.47286	+	2.20429i	0.0552365	+	0.0826672i
$712$	3.54519	−	43.0432i	0.132862	−	1.61311i
$713$	15.7481	+	10.5226i	0.589772	+	0.394073i
$714$	11.1994	+	0.674095i	0.419128	+	0.0252274i
$715$	−0.707457	−	2.33217i	−0.0264574	−	0.0872183i
$716$	0.335932	−	0.479512i	0.0125544	−	0.0179202i
$717$	−3.45472	+	4.20959i	−0.129019	+	0.157210i
$718$	−47.5486	−	7.59008i	−1.77450	−	0.283259i
$719$	−9.51057	+	22.9605i	−0.354684	+	0.856284i	0.641345	+	0.767253i	$0.278377\pi$
$719$	−9.51057	+	22.9605i	−0.354684	+	0.856284i	−0.996029	+	0.0890308i	$0.971623\pi$
$720$	−9.23628	+	2.36238i	−0.344216	+	0.0880406i
$721$	−2.06760	−	4.99164i	−0.0770016	−	0.185898i
$722$	9.28604	+	38.8869i	0.345591	+	1.44722i
$723$	−22.3569	+	2.20196i	−0.831461	+	0.0818917i
$724$	−9.32292	−	23.9912i	−0.346484	−	0.891625i
$725$	0.494914	+	0.264537i	0.0183807	+	0.00982467i
$726$	−23.6457	−	11.5044i	−0.877573	−	0.426969i
$727$	2.46513	+	12.3931i	0.0914268	+	0.459633i	0.999193	+	0.0401577i	$0.0127860\pi$
$727$	2.46513	+	12.3931i	0.0914268	+	0.459633i	−0.907767	+	0.419476i	$0.862214\pi$
$728$	0.0263889	+	1.64951i	0.000978039	+	0.0611348i
$729$	−0.811952	−	0.161507i	−0.0300723	−	0.00598175i
$730$	0.153100	−	0.0209871i	0.00566648	−	0.000776766i
$731$	13.1267	+	1.29287i	0.485509	+	0.0478184i
$732$	16.8229	+	9.47493i	0.621791	+	0.350204i
$733$	−7.58209	−	2.30000i	−0.280051	−	0.0849525i	0.147135	−	0.989116i	$-0.452995\pi$
$733$	−7.58209	−	2.30000i	−0.280051	−	0.0849525i	−0.427186	+	0.904164i	$0.640495\pi$
$734$	20.5706	+	44.7637i	0.759274	+	1.65226i
$735$	−2.78383	+	2.78383i	−0.102683	+	0.102683i
$736$	−6.97776	−	17.1390i	−0.257204	−	0.631753i
$737$	29.4633	+	29.4633i	1.08529	+	1.08529i
$738$	0.251792	−	0.679970i	0.00926858	−	0.0250301i
$739$	10.6088	−	34.9726i	0.390252	−	1.28649i	−0.513374	−	0.858165i	$-0.671605\pi$
$739$	10.6088	−	34.9726i	0.390252	−	1.28649i	0.903626	−	0.428322i	$-0.140895\pi$
$740$	4.09787	+	5.22414i	0.150641	+	0.192043i
$741$	−0.218997	+	2.22351i	−0.00804505	+	0.0816827i
$742$	−7.00943	+	9.23643i	−0.257324	+	0.339080i
$743$	2.59058	−	13.0237i	0.0950392	−	0.477794i	−0.903726	−	0.428112i	$-0.859179\pi$
$743$	2.59058	−	13.0237i	0.0950392	−	0.477794i	0.998765	−	0.0496827i	$-0.0158210\pi$
$744$	−2.30664	+	12.6506i	−0.0845657	+	0.463795i
$745$	4.68635	−	0.932173i	0.171695	−	0.0341522i
$746$	−3.20571	−	9.28082i	−0.117369	−	0.339795i
$747$	−4.81117	+	9.00107i	−0.176032	+	0.329332i
$748$	−61.0047	+	58.3708i	−2.23055	+	2.13425i
$749$	0.292881	+	2.97367i	0.0107016	+	0.108655i
$750$	0.946148	+	0.581380i	0.0345484	+	0.0212290i
$751$	−9.33452	+	3.86648i	−0.340621	+	0.141090i	−0.546436	−	0.837501i	$-0.684016\pi$
$751$	−9.33452	+	3.86648i	−0.340621	+	0.141090i	0.205814	+	0.978591i	$0.434016\pi$
$752$	21.6485	+	35.7148i	0.789438	+	1.30239i
$753$	−9.78420	−	4.05275i	−0.356556	−	0.147690i
$754$	0.192729	+	0.265947i	0.00701879	+	0.00968522i
$755$	0.907404	+	0.744687i	0.0330238	+	0.0271019i
$756$	6.39975	+	10.0510i	0.232757	+	0.365551i
$757$	33.8713	−	10.2748i	1.23107	−	0.373442i	0.393275	−	0.919421i	$-0.371342\pi$
$757$	33.8713	−	10.2748i	1.23107	−	0.373442i	0.837799	+	0.545979i	$0.183842\pi$
$758$	−23.4667	+	20.8021i	−0.852348	+	0.755567i
$759$	8.40408	−	12.5776i	0.305049	−	0.456538i
$760$	15.2277	+	12.0946i	0.552366	+	0.438718i
$761$	−21.9375	+	14.6582i	−0.795235	+	0.531359i	−0.885544	−	0.464555i	$-0.846214\pi$
$761$	−21.9375	+	14.6582i	−0.795235	+	0.531359i	0.0903097	+	0.995914i	$0.471214\pi$
$762$	11.0600	+	18.9227i	0.400662	+	0.685499i
$763$	0.288087	+	0.351034i	0.0104294	+	0.0127083i
$764$	−2.21889	−	29.0958i	−0.0802767	−	1.05265i
$765$	−15.0684	+	8.05423i	−0.544799	+	0.291201i
$766$	−0.0466337	−	1.22477i	−0.00168494	−	0.0442527i
$767$	−1.40982			−0.0509058
$768$	8.79527	−	8.97176i	0.317372	−	0.323741i
$769$	22.2074			0.800820			0.400410	−	0.916336i	$-0.368868\pi$
$769$	22.2074			0.800820			0.400410	+	0.916336i	$0.368868\pi$
$770$	0.446588	+	11.7290i	0.0160939	+	0.422683i
$771$	−4.04185	+	2.16041i	−0.145563	+	0.0778053i
$772$	−0.177638	−	2.32932i	−0.00639333	−	0.0838341i
$773$	26.7018	+	32.5363i	0.960398	+	1.17025i	0.985347	+	0.170560i	$0.0545575\pi$
$773$	26.7018	+	32.5363i	0.960398	+	1.17025i	−0.0249494	+	0.999689i	$0.507942\pi$
$774$	3.12954	+	5.35438i	0.112489	+	0.192459i
$775$	−4.81409	+	3.21667i	−0.172927	+	0.115546i
$776$	−4.52410	+	5.69605i	−0.162406	+	0.204476i
$777$	2.04116	−	3.05481i	0.0732261	−	0.109591i
$778$	−11.1402	+	9.87532i	−0.399397	+	0.354047i
$779$	−1.41534	+	0.429338i	−0.0507097	+	0.0153826i
$780$	0.349077	+	0.548237i	0.0124990	+	0.0196300i
$781$	−50.6923	−	41.6021i	−1.81391	−	1.48864i
$782$	−19.4609	−	26.8540i	−0.695920	−	0.960298i
$783$	2.19166	+	0.907816i	0.0783236	+	0.0324427i
$784$	−4.77622	+	19.4777i	−0.170579	+	0.695631i
$785$	−0.983742	+	0.407479i	−0.0351113	+	0.0145436i
$786$	−12.3499	−	7.58864i	−0.440506	−	0.270678i
$787$	2.02279	+	20.5377i	0.0721046	+	0.732090i	0.961473	+	0.274899i	$0.0886444\pi$
$787$	2.02279	+	20.5377i	0.0721046	+	0.732090i	−0.889369	+	0.457191i	$0.848856\pi$
$788$	40.3098	−	38.5694i	1.43598	−	1.37398i
$789$	5.70355	−	10.6706i	0.203052	−	0.379883i
$790$	−0.513572	−	1.48684i	−0.0182721	−	0.0528994i
$791$	25.0463	−	4.98202i	0.890544	−	0.177140i
$792$	−39.0549	−	7.12104i	−1.38776	−	0.253035i
$793$	−0.992596	+	4.99012i	−0.0352481	+	0.177204i
$794$	26.1119	−	34.4080i	0.926677	−	1.22110i
$795$	−0.447748	+	4.54607i	−0.0158800	+	0.161232i
$796$	−29.2619	−	37.3043i	−1.03716	−	1.32222i
$797$	12.3151	−	40.5973i	0.436222	−	1.43803i	−0.413357	−	0.910569i	$-0.635644\pi$
$797$	12.3151	−	40.5973i	0.436222	−	1.43803i	0.849579	−	0.527462i	$-0.176856\pi$
$798$	3.73665	−	10.0909i	0.132276	−	0.357215i
$799$	52.9254	+	52.9254i	1.87237	+	1.87237i
$800$	5.65675	+	0.0343014i	0.199996	+	0.00121274i
$801$	25.7341	−	25.7341i	0.909271	−	0.909271i
$802$	−18.8496	−	41.0187i	−0.665602	−	1.44842i
$803$	0.615776	+	0.186794i	0.0217303	+	0.00659180i
$804$	−9.68197	−	5.45306i	−0.341457	−	0.192314i
$805$	−4.58820	−	0.451898i	−0.161713	−	0.0159273i
$806$	−3.35723	+	0.460212i	−0.118253	+	0.0162103i
$807$	−24.7354	−	4.92018i	−0.870729	−	0.173199i
$808$	−14.1109	+	0.225747i	−0.496419	+	0.00794176i
$809$	9.87832	+	49.6617i	0.347303	+	1.74601i	0.620642	+	0.784094i	$0.286872\pi$
$809$	9.87832	+	49.6617i	0.347303	+	1.74601i	−0.273339	+	0.961918i	$0.588128\pi$
$810$	−4.87158	−	2.37019i	−0.171170	−	0.0832800i
$811$	1.41962	+	0.758803i	0.0498496	+	0.0266452i	0.496133	−	0.868246i	$-0.334753\pi$
$811$	1.41962	+	0.758803i	0.0498496	+	0.0266452i	−0.446284	+	0.894892i	$0.647253\pi$
$812$	−0.572949	−	1.47440i	−0.0201066	−	0.0517413i
$813$	−0.299928	+	0.0295403i	−0.0105189	+	0.00103602i
$814$	6.42166	+	26.8918i	0.225079	+	0.942556i
$815$	−1.35163	−	3.26312i	−0.0473456	−	0.114302i
$816$	11.4798	−	19.3703i	0.401872	−	0.678098i
$817$	4.84112	−	11.6875i	0.169369	−	0.408893i
$818$	−24.3820	−	3.89204i	−0.852496	−	0.136082i
$819$	−0.881902	+	1.07460i	−0.0308161	+	0.0375496i
$820$	−0.246862	+	0.352372i	−0.00862078	+	0.0123054i
$821$	−2.54913	−	8.40337i	−0.0889654	−	0.293280i	0.901155	−	0.433496i	$-0.142720\pi$
$821$	−2.54913	−	8.40337i	−0.0889654	−	0.293280i	−0.990121	+	0.140216i	$0.955220\pi$
$822$	6.96717	+	0.419355i	0.243008	+	0.0146267i
$823$	−36.9216	−	24.6702i	−1.28701	−	0.859949i	−0.291679	−	0.956516i	$-0.594214\pi$
$823$	−36.9216	−	24.6702i	−1.28701	−	0.859949i	−0.995326	+	0.0965670i	$0.969214\pi$
$824$	−10.8064	−	0.890051i	−0.376458	−	0.0310064i
$825$	2.56907	+	3.84489i	0.0894436	+	0.133862i
$826$	6.56783	+	1.72236i	0.228524	+	0.0599287i
$827$	25.3402	−	20.7962i	0.881166	−	0.723154i	−0.0806816	−	0.996740i	$-0.525710\pi$
$827$	25.3402	−	20.7962i	0.881166	−	0.723154i	0.961848	+	0.273586i	$0.0882097\pi$
$828$	4.85459	−	14.8185i	0.168709	−	0.514978i
$829$	−22.2094	−	41.5508i	−0.771363	−	1.44312i	−0.892769	−	0.450515i	$-0.851240\pi$
$829$	−22.2094	−	41.5508i	−0.771363	−	1.44312i	0.121406	−	0.992603i	$-0.461260\pi$
$830$	4.11617	−	4.44203i	0.142875	−	0.154185i
$831$		−	18.5235i		−	0.642573i
$832$	2.96827	+	1.46649i	0.102906	+	0.0508414i
$833$			35.9416i			1.24530i
$834$	−12.0538	−	11.1695i	−0.417388	−	0.386769i
$835$	1.76160	+	3.29573i	0.0609628	+	0.114053i
$836$	36.5875	+	72.2397i	1.26541	+	2.49846i
$837$	−18.9196	+	15.5269i	−0.653957	+	0.536688i
$838$	9.43424	−	35.9753i	0.325901	−	1.24275i
$839$	19.2293	+	28.7786i	0.663868	+	0.993549i	0.998685	+	0.0512656i	$0.0163255\pi$
$839$	19.2293	+	28.7786i	0.663868	+	0.993549i	−0.334817	+	0.942283i	$0.608675\pi$
$840$	−0.956445	−	2.98049i	−0.0330005	−	0.102837i
$841$	23.8508	+	15.9366i	0.822440	+	0.549537i
$842$	3.00895	−	49.9907i	0.103695	−	1.72279i
$843$	−1.72158	−	5.67528i	−0.0592943	−	0.195467i
$844$	15.4433	−	2.71919i	0.531581	−	0.0935985i
$845$	8.13846	−	9.91674i	0.279972	−	0.341146i
$846$	−5.54748	+	34.7526i	−0.190726	+	1.19482i
$847$	−12.7713	+	30.8326i	−0.438826	+	1.05942i
$848$	10.0534	+	20.9859i	0.345236	+	0.720658i
$849$	−8.76668	−	21.1646i	−0.300872	−	0.726368i
$850$	9.86082	−	2.35473i	0.338223	−	0.0807665i
$851$	−10.8076	+	1.06446i	−0.370480	+	0.0364891i
$852$	16.0057	+	7.04733i	0.548346	+	0.241438i
$853$	10.2290	+	5.46752i	0.350234	+	0.187204i	0.637127	−	0.770758i	$-0.280122\pi$
$853$	10.2290	+	5.46752i	0.350234	+	0.187204i	−0.286893	+	0.957963i	$0.592622\pi$
$854$	10.7205	−	22.0344i	0.366847	−	0.754002i
$855$	3.19688	+	16.0718i	0.109331	+	0.549645i
$856$	5.57619	+	2.20591i	0.190590	+	0.0753964i
$857$	−2.60545	−	0.518257i	−0.0890006	−	0.0177033i	0.150389	−	0.988627i	$-0.451947\pi$
$857$	−2.60545	−	0.518257i	−0.0890006	−	0.0177033i	−0.239390	+	0.970924i	$0.576947\pi$
$858$	0.367559	+	2.68133i	0.0125483	+	0.0915389i
$859$	31.3884	+	3.09149i	1.07096	+	0.105480i	0.618099	−	0.786101i	$-0.287903\pi$
$859$	31.3884	+	3.09149i	1.07096	+	0.105480i	0.452861	+	0.891581i	$0.350403\pi$
$860$	−0.990293	−	3.54420i	−0.0337687	−	0.120856i
$861$	0.227820	+	0.0691084i	0.00776409	+	0.00235521i
$862$	−35.7352	+	16.4216i	−1.21714	+	0.559322i
$863$	40.6723	−	40.6723i	1.38450	−	1.38450i	0.548063	−	0.836437i	$-0.315365\pi$
$863$	40.6723	−	40.6723i	1.38450	−	1.38450i	0.836437	−	0.548063i	$-0.184635\pi$
$864$	23.8116	−	2.19953i	0.810086	−	0.0748296i
$865$	−7.35159	−	7.35159i	−0.249962	−	0.249962i
$866$	18.2502	+	6.75802i	0.620168	+	0.229647i
$867$	7.83901	−	25.8417i	0.266227	−	0.877631i
$868$	16.2023	+	1.95753i	0.549941	+	0.0664427i
$869$	0.642040	−	6.51874i	0.0217797	−	0.221133i
$870$	−0.496421	−	0.376729i	−0.0168303	−	0.0127723i
$871$	0.571264	−	2.87194i	0.0193565	−	0.0973118i
$872$	0.890880	−	0.192071i	0.0301690	−	0.00650433i
$873$	−6.01181	+	1.19582i	−0.203469	+	0.0404725i
$874$	−30.0641	+	10.3845i	−1.01693	+	0.351261i
$875$	0.664372	−	1.24295i	0.0224599	−	0.0420194i
$876$	−0.171565	−	0.00378541i	−0.00579663	−	0.000127897i
$877$	2.83545	+	28.7888i	0.0957464	+	0.972130i	0.916282	+	0.400534i	$0.131175\pi$
$877$	2.83545	+	28.7888i	0.0957464	+	0.972130i	−0.820535	+	0.571596i	$0.806325\pi$
$878$	−18.8963	+	30.7521i	−0.637718	+	1.03783i
$879$	1.88802	−	0.782045i	0.0636815	−	0.0263777i
$880$	21.3438	+	9.96547i	0.719501	+	0.335936i
$881$	−42.4712	−	17.5921i	−1.43089	−	0.592694i	−0.473318	−	0.880891i	$-0.656944\pi$
$881$	−42.4712	−	17.5921i	−1.43089	−	0.592694i	−0.957571	+	0.288198i	$0.906944\pi$
$882$	−13.6839	+	9.91658i	−0.460760	+	0.333908i
$883$	−24.9105	−	20.4435i	−0.838304	−	0.687978i	0.113883	−	0.993494i	$-0.463671\pi$
$883$	−24.9105	−	20.4435i	−0.838304	−	0.687978i	−0.952187	+	0.305516i	$0.901171\pi$
$884$	5.79253	+	1.28566i	0.194824	+	0.0432413i
$885$	2.55983	−	0.776516i	0.0860478	−	0.0261023i
$886$	2.31388	+	2.61027i	0.0777363	+	0.0876936i
$887$	1.24089	−	1.85712i	0.0416650	−	0.0623561i	−0.810052	−	0.586358i	$-0.800561\pi$
$887$	1.24089	−	1.85712i	0.0416650	−	0.0623561i	0.851717	+	0.524001i	$0.175561\pi$
$888$	−3.57929	−	6.44618i	−0.120113	−	0.216320i
$889$	23.1288	−	15.4542i	0.775715	−	0.518316i
$890$	−18.6435	+	10.8968i	−0.624932	+	0.365261i
$891$	−14.3115	−	17.4386i	−0.479452	−	0.584214i
$892$	−7.50304	+	8.74191i	−0.251220	+	0.292701i
$893$	63.3086	−	33.8391i	2.11854	−	1.13238i
$894$	−5.30228	+	0.201887i	−0.177335	+	0.00675212i
$895$	−0.292738			−0.00978515
$896$	−12.0365	−	10.4581i	−0.402110	−	0.349381i
$897$	−1.06306			−0.0354944
$898$	22.7771	−	0.867250i	0.760081	−	0.0289405i
$899$	2.86549	−	1.53163i	0.0955693	−	0.0510828i
$900$	3.61719	+	3.10457i	0.120573	+	0.103486i
$901$	26.4563	+	32.2371i	0.881388	+	1.07397i
$902$	−1.54674	+	0.904041i	−0.0515008	+	0.0301013i
$903$	−1.69311	+	1.13130i	−0.0563430	+	0.0376472i
$904$	14.0906	−	49.2745i	0.468645	−	1.63884i
$905$	−7.14989	+	10.7006i	−0.237670	+	0.355699i
$906$	−0.864712	−	0.975473i	−0.0287281	−	0.0324079i
$907$	−10.5599	+	3.20331i	−0.350636	+	0.106364i	−0.460689	−	0.887561i	$-0.652398\pi$
$907$	−10.5599	+	3.20331i	−0.350636	+	0.106364i	0.110054	+	0.993926i	$0.464898\pi$
$908$	5.02876	−	22.6571i	0.166885	−	0.751903i
$909$	−9.19279	−	7.54433i	−0.304906	−	0.250230i
$910$	0.667912	−	0.484030i	0.0221411	−	0.0160454i
$911$	−34.4122	−	14.2540i	−1.14013	−	0.472257i	−0.268916	−	0.963164i	$-0.586666\pi$
$911$	−34.4122	−	14.2540i	−1.14013	−	0.472257i	−0.871212	+	0.490907i	$0.836666\pi$
$912$	−14.5817	−	15.9287i	−0.482848	−	0.527452i
$913$	23.2980	−	9.65034i	0.771051	−	0.319380i
$914$	−19.0873	+	31.0630i	−0.631352	+	1.02747i
$915$	−0.946237	−	9.60731i	−0.0312816	−	0.317608i
$916$	0.475863	−	21.5674i	0.0157230	−	0.712606i
$917$	−8.67191	+	16.2240i	−0.286372	+	0.535764i
$918$	40.5078	−	13.9919i	1.33696	−	0.461800i
$919$	−1.21448	+	0.241576i	−0.0400621	+	0.00796885i	−0.215081	−	0.976596i	$-0.569001\pi$
$919$	−1.21448	+	0.241576i	−0.0400621	+	0.00796885i	0.175019	+	0.984565i	$0.444001\pi$
$920$	−5.01670	+	7.77442i	−0.165396	+	0.256315i
$921$	−4.03960	+	20.3084i	−0.133109	+	0.669185i
$922$	22.1512	+	16.8103i	0.729512	+	0.553619i
$923$	−0.451713	+	4.58632i	−0.0148683	+	0.150961i
$924$	1.56342	−	12.9403i	0.0514328	−	0.425705i
$925$	0.963686	−	3.17685i	0.0316858	−	0.104454i
$926$	40.2166	+	14.8921i	1.32160	+	0.489385i
$927$	−6.46078	−	6.46078i	−0.212200	−	0.212200i
$928$	−3.15727	−	0.330306i	−0.103642	−	0.0108428i
$929$	−17.9016	+	17.9016i	−0.587332	+	0.587332i	−0.936908	−	0.349576i	$-0.886326\pi$
$929$	−17.9016	+	17.9016i	−0.587332	+	0.587332i	0.349576	+	0.936908i	$0.386326\pi$
$930$	5.84227	−	2.68474i	0.191575	−	0.0880359i
$931$	32.9865	+	10.0063i	1.08109	+	0.327944i
$932$	39.8090	−	11.1231i	1.30399	−	0.364350i
$933$	−24.9699	−	2.45932i	−0.817476	−	0.0805144i
$934$	−2.44785	−	17.8570i	−0.0800961	−	0.584298i
$935$	41.4047	+	8.23591i	1.35408	+	0.269343i
$936$	1.10873	+	2.56009i	0.0362398	+	0.0836790i
$937$	−2.29209	−	11.5231i	−0.0748794	−	0.376444i	0.925115	−	0.379686i	$-0.123968\pi$
$937$	−2.29209	−	11.5231i	−0.0748794	−	0.376444i	−0.999995	+	0.00324197i	$0.998968\pi$
$938$	−6.16990	+	12.6813i	−0.201454	+	0.414061i
$939$	17.9283	+	9.58289i	0.585069	+	0.312726i
$940$	8.41475	−	19.1113i	0.274459	−	0.623343i
$941$	−50.1698	+	4.94130i	−1.63549	+	0.161082i	−0.873607	−	0.486633i	$-0.838225\pi$
$941$	−50.1698	+	4.94130i	−1.63549	+	0.161082i	−0.761883	+	0.647715i	$0.775725\pi$
$942$	1.15011	−	0.274643i	0.0374727	−	0.00894834i
$943$	−0.269299	−	0.650146i	−0.00876959	−	0.0211717i
$944$	9.10075	−	10.1419i	0.296204	−	0.330091i
$945$	2.27993	−	5.50425i	0.0741663	−	0.179053i
$946$	2.41550	−	15.1321i	0.0785347	−	0.491986i
$947$	−10.1057	+	12.3138i	−0.328391	+	0.400146i	−0.910865	−	0.412703i	$-0.864585\pi$
$947$	−10.1057	+	12.3138i	−0.328391	+	0.400146i	0.582474	+	0.812849i	$0.302085\pi$
$948$	0.302918	+	1.72039i	0.00983832	+	0.0558756i
$949$	−0.0131270	−	0.0432740i	−0.000426121	−	0.00140473i
$950$	0.584183	−	9.70563i	0.0189534	−	0.314892i
$951$	12.9045	+	8.62248i	0.418456	+	0.279603i
$952$	−25.4145	−	13.0660i	−0.823690	−	0.423473i
$953$	−19.4586	−	29.1218i	−0.630325	−	0.943348i	−0.999900	−	0.0141469i	$-0.995497\pi$
$953$	−19.4586	−	29.1218i	−0.630325	−	0.943348i	0.369575	−	0.929201i	$-0.379503\pi$
$954$	−4.97397	+	18.9671i	−0.161038	+	0.614082i
$955$	−11.2783	+	9.25588i	−0.364958	+	0.299513i
$956$	12.3737	−	6.26695i	0.400194	−	0.202688i
$957$	−1.22327	−	2.28859i	−0.0395428	−	0.0739794i
$958$	35.9277	+	33.2922i	1.16077	+	1.07562i
$959$		−	8.85828i		−	0.286049i
$960$	−6.19725	−	1.02783i	−0.200015	−	0.0331730i
$961$			2.52249i			0.0813707i
$962$	1.32062	−	1.42517i	0.0425785	−	0.0459492i
$963$	2.38204	+	4.45647i	0.0767600	+	0.143608i
$964$	54.3749	+	17.8134i	1.75130	+	0.573731i
$965$	−0.902909	+	0.740999i	−0.0290657	+	0.0238536i
$966$	4.95237	+	1.29872i	0.159340	+	0.0417856i
$967$	−17.7769	−	26.6051i	−0.571668	−	0.855562i	0.427149	−	0.904181i	$-0.359518\pi$
$967$	−17.7769	−	26.6051i	−0.571668	−	0.855562i	−0.998817	+	0.0486194i	$0.984518\pi$
$968$	43.3115	+	51.0864i	1.39208	+	1.64198i
$969$	−32.1797	−	21.5018i	−1.03376	−	0.690737i
$970$	3.63048	+	0.218519i	0.116568	+	0.00701622i
$971$	7.08603	+	23.3595i	0.227402	+	0.749642i	0.994180	+	0.107731i	$0.0343584\pi$
$971$	7.08603	+	23.3595i	0.227402	+	0.749642i	−0.766779	+	0.641912i	$0.778142\pi$
$972$	25.7004	+	18.0049i	0.824339	+	0.577508i
$973$	−13.2309	+	16.1219i	−0.424164	+	0.516846i
$974$	−42.1102	−	6.72196i	−1.34930	−	0.215386i
$975$	0.124360	−	0.300232i	0.00398271	−	0.00961512i
$976$	−29.4902	−	39.3529i	−0.943957	−	1.25965i
$977$	−2.21434	−	5.34589i	−0.0708430	−	0.171030i	0.884492	−	0.466556i	$-0.154505\pi$
$977$	−2.21434	−	5.34589i	−0.0708430	−	0.171030i	−0.955335	+	0.295526i	$0.904505\pi$
$978$	0.911004	+	3.81498i	0.0291307	+	0.121990i
$979$	−89.4884	+	8.81384i	−2.86006	+	0.281691i
$980$	9.34647	−	3.63202i	0.298562	−	0.116021i
$981$	0.677278	+	0.362013i	0.0216238	+	0.0115582i
$982$	28.5934	+	13.9117i	0.912452	+	0.443939i
$983$	0.758456	+	3.81301i	0.0241910	+	0.121616i	0.990994	−	0.133907i	$-0.0427523\pi$
$983$	0.758456	+	3.81301i	0.0241910	+	0.121616i	−0.966803	+	0.255523i	$0.917752\pi$
$984$	0.332394	−	0.343202i	0.0105963	−	0.0109409i
$985$	−27.3588	−	5.44200i	−0.871723	−	0.173397i
$986$	−5.63655	+	0.772663i	−0.179504	+	0.0246066i
$987$	−11.4992	−	1.13257i	−0.366024	−	0.0360502i
$988$	2.79262	−	4.95834i	0.0888451	−	0.157746i
$989$	5.75985	+	1.74723i	0.183152	+	0.0555587i
$990$	8.28828	+	18.0362i	0.263419	+	0.573227i
$991$	29.7812	−	29.7812i	0.946031	−	0.946031i	−0.0525859	−	0.998616i	$-0.516746\pi$
$991$	29.7812	−	29.7812i	0.946031	−	0.946031i	0.998616	+	0.0525859i	$0.0167463\pi$
$992$	18.3611	−	27.1218i	0.582964	−	0.861118i
$993$	7.73704	+	7.73704i	0.245528	+	0.245528i
$994$	7.70741	−	20.8141i	0.244464	−	0.660182i
$995$	−6.88145	+	22.6851i	−0.218157	+	0.719166i
$996$	−5.29142	+	4.15065i	−0.167665	+	0.131518i
$997$	4.09593	−	41.5867i	0.129719	−	1.31706i	−0.681283	−	0.732020i	$-0.738578\pi$
$997$	4.09593	−	41.5867i	0.129719	−	1.31706i	0.811002	−	0.585043i	$-0.198922\pi$
$998$	9.06529	−	11.9455i	0.286957	−	0.378127i
$999$	2.73782	−	13.7640i	0.0866208	−	0.435472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.31	✓	1024
128.109	even	32	inner	640.2.bm.a.621.31	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.31	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.31	yes	1024	128.109	even	32	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0538080 - 1.41319i) q^{2} +(0.692518 - 0.370159i) q^{3} +(-1.99421 + 0.152082i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-0.560367 - 0.958742i) q^{6} +(-1.17185 + 0.783003i) q^{7} +(0.322225 + 2.81001i) q^{8} +(-1.32415 + 1.98173i) q^{9} +(1.05827 - 0.938112i) q^{10} +(5.63534 - 1.70946i) q^{11} +(-1.32473 + 0.843493i) q^{12} +(-0.319908 - 0.262542i) q^{13} +(1.16959 + 1.61391i) q^{14} +(0.725465 + 0.300498i) q^{15} +(3.95374 - 0.606566i) q^{16} +(6.62302 - 2.74334i) q^{17} +(2.87180 + 1.76464i) q^{18} +(-0.673901 - 6.84223i) q^{19} +(-1.38267 - 1.44507i) q^{20} +(-0.521690 + 0.976013i) q^{21} +(-2.71902 - 7.87183i) q^{22} +(3.20840 - 0.638190i) q^{23} +(1.26330 + 1.82671i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-0.353808 + 0.466218i) q^{26} +(-0.414343 + 4.20690i) q^{27} +(2.21783 - 1.73969i) q^{28} +(0.162901 - 0.537013i) q^{29} +(0.385624 - 1.04139i) q^{30} +(4.09405 + 4.09405i) q^{31} +(-1.06993 - 5.55475i) q^{32} +(3.26981 - 3.26981i) q^{33} +(-4.23323 - 9.21196i) q^{34} +(-1.34868 - 0.409118i) q^{35} +(2.33924 - 4.15335i) q^{36} +(-3.30381 - 0.325397i) q^{37} +(-9.63311 + 1.32052i) q^{38} +(-0.318725 - 0.0633982i) q^{39} +(-1.96775 + 2.03174i) q^{40} +(-0.0419679 - 0.210987i) q^{41} +(1.40736 + 0.684729i) q^{42} +(1.62271 + 0.867358i) q^{43} +(-10.9781 + 4.26606i) q^{44} +(-2.37192 + 0.233614i) q^{45} +(-1.07452 - 4.49974i) q^{46} +(3.99557 + 9.64615i) q^{47} +(2.51351 - 1.88357i) q^{48} +(-1.91865 + 4.63204i) q^{49} +(1.39653 + 0.222926i) q^{50} +(3.57109 - 4.35138i) q^{51} +(0.677892 + 0.474911i) q^{52} +(1.68871 + 5.56693i) q^{53} +(5.96744 + 0.359181i) q^{54} +(4.89646 + 3.27171i) q^{55} +(-2.57785 - 3.04060i) q^{56} +(-2.99940 - 4.48892i) q^{57} +(-0.767667 - 0.201315i) q^{58} +(2.63336 - 2.16114i) q^{59} +(-1.49243 - 0.488925i) q^{60} +(-5.79540 - 10.8424i) q^{61} +(5.56538 - 6.00596i) q^{62} -3.35909i q^{63} +(-7.79234 + 1.81091i) q^{64} -0.413847i q^{65} +(-4.79680 - 4.44491i) q^{66} +(3.33539 + 6.24008i) q^{67} +(-12.7905 + 6.47804i) q^{68} +(1.98564 - 1.62957i) q^{69} +(-0.505591 + 1.92796i) q^{70} +(-6.18671 - 9.25907i) q^{71} +(-5.99535 - 3.08231i) q^{72} +(0.0908549 + 0.0607073i) q^{73} +(-0.282076 + 4.68642i) q^{74} +(0.227943 + 0.751426i) q^{75} +(2.38448 + 13.5424i) q^{76} +(-5.26525 + 6.41572i) q^{77} +(-0.0724438 + 0.453829i) q^{78} +(0.425661 - 1.02764i) q^{79} +(2.97711 + 2.67148i) q^{80} +(-1.46598 - 3.53920i) q^{81} +(-0.295906 + 0.0706613i) q^{82} +(4.26158 - 0.419729i) q^{83} +(0.891925 - 2.02571i) q^{84} +(6.32223 + 3.37930i) q^{85} +(1.13843 - 2.33987i) q^{86} +(-0.0859681 - 0.432191i) q^{87} +(6.61946 + 15.2846i) q^{88} +(-14.9762 - 2.97895i) q^{89} +(0.457769 + 3.33941i) q^{90} +(0.580455 + 0.0571698i) q^{91} +(-6.30116 + 1.76062i) q^{92} +(4.35065 + 1.31976i) q^{93} +(13.4168 - 6.16553i) q^{94} +(4.86160 - 4.86160i) q^{95} +(-2.79709 - 3.45072i) q^{96} +(1.81852 + 1.81852i) q^{97} +(6.64919 + 2.46218i) q^{98} +(-4.07434 + 13.4313i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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