LMFDB - Embedded newform 460.2.o.b.159.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			159.40
Character	$\chi$	$=$	460.159
Dual form			460.2.o.b.379.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.450881 - 1.34041i) q^{2} +(0.195566 + 1.36019i) q^{3} +(-1.59341 - 1.20873i) q^{4} +(-2.10352 + 0.758423i) q^{5} +(1.91140 + 0.351145i) q^{6} +(2.25392 + 1.95304i) q^{7} +(-2.33864 + 1.59084i) q^{8} +(1.06660 - 0.313183i) q^{9} +O(q^{10})$	\(q+(0.450881 - 1.34041i) q^{2} +(0.195566 + 1.36019i) q^{3} +(-1.59341 - 1.20873i) q^{4} +(-2.10352 + 0.758423i) q^{5} +(1.91140 + 0.351145i) q^{6} +(2.25392 + 1.95304i) q^{7} +(-2.33864 + 1.59084i) q^{8} +(1.06660 - 0.313183i) q^{9} +(0.0681638 + 3.16154i) q^{10} +(-1.97726 + 1.27071i) q^{11} +(1.33249 - 2.40373i) q^{12} +(-1.81550 + 1.57314i) q^{13} +(3.63413 - 2.14060i) q^{14} +(-1.44298 - 2.71287i) q^{15} +(1.07793 + 3.85202i) q^{16} +(-2.71880 + 5.95333i) q^{17} +(0.0611166 - 1.57090i) q^{18} +(0.209168 + 0.458013i) q^{19} +(4.26851 + 1.33411i) q^{20} +(-2.21571 + 3.44772i) q^{21} +(0.811764 + 3.22328i) q^{22} +(-0.0393105 + 4.79567i) q^{23} +(-2.62120 - 2.86989i) q^{24} +(3.84959 - 3.19072i) q^{25} +(1.29008 + 3.14281i) q^{26} +(2.34714 + 5.13953i) q^{27} +(-1.23073 - 5.83639i) q^{28} +(3.03076 - 6.63644i) q^{29} +(-4.28697 + 0.711006i) q^{30} +(8.59592 + 1.23591i) q^{31} +(5.64932 + 0.291933i) q^{32} +(-2.11509 - 2.44095i) q^{33} +(6.75407 + 6.32855i) q^{34} +(-6.22240 - 2.39882i) q^{35} +(-2.07809 - 0.790209i) q^{36} +(4.42954 - 1.30063i) q^{37} +(0.708237 - 0.0738616i) q^{38} +(-2.49482 - 2.16177i) q^{39} +(3.71285 - 5.12003i) q^{40} +(-0.227570 - 0.0668207i) q^{41} +(3.62234 + 4.52448i) q^{42} +(-11.1114 + 1.59758i) q^{43} +(4.68654 + 0.365217i) q^{44} +(-2.00610 + 1.46772i) q^{45} +(6.41045 + 2.21497i) q^{46} -8.41857 q^{47} +(-5.02868 + 2.21951i) q^{48} +(0.269620 + 1.87525i) q^{49} +(-2.54117 - 6.59867i) q^{50} +(-8.62938 - 2.53381i) q^{51} +(4.79434 - 0.312205i) q^{52} +(2.79031 - 3.22019i) q^{53} +(7.94737 - 0.828827i) q^{54} +(3.19547 - 4.17256i) q^{55} +(-8.37808 - 0.981826i) q^{56} +(-0.582080 + 0.374080i) q^{57} +(-7.52906 - 7.05471i) q^{58} +(-8.81293 + 7.63645i) q^{59} +(-0.979873 + 6.06689i) q^{60} +(-7.90931 - 1.13719i) q^{61} +(5.53236 - 10.9648i) q^{62} +(3.01570 + 1.37723i) q^{63} +(2.93848 - 7.44079i) q^{64} +(2.62583 - 4.68604i) q^{65} +(-4.22553 + 1.73452i) q^{66} +(4.03312 - 6.27565i) q^{67} +(11.5282 - 6.19982i) q^{68} +(-6.53072 + 0.884400i) q^{69} +(-6.02097 + 7.25901i) q^{70} +(2.76141 - 4.29683i) q^{71} +(-1.99618 + 2.42921i) q^{72} +(8.40122 - 3.83671i) q^{73} +(0.253814 - 6.52385i) q^{74} +(5.09284 + 4.61218i) q^{75} +(0.220325 - 0.982632i) q^{76} +(-6.93834 - 0.997582i) q^{77} +(-4.02253 + 2.36938i) q^{78} +(0.508994 + 0.587411i) q^{79} +(-5.18891 - 7.28528i) q^{80} +(-3.72623 + 2.39470i) q^{81} +(-0.192174 + 0.274910i) q^{82} +(-0.865999 - 2.94932i) q^{83} +(7.69792 - 2.81543i) q^{84} +(1.20389 - 14.5849i) q^{85} +(-2.86850 + 15.6142i) q^{86} +(9.61954 + 2.82455i) q^{87} +(2.60261 - 6.11723i) q^{88} +(-3.79418 + 0.545520i) q^{89} +(1.06285 + 3.35077i) q^{90} -7.16438 q^{91} +(5.85932 - 7.59397i) q^{92} +11.9338i q^{93} +(-3.79577 + 11.2844i) q^{94} +(-0.787356 - 0.804802i) q^{95} +(0.707729 + 7.74124i) q^{96} +(-2.41301 - 0.708525i) q^{97} +(2.63517 + 0.484111i) q^{98} +(-1.71099 + 1.97459i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.450881	−	1.34041i	0.318821	−	0.947815i
$2$	0.450881	−	1.34041i	0.318821	−	0.947815i
$3$	0.195566	+	1.36019i	0.112910	+	0.785307i	0.965064	+	0.262015i	$0.0843871\pi$
$3$	0.195566	+	1.36019i	0.112910	+	0.785307i	−0.852154	+	0.523292i	$0.824704\pi$
$4$	−1.59341	−	1.20873i	−0.796706	−	0.604367i
$5$	−2.10352	+	0.758423i	−0.940722	+	0.339177i
$5$	−2.10352	+	0.758423i	−0.940722	+	0.339177i
$6$	1.91140	+	0.351145i	0.780324	+	0.143354i
$7$	2.25392	+	1.95304i	0.851903	+	0.738179i	0.966891	−	0.255188i	$-0.0821375\pi$
$7$	2.25392	+	1.95304i	0.851903	+	0.738179i	−0.114988	+	0.993367i	$0.536683\pi$
$8$	−2.33864	+	1.59084i	−0.826834	+	0.562446i
$9$	1.06660	−	0.313183i	0.355535	−	0.104394i
$10$	0.0681638	+	3.16154i	0.0215553	+	0.999768i
$11$	−1.97726	+	1.27071i	−0.596166	+	0.383133i	−0.803647	−	0.595106i	$-0.797110\pi$
$11$	−1.97726	+	1.27071i	−0.596166	+	0.383133i	0.207481	+	0.978239i	$0.433474\pi$
$12$	1.33249	−	2.40373i	0.384657	−	0.693898i
$13$	−1.81550	+	1.57314i	−0.503528	+	0.436309i	−0.869219	−	0.494427i	$-0.835378\pi$
$13$	−1.81550	+	1.57314i	−0.503528	+	0.436309i	0.365691	+	0.930736i	$0.380833\pi$
$14$	3.63413	−	2.14060i	0.971261	−	0.572100i
$15$	−1.44298	−	2.71287i	−0.372575	−	0.700459i
$16$	1.07793	+	3.85202i	0.269482	+	0.963005i
$17$	−2.71880	+	5.95333i	−0.659405	+	1.44390i	0.223671	+	0.974665i	$0.428196\pi$
$17$	−2.71880	+	5.95333i	−0.659405	+	1.44390i	−0.883076	+	0.469231i	$0.844531\pi$
$18$	0.0611166	−	1.57090i	0.0144053	−	0.370264i
$19$	0.209168	+	0.458013i	0.0479864	+	0.105075i	0.932107	−	0.362184i	$-0.117969\pi$
$19$	0.209168	+	0.458013i	0.0479864	+	0.105075i	−0.884120	+	0.467259i	$0.845241\pi$
$20$	4.26851	+	1.33411i	0.954467	+	0.298316i
$21$	−2.21571	+	3.44772i	−0.483508	+	0.752354i
$22$	0.811764	+	3.22328i	0.173069	+	0.687206i
$23$	−0.0393105	+	4.79567i	−0.00819680	+	0.999966i
$23$	−0.0393105	+	4.79567i	−0.00819680	+	0.999966i
$24$	−2.62120	−	2.86989i	−0.535050	−	0.585813i
$25$	3.84959	−	3.19072i	0.769918	−	0.638143i
$26$	1.29008	+	3.14281i	0.253005	+	0.616356i
$27$	2.34714	+	5.13953i	0.451708	+	0.989103i
$28$	−1.23073	−	5.83639i	−0.232587	−	1.10297i
$29$	3.03076	−	6.63644i	0.562798	−	1.23236i	−0.387746	−	0.921766i	$-0.626746\pi$
$29$	3.03076	−	6.63644i	0.562798	−	1.23236i	0.950544	−	0.310590i	$-0.100527\pi$
$30$	−4.28697	+	0.711006i	−0.782691	+	0.129811i
$31$	8.59592	+	1.23591i	1.54387	+	0.221975i	0.861016	−	0.508577i	$-0.169828\pi$
$31$	8.59592	+	1.23591i	1.54387	+	0.221975i	0.682856	+	0.730553i	$0.260738\pi$
$32$	5.64932	+	0.291933i	0.998667	+	0.0516070i
$33$	−2.11509	−	2.44095i	−0.368190	−	0.424914i
$34$	6.75407	+	6.32855i	1.15831	+	1.08534i
$35$	−6.22240	−	2.39882i	−1.05178	−	0.405475i
$36$	−2.07809	−	0.790209i	−0.346349	−	0.131702i
$37$	4.42954	−	1.30063i	0.728213	−	0.213822i	0.103447	−	0.994635i	$-0.467013\pi$
$37$	4.42954	−	1.30063i	0.728213	−	0.213822i	0.624765	+	0.780812i	$0.285195\pi$
$38$	0.708237	−	0.0738616i	0.114891	−	0.0119819i
$39$	−2.49482	−	2.16177i	−0.399490	−	0.346160i
$40$	3.71285	−	5.12003i	0.587053	−	0.809549i
$41$	−0.227570	−	0.0668207i	−0.0355405	−	0.0104356i	0.263914	−	0.964546i	$-0.414986\pi$
$41$	−0.227570	−	0.0668207i	−0.0355405	−	0.0104356i	−0.299454	+	0.954111i	$0.596805\pi$
$42$	3.62234	+	4.52448i	0.558939	+	0.698142i
$43$	−11.1114	+	1.59758i	−1.69447	+	0.243628i	−0.920821	−	0.389984i	$-0.872480\pi$
$43$	−11.1114	+	1.59758i	−1.69447	+	0.243628i	−0.773650	+	0.633613i	$0.781571\pi$
$44$	4.68654	+	0.365217i	0.706522	+	0.0550586i
$45$	−2.00610	+	1.46772i	−0.299051	+	0.218795i
$46$	6.41045	+	2.21497i	0.945170	+	0.326579i
$47$	−8.41857			−1.22797			−0.613987	−	0.789316i	$-0.710435\pi$
$47$	−8.41857			−1.22797			−0.613987	+	0.789316i	$0.710435\pi$
$48$	−5.02868	+	2.21951i	−0.725828	+	0.320359i
$49$	0.269620	+	1.87525i	0.0385171	+	0.267892i
$50$	−2.54117	−	6.59867i	−0.359376	−	0.933193i
$51$	−8.62938	−	2.53381i	−1.20835	−	0.354805i
$52$	4.79434	−	0.312205i	0.664855	−	0.0432951i
$53$	2.79031	−	3.22019i	0.383279	−	0.442328i	−0.531025	−	0.847356i	$-0.678193\pi$
$53$	2.79031	−	3.22019i	0.383279	−	0.442328i	0.914304	+	0.405028i	$0.132738\pi$
$54$	7.94737	−	0.828827i	1.08150	−	0.112789i
$55$	3.19547	−	4.17256i	0.430877	−	0.562628i
$56$	−8.37808	−	0.981826i	−1.11957	−	0.131202i
$57$	−0.582080	+	0.374080i	−0.0770984	+	0.0495481i
$58$	−7.52906	−	7.05471i	−0.988614	−	0.926329i
$59$	−8.81293	+	7.63645i	−1.14735	+	0.994181i	−0.147359	+	0.989083i	$0.547077\pi$
$59$	−8.81293	+	7.63645i	−1.14735	+	0.994181i	−0.999987	+	0.00509789i	$0.998377\pi$
$60$	−0.979873	+	6.06689i	−0.126501	+	0.783233i
$61$	−7.90931	−	1.13719i	−1.01268	−	0.145602i	−0.384057	−	0.923309i	$-0.625473\pi$
$61$	−7.90931	−	1.13719i	−1.01268	−	0.145602i	−0.628626	+	0.777708i	$0.716382\pi$
$62$	5.53236	−	10.9648i	0.702610	−	1.39254i
$63$	3.01570	+	1.37723i	0.379943	+	0.173514i
$64$	2.93848	−	7.44079i	0.367310	−	0.930099i
$65$	2.62583	−	4.68604i	0.325694	−	0.581231i
$66$	−4.22553	+	1.73452i	−0.520127	+	0.213505i
$67$	4.03312	−	6.27565i	0.492724	−	0.766693i	−0.502473	−	0.864593i	$-0.667576\pi$
$67$	4.03312	−	6.27565i	0.492724	−	0.766693i	0.995196	+	0.0979002i	$0.0312126\pi$
$68$	11.5282	−	6.19982i	1.39799	−	0.751838i
$69$	−6.53072	+	0.884400i	−0.786206	+	0.106469i
$70$	−6.02097	+	7.25901i	−0.719644	+	0.867617i
$71$	2.76141	−	4.29683i	0.327719	−	0.509940i	−0.637825	−	0.770181i	$-0.720166\pi$
$71$	2.76141	−	4.29683i	0.327719	−	0.509940i	0.965544	+	0.260241i	$0.0838020\pi$
$72$	−1.99618	+	2.42921i	−0.235252	+	0.286286i
$73$	8.40122	−	3.83671i	0.983289	−	0.449053i	0.142134	−	0.989847i	$-0.454604\pi$
$73$	8.40122	−	3.83671i	0.983289	−	0.449053i	0.841155	+	0.540795i	$0.181876\pi$
$74$	0.253814	−	6.52385i	0.0295052	−	0.758382i
$75$	5.09284	+	4.61218i	0.588070	+	0.532569i
$76$	0.220325	−	0.982632i	0.0252731	−	0.112716i
$77$	−6.93834	−	0.997582i	−0.790697	−	0.113685i
$78$	−4.02253	+	2.36938i	−0.455462	+	0.268280i
$79$	0.508994	+	0.587411i	0.0572663	+	0.0660889i	0.783660	−	0.621190i	$-0.213350\pi$
$79$	0.508994	+	0.587411i	0.0572663	+	0.0660889i	−0.726394	+	0.687279i	$0.758805\pi$
$80$	−5.18891	−	7.28528i	−0.580138	−	0.814519i
$81$	−3.72623	+	2.39470i	−0.414025	+	0.266078i
$82$	−0.192174	+	0.274910i	−0.0212221	+	0.0303587i
$83$	−0.865999	−	2.94932i	−0.0950557	−	0.323730i	0.898213	−	0.439560i	$-0.144866\pi$
$83$	−0.865999	−	2.94932i	−0.0950557	−	0.323730i	−0.993269	+	0.115830i	$0.963047\pi$
$84$	7.69792	−	2.81543i	0.839911	−	0.307189i
$85$	1.20389	−	14.5849i	0.130581	−	1.58196i
$86$	−2.86850	+	15.6142i	−0.309319	+	1.68372i
$87$	9.61954	+	2.82455i	1.03132	+	0.302824i
$88$	2.60261	−	6.11723i	0.277439	−	0.652099i
$89$	−3.79418	+	0.545520i	−0.402182	+	0.0578250i	−0.340438	−	0.940267i	$-0.610575\pi$
$89$	−3.79418	+	0.545520i	−0.402182	+	0.0578250i	−0.0617440	+	0.998092i	$0.519666\pi$
$90$	1.06285	+	3.35077i	0.112034	+	0.353202i
$91$	−7.16438			−0.751031
$92$	5.85932	−	7.59397i	0.610877	−	0.791726i
$93$			11.9338i			1.23748i
$94$	−3.79577	+	11.2844i	−0.391504	+	1.16389i
$95$	−0.787356	−	0.804802i	−0.0807811	−	0.0825710i
$96$	0.707729	+	7.74124i	0.0722323	+	0.790088i
$97$	−2.41301	−	0.708525i	−0.245005	−	0.0719398i	0.156925	−	0.987611i	$-0.449842\pi$
$97$	−2.41301	−	0.708525i	−0.245005	−	0.0719398i	−0.401929	+	0.915671i	$0.631660\pi$
$98$	2.63517	+	0.484111i	0.266192	+	0.0489026i
$99$	−1.71099	+	1.97459i	−0.171961	+	0.198453i
$100$	−9.99071	+	0.431006i	−0.999071	+	0.0431006i
$101$	14.1151	−	4.14456i	1.40450	−	0.412400i	0.510276	−	0.860011i	$-0.329543\pi$
$101$	14.1151	−	4.14456i	1.40450	−	0.412400i	0.894228	+	0.447611i	$0.147725\pi$
$102$	−7.28718	+	10.4245i	−0.721538	+	1.03218i
$103$	−0.00872923	−	0.0135830i	−0.000860117	−	0.00133837i	0.840823	−	0.541310i	$-0.182071\pi$
$103$	−0.00872923	−	0.0135830i	−0.000860117	−	0.00133837i	−0.841683	+	0.539971i	$0.818435\pi$
$104$	1.74319	−	6.56716i	0.170934	−	0.643963i
$105$	2.04597	−	8.93279i	0.199666	−	0.871751i
$106$	−3.05829	−	5.19210i	−0.297047	−	0.504301i
$107$	10.1660	+	1.46164i	0.982780	+	0.141302i	0.614929	−	0.788582i	$-0.289185\pi$
$107$	10.1660	+	1.46164i	0.982780	+	0.141302i	0.367851	+	0.929885i	$0.380094\pi$
$108$	2.47235	−	11.0265i	0.237902	−	1.06102i
$109$	2.94104	+	1.34313i	0.281701	+	0.128648i	0.551255	−	0.834337i	$-0.314149\pi$
$109$	2.94104	+	1.34313i	0.281701	+	0.128648i	−0.269554	+	0.962985i	$0.586876\pi$
$110$	−4.15218	−	6.16458i	−0.395894	−	0.587769i
$111$	2.63538	+	5.77067i	0.250139	+	0.547728i
$112$	−5.09357	+	10.7874i	−0.481297	+	1.01931i
$113$	13.3948	+	8.60833i	1.26008	+	0.809804i	0.988295	−	0.152554i	$-0.0487499\pi$
$113$	13.3948	+	8.60833i	1.26008	+	0.809804i	0.271784	+	0.962358i	$0.412386\pi$
$114$	0.238973	+	0.948893i	0.0223819	+	0.0888720i
$115$	−3.55446	−	10.1176i	−0.331455	−	0.943471i
$116$	−12.8509	+	6.91121i	−1.19318	+	0.641690i
$117$	−1.44373	+	2.24650i	−0.133473	+	0.207689i
$118$	6.26241	+	15.2561i	0.576502	+	1.40444i
$119$	−17.7550	+	8.10845i	−1.62760	+	0.743301i
$120$	7.69034	+	4.04888i	0.702028	+	0.369611i
$121$	−2.27471	+	4.98091i	−0.206791	+	0.452810i
$122$	−5.09046	+	10.0890i	−0.460868	+	0.913415i
$123$	0.0463839	−	0.322607i	0.00418230	−	0.0290885i
$124$	−12.2030	−	12.3595i	−1.09586	−	1.10991i
$125$	−5.67777	+	9.63135i	−0.507835	+	0.861454i
$126$	3.20577	−	3.42132i	0.285593	−	0.304796i
$127$	16.6574	−	10.7050i	1.47810	−	0.949919i	0.480777	−	0.876843i	$-0.340355\pi$
$127$	16.6574	−	10.7050i	1.47810	−	0.949919i	0.997326	−	0.0730762i	$-0.0232816\pi$
$128$	−8.64882	−	7.29369i	−0.764455	−	0.644677i
$129$	−4.34602	−	14.8012i	−0.382646	−	1.30317i
$130$	−5.09729	−	5.63254i	−0.447062	−	0.494006i
$131$	5.14593	+	4.45898i	0.449602	+	0.389583i	0.850020	−	0.526750i	$-0.176590\pi$
$131$	5.14593	+	4.45898i	0.449602	+	0.389583i	−0.400418	+	0.916333i	$0.631135\pi$
$132$	0.419762	+	6.44602i	0.0365356	+	0.561054i
$133$	−0.423069	+	1.44084i	−0.0366847	+	0.124937i
$134$	−6.59351	−	8.23561i	−0.569592	−	0.711449i
$135$	−8.83520	−	9.03097i	−0.760413	−	0.777262i
$136$	−3.11249	−	18.2479i	−0.266894	−	1.56474i
$137$	3.33050			0.284544			0.142272	−	0.989828i	$-0.454559\pi$
$137$	3.33050			0.284544			0.142272	+	0.989828i	$0.454559\pi$
$138$	−1.75911	+	9.15262i	−0.149746	+	0.779123i
$139$			3.03121i			0.257104i	0.991703	+	0.128552i	$0.0410330\pi$
$139$			3.03121i			0.257104i	−0.991703	+	0.128552i	$0.958967\pi$
$140$	7.01532	+	11.3435i	0.592903	+	0.958704i
$141$	−1.64639	−	11.4509i	−0.138651	−	0.964337i
$142$	−4.51447	−	5.63879i	−0.378846	−	0.473196i
$143$	1.59071	−	5.41746i	0.133022	−	0.453031i
$144$	2.35611	+	3.77099i	0.196343	+	0.314249i
$145$	−1.34203	+	16.2585i	−0.111450	+	1.35019i
$146$	−1.35482	−	12.9910i	−0.112126	−	1.07514i
$147$	−2.49797	+	0.733469i	−0.206029	+	0.0604955i
$148$	−8.63021	−	3.28169i	−0.709399	−	0.269754i
$149$	−0.383854	−	0.597288i	−0.0314465	−	0.0489317i	0.825174	−	0.564878i	$-0.191077\pi$
$149$	−0.383854	−	0.597288i	−0.0314465	−	0.0489317i	−0.856621	+	0.515946i	$0.827440\pi$
$150$	8.47849	−	4.74696i	0.692266	−	0.387587i
$151$	14.6493	−	12.6937i	1.19214	−	1.03300i	0.193487	−	0.981103i	$-0.438020\pi$
$151$	14.6493	−	12.6937i	1.19214	−	1.03300i	0.998653	−	0.0518925i	$-0.0165253\pi$
$152$	−1.21779	−	0.738377i	−0.0987760	−	0.0598903i
$153$	−1.03539	+	7.20133i	−0.0837067	+	0.582193i
$154$	−4.46553	+	8.85044i	−0.359843	+	0.713189i
$155$	−19.0190	+	3.91959i	−1.52764	+	0.314829i
$156$	1.36227	+	6.46016i	0.109069	+	0.517227i
$157$	0.957563	+	2.09677i	0.0764219	+	0.167341i	0.943987	−	0.329984i	$-0.107043\pi$
$157$	0.957563	+	2.09677i	0.0764219	+	0.167341i	−0.867565	+	0.497324i	$0.834316\pi$
$158$	1.01687	−	0.417410i	0.0808977	−	0.0332074i
$159$	4.92577	+	3.16560i	0.390639	+	0.251049i
$160$	−12.1049	+	3.67049i	−0.956973	+	0.290177i
$161$	−9.45472	+	10.7323i	−0.745137	+	0.845824i
$162$	1.52980	+	6.07441i	0.120193	+	0.477251i
$163$	−12.3554	−	7.94035i	−0.967751	−	0.621936i	−0.0416185	−	0.999134i	$-0.513251\pi$
$163$	−12.3554	−	7.94035i	−0.967751	−	0.621936i	−0.926133	+	0.377198i	$0.876888\pi$
$164$	0.281845	+	0.381545i	0.0220084	+	0.0297936i
$165$	6.30041	+	3.53044i	0.490486	+	0.274845i
$166$	−4.34377	−	0.168997i	−0.337142	−	0.0131167i
$167$	−5.17782	+	11.3379i	−0.400672	+	0.877349i	0.596530	+	0.802591i	$0.296546\pi$
$167$	−5.17782	+	11.3379i	−0.400672	+	0.877349i	−0.997202	+	0.0747582i	$0.976181\pi$
$168$	−0.302997	−	11.5878i	−0.0233767	−	0.894019i
$169$	−1.02883	+	7.15564i	−0.0791404	+	0.550434i
$170$	−19.0070	−	8.18979i	−1.45777	−	0.628128i
$171$	0.366541	+	0.423011i	0.0280301	+	0.0323485i
$172$	19.6361	+	10.8851i	1.49724	+	0.829982i
$173$	−10.9967	−	17.1112i	−0.836065	−	1.30094i	−0.951507	−	0.307628i	$-0.900465\pi$
$173$	−10.9967	−	17.1112i	−0.836065	−	1.30094i	0.115442	−	0.993314i	$-0.463172\pi$
$174$	8.12334	−	11.6206i	0.615828	−	0.880957i
$175$	14.9083	+	0.326751i	1.12696	+	0.0247000i
$176$	−7.02614	−	6.24672i	−0.529615	−	0.470864i
$177$	−12.1105	−	10.4938i	−0.910284	−	0.788766i
$178$	−0.979499	+	5.33173i	−0.0734166	+	0.399630i
$179$	−6.43768	+	21.9247i	−0.481175	+	1.63873i	0.258678	+	0.965963i	$0.416713\pi$
$179$	−6.43768	+	21.9247i	−0.481175	+	1.63873i	−0.739853	+	0.672768i	$0.765105\pi$
$180$	4.97063	+	0.0861444i	0.370489	+	0.00642082i
$181$	24.0045	−	3.45132i	1.78424	−	0.256535i	0.830466	−	0.557069i	$-0.188074\pi$
$181$	24.0045	−	3.45132i	1.78424	−	0.256535i	0.953771	+	0.300535i	$0.0971651\pi$
$182$	−3.23028	+	9.60323i	−0.239445	+	0.711839i
$183$		−	10.9806i		−	0.811707i
$184$	−7.53719	−	11.2779i	−0.555649	−	0.831417i
$185$	−8.33120	+	6.09537i	−0.612522	+	0.448141i
$186$	15.9962	+	5.38072i	1.17290	+	0.394534i
$187$	−2.18918	−	15.2261i	−0.160089	−	1.11344i
$188$	13.4143	+	10.1758i	0.978336	+	0.742147i
$189$	−4.74740	+	16.1682i	−0.345323	+	1.17606i
$190$	−1.43377	+	0.692513i	−0.104017	+	0.0502401i
$191$	3.88935	−	4.48855i	0.281424	−	0.324780i	−0.597385	−	0.801955i	$-0.703794\pi$
$191$	3.88935	−	4.48855i	0.281424	−	0.324780i	0.878809	+	0.477174i	$0.158339\pi$
$192$	10.6956	+	2.54173i	0.771886	+	0.183434i
$193$	0.218522	+	0.744218i	0.0157296	+	0.0535700i	0.966984	−	0.254838i	$-0.0820221\pi$
$193$	0.218522	+	0.744218i	0.0157296	+	0.0535700i	−0.951254	+	0.308408i	$0.900204\pi$
$194$	−2.03770	+	2.91498i	−0.146298	+	0.209283i
$195$	6.88743	+	2.65520i	0.493219	+	0.190143i
$196$	1.83706	−	3.31394i	0.131218	−	0.236710i
$197$	10.4042	−	9.01530i	0.741269	−	0.642314i	−0.200067	−	0.979782i	$-0.564116\pi$
$197$	10.4042	−	9.01530i	0.741269	−	0.642314i	0.941337	+	0.337468i	$0.109571\pi$
$198$	1.87531	+	3.18374i	0.133272	+	0.226258i
$199$	−1.00416	+	6.98406i	−0.0711827	+	0.495087i	0.922776	+	0.385336i	$0.125914\pi$
$199$	−1.00416	+	6.98406i	−0.0711827	+	0.495087i	−0.993959	+	0.109751i	$0.964995\pi$
$200$	−3.92689	+	13.5860i	−0.277673	+	0.960676i
$201$	9.32483	+	4.25851i	0.657723	+	0.300372i
$202$	0.808797	−	20.7888i	0.0569068	−	1.46269i
$203$	19.7923	−	9.03885i	1.38915	−	0.634403i
$204$	10.6875	+	14.4680i	0.748272	+	1.01296i
$205$	0.529377	−	0.0320361i	0.0369733	−	0.00223750i
$206$	−0.0221426	+	0.00557648i	−0.00154275	+	0.000388532i
$207$	1.45999	+	5.12739i	0.101477	+	0.356378i
$208$	−8.01673	−	5.29760i	−0.555860	−	0.367322i
$209$	−0.995580	−	0.639821i	−0.0688657	−	0.0442573i
$210$	−11.0511	−	6.77006i	−0.762601	−	0.467179i
$211$	11.6620	−	5.32585i	0.802844	−	0.366647i	0.0286459	−	0.999590i	$-0.490880\pi$
$211$	11.6620	−	5.32585i	0.802844	−	0.366647i	0.774198	+	0.632943i	$0.218153\pi$
$212$	−8.33848	+	1.75835i	−0.572689	+	0.120764i
$213$	6.38456	+	2.91573i	0.437463	+	0.199782i
$214$	6.54284	−	12.9676i	0.447260	−	0.886444i
$215$	22.1614	−	11.7877i	1.51139	−	0.803913i
$216$	−13.6653	−	8.28559i	−0.929804	−	0.563763i
$217$	16.9608	+	19.5738i	1.15137	+	1.32876i
$218$	3.12641	−	3.33662i	0.211747	−	0.225984i
$219$	6.86165	+	10.6769i	0.463668	+	0.721481i
$220$	−10.1352	+	2.78614i	−0.683316	+	0.187841i
$221$	−4.42944	−	15.0853i	−0.297956	−	1.01475i
$222$	8.92332	−	0.930608i	0.598894	−	0.0624583i
$223$	−0.232665	+	0.268510i	−0.0155804	+	0.0179807i	−0.763486	−	0.645824i	$-0.776514\pi$
$223$	−0.232665	+	0.268510i	−0.0155804	+	0.0179807i	0.747906	+	0.663805i	$0.231059\pi$
$224$	12.1630	+	11.6913i	0.812673	+	0.781159i
$225$	3.10671	−	4.60886i	0.207114	−	0.307257i
$226$	17.5782	−	14.0733i	1.16928	−	0.936140i
$227$	0.978245	−	0.140650i	0.0649284	−	0.00933530i	−0.109774	−	0.993957i	$-0.535013\pi$
$227$	0.978245	−	0.140650i	0.0649284	−	0.00933530i	0.174702	+	0.984621i	$0.444104\pi$
$228$	1.37966	+	0.107515i	0.0913700	+	0.00712037i
$229$			26.9520i			1.78104i	0.454944	+	0.890520i	$0.349659\pi$
$229$			26.9520i			1.78104i	−0.454944	+	0.890520i	$0.650341\pi$
$230$	−15.1644	+	0.202609i	−0.999911	+	0.0133597i
$231$		−	9.63256i		−	0.633776i
$232$	3.46963	+	20.3417i	0.227792	+	1.33550i
$233$	−16.5377	+	2.37776i	−1.08342	+	0.155772i	−0.660820	−	0.750545i	$-0.729791\pi$
$233$	−16.5377	+	2.37776i	−1.08342	+	0.155772i	−0.422599	+	0.906317i	$0.638882\pi$
$234$	2.36028	+	2.94810i	0.154296	+	0.192723i
$235$	17.7086	−	6.38484i	1.15518	−	0.416501i
$236$	23.2731	−	1.51553i	1.51495	−	0.0986529i
$237$	−0.699449	+	0.807207i	−0.0454341	+	0.0524337i
$238$	2.86327	+	27.4550i	0.185598	+	1.77965i
$239$	−4.21297	−	14.3481i	−0.272515	−	0.928099i	−0.976070	−	0.217459i	$-0.930223\pi$
$239$	−4.21297	−	14.3481i	−0.272515	−	0.928099i	0.703555	−	0.710641i	$-0.251595\pi$
$240$	8.89460	−	8.48266i	0.574144	−	0.547553i
$241$	10.5646	+	16.4388i	0.680523	+	1.05891i	0.994007	+	0.109320i	$0.0348675\pi$
$241$	10.5646	+	16.4388i	0.680523	+	1.05891i	−0.313484	+	0.949594i	$0.601496\pi$
$242$	5.65085	+	5.29484i	0.363251	+	0.340365i
$243$	7.11415	+	8.21016i	0.456373	+	0.526682i
$244$	11.2282	+	11.3723i	0.718814	+	0.728034i
$245$	−1.98938	−	3.74013i	−0.127097	−	0.238948i
$246$	−0.411513	−	0.207631i	−0.0262371	−	0.0132381i
$247$	−1.10026	−	0.502472i	−0.0700079	−	0.0319715i
$248$	−22.0689	+	10.7844i	−1.40138	+	0.684807i
$249$	3.84228	−	1.75471i	0.243495	−	0.111200i
$250$	10.3500	+	11.9531i	0.654591	+	0.755983i
$251$	−5.34769	−	3.43675i	−0.337543	−	0.216926i	0.360878	−	0.932613i	$-0.382477\pi$
$251$	−5.34769	−	3.43675i	−0.337543	−	0.216926i	−0.698421	+	0.715687i	$0.746114\pi$
$252$	−3.14056	−	5.83967i	−0.197837	−	0.367865i
$253$	−6.01617	−	9.53224i	−0.378233	−	0.599287i
$254$	−6.83869	−	27.1545i	−0.429097	−	1.70382i
$255$	20.0738	−	1.21480i	1.25707	−	0.0760735i
$256$	−13.6761	+	8.30441i	−0.854759	+	0.519026i
$257$	11.3805	−	5.19731i	0.709897	−	0.324199i	−0.0275345	−	0.999621i	$-0.508766\pi$
$257$	11.3805	−	5.19731i	0.709897	−	0.324199i	0.737432	+	0.675422i	$0.236038\pi$
$258$	−21.7992	−	0.848111i	−1.35716	−	0.0528011i
$259$	12.5240	+	5.71954i	0.778206	+	0.355395i
$260$	−9.84819	+	4.29287i	−0.610759	+	0.266232i
$261$	1.15420	−	8.02764i	0.0714432	−	0.496898i
$262$	8.29707	−	4.88721i	0.512595	−	0.301933i
$263$	−11.1644	+	9.67400i	−0.688426	+	0.596525i	−0.927207	−	0.374549i	$-0.877798\pi$
$263$	−11.1644	+	9.67400i	−0.688426	+	0.596525i	0.238781	+	0.971073i	$0.423252\pi$
$264$	8.82958	+	2.34373i	0.543423	+	0.144247i
$265$	−3.42721	+	8.88998i	−0.210532	+	0.546107i
$266$	1.74057	+	1.21673i	0.106721	+	0.0746027i
$267$	−1.48402	−	5.05412i	−0.0908208	−	0.309307i
$268$	−14.0120	+	5.12474i	−0.855920	+	0.313043i
$269$	14.9415	−	17.2434i	0.910997	−	1.05135i	−0.0874789	−	0.996166i	$-0.527881\pi$
$269$	14.9415	−	17.2434i	0.910997	−	1.05135i	0.998476	−	0.0551807i	$-0.0175735\pi$
$270$	−16.0888	+	7.77093i	−0.979136	+	0.472924i
$271$	0.135663	−	0.462025i	0.00824092	−	0.0280660i	−0.955270	−	0.295735i	$-0.904435\pi$
$271$	0.135663	−	0.462025i	0.00824092	−	0.0280660i	0.963511	+	0.267669i	$0.0862535\pi$
$272$	−25.8630	−	4.05559i	−1.56818	−	0.245906i
$273$	−1.40111	−	9.74493i	−0.0847990	−	0.589790i
$274$	1.50166	−	4.46425i	0.0907186	−	0.269695i
$275$	−3.55717	+	11.2006i	−0.214505	+	0.675420i
$276$	11.4751	+	6.48468i	0.690722	+	0.390332i
$277$			7.37704i			0.443243i	0.975133	+	0.221622i	$0.0711350\pi$
$277$			7.37704i			0.443243i	−0.975133	+	0.221622i	$0.928865\pi$
$278$	4.06308	+	1.36672i	0.243687	+	0.0819702i
$279$	9.55550	−	1.37387i	0.572073	−	0.0822517i
$280$	18.3681	−	4.28884i	1.09770	−	0.256307i
$281$	−1.99948	+	6.80960i	−0.119279	+	0.406227i	−0.997388	−	0.0722344i	$-0.976987\pi$
$281$	−1.99948	+	6.80960i	−0.119279	+	0.406227i	0.878109	+	0.478461i	$0.158805\pi$
$282$	−16.0912	−	2.95614i	−0.958218	−	0.176036i
$283$	1.08790	+	0.942673i	0.0646691	+	0.0560361i	0.686596	−	0.727040i	$-0.259104\pi$
$283$	1.08790	+	0.942673i	0.0646691	+	0.0560361i	−0.621927	+	0.783076i	$0.713650\pi$
$284$	−9.59379	+	3.50883i	−0.569287	+	0.208211i
$285$	0.940705	−	1.22835i	0.0557226	−	0.0727610i
$286$	−6.54442	−	4.57484i	−0.386980	−	0.270516i
$287$	−0.382423	−	0.595062i	−0.0225737	−	0.0351254i
$288$	6.11701	−	1.45789i	0.360448	−	0.0859072i
$289$	−16.9177	−	19.5240i	−0.995158	−	1.14847i
$290$	21.1880	+	9.12952i	1.24420	+	0.536104i
$291$	0.491826	−	3.42073i	0.0288314	−	0.200526i
$292$	−18.0242	−	4.04137i	−1.05478	−	0.236503i
$293$	7.14599	−	15.6475i	0.417473	−	0.914138i	−0.577723	−	0.816233i	$-0.696059\pi$
$293$	7.14599	−	15.6475i	0.417473	−	0.914138i	0.995196	−	0.0979053i	$-0.0312142\pi$
$294$	−0.143134	+	3.67901i	−0.00834774	+	0.214564i
$295$	12.7465	−	22.7474i	0.742131	−	1.32440i
$296$	−8.29002	+	10.0884i	−0.481848	+	0.586376i
$297$	−11.1718	−	7.17965i	−0.648251	−	0.416606i
$298$	−0.973685	+	0.245217i	−0.0564040	+	0.0142050i
$299$	−7.47287	−	8.76836i	−0.432167	−	0.507087i
$300$	−2.54009	−	13.5050i	−0.146652	−	0.779711i
$301$	−28.1644	−	18.1001i	−1.62337	−	1.04328i
$302$	−10.4097	−	25.3594i	−0.599009	−	1.45927i
$303$	8.39783	+	18.3887i	0.482443	+	1.05640i
$304$	−1.53881	+	1.29942i	−0.0882568	+	0.0745271i
$305$	17.4999	−	3.60651i	1.00204	−	0.206508i
$306$	9.18591	+	4.63480i	0.525124	+	0.264954i
$307$	0.980680	−	6.82078i	0.0559704	−	0.389282i	−0.942510	−	0.334177i	$-0.891542\pi$
$307$	0.980680	−	6.82078i	0.0559704	−	0.389282i	0.998481	−	0.0551051i	$-0.0175494\pi$
$308$	9.84982	+	9.97616i	0.561246	+	0.568444i
$309$	0.0167683	−	0.0145298i	0.000953914	−	0.000826571i
$310$	−3.32144	+	27.2606i	−0.188645	+	1.54830i
$311$	−10.4231	−	16.2187i	−0.591041	−	0.919677i	−0.999975	−	0.00711339i	$-0.997736\pi$
$311$	−10.4231	−	16.2187i	−0.591041	−	0.919677i	0.408934	−	0.912564i	$-0.365901\pi$
$312$	9.27350	+	1.08676i	0.525009	+	0.0615257i
$313$	−8.50993	+	2.49874i	−0.481010	+	0.141237i	−0.513243	−	0.858243i	$-0.671556\pi$
$313$	−8.50993	+	2.49874i	−0.481010	+	0.141237i	0.0322335	+	0.999480i	$0.489738\pi$
$314$	3.24229	−	0.338136i	0.182973	−	0.0190821i
$315$	−7.38811	−	0.609840i	−0.416273	−	0.0343606i
$316$	−0.101015	−	1.55123i	−0.00568255	−	0.0872633i
$317$	−6.34587	+	21.6120i	−0.356419	+	1.21385i	0.564937	+	0.825134i	$0.308900\pi$
$317$	−6.34587	+	21.6120i	−0.356419	+	1.21385i	−0.921356	+	0.388719i	$0.872918\pi$
$318$	6.46415	−	5.17526i	0.362491	−	0.290214i
$319$	2.44038	+	16.9732i	0.136635	+	0.950316i
$320$	−0.537880	+	17.8805i	−0.0300684	+	0.999548i
$321$			14.1135i			0.787739i
$322$	10.1228	+	17.5122i	0.564120	+	0.975918i
$323$	−3.29539			−0.183360
$324$	8.83197	+	0.688267i	0.490665	+	0.0382370i
$325$	−1.96948	+	11.8487i	−0.109247	+	0.657245i
$326$	−16.2142	+	12.9812i	−0.898020	+	0.718963i
$327$	−1.25174	+	4.26305i	−0.0692216	+	0.235747i
$328$	0.638506	−	0.205758i	0.0352556	−	0.0113611i
$329$	−18.9748	−	16.4418i	−1.04612	−	0.906465i
$330$	7.57298	−	6.85334i	0.416879	−	0.377264i
$331$	6.81531	+	23.2108i	0.374603	+	1.27578i	0.904046	+	0.427436i	$0.140583\pi$
$331$	6.81531	+	23.2108i	0.374603	+	1.27578i	−0.529442	+	0.848346i	$0.677599\pi$
$332$	−2.18505	+	5.74625i	−0.119920	+	0.315366i
$333$	4.31723	−	2.77452i	0.236583	−	0.152043i
$334$	12.8628	+	12.0524i	0.703822	+	0.659480i
$335$	−3.72414	+	16.2598i	−0.203471	+	0.888366i
$336$	−15.6691	−	4.81858i	−0.854817	−	0.262875i
$337$	−1.32772	+	9.23447i	−0.0723253	+	0.503034i	0.921170	+	0.389161i	$0.127235\pi$
$337$	−1.32772	+	9.23447i	−0.0723253	+	0.503034i	−0.993495	+	0.113873i	$0.963674\pi$
$338$	9.12763	+	4.60539i	0.496478	+	0.250500i
$339$	−9.08941	+	19.9030i	−0.493669	+	1.08098i
$340$	−19.5476	+	21.7847i	−1.06012	+	1.18144i
$341$	−18.5668	+	8.47919i	−1.00545	+	0.459174i
$342$	0.732276	−	0.300589i	0.0395969	−	0.0162540i
$343$	8.23201	−	12.8093i	0.444487	−	0.691635i
$344$	23.4441	−	21.4126i	1.26402	−	1.15449i
$345$	13.0667	−	6.81340i	0.703490	−	0.366821i
$346$	−27.8943	+	7.02502i	−1.49961	+	0.377667i
$347$	−22.5718	−	14.5060i	−1.21172	−	0.778723i	−0.230771	−	0.973008i	$-0.574125\pi$
$347$	−22.5718	−	14.5060i	−1.21172	−	0.778723i	−0.980945	+	0.194285i	$0.937761\pi$
$348$	−11.9138	−	16.1281i	−0.638645	−	0.864559i
$349$	3.14412	+	6.88467i	0.168301	+	0.368528i	0.974924	−	0.222539i	$-0.0714343\pi$
$349$	3.14412	+	6.88467i	0.168301	+	0.368528i	−0.806623	+	0.591067i	$0.798707\pi$
$350$	7.15983	−	19.8359i	0.382709	−	1.06027i
$351$	−12.3464	−	5.63842i	−0.659002	−	0.300956i
$352$	−11.5411	+	6.60140i	−0.615144	+	0.351856i
$353$	−1.82586	−	0.262519i	−0.0971809	−	0.0139725i	0.0935528	−	0.995614i	$-0.470178\pi$
$353$	−1.82586	−	0.262519i	−0.0971809	−	0.0139725i	−0.190734	+	0.981642i	$0.561087\pi$
$354$	−19.5265	+	11.5017i	−1.03782	+	0.611306i
$355$	−2.54985	+	11.1328i	−0.135332	+	0.590867i
$356$	6.70508	+	3.71691i	0.355368	+	0.196996i
$357$	−14.5013	−	22.5645i	−0.767492	−	1.19424i
$358$	26.4856	+	18.5146i	1.39981	+	0.978527i
$359$	−5.03132	+	1.47733i	−0.265543	+	0.0779704i	−0.411794	−	0.911277i	$-0.635098\pi$
$359$	−5.03132	+	1.47733i	−0.265543	+	0.0779704i	0.146251	+	0.989248i	$0.453279\pi$
$360$	2.35663	−	6.62385i	0.124205	−	0.349108i
$361$	12.2763	−	14.1676i	0.646123	−	0.745665i
$362$	6.19696	−	33.7320i	0.325705	−	1.77291i
$363$	−7.21985	−	2.11994i	−0.378944	−	0.111268i
$364$	11.4158	+	8.65983i	0.598352	+	0.453898i
$365$	−14.7623	+	14.4423i	−0.772693	+	0.755943i
$366$	−14.7185	−	4.95093i	−0.769348	−	0.258789i
$367$			25.4523i			1.32860i	0.747467	+	0.664299i	$0.231270\pi$
$367$			25.4523i			1.32860i	−0.747467	+	0.664299i	$0.768730\pi$
$368$	−18.5154	+	5.01797i	−0.965182	+	0.261580i
$369$	−0.263654			−0.0137253
$370$	4.41394	+	13.9155i	0.229470	+	0.723434i
$371$	12.5783	−	1.80849i	0.653034	−	0.0938921i
$372$	14.4248	−	19.0155i	0.747890	−	0.985906i
$373$	−10.8478	−	3.18522i	−0.561680	−	0.164924i	−0.0114459	−	0.999934i	$-0.503643\pi$
$373$	−10.8478	−	3.18522i	−0.561680	−	0.164924i	−0.550234	+	0.835010i	$0.685462\pi$
$374$	−21.3963	−	3.93075i	−1.10638	−	0.203254i
$375$	−14.2109	−	5.83929i	−0.733846	−	0.301539i
$376$	19.6880	−	13.3926i	1.01533	−	0.690669i
$377$	4.93769	+	16.8162i	0.254304	+	0.866080i
$378$	19.5315	+	13.6534i	1.00459	+	0.702255i
$379$	−4.34830	+	2.79448i	−0.223357	+	0.143543i	−0.647534	−	0.762036i	$-0.724200\pi$
$379$	−4.34830	+	2.79448i	−0.223357	+	0.143543i	0.424177	+	0.905579i	$0.360563\pi$
$380$	0.281793	+	2.23409i	0.0144557	+	0.114606i
$381$	17.8185	+	20.5637i	0.912871	+	1.05351i
$382$	−4.26288	−	7.23714i	−0.218108	−	0.370284i
$383$	15.5961	+	2.24238i	0.796924	+	0.114580i	0.528736	−	0.848786i	$-0.322666\pi$
$383$	15.5961	+	2.24238i	0.796924	+	0.114580i	0.268188	+	0.963367i	$0.413575\pi$
$384$	8.22939	−	13.1905i	0.419954	−	0.673123i
$385$	15.3515	−	3.16376i	0.782386	−	0.161240i
$386$	1.09609	+	0.0426438i	0.0557894	+	0.00217051i
$387$	−11.3511	+	5.18388i	−0.577010	+	0.263512i
$388$	2.98851	+	4.04566i	0.151719	+	0.205387i
$389$	−4.68374	+	7.28804i	−0.237475	+	0.369518i	−0.939452	−	0.342682i	$-0.888665\pi$
$389$	−4.68374	+	7.28804i	−0.237475	+	0.369518i	0.701977	+	0.712200i	$0.252301\pi$
$390$	6.66447	−	8.03482i	0.337469	−	0.406859i
$391$	−28.4433	−	13.2725i	−1.43844	−	0.671218i
$392$	−3.61375	−	3.95661i	−0.182522	−	0.199839i
$393$	−5.05869	+	7.87148i	−0.255177	+	0.397064i
$394$	−7.39316	−	18.0108i	−0.372462	−	0.907369i
$395$	−1.51619	−	0.849596i	−0.0762876	−	0.0427478i
$396$	5.11306	−	1.07820i	0.256941	−	0.0541817i
$397$	22.2933	+	10.1810i	1.11887	+	0.510969i	0.886996	−	0.461777i	$-0.152788\pi$
$397$	22.2933	+	10.1810i	1.11887	+	0.510969i	0.231871	+	0.972747i	$0.425515\pi$
$398$	8.90877	+	4.49496i	0.446556	+	0.225312i
$399$	−2.04256	−	0.293675i	−0.102256	−	0.0147022i
$400$	16.4403	+	11.3893i	0.822015	+	0.569466i
$401$	18.8608	−	16.3430i	0.941863	−	0.816129i	−0.0412461	−	0.999149i	$-0.513133\pi$
$401$	18.8608	−	16.3430i	0.941863	−	0.816129i	0.983109	+	0.183020i	$0.0585873\pi$
$402$	9.91254	−	10.5790i	0.494393	−	0.527635i
$403$	−17.5501	+	11.2788i	−0.874233	+	0.561835i
$404$	−27.5008	−	10.4574i	−1.36822	−	0.520274i
$405$	6.02199	−	7.86336i	0.299235	−	0.390733i
$406$	−3.19181	−	30.6053i	−0.158407	−	1.51892i
$407$	−7.10564	+	8.20034i	−0.352213	+	0.406476i
$408$	24.2119	−	7.80225i	1.19867	−	0.386269i
$409$	−16.5670	−	4.86451i	−0.819186	−	0.240535i	−0.154820	−	0.987943i	$-0.549480\pi$
$409$	−16.5670	−	4.86451i	−0.819186	−	0.240535i	−0.664365	+	0.747408i	$0.731298\pi$
$410$	0.195744	−	0.724028i	0.00966713	−	0.0357572i
$411$	0.651333	+	4.53012i	0.0321279	+	0.223454i
$412$	−0.00250889	+	0.0321946i	−0.000123604	+	0.00158611i
$413$	−34.7780			−1.71131
$414$	7.53110	+	0.354848i	0.370134	+	0.0174398i
$415$	4.05848	+	5.54716i	0.199223	+	0.272299i
$416$	−10.7156	+	8.35714i	−0.525374	+	0.409742i
$417$	−4.12303	+	0.592803i	−0.201906	+	0.0290297i
$418$	−1.30651	+	1.04601i	−0.0639036	+	0.0511618i
$419$	−12.2265	−	3.59001i	−0.597301	−	0.175384i	−0.0309132	−	0.999522i	$-0.509842\pi$
$419$	−12.2265	−	3.59001i	−0.597301	−	0.175384i	−0.566388	+	0.824139i	$0.691660\pi$
$420$	−14.0574	+	11.7606i	−0.685932	+	0.573858i
$421$	−7.36145	−	6.37873i	−0.358775	−	0.310880i	0.456758	−	0.889591i	$-0.349011\pi$
$421$	−7.36145	−	6.37873i	−0.358775	−	0.310880i	−0.815533	+	0.578711i	$0.803556\pi$
$422$	−1.88067	−	18.0332i	−0.0915497	−	0.877843i
$423$	−8.97928	+	2.63655i	−0.436588	+	0.128194i
$424$	−1.40274	+	11.9698i	−0.0681231	+	0.581305i
$425$	8.52916	+	31.5928i	0.413725	+	1.53248i
$426$	6.78695	−	7.24329i	0.328829	−	0.350939i
$427$	−15.6060	−	18.0103i	−0.755228	−	0.871580i
$428$	−14.4318	−	14.6169i	−0.697589	−	0.706536i
$429$	7.67988	+	1.10420i	0.370788	+	0.0533113i
$430$	−5.80820	−	35.0203i	−0.280097	−	1.68883i
$431$	−0.149866	+	0.328161i	−0.00721879	+	0.0158069i	−0.913207	−	0.407496i	$-0.866402\pi$
$431$	−0.149866	+	0.328161i	−0.00721879	+	0.0158069i	0.905988	+	0.423303i	$0.139129\pi$
$432$	−17.2675	+	14.5813i	−0.830784	+	0.701543i
$433$	−13.5445	−	29.6582i	−0.650905	−	1.42528i	−0.890760	−	0.454474i	$-0.849827\pi$
$433$	−13.5445	−	29.6582i	−0.650905	−	1.42528i	0.239855	−	0.970809i	$-0.422900\pi$
$434$	33.8842	−	13.9090i	1.62650	−	0.667653i
$435$	−22.3771	+	1.35419i	−1.07290	+	0.0649283i
$436$	−3.06281	−	5.69509i	−0.146682	−	0.272745i
$437$	−2.20470	+	0.985095i	−0.105465	+	0.0471235i
$438$	17.4053	−	4.38342i	0.831657	−	0.209448i
$439$	−3.54381	+	5.51427i	−0.169137	+	0.263182i	−0.915466	−	0.402395i	$-0.868178\pi$
$439$	−3.54381	+	5.51427i	−0.169137	+	0.263182i	0.746330	+	0.665577i	$0.231814\pi$
$440$	−0.835198	+	14.8416i	−0.0398165	+	0.707545i
$441$	0.874873	+	1.91570i	0.0416606	+	0.0912240i
$442$	−22.2177	−	0.864390i	−1.05679	−	0.0411148i
$443$	−1.05914	+	2.31919i	−0.0503211	+	0.110188i	−0.933123	−	0.359558i	$-0.882927\pi$
$443$	−1.05914	+	2.31919i	−0.0503211	+	0.110188i	0.882801	+	0.469746i	$0.155655\pi$
$444$	2.77596	−	12.3805i	0.131741	−	0.587554i
$445$	7.56739	−	4.02510i	0.358729	−	0.190808i
$446$	0.255010	+	0.432933i	0.0120751	+	0.0205000i
$447$	0.737357	−	0.638924i	0.0348758	−	0.0302201i
$448$	21.1552	−	11.0320i	0.999491	−	0.521214i
$449$	19.2786	−	12.3896i	0.909813	−	0.584702i	0.000128180	−	1.00000i	$-0.499959\pi$
$449$	19.2786	−	12.3896i	0.909813	−	0.584702i	0.909685	+	0.415298i	$0.136323\pi$
$450$	−4.77702	−	6.24231i	−0.225191	−	0.294265i
$451$	0.534875	−	0.157054i	0.0251863	−	0.00739536i
$452$	−10.9383	−	29.9074i	−0.514495	−	1.40673i
$453$	20.1307	+	17.4434i	0.945823	+	0.819560i
$454$	0.252542	−	1.37467i	0.0118524	−	0.0645164i
$455$	15.0704	−	5.43364i	0.706512	−	0.254733i
$456$	0.766176	−	1.80083i	0.0358795	−	0.0843317i
$457$	−4.47837	−	31.1477i	−0.209489	−	1.45703i	−0.774828	−	0.632172i	$-0.782164\pi$
$457$	−4.47837	−	31.1477i	−0.209489	−	1.45703i	0.565339	−	0.824859i	$-0.308745\pi$
$458$	36.1268	+	12.1522i	1.68810	+	0.567833i
$459$	−36.9787			−1.72602
$460$	−6.56576	+	20.4179i	−0.306130	+	0.951990i
$461$	24.8482			1.15730			0.578648	−	0.815577i	$-0.303580\pi$
$461$	24.8482			1.15730			0.578648	+	0.815577i	$0.303580\pi$
$462$	−12.9116	−	4.34314i	−0.600702	−	0.202061i
$463$	−2.73665	−	19.0338i	−0.127183	−	0.884577i	−0.949101	−	0.314972i	$-0.898005\pi$
$463$	−2.73665	−	19.0338i	−0.127183	−	0.884577i	0.821918	−	0.569606i	$-0.192904\pi$
$464$	28.8307	+	4.52094i	1.33843	+	0.209880i
$465$	−9.05087	−	25.1030i	−0.419724	−	1.16412i
$466$	−4.26934	+	23.2394i	−0.197773	+	1.07654i
$467$	12.2923	+	10.6513i	0.568819	+	0.492885i	0.891129	−	0.453750i	$-0.149914\pi$
$467$	12.2923	+	10.6513i	0.568819	+	0.492885i	−0.322310	+	0.946634i	$0.604459\pi$
$468$	5.01588	−	1.83450i	0.231859	−	0.0848000i
$469$	21.3469	−	6.26802i	0.985709	−	0.289430i
$470$	−0.573842	−	26.6157i	−0.0264694	−	1.22769i
$471$	−2.66474	+	1.71253i	−0.122785	+	0.0789091i
$472$	8.46194	−	31.8788i	0.389492	−	1.46734i
$473$	19.9401	−	17.2782i	0.916845	−	0.794451i
$474$	0.766623	+	1.30150i	0.0352121	+	0.0597801i
$475$	2.26660	+	1.09577i	0.103999	+	0.0502773i
$476$	38.0921	+	8.54099i	1.74595	+	0.391475i
$477$	1.96765	−	4.30855i	0.0900925	−	0.197275i
$478$	−21.1319	−	0.822147i	−0.966550	−	0.0376041i
$479$	−9.35204	−	20.4781i	−0.427306	−	0.935669i	−0.993756	−	0.111573i	$-0.964411\pi$
$479$	−9.35204	−	20.4781i	−0.427306	−	0.935669i	0.566450	−	0.824096i	$-0.308316\pi$
$480$	−7.35986	−	15.7471i	−0.335930	−	0.718754i
$481$	−5.99575	+	9.32957i	−0.273383	+	0.425392i
$482$	26.7981	−	6.74894i	1.22062	−	0.307406i
$483$	−16.4470	−	10.7614i	−0.748365	−	0.489659i
$484$	9.64514	−	5.18713i	0.438415	−	0.235779i
$485$	5.61318	−	0.339691i	0.254882	−	0.0154246i
$486$	14.2126	−	5.83409i	0.644698	−	0.264640i
$487$	−5.84736	−	12.8039i	−0.264969	−	0.580201i	0.729648	−	0.683823i	$-0.239684\pi$
$487$	−5.84736	−	12.8039i	−0.264969	−	0.580201i	−0.994617	+	0.103622i	$0.966957\pi$
$488$	20.3061	−	9.92295i	0.919214	−	0.449191i
$489$	8.38409	−	18.3586i	0.379142	−	0.830205i
$490$	−5.91029	+	0.980238i	−0.267000	+	0.0442826i
$491$	−24.9758	−	3.59097i	−1.12714	−	0.162058i	−0.446575	−	0.894746i	$-0.647357\pi$
$491$	−24.9758	−	3.59097i	−1.12714	−	0.162058i	−0.680565	+	0.732688i	$0.738266\pi$
$492$	−0.463855	+	0.457981i	−0.0209122	+	0.0206474i
$493$	31.2689	+	36.0863i	1.40828	+	1.62524i
$494$	−1.16961	+	1.24825i	−0.0526231	+	0.0561613i
$495$	2.10153	−	5.45124i	0.0944566	−	0.245015i
$496$	4.50505	+	34.4439i	0.202283	+	1.54658i
$497$	14.6159	−	4.29161i	0.655612	−	0.192505i
$498$	−0.619626	−	5.94141i	−0.0277661	−	0.266241i
$499$	−2.88149	−	2.49683i	−0.128993	−	0.111773i	0.587975	−	0.808879i	$-0.299925\pi$
$499$	−2.88149	−	2.49683i	−0.128993	−	0.111773i	−0.716968	+	0.697106i	$0.754471\pi$
$500$	20.6888	−	8.48382i	0.925230	−	0.379408i
$501$	−16.4343	−	4.82553i	−0.734228	−	0.215589i
$502$	−7.01783	+	5.61854i	−0.313221	+	0.250768i
$503$	33.4604	−	4.81088i	1.49193	−	0.214507i	0.652420	−	0.757857i	$-0.273754\pi$
$503$	33.4604	−	4.81088i	1.49193	−	0.214507i	0.839506	+	0.543351i	$0.182845\pi$
$504$	−9.24358	+	1.57665i	−0.411742	+	0.0702298i
$505$	−26.5480	+	19.4234i	−1.18137	+	0.864329i
$506$	−15.4897	+	3.76625i	−0.688602	+	0.167430i
$507$	−9.93424			−0.441195
$508$	−39.4816	−	3.07676i	−1.75171	−	0.136509i
$509$	−0.390539	−	2.71626i	−0.0173103	−	0.120396i	0.979334	−	0.202249i	$-0.0648252\pi$
$509$	−0.390539	−	2.71626i	−0.0173103	−	0.120396i	−0.996644	+	0.0818534i	$0.973916\pi$
$510$	7.42255	−	27.4549i	0.328676	−	1.21572i
$511$	26.4290	+	7.76024i	1.16915	+	0.343293i
$512$	4.96503	+	22.0760i	0.219425	+	0.975629i
$513$	−1.86303	+	2.15005i	−0.0822546	+	0.0949269i
$514$	−1.83528	−	17.5980i	−0.0809508	−	0.776213i
$515$	0.0286637	+	0.0219516i	0.00126308	+	0.000967301i
$516$	−10.9657	+	28.8376i	−0.482737	+	1.26950i
$517$	16.6457	−	10.6975i	0.732077	−	0.470478i
$518$	13.3134	−	14.2086i	0.584957	−	0.624288i
$519$	21.1240	−	18.3040i	0.927239	−	0.803457i
$520$	1.31385	+	15.1362i	0.0576162	+	0.663767i
$521$	−8.84431	−	1.27162i	−0.387476	−	0.0557107i	−0.0541759	−	0.998531i	$-0.517253\pi$
$521$	−8.84431	−	1.27162i	−0.387476	−	0.0557107i	−0.333300	+	0.942821i	$0.608162\pi$
$522$	−10.2399	−	5.16661i	−0.448190	−	0.226136i
$523$	20.1970	+	9.22368i	0.883155	+	0.403323i	0.804761	−	0.593599i	$-0.202294\pi$
$523$	20.1970	+	9.22368i	0.883155	+	0.403323i	0.0783940	+	0.996922i	$0.475021\pi$
$524$	−2.80988	−	13.3251i	−0.122750	−	0.582108i
$525$	2.47111	+	20.3420i	0.107848	+	0.887798i
$526$	7.93335	+	19.3267i	0.345910	+	0.842685i
$527$	−30.7283	+	47.8142i	−1.33855	+	2.08282i
$528$	7.12266	−	10.7785i	0.309974	−	0.469076i
$529$	−22.9969	−	0.377040i	−0.999866	−	0.0163930i
$530$	10.3710	+	8.60220i	0.450487	+	0.373656i
$531$	−7.00830	+	10.9051i	−0.304134	+	0.473242i
$532$	2.41571	−	1.78448i	0.104734	−	0.0773668i
$533$	0.518271	−	0.236686i	0.0224488	−	0.0102520i
$534$	−7.44373	−	0.289602i	−0.322122	−	0.0125323i
$535$	−22.4928	+	4.63551i	−0.972450	+	0.200410i
$536$	0.551525	+	21.0925i	0.0238222	+	0.911058i
$537$	−31.0808	−	4.46875i	−1.34124	−	0.192841i
$538$	−16.3764	−	27.8024i	−0.706037	−	1.19865i
$539$	−2.91600	−	3.36524i	−0.125601	−	0.144951i
$540$	3.16209	+	25.0695i	0.136075	+	1.07882i
$541$	−20.1321	+	12.9381i	−0.865548	+	0.556254i	−0.896388	−	0.443270i	$-0.853818\pi$
$541$	−20.1321	+	12.9381i	−0.865548	+	0.556254i	0.0308400	+	0.999524i	$0.490182\pi$
$542$	−0.558136	−	0.390162i	−0.0239740	−	0.0167589i
$543$	9.38891	+	31.9757i	0.402917	+	1.37221i
$544$	−17.0973	+	32.8386i	−0.733041	+	1.40794i
$545$	−7.20520	−	0.594742i	−0.308637	−	0.0254760i
$546$	−13.6940	−	2.51574i	−0.586048	−	0.107664i
$547$	−18.0910	−	5.31199i	−0.773514	−	0.227124i	−0.128926	−	0.991654i	$-0.541153\pi$
$547$	−18.0910	−	5.31199i	−0.773514	−	0.227124i	−0.644588	+	0.764530i	$0.722971\pi$
$548$	−5.30686	−	4.02569i	−0.226698	−	0.171969i
$549$	−8.79225	+	1.26413i	−0.375244	+	0.0539519i
$550$	13.4095	+	9.81820i	0.571785	+	0.418649i
$551$	3.67352			0.156497
$552$	13.8661	−	12.4576i	0.590179	−	0.530231i
$553$			2.31806i			0.0985741i
$554$	9.88827	+	3.32616i	0.420112	+	0.141315i
$555$	−9.92018	−	10.1400i	−0.421088	−	0.430418i
$556$	3.66393	−	4.82998i	0.155385	−	0.204837i
$557$	2.97377	+	0.873177i	0.126003	+	0.0369977i	0.344126	−	0.938924i	$-0.388175\pi$
$557$	2.97377	+	0.873177i	0.126003	+	0.0369977i	−0.218123	+	0.975921i	$0.569994\pi$
$558$	2.46684	−	13.4278i	0.104429	−	0.568443i
$559$	17.6595	−	20.3801i	0.746917	−	0.861988i
$560$	2.53300	−	26.5546i	0.107039	−	1.12214i
$561$	20.2823	−	5.95541i	0.856318	−	0.251438i
$562$	8.22615	+	5.75045i	0.346999	+	0.242568i
$563$	1.24438	+	1.93629i	0.0524443	+	0.0816049i	0.866486	−	0.499202i	$-0.166373\pi$
$563$	1.24438	+	1.93629i	0.0524443	+	0.0816049i	−0.814041	+	0.580807i	$0.802737\pi$
$564$	−11.2177	+	20.2360i	−0.472349	+	0.852090i
$565$	−34.7050	−	7.94884i	−1.46005	−	0.334410i
$566$	1.75408	−	1.03320i	0.0737297	−	0.0434288i
$567$	−13.0756	−	1.87998i	−0.549123	−	0.0789519i
$568$	0.377620	+	14.4417i	0.0158446	+	0.605960i
$569$	18.3290	+	8.37059i	0.768393	+	0.350913i	0.760739	−	0.649057i	$-0.224837\pi$
$569$	18.3290	+	8.37059i	0.768393	+	0.350913i	0.00765347	+	0.999971i	$0.497564\pi$
$570$	−1.22235	−	1.81477i	−0.0511985	−	0.0760124i
$571$	19.5105	+	42.7220i	0.816488	+	1.78786i	0.576527	+	0.817078i	$0.304407\pi$
$571$	19.5105	+	42.7220i	0.816488	+	1.78786i	0.239961	+	0.970783i	$0.422865\pi$
$572$	−9.08293	+	6.70951i	−0.379776	+	0.280539i
$573$	6.86591	+	4.41245i	0.286828	+	0.184333i
$574$	−0.970056	+	0.244303i	−0.0404894	+	0.0101970i
$575$	15.1503	+	18.5868i	0.631811	+	0.775122i
$576$	0.803864	−	8.85666i	0.0334943	−	0.369027i
$577$	7.31254	−	11.3785i	0.304425	−	0.473694i	−0.655012	−	0.755619i	$-0.727336\pi$
$577$	7.31254	−	11.3785i	0.304425	−	0.473694i	0.959437	+	0.281924i	$0.0909727\pi$
$578$	−33.7981	+	13.8737i	−1.40582	+	0.577068i
$579$	−0.969544	+	0.442776i	−0.0402929	+	0.0184011i
$580$	21.7906	−	24.2843i	0.904804	−	1.00835i
$581$	3.80824	−	8.33887i	0.157992	−	0.345955i
$582$	−4.36343	−	2.20159i	−0.180870	−	0.0912588i
$583$	−1.42525	+	9.91284i	−0.0590279	+	0.410548i
$584$	−13.5439	+	22.3377i	−0.560449	+	0.924339i
$585$	1.33313	−	5.82051i	0.0551181	−	0.240648i
$586$	−17.7522	−	16.6337i	−0.733335	−	0.687134i
$587$	7.80484	−	5.01587i	0.322140	−	0.207027i	−0.369569	−	0.929203i	$-0.620494\pi$
$587$	7.80484	−	5.01587i	0.322140	−	0.207027i	0.691709	+	0.722176i	$0.256858\pi$
$588$	4.86686	+	1.85065i	0.200706	+	0.0763197i
$589$	1.23193	+	4.19556i	0.0507607	+	0.172875i
$590$	−24.7437	−	27.3419i	−1.01868	−	1.12565i
$591$	14.2972	+	12.3886i	0.588110	+	0.509600i
$592$	9.78479	+	15.6607i	0.402153	+	0.643651i
$593$	−0.123479	+	0.420530i	−0.00507067	+	0.0172691i	−0.961989	−	0.273087i	$-0.911955\pi$
$593$	−0.123479	+	0.420530i	−0.00507067	+	0.0172691i	0.956919	+	0.290356i	$0.0937736\pi$
$594$	−14.6608	+	11.7376i	−0.601541	+	0.481599i
$595$	31.1984	−	30.5221i	1.27901	−	1.25129i
$596$	−0.110324	+	1.41570i	−0.00451906	+	0.0579894i
$597$	−9.69604			−0.396832
$598$	−15.1226	+	6.06325i	−0.618409	+	0.247945i
$599$			0.105608i			0.00431502i	0.999998	+	0.00215751i	$0.000686758\pi$
$599$			0.105608i			0.00431502i	−0.999998	+	0.00215751i	$0.999313\pi$
$600$	−19.2475	−	2.68437i	−0.785777	−	0.109589i
$601$	−0.769648	−	5.35302i	−0.0313946	−	0.218354i	0.968085	−	0.250624i	$-0.0806356\pi$
$601$	−0.769648	−	5.35302i	−0.0313946	−	0.218354i	−0.999479	+	0.0322694i	$0.989727\pi$
$602$	−36.9604	+	29.5909i	−1.50640	+	1.20603i
$603$	2.33631	−	7.95674i	0.0951419	−	0.324023i
$604$	−38.6856	+	2.51919i	−1.57409	+	0.102504i
$605$	1.00725	−	12.2026i	0.0409504	−	0.496107i
$606$	28.4349	−	2.96545i	1.15509	−	0.120463i
$607$	−3.01020	+	0.883875i	−0.122180	+	0.0358754i	−0.342251	−	0.939609i	$-0.611189\pi$
$607$	−3.01020	+	0.883875i	−0.122180	+	0.0358754i	0.220071	+	0.975484i	$0.429371\pi$
$608$	1.04795	+	2.64853i	0.0424998	+	0.107412i
$609$	16.1653	+	25.1537i	0.655050	+	1.01928i
$610$	3.05614	−	25.0831i	0.123739	−	1.01559i
$611$	15.2839	−	13.2436i	0.618320	−	0.535777i
$612$	10.3543	−	10.2232i	0.418548	−	0.413247i
$613$	−3.53145	+	24.5618i	−0.142634	+	0.992042i	0.785252	+	0.619177i	$0.212534\pi$
$613$	−3.53145	+	24.5618i	−0.142634	+	0.992042i	−0.927886	+	0.372865i	$0.878375\pi$
$614$	−8.70049	−	4.38988i	−0.351123	−	0.177161i
$615$	0.147103	+	0.713789i	0.00593178	+	0.0287827i
$616$	17.8133	−	8.70477i	0.717717	−	0.350725i
$617$	−17.0071	−	37.2404i	−0.684682	−	1.49924i	−0.857605	−	0.514308i	$-0.828049\pi$
$617$	−17.0071	−	37.2404i	−0.684682	−	1.49924i	0.172924	−	0.984935i	$-0.444679\pi$
$618$	−0.0119154	−	0.0290276i	−0.000479309	−	0.00116766i
$619$	18.9003	+	12.1465i	0.759666	+	0.488207i	0.862229	−	0.506519i	$-0.169068\pi$
$619$	18.9003	+	12.1465i	0.759666	+	0.488207i	−0.102563	+	0.994726i	$0.532704\pi$
$620$	35.0429	+	16.7434i	1.40736	+	0.672431i
$621$	−24.7398	+	11.0541i	−0.992772	+	0.443585i
$622$	−26.4393	+	6.65858i	−1.06012	+	0.266985i
$623$	−9.61721	−	6.18060i	−0.385305	−	0.247621i
$624$	5.63795	−	11.9403i	0.225699	−	0.477995i
$625$	4.63865	−	24.5659i	0.185546	−	0.982636i
$626$	−0.487621	+	12.5335i	−0.0194892	+	0.500938i
$627$	0.675577	−	1.47931i	0.0269799	−	0.0590778i
$628$	1.00864	−	4.49846i	0.0402492	−	0.179508i
$629$	−4.29993	+	29.9067i	−0.171450	+	1.19246i
$630$	−4.14860	+	9.62815i	−0.165284	+	0.383595i
$631$	−31.4217	−	36.2626i	−1.25088	−	1.44359i	−0.849425	−	0.527710i	$-0.823051\pi$
$631$	−31.4217	−	36.2626i	−1.25088	−	1.44359i	−0.401453	−	0.915880i	$-0.631495\pi$
$632$	−2.12483	−	0.564016i	−0.0845211	−	0.0224353i
$633$	9.52487	+	14.8210i	0.378579	+	0.589081i
$634$	26.1078	+	18.2505i	1.03687	+	0.724821i
$635$	−26.9202	+	35.1516i	−1.06829	+	1.39495i
$636$	−4.02242	−	10.9981i	−0.159499	−	0.436101i
$637$	−3.43951	−	2.98035i	−0.136278	−	0.118086i
$638$	23.8514	+	4.38177i	0.944286	+	0.173476i
$639$	1.59963	−	5.44785i	0.0632805	−	0.215513i
$640$	23.7247	+	8.78294i	0.937800	+	0.347176i
$641$	−36.7810	+	5.28831i	−1.45276	+	0.208876i	−0.823058	−	0.567958i	$-0.807734\pi$
$641$	−36.7810	+	5.28831i	−1.45276	+	0.208876i	−0.629706	+	0.776834i	$0.716825\pi$
$642$	18.9179	+	6.36351i	0.746631	+	0.251148i
$643$		−	17.6036i		−	0.694218i	−0.937825	−	0.347109i	$-0.887163\pi$
$643$		−	17.6036i		−	0.694218i	0.937825	−	0.347109i	$-0.112837\pi$
$644$	28.0378	−	5.67276i	1.10484	−	0.223538i
$645$	20.3675	+	27.8385i	0.801970	+	1.09614i
$646$	−1.48583	+	4.41718i	−0.0584591	+	0.173792i
$647$	−2.40522	−	16.7287i	−0.0945591	−	0.657673i	−0.980882	−	0.194605i	$-0.937658\pi$
$647$	−2.40522	−	16.7287i	−0.0945591	−	0.657673i	0.886323	−	0.463068i	$-0.153251\pi$
$648$	4.90473	−	11.5282i	0.192676	−	0.452869i
$649$	7.72176	−	26.2979i	0.303106	−	1.03228i
$650$	14.9941	+	7.98225i	0.588117	+	0.313089i
$651$	−23.3071	+	26.8979i	−0.913479	+	1.05421i
$652$	10.0895	+	27.5867i	0.395136	+	1.08038i
$653$	3.98733	+	13.5796i	0.156036	+	0.531411i	0.999987	−	0.00500893i	$-0.00159440\pi$
$653$	3.98733	+	13.5796i	0.156036	+	0.531411i	−0.843951	+	0.536420i	$0.819776\pi$
$654$	5.14986	+	3.59998i	0.201375	+	0.140770i
$655$	−14.2064	−	5.47675i	−0.555089	−	0.213994i
$656$	0.0120900	−	0.948634i	0.000472037	−	0.0370379i
$657$	7.75918	−	6.72337i	0.302715	−	0.262304i
$658$	−30.5942	+	18.0208i	−1.19268	+	0.702525i
$659$	0.644009	−	4.47918i	0.0250870	−	0.174484i	−0.973426	−	0.229003i	$-0.926453\pi$
$659$	0.644009	−	4.47918i	0.0250870	−	0.174484i	0.998513	+	0.0545189i	$0.0173625\pi$
$660$	−5.77179	−	13.2410i	−0.224667	−	0.515404i
$661$	−5.82277	−	2.65917i	−0.226479	−	0.103430i	0.298944	−	0.954271i	$-0.403366\pi$
$661$	−5.82277	−	2.65917i	−0.226479	−	0.103430i	−0.525423	+	0.850841i	$0.676093\pi$
$662$	34.1850	+	1.32998i	1.32864	+	0.0516913i
$663$	19.6526	−	8.97506i	0.763245	−	0.348562i
$664$	6.71715	+	5.51974i	0.260676	+	0.214207i
$665$	−0.202833	−	3.35170i	−0.00786554	−	0.129973i
$666$	−1.77244	−	7.03785i	−0.0686807	−	0.272711i
$667$	31.7070	+	14.7954i	1.22770	+	0.572881i
$668$	21.9548	−	11.8073i	0.849458	−	0.456837i
$669$	−0.410726	−	0.263957i	−0.0158796	−	0.0102052i
$670$	20.1157	+	12.3231i	0.777136	+	0.476083i
$671$	17.0838	−	7.80191i	0.659513	−	0.301189i
$672$	−13.5238	+	18.8304i	−0.521691	+	0.726399i
$673$	−9.03202	−	4.12478i	−0.348159	−	0.158999i	0.233658	−	0.972319i	$-0.424930\pi$
$673$	−9.03202	−	4.12478i	−0.348159	−	0.158999i	−0.581816	+	0.813320i	$0.697658\pi$
$674$	11.7794	+	5.94334i	0.453724	+	0.228929i
$675$	25.4343	+	12.2960i	0.978967	+	0.473273i
$676$	10.2886	−	10.1583i	0.395715	−	0.390704i
$677$	−28.6879	−	33.1077i	−1.10257	−	1.27243i	−0.959190	−	0.282762i	$-0.908749\pi$
$677$	−28.6879	−	33.1077i	−1.10257	−	1.27243i	−0.143377	−	0.989668i	$-0.545796\pi$
$678$	22.5800	+	21.1575i	0.867181	+	0.812547i
$679$	−4.05498	−	6.30967i	−0.155616	−	0.242143i
$680$	20.3868	+	36.0242i	0.781798	+	1.38146i
$681$	0.382623	+	1.30309i	0.0146621	+	0.0499347i
$682$	2.99418	+	28.7103i	0.114653	+	1.09938i
$683$	−16.2596	+	18.7646i	−0.622156	+	0.718007i	−0.976115	−	0.217254i	$-0.930290\pi$
$683$	−16.2596	+	18.7646i	−0.622156	+	0.718007i	0.353959	+	0.935261i	$0.384835\pi$
$684$	−0.0727440	−	1.11708i	−0.00278143	−	0.0427127i
$685$	−7.00577	+	2.52593i	−0.267677	+	0.0965108i
$686$	−13.4580	−	16.8097i	−0.513830	−	0.641799i
$687$	−36.6599	+	5.27090i	−1.39866	+	0.201097i
$688$	−18.1312	−	41.0793i	−0.691245	−	1.56613i
$689$			10.2358i			0.389953i
$690$	−3.24123	−	20.5869i	−0.123391	−	0.783728i
$691$			14.4577i			0.549998i	0.961445	+	0.274999i	$0.0886775\pi$
$691$			14.4577i			0.549998i	−0.961445	+	0.274999i	$0.911323\pi$
$692$	−3.16059	+	40.5573i	−0.120148	+	1.54176i
$693$	−7.71288	+	1.10894i	−0.292988	+	0.0421253i
$694$	−29.6212	+	23.7150i	−1.12441	+	0.900210i
$695$	−2.29894	−	6.37622i	−0.0872039	−	0.241864i
$696$	−26.9901	+	8.69751i	−1.02306	+	0.329678i
$697$	1.01652	−	1.17313i	0.0385036	−	0.0444355i
$698$	10.6459	−	1.11026i	0.402954	−	0.0420238i
$699$	−6.46841	−	22.0294i	−0.244658	−	0.833228i
$700$	−23.3601	−	18.5408i	−0.882928	−	0.700775i
$701$	14.8245	+	23.0674i	0.559913	+	0.871242i	0.999638	−	0.0268902i	$-0.00856043\pi$
$701$	14.8245	+	23.0674i	0.559913	+	0.871242i	−0.439725	+	0.898132i	$0.644924\pi$
$702$	−13.1246	+	14.0070i	−0.495355	+	0.528661i
$703$	1.52222	+	1.75674i	0.0574118	+	0.0662567i
$704$	3.64493	+	18.4463i	0.137374	+	0.695222i
$705$	12.1478	+	22.8385i	0.457513	+	0.860147i
$706$	−1.17513	+	2.32905i	−0.0442266	+	0.0876548i
$707$	39.9088	+	18.2258i	1.50093	+	0.685450i
$708$	6.61284	+	31.3594i	0.248526	+	1.17856i
$709$	−1.88686	+	0.861702i	−0.0708627	+	0.0323619i	−0.450531	−	0.892761i	$-0.648765\pi$
$709$	−1.88686	+	0.861702i	−0.0708627	+	0.0323619i	0.379668	+	0.925123i	$0.376038\pi$
$710$	13.7729	+	8.43742i	0.516886	+	0.316651i
$711$	0.726862	+	0.467126i	0.0272595	+	0.0175186i
$712$	8.00538	−	7.31169i	0.300014	−	0.274017i
$713$	−6.26491	+	41.1746i	−0.234623	+	1.54200i
$714$	−36.7841	+	9.26386i	−1.37661	+	0.346691i
$715$	0.762641	+	12.6022i	0.0285211	+	0.471295i
$716$	36.7590	−	27.1537i	1.37375	−	1.01478i
$717$	18.6922	−	8.53645i	0.698073	−	0.318799i
$718$	−0.288296	+	7.41015i	−0.0107591	+	0.276544i
$719$	37.9817	+	17.3457i	1.41648	+	0.646884i	0.968921	−	0.247371i	$-0.0795668\pi$
$719$	37.9817	+	17.3457i	1.41648	+	0.646884i	0.447557	+	0.894255i	$0.352294\pi$
$720$	−7.81613	−	6.14542i	−0.291290	−	0.229026i
$721$	0.00685297	−	0.0476635i	0.000255218	−	0.00177508i
$722$	−13.4553	−	22.8433i	−0.500755	−	0.850138i
$723$	−20.2938	+	17.5847i	−0.754735	+	0.653981i
$724$	−42.4207	−	23.5156i	−1.57655	−	0.873950i
$725$	−9.50782	−	35.2179i	−0.353112	−	1.30796i
$726$	−6.09688	+	8.72174i	−0.226277	+	0.323694i
$727$	4.41547	+	15.0377i	0.163761	+	0.557718i	0.999957	+	0.00928735i	$0.00295630\pi$
$727$	4.41547	+	15.0377i	0.163761	+	0.557718i	−0.836196	+	0.548431i	$0.815226\pi$
$728$	16.7549	−	11.3974i	0.620979	−	0.422414i
$729$	−18.4780	+	21.3247i	−0.684370	+	0.789805i
$730$	12.7026	+	26.2993i	0.470144	+	0.973381i
$731$	20.6987	−	70.4933i	0.765569	−	2.60729i
$732$	−13.2726	+	17.4966i	−0.490569	+	0.646692i
$733$	−5.15048	−	35.8224i	−0.190237	−	1.32313i	−0.831378	−	0.555707i	$-0.812448\pi$
$733$	−5.15048	−	35.8224i	−0.190237	−	1.32313i	0.641141	−	0.767423i	$-0.278461\pi$
$734$	34.1166	+	11.4760i	1.25927	+	0.423585i
$735$	4.69824	−	3.43738i	0.173297	−	0.126790i
$736$	−1.62209	+	27.0808i	−0.0597911	+	0.998211i
$737$			17.5335i			0.645855i
$738$	−0.118877	+	0.353406i	−0.00437591	+	0.0130090i
$739$	46.1562	−	6.63626i	1.69788	−	0.244119i	0.775763	−	0.631024i	$-0.217365\pi$
$739$	46.1562	−	6.63626i	1.69788	−	0.244119i	0.922119	+	0.386906i	$0.126456\pi$
$740$	20.6427	+	0.357753i	0.758842	+	0.0131513i
$741$	0.468285	−	1.59483i	0.0172029	−	0.0585876i
$742$	3.24720	−	17.6755i	0.119209	−	0.648890i
$743$	−15.4876	−	13.4201i	−0.568186	−	0.492336i	0.322738	−	0.946488i	$-0.395397\pi$
$743$	−15.4876	−	13.4201i	−0.568186	−	0.492336i	−0.890924	+	0.454153i	$0.849942\pi$
$744$	−18.9847	−	27.9089i	−0.696014	−	1.02319i
$745$	1.26044	+	0.965283i	0.0461790	+	0.0353652i
$746$	−9.16059	+	13.1044i	−0.335393	+	0.479788i
$747$	−1.84735	−	2.87454i	−0.0675912	−	0.105174i
$748$	−14.9160	+	26.9076i	−0.545383	+	0.983838i
$749$	20.0587	+	23.1489i	0.732928	+	0.845844i
$750$	−14.2345	+	16.4156i	−0.519769	+	0.599413i
$751$	−6.81141	+	47.3744i	−0.248552	+	1.72872i	0.358043	+	0.933705i	$0.383444\pi$
$751$	−6.81141	+	47.3744i	−0.248552	+	1.72872i	−0.606595	+	0.795011i	$0.707465\pi$
$752$	−9.07462	−	32.4285i	−0.330917	−	1.18255i
$753$	3.62881	−	7.94599i	0.132241	−	0.289568i
$754$	24.7670	+	0.963573i	0.901961	+	0.0350913i
$755$	−21.1878	+	37.8117i	−0.771104	+	1.37611i
$756$	27.1076	−	20.0242i	0.985893	−	0.728274i
$757$	5.92411	+	3.80719i	0.215315	+	0.138375i	0.643853	−	0.765149i	$-0.277335\pi$
$757$	5.92411	+	3.80719i	0.215315	+	0.138375i	−0.428538	+	0.903524i	$0.640971\pi$
$758$	1.78520	+	7.08850i	0.0648412	+	0.257466i
$759$	11.7891	−	10.0473i	0.427918	−	0.364695i
$760$	3.12165	+	0.629588i	0.113234	+	0.0228376i
$761$	−21.5563	−	13.8534i	−0.781414	−	0.502184i	0.0880886	−	0.996113i	$-0.471924\pi$
$761$	−21.5563	−	13.8534i	−0.781414	−	0.502184i	−0.869503	+	0.493928i	$0.835561\pi$
$762$	35.5979	−	14.6124i	1.28957	−	0.529352i
$763$	4.00571	+	8.77127i	0.145016	+	0.317541i
$764$	−11.6228	+	2.45093i	−0.420498	+	0.0886714i
$765$	−3.28368	−	15.9334i	−0.118722	−	0.576073i
$766$	10.0377	−	19.8942i	0.362677	−	0.718806i
$767$	3.98667	−	27.7279i	0.143950	−	1.00120i
$768$	−13.9702	−	16.9781i	−0.504105	−	0.612645i
$769$	13.4402	−	11.6460i	0.484665	−	0.419964i	−0.377950	−	0.925826i	$-0.623371\pi$
$769$	13.4402	−	11.6460i	0.484665	−	0.419964i	0.862615	+	0.505862i	$0.168825\pi$
$770$	2.68096	−	22.0038i	0.0966149	−	0.792964i
$771$	9.29498	+	14.4633i	0.334751	+	0.520882i
$772$	0.551365	−	1.44998i	0.0198441	−	0.0521860i
$773$	15.0642	−	4.42326i	0.541823	−	0.159094i	0.000641995	−	1.00000i	$-0.499796\pi$
$773$	15.0642	−	4.42326i	0.541823	−	0.159094i	0.541181	+	0.840906i	$0.317977\pi$
$774$	1.83054	+	17.5525i	0.0657974	+	0.630912i
$775$	37.0342	−	22.6694i	1.33031	−	0.814309i
$776$	6.77032	−	2.18173i	0.243040	−	0.0783194i
$777$	−5.33039	+	18.1536i	−0.191227	+	0.651258i
$778$	7.65718	+	9.56418i	0.274523	+	0.342893i
$779$	−0.0169956	−	0.118207i	−0.000608931	−	0.00423520i
$780$	−7.76509	−	12.5559i	−0.278035	−	0.449573i
$781$			12.0049i			0.429569i
$782$	−30.6152	+	32.1415i	−1.09480	+	1.14938i
$783$	41.2218			1.47315
$784$	−6.93286	+	3.05996i	−0.247602	+	0.109284i
$785$	−3.60449	−	3.68436i	−0.128650	−	0.131500i
$786$	8.27017	+	10.3298i	0.294987	+	0.368453i
$787$	9.85003	−	33.5461i	0.351116	−	1.19579i	−0.574874	−	0.818242i	$-0.694949\pi$
$787$	9.85003	−	33.5461i	0.351116	−	1.19579i	0.925990	−	0.377549i	$-0.123233\pi$
$788$	−27.4753	+	1.78918i	−0.978767	+	0.0637370i
$789$	−15.3419	−	13.2938i	−0.546185	−	0.473272i
$790$	−1.82243	+	1.64925i	−0.0648391	+	0.0586776i
$791$	13.3785	+	45.5631i	0.475686	+	1.62004i
$792$	0.860144	−	7.33975i	0.0305639	−	0.260807i
$793$	16.1483	−	10.3779i	0.573442	−	0.368529i
$794$	23.6983	−	25.2918i	0.841023	−	0.897571i
$795$	−12.7623	−	2.92308i	−0.452633	−	0.103671i
$796$	10.0419	−	9.91473i	0.355926	−	0.351418i
$797$	−0.631284	+	4.39068i	−0.0223612	+	0.155526i	−0.997943	−	0.0641120i	$-0.979578\pi$
$797$	−0.631284	+	4.39068i	−0.0223612	+	0.155526i	0.975581	+	0.219638i	$0.0704876\pi$
$798$	−1.31460	+	2.60546i	−0.0465362	+	0.0922321i
$799$	22.8884	−	50.1186i	0.809733	−	1.77307i
$800$	22.6790	−	16.9015i	0.801824	−	0.597560i
$801$	−3.87603	+	1.77013i	−0.136953	+	0.0625443i
$802$	−13.4024	−	32.6500i	−0.473254	−	1.15291i
$803$	−11.7361	+	18.2617i	−0.414157	+	0.644441i
$804$	−9.71090	−	18.0568i	−0.342477	−	0.636814i
$805$	11.7486	−	29.7463i	0.414082	−	1.04842i
$806$	7.20520	+	28.6098i	0.253792	+	1.00774i
$807$	26.3763	+	16.9510i	0.928491	+	0.596705i
$808$	−26.4168	+	32.1474i	−0.929340	+	1.13094i
$809$	0.420549	+	0.920874i	0.0147857	+	0.0323762i	0.916881	−	0.399161i	$-0.130699\pi$
$809$	0.420549	+	0.920874i	0.0147857	+	0.0323762i	−0.902095	+	0.431537i	$0.857971\pi$
$810$	−7.82494	−	11.6174i	−0.274940	−	0.408194i
$811$	−21.9495	−	10.0240i	−0.770753	−	0.351991i	−0.00908499	−	0.999959i	$-0.502892\pi$
$811$	−21.9495	−	10.0240i	−0.770753	−	0.351991i	−0.761668	+	0.647968i	$0.775619\pi$
$812$	−42.4629	−	9.52101i	−1.49016	−	0.334122i
$813$	0.654973	+	0.0941709i	0.0229709	+	0.00330272i
$814$	7.78805	+	13.2219i	0.272971	+	0.463426i
$815$	32.0120	+	7.33203i	1.12133	+	0.256830i
$816$	0.458449	−	35.9718i	0.0160489	−	1.25927i
$817$	−3.05586	−	4.75501i	−0.106911	−	0.166357i
$818$	−13.9902	+	20.0133i	−0.489156	+	0.699749i
$819$	−7.64156	+	2.24376i	−0.267018	+	0.0784035i
$820$	−0.882239	−	0.588829i	−0.0308091	−	0.0205628i
$821$	29.8118	−	34.4047i	1.04044	−	1.20073i	0.0611797	−	0.998127i	$-0.480514\pi$
$821$	29.8118	−	34.4047i	1.04044	−	1.20073i	0.979260	−	0.202605i	$-0.0649408\pi$
$822$	6.36590	+	1.16949i	0.222036	+	0.0407906i
$823$	−35.0417	−	10.2892i	−1.22148	−	0.358658i	−0.393450	−	0.919346i	$-0.628719\pi$
$823$	−35.0417	−	10.2892i	−1.22148	−	0.358658i	−0.828027	+	0.560688i	$0.810537\pi$
$824$	0.0420228	+	0.0178789i	0.00146393	+	0.000622840i
$825$	−15.9306	−	2.64798i	−0.554632	−	0.0921907i
$826$	−15.6807	+	46.6168i	−0.545602	+	1.62201i
$827$		−	46.5807i		−	1.61977i	−0.586590	−	0.809884i	$-0.699530\pi$
$827$		−	46.5807i		−	1.61977i	0.586590	−	0.809884i	$-0.300470\pi$
$828$	3.87127	−	9.93479i	0.134536	−	0.345258i
$829$	−19.4667			−0.676106			−0.338053	−	0.941127i	$-0.609768\pi$
$829$	−19.4667			−0.676106			−0.338053	+	0.941127i	$0.609768\pi$
$830$	9.26537	−	2.93893i	0.321606	−	0.102012i
$831$	−10.0342	+	1.44270i	−0.348082	+	0.0500466i
$832$	6.37058	+	18.1313i	0.220860	+	0.628591i
$833$	−11.8970	−	3.49328i	−0.412207	−	0.121035i
$834$	−1.06440	+	5.79385i	−0.0368570	+	0.200625i
$835$	2.29276	−	27.7764i	0.0793442	−	0.961241i
$836$	0.812998	+	2.22289i	0.0281181	+	0.0768802i
$837$	13.8239	+	47.0798i	0.477823	+	1.62732i
$838$	−10.3248	+	14.7698i	−0.356663	+	0.510215i
$839$	−42.1411	+	27.0824i	−1.45487	+	0.934989i	−0.455881	+	0.890041i	$0.650676\pi$
$839$	−42.1411	+	27.0824i	−1.45487	+	0.934989i	−0.998989	+	0.0449480i	$0.985688\pi$
$840$	9.42583	+	24.1454i	0.325222	+	0.833095i
$841$	−15.8659	−	18.3102i	−0.547099	−	0.631386i
$842$	−11.8693	+	6.99133i	−0.409042	+	0.240937i
$843$	−9.65339	−	1.38795i	−0.332480	−	0.0478035i
$844$	−25.0199	−	5.60995i	−0.861220	−	0.193102i
$845$	−3.26285	−	15.8323i	−0.112245	−	0.544648i
$846$	−0.514514	+	13.2247i	−0.0176894	+	0.454675i
$847$	−14.8549	+	6.78401i	−0.510421	+	0.233101i
$848$	15.4120	+	7.27721i	0.529251	+	0.249900i
$849$	−1.06946	+	1.66411i	−0.0367037	+	0.0571121i
$850$	46.1930	+	2.81199i	1.58441	+	0.0964506i
$851$	6.06327	+	21.2938i	0.207846	+	0.729941i
$852$	−6.64890	−	12.3632i	−0.227787	−	0.423556i
$853$	11.4330	−	17.7900i	0.391457	−	0.609119i	−0.588459	−	0.808527i	$-0.700265\pi$
$853$	11.4330	−	17.7900i	0.391457	−	0.609119i	0.979917	+	0.199407i	$0.0639017\pi$
$854$	−31.1777	+	12.7980i	−1.06688	+	0.437939i
$855$	−1.09185	−	0.611818i	−0.0373404	−	0.0209237i
$856$	−26.0998	+	12.7541i	−0.892072	+	0.435927i
$857$	39.7757	+	18.1649i	1.35871	+	0.620503i	0.955605	−	0.294650i	$-0.0952032\pi$
$857$	39.7757	+	18.1649i	1.35871	+	0.620503i	0.403106	+	0.915153i	$0.367930\pi$
$858$	4.94279	−	9.79635i	0.168744	−	0.334442i
$859$	−39.0480	−	5.61425i	−1.33230	−	0.191556i	−0.560888	−	0.827892i	$-0.689540\pi$
$859$	−39.0480	−	5.61425i	−1.33230	−	0.191556i	−0.771412	+	0.636336i	$0.780449\pi$
$860$	−49.5604	−	8.00457i	−1.69000	−	0.272954i
$861$	0.734609	−	0.636543i	0.0250354	−	0.0216933i
$862$	0.372299	+	0.348844i	0.0126806	+	0.0118817i
$863$	16.5400	−	10.6296i	0.563027	−	0.361835i	−0.227958	−	0.973671i	$-0.573205\pi$
$863$	16.5400	−	10.6296i	0.563027	−	0.361835i	0.790985	+	0.611836i	$0.209569\pi$
$864$	11.7594	+	29.7200i	0.400062	+	1.01110i
$865$	36.1094	+	27.6536i	1.22776	+	0.940252i
$866$	−45.8612	+	4.78284i	−1.55843	+	0.162527i
$867$	23.2479	−	26.8295i	0.789541	−	0.911179i
$868$	−3.36605	−	51.6902i	−0.114251	−	1.75448i
$869$	−1.75284	−	0.514681i	−0.0594611	−	0.0174593i
$870$	−8.27424	+	30.6051i	−0.280523	+	1.03761i
$871$	2.55035	+	17.7381i	0.0864152	+	0.601031i
$872$	−9.01474	+	1.53762i	−0.305278	+	0.0520704i
$873$	−2.79563			−0.0946177
$874$	0.326375	+	3.39937i	0.0110398	+	0.114986i
$875$	−31.6076	+	10.6195i	−1.06853	+	0.359003i
$876$	1.97212	−	25.3067i	0.0666319	−	0.855034i
$877$	−29.0151	+	4.17175i	−0.979772	+	0.140870i	−0.613549	−	0.789657i	$-0.710259\pi$
$877$	−29.0151	+	4.17175i	−0.979772	+	0.140870i	−0.366223	+	0.930527i	$0.619349\pi$
$878$	5.79356	+	7.23644i	0.195523	+	0.244218i
$879$	22.6811	+	6.65979i	0.765016	+	0.224629i
$880$	19.5173	+	7.81130i	0.657927	+	0.263319i
$881$	7.29366	+	6.31999i	0.245730	+	0.212926i	0.769014	−	0.639232i	$-0.220748\pi$
$881$	7.29366	+	6.31999i	0.245730	+	0.212926i	−0.523284	+	0.852158i	$0.675293\pi$
$882$	2.96230	−	0.308936i	0.0997458	−	0.0104024i
$883$	−20.3226	+	5.96724i	−0.683909	+	0.200814i	−0.605188	−	0.796083i	$-0.706902\pi$
$883$	−20.3226	+	5.96724i	−0.683909	+	0.200814i	−0.0787212	+	0.996897i	$0.525084\pi$
$884$	−11.1762	+	29.3911i	−0.375895	+	0.988530i
$885$	33.4335	+	12.8891i	1.12386	+	0.433262i
$886$	2.63112	+	2.46536i	0.0883943	+	0.0828253i
$887$	−13.5666	−	15.6567i	−0.455522	−	0.525700i	0.480806	−	0.876827i	$-0.340344\pi$
$887$	−13.5666	−	15.6567i	−0.455522	−	0.525700i	−0.936328	+	0.351127i	$0.885799\pi$
$888$	−15.3434	−	9.30307i	−0.514890	−	0.312191i
$889$	58.4518	+	8.40410i	1.96041	+	0.281865i
$890$	−1.98331	−	11.9583i	−0.0664807	−	0.400842i
$891$	4.32476	−	9.46989i	0.144885	−	0.317253i
$892$	0.695288	−	0.146617i	0.0232800	−	0.00490910i
$893$	−1.76089	−	3.85582i	−0.0589261	−	0.129030i
$894$	−0.523961	−	1.27644i	−0.0175239	−	0.0426906i
$895$	−3.08644	−	51.0016i	−0.103168	−	1.70480i
$896$	−5.24896	−	33.3309i	−0.175356	−	1.11351i
$897$	10.4652	−	11.8793i	0.349423	−	0.396639i
$898$	−7.91483	−	31.4275i	−0.264121	−	1.04875i
$899$	34.2542	−	53.3006i	1.14244	−	1.77767i
$900$	−10.5211	+	3.58863i	−0.350705	+	0.119621i
$901$	11.5846	+	25.3667i	0.385939	+	0.845088i
$902$	0.0306485	−	0.787766i	0.00102048	−	0.0262297i
$903$	19.1117	−	41.8487i	0.635997	−	1.39264i
$904$	−45.0201	+	1.17718i	−1.49735	+	0.0391525i
$905$	−47.8763	+	25.4655i	−1.59146	+	0.846500i
$906$	32.4578	−	19.1186i	1.07834	−	0.635172i
$907$	15.0533	−	13.0437i	0.499835	−	0.433110i	−0.368101	−	0.929786i	$-0.619992\pi$
$907$	15.0533	−	13.0437i	0.499835	−	0.433110i	0.867936	+	0.496676i	$0.165446\pi$
$908$	−1.72876	−	0.958323i	−0.0573708	−	0.0318031i
$909$	13.7572	−	8.84122i	0.456298	−	0.293245i
$910$	−0.488352	−	22.6505i	−0.0161887	−	0.750857i
$911$	47.5144	−	13.9515i	1.57422	−	0.462233i	0.625995	−	0.779827i	$-0.284693\pi$
$911$	47.5144	−	13.9515i	1.57422	−	0.462233i	0.948227	+	0.317594i	$0.102875\pi$
$912$	−2.06841	−	1.83895i	−0.0684917	−	0.0608938i
$913$	5.46003	+	4.73114i	0.180701	+	0.156578i
$914$	−43.7700	−	8.04106i	−1.44778	−	0.265975i
$915$	8.32792	+	23.0978i	0.275313	+	0.763591i
$916$	32.5778	−	42.9457i	1.07640	−	1.41897i
$917$	2.89000	+	20.1004i	0.0954363	+	0.663774i
$918$	−16.6730	+	49.5668i	−0.550291	+	1.63595i
$919$	11.0732			0.365271			0.182635	−	0.983181i	$-0.441537\pi$
$919$	11.0732			0.365271			0.182635	+	0.983181i	$0.441537\pi$
$920$	24.4080	+	18.0069i	0.804709	+	0.593669i
$921$	9.46936			0.312026
$922$	11.2036	−	33.3068i	0.368970	−	1.09690i
$923$	1.74618	+	12.1450i	0.0574762	+	0.399756i
$924$	−11.6432	+	15.3486i	−0.383033	+	0.504933i
$925$	12.9020	−	19.1403i	0.424214	−	0.629330i
$926$	−26.7471	−	4.91375i	−0.878964	−	0.161476i
$927$	−0.0135646	−	0.0117538i	−0.000445519	−	0.000386045i
$928$	19.0591	−	36.6066i	0.625646	−	1.20167i
$929$	−40.6182	+	11.9266i	−1.33264	+	0.391299i	−0.869038	−	0.494745i	$-0.835262\pi$
$929$	−40.6182	+	11.9266i	−1.33264	+	0.391299i	−0.463602	+	0.886043i	$0.653443\pi$
$930$	−37.7292	+	0.813453i	−1.23719	+	0.0266742i
$931$	−0.802492	+	0.515730i	−0.0263006	+	0.0169024i
$932$	29.2254	+	16.2009i	0.957310	+	0.530677i
$933$	20.0221	−	17.3493i	0.655495	−	0.567989i
$934$	19.8195	−	11.6743i	0.648515	−	0.381993i
$935$	16.1528	+	30.3680i	0.528253	+	0.993141i
$936$	−0.197429	−	7.55049i	−0.00645318	−	0.246796i
$937$	−15.0429	+	32.9395i	−0.491432	+	1.07609i	0.487728	+	0.872995i	$0.337826\pi$
$937$	−15.0429	+	32.9395i	−0.491432	+	1.07609i	−0.979160	+	0.203090i	$0.934902\pi$
$938$	1.22318	−	31.4398i	0.0399383	−	1.02655i
$939$	−5.06302	−	11.0865i	−0.165225	−	0.361793i
$940$	−35.9347	−	11.2313i	−1.17206	−	0.366325i
$941$	−14.6109	+	22.7351i	−0.476303	+	0.741142i	−0.993390	−	0.114791i	$-0.963380\pi$
$941$	−14.6109	+	22.7351i	−0.476303	+	0.741142i	0.517087	+	0.855933i	$0.327016\pi$
$942$	1.09401	+	4.34400i	0.0356448	+	0.141535i
$943$	0.329396	−	1.08873i	0.0107266	−	0.0354538i
$944$	−38.9155	−	25.7161i	−1.26659	−	0.836986i
$945$	−2.27607	−	37.6106i	−0.0740404	−	1.22347i
$946$	−14.1693	−	34.5183i	−0.460683	−	1.12229i
$947$	15.1042	+	33.0737i	0.490822	+	1.07475i	0.979345	+	0.202199i	$0.0648087\pi$
$947$	15.1042	+	33.0737i	0.490822	+	1.07475i	−0.488523	+	0.872551i	$0.662464\pi$
$948$	2.09021	−	0.440767i	0.0678868	−	0.0143155i
$949$	−9.21672	+	20.1818i	−0.299187	+	0.655129i
$950$	2.49075	−	2.54412i	0.0808105	−	0.0825421i
$951$	−30.6376	−	4.40501i	−0.993491	−	0.142842i
$952$	28.6234	−	47.2081i	0.927691	−	1.53002i
$953$	30.0383	+	34.6660i	0.973035	+	1.12294i	0.992391	+	0.123130i	$0.0392932\pi$
$953$	30.0383	+	34.6660i	0.973035	+	1.12294i	−0.0193552	+	0.999813i	$0.506161\pi$
$954$	−4.88806	−	4.58011i	−0.158257	−	0.148286i
$955$	−4.77710	+	12.3915i	−0.154583	+	0.400980i
$956$	−10.6300	+	27.9548i	−0.343798	+	0.904121i
$957$	−22.6095	+	6.63876i	−0.730862	+	0.214601i
$958$	−31.6658	+	3.30241i	−1.02308	+	0.106696i
$959$	7.50670	+	6.50459i	0.242404	+	0.210044i
$960$	−24.4260	+	2.76519i	−0.788347	+	0.0892461i
$961$	42.6181	+	12.5138i	1.37478	+	0.403671i
$962$	9.80210	+	12.2433i	0.316032	+	0.394740i
$963$	11.3008	−	1.62481i	0.364164	−	0.0523588i
$964$	3.03638	−	38.9635i	0.0977954	−	1.25493i
$965$	−1.02410	−	1.39975i	−0.0329669	−	0.0450594i
$966$	−21.8403	+	17.1937i	−0.702701	+	0.553198i
$967$	−17.3550			−0.558100			−0.279050	−	0.960277i	$-0.590020\pi$
$967$	−17.3550			−0.558100			−0.279050	+	0.960277i	$0.590020\pi$
$968$	−2.60409	−	15.2672i	−0.0836988	−	0.490708i
$969$	−0.644466	−	4.48236i	−0.0207032	−	0.143994i
$970$	2.07555	−	7.67714i	0.0666420	−	0.246498i
$971$	−46.2963	−	13.5938i	−1.48572	−	0.436247i	−0.564547	−	0.825401i	$-0.690949\pi$
$971$	−46.2963	−	13.5938i	−1.48572	−	0.436247i	−0.921173	+	0.389154i	$0.872767\pi$
$972$	−1.41188	−	21.6813i	−0.0452860	−	0.695427i
$973$	−5.92007	+	6.83213i	−0.189789	+	0.219028i
$974$	−19.7990	+	2.06483i	−0.634401	+	0.0661613i
$975$	−16.5016	−	0.361673i	−0.528474	−	0.0115828i
$976$	−4.14520	−	31.6926i	−0.132685	−	1.01446i
$977$	−18.8134	+	12.0907i	−0.601895	+	0.386814i	−0.805810	−	0.592174i	$-0.798270\pi$
$977$	−18.8134	+	12.0907i	−0.601895	+	0.386814i	0.203915	+	0.978989i	$0.434633\pi$
$978$	−20.8279	−	19.5157i	−0.666002	−	0.624043i
$979$	6.80888	−	5.89993i	0.217613	−	0.188562i
$980$	−1.35091	+	8.36420i	−0.0431534	+	0.267185i
$981$	3.55757	+	0.511501i	0.113585	+	0.0163310i
$982$	−16.0745	+	31.8587i	−0.512957	+	1.01665i
$983$	6.63609	+	3.03060i	0.211658	+	0.0966612i	0.518423	−	0.855124i	$-0.326519\pi$
$983$	6.63609	+	3.03060i	0.211658	+	0.0966612i	−0.306765	+	0.951785i	$0.599246\pi$
$984$	0.404740	+	0.828251i	0.0129026	+	0.0264037i
$985$	−15.0480	+	26.8547i	−0.479471	+	0.855661i
$986$	62.4690	−	25.6427i	1.98942	−	0.816628i
$987$	18.6531	−	29.0249i	0.593736	−	0.923871i
$988$	1.14581	+	2.13057i	0.0364532	+	0.0677824i
$989$	−7.22466	−	53.3494i	−0.229731	−	1.69641i
$990$	−6.35937	−	5.27477i	−0.202114	−	0.167643i
$991$	10.3948	−	16.1746i	0.330201	−	0.513802i	−0.635967	−	0.771716i	$-0.719399\pi$
$991$	10.3948	−	16.1746i	0.330201	−	0.513802i	0.966168	+	0.257914i	$0.0830350\pi$
$992$	48.2003	+	9.49146i	1.53036	+	0.301354i
$993$	−30.2383	+	13.8094i	−0.959584	+	0.438227i
$994$	0.837493	−	21.5263i	0.0265637	−	0.682773i
$995$	−3.18461	−	15.4527i	−0.100959	−	0.489883i
$996$	−8.24332	−	1.84831i	−0.261200	−	0.0585660i
$997$	−25.4190	−	3.65471i	−0.805029	−	0.115746i	−0.272498	−	0.962156i	$-0.587850\pi$
$997$	−25.4190	−	3.65471i	−0.805029	−	0.115746i	−0.532531	+	0.846411i	$0.678759\pi$
$998$	−4.64599	+	2.73662i	−0.147066	+	0.0866261i
$999$	17.0814	+	19.7130i	0.540432	+	0.623692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.b.159.40	yes	640
4.3	odd	2	inner	460.2.o.b.159.51	yes	640
5.4	even	2	inner	460.2.o.b.159.25	yes	640
20.19	odd	2	inner	460.2.o.b.159.14	✓	640
23.11	odd	22	inner	460.2.o.b.379.14	yes	640
92.11	even	22	inner	460.2.o.b.379.25	yes	640
115.34	odd	22	inner	460.2.o.b.379.51	yes	640
460.379	even	22	inner	460.2.o.b.379.40	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.b.159.14	✓	640	20.19	odd	2	inner
460.2.o.b.159.25	yes	640	5.4	even	2	inner
460.2.o.b.159.40	yes	640	1.1	even	1	trivial
460.2.o.b.159.51	yes	640	4.3	odd	2	inner
460.2.o.b.379.14	yes	640	23.11	odd	22	inner
460.2.o.b.379.25	yes	640	92.11	even	22	inner
460.2.o.b.379.40	yes	640	460.379	even	22	inner
460.2.o.b.379.51	yes	640	115.34	odd	22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.450881 - 1.34041i) q^{2} +(0.195566 + 1.36019i) q^{3} +(-1.59341 - 1.20873i) q^{4} +(-2.10352 + 0.758423i) q^{5} +(1.91140 + 0.351145i) q^{6} +(2.25392 + 1.95304i) q^{7} +(-2.33864 + 1.59084i) q^{8} +(1.06660 - 0.313183i) q^{9} +O(q^{10})\)	\(q+(0.450881 - 1.34041i) q^{2} +(0.195566 + 1.36019i) q^{3} +(-1.59341 - 1.20873i) q^{4} +(-2.10352 + 0.758423i) q^{5} +(1.91140 + 0.351145i) q^{6} +(2.25392 + 1.95304i) q^{7} +(-2.33864 + 1.59084i) q^{8} +(1.06660 - 0.313183i) q^{9} +(0.0681638 + 3.16154i) q^{10} +(-1.97726 + 1.27071i) q^{11} +(1.33249 - 2.40373i) q^{12} +(-1.81550 + 1.57314i) q^{13} +(3.63413 - 2.14060i) q^{14} +(-1.44298 - 2.71287i) q^{15} +(1.07793 + 3.85202i) q^{16} +(-2.71880 + 5.95333i) q^{17} +(0.0611166 - 1.57090i) q^{18} +(0.209168 + 0.458013i) q^{19} +(4.26851 + 1.33411i) q^{20} +(-2.21571 + 3.44772i) q^{21} +(0.811764 + 3.22328i) q^{22} +(-0.0393105 + 4.79567i) q^{23} +(-2.62120 - 2.86989i) q^{24} +(3.84959 - 3.19072i) q^{25} +(1.29008 + 3.14281i) q^{26} +(2.34714 + 5.13953i) q^{27} +(-1.23073 - 5.83639i) q^{28} +(3.03076 - 6.63644i) q^{29} +(-4.28697 + 0.711006i) q^{30} +(8.59592 + 1.23591i) q^{31} +(5.64932 + 0.291933i) q^{32} +(-2.11509 - 2.44095i) q^{33} +(6.75407 + 6.32855i) q^{34} +(-6.22240 - 2.39882i) q^{35} +(-2.07809 - 0.790209i) q^{36} +(4.42954 - 1.30063i) q^{37} +(0.708237 - 0.0738616i) q^{38} +(-2.49482 - 2.16177i) q^{39} +(3.71285 - 5.12003i) q^{40} +(-0.227570 - 0.0668207i) q^{41} +(3.62234 + 4.52448i) q^{42} +(-11.1114 + 1.59758i) q^{43} +(4.68654 + 0.365217i) q^{44} +(-2.00610 + 1.46772i) q^{45} +(6.41045 + 2.21497i) q^{46} -8.41857 q^{47} +(-5.02868 + 2.21951i) q^{48} +(0.269620 + 1.87525i) q^{49} +(-2.54117 - 6.59867i) q^{50} +(-8.62938 - 2.53381i) q^{51} +(4.79434 - 0.312205i) q^{52} +(2.79031 - 3.22019i) q^{53} +(7.94737 - 0.828827i) q^{54} +(3.19547 - 4.17256i) q^{55} +(-8.37808 - 0.981826i) q^{56} +(-0.582080 + 0.374080i) q^{57} +(-7.52906 - 7.05471i) q^{58} +(-8.81293 + 7.63645i) q^{59} +(-0.979873 + 6.06689i) q^{60} +(-7.90931 - 1.13719i) q^{61} +(5.53236 - 10.9648i) q^{62} +(3.01570 + 1.37723i) q^{63} +(2.93848 - 7.44079i) q^{64} +(2.62583 - 4.68604i) q^{65} +(-4.22553 + 1.73452i) q^{66} +(4.03312 - 6.27565i) q^{67} +(11.5282 - 6.19982i) q^{68} +(-6.53072 + 0.884400i) q^{69} +(-6.02097 + 7.25901i) q^{70} +(2.76141 - 4.29683i) q^{71} +(-1.99618 + 2.42921i) q^{72} +(8.40122 - 3.83671i) q^{73} +(0.253814 - 6.52385i) q^{74} +(5.09284 + 4.61218i) q^{75} +(0.220325 - 0.982632i) q^{76} +(-6.93834 - 0.997582i) q^{77} +(-4.02253 + 2.36938i) q^{78} +(0.508994 + 0.587411i) q^{79} +(-5.18891 - 7.28528i) q^{80} +(-3.72623 + 2.39470i) q^{81} +(-0.192174 + 0.274910i) q^{82} +(-0.865999 - 2.94932i) q^{83} +(7.69792 - 2.81543i) q^{84} +(1.20389 - 14.5849i) q^{85} +(-2.86850 + 15.6142i) q^{86} +(9.61954 + 2.82455i) q^{87} +(2.60261 - 6.11723i) q^{88} +(-3.79418 + 0.545520i) q^{89} +(1.06285 + 3.35077i) q^{90} -7.16438 q^{91} +(5.85932 - 7.59397i) q^{92} +11.9338i q^{93} +(-3.79577 + 11.2844i) q^{94} +(-0.787356 - 0.804802i) q^{95} +(0.707729 + 7.74124i) q^{96} +(-2.41301 - 0.708525i) q^{97} +(2.63517 + 0.484111i) q^{98} +(-1.71099 + 1.97459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Introduction

L-functions

Modular forms

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