LMFDB - Embedded newform 725.2.bd.a.482.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(43,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([21, 13]))

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

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

chi := DirichletCharacter("725.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.bd (of order $28$, degree $12$, 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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			482.7
Character	$\chi$	$=$	725.482
Dual form			725.2.bd.a.543.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.177554 - 0.368695i) q^{2} +(1.94143 - 2.43448i) q^{3} +(1.14257 + 1.43274i) q^{4} +(-0.552871 - 1.14805i) q^{6} +(3.34071 - 0.376408i) q^{7} +(1.52903 - 0.348992i) q^{8} +(-1.48996 - 6.52795i) q^{9} +(0.822283 - 0.516675i) q^{11} +5.70618 q^{12} +(-2.05464 + 1.29101i) q^{13} +(0.454377 - 1.29854i) q^{14} +(-0.672742 + 2.94747i) q^{16} +6.45849i q^{17} +(-2.67137 - 0.609723i) q^{18} +(-6.60252 - 0.743926i) q^{19} +(5.56940 - 8.86365i) q^{21} +(-0.0444956 - 0.394910i) q^{22} +(0.540188 - 1.54377i) q^{23} +(2.11890 - 4.39994i) q^{24} +(0.111181 + 0.986759i) q^{26} +(-10.3684 - 4.99318i) q^{27} +(4.35628 + 4.35628i) q^{28} +(-3.75211 + 3.86286i) q^{29} +(0.744261 + 2.12697i) q^{31} +(3.41965 + 2.72708i) q^{32} +(0.338573 - 3.00492i) q^{33} +(2.38121 + 1.14673i) q^{34} +(7.65044 - 9.59335i) q^{36} +(-0.761473 - 3.33623i) q^{37} +(-1.44659 + 2.30223i) q^{38} +(-0.845991 + 7.50838i) q^{39} +(4.23097 - 4.23097i) q^{41} +(-2.27911 - 3.62719i) q^{42} +(-6.22552 + 2.99805i) q^{43} +(1.67977 + 0.587778i) q^{44} +(-0.473268 - 0.473268i) q^{46} +(1.78903 - 7.83824i) q^{47} +(5.86947 + 7.36009i) q^{48} +(4.19416 - 0.957290i) q^{49} +(15.7230 + 12.5387i) q^{51} +(-4.19725 - 1.46868i) q^{52} +(1.97396 - 0.690719i) q^{53} +(-3.68192 + 2.93624i) q^{54} +(4.97669 - 1.74142i) q^{56} +(-14.6294 + 14.6294i) q^{57} +(0.758015 + 2.06925i) q^{58} -9.81641i q^{59} +(-14.5399 + 1.63826i) q^{61} +(0.916352 + 0.103248i) q^{62} +(-7.43470 - 21.2471i) q^{63} +(-3.83512 + 1.84690i) q^{64} +(-1.04778 - 0.658366i) q^{66} +(-1.73785 - 1.09196i) q^{67} +(-9.25331 + 7.37927i) q^{68} +(-2.70953 - 4.31220i) q^{69} +(-6.27144 - 1.43141i) q^{71} +(-4.55640 - 9.46146i) q^{72} +(6.36386 + 13.2147i) q^{73} +(-1.36525 - 0.311611i) q^{74} +(-6.47799 - 10.3097i) q^{76} +(2.55253 - 2.03557i) q^{77} +(2.61809 + 1.64506i) q^{78} +(-12.1834 - 7.65532i) q^{79} +(-14.1872 + 6.83220i) q^{81} +(-0.808712 - 2.31117i) q^{82} +(-6.43840 - 0.725433i) q^{83} +(19.0627 - 2.14785i) q^{84} +2.82764i q^{86} +(2.11958 + 16.6339i) q^{87} +(1.07698 - 1.07698i) q^{88} +(10.7763 - 3.77081i) q^{89} +(-6.37799 + 5.08628i) q^{91} +(2.82902 - 0.989916i) q^{92} +(6.62300 + 2.31749i) q^{93} +(-2.57227 - 2.05132i) q^{94} +(13.2780 - 3.03062i) q^{96} +(3.17277 + 3.97853i) q^{97} +(0.391743 - 1.71634i) q^{98} +(-4.59800 - 4.59800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{4} - 28 q^{9} - 12 q^{11} + 20 q^{16} - 4 q^{19} + 4 q^{21} - 12 q^{29} - 32 q^{31} + 40 q^{34} - 16 q^{36} + 184 q^{39} - 4 q^{41} - 36 q^{44} + 76 q^{46} + 84 q^{49} + 112 q^{51} - 168 q^{54}+ \cdots + 208 q^{99}+O(q^{100}) $ 120 * q + 20 * q^4 - 28 * q^9 - 12 * q^11 + 20 * q^16 - 4 * q^19 + 4 * q^21 - 12 * q^29 - 32 * q^31 + 40 * q^34 - 16 * q^36 + 184 * q^39 - 4 * q^41 - 36 * q^44 + 76 * q^46 + 84 * q^49 + 112 * q^51 - 168 * q^54 + 180 * q^56 + 124 * q^61 + 196 * q^64 + 144 * q^66 - 152 * q^69 + 56 * q^71 + 112 * q^74 + 12 * q^76 - 220 * q^79 - 76 * q^81 - 136 * q^84 + 208 * q^89 - 84 * q^94 - 84 * q^96 + 208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.177554	−	0.368695i	0.125550	−	0.260707i	−0.828714	−	0.559672i	$-0.810927\pi$
$2$	0.177554	−	0.368695i	0.125550	−	0.260707i	0.954264	+	0.298965i	$0.0966414\pi$
$3$	1.94143	−	2.43448i	1.12089	−	1.40555i	0.217848	−	0.975983i	$-0.430096\pi$
$3$	1.94143	−	2.43448i	1.12089	−	1.40555i	0.903037	−	0.429563i	$-0.141332\pi$
$4$	1.14257	+	1.43274i	0.571284	+	0.716368i
$5$		0			0
$5$		0			0
$6$	−0.552871	−	1.14805i	−0.225708	−	0.468688i
$7$	3.34071	−	0.376408i	1.26267	−	0.142269i	0.544871	−	0.838520i	$-0.316579\pi$
$7$	3.34071	−	0.376408i	1.26267	−	0.142269i	0.717798	+	0.696251i	$0.245150\pi$
$8$	1.52903	−	0.348992i	0.540595	−	0.123387i
$9$	−1.48996	−	6.52795i	−0.496654	−	2.17598i
$10$		0			0
$11$	0.822283	−	0.516675i	0.247928	−	0.155783i	−0.402336	−	0.915492i	$-0.631801\pi$
$11$	0.822283	−	0.516675i	0.247928	−	0.155783i	0.650263	+	0.759709i	$0.274659\pi$
$12$	5.70618			1.64723
$13$	−2.05464	+	1.29101i	−0.569854	+	0.358063i	−0.785932	−	0.618313i	$-0.787816\pi$
$13$	−2.05464	+	1.29101i	−0.569854	+	0.358063i	0.216078	+	0.976376i	$0.430673\pi$
$14$	0.454377	−	1.29854i	0.121437	−	0.347048i
$15$		0			0
$16$	−0.672742	+	2.94747i	−0.168185	+	0.736868i
$17$			6.45849i			1.56641i	0.621761	+	0.783207i	$0.286418\pi$
$17$			6.45849i			1.56641i	−0.621761	+	0.783207i	$0.713582\pi$
$18$	−2.67137	−	0.609723i	−0.629648	−	0.143713i
$19$	−6.60252	−	0.743926i	−1.51472	−	0.170668i	−0.684876	−	0.728660i	$-0.740144\pi$
$19$	−6.60252	−	0.743926i	−1.51472	−	0.170668i	−0.829847	+	0.557991i	$0.811572\pi$
$20$		0			0
$21$	5.56940	−	8.86365i	1.21534	−	1.93421i
$22$	−0.0444956	−	0.394910i	−0.00948650	−	0.0841950i
$23$	0.540188	−	1.54377i	0.112637	−	0.321898i	−0.873741	−	0.486391i	$-0.838313\pi$
$23$	0.540188	−	1.54377i	0.112637	−	0.321898i	0.986378	+	0.164493i	$0.0525988\pi$
$24$	2.11890	−	4.39994i	0.432518	−	0.898133i
$25$		0			0
$26$	0.111181	+	0.986759i	0.0218044	+	0.193519i
$27$	−10.3684	−	4.99318i	−1.99541	−	0.960938i
$28$	4.35628	+	4.35628i	0.823260	+	0.823260i
$29$	−3.75211	+	3.86286i	−0.696749	+	0.717315i
$29$	−3.75211	+	3.86286i	−0.696749	+	0.717315i
$30$		0			0
$31$	0.744261	+	2.12697i	0.133673	+	0.382016i	0.991191	−	0.132438i	$-0.0422805\pi$
$31$	0.744261	+	2.12697i	0.133673	+	0.382016i	−0.857518	+	0.514454i	$0.827995\pi$
$32$	3.41965	+	2.72708i	0.604514	+	0.482084i
$33$	0.338573	−	3.00492i	0.0589380	−	0.523089i
$34$	2.38121	+	1.14673i	0.408375	+	0.196663i
$35$		0			0
$36$	7.65044	−	9.59335i	1.27507	−	1.59889i
$37$	−0.761473	−	3.33623i	−0.125185	−	0.548473i	−0.998156	−	0.0607003i	$-0.980667\pi$
$37$	−0.761473	−	3.33623i	−0.125185	−	0.548473i	0.872971	−	0.487773i	$-0.162191\pi$
$38$	−1.44659	+	2.30223i	−0.234668	+	0.373471i
$39$	−0.845991	+	7.50838i	−0.135467	+	1.20230i
$40$		0			0
$41$	4.23097	−	4.23097i	0.660767	−	0.660767i	−0.294794	−	0.955561i	$-0.595251\pi$
$41$	4.23097	−	4.23097i	0.660767	−	0.660767i	0.955561	+	0.294794i	$0.0952511\pi$
$42$	−2.27911	−	3.62719i	−0.351675	−	0.559687i
$43$	−6.22552	+	2.99805i	−0.949383	+	0.457199i	−0.843470	−	0.537176i	$-0.819491\pi$
$43$	−6.22552	+	2.99805i	−0.949383	+	0.457199i	−0.105913	+	0.994375i	$0.533777\pi$
$44$	1.67977	+	0.587778i	0.253235	+	0.0886109i
$45$		0			0
$46$	−0.473268	−	0.473268i	−0.0697795	−	0.0697795i
$47$	1.78903	−	7.83824i	0.260956	−	1.14332i	−0.659260	−	0.751915i	$-0.729130\pi$
$47$	1.78903	−	7.83824i	0.260956	−	1.14332i	0.920216	−	0.391410i	$-0.128013\pi$
$48$	5.86947	+	7.36009i	0.847186	+	1.06234i
$49$	4.19416	−	0.957290i	0.599166	−	0.136756i
$50$		0			0
$51$	15.7230	+	12.5387i	2.20167	+	1.75577i
$52$	−4.19725	−	1.46868i	−0.582053	−	0.203669i
$53$	1.97396	−	0.690719i	0.271144	−	0.0948775i	−0.191282	−	0.981535i	$-0.561265\pi$
$53$	1.97396	−	0.690719i	0.271144	−	0.0948775i	0.462427	+	0.886658i	$0.346979\pi$
$54$	−3.68192	+	2.93624i	−0.501046	+	0.399571i
$55$		0			0
$56$	4.97669	−	1.74142i	0.665038	−	0.232707i
$57$	−14.6294	+	14.6294i	−1.93771	+	1.93771i
$58$	0.758015	+	2.06925i	0.0995322	+	0.271706i
$59$		−	9.81641i		−	1.27799i	−0.769212	−	0.638994i	$-0.779351\pi$
$59$		−	9.81641i		−	1.27799i	0.769212	−	0.638994i	$-0.220649\pi$
$60$		0			0
$61$	−14.5399	+	1.63826i	−1.86165	+	0.209757i	−0.970022	−	0.243019i	$-0.921862\pi$
$61$	−14.5399	+	1.63826i	−1.86165	+	0.209757i	−0.891624	+	0.452776i	$0.850434\pi$
$62$	0.916352	+	0.103248i	0.116377	+	0.0131125i
$63$	−7.43470	−	21.2471i	−0.936684	−	2.67689i
$64$	−3.83512	+	1.84690i	−0.479390	+	0.230862i
$65$		0			0
$66$	−1.04778	−	0.658366i	−0.128973	−	0.0810392i
$67$	−1.73785	−	1.09196i	−0.212312	−	0.133404i	0.421678	−	0.906745i	$-0.361441\pi$
$67$	−1.73785	−	1.09196i	−0.212312	−	0.133404i	−0.633990	+	0.773341i	$0.718584\pi$
$68$	−9.25331	+	7.37927i	−1.12213	+	0.894868i
$69$	−2.70953	−	4.31220i	−0.326189	−	0.519127i
$70$		0			0
$71$	−6.27144	−	1.43141i	−0.744283	−	0.169878i	−0.166469	−	0.986047i	$-0.553237\pi$
$71$	−6.27144	−	1.43141i	−0.744283	−	0.169878i	−0.577813	+	0.816169i	$0.696094\pi$
$72$	−4.55640	−	9.46146i	−0.536977	−	1.11504i
$73$	6.36386	+	13.2147i	0.744833	+	1.54666i	0.834698	+	0.550708i	$0.185642\pi$
$73$	6.36386	+	13.2147i	0.744833	+	1.54666i	−0.0898647	+	0.995954i	$0.528643\pi$
$74$	−1.36525	−	0.311611i	−0.158708	−	0.0362240i
$75$		0			0
$76$	−6.47799	−	10.3097i	−0.743076	−	1.18260i
$77$	2.55253	−	2.03557i	0.290888	−	0.231975i
$78$	2.61809	+	1.64506i	0.296441	+	0.186266i
$79$	−12.1834	−	7.65532i	−1.37074	−	0.861291i	−0.372954	−	0.927850i	$-0.621655\pi$
$79$	−12.1834	−	7.65532i	−1.37074	−	0.861291i	−0.997782	+	0.0665589i	$0.978798\pi$
$80$		0			0
$81$	−14.1872	+	6.83220i	−1.57636	+	0.759133i
$82$	−0.808712	−	2.31117i	−0.0893073	−	0.255226i
$83$	−6.43840	−	0.725433i	−0.706706	−	0.0796267i	−0.248706	−	0.968579i	$-0.580005\pi$
$83$	−6.43840	−	0.725433i	−0.706706	−	0.0796267i	−0.458000	+	0.888952i	$0.651434\pi$
$84$	19.0627	−	2.14785i	2.07991	−	0.234350i
$85$		0			0
$86$			2.82764i			0.304912i
$87$	2.11958	+	16.6339i	0.227243	+	1.78334i
$88$	1.07698	−	1.07698i	0.114807	−	0.114807i
$89$	10.7763	−	3.77081i	1.14229	−	0.399705i	0.308194	−	0.951323i	$-0.400275\pi$
$89$	10.7763	−	3.77081i	1.14229	−	0.399705i	0.834096	+	0.551619i	$0.185990\pi$
$90$		0			0
$91$	−6.37799	+	5.08628i	−0.668596	+	0.533187i
$92$	2.82902	−	0.989916i	0.294945	−	0.103206i
$93$	6.62300	+	2.31749i	0.686773	+	0.240312i
$94$	−2.57227	−	2.05132i	−0.265310	−	0.211577i
$95$		0			0
$96$	13.2780	−	3.03062i	1.35518	−	0.309311i
$97$	3.17277	+	3.97853i	0.322146	+	0.403958i	0.916364	−	0.400345i	$-0.131110\pi$
$97$	3.17277	+	3.97853i	0.322146	+	0.403958i	−0.594218	+	0.804304i	$0.702538\pi$
$98$	0.391743	−	1.71634i	0.0395720	−	0.173376i
$99$	−4.59800	−	4.59800i	−0.462116	−	0.462116i
$100$		0			0
$101$	17.6481	+	6.17534i	1.75605	+	0.614469i	0.999233	−	0.0391557i	$-0.0124668\pi$
$101$	17.6481	+	6.17534i	1.75605	+	0.614469i	0.756819	+	0.653625i	$0.226753\pi$
$102$	7.41465	−	3.57071i	0.734160	−	0.353553i
$103$	−2.50394	−	3.98499i	−0.246720	−	0.392653i	0.700289	−	0.713860i	$-0.253055\pi$
$103$	−2.50394	−	3.98499i	−0.246720	−	0.392653i	−0.947009	+	0.321206i	$0.895912\pi$
$104$	−2.69105	+	2.69105i	−0.263879	+	0.263879i
$105$		0			0
$106$	0.0958204	−	0.850430i	0.00930690	−	0.0826011i
$107$	6.59492	−	10.4958i	0.637555	−	1.01466i	−0.359129	−	0.933288i	$-0.616926\pi$
$107$	6.59492	−	10.4958i	0.637555	−	1.01466i	0.996684	−	0.0813745i	$-0.0259310\pi$
$108$	−4.69275	−	20.5603i	−0.451561	−	1.97842i
$109$	1.30985	−	1.64250i	0.125461	−	0.157323i	−0.715134	−	0.698988i	$-0.753634\pi$
$109$	1.30985	−	1.64250i	0.125461	−	0.157323i	0.840595	+	0.541664i	$0.182206\pi$
$110$		0			0
$111$	−9.60032	−	4.62327i	−0.911222	−	0.438822i
$112$	−1.13798	+	10.0999i	−0.107529	+	0.954349i
$113$	10.9795	+	8.75582i	1.03286	+	0.823679i	0.984541	−	0.175153i	$-0.0560421\pi$
$113$	10.9795	+	8.75582i	1.03286	+	0.823679i	0.0483193	+	0.998832i	$0.484614\pi$
$114$	2.79628	+	7.99131i	0.261896	+	0.748454i
$115$		0			0
$116$	−9.82150	−	0.962198i	−0.911903	−	0.0893378i
$117$	11.4890	+	11.4890i	1.06216	+	1.06216i
$118$	−3.61926	−	1.74295i	−0.333180	−	0.160451i
$119$	2.43102	+	21.5759i	0.222852	+	1.97786i
$120$		0			0
$121$	−4.36352	+	9.06095i	−0.396684	+	0.823723i
$122$	−1.97761	+	5.65168i	−0.179044	+	0.511679i
$123$	−2.08606	−	18.5143i	−0.188094	−	1.66938i
$124$	−2.19702	+	3.49654i	−0.197299	+	0.313999i
$125$		0			0
$126$	−9.15378	−	1.03138i	−0.815484	−	0.0918829i
$127$	12.5264	+	2.85906i	1.11154	+	0.253701i	0.738592	−	0.674153i	$-0.235491\pi$
$127$	12.5264	+	2.85906i	1.11154	+	0.253701i	0.372944	+	0.927854i	$0.378348\pi$
$128$			10.4897i			0.927167i
$129$	−4.78773	+	20.9764i	−0.421536	+	1.84687i
$130$		0			0
$131$	−0.641091	+	1.83213i	−0.0560124	+	0.160074i	−0.968490	−	0.249052i	$-0.919881\pi$
$131$	−0.641091	+	1.83213i	−0.0560124	+	0.160074i	0.912478	+	0.409127i	$0.134167\pi$
$132$	4.69210	−	2.94824i	0.408395	−	0.256611i
$133$	−22.3371			−1.93688
$134$	−0.711163	+	0.446853i	−0.0614351	+	0.0386022i
$135$		0			0
$136$	2.25396	+	9.87524i	0.193275	+	0.846795i
$137$	12.6489	−	2.88703i	1.08067	−	0.246656i	0.355117	−	0.934822i	$-0.384441\pi$
$137$	12.6489	−	2.88703i	1.08067	−	0.246656i	0.725553	+	0.688166i	$0.241584\pi$
$138$	−2.07097	+	0.233343i	−0.176293	+	0.0198635i
$139$	−3.97416	−	8.25242i	−0.337083	−	0.699961i	0.661674	−	0.749791i	$-0.269846\pi$
$139$	−3.97416	−	8.25242i	−0.337083	−	0.699961i	−0.998758	+	0.0498304i	$0.984132\pi$
$140$		0			0
$141$	−15.6087	−	19.5727i	−1.31449	−	1.64832i
$142$	−1.64128	+	2.05809i	−0.137733	+	0.172711i
$143$	−1.02246	+	2.12316i	−0.0855023	+	0.177547i
$144$	20.2433			1.68694
$145$		0			0
$146$	6.00212			0.496739
$147$	5.81217	−	12.0691i	0.479380	−	0.995442i
$148$	3.90990	−	4.90286i	0.321392	−	0.403013i
$149$	5.48621	+	6.87949i	0.449448	+	0.563589i	0.954006	−	0.299788i	$-0.0969160\pi$
$149$	5.48621	+	6.87949i	0.449448	+	0.563589i	−0.504558	+	0.863378i	$0.668345\pi$
$150$		0			0
$151$	0.851278	+	1.76770i	0.0692760	+	0.143853i	0.932731	−	0.360572i	$-0.117419\pi$
$151$	0.851278	+	1.76770i	0.0692760	+	0.143853i	−0.863455	+	0.504425i	$0.831704\pi$
$152$	−10.3551	+	1.16674i	−0.839909	+	0.0946350i
$153$	42.1607	−	9.62290i	3.40849	−	0.777966i
$154$	−0.297294	−	1.30253i	−0.0239566	−	0.104961i
$155$		0			0
$156$	−11.7241	+	7.36676i	−0.938681	+	0.589812i
$157$	9.57129			0.763872			0.381936	−	0.924189i	$-0.375257\pi$
$157$	9.57129			0.763872			0.381936	+	0.924189i	$0.375257\pi$
$158$	−4.98569	+	3.13272i	−0.396640	+	0.249226i
$159$	2.15077	−	6.14654i	0.170567	−	0.487453i
$160$		0			0
$161$	1.22353	−	5.36062i	0.0964273	−	0.422476i
$162$			6.44384i			0.506276i
$163$	20.5394	+	4.68798i	1.60877	+	0.367191i	0.930115	−	0.367268i	$-0.119707\pi$
$163$	20.5394	+	4.68798i	1.60877	+	0.367191i	0.678653	+	0.734459i	$0.262564\pi$
$164$	10.8960	+	1.22769i	0.850838	+	0.0958664i
$165$		0			0
$166$	−1.41063	+	2.24500i	−0.109486	+	0.174246i
$167$	−1.32434	−	11.7539i	−0.102481	−	0.909543i	−0.934783	−	0.355220i	$-0.884406\pi$
$167$	−1.32434	−	11.7539i	−0.102481	−	0.909543i	0.832302	−	0.554323i	$-0.187023\pi$
$168$	5.42245	−	15.4965i	0.418351	−	1.19558i
$169$	−3.08567	+	6.40747i	−0.237360	+	0.492882i
$170$		0			0
$171$	4.98120	+	44.2094i	0.380922	+	3.38077i
$172$	−11.4085	−	5.49405i	−0.869891	−	0.418917i
$173$	−3.61857	−	3.61857i	−0.275115	−	0.275115i	0.556041	−	0.831155i	$-0.312320\pi$
$173$	−3.61857	−	3.61857i	−0.275115	−	0.275115i	−0.831155	+	0.556041i	$0.812320\pi$
$174$	6.50918	+	2.17194i	0.493459	+	0.164654i
$175$		0			0
$176$	0.969701	+	2.77125i	0.0730940	+	0.208891i
$177$	−23.8978	−	19.0579i	−1.79627	−	1.43248i
$178$	0.523108	−	4.64271i	0.0392086	−	0.347986i
$179$	−9.13064	−	4.39709i	−0.682456	−	0.328654i	0.0603336	−	0.998178i	$-0.480784\pi$
$179$	−9.13064	−	4.39709i	−0.682456	−	0.328654i	−0.742790	+	0.669525i	$0.766498\pi$
$180$		0			0
$181$	−5.67771	+	7.11962i	−0.422021	+	0.529197i	−0.946706	−	0.322099i	$-0.895612\pi$
$181$	−5.67771	+	7.11962i	−0.422021	+	0.529197i	0.524685	+	0.851296i	$0.324183\pi$
$182$	0.742847	+	3.25463i	0.0550635	+	0.241249i
$183$	−24.2399	+	38.5776i	−1.79187	+	2.85174i
$184$	0.287203	−	2.54899i	0.0211729	−	0.187914i
$185$		0			0
$186$	2.03039	−	2.03039i	0.148875	−	0.148875i
$187$	3.33694	+	5.31071i	0.244021	+	0.388357i
$188$	13.2742	−	6.39253i	0.968122	−	0.466223i
$189$	−36.5174	−	12.7780i	−2.65625	−	0.929463i
$190$		0			0
$191$	−9.21557	−	9.21557i	−0.666815	−	0.666815i	0.290162	−	0.956977i	$-0.406291\pi$
$191$	−9.21557	−	9.21557i	−0.666815	−	0.666815i	−0.956977	+	0.290162i	$0.906291\pi$
$192$	−2.94939	+	12.9221i	−0.212854	+	0.932574i
$193$	6.28591	+	7.88229i	0.452470	+	0.567379i	0.954782	−	0.297307i	$-0.0960885\pi$
$193$	6.28591	+	7.88229i	0.452470	+	0.567379i	−0.502312	+	0.864686i	$0.667517\pi$
$194$	2.03020	−	0.463381i	0.145760	−	0.0332688i
$195$		0			0
$196$	6.16366	+	4.91536i	0.440262	+	0.351097i
$197$	−15.4593	−	5.40945i	−1.10143	−	0.385408i	−0.282482	−	0.959273i	$-0.591158\pi$
$197$	−15.4593	−	5.40945i	−1.10143	−	0.385408i	−0.818950	+	0.573865i	$0.805443\pi$
$198$	−2.51165	+	0.878865i	−0.178495	+	0.0624582i
$199$	9.36325	−	7.46694i	0.663743	−	0.529318i	−0.232659	−	0.972558i	$-0.574743\pi$
$199$	9.36325	−	7.46694i	0.663743	−	0.529318i	0.896403	+	0.443241i	$0.146171\pi$
$200$		0			0
$201$	−6.03226	+	2.11078i	−0.425483	+	0.148883i
$202$	5.41031	−	5.41031i	0.380668	−	0.380668i
$203$	−11.0807	+	14.3170i	−0.777712	+	1.00486i
$204$			36.8533i			2.58025i
$205$		0			0
$206$	−1.91383	+	0.215637i	−0.133343	+	0.0150242i
$207$	−10.8825	−	1.22616i	−0.756386	−	0.0852243i
$208$	−2.42299	−	6.92450i	−0.168004	−	0.480128i
$209$	−5.81351	+	2.79964i	−0.402129	+	0.193655i
$210$		0			0
$211$	6.25359	+	3.92939i	0.430515	+	0.270510i	0.729810	−	0.683650i	$-0.239609\pi$
$211$	6.25359	+	3.92939i	0.430515	+	0.270510i	−0.299295	+	0.954161i	$0.596751\pi$
$212$	3.24500	+	2.03897i	0.222868	+	0.140037i
$213$	−15.6603	+	12.4887i	−1.07303	+	0.855710i
$214$	−2.69878	−	4.29508i	−0.184485	−	0.293606i
$215$		0			0
$216$	−17.5963	−	4.01623i	−1.19727	−	0.273270i
$217$	3.28697	+	6.82546i	0.223134	+	0.463342i
$218$	−0.373013	−	0.774570i	−0.0252636	−	0.0524605i
$219$	44.5258	+	10.1627i	3.00878	+	0.686734i
$220$		0			0
$221$	−8.33800	−	13.2698i	−0.560874	−	0.892627i
$222$	−3.40916	+	2.71871i	−0.228808	+	0.182468i
$223$	9.33568	+	5.86600i	0.625164	+	0.392816i	0.807033	−	0.590506i	$-0.201072\pi$
$223$	9.33568	+	5.86600i	0.625164	+	0.392816i	−0.181869	+	0.983323i	$0.558215\pi$
$224$	12.4505	+	7.82320i	0.831887	+	0.522709i
$225$		0			0
$226$	5.17768	−	2.49344i	0.344414	−	0.165861i
$227$	−1.24599	−	3.56082i	−0.0826990	−	0.236340i	0.895107	−	0.445851i	$-0.147099\pi$
$227$	−1.24599	−	3.56082i	−0.0826990	−	0.236340i	−0.977806	+	0.209510i	$0.932813\pi$
$228$	−37.6752	−	4.24497i	−2.49510	−	0.281130i
$229$	−8.55442	+	0.963852i	−0.565292	+	0.0636931i	−0.389986	−	0.920821i	$-0.627520\pi$
$229$	−8.55442	+	0.963852i	−0.565292	+	0.0636931i	−0.175306	+	0.984514i	$0.556092\pi$
$230$		0			0
$231$		−	10.1660i		−	0.668873i
$232$	−4.38899	+	7.21589i	−0.288151	+	0.473746i
$233$	1.57326	−	1.57326i	0.103068	−	0.103068i	−0.653692	−	0.756760i	$-0.726781\pi$
$233$	1.57326	−	1.57326i	0.103068	−	0.103068i	0.756760	+	0.653692i	$0.226781\pi$
$234$	6.27586	−	2.19602i	0.410266	−	0.143558i
$235$		0			0
$236$	14.0643	−	11.2159i	0.915510	−	0.730095i
$237$	−42.2899	+	14.7979i	−2.74702	+	0.961225i
$238$	8.38658	+	2.93459i	0.543621	+	0.190221i
$239$	5.34017	+	4.25865i	0.345427	+	0.275469i	0.780800	−	0.624781i	$-0.214812\pi$
$239$	5.34017	+	4.25865i	0.345427	+	0.275469i	−0.435373	+	0.900250i	$0.643383\pi$
$240$		0			0
$241$	6.54369	−	1.49355i	0.421516	−	0.0962083i	−0.00650118	−	0.999979i	$-0.502069\pi$
$241$	6.54369	−	1.49355i	0.421516	−	0.0962083i	0.428017	+	0.903771i	$0.359212\pi$
$242$	2.56597	+	3.21762i	0.164947	+	0.206836i
$243$	−3.22826	+	14.1439i	−0.207093	+	0.907333i
$244$	−18.9600	−	18.9600i	−1.21379	−	1.21379i
$245$		0			0
$246$	−7.19653	−	2.51818i	−0.458834	−	0.160553i
$247$	14.5262	−	6.99545i	0.924280	−	0.445110i
$248$	1.88029	+	2.99247i	0.119399	+	0.190022i
$249$	−14.2658	+	14.2658i	−0.904055	+	0.904055i
$250$		0			0
$251$	0.287687	−	2.55329i	0.0181586	−	0.161162i	−0.981360	−	0.192177i	$-0.938445\pi$
$251$	0.287687	−	2.55329i	0.0181586	−	0.161162i	0.999519	+	0.0310146i	$0.00987384\pi$
$252$	21.9469	−	34.9283i	1.38252	−	2.20028i
$253$	−0.353439	−	1.54852i	−0.0222205	−	0.0973544i
$254$	3.27823	−	4.11078i	0.205695	−	0.257933i
$255$		0			0
$256$	−3.80273	−	1.83130i	−0.237671	−	0.114456i
$257$	−2.99776	+	26.6059i	−0.186995	+	1.65963i	0.453194	+	0.891412i	$0.350285\pi$
$257$	−2.99776	+	26.6059i	−0.186995	+	1.65963i	−0.640189	+	0.768218i	$0.721144\pi$
$258$	6.88382	+	5.48966i	0.428568	+	0.341771i
$259$	−3.79964	−	10.8588i	−0.236098	−	0.674730i
$260$		0			0
$261$	30.8070	+	18.7381i	1.90691	+	1.15986i
$262$	0.561670	+	0.561670i	0.0347001	+	0.0347001i
$263$	1.45037	+	0.698461i	0.0894336	+	0.0430689i	0.478066	−	0.878324i	$-0.341338\pi$
$263$	1.45037	+	0.698461i	0.0894336	+	0.0430689i	−0.388632	+	0.921393i	$0.627052\pi$
$264$	−0.531002	−	4.71277i	−0.0326809	−	0.290051i
$265$		0			0
$266$	−3.96605	+	8.23559i	−0.243174	+	0.504957i
$267$	11.7416	−	33.5555i	0.718573	−	2.05356i
$268$	−0.421117	−	3.73752i	−0.0257238	−	0.228305i
$269$	2.51693	−	4.00567i	0.153460	−	0.244230i	−0.761142	−	0.648585i	$-0.775361\pi$
$269$	2.51693	−	4.00567i	0.153460	−	0.244230i	0.914602	+	0.404355i	$0.132504\pi$
$270$		0			0
$271$	−9.25283	−	1.04254i	−0.562069	−	0.0633300i	−0.173641	−	0.984809i	$-0.555553\pi$
$271$	−9.25283	−	1.04254i	−0.562069	−	0.0633300i	−0.388428	+	0.921479i	$0.626982\pi$
$272$	−19.0362	−	4.34490i	−1.15424	−	0.263448i
$273$			25.4017i			1.53738i
$274$	1.18143	−	5.17620i	0.0713730	−	0.312706i
$275$		0			0
$276$	3.08241	−	8.80903i	0.185539	−	0.530241i
$277$	2.97647	−	1.87024i	0.178839	−	0.112372i	−0.439638	−	0.898175i	$-0.644893\pi$
$277$	2.97647	−	1.87024i	0.178839	−	0.112372i	0.618476	+	0.785803i	$0.287750\pi$
$278$	−3.74825			−0.224805
$279$	12.7759	−	8.02760i	0.764871	−	0.480600i
$280$		0			0
$281$	−0.994732	−	4.35821i	−0.0593407	−	0.259989i	0.936552	−	0.350528i	$-0.113998\pi$
$281$	−0.994732	−	4.35821i	−0.0593407	−	0.259989i	−0.995893	+	0.0905396i	$0.971141\pi$
$282$	−9.98777	+	2.27964i	−0.594763	+	0.135751i
$283$	−17.5096	+	1.97286i	−1.04084	+	0.117274i	−0.615800	−	0.787902i	$-0.711167\pi$
$283$	−17.5096	+	1.97286i	−1.04084	+	0.117274i	−0.425036	+	0.905176i	$0.639739\pi$
$284$	−5.11471	−	10.6208i	−0.303502	−	0.630229i
$285$		0			0
$286$	0.601256	+	0.753951i	0.0355530	+	0.0445821i
$287$	12.5419	−	15.7270i	0.740323	−	0.928336i
$288$	12.7071	−	26.3865i	0.748772	−	1.55484i
$289$	−24.7121			−1.45365
$290$		0			0
$291$	15.8453			0.928871
$292$	−11.6620	+	24.2164i	−0.682468	+	1.41716i
$293$	−5.65066	+	7.08570i	−0.330115	+	0.413951i	−0.918995	−	0.394269i	$-0.870998\pi$
$293$	−5.65066	+	7.08570i	−0.330115	+	0.413951i	0.588880	+	0.808221i	$0.299569\pi$
$294$	−3.41784	−	4.28584i	−0.199333	−	0.249955i
$295$		0			0
$296$	−2.32863	−	4.83546i	−0.135349	−	0.281055i
$297$	−11.1056	+	1.25131i	−0.644415	+	0.0726082i
$298$	3.51053	−	0.801256i	0.203360	−	0.0464155i
$299$	0.883137	+	3.86927i	0.0510731	+	0.223766i
$300$		0			0
$301$	−19.6692	+	12.3590i	−1.13371	+	0.712359i
$302$	0.802889			0.0462011
$303$	49.2963	−	30.9749i	2.83200	−	1.77946i
$304$	6.63450	−	18.9603i	0.380514	−	1.08745i
$305$		0			0
$306$	3.93789	−	17.2530i	0.225114	−	0.986290i
$307$			9.63676i			0.549999i	0.961444	+	0.274999i	$0.0886777\pi$
$307$			9.63676i			0.549999i	−0.961444	+	0.274999i	$0.911322\pi$
$308$	5.83288	+	1.33132i	0.332359	+	0.0758588i
$309$	−14.5626	−	1.64081i	−0.828437	−	0.0933424i
$310$		0			0
$311$	−11.8375	+	18.8393i	−0.671242	+	1.06828i	0.321371	+	0.946953i	$0.395856\pi$
$311$	−11.8375	+	18.8393i	−0.671242	+	1.06828i	−0.992613	+	0.121323i	$0.961286\pi$
$312$	1.32681	+	11.7758i	0.0751160	+	0.666673i
$313$	10.0042	−	28.5902i	0.565469	−	1.61602i	−0.205158	−	0.978729i	$-0.565771\pi$
$313$	10.0042	−	28.5902i	0.565469	−	1.61602i	0.770626	−	0.637288i	$-0.219944\pi$
$314$	1.69942	−	3.52889i	0.0959040	−	0.199147i
$315$		0			0
$316$	−2.95229	−	26.2023i	−0.166079	−	1.47399i
$317$	19.8654	+	9.56669i	1.11575	+	0.537319i	0.898578	−	0.438814i	$-0.144601\pi$
$317$	19.8654	+	9.56669i	1.11575	+	0.537319i	0.217176	+	0.976133i	$0.430316\pi$
$318$	−1.88432	−	1.88432i	−0.105668	−	0.105668i
$319$	−1.08945	+	5.11498i	−0.0609977	+	0.286384i
$320$		0			0
$321$	−12.7481	−	36.4319i	−0.711529	−	2.03343i
$322$	−1.75919	−	1.40291i	−0.0980359	−	0.0781810i
$323$	4.80464	−	42.6423i	0.267337	−	2.37268i
$324$	−25.9986	−	12.5203i	−1.44437	−	0.695570i
$325$		0			0
$326$	5.37529	−	6.74040i	0.297710	−	0.373316i
$327$	−1.45565	−	6.37761i	−0.0804975	−	0.352683i
$328$	4.99272	−	7.94587i	0.275677	−	0.438737i
$329$	3.02625	−	26.8587i	0.166842	−	1.48077i
$330$		0			0
$331$	−7.91949	+	7.91949i	−0.435295	+	0.435295i	−0.890425	−	0.455130i	$-0.849593\pi$
$331$	−7.91949	+	7.91949i	−0.435295	+	0.435295i	0.455130	+	0.890425i	$0.349593\pi$
$332$	−6.31696	−	10.0534i	−0.346688	−	0.551751i
$333$	−20.6442	+	9.94171i	−1.13129	+	0.544802i
$334$	−4.56874	−	1.59867i	−0.249990	−	0.0874754i
$335$		0			0
$336$	22.3786	+	22.3786i	1.22085	+	1.22085i
$337$	4.79466	−	21.0068i	0.261182	−	1.14431i	−0.658789	−	0.752327i	$-0.728931\pi$
$337$	4.79466	−	21.0068i	0.261182	−	1.14431i	0.919971	−	0.391986i	$-0.128212\pi$
$338$	1.81453	+	2.27535i	0.0986973	+	0.123763i
$339$	42.6317	−	9.73041i	2.31544	−	0.528483i
$340$		0			0
$341$	1.71095	+	1.36443i	0.0926530	+	0.0738883i
$342$	17.1842	+	6.01301i	0.929215	+	0.325147i
$343$	−8.56121	+	2.99570i	−0.462262	+	0.161752i
$344$	−8.47273	+	6.75678i	−0.456819	+	0.364301i
$345$		0			0
$346$	−1.97664	+	0.691657i	−0.106265	+	0.0371837i
$347$	−0.543822	+	0.543822i	−0.0291939	+	0.0291939i	−0.721553	−	0.692359i	$-0.756571\pi$
$347$	−0.543822	+	0.543822i	−0.0291939	+	0.0291939i	0.692359	+	0.721553i	$0.256571\pi$
$348$	−21.4102	+	22.0422i	−1.14771	+	1.18158i
$349$		−	4.38642i		−	0.234800i	−0.993085	−	0.117400i	$-0.962544\pi$
$349$		−	4.38642i		−	0.234800i	0.993085	−	0.117400i	$-0.0374559\pi$
$350$		0			0
$351$	27.7496	−	3.12663i	1.48117	−	0.166887i
$352$	4.22093	+	0.475585i	0.224976	+	0.0253488i
$353$	−8.73188	−	24.9543i	−0.464751	−	1.32818i	−0.903120	−	0.429387i	$-0.858730\pi$
$353$	−8.73188	−	24.9543i	−0.464751	−	1.32818i	0.438369	−	0.898795i	$-0.355556\pi$
$354$	−11.2697	+	5.42721i	−0.598978	+	0.288453i
$355$		0			0
$356$	17.7153	+	11.1313i	0.938909	+	0.589955i
$357$	57.2458	+	35.9699i	3.02977	+	1.90373i
$358$	−3.24237	+	2.58570i	−0.171364	+	0.136659i
$359$	12.0702	+	19.2097i	0.637042	+	1.01385i	0.996732	+	0.0807752i	$0.0257396\pi$
$359$	12.0702	+	19.2097i	0.637042	+	1.01385i	−0.359690	+	0.933072i	$0.617118\pi$
$360$		0			0
$361$	24.5163	+	5.59568i	1.29033	+	0.294509i
$362$	1.61687	+	3.35746i	0.0849807	+	0.176464i
$363$	13.5872	+	28.2141i	0.713143	+	1.48086i
$364$	−14.5746	−	3.32656i	−0.763917	−	0.174359i
$365$		0			0
$366$	9.91949	+	15.7868i	0.518500	+	0.825188i
$367$	2.05179	−	1.63625i	0.107103	−	0.0854115i	−0.568474	−	0.822701i	$-0.692466\pi$
$367$	2.05179	−	1.63625i	0.107103	−	0.0854115i	0.675577	+	0.737290i	$0.263895\pi$
$368$	4.18681	+	2.63075i	0.218253	+	0.137137i
$369$	−33.9235	−	21.3156i	−1.76599	−	1.10964i
$370$		0			0
$371$	6.33444	−	3.05050i	0.328868	−	0.158374i
$372$	4.24688	+	12.1369i	0.220191	+	0.629269i
$373$	−3.50003	−	0.394358i	−0.181225	−	0.0204191i	0.0208857	−	0.999782i	$-0.493351\pi$
$373$	−3.50003	−	0.394358i	−0.181225	−	0.0204191i	−0.202110	+	0.979363i	$0.564780\pi$
$374$	2.55052	−	0.287375i	0.131884	−	0.0148598i
$375$		0			0
$376$		−	12.6093i		−	0.650274i
$377$	2.72221	−	12.7808i	0.140201	−	0.658244i
$378$	−11.1950	+	11.1950i	−0.575809	+	0.575809i
$379$	23.0211	−	8.05542i	1.18251	−	0.413779i	0.333805	−	0.942642i	$-0.391667\pi$
$379$	23.0211	−	8.05542i	1.18251	−	0.413779i	0.848707	+	0.528863i	$0.177381\pi$
$380$		0			0
$381$	31.2794	−	24.9445i	1.60249	−	1.27795i
$382$	−5.03400	+	1.76147i	−0.257562	+	0.0901247i
$383$	−16.7325	−	5.85497i	−0.854992	−	0.299175i	−0.133034	−	0.991111i	$-0.542472\pi$
$383$	−16.7325	−	5.85497i	−0.854992	−	0.299175i	−0.721958	+	0.691937i	$0.756758\pi$
$384$	25.5369	+	20.3650i	1.30318	+	1.03925i
$385$		0			0
$386$	4.02225	−	0.918053i	0.204727	−	0.0467277i
$387$	28.8469	+	36.1729i	1.46637	+	1.83877i
$388$	−2.07507	+	9.09149i	−0.105346	+	0.461550i
$389$	20.9074	+	20.9074i	1.06005	+	1.06005i	0.998078	+	0.0619714i	$0.0197387\pi$
$389$	20.9074	+	20.9074i	1.06005	+	1.06005i	0.0619714	+	0.998078i	$0.480261\pi$
$390$		0			0
$391$	9.97042	+	3.48880i	0.504226	+	0.176436i
$392$	6.07892	−	2.92745i	0.307032	−	0.147859i
$393$	3.21565	+	5.11768i	0.162208	+	0.258153i
$394$	−4.73931	+	4.73931i	−0.238763	+	0.238763i
$395$		0			0
$396$	1.33419	−	11.8412i	0.0670455	−	0.595045i
$397$	−4.77899	+	7.60573i	−0.239851	+	0.381720i	−0.944858	−	0.327479i	$-0.893801\pi$
$397$	−4.77899	+	7.60573i	−0.239851	+	0.381720i	0.705007	+	0.709200i	$0.250944\pi$
$398$	−1.09054	−	4.77797i	−0.0546639	−	0.239498i
$399$	−43.3660	+	54.3792i	−2.17101	+	2.72237i
$400$		0			0
$401$	−16.1128	−	7.75950i	−0.804634	−	0.387491i	−0.0140930	−	0.999901i	$-0.504486\pi$
$401$	−16.1128	−	7.75950i	−0.804634	−	0.387491i	−0.790541	+	0.612410i	$0.790200\pi$
$402$	−0.292819	+	2.59884i	−0.0146045	+	0.129619i
$403$	−4.27514	−	3.40931i	−0.212960	−	0.169830i
$404$	11.3165	+	32.3408i	0.563019	+	1.60902i
$405$		0			0
$406$	3.31119	+	6.62744i	0.164332	+	0.328915i
$407$	−2.34989	−	2.34989i	−0.116480	−	0.116480i
$408$	28.4169	+	13.6849i	1.40685	+	0.677503i
$409$	−1.88589	−	16.7378i	−0.0932513	−	0.827628i	−0.950076	−	0.312020i	$-0.898994\pi$
$409$	−1.88589	−	16.7378i	−0.0932513	−	0.827628i	0.856824	−	0.515609i	$-0.172434\pi$
$410$		0			0
$411$	17.5286	−	36.3985i	0.864621	−	1.79540i
$412$	2.84852	−	8.14061i	0.140337	−	0.401059i
$413$	−3.69497	−	32.7938i	−0.181818	−	1.61368i
$414$	−2.38432	+	3.79462i	−0.117183	+	0.186495i
$415$		0			0
$416$	−10.5468	−	1.18834i	−0.517101	−	0.0582633i
$417$	−27.8059	−	6.34651i	−1.36166	−	0.310790i
$418$			2.64050i			0.129151i
$419$	0.726862	−	3.18459i	0.0355095	−	0.155577i	−0.954065	−	0.299600i	$-0.903147\pi$
$419$	0.726862	−	3.18459i	0.0355095	−	0.155577i	0.989574	+	0.144023i	$0.0460038\pi$
$420$		0			0
$421$	−2.10095	+	6.00416i	−0.102394	+	0.292625i	−0.983671	−	0.179975i	$-0.942398\pi$
$421$	−2.10095	+	6.00416i	−0.102394	+	0.292625i	0.881277	+	0.472599i	$0.156684\pi$
$422$	2.55910	−	1.60799i	0.124575	−	0.0782756i
$423$	−53.8332			−2.61746
$424$	2.77719	−	1.74503i	0.134873	−	0.0847460i
$425$		0			0
$426$	1.82396	+	7.99129i	0.0883712	+	0.387179i
$427$	−47.9570	+	10.9459i	−2.32080	+	0.529708i
$428$	22.5728	−	2.54334i	1.09110	−	0.122937i
$429$	3.18374	+	6.61111i	0.153713	+	0.319188i
$430$		0			0
$431$	22.7217	+	28.4921i	1.09447	+	1.37242i	0.921904	+	0.387418i	$0.126633\pi$
$431$	22.7217	+	28.4921i	1.09447	+	1.37242i	0.172561	+	0.984999i	$0.444796\pi$
$432$	21.6926	−	27.2016i	1.04368	−	1.30874i
$433$	12.2296	−	25.3951i	0.587718	−	1.22041i	−0.369010	−	0.929425i	$-0.620303\pi$
$433$	12.2296	−	25.3951i	0.587718	−	1.22041i	0.956728	−	0.290983i	$-0.0939824\pi$
$434$	3.10013			0.148811
$435$		0			0
$436$	3.84987			0.184375
$437$	−4.71506	+	9.79091i	−0.225552	+	0.468363i
$438$	11.6527	−	14.6120i	0.556787	−	0.698189i
$439$	−21.5771	−	27.0568i	−1.02982	−	1.29135i	−0.955775	−	0.294097i	$-0.904981\pi$
$439$	−21.5771	−	27.0568i	−1.02982	−	1.29135i	−0.0740437	−	0.997255i	$-0.523590\pi$
$440$		0			0
$441$	−12.4983	−	25.9529i	−0.595156	−	1.23585i
$442$	−6.37298	+	0.718062i	−0.303132	+	0.0341547i
$443$	15.1035	−	3.44728i	0.717590	−	0.163785i	0.151891	−	0.988397i	$-0.451464\pi$
$443$	15.1035	−	3.44728i	0.717590	−	0.163785i	0.565699	+	0.824612i	$0.308606\pi$
$444$	−4.34510	−	19.0371i	−0.206209	−	0.903462i
$445$		0			0
$446$	3.82035	−	2.40049i	0.180899	−	0.113666i
$447$	27.3990			1.29593
$448$	−12.1168	+	7.61351i	−0.572466	+	0.359704i
$449$	−10.5740	+	30.2189i	−0.499020	+	1.42612i	0.368926	+	0.929459i	$0.379725\pi$
$449$	−10.5740	+	30.2189i	−0.499020	+	1.42612i	−0.867946	+	0.496658i	$0.834560\pi$
$450$		0			0
$451$	1.29302	−	5.66509i	0.0608860	−	0.266759i
$452$			25.7348i			1.21046i
$453$	5.95611	+	1.35944i	0.279843	+	0.0638722i
$454$	−1.53409	−	0.172850i	−0.0719983	−	0.00811226i
$455$		0			0
$456$	−17.2633	+	27.4744i	−0.808428	+	1.28661i
$457$	−2.99861	−	26.6134i	−0.140269	−	1.24492i	−0.844735	−	0.535184i	$-0.820242\pi$
$457$	−2.99861	−	26.6134i	−0.140269	−	1.24492i	0.704466	−	0.709738i	$-0.251186\pi$
$458$	−1.16351	+	3.32511i	−0.0543671	+	0.155372i
$459$	32.2484	−	66.9645i	1.50523	−	3.12564i
$460$		0			0
$461$	−4.40376	−	39.0844i	−0.205103	−	1.82034i	−0.501365	−	0.865236i	$-0.667169\pi$
$461$	−4.40376	−	39.0844i	−0.205103	−	1.82034i	0.296262	−	0.955107i	$-0.404260\pi$
$462$	−3.74815	−	1.80502i	−0.174380	−	0.0839769i
$463$	17.3288	+	17.3288i	0.805338	+	0.805338i	0.983924	−	0.178586i	$-0.0571522\pi$
$463$	17.3288	+	17.3288i	0.805338	+	0.805338i	−0.178586	+	0.983924i	$0.557152\pi$
$464$	−8.86148	−	13.6579i	−0.411384	−	0.634054i
$465$		0			0
$466$	−0.300715	−	0.859394i	−0.0139304	−	0.0398107i
$467$	−14.6224	−	11.6610i	−0.676646	−	0.539607i	0.223767	−	0.974643i	$-0.428164\pi$
$467$	−14.6224	−	11.6610i	−0.676646	−	0.539607i	−0.900413	+	0.435035i	$0.856736\pi$
$468$	−3.33373	+	29.5877i	−0.154102	+	1.36769i
$469$	−6.21666	−	2.99379i	−0.287059	−	0.138240i
$470$		0			0
$471$	18.5820	−	23.3011i	0.856213	−	1.07366i
$472$	−3.42585	−	15.0096i	−0.157687	−	0.690873i
$473$	−3.57012	+	5.68182i	−0.164154	+	0.261250i
$474$	−2.05284	+	18.2195i	−0.0942902	+	0.836849i
$475$		0			0
$476$	−28.1350	+	28.1350i	−1.28957	+	1.28957i
$477$	−7.45010	−	11.8568i	−0.341117	−	0.542884i
$478$	2.51831	−	1.21276i	0.115185	−	0.0554701i
$479$	−30.1049	−	10.5342i	−1.37553	−	0.481319i	−0.461563	−	0.887107i	$-0.652711\pi$
$479$	−30.1049	−	10.5342i	−1.37553	−	0.481319i	−0.913967	+	0.405789i	$0.866997\pi$
$480$		0			0
$481$	5.87167	+	5.87167i	0.267725	+	0.267725i
$482$	0.611193	−	2.67781i	0.0278391	−	0.121971i
$483$	−10.6749	−	13.3859i	−0.485725	−	0.609080i
$484$	−17.9676	+	4.10098i	−0.816708	+	0.186408i
$485$		0			0
$486$	4.64160	+	3.70155i	0.210547	+	0.167906i
$487$	−19.1858	−	6.71341i	−0.869393	−	0.304214i	−0.141528	−	0.989934i	$-0.545202\pi$
$487$	−19.1858	−	6.71341i	−0.869393	−	0.304214i	−0.727865	+	0.685720i	$0.759487\pi$
$488$	−21.6603	+	7.57926i	−0.980514	+	0.343097i
$489$	51.2885	−	40.9012i	2.31935	−	1.84962i
$490$		0			0
$491$	9.57151	−	3.34922i	0.431956	−	0.151148i	−0.105538	−	0.994415i	$-0.533657\pi$
$491$	9.57151	−	3.34922i	0.431956	−	0.151148i	0.537495	+	0.843267i	$0.319371\pi$
$492$	24.1427	−	24.1427i	1.08844	−	1.08844i
$493$	−24.9482	−	24.2330i	−1.12361	−	1.09140i
$494$		−	6.59781i		−	0.296850i
$495$		0			0
$496$	−6.76990	+	0.762784i	−0.303977	+	0.0342500i
$497$	−21.4898	−	2.42132i	−0.963951	−	0.108611i
$498$	2.72677	+	7.79266i	0.122189	+	0.349197i
$499$	−1.40772	+	0.677923i	−0.0630183	+	0.0303480i	−0.465127	−	0.885244i	$-0.653992\pi$
$499$	−1.40772	+	0.677923i	−0.0630183	+	0.0303480i	0.402109	+	0.915592i	$0.368277\pi$
$500$		0			0
$501$	−31.1857	−	19.5953i	−1.39327	−	0.875451i
$502$	−0.890306	−	0.559416i	−0.0397363	−	0.0249680i
$503$	11.4829	−	9.15733i	0.511998	−	0.408305i	−0.333120	−	0.942884i	$-0.608101\pi$
$503$	11.4829	−	9.15733i	0.511998	−	0.408305i	0.845118	+	0.534579i	$0.179530\pi$
$504$	−18.7830	−	29.8929i	−0.836660	−	1.33154i
$505$		0			0
$506$	−0.633685	−	0.144635i	−0.0281708	−	0.00642979i
$507$	9.60821	+	19.9517i	0.426716	+	0.886084i
$508$	10.2160	+	21.2137i	0.453260	+	0.941204i
$509$	−10.9409	−	2.49719i	−0.484947	−	0.110686i	−0.0269447	−	0.999637i	$-0.508578\pi$
$509$	−10.9409	−	2.49719i	−0.484947	−	0.110686i	−0.458003	+	0.888951i	$0.651435\pi$
$510$		0			0
$511$	26.2339	+	41.7510i	1.16052	+	1.84696i
$512$	−17.7527	+	14.1573i	−0.784568	+	0.625672i
$513$	64.7434	+	40.6810i	2.85849	+	1.79611i
$514$	9.27720	+	5.82925i	0.409200	+	0.257117i
$515$		0			0
$516$	−35.5240	+	17.1074i	−1.56385	+	0.753113i
$517$	−2.57873	−	7.36960i	−0.113413	−	0.324115i
$518$	−4.67821	−	0.527108i	−0.205549	−	0.0231598i
$519$	−15.8345	+	1.78412i	−0.695058	+	0.0783143i
$520$		0			0
$521$		−	28.5240i		−	1.24966i	−0.780762	−	0.624829i	$-0.785169\pi$
$521$		−	28.5240i		−	1.24966i	0.780762	−	0.624829i	$-0.214831\pi$
$522$	12.3786	−	8.03139i	0.541794	−	0.351524i
$523$	3.65812	−	3.65812i	0.159958	−	0.159958i	−0.622590	−	0.782548i	$-0.713919\pi$
$523$	3.65812	−	3.65812i	0.159958	−	0.159958i	0.782548	+	0.622590i	$0.213919\pi$
$524$	−3.35745	+	1.17482i	−0.146671	+	0.0513224i
$525$		0			0
$526$	0.515038	−	0.410729i	0.0224567	−	0.0179086i
$527$	−13.7370	+	4.80680i	−0.598395	+	0.209387i
$528$	8.62914	+	3.01947i	0.375535	+	0.131405i
$529$	15.8907	+	12.6724i	0.690900	+	0.550974i
$530$		0			0
$531$	−64.0810	+	14.6261i	−2.78088	+	0.634718i
$532$	−25.5217	−	32.0032i	−1.10651	−	1.38752i
$533$	−3.23087	+	14.1553i	−0.139944	+	0.613136i
$534$	−10.2870	−	10.2870i	−0.445162	−	0.445162i
$535$		0			0
$536$	−3.03831	−	1.06315i	−0.131235	−	0.0459211i
$537$	−28.4311	+	13.6917i	−1.22689	+	0.590840i
$538$	−1.02998	−	1.63920i	−0.0444056	−	0.0706711i
$539$	2.95418	−	2.95418i	0.127246	−	0.127246i
$540$		0			0
$541$	−1.69761	+	15.0667i	−0.0729858	+	0.647767i	0.902956	+	0.429734i	$0.141393\pi$
$541$	−1.69761	+	15.0667i	−0.0729858	+	0.647767i	−0.975941	+	0.218033i	$0.930036\pi$
$542$	−2.02726	+	3.22637i	−0.0870783	+	0.138584i
$543$	6.30967	+	27.6445i	0.270774	+	1.18634i
$544$	−17.6128	+	22.0858i	−0.755143	+	0.946920i
$545$		0			0
$546$	9.36550	+	4.51019i	0.400806	+	0.193018i
$547$	2.90217	−	25.7574i	0.124088	−	1.10131i	−0.765146	−	0.643856i	$-0.777333\pi$
$547$	2.90217	−	25.7574i	0.124088	−	1.10131i	0.889234	−	0.457452i	$-0.151238\pi$
$548$	18.5886	+	14.8239i	0.794067	+	0.633247i
$549$	32.3584	+	92.4749i	1.38102	+	3.94673i
$550$		0			0
$551$	27.6471	−	22.7133i	1.17780	−	0.967621i
$552$	−5.64788	−	5.64788i	−0.240390	−	0.240390i
$553$	−43.5826	−	20.9883i	−1.85332	−	0.892513i
$554$	−0.161064	−	1.42948i	−0.00684294	−	0.0607328i
$555$		0			0
$556$	7.28279	−	15.1229i	0.308859	−	0.641353i
$557$	−9.53025	+	27.2359i	−0.403810	+	1.15402i	0.545072	+	0.838389i	$0.316502\pi$
$557$	−9.53025	+	27.2359i	−0.403810	+	1.15402i	−0.948882	+	0.315632i	$0.897783\pi$
$558$	−0.691331	−	6.13573i	−0.0292664	−	0.259746i
$559$	8.92066	−	14.1971i	0.377304	−	0.600475i
$560$		0			0
$561$	19.4072	+	2.18667i	0.819374	+	0.0923213i
$562$	−1.78347	−	0.407065i	−0.0752311	−	0.0171710i
$563$			17.8844i			0.753737i	0.926267	+	0.376868i	$0.122999\pi$
$563$			17.8844i			0.753737i	−0.926267	+	0.376868i	$0.877001\pi$
$564$	10.2085	−	44.7264i	0.429856	−	1.88332i
$565$		0			0
$566$	−2.38152	+	6.80598i	−0.100103	+	0.286077i
$567$	−44.8236	+	28.1646i	−1.88242	+	1.18280i
$568$	−10.0888			−0.423316
$569$	5.61413	−	3.52759i	0.235357	−	0.147884i	−0.409190	−	0.912449i	$-0.634189\pi$
$569$	5.61413	−	3.52759i	0.235357	−	0.147884i	0.644547	+	0.764565i	$0.277046\pi$
$570$		0			0
$571$	−2.44233	−	10.7005i	−0.102208	−	0.447804i	−0.999973	−	0.00732878i	$-0.997667\pi$
$571$	−2.44233	−	10.7005i	−0.102208	−	0.447804i	0.897765	−	0.440475i	$-0.145190\pi$
$572$	−4.21015	+	0.960940i	−0.176035	+	0.0401789i
$573$	−40.3265	+	4.54370i	−1.68466	+	0.189816i
$574$	−3.57161	−	7.41653i	−0.149076	−	0.309560i
$575$		0			0
$576$	17.7706	+	22.2836i	0.740442	+	0.928485i
$577$	4.44160	−	5.56959i	0.184906	−	0.231865i	−0.680735	−	0.732530i	$-0.738340\pi$
$577$	4.44160	−	5.56959i	0.184906	−	0.231865i	0.865641	+	0.500664i	$0.166911\pi$
$578$	−4.38774	+	9.11123i	−0.182506	+	0.378977i
$579$	31.3929			1.30464
$580$		0			0
$581$	−21.7819			−0.903665
$582$	2.81341	−	5.84210i	0.116620	−	0.242163i
$583$	1.26628	−	1.58786i	0.0524439	−	0.0657625i
$584$	14.3424	+	17.9848i	0.593491	+	0.744214i
$585$		0			0
$586$	1.60917	+	3.34147i	0.0664740	+	0.138035i
$587$	12.9726	−	1.46166i	0.535435	−	0.0603290i	0.159893	−	0.987134i	$-0.448885\pi$
$587$	12.9726	−	1.46166i	0.535435	−	0.0603290i	0.375542	+	0.926805i	$0.377457\pi$
$588$	23.9326	−	5.46247i	0.986965	−	0.225268i
$589$	−3.33169	−	14.5971i	−0.137280	−	0.601462i
$590$		0			0
$591$	−43.1824	+	27.1333i	−1.77629	+	1.11611i
$592$	10.3457			0.425207
$593$	−0.627634	+	0.394369i	−0.0257739	+	0.0161948i	−0.544857	−	0.838529i	$-0.683416\pi$
$593$	−0.627634	+	0.394369i	−0.0257739	+	0.0161948i	0.519084	+	0.854724i	$0.326273\pi$
$594$	−1.51050	+	4.31677i	−0.0619768	+	0.177119i
$595$		0			0
$596$	−3.58812	+	15.7206i	−0.146975	+	0.643940i
$597$		−	37.2912i		−	1.52623i
$598$	1.58339	+	0.361398i	0.0647495	+	0.0147787i
$599$	5.63173	+	0.634544i	0.230106	+	0.0259267i	0.226265	−	0.974066i	$-0.427349\pi$
$599$	5.63173	+	0.634544i	0.230106	+	0.0259267i	0.00384165	+	0.999993i	$0.498777\pi$
$600$		0			0
$601$	−10.8716	+	17.3020i	−0.443462	+	0.705765i	−0.991416	−	0.130743i	$-0.958264\pi$
$601$	−10.8716	+	17.3020i	−0.443462	+	0.705765i	0.547955	+	0.836508i	$0.315407\pi$
$602$	1.06434	+	9.44631i	0.0433794	+	0.385003i
$603$	−4.53894	+	12.9716i	−0.184840	+	0.528242i
$604$	−1.56000	+	3.23937i	−0.0634755	+	0.131808i
$605$		0			0
$606$	−2.66753	−	23.6750i	−0.108361	−	0.961732i
$607$	−9.19377	−	4.42748i	−0.373163	−	0.179706i	0.237896	−	0.971291i	$-0.423542\pi$
$607$	−9.19377	−	4.42748i	−0.373163	−	0.179706i	−0.611060	+	0.791585i	$0.709256\pi$
$608$	−20.5496	−	20.5496i	−0.833395	−	0.833395i
$609$	13.3420	+	54.7712i	0.540647	+	2.21944i
$610$		0			0
$611$	6.44347	+	18.4144i	0.260675	+	0.744966i
$612$	61.9586	+	49.4103i	2.50453	+	1.99729i
$613$	1.41538	−	12.5618i	0.0571667	−	0.507368i	−0.932202	−	0.361939i	$-0.882115\pi$
$613$	1.41538	−	12.5618i	0.0571667	−	0.507368i	0.989369	−	0.145430i	$-0.0464564\pi$
$614$	3.55303	+	1.71105i	0.143388	+	0.0690522i
$615$		0			0
$616$	3.19250	−	4.00327i	0.128630	−	0.161296i
$617$	−5.57635	−	24.4316i	−0.224495	−	0.983579i	−0.954048	−	0.299654i	$-0.903129\pi$
$617$	−5.57635	−	24.4316i	−0.224495	−	0.983579i	0.729553	−	0.683925i	$-0.239728\pi$
$618$	−3.19061	+	5.07783i	−0.128345	+	0.204260i
$619$	−2.36418	+	20.9827i	−0.0950245	+	0.843366i	0.852292	+	0.523066i	$0.175212\pi$
$619$	−2.36418	+	20.9827i	−0.0950245	+	0.843366i	−0.947316	+	0.320299i	$0.896217\pi$
$620$		0			0
$621$	−13.3092	+	13.3092i	−0.534081	+	0.534081i
$622$	4.84415	+	7.70941i	0.194233	+	0.309119i
$623$	34.5813	−	16.6535i	1.38547	−	0.667207i
$624$	−21.5616	−	7.54473i	−0.863155	−	0.302031i
$625$		0			0
$626$	−8.76481	−	8.76481i	−0.350312	−	0.350312i
$627$	−4.47087	+	19.5882i	−0.178549	+	0.782276i
$628$	10.9359	+	13.7131i	0.436388	+	0.547214i
$629$	21.5470	−	4.91797i	0.859136	−	0.196092i
$630$		0			0
$631$	−14.8022	−	11.8044i	−0.589268	−	0.469926i	0.282888	−	0.959153i	$-0.408707\pi$
$631$	−14.8022	−	11.8044i	−0.589268	−	0.469926i	−0.872156	+	0.489227i	$0.837279\pi$
$632$	−21.3004	−	7.45334i	−0.847285	−	0.296478i
$633$	21.7069	−	7.59558i	0.862772	−	0.301897i
$634$	7.05438	−	5.62568i	0.280165	−	0.223424i
$635$		0			0
$636$	11.2638	−	3.94137i	0.446638	−	0.156285i
$637$	−7.38160	+	7.38160i	−0.292470	+	0.292470i
$638$	1.69243	+	1.30986i	0.0670041	+	0.0518580i
$639$			43.0724i			1.70392i
$640$		0			0
$641$	34.3580	−	3.87121i	1.35706	−	0.152904i	0.596729	−	0.802443i	$-0.296467\pi$
$641$	34.3580	−	3.87121i	1.35706	−	0.152904i	0.760328	+	0.649539i	$0.225038\pi$
$642$	−15.6958	−	1.76849i	−0.619462	−	0.0697966i
$643$	−8.58638	−	24.5385i	−0.338614	−	0.967703i	−0.979741	−	0.200268i	$-0.935819\pi$
$643$	−8.58638	−	24.5385i	−0.338614	−	0.967703i	0.641127	−	0.767434i	$-0.278467\pi$
$644$	9.07831	−	4.37188i	0.357736	−	0.172276i
$645$		0			0
$646$	−14.8689	−	9.34278i	−0.585011	−	0.367587i
$647$	−22.3019	−	14.0132i	−0.876778	−	0.550916i	0.0167822	−	0.999859i	$-0.494658\pi$
$647$	−22.3019	−	14.0132i	−0.876778	−	0.550916i	−0.893560	+	0.448943i	$0.851801\pi$
$648$	−19.3083	+	15.3979i	−0.758502	+	0.604885i
$649$	−5.07189	−	8.07187i	−0.199089	−	0.316849i
$650$		0			0
$651$	22.9978	+	5.24911i	0.901356	+	0.205729i
$652$	16.7510	+	34.7838i	0.656020	+	1.36224i
$653$	−10.1819	−	21.1430i	−0.398449	−	0.827389i	−0.999601	−	0.0282535i	$-0.991005\pi$
$653$	−10.1819	−	21.1430i	−0.398449	−	0.827389i	0.601151	−	0.799135i	$-0.294709\pi$
$654$	−2.60985	−	0.595682i	−0.102053	−	0.0232930i
$655$		0			0
$656$	9.62433	+	15.3170i	0.375767	+	0.598029i
$657$	76.7829	−	61.2323i	2.99559	−	2.38890i
$658$	−9.36534	−	5.88464i	−0.365099	−	0.229407i
$659$	−4.29921	−	2.70137i	−0.167473	−	0.105230i	0.445687	−	0.895189i	$-0.352959\pi$
$659$	−4.29921	−	2.70137i	−0.167473	−	0.105230i	−0.613161	+	0.789958i	$0.710102\pi$
$660$		0			0
$661$	−8.41615	+	4.05301i	−0.327350	+	0.157644i	−0.590339	−	0.807155i	$-0.701006\pi$
$661$	−8.41615	+	4.05301i	−0.327350	+	0.157644i	0.262989	+	0.964799i	$0.415292\pi$
$662$	1.51374	+	4.32602i	0.0588331	+	0.168135i
$663$	−48.4928	−	5.46382i	−1.88330	−	0.212197i
$664$	−10.0977	+	1.13774i	−0.391866	+	0.0441527i
$665$		0			0
$666$			9.37660i			0.363336i
$667$	3.93652	+	7.87906i	0.152423	+	0.305078i
$668$	15.3271	−	15.3271i	0.593022	−	0.593022i
$669$	32.4052	−	11.3391i	1.25286	−	0.438394i
$670$		0			0
$671$	−11.1095	+	8.85952i	−0.428877	+	0.342018i
$672$	43.2172	−	15.1224i	1.66714	−	0.583358i
$673$	47.8420	+	16.7407i	1.84417	+	0.645305i	0.992655	+	0.120983i	$0.0386046\pi$
$673$	47.8420	+	16.7407i	1.84417	+	0.645305i	0.851520	+	0.524322i	$0.175681\pi$
$674$	−6.89379	−	5.49761i	−0.265539	−	0.211760i
$675$		0			0
$676$	−12.7058	+	2.90002i	−0.488685	+	0.111539i
$677$	20.2159	+	25.3499i	0.776960	+	0.974277i	1.00000		0.000532135i	$-0.000169384\pi$
$677$	20.2159	+	25.3499i	0.776960	+	0.974277i	−0.223040	+	0.974809i	$0.571598\pi$
$678$	3.98188	−	17.4458i	0.152923	−	0.670001i
$679$	12.0969	+	12.0969i	0.464235	+	0.464235i
$680$		0			0
$681$	−11.0877	−	3.87977i	−0.424883	−	0.148673i
$682$	0.806846	−	0.388557i	0.0308957	−	0.0148786i
$683$	22.5210	+	35.8420i	0.861743	+	1.37146i	0.927580	+	0.373625i	$0.121885\pi$
$683$	22.5210	+	35.8420i	0.861743	+	1.37146i	−0.0658371	+	0.997830i	$0.520972\pi$
$684$	−57.6490	+	57.6490i	−2.20426	+	2.20426i
$685$		0			0
$686$	−0.415580	+	3.68837i	−0.0158669	+	0.140823i
$687$	−14.2613	+	22.6968i	−0.544104	+	0.865937i
$688$	−4.64852	−	20.3665i	−0.177223	−	0.776465i
$689$	−3.16404	+	3.96759i	−0.120540	+	0.151153i
$690$		0			0
$691$	−39.8969	−	19.2134i	−1.51775	−	0.730910i	−0.525000	−	0.851102i	$-0.675935\pi$
$691$	−39.8969	−	19.2134i	−1.51775	−	0.730910i	−0.992751	+	0.120192i	$0.961649\pi$
$692$	1.04999	−	9.31892i	0.0399146	−	0.354252i
$693$	−17.0913	−	13.6298i	−0.649244	−	0.517755i
$694$	0.103947	+	0.297063i	0.00394576	+	0.0112763i
$695$		0			0
$696$	9.04600	+	24.6940i	0.342888	+	0.936025i
$697$	27.3257	+	27.3257i	1.03503	+	1.03503i
$698$	−1.61725	−	0.778828i	−0.0612139	−	0.0294791i
$699$	−0.775692	−	6.88445i	−0.0293393	−	0.260394i
$700$		0			0
$701$	−11.2723	+	23.4071i	−0.425747	+	0.884074i	0.572205	+	0.820111i	$0.306088\pi$
$701$	−11.2723	+	23.4071i	−0.425747	+	0.884074i	−0.997952	+	0.0639630i	$0.979626\pi$
$702$	3.77429	−	10.7863i	0.142451	−	0.407103i
$703$	2.54574	+	22.5940i	0.0960142	+	0.852150i
$704$	−2.19931	+	3.50018i	−0.0828895	+	0.131918i
$705$		0			0
$706$	−10.7509	−	1.21134i	−0.404616	−	0.0455892i
$707$	61.2816	+	13.9871i	2.30473	+	0.526040i
$708$		−	56.0142i		−	2.10514i
$709$	−1.44196	+	6.31766i	−0.0541541	+	0.237265i	−0.994760	−	0.102235i	$-0.967401\pi$
$709$	−1.44196	+	6.31766i	−0.0541541	+	0.237265i	0.940606	+	0.339500i	$0.110258\pi$
$710$		0			0
$711$	−31.8208	+	90.9386i	−1.19337	+	3.41046i
$712$	15.1614	−	9.52654i	0.568198	−	0.357022i
$713$	3.68560			0.138027
$714$	23.4262	−	14.7196i	0.876702	−	0.550868i
$715$		0			0
$716$	−4.13253	−	18.1058i	−0.154440	−	0.676645i
$717$	20.7351	−	4.73266i	0.774368	−	0.176744i
$718$	9.22563	−	1.03948i	0.344297	−	0.0387930i
$719$	−4.39780	−	9.13213i	−0.164010	−	0.340571i	0.802725	−	0.596349i	$-0.203383\pi$
$719$	−4.39780	−	9.13213i	−0.164010	−	0.340571i	−0.966735	+	0.255778i	$0.917668\pi$
$720$		0			0
$721$	−9.86491	−	12.3702i	−0.367388	−	0.460691i
$722$	6.41607	−	8.04549i	0.238781	−	0.299422i
$723$	9.06809	−	18.8301i	0.337246	−	0.700298i
$724$	−16.6877			−0.620194
$725$		0			0
$726$	12.8149			0.475604
$727$	−3.91438	+	8.12829i	−0.145176	+	0.301461i	−0.960859	−	0.277038i	$-0.910647\pi$
$727$	−3.91438	+	8.12829i	−0.145176	+	0.301461i	0.815683	+	0.578499i	$0.196362\pi$
$728$	−7.97709	+	10.0030i	−0.295651	+	0.370734i
$729$	−1.28795	−	1.61504i	−0.0477020	−	0.0598164i
$730$		0			0
$731$	−19.3629	−	40.2075i	−0.716163	−	1.48713i
$732$	−82.9674	+	9.34818i	−3.06656	+	0.345519i
$733$	−47.5277	+	10.8479i	−1.75548	+	0.400676i	−0.974590	−	0.223998i	$-0.928089\pi$
$733$	−47.5277	+	10.8479i	−1.75548	+	0.400676i	−0.780886	+	0.624674i	$0.785232\pi$
$734$	−0.238973	−	1.04701i	−0.00882065	−	0.0386458i
$735$		0			0
$736$	6.05723	−	3.80601i	0.223273	−	0.140291i
$737$	−1.99319			−0.0734201
$738$	−13.8822	+	8.72277i	−0.511011	+	0.321090i
$739$	−7.43283	+	21.2418i	−0.273421	+	0.781392i	0.722517	+	0.691353i	$0.242985\pi$
$739$	−7.43283	+	21.2418i	−0.273421	+	0.781392i	−0.995938	+	0.0900393i	$0.971301\pi$
$740$		0			0
$741$	11.1713	−	48.9449i	0.410390	−	1.79803i
$742$		−	2.87711i		−	0.105622i
$743$	15.9607	+	3.64293i	0.585542	+	0.133646i	0.505021	−	0.863107i	$-0.331485\pi$
$743$	15.9607	+	3.64293i	0.585542	+	0.133646i	0.0805206	+	0.996753i	$0.474342\pi$
$744$	10.9356	+	1.23214i	0.400917	+	0.0451725i
$745$		0			0
$746$	−0.766843	+	1.22042i	−0.0280761	+	0.0446829i
$747$	4.85738	+	43.1104i	0.177722	+	1.57733i
$748$	−3.79616	+	10.8488i	−0.138801	+	0.396672i
$749$	18.0810	−	37.5456i	0.660666	−	1.37189i
$750$		0			0
$751$	3.39925	+	30.1691i	0.124040	+	1.10089i	0.889351	+	0.457226i	$0.151157\pi$
$751$	3.39925	+	30.1691i	0.124040	+	1.10089i	−0.765310	+	0.643661i	$0.777414\pi$
$752$	21.8995	+	10.5462i	0.798591	+	0.384581i
$753$	−5.65740	−	5.65740i	−0.206167	−	0.206167i
$754$	−4.22888	−	3.27295i	−0.154007	−	0.119194i
$755$		0			0
$756$	−23.4162	−	66.9196i	−0.851638	−	2.43384i
$757$	6.15003	+	4.90448i	0.223527	+	0.178256i	0.728850	−	0.684674i	$-0.240055\pi$
$757$	6.15003	+	4.90448i	0.223527	+	0.178256i	−0.505323	+	0.862930i	$0.668627\pi$
$758$	1.11749	−	9.91803i	0.0405892	−	0.360239i
$759$	−4.45601	−	2.14590i	−0.161743	−	0.0778912i
$760$		0			0
$761$	−13.9346	+	17.4735i	−0.505130	+	0.633412i	−0.967378	−	0.253338i	$-0.918471\pi$
$761$	−13.9346	+	17.4735i	−0.505130	+	0.633412i	0.462248	+	0.886751i	$0.347043\pi$
$762$	−3.64312	−	15.9616i	−0.131976	−	0.578227i
$763$	3.75759	−	5.98017i	0.136034	−	0.216497i
$764$	2.67406	−	23.7329i	0.0967439	−	0.858626i
$765$		0			0
$766$	−5.12963	+	5.12963i	−0.185341	+	0.185341i
$767$	12.6731	+	20.1692i	0.457600	+	0.728266i
$768$	−11.8410	+	5.70232i	−0.427275	+	0.205765i
$769$	22.2341	+	7.78004i	0.801782	+	0.280556i	0.699900	−	0.714241i	$-0.253228\pi$
$769$	22.2341	+	7.78004i	0.801782	+	0.280556i	0.101882	+	0.994797i	$0.467514\pi$
$770$		0			0
$771$	58.9515	+	58.9515i	2.12308	+	2.12308i
$772$	−4.11115	+	18.0121i	−0.147963	+	0.648270i
$773$	−21.4144	−	26.8528i	−0.770223	−	0.965829i	0.229750	−	0.973250i	$-0.426209\pi$
$773$	−21.4144	−	26.8528i	−0.770223	−	0.965829i	−0.999972	+	0.00742075i	$0.997638\pi$
$774$	18.4587	−	4.21307i	0.663483	−	0.151436i
$775$		0			0
$776$	6.23974	+	4.97603i	0.223994	+	0.178629i
$777$	−33.8121	−	11.8314i	−1.21300	−	0.424448i
$778$	11.4207	−	3.99627i	0.409451	−	0.143273i
$779$	−31.0826	+	24.7876i	−1.11365	+	0.888107i
$780$		0			0
$781$	−5.89647	+	2.06326i	−0.210992	+	0.0738294i
$782$	3.05659	−	3.05659i	0.109304	−	0.109304i
$783$	58.1915	−	21.3169i	2.07959	−	0.761804i
$784$			13.0062i			0.464507i
$785$		0			0
$786$	2.45781	−	0.276929i	0.0876673	−	0.00987774i
$787$	−6.72156	−	0.757338i	−0.239598	−	0.0269962i	−0.00865096	−	0.999963i	$-0.502754\pi$
$787$	−6.72156	−	0.757338i	−0.239598	−	0.0269962i	−0.230947	+	0.972966i	$0.574182\pi$
$788$	−9.91303	−	28.3298i	−0.353137	−	1.00921i
$789$	4.51618	−	2.17488i	0.160780	−	0.0774276i
$790$		0			0
$791$	39.9749	+	25.1179i	1.42134	+	0.893090i
$792$	−8.63515	−	5.42582i	−0.306837	−	0.192798i
$793$	27.7592	−	22.1373i	0.985759	−	0.786117i
$794$	1.95566	+	3.11242i	0.0694039	+	0.110456i
$795$		0			0
$796$	21.3963	+	4.88357i	0.758373	+	0.173094i
$797$	−18.9538	−	39.3580i	−0.671379	−	1.39413i	−0.906516	−	0.422171i	$-0.861268\pi$
$797$	−18.9538	−	39.3580i	−0.671379	−	1.39413i	0.235137	−	0.971962i	$-0.424446\pi$
$798$	12.3495	+	25.6441i	0.437169	+	0.907791i
$799$	50.6232	+	11.5544i	1.79092	+	0.408766i
$800$		0			0
$801$	−40.6720	−	64.7291i	−1.43707	−	2.28709i
$802$	−5.72178	+	4.56297i	−0.202043	+	0.161124i
$803$	12.0606	+	7.57817i	0.425609	+	0.267428i
$804$	−9.91646	−	6.23093i	−0.349727	−	0.219748i
$805$		0			0
$806$	−2.01606	+	0.970885i	−0.0710128	+	0.0341980i
$807$	−4.86527	−	13.9041i	−0.171266	−	0.489449i
$808$	29.1397	+	3.28325i	1.02513	+	0.115504i
$809$	−25.1469	+	2.83338i	−0.884120	+	0.0996164i	−0.542335	−	0.840162i	$-0.682460\pi$
$809$	−25.1469	+	2.83338i	−0.884120	+	0.0996164i	−0.341784	+	0.939778i	$0.611031\pi$
$810$		0			0
$811$			16.4826i			0.578783i	0.957211	+	0.289392i	$0.0934530\pi$
$811$			16.4826i			0.578783i	−0.957211	+	0.289392i	$0.906547\pi$
$812$	−33.1730	+	0.482463i	−1.16414	+	0.0169311i
$813$	−20.5018	+	20.5018i	−0.719028	+	0.719028i
$814$	−1.28363	+	0.449161i	−0.0449911	+	0.0157431i
$815$		0			0
$816$	−47.5351	+	37.9079i	−1.66406	+	1.32704i
$817$	43.3345	−	15.1634i	1.51608	−	0.530500i
$818$	−6.50598	−	2.27654i	−0.227476	−	0.0795973i
$819$	42.7059	+	34.0569i	1.49227	+	1.19004i
$820$		0			0
$821$	25.1655	−	5.74385i	0.878281	−	0.200462i	0.240471	−	0.970656i	$-0.422698\pi$
$821$	25.1655	−	5.74385i	0.878281	−	0.200462i	0.637809	+	0.770194i	$0.279841\pi$
$822$	−10.3077	−	12.9254i	−0.359521	−	0.450825i
$823$	7.33020	−	32.1157i	0.255515	−	1.11948i	−0.670475	−	0.741933i	$-0.733909\pi$
$823$	7.33020	−	32.1157i	0.255515	−	1.11948i	0.925989	−	0.377550i	$-0.123233\pi$
$824$	−5.21933	−	5.21933i	−0.181824	−	0.181824i
$825$		0			0
$826$	−12.7470	−	4.46036i	−0.443524	−	0.155196i
$827$	8.27938	−	3.98714i	0.287902	−	0.138646i	−0.284359	−	0.958718i	$-0.591781\pi$
$827$	8.27938	−	3.98714i	0.287902	−	0.138646i	0.572261	+	0.820071i	$0.306066\pi$
$828$	−10.6772	−	16.9927i	−0.371060	−	0.590538i
$829$	−21.1823	+	21.1823i	−0.735693	+	0.735693i	−0.971741	−	0.236048i	$-0.924148\pi$
$829$	−21.1823	+	21.1823i	−0.735693	+	0.735693i	0.236048	+	0.971741i	$0.424148\pi$
$830$		0			0
$831$	1.22555	−	10.8771i	0.0425140	−	0.377322i
$832$	5.49540	−	8.74588i	0.190519	−	0.303209i
$833$	6.18265	+	27.0879i	0.214216	+	0.938542i
$834$	−7.27697	+	9.12504i	−0.251981	+	0.315974i
$835$		0			0
$836$	−10.6535	−	5.13045i	−0.368458	−	0.177440i
$837$	2.90354	−	25.7696i	0.100361	−	0.890729i
$838$	−1.04509	−	0.833428i	−0.0361019	−	0.0287903i
$839$	−4.98865	−	14.2567i	−0.172227	−	0.492197i	0.825123	−	0.564954i	$-0.191106\pi$
$839$	−4.98865	−	14.2567i	−0.172227	−	0.492197i	−0.997350	+	0.0727568i	$0.976820\pi$
$840$		0			0
$841$	−0.843366	−	28.9877i	−0.0290816	−	0.999577i
$842$	1.84067	+	1.84067i	0.0634338	+	0.0634338i
$843$	−12.5412	−	6.03950i	−0.431940	−	0.208011i
$844$	1.51538	+	13.4493i	0.0521614	+	0.462945i
$845$		0			0
$846$	−9.55831	+	19.8480i	−0.328622	+	0.682390i
$847$	−11.1667	+	31.9125i	−0.383691	+	1.09653i
$848$	0.707910	+	6.28287i	0.0243097	+	0.215755i
$849$	−29.1907	+	46.4568i	−1.00182	+	1.59439i
$850$		0			0
$851$	−5.56171	−	0.626654i	−0.190653	−	0.0214814i
$852$	−35.7859	−	8.16791i	−1.22601	−	0.279828i
$853$			41.9677i			1.43695i	0.695554	+	0.718474i	$0.255159\pi$
$853$			41.9677i			1.43695i	−0.695554	+	0.718474i	$0.744841\pi$
$854$	−4.47928	+	19.6250i	−0.153278	+	0.671554i
$855$		0			0
$856$	6.42091	−	18.3499i	0.219462	−	0.627187i
$857$	24.1425	−	15.1697i	0.824692	−	0.518189i	−0.0523346	−	0.998630i	$-0.516666\pi$
$857$	24.1425	−	15.1697i	0.824692	−	0.518189i	0.877027	+	0.480441i	$0.159523\pi$
$858$	3.00277			0.102513
$859$	13.3099	−	8.36320i	0.454130	−	0.285349i	−0.285480	−	0.958385i	$-0.592153\pi$
$859$	13.3099	−	8.36320i	0.454130	−	0.285349i	0.739610	+	0.673036i	$0.235010\pi$
$860$		0			0
$861$	−13.9379	−	61.0658i	−0.475001	−	2.08112i
$862$	14.5392	−	3.31849i	0.495208	−	0.113028i
$863$	−20.0904	+	2.26364i	−0.683884	+	0.0770552i	−0.447069	−	0.894500i	$-0.647532\pi$
$863$	−20.0904	+	2.26364i	−0.683884	+	0.0770552i	−0.236815	+	0.971555i	$0.576104\pi$
$864$	−21.8396	−	45.3505i	−0.743000	−	1.54286i
$865$		0			0
$866$	−7.19161	−	9.01800i	−0.244381	−	0.306444i
$867$	−47.9768	+	60.1610i	−1.62938	+	2.04318i
$868$	−6.02349	+	12.5079i	−0.204451	+	0.424546i
$869$	−13.9735			−0.474018
$870$		0			0
$871$	4.98038			0.168754
$872$	1.42959	−	2.96857i	0.0484119	−	0.100528i
$873$	21.2443	−	26.6395i	0.719011	−	0.901612i
$874$	2.77268	+	3.47684i	0.0937875	+	0.117606i
$875$		0			0
$876$	36.3133	+	75.4054i	1.22691	+	2.54771i
$877$	24.1689	−	2.72318i	0.816126	−	0.0919553i	0.305974	−	0.952040i	$-0.401018\pi$
$877$	24.1689	−	2.72318i	0.816126	−	0.0919553i	0.510152	+	0.860084i	$0.329589\pi$
$878$	−13.8068	+	3.15132i	−0.465958	+	0.106352i
$879$	6.27962	+	27.5128i	0.211806	+	0.927983i
$880$		0			0
$881$	19.1587	−	12.0382i	0.645472	−	0.405577i	−0.169133	−	0.985593i	$-0.554097\pi$
$881$	19.1587	−	12.0382i	0.645472	−	0.405577i	0.814605	+	0.580016i	$0.196954\pi$
$882$	−11.7878			−0.396917
$883$	−7.66575	+	4.81671i	−0.257973	+	0.162095i	−0.654809	−	0.755794i	$-0.727251\pi$
$883$	−7.66575	+	4.81671i	−0.257973	+	0.162095i	0.396836	+	0.917889i	$0.370108\pi$
$884$	9.48545	−	27.1079i	0.319030	−	0.911736i
$885$		0			0
$886$	1.41070	−	6.18068i	0.0473934	−	0.207644i
$887$		−	1.17437i		−	0.0394316i	−0.999806	−	0.0197158i	$-0.993724\pi$
$887$		−	1.17437i		−	0.0394316i	0.999806	−	0.0197158i	$-0.00627614\pi$
$888$	−16.2927	−	3.71870i	−0.546747	−	0.124791i
$889$	42.9232	+	4.83628i	1.43960	+	0.162204i
$890$		0			0
$891$	−8.13587	+	12.9482i	−0.272562	+	0.433780i
$892$	2.26223	+	20.0779i	0.0757452	+	0.672257i
$893$	−17.6432	+	50.4213i	−0.590406	+	1.68728i
$894$	4.86481	−	10.1019i	0.162704	−	0.337858i
$895$		0			0
$896$	3.94840	+	35.0430i	0.131907	+	1.17071i
$897$	11.1342	+	5.36195i	0.371760	+	0.179030i
$898$	9.26409	+	9.26409i	0.309147	+	0.309147i
$899$	−11.0087	−	5.10566i	−0.367162	−	0.170283i
$900$		0			0
$901$	4.46100	+	12.7488i	0.148617	+	0.424724i
$902$	−1.85911	−	1.48259i	−0.0619016	−	0.0493649i
$903$	−8.09873	+	71.8782i	−0.269509	+	2.39196i
$904$	19.8437	+	9.55620i	0.659990	+	0.317834i
$905$		0			0
$906$	1.55875	−	1.95461i	0.0517861	−	0.0649377i
$907$	−2.31122	−	10.1261i	−0.0767427	−	0.336232i	0.921952	−	0.387304i	$-0.126593\pi$
$907$	−2.31122	−	10.1261i	−0.0767427	−	0.336232i	−0.998695	+	0.0510717i	$0.983736\pi$
$908$	3.67810	−	5.85366i	0.122062	−	0.194260i
$909$	14.0173	−	124.407i	0.464924	−	4.12632i
$910$		0			0
$911$	24.7498	−	24.7498i	0.819996	−	0.819996i	−0.166111	−	0.986107i	$-0.553121\pi$
$911$	24.7498	−	24.7498i	0.819996	−	0.819996i	0.986107	+	0.166111i	$0.0531209\pi$
$912$	−33.2780	−	52.9616i	−1.10194	−	1.75373i
$913$	−5.66900	+	2.73005i	−0.187617	+	0.0903514i
$914$	−10.3446	−	3.61975i	−0.342170	−	0.119731i
$915$		0			0
$916$	−11.1550	−	11.1550i	−0.368570	−	0.368570i
$917$	−1.45207	+	6.36193i	−0.0479516	+	0.210089i
$918$	−18.9637	−	23.7797i	−0.625894	−	0.784846i
$919$	18.3243	−	4.18239i	0.604461	−	0.137964i	0.0906722	−	0.995881i	$-0.471098\pi$
$919$	18.3243	−	4.18239i	0.604461	−	0.137964i	0.513789	+	0.857916i	$0.328241\pi$
$920$		0			0
$921$	23.4605	+	18.7091i	0.773048	+	0.616486i
$922$	−15.1921	−	5.31596i	−0.500326	−	0.175072i
$923$	14.7335	−	5.15547i	0.484959	−	0.169694i
$924$	14.5652	−	11.6154i	0.479160	−	0.382117i
$925$		0			0
$926$	9.46586	−	3.31225i	0.311067	−	0.108847i
$927$	−22.2831	+	22.2831i	−0.731872	+	0.731872i
$928$	−23.3652	+	2.97733i	−0.767001	+	0.0977355i
$929$			30.7214i			1.00794i	0.863722	+	0.503968i	$0.168127\pi$
$929$			30.7214i			1.00794i	−0.863722	+	0.503968i	$0.831873\pi$
$930$		0			0
$931$	−28.4042	+	3.20038i	−0.930910	+	0.104888i
$932$	4.05163	+	0.456509i	0.132716	+	0.0149535i
$933$	22.8821	+	65.3932i	0.749125	+	2.14088i
$934$	−6.89563	+	3.32076i	−0.225632	+	0.108659i
$935$		0			0
$936$	21.5766	+	13.5575i	0.705254	+	0.443140i
$937$	−13.4568	−	8.45546i	−0.439614	−	0.276228i	0.293985	−	0.955810i	$-0.405018\pi$
$937$	−13.4568	−	8.45546i	−0.439614	−	0.276228i	−0.733599	+	0.679582i	$0.762161\pi$
$938$	−2.20759	+	1.76049i	−0.0720803	+	0.0574822i
$939$	−50.1799	−	79.8609i	−1.63756	−	2.60616i
$940$		0			0
$941$	−29.7233	−	6.78416i	−0.968953	−	0.221157i	−0.291376	−	0.956609i	$-0.594113\pi$
$941$	−29.7233	−	6.78416i	−0.968953	−	0.221157i	−0.677578	+	0.735451i	$0.736970\pi$
$942$	−5.29169	−	10.9883i	−0.172412	−	0.358018i
$943$	−4.24612	−	8.81716i	−0.138273	−	0.287126i
$944$	28.9336	+	6.60391i	0.941709	+	0.214939i
$945$		0			0
$946$	1.46097	+	2.32512i	0.0475002	+	0.0755961i
$947$	−4.29539	+	3.42546i	−0.139581	+	0.111312i	−0.690791	−	0.723054i	$-0.742738\pi$
$947$	−4.29539	+	3.42546i	−0.139581	+	0.111312i	0.551210	+	0.834367i	$0.314166\pi$
$948$	−69.5205	−	43.6826i	−2.25792	−	1.41875i
$949$	−30.1358	−	18.9355i	−0.978248	−	0.614674i
$950$		0			0
$951$	61.8572	−	29.7889i	2.00586	−	0.965970i
$952$	11.2469	+	32.1419i	0.364515	+	1.04173i
$953$	20.7685	+	2.34005i	0.672758	+	0.0758016i	0.441734	−	0.897146i	$-0.354364\pi$
$953$	20.7685	+	2.34005i	0.672758	+	0.0758016i	0.231025	+	0.972948i	$0.425792\pi$
$954$	−5.69433	+	0.641597i	−0.184361	+	0.0207725i
$955$		0			0
$956$			12.5169i			0.404824i
$957$	10.3372	+	12.5826i	0.334155	+	0.406739i
$958$	−9.22916	+	9.22916i	−0.298181	+	0.298181i
$959$	41.1697	−	14.4059i	1.32944	−	0.465190i
$960$		0			0
$961$	20.2667	−	16.1621i	0.653764	−	0.521359i
$962$	3.20740	−	1.12232i	0.103411	−	0.0361849i
$963$	−78.3419	−	27.4130i	−2.52453	−	0.883372i
$964$	9.61648	+	7.66889i	0.309726	+	0.246998i
$965$		0			0
$966$	−6.83069	+	1.55906i	−0.219774	+	0.0501620i
$967$	5.39600	+	6.76637i	0.173524	+	0.217592i	0.860987	−	0.508628i	$-0.169847\pi$
$967$	5.39600	+	6.76637i	0.173524	+	0.217592i	−0.687463	+	0.726220i	$0.741276\pi$
$968$	−3.50977	+	15.3773i	−0.112808	+	0.494246i
$969$	−94.4839	−	94.4839i	−3.03526	−	3.03526i
$970$		0			0
$971$	−26.5825	−	9.30161i	−0.853072	−	0.298503i	−0.131903	−	0.991263i	$-0.542109\pi$
$971$	−26.5825	−	9.30161i	−0.853072	−	0.298503i	−0.721168	+	0.692760i	$0.756395\pi$
$972$	−23.9530	+	11.5352i	−0.768293	+	0.369990i
$973$	−16.3828	−	26.0730i	−0.525207	−	0.835863i
$974$	−5.88173	+	5.88173i	−0.188463	+	0.188463i
$975$		0			0
$976$	4.95289	−	43.9582i	0.158538	−	1.40707i
$977$	−21.1503	+	33.6606i	−0.676659	+	1.07690i	0.315134	+	0.949047i	$0.397950\pi$
$977$	−21.1503	+	33.6606i	−0.676659	+	1.07690i	−0.991794	+	0.127850i	$0.959192\pi$
$978$	−5.97359	−	26.1720i	−0.191014	−	0.836889i
$979$	6.91293	−	8.66854i	0.220938	−	0.277048i
$980$		0			0
$981$	−12.6738	−	6.10339i	−0.404644	−	0.194866i
$982$	0.464623	−	4.12364i	0.0148267	−	0.131591i
$983$	10.6815	+	8.51823i	0.340688	+	0.271689i	0.778855	−	0.627204i	$-0.215801\pi$
$983$	10.6815	+	8.51823i	0.340688	+	0.271689i	−0.438167	+	0.898893i	$0.644372\pi$
$984$	−9.65101	−	27.5810i	−0.307663	−	0.879250i
$985$		0			0
$986$	−13.3642	+	4.89563i	−0.425604	+	0.155909i
$987$	−59.5116	−	59.5116i	−1.89427	−	1.89427i
$988$	26.6198	+	12.8194i	0.846889	+	0.407840i
$989$	1.26535	+	11.2303i	0.0402358	+	0.357102i
$990$		0			0
$991$	−13.7568	+	28.5662i	−0.436998	+	0.907435i	0.559887	+	0.828569i	$0.310844\pi$
$991$	−13.7568	+	28.5662i	−0.436998	+	0.907435i	−0.996885	+	0.0788666i	$0.974870\pi$
$992$	−3.25532	+	9.30316i	−0.103356	+	0.295376i
$993$	3.90468	+	34.6550i	0.123911	+	1.09974i
$994$	−4.70834	+	7.49328i	−0.149340	+	0.237673i
$995$		0			0
$996$	−36.7387	−	4.13945i	−1.16411	−	0.131164i
$997$	−10.1631	−	2.31966i	−0.321868	−	0.0734642i	0.0585343	−	0.998285i	$-0.481357\pi$
$997$	−10.1631	−	2.31966i	−0.321868	−	0.0734642i	−0.380402	+	0.924821i	$0.624214\pi$
$998$			0.639388i			0.0202395i
$999$	−8.76311	+	38.3937i	−0.277253	+	1.21472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.bd.a.482.7	yes	120
5.2	odd	4		725.2.y.a.18.7	yes	120
5.3	odd	4		725.2.y.a.18.4	✓	120
5.4	even	2	inner	725.2.bd.a.482.4	yes	120
29.21	odd	28		725.2.y.a.282.4	yes	120
145.79	odd	28		725.2.y.a.282.7	yes	120
145.108	even	28	inner	725.2.bd.a.543.7	yes	120
145.137	even	28	inner	725.2.bd.a.543.4	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.y.a.18.4	✓	120	5.3	odd	4
725.2.y.a.18.7	yes	120	5.2	odd	4
725.2.y.a.282.4	yes	120	29.21	odd	28
725.2.y.a.282.7	yes	120	145.79	odd	28
725.2.bd.a.482.4	yes	120	5.4	even	2	inner
725.2.bd.a.482.7	yes	120	1.1	even	1	trivial
725.2.bd.a.543.4	yes	120	145.137	even	28	inner
725.2.bd.a.543.7	yes	120	145.108	even	28	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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.bd (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.177554 - 0.368695i) q^{2} +(1.94143 - 2.43448i) q^{3} +(1.14257 + 1.43274i) q^{4} +(-0.552871 - 1.14805i) q^{6} +(3.34071 - 0.376408i) q^{7} +(1.52903 - 0.348992i) q^{8} +(-1.48996 - 6.52795i) q^{9} +(0.822283 - 0.516675i) q^{11} +5.70618 q^{12} +(-2.05464 + 1.29101i) q^{13} +(0.454377 - 1.29854i) q^{14} +(-0.672742 + 2.94747i) q^{16} +6.45849i q^{17} +(-2.67137 - 0.609723i) q^{18} +(-6.60252 - 0.743926i) q^{19} +(5.56940 - 8.86365i) q^{21} +(-0.0444956 - 0.394910i) q^{22} +(0.540188 - 1.54377i) q^{23} +(2.11890 - 4.39994i) q^{24} +(0.111181 + 0.986759i) q^{26} +(-10.3684 - 4.99318i) q^{27} +(4.35628 + 4.35628i) q^{28} +(-3.75211 + 3.86286i) q^{29} +(0.744261 + 2.12697i) q^{31} +(3.41965 + 2.72708i) q^{32} +(0.338573 - 3.00492i) q^{33} +(2.38121 + 1.14673i) q^{34} +(7.65044 - 9.59335i) q^{36} +(-0.761473 - 3.33623i) q^{37} +(-1.44659 + 2.30223i) q^{38} +(-0.845991 + 7.50838i) q^{39} +(4.23097 - 4.23097i) q^{41} +(-2.27911 - 3.62719i) q^{42} +(-6.22552 + 2.99805i) q^{43} +(1.67977 + 0.587778i) q^{44} +(-0.473268 - 0.473268i) q^{46} +(1.78903 - 7.83824i) q^{47} +(5.86947 + 7.36009i) q^{48} +(4.19416 - 0.957290i) q^{49} +(15.7230 + 12.5387i) q^{51} +(-4.19725 - 1.46868i) q^{52} +(1.97396 - 0.690719i) q^{53} +(-3.68192 + 2.93624i) q^{54} +(4.97669 - 1.74142i) q^{56} +(-14.6294 + 14.6294i) q^{57} +(0.758015 + 2.06925i) q^{58} -9.81641i q^{59} +(-14.5399 + 1.63826i) q^{61} +(0.916352 + 0.103248i) q^{62} +(-7.43470 - 21.2471i) q^{63} +(-3.83512 + 1.84690i) q^{64} +(-1.04778 - 0.658366i) q^{66} +(-1.73785 - 1.09196i) q^{67} +(-9.25331 + 7.37927i) q^{68} +(-2.70953 - 4.31220i) q^{69} +(-6.27144 - 1.43141i) q^{71} +(-4.55640 - 9.46146i) q^{72} +(6.36386 + 13.2147i) q^{73} +(-1.36525 - 0.311611i) q^{74} +(-6.47799 - 10.3097i) q^{76} +(2.55253 - 2.03557i) q^{77} +(2.61809 + 1.64506i) q^{78} +(-12.1834 - 7.65532i) q^{79} +(-14.1872 + 6.83220i) q^{81} +(-0.808712 - 2.31117i) q^{82} +(-6.43840 - 0.725433i) q^{83} +(19.0627 - 2.14785i) q^{84} +2.82764i q^{86} +(2.11958 + 16.6339i) q^{87} +(1.07698 - 1.07698i) q^{88} +(10.7763 - 3.77081i) q^{89} +(-6.37799 + 5.08628i) q^{91} +(2.82902 - 0.989916i) q^{92} +(6.62300 + 2.31749i) q^{93} +(-2.57227 - 2.05132i) q^{94} +(13.2780 - 3.03062i) q^{96} +(3.17277 + 3.97853i) q^{97} +(0.391743 - 1.71634i) q^{98} +(-4.59800 - 4.59800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 28 q^{9} - 12 q^{11} + 20 q^{16} - 4 q^{19} + 4 q^{21} - 12 q^{29} - 32 q^{31} + 40 q^{34} - 16 q^{36} + 184 q^{39} - 4 q^{41} - 36 q^{44} + 76 q^{46} + 84 q^{49} + 112 q^{51} - 168 q^{54}+ \cdots + 208 q^{99}+O(q^{100}) \) 120 * q + 20 * q^4 - 28 * q^9 - 12 * q^11 + 20 * q^16 - 4 * q^19 + 4 * q^21 - 12 * q^29 - 32 * q^31 + 40 * q^34 - 16 * q^36 + 184 * q^39 - 4 * q^41 - 36 * q^44 + 76 * q^46 + 84 * q^49 + 112 * q^51 - 168 * q^54 + 180 * q^56 + 124 * q^61 + 196 * q^64 + 144 * q^66 - 152 * q^69 + 56 * q^71 + 112 * q^74 + 12 * q^76 - 220 * q^79 - 76 * q^81 - 136 * q^84 + 208 * q^89 - 84 * q^94 - 84 * q^96 + 208 * q^99

Introduction

L-functions

Modular forms

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Groups

Database

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