LMFDB - Embedded newform 725.2.y.a.18.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(18,725)]

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, 11]))

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

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

chi := DirichletCharacter("725.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.y (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			18.7
Character	$\chi$	$=$	725.18
Dual form			725.2.y.a.282.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.368695 + 0.177554i) q^{2} +(-2.43448 - 1.94143i) q^{3} +(-1.14257 - 1.43274i) q^{4} +(-0.552871 - 1.14805i) q^{6} +(0.376408 + 3.34071i) q^{7} +(-0.348992 - 1.52903i) q^{8} +(1.48996 + 6.52795i) q^{9} +(0.822283 - 0.516675i) q^{11} +5.70618i q^{12} +(1.29101 + 2.05464i) q^{13} +(-0.454377 + 1.29854i) q^{14} +(-0.672742 + 2.94747i) q^{16} -6.45849 q^{17} +(-0.609723 + 2.67137i) q^{18} +(6.60252 + 0.743926i) q^{19} +(5.56940 - 8.86365i) q^{21} +(0.394910 - 0.0444956i) q^{22} +(-1.54377 - 0.540188i) q^{23} +(-2.11890 + 4.39994i) q^{24} +(0.111181 + 0.986759i) q^{26} +(4.99318 - 10.3684i) q^{27} +(4.35628 - 4.35628i) q^{28} +(3.75211 - 3.86286i) q^{29} +(0.744261 + 2.12697i) q^{31} +(-2.72708 + 3.41965i) q^{32} +(-3.00492 - 0.338573i) q^{33} +(-2.38121 - 1.14673i) q^{34} +(7.65044 - 9.59335i) q^{36} +(3.33623 - 0.761473i) q^{37} +(2.30223 + 1.44659i) q^{38} +(0.845991 - 7.50838i) q^{39} +(4.23097 - 4.23097i) q^{41} +(3.62719 - 2.27911i) q^{42} +(2.99805 + 6.22552i) q^{43} +(-1.67977 - 0.587778i) q^{44} +(-0.473268 - 0.473268i) q^{46} +(7.83824 + 1.78903i) q^{47} +(7.36009 - 5.86947i) q^{48} +(-4.19416 + 0.957290i) q^{49} +(15.7230 + 12.5387i) q^{51} +(1.46868 - 4.19725i) q^{52} +(-0.690719 - 1.97396i) q^{53} +(3.68192 - 2.93624i) q^{54} +(4.97669 - 1.74142i) q^{56} +(-14.6294 - 14.6294i) q^{57} +(2.06925 - 0.758015i) q^{58} +9.81641i q^{59} +(-14.5399 + 1.63826i) q^{61} +(-0.103248 + 0.916352i) q^{62} +(-21.2471 + 7.43470i) q^{63} +(3.83512 - 1.84690i) q^{64} +(-1.04778 - 0.658366i) q^{66} +(1.09196 - 1.73785i) q^{67} +(7.37927 + 9.25331i) q^{68} +(2.70953 + 4.31220i) q^{69} +(-6.27144 - 1.43141i) q^{71} +(9.46146 - 4.55640i) q^{72} +(13.2147 - 6.36386i) q^{73} +(1.36525 + 0.311611i) q^{74} +(-6.47799 - 10.3097i) q^{76} +(2.03557 + 2.55253i) q^{77} +(1.64506 - 2.61809i) q^{78} +(12.1834 + 7.65532i) q^{79} +(-14.1872 + 6.83220i) q^{81} +(2.31117 - 0.808712i) q^{82} +(-0.725433 + 6.43840i) q^{83} +(-19.0627 + 2.14785i) q^{84} +2.82764i q^{86} +(-16.6339 + 2.11958i) q^{87} +(-1.07698 - 1.07698i) q^{88} +(-10.7763 + 3.77081i) q^{89} +(-6.37799 + 5.08628i) q^{91} +(0.989916 + 2.82902i) q^{92} +(2.31749 - 6.62300i) q^{93} +(2.57227 + 2.05132i) q^{94} +(13.2780 - 3.03062i) q^{96} +(-3.97853 + 3.17277i) q^{97} +(-1.71634 - 0.391743i) 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 $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.368695	+	0.177554i	0.260707	+	0.125550i	0.559672	−	0.828714i	$-0.310927\pi$
$2$	0.368695	+	0.177554i	0.260707	+	0.125550i	−0.298965	+	0.954264i	$0.596641\pi$
$3$	−2.43448	−	1.94143i	−1.40555	−	1.12089i	−0.975983	−	0.217848i	$-0.930096\pi$
$3$	−2.43448	−	1.94143i	−1.40555	−	1.12089i	−0.429563	−	0.903037i	$-0.641332\pi$
$4$	−1.14257	−	1.43274i	−0.571284	−	0.716368i
$5$		0			0
$5$		0			0
$6$	−0.552871	−	1.14805i	−0.225708	−	0.468688i
$7$	0.376408	+	3.34071i	0.142269	+	1.26267i	0.838520	+	0.544871i	$0.183421\pi$
$7$	0.376408	+	3.34071i	0.142269	+	1.26267i	−0.696251	+	0.717798i	$0.745150\pi$
$8$	−0.348992	−	1.52903i	−0.123387	−	0.540595i
$9$	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	$0.274659\pi$
$12$			5.70618i			1.64723i
$13$	1.29101	+	2.05464i	0.358063	+	0.569854i	0.976376	−	0.216078i	$-0.0693266\pi$
$13$	1.29101	+	2.05464i	0.358063	+	0.569854i	−0.618313	+	0.785932i	$0.712184\pi$
$14$	−0.454377	+	1.29854i	−0.121437	+	0.347048i
$15$		0			0
$16$	−0.672742	+	2.94747i	−0.168185	+	0.736868i
$17$	−6.45849			−1.56641			−0.783207	−	0.621761i	$-0.786418\pi$
$17$	−6.45849			−1.56641			−0.783207	+	0.621761i	$0.786418\pi$
$18$	−0.609723	+	2.67137i	−0.143713	+	0.629648i
$19$	6.60252	+	0.743926i	1.51472	+	0.170668i	0.829847	−	0.557991i	$-0.188428\pi$
$19$	6.60252	+	0.743926i	1.51472	+	0.170668i	0.684876	+	0.728660i	$0.259856\pi$
$20$		0			0
$21$	5.56940	−	8.86365i	1.21534	−	1.93421i
$22$	0.394910	−	0.0444956i	0.0841950	−	0.00948650i
$23$	−1.54377	−	0.540188i	−0.321898	−	0.112637i	0.164493	−	0.986378i	$-0.447401\pi$
$23$	−1.54377	−	0.540188i	−0.321898	−	0.112637i	−0.486391	+	0.873741i	$0.661687\pi$
$24$	−2.11890	+	4.39994i	−0.432518	+	0.898133i
$25$		0			0
$26$	0.111181	+	0.986759i	0.0218044	+	0.193519i
$27$	4.99318	−	10.3684i	0.960938	−	1.99541i
$28$	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	$0.827995\pi$
$32$	−2.72708	+	3.41965i	−0.482084	+	0.604514i
$33$	−3.00492	−	0.338573i	−0.523089	−	0.0589380i
$34$	−2.38121	−	1.14673i	−0.408375	−	0.196663i
$35$		0			0
$36$	7.65044	−	9.59335i	1.27507	−	1.59889i
$37$	3.33623	−	0.761473i	0.548473	−	0.125185i	0.0607003	−	0.998156i	$-0.480667\pi$
$37$	3.33623	−	0.761473i	0.548473	−	0.125185i	0.487773	+	0.872971i	$0.337809\pi$
$38$	2.30223	+	1.44659i	0.373471	+	0.234668i
$39$	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	$0.0952511\pi$
$42$	3.62719	−	2.27911i	0.559687	−	0.351675i
$43$	2.99805	+	6.22552i	0.457199	+	0.949383i	0.994375	+	0.105913i	$0.0337766\pi$
$43$	2.99805	+	6.22552i	0.457199	+	0.949383i	−0.537176	+	0.843470i	$0.680509\pi$
$44$	−1.67977	−	0.587778i	−0.253235	−	0.0886109i
$45$		0			0
$46$	−0.473268	−	0.473268i	−0.0697795	−	0.0697795i
$47$	7.83824	+	1.78903i	1.14332	+	0.260956i	0.751915	−	0.659260i	$-0.229130\pi$
$47$	7.83824	+	1.78903i	1.14332	+	0.260956i	0.391410	+	0.920216i	$0.371987\pi$
$48$	7.36009	−	5.86947i	1.06234	−	0.847186i
$49$	−4.19416	+	0.957290i	−0.599166	+	0.136756i
$50$		0			0
$51$	15.7230	+	12.5387i	2.20167	+	1.75577i
$52$	1.46868	−	4.19725i	0.203669	−	0.582053i
$53$	−0.690719	−	1.97396i	−0.0948775	−	0.271144i	0.886658	−	0.462427i	$-0.153021\pi$
$53$	−0.690719	−	1.97396i	−0.0948775	−	0.271144i	−0.981535	+	0.191282i	$0.938735\pi$
$54$	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
$58$	2.06925	−	0.758015i	0.271706	−	0.0995322i
$59$			9.81641i			1.27799i	0.769212	+	0.638994i	$0.220649\pi$
$59$			9.81641i			1.27799i	−0.769212	+	0.638994i	$0.779351\pi$
$60$		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	$0.850434\pi$
$62$	−0.103248	+	0.916352i	−0.0131125	+	0.116377i
$63$	−21.2471	+	7.43470i	−2.67689	+	0.936684i
$64$	3.83512	−	1.84690i	0.479390	−	0.230862i
$65$		0			0
$66$	−1.04778	−	0.658366i	−0.128973	−	0.0810392i
$67$	1.09196	−	1.73785i	0.133404	−	0.212312i	−0.773341	−	0.633990i	$-0.781416\pi$
$67$	1.09196	−	1.73785i	0.133404	−	0.212312i	0.906745	+	0.421678i	$0.138559\pi$
$68$	7.37927	+	9.25331i	0.894868	+	1.12213i
$69$	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	$0.696094\pi$
$72$	9.46146	−	4.55640i	1.11504	−	0.536977i
$73$	13.2147	−	6.36386i	1.54666	−	0.744833i	0.550708	−	0.834698i	$-0.314358\pi$
$73$	13.2147	−	6.36386i	1.54666	−	0.744833i	0.995954	+	0.0898647i	$0.0286435\pi$
$74$	1.36525	+	0.311611i	0.158708	+	0.0362240i
$75$		0			0
$76$	−6.47799	−	10.3097i	−0.743076	−	1.18260i
$77$	2.03557	+	2.55253i	0.231975	+	0.290888i
$78$	1.64506	−	2.61809i	0.186266	−	0.296441i
$79$	12.1834	+	7.65532i	1.37074	+	0.861291i	0.997782	−	0.0665589i	$-0.0212020\pi$
$79$	12.1834	+	7.65532i	1.37074	+	0.861291i	0.372954	+	0.927850i	$0.378345\pi$
$80$		0			0
$81$	−14.1872	+	6.83220i	−1.57636	+	0.759133i
$82$	2.31117	−	0.808712i	0.255226	−	0.0893073i
$83$	−0.725433	+	6.43840i	−0.0796267	+	0.706706i	0.888952	+	0.458000i	$0.151434\pi$
$83$	−0.725433	+	6.43840i	−0.0796267	+	0.706706i	−0.968579	+	0.248706i	$0.919995\pi$
$84$	−19.0627	+	2.14785i	−2.07991	+	0.234350i
$85$		0			0
$86$			2.82764i			0.304912i
$87$	−16.6339	+	2.11958i	−1.78334	+	0.227243i
$88$	−1.07698	−	1.07698i	−0.114807	−	0.114807i
$89$	−10.7763	+	3.77081i	−1.14229	+	0.399705i	−0.834096	−	0.551619i	$-0.814010\pi$
$89$	−10.7763	+	3.77081i	−1.14229	+	0.399705i	−0.308194	+	0.951323i	$0.599725\pi$
$90$		0			0
$91$	−6.37799	+	5.08628i	−0.668596	+	0.533187i
$92$	0.989916	+	2.82902i	0.103206	+	0.294945i
$93$	2.31749	−	6.62300i	0.240312	−	0.686773i
$94$	2.57227	+	2.05132i	0.265310	+	0.211577i
$95$		0			0
$96$	13.2780	−	3.03062i	1.35518	−	0.309311i
$97$	−3.97853	+	3.17277i	−0.403958	+	0.322146i	−0.804304	−	0.594218i	$-0.797462\pi$
$97$	−3.97853	+	3.17277i	−0.403958	+	0.322146i	0.400345	+	0.916364i	$0.368890\pi$
$98$	−1.71634	−	0.391743i	−0.173376	−	0.0395720i
$99$	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	$0.226753\pi$
$102$	3.57071	+	7.41465i	0.353553	+	0.734160i
$103$	−3.98499	+	2.50394i	−0.392653	+	0.246720i	−0.713860	−	0.700289i	$-0.753055\pi$
$103$	−3.98499	+	2.50394i	−0.392653	+	0.246720i	0.321206	+	0.947009i	$0.395912\pi$
$104$	2.69105	−	2.69105i	0.263879	−	0.263879i
$105$		0			0
$106$	0.0958204	−	0.850430i	0.00930690	−	0.0826011i
$107$	10.4958	+	6.59492i	1.01466	+	0.637555i	0.933288	−	0.359129i	$-0.116926\pi$
$107$	10.4958	+	6.59492i	1.01466	+	0.637555i	0.0813745	+	0.996684i	$0.474069\pi$
$108$	−20.5603	+	4.69275i	−1.97842	+	0.451561i
$109$	−1.30985	+	1.64250i	−0.125461	+	0.157323i	−0.840595	−	0.541664i	$-0.817794\pi$
$109$	−1.30985	+	1.64250i	−0.125461	+	0.157323i	0.715134	+	0.698988i	$0.246366\pi$
$110$		0			0
$111$	−9.60032	−	4.62327i	−0.911222	−	0.438822i
$112$	−10.0999	−	1.13798i	−0.954349	−	0.107529i
$113$	8.75582	−	10.9795i	0.823679	−	1.03286i	−0.175153	−	0.984541i	$-0.556042\pi$
$113$	8.75582	−	10.9795i	0.823679	−	1.03286i	0.998832	−	0.0483193i	$-0.0153865\pi$
$114$	−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
$118$	−1.74295	+	3.61926i	−0.160451	+	0.333180i
$119$	−2.43102	−	21.5759i	−0.222852	−	1.97786i
$120$		0			0
$121$	−4.36352	+	9.06095i	−0.396684	+	0.823723i
$122$	−5.65168	−	1.97761i	−0.511679	−	0.179044i
$123$	−18.5143	+	2.08606i	−1.66938	+	0.188094i
$124$	2.19702	−	3.49654i	0.197299	−	0.313999i
$125$		0			0
$126$	−9.15378	−	1.03138i	−0.815484	−	0.0918829i
$127$	−2.85906	+	12.5264i	−0.253701	+	1.11154i	0.674153	+	0.738592i	$0.264509\pi$
$127$	−2.85906	+	12.5264i	−0.253701	+	1.11154i	−0.927854	+	0.372944i	$0.878348\pi$
$128$	10.4897			0.927167
$129$	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	$0.134167\pi$
$132$	2.94824	+	4.69210i	0.256611	+	0.408395i
$133$			22.3371i			1.93688i
$134$	0.711163	−	0.446853i	0.0614351	−	0.0386022i
$135$		0			0
$136$	2.25396	+	9.87524i	0.193275	+	0.846795i
$137$	2.88703	+	12.6489i	0.246656	+	1.08067i	0.934822	+	0.355117i	$0.115559\pi$
$137$	2.88703	+	12.6489i	0.246656	+	1.08067i	−0.688166	+	0.725553i	$0.741584\pi$
$138$	0.233343	+	2.07097i	0.0198635	+	0.176293i
$139$	3.97416	+	8.25242i	0.337083	+	0.699961i	0.998758	−	0.0498304i	$-0.0158681\pi$
$139$	3.97416	+	8.25242i	0.337083	+	0.699961i	−0.661674	+	0.749791i	$0.730154\pi$
$140$		0			0
$141$	−15.6087	−	19.5727i	−1.31449	−	1.64832i
$142$	−2.05809	−	1.64128i	−0.172711	−	0.137733i
$143$	2.12316	+	1.02246i	0.177547	+	0.0855023i
$144$	−20.2433			−1.68694
$145$		0			0
$146$	6.00212			0.496739
$147$	12.0691	+	5.81217i	0.995442	+	0.479380i
$148$	−4.90286	−	3.90990i	−0.403013	−	0.321392i
$149$	−5.48621	−	6.87949i	−0.449448	−	0.563589i	0.504558	−	0.863378i	$-0.331655\pi$
$149$	−5.48621	−	6.87949i	−0.449448	−	0.563589i	−0.954006	+	0.299788i	$0.903084\pi$
$150$		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	$0.831704\pi$
$152$	−1.16674	−	10.3551i	−0.0946350	−	0.839909i
$153$	−9.62290	−	42.1607i	−0.777966	−	3.40849i
$154$	0.297294	+	1.30253i	0.0239566	+	0.104961i
$155$		0			0
$156$	−11.7241	+	7.36676i	−0.938681	+	0.589812i
$157$			9.57129i			0.763872i	0.924189	+	0.381936i	$0.124743\pi$
$157$			9.57129i			0.763872i	−0.924189	+	0.381936i	$0.875257\pi$
$158$	3.13272	+	4.98569i	0.249226	+	0.396640i
$159$	−2.15077	+	6.14654i	−0.170567	+	0.487453i
$160$		0			0
$161$	1.22353	−	5.36062i	0.0964273	−	0.422476i
$162$	−6.44384			−0.506276
$163$	4.68798	−	20.5394i	0.367191	−	1.60877i	−0.367268	−	0.930115i	$-0.619707\pi$
$163$	4.68798	−	20.5394i	0.367191	−	1.60877i	0.734459	−	0.678653i	$-0.237436\pi$
$164$	−10.8960	−	1.22769i	−0.850838	−	0.0958664i
$165$		0			0
$166$	−1.41063	+	2.24500i	−0.109486	+	0.174246i
$167$	11.7539	−	1.32434i	0.909543	−	0.102481i	0.355220	−	0.934783i	$-0.384406\pi$
$167$	11.7539	−	1.32434i	0.909543	−	0.102481i	0.554323	+	0.832302i	$0.312977\pi$
$168$	−15.4965	−	5.42245i	−1.19558	−	0.418351i
$169$	3.08567	−	6.40747i	0.237360	−	0.492882i
$170$		0			0
$171$	4.98120	+	44.2094i	0.380922	+	3.38077i
$172$	5.49405	−	11.4085i	0.418917	−	0.869891i
$173$	−3.61857	+	3.61857i	−0.275115	+	0.275115i	−0.831155	−	0.556041i	$-0.812320\pi$
$173$	−3.61857	+	3.61857i	−0.275115	+	0.275115i	0.556041	+	0.831155i	$0.312320\pi$
$174$	−6.50918	−	2.17194i	−0.493459	−	0.164654i
$175$		0			0
$176$	0.969701	+	2.77125i	0.0730940	+	0.208891i
$177$	19.0579	−	23.8978i	1.43248	−	1.79627i
$178$	−4.64271	−	0.523108i	−0.347986	−	0.0392086i
$179$	9.13064	+	4.39709i	0.682456	+	0.328654i	0.742790	−	0.669525i	$-0.233502\pi$
$179$	9.13064	+	4.39709i	0.682456	+	0.328654i	−0.0603336	+	0.998178i	$0.519216\pi$
$180$		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	$0.324183\pi$
$182$	−3.25463	+	0.742847i	−0.241249	+	0.0550635i
$183$	38.5776	+	24.2399i	2.85174	+	1.79187i
$184$	−0.287203	+	2.54899i	−0.0211729	+	0.187914i
$185$		0			0
$186$	2.03039	−	2.03039i	0.148875	−	0.148875i
$187$	−5.31071	+	3.33694i	−0.388357	+	0.244021i
$188$	−6.39253	−	13.2742i	−0.466223	−	0.968122i
$189$	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	$0.906291\pi$
$192$	−12.9221	−	2.94939i	−0.932574	−	0.212854i
$193$	7.88229	−	6.28591i	0.567379	−	0.452470i	−0.297307	−	0.954782i	$-0.596089\pi$
$193$	7.88229	−	6.28591i	0.567379	−	0.452470i	0.864686	+	0.502312i	$0.167517\pi$
$194$	−2.03020	+	0.463381i	−0.145760	+	0.0332688i
$195$		0			0
$196$	6.16366	+	4.91536i	0.440262	+	0.351097i
$197$	5.40945	−	15.4593i	0.385408	−	1.10143i	−0.573865	−	0.818950i	$-0.694557\pi$
$197$	5.40945	−	15.4593i	0.385408	−	1.10143i	0.959273	−	0.282482i	$-0.0911577\pi$
$198$	0.878865	+	2.51165i	0.0624582	+	0.178495i
$199$	−9.36325	+	7.46694i	−0.663743	+	0.529318i	−0.896403	−	0.443241i	$-0.853829\pi$
$199$	−9.36325	+	7.46694i	−0.663743	+	0.529318i	0.232659	+	0.972558i	$0.425257\pi$
$200$		0			0
$201$	−6.03226	+	2.11078i	−0.425483	+	0.148883i
$202$	5.41031	+	5.41031i	0.380668	+	0.380668i
$203$	14.3170	+	11.0807i	1.00486	+	0.777712i
$204$		−	36.8533i		−	2.58025i
$205$		0			0
$206$	−1.91383	+	0.215637i	−0.133343	+	0.0150242i
$207$	1.22616	−	10.8825i	0.0852243	−	0.756386i
$208$	−6.92450	+	2.42299i	−0.480128	+	0.168004i
$209$	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	$0.596751\pi$
$212$	−2.03897	+	3.24500i	−0.140037	+	0.222868i
$213$	12.4887	+	15.6603i	0.855710	+	1.07303i
$214$	2.69878	+	4.29508i	0.184485	+	0.293606i
$215$		0			0
$216$	−17.5963	−	4.01623i	−1.19727	−	0.273270i
$217$	−6.82546	+	3.28697i	−0.463342	+	0.223134i
$218$	−0.774570	+	0.373013i	−0.0524605	+	0.0252636i
$219$	−44.5258	−	10.1627i	−3.00878	−	0.686734i
$220$		0			0
$221$	−8.33800	−	13.2698i	−0.560874	−	0.892627i
$222$	−2.71871	−	3.40916i	−0.182468	−	0.228808i
$223$	5.86600	−	9.33568i	0.392816	−	0.625164i	−0.590506	−	0.807033i	$-0.701072\pi$
$223$	5.86600	−	9.33568i	0.392816	−	0.625164i	0.983323	+	0.181869i	$0.0582148\pi$
$224$	−12.4505	−	7.82320i	−0.831887	−	0.522709i
$225$		0			0
$226$	5.17768	−	2.49344i	0.344414	−	0.165861i
$227$	3.56082	−	1.24599i	0.236340	−	0.0826990i	−0.209510	−	0.977806i	$-0.567187\pi$
$227$	3.56082	−	1.24599i	0.236340	−	0.0826990i	0.445851	+	0.895107i	$0.352901\pi$
$228$	−4.24497	+	37.6752i	−0.281130	+	2.49510i
$229$	8.55442	−	0.963852i	0.565292	−	0.0636931i	0.175306	−	0.984514i	$-0.443908\pi$
$229$	8.55442	−	0.963852i	0.565292	−	0.0636931i	0.389986	+	0.920821i	$0.372480\pi$
$230$		0			0
$231$		−	10.1660i		−	0.668873i
$232$	−7.21589	−	4.38899i	−0.473746	−	0.288151i
$233$	−1.57326	−	1.57326i	−0.103068	−	0.103068i	0.653692	−	0.756760i	$-0.273219\pi$
$233$	−1.57326	−	1.57326i	−0.103068	−	0.103068i	−0.756760	+	0.653692i	$0.773219\pi$
$234$	−6.27586	+	2.19602i	−0.410266	+	0.143558i
$235$		0			0
$236$	14.0643	−	11.2159i	0.915510	−	0.730095i
$237$	−14.7979	−	42.2899i	−0.961225	−	2.74702i
$238$	2.93459	−	8.38658i	0.190221	−	0.543621i
$239$	−5.34017	−	4.25865i	−0.345427	−	0.275469i	0.435373	−	0.900250i	$-0.356617\pi$
$239$	−5.34017	−	4.25865i	−0.345427	−	0.275469i	−0.780800	+	0.624781i	$0.785188\pi$
$240$		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	$0.359212\pi$
$242$	−3.21762	+	2.56597i	−0.206836	+	0.164947i
$243$	14.1439	+	3.22826i	0.907333	+	0.207093i
$244$	18.9600	+	18.9600i	1.21379	+	1.21379i
$245$		0			0
$246$	−7.19653	−	2.51818i	−0.458834	−	0.160553i
$247$	6.99545	+	14.5262i	0.445110	+	0.924280i
$248$	2.99247	−	1.88029i	0.190022	−	0.119399i
$249$	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	$0.00987384\pi$
$252$	34.9283	+	21.9469i	2.20028	+	1.38252i
$253$	−1.54852	+	0.353439i	−0.0973544	+	0.0222205i
$254$	−3.27823	+	4.11078i	−0.205695	+	0.257933i
$255$		0			0
$256$	−3.80273	−	1.83130i	−0.237671	−	0.114456i
$257$	−26.6059	−	2.99776i	−1.65963	−	0.186995i	−0.768218	−	0.640189i	$-0.778856\pi$
$257$	−26.6059	−	2.99776i	−1.65963	−	0.186995i	−0.891412	+	0.453194i	$0.850285\pi$
$258$	5.48966	−	6.88382i	0.341771	−	0.428568i
$259$	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
$263$	0.698461	−	1.45037i	0.0430689	−	0.0894336i	−0.878324	−	0.478066i	$-0.841338\pi$
$263$	0.698461	−	1.45037i	0.0430689	−	0.0894336i	0.921393	+	0.388632i	$0.127052\pi$
$264$	0.531002	+	4.71277i	0.0326809	+	0.290051i
$265$		0			0
$266$	−3.96605	+	8.23559i	−0.243174	+	0.504957i
$267$	33.5555	+	11.7416i	2.05356	+	0.718573i
$268$	−3.73752	+	0.421117i	−0.228305	+	0.0257238i
$269$	−2.51693	+	4.00567i	−0.153460	+	0.244230i	−0.914602	−	0.404355i	$-0.867496\pi$
$269$	−2.51693	+	4.00567i	−0.153460	+	0.244230i	0.761142	+	0.648585i	$0.224639\pi$
$270$		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	$0.626982\pi$
$272$	4.34490	−	19.0362i	0.263448	−	1.15424i
$273$	25.4017			1.53738
$274$	−1.18143	+	5.17620i	−0.0713730	+	0.312706i
$275$		0			0
$276$	3.08241	−	8.80903i	0.185539	−	0.530241i
$277$	1.87024	+	2.97647i	0.112372	+	0.178839i	0.898175	−	0.439638i	$-0.144893\pi$
$277$	1.87024	+	2.97647i	0.112372	+	0.178839i	−0.785803	+	0.618476i	$0.787750\pi$
$278$			3.74825i			0.224805i
$279$	−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	$0.971141\pi$
$282$	−2.27964	−	9.98777i	−0.135751	−	0.594763i
$283$	1.97286	+	17.5096i	0.117274	+	1.04084i	0.905176	+	0.425036i	$0.139739\pi$
$283$	1.97286	+	17.5096i	0.117274	+	1.04084i	−0.787902	+	0.615800i	$0.788833\pi$
$284$	5.11471	+	10.6208i	0.303502	+	0.630229i
$285$		0			0
$286$	0.601256	+	0.753951i	0.0355530	+	0.0445821i
$287$	15.7270	+	12.5419i	0.928336	+	0.740323i
$288$	−26.3865	−	12.7071i	−1.55484	−	0.748772i
$289$	24.7121			1.45365
$290$		0			0
$291$	15.8453			0.928871
$292$	−24.2164	−	11.6620i	−1.41716	−	0.682468i
$293$	7.08570	+	5.65066i	0.413951	+	0.330115i	0.808221	−	0.588880i	$-0.200431\pi$
$293$	7.08570	+	5.65066i	0.413951	+	0.330115i	−0.394269	+	0.918995i	$0.629002\pi$
$294$	3.41784	+	4.28584i	0.199333	+	0.249955i
$295$		0			0
$296$	−2.32863	−	4.83546i	−0.135349	−	0.281055i
$297$	−1.25131	−	11.1056i	−0.0726082	−	0.644415i
$298$	−0.801256	−	3.51053i	−0.0464155	−	0.203360i
$299$	−0.883137	−	3.86927i	−0.0510731	−	0.223766i
$300$		0			0
$301$	−19.6692	+	12.3590i	−1.13371	+	0.712359i
$302$			0.802889i			0.0462011i
$303$	−30.9749	−	49.2963i	−1.77946	−	2.83200i
$304$	−6.63450	+	18.9603i	−0.380514	+	1.08745i
$305$		0			0
$306$	3.93789	−	17.2530i	0.225114	−	0.986290i
$307$	−9.63676			−0.549999			−0.274999	−	0.961444i	$-0.588678\pi$
$307$	−9.63676			−0.549999			−0.274999	+	0.961444i	$0.588678\pi$
$308$	1.33132	−	5.83288i	0.0758588	−	0.332359i
$309$	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	$0.961286\pi$
$312$	−11.7758	+	1.32681i	−0.666673	+	0.0751160i
$313$	−28.5902	−	10.0042i	−1.61602	−	0.565469i	−0.637288	−	0.770626i	$-0.719944\pi$
$313$	−28.5902	−	10.0042i	−1.61602	−	0.565469i	−0.978729	+	0.205158i	$0.934229\pi$
$314$	−1.69942	+	3.52889i	−0.0959040	+	0.199147i
$315$		0			0
$316$	−2.95229	−	26.2023i	−0.166079	−	1.47399i
$317$	−9.56669	+	19.8654i	−0.537319	+	1.11575i	0.438814	+	0.898578i	$0.355399\pi$
$317$	−9.56669	+	19.8654i	−0.537319	+	1.11575i	−0.976133	+	0.217176i	$0.930316\pi$
$318$	−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
$322$	1.40291	−	1.75919i	0.0781810	−	0.0980359i
$323$	−42.6423	−	4.80464i	−2.37268	−	0.267337i
$324$	25.9986	+	12.5203i	1.44437	+	0.695570i
$325$		0			0
$326$	5.37529	−	6.74040i	0.297710	−	0.373316i
$327$	6.37761	−	1.45565i	0.352683	−	0.0804975i
$328$	−7.94587	−	4.99272i	−0.438737	−	0.275677i
$329$	−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	$0.349593\pi$
$332$	10.0534	−	6.31696i	0.551751	−	0.346688i
$333$	9.94171	+	20.6442i	0.544802	+	1.13129i
$334$	4.56874	+	1.59867i	0.249990	+	0.0874754i
$335$		0			0
$336$	22.3786	+	22.3786i	1.22085	+	1.22085i
$337$	21.0068	+	4.79466i	1.14431	+	0.261182i	0.752327	−	0.658789i	$-0.228931\pi$
$337$	21.0068	+	4.79466i	1.14431	+	0.261182i	0.391986	+	0.919971i	$0.371788\pi$
$338$	2.27535	−	1.81453i	0.123763	−	0.0986973i
$339$	−42.6317	+	9.73041i	−2.31544	+	0.528483i
$340$		0			0
$341$	1.71095	+	1.36443i	0.0926530	+	0.0738883i
$342$	−6.01301	+	17.1842i	−0.325147	+	0.929215i
$343$	2.99570	+	8.56121i	0.161752	+	0.462262i
$344$	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	0.692359	−	0.721553i	$-0.256571\pi$
$347$	−0.543822	−	0.543822i	−0.0291939	−	0.0291939i	−0.721553	+	0.692359i	$0.756571\pi$
$348$	22.0422	+	21.4102i	1.18158	+	1.14771i
$349$			4.38642i			0.234800i	0.993085	+	0.117400i	$0.0374559\pi$
$349$			4.38642i			0.234800i	−0.993085	+	0.117400i	$0.962544\pi$
$350$		0			0
$351$	27.7496	−	3.12663i	1.48117	−	0.166887i
$352$	−0.475585	+	4.22093i	−0.0253488	+	0.224976i
$353$	−24.9543	+	8.73188i	−1.32818	+	0.464751i	−0.898795	−	0.438369i	$-0.855556\pi$
$353$	−24.9543	+	8.73188i	−1.32818	+	0.464751i	−0.429387	+	0.903120i	$0.641270\pi$
$354$	11.2697	−	5.42721i	0.598978	−	0.288453i
$355$		0			0
$356$	17.7153	+	11.1313i	0.938909	+	0.589955i
$357$	−35.9699	+	57.2458i	−1.90373	+	3.02977i
$358$	2.58570	+	3.24237i	0.136659	+	0.171364i
$359$	−12.0702	−	19.2097i	−0.637042	−	1.01385i	−0.996732	−	0.0807752i	$-0.974260\pi$
$359$	−12.0702	−	19.2097i	−0.637042	−	1.01385i	0.359690	−	0.933072i	$-0.382882\pi$
$360$		0			0
$361$	24.5163	+	5.59568i	1.29033	+	0.294509i
$362$	−3.35746	+	1.61687i	−0.176464	+	0.0849807i
$363$	28.2141	−	13.5872i	1.48086	−	0.713143i
$364$	14.5746	+	3.32656i	0.763917	+	0.174359i
$365$		0			0
$366$	9.91949	+	15.7868i	0.518500	+	0.825188i
$367$	1.63625	+	2.05179i	0.0854115	+	0.107103i	0.822701	−	0.568474i	$-0.192466\pi$
$367$	1.63625	+	2.05179i	0.0854115	+	0.107103i	−0.737290	+	0.675577i	$0.763895\pi$
$368$	2.63075	−	4.18681i	0.137137	−	0.218253i
$369$	33.9235	+	21.3156i	1.76599	+	1.10964i
$370$		0			0
$371$	6.33444	−	3.05050i	0.328868	−	0.158374i
$372$	−12.1369	+	4.24688i	−0.629269	+	0.220191i
$373$	−0.394358	+	3.50003i	−0.0204191	+	0.181225i	−0.999782	−	0.0208857i	$-0.993351\pi$
$373$	−0.394358	+	3.50003i	−0.0204191	+	0.181225i	0.979363	+	0.202110i	$0.0647800\pi$
$374$	−2.55052	+	0.287375i	−0.131884	+	0.0148598i
$375$		0			0
$376$		−	12.6093i		−	0.650274i
$377$	12.7808	+	2.72221i	0.658244	+	0.140201i
$378$	11.1950	+	11.1950i	0.575809	+	0.575809i
$379$	−23.0211	+	8.05542i	−1.18251	+	0.413779i	−0.848707	−	0.528863i	$-0.822619\pi$
$379$	−23.0211	+	8.05542i	−1.18251	+	0.413779i	−0.333805	+	0.942642i	$0.608333\pi$
$380$		0			0
$381$	31.2794	−	24.9445i	1.60249	−	1.27795i
$382$	−1.76147	−	5.03400i	−0.0901247	−	0.257562i
$383$	−5.85497	+	16.7325i	−0.299175	+	0.854992i	0.691937	+	0.721958i	$0.256758\pi$
$383$	−5.85497	+	16.7325i	−0.299175	+	0.854992i	−0.991111	+	0.133034i	$0.957528\pi$
$384$	−25.5369	−	20.3650i	−1.30318	−	1.03925i
$385$		0			0
$386$	4.02225	−	0.918053i	0.204727	−	0.0467277i
$387$	−36.1729	+	28.8469i	−1.83877	+	1.46637i
$388$	9.09149	+	2.07507i	0.461550	+	0.105346i
$389$	−20.9074	−	20.9074i	−1.06005	−	1.06005i	−0.998078	−	0.0619714i	$-0.980261\pi$
$389$	−20.9074	−	20.9074i	−1.06005	−	1.06005i	−0.0619714	−	0.998078i	$-0.519739\pi$
$390$		0			0
$391$	9.97042	+	3.48880i	0.504226	+	0.176436i
$392$	2.92745	+	6.07892i	0.147859	+	0.307032i
$393$	5.11768	−	3.21565i	0.258153	−	0.162208i
$394$	4.73931	−	4.73931i	0.238763	−	0.238763i
$395$		0			0
$396$	1.33419	−	11.8412i	0.0670455	−	0.595045i
$397$	−7.60573	−	4.77899i	−0.381720	−	0.239851i	0.327479	−	0.944858i	$-0.393801\pi$
$397$	−7.60573	−	4.77899i	−0.381720	−	0.239851i	−0.709200	+	0.705007i	$0.750944\pi$
$398$	−4.77797	+	1.09054i	−0.239498	+	0.0546639i
$399$	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	$0.790200\pi$
$402$	−2.59884	−	0.292819i	−0.129619	−	0.0146045i
$403$	−3.40931	+	4.27514i	−0.169830	+	0.212960i
$404$	−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
$408$	13.6849	−	28.4169i	0.677503	−	1.40685i
$409$	1.88589	+	16.7378i	0.0932513	+	0.827628i	0.950076	+	0.312020i	$0.101006\pi$
$409$	1.88589	+	16.7378i	0.0932513	+	0.827628i	−0.856824	+	0.515609i	$0.827566\pi$
$410$		0			0
$411$	17.5286	−	36.3985i	0.864621	−	1.79540i
$412$	8.14061	+	2.84852i	0.401059	+	0.140337i
$413$	−32.7938	+	3.69497i	−1.61368	+	0.181818i
$414$	2.38432	−	3.79462i	0.117183	−	0.186495i
$415$		0			0
$416$	−10.5468	−	1.18834i	−0.517101	−	0.0582633i
$417$	6.34651	−	27.8059i	0.310790	−	1.36166i
$418$	2.64050			0.129151
$419$	−0.726862	+	3.18459i	−0.0355095	+	0.155577i	−0.989574	−	0.144023i	$-0.953996\pi$
$419$	−0.726862	+	3.18459i	−0.0355095	+	0.155577i	0.954065	+	0.299600i	$0.0968533\pi$
$420$		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	$0.156684\pi$
$422$	1.60799	+	2.55910i	0.0782756	+	0.124575i
$423$			53.8332i			2.61746i
$424$	−2.77719	+	1.74503i	−0.134873	+	0.0847460i
$425$		0			0
$426$	1.82396	+	7.99129i	0.0883712	+	0.387179i
$427$	−10.9459	−	47.9570i	−0.529708	−	2.32080i
$428$	−2.54334	−	22.5728i	−0.122937	−	1.09110i
$429$	−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	$0.444796\pi$
$432$	27.2016	+	21.6926i	1.30874	+	1.04368i
$433$	−25.3951	−	12.2296i	−1.22041	−	0.587718i	−0.290983	−	0.956728i	$-0.593982\pi$
$433$	−25.3951	−	12.2296i	−1.22041	−	0.587718i	−0.929425	+	0.369010i	$0.879697\pi$
$434$	−3.10013			−0.148811
$435$		0			0
$436$	3.84987			0.184375
$437$	−9.79091	−	4.71506i	−0.468363	−	0.225552i
$438$	−14.6120	−	11.6527i	−0.698189	−	0.556787i
$439$	21.5771	+	27.0568i	1.02982	+	1.29135i	0.955775	+	0.294097i	$0.0950190\pi$
$439$	21.5771	+	27.0568i	1.02982	+	1.29135i	0.0740437	+	0.997255i	$0.476410\pi$
$440$		0			0
$441$	−12.4983	−	25.9529i	−0.595156	−	1.23585i
$442$	−0.718062	−	6.37298i	−0.0341547	−	0.303132i
$443$	−3.44728	−	15.1035i	−0.163785	−	0.717590i	−0.988397	−	0.151891i	$-0.951464\pi$
$443$	−3.44728	−	15.1035i	−0.163785	−	0.717590i	0.824612	−	0.565699i	$-0.191394\pi$
$444$	4.34510	+	19.0371i	0.206209	+	0.903462i
$445$		0			0
$446$	3.82035	−	2.40049i	0.180899	−	0.113666i
$447$			27.3990i			1.29593i
$448$	7.61351	+	12.1168i	0.359704	+	0.572466i
$449$	10.5740	−	30.2189i	0.499020	−	1.42612i	−0.368926	−	0.929459i	$-0.620275\pi$
$449$	10.5740	−	30.2189i	0.499020	−	1.42612i	0.867946	−	0.496658i	$-0.165440\pi$
$450$		0			0
$451$	1.29302	−	5.66509i	0.0608860	−	0.266759i
$452$	−25.7348			−1.21046
$453$	1.35944	−	5.95611i	0.0638722	−	0.279843i
$454$	1.53409	+	0.172850i	0.0719983	+	0.00811226i
$455$		0			0
$456$	−17.2633	+	27.4744i	−0.808428	+	1.28661i
$457$	26.6134	−	2.99861i	1.24492	−	0.140269i	0.535184	−	0.844735i	$-0.320242\pi$
$457$	26.6134	−	2.99861i	1.24492	−	0.140269i	0.709738	+	0.704466i	$0.248814\pi$
$458$	3.32511	+	1.16351i	0.155372	+	0.0543671i
$459$	−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	$-0.404260\pi$
$462$	1.80502	−	3.74815i	0.0839769	−	0.174380i
$463$	17.3288	−	17.3288i	0.805338	−	0.805338i	−0.178586	−	0.983924i	$-0.557152\pi$
$463$	17.3288	−	17.3288i	0.805338	−	0.805338i	0.983924	+	0.178586i	$0.0571522\pi$
$464$	8.86148	+	13.6579i	0.411384	+	0.634054i
$465$		0			0
$466$	−0.300715	−	0.859394i	−0.0139304	−	0.0398107i
$467$	11.6610	−	14.6224i	0.539607	−	0.676646i	−0.435035	−	0.900413i	$-0.643264\pi$
$467$	11.6610	−	14.6224i	0.539607	−	0.676646i	0.974643	+	0.223767i	$0.0718356\pi$
$468$	29.5877	+	3.33373i	1.36769	+	0.154102i
$469$	6.21666	+	2.99379i	0.287059	+	0.138240i
$470$		0			0
$471$	18.5820	−	23.3011i	0.856213	−	1.07366i
$472$	15.0096	−	3.42585i	0.690873	−	0.157687i
$473$	5.68182	+	3.57012i	0.261250	+	0.164154i
$474$	2.05284	−	18.2195i	0.0942902	−	0.836849i
$475$		0			0
$476$	−28.1350	+	28.1350i	−1.28957	+	1.28957i
$477$	11.8568	−	7.45010i	0.542884	−	0.341117i
$478$	−1.21276	−	2.51831i	−0.0554701	−	0.115185i
$479$	30.1049	+	10.5342i	1.37553	+	0.481319i	0.913967	−	0.405789i	$-0.133003\pi$
$479$	30.1049	+	10.5342i	1.37553	+	0.481319i	0.461563	+	0.887107i	$0.347289\pi$
$480$		0			0
$481$	5.87167	+	5.87167i	0.267725	+	0.267725i
$482$	2.67781	+	0.611193i	0.121971	+	0.0278391i
$483$	−13.3859	+	10.6749i	−0.609080	+	0.485725i
$484$	17.9676	−	4.10098i	0.816708	−	0.186408i
$485$		0			0
$486$	4.64160	+	3.70155i	0.210547	+	0.167906i
$487$	6.71341	−	19.1858i	0.304214	−	0.869393i	−0.685720	−	0.727865i	$-0.740513\pi$
$487$	6.71341	−	19.1858i	0.304214	−	0.869393i	0.989934	−	0.141528i	$-0.0452015\pi$
$488$	7.57926	+	21.6603i	0.343097	+	0.980514i
$489$	−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
$493$	−24.2330	+	24.9482i	−1.09140	+	1.12361i
$494$			6.59781i			0.296850i
$495$		0			0
$496$	−6.76990	+	0.762784i	−0.303977	+	0.0342500i
$497$	2.42132	−	21.4898i	0.108611	−	0.963951i
$498$	7.79266	−	2.72677i	0.349197	−	0.122189i
$499$	1.40772	−	0.677923i	0.0630183	−	0.0303480i	−0.402109	−	0.915592i	$-0.631723\pi$
$499$	1.40772	−	0.677923i	0.0630183	−	0.0303480i	0.465127	+	0.885244i	$0.346008\pi$
$500$		0			0
$501$	−31.1857	−	19.5953i	−1.39327	−	0.875451i
$502$	0.559416	−	0.890306i	0.0249680	−	0.0397363i
$503$	−9.15733	−	11.4829i	−0.408305	−	0.511998i	0.534579	−	0.845118i	$-0.320470\pi$
$503$	−9.15733	−	11.4829i	−0.408305	−	0.511998i	−0.942884	+	0.333120i	$0.891899\pi$
$504$	18.7830	+	29.8929i	0.836660	+	1.33154i
$505$		0			0
$506$	−0.633685	−	0.144635i	−0.0281708	−	0.00642979i
$507$	−19.9517	+	9.60821i	−0.886084	+	0.426716i
$508$	21.2137	−	10.2160i	0.941204	−	0.453260i
$509$	10.9409	+	2.49719i	0.484947	+	0.110686i	0.458003	−	0.888951i	$-0.348565\pi$
$509$	10.9409	+	2.49719i	0.484947	+	0.110686i	0.0269447	+	0.999637i	$0.491422\pi$
$510$		0			0
$511$	26.2339	+	41.7510i	1.16052	+	1.84696i
$512$	−14.1573	−	17.7527i	−0.625672	−	0.784568i
$513$	40.6810	−	64.7434i	1.79611	−	2.85849i
$514$	−9.27720	−	5.82925i	−0.409200	−	0.257117i
$515$		0			0
$516$	−35.5240	+	17.1074i	−1.56385	+	0.753113i
$517$	7.36960	−	2.57873i	0.324115	−	0.113413i
$518$	−0.527108	+	4.67821i	−0.0231598	+	0.205549i
$519$	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	$-0.214831\pi$
$522$	8.03139	+	12.3786i	0.351524	+	0.541794i
$523$	−3.65812	−	3.65812i	−0.159958	−	0.159958i	0.622590	−	0.782548i	$-0.286081\pi$
$523$	−3.65812	−	3.65812i	−0.159958	−	0.159958i	−0.782548	+	0.622590i	$0.786081\pi$
$524$	3.35745	−	1.17482i	0.146671	−	0.0513224i
$525$		0			0
$526$	0.515038	−	0.410729i	0.0224567	−	0.0179086i
$527$	−4.80680	−	13.7370i	−0.209387	−	0.598395i
$528$	3.01947	−	8.62914i	0.131405	−	0.375535i
$529$	−15.8907	−	12.6724i	−0.690900	−	0.550974i
$530$		0			0
$531$	−64.0810	+	14.6261i	−2.78088	+	0.634718i
$532$	32.0032	−	25.5217i	1.38752	−	1.10651i
$533$	14.1553	+	3.23087i	0.613136	+	0.139944i
$534$	10.2870	+	10.2870i	0.445162	+	0.445162i
$535$		0			0
$536$	−3.03831	−	1.06315i	−0.131235	−	0.0459211i
$537$	−13.6917	−	28.4311i	−0.590840	−	1.22689i
$538$	−1.63920	+	1.02998i	−0.0706711	+	0.0444056i
$539$	−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	$0.930036\pi$
$542$	−3.22637	−	2.02726i	−0.138584	−	0.0870783i
$543$	27.6445	−	6.30967i	1.18634	−	0.270774i
$544$	17.6128	−	22.0858i	0.755143	−	0.946920i
$545$		0			0
$546$	9.36550	+	4.51019i	0.400806	+	0.193018i
$547$	25.7574	+	2.90217i	1.10131	+	0.124088i	0.643856	−	0.765146i	$-0.277333\pi$
$547$	25.7574	+	2.90217i	1.10131	+	0.124088i	0.457452	+	0.889234i	$0.348762\pi$
$548$	14.8239	−	18.5886i	0.633247	−	0.794067i
$549$	−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
$553$	−20.9883	+	43.5826i	−0.892513	+	1.85332i
$554$	0.161064	+	1.42948i	0.00684294	+	0.0607328i
$555$		0			0
$556$	7.28279	−	15.1229i	0.308859	−	0.641353i
$557$	−27.2359	−	9.53025i	−1.15402	−	0.403810i	−0.315632	−	0.948882i	$-0.602217\pi$
$557$	−27.2359	−	9.53025i	−1.15402	−	0.403810i	−0.838389	+	0.545072i	$0.816502\pi$
$558$	−6.13573	+	0.691331i	−0.259746	+	0.0292664i
$559$	−8.92066	+	14.1971i	−0.377304	+	0.600475i
$560$		0			0
$561$	19.4072	+	2.18667i	0.819374	+	0.0923213i
$562$	0.407065	−	1.78347i	0.0171710	−	0.0752311i
$563$	17.8844			0.753737			0.376868	−	0.926267i	$-0.377001\pi$
$563$	17.8844			0.753737			0.376868	+	0.926267i	$0.377001\pi$
$564$	−10.2085	+	44.7264i	−0.429856	+	1.88332i
$565$		0			0
$566$	−2.38152	+	6.80598i	−0.100103	+	0.286077i
$567$	−28.1646	−	44.8236i	−1.18280	−	1.88242i
$568$			10.0888i			0.423316i
$569$	−5.61413	+	3.52759i	−0.235357	+	0.147884i	−0.644547	−	0.764565i	$-0.722954\pi$
$569$	−5.61413	+	3.52759i	−0.235357	+	0.147884i	0.409190	+	0.912449i	$0.365811\pi$
$570$		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	$-0.145190\pi$
$572$	−0.960940	−	4.21015i	−0.0401789	−	0.176035i
$573$	4.54370	+	40.3265i	0.189816	+	1.68466i
$574$	3.57161	+	7.41653i	0.149076	+	0.309560i
$575$		0			0
$576$	17.7706	+	22.2836i	0.740442	+	0.928485i
$577$	5.56959	+	4.44160i	0.231865	+	0.184906i	0.732530	−	0.680735i	$-0.238340\pi$
$577$	5.56959	+	4.44160i	0.231865	+	0.184906i	−0.500664	+	0.865641i	$0.666911\pi$
$578$	9.11123	+	4.38774i	0.378977	+	0.182506i
$579$	−31.3929			−1.30464
$580$		0			0
$581$	−21.7819			−0.903665
$582$	5.84210	+	2.81341i	0.242163	+	0.116620i
$583$	−1.58786	−	1.26628i	−0.0657625	−	0.0524439i
$584$	−14.3424	−	17.9848i	−0.593491	−	0.744214i
$585$		0			0
$586$	1.60917	+	3.34147i	0.0664740	+	0.138035i
$587$	1.46166	+	12.9726i	0.0603290	+	0.535435i	0.987134	+	0.159893i	$0.0511148\pi$
$587$	1.46166	+	12.9726i	0.0603290	+	0.535435i	−0.926805	+	0.375542i	$0.877457\pi$
$588$	−5.46247	−	23.9326i	−0.225268	−	0.986965i
$589$	3.33169	+	14.5971i	0.137280	+	0.601462i
$590$		0			0
$591$	−43.1824	+	27.1333i	−1.77629	+	1.11611i
$592$			10.3457i			0.425207i
$593$	0.394369	+	0.627634i	0.0161948	+	0.0257739i	0.854724	−	0.519084i	$-0.173727\pi$
$593$	0.394369	+	0.627634i	0.0161948	+	0.0257739i	−0.838529	+	0.544857i	$0.816584\pi$
$594$	1.51050	−	4.31677i	0.0619768	−	0.177119i
$595$		0			0
$596$	−3.58812	+	15.7206i	−0.146975	+	0.643940i
$597$	37.2912			1.52623
$598$	0.361398	−	1.58339i	0.0147787	−	0.0647495i
$599$	−5.63173	−	0.634544i	−0.230106	−	0.0259267i	−0.00384165	−	0.999993i	$-0.501223\pi$
$599$	−5.63173	−	0.634544i	−0.230106	−	0.0259267i	−0.226265	+	0.974066i	$0.572651\pi$
$600$		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	$0.315407\pi$
$602$	−9.44631	+	1.06434i	−0.385003	+	0.0433794i
$603$	12.9716	+	4.53894i	0.528242	+	0.184840i
$604$	1.56000	−	3.23937i	0.0634755	−	0.131808i
$605$		0			0
$606$	−2.66753	−	23.6750i	−0.108361	−	0.961732i
$607$	4.42748	−	9.19377i	0.179706	−	0.373163i	−0.791585	−	0.611060i	$-0.790744\pi$
$607$	4.42748	−	9.19377i	0.179706	−	0.373163i	0.971291	+	0.237896i	$0.0764578\pi$
$608$	−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
$612$	−49.4103	+	61.9586i	−1.99729	+	2.50453i
$613$	−12.5618	−	1.41538i	−0.507368	−	0.0571667i	−0.145430	−	0.989369i	$-0.546456\pi$
$613$	−12.5618	−	1.41538i	−0.507368	−	0.0571667i	−0.361939	+	0.932202i	$0.617885\pi$
$614$	−3.55303	−	1.71105i	−0.143388	−	0.0690522i
$615$		0			0
$616$	3.19250	−	4.00327i	0.128630	−	0.161296i
$617$	24.4316	−	5.57635i	0.983579	−	0.224495i	0.299654	−	0.954048i	$-0.403129\pi$
$617$	24.4316	−	5.57635i	0.983579	−	0.224495i	0.683925	+	0.729553i	$0.260272\pi$
$618$	5.07783	+	3.19061i	0.204260	+	0.128345i
$619$	2.36418	−	20.9827i	0.0950245	−	0.843366i	−0.852292	−	0.523066i	$-0.824788\pi$
$619$	2.36418	−	20.9827i	0.0950245	−	0.843366i	0.947316	−	0.320299i	$-0.103783\pi$
$620$		0			0
$621$	−13.3092	+	13.3092i	−0.534081	+	0.534081i
$622$	−7.70941	+	4.84415i	−0.309119	+	0.194233i
$623$	−16.6535	−	34.5813i	−0.667207	−	1.38547i
$624$	21.5616	+	7.54473i	0.863155	+	0.302031i
$625$		0			0
$626$	−8.76481	−	8.76481i	−0.350312	−	0.350312i
$627$	−19.5882	−	4.47087i	−0.782276	−	0.178549i
$628$	13.7131	−	10.9359i	0.547214	−	0.436388i
$629$	−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	$0.837279\pi$
$632$	7.45334	−	21.3004i	0.296478	−	0.847285i
$633$	−7.59558	−	21.7069i	−0.301897	−	0.862772i
$634$	−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
$638$	1.30986	−	1.69243i	0.0518580	−	0.0670041i
$639$		−	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	$0.225038\pi$
$642$	1.76849	−	15.6958i	0.0697966	−	0.619462i
$643$	−24.5385	+	8.58638i	−0.967703	+	0.338614i	−0.767434	−	0.641127i	$-0.778467\pi$
$643$	−24.5385	+	8.58638i	−0.967703	+	0.338614i	−0.200268	+	0.979741i	$0.564181\pi$
$644$	−9.07831	+	4.37188i	−0.357736	+	0.172276i
$645$		0			0
$646$	−14.8689	−	9.34278i	−0.585011	−	0.367587i
$647$	14.0132	−	22.3019i	0.550916	−	0.876778i	−0.448943	−	0.893560i	$-0.648199\pi$
$647$	14.0132	−	22.3019i	0.550916	−	0.876778i	0.999859	+	0.0167822i	$0.00534220\pi$
$648$	15.3979	+	19.3083i	0.604885	+	0.758502i
$649$	5.07189	+	8.07187i	0.199089	+	0.316849i
$650$		0			0
$651$	22.9978	+	5.24911i	0.901356	+	0.205729i
$652$	−34.7838	+	16.7510i	−1.36224	+	0.656020i
$653$	−21.1430	+	10.1819i	−0.827389	+	0.398449i	−0.799135	−	0.601151i	$-0.794709\pi$
$653$	−21.1430	+	10.1819i	−0.827389	+	0.398449i	−0.0282535	+	0.999601i	$0.508995\pi$
$654$	2.60985	+	0.595682i	0.102053	+	0.0232930i
$655$		0			0
$656$	9.62433	+	15.3170i	0.375767	+	0.598029i
$657$	61.2323	+	76.7829i	2.38890	+	2.99559i
$658$	−5.88464	+	9.36534i	−0.229407	+	0.365099i
$659$	4.29921	+	2.70137i	0.167473	+	0.105230i	0.613161	−	0.789958i	$-0.289898\pi$
$659$	4.29921	+	2.70137i	0.167473	+	0.105230i	−0.445687	+	0.895189i	$0.647041\pi$
$660$		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	$0.415292\pi$
$662$	−4.32602	+	1.51374i	−0.168135	+	0.0588331i
$663$	−5.46382	+	48.4928i	−0.212197	+	1.88330i
$664$	10.0977	−	1.13774i	0.391866	−	0.0441527i
$665$		0			0
$666$			9.37660i			0.363336i
$667$	−7.87906	+	3.93652i	−0.305078	+	0.152423i
$668$	−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
$672$	15.1224	+	43.2172i	0.583358	+	1.66714i
$673$	16.7407	−	47.8420i	0.645305	−	1.84417i	0.120983	−	0.992655i	$-0.461395\pi$
$673$	16.7407	−	47.8420i	0.645305	−	1.84417i	0.524322	−	0.851520i	$-0.324319\pi$
$674$	6.89379	+	5.49761i	0.265539	+	0.211760i
$675$		0			0
$676$	−12.7058	+	2.90002i	−0.488685	+	0.111539i
$677$	−25.3499	+	20.2159i	−0.974277	+	0.776960i	−0.974809	−	0.223040i	$-0.928402\pi$
$677$	−25.3499	+	20.2159i	−0.974277	+	0.776960i	0.000532135		1.00000i	$0.499831\pi$
$678$	−17.4458	−	3.98188i	−0.670001	−	0.152923i
$679$	−12.0969	−	12.0969i	−0.464235	−	0.464235i
$680$		0			0
$681$	−11.0877	−	3.87977i	−0.424883	−	0.148673i
$682$	0.388557	+	0.806846i	0.0148786	+	0.0308957i
$683$	35.8420	−	22.5210i	1.37146	−	0.861743i	0.373625	−	0.927580i	$-0.378115\pi$
$683$	35.8420	−	22.5210i	1.37146	−	0.861743i	0.997830	+	0.0658371i	$0.0209718\pi$
$684$	57.6490	−	57.6490i	2.20426	−	2.20426i
$685$		0			0
$686$	−0.415580	+	3.68837i	−0.0158669	+	0.140823i
$687$	−22.6968	−	14.2613i	−0.865937	−	0.544104i
$688$	−20.3665	+	4.64852i	−0.776465	+	0.177223i
$689$	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	$0.961649\pi$
$692$	9.31892	+	1.04999i	0.354252	+	0.0399146i
$693$	−13.6298	+	17.0913i	−0.517755	+	0.649244i
$694$	−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
$698$	−0.778828	+	1.61725i	−0.0294791	+	0.0612139i
$699$	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	$0.979626\pi$
$702$	10.7863	+	3.77429i	0.407103	+	0.142451i
$703$	22.5940	−	2.54574i	0.852150	−	0.0960142i
$704$	2.19931	−	3.50018i	0.0828895	−	0.131918i
$705$		0			0
$706$	−10.7509	−	1.21134i	−0.404616	−	0.0455892i
$707$	−13.9871	+	61.2816i	−0.526040	+	2.30473i
$708$	−56.0142			−2.10514
$709$	1.44196	−	6.31766i	0.0541541	−	0.237265i	−0.940606	−	0.339500i	$-0.889742\pi$
$709$	1.44196	−	6.31766i	0.0541541	−	0.237265i	0.994760	+	0.102235i	$0.0325994\pi$
$710$		0			0
$711$	−31.8208	+	90.9386i	−1.19337	+	3.41046i
$712$	9.52654	+	15.1614i	0.357022	+	0.568198i
$713$		−	3.68560i		−	0.138027i
$714$	−23.4262	+	14.7196i	−0.876702	+	0.550868i
$715$		0			0
$716$	−4.13253	−	18.1058i	−0.154440	−	0.676645i
$717$	4.73266	+	20.7351i	0.176744	+	0.774368i
$718$	−1.03948	−	9.22563i	−0.0387930	−	0.344297i
$719$	4.39780	+	9.13213i	0.164010	+	0.340571i	0.966735	−	0.255778i	$-0.0823317\pi$
$719$	4.39780	+	9.13213i	0.164010	+	0.340571i	−0.802725	+	0.596349i	$0.796617\pi$
$720$		0			0
$721$	−9.86491	−	12.3702i	−0.367388	−	0.460691i
$722$	8.04549	+	6.41607i	0.299422	+	0.238781i
$723$	−18.8301	−	9.06809i	−0.700298	−	0.337246i
$724$	16.6877			0.620194
$725$		0			0
$726$	12.8149			0.475604
$727$	−8.12829	−	3.91438i	−0.301461	−	0.145176i	0.277038	−	0.960859i	$-0.410647\pi$
$727$	−8.12829	−	3.91438i	−0.301461	−	0.145176i	−0.578499	+	0.815683i	$0.696362\pi$
$728$	10.0030	+	7.97709i	0.370734	+	0.295651i
$729$	1.28795	+	1.61504i	0.0477020	+	0.0598164i
$730$		0			0
$731$	−19.3629	−	40.2075i	−0.716163	−	1.48713i
$732$	−9.34818	−	82.9674i	−0.345519	−	3.06656i
$733$	10.8479	+	47.5277i	0.400676	+	1.75548i	0.624674	+	0.780886i	$0.285232\pi$
$733$	10.8479	+	47.5277i	0.400676	+	1.75548i	−0.223998	+	0.974590i	$0.571911\pi$
$734$	0.238973	+	1.04701i	0.00882065	+	0.0386458i
$735$		0			0
$736$	6.05723	−	3.80601i	0.223273	−	0.140291i
$737$		−	1.99319i		−	0.0734201i
$738$	8.72277	+	13.8822i	0.321090	+	0.511011i
$739$	7.43283	−	21.2418i	0.273421	−	0.781392i	−0.722517	−	0.691353i	$-0.757015\pi$
$739$	7.43283	−	21.2418i	0.273421	−	0.781392i	0.995938	−	0.0900393i	$-0.0286993\pi$
$740$		0			0
$741$	11.1713	−	48.9449i	0.410390	−	1.79803i
$742$	2.87711			0.105622
$743$	3.64293	−	15.9607i	0.133646	−	0.585542i	−0.863107	−	0.505021i	$-0.831485\pi$
$743$	3.64293	−	15.9607i	0.133646	−	0.585542i	0.996753	−	0.0805206i	$-0.0256583\pi$
$744$	−10.9356	−	1.23214i	−0.400917	−	0.0451725i
$745$		0			0
$746$	−0.766843	+	1.22042i	−0.0280761	+	0.0446829i
$747$	−43.1104	+	4.85738i	−1.57733	+	0.177722i
$748$	10.8488	+	3.79616i	0.396672	+	0.138801i
$749$	−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	$0.777414\pi$
$752$	−10.5462	+	21.8995i	−0.384581	+	0.798591i
$753$	−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
$757$	−4.90448	+	6.15003i	−0.178256	+	0.223527i	−0.862930	−	0.505323i	$-0.831373\pi$
$757$	−4.90448	+	6.15003i	−0.178256	+	0.223527i	0.684674	+	0.728850i	$0.259945\pi$
$758$	−9.91803	−	1.11749i	−0.360239	−	0.0405892i
$759$	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	$0.347043\pi$
$762$	15.9616	−	3.64312i	0.578227	−	0.131976i
$763$	−5.98017	−	3.75759i	−0.216497	−	0.136034i
$764$	−2.67406	+	23.7329i	−0.0967439	+	0.858626i
$765$		0			0
$766$	−5.12963	+	5.12963i	−0.185341	+	0.185341i
$767$	−20.1692	+	12.6731i	−0.728266	+	0.457600i
$768$	5.70232	+	11.8410i	0.205765	+	0.427275i
$769$	−22.2341	−	7.78004i	−0.801782	−	0.280556i	−0.101882	−	0.994797i	$-0.532486\pi$
$769$	−22.2341	−	7.78004i	−0.801782	−	0.280556i	−0.699900	+	0.714241i	$0.746772\pi$
$770$		0			0
$771$	58.9515	+	58.9515i	2.12308	+	2.12308i
$772$	−18.0121	−	4.11115i	−0.648270	−	0.147963i
$773$	−26.8528	+	21.4144i	−0.965829	+	0.770223i	−0.973250	−	0.229750i	$-0.926209\pi$
$773$	−26.8528	+	21.4144i	−0.965829	+	0.770223i	0.00742075	+	0.999972i	$0.497638\pi$
$774$	−18.4587	+	4.21307i	−0.663483	+	0.151436i
$775$		0			0
$776$	6.23974	+	4.97603i	0.223994	+	0.178629i
$777$	11.8314	−	33.8121i	0.424448	−	1.21300i
$778$	−3.99627	−	11.4207i	−0.143273	−	0.409451i
$779$	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
$783$	−21.3169	−	58.1915i	−0.761804	−	2.07959i
$784$		−	13.0062i		−	0.464507i
$785$		0			0
$786$	2.45781	−	0.276929i	0.0876673	−	0.00987774i
$787$	0.757338	−	6.72156i	0.0269962	−	0.239598i	−0.972966	−	0.230947i	$-0.925818\pi$
$787$	0.757338	−	6.72156i	0.0269962	−	0.239598i	0.999963	−	0.00865096i	$-0.00275372\pi$
$788$	−28.3298	+	9.91303i	−1.00921	+	0.353137i
$789$	−4.51618	+	2.17488i	−0.160780	+	0.0774276i
$790$		0			0
$791$	39.9749	+	25.1179i	1.42134	+	0.893090i
$792$	5.42582	−	8.63515i	0.192798	−	0.306837i
$793$	−22.1373	−	27.7592i	−0.786117	−	0.985759i
$794$	−1.95566	−	3.11242i	−0.0694039	−	0.110456i
$795$		0			0
$796$	21.3963	+	4.88357i	0.758373	+	0.173094i
$797$	39.3580	−	18.9538i	1.39413	−	0.671379i	0.422171	−	0.906516i	$-0.361268\pi$
$797$	39.3580	−	18.9538i	1.39413	−	0.671379i	0.971962	+	0.235137i	$0.0755538\pi$
$798$	25.6441	−	12.3495i	0.907791	−	0.437169i
$799$	−50.6232	−	11.5544i	−1.79092	−	0.408766i
$800$		0			0
$801$	−40.6720	−	64.7291i	−1.43707	−	2.28709i
$802$	−4.56297	−	5.72178i	−0.161124	−	0.202043i
$803$	7.57817	−	12.0606i	0.267428	−	0.425609i
$804$	9.91646	+	6.23093i	0.349727	+	0.219748i
$805$		0			0
$806$	−2.01606	+	0.970885i	−0.0710128	+	0.0341980i
$807$	13.9041	−	4.86527i	0.489449	−	0.171266i
$808$	3.28325	−	29.1397i	0.115504	−	1.02513i
$809$	25.1469	−	2.83338i	0.884120	−	0.0996164i	0.341784	−	0.939778i	$-0.388969\pi$
$809$	25.1469	−	2.83338i	0.884120	−	0.0996164i	0.542335	+	0.840162i	$0.317540\pi$
$810$		0			0
$811$			16.4826i			0.578783i	0.957211	+	0.289392i	$0.0934530\pi$
$811$			16.4826i			0.578783i	−0.957211	+	0.289392i	$0.906547\pi$
$812$	−0.482463	−	33.1730i	−0.0169311	−	1.16414i
$813$	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
$817$	15.1634	+	43.3345i	0.530500	+	1.51608i
$818$	−2.27654	+	6.50598i	−0.0795973	+	0.227476i
$819$	−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	$0.279841\pi$
$822$	12.9254	−	10.3077i	0.450825	−	0.359521i
$823$	−32.1157	−	7.33020i	−1.11948	−	0.255515i	−0.377550	−	0.925989i	$-0.623233\pi$
$823$	−32.1157	−	7.33020i	−1.11948	−	0.255515i	−0.741933	+	0.670475i	$0.766091\pi$
$824$	5.21933	+	5.21933i	0.181824	+	0.181824i
$825$		0			0
$826$	−12.7470	−	4.46036i	−0.443524	−	0.155196i
$827$	3.98714	+	8.27938i	0.138646	+	0.287902i	0.958718	−	0.284359i	$-0.0917807\pi$
$827$	3.98714	+	8.27938i	0.138646	+	0.287902i	−0.820071	+	0.572261i	$0.806066\pi$
$828$	−16.9927	+	10.6772i	−0.590538	+	0.371060i
$829$	21.1823	−	21.1823i	0.735693	−	0.735693i	−0.236048	−	0.971741i	$-0.575852\pi$
$829$	21.1823	−	21.1823i	0.735693	−	0.735693i	0.971741	+	0.236048i	$0.0758523\pi$
$830$		0			0
$831$	1.22555	−	10.8771i	0.0425140	−	0.377322i
$832$	8.74588	+	5.49540i	0.303209	+	0.190519i
$833$	27.0879	−	6.18265i	0.938542	−	0.214216i
$834$	7.27697	−	9.12504i	0.251981	−	0.315974i
$835$		0			0
$836$	−10.6535	−	5.13045i	−0.368458	−	0.177440i
$837$	25.7696	+	2.90354i	0.890729	+	0.100361i
$838$	−0.833428	+	1.04509i	−0.0287903	+	0.0361019i
$839$	4.98865	+	14.2567i	0.172227	+	0.492197i	0.997350	−	0.0727568i	$-0.0231797\pi$
$839$	4.98865	+	14.2567i	0.172227	+	0.492197i	−0.825123	+	0.564954i	$0.808894\pi$
$840$		0			0
$841$	−0.843366	−	28.9877i	−0.0290816	−	0.999577i
$842$	−1.84067	+	1.84067i	−0.0634338	+	0.0634338i
$843$	−6.03950	+	12.5412i	−0.208011	+	0.431940i
$844$	−1.51538	−	13.4493i	−0.0521614	−	0.462945i
$845$		0			0
$846$	−9.55831	+	19.8480i	−0.328622	+	0.682390i
$847$	−31.9125	−	11.1667i	−1.09653	−	0.383691i
$848$	6.28287	−	0.707910i	0.215755	−	0.0243097i
$849$	29.1907	−	46.4568i	1.00182	−	1.59439i
$850$		0			0
$851$	−5.56171	−	0.626654i	−0.190653	−	0.0214814i
$852$	8.16791	−	35.7859i	0.279828	−	1.22601i
$853$	41.9677			1.43695			0.718474	−	0.695554i	$-0.244841\pi$
$853$	41.9677			1.43695			0.718474	+	0.695554i	$0.244841\pi$
$854$	4.47928	−	19.6250i	0.153278	−	0.671554i
$855$		0			0
$856$	6.42091	−	18.3499i	0.219462	−	0.627187i
$857$	15.1697	+	24.1425i	0.518189	+	0.824692i	0.998630	−	0.0523346i	$-0.0166662\pi$
$857$	15.1697	+	24.1425i	0.518189	+	0.824692i	−0.480441	+	0.877027i	$0.659523\pi$
$858$		−	3.00277i		−	0.102513i
$859$	−13.3099	+	8.36320i	−0.454130	+	0.285349i	−0.739610	−	0.673036i	$-0.764990\pi$
$859$	−13.3099	+	8.36320i	−0.454130	+	0.285349i	0.285480	+	0.958385i	$0.407847\pi$
$860$		0			0
$861$	−13.9379	−	61.0658i	−0.475001	−	2.08112i
$862$	3.31849	+	14.5392i	0.113028	+	0.495208i
$863$	2.26364	+	20.0904i	0.0770552	+	0.683884i	0.971555	+	0.236815i	$0.0761035\pi$
$863$	2.26364	+	20.0904i	0.0770552	+	0.683884i	−0.894500	+	0.447069i	$0.852468\pi$
$864$	21.8396	+	45.3505i	0.743000	+	1.54286i
$865$		0			0
$866$	−7.19161	−	9.01800i	−0.244381	−	0.306444i
$867$	−60.1610	−	47.9768i	−2.04318	−	1.62938i
$868$	12.5079	+	6.02349i	0.424546	+	0.204451i
$869$	13.9735			0.474018
$870$		0			0
$871$	4.98038			0.168754
$872$	2.96857	+	1.42959i	0.100528	+	0.0484119i
$873$	−26.6395	−	21.2443i	−0.901612	−	0.719011i
$874$	−2.77268	−	3.47684i	−0.0937875	−	0.117606i
$875$		0			0
$876$	36.3133	+	75.4054i	1.22691	+	2.54771i
$877$	2.72318	+	24.1689i	0.0919553	+	0.816126i	0.952040	+	0.305974i	$0.0989821\pi$
$877$	2.72318	+	24.1689i	0.0919553	+	0.816126i	−0.860084	+	0.510152i	$0.829589\pi$
$878$	3.15132	+	13.8068i	0.106352	+	0.465958i
$879$	−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	$0.196954\pi$
$882$		−	11.7878i		−	0.396917i
$883$	4.81671	+	7.66575i	0.162095	+	0.257973i	0.917889	−	0.396836i	$-0.129892\pi$
$883$	4.81671	+	7.66575i	0.162095	+	0.257973i	−0.755794	+	0.654809i	$0.772749\pi$
$884$	−9.48545	+	27.1079i	−0.319030	+	0.911736i
$885$		0			0
$886$	1.41070	−	6.18068i	0.0473934	−	0.207644i
$887$	1.17437			0.0394316			0.0197158	−	0.999806i	$-0.493724\pi$
$887$	1.17437			0.0394316			0.0197158	+	0.999806i	$0.493724\pi$
$888$	−3.71870	+	16.2927i	−0.124791	+	0.546747i
$889$	−42.9232	−	4.83628i	−1.43960	−	0.162204i
$890$		0			0
$891$	−8.13587	+	12.9482i	−0.272562	+	0.433780i
$892$	−20.0779	+	2.26223i	−0.672257	+	0.0757452i
$893$	50.4213	+	17.6432i	1.68728	+	0.590406i
$894$	−4.86481	+	10.1019i	−0.162704	+	0.337858i
$895$		0			0
$896$	3.94840	+	35.0430i	0.131907	+	1.17071i
$897$	−5.36195	+	11.1342i	−0.179030	+	0.371760i
$898$	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
$902$	1.48259	−	1.85911i	0.0493649	−	0.0619016i
$903$	71.8782	+	8.09873i	2.39196	+	0.269509i
$904$	−19.8437	−	9.55620i	−0.659990	−	0.317834i
$905$		0			0
$906$	1.55875	−	1.95461i	0.0517861	−	0.0649377i
$907$	10.1261	−	2.31122i	0.336232	−	0.0767427i	−0.0510717	−	0.998695i	$-0.516264\pi$
$907$	10.1261	−	2.31122i	0.336232	−	0.0767427i	0.387304	+	0.921952i	$0.373407\pi$
$908$	−5.85366	−	3.67810i	−0.194260	−	0.122062i
$909$	−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	$0.0531209\pi$
$912$	52.9616	−	33.2780i	1.75373	−	1.10194i
$913$	2.73005	+	5.66900i	0.0903514	+	0.187617i
$914$	10.3446	+	3.61975i	0.342170	+	0.119731i
$915$		0			0
$916$	−11.1550	−	11.1550i	−0.368570	−	0.368570i
$917$	−6.36193	−	1.45207i	−0.210089	−	0.0479516i
$918$	−23.7797	+	18.9637i	−0.784846	+	0.625894i
$919$	−18.3243	+	4.18239i	−0.604461	+	0.137964i	−0.513789	−	0.857916i	$-0.671759\pi$
$919$	−18.3243	+	4.18239i	−0.604461	+	0.137964i	−0.0906722	+	0.995881i	$0.528902\pi$
$920$		0			0
$921$	23.4605	+	18.7091i	0.773048	+	0.616486i
$922$	5.31596	−	15.1921i	0.175072	−	0.500326i
$923$	−5.15547	−	14.7335i	−0.169694	−	0.484959i
$924$	−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
$928$	2.97733	+	23.3652i	0.0977355	+	0.767001i
$929$		−	30.7214i		−	1.00794i	−0.863722	−	0.503968i	$-0.831873\pi$
$929$		−	30.7214i		−	1.00794i	0.863722	−	0.503968i	$-0.168127\pi$
$930$		0			0
$931$	−28.4042	+	3.20038i	−0.930910	+	0.104888i
$932$	−0.456509	+	4.05163i	−0.0149535	+	0.132716i
$933$	65.3932	−	22.8821i	2.14088	−	0.749125i
$934$	6.89563	−	3.32076i	0.225632	−	0.108659i
$935$		0			0
$936$	21.5766	+	13.5575i	0.705254	+	0.443140i
$937$	8.45546	−	13.4568i	0.276228	−	0.439614i	−0.679582	−	0.733599i	$-0.737839\pi$
$937$	8.45546	−	13.4568i	0.276228	−	0.439614i	0.955810	+	0.293985i	$0.0949817\pi$
$938$	1.76049	+	2.20759i	0.0574822	+	0.0720803i
$939$	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	$0.736970\pi$
$942$	10.9883	−	5.29169i	0.358018	−	0.172412i
$943$	−8.81716	+	4.24612i	−0.287126	+	0.138273i
$944$	−28.9336	−	6.60391i	−0.941709	−	0.214939i
$945$		0			0
$946$	1.46097	+	2.32512i	0.0475002	+	0.0755961i
$947$	−3.42546	−	4.29539i	−0.111312	−	0.139581i	0.723054	−	0.690791i	$-0.242738\pi$
$947$	−3.42546	−	4.29539i	−0.111312	−	0.139581i	−0.834367	+	0.551210i	$0.814166\pi$
$948$	−43.6826	+	69.5205i	−1.41875	+	2.25792i
$949$	30.1358	+	18.9355i	0.978248	+	0.614674i
$950$		0			0
$951$	61.8572	−	29.7889i	2.00586	−	0.965970i
$952$	−32.1419	+	11.2469i	−1.04173	+	0.364515i
$953$	2.34005	−	20.7685i	0.0758016	−	0.672758i	−0.897146	−	0.441734i	$-0.854364\pi$
$953$	2.34005	−	20.7685i	0.0758016	−	0.672758i	0.972948	−	0.231025i	$-0.0742078\pi$
$954$	5.69433	−	0.641597i	0.184361	−	0.0207725i
$955$		0			0
$956$			12.5169i			0.404824i
$957$	−12.5826	+	10.3372i	−0.406739	+	0.334155i
$958$	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
$962$	1.12232	+	3.20740i	0.0361849	+	0.103411i
$963$	−27.4130	+	78.3419i	−0.883372	+	2.52453i
$964$	−9.61648	−	7.66889i	−0.309726	−	0.246998i
$965$		0			0
$966$	−6.83069	+	1.55906i	−0.219774	+	0.0501620i
$967$	−6.76637	+	5.39600i	−0.217592	+	0.173524i	−0.726220	−	0.687463i	$-0.758724\pi$
$967$	−6.76637	+	5.39600i	−0.217592	+	0.173524i	0.508628	+	0.860987i	$0.330153\pi$
$968$	15.3773	+	3.50977i	0.494246	+	0.112808i
$969$	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	$0.756395\pi$
$972$	−11.5352	−	23.9530i	−0.369990	−	0.768293i
$973$	−26.0730	+	16.3828i	−0.835863	+	0.525207i
$974$	5.88173	−	5.88173i	0.188463	−	0.188463i
$975$		0			0
$976$	4.95289	−	43.9582i	0.158538	−	1.40707i
$977$	−33.6606	−	21.1503i	−1.07690	−	0.676659i	−0.127850	−	0.991794i	$-0.540808\pi$
$977$	−33.6606	−	21.1503i	−1.07690	−	0.676659i	−0.949047	+	0.315134i	$0.897950\pi$
$978$	−26.1720	+	5.97359i	−0.836889	+	0.191014i
$979$	−6.91293	+	8.66854i	−0.220938	+	0.277048i
$980$		0			0
$981$	−12.6738	−	6.10339i	−0.404644	−	0.194866i
$982$	4.12364	+	0.464623i	0.131591	+	0.0148267i
$983$	8.51823	−	10.6815i	0.271689	−	0.340688i	−0.627204	−	0.778855i	$-0.715801\pi$
$983$	8.51823	−	10.6815i	0.271689	−	0.340688i	0.898893	+	0.438167i	$0.144372\pi$
$984$	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
$988$	12.8194	−	26.6198i	0.407840	−	0.846889i
$989$	−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	$0.974870\pi$
$992$	−9.30316	−	3.25532i	−0.295376	−	0.103356i
$993$	34.6550	−	3.90468i	1.09974	−	0.123911i
$994$	4.70834	−	7.49328i	0.149340	−	0.237673i
$995$		0			0
$996$	−36.7387	−	4.13945i	−1.16411	−	0.131164i
$997$	2.31966	−	10.1631i	0.0734642	−	0.321868i	−0.924821	−	0.380402i	$-0.875786\pi$
$997$	2.31966	−	10.1631i	0.0734642	−	0.321868i	0.998285	+	0.0585343i	$0.0186427\pi$
$998$	0.639388			0.0202395
$999$	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.y.a.18.7	yes	120
5.2	odd	4		725.2.bd.a.482.4	yes	120
5.3	odd	4		725.2.bd.a.482.7	yes	120
5.4	even	2	inner	725.2.y.a.18.4	✓	120
29.21	odd	28		725.2.bd.a.543.4	yes	120
145.79	odd	28		725.2.bd.a.543.7	yes	120
145.108	even	28	inner	725.2.y.a.282.4	yes	120
145.137	even	28	inner	725.2.y.a.282.7	yes	120

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

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.y (of order \(28\), degree \(12\), minimal)

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

Varieties

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Database

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