LMFDB - Embedded newform 925.2.bb.e.176.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(151,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			176.3
Character	$\chi$	$=$	925.176
Dual form			925.2.bb.e.226.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.22054 + 0.391541i) q^{2} +(-0.457886 + 2.59680i) q^{3} +(2.89811 - 1.05483i) q^{4} -5.94558i q^{6} +(0.761600 + 0.639059i) q^{7} +(-2.11694 + 1.22222i) q^{8} +(-3.71464 - 1.35202i) q^{9} +(-2.23710 - 3.87477i) q^{11} +(1.41217 + 8.00880i) q^{12} +(0.156821 + 0.430863i) q^{13} +(-1.94138 - 1.12086i) q^{14} +(-0.502918 + 0.421999i) q^{16} +(1.31622 - 3.61628i) q^{17} +(8.77787 + 1.54777i) q^{18} +(6.33129 + 1.11638i) q^{19} +(-2.00823 + 1.68511i) q^{21} +(6.48469 + 7.72816i) q^{22} +(-1.59935 - 0.923384i) q^{23} +(-2.20453 - 6.05691i) q^{24} +(-0.516929 - 0.895348i) q^{26} +(1.25651 - 2.17633i) q^{27} +(2.88130 + 1.04871i) q^{28} +(6.71853 - 3.87895i) q^{29} -1.28733i q^{31} +(4.09402 - 4.87906i) q^{32} +(11.0863 - 4.03509i) q^{33} +(-1.50679 + 8.54544i) q^{34} -12.1916 q^{36} +(-5.40445 + 2.79140i) q^{37} -14.4960 q^{38} +(-1.19067 + 0.209948i) q^{39} +(10.2048 - 3.71426i) q^{41} +(3.79957 - 4.52816i) q^{42} -4.21419i q^{43} +(-10.5706 - 8.86975i) q^{44} +(3.91296 + 1.42420i) q^{46} +(6.11134 - 10.5851i) q^{47} +(-0.865567 - 1.49921i) q^{48} +(-1.04390 - 5.92024i) q^{49} +(8.78807 + 5.07379i) q^{51} +(0.908971 + 1.08327i) q^{52} +(-2.19000 + 1.83762i) q^{53} +(-1.93800 + 5.32461i) q^{54} +(-2.39333 - 0.422009i) q^{56} +(-5.79802 + 15.9299i) q^{57} +(-13.4000 + 11.2439i) q^{58} +(4.99958 + 5.95827i) q^{59} +(-0.980592 - 2.69415i) q^{61} +(0.504044 + 2.85858i) q^{62} +(-1.96505 - 3.40357i) q^{63} +(-6.52407 + 11.3000i) q^{64} +(-23.0377 + 13.3008i) q^{66} +(-1.35393 - 1.13608i) q^{67} -11.8687i q^{68} +(3.13016 - 3.73038i) q^{69} +(-1.98450 + 11.2547i) q^{71} +(9.51611 - 1.67795i) q^{72} +12.7316 q^{73} +(10.9079 - 8.31448i) q^{74} +(19.5263 - 3.44302i) q^{76} +(0.772428 - 4.38066i) q^{77} +(2.56173 - 0.932395i) q^{78} +(-9.83583 + 11.7219i) q^{79} +(-4.00843 - 3.36347i) q^{81} +(-21.2060 + 12.2433i) q^{82} +(2.25275 + 0.819933i) q^{83} +(-4.04259 + 7.00196i) q^{84} +(1.65003 + 9.35777i) q^{86} +(6.99653 + 19.2228i) q^{87} +(9.47160 + 5.46843i) q^{88} +(0.0452057 + 0.0538740i) q^{89} +(-0.155912 + 0.428364i) q^{91} +(-5.60910 - 0.989035i) q^{92} +(3.34295 + 0.589452i) q^{93} +(-9.42595 + 25.8976i) q^{94} +(10.7954 + 12.8654i) q^{96} +(11.3598 + 6.55858i) q^{97} +(4.63604 + 12.7374i) q^{98} +(3.07125 + 17.4179i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) $ 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.22054	+	0.391541i	−1.57016	+	0.276861i	−0.889916	−	0.456125i	$-0.849237\pi$
$2$	−2.22054	+	0.391541i	−1.57016	+	0.276861i	−0.680243	+	0.732986i	$0.738126\pi$
$3$	−0.457886	+	2.59680i	−0.264361	+	1.49926i	0.506489	+	0.862246i	$0.330943\pi$
$3$	−0.457886	+	2.59680i	−0.264361	+	1.49926i	−0.770850	+	0.637017i	$0.780168\pi$
$4$	2.89811	−	1.05483i	1.44905	−	0.527413i
$5$		0			0
$5$		0			0
$6$		−	5.94558i		−	2.42727i
$7$	0.761600	+	0.639059i	0.287858	+	0.241541i	0.775269	−	0.631631i	$-0.217614\pi$
$7$	0.761600	+	0.639059i	0.287858	+	0.241541i	−0.487411	+	0.873173i	$0.662059\pi$
$8$	−2.11694	+	1.22222i	−0.748451	+	0.432119i
$9$	−3.71464	−	1.35202i	−1.23821	−	0.450672i
$10$		0			0
$11$	−2.23710	−	3.87477i	−0.674510	−	1.16829i	−0.976612	−	0.215010i	$-0.931022\pi$
$11$	−2.23710	−	3.87477i	−0.674510	−	1.16829i	0.302102	−	0.953276i	$-0.402312\pi$
$12$	1.41217	+	8.00880i	0.407658	+	2.31194i
$13$	0.156821	+	0.430863i	0.0434945	+	0.119500i	0.959538	−	0.281578i	$-0.0908578\pi$
$13$	0.156821	+	0.430863i	0.0434945	+	0.119500i	−0.916044	+	0.401078i	$0.868636\pi$
$14$	−1.94138	−	1.12086i	−0.518856	−	0.299562i
$15$		0			0
$16$	−0.502918	+	0.421999i	−0.125730	+	0.105500i
$17$	1.31622	−	3.61628i	0.319229	−	0.877076i	−0.671473	−	0.741029i	$-0.734338\pi$
$17$	1.31622	−	3.61628i	0.319229	−	0.877076i	0.990702	−	0.136047i	$-0.0434397\pi$
$18$	8.77787	+	1.54777i	2.06896	+	0.364814i
$19$	6.33129	+	1.11638i	1.45250	+	0.256114i	0.843530	−	0.537081i	$-0.180473\pi$
$19$	6.33129	+	1.11638i	1.45250	+	0.256114i	0.608967	+	0.793196i	$0.291584\pi$
$20$		0			0
$21$	−2.00823	+	1.68511i	−0.438232	+	0.367721i
$22$	6.48469	+	7.72816i	1.38254	+	1.64765i
$23$	−1.59935	−	0.923384i	−0.333487	−	0.192539i	0.323901	−	0.946091i	$-0.395006\pi$
$23$	−1.59935	−	0.923384i	−0.333487	−	0.192539i	−0.657388	+	0.753552i	$0.728339\pi$
$24$	−2.20453	−	6.05691i	−0.449998	−	1.23636i
$25$		0			0
$26$	−0.516929	−	0.895348i	−0.101378	−	0.175592i
$27$	1.25651	−	2.17633i	0.241815	−	0.418835i
$28$	2.88130	+	1.04871i	0.544514	+	0.198187i
$29$	6.71853	−	3.87895i	1.24760	−	0.720302i	0.276970	−	0.960879i	$-0.410670\pi$
$29$	6.71853	−	3.87895i	1.24760	−	0.720302i	0.970630	+	0.240576i	$0.0773363\pi$
$30$		0			0
$31$		−	1.28733i		−	0.231212i	−0.993295	−	0.115606i	$-0.963119\pi$
$31$		−	1.28733i		−	0.231212i	0.993295	−	0.115606i	$-0.0368810\pi$
$32$	4.09402	−	4.87906i	0.723728	−	0.862505i
$33$	11.0863	−	4.03509i	1.92988	−	0.702420i
$34$	−1.50679	+	8.54544i	−0.258413	+	1.46553i
$35$		0			0
$36$	−12.1916			−2.03193
$37$	−5.40445	+	2.79140i	−0.888486	+	0.458903i
$37$	−5.40445	+	2.79140i	−0.888486	+	0.458903i
$38$	−14.4960			−2.35156
$39$	−1.19067	+	0.209948i	−0.190660	+	0.0336185i
$40$		0			0
$41$	10.2048	−	3.71426i	1.59373	−	0.580070i	0.615598	−	0.788060i	$-0.288915\pi$
$41$	10.2048	−	3.71426i	1.59373	−	0.580070i	0.978131	+	0.207990i	$0.0666923\pi$
$42$	3.79957	−	4.52816i	0.586287	−	0.698710i
$43$		−	4.21419i		−	0.642658i	−0.946968	−	0.321329i	$-0.895871\pi$
$43$		−	4.21419i		−	0.642658i	0.946968	−	0.321329i	$-0.104129\pi$
$44$	−10.5706	−	8.86975i	−1.59357	−	1.33716i
$45$		0			0
$46$	3.91296	+	1.42420i	0.576935	+	0.209987i
$47$	6.11134	−	10.5851i	0.891430	−	1.54400i	0.0532682	−	0.998580i	$-0.483036\pi$
$47$	6.11134	−	10.5851i	0.891430	−	1.54400i	0.838162	−	0.545422i	$-0.183630\pi$
$48$	−0.865567	−	1.49921i	−0.124934	−	0.216392i
$49$	−1.04390	−	5.92024i	−0.149128	−	0.845749i
$50$		0			0
$51$	8.78807	+	5.07379i	1.23058	+	0.710473i
$52$	0.908971	+	1.08327i	0.126052	+	0.150223i
$53$	−2.19000	+	1.83762i	−0.300819	+	0.252417i	−0.780685	−	0.624925i	$-0.785130\pi$
$53$	−2.19000	+	1.83762i	−0.300819	+	0.252417i	0.479866	+	0.877342i	$0.340685\pi$
$54$	−1.93800	+	5.32461i	−0.263728	+	0.724587i
$55$		0			0
$56$	−2.39333	−	0.422009i	−0.319822	−	0.0563933i
$57$	−5.79802	+	15.9299i	−0.767966	+	2.10997i
$58$	−13.4000	+	11.2439i	−1.75951	+	1.47640i
$59$	4.99958	+	5.95827i	0.650890	+	0.775700i	0.986048	−	0.166462i	$-0.0532342\pi$
$59$	4.99958	+	5.95827i	0.650890	+	0.775700i	−0.335158	+	0.942162i	$0.608790\pi$
$60$		0			0
$61$	−0.980592	−	2.69415i	−0.125552	−	0.344951i	0.860953	−	0.508685i	$-0.169868\pi$
$61$	−0.980592	−	2.69415i	−0.125552	−	0.344951i	−0.986504	+	0.163734i	$0.947646\pi$
$62$	0.504044	+	2.85858i	0.0640137	+	0.363040i
$63$	−1.96505	−	3.40357i	−0.247573	−	0.428809i
$64$	−6.52407	+	11.3000i	−0.815509	+	1.41250i
$65$		0			0
$66$	−23.0377	+	13.3008i	−2.83575	+	1.63722i
$67$	−1.35393	−	1.13608i	−0.165409	−	0.138794i	0.556326	−	0.830964i	$-0.312211\pi$
$67$	−1.35393	−	1.13608i	−0.165409	−	0.138794i	−0.721735	+	0.692170i	$0.756655\pi$
$68$		−	11.8687i		−	1.43930i
$69$	3.13016	−	3.73038i	0.376828	−	0.449086i
$70$		0			0
$71$	−1.98450	+	11.2547i	−0.235517	+	1.33569i	0.606004	+	0.795461i	$0.292771\pi$
$71$	−1.98450	+	11.2547i	−0.235517	+	1.33569i	−0.841521	+	0.540224i	$0.818340\pi$
$72$	9.51611	−	1.67795i	1.12148	−	0.197748i
$73$	12.7316			1.49012			0.745059	−	0.666999i	$-0.232422\pi$
$73$	12.7316			1.49012			0.745059	+	0.666999i	$0.232422\pi$
$74$	10.9079	−	8.31448i	1.26801	−	0.966539i
$75$		0			0
$76$	19.5263	−	3.44302i	2.23983	−	0.394942i
$77$	0.772428	−	4.38066i	0.0880264	−	0.499222i
$78$	2.56173	−	0.932395i	0.290059	−	0.105573i
$79$	−9.83583	+	11.7219i	−1.10662	+	1.31881i	−0.163429	+	0.986555i	$0.552255\pi$
$79$	−9.83583	+	11.7219i	−1.10662	+	1.31881i	−0.943188	+	0.332260i	$0.892189\pi$
$80$		0			0
$81$	−4.00843	−	3.36347i	−0.445381	−	0.373719i
$82$	−21.2060	+	12.2433i	−2.34181	+	1.35204i
$83$	2.25275	+	0.819933i	0.247271	+	0.0899993i	0.462682	−	0.886524i	$-0.346887\pi$
$83$	2.25275	+	0.819933i	0.247271	+	0.0899993i	−0.215411	+	0.976523i	$0.569109\pi$
$84$	−4.04259	+	7.00196i	−0.441082	+	0.763977i
$85$		0			0
$86$	1.65003	+	9.35777i	0.177927	+	1.00907i
$87$	6.99653	+	19.2228i	0.750107	+	2.06090i
$88$	9.47160	+	5.46843i	1.00968	+	0.582937i
$89$	0.0452057	+	0.0538740i	0.00479179	+	0.00571064i	0.768435	−	0.639928i	$-0.221036\pi$
$89$	0.0452057	+	0.0538740i	0.00479179	+	0.00571064i	−0.763643	+	0.645638i	$0.776591\pi$
$90$		0			0
$91$	−0.155912	+	0.428364i	−0.0163440	+	0.0449047i
$92$	−5.60910	−	0.989035i	−0.584789	−	0.103114i
$93$	3.34295	+	0.589452i	0.346648	+	0.0611234i
$94$	−9.42595	+	25.8976i	−0.972212	+	2.67113i
$95$		0			0
$96$	10.7954	+	12.8654i	1.10180	+	1.31307i
$97$	11.3598	+	6.55858i	1.15341	+	0.665923i	0.949717	−	0.313111i	$-0.101371\pi$
$97$	11.3598	+	6.55858i	1.15341	+	0.665923i	0.203696	+	0.979034i	$0.434704\pi$
$98$	4.63604	+	12.7374i	0.468310	+	1.28667i
$99$	3.07125	+	17.4179i	0.308672	+	1.75057i
$100$		0			0
$101$	0.814832	−	1.41133i	0.0810789	−	0.140433i	−0.822635	−	0.568570i	$-0.807497\pi$
$101$	0.814832	−	1.41133i	0.0810789	−	0.140433i	0.903714	+	0.428137i	$0.140830\pi$
$102$	−21.5009	−	7.82567i	−2.12890	−	0.774857i
$103$	−5.36795	+	3.09919i	−0.528920	+	0.305372i	−0.740576	−	0.671972i	$-0.765447\pi$
$103$	−5.36795	+	3.09919i	−0.528920	+	0.305372i	0.211657	+	0.977344i	$0.432114\pi$
$104$	−0.858590	−	0.720442i	−0.0841916	−	0.0706452i
$105$		0			0
$106$	4.14347	−	4.93799i	0.402449	−	0.479620i
$107$	−3.05633	+	1.11241i	−0.295467	+	0.107541i	−0.485500	−	0.874236i	$-0.661363\pi$
$107$	−3.05633	+	1.11241i	−0.295467	+	0.107541i	0.190033	+	0.981778i	$0.439140\pi$
$108$	1.34584	−	7.63264i	0.129504	−	0.734452i
$109$	3.74867	−	0.660992i	0.359058	−	0.0633116i	0.00879045	−	0.999961i	$-0.497202\pi$
$109$	3.74867	−	0.660992i	0.359058	−	0.0633116i	0.350267	+	0.936650i	$0.386091\pi$
$110$		0			0
$111$	−4.77409	−	15.3124i	−0.453136	−	1.45339i
$112$	−0.652705			−0.0616748
$113$	−7.49985	+	1.32243i	−0.705526	+	0.124403i	−0.514889	−	0.857257i	$-0.672167\pi$
$113$	−7.49985	+	1.32243i	−0.705526	+	0.124403i	−0.190638	+	0.981660i	$0.561056\pi$
$114$	6.63751	−	37.6432i	0.621660	−	3.52561i
$115$		0			0
$116$	15.3794	−	18.3285i	1.42794	−	1.70176i
$117$		−	1.81253i		−	0.167568i
$118$	−13.4347	−	11.2730i	−1.23676	−	1.03777i
$119$	3.31344	−	1.91302i	0.303743	−	0.175366i
$120$		0			0
$121$	−4.50921	+	7.81017i	−0.409928	+	0.710016i
$122$	3.23232	+	5.59854i	0.292640	+	0.506868i
$123$	4.97254	+	28.2007i	0.448358	+	2.54277i
$124$	−1.35791	−	3.73084i	−0.121944	−	0.335039i
$125$		0			0
$126$	5.69611	+	6.78836i	0.507450	+	0.604755i
$127$	6.99265	−	5.86753i	0.620497	−	0.520659i	−0.277463	−	0.960736i	$-0.589493\pi$
$127$	6.99265	−	5.86753i	0.620497	−	0.520659i	0.897960	+	0.440078i	$0.145049\pi$
$128$	5.70577	−	15.6765i	0.504324	−	1.38562i
$129$	10.9434	+	1.92962i	0.963513	+	0.169893i
$130$		0			0
$131$	1.32337	−	3.63592i	0.115623	−	0.317672i	−0.868360	−	0.495935i	$-0.834825\pi$
$131$	1.32337	−	3.63592i	0.115623	−	0.317672i	0.983983	+	0.178263i	$0.0570477\pi$
$132$	27.8731	−	23.3883i	2.42604	−	2.03569i
$133$	4.10848	+	4.89630i	0.356250	+	0.424563i
$134$	3.45127	+	1.99259i	0.298145	+	0.172134i
$135$		0			0
$136$	1.63352	+	9.26414i	0.140073	+	0.794393i
$137$	−8.51914	−	14.7556i	−0.727839	−	1.26065i	−0.957795	−	0.287453i	$-0.907191\pi$
$137$	−8.51914	−	14.7556i	−0.727839	−	1.26065i	0.229956	−	0.973201i	$-0.426142\pi$
$138$	−5.49006	+	9.50906i	−0.467345	+	0.809465i
$139$	14.2563	+	5.18888i	1.20921	+	0.440115i	0.866428	−	0.499301i	$-0.166410\pi$
$139$	14.2563	+	5.18888i	1.20921	+	0.440115i	0.342778	+	0.939416i	$0.388632\pi$
$140$		0			0
$141$	24.6892	+	20.7167i	2.07921	+	1.74466i
$142$		−	25.7685i		−	2.16244i
$143$	1.31867	−	1.57153i	0.110273	−	0.131418i
$144$	2.43871	−	0.887617i	0.203226	−	0.0739681i
$145$		0			0
$146$	−28.2710	+	4.98493i	−2.33972	+	0.412556i
$147$	15.8517			1.30742
$148$	−12.7182	+	13.7905i	−1.04543	+	1.13357i
$149$	−20.4534			−1.67560			−0.837802	−	0.545974i	$-0.816160\pi$
$149$	−20.4534			−1.67560			−0.837802	+	0.545974i	$0.816160\pi$
$150$		0			0
$151$	−0.605408	+	3.43344i	−0.0492674	+	0.279409i	−0.999482	−	0.0321873i	$-0.989753\pi$
$151$	−0.605408	+	3.43344i	−0.0492674	+	0.279409i	0.950214	+	0.311597i	$0.100864\pi$
$152$	−14.7674	+	5.37490i	−1.19780	+	0.435962i
$153$	−9.77853	+	11.6536i	−0.790547	+	0.942138i
$154$			10.0299i			0.808230i
$155$		0			0
$156$	−3.22924	+	1.86440i	−0.258546	+	0.149272i
$157$	8.46721	+	3.08181i	0.675757	+	0.245955i	0.657025	−	0.753869i	$-0.271815\pi$
$157$	8.46721	+	3.08181i	0.675757	+	0.245955i	0.0187324	+	0.999825i	$0.494037\pi$
$158$	17.2512	−	29.8800i	1.37244	−	2.37713i
$159$	−3.76918	−	6.52840i	−0.298915	−	0.517736i
$160$		0			0
$161$	−0.627968	−	1.72533i	−0.0494908	−	0.135975i
$162$	10.2178	+	5.89926i	0.802788	+	0.463490i
$163$	−3.23664	−	3.85727i	−0.253513	−	0.302125i	0.624246	−	0.781228i	$-0.285406\pi$
$163$	−3.23664	−	3.85727i	−0.253513	−	0.302125i	−0.877759	+	0.479103i	$0.840962\pi$
$164$	25.6569	−	21.5287i	2.00346	−	1.68111i
$165$		0			0
$166$	−5.32335	−	0.938651i	−0.413172	−	0.0728534i
$167$	−5.30997	−	0.936291i	−0.410898	−	0.0724524i	−0.0356215	−	0.999365i	$-0.511341\pi$
$167$	−5.30997	−	0.936291i	−0.410898	−	0.0724524i	−0.375276	+	0.926913i	$0.622452\pi$
$168$	2.19174	−	6.02177i	0.169097	−	0.464589i
$169$	9.79753	−	8.22110i	0.753656	−	0.632392i
$170$		0			0
$171$	−22.0091	−	12.7069i	−1.68308	−	0.971724i
$172$	−4.44523	−	12.2132i	−0.338946	−	0.931246i
$173$	1.88053	+	10.6650i	0.142974	+	0.810847i	0.968971	+	0.247173i	$0.0795015\pi$
$173$	1.88053	+	10.6650i	0.142974	+	0.810847i	−0.825997	+	0.563674i	$0.809387\pi$
$174$	−23.0626	−	39.9456i	−1.74837	−	3.02827i
$175$		0			0
$176$	2.76022	+	1.00464i	0.208060	+	0.0757275i
$177$	−17.7617	+	10.2547i	−1.33505	+	0.770791i
$178$	−0.121475	−	0.101930i	−0.00910493	−	0.00763995i
$179$			14.8784i			1.11207i	0.831161	+	0.556033i	$0.187677\pi$
$179$			14.8784i			1.11207i	−0.831161	+	0.556033i	$0.812323\pi$
$180$		0			0
$181$	9.10190	−	3.31282i	0.676539	−	0.246240i	0.0191782	−	0.999816i	$-0.493895\pi$
$181$	9.10190	−	3.31282i	0.676539	−	0.246240i	0.657361	+	0.753576i	$0.271673\pi$
$182$	0.178486	−	1.01224i	0.0132303	−	0.0750326i
$183$	7.44518	−	1.31279i	0.550363	−	0.0970439i
$184$	4.51430			0.332799
$185$		0			0
$186$	−7.65395			−0.561215
$187$	−16.9567	+	2.98993i	−1.24000	+	0.218645i
$188$	6.54584	−	37.1233i	0.477404	−	2.70749i
$189$	2.34776	−	0.854515i	0.170774	−	0.0621568i
$190$		0			0
$191$		−	6.01672i		−	0.435355i	−0.976021	−	0.217677i	$-0.930152\pi$
$191$		−	6.01672i		−	0.435355i	0.976021	−	0.217677i	$-0.0698480\pi$
$192$	−26.3566	−	22.1158i	−1.90213	−	1.59607i
$193$	−2.39428	+	1.38234i	−0.172344	+	0.0995030i	−0.583691	−	0.811976i	$-0.698392\pi$
$193$	−2.39428	+	1.38234i	−0.172344	+	0.0995030i	0.411346	+	0.911479i	$0.365059\pi$
$194$	−27.7929	−	10.1158i	−1.99541	−	0.726270i
$195$		0			0
$196$	−9.27015	−	16.0564i	−0.662154	−	1.14688i
$197$	−2.77328	−	15.7281i	−0.197588	−	1.12058i	−0.908685	−	0.417483i	$-0.862912\pi$
$197$	−2.77328	−	15.7281i	−0.197588	−	1.12058i	0.711096	−	0.703094i	$-0.248199\pi$
$198$	−13.6397	−	37.4747i	−0.969330	−	2.66321i
$199$	7.86460	+	4.54063i	0.557507	+	0.321877i	0.752144	−	0.658999i	$-0.229020\pi$
$199$	7.86460	+	4.54063i	0.557507	+	0.321877i	−0.194637	+	0.980875i	$0.562353\pi$
$200$		0			0
$201$	3.57012	−	2.99569i	0.251817	−	0.211299i
$202$	−1.25677	+	3.45296i	−0.0884263	+	0.242949i
$203$	7.59571	+	1.33933i	0.533114	+	0.0940025i
$204$	30.8208	+	5.43453i	2.15788	+	0.380493i
$205$		0			0
$206$	10.7063	−	8.98364i	0.745943	−	0.625920i
$207$	4.69257	+	5.59238i	0.326156	+	0.388697i
$208$	−0.260692	−	0.150511i	−0.0180758	−	0.0104360i
$209$	−9.83801	−	27.0297i	−0.680509	−	1.86968i
$210$		0			0
$211$	−1.01424	−	1.75671i	−0.0698231	−	0.120937i	0.829000	−	0.559248i	$-0.188910\pi$
$211$	−1.01424	−	1.75671i	−0.0698231	−	0.120937i	−0.898823	+	0.438311i	$0.855577\pi$
$212$	−4.40847	+	7.63570i	−0.302775	+	0.524422i
$213$	−28.3175	−	10.3067i	−1.94028	−	0.706205i
$214$	6.35116	−	3.66684i	0.434156	−	0.250660i
$215$		0			0
$216$			6.14289i			0.417971i
$217$	0.822682	−	0.980434i	0.0558473	−	0.0665562i
$218$	−8.06527	+	2.93552i	−0.546249	+	0.198818i
$219$	−5.82961	+	33.0613i	−0.393928	+	2.23408i
$220$		0			0
$221$	1.76453			0.118695
$222$	16.5965	+	32.1326i	1.11388	+	2.15660i
$223$	15.4373			1.03376			0.516880	−	0.856058i	$-0.327093\pi$
$223$	15.4373			1.03376			0.516880	+	0.856058i	$0.327093\pi$
$224$	6.23602	−	1.09958i	0.416661	−	0.0734686i
$225$		0			0
$226$	16.1359	−	5.87300i	1.07335	−	0.390666i
$227$	−5.78477	+	6.89403i	−0.383949	+	0.457573i	−0.923057	−	0.384664i	$-0.874317\pi$
$227$	−5.78477	+	6.89403i	−0.383949	+	0.457573i	0.539108	+	0.842237i	$0.318762\pi$
$228$			52.2825i			3.46250i
$229$	−11.3105	−	9.49061i	−0.747417	−	0.627157i	0.187402	−	0.982283i	$-0.439993\pi$
$229$	−11.3105	−	9.49061i	−0.747417	−	0.627157i	−0.934818	+	0.355126i	$0.884438\pi$
$230$		0			0
$231$	11.0220	+	4.01168i	0.725195	+	0.263949i
$232$	−9.48182	+	16.4230i	−0.622512	+	1.07822i
$233$	−7.37735	−	12.7780i	−0.483307	−	0.837112i	0.516510	−	0.856281i	$-0.327231\pi$
$233$	−7.37735	−	12.7780i	−0.483307	−	0.837112i	−0.999816	+	0.0191698i	$0.993898\pi$
$234$	0.709678	+	4.02479i	0.0463931	+	0.263109i
$235$		0			0
$236$	20.7743	+	11.9940i	1.35229	+	0.780744i
$237$	−25.9357	−	30.9090i	−1.68470	−	2.00775i
$238$	−6.60861	+	5.54528i	−0.428372	+	0.359447i
$239$	2.49066	−	6.84304i	0.161108	−	0.442640i	−0.832704	−	0.553718i	$-0.813208\pi$
$239$	2.49066	−	6.84304i	0.161108	−	0.442640i	0.993812	+	0.111079i	$0.0354306\pi$
$240$		0			0
$241$	−14.2166	−	2.50678i	−0.915774	−	0.161476i	−0.304150	−	0.952624i	$-0.598372\pi$
$241$	−14.2166	−	2.50678i	−0.915774	−	0.161476i	−0.611624	+	0.791148i	$0.709484\pi$
$242$	6.95487	−	19.1083i	0.447076	−	1.22833i
$243$	16.3449	−	13.7150i	1.04853	−	0.879818i
$244$	−5.68372	−	6.77360i	−0.363863	−	0.433635i
$245$		0			0
$246$	−22.0834	−	60.6737i	−1.40799	−	3.86842i
$247$	0.511876	+	2.90299i	0.0325699	+	0.184713i
$248$	1.57340	+	2.72521i	0.0999110	+	0.173051i
$249$	−3.16070	+	5.47450i	−0.200301	+	0.346932i
$250$		0			0
$251$	−3.50298	+	2.02245i	−0.221106	+	0.127656i	−0.606462	−	0.795112i	$-0.707412\pi$
$251$	−3.50298	+	2.02245i	−0.221106	+	0.127656i	0.385356	+	0.922768i	$0.374079\pi$
$252$	−9.28510	−	7.79112i	−0.584906	−	0.490794i
$253$			8.26280i			0.519478i
$254$	−13.2301	+	15.7670i	−0.830129	+	0.989309i
$255$		0			0
$256$	−2.00034	+	11.3445i	−0.125021	+	0.709030i
$257$	4.36174	−	0.769093i	0.272078	−	0.0479747i	−0.0359444	−	0.999354i	$-0.511444\pi$
$257$	4.36174	−	0.769093i	0.272078	−	0.0479747i	0.308022	+	0.951379i	$0.400333\pi$
$258$	−25.0558			−1.55991
$259$	−5.89990	−	1.32783i	−0.366602	−	0.0825073i
$260$		0			0
$261$	−30.2013	+	5.32530i	−1.86941	+	0.329628i
$262$	−1.51498	+	8.59186i	−0.0935956	+	0.530807i
$263$	19.1430	−	6.96750i	1.18041	−	0.429634i	0.324064	−	0.946035i	$-0.394951\pi$
$263$	19.1430	−	6.96750i	1.18041	−	0.429634i	0.856347	+	0.516401i	$0.172729\pi$
$264$	−18.5373	+	22.0919i	−1.14089	+	1.35966i
$265$		0			0
$266$	−11.0401	−	9.26378i	−0.676915	−	0.567999i
$267$	−0.160599	+	0.0927220i	−0.00982851	+	0.00567449i
$268$	−5.12220	−	1.86433i	−0.312888	−	0.113882i
$269$	−1.97618	+	3.42284i	−0.120490	+	0.208694i	−0.919961	−	0.392010i	$-0.871780\pi$
$269$	−1.97618	+	3.42284i	−0.120490	+	0.208694i	0.799471	+	0.600704i	$0.205113\pi$
$270$		0			0
$271$	0.867241	+	4.91837i	0.0526811	+	0.298770i	0.999752	−	0.0222540i	$-0.00708424\pi$
$271$	0.867241	+	4.91837i	0.0526811	+	0.298770i	−0.947071	+	0.321024i	$0.895973\pi$
$272$	0.864114	+	2.37413i	0.0523946	+	0.143953i
$273$	−1.04099	−	0.601013i	−0.0630033	−	0.0363750i
$274$	24.6945	+	29.4298i	1.49185	+	1.77792i
$275$		0			0
$276$	5.13665	−	14.1128i	0.309190	−	0.849493i
$277$	24.8800	+	4.38701i	1.49489	+	0.263590i	0.860511	−	0.509431i	$-0.170144\pi$
$277$	24.8800	+	4.38701i	1.49489	+	0.263590i	0.634380	+	0.773021i	$0.281255\pi$
$278$	−33.6884	−	5.94018i	−2.02050	−	0.356268i
$279$	−1.74050	+	4.78198i	−0.104201	+	0.286290i
$280$		0			0
$281$	−17.4703	−	20.8203i	−1.04219	−	1.24204i	−0.969605	−	0.244674i	$-0.921319\pi$
$281$	−17.4703	−	20.8203i	−1.04219	−	1.24204i	−0.0725871	−	0.997362i	$-0.523126\pi$
$282$	−62.9348	−	36.3354i	−3.74771	−	2.16374i
$283$	3.50550	+	9.63127i	0.208380	+	0.572520i	0.999219	−	0.0395042i	$-0.0125779\pi$
$283$	3.50550	+	9.63127i	0.208380	+	0.572520i	−0.790839	+	0.612024i	$0.790356\pi$
$284$	6.12042	+	34.7106i	0.363180	+	2.05970i
$285$		0			0
$286$	−2.31284	+	4.00596i	−0.136761	+	0.236877i
$287$	10.1456	+	3.69271i	0.598878	+	0.217974i
$288$	−21.8044	+	12.5888i	−1.28483	+	0.741800i
$289$	1.67773	+	1.40778i	0.0986900	+	0.0828108i
$290$		0			0
$291$	−22.2328	+	26.4961i	−1.30331	+	1.55323i
$292$	36.8975	−	13.4296i	2.15926	−	0.785907i
$293$	0.127471	−	0.722926i	0.00744696	−	0.0422338i	−0.980858	−	0.194725i	$-0.937619\pi$
$293$	0.127471	−	0.722926i	0.00744696	−	0.0422338i	0.988305	+	0.152491i	$0.0487296\pi$
$294$	−35.1993	+	6.20658i	−2.05286	+	0.361975i
$295$		0			0
$296$	8.02920	−	12.5146i	0.466688	−	0.727398i
$297$	−11.2437			−0.652426
$298$	45.4175	−	8.00833i	2.63097	−	0.463910i
$299$	0.147040	−	0.833907i	0.00850356	−	0.0482261i
$300$		0			0
$301$	2.69311	−	3.20953i	0.155228	−	0.184994i
$302$		−	7.86113i		−	0.452357i
$303$	3.29184	+	2.76219i	0.189112	+	0.158683i
$304$	−3.65523	+	2.11035i	−0.209642	+	0.121037i
$305$		0			0
$306$	17.1508	−	29.7060i	0.980444	−	1.69818i
$307$	4.03299	+	6.98534i	0.230175	+	0.398674i	0.957859	−	0.287238i	$-0.0927369\pi$
$307$	4.03299	+	6.98534i	0.230175	+	0.398674i	−0.727685	+	0.685912i	$0.759404\pi$
$308$	−2.38225	−	13.5104i	−0.135741	−	0.769827i
$309$	−5.59006	−	15.3586i	−0.318008	−	0.873718i
$310$		0			0
$311$	15.4097	+	18.3646i	0.873805	+	1.04136i	0.998789	+	0.0492012i	$0.0156675\pi$
$311$	15.4097	+	18.3646i	0.873805	+	1.04136i	−0.124984	+	0.992159i	$0.539888\pi$
$312$	2.26398	−	1.89971i	0.128173	−	0.107550i
$313$	0.328171	−	0.901643i	0.0185493	−	0.0509639i	−0.930072	−	0.367376i	$-0.880256\pi$
$313$	0.328171	−	0.901643i	0.0185493	−	0.0509639i	0.948622	+	0.316412i	$0.102478\pi$
$314$	−20.0084	−	3.52803i	−1.12914	−	0.199098i
$315$		0			0
$316$	−16.1408	+	44.3464i	−0.907989	+	2.49468i
$317$	3.17291	−	2.66239i	0.178208	−	0.149535i	−0.549320	−	0.835612i	$-0.685113\pi$
$317$	3.17291	−	2.66239i	0.178208	−	0.149535i	0.727529	+	0.686077i	$0.240669\pi$
$318$	10.9257	+	13.0208i	0.612685	+	0.730170i
$319$	−30.0600	−	17.3552i	−1.68304	−	0.971703i
$320$		0			0
$321$	−1.48927	−	8.44605i	−0.0831227	−	0.471412i
$322$	2.06996	+	3.58528i	0.115355	+	0.199800i
$323$	12.3705	−	21.4263i	0.688312	−	1.19219i
$324$	−15.1647	−	5.51951i	−0.842486	−	0.306640i
$325$		0			0
$326$	8.69736	+	7.29795i	0.481702	+	0.404196i
$327$			10.0372i			0.555059i
$328$	−17.0634	+	20.3354i	−0.942169	+	1.12283i
$329$	11.4189	−	4.15615i	0.629546	−	0.229136i
$330$		0			0
$331$	8.04029	−	1.41772i	0.441934	−	0.0779250i	0.0517466	−	0.998660i	$-0.483521\pi$
$331$	8.04029	−	1.41772i	0.441934	−	0.0779250i	0.390188	+	0.920735i	$0.372410\pi$
$332$	7.39359			0.405776
$333$	23.8496	−	3.06213i	1.30695	−	0.167803i
$334$	12.1576			0.665234
$335$		0			0
$336$	0.298864	−	1.69494i	0.0163044	−	0.0924668i
$337$	22.9481	−	8.35241i	1.25006	−	0.454985i	0.369639	−	0.929176i	$-0.379481\pi$
$337$	22.9481	−	8.35241i	1.25006	−	0.454985i	0.880422	+	0.474191i	$0.157259\pi$
$338$	−18.5369	+	22.0914i	−1.00827	+	1.20161i
$339$		−	20.0811i		−	1.09066i
$340$		0			0
$341$	−4.98812	+	2.87989i	−0.270122	+	0.155955i
$342$	53.8473	+	19.5988i	2.91173	+	1.05978i
$343$	6.46804	−	11.2030i	0.349241	−	0.604904i
$344$	5.15065	+	8.92118i	0.277704	+	0.480998i
$345$		0			0
$346$	−8.35159	−	22.9458i	−0.448984	−	1.23357i
$347$	22.4263	+	12.9478i	1.20391	+	0.695076i	0.961422	−	0.275079i	$-0.0887041\pi$
$347$	22.4263	+	12.9478i	1.20391	+	0.695076i	0.242485	+	0.970155i	$0.422037\pi$
$348$	40.5534	+	48.3297i	2.17389	+	2.59074i
$349$	16.6941	−	14.0080i	0.893616	−	0.749833i	−0.0753162	−	0.997160i	$-0.523997\pi$
$349$	16.6941	−	14.0080i	0.893616	−	0.749833i	0.968932	+	0.247327i	$0.0795522\pi$
$350$		0			0
$351$	1.13475	+	0.200087i	0.0605684	+	0.0106799i
$352$	−28.0640	−	4.94843i	−1.49581	−	0.263752i
$353$	−2.45743	+	6.75174i	−0.130796	+	0.359359i	−0.987752	−	0.156030i	$-0.950130\pi$
$353$	−2.45743	+	6.75174i	−0.130796	+	0.359359i	0.856956	+	0.515389i	$0.172353\pi$
$354$	35.4254	−	29.7254i	1.88284	−	1.57989i
$355$		0			0
$356$	0.187839	+	0.108449i	0.00995543	+	0.00574777i
$357$	3.45054	+	9.48029i	0.182622	+	0.501750i
$358$	−5.82551	−	33.0381i	−0.307888	−	1.74612i
$359$	12.2092	+	21.1469i	0.644375	+	1.11609i	0.984445	+	0.175691i	$0.0562158\pi$
$359$	12.2092	+	21.1469i	0.644375	+	1.11609i	−0.340070	+	0.940400i	$0.610451\pi$
$360$		0			0
$361$	20.9848	+	7.63783i	1.10446	+	0.401991i
$362$	−18.9140	+	10.9200i	−0.994099	+	0.573944i
$363$	−18.2168	−	15.2857i	−0.956132	−	0.802290i
$364$			1.40590i			0.0736894i
$365$		0			0
$366$	−16.0183	+	5.83019i	−0.837290	+	0.304749i
$367$	4.45604	−	25.2715i	0.232603	−	1.31916i	−0.614999	−	0.788528i	$-0.710844\pi$
$367$	4.45604	−	25.2715i	0.232603	−	1.31916i	0.847602	−	0.530632i	$-0.178045\pi$
$368$	1.19401	−	0.210536i	0.0622420	−	0.0109749i
$369$	−42.9290			−2.23480
$370$		0			0
$371$	−2.84225			−0.147562
$372$	10.3100	−	1.81793i	0.534549	−	0.0942554i
$373$	5.46836	−	31.0126i	0.283141	−	1.60577i	−0.428711	−	0.903442i	$-0.641032\pi$
$373$	5.46836	−	31.0126i	0.283141	−	1.60577i	0.711852	−	0.702330i	$-0.247857\pi$
$374$	36.4824	−	13.2785i	1.88646	−	0.686616i
$375$		0			0
$376$			29.8775i			1.54081i
$377$	2.72491	+	2.28647i	0.140340	+	0.117759i
$378$	−4.87872	+	2.81673i	−0.250934	+	0.144877i
$379$	0.481376	+	0.175207i	0.0247266	+	0.00899976i	0.354354	−	0.935111i	$-0.384701\pi$
$379$	0.481376	+	0.175207i	0.0247266	+	0.00899976i	−0.329627	+	0.944111i	$0.606923\pi$
$380$		0			0
$381$	12.0350	+	20.8452i	0.616570	+	1.06793i
$382$	2.35579	+	13.3604i	0.120533	+	0.683576i
$383$	7.57838	+	20.8214i	0.387237	+	1.06392i	0.968240	+	0.250023i	$0.0804382\pi$
$383$	7.57838	+	20.8214i	0.387237	+	1.06392i	−0.581003	+	0.813901i	$0.697340\pi$
$384$	38.0961	+	21.9948i	1.94408	+	1.12242i
$385$		0			0
$386$	4.77536	−	4.00700i	0.243059	−	0.203951i
$387$	−5.69765	+	15.6542i	−0.289628	+	0.795746i
$388$	39.8401	+	7.02489i	2.02258	+	0.356635i
$389$	15.8562	+	2.79587i	0.803940	+	0.141756i	0.560494	−	0.828158i	$-0.310611\pi$
$389$	15.8562	+	2.79587i	0.803940	+	0.141756i	0.243446	+	0.969915i	$0.421722\pi$
$390$		0			0
$391$	−5.44430	+	4.56831i	−0.275330	+	0.231029i
$392$	9.44568	+	11.2569i	0.477079	+	0.568560i
$393$	8.83581	+	5.10136i	0.445708	+	0.257330i
$394$	12.3164	+	33.8389i	0.620489	+	1.70478i
$395$		0			0
$396$	27.2737	+	47.2394i	1.37056	+	2.37387i
$397$	−4.59649	+	7.96135i	−0.230691	+	0.399569i	−0.958012	−	0.286729i	$-0.907432\pi$
$397$	−4.59649	+	7.96135i	−0.230691	+	0.399569i	0.727321	+	0.686298i	$0.240765\pi$
$398$	−19.2415	−	7.00334i	−0.964490	−	0.351046i
$399$	−14.5959	+	8.42696i	−0.730710	+	0.421876i
$400$		0			0
$401$		−	4.16082i		−	0.207782i	−0.994589	−	0.103891i	$-0.966871\pi$
$401$		−	4.16082i		−	0.207782i	0.994589	−	0.103891i	$-0.0331292\pi$
$402$	−6.75466	+	8.04989i	−0.336892	+	0.401492i
$403$	0.554665	−	0.201882i	0.0276299	−	0.0100564i
$404$	0.872765	−	4.94970i	0.0434217	−	0.246257i
$405$		0			0
$406$	−17.3910			−0.863100
$407$	22.9063	+	14.6963i	1.13542	+	0.728471i
$408$	−24.8051			−1.22803
$409$	−13.7539	+	2.42518i	−0.680087	+	0.119918i	−0.503012	−	0.864280i	$-0.667775\pi$
$409$	−13.7539	+	2.42518i	−0.680087	+	0.119918i	−0.177075	+	0.984197i	$0.556664\pi$
$410$		0			0
$411$	42.2181	−	15.3661i	2.08246	−	0.757955i
$412$	−12.2878	+	14.6440i	−0.605377	+	0.721460i
$413$			7.73284i			0.380508i
$414$	−12.6097	−	10.5808i	−0.619732	−	0.520017i
$415$		0			0
$416$	2.74424	+	0.998822i	0.134547	+	0.0489713i
$417$	−20.0023	+	34.6449i	−0.979515	+	1.69657i
$418$	32.4289	+	56.1686i	1.58615	+	2.74729i
$419$	−5.13898	−	29.1446i	−0.251055	−	1.42381i	−0.805998	−	0.591918i	$-0.798371\pi$
$419$	−5.13898	−	29.1446i	−0.251055	−	1.42381i	0.554943	−	0.831888i	$-0.312740\pi$
$420$		0			0
$421$	−0.713500	−	0.411939i	−0.0347739	−	0.0200767i	0.482512	−	0.875889i	$-0.339724\pi$
$421$	−0.713500	−	0.411939i	−0.0347739	−	0.0200767i	−0.517286	+	0.855813i	$0.673058\pi$
$422$	2.93999	+	3.50374i	0.143116	+	0.170559i
$423$	−37.0127	+	31.0573i	−1.79962	+	1.51006i
$424$	2.39012	−	6.56679i	0.116074	−	0.318911i
$425$		0			0
$426$	66.9156	+	11.7990i	3.24207	+	0.571665i
$427$	0.974903	−	2.67852i	0.0471789	−	0.129623i
$428$	−7.68419	+	6.44780i	−0.371429	+	0.311666i
$429$	3.47715	+	4.14390i	0.167878	+	0.200070i
$430$		0			0
$431$	7.24643	+	19.9094i	0.349048	+	0.959002i	0.982671	+	0.185359i	$0.0593450\pi$
$431$	7.24643	+	19.9094i	0.349048	+	0.959002i	−0.633623	+	0.773642i	$0.718433\pi$
$432$	0.286489	+	1.62476i	0.0137837	+	0.0781714i
$433$	9.37498	+	16.2379i	0.450533	+	0.780346i	0.998419	−	0.0562071i	$-0.0179007\pi$
$433$	9.37498	+	16.2379i	0.450533	+	0.780346i	−0.547886	+	0.836553i	$0.684567\pi$
$434$	−1.44292	+	2.49921i	−0.0692623	+	0.119966i
$435$		0			0
$436$	10.1668	−	5.86982i	0.486903	−	0.281114i
$437$	−9.09509	−	7.63169i	−0.435077	−	0.365073i
$438$		−	75.6966i		−	3.61692i
$439$	18.1999	−	21.6898i	0.868634	−	1.03520i	−0.130409	−	0.991460i	$-0.541629\pi$
$439$	18.1999	−	21.6898i	0.868634	−	1.03520i	0.999043	−	0.0437376i	$-0.0139266\pi$
$440$		0			0
$441$	−4.12656	+	23.4029i	−0.196503	+	1.11442i
$442$	−3.91821	+	0.690887i	−0.186370	+	0.0328621i
$443$	−4.48612			−0.213142			−0.106571	−	0.994305i	$-0.533987\pi$
$443$	−4.48612			−0.213142			−0.106571	+	0.994305i	$0.533987\pi$
$444$	−29.9878	−	39.3412i	−1.42316	−	1.86705i
$445$		0			0
$446$	−34.2792	+	6.04435i	−1.62317	+	0.286208i
$447$	9.36531	−	53.1133i	0.442964	−	2.51217i
$448$	−12.1901	+	4.43684i	−0.575929	+	0.209621i
$449$	−3.67299	+	4.37730i	−0.173339	+	0.206577i	−0.845719	−	0.533629i	$-0.820828\pi$
$449$	−3.67299	+	4.37730i	−0.173339	+	0.206577i	0.672380	+	0.740207i	$0.265272\pi$
$450$		0			0
$451$	−37.2211	−	31.2322i	−1.75267	−	1.47067i
$452$	−20.3405	+	11.7436i	−0.956734	+	0.552371i
$453$	−8.63875	−	3.14425i	−0.405884	−	0.147730i
$454$	10.1460	−	17.5734i	0.476177	−	0.824762i
$455$		0			0
$456$	−7.19575	−	40.8091i	−0.336972	−	1.91106i
$457$	−9.30079	−	25.5537i	−0.435073	−	1.19535i	−0.942661	−	0.333752i	$-0.891685\pi$
$457$	−9.30079	−	25.5537i	−0.435073	−	1.19535i	0.507588	−	0.861600i	$-0.330537\pi$
$458$	28.8313	+	16.6458i	1.34720	+	0.777806i
$459$	−6.21639	−	7.40840i	−0.290156	−	0.345794i
$460$		0			0
$461$	−4.65287	+	12.7837i	−0.216706	+	0.595394i	−0.999643	−	0.0267060i	$-0.991498\pi$
$461$	−4.65287	+	12.7837i	−0.216706	+	0.595394i	0.782937	+	0.622100i	$0.213720\pi$
$462$	−26.0456	−	4.59254i	−1.21175	−	0.213664i
$463$	−12.7440	−	2.24711i	−0.592262	−	0.104432i	−0.130520	−	0.991446i	$-0.541665\pi$
$463$	−12.7440	−	2.24711i	−0.592262	−	0.104432i	−0.461743	+	0.887014i	$0.652776\pi$
$464$	−1.74196	+	4.78601i	−0.0808686	+	0.222185i
$465$		0			0
$466$	21.3848	+	25.4854i	0.990632	+	1.18059i
$467$	−13.9911	−	8.07776i	−0.647431	−	0.373794i	0.140040	−	0.990146i	$-0.455277\pi$
$467$	−13.9911	−	8.07776i	−0.647431	−	0.373794i	−0.787471	+	0.616351i	$0.788610\pi$
$468$	−1.91190	−	5.25290i	−0.0883775	−	0.242815i
$469$	−0.305130	−	1.73048i	−0.0140896	−	0.0799061i
$470$		0			0
$471$	−11.8799	+	20.5765i	−0.547396	+	0.948117i
$472$	−17.8661	−	6.50273i	−0.822354	−	0.299312i
$473$	−16.3290	+	9.42755i	−0.750808	+	0.433479i
$474$	69.6934	+	58.4797i	3.20112	+	2.68606i
$475$		0			0
$476$	7.58482	−	9.03924i	0.347650	−	0.414313i
$477$	10.6195	−	3.86519i	0.486235	−	0.176975i
$478$	−2.85129	+	16.1704i	−0.130415	+	0.739619i
$479$	6.26813	−	1.10524i	0.286398	−	0.0504998i	−0.0286034	−	0.999591i	$-0.509106\pi$
$479$	6.26813	−	1.10524i	0.286398	−	0.0504998i	0.315002	+	0.949091i	$0.397995\pi$
$480$		0			0
$481$	−2.05025	−	1.89083i	−0.0934832	−	0.0862144i
$482$	32.5501			1.48262
$483$	4.76787	−	0.840704i	0.216946	−	0.0382533i
$484$	−4.82980	+	27.3912i	−0.219536	+	1.24505i
$485$		0			0
$486$	−30.9245	+	36.8544i	−1.40277	+	1.67175i
$487$			8.81435i			0.399416i	0.979855	+	0.199708i	$0.0639994\pi$
$487$			8.81435i			0.399416i	−0.979855	+	0.199708i	$0.936001\pi$
$488$	5.36869	+	4.50487i	0.243029	+	0.203926i
$489$	11.4986	−	6.63871i	0.519984	−	0.300213i
$490$		0			0
$491$	−19.2408	+	33.3261i	−0.868327	+	1.50399i	−0.00462244	+	0.999989i	$0.501471\pi$
$491$	−19.2408	+	33.3261i	−0.868327	+	1.50399i	−0.863705	+	0.503998i	$0.831862\pi$
$492$	44.1577	+	76.4834i	1.99078	+	3.44814i
$493$	−5.18430	−	29.4016i	−0.233489	−	1.32418i
$494$	−2.27328	−	6.24579i	−0.102280	−	0.281011i
$495$		0			0
$496$	0.543253	+	0.647424i	0.0243928	+	0.0290702i
$497$	−8.70380	+	7.30336i	−0.390419	+	0.327600i
$498$	4.87498	−	13.3939i	0.218453	−	0.600194i
$499$	8.38718	+	1.47889i	0.375462	+	0.0662040i	0.358195	−	0.933647i	$-0.383392\pi$
$499$	8.38718	+	1.47889i	0.375462	+	0.0662040i	0.0172670	+	0.999851i	$0.494503\pi$
$500$		0			0
$501$	4.86272	−	13.3602i	0.217250	−	0.596891i
$502$	6.98664	−	5.86249i	0.311829	−	0.261656i
$503$	−19.7191	−	23.5003i	−0.879232	−	1.04783i	−0.998488	−	0.0549647i	$-0.982495\pi$
$503$	−19.7191	−	23.5003i	−0.879232	−	1.04783i	0.119256	−	0.992864i	$-0.461949\pi$
$504$	8.31978	+	4.80343i	0.370593	+	0.213962i
$505$		0			0
$506$	−3.23523	−	18.3479i	−0.143823	−	0.815663i
$507$	16.8624	+	29.2066i	0.748886	+	1.29711i
$508$	14.0762	−	24.3808i	0.624532	−	1.08172i
$509$	18.1588	+	6.60926i	0.804875	+	0.292950i	0.711505	−	0.702681i	$-0.248014\pi$
$509$	18.1588	+	6.60926i	0.804875	+	0.292950i	0.0933697	+	0.995632i	$0.470236\pi$
$510$		0			0
$511$	9.69636	+	8.13622i	0.428942	+	0.359925i
$512$			7.39105i			0.326641i
$513$	10.3849	−	12.3763i	0.458505	−	0.546425i
$514$	−9.38429	+	3.41560i	−0.413923	+	0.150656i
$515$		0			0
$516$	33.7506	−	5.95114i	1.48579	−	0.261984i
$517$	−54.6866			−2.40511
$518$	13.6209	+	0.638445i	0.598466	+	0.0280517i
$519$	−28.5560			−1.25347
$520$		0			0
$521$	7.38927	−	41.9066i	0.323730	−	1.83596i	−0.194724	−	0.980858i	$-0.562381\pi$
$521$	7.38927	−	41.9066i	0.323730	−	1.83596i	0.518454	−	0.855105i	$-0.326508\pi$
$522$	64.9781	−	23.6501i	2.84402	−	1.03514i
$523$	−19.8137	+	23.6131i	−0.866393	+	1.03253i	0.132751	+	0.991149i	$0.457619\pi$
$523$	−19.8137	+	23.6131i	−0.866393	+	1.03253i	−0.999144	+	0.0413775i	$0.986825\pi$
$524$		−	11.9332i		−	0.521305i
$525$		0			0
$526$	−39.7798	+	22.9669i	−1.73448	+	1.00140i
$527$	−4.65536	−	1.69441i	−0.202791	−	0.0738097i
$528$	−3.87271	+	6.70774i	−0.168538	+	0.291917i
$529$	−9.79472	−	16.9650i	−0.425857	−	0.737607i
$530$		0			0
$531$	−10.5159	−	28.8923i	−0.456353	−	1.25382i
$532$	17.0716	+	9.85627i	0.740146	+	0.427324i
$533$	3.20068	+	3.81442i	0.138637	+	0.165221i
$534$	0.320313	−	0.268774i	0.0138613	−	0.0116310i
$535$		0			0
$536$	4.25472	+	0.750222i	0.183776	+	0.0324046i
$537$	−38.6363	−	6.81262i	−1.66728	−	0.293986i
$538$	3.04800	−	8.37430i	0.131408	−	0.361042i
$539$	−20.6042	+	17.2890i	−0.887488	+	0.744690i
$540$		0			0
$541$	1.16602	+	0.673201i	0.0501311	+	0.0289432i	0.524856	−	0.851191i	$-0.324119\pi$
$541$	1.16602	+	0.673201i	0.0501311	+	0.0289432i	−0.474725	+	0.880134i	$0.657452\pi$
$542$	−3.85149	−	10.5819i	−0.165436	−	0.454530i
$543$	4.43510	+	25.1527i	0.190328	+	1.07941i
$544$	−12.2554	−	21.2270i	−0.525447	−	0.910101i
$545$		0			0
$546$	2.54687	+	0.926986i	0.108996	+	0.0396713i
$547$	18.1194	−	10.4612i	0.774729	−	0.447290i	−0.0598299	−	0.998209i	$-0.519056\pi$
$547$	18.1194	−	10.4612i	0.774729	−	0.447290i	0.834559	+	0.550919i	$0.185723\pi$
$548$	−40.2539	−	33.7771i	−1.71956	−	1.44289i
$549$			11.3336i			0.483705i
$550$		0			0
$551$	46.8673	−	17.0583i	1.99662	−	0.726709i
$552$	−2.06703	+	11.7227i	−0.0879788	+	0.498953i
$553$	−14.9819	+	2.64172i	−0.637097	+	0.112337i
$554$	−56.9646			−2.42020
$555$		0			0
$556$	46.7898			1.98433
$557$	−15.8193	+	2.78938i	−0.670287	+	0.118190i	−0.498427	−	0.866932i	$-0.666089\pi$
$557$	−15.8193	+	2.78938i	−0.670287	+	0.118190i	−0.171860	+	0.985121i	$0.554978\pi$
$558$	1.99250	−	11.3001i	0.0843494	−	0.478369i
$559$	1.81574	−	0.660875i	0.0767976	−	0.0279520i
$560$		0			0
$561$		−	45.4023i		−	1.91689i
$562$	46.9456	+	39.3920i	1.98028	+	1.66165i
$563$	20.2757	−	11.7062i	0.854517	−	0.493356i	−0.00765524	−	0.999971i	$-0.502437\pi$
$563$	20.2757	−	11.7062i	0.854517	−	0.493356i	0.862172	+	0.506615i	$0.169103\pi$
$564$	93.4045	+	33.9965i	3.93304	+	1.43151i
$565$		0			0
$566$	−11.5551	−	20.0141i	−0.485699	−	0.841255i
$567$	−0.903366	−	5.12324i	−0.0379378	−	0.215156i
$568$	−9.55457	−	26.2510i	−0.400901	−	1.10147i
$569$	0.863312	+	0.498434i	0.0361919	+	0.0208954i	0.517987	−	0.855389i	$-0.326682\pi$
$569$	0.863312	+	0.498434i	0.0361919	+	0.0208954i	−0.481795	+	0.876284i	$0.660015\pi$
$570$		0			0
$571$	−2.21656	+	1.85991i	−0.0927599	+	0.0778348i	−0.687988	−	0.725722i	$-0.741506\pi$
$571$	−2.21656	+	1.85991i	−0.0927599	+	0.0778348i	0.595228	+	0.803557i	$0.297062\pi$
$572$	2.16396	−	5.94543i	0.0904797	−	0.248591i
$573$	15.6242	+	2.75497i	0.652711	+	0.115091i
$574$	−23.9747	−	4.22738i	−1.00068	−	0.176447i
$575$		0			0
$576$	39.5124	−	33.1548i	1.64635	−	1.38145i
$577$	11.2691	+	13.4300i	0.469141	+	0.559100i	0.947785	−	0.318909i	$-0.103316\pi$
$577$	11.2691	+	13.4300i	0.469141	+	0.559100i	−0.478645	+	0.878009i	$0.658872\pi$
$578$	−4.27667	−	2.46914i	−0.177886	−	0.102703i
$579$	−2.49335	−	6.85043i	−0.103620	−	0.284694i
$580$		0			0
$581$	1.19171	+	2.06410i	0.0494404	+	0.0856332i
$582$	38.9946	−	67.5406i	1.61638	−	2.79965i
$583$	12.0196	+	4.37478i	0.497801	+	0.181185i
$584$	−26.9520	+	15.5607i	−1.11528	+	0.643907i
$585$		0			0
$586$			1.65520i			0.0683755i
$587$	11.9531	−	14.2451i	0.493356	−	0.587959i	−0.460711	−	0.887550i	$-0.652406\pi$
$587$	11.9531	−	14.2451i	0.493356	−	0.587959i	0.954068	+	0.299591i	$0.0968502\pi$
$588$	45.9399	−	16.7207i	1.89453	−	0.689552i
$589$	1.43715	−	8.15049i	0.0592168	−	0.335835i
$590$		0			0
$591$	42.1125			1.73228
$592$	1.54003	−	3.68452i	0.0632949	−	0.151433i
$593$	−35.6659			−1.46462			−0.732312	−	0.680969i	$-0.761559\pi$
$593$	−35.6659			−1.46462			−0.732312	+	0.680969i	$0.761559\pi$
$594$	24.9671	−	4.40237i	1.02441	−	0.180632i
$595$		0			0
$596$	−59.2761	+	21.5747i	−2.42804	+	0.883735i
$597$	−15.3922	+	18.3437i	−0.629961	+	0.750758i
$598$			1.90930i			0.0780770i
$599$	−17.1168	−	14.3627i	−0.699375	−	0.586845i	0.222221	−	0.974996i	$-0.428669\pi$
$599$	−17.1168	−	14.3627i	−0.699375	−	0.586845i	−0.921596	+	0.388151i	$0.873114\pi$
$600$		0			0
$601$	−43.0749	−	15.6780i	−1.75706	−	0.639518i	−0.757155	−	0.653236i	$-0.773411\pi$
$601$	−43.0749	−	15.6780i	−1.75706	−	0.639518i	−0.999906	+	0.0137178i	$0.995633\pi$
$602$	−4.72350	+	8.18135i	−0.192516	+	0.333447i
$603$	3.49335	+	6.05066i	0.142260	+	0.246402i
$604$	1.86714	+	10.5891i	0.0759729	+	0.430864i
$605$		0			0
$606$	−8.39118	−	4.84465i	−0.340869	−	0.196801i
$607$	2.25898	+	2.69214i	0.0916891	+	0.109271i	0.809938	−	0.586515i	$-0.199501\pi$
$607$	2.25898	+	2.69214i	0.0916891	+	0.109271i	−0.718249	+	0.695786i	$0.755056\pi$
$608$	31.3673	−	26.3203i	1.27211	−	1.06743i
$609$	−6.95594	+	19.1113i	−0.281869	+	0.774428i
$610$		0			0
$611$	5.51914	+	0.973173i	0.223281	+	0.0393704i
$612$	−16.0467	+	44.0880i	−0.648651	+	1.78215i
$613$	−33.5958	+	28.1902i	−1.35692	+	1.13859i	−0.380001	+	0.924986i	$0.624076\pi$
$613$	−33.5958	+	28.1902i	−1.35692	+	1.13859i	−0.976920	+	0.213606i	$0.931479\pi$
$614$	−11.6905	−	13.9321i	−0.471788	−	0.562255i
$615$		0			0
$616$	3.71893	+	10.2177i	0.149840	+	0.411681i
$617$	4.53642	+	25.7273i	0.182629	+	1.03574i	0.928964	+	0.370171i	$0.120701\pi$
$617$	4.53642	+	25.7273i	0.182629	+	1.03574i	−0.746334	+	0.665571i	$0.768188\pi$
$618$	18.4265	+	31.9156i	0.741221	+	1.28383i
$619$	−7.25750	+	12.5704i	−0.291703	+	0.505245i	−0.974213	−	0.225632i	$-0.927555\pi$
$619$	−7.25750	+	12.5704i	−0.291703	+	0.505245i	0.682509	+	0.730877i	$0.260889\pi$
$620$		0			0
$621$	−4.01918	+	2.32048i	−0.161284	+	0.0931175i
$622$	−41.4084	−	34.7458i	−1.66032	−	1.39318i
$623$			0.0699196i			0.00280127i
$624$	0.510214	−	0.608049i	0.0204249	−	0.0243414i
$625$		0			0
$626$	−0.375687	+	2.13063i	−0.0150155	+	0.0851570i
$627$	74.6954	−	13.1708i	2.98305	−	0.525992i
$628$	27.7897			1.10893
$629$	2.98104	+	23.2181i	0.118862	+	0.925765i
$630$		0			0
$631$	−27.7172	+	4.88728i	−1.10340	+	0.194560i	−0.695543	−	0.718485i	$-0.744836\pi$
$631$	−27.7172	+	4.88728i	−1.10340	+	0.194560i	−0.407860	+	0.913044i	$0.633725\pi$
$632$	6.49518	−	36.8360i	0.258365	−	1.46526i
$633$	5.02624	−	1.82940i	0.199775	−	0.0727122i
$634$	−6.00314	+	7.15426i	−0.238415	+	0.284132i
$635$		0			0
$636$	−17.8098	−	14.9442i	−0.706205	−	0.592576i
$637$	2.38711	−	1.37820i	0.0945807	−	0.0546062i
$638$	73.5448	+	26.7681i	2.91166	+	1.05976i
$639$	22.5882	−	39.1240i	0.893577	−	1.54772i
$640$		0			0
$641$	−6.53812	−	37.0795i	−0.258240	−	1.46455i	−0.787616	−	0.616166i	$-0.788685\pi$
$641$	−6.53812	−	37.0795i	−0.258240	−	1.46455i	0.529376	−	0.848387i	$-0.322426\pi$
$642$	6.61395	+	18.1717i	0.261032	+	0.717179i
$643$	30.9482	+	17.8680i	1.22048	+	0.704644i	0.965020	−	0.262176i	$-0.0844402\pi$
$643$	30.9482	+	17.8680i	1.22048	+	0.704644i	0.255459	+	0.966820i	$0.417774\pi$
$644$	−3.63984	−	4.33779i	−0.143430	−	0.170933i
$645$		0			0
$646$	−19.0799	+	52.4215i	−0.750687	+	2.06250i
$647$	−33.2272	−	5.85886i	−1.30630	−	0.230335i	−0.523187	−	0.852218i	$-0.675257\pi$
$647$	−33.2272	−	5.85886i	−1.30630	−	0.230335i	−0.783110	+	0.621883i	$0.786368\pi$
$648$	12.5965	+	2.22110i	0.494837	+	0.0872531i
$649$	11.9023	−	32.7014i	0.467208	−	1.28364i
$650$		0			0
$651$	2.16930	+	2.58527i	0.0850215	+	0.101325i
$652$	−13.4489	−	7.76471i	−0.526698	−	0.304089i
$653$	−10.7760	−	29.6067i	−0.421696	−	1.15860i	−0.950736	−	0.310003i	$-0.899670\pi$
$653$	−10.7760	−	29.6067i	−0.421696	−	1.15860i	0.529040	−	0.848597i	$-0.322552\pi$
$654$	−3.92998	−	22.2880i	−0.153674	−	0.871531i
$655$		0			0
$656$	−3.56479	+	6.17440i	−0.139182	+	0.241070i
$657$	−47.2931	−	17.2133i	−1.84508	−	0.671554i
$658$	−23.7289	+	13.6999i	−0.925048	+	0.534077i
$659$	−9.49140	−	7.96423i	−0.369732	−	0.310242i	0.438923	−	0.898525i	$-0.355360\pi$
$659$	−9.49140	−	7.96423i	−0.369732	−	0.310242i	−0.808656	+	0.588282i	$0.799804\pi$
$660$		0			0
$661$	−18.8674	+	22.4853i	−0.733856	+	0.874576i	−0.995898	−	0.0904805i	$-0.971160\pi$
$661$	−18.8674	+	22.4853i	−0.733856	+	0.874576i	0.262042	+	0.965057i	$0.415604\pi$
$662$	−17.2987	+	6.29621i	−0.672333	+	0.244709i
$663$	−0.807955	+	4.58214i	−0.0313784	+	0.177955i
$664$	−5.77106	+	1.01759i	−0.223961	+	0.0394903i
$665$		0			0
$666$	−51.7600	+	16.1377i	−2.00566	+	0.625322i
$667$	−14.3270			−0.554745
$668$	−16.3765	+	2.88762i	−0.633626	+	0.111725i
$669$	−7.06854	+	40.0877i	−0.273286	+	1.54988i
$670$		0			0
$671$	−8.24554	+	9.82665i	−0.318315	+	0.379354i
$672$			16.6972i			0.644107i
$673$	−5.83800	−	4.89867i	−0.225038	−	0.188830i	0.523297	−	0.852151i	$-0.324702\pi$
$673$	−5.83800	−	4.89867i	−0.225038	−	0.188830i	−0.748335	+	0.663321i	$0.769146\pi$
$674$	−47.6868	+	27.5320i	−1.83683	+	1.06049i
$675$		0			0
$676$	19.7225	−	34.1603i	0.758557	−	1.31386i
$677$	3.06301	+	5.30530i	0.117721	+	0.203899i	0.918864	−	0.394574i	$-0.129108\pi$
$677$	3.06301	+	5.30530i	0.117721	+	0.203899i	−0.801143	+	0.598473i	$0.795774\pi$
$678$	7.86259	+	44.5910i	0.301961	+	1.71251i
$679$	4.46031	+	12.2546i	0.171171	+	0.470288i
$680$		0			0
$681$	−15.2536	−	18.1786i	−0.584521	−	0.696605i
$682$	9.94872	−	8.34797i	0.380956	−	0.319660i
$683$	−13.6360	+	37.4647i	−0.521769	+	1.43355i	0.346782	+	0.937946i	$0.387275\pi$
$683$	−13.6360	+	37.4647i	−0.521769	+	1.43355i	−0.868550	+	0.495601i	$0.834948\pi$
$684$	−77.1883	−	13.6104i	−2.95137	−	0.520406i
$685$		0			0
$686$	−9.97612	+	27.4092i	−0.380890	+	1.04649i
$687$	29.8241	−	25.0254i	1.13786	−	0.954779i
$688$	1.77838	+	2.11939i	0.0678002	+	0.0808011i
$689$	−1.13520	−	0.655410i	−0.0432478	−	0.0249691i
$690$		0			0
$691$	−4.99430	−	28.3241i	−0.189992	−	1.07750i	−0.919372	−	0.393390i	$-0.871302\pi$
$691$	−4.99430	−	28.3241i	−0.189992	−	1.07750i	0.729379	−	0.684109i	$-0.239809\pi$
$692$	16.6997	+	28.9248i	0.634828	+	1.09955i
$693$	−8.79201	+	15.2282i	−0.333981	+	0.578472i
$694$	−54.8681	−	19.9704i	−2.08276	−	0.758064i
$695$		0			0
$696$	−38.3057	−	32.1423i	−1.45197	−	1.21835i
$697$		−	41.7923i		−	1.58300i
$698$	−31.5852	+	37.6418i	−1.19552	+	1.42476i
$699$	36.5598	−	13.3067i	1.38282	−	0.503305i
$700$		0			0
$701$	21.2827	−	3.75272i	0.803837	−	0.141738i	0.243390	−	0.969928i	$-0.421740\pi$
$701$	21.2827	−	3.75272i	0.803837	−	0.141738i	0.560447	+	0.828190i	$0.310629\pi$
$702$	−2.59810			−0.0980589
$703$	−37.3334	+	11.6398i	−1.40806	+	0.439002i
$704$	58.3799			2.20028
$705$		0			0
$706$	2.81324	−	15.9547i	0.105878	−	0.600463i
$707$	1.52250	−	0.554145i	0.0572595	−	0.0208408i
$708$	−40.6583	+	48.4547i	−1.52803	+	1.82104i
$709$			21.2461i			0.797913i	0.916970	+	0.398956i	$0.130627\pi$
$709$			21.2461i			0.797913i	−0.916970	+	0.398956i	$0.869373\pi$
$710$		0			0
$711$	52.3847	−	30.2443i	1.96458	−	1.13425i
$712$	−0.161543	−	0.0587970i	−0.00605410	−	0.00220351i
$713$	−1.18870	+	2.05890i	−0.0445173	+	0.0771063i
$714$	−11.3740	−	19.7003i	−0.425661	−	0.737267i
$715$		0			0
$716$	15.6941	+	43.1193i	0.586517	+	1.61144i
$717$	16.6296	+	9.60109i	0.621043	+	0.358559i
$718$	−35.3908	−	42.1771i	−1.32077	−	1.57404i
$719$	−20.7120	+	17.3794i	−0.772428	+	0.648144i	−0.941330	−	0.337489i	$-0.890422\pi$
$719$	−20.7120	+	17.3794i	−0.772428	+	0.648144i	0.168902	+	0.985633i	$0.445978\pi$
$720$		0			0
$721$	−6.06879	−	1.07009i	−0.226014	−	0.0398523i
$722$	−49.5880	−	8.74371i	−1.84547	−	0.325407i
$723$	13.0192	−	35.7700i	0.484189	−	1.33030i
$724$	22.8839	−	19.2018i	0.850472	−	0.713630i
$725$		0			0
$726$	46.4360	+	26.8099i	1.72340	+	0.995007i
$727$	13.3788	+	36.7580i	0.496192	+	1.36328i	0.894928	+	0.446211i	$0.147227\pi$
$727$	13.3788	+	36.7580i	0.496192	+	1.36328i	−0.398735	+	0.917066i	$0.630551\pi$
$728$	−0.193497	−	1.09738i	−0.00717149	−	0.0406715i
$729$	20.2821	+	35.1296i	0.751188	+	1.30110i
$730$		0			0
$731$	−15.2397	−	5.54679i	−0.563659	−	0.205155i
$732$	20.1922	−	11.6580i	0.746325	−	0.430891i
$733$	2.35907	+	1.97949i	0.0871341	+	0.0731142i	0.685314	−	0.728247i	$-0.259665\pi$
$733$	2.35907	+	1.97949i	0.0871341	+	0.0731142i	−0.598180	+	0.801362i	$0.704109\pi$
$734$			57.8610i			2.13569i
$735$		0			0
$736$	−11.0530	+	4.02297i	−0.407420	+	0.148289i
$737$	−1.37318	+	7.78767i	−0.0505816	+	0.286863i
$738$	95.3256	−	16.8085i	3.50898	−	0.618729i
$739$	32.6502			1.20106			0.600529	−	0.799603i	$-0.294957\pi$
$739$	32.6502			1.20106			0.600529	+	0.799603i	$0.294957\pi$
$740$		0			0
$741$	−7.77287			−0.285544
$742$	6.31133	−	1.11286i	0.231696	−	0.0408543i
$743$	1.99228	−	11.2988i	0.0730895	−	0.414511i	−0.926207	−	0.377015i	$-0.876951\pi$
$743$	1.99228	−	11.2988i	0.0730895	−	0.414511i	0.999297	−	0.0374965i	$-0.0119383\pi$
$744$	−7.79726	+	2.83797i	−0.285862	+	0.104045i
$745$		0			0
$746$			71.0058i			2.59971i
$747$	−7.25957	−	6.09150i	−0.265614	−	0.222876i
$748$	−45.9886	+	26.5515i	−1.68151	+	0.970820i
$749$	−3.03860	−	1.10596i	−0.111028	−	0.0404109i
$750$		0			0
$751$	−11.8473	−	20.5201i	−0.432313	−	0.748787i	0.564759	−	0.825256i	$-0.308969\pi$
$751$	−11.8473	−	20.5201i	−0.432313	−	0.748787i	−0.997072	+	0.0764682i	$0.975636\pi$
$752$	1.39341	+	7.90244i	0.0508126	+	0.288172i
$753$	−3.64793	−	10.0226i	−0.132938	−	0.365244i
$754$	−6.94601	−	4.01028i	−0.252959	−	0.146046i
$755$		0			0
$756$	5.90270	−	4.95295i	0.214679	−	0.180137i
$757$	−9.24748	+	25.4072i	−0.336105	+	0.923441i	0.650383	+	0.759607i	$0.274609\pi$
$757$	−9.24748	+	25.4072i	−0.336105	+	0.923441i	−0.986488	+	0.163835i	$0.947614\pi$
$758$	−1.13752	−	0.200575i	−0.0413164	−	0.00728520i
$759$	−21.4568	−	3.78342i	−0.778834	−	0.137329i
$760$		0			0
$761$	−14.7399	+	12.3682i	−0.534320	+	0.448348i	−0.869590	−	0.493774i	$-0.835617\pi$
$761$	−14.7399	+	12.3682i	−0.534320	+	0.448348i	0.335270	+	0.942122i	$0.391173\pi$
$762$	−34.8859	−	41.5754i	−1.26378	−	1.50612i
$763$	3.27740	+	1.89221i	0.118650	+	0.0685026i
$764$	−6.34659	−	17.4371i	−0.229612	−	0.630853i
$765$		0			0
$766$	−24.9805	−	43.2675i	−0.902583	−	1.56332i
$767$	−1.78316	+	3.08852i	−0.0643861	+	0.111520i
$768$	−28.5434	−	10.3890i	−1.02997	−	0.374879i
$769$	12.5264	−	7.23213i	0.451714	−	0.260797i	−0.256840	−	0.966454i	$-0.582681\pi$
$769$	12.5264	−	7.23213i	0.451714	−	0.260797i	0.708554	+	0.705657i	$0.249348\pi$
$770$		0			0
$771$			11.6787i			0.420599i
$772$	−5.48077	+	6.53172i	−0.197257	+	0.235082i
$773$	8.26357	−	3.00769i	0.297220	−	0.108179i	−0.189106	−	0.981957i	$-0.560559\pi$
$773$	8.26357	−	3.00769i	0.297220	−	0.108179i	0.486326	+	0.873777i	$0.338337\pi$
$774$	6.52261	−	36.9916i	0.234451	−	1.32963i
$775$		0			0
$776$	−32.0640			−1.15103
$777$	6.14959	−	14.7129i	0.220615	−	0.527821i
$778$	−36.3040			−1.30156
$779$	68.7563	−	12.1236i	2.46345	−	0.434373i
$780$		0			0
$781$	48.0488	−	17.4883i	1.71932	−	0.625782i
$782$	10.3006	−	12.2758i	0.368349	−	0.438981i
$783$		−	19.4957i		−	0.696719i
$784$	3.02333	+	2.53687i	0.107976	+	0.0906026i
$785$		0			0
$786$	−21.6177	−	7.86819i	−0.771077	−	0.280649i
$787$	−23.2485	+	40.2675i	−0.828718	+	1.43538i	0.0703259	+	0.997524i	$0.477596\pi$
$787$	−23.2485	+	40.2675i	−0.828718	+	1.43538i	−0.899044	+	0.437858i	$0.855737\pi$
$788$	−24.6276	−	42.6563i	−0.877323	−	1.51957i
$789$	9.32787	+	52.9010i	0.332081	+	1.88332i
$790$		0			0
$791$	−6.55699	−	3.78568i	−0.233140	−	0.134603i
$792$	−27.7901	−	33.1190i	−0.987479	−	1.17683i
$793$	1.00703	−	0.845002i	0.0357608	−	0.0300069i
$794$	7.08949	−	19.4782i	0.251597	−	0.691256i
$795$		0			0
$796$	27.5820	+	4.86346i	0.977620	+	0.172381i
$797$	−7.83286	+	21.5206i	−0.277454	+	0.762299i	0.720195	+	0.693772i	$0.244052\pi$
$797$	−7.83286	+	21.5206i	−0.277454	+	0.762299i	−0.997649	+	0.0685274i	$0.978170\pi$
$798$	29.1113	−	24.4273i	1.03053	−	0.864717i
$799$	−30.2350	−	36.0326i	−1.06964	−	1.27474i
$800$		0			0
$801$	−0.0950840	−	0.261241i	−0.00335963	−	0.00923051i
$802$	1.62913	+	9.23928i	0.0575267	+	0.326250i
$803$	−28.4817	−	49.3318i	−1.00510	−	1.74088i
$804$	7.18667	−	12.4477i	0.253454	−	0.438996i
$805$		0			0
$806$	−1.15261	+	0.665461i	−0.0405990	+	0.0234399i
$807$	−7.98356	−	6.69900i	−0.281035	−	0.235816i
$808$			3.98360i			0.140143i
$809$	−11.5836	+	13.8048i	−0.407256	+	0.485349i	−0.930218	−	0.367007i	$-0.880383\pi$
$809$	−11.5836	+	13.8048i	−0.407256	+	0.485349i	0.522962	+	0.852356i	$0.324827\pi$
$810$		0			0
$811$	6.53215	−	37.0456i	0.229375	−	1.30085i	−0.624768	−	0.780810i	$-0.714807\pi$
$811$	6.53215	−	37.0456i	0.229375	−	1.30085i	0.854143	−	0.520038i	$-0.174082\pi$
$812$	23.4260	−	4.13063i	0.822090	−	0.144957i
$813$	−13.1691			−0.461861
$814$	−56.6186	−	23.6651i	−1.98448	−	0.829460i
$815$		0			0
$816$	−6.56082	+	1.15685i	−0.229674	+	0.0404978i
$817$	4.70462	−	26.6812i	0.164594	−	0.933458i
$818$	29.5915	−	10.7704i	1.03464	−	0.376580i
$819$	1.15831	−	1.38042i	0.0404746	−	0.0482358i
$820$		0			0
$821$	35.1467	+	29.4916i	1.22663	+	1.02926i	0.998451	+	0.0556457i	$0.0177217\pi$
$821$	35.1467	+	29.4916i	1.22663	+	1.02926i	0.228179	+	0.973619i	$0.426723\pi$
$822$	−87.7305	+	50.6512i	−3.05995	+	1.76666i
$823$	−16.8809	−	6.14415i	−0.588431	−	0.214172i	0.0306079	−	0.999531i	$-0.490256\pi$
$823$	−16.8809	−	6.14415i	−0.588431	−	0.214172i	−0.619039	+	0.785360i	$0.712478\pi$
$824$	7.57575	−	13.1216i	0.263914	−	0.457112i
$825$		0			0
$826$	−3.02773	−	17.1711i	−0.105348	−	0.597458i
$827$	−3.79185	−	10.4180i	−0.131856	−	0.362270i	0.856142	−	0.516741i	$-0.172855\pi$
$827$	−3.79185	−	10.4180i	−0.131856	−	0.362270i	−0.987997	+	0.154471i	$0.950633\pi$
$828$	19.4986	+	11.2575i	0.677622	+	0.391225i
$829$	−23.8292	−	28.3986i	−0.827623	−	0.986323i	−0.999999	−	0.00129183i	$-0.999589\pi$
$829$	−23.8292	−	28.3986i	−0.827623	−	0.986323i	0.172376	−	0.985031i	$-0.444856\pi$
$830$		0			0
$831$	−22.7844	+	62.5995i	−0.790381	+	2.17155i
$832$	−5.89188	−	1.03890i	−0.204264	−	0.0360173i
$833$	−22.7832	−	4.01730i	−0.789392	−	0.139191i
$834$	30.8509	−	84.7622i	1.06828	−	2.93507i
$835$		0			0
$836$	−57.0232	−	67.9576i	−1.97219	−	2.35036i
$837$	−2.80167	−	1.61754i	−0.0968398	−	0.0559105i
$838$	22.8226	+	62.7046i	0.788394	+	2.16609i
$839$	−3.24095	−	18.3803i	−0.111890	−	0.634559i	−0.988243	−	0.152890i	$-0.951142\pi$
$839$	−3.24095	−	18.3803i	−0.111890	−	0.634559i	0.876353	−	0.481669i	$-0.159969\pi$
$840$		0			0
$841$	15.5925	−	27.0069i	0.537671	−	0.931274i
$842$	1.74565	+	0.635363i	0.0601590	+	0.0218961i
$843$	62.0657	−	35.8336i	2.13765	−	1.23418i
$844$	−4.79240	−	4.02131i	−0.164961	−	0.138419i
$845$		0			0
$846$	70.0279	−	83.4560i	2.40761	−	2.86928i
$847$	−8.42537	+	3.06658i	−0.289499	+	0.105369i
$848$	0.325914	−	1.84835i	0.0111919	−	0.0634726i
$849$	−26.6156	+	4.69305i	−0.913445	+	0.161065i
$850$		0			0
$851$	11.2211	+	0.525964i	0.384656	+	0.0180298i
$852$	−92.9390			−3.18404
$853$	7.07640	−	1.24776i	0.242291	−	0.0427225i	−0.0511837	−	0.998689i	$-0.516299\pi$
$853$	7.07640	−	1.24776i	0.242291	−	0.0427225i	0.293475	+	0.955967i	$0.405188\pi$
$854$	−1.11606	+	6.32948i	−0.0381908	+	0.216591i
$855$		0			0
$856$	5.11046	−	6.09041i	0.174672	−	0.208166i
$857$		−	35.4385i		−	1.21056i	−0.796014	−	0.605278i	$-0.793062\pi$
$857$		−	35.4385i		−	1.21056i	0.796014	−	0.605278i	$-0.206938\pi$
$858$	−9.34366	−	7.84026i	−0.318987	−	0.267662i
$859$	−16.1227	+	9.30843i	−0.550098	+	0.317599i	−0.749162	−	0.662387i	$-0.769543\pi$
$859$	−16.1227	+	9.30843i	−0.550098	+	0.317599i	0.199063	+	0.979987i	$0.436210\pi$
$860$		0			0
$861$	−14.2348	+	24.6554i	−0.485120	+	0.840253i
$862$	−23.8863	−	41.3723i	−0.813572	−	1.40915i
$863$	−3.08008	−	17.4680i	−0.104847	−	0.594617i	−0.991281	−	0.131762i	$-0.957936\pi$
$863$	−3.08008	−	17.4680i	−0.104847	−	0.594617i	0.886434	−	0.462854i	$-0.153175\pi$
$864$	−5.47430	−	15.0405i	−0.186240	−	0.511689i
$865$		0			0
$866$	−27.1753	−	32.3863i	−0.923456	−	1.10053i
$867$	−4.42394	+	3.71213i	−0.150245	+	0.126070i
$868$	1.35004	−	3.70919i	0.0458232	−	0.125898i
$869$	67.4232	+	11.8885i	2.28718	+	0.403291i
$870$		0			0
$871$	0.277171	−	0.761520i	0.00939157	−	0.0258031i
$872$	−7.12784	+	5.98097i	−0.241379	+	0.202541i
$873$	−33.3302	−	39.7214i	−1.12806	−	1.34437i
$874$	23.1841	+	13.3854i	0.784215	+	0.452767i
$875$		0			0
$876$	17.9791	+	101.965i	0.607458	+	3.44506i
$877$	11.7858	+	20.4136i	0.397977	+	0.689317i	0.993476	−	0.114039i	$-0.0363789\pi$
$877$	11.7858	+	20.4136i	0.397977	+	0.689317i	−0.595499	+	0.803356i	$0.703046\pi$
$878$	−31.9212	+	55.2891i	−1.07729	+	1.86592i
$879$	1.81893	+	0.662035i	0.0613509	+	0.0223299i
$880$		0			0
$881$	40.6015	+	34.0687i	1.36790	+	1.14780i	0.973453	+	0.228886i	$0.0735083\pi$
$881$	40.6015	+	34.0687i	1.36790	+	1.14780i	0.394447	+	0.918919i	$0.370936\pi$
$882$		−	53.5828i		−	1.80423i
$883$	18.1219	−	21.5969i	0.609851	−	0.726792i	−0.369439	−	0.929255i	$-0.620450\pi$
$883$	18.1219	−	21.5969i	0.609851	−	0.726792i	0.979290	+	0.202463i	$0.0648945\pi$
$884$	5.11381	−	1.86127i	0.171996	−	0.0626014i
$885$		0			0
$886$	9.96161	−	1.75650i	0.334667	−	0.0590108i
$887$	−25.0397			−0.840751			−0.420376	−	0.907350i	$-0.638102\pi$
$887$	−25.0397			−0.840751			−0.420376	+	0.907350i	$0.638102\pi$
$888$	28.8215	+	26.5805i	0.967187	+	0.891984i
$889$	9.07530			0.304376
$890$		0			0
$891$	−4.06542	+	23.0561i	−0.136197	+	0.772410i
$892$	44.7391	−	16.2837i	1.49798	−	0.545219i
$893$	50.5096	−	60.1950i	1.69024	−	2.01435i
$894$			121.607i			4.06715i
$895$		0			0
$896$	14.3637	−	8.29289i	0.479858	−	0.277046i
$897$	2.09816	+	0.763669i	0.0700556	+	0.0254982i
$898$	6.44213	−	11.1581i	0.214977	−	0.372350i
$899$	−4.99350	−	8.64900i	−0.166543	−	0.288460i
$900$		0			0
$901$	3.76285	+	10.3383i	0.125359	+	0.344420i
$902$	94.8797	+	54.7788i	3.15915	+	1.82393i
$903$	7.10136	+	8.46307i	0.236319	+	0.281633i
$904$	14.2604	−	11.9659i	0.474295	−	0.397981i
$905$		0			0
$906$	20.4138	+	3.59950i	0.678203	+	0.119585i
$907$	46.7556	+	8.24428i	1.55249	+	0.273747i	0.883109	−	0.469168i	$-0.155446\pi$
$907$	46.7556	+	8.24428i	1.55249	+	0.273747i	0.669386	+	0.742915i	$0.266557\pi$
$908$	−9.49291	+	26.0816i	−0.315033	+	0.865547i
$909$	−4.93495	+	4.14091i	−0.163682	+	0.137345i
$910$		0			0
$911$	−31.4589	−	18.1628i	−1.04228	−	0.601761i	−0.121803	−	0.992554i	$-0.538868\pi$
$911$	−31.4589	−	18.1628i	−1.04228	−	0.601761i	−0.920479	+	0.390793i	$0.872201\pi$
$912$	−3.80647	−	10.4582i	−0.126045	−	0.346306i
$913$	−1.86257	−	10.5631i	−0.0616419	−	0.349589i
$914$	30.6581	+	53.1014i	1.01408	+	1.75644i
$915$		0			0
$916$	−42.7899	−	15.5743i	−1.41382	−	0.514588i
$917$	3.33144	−	1.92341i	0.110014	−	0.0635166i
$918$	16.7044	+	14.0167i	0.551328	+	0.462619i
$919$			6.82416i			0.225108i	0.993646	+	0.112554i	$0.0359032\pi$
$919$			6.82416i			0.225108i	−0.993646	+	0.112554i	$0.964097\pi$
$920$		0			0
$921$	−19.9862	+	7.27437i	−0.658567	+	0.239699i
$922$	5.32656	−	30.2084i	0.175421	−	0.994861i
$923$	−5.16044	+	0.909926i	−0.169858	+	0.0299506i
$924$	36.1746			1.19006
$925$		0			0
$926$	29.1783			0.958859
$927$	24.1301	−	4.25479i	0.792537	−	0.139746i
$928$	8.58019	−	48.6607i	0.281658	−	1.59736i
$929$	−0.601856	+	0.219058i	−0.0197463	+	0.00718705i	−0.351874	−	0.936047i	$-0.614456\pi$
$929$	−0.601856	+	0.219058i	−0.0197463	+	0.00718705i	0.332128	+	0.943234i	$0.392233\pi$
$930$		0			0
$931$		−	38.6481i		−	1.26664i
$932$	−34.8589	−	29.2501i	−1.14184	−	0.958118i
$933$	−54.7450	+	31.6071i	−1.79227	+	1.03477i
$934$	34.2306	+	12.4589i	1.12006	+	0.407668i
$935$		0			0
$936$	2.21530	+	3.83701i	0.0724093	+	0.125417i
$937$	−0.663231	−	3.76137i	−0.0216668	−	0.122879i	0.972056	−	0.234749i	$-0.0754269\pi$
$937$	−0.663231	−	3.76137i	−0.0216668	−	0.122879i	−0.993723	+	0.111871i	$0.964316\pi$
$938$	1.35511	+	3.72313i	0.0442458	+	0.121564i
$939$	2.19112	+	1.26505i	0.0715046	+	0.0412832i
$940$		0			0
$941$	−24.6544	+	20.6875i	−0.803711	+	0.674394i	−0.949098	−	0.314981i	$-0.898002\pi$
$941$	−24.6544	+	20.6875i	−0.803711	+	0.674394i	0.145387	+	0.989375i	$0.453557\pi$
$942$	18.3232	−	50.3425i	0.597001	−	1.64025i
$943$	−19.7508	−	3.48260i	−0.643174	−	0.113409i
$944$	−5.02876	−	0.886706i	−0.163672	−	0.0288598i
$945$		0			0
$946$	32.5679	−	27.3277i	1.05887	−	0.888501i
$947$	−25.1449	−	29.9666i	−0.817101	−	0.973783i	0.182856	−	0.983140i	$-0.441466\pi$
$947$	−25.1449	−	29.9666i	−0.817101	−	0.973783i	−0.999956	+	0.00935710i	$0.997022\pi$
$948$	−107.768	−	62.2199i	−3.50014	−	2.02081i
$949$	1.99658	+	5.48557i	0.0648118	+	0.178069i
$950$		0			0
$951$	5.46086	+	9.45848i	0.177080	+	0.306712i
$952$	−4.67624	+	8.09948i	−0.151558	+	0.262506i
$953$	36.9080	+	13.4334i	1.19557	+	0.435151i	0.861675	−	0.507461i	$-0.169416\pi$
$953$	36.9080	+	13.4334i	1.19557	+	0.435151i	0.333892	+	0.942611i	$0.391638\pi$
$954$	−22.0677	+	12.7408i	−0.714469	+	0.412499i
$955$		0			0
$956$		−	22.4591i		−	0.726379i
$957$	58.8320	−	70.1132i	1.90177	−	2.26644i
$958$	−13.4859	+	4.90846i	−0.435709	+	0.158585i
$959$	2.94150	−	16.6821i	0.0949860	−	0.538692i
$960$		0			0
$961$	29.3428			0.946541
$962$	5.29299	+	3.39591i	0.170653	+	0.109488i
$963$	12.8572			0.414316
$964$	−43.8456	+	7.73116i	−1.41217	+	0.249004i
$965$		0			0
$966$	−10.2581	+	3.73363i	−0.330048	+	0.120128i
$967$	−11.6487	+	13.8824i	−0.374597	+	0.446428i	−0.920101	−	0.391681i	$-0.871894\pi$
$967$	−11.6487	+	13.8824i	−0.374597	+	0.446428i	0.545504	+	0.838108i	$0.316338\pi$
$968$		−	22.0449i		−	0.708550i
$969$	49.9755	+	41.9345i	1.60545	+	1.34713i
$970$		0			0
$971$	33.5219	+	12.2010i	1.07577	+	0.391548i	0.818331	−	0.574747i	$-0.194899\pi$
$971$	33.5219	+	12.2010i	1.07577	+	0.391548i	0.257438	+	0.966295i	$0.417122\pi$
$972$	32.9024	−	56.9886i	1.05534	−	1.82791i
$973$	7.54163	+	13.0625i	0.241773	+	0.418764i
$974$	−3.45118	−	19.5726i	−0.110583	−	0.627147i
$975$		0			0
$976$	1.63009	+	0.941131i	0.0521778	+	0.0301249i
$977$	−22.4068	−	26.7033i	−0.716856	−	0.854315i	0.277465	−	0.960736i	$-0.410506\pi$
$977$	−22.4068	−	26.7033i	−0.716856	−	0.854315i	−0.994321	+	0.106420i	$0.966061\pi$
$978$	−22.9337	+	19.2437i	−0.733340	+	0.615345i
$979$	0.107620	−	0.295683i	0.00343954	−	0.00945007i
$980$		0			0
$981$	−14.8186	−	2.61292i	−0.473122	−	0.0834242i
$982$	29.6765	−	81.5356i	0.947016	−	2.60191i
$983$	16.0808	−	13.4934i	0.512897	−	0.430371i	−0.349251	−	0.937029i	$-0.613564\pi$
$983$	16.0808	−	13.4934i	0.512897	−	0.430371i	0.862147	+	0.506658i	$0.169119\pi$
$984$	−44.9938	−	53.6216i	−1.43435	−	1.70939i
$985$		0			0
$986$	23.0239	+	63.2576i	0.733230	+	2.01453i
$987$	5.56412	+	31.5557i	0.177108	+	1.00443i
$988$	4.54562	+	7.87325i	0.144616	+	0.250481i
$989$	−3.89132	+	6.73996i	−0.123737	+	0.214318i
$990$		0			0
$991$	43.6715	−	25.2138i	1.38727	−	0.800942i	0.394265	−	0.918997i	$-0.370999\pi$
$991$	43.6715	−	25.2138i	1.38727	−	0.800942i	0.993007	+	0.118055i	$0.0376659\pi$
$992$	−6.28099	−	5.27037i	−0.199422	−	0.167335i
$993$			21.5282i			0.683176i
$994$	16.4676	−	19.6253i	0.522320	−	0.622476i
$995$		0			0
$996$	−3.38542	+	19.1997i	−0.107271	+	0.608365i
$997$	−2.95424	+	0.520912i	−0.0935617	+	0.0164975i	−0.220233	−	0.975447i	$-0.570682\pi$
$997$	−2.95424	+	0.520912i	−0.0935617	+	0.0164975i	0.126671	+	0.991945i	$0.459571\pi$
$998$	−19.2031			−0.607864
$999$	−0.715711	+	15.2693i	−0.0226441	+	0.483099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bb.e.176.3		96
5.2	odd	4		185.2.v.a.139.3	yes	96
5.3	odd	4		185.2.v.a.139.14	yes	96
5.4	even	2	inner	925.2.bb.e.176.14		96
37.4	even	18	inner	925.2.bb.e.226.3		96
185.4	even	18	inner	925.2.bb.e.226.14		96
185.78	odd	36		185.2.v.a.4.3	✓	96
185.152	odd	36		185.2.v.a.4.14	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.4.3	✓	96	185.78	odd	36
185.2.v.a.4.14	yes	96	185.152	odd	36
185.2.v.a.139.3	yes	96	5.2	odd	4
185.2.v.a.139.14	yes	96	5.3	odd	4
925.2.bb.e.176.3		96	1.1	even	1	trivial
925.2.bb.e.176.14		96	5.4	even	2	inner
925.2.bb.e.226.3		96	37.4	even	18	inner
925.2.bb.e.226.14		96	185.4	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.22054 + 0.391541i) q^{2} +(-0.457886 + 2.59680i) q^{3} +(2.89811 - 1.05483i) q^{4} -5.94558i q^{6} +(0.761600 + 0.639059i) q^{7} +(-2.11694 + 1.22222i) q^{8} +(-3.71464 - 1.35202i) q^{9} +(-2.23710 - 3.87477i) q^{11} +(1.41217 + 8.00880i) q^{12} +(0.156821 + 0.430863i) q^{13} +(-1.94138 - 1.12086i) q^{14} +(-0.502918 + 0.421999i) q^{16} +(1.31622 - 3.61628i) q^{17} +(8.77787 + 1.54777i) q^{18} +(6.33129 + 1.11638i) q^{19} +(-2.00823 + 1.68511i) q^{21} +(6.48469 + 7.72816i) q^{22} +(-1.59935 - 0.923384i) q^{23} +(-2.20453 - 6.05691i) q^{24} +(-0.516929 - 0.895348i) q^{26} +(1.25651 - 2.17633i) q^{27} +(2.88130 + 1.04871i) q^{28} +(6.71853 - 3.87895i) q^{29} -1.28733i q^{31} +(4.09402 - 4.87906i) q^{32} +(11.0863 - 4.03509i) q^{33} +(-1.50679 + 8.54544i) q^{34} -12.1916 q^{36} +(-5.40445 + 2.79140i) q^{37} -14.4960 q^{38} +(-1.19067 + 0.209948i) q^{39} +(10.2048 - 3.71426i) q^{41} +(3.79957 - 4.52816i) q^{42} -4.21419i q^{43} +(-10.5706 - 8.86975i) q^{44} +(3.91296 + 1.42420i) q^{46} +(6.11134 - 10.5851i) q^{47} +(-0.865567 - 1.49921i) q^{48} +(-1.04390 - 5.92024i) q^{49} +(8.78807 + 5.07379i) q^{51} +(0.908971 + 1.08327i) q^{52} +(-2.19000 + 1.83762i) q^{53} +(-1.93800 + 5.32461i) q^{54} +(-2.39333 - 0.422009i) q^{56} +(-5.79802 + 15.9299i) q^{57} +(-13.4000 + 11.2439i) q^{58} +(4.99958 + 5.95827i) q^{59} +(-0.980592 - 2.69415i) q^{61} +(0.504044 + 2.85858i) q^{62} +(-1.96505 - 3.40357i) q^{63} +(-6.52407 + 11.3000i) q^{64} +(-23.0377 + 13.3008i) q^{66} +(-1.35393 - 1.13608i) q^{67} -11.8687i q^{68} +(3.13016 - 3.73038i) q^{69} +(-1.98450 + 11.2547i) q^{71} +(9.51611 - 1.67795i) q^{72} +12.7316 q^{73} +(10.9079 - 8.31448i) q^{74} +(19.5263 - 3.44302i) q^{76} +(0.772428 - 4.38066i) q^{77} +(2.56173 - 0.932395i) q^{78} +(-9.83583 + 11.7219i) q^{79} +(-4.00843 - 3.36347i) q^{81} +(-21.2060 + 12.2433i) q^{82} +(2.25275 + 0.819933i) q^{83} +(-4.04259 + 7.00196i) q^{84} +(1.65003 + 9.35777i) q^{86} +(6.99653 + 19.2228i) q^{87} +(9.47160 + 5.46843i) q^{88} +(0.0452057 + 0.0538740i) q^{89} +(-0.155912 + 0.428364i) q^{91} +(-5.60910 - 0.989035i) q^{92} +(3.34295 + 0.589452i) q^{93} +(-9.42595 + 25.8976i) q^{94} +(10.7954 + 12.8654i) q^{96} +(11.3598 + 6.55858i) q^{97} +(4.63604 + 12.7374i) q^{98} +(3.07125 + 17.4179i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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