LMFDB - Embedded newform 345.2.t.a.4.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [345,2,Mod(4,345)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(345, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("345.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.t (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			4.12
Character	$\chi$	$=$	345.4
Dual form			345.2.t.a.259.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.00990606 + 0.00452394i) q^{2} +(0.281733 + 0.959493i) q^{3} +(-1.30964 + 1.51141i) q^{4} +(-0.715854 + 2.11838i) q^{5} +(-0.00713155 - 0.00823025i) q^{6} +(-0.520522 + 0.0748397i) q^{7} +(0.0122721 - 0.0417950i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(-0.00249216 - 0.0242233i) q^{10} +(1.18617 - 2.59736i) q^{11} +(-1.81916 - 0.830781i) q^{12} +(-3.11331 - 0.447626i) q^{13} +(0.00481775 - 0.00309618i) q^{14} +(-2.23425 - 0.0900389i) q^{15} +(-0.569158 - 3.95858i) q^{16} +(-3.43438 + 2.97590i) q^{17} +(0.00588768 - 0.00916140i) q^{18} +(-0.732287 + 0.845104i) q^{19} +(-2.26423 - 3.85628i) q^{20} +(-0.218456 - 0.478352i) q^{21} +0.0310958i q^{22} +(0.775939 + 4.73264i) q^{23} +0.0435594 q^{24} +(-3.97511 - 3.03291i) q^{25} +(0.0328656 - 0.00965022i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(0.568584 - 0.884735i) q^{28} +(4.90475 + 5.66038i) q^{29} +(0.0225400 - 0.00921571i) q^{30} +(-0.310721 - 0.0912358i) q^{31} +(0.0706465 + 0.109928i) q^{32} +(2.82633 + 0.406365i) q^{33} +(0.0205583 - 0.0450164i) q^{34} +(0.214078 - 1.15624i) q^{35} +(0.284613 - 1.97953i) q^{36} +(2.23090 + 3.47135i) q^{37} +(0.00343087 - 0.0116845i) q^{38} +(-0.447626 - 3.11331i) q^{39} +(0.0797528 + 0.0559161i) q^{40} +(6.17403 + 3.96781i) q^{41} +(0.00432808 + 0.00375030i) q^{42} +(0.441423 + 1.50335i) q^{43} +(2.37221 + 5.19441i) q^{44} +(-0.543071 - 2.16912i) q^{45} +(-0.0290967 - 0.0433715i) q^{46} -2.35771i q^{47} +(3.63788 - 1.66136i) q^{48} +(-6.45111 + 1.89422i) q^{49} +(0.0530983 + 0.0120610i) q^{50} +(-3.82293 - 2.45685i) q^{51} +(4.75387 - 4.11925i) q^{52} +(4.26337 - 0.612980i) q^{53} +(0.0104491 + 0.00306812i) q^{54} +(4.65308 + 4.37210i) q^{55} +(-0.00325997 + 0.0226736i) q^{56} +(-1.01718 - 0.464531i) q^{57} +(-0.0741939 - 0.0338832i) q^{58} +(-1.77924 + 12.3749i) q^{59} +(3.06216 - 3.25895i) q^{60} +(-8.58375 - 2.52042i) q^{61} +(0.00349076 - 0.000501896i) q^{62} +(0.397429 - 0.344374i) q^{63} +(6.72763 + 4.32359i) q^{64} +(3.17692 - 6.27475i) q^{65} +(-0.0298362 + 0.00876069i) q^{66} +(10.0411 - 4.58563i) q^{67} -9.08812i q^{68} +(-4.32233 + 2.07785i) q^{69} +(0.00311009 + 0.0124222i) q^{70} +(3.42206 + 7.49326i) q^{71} +(0.0122721 + 0.0417950i) q^{72} +(-9.01868 - 7.81473i) q^{73} +(-0.0378036 - 0.0242949i) q^{74} +(1.79014 - 4.66856i) q^{75} +(-0.318263 - 2.21357i) q^{76} +(-0.423044 + 1.44076i) q^{77} +(0.0185186 + 0.0288156i) q^{78} +(0.345206 - 2.40096i) q^{79} +(8.79323 + 1.62807i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-0.0791105 - 0.0113744i) q^{82} +(4.09529 + 6.37239i) q^{83} +(1.00909 + 0.296294i) q^{84} +(-3.84560 - 9.40564i) q^{85} +(-0.0111738 - 0.0128953i) q^{86} +(-4.04927 + 6.30078i) q^{87} +(-0.0939997 - 0.0814512i) q^{88} +(-1.34903 + 0.396110i) q^{89} +(0.0151927 + 0.0190306i) q^{90} +1.65404 q^{91} +(-8.16917 - 5.02532i) q^{92} -0.323838i q^{93} +(0.0106662 + 0.0233556i) q^{94} +(-1.26605 - 2.15624i) q^{95} +(-0.0855718 + 0.0987552i) q^{96} +(5.66197 - 8.81019i) q^{97} +(0.0553357 - 0.0479487i) q^{98} +(0.406365 + 2.82633i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) $ 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.00990606	+	0.00452394i	−0.00700464	+	0.00319891i	−0.418914	−	0.908026i	$-0.637589\pi$
$2$	−0.00990606	+	0.00452394i	−0.00700464	+	0.00319891i	0.411910	+	0.911225i	$0.364862\pi$
$3$	0.281733	+	0.959493i	0.162658	+	0.553964i
$3$	0.281733	+	0.959493i	0.162658	+	0.553964i
$4$	−1.30964	+	1.51141i	−0.654822	+	0.755705i
$5$	−0.715854	+	2.11838i	−0.320140	+	0.947370i
$5$	−0.715854	+	2.11838i	−0.320140	+	0.947370i
$6$	−0.00713155	−	0.00823025i	−0.00291144	−	0.00335998i
$7$	−0.520522	+	0.0748397i	−0.196739	+	0.0282868i	−0.239980	−	0.970778i	$-0.577141\pi$
$7$	−0.520522	+	0.0748397i	−0.196739	+	0.0282868i	0.0432410	+	0.999065i	$0.486232\pi$
$8$	0.0122721	−	0.0417950i	0.00433885	−	0.0147768i
$9$	−0.841254	+	0.540641i	−0.280418	+	0.180214i
$10$	−0.00249216	−	0.0242233i	−0.000788092	−	0.00766009i
$11$	1.18617	−	2.59736i	0.357645	−	0.783134i	−0.642217	−	0.766523i	$-0.721985\pi$
$11$	1.18617	−	2.59736i	0.357645	−	0.783134i	0.999862	−	0.0166106i	$-0.00528757\pi$
$12$	−1.81916	−	0.830781i	−0.525145	−	0.239826i
$13$	−3.11331	−	0.447626i	−0.863476	−	0.124149i	−0.303674	−	0.952776i	$-0.598214\pi$
$13$	−3.11331	−	0.447626i	−0.863476	−	0.124149i	−0.559802	+	0.828627i	$0.689123\pi$
$14$	0.00481775	−	0.00309618i	0.00128760	−	0.000827488i
$15$	−2.23425	−	0.0900389i	−0.576882	−	0.0232479i
$16$	−0.569158	−	3.95858i	−0.142290	−	0.989645i
$17$	−3.43438	+	2.97590i	−0.832958	+	0.721763i	−0.962929	−	0.269755i	$-0.913057\pi$
$17$	−3.43438	+	2.97590i	−0.832958	+	0.721763i	0.129971	+	0.991518i	$0.458512\pi$
$18$	0.00588768	−	0.00916140i	0.00138774	−	0.00215936i
$19$	−0.732287	+	0.845104i	−0.167998	+	0.193880i	−0.833506	−	0.552511i	$-0.813670\pi$
$19$	−0.732287	+	0.845104i	−0.167998	+	0.193880i	0.665507	+	0.746391i	$0.268215\pi$
$20$	−2.26423	−	3.85628i	−0.506298	−	0.862290i
$21$	−0.218456	−	0.478352i	−0.0476710	−	0.104385i
$22$			0.0310958i			0.00662964i
$23$	0.775939	+	4.73264i	0.161794	+	0.986824i
$23$	0.775939	+	4.73264i	0.161794	+	0.986824i
$24$	0.0435594			0.00889153
$25$	−3.97511	−	3.03291i	−0.795021	−	0.606582i
$26$	0.0328656	−	0.00965022i	0.00644548	−	0.00189256i
$27$	−0.755750	−	0.654861i	−0.145444	−	0.126028i
$28$	0.568584	−	0.884735i	0.107452	−	0.167199i
$29$	4.90475	+	5.66038i	0.910789	+	1.05111i	0.998489	+	0.0549591i	$0.0175029\pi$
$29$	4.90475	+	5.66038i	0.910789	+	1.05111i	−0.0877000	+	0.996147i	$0.527952\pi$
$30$	0.0225400	−	0.00921571i	0.00411522	−	0.00168255i
$31$	−0.310721	−	0.0912358i	−0.0558071	−	0.0163864i	0.253710	−	0.967280i	$-0.418349\pi$
$31$	−0.310721	−	0.0912358i	−0.0558071	−	0.0163864i	−0.309517	+	0.950894i	$0.600167\pi$
$32$	0.0706465	+	0.109928i	0.0124887	+	0.0194327i
$33$	2.82633	+	0.406365i	0.492001	+	0.0707391i
$34$	0.0205583	−	0.0450164i	0.00352572	−	0.00772025i
$35$	0.214078	−	1.15624i	0.0361858	−	0.195440i
$36$	0.284613	−	1.97953i	0.0474355	−	0.329921i
$37$	2.23090	+	3.47135i	0.366758	+	0.570687i	0.974762	−	0.223247i	$-0.0716658\pi$
$37$	2.23090	+	3.47135i	0.366758	+	0.570687i	−0.608004	+	0.793934i	$0.708029\pi$
$38$	0.00343087	−	0.0116845i	0.000556561	−	0.00189547i
$39$	−0.447626	−	3.11331i	−0.0716775	−	0.498528i
$40$	0.0797528	+	0.0559161i	0.0126100	+	0.00884112i
$41$	6.17403	+	3.96781i	0.964222	+	0.619668i	0.925163	−	0.379569i	$-0.123928\pi$
$41$	6.17403	+	3.96781i	0.964222	+	0.619668i	0.0390585	+	0.999237i	$0.487564\pi$
$42$	0.00432808	+	0.00375030i	0.000667837	+	0.000578684i
$43$	0.441423	+	1.50335i	0.0673164	+	0.229259i	0.986279	−	0.165085i	$-0.0527900\pi$
$43$	0.441423	+	1.50335i	0.0673164	+	0.229259i	−0.918963	+	0.394344i	$0.870972\pi$
$44$	2.37221	+	5.19441i	0.357624	+	0.783087i
$45$	−0.543071	−	2.16912i	−0.0809562	−	0.323353i
$46$	−0.0290967	−	0.0433715i	−0.00429008	−	0.00639478i
$47$		−	2.35771i		−	0.343908i	−0.985105	−	0.171954i	$-0.944992\pi$
$47$		−	2.35771i		−	0.343908i	0.985105	−	0.171954i	$-0.0550080\pi$
$48$	3.63788	−	1.66136i	0.525083	−	0.239797i
$49$	−6.45111	+	1.89422i	−0.921587	+	0.270602i
$50$	0.0530983	+	0.0120610i	0.00750924	+	0.00170568i
$51$	−3.82293	−	2.45685i	−0.535318	−	0.344028i
$52$	4.75387	−	4.11925i	0.659243	−	0.571237i
$53$	4.26337	−	0.612980i	0.585618	−	0.0841992i	0.156864	−	0.987620i	$-0.449862\pi$
$53$	4.26337	−	0.612980i	0.585618	−	0.0841992i	0.428755	+	0.903421i	$0.358953\pi$
$54$	0.0104491	+	0.00306812i	0.00142194	+	0.000417518i
$55$	4.65308	+	4.37210i	0.627421	+	0.589534i
$56$	−0.00325997	+	0.0226736i	−0.000435632	+	0.00302989i
$57$	−1.01718	−	0.464531i	−0.134729	−	0.0615286i
$58$	−0.0741939	−	0.0338832i	−0.00974214	−	0.00444909i
$59$	−1.77924	+	12.3749i	−0.231637	+	1.61107i	0.459383	+	0.888238i	$0.348070\pi$
$59$	−1.77924	+	12.3749i	−0.231637	+	1.61107i	−0.691021	+	0.722835i	$0.742839\pi$
$60$	3.06216	−	3.25895i	0.395324	−	0.420729i
$61$	−8.58375	−	2.52042i	−1.09904	−	0.322706i	−0.318567	−	0.947900i	$-0.603202\pi$
$61$	−8.58375	−	2.52042i	−1.09904	−	0.322706i	−0.780469	+	0.625194i	$0.785020\pi$
$62$	0.00349076		0.000501896i	0.000443327		6.37408e-5i
$63$	0.397429	−	0.344374i	0.0500714	−	0.0433871i
$64$	6.72763	+	4.32359i	0.840954	+	0.540448i
$65$	3.17692	−	6.27475i	0.394048	−	0.778287i
$66$	−0.0298362	+	0.00876069i	−0.00367258	+	0.00107837i
$67$	10.0411	−	4.58563i	1.22672	−	0.560224i	0.306591	−	0.951841i	$-0.400812\pi$
$67$	10.0411	−	4.58563i	1.22672	−	0.560224i	0.920128	+	0.391618i	$0.128084\pi$
$68$		−	9.08812i		−	1.10210i
$69$	−4.32233	+	2.07785i	−0.520348	+	0.250143i
$70$	0.00311009	+	0.0124222i	0.000371727	+	0.00148474i
$71$	3.42206	+	7.49326i	0.406124	+	0.889287i	0.996612	+	0.0822410i	$0.0262077\pi$
$71$	3.42206	+	7.49326i	0.406124	+	0.889287i	−0.590489	+	0.807046i	$0.701065\pi$
$72$	0.0122721	+	0.0417950i	0.00144628	+	0.00492558i
$73$	−9.01868	−	7.81473i	−1.05556	−	0.914645i	−0.0590583	−	0.998255i	$-0.518810\pi$
$73$	−9.01868	−	7.81473i	−1.05556	−	0.914645i	−0.996499	+	0.0836093i	$0.973355\pi$
$74$	−0.0378036	−	0.0242949i	−0.00439458	−	0.00282423i
$75$	1.79014	−	4.66856i	0.206707	−	0.539078i
$76$	−0.318263	−	2.21357i	−0.0365073	−	0.253914i
$77$	−0.423044	+	1.44076i	−0.0482103	+	0.164189i
$78$	0.0185186	+	0.0288156i	0.00209682	+	0.00326272i
$79$	0.345206	−	2.40096i	0.0388387	−	0.270129i	−0.961144	−	0.276048i	$-0.910975\pi$
$79$	0.345206	−	2.40096i	0.0388387	−	0.270129i	0.999982	+	0.00591927i	$0.00188417\pi$
$80$	8.79323	+	1.62807i	0.983113	+	0.182024i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−0.0791105	−	0.0113744i	−0.00873629	−	0.00125609i
$83$	4.09529	+	6.37239i	0.449516	+	0.699461i	0.989870	−	0.141977i	$-0.0453459\pi$
$83$	4.09529	+	6.37239i	0.449516	+	0.699461i	−0.540354	+	0.841438i	$0.681710\pi$
$84$	1.00909	+	0.296294i	0.110100	+	0.0323284i
$85$	−3.84560	−	9.40564i	−0.417113	−	1.02018i
$86$	−0.0111738	−	0.0128953i	−0.00120490	−	0.00139053i
$87$	−4.04927	+	6.30078i	−0.434127	+	0.675515i
$88$	−0.0939997	−	0.0814512i	−0.0100204	−	0.00868273i
$89$	−1.34903	+	0.396110i	−0.142997	+	0.0419876i	−0.352448	−	0.935832i	$-0.614651\pi$
$89$	−1.34903	+	0.396110i	−0.142997	+	0.0419876i	0.209451	+	0.977819i	$0.432832\pi$
$90$	0.0151927	+	0.0190306i	0.00160145	+	0.00200600i
$91$	1.65404			0.173391
$92$	−8.16917	−	5.02532i	−0.851694	−	0.523925i
$93$		−	0.323838i		−	0.0335805i
$94$	0.0106662	+	0.0233556i	0.00110013	+	0.00240895i
$95$	−1.26605	−	2.15624i	−0.129893	−	0.221225i
$96$	−0.0855718	+	0.0987552i	−0.00873364	+	0.0100792i
$97$	5.66197	−	8.81019i	0.574886	−	0.894539i	−0.425058	−	0.905166i	$-0.639746\pi$
$97$	5.66197	−	8.81019i	0.574886	−	0.894539i	0.999944	+	0.0106267i	$0.00338264\pi$
$98$	0.0553357	−	0.0479487i	0.00558975	−	0.00484355i
$99$	0.406365	+	2.82633i	0.0408413	+	0.284057i
$100$	9.78994	−	2.03598i	0.978994	−	0.203598i
$101$	3.40568	−	2.18870i	0.338878	−	0.217784i	−0.360122	−	0.932905i	$-0.617265\pi$
$101$	3.40568	−	2.18870i	0.338878	−	0.217784i	0.699000	+	0.715122i	$0.253629\pi$
$102$	0.0489848	+	0.00704296i	0.00485022	+	0.000697357i
$103$	−0.151664	−	0.0692629i	−0.0149439	−	0.00682467i	0.407929	−	0.913014i	$-0.366251\pi$
$103$	−0.151664	−	0.0692629i	−0.0149439	−	0.00682467i	−0.422873	+	0.906189i	$0.638978\pi$
$104$	−0.0569154	+	0.124627i	−0.00558101	+	0.0122207i
$105$	1.16972	−	0.120344i	0.114153	−	0.0117443i
$106$	−0.0394601	+	0.0253594i	−0.00383270	+	0.00246313i
$107$	−1.70597	+	5.81000i	−0.164922	+	0.561674i	0.835012	+	0.550232i	$0.185461\pi$
$107$	−1.70597	+	5.81000i	−0.164922	+	0.561674i	−0.999935	+	0.0114426i	$0.996358\pi$
$108$	1.97953	−	0.284613i	0.190480	−	0.0273869i
$109$	12.0600	+	13.9180i	1.15514	+	1.33310i	0.933752	+	0.357919i	$0.116514\pi$
$109$	12.0600	+	13.9180i	1.15514	+	1.33310i	0.221389	+	0.975185i	$0.428941\pi$
$110$	−0.0658728	−	0.0222600i	−0.00628073	−	0.00212241i
$111$	−2.70222	+	3.11853i	−0.256483	+	0.295998i
$112$	0.592518	+	2.01793i	0.0559877	+	0.190677i
$113$	3.14225	−	1.43502i	0.295598	−	0.134995i	−0.262096	−	0.965042i	$-0.584414\pi$
$113$	3.14225	−	1.43502i	0.295598	−	0.134995i	0.557694	+	0.830047i	$0.311686\pi$
$114$	0.0121778			0.00114055
$115$	−10.5810	−	1.74415i	−0.986685	−	0.162642i
$116$	−14.9786			−1.39073
$117$	2.86109	−	1.30661i	0.264507	−	0.120796i
$118$	−0.0383580	−	0.130636i	−0.00353114	−	0.0120260i
$119$	1.56495	−	1.80605i	0.143459	−	0.165560i
$120$	−0.0311822	+	0.0922756i	−0.00284653	+	0.00842357i
$121$	1.86420	+	2.15140i	0.169473	+	0.195582i
$122$	0.0964333	−	0.0138650i	0.00873066	−	0.00125528i
$123$	−2.06766	+	7.04180i	−0.186435	+	0.634938i
$124$	0.544828	−	0.350140i	0.0489270	−	0.0314435i
$125$	9.27046	−	6.24968i	0.829175	−	0.558989i
$126$	−0.00237903	+	0.00520934i	−0.000211940	+	0.000464085i
$127$	17.9256	+	8.18635i	1.59064	+	0.726421i	0.996933	−	0.0782610i	$-0.0249367\pi$
$127$	17.9256	+	8.18635i	1.59064	+	0.726421i	0.593707	+	0.804682i	$0.297664\pi$
$128$	−0.344888	−	0.0495873i	−0.0304840	−	0.00438294i
$129$	−1.31809	+	0.847085i	−0.116051	+	0.0745817i
$130$	−0.00308411	+	0.0765302i	−0.000270495	+	0.00671214i
$131$	−2.52412	−	17.5556i	−0.220533	−	1.53384i	−0.736029	−	0.676950i	$-0.763301\pi$
$131$	−2.52412	−	17.5556i	−0.220533	−	1.53384i	0.515496	−	0.856892i	$-0.327608\pi$
$132$	−4.31567	+	3.73955i	−0.375631	+	0.325486i
$133$	0.317924	−	0.494699i	0.0275675	−	0.0428959i
$134$	−0.0787228	+	0.0908510i	−0.00680062	+	0.00784833i
$135$	1.92825	−	1.13218i	0.165958	−	0.0974429i
$136$	0.0822307	+	0.180060i	0.00705123	+	0.0154400i
$137$		−	2.49325i		−	0.213013i	−0.994312	−	0.106507i	$-0.966034\pi$
$137$		−	2.49325i		−	0.213013i	0.994312	−	0.106507i	$-0.0339665\pi$
$138$	0.0334172	−	0.0401373i	0.00284466	−	0.00341671i
$139$	−11.7943			−1.00038			−0.500190	−	0.865916i	$-0.666737\pi$
$139$	−11.7943			−1.00038			−0.500190	+	0.865916i	$0.666737\pi$
$140$	1.46718	+	1.83782i	0.124000	+	0.155324i
$141$	2.26221	−	0.664245i	0.190512	−	0.0559395i
$142$	−0.0677982	−	0.0587475i	−0.00568950	−	0.00492998i
$143$	−4.85557	+	7.55542i	−0.406043	+	0.631816i
$144$	2.61898	+	3.02246i	0.218248	+	0.251872i
$145$	−15.5019	+	6.33813i	−1.28737	+	0.526353i
$146$	0.124693	+	0.0366132i	0.0103197	+	0.00303013i
$147$	−3.63497	−	5.65613i	−0.299808	−	0.466510i
$148$	−8.16832	−	1.17443i	−0.671432	−	0.0965373i
$149$	7.18098	−	15.7241i	0.588289	−	1.28817i	−0.348182	−	0.937427i	$-0.613201\pi$
$149$	7.18098	−	15.7241i	0.588289	−	1.28817i	0.936471	−	0.350746i	$-0.114072\pi$
$150$	0.00338709	+	0.0543454i	0.000276555	+	0.00443729i
$151$	−1.75461	+	12.2036i	−0.142788	+	0.993115i	0.784864	+	0.619669i	$0.212733\pi$
$151$	−1.75461	+	12.2036i	−0.142788	+	0.993115i	−0.927652	+	0.373446i	$0.878176\pi$
$152$	0.0263344	+	0.0409771i	0.00213600	+	0.00332368i
$153$	1.28029	−	4.36025i	0.103505	−	0.352506i
$154$	−0.00232720	−	0.0161860i	−0.000187531	−	0.00130431i
$155$	0.415703	−	0.592914i	0.0333901	−	0.0476240i
$156$	5.29171	+	3.40078i	0.423676	+	0.272280i
$157$	−3.73320	−	3.23483i	−0.297941	−	0.258168i	0.493042	−	0.870006i	$-0.335885\pi$
$157$	−3.73320	−	3.23483i	−0.297941	−	0.258168i	−0.790983	+	0.611838i	$0.790430\pi$
$158$	0.00744217	+	0.0253457i	0.000592067	+	0.00201640i
$159$	1.78928	+	3.91797i	0.141899	+	0.310716i
$160$	−0.283443	+	0.0709640i	−0.0224081	+	0.00561020i
$161$	−0.758083	−	2.40537i	−0.0597453	−	0.189570i
$162$			0.0108902i			0.000855613i
$163$	−22.0234	+	10.0577i	−1.72500	+	0.787783i	−0.730522	+	0.682890i	$0.760723\pi$
$163$	−22.0234	+	10.0577i	−1.72500	+	0.787783i	−0.994483	+	0.104894i	$0.966550\pi$
$164$	−14.0828	+	4.13507i	−1.09968	+	0.322895i
$165$	−2.88408	+	5.69636i	−0.224525	+	0.443461i
$166$	−0.0693965	−	0.0445984i	−0.00538621	−	0.00346151i
$167$	−1.69464	+	1.46841i	−0.131135	+	0.113629i	−0.717959	−	0.696085i	$-0.754924\pi$
$167$	−1.69464	+	1.46841i	−0.131135	+	0.113629i	0.586824	+	0.809715i	$0.300378\pi$
$168$	−0.0226736	+	0.00325997i	−0.00174931	+	0.000251513i
$169$	−2.98110	−	0.875329i	−0.229315	−	0.0673330i
$170$	0.0806453	+	0.0757755i	0.00618521	+	0.00581172i
$171$	0.159141	−	1.10685i	0.0121698	−	0.0846430i
$172$	−2.85028	−	1.30168i	−0.217332	−	0.0992522i
$173$	−9.63999	−	4.40244i	−0.732915	−	0.334711i	0.0137553	−	0.999905i	$-0.495621\pi$
$173$	−9.63999	−	4.40244i	−0.732915	−	0.334711i	−0.746670	+	0.665194i	$0.768349\pi$
$174$	0.0116079	−	0.0807346i	0.000879991	−	0.00612047i
$175$	2.29611	+	1.28120i	0.173570	+	0.0968495i
$176$	−10.9570	−	3.21726i	−0.825914	−	0.242510i
$177$	−12.3749	+	1.77924i	−0.930153	+	0.133736i
$178$	0.0115716	−	0.0100268i	0.000867325	−	0.000751541i
$179$	−2.20316	−	1.41589i	−0.164672	−	0.105828i	0.455709	−	0.890129i	$-0.349386\pi$
$179$	−2.20316	−	1.41589i	−0.164672	−	0.105828i	−0.620381	+	0.784300i	$0.713022\pi$
$180$	3.98966	+	2.01997i	0.297371	+	0.150560i
$181$	16.6312	−	4.88336i	1.23619	−	0.362977i	0.402605	−	0.915374i	$-0.368105\pi$
$181$	16.6312	−	4.88336i	1.23619	−	0.362977i	0.833582	+	0.552396i	$0.186287\pi$
$182$	−0.0163850	+	0.00748280i	−0.00121454	+	0.000554662i
$183$		−	8.94613i		−	0.661317i
$184$	0.207323	+	0.0256492i	0.0152841	+	0.00189088i
$185$	−8.95066	+	2.24093i	−0.658065	+	0.164756i
$186$	0.00146503	+	0.00320796i	0.000107421	+	0.000235219i
$187$	3.65572	+	12.4503i	0.267333	+	0.910453i
$188$	3.56347	+	3.08777i	0.259893	+	0.225198i
$189$	0.442394	+	0.284309i	0.0321794	+	0.0206804i
$190$	0.0222962	+	0.0156323i	0.00161754	+	0.00113408i
$191$	1.49793	+	10.4184i	0.108387	+	0.753846i	0.969439	+	0.245331i	$0.0788965\pi$
$191$	1.49793	+	10.4184i	0.108387	+	0.753846i	−0.861053	+	0.508516i	$0.830194\pi$
$192$	−2.25306	+	7.67321i	−0.162600	+	0.553766i
$193$	0.155735	+	0.242328i	0.0112100	+	0.0174431i	0.846813	−	0.531890i	$-0.178518\pi$
$193$	0.155735	+	0.242328i	0.0112100	+	0.0174431i	−0.835603	+	0.549333i	$0.814882\pi$
$194$	−0.0162309	+	0.112889i	−0.00116531	+	0.00810493i
$195$	6.91562	+	1.28043i	0.495238	+	0.0916934i
$196$	5.58572	−	12.2310i	0.398980	−	0.873644i
$197$	−14.5747	−	2.09553i	−1.03840	−	0.149300i	−0.398037	−	0.917369i	$-0.630309\pi$
$197$	−14.5747	−	2.09553i	−1.03840	−	0.149300i	−0.640367	+	0.768069i	$0.721218\pi$
$198$	−0.0168116	−	0.0261594i	−0.00119475	−	0.00185907i
$199$	5.95235	+	1.74777i	0.421951	+	0.123896i	0.485813	−	0.874063i	$-0.338524\pi$
$199$	5.95235	+	1.74777i	0.421951	+	0.123896i	−0.0638620	+	0.997959i	$0.520342\pi$
$200$	−0.175543	+	0.128919i	−0.0124128	+	0.00911597i
$201$	7.22879	+	8.34247i	0.509879	+	0.588432i
$202$	−0.0238353	+	0.0370885i	−0.00167705	+	0.00260954i
$203$	−2.97665	−	2.57928i	−0.208920	−	0.181030i
$204$	8.71999	−	2.56042i	0.610521	−	0.179265i
$205$	−12.8251	+	10.2386i	−0.895740	+	0.715095i
$206$	0.00181574			0.000126508
$207$	−3.21142	−	3.56185i	−0.223209	−	0.247566i
$208$			12.5790i			0.872200i
$209$	1.32642	+	2.90445i	0.0917504	+	0.200905i
$210$	−0.0110428	+	0.00648386i	−0.000762029	+	0.000447429i
$211$	−3.25800	+	3.75994i	−0.224290	+	0.258845i	−0.856730	−	0.515765i	$-0.827508\pi$
$211$	−3.25800	+	3.75994i	−0.224290	+	0.258845i	0.632440	+	0.774609i	$0.282053\pi$
$212$	−4.65703	+	7.24648i	−0.319846	+	0.497690i
$213$	−6.22563	+	5.39454i	−0.426573	+	0.369628i
$214$	−0.00938469	−	0.0652719i	−0.000641524	−	0.00446190i
$215$	−3.50067	−	0.141074i	−0.238743	−	0.00962120i
$216$	−0.0366445	+	0.0235500i	−0.00249334	+	0.00160237i
$217$	0.168565	+	0.0242360i	0.0114429	+	0.00164525i
$218$	−0.182432	−	0.0833138i	−0.0123558	−	0.00564272i
$219$	4.95732	−	10.8550i	0.334985	−	0.733515i
$220$	−12.7019	+	1.30681i	−0.856363	+	0.0881051i
$221$	12.0244	−	7.72758i	0.808846	−	0.519814i
$222$	0.0126603	−	0.0431170i	0.000849703	−	0.00289382i
$223$	25.5363	−	3.67156i	1.71004	−	0.245866i	0.783318	−	0.621621i	$-0.213526\pi$
$223$	25.5363	−	3.67156i	1.71004	−	0.245866i	0.926719	+	0.375755i	$0.122617\pi$
$224$	−0.0450000	−	0.0519328i	−0.00300669	−	0.00346991i
$225$	4.98379	+	0.402340i	0.332252	+	0.0268226i
$226$	−0.0246353	+	0.0284307i	−0.00163872	+	0.00189118i
$227$	−1.11468	−	3.79623i	−0.0739836	−	0.251965i	0.914194	−	0.405276i	$-0.132825\pi$
$227$	−1.11468	−	3.79623i	−0.0739836	−	0.251965i	−0.988178	+	0.153311i	$0.951006\pi$
$228$	2.03424	−	0.929006i	0.134721	−	0.0615250i
$229$	−23.2812			−1.53847			−0.769233	−	0.638969i	$-0.779361\pi$
$229$	−23.2812			−1.53847			−0.769233	+	0.638969i	$0.779361\pi$
$230$	0.112707	−	0.0305903i	0.00743165	−	0.00201707i
$231$	−1.50158			−0.0987967
$232$	0.296767	−	0.135529i	0.0194837	−	0.00889791i
$233$	−5.26822	−	17.9419i	−0.345133	−	1.17541i	−0.931004	−	0.365010i	$-0.881066\pi$
$233$	−5.26822	−	17.9419i	−0.345133	−	1.17541i	0.585871	−	0.810404i	$-0.300752\pi$
$234$	−0.0224310	+	0.0258868i	−0.00146636	+	0.00169227i
$235$	4.99455	+	1.68778i	0.325808	+	0.110099i
$236$	−16.3734	−	18.8959i	−1.06581	−	1.23002i
$237$	2.40096	−	0.345206i	0.155959	−	0.0224235i
$238$	−0.00733202	+	0.0249706i	−0.000475264	+	0.00161860i
$239$	−7.84729	+	5.04314i	−0.507599	+	0.326214i	−0.769249	−	0.638949i	$-0.779370\pi$
$239$	−7.84729	+	5.04314i	−0.507599	+	0.326214i	0.261651	+	0.965163i	$0.415733\pi$
$240$	0.915218	+	8.89572i	0.0590770	+	0.574217i
$241$	5.55324	−	12.1599i	0.357716	−	0.783289i	−0.642145	−	0.766584i	$-0.721955\pi$
$241$	5.55324	−	12.1599i	0.357716	−	0.783289i	0.999860	−	0.0167051i	$-0.00531763\pi$
$242$	−0.0281997	−	0.0128784i	−0.00181274	−	0.000827852i
$243$	0.989821	+	0.142315i	0.0634971	+	0.00912950i
$244$	15.0510	−	9.67271i	0.963544	−	0.619232i
$245$	0.605373	−	15.0219i	0.0386758	−	0.959715i
$246$	−0.0113744	−	0.0791105i	−0.000725203	−	0.00504390i
$247$	2.65812	−	2.30328i	0.169132	−	0.146554i
$248$	−0.00762640	+	0.0118669i	−0.000484277	+	0.000753549i
$249$	−4.96049	+	5.72471i	−0.314358	+	0.362789i
$250$	−0.0635605	+	0.103849i	−0.00401992	+	0.00656797i
$251$	2.03647	+	4.45924i	0.128541	+	0.281465i	0.962950	−	0.269681i	$-0.0869182\pi$
$251$	2.03647	+	4.45924i	0.128541	+	0.281465i	−0.834409	+	0.551146i	$0.814191\pi$
$252$			1.05169i			0.0662500i
$253$	13.2128	+	3.59835i	0.830680	+	0.226226i
$254$	−0.214607			−0.0134656
$255$	7.94122	−	6.33970i	0.497298	−	0.397007i
$256$	−15.3428	+	4.50505i	−0.958924	+	0.281566i
$257$	8.89193	+	7.70490i	0.554663	+	0.480619i	0.886507	−	0.462716i	$-0.153125\pi$
$257$	8.89193	+	7.70490i	0.554663	+	0.480619i	−0.331843	+	0.943335i	$0.607670\pi$
$258$	0.00922491	−	0.0143542i	0.000574318	−	0.000893655i
$259$	−1.42103	−	1.63995i	−0.0882984	−	0.101902i
$260$	5.32308	+	13.0193i	0.330124	+	0.807423i
$261$	−7.18637	−	2.11011i	−0.444825	−	0.130612i
$262$	0.104425	+	0.162488i	0.00645138	+	0.0100385i
$263$	17.1413	+	2.46454i	1.05698	+	0.151970i	0.648820	−	0.760942i	$-0.275263\pi$
$263$	17.1413	+	2.46454i	1.05698	+	0.151970i	0.408156	+	0.912912i	$0.366172\pi$
$264$	0.0516691	−	0.113140i	0.00318001	−	0.00696326i
$265$	−1.75342	+	9.47025i	−0.107712	+	0.581753i
$266$	−0.000911380		0.00633879i	−5.58803e−5		0.000388656i
$267$	−0.760130	−	1.18279i	−0.0465192	−	0.0723853i
$268$	−6.21953	+	21.1818i	−0.379919	+	1.29388i
$269$	−3.29252	−	22.9000i	−0.200748	−	1.39624i	−0.802071	−	0.597229i	$-0.796268\pi$
$269$	−3.29252	−	22.9000i	−0.200748	−	1.39624i	0.601323	−	0.799006i	$-0.294641\pi$
$270$	−0.0139794	+	0.0199388i	−0.000850762	+	0.00121344i
$271$	20.6855	+	13.2938i	1.25656	+	0.807539i	0.987809	−	0.155672i	$-0.0497542\pi$
$271$	20.6855	+	13.2938i	1.25656	+	0.807539i	0.268747	+	0.963211i	$0.413391\pi$
$272$	13.7351	+	11.9015i	0.832810	+	0.721634i
$273$	0.465998	+	1.58704i	0.0282035	+	0.0960522i
$274$	0.0112793	+	0.0246983i	0.000681410	+	0.00149208i
$275$	−12.5927	+	6.72722i	−0.759370	+	0.405667i
$276$	2.52024	−	9.25405i	0.151700	−	0.557029i
$277$		−	29.4647i		−	1.77036i	−0.465248	−	0.885180i	$-0.654035\pi$
$277$		−	29.4647i		−	1.77036i	0.465248	−	0.885180i	$-0.345965\pi$
$278$	0.116835	−	0.0533568i	0.00700730	−	0.00320013i
$279$	0.310721	−	0.0912358i	0.0186024	−	0.00546215i
$280$	−0.0456978	−	0.0231369i	−0.00273097	−	0.00138269i
$281$	17.4244	+	11.1980i	1.03945	+	0.668016i	0.944851	−	0.327499i	$-0.106206\pi$
$281$	17.4244	+	11.1980i	1.03945	+	0.668016i	0.0946016	+	0.995515i	$0.469842\pi$
$282$	−0.0194046	+	0.0168142i	−0.00115553	+	0.00100127i
$283$	7.68200	−	1.10450i	0.456647	−	0.0656560i	0.0898469	−	0.995956i	$-0.471362\pi$
$283$	7.68200	−	1.10450i	0.456647	−	0.0656560i	0.366801	+	0.930300i	$0.380453\pi$
$284$	−15.8071	−	4.64137i	−0.937977	−	0.275415i
$285$	1.71221	−	1.82224i	0.101422	−	0.107940i
$286$	0.0139193	−	0.0968107i	0.000823064	−	0.00572454i
$287$	−3.51067	−	1.60327i	−0.207228	−	0.0946379i
$288$	−0.118863	−	0.0542830i	−0.00700409	−	0.00319866i
$289$	0.519582	−	3.61377i	0.0305637	−	0.212575i
$290$	0.124890	−	0.132916i	0.00733378	−	0.00780509i
$291$	10.0485	+	2.95050i	0.589052	+	0.172961i
$292$	23.6225	−	3.39641i	1.38240	−	0.198760i
$293$	12.2739	−	10.6354i	0.717048	−	0.621326i	−0.217958	−	0.975958i	$-0.569939\pi$
$293$	12.2739	−	10.6354i	0.717048	−	0.621326i	0.935006	+	0.354633i	$0.115394\pi$
$294$	0.0615963	+	0.0395855i	0.00359237	+	0.00230867i
$295$	−24.9411	−	12.6277i	−1.45213	−	0.735215i
$296$	0.172463	−	0.0506397i	0.0100242	−	0.00294337i
$297$	−2.59736	+	1.18617i	−0.150714	+	0.0688288i
$298$			0.188251i			0.0109051i
$299$	−0.297281	−	15.0815i	−0.0171922	−	0.872186i
$300$	4.71166	+	8.81977i	0.272028	+	0.509210i
$301$	−0.342280	−	0.749490i	−0.0197287	−	0.0431999i
$302$	−0.0378271	−	0.128827i	−0.00217671	−	0.00741318i
$303$	3.05953	+	2.65110i	0.175765	+	0.152302i
$304$	3.76220	+	2.41782i	0.215777	+	0.138671i
$305$	11.4839	−	16.3794i	0.657567	−	0.937884i
$306$	0.00704296	+	0.0489848i	0.000402619	+	0.00280028i
$307$	9.13563	−	31.1131i	0.521398	−	1.77572i	−0.103076	−	0.994673i	$-0.532869\pi$
$307$	9.13563	−	31.1131i	0.521398	−	1.77572i	0.624474	−	0.781045i	$-0.285313\pi$
$308$	−1.62353	−	2.52627i	−0.0925094	−	0.143948i
$309$	0.0237284	−	0.165035i	0.00134986	−	0.00938849i
$310$	−0.00143567	+	0.00775406i	−8.15404e−5	+	0.000440401i
$311$	−8.49706	+	18.6060i	−0.481824	+	1.05505i	0.500134	+	0.865948i	$0.333284\pi$
$311$	−8.49706	+	18.6060i	−0.481824	+	1.05505i	−0.981958	+	0.189099i	$0.939443\pi$
$312$	−0.135614	−	0.0194983i	−0.00767762	−	0.00110388i
$313$	−6.08344	−	9.46602i	−0.343856	−	0.535051i	0.625654	−	0.780100i	$-0.284832\pi$
$313$	−6.08344	−	9.46602i	−0.343856	−	0.535051i	−0.969511	+	0.245050i	$0.921196\pi$
$314$	0.0516154	+	0.0151557i	0.00291283	+	0.000855283i
$315$	0.445016	+	1.08843i	0.0250738	+	0.0613261i
$316$	3.17673	+	3.66615i	0.178705	+	0.206237i
$317$	−4.66785	+	7.26332i	−0.262173	+	0.407949i	−0.947237	−	0.320534i	$-0.896138\pi$
$317$	−4.66785	+	7.26332i	−0.262173	+	0.407949i	0.685064	+	0.728483i	$0.259774\pi$
$318$	−0.0354494	−	0.0307171i	−0.00198790	−	0.00172253i
$319$	20.5199	−	6.02520i	1.14890	−	0.337346i
$320$	−13.9750	+	11.1567i	−0.781228	+	0.623676i
$321$	−6.05528			−0.337973
$322$	0.0183914	+	0.0203982i	0.00102491	+	0.00113675i
$323$		−	5.08162i		−	0.282749i
$324$	0.830781	+	1.81916i	0.0461545	+	0.101064i
$325$	11.0181	+	11.2217i	0.611175	+	0.622470i
$326$	0.172664	−	0.199265i	0.00956299	−	0.0110363i
$327$	−9.95654	+	15.4927i	−0.550598	+	0.856747i
$328$	0.241603	−	0.209350i	0.0133403	−	0.0115594i
$329$	0.176451	+	1.22724i	0.00972804	+	0.0676600i
$330$	0.00279983	−	0.0694759i	0.000154126	−	0.00382452i
$331$	−17.9746	+	11.5516i	−0.987975	+	0.634933i	−0.931603	−	0.363477i	$-0.881590\pi$
$331$	−17.9746	+	11.5516i	−0.987975	+	0.634933i	−0.0563721	+	0.998410i	$0.517953\pi$
$332$	−14.9947	−	2.15591i	−0.822939	−	0.118321i
$333$	−3.75351	−	1.71417i	−0.205691	−	0.0939359i
$334$	0.0101442	−	0.0222127i	0.000555065	−	0.00121542i
$335$	2.52614	+	24.5536i	0.138018	+	1.34151i
$336$	−1.76926	+	1.13703i	−0.0965210	+	0.0620303i
$337$	0.860568	−	2.93082i	0.0468781	−	0.159652i	−0.932728	−	0.360582i	$-0.882578\pi$
$337$	0.860568	−	2.93082i	0.0468781	−	0.159652i	0.979606	+	0.200930i	$0.0643963\pi$
$338$	0.0334909	−	0.00481526i	0.00182166	−	0.000261916i
$339$	2.26216	+	2.61067i	0.122864	+	0.141792i
$340$	19.2521	+	6.50577i	1.04409	+	0.352825i
$341$	−0.605541	+	0.698832i	−0.0327919	+	0.0378439i
$342$	0.00343087	+	0.0116845i	0.000185520	+	0.000631824i
$343$	6.56464	−	2.99797i	0.354457	−	0.161875i
$344$	0.0682496			0.00367977
$345$	−1.30752	−	10.6438i	−0.0703946	−	0.573043i
$346$	0.115411			0.00620452
$347$	17.7956	−	8.12697i	0.955317	−	0.436279i	0.124127	−	0.992266i	$-0.460387\pi$
$347$	17.7956	−	8.12697i	0.955317	−	0.436279i	0.831191	+	0.555988i	$0.187660\pi$
$348$	−4.21997	−	14.3719i	−0.226214	−	0.770414i
$349$	5.67498	−	6.54927i	0.303775	−	0.350575i	−0.583253	−	0.812290i	$-0.698221\pi$
$349$	5.67498	−	6.54927i	0.303775	−	0.350575i	0.887028	+	0.461716i	$0.152766\pi$
$350$	−0.0285415	−	0.00230414i	−0.00152561	−	0.000123162i
$351$	2.05975	+	2.37708i	0.109941	+	0.126879i
$352$	0.369322	−	0.0531005i	0.0196849	−	0.00283027i
$353$	−9.44710	+	32.1739i	−0.502818	+	1.71244i	0.181618	+	0.983369i	$0.441867\pi$
$353$	−9.44710	+	32.1739i	−0.502818	+	1.71244i	−0.684436	+	0.729073i	$0.739952\pi$
$354$	0.114537	−	0.0736085i	0.00608758	−	0.00391225i
$355$	−18.3233	+	1.88515i	−0.972500	+	0.100054i
$356$	1.16806	−	2.55770i	0.0619071	−	0.135558i
$357$	2.17379	+	0.992736i	0.115049	+	0.0525412i
$358$	0.0282300	+	0.00405887i	0.00149200	+	0.000214518i
$359$	24.4155	−	15.6909i	1.28860	−	0.828133i	0.296678	−	0.954978i	$-0.404121\pi$
$359$	24.4155	−	15.6909i	1.28860	−	0.828133i	0.991923	+	0.126845i	$0.0404850\pi$
$360$	−0.0973228	−	0.00392204i	−0.00512936	−	0.000206710i
$361$	2.52603	+	17.5689i	0.132949	+	0.924678i
$362$	−0.142657	+	0.123613i	−0.00749791	+	0.00649698i
$363$	−1.53905	+	2.39480i	−0.0807790	+	0.125695i
$364$	−2.16621	+	2.49994i	−0.113540	+	0.131032i
$365$	23.0107	−	13.5108i	1.20443	−	0.707189i
$366$	0.0404718	+	0.0886209i	0.00211549	+	0.00463229i
$367$			30.3906i			1.58638i	0.608976	+	0.793188i	$0.291580\pi$
$367$			30.3906i			1.58638i	−0.608976	+	0.793188i	$0.708420\pi$
$368$	18.2929	−	5.76524i	0.953585	−	0.300534i
$369$	−7.33909			−0.382058
$370$	0.0785279	−	0.0626910i	0.00408247	−	0.00325915i
$371$	−2.17330	+	0.638138i	−0.112832	+	0.0331305i
$372$	0.489452	+	0.424113i	0.0253769	+	0.0219892i
$373$	11.7280	−	18.2492i	0.607254	−	0.944905i	−0.392430	−	0.919782i	$-0.628366\pi$
$373$	11.7280	−	18.2492i	0.607254	−	0.944905i	0.999684	−	0.0251238i	$-0.00799800\pi$
$374$	−0.0925380	−	0.106795i	−0.00478503	−	0.00552222i
$375$	8.60832	+	7.13420i	0.444532	+	0.368409i
$376$	−0.0985406	−	0.0289341i	−0.00508184	−	0.00149216i
$377$	−12.7362	−	19.8180i	−0.655950	−	1.02068i
$378$	−0.00566857		0.000815018i	−0.000291560		4.19200e-5i
$379$	12.1262	−	26.5526i	0.622880	−	1.36392i	−0.290527	−	0.956867i	$-0.593831\pi$
$379$	12.1262	−	26.5526i	0.622880	−	1.36392i	0.913406	−	0.407049i	$-0.133442\pi$
$380$	4.91702	+	0.910389i	0.252238	+	0.0467020i
$381$	−2.80452	+	19.5058i	−0.143680	+	0.999315i
$382$	−0.0619707	−	0.0964283i	−0.00317070	−	0.00493370i
$383$	3.41382	−	11.6264i	0.174438	−	0.594081i	−0.825137	−	0.564933i	$-0.808902\pi$
$383$	3.41382	−	11.6264i	0.174438	−	0.594081i	0.999575	−	0.0291488i	$-0.00927966\pi$
$384$	−0.0495873	−	0.344888i	−0.00253049	−	0.0176000i
$385$	−2.74924	−	1.92754i	−0.140114	−	0.0982365i
$386$	−0.00263899	−	0.00169598i	−0.000134321	−	8.63230e-5i
$387$	−1.18412	−	1.02605i	−0.0601922	−	0.0521569i
$388$	5.90065	+	20.0958i	0.299560	+	1.02021i
$389$	−13.2531	−	29.0203i	−0.671959	−	1.47139i	−0.870944	−	0.491383i	$-0.836492\pi$
$389$	−13.2531	−	29.0203i	−0.671959	−	1.47139i	0.198985	−	0.980003i	$-0.436236\pi$
$390$	−0.0742991	+	0.0186019i	−0.00376228	+	0.000941942i
$391$	−16.7488	−	13.9446i	−0.847021	−	0.705207i
$392$			0.292870i			0.0147922i
$393$	16.1334	−	7.36786i	0.813821	−	0.371659i
$394$	0.153858	−	0.0451767i	0.00775124	−	0.00227597i
$395$	4.83903	+	2.45001i	0.243478	+	0.123274i
$396$	−4.80394	−	3.08731i	−0.241407	−	0.155143i
$397$	−1.16670	+	1.01095i	−0.0585548	+	0.0507380i	−0.683647	−	0.729813i	$-0.739607\pi$
$397$	−1.16670	+	1.01095i	−0.0585548	+	0.0507380i	0.625092	+	0.780551i	$0.285062\pi$
$398$	−0.0668711	+	0.00961462i	−0.00335195	+	0.000481937i
$399$	0.564230	+	0.165673i	0.0282468	+	0.00829401i
$400$	−9.74355	+	17.4620i	−0.487177	+	0.873099i
$401$	−2.03073	+	14.1240i	−0.101410	+	0.705321i	0.874161	+	0.485636i	$0.161412\pi$
$401$	−2.03073	+	14.1240i	−0.101410	+	0.705321i	−0.975571	+	0.219685i	$0.929497\pi$
$402$	−0.109350	−	0.0499383i	−0.00545386	−	0.00249070i
$403$	0.926529	+	0.423132i	0.0461537	+	0.0210777i
$404$	−1.15221	+	8.01379i	−0.0573246	+	0.398701i
$405$	1.62957	+	1.53117i	0.0809742	+	0.0760846i
$406$	0.0411554	+	0.0120843i	0.00204251	+	0.000599734i
$407$	11.6626	−	1.67683i	0.578093	−	0.0831172i
$408$	−0.149599	+	0.129629i	−0.00740627	+	0.00641757i
$409$	−16.7328	−	10.7535i	−0.827381	−	0.531726i	0.0570634	−	0.998371i	$-0.481826\pi$
$409$	−16.7328	−	10.7535i	−0.827381	−	0.531726i	−0.884445	+	0.466645i	$0.845463\pi$
$410$	0.0807268	−	0.159444i	0.00398681	−	0.00787438i
$411$	2.39226	−	0.702431i	0.118001	−	0.0346483i
$412$	0.303311	−	0.138517i	0.0149431	−	0.00682427i
$413$		−	6.57455i		−	0.323513i
$414$	0.0479261	+	0.0207556i	0.00235544	+	0.00102008i
$415$	−16.4308	+	4.11369i	−0.806557	+	0.201933i
$416$	−0.170738	−	0.373863i	−0.00837110	−	0.0183302i
$417$	−3.32284	−	11.3166i	−0.162720	−	0.554174i
$418$	−0.0262792	−	0.0227710i	−0.00128536	−	0.00111377i
$419$	18.7778	+	12.0678i	0.917356	+	0.589549i	0.911889	−	0.410436i	$-0.134624\pi$
$419$	18.7778	+	12.0678i	0.917356	+	0.589549i	0.00546661	+	0.999985i	$0.498260\pi$
$420$	−1.35002	+	1.92553i	−0.0658744	+	0.0939561i
$421$	4.58634	+	31.8987i	0.223524	+	1.55465i	0.724555	+	0.689217i	$0.242045\pi$
$421$	4.58634	+	31.8987i	0.223524	+	1.55465i	−0.501030	+	0.865430i	$0.667045\pi$
$422$	0.0152642	−	0.0519851i	0.000743050	−	0.00253060i
$423$	1.27468	+	1.98344i	0.0619769	+	0.0964379i
$424$	0.0267010	−	0.185710i	0.00129672	−	0.00901886i
$425$	22.6776	−	1.41339i	1.10003	−	0.0685594i
$426$	0.0372668	−	0.0816030i	0.00180558	−	0.00395368i
$427$	4.65665	+	0.669526i	0.225351	+	0.0324006i
$428$	−6.54708	−	10.1875i	−0.316465	−	0.492429i
$429$	−8.61734	−	2.53028i	−0.416049	−	0.122163i
$430$	0.0353160	−	0.0144393i	0.00170309	−	0.000696326i
$431$	−2.08545	−	2.40674i	−0.100453	−	0.115929i	0.703297	−	0.710896i	$-0.251710\pi$
$431$	−2.08545	−	2.40674i	−0.100453	−	0.115929i	−0.803750	+	0.594967i	$0.797165\pi$
$432$	−2.16218	+	3.36442i	−0.104028	+	0.161871i
$433$	−10.1812	−	8.82202i	−0.489275	−	0.423959i	0.374965	−	0.927039i	$-0.377655\pi$
$433$	−10.1812	−	8.82202i	−0.489275	−	0.423959i	−0.864240	+	0.503080i	$0.832200\pi$
$434$	−0.00177946		0.000522495i	−8.54166e−5		2.50806e-5i
$435$	−10.4488	−	13.0883i	−0.500982	−	0.627538i
$436$	−36.8302			−1.76385
$437$	−4.56779	−	2.80990i	−0.218507	−	0.134416i
$438$			0.129957i			0.00620959i
$439$	−4.46392	−	9.77463i	−0.213051	−	0.466518i	0.772690	−	0.634783i	$-0.218911\pi$
$439$	−4.46392	−	9.77463i	−0.213051	−	0.466518i	−0.985742	+	0.168266i	$0.946183\pi$
$440$	0.239835	−	0.140820i	0.0114337	−	0.00671335i
$441$	4.40293	−	5.08125i	0.209663	−	0.241964i
$442$	−0.0841548	+	0.130947i	−0.00400283	+	0.00622853i
$443$	−24.4811	+	21.2130i	−1.16313	+	1.00786i	−0.163359	+	0.986567i	$0.552233\pi$
$443$	−24.4811	+	21.2130i	−1.16313	+	1.00786i	−0.999773	+	0.0212929i	$0.993222\pi$
$444$	−1.17443	−	8.16832i	−0.0557358	−	0.387651i
$445$	0.126593	−	3.14132i	0.00600108	−	0.148913i
$446$	−0.236354	+	0.151895i	−0.0111917	+	0.00719246i
$447$	17.1103	+	2.46009i	0.809291	+	0.116358i
$448$	−3.82545	−	1.74703i	−0.180736	−	0.0825393i
$449$	0.658669	−	1.44228i	0.0310845	−	0.0680656i	−0.893453	−	0.449157i	$-0.851724\pi$
$449$	0.658669	−	1.44228i	0.0310845	−	0.0680656i	0.924537	+	0.381091i	$0.124452\pi$
$450$	−0.0511898	+	0.0185608i	−0.00241311	+	0.000874963i
$451$	17.6293	−	11.3297i	0.830132	−	0.533493i
$452$	−1.94633	+	6.62858i	−0.0915475	+	0.311782i
$453$	−12.2036	+	1.75461i	−0.573375	+	0.0824389i
$454$	0.0282160	+	0.0325630i	0.00132424	+	0.00152826i
$455$	−1.18405	+	3.50390i	−0.0555093	+	0.164265i
$456$	−0.0318980	+	0.0368123i	−0.00149376	+	0.00172389i
$457$	3.03241	+	10.3274i	0.141850	+	0.483097i	0.999516	−	0.0311104i	$-0.00990435\pi$
$457$	3.03241	+	10.3274i	0.141850	+	0.483097i	−0.857666	+	0.514207i	$0.828086\pi$
$458$	0.230625	−	0.105323i	0.0107764	−	0.00492142i
$459$	4.54433			0.212111
$460$	16.4935	−	13.7080i	0.769013	−	0.639141i
$461$	−20.6162			−0.960190			−0.480095	−	0.877216i	$-0.659398\pi$
$461$	−20.6162			−0.960190			−0.480095	+	0.877216i	$0.659398\pi$
$462$	0.0148747	−	0.00679306i	0.000692035	−	0.000316042i
$463$	1.47772	+	5.03264i	0.0686753	+	0.233886i	0.986677	−	0.162689i	$-0.0520167\pi$
$463$	1.47772	+	5.03264i	0.0686753	+	0.233886i	−0.918002	+	0.396575i	$0.870199\pi$
$464$	19.6155	−	22.6375i	0.910627	−	1.05092i
$465$	0.686014	+	0.231821i	0.0318132	+	0.0107504i
$466$	0.133355	+	0.153900i	0.00617757	+	0.00712930i
$467$	−32.2876	+	4.64225i	−1.49409	+	0.214818i	−0.840409	−	0.541953i	$-0.817685\pi$
$467$	−32.2876	+	4.64225i	−1.49409	+	0.214818i	−0.653681	+	0.756770i	$0.726776\pi$
$468$	−1.77217	+	6.03547i	−0.0819188	+	0.278990i
$469$	−4.88344	+	3.13839i	−0.225496	+	0.144918i
$470$	−0.0571117	+	0.00587581i	−0.00263436	+	0.000271031i
$471$	2.05204	−	4.49333i	0.0945528	−	0.207042i
$472$	0.495373	+	0.226229i	0.0228014	+	0.0104130i
$473$	4.42834	+	0.636700i	0.203615	+	0.0292755i
$474$	−0.0222223	+	0.0142814i	−0.00102071	+	0.000655968i
$475$	5.47404	−	1.13842i	0.251166	−	0.0522343i
$476$	0.680152	+	4.73056i	0.0311747	+	0.216825i
$477$	−3.25517	+	2.82062i	−0.149044	+	0.129147i
$478$	0.0549207	−	0.0854584i	0.00251202	−	0.00390877i
$479$	−16.5369	+	19.0845i	−0.755588	+	0.871995i	−0.995097	−	0.0988990i	$-0.968468\pi$
$479$	−16.5369	+	19.0845i	−0.755588	+	0.871995i	0.239509	+	0.970894i	$0.423013\pi$
$480$	−0.147944	−	0.251968i	−0.00675271	−	0.0115007i
$481$	−5.39162	−	11.8060i	−0.245837	−	0.538307i
$482$			0.145579i			0.00663096i
$483$	2.09436	−	1.40505i	0.0952967	−	0.0639318i
$484$	−5.69308			−0.258776
$485$	14.6102	+	18.3010i	0.663417	+	0.831007i
$486$	−0.0104491	+	0.00306812i	−0.000473979	+	0.000139173i
$487$	15.3795	+	13.3264i	0.696912	+	0.603878i	0.929555	−	0.368685i	$-0.120192\pi$
$487$	15.3795	+	13.3264i	0.696912	+	0.603878i	−0.232643	+	0.972562i	$0.574737\pi$
$488$	−0.210681	+	0.327827i	−0.00953710	+	0.0148400i
$489$	−15.8550	−	18.2977i	−0.716990	−	0.827450i
$490$	0.0619614	+	0.151547i	0.00279913	+	0.00684618i
$491$	24.7133	+	7.25648i	1.11530	+	0.327480i	0.786913	−	0.617064i	$-0.211678\pi$
$491$	24.7133	+	7.25648i	1.11530	+	0.327480i	0.328383	+	0.944545i	$0.393496\pi$
$492$	−7.93515	−	12.3473i	−0.357744	−	0.556661i
$493$	−33.6895	−	4.84382i	−1.51730	−	0.218155i
$494$	−0.0159116	+	0.0348416i	−0.000715898	+	0.00156760i
$495$	−6.27816	−	1.16240i	−0.282182	−	0.0522462i
$496$	−0.184315	+	1.28194i	−0.00827600	+	0.0575608i
$497$	−2.34205	−	3.64430i	−0.105055	−	0.163469i
$498$	0.0232406	−	0.0791503i	0.00104144	−	0.00354681i
$499$	−3.80205	−	26.4439i	−0.170203	−	1.18379i	−0.878453	−	0.477828i	$-0.841424\pi$
$499$	−3.80205	−	26.4439i	−0.170203	−	1.18379i	0.708250	−	0.705962i	$-0.249485\pi$
$500$	−2.69517	+	22.1963i	−0.120532	+	0.992650i
$501$	−1.88637	−	1.21230i	−0.0842767	−	0.0541614i
$502$	−0.0403467	−	0.0349606i	−0.00180076	−	0.00156037i
$503$	9.30080	+	31.6756i	0.414702	+	1.41235i	0.856925	+	0.515441i	$0.172372\pi$
$503$	9.30080	+	31.6756i	0.414702	+	1.41235i	−0.442223	+	0.896905i	$0.645810\pi$
$504$	−0.00951582	−	0.0208367i	−0.000423868	−	0.000928142i
$505$	2.19853	+	8.78133i	0.0978335	+	0.390764i
$506$	−0.147165	+	0.0241284i	−0.00654229	+	0.00107264i
$507$		−	3.10695i		−	0.137985i
$508$	−35.8491	+	16.3717i	−1.59055	+	0.726378i
$509$	−6.51459	+	1.91286i	−0.288754	+	0.0847859i	−0.422902	−	0.906175i	$-0.638989\pi$
$509$	−6.51459	+	1.91286i	−0.288754	+	0.0847859i	0.134148	+	0.990961i	$0.457170\pi$
$510$	−0.0499857	+	0.0987270i	−0.00221340	+	0.00437171i
$511$	5.27927	+	3.39278i	0.233541	+	0.150088i
$512$	0.658264	−	0.570389i	0.0290914	−	0.0252079i
$513$	1.10685	−	0.159141i	0.0488687	−	0.00702625i
$514$	−0.122940	−	0.0360986i	−0.00542267	−	0.00159224i
$515$	0.255295	−	0.271702i	0.0112496	−	0.0119726i
$516$	0.445936	−	3.10155i	0.0196312	−	0.136538i
$517$	−6.12383	−	2.79666i	−0.269326	−	0.122997i
$518$	0.0214958	+	0.00981682i	0.000944473	+	0.000431326i
$519$	1.50821	−	10.4898i	0.0662030	−	0.460452i
$520$	−0.223265	−	0.209783i	−0.00979083	−	0.00919961i
$521$	25.6154	+	7.52135i	1.12223	+	0.329516i	0.789649	−	0.613559i	$-0.210263\pi$
$521$	25.6154	+	7.52135i	1.12223	+	0.329516i	0.332580	+	0.943075i	$0.392081\pi$
$522$	0.0807346	−	0.0116079i	0.00353366	−	0.000508063i
$523$	−5.55874	+	4.81667i	−0.243067	+	0.210618i	−0.767871	−	0.640604i	$-0.778684\pi$
$523$	−5.55874	+	4.81667i	−0.243067	+	0.210618i	0.524804	+	0.851223i	$0.324138\pi$
$524$	29.8394	+	19.1766i	1.30354	+	0.837735i
$525$	−0.582412	+	2.56406i	−0.0254185	+	0.111905i
$526$	−0.180952	+	0.0531323i	−0.00788988	+	0.00231668i
$527$	1.33864	−	0.611337i	0.0583121	−	0.0266302i
$528$		−	11.4196i		−	0.496972i
$529$	−21.7958	+	7.34448i	−0.947645	+	0.319325i
$530$	−0.0254734	−	0.101745i	−0.00110649	−	0.00441953i
$531$	−5.19358	−	11.3723i	−0.225382	−	0.493518i
$532$	0.331326	+	1.12839i	0.0143648	+	0.0489220i
$533$	−17.4456	−	15.1167i	−0.755651	−	0.654776i
$534$	0.0128807	+	0.00827795i	0.000557404	+	0.000358222i
$535$	−11.0866	−	7.77302i	−0.479315	−	0.336057i
$536$	−0.0684304	−	0.475944i	−0.00295574	−	0.0205576i
$537$	0.737831	−	2.51282i	0.0318397	−	0.108436i
$538$	0.136214	+	0.211953i	0.00587260	+	0.00913795i
$539$	−2.73218	+	19.0027i	−0.117683	+	0.818505i
$540$	−0.814132	+	4.39714i	−0.0350347	+	0.189223i
$541$	1.61744	−	3.54169i	0.0695390	−	0.152269i	−0.871671	−	0.490092i	$-0.836963\pi$
$541$	1.61744	−	3.54169i	0.0695390	−	0.152269i	0.941210	+	0.337823i	$0.109690\pi$
$542$	−0.265052	−	0.0381087i	−0.0113850	−	0.00163691i
$543$	9.37110	+	14.5817i	0.402152	+	0.625761i
$544$	−0.569762	−	0.167297i	−0.0244284	−	0.00717281i
$545$	−38.1169	+	15.5845i	−1.63275	+	0.667568i
$546$	−0.0117959	−	0.0136132i	−0.000504818	−	0.000582591i
$547$	−7.87865	+	12.2594i	−0.336867	+	0.524175i	−0.967819	−	0.251647i	$-0.919028\pi$
$547$	−7.87865	+	12.2594i	−0.336867	+	0.524175i	0.630952	+	0.775821i	$0.282664\pi$
$548$	3.76833	+	3.26527i	0.160975	+	0.139486i
$549$	8.58375	−	2.52042i	0.366345	−	0.107569i
$550$	0.0943106	−	0.123609i	0.00402142	−	0.00527071i
$551$	−8.37529			−0.356799
$552$	0.0337994	+	0.206151i	0.00143860	+	0.00877438i
$553$			1.27559i			0.0542434i
$554$	0.133297	+	0.291879i	0.00566323	+	0.0124007i
$555$	−4.67185	−	7.95675i	−0.198309	−	0.337745i
$556$	15.4463	−	17.8260i	0.655071	−	0.755992i
$557$	−20.6454	+	32.1248i	−0.874772	+	1.36117i	0.0570940	+	0.998369i	$0.481817\pi$
$557$	−20.6454	+	32.1248i	−0.874772	+	1.36117i	−0.931866	+	0.362803i	$0.881820\pi$
$558$	−0.00266527	+	0.00230947i	−0.000112830	+	9.77677e-5i
$559$	−0.701348	−	4.87798i	−0.0296638	−	0.206317i
$560$	−4.69891	−	0.189363i	−0.198565	−	0.00800204i
$561$	−10.9160	+	7.01528i	−0.460874	+	0.296185i
$562$	−0.223266	−	0.0321008i	−0.00941792	−	0.00135409i
$563$	−15.7184	−	7.17833i	−0.662450	−	0.302531i	0.0556710	−	0.998449i	$-0.482270\pi$
$563$	−15.7184	−	7.17833i	−0.662450	−	0.302531i	−0.718121	+	0.695919i	$0.754997\pi$
$564$	−1.95874	+	4.28905i	−0.0824780	+	0.180602i
$565$	0.790526	+	7.68375i	0.0332577	+	0.323258i
$566$	−0.0711016	+	0.0456942i	−0.00298862	+	0.00192067i
$567$	−0.148156	+	0.504573i	−0.00622196	+	0.0211901i
$568$	0.355177	−	0.0510667i	0.0149029	−	0.00214271i
$569$	9.51395	+	10.9797i	0.398845	+	0.460292i	0.919277	−	0.393611i	$-0.128774\pi$
$569$	9.51395	+	10.9797i	0.398845	+	0.460292i	−0.520432	+	0.853903i	$0.674229\pi$
$570$	−0.00871750	+	0.0257972i	−0.000365136	+	0.00108052i
$571$	8.39628	−	9.68983i	0.351374	−	0.405507i	−0.552358	−	0.833607i	$-0.686272\pi$
$571$	8.39628	−	9.68983i	0.351374	−	0.405507i	0.903731	+	0.428101i	$0.140817\pi$
$572$	−5.06026	−	17.2337i	−0.211580	−	0.720576i
$573$	−9.57433	+	4.37245i	−0.399973	+	0.182662i
$574$	0.0420300			0.00175430
$575$	11.2692	−	21.1661i	0.469960	−	0.882688i
$576$	−7.99715			−0.333215
$577$	−24.9401	+	11.3897i	−1.03827	+	0.474161i	−0.860253	−	0.509867i	$-0.829695\pi$
$577$	−24.9401	+	11.3897i	−1.03827	+	0.474161i	−0.178015	+	0.984028i	$0.556967\pi$
$578$	0.0112015	+	0.0381488i	0.000465921	+	0.00158678i
$579$	−0.188636	+	0.217698i	−0.00783946	+	0.00904722i
$580$	10.7225	−	31.7305i	0.445228	−	1.31754i
$581$	−2.60859	−	3.01048i	−0.108223	−	0.124896i
$582$	−0.112889	+	0.0162309i	−0.00467939	+	0.000672794i
$583$	3.46497	−	11.8006i	0.143504	−	0.488731i
$584$	−0.437295	+	0.281032i	−0.0180954	+	0.0116292i
$585$	0.719792	+	6.99622i	0.0297597	+	0.289258i
$586$	−0.0734719	+	0.160881i	−0.00303510	+	0.00664594i
$587$	−4.39767	−	2.00835i	−0.181511	−	0.0828935i	0.322587	−	0.946540i	$-0.395448\pi$
$587$	−4.39767	−	2.00835i	−0.181511	−	0.0828935i	−0.504098	+	0.863646i	$0.668175\pi$
$588$	13.3093	+	1.91358i	0.548864	+	0.0789148i
$589$	0.304640	−	0.195781i	0.0125525	−	0.00806700i
$590$	0.304195	+	0.0122588i	0.0125235	+	0.000504689i
$591$	−2.09553	−	14.5747i	−0.0861984	−	0.599523i
$592$	12.4719	−	10.8070i	0.512592	−	0.444163i
$593$	−1.85664	+	2.88899i	−0.0762431	+	0.118637i	−0.877281	−	0.479977i	$-0.840645\pi$
$593$	−1.85664	+	2.88899i	−0.0762431	+	0.118637i	0.801038	+	0.598613i	$0.204281\pi$
$594$	0.0203634	−	0.0235006i	0.000835521	−	0.000964242i
$595$	2.70563	+	4.60804i	0.110920	+	0.188911i
$596$	14.3611	+	31.4464i	0.588254	+	1.28810i
$597$			6.20364i			0.253898i
$598$	0.0711728	+	0.148053i	0.00291047	+	0.00605435i
$599$	4.73251			0.193365			0.0966827	−	0.995315i	$-0.469177\pi$
$599$	4.73251			0.193365			0.0966827	+	0.995315i	$0.469177\pi$
$600$	−0.173153	−	0.132112i	−0.00706896	−	0.00539344i
$601$	−17.0156	+	4.99624i	−0.694082	+	0.203801i	−0.609700	−	0.792633i	$-0.708710\pi$
$601$	−17.0156	+	4.99624i	−0.694082	+	0.203801i	−0.0843825	+	0.996433i	$0.526892\pi$
$602$	0.00678130	+	0.00587603i	0.000276385	+	0.000239489i
$603$	−5.96795	+	9.28632i	−0.243034	+	0.378168i
$604$	−16.1467	−	18.6343i	−0.657001	−	0.758219i
$605$	−5.89198	+	2.40900i	−0.239543	+	0.0979398i
$606$	−0.0423013	−	0.0124208i	−0.00171837	−	0.000504560i
$607$	−0.896993	−	1.39575i	−0.0364078	−	0.0566517i	0.822573	−	0.568660i	$-0.192538\pi$
$607$	−0.896993	−	1.39575i	−0.0364078	−	0.0566517i	−0.858980	+	0.512008i	$0.828902\pi$
$608$	−0.144634	−	0.0207953i	−0.00586569	−	0.000843359i
$609$	1.63618	−	3.58274i	0.0663015	−	0.145180i
$610$	−0.0396607	+	0.214208i	−0.00160582	+	0.00867304i
$611$	−1.05537	+	7.34029i	−0.0426959	+	0.296956i
$612$	4.91341	+	7.64541i	0.198613	+	0.309048i
$613$	11.7418	−	39.9890i	0.474248	−	1.61514i	−0.281005	−	0.959706i	$-0.590668\pi$
$613$	11.7418	−	39.9890i	0.474248	−	1.61514i	0.755253	−	0.655433i	$-0.227514\pi$
$614$	0.0502559	+	0.349537i	0.00202816	+	0.0141062i
$615$	−13.4371	−	9.42100i	−0.541836	−	0.379891i
$616$	0.0550247	+	0.0353622i	0.00221701	+	0.00142478i
$617$	34.4537	+	29.8543i	1.38705	+	1.20189i	0.953736	+	0.300646i	$0.0972024\pi$
$617$	34.4537	+	29.8543i	1.38705	+	1.20189i	0.433317	+	0.901242i	$0.357343\pi$
$618$	0.000511553		0.00174219i	2.05777e−5		7.00811e-5i
$619$	12.3215	+	26.9804i	0.495244	+	1.08443i	0.977986	+	0.208670i	$0.0669134\pi$
$619$	12.3215	+	26.9804i	0.495244	+	1.08443i	−0.482743	+	0.875762i	$0.660359\pi$
$620$	0.351713	+	1.40480i	0.0141251	+	0.0564183i
$621$	2.51281	−	4.08483i	0.100835	−	0.163918i
$622$		−	0.222752i		−	0.00893154i
$623$	0.672553	−	0.307145i	0.0269453	−	0.0123055i
$624$	−12.0695	+	3.54393i	−0.483167	+	0.141871i
$625$	6.60294	+	24.1123i	0.264118	+	0.964490i
$626$	0.103087	+	0.0662497i	0.00412017	+	0.00264787i
$627$	−2.41311	+	2.09097i	−0.0963702	+	0.0835053i
$628$	9.77831	−	1.40591i	0.390197	−	0.0561019i
$629$	−17.9922	−	5.28298i	−0.717394	−	0.210646i
$630$	−0.00933235	−	0.00876882i	−0.000371810	−	0.000349358i
$631$	4.11893	−	28.6478i	0.163972	−	1.14045i	−0.727082	−	0.686551i	$-0.759124\pi$
$631$	4.11893	−	28.6478i	0.163972	−	1.14045i	0.891053	−	0.453898i	$-0.149967\pi$
$632$	−0.0961115	−	0.0438927i	−0.00382311	−	0.00174596i
$633$	−4.52552	−	2.06673i	−0.179873	−	0.0821453i
$634$	0.0133811	−	0.0930679i	0.000531433	−	0.00369620i
$635$	−30.1739	+	32.1131i	−1.19742	+	1.27437i
$636$	−8.26498	−	2.42682i	−0.327728	−	0.0962296i
$637$	20.9322	−	3.00959i	0.829363	−	0.119244i
$638$	−0.176014	+	0.152517i	−0.00696846	+	0.00603820i
$639$	−6.92998	−	4.45363i	−0.274146	−	0.176183i
$640$	0.351934	−	0.695107i	0.0139114	−	0.0274765i
$641$	33.3128	−	9.78154i	1.31578	−	0.386347i	0.452811	−	0.891607i	$-0.350421\pi$
$641$	33.3128	−	9.78154i	1.31578	−	0.386347i	0.862968	+	0.505259i	$0.168603\pi$
$642$	0.0599840	−	0.0273938i	0.00236738	−	0.00108115i
$643$		−	18.3335i		−	0.723004i	−0.932371	−	0.361502i	$-0.882264\pi$
$643$		−	18.3335i		−	0.723004i	0.932371	−	0.361502i	$-0.117736\pi$
$644$	4.62832	+	2.00441i	0.182381	+	0.0789847i
$645$	−0.850892	−	3.39861i	−0.0335038	−	0.133820i
$646$	0.0229890	+	0.0503388i	0.000904489	+	0.00198055i
$647$	−0.672209	−	2.28933i	−0.0264272	−	0.0900029i	0.945223	−	0.326424i	$-0.105844\pi$
$647$	−0.672209	−	2.28933i	−0.0264272	−	0.0900029i	−0.971651	+	0.236421i	$0.924026\pi$
$648$	−0.0329200	−	0.0285254i	−0.00129322	−	0.00112058i
$649$	30.0316	+	19.3001i	1.17884	+	0.757595i
$650$	−0.159913	−	0.0613178i	−0.00627229	−	0.00240508i
$651$	0.0242360	+	0.168565i	0.000949883	+	0.00660658i
$652$	13.6414	−	46.4584i	0.534239	−	1.81945i
$653$	4.77122	+	7.42416i	0.186712	+	0.290530i	0.921973	−	0.387255i	$-0.126577\pi$
$653$	4.77122	+	7.42416i	0.186712	+	0.290530i	−0.735261	+	0.677785i	$0.762940\pi$
$654$	0.0285420	−	0.198514i	0.00111608	−	0.00776252i
$655$	38.9965	+	7.22021i	1.52372	+	0.282117i
$656$	12.1929	−	26.6987i	0.476053	−	1.04241i
$657$	11.8120	+	1.69830i	0.460829	+	0.0662571i
$658$	−0.00729990	−	0.0113589i	−0.000284580	−	0.000442815i
$659$	−3.60879	−	1.05964i	−0.140578	−	0.0412776i	0.210686	−	0.977554i	$-0.432430\pi$
$659$	−3.60879	−	1.05964i	−0.140578	−	0.0412776i	−0.351265	+	0.936276i	$0.614248\pi$
$660$	−4.83242	−	11.8192i	−0.188102	−	0.460063i
$661$	−2.32693	−	2.68542i	−0.0905071	−	0.104451i	0.708689	−	0.705521i	$-0.249287\pi$
$661$	−2.32693	−	2.68542i	−0.0905071	−	0.104451i	−0.799196	+	0.601070i	$0.794741\pi$
$662$	0.125799	−	0.195747i	0.00488932	−	0.00760792i
$663$	10.8022	+	9.36017i	0.419523	+	0.363519i
$664$	0.316592	−	0.0929597i	0.0122861	−	0.00360754i
$665$	0.820376	+	1.02762i	0.0318128	+	0.0398493i
$666$	0.0449373			0.00174128
$667$	−22.9828	+	27.6045i	−0.889897	+	1.06885i
$668$		−	4.48440i		−	0.173506i
$669$	10.7172	+	23.4675i	0.414353	+	0.907306i
$670$	−0.136103	−	0.231801i	−0.00525813	−	0.00895526i
$671$	−16.7283	+	19.3054i	−0.645787	+	0.745278i
$672$	0.0371512	−	0.0578084i	0.00143314	−	0.00223001i
$673$	0.515143	−	0.446374i	0.0198573	−	0.0172065i	−0.644876	−	0.764288i	$-0.723091\pi$
$673$	0.515143	−	0.446374i	0.0198573	−	0.0172065i	0.664733	+	0.747081i	$0.268545\pi$
$674$	0.00473405	+	0.0329261i	0.000182349	+	0.00126827i
$675$	1.01805	+	4.89526i	0.0391849	+	0.188419i
$676$	5.22716	−	3.35929i	0.201044	−	0.129203i
$677$	37.2105	+	5.35006i	1.43011	+	0.205619i	0.813463	−	0.581617i	$-0.197580\pi$
$677$	37.2105	+	5.35006i	1.43011	+	0.205619i	0.616651	+	0.787236i	$0.288489\pi$
$678$	−0.0342196	−	0.0156276i	−0.00131420	−	0.000600174i
$679$	−2.28782	+	5.00964i	−0.0877986	+	0.192252i
$680$	−0.440302	+	0.0452995i	−0.0168848	+	0.00173716i
$681$	3.32842	−	2.13905i	0.127545	−	0.0819684i
$682$	0.00283705	−	0.00966210i	0.000108636	−	0.000369981i
$683$	−7.24408	+	1.04154i	−0.277187	+	0.0398535i	−0.279506	−	0.960144i	$-0.590171\pi$
$683$	−7.24408	+	1.04154i	−0.277187	+	0.0398535i	0.00231934	+	0.999997i	$0.499262\pi$
$684$	1.46449	+	1.69011i	0.0559961	+	0.0646229i
$685$	5.28167	+	1.78481i	0.201802	+	0.0681939i
$686$	−0.0514671	+	0.0593962i	−0.00196502	+	0.00226776i
$687$	−6.55907	−	22.3382i	−0.250244	−	0.852254i
$688$	5.69989	−	2.60305i	0.217306	−	0.0992405i
$689$	−13.5476			−0.516121
$690$	0.0611043	+	0.0995229i	0.00232620	+	0.00378877i
$691$	9.72627			0.370005			0.185002	−	0.982738i	$-0.440771\pi$
$691$	9.72627			0.370005			0.185002	+	0.982738i	$0.440771\pi$
$692$	19.2788	−	8.80435i	0.732872	−	0.334691i
$693$	−0.423044	−	1.44076i	−0.0160701	−	0.0547298i
$694$	−0.139518	+	0.161013i	−0.00529604	+	0.00611195i
$695$	8.44300	−	24.9849i	0.320261	−	0.947731i
$696$	0.213648	+	0.246563i	0.00809830	+	0.00934594i
$697$	−33.0118	+	4.74637i	−1.25041	+	0.179782i
$698$	−0.0265881	+	0.0905508i	−0.00100637	+	0.00342740i
$699$	15.7309	−	10.1096i	0.594998	−	0.382382i
$700$	−4.94350	+	1.79245i	−0.186847	+	0.0677482i
$701$	7.26054	−	15.8984i	0.274227	−	0.600473i	−0.721542	−	0.692371i	$-0.756566\pi$
$701$	7.26054	−	15.8984i	0.274227	−	0.600473i	0.995768	+	0.0918982i	$0.0292934\pi$
$702$	−0.0311577	−	0.0142293i	−0.00117597	−	0.000537049i
$703$	−4.56731	−	0.656681i	−0.172260	−	0.0247672i
$704$	19.2101	−	12.3456i	0.724007	−	0.465291i
$705$	−0.212286	+	5.26773i	−0.00799515	+	0.198394i
$706$	−0.0519693	−	0.361454i	−0.00195589	−	0.0136035i
$707$	−1.60893	+	1.39414i	−0.0605100	+	0.0524322i
$708$	13.5175	−	21.0337i	0.508020	−	0.790495i
$709$	−19.8337	+	22.8893i	−0.744869	+	0.859625i	−0.994060	−	0.108830i	$-0.965290\pi$
$709$	−19.8337	+	22.8893i	−0.744869	+	0.859625i	0.249191	+	0.968454i	$0.419835\pi$
$710$	0.172983	−	0.101568i	0.00649195	−	0.00381178i
$711$	1.00765	+	2.20645i	0.0377898	+	0.0827482i
$712$			0.0612437i			0.00229520i
$713$	0.190686	−	1.54132i	0.00714127	−	0.0577230i
$714$	−0.0260248			−0.000973952
$715$	−12.5294	−	15.6945i	−0.468573	−	0.586943i
$716$	5.02534	−	1.47557i	0.187806	−	0.0551448i
$717$	−7.04970	−	6.10860i	−0.263276	−	0.228130i
$718$	−0.170877	+	0.265889i	−0.00637705	+	0.00992289i
$719$	22.5650	+	26.0414i	0.841532	+	0.971179i	0.999869	−	0.0162058i	$-0.00515869\pi$
$719$	22.5650	+	26.0414i	0.841532	+	0.971179i	−0.158337	+	0.987385i	$0.550613\pi$
$720$	−8.27754	+	3.38436i	−0.308486	+	0.126128i
$721$	0.0841283	+	0.0247023i	0.00313310	+	0.000919961i
$722$	−0.104504	−	0.162611i	−0.00388922	−	0.00605175i
$723$	13.2319	+	1.90246i	0.492099	+	0.0707531i
$724$	−14.4002	+	31.5320i	−0.535179	+	1.17188i
$725$	−2.32948	−	37.3763i	−0.0865147	−	1.38812i
$726$	0.00441193	−	0.0306856i	0.000163742	−	0.00113885i
$727$	−14.6637	−	22.8172i	−0.543848	−	0.846243i	0.455177	−	0.890401i	$-0.349576\pi$
$727$	−14.6637	−	22.8172i	−0.543848	−	0.846243i	−0.999025	+	0.0441576i	$0.985940\pi$
$728$	0.0202986	−	0.0691307i	0.000752316	−	0.00256215i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	−0.166823	+	0.237938i	−0.00617439	+	0.00880648i
$731$	−5.98983	−	3.84943i	−0.221542	−	0.142376i
$732$	13.5213	+	11.7162i	0.499760	+	0.433045i
$733$	10.7660	+	36.6658i	0.397653	+	1.35428i	0.878611	+	0.477538i	$0.158471\pi$
$733$	10.7660	+	36.6658i	0.397653	+	1.35428i	−0.480959	+	0.876743i	$0.659711\pi$
$734$	−0.137485	−	0.301051i	−0.00507468	−	0.0111120i
$735$	14.5840	−	3.65131i	0.537938	−	0.134681i
$736$	−0.465433	+	0.419642i	−0.0171561	+	0.0154682i
$737$		−	31.5198i		−	1.16105i
$738$	0.0727014	−	0.0332016i	0.00267618	−	0.00122217i
$739$	−3.60933	+	1.05980i	−0.132772	+	0.0389852i	−0.347443	−	0.937701i	$-0.612950\pi$
$739$	−3.60933	+	1.05980i	−0.132772	+	0.0389852i	0.214672	+	0.976686i	$0.431132\pi$
$740$	8.33521	−	16.4629i	0.306409	−	0.605189i
$741$	2.95886	+	1.90154i	0.108696	+	0.0698549i
$742$	0.0186419	−	0.0161533i	0.000684366	−	0.000593007i
$743$	44.1096	−	6.34200i	1.61822	−	0.232665i	0.727135	−	0.686495i	$-0.240852\pi$
$743$	44.1096	−	6.34200i	1.61822	−	0.232665i	0.891089	+	0.453829i	$0.149942\pi$
$744$	−0.0135348	−	0.00397418i	−0.000496210	−	0.000145701i
$745$	28.1693	+	26.4683i	1.03204	+	0.969722i
$746$	−0.0336203	+	0.233834i	−0.00123093	+	0.00856127i
$747$	−6.89035	−	3.14672i	−0.252105	−	0.115132i
$748$	−23.6051	−	10.7801i	−0.863089	−	0.394159i
$749$	0.453176	−	3.15191i	0.0165587	−	0.115168i
$750$	−0.117549	−	0.0317282i	−0.00429229	−	0.00115855i
$751$	−2.07370	−	0.608894i	−0.0756705	−	0.0222189i	0.243678	−	0.969856i	$-0.421646\pi$
$751$	−2.07370	−	0.608894i	−0.0756705	−	0.0222189i	−0.319349	+	0.947637i	$0.603464\pi$
$752$	−9.33320	+	1.34191i	−0.340347	+	0.0489345i
$753$	−3.70487	+	3.21029i	−0.135013	+	0.116989i
$754$	0.215821	+	0.138700i	0.00785975	+	0.00505116i
$755$	−24.5959	−	12.4529i	−0.895135	−	0.453209i
$756$	−1.00909	+	0.296294i	−0.0367001	+	0.0107761i
$757$	45.6677	−	20.8557i	1.65982	−	0.758015i	0.659842	−	0.751404i	$-0.270623\pi$
$757$	45.6677	−	20.8557i	1.65982	−	0.758015i	0.999978	−	0.00661032i	$-0.00210414\pi$
$758$			0.317890i			0.0115463i
$759$	0.269879	+	13.6913i	0.00979597	+	0.496964i
$760$	−0.105657	+	0.0264527i	−0.00383258	+	0.000959542i
$761$	−12.6312	−	27.6585i	−0.457882	−	1.00262i	−0.987965	−	0.154676i	$-0.950567\pi$
$761$	−12.6312	−	27.6585i	−0.457882	−	1.00262i	0.530084	−	0.847945i	$-0.322161\pi$
$762$	−0.0604616	−	0.205913i	−0.00219029	−	0.00745946i
$763$	−7.31913	−	6.34206i	−0.264970	−	0.229598i
$764$	−17.7082	−	11.3804i	−0.640659	−	0.411727i
$765$	8.32019	+	5.83344i	0.300817	+	0.210909i
$766$	0.0187797	+	0.130616i	0.000678538	+	0.00471934i
$767$	11.0786	−	37.7304i	0.400027	−	1.36237i
$768$	−8.64512	−	13.4521i	−0.311954	−	0.485410i
$769$	2.23237	−	15.5265i	0.0805014	−	0.559899i	−0.909157	−	0.416454i	$-0.863273\pi$
$769$	2.23237	−	15.5265i	0.0805014	−	0.559899i	0.989658	−	0.143445i	$-0.0458182\pi$
$770$	0.0359542	+	0.00665693i	0.00129570	+	0.000239899i
$771$	−4.88765	+	10.7025i	−0.176024	+	0.385440i
$772$	−0.570213	−	0.0819843i	−0.0205224	−	0.00295068i
$773$	22.8573	+	35.5667i	0.822120	+	1.27924i	0.957495	+	0.288449i	$0.0931397\pi$
$773$	22.8573	+	35.5667i	0.822120	+	1.27924i	−0.135375	+	0.990794i	$0.543224\pi$
$774$	0.0163717	+	0.00480718i	0.000588470	+	0.000172790i
$775$	0.958438	+	1.30506i	0.0344281	+	0.0468791i
$776$	−0.298737	−	0.344761i	−0.0107240	−	0.0123762i
$777$	1.17317	−	1.82549i	0.0420874	−	0.0654892i
$778$	0.262572	+	0.227520i	0.00941366	+	0.00815698i
$779$	−7.87438	+	2.31213i	−0.282129	+	0.0828405i
$780$	−10.9922	+	8.77542i	−0.393586	+	0.314211i
$781$	23.5219			0.841679
$782$	0.228998	+	0.0623651i	0.00818897	+	0.00223017i
$783$		−	7.48976i		−	0.267662i
$784$	11.1701	+	24.4591i	0.398933	+	0.873540i
$785$	9.52504	−	5.59268i	0.339963	−	0.199611i
$786$	−0.126486	+	0.145973i	−0.00451161	+	0.00520668i
$787$	−20.6552	+	32.1401i	−0.736277	+	1.14567i	0.247952	+	0.968772i	$0.420242\pi$
$787$	−20.6552	+	32.1401i	−0.736277	+	1.14567i	−0.984229	+	0.176897i	$0.943394\pi$
$788$	22.2549	−	19.2839i	0.792797	−	0.686962i
$789$	2.46454	+	17.1413i	0.0877401	+	0.610246i
$790$	−0.0590195	−	0.00237844i	−0.00209982	−	8.46212e-5i
$791$	−1.52821	+	0.982122i	−0.0543369	+	0.0349202i
$792$	0.123113	+	0.0177010i	0.00437465	+	0.000628979i
$793$	25.5956	+	11.6891i	0.908928	+	0.415093i
$794$	0.00698388	−	0.0152926i	0.000247849	−	0.000542713i
$795$	−9.58064	+	0.985683i	−0.339790	+	0.0349586i
$796$	−10.4371	+	6.70749i	−0.369932	+	0.237741i
$797$	−9.12436	+	31.0747i	−0.323201	+	1.10072i	0.624357	+	0.781139i	$0.285361\pi$
$797$	−9.12436	+	31.0747i	−0.323201	+	1.10072i	−0.947558	+	0.319583i	$0.896457\pi$
$798$	−0.00633879		0.000911380i	−0.000224391		3.22625e-5i
$799$	7.01633	+	8.09728i	0.248220	+	0.286461i
$800$	0.0525745	−	0.651240i	0.00185879	−	0.0230248i
$801$	0.920721	−	1.06257i	0.0325321	−	0.0375440i
$802$	−0.0437798	−	0.149100i	−0.00154592	−	0.00526492i
$803$	−30.9954	+	14.1551i	−1.09380	+	0.499524i
$804$	−22.0760			−0.778561
$805$	5.63818	+	0.115985i	0.198720	+	0.00408793i
$806$	−0.0110925			−0.000390716
$807$	21.0447	−	9.61081i	0.740810	−	0.338317i
$808$	−0.0496817	−	0.169200i	−0.00174779	−	0.00595244i
$809$	−27.7065	+	31.9750i	−0.974109	+	1.12418i	0.0181299	+	0.999836i	$0.494229\pi$
$809$	−27.7065	+	31.9750i	−0.974109	+	1.12418i	−0.992239	+	0.124346i	$0.960317\pi$
$810$	−0.0230696	−	0.00779578i	−0.000810583	−	0.000273916i
$811$	7.21723	+	8.32913i	0.253431	+	0.292475i	0.868182	−	0.496246i	$-0.165289\pi$
$811$	7.21723	+	8.32913i	0.253431	+	0.292475i	−0.614750	+	0.788722i	$0.710743\pi$
$812$	7.79670	−	1.12100i	0.273610	−	0.0393392i
$813$	−6.92750	+	23.5929i	−0.242958	+	0.827439i
$814$	−0.107944	+	0.0693716i	−0.00378345	+	0.00243148i
$815$	−5.54064	−	53.8539i	−0.194080	−	1.88642i
$816$	−7.54979	+	16.5317i	−0.264295	+	0.578726i
$817$	−1.59373	−	0.727834i	−0.0557577	−	0.0254637i
$818$	0.214404	+	0.0308266i	0.00749645	+	0.00107783i
$819$	−1.39147	+	0.894244i	−0.0486219	+	0.0312474i
$820$	1.32153	−	32.7928i	0.0461498	−	1.14518i
$821$	−4.45701	−	30.9992i	−0.155551	−	1.08188i	−0.906709	−	0.421756i	$-0.861414\pi$
$821$	−4.45701	−	30.9992i	−0.155551	−	1.08188i	0.751159	−	0.660122i	$-0.229495\pi$
$822$	−0.0205201	+	0.0177808i	−0.000715720	+	0.000620175i
$823$	19.2039	−	29.8819i	0.669407	−	1.04162i	−0.325952	−	0.945386i	$-0.605685\pi$
$823$	19.2039	−	29.8819i	0.669407	−	1.04162i	0.995359	−	0.0962318i	$-0.0306790\pi$
$824$	−0.00475608	+	0.00548881i	−0.000165686	+	0.000191212i
$825$	−10.0025	−	10.1874i	−0.348243	−	0.354678i
$826$	0.0297429	+	0.0651279i	0.00103489	+	0.00226609i
$827$		−	18.4279i		−	0.640801i	−0.947282	−	0.320400i	$-0.896183\pi$
$827$		−	18.4279i		−	0.640801i	0.947282	−	0.320400i	$-0.103817\pi$
$828$	9.58923	−	0.189019i	0.333249	−	0.00656888i
$829$	−19.1208			−0.664091			−0.332046	−	0.943263i	$-0.607739\pi$
$829$	−19.1208			−0.664091			−0.332046	+	0.943263i	$0.607739\pi$
$830$	0.144154	−	0.115083i	0.00500367	−	0.00399457i
$831$	28.2711	−	8.30116i	0.980715	−	0.287964i
$832$	−19.0098	−	16.4721i	−0.659048	−	0.571068i
$833$	16.5185	−	25.7033i	0.572333	−	0.890567i
$834$	0.0841117	+	0.0970701i	0.00291255	+	0.00336126i
$835$	−1.89755	−	4.64107i	−0.0656675	−	0.160611i
$836$	−6.12696	−	1.79904i	−0.211905	−	0.0622210i
$837$	0.175080	+	0.272430i	0.00605166	+	0.00941657i
$838$	−0.240608	−	0.0345942i	−0.00831166	−	0.00119504i
$839$	−4.36192	+	9.55127i	−0.150590	+	0.329747i	−0.969860	−	0.243661i	$-0.921652\pi$
$839$	−4.36192	+	9.55127i	−0.150590	+	0.329747i	0.819270	+	0.573408i	$0.194379\pi$
$840$	0.00932512	−	0.0503651i	0.000321747	−	0.00173776i
$841$	−3.85622	+	26.8206i	−0.132973	+	0.924849i
$842$	−0.189740	−	0.295242i	−0.00653889	−	0.0101747i
$843$	−5.83537	+	19.8734i	−0.200981	+	0.684477i
$844$	−1.41598	−	9.84835i	−0.0487400	−	0.338994i
$845$	3.98831	−	5.68850i	0.137202	−	0.195690i
$846$	−0.0216000	−	0.0138815i	−0.000742622	−	0.000477254i
$847$	−1.13137	−	0.980334i	−0.0388742	−	0.0336847i
$848$	−4.85306	−	16.5280i	−0.166655	−	0.567574i
$849$	3.22403	+	7.05965i	0.110649	+	0.242287i
$850$	−0.218252	+	0.116594i	−0.00748598	+	0.00399912i
$851$	−14.6976	+	13.2516i	−0.503828	+	0.454260i
$852$		−	16.4744i		−	0.564404i
$853$	−1.04470	+	0.477098i	−0.0357698	+	0.0163355i	−0.433220	−	0.901288i	$-0.642623\pi$
$853$	−1.04470	+	0.477098i	−0.0357698	+	0.0163355i	0.397450	+	0.917624i	$0.369895\pi$
$854$	−0.0491580	+	0.0144341i	−0.00168215	+	0.000493924i
$855$	2.23081	+	1.12947i	0.0762922	+	0.0386269i
$856$	0.221893	+	0.142602i	0.00758415	+	0.00487403i
$857$	−10.0146	+	8.67773i	−0.342093	+	0.296426i	−0.808915	−	0.587926i	$-0.799945\pi$
$857$	−10.0146	+	8.67773i	−0.342093	+	0.296426i	0.466821	+	0.884352i	$0.345399\pi$
$858$	0.0968107	−	0.0139193i	0.00330506	−	0.000475196i
$859$	29.5825	+	8.68622i	1.00934	+	0.296370i	0.744285	−	0.667862i	$-0.232791\pi$
$859$	29.5825	+	8.68622i	1.00934	+	0.296370i	0.265058	+	0.964232i	$0.414609\pi$
$860$	4.79785	−	5.10618i	0.163605	−	0.174119i
$861$	0.549255	−	3.82015i	0.0187186	−	0.130190i
$862$	0.0315466	+	0.0144068i	0.00107448	+	0.000490699i
$863$	−7.38451	−	3.37239i	−0.251372	−	0.114798i	0.285745	−	0.958306i	$-0.407759\pi$
$863$	−7.38451	−	3.37239i	−0.251372	−	0.114798i	−0.537116	+	0.843508i	$0.680486\pi$
$864$	0.0185965	−	0.129342i	0.000632667	−	0.00440030i
$865$	16.2269	−	17.2697i	0.551730	−	0.587188i
$866$	0.140765	+	0.0413325i	0.00478340	+	0.00140453i
$867$	3.61377	−	0.519582i	0.122730	−	0.0176459i
$868$	−0.257390	+	0.223030i	−0.00873640	+	0.00757014i
$869$	−5.82668	−	3.74458i	−0.197657	−	0.127026i
$870$	0.162717	+	0.0823841i	0.00551663	+	0.00279308i
$871$	−33.3137	+	9.78180i	−1.12879	+	0.331444i
$872$	0.729705	−	0.333245i	0.0247109	−	0.0112851i
$873$			10.4727i			0.354447i
$874$	0.0579606	+	0.00717066i	0.00196055	+	0.000242551i
$875$	−4.35775	+	3.94689i	−0.147319	+	0.133429i
$876$	9.91406	+	21.7088i	0.334965	+	0.733471i
$877$	12.5028	+	42.5805i	0.422188	+	1.43784i	0.846531	+	0.532339i	$0.178687\pi$
$877$	12.5028	+	42.5805i	0.422188	+	1.43784i	−0.424343	+	0.905501i	$0.639495\pi$
$878$	0.0884398	+	0.0766335i	0.00298470	+	0.00258625i
$879$	13.6625	+	8.78037i	0.460826	+	0.296155i
$880$	14.6590	−	20.9080i	0.494155	−	0.704809i
$881$	−1.41093	−	9.81323i	−0.0475354	−	0.330616i	−0.999688	−	0.0249919i	$-0.992044\pi$
$881$	−1.41093	−	9.81323i	−0.0475354	−	0.330616i	0.952152	−	0.305624i	$-0.0988651\pi$
$882$	−0.0206284	+	0.0702537i	−0.000694593	+	0.00236557i
$883$	15.0470	+	23.4136i	0.506373	+	0.787932i	0.996489	−	0.0837255i	$-0.0266819\pi$
$883$	15.0470	+	23.4136i	0.506373	+	0.787932i	−0.490116	+	0.871657i	$0.663046\pi$
$884$	−4.06808	+	28.2941i	−0.136824	+	0.951634i
$885$	5.08950	−	27.4884i	0.171082	−	0.924014i
$886$	0.146545	−	0.320888i	0.00492327	−	0.0107804i
$887$	46.1924	+	6.64146i	1.55099	+	0.222998i	0.863933	−	0.503607i	$-0.167994\pi$
$887$	46.1924	+	6.64146i	1.55099	+	0.222998i	0.687055	+	0.726606i	$0.258903\pi$
$888$	0.0971768	+	0.151210i	0.00326104	+	0.00507428i
$889$	−9.94332	−	2.91962i	−0.333488	−	0.0979210i
$890$	0.0129571	+	0.0316907i	0.000434323	+	0.00106228i
$891$	−1.86989	−	2.15796i	−0.0626436	−	0.0722945i
$892$	−27.8942	+	43.4042i	−0.933967	+	1.45328i
$893$	1.99251	+	1.72652i	0.0666769	+	0.0577759i
$894$	−0.180625	+	0.0530363i	−0.00604101	+	0.00177380i
$895$	4.57653	−	3.65358i	0.152977	−	0.122126i
$896$	0.183233			0.00612137
$897$	14.3868	−	4.53419i	0.480363	−	0.151392i
$898$			0.0172671i			0.000576212i
$899$	−1.00758	−	2.20629i	−0.0336046	−	0.0735837i
$900$	−7.13508	+	7.00562i	−0.237836	+	0.233521i
$901$	−12.8178	+	14.7926i	−0.427024	+	0.492812i
$902$	−0.123382	+	0.191986i	−0.00410818	+	0.00639245i
$903$	0.622699	−	0.539571i	0.0207221	−	0.0179558i
$904$	−0.0214145	−	0.148941i	−0.000712234	−	0.00495370i
$905$	−1.56067	+	38.7270i	−0.0518785	+	1.28733i
$906$	0.112952	−	0.0725897i	0.00375257	−	0.00241163i
$907$	−52.8579	−	7.59982i	−1.75512	−	0.252348i	−0.811729	−	0.584034i	$-0.801473\pi$
$907$	−52.8579	−	7.59982i	−1.75512	−	0.252348i	−0.943390	+	0.331686i	$0.892382\pi$
$908$	7.19749	+	3.28698i	0.238857	+	0.109082i
$909$	−1.68174	+	3.68250i	−0.0557798	+	0.122141i
$910$	−0.00412215	−	0.0400664i	−0.000136648	−	0.00132819i
$911$	−40.8247	+	26.2364i	−1.35258	+	0.869252i	−0.997839	−	0.0657119i	$-0.979068\pi$
$911$	−40.8247	+	26.2364i	−1.35258	+	0.869252i	−0.354743	+	0.934964i	$0.615432\pi$
$912$	−1.25995	+	4.29098i	−0.0417210	+	0.142089i
$913$	21.4091	−	3.07817i	0.708539	−	0.101873i
$914$	−0.0767599	−	0.0885857i	−0.00253899	−	0.00293015i
$915$	18.9513	+	6.40412i	0.626512	+	0.211714i
$916$	30.4901	−	35.1874i	1.00742	−	1.16263i
$917$	2.62771	+	8.94917i	0.0867748	+	0.295528i
$918$	−0.0450164	+	0.0205583i	−0.00148576	+	0.000678525i
$919$	59.1683			1.95178			0.975891	−	0.218261i	$-0.0700383\pi$
$919$	59.1683			1.95178			0.975891	+	0.218261i	$0.0700383\pi$
$920$	−0.202748	+	0.420829i	−0.00668440	+	0.0138743i
$921$	32.4266			1.06849
$922$	0.204225	−	0.0932664i	0.00672579	−	0.00307156i
$923$	−7.29974	−	24.8606i	−0.240274	−	0.818298i
$924$	1.96653	−	2.26950i	0.0646942	−	0.0746611i
$925$	1.66022	−	20.5651i	0.0545876	−	0.676177i
$926$	−0.0374057	−	0.0431685i	−0.00122923	−	0.00141860i
$927$	0.165035	−	0.0237284i	0.00542045	−	0.000779343i
$928$	−0.275732	+	0.939056i	−0.00905133	+	0.0308260i
$929$	−24.9953	+	16.0635i	−0.820070	+	0.527027i	−0.882108	−	0.471047i	$-0.843876\pi$
$929$	−24.9953	+	16.0635i	−0.820070	+	0.527027i	0.0620383	+	0.998074i	$0.480240\pi$
$930$	−0.00784444		0.000807059i	−0.000257229		2.64645e-5i
$931$	3.12325	−	6.83897i	0.102360	−	0.224138i
$932$	34.0171	+	15.5351i	1.11427	+	0.508868i
$933$	−20.2462	−	2.91096i	−0.662830	−	0.0953006i
$934$	0.298841	−	0.192053i	0.00977838	−	0.00628418i
$935$	−28.9914	−	1.16833i	−0.948120	−	0.0382086i
$936$	−0.0194983	−	0.135614i	−0.000637323	−	0.00443268i
$937$	−24.7611	+	21.4556i	−0.808911	+	0.700925i	−0.957645	−	0.287952i	$-0.907026\pi$
$937$	−24.7611	+	21.4556i	−0.808911	+	0.700925i	0.148734	+	0.988877i	$0.452480\pi$
$938$	0.0341777	−	0.0531815i	0.00111594	−	0.00173644i
$939$	7.36867	−	8.50390i	0.240468	−	0.277514i
$940$	−9.09200	+	5.33841i	−0.296548	+	0.174120i
$941$	−10.6161	−	23.2461i	−0.346076	−	0.757801i	−0.999999	−	0.00123982i	$-0.999605\pi$
$941$	−10.6161	−	23.2461i	−0.346076	−	0.757801i	0.653923	−	0.756561i	$-0.273122\pi$
$942$			0.0537945i			0.00175272i
$943$	−13.9876	+	32.2983i	−0.455498	+	1.05178i
$944$	49.9997			1.62735
$945$	−0.918965	+	0.733636i	−0.0298939	+	0.0238652i
$946$	−0.0467478	+	0.0137264i	−0.00151990	+	0.000446284i
$947$	−26.5671	−	23.0205i	−0.863313	−	0.748065i	0.105877	−	0.994379i	$-0.466235\pi$
$947$	−26.5671	−	23.0205i	−0.863313	−	0.748065i	−0.969190	+	0.246314i	$0.920781\pi$
$948$	−2.62265	+	4.08093i	−0.0851798	+	0.132542i
$949$	24.5798	+	28.3667i	0.797896	+	0.920821i
$950$	−0.0490760	+	0.0360415i	−0.00159224	+	0.00116934i
$951$	−8.28419	−	2.43246i	−0.268633	−	0.0788778i
$952$	−0.0562785	−	0.0875711i	−0.00182400	−	0.00283820i
$953$	12.7669	+	1.83560i	0.413559	+	0.0594608i	0.345954	−	0.938251i	$-0.387555\pi$
$953$	12.7669	+	1.83560i	0.413559	+	0.0594608i	0.0676048	+	0.997712i	$0.478464\pi$
$954$	0.0194856	−	0.0426674i	0.000630868	−	0.00138141i
$955$	−23.1424	−	4.28482i	−0.748870	−	0.138654i
$956$	2.65489	−	18.4652i	0.0858654	−	0.597207i
$957$	11.5623	+	17.9912i	0.373755	+	0.581574i
$958$	0.0774776	−	0.263864i	0.00250319	−	0.00852507i
$959$	0.186594	+	1.29779i	0.00602545	+	0.0419079i
$960$	−14.6420	−	10.2657i	−0.472567	−	0.331325i
$961$	−25.9906	−	16.7032i	−0.838408	−	0.538812i
$962$	0.106819	+	0.0925594i	0.00344399	+	0.00298424i
$963$	−1.70597	−	5.81000i	−0.0549741	−	0.187225i
$964$	11.1058	+	24.3184i	0.357695	+	0.783242i
$965$	−0.624827	+	0.156434i	−0.0201139	+	0.00503580i
$966$	−0.0143905	+	0.0233932i	−0.000463007	+	0.000752665i
$967$			11.4820i			0.369238i	0.982810	+	0.184619i	$0.0591051\pi$
$967$			11.4820i			0.369238i	−0.982810	+	0.184619i	$0.940895\pi$
$968$	0.112795	−	0.0515119i	0.00362538	−	0.00165565i
$969$	4.87578	−	1.43166i	0.156633	−	0.0459915i
$970$	−0.227523	−	0.115195i	−0.00730531	−	0.00369869i
$971$	−43.1360	−	27.7218i	−1.38430	−	0.889635i	−0.384856	−	0.922977i	$-0.625749\pi$
$971$	−43.1360	−	27.7218i	−1.38430	−	0.889635i	−0.999444	+	0.0333414i	$0.989385\pi$
$972$	−1.51141	+	1.30964i	−0.0484785	+	0.0420068i
$973$	6.13919	−	0.882683i	0.196813	−	0.0282975i
$974$	−0.212638	−	0.0624362i	−0.00681337	−	0.00200059i
$975$	−7.66301	+	13.7333i	−0.245413	+	0.439819i
$976$	−5.09176	+	35.4140i	−0.162983	+	1.13357i
$977$	−52.7598	−	24.0946i	−1.68794	−	0.770854i	−0.998937	−	0.0460913i	$-0.985323\pi$
$977$	−52.7598	−	24.0946i	−1.68794	−	0.770854i	−0.688998	−	0.724763i	$-0.741949\pi$
$978$	0.239839	+	0.109531i	0.00766919	+	0.00350240i
$979$	−0.571341	+	3.97377i	−0.0182601	+	0.127002i
$980$	21.9114	+	20.5883i	0.699935	+	0.657670i
$981$	−17.6702	−	5.18844i	−0.564166	−	0.165654i
$982$	−0.277639	+	0.0399185i	−0.00885983	+	0.00127385i
$983$	−36.0810	+	31.2644i	−1.15081	+	0.997179i	−0.150843	+	0.988558i	$0.548199\pi$
$983$	−36.0810	+	31.2644i	−1.15081	+	0.997179i	−0.999963	+	0.00862135i	$0.997256\pi$
$984$	0.268937	+	0.172836i	0.00857341	+	0.00550979i
$985$	14.8725	−	29.3747i	0.473877	−	0.935957i
$986$	0.355643	−	0.104426i	0.0113260	−	0.00332561i
$987$	−1.12782	+	0.515057i	−0.0358988	+	0.0163944i
$988$			7.03399i			0.223781i
$989$	−6.77230	+	3.25561i	−0.215347	+	0.103522i
$990$	0.0674504	−	0.0168872i	0.00214372	−	0.000536711i
$991$	1.97240	+	4.31894i	0.0626552	+	0.137196i	0.938369	−	0.345634i	$-0.112336\pi$
$991$	1.97240	+	4.31894i	0.0626552	+	0.137196i	−0.875714	+	0.482830i	$0.839609\pi$
$992$	−0.0119220	−	0.0406024i	−0.000378522	−	0.00128913i
$993$	−16.1477	−	13.9921i	−0.512432	−	0.444025i
$994$	0.0396871	+	0.0255053i	0.00125880	+	0.000808980i
$995$	−7.96346	+	11.3582i	−0.252459	+	0.360080i
$996$	−2.15591	−	14.9947i	−0.0683125	−	0.475124i
$997$	4.10475	−	13.9795i	0.129999	−	0.442735i	−0.868608	−	0.495499i	$-0.834985\pi$
$997$	4.10475	−	13.9795i	0.129999	−	0.442735i	0.998607	+	0.0527647i	$0.0168033\pi$
$998$	0.157294	+	0.244754i	0.00497905	+	0.00774756i
$999$	0.587248	−	4.08440i	0.0185797	−	0.129225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.t.a.4.12	✓	240
5.4	even	2	inner	345.2.t.a.4.13	yes	240
23.6	even	11	inner	345.2.t.a.259.13	yes	240
115.29	even	22	inner	345.2.t.a.259.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.t.a.4.12	✓	240	1.1	even	1	trivial
345.2.t.a.4.13	yes	240	5.4	even	2	inner
345.2.t.a.259.12	yes	240	115.29	even	22	inner
345.2.t.a.259.13	yes	240	23.6	even	11	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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.00990606 + 0.00452394i) q^{2} +(0.281733 + 0.959493i) q^{3} +(-1.30964 + 1.51141i) q^{4} +(-0.715854 + 2.11838i) q^{5} +(-0.00713155 - 0.00823025i) q^{6} +(-0.520522 + 0.0748397i) q^{7} +(0.0122721 - 0.0417950i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(-0.00249216 - 0.0242233i) q^{10} +(1.18617 - 2.59736i) q^{11} +(-1.81916 - 0.830781i) q^{12} +(-3.11331 - 0.447626i) q^{13} +(0.00481775 - 0.00309618i) q^{14} +(-2.23425 - 0.0900389i) q^{15} +(-0.569158 - 3.95858i) q^{16} +(-3.43438 + 2.97590i) q^{17} +(0.00588768 - 0.00916140i) q^{18} +(-0.732287 + 0.845104i) q^{19} +(-2.26423 - 3.85628i) q^{20} +(-0.218456 - 0.478352i) q^{21} +0.0310958i q^{22} +(0.775939 + 4.73264i) q^{23} +0.0435594 q^{24} +(-3.97511 - 3.03291i) q^{25} +(0.0328656 - 0.00965022i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(0.568584 - 0.884735i) q^{28} +(4.90475 + 5.66038i) q^{29} +(0.0225400 - 0.00921571i) q^{30} +(-0.310721 - 0.0912358i) q^{31} +(0.0706465 + 0.109928i) q^{32} +(2.82633 + 0.406365i) q^{33} +(0.0205583 - 0.0450164i) q^{34} +(0.214078 - 1.15624i) q^{35} +(0.284613 - 1.97953i) q^{36} +(2.23090 + 3.47135i) q^{37} +(0.00343087 - 0.0116845i) q^{38} +(-0.447626 - 3.11331i) q^{39} +(0.0797528 + 0.0559161i) q^{40} +(6.17403 + 3.96781i) q^{41} +(0.00432808 + 0.00375030i) q^{42} +(0.441423 + 1.50335i) q^{43} +(2.37221 + 5.19441i) q^{44} +(-0.543071 - 2.16912i) q^{45} +(-0.0290967 - 0.0433715i) q^{46} -2.35771i q^{47} +(3.63788 - 1.66136i) q^{48} +(-6.45111 + 1.89422i) q^{49} +(0.0530983 + 0.0120610i) q^{50} +(-3.82293 - 2.45685i) q^{51} +(4.75387 - 4.11925i) q^{52} +(4.26337 - 0.612980i) q^{53} +(0.0104491 + 0.00306812i) q^{54} +(4.65308 + 4.37210i) q^{55} +(-0.00325997 + 0.0226736i) q^{56} +(-1.01718 - 0.464531i) q^{57} +(-0.0741939 - 0.0338832i) q^{58} +(-1.77924 + 12.3749i) q^{59} +(3.06216 - 3.25895i) q^{60} +(-8.58375 - 2.52042i) q^{61} +(0.00349076 - 0.000501896i) q^{62} +(0.397429 - 0.344374i) q^{63} +(6.72763 + 4.32359i) q^{64} +(3.17692 - 6.27475i) q^{65} +(-0.0298362 + 0.00876069i) q^{66} +(10.0411 - 4.58563i) q^{67} -9.08812i q^{68} +(-4.32233 + 2.07785i) q^{69} +(0.00311009 + 0.0124222i) q^{70} +(3.42206 + 7.49326i) q^{71} +(0.0122721 + 0.0417950i) q^{72} +(-9.01868 - 7.81473i) q^{73} +(-0.0378036 - 0.0242949i) q^{74} +(1.79014 - 4.66856i) q^{75} +(-0.318263 - 2.21357i) q^{76} +(-0.423044 + 1.44076i) q^{77} +(0.0185186 + 0.0288156i) q^{78} +(0.345206 - 2.40096i) q^{79} +(8.79323 + 1.62807i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-0.0791105 - 0.0113744i) q^{82} +(4.09529 + 6.37239i) q^{83} +(1.00909 + 0.296294i) q^{84} +(-3.84560 - 9.40564i) q^{85} +(-0.0111738 - 0.0128953i) q^{86} +(-4.04927 + 6.30078i) q^{87} +(-0.0939997 - 0.0814512i) q^{88} +(-1.34903 + 0.396110i) q^{89} +(0.0151927 + 0.0190306i) q^{90} +1.65404 q^{91} +(-8.16917 - 5.02532i) q^{92} -0.323838i q^{93} +(0.0106662 + 0.0233556i) q^{94} +(-1.26605 - 2.15624i) q^{95} +(-0.0855718 + 0.0987552i) q^{96} +(5.66197 - 8.81019i) q^{97} +(0.0553357 - 0.0479487i) q^{98} +(0.406365 + 2.82633i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) \) 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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