LMFDB - Embedded newform 990.2.bg.a.841.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(31,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 0, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,11,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			841.4
Character	$\chi$	$=$	990.841
Dual form			990.2.bg.a.691.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.669131 - 0.743145i) q^{2} +(-0.790547 + 1.54112i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(0.669131 + 0.743145i) q^{5} +(0.616293 + 1.61870i) q^{6} +(-0.458335 - 0.204064i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-1.75007 - 2.43665i) q^{9} +1.00000 q^{10} +(-2.50337 + 2.17558i) q^{11} +(1.61531 + 0.625126i) q^{12} +(-4.31860 - 0.917946i) q^{13} +(-0.458335 + 0.204064i) q^{14} +(-1.67425 + 0.443717i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-0.791452 + 2.43584i) q^{17} +(-2.98181 - 0.329879i) q^{18} +(-0.146517 - 0.106451i) q^{19} +(0.669131 - 0.743145i) q^{20} +(0.676821 - 0.545025i) q^{21} +(-0.0583144 + 3.31611i) q^{22} +(-0.385331 + 0.667413i) q^{23} +(1.54541 - 0.782117i) q^{24} +(-0.104528 + 0.994522i) q^{25} +(-3.57187 + 2.59512i) q^{26} +(5.13867 - 0.770778i) q^{27} +(-0.155037 + 0.477155i) q^{28} +(-2.62836 - 1.17022i) q^{29} +(-0.790547 + 1.54112i) q^{30} +(-9.42092 - 2.00248i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.37378 - 5.57788i) q^{33} +(1.28060 + 2.21806i) q^{34} +(-0.155037 - 0.477155i) q^{35} +(-2.24037 + 1.99518i) q^{36} +(-0.841887 + 0.611667i) q^{37} +(-0.177147 + 0.0376537i) q^{38} +(4.82872 - 5.92978i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-0.537342 + 0.239240i) q^{41} +(0.0478493 - 0.867669i) q^{42} +(3.57269 + 6.18808i) q^{43} +(2.42533 + 2.26225i) q^{44} +(0.639755 - 2.93099i) q^{45} +(0.238148 + 0.732943i) q^{46} +(-0.116154 + 1.10513i) q^{47} +(0.452856 - 1.67180i) q^{48} +(-4.51549 - 5.01495i) q^{49} +(0.669131 + 0.743145i) q^{50} +(-3.12823 - 3.14536i) q^{51} +(-0.461501 + 4.39089i) q^{52} +(-2.91276 - 8.96457i) q^{53} +(2.86564 - 4.33453i) q^{54} +(-3.29185 - 0.404623i) q^{55} +(0.250855 + 0.434494i) q^{56} +(0.279881 - 0.141645i) q^{57} +(-2.62836 + 1.17022i) q^{58} +(0.275918 + 2.62518i) q^{59} +(0.616293 + 1.61870i) q^{60} +(-3.94297 + 0.838103i) q^{61} +(-7.79196 + 5.66119i) q^{62} +(0.304888 + 1.47393i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-2.20754 - 3.82357i) q^{65} +(-5.06441 - 2.71141i) q^{66} +(-2.85511 + 4.94520i) q^{67} +(2.50523 + 0.532502i) q^{68} +(-0.723938 - 1.12146i) q^{69} +(-0.458335 - 0.204064i) q^{70} +(-1.08364 + 3.33511i) q^{71} +(-0.0163876 + 2.99996i) q^{72} +(-2.39794 + 1.74220i) q^{73} +(-0.108775 + 1.03493i) q^{74} +(-1.45004 - 0.947306i) q^{75} +(-0.0905523 + 0.156841i) q^{76} +(1.59134 - 0.486295i) q^{77} +(-1.17564 - 7.55623i) q^{78} +(-0.797324 + 0.885518i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-2.87450 + 8.52861i) q^{81} +(-0.181762 + 0.559405i) q^{82} +(3.30169 - 0.701797i) q^{83} +(-0.612787 - 0.616143i) q^{84} +(-2.33977 + 1.04173i) q^{85} +(6.98924 + 1.48561i) q^{86} +(3.88129 - 3.12550i) q^{87} +(3.30404 - 0.288633i) q^{88} -2.22432 q^{89} +(-1.75007 - 2.43665i) q^{90} +(1.79205 + 1.30200i) q^{91} +(0.704035 + 0.313457i) q^{92} +(10.5337 - 12.9357i) q^{93} +(0.743547 + 0.825793i) q^{94} +(-0.0189306 - 0.180112i) q^{95} +(-0.939371 - 1.45519i) q^{96} +(-3.97204 + 4.41140i) q^{97} -6.74829 q^{98} +(9.68219 + 2.29242i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) $ 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.669131	−	0.743145i	0.473147	−	0.525483i
$2$	0.669131	−	0.743145i	0.473147	−	0.525483i
$3$	−0.790547	+	1.54112i	−0.456422	+	0.889763i
$3$	−0.790547	+	1.54112i	−0.456422	+	0.889763i
$4$	−0.104528	−	0.994522i	−0.0522642	−	0.497261i
$5$	0.669131	+	0.743145i	0.299244	+	0.332344i
$5$	0.669131	+	0.743145i	0.299244	+	0.332344i
$6$	0.616293	+	1.61870i	0.251600	+	0.660831i
$7$	−0.458335	−	0.204064i	−0.173234	−	0.0771289i	0.318287	−	0.947994i	$-0.396892\pi$
$7$	−0.458335	−	0.204064i	−0.173234	−	0.0771289i	−0.491521	+	0.870865i	$0.663559\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−1.75007	−	2.43665i	−0.583357	−	0.812216i
$10$	1.00000			0.316228
$11$	−2.50337	+	2.17558i	−0.754795	+	0.655961i
$11$	−2.50337	+	2.17558i	−0.754795	+	0.655961i
$12$	1.61531	+	0.625126i	0.466299	+	0.180458i
$13$	−4.31860	−	0.917946i	−1.19776	−	0.254593i	−0.434495	−	0.900674i	$-0.643073\pi$
$13$	−4.31860	−	0.917946i	−1.19776	−	0.254593i	−0.763268	+	0.646082i	$0.776407\pi$
$14$	−0.458335	+	0.204064i	−0.122495	+	0.0545384i
$15$	−1.67425	+	0.443717i	−0.432290	+	0.114567i
$16$	−0.978148	+	0.207912i	−0.244537	+	0.0519779i
$17$	−0.791452	+	2.43584i	−0.191955	+	0.590778i	0.808043	+	0.589123i	$0.200527\pi$
$17$	−0.791452	+	2.43584i	−0.191955	+	0.590778i	−0.999999	+	0.00165479i	$0.999473\pi$
$18$	−2.98181	−	0.329879i	−0.702819	−	0.0777531i
$19$	−0.146517	−	0.106451i	−0.0336132	−	0.0244214i	0.570852	−	0.821053i	$-0.306613\pi$
$19$	−0.146517	−	0.106451i	−0.0336132	−	0.0244214i	−0.604465	+	0.796632i	$0.706613\pi$
$20$	0.669131	−	0.743145i	0.149622	−	0.166172i
$21$	0.676821	−	0.545025i	0.147695	−	0.118934i
$22$	−0.0583144	+	3.31611i	−0.0124327	+	0.706997i
$23$	−0.385331	+	0.667413i	−0.0803471	+	0.139165i	−0.903399	−	0.428801i	$-0.858936\pi$
$23$	−0.385331	+	0.667413i	−0.0803471	+	0.139165i	0.823052	+	0.567966i	$0.192270\pi$
$24$	1.54541	−	0.782117i	0.315456	−	0.159649i
$25$	−0.104528	+	0.994522i	−0.0209057	+	0.198904i
$26$	−3.57187	+	2.59512i	−0.700502	+	0.508945i
$27$	5.13867	−	0.770778i	0.988937	−	0.148336i
$28$	−0.155037	+	0.477155i	−0.0292992	+	0.0901738i
$29$	−2.62836	−	1.17022i	−0.488075	−	0.217305i	0.147918	−	0.989000i	$-0.452743\pi$
$29$	−2.62836	−	1.17022i	−0.488075	−	0.217305i	−0.635993	+	0.771695i	$0.719409\pi$
$30$	−0.790547	+	1.54112i	−0.144333	+	0.281368i
$31$	−9.42092	−	2.00248i	−1.69205	−	0.359656i	−0.741672	−	0.670762i	$-0.765967\pi$
$31$	−9.42092	−	2.00248i	−1.69205	−	0.359656i	−0.950375	+	0.311106i	$0.899300\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.37378	−	5.57788i	−0.239145	−	0.970984i
$34$	1.28060	+	2.21806i	0.219621	+	0.380394i
$35$	−0.155037	−	0.477155i	−0.0262060	−	0.0806539i
$36$	−2.24037	+	1.99518i	−0.373394	+	0.332531i
$37$	−0.841887	+	0.611667i	−0.138405	+	0.100557i	−0.654834	−	0.755773i	$-0.727261\pi$
$37$	−0.841887	+	0.611667i	−0.138405	+	0.100557i	0.516428	+	0.856330i	$0.327261\pi$
$38$	−0.177147	+	0.0376537i	−0.0287370	+	0.00610824i
$39$	4.82872	−	5.92978i	0.773213	−	0.949524i
$40$	−0.104528	−	0.994522i	−0.0165274	−	0.157248i
$41$	−0.537342	+	0.239240i	−0.0839187	+	0.0373630i	−0.448267	−	0.893900i	$-0.647959\pi$
$41$	−0.537342	+	0.239240i	−0.0839187	+	0.0373630i	0.364348	+	0.931263i	$0.381292\pi$
$42$	0.0478493	−	0.867669i	0.00738331	−	0.133884i
$43$	3.57269	+	6.18808i	0.544830	+	0.943674i	0.998618	+	0.0525635i	$0.0167392\pi$
$43$	3.57269	+	6.18808i	0.544830	+	0.943674i	−0.453787	+	0.891110i	$0.649927\pi$
$44$	2.42533	+	2.26225i	0.365632	+	0.341047i
$45$	0.639755	−	2.93099i	0.0953691	−	0.436926i
$46$	0.238148	+	0.732943i	0.0351130	+	0.108067i
$47$	−0.116154	+	1.10513i	−0.0169427	+	0.161199i	−0.999722	−	0.0235850i	$-0.992492\pi$
$47$	−0.116154	+	1.10513i	−0.0169427	+	0.161199i	0.982779	+	0.184784i	$0.0591586\pi$
$48$	0.452856	−	1.67180i	0.0653641	−	0.241304i
$49$	−4.51549	−	5.01495i	−0.645069	−	0.716422i
$50$	0.669131	+	0.743145i	0.0946294	+	0.105097i
$51$	−3.12823	−	3.14536i	−0.438040	−	0.440439i
$52$	−0.461501	+	4.39089i	−0.0639987	+	0.608907i
$53$	−2.91276	−	8.96457i	−0.400099	−	1.23138i	−0.924919	−	0.380165i	$-0.875867\pi$
$53$	−2.91276	−	8.96457i	−0.400099	−	1.23138i	0.524820	−	0.851213i	$-0.324133\pi$
$54$	2.86564	−	4.33453i	0.389964	−	0.589854i
$55$	−3.29185	−	0.404623i	−0.443873	−	0.0545594i
$56$	0.250855	+	0.434494i	0.0335219	+	0.0580617i
$57$	0.279881	−	0.141645i	0.0370711	−	0.0187613i
$58$	−2.62836	+	1.17022i	−0.345121	+	0.153658i
$59$	0.275918	+	2.62518i	0.0359214	+	0.341769i	0.997691	+	0.0679109i	$0.0216334\pi$
$59$	0.275918	+	2.62518i	0.0359214	+	0.341769i	−0.961770	+	0.273859i	$0.911700\pi$
$60$	0.616293	+	1.61870i	0.0795630	+	0.208973i
$61$	−3.94297	+	0.838103i	−0.504845	+	0.107308i	−0.453292	−	0.891362i	$-0.649750\pi$
$61$	−3.94297	+	0.838103i	−0.504845	+	0.107308i	−0.0515531	+	0.998670i	$0.516417\pi$
$62$	−7.79196	+	5.66119i	−0.989580	+	0.718972i
$63$	0.304888	+	1.47393i	0.0384122	+	0.185697i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−2.20754	−	3.82357i	−0.273812	−	0.474256i
$66$	−5.06441	−	2.71141i	−0.623386	−	0.333752i
$67$	−2.85511	+	4.94520i	−0.348808	+	0.604153i	−0.986038	−	0.166521i	$-0.946747\pi$
$67$	−2.85511	+	4.94520i	−0.348808	+	0.604153i	0.637230	+	0.770674i	$0.280080\pi$
$68$	2.50523	+	0.532502i	0.303803	+	0.0645754i
$69$	−0.723938	−	1.12146i	−0.0871519	−	0.135008i
$70$	−0.458335	−	0.204064i	−0.0547815	−	0.0243903i
$71$	−1.08364	+	3.33511i	−0.128605	+	0.395805i	−0.994541	−	0.104350i	$-0.966724\pi$
$71$	−1.08364	+	3.33511i	−0.128605	+	0.395805i	0.865936	+	0.500155i	$0.166724\pi$
$72$	−0.0163876	+	2.99996i	−0.00193130	+	0.353548i
$73$	−2.39794	+	1.74220i	−0.280657	+	0.203909i	−0.719204	−	0.694799i	$-0.755493\pi$
$73$	−2.39794	+	1.74220i	−0.280657	+	0.203909i	0.438547	+	0.898708i	$0.355493\pi$
$74$	−0.108775	+	1.03493i	−0.0126449	+	0.120308i
$75$	−1.45004	−	0.947306i	−0.167436	−	0.109386i
$76$	−0.0905523	+	0.156841i	−0.0103871	+	0.0179909i
$77$	1.59134	−	0.486295i	0.181350	−	0.0554185i
$78$	−1.17564	−	7.55623i	−0.133115	−	0.855575i
$79$	−0.797324	+	0.885518i	−0.0897060	+	0.0996286i	−0.786326	−	0.617811i	$-0.788020\pi$
$79$	−0.797324	+	0.885518i	−0.0897060	+	0.0996286i	0.696620	+	0.717440i	$0.254686\pi$
$80$	−0.809017	−	0.587785i	−0.0904508	−	0.0657164i
$81$	−2.87450	+	8.52861i	−0.319389	+	0.947624i
$82$	−0.181762	+	0.559405i	−0.0200722	+	0.0617760i
$83$	3.30169	−	0.701797i	0.362408	−	0.0770322i	−0.0231090	−	0.999733i	$-0.507356\pi$
$83$	3.30169	−	0.701797i	0.362408	−	0.0770322i	0.385517	+	0.922701i	$0.374023\pi$
$84$	−0.612787	−	0.616143i	−0.0668605	−	0.0672267i
$85$	−2.33977	+	1.04173i	−0.253783	+	0.112992i
$86$	6.98924	+	1.48561i	0.753669	+	0.160197i
$87$	3.88129	−	3.12550i	0.416118	−	0.335088i
$88$	3.30404	−	0.288633i	0.352212	−	0.0307684i
$89$	−2.22432			−0.235778			−0.117889	−	0.993027i	$-0.537613\pi$
$89$	−2.22432			−0.235778			−0.117889	+	0.993027i	$0.537613\pi$
$90$	−1.75007	−	2.43665i	−0.184474	−	0.256845i
$91$	1.79205	+	1.30200i	0.187857	+	0.136486i
$92$	0.704035	+	0.313457i	0.0734007	+	0.0326801i
$93$	10.5337	−	12.9357i	1.09230	−	1.34137i
$94$	0.743547	+	0.825793i	0.0766911	+	0.0851740i
$95$	−0.0189306	−	0.180112i	−0.00194224	−	0.0184791i
$96$	−0.939371	−	1.45519i	−0.0958742	−	0.148520i
$97$	−3.97204	+	4.41140i	−0.403300	+	0.447910i	−0.910246	−	0.414068i	$-0.864108\pi$
$97$	−3.97204	+	4.41140i	−0.403300	+	0.447910i	0.506946	+	0.861978i	$0.330774\pi$
$98$	−6.74829			−0.681680
$99$	9.68219	+	2.29242i	0.973097	+	0.230397i
$100$	1.00000			0.100000
$101$	2.99391	−	3.32508i	0.297906	−	0.330858i	−0.575545	−	0.817770i	$-0.695210\pi$
$101$	2.99391	−	3.32508i	0.297906	−	0.330858i	0.873451	+	0.486912i	$0.161877\pi$
$102$	−4.43066	+	0.220068i	−0.438700	+	0.0217900i
$103$	1.39530	+	13.2754i	0.137483	+	1.30806i	0.817952	+	0.575287i	$0.195110\pi$
$103$	1.39530	+	13.2754i	0.137483	+	1.30806i	−0.680469	+	0.732777i	$0.738224\pi$
$104$	2.95426	+	3.28104i	0.289689	+	0.321733i
$105$	0.857915	+	0.138283i	0.0837239	+	0.0134951i
$106$	−8.61099	−	3.83386i	−0.836373	−	0.372377i
$107$	13.0943	+	9.51357i	1.26587	+	0.919711i	0.999030	−	0.0440283i	$-0.0140192\pi$
$107$	13.0943	+	9.51357i	1.26587	+	0.919711i	0.266844	+	0.963740i	$0.414019\pi$
$108$	−1.30369	−	5.02995i	−0.125448	−	0.484007i
$109$	3.70074			0.354466			0.177233	−	0.984169i	$-0.443285\pi$
$109$	3.70074			0.354466			0.177233	+	0.984169i	$0.443285\pi$
$110$	−2.50337	+	2.17558i	−0.238687	+	0.207433i
$111$	−0.277098	−	1.78100i	−0.0263010	−	0.169045i
$112$	0.490747	+	0.104311i	0.0463712	+	0.00985650i
$113$	−6.80622	+	3.03033i	−0.640275	+	0.285069i	−0.701082	−	0.713081i	$-0.747299\pi$
$113$	−6.80622	+	3.03033i	−0.640275	+	0.285069i	0.0608066	+	0.998150i	$0.480633\pi$
$114$	0.0820142	−	0.302771i	0.00768133	−	0.0283571i
$115$	−0.753821	+	0.160230i	−0.0702942	+	0.0149415i
$116$	−0.889074	+	2.73629i	−0.0825484	+	0.254058i
$117$	5.32115	+	12.1294i	0.491940	+	1.12136i
$118$	2.13551	+	1.55154i	0.196590	+	0.142831i
$119$	0.859818	−	0.954924i	0.0788194	−	0.0875378i
$120$	1.61531	+	0.625126i	0.147457	+	0.0570659i
$121$	1.53374	−	10.8926i	0.139431	−	0.990232i
$122$	−2.01553	+	3.49099i	−0.182477	+	0.316060i
$123$	0.0560975	−	1.01724i	0.00505814	−	0.0917211i
$124$	−1.00675	+	9.57863i	−0.0904092	+	0.860186i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$	1.29935	+	0.759675i	0.115755	+	0.0676772i
$127$	−1.98451	+	6.10771i	−0.176097	+	0.541971i	−0.999682	−	0.0252219i	$-0.991971\pi$
$127$	−1.98451	+	6.10771i	−0.176097	+	0.541971i	0.823585	+	0.567193i	$0.191971\pi$
$128$	0.913545	+	0.406737i	0.0807468	+	0.0359508i
$129$	−12.3609	+	0.613959i	−1.08832	+	0.0540561i
$130$	−4.31860	−	0.917946i	−0.378766	−	0.0805092i
$131$	5.96537	−	10.3323i	0.521196	−	0.902739i	−0.478500	−	0.878088i	$-0.658819\pi$
$131$	5.96537	−	10.3323i	0.521196	−	0.902739i	0.999696	−	0.0246510i	$-0.00784746\pi$
$132$	−5.40372	+	1.94930i	−0.470334	+	0.169665i
$133$	0.0454310	+	0.0786888i	0.00393937	+	0.00682318i
$134$	1.76456	+	5.43075i	0.152435	+	0.469145i
$135$	4.01124	+	3.30302i	0.345233	+	0.284279i
$136$	2.07205	−	1.50543i	0.177677	−	0.129090i
$137$	20.3348	−	4.32229i	1.73732	−	0.369278i	0.773078	−	0.634311i	$-0.218716\pi$
$137$	20.3348	−	4.32229i	1.73732	−	0.369278i	0.964239	+	0.265033i	$0.0853828\pi$
$138$	−1.31782	−	0.212413i	−0.112180	−	0.0180818i
$139$	−1.75322	−	16.6808i	−0.148706	−	1.41485i	−0.773371	−	0.633953i	$-0.781431\pi$
$139$	−1.75322	−	16.6808i	−0.148706	−	1.41485i	0.624665	−	0.780893i	$-0.285236\pi$
$140$	−0.458335	+	0.204064i	−0.0387364	+	0.0172466i
$141$	−1.61130	−	1.05266i	−0.135696	−	0.0886500i
$142$	1.75337	+	3.03693i	0.147140	+	0.254854i
$143$	12.8081	−	7.09748i	1.07107	−	0.593521i
$144$	2.21844	+	2.01954i	0.184870	+	0.168295i
$145$	−0.889074	−	2.73629i	−0.0738336	−	0.227236i
$146$	−0.309824	+	2.94777i	−0.0256412	+	0.243960i
$147$	11.2983	−	2.99433i	0.931870	−	0.246968i
$148$	0.696317	+	0.773338i	0.0572369	+	0.0635680i
$149$	−4.04335	−	4.49059i	−0.331244	−	0.367884i	0.554399	−	0.832251i	$-0.312948\pi$
$149$	−4.04335	−	4.49059i	−0.331244	−	0.367884i	−0.885643	+	0.464368i	$0.846282\pi$
$150$	−1.67425	+	0.443717i	−0.136702	+	0.0362293i
$151$	0.964809	−	9.17954i	0.0785150	−	0.747021i	−0.882460	−	0.470387i	$-0.844114\pi$
$151$	0.964809	−	9.17954i	0.0785150	−	0.747021i	0.960975	−	0.276634i	$-0.0892189\pi$
$152$	0.0559644	+	0.172241i	0.00453931	+	0.0139706i
$153$	7.32038	−	2.33440i	0.591818	−	0.188725i
$154$	0.703427	−	1.50799i	0.0566837	−	0.121517i
$155$	−4.81570	−	8.34103i	−0.386806	−	0.669968i
$156$	−6.40203	−	4.18243i	−0.512573	−	0.334863i
$157$	−8.86508	+	3.94699i	−0.707510	+	0.315004i	−0.728759	−	0.684770i	$-0.759903\pi$
$157$	−8.86508	+	3.94699i	−0.707510	+	0.315004i	0.0212485	+	0.999774i	$0.493236\pi$
$158$	0.124554	+	1.18506i	0.00990901	+	0.0942779i
$159$	16.1181	+	2.59800i	1.27825	+	0.206035i
$160$	−0.978148	+	0.207912i	−0.0773294	+	0.0164369i
$161$	0.312806	−	0.227267i	0.0246526	−	0.0179111i
$162$	4.41458	+	7.84293i	0.346842	+	0.616198i
$163$	2.00556	+	6.17249i	0.157088	+	0.483467i	0.998366	−	0.0571350i	$-0.0181966\pi$
$163$	2.00556	+	6.17249i	0.157088	+	0.483467i	−0.841279	+	0.540602i	$0.818197\pi$
$164$	0.294097	+	0.509391i	0.0229651	+	0.0397767i
$165$	3.22593	−	4.75325i	0.251139	−	0.370040i
$166$	1.68773	−	2.92323i	0.130993	−	0.226887i
$167$	19.3797	+	4.11929i	1.49965	+	0.318760i	0.883335	−	0.468742i	$-0.155293\pi$
$167$	19.3797	+	4.11929i	1.49965	+	0.318760i	0.616312	+	0.787502i	$0.288626\pi$
$168$	−0.867918	+	0.0431089i	−0.0669613	+	0.00332593i
$169$	5.93158	+	2.64091i	0.456275	+	0.203147i
$170$	−0.791452	+	2.43584i	−0.0607016	+	0.186820i
$171$	−0.00296787	+	0.543305i	−0.000226958	+	0.0415476i
$172$	5.78073	−	4.19995i	0.440777	−	0.320243i
$173$	1.31003	−	12.4641i	0.0995996	−	0.947627i	−0.824600	−	0.565717i	$-0.808600\pi$
$173$	1.31003	−	12.4641i	0.0995996	−	0.947627i	0.924199	−	0.381910i	$-0.124734\pi$
$174$	0.274396	−	4.97573i	0.0208019	−	0.377209i
$175$	0.250855	−	0.434494i	0.0189629	−	0.0328447i
$176$	1.99634	−	2.64851i	0.150480	−	0.199639i
$177$	−4.26383	−	1.65011i	−0.320489	−	0.124030i
$178$	−1.48836	+	1.65299i	−0.111557	+	0.123897i
$179$	14.6007	+	10.6080i	1.09131	+	0.792882i	0.979620	−	0.200861i	$-0.0643739\pi$
$179$	14.6007	+	10.6080i	1.09131	+	0.792882i	0.111689	+	0.993743i	$0.464374\pi$
$180$	−2.98181	−	0.329879i	−0.222251	−	0.0245877i
$181$	−6.56043	+	20.1909i	−0.487633	+	1.50078i	0.340498	+	0.940245i	$0.389404\pi$
$181$	−6.56043	+	20.1909i	−0.487633	+	1.50078i	−0.828131	+	0.560535i	$0.810596\pi$
$182$	2.16669	−	0.460543i	0.160605	−	0.0341377i
$183$	1.82549	−	6.73912i	0.134944	−	0.498170i
$184$	0.704035	−	0.313457i	0.0519022	−	0.0231083i
$185$	−1.01789	−	0.216359i	−0.0748367	−	0.0159070i
$186$	−2.56464	−	16.4837i	−0.188048	−	1.20865i
$187$	−3.31806	−	7.81968i	−0.242640	−	0.571831i
$188$	1.11121			0.0810436
$189$	−2.51252	−	0.695342i	−0.182759	−	0.0505787i
$190$	−0.146517	−	0.106451i	−0.0106294	−	0.00772274i
$191$	−3.37280	−	1.50167i	−0.244047	−	0.108657i	0.281068	−	0.959688i	$-0.409311\pi$
$191$	−3.37280	−	1.50167i	−0.244047	−	0.108657i	−0.525116	+	0.851031i	$0.675978\pi$
$192$	−1.70998	−	0.275624i	−0.123407	−	0.0198914i
$193$	−6.24075	−	6.93105i	−0.449219	−	0.498908i	0.475417	−	0.879761i	$-0.342297\pi$
$193$	−6.24075	−	6.93105i	−0.449219	−	0.498908i	−0.924636	+	0.380853i	$0.875631\pi$
$194$	0.620494	+	5.90360i	0.0445489	+	0.423854i
$195$	7.63773	−	0.379361i	0.546949	−	0.0271666i
$196$	−4.51549	+	5.01495i	−0.322535	+	0.358211i
$197$	21.2493			1.51395			0.756977	−	0.653442i	$-0.226676\pi$
$197$	21.2493			1.51395			0.756977	+	0.653442i	$0.226676\pi$
$198$	8.18225	−	5.66134i	0.581487	−	0.402334i
$199$	−21.6690			−1.53608			−0.768038	−	0.640405i	$-0.778767\pi$
$199$	−21.6690			−1.53608			−0.768038	+	0.640405i	$0.778767\pi$
$200$	0.669131	−	0.743145i	0.0473147	−	0.0525483i
$201$	−5.36403	−	8.30947i	−0.378349	−	0.586105i
$202$	−0.467695	−	4.44982i	−0.0329069	−	0.313088i
$203$	0.965871	+	1.07271i	0.0677909	+	0.0752894i
$204$	−2.80115	+	3.43987i	−0.196119	+	0.240839i
$205$	−0.537342	−	0.239240i	−0.0375296	−	0.0167092i
$206$	10.7992	+	7.84607i	0.752415	+	0.546661i
$207$	2.30061	−	0.229105i	0.159903	−	0.0159239i
$208$	4.41508			0.306131
$209$	0.598377	−	0.0522728i	0.0413906	−	0.00361578i
$210$	0.676821	−	0.545025i	0.0467051	−	0.0376103i
$211$	27.0621	+	5.75223i	1.86303	+	0.396000i	0.994946	−	0.100414i	$-0.0320166\pi$
$211$	27.0621	+	5.75223i	1.86303	+	0.396000i	0.868086	+	0.496413i	$0.165350\pi$
$212$	−8.61099	+	3.83386i	−0.591405	+	0.263311i
$213$	−4.28312	−	4.30658i	−0.293475	−	0.295082i
$214$	15.8318	−	3.36514i	1.08224	−	0.230037i
$215$	−2.20804	+	6.79566i	−0.150587	+	0.463460i
$216$	−4.61032	−	2.39686i	−0.313693	−	0.163086i
$217$	3.90931	+	2.84028i	0.265381	+	0.192811i
$218$	2.47628	−	2.75018i	0.167715	−	0.186266i
$219$	−0.789254	−	5.07279i	−0.0533328	−	0.342787i
$220$	−0.0583144	+	3.31611i	−0.00393156	+	0.223572i
$221$	5.65394	−	9.79290i	0.380325	−	0.658742i
$222$	−1.50895	−	0.985795i	−0.101274	−	0.0661622i
$223$	−1.68206	+	16.0037i	−0.112639	+	1.07169i	0.781502	+	0.623903i	$0.214454\pi$
$223$	−1.68206	+	16.0037i	−0.112639	+	1.07169i	−0.894141	+	0.447785i	$0.852213\pi$
$224$	0.405892	−	0.294898i	0.0271198	−	0.0197037i
$225$	2.60623	−	1.48579i	0.173749	−	0.0990524i
$226$	−2.30228	+	7.08569i	−0.153145	+	0.471333i
$227$	5.37201	+	2.39177i	0.356553	+	0.158748i	0.577193	−	0.816608i	$-0.304148\pi$
$227$	5.37201	+	2.39177i	0.356553	+	0.158748i	−0.220640	+	0.975355i	$0.570815\pi$
$228$	−0.170124	−	0.263542i	−0.0112668	−	0.0174535i
$229$	−20.6121	−	4.38123i	−1.36208	−	0.289520i	−0.531804	−	0.846867i	$-0.678486\pi$
$229$	−20.6121	−	4.38123i	−1.36208	−	0.289520i	−0.830279	+	0.557347i	$0.811819\pi$
$230$	−0.385331	+	0.667413i	−0.0254080	+	0.0440079i
$231$	−0.508592	+	2.83688i	−0.0334629	+	0.186653i
$232$	1.43855	+	2.49164i	0.0944455	+	0.163584i
$233$	3.78870	+	11.6604i	0.248206	+	0.763899i	0.995093	+	0.0989479i	$0.0315477\pi$
$233$	3.78870	+	11.6604i	0.248206	+	0.763899i	−0.746887	+	0.664951i	$0.768452\pi$
$234$	12.5744	+	4.16175i	0.822016	+	0.272062i
$235$	−0.898991	+	0.653155i	−0.0586437	+	0.0426072i
$236$	2.58196	−	0.548812i	0.168071	−	0.0357246i
$237$	−0.734364	−	1.92881i	−0.0477020	−	0.125290i
$238$	−0.134317	−	1.27794i	−0.00870646	−	0.0828364i
$239$	−5.87074	+	2.61382i	−0.379747	+	0.169074i	−0.587728	−	0.809059i	$-0.699977\pi$
$239$	−5.87074	+	2.61382i	−0.379747	+	0.169074i	0.207981	+	0.978133i	$0.433311\pi$
$240$	1.54541	−	0.782117i	0.0997558	−	0.0504854i
$241$	−2.88972	−	5.00515i	−0.186143	−	0.322410i	0.757818	−	0.652466i	$-0.226266\pi$
$241$	−2.88972	−	5.00515i	−0.186143	−	0.322410i	−0.943961	+	0.330056i	$0.892932\pi$
$242$	−7.06847	−	8.42833i	−0.454379	−	0.541793i
$243$	−10.8712	−	11.1722i	−0.697385	−	0.716697i
$244$	1.24566	+	3.83376i	0.0797455	+	0.245431i
$245$	0.705388	−	6.71132i	0.0450656	−	0.428770i
$246$	−0.718417	−	0.722352i	−0.0458046	−	0.0460555i
$247$	0.535031	+	0.594212i	0.0340432	+	0.0378088i
$248$	6.44466	+	7.15752i	0.409236	+	0.454503i
$249$	−1.52859	+	5.64309i	−0.0968707	+	0.357616i
$250$	−0.104528	+	0.994522i	−0.00661096	+	0.0628991i
$251$	2.13062	+	6.55739i	0.134484	+	0.413899i	0.995509	−	0.0946631i	$-0.0301774\pi$
$251$	2.13062	+	6.55739i	0.134484	+	0.413899i	−0.861026	+	0.508562i	$0.830177\pi$
$252$	1.43398	−	0.457285i	0.0903325	−	0.0288062i
$253$	−0.487381	−	2.50910i	−0.0306414	−	0.157746i
$254$	3.21101	+	5.56164i	0.201477	+	0.348968i
$255$	0.244267	−	4.42939i	0.0152966	−	0.277379i
$256$	0.913545	−	0.406737i	0.0570966	−	0.0254210i
$257$	−0.0587283	−	0.558763i	−0.00366337	−	0.0348547i	0.992538	−	0.121940i	$-0.0389115\pi$
$257$	−0.0587283	−	0.558763i	−0.00366337	−	0.0348547i	−0.996201	+	0.0870851i	$0.972245\pi$
$258$	−7.81481	+	9.59678i	−0.486529	+	0.597469i
$259$	0.510685	−	0.108550i	0.0317325	−	0.00674494i
$260$	−3.57187	+	2.59512i	−0.221518	+	0.160942i
$261$	1.74840	+	8.45237i	0.108224	+	0.523189i
$262$	−3.68680	−	11.3468i	−0.227771	−	0.701008i
$263$	−11.1773	−	19.3597i	−0.689223	−	1.19377i	−0.972090	−	0.234610i	$-0.924619\pi$
$263$	−11.1773	−	19.3597i	−0.689223	−	1.19377i	0.282867	−	0.959159i	$-0.408715\pi$
$264$	−2.16718	+	5.32009i	−0.133381	+	0.327429i
$265$	4.71295	−	8.16307i	0.289514	−	0.501454i
$266$	0.0888764	+	0.0188913i	0.00544936	+	0.00115830i
$267$	1.75843	−	3.42794i	0.107614	−	0.209786i
$268$	5.21655	+	2.32256i	0.318652	+	0.141873i
$269$	−6.83206	+	21.0269i	−0.416558	+	1.28203i	0.494292	+	0.869296i	$0.335428\pi$
$269$	−6.83206	+	21.0269i	−0.416558	+	1.28203i	−0.910850	+	0.412738i	$0.864572\pi$
$270$	5.13867	−	0.770778i	0.312729	−	0.0469081i
$271$	−23.0218	+	16.7264i	−1.39848	+	1.01605i	−0.403604	+	0.914934i	$0.632242\pi$
$271$	−23.0218	+	16.7264i	−1.39848	+	1.01605i	−0.994874	+	0.101120i	$0.967758\pi$
$272$	0.267718	−	2.54716i	0.0162328	−	0.154444i
$273$	−3.42322	+	1.73246i	−0.207183	+	0.104853i
$274$	10.3945	−	18.0039i	0.627957	−	1.08765i
$275$	−1.90198	−	2.71707i	−0.114694	−	0.163845i
$276$	−1.03965	+	0.837197i	−0.0625793	+	0.0503933i
$277$	14.0314	−	15.5835i	0.843068	−	0.936322i	−0.155605	−	0.987819i	$-0.549733\pi$
$277$	14.0314	−	15.5835i	0.843068	−	0.936322i	0.998673	+	0.0514978i	$0.0163995\pi$
$278$	−13.5694	−	9.85873i	−0.813837	−	0.591287i
$279$	11.6080	+	26.4599i	0.694950	+	1.58412i
$280$	−0.155037	+	0.477155i	−0.00926523	+	0.0285155i
$281$	−21.4484	+	4.55901i	−1.27951	+	0.271967i	−0.797029	−	0.603941i	$-0.793596\pi$
$281$	−21.4484	+	4.55901i	−1.27951	+	0.271967i	−0.482477	+	0.875908i	$0.660263\pi$
$282$	−1.86045	+	0.493064i	−0.110788	+	0.0293615i
$283$	1.44113	−	0.641632i	0.0856663	−	0.0381411i	−0.363456	−	0.931611i	$-0.618403\pi$
$283$	1.44113	−	0.641632i	0.0856663	−	0.0381411i	0.449122	+	0.893470i	$0.351737\pi$
$284$	3.43012	+	0.729094i	0.203540	+	0.0432637i
$285$	0.292539	+	0.113213i	0.0173285	+	0.00670616i
$286$	3.29585	−	14.2674i	0.194888	−	0.843651i
$287$	0.295103			0.0174194
$288$	2.98523	−	0.297283i	0.175907	−	0.0175176i
$289$	8.44637	+	6.13665i	0.496845	+	0.360979i
$290$	−2.62836	−	1.17022i	−0.154343	−	0.0687179i
$291$	−3.65839	−	9.60879i	−0.214459	−	0.563277i
$292$	1.98331	+	2.20269i	0.116064	+	0.128903i
$293$	1.68003	+	15.9844i	0.0981482	+	0.933818i	0.927180	+	0.374616i	$0.122226\pi$
$293$	1.68003	+	15.9844i	0.0981482	+	0.933818i	−0.829032	+	0.559202i	$0.811108\pi$
$294$	5.33484	−	10.3999i	0.311134	−	0.606534i
$295$	−1.76626	+	1.96164i	−0.102836	+	0.114211i
$296$	1.04063			0.0604854
$297$	−11.1871	+	13.1091i	−0.649142	+	0.760667i
$298$	−6.04269			−0.350044
$299$	2.27674	−	2.52858i	0.131667	−	0.146231i
$300$	−0.790547	+	1.54112i	−0.0456422	+	0.0889763i
$301$	−0.374725	−	3.56527i	−0.0215988	−	0.205499i
$302$	−6.17615	−	6.85931i	−0.355397	−	0.394709i
$303$	2.75750	+	7.24259i	0.158414	+	0.416076i
$304$	0.165447	+	0.0736618i	0.00948905	+	0.00422480i
$305$	−3.26119	−	2.36939i	−0.186735	−	0.135671i
$306$	3.16349	−	7.00212i	0.180845	−	0.400285i
$307$	23.9731			1.36822			0.684108	−	0.729381i	$-0.260192\pi$
$307$	23.9731			1.36822			0.684108	+	0.729381i	$0.260192\pi$
$308$	−0.649971	−	1.53179i	−0.0370356	−	0.0872819i
$309$	−21.5620	−	8.34451i	−1.22662	−	0.474702i
$310$	−9.42092	−	2.00248i	−0.535072	−	0.113733i
$311$	−4.77308	+	2.12511i	−0.270657	+	0.120504i	−0.537578	−	0.843214i	$-0.680660\pi$
$311$	−4.77308	+	2.12511i	−0.270657	+	0.120504i	0.266921	+	0.963718i	$0.413994\pi$
$312$	−7.39195	+	1.95904i	−0.418487	+	0.110909i
$313$	−19.2015	+	4.08141i	−1.08533	+	0.230695i	−0.715648	−	0.698461i	$-0.753868\pi$
$313$	−19.2015	+	4.08141i	−1.08533	+	0.230695i	−0.369687	+	0.929156i	$0.620535\pi$
$314$	−2.99871	+	9.22909i	−0.169227	+	0.520828i
$315$	−0.891332	+	1.21283i	−0.0502209	+	0.0683350i
$316$	0.964011	+	0.700395i	0.0542298	+	0.0394003i
$317$	5.63718	−	6.26073i	0.316616	−	0.351637i	−0.563739	−	0.825953i	$-0.690638\pi$
$317$	5.63718	−	6.26073i	0.316616	−	0.351637i	0.880355	+	0.474315i	$0.157304\pi$
$318$	12.7158	−	10.2397i	0.713067	−	0.574213i
$319$	9.12568	−	2.78870i	0.510940	−	0.156137i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−25.0132	+	12.6589i	−1.39610	+	0.706551i
$322$	0.0404158	−	0.384531i	0.00225229	−	0.0214291i
$323$	0.375257	−	0.272641i	0.0208799	−	0.0151701i
$324$	8.78236	+	1.96727i	0.487909	+	0.109293i
$325$	1.36433	−	4.19899i	0.0756797	−	0.232918i
$326$	5.92904	+	2.63978i	0.328379	+	0.146204i
$327$	−2.92561	+	5.70326i	−0.161786	+	0.315391i
$328$	0.575340	+	0.122292i	0.0317679	+	0.00675247i
$329$	0.278754	−	0.482816i	0.0153682	−	0.0266185i
$330$	−1.37378	−	5.57788i	−0.0756241	−	0.307052i
$331$	−16.0079	−	27.7266i	−0.879876	−	1.52399i	−0.851476	−	0.524393i	$-0.824292\pi$
$331$	−16.0079	−	27.7266i	−0.879876	−	1.52399i	−0.0283994	−	0.999597i	$-0.509041\pi$
$332$	−1.04307	−	3.21025i	−0.0572461	−	0.176185i
$333$	2.96378	+	0.980921i	0.162414	+	0.0537541i
$334$	16.0288	−	11.6456i	0.877056	−	0.637219i
$335$	−5.58545	+	1.18722i	−0.305166	+	0.0648649i
$336$	−0.548714	+	0.673834i	−0.0299348	+	0.0367607i
$337$	−2.56244	−	24.3800i	−0.139585	−	1.32806i	−0.810154	−	0.586217i	$-0.800616\pi$
$337$	−2.56244	−	24.3800i	−0.139585	−	1.32806i	0.670569	−	0.741848i	$-0.266050\pi$
$338$	5.93158	−	2.64091i	0.322635	−	0.143646i
$339$	0.710557	−	12.8848i	0.0385921	−	0.699805i
$340$	1.28060	+	2.21806i	0.0694501	+	0.120291i
$341$	27.9406	−	15.4830i	1.51307	−	0.838451i
$342$	0.401769	+	0.365748i	0.0217252	+	0.0197774i
$343$	2.13149	+	6.56006i	0.115090	+	0.354210i
$344$	0.746896	−	7.10624i	0.0402699	−	0.383143i
$345$	0.348999	−	1.28839i	0.0187895	−	0.0693648i
$346$	−8.38604	−	9.31364i	−0.450836	−	0.500705i
$347$	−10.4903	−	11.6507i	−0.563149	−	0.625440i	0.392570	−	0.919722i	$-0.371586\pi$
$347$	−10.4903	−	11.6507i	−0.563149	−	0.625440i	−0.955719	+	0.294282i	$0.904919\pi$
$348$	−3.51408	−	3.53333i	−0.188374	−	0.189406i
$349$	1.55847	−	14.8279i	0.0834230	−	0.793717i	−0.870197	−	0.492704i	$-0.836009\pi$
$349$	1.55847	−	14.8279i	0.0834230	−	0.793717i	0.953620	−	0.301013i	$-0.0973247\pi$
$350$	−0.155037	−	0.477155i	−0.00828708	−	0.0255050i
$351$	−22.8994	−	1.38834i	−1.22228	−	0.0741041i
$352$	−0.632418	−	3.25577i	−0.0337080	−	0.173533i
$353$	−2.84834	−	4.93347i	−0.151602	−	0.262582i	0.780215	−	0.625512i	$-0.215110\pi$
$353$	−2.84834	−	4.93347i	−0.151602	−	0.262582i	−0.931816	+	0.362930i	$0.881776\pi$
$354$	−4.07933	+	2.06451i	−0.216814	+	0.109727i
$355$	−3.20357	+	1.42632i	−0.170028	+	0.0757013i
$356$	0.232505	+	2.21214i	0.0123227	+	0.117243i
$357$	0.791922	+	2.07999i	0.0419130	+	0.110085i
$358$	17.6531	−	3.75228i	0.932995	−	0.198314i
$359$	−4.37876	+	3.18136i	−0.231102	+	0.167906i	−0.697310	−	0.716770i	$-0.745620\pi$
$359$	−4.37876	+	3.18136i	−0.231102	+	0.167906i	0.466208	+	0.884675i	$0.345620\pi$
$360$	−2.24037	+	1.99518i	−0.118078	+	0.105155i
$361$	−5.86119	−	18.0389i	−0.308484	−	0.949415i
$362$	10.6150	+	18.3857i	0.557912	+	0.966332i
$363$	15.5742	+	10.9747i	0.817433	+	0.576024i
$364$	1.10755	−	1.91832i	0.0580511	−	0.100548i
$365$	−2.89924	−	0.616253i	−0.151753	−	0.0322561i
$366$	−3.78666	−	5.86595i	−0.197932	−	0.306618i
$367$	−5.50034	−	2.44891i	−0.287116	−	0.127832i	0.258125	−	0.966111i	$-0.416895\pi$
$367$	−5.50034	−	2.44891i	−0.287116	−	0.127832i	−0.545241	+	0.838279i	$0.683562\pi$
$368$	0.238148	−	0.732943i	0.0124143	−	0.0382073i
$369$	1.52333	+	0.890625i	0.0793014	+	0.0463641i
$370$	−0.841887	+	0.611667i	−0.0437676	+	0.0317990i
$371$	−0.494323	+	4.70317i	−0.0256640	+	0.244176i
$372$	−13.9659	−	9.12388i	−0.724097	−	0.473051i
$373$	−1.48929	+	2.57953i	−0.0771125	+	0.133563i	−0.902003	−	0.431730i	$-0.857903\pi$
$373$	−1.48929	+	2.57953i	−0.0771125	+	0.133563i	0.824890	+	0.565293i	$0.191237\pi$
$374$	−8.03137	−	2.76659i	−0.415292	−	0.143057i
$375$	−0.266279	−	1.71146i	−0.0137506	−	0.0883794i
$376$	0.743547	−	0.825793i	0.0383455	−	0.0425870i
$377$	10.2766	+	7.46642i	0.529274	+	0.384540i
$378$	−2.19794	+	1.40189i	−0.113050	+	0.0721055i
$379$	−11.5833	+	35.6497i	−0.594994	+	1.83120i	−0.0402384	+	0.999190i	$0.512812\pi$
$379$	−11.5833	+	35.6497i	−0.594994	+	1.83120i	−0.554756	+	0.832013i	$0.687188\pi$
$380$	−0.177147	+	0.0376537i	−0.00908745	+	0.00193160i
$381$	−7.84383	−	7.88679i	−0.401852	−	0.404053i
$382$	−3.37280	+	1.50167i	−0.172568	+	0.0768321i
$383$	1.82938	+	0.388848i	0.0934772	+	0.0198692i	0.254413	−	0.967096i	$-0.418118\pi$
$383$	1.82938	+	0.388848i	0.0934772	+	0.0198692i	−0.160936	+	0.986965i	$0.551451\pi$
$384$	−1.34903	+	1.08633i	−0.0688423	+	0.0554368i
$385$	1.42620	+	0.857201i	0.0726860	+	0.0436870i
$386$	−9.32665			−0.474714
$387$	8.82571	−	19.5350i	0.448636	−	0.993018i
$388$	4.80242	+	3.48917i	0.243806	+	0.177136i
$389$	14.2096	+	6.32652i	0.720455	+	0.320767i	0.734008	−	0.679141i	$-0.237647\pi$
$389$	14.2096	+	6.32652i	0.720455	+	0.320767i	−0.0135526	+	0.999908i	$0.504314\pi$
$390$	4.82872	−	5.92978i	0.244512	−	0.300266i
$391$	−1.32074	−	1.46683i	−0.0667927	−	0.0741808i
$392$	0.705388	+	6.71132i	0.0356275	+	0.338973i
$393$	11.2074	+	17.3615i	0.565338	+	0.875772i
$394$	14.2186	−	15.7913i	0.716322	−	0.795556i
$395$	−1.19158			−0.0599550
$396$	1.26780	−	9.86877i	0.0637092	−	0.495925i
$397$	−16.0139			−0.803716			−0.401858	−	0.915702i	$-0.631635\pi$
$397$	−16.0139			−0.803716			−0.401858	+	0.915702i	$0.631635\pi$
$398$	−14.4994	+	16.1032i	−0.726789	+	0.807181i
$399$	−0.157184	+	0.00780722i	−0.00786903	+	0.000390850i
$400$	−0.104528	−	0.994522i	−0.00522642	−	0.0497261i
$401$	−17.1151	−	19.0082i	−0.854685	−	0.949224i	0.144503	−	0.989504i	$-0.453842\pi$
$401$	−17.1151	−	19.0082i	−0.854685	−	0.949224i	−0.999188	+	0.0402801i	$0.987175\pi$
$402$	−9.76438	−	1.57388i	−0.487003	−	0.0784978i
$403$	38.8470	+	17.2958i	1.93511	+	0.861565i
$404$	−3.61981	−	2.62995i	−0.180092	−	0.130845i
$405$	−8.26141	+	3.57059i	−0.410513	+	0.177424i
$406$	1.44347			0.0716383
$407$	0.776828	−	3.36282i	0.0385060	−	0.166689i
$408$	0.681992	+	4.38338i	0.0337636	+	0.217010i
$409$	−24.7891	−	5.26909i	−1.22574	−	0.260540i	−0.450831	−	0.892609i	$-0.648872\pi$
$409$	−24.7891	−	5.26909i	−1.22574	−	0.260540i	−0.774911	+	0.632070i	$0.782206\pi$
$410$	−0.537342	+	0.239240i	−0.0265374	+	0.0118152i
$411$	−9.41445	+	34.7552i	−0.464380	+	1.71435i
$412$	13.0568	−	2.77531i	0.643264	−	0.136730i
$413$	0.409242	−	1.25952i	0.0201375	−	0.0619768i
$414$	1.36915	−	1.86299i	0.0672900	−	0.0915607i
$415$	2.73080	+	1.98404i	0.134050	+	0.0973928i
$416$	2.95426	−	3.28104i	0.144845	−	0.160866i
$417$	27.0930	+	10.4850i	1.32675	+	0.513454i
$418$	0.361546	−	0.479658i	0.0176838	−	0.0234608i
$419$	−11.3454	+	19.6507i	−0.554257	+	0.960001i	0.443704	+	0.896173i	$0.353664\pi$
$419$	−11.3454	+	19.6507i	−0.554257	+	0.960001i	−0.997961	+	0.0638276i	$0.979669\pi$
$420$	0.0478493	−	0.867669i	0.00233481	−	0.0423379i
$421$	1.67137	−	15.9020i	0.0814576	−	0.775017i	−0.875192	−	0.483776i	$-0.839265\pi$
$421$	1.67137	−	15.9020i	0.0814576	−	0.775017i	0.956650	−	0.291241i	$-0.0940683\pi$
$422$	22.3828	−	16.2621i	1.08958	−	0.791625i
$423$	2.89608	−	1.65103i	0.140812	−	0.0802756i
$424$	−2.91276	+	8.96457i	−0.141456	+	0.435358i
$425$	−2.33977	−	1.04173i	−0.113495	−	0.0505314i
$426$	−6.06638	+	0.301314i	−0.293917	+	0.0145987i
$427$	1.97823	+	0.420485i	0.0957331	+	0.0203487i
$428$	8.09273	−	14.0170i	0.391177	−	0.677538i
$429$	0.812614	+	25.3497i	0.0392334	+	1.22389i
$430$	3.57269	+	6.18808i	0.172290	+	0.298416i
$431$	−8.77404	−	27.0037i	−0.422631	−	1.30072i	−0.905245	−	0.424891i	$-0.860313\pi$
$431$	−8.77404	−	27.0037i	−0.422631	−	1.30072i	0.482614	−	0.875833i	$-0.339687\pi$
$432$	−4.86612	+	1.82232i	−0.234121	+	0.0876766i
$433$	−17.7655	+	12.9074i	−0.853753	+	0.620288i	−0.926178	−	0.377086i	$-0.876926\pi$
$433$	−17.7655	+	12.9074i	−0.853753	+	0.620288i	0.0724250	+	0.997374i	$0.476926\pi$
$434$	4.72657	−	1.00466i	0.226883	−	0.0482254i
$435$	4.91979	+	0.792998i	0.235886	+	0.0380214i
$436$	−0.386832	−	3.68046i	−0.0185259	−	0.176262i
$437$	0.127504	−	0.0567684i	0.00609934	−	0.00271560i
$438$	−4.29793	−	2.80783i	−0.205363	−	0.134163i
$439$	9.77054	+	16.9231i	0.466323	+	0.807694i	0.999260	−	0.0384602i	$-0.0122453\pi$
$439$	9.77054	+	16.9231i	0.466323	+	0.807694i	−0.532938	+	0.846155i	$0.678912\pi$
$440$	2.42533	+	2.26225i	0.115623	+	0.107848i
$441$	−4.31725	+	19.7792i	−0.205583	+	0.941865i
$442$	−3.49432	−	10.7544i	−0.166208	−	0.511536i
$443$	−1.49314	+	14.2062i	−0.0709410	+	0.674959i	0.900041	+	0.435806i	$0.143536\pi$
$443$	−1.49314	+	14.2062i	−0.0709410	+	0.674959i	−0.970982	+	0.239153i	$0.923130\pi$
$444$	−1.74227	+	0.461744i	−0.0826847	+	0.0219134i
$445$	−1.48836	−	1.65299i	−0.0705551	−	0.0783594i
$446$	10.7676	+	11.9586i	0.509859	+	0.566255i
$447$	10.1170	−	2.68124i	0.478517	−	0.126818i
$448$	0.0524430	−	0.498962i	0.00247770	−	0.0235737i
$449$	3.10427	+	9.55395i	0.146499	+	0.450879i	0.997201	−	0.0747704i	$-0.0238224\pi$
$449$	3.10427	+	9.55395i	0.146499	+	0.450879i	−0.850701	+	0.525649i	$0.823822\pi$
$450$	0.639755	−	2.93099i	0.0301584	−	0.138168i
$451$	0.824681	−	1.76793i	0.0388327	−	0.0832488i
$452$	3.72517	+	6.45218i	0.175217	+	0.303485i
$453$	13.3840	+	8.74374i	0.628835	+	0.410817i
$454$	5.37201	−	2.39177i	0.252121	−	0.112251i
$455$	0.231540	+	2.20296i	0.0108548	+	0.103276i
$456$	−0.309685	−	0.0499167i	−0.0145023	−	0.00233757i
$457$	−4.85419	+	1.03179i	−0.227069	+	0.0482651i	−0.320041	−	0.947404i	$-0.603697\pi$
$457$	−4.85419	+	1.03179i	−0.227069	+	0.0482651i	0.0929718	+	0.995669i	$0.470363\pi$
$458$	−17.0481	+	12.3861i	−0.796603	+	0.578766i
$459$	−2.18952	+	13.1270i	−0.102198	+	0.612716i
$460$	0.238148	+	0.732943i	0.0111037	+	0.0341737i
$461$	20.6778	+	35.8151i	0.963063	+	1.66807i	0.714731	+	0.699399i	$0.246549\pi$
$461$	20.6778	+	35.8151i	0.963063	+	1.66807i	0.248332	+	0.968675i	$0.420118\pi$
$462$	1.76790	+	2.27620i	0.0822500	+	0.105898i
$463$	−14.1429	+	24.4962i	−0.657276	+	1.13844i	0.324042	+	0.946043i	$0.394958\pi$
$463$	−14.1429	+	24.4962i	−0.657276	+	1.13844i	−0.981318	+	0.192393i	$0.938375\pi$
$464$	2.81423	+	0.598183i	0.130647	+	0.0277700i
$465$	16.6615	−	0.827567i	0.772659	−	0.0383775i
$466$	11.2005	+	4.98679i	0.518854	+	0.231009i
$467$	2.59374	−	7.98272i	0.120024	−	0.369396i	−0.872938	−	0.487832i	$-0.837788\pi$
$467$	2.59374	−	7.98272i	0.120024	−	0.369396i	0.992962	+	0.118436i	$0.0377879\pi$
$468$	11.5067	−	6.55986i	0.531898	−	0.303230i
$469$	2.31774	−	1.68393i	0.107023	−	0.0777569i
$470$	−0.116154	+	1.10513i	−0.00535776	+	0.0509757i
$471$	0.925498	−	16.7824i	0.0426447	−	0.773292i
$472$	1.31982	−	2.28600i	0.0607497	−	0.105222i
$473$	−22.4064	−	7.71841i	−1.03025	−	0.354893i
$474$	−1.92477	−	0.744889i	−0.0884077	−	0.0342139i
$475$	0.121183	−	0.134587i	0.00556024	−	0.00617527i
$476$	−1.03957	−	0.755291i	−0.0476485	−	0.0346187i
$477$	−16.7459	+	22.7860i	−0.766744	+	1.04330i
$478$	−1.98584	+	6.11180i	−0.0908304	+	0.279547i
$479$	−25.0314	+	5.32059i	−1.14371	+	0.243104i	−0.740535	−	0.672017i	$-0.765428\pi$
$479$	−25.0314	+	5.32059i	−1.14371	+	0.243104i	−0.403178	+	0.915121i	$0.632095\pi$
$480$	0.452856	−	1.67180i	0.0206699	−	0.0763070i
$481$	4.19725	−	1.86874i	0.191378	−	0.0852070i
$482$	−5.65315	−	1.20161i	−0.257494	−	0.0547320i
$483$	0.102957	+	0.661735i	0.00468469	+	0.0301100i
$484$	−10.9932	−	0.386754i	−0.499691	−	0.0175797i
$485$	−5.93612			−0.269545
$486$	−15.5768	+	0.603177i	−0.706577	+	0.0273607i
$487$	7.39497	+	5.37276i	0.335098	+	0.243463i	0.742591	−	0.669746i	$-0.233597\pi$
$487$	7.39497	+	5.37276i	0.335098	+	0.243463i	−0.407493	+	0.913208i	$0.633597\pi$
$488$	3.68255	+	1.63958i	0.166701	+	0.0742202i
$489$	−11.0980	−	1.78884i	−0.501869	−	0.0808940i
$490$	−4.51549	−	5.01495i	−0.203989	−	0.226553i
$491$	3.08551	+	29.3567i	0.139247	+	1.32485i	0.811424	+	0.584458i	$0.198693\pi$
$491$	3.08551	+	29.3567i	0.139247	+	1.32485i	−0.672177	+	0.740391i	$0.734641\pi$
$492$	−1.01753	+	0.0505399i	−0.0458737	+	0.00227852i
$493$	4.93070	−	5.47610i	0.222068	−	0.246631i
$494$	0.799591			0.0359753
$495$	4.77505	+	8.72920i	0.214623	+	0.392348i
$496$	9.63139			0.432462
$497$	1.17725	−	1.30747i	0.0528068	−	0.0586479i
$498$	3.17081	+	4.91193i	0.142087	+	0.220109i
$499$	−0.574255	−	5.46368i	−0.0257072	−	0.244588i	−0.999828	−	0.0185587i	$-0.994092\pi$
$499$	−0.574255	−	5.46368i	−0.0257072	−	0.244588i	0.974121	−	0.226029i	$-0.0725744\pi$
$500$	0.669131	+	0.743145i	0.0299244	+	0.0332344i
$501$	−21.6689	+	26.6099i	−0.968094	+	1.18884i
$502$	6.29875	+	2.80439i	0.281127	+	0.125166i
$503$	−21.2513	−	15.4400i	−0.947551	−	0.688436i	0.00267571	−	0.999996i	$-0.499148\pi$
$503$	−21.2513	−	15.4400i	−0.947551	−	0.688436i	−0.950226	+	0.311561i	$0.899148\pi$
$504$	0.619694	−	1.37164i	0.0276034	−	0.0610977i
$505$	4.47433			0.199105
$506$	−2.19075	−	1.31672i	−0.0973906	−	0.0585354i
$507$	−8.75913	+	7.05348i	−0.389007	+	0.313256i
$508$	6.28169	+	1.33521i	0.278705	+	0.0592405i
$509$	−16.1049	+	7.17038i	−0.713839	+	0.317822i	−0.731329	−	0.682025i	$-0.761099\pi$
$509$	−16.1049	+	7.17038i	−0.713839	+	0.317822i	0.0174893	+	0.999847i	$0.494433\pi$
$510$	−3.12823	−	3.14536i	−0.138520	−	0.139279i
$511$	1.45458	−	0.309180i	0.0643468	−	0.0136773i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−0.834950	−	0.434082i	−0.0368639	−	0.0191652i
$514$	−0.454539	−	0.330242i	−0.0200488	−	0.0145663i
$515$	−8.93191	+	9.91989i	−0.393587	+	0.437123i
$516$	1.90266	+	12.2290i	0.0837601	+	0.538353i
$517$	−2.11351	−	3.01924i	−0.0929521	−	0.132786i
$518$	0.261047	−	0.452147i	0.0114698	−	0.0198662i
$519$	18.1730	+	11.8724i	0.797704	+	0.521138i
$520$	−0.461501	+	4.39089i	−0.0202382	+	0.192553i
$521$	34.0437	−	24.7342i	1.49148	−	1.08362i	0.517855	−	0.855468i	$-0.326731\pi$
$521$	34.0437	−	24.7342i	1.49148	−	1.08362i	0.973625	−	0.228156i	$-0.0732695\pi$
$522$	7.45125	+	4.35642i	0.326132	+	0.190675i
$523$	−8.44042	+	25.9769i	−0.369074	+	1.13589i	0.578317	+	0.815812i	$0.303710\pi$
$523$	−8.44042	+	25.9769i	−0.369074	+	1.13589i	−0.947391	+	0.320080i	$0.896290\pi$
$524$	−10.8993	−	4.85267i	−0.476137	−	0.211990i
$525$	0.471292	+	0.730084i	0.0205689	+	0.0318635i
$526$	−21.8661	−	4.64779i	−0.953409	−	0.202653i
$527$	12.3339	−	21.3630i	0.537274	−	0.930587i
$528$	2.50347	+	5.17036i	0.108949	+	0.225011i
$529$	11.2030	+	19.4042i	0.487089	+	0.843662i
$530$	−2.91276	−	8.96457i	−0.126522	−	0.389396i
$531$	5.91376	−	5.26657i	0.256636	−	0.228550i
$532$	0.0735089	−	0.0534073i	0.00318702	−	0.00231550i
$533$	2.54017	−	0.539930i	0.110027	−	0.0233870i
$534$	−1.37083	−	3.60051i	−0.0593218	−	0.155809i
$535$	1.69184	+	16.0968i	0.0731446	+	0.695925i
$536$	5.21655	−	2.32256i	0.225321	−	0.100319i
$537$	−27.8908	+	14.1152i	−1.20358	+	0.609117i
$538$	11.0545	+	19.1470i	0.476594	+	0.825485i
$539$	22.2144	+	2.73051i	0.956840	+	0.117612i
$540$	2.86564	−	4.33453i	0.123317	−	0.186528i
$541$	−10.1612	−	31.2730i	−0.436865	−	1.34453i	−0.891163	−	0.453682i	$-0.850110\pi$
$541$	−10.1612	−	31.2730i	−0.436865	−	1.34453i	0.454299	−	0.890849i	$-0.349890\pi$
$542$	−2.97452	+	28.3007i	−0.127767	+	1.21562i
$543$	−25.9302	−	26.0723i	−1.11277	−	1.11887i
$544$	−1.71377	−	1.90334i	−0.0734774	−	0.0816049i
$545$	2.47628	+	2.75018i	0.106072	+	0.117805i
$546$	−1.00312	+	3.70319i	−0.0429294	+	0.158482i
$547$	3.41963	−	32.5356i	0.146213	−	1.39112i	−0.637715	−	0.770272i	$-0.720120\pi$
$547$	3.41963	−	32.5356i	0.146213	−	1.39112i	0.783928	−	0.620852i	$-0.213213\pi$
$548$	−6.42418	−	19.7716i	−0.274427	−	0.844600i
$549$	8.94263	+	8.14088i	0.381662	+	0.347444i
$550$	−3.29185	−	0.404623i	−0.140365	−	0.0172532i
$551$	0.260528	+	0.451248i	0.0110989	+	0.0192238i
$552$	−0.0734999	+	1.33280i	−0.00312836	+	0.0567278i
$553$	0.546144	−	0.243159i	0.0232244	−	0.0103402i
$554$	−2.19193	−	20.8548i	−0.0931260	−	0.886035i
$555$	1.13812	−	1.39764i	0.0483106	−	0.0593266i
$556$	−16.4061	+	3.48723i	−0.695776	+	0.147892i
$557$	−14.4020	+	10.4636i	−0.610230	+	0.443358i	−0.849495	−	0.527596i	$-0.823094\pi$
$557$	−14.4020	+	10.4636i	−0.610230	+	0.443358i	0.239265	+	0.970954i	$0.423094\pi$
$558$	27.4308	+	9.07877i	1.16124	+	0.384335i
$559$	−9.74869	−	30.0034i	−0.412326	−	1.26901i
$560$	0.250855	+	0.434494i	0.0106006	+	0.0183607i
$561$	14.6741	+	1.06831i	0.619541	+	0.0451043i
$562$	−10.9638	+	18.9899i	−0.462480	+	0.801039i
$563$	1.37861	+	0.293032i	0.0581013	+	0.0123498i	0.236871	−	0.971541i	$-0.423878\pi$
$563$	1.37861	+	0.293032i	0.0581013	+	0.0123498i	−0.178769	+	0.983891i	$0.557212\pi$
$564$	−0.878467	+	1.71251i	−0.0369901	+	0.0721096i
$565$	−6.80622	−	3.03033i	−0.286340	−	0.127487i
$566$	0.487478	−	1.50030i	0.0204902	−	0.0630625i
$567$	3.05787	−	3.32238i	0.128418	−	0.139527i
$568$	2.83702	−	2.06121i	0.119039	−	0.0864866i
$569$	0.682092	−	6.48967i	0.0285948	−	0.272061i	−0.970877	−	0.239577i	$-0.922991\pi$
$569$	0.682092	−	6.48967i	0.0285948	−	0.272061i	0.999472	−	0.0324845i	$-0.0103420\pi$
$570$	0.279881	−	0.141645i	0.0117229	−	0.00593285i
$571$	9.07930	−	15.7258i	0.379957	−	0.658104i	−0.611099	−	0.791554i	$-0.709272\pi$
$571$	9.07930	−	15.7258i	0.379957	−	0.658104i	0.991056	+	0.133450i	$0.0426055\pi$
$572$	−8.39741	−	11.9961i	−0.351113	−	0.501581i
$573$	4.98060	−	4.01074i	0.208068	−	0.167551i
$574$	0.197462	−	0.219304i	0.00824192	−	0.00915358i
$575$	−0.623479	−	0.452984i	−0.0260009	−	0.0188907i
$576$	1.77659	−	2.41738i	0.0740245	−	0.100724i
$577$	−5.53051	+	17.0212i	−0.230238	+	0.708601i	0.767479	+	0.641074i	$0.221511\pi$
$577$	−5.53051	+	17.0212i	−0.230238	+	0.708601i	−0.997717	+	0.0675268i	$0.978489\pi$
$578$	10.2121	−	2.17066i	0.424769	−	0.0902875i
$579$	15.6152	−	4.13839i	0.648944	−	0.171986i
$580$	−2.62836	+	1.17022i	−0.109137	+	0.0485909i
$581$	−1.65649	−	0.352099i	−0.0687229	−	0.0146075i
$582$	−9.58866	−	3.71082i	−0.397463	−	0.153819i
$583$	26.7948	+	16.1047i	1.10973	+	0.666989i
$584$	2.96401			0.122652
$585$	−5.45334	+	12.0705i	−0.225468	+	0.499054i
$586$	13.0029	+	9.44714i	0.537144	+	0.390258i
$587$	−28.0617	−	12.4939i	−1.15823	−	0.515678i	−0.264546	−	0.964373i	$-0.585222\pi$
$587$	−28.0617	−	12.4939i	−1.15823	−	0.515678i	−0.893685	+	0.448695i	$0.851889\pi$
$588$	−4.15892	−	10.9234i	−0.171511	−	0.450475i
$589$	1.16716	+	1.29626i	0.0480919	+	0.0534114i
$590$	0.275918	+	2.62518i	0.0113594	+	0.108077i
$591$	−16.7986	+	32.7477i	−0.691002	+	1.34706i
$592$	0.696317	−	0.773338i	0.0286185	−	0.0317840i
$593$	−28.5544			−1.17259			−0.586295	−	0.810098i	$-0.699414\pi$
$593$	−28.5544			−1.17259			−0.586295	+	0.810098i	$0.699414\pi$
$594$	2.25633	+	17.0853i	0.0925783	+	0.701020i
$595$	1.28498			0.0526789
$596$	−4.04335	+	4.49059i	−0.165622	+	0.183942i
$597$	17.1304	−	33.3944i	0.701099	−	1.36674i
$598$	−0.355662	−	3.38390i	−0.0145441	−	0.138378i
$599$	−29.0096	−	32.2184i	−1.18530	−	1.31641i	−0.937659	−	0.347556i	$-0.887012\pi$
$599$	−29.0096	−	32.2184i	−1.18530	−	1.31641i	−0.247640	−	0.968852i	$-0.579655\pi$
$600$	0.616293	+	1.61870i	0.0251600	+	0.0660831i
$601$	32.8676	+	14.6336i	1.34070	+	0.596917i	0.946677	−	0.322185i	$-0.104417\pi$
$601$	32.8676	+	14.6336i	1.34070	+	0.596917i	0.394020	+	0.919102i	$0.371084\pi$
$602$	−2.90025	−	2.10716i	−0.118206	−	0.0858813i
$603$	17.0464	−	1.69755i	0.694182	−	0.0691297i
$604$	−9.23011			−0.375568
$605$	9.12101	−	6.14875i	0.370822	−	0.249982i
$606$	7.22742	+	2.79702i	0.293594	+	0.113621i
$607$	33.8210	+	7.18887i	1.37275	+	0.291787i	0.834505	−	0.551000i	$-0.185754\pi$
$607$	33.8210	+	7.18887i	1.37275	+	0.291787i	0.538246	+	0.842788i	$0.319087\pi$
$608$	0.165447	−	0.0736618i	0.00670977	−	0.00298738i
$609$	−2.41673	+	0.640493i	−0.0979310	+	0.0259541i
$610$	−3.94297	+	0.838103i	−0.159646	+	0.0339338i
$611$	1.51607	−	4.66598i	0.0613335	−	0.188765i
$612$	−3.08680	−	7.03627i	−0.124777	−	0.284424i
$613$	−29.0612	−	21.1142i	−1.17377	−	0.852793i	−0.182314	−	0.983240i	$-0.558359\pi$
$613$	−29.0612	−	21.1142i	−1.17377	−	0.852793i	−0.991455	+	0.130447i	$0.958359\pi$
$614$	16.0411	−	17.8155i	0.647367	−	0.718974i
$615$	0.793490	−	0.638975i	0.0319966	−	0.0257660i
$616$	−1.57326	−	0.541945i	−0.0633884	−	0.0218356i
$617$	−11.9753	+	20.7418i	−0.482107	+	0.835034i	−0.999789	−	0.0205389i	$-0.993462\pi$
$617$	−11.9753	+	20.7418i	−0.482107	+	0.835034i	0.517682	+	0.855573i	$0.326795\pi$
$618$	−20.6290	+	10.4401i	−0.829818	+	0.419963i
$619$	0.415029	−	3.94873i	0.0166814	−	0.158713i	−0.983010	−	0.183552i	$-0.941241\pi$
$619$	0.415029	−	3.94873i	0.0166814	−	0.158713i	0.999691	+	0.0248386i	$0.00790720\pi$
$620$	−7.79196	+	5.66119i	−0.312933	+	0.227359i
$621$	−1.46566	+	3.72662i	−0.0588149	+	0.149544i
$622$	−1.61455	+	4.96907i	−0.0647375	+	0.199242i
$623$	1.01948	+	0.453904i	0.0408448	+	0.0181853i
$624$	−3.49033	+	6.80414i	−0.139725	+	0.272384i
$625$	−0.978148	−	0.207912i	−0.0391259	−	0.00831647i
$626$	−9.81525	+	17.0005i	−0.392296	+	0.679477i
$627$	−0.392487	+	0.963492i	−0.0156744	+	0.0384781i
$628$	4.85202	+	8.40394i	0.193617	+	0.335354i
$629$	−0.823609	−	2.53481i	−0.0328394	−	0.101069i
$630$	0.304888	+	1.47393i	0.0121470	+	0.0587227i
$631$	−36.9811	+	26.8684i	−1.47220	+	1.06961i	−0.492226	+	0.870467i	$0.663817\pi$
$631$	−36.9811	+	26.8684i	−1.47220	+	1.06961i	−0.979970	+	0.199146i	$0.936183\pi$
$632$	1.16554	−	0.247744i	0.0463628	−	0.00985473i
$633$	−30.2587	+	37.1584i	−1.20268	+	1.47691i
$634$	−0.880615	−	8.37849i	−0.0349737	−	0.332752i
$635$	−5.86681	+	2.61207i	−0.232817	+	0.103657i
$636$	0.898971	−	16.3014i	0.0356465	−	0.646392i
$637$	14.8971	+	25.8025i	0.590245	+	1.02233i
$638$	4.03386	−	8.64771i	0.159702	−	0.342366i
$639$	10.0230	−	3.19623i	0.396502	−	0.126441i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−0.902310	+	8.58490i	−0.0356391	+	0.339083i	0.962144	+	0.272540i	$0.0878637\pi$
$641$	−0.902310	+	8.58490i	−0.0356391	+	0.339083i	−0.997784	+	0.0665433i	$0.978803\pi$
$642$	−7.32967	+	27.0589i	−0.289279	+	1.06793i
$643$	18.3234	+	20.3502i	0.722605	+	0.802534i	0.986801	−	0.161935i	$-0.0517734\pi$
$643$	18.3234	+	20.3502i	0.722605	+	0.802534i	−0.264197	+	0.964469i	$0.585107\pi$
$644$	−0.258719	−	0.287336i	−0.0101950	−	0.0113226i
$645$	−8.72733	−	8.77514i	−0.343638	−	0.345521i
$646$	0.0484849	−	0.461303i	0.00190761	−	0.0181497i
$647$	−3.23866	−	9.96756i	−0.127325	−	0.391865i	0.866993	−	0.498321i	$-0.166050\pi$
$647$	−3.23866	−	9.96756i	−0.127325	−	0.391865i	−0.994317	+	0.106456i	$0.966050\pi$
$648$	7.33851	−	5.21021i	0.288284	−	0.204676i
$649$	−6.40201	−	5.97152i	−0.251301	−	0.234403i
$650$	−2.20754	−	3.82357i	−0.0865868	−	0.149973i
$651$	−7.46768	+	3.77932i	−0.292682	+	0.148123i
$652$	5.92904	−	2.63978i	0.232199	−	0.103382i
$653$	−1.61463	−	15.3622i	−0.0631855	−	0.601170i	−0.979602	−	0.200945i	$-0.935599\pi$
$653$	−1.61463	−	15.3622i	−0.0631855	−	0.601170i	0.916417	−	0.400225i	$-0.131068\pi$
$654$	2.28074	+	5.99038i	0.0891839	+	0.234242i
$655$	11.6700	−	2.48054i	0.455985	−	0.0969227i
$656$	0.475859	−	0.345732i	0.0185792	−	0.0134986i
$657$	8.44169	+	2.79394i	0.329342	+	0.109002i
$658$	−0.172279	−	0.530221i	−0.00671615	−	0.0206702i
$659$	−24.6956	−	42.7740i	−0.962003	−	1.66624i	−0.717460	−	0.696599i	$-0.754696\pi$
$659$	−24.6956	−	42.7740i	−0.962003	−	1.66624i	−0.244543	−	0.969639i	$-0.578638\pi$
$660$	−5.06441	−	2.71141i	−0.197132	−	0.105542i
$661$	15.0634	−	26.0906i	0.585900	−	1.01481i	−0.408863	−	0.912596i	$-0.634075\pi$
$661$	15.0634	−	26.0906i	0.585900	−	1.01481i	0.994763	−	0.102212i	$-0.0325920\pi$
$662$	−31.3163	−	6.65647i	−1.21714	−	0.258711i
$663$	10.6223	+	16.4551i	0.412536	+	0.639064i
$664$	−3.08363	−	1.37292i	−0.119668	−	0.0532797i
$665$	−0.0280779	+	0.0864149i	−0.00108881	+	0.00335103i
$666$	2.71212	−	1.54615i	0.105093	−	0.0599122i
$667$	1.79381	−	1.30328i	0.0694567	−	0.0504633i
$668$	2.07099	−	19.7041i	0.0801289	−	0.762376i
$669$	−23.3338	−	15.2439i	−0.902138	−	0.589364i
$670$	−2.85511	+	4.94520i	−0.110303	+	0.191050i
$671$	8.04735	−	10.6763i	0.310665	−	0.412154i
$672$	0.133595	+	0.858657i	0.00515354	+	0.0331234i
$673$	−11.6785	+	12.9703i	−0.450174	+	0.499969i	−0.924924	−	0.380152i	$-0.875872\pi$
$673$	−11.6785	+	12.9703i	−0.450174	+	0.499969i	0.474750	+	0.880121i	$0.342538\pi$
$674$	−19.8325	−	14.4092i	−0.763920	−	0.555020i
$675$	0.229419	+	5.19109i	0.00883034	+	0.199805i
$676$	2.00642	−	6.17513i	0.0771701	−	0.237505i
$677$	−22.4298	+	4.76760i	−0.862047	+	0.183234i	−0.617661	−	0.786444i	$-0.711920\pi$
$677$	−22.4298	+	4.76760i	−0.862047	+	0.183234i	−0.244386	+	0.969678i	$0.578586\pi$
$678$	−9.09981	−	9.14965i	−0.349476	−	0.351390i
$679$	2.72073	−	1.21135i	0.104412	−	0.0464873i
$680$	2.50523	+	0.532502i	0.0960710	+	0.0204205i
$681$	−7.93282	+	6.38808i	−0.303986	+	0.244792i
$682$	7.18982	−	31.1241i	0.275312	−	1.19180i
$683$	−31.3640			−1.20011			−0.600054	−	0.799959i	$-0.704854\pi$
$683$	−31.3640			−1.20011			−0.600054	+	0.799959i	$0.704854\pi$
$684$	0.540639	−	0.0538393i	0.0206719	−	0.00205860i
$685$	16.8187	+	12.2195i	0.642610	+	0.466883i
$686$	6.30132	+	2.80553i	0.240586	+	0.107116i
$687$	23.0468	−	28.3020i	0.879290	−	1.07979i
$688$	−4.78119	−	5.31005i	−0.182281	−	0.202444i
$689$	4.35007	+	41.3881i	0.165724	+	1.57676i
$690$	−0.723938	−	1.12146i	−0.0275599	−	0.0426933i
$691$	27.9629	−	31.0560i	1.06376	−	1.18142i	0.0809661	−	0.996717i	$-0.474199\pi$
$691$	27.9629	−	31.0560i	1.06376	−	1.18142i	0.982793	−	0.184708i	$-0.0591339\pi$
$692$	−12.5327			−0.476423
$693$	−3.96989	−	3.02648i	−0.150804	−	0.114967i
$694$	−15.6775			−0.595110
$695$	11.2231	−	12.4645i	0.425717	−	0.472806i
$696$	−4.97715	+	0.247212i	−0.188658	+	0.00937055i
$697$	−0.157470	−	1.49823i	−0.00596460	−	0.0567493i
$698$	−9.97642	−	11.0799i	−0.377613	−	0.419382i
$699$	−20.9652	−	3.37928i	−0.792976	−	0.127816i
$700$	−0.458335	−	0.204064i	−0.0173234	−	0.00771289i
$701$	−10.3804	−	7.54181i	−0.392063	−	0.284850i	0.374237	−	0.927333i	$-0.377905\pi$
$701$	−10.3804	−	7.54181i	−0.392063	−	0.284850i	−0.766300	+	0.642483i	$0.777905\pi$
$702$	−16.3544	+	16.0886i	−0.617257	+	0.607224i
$703$	0.188463			0.00710800
$704$	−2.84268	−	1.70856i	−0.107138	−	0.0643937i
$705$	−0.295893	−	1.90180i	−0.0111440	−	0.0716259i
$706$	−5.57219	−	1.18441i	−0.209712	−	0.0445757i
$707$	−2.05074	+	0.913050i	−0.0771262	+	0.0343388i
$708$	−1.19538	+	4.41296i	−0.0449250	+	0.165849i
$709$	−9.76120	+	2.07481i	−0.366590	+	0.0779210i	−0.387523	−	0.921860i	$-0.626669\pi$
$709$	−9.76120	+	2.07481i	−0.366590	+	0.0779210i	0.0209339	+	0.999781i	$0.493336\pi$
$710$	−1.08364	+	3.33511i	−0.0406684	+	0.125165i
$711$	3.55307	+	0.393078i	0.133251	+	0.0147416i
$712$	1.79951	+	1.30742i	0.0674396	+	0.0489978i
$713$	4.96666	−	5.51603i	0.186003	−	0.206577i
$714$	2.07563	+	0.803272i	0.0776786	+	0.0300617i
$715$	13.8448	+	4.76915i	0.517765	+	0.178356i
$716$	9.02374	−	15.6296i	0.337233	−	0.584105i
$717$	0.612894	−	11.1138i	0.0228890	−	0.415054i
$718$	−0.565755	+	5.38280i	−0.0211138	+	0.200884i
$719$	36.6112	−	26.5996i	1.36537	−	0.991997i	0.367283	−	0.930109i	$-0.380288\pi$
$719$	36.6112	−	26.5996i	1.36537	−	0.991997i	0.998083	−	0.0618874i	$-0.0197120\pi$
$720$	−0.0163876	+	2.99996i	−0.000610729	+	0.111802i
$721$	2.06952	−	6.36932i	0.0770728	−	0.237206i
$722$	−17.3274	−	7.71466i	−0.644859	−	0.287110i
$723$	9.99797	−	0.496593i	0.371829	−	0.0184685i
$724$	20.7661	+	4.41397i	0.771765	+	0.164044i
$725$	1.43855	−	2.49164i	0.0534265	−	0.0925373i
$726$	18.5770	−	4.23034i	0.689456	−	0.157003i
$727$	−9.41599	−	16.3090i	−0.349220	−	0.604866i	0.636891	−	0.770954i	$-0.280220\pi$
$727$	−9.41599	−	16.3090i	−0.349220	−	0.604866i	−0.986111	+	0.166087i	$0.946887\pi$
$728$	−0.684501	−	2.10668i	−0.0253693	−	0.0780786i
$729$	25.8118	−	7.92155i	0.955993	−	0.293391i
$730$	−2.39794	+	1.74220i	−0.0887516	+	0.0644818i
$731$	−17.9008	+	3.80493i	−0.662085	+	0.140730i
$732$	−6.89302	−	1.11105i	−0.254773	−	0.0410658i
$733$	2.45537	+	23.3613i	0.0906912	+	0.862869i	0.941414	+	0.337254i	$0.109498\pi$
$733$	2.45537	+	23.3613i	0.0906912	+	0.862869i	−0.850722	+	0.525615i	$0.823835\pi$
$734$	−5.50034	+	2.44891i	−0.203021	+	0.0903909i
$735$	9.78527	+	6.39270i	0.360935	+	0.235798i
$736$	−0.385331	−	0.667413i	−0.0142035	−	0.0246012i
$737$	−3.61125	−	18.5912i	−0.133022	−	0.684816i
$738$	1.68117	−	0.536110i	0.0618847	−	0.0197345i
$739$	−7.12086	−	21.9158i	−0.261945	−	0.806185i	−0.992381	−	0.123204i	$-0.960683\pi$
$739$	−7.12086	−	21.9158i	−0.261945	−	0.806185i	0.730436	−	0.682981i	$-0.239317\pi$
$740$	−0.108775	+	1.03493i	−0.00399866	+	0.0380447i
$741$	−1.33872	+	0.354792i	−0.0491789	+	0.0130336i
$742$	3.16437	+	3.51439i	0.116168	+	0.129017i
$743$	9.04300	+	10.0433i	0.331756	+	0.368452i	0.885826	−	0.464018i	$-0.153593\pi$
$743$	9.04300	+	10.0433i	0.331756	+	0.368452i	−0.554070	+	0.832470i	$0.686926\pi$
$744$	−16.1254	+	4.27361i	−0.591185	+	0.156678i
$745$	0.631633	−	6.00959i	0.0231412	−	0.220174i
$746$	0.920432	+	2.83280i	0.0336994	+	0.103716i
$747$	−7.48823	−	6.81687i	−0.273980	−	0.249416i
$748$	−7.43001	+	4.11726i	−0.271668	+	0.150542i
$749$	−4.06020	−	7.03248i	−0.148357	−	0.256961i
$750$	−1.45004	−	0.947306i	−0.0529479	−	0.0345907i
$751$	33.2227	−	14.7917i	1.21231	−	0.539757i	0.301854	−	0.953354i	$-0.402394\pi$
$751$	33.2227	−	14.7917i	1.21231	−	0.539757i	0.910460	+	0.413597i	$0.135728\pi$
$752$	−0.116154	−	1.10513i	−0.00423568	−	0.0402998i
$753$	−11.7900	−	1.90038i	−0.429653	−	0.0692538i
$754$	12.4251	−	2.64103i	0.452494	−	0.0961805i
$755$	7.46731	−	5.42532i	0.271763	−	0.197448i
$756$	−0.428903	+	2.57144i	−0.0155991	+	0.0935223i
$757$	9.79431	+	30.1438i	0.355980	+	1.09559i	0.955439	+	0.295189i	$0.0953827\pi$
$757$	9.79431	+	30.1438i	0.355980	+	1.09559i	−0.599458	+	0.800406i	$0.704617\pi$
$758$	18.7422	+	32.4624i	0.680746	+	1.17909i
$759$	4.25211	+	1.23245i	0.154342	+	0.0447351i
$760$	−0.0905523	+	0.156841i	−0.00328468	+	0.00568922i
$761$	−29.2239	−	6.21174i	−1.05937	−	0.225175i	−0.354894	−	0.934906i	$-0.615483\pi$
$761$	−29.2239	−	6.21174i	−1.05937	−	0.225175i	−0.704473	+	0.709731i	$0.748816\pi$
$762$	−11.1096	+	0.551806i	−0.402458	+	0.0199898i
$763$	−1.69618	−	0.755187i	−0.0614058	−	0.0273396i
$764$	−1.14089	+	3.51129i	−0.0412759	+	0.127034i
$765$	6.63309	+	3.87808i	0.239820	+	0.140212i
$766$	1.51307	−	1.09931i	0.0546693	−	0.0397196i
$767$	1.21820	−	11.5904i	0.0439866	−	0.418504i
$768$	−0.0953724	+	1.72942i	−0.00344146	+	0.0624052i
$769$	−0.930722	+	1.61206i	−0.0335627	+	0.0581323i	−0.882319	−	0.470652i	$-0.844019\pi$
$769$	−0.930722	+	1.61206i	−0.0335627	+	0.0581323i	0.848756	+	0.528784i	$0.177352\pi$
$770$	1.59134	−	0.486295i	0.0573479	−	0.0175249i
$771$	0.907545	+	0.351221i	0.0326844	+	0.0126489i
$772$	−6.24075	+	6.93105i	−0.224609	+	0.249454i
$773$	−41.6558	−	30.2647i	−1.49825	−	1.08855i	−0.971070	−	0.238794i	$-0.923248\pi$
$773$	−41.6558	−	30.2647i	−1.49825	−	1.08855i	−0.527184	−	0.849751i	$-0.676752\pi$
$774$	−8.61176	−	19.6302i	−0.309543	−	0.705594i
$775$	2.97626	−	9.16000i	0.106911	−	0.329037i
$776$	5.80640	−	1.23419i	0.208438	−	0.0443048i
$777$	−0.236433	+	0.872839i	−0.00848200	+	0.0313129i
$778$	14.2096	−	6.32652i	0.509439	−	0.226817i
$779$	0.104197	+	0.0221477i	0.00373323	+	0.000793524i
$780$	−1.17564	−	7.55623i	−0.0420948	−	0.270556i
$781$	−4.54303	−	10.7066i	−0.162562	−	0.383112i
$782$	−1.97382			−0.0705835
$783$	−14.4083	−	3.98750i	−0.514910	−	0.142502i
$784$	5.45948	+	3.96654i	0.194981	+	0.141662i
$785$	−8.86508	−	3.94699i	−0.316408	−	0.140874i
$786$	20.4013	+	3.28839i	0.727691	+	0.117293i
$787$	−11.4719	−	12.7408i	−0.408928	−	0.454161i	0.503137	−	0.864207i	$-0.332179\pi$
$787$	−11.4719	−	12.7408i	−0.408928	−	0.454161i	−0.912065	+	0.410046i	$0.865513\pi$
$788$	−2.22116	−	21.1329i	−0.0791256	−	0.752830i
$789$	38.6717	−	1.92080i	1.37675	−	0.0683823i
$790$	−0.797324	+	0.885518i	−0.0283675	+	0.0315053i
$791$	3.73791			0.132905
$792$	−6.48561	−	7.54565i	−0.230456	−	0.268123i
$793$	17.7974			0.632005
$794$	−10.7154	+	11.9007i	−0.380276	+	0.422339i
$795$	8.85443	+	13.7165i	0.314034	+	0.486474i
$796$	2.26503	+	21.5503i	0.0802818	+	0.763830i
$797$	−2.01988	−	2.24330i	−0.0715477	−	0.0794617i	0.706308	−	0.707904i	$-0.250359\pi$
$797$	−2.01988	−	2.24330i	−0.0715477	−	0.0794617i	−0.777856	+	0.628443i	$0.783693\pi$
$798$	−0.0993746	+	0.122034i	−0.00351782	+	0.00431997i
$799$	−2.59998	−	1.15759i	−0.0919808	−	0.0409525i
$800$	−0.809017	−	0.587785i	−0.0286031	−	0.0207813i
$801$	3.89272	+	5.41989i	0.137543	+	0.191502i
$802$	−25.5781			−0.903193
$803$	2.21263	−	9.57827i	0.0780820	−	0.338010i
$804$	−7.70326	+	6.20322i	−0.271673	+	0.218771i
$805$	0.378200	+	0.0803889i	0.0133298	+	0.00283334i
$806$	38.8470	−	17.2958i	1.36833	−	0.609219i
$807$	−27.0038	−	27.1518i	−0.950581	−	0.955787i
$808$	−4.37656	+	0.930266i	−0.153967	+	0.0327267i
$809$	−2.12054	+	6.52635i	−0.0745542	+	0.229454i	−0.981388	−	0.192033i	$-0.938492\pi$
$809$	−2.12054	+	6.52635i	−0.0745542	+	0.229454i	0.906834	+	0.421488i	$0.138492\pi$
$810$	−2.87450	+	8.52861i	−0.101000	+	0.299665i
$811$	−5.53723	−	4.02303i	−0.194438	−	0.141268i	0.486307	−	0.873788i	$-0.338344\pi$
$811$	−5.53723	−	4.02303i	−0.194438	−	0.141268i	−0.680745	+	0.732520i	$0.738344\pi$
$812$	0.965871	−	1.07271i	0.0338954	−	0.0376447i
$813$	−7.57739	−	48.7023i	−0.265751	−	1.70806i
$814$	−1.97926	−	2.82746i	−0.0693731	−	0.0991024i
$815$	−3.24507	+	5.62063i	−0.113670	+	0.196882i
$816$	3.71383	+	2.42624i	0.130010	+	0.0849352i
$817$	0.135266	−	1.28697i	0.00473236	−	0.0450254i
$818$	−20.5028	+	14.8962i	−0.716865	+	0.520833i
$819$	0.0363000	−	6.64517i	0.00126842	−	0.232201i
$820$	−0.181762	+	0.559405i	−0.00634740	+	0.0195353i
$821$	21.0276	+	9.36209i	0.733868	+	0.326739i	0.739419	−	0.673245i	$-0.235100\pi$
$821$	21.0276	+	9.36209i	0.733868	+	0.326739i	−0.00555084	+	0.999985i	$0.501767\pi$
$822$	19.5287	+	30.2521i	0.681140	+	1.05516i
$823$	−48.0087	−	10.2046i	−1.67348	−	0.355709i	−0.729060	−	0.684450i	$-0.760042\pi$
$823$	−48.0087	−	10.2046i	−1.67348	−	0.355709i	−0.944420	+	0.328741i	$0.893376\pi$
$824$	6.67426	−	11.5602i	0.232509	−	0.402717i
$825$	5.69092	−	0.783208i	0.198132	−	0.0272678i
$826$	−0.662168	−	1.14691i	−0.0230398	−	0.0399060i
$827$	15.3444	+	47.2253i	0.533578	+	1.64218i	0.746702	+	0.665158i	$0.231636\pi$
$827$	15.3444	+	47.2253i	0.533578	+	1.64218i	−0.213124	+	0.977025i	$0.568364\pi$
$828$	−0.468329	−	2.26406i	−0.0162755	−	0.0786814i
$829$	28.7456	−	20.8849i	0.998376	−	0.725362i	0.0366363	−	0.999329i	$-0.488336\pi$
$829$	28.7456	−	20.8849i	0.998376	−	0.725362i	0.961739	+	0.273966i	$0.0883357\pi$
$830$	3.30169	−	0.701797i	0.114603	−	0.0243597i
$831$	12.9234	+	33.9436i	0.448309	+	1.17749i
$832$	−0.461501	−	4.39089i	−0.0159997	−	0.152227i
$833$	15.7894	−	7.02990i	0.547071	−	0.243572i
$834$	25.9207	−	13.1182i	0.897559	−	0.454246i
$835$	9.90634	+	17.1583i	0.342823	+	0.593787i
$836$	−0.114534	−	0.589635i	−0.00396123	−	0.0203929i
$837$	−49.9545	−	3.02863i	−1.72668	−	0.104685i
$838$	7.01181	+	21.5801i	0.242219	+	0.745474i
$839$	0.794971	−	7.56364i	0.0274454	−	0.261126i	−0.972192	−	0.234187i	$-0.924757\pi$
$839$	0.794971	−	7.56364i	0.0274454	−	0.261126i	0.999637	−	0.0269392i	$-0.00857604\pi$
$840$	−0.612787	−	0.616143i	−0.0211431	−	0.0212590i
$841$	−13.8659	−	15.3997i	−0.478135	−	0.531023i
$842$	−10.6991	−	11.8826i	−0.368717	−	0.409501i
$843$	9.93004	−	36.6586i	0.342009	−	1.26259i
$844$	2.89196	−	27.5151i	0.0995452	−	0.947110i
$845$	2.00642	+	6.17513i	0.0690230	+	0.212431i
$846$	0.710905	−	3.25696i	0.0244414	−	0.111977i
$847$	−2.92574	+	4.67946i	−0.100530	+	0.160788i
$848$	4.71295	+	8.16307i	0.161843	+	0.280321i
$849$	−0.150451	+	2.72819i	−0.00516347	+	0.0936311i
$850$	−2.33977	+	1.04173i	−0.0802533	+	0.0357311i
$851$	−0.0838291	−	0.797581i	−0.00287362	−	0.0273407i
$852$	−3.83528	+	4.70982i	−0.131395	+	0.161356i
$853$	9.65943	−	2.05317i	0.330732	−	0.0702993i	−0.0395527	−	0.999217i	$-0.512593\pi$
$853$	9.65943	−	2.05317i	0.330732	−	0.0702993i	0.370285	+	0.928918i	$0.379260\pi$
$854$	1.63617	−	1.18875i	0.0559887	−	0.0406782i
$855$	−0.405740	+	0.361337i	−0.0138760	+	0.0123575i
$856$	−5.00158	−	15.3933i	−0.170950	−	0.526131i
$857$	19.2745	+	33.3845i	0.658406	+	1.14039i	0.981028	+	0.193864i	$0.0621022\pi$
$857$	19.2745	+	33.3845i	0.658406	+	1.14039i	−0.322623	+	0.946528i	$0.604564\pi$
$858$	19.3822	+	16.3584i	0.661698	+	0.558465i
$859$	−9.89391	+	17.1367i	−0.337576	+	0.584698i	−0.983976	−	0.178300i	$-0.942940\pi$
$859$	−9.89391	+	17.1367i	−0.337576	+	0.584698i	0.646400	+	0.762998i	$0.276274\pi$
$860$	6.98924	+	1.48561i	0.238331	+	0.0506588i
$861$	−0.233293	+	0.454787i	−0.00795059	+	0.0154991i
$862$	−25.9387	−	11.5486i	−0.883474	−	0.393348i
$863$	7.67217	−	23.6125i	0.261164	−	0.803779i	−0.731389	−	0.681961i	$-0.761127\pi$
$863$	7.67217	−	23.6125i	0.261164	−	0.803779i	0.992552	−	0.121819i	$-0.0388726\pi$
$864$	−1.90182	+	4.83561i	−0.0647012	+	0.164511i
$865$	10.1392	−	7.36656i	0.344743	−	0.250471i
$866$	−2.29537	+	21.8390i	−0.0780000	+	0.742120i
$867$	−16.1345	+	8.16552i	−0.547957	+	0.277316i
$868$	2.41608	−	4.18478i	0.0820072	−	0.142041i
$869$	0.0694865	−	3.95142i	0.00235717	−	0.134043i
$870$	3.88129	−	3.12550i	0.131588	−	0.105964i
$871$	16.8695	−	18.7355i	0.571602	−	0.634828i
$872$	−2.99396	−	2.17524i	−0.101388	−	0.0736629i
$873$	17.7004	+	1.95820i	0.599067	+	0.0662750i
$874$	0.0431296	−	0.132739i	0.00145888	−	0.00448998i
$875$	0.490747	−	0.104311i	0.0165903	−	0.00352637i
$876$	−4.96250	+	1.31518i	−0.167667	+	0.0444358i
$877$	10.8769	−	4.84273i	0.367288	−	0.163527i	−0.214790	−	0.976660i	$-0.568907\pi$
$877$	10.8769	−	4.84273i	0.367288	−	0.163527i	0.582078	+	0.813133i	$0.302240\pi$
$878$	19.1141	+	4.06282i	0.645068	+	0.137114i
$879$	−25.9619	−	10.0473i	−0.875674	−	0.338887i
$880$	3.30404	−	0.288633i	0.111379	−	0.00972982i
$881$	27.5072			0.926742			0.463371	−	0.886164i	$-0.346640\pi$
$881$	27.5072			0.926742			0.463371	+	0.886164i	$0.346640\pi$
$882$	11.8100	+	16.4432i	0.397663	+	0.553671i
$883$	34.7423	+	25.2418i	1.16917	+	0.849453i	0.990910	−	0.134530i	$-0.0429523\pi$
$883$	34.7423	+	25.2418i	1.16917	+	0.849453i	0.178263	+	0.983983i	$0.442952\pi$
$884$	−10.3303	−	4.59933i	−0.347444	−	0.154692i
$885$	−1.62679	−	4.27278i	−0.0546840	−	0.143628i
$886$	9.55819	+	10.6154i	0.321114	+	0.356633i
$887$	4.90004	+	46.6208i	0.164527	+	1.56537i	0.695840	+	0.718196i	$0.255032\pi$
$887$	4.90004	+	46.6208i	0.164527	+	1.56537i	−0.531313	+	0.847175i	$0.678301\pi$
$888$	−0.822666	+	1.60373i	−0.0276069	+	0.0538176i
$889$	2.15594	−	2.39441i	0.0723078	−	0.0803059i
$890$	−2.22432			−0.0745594
$891$	−11.3587	−	27.6040i	−0.380531	−	0.924768i
$892$	16.0919			0.538796
$893$	0.134660	−	0.149555i	0.00450622	−	0.00500466i
$894$	4.77703	−	9.31248i	0.159768	−	0.311456i
$895$	1.88648	+	17.9486i	0.0630579	+	0.599956i
$896$	−0.335710	−	0.372843i	−0.0112153	−	0.0124558i
$897$	2.09696	+	5.50768i	0.0700154	+	0.183896i
$898$	9.17713	+	4.08592i	0.306245	+	0.136349i
$899$	22.4183	+	16.2878i	0.747691	+	0.543229i
$900$	−1.75007	−	2.43665i	−0.0583357	−	0.0812216i
$901$	24.1416			0.804272
$902$	−0.762012	−	1.79584i	−0.0253722	−	0.0597948i
$903$	5.79073	+	2.24102i	0.192704	+	0.0745765i
$904$	7.28753	+	1.54901i	0.242380	+	0.0515194i
$905$	−19.3946	+	8.63502i	−0.644697	+	0.287038i
$906$	15.4535	−	4.09555i	0.513409	−	0.136066i
$907$	−16.1187	+	3.42614i	−0.535214	+	0.113763i	−0.467586	−	0.883948i	$-0.654876\pi$
$907$	−16.1187	+	3.42614i	−0.535214	+	0.113763i	−0.0676274	+	0.997711i	$0.521543\pi$
$908$	1.81714	−	5.59259i	0.0603040	−	0.185597i
$909$	−13.3416	−	1.47599i	−0.442513	−	0.0489554i
$910$	1.79205	+	1.30200i	0.0594057	+	0.0431608i
$911$	−8.84071	+	9.81860i	−0.292906	+	0.325305i	−0.871579	−	0.490254i	$-0.836904\pi$
$911$	−8.84071	+	9.81860i	−0.292906	+	0.325305i	0.578674	+	0.815559i	$0.303571\pi$
$912$	−0.244315	+	0.196740i	−0.00809008	+	0.00651471i
$913$	−6.73855	+	8.93994i	−0.223014	+	0.295869i
$914$	−2.48132	+	4.29776i	−0.0820746	+	0.142157i
$915$	6.22963	−	3.15275i	0.205945	−	0.104227i
$916$	−2.20268	+	20.9571i	−0.0727786	+	0.692443i
$917$	−4.84259	+	3.51835i	−0.159916	+	0.116186i
$918$	8.29019	+	10.4108i	0.273617	+	0.343608i
$919$	−7.16028	+	22.0371i	−0.236196	+	0.726936i	0.760765	+	0.649028i	$0.224824\pi$
$919$	−7.16028	+	22.0371i	−0.236196	+	0.726936i	−0.996961	+	0.0779085i	$0.975176\pi$
$920$	0.704035	+	0.313457i	0.0232113	+	0.0103344i
$921$	−18.9518	+	36.9453i	−0.624484	+	1.21739i
$922$	40.4520	+	8.59833i	1.33221	+	0.283171i
$923$	7.74128	−	13.4083i	0.254807	−	0.441339i
$924$	2.87450	+	0.209271i	0.0945641	+	0.00688452i
$925$	−0.520315	−	0.901211i	−0.0171078	−	0.0296317i
$926$	8.74079	+	26.9014i	0.287240	+	0.884034i
$927$	29.9056	−	26.6328i	0.982229	−	0.874735i
$928$	2.32763	−	1.69112i	0.0764080	−	0.0555137i
$929$	28.9999	−	6.16411i	0.951454	−	0.202238i	0.294062	−	0.955786i	$-0.404993\pi$
$929$	28.9999	−	6.16411i	0.951454	−	0.202238i	0.657392	+	0.753548i	$0.271659\pi$
$930$	10.5337	−	12.9357i	0.345415	−	0.424177i
$931$	0.127749	+	1.21545i	0.00418680	+	0.0398348i
$932$	11.2005	−	4.98679i	0.366885	−	0.163348i
$933$	0.498301	−	9.03588i	0.0163136	−	0.295821i
$934$	−4.19677	−	7.26901i	−0.137322	−	0.237849i
$935$	3.59094	−	7.69818i	0.117436	−	0.251757i
$936$	2.82457	−	12.9406i	0.0923240	−	0.422975i
$937$	−10.4218	−	32.0750i	−0.340465	−	1.04784i	−0.963967	−	0.266023i	$-0.914290\pi$
$937$	−10.4218	−	32.0750i	−0.340465	−	1.04784i	0.623501	−	0.781822i	$-0.285710\pi$
$938$	0.299462	−	2.84919i	0.00977777	−	0.0930292i
$939$	8.88979	−	32.8183i	0.290107	−	1.07099i
$940$	0.743547	+	0.825793i	0.0242518	+	0.0269344i
$941$	23.4207	+	26.0114i	0.763494	+	0.847946i	0.992084	−	0.125577i	$-0.0400781\pi$
$941$	23.4207	+	26.0114i	0.763494	+	0.847946i	−0.228590	+	0.973523i	$0.573411\pi$
$942$	−11.8525	−	11.9174i	−0.386174	−	0.388290i
$943$	0.0473826	−	0.450815i	0.00154299	−	0.0146806i
$944$	−0.815694	−	2.51045i	−0.0265486	−	0.0817081i
$945$	−1.16446	−	2.33244i	−0.0378800	−	0.0758743i
$946$	−20.7287	+	11.4866i	−0.673948	+	0.373461i
$947$	3.68684	+	6.38580i	0.119806	+	0.207511i	0.919691	−	0.392643i	$-0.128439\pi$
$947$	3.68684	+	6.38580i	0.119806	+	0.207511i	−0.799885	+	0.600154i	$0.795106\pi$
$948$	−1.84148	+	0.931957i	−0.0598086	+	0.0302685i
$949$	11.9550	−	5.32270i	0.388075	−	0.172782i
$950$	−0.0189306	−	0.180112i	−0.000614189	−	0.00584362i
$951$	5.19204	+	13.6369i	0.168364	+	0.442208i
$952$	−1.25690	+	0.267162i	−0.0407363	+	0.00865876i
$953$	−25.6323	+	18.6230i	−0.830312	+	0.603257i	−0.919648	−	0.392744i	$-0.871526\pi$
$953$	−25.6323	+	18.6230i	−0.830312	+	0.603257i	0.0893354	+	0.996002i	$0.471526\pi$
$954$	5.72809	+	27.6915i	0.185454	+	0.896545i
$955$	−1.14089	−	3.51129i	−0.0369183	−	0.113623i
$956$	3.21316	+	5.56536i	0.103921	+	0.179997i
$957$	−2.91657	+	16.2683i	−0.0942792	+	0.525880i
$958$	−12.7953	+	22.1621i	−0.413398	+	0.716026i
$959$	−10.2022	−	2.16854i	−0.329445	−	0.0700257i
$960$	−0.939371	−	1.45519i	−0.0303181	−	0.0469661i
$961$	56.4239	+	25.1216i	1.82013	+	0.810373i
$962$	1.41977	−	4.36959i	0.0457751	−	0.140881i
$963$	0.265241	−	48.5556i	0.00854726	−	1.56468i
$964$	−4.67567	+	3.39707i	−0.150593	+	0.109412i
$965$	0.974901	−	9.27556i	0.0313832	−	0.298591i
$966$	0.560656	+	0.366275i	0.0180388	+	0.0117847i
$967$	−9.61728	+	16.6576i	−0.309271	+	0.535673i	−0.978203	−	0.207650i	$-0.933418\pi$
$967$	−9.61728	+	16.6576i	−0.309271	+	0.535673i	0.668932	+	0.743324i	$0.266752\pi$
$968$	−7.64330	+	7.91075i	−0.245665	+	0.254261i
$969$	0.123512	+	0.793850i	0.00396777	+	0.0255021i
$970$	−3.97204	+	4.41140i	−0.127535	+	0.141641i
$971$	−25.3262	−	18.4006i	−0.812757	−	0.590503i	0.101871	−	0.994798i	$-0.467517\pi$
$971$	−25.3262	−	18.4006i	−0.812757	−	0.590503i	−0.914629	+	0.404295i	$0.867517\pi$
$972$	−9.97465	+	11.9794i	−0.319937	+	0.384240i
$973$	−2.60038	+	8.00316i	−0.0833645	+	0.256570i
$974$	8.94093	−	1.90045i	0.286486	−	0.0608945i
$975$	5.39256	+	5.42209i	0.172700	+	0.173646i
$976$	3.68255	−	1.63958i	0.117876	−	0.0524816i
$977$	53.6567	+	11.4051i	1.71663	+	0.364881i	0.958028	−	0.286673i	$-0.0925495\pi$
$977$	53.6567	+	11.4051i	1.71663	+	0.364881i	0.758602	+	0.651554i	$0.225883\pi$
$978$	−8.75538	+	7.05046i	−0.279966	+	0.225449i
$979$	5.56830	−	4.83918i	0.177964	−	0.154661i
$980$	−6.74829			−0.215566
$981$	−6.47656	−	9.01739i	−0.206781	−	0.287903i
$982$	23.8809	+	17.3505i	0.762069	+	0.553676i
$983$	−48.6313	−	21.6520i	−1.55110	−	0.690593i	−0.560595	−	0.828090i	$-0.689427\pi$
$983$	−48.6313	−	21.6520i	−1.55110	−	0.690593i	−0.990502	+	0.137498i	$0.956094\pi$
$984$	−0.643300	+	0.789988i	−0.0205077	+	0.0251839i
$985$	14.2186	+	15.7913i	0.453042	+	0.503154i
$986$	−0.770251	−	7.32845i	−0.0245298	−	0.233385i
$987$	0.523707	+	0.811280i	0.0166698	+	0.0258233i
$988$	0.535031	−	0.594212i	0.0170216	−	0.0189044i
$989$	−5.50668			−0.175102
$990$	9.68219	+	2.29242i	0.307720	+	0.0728579i
$991$	47.8721			1.52071			0.760354	−	0.649509i	$-0.225025\pi$
$991$	47.8721			1.52071			0.760354	+	0.649509i	$0.225025\pi$
$992$	6.44466	−	7.15752i	0.204618	−	0.227251i
$993$	55.3848	−	2.75093i	1.75758	−	0.0872982i
$994$	−0.183904	−	1.74973i	−0.00583309	−	0.0554982i
$995$	−14.4994	−	16.1032i	−0.459662	−	0.510506i
$996$	5.77196	+	0.930356i	0.182892	+	0.0294795i
$997$	−41.9918	−	18.6959i	−1.32989	−	0.592106i	−0.386043	−	0.922481i	$-0.626158\pi$
$997$	−41.9918	−	18.6959i	−1.32989	−	0.592106i	−0.943850	+	0.330375i	$0.892825\pi$
$998$	−4.44455	−	3.22916i	−0.140690	−	0.102217i
$999$	−3.85472	+	3.79206i	−0.121958	+	0.119975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bg.a.841.4	yes	88
9.7	even	3	inner	990.2.bg.a.511.9	yes	88
11.9	even	5	inner	990.2.bg.a.31.9	✓	88
99.97	even	15	inner	990.2.bg.a.691.4	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.bg.a.31.9	✓	88	11.9	even	5	inner
990.2.bg.a.511.9	yes	88	9.7	even	3	inner
990.2.bg.a.691.4	yes	88	99.97	even	15	inner
990.2.bg.a.841.4	yes	88	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.669131 - 0.743145i) q^{2} +(-0.790547 + 1.54112i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(0.669131 + 0.743145i) q^{5} +(0.616293 + 1.61870i) q^{6} +(-0.458335 - 0.204064i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-1.75007 - 2.43665i) q^{9} +1.00000 q^{10} +(-2.50337 + 2.17558i) q^{11} +(1.61531 + 0.625126i) q^{12} +(-4.31860 - 0.917946i) q^{13} +(-0.458335 + 0.204064i) q^{14} +(-1.67425 + 0.443717i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-0.791452 + 2.43584i) q^{17} +(-2.98181 - 0.329879i) q^{18} +(-0.146517 - 0.106451i) q^{19} +(0.669131 - 0.743145i) q^{20} +(0.676821 - 0.545025i) q^{21} +(-0.0583144 + 3.31611i) q^{22} +(-0.385331 + 0.667413i) q^{23} +(1.54541 - 0.782117i) q^{24} +(-0.104528 + 0.994522i) q^{25} +(-3.57187 + 2.59512i) q^{26} +(5.13867 - 0.770778i) q^{27} +(-0.155037 + 0.477155i) q^{28} +(-2.62836 - 1.17022i) q^{29} +(-0.790547 + 1.54112i) q^{30} +(-9.42092 - 2.00248i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.37378 - 5.57788i) q^{33} +(1.28060 + 2.21806i) q^{34} +(-0.155037 - 0.477155i) q^{35} +(-2.24037 + 1.99518i) q^{36} +(-0.841887 + 0.611667i) q^{37} +(-0.177147 + 0.0376537i) q^{38} +(4.82872 - 5.92978i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-0.537342 + 0.239240i) q^{41} +(0.0478493 - 0.867669i) q^{42} +(3.57269 + 6.18808i) q^{43} +(2.42533 + 2.26225i) q^{44} +(0.639755 - 2.93099i) q^{45} +(0.238148 + 0.732943i) q^{46} +(-0.116154 + 1.10513i) q^{47} +(0.452856 - 1.67180i) q^{48} +(-4.51549 - 5.01495i) q^{49} +(0.669131 + 0.743145i) q^{50} +(-3.12823 - 3.14536i) q^{51} +(-0.461501 + 4.39089i) q^{52} +(-2.91276 - 8.96457i) q^{53} +(2.86564 - 4.33453i) q^{54} +(-3.29185 - 0.404623i) q^{55} +(0.250855 + 0.434494i) q^{56} +(0.279881 - 0.141645i) q^{57} +(-2.62836 + 1.17022i) q^{58} +(0.275918 + 2.62518i) q^{59} +(0.616293 + 1.61870i) q^{60} +(-3.94297 + 0.838103i) q^{61} +(-7.79196 + 5.66119i) q^{62} +(0.304888 + 1.47393i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-2.20754 - 3.82357i) q^{65} +(-5.06441 - 2.71141i) q^{66} +(-2.85511 + 4.94520i) q^{67} +(2.50523 + 0.532502i) q^{68} +(-0.723938 - 1.12146i) q^{69} +(-0.458335 - 0.204064i) q^{70} +(-1.08364 + 3.33511i) q^{71} +(-0.0163876 + 2.99996i) q^{72} +(-2.39794 + 1.74220i) q^{73} +(-0.108775 + 1.03493i) q^{74} +(-1.45004 - 0.947306i) q^{75} +(-0.0905523 + 0.156841i) q^{76} +(1.59134 - 0.486295i) q^{77} +(-1.17564 - 7.55623i) q^{78} +(-0.797324 + 0.885518i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-2.87450 + 8.52861i) q^{81} +(-0.181762 + 0.559405i) q^{82} +(3.30169 - 0.701797i) q^{83} +(-0.612787 - 0.616143i) q^{84} +(-2.33977 + 1.04173i) q^{85} +(6.98924 + 1.48561i) q^{86} +(3.88129 - 3.12550i) q^{87} +(3.30404 - 0.288633i) q^{88} -2.22432 q^{89} +(-1.75007 - 2.43665i) q^{90} +(1.79205 + 1.30200i) q^{91} +(0.704035 + 0.313457i) q^{92} +(10.5337 - 12.9357i) q^{93} +(0.743547 + 0.825793i) q^{94} +(-0.0189306 - 0.180112i) q^{95} +(-0.939371 - 1.45519i) q^{96} +(-3.97204 + 4.41140i) q^{97} -6.74829 q^{98} +(9.68219 + 2.29242i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) \) 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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