LMFDB - Embedded newform 378.2.v.b.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	378.67
Dual form			378.2.v.b.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-1.73077 + 0.0664993i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.294369 + 1.66945i) q^{5} +(-1.28310 + 1.16346i) q^{6} +(-2.64575 - 0.00486080i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.99116 - 0.230191i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-1.73077 + 0.0664993i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.294369 + 1.66945i) q^{5} +(-1.28310 + 1.16346i) q^{6} +(-2.64575 - 0.00486080i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.99116 - 0.230191i) q^{9} +(0.847602 + 1.46809i) q^{10} +(1.08481 + 6.15227i) q^{11} +(-0.235057 + 1.71603i) q^{12} +(-0.226902 + 1.28683i) q^{13} +(-2.02988 + 1.69693i) q^{14} +(0.398469 - 2.90902i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.03612 - 1.79461i) q^{17} +(2.14339 - 2.09901i) q^{18} +(-3.71970 + 6.44271i) q^{19} +(1.59297 + 0.579794i) q^{20} +(4.57951 - 0.167527i) q^{21} +(4.78562 + 4.01561i) q^{22} +(4.05743 + 3.40459i) q^{23} +(0.922977 + 1.46564i) q^{24} +(1.99805 + 0.727232i) q^{25} +(0.653339 + 1.13162i) q^{26} +(-5.16171 + 0.597318i) q^{27} +(-0.464216 + 2.60471i) q^{28} +(-0.726953 - 4.12275i) q^{29} +(-1.56463 - 2.48457i) q^{30} +(-0.490802 + 2.78347i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-2.28669 - 10.5761i) q^{33} +(-1.94727 - 0.708747i) q^{34} +(0.786941 - 4.41551i) q^{35} +(0.292715 - 2.98569i) q^{36} -9.35873 q^{37} +(1.29184 + 7.32638i) q^{38} +(0.307144 - 2.24230i) q^{39} +(1.59297 - 0.579794i) q^{40} +(0.943258 - 5.34948i) q^{41} +(3.40043 - 3.07199i) q^{42} +(1.44997 - 1.21667i) q^{43} +6.24718 q^{44} +(-0.496212 + 5.06135i) q^{45} +5.29660 q^{46} +(-0.218830 - 1.24105i) q^{47} +(1.64914 + 0.529471i) q^{48} +(6.99995 + 0.0257209i) q^{49} +(1.99805 - 0.727232i) q^{50} +(1.91263 + 3.03716i) q^{51} +(1.22788 + 0.446910i) q^{52} +(0.611155 - 1.05855i) q^{53} +(-3.57015 + 3.77545i) q^{54} -10.5902 q^{55} +(1.31866 + 2.29371i) q^{56} +(6.00952 - 11.3982i) q^{57} +(-3.20693 - 2.69094i) q^{58} +(1.36405 - 0.496475i) q^{59} +(-2.79563 - 0.897561i) q^{60} +(1.48009 + 8.39399i) q^{61} +(1.41321 + 2.44775i) q^{62} +(-7.91496 + 0.594487i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.08150 - 0.757604i) q^{65} +(-8.54986 - 6.63187i) q^{66} +(-4.26770 - 3.58102i) q^{67} +(-1.94727 + 0.708747i) q^{68} +(-7.24890 - 5.62276i) q^{69} +(-2.23540 - 3.88831i) q^{70} +(4.83278 - 8.37063i) q^{71} +(-1.69493 - 2.47532i) q^{72} -5.04256 q^{73} +(-7.16920 + 6.01568i) q^{74} +(-3.50654 - 1.12580i) q^{75} +(5.69891 + 4.78195i) q^{76} +(-2.84023 - 16.2826i) q^{77} +(-1.20603 - 1.91513i) q^{78} +(-5.05574 + 4.24227i) q^{79} +(0.847602 - 1.46809i) q^{80} +(8.89402 - 1.37707i) q^{81} +(-2.71600 - 4.70425i) q^{82} +(1.19636 + 6.78487i) q^{83} +(0.630242 - 4.53903i) q^{84} +(3.30101 - 1.20147i) q^{85} +(0.328683 - 1.86405i) q^{86} +(1.53235 + 7.08721i) q^{87} +(4.78562 - 4.01561i) q^{88} +(-3.26175 + 5.64952i) q^{89} +(2.87325 + 4.19617i) q^{90} +(0.606581 - 3.40352i) q^{91} +(4.05743 - 3.40459i) q^{92} +(0.664367 - 4.85020i) q^{93} +(-0.965365 - 0.810037i) q^{94} +(-9.66081 - 8.10638i) q^{95} +(1.60365 - 0.654448i) q^{96} +(7.24932 - 6.08290i) q^{97} +(5.37881 - 4.47978i) q^{98} +(4.66104 + 18.1527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−1.73077	+	0.0664993i	−0.999263	+	0.0383934i
$3$	−1.73077	+	0.0664993i	−0.999263	+	0.0383934i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.294369	+	1.66945i	−0.131646	+	0.746601i	0.845491	+	0.533990i	$0.179308\pi$
$5$	−0.294369	+	1.66945i	−0.131646	+	0.746601i	−0.977137	+	0.212611i	$0.931803\pi$
$6$	−1.28310	+	1.16346i	−0.523825	+	0.474981i
$7$	−2.64575	−	0.00486080i	−0.999998	−	0.00183721i
$7$	−2.64575	−	0.00486080i	−0.999998	−	0.00183721i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.99116	−	0.230191i	0.997052	−	0.0767302i
$10$	0.847602	+	1.46809i	0.268035	+	0.464251i
$11$	1.08481	+	6.15227i	0.327083	+	1.85498i	0.494613	+	0.869113i	$0.335310\pi$
$11$	1.08481	+	6.15227i	0.327083	+	1.85498i	−0.167530	+	0.985867i	$0.553579\pi$
$12$	−0.235057	+	1.71603i	−0.0678550	+	0.495374i
$13$	−0.226902	+	1.28683i	−0.0629314	+	0.356902i	0.937039	+	0.349224i	$0.113555\pi$
$13$	−0.226902	+	1.28683i	−0.0629314	+	0.356902i	−0.999971	+	0.00767732i	$0.997556\pi$
$14$	−2.02988	+	1.69693i	−0.542509	+	0.453524i
$15$	0.398469	−	2.90902i	0.102884	−	0.751105i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−1.03612	−	1.79461i	−0.251296	−	0.435257i	0.712587	−	0.701584i	$-0.247523\pi$
$17$	−1.03612	−	1.79461i	−0.251296	−	0.435257i	−0.963883	+	0.266327i	$0.914190\pi$
$18$	2.14339	−	2.09901i	0.505203	−	0.494742i
$19$	−3.71970	+	6.44271i	−0.853357	+	1.47806i	0.0248031	+	0.999692i	$0.492104\pi$
$19$	−3.71970	+	6.44271i	−0.853357	+	1.47806i	−0.878161	+	0.478366i	$0.841229\pi$
$20$	1.59297	+	0.579794i	0.356199	+	0.129646i
$21$	4.57951	−	0.167527i	0.999332	−	0.0365575i
$22$	4.78562	+	4.01561i	1.02030	+	0.856131i
$23$	4.05743	+	3.40459i	0.846033	+	0.709906i	0.958912	−	0.283703i	$-0.0915630\pi$
$23$	4.05743	+	3.40459i	0.846033	+	0.709906i	−0.112879	+	0.993609i	$0.536007\pi$
$24$	0.922977	+	1.46564i	0.188402	+	0.299173i
$25$	1.99805	+	0.727232i	0.399611	+	0.145446i
$26$	0.653339	+	1.13162i	0.128130	+	0.221928i
$27$	−5.16171	+	0.597318i	−0.993371	+	0.114954i
$28$	−0.464216	+	2.60471i	−0.0877286	+	0.492244i
$29$	−0.726953	−	4.12275i	−0.134992	−	0.765576i	−0.974865	−	0.222794i	$-0.928482\pi$
$29$	−0.726953	−	4.12275i	−0.134992	−	0.765576i	0.839874	−	0.542782i	$-0.182629\pi$
$30$	−1.56463	−	2.48457i	−0.285662	−	0.453618i
$31$	−0.490802	+	2.78347i	−0.0881506	+	0.499927i	0.908482	+	0.417925i	$0.137242\pi$
$31$	−0.490802	+	2.78347i	−0.0881506	+	0.499927i	−0.996632	+	0.0820019i	$0.973869\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−2.28669	−	10.5761i	−0.398061	−	1.84105i
$34$	−1.94727	−	0.708747i	−0.333953	−	0.121549i
$35$	0.786941	−	4.41551i	0.133017	−	0.746358i
$36$	0.292715	−	2.98569i	0.0487859	−	0.497614i
$37$	−9.35873			−1.53857			−0.769283	−	0.638908i	$-0.779386\pi$
$37$	−9.35873			−1.53857			−0.769283	+	0.638908i	$0.779386\pi$
$38$	1.29184	+	7.32638i	0.209564	+	1.18850i
$39$	0.307144	−	2.24230i	0.0491823	−	0.359055i
$40$	1.59297	−	0.579794i	0.251871	−	0.0916735i
$41$	0.943258	−	5.34948i	0.147312	−	0.835449i	−0.818169	−	0.574977i	$-0.805011\pi$
$41$	0.943258	−	5.34948i	0.147312	−	0.835449i	0.965482	−	0.260471i	$-0.0838780\pi$
$42$	3.40043	−	3.07199i	0.524697	−	0.474018i
$43$	1.44997	−	1.21667i	0.221119	−	0.185541i	−0.525498	−	0.850795i	$-0.676121\pi$
$43$	1.44997	−	1.21667i	0.221119	−	0.185541i	0.746617	+	0.665254i	$0.231677\pi$
$44$	6.24718			0.941798
$45$	−0.496212	+	5.06135i	−0.0739709	+	0.754501i
$46$	5.29660			0.780941
$47$	−0.218830	−	1.24105i	−0.0319197	−	0.181026i	0.964680	−	0.263426i	$-0.0848525\pi$
$47$	−0.218830	−	1.24105i	−0.0319197	−	0.181026i	−0.996599	+	0.0824004i	$0.973741\pi$
$48$	1.64914	+	0.529471i	0.238033	+	0.0764225i
$49$	6.99995	+	0.0257209i	0.999993	+	0.00367442i
$50$	1.99805	−	0.727232i	0.282567	−	0.102846i
$51$	1.91263	+	3.03716i	0.267821	+	0.425288i
$52$	1.22788	+	0.446910i	0.170276	+	0.0619753i
$53$	0.611155	−	1.05855i	0.0839486	−	0.145403i	−0.820994	−	0.570937i	$-0.806580\pi$
$53$	0.611155	−	1.05855i	0.0839486	−	0.145403i	0.904943	+	0.425533i	$0.139914\pi$
$54$	−3.57015	+	3.77545i	−0.485836	+	0.513774i
$55$	−10.5902			−1.42799
$56$	1.31866	+	2.29371i	0.176214	+	0.306510i
$57$	6.00952	−	11.3982i	0.795981	−	1.50973i
$58$	−3.20693	−	2.69094i	−0.421091	−	0.353337i
$59$	1.36405	−	0.496475i	0.177585	−	0.0646355i	−0.251698	−	0.967806i	$-0.580989\pi$
$59$	1.36405	−	0.496475i	0.177585	−	0.0646355i	0.429282	+	0.903170i	$0.358767\pi$
$60$	−2.79563	−	0.897561i	−0.360914	−	0.115875i
$61$	1.48009	+	8.39399i	0.189506	+	1.07474i	0.920028	+	0.391852i	$0.128165\pi$
$61$	1.48009	+	8.39399i	0.189506	+	1.07474i	−0.730523	+	0.682889i	$0.760723\pi$
$62$	1.41321	+	2.44775i	0.179477	+	0.310864i
$63$	−7.91496	+	0.594487i	−0.997191	+	0.0748983i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.08150	−	0.757604i	−0.258178	−	0.0939693i
$66$	−8.54986	−	6.63187i	−1.05242	−	0.816327i
$67$	−4.26770	−	3.58102i	−0.521382	−	0.437492i	0.343731	−	0.939068i	$-0.388309\pi$
$67$	−4.26770	−	3.58102i	−0.521382	−	0.437492i	−0.865113	+	0.501577i	$0.832754\pi$
$68$	−1.94727	+	0.708747i	−0.236141	+	0.0859481i
$69$	−7.24890	−	5.62276i	−0.872665	−	0.676900i
$70$	−2.23540	−	3.88831i	−0.267182	−	0.464742i
$71$	4.83278	−	8.37063i	0.573546	−	0.993410i	−0.422652	−	0.906292i	$-0.638901\pi$
$71$	4.83278	−	8.37063i	0.573546	−	0.993410i	0.996198	−	0.0871185i	$-0.0277659\pi$
$72$	−1.69493	−	2.47532i	−0.199749	−	0.291719i
$73$	−5.04256			−0.590187			−0.295093	−	0.955468i	$-0.595351\pi$
$73$	−5.04256			−0.590187			−0.295093	+	0.955468i	$0.595351\pi$
$74$	−7.16920	+	6.01568i	−0.833403	+	0.699308i
$75$	−3.50654	−	1.12580i	−0.404900	−	0.129997i
$76$	5.69891	+	4.78195i	0.653710	+	0.548528i
$77$	−2.84023	−	16.2826i	−0.323675	−	1.85558i
$78$	−1.20603	−	1.91513i	−0.136557	−	0.216845i
$79$	−5.05574	+	4.24227i	−0.568815	+	0.477292i	−0.881252	−	0.472646i	$-0.843299\pi$
$79$	−5.05574	+	4.24227i	−0.568815	+	0.477292i	0.312437	+	0.949938i	$0.398855\pi$
$80$	0.847602	−	1.46809i	0.0947648	−	0.164137i
$81$	8.89402	−	1.37707i	0.988225	−	0.153008i
$82$	−2.71600	−	4.70425i	−0.299932	−	0.519498i
$83$	1.19636	+	6.78487i	0.131317	+	0.744737i	0.977354	+	0.211612i	$0.0678713\pi$
$83$	1.19636	+	6.78487i	0.131317	+	0.744737i	−0.846037	+	0.533125i	$0.821018\pi$
$84$	0.630242	−	4.53903i	0.0687650	−	0.495249i
$85$	3.30101	−	1.20147i	0.358045	−	0.130318i
$86$	0.328683	−	1.86405i	0.0354427	−	0.201006i
$87$	1.53235	+	7.08721i	0.164285	+	0.759829i
$88$	4.78562	−	4.01561i	0.510149	−	0.428066i
$89$	−3.26175	+	5.64952i	−0.345745	+	0.598848i	−0.985489	−	0.169740i	$-0.945707\pi$
$89$	−3.26175	+	5.64952i	−0.345745	+	0.598848i	0.639744	+	0.768588i	$0.279040\pi$
$90$	2.87325	+	4.19617i	0.302867	+	0.442316i
$91$	0.606581	−	3.40352i	0.0635870	−	0.356785i
$92$	4.05743	−	3.40459i	0.423016	−	0.354953i
$93$	0.664367	−	4.85020i	0.0688917	−	0.502943i
$94$	−0.965365	−	0.810037i	−0.0995698	−	0.0835490i
$95$	−9.66081	−	8.10638i	−0.991178	−	0.831697i
$96$	1.60365	−	0.654448i	0.163672	−	0.0667944i
$97$	7.24932	−	6.08290i	0.736057	−	0.617625i	−0.195719	−	0.980660i	$-0.562704\pi$
$97$	7.24932	−	6.08290i	0.736057	−	0.617625i	0.931776	+	0.363035i	$0.118259\pi$
$98$	5.37881	−	4.47978i	0.543342	−	0.452526i
$99$	4.66104	+	18.1527i	0.468452	+	1.82441i
$100$	1.06314	−	1.84142i	0.106314	−	0.184142i
$101$	8.96195	−	7.51997i	0.891747	−	0.748265i	−0.0768128	−	0.997046i	$-0.524474\pi$
$101$	8.96195	−	7.51997i	0.891747	−	0.748265i	0.968560	+	0.248781i	$0.0800299\pi$
$102$	3.41741	+	1.09719i	0.338374	+	0.108638i
$103$	2.57181	−	14.5855i	0.253408	−	1.43715i	−0.546718	−	0.837317i	$-0.684123\pi$
$103$	2.57181	−	14.5855i	0.253408	−	1.43715i	0.800126	−	0.599832i	$-0.204766\pi$
$104$	1.22788	−	0.446910i	0.120403	−	0.0438232i
$105$	−1.06839	+	7.69458i	−0.104264	+	0.750914i
$106$	−0.212252	−	1.20374i	−0.0206157	−	0.116918i
$107$	−4.50839	−	7.80876i	−0.435842	−	0.754901i	0.561522	−	0.827462i	$-0.310216\pi$
$107$	−4.50839	−	7.80876i	−0.435842	−	0.754901i	−0.997364	+	0.0725610i	$0.976883\pi$
$108$	−0.308078	+	5.18701i	−0.0296448	+	0.499120i
$109$	−9.27298	+	16.0613i	−0.888190	+	1.53839i	−0.0461775	+	0.998933i	$0.514704\pi$
$109$	−9.27298	+	16.0613i	−0.888190	+	1.53839i	−0.842013	+	0.539457i	$0.818629\pi$
$110$	−8.11260	+	6.80728i	−0.773506	+	0.649049i
$111$	16.1978	−	0.622349i	1.53743	−	0.0590708i
$112$	2.48453	+	0.909466i	0.234766	+	0.0859365i
$113$	15.9066	+	13.3472i	1.49637	+	1.25560i	0.886177	+	0.463346i	$0.153351\pi$
$113$	15.9066	+	13.3472i	1.49637	+	1.25560i	0.610190	+	0.792255i	$0.291093\pi$
$114$	−2.72308	−	12.5944i	−0.255040	−	1.17957i
$115$	−6.87817	+	5.77147i	−0.641393	+	0.538192i
$116$	−4.18635			−0.388693
$117$	−0.382485	+	3.90133i	−0.0353607	+	0.360678i
$118$	0.725798	−	1.25712i	0.0668151	−	0.115727i
$119$	2.73258	+	4.75312i	0.250495	+	0.435718i
$120$	−2.71852	+	1.10942i	−0.248165	+	0.101276i
$121$	−26.3370	+	9.58590i	−2.39428	+	0.871445i
$122$	6.52937	+	5.47879i	0.591141	+	0.496026i
$123$	−1.27683	+	9.32147i	−0.115128	+	0.840488i
$124$	2.65596	+	0.966690i	0.238512	+	0.0868114i
$125$	−6.04025	+	10.4620i	−0.540257	+	0.935752i
$126$	−5.68108	+	5.54304i	−0.506111	+	0.493813i
$127$	−1.57627	−	2.73017i	−0.139871	−	0.242264i	0.787577	−	0.616217i	$-0.211335\pi$
$127$	−1.57627	−	2.73017i	−0.139871	−	0.242264i	−0.927448	+	0.373953i	$0.878002\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−2.42867	+	2.20221i	−0.213832	+	0.193894i
$130$	−2.08150	+	0.757604i	−0.182560	+	0.0664463i
$131$	16.5994	+	13.9286i	1.45030	+	1.21695i	0.932362	+	0.361527i	$0.117745\pi$
$131$	16.5994	+	13.9286i	1.45030	+	1.21695i	0.517938	+	0.855418i	$0.326700\pi$
$132$	−10.8125	+	0.415434i	−0.941104	+	0.0361588i
$133$	9.87270	−	17.0277i	0.856071	−	1.47649i
$134$	−5.57108			−0.481268
$135$	0.522255	−	8.79304i	0.0449485	−	0.756785i
$136$	−1.03612	+	1.79461i	−0.0888464	+	0.153886i
$137$	17.4902	+	6.36590i	1.49429	+	0.543876i	0.954574	−	0.297974i	$-0.0963109\pi$
$137$	17.4902	+	6.36590i	1.49429	+	0.543876i	0.539712	+	0.841850i	$0.318533\pi$
$138$	−9.16722	+	0.352220i	−0.780365	+	0.0299830i
$139$	7.38333	−	2.68731i	0.626246	−	0.227935i	−0.00935072	−	0.999956i	$-0.502976\pi$
$139$	7.38333	−	2.68731i	0.626246	−	0.227935i	0.635596	+	0.772021i	$0.280754\pi$
$140$	−4.21178	−	1.54173i	−0.355960	−	0.130300i
$141$	0.461275	+	2.13342i	0.0388464	+	0.179667i
$142$	−1.67841	−	9.51872i	−0.140849	−	0.798794i
$143$	−8.16306			−0.682629
$144$	−2.88950	−	0.806727i	−0.240791	−	0.0672273i
$145$	7.09672			0.589351
$146$	−3.86282	+	3.24129i	−0.319689	+	0.268251i
$147$	−12.1170	+	0.420975i	−0.999397	+	0.0347214i
$148$	−1.62513	+	9.21655i	−0.133585	+	0.757596i
$149$	7.92344	−	2.88390i	0.649113	−	0.236258i	0.00358421	−	0.999994i	$-0.498859\pi$
$149$	7.92344	−	2.88390i	0.649113	−	0.236258i	0.645529	+	0.763736i	$0.276637\pi$
$150$	−3.40982	+	1.39154i	−0.278410	+	0.113619i
$151$	−2.13898	−	12.1308i	−0.174068	−	0.987187i	−0.939215	−	0.343331i	$-0.888445\pi$
$151$	−2.13898	−	12.1308i	−0.174068	−	0.987187i	0.765147	−	0.643856i	$-0.222666\pi$
$152$	7.43940			0.603415
$153$	−3.51229	−	5.12945i	−0.283952	−	0.414692i
$154$	−12.6420	−	10.6476i	−1.01872	−	0.858004i
$155$	−4.50239	−	1.63874i	−0.361641	−	0.131627i
$156$	−2.15490	−	0.691848i	−0.172530	−	0.0553922i
$157$	11.5374	−	4.19928i	0.920787	−	0.335139i	0.162235	−	0.986752i	$-0.448130\pi$
$157$	11.5374	−	4.19928i	0.920787	−	0.335139i	0.758551	+	0.651613i	$0.225907\pi$
$158$	−1.14604	+	6.49953i	−0.0911743	+	0.517075i
$159$	−0.987378	+	1.87275i	−0.0783042	+	0.148519i
$160$	−0.294369	−	1.66945i	−0.0232719	−	0.131982i
$161$	−10.7184	−	9.02740i	−0.844727	−	0.711459i
$162$	5.92805	−	6.77187i	0.465752	−	0.532048i
$163$	2.02983	+	3.51577i	0.158988	+	0.275376i	0.934504	−	0.355952i	$-0.115843\pi$
$163$	2.02983	+	3.51577i	0.158988	+	0.275376i	−0.775516	+	0.631328i	$0.782510\pi$
$164$	−5.10442	−	1.85786i	−0.398588	−	0.145074i
$165$	18.3293	−	0.704245i	1.42694	−	0.0548254i
$166$	5.27770	+	4.42851i	0.409629	+	0.343719i
$167$	3.47271	+	2.91395i	0.268726	+	0.225488i	0.767186	−	0.641425i	$-0.221656\pi$
$167$	3.47271	+	2.91395i	0.268726	+	0.225488i	−0.498460	+	0.866913i	$0.666101\pi$
$168$	−2.43484	−	3.88221i	−0.187852	−	0.299519i
$169$	10.6116	+	3.86229i	0.816274	+	0.297099i
$170$	1.75643	−	3.04223i	0.134712	−	0.233328i
$171$	−9.64315	+	20.1274i	−0.737430	+	1.53918i
$172$	−0.946404	−	1.63922i	−0.0721626	−	0.124989i
$173$	11.0308	+	4.01490i	0.838660	+	0.305247i	0.725408	−	0.688319i	$-0.241651\pi$
$173$	11.0308	+	4.01490i	0.838660	+	0.305247i	0.113252	+	0.993566i	$0.463873\pi$
$174$	5.72942	+	4.44414i	0.434346	+	0.336910i
$175$	−5.28281	−	1.93378i	−0.399343	−	0.146180i
$176$	1.08481	−	6.15227i	0.0817708	−	0.463745i
$177$	−2.32785	+	0.949994i	−0.174972	+	0.0714059i
$178$	1.13279	+	6.42440i	0.0849066	+	0.481529i
$179$	−1.42864	−	2.47448i	−0.106782	−	0.184951i	0.807683	−	0.589617i	$-0.200721\pi$
$179$	−1.42864	−	2.47448i	−0.106782	−	0.184951i	−0.914465	+	0.404666i	$0.867388\pi$
$180$	4.89829	+	1.36757i	0.365097	+	0.101932i
$181$	5.39816	+	9.34989i	0.401242	+	0.694972i	0.993876	−	0.110500i	$-0.0352452\pi$
$181$	5.39816	+	9.34989i	0.401242	+	0.694972i	−0.592634	+	0.805472i	$0.701912\pi$
$182$	−1.72307	−	2.99715i	−0.127722	−	0.222163i
$183$	−3.11989	−	14.4297i	−0.230629	−	1.06667i
$184$	0.919745	−	5.21613i	0.0678045	−	0.384538i
$185$	2.75492	−	15.6239i	0.202546	−	1.14869i
$186$	−2.60871	−	4.14252i	−0.191280	−	0.303744i
$187$	9.91694	−	8.32130i	0.725198	−	0.608513i
$188$	−1.26019			−0.0919091
$189$	13.6595	−	1.55526i	0.993580	−	0.113129i
$190$	−12.6113			−0.914920
$191$	−15.3321	+	12.8652i	−1.10939	+	0.930893i	−0.998021	−	0.0628859i	$-0.979970\pi$
$191$	−15.3321	+	12.8652i	−1.10939	+	0.930893i	−0.111374	+	0.993779i	$0.535525\pi$
$192$	0.807797	−	1.53214i	0.0582977	−	0.110573i
$193$	−3.64662	+	20.6810i	−0.262489	+	1.48865i	0.513601	+	0.858029i	$0.328311\pi$
$193$	−3.64662	+	20.6810i	−0.262489	+	1.48865i	−0.776090	+	0.630622i	$0.782800\pi$
$194$	1.64329	−	9.31955i	0.117981	−	0.669104i
$195$	3.65299	+	1.17282i	0.261596	+	0.0839876i
$196$	1.24086	−	6.88914i	0.0886328	−	0.492082i
$197$	−4.04409	−	7.00458i	−0.288130	−	0.499055i	0.685234	−	0.728323i	$-0.259700\pi$
$197$	−4.04409	−	7.00458i	−0.288130	−	0.499055i	−0.973363	+	0.229268i	$0.926367\pi$
$198$	15.2389	+	10.9097i	1.08298	+	0.775320i
$199$	7.02511	+	12.1678i	0.497997	+	0.862555i	0.999997	−	0.00231187i	$-0.000735891\pi$
$199$	7.02511	+	12.1678i	0.497997	+	0.862555i	−0.502001	+	0.864867i	$0.667403\pi$
$200$	−0.369225	−	2.09398i	−0.0261082	−	0.148067i
$201$	7.62455	+	5.91414i	0.537794	+	0.417151i
$202$	2.03151	−	11.5213i	0.142936	−	0.810633i
$203$	1.90329	+	10.9113i	0.133585	+	0.765823i
$204$	3.32314	−	1.35617i	0.232667	−	0.0949510i
$205$	8.65302	+	3.14944i	0.604353	+	0.219967i
$206$	−7.40524	−	12.8262i	−0.515947	−	0.893647i
$207$	12.9201	+	9.24967i	0.898010	+	0.642897i
$208$	0.653339	−	1.13162i	0.0453009	−	0.0784635i
$209$	−43.6725	−	15.8955i	−3.02089	−	1.09951i
$210$	4.12755	+	6.58114i	0.284828	+	0.454142i
$211$	7.20837	+	6.04854i	0.496245	+	0.416399i	0.856258	−	0.516549i	$-0.172783\pi$
$211$	7.20837	+	6.04854i	0.496245	+	0.416399i	−0.360013	+	0.932947i	$0.617228\pi$
$212$	−0.936344	−	0.785686i	−0.0643083	−	0.0539611i
$213$	−7.80781	+	14.8090i	−0.534982	+	1.01470i
$214$	−8.47300	−	3.08392i	−0.579202	−	0.210812i
$215$	1.60435	+	2.77881i	0.109416	+	0.189513i
$216$	3.09815	+	4.17151i	0.210802	+	0.283835i
$217$	1.31207	−	7.36198i	0.0890689	−	0.499764i
$218$	3.22047	+	18.2642i	0.218118	+	1.23701i
$219$	8.72752	−	0.335327i	0.589751	−	0.0226593i
$220$	−1.83898	+	10.4294i	−0.123984	+	0.703147i
$221$	2.54445	−	0.926104i	0.171158	−	0.0622965i
$222$	12.0082	−	10.8885i	0.805940	−	0.730790i
$223$	−20.6225	−	7.50597i	−1.38098	−	0.502637i	−0.458507	−	0.888691i	$-0.651616\pi$
$223$	−20.6225	−	7.50597i	−1.38098	−	0.502637i	−0.922476	+	0.386054i	$0.873838\pi$
$224$	2.48785	−	0.900331i	0.166227	−	0.0601559i
$225$	6.14389	+	1.71533i	0.409593	+	0.114355i
$226$	20.7646			1.38124
$227$	−1.97838	−	11.2199i	−0.131309	−	0.744693i	−0.977359	−	0.211588i	$-0.932136\pi$
$227$	−1.97838	−	11.2199i	−0.131309	−	0.744693i	0.846049	−	0.533104i	$-0.178975\pi$
$228$	−10.1815	−	7.89750i	−0.674288	−	0.523025i
$229$	19.5625	−	7.12016i	1.29273	−	0.470514i	0.398105	−	0.917340i	$-0.369668\pi$
$229$	19.5625	−	7.12016i	1.29273	−	0.470514i	0.894621	+	0.446826i	$0.147446\pi$
$230$	−1.55915	+	8.84241i	−0.102808	+	0.583051i
$231$	5.99858	+	27.9927i	0.394678	+	1.84178i
$232$	−3.20693	+	2.69094i	−0.210545	+	0.176669i
$233$	−2.96744			−0.194403			−0.0972017	−	0.995265i	$-0.530989\pi$
$233$	−2.96744			−0.194403			−0.0972017	+	0.995265i	$0.530989\pi$
$234$	2.21473	+	3.23445i	0.144781	+	0.211443i
$235$	2.13629			0.139356
$236$	−0.252067	−	1.42954i	−0.0164082	−	0.0930553i
$237$	8.46823	−	7.67861i	0.550071	−	0.498779i
$238$	5.14853	+	1.88463i	0.333729	+	0.122162i
$239$	0.0373684	−	0.0136010i	0.00241716	−	0.000879776i	−0.340811	−	0.940132i	$-0.610702\pi$
$239$	0.0373684	−	0.0136010i	0.00241716	−	0.000879776i	0.343228	+	0.939252i	$0.388479\pi$
$240$	−1.36938	+	2.59730i	−0.0883931	+	0.167655i
$241$	−17.7989	−	6.47826i	−1.14653	−	0.417301i	−0.302260	−	0.953226i	$-0.597741\pi$
$241$	−17.7989	−	6.47826i	−1.14653	−	0.417301i	−0.844266	+	0.535924i	$0.819963\pi$
$242$	−14.0136	+	24.2723i	−0.900831	+	1.56029i
$243$	−15.3020	+	2.97485i	−0.981622	+	0.190837i
$244$	8.52348			0.545660
$245$	−2.10351	+	11.6785i	−0.134388	+	0.746112i
$246$	5.01362	+	7.96139i	0.319656	+	0.507600i
$247$	−7.44664	−	6.24848i	−0.473819	−	0.397581i
$248$	2.65596	−	0.966690i	0.168654	−	0.0613849i
$249$	−2.52181	−	11.6635i	−0.159813	−	0.739146i
$250$	2.09776	+	11.8970i	0.132674	+	0.752431i
$251$	−9.77360	−	16.9284i	−0.616904	−	1.06851i	−0.990047	−	0.140736i	$-0.955053\pi$
$251$	−9.77360	−	16.9284i	−0.616904	−	1.06851i	0.373143	−	0.927774i	$-0.378280\pi$
$252$	−0.788963	+	7.89795i	−0.0497000	+	0.497524i
$253$	−16.5444	+	28.6558i	−1.04014	+	1.80157i
$254$	−2.96241	−	1.07823i	−0.185878	−	0.0676542i
$255$	−5.63341	+	2.29899i	−0.352778	+	0.143968i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−12.9421	+	4.71055i	−0.807308	+	0.293836i	−0.712511	−	0.701661i	$-0.752442\pi$
$257$	−12.9421	+	4.71055i	−0.807308	+	0.293836i	−0.0947967	+	0.995497i	$0.530220\pi$
$258$	−0.444917	+	3.24811i	−0.0276993	+	0.202218i
$259$	24.7608	+	0.0454909i	1.53856	+	0.00282667i
$260$	−1.10754	+	1.91832i	−0.0686869	+	0.118969i
$261$	−3.12345	−	12.1645i	−0.193337	−	0.752961i
$262$	21.6690			1.33872
$263$	10.0155	−	8.40396i	0.617579	−	0.518211i	−0.279462	−	0.960157i	$-0.590156\pi$
$263$	10.0155	−	8.40396i	0.617579	−	0.518211i	0.897042	+	0.441946i	$0.145712\pi$
$264$	−8.01579	+	7.26836i	−0.493338	+	0.447336i
$265$	1.58729	+	1.33190i	0.0975066	+	0.0818178i
$266$	−3.38226	−	19.3900i	−0.207380	−	1.18888i
$267$	5.26967	−	9.99495i	0.322498	−	0.611681i
$268$	−4.26770	+	3.58102i	−0.260691	+	0.218746i
$269$	7.37085	−	12.7667i	0.449409	−	0.778399i	−0.548939	−	0.835862i	$-0.684968\pi$
$269$	7.37085	−	12.7667i	0.449409	−	0.778399i	0.998348	+	0.0574638i	$0.0183014\pi$
$270$	−5.25199	−	7.07156i	−0.319626	−	0.430361i
$271$	−9.09135	−	15.7467i	−0.552260	−	0.956542i	−0.998111	−	0.0614351i	$-0.980432\pi$
$271$	−9.09135	−	15.7467i	−0.552260	−	0.956542i	0.445851	−	0.895107i	$-0.352901\pi$
$272$	0.359840	+	2.04075i	0.0218185	+	0.123739i
$273$	−0.823523	+	5.93105i	−0.0498419	+	0.358964i
$274$	17.4902	−	6.36590i	1.05662	−	0.384578i
$275$	−2.30662	+	13.0815i	−0.139094	+	0.788843i
$276$	−6.79609	+	6.16239i	−0.409077	+	0.370932i
$277$	10.5416	−	8.84542i	0.633381	−	0.531470i	−0.268597	−	0.963253i	$-0.586560\pi$
$277$	10.5416	−	8.84542i	0.633381	−	0.531470i	0.901977	+	0.431783i	$0.142115\pi$
$278$	3.92859	−	6.80451i	0.235621	−	0.408108i
$279$	−0.827334	+	8.43878i	−0.0495312	+	0.505217i
$280$	−4.21742	+	1.52624i	−0.252039	+	0.0912106i
$281$	−12.2374	+	10.2684i	−0.730021	+	0.612561i	−0.930137	−	0.367212i	$-0.880312\pi$
$281$	−12.2374	+	10.2684i	−0.730021	+	0.612561i	0.200116	+	0.979772i	$0.435868\pi$
$282$	1.72470	+	1.33780i	0.102704	+	0.0796646i
$283$	6.79540	+	5.70201i	0.403944	+	0.338950i	0.822016	−	0.569465i	$-0.192849\pi$
$283$	6.79540	+	5.70201i	0.403944	+	0.338950i	−0.418072	+	0.908414i	$0.637294\pi$
$284$	−7.40425	−	6.21291i	−0.439362	−	0.368668i
$285$	17.2597	+	13.3879i	1.02238	+	0.793030i
$286$	−6.25327	+	5.24711i	−0.369763	+	0.310268i
$287$	−2.52162	+	14.1488i	−0.148847	+	0.835177i
$288$	−2.73204	+	1.23934i	−0.160987	+	0.0730290i
$289$	6.35292	−	11.0036i	0.373701	−	0.647269i
$290$	5.43641	−	4.56169i	0.319237	−	0.267871i
$291$	−12.1424	+	11.0102i	−0.711802	+	0.645429i
$292$	−0.875631	+	4.96595i	−0.0512424	+	0.290610i
$293$	−18.0435	+	6.56729i	−1.05411	+	0.383665i	−0.810213	−	0.586135i	$-0.800649\pi$
$293$	−18.0435	+	6.56729i	−1.05411	+	0.383665i	−0.243899	+	0.969801i	$0.578427\pi$
$294$	−9.01160	+	8.11117i	−0.525567	+	0.473053i
$295$	0.427305	+	2.42337i	0.0248786	+	0.141094i
$296$	4.67936	+	8.10490i	0.271983	+	0.471088i
$297$	−9.27434	−	31.1083i	−0.538152	−	1.80508i
$298$	4.21597	−	7.30228i	0.244225	−	0.423010i
$299$	−5.30176	+	4.44870i	−0.306609	+	0.257275i
$300$	−1.71761	+	3.25777i	−0.0991660	+	0.188088i
$301$	−3.84218	+	3.21196i	−0.221460	+	0.185134i
$302$	−9.43605	−	7.91779i	−0.542984	−	0.455617i
$303$	−15.0110	+	13.6113i	−0.862361	+	0.781950i
$304$	5.69891	−	4.78195i	0.326855	−	0.274264i
$305$	−14.4490			−0.827350
$306$	−5.98772	−	1.67173i	−0.342295	−	0.0955664i
$307$	4.64779	−	8.05021i	0.265264	−	0.459450i	−0.702369	−	0.711813i	$-0.747874\pi$
$307$	4.64779	−	8.05021i	0.265264	−	0.459450i	0.967633	+	0.252363i	$0.0812077\pi$
$308$	−16.5285	−	0.0303663i	−0.941797	−	0.00173028i
$309$	−3.48130	+	25.4152i	−0.198044	+	1.44582i
$310$	−4.50239	+	1.63874i	−0.255719	+	0.0930740i
$311$	17.2554	+	14.4790i	0.978466	+	0.821030i	0.983857	−	0.178955i	$-0.0572717\pi$
$311$	17.2554	+	14.4790i	0.978466	+	0.821030i	−0.00539151	+	0.999985i	$0.501716\pi$
$312$	−2.09546	+	0.855154i	−0.118632	+	0.0484136i
$313$	−13.3198	−	4.84803i	−0.752882	−	0.274027i	−0.0630642	−	0.998009i	$-0.520087\pi$
$313$	−13.3198	−	4.84803i	−0.752882	−	0.274027i	−0.689818	+	0.723983i	$0.742310\pi$
$314$	6.13893	−	10.6329i	0.346440	−	0.600052i
$315$	1.33745	−	13.3886i	0.0753570	−	0.754364i
$316$	3.29990	+	5.71559i	0.185634	+	0.321527i
$317$	−0.460115	−	2.60944i	−0.0258427	−	0.146561i	0.969156	−	0.246447i	$-0.0792632\pi$
$317$	−0.460115	−	2.60944i	−0.0258427	−	0.146561i	−0.994999	+	0.0998863i	$0.968152\pi$
$318$	0.447408	+	2.06929i	0.0250894	+	0.116040i
$319$	24.5757	−	8.94483i	1.37598	−	0.500814i
$320$	−1.29860	−	1.08966i	−0.0725940	−	0.0609136i
$321$	8.32228	+	13.2154i	0.464504	+	0.737611i
$322$	−14.0135	−	0.0257457i	−0.780940	−	0.00143475i
$323$	15.4162			0.857780
$324$	0.188280	−	8.99803i	0.0104600	−	0.499891i
$325$	−1.38919	+	2.40614i	−0.0770581	+	0.133469i
$326$	3.81483	+	1.38848i	0.211284	+	0.0769011i
$327$	14.9814	−	28.4151i	0.828471	−	1.57136i
$328$	−5.10442	+	1.85786i	−0.281844	+	0.102583i
$329$	0.572938	+	3.28457i	0.0315871	+	0.181084i
$330$	13.5884	−	12.3213i	0.748017	−	0.678268i
$331$	2.80470	+	15.9062i	0.154160	+	0.874287i	0.959549	+	0.281540i	$0.0908453\pi$
$331$	2.80470	+	15.9062i	0.154160	+	0.874287i	−0.805389	+	0.592746i	$0.798044\pi$
$332$	6.88954			0.378113
$333$	−27.9934	+	2.15429i	−1.53403	+	0.118054i
$334$	4.53330			0.248051
$335$	7.23462	−	6.07056i	0.395269	−	0.331670i
$336$	−4.36063	−	1.40886i	−0.237892	−	0.0768597i
$337$	3.43130	−	19.4599i	0.186915	−	1.06005i	−0.736556	−	0.676377i	$-0.763549\pi$
$337$	3.43130	−	19.4599i	0.186915	−	1.06005i	0.923470	−	0.383670i	$-0.125340\pi$
$338$	10.6116	−	3.86229i	0.577193	−	0.210081i
$339$	−28.4183	−	22.0432i	−1.54347	−	1.19722i
$340$	−0.610002	−	3.45949i	−0.0330820	−	0.187617i
$341$	−17.6571			−0.956187
$342$	5.55055	+	21.6170i	0.300139	+	1.16891i
$343$	−18.5200	−	0.102076i	−0.999985	−	0.00551161i
$344$	−1.77866	−	0.647378i	−0.0958988	−	0.0349043i
$345$	11.5208	−	10.4465i	0.620257	−	0.562421i
$346$	11.0308	−	4.01490i	0.593022	−	0.215842i
$347$	−0.399049	+	2.26312i	−0.0214221	+	0.121491i	−0.993644	−	0.112572i	$-0.964091\pi$
$347$	−0.399049	+	2.26312i	−0.0214221	+	0.121491i	0.972221	+	0.234063i	$0.0752021\pi$
$348$	7.24563	−	0.278390i	0.388407	−	0.0149233i
$349$	−1.98276	−	11.2448i	−0.106135	−	0.601920i	−0.990761	−	0.135619i	$-0.956698\pi$
$349$	−1.98276	−	11.2448i	−0.106135	−	0.601920i	0.884626	−	0.466301i	$-0.154413\pi$
$350$	−5.28988	+	1.91436i	−0.282756	+	0.102327i
$351$	0.402559	−	6.77776i	0.0214870	−	0.361770i
$352$	−3.12359	−	5.41022i	−0.166488	−	0.288366i
$353$	8.03755	+	2.92543i	0.427795	+	0.155705i	0.546939	−	0.837172i	$-0.315793\pi$
$353$	8.03755	+	2.92543i	0.427795	+	0.155705i	−0.119144	+	0.992877i	$0.538015\pi$
$354$	−1.17259	+	2.22405i	−0.0623227	+	0.118207i
$355$	12.5517	+	10.5321i	0.666176	+	0.558988i
$356$	4.99730	+	4.19323i	0.264856	+	0.222241i
$357$	−5.04556	−	8.04486i	−0.267039	−	0.425779i
$358$	−2.68497	−	0.977249i	−0.141905	−	0.0516492i
$359$	4.47980	−	7.75924i	0.236435	−	0.409517i	−0.723254	−	0.690582i	$-0.757354\pi$
$359$	4.47980	−	7.75924i	0.236435	−	0.409517i	0.959689	+	0.281065i	$0.0906877\pi$
$360$	4.63136	−	2.10094i	0.244094	−	0.110729i
$361$	−18.1723	−	31.4754i	−0.956438	−	1.65660i
$362$	10.1452	+	3.69256i	0.533221	+	0.194077i
$363$	44.9460	−	18.3424i	2.35905	−	0.962727i
$364$	−3.24648	−	1.18838i	−0.170162	−	0.0622881i
$365$	1.48437	−	8.41829i	0.0776956	−	0.440634i
$366$	−11.6652	−	9.04835i	−0.609749	−	0.472965i
$367$	1.66934	+	9.46732i	0.0871391	+	0.494190i	0.996874	+	0.0790017i	$0.0251733\pi$
$367$	1.66934	+	9.46732i	0.0871391	+	0.494190i	−0.909735	+	0.415188i	$0.863716\pi$
$368$	−2.64830	−	4.58699i	−0.138052	−	0.239113i
$369$	1.59003	−	16.2183i	0.0827737	−	0.844289i
$370$	−7.93248	−	13.7395i	−0.412390	−	0.714280i
$371$	−1.62211	+	2.79769i	−0.0842156	+	0.145249i
$372$	−4.66115	−	1.49650i	−0.241669	−	0.0775901i
$373$	0.268372	−	1.52201i	0.0138958	−	0.0788068i	−0.977071	−	0.212913i	$-0.931705\pi$
$373$	0.268372	−	1.52201i	0.0138958	−	0.0788068i	0.990967	+	0.134106i	$0.0428162\pi$
$374$	2.24799	−	12.7490i	0.116241	−	0.659233i
$375$	9.75859	−	18.5091i	0.503932	−	0.955804i
$376$	−0.965365	+	0.810037i	−0.0497849	+	0.0417745i
$377$	5.47022			0.281731
$378$	9.46406	−	9.97154i	0.486779	−	0.512881i
$379$	−11.2455			−0.577644			−0.288822	−	0.957383i	$-0.593264\pi$
$379$	−11.2455			−0.577644			−0.288822	+	0.957383i	$0.593264\pi$
$380$	−9.66081	+	8.10638i	−0.495589	+	0.415849i
$381$	2.90972	+	4.62049i	0.149069	+	0.236715i
$382$	−3.47551	+	19.7106i	−0.177823	+	1.00848i
$383$	4.04411	−	22.9353i	0.206644	−	1.17194i	−0.688187	−	0.725533i	$-0.741593\pi$
$383$	4.04411	−	22.9353i	0.206644	−	1.17194i	0.894831	−	0.446404i	$-0.147296\pi$
$384$	−0.366035	−	1.69293i	−0.0186791	−	0.0863921i
$385$	28.0191	+	0.0514771i	1.42799	+	0.00262352i
$386$	10.5000	+	18.1866i	0.534437	+	0.925672i
$387$	4.05703	−	3.97303i	0.206231	−	0.201960i
$388$	−4.73166	−	8.19547i	−0.240214	−	0.416062i
$389$	−1.53598	−	8.71099i	−0.0778774	−	0.441665i	−0.998668	−	0.0516063i	$-0.983566\pi$
$389$	−1.53598	−	8.71099i	−0.0778774	−	0.441665i	0.920790	−	0.390058i	$-0.127545\pi$
$390$	3.55223	−	1.44966i	0.179874	−	0.0734064i
$391$	1.90593	−	10.8091i	0.0963870	−	0.546638i
$392$	−3.47770	−	6.07500i	−0.175650	−	0.306834i
$393$	−29.6561	−	23.0034i	−1.49595	−	1.16037i
$394$	−7.60041	−	2.76632i	−0.382903	−	0.139365i
$395$	−5.59400	−	9.68909i	−0.281465	−	0.487511i
$396$	18.6863	−	1.43804i	0.939022	−	0.0722644i
$397$	−1.63892	+	2.83870i	−0.0822552	+	0.142470i	−0.904218	−	0.427071i	$-0.859546\pi$
$397$	−1.63892	+	2.83870i	−0.0822552	+	0.142470i	0.821963	+	0.569541i	$0.192879\pi$
$398$	13.2029	+	4.80546i	0.661801	+	0.240876i
$399$	−15.9551	+	30.1276i	−0.798753	+	1.50827i
$400$	−1.62883	−	1.36675i	−0.0814414	−	0.0683375i
$401$	17.5385	+	14.7166i	0.875833	+	0.734911i	0.965318	−	0.261077i	$-0.0840777\pi$
$401$	17.5385	+	14.7166i	0.875833	+	0.734911i	−0.0894852	+	0.995988i	$0.528522\pi$
$402$	9.64228	−	0.370473i	0.480913	−	0.0184775i
$403$	−3.47049	−	1.26315i	−0.172877	−	0.0629222i
$404$	−5.84950	−	10.1316i	−0.291023	−	0.504067i
$405$	−0.319173	+	15.2535i	−0.0158598	+	0.757952i
$406$	8.47165	+	7.13513i	0.420441	+	0.354110i
$407$	−10.1525	−	57.5775i	−0.503239	−	2.85401i
$408$	1.67395	−	3.17496i	0.0828727	−	0.157184i
$409$	−4.49402	+	25.4869i	−0.222215	+	1.26024i	0.645723	+	0.763572i	$0.276556\pi$
$409$	−4.49402	+	25.4869i	−0.222215	+	1.26024i	−0.867938	+	0.496673i	$0.834555\pi$
$410$	8.65302	−	3.14944i	0.427342	−	0.155540i
$411$	−30.6949	−	9.85485i	−1.51407	−	0.486104i
$412$	−13.9173	−	5.06548i	−0.685656	−	0.249558i
$413$	−3.61135	+	1.30692i	−0.177703	+	0.0643091i
$414$	15.8430	−	1.21923i	0.778639	−	0.0599218i
$415$	−11.6792			−0.573308
$416$	−0.226902	−	1.28683i	−0.0111248	−	0.0630919i
$417$	−12.6002	+	5.14212i	−0.617033	+	0.251810i
$418$	−43.6725	+	15.8955i	−2.13609	+	0.777473i
$419$	0.330193	−	1.87262i	0.0161310	−	0.0914835i	−0.975679	−	0.219202i	$-0.929654\pi$
$419$	0.330193	−	1.87262i	0.0161310	−	0.0914835i	0.991810	+	0.127719i	$0.0407656\pi$
$420$	7.39216	+	2.38831i	0.360700	+	0.116537i
$421$	1.82280	−	1.52951i	0.0888380	−	0.0745439i	−0.597287	−	0.802027i	$-0.703755\pi$
$421$	1.82280	−	1.52951i	0.0888380	−	0.0745439i	0.686125	+	0.727484i	$0.259310\pi$
$422$	9.40986			0.458065
$423$	−0.940234	−	3.66180i	−0.0457157	−	0.178043i
$424$	−1.22231			−0.0593606
$425$	−0.765122	−	4.33922i	−0.0371139	−	0.210483i
$426$	3.53793	+	16.3631i	0.171413	+	0.792797i
$427$	−3.87513	−	22.2156i	−0.187531	−	1.07509i
$428$	−8.47300	+	3.08392i	−0.409558	+	0.149067i
$429$	14.1284	−	0.542838i	0.682126	−	0.0262085i
$430$	3.01519	+	1.09744i	0.145405	+	0.0529232i
$431$	−9.56044	+	16.5592i	−0.460510	+	0.797627i	−0.998986	−	0.0450138i	$-0.985667\pi$
$431$	−9.56044	+	16.5592i	−0.460510	+	0.797627i	0.538476	+	0.842641i	$0.319000\pi$
$432$	5.05471	+	1.20411i	0.243195	+	0.0579329i
$433$	39.3705			1.89202			0.946012	−	0.324132i	$-0.105072\pi$
$433$	39.3705			1.89202			0.946012	+	0.324132i	$0.105072\pi$
$434$	−3.72709	−	6.48299i	−0.178906	−	0.311193i
$435$	−12.2828	+	0.471927i	−0.588916	+	0.0226272i
$436$	14.2070	+	11.9211i	0.680393	+	0.570918i
$437$	−37.0272	+	13.4768i	−1.77125	+	0.644682i
$438$	6.47013	−	5.86682i	0.309155	−	0.280327i
$439$	−3.91770	−	22.2184i	−0.186982	−	1.06043i	−0.923383	−	0.383881i	$-0.874587\pi$
$439$	−3.91770	−	22.2184i	−0.186982	−	1.06043i	0.736401	−	0.676546i	$-0.236524\pi$
$440$	5.29512	+	9.17142i	0.252435	+	0.437230i
$441$	20.9439	−	1.53439i	0.997327	−	0.0730661i
$442$	1.35387	−	2.34498i	0.0643972	−	0.111539i
$443$	21.7579	+	7.91924i	1.03375	+	0.376254i	0.802508	−	0.596642i	$-0.203499\pi$
$443$	21.7579	+	7.91924i	1.03375	+	0.376254i	0.231243	+	0.972896i	$0.425721\pi$
$444$	2.19983	−	16.0598i	0.104399	−	0.762166i
$445$	−8.47143	−	7.10838i	−0.401585	−	0.336969i
$446$	−20.6225	+	7.50597i	−0.976503	+	0.355418i
$447$	−13.5219	+	5.51827i	−0.639564	+	0.261005i
$448$	1.32708	−	2.28885i	0.0626988	−	0.108138i
$449$	−17.1874	+	29.7695i	−0.811125	+	1.40491i	0.100953	+	0.994891i	$0.467811\pi$
$449$	−17.1874	+	29.7695i	−0.811125	+	1.40491i	−0.912078	+	0.410018i	$0.865522\pi$
$450$	5.80909	−	2.63520i	0.273843	−	0.124224i
$451$	33.9347			1.59792
$452$	15.9066	−	13.3472i	0.748184	−	0.627801i
$453$	4.50878	+	20.8533i	0.211841	+	0.979776i
$454$	−8.72755	−	7.32329i	−0.409604	−	0.343699i
$455$	5.50344	+	2.01455i	0.258005	+	0.0944434i
$456$	−12.8759	+	0.494715i	−0.602970	+	0.0231672i
$457$	−5.95597	+	4.99766i	−0.278609	+	0.233780i	−0.771374	−	0.636382i	$-0.780430\pi$
$457$	−5.95597	+	4.99766i	−0.278609	+	0.233780i	0.492766	+	0.870162i	$0.335986\pi$
$458$	10.4090	−	18.0289i	0.486380	−	0.842435i
$459$	6.42009	+	8.64435i	0.299664	+	0.403484i
$460$	4.48941	+	7.77588i	0.209320	+	0.362552i
$461$	−3.93791	−	22.3330i	−0.183407	−	1.04015i	−0.927985	−	0.372617i	$-0.878461\pi$
$461$	−3.93791	−	22.3330i	−0.183407	−	1.04015i	0.744578	−	0.667535i	$-0.232651\pi$
$462$	22.5885	+	17.5878i	1.05091	+	0.818260i
$463$	−32.9983	+	12.0104i	−1.53356	+	0.558170i	−0.964490	−	0.264119i	$-0.914919\pi$
$463$	−32.9983	+	12.0104i	−1.53356	+	0.558170i	−0.569070	+	0.822289i	$0.692696\pi$
$464$	−0.726953	+	4.12275i	−0.0337479	+	0.191394i
$465$	7.90160	+	2.53688i	0.366428	+	0.117645i
$466$	−2.27319	+	1.90743i	−0.105303	+	0.0883601i
$467$	−4.99826	+	8.65724i	−0.231292	+	0.400609i	−0.958189	−	0.286138i	$-0.907629\pi$
$467$	−4.99826	+	8.65724i	−0.231292	+	0.400609i	0.726897	+	0.686747i	$0.240962\pi$
$468$	3.77564	+	1.05413i	0.174529	+	0.0487273i
$469$	11.2738	+	9.49522i	0.520577	+	0.438449i
$470$	1.63649	−	1.37318i	0.0754857	−	0.0633400i
$471$	−19.6894	+	8.03523i	−0.907241	+	0.370244i
$472$	−1.11199	−	0.933067i	−0.0511833	−	0.0429479i
$473$	9.05826	+	7.60078i	0.416499	+	0.349484i
$474$	1.55133	−	11.3254i	0.0712548	−	0.520194i
$475$	−12.1175	+	10.1678i	−0.555989	+	0.466530i
$476$	5.15542	−	1.86570i	0.236298	−	0.0855142i
$477$	1.58439	−	3.30697i	0.0725443	−	0.151416i
$478$	0.0198833	−	0.0344389i	0.000909443	−	0.00157520i
$479$	14.8336	−	12.4469i	0.677765	−	0.568712i	−0.237587	−	0.971366i	$-0.576357\pi$
$479$	14.8336	−	12.4469i	0.677765	−	0.568712i	0.915352	+	0.402654i	$0.131912\pi$
$480$	0.620504	+	2.86986i	0.0283220	+	0.130991i
$481$	2.12352	−	12.0431i	0.0968241	−	0.549117i
$482$	−17.7989	+	6.47826i	−0.810716	+	0.295077i
$483$	19.1514	+	14.9116i	0.871420	+	0.678502i
$484$	4.86689	+	27.6015i	0.221222	+	1.25461i
$485$	8.02112	+	13.8930i	0.364220	+	0.630848i
$486$	−9.80979	+	12.1148i	−0.444981	+	0.549538i
$487$	8.70939	−	15.0851i	0.394660	−	0.683571i	−0.598398	−	0.801199i	$-0.704196\pi$
$487$	8.70939	−	15.0851i	0.394660	−	0.683571i	0.993058	+	0.117628i	$0.0375290\pi$
$488$	6.52937	−	5.47879i	0.295571	−	0.248013i
$489$	−3.74697	−	5.95002i	−0.169444	−	0.269069i
$490$	5.89541	+	10.2984i	0.266328	+	0.465232i
$491$	14.8274	+	12.4416i	0.669149	+	0.561483i	0.912813	−	0.408377i	$-0.133905\pi$
$491$	14.8274	+	12.4416i	0.669149	+	0.561483i	−0.243664	+	0.969860i	$0.578349\pi$
$492$	8.95813	+	2.87609i	0.403864	+	0.129664i
$493$	−6.64552	+	5.57626i	−0.299299	+	0.251142i
$494$	−9.72090			−0.437364
$495$	−31.6771	+	2.43778i	−1.42378	+	0.109570i
$496$	1.41321	−	2.44775i	0.0634549	−	0.109907i
$497$	−12.8270	+	22.1231i	−0.575370	+	0.992355i
$498$	−9.42899	−	7.31379i	−0.422523	−	0.327739i
$499$	−36.1469	+	13.1564i	−1.61816	+	0.588961i	−0.983030	−	0.183447i	$-0.941274\pi$
$499$	−36.1469	+	13.1564i	−1.61816	+	0.588961i	−0.635127	+	0.772408i	$0.719052\pi$
$500$	9.25420	+	7.76520i	0.413861	+	0.347270i
$501$	−6.20425	−	4.81246i	−0.277186	−	0.215005i
$502$	−18.3684	−	6.68554i	−0.819820	−	0.298390i
$503$	−10.1741	+	17.6220i	−0.453640	+	0.785727i	−0.998609	−	0.0527289i	$-0.983208\pi$
$503$	−10.1741	+	17.6220i	−0.453640	+	0.785727i	0.544969	+	0.838456i	$0.316541\pi$
$504$	4.47232	+	6.55731i	0.199213	+	0.292086i
$505$	9.91609	+	17.1752i	0.441260	+	0.764285i
$506$	5.74581	+	32.5861i	0.255433	+	1.44863i
$507$	−18.6231	−	5.97909i	−0.827079	−	0.265541i
$508$	−2.96241	+	1.07823i	−0.131436	+	0.0478387i
$509$	9.70115	+	8.14024i	0.429996	+	0.360810i	0.831950	−	0.554850i	$-0.187224\pi$
$509$	9.70115	+	8.14024i	0.429996	+	0.360810i	−0.401954	+	0.915660i	$0.631669\pi$
$510$	−2.83768	+	5.38221i	−0.125655	+	0.238328i
$511$	13.3413	+	0.0245109i	0.590186	+	0.00108430i
$512$	1.00000			0.0441942
$513$	15.3516	−	35.4772i	0.677792	−	1.56636i
$514$	−6.88636	+	11.9275i	−0.303745	+	0.526101i
$515$	23.5926	+	8.58702i	1.03962	+	0.378389i
$516$	1.74702	+	2.77418i	0.0769082	+	0.122127i
$517$	7.39789	−	2.69261i	0.325359	−	0.118421i
$518$	18.9971	−	15.8811i	0.834686	−	0.697776i
$519$	−19.3589	−	6.21534i	−0.849761	−	0.272823i
$520$	0.384646	+	2.18143i	0.0168678	+	0.0956622i
$521$	13.9161			0.609676			0.304838	−	0.952404i	$-0.401398\pi$
$521$	13.9161			0.609676			0.304838	+	0.952404i	$0.401398\pi$
$522$	−10.2119	−	7.31080i	−0.446961	−	0.319985i
$523$	−9.94983			−0.435075			−0.217538	−	0.976052i	$-0.569803\pi$
$523$	−9.94983			−0.435075			−0.217538	+	0.976052i	$0.569803\pi$
$524$	16.5994	−	13.9286i	0.725150	−	0.608473i
$525$	9.27194	+	2.99564i	0.404661	+	0.130740i
$526$	2.27032	−	12.8756i	0.0989906	−	0.561404i
$527$	5.50378	−	2.00321i	0.239748	−	0.0872612i
$528$	−1.46844	+	10.7203i	−0.0639057	+	0.466543i
$529$	0.877612	+	4.97718i	0.0381570	+	0.216399i
$530$	2.07206			0.0900047
$531$	3.96581	−	1.79903i	0.172102	−	0.0780711i
$532$	−15.0546	−	12.6795i	−0.652701	−	0.549728i
$533$	6.66983	+	2.42762i	0.288902	+	0.105152i
$534$	−2.38783	−	11.0439i	−0.103332	−	0.477914i
$535$	14.3635	−	5.22787i	0.620986	−	0.226021i
$536$	−0.967408	+	5.48644i	−0.0417857	+	0.236978i
$537$	2.63721	+	4.18776i	0.113804	+	0.180715i
$538$	−2.55987	−	14.5177i	−0.110364	−	0.625904i
$539$	7.43539	+	43.0935i	0.320265	+	1.85617i
$540$	−8.56877	−	2.04122i	−0.368741	−	0.0878399i
$541$	9.79775	+	16.9702i	0.421238	+	0.729606i	0.996061	−	0.0886719i	$-0.0282623\pi$
$541$	9.79775	+	16.9702i	0.421238	+	0.729606i	−0.574823	+	0.818278i	$0.694929\pi$
$542$	−17.0861	−	6.21885i	−0.733913	−	0.267122i
$543$	−9.96476	−	15.8236i	−0.427629	−	0.679054i
$544$	1.58743	+	1.33201i	0.0680603	+	0.0571094i
$545$	−24.0838	−	20.2087i	−1.03164	−	0.865646i
$546$	3.18155	+	5.07280i	0.136158	+	0.217096i
$547$	−14.4391	−	5.25541i	−0.617372	−	0.224705i	0.0143537	−	0.999897i	$-0.495431\pi$
$547$	−14.4391	−	5.25541i	−0.617372	−	0.224705i	−0.631726	+	0.775192i	$0.717653\pi$
$548$	9.30633	−	16.1190i	0.397547	−	0.688571i
$549$	6.35939	+	24.7670i	0.271412	+	1.05703i
$550$	6.64164	+	11.5037i	0.283201	+	0.490518i
$551$	29.2657	+	10.6519i	1.24676	+	0.453784i
$552$	−1.24500	+	9.08911i	−0.0529908	+	0.386858i
$553$	13.3968	−	11.1994i	0.569691	−	0.476247i
$554$	2.38958	−	13.5520i	0.101523	−	0.575768i
$555$	−3.72916	+	27.2247i	−0.158294	+	1.15562i
$556$	−1.36438	−	7.73781i	−0.0578628	−	0.328156i
$557$	0.0271240	+	0.0469801i	0.00114928	+	0.00199061i	0.866599	−	0.499004i	$-0.166301\pi$
$557$	0.0271240	+	0.0469801i	0.00114928	+	0.00199061i	−0.865450	+	0.500995i	$0.832968\pi$
$558$	4.79057	+	6.99628i	0.202801	+	0.296176i
$559$	1.23665	+	2.14193i	0.0523045	+	0.0905941i
$560$	−2.24968	+	3.88007i	−0.0950662	+	0.163963i
$561$	−16.6106	+	15.0618i	−0.701301	+	0.635908i
$562$	−2.77399	+	15.7321i	−0.117014	+	0.663618i
$563$	−2.64187	+	14.9828i	−0.111342	+	0.631449i	0.877155	+	0.480207i	$0.159438\pi$
$563$	−2.64187	+	14.9828i	−0.111342	+	0.631449i	−0.988497	+	0.151242i	$0.951673\pi$
$564$	2.18111	−	0.0838021i	0.0918414	−	0.00352871i
$565$	−26.9649	+	22.6263i	−1.13442	+	0.951894i
$566$	8.87076			0.372866
$567$	−23.5380	+	3.60015i	−0.988504	+	0.151192i
$568$	−9.66557			−0.405558
$569$	−17.9447	+	15.0574i	−0.752283	+	0.631240i	−0.936106	−	0.351719i	$-0.885597\pi$
$569$	−17.9447	+	15.0574i	−0.752283	+	0.631240i	0.183823	+	0.982959i	$0.441153\pi$
$570$	21.8273	−	0.838643i	0.914245	−	0.0351269i
$571$	−1.60735	+	9.11572i	−0.0672654	+	0.381481i	0.932527	+	0.361101i	$0.117599\pi$
$571$	−1.60735	+	9.11572i	−0.0672654	+	0.381481i	−0.999792	+	0.0203806i	$0.993512\pi$
$572$	−1.41750	+	8.03905i	−0.0592687	+	0.336129i
$573$	25.6809	−	23.2863i	1.07284	−	0.972800i
$574$	7.16299	+	12.4595i	0.298977	+	0.520048i
$575$	5.63104	+	9.75324i	0.234830	+	0.406738i
$576$	−1.29623	+	2.70551i	−0.0540095	+	0.112730i
$577$	13.1250	+	22.7331i	0.546400	+	0.946393i	0.998517	+	0.0544343i	$0.0173355\pi$
$577$	13.1250	+	22.7331i	0.546400	+	0.946393i	−0.452117	+	0.891959i	$0.649331\pi$
$578$	−2.20635	−	12.5128i	−0.0917719	−	0.520464i
$579$	4.93620	−	36.0366i	0.205141	−	1.49763i
$580$	1.23233	−	6.98891i	0.0511698	−	0.290199i
$581$	−3.13228	−	17.9569i	−0.129949	−	0.744977i
$582$	−2.22442	+	16.2393i	−0.0922050	+	0.673141i
$583$	7.17549	+	2.61166i	0.297178	+	0.108164i
$584$	2.52128	+	4.36698i	0.104331	+	0.180707i
$585$	−6.40049	−	1.78697i	−0.264628	−	0.0738821i
$586$	−9.60074	+	16.6290i	−0.396603	+	0.686937i
$587$	38.4208	+	13.9840i	1.58580	+	0.577183i	0.976454	−	0.215724i	$-0.0692112\pi$
$587$	38.4208	+	13.9840i	1.58580	+	0.577183i	0.609343	+	0.792907i	$0.291433\pi$
$588$	−1.68952	+	12.0061i	−0.0696748	+	0.495122i
$589$	−16.1075	−	13.5158i	−0.663697	−	0.556908i
$590$	1.88504	+	1.58174i	0.0776060	+	0.0651192i
$591$	7.46521	+	11.8544i	0.307078	+	0.487625i
$592$	8.79433	+	3.20087i	0.361445	+	0.131555i
$593$	14.1694	+	24.5421i	0.581867	+	1.00782i	0.995258	+	0.0972697i	$0.0310109\pi$
$593$	14.1694	+	24.5421i	0.581867	+	1.00782i	−0.413391	+	0.910554i	$0.635656\pi$
$594$	−27.1006	−	17.8689i	−1.11195	−	0.733169i
$595$	−8.73948	+	3.16274i	−0.358284	+	0.129660i
$596$	−1.46419	−	8.30385i	−0.0599757	−	0.340139i
$597$	−12.9680	−	20.5926i	−0.530746	−	0.842800i
$598$	−1.20181	+	6.81581i	−0.0491457	+	0.278719i
$599$	25.9357	−	9.43981i	1.05970	−	0.385700i	0.247386	−	0.968917i	$-0.420428\pi$
$599$	25.9357	−	9.43981i	1.05970	−	0.385700i	0.812316	+	0.583217i	$0.198206\pi$
$600$	0.778294	+	3.59965i	0.0317737	+	0.146955i
$601$	25.9677	+	9.45146i	1.05924	+	0.385533i	0.812144	−	0.583457i	$-0.198300\pi$
$601$	25.9677	+	9.45146i	1.05924	+	0.385533i	0.247099	+	0.968990i	$0.420523\pi$
$602$	−0.878671	+	4.93021i	−0.0358120	+	0.200940i
$603$	−13.5897	−	9.72901i	−0.553414	−	0.396196i
$604$	−12.3179			−0.501208
$605$	−8.25037	−	46.7902i	−0.335425	−	1.90229i
$606$	−2.74993	+	20.0758i	−0.111708	+	0.815523i
$607$	−6.02460	+	2.19278i	−0.244531	+	0.0890020i	−0.461378	−	0.887204i	$-0.652645\pi$
$607$	−6.02460	+	2.19278i	−0.244531	+	0.0890020i	0.216847	+	0.976206i	$0.430423\pi$
$608$	1.29184	−	7.32638i	0.0523909	−	0.297124i
$609$	−4.01976	−	18.7584i	−0.162889	−	0.760130i
$610$	−11.0686	+	9.28766i	−0.448155	+	0.376047i
$611$	1.64667			0.0666171
$612$	−5.66143	+	2.56821i	−0.228850	+	0.103814i
$613$	−43.5017			−1.75702			−0.878508	−	0.477728i	$-0.841461\pi$
$613$	−43.5017			−1.75702			−0.878508	+	0.477728i	$0.841461\pi$
$614$	−1.61416	−	9.15437i	−0.0651423	−	0.369440i
$615$	−15.1859	−	4.87555i	−0.612353	−	0.196601i
$616$	−12.6811	+	10.6010i	−0.510934	+	0.427128i
$617$	26.4638	−	9.63205i	1.06539	−	0.387772i	0.250942	−	0.968002i	$-0.419260\pi$
$617$	26.4638	−	9.63205i	1.06539	−	0.387772i	0.814452	+	0.580231i	$0.197038\pi$
$618$	13.6697	+	21.7069i	0.549877	+	0.873179i
$619$	22.9006	+	8.33513i	0.920452	+	0.335017i	0.758418	−	0.651768i	$-0.225973\pi$
$619$	22.9006	+	8.33513i	0.920452	+	0.335017i	0.162034	+	0.986785i	$0.448195\pi$
$620$	−2.39567	+	4.14943i	−0.0962126	+	0.166645i
$621$	−22.9769	−	15.1499i	−0.922031	−	0.607945i
$622$	22.5254			0.903185
$623$	8.65723	−	14.9314i	0.346845	−	0.598212i
$624$	−1.05553	+	2.00202i	−0.0422551	+	0.0801449i
$625$	−7.54362	−	6.32985i	−0.301745	−	0.253194i
$626$	−13.3198	+	4.84803i	−0.532368	+	0.193766i
$627$	76.6442	+	24.6073i	3.06087	+	0.982721i
$628$	−2.13203	−	12.0913i	−0.0850772	−	0.482497i
$629$	9.69675	+	16.7953i	0.386635	+	0.669671i
$630$	−7.58149	−	11.1160i	−0.302054	−	0.442871i
$631$	12.4789	−	21.6141i	0.496778	−	0.860445i	−0.503215	−	0.864161i	$-0.667850\pi$
$631$	12.4789	−	21.6141i	0.496778	−	0.860445i	0.999993	+	0.00371657i	$0.00118303\pi$
$632$	6.20178	+	2.25726i	0.246694	+	0.0897891i
$633$	−12.8783	−	9.98930i	−0.511866	−	0.397039i
$634$	−2.02979	−	1.70319i	−0.0806132	−	0.0676425i
$635$	5.02189	−	1.82782i	0.199288	−	0.0725348i
$636$	1.67285	+	1.29758i	0.0663327	+	0.0514523i
$637$	−1.62140	+	9.00189i	−0.0642424	+	0.356668i
$638$	13.0765	−	22.6491i	0.517702	−	0.896686i
$639$	12.5288	−	26.1503i	0.495630	−	1.03449i
$640$	−1.69520			−0.0670088
$641$	−18.2420	+	15.3069i	−0.720516	+	0.604585i	−0.927528	−	0.373754i	$-0.878070\pi$
$641$	−18.2420	+	15.3069i	−0.720516	+	0.604585i	0.207012	+	0.978338i	$0.433626\pi$
$642$	14.8699	+	4.77412i	0.586869	+	0.188419i
$643$	14.0311	+	11.7735i	0.553331	+	0.464300i	0.876067	−	0.482189i	$-0.160158\pi$
$643$	14.0311	+	11.7735i	0.553331	+	0.464300i	−0.322736	+	0.946489i	$0.604603\pi$
$644$	−10.7515	+	8.98796i	−0.423668	+	0.354175i
$645$	−2.96155	−	4.70280i	−0.116611	−	0.185173i
$646$	11.8095	−	9.90934i	0.464638	−	0.389878i
$647$	18.0908	−	31.3343i	0.711225	−	1.23188i	−0.253173	−	0.967421i	$-0.581474\pi$
$647$	18.0908	−	31.3343i	0.711225	−	1.23188i	0.964398	−	0.264456i	$-0.0851925\pi$
$648$	−5.63959	−	7.01392i	−0.221544	−	0.275533i
$649$	4.53419	+	7.85345i	0.177983	+	0.308275i
$650$	0.482459	+	2.73616i	0.0189236	+	0.107321i
$651$	−1.78132	+	12.8292i	−0.0698156	+	0.502815i
$652$	3.81483	−	1.38848i	0.149400	−	0.0543773i
$653$	1.93084	−	10.9503i	0.0755595	−	0.428519i	−0.923438	−	0.383748i	$-0.874633\pi$
$653$	1.93084	−	10.9503i	0.0755595	−	0.428519i	0.998997	−	0.0447709i	$-0.0142558\pi$
$654$	−6.78847	−	31.3970i	−0.265450	−	1.22772i
$655$	−28.1394	+	23.6118i	−1.09950	+	0.922589i
$656$	−2.71600	+	4.70425i	−0.106042	+	0.183670i
$657$	−15.0831	+	1.16075i	−0.588447	+	0.0452851i
$658$	2.55017	+	2.14785i	0.0994161	+	0.0837318i
$659$	13.7667	−	11.5517i	0.536276	−	0.449989i	−0.333986	−	0.942578i	$-0.608394\pi$
$659$	13.7667	−	11.5517i	0.536276	−	0.449989i	0.870262	+	0.492589i	$0.163949\pi$
$660$	2.48931	−	18.1732i	0.0968962	−	0.707389i
$661$	−36.2561	−	30.4225i	−1.41020	−	1.18330i	−0.956352	−	0.292216i	$-0.905607\pi$
$661$	−36.2561	−	30.4225i	−1.41020	−	1.18330i	−0.453846	−	0.891080i	$-0.649948\pi$
$662$	12.3729	+	10.3821i	0.480885	+	0.403510i
$663$	−4.34228	+	1.77208i	−0.168640	+	0.0688219i
$664$	5.27770	−	4.42851i	0.204814	−	0.171860i
$665$	25.5207	+	21.4944i	0.989649	+	0.833517i
$666$	−20.0595	+	19.6441i	−0.777288	+	0.761194i
$667$	11.0867	−	19.2028i	0.429280	−	0.743534i
$668$	3.47271	−	2.91395i	0.134363	−	0.112744i
$669$	36.1920	+	11.6198i	1.39926	+	0.449246i
$670$	1.63995	−	9.30064i	0.0633570	−	0.359315i
$671$	−50.0365	+	18.2118i	−1.93164	+	0.703059i
$672$	−4.24604	+	1.72371i	−0.163794	+	0.0664936i
$673$	4.00665	+	22.7229i	0.154445	+	0.875902i	0.959291	+	0.282418i	$0.0911367\pi$
$673$	4.00665	+	22.7229i	0.154445	+	0.875902i	−0.804846	+	0.593483i	$0.797752\pi$
$674$	−9.88003	−	17.1127i	−0.380565	−	0.659157i
$675$	−10.7478	−	2.56028i	−0.413681	−	0.0985454i
$676$	5.64630	−	9.77967i	0.217165	−	0.376141i
$677$	1.23585	−	1.03700i	0.0474977	−	0.0398553i	−0.618730	−	0.785604i	$-0.712352\pi$
$677$	1.23585	−	1.03700i	0.0474977	−	0.0398553i	0.666227	+	0.745749i	$0.267908\pi$
$678$	−35.9388	+	1.38083i	−1.38022	+	0.0530305i
$679$	−19.2094	+	16.0586i	−0.737190	+	0.616272i
$680$	−2.69101	−	2.25802i	−0.103195	−	0.0865913i
$681$	4.17024	+	19.2876i	0.159804	+	0.739102i
$682$	−13.5261	+	11.3498i	−0.517943	+	0.434606i
$683$	−2.97731			−0.113924			−0.0569619	−	0.998376i	$-0.518141\pi$
$683$	−2.97731			−0.113924			−0.0569619	+	0.998376i	$0.518141\pi$
$684$	18.1471	+	12.9917i	0.693871	+	0.496751i
$685$	−15.7761	+	27.3250i	−0.602774	+	1.04404i
$686$	−14.2527	+	11.8262i	−0.544172	+	0.451527i
$687$	−33.3848	+	13.6243i	−1.27371	+	0.519799i
$688$	−1.77866	+	0.647378i	−0.0678107	+	0.0246811i
$689$	1.22350	+	1.02664i	0.0466117	+	0.0391118i
$690$	2.11053	−	15.4079i	0.0803465	−	0.586568i
$691$	−25.3368	−	9.22183i	−0.963856	−	0.350815i	−0.188313	−	0.982109i	$-0.560302\pi$
$691$	−25.3368	−	9.22183i	−0.963856	−	0.350815i	−0.775543	+	0.631294i	$0.782524\pi$
$692$	5.86939	−	10.1661i	0.223121	−	0.386456i
$693$	−12.2437	−	48.0501i	−0.465099	−	1.82527i
$694$	1.14902	+	1.99015i	0.0436160	+	0.0755452i
$695$	2.31291	+	13.1172i	0.0877336	+	0.497562i
$696$	5.37153	−	4.87066i	0.203607	−	0.184622i
$697$	−10.5776	+	3.84992i	−0.400653	+	0.145826i
$698$	−8.74689	−	7.33952i	−0.331075	−	0.277805i
$699$	5.13596	−	0.197333i	0.194260	−	0.00746381i
$700$	−2.82176	+	4.86675i	−0.106652	+	0.183946i
$701$	12.4466			0.470101			0.235050	−	0.971983i	$-0.424475\pi$
$701$	12.4466			0.470101			0.235050	+	0.971983i	$0.424475\pi$
$702$	−4.04828	−	5.45082i	−0.152793	−	0.205728i
$703$	34.8117	−	60.2956i	1.31295	−	2.27409i
$704$	−5.87043	−	2.13666i	−0.221250	−	0.0805285i
$705$	−3.69743	+	0.142062i	−0.139253	+	0.00535035i
$706$	8.03755	−	2.92543i	0.302497	−	0.110100i
$707$	−23.7476	+	19.8524i	−0.893120	+	0.746625i
$708$	0.531334	+	2.45745i	0.0199688	+	0.0923567i
$709$	3.60082	+	20.4213i	0.135232	+	0.766936i	0.974698	+	0.223525i	$0.0717564\pi$
$709$	3.60082	+	20.4213i	0.135232	+	0.766936i	−0.839467	+	0.543411i	$0.817132\pi$
$710$	16.3851			0.614922
$711$	−14.1460	+	13.8531i	−0.530515	+	0.519531i
$712$	6.52351			0.244479
$713$	−11.4680	+	9.62278i	−0.429479	+	0.360376i
$714$	−9.03626	−	2.91949i	−0.338174	−	0.109259i
$715$	2.40295	−	13.6278i	0.0898653	−	0.509652i
$716$	−2.68497	+	0.977249i	−0.100342	+	0.0365215i
$717$	−0.0637719	+	0.0260252i	−0.00238160	+	0.000971930i
$718$	−1.55582	−	8.82348i	−0.0580626	−	0.329289i
$719$	18.6950			0.697205			0.348603	−	0.937271i	$-0.386656\pi$
$719$	18.6950			0.697205			0.348603	+	0.937271i	$0.386656\pi$
$720$	2.19737	−	4.58639i	0.0818911	−	0.170925i
$721$	−6.87526	+	38.5770i	−0.256048	+	1.43668i
$722$	−34.1528	−	12.4306i	−1.27104	−	0.462619i
$723$	31.2366	+	10.0288i	1.16170	+	0.372975i
$724$	10.1452	−	3.69256i	0.377044	−	0.137233i
$725$	1.54571	−	8.76615i	0.0574062	−	0.325567i
$726$	22.6404	−	42.9418i	0.840262	−	1.59372i
$727$	4.18619	+	23.7411i	0.155257	+	0.880507i	0.958550	+	0.284923i	$0.0919681\pi$
$727$	4.18619	+	23.7411i	0.155257	+	0.880507i	−0.803293	+	0.595584i	$0.796921\pi$
$728$	−3.25082	+	1.17644i	−0.120483	+	0.0436019i
$729$	26.2864	−	6.16636i	0.973571	−	0.228384i
$730$	−4.27408	−	7.40292i	−0.158191	−	0.273995i
$731$	−3.68580	−	1.34152i	−0.136324	−	0.0496179i
$732$	−14.7522	+	0.566806i	−0.545258	+	0.0209498i
$733$	9.85742	+	8.27136i	0.364092	+	0.305510i	0.806419	−	0.591344i	$-0.201403\pi$
$733$	9.85742	+	8.27136i	0.364092	+	0.305510i	−0.442327	+	0.896854i	$0.645847\pi$
$734$	7.36427	+	6.17936i	0.271820	+	0.228084i
$735$	2.86409	−	20.3527i	0.105643	−	0.750721i
$736$	−4.97718	−	1.81154i	−0.183461	−	0.0667744i
$737$	17.4018	−	30.1408i	0.641003	−	1.11025i
$738$	−9.20686	−	13.4460i	−0.338909	−	0.494953i
$739$	−11.8507	−	20.5261i	−0.435936	−	0.755063i	0.561435	−	0.827521i	$-0.310249\pi$
$739$	−11.8507	−	20.5261i	−0.435936	−	0.755063i	−0.997372	+	0.0724571i	$0.976916\pi$
$740$	−14.9082	−	5.42613i	−0.548036	−	0.199469i
$741$	13.3040	+	10.3195i	0.488734	+	0.379096i
$742$	0.555714	+	3.18582i	0.0204009	+	0.116955i
$743$	−5.30199	+	30.0691i	−0.194511	+	1.10313i	0.718602	+	0.695421i	$0.244782\pi$
$743$	−5.30199	+	30.0691i	−0.194511	+	1.10313i	−0.913113	+	0.407706i	$0.866329\pi$
$744$	−4.53258	+	1.84974i	−0.166173	+	0.0678148i
$745$	2.48210	+	14.0767i	0.0909373	+	0.515731i
$746$	−0.772745	−	1.33843i	−0.0282922	−	0.0490036i
$747$	5.14030	+	20.0192i	0.188074	+	0.732465i
$748$	−6.47282	−	11.2113i	−0.236670	−	0.409924i
$749$	11.8901	+	20.6819i	0.434455	+	0.755700i
$750$	−4.42188	−	20.4515i	−0.161464	−	0.746782i
$751$	3.36612	−	19.0902i	0.122831	−	0.696611i	−0.859741	−	0.510730i	$-0.829375\pi$
$751$	3.36612	−	19.0902i	0.122831	−	0.696611i	0.982572	−	0.185881i	$-0.0595138\pi$
$752$	−0.218830	+	1.24105i	−0.00797993	+	0.0452564i
$753$	18.0416	+	28.6493i	0.657473	+	1.04404i
$754$	4.19043	−	3.51619i	0.152607	−	0.128052i
$755$	20.8813			0.759950
$756$	0.840309	−	13.7220i	0.0305617	−	0.499065i
$757$	−21.3375			−0.775525			−0.387763	−	0.921759i	$-0.626752\pi$
$757$	−21.3375			−0.775525			−0.387763	+	0.921759i	$0.626752\pi$
$758$	−8.61457	+	7.22848i	−0.312895	+	0.262550i
$759$	26.7290	−	50.6968i	0.970203	−	1.84018i
$760$	−2.18993	+	12.4197i	−0.0794371	+	0.450510i
$761$	1.09521	−	6.21124i	0.0397013	−	0.225157i	−0.958501	−	0.285088i	$-0.907977\pi$
$761$	1.09521	−	6.21124i	0.0397013	−	0.225157i	0.998203	+	0.0599312i	$0.0190881\pi$
$762$	5.19897	+	1.66917i	0.188339	+	0.0604678i
$763$	24.6120	−	42.4490i	0.891015	−	1.53676i
$764$	10.0073	+	17.3332i	0.362053	+	0.627094i
$765$	9.59727	−	4.35365i	0.346990	−	0.157406i
$766$	−11.6445	−	20.1689i	−0.420734	−	0.728733i
$767$	0.329370	+	1.86795i	0.0118929	+	0.0674479i
$768$	−1.36859	−	1.06158i	−0.0493849	−	0.0383064i
$769$	3.06136	−	17.3618i	0.110396	−	0.626084i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-1.73077 + 0.0664993i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.294369 + 1.66945i) q^{5} +(-1.28310 + 1.16346i) q^{6} +(-2.64575 - 0.00486080i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.99116 - 0.230191i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-1.73077 + 0.0664993i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.294369 + 1.66945i) q^{5} +(-1.28310 + 1.16346i) q^{6} +(-2.64575 - 0.00486080i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.99116 - 0.230191i) q^{9} +(0.847602 + 1.46809i) q^{10} +(1.08481 + 6.15227i) q^{11} +(-0.235057 + 1.71603i) q^{12} +(-0.226902 + 1.28683i) q^{13} +(-2.02988 + 1.69693i) q^{14} +(0.398469 - 2.90902i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.03612 - 1.79461i) q^{17} +(2.14339 - 2.09901i) q^{18} +(-3.71970 + 6.44271i) q^{19} +(1.59297 + 0.579794i) q^{20} +(4.57951 - 0.167527i) q^{21} +(4.78562 + 4.01561i) q^{22} +(4.05743 + 3.40459i) q^{23} +(0.922977 + 1.46564i) q^{24} +(1.99805 + 0.727232i) q^{25} +(0.653339 + 1.13162i) q^{26} +(-5.16171 + 0.597318i) q^{27} +(-0.464216 + 2.60471i) q^{28} +(-0.726953 - 4.12275i) q^{29} +(-1.56463 - 2.48457i) q^{30} +(-0.490802 + 2.78347i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-2.28669 - 10.5761i) q^{33} +(-1.94727 - 0.708747i) q^{34} +(0.786941 - 4.41551i) q^{35} +(0.292715 - 2.98569i) q^{36} -9.35873 q^{37} +(1.29184 + 7.32638i) q^{38} +(0.307144 - 2.24230i) q^{39} +(1.59297 - 0.579794i) q^{40} +(0.943258 - 5.34948i) q^{41} +(3.40043 - 3.07199i) q^{42} +(1.44997 - 1.21667i) q^{43} +6.24718 q^{44} +(-0.496212 + 5.06135i) q^{45} +5.29660 q^{46} +(-0.218830 - 1.24105i) q^{47} +(1.64914 + 0.529471i) q^{48} +(6.99995 + 0.0257209i) q^{49} +(1.99805 - 0.727232i) q^{50} +(1.91263 + 3.03716i) q^{51} +(1.22788 + 0.446910i) q^{52} +(0.611155 - 1.05855i) q^{53} +(-3.57015 + 3.77545i) q^{54} -10.5902 q^{55} +(1.31866 + 2.29371i) q^{56} +(6.00952 - 11.3982i) q^{57} +(-3.20693 - 2.69094i) q^{58} +(1.36405 - 0.496475i) q^{59} +(-2.79563 - 0.897561i) q^{60} +(1.48009 + 8.39399i) q^{61} +(1.41321 + 2.44775i) q^{62} +(-7.91496 + 0.594487i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.08150 - 0.757604i) q^{65} +(-8.54986 - 6.63187i) q^{66} +(-4.26770 - 3.58102i) q^{67} +(-1.94727 + 0.708747i) q^{68} +(-7.24890 - 5.62276i) q^{69} +(-2.23540 - 3.88831i) q^{70} +(4.83278 - 8.37063i) q^{71} +(-1.69493 - 2.47532i) q^{72} -5.04256 q^{73} +(-7.16920 + 6.01568i) q^{74} +(-3.50654 - 1.12580i) q^{75} +(5.69891 + 4.78195i) q^{76} +(-2.84023 - 16.2826i) q^{77} +(-1.20603 - 1.91513i) q^{78} +(-5.05574 + 4.24227i) q^{79} +(0.847602 - 1.46809i) q^{80} +(8.89402 - 1.37707i) q^{81} +(-2.71600 - 4.70425i) q^{82} +(1.19636 + 6.78487i) q^{83} +(0.630242 - 4.53903i) q^{84} +(3.30101 - 1.20147i) q^{85} +(0.328683 - 1.86405i) q^{86} +(1.53235 + 7.08721i) q^{87} +(4.78562 - 4.01561i) q^{88} +(-3.26175 + 5.64952i) q^{89} +(2.87325 + 4.19617i) q^{90} +(0.606581 - 3.40352i) q^{91} +(4.05743 - 3.40459i) q^{92} +(0.664367 - 4.85020i) q^{93} +(-0.965365 - 0.810037i) q^{94} +(-9.66081 - 8.10638i) q^{95} +(1.60365 - 0.654448i) q^{96} +(7.24932 - 6.08290i) q^{97} +(5.37881 - 4.47978i) q^{98} +(4.66104 + 18.1527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more