LMFDB - Embedded newform 680.2.l.a.101.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(101,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,-4] 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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.12
Character	$\chi$	$=$	680.101
Dual form			680.2.l.a.101.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.775550 + 1.18259i) q^{2} -0.0722782 q^{3} +(-0.797044 - 1.83432i) q^{4} +1.00000 q^{5} +(0.0560554 - 0.0854756i) q^{6} -0.600402i q^{7} +(2.78740 + 0.480027i) q^{8} -2.99478 q^{9} +(-0.775550 + 1.18259i) q^{10} -3.24363 q^{11} +(0.0576089 + 0.132581i) q^{12} -2.10838i q^{13} +(0.710030 + 0.465642i) q^{14} -0.0722782 q^{15} +(-2.72944 + 2.92406i) q^{16} +(-3.65966 + 1.89918i) q^{17} +(2.32260 - 3.54160i) q^{18} +1.70170i q^{19} +(-0.797044 - 1.83432i) q^{20} +0.0433960i q^{21} +(2.51560 - 3.83589i) q^{22} +8.88923i q^{23} +(-0.201468 - 0.0346955i) q^{24} +1.00000 q^{25} +(2.49335 + 1.63515i) q^{26} +0.433292 q^{27} +(-1.10133 + 0.478547i) q^{28} -5.60163 q^{29} +(0.0560554 - 0.0854756i) q^{30} +6.14500i q^{31} +(-1.34115 - 5.49557i) q^{32} +0.234444 q^{33} +(0.592295 - 5.80079i) q^{34} -0.600402i q^{35} +(2.38697 + 5.49337i) q^{36} -6.98930 q^{37} +(-2.01242 - 1.31975i) q^{38} +0.152390i q^{39} +(2.78740 + 0.480027i) q^{40} +4.41572i q^{41} +(-0.0513197 - 0.0336558i) q^{42} -2.96494i q^{43} +(2.58532 + 5.94985i) q^{44} -2.99478 q^{45} +(-10.5123 - 6.89404i) q^{46} -10.8952 q^{47} +(0.197279 - 0.211346i) q^{48} +6.63952 q^{49} +(-0.775550 + 1.18259i) q^{50} +(0.264514 - 0.137269i) q^{51} +(-3.86743 + 1.68047i) q^{52} -12.8747i q^{53} +(-0.336039 + 0.512407i) q^{54} -3.24363 q^{55} +(0.288209 - 1.67356i) q^{56} -0.122996i q^{57} +(4.34434 - 6.62443i) q^{58} +2.86583i q^{59} +(0.0576089 + 0.132581i) q^{60} -3.10854 q^{61} +(-7.26703 - 4.76576i) q^{62} +1.79807i q^{63} +(7.53915 + 2.67605i) q^{64} -2.10838i q^{65} +(-0.181823 + 0.277251i) q^{66} -8.26082i q^{67} +(6.40061 + 5.19925i) q^{68} -0.642498i q^{69} +(0.710030 + 0.465642i) q^{70} -0.467480i q^{71} +(-8.34762 - 1.43757i) q^{72} -11.4399i q^{73} +(5.42055 - 8.26548i) q^{74} -0.0722782 q^{75} +(3.12146 - 1.35633i) q^{76} +1.94748i q^{77} +(-0.180215 - 0.118186i) q^{78} +10.3817i q^{79} +(-2.72944 + 2.92406i) q^{80} +8.95301 q^{81} +(-5.22199 - 3.42461i) q^{82} +5.97721i q^{83} +(0.0796020 - 0.0345885i) q^{84} +(-3.65966 + 1.89918i) q^{85} +(3.50631 + 2.29946i) q^{86} +0.404876 q^{87} +(-9.04128 - 1.55703i) q^{88} -5.24445 q^{89} +(2.32260 - 3.54160i) q^{90} -1.26587 q^{91} +(16.3057 - 7.08511i) q^{92} -0.444150i q^{93} +(8.44976 - 12.8846i) q^{94} +1.70170i q^{95} +(0.0969363 + 0.397210i) q^{96} -13.7724i q^{97} +(-5.14928 + 7.85184i) q^{98} +9.71395 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{3} + 2 q^{4} + 36 q^{5} + 36 q^{9} - 8 q^{11} - 2 q^{12} + 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} + 2 q^{20} + 26 q^{24} + 36 q^{25} + 6 q^{26} - 16 q^{27} + 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots - 40 q^{99}+O(q^{100}) $ 36 * q - 4 * q^3 + 2 * q^4 + 36 * q^5 + 36 * q^9 - 8 * q^11 - 2 * q^12 + 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 + 2 * q^20 + 26 * q^24 + 36 * q^25 + 6 * q^26 - 16 * q^27 + 14 * q^28 - 10 * q^32 - 8 * q^33 - 24 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 + 6 * q^44 + 36 * q^45 + 24 * q^46 + 20 * q^47 - 4 * q^48 - 36 * q^49 + 6 * q^52 - 56 * q^54 - 8 * q^55 + 20 * q^56 - 18 * q^58 - 2 * q^60 - 24 * q^62 + 14 * q^64 - 16 * q^66 - 40 * q^68 + 2 * q^70 - 54 * q^72 + 6 * q^74 - 4 * q^75 + 2 * q^76 - 14 * q^78 + 6 * q^80 + 44 * q^81 + 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 - 58 * q^88 - 10 * q^90 - 56 * q^91 - 12 * q^92 + 14 * q^94 - 24 * q^96 + 10 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.775550	+	1.18259i	−0.548397	+	0.836218i
$2$	−0.775550	+	1.18259i	−0.548397	+	0.836218i
$3$	−0.0722782			−0.0417299			−0.0208649	−	0.999782i	$-0.506642\pi$
$3$	−0.0722782			−0.0417299			−0.0208649	+	0.999782i	$0.506642\pi$
$4$	−0.797044	−	1.83432i	−0.398522	−	0.917159i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.0560554	−	0.0854756i	0.0228845	−	0.0348953i
$7$		−	0.600402i		−	0.226931i	−0.993542	−	0.113465i	$-0.963805\pi$
$7$		−	0.600402i		−	0.226931i	0.993542	−	0.113465i	$-0.0361951\pi$
$8$	2.78740	+	0.480027i	0.985493	+	0.169715i
$9$	−2.99478			−0.998259
$10$	−0.775550	+	1.18259i	−0.245250	+	0.373968i
$11$	−3.24363			−0.977991			−0.488996	−	0.872286i	$-0.662637\pi$
$11$	−3.24363			−0.977991			−0.488996	+	0.872286i	$0.662637\pi$
$12$	0.0576089	+	0.132581i	0.0166303	+	0.0382729i
$13$		−	2.10838i		−	0.584759i	−0.956302	−	0.292379i	$-0.905553\pi$
$13$		−	2.10838i		−	0.584759i	0.956302	−	0.292379i	$-0.0944470\pi$
$14$	0.710030	+	0.465642i	0.189764	+	0.124448i
$15$	−0.0722782			−0.0186622
$16$	−2.72944	+	2.92406i	−0.682360	+	0.731016i
$17$	−3.65966	+	1.89918i	−0.887598	+	0.460619i
$17$	−3.65966	+	1.89918i	−0.887598	+	0.460619i
$18$	2.32260	−	3.54160i	0.547442	−	0.834762i
$19$			1.70170i			0.390397i	0.980764	+	0.195198i	$0.0625351\pi$
$19$			1.70170i			0.390397i	−0.980764	+	0.195198i	$0.937465\pi$
$20$	−0.797044	−	1.83432i	−0.178225	−	0.410166i
$21$			0.0433960i			0.00946978i
$22$	2.51560	−	3.83589i	0.536327	−	0.817814i
$23$			8.88923i			1.85353i	0.375639	+	0.926766i	$0.377423\pi$
$23$			8.88923i			1.85353i	−0.375639	+	0.926766i	$0.622577\pi$
$24$	−0.201468	−	0.0346955i	−0.0411245	−	0.00708220i
$25$	1.00000			0.200000
$26$	2.49335	+	1.63515i	0.488986	+	0.320680i
$27$	0.433292			0.0833870
$28$	−1.10133	+	0.478547i	−0.208131	+	0.0904369i
$29$	−5.60163			−1.04020			−0.520098	−	0.854107i	$-0.674105\pi$
$29$	−5.60163			−1.04020			−0.520098	+	0.854107i	$0.674105\pi$
$30$	0.0560554	−	0.0854756i	0.0102343	−	0.0156056i
$31$			6.14500i			1.10367i	0.833952	+	0.551837i	$0.186073\pi$
$31$			6.14500i			1.10367i	−0.833952	+	0.551837i	$0.813927\pi$
$32$	−1.34115	−	5.49557i	−0.237085	−	0.971489i
$33$	0.234444			0.0408114
$34$	0.592295	−	5.80079i	0.101578	−	0.994828i
$35$		−	0.600402i		−	0.101486i
$36$	2.38697	+	5.49337i	0.397828	+	0.915562i
$37$	−6.98930			−1.14903			−0.574517	−	0.818493i	$-0.694810\pi$
$37$	−6.98930			−1.14903			−0.574517	+	0.818493i	$0.694810\pi$
$38$	−2.01242	−	1.31975i	−0.326457	−	0.214092i
$39$			0.152390i			0.0244019i
$40$	2.78740	+	0.480027i	0.440726	+	0.0758990i
$41$			4.41572i			0.689619i	0.938673	+	0.344809i	$0.112056\pi$
$41$			4.41572i			0.689619i	−0.938673	+	0.344809i	$0.887944\pi$
$42$	−0.0513197	−	0.0336558i	−0.00791881	−	0.00519320i
$43$		−	2.96494i		−	0.452148i	−0.974110	−	0.226074i	$-0.927411\pi$
$43$		−	2.96494i		−	0.452148i	0.974110	−	0.226074i	$-0.0725892\pi$
$44$	2.58532	+	5.94985i	0.389751	+	0.896973i
$45$	−2.99478			−0.446435
$46$	−10.5123	−	6.89404i	−1.54996	−	1.01647i
$47$	−10.8952			−1.58923			−0.794613	−	0.607116i	$-0.792326\pi$
$47$	−10.8952			−1.58923			−0.794613	+	0.607116i	$0.792326\pi$
$48$	0.197279	−	0.211346i	0.0284748	−	0.0305052i
$49$	6.63952			0.948502
$50$	−0.775550	+	1.18259i	−0.109679	+	0.167244i
$51$	0.264514	−	0.137269i	0.0370393	−	0.0192216i
$52$	−3.86743	+	1.68047i	−0.536317	+	0.233039i
$53$		−	12.8747i		−	1.76848i	−0.467032	−	0.884240i	$-0.654677\pi$
$53$		−	12.8747i		−	1.76848i	0.467032	−	0.884240i	$-0.345323\pi$
$54$	−0.336039	+	0.512407i	−0.0457292	+	0.0697298i
$55$	−3.24363			−0.437371
$56$	0.288209	−	1.67356i	0.0385136	−	0.223639i
$57$		−	0.122996i		−	0.0162912i
$58$	4.34434	−	6.62443i	0.570440	−	0.869831i
$59$			2.86583i			0.373099i	0.982446	+	0.186550i	$0.0597305\pi$
$59$			2.86583i			0.373099i	−0.982446	+	0.186550i	$0.940269\pi$
$60$	0.0576089	+	0.132581i	0.00743728	+	0.0171162i
$61$	−3.10854			−0.398008			−0.199004	−	0.979999i	$-0.563771\pi$
$61$	−3.10854			−0.398008			−0.199004	+	0.979999i	$0.563771\pi$
$62$	−7.26703	−	4.76576i	−0.922913	−	0.605252i
$63$			1.79807i			0.226535i
$64$	7.53915	+	2.67605i	0.942393	+	0.334507i
$65$		−	2.10838i		−	0.261512i
$66$	−0.181823	+	0.277251i	−0.0223809	+	0.0341273i
$67$		−	8.26082i		−	1.00922i	−0.863347	−	0.504610i	$-0.831636\pi$
$67$		−	8.26082i		−	1.00922i	0.863347	−	0.504610i	$-0.168364\pi$
$68$	6.40061	+	5.19925i	0.776188	+	0.630501i
$69$		−	0.642498i		−	0.0773476i
$70$	0.710030	+	0.465642i	0.0848648	+	0.0556548i
$71$		−	0.467480i		−	0.0554797i	−0.999615	−	0.0277398i	$-0.991169\pi$
$71$		−	0.467480i		−	0.0554797i	0.999615	−	0.0277398i	$-0.00883099\pi$
$72$	−8.34762	−	1.43757i	−0.983777	−	0.169420i
$73$		−	11.4399i		−	1.33894i	−0.742839	−	0.669470i	$-0.766521\pi$
$73$		−	11.4399i		−	1.33894i	0.742839	−	0.669470i	$-0.233479\pi$
$74$	5.42055	−	8.26548i	0.630126	−	0.960843i
$75$	−0.0722782			−0.00834597
$76$	3.12146	−	1.35633i	0.358056	−	0.155582i
$77$			1.94748i			0.221936i
$78$	−0.180215	−	0.118186i	−0.0204053	−	0.0133819i
$79$			10.3817i			1.16804i	0.811740	+	0.584019i	$0.198520\pi$
$79$			10.3817i			1.16804i	−0.811740	+	0.584019i	$0.801480\pi$
$80$	−2.72944	+	2.92406i	−0.305161	+	0.326920i
$81$	8.95301			0.994779
$82$	−5.22199	−	3.42461i	−0.576672	−	0.378185i
$83$			5.97721i			0.656084i	0.944663	+	0.328042i	$0.106389\pi$
$83$			5.97721i			0.656084i	−0.944663	+	0.328042i	$0.893611\pi$
$84$	0.0796020	−	0.0345885i	0.00868529	−	0.00377392i
$85$	−3.65966	+	1.89918i	−0.396946	+	0.205995i
$86$	3.50631	+	2.29946i	0.378095	+	0.247957i
$87$	0.404876			0.0434072
$88$	−9.04128	−	1.55703i	−0.963804	−	0.165980i
$89$	−5.24445			−0.555911			−0.277955	−	0.960594i	$-0.589657\pi$
$89$	−5.24445			−0.555911			−0.277955	+	0.960594i	$0.589657\pi$
$90$	2.32260	−	3.54160i	0.244823	−	0.373317i
$91$	−1.26587			−0.132700
$92$	16.3057	−	7.08511i	1.69998	−	0.738674i
$93$		−	0.444150i		−	0.0460562i
$94$	8.44976	−	12.8846i	0.871527	−	1.32894i
$95$			1.70170i			0.174591i
$96$	0.0969363	+	0.397210i	0.00989352	+	0.0405401i
$97$		−	13.7724i		−	1.39837i	−0.714939	−	0.699186i	$-0.753546\pi$
$97$		−	13.7724i		−	1.39837i	0.714939	−	0.699186i	$-0.246454\pi$
$98$	−5.14928	+	7.85184i	−0.520156	+	0.793155i
$99$	9.71395			0.976288
$100$	−0.797044	−	1.83432i	−0.0797044	−	0.183432i
$101$			3.84878i			0.382968i	0.981496	+	0.191484i	$0.0613300\pi$
$101$			3.84878i			0.382968i	−0.981496	+	0.191484i	$0.938670\pi$
$102$	−0.0428101	+	0.419271i	−0.00423883	+	0.0415140i
$103$	5.90603			0.581938			0.290969	−	0.956732i	$-0.406022\pi$
$103$	5.90603			0.581938			0.290969	+	0.956732i	$0.406022\pi$
$104$	1.01208	−	5.87688i	0.0992425	−	0.576276i
$105$			0.0433960i			0.00423502i
$106$	15.2255	+	9.98500i	1.47884	+	0.969829i
$107$	3.95376			0.382225			0.191112	−	0.981568i	$-0.438791\pi$
$107$	3.95376			0.382225			0.191112	+	0.981568i	$0.438791\pi$
$108$	−0.345353	−	0.794795i	−0.0332316	−	0.0764792i
$109$	1.65160			0.158195			0.0790975	−	0.996867i	$-0.474796\pi$
$109$	1.65160			0.158195			0.0790975	+	0.996867i	$0.474796\pi$
$110$	2.51560	−	3.83589i	0.239853	−	0.365738i
$111$	0.505174			0.0479490
$112$	1.75561	+	1.63876i	0.165890	+	0.154848i
$113$			11.0712i			1.04149i	0.853712	+	0.520746i	$0.174346\pi$
$113$			11.0712i			1.04149i	−0.853712	+	0.520746i	$0.825654\pi$
$114$	0.145454	+	0.0953894i	0.0136230	+	0.00893404i
$115$			8.88923i			0.828925i
$116$	4.46474	+	10.2752i	0.414541	+	0.954025i
$117$			6.31412i			0.583740i
$118$	−3.38911	−	2.22259i	−0.311992	−	0.204606i
$119$	1.14027	+	2.19727i	0.104529	+	0.201423i
$120$	−0.201468	−	0.0346955i	−0.0183914	−	0.00316725i
$121$	−0.478864			−0.0435330
$122$	2.41083	−	3.67614i	0.218266	−	0.332822i
$123$		−	0.319160i		−	0.0287777i
$124$	11.2719	−	4.89784i	1.01225	−	0.439839i
$125$	1.00000			0.0894427
$126$	−2.12638	−	1.39449i	−0.189433	−	0.124231i
$127$	−15.3744			−1.36426			−0.682128	−	0.731233i	$-0.738945\pi$
$127$	−15.3744			−1.36426			−0.682128	+	0.731233i	$0.738945\pi$
$128$	−9.01166	+	6.84032i	−0.796526	+	0.604604i
$129$			0.214300i			0.0188681i
$130$	2.49335	+	1.63515i	0.218681	+	0.143412i
$131$	14.1739			1.23838			0.619188	−	0.785243i	$-0.287462\pi$
$131$	14.1739			1.23838			0.619188	+	0.785243i	$0.287462\pi$
$132$	−0.186862	−	0.430044i	−0.0162643	−	0.0374306i
$133$	1.02170			0.0885930
$134$	9.76918	+	6.40668i	0.843928	+	0.553453i
$135$	0.433292			0.0372918
$136$	−11.1126	+	3.53703i	−0.952896	+	0.303298i
$137$	−5.31352			−0.453965			−0.226982	−	0.973899i	$-0.572886\pi$
$137$	−5.31352			−0.453965			−0.226982	+	0.973899i	$0.572886\pi$
$138$	0.759812	+	0.498289i	0.0646795	+	0.0424172i
$139$	−17.9875			−1.52568			−0.762841	−	0.646587i	$-0.776196\pi$
$139$	−17.9875			−1.52568			−0.762841	+	0.646587i	$0.776196\pi$
$140$	−1.10133	+	0.478547i	−0.0930792	+	0.0404446i
$141$	0.787485			0.0663182
$142$	0.552838	+	0.362554i	0.0463931	+	0.0304249i
$143$			6.83880i			0.571889i
$144$	8.17406	−	8.75692i	0.681172	−	0.729743i
$145$	−5.60163			−0.465190
$146$	13.5287	+	8.87223i	1.11965	+	0.734271i
$147$	−0.479893			−0.0395809
$148$	5.57078	+	12.8206i	0.457915	+	1.05385i
$149$		−	1.20281i		−	0.0985381i	−0.998786	−	0.0492691i	$-0.984311\pi$
$149$		−	1.20281i		−	0.0985381i	0.998786	−	0.0492691i	$-0.0156892\pi$
$150$	0.0560554	−	0.0854756i	0.00457690	−	0.00697905i
$151$	−11.2014			−0.911553			−0.455777	−	0.890094i	$-0.650638\pi$
$151$	−11.2014			−0.911553			−0.455777	+	0.890094i	$0.650638\pi$
$152$	−0.816863	+	4.74331i	−0.0662563	+	0.384733i
$153$	10.9599	−	5.68762i	0.886052	−	0.459817i
$154$	−2.30308	−	1.51037i	−0.185587	−	0.121709i
$155$			6.14500i			0.493578i
$156$	0.279531	−	0.121461i	0.0223804	−	0.00972470i
$157$		−	7.88359i		−	0.629179i	−0.949228	−	0.314590i	$-0.898133\pi$
$157$		−	7.88359i		−	0.629179i	0.949228	−	0.314590i	$-0.101867\pi$
$158$	−12.2774	−	8.05156i	−0.976734	−	0.640548i
$159$			0.930563i			0.0737984i
$160$	−1.34115	−	5.49557i	−0.106028	−	0.434463i
$161$	5.33711			0.420623
$162$	−6.94351	+	10.5878i	−0.545533	+	0.831852i
$163$	16.4803			1.29084			0.645418	−	0.763830i	$-0.276683\pi$
$163$	16.4803			1.29084			0.645418	+	0.763830i	$0.276683\pi$
$164$	8.09982	−	3.51952i	0.632490	−	0.274828i
$165$	0.234444			0.0182514
$166$	−7.06860	−	4.63563i	−0.548630	−	0.359795i
$167$			17.4160i			1.34769i	0.738871	+	0.673846i	$0.235359\pi$
$167$			17.4160i			1.34769i	−0.738871	+	0.673846i	$0.764641\pi$
$168$	−0.0208313	+	0.120962i	−0.00160717	+	0.00933241i
$169$	8.55474			0.658057
$170$	0.592295	−	5.80079i	0.0454270	−	0.444900i
$171$		−	5.09621i		−	0.389717i
$172$	−5.43863	+	2.36318i	−0.414692	+	0.180191i
$173$	12.5295			0.952597			0.476298	−	0.879284i	$-0.341978\pi$
$173$	12.5295			0.952597			0.476298	+	0.879284i	$0.341978\pi$
$174$	−0.314001	+	0.478802i	−0.0238044	+	0.0362979i
$175$		−	0.600402i		−	0.0453861i
$176$	8.85330	−	9.48458i	0.667342	−	0.714927i
$177$		−	0.207137i		−	0.0155694i
$178$	4.06733	−	6.20204i	0.304860	−	0.464863i
$179$			17.1015i			1.27823i	0.769111	+	0.639115i	$0.220699\pi$
$179$			17.1015i			1.27823i	−0.769111	+	0.639115i	$0.779301\pi$
$180$	2.38697	+	5.49337i	0.177914	+	0.409452i
$181$	−22.0934			−1.64219			−0.821093	−	0.570795i	$-0.806635\pi$
$181$	−22.0934			−1.64219			−0.821093	+	0.570795i	$0.806635\pi$
$182$	0.981749	−	1.49701i	0.0727721	−	0.110966i
$183$	0.224680			0.0166088
$184$	−4.26707	+	24.7778i	−0.314573	+	1.82664i
$185$	−6.98930			−0.513863
$186$	0.525248	+	0.344460i	0.0385130	+	0.0252571i
$187$	11.8706	−	6.16024i	0.868063	−	0.450481i
$188$	8.68395	+	19.9852i	0.633342	+	1.45757i
$189$		−	0.260149i		−	0.0189231i
$190$	−2.01242	−	1.31975i	−0.145996	−	0.0957450i
$191$	10.5298			0.761907			0.380954	−	0.924594i	$-0.375596\pi$
$191$	10.5298			0.761907			0.380954	+	0.924594i	$0.375596\pi$
$192$	−0.544916	−	0.193420i	−0.0393259	−	0.0139589i
$193$			8.45792i			0.608814i	0.952542	+	0.304407i	$0.0984583\pi$
$193$			8.45792i			0.608814i	−0.952542	+	0.304407i	$0.901542\pi$
$194$	16.2871	+	10.6812i	1.16934	+	0.766863i
$195$			0.152390i			0.0109129i
$196$	−5.29199	−	12.1790i	−0.377999	−	0.869927i
$197$	21.8192			1.55455			0.777275	−	0.629160i	$-0.216601\pi$
$197$	21.8192			1.55455			0.777275	+	0.629160i	$0.216601\pi$
$198$	−7.53365	+	11.4876i	−0.535393	+	0.816390i
$199$		−	0.867086i		−	0.0614661i	−0.999528	−	0.0307330i	$-0.990216\pi$
$199$		−	0.867086i		−	0.0614661i	0.999528	−	0.0307330i	$-0.00978417\pi$
$200$	2.78740	+	0.480027i	0.197099	+	0.0339431i
$201$			0.597078i			0.0421146i
$202$	−4.55153	−	2.98492i	−0.320245	−	0.210018i
$203$			3.36323i			0.236052i
$204$	−0.462625	−	0.375792i	−0.0323902	−	0.0263107i
$205$			4.41572i			0.308407i
$206$	−4.58042	+	6.98441i	−0.319133	+	0.486627i
$207$		−	26.6212i		−	1.85030i
$208$	6.16503	+	5.75469i	0.427468	+	0.399016i
$209$		−	5.51968i		−	0.381805i
$210$	−0.0513197	−	0.0336558i	−0.00354140	−	0.00232247i
$211$	20.4773			1.40971			0.704857	−	0.709350i	$-0.251011\pi$
$211$	20.4773			1.40971			0.704857	+	0.709350i	$0.251011\pi$
$212$	−23.6163	+	10.2617i	−1.62198	+	0.704779i
$213$			0.0337886i			0.00231516i
$214$	−3.06634	+	4.67568i	−0.209611	+	0.319623i
$215$		−	2.96494i		−	0.202207i
$216$	1.20776	+	0.207992i	0.0821774	+	0.0141521i
$217$	3.68947			0.250458
$218$	−1.28090	+	1.95317i	−0.0867536	+	0.132286i
$219$			0.826857i			0.0558738i
$220$	2.58532	+	5.94985i	0.174302	+	0.401139i
$221$	4.00419	+	7.71595i	0.269351	+	0.519031i
$222$	−0.391788	+	0.597414i	−0.0262951	+	0.0400958i
$223$	15.6305			1.04669			0.523347	−	0.852120i	$-0.324683\pi$
$223$	15.6305			1.04669			0.523347	+	0.852120i	$0.324683\pi$
$224$	−3.29955	+	0.805232i	−0.220461	+	0.0538018i
$225$	−2.99478			−0.199652
$226$	−13.0927	−	8.58628i	−0.870915	−	0.571151i
$227$	7.35013			0.487845			0.243923	−	0.969795i	$-0.421566\pi$
$227$	7.35013			0.487845			0.243923	+	0.969795i	$0.421566\pi$
$228$	−0.225613	+	0.0980331i	−0.0149416	+	0.00649240i
$229$			26.0928i			1.72426i	0.506688	+	0.862129i	$0.330869\pi$
$229$			26.0928i			1.72426i	−0.506688	+	0.862129i	$0.669131\pi$
$230$	−10.5123	−	6.89404i	−0.693162	−	0.454580i
$231$		−	0.140761i		−	0.00926136i
$232$	−15.6139	−	2.68893i	−1.02511	−	0.176537i
$233$		−	20.1080i		−	1.31732i	−0.752440	−	0.658661i	$-0.771123\pi$
$233$		−	20.1080i		−	1.31732i	0.752440	−	0.658661i	$-0.228877\pi$
$234$	−7.46702	−	4.89691i	−0.488134	−	0.320121i
$235$	−10.8952			−0.710724
$236$	5.25684	−	2.28419i	0.342191	−	0.148688i
$237$		−	0.750374i		−	0.0487420i
$238$	−3.48281	−	0.355615i	−0.225757	−	0.0230511i
$239$	−12.0248			−0.777822			−0.388911	−	0.921275i	$-0.627149\pi$
$239$	−12.0248			−0.777822			−0.388911	+	0.921275i	$0.627149\pi$
$240$	0.197279	−	0.211346i	0.0127343	−	0.0136423i
$241$		−	18.6565i		−	1.20177i	−0.799336	−	0.600885i	$-0.794815\pi$
$241$		−	18.6565i		−	1.20177i	0.799336	−	0.600885i	$-0.205185\pi$
$242$	0.371383	−	0.566300i	0.0238734	−	0.0364031i
$243$	−1.94698			−0.124899
$244$	2.47765	+	5.70205i	0.158615	+	0.365037i
$245$	6.63952			0.424183
$246$	0.377436	+	0.247525i	0.0240644	+	0.0157816i
$247$	3.58783			0.228288
$248$	−2.94977	+	17.1286i	−0.187311	+	1.08766i
$249$		−	0.432022i		−	0.0273783i
$250$	−0.775550	+	1.18259i	−0.0490501	+	0.0747936i
$251$		−	24.6401i		−	1.55527i	−0.628718	−	0.777633i	$-0.716420\pi$
$251$		−	24.6401i		−	1.55527i	0.628718	−	0.777633i	$-0.283580\pi$
$252$	3.29823	−	1.43314i	0.207769	−	0.0902794i
$253$		−	28.8334i		−	1.81274i
$254$	11.9236	−	18.1816i	0.748153	−	1.14082i
$255$	0.264514	−	0.137269i	0.0165645	−	0.00859614i
$256$	−1.10030	−	15.9621i	−0.0687689	−	0.997633i
$257$	6.72149			0.419275			0.209638	−	0.977779i	$-0.432772\pi$
$257$	6.72149			0.419275			0.209638	+	0.977779i	$0.432772\pi$
$258$	−0.253430	−	0.166201i	−0.0157778	−	0.0103472i
$259$			4.19639i			0.260751i
$260$	−3.86743	+	1.68047i	−0.239848	+	0.104218i
$261$	16.7756			1.03838
$262$	−10.9925	+	16.7619i	−0.679122	+	1.03555i
$263$	13.6373			0.840912			0.420456	−	0.907313i	$-0.361870\pi$
$263$	13.6373			0.840912			0.420456	+	0.907313i	$0.361870\pi$
$264$	0.653488	+	0.112539i	0.0402194	+	0.00692633i
$265$		−	12.8747i		−	0.790889i
$266$	−0.792382	+	1.20826i	−0.0485841	+	0.0740831i
$267$	0.379060			0.0231981
$268$	−15.1530	+	6.58424i	−0.925615	+	0.402196i
$269$	−24.0488			−1.46628			−0.733140	−	0.680077i	$-0.761946\pi$
$269$	−24.0488			−1.46628			−0.733140	+	0.680077i	$0.761946\pi$
$270$	−0.336039	+	0.512407i	−0.0204507	+	0.0311841i
$271$	−9.39314			−0.570592			−0.285296	−	0.958439i	$-0.592092\pi$
$271$	−9.39314			−0.570592			−0.285296	+	0.958439i	$0.592092\pi$
$272$	4.43550	−	15.8848i	0.268942	−	0.963156i
$273$	0.0914951			0.00553754
$274$	4.12090	−	6.28372i	0.248953	−	0.379614i
$275$	−3.24363			−0.195598
$276$	−1.17854	+	0.512099i	−0.0709401	+	0.0308247i
$277$	−28.9718			−1.74075			−0.870373	−	0.492393i	$-0.836122\pi$
$277$	−28.9718			−1.74075			−0.870373	+	0.492393i	$0.836122\pi$
$278$	13.9502	−	21.2719i	0.836679	−	1.27580i
$279$		−	18.4029i		−	1.10175i
$280$	0.288209	−	1.67356i	0.0172238	−	0.100014i
$281$	13.2167			0.788444			0.394222	−	0.919015i	$-0.371014\pi$
$281$	13.2167			0.788444			0.394222	+	0.919015i	$0.371014\pi$
$282$	−0.610734	+	0.931273i	−0.0363687	+	0.0554565i
$283$	−26.9621			−1.60273			−0.801364	−	0.598176i	$-0.795892\pi$
$283$	−26.9621			−1.60273			−0.801364	+	0.598176i	$0.795892\pi$
$284$	−0.857507	+	0.372602i	−0.0508837	+	0.0221099i
$285$		−	0.122996i		−	0.00728564i
$286$	−8.08750	−	5.30383i	−0.478224	−	0.313622i
$287$	2.65120			0.156496
$288$	4.01646	+	16.4580i	0.236672	+	0.969797i
$289$	9.78623	−	13.9007i	0.575660	−	0.817689i
$290$	4.34434	−	6.62443i	0.255109	−	0.389000i
$291$			0.995443i			0.0583539i
$292$	−20.9844	+	9.11812i	−1.22802	+	0.533597i
$293$		−	6.29350i		−	0.367670i	−0.982957	−	0.183835i	$-0.941149\pi$
$293$		−	6.29350i		−	0.367670i	0.982957	−	0.183835i	$-0.0588513\pi$
$294$	0.372181	−	0.567517i	0.0217060	−	0.0330983i
$295$			2.86583i			0.166855i
$296$	−19.4819	−	3.35505i	−1.13236	−	0.195009i
$297$	−1.40544			−0.0815518
$298$	1.42243	+	0.932840i	0.0823994	+	0.0540380i
$299$	18.7419			1.08387
$300$	0.0576089	+	0.132581i	0.00332605	+	0.00765458i
$301$	−1.78015			−0.102606
$302$	8.68721	−	13.2466i	0.499893	−	0.762258i
$303$		−	0.278183i		−	0.0159812i
$304$	−4.97588	−	4.64469i	−0.285386	−	0.266391i
$305$	−3.10854			−0.177995
$306$	−1.77379	+	17.3721i	−0.101401	+	0.993095i
$307$			27.4747i			1.56806i	0.620721	+	0.784032i	$0.286840\pi$
$307$			27.4747i			1.56806i	−0.620721	+	0.784032i	$0.713160\pi$
$308$	3.57230	−	1.55223i	0.203551	−	0.0884465i
$309$	−0.426877			−0.0242842
$310$	−7.26703	−	4.76576i	−0.412739	−	0.270677i
$311$			18.2426i			1.03445i	0.855851	+	0.517223i	$0.173034\pi$
$311$			18.2426i			1.03445i	−0.855851	+	0.517223i	$0.826966\pi$
$312$	−0.0731513	+	0.424771i	−0.00414138	+	0.0240479i
$313$			14.3390i			0.810490i	0.914208	+	0.405245i	$0.132814\pi$
$313$			14.3390i			0.810490i	−0.914208	+	0.405245i	$0.867186\pi$
$314$	9.32307	+	6.11412i	0.526131	+	0.345040i
$315$			1.79807i			0.101310i
$316$	19.0434	−	8.27471i	1.07128	−	0.465489i
$317$	−8.71699			−0.489595			−0.244797	−	0.969574i	$-0.578721\pi$
$317$	−8.71699			−0.489595			−0.244797	+	0.969574i	$0.578721\pi$
$318$	−1.10048	−	0.721698i	−0.0617116	−	0.0404708i
$319$	18.1696			1.01730
$320$	7.53915	+	2.67605i	0.421451	+	0.149596i
$321$	−0.285771			−0.0159502
$322$	−4.13920	+	6.31162i	−0.230668	+	0.351733i
$323$	−3.23183	−	6.22764i	−0.179824	−	0.346515i
$324$	−7.13594	−	16.4227i	−0.396441	−	0.912370i
$325$		−	2.10838i		−	0.116952i
$326$	−12.7813	+	19.4894i	−0.707890	+	1.07942i
$327$	−0.119375			−0.00660146
$328$	−2.11966	+	12.3083i	−0.117039	+	0.679615i
$329$			6.54149i			0.360644i
$330$	−0.181823	+	0.277251i	−0.0100090	+	0.0152622i
$331$		−	20.7382i		−	1.13987i	−0.821689	−	0.569936i	$-0.806968\pi$
$331$		−	20.7382i		−	1.13987i	0.821689	−	0.569936i	$-0.193032\pi$
$332$	10.9641	−	4.76410i	0.601734	−	0.261464i
$333$	20.9314			1.14703
$334$	−20.5960	−	13.5070i	−1.12697	−	0.739070i
$335$		−	8.26082i		−	0.451337i
$336$	−0.126893	−	0.118447i	−0.00692256	−	0.00646180i
$337$		−	5.54913i		−	0.302280i	−0.988512	−	0.151140i	$-0.951706\pi$
$337$		−	5.54913i		−	0.302280i	0.988512	−	0.151140i	$-0.0482945\pi$
$338$	−6.63463	+	10.1168i	−0.360876	+	0.550279i
$339$		−	0.800208i		−	0.0434613i
$340$	6.40061	+	5.19925i	0.347122	+	0.281969i
$341$		−	19.9321i		−	1.07938i
$342$	6.02673	+	3.95237i	0.325888	+	0.213719i
$343$		−	8.18919i		−	0.442175i
$344$	1.42325	−	8.26445i	0.0767365	−	0.445589i
$345$		−	0.642498i		−	0.0345909i
$346$	−9.71722	+	14.8172i	−0.522401	+	0.796579i
$347$	−30.8060			−1.65375			−0.826877	−	0.562383i	$-0.809885\pi$
$347$	−30.8060			−1.65375			−0.826877	+	0.562383i	$0.809885\pi$
$348$	−0.322704	−	0.742671i	−0.0172987	−	0.0398113i
$349$			5.21987i			0.279413i	0.990193	+	0.139707i	$0.0446159\pi$
$349$			5.21987i			0.279413i	−0.990193	+	0.139707i	$0.955384\pi$
$350$	0.710030	+	0.465642i	0.0379527	+	0.0248896i
$351$		−	0.913543i		−	0.0487613i
$352$	4.35021	+	17.8256i	0.231867	+	0.950108i
$353$	−22.8777			−1.21766			−0.608828	−	0.793303i	$-0.708360\pi$
$353$	−22.8777			−1.21766			−0.608828	+	0.793303i	$0.708360\pi$
$354$	0.244959	+	0.160645i	0.0130194	+	0.00853820i
$355$		−	0.467480i		−	0.0248113i
$356$	4.18006	+	9.61999i	0.221543	+	0.509858i
$357$	−0.0824168	−	0.158815i	−0.00436196	−	0.00840536i
$358$	−20.2241	−	13.2631i	−1.06888	−	0.700977i
$359$	−12.2004			−0.643910			−0.321955	−	0.946755i	$-0.604340\pi$
$359$	−12.2004			−0.643910			−0.321955	+	0.946755i	$0.604340\pi$
$360$	−8.34762	−	1.43757i	−0.439958	−	0.0757668i
$361$	16.1042			0.847590
$362$	17.1345	−	26.1274i	0.900569	−	1.37323i
$363$	0.0346114			0.00181663
$364$	1.00896	+	2.32201i	0.0528837	+	0.121707i
$365$		−	11.4399i		−	0.598792i
$366$	−0.174251	+	0.265705i	−0.00910822	+	0.0138886i
$367$			0.161194i			0.00841425i	0.999991	+	0.00420713i	$0.00133917\pi$
$367$			0.161194i			0.00841425i	−0.999991	+	0.00420713i	$0.998661\pi$
$368$	−25.9927	−	24.2626i	−1.35496	−	1.26478i
$369$		−	13.2241i		−	0.688418i
$370$	5.42055	−	8.26548i	0.281801	−	0.429702i
$371$	−7.73002			−0.401322
$372$	−0.814712	+	0.354007i	−0.0422408	+	0.0183544i
$373$		−	25.0872i		−	1.29897i	−0.760376	−	0.649483i	$-0.774985\pi$
$373$		−	25.0872i		−	1.29897i	0.760376	−	0.649483i	$-0.225015\pi$
$374$	−1.92119	+	18.8156i	−0.0993422	+	0.972933i
$375$	−0.0722782			−0.00373243
$376$	−30.3692	−	5.22999i	−1.56617	−	0.269716i
$377$			11.8103i			0.608264i
$378$	0.307650	+	0.201759i	0.0158238	+	0.0103774i
$379$	−13.0004			−0.667783			−0.333892	−	0.942611i	$-0.608362\pi$
$379$	−13.0004			−0.667783			−0.333892	+	0.942611i	$0.608362\pi$
$380$	3.12146	−	1.35633i	0.160127	−	0.0695783i
$381$	1.11123			0.0569302
$382$	−8.16636	+	12.4524i	−0.417827	+	0.637121i
$383$	−10.3152			−0.527083			−0.263542	−	0.964648i	$-0.584891\pi$
$383$	−10.3152			−0.527083			−0.263542	+	0.964648i	$0.584891\pi$
$384$	0.651347	−	0.494406i	0.0332389	−	0.0252301i
$385$			1.94748i			0.0992529i
$386$	−10.0023	−	6.55954i	−0.509102	−	0.333872i
$387$			8.87932i			0.451361i
$388$	−25.2629	+	10.9772i	−1.28253	+	0.557283i
$389$			29.7338i			1.50756i	0.657124	+	0.753782i	$0.271773\pi$
$389$			29.7338i			1.50756i	−0.657124	+	0.753782i	$0.728227\pi$
$390$	−0.180215	−	0.118186i	−0.00912553	−	0.00598458i
$391$	−16.8823	−	32.5316i	−0.853772	−	1.64519i
$392$	18.5070	+	3.18715i	0.934743	+	0.160975i
$393$	−1.02446			−0.0516773
$394$	−16.9219	+	25.8031i	−0.852511	+	1.29994i
$395$			10.3817i			0.522362i
$396$	−7.74244	−	17.8185i	−0.389072	−	0.895411i
$397$	12.5346			0.629093			0.314546	−	0.949242i	$-0.398148\pi$
$397$	12.5346			0.629093			0.314546	+	0.949242i	$0.398148\pi$
$398$	1.02541	+	0.672468i	0.0513991	+	0.0337078i
$399$	−0.0738469			−0.00369697
$400$	−2.72944	+	2.92406i	−0.136472	+	0.146203i
$401$			5.73963i			0.286623i	0.989678	+	0.143312i	$0.0457751\pi$
$401$			5.73963i			0.286623i	−0.989678	+	0.143312i	$0.954225\pi$
$402$	−0.706099	−	0.463064i	−0.0352170	−	0.0230955i
$403$	12.9560			0.645384
$404$	7.05988	−	3.06765i	0.351242	−	0.152621i
$405$	8.95301			0.444879
$406$	−3.97732	−	2.60835i	−0.197391	−	0.129450i
$407$	22.6707			1.12374
$408$	0.803198	−	0.255650i	0.0397642	−	0.0126566i
$409$	5.00882			0.247670			0.123835	−	0.992303i	$-0.460481\pi$
$409$	5.00882			0.247670			0.123835	+	0.992303i	$0.460481\pi$
$410$	−5.22199	−	3.42461i	−0.257896	−	0.169129i
$411$	0.384052			0.0189439
$412$	−4.70736	−	10.8335i	−0.231915	−	0.533729i
$413$	1.72065			0.0846677
$414$	31.4821	+	20.6461i	1.54726	+	1.01470i
$415$			5.97721i			0.293410i
$416$	−11.5867	+	2.82766i	−0.568087	+	0.138637i
$417$	1.30011			0.0636665
$418$	6.52753	+	4.28079i	0.319272	+	0.209380i
$419$	−19.0222			−0.929296			−0.464648	−	0.885495i	$-0.653819\pi$
$419$	−19.0222			−0.929296			−0.464648	+	0.885495i	$0.653819\pi$
$420$	0.0796020	−	0.0345885i	0.00388418	−	0.00168775i
$421$			13.5055i			0.658217i	0.944292	+	0.329108i	$0.106748\pi$
$421$			13.5055i			0.658217i	−0.944292	+	0.329108i	$0.893252\pi$
$422$	−15.8811	+	24.2162i	−0.773082	+	1.17883i
$423$	32.6286			1.58646
$424$	6.18023	−	35.8870i	0.300138	−	1.74283i
$425$	−3.65966	+	1.89918i	−0.177520	+	0.0921238i
$426$	−0.0399581	−	0.0262048i	−0.00193598	−	0.00126963i
$427$			1.86638i			0.0903202i
$428$	−3.15132	−	7.25245i	−0.152325	−	0.350561i
$429$		−	0.494296i		−	0.0238648i
$430$	3.50631	+	2.29946i	0.169089	+	0.110890i
$431$		−	17.5514i		−	0.845421i	−0.906265	−	0.422710i	$-0.861079\pi$
$431$		−	17.5514i		−	0.845421i	0.906265	−	0.422710i	$-0.138921\pi$
$432$	−1.18264	+	1.26697i	−0.0569000	+	0.0609573i
$433$	−14.0622			−0.675787			−0.337894	−	0.941184i	$-0.609714\pi$
$433$	−14.0622			−0.675787			−0.337894	+	0.941184i	$0.609714\pi$
$434$	−2.86137	+	4.36314i	−0.137350	+	0.209437i
$435$	0.404876			0.0194123
$436$	−1.31640	−	3.02957i	−0.0630442	−	0.145090i
$437$	−15.1268			−0.723613
$438$	−0.977833	−	0.641269i	−0.0467227	−	0.0306410i
$439$			0.897327i			0.0428271i	0.999771	+	0.0214135i	$0.00681666\pi$
$439$			0.897327i			0.0428271i	−0.999771	+	0.0214135i	$0.993183\pi$
$440$	−9.04128	−	1.55703i	−0.431026	−	0.0742286i
$441$	−19.8839			−0.946851
$442$	−12.2303	−	1.24878i	−0.581734	−	0.0593985i
$443$			9.90397i			0.470552i	0.971929	+	0.235276i	$0.0755994\pi$
$443$			9.90397i			0.470552i	−0.971929	+	0.235276i	$0.924401\pi$
$444$	−0.402646	−	0.926650i	−0.0191087	−	0.0439768i
$445$	−5.24445			−0.248611
$446$	−12.1222	+	18.4845i	−0.574003	+	0.875264i
$447$			0.0869371i			0.00411198i
$448$	1.60671	−	4.52652i	0.0759098	−	0.213858i
$449$			41.1008i			1.93967i	0.243772	+	0.969833i	$0.421615\pi$
$449$			41.1008i			1.93967i	−0.243772	+	0.969833i	$0.578385\pi$
$450$	2.32260	−	3.54160i	0.109488	−	0.166952i
$451$		−	14.3229i		−	0.674441i
$452$	20.3081	−	8.82425i	0.955214	−	0.415058i
$453$	0.809614			0.0380390
$454$	−5.70039	+	8.69220i	−0.267533	+	0.407945i
$455$	−1.26587			−0.0593451
$456$	0.0590414	−	0.342838i	0.00276487	−	0.0160549i
$457$	3.84405			0.179817			0.0899086	−	0.995950i	$-0.471342\pi$
$457$	3.84405			0.179817			0.0899086	+	0.995950i	$0.471342\pi$
$458$	−30.8571	−	20.2362i	−1.44186	−	0.945578i
$459$	−1.58570	+	0.822899i	−0.0740142	+	0.0384097i
$460$	16.3057	−	7.08511i	0.760256	−	0.330345i
$461$			20.6103i			0.959918i	0.877291	+	0.479959i	$0.159348\pi$
$461$			20.6103i			0.959918i	−0.877291	+	0.479959i	$0.840652\pi$
$462$	0.166462	+	0.109167i	0.00774452	+	0.00507890i
$463$	11.7981			0.548302			0.274151	−	0.961687i	$-0.411603\pi$
$463$	11.7981			0.548302			0.274151	+	0.961687i	$0.411603\pi$
$464$	15.2893	−	16.3795i	0.709788	−	0.760400i
$465$		−	0.444150i		−	0.0205970i
$466$	23.7796	+	15.5948i	1.10157	+	0.722415i
$467$		−	29.7822i		−	1.37815i	−0.724688	−	0.689077i	$-0.758016\pi$
$467$		−	29.7822i		−	1.37815i	0.724688	−	0.689077i	$-0.241984\pi$
$468$	11.5821	−	5.03263i	0.535383	−	0.232633i
$469$	−4.95981			−0.229023
$470$	8.44976	−	12.8846i	0.389759	−	0.594320i
$471$			0.569812i			0.0262556i
$472$	−1.37568	+	7.98820i	−0.0633207	+	0.367687i
$473$			9.61715i			0.442197i
$474$	0.887386	+	0.581952i	0.0407590	+	0.0267300i
$475$			1.70170i			0.0780793i
$476$	3.12164	−	3.84294i	0.143080	−	0.176141i
$477$			38.5569i			1.76540i
$478$	9.32587	−	14.2205i	0.426555	−	0.650429i
$479$		−	29.1071i		−	1.32994i	−0.746872	−	0.664968i	$-0.768445\pi$
$479$		−	29.1071i		−	1.32994i	0.746872	−	0.664968i	$-0.231555\pi$
$480$	0.0969363	+	0.397210i	0.00442452	+	0.0181301i
$481$			14.7361i			0.671907i
$482$	22.0630	+	14.4690i	1.00494	+	0.659046i
$483$	−0.385757			−0.0175525
$484$	0.381675	+	0.878388i	0.0173489	+	0.0399267i
$485$		−	13.7724i		−	0.625371i
$486$	1.50998	−	2.30249i	0.0684942	−	0.104443i
$487$			7.71241i			0.349483i	0.984614	+	0.174741i	$0.0559089\pi$
$487$			7.71241i			0.349483i	−0.984614	+	0.174741i	$0.944091\pi$
$488$	−8.66474	−	1.49219i	−0.392234	−	0.0675481i
$489$	−1.19117			−0.0538664
$490$	−5.14928	+	7.85184i	−0.232621	+	0.354710i
$491$		−	21.0539i		−	0.950151i	−0.879945	−	0.475076i	$-0.842421\pi$
$491$		−	21.0539i		−	0.950151i	0.879945	−	0.475076i	$-0.157579\pi$
$492$	−0.585441	+	0.254385i	−0.0263937	+	0.0114685i
$493$	20.5001	−	10.6385i	0.923276	−	0.479134i
$494$	−2.78254	+	4.24293i	−0.125192	+	0.190898i
$495$	9.71395			0.436609
$496$	−17.9684	−	16.7724i	−0.806804	−	0.753104i
$497$	−0.280676			−0.0125900
$498$	0.510906	+	0.335055i	0.0228942	+	0.0150142i
$499$	10.3562			0.463607			0.231803	−	0.972763i	$-0.425537\pi$
$499$	10.3562			0.463607			0.231803	+	0.972763i	$0.425537\pi$
$500$	−0.797044	−	1.83432i	−0.0356449	−	0.0820332i
$501$		−	1.25880i		−	0.0562390i
$502$	29.1391	+	19.1096i	1.30054	+	0.852903i
$503$		−	6.63644i		−	0.295904i	−0.988995	−	0.147952i	$-0.952732\pi$
$503$		−	6.63644i		−	0.295904i	0.988995	−	0.147952i	$-0.0472681\pi$
$504$	−0.863123	+	5.01193i	−0.0384465	+	0.223249i
$505$			3.84878i			0.171268i
$506$	34.0981	+	22.3617i	1.51585	+	0.994100i
$507$	−0.618322			−0.0274606
$508$	12.2541	+	28.2015i	0.543686	+	1.25124i
$509$			29.4523i			1.30545i	0.757596	+	0.652724i	$0.226374\pi$
$509$			29.4523i			1.30545i	−0.757596	+	0.652724i	$0.773626\pi$
$510$	−0.0428101	+	0.419271i	−0.00189566	+	0.0185656i
$511$	−6.86855			−0.303847
$512$	19.7300	+	11.0782i	0.871951	+	0.489593i
$513$			0.737332i			0.0325540i
$514$	−5.21285	+	7.94878i	−0.229929	+	0.350605i
$515$	5.90603			0.260251
$516$	0.393095	−	0.170807i	0.0173050	−	0.00751935i
$517$	35.3400			1.55425
$518$	−4.96261	−	3.25451i	−0.218045	−	0.142995i
$519$	−0.905607			−0.0397517
$520$	1.01208	−	5.87688i	0.0443826	−	0.257718i
$521$			15.0438i			0.659082i	0.944141	+	0.329541i	$0.106894\pi$
$521$			15.0438i			0.659082i	−0.944141	+	0.329541i	$0.893106\pi$
$522$	−13.0103	+	19.8387i	−0.569447	+	0.868316i
$523$			9.50197i			0.415492i	0.978183	+	0.207746i	$0.0666128\pi$
$523$			9.50197i			0.415492i	−0.978183	+	0.207746i	$0.933387\pi$
$524$	−11.2972	−	25.9994i	−0.493520	−	1.13579i
$525$			0.0433960i			0.00189396i
$526$	−10.5764	+	16.1273i	−0.461153	+	0.703186i
$527$	−11.6705	−	22.4886i	−0.508374	−	0.979620i
$528$	−0.639901	+	0.685529i	−0.0278481	+	0.0298338i
$529$	−56.0184			−2.43558
$530$	15.2255	+	9.98500i	0.661356	+	0.433721i
$531$		−	8.58252i		−	0.372450i
$532$	−0.814343	−	1.87413i	−0.0353063	−	0.0812538i
$533$	9.31000			0.403261
$534$	−0.293980	+	0.448273i	−0.0127217	+	0.0193987i
$535$	3.95376			0.170936
$536$	3.96542	−	23.0262i	0.171280	−	0.994579i
$537$		−	1.23607i		−	0.0533403i
$538$	18.6510	−	28.4399i	0.804104	−	1.22613i
$539$	−21.5361			−0.927627
$540$	−0.345353	−	0.794795i	−0.0148616	−	0.0342025i
$541$	−9.89478			−0.425410			−0.212705	−	0.977116i	$-0.568227\pi$
$541$	−9.89478			−0.425410			−0.212705	+	0.977116i	$0.568227\pi$
$542$	7.28485	−	11.1082i	0.312911	−	0.477140i
$543$	1.59687			0.0685282
$544$	15.3453	+	17.5648i	0.657922	+	0.753086i
$545$	1.65160			0.0707470
$546$	−0.0709591	+	0.108201i	−0.00303677	+	0.00463059i
$547$	9.85752			0.421477			0.210739	−	0.977542i	$-0.432413\pi$
$547$	9.85752			0.421477			0.210739	+	0.977542i	$0.432413\pi$
$548$	4.23511	+	9.74669i	0.180915	+	0.416358i
$549$	9.30939			0.397315
$550$	2.51560	−	3.83589i	0.107265	−	0.163563i
$551$		−	9.53229i		−	0.406089i
$552$	0.308417	−	1.79090i	0.0131271	−	0.0762256i
$553$	6.23322			0.265063
$554$	22.4691	−	34.2618i	0.954619	−	1.45564i
$555$	0.505174			0.0214434
$556$	14.3368	+	32.9948i	0.608018	+	1.39929i
$557$			6.85866i			0.290611i	0.989387	+	0.145305i	$0.0464165\pi$
$557$			6.85866i			0.290611i	−0.989387	+	0.145305i	$0.953584\pi$
$558$	21.7631	+	14.2724i	0.921306	+	0.604198i
$559$	−6.25120			−0.264398
$560$	1.75561	+	1.63876i	0.0741882	+	0.0692503i
$561$	−0.857985	+	0.445251i	−0.0362241	+	0.0187985i
$562$	−10.2502	+	15.6300i	−0.432380	+	0.659311i
$563$		−	6.24108i		−	0.263030i	−0.991314	−	0.131515i	$-0.958016\pi$
$563$		−	6.24108i		−	0.263030i	0.991314	−	0.131515i	$-0.0419842\pi$
$564$	−0.627660	−	1.44450i	−0.0264293	−	0.0608243i
$565$			11.0712i			0.465769i
$566$	20.9104	−	31.8851i	0.878931	−	1.34023i
$567$		−	5.37541i		−	0.225746i
$568$	0.224403	−	1.30305i	0.00941575	−	0.0546748i
$569$	10.1745			0.426536			0.213268	−	0.976994i	$-0.431589\pi$
$569$	10.1745			0.426536			0.213268	+	0.976994i	$0.431589\pi$
$570$	0.145454	+	0.0953894i	0.00609239	+	0.00399542i
$571$	31.1761			1.30468			0.652339	−	0.757927i	$-0.273788\pi$
$571$	31.1761			1.30468			0.652339	+	0.757927i	$0.273788\pi$
$572$	12.5445	−	5.45082i	0.524513	−	0.227910i
$573$	−0.761073			−0.0317943
$574$	−2.05614	+	3.13529i	−0.0858217	+	0.130865i
$575$			8.88923i			0.370706i
$576$	−22.5781	−	8.01418i	−0.940752	−	0.333924i
$577$	29.3283			1.22095			0.610476	−	0.792035i	$-0.290978\pi$
$577$	29.3283			1.22095			0.610476	+	0.792035i	$0.290978\pi$
$578$	8.84915	+	22.3538i	0.368076	+	0.929796i
$579$		−	0.611323i		−	0.0254057i
$580$	4.46474	+	10.2752i	0.185388	+	0.426653i
$581$	3.58873			0.148886
$582$	−1.17720	−	0.772016i	−0.0487966	−	0.0320011i
$583$			41.7609i			1.72956i
$584$	5.49147	−	31.8876i	0.227239	−	1.31952i
$585$			6.31412i			0.261057i
$586$	7.44264	+	4.88093i	0.307453	+	0.201629i
$587$		−	17.6605i		−	0.728929i	−0.931217	−	0.364464i	$-0.881252\pi$
$587$		−	17.6605i		−	0.728929i	0.931217	−	0.364464i	$-0.118748\pi$
$588$	0.382496	+	0.880275i	0.0157739	+	0.0363019i
$589$	−10.4569			−0.430871
$590$	−3.38911	−	2.22259i	−0.139527	−	0.0915028i
$591$	−1.57705			−0.0648712
$592$	19.0769	−	20.4372i	0.784055	−	0.839962i
$593$	8.67511			0.356244			0.178122	−	0.984008i	$-0.442998\pi$
$593$	8.67511			0.356244			0.178122	+	0.984008i	$0.442998\pi$
$594$	1.08999	−	1.66206i	0.0447227	−	0.0681951i
$595$	1.14027	+	2.19727i	0.0467466	+	0.0900792i
$596$	−2.20634	+	0.958694i	−0.0903751	+	0.0392696i
$597$			0.0626714i			0.00256497i
$598$	−14.5352	+	22.1640i	−0.594390	+	0.906351i
$599$	−36.1426			−1.47674			−0.738372	−	0.674393i	$-0.764405\pi$
$599$	−36.1426			−1.47674			−0.738372	+	0.674393i	$0.764405\pi$
$600$	−0.201468	−	0.0346955i	−0.00822490	−	0.00141644i
$601$			29.1531i			1.18918i	0.804029	+	0.594590i	$0.202686\pi$
$601$			29.1531i			1.18918i	−0.804029	+	0.594590i	$0.797314\pi$
$602$	1.38060	−	2.10519i	0.0562690	−	0.0858013i
$603$			24.7393i			1.00746i
$604$	8.92797	+	20.5468i	0.363274	+	0.836039i
$605$	−0.478864			−0.0194686
$606$	0.328977	+	0.215745i	0.0133638	+	0.00876404i
$607$			27.3526i			1.11021i	0.831781	+	0.555104i	$0.187322\pi$
$607$			27.3526i			1.11021i	−0.831781	+	0.555104i	$0.812678\pi$
$608$	9.35181	−	2.28224i	0.379266	−	0.0925572i
$609$		−	0.243088i		−	0.00985043i
$610$	2.41083	−	3.67614i	0.0976117	−	0.148842i
$611$			22.9712i			0.929314i
$612$	−19.1684	−	15.5706i	−0.774836	−	0.629403i
$613$		−	45.5742i		−	1.84073i	−0.391065	−	0.920363i	$-0.627893\pi$
$613$		−	45.5742i		−	1.84073i	0.391065	−	0.920363i	$-0.372107\pi$
$614$	−32.4913	−	21.3080i	−1.31124	−	0.859921i
$615$		−	0.319160i		−	0.0128698i
$616$	−0.934845	+	5.42840i	−0.0376660	+	0.218717i
$617$			36.9239i			1.48650i	0.669013	+	0.743250i	$0.266717\pi$
$617$			36.9239i			1.48650i	−0.669013	+	0.743250i	$0.733283\pi$
$618$	0.331065	−	0.504821i	0.0133174	−	0.0203069i
$619$	−0.856032			−0.0344068			−0.0172034	−	0.999852i	$-0.505476\pi$
$619$	−0.856032			−0.0344068			−0.0172034	+	0.999852i	$0.505476\pi$
$620$	11.2719	−	4.89784i	0.452690	−	0.196702i
$621$			3.85163i			0.154561i
$622$	−21.5736	−	14.1481i	−0.865022	−	0.567286i
$623$			3.14878i			0.126153i
$624$	−0.445598	−	0.415939i	−0.0178382	−	0.0166509i
$625$	1.00000			0.0400000
$626$	−16.9572	−	11.1206i	−0.677747	−	0.444470i
$627$			0.398953i			0.0159326i
$628$	−14.4610	+	6.28357i	−0.577057	+	0.250742i
$629$	25.5785	−	13.2739i	1.01988	−	0.529267i
$630$	−2.12638	−	1.39449i	−0.0847171	−	0.0555579i
$631$	−7.32017			−0.291412			−0.145706	−	0.989328i	$-0.546545\pi$
$631$	−7.32017			−0.291412			−0.145706	+	0.989328i	$0.546545\pi$
$632$	−4.98352	+	28.9380i	−0.198234	+	1.15109i
$633$	−1.48006			−0.0588271
$634$	6.76046	−	10.3086i	0.268492	−	0.409408i
$635$	−15.3744			−0.610114
$636$	1.70695	−	0.741700i	0.0676849	−	0.0294103i
$637$		−	13.9986i		−	0.554645i
$638$	−14.0914	+	21.4872i	−0.557885	+	0.850687i
$639$			1.40000i			0.0553830i
$640$	−9.01166	+	6.84032i	−0.356217	+	0.270387i
$641$			15.1115i			0.596869i	0.954430	+	0.298434i	$0.0964644\pi$
$641$			15.1115i			0.596869i	−0.954430	+	0.298434i	$0.903536\pi$
$642$	0.221630	−	0.337950i	0.00874702	−	0.0133378i
$643$	−7.16882			−0.282711			−0.141355	−	0.989959i	$-0.545146\pi$
$643$	−7.16882			−0.282711			−0.141355	+	0.989959i	$0.545146\pi$
$644$	−4.25391	−	9.78996i	−0.167628	−	0.385778i
$645$			0.214300i			0.00843807i
$646$	9.87121	+	1.00791i	0.388377	+	0.0396556i
$647$	20.8410			0.819346			0.409673	−	0.912233i	$-0.365643\pi$
$647$	20.8410			0.819346			0.409673	+	0.912233i	$0.365643\pi$
$648$	24.9556	+	4.29769i	0.980348	+	0.168829i
$649$		−	9.29569i		−	0.364888i
$650$	2.49335	+	1.63515i	0.0977972	+	0.0641360i
$651$	−0.266668			−0.0104516
$652$	−13.1355	−	30.2301i	−0.514426	−	1.18390i
$653$	2.07393			0.0811591			0.0405796	−	0.999176i	$-0.487080\pi$
$653$	2.07393			0.0811591			0.0405796	+	0.999176i	$0.487080\pi$
$654$	0.0925813	−	0.141172i	0.00362022	−	0.00552026i
$655$	14.1739			0.553819
$656$	−12.9118	−	12.0524i	−0.504123	−	0.470569i
$657$			34.2600i			1.33661i
$658$	−7.73591	−	5.07326i	−0.301577	−	0.197776i
$659$		−	6.06141i		−	0.236119i	−0.993007	−	0.118060i	$-0.962333\pi$
$659$		−	6.06141i		−	0.236119i	0.993007	−	0.118060i	$-0.0376674\pi$
$660$	−0.186862	−	0.430044i	−0.00727360	−	0.0167395i
$661$			20.3183i			0.790289i	0.918619	+	0.395145i	$0.129306\pi$
$661$			20.3183i			0.790289i	−0.918619	+	0.395145i	$0.870694\pi$
$662$	24.5248	+	16.0835i	0.953182	+	0.625102i
$663$	−0.289416	−	0.557695i	−0.0112400	−	0.0216591i
$664$	−2.86923	+	16.6609i	−0.111348	+	0.646567i
$665$	1.02170			0.0396200
$666$	−16.2333	+	24.7533i	−0.629029	+	0.959170i
$667$		−	49.7941i		−	1.92804i
$668$	31.9465	−	13.8813i	1.23605	−	0.537085i
$669$	−1.12974			−0.0436784
$670$	9.76918	+	6.40668i	0.377416	+	0.247512i
$671$	10.0830			0.389249
$672$	0.238486	−	0.0582007i	0.00919979	−	0.00224514i
$673$		−	48.1640i		−	1.85659i	−0.371848	−	0.928294i	$-0.621276\pi$
$673$		−	48.1640i		−	1.85659i	0.371848	−	0.928294i	$-0.378724\pi$
$674$	6.56235	+	4.30362i	0.252772	+	0.165769i
$675$	0.433292			0.0166774
$676$	−6.81851	−	15.6921i	−0.262250	−	0.603543i
$677$	−6.64023			−0.255205			−0.127602	−	0.991825i	$-0.540728\pi$
$677$	−6.64023			−0.255205			−0.127602	+	0.991825i	$0.540728\pi$
$678$	0.946319	+	0.620601i	0.0363431	+	0.0238340i
$679$	−8.26896			−0.317334
$680$	−11.1126	+	3.53703i	−0.426148	+	0.135639i
$681$	−0.531254			−0.0203577
$682$	23.5715	+	15.4584i	0.902601	+	0.591931i
$683$	−37.0078			−1.41606			−0.708032	−	0.706180i	$-0.750417\pi$
$683$	−37.0078			−1.41606			−0.708032	+	0.706180i	$0.750417\pi$
$684$	−9.34806	+	4.06190i	−0.357432	+	0.155311i
$685$	−5.31352			−0.203019
$686$	9.68447	+	6.35113i	0.369755	+	0.242487i
$687$		−	1.88594i		−	0.0719531i
$688$	8.66966	+	8.09262i	0.330528	+	0.308528i
$689$	−27.1448			−1.03413
$690$	0.759812	+	0.498289i	0.0289256	+	0.0189695i
$691$	−5.25264			−0.199820			−0.0999100	−	0.994996i	$-0.531855\pi$
$691$	−5.25264			−0.199820			−0.0999100	+	0.994996i	$0.531855\pi$
$692$	−9.98653	−	22.9830i	−0.379631	−	0.873682i
$693$		−	5.83227i		−	0.221550i
$694$	23.8916	−	36.4309i	0.906913	−	1.38290i
$695$	−17.9875			−0.682305
$696$	1.12855	+	0.194351i	0.0427775	+	0.00736687i
$697$	−8.38624	−	16.1600i	−0.317652	−	0.612104i
$698$	−6.17297	−	4.04827i	−0.233650	−	0.153229i
$699$			1.45337i			0.0549717i
$700$	−1.10133	+	0.478547i	−0.0416263	+	0.0180874i
$701$			15.2674i			0.576640i	0.957534	+	0.288320i	$0.0930967\pi$
$701$			15.2674i			0.576640i	−0.957534	+	0.288320i	$0.906903\pi$
$702$	1.08035	+	0.708498i	0.0407751	+	0.0267405i
$703$		−	11.8937i		−	0.448579i
$704$	−24.4542	−	8.68013i	−0.921653	−	0.327145i
$705$	0.787485			0.0296584
$706$	17.7428	−	27.0549i	0.667758	−	1.01823i
$707$	2.31082			0.0869072
$708$	−0.379955	+	0.165097i	−0.0142796	+	0.00620474i
$709$	11.8011			0.443200			0.221600	−	0.975138i	$-0.428872\pi$
$709$	11.8011			0.443200			0.221600	+	0.975138i	$0.428872\pi$
$710$	0.552838	+	0.362554i	0.0207476	+	0.0136064i
$711$		−	31.0910i		−	1.16600i
$712$	−14.6184	−	2.51748i	−0.547846	−	0.0943466i
$713$	−54.6243			−2.04570
$714$	0.251731	+	0.0257032i	0.00942080	+	0.000961920i
$715$			6.83880i			0.255757i
$716$	31.3697	−	13.6307i	1.17234	−	0.509403i
$717$	0.869134			0.0324584
$718$	9.46199	−	14.4280i	0.353118	−	0.538449i
$719$			41.5687i			1.55025i	0.631807	+	0.775125i	$0.282313\pi$
$719$			41.5687i			1.55025i	−0.631807	+	0.775125i	$0.717687\pi$
$720$	8.17406	−	8.75692i	0.304629	−	0.326351i
$721$		−	3.54599i		−	0.132060i
$722$	−12.4896	+	19.0447i	−0.464816	+	0.708771i
$723$			1.34846i			0.0501497i
$724$	17.6094	+	40.5262i	0.654447	+	1.50615i
$725$	−5.60163			−0.208039
$726$	−0.0268429	+	0.0409312i	−0.000996233	+	0.00151910i
$727$	16.5087			0.612273			0.306136	−	0.951988i	$-0.400964\pi$
$727$	16.5087			0.612273			0.306136	+	0.951988i	$0.400964\pi$
$728$	−3.52849	−	0.607654i	−0.130775	−	0.0225212i
$729$	−26.7183			−0.989567
$730$	13.5287	+	8.87223i	0.500721	+	0.328376i
$731$	5.63095	+	10.8507i	0.208268	+	0.401326i
$732$	−0.179080	−	0.412134i	−0.00661898	−	0.0152329i
$733$			7.56946i			0.279584i	0.990181	+	0.139792i	$0.0446435\pi$
$733$			7.56946i			0.279584i	−0.990181	+	0.139792i	$0.955357\pi$
$734$	−0.190627	−	0.125014i	−0.00703615	−	0.00461435i
$735$	−0.479893			−0.0177011
$736$	48.8514	−	11.9218i	1.80069	−	0.439445i
$737$			26.7950i			0.987008i
$738$	15.6387	+	10.2559i	0.575668	+	0.377526i
$739$			28.7104i			1.05613i	0.849204	+	0.528064i	$0.177082\pi$
$739$			28.7104i			1.05613i	−0.849204	+	0.528064i	$0.822918\pi$
$740$	5.57078	+	12.8206i	0.204786	+	0.471294i
$741$	−0.259322			−0.00952642
$742$	5.99501	−	9.14145i	0.220084	−	0.335593i
$743$		−	9.41700i		−	0.345476i	−0.984968	−	0.172738i	$-0.944739\pi$
$743$		−	9.41700i		−	0.345476i	0.984968	−	0.172738i	$-0.0552614\pi$
$744$	0.213204	−	1.23802i	0.00781644	−	0.0453881i
$745$		−	1.20281i		−	0.0440676i
$746$	29.6679	+	19.4564i	1.08622	+	0.712349i
$747$		−	17.9004i		−	0.654942i
$748$	−20.7612	−	16.8644i	−0.759105	−	0.616625i
$749$		−	2.37385i		−	0.0867384i
$750$	0.0560554	−	0.0854756i	0.00204685	−	0.00312113i
$751$		−	6.20328i		−	0.226361i	−0.993574	−	0.113181i	$-0.963896\pi$
$751$		−	6.20328i		−	0.226361i	0.993574	−	0.113181i	$-0.0361038\pi$
$752$	29.7378	−	31.8582i	1.08443	−	1.16175i
$753$			1.78094i			0.0649011i
$754$	−13.9668	−	9.15951i	−0.508641	−	0.333570i
$755$	−11.2014			−0.407659
$756$	−0.477196	+	0.207350i	−0.0173555	+	0.00754126i
$757$			22.6850i			0.824499i	0.911071	+	0.412250i	$0.135257\pi$
$757$			22.6850i			0.824499i	−0.911071	+	0.412250i	$0.864743\pi$
$758$	10.0824	−	15.3741i	0.366210	−	0.558413i
$759$			2.08403i			0.0756453i
$760$	−0.816863	+	4.74331i	−0.0296307	+	0.172058i
$761$	16.4440			0.596096			0.298048	−	0.954551i	$-0.403664\pi$
$761$	16.4440			0.596096			0.298048	+	0.954551i	$0.403664\pi$
$762$	−0.861817	+	1.31413i	−0.0312203	+	0.0476061i
$763$		−	0.991627i		−	0.0358993i
$764$	−8.39269	−	19.3149i	−0.303637	−	0.698790i
$765$	10.9599	−	5.68762i	0.396255	−	0.205636i
$766$	7.99997	−	12.1987i	0.289051	−	0.440757i
$767$	6.04225			0.218173
$768$	0.0795280	+	1.15371i	0.00286972	+	0.0416311i
$769$	19.4363			0.700892			0.350446	−	0.936583i	$-0.386030\pi$
$769$	19.4363			0.700892			0.350446	+	0.936583i	$0.386030\pi$
$770$	−2.30308	−	1.51037i	−0.0829971	−	0.0544299i
$771$	−0.485817			−0.0174963
$772$	15.5145	−	6.74133i	0.558379	−	0.242626i
$773$			27.8588i			1.00201i	0.865444	+	0.501006i	$0.167037\pi$
$773$			27.8588i			1.00201i	−0.865444	+	0.501006i	$0.832963\pi$
$774$	−10.5006	−	6.88636i	−0.377436	−	0.247525i
$775$			6.14500i			0.220735i
$776$	6.61112	−	38.3891i	0.237325	−	1.37809i
$777$		−	0.303308i		−	0.0108811i
$778$	−35.1630	−	23.0601i	−1.26065	−	0.826743i
$779$	−7.51422			−0.269225
$780$	0.279531	−	0.121461i	0.0100088	−	0.00434902i
$781$			1.51633i			0.0542586i
$782$	51.5646	+	5.26505i	1.84395	+	0.188278i
$783$	−2.42714			−0.0867389
$784$	−18.1222	+	19.4144i	−0.647220	+	0.693371i
$785$		−	7.88359i		−	0.281378i
$786$	0.794522	−	1.21152i	0.0283396	−	0.0432135i
$787$	46.8253			1.66914			0.834572	−	0.550899i	$-0.185715\pi$
$787$	46.8253			1.66914			0.834572	+	0.550899i	$0.185715\pi$
$788$	−17.3908	−	40.0233i	−0.619523	−	1.42577i
$789$	−0.985680			−0.0350911
$790$	−12.2774	−	8.05156i	−0.436809	−	0.286462i
$791$	6.64718			0.236346
$792$	27.0766	+	4.66296i	0.962125	+	0.165691i
$793$			6.55398i			0.232739i
$794$	−9.72120	+	14.8233i	−0.344992	+	0.526059i
$795$			0.930563i			0.0330037i
$796$	−1.59051	+	0.691106i	−0.0563742	+	0.0244956i
$797$		−	19.4665i		−	0.689540i	−0.938687	−	0.344770i	$-0.887957\pi$
$797$		−	19.4665i		−	0.689540i	0.938687	−	0.344770i	$-0.112043\pi$
$798$	0.0572720	−	0.0873308i	0.00202741	−	0.00309148i
$799$	39.8727	−	20.6919i	1.41059	−	0.732028i
$800$	−1.34115	−	5.49557i	−0.0474170	−	0.194298i
$801$	15.7060			0.554943
$802$	−6.78763	−	4.45137i	−0.239680	−	0.157183i
$803$			37.1068i			1.30947i
$804$	1.09523	−	0.475897i	0.0386258	−	0.0167836i
$805$	5.33711			0.188108
$806$	−10.0480	+	15.3216i	−0.353926	+	0.539682i
$807$	1.73820			0.0611877
$808$	−1.84752	+	10.7281i	−0.0649955	+	0.377412i
$809$		−	15.4185i		−	0.542085i	−0.962567	−	0.271043i	$-0.912632\pi$
$809$		−	15.4185i		−	0.542085i	0.962567	−	0.271043i	$-0.0873684\pi$
$810$	−6.94351	+	10.5878i	−0.243970	+	0.372016i
$811$	−41.0529			−1.44156			−0.720781	−	0.693163i	$-0.756217\pi$
$811$	−41.0529			−1.44156			−0.720781	+	0.693163i	$0.756217\pi$
$812$	6.16923	−	2.68064i	0.216497	−	0.0940721i
$813$	0.678919			0.0238107
$814$	−17.5823	+	26.8102i	−0.616258	+	0.939696i
$815$	16.4803			0.577279
$816$	−0.320590	+	1.14812i	−0.0112229	+	0.0401924i
$817$	5.04543			0.176517
$818$	−3.88459	+	5.92339i	−0.135822	+	0.207107i
$819$	3.79101			0.132469
$820$	8.09982	−	3.51952i	0.282858	−	0.122907i
$821$	−34.2501			−1.19534			−0.597668	−	0.801744i	$-0.703906\pi$
$821$	−34.2501			−1.19534			−0.597668	+	0.801744i	$0.703906\pi$
$822$	−0.297852	+	0.454177i	−0.0103888	+	0.0158412i
$823$			2.29212i			0.0798982i	0.999202	+	0.0399491i	$0.0127196\pi$
$823$			2.29212i			0.0798982i	−0.999202	+	0.0399491i	$0.987280\pi$
$824$	16.4624	+	2.83505i	0.573496	+	0.0987638i
$825$	0.234444			0.00816229
$826$	−1.33445	+	2.03483i	−0.0464315	+	0.0708007i
$827$	−30.0936			−1.04646			−0.523229	−	0.852192i	$-0.675273\pi$
$827$	−30.0936			−1.04646			−0.523229	+	0.852192i	$0.675273\pi$
$828$	−48.8318	+	21.2183i	−1.69702	+	0.737387i
$829$		−	47.5949i		−	1.65304i	−0.562908	−	0.826519i	$-0.690318\pi$
$829$		−	47.5949i		−	1.65304i	0.562908	−	0.826519i	$-0.309682\pi$
$830$	−7.06860	−	4.63563i	−0.245355	−	0.160905i
$831$	2.09403			0.0726411
$832$	5.64213	−	15.8954i	0.195606	−	0.551073i
$833$	−24.2984	+	12.6096i	−0.841889	+	0.436898i
$834$	−1.00830	+	1.53749i	−0.0349145	+	0.0532391i
$835$			17.4160i			0.602707i
$836$	−10.1249	+	4.39943i	−0.350175	+	0.152158i
$837$			2.66258i			0.0920322i
$838$	14.7527	−	22.4955i	0.509623	−	0.777094i
$839$		−	33.5374i		−	1.15784i	−0.815385	−	0.578920i	$-0.803474\pi$
$839$		−	33.5374i		−	1.15784i	0.815385	−	0.578920i	$-0.196526\pi$
$840$	−0.0208313	+	0.120962i	−0.000718747	+	0.00417358i
$841$	2.37822			0.0820077
$842$	−15.9715	−	10.4742i	−0.550413	−	0.360964i
$843$	−0.955282			−0.0329017
$844$	−16.3213	−	37.5618i	−0.561802	−	1.29293i
$845$	8.55474			0.294292
$846$	−25.3051	+	38.5864i	−0.870009	+	1.32663i
$847$			0.287511i			0.00987898i
$848$	37.6465	+	35.1408i	1.29279	+	1.20674i
$849$	1.94877			0.0668816
$850$	0.592295	−	5.80079i	0.0203156	−	0.198966i
$851$		−	62.1295i		−	2.12977i
$852$	0.0619791	−	0.0269310i	0.00212337	−	0.000922642i
$853$	−1.81771			−0.0622373			−0.0311186	−	0.999516i	$-0.509907\pi$
$853$	−1.81771			−0.0622373			−0.0311186	+	0.999516i	$0.509907\pi$
$854$	−2.20716	−	1.44747i	−0.0755274	−	0.0495313i
$855$		−	5.09621i		−	0.174287i
$856$	11.0207	+	1.89791i	0.376680	+	0.0648694i
$857$			10.8395i			0.370271i	0.982713	+	0.185135i	$0.0592724\pi$
$857$			10.8395i			0.370271i	−0.982713	+	0.185135i	$0.940728\pi$
$858$	0.584550	+	0.383351i	0.0199562	+	0.0130874i
$859$			8.54352i			0.291501i	0.989321	+	0.145751i	$0.0465597\pi$
$859$			8.54352i			0.291501i	−0.989321	+	0.145751i	$0.953440\pi$
$860$	−5.43863	+	2.36318i	−0.185456	+	0.0805839i
$861$	−0.191624			−0.00653054
$862$	20.7561	+	13.6120i	0.706956	+	0.463626i
$863$	−10.5865			−0.360369			−0.180185	−	0.983633i	$-0.557670\pi$
$863$	−10.5865			−0.360369			−0.180185	+	0.983633i	$0.557670\pi$
$864$	−0.581111	−	2.38119i	−0.0197698	−	0.0810096i
$865$	12.5295			0.426014
$866$	10.9060	−	16.6299i	0.370600	−	0.565106i
$867$	−0.707331	+	1.00472i	−0.0240222	+	0.0341220i
$868$	−2.94067	−	6.76766i	−0.0998129	−	0.229709i
$869$		−	33.6745i		−	1.14233i
$870$	−0.314001	+	0.478802i	−0.0106456	+	0.0162329i
$871$	−17.4169			−0.590150
$872$	4.60368	+	0.792816i	0.155900	+	0.0268481i
$873$			41.2452i			1.39594i
$874$	11.7316	−	17.8888i	0.396827	−	0.605098i
$875$		−	0.600402i		−	0.0202973i
$876$	1.51672	−	0.659041i	0.0512451	−	0.0222669i
$877$	−16.2737			−0.549524			−0.274762	−	0.961512i	$-0.588599\pi$
$877$	−16.2737			−0.549524			−0.274762	+	0.961512i	$0.588599\pi$
$878$	−1.06117	−	0.695922i	−0.0358128	−	0.0234862i
$879$			0.454883i			0.0153428i
$880$	8.85330	−	9.48458i	0.298445	−	0.319725i
$881$			30.7607i			1.03635i	0.855273	+	0.518177i	$0.173389\pi$
$881$			30.7607i			1.03635i	−0.855273	+	0.518177i	$0.826611\pi$
$882$	15.4209	−	23.5145i	0.519250	−	0.791774i
$883$			34.3181i			1.15489i	0.816428	+	0.577447i	$0.195951\pi$
$883$			34.3181i			1.15489i	−0.816428	+	0.577447i	$0.804049\pi$
$884$	10.9620	−	13.4949i	0.368691	−	0.453883i
$885$		−	0.207137i		−	0.00696284i
$886$	−11.7123	−	7.68102i	−0.393484	−	0.258049i
$887$		−	30.5930i		−	1.02721i	−0.858026	−	0.513607i	$-0.828309\pi$
$887$		−	30.5930i		−	1.02721i	0.858026	−	0.513607i	$-0.171691\pi$
$888$	1.40812	+	0.242497i	0.0472534	+	0.00813768i
$889$			9.23081i			0.309591i
$890$	4.06733	−	6.20204i	0.136337	−	0.207893i
$891$	−29.0403			−0.972885
$892$	−12.4582	−	28.6712i	−0.417130	−	0.959984i
$893$		−	18.5403i		−	0.620429i
$894$	−0.102811	−	0.0674240i	−0.00343851	−	0.00225500i
$895$			17.1015i			0.571642i
$896$	4.10694	+	5.41062i	0.137203	+	0.180756i
$897$	−1.35463			−0.0452297
$898$	−48.6054	−	31.8757i	−1.62198	−	1.06371i
$899$		−	34.4220i		−	1.14804i
$900$	2.38697	+	5.49337i	0.0795656	+	0.183112i
$901$	24.4514	+	47.1172i	0.814596	+	1.56970i
$902$	16.9382	+	11.1082i	0.563980	+	0.369861i
$903$	0.128666			0.00428175
$904$	−5.31449	+	30.8598i	−0.176757	+	1.02638i
$905$	−22.0934			−0.734408
$906$	−0.627896	+	0.957443i	−0.0208605	+	0.0318089i
$907$	−25.1500			−0.835093			−0.417547	−	0.908655i	$-0.637110\pi$
$907$	−25.1500			−0.835093			−0.417547	+	0.908655i	$0.637110\pi$
$908$	−5.85838	−	13.4825i	−0.194417	−	0.447432i
$909$		−	11.5262i		−	0.382301i
$910$	0.981749	−	1.49701i	0.0325447	−	0.0496255i
$911$			46.0371i			1.52528i	0.646825	+	0.762639i	$0.276097\pi$
$911$			46.0371i			1.52528i	−0.646825	+	0.762639i	$0.723903\pi$
$912$	0.359648	+	0.335710i	0.0119091	+	0.0111165i
$913$		−	19.3879i		−	0.641645i
$914$	−2.98126	+	4.54594i	−0.0986112	+	0.150366i
$915$	0.224680			0.00742769
$916$	47.8624	−	20.7971i	1.58142	−	0.687155i
$917$		−	8.51002i		−	0.281026i
$918$	0.256637	−	2.51344i	0.00847027	−	0.0829557i
$919$	−10.1555			−0.334998			−0.167499	−	0.985872i	$-0.553569\pi$
$919$	−10.1555			−0.334998			−0.167499	+	0.985872i	$0.553569\pi$
$920$	−4.26707	+	24.7778i	−0.140681	+	0.816900i
$921$		−	1.98582i		−	0.0654350i
$922$	−24.3736	−	15.9843i	−0.802701	−	0.526416i
$923$	−0.985624			−0.0324422
$924$	−0.258200	+	0.112192i	−0.00849414	+	0.00369086i
$925$	−6.98930			−0.229807
$926$	−9.14999	+	13.9523i	−0.300687	+	0.458501i
$927$	−17.6872			−0.580925
$928$	7.51265	+	30.7841i	0.246615	+	1.01054i
$929$			7.21799i			0.236815i	0.992965	+	0.118407i	$0.0377789\pi$
$929$			7.21799i			0.236815i	−0.992965	+	0.118407i	$0.962221\pi$
$930$	0.525248	+	0.344460i	0.0172236	+	0.0112953i
$931$			11.2985i			0.370292i
$932$	−36.8845	+	16.0270i	−1.20819	+	0.524982i
$933$		−	1.31855i		−	0.0431673i
$934$	35.2201	+	23.0976i	1.15244	+	0.755775i
$935$	11.8706	−	6.16024i	0.388210	−	0.201461i
$936$	−3.03095	+	17.5999i	−0.0990697	+	0.575272i
$937$	47.6772			1.55755			0.778774	−	0.627305i	$-0.215842\pi$
$937$	47.6772			1.55755			0.778774	+	0.627305i	$0.215842\pi$
$938$	3.84658	−	5.86543i	0.125595	−	0.191513i
$939$		−	1.03640i		−	0.0338216i
$940$	8.68395	+	19.9852i	0.283239	+	0.651846i
$941$	13.9923			0.456137			0.228069	−	0.973645i	$-0.426759\pi$
$941$	13.9923			0.456137			0.228069	+	0.973645i	$0.426759\pi$
$942$	−0.673855	−	0.441918i	−0.0219554	−	0.0143985i
$943$	−39.2523			−1.27823
$944$	−8.37987	−	7.82212i	−0.272742	−	0.254588i
$945$		−	0.260149i		−	0.00846266i
$946$	−11.3732	−	7.45858i	−0.369773	−	0.242500i
$947$	36.7607			1.19456			0.597281	−	0.802032i	$-0.296248\pi$
$947$	36.7607			1.19456			0.597281	+	0.802032i	$0.296248\pi$
$948$	−1.37642	+	0.598081i	−0.0447042	+	0.0194248i
$949$	−24.1197			−0.782957
$950$	−2.01242	−	1.31975i	−0.0652914	−	0.0428184i
$951$	0.630048			0.0204307
$952$	2.12364	+	6.67201i	0.0688276	+	0.216241i
$953$	−43.3201			−1.40328			−0.701638	−	0.712534i	$-0.747547\pi$
$953$	−43.3201			−1.40328			−0.701638	+	0.712534i	$0.747547\pi$
$954$	−45.5971	−	29.9028i	−1.47626	−	0.968140i
$955$	10.5298			0.340735
$956$	9.58433	+	22.0574i	0.309979	+	0.713386i
$957$	−1.31327			−0.0424519
$958$	34.4218	+	22.5740i	1.11212	+	0.729333i
$959$			3.19025i			0.103019i
$960$	−0.544916	−	0.193420i	−0.0175871	−	0.00624262i
$961$	−6.76105			−0.218098
$962$	−17.4268	−	11.4286i	−0.561861	−	0.368472i
$963$	−11.8406			−0.381559
$964$	−34.2219	+	14.8700i	−1.10221	+	0.478932i
$965$			8.45792i			0.272270i
$966$	0.299174	−	0.456193i	0.00962576	−	0.0146778i
$967$	−56.8267			−1.82742			−0.913711	−	0.406364i	$-0.866797\pi$
$967$	−56.8267			−1.82742			−0.913711	+	0.406364i	$0.866797\pi$
$968$	−1.33478	−	0.229868i	−0.0429015	−	0.00738823i
$969$	0.233591	+	0.450123i	0.00750403	+	0.0144600i
$970$	16.2871	+	10.6812i	0.522947	+	0.342952i
$971$		−	18.6599i		−	0.598823i	−0.954124	−	0.299412i	$-0.903210\pi$
$971$		−	18.6599i		−	0.598823i	0.954124	−	0.299412i	$-0.0967904\pi$
$972$	1.55183	+	3.57139i	0.0497750	+	0.114552i
$973$			10.7997i			0.346224i
$974$	−9.12063	−	5.98136i	−0.292244	−	0.191655i
$975$			0.152390i			0.00488038i
$976$	8.48459	−	9.08958i	0.271585	−	0.290950i
$977$	−6.17905			−0.197685			−0.0988427	−	0.995103i	$-0.531514\pi$
$977$	−6.17905			−0.197685			−0.0988427	+	0.995103i	$0.531514\pi$
$978$	0.923808	−	1.40866i	0.0295401	−	0.0450440i
$979$	17.0111			0.543676
$980$	−5.29199	−	12.1790i	−0.169046	−	0.389043i
$981$	−4.94619			−0.157920
$982$	24.8982	+	16.3284i	0.794534	+	0.521060i
$983$		−	2.60855i		−	0.0832000i	−0.999134	−	0.0416000i	$-0.986754\pi$
$983$		−	2.60855i		−	0.0832000i	0.999134	−	0.0416000i	$-0.0132455\pi$
$984$	0.153206	−	0.889626i	0.00488402	−	0.0283602i
$985$	21.8192			0.695216
$986$	−3.31782	+	32.4939i	−0.105661	+	1.03482i
$987$		−	0.472808i		−	0.0150496i
$988$	−2.85966	−	6.58121i	−0.0909778	−	0.209376i
$989$	26.3560			0.838072
$990$	−7.53365	+	11.4876i	−0.239435	+	0.365101i
$991$			31.1921i			0.990850i	0.868651	+	0.495425i	$0.164988\pi$
$991$			31.1921i			0.990850i	−0.868651	+	0.495425i	$0.835012\pi$
$992$	33.7703	−	8.24140i	1.07221	−	0.261665i
$993$			1.49892i			0.0475667i
$994$	0.217678	−	0.331925i	0.00690433	−	0.0105280i
$995$		−	0.867086i		−	0.0274885i
$996$	−0.792466	+	0.344341i	−0.0251103	+	0.0109109i
$997$	−22.5159			−0.713084			−0.356542	−	0.934279i	$-0.616044\pi$
$997$	−22.5159			−0.713084			−0.356542	+	0.934279i	$0.616044\pi$
$998$	−8.03174	+	12.2471i	−0.254240	+	0.387676i
$999$	−3.02841			−0.0958145

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.l.a.101.12	yes	36
4.3	odd	2		2720.2.l.b.2481.17		36
8.3	odd	2		2720.2.l.a.2481.19		36
8.5	even	2		680.2.l.b.101.11	yes	36
17.16	even	2		680.2.l.b.101.12	yes	36
68.67	odd	2		2720.2.l.a.2481.20		36
136.67	odd	2		2720.2.l.b.2481.18		36
136.101	even	2	inner	680.2.l.a.101.11	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.l.a.101.11	✓	36	136.101	even	2	inner
680.2.l.a.101.12	yes	36	1.1	even	1	trivial
680.2.l.b.101.11	yes	36	8.5	even	2
680.2.l.b.101.12	yes	36	17.16	even	2
2720.2.l.a.2481.19		36	8.3	odd	2
2720.2.l.a.2481.20		36	68.67	odd	2
2720.2.l.b.2481.17		36	4.3	odd	2
2720.2.l.b.2481.18		36	136.67	odd	2

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.775550 + 1.18259i) q^{2} -0.0722782 q^{3} +(-0.797044 - 1.83432i) q^{4} +1.00000 q^{5} +(0.0560554 - 0.0854756i) q^{6} -0.600402i q^{7} +(2.78740 + 0.480027i) q^{8} -2.99478 q^{9} +(-0.775550 + 1.18259i) q^{10} -3.24363 q^{11} +(0.0576089 + 0.132581i) q^{12} -2.10838i q^{13} +(0.710030 + 0.465642i) q^{14} -0.0722782 q^{15} +(-2.72944 + 2.92406i) q^{16} +(-3.65966 + 1.89918i) q^{17} +(2.32260 - 3.54160i) q^{18} +1.70170i q^{19} +(-0.797044 - 1.83432i) q^{20} +0.0433960i q^{21} +(2.51560 - 3.83589i) q^{22} +8.88923i q^{23} +(-0.201468 - 0.0346955i) q^{24} +1.00000 q^{25} +(2.49335 + 1.63515i) q^{26} +0.433292 q^{27} +(-1.10133 + 0.478547i) q^{28} -5.60163 q^{29} +(0.0560554 - 0.0854756i) q^{30} +6.14500i q^{31} +(-1.34115 - 5.49557i) q^{32} +0.234444 q^{33} +(0.592295 - 5.80079i) q^{34} -0.600402i q^{35} +(2.38697 + 5.49337i) q^{36} -6.98930 q^{37} +(-2.01242 - 1.31975i) q^{38} +0.152390i q^{39} +(2.78740 + 0.480027i) q^{40} +4.41572i q^{41} +(-0.0513197 - 0.0336558i) q^{42} -2.96494i q^{43} +(2.58532 + 5.94985i) q^{44} -2.99478 q^{45} +(-10.5123 - 6.89404i) q^{46} -10.8952 q^{47} +(0.197279 - 0.211346i) q^{48} +6.63952 q^{49} +(-0.775550 + 1.18259i) q^{50} +(0.264514 - 0.137269i) q^{51} +(-3.86743 + 1.68047i) q^{52} -12.8747i q^{53} +(-0.336039 + 0.512407i) q^{54} -3.24363 q^{55} +(0.288209 - 1.67356i) q^{56} -0.122996i q^{57} +(4.34434 - 6.62443i) q^{58} +2.86583i q^{59} +(0.0576089 + 0.132581i) q^{60} -3.10854 q^{61} +(-7.26703 - 4.76576i) q^{62} +1.79807i q^{63} +(7.53915 + 2.67605i) q^{64} -2.10838i q^{65} +(-0.181823 + 0.277251i) q^{66} -8.26082i q^{67} +(6.40061 + 5.19925i) q^{68} -0.642498i q^{69} +(0.710030 + 0.465642i) q^{70} -0.467480i q^{71} +(-8.34762 - 1.43757i) q^{72} -11.4399i q^{73} +(5.42055 - 8.26548i) q^{74} -0.0722782 q^{75} +(3.12146 - 1.35633i) q^{76} +1.94748i q^{77} +(-0.180215 - 0.118186i) q^{78} +10.3817i q^{79} +(-2.72944 + 2.92406i) q^{80} +8.95301 q^{81} +(-5.22199 - 3.42461i) q^{82} +5.97721i q^{83} +(0.0796020 - 0.0345885i) q^{84} +(-3.65966 + 1.89918i) q^{85} +(3.50631 + 2.29946i) q^{86} +0.404876 q^{87} +(-9.04128 - 1.55703i) q^{88} -5.24445 q^{89} +(2.32260 - 3.54160i) q^{90} -1.26587 q^{91} +(16.3057 - 7.08511i) q^{92} -0.444150i q^{93} +(8.44976 - 12.8846i) q^{94} +1.70170i q^{95} +(0.0969363 + 0.397210i) q^{96} -13.7724i q^{97} +(-5.14928 + 7.85184i) q^{98} +9.71395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{3} + 2 q^{4} + 36 q^{5} + 36 q^{9} - 8 q^{11} - 2 q^{12} + 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} + 2 q^{20} + 26 q^{24} + 36 q^{25} + 6 q^{26} - 16 q^{27} + 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots - 40 q^{99}+O(q^{100}) \) 36 * q - 4 * q^3 + 2 * q^4 + 36 * q^5 + 36 * q^9 - 8 * q^11 - 2 * q^12 + 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 + 2 * q^20 + 26 * q^24 + 36 * q^25 + 6 * q^26 - 16 * q^27 + 14 * q^28 - 10 * q^32 - 8 * q^33 - 24 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 + 6 * q^44 + 36 * q^45 + 24 * q^46 + 20 * q^47 - 4 * q^48 - 36 * q^49 + 6 * q^52 - 56 * q^54 - 8 * q^55 + 20 * q^56 - 18 * q^58 - 2 * q^60 - 24 * q^62 + 14 * q^64 - 16 * q^66 - 40 * q^68 + 2 * q^70 - 54 * q^72 + 6 * q^74 - 4 * q^75 + 2 * q^76 - 14 * q^78 + 6 * q^80 + 44 * q^81 + 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 - 58 * q^88 - 10 * q^90 - 56 * q^91 - 12 * q^92 + 14 * q^94 - 24 * q^96 + 10 * q^98 - 40 * q^99

Introduction

L-functions

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