LMFDB - Embedded newform 392.2.z.a.109.49

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(37,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([0, 21, 32])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.z (of order $42$, degree $12$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			109.49
Character	$\chi$	$=$	392.109
Dual form			392.2.z.a.205.49

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34520 - 0.436384i) q^{2} +(0.296979 + 1.97033i) q^{3} +(1.61914 - 1.17405i) q^{4} +(0.830993 + 0.326141i) q^{5} +(1.25932 + 2.52089i) q^{6} +(1.00756 - 2.44639i) q^{7} +(1.66573 - 2.28590i) q^{8} +(-0.927279 + 0.286028i) q^{9} +(1.26018 + 0.0760928i) q^{10} +(-0.0695882 + 0.225599i) q^{11} +(2.79411 + 2.84156i) q^{12} +(-1.87545 + 0.428060i) q^{13} +(0.287799 - 3.73057i) q^{14} +(-0.395817 + 1.73419i) q^{15} +(1.24321 - 3.80190i) q^{16} +(-5.72947 + 3.90628i) q^{17} +(-1.12256 + 0.789415i) q^{18} +(-2.06708 + 1.19343i) q^{19} +(1.72840 - 0.447561i) q^{20} +(5.11942 + 1.25869i) q^{21} +(0.00483787 + 0.333844i) q^{22} +(5.14256 + 3.50614i) q^{23} +(4.99866 + 2.60317i) q^{24} +(-3.08108 - 2.85882i) q^{25} +(-2.33607 + 1.39425i) q^{26} +(1.75470 + 3.64367i) q^{27} +(-1.24082 - 5.14397i) q^{28} +(0.663324 - 1.37741i) q^{29} +(0.224318 + 2.50556i) q^{30} +(0.282206 - 0.488795i) q^{31} +(0.0132814 - 5.65684i) q^{32} +(-0.465171 - 0.0701133i) q^{33} +(-6.00265 + 7.75499i) q^{34} +(1.63514 - 1.70433i) q^{35} +(-1.16558 + 1.55179i) q^{36} +(-11.9524 + 0.895709i) q^{37} +(-2.25985 + 2.50745i) q^{38} +(-1.40039 - 3.56813i) q^{39} +(2.12974 - 1.35631i) q^{40} +(-3.07554 - 3.85661i) q^{41} +(7.43592 - 0.540843i) q^{42} +(4.72536 + 3.76835i) q^{43} +(0.152192 + 0.446976i) q^{44} +(-0.863848 - 0.0647364i) q^{45} +(8.44780 + 2.47233i) q^{46} +(4.25334 - 3.94653i) q^{47} +(7.86019 + 1.32045i) q^{48} +(-4.96966 - 4.92975i) q^{49} +(-5.39222 - 2.50116i) q^{50} +(-9.39819 - 10.1288i) q^{51} +(-2.53405 + 2.89497i) q^{52} +(-1.27621 - 0.0956390i) q^{53} +(3.95046 + 4.13575i) q^{54} +(-0.131405 + 0.164776i) q^{55} +(-3.91389 - 6.37820i) q^{56} +(-2.96533 - 3.71841i) q^{57} +(0.291226 - 2.14235i) q^{58} +(-7.44878 + 2.92343i) q^{59} +(1.39514 + 3.27260i) q^{60} +(12.7297 - 0.953956i) q^{61} +(0.166322 - 0.780679i) q^{62} +(-0.234550 + 2.55668i) q^{63} +(-2.45069 - 7.61539i) q^{64} +(-1.69810 - 0.255947i) q^{65} +(-0.656345 + 0.108677i) q^{66} +(-5.72433 - 3.30494i) q^{67} +(-4.69062 + 13.0515i) q^{68} +(-5.38101 + 11.1738i) q^{69} +(1.45585 - 3.00622i) q^{70} +(6.57661 - 3.16713i) q^{71} +(-0.890765 + 2.59611i) q^{72} +(-7.04465 - 6.53648i) q^{73} +(-15.6875 + 6.42076i) q^{74} +(4.71780 - 6.91974i) q^{75} +(-1.94574 + 4.35919i) q^{76} +(0.481790 + 0.397544i) q^{77} +(-3.44089 - 4.18875i) q^{78} +(-0.456582 - 0.790823i) q^{79} +(2.27305 - 2.75389i) q^{80} +(-9.06344 + 6.17935i) q^{81} +(-5.82019 - 3.84580i) q^{82} +(6.00526 + 1.37066i) q^{83} +(9.76680 - 3.97246i) q^{84} +(-6.03515 + 1.37748i) q^{85} +(8.00102 + 3.00712i) q^{86} +(2.91094 + 0.897905i) q^{87} +(0.399783 + 0.534859i) q^{88} +(8.44981 - 2.60642i) q^{89} +(-1.19030 + 0.289886i) q^{90} +(-0.842422 + 5.01939i) q^{91} +(12.4429 - 0.360706i) q^{92} +(1.04690 + 0.410877i) q^{93} +(3.99940 - 7.16497i) q^{94} +(-2.10696 + 0.317573i) q^{95} +(11.1498 - 1.65379i) q^{96} +4.64123 q^{97} +(-8.83647 - 4.46283i) q^{98} -0.229098i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25}+ \cdots + 151 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{20}{21}\right)$

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 $

$2$	1.34520	−	0.436384i	0.951202	−	0.308570i
$2$	1.34520	−	0.436384i	0.951202	−	0.308570i
$3$	0.296979	+	1.97033i	0.171461	+	1.13757i	0.894600	+	0.446867i	$0.147460\pi$
$3$	0.296979	+	1.97033i	0.171461	+	1.13757i	−0.723139	+	0.690702i	$0.757302\pi$
$4$	1.61914	−	1.17405i	0.809569	−	0.587025i
$5$	0.830993	+	0.326141i	0.371632	+	0.145855i	0.543804	−	0.839212i	$-0.316983\pi$
$5$	0.830993	+	0.326141i	0.371632	+	0.145855i	−0.172173	+	0.985067i	$0.555079\pi$
$6$	1.25932	+	2.52089i	0.514114	+	1.02915i
$7$	1.00756	−	2.44639i	0.380820	−	0.924649i
$7$	1.00756	−	2.44639i	0.380820	−	0.924649i
$8$	1.66573	−	2.28590i	0.588924	−	0.808188i
$9$	−0.927279	+	0.286028i	−0.309093	+	0.0953425i
$10$	1.26018	+	0.0760928i	0.398503	+	0.0240627i
$11$	−0.0695882	+	0.225599i	−0.0209816	+	0.0680208i	−0.965458	−	0.260558i	$-0.916093\pi$
$11$	−0.0695882	+	0.225599i	−0.0209816	+	0.0680208i	0.944477	+	0.328579i	$0.106570\pi$
$12$	2.79411	+	2.84156i	0.806592	+	0.820289i
$13$	−1.87545	+	0.428060i	−0.520157	+	0.118722i	−0.474536	−	0.880236i	$-0.657384\pi$
$13$	−1.87545	+	0.428060i	−0.520157	+	0.118722i	−0.0456216	+	0.998959i	$0.514527\pi$
$14$	0.287799	−	3.73057i	0.0769176	−	0.997037i
$15$	−0.395817	+	1.73419i	−0.102199	+	0.447765i
$16$	1.24321	−	3.80190i	0.310803	−	0.950474i
$17$	−5.72947	+	3.90628i	−1.38960	+	0.947413i	−0.389953	+	0.920835i	$0.627509\pi$
$17$	−5.72947	+	3.90628i	−1.38960	+	0.947413i	−0.999647	+	0.0265780i	$0.991539\pi$
$18$	−1.12256	+	0.789415i	−0.264590	+	0.186067i
$19$	−2.06708	+	1.19343i	−0.474222	+	0.273792i	−0.718005	−	0.696038i	$-0.754945\pi$
$19$	−2.06708	+	1.19343i	−0.474222	+	0.273792i	0.243784	+	0.969830i	$0.421611\pi$
$20$	1.72840	−	0.447561i	0.386482	−	0.100078i
$21$	5.11942	+	1.25869i	1.11715	+	0.274668i
$22$	0.00483787	+	0.333844i	0.00103144	+	0.0711758i
$23$	5.14256	+	3.50614i	1.07230	+	0.731080i	0.964763	−	0.263121i	$-0.0847520\pi$
$23$	5.14256	+	3.50614i	1.07230	+	0.731080i	0.107535	+	0.994201i	$0.465704\pi$
$24$	4.99866	+	2.60317i	1.02035	+	0.531370i
$25$	−3.08108	−	2.85882i	−0.616215	−	0.571764i
$26$	−2.33607	+	1.39425i	−0.458140	+	0.273434i
$27$	1.75470	+	3.64367i	0.337692	+	0.701224i
$28$	−1.24082	−	5.14397i	−0.234492	−	0.972118i
$29$	0.663324	−	1.37741i	0.123176	−	0.255778i	−0.830258	−	0.557379i	$-0.811807\pi$
$29$	0.663324	−	1.37741i	0.123176	−	0.255778i	0.953434	+	0.301601i	$0.0975212\pi$
$30$	0.224318	+	2.50556i	0.0409548	+	0.457451i
$31$	0.282206	−	0.488795i	0.0506857	−	0.0877902i	−0.839569	−	0.543252i	$-0.817193\pi$
$31$	0.282206	−	0.488795i	0.0506857	−	0.0877902i	0.890255	+	0.455462i	$0.150526\pi$
$32$	0.0132814	−	5.65684i	0.00234785	−	0.999997i
$33$	−0.465171	−	0.0701133i	−0.0809759	−	0.0122052i
$34$	−6.00265	+	7.75499i	−1.02945	+	1.32997i
$35$	1.63514	−	1.70433i	0.276389	−	0.288084i
$36$	−1.16558	+	1.55179i	−0.194263	+	0.258632i
$37$	−11.9524	+	0.895709i	−1.96496	+	0.147254i	−0.995276	−	0.0970899i	$-0.969047\pi$
$37$	−11.9524	+	0.895709i	−1.96496	+	0.147254i	−0.969689	+	0.244344i	$0.921428\pi$
$38$	−2.25985	+	2.50745i	−0.366596	+	0.406762i
$39$	−1.40039	−	3.56813i	−0.224242	−	0.571359i
$40$	2.12974	−	1.35631i	0.336741	−	0.214451i
$41$	−3.07554	−	3.85661i	−0.480319	−	0.602301i	0.481345	−	0.876531i	$-0.340149\pi$
$41$	−3.07554	−	3.85661i	−0.480319	−	0.602301i	−0.961664	+	0.274230i	$0.911577\pi$
$42$	7.43592	−	0.540843i	1.14739	−	0.0834539i
$43$	4.72536	+	3.76835i	0.720611	+	0.574668i	0.913640	−	0.406525i	$-0.133260\pi$
$43$	4.72536	+	3.76835i	0.720611	+	0.574668i	−0.193028	+	0.981193i	$0.561831\pi$
$44$	0.152192	+	0.446976i	0.0229438	+	0.0673842i
$45$	−0.863848	−	0.0647364i	−0.128775	−	0.00965034i
$46$	8.44780	+	2.47233i	1.24556	+	0.364525i
$47$	4.25334	−	3.94653i	0.620414	−	0.575660i	−0.306063	−	0.952011i	$-0.599012\pi$
$47$	4.25334	−	3.94653i	0.620414	−	0.575660i	0.926477	+	0.376351i	$0.122821\pi$
$48$	7.86019	+	1.32045i	1.13452	+	0.190590i
$49$	−4.96966	−	4.92975i	−0.709952	−	0.704250i
$50$	−5.39222	−	2.50116i	−0.762575	−	0.353717i
$51$	−9.39819	−	10.1288i	−1.31601	−	1.41832i
$52$	−2.53405	+	2.89497i	−0.351410	+	0.401459i
$53$	−1.27621	−	0.0956390i	−0.175301	−	0.0131370i	−0.0132098	−	0.999913i	$-0.504205\pi$
$53$	−1.27621	−	0.0956390i	−0.175301	−	0.0131370i	−0.162092	+	0.986776i	$0.551824\pi$
$54$	3.95046	+	4.13575i	0.537590	+	0.562804i
$55$	−0.131405	+	0.164776i	−0.0177186	+	0.0222184i
$56$	−3.91389	−	6.37820i	−0.523016	−	0.852323i
$57$	−2.96533	−	3.71841i	−0.392768	−	0.492516i
$58$	0.291226	−	2.14235i	0.0382399	−	0.281305i
$59$	−7.44878	+	2.92343i	−0.969749	+	0.380599i	−0.796740	−	0.604322i	$-0.793444\pi$
$59$	−7.44878	+	2.92343i	−0.969749	+	0.380599i	−0.173009	+	0.984920i	$0.555349\pi$
$60$	1.39514	+	3.27260i	0.180112	+	0.422490i
$61$	12.7297	−	0.953956i	1.62987	−	0.122142i	0.771864	−	0.635788i	$-0.219325\pi$
$61$	12.7297	−	0.953956i	1.62987	−	0.122142i	0.858002	+	0.513646i	$0.171706\pi$
$62$	0.166322	−	0.780679i	0.0211229	−	0.0991463i
$63$	−0.234550	+	2.55668i	−0.0295505	+	0.322111i
$64$	−2.45069	−	7.61539i	−0.306336	−	0.951923i
$65$	−1.69810	−	0.255947i	−0.210623	−	0.0317463i
$66$	−0.656345	+	0.108677i	−0.0807905	+	0.0133772i
$67$	−5.72433	−	3.30494i	−0.699338	−	0.403763i	0.107763	−	0.994177i	$-0.465631\pi$
$67$	−5.72433	−	3.30494i	−0.699338	−	0.403763i	−0.807101	+	0.590414i	$0.798965\pi$
$68$	−4.69062	+	13.0515i	−0.568821	+	1.58273i
$69$	−5.38101	+	11.1738i	−0.647797	+	1.34516i
$70$	1.45585	−	3.00622i	0.174008	−	0.359312i
$71$	6.57661	−	3.16713i	0.780500	−	0.375869i	−0.000820196	−	1.00000i	$-0.500261\pi$
$71$	6.57661	−	3.16713i	0.780500	−	0.375869i	0.781320	+	0.624131i	$0.214547\pi$
$72$	−0.890765	+	2.59611i	−0.104978	+	0.305955i
$73$	−7.04465	−	6.53648i	−0.824514	−	0.765037i	0.150162	−	0.988661i	$-0.452021\pi$
$73$	−7.04465	−	6.53648i	−0.824514	−	0.765037i	−0.974675	+	0.223624i	$0.928211\pi$
$74$	−15.6875	+	6.42076i	−1.82364	+	0.746398i
$75$	4.71780	−	6.91974i	0.544765	−	0.799023i
$76$	−1.94574	+	4.35919i	−0.223192	+	0.500034i
$77$	0.481790	+	0.397544i	0.0549051	+	0.0453043i
$78$	−3.44089	−	4.18875i	−0.389604	−	0.474283i
$79$	−0.456582	−	0.790823i	−0.0513694	−	0.0889745i	0.839197	−	0.543827i	$-0.183025\pi$
$79$	−0.456582	−	0.790823i	−0.0513694	−	0.0889745i	−0.890567	+	0.454853i	$0.849692\pi$
$80$	2.27305	−	2.75389i	0.254135	−	0.307894i
$81$	−9.06344	+	6.17935i	−1.00705	+	0.686594i
$82$	−5.82019	−	3.84580i	−0.642733	−	0.424698i
$83$	6.00526	+	1.37066i	0.659163	+	0.150450i	0.539002	−	0.842305i	$-0.318802\pi$
$83$	6.00526	+	1.37066i	0.659163	+	0.150450i	0.120161	+	0.992754i	$0.461659\pi$
$84$	9.76680	−	3.97246i	1.06565	−	0.433431i
$85$	−6.03515	+	1.37748i	−0.654604	+	0.149409i
$86$	8.00102	+	3.00712i	0.862772	+	0.324266i
$87$	2.91094	+	0.897905i	0.312085	+	0.0962655i
$88$	0.399783	+	0.534859i	0.0426170	+	0.0570162i
$89$	8.44981	−	2.60642i	0.895678	−	0.276280i	0.187458	−	0.982273i	$-0.439975\pi$
$89$	8.44981	−	2.60642i	0.895678	−	0.276280i	0.708219	+	0.705993i	$0.249499\pi$
$90$	−1.19030	+	0.289886i	−0.125469	+	0.0305567i
$91$	−0.842422	+	5.01939i	−0.0883098	+	0.526175i
$92$	12.4429	−	0.360706i	1.29726	−	0.0376062i
$93$	1.04690	+	0.410877i	0.108558	+	0.0426059i
$94$	3.99940	−	7.16497i	0.412507	−	0.739010i
$95$	−2.10696	+	0.317573i	−0.216170	+	0.0325823i
$96$	11.1498	−	1.65379i	1.13797	−	0.168790i
$97$	4.64123			0.471246			0.235623	−	0.971845i	$-0.424287\pi$
$97$	4.64123			0.471246			0.235623	+	0.971845i	$0.424287\pi$
$98$	−8.83647	−	4.46283i	−0.892618	−	0.450814i
$99$		−	0.229098i		−	0.0230252i
$100$	−8.34509	−	1.01149i	−0.834509	−	0.101149i
$101$	0.162441	+	1.07772i	0.0161634	+	0.107237i	0.995458	−	0.0952043i	$-0.0303504\pi$
$101$	0.162441	+	1.07772i	0.0161634	+	0.107237i	−0.979294	+	0.202442i	$0.935112\pi$
$102$	−17.0625	−	9.52412i	−1.68944	−	0.943028i
$103$	−2.21422	+	5.64174i	−0.218174	+	0.555897i	−0.997496	−	0.0707262i	$-0.977468\pi$
$103$	−2.21422	+	5.64174i	−0.218174	+	0.555897i	0.779322	+	0.626623i	$0.215564\pi$
$104$	−2.14550	+	5.00013i	−0.210383	+	0.490304i
$105$	3.84369	+	2.71561i	0.375106	+	0.265017i
$106$	−1.75850	+	0.428266i	−0.170801	+	0.0415969i
$107$	−4.83980	−	15.6902i	−0.467881	−	1.51683i	−0.815252	−	0.579106i	$-0.803402\pi$
$107$	−4.83980	−	15.6902i	−0.467881	−	1.51683i	0.347371	−	0.937728i	$-0.387074\pi$
$108$	7.11895	+	3.83950i	0.685021	+	0.369456i
$109$	−3.19735	+	10.3655i	−0.306250	+	0.992839i	0.663384	+	0.748279i	$0.269120\pi$
$109$	−3.19735	+	10.3655i	−0.306250	+	0.992839i	−0.969634	+	0.244560i	$0.921356\pi$
$110$	−0.104860	+	0.279000i	−0.00999800	+	0.0266016i
$111$	−5.31446	−	23.2842i	−0.504426	−	2.21004i
$112$	−8.04832	−	6.87201i	−0.760495	−	0.649344i
$113$	−1.75028	+	7.66849i	−0.164653	+	0.721391i	0.823424	+	0.567427i	$0.192061\pi$
$113$	−1.75028	+	7.66849i	−0.164653	+	0.721391i	−0.988076	+	0.153964i	$0.950796\pi$
$114$	−5.61163	−	3.70799i	−0.525577	−	0.347285i
$115$	3.12994	+	4.59077i	0.291868	+	0.428092i
$116$	−0.543132	−	3.00899i	−0.0504286	−	0.279377i
$117$	1.61663	−	0.933363i	0.149458	−	0.0862894i
$118$	−8.74438	+	7.18314i	−0.804985	+	0.661262i
$119$	3.78354	+	17.9523i	0.346837	+	1.64569i
$120$	3.30486	+	3.79348i	0.301691	+	0.346296i
$121$	9.04257	+	6.16512i	0.822052	+	0.560466i
$122$	16.7077	−	6.83829i	1.51264	−	0.619110i
$123$	6.68542	−	7.20517i	0.602804	−	0.649668i
$124$	−0.116940	−	1.12275i	−0.0105015	−	0.100826i
$125$	−3.56462	−	7.40201i	−0.318829	−	0.662056i
$126$	0.800177	+	3.54160i	0.0712854	+	0.315511i
$127$	13.1779	+	6.34614i	1.16935	+	0.563129i	0.914790	−	0.403929i	$-0.132356\pi$
$127$	13.1779	+	6.34614i	1.16935	+	0.563129i	0.254558	+	0.967057i	$0.418070\pi$
$128$	−6.61991	−	9.17479i	−0.585123	−	0.810945i
$129$	−6.02156	+	10.4296i	−0.530169	+	0.918279i
$130$	−2.39598	+	0.396723i	−0.210141	+	0.0347949i
$131$	−0.328571	+	2.17993i	−0.0287074	+	0.190461i	−0.998588	−	0.0531188i	$-0.983084\pi$
$131$	−0.328571	+	2.17993i	−0.0287074	+	0.190461i	0.969881	+	0.243580i	$0.0783219\pi$
$132$	−0.835492	+	0.432611i	−0.0727203	+	0.0376540i
$133$	0.836898	+	6.25935i	0.0725683	+	0.542754i
$134$	−9.14260	−	1.94781i	−0.789800	−	0.168265i
$135$	0.269793	+	3.60014i	0.0232201	+	0.309851i
$136$	−0.614362	+	19.6038i	−0.0526811	+	1.68101i
$137$	8.00578	+	20.3984i	0.683980	+	1.74275i	0.669450	+	0.742857i	$0.266530\pi$
$137$	8.00578	+	20.3984i	0.683980	+	1.74275i	0.0145295	+	0.999894i	$0.495375\pi$
$138$	−2.36248	+	17.3792i	−0.201108	+	1.47941i
$139$	−5.07510	+	4.04725i	−0.430464	+	0.343284i	−0.814631	−	0.579980i	$-0.803060\pi$
$139$	−5.07510	+	4.04725i	−0.430464	+	0.343284i	0.384167	+	0.923264i	$0.374489\pi$
$140$	0.646548	−	4.67928i	0.0546433	−	0.395471i
$141$	9.03911	+	7.20845i	0.761230	+	0.607061i
$142$	7.46478	−	7.13035i	0.626430	−	0.598366i
$143$	0.0339393	−	0.452889i	0.00283815	−	0.0378725i
$144$	−0.0653556	+	3.88101i	−0.00544630	+	0.323418i
$145$	1.00045	−	0.928279i	0.0830826	−	0.0770894i
$146$	−12.3289	−	5.71871i	−1.02035	−	0.473284i
$147$	8.23735	−	11.2559i	0.679405	−	0.928371i
$148$	−18.3010	+	15.4830i	−1.50433	+	1.27270i
$149$	3.73478	+	4.02514i	0.305965	+	0.329752i	0.867252	−	0.497869i	$-0.165884\pi$
$149$	3.73478	+	4.02514i	0.305965	+	0.329752i	−0.561287	+	0.827621i	$0.689694\pi$
$150$	3.32673	−	11.3672i	0.271626	−	0.928130i
$151$	0.444487	−	5.93126i	0.0361718	−	0.482679i	−0.949473	−	0.313848i	$-0.898382\pi$
$151$	0.444487	−	5.93126i	0.0361718	−	0.482679i	0.985645	−	0.168831i	$-0.0539993\pi$
$152$	−0.715137	+	6.71309i	−0.0580052	+	0.544503i
$153$	4.19551	−	5.26100i	0.339187	−	0.425327i
$154$	0.821587	+	0.324531i	0.0662054	+	0.0261515i
$155$	0.393927	−	0.314147i	0.0316410	−	0.0252329i
$156$	−6.45659	−	4.13317i	−0.516941	−	0.330919i
$157$	−2.95337	+	1.15911i	−0.235704	+	0.0925072i	−0.480253	−	0.877130i	$-0.659455\pi$
$157$	−2.95337	+	1.15911i	−0.235704	+	0.0925072i	0.244549	+	0.969637i	$0.421360\pi$
$158$	−0.959297	−	0.864571i	−0.0763176	−	0.0687816i
$159$	−0.190569	−	2.54296i	−0.0151131	−	0.201670i
$160$	1.85596	−	4.69646i	0.146727	−	0.371288i
$161$	13.7588	−	9.04808i	1.08434	−	0.713089i
$162$	−9.49558	+	12.2676i	−0.746044	+	0.963835i
$163$	0.0459340	−	0.304752i	0.00359783	−	0.0238700i	−0.986960	−	0.160966i	$-0.948539\pi$
$163$	0.0459340	−	0.304752i	0.00359783	−	0.0238700i	0.990558	+	0.137096i	$0.0437770\pi$
$164$	−9.50758	−	2.63354i	−0.742418	−	0.205645i
$165$	−0.363687	−	0.209975i	−0.0283130	−	0.0163465i
$166$	8.67643	−	0.776785i	0.673421	−	0.0602902i
$167$	6.35851	+	3.06210i	0.492036	+	0.236952i	0.663413	−	0.748253i	$-0.269107\pi$
$167$	6.35851	+	3.06210i	0.492036	+	0.236952i	−0.171377	+	0.985206i	$0.554822\pi$
$168$	11.4048	−	9.60585i	0.879900	−	0.741107i
$169$	−8.37850	+	4.03488i	−0.644500	+	0.310375i
$170$	−7.51738	+	4.48664i	−0.576557	+	0.344109i
$171$	1.57541	−	1.69789i	0.120475	−	0.129841i
$172$	12.0753	+	0.553664i	0.920729	+	0.0422165i
$173$	11.9695	−	17.5560i	0.910023	−	1.33476i	−0.0320973	−	0.999485i	$-0.510219\pi$
$173$	11.9695	−	17.5560i	0.910023	−	1.33476i	0.942121	−	0.335274i	$-0.108829\pi$
$174$	4.30763	−	0.0624236i	0.326561	−	0.00473232i
$175$	−10.0982	+	4.65710i	−0.763349	+	0.352043i
$176$	0.771193	+	0.545035i	0.0581309	+	0.0410835i
$177$	−7.97226	−	13.8084i	−0.599231	−	1.03790i
$178$	10.2293	−	7.19353i	0.766718	−	0.539178i
$179$	1.20576	+	1.76853i	0.0901230	+	0.132186i	0.868653	−	0.495422i	$-0.164986\pi$
$179$	1.20576	+	1.76853i	0.0901230	+	0.132186i	−0.778530	+	0.627608i	$0.784034\pi$
$180$	−1.47469	+	0.909384i	−0.109917	+	0.0677815i
$181$	−20.1386	−	4.59652i	−1.49689	−	0.341656i	−0.605852	−	0.795577i	$-0.707168\pi$
$181$	−20.1386	−	4.59652i	−1.49689	−	0.341656i	−0.891042	+	0.453921i	$0.850025\pi$
$182$	1.05715	+	7.11971i	0.0783615	+	0.527748i
$183$	5.66005	+	24.7983i	0.418403	+	1.83314i
$184$	16.5808	−	5.91510i	1.22235	−	0.436067i
$185$	−10.2245	−	3.15384i	−0.751720	−	0.231875i
$186$	1.58759	+	0.0958627i	0.116408	+	0.00702900i
$187$	−0.482552	−	1.56439i	−0.0352877	−	0.114400i
$188$	2.25333	−	11.3836i	0.164341	−	0.830235i
$189$	10.6818	−	0.621479i	0.776986	−	0.0452059i
$190$	−2.69570	+	1.34665i	−0.195567	+	0.0976959i
$191$	7.28275	−	18.5562i	0.526962	−	1.34268i	−0.381369	−	0.924423i	$-0.624547\pi$
$191$	7.28275	−	18.5562i	0.526962	−	1.34268i	0.908330	−	0.418253i	$-0.137358\pi$
$192$	14.2770	−	7.09028i	1.03035	−	0.511697i
$193$	11.7348	−	1.76873i	0.844686	−	0.127316i	0.287579	−	0.957757i	$-0.407150\pi$
$193$	11.7348	−	1.76873i	0.844686	−	0.127316i	0.557107	+	0.830441i	$0.311911\pi$
$194$	6.24340	−	2.02536i	0.448250	−	0.145413i
$195$		−	3.42182i		−	0.245042i
$196$	−13.8343	−	2.14731i	−0.988167	−	0.153380i
$197$		−	12.6863i		−	0.903861i	−0.892053	−	0.451931i	$-0.850735\pi$
$197$		−	12.6863i		−	0.903861i	0.892053	−	0.451931i	$-0.149265\pi$
$198$	−0.0999746	−	0.308183i	−0.00710489	−	0.0219016i
$199$	4.93328	−	0.743572i	0.349711	−	0.0527104i	0.0281618	−	0.999603i	$-0.491035\pi$
$199$	4.93328	−	0.743572i	0.349711	−	0.0527104i	0.321549	+	0.946893i	$0.395797\pi$
$200$	−11.6672	+	2.28101i	−0.824997	+	0.161292i
$201$	4.81181	−	12.2603i	0.339399	−	0.864775i
$202$	0.688817	+	1.37887i	0.0484650	+	0.0970169i
$203$	−2.70134	−	3.01057i	−0.189597	−	0.211300i
$204$	−27.1087	−	5.36604i	−1.89799	−	0.375698i
$205$	−1.29796	−	4.20788i	−0.0906534	−	0.293891i
$206$	−0.516606	+	8.55553i	−0.0359936	+	0.596092i
$207$	−5.77144	−	1.78025i	−0.401143	−	0.123736i
$208$	−0.704144	+	7.66245i	−0.0488236	+	0.531295i
$209$	−0.125393	−	0.549382i	−0.00867360	−	0.0380015i
$210$	6.35559	+	1.97572i	0.438578	+	0.136338i
$211$	16.5791	+	3.78408i	1.14136	+	0.260507i	0.751093	−	0.660197i	$-0.229527\pi$
$211$	16.5791	+	3.78408i	1.14136	+	0.260507i	0.390263	+	0.920704i	$0.372384\pi$
$212$	−2.17865	+	1.34349i	−0.149630	+	0.0922710i
$213$	8.19340	+	12.0175i	0.561402	+	0.823426i
$214$	−13.3575	−	18.9945i	−0.913099	−	1.29844i
$215$	2.69773	+	4.67261i	0.183984	+	0.318669i
$216$	11.2519	+	2.05830i	0.765596	+	0.140050i
$217$	−0.911446	−	1.18287i	−0.0618730	−	0.0802988i
$218$	0.222284	+	15.3390i	0.0150550	+	1.03889i
$219$	10.7869	−	15.8215i	0.728911	−	1.06912i
$220$	−0.0193066	+	0.421071i	−0.00130165	+	0.0283886i
$221$	9.07322	−	9.77861i	0.610331	−	0.657780i
$222$	−17.3099	−	29.0028i	−1.16176	−	1.94654i
$223$	−16.5746	+	7.98189i	−1.10991	+	0.534507i	−0.896762	−	0.442512i	$-0.854087\pi$
$223$	−16.5746	+	7.98189i	−1.10991	+	0.534507i	−0.213152	+	0.977019i	$0.568373\pi$
$224$	−13.8255	−	5.73207i	−0.923752	−	0.382990i
$225$	3.67472	+	1.76965i	0.244981	+	0.117977i
$226$	0.991926	+	11.0795i	0.0659819	+	0.736995i
$227$	6.80198	+	3.92713i	0.451463	+	0.260653i	0.708448	−	0.705763i	$-0.249396\pi$
$227$	6.80198	+	3.92713i	0.451463	+	0.260653i	−0.256985	+	0.966415i	$0.582729\pi$
$228$	−9.16689	−	2.53917i	−0.607092	−	0.168160i
$229$	2.56701	−	17.0310i	0.169633	−	1.12544i	−0.728284	−	0.685276i	$-0.759682\pi$
$229$	2.56701	−	17.0310i	0.169633	−	1.12544i	0.897917	−	0.440166i	$-0.145080\pi$
$230$	6.21374	+	4.80966i	0.409722	+	0.317140i
$231$	−0.640210	+	1.06735i	−0.0421228	+	0.0702263i
$232$	−2.04370	−	3.81068i	−0.134175	−	0.250183i
$233$	−0.0298007	−	0.397663i	−0.00195231	−	0.0260518i	0.996143	−	0.0877496i	$-0.0279675\pi$
$233$	−0.0298007	−	0.397663i	−0.00195231	−	0.0260518i	−0.998095	+	0.0616978i	$0.980348\pi$
$234$	1.76739	−	1.96103i	0.115538	−	0.128197i
$235$	4.82162	−	1.89235i	0.314528	−	0.123443i
$236$	−8.62835	+	13.4787i	−0.561658	+	0.877388i
$237$	1.42258	−	1.13447i	0.0924068	−	0.0736920i
$238$	12.9237	+	22.4984i	0.837721	+	1.45836i
$239$	−3.61005	+	4.52685i	−0.233514	+	0.292818i	−0.884758	−	0.466051i	$-0.845676\pi$
$239$	−3.61005	+	4.52685i	−0.233514	+	0.292818i	0.651243	+	0.758869i	$0.274248\pi$
$240$	6.10112	+	3.66082i	0.393825	+	0.236305i
$241$	−0.686420	+	9.15964i	−0.0442162	+	0.590024i	0.930459	+	0.366397i	$0.119409\pi$
$241$	−0.686420	+	9.15964i	−0.0442162	+	0.590024i	−0.974675	+	0.223627i	$0.928210\pi$
$242$	14.8545	+	4.34730i	0.954880	+	0.279455i
$243$	−6.61480	−	7.12906i	−0.424340	−	0.457329i
$244$	19.4911	−	16.4898i	1.24779	−	1.05565i
$245$	−2.52196	−	5.71740i	−0.161122	−	0.365271i
$246$	5.84902	−	12.6098i	0.372920	−	0.803973i
$247$	3.36586	−	3.12306i	0.214165	−	0.198716i
$248$	−0.647259	−	1.45930i	−0.0411010	−	0.0926654i
$249$	−0.917216	+	12.2394i	−0.0581262	+	0.775640i
$250$	−8.02526	−	8.40166i	−0.507562	−	0.531368i
$251$	14.9427	+	11.9164i	0.943177	+	0.752158i	0.968885	−	0.247511i	$-0.0796126\pi$
$251$	14.9427	+	11.9164i	0.943177	+	0.752158i	−0.0257082	+	0.999669i	$0.508184\pi$
$252$	2.62190	+	4.41498i	0.165164	+	0.278118i
$253$	−1.14884	+	0.916172i	−0.0722272	+	0.0575992i
$254$	20.4963	+	2.78621i	1.28605	+	0.174822i
$255$	−4.50641	−	11.4821i	−0.282202	−	0.719039i
$256$	−12.9089	−	9.45312i	−0.806803	−	0.590820i
$257$	1.98320	+	26.4639i	0.123708	+	1.65077i	0.621454	+	0.783451i	$0.286542\pi$
$257$	1.98320	+	26.4639i	0.123708	+	1.65077i	−0.497746	+	0.867323i	$0.665839\pi$
$258$	−3.54888	+	16.6577i	−0.220943	+	1.03706i
$259$	−9.85147	+	30.1428i	−0.612140	+	1.87298i
$260$	−3.04995	+	1.57924i	−0.189150	+	0.0979402i
$261$	−0.221110	+	1.46697i	−0.0136864	+	0.0908031i
$262$	0.509292	+	3.07583i	0.0314642	+	0.190025i
$263$	−3.18330	+	5.51363i	−0.196291	+	0.339985i	−0.947323	−	0.320280i	$-0.896223\pi$
$263$	−3.18330	+	5.51363i	−0.196291	+	0.339985i	0.751032	+	0.660266i	$0.229556\pi$
$264$	−0.935121	+	0.946545i	−0.0575527	+	0.0582558i
$265$	−1.02933	−	0.495701i	−0.0632314	−	0.0304507i
$266$	3.85728	+	8.05488i	0.236505	+	0.493876i
$267$	7.64492	+	15.8748i	0.467862	+	0.971525i
$268$	−13.1486	+	1.36949i	−0.803181	+	0.0836552i
$269$	19.1261	−	20.6130i	1.16614	−	1.25680i	0.205603	−	0.978636i	$-0.434085\pi$
$269$	19.1261	−	20.6130i	1.16614	−	1.25680i	0.960534	−	0.278161i	$-0.0897250\pi$
$270$	1.93397	+	4.72519i	0.117698	+	0.287566i
$271$	−9.20580	−	6.27641i	−0.559212	−	0.381265i	0.250478	−	0.968122i	$-0.419412\pi$
$271$	−9.20580	−	6.27641i	−0.559212	−	0.381265i	−0.809690	+	0.586858i	$0.800365\pi$
$272$	7.72835	+	26.6392i	0.468600	+	1.61524i
$273$	−10.1400	−	0.169194i	−0.613702	−	0.0102401i
$274$	19.6709	+	23.9464i	1.18836	+	1.44665i
$275$	0.859355	−	0.496149i	0.0518211	−	0.0299189i
$276$	4.40599	+	24.4095i	0.265209	+	1.46928i
$277$	3.32708	+	4.87993i	0.199905	+	0.293206i	0.913081	−	0.407778i	$-0.133696\pi$
$277$	3.32708	+	4.87993i	0.199905	+	0.293206i	−0.713176	+	0.700985i	$0.752744\pi$
$278$	−5.06087	+	7.65907i	−0.303531	+	0.459360i
$279$	−0.121875	+	0.533968i	−0.00729645	+	0.0319678i
$280$	−1.17223	−	6.57672i	−0.0700540	−	0.393034i
$281$	−2.39382	−	10.4880i	−0.142803	−	0.625661i	−0.994777	−	0.102076i	$-0.967451\pi$
$281$	−2.39382	−	10.4880i	−0.142803	−	0.625661i	0.851974	−	0.523585i	$-0.175406\pi$
$282$	15.3051	+	5.75229i	0.911404	+	0.342544i
$283$	−8.47460	+	27.4740i	−0.503763	+	1.63316i	0.244423	+	0.969669i	$0.421401\pi$
$283$	−8.47460	+	27.4740i	−0.503763	+	1.63316i	−0.748186	+	0.663490i	$0.769075\pi$
$284$	6.93006	−	12.8493i	0.411224	−	0.762465i
$285$	−1.25145	−	4.05709i	−0.0741293	−	0.240321i
$286$	−0.151978	−	0.624038i	−0.00898667	−	0.0369001i
$287$	−12.5336	+	3.63823i	−0.739833	+	0.214758i
$288$	1.60570	+	5.24927i	0.0946166	+	0.309316i
$289$	11.3569	−	28.9370i	0.668055	−	1.70218i
$290$	0.940717	−	1.68530i	0.0552408	−	0.0989643i
$291$	1.37835	+	9.14476i	0.0808003	+	0.536075i
$292$	−19.0804	−	2.31268i	−1.11660	−	0.135340i
$293$			1.99475i			0.116534i	0.998301	+	0.0582672i	$0.0185575\pi$
$293$			1.99475i			0.116534i	−0.998301	+	0.0582672i	$0.981442\pi$
$294$	6.16900	−	18.7361i	0.359783	−	1.09271i
$295$	−7.14334			−0.415901
$296$	−17.8620	+	28.8140i	−1.03821	+	1.67478i
$297$	−0.944116	+	0.142303i	−0.0547831	+	0.00825723i
$298$	6.78054	+	3.78482i	0.392786	+	0.219249i
$299$	−11.1455	−	4.37427i	−0.644559	−	0.252971i
$300$	−0.485360	−	16.7430i	−0.0280223	−	0.966655i
$301$	13.9799	−	7.76327i	0.805790	−	0.447467i
$302$	−1.99039	−	8.17272i	−0.114534	−	0.470287i
$303$	−2.07523	+	0.640123i	−0.119219	+	0.0367741i
$304$	1.96748	+	9.34253i	0.112843	+	0.535831i
$305$	10.8894	+	3.35893i	0.623525	+	0.192332i
$306$	3.34799	−	8.90796i	0.191392	−	0.509234i
$307$	−31.8911	+	7.27893i	−1.82012	+	0.415430i	−0.989872	−	0.141965i	$-0.954658\pi$
$307$	−31.8911	+	7.27893i	−1.82012	+	0.415430i	−0.830247	+	0.557395i	$0.811801\pi$
$308$	1.24682	+	0.0780321i	0.0710442	+	0.00444629i
$309$	−11.7737	−	2.68726i	−0.669780	−	0.152873i
$310$	0.392823	−	0.594495i	0.0223109	−	0.0337650i
$311$	19.2506	−	13.1248i	1.09160	−	0.744242i	0.122888	−	0.992421i	$-0.460784\pi$
$311$	19.2506	−	13.1248i	1.09160	−	0.744242i	0.968714	+	0.248179i	$0.0798320\pi$
$312$	−10.4891	−	2.74239i	−0.593827	−	0.155258i
$313$	8.71345	+	15.0921i	0.492513	+	0.853058i	0.999963	−	0.00862354i	$-0.00274499\pi$
$313$	8.71345	+	15.0921i	0.492513	+	0.853058i	−0.507450	+	0.861681i	$0.669412\pi$
$314$	−3.46706	+	2.84804i	−0.195657	+	0.160724i
$315$	−1.02875	+	2.04808i	−0.0579633	+	0.115396i
$316$	−1.66773	−	0.744400i	−0.0938174	−	0.0418758i
$317$	−13.6441	+	20.0123i	−0.766331	+	1.12400i	0.222496	+	0.974934i	$0.428580\pi$
$317$	−13.6441	+	20.0123i	−0.766331	+	1.12400i	−0.988827	+	0.149068i	$0.952373\pi$
$318$	−1.36606	−	3.33764i	−0.0766050	−	0.187165i
$319$	0.264583	+	0.245497i	0.0148138	+	0.0137452i
$320$	0.447182	−	7.12761i	0.0249982	−	0.398445i
$321$	29.4776	−	14.1957i	1.64528	−	0.792325i
$322$	14.5599	−	18.1756i	0.811393	−	1.01289i
$323$	7.18141	−	14.9123i	0.399584	−	0.829745i
$324$	−7.42008	+	20.6461i	−0.412227	+	1.14701i
$325$	7.00216	+	4.04270i	0.388410	+	0.224249i
$326$	−0.0711986	−	0.429998i	−0.00394332	−	0.0238154i
$327$	−21.3731	−	3.22147i	−1.18193	−	0.178148i
$328$	−13.9389	+	0.606321i	−0.769645	+	0.0334785i
$329$	−5.36927	−	14.3817i	−0.296017	−	0.792888i
$330$	−0.580863	−	0.123751i	−0.0319754	−	0.00681228i
$331$	−18.9968	+	1.42362i	−1.04416	+	0.0782490i	−0.585750	−	0.810492i	$-0.699200\pi$
$331$	−18.9968	+	1.42362i	−1.04416	+	0.0782490i	−0.458410	+	0.888741i	$0.651581\pi$
$332$	11.3326	−	4.83119i	0.621956	−	0.265146i
$333$	10.8270	−	4.24929i	0.593317	−	0.232860i
$334$	9.88973	+	1.34438i	0.541142	+	0.0735614i
$335$	−3.67900	−	4.61332i	−0.201005	−	0.252053i
$336$	11.1499	−	17.8987i	0.608278	−	0.976453i
$337$	12.7640	−	16.0056i	0.695301	−	0.871880i	−0.301361	−	0.953510i	$-0.597441\pi$
$337$	12.7640	−	16.0056i	0.695301	−	0.871880i	0.996663	+	0.0816296i	$0.0260125\pi$
$338$	−9.51002	+	9.08397i	−0.517277	+	0.494103i
$339$	−15.6293	−	1.17125i	−0.848864	−	0.0636136i
$340$	−8.15450	+	9.31590i	−0.442240	+	0.505226i
$341$	0.0906337	+	0.0976799i	0.00490809	+	0.00528966i
$342$	1.37831	−	2.97149i	0.0745306	−	0.160680i
$343$	−17.0673	+	7.19074i	−0.921549	+	0.388263i
$344$	16.4853	−	4.52466i	0.888826	−	0.243953i
$345$	−8.11581	+	7.53037i	−0.436940	+	0.405421i
$346$	8.44021	−	28.8397i	0.453748	−	1.55043i
$347$	16.6218	+	1.24563i	0.892306	+	0.0668691i	0.512987	−	0.858397i	$-0.328539\pi$
$347$	16.6218	+	1.24563i	0.892306	+	0.0668691i	0.379320	+	0.925266i	$0.376158\pi$
$348$	5.76739	−	1.96376i	0.309165	−	0.105268i
$349$	−26.5037	−	21.1360i	−1.41871	−	1.13138i	−0.971524	−	0.236940i	$-0.923856\pi$
$349$	−26.5037	−	21.1360i	−1.41871	−	1.13138i	−0.447184	−	0.894442i	$-0.647573\pi$
$350$	−11.5518	+	10.6714i	−0.617468	+	0.570411i
$351$	−4.85056	−	6.08242i	−0.258904	−	0.324655i
$352$	1.27525	+	0.396645i	0.0679713	+	0.0211413i
$353$	−2.02401	−	5.15709i	−0.107727	−	0.274484i	0.866838	−	0.498591i	$-0.166149\pi$
$353$	−2.02401	−	5.15709i	−0.107727	−	0.274484i	−0.974565	+	0.224106i	$0.928054\pi$
$354$	−16.7500	−	15.0961i	−0.890255	−	0.802346i
$355$	6.49805	−	0.486961i	0.344881	−	0.0258452i
$356$	10.6213	−	14.1407i	0.562929	−	0.749453i
$357$	−34.2483	+	12.7863i	−1.81261	+	0.676722i
$358$	2.39376	+	1.85285i	0.126514	+	0.0979264i
$359$	29.7980	+	4.49133i	1.57268	+	0.237043i	0.876707	−	0.481024i	$-0.159735\pi$
$359$	29.7980	+	4.49133i	1.57268	+	0.237043i	0.695973	+	0.718068i	$0.254973\pi$
$360$	−1.58692	+	1.86684i	−0.0836379	+	0.0983910i
$361$	−6.65144	+	11.5206i	−0.350076	+	0.606349i
$362$	−29.0964	+	2.60495i	−1.52927	+	0.136913i
$363$	−9.46186	+	19.6478i	−0.496619	+	1.03124i
$364$	4.52902	+	9.11612i	0.237385	+	0.477815i
$365$	−3.72224	−	7.72932i	−0.194831	−	0.404571i
$366$	18.4355	+	30.8888i	0.963639	+	1.61458i
$367$	−13.7432	−	12.7518i	−0.717389	−	0.665639i	0.234489	−	0.972119i	$-0.424658\pi$
$367$	−13.7432	−	12.7518i	−0.717389	−	0.665639i	−0.951877	+	0.306479i	$0.900849\pi$
$368$	19.7233	−	15.1926i	1.02815	−	0.791969i
$369$	3.95498	+	2.69646i	0.205888	+	0.140372i
$370$	−15.1303	+	0.219260i	−0.786587	+	0.0113988i
$371$	−1.51983	+	3.02576i	−0.0789055	+	0.157089i
$372$	2.17746	−	0.563844i	0.112896	−	0.0292339i
$373$	12.2029	−	7.04536i	0.631843	−	0.364795i	−0.149622	−	0.988743i	$-0.547806\pi$
$373$	12.2029	−	7.04536i	0.631843	−	0.364795i	0.781466	+	0.623948i	$0.214472\pi$
$374$	−1.33181	−	1.89385i	−0.0688661	−	0.0979286i
$375$	13.5258	−	9.22172i	0.698468	−	0.476208i
$376$	−1.93645	−	16.2966i	−0.0998648	−	0.840431i
$377$	−0.654421	+	2.86721i	−0.0337044	+	0.147669i
$378$	14.0980	−	5.49738i	0.725121	−	0.282755i
$379$	−6.25261	+	1.42712i	−0.321175	+	0.0733061i	−0.380069	−	0.924958i	$-0.624100\pi$
$379$	−6.25261	+	1.42712i	−0.321175	+	0.0733061i	0.0588940	+	0.998264i	$0.481243\pi$
$380$	−3.03861	+	2.98787i	−0.155878	+	0.153275i
$381$	−8.59042	+	27.8494i	−0.440100	+	1.42677i
$382$	1.69916	−	28.1399i	0.0869366	−	1.43976i
$383$	7.14766	−	2.20476i	0.365228	−	0.112658i	−0.106709	−	0.994290i	$-0.534031\pi$
$383$	7.14766	−	2.20476i	0.365228	−	0.112658i	0.471937	+	0.881632i	$0.343555\pi$
$384$	16.1114	−	15.7681i	0.822180	−	0.804663i
$385$	0.270709	+	0.487488i	0.0137966	+	0.0248447i
$386$	15.0138	−	7.50016i	0.764181	−	0.381748i
$387$	−5.45958	−	2.14273i	−0.277526	−	0.108921i
$388$	7.51480	−	5.44904i	0.381506	−	0.276633i
$389$	2.07719	+	13.7812i	0.105317	+	0.698736i	0.977715	+	0.209938i	$0.0673263\pi$
$389$	2.07719	+	13.7812i	0.105317	+	0.698736i	−0.872397	+	0.488798i	$0.837436\pi$
$390$	−1.49323	−	4.60304i	−0.0756126	−	0.233084i
$391$	−43.1601			−2.18270
$392$	−19.5470	+	3.14852i	−0.987275	+	0.159024i
$393$	−4.39276			−0.221585
$394$	−5.53610	−	17.0656i	−0.278905	−	0.859754i
$395$	−0.121497	−	0.806078i	−0.00611316	−	0.0405582i
$396$	−0.268972	−	0.370941i	−0.0135164	−	0.0186405i
$397$	−25.3725	−	9.95796i	−1.27341	−	0.499776i	−0.370189	−	0.928957i	$-0.620707\pi$
$397$	−25.3725	−	9.95796i	−1.27341	−	0.499776i	−0.903218	+	0.429181i	$0.858802\pi$
$398$	6.31177	−	3.15306i	0.316380	−	0.158049i
$399$	−12.0844	+	3.50786i	−0.604978	+	0.175613i
$400$	−14.6994	+	8.15982i	−0.734969	+	0.407991i
$401$	−31.6571	+	9.76492i	−1.58088	+	0.487637i	−0.956069	−	0.293140i	$-0.905300\pi$
$401$	−31.6571	+	9.76492i	−1.58088	+	0.487637i	−0.624810	+	0.780777i	$0.714823\pi$
$402$	1.12266	−	18.5924i	0.0559931	−	0.927304i
$403$	−0.320031	+	1.03751i	−0.0159419	+	0.0516822i
$404$	1.52832	+	1.55427i	0.0760365	+	0.0773277i
$405$	−9.54699	+	2.17904i	−0.474394	+	0.108277i
$406$	−4.94761	−	2.87100i	−0.245546	−	0.142485i
$407$	0.629675	−	2.75879i	0.0312118	−	0.136748i
$408$	−38.8084	+	4.61143i	−1.92130	+	0.228300i
$409$	12.4181	−	8.46650i	0.614034	−	0.418641i	−0.215969	−	0.976400i	$-0.569291\pi$
$409$	12.4181	−	8.46650i	0.614034	−	0.418641i	0.830003	+	0.557759i	$0.188339\pi$
$410$	−3.58227	−	5.09404i	−0.176916	−	0.251577i
$411$	−37.8140	+	21.8319i	−1.86523	+	1.07689i
$412$	3.03856	+	11.7344i	0.149699	+	0.578110i
$413$	−0.353208	+	21.1682i	−0.0173802	+	1.04162i
$414$	−8.54062	+	0.123766i	−0.419749	+	0.00608275i
$415$	4.54330	+	3.09757i	0.223022	+	0.152054i
$416$	2.39656	+	10.6148i	0.117501	+	0.520435i
$417$	−9.48162	−	8.79766i	−0.464317	−	0.430823i
$418$	−0.408420	−	0.684310i	−0.0199765	−	0.0334707i
$419$	−9.84647	−	20.4464i	−0.481032	−	0.998872i	−0.990388	−	0.138317i	$-0.955831\pi$
$419$	−9.84647	−	20.4464i	−0.481032	−	0.998872i	0.509357	−	0.860556i	$-0.329883\pi$
$420$	9.41173	−	0.115738i	0.459246	−	0.00564742i
$421$	4.26313	−	8.85248i	0.207772	−	0.431444i	−0.770876	−	0.636985i	$-0.780181\pi$
$421$	4.26313	−	8.85248i	0.207772	−	0.431444i	0.978648	+	0.205541i	$0.0658955\pi$
$422$	23.9536	−	2.14453i	1.16604	−	0.104394i
$423$	−2.81522	+	4.87610i	−0.136881	+	0.237084i
$424$	−2.34445	+	2.75799i	−0.113856	+	0.133940i
$425$	28.8203	+	4.34396i	1.39799	+	0.210713i
$426$	16.2660	+	12.5905i	0.788091	+	0.610012i
$427$	10.4921	−	32.1029i	0.507748	−	1.55357i
$428$	−26.2574	−	19.7225i	−1.26920	−	0.953323i
$429$	0.902419	−	0.0676270i	0.0435692	−	0.00326506i
$430$	5.66805	+	5.10836i	0.273338	+	0.246347i
$431$	−3.52052	−	8.97013i	−0.169577	−	0.432076i	0.820669	−	0.571404i	$-0.193601\pi$
$431$	−3.52052	−	8.97013i	−0.169577	−	0.432076i	−0.990246	+	0.139328i	$0.955506\pi$
$432$	16.0343	−	2.14133i	0.771451	−	0.103025i
$433$	15.1080	+	18.9449i	0.726046	+	0.910433i	0.998663	−	0.0516896i	$-0.0164606\pi$
$433$	15.1080	+	18.9449i	0.726046	+	0.910433i	−0.272617	+	0.962123i	$0.587889\pi$
$434$	−1.74227	−	1.19347i	−0.0836315	−	0.0572882i
$435$	2.12613	+	1.69553i	0.101940	+	0.0812944i
$436$	6.99273	+	20.5371i	0.334891	+	0.983548i
$437$	−14.8144	−	1.11019i	−0.708671	−	0.0531075i
$438$	7.60631	−	25.9903i	0.363444	−	1.24187i
$439$	11.7701	−	10.9210i	0.561755	−	0.521233i	−0.347385	−	0.937723i	$-0.612930\pi$
$439$	11.7701	−	10.9210i	0.561755	−	0.521233i	0.909140	+	0.416490i	$0.136740\pi$
$440$	0.157777	+	0.574850i	0.00752174	+	0.0274049i
$441$	6.01831	+	3.14979i	0.286586	+	0.149990i
$442$	7.93809	−	17.1136i	0.377576	−	0.814012i
$443$	28.2074	+	30.4004i	1.34018	+	1.44437i	0.795854	+	0.605489i	$0.207022\pi$
$443$	28.2074	+	30.4004i	1.34018	+	1.44437i	0.544321	+	0.838877i	$0.316787\pi$
$444$	−35.9416	−	31.4608i	−1.70571	−	1.49306i
$445$	7.87179	+	0.589909i	0.373159	+	0.0279644i
$446$	−18.8130	+	17.9701i	−0.890819	+	0.850910i
$447$	−6.82169	+	8.55412i	−0.322655	+	0.404596i
$448$	−21.0994	−	1.67758i	−0.996854	−	0.0792583i
$449$	−11.2371	−	14.0909i	−0.530311	−	0.664989i	0.442452	−	0.896792i	$-0.354109\pi$
$449$	−11.2371	−	14.0909i	−0.530311	−	0.664989i	−0.972763	+	0.231804i	$0.925537\pi$
$450$	5.71549	+	0.776949i	0.269431	+	0.0366257i
$451$	1.08407	−	0.425466i	0.0510469	−	0.0200344i
$452$	6.16925	+	14.4713i	0.290177	+	0.680671i
$453$	11.8185	−	0.885677i	0.555284	−	0.0416127i
$454$	10.8638	+	2.31450i	0.509862	+	0.108625i
$455$	−2.33708	+	3.89633i	−0.109564	+	0.182663i
$456$	−13.4394	+	0.584593i	−0.629356	+	0.0273761i
$457$	10.5326	+	1.58754i	0.492695	+	0.0742618i	0.390691	−	0.920522i	$-0.372236\pi$
$457$	10.5326	+	1.58754i	0.492695	+	0.0742618i	0.102005	+	0.994784i	$0.467474\pi$
$458$	−3.97892	−	24.0304i	−0.185923	−	1.12287i
$459$	−24.2867	−	14.0219i	−1.13361	−	0.654487i
$460$	10.4576	+	3.75839i	0.487588	+	0.175236i
$461$	1.04944	−	2.17918i	0.0488771	−	0.101494i	−0.875100	−	0.483942i	$-0.839205\pi$
$461$	1.04944	−	2.17918i	0.0488771	−	0.101494i	0.923977	+	0.382448i	$0.124919\pi$
$462$	−0.395439	+	1.71518i	−0.0183975	+	0.0797972i
$463$	−13.0979	+	6.30763i	−0.608712	+	0.293140i	−0.712734	−	0.701435i	$-0.752543\pi$
$463$	−13.0979	+	6.30763i	−0.608712	+	0.293140i	0.104022	+	0.994575i	$0.466829\pi$
$464$	−4.41211	−	4.23430i	−0.204827	−	0.196572i
$465$	0.735960	+	0.682871i	0.0341293	+	0.0316674i
$466$	−0.213622	−	0.521932i	−0.00989584	−	0.0241780i
$467$	−1.30311	+	1.91131i	−0.0603006	+	0.0884447i	−0.855205	−	0.518290i	$-0.826569\pi$
$467$	−1.30311	+	1.91131i	−0.0603006	+	0.0884447i	0.794904	+	0.606735i	$0.207521\pi$
$468$	1.52173	−	3.40925i	0.0703422	−	0.157593i
$469$	−13.8528	+	10.6740i	−0.639661	+	0.492881i
$470$	5.66027	−	4.64967i	0.261089	−	0.214473i
$471$	−3.16092	−	5.47487i	−0.145648	−	0.252269i
$472$	−5.72498	+	21.8968i	−0.263514	+	1.00788i
$473$	−1.17897	+	0.803806i	−0.0542090	+	0.0369591i
$474$	1.41860	−	2.14689i	0.0651583	−	0.0986099i
$475$	9.78066	+	2.23237i	0.448767	+	0.102428i
$476$	27.2030	+	24.6252i	1.24685	+	1.12869i
$477$	1.21076	−	0.276348i	0.0554369	−	0.0126531i
$478$	−2.88079	+	7.66490i	−0.131764	+	0.350584i
$479$	−7.61825	−	2.34992i	−0.348087	−	0.107371i	0.115782	−	0.993275i	$-0.463063\pi$
$479$	−7.61825	−	2.34992i	−0.348087	−	0.107371i	−0.463868	+	0.885904i	$0.653539\pi$
$480$	9.80476	+	2.26210i	0.447524	+	0.103250i
$481$	22.0328	−	6.79621i	1.00461	−	0.309881i
$482$	3.07375	+	12.6211i	0.140005	+	0.574876i
$483$	21.9138	+	24.4223i	0.997111	+	1.11125i
$484$	21.8793	−	0.634258i	0.994515	−	0.0288299i
$485$	3.85684	+	1.51370i	0.175130	+	0.0687334i
$486$	−12.0093	−	6.70343i	−0.544751	−	0.304074i
$487$	−27.9997	+	4.22027i	−1.26879	+	0.191239i	−0.748720	−	0.662887i	$-0.769331\pi$
$487$	−27.9997	+	4.22027i	−1.26879	+	0.191239i	−0.520067	+	0.854125i	$0.674093\pi$
$488$	19.0235	−	30.6878i	0.861154	−	1.38917i
$489$	0.614103			0.0277707
$490$	−5.88753	−	6.59052i	−0.265972	−	0.297729i
$491$		−	33.5081i		−	1.51220i	−0.654456	−	0.756100i	$-0.727102\pi$
$491$		−	33.5081i		−	1.51220i	0.654456	−	0.756100i	$-0.272898\pi$
$492$	2.36538	−	19.5152i	0.106640	−	0.879812i
$493$	1.58005	+	10.4829i	0.0711618	+	0.472128i
$494$	3.16491	−	5.66996i	0.142396	−	0.255104i
$495$	0.0747181	−	0.190379i	0.00335833	−	0.00855688i
$496$	−1.50751	−	1.68059i	−0.0676891	−	0.0754609i
$497$	−1.12173	−	19.2800i	−0.0503166	−	0.864827i
$498$	4.10724	+	16.8647i	0.184050	+	0.755726i
$499$	3.82644	+	12.4050i	0.171295	+	0.555325i	0.999990	−	0.00437478i	$-0.00139254\pi$
$499$	3.82644	+	12.4050i	0.171295	+	0.555325i	−0.828695	+	0.559700i	$0.810916\pi$
$500$	−14.4619	−	7.79983i	−0.646758	−	0.348819i
$501$	−4.14499	+	13.4377i	−0.185185	+	0.600354i
$502$	25.3011	+	9.50923i	1.12925	+	0.424418i
$503$	6.39749	+	28.0292i	0.285250	+	1.24976i	0.890962	+	0.454077i	$0.150031\pi$
$503$	6.39749	+	28.0292i	0.285250	+	1.24976i	−0.605713	+	0.795684i	$0.707112\pi$
$504$	5.45361	+	4.79489i	0.242923	+	0.213581i
$505$	−0.216503	+	0.948559i	−0.00963424	+	0.0422103i
$506$	−1.14562	+	1.73377i	−0.0509292	+	0.0770756i
$507$	−10.4383	−	15.3101i	−0.463580	−	0.679947i
$508$	28.7875	−	5.19624i	1.27724	−	0.230546i
$509$	−17.6837	+	10.2097i	−0.783818	+	0.452537i	−0.837782	−	0.546005i	$-0.816148\pi$
$509$	−17.6837	+	10.2097i	−0.783818	+	0.452537i	0.0539638	+	0.998543i	$0.482814\pi$
$510$	−11.0727	−	13.4793i	−0.490305	−	0.596872i
$511$	−23.0887	+	10.6481i	−1.02138	+	0.471044i
$512$	−21.4902	−	7.08314i	−0.949742	−	0.313034i
$513$	−7.97558	−	5.43766i	−0.352131	−	0.240079i
$514$	14.2162	+	34.7339i	0.627051	+	1.53205i
$515$	−3.68001	+	3.96610i	−0.162160	+	0.174767i
$516$	2.49520	+	23.9566i	0.109845	+	1.05463i
$517$	0.594351	+	1.23418i	0.0261395	+	0.0542793i
$518$	−0.0983881	+	44.8471i	−0.00432292	+	1.97047i
$519$	38.1458	+	18.3700i	1.67441	+	0.806356i
$520$	−3.41364	+	3.45534i	−0.149698	+	0.151527i
$521$	−3.34578	+	5.79507i	−0.146581	+	0.253887i	−0.929962	−	0.367656i	$-0.880160\pi$
$521$	−3.34578	+	5.79507i	−0.146581	+	0.253887i	0.783380	+	0.621543i	$0.213494\pi$
$522$	0.342725	+	2.06986i	0.0150007	+	0.0905953i
$523$	1.56574	−	10.3880i	0.0684650	−	0.454236i	−0.928162	−	0.372175i	$-0.878612\pi$
$523$	1.56574	−	10.3880i	0.0684650	−	0.454236i	0.996627	−	0.0820601i	$-0.0261500\pi$
$524$	2.02734	+	3.91536i	0.0885650	+	0.171043i
$525$	−12.1750	−	18.5136i	−0.531359	−	0.808001i
$526$	−1.87612	+	8.80609i	−0.0818025	+	0.383964i
$527$	0.292483	+	3.90291i	0.0127408	+	0.170014i
$528$	−0.844869	+	1.68137i	−0.0367682	+	0.0731721i
$529$	5.75006	+	14.6509i	0.250003	+	0.636996i
$530$	−1.60098	−	0.217633i	−0.0695420	−	0.00945336i
$531$	6.07092	−	4.84140i	0.263455	−	0.210099i
$532$	8.70384	+	9.15218i	0.377359	+	0.396797i
$533$	7.41890	+	5.91638i	0.321348	+	0.256267i
$534$	17.2115	+	18.0187i	0.744814	+	0.779747i
$535$	1.09539	−	14.6169i	0.0473578	−	0.631946i
$536$	−17.0899	+	7.58011i	−0.738173	+	0.327411i
$537$	−3.12650	+	2.90097i	−0.134918	+	0.125186i
$538$	16.7332	−	36.0750i	0.721421	−	1.55530i
$539$	1.45798	−	0.778100i	0.0627996	−	0.0335151i
$540$	4.66358	+	5.51238i	0.200689	+	0.237215i
$541$	−2.82164	−	3.04100i	−0.121312	−	0.130743i	0.669475	−	0.742834i	$-0.266519\pi$
$541$	−2.82164	−	3.04100i	−0.121312	−	0.130743i	−0.790787	+	0.612091i	$0.790328\pi$
$542$	−15.1226	−	4.42577i	−0.649571	−	0.190103i
$543$	3.07588	−	41.0448i	0.131999	−	1.76140i
$544$	22.0211	+	32.4625i	0.944148	+	1.39182i
$545$	−6.03760	+	7.57092i	−0.258623	+	0.324302i
$546$	−13.7142	+	4.19735i	−0.586914	+	0.179630i
$547$	29.5965	−	23.6024i	1.26545	−	1.00917i	0.266481	−	0.963840i	$-0.414139\pi$
$547$	29.5965	−	23.6024i	1.26545	−	1.00917i	0.998972	−	0.0453252i	$-0.0144324\pi$
$548$	36.9112	+	23.6286i	1.57677	+	1.00936i
$549$	−11.5311	+	4.52562i	−0.492135	+	0.193149i
$550$	0.939494	−	1.04243i	0.0400602	−	0.0444493i
$551$	0.272694	+	3.63885i	0.0116172	+	0.155020i
$552$	16.5788	+	30.9129i	0.705643	+	1.31574i
$553$	−2.39469	+	0.320179i	−0.101833	+	0.0136154i
$554$	6.60511	+	5.11260i	0.280624	+	0.217214i
$555$	3.17764	−	21.0823i	0.134883	−	0.894892i
$556$	−3.46560	+	12.5115i	−0.146974	+	0.530605i
$557$	27.4040	+	15.8217i	1.16115	+	0.670388i	0.951578	−	0.307407i	$-0.0994612\pi$
$557$	27.4040	+	15.8217i	1.16115	+	0.670388i	0.209567	+	0.977794i	$0.432795\pi$
$558$	0.0690692	+	0.771479i	0.00292393	+	0.0326593i
$559$	−10.4753	−	5.04463i	−0.443057	−	0.213365i
$560$	−4.44686	−	8.33548i	−0.187914	−	0.352238i
$561$	2.93906	−	1.41538i	0.124087	−	0.0597573i
$562$	−7.79696	−	13.0638i	−0.328895	−	0.551065i
$563$	25.3524	−	27.3234i	1.06848	−	1.15155i	0.0805307	−	0.996752i	$-0.474338\pi$
$563$	25.3524	−	27.3234i	1.06848	−	1.15155i	0.987947	−	0.154793i	$-0.0494710\pi$
$564$	23.0986	+	1.05910i	0.972628	+	0.0445961i
$565$	−3.95548	+	5.80163i	−0.166408	+	0.244076i
$566$	0.589166	+	40.6562i	0.0247645	+	1.70891i
$567$	5.98518	+	28.3988i	0.251354	+	1.19264i
$568$	3.71511	−	20.3091i	0.155883	−	0.852149i
$569$	−9.30351	−	16.1142i	−0.390024	−	0.675541i	0.602429	−	0.798173i	$-0.294200\pi$
$569$	−9.30351	−	16.1142i	−0.390024	−	0.675541i	−0.992452	+	0.122632i	$0.960866\pi$
$570$	−3.45390	−	4.91150i	−0.144668	−	0.205720i
$571$	20.1842	+	29.6048i	0.844682	+	1.23892i	0.969094	+	0.246690i	$0.0793430\pi$
$571$	20.1842	+	29.6048i	0.844682	+	1.23892i	−0.124412	+	0.992231i	$0.539705\pi$
$572$	−0.476762	−	0.773136i	−0.0199344	−	0.0323264i
$573$	38.7245	+	8.83862i	1.61774	+	0.369239i
$574$	−15.2725	+	10.3636i	−0.637462	+	0.432569i
$575$	−5.82120	−	25.5043i	−0.242761	−	1.06360i
$576$	4.45068	+	6.36062i	0.185445	+	0.265026i
$577$	−36.9563	−	11.3995i	−1.53851	−	0.474568i	−0.594393	−	0.804175i	$-0.702608\pi$
$577$	−36.9563	−	11.3995i	−1.53851	−	0.474568i	−0.944118	+	0.329607i	$0.893084\pi$
$578$	2.64972	−	43.8821i	0.110214	−	1.82525i
$579$	6.96995	+	22.5960i	0.289661	+	0.939059i
$580$	0.530014	−	2.67759i	0.0220076	−	0.111181i
$581$	9.40381	−	13.3102i	0.390136	−	0.552200i
$582$	5.84479	+	11.7001i	0.242274	+	0.484983i
$583$	0.110385	−	0.281258i	0.00457170	−	0.0116485i
$584$	−26.6762	+	5.21537i	−1.10387	+	0.215813i
$585$	1.64782	−	0.248369i	0.0681289	−	0.0102688i
$586$	0.870477	+	2.68334i	0.0359591	+	0.110848i
$587$		−	26.5541i		−	1.09600i	−0.836477	−	0.548002i	$-0.815389\pi$
$587$		−	26.5541i		−	1.09600i	0.836477	−	0.548002i	$-0.184611\pi$
$588$	0.122400	−	27.8959i	0.00504768	−	1.15041i
$589$			1.34717i			0.0555094i
$590$	−9.60924	+	3.11724i	−0.395606	+	0.128335i
$591$	24.9962	−	3.76757i	1.02821	−	0.154977i
$592$	−11.4540	+	46.5554i	−0.470756	+	1.91342i
$593$	−1.19895	+	3.05486i	−0.0492348	+	0.125448i	−0.953376	−	0.301787i	$-0.902417\pi$
$593$	−1.19895	+	3.05486i	−0.0492348	+	0.125448i	0.904141	+	0.427235i	$0.140512\pi$
$594$	−1.20793	+	0.603423i	−0.0495619	+	0.0247587i
$595$	−2.71089	+	16.1522i	−0.111136	+	0.662177i
$596$	10.7728	+	2.13243i	0.441272	+	0.0873476i
$597$	2.93016	+	9.49935i	0.119924	+	0.388782i
$598$	−16.9018	−	1.02057i	−0.691165	−	0.0417344i
$599$	27.6150	+	8.51811i	1.12832	+	0.348040i	0.802062	−	0.597241i	$-0.203736\pi$
$599$	27.6150	+	8.51811i	1.12832	+	0.348040i	0.326257	+	0.945281i	$0.394212\pi$
$600$	−7.95927	−	22.3109i	−0.324936	−	0.910837i
$601$	−8.42509	−	36.9127i	−0.343667	−	1.50570i	−0.791269	−	0.611469i	$-0.790579\pi$
$601$	−8.42509	−	36.9127i	−0.343667	−	1.50570i	0.447602	−	0.894233i	$-0.352278\pi$
$602$	15.4181	−	16.5438i	0.628394	−	0.674274i
$603$	6.25335	+	1.42729i	0.254656	+	0.0581236i
$604$	−6.24392	−	10.1254i	−0.254061	−	0.411996i
$605$	5.50362	+	8.07233i	0.223754	+	0.328187i
$606$	−2.51226	+	1.76669i	−0.102054	+	0.0717669i
$607$	−14.8184	−	25.6662i	−0.601459	−	1.04176i	−0.992600	−	0.121427i	$-0.961253\pi$
$607$	−14.8184	−	25.6662i	−0.601459	−	1.04176i	0.391141	−	0.920331i	$-0.372080\pi$
$608$	6.72360	+	11.7090i	0.272678	+	0.474863i
$609$	5.12956	−	6.21660i	0.207860	−	0.251909i
$610$	16.1142	−	0.233518i	0.652445	−	0.00945485i
$611$	−6.28760	+	9.22221i	−0.254369	+	0.373091i
$612$	0.616423	−	13.4440i	0.0249174	−	0.543442i
$613$	31.0975	−	33.5152i	1.25602	−	1.35366i	0.346471	−	0.938061i	$-0.387380\pi$
$613$	31.0975	−	33.5152i	1.25602	−	1.35366i	0.909546	−	0.415604i	$-0.136430\pi$
$614$	−39.7235	+	23.7084i	−1.60311	+	0.956793i
$615$	7.90544	−	3.80706i	0.318778	−	0.153515i
$616$	1.71128	−	0.439124i	0.0689494	−	0.0176928i
$617$	−0.136009	−	0.0654984i	−0.00547551	−	0.00263687i	0.431144	−	0.902283i	$-0.358110\pi$
$617$	−0.136009	−	0.0654984i	−0.00547551	−	0.00263687i	−0.436619	+	0.899646i	$0.643824\pi$
$618$	−17.0106	+	1.52293i	−0.684268	+	0.0612613i
$619$	−28.1069	−	16.2275i	−1.12971	−	0.652240i	−0.185850	−	0.982578i	$-0.559504\pi$
$619$	−28.1069	−	16.2275i	−1.12971	−	0.652240i	−0.943863	+	0.330338i	$0.892837\pi$
$620$	0.268999	−	0.971137i	0.0108032	−	0.0390018i
$621$	−3.75156	+	24.8900i	−0.150545	+	0.998801i
$622$	20.1685	−	26.0562i	0.808683	−	1.04476i
$623$	2.13733	−	23.2976i	0.0856303	−	0.933401i
$624$	−15.3067	+	0.888193i	−0.612757	+	0.0355562i
$625$	1.02241	+	13.6431i	0.0408962	+	0.545722i
$626$	18.3073	+	16.4996i	0.731708	+	0.659455i
$627$	1.04522	−	0.410220i	0.0417422	−	0.0163826i
$628$	−3.42105	+	5.34416i	−0.136515	+	0.213255i
$629$	64.9820	−	51.8214i	2.59100	−	2.06626i
$630$	−0.490119	+	3.20402i	−0.0195268	+	0.127651i
$631$	−9.95370	+	12.4815i	−0.396251	+	0.496882i	−0.939433	−	0.342732i	$-0.888648\pi$
$631$	−9.95370	+	12.4815i	−0.396251	+	0.496882i	0.543183	+	0.839615i	$0.317219\pi$
$632$	−2.56828	−	0.273596i	−0.102161	−	0.0108831i
$633$	−2.53222	+	33.7902i	−0.100647	+	1.34304i
$634$	−9.62108	+	32.8746i	−0.382102	+	1.30562i
$635$	8.88101	+	9.57145i	0.352432	+	0.379831i
$636$	−3.29412	−	3.89367i	−0.130620	−	0.154394i
$637$	11.4306	+	7.11821i	0.452897	+	0.282034i
$638$	0.463048	+	0.214783i	0.0183322	+	0.00850334i
$639$	−5.19246	+	4.81790i	−0.205411	+	0.190593i
$640$	−2.50883	−	9.78321i	−0.0991701	−	0.386716i
$641$	−2.20670	+	29.4463i	−0.0871594	+	1.16306i	0.766505	+	0.642238i	$0.221994\pi$
$641$	−2.20670	+	29.4463i	−0.0871594	+	1.16306i	−0.853665	+	0.520823i	$0.825625\pi$
$642$	33.4586	−	31.9596i	1.32051	−	1.26135i
$643$	1.20678	+	0.962376i	0.0475908	+	0.0379524i	0.646996	−	0.762493i	$-0.276025\pi$
$643$	1.20678	+	0.962376i	0.0475908	+	0.0379524i	−0.599406	+	0.800445i	$0.704596\pi$
$644$	11.6545	−	30.8036i	0.459251	−	1.21383i
$645$	−8.40541	+	6.70309i	−0.330963	+	0.263934i
$646$	3.15293	−	23.1940i	0.124050	−	0.912555i
$647$	7.90534	+	20.1425i	0.310791	+	0.791882i	0.997866	+	0.0652959i	$0.0207991\pi$
$647$	7.90534	+	20.1425i	0.310791	+	0.791882i	−0.687075	+	0.726587i	$0.741106\pi$
$648$	−0.971858	+	31.0112i	−0.0381782	+	1.21824i
$649$	−0.141177	−	1.88388i	−0.00554169	−	0.0739487i
$650$	11.1835	+	2.38262i	0.438653	+	0.0934539i
$651$	2.05997	−	2.14714i	0.0807366	−	0.0841529i
$652$	−0.283421	−	0.547364i	−0.0110996	−	0.0214364i
$653$	−1.36702	+	9.06961i	−0.0534958	+	0.354921i	0.946029	+	0.324083i	$0.105056\pi$
$653$	−1.36702	+	9.06961i	−0.0534958	+	0.354921i	−0.999524	+	0.0308381i	$0.990182\pi$
$654$	−30.1569	+	4.99335i	−1.17923	+	0.195255i
$655$	−0.984005	+	1.70435i	−0.0384483	+	0.0665943i
$656$	−18.4860	+	6.89832i	−0.721757	+	0.269334i
$657$	8.40197	+	4.04617i	0.327792	+	0.157856i
$658$	−13.4987	−	17.0032i	−0.526234	−	0.662854i
$659$	−9.84431	−	20.4419i	−0.383480	−	0.796304i	−0.999960	−	0.00893367i	$-0.997156\pi$
$659$	−9.84431	−	20.4419i	−0.383480	−	0.796304i	0.616480	−	0.787370i	$-0.288558\pi$
$660$	−0.835381	+	0.0870089i	−0.0325172	+	0.00338682i
$661$	7.63649	−	8.23018i	0.297025	−	0.320117i	−0.566852	−	0.823820i	$-0.691839\pi$
$661$	7.63649	−	8.23018i	0.297025	−	0.320117i	0.863877	+	0.503703i	$0.168029\pi$
$662$	−24.9333	+	10.2050i	−0.969062	+	0.396628i
$663$	21.9616	+	14.9732i	0.852919	+	0.581510i
$664$	13.1363	−	11.4443i	0.509789	−	0.444124i
$665$	−1.34597	+	5.47442i	−0.0521946	+	0.212289i
$666$	12.7102	−	10.4409i	0.492510	−	0.404577i
$667$	8.24056	−	4.75769i	0.319076	−	0.184218i
$668$	13.8904	−	2.50726i	0.537434	−	0.0970086i
$669$	−20.6492	−	30.2869i	−0.798346	−	1.17096i
$670$	−6.96218	−	4.60039i	−0.268973	−	0.177729i
$671$	−0.670622	+	2.93819i	−0.0258891	+	0.113427i
$672$	7.18819	−	28.9430i	0.277291	−	1.11650i
$673$	−8.28607	−	36.3037i	−0.319405	−	1.39940i	−0.838600	−	0.544748i	$-0.816625\pi$
$673$	−8.28607	−	36.3037i	−0.319405	−	1.39940i	0.519195	−	0.854656i	$-0.326232\pi$
$674$	10.1856	−	27.1008i	0.392335	−	1.04388i
$675$	5.01024	−	16.2428i	0.192844	−	0.625185i
$676$	−8.82880	+	16.3698i	−0.339569	+	0.629608i
$677$	1.08561	+	3.51945i	0.0417233	+	0.135264i	0.974038	−	0.226384i	$-0.0726905\pi$
$677$	1.08561	+	3.51945i	0.0417233	+	0.135264i	−0.932315	+	0.361648i	$0.882214\pi$
$678$	−21.5356	+	5.24479i	−0.827070	+	0.201425i
$679$	4.67630	−	11.3543i	0.179460	−	0.435737i
$680$	−6.90413	+	16.0903i	−0.264761	+	0.617033i
$681$	−5.71768	+	14.5684i	−0.219102	+	0.558263i
$682$	0.164547	+	0.0918480i	0.00630081	+	0.00351704i
$683$	3.41275	+	22.6421i	0.130585	+	0.866377i	0.954188	+	0.299209i	$0.0967228\pi$
$683$	3.41275	+	22.6421i	0.130585	+	0.866377i	−0.823602	+	0.567168i	$0.808039\pi$
$684$	0.557399	−	4.59872i	0.0213127	−	0.175837i
$685$			19.5619i			0.747423i
$686$	−19.8211	+	17.1209i	−0.756772	+	0.653679i
$687$	34.3191			1.30935
$688$	20.2015	−	13.2805i	0.770176	−	0.506314i
$689$	2.43442	−	0.366930i	0.0927440	−	0.0139789i
$690$	−7.63126	+	13.6715i	−0.290517	+	0.520464i
$691$	39.5427	+	15.5194i	1.50428	+	0.590385i	0.967395	−	0.253273i	$-0.0815071\pi$
$691$	39.5427	+	15.5194i	1.50428	+	0.590385i	0.536881	+	0.843658i	$0.319602\pi$
$692$	−1.23140	−	42.4784i	−0.0468109	−	1.61479i
$693$	−0.560463	−	0.230829i	−0.0212902	−	0.00876846i
$694$	22.9033	−	5.57788i	0.869397	−	0.211733i
$695$	−5.53735	+	1.70805i	−0.210044	+	0.0647899i
$696$	6.90136	−	5.15845i	0.261595	−	0.195530i
$697$	32.6862	+	10.0824i	1.23808	+	0.381897i
$698$	−44.8762	−	16.8664i	−1.69859	−	0.638401i
$699$	0.774676	−	0.176815i	0.0293009	−	0.00668775i
$700$	−10.8826	+	19.3962i	−0.411325	+	0.733108i
$701$	−20.0048	−	4.56596i	−0.755569	−	0.172454i	−0.172649	−	0.984983i	$-0.555233\pi$
$701$	−20.0048	−	4.56596i	−0.755569	−	0.172454i	−0.582920	+	0.812530i	$0.698090\pi$
$702$	−9.17926	−	6.06537i	−0.346449	−	0.228923i
$703$	23.6377	−	16.1159i	0.891512	−	0.607823i
$704$	1.88857	−	0.0229331i	0.0711780	−	0.000864325i
$705$	5.16047	+	8.93820i	0.194355	+	0.336632i
$706$	−4.97317	−	6.05408i	−0.187168	−	0.227848i
$707$	2.80020	+	0.688473i	0.105312	+	0.0258927i
$708$	−29.1199	−	12.9978i	−1.09439	−	0.488487i
$709$	27.7023	−	40.6318i	1.04038	−	1.52596i	0.203123	−	0.979153i	$-0.434891\pi$
$709$	27.7023	−	40.6318i	1.04038	−	1.52596i	0.837259	−	0.546807i	$-0.184157\pi$
$710$	8.52868	−	3.49071i	0.320076	−	0.131004i
$711$	0.649576	+	0.602718i	0.0243610	+	0.0226037i
$712$	8.11707	−	23.6570i	0.304200	−	0.886584i
$713$	3.16504	−	1.52420i	0.118532	−	0.0570819i
$714$	−40.4912	+	32.1456i	−1.51534	+	1.20302i
$715$	0.175909	−	0.365279i	0.00657862	−	0.0136607i
$716$	4.02864	+	1.44787i	0.150557	+	0.0541093i
$717$	−9.99150	−	5.76859i	−0.373139	−	0.215432i
$718$	42.0443	−	6.96165i	1.56908	−	0.259807i
$719$	−49.3408	−	7.43692i	−1.84010	−	0.277350i	−0.865435	−	0.501021i	$-0.832958\pi$
$719$	−49.3408	−	7.43692i	−1.84010	−	0.277350i	−0.974665	+	0.223671i	$0.928196\pi$
$720$	−1.32007	+	3.20378i	−0.0491960	+	0.119398i
$721$	11.5710	+	11.1012i	0.430925	+	0.413431i
$722$	−3.92011	+	18.4002i	−0.145891	+	0.684783i
$723$	−18.2513	+	1.36775i	−0.678775	+	0.0508671i
$724$	−38.0038	+	16.2014i	−1.41240	+	0.602120i
$725$	−5.98151	+	2.34757i	−0.222148	+	0.0871866i
$726$	−4.15414	+	30.5592i	−0.154175	+	1.13416i
$727$	27.6290	+	34.6457i	1.02470	+	1.28494i	0.957879	+	0.287171i	$0.0927149\pi$
$727$	27.6290	+	34.6457i	1.02470	+	1.28494i	0.0668230	+	0.997765i	$0.478714\pi$
$728$	10.0706	+	10.2866i	0.373240	+	0.381248i
$729$	−8.43601	+	10.5784i	−0.312445	+	0.391794i
$730$	−8.38013	−	8.77317i	−0.310162	−	0.324710i
$731$	−41.7941	−	3.13203i	−1.54581	−	0.115842i
$732$	38.2789	+	33.5067i	1.41483	+	1.23844i
$733$	−3.26284	−	3.51650i	−0.120516	−	0.129885i	0.669912	−	0.742441i	$-0.266332\pi$
$733$	−3.26284	−	3.51650i	−0.120516	−	0.129885i	−0.790427	+	0.612556i	$0.790141\pi$
$734$	−24.0521	−	11.1565i	−0.887778	−	0.411792i
$735$	10.5162	−	6.66704i	0.387895	−	0.245918i
$736$	19.9019	−	29.0440i	0.733595	−	1.07058i
$737$	1.14394	−	1.06142i	0.0421375	−	0.0390979i
$738$	6.49695	+	1.90139i	0.239156	+	0.0699913i
$739$	−27.5378	−	2.06368i	−1.01300	−	0.0759135i	−0.442125	−	0.896954i	$-0.645775\pi$
$739$	−27.5378	−	2.06368i	−1.01300	−	0.0759135i	−0.570871	+	0.821040i	$0.693394\pi$
$740$	−20.2576	+	6.89758i	−0.744686	+	0.253560i
$741$	7.15305	+	5.70437i	0.262774	+	0.209555i
$742$	−0.724082	+	4.73348i	−0.0265819	+	0.173772i
$743$	13.7458	+	17.2367i	0.504284	+	0.632352i	0.967190	−	0.254055i	$-0.0817645\pi$
$743$	13.7458	+	17.2367i	0.504284	+	0.632352i	−0.462906	+	0.886408i	$0.653193\pi$
$744$	2.68307	−	1.70869i	0.0983661	−	0.0626437i
$745$	1.79082	+	4.56293i	0.0656104	+	0.167173i
$746$	13.3409	−	14.8026i	0.488446	−	0.541962i
$747$	−5.96060	+	0.446685i	−0.218087	+	0.0163434i
$748$	−2.61800	−	1.96643i	−0.0957234	−	0.0718998i
$749$	−43.2609	−	3.96876i	−1.58072	−	0.145015i
$750$	14.1707	−	18.3075i	0.517440	−	0.668496i
$751$	36.7223	+	5.53500i	1.34002	+	0.201975i	0.779622	−	0.626250i	$-0.215411\pi$
$751$	36.7223	+	5.53500i	1.34002	+	0.201975i	0.560395	+	0.828225i	$0.310649\pi$
$752$	−9.71649	−	21.0771i	−0.354324	−	0.768604i
$753$	−19.0416	+	32.9810i	−0.693915	+	1.20190i
$754$	0.370875	+	4.14255i	0.0135065	+	0.150863i
$755$	2.30379	−	4.78388i	0.0838436	−	0.174103i
$756$	16.5656	−	13.5472i	0.602487	−	0.492708i
$757$	10.4881	+	21.7788i	0.381197	+	0.791564i	0.999982	+	0.00600323i	$0.00191090\pi$
$757$	10.4881	+	21.7788i	0.381197	+	0.791564i	−0.618785	+	0.785560i	$0.712375\pi$
$758$	−7.78825	+	4.64830i	−0.282882	+	0.168834i
$759$	−2.14634	−	1.99151i	−0.0779073	−	0.0722874i
$760$	−2.78369	+	5.34530i	−0.100975	+	0.193894i
$761$	−18.0337	−	12.2952i	−0.653722	−	0.445700i	0.190505	−	0.981686i	$-0.438987\pi$
$761$	−18.0337	−	12.2952i	−0.653722	−	0.445700i	−0.844227	+	0.535986i	$0.819940\pi$
$762$	0.597218	+	41.2119i	0.0216349	+	1.49295i
$763$	22.1367	+	18.2658i	0.801402	+	0.661268i
$764$	−9.99408	−	38.5953i	−0.361573	−	1.39633i
$765$	5.20227	−	3.00353i	0.188088	−	0.108593i
$766$	8.65292	−	6.08498i	0.312643	−	0.219859i
$767$	12.7184	−	8.67129i	0.459236	−	0.313102i
$768$	14.7921	−	28.2421i	0.533764	−	1.01910i
$769$	−0.0945013	+	0.414037i	−0.00340781	+	0.0149306i	−0.976603	−	0.215049i	$-0.931009\pi$
$769$	−0.0945013	+	0.414037i	−0.00340781	+	0.0149306i	0.973195	+	0.229980i	$0.0738660\pi$
$770$	0.576891	+	0.537636i	0.0207897	+	0.0193751i
$771$	−51.5536	+	11.7668i	−1.85666	+	0.423770i
$772$	16.9236	−	16.6410i	0.609094	−	0.598923i
$773$	−4.21801	+	13.6745i	−0.151711	+	0.491836i	−0.999243	−	0.0389090i	$-0.987612\pi$
$773$	−4.21801	+	13.6745i	−0.151711	+	0.491836i	0.847531	+	0.530745i	$0.178088\pi$
$774$	−8.27930	−	0.499926i	−0.297593	−	0.0179695i
$775$	−2.26688	+	0.699239i	−0.0814286	+	0.0251174i
$776$	7.73104	−	10.6094i	0.277528	−	0.380855i
$777$	−62.3168	−	10.4589i	−2.23560	−	0.375209i
$778$	8.80814	+	17.6321i	0.315787	+	0.632141i
$779$	10.9600	+	4.30149i	0.392683	+	0.154117i
$780$	−4.01739	−	5.54040i	−0.143846	−	0.198378i
$781$	0.256848	+	1.70407i	0.00919073	+	0.0609765i
$782$	−58.0590	+	18.8344i	−2.07619	+	0.673516i
$783$	6.18275			0.220953
$784$	−24.9208	+	12.7654i	−0.890027	+	0.455908i
$785$	−2.83226			−0.101088
$786$	−5.90914	+	1.91693i	−0.210772	+	0.0683746i
$787$	−4.63360	−	30.7419i	−0.165170	−	1.09583i	−0.905734	−	0.423846i	$-0.860680\pi$
$787$	−4.63360	−	30.7419i	−0.165170	−	1.09583i	0.740565	−	0.671985i	$-0.234558\pi$
$788$	−14.8944	−	20.5409i	−0.530589	−	0.731738i
$789$	−11.8090	−	4.63471i	−0.420413	−	0.165000i
$790$	−0.515198	−	1.03132i	−0.0183299	−	0.0366927i
$791$	16.9966	+	12.0083i	0.604331	+	0.426967i
$792$	−0.523695	−	0.381615i	−0.0186087	−	0.0135601i
$793$	−23.4655	+	7.23816i	−0.833286	+	0.257035i
$794$	−38.4766	−	2.32332i	−1.36548	−	0.0824515i
$795$	0.671003	−	2.17534i	0.0237980	−	0.0771513i
$796$	7.11466	−	6.99586i	0.252172	−	0.247962i
$797$	−16.8482	+	3.84549i	−0.596794	+	0.136214i	−0.510239	−	0.860033i	$-0.670443\pi$
$797$	−16.8482	+	3.84549i	−0.596794	+	0.136214i	−0.0865550	+	0.996247i	$0.527586\pi$
$798$	−14.7252	+	9.99224i	−0.521267	+	0.353721i
$799$	−8.95314	+	39.2263i	−0.316739	+	1.38773i
$800$	−16.2128	+	17.3912i	−0.573210	+	0.614871i
$801$	−7.08982	+	4.83376i	−0.250506	+	0.170792i
$802$	−38.3239	+	26.9504i	−1.35326	+	0.951653i
$803$	1.96485	−	1.13441i	0.0693381	−	0.0400323i
$804$	−6.60322	−	25.5004i	−0.232878	−	0.899331i
$805$	14.3844	−	3.03159i	0.506984	−	0.106849i
$806$	0.0222490	+	1.53532i	0.000783687	+	0.0540794i
$807$	46.2944	+	31.5630i	1.62964	+	1.11107i
$808$	2.73415	+	1.42387i	0.0961871	+	0.0500916i
$809$	−21.5412	−	19.9873i	−0.757349	−	0.702717i	0.203719	−	0.979029i	$-0.434697\pi$
$809$	−21.5412	−	19.9873i	−0.757349	−	0.702717i	−0.961068	+	0.276312i	$0.910888\pi$
$810$	−11.8917	+	7.09741i	−0.417833	+	0.249377i
$811$	9.69268	+	20.1271i	0.340356	+	0.706757i	0.998953	−	0.0457389i	$-0.0145642\pi$
$811$	9.69268	+	20.1271i	0.340356	+	0.706757i	−0.658597	+	0.752496i	$0.728850\pi$
$812$	−7.90840	−	1.70301i	−0.277530	−	0.0597639i
$813$	9.63265	−	20.0024i	0.337832	−	0.701515i
$814$	−0.356851	−	3.98591i	−0.0125076	−	0.139706i
$815$	0.137563	−	0.238266i	0.00481862	−	0.00834610i
$816$	−50.1928	+	23.1387i	−1.75710	+	0.810016i
$817$	−14.2650	−	2.15010i	−0.499069	−	0.0752226i
$818$	13.0102	−	16.8082i	0.454890	−	0.587685i
$819$	−0.654523	−	4.89533i	−0.0228709	−	0.171057i
$820$	−7.04184	−	5.28927i	−0.245912	−	0.184709i
$821$	−46.4716	+	3.48256i	−1.62187	+	0.121542i	−0.854425	−	0.519574i	$-0.826091\pi$
$821$	−46.4716	+	3.48256i	−1.62187	+	0.121542i	−0.767444	+	0.641116i	$0.778472\pi$
$822$	−41.3403	+	45.8697i	−1.44191	+	1.59989i
$823$	13.6572	+	34.7979i	0.476059	+	1.21298i	0.944214	+	0.329332i	$0.106823\pi$
$823$	13.6572	+	34.7979i	0.476059	+	1.21298i	−0.468156	+	0.883646i	$0.655081\pi$
$824$	9.20817	+	14.4591i	0.320782	+	0.503707i
$825$	1.23279	+	1.54587i	0.0429201	+	0.0538201i
$826$	8.76232	+	28.6296i	0.304880	+	0.996151i
$827$	−4.14750	−	3.30752i	−0.144223	−	0.115014i	0.548721	−	0.836006i	$-0.315115\pi$
$827$	−4.14750	−	3.30752i	−0.144223	−	0.115014i	−0.692943	+	0.720992i	$0.743686\pi$
$828$	−11.4349	+	3.89348i	−0.397389	+	0.135308i
$829$	−24.7155	−	1.85217i	−0.858404	−	0.0643285i	−0.361748	−	0.932276i	$-0.617820\pi$
$829$	−24.7155	−	1.85217i	−0.858404	−	0.0643285i	−0.496656	+	0.867948i	$0.665439\pi$
$830$	7.46339	+	2.18423i	0.259058	+	0.0758159i
$831$	−8.62698	+	8.00467i	−0.299267	+	0.277679i
$832$	7.85600	+	13.2333i	0.272358	+	0.458781i
$833$	47.7305	+	8.83194i	1.65376	+	0.306009i
$834$	−16.5939	−	7.69700i	−0.574598	−	0.266525i
$835$	4.28520	+	4.61835i	0.148296	+	0.159825i
$836$	−0.848030	−	0.742307i	−0.0293297	−	0.0256732i
$837$	2.27619	+	0.170577i	0.0786768	+	0.00589601i
$838$	−22.1680	−	23.2077i	−0.765780	−	0.801697i
$839$	20.7775	−	26.0541i	0.717318	−	0.899489i	−0.280864	−	0.959747i	$-0.590621\pi$
$839$	20.7775	−	26.0541i	0.717318	−	0.899489i	0.998183	+	0.0602586i	$0.0191925\pi$
$840$	12.6102	−	4.26282i	0.435092	−	0.147081i
$841$	16.6240	+	20.8458i	0.573240	+	0.718820i
$842$	1.87169	−	13.7687i	0.0645026	−	0.474502i
$843$	19.9539	−	7.83132i	0.687248	−	0.269725i
$844$	31.2866	−	13.3378i	1.07693	−	0.459106i
$845$	−8.27842	+	0.620382i	−0.284786	+	0.0213418i
$846$	−1.65918	+	7.78786i	−0.0570439	+	0.267752i
$847$	24.1932	−	15.9100i	0.831288	−	0.546673i
$848$	−1.95021	+	4.73313i	−0.0669706	+	0.162536i
$849$	−56.6495	−	8.53854i	−1.94421	−	0.293042i
$850$	40.6648	−	6.73322i	1.39479	−	0.230948i
$851$	−64.6064	−	37.3005i	−2.21468	−	1.27865i
$852$	27.3754	+	9.83853i	0.937865	+	0.337062i
$853$	4.99744	−	10.3773i	0.171109	−	0.355311i	−0.797725	−	0.603021i	$-0.793964\pi$
$853$	4.99744	−	10.3773i	0.171109	−	0.355311i	0.968834	+	0.247709i	$0.0796778\pi$
$854$	0.104786	−	47.7635i	0.00358571	−	1.63443i
$855$	1.86291	−	0.897128i	0.0637100	−	0.0306811i
$856$	−43.9282	−	15.0724i	−1.50143	−	0.515164i
$857$	12.9253	+	11.9929i	0.441519	+	0.409670i	0.869356	−	0.494186i	$-0.164534\pi$
$857$	12.9253	+	11.9929i	0.441519	+	0.409670i	−0.427837	+	0.903856i	$0.640724\pi$
$858$	1.18443	−	0.484774i	0.0404356	−	0.0165499i
$859$	12.7739	−	18.7358i	0.435839	−	0.639258i	−0.543991	−	0.839091i	$-0.683088\pi$
$859$	12.7739	−	18.7358i	0.435839	−	0.639258i	0.979830	+	0.199833i	$0.0640400\pi$
$860$	9.85388	+	4.39832i	0.336015	+	0.149982i
$861$	−10.8907	−	23.6148i	−0.371155	−	0.804789i
$862$	−8.65023	−	10.5303i	−0.294628	−	0.358665i
$863$	−7.09831	−	12.2946i	−0.241629	−	0.418514i	0.719549	−	0.694441i	$-0.244348\pi$
$863$	−7.09831	−	12.2946i	−0.241629	−	0.418514i	−0.961179	+	0.275927i	$0.911015\pi$
$864$	20.6350	−	9.87765i	0.702015	−	0.336045i
$865$	15.6723	−	10.6852i	0.532874	−	0.363307i
$866$	28.5906	+	18.8918i	0.971549	+	0.641969i
$867$	60.3881	+	13.7832i	2.05089	+	0.468102i
$868$	−2.86451	−	0.845153i	−0.0972278	−	0.0286864i
$869$	0.210182	−	0.0479726i	0.00712993	−	0.00162736i
$870$	3.59997	+	1.35302i	0.122050	+	0.0458717i
$871$	12.1504	+	3.74791i	0.411701	+	0.126993i
$872$	18.3687	+	24.5750i	0.622043	+	0.832215i
$873$	−4.30372	+	1.32752i	−0.145659	+	0.0449298i
$874$	−20.4129	+	4.97136i	−0.690476	+	0.168159i
$875$	−21.6998	+	1.26252i	−0.733586	+	0.0426809i
$876$	−1.10974	−	38.2815i	−0.0374946	−	1.29341i
$877$	−24.2965	−	9.53569i	−0.820436	−	0.321997i	−0.0822646	−	0.996611i	$-0.526215\pi$
$877$	−24.2965	−	9.53569i	−0.820436	−	0.321997i	−0.738172	+	0.674613i	$0.764310\pi$
$878$	11.0674	−	19.8273i	0.373506	−	0.669139i
$879$	−3.93031	+	0.592399i	−0.132566	+	0.0199811i
$880$	0.463098	+	0.704438i	0.0156110	+	0.0237466i
$881$	12.3275			0.415325			0.207663	−	0.978200i	$-0.433414\pi$
$881$	12.3275			0.415325			0.207663	+	0.978200i	$0.433414\pi$
$882$	9.47036	+	1.61081i	0.318884	+	0.0542390i
$883$		−	41.8053i		−	1.40686i	−0.710765	−	0.703429i	$-0.751651\pi$
$883$		−	41.8053i		−	1.40686i	0.710765	−	0.703429i	$-0.248349\pi$
$884$	3.21021	−	26.4853i	0.107971	−	0.890798i
$885$	−2.12142	−	14.0747i	−0.0713109	−	0.473117i
$886$	51.2109	+	28.5854i	1.72047	+	0.960344i
$887$	7.10092	−	18.0929i	0.238426	−	0.607499i	−0.760709	−	0.649093i	$-0.775149\pi$
$887$	7.10092	−	18.0929i	0.238426	−	0.607499i	0.999135	+	0.0415946i	$0.0132438\pi$
$888$	−62.0778	−	26.6368i	−2.08319	−	0.893872i
$889$	28.8026	−	25.8442i	0.966008	−	0.866786i
$890$	10.8466	−	2.64158i	0.363578	−	0.0885460i
$891$	−0.763349	−	2.47472i	−0.0255731	−	0.0829061i
$892$	−17.4653	+	32.3831i	−0.584783	+	1.08427i
$893$	−4.08211	+	13.2339i	−0.136603	+	0.442855i
$894$	−5.44366	+	14.4839i	−0.182063	+	0.484414i
$895$	0.425192	+	1.86289i	0.0142126	+	0.0622694i
$896$	−29.1151	+	6.95077i	−0.972666	+	0.232209i
$897$	5.30878	−	23.2593i	0.177255	−	0.776605i
$898$	−21.2652	−	14.0514i	−0.709628	−	0.468900i
$899$	−0.486076	−	0.712942i	−0.0162115	−	0.0237780i
$900$	8.02754	−	1.44900i	0.267585	−	0.0482999i
$901$	7.68561	−	4.43729i	0.256045	−	0.147828i
$902$	1.27263	−	1.04541i	0.0423738	−	0.0348083i
$903$	19.4479	+	25.2395i	0.647187	+	0.839919i
$904$	14.6139	+	16.7746i	0.486052	+	0.557915i
$905$	−15.2360	−	10.3877i	−0.506461	−	0.345299i
$906$	15.5118	−	6.34884i	0.515346	−	0.210926i
$907$	−10.5512	+	11.3715i	−0.350347	+	0.377584i	−0.883497	−	0.468436i	$-0.844818\pi$
$907$	−10.5512	+	11.3715i	−0.350347	+	0.377584i	0.533150	+	0.846021i	$0.321008\pi$
$908$	15.6240	−	1.62731i	0.518500	−	0.0540043i
$909$	−0.458886	−	0.952887i	−0.0152203	−	0.0316053i
$910$	−1.44354	+	6.26121i	−0.0478529	+	0.207557i
$911$	−46.3593	−	22.3255i	−1.53595	−	0.739675i	−0.541094	−	0.840962i	$-0.681990\pi$
$911$	−46.3593	−	22.3255i	−1.53595	−	0.739675i	−0.994857	+	0.101287i	$0.967704\pi$
$912$	−17.8236	+	6.65113i	−0.590197	+	0.220241i
$913$	−0.727116	+	1.25940i	−0.0240640	+	0.0416801i
$914$	14.8613	−	2.46071i	0.491567	−	0.0813931i
$915$	−3.38428	+	22.4532i	−0.111881	+	0.742280i
$916$	−15.8389	−	30.5894i	−0.523333	−	1.01070i
$917$	5.00191	+	3.00022i	0.165177	+	0.0990758i
$918$	−38.7894	−	8.26399i	−1.28024	−	0.272752i
$919$	−0.832261	−	11.1057i	−0.0274537	−	0.366345i	−0.993963	−	0.109714i	$-0.965007\pi$
$919$	−0.832261	−	11.1057i	−0.0274537	−	0.366345i	0.966509	−	0.256631i	$-0.0826125\pi$
$920$	15.7077	+	0.492261i	0.517867	+	0.0162294i
$921$	−23.8129	−	60.6742i	−0.784660	−	1.99928i
$922$	0.460745	−	3.38939i	0.0151738	−	0.111624i
$923$	−10.9784	+	8.75498i	−0.361358	+	0.288174i
$924$	0.216531	+	2.47982i	0.00712335	+	0.0815801i
$925$	39.3870	+	31.4101i	1.29504	+	1.03276i
$926$	−14.8668	+	14.2008i	−0.488553	+	0.466666i
$927$	0.439506	−	5.86480i	0.0144353	−	0.192625i
$928$	−7.78296	−	3.77061i	−0.255488	−	0.123776i
$929$	−29.6104	+	27.4744i	−0.971485	+	0.901406i	−0.995155	−	0.0983136i	$-0.968655\pi$
$929$	−29.6104	+	27.4744i	−0.971485	+	0.901406i	0.0236707	+	0.999720i	$0.492465\pi$
$930$	1.28801	+	0.597438i	0.0422355	+	0.0195908i
$931$	16.1560	+	4.25926i	0.529493	+	0.139592i
$932$	−0.515128	−	0.608883i	−0.0168736	−	0.0199446i
$933$	31.5773	+	34.0322i	1.03379	+	1.11417i
$934$	−0.918878	+	3.13975i	−0.0300666	+	0.102736i
$935$	0.109216	−	1.45738i	0.00357173	−	0.0476615i
$936$	0.559296	−	5.25019i	0.0182812	−	0.171608i
$937$	9.43528	−	11.8315i	0.308237	−	0.386517i	−0.603451	−	0.797400i	$-0.706208\pi$
$937$	9.43528	−	11.8315i	0.308237	−	0.386517i	0.911688	+	0.410883i	$0.134779\pi$
$938$	−13.9768	+	20.4039i	−0.456358	+	0.666209i
$939$	−27.1487	+	21.6504i	−0.885966	+	0.706534i
$940$	5.58516	−	8.72480i	0.182168	−	0.284572i
$941$	−5.56477	+	2.18401i	−0.181406	+	0.0711967i	−0.454306	−	0.890846i	$-0.650113\pi$
$941$	−5.56477	+	2.18401i	−0.181406	+	0.0711967i	0.272899	+	0.962043i	$0.412017\pi$
$942$	−6.64123	−	5.98544i	−0.216383	−	0.195016i
$943$	−2.29436	−	30.6161i	−0.0747147	−	0.996998i
$944$	1.85418	+	31.9540i	0.0603484	+	1.04001i
$945$	9.07919	+	2.96733i	0.295346	+	0.0965271i
$946$	−1.23518	+	1.59577i	−0.0401592	+	0.0518828i
$947$	−8.38123	+	55.6058i	−0.272353	+	1.80695i	0.265722	+	0.964050i	$0.414390\pi$
$947$	−8.38123	+	55.6058i	−0.272353	+	1.80695i	−0.538075	+	0.842897i	$0.680848\pi$
$948$	0.971431	−	3.50705i	0.0315506	−	0.113904i
$949$	16.0099	+	9.24333i	0.519704	+	0.300051i
$950$	14.1311	−	1.26514i	0.458474	−	0.0410464i
$951$	−43.4828	−	20.9402i	−1.41003	−	0.679033i
$952$	47.3396	+	21.2549i	1.53428	+	0.688875i
$953$	−6.96492	+	3.35413i	−0.225616	+	0.108651i	−0.543277	−	0.839553i	$-0.682817\pi$
$953$	−6.96492	+	3.35413i	−0.225616	+	0.108651i	0.317661	+	0.948204i	$0.397103\pi$
$954$	1.50812	−	0.900102i	0.0488273	−	0.0291419i
$955$	12.1038	−	13.0448i	0.391671	−	0.422121i
$956$	−0.530405	+	11.5680i	−0.0171545	+	0.374135i
$957$	−0.405134	+	0.594222i	−0.0130961	+	0.0192085i
$958$	−11.2736	+	0.163370i	−0.364232	+	0.00527824i
$959$	57.9687	+	0.967254i	1.87191	+	0.0312343i
$960$	14.1765	−	1.23566i	0.457546	−	0.0398806i
$961$	15.3407	+	26.5709i	0.494862	+	0.857126i
$962$	26.6728	−	18.7570i	0.859965	−	0.604751i
$963$	8.97569	+	13.1649i	0.289238	+	0.424234i
$964$	9.64247	+	15.6366i	0.310563	+	0.503621i
$965$	10.3284	+	2.35738i	0.332482	+	0.0758867i
$966$	40.1359	+	23.2900i	1.29135	+	0.749345i
$967$	3.93819	+	17.2543i	0.126644	+	0.554862i	0.997943	+	0.0641100i	$0.0204208\pi$
$967$	3.93819	+	17.2543i	0.126644	+	0.554862i	−0.871299	+	0.490752i	$0.836722\pi$
$968$	29.1553	−	10.4010i	0.937088	−	0.334301i
$969$	31.5149	+	9.72107i	1.01241	+	0.312286i
$970$	5.84878	+	0.353165i	0.187793	+	0.0113394i
$971$	−12.9816	−	42.0852i	−0.416598	−	1.35058i	−0.884394	−	0.466741i	$-0.845428\pi$
$971$	−12.9816	−	42.0852i	−0.416598	−	1.35058i	0.467796	−	0.883837i	$-0.345048\pi$
$972$	−19.0801	−	3.77682i	−0.611996	−	0.121141i
$973$	4.78772	+	16.4935i	0.153487	+	0.528758i
$974$	−35.8236	+	17.8957i	−1.14786	+	0.573417i
$975$	−5.88595	+	14.9972i	−0.188501	+	0.480294i
$976$	12.1988	−	49.5828i	0.390474	−	1.58711i
$977$	−51.4164	+	7.74978i	−1.64496	+	0.247937i	−0.905215	−	0.424953i	$-0.860291\pi$
$977$	−51.4164	+	7.74978i	−1.64496	+	0.247937i	−0.739742	+	0.672890i	$0.765053\pi$
$978$	0.826093	−	0.267985i	0.0264155	−	0.00856922i
$979$			2.08765i			0.0667215i
$980$	−10.7959	−	6.29635i	−0.344863	−	0.201129i
$981$		−	10.5263i		−	0.336078i
$982$	−14.6224	−	45.0752i	−0.466620	−	1.43841i
$983$	−20.2612	+	3.05388i	−0.646232	+	0.0974038i	−0.463977	−	0.885847i	$-0.653578\pi$
$983$	−20.2612	+	3.05388i	−0.646232	+	0.0974038i	−0.182255	+	0.983251i	$0.558340\pi$
$984$	−5.33420	−	27.2841i	−0.170048	−	0.869784i
$985$	4.13752	−	10.5422i	0.131832	−	0.335903i
$986$	6.70007	+	13.4122i	0.213374	+	0.427130i
$987$	26.7421	−	14.8503i	0.851210	−	0.472690i
$988$	1.78316	−	9.00836i	0.0567298	−	0.286594i
$989$	11.0881	+	35.9467i	0.352581	+	1.14304i
$990$	0.0174327	−	0.288704i	0.000554047	−	0.00917560i
$991$	−50.1886	−	15.4811i	−1.59429	−	0.491774i	−0.634603	−	0.772838i	$-0.718836\pi$
$991$	−50.1886	−	15.4811i	−1.59429	−	0.491774i	−0.959689	+	0.281064i	$0.909313\pi$
$992$	−2.76129	−	1.60289i	−0.0876710	−	0.0508917i
$993$	−8.44666	−	37.0072i	−0.268047	−	1.17439i
$994$	−9.92245	−	25.4460i	−0.314721	−	0.807098i
$995$	4.34203	+	0.991040i	0.137652	+	0.0314181i
$996$	12.8846	+	20.8941i	0.408263	+	0.662056i
$997$	4.57983	+	6.71738i	0.145045	+	0.212742i	0.891885	−	0.452261i	$-0.149383\pi$
$997$	4.57983	+	6.71738i	0.145045	+	0.212742i	−0.746841	+	0.665003i	$0.768430\pi$
$998$	10.5607	+	15.0175i	0.334293	+	0.475370i
$999$	−24.2365	−	41.9789i	−0.766810	−	1.32815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.z.a.109.49	yes	648
8.5	even	2	inner	392.2.z.a.109.35	✓	648
49.9	even	21	inner	392.2.z.a.205.35	yes	648
392.205	even	42	inner	392.2.z.a.205.49	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.109.35	✓	648	8.5	even	2	inner
392.2.z.a.109.49	yes	648	1.1	even	1	trivial
392.2.z.a.205.35	yes	648	49.9	even	21	inner
392.2.z.a.205.49	yes	648	392.205	even	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34520 - 0.436384i) q^{2} +(0.296979 + 1.97033i) q^{3} +(1.61914 - 1.17405i) q^{4} +(0.830993 + 0.326141i) q^{5} +(1.25932 + 2.52089i) q^{6} +(1.00756 - 2.44639i) q^{7} +(1.66573 - 2.28590i) q^{8} +(-0.927279 + 0.286028i) q^{9} +(1.26018 + 0.0760928i) q^{10} +(-0.0695882 + 0.225599i) q^{11} +(2.79411 + 2.84156i) q^{12} +(-1.87545 + 0.428060i) q^{13} +(0.287799 - 3.73057i) q^{14} +(-0.395817 + 1.73419i) q^{15} +(1.24321 - 3.80190i) q^{16} +(-5.72947 + 3.90628i) q^{17} +(-1.12256 + 0.789415i) q^{18} +(-2.06708 + 1.19343i) q^{19} +(1.72840 - 0.447561i) q^{20} +(5.11942 + 1.25869i) q^{21} +(0.00483787 + 0.333844i) q^{22} +(5.14256 + 3.50614i) q^{23} +(4.99866 + 2.60317i) q^{24} +(-3.08108 - 2.85882i) q^{25} +(-2.33607 + 1.39425i) q^{26} +(1.75470 + 3.64367i) q^{27} +(-1.24082 - 5.14397i) q^{28} +(0.663324 - 1.37741i) q^{29} +(0.224318 + 2.50556i) q^{30} +(0.282206 - 0.488795i) q^{31} +(0.0132814 - 5.65684i) q^{32} +(-0.465171 - 0.0701133i) q^{33} +(-6.00265 + 7.75499i) q^{34} +(1.63514 - 1.70433i) q^{35} +(-1.16558 + 1.55179i) q^{36} +(-11.9524 + 0.895709i) q^{37} +(-2.25985 + 2.50745i) q^{38} +(-1.40039 - 3.56813i) q^{39} +(2.12974 - 1.35631i) q^{40} +(-3.07554 - 3.85661i) q^{41} +(7.43592 - 0.540843i) q^{42} +(4.72536 + 3.76835i) q^{43} +(0.152192 + 0.446976i) q^{44} +(-0.863848 - 0.0647364i) q^{45} +(8.44780 + 2.47233i) q^{46} +(4.25334 - 3.94653i) q^{47} +(7.86019 + 1.32045i) q^{48} +(-4.96966 - 4.92975i) q^{49} +(-5.39222 - 2.50116i) q^{50} +(-9.39819 - 10.1288i) q^{51} +(-2.53405 + 2.89497i) q^{52} +(-1.27621 - 0.0956390i) q^{53} +(3.95046 + 4.13575i) q^{54} +(-0.131405 + 0.164776i) q^{55} +(-3.91389 - 6.37820i) q^{56} +(-2.96533 - 3.71841i) q^{57} +(0.291226 - 2.14235i) q^{58} +(-7.44878 + 2.92343i) q^{59} +(1.39514 + 3.27260i) q^{60} +(12.7297 - 0.953956i) q^{61} +(0.166322 - 0.780679i) q^{62} +(-0.234550 + 2.55668i) q^{63} +(-2.45069 - 7.61539i) q^{64} +(-1.69810 - 0.255947i) q^{65} +(-0.656345 + 0.108677i) q^{66} +(-5.72433 - 3.30494i) q^{67} +(-4.69062 + 13.0515i) q^{68} +(-5.38101 + 11.1738i) q^{69} +(1.45585 - 3.00622i) q^{70} +(6.57661 - 3.16713i) q^{71} +(-0.890765 + 2.59611i) q^{72} +(-7.04465 - 6.53648i) q^{73} +(-15.6875 + 6.42076i) q^{74} +(4.71780 - 6.91974i) q^{75} +(-1.94574 + 4.35919i) q^{76} +(0.481790 + 0.397544i) q^{77} +(-3.44089 - 4.18875i) q^{78} +(-0.456582 - 0.790823i) q^{79} +(2.27305 - 2.75389i) q^{80} +(-9.06344 + 6.17935i) q^{81} +(-5.82019 - 3.84580i) q^{82} +(6.00526 + 1.37066i) q^{83} +(9.76680 - 3.97246i) q^{84} +(-6.03515 + 1.37748i) q^{85} +(8.00102 + 3.00712i) q^{86} +(2.91094 + 0.897905i) q^{87} +(0.399783 + 0.534859i) q^{88} +(8.44981 - 2.60642i) q^{89} +(-1.19030 + 0.289886i) q^{90} +(-0.842422 + 5.01939i) q^{91} +(12.4429 - 0.360706i) q^{92} +(1.04690 + 0.410877i) q^{93} +(3.99940 - 7.16497i) q^{94} +(-2.10696 + 0.317573i) q^{95} +(11.1498 - 1.65379i) q^{96} +4.64123 q^{97} +(-8.83647 - 4.46283i) q^{98} -0.229098i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25}+ \cdots + 151 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more