LMFDB - Embedded newform 418.2.v.b.29.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			29.9
Character	$\chi$	$=$	418.29
Dual form			418.2.v.b.173.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.438371 - 0.898794i) q^{2} +(2.45510 - 0.991923i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(2.52718 - 0.724656i) q^{5} +(0.184709 - 2.64146i) q^{6} +(-0.616865 + 2.90212i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(2.88556 - 2.78656i) q^{9} +O(q^{10})$	\(q+(0.438371 - 0.898794i) q^{2} +(2.45510 - 0.991923i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(2.52718 - 0.724656i) q^{5} +(0.184709 - 2.64146i) q^{6} +(-0.616865 + 2.90212i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(2.88556 - 2.78656i) q^{9} +(0.456524 - 2.58908i) q^{10} +(-3.06365 - 1.27045i) q^{11} +(-2.29315 - 1.32395i) q^{12} +(-0.145391 - 0.583133i) q^{13} +(2.33799 + 1.82664i) q^{14} +(5.48565 - 4.28586i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-3.48371 + 3.60748i) q^{17} +(-1.23959 - 3.81507i) q^{18} +(3.97974 + 1.77810i) q^{19} +(-2.12692 - 1.54530i) q^{20} +(1.36422 + 7.73687i) q^{21} +(-2.48489 + 2.19666i) q^{22} +(0.972583 - 0.353991i) q^{23} +(-2.19521 + 1.48069i) q^{24} +(1.62125 - 1.01307i) q^{25} +(-0.587852 - 0.124952i) q^{26} +(1.08928 - 2.44657i) q^{27} +(2.66668 - 1.30063i) q^{28} +(-7.25784 + 1.02002i) q^{29} +(-1.44736 - 6.80927i) q^{30} +(-3.02586 - 6.79618i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-8.78174 - 0.0801801i) q^{33} +(1.71523 + 4.71255i) q^{34} +(0.544114 + 7.78119i) q^{35} +(-3.97237 - 0.558280i) q^{36} +(-5.31368 + 1.72652i) q^{37} +(3.34275 - 2.79750i) q^{38} +(-0.935373 - 1.28743i) q^{39} +(-2.32129 + 1.23425i) q^{40} +(3.14482 + 7.78369i) q^{41} +(7.55189 + 2.16547i) q^{42} +(4.40990 - 12.1161i) q^{43} +(0.885040 + 3.19636i) q^{44} +(5.27303 - 9.13316i) q^{45} +(0.108187 - 1.02933i) q^{46} +(1.60307 + 0.852368i) q^{47} +(0.368517 + 2.62214i) q^{48} +(-1.64698 - 0.733281i) q^{49} +(-0.199831 - 1.90127i) q^{50} +(-4.97449 + 12.3123i) q^{51} +(-0.370003 + 0.473583i) q^{52} +(0.780215 - 2.72093i) q^{53} +(-1.72145 - 2.05155i) q^{54} +(-8.66302 - 0.990567i) q^{55} -2.96696i q^{56} +(11.5344 + 0.417798i) q^{57} +(-2.26484 + 6.97045i) q^{58} +(0.224370 + 0.421978i) q^{59} +(-6.75461 - 1.68411i) q^{60} +(3.32907 + 2.24548i) q^{61} +(-7.43482 - 0.259630i) q^{62} +(6.30692 + 10.0932i) q^{63} +(0.913545 - 0.406737i) q^{64} +(-0.790001 - 1.36832i) q^{65} +(-3.92173 + 7.85783i) q^{66} +(2.52145 + 0.444600i) q^{67} +(4.98752 + 0.524209i) q^{68} +(2.03665 - 1.83381i) q^{69} +(7.23221 + 2.92200i) q^{70} +(-2.25938 - 7.87941i) q^{71} +(-2.24315 + 3.32561i) q^{72} +(5.96223 - 9.54156i) q^{73} +(-0.777578 + 5.53276i) q^{74} +(2.97543 - 4.09533i) q^{75} +(-1.04902 - 4.23079i) q^{76} +(5.57687 - 8.10739i) q^{77} +(-1.56718 + 0.276335i) q^{78} +(-0.754823 + 0.0527823i) q^{79} +(0.0917514 + 2.62742i) q^{80} +(-0.172503 + 4.93983i) q^{81} +(8.37453 + 0.585604i) q^{82} +(-11.2057 + 1.17776i) q^{83} +(5.25684 - 5.83831i) q^{84} +(-6.18975 + 11.6412i) q^{85} +(-8.95671 - 9.27494i) q^{86} +(-16.8069 + 9.70347i) q^{87} +(3.26084 + 0.605722i) q^{88} +(-7.69708 + 9.17302i) q^{89} +(-5.89728 - 8.74308i) q^{90} +(1.78201 - 0.0622292i) q^{91} +(-0.877731 - 0.548467i) q^{92} +(-14.1701 - 13.6839i) q^{93} +(1.46884 - 1.06718i) q^{94} +(11.3460 + 1.60962i) q^{95} +(2.51831 + 0.818248i) q^{96} +(13.5966 + 6.63149i) q^{97} +(-1.38106 + 1.15884i) q^{98} +(-12.3805 + 4.87106i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	0.438371	−	0.898794i	0.309975	−	0.635543i
$2$	0.438371	−	0.898794i	0.309975	−	0.635543i
$3$	2.45510	−	0.991923i	1.41745	−	0.572687i	0.467193	−	0.884155i	$-0.345265\pi$
$3$	2.45510	−	0.991923i	1.41745	−	0.572687i	0.950257	+	0.311468i	$0.100821\pi$
$4$	−0.615661	−	0.788011i	−0.307831	−	0.394005i
$5$	2.52718	−	0.724656i	1.13019	−	0.324076i	0.342115	−	0.939658i	$-0.388857\pi$
$5$	2.52718	−	0.724656i	1.13019	−	0.324076i	0.788073	+	0.615582i	$0.211079\pi$
$6$	0.184709	−	2.64146i	0.0754070	−	1.07837i
$7$	−0.616865	+	2.90212i	−0.233153	+	1.09690i	0.693347	+	0.720604i	$0.256135\pi$
$7$	−0.616865	+	2.90212i	−0.233153	+	1.09690i	−0.926500	+	0.376295i	$0.877198\pi$
$8$	−0.978148	+	0.207912i	−0.345827	+	0.0735079i
$9$	2.88556	−	2.78656i	0.961855	−	0.928852i
$10$	0.456524	−	2.58908i	0.144366	−	0.818738i
$11$	−3.06365	−	1.27045i	−0.923725	−	0.383056i
$11$	−3.06365	−	1.27045i	−0.923725	−	0.383056i
$12$	−2.29315	−	1.32395i	−0.661976	−	0.382192i
$13$	−0.145391	−	0.583133i	−0.0403243	−	0.161732i	0.946758	−	0.321946i	$-0.104337\pi$
$13$	−0.145391	−	0.583133i	−0.0403243	−	0.161732i	−0.987082	+	0.160214i	$0.948782\pi$
$14$	2.33799	+	1.82664i	0.624855	+	0.488191i
$15$	5.48565	−	4.28586i	1.41639	−	1.10660i
$16$	−0.241922	+	0.970296i	−0.0604805	+	0.242574i
$17$	−3.48371	+	3.60748i	−0.844923	+	0.874943i	−0.993485	−	0.113960i	$-0.963647\pi$
$17$	−3.48371	+	3.60748i	−0.844923	+	0.874943i	0.148562	+	0.988903i	$0.452535\pi$
$18$	−1.23959	−	3.81507i	−0.292175	−	0.899221i
$19$	3.97974	+	1.77810i	0.913016	+	0.407923i
$19$	3.97974	+	1.77810i	0.913016	+	0.407923i
$20$	−2.12692	−	1.54530i	−0.475594	−	0.345539i
$21$	1.36422	+	7.73687i	0.297697	+	1.68832i
$22$	−2.48489	+	2.19666i	−0.529781	+	0.468329i
$23$	0.972583	−	0.353991i	0.202798	−	0.0738123i	−0.238624	−	0.971112i	$-0.576696\pi$
$23$	0.972583	−	0.353991i	0.202798	−	0.0738123i	0.441422	+	0.897300i	$0.354474\pi$
$24$	−2.19521	+	1.48069i	−0.448096	+	0.302245i
$25$	1.62125	−	1.01307i	0.324250	−	0.202614i
$26$	−0.587852	−	0.124952i	−0.115287	−	0.0245051i
$27$	1.08928	−	2.44657i	0.209633	−	0.470843i
$28$	2.66668	−	1.30063i	0.503956	−	0.245796i
$29$	−7.25784	+	1.02002i	−1.34775	+	0.189413i	−0.775853	−	0.630914i	$-0.782680\pi$
$29$	−7.25784	+	1.02002i	−1.34775	+	0.189413i	−0.571894	+	0.820328i	$0.693791\pi$
$30$	−1.44736	−	6.80927i	−0.264250	−	1.24320i
$31$	−3.02586	−	6.79618i	−0.543460	−	1.22063i	−0.951495	−	0.307664i	$-0.900453\pi$
$31$	−3.02586	−	6.79618i	−0.543460	−	1.22063i	0.408035	−	0.912966i	$-0.366214\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−8.78174	−	0.0801801i	−1.52871	−	0.0139576i
$34$	1.71523	+	4.71255i	0.294159	+	0.808196i
$35$	0.544114	+	7.78119i	0.0919720	+	1.31526i
$36$	−3.97237	−	0.558280i	−0.662061	−	0.0930466i
$37$	−5.31368	+	1.72652i	−0.873563	+	0.283838i	−0.711282	−	0.702907i	$-0.751885\pi$
$37$	−5.31368	+	1.72652i	−0.873563	+	0.283838i	−0.162281	+	0.986745i	$0.551885\pi$
$38$	3.34275	−	2.79750i	0.542265	−	0.453815i
$39$	−0.935373	−	1.28743i	−0.149780	−	0.206154i
$40$	−2.32129	+	1.23425i	−0.367028	+	0.195152i
$41$	3.14482	+	7.78369i	0.491138	+	1.21561i	0.945743	+	0.324915i	$0.105336\pi$
$41$	3.14482	+	7.78369i	0.491138	+	1.21561i	−0.454605	+	0.890693i	$0.650220\pi$
$42$	7.55189	+	2.16547i	1.16528	+	0.334139i
$43$	4.40990	−	12.1161i	0.672503	−	1.84769i	0.164396	−	0.986394i	$-0.447433\pi$
$43$	4.40990	−	12.1161i	0.672503	−	1.84769i	0.508108	−	0.861293i	$-0.330345\pi$
$44$	0.885040	+	3.19636i	0.133425	+	0.481869i
$45$	5.27303	−	9.13316i	0.786057	−	1.36149i
$46$	0.108187	−	1.02933i	0.0159513	−	0.151767i
$47$	1.60307	+	0.852368i	0.233832	+	0.124331i	0.582254	−	0.813007i	$-0.302171\pi$
$47$	1.60307	+	0.852368i	0.233832	+	0.124331i	−0.348422	+	0.937338i	$0.613282\pi$
$48$	0.368517	+	2.62214i	0.0531909	+	0.378473i
$49$	−1.64698	−	0.733281i	−0.235282	−	0.104754i
$50$	−0.199831	−	1.90127i	−0.0282604	−	0.268880i
$51$	−4.97449	+	12.3123i	−0.696567	+	1.72406i
$52$	−0.370003	+	0.473583i	−0.0513102	+	0.0656741i
$53$	0.780215	−	2.72093i	0.107171	−	0.373749i	−0.889337	−	0.457253i	$-0.848833\pi$
$53$	0.780215	−	2.72093i	0.107171	−	0.373749i	0.996507	+	0.0835041i	$0.0266112\pi$
$54$	−1.72145	−	2.05155i	−0.234260	−	0.279180i
$55$	−8.66302	−	0.990567i	−1.16812	−	0.133568i
$56$		−	2.96696i		−	0.396476i
$57$	11.5344	+	0.417798i	1.52777	+	0.0553387i
$58$	−2.26484	+	6.97045i	−0.297388	+	0.915265i
$59$	0.224370	+	0.421978i	0.0292105	+	0.0549369i	0.897125	−	0.441776i	$-0.145651\pi$
$59$	0.224370	+	0.421978i	0.0292105	+	0.0549369i	−0.867915	+	0.496713i	$0.834540\pi$
$60$	−6.75461	−	1.68411i	−0.872017	−	0.217418i
$61$	3.32907	+	2.24548i	0.426243	+	0.287505i	0.753521	−	0.657423i	$-0.228354\pi$
$61$	3.32907	+	2.24548i	0.426243	+	0.287505i	−0.327278	+	0.944928i	$0.606131\pi$
$62$	−7.43482	−	0.259630i	−0.944223	−	0.0329730i
$63$	6.30692	+	10.0932i	0.794598	+	1.27162i
$64$	0.913545	−	0.406737i	0.114193	−	0.0508421i
$65$	−0.790001	−	1.36832i	−0.0979875	−	0.169719i
$66$	−3.92173	+	7.85783i	−0.482731	+	0.967232i
$67$	2.52145	+	0.444600i	0.308044	+	0.0543165i	0.325533	−	0.945531i	$-0.394456\pi$
$67$	2.52145	+	0.444600i	0.308044	+	0.0543165i	−0.0174892	+	0.999847i	$0.505567\pi$
$68$	4.98752	+	0.524209i	0.604826	+	0.0635697i
$69$	2.03665	−	1.83381i	0.245184	−	0.220765i
$70$	7.23221	+	2.92200i	0.864414	+	0.349246i
$71$	−2.25938	−	7.87941i	−0.268140	−	0.935114i	−0.973959	−	0.226722i	$-0.927199\pi$
$71$	−2.25938	−	7.87941i	−0.268140	−	0.935114i	0.705820	−	0.708391i	$-0.250579\pi$
$72$	−2.24315	+	3.32561i	−0.264358	+	0.391926i
$73$	5.96223	−	9.54156i	0.697826	−	1.11676i	−0.289366	−	0.957219i	$-0.593444\pi$
$73$	5.96223	−	9.54156i	0.697826	−	1.11676i	0.987192	−	0.159537i	$-0.0510000\pi$
$74$	−0.777578	+	5.53276i	−0.0903916	+	0.643170i
$75$	2.97543	−	4.09533i	0.343574	−	0.472888i
$76$	−1.04902	−	4.23079i	−0.120330	−	0.485305i
$77$	5.57687	−	8.10739i	0.635543	−	0.923923i
$78$	−1.56718	+	0.276335i	−0.177448	+	0.0312888i
$79$	−0.754823	+	0.0527823i	−0.0849242	+	0.00593848i	−0.112155	−	0.993691i	$-0.535775\pi$
$79$	−0.754823	+	0.0527823i	−0.0849242	+	0.00593848i	0.0272312	+	0.999629i	$0.491331\pi$
$80$	0.0917514	+	2.62742i	0.0102581	+	0.293754i
$81$	−0.172503	+	4.93983i	−0.0191670	+	0.548870i
$82$	8.37453	+	0.585604i	0.924812	+	0.0646692i
$83$	−11.2057	+	1.17776i	−1.22998	+	0.129276i	−0.697137	−	0.716938i	$-0.745543\pi$
$83$	−11.2057	+	1.17776i	−1.22998	+	0.129276i	−0.532843	+	0.846214i	$0.678876\pi$
$84$	5.25684	−	5.83831i	0.573568	−	0.637012i
$85$	−6.18975	+	11.6412i	−0.671373	+	1.26267i
$86$	−8.95671	−	9.27494i	−0.965826	−	1.00014i
$87$	−16.8069	+	9.70347i	−1.80189	+	1.04032i
$88$	3.26084	+	0.605722i	0.347607	+	0.0645702i
$89$	−7.69708	+	9.17302i	−0.815889	+	0.972338i	−0.999944	−	0.0105775i	$-0.996633\pi$
$89$	−7.69708	+	9.17302i	−0.815889	+	0.972338i	0.184055	+	0.982916i	$0.441077\pi$
$90$	−5.89728	−	8.74308i	−0.621628	−	0.921602i
$91$	1.78201	−	0.0622292i	0.186806	−	0.00652339i
$92$	−0.877731	−	0.548467i	−0.0915098	−	0.0571816i
$93$	−14.1701	−	13.6839i	−1.46937	−	1.41895i
$94$	1.46884	−	1.06718i	0.151500	−	0.110071i
$95$	11.3460	+	1.60962i	1.16408	+	0.165143i
$96$	2.51831	+	0.818248i	0.257024	+	0.0835121i
$97$	13.5966	+	6.63149i	1.38052	+	0.673326i	0.971023	−	0.238985i	$-0.0768147\pi$
$97$	13.5966	+	6.63149i	1.38052	+	0.673326i	0.409499	+	0.912311i	$0.365704\pi$
$98$	−1.38106	+	1.15884i	−0.139508	+	0.117061i
$99$	−12.3805	+	4.87106i	−1.24429	+	0.489560i
$100$	−1.79645	−	0.653854i	−0.179645	−	0.0653854i
$101$	13.4706	−	3.35859i	1.34037	−	0.334192i	0.495243	−	0.868754i	$-0.335079\pi$
$101$	13.4706	−	3.35859i	1.34037	−	0.334192i	0.845129	+	0.534562i	$0.179523\pi$
$102$	8.88554	+	9.86839i	0.879799	+	0.977116i
$103$	8.15064	+	7.33887i	0.803107	+	0.723121i	0.964590	−	0.263755i	$-0.0849610\pi$
$103$	8.15064	+	7.33887i	0.803107	+	0.723121i	−0.161483	+	0.986876i	$0.551628\pi$
$104$	0.263455	+	0.540162i	0.0258338	+	0.0529672i
$105$	9.05419	+	18.5638i	0.883599	+	1.81165i
$106$	−2.10353	−	1.89403i	−0.204313	−	0.183965i
$107$	−5.48779	−	6.09481i	−0.530524	−	0.589207i	0.416994	−	0.908909i	$-0.363084\pi$
$107$	−5.48779	−	6.09481i	−0.530524	−	0.589207i	−0.947518	+	0.319702i	$0.896417\pi$
$108$	−2.59855	+	0.647893i	−0.250046	+	0.0623435i
$109$	−7.49307	−	2.72725i	−0.717706	−	0.261223i	−0.0427542	−	0.999086i	$-0.513613\pi$
$109$	−7.49307	−	2.72725i	−0.717706	−	0.261223i	−0.674951	+	0.737862i	$0.735835\pi$
$110$	−4.68793	+	7.35204i	−0.446977	+	0.700989i
$111$	−11.3330	+	9.50952i	−1.07568	+	0.902604i
$112$	−2.66668	−	1.30063i	−0.251978	−	0.122898i
$113$	13.3186	+	4.32748i	1.25291	+	0.407095i	0.858963	−	0.512037i	$-0.171109\pi$
$113$	13.3186	+	4.32748i	1.25291	+	0.407095i	0.393948	+	0.919133i	$0.371109\pi$
$114$	5.43186	−	10.1839i	0.508740	−	0.953809i
$115$	2.20137	−	1.59939i	0.205278	−	0.149144i
$116$	5.27216	+	5.09127i	0.489508	+	0.472712i
$117$	−2.04447	−	1.27753i	−0.189011	−	0.118107i
$118$	0.477629	−	0.0166792i	0.0439693	−	0.00153544i
$119$	−8.32038	−	12.3355i	−0.762728	−	1.13079i
$120$	−4.47470	+	5.33274i	−0.408482	+	0.486810i
$121$	7.77190	+	7.78445i	0.706536	+	0.707677i
$122$	3.47759	−	2.00779i	0.314846	−	0.181777i
$123$	15.4416	+	15.9903i	1.39233	+	1.44180i
$124$	−3.49256	+	6.56856i	−0.313641	+	0.589874i
$125$	−5.43273	+	6.03366i	−0.485918	+	0.539667i
$126$	11.8365	−	1.24406i	1.05448	−	0.110830i
$127$	6.95677	+	0.486465i	0.617314	+	0.0431668i	0.374990	−	0.927029i	$-0.377646\pi$
$127$	6.95677	+	0.486465i	0.617314	+	0.0431668i	0.242323	+	0.970196i	$0.422090\pi$
$128$	0.0348995	−	0.999391i	0.00308471	−	0.0883345i
$129$	−1.19151	−	34.1205i	−0.104907	−	3.00414i
$130$	−1.57615	+	0.110215i	−0.138238	+	0.00966652i
$131$	−9.36162	+	1.65071i	−0.817929	+	0.144223i	−0.566932	−	0.823765i	$-0.691870\pi$
$131$	−9.36162	+	1.65071i	−0.817929	+	0.144223i	−0.250997	+	0.967988i	$0.580759\pi$
$132$	5.34340	+	6.96947i	0.465083	+	0.606615i
$133$	−7.61522	+	10.4529i	−0.660324	+	0.906378i
$134$	1.50493	−	2.07136i	0.130007	−	0.178939i
$135$	0.979889	−	6.97227i	0.0843354	−	0.600078i
$136$	2.65754	−	4.25295i	0.227882	−	0.364688i
$137$	8.96389	−	13.2895i	0.765837	−	1.13540i	−0.221250	−	0.975217i	$-0.571014\pi$
$137$	8.96389	−	13.2895i	0.765837	−	1.13540i	0.987087	−	0.160183i	$-0.0512084\pi$
$138$	−0.755408	−	2.63442i	−0.0643046	−	0.224257i
$139$	4.50887	+	1.82170i	0.382438	+	0.154515i	0.557772	−	0.829994i	$-0.311656\pi$
$139$	4.50887	+	1.82170i	0.382438	+	0.154515i	−0.175335	+	0.984509i	$0.556101\pi$
$140$	5.79667	−	5.21935i	0.489908	−	0.441115i
$141$	4.78118	+	0.502522i	0.402648	+	0.0423200i
$142$	−8.07241	−	1.42338i	−0.677422	−	0.119448i
$143$	−0.295415	+	1.97123i	−0.0247039	+	0.164842i
$144$	2.00570	+	3.47398i	0.167142	+	0.289498i
$145$	−17.6027	+	7.83721i	−1.46182	+	0.650845i
$146$	−5.96223	−	9.54156i	−0.493438	−	0.789665i
$147$	−4.77084	−	0.166602i	−0.393492	−	0.0137411i
$148$	4.63194	+	3.12428i	0.380743	+	0.256814i
$149$	8.99442	+	2.24256i	0.736851	+	0.183718i	0.592229	−	0.805769i	$-0.298248\pi$
$149$	8.99442	+	2.24256i	0.736851	+	0.183718i	0.144622	+	0.989487i	$0.453803\pi$
$150$	−2.37652	−	4.46958i	−0.194042	−	0.364940i
$151$	−1.17983	+	3.63113i	−0.0960128	+	0.295497i	−0.987516	−	0.157517i	$-0.949651\pi$
$151$	−1.17983	+	3.63113i	−0.0960128	+	0.295497i	0.891504	+	0.453014i	$0.149651\pi$
$152$	−4.26247	−	0.911806i	−0.345732	−	0.0739572i
$153$			20.1172i			1.62638i
$154$	−4.84213	−	8.56650i	−0.390190	−	0.690309i
$155$	−12.5718	−	14.9824i	−1.00979	−	1.20342i
$156$	−0.438636	+	1.52971i	−0.0351190	+	0.122474i
$157$	−6.43630	+	8.23809i	−0.513673	+	0.657471i	−0.973003	−	0.230795i	$-0.925867\pi$
$157$	−6.43630	+	8.23809i	−0.513673	+	0.657471i	0.459330	+	0.888266i	$0.348090\pi$
$158$	−0.283452	+	0.701568i	−0.0225502	+	0.0558138i
$159$	−0.783454	−	7.45406i	−0.0621319	−	0.591146i
$160$	2.40173	+	1.06932i	0.189873	+	0.0845370i
$161$	0.427373	+	3.04092i	0.0336817	+	0.239658i
$162$	4.36427	+	2.32052i	0.342890	+	0.182318i
$163$	1.18058	−	11.2325i	0.0924705	−	0.879798i	−0.845708	−	0.533646i	$-0.820821\pi$
$163$	1.18058	−	11.2325i	0.0924705	−	0.879798i	0.938178	−	0.346152i	$-0.112512\pi$
$164$	4.19749	−	7.27027i	0.327769	−	0.567712i
$165$	−22.2511	+	6.16111i	−1.73225	+	0.479642i
$166$	−3.85367	+	10.5879i	−0.299103	+	0.821778i
$167$	−7.44799	−	2.13568i	−0.576343	−	0.165264i	−0.0252115	−	0.999682i	$-0.508026\pi$
$167$	−7.44799	−	2.13568i	−0.576343	−	0.165264i	−0.551131	+	0.834418i	$0.685804\pi$
$168$	−2.94299	−	7.28417i	−0.227057	−	0.561986i
$169$	11.1594	−	5.93357i	0.858416	−	0.456428i
$170$	7.74966	+	10.6665i	0.594372	+	0.818083i
$171$	16.4386	−	5.95897i	1.25709	−	0.455694i
$172$	−12.2626	+	3.98437i	−0.935016	+	0.303805i
$173$	−21.3213	−	2.99652i	−1.62103	−	0.227821i	−0.730555	−	0.682854i	$-0.760739\pi$
$173$	−21.3213	−	2.99652i	−1.62103	−	0.227821i	−0.890475	+	0.455033i	$0.849628\pi$
$174$	1.35376	+	19.3597i	0.102628	+	1.46765i
$175$	1.93996	+	5.32999i	0.146647	+	0.402909i
$176$	1.97388	−	2.66530i	0.148787	−	0.200904i
$177$	0.969419	+	0.813439i	0.0728660	+	0.0611418i
$178$	4.87048	+	10.9393i	0.365058	+	0.819934i
$179$	−4.01147	−	18.8725i	−0.299831	−	1.41059i	−0.827654	−	0.561239i	$-0.810325\pi$
$179$	−4.01147	−	18.8725i	−0.299831	−	1.41059i	0.527823	−	0.849355i	$-0.323009\pi$
$180$	−10.4434	+	1.46773i	−0.778407	+	0.109398i
$181$	−17.6208	+	8.59425i	−1.30975	+	0.638806i	−0.955125	−	0.296204i	$-0.904279\pi$
$181$	−17.6208	+	8.59425i	−1.30975	+	0.638806i	−0.354621	+	0.935010i	$0.615390\pi$
$182$	0.725251	−	1.62894i	0.0537592	−	0.120745i
$183$	10.4005	+	2.21070i	0.768828	+	0.163420i
$184$	−0.877731	+	0.548467i	−0.0647072	+	0.0404335i
$185$	−12.1775	+	8.21380i	−0.895305	+	0.603891i
$186$	−18.5107	+	6.73735i	−1.35727	+	0.494007i
$187$	15.2560	−	6.62618i	1.11563	−	0.484554i
$188$	−0.315274	−	1.78801i	−0.0229937	−	0.130404i
$189$	6.42831	+	4.67044i	0.467591	+	0.339725i
$190$	6.42048	−	9.49213i	0.465791	−	0.688631i
$191$	5.36428	+	16.5096i	0.388146	+	1.19459i	0.934172	+	0.356822i	$0.116140\pi$
$191$	5.36428	+	16.5096i	0.388146	+	1.19459i	−0.546026	+	0.837768i	$0.683860\pi$
$192$	1.83939	−	1.90474i	0.132747	−	0.137463i
$193$	−1.30995	+	5.25393i	−0.0942923	+	0.378186i	−0.998838	−	0.0481906i	$-0.984655\pi$
$193$	−1.30995	+	5.25393i	−0.0942923	+	0.378186i	0.904546	+	0.426376i	$0.140210\pi$
$194$	11.9207	−	9.31346i	0.855855	−	0.668667i
$195$	−3.29680	−	2.57574i	−0.236089	−	0.184453i
$196$	0.436147	+	1.74929i	0.0311533	+	0.124949i
$197$	−13.5615	−	7.82974i	−0.966217	−	0.557846i	−0.0681365	−	0.997676i	$-0.521705\pi$
$197$	−13.5615	−	7.82974i	−0.966217	−	0.557846i	−0.898081	+	0.439830i	$0.855039\pi$
$198$	−1.04920	+	13.2629i	−0.0745631	+	0.942553i
$199$	4.34369	−	24.6343i	0.307916	−	1.74628i	−0.301534	−	0.953455i	$-0.597499\pi$
$199$	4.34369	−	24.6343i	0.307916	−	1.74628i	0.609450	−	0.792824i	$-0.291390\pi$
$200$	−1.37519	+	1.32801i	−0.0972407	+	0.0939043i
$201$	6.63141	−	1.40955i	0.467744	−	0.0994220i
$202$	2.88643	−	13.5796i	0.203089	−	0.955456i
$203$	1.51688	−	21.6924i	0.106464	−	1.52250i
$204$	12.7648	−	3.66025i	0.893716	−	0.256269i
$205$	13.5880	+	17.3918i	0.949027	+	1.21470i
$206$	10.1691	−	4.10860i	0.708518	−	0.286260i
$207$	1.82003	−	3.73162i	0.126501	−	0.259366i
$208$	0.600985			0.0416708
$209$	−9.93355	−	10.5035i	−0.687118	−	0.726546i
$210$	20.6542			1.42527
$211$	7.42114	−	15.2156i	0.510892	−	1.04748i	−0.474981	−	0.879996i	$-0.657545\pi$
$211$	7.42114	−	15.2156i	0.510892	−	1.04748i	0.985874	−	0.167489i	$-0.0535659\pi$
$212$	−2.62447	+	1.06036i	−0.180250	+	0.0728255i
$213$	−13.3628	−	17.1036i	−0.915602	−	1.17192i
$214$	−7.88366	+	2.26060i	−0.538916	+	0.154532i
$215$	2.36459	−	33.8152i	0.161263	−	2.30618i
$216$	−0.556810	+	2.61958i	−0.0378861	+	0.178240i
$217$	21.5899	−	4.58908i	1.46562	−	0.311527i
$218$	−5.73598	+	5.53917i	−0.388490	+	0.375160i
$219$	5.17335	−	29.3395i	0.349583	−	1.98258i
$220$	4.55291	+	7.43641i	0.306957	+	0.501362i
$221$	2.61015	+	1.50697i	0.175577	+	0.101370i
$222$	3.57904	+	14.3547i	0.240209	+	0.963427i
$223$	−0.651824	−	0.509260i	−0.0436493	−	0.0341026i	0.593601	−	0.804760i	$-0.297706\pi$
$223$	−0.651824	−	0.509260i	−0.0436493	−	0.0341026i	−0.637250	+	0.770657i	$0.719928\pi$
$224$	−2.33799	+	1.82664i	−0.156214	+	0.122048i
$225$	1.85524	−	7.44097i	0.123683	−	0.496065i
$226$	9.72802	−	10.0737i	0.647098	−	0.670090i
$227$	−4.15394	−	12.7845i	−0.275706	−	0.848537i	−0.989032	−	0.147704i	$-0.952812\pi$
$227$	−4.15394	−	12.7845i	−0.275706	−	0.848537i	0.713325	−	0.700833i	$-0.247188\pi$
$228$	−6.77205	−	9.34645i	−0.448490	−	0.618983i
$229$	0.582233	+	0.423017i	0.0384750	+	0.0279537i	0.606857	−	0.794811i	$-0.292430\pi$
$229$	0.582233	+	0.423017i	0.0384750	+	0.0279537i	−0.568382	+	0.822765i	$0.692430\pi$
$230$	−0.472503	−	2.67970i	−0.0311559	−	0.176694i
$231$	5.64985	−	25.4362i	0.371733	−	1.67358i
$232$	6.88716	−	2.50672i	0.452164	−	0.164574i
$233$	14.5582	−	9.81962i	0.953739	−	0.643305i	0.0194456	−	0.999811i	$-0.493810\pi$
$233$	14.5582	−	9.81962i	0.953739	−	0.643305i	0.934293	+	0.356506i	$0.116032\pi$
$234$	−2.04447	+	1.27753i	−0.133651	+	0.0835145i
$235$	4.66892	+	0.992409i	0.304567	+	0.0647376i
$236$	0.194388	−	0.436602i	0.0126536	−	0.0284203i
$237$	−1.80081	+	0.878312i	−0.116975	+	0.0570525i
$238$	−14.7345	+	2.07079i	−0.955094	+	0.134230i
$239$	0.699981	+	3.29315i	0.0452780	+	0.213016i	0.994971	−	0.100167i	$-0.0319378\pi$
$239$	0.699981	+	3.29315i	0.0452780	+	0.213016i	−0.949693	+	0.313184i	$0.898604\pi$
$240$	2.83145	+	6.35955i	0.182770	+	0.410507i
$241$	13.1597	+	11.0423i	0.847690	+	0.711297i	0.959280	−	0.282458i	$-0.0911497\pi$
$241$	13.1597	+	11.0423i	0.847690	+	0.711297i	−0.111589	+	0.993754i	$0.535594\pi$
$242$	10.4036	−	3.57286i	0.668768	−	0.229672i
$243$	7.22432	+	19.8487i	0.463440	+	1.27329i
$244$	−0.280113	−	4.00580i	−0.0179324	−	0.256445i
$245$	−4.69357	−	0.659639i	−0.299861	−	0.0421428i
$246$	21.1412	−	6.86918i	1.34791	−	0.437963i
$247$	0.458247	−	2.57924i	0.0291575	−	0.164113i
$248$	4.37274	+	6.01856i	0.277669	+	0.382179i
$249$	−26.3427	+	14.0067i	−1.66940	+	0.887636i
$250$	3.04147	+	7.52789i	0.192359	+	0.476106i
$251$	5.74708	+	1.64795i	0.362752	+	0.104018i	0.452062	−	0.891986i	$-0.350688\pi$
$251$	5.74708	+	1.64795i	0.362752	+	0.104018i	−0.0893102	+	0.996004i	$0.528466\pi$
$252$	4.07061	−	11.1839i	0.256424	−	0.704520i
$253$	−3.42938	−	0.151116i	−0.215603	−	0.00950059i
$254$	3.48688	−	6.03945i	0.218786	−	0.378949i
$255$	−3.64923	+	34.7201i	−0.228524	+	2.17426i
$256$	−0.882948	−	0.469472i	−0.0551842	−	0.0293420i
$257$	−0.680701	−	4.84344i	−0.0424609	−	0.302125i	−0.999909	−	0.0135184i	$-0.995697\pi$
$257$	−0.680701	−	4.84344i	−0.0424609	−	0.302125i	0.957448	−	0.288607i	$-0.0931921\pi$
$258$	−31.1896	−	13.8865i	−1.94178	−	0.864536i
$259$	−1.73275	−	16.4860i	−0.107668	−	1.02439i
$260$	−0.591879	+	1.46495i	−0.0367068	+	0.0908525i
$261$	−18.1006	+	23.1677i	−1.12040	+	1.43405i
$262$	−2.62022	+	9.13780i	−0.161878	+	0.564535i
$263$	−5.63512	−	6.71568i	−0.347477	−	0.414106i	0.563793	−	0.825916i	$-0.309341\pi$
$263$	−5.63512	−	6.71568i	−0.347477	−	0.414106i	−0.911270	+	0.411809i	$0.864897\pi$
$264$	8.60651	−	1.74740i	0.529694	−	0.107545i
$265$		−	7.44166i		−	0.457138i
$266$	6.05668	+	11.4268i	0.371359	+	0.700619i
$267$	−9.79813	+	30.1556i	−0.599636	+	1.84549i
$268$	−1.20201	−	2.26065i	−0.0734245	−	0.138091i
$269$	−19.1613	−	4.77746i	−1.16829	−	0.291287i	−0.390974	−	0.920402i	$-0.627862\pi$
$269$	−19.1613	−	4.77746i	−1.16829	−	0.291287i	−0.777312	+	0.629115i	$0.783417\pi$
$270$	−5.83708	−	3.93716i	−0.355233	−	0.239608i
$271$	9.40869	+	0.328559i	0.571537	+	0.0199585i	0.319211	−	0.947684i	$-0.396582\pi$
$271$	9.40869	+	0.328559i	0.571537	+	0.0199585i	0.252326	+	0.967642i	$0.418804\pi$
$272$	−2.65754	−	4.25295i	−0.161137	−	0.257873i
$273$	4.31328	−	1.92040i	0.261052	−	0.116228i
$274$	−8.01503	−	13.8824i	−0.484205	−	0.838669i
$275$	−6.25399	+	1.04397i	−0.377130	+	0.0629535i
$276$	−2.69895	−	0.475898i	−0.162458	−	0.0286457i
$277$	−27.9981	−	2.94272i	−1.68224	−	0.176811i	−0.785348	−	0.619055i	$-0.787516\pi$
$277$	−27.9981	−	2.94272i	−1.68224	−	0.176811i	−0.896895	+	0.442244i	$0.854183\pi$
$278$	3.61390	−	3.25397i	0.216747	−	0.195160i
$279$	−27.6692	−	11.1791i	−1.65651	−	0.669275i
$280$	−2.15002	−	7.49802i	−0.128488	−	0.448093i
$281$	3.81141	−	5.65065i	0.227370	−	0.337090i	−0.698039	−	0.716060i	$-0.745944\pi$
$281$	3.81141	−	5.65065i	0.227370	−	0.337090i	0.925409	+	0.378970i	$0.123722\pi$
$282$	2.54759	−	4.07700i	0.151707	−	0.242782i
$283$	−3.20541	+	22.8077i	−0.190542	+	1.35578i	0.626600	+	0.779341i	$0.284446\pi$
$283$	−3.20541	+	22.8077i	−0.190542	+	1.35578i	−0.817142	+	0.576436i	$0.804443\pi$
$284$	−4.81804	+	6.63147i	−0.285898	+	0.393505i
$285$	29.4522	−	7.30261i	1.74460	−	0.432570i
$286$	1.64223	+	1.12965i	0.0971070	+	0.0667975i
$287$	−24.5292	+	4.32515i	−1.44791	+	0.255306i
$288$	4.00163	−	0.279821i	0.235799	−	0.0164886i
$289$	−0.284436	−	8.14519i	−0.0167315	−	0.479129i
$290$	−0.672461	+	19.2568i	−0.0394883	+	1.13080i
$291$	39.9588	+	2.79419i	2.34243	+	0.163798i
$292$	−11.1896	+	1.17607i	−0.654820	+	0.0688243i
$293$	−20.4173	+	22.6757i	−1.19279	+	1.32473i	−0.259444	+	0.965758i	$0.583539\pi$
$293$	−20.4173	+	22.6757i	−1.19279	+	1.32473i	−0.933348	+	0.358972i	$0.883127\pi$
$294$	−2.24114	+	4.21497i	−0.130706	+	0.245822i
$295$	0.872811	+	0.903822i	0.0508170	+	0.0526226i
$296$	4.83860	−	2.79356i	0.281238	−	0.162373i
$297$	−6.44544	+	6.11155i	−0.374002	+	0.354628i
$298$	5.95849	−	7.10105i	0.345166	−	0.411353i
$299$	−0.347829	−	0.515678i	−0.0201155	−	0.0298224i
$300$	−5.05903	+	0.176665i	−0.292083	+	0.0101998i
$301$	32.4421	+	20.2721i	1.86993	+	1.16846i
$302$	2.74644	+	2.65220i	0.158040	+	0.152617i
$303$	29.7401	−	21.6074i	1.70852	−	1.24132i
$304$	−2.68807	+	3.43137i	−0.154171	+	0.196803i
$305$	10.0403	+	3.26230i	0.574908	+	0.186799i
$306$	18.0812	+	8.81879i	1.03363	+	0.504136i
$307$	−9.17239	+	7.69655i	−0.523496	+	0.439265i	−0.865849	−	0.500306i	$-0.833221\pi$
$307$	−9.17239	+	7.69655i	−0.523496	+	0.439265i	0.342352	+	0.939572i	$0.388776\pi$
$308$	−9.82217	+	0.596773i	−0.559670	+	0.0340043i
$309$	27.2902	+	9.93282i	1.55249	+	0.565059i
$310$	−18.9772	+	4.73155i	−1.07783	+	0.268734i
$311$	−17.0498	−	18.9357i	−0.966805	−	1.07375i	−0.997243	−	0.0742088i	$-0.976357\pi$
$311$	−17.0498	−	18.9357i	−0.966805	−	1.07375i	0.0304380	−	0.999537i	$-0.490310\pi$
$312$	1.18261	+	1.06482i	0.0669518	+	0.0602837i
$313$	−4.21125	−	8.63434i	−0.238034	−	0.488042i	0.746017	−	0.665926i	$-0.231964\pi$
$313$	−4.21125	−	8.63434i	−0.238034	−	0.488042i	−0.984051	+	0.177884i	$0.943075\pi$
$314$	4.58286	+	9.39625i	0.258626	+	0.530261i
$315$	23.2528	+	20.9369i	1.31015	+	1.17966i
$316$	0.506308	+	0.562312i	0.0284821	+	0.0316325i
$317$	−2.94369	+	0.733944i	−0.165334	+	0.0412224i	−0.323709	−	0.946157i	$-0.604930\pi$
$317$	−2.94369	+	0.733944i	−0.165334	+	0.0412224i	0.158375	+	0.987379i	$0.449374\pi$
$318$	−7.04311	−	2.56348i	−0.394958	−	0.143753i
$319$	23.5314	+	6.09575i	1.31750	+	0.341297i
$320$	2.01395	−	1.68990i	0.112583	−	0.0944683i
$321$	−19.5186	−	9.51987i	−1.08942	−	0.531347i
$322$	2.92051	+	0.948931i	0.162754	+	0.0528819i
$323$	−20.2787	+	8.16250i	−1.12834	+	0.454173i
$324$	3.99884	−	2.90533i	0.222158	−	0.161407i
$325$	−0.826470	−	0.798113i	−0.0458443	−	0.0442713i
$326$	−9.57818	−	5.98511i	−0.530486	−	0.331485i
$327$	−21.1014	+	0.736878i	−1.16691	+	0.0407494i
$328$	−4.69441	−	6.95976i	−0.259206	−	0.384288i
$329$	−3.46256	+	4.12651i	−0.190897	+	0.227502i
$330$	−4.21667	+	22.7000i	−0.232120	+	1.24959i
$331$	−13.8690	+	8.00728i	−0.762310	+	0.440120i	−0.830125	−	0.557578i	$-0.811731\pi$
$331$	−13.8690	+	8.00728i	−0.762310	+	0.440120i	0.0678143	+	0.997698i	$0.478397\pi$
$332$	7.82698	+	8.10507i	0.429561	+	0.444824i
$333$	−10.5219	+	19.7888i	−0.576597	+	1.08442i
$334$	−5.18452	+	5.75799i	−0.283684	+	0.315063i
$335$	6.69433	−	0.703602i	0.365750	−	0.0384419i
$336$	−7.83709	−	0.548023i	−0.427548	−	0.0298971i
$337$	0.934493	−	26.7604i	0.0509051	−	1.45773i	−0.658315	−	0.752743i	$-0.728730\pi$
$337$	0.934493	−	26.7604i	0.0509051	−	1.45773i	0.709220	−	0.704987i	$-0.249047\pi$
$338$	−0.441088	−	12.6311i	−0.0239920	−	0.687042i
$339$	36.9910	−	2.58667i	2.00908	−	0.140488i
$340$	12.9842	−	2.28947i	0.704168	−	0.124164i
$341$	0.635927	+	24.6653i	0.0344374	+	1.33570i
$342$	1.85031	−	17.3871i	0.100053	−	0.940189i
$343$	−9.06350	+	12.4748i	−0.489383	+	0.673578i
$344$	−1.79445	+	12.7682i	−0.0967505	+	0.688415i
$345$	3.81810	−	6.11023i	0.205559	−	0.328964i
$346$	−12.0399	+	17.8499i	−0.647269	+	0.959616i
$347$	−2.72115	−	9.48977i	−0.146079	−	0.509437i	0.853860	−	0.520503i	$-0.174255\pi$
$347$	−2.72115	−	9.48977i	−0.146079	−	0.509437i	−0.999939	+	0.0110654i	$0.996478\pi$
$348$	17.9938	+	7.26997i	0.964569	+	0.389711i
$349$	0.100379	−	0.0903815i	0.00537315	−	0.00483801i	−0.666440	−	0.745559i	$-0.732183\pi$
$349$	0.100379	−	0.0903815i	0.00537315	−	0.00483801i	0.671813	+	0.740721i	$0.265516\pi$
$350$	5.64098	+	0.592891i	0.301523	+	0.0316914i
$351$	−1.58505	−	0.279487i	−0.0846037	−	0.0149179i
$352$	−1.53026	−	2.94250i	−0.0815631	−	0.156836i
$353$	8.79905	+	15.2404i	0.468326	+	0.811165i	0.999345	−	0.0361955i	$-0.0115239\pi$
$353$	8.79905	+	15.2404i	0.468326	+	0.811165i	−0.531019	+	0.847360i	$0.678191\pi$
$354$	1.15608	−	0.514720i	0.0614450	−	0.0273571i
$355$	−11.4197	−	18.2754i	−0.606096	−	0.969956i
$356$	11.9672	+	0.417905i	0.634262	+	0.0221489i
$357$	−32.6632	−	22.0316i	−1.72872	−	1.16604i
$358$	−18.7210	−	4.66766i	−0.989434	−	0.246694i
$359$	14.4436	+	27.1644i	0.762302	+	1.43368i	0.896646	+	0.442747i	$0.145996\pi$
$359$	14.4436	+	27.1644i	0.762302	+	1.43368i	−0.134344	+	0.990935i	$0.542893\pi$
$360$	−3.25891	+	10.0299i	−0.171760	+	0.528622i
$361$	12.6767	+	14.1527i	0.667197	+	0.744881i
$362$			19.6050i			1.03041i
$363$	26.8023	+	11.4024i	1.40676	+	0.598473i
$364$	−1.14615	−	1.36593i	−0.0600748	−	0.0715943i
$365$	8.15325	−	28.4338i	0.426761	−	1.48829i
$366$	6.54625	−	8.37882i	0.342178	−	0.437968i
$367$	−10.1428	+	25.1044i	−0.529452	+	1.31044i	0.391290	+	0.920268i	$0.372029\pi$
$367$	−10.1428	+	25.1044i	−0.529452	+	1.31044i	−0.920742	+	0.390172i	$0.872415\pi$
$368$	0.108187	+	1.02933i	0.00563964	+	0.0536576i
$369$	30.7643	+	13.6971i	1.60152	+	0.713044i
$370$	2.04427	+	14.5457i	0.106276	+	0.756196i
$371$	7.41519	+	3.94273i	0.384978	+	0.204696i
$372$	−2.05907	+	19.5908i	−0.106758	+	1.01573i
$373$	12.1241	−	20.9996i	0.627764	−	1.08732i	−0.360235	−	0.932862i	$-0.617304\pi$
$373$	12.1241	−	20.9996i	0.627764	−	1.08732i	0.987999	−	0.154458i	$-0.0493632\pi$
$374$	0.732218	−	16.6167i	0.0378621	−	0.859230i
$375$	−7.35295	+	20.2021i	−0.379705	+	1.04323i
$376$	−1.74526	−	0.500445i	−0.0900048	−	0.0258085i
$377$	1.65004	+	4.08398i	0.0849812	+	0.210336i
$378$	7.01575	−	3.73034i	0.360851	−	0.191868i
$379$	−16.3411	−	22.4916i	−0.839385	−	1.15532i	−0.986103	−	0.166137i	$-0.946871\pi$
$379$	−16.3411	−	22.4916i	−0.839385	−	1.15532i	0.146717	−	0.989178i	$-0.453129\pi$
$380$	−5.71691	−	9.93177i	−0.293271	−	0.509489i
$381$	17.5621	−	5.70626i	0.899732	−	0.292341i
$382$	17.1902	+	2.41593i	0.879529	+	0.123610i
$383$	−0.963238	−	13.7749i	−0.0492192	−	0.703867i	−0.958032	−	0.286662i	$-0.907454\pi$
$383$	−0.963238	−	13.7749i	−0.0492192	−	0.703867i	0.908813	−	0.417205i	$-0.136990\pi$
$384$	−0.905637	−	2.48822i	−0.0462156	−	0.126976i
$385$	8.21866	−	24.5301i	0.418862	−	1.25017i
$386$	4.14795	+	3.48055i	0.211125	+	0.177155i
$387$	−21.0371	−	47.2502i	−1.06938	−	2.40186i
$388$	−3.14520	−	14.7970i	−0.159673	−	0.751203i
$389$	15.2555	−	2.14403i	0.773486	−	0.108706i	0.258623	−	0.965978i	$-0.416731\pi$
$389$	15.2555	−	2.14403i	0.773486	−	0.108706i	0.514864	+	0.857272i	$0.327843\pi$
$390$	−3.76028	+	1.83401i	−0.190409	+	0.0928688i
$391$	−2.11118	+	4.74178i	−0.106767	+	0.239802i
$392$	1.76344	+	0.374832i	0.0890674	+	0.0189319i
$393$	−21.3463	+	13.3387i	−1.07678	+	0.672846i
$394$	−12.9823	+	8.75667i	−0.654039	+	0.441155i
$395$	−1.86932	+	0.680377i	−0.0940557	+	0.0342335i
$396$	11.4607	+	6.75708i	0.575920	+	0.339556i
$397$	4.98478	+	28.2701i	0.250179	+	1.41884i	0.808151	+	0.588976i	$0.200469\pi$
$397$	4.98478	+	28.2701i	0.250179	+	1.41884i	−0.557971	+	0.829860i	$0.688420\pi$
$398$	−20.2370	−	14.7031i	−1.01439	−	0.736998i
$399$	−8.32767	+	33.2165i	−0.416905	+	1.66290i
$400$	0.590761	+	1.81817i	0.0295380	+	0.0909087i
$401$	−6.73565	+	6.97497i	−0.336363	+	0.348314i	−0.866120	−	0.499835i	$-0.833394\pi$
$401$	−6.73565	+	6.97497i	−0.336363	+	0.348314i	0.529758	+	0.848149i	$0.322283\pi$
$402$	1.64012	−	6.57818i	0.0818020	−	0.328090i
$403$	−3.52315	+	2.75258i	−0.175500	+	0.137116i
$404$	−10.9399	−	8.54721i	−0.544282	−	0.425239i
$405$	3.14373	+	12.6088i	0.156213	+	0.626538i
$406$	−18.8320	−	10.8727i	−0.934617	−	0.539601i
$407$	18.4727	+	1.46133i	0.915658	+	0.0724355i
$408$	2.30591	−	13.0775i	0.114160	−	0.647432i
$409$	−19.6870	+	19.0115i	−0.973461	+	0.940060i	−0.998220	−	0.0596335i	$-0.981007\pi$
$409$	−19.6870	+	19.0115i	−0.973461	+	0.940060i	0.0247598	+	0.999693i	$0.492118\pi$
$410$	21.5883	−	4.58873i	1.06617	−	0.226621i
$411$	8.82503	−	41.5185i	0.435307	−	2.04796i
$412$	0.765073	−	10.9411i	0.0376925	−	0.539027i
$413$	−1.36304	+	0.390845i	−0.0670707	+	0.0192322i
$414$	−2.55611	−	3.27167i	−0.125626	−	0.160794i
$415$	−27.4652	+	11.0967i	−1.34821	+	0.544713i
$416$	0.263455	−	0.540162i	0.0129169	−	0.0264836i
$417$	12.8767			0.630575
$418$	−13.7951	+	4.32377i	−0.674741	+	0.211482i
$419$	6.16756			0.301305			0.150653	−	0.988587i	$-0.451863\pi$
$419$	6.16756			0.301305			0.150653	+	0.988587i	$0.451863\pi$
$420$	9.05419	−	18.5638i	0.441799	−	0.905823i
$421$	33.9905	−	13.7331i	1.65660	−	0.669308i	0.659963	−	0.751298i	$-0.270572\pi$
$421$	33.9905	−	13.7331i	1.65660	−	0.669308i	0.996633	+	0.0819898i	$0.0261275\pi$
$422$	−10.4225	−	13.3402i	−0.507358	−	0.649389i
$423$	7.00094	−	2.00749i	0.340397	−	0.0976073i
$424$	−0.197452	+	2.82369i	−0.00958910	+	0.137130i
$425$	−1.99333	+	9.37786i	−0.0966905	+	0.454893i
$426$	−21.2304	+	4.51267i	−1.02862	+	0.218639i
$427$	−8.57025	+	8.27620i	−0.414744	+	0.400513i
$428$	−1.42415	+	8.07677i	−0.0688390	+	0.390406i
$429$	1.23004	+	5.13259i	0.0593867	+	0.247804i
$430$	−29.3563	−	16.9489i	−1.41569	−	0.817347i
$431$	−0.487913	−	1.95691i	−0.0235020	−	0.0942612i	0.957399	−	0.288767i	$-0.0932453\pi$
$431$	−0.487913	−	1.95691i	−0.0235020	−	0.0942612i	−0.980901	+	0.194506i	$0.937690\pi$
$432$	2.11038	+	1.64881i	0.101536	+	0.0793283i
$433$	−1.72086	+	1.34448i	−0.0826993	+	0.0646118i	−0.656163	−	0.754619i	$-0.727822\pi$
$433$	−1.72086	+	1.34448i	−0.0826993	+	0.0646118i	0.573464	+	0.819231i	$0.305599\pi$
$434$	5.33976	−	21.4166i	0.256317	−	1.02803i
$435$	−35.4423	+	36.7016i	−1.69933	+	1.75971i
$436$	2.46409	+	7.58368i	0.118008	+	0.363192i
$437$	4.50006	+	0.320552i	0.215267	+	0.0153341i
$438$	−24.1023	−	17.5114i	−1.15165	−	0.836726i
$439$	−1.04126	−	5.90528i	−0.0496966	−	0.281844i	0.949825	−	0.312783i	$-0.101261\pi$
$439$	−1.04126	−	5.90528i	−0.0496966	−	0.281844i	−0.999521	+	0.0309393i	$0.990150\pi$
$440$	8.67966	−	0.832223i	0.413787	−	0.0396747i
$441$	−6.79578	+	2.47346i	−0.323609	+	0.117784i
$442$	2.49867	−	1.68537i	0.118849	−	0.0801650i
$443$	−11.8825	+	7.42502i	−0.564556	+	0.352774i	−0.781980	−	0.623304i	$-0.785790\pi$
$443$	−11.8825	+	7.42502i	−0.564556	+	0.352774i	0.217424	+	0.976077i	$0.430234\pi$
$444$	14.4709	+	3.07589i	0.686759	+	0.145975i
$445$	−12.8046	+	28.7596i	−0.606996	+	1.36333i
$446$	−0.743461	+	0.362610i	−0.0352039	+	0.0171701i
$447$	24.3066	−	3.41607i	1.14966	−	0.161575i
$448$	0.616865	+	2.90212i	0.0291441	+	0.137112i
$449$	2.52234	+	5.66527i	0.119037	+	0.267360i	0.963230	−	0.268678i	$-0.0865868\pi$
$449$	2.52234	+	5.66527i	0.119037	+	0.267360i	−0.844193	+	0.536039i	$0.819920\pi$
$450$	−5.87462	−	4.92939i	−0.276932	−	0.232374i
$451$	0.254205	−	27.8418i	0.0119700	−	1.31102i
$452$	−4.78966	−	13.1595i	−0.225287	−	0.618970i
$453$	0.705216	+	10.0851i	0.0331340	+	0.473838i
$454$	−13.3116	−	1.87082i	−0.624744	−	0.0878021i
$455$	4.45836	−	1.44861i	0.209011	−	0.0679119i
$456$	−11.3692	+	1.98947i	−0.532412	+	0.0931653i
$457$	11.8191	+	16.2675i	0.552873	+	0.760964i	0.990398	−	0.138242i	$-0.0441452\pi$
$457$	11.8191	+	16.2675i	0.552873	+	0.760964i	−0.437526	+	0.899206i	$0.644145\pi$
$458$	0.635439	−	0.337869i	0.0296921	−	0.0157876i
$459$	5.03122	+	12.4527i	0.234837	+	0.581243i
$460$	−2.61563	−	0.750020i	−0.121954	−	0.0349698i
$461$	−3.33254	+	9.15609i	−0.155212	+	0.426441i	−0.992789	−	0.119879i	$-0.961749\pi$
$461$	−3.33254	+	9.15609i	−0.155212	+	0.426441i	0.837577	+	0.546320i	$0.183972\pi$
$462$	−20.3852	−	16.2286i	−0.948406	−	0.755021i
$463$	13.9905	−	24.2322i	0.650192	−	1.12617i	−0.332884	−	0.942968i	$-0.608022\pi$
$463$	13.9905	−	24.2322i	0.650192	−	1.12617i	0.983076	−	0.183198i	$-0.0586451\pi$
$464$	0.766106	−	7.28901i	0.0355656	−	0.338384i
$465$	−45.7263	−	24.3131i	−2.12051	−	1.12749i
$466$	−2.44393	−	17.3895i	−0.113213	−	0.805551i
$467$	20.5267	+	9.13907i	0.949862	+	0.422906i	0.822382	−	0.568935i	$-0.192645\pi$
$467$	20.5267	+	9.13907i	0.949862	+	0.422906i	0.127480	+	0.991841i	$0.459311\pi$
$468$	0.251997	+	2.39759i	0.0116486	+	0.110829i
$469$	−2.84568	+	7.04330i	−0.131401	+	0.325229i
$470$	2.93869	−	3.76135i	0.135552	−	0.173498i
$471$	−7.63019	+	26.6096i	−0.351580	+	1.22611i
$472$	−0.307201	−	0.366108i	−0.0141401	−	0.0168515i
$473$	−28.9033	+	31.5169i	−1.32898	+	1.44915i
$474$			2.00358i			0.0920275i
$475$	8.25349	−	1.14902i	0.378696	−	0.0527205i
$476$	−4.59795	+	14.1510i	−0.210747	+	0.648611i
$477$	−5.33067	−	10.0255i	−0.244075	−	0.459038i
$478$	3.26671	+	0.814483i	0.149416	+	0.0372536i
$479$	24.0027	+	16.1901i	1.09671	+	0.739743i	0.967751	−	0.251907i	$-0.0810577\pi$
$479$	24.0027	+	16.1901i	1.09671	+	0.739743i	0.128962	+	0.991650i	$0.458835\pi$
$480$	6.95715	+	0.242949i	0.317549	+	0.0110891i
$481$	1.77935	+	2.84756i	0.0811315	+	0.129838i
$482$	15.6936	−	6.98723i	0.714823	−	0.318260i
$483$	4.06560	+	7.04183i	0.184991	+	0.320414i
$484$	1.34937	−	10.9169i	0.0613351	−	0.496224i
$485$	39.1665	+	6.90610i	1.77846	+	0.313590i
$486$	21.0068	+	2.20790i	0.952887	+	0.100152i
$487$	−8.76432	+	7.89143i	−0.397149	+	0.357595i	−0.843375	−	0.537326i	$-0.819435\pi$
$487$	−8.76432	+	7.89143i	−0.397149	+	0.357595i	0.446226	+	0.894921i	$0.352768\pi$
$488$	−3.72318	−	1.50426i	−0.168540	−	0.0680947i
$489$	−8.24334	−	28.7479i	−0.372777	−	1.30003i
$490$	−2.65041	+	3.92939i	−0.119733	+	0.177512i
$491$	−21.4265	+	34.2895i	−0.966963	+	1.54746i	−0.136316	+	0.990665i	$0.543526\pi$
$491$	−21.4265	+	34.2895i	−0.966963	+	1.54746i	−0.830647	+	0.556799i	$0.812029\pi$
$492$	3.09370	−	22.0128i	0.139475	−	0.992413i
$493$	21.6045	−	29.7360i	0.973016	−	1.33924i
$494$	−2.11733	−	1.54253i	−0.0952630	−	0.0694019i
$495$	−27.7580	+	21.2817i	−1.24763	+	0.956539i
$496$	7.32633	−	1.29183i	0.328962	−	0.0580049i
$497$	24.2607	−	1.69648i	1.08824	−	0.0760974i
$498$	1.04122	+	29.8168i	0.0466584	+	1.33612i
$499$	−0.432338	+	12.3805i	−0.0193541	+	0.554229i	0.950526	+	0.310646i	$0.100545\pi$
$499$	−0.432338	+	12.3805i	−0.0193541	+	0.554229i	−0.969880	+	0.243584i	$0.921677\pi$
$500$	8.09931	+	0.566359i	0.362212	+	0.0253284i
$501$	−20.4040	+	2.14454i	−0.911582	+	0.0958111i
$502$	4.00052	−	4.44302i	0.178552	−	0.198302i
$503$	5.80500	−	10.9176i	0.258832	−	0.486793i	−0.719321	−	0.694678i	$-0.755547\pi$
$503$	5.80500	−	10.9176i	0.258832	−	0.486793i	0.978153	+	0.207885i	$0.0666581\pi$
$504$	−8.26760	−	8.56135i	−0.368268	−	0.381353i
$505$	31.6087	−	18.2493i	1.40657	−	0.812083i
$506$	−1.63916	+	3.01606i	−0.0728698	+	0.134080i
$507$	21.5118	−	25.6367i	0.955372	−	1.13857i
$508$	−3.89968	−	5.78151i	−0.173020	−	0.256513i
$509$	−0.852339	+	0.0297643i	−0.0377792	+	0.00131928i	−0.0537829	−	0.998553i	$-0.517128\pi$
$509$	−0.852339	+	0.0297643i	−0.0377792	+	0.00131928i	0.0160036	+	0.999872i	$0.494906\pi$
$510$	29.6065	+	18.5002i	1.31100	+	0.819202i
$511$	24.0129	+	23.1890i	1.06227	+	1.02582i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	8.68531	−	7.79988i	0.383466	−	0.344373i
$514$	−4.65165	−	1.51141i	−0.205176	−	0.0666656i
$515$	25.9163	+	12.6402i	1.14201	+	0.556994i
$516$	−26.1537	+	21.9456i	−1.15135	+	0.966100i
$517$	−3.82836	−	4.64799i	−0.168371	−	0.204418i
$518$	−15.5771	−	5.66959i	−0.684417	−	0.249108i
$519$	−55.3182	+	13.7924i	−2.42820	+	0.605418i
$520$	1.05723	+	1.17417i	0.0463625	+	0.0514908i
$521$	−0.251762	−	0.226688i	−0.0110299	−	0.00993138i	0.663597	−	0.748090i	$-0.269029\pi$
$521$	−0.251762	−	0.226688i	−0.0110299	−	0.00993138i	−0.674627	+	0.738159i	$0.735696\pi$
$522$	12.8882	+	26.4248i	0.564102	+	1.15658i
$523$	6.55343	+	13.4365i	0.286562	+	0.587538i	0.992710	−	0.120525i	$-0.0384579\pi$
$523$	6.55343	+	13.4365i	0.286562	+	0.587538i	−0.706149	+	0.708064i	$0.749569\pi$
$524$	7.06437	+	6.36078i	0.308608	+	0.277872i
$525$	10.0497	+	11.1613i	0.438606	+	0.487121i
$526$	−8.50629	+	2.12086i	−0.370892	+	0.0924737i
$527$	35.0583	+	12.7602i	1.52716	+	0.555842i
$528$	2.20229	−	8.50149i	0.0958426	−	0.369980i
$529$	−16.7984	+	14.0955i	−0.730366	+	0.612850i
$530$	−6.68852	−	3.26221i	−0.290531	−	0.141701i
$531$	1.82330	+	0.592426i	0.0791245	+	0.0257091i
$532$	12.9254	−	0.434547i	0.560386	−	0.0188400i
$533$	4.08170	−	2.96553i	0.176798	−	0.128451i
$534$	22.8084	+	22.0258i	0.987017	+	0.953151i
$535$	−18.2852	−	11.4259i	−0.790540	−	0.493984i
$536$	−2.55879	+	0.0893549i	−0.110523	+	0.00385954i
$537$	−28.5686	−	42.3546i	−1.23282	−	1.82774i
$538$	−12.6937	+	15.1278i	−0.547265	+	0.652205i
$539$	4.11416	+	4.33892i	0.177209	+	0.186891i
$540$	−6.09750	+	3.52040i	−0.262395	+	0.151494i
$541$	−15.0342	−	15.5683i	−0.646370	−	0.669335i	0.313563	−	0.949568i	$-0.398477\pi$
$541$	−15.0342	−	15.5683i	−0.646370	−	0.669335i	−0.959932	+	0.280232i	$0.909589\pi$
$542$	4.41980	−	8.31244i	0.189847	−	0.357050i
$543$	−34.7360	+	38.5782i	−1.49066	+	1.65555i
$544$	−4.98752	+	0.524209i	−0.213838	+	0.0224753i
$545$	−20.9126	−	1.46235i	−0.895798	−	0.0626403i
$546$	0.164777	−	4.71860i	0.00705181	−	0.201937i
$547$	−0.468044	−	13.4030i	−0.0200121	−	0.573072i	−0.967440	−	0.253102i	$-0.918549\pi$
$547$	−0.468044	−	13.4030i	−0.0200121	−	0.573072i	0.947428	−	0.319970i	$-0.103673\pi$
$548$	−15.9910	+	1.11820i	−0.683102	+	0.0477671i
$549$	15.8634	−	2.79714i	0.677033	−	0.119379i
$550$	−1.80326	+	6.07870i	−0.0768913	+	0.259197i
$551$	−30.6980	−	8.84571i	−1.30778	−	0.376840i
$552$	−1.61088	+	2.21718i	−0.0685634	+	0.0943695i
$553$	0.312443	−	2.22315i	0.0132864	−	0.0945379i
$554$	−14.9185	+	23.8745i	−0.633825	+	1.01433i
$555$	−21.7494	+	32.2448i	−0.923209	+	1.36871i
$556$	−1.34042	−	4.67459i	−0.0568464	−	0.198247i
$557$	−28.5454	−	11.5331i	−1.20951	−	0.488673i	−0.320801	−	0.947147i	$-0.603952\pi$
$557$	−28.5454	−	11.5331i	−1.20951	−	0.488673i	−0.888708	+	0.458473i	$0.848397\pi$
$558$	−22.1771	+	19.9684i	−0.938832	+	0.845328i
$559$	−7.70646	−	0.809982i	−0.325949	−	0.0342586i
$560$	−7.68169	−	1.35449i	−0.324611	−	0.0572376i
$561$	30.8823	−	31.4007i	1.30385	−	1.32574i
$562$	−3.40796	−	5.90276i	−0.143756	−	0.248993i
$563$	33.3711	−	14.8578i	1.40642	−	0.626180i	0.443578	−	0.896236i	$-0.353709\pi$
$563$	33.3711	−	14.8578i	1.40642	−	0.626180i	0.962845	+	0.270056i	$0.0870421\pi$
$564$	−2.54759	−	4.07700i	−0.107273	−	0.171673i
$565$	36.7944	+	1.28489i	1.54795	+	0.0540557i
$566$	19.0943	+	12.8792i	0.802592	+	0.541355i
$567$	−14.2296	−	3.54784i	−0.597587	−	0.148995i
$568$	3.84823	+	7.23747i	0.161468	+	0.303678i
$569$	4.85599	−	14.9452i	0.203574	−	0.626535i	−0.796195	−	0.605040i	$-0.793157\pi$
$569$	4.85599	−	14.9452i	0.203574	−	0.626535i	0.999769	−	0.0214953i	$-0.00684270\pi$
$570$	6.34744	−	29.6727i	0.265865	−	1.24285i
$571$		−	8.23857i		−	0.344773i	−0.985029	−	0.172387i	$-0.944852\pi$
$571$		−	8.23857i		−	0.344773i	0.985029	−	0.172387i	$-0.0551479\pi$
$572$	1.73523	−	0.980820i	0.0725534	−	0.0410101i
$573$	29.5460	+	35.2116i	1.23430	+	1.47099i
$574$	−6.86545	+	23.9427i	−0.286558	+	0.999348i
$575$	1.21818	−	1.55920i	0.0508017	−	0.0650232i
$576$	1.50270	−	3.71931i	0.0626125	−	0.154971i
$577$	4.07949	+	38.8137i	0.169831	+	1.61584i	0.664865	+	0.746963i	$0.268489\pi$
$577$	4.07949	+	38.8137i	0.169831	+	1.61584i	−0.495034	+	0.868874i	$0.664844\pi$
$578$	−7.44553	−	3.31497i	−0.309693	−	0.137884i
$579$	1.99544	+	14.1983i	0.0829275	+	0.590059i
$580$	17.0131	+	9.04602i	0.706430	+	0.375615i
$581$	3.49437	−	33.2467i	0.144971	−	1.37931i
$582$	20.0282	−	34.6898i	0.830195	−	1.43794i
$583$	−5.84712	+	7.34476i	−0.242163	+	0.304189i
$584$	−3.84814	+	10.5727i	−0.159237	+	0.437500i
$585$	−6.09250	−	1.74700i	−0.251894	−	0.0722294i
$586$	11.4304	+	28.2914i	0.472187	+	1.16870i
$587$	25.6235	−	13.6243i	1.05760	−	0.562334i	0.152835	−	0.988252i	$-0.451160\pi$
$587$	25.6235	−	13.6243i	1.05760	−	0.562334i	0.904762	+	0.425917i	$0.140049\pi$
$588$	2.80594	+	3.86205i	0.115715	+	0.159268i
$589$	0.0421408	−	32.4273i	0.00173638	−	1.33615i
$590$	1.19497	−	0.388268i	0.0491959	−	0.0159847i
$591$	−41.0613	−	5.77079i	−1.68904	−	0.237379i
$592$	−0.389738	−	5.57352i	−0.0160181	−	0.229070i
$593$	−5.08577	−	13.9730i	−0.208848	−	0.573804i	0.790400	−	0.612591i	$-0.209873\pi$
$593$	−5.08577	−	13.9730i	−0.208848	−	0.573804i	−0.999247	+	0.0387871i	$0.987651\pi$
$594$	2.66753	+	8.47225i	0.109450	+	0.347621i
$595$	−29.9660	−	25.1445i	−1.22849	−	1.03082i
$596$	−3.77035	−	8.46835i	−0.154440	−	0.346877i
$597$	−13.7712	−	64.7882i	−0.563616	−	2.65160i
$598$	−0.615967	+	0.0865685i	−0.0251888	+	0.00354005i
$599$	−12.4005	+	6.04811i	−0.506669	+	0.247119i	−0.673932	−	0.738793i	$-0.735396\pi$
$599$	−12.4005	+	6.04811i	−0.506669	+	0.247119i	0.167263	+	0.985912i	$0.446507\pi$
$600$	−2.05895	+	4.62447i	−0.0840561	+	0.188793i
$601$	18.1216	+	3.85187i	0.739196	+	0.157121i	0.562096	−	0.827072i	$-0.309995\pi$
$601$	18.1216	+	3.85187i	0.739196	+	0.157121i	0.177100	+	0.984193i	$0.443328\pi$
$602$	32.4421	−	20.2721i	1.32224	−	0.826228i
$603$	8.51471	−	5.74324i	0.346746	−	0.233883i
$604$	3.58774	−	1.30583i	0.145983	−	0.0531335i
$605$	25.2820	+	14.0407i	1.02786	+	0.570836i
$606$	−6.38344	−	36.2023i	−0.259310	−	1.47062i
$607$	−1.59609	−	1.15962i	−0.0647831	−	0.0470677i	0.554922	−	0.831902i	$-0.312748\pi$
$607$	−1.59609	−	1.15962i	−0.0647831	−	0.0470677i	−0.619705	+	0.784834i	$0.712748\pi$
$608$	1.90572	+	3.92023i	0.0772873	+	0.158986i
$609$	−17.7931	−	54.7614i	−0.721011	−	2.21904i
$610$	7.33353	−	7.59409i	0.296926	−	0.307476i
$611$	0.263971	−	1.05873i	0.0106791	−	0.0428317i
$612$	15.8525	−	12.3854i	0.640801	−	0.500649i
$613$	7.77541	+	6.07482i	0.314046	+	0.245360i	0.760338	−	0.649528i	$-0.225033\pi$
$613$	7.77541	+	6.07482i	0.314046	+	0.245360i	−0.446292	+	0.894887i	$0.647256\pi$
$614$	2.89670	+	11.6180i	0.116901	+	0.468866i
$615$	50.6112	+	29.2204i	2.04084	+	1.17828i
$616$	−3.76938	+	9.08972i	−0.151873	+	0.366235i
$617$	4.11932	−	23.3618i	0.165838	−	0.940512i	−0.782359	−	0.622828i	$-0.785984\pi$
$617$	4.11932	−	23.3618i	0.165838	−	0.940512i	0.948197	−	0.317684i	$-0.102905\pi$
$618$	20.8908	−	20.1740i	0.840351	−	0.811518i
$619$	31.5169	−	6.69913i	1.26677	−	0.269261i	0.474950	−	0.880013i	$-0.342466\pi$
$619$	31.5169	−	6.69913i	1.26677	−	0.269261i	0.791822	+	0.610752i	$0.209133\pi$
$620$	−4.06638	+	19.1308i	−0.163310	+	0.768311i
$621$	0.193354	−	2.76509i	0.00775903	−	0.110959i
$622$	−24.4934	+	7.02338i	−0.982097	+	0.281612i
$623$	−21.8732	−	27.9964i	−0.876330	−	1.12165i
$624$	1.47548	−	0.596131i	0.0590663	−	0.0238643i
$625$	−13.5474	+	27.7763i	−0.541896	+	1.11105i
$626$	−9.60659			−0.383956
$627$	−34.8065	−	15.9339i	−1.39004	−	0.636338i
$628$	10.4543			0.417172
$629$	12.2829	−	25.1837i	0.489751	−	1.00414i
$630$	29.0113	−	11.7213i	1.15584	−	0.466989i
$631$	20.2428	+	25.9096i	0.805852	+	1.03144i	0.998738	+	0.0502220i	$0.0159929\pi$
$631$	20.2428	+	25.9096i	0.805852	+	1.03144i	−0.192886	+	0.981221i	$0.561785\pi$
$632$	0.727354	−	0.208565i	0.0289326	−	0.00829628i
$633$	3.12691	−	44.7169i	0.124284	−	1.77734i
$634$	−0.630764	+	2.96751i	−0.0250508	+	0.117855i
$635$	17.9335	−	3.81188i	0.711669	−	0.151270i
$636$	−5.39154	+	5.20655i	−0.213788	+	0.206453i
$637$	−0.188144	+	1.06702i	−0.00745455	+	0.0422769i
$638$	15.7943	−	18.4776i	0.625302	−	0.731537i
$639$	−28.4760	−	16.4406i	−1.12649	−	0.650381i
$640$	−0.636017	−	2.55093i	−0.0251408	−	0.100834i
$641$	1.84876	+	1.44441i	0.0730217	+	0.0570508i	0.651511	−	0.758639i	$-0.274135\pi$
$641$	1.84876	+	1.44441i	0.0730217	+	0.0570508i	−0.578489	+	0.815690i	$0.696358\pi$
$642$	−17.1128	+	13.3700i	−0.675388	+	0.527671i
$643$	3.65947	−	14.6773i	0.144315	−	0.578817i	−0.853972	−	0.520319i	$-0.825813\pi$
$643$	3.65947	−	14.6773i	0.144315	−	0.578817i	0.998287	−	0.0584985i	$-0.0186313\pi$
$644$	2.13316	−	2.20895i	0.0840583	−	0.0870449i
$645$	−27.7368	−	85.3650i	−1.09213	−	3.36124i
$646$	−1.55320	+	21.8046i	−0.0611100	+	0.857890i
$647$	8.30014	+	6.03041i	0.326312	+	0.237080i	0.738864	−	0.673854i	$-0.235362\pi$
$647$	8.30014	+	6.03041i	0.326312	+	0.237080i	−0.412552	+	0.910934i	$0.635362\pi$
$648$	−0.858316	−	4.86775i	−0.0337178	−	0.191223i
$649$	−0.151287	−	1.57784i	−0.00593853	−	0.0619358i
$650$	−1.07964	+	0.392957i	−0.0423469	+	0.0154130i
$651$	48.4533	−	32.6821i	1.89903	−	1.28091i
$652$	−9.57818	+	5.98511i	−0.375111	+	0.234395i
$653$	27.7342	+	5.89508i	1.08532	+	0.230692i	0.715642	−	0.698467i	$-0.246134\pi$
$653$	27.7342	+	5.89508i	1.08532	+	0.230692i	0.369680	+	0.929159i	$0.379467\pi$
$654$	−8.58795	+	19.2889i	−0.335815	+	0.754254i
$655$	−22.4623	+	10.9556i	−0.877674	+	0.428070i
$656$	−8.31328	+	1.16836i	−0.324579	+	0.0456166i
$657$	−9.38371	−	44.1469i	−0.366093	−	1.72233i
$658$	2.19100	+	4.92107i	0.0854141	+	0.191843i
$659$	−2.45136	−	2.05694i	−0.0954915	−	0.0801269i	0.593792	−	0.804619i	$-0.297630\pi$
$659$	−2.45136	−	2.05694i	−0.0954915	−	0.0801269i	−0.689284	+	0.724492i	$0.742075\pi$
$660$	18.5542	+	13.7410i	0.722220	+	0.534866i
$661$	8.19474	+	22.5149i	0.318738	+	0.875726i	0.990813	+	0.135242i	$0.0431813\pi$
$661$	8.19474	+	22.5149i	0.318738	+	0.875726i	−0.672074	+	0.740484i	$0.734596\pi$
$662$	1.11712	+	15.9756i	0.0434181	+	0.620908i
$663$	7.90295	+	1.11069i	0.306925	+	0.0431355i
$664$	10.7159	−	3.48181i	0.415858	−	0.135120i
$665$	−11.6703	+	31.9346i	−0.452554	+	1.23837i
$666$	13.1736	+	18.1319i	0.510466	+	0.702596i
$667$	−6.69777	+	3.56127i	−0.259339	+	0.137893i
$668$	2.90250	+	7.18395i	0.112301	+	0.277955i
$669$	−2.10544	−	0.603724i	−0.0814009	−	0.0233413i
$670$	2.30221	−	6.32526i	0.0889420	−	0.244366i
$671$	−7.34631	−	11.1088i	−0.283601	−	0.428850i
$672$	−3.92811	+	6.80369i	−0.151530	+	0.262458i
$673$	−1.91545	+	18.2243i	−0.0738352	+	0.702495i	0.893512	+	0.449040i	$0.148234\pi$
$673$	−1.91545	+	18.2243i	−0.0738352	+	0.702495i	−0.967347	+	0.253456i	$0.918433\pi$
$674$	−23.6424	−	12.5709i	−0.910671	−	0.484213i
$675$	−0.712545	−	5.07002i	−0.0274259	−	0.195145i
$676$	−11.5461	−	5.14067i	−0.444082	−	0.197718i
$677$	−3.00489	−	28.5896i	−0.115487	−	1.09879i	−0.886743	−	0.462263i	$-0.847038\pi$
$677$	−3.00489	−	28.5896i	−0.115487	−	1.09879i	0.771255	−	0.636526i	$-0.219629\pi$
$678$	13.8909	−	34.3812i	0.533478	−	1.32040i
$679$	−27.6326	+	35.3682i	−1.06044	+	1.35731i
$680$	3.63414	−	12.6738i	0.139363	−	0.486017i
$681$	−22.8795	−	27.2668i	−0.876746	−	1.04487i
$682$	22.4478	+	10.2410i	0.859572	+	0.392148i
$683$			45.5859i			1.74430i	0.489242	+	0.872148i	$0.337273\pi$
$683$			45.5859i			1.74430i	−0.489242	+	0.872148i	$0.662727\pi$
$684$	−14.8163	−	9.28507i	−0.566517	−	0.355023i
$685$	13.0230	−	40.0807i	0.497583	−	1.53140i
$686$	7.23914	+	13.6148i	0.276392	+	0.519817i
$687$	1.84904	+	0.461017i	0.0705452	+	0.0175889i
$688$	10.6893	+	7.21006i	0.407528	+	0.274881i
$689$	−1.70010	−	0.0593689i	−0.0647688	−	0.00226178i
$690$	−3.81810	−	6.11023i	−0.145352	−	0.232613i
$691$	37.3336	−	16.6220i	1.42024	−	0.632329i	0.454238	−	0.890881i	$-0.349912\pi$
$691$	37.3336	−	16.6220i	1.42024	−	0.632329i	0.965998	+	0.258551i	$0.0832450\pi$
$692$	10.7654	+	18.6463i	0.409240	+	0.708825i
$693$	−6.49928	−	38.9346i	−0.246887	−	1.47901i
$694$	−9.72222	−	1.71429i	−0.369050	−	0.0650735i
$695$	12.7148	+	1.33638i	0.482301	+	0.0506919i
$696$	14.4222	−	12.9858i	0.546671	−	0.492225i
$697$	−39.0352	−	15.7712i	−1.47856	−	0.597378i
$698$	−0.0372312	−	0.129840i	−0.00140922	−	0.00491453i
$699$	26.0014	−	38.5487i	0.983465	−	1.45805i
$700$	3.00573	−	4.81018i	0.113606	−	0.181808i
$701$	−2.23640	+	15.9128i	−0.0844677	+	0.601019i	0.901336	+	0.433120i	$0.142587\pi$
$701$	−2.23640	+	15.9128i	−0.0844677	+	0.601019i	−0.985804	+	0.167899i	$0.946302\pi$
$702$	−0.946042	+	1.30211i	−0.0357060	+	0.0491451i
$703$	−24.2170	−	2.57713i	−0.913361	−	0.0971983i
$704$	−3.31552	+	0.0854816i	−0.124958	+	0.00322171i
$705$	12.4470	−	2.19475i	0.468782	−	0.0826590i
$706$	17.5552	−	1.22758i	0.660700	−	0.0462006i
$707$	1.43752	+	41.1651i	0.0540634	+	1.54817i
$708$	0.0441649	−	1.26472i	0.00165982	−	0.0475309i
$709$	29.4334	+	2.05818i	1.10539	+	0.0772967i	0.610769	−	0.791809i	$-0.290861\pi$
$709$	29.4334	+	2.05818i	1.10539	+	0.0772967i	0.494626	+	0.869106i	$0.335305\pi$
$710$	−21.4319	+	2.25258i	−0.804324	+	0.0845378i
$711$	−2.03101	+	2.25566i	−0.0761687	+	0.0845940i
$712$	5.62170	−	10.5729i	0.210682	−	0.396236i
$713$	−5.34869	−	5.53873i	−0.200310	−	0.207427i
$714$	−34.1205	+	19.6995i	−1.27693	+	0.737234i
$715$	0.681897	+	5.19572i	0.0255015	+	0.194309i
$716$	−12.4020	+	14.7801i	−0.463484	+	0.552359i
$717$	4.98507	+	7.39067i	0.186171	+	0.276010i
$718$	30.7468	−	1.07370i	1.14746	−	0.0400703i
$719$	23.3765	+	14.6073i	0.871797	+	0.544759i	0.890457	−	0.455067i	$-0.150385\pi$
$719$	23.3765	+	14.6073i	0.871797	+	0.544759i	−0.0186605	+	0.999826i	$0.505940\pi$
$720$	7.58620	+	7.32591i	0.282721	+	0.273021i
$721$	−26.3262	+	19.1271i	−0.980437	+	0.712329i
$722$	18.2775	−	5.18962i	0.680219	−	0.193138i
$723$	43.2614	+	14.0565i	1.60891	+	0.522766i
$724$	17.6208	+	8.59425i	0.654873	+	0.319403i
$725$	−10.7334	+	9.00640i	−0.398629	+	0.334489i
$726$	21.9978	−	19.0913i	0.816415	−	0.708543i
$727$	−27.7923	−	10.1156i	−1.03076	−	0.375165i	−0.229389	−	0.973335i	$-0.573673\pi$
$727$	−27.7923	−	10.1156i	−1.03076	−	0.375165i	−0.801370	+	0.598169i	$0.795895\pi$
$728$	−1.73013	+	0.431370i	−0.0641230	+	0.0159877i
$729$	27.5025	+	30.5446i	1.01861	+	1.13128i
$730$	−21.9819	−	19.7926i	−0.813588	−	0.732558i
$731$	28.3458	+	58.1176i	1.04841	+	2.14956i
$732$	−4.66114	−	9.55676i	−0.172281	−	0.353228i
$733$	−9.15475	−	8.24298i	−0.338139	−	0.304461i	0.482515	−	0.875888i	$-0.339724\pi$
$733$	−9.15475	−	8.24298i	−0.338139	−	0.304461i	−0.820653	+	0.571427i	$0.806390\pi$
$734$	18.1174	+	20.1214i	0.668724	+	0.742694i
$735$	−12.1775	+	3.03619i	−0.449173	+	0.111991i
$736$	0.972583	+	0.353991i	0.0358499	+	0.0130483i
$737$	−7.16000	−	4.56548i	−0.263742	−	0.168172i
$738$	25.7971	−	21.6463i	0.949603	−	0.796812i
$739$	−8.88459	−	4.33330i	−0.326825	−	0.159403i	0.267652	−	0.963516i	$-0.413752\pi$
$739$	−8.88459	−	4.33330i	−0.326825	−	0.159403i	−0.594477	+	0.804112i	$0.702641\pi$
$740$	13.9698	+	4.53905i	0.513538	+	0.166859i
$741$	−1.43337	−	6.78683i	−0.0526562	−	0.249321i
$742$	6.79431	−	4.93635i	0.249427	−	0.181219i
$743$	−1.33085	−	1.28519i	−0.0488241	−	0.0471489i	0.669846	−	0.742500i	$-0.266360\pi$
$743$	−1.33085	−	1.28519i	−0.0488241	−	0.0471489i	−0.718670	+	0.695351i	$0.755249\pi$
$744$	16.7054	+	10.4387i	0.612451	+	0.382702i
$745$	24.3555	−	0.850514i	0.892318	−	0.0311604i
$746$	−13.5595	−	20.1027i	−0.496447	−	0.736014i
$747$	−29.0527	+	34.6237i	−1.06298	+	1.26681i
$748$	−14.6140	−	7.94241i	−0.534342	−	0.290403i
$749$	21.0731	−	12.1666i	0.769994	−	0.444556i
$750$	14.9342	+	15.4648i	0.545319	+	0.564694i
$751$	6.33434	−	11.9132i	0.231143	−	0.434717i	−0.740204	−	0.672383i	$-0.765271\pi$
$751$	6.33434	−	11.9132i	0.231143	−	0.434717i	0.971347	+	0.237665i	$0.0763821\pi$
$752$	−1.21487	+	1.34925i	−0.0443017	+	0.0492020i
$753$	15.7443	−	1.65479i	0.573753	−	0.0603038i
$754$	4.39399	+	0.307258i	0.160020	+	0.0111897i
$755$	−0.350306	+	10.0315i	−0.0127490	+	0.365082i
$756$	−0.277305	−	7.94099i	−0.0100855	−	0.288811i
$757$	−19.2739	+	1.34776i	−0.700523	+	0.0489853i	−0.415577	−	0.909558i	$-0.636420\pi$
$757$	−19.2739	+	1.34776i	−0.700523	+	0.0489853i	−0.284946	+	0.958543i	$0.591976\pi$
$758$	−27.3788	+	4.82761i	−0.994441	+	0.175347i
$759$	−8.56936	+	3.03068i	−0.311048	+	0.110007i
$760$	−11.4327	+	0.784527i	−0.414709	+	0.0284578i
$761$	−18.9427	+	26.0723i	−0.686671	+	0.945122i	−0.999990	−	0.00452632i	$-0.998559\pi$
$761$	−18.9427	+	26.0723i	−0.686671	+	0.945122i	0.313319	+	0.949648i	$0.398559\pi$
$762$	2.56995	−	18.2862i	0.0930995	−	0.662437i
$763$	12.5370	−	20.0635i	0.453871	−	0.726346i
$764$	9.70713	−	14.3914i	0.351192	−	0.520663i
$765$	14.5780	+	50.8396i	0.527070	+	1.83811i
$766$	−12.8031	−	5.17278i	−0.462595	−	0.186900i
$767$	0.213448	−	0.192190i	0.00770717	−	0.00693956i
$768$	−2.63340	−	0.276782i	−0.0950246	−	0.00998749i
$769$	0.0897496	+	0.0158253i	0.00323645	+	0.000570674i	0.175266	−	0.984521i	$-0.443921\pi$
$769$	0.0897496	+	0.0158253i	0.00323645	+	0.000570674i	−0.172030	+	0.985092i	$0.555033\pi$
$770$	−18.4447	−	18.1402i	−0.664700	−	0.653727i
$771$	−6.47550	−	11.2159i	−0.233209	−	0.403931i
$772$	4.94664	−	2.20238i	0.178033	−	0.0792655i
$773$	−13.7393	−	21.9874i	−0.494167	−	0.790833i	0.503137	−	0.864206i	$-0.332179\pi$
$773$	−13.7393	−	21.9874i	−0.494167	−	0.790833i	−0.997305	+	0.0733737i	$0.976623\pi$
$774$	−51.6903	−	1.80506i	−1.85797	−	0.0648817i
$775$	−11.7907	−	7.95290i	−0.423533	−	0.285677i
$776$	−14.6782	−	3.65969i	−0.526917	−	0.131375i
$777$	−20.6069	−	38.7559i	−0.739267	−	1.39036i
$778$	4.76055	−	14.6515i	0.170674	−	0.525280i
$779$	−1.32460	+	36.5689i	−0.0474586	+	1.31022i
$780$			4.18370i			0.149800i
$781$	−3.08846	+	27.0102i	−0.110514	+	0.966500i
$782$	3.33640	+	3.97617i	0.119310	+	0.142188i
$783$	−5.41029	+	18.8679i	−0.193348	+	0.674284i
$784$	1.10994	−	1.42066i	0.0396407	−	0.0507378i
$785$	−10.2959	+	25.4832i	−0.367476	+	0.909535i
$786$	2.63110	+	25.0332i	0.0938481	+	0.892905i
$787$	29.3430	+	13.0643i	1.04596	+	0.465693i	0.856475	−	0.516189i	$-0.172650\pi$
$787$	29.3430	+	13.0643i	1.04596	+	0.465693i	0.189490	+	0.981883i	$0.439317\pi$
$788$	2.17938	+	15.5071i	0.0776371	+	0.552417i
$789$	−20.4962	−	10.8980i	−0.729684	−	0.387980i
$790$	−0.207937	+	1.97839i	−0.00739808	+	0.0703880i
$791$	−20.7747	+	35.9828i	−0.738663	+	1.27940i
$792$	11.0973	−	7.33867i	0.394324	−	0.260768i
$793$	0.825398	−	2.26776i	0.0293108	−	0.0805306i
$794$	27.5942	+	7.91251i	0.979281	+	0.280804i
$795$	−7.38155	−	18.2700i	−0.261797	−	0.647970i
$796$	−22.0863	+	11.7435i	−0.782830	+	0.416238i
$797$	0.228737	+	0.314829i	0.00810227	+	0.0111518i	0.813049	−	0.582195i	$-0.197806\pi$
$797$	0.228737	+	0.314829i	0.00810227	+	0.0111518i	−0.804947	+	0.593347i	$0.797806\pi$
$798$	26.2042	+	22.0460i	0.927618	+	0.780420i
$799$	−8.65954	+	2.81365i	−0.306352	+	0.0995399i
$800$	1.89314	+	0.266063i	0.0669325	+	0.00940675i
$801$	3.35073	+	47.9177i	0.118392	+	1.69309i
$802$	3.31635	+	9.11159i	0.117104	+	0.321742i
$803$	−30.3883	+	21.6573i	−1.07238	+	0.764268i
$804$	−5.19344	−	4.35782i	−0.183159	−	0.153688i
$805$	3.28367	+	7.37524i	0.115734	+	0.259943i
$806$	0.929560	+	4.37324i	0.0327424	+	0.154041i
$807$	−51.7818	+	7.27745i	−1.82280	+	0.256178i
$808$	−12.4779	+	6.08589i	−0.438972	+	0.214101i
$809$	−1.59055	+	3.57242i	−0.0559206	+	0.125600i	−0.939345	−	0.342975i	$-0.888566\pi$
$809$	−1.59055	+	3.57242i	−0.0559206	+	0.125600i	0.883424	+	0.468574i	$0.155232\pi$
$810$	12.7109	+	2.70178i	0.446614	+	0.0949308i
$811$	44.9103	−	28.0631i	1.57701	−	0.985427i	0.593449	−	0.804872i	$-0.297766\pi$
$811$	44.9103	−	28.0631i	1.57701	−	0.985427i	0.983565	−	0.180556i	$-0.0577895\pi$
$812$	−18.0277	+	12.1598i	−0.632648	+	0.426726i
$813$	23.4251	−	8.52605i	0.821555	−	0.299022i
$814$	9.41133	−	15.9625i	0.329867	−	0.559487i
$815$	−5.15616	−	29.2420i	−0.180612	−	1.02430i
$816$	−10.7431	−	7.80533i	−0.376084	−	0.273241i
$817$	39.0939	−	40.3778i	1.36772	−	1.41264i
$818$	8.45723	+	26.0287i	0.295700	+	0.910072i
$819$	4.96870	−	5.14524i	0.173621	−	0.179789i
$820$	5.33935	−	21.4150i	0.186458	−	0.747843i
$821$	−38.9813	+	30.4555i	−1.36046	+	1.06290i	−0.369427	+	0.929260i	$0.620446\pi$
$821$	−38.9813	+	30.4555i	−1.36046	+	1.06290i	−0.991029	+	0.133645i	$0.957332\pi$
$822$	−33.4480	−	26.1324i	−1.16663	−	0.911473i
$823$	−7.13257	−	28.6072i	−0.248626	−	0.997184i	−0.956707	−	0.291053i	$-0.905994\pi$
$823$	−7.13257	−	28.6072i	−0.248626	−	0.997184i	0.708081	−	0.706131i	$-0.249561\pi$
$824$	−9.49837	−	5.48389i	−0.330891	−	0.191040i
$825$	−14.3186	+	8.76652i	−0.498510	+	0.305211i
$826$	−0.246228	+	1.39643i	−0.00856735	+	0.0485879i
$827$	7.48297	−	7.22622i	0.260208	−	0.251280i	−0.553098	−	0.833116i	$-0.686554\pi$
$827$	7.48297	−	7.22622i	0.260208	−	0.251280i	0.813306	+	0.581836i	$0.197666\pi$
$828$	−4.06108	+	0.863210i	−0.141132	+	0.0299986i
$829$	−4.57007	+	21.5005i	−0.158725	+	0.746743i	0.824721	+	0.565540i	$0.191332\pi$
$829$	−4.57007	+	21.5005i	−0.158725	+	0.746743i	−0.983446	+	0.181202i	$0.942001\pi$
$830$	−2.06634	+	29.5500i	−0.0717236	+	1.02570i
$831$	−71.6570	+	20.5473i	−2.48575	+	0.712778i
$832$	−0.370003	−	0.473583i	−0.0128276	−	0.0164185i
$833$	8.38288	−	3.38690i	0.290450	−	0.117349i
$834$	5.64478	−	11.5735i	0.195463	−	0.400758i
$835$	−20.3700			−0.704933
$836$	−2.16120	+	14.2944i	−0.0747467	+	0.494381i
$837$	−19.9234			−0.688652
$838$	2.70368	−	5.54337i	0.0933971	−	0.191493i
$839$	−42.3009	+	17.0907i	−1.46039	+	0.590036i	−0.961051	−	0.276371i	$-0.910868\pi$
$839$	−42.3009	+	17.0907i	−1.46039	+	0.590036i	−0.499339	+	0.866407i	$0.666424\pi$
$840$	−12.7160	−	16.2757i	−0.438743	−	0.561565i
$841$	23.7592	−	6.81283i	0.819282	−	0.234925i
$842$	2.55727	−	36.5706i	0.0881293	−	1.26031i
$843$	3.75237	−	17.6535i	0.129239	−	0.608020i
$844$	−16.5590	+	3.51972i	−0.569983	+	0.121154i
$845$	23.9020	−	23.0819i	0.822254	−	0.794041i
$846$	1.26469	−	7.17243i	0.0434810	−	0.246593i
$847$	−27.3856	+	17.7530i	−0.940982	+	0.610002i
$848$	2.45136	+	1.41529i	0.0841800	+	0.0486013i
$849$	14.7539	+	59.1746i	0.506352	+	2.03087i
$850$	7.55495	+	5.90257i	0.259133	+	0.202457i
$851$	−4.55682	+	3.56018i	−0.156206	+	0.122041i
$852$	−5.25085	+	21.0600i	−0.179891	+	0.721504i
$853$	−11.4308	+	11.8370i	−0.391384	+	0.405290i	−0.885898	−	0.463879i	$-0.846457\pi$
$853$	−11.4308	+	11.8370i	−0.391384	+	0.405290i	0.494514	+	0.869170i	$0.335346\pi$
$854$	3.68164	+	11.3309i	0.125983	+	0.387737i
$855$	37.2250	−	26.9717i	1.27307	−	0.922412i
$856$	6.63505	+	4.82064i	0.226781	+	0.164766i
$857$	−0.892918	−	5.06399i	−0.0305015	−	0.172983i	0.965752	−	0.259468i	$-0.0835474\pi$
$857$	−0.892918	−	5.06399i	−0.0305015	−	0.172983i	−0.996253	+	0.0864859i	$0.972436\pi$
$858$	5.15235	+	1.14443i	0.175898	+	0.0390702i
$859$	5.77574	−	2.10220i	0.197066	−	0.0717261i	−0.241602	−	0.970375i	$-0.577673\pi$
$859$	5.77574	−	2.10220i	0.197066	−	0.0717261i	0.438668	+	0.898649i	$0.355451\pi$
$860$	−28.1025	+	18.9554i	−0.958287	+	0.646373i
$861$	−55.9312	+	34.9497i	−1.90613	+	1.19108i
$862$	−1.97275	−	0.419321i	−0.0671921	−	0.0142821i
$863$	−4.68568	+	10.5242i	−0.159503	+	0.358249i	−0.975564	−	0.219717i	$-0.929487\pi$
$863$	−4.68568	+	10.5242i	−0.159503	+	0.358249i	0.816061	+	0.577966i	$0.196153\pi$
$864$	2.40707	−	1.17400i	0.0818900	−	0.0399404i
$865$	−56.0542	+	7.87790i	−1.90590	+	0.267857i
$866$	0.454038	+	2.13608i	0.0154288	+	0.0725870i
$867$	−8.77772	−	19.7151i	−0.298107	−	0.669559i
$868$	−16.9083	−	14.1878i	−0.573906	−	0.481564i
$869$	2.37957	+	0.797260i	0.0807214	+	0.0270452i
$870$	17.4503	+	47.9443i	0.591620	+	1.62546i
$871$	−0.107336	−	1.53498i	−0.00363696	−	0.0520109i
$872$	7.89635	+	1.10976i	0.267404	+	0.0375812i
$873$	57.7128	−	18.7520i	1.95328	−	0.634660i
$874$	2.26081	−	3.90411i	0.0764730	−	0.132058i
$875$	−14.1592	−	19.4884i	−0.478667	−	0.658829i
$876$	−26.3049	+	13.9866i	−0.888760	+	0.472562i
$877$	−13.8064	−	34.1719i	−0.466207	−	1.15390i	−0.958911	−	0.283707i	$-0.908436\pi$
$877$	−13.8064	−	34.1719i	−0.466207	−	1.15390i	0.492704	−	0.870197i	$-0.336009\pi$
$878$	−5.76409	−	1.65283i	−0.194529	−	0.0557802i
$879$	−27.6339	+	75.9235i	−0.932068	+	2.56084i
$880$	3.05692	−	8.16605i	0.103049	−	0.275278i
$881$	−2.55287	+	4.42170i	−0.0860084	+	0.148971i	−0.905820	−	0.423662i	$-0.860745\pi$
$881$	−2.55287	+	4.42170i	−0.0860084	+	0.148971i	0.819812	+	0.572633i	$0.194078\pi$
$882$	−0.755942	+	7.19231i	−0.0254539	+	0.242178i
$883$	−20.5092	−	10.9050i	−0.690191	−	0.366981i	0.0870326	−	0.996205i	$-0.472262\pi$
$883$	−20.5092	−	10.9050i	−0.690191	−	0.366981i	−0.777224	+	0.629224i	$0.783373\pi$
$884$	−0.419459	−	2.98461i	−0.0141079	−	0.100383i
$885$	3.03936	+	1.35321i	0.102167	+	0.0454876i
$886$	1.46461	+	13.9349i	0.0492046	+	0.468151i
$887$	10.9266	−	27.0443i	0.366880	−	0.908059i	−0.624970	−	0.780648i	$-0.714889\pi$
$887$	10.9266	−	27.0443i	0.366880	−	0.908059i	0.991850	−	0.127411i	$-0.0406666\pi$
$888$	9.10821	−	11.6580i	0.305652	−	0.391216i
$889$	−5.70317	+	19.8893i	−0.191278	+	0.667067i
$890$	20.2358	+	24.1161i	0.678305	+	0.808372i
$891$	6.80431	−	14.9148i	0.227953	−	0.499663i
$892$			0.827176i			0.0276959i
$893$	4.86422	+	6.24263i	0.162775	+	0.208902i
$894$	7.58497	−	23.3441i	0.253679	−	0.780744i
$895$	−23.8137	−	44.7871i	−0.796005	−	1.49707i
$896$	2.87883	+	0.717772i	0.0961749	+	0.0239791i
$897$	−1.36547	−	0.921019i	−0.0455916	−	0.0307519i
$898$	6.19763	+	0.216426i	0.206818	+	0.00722223i
$899$	28.8934	+	46.2392i	0.963650	+	1.54216i
$900$	−7.00577	+	3.11917i	−0.233526	+	0.103972i
$901$	7.09768	+	12.2935i	0.236458	+	0.409557i
$902$	−24.9126	−	12.4335i	−0.829500	−	0.413992i
$903$	99.7568	+	17.5898i	3.31970	+	0.585352i
$904$	−13.9273	−	1.46382i	−0.463216	−	0.0486859i
$905$	−38.3030	+	34.4882i	−1.27324	+	1.14643i
$906$	9.37354	+	3.78716i	0.311415	+	0.125820i
$907$	−0.00138695	−	0.00483687i	−4.60530e−5	−	0.000160606i	0.961239	−	0.275718i	$-0.0889155\pi$
$907$	−0.00138695	−	0.00483687i	−4.60530e−5	−	0.000160606i	−0.961285	+	0.275557i	$0.911138\pi$
$908$	−7.51691	+	11.1443i	−0.249457	+	0.369836i
$909$	29.5113	−	47.2280i	0.978828	−	1.56645i
$910$	0.652415	−	4.64218i	0.0216274	−	0.153887i
$911$	29.0780	−	40.0225i	0.963399	−	1.32600i	0.0180867	−	0.999836i	$-0.494243\pi$
$911$	29.0780	−	40.0225i	0.963399	−	1.32600i	0.945312	−	0.326168i	$-0.105757\pi$
$912$	−3.19581	+	11.0907i	−0.105824	+	0.367250i
$913$	35.8265	+	10.6280i	1.18568	+	0.351736i
$914$	19.8023	−	3.49168i	0.655002	−	0.115495i
$915$	27.8859	−	1.94997i	0.921880	−	0.0644642i
$916$	−0.0251164	−	0.719241i	−0.000829871	−	0.0237644i
$917$	0.984306	−	28.1868i	0.0325047	−	0.930812i
$918$	13.3980	+	0.936877i	0.442199	+	0.0309216i
$919$	−24.9207	+	2.61927i	−0.822057	+	0.0864017i	−0.506212	−	0.862409i	$-0.668955\pi$
$919$	−24.9207	+	2.61927i	−0.822057	+	0.0864017i	−0.315845	+	0.948811i	$0.602288\pi$
$920$	−1.82073	+	2.02213i	−0.0600277	+	0.0666675i
$921$	−14.8847	+	27.9941i	−0.490468	+	0.922436i
$922$	6.76854	+	7.00903i	0.222910	+	0.230830i
$923$	−4.26625	+	2.46312i	−0.140425	+	0.0810746i
$924$	−23.5224	+	11.2080i	−0.773831	+	0.368715i
$925$	−6.86571	+	8.18223i	−0.225743	+	0.269030i
$926$	−15.6467	−	23.1973i	−0.514184	−	0.762309i
$927$	43.9694	−	1.53544i	1.44414	−	0.0504306i
$928$	−6.21548	−	3.88387i	−0.204033	−	0.127494i
$929$	30.3434	+	29.3022i	0.995533	+	0.961375i	0.999254	−	0.0386177i	$-0.0122955\pi$
$929$	30.3434	+	29.3022i	0.995533	+	0.961375i	−0.00372075	+	0.999993i	$0.501184\pi$
$930$	−41.8976	+	30.4404i	−1.37388	+	0.998179i
$931$	−5.25070	−	5.84676i	−0.172085	−	0.191620i
$932$	−16.7009	−	5.42645i	−0.547056	−	0.177749i
$933$	−60.6416	−	29.5769i	−1.98532	−	0.968304i
$934$	17.2124	−	14.4430i	0.563209	−	0.472588i
$935$	33.7529	−	27.8009i	1.10384	−	0.909185i
$936$	2.26541	+	0.824541i	0.0740471	+	0.0269510i
$937$	13.2414	−	3.30145i	0.432578	−	0.107854i	−0.0195460	−	0.999809i	$-0.506222\pi$
$937$	13.2414	−	3.30145i	0.432578	−	0.107854i	0.452124	+	0.891955i	$0.350667\pi$
$938$	5.08301	+	5.64526i	0.165966	+	0.184324i
$939$	−18.9036	−	17.0209i	−0.616897	−	0.555456i
$940$	−2.09244	−	4.29014i	−0.0682480	−	0.139929i
$941$	9.14357	+	18.7471i	0.298072	+	0.611138i	0.994292	−	0.106690i	$-0.0340252\pi$
$941$	9.14357	+	18.7471i	0.298072	+	0.611138i	−0.696220	+	0.717828i	$0.745136\pi$
$942$	20.5717	+	18.5229i	0.670263	+	0.603507i
$943$	5.81395	+	6.45705i	0.189328	+	0.210270i
$944$	−0.463724	+	0.115619i	−0.0150929	+	0.00376309i
$945$	19.6299	+	7.14471i	0.638562	+	0.232417i
$946$	15.6568	+	39.7942i	0.509047	+	1.29382i
$947$	−33.8650	+	28.4161i	−1.10046	+	0.923400i	−0.997456	−	0.0712808i	$-0.977291\pi$
$947$	−33.8650	+	28.4161i	−1.10046	+	0.923400i	−0.103009	+	0.994680i	$0.532847\pi$
$948$	1.80081	+	0.878312i	0.0584874	+	0.0285262i
$949$	−6.43086	−	2.08951i	−0.208755	−	0.0678285i
$950$	2.58536	−	7.92188i	0.0838802	−	0.257020i
$951$	−6.49902	+	4.72181i	−0.210745	+	0.153115i
$952$	10.7033	+	10.3360i	0.346894	+	0.334992i
$953$	−26.4651	−	16.5372i	−0.857288	−	0.535693i	0.0286009	−	0.999591i	$-0.490895\pi$
$953$	−26.4651	−	16.5372i	−0.857288	−	0.535693i	−0.885889	+	0.463898i	$0.846450\pi$
$954$	−11.3477	+	0.396271i	−0.367396	+	0.0128297i
$955$	25.5202	+	37.8353i	0.825815	+	1.22432i
$956$	2.16409	−	2.57906i	0.0699915	−	0.0834127i
$957$	63.8183	−	8.37564i	2.06295	−	0.270746i
$958$	25.0736	−	14.4763i	0.810093	−	0.467707i
$959$	33.0383	+	34.2122i	1.06686	+	1.10477i
$960$	3.26818	−	6.14655i	0.105480	−	0.198379i
$961$	−16.2893	+	18.0911i	−0.525460	+	0.583582i
$962$	3.33939	−	0.350984i	0.107666	−	0.0113162i
$963$	−32.8189	−	2.29492i	−1.05757	−	0.0739528i
$964$	0.599530	−	17.1683i	0.0193096	−	0.552954i
$965$	0.496813	+	14.2269i	0.0159930	+	0.457979i
$966$	8.11140	−	0.567204i	0.260980	−	0.0182495i
$967$	34.1166	−	6.01568i	1.09712	−	0.193451i	0.404344	−	0.914607i	$-0.367500\pi$
$967$	34.1166	−	6.01568i	1.09712	−	0.193451i	0.692773	+	0.721156i	$0.256389\pi$
$968$	−9.22054	−	5.99847i	−0.296359	−	0.192798i
$969$	−41.6896	+	40.1546i	−1.33926	+	1.28995i
$970$	23.3766	−	32.1751i	0.750578	−	1.03308i
$971$	−8.16528	+	58.0990i	−0.262036	+	1.86449i	0.202979	+	0.979183i	$0.434938\pi$
$971$	−8.16528	+	58.0990i	−0.262036	+	1.86449i	−0.465015	+	0.885303i	$0.653951\pi$
$972$	11.1932	−	17.9129i	0.359023	−	0.574556i
$973$	−8.06818	+	11.9616i	−0.258654	+	0.383470i
$974$	3.25074	+	11.3367i	0.104161	+	0.363251i
$975$	−2.82073	−	1.13965i	−0.0903356	−	0.0364980i
$976$	−2.98416	+	2.68695i	−0.0955205	+	0.0860071i
$977$	−20.7071	−	2.17641i	−0.662480	−	0.0696294i	−0.232680	−	0.972553i	$-0.574749\pi$
$977$	−20.7071	−	2.17641i	−0.662480	−	0.0696294i	−0.429800	+	0.902924i	$0.641416\pi$
$978$	−29.4521	−	5.19320i	−0.941775	−	0.166060i
$979$	35.2351	−	18.3241i	1.12612	−	0.585642i
$980$	2.36985	+	4.10470i	0.0757021	+	0.131120i
$981$	−29.2214	+	13.0102i	−0.932966	+	0.415383i
$982$	21.4265	+	34.2895i	0.683746	+	1.09422i
$983$	−8.89785	−	0.310720i	−0.283797	−	0.00991042i	−0.107353	−	0.994221i	$-0.534237\pi$
$983$	−8.89785	−	0.310720i	−0.283797	−	0.00991042i	−0.176445	+	0.984311i	$0.556460\pi$
$984$	−18.4288	−	12.4304i	−0.587488	−	0.396266i
$985$	−39.9462	−	9.95970i	−1.27279	−	0.317342i
$986$	−17.2558	−	32.4534i	−0.549535	−	1.03353i
$987$	−4.40772	+	13.5656i	−0.140299	+	0.431797i
$988$	−2.31460	+	1.22684i	−0.0736371	+	0.0390309i
$989$		−	13.3450i		−	0.424346i
$990$	6.95953	+	34.2780i	0.221188	+	1.08943i
$991$	17.3161	+	20.6365i	0.550063	+	0.655539i	0.967412	−	0.253207i	$-0.0814853\pi$
$991$	17.3161	+	20.6365i	0.550063	+	0.655539i	−0.417349	+	0.908746i	$0.637041\pi$
$992$	2.05056	−	7.15116i	0.0651054	−	0.227050i
$993$	−26.1072	+	33.4156i	−0.828486	+	1.06041i
$994$	9.11043	−	22.5491i	0.288965	−	0.715214i
$995$	−6.87412	−	65.4029i	−0.217924	−	2.07341i
$996$	27.2556	+	12.1350i	0.863626	+	0.384511i
$997$	−1.74350	−	12.4057i	−0.0552173	−	0.392891i	−0.998196	−	0.0600385i	$-0.980878\pi$
$997$	−1.74350	−	12.4057i	−0.0552173	−	0.392891i	0.942979	−	0.332853i	$-0.108011\pi$
$998$	10.9380	+	5.81586i	0.346237	+	0.184098i
$999$	−1.56405	+	14.8810i	−0.0494844	+	0.470813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.b.29.9	yes	240
11.8	odd	10		418.2.v.a.371.2	yes	240
19.2	odd	18		418.2.v.a.249.2	✓	240
209.173	even	90	inner	418.2.v.b.173.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.249.2	✓	240	19.2	odd	18
418.2.v.a.371.2	yes	240	11.8	odd	10
418.2.v.b.29.9	yes	240	1.1	even	1	trivial
418.2.v.b.173.9	yes	240	209.173	even	90	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.438371 - 0.898794i) q^{2} +(2.45510 - 0.991923i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(2.52718 - 0.724656i) q^{5} +(0.184709 - 2.64146i) q^{6} +(-0.616865 + 2.90212i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(2.88556 - 2.78656i) q^{9} +O(q^{10})\)	\(q+(0.438371 - 0.898794i) q^{2} +(2.45510 - 0.991923i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(2.52718 - 0.724656i) q^{5} +(0.184709 - 2.64146i) q^{6} +(-0.616865 + 2.90212i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(2.88556 - 2.78656i) q^{9} +(0.456524 - 2.58908i) q^{10} +(-3.06365 - 1.27045i) q^{11} +(-2.29315 - 1.32395i) q^{12} +(-0.145391 - 0.583133i) q^{13} +(2.33799 + 1.82664i) q^{14} +(5.48565 - 4.28586i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-3.48371 + 3.60748i) q^{17} +(-1.23959 - 3.81507i) q^{18} +(3.97974 + 1.77810i) q^{19} +(-2.12692 - 1.54530i) q^{20} +(1.36422 + 7.73687i) q^{21} +(-2.48489 + 2.19666i) q^{22} +(0.972583 - 0.353991i) q^{23} +(-2.19521 + 1.48069i) q^{24} +(1.62125 - 1.01307i) q^{25} +(-0.587852 - 0.124952i) q^{26} +(1.08928 - 2.44657i) q^{27} +(2.66668 - 1.30063i) q^{28} +(-7.25784 + 1.02002i) q^{29} +(-1.44736 - 6.80927i) q^{30} +(-3.02586 - 6.79618i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-8.78174 - 0.0801801i) q^{33} +(1.71523 + 4.71255i) q^{34} +(0.544114 + 7.78119i) q^{35} +(-3.97237 - 0.558280i) q^{36} +(-5.31368 + 1.72652i) q^{37} +(3.34275 - 2.79750i) q^{38} +(-0.935373 - 1.28743i) q^{39} +(-2.32129 + 1.23425i) q^{40} +(3.14482 + 7.78369i) q^{41} +(7.55189 + 2.16547i) q^{42} +(4.40990 - 12.1161i) q^{43} +(0.885040 + 3.19636i) q^{44} +(5.27303 - 9.13316i) q^{45} +(0.108187 - 1.02933i) q^{46} +(1.60307 + 0.852368i) q^{47} +(0.368517 + 2.62214i) q^{48} +(-1.64698 - 0.733281i) q^{49} +(-0.199831 - 1.90127i) q^{50} +(-4.97449 + 12.3123i) q^{51} +(-0.370003 + 0.473583i) q^{52} +(0.780215 - 2.72093i) q^{53} +(-1.72145 - 2.05155i) q^{54} +(-8.66302 - 0.990567i) q^{55} -2.96696i q^{56} +(11.5344 + 0.417798i) q^{57} +(-2.26484 + 6.97045i) q^{58} +(0.224370 + 0.421978i) q^{59} +(-6.75461 - 1.68411i) q^{60} +(3.32907 + 2.24548i) q^{61} +(-7.43482 - 0.259630i) q^{62} +(6.30692 + 10.0932i) q^{63} +(0.913545 - 0.406737i) q^{64} +(-0.790001 - 1.36832i) q^{65} +(-3.92173 + 7.85783i) q^{66} +(2.52145 + 0.444600i) q^{67} +(4.98752 + 0.524209i) q^{68} +(2.03665 - 1.83381i) q^{69} +(7.23221 + 2.92200i) q^{70} +(-2.25938 - 7.87941i) q^{71} +(-2.24315 + 3.32561i) q^{72} +(5.96223 - 9.54156i) q^{73} +(-0.777578 + 5.53276i) q^{74} +(2.97543 - 4.09533i) q^{75} +(-1.04902 - 4.23079i) q^{76} +(5.57687 - 8.10739i) q^{77} +(-1.56718 + 0.276335i) q^{78} +(-0.754823 + 0.0527823i) q^{79} +(0.0917514 + 2.62742i) q^{80} +(-0.172503 + 4.93983i) q^{81} +(8.37453 + 0.585604i) q^{82} +(-11.2057 + 1.17776i) q^{83} +(5.25684 - 5.83831i) q^{84} +(-6.18975 + 11.6412i) q^{85} +(-8.95671 - 9.27494i) q^{86} +(-16.8069 + 9.70347i) q^{87} +(3.26084 + 0.605722i) q^{88} +(-7.69708 + 9.17302i) q^{89} +(-5.89728 - 8.74308i) q^{90} +(1.78201 - 0.0622292i) q^{91} +(-0.877731 - 0.548467i) q^{92} +(-14.1701 - 13.6839i) q^{93} +(1.46884 - 1.06718i) q^{94} +(11.3460 + 1.60962i) q^{95} +(2.51831 + 0.818248i) q^{96} +(13.5966 + 6.63149i) q^{97} +(-1.38106 + 1.15884i) q^{98} +(-12.3805 + 4.87106i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Introduction

L-functions

Modular forms

Varieties

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