LMFDB - Embedded newform 418.2.v.b.29.3

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			29.3
Character	$\chi$	$=$	418.29
Dual form			418.2.v.b.173.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.438371 - 0.898794i) q^{2} +(-1.31507 + 0.531324i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(2.95966 - 0.848670i) q^{5} +(-0.0989393 + 1.41490i) q^{6} +(0.318233 - 1.49717i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(-0.710907 + 0.686515i) q^{9} +O(q^{10})$	\(q+(0.438371 - 0.898794i) q^{2} +(-1.31507 + 0.531324i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(2.95966 - 0.848670i) q^{5} +(-0.0989393 + 1.41490i) q^{6} +(0.318233 - 1.49717i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(-0.710907 + 0.686515i) q^{9} +(0.534652 - 3.03216i) q^{10} +(2.43848 - 2.24807i) q^{11} +(1.22833 + 0.709176i) q^{12} +(0.142618 + 0.572011i) q^{13} +(-1.20614 - 0.942340i) q^{14} +(-3.44126 + 2.68860i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-0.429292 + 0.444544i) q^{17} +(0.305394 + 0.939907i) q^{18} +(0.527207 - 4.32690i) q^{19} +(-2.49091 - 1.80975i) q^{20} +(0.376982 + 2.13797i) q^{21} +(-0.951588 - 3.17718i) q^{22} +(8.56246 - 3.11648i) q^{23} +(1.17587 - 0.793133i) q^{24} +(3.79913 - 2.37396i) q^{25} +(0.576639 + 0.122568i) q^{26} +(2.30082 - 5.16773i) q^{27} +(-1.37571 + 0.670977i) q^{28} +(-6.28270 + 0.882976i) q^{29} +(0.907954 + 4.27159i) q^{30} +(-3.15235 - 7.08030i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-2.01233 + 4.25200i) q^{33} +(0.211365 + 0.580720i) q^{34} +(-0.328739 - 4.70119i) q^{35} +(0.978659 + 0.137542i) q^{36} +(-1.54182 + 0.500967i) q^{37} +(-3.65788 - 2.37064i) q^{38} +(-0.491476 - 0.676459i) q^{39} +(-2.71854 + 1.44547i) q^{40} +(1.82884 + 4.52653i) q^{41} +(2.08685 + 0.598395i) q^{42} +(-2.28447 + 6.27653i) q^{43} +(-3.27278 - 0.537503i) q^{44} +(-1.52142 + 2.63518i) q^{45} +(0.952462 - 9.06207i) q^{46} +(-2.15679 - 1.14678i) q^{47} +(-0.197396 - 1.40455i) q^{48} +(4.25458 + 1.89426i) q^{49} +(-0.468273 - 4.45532i) q^{50} +(0.328353 - 0.812701i) q^{51} +(0.362946 - 0.464550i) q^{52} +(0.794197 - 2.76969i) q^{53} +(-3.63611 - 4.33335i) q^{54} +(5.30923 - 8.72299i) q^{55} +1.53061i q^{56} +(1.60567 + 5.97031i) q^{57} +(-1.96054 + 6.03392i) q^{58} +(5.05250 + 9.50238i) q^{59} +(4.23730 + 1.05648i) q^{60} +(9.22922 + 6.22519i) q^{61} +(-7.74563 - 0.270483i) q^{62} +(0.801593 + 1.28282i) q^{63} +(0.913545 - 0.406737i) q^{64} +(0.907551 + 1.57192i) q^{65} +(2.93952 + 3.67262i) q^{66} +(-7.02601 - 1.23888i) q^{67} +(0.614604 + 0.0645975i) q^{68} +(-9.60441 + 8.64785i) q^{69} +(-4.36951 - 1.76540i) q^{70} +(3.89345 + 13.5781i) q^{71} +(0.552637 - 0.819318i) q^{72} +(-5.87265 + 9.39821i) q^{73} +(-0.225622 + 1.60539i) q^{74} +(-3.73480 + 5.14051i) q^{75} +(-3.73422 + 2.24846i) q^{76} +(-2.58973 - 4.36622i) q^{77} +(-0.823447 + 0.145196i) q^{78} +(-0.752229 + 0.0526010i) q^{79} +(0.107453 + 3.07706i) q^{80} +(-0.176538 + 5.05540i) q^{81} +(4.87013 + 0.340553i) q^{82} +(-6.84110 + 0.719029i) q^{83} +(1.45265 - 1.61333i) q^{84} +(-0.893287 + 1.68003i) q^{85} +(4.63986 + 4.80472i) q^{86} +(7.79306 - 4.49933i) q^{87} +(-1.91780 + 2.70593i) q^{88} +(-2.37357 + 2.82872i) q^{89} +(1.70154 + 2.52263i) q^{90} +(0.901781 - 0.0314909i) q^{91} +(-7.72740 - 4.82862i) q^{92} +(7.90751 + 7.63619i) q^{93} +(-1.97620 + 1.43579i) q^{94} +(-2.11175 - 13.2536i) q^{95} +(-1.34893 - 0.438295i) q^{96} +(-6.78173 - 3.30767i) q^{97} +(3.56764 - 2.99360i) q^{98} +(-0.190204 + 3.27222i) 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
$3$	−1.31507	+	0.531324i	−0.759258	+	0.306760i	−0.721396	−	0.692523i	$-0.756499\pi$
$3$	−1.31507	+	0.531324i	−0.759258	+	0.306760i	−0.0378620	+	0.999283i	$0.512055\pi$
$4$	−0.615661	−	0.788011i	−0.307831	−	0.394005i
$5$	2.95966	−	0.848670i	1.32360	−	0.379537i	0.461891	−	0.886936i	$-0.347171\pi$
$5$	2.95966	−	0.848670i	1.32360	−	0.379537i	0.861711	+	0.507400i	$0.169393\pi$
$6$	−0.0989393	+	1.41490i	−0.0403918	+	0.577629i
$7$	0.318233	−	1.49717i	0.120281	−	0.565876i	−0.876192	−	0.481962i	$-0.839924\pi$
$7$	0.318233	−	1.49717i	0.120281	−	0.565876i	0.996473	−	0.0839143i	$-0.0267422\pi$
$8$	−0.978148	+	0.207912i	−0.345827	+	0.0735079i
$9$	−0.710907	+	0.686515i	−0.236969	+	0.228838i
$10$	0.534652	−	3.03216i	0.169072	−	0.958854i
$11$	2.43848	−	2.24807i	0.735230	−	0.677817i
$11$	2.43848	−	2.24807i	0.735230	−	0.677817i
$12$	1.22833	+	0.709176i	0.354588	+	0.204722i
$13$	0.142618	+	0.572011i	0.0395552	+	0.158647i	0.986825	−	0.161789i	$-0.0517262\pi$
$13$	0.142618	+	0.572011i	0.0395552	+	0.158647i	−0.947270	+	0.320436i	$0.896171\pi$
$14$	−1.20614	−	0.942340i	−0.322355	−	0.251851i
$15$	−3.44126	+	2.68860i	−0.888529	+	0.694195i
$16$	−0.241922	+	0.970296i	−0.0604805	+	0.242574i
$17$	−0.429292	+	0.444544i	−0.104118	+	0.107818i	−0.769376	−	0.638796i	$-0.779433\pi$
$17$	−0.429292	+	0.444544i	−0.104118	+	0.107818i	0.665258	+	0.746614i	$0.268322\pi$
$18$	0.305394	+	0.939907i	0.0719821	+	0.221538i
$19$	0.527207	−	4.32690i	0.120950	−	0.992659i
$19$	0.527207	−	4.32690i	0.120950	−	0.992659i
$20$	−2.49091	−	1.80975i	−0.556985	−	0.404673i
$21$	0.376982	+	2.13797i	0.0822641	+	0.466543i
$22$	−0.951588	−	3.17718i	−0.202879	−	0.677377i
$23$	8.56246	−	3.11648i	1.78540	−	0.649831i	0.785892	−	0.618363i	$-0.212204\pi$
$23$	8.56246	−	3.11648i	1.78540	−	0.649831i	0.999505	−	0.0314682i	$-0.0100183\pi$
$24$	1.17587	−	0.793133i	0.240023	−	0.161898i
$25$	3.79913	−	2.37396i	0.759827	−	0.474792i
$26$	0.576639	+	0.122568i	0.113088	+	0.0240377i
$27$	2.30082	−	5.16773i	0.442793	−	0.994530i
$28$	−1.37571	+	0.670977i	−0.259984	+	0.126803i
$29$	−6.28270	+	0.882976i	−1.16667	+	0.163964i	−0.695797	−	0.718238i	$-0.744949\pi$
$29$	−6.28270	+	0.882976i	−1.16667	+	0.163964i	−0.470870	+	0.882203i	$0.656060\pi$
$30$	0.907954	+	4.27159i	0.165769	+	0.779882i
$31$	−3.15235	−	7.08030i	−0.566179	−	1.27166i	−0.939051	−	0.343777i	$-0.888294\pi$
$31$	−3.15235	−	7.08030i	−0.566179	−	1.27166i	0.372872	−	0.927883i	$-0.378373\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−2.01233	+	4.25200i	−0.350302	+	0.740178i
$34$	0.211365	+	0.580720i	0.0362488	+	0.0995927i
$35$	−0.328739	−	4.70119i	−0.0555670	−	0.794646i
$36$	0.978659	+	0.137542i	0.163110	+	0.0229236i
$37$	−1.54182	+	0.500967i	−0.253473	+	0.0823585i	−0.432998	−	0.901395i	$-0.642544\pi$
$37$	−1.54182	+	0.500967i	−0.253473	+	0.0823585i	0.179524	+	0.983754i	$0.442544\pi$
$38$	−3.65788	−	2.37064i	−0.593386	−	0.384568i
$39$	−0.491476	−	0.676459i	−0.0786992	−	0.108320i
$40$	−2.71854	+	1.44547i	−0.429839	+	0.228549i
$41$	1.82884	+	4.52653i	0.285616	+	0.706926i	0.999974	+	0.00714511i	$0.00227438\pi$
$41$	1.82884	+	4.52653i	0.285616	+	0.706926i	−0.714358	+	0.699780i	$0.753281\pi$
$42$	2.08685	+	0.598395i	0.322008	+	0.0923344i
$43$	−2.28447	+	6.27653i	−0.348378	+	0.957162i	0.634503	+	0.772921i	$0.281205\pi$
$43$	−2.28447	+	6.27653i	−0.348378	+	0.957162i	−0.982881	+	0.184241i	$0.941017\pi$
$44$	−3.27278	−	0.537503i	−0.493390	−	0.0810316i
$45$	−1.52142	+	2.63518i	−0.226800	+	0.392829i
$46$	0.952462	−	9.06207i	0.140433	−	1.33613i
$47$	−2.15679	−	1.14678i	−0.314600	−	0.167276i	0.304662	−	0.952461i	$-0.401457\pi$
$47$	−2.15679	−	1.14678i	−0.314600	−	0.167276i	−0.619261	+	0.785185i	$0.712568\pi$
$48$	−0.197396	−	1.40455i	−0.0284917	−	0.202729i
$49$	4.25458	+	1.89426i	0.607797	+	0.270609i
$50$	−0.468273	−	4.45532i	−0.0662237	−	0.630077i
$51$	0.328353	−	0.812701i	0.0459786	−	0.113801i
$52$	0.362946	−	0.464550i	0.0503315	−	0.0644214i
$53$	0.794197	−	2.76969i	0.109091	−	0.380447i	−0.887706	−	0.460410i	$-0.847702\pi$
$53$	0.794197	−	2.76969i	0.109091	−	0.380447i	0.996798	+	0.0799631i	$0.0254802\pi$
$54$	−3.63611	−	4.33335i	−0.494812	−	0.589694i
$55$	5.30923	−	8.72299i	0.715896	−	1.17621i
$56$			1.53061i			0.204537i
$57$	1.60567	+	5.97031i	0.212676	+	0.790786i
$58$	−1.96054	+	6.03392i	−0.257432	+	0.792293i
$59$	5.05250	+	9.50238i	0.657780	+	1.23710i	0.958961	+	0.283537i	$0.0915080\pi$
$59$	5.05250	+	9.50238i	0.657780	+	1.23710i	−0.301181	+	0.953567i	$0.597381\pi$
$60$	4.23730	+	1.05648i	0.547033	+	0.136391i
$61$	9.22922	+	6.22519i	1.18168	+	0.797054i	0.983107	−	0.183032i	$-0.0585913\pi$
$61$	9.22922	+	6.22519i	1.18168	+	0.797054i	0.198574	+	0.980086i	$0.436369\pi$
$62$	−7.74563	−	0.270483i	−0.983696	−	0.0343514i
$63$	0.801593	+	1.28282i	0.100991	+	0.161620i
$64$	0.913545	−	0.406737i	0.114193	−	0.0508421i
$65$	0.907551	+	1.57192i	0.112568	+	0.194973i
$66$	2.93952	+	3.67262i	0.361830	+	0.452069i
$67$	−7.02601	−	1.23888i	−0.858364	−	0.151353i	−0.272891	−	0.962045i	$-0.587980\pi$
$67$	−7.02601	−	1.23888i	−0.858364	−	0.151353i	−0.585473	+	0.810692i	$0.699091\pi$
$68$	0.614604	+	0.0645975i	0.0745317	+	0.00783360i
$69$	−9.60441	+	8.64785i	−1.15623	+	1.04108i
$70$	−4.36951	−	1.76540i	−0.522256	−	0.211005i
$71$	3.89345	+	13.5781i	0.462068	+	1.61142i	0.755299	+	0.655380i	$0.227491\pi$
$71$	3.89345	+	13.5781i	0.462068	+	1.61142i	−0.293232	+	0.956041i	$0.594731\pi$
$72$	0.552637	−	0.819318i	0.0651289	−	0.0965576i
$73$	−5.87265	+	9.39821i	−0.687342	+	1.09998i	0.301851	+	0.953355i	$0.402396\pi$
$73$	−5.87265	+	9.39821i	−0.687342	+	1.09998i	−0.989193	+	0.146622i	$0.953160\pi$
$74$	−0.225622	+	1.60539i	−0.0262281	+	0.186622i
$75$	−3.73480	+	5.14051i	−0.431257	+	0.593575i
$76$	−3.73422	+	2.24846i	−0.428345	+	0.257916i
$77$	−2.58973	−	4.36622i	−0.295127	−	0.497577i
$78$	−0.823447	+	0.145196i	−0.0932370	+	0.0164402i
$79$	−0.752229	+	0.0526010i	−0.0846324	+	0.00591808i	−0.112010	−	0.993707i	$-0.535729\pi$
$79$	−0.752229	+	0.0526010i	−0.0846324	+	0.00591808i	0.0273775	+	0.999625i	$0.491284\pi$
$80$	0.107453	+	3.07706i	0.0120137	+	0.344026i
$81$	−0.176538	+	5.05540i	−0.0196154	+	0.561711i
$82$	4.87013	+	0.340553i	0.537816	+	0.0376077i
$83$	−6.84110	+	0.719029i	−0.750908	+	0.0789236i	−0.472248	−	0.881466i	$-0.656557\pi$
$83$	−6.84110	+	0.719029i	−0.750908	+	0.0789236i	−0.278661	+	0.960390i	$0.589891\pi$
$84$	1.45265	−	1.61333i	0.158497	−	0.176029i
$85$	−0.893287	+	1.68003i	−0.0968906	+	0.182225i
$86$	4.63986	+	4.80472i	0.500329	+	0.518106i
$87$	7.79306	−	4.49933i	0.835504	−	0.482378i
$88$	−1.91780	+	2.70593i	−0.204438	+	0.288453i
$89$	−2.37357	+	2.82872i	−0.251598	+	0.299843i	−0.877030	−	0.480436i	$-0.840479\pi$
$89$	−2.37357	+	2.82872i	−0.251598	+	0.299843i	0.625432	+	0.780279i	$0.284923\pi$
$90$	1.70154	+	2.52263i	0.179358	+	0.265909i
$91$	0.901781	−	0.0314909i	0.0945323	−	0.00330114i
$92$	−7.72740	−	4.82862i	−0.805637	−	0.503418i
$93$	7.90751	+	7.63619i	0.819971	+	0.791836i
$94$	−1.97620	+	1.43579i	−0.203829	+	0.148090i
$95$	−2.11175	−	13.2536i	−0.216661	−	1.35979i
$96$	−1.34893	−	0.438295i	−0.137675	−	0.0447333i
$97$	−6.78173	−	3.30767i	−0.688580	−	0.335843i	0.0606440	−	0.998159i	$-0.480685\pi$
$97$	−6.78173	−	3.30767i	−0.688580	−	0.335843i	−0.749224	+	0.662316i	$0.769573\pi$
$98$	3.56764	−	2.99360i	0.360386	−	0.302400i
$99$	−0.190204	+	3.27222i	−0.0191162	+	0.328870i
$100$	−4.20969	−	1.53220i	−0.420969	−	0.153220i
$101$	−0.585288	+	0.145929i	−0.0582383	+	0.0145205i	−0.270932	−	0.962598i	$-0.587332\pi$
$101$	−0.585288	+	0.145929i	−0.0582383	+	0.0145205i	0.212694	+	0.977119i	$0.431776\pi$
$102$	−0.586511	−	0.651386i	−0.0580732	−	0.0644969i
$103$	11.3605	+	10.2291i	1.11939	+	1.00790i	0.999887	+	0.0150645i	$0.00479535\pi$
$103$	11.3605	+	10.2291i	1.11939	+	1.00790i	0.119499	+	0.992834i	$0.461871\pi$
$104$	−0.258429	−	0.529859i	−0.0253411	−	0.0519569i
$105$	2.93017	+	6.00774i	0.285955	+	0.586295i
$106$	−2.14123	−	1.92797i	−0.207975	−	0.187261i
$107$	−6.26010	−	6.95255i	−0.605187	−	0.672128i	0.360223	−	0.932866i	$-0.382701\pi$
$107$	−6.26010	−	6.95255i	−0.605187	−	0.672128i	−0.965410	+	0.260738i	$0.916034\pi$
$108$	−5.48875	+	1.36850i	−0.528155	+	0.131684i
$109$	14.4217	+	5.24906i	1.38135	+	0.502769i	0.922586	−	0.385792i	$-0.126072\pi$
$109$	14.4217	+	5.24906i	1.38135	+	0.502769i	0.458760	+	0.888560i	$0.348294\pi$
$110$	−5.51276	−	8.59581i	−0.525621	−	0.819578i
$111$	1.76143	−	1.47801i	0.167187	−	0.140287i
$112$	1.37571	+	0.670977i	0.129992	+	0.0634014i
$113$	−8.29171	−	2.69414i	−0.780018	−	0.253443i	−0.108170	−	0.994132i	$-0.534499\pi$
$113$	−8.29171	−	2.69414i	−0.780018	−	0.253443i	−0.671848	+	0.740689i	$0.734499\pi$
$114$	6.06996	+	1.17404i	0.568503	+	0.109959i
$115$	22.6972	−	16.4905i	2.11652	−	1.53774i
$116$	4.56381	+	4.40722i	0.423739	+	0.409200i
$117$	−0.494082	−	0.308737i	−0.0456779	−	0.0285427i
$118$	10.7556	−	0.375592i	0.990129	−	0.0345761i
$119$	0.528943	+	0.784190i	0.0484881	+	0.0718865i
$120$	2.80707	−	3.34533i	0.256249	−	0.305385i
$121$	0.892397	−	10.9637i	0.0811270	−	0.996704i
$122$	9.64098	−	5.56623i	0.872854	−	0.503942i
$123$	−4.81011	−	4.98102i	−0.433713	−	0.449123i
$124$	−3.63857	+	6.84316i	−0.326753	+	0.614534i
$125$	−1.07161	+	1.19014i	−0.0958473	+	0.106449i
$126$	1.50438	−	0.158117i	0.134021	−	0.0140862i
$127$	−7.42991	−	0.519550i	−0.659298	−	0.0461026i	−0.263811	−	0.964574i	$-0.584980\pi$
$127$	−7.42991	−	0.519550i	−0.659298	−	0.0461026i	−0.395487	+	0.918472i	$0.629424\pi$
$128$	0.0348995	−	0.999391i	0.00308471	−	0.0883345i
$129$	−0.330626	−	9.46789i	−0.0291100	−	0.833601i
$130$	1.81068	−	0.126615i	0.158807	−	0.0111049i
$131$	−14.2012	+	2.50405i	−1.24076	+	0.218780i	−0.755243	−	0.655445i	$-0.772481\pi$
$131$	−14.2012	+	2.50405i	−1.24076	+	0.218780i	−0.485520	+	0.874225i	$0.661370\pi$
$132$	4.58953	−	1.03205i	0.399468	−	0.0898285i
$133$	−6.31031	−	2.16628i	−0.547174	−	0.187840i
$134$	−4.19349	+	5.77185i	−0.362263	+	0.498612i
$135$	2.42396	−	17.2474i	0.208621	−	1.48442i
$136$	0.327485	−	0.524085i	0.0280816	−	0.0449399i
$137$	2.80082	−	4.15238i	0.239290	−	0.354762i	−0.690194	−	0.723624i	$-0.742475\pi$
$137$	2.80082	−	4.15238i	0.239290	−	0.354762i	0.929484	+	0.368863i	$0.120253\pi$
$138$	3.56234	+	12.4233i	0.303246	+	1.05755i
$139$	7.43540	+	3.00410i	0.630662	+	0.254804i	0.667608	−	0.744513i	$-0.267318\pi$
$139$	7.43540	+	3.00410i	0.630662	+	0.254804i	−0.0369454	+	0.999317i	$0.511763\pi$
$140$	−3.50219	+	3.15339i	−0.295989	+	0.266510i
$141$	3.44565	+	0.362152i	0.290176	+	0.0304987i
$142$	13.9107	+	2.45283i	1.16736	+	0.205837i
$143$	1.63369	+	1.07422i	0.136616	+	0.0898310i
$144$	−0.494138	−	0.855873i	−0.0411782	−	0.0713227i
$145$	−17.8453	+	7.94525i	−1.48197	+	0.659817i
$146$	5.87265	+	9.39821i	0.486024	+	0.777801i
$147$	−6.60155	−	0.230531i	−0.544487	−	0.0190139i
$148$	1.34401	+	0.906543i	0.110477	+	0.0745174i
$149$	2.01649	+	0.502768i	0.165198	+	0.0411884i	0.323642	−	0.946179i	$-0.395092\pi$
$149$	2.01649	+	0.502768i	0.165198	+	0.0411884i	−0.158445	+	0.987368i	$0.550648\pi$
$150$	2.98303	+	5.61026i	0.243563	+	0.458076i
$151$	−5.46553	+	16.8212i	−0.444779	+	1.36889i	0.437948	+	0.899000i	$0.355706\pi$
$151$	−5.46553	+	16.8212i	−0.444779	+	1.36889i	−0.882726	+	0.469887i	$0.844294\pi$
$152$	0.383927	+	4.34196i	0.0311406	+	0.352179i
$153$		−	0.610745i		−	0.0493758i
$154$	−5.05960	+	0.413603i	−0.407714	+	0.0333291i
$155$	−15.3387	−	18.2800i	−1.23204	−	1.46829i
$156$	−0.230474	+	0.803759i	−0.0184527	+	0.0643522i
$157$	12.4698	−	15.9606i	0.995196	−	1.27379i	0.0335685	−	0.999436i	$-0.489313\pi$
$157$	12.4698	−	15.9606i	0.995196	−	1.27379i	0.961628	−	0.274357i	$-0.0884650\pi$
$158$	−0.282478	+	0.699158i	−0.0224728	+	0.0556220i
$159$	0.427178	+	4.06433i	0.0338774	+	0.322322i
$160$	2.81275	+	1.25232i	0.222367	+	0.0990043i
$161$	−1.94104	−	13.8112i	−0.152975	−	1.08848i
$162$	4.46637	+	2.37481i	0.350911	+	0.186583i
$163$	−1.51978	+	14.4597i	−0.119038	+	1.13257i	0.758034	+	0.652215i	$0.226160\pi$
$163$	−1.51978	+	14.4597i	−0.119038	+	1.13257i	−0.877072	+	0.480359i	$0.840506\pi$
$164$	2.44101	−	4.22795i	0.190611	−	0.330148i
$165$	−2.34729	+	14.2923i	−0.182736	+	1.11265i
$166$	−2.35268	+	6.46394i	−0.182604	+	0.501699i
$167$	−2.48979	−	0.713936i	−0.192666	−	0.0552460i	0.177917	−	0.984046i	$-0.443064\pi$
$167$	−2.48979	−	0.713936i	−0.192666	−	0.0552460i	−0.370583	+	0.928800i	$0.620842\pi$
$168$	−0.813252	−	2.01287i	−0.0627438	−	0.155296i
$169$	11.1715	−	5.93997i	0.859343	−	0.456921i
$170$	1.11841	+	1.53936i	0.0857781	+	0.118063i
$171$	2.59568	+	3.43796i	0.198497	+	0.262907i
$172$	6.35243	−	2.06403i	0.484369	−	0.157381i
$173$	−4.89117	−	0.687410i	−0.371869	−	0.0522628i	−0.0492367	−	0.998787i	$-0.515679\pi$
$173$	−4.89117	−	0.687410i	−0.371869	−	0.0522628i	−0.322632	+	0.946524i	$0.604568\pi$
$174$	−0.627714	−	8.97673i	−0.0475869	−	0.680524i
$175$	−2.34521	−	6.44341i	−0.177281	−	0.487076i
$176$	1.59137	+	2.90991i	0.119954	+	0.219342i
$177$	−11.6933	−	9.81181i	−0.878919	−	0.737501i
$178$	1.50193	+	3.37338i	0.112574	+	0.252846i
$179$	−1.33366	−	6.27439i	−0.0996827	−	0.468970i	−0.999467	−	0.0326358i	$-0.989610\pi$
$179$	−1.33366	−	6.27439i	−0.0996827	−	0.468970i	0.899785	−	0.436334i	$-0.143723\pi$
$180$	3.01323	−	0.423482i	0.224593	−	0.0315645i
$181$	18.7251	−	9.13282i	1.39182	−	0.678837i	0.418487	−	0.908223i	$-0.362561\pi$
$181$	18.7251	−	9.13282i	1.39182	−	0.678837i	0.973336	+	0.229386i	$0.0736718\pi$
$182$	0.367011	−	0.824320i	0.0272047	−	0.0611027i
$183$	−15.4447	−	3.28287i	−1.14170	−	0.242677i
$184$	−7.72740	+	4.82862i	−0.569672	+	0.355970i
$185$	−4.13811	+	2.79119i	−0.304240	+	0.205212i
$186$	10.3298	−	3.75974i	0.757417	−	0.275677i
$187$	−0.0474548	+	2.04909i	−0.00347024	+	0.149844i
$188$	0.424172	+	2.40560i	0.0309360	+	0.175447i
$189$	−7.00475	−	5.08925i	−0.509521	−	0.370189i
$190$	−12.8380	−	3.91196i	−0.931365	−	0.283803i
$191$	−6.00270	−	18.4744i	−0.434340	−	1.33676i	−0.893761	−	0.448543i	$-0.851943\pi$
$191$	−6.00270	−	18.4744i	−0.434340	−	1.33676i	0.459421	−	0.888219i	$-0.348057\pi$
$192$	−0.985270	+	1.02028i	−0.0711058	+	0.0736322i
$193$	−1.48394	+	5.95176i	−0.106816	+	0.428417i	−0.999764	−	0.0217445i	$-0.993078\pi$
$193$	−1.48394	+	5.95176i	−0.106816	+	0.428417i	0.892947	+	0.450161i	$0.148634\pi$
$194$	−5.94583	+	4.64539i	−0.426886	+	0.333520i
$195$	−2.02870	−	1.58499i	−0.145278	−	0.113504i
$196$	−1.12668	−	4.51888i	−0.0804774	−	0.322777i
$197$	−2.34898	−	1.35618i	−0.167358	−	0.0966241i	0.413982	−	0.910285i	$-0.364138\pi$
$197$	−2.34898	−	1.35618i	−0.167358	−	0.0966241i	−0.581339	+	0.813661i	$0.697471\pi$
$198$	2.85767	+	1.60540i	0.203086	+	0.114091i
$199$	−4.53872	+	25.7403i	−0.321741	+	1.82468i	0.209910	+	0.977721i	$0.432683\pi$
$199$	−4.53872	+	25.7403i	−0.321741	+	1.82468i	−0.531651	+	0.846964i	$0.678428\pi$
$200$	−3.22254	+	3.11197i	−0.227868	+	0.220050i
$201$	9.89797	−	2.10388i	0.698149	−	0.148396i
$202$	−0.125414	+	0.590024i	−0.00882407	+	0.0415140i
$203$	−0.677398	+	9.68724i	−0.0475440	+	0.679911i
$204$	−0.842572	+	0.241604i	−0.0589918	+	0.0169156i
$205$	9.25428	+	11.8449i	0.646347	+	0.827286i
$206$	14.1739	−	5.72664i	0.987545	−	0.398994i
$207$	−3.94760	+	8.09378i	−0.274377	+	0.562557i
$208$	−0.589522			−0.0408760
$209$	−8.44157	−	11.7363i	−0.583916	−	0.811814i
$210$	6.68422			0.461255
$211$	2.28696	−	4.68896i	0.157441	−	0.322802i	−0.805463	−	0.592646i	$-0.798083\pi$
$211$	2.28696	−	4.68896i	0.157441	−	0.322802i	0.962904	+	0.269844i	$0.0869722\pi$
$212$	−2.67151	+	1.07936i	−0.183480	+	0.0741306i
$213$	−12.3345	−	15.7875i	−0.845148	−	1.08174i
$214$	−8.99316	+	2.57875i	−0.614759	+	0.176279i
$215$	−1.43456	+	20.5152i	−0.0978363	+	1.39912i
$216$	−1.17611	+	5.53317i	−0.0800242	+	0.376484i
$217$	−11.6036	+	2.46642i	−0.787702	+	0.167431i
$218$	11.0399	−	10.6611i	0.747714	−	0.722059i
$219$	2.72947	−	15.4796i	0.184441	−	1.04602i
$220$	−10.1425	+	1.18668i	−0.683807	+	0.0800061i
$221$	−0.315509	−	0.182159i	−0.0212234	−	0.0122534i
$222$	−0.556271	−	2.23108i	−0.0373344	−	0.149740i
$223$	0.590575	+	0.461408i	0.0395478	+	0.0308982i	0.635242	−	0.772314i	$-0.280901\pi$
$223$	0.590575	+	0.461408i	0.0395478	+	0.0308982i	−0.595694	+	0.803212i	$0.703123\pi$
$224$	1.20614	−	0.942340i	0.0805887	−	0.0629628i
$225$	−1.07107	+	4.29583i	−0.0714047	+	0.286388i
$226$	−6.05632	+	6.27150i	−0.402861	+	0.417174i
$227$	−3.85734	−	11.8717i	−0.256021	−	0.787951i	−0.993627	−	0.112720i	$-0.964044\pi$
$227$	−3.85734	−	11.8717i	−0.256021	−	0.787951i	0.737606	−	0.675231i	$-0.235956\pi$
$228$	3.71612	−	4.94097i	0.246106	−	0.327224i
$229$	3.56593	+	2.59080i	0.235643	+	0.171205i	0.699340	−	0.714789i	$-0.253477\pi$
$229$	3.56593	+	2.59080i	0.235643	+	0.171205i	−0.463697	+	0.885994i	$0.653477\pi$
$230$	−4.87174	−	27.6290i	−0.321233	−	1.82180i
$231$	5.72556	+	4.36592i	0.376714	+	0.287257i
$232$	5.96182	−	2.16993i	0.391413	−	0.142463i
$233$	−18.6892	+	12.6060i	−1.22437	+	0.825848i	−0.989266	−	0.146123i	$-0.953321\pi$
$233$	−18.6892	+	12.6060i	−1.22437	+	0.825848i	−0.235103	+	0.971970i	$0.575543\pi$
$234$	−0.494082	+	0.308737i	−0.0322991	+	0.0201827i
$235$	−7.35661	−	1.56369i	−0.479892	−	0.102004i
$236$	4.37734	−	9.83168i	0.284941	−	0.639988i
$237$	0.961289	−	0.468852i	0.0624424	−	0.0304552i
$238$	0.936698	−	0.131644i	0.0607171	−	0.00853323i
$239$	−5.08085	−	23.9035i	−0.328653	−	1.54619i	−0.763574	−	0.645720i	$-0.776557\pi$
$239$	−5.08085	−	23.9035i	−0.328653	−	1.54619i	0.434921	−	0.900468i	$-0.356776\pi$
$240$	−1.77623	−	3.98947i	−0.114655	−	0.257519i
$241$	3.60294	+	3.02323i	0.232086	+	0.194743i	0.751413	−	0.659833i	$-0.229373\pi$
$241$	3.60294	+	3.02323i	0.232086	+	0.194743i	−0.519327	+	0.854576i	$0.673817\pi$
$242$	−9.46294	−	5.60827i	−0.608301	−	0.360513i
$243$	3.35031	+	9.20489i	0.214922	+	0.590494i
$244$	−0.776560	−	11.1053i	−0.0497142	−	0.710946i
$245$	14.1997	+	1.99564i	0.907188	+	0.127497i
$246$	−6.58552	+	2.13977i	−0.419878	+	0.136426i
$247$	2.55022	−	0.315527i	0.162267	−	0.0200765i
$248$	4.55554	+	6.27017i	0.289277	+	0.398156i
$249$	8.61451	−	4.58042i	0.545923	−	0.290272i
$250$	0.599928	+	1.48487i	0.0379428	+	0.0939117i
$251$	23.1112	+	6.62702i	1.45876	+	0.418294i	0.908919	−	0.416973i	$-0.136909\pi$
$251$	23.1112	+	6.62702i	1.45876	+	0.418294i	0.549845	+	0.835267i	$0.314687\pi$
$252$	0.517364	−	1.42145i	0.0325909	−	0.0895426i
$253$	13.8734	−	26.8485i	0.872211	−	1.68795i
$254$	−3.72403	+	6.45020i	−0.233666	+	0.404722i
$255$	0.282098	−	2.68399i	0.0176657	−	0.168078i
$256$	−0.882948	−	0.469472i	−0.0551842	−	0.0293420i
$257$	0.498473	+	3.54682i	0.0310939	+	0.221245i	0.999617	−	0.0276797i	$-0.00881184\pi$
$257$	0.498473	+	3.54682i	0.0310939	+	0.221245i	−0.968523	+	0.248924i	$0.919923\pi$
$258$	−8.65462	−	3.85329i	−0.538813	−	0.239895i
$259$	0.259374	+	2.46778i	0.0161167	+	0.153341i
$260$	0.679949	−	1.68293i	0.0421686	−	0.104371i
$261$	3.86024	−	4.94088i	0.238943	−	0.305833i
$262$	−3.97476	+	13.8616i	−0.245562	+	0.856375i
$263$	−14.6292	−	17.4344i	−0.902077	−	1.07505i	−0.996831	−	0.0795523i	$-0.974651\pi$
$263$	−14.6292	−	17.4344i	−0.902077	−	1.07505i	0.0947541	−	0.995501i	$-0.469794\pi$
$264$	1.08432	−	4.57747i	0.0667352	−	0.281724i
$265$		−	8.87138i		−	0.544964i
$266$	−4.71330	+	4.72204i	−0.288991	+	0.289527i
$267$	1.61846	−	4.98111i	0.0990481	−	0.304839i
$268$	3.34940	+	6.29930i	0.204597	+	0.384791i
$269$	15.5521	+	3.87757i	0.948228	+	0.236420i	0.685189	−	0.728365i	$-0.259720\pi$
$269$	15.5521	+	3.87757i	0.948228	+	0.236420i	0.263039	+	0.964785i	$0.415275\pi$
$270$	−14.4392	−	9.73939i	−0.878745	−	0.592721i
$271$	−16.9400	−	0.591559i	−1.02903	−	0.0359347i	−0.484598	−	0.874737i	$-0.661034\pi$
$271$	−16.9400	−	0.591559i	−1.02903	−	0.0359347i	−0.544436	+	0.838802i	$0.683256\pi$
$272$	−0.327485	−	0.524085i	−0.0198567	−	0.0317773i
$273$	−1.16918	+	0.520551i	−0.0707618	+	0.0315052i
$274$	−2.50434	−	4.33764i	−0.151293	−	0.262046i
$275$	3.92730	−	14.3296i	0.236825	−	0.864106i
$276$	12.7277	+	2.24423i	0.766115	+	0.135087i
$277$	1.36559	+	0.143529i	0.0820503	+	0.00862383i	0.145465	−	0.989363i	$-0.453532\pi$
$277$	1.36559	+	0.143529i	0.0820503	+	0.00862383i	−0.0634143	+	0.997987i	$0.520199\pi$
$278$	5.95953	−	5.36598i	0.357429	−	0.321830i
$279$	7.10176	+	2.86930i	0.425171	+	0.171780i
$280$	1.29899	+	4.53011i	0.0776293	+	0.270726i
$281$	−13.4043	+	19.8727i	−0.799634	+	1.18551i	0.179792	+	0.983705i	$0.442458\pi$
$281$	−13.4043	+	19.8727i	−0.799634	+	1.18551i	−0.979426	+	0.201802i	$0.935320\pi$
$282$	1.83597	−	2.93817i	0.109331	−	0.174965i
$283$	4.10588	−	29.2148i	0.244069	−	1.73664i	−0.354043	−	0.935229i	$-0.615193\pi$
$283$	4.10588	−	29.2148i	0.244069	−	1.73664i	0.598112	−	0.801413i	$-0.295918\pi$
$284$	8.30262	−	11.4276i	0.492670	−	0.678102i
$285$	9.81907	+	16.3074i	0.581631	+	0.965968i
$286$	1.68167	−	0.997442i	0.0994391	−	0.0589800i
$287$	7.35897	−	1.29758i	0.434386	−	0.0765940i
$288$	−0.985869	+	0.0689387i	−0.0580929	+	0.00406225i
$289$	0.579963	+	16.6080i	0.0341155	+	0.976939i
$290$	−0.681732	+	19.5222i	−0.0400327	+	1.14639i
$291$	10.6759	+	0.746533i	0.625833	+	0.0437625i
$292$	11.0215	−	1.15840i	0.644982	−	0.0677903i
$293$	7.33328	−	8.14444i	0.428415	−	0.475803i	−0.489829	−	0.871819i	$-0.662941\pi$
$293$	7.33328	−	8.14444i	0.428415	−	0.475803i	0.918244	+	0.396016i	$0.129607\pi$
$294$	−3.10113	+	5.83238i	−0.180862	+	0.340151i
$295$	23.0181	+	23.8359i	1.34017	+	1.38778i
$296$	1.40397	−	0.810582i	0.0816040	−	0.0471141i
$297$	−6.00688	−	17.7738i	−0.348555	−	1.03134i
$298$	1.33586	−	1.59201i	0.0773841	−	0.0922228i
$299$	3.00382	+	4.45335i	0.173716	+	0.257544i
$300$	6.35014	−	0.221752i	0.366626	−	0.0128029i
$301$	8.67002	+	5.41763i	0.499732	+	0.312267i
$302$	12.7228	+	12.2863i	0.732117	+	0.706997i
$303$	0.692161	−	0.502885i	0.0397636	−	0.0288900i
$304$	4.07083	+	1.55832i	0.233478	+	0.0893757i
$305$	32.5985	+	10.5919i	1.86659	+	0.606491i
$306$	−0.548934	−	0.267733i	−0.0313804	−	0.0153053i
$307$	14.7459	−	12.3733i	0.841591	−	0.706179i	−0.116330	−	0.993211i	$-0.537113\pi$
$307$	14.7459	−	12.3733i	0.841591	−	0.706179i	0.957921	+	0.287032i	$0.0926686\pi$
$308$	−1.84624	+	4.72885i	−0.105199	+	0.269451i
$309$	−20.3749	−	7.41584i	−1.15909	−	0.421873i
$310$	−23.1540	+	5.77295i	−1.31506	+	0.327881i
$311$	−10.2515	−	11.3854i	−0.581307	−	0.645607i	0.378721	−	0.925511i	$-0.376364\pi$
$311$	−10.2515	−	11.3854i	−0.581307	−	0.645607i	−0.960028	+	0.279904i	$0.909697\pi$
$312$	0.621380	+	0.559493i	0.0351787	+	0.0316751i
$313$	5.50972	+	11.2966i	0.311428	+	0.638522i	0.995894	−	0.0905223i	$-0.0288537\pi$
$313$	5.50972	+	11.2966i	0.311428	+	0.638522i	−0.684466	+	0.729044i	$0.739965\pi$
$314$	−8.87889	−	18.2044i	−0.501065	−	1.02733i
$315$	3.46114	+	3.11642i	0.195013	+	0.175590i
$316$	0.504569	+	0.560380i	0.0283842	+	0.0315239i
$317$	−2.28160	+	0.568866i	−0.128147	+	0.0319507i	−0.305467	−	0.952203i	$-0.598813\pi$
$317$	−2.28160	+	0.568866i	−0.128147	+	0.0319507i	0.177320	+	0.984153i	$0.443257\pi$
$318$	3.84026	+	1.39774i	0.215351	+	0.0783813i
$319$	−13.3353	+	16.2770i	−0.746631	+	0.911339i
$320$	2.35860	−	1.97910i	0.131850	−	0.110635i
$321$	11.9265	+	5.81697i	0.665675	+	0.324671i
$322$	−13.2643	−	4.30984i	−0.739192	−	0.240178i
$323$	1.69717	+	2.09187i	0.0944332	+	0.116395i
$324$	4.09240	−	2.97330i	0.227355	−	0.165183i
$325$	1.89976	+	1.83457i	0.105380	+	0.101764i
$326$	12.3301	+	7.70470i	0.682901	+	0.426724i
$327$	−21.7545	+	0.759684i	−1.20303	+	0.0420106i
$328$	−2.72999	−	4.04738i	−0.150739	−	0.223479i
$329$	−2.40329	+	2.86412i	−0.132497	+	0.157904i
$330$	11.8168	+	8.37505i	0.650496	+	0.461032i
$331$	5.39970	−	3.11752i	0.296795	−	0.171354i	−0.344207	−	0.938894i	$-0.611852\pi$
$331$	5.39970	−	3.11752i	0.296795	−	0.171354i	0.641002	+	0.767539i	$0.278519\pi$
$332$	4.77840	+	4.94818i	0.262249	+	0.271567i
$333$	0.752167	−	1.41462i	0.0412185	−	0.0775208i
$334$	−1.73313	+	1.92484i	−0.0948329	+	0.105323i
$335$	−21.8460	+	2.29611i	−1.19358	+	0.125450i
$336$	−2.16566	−	0.151438i	−0.118147	−	0.00826161i
$337$	−0.347716	+	9.95728i	−0.0189413	+	0.542407i	0.952418	+	0.304794i	$0.0985875\pi$
$337$	−0.347716	+	9.95728i	−0.0189413	+	0.542407i	−0.971360	+	0.237614i	$0.923635\pi$
$338$	−0.441565	−	12.6448i	−0.0240179	−	0.687784i
$339$	12.3357	−	0.862594i	0.669981	−	0.0468497i
$340$	1.87384	−	0.330409i	0.101623	−	0.0179190i
$341$	−23.6039	−	10.1785i	−1.27823	−	0.551196i
$342$	4.22789	−	0.825885i	0.228618	−	0.0446587i
$343$	10.4877	−	14.4351i	0.566282	−	0.779420i
$344$	0.929585	−	6.61434i	0.0501199	−	0.356621i
$345$	−21.0867	+	33.7457i	−1.13527	+	1.81681i
$346$	−2.76199	+	4.09482i	−0.148485	+	0.220139i
$347$	−0.511343	−	1.78326i	−0.0274503	−	0.0957307i	0.946344	−	0.323161i	$-0.104745\pi$
$347$	−0.511343	−	1.78326i	−0.0274503	−	0.0957307i	−0.973794	+	0.227430i	$0.926968\pi$
$348$	−8.34341	−	3.37095i	−0.447253	−	0.180702i
$349$	−11.2718	+	10.1491i	−0.603364	+	0.543271i	−0.913196	−	0.407520i	$-0.866394\pi$
$349$	−11.2718	+	10.1491i	−0.603364	+	0.543271i	0.309832	+	0.950791i	$0.399727\pi$
$350$	−6.81937	−	0.716745i	−0.364511	−	0.0383116i
$351$	3.28413	+	0.579081i	0.175294	+	0.0309091i
$352$	3.31302	−	0.154692i	0.176584	−	0.00824511i
$353$	1.81991	+	3.15218i	0.0968641	+	0.167774i	0.910385	−	0.413762i	$-0.135785\pi$
$353$	1.81991	+	3.15218i	0.0968641	+	0.167774i	−0.813521	+	0.581536i	$0.802452\pi$
$354$	−13.9448	+	6.20862i	−0.741157	+	0.329984i
$355$	23.0466	+	36.8823i	1.22319	+	1.95751i
$356$	3.69038	+	0.128871i	0.195590	+	0.00683014i
$357$	−1.11226	−	0.750227i	−0.0588669	−	0.0397062i
$358$	−6.22403	−	1.55182i	−0.328950	−	0.0820164i
$359$	0.0355133	+	0.0667908i	0.00187432	+	0.00352508i	0.883883	−	0.467708i	$-0.154920\pi$
$359$	0.0355133	+	0.0667908i	0.00187432	+	0.00352508i	−0.882009	+	0.471233i	$0.843809\pi$
$360$	0.940290	−	2.89391i	0.0495576	−	0.152523i
$361$	−18.4441	−	4.56234i	−0.970742	−	0.240123i
$362$		−	20.8335i		−	1.09499i
$363$	4.65173	+	14.8923i	0.244153	+	0.781642i
$364$	−0.580007	−	0.691225i	−0.0304006	−	0.0362301i
$365$	−9.40510	+	32.7995i	−0.492286	+	1.71680i
$366$	−9.72113	+	12.4425i	−0.508132	+	0.650379i
$367$	5.35639	−	13.2575i	0.279601	−	0.692037i	−0.720398	−	0.693561i	$-0.756041\pi$
$367$	5.35639	−	13.2575i	0.279601	−	0.692037i	0.999999	+	0.00152419i	$0.000485166\pi$
$368$	0.952462	+	9.06207i	0.0496505	+	0.472393i
$369$	−4.40766	−	1.96242i	−0.229454	−	0.102159i
$370$	0.694677	+	4.94288i	0.0361145	+	0.256968i
$371$	−3.89396	−	2.07045i	−0.202164	−	0.107493i
$372$	1.14905	−	10.9325i	0.0595757	−	0.566824i
$373$	−8.67675	+	15.0286i	−0.449265	+	0.778150i	−0.998338	−	0.0576240i	$-0.981648\pi$
$373$	−8.67675	+	15.0286i	−0.449265	+	0.778150i	0.549073	+	0.835774i	$0.314981\pi$
$374$	1.82091	+	0.940914i	0.0941569	+	0.0486535i
$375$	0.776890	−	2.13449i	0.0401184	−	0.110225i
$376$	2.34808	+	0.673303i	0.121093	+	0.0347229i
$377$	−1.40110	−	3.46784i	−0.0721603	−	0.178603i
$378$	−7.64487	+	4.06485i	−0.393210	+	0.209073i
$379$	−15.4961	−	21.3286i	−0.795982	−	1.09558i	−0.993337	−	0.115243i	$-0.963235\pi$
$379$	−15.4961	−	21.3286i	−0.795982	−	1.09558i	0.197355	−	0.980332i	$-0.436765\pi$
$380$	−9.14385	+	9.82381i	−0.469070	+	0.503951i
$381$	10.0469	−	3.26444i	0.514720	−	0.167243i
$382$	−19.2361	−	2.70346i	−0.984205	−	0.138321i
$383$	0.400491	+	5.72729i	0.0204641	+	0.292651i	0.997006	+	0.0773235i	$0.0246374\pi$
$383$	0.400491	+	5.72729i	0.0204641	+	0.292651i	−0.976542	+	0.215327i	$0.930918\pi$
$384$	0.485105	+	1.33282i	0.0247554	+	0.0680149i
$385$	−11.3702	−	10.7247i	−0.579479	−	0.546583i
$386$	4.69889	+	3.94283i	0.239167	+	0.200685i
$387$	−2.68488	−	6.03035i	−0.136480	−	0.306540i
$388$	1.56877	+	7.38048i	0.0796422	+	0.374687i
$389$	6.59934	−	0.927476i	0.334600	−	0.0470249i	0.0301272	−	0.999546i	$-0.490409\pi$
$389$	6.59934	−	0.927476i	0.334600	−	0.0470249i	0.304472	+	0.952521i	$0.401520\pi$
$390$	−2.31390	+	1.12857i	−0.117169	+	0.0571472i
$391$	−2.29038	+	5.14427i	−0.115829	+	0.260157i
$392$	−4.55545	−	0.968290i	−0.230085	−	0.0489060i
$393$	17.3451	−	10.8384i	0.874946	−	0.546727i
$394$	−2.24866	+	1.51674i	−0.113286	+	0.0764121i
$395$	−2.18171	+	0.794076i	−0.109774	+	0.0399543i
$396$	2.69565	−	1.86470i	0.135461	−	0.0937046i
$397$	0.0100166	+	0.0568072i	0.000502721	+	0.00285107i	0.985058	−	0.172222i	$-0.0550948\pi$
$397$	0.0100166	+	0.0568072i	0.000502721	+	0.00285107i	−0.984555	+	0.175074i	$0.943984\pi$
$398$	21.1456	+	15.3632i	1.05993	+	0.770087i
$399$	9.44952	−	0.504010i	0.473068	−	0.0252320i
$400$	1.38435	+	4.26060i	0.0692176	+	0.213030i
$401$	−14.8754	+	15.4039i	−0.742841	+	0.769234i	−0.979301	−	0.202407i	$-0.935124\pi$
$401$	−14.8754	+	15.4039i	−0.742841	+	0.769234i	0.236461	+	0.971641i	$0.424013\pi$
$402$	2.44803	−	9.81851i	0.122097	−	0.489703i
$403$	3.60042	−	2.81296i	0.179350	−	0.140123i
$404$	0.475333	+	0.371371i	0.0236487	+	0.0184764i
$405$	3.76787	+	15.1121i	0.187227	+	0.750927i
$406$	8.40988	+	4.85545i	0.417375	+	0.240972i
$407$	−2.63349	+	4.68771i	−0.130537	+	0.232361i
$408$	−0.152207	+	0.863210i	−0.00753538	+	0.0427353i
$409$	23.7912	−	22.9749i	1.17640	−	1.13603i	0.188315	−	0.982109i	$-0.439697\pi$
$409$	23.7912	−	22.9749i	1.17640	−	1.13603i	0.988083	−	0.153925i	$-0.0491914\pi$
$410$	14.7030	−	3.12521i	0.726128	−	0.154343i
$411$	−1.47702	+	6.94882i	−0.0728559	+	0.342760i
$412$	1.06637	−	15.2498i	0.0525364	−	0.751306i
$413$	15.8345	−	4.54047i	0.779166	−	0.223422i
$414$	5.54413	+	7.09616i	0.272479	+	0.348757i
$415$	−19.6371	+	7.93392i	−0.963950	+	0.389461i
$416$	−0.258429	+	0.529859i	−0.0126705	+	0.0259785i
$417$	−11.3742			−0.556999
$418$	−14.2490	+	2.44239i	−0.696943	+	0.119461i
$419$	14.3618			0.701618			0.350809	−	0.936447i	$-0.385907\pi$
$419$	14.3618			0.701618			0.350809	+	0.936447i	$0.385907\pi$
$420$	2.93017	−	6.00774i	0.142978	−	0.293148i
$421$	−12.3297	+	4.98151i	−0.600912	+	0.242784i	−0.654848	−	0.755760i	$-0.727268\pi$
$421$	−12.3297	+	4.98151i	−0.600912	+	0.242784i	0.0539367	+	0.998544i	$0.482823\pi$
$422$	−3.21188	−	4.11101i	−0.156352	−	0.200121i
$423$	2.32056	−	0.665409i	0.112829	−	0.0323533i
$424$	−0.200990	+	2.87429i	−0.00976094	+	0.139588i
$425$	−0.575604	+	2.70801i	−0.0279209	+	0.131358i
$426$	−19.5968	+	4.16543i	−0.949468	+	0.201816i
$427$	12.2572	−	11.8366i	0.593167	−	0.572814i
$428$	−1.62458	+	9.21344i	−0.0785270	+	0.445349i
$429$	−2.71918	−	0.544663i	−0.131283	−	0.0262966i
$430$	17.8101	+	10.2826i	0.858877	+	0.495873i
$431$	8.21177	+	32.9356i	0.395547	+	1.58645i	0.756581	+	0.653900i	$0.226868\pi$
$431$	8.21177	+	32.9356i	0.395547	+	1.58645i	−0.361034	+	0.932553i	$0.617576\pi$
$432$	4.45760	+	3.48266i	0.214467	+	0.167560i
$433$	−0.726642	+	0.567715i	−0.0349202	+	0.0272827i	−0.632970	−	0.774176i	$-0.718165\pi$
$433$	−0.726642	+	0.567715i	−0.0349202	+	0.0272827i	0.598050	+	0.801459i	$0.295942\pi$
$434$	−2.86987	+	11.5104i	−0.137758	+	0.552518i
$435$	19.2464	−	19.9302i	0.922795	−	0.955582i
$436$	−4.74255	−	14.5961i	−0.227127	−	0.699025i
$437$	−8.97051	−	38.6919i	−0.429118	−	1.85089i
$438$	−12.7165	−	9.23905i	−0.607616	−	0.441459i
$439$	1.74951	+	9.92194i	0.0834993	+	0.473548i	0.997670	+	0.0682195i	$0.0217318\pi$
$439$	1.74951	+	9.92194i	0.0834993	+	0.473548i	−0.914171	+	0.405329i	$0.867157\pi$
$440$	−3.37959	+	9.63622i	−0.161116	+	0.459389i
$441$	−4.32505	+	1.57419i	−0.205955	+	0.0749614i
$442$	−0.302034	+	0.203724i	−0.0143663	+	0.00969017i
$443$	−25.4977	+	15.9328i	−1.21143	+	0.756988i	−0.976603	−	0.215048i	$-0.931009\pi$
$443$	−25.4977	+	15.9328i	−1.21143	+	0.756988i	−0.234831	+	0.972036i	$0.575454\pi$
$444$	−2.24913	−	0.478068i	−0.106739	−	0.0226881i
$445$	−4.62434	+	10.3864i	−0.219215	+	0.492364i
$446$	0.673602	−	0.328537i	0.0318960	−	0.0155567i
$447$	−2.91897	+	0.410234i	−0.138062	+	0.0194034i
$448$	−0.318233	−	1.49717i	−0.0150351	−	0.0707345i
$449$	5.91544	+	13.2863i	0.279167	+	0.627019i	0.997649	−	0.0685262i	$-0.0218297\pi$
$449$	5.91544	+	13.2863i	0.279167	+	0.627019i	−0.718483	+	0.695545i	$0.755163\pi$
$450$	3.39154	+	2.84584i	0.159879	+	0.134154i
$451$	14.6355	+	6.92652i	0.689160	+	0.326157i
$452$	2.98187	+	8.19263i	0.140256	+	0.385349i
$453$	−1.74992	−	25.0251i	−0.0822185	−	1.17578i
$454$	−12.3611	−	1.73724i	−0.580137	−	0.0815329i
$455$	2.64224	−	0.858517i	0.123870	−	0.0402479i
$456$	−2.81188	−	5.50600i	−0.131678	−	0.257842i
$457$	−1.53754	−	2.11625i	−0.0719232	−	0.0989938i	0.771540	−	0.636181i	$-0.219487\pi$
$457$	−1.53754	−	2.11625i	−0.0719232	−	0.0989938i	−0.843463	+	0.537187i	$0.819487\pi$
$458$	3.89180	−	2.06931i	0.181852	−	0.0966923i
$459$	1.30956	+	3.24128i	0.0611251	+	0.151290i
$460$	−26.9684	−	7.73307i	−1.25741	−	0.360556i
$461$	−0.478296	+	1.31411i	−0.0222764	+	0.0612040i	−0.950332	−	0.311237i	$-0.899257\pi$
$461$	−0.478296	+	1.31411i	−0.0222764	+	0.0612040i	0.928056	+	0.372441i	$0.121479\pi$
$462$	6.43398	−	3.23220i	0.299336	−	0.150376i
$463$	3.52083	−	6.09825i	0.163627	−	0.283410i	−0.772540	−	0.634966i	$-0.781014\pi$
$463$	3.52083	−	6.09825i	0.163627	−	0.283410i	0.936167	+	0.351556i	$0.114347\pi$
$464$	0.663175	−	6.30969i	0.0307871	−	0.292920i
$465$	29.8842	+	15.8897i	1.38585	+	0.736868i
$466$	3.13741	+	22.3238i	0.145338	+	1.03413i
$467$	−1.37782	−	0.613445i	−0.0637579	−	0.0283869i	0.374610	−	0.927182i	$-0.377777\pi$
$467$	−1.37782	−	0.613445i	−0.0637579	−	0.0283869i	−0.438368	+	0.898796i	$0.644443\pi$
$468$	0.0608994	+	0.579419i	0.00281508	+	0.0267837i
$469$	−4.09071	+	10.1249i	−0.188891	+	0.467523i
$470$	−4.63036	+	5.92659i	−0.213583	+	0.273373i
$471$	−7.91843	+	27.6148i	−0.364862	+	1.27242i
$472$	−6.91775	−	8.24425i	−0.318415	−	0.379473i
$473$	8.53941	+	20.4409i	0.392643	+	0.939871i
$474$		−	1.06953i		−	0.0491252i
$475$	−8.26897	−	17.6900i	−0.379406	−	0.811675i
$476$	0.292300	−	0.899608i	0.0133976	−	0.0412335i
$477$	1.33684	+	2.51422i	0.0612095	+	0.115118i
$478$	−23.7116	−	5.91197i	−1.08454	−	0.270407i
$479$	−22.3315	−	15.0628i	−1.02035	−	0.688236i	−0.0694042	−	0.997589i	$-0.522110\pi$
$479$	−22.3315	−	15.0628i	−1.02035	−	0.688236i	−0.950947	+	0.309353i	$0.899888\pi$
$480$	−4.36436	−	0.152407i	−0.199205	−	0.00695638i
$481$	−0.506450	−	0.810489i	−0.0230921	−	0.0369551i
$482$	4.29668	−	1.91301i	0.195709	−	0.0871351i
$483$	9.89083	+	17.1314i	0.450048	+	0.779507i
$484$	−9.18896	+	6.04673i	−0.417680	+	0.274852i
$485$	−22.8788	−	4.03414i	−1.03887	−	0.183181i
$486$	9.74198	+	1.02392i	0.441905	+	0.0464461i
$487$	−22.5798	+	20.3310i	−1.02319	+	0.921284i	−0.996924	−	0.0783712i	$-0.975028\pi$
$487$	−22.5798	+	20.3310i	−1.02319	+	0.921284i	−0.0262651	+	0.999655i	$0.508361\pi$
$488$	−10.3218	−	4.17029i	−0.467247	−	0.188780i
$489$	−5.68419	−	19.8231i	−0.257048	−	0.896432i
$490$	8.01843	−	11.8878i	0.362236	−	0.537036i
$491$	−10.3374	+	16.5432i	−0.466519	+	0.746586i	−0.994730	−	0.102527i	$-0.967307\pi$
$491$	−10.3374	+	16.5432i	−0.466519	+	0.746586i	0.528211	+	0.849113i	$0.322863\pi$
$492$	−0.963694	+	6.85704i	−0.0434467	+	0.309139i
$493$	2.30459	−	3.17199i	0.103793	−	0.142859i
$494$	0.834350	−	2.43044i	0.0375392	−	0.109351i
$495$	2.21410	+	9.84609i	0.0995162	+	0.442549i
$496$	7.63261	−	1.34583i	0.342714	−	0.0604298i
$497$	21.5677	−	1.50816i	0.967442	−	0.0676501i
$498$	−0.340498	−	9.75060i	−0.0152581	−	0.436935i
$499$	0.562606	−	16.1109i	0.0251857	−	0.721224i	−0.919470	−	0.393160i	$-0.871382\pi$
$499$	0.562606	−	16.1109i	0.0251857	−	0.721224i	0.944656	−	0.328064i	$-0.106396\pi$
$500$	1.59759	+	0.111714i	0.0714463	+	0.00499601i
$501$	3.65359	−	0.384008i	0.163230	−	0.0171562i
$502$	16.0876	−	17.8671i	0.718024	−	0.797447i
$503$	−14.3689	+	27.0239i	−0.640677	+	1.20494i	0.325129	+	0.945670i	$0.394592\pi$
$503$	−14.3689	+	27.0239i	−0.640677	+	1.20494i	−0.965805	+	0.259268i	$0.916519\pi$
$504$	−1.05079	−	1.08812i	−0.0468059	−	0.0484689i
$505$	−1.60841	+	0.928617i	−0.0715734	+	0.0413229i
$506$	−18.0496	−	24.2389i	−0.802401	−	1.07755i
$507$	−11.5352	+	13.7472i	−0.512298	+	0.610533i
$508$	4.16490	+	6.17472i	0.184788	+	0.273959i
$509$	20.9630	−	0.732044i	0.929169	−	0.0324473i	0.433685	−	0.901064i	$-0.357213\pi$
$509$	20.9630	−	0.732044i	0.929169	−	0.0324473i	0.495484	+	0.868617i	$0.334991\pi$
$510$	−2.28869	−	1.43013i	−0.101345	−	0.0633273i
$511$	12.2018	+	11.7832i	0.539777	+	0.521256i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−21.1472	−	12.6799i	−0.933673	−	0.559830i
$514$	3.40638	+	1.10680i	0.150249	+	0.0488188i
$515$	42.3044	+	20.6332i	1.86416	+	0.909209i
$516$	−7.25725	+	6.08955i	−0.319483	+	0.268078i
$517$	−7.83733	+	2.05219i	−0.344685	+	0.0902550i
$518$	2.33173	+	0.848681i	0.102450	+	0.0372889i
$519$	6.79749	−	1.69480i	0.298377	−	0.0743937i
$520$	−1.21454	−	1.34888i	−0.0532611	−	0.0591524i
$521$	−6.90509	−	6.21737i	−0.302518	−	0.272388i	0.503865	−	0.863783i	$-0.331911\pi$
$521$	−6.90509	−	6.21737i	−0.302518	−	0.272388i	−0.806382	+	0.591394i	$0.798578\pi$
$522$	−2.74861	−	5.63549i	−0.120304	−	0.246659i
$523$	−10.3677	−	21.2569i	−0.453347	−	0.929499i	−0.995984	−	0.0895317i	$-0.971463\pi$
$523$	−10.3677	−	21.2569i	−0.453347	−	0.929499i	0.542637	−	0.839967i	$-0.317426\pi$
$524$	10.7163	+	9.64904i	0.468145	+	0.421520i
$525$	6.50766	+	7.22749i	0.284018	+	0.315434i
$526$	−22.0830	+	5.50591i	−0.962864	+	0.240069i
$527$	4.50079	+	1.63815i	0.196057	+	0.0713590i
$528$	−3.63887	−	2.98121i	−0.158361	−	0.129740i
$529$	45.9843	−	38.5854i	1.99932	−	1.67763i
$530$	−7.97354	−	3.88896i	−0.346349	−	0.168925i
$531$	−10.1154	−	3.28669i	−0.438970	−	0.142630i
$532$	2.17797	+	6.30629i	0.0944269	+	0.273412i
$533$	−2.32840	+	1.69168i	−0.100854	+	0.0732748i
$534$	−3.76750	−	3.63824i	−0.163036	−	0.157442i
$535$	−24.4282	−	15.2644i	−1.05612	−	0.659940i
$536$	7.13005	−	0.248987i	0.307971	−	0.0107546i
$537$	5.08760	+	7.54268i	0.219546	+	0.325491i
$538$	10.3027	−	12.2783i	0.444182	−	0.529356i
$539$	14.6332	−	4.94546i	0.630294	−	0.213016i
$540$	−15.0835	+	8.70844i	−0.649089	+	0.374752i
$541$	4.01849	+	4.16127i	0.172768	+	0.178907i	0.800140	−	0.599813i	$-0.204758\pi$
$541$	4.01849	+	4.16127i	0.172768	+	0.178907i	−0.627372	+	0.778720i	$0.715869\pi$
$542$	−7.95771	+	14.9663i	−0.341813	+	0.642857i
$543$	−19.7723	+	21.9594i	−0.848512	+	0.942368i
$544$	−0.614604	+	0.0645975i	−0.0263509	+	0.00276959i
$545$	47.1380	+	3.29621i	2.01917	+	0.141194i
$546$	−0.0446652	+	1.27904i	−0.00191149	+	0.0547380i
$547$	−1.40405	−	40.2068i	−0.0600330	−	1.71912i	−0.539858	−	0.841756i	$-0.681522\pi$
$547$	−1.40405	−	40.2068i	−0.0600330	−	1.71912i	0.479825	−	0.877364i	$-0.340700\pi$
$548$	−4.99647	+	0.349387i	−0.213439	+	0.0149251i
$549$	−10.8348	+	1.91047i	−0.462418	+	0.0815367i
$550$	−11.1577	−	9.81150i	−0.475767	−	0.418364i
$551$	0.508265	+	27.6501i	0.0216528	+	1.17793i
$552$	7.59654	−	10.4557i	0.323330	−	0.445026i
$553$	−0.160631	+	1.14295i	−0.00683074	+	0.0486033i
$554$	0.727638	−	1.16446i	0.0309144	−	0.0494733i
$555$	3.95889	−	5.86930i	0.168046	−	0.249138i
$556$	−2.21043	−	7.70868i	−0.0937431	−	0.326921i
$557$	−18.8275	−	7.60682i	−0.797749	−	0.322311i	−0.0607044	−	0.998156i	$-0.519335\pi$
$557$	−18.8275	−	7.60682i	−0.797749	−	0.322311i	−0.737044	+	0.675844i	$0.763779\pi$
$558$	5.69211	−	5.12520i	0.240966	−	0.216967i
$559$	−3.91605	−	0.411593i	−0.165631	−	0.0174085i
$560$	4.64107	+	0.818346i	0.196121	+	0.0345814i
$561$	−1.02632	−	2.71992i	−0.0433314	−	0.114835i
$562$	11.9854	+	20.7593i	0.505574	+	0.875680i
$563$	19.9040	−	8.86184i	0.838854	−	0.373482i	0.0580926	−	0.998311i	$-0.481498\pi$
$563$	19.9040	−	8.86184i	0.838854	−	0.373482i	0.780761	+	0.624829i	$0.214831\pi$
$564$	−1.83597	−	2.93817i	−0.0773084	−	0.123719i
$565$	−26.8271	−	0.936823i	−1.12863	−	0.0394125i
$566$	−24.4582	−	16.4973i	−1.02806	−	0.693432i
$567$	7.51259	+	1.87310i	0.315499	+	0.0786628i
$568$	−6.63141	−	12.4719i	−0.278248	−	0.523308i
$569$	9.47875	−	29.1726i	0.397370	−	1.22298i	−0.529730	−	0.848166i	$-0.677707\pi$
$569$	9.47875	−	29.1726i	0.397370	−	1.22298i	0.927100	−	0.374813i	$-0.122293\pi$
$570$	18.9614	−	1.67662i	0.794206	−	0.0702257i
$571$			22.0637i			0.923338i	0.887052	+	0.461669i	$0.152749\pi$
$571$			22.0637i			0.923338i	−0.887052	+	0.461669i	$0.847251\pi$
$572$	−0.159301	−	1.94872i	−0.00666070	−	0.0814802i
$573$	17.7099	+	21.1058i	0.739842	+	0.881709i
$574$	2.05970	−	7.18302i	0.0859701	−	0.299814i
$575$	25.1315	−	32.1669i	1.04806	−	1.34145i
$576$	−0.370215	+	0.916314i	−0.0154256	+	0.0381798i
$577$	3.01062	+	28.6441i	0.125334	+	1.19247i	0.858643	+	0.512575i	$0.171308\pi$
$577$	3.01062	+	28.6441i	0.125334	+	1.19247i	−0.733309	+	0.679896i	$0.762025\pi$
$578$	15.1814	+	6.75919i	0.631462	+	0.281145i
$579$	−1.21082	−	8.61545i	−0.0503201	−	0.358046i
$580$	17.2476	+	9.17072i	0.716168	+	0.380794i
$581$	−1.10056	+	10.4711i	−0.0456587	+	0.434414i
$582$	5.35099	−	9.26819i	0.221806	−	0.384179i
$583$	−4.28982	−	8.53926i	−0.177666	−	0.353660i
$584$	3.79032	−	10.4138i	0.156845	−	0.430927i
$585$	−1.72433	−	0.494444i	−0.0712924	−	0.0204428i
$586$	−4.10547	−	10.1614i	−0.169595	−	0.419763i
$587$	30.2992	−	16.1103i	1.25058	−	0.664945i	0.293830	−	0.955858i	$-0.405070\pi$
$587$	30.2992	−	16.1103i	1.25058	−	0.664945i	0.956750	+	0.290913i	$0.0939589\pi$
$588$	3.88266	+	5.34403i	0.160118	+	0.220384i
$589$	−32.2977	+	9.90713i	−1.33080	+	0.408216i
$590$	31.5141	−	10.2395i	1.29741	−	0.421555i
$591$	3.80965	+	0.535412i	0.156708	+	0.0220239i
$592$	−0.113087	−	1.61721i	−0.00464783	−	0.0664671i
$593$	−11.2699	−	30.9637i	−0.462798	−	1.27153i	−0.923373	−	0.383905i	$-0.874579\pi$
$593$	−11.2699	−	30.9637i	−0.462798	−	1.27153i	0.460575	−	0.887621i	$-0.347643\pi$
$594$	−18.6082	−	2.39258i	−0.763505	−	0.0981686i
$595$	2.23101	+	1.87204i	0.0914625	+	0.0767462i
$596$	−0.845290	−	1.89855i	−0.0346244	−	0.0777678i
$597$	−7.70772	−	36.2620i	−0.315456	−	1.48410i
$598$	5.31944	−	0.747598i	0.217528	−	0.0305716i
$599$	13.7618	−	6.71207i	0.562291	−	0.274248i	−0.135227	−	0.990815i	$-0.543176\pi$
$599$	13.7618	−	6.71207i	0.562291	−	0.274248i	0.697518	+	0.716567i	$0.254288\pi$
$600$	2.58441	−	5.80468i	0.105508	−	0.236975i
$601$	41.6794	+	8.85924i	1.70014	+	0.361376i	0.952925	−	0.303207i	$-0.0980572\pi$
$601$	41.6794	+	8.85924i	1.70014	+	0.361376i	0.747215	+	0.664582i	$0.231391\pi$
$602$	8.67002	−	5.41763i	0.353364	−	0.220806i
$603$	5.84535	−	3.94274i	0.238041	−	0.160561i
$604$	16.6202	−	6.04925i	0.676266	−	0.246141i
$605$	−6.66340	−	33.2064i	−0.270906	−	1.35003i
$606$	−0.148566	−	0.842561i	−0.00603509	−	0.0342267i
$607$	4.44488	+	3.22939i	0.180412	+	0.131077i	0.674326	−	0.738434i	$-0.264434\pi$
$607$	4.44488	+	3.22939i	0.180412	+	0.131077i	−0.493914	+	0.869511i	$0.664434\pi$
$608$	3.18514	−	2.97571i	0.129175	−	0.120681i
$609$	−4.25624	−	13.0993i	−0.172471	−	0.530812i
$610$	23.8102	−	24.6562i	0.964047	−	0.998299i
$611$	0.348375	−	1.39726i	0.0140938	−	0.0565270i
$612$	−0.481273	+	0.376012i	−0.0194543	+	0.0151994i
$613$	5.35635	+	4.18484i	0.216341	+	0.169024i	0.718004	−	0.696039i	$-0.245056\pi$
$613$	5.35635	+	4.18484i	0.216341	+	0.169024i	−0.501663	+	0.865063i	$0.667278\pi$
$614$	−4.65684	−	18.6776i	−0.187935	−	0.753765i
$615$	−18.4636	−	10.6599i	−0.744522	−	0.429850i
$616$	3.44092	+	3.73238i	0.138639	+	0.150382i
$617$	0.660579	−	3.74633i	0.0265939	−	0.150821i	−0.968619	−	0.248549i	$-0.920046\pi$
$617$	0.660579	−	3.74633i	0.0265939	−	0.150821i	0.995213	+	0.0977276i	$0.0311574\pi$
$618$	−15.5971	+	15.0619i	−0.627406	+	0.605879i
$619$	33.1993	−	7.05673i	1.33439	−	0.283634i	0.515159	−	0.857095i	$-0.327733\pi$
$619$	33.1993	−	7.05673i	1.33439	−	0.283634i	0.819233	+	0.573461i	$0.194400\pi$
$620$	−4.96137	+	23.3414i	−0.199253	+	0.937413i
$621$	3.59556	−	51.4189i	0.144285	−	2.06337i
$622$	−14.7271	+	4.22292i	−0.590502	+	0.169324i
$623$	3.47971	+	4.45383i	0.139412	+	0.178439i
$624$	0.775265	−	0.313227i	0.0310354	−	0.0125391i
$625$	−11.9808	+	24.5642i	−0.479230	+	0.982568i
$626$	12.5686			0.502343
$627$	17.3370	+	10.9488i	0.692375	+	0.437255i
$628$	−20.2543			−0.808233
$629$	0.439187	−	0.900467i	0.0175115	−	0.0359040i
$630$	4.31828	−	1.74470i	0.172045	−	0.0695105i
$631$	17.7141	+	22.6730i	0.705187	+	0.902599i	0.998573	−	0.0533954i	$-0.0170044\pi$
$631$	17.7141	+	22.6730i	0.705187	+	0.902599i	−0.293386	+	0.955994i	$0.594782\pi$
$632$	0.724855	−	0.207849i	0.0288332	−	0.00826778i
$633$	−0.516161	+	7.38145i	−0.0205156	+	0.293386i
$634$	−0.488893	+	2.30006i	−0.0194164	+	0.0913470i
$635$	−22.4310	+	4.76785i	−0.890146	+	0.189206i
$636$	2.93974	−	2.83887i	0.116568	−	0.112569i
$637$	−0.476757	+	2.70382i	−0.0188898	+	0.107129i
$638$	8.78391	+	19.1210i	0.347758	+	0.757009i
$639$	−12.0894	−	6.97983i	−0.478250	−	0.276118i
$640$	−0.744862	−	2.98748i	−0.0294433	−	0.118091i
$641$	−30.0793	−	23.5006i	−1.18806	−	0.928216i	−0.189503	−	0.981880i	$-0.560688\pi$
$641$	−30.0793	−	23.5006i	−1.18806	−	0.928216i	−0.998559	+	0.0536640i	$0.982910\pi$
$642$	10.4565	−	8.16952i	0.412686	−	0.322425i
$643$	−1.04684	+	4.19866i	−0.0412835	+	0.165579i	−0.987399	−	0.158250i	$-0.949415\pi$
$643$	−1.04684	+	4.19866i	−0.0412835	+	0.165579i	0.946116	+	0.323829i	$0.104970\pi$
$644$	−9.68835	+	10.0326i	−0.381775	+	0.395339i
$645$	−9.01366	−	27.7412i	−0.354913	−	1.09231i
$646$	2.62415	−	0.608395i	0.103246	−	0.0239370i
$647$	−27.2722	−	19.8144i	−1.07218	−	0.778984i	−0.0958769	−	0.995393i	$-0.530566\pi$
$647$	−27.2722	−	19.8144i	−1.07218	−	0.778984i	−0.976303	+	0.216409i	$0.930566\pi$
$648$	−0.878396	−	4.98163i	−0.0345066	−	0.195697i
$649$	33.6824	+	11.8130i	1.32215	+	0.463702i
$650$	2.48170	−	0.903266i	0.0973404	−	0.0354290i
$651$	13.9491	−	9.40878i	0.546708	−	0.368759i
$652$	12.3301	−	7.70470i	0.482884	−	0.301739i
$653$	−10.2994	−	2.18921i	−0.403048	−	0.0856704i	0.00192739	−	0.999998i	$-0.499386\pi$
$653$	−10.2994	−	2.18921i	−0.403048	−	0.0856704i	−0.404975	+	0.914328i	$0.632720\pi$
$654$	−8.85375	+	19.8858i	−0.346209	+	0.777598i
$655$	−39.9056	+	19.4633i	−1.55924	+	0.760493i
$656$	−4.83451	+	0.679446i	−0.188756	+	0.0265279i
$657$	−2.27710	−	10.7129i	−0.0888381	−	0.417950i
$658$	1.52073	+	3.41561i	0.0592841	+	0.133154i
$659$	10.4986	+	8.80938i	0.408968	+	0.343165i	0.823948	−	0.566666i	$-0.191767\pi$
$659$	10.4986	+	8.80938i	0.408968	+	0.343165i	−0.414980	+	0.909831i	$0.636211\pi$
$660$	12.7076	−	6.94953i	0.494643	−	0.270510i
$661$	−10.9060	−	29.9640i	−0.424195	−	1.16547i	−0.949285	−	0.314418i	$-0.898191\pi$
$661$	−10.9060	−	29.9640i	−0.424195	−	1.16547i	0.525090	−	0.851047i	$-0.324032\pi$
$662$	−0.434935	−	6.21985i	−0.0169042	−	0.241741i
$663$	0.511703	+	0.0719152i	0.0198729	+	0.00279295i
$664$	6.54211	−	2.12566i	0.253883	−	0.0824916i
$665$	−20.5149	−	1.05608i	−0.795533	−	0.0409529i
$666$	−0.941725	−	1.29617i	−0.0364911	−	0.0502257i
$667$	−51.0436	+	27.1404i	−1.97642	+	1.05088i
$668$	0.970279	+	2.40152i	0.0375412	+	0.0929178i
$669$	−1.02181	−	0.292998i	−0.0395053	−	0.0113280i
$670$	−7.51294	+	20.6416i	−0.290250	+	0.797456i
$671$	36.4999	−	5.56788i	1.40906	−	0.214946i
$672$	−1.08548	+	1.88010i	−0.0418731	+	0.0725264i
$673$	5.20558	−	49.5278i	0.200660	−	1.90916i	−0.178693	−	0.983905i	$-0.557187\pi$
$673$	5.20558	−	49.5278i	0.200660	−	1.90916i	0.379354	−	0.925252i	$-0.376146\pi$
$674$	8.79711	+	4.67751i	0.338852	+	0.180171i
$675$	−3.52686	−	25.0949i	−0.135749	−	0.965905i
$676$	−11.5586	−	5.14622i	−0.444562	−	0.197932i
$677$	3.56786	+	33.9459i	0.137124	+	1.30465i	0.819260	+	0.573422i	$0.194384\pi$
$677$	3.56786	+	33.9459i	0.137124	+	1.30465i	−0.682136	+	0.731225i	$0.738949\pi$
$678$	4.63231	−	11.4654i	0.177903	−	0.440324i
$679$	−7.11030	+	9.10077i	−0.272868	+	0.349256i
$680$	0.524469	−	1.82904i	0.0201125	−	0.0701405i
$681$	11.3804	+	13.5626i	0.436098	+	0.519721i
$682$	−19.4957	+	16.7531i	−0.746527	+	0.641510i
$683$		−	14.4420i		−	0.552609i	−0.961070	−	0.276305i	$-0.910890\pi$
$683$		−	14.4420i		−	0.552609i	0.961070	−	0.276305i	$-0.0891099\pi$
$684$	1.11108	−	4.16204i	0.0424834	−	0.159140i
$685$	4.76547	−	14.6666i	0.182079	−	0.560383i
$686$	−8.37664	−	15.7542i	−0.319822	−	0.601497i
$687$	−6.06602	−	1.51243i	−0.231433	−	0.0577027i
$688$	−5.53743	−	3.73504i	−0.211112	−	0.142397i
$689$	1.69756	+	0.0592802i	0.0646719	+	0.00225839i
$690$	21.0867	+	33.7457i	0.802755	+	1.28468i
$691$	15.3300	−	6.82535i	0.583180	−	0.259648i	−0.0938713	−	0.995584i	$-0.529924\pi$
$691$	15.3300	−	6.82535i	0.583180	−	0.259648i	0.677051	+	0.735936i	$0.263258\pi$
$692$	2.46962	+	4.27751i	0.0938809	+	0.162606i
$693$	4.83853	+	1.32609i	0.183801	+	0.0503741i
$694$	−1.82695	−	0.322140i	−0.0693499	−	0.0122283i
$695$	24.5558	+	2.58092i	0.931454	+	0.0978998i
$696$	−6.68730	+	6.02127i	−0.253482	+	0.228236i
$697$	−2.79735	−	1.13020i	−0.105957	−	0.0428095i
$698$	4.18077	+	14.5801i	0.158245	+	0.551865i
$699$	17.8798	−	26.5079i	0.676275	−	1.00262i
$700$	−3.63362	+	5.81501i	−0.137338	+	0.219787i
$701$	−7.09150	+	50.4586i	−0.267842	+	1.90580i	0.135554	+	0.990770i	$0.456719\pi$
$701$	−7.09150	+	50.4586i	−0.267842	+	1.90580i	−0.403396	+	0.915026i	$0.632170\pi$
$702$	1.96014	−	2.69791i	0.0739809	−	0.101826i
$703$	1.35478	+	6.93540i	0.0510964	+	0.261574i
$704$	1.31329	−	3.04553i	0.0494966	−	0.114783i
$705$	10.5053	−	1.85237i	0.395653	−	0.0697642i
$706$	3.63096	−	0.253901i	0.136653	−	0.00955570i
$707$	0.0322219	+	0.922713i	0.00121183	+	0.0347022i
$708$	−0.532722	+	15.2552i	−0.0200209	+	0.573324i
$709$	−0.123752	−	0.00865357i	−0.00464760	−	0.000324992i	0.0674325	−	0.997724i	$-0.478519\pi$
$709$	−0.123752	−	0.00865357i	−0.00464760	−	0.000324992i	−0.0720801	+	0.997399i	$0.522964\pi$
$710$	43.2526	−	4.54603i	1.62324	−	0.170609i
$711$	0.498654	−	0.553811i	0.0187010	−	0.0207695i
$712$	1.73358	−	3.26040i	0.0649688	−	0.122188i
$713$	−49.0575	−	50.8006i	−1.83722	−	1.90250i
$714$	−1.16188	+	0.670812i	−0.0434823	+	0.0251045i
$715$	5.74683	+	1.79288i	0.214919	+	0.0670497i
$716$	−4.12320	+	4.91384i	−0.154091	+	0.183639i
$717$	19.3822	+	28.7353i	0.723841	+	1.07314i
$718$	0.0755992	−	0.00263998i	0.00282134	−	9.85233e-5i
$719$	3.71768	+	2.32307i	0.138646	+	0.0866358i	0.597469	−	0.801892i	$-0.296173\pi$
$719$	3.71768	+	2.32307i	0.138646	+	0.0866358i	−0.458823	+	0.888528i	$0.651729\pi$
$720$	−2.18884	−	2.11374i	−0.0815732	−	0.0787743i
$721$	18.9299	−	13.7534i	0.704986	−	0.512202i
$722$	−12.1860	+	14.5775i	−0.453515	+	0.542517i
$723$	−6.34444	−	2.06144i	−0.235952	−	0.0766656i
$724$	−18.7251	−	9.13282i	−0.695911	−	0.339419i
$725$	−21.7727	+	18.2694i	−0.808616	+	0.678510i
$726$	15.4243	+	2.34740i	0.572449	+	0.0871200i
$727$	−25.8627	−	9.41326i	−0.959195	−	0.349119i	−0.185477	−	0.982649i	$-0.559383\pi$
$727$	−25.8627	−	9.41326i	−0.959195	−	0.349119i	−0.773718	+	0.633530i	$0.781605\pi$
$728$	−0.875528	+	0.218294i	−0.0324492	+	0.00809050i
$729$	−19.4510	−	21.6026i	−0.720408	−	0.800095i
$730$	25.3571	+	22.8316i	0.938507	+	0.845035i
$731$	−1.80949	−	3.71001i	−0.0669265	−	0.137220i
$732$	6.92177	+	14.1917i	0.255836	+	0.524541i
$733$	20.2108	+	18.1979i	0.746503	+	0.672154i	0.951860	−	0.306533i	$-0.0991690\pi$
$733$	20.2108	+	18.1979i	0.746503	+	0.672154i	−0.205357	+	0.978687i	$0.565836\pi$
$734$	−9.56770	−	10.6260i	−0.353150	−	0.392213i
$735$	−19.7340	+	4.92025i	−0.727901	+	0.181486i
$736$	8.56246	+	3.11648i	0.315617	+	0.114875i
$737$	−19.9179	+	12.7740i	−0.733685	+	0.470535i
$738$	−3.69600	+	3.10131i	−0.136052	+	0.114161i
$739$	−16.1001	−	7.85257i	−0.592253	−	0.288861i	0.117768	−	0.993041i	$-0.462426\pi$
$739$	−16.1001	−	7.85257i	−0.592253	−	0.288861i	−0.710022	+	0.704180i	$0.751315\pi$
$740$	4.74716	+	1.54245i	0.174509	+	0.0567014i
$741$	−3.18608	+	1.76994i	−0.117044	+	0.0650202i
$742$	−3.56791	+	2.59224i	−0.130982	+	0.0951640i
$743$	−19.5091	−	18.8397i	−0.715719	−	0.691161i	0.244739	−	0.969589i	$-0.421298\pi$
$743$	−19.5091	−	18.8397i	−0.715719	−	0.691161i	−0.960457	+	0.278428i	$0.910187\pi$
$744$	−9.32237	−	5.82526i	−0.341775	−	0.213564i
$745$	6.39483	−	0.223312i	0.234288	−	0.00818153i
$746$	9.70396	+	14.3867i	0.355287	+	0.526735i
$747$	4.36976	−	5.20768i	0.159881	−	0.190539i
$748$	1.64392	−	1.22415i	0.0601077	−	0.0447594i
$749$	−12.4013	+	7.15989i	−0.453133	+	0.261617i
$750$	−1.57790	−	1.63396i	−0.0576167	−	0.0596639i
$751$	−22.3581	+	42.0495i	−0.815859	+	1.53441i	0.0290998	+	0.999577i	$0.490736\pi$
$751$	−22.3581	+	42.0495i	−0.815859	+	1.53441i	−0.844959	+	0.534831i	$0.820375\pi$
$752$	1.63449	−	1.81529i	0.0596038	−	0.0661968i
$753$	−33.9140	+	3.56450i	−1.23589	+	0.129898i
$754$	−3.73108	−	0.260902i	−0.135878	−	0.00950150i
$755$	−1.90051	+	54.4235i	−0.0691666	+	1.98067i
$756$	0.302172	+	8.65308i	0.0109899	+	0.314709i
$757$	−1.01509	+	0.0709822i	−0.0368942	+	0.00257989i	−0.0881916	−	0.996104i	$-0.528109\pi$
$757$	−1.01509	+	0.0709822i	−0.0368942	+	0.00257989i	0.0512975	+	0.998683i	$0.483664\pi$
$758$	−25.9630	+	4.57798i	−0.943020	+	0.166280i
$759$	−3.97925	+	42.6790i	−0.144438	+	1.54915i
$760$	4.82119	+	12.5249i	0.174883	+	0.454326i
$761$	−10.3674	+	14.2695i	−0.375818	+	0.517269i	−0.954471	−	0.298305i	$-0.903579\pi$
$761$	−10.3674	+	14.2695i	−0.375818	+	0.517269i	0.578653	+	0.815574i	$0.303579\pi$
$762$	1.47022	−	10.4612i	0.0532604	−	0.378968i
$763$	12.4482	−	19.9212i	0.450654	−	0.721197i
$764$	−10.8624	+	16.1042i	−0.392988	+	0.582629i
$765$	−0.518321	−	1.80760i	−0.0187399	−	0.0653539i
$766$	5.32322	+	2.15072i	0.192336	+	0.0777087i
$767$	−4.71488	+	4.24530i	−0.170245	+	0.153289i
$768$	1.41058	+	0.148258i	0.0509000	+	0.00534981i
$769$	−37.3864	−	6.59223i	−1.34819	−	0.237722i	−0.547501	−	0.836805i	$-0.684421\pi$
$769$	−37.3864	−	6.59223i	−1.34819	−	0.237722i	−0.800687	+	0.599083i	$0.795532\pi$
$770$	−14.6237	+	5.51806i	−0.527001	+	0.198857i
$771$	−2.54004	−	4.39948i	−0.0914773	−	0.158443i
$772$	5.60365	−	2.49491i	0.201680	−	0.0897936i
$773$	−10.8815	−	17.4141i	−0.391381	−	0.626341i	0.592415	−	0.805633i	$-0.298175\pi$
$773$	−10.8815	−	17.4141i	−0.391381	−	0.626341i	−0.983796	+	0.179292i	$0.942619\pi$
$774$	−6.59702	−	0.230373i	−0.237125	−	0.00828059i
$775$	−28.7846	−	19.4154i	−1.03397	−	0.697423i
$776$	7.32124	+	1.82539i	0.262817	+	0.0655276i
$777$	−1.65229	−	3.10750i	−0.0592755	−	0.111481i
$778$	2.05935	−	6.33802i	0.0738312	−	0.227229i
$779$	20.5500	−	5.52678i	0.736281	−	0.198017i
$780$			2.57445i			0.0921802i
$781$	40.0185	+	24.3572i	1.43198	+	0.871568i
$782$	3.61961	+	4.31368i	0.129437	+	0.154257i
$783$	−9.89238	+	34.4988i	−0.353525	+	1.23289i
$784$	−2.86727	+	3.66994i	−0.102403	+	0.131069i
$785$	23.3611	−	57.8207i	0.833793	−	2.06371i
$786$	−2.13792	−	20.3410i	−0.0762571	−	0.725538i
$787$	−7.23961	−	3.22328i	−0.258064	−	0.114898i	0.273627	−	0.961836i	$-0.411777\pi$
$787$	−7.23961	−	3.22328i	−0.258064	−	0.114898i	−0.531691	+	0.846938i	$0.678443\pi$
$788$	0.377489	+	2.68597i	0.0134475	+	0.0956838i
$789$	28.5018	+	15.1547i	1.01469	+	0.539521i
$790$	−0.242686	+	2.30900i	−0.00863439	+	0.0821507i
$791$	−6.67227	+	11.5567i	−0.237239	+	0.410909i
$792$	−0.494286	−	3.24026i	−0.0175637	−	0.115138i
$793$	−2.24462	+	6.16704i	−0.0797087	+	0.218998i
$794$	0.0554490	+	0.0158998i	0.00196781	+	0.000564261i
$795$	4.71358	+	11.6665i	0.167173	+	0.413769i
$796$	23.0780	−	12.2708i	0.817977	−	0.434926i
$797$	5.20875	+	7.16923i	0.184503	+	0.253947i	0.891242	−	0.453527i	$-0.149834\pi$
$797$	5.20875	+	7.16923i	0.184503	+	0.253947i	−0.706739	+	0.707474i	$0.749834\pi$
$798$	3.68940	−	8.71412i	0.130603	−	0.308476i
$799$	1.43569	−	0.466483i	0.0507909	−	0.0165030i
$800$	4.43626	+	0.623476i	0.156845	+	0.0220432i
$801$	−0.254565	−	3.64045i	−0.00899461	−	0.128629i
$802$	7.32400	+	20.1225i	0.258619	+	0.710551i
$803$	6.80743	+	36.1195i	0.240229	+	1.27463i
$804$	−7.75167	−	6.50443i	−0.273380	−	0.229393i
$805$	−17.4660	−	39.2292i	−0.615595	−	1.38265i
$806$	−0.949949	−	4.46916i	−0.0334605	−	0.157419i
$807$	−22.5124	+	3.16391i	−0.792474	+	0.111375i
$808$	0.542158	−	0.264428i	0.0190730	−	0.00930255i
$809$	3.48178	−	7.82021i	0.122413	−	0.274944i	−0.841936	−	0.539577i	$-0.818584\pi$
$809$	3.48178	−	7.82021i	0.122413	−	0.274944i	0.964349	+	0.264633i	$0.0852508\pi$
$810$	15.2344	+	3.23817i	0.535282	+	0.113778i
$811$	28.1879	−	17.6137i	0.989810	−	0.618502i	0.0645815	−	0.997912i	$-0.479429\pi$
$811$	28.1879	−	17.6137i	0.989810	−	0.618502i	0.925228	+	0.379411i	$0.123873\pi$
$812$	8.05069	−	5.43026i	0.282524	−	0.190565i
$813$	22.5917	−	8.22271i	0.792326	−	0.288383i
$814$	3.05884	+	4.42192i	0.107212	+	0.154988i
$815$	7.77351	+	44.0858i	0.272294	+	1.54426i
$816$	0.709125	+	0.515210i	0.0248243	+	0.0180359i
$817$	25.9535	+	13.1937i	0.907999	+	0.461589i
$818$	−10.2203	−	31.4549i	−0.357345	−	1.09979i
$819$	−0.619463	+	0.641473i	−0.0216458	+	0.0224149i
$820$	3.63643	−	14.5849i	0.126990	−	0.509328i
$821$	17.0423	−	13.3149i	0.594781	−	0.464694i	−0.272745	−	0.962086i	$-0.587931\pi$
$821$	17.0423	−	13.3149i	0.594781	−	0.464694i	0.867525	+	0.497393i	$0.165709\pi$
$822$	5.59808	+	4.37370i	0.195255	+	0.152550i
$823$	−5.95990	−	23.9039i	−0.207749	−	0.833236i	−0.980175	−	0.198132i	$-0.936513\pi$
$823$	−5.95990	−	23.9039i	−0.207749	−	0.833236i	0.772426	−	0.635104i	$-0.219043\pi$
$824$	−13.2390	−	7.64354i	−0.461203	−	0.266275i
$825$	2.44896	+	20.9311i	0.0852619	+	0.728728i
$826$	2.86044	−	16.2224i	0.0995276	−	0.564449i
$827$	−19.2555	+	18.5948i	−0.669580	+	0.646606i	−0.949628	−	0.313380i	$-0.898539\pi$
$827$	−19.2555	+	18.5948i	−0.669580	+	0.646606i	0.280048	+	0.959986i	$0.409650\pi$
$828$	8.80838	−	1.87228i	0.306112	−	0.0650662i
$829$	2.07066	−	9.74170i	0.0719171	−	0.338343i	−0.927449	−	0.373950i	$-0.878003\pi$
$829$	2.07066	−	9.74170i	0.0719171	−	0.338343i	0.999366	+	0.0356069i	$0.0113364\pi$
$830$	−1.47740	+	21.1278i	−0.0512812	+	0.733355i
$831$	−1.87211	+	0.536819i	−0.0649428	+	0.0186220i
$832$	0.362946	+	0.464550i	0.0125829	+	0.0161054i
$833$	−2.66854	+	1.07816i	−0.0924594	+	0.0373560i
$834$	−4.98614	+	10.2231i	−0.172656	+	0.353997i
$835$	−7.97484			−0.275981
$836$	−4.05115	+	13.8776i	−0.140112	+	0.479967i
$837$	−43.8421			−1.51540
$838$	6.29578	−	12.9083i	0.217484	−	0.445909i
$839$	11.0772	−	4.47546i	0.382426	−	0.154510i	−0.175341	−	0.984508i	$-0.556103\pi$
$839$	11.0772	−	4.47546i	0.382426	−	0.154510i	0.557767	+	0.829998i	$0.311658\pi$
$840$	−4.11522	−	5.26724i	−0.141988	−	0.181737i
$841$	10.8160	−	3.10145i	0.372967	−	0.106947i
$842$	−0.927620	+	13.2656i	−0.0319679	+	0.457162i
$843$	7.06881	−	33.2561i	0.243463	−	1.14540i
$844$	−5.10295	+	1.08467i	−0.175651	+	0.0373357i
$845$	28.0227	−	27.0612i	0.964010	−	0.930934i
$846$	0.419200	−	2.37740i	0.0144124	−	0.0817367i
$847$	−16.1306	−	4.82509i	−0.554253	−	0.165792i
$848$	2.49529	+	1.44066i	0.0856886	+	0.0494723i
$849$	10.1230	+	40.6012i	0.347421	+	1.39343i
$850$	2.18161	+	1.70446i	0.0748286	+	0.0584625i
$851$	−11.6405	+	9.09456i	−0.399031	+	0.311757i
$852$	−4.84681	+	19.4395i	−0.166049	+	0.665986i
$853$	23.1232	−	23.9447i	0.791722	−	0.819852i	−0.195249	−	0.980754i	$-0.562551\pi$
$853$	23.1232	−	23.9447i	0.791722	−	0.819852i	0.986970	+	0.160902i	$0.0514403\pi$
$854$	−5.26549	−	16.2055i	−0.180181	−	0.554541i
$855$	10.6000	+	7.97232i	0.362514	+	0.272648i
$856$	7.56882	+	5.49907i	0.258697	+	0.187954i
$857$	5.56412	+	31.5557i	0.190067	+	1.07792i	0.919271	+	0.393626i	$0.128779\pi$
$857$	5.56412	+	31.5557i	0.190067	+	1.07792i	−0.729204	+	0.684296i	$0.760110\pi$
$858$	−1.68155	+	2.20522i	−0.0574072	+	0.0752850i
$859$	0.656014	−	0.238770i	0.0223829	−	0.00814672i	−0.330804	−	0.943699i	$-0.607320\pi$
$859$	0.656014	−	0.238770i	0.0223829	−	0.00814672i	0.353187	+	0.935553i	$0.385098\pi$
$860$	17.0494	−	11.5000i	0.581379	−	0.392145i
$861$	−8.98815	+	5.61642i	−0.306315	+	0.191407i
$862$	33.2021	+	7.05733i	1.13087	+	0.240374i
$863$	10.6570	−	23.9360i	0.362768	−	0.814791i	−0.636292	−	0.771448i	$-0.719533\pi$
$863$	10.6570	−	23.9360i	0.362768	−	0.814791i	0.999060	−	0.0433425i	$-0.0138007\pi$
$864$	5.08428	−	2.47977i	0.172971	−	0.0843635i
$865$	−15.0596	+	2.11649i	−0.512042	+	0.0719629i
$866$	0.191720	+	0.901972i	0.00651491	+	0.0306502i
$867$	−9.58691	−	21.5325i	−0.325588	−	0.731284i
$868$	9.08744	+	7.62526i	0.308448	+	0.258818i
$869$	−1.71605	+	1.81933i	−0.0582129	+	0.0617165i
$870$	−9.47611	−	26.0354i	−0.321270	−	0.882683i
$871$	−0.293388	−	4.19564i	−0.00994106	−	0.142164i
$872$	−15.1979	−	2.13592i	−0.514665	−	0.0723314i
$873$	7.09194	−	2.30431i	0.240026	−	0.0779891i
$874$	−38.7085	−	8.89879i	−1.30933	−	0.301006i
$875$	1.44082	+	1.98311i	0.0487085	+	0.0670414i
$876$	−13.8785	+	7.37935i	−0.468912	+	0.249325i
$877$	−18.1684	−	44.9685i	−0.613505	−	1.51848i	−0.838943	−	0.544220i	$-0.816826\pi$
$877$	−18.1684	−	44.9685i	−0.613505	−	1.51848i	0.225438	−	0.974258i	$-0.427619\pi$
$878$	9.68471	+	2.77705i	0.326843	+	0.0937208i
$879$	−5.31647	+	14.6069i	−0.179320	+	0.492678i
$880$	7.17946	+	7.26180i	0.242020	+	0.244795i
$881$	14.3791	−	24.9053i	0.484444	−	0.839082i	−0.515396	−	0.856952i	$-0.672355\pi$
$881$	14.3791	−	24.9053i	0.484444	−	0.839082i	0.999840	+	0.0178703i	$0.00568861\pi$
$882$	−0.481105	+	4.57741i	−0.0161996	+	0.154129i
$883$	16.1469	+	8.58545i	0.543386	+	0.288923i	0.718386	−	0.695645i	$-0.244881\pi$
$883$	16.1469	+	8.58545i	0.543386	+	0.288923i	−0.175000	+	0.984568i	$0.555992\pi$
$884$	0.0507033	+	0.360773i	0.00170534	+	0.0121341i
$885$	−42.9351	−	19.1159i	−1.44325	−	0.642575i
$886$	3.14279	+	29.9017i	0.105584	+	1.00457i
$887$	−6.16027	+	15.2472i	−0.206842	+	0.511951i	−0.994570	−	0.104072i	$-0.966813\pi$
$887$	−6.16027	+	15.2472i	−0.206842	+	0.511951i	0.787728	+	0.616023i	$0.211257\pi$
$888$	−1.41564	+	1.81194i	−0.0475058	+	0.0608046i
$889$	−3.14229	+	10.9585i	−0.105389	+	0.367536i
$890$	7.30809	+	8.70944i	0.244968	+	0.291941i
$891$	10.9344	+	12.7244i	0.366316	+	0.426282i
$892$		−	0.749451i		−	0.0250935i
$893$	−6.09909	+	8.72760i	−0.204098	+	0.292058i
$894$	−0.910875	+	2.80339i	−0.0304642	+	0.0937593i
$895$	−9.27209	−	17.4383i	−0.309932	−	0.582897i
$896$	−1.48515	−	0.370289i	−0.0496153	−	0.0123705i
$897$	−6.31642	−	4.26048i	−0.210899	−	0.142253i
$898$	14.5348	+	0.507566i	0.485032	+	0.0169377i
$899$	26.0570	+	41.6999i	0.869050	+	1.39077i
$900$	4.04457	−	1.80076i	0.134819	−	0.0600253i
$901$	0.890310	+	1.54206i	0.0296605	+	0.0513735i
$902$	12.6413	−	10.1179i	0.420910	−	0.336891i
$903$	−14.2802	−	2.51799i	−0.475216	−	0.0837935i
$904$	8.67066	+	0.911323i	0.288382	+	0.0303101i
$905$	47.6691	−	42.9215i	1.58458	−	1.42676i
$906$	−23.2595	−	9.39744i	−0.772745	−	0.312209i
$907$	−2.50109	−	8.72234i	−0.0830474	−	0.289621i	0.908768	−	0.417302i	$-0.137024\pi$
$907$	−2.50109	−	8.72234i	−0.0830474	−	0.289621i	−0.991815	+	0.127681i	$0.959246\pi$
$908$	−6.98019	+	10.3486i	−0.231646	+	0.343429i
$909$	0.315903	−	0.505551i	0.0104778	−	0.0167681i
$910$	0.386653	−	2.75118i	0.0128174	−	0.0912008i
$911$	−21.6339	+	29.7766i	−0.716764	+	0.986542i	0.282861	+	0.959161i	$0.408717\pi$
$911$	−21.6339	+	29.7766i	−0.716764	+	0.986542i	−0.999625	+	0.0273807i	$0.991283\pi$
$912$	−6.18141	+	0.113627i	−0.204687	+	0.00376256i
$913$	−15.0655	+	17.1326i	−0.498595	+	0.567006i
$914$	−2.57608	+	0.454233i	−0.0852093	+	0.0150247i
$915$	−48.4972	+	3.39125i	−1.60327	+	0.112111i
$916$	−0.153828	−	4.40505i	−0.00508261	−	0.145547i
$917$	−0.770297	+	22.0584i	−0.0254374	+	0.728433i
$918$	3.48732	+	0.243857i	0.115099	+	0.00804848i
$919$	8.01760	−	0.842684i	0.264476	−	0.0277976i	0.0286378	−	0.999590i	$-0.490883\pi$
$919$	8.01760	−	0.842684i	0.264476	−	0.0277976i	0.235838	+	0.971792i	$0.424216\pi$
$920$	−18.7726	+	20.8491i	−0.618915	+	0.687374i
$921$	−12.8177	+	24.1066i	−0.422357	+	0.794338i
$922$	0.971440	+	1.00596i	0.0319927	+	0.0331294i
$923$	−7.21153	+	4.16358i	−0.237370	+	0.137046i
$924$	−0.0846132	−	7.19973i	−0.00278357	−	0.236854i
$925$	−4.66830	+	5.56346i	−0.153493	+	0.182925i
$926$	−3.93764	−	5.83779i	−0.129399	−	0.191842i
$927$	−15.0987	+	0.527257i	−0.495905	+	0.0173174i
$928$	−5.38039	−	3.36204i	−0.176620	−	0.110364i
$929$	15.4850	+	14.9537i	0.508046	+	0.490615i	0.903927	−	0.427687i	$-0.140672\pi$
$929$	15.4850	+	14.9537i	0.508046	+	0.490615i	−0.395880	+	0.918302i	$0.629560\pi$
$930$	27.3819	−	19.8941i	0.897889	−	0.652355i
$931$	10.4393	−	17.4105i	0.342135	−	0.570605i
$932$	21.4399	+	6.96624i	0.702287	+	0.228187i
$933$	19.5308	+	9.52579i	0.639409	+	0.311860i
$934$	−1.15536	+	0.969460i	−0.0378045	+	0.0317217i
$935$	1.59855	+	6.10489i	0.0522782	+	0.199651i
$936$	0.547475	+	0.199265i	0.0178948	+	0.00651317i
$937$	−42.5122	+	10.5995i	−1.38881	+	0.346270i	−0.863375	−	0.504563i	$-0.831654\pi$
$937$	−42.5122	+	10.5995i	−1.38881	+	0.346270i	−0.525437	+	0.850833i	$0.676098\pi$
$938$	7.30692	+	8.11515i	0.238579	+	0.264969i
$939$	−13.2479	−	11.9284i	−0.432327	−	0.389269i
$940$	3.29697	+	6.75979i	0.107535	+	0.220480i
$941$	−23.8879	−	48.9774i	−0.778722	−	1.59662i	−0.802319	−	0.596895i	$-0.796401\pi$
$941$	−23.8879	−	48.9774i	−0.778722	−	1.59662i	0.0235976	−	0.999722i	$-0.492488\pi$
$942$	21.3488	+	19.2226i	0.695583	+	0.626306i
$943$	29.7662	+	33.0587i	0.969321	+	1.07654i
$944$	−10.4424	+	2.60359i	−0.339872	+	0.0847396i
$945$	−25.0508	−	9.11775i	−0.814903	−	0.296600i
$946$	22.1155	+	1.28551i	0.719039	+	0.0417954i
$947$	15.4145	−	12.9343i	0.500903	−	0.420307i	−0.357012	−	0.934100i	$-0.616204\pi$
$947$	15.4145	−	12.9343i	0.500903	−	0.420307i	0.857914	+	0.513793i	$0.171760\pi$
$948$	−0.961289	−	0.468852i	−0.0312212	−	0.0152276i
$949$	−6.21342	−	2.01886i	−0.201696	−	0.0655351i
$950$	−19.5246	−	0.322705i	−0.633461	−	0.0104699i
$951$	2.69821	−	1.96037i	0.0874956	−	0.0635693i
$952$	−0.680426	−	0.657080i	−0.0220527	−	0.0212961i
$953$	40.4049	+	25.2478i	1.30884	+	0.817855i	0.991456	−	0.130442i	$-0.0416395\pi$
$953$	40.4049	+	25.2478i	1.30884	+	0.817855i	0.317386	+	0.948297i	$0.397195\pi$
$954$	2.84580	−	0.0993775i	0.0921361	−	0.00321746i
$955$	−33.4447	−	49.5838i	−1.08224	−	1.60449i
$956$	−15.7081	+	18.7202i	−0.508037	+	0.605455i
$957$	8.88846	−	28.4908i	0.287323	−	0.920978i
$958$	−23.3278	+	13.4683i	−0.753687	+	0.435142i
$959$	−5.32549	−	5.51471i	−0.171969	−	0.178079i
$960$	−2.05019	+	3.85585i	−0.0661696	+	0.124447i
$961$	−19.4503	+	21.6017i	−0.627429	+	0.696830i
$962$	−0.950476	+	0.0998990i	−0.0306446	+	0.00322087i
$963$	9.22337	+	0.644961i	0.297219	+	0.0207836i
$964$	0.164143	−	4.70044i	0.00528669	−	0.151391i
$965$	0.659115	+	18.8746i	0.0212177	+	0.607594i
$966$	19.7335	−	1.37990i	0.634914	−	0.0443975i
$967$	42.7094	−	7.53082i	1.37344	−	0.242175i	0.562255	−	0.826964i	$-0.309934\pi$
$967$	42.7094	−	7.53082i	1.37344	−	0.242175i	0.811186	+	0.584789i	$0.198823\pi$
$968$	1.40659	+	10.9097i	0.0452096	+	0.350651i
$969$	−3.34337	−	1.84921i	−0.107404	−	0.0594052i
$970$	−13.6553	+	18.7948i	−0.438444	+	0.603466i
$971$	−1.44778	+	10.3015i	−0.0464615	+	0.330591i	0.953144	+	0.302516i	$0.0978266\pi$
$971$	−1.44778	+	10.3015i	−0.0464615	+	0.330591i	−0.999606	+	0.0280748i	$0.991062\pi$
$972$	5.19090	−	8.30717i	0.166498	−	0.266453i
$973$	6.86382	−	10.1760i	0.220044	−	0.326229i
$974$	8.37501	+	29.2071i	0.268352	+	0.935856i
$975$	−3.47307	−	1.40321i	−0.111227	−	0.0449388i
$976$	−8.27302	+	7.44906i	−0.264813	+	0.238439i
$977$	−33.4247	−	3.51308i	−1.06935	−	0.112393i	−0.446538	−	0.894765i	$-0.647343\pi$
$977$	−33.4247	−	3.51308i	−1.06935	−	0.112393i	−0.622812	+	0.782371i	$0.714010\pi$
$978$	−20.3087	−	3.58097i	−0.649400	−	0.114507i
$979$	0.571220	+	12.2337i	0.0182563	+	0.390992i
$980$	−7.16964	−	12.4182i	−0.229026	−	0.396684i
$981$	−13.8560	+	6.16910i	−0.442389	+	0.196964i
$982$	10.3374	+	16.5432i	0.329879	+	0.527916i
$983$	13.6164	+	0.475495i	0.434295	+	0.0151659i	0.251213	−	0.967932i	$-0.419170\pi$
$983$	13.6164	+	0.475495i	0.434295	+	0.0151659i	0.183082	+	0.983098i	$0.441393\pi$
$984$	5.74061	+	3.87209i	0.183004	+	0.123438i
$985$	−8.10315	−	2.02034i	−0.258188	−	0.0643734i
$986$	−1.84070	−	3.46186i	−0.0586199	−	0.110248i
$987$	1.63872	−	5.04346i	0.0521610	−	0.160535i
$988$	−1.81871	−	1.81534i	−0.0578609	−	0.0577538i
$989$			60.8621i			1.93530i
$990$	9.82021	+	2.32623i	0.312107	+	0.0739323i
$991$	−38.4991	−	45.8814i	−1.22296	−	1.45747i	−0.847635	−	0.530580i	$-0.821974\pi$
$991$	−38.4991	−	45.8814i	−1.22296	−	1.45747i	−0.375329	−	0.926892i	$-0.622470\pi$
$992$	2.13629	−	7.45012i	0.0678272	−	0.236542i
$993$	−5.44459	+	6.96876i	−0.172779	+	0.221147i
$994$	8.09912	−	20.0460i	0.256888	−	0.635821i
$995$	8.41198	+	80.0346i	0.266678	+	2.53727i
$996$	−8.91304	−	3.96834i	−0.282421	−	0.125742i
$997$	8.04353	+	57.2327i	0.254741	+	1.81258i	0.526458	+	0.850201i	$0.323520\pi$
$997$	8.04353	+	57.2327i	0.254741	+	1.81258i	−0.271717	+	0.962377i	$0.587591\pi$
$998$	−14.2338	−	7.56823i	−0.450562	−	0.239568i
$999$	−0.958585	+	9.12033i	−0.0303283	+	0.288554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.b.29.3	yes	240
11.8	odd	10		418.2.v.a.371.8	yes	240
19.2	odd	18		418.2.v.a.249.8	✓	240
209.173	even	90	inner	418.2.v.b.173.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.249.8	✓	240	19.2	odd	18
418.2.v.a.371.8	yes	240	11.8	odd	10
418.2.v.b.29.3	yes	240	1.1	even	1	trivial
418.2.v.b.173.3	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)

\(f(q)\)	\(=\)	\(q+(0.438371 - 0.898794i) q^{2} +(-1.31507 + 0.531324i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(2.95966 - 0.848670i) q^{5} +(-0.0989393 + 1.41490i) q^{6} +(0.318233 - 1.49717i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(-0.710907 + 0.686515i) q^{9} +O(q^{10})\)	\(q+(0.438371 - 0.898794i) q^{2} +(-1.31507 + 0.531324i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(2.95966 - 0.848670i) q^{5} +(-0.0989393 + 1.41490i) q^{6} +(0.318233 - 1.49717i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(-0.710907 + 0.686515i) q^{9} +(0.534652 - 3.03216i) q^{10} +(2.43848 - 2.24807i) q^{11} +(1.22833 + 0.709176i) q^{12} +(0.142618 + 0.572011i) q^{13} +(-1.20614 - 0.942340i) q^{14} +(-3.44126 + 2.68860i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-0.429292 + 0.444544i) q^{17} +(0.305394 + 0.939907i) q^{18} +(0.527207 - 4.32690i) q^{19} +(-2.49091 - 1.80975i) q^{20} +(0.376982 + 2.13797i) q^{21} +(-0.951588 - 3.17718i) q^{22} +(8.56246 - 3.11648i) q^{23} +(1.17587 - 0.793133i) q^{24} +(3.79913 - 2.37396i) q^{25} +(0.576639 + 0.122568i) q^{26} +(2.30082 - 5.16773i) q^{27} +(-1.37571 + 0.670977i) q^{28} +(-6.28270 + 0.882976i) q^{29} +(0.907954 + 4.27159i) q^{30} +(-3.15235 - 7.08030i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-2.01233 + 4.25200i) q^{33} +(0.211365 + 0.580720i) q^{34} +(-0.328739 - 4.70119i) q^{35} +(0.978659 + 0.137542i) q^{36} +(-1.54182 + 0.500967i) q^{37} +(-3.65788 - 2.37064i) q^{38} +(-0.491476 - 0.676459i) q^{39} +(-2.71854 + 1.44547i) q^{40} +(1.82884 + 4.52653i) q^{41} +(2.08685 + 0.598395i) q^{42} +(-2.28447 + 6.27653i) q^{43} +(-3.27278 - 0.537503i) q^{44} +(-1.52142 + 2.63518i) q^{45} +(0.952462 - 9.06207i) q^{46} +(-2.15679 - 1.14678i) q^{47} +(-0.197396 - 1.40455i) q^{48} +(4.25458 + 1.89426i) q^{49} +(-0.468273 - 4.45532i) q^{50} +(0.328353 - 0.812701i) q^{51} +(0.362946 - 0.464550i) q^{52} +(0.794197 - 2.76969i) q^{53} +(-3.63611 - 4.33335i) q^{54} +(5.30923 - 8.72299i) q^{55} +1.53061i q^{56} +(1.60567 + 5.97031i) q^{57} +(-1.96054 + 6.03392i) q^{58} +(5.05250 + 9.50238i) q^{59} +(4.23730 + 1.05648i) q^{60} +(9.22922 + 6.22519i) q^{61} +(-7.74563 - 0.270483i) q^{62} +(0.801593 + 1.28282i) q^{63} +(0.913545 - 0.406737i) q^{64} +(0.907551 + 1.57192i) q^{65} +(2.93952 + 3.67262i) q^{66} +(-7.02601 - 1.23888i) q^{67} +(0.614604 + 0.0645975i) q^{68} +(-9.60441 + 8.64785i) q^{69} +(-4.36951 - 1.76540i) q^{70} +(3.89345 + 13.5781i) q^{71} +(0.552637 - 0.819318i) q^{72} +(-5.87265 + 9.39821i) q^{73} +(-0.225622 + 1.60539i) q^{74} +(-3.73480 + 5.14051i) q^{75} +(-3.73422 + 2.24846i) q^{76} +(-2.58973 - 4.36622i) q^{77} +(-0.823447 + 0.145196i) q^{78} +(-0.752229 + 0.0526010i) q^{79} +(0.107453 + 3.07706i) q^{80} +(-0.176538 + 5.05540i) q^{81} +(4.87013 + 0.340553i) q^{82} +(-6.84110 + 0.719029i) q^{83} +(1.45265 - 1.61333i) q^{84} +(-0.893287 + 1.68003i) q^{85} +(4.63986 + 4.80472i) q^{86} +(7.79306 - 4.49933i) q^{87} +(-1.91780 + 2.70593i) q^{88} +(-2.37357 + 2.82872i) q^{89} +(1.70154 + 2.52263i) q^{90} +(0.901781 - 0.0314909i) q^{91} +(-7.72740 - 4.82862i) q^{92} +(7.90751 + 7.63619i) q^{93} +(-1.97620 + 1.43579i) q^{94} +(-2.11175 - 13.2536i) q^{95} +(-1.34893 - 0.438295i) q^{96} +(-6.78173 - 3.30767i) q^{97} +(3.56764 - 2.99360i) q^{98} +(-0.190204 + 3.27222i) 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

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