LMFDB - Embedded newform 418.2.v.b.29.1

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			29.1
Character	$\chi$	$=$	418.29
Dual form			418.2.v.b.173.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.438371 - 0.898794i) q^{2} +(-2.63027 + 1.06270i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(1.03456 - 0.296655i) q^{5} +(-0.197888 + 2.82992i) q^{6} +(0.0323920 - 0.152392i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(3.63096 - 3.50638i) q^{9} +O(q^{10})$	\(q+(0.438371 - 0.898794i) q^{2} +(-2.63027 + 1.06270i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(1.03456 - 0.296655i) q^{5} +(-0.197888 + 2.82992i) q^{6} +(0.0323920 - 0.152392i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(3.63096 - 3.50638i) q^{9} +(0.186889 - 1.05990i) q^{10} +(-3.24638 + 0.678977i) q^{11} +(2.45677 + 1.41842i) q^{12} +(-0.240063 - 0.962840i) q^{13} +(-0.122770 - 0.0959182i) q^{14} +(-2.40591 + 1.87970i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-2.99998 + 3.10657i) q^{17} +(-1.55980 - 4.80058i) q^{18} +(-4.20706 - 1.14045i) q^{19} +(-0.870704 - 0.632604i) q^{20} +(0.0767474 + 0.435256i) q^{21} +(-0.812859 + 3.21547i) q^{22} +(-7.69516 + 2.80081i) q^{23} +(2.35184 - 1.58634i) q^{24} +(-3.25794 + 2.03578i) q^{25} +(-0.970631 - 0.206314i) q^{26} +(-2.36265 + 5.30660i) q^{27} +(-0.140029 + 0.0682969i) q^{28} +(2.58063 - 0.362684i) q^{29} +(0.634784 + 2.98642i) q^{30} +(-2.20948 - 4.96257i) q^{31} +(0.766044 + 0.642788i) q^{32} +(7.81730 - 5.23581i) q^{33} +(1.47706 + 4.05819i) q^{34} +(-0.0116965 - 0.167268i) q^{35} +(-4.99851 - 0.702495i) q^{36} +(-4.58373 + 1.48934i) q^{37} +(-2.86928 + 3.28134i) q^{38} +(1.65464 + 2.27741i) q^{39} +(-0.950272 + 0.505269i) q^{40} +(0.571969 + 1.41567i) q^{41} +(0.424849 + 0.121824i) q^{42} +(-0.889121 + 2.44284i) q^{43} +(2.53371 + 2.14016i) q^{44} +(2.71626 - 4.70469i) q^{45} +(-0.855985 + 8.14416i) q^{46} +(4.33430 + 2.30459i) q^{47} +(-0.394811 - 2.80923i) q^{48} +(6.37264 + 2.83728i) q^{49} +(0.401566 + 3.82064i) q^{50} +(4.58940 - 11.3592i) q^{51} +(-0.610931 + 0.781955i) q^{52} +(2.05315 - 7.16018i) q^{53} +(3.73382 + 4.44980i) q^{54} +(-3.15715 + 1.66549i) q^{55} +0.155797i q^{56} +(12.2777 - 1.47115i) q^{57} +(0.805296 - 2.47844i) q^{58} +(-1.20489 - 2.26607i) q^{59} +(2.96245 + 0.738622i) q^{60} +(-12.0498 - 8.12770i) q^{61} +(-5.42890 - 0.189581i) q^{62} +(-0.416732 - 0.666910i) q^{63} +(0.913545 - 0.406737i) q^{64} +(-0.533990 - 0.924897i) q^{65} +(-1.27904 - 9.32138i) q^{66} +(-4.93074 - 0.869423i) q^{67} +(4.29498 + 0.451420i) q^{68} +(17.2639 - 15.5445i) q^{69} +(-0.155467 - 0.0628127i) q^{70} +(1.47731 + 5.15199i) q^{71} +(-2.82260 + 4.18468i) q^{72} +(1.37235 - 2.19621i) q^{73} +(-0.670761 + 4.77271i) q^{74} +(6.40582 - 8.81685i) q^{75} +(1.69144 + 4.01734i) q^{76} +(-0.00168583 + 0.516718i) q^{77} +(2.77227 - 0.488826i) q^{78} +(13.0429 - 0.912047i) q^{79} +(0.0375606 + 1.07559i) q^{80} +(0.0466153 - 1.33489i) q^{81} +(1.52313 + 0.106508i) q^{82} +(2.74529 - 0.288542i) q^{83} +(0.295736 - 0.328448i) q^{84} +(-2.18207 + 4.10388i) q^{85} +(1.80585 + 1.87001i) q^{86} +(-6.40232 + 3.69638i) q^{87} +(3.03427 - 1.33910i) q^{88} +(7.79440 - 9.28901i) q^{89} +(-3.03782 - 4.50376i) q^{90} +(-0.154506 + 0.00539546i) q^{91} +(6.94468 + 4.33952i) q^{92} +(11.0852 + 10.7049i) q^{93} +(3.97138 - 2.88538i) q^{94} +(-4.69077 + 0.0681840i) q^{95} +(-2.69799 - 0.876630i) q^{96} +(-0.254392 - 0.124075i) q^{97} +(5.34372 - 4.48391i) q^{98} +(-9.40674 + 13.8484i) 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
$3$	−2.63027	+	1.06270i	−1.51859	+	0.613548i	−0.974280	−	0.225339i	$-0.927651\pi$
$3$	−2.63027	+	1.06270i	−1.51859	+	0.613548i	−0.544305	+	0.838887i	$0.683207\pi$
$4$	−0.615661	−	0.788011i	−0.307831	−	0.394005i
$5$	1.03456	−	0.296655i	0.462668	−	0.132668i	−0.0362024	−	0.999344i	$-0.511526\pi$
$5$	1.03456	−	0.296655i	0.462668	−	0.132668i	0.498871	+	0.866677i	$0.333748\pi$
$6$	−0.197888	+	2.82992i	−0.0807873	+	1.15531i
$7$	0.0323920	−	0.152392i	0.0122430	−	0.0575989i	−0.971602	−	0.236621i	$-0.923960\pi$
$7$	0.0323920	−	0.152392i	0.0122430	−	0.0575989i	0.983845	+	0.179022i	$0.0572934\pi$
$8$	−0.978148	+	0.207912i	−0.345827	+	0.0735079i
$9$	3.63096	−	3.50638i	1.21032	−	1.16879i
$10$	0.186889	−	1.05990i	0.0590994	−	0.335169i
$11$	−3.24638	+	0.678977i	−0.978821	+	0.204719i
$11$	−3.24638	+	0.678977i	−0.978821	+	0.204719i
$12$	2.45677	+	1.41842i	0.709209	+	0.409462i
$13$	−0.240063	−	0.962840i	−0.0665815	−	0.267044i	0.927774	−	0.373142i	$-0.121720\pi$
$13$	−0.240063	−	0.962840i	−0.0665815	−	0.267044i	−0.994356	+	0.106099i	$0.966164\pi$
$14$	−0.122770	−	0.0959182i	−0.0328116	−	0.0256352i
$15$	−2.40591	+	1.87970i	−0.621203	+	0.485337i
$16$	−0.241922	+	0.970296i	−0.0604805	+	0.242574i
$17$	−2.99998	+	3.10657i	−0.727601	+	0.753453i	−0.976603	−	0.215050i	$-0.931009\pi$
$17$	−2.99998	+	3.10657i	−0.727601	+	0.753453i	0.249002	+	0.968503i	$0.419897\pi$
$18$	−1.55980	−	4.80058i	−0.367649	−	1.13151i
$19$	−4.20706	−	1.14045i	−0.965166	−	0.261637i
$19$	−4.20706	−	1.14045i	−0.965166	−	0.261637i
$20$	−0.870704	−	0.632604i	−0.194695	−	0.141454i
$21$	0.0767474	+	0.435256i	0.0167476	+	0.0949806i
$22$	−0.812859	+	3.21547i	−0.173302	+	0.685541i
$23$	−7.69516	+	2.80081i	−1.60455	+	0.584009i	−0.980352	−	0.197256i	$-0.936797\pi$
$23$	−7.69516	+	2.80081i	−1.60455	+	0.584009i	−0.624199	+	0.781265i	$0.714575\pi$
$24$	2.35184	−	1.58634i	0.480068	−	0.323810i
$25$	−3.25794	+	2.03578i	−0.651587	+	0.407157i
$26$	−0.970631	−	0.206314i	−0.190356	−	0.0404615i
$27$	−2.36265	+	5.30660i	−0.454692	+	1.02126i
$28$	−0.140029	+	0.0682969i	−0.0264631	+	0.0129069i
$29$	2.58063	−	0.362684i	0.479211	−	0.0673487i	0.104568	−	0.994518i	$-0.466654\pi$
$29$	2.58063	−	0.362684i	0.479211	−	0.0673487i	0.374643	+	0.927169i	$0.377765\pi$
$30$	0.634784	+	2.98642i	0.115895	+	0.545244i
$31$	−2.20948	−	4.96257i	−0.396834	−	0.891303i	−0.995888	−	0.0905947i	$-0.971123\pi$
$31$	−2.20948	−	4.96257i	−0.396834	−	0.891303i	0.599054	−	0.800709i	$-0.295543\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	7.81730	−	5.23581i	1.36082	−	0.911438i
$34$	1.47706	+	4.05819i	0.253314	+	0.695974i
$35$	−0.0116965	−	0.167268i	−0.00197707	−	0.0282735i
$36$	−4.99851	−	0.702495i	−0.833085	−	0.117082i
$37$	−4.58373	+	1.48934i	−0.753560	+	0.244846i	−0.660512	−	0.750815i	$-0.729661\pi$
$37$	−4.58373	+	1.48934i	−0.753560	+	0.244846i	−0.0930475	+	0.995662i	$0.529661\pi$
$38$	−2.86928	+	3.28134i	−0.465459	+	0.532304i
$39$	1.65464	+	2.27741i	0.264954	+	0.364678i
$40$	−0.950272	+	0.505269i	−0.150251	+	0.0798900i
$41$	0.571969	+	1.41567i	0.0893266	+	0.221091i	0.965234	−	0.261389i	$-0.0841805\pi$
$41$	0.571969	+	1.41567i	0.0893266	+	0.221091i	−0.875907	+	0.482480i	$0.839736\pi$
$42$	0.424849	+	0.121824i	0.0655557	+	0.0187978i
$43$	−0.889121	+	2.44284i	−0.135590	+	0.372530i	−0.988842	−	0.148969i	$-0.952405\pi$
$43$	−0.889121	+	2.44284i	−0.135590	+	0.372530i	0.853252	+	0.521499i	$0.174627\pi$
$44$	2.53371	+	2.14016i	0.381972	+	0.322642i
$45$	2.71626	−	4.70469i	0.404916	−	0.701334i
$46$	−0.855985	+	8.14416i	−0.126208	+	1.20079i
$47$	4.33430	+	2.30459i	0.632222	+	0.336159i	0.754464	−	0.656342i	$-0.227897\pi$
$47$	4.33430	+	2.30459i	0.632222	+	0.336159i	−0.122241	+	0.992500i	$0.539008\pi$
$48$	−0.394811	−	2.80923i	−0.0569861	−	0.405477i
$49$	6.37264	+	2.83728i	0.910378	+	0.405326i
$50$	0.401566	+	3.82064i	0.0567900	+	0.540320i
$51$	4.58940	−	11.3592i	0.642645	−	1.59060i
$52$	−0.610931	+	0.781955i	−0.0847208	+	0.108438i
$53$	2.05315	−	7.16018i	0.282022	−	0.983526i	−0.684939	−	0.728600i	$-0.740171\pi$
$53$	2.05315	−	7.16018i	0.282022	−	0.983526i	0.966961	−	0.254926i	$-0.0820510\pi$
$54$	3.73382	+	4.44980i	0.508109	+	0.605541i
$55$	−3.15715	+	1.66549i	−0.425710	+	0.224575i
$56$			0.155797i			0.0208193i
$57$	12.2777	−	1.47115i	1.62621	−	0.194858i
$58$	0.805296	−	2.47844i	0.105740	−	0.325436i
$59$	−1.20489	−	2.26607i	−0.156863	−	0.295017i	0.792107	−	0.610382i	$-0.208984\pi$
$59$	−1.20489	−	2.26607i	−0.156863	−	0.295017i	−0.948970	+	0.315365i	$0.897873\pi$
$60$	2.96245	+	0.738622i	0.382451	+	0.0953557i
$61$	−12.0498	−	8.12770i	−1.54282	−	1.04065i	−0.976254	−	0.216630i	$-0.930494\pi$
$61$	−12.0498	−	8.12770i	−1.54282	−	1.04065i	−0.566567	−	0.824016i	$-0.691729\pi$
$62$	−5.42890	−	0.189581i	−0.689471	−	0.0240768i
$63$	−0.416732	−	0.666910i	−0.0525033	−	0.0840228i
$64$	0.913545	−	0.406737i	0.114193	−	0.0508421i
$65$	−0.533990	−	0.924897i	−0.0662333	−	0.114719i
$66$	−1.27904	−	9.32138i	−0.157438	−	1.14738i
$67$	−4.93074	−	0.869423i	−0.602386	−	0.106217i	−0.135866	−	0.990727i	$-0.543382\pi$
$67$	−4.93074	−	0.869423i	−0.602386	−	0.106217i	−0.466521	+	0.884510i	$0.654493\pi$
$68$	4.29498	+	0.451420i	0.520843	+	0.0547428i
$69$	17.2639	−	15.5445i	2.07833	−	1.87134i
$70$	−0.155467	−	0.0628127i	−0.0185819	−	0.00750756i
$71$	1.47731	+	5.15199i	0.175324	+	0.611429i	0.999014	+	0.0443885i	$0.0141339\pi$
$71$	1.47731	+	5.15199i	0.175324	+	0.611429i	−0.823690	+	0.567041i	$0.808088\pi$
$72$	−2.82260	+	4.18468i	−0.332647	+	0.493169i
$73$	1.37235	−	2.19621i	0.160621	−	0.257047i	−0.757942	−	0.652322i	$-0.773795\pi$
$73$	1.37235	−	2.19621i	0.160621	−	0.257047i	0.918563	+	0.395275i	$0.129351\pi$
$74$	−0.670761	+	4.77271i	−0.0779743	+	0.554816i
$75$	6.40582	−	8.81685i	0.739680	−	1.01808i
$76$	1.69144	+	4.01734i	0.194021	+	0.460821i
$77$	−0.00168583	+	0.516718i	−0.000192118	+	0.0588854i
$78$	2.77227	−	0.488826i	0.313898	−	0.0553486i
$79$	13.0429	−	0.912047i	1.46744	−	0.102613i	0.686458	−	0.727169i	$-0.259164\pi$
$79$	13.0429	−	0.912047i	1.46744	−	0.102613i	0.780980	+	0.624556i	$0.214720\pi$
$80$	0.0375606	+	1.07559i	0.00419940	+	0.120255i
$81$	0.0466153	−	1.33489i	0.00517948	−	0.148321i
$82$	1.52313	+	0.106508i	0.168202	+	0.0117618i
$83$	2.74529	−	0.288542i	0.301335	−	0.0316715i	0.0473454	−	0.998879i	$-0.484924\pi$
$83$	2.74529	−	0.288542i	0.301335	−	0.0316715i	0.253989	+	0.967207i	$0.418257\pi$
$84$	0.295736	−	0.328448i	0.0322674	−	0.0358366i
$85$	−2.18207	+	4.10388i	−0.236679	+	0.445128i
$86$	1.80585	+	1.87001i	0.194729	+	0.201648i
$87$	−6.40232	+	3.69638i	−0.686401	+	0.396294i
$88$	3.03427	−	1.33910i	0.323455	−	0.142749i
$89$	7.79440	−	9.28901i	0.826205	−	0.984633i	−0.173795	−	0.984782i	$-0.555603\pi$
$89$	7.79440	−	9.28901i	0.826205	−	0.984633i	1.00000		0.000148890i	$4.73931e-5\pi$
$90$	−3.03782	−	4.50376i	−0.320215	−	0.474738i
$91$	−0.154506	+	0.00539546i	−0.0161966	+	0.000565598i
$92$	6.94468	+	4.33952i	0.724033	+	0.452426i
$93$	11.0852	+	10.7049i	1.14948	+	1.11004i
$94$	3.97138	−	2.88538i	0.409617	−	0.297604i
$95$	−4.69077	+	0.0681840i	−0.481263	+	0.00699553i
$96$	−2.69799	−	0.876630i	−0.275362	−	0.0894707i
$97$	−0.254392	−	0.124075i	−0.0258296	−	0.0125979i	0.425411	−	0.905000i	$-0.360130\pi$
$97$	−0.254392	−	0.124075i	−0.0258296	−	0.0125979i	−0.451241	+	0.892402i	$0.649018\pi$
$98$	5.34372	−	4.48391i	0.539797	−	0.452943i
$99$	−9.40674	+	13.8484i	−0.945413	+	1.39182i
$100$	3.61000	+	1.31393i	0.361000	+	0.131393i
$101$	−14.8240	+	3.69604i	−1.47504	+	0.367770i	−0.894725	−	0.446618i	$-0.852628\pi$
$101$	−14.8240	+	3.69604i	−1.47504	+	0.367770i	−0.580320	+	0.814388i	$0.697073\pi$
$102$	−8.19769	−	9.10446i	−0.811692	−	0.901476i
$103$	2.65344	+	2.38917i	0.261452	+	0.235412i	0.789422	−	0.613850i	$-0.210380\pi$
$103$	2.65344	+	2.38917i	0.261452	+	0.235412i	−0.527971	+	0.849263i	$0.677047\pi$
$104$	0.435003	+	0.891888i	0.0426555	+	0.0874568i
$105$	0.208520	+	0.427530i	0.0203495	+	0.0417226i
$106$	−5.53548	−	4.98417i	−0.537654	−	0.484106i
$107$	8.36897	+	9.29468i	0.809059	+	0.898551i	0.996489	−	0.0837272i	$-0.0266824\pi$
$107$	8.36897	+	9.29468i	0.809059	+	0.898551i	−0.187430	+	0.982278i	$0.560016\pi$
$108$	5.63625	−	1.40528i	0.542349	−	0.135223i
$109$	−13.7870	−	5.01806i	−1.32056	−	0.480643i	−0.416919	−	0.908944i	$-0.636890\pi$
$109$	−13.7870	−	5.01806i	−1.32056	−	0.480643i	−0.903636	+	0.428301i	$0.859112\pi$
$110$	0.112935	+	3.56773i	0.0107679	+	0.340170i
$111$	10.4737	−	8.78848i	0.994120	−	0.834166i
$112$	0.140029	+	0.0682969i	0.0132315	+	0.00645345i
$113$	9.06045	+	2.94392i	0.852335	+	0.276940i	0.702424	−	0.711759i	$-0.252101\pi$
$113$	9.06045	+	2.94392i	0.852335	+	0.276940i	0.149911	+	0.988699i	$0.452101\pi$
$114$	4.05991	−	11.6800i	0.380246	−	1.09393i
$115$	−7.13021	+	5.18040i	−0.664896	+	0.483075i
$116$	−1.87459	−	1.81027i	−0.174052	−	0.168080i
$117$	−4.24774	−	2.65428i	−0.392704	−	0.245389i
$118$	−2.56492	+	0.0895689i	−0.236120	+	0.00824549i
$119$	0.376242	+	0.557802i	0.0344901	+	0.0511336i
$120$	1.96252	−	2.33884i	0.179153	−	0.213506i
$121$	10.0780	−	4.40844i	0.916180	−	0.400767i
$122$	−12.5874	+	7.26735i	−1.13961	+	0.657955i
$123$	−3.00886	−	3.11577i	−0.271300	−	0.280940i
$124$	−2.55027	+	4.79635i	−0.229021	+	0.430725i
$125$	−6.36735	+	7.07166i	−0.569514	+	0.632509i
$126$	−0.782098	+	0.0822018i	−0.0696748	+	0.00732312i
$127$	−6.75233	−	0.472169i	−0.599172	−	0.0418982i	−0.233050	−	0.972465i	$-0.574870\pi$
$127$	−6.75233	−	0.472169i	−0.599172	−	0.0418982i	−0.366123	+	0.930567i	$0.619315\pi$
$128$	0.0348995	−	0.999391i	0.00308471	−	0.0883345i
$129$	−0.257373	−	7.37019i	−0.0226604	−	0.648909i
$130$	−1.06538	+	0.0744985i	−0.0934398	+	0.00653395i
$131$	2.02971	−	0.357893i	0.177337	−	0.0312693i	−0.0842744	−	0.996443i	$-0.526857\pi$
$131$	2.02971	−	0.357893i	0.177337	−	0.0312693i	0.261611	+	0.965173i	$0.415746\pi$
$132$	−8.93869	−	2.93663i	−0.778013	−	0.255601i
$133$	−0.310071	+	0.604183i	−0.0268866	+	0.0523893i
$134$	−2.94293	+	4.05059i	−0.254230	+	0.349918i
$135$	−0.870071	+	6.19088i	−0.0748838	+	0.532826i
$136$	2.28853	−	3.66241i	0.196240	−	0.314049i
$137$	−9.79968	+	14.5286i	−0.837243	+	1.24126i	0.131032	+	0.991378i	$0.458171\pi$
$137$	−9.79968	+	14.5286i	−0.837243	+	1.24126i	−0.968275	+	0.249886i	$0.919607\pi$
$138$	−6.40330	−	22.3310i	−0.545085	−	1.90094i
$139$	−13.3832	−	5.40715i	−1.13514	−	0.458628i	−0.271354	−	0.962480i	$-0.587472\pi$
$139$	−13.3832	−	5.40715i	−1.13514	−	0.458628i	−0.863790	+	0.503851i	$0.831916\pi$
$140$	−0.124608	+	0.112197i	−0.0105313	+	0.00948242i
$141$	−13.8494	−	1.45563i	−1.16633	−	0.122587i
$142$	5.27819	+	0.930687i	0.442936	+	0.0781015i
$143$	1.43308	+	2.96275i	0.119840	+	0.247757i
$144$	2.52382	+	4.37138i	0.210318	+	0.364282i
$145$	2.56222	−	1.14077i	0.212781	−	0.0947361i
$146$	−1.37235	−	2.19621i	−0.113576	−	0.181760i
$147$	−19.7769	−	0.690626i	−1.63117	−	0.0569618i
$148$	3.99564	+	2.69509i	0.328440	+	0.221535i
$149$	1.00044	+	0.249438i	0.0819594	+	0.0204348i	0.282686	−	0.959213i	$-0.408775\pi$
$149$	1.00044	+	0.249438i	0.0819594	+	0.0204348i	−0.200726	+	0.979647i	$0.564330\pi$
$150$	−5.11641	−	9.62257i	−0.417753	−	0.785679i
$151$	4.69975	−	14.4644i	0.382461	−	1.17709i	−0.555845	−	0.831286i	$-0.687605\pi$
$151$	4.69975	−	14.4644i	0.382461	−	1.17709i	0.938306	−	0.345807i	$-0.112395\pi$
$152$	4.35224	+	0.240830i	0.353013	+	0.0195339i
$153$			21.7989i			1.76234i
$154$	0.463684	+	0.228029i	0.0373647	+	0.0183751i
$155$	−3.75800	−	4.47861i	−0.301850	−	0.359731i
$156$	0.775929	−	2.70599i	0.0621240	−	0.216652i
$157$	6.82734	−	8.73860i	0.544881	−	0.697416i	−0.434216	−	0.900809i	$-0.642975\pi$
$157$	6.82734	−	8.73860i	0.544881	−	0.697416i	0.979097	+	0.203393i	$0.0651968\pi$
$158$	4.89788	−	12.1227i	0.389654	−	0.964428i
$159$	2.20877	+	21.0151i	0.175167	+	1.66660i
$160$	0.983203	+	0.437750i	0.0777290	+	0.0346072i
$161$	0.177560	+	1.26341i	0.0139937	+	0.0995705i
$162$	−1.17935	−	0.627074i	−0.0926588	−	0.0492676i
$163$	−1.04134	+	9.90773i	−0.0815644	+	0.776034i	0.874923	+	0.484261i	$0.160912\pi$
$163$	−1.04134	+	9.90773i	−0.0815644	+	0.776034i	−0.956488	+	0.291772i	$0.905755\pi$
$164$	0.763427	−	1.32229i	0.0596136	−	0.103254i
$165$	6.53422	−	7.73579i	0.508689	−	0.602230i
$166$	0.944116	−	2.59394i	0.0732776	−	0.201329i
$167$	−15.0812	−	4.32446i	−1.16702	−	0.334637i	−0.364464	−	0.931217i	$-0.618748\pi$
$167$	−15.0812	−	4.32446i	−1.16702	−	0.334637i	−0.802553	+	0.596581i	$0.796526\pi$
$168$	−0.165565	−	0.409788i	−0.0127736	−	0.0316158i
$169$	10.6089	−	5.64085i	0.816068	−	0.433911i
$170$	2.73199	+	3.76025i	0.209534	+	0.288398i
$171$	−19.2745	+	10.6106i	−1.47396	+	0.811415i
$172$	2.47238	−	0.803326i	0.188517	−	0.0612530i
$173$	4.69721	+	0.660150i	0.357123	+	0.0501903i	0.315453	−	0.948941i	$-0.397843\pi$
$173$	4.69721	+	0.660150i	0.357123	+	0.0501903i	0.0416694	+	0.999131i	$0.486732\pi$
$174$	0.515693	+	7.37476i	0.0390946	+	0.559079i
$175$	0.204707	+	0.562428i	0.0154744	+	0.0425156i
$176$	0.126562	−	3.31421i	0.00953997	−	0.249818i
$177$	5.57733	+	4.67994i	0.419218	+	0.351765i
$178$	−4.93206	−	11.0776i	−0.369674	−	0.830301i
$179$	0.891582	+	4.19456i	0.0666400	+	0.313516i	0.998825	−	0.0484661i	$-0.0154333\pi$
$179$	0.891582	+	4.19456i	0.0666400	+	0.313516i	−0.932185	+	0.361983i	$0.882100\pi$
$180$	−5.37964	+	0.756060i	−0.400975	+	0.0563534i
$181$	3.10286	−	1.51337i	0.230634	−	0.112488i	−0.319431	−	0.947609i	$-0.603492\pi$
$181$	3.10286	−	1.51337i	0.230634	−	0.112488i	0.550065	+	0.835122i	$0.314603\pi$
$182$	−0.0628814	+	0.141234i	−0.00466108	+	0.0104690i
$183$	40.3315	+	8.57273i	2.98139	+	0.633714i
$184$	6.94468	−	4.33952i	0.511969	−	0.319913i
$185$	−4.30031	+	2.90059i	−0.316165	+	0.213256i
$186$	14.4809	−	5.27062i	1.06179	−	0.386461i
$187$	7.62978	−	12.1220i	0.557945	−	0.886450i
$188$	−0.852421	−	4.83432i	−0.0621692	−	0.352579i
$189$	0.732155	+	0.531942i	0.0532564	+	0.0386931i
$190$	−1.99501	+	4.24592i	−0.144734	+	0.308032i
$191$	7.37114	+	22.6860i	0.533357	+	1.64150i	0.747173	+	0.664630i	$0.231411\pi$
$191$	7.37114	+	22.6860i	0.533357	+	1.64150i	−0.213816	+	0.976874i	$0.568589\pi$
$192$	−1.97063	+	2.04065i	−0.142218	+	0.147271i
$193$	−5.70848	+	22.8955i	−0.410905	+	1.64805i	0.306851	+	0.951757i	$0.400725\pi$
$193$	−5.70848	+	22.8955i	−0.410905	+	1.64805i	−0.717757	+	0.696294i	$0.754831\pi$
$194$	−0.223036	+	0.174255i	−0.0160131	+	0.0125108i
$195$	2.38742	+	1.86526i	0.170967	+	0.133574i
$196$	−1.68758	−	6.76852i	−0.120542	−	0.483466i
$197$	9.21618	+	5.32096i	0.656625	+	0.379103i	0.790990	−	0.611829i	$-0.209566\pi$
$197$	9.21618	+	5.32096i	0.656625	+	0.379103i	−0.134365	+	0.990932i	$0.542899\pi$
$198$	8.32321	+	14.5255i	0.591505	+	1.03228i
$199$	1.32633	−	7.52201i	0.0940213	−	0.533221i	−0.901022	−	0.433774i	$-0.857182\pi$
$199$	1.32633	−	7.52201i	0.0940213	−	0.533221i	0.995043	−	0.0994470i	$-0.0317074\pi$
$200$	2.76348	−	2.66866i	0.195407	−	0.188703i
$201$	13.8931	−	2.95307i	0.979944	−	0.208294i
$202$	−3.17644	+	14.9440i	−0.223494	+	1.05145i
$203$	0.0283215	−	0.405017i	0.00198778	−	0.0284266i
$204$	−11.7767	+	3.37690i	−0.824532	+	0.236431i
$205$	1.01170	+	1.29492i	0.0706603	+	0.0904410i
$206$	3.31057	−	1.33756i	0.230658	−	0.0931919i
$207$	−18.1201	+	37.1518i	−1.25944	+	2.58223i
$208$	0.992316			0.0688047
$209$	14.4321	+	0.845834i	0.998287	+	0.0585075i
$210$	0.475671			0.0328244
$211$	10.5403	−	21.6109i	0.725627	−	1.48776i	−0.141643	−	0.989918i	$-0.545238\pi$
$211$	10.5403	−	21.6109i	0.725627	−	1.48776i	0.867270	−	0.497838i	$-0.165873\pi$
$212$	−6.90634	+	2.79034i	−0.474330	+	0.191642i
$213$	−9.36073	−	11.9812i	−0.641387	−	0.820937i
$214$	12.0227	−	3.44746i	0.821856	−	0.235663i
$215$	−0.195167	+	2.79102i	−0.0133103	+	0.190346i
$216$	1.20772	−	5.68186i	0.0821747	−	0.386602i
$217$	−0.827827	+	0.175960i	−0.0561966	+	0.0119450i
$218$	−10.5540	+	10.1919i	−0.714809	+	0.690283i
$219$	−1.27573	+	7.23501i	−0.0862057	+	0.488897i
$220$	3.25616	+	1.46248i	0.219530	+	0.0986007i
$221$	3.71131	+	2.14273i	0.249650	+	0.144135i
$222$	−3.30767	−	13.2663i	−0.221996	−	0.890377i
$223$	−14.5731	−	11.3857i	−0.975884	−	0.762444i	−0.00450782	−	0.999990i	$-0.501435\pi$
$223$	−14.5731	−	11.3857i	−0.975884	−	0.762444i	−0.971376	+	0.237546i	$0.923657\pi$
$224$	0.122770	−	0.0959182i	0.00820290	−	0.00640881i
$225$	−4.69121	+	18.8154i	−0.312747	+	1.25436i
$226$	6.61781	−	6.85295i	0.440210	−	0.455851i
$227$	0.851188	+	2.61969i	0.0564953	+	0.173875i	0.975322	−	0.220786i	$-0.0708622\pi$
$227$	0.851188	+	2.61969i	0.0564953	+	0.173875i	−0.918827	+	0.394661i	$0.870862\pi$
$228$	−8.71816	−	8.76919i	−0.577374	−	0.580754i
$229$	−15.3759	−	11.1712i	−1.01607	−	0.738215i	−0.0505934	−	0.998719i	$-0.516111\pi$
$229$	−15.3759	−	11.1712i	−1.01607	−	0.738215i	−0.965473	+	0.260504i	$0.916111\pi$
$230$	1.53044	+	8.67953i	0.100914	+	0.572311i
$231$	−0.544680	−	1.36090i	−0.0358373	−	0.0895404i
$232$	−2.44883	+	0.891302i	−0.160774	+	0.0585168i
$233$	−11.7896	+	7.95221i	−0.772365	+	0.520967i	−0.881001	−	0.473115i	$-0.843130\pi$
$233$	−11.7896	+	7.95221i	−0.772365	+	0.520967i	0.108636	+	0.994082i	$0.465352\pi$
$234$	−4.24774	+	2.65428i	−0.277684	+	0.173516i
$235$	5.16775	+	1.09844i	0.337107	+	0.0716542i
$236$	−1.04388	+	2.34460i	−0.0679510	+	0.152620i
$237$	−33.3370	+	16.2596i	−2.16547	+	1.05617i
$238$	0.666283	−	0.0936399i	0.0431887	−	0.00606978i
$239$	−2.72850	−	12.8366i	−0.176492	−	0.830329i	−0.973916	−	0.226910i	$-0.927138\pi$
$239$	−2.72850	−	12.8366i	−0.176492	−	0.830329i	0.797424	−	0.603420i	$-0.206196\pi$
$240$	−1.24183	−	2.78918i	−0.0801595	−	0.180041i
$241$	−14.7562	−	12.3820i	−0.950533	−	0.797592i	0.0288543	−	0.999584i	$-0.490814\pi$
$241$	−14.7562	−	12.3820i	−0.950533	−	0.797592i	−0.979387	+	0.201992i	$0.935259\pi$
$242$	0.455618	−	10.9906i	0.0292883	−	0.706500i
$243$	−4.66421	−	12.8148i	−0.299209	−	0.822070i
$244$	1.01389	+	14.4993i	0.0649076	+	0.928222i
$245$	7.43456	+	1.04486i	0.474977	+	0.0667536i
$246$	−4.11944	+	1.33849i	−0.262646	+	0.0853387i
$247$	−0.0881102	+	4.32451i	−0.00560632	+	0.275162i
$248$	3.19297	+	4.39475i	0.202754	+	0.279067i
$249$	−6.91421	+	3.67635i	−0.438170	+	0.232979i
$250$	3.56470	+	8.82295i	0.225452	+	0.558013i
$251$	21.6666	+	6.21280i	1.36758	+	0.392149i	0.877521	−	0.479538i	$-0.159196\pi$
$251$	21.6666	+	6.21280i	1.36758	+	0.392149i	0.490064	+	0.871687i	$0.336973\pi$
$252$	−0.268967	+	0.738980i	−0.0169433	+	0.0465514i
$253$	23.0797	−	14.3173i	1.45101	−	0.900123i
$254$	−3.38441	+	5.86197i	−0.212357	+	0.367813i
$255$	1.37825	−	13.1132i	0.0863094	−	0.821179i
$256$	−0.882948	−	0.469472i	−0.0551842	−	0.0293420i
$257$	1.94149	+	13.8144i	0.121107	+	0.861721i	0.952176	+	0.305551i	$0.0988407\pi$
$257$	1.94149	+	13.8144i	0.121107	+	0.861721i	−0.831069	+	0.556170i	$0.812270\pi$
$258$	−6.73711	−	2.99955i	−0.419434	−	0.186744i
$259$	0.0784885	+	0.746768i	0.00487704	+	0.0464019i
$260$	−0.400072	+	0.990213i	−0.0248114	+	0.0614104i
$261$	8.09847	−	10.3656i	0.501282	−	0.641612i
$262$	0.568096	−	1.98118i	0.0350971	−	0.122398i
$263$	−6.17931	−	7.36422i	−0.381033	−	0.454097i	0.541107	−	0.840954i	$-0.318005\pi$
$263$	−6.17931	−	7.36422i	−0.381033	−	0.454097i	−0.922140	+	0.386856i	$0.873561\pi$
$264$	−6.55789	+	6.74671i	−0.403610	+	0.415231i
$265$		−	8.01669i		−	0.492462i
$266$	0.407110	+	0.543547i	0.0249615	+	0.0333270i
$267$	−10.6300	+	32.7157i	−0.650543	+	2.00217i
$268$	2.35055	+	4.42075i	0.143583	+	0.270040i
$269$	−19.6292	−	4.89411i	−1.19681	−	0.298399i	−0.407972	−	0.912995i	$-0.633764\pi$
$269$	−19.6292	−	4.89411i	−1.19681	−	0.298399i	−0.788843	+	0.614595i	$0.789319\pi$
$270$	5.18291	+	3.49592i	0.315422	+	0.212755i
$271$	11.9291	+	0.416574i	0.724643	+	0.0253051i	0.394847	−	0.918747i	$-0.370798\pi$
$271$	11.9291	+	0.416574i	0.724643	+	0.0253051i	0.329796	+	0.944052i	$0.393020\pi$
$272$	−2.28853	−	3.66241i	−0.138762	−	0.222066i
$273$	0.400658	−	0.178384i	0.0242489	−	0.0107963i
$274$	8.76234	+	15.1768i	0.529352	+	0.916865i
$275$	9.19425	−	8.82099i	0.554434	−	0.531926i
$276$	−22.8780	−	4.03400i	−1.37709	−	0.242818i
$277$	−13.7878	−	1.44915i	−0.828426	−	0.0870711i	−0.319182	−	0.947693i	$-0.603408\pi$
$277$	−13.7878	−	1.44915i	−0.828426	−	0.0870711i	−0.509244	+	0.860622i	$0.670075\pi$
$278$	−10.7267	+	9.65837i	−0.643345	+	0.579270i
$279$	−25.4232	−	10.2716i	−1.52205	−	0.614946i
$280$	0.0462179	+	0.161181i	0.00276205	+	0.00963241i
$281$	5.76601	−	8.54846i	0.343971	−	0.509958i	−0.616867	−	0.787067i	$-0.711599\pi$
$281$	5.76601	−	8.54846i	0.343971	−	0.509958i	0.960839	+	0.277109i	$0.0893763\pi$
$282$	−7.37951	+	11.8097i	−0.439443	+	0.703256i
$283$	0.604695	−	4.30263i	0.0359454	−	0.255765i	−0.964003	−	0.265890i	$-0.914334\pi$
$283$	0.604695	−	4.30263i	0.0359454	−	0.255765i	0.999949	+	0.0101254i	$0.00322308\pi$
$284$	3.15030	−	4.33602i	0.186936	−	0.257295i
$285$	12.2655	−	5.16421i	0.726546	−	0.305901i
$286$	3.29112	+	0.0107375i	0.194608	+	0.000634924i
$287$	0.234265	−	0.0413073i	0.0138282	−	0.00243829i
$288$	5.03534	−	0.352105i	0.296710	−	0.0207480i
$289$	−0.0576058	−	1.64961i	−0.00338858	−	0.0970361i
$290$	0.0978825	−	2.80299i	0.00574786	−	0.164597i
$291$	0.800973	+	0.0560095i	0.0469539	+	0.00328334i
$292$	−2.57554	+	0.270700i	−0.150722	+	0.0158415i
$293$	0.105915	−	0.117630i	0.00618762	−	0.00687205i	−0.740043	−	0.672559i	$-0.765195\pi$
$293$	0.105915	−	0.117630i	0.00618762	−	0.00687205i	0.746231	+	0.665687i	$0.231862\pi$
$294$	−9.29037	+	17.4726i	−0.541825	+	1.01903i
$295$	−1.91877	−	1.98694i	−0.111715	−	0.115684i
$296$	4.17391	−	2.40981i	0.242603	−	0.140067i
$297$	4.06700	−	18.8314i	0.235992	−	1.09271i
$298$	0.662758	−	0.789844i	0.0383926	−	0.0457545i
$299$	4.54405	+	6.73683i	0.262789	+	0.389601i
$300$	−10.8916	+	0.380343i	−0.628826	+	0.0219591i
$301$	0.343470	+	0.214624i	0.0197973	+	0.0123707i
$302$	−10.9402	−	10.5649i	−0.629540	−	0.607940i
$303$	35.0634	−	25.4750i	2.01434	−	1.46350i
$304$	2.12435	−	3.80620i	0.121840	−	0.218300i
$305$	−14.8773	−	4.83394i	−0.851874	−	0.276791i
$306$	19.5927	+	9.55601i	1.12004	+	0.546280i
$307$	10.1061	−	8.48005i	0.576787	−	0.483982i	−0.307103	−	0.951676i	$-0.599360\pi$
$307$	10.1061	−	8.48005i	0.576787	−	0.483982i	0.883890	+	0.467694i	$0.154915\pi$
$308$	0.408217	−	0.316795i	0.0232603	−	0.0180510i
$309$	−9.51824	−	3.46435i	−0.541474	−	0.197080i
$310$	−5.67275	+	1.41437i	−0.322190	+	0.0803311i
$311$	−6.46545	−	7.18061i	−0.366622	−	0.407175i	0.531403	−	0.847119i	$-0.321665\pi$
$311$	−6.46545	−	7.18061i	−0.366622	−	0.407175i	−0.898025	+	0.439944i	$0.854998\pi$
$312$	−2.09198	−	1.88363i	−0.118435	−	0.106639i
$313$	−12.7388	−	26.1185i	−0.720041	−	1.47630i	−0.872820	−	0.488043i	$-0.837711\pi$
$313$	−12.7388	−	26.1185i	−0.720041	−	1.47630i	0.152779	−	0.988260i	$-0.451178\pi$
$314$	−4.86129	−	9.96712i	−0.274338	−	0.562477i
$315$	−0.628975	−	0.566332i	−0.0354387	−	0.0319092i
$316$	−8.74870	−	9.71642i	−0.492153	−	0.546591i
$317$	−30.4531	+	7.59282i	−1.71042	+	0.426455i	−0.969490	−	0.245130i	$-0.921169\pi$
$317$	−30.4531	+	7.59282i	−1.71042	+	0.426455i	−0.740928	+	0.671585i	$0.765614\pi$
$318$	19.8565	+	7.22717i	1.11350	+	0.405279i
$319$	−8.13145	+	2.92960i	−0.455274	+	0.164026i
$320$	0.824455	−	0.691800i	0.0460884	−	0.0386728i
$321$	−31.8901	−	15.5538i	−1.77993	−	0.868130i
$322$	1.21338	+	0.394251i	0.0676191	+	0.0219708i
$323$	16.1640	−	9.64820i	0.899387	−	0.536840i
$324$	−1.08060	+	0.785105i	−0.0600336	+	0.0436170i
$325$	2.74224	+	2.64815i	0.152112	+	0.146893i
$326$	8.44852	+	5.27922i	0.467920	+	0.292389i
$327$	41.5962	−	1.45257i	2.30027	−	0.0803273i
$328$	−0.853806	−	1.26582i	−0.0471435	−	0.0698932i
$329$	0.491598	−	0.585864i	0.0271027	−	0.0322997i
$330$	−4.08846	−	9.26407i	−0.225063	−	0.509970i
$331$	−21.1825	+	12.2297i	−1.16430	+	0.672207i	−0.952330	−	0.305070i	$-0.901320\pi$
$331$	−21.1825	+	12.2297i	−1.16430	+	0.672207i	−0.211967	+	0.977277i	$0.567987\pi$
$332$	−1.91754	−	1.98567i	−0.105239	−	0.108978i
$333$	−11.4211	+	21.4800i	−0.625874	+	1.17710i
$334$	−10.4980	+	11.6592i	−0.574423	+	0.637961i
$335$	−5.35906	+	0.563259i	−0.292797	+	0.0307742i
$336$	−0.440894	−	0.0308303i	−0.0240527	−	0.00168193i
$337$	−0.916572	+	26.2472i	−0.0499288	+	1.42978i	0.673404	+	0.739275i	$0.264832\pi$
$337$	−0.916572	+	26.2472i	−0.0499288	+	1.42978i	−0.723332	+	0.690500i	$0.757391\pi$
$338$	−0.419328	−	12.0080i	−0.0228085	−	0.653149i
$339$	−26.9599	+	1.88522i	−1.46426	+	0.102391i
$340$	4.57732	−	0.807105i	0.248240	−	0.0437714i
$341$	10.5423	+	14.6102i	0.570896	+	0.791187i
$342$	1.08737	+	21.9752i	0.0587983	+	1.18828i
$343$	1.27983	−	1.76153i	0.0691043	−	0.0951139i
$344$	0.361797	−	2.57432i	0.0195068	−	0.138798i
$345$	13.2492	−	21.2031i	0.713311	−	1.14154i
$346$	2.65246	−	3.93244i	0.142597	−	0.211409i
$347$	−1.08292	−	3.77658i	−0.0581340	−	0.202737i	0.926835	−	0.375469i	$-0.122518\pi$
$347$	−1.08292	−	3.77658i	−0.0581340	−	0.202737i	−0.984969	+	0.172732i	$0.944741\pi$
$348$	6.85445	+	2.76938i	0.367437	+	0.148454i
$349$	8.08889	−	7.28327i	0.432988	−	0.389864i	−0.423613	−	0.905843i	$-0.639238\pi$
$349$	8.08889	−	7.28327i	0.432988	−	0.389864i	0.856601	+	0.515979i	$0.172572\pi$
$350$	0.595245	+	0.0625627i	0.0318172	+	0.00334412i
$351$	5.67659	+	1.00094i	0.302994	+	0.0534260i
$352$	−2.92331	−	1.56661i	−0.155813	−	0.0835004i
$353$	16.0380	+	27.7787i	0.853618	+	1.47851i	0.877921	+	0.478805i	$0.158930\pi$
$353$	16.0380	+	27.7787i	0.853618	+	1.47851i	−0.0243036	+	0.999705i	$0.507737\pi$
$354$	6.65124	−	2.96132i	0.353509	−	0.157392i
$355$	3.05672	+	4.89178i	0.162234	+	0.259629i
$356$	−12.1186	−	0.423189i	−0.642282	−	0.0224290i
$357$	−1.58239	−	1.06734i	−0.0837491	−	0.0564895i
$358$	4.16089	+	1.03743i	0.219910	+	0.0548297i
$359$	−9.50271	−	17.8720i	−0.501534	−	0.943248i	−0.997203	−	0.0747367i	$-0.976188\pi$
$359$	−9.50271	−	17.8720i	−0.501534	−	0.943248i	0.495669	−	0.868511i	$-0.334923\pi$
$360$	−1.67874	+	5.16663i	−0.0884773	+	0.272305i
$361$	16.3988	+	9.59588i	0.863092	+	0.505046i
$362$		−	3.45225i		−	0.181446i
$363$	−21.8230	+	22.3052i	−1.14541	+	1.17072i
$364$	0.0993749	+	0.118430i	0.00520866	+	0.00620744i
$365$	0.768254	−	2.67922i	0.0402122	−	0.140237i
$366$	25.3853	−	32.4917i	1.32691	−	1.69837i
$367$	−9.62066	+	23.8120i	−0.502195	+	1.24298i	0.436960	+	0.899481i	$0.356055\pi$
$367$	−9.62066	+	23.8120i	−0.502195	+	1.24298i	−0.939155	+	0.343494i	$0.888389\pi$
$368$	−0.855985	−	8.14416i	−0.0446213	−	0.424543i
$369$	7.04069	+	3.13472i	0.366524	+	0.163187i
$370$	0.721906	+	5.13663i	0.0375301	+	0.267041i
$371$	−1.02465	−	0.544817i	−0.0531973	−	0.0282855i
$372$	1.61081	−	15.3259i	0.0835167	−	0.794608i
$373$	10.2477	−	17.7496i	0.530607	−	0.919039i	−0.468755	−	0.883328i	$-0.655297\pi$
$373$	10.2477	−	17.7496i	0.530607	−	0.919039i	0.999362	−	0.0357104i	$-0.0113694\pi$
$374$	−7.55052	−	12.1715i	−0.390428	−	0.629375i
$375$	9.23281	−	25.3669i	0.476780	−	1.30994i
$376$	−4.71873	−	1.35307i	−0.243350	−	0.0697795i
$377$	−0.968720	−	2.39767i	−0.0498916	−	0.123486i
$378$	0.799062	−	0.424869i	0.0410993	−	0.0218529i
$379$	16.2778	+	22.4045i	0.836136	+	1.15084i	0.986750	+	0.162249i	$0.0518749\pi$
$379$	16.2778	+	22.4045i	0.836136	+	1.15084i	−0.150614	+	0.988593i	$0.548125\pi$
$380$	2.94165	+	3.65440i	0.150904	+	0.187467i
$381$	18.2622	−	5.93375i	0.935601	−	0.303995i
$382$	23.6214	+	3.31977i	1.20857	+	0.169854i
$383$	1.05532	+	15.0918i	0.0539243	+	0.771154i	0.946997	+	0.321242i	$0.104100\pi$
$383$	1.05532	+	15.0918i	0.0539243	+	0.771154i	−0.893073	+	0.449912i	$0.851455\pi$
$384$	0.970255	+	2.66575i	0.0495131	+	0.136036i
$385$	0.151543	+	0.535074i	0.00772332	+	0.0272699i
$386$	18.0759	+	15.1675i	0.920038	+	0.772003i
$387$	5.33716	+	11.9875i	0.271303	+	0.609357i
$388$	0.0588467	+	0.276852i	0.00298749	+	0.0140550i
$389$	12.6404	−	1.77649i	0.640893	−	0.0900716i	0.188762	−	0.982023i	$-0.439553\pi$
$389$	12.6404	−	1.77649i	0.640893	−	0.0900716i	0.452131	+	0.891951i	$0.350664\pi$
$390$	2.72306	−	1.32813i	0.137887	−	0.0672522i
$391$	14.3844	−	32.3079i	0.727450	−	1.63388i
$392$	−6.82329	−	1.45034i	−0.344628	−	0.0732530i
$393$	−4.95836	+	3.09833i	−0.250116	+	0.156290i
$394$	8.82255	−	5.95089i	0.444474	−	0.299801i
$395$	13.2230	−	4.81280i	0.665324	−	0.242158i
$396$	16.7040	−	1.11331i	0.839410	−	0.0559459i
$397$	3.01689	+	17.1096i	0.151413	+	0.858707i	0.961992	+	0.273078i	$0.0880416\pi$
$397$	3.01689	+	17.1096i	0.151413	+	0.858707i	−0.810579	+	0.585630i	$0.800847\pi$
$398$	−6.17931	−	4.48953i	−0.309741	−	0.225040i
$399$	0.173506	−	1.91868i	0.00868618	−	0.0960539i
$400$	−1.18715	−	3.65366i	−0.0593573	−	0.182683i
$401$	−10.6769	+	11.0563i	−0.533181	+	0.552125i	−0.930849	−	0.365405i	$-0.880931\pi$
$401$	−10.6769	+	11.0563i	−0.533181	+	0.552125i	0.397668	+	0.917529i	$0.369820\pi$
$402$	3.43613	−	13.7816i	0.171379	−	0.687363i
$403$	−4.24774	+	3.31870i	−0.211595	+	0.165316i
$404$	12.0391	+	9.40597i	0.598968	+	0.467965i
$405$	−0.347774	−	1.39485i	−0.0172810	−	0.0693105i
$406$	−0.351611	−	0.203003i	−0.0174502	−	0.0100749i
$407$	13.8693	−	7.94722i	0.687475	−	0.393929i
$408$	−2.12741	+	12.0651i	−0.105322	+	0.597313i
$409$	7.98077	−	7.70694i	0.394624	−	0.381084i	−0.470703	−	0.882292i	$-0.656000\pi$
$409$	7.98077	−	7.70694i	0.394624	−	0.381084i	0.865327	+	0.501208i	$0.167111\pi$
$410$	1.60737	−	0.341656i	0.0793821	−	0.0168732i
$411$	10.3363	−	48.6282i	0.509850	−	2.39865i
$412$	0.249070	−	3.56186i	0.0122708	−	0.175480i
$413$	−0.384361	+	0.110214i	−0.0189132	+	0.00542326i
$414$	25.4485	+	32.5725i	1.25072	+	1.60085i
$415$	2.75456	−	1.11292i	0.135216	−	0.0546309i
$416$	0.435003	−	0.891888i	0.0213278	−	0.0437284i
$417$	40.9475			2.00521
$418$	7.08683	−	12.6007i	0.346628	−	0.616319i
$419$	−8.53492			−0.416958			−0.208479	−	0.978027i	$-0.566851\pi$
$419$	−8.53492			−0.416958			−0.208479	+	0.978027i	$0.566851\pi$
$420$	0.208520	−	0.427530i	0.0101747	−	0.0208613i
$421$	−28.6815	+	11.5881i	−1.39785	+	0.564768i	−0.945074	−	0.326856i	$-0.894011\pi$
$421$	−28.6815	+	11.5881i	−1.39785	+	0.564768i	−0.452776	+	0.891624i	$0.649566\pi$
$422$	−14.8032	−	18.9472i	−0.720607	−	0.922335i
$423$	23.8184	−	6.82983i	1.15809	−	0.332077i
$424$	−0.519597	+	7.43059i	−0.0252339	+	0.360861i
$425$	3.44943	−	16.2283i	0.167322	−	0.787188i
$426$	−14.8721	+	3.16116i	−0.720555	+	0.153159i
$427$	−1.62892	+	1.57303i	−0.0788289	+	0.0761242i
$428$	2.17186	−	12.3172i	0.104981	−	0.595375i
$429$	−6.91789	−	6.26989i	−0.333999	−	0.302713i
$430$	2.42300	+	1.39892i	0.116847	+	0.0674618i
$431$	3.24040	+	12.9965i	0.156085	+	0.626021i	0.996464	+	0.0840225i	$0.0267767\pi$
$431$	3.24040	+	12.9965i	0.156085	+	0.626021i	−0.840379	+	0.541999i	$0.817668\pi$
$432$	−4.57739	−	3.57625i	−0.220230	−	0.172063i
$433$	−16.2478	+	12.6942i	−0.780822	+	0.610045i	−0.925201	−	0.379478i	$-0.876104\pi$
$433$	−16.2478	+	12.6942i	−0.780822	+	0.610045i	0.144379	+	0.989522i	$0.453881\pi$
$434$	−0.204744	+	0.821182i	−0.00982801	+	0.0394180i
$435$	−5.52702	+	5.72340i	−0.265001	+	0.274416i
$436$	4.53384	+	13.9537i	0.217132	+	0.668262i
$437$	35.5682	−	3.00724i	1.70146	−	0.143856i
$438$	5.94354	+	4.31824i	0.283993	+	0.206333i
$439$	0.630806	+	3.57748i	0.0301067	+	0.170744i	0.996154	−	0.0876227i	$-0.0279270\pi$
$439$	0.630806	+	3.57748i	0.0301067	+	0.170744i	−0.966047	+	0.258366i	$0.916816\pi$
$440$	2.74188	−	2.28551i	0.130714	−	0.108957i
$441$	33.0874	−	12.0428i	1.57559	−	0.573469i
$442$	3.55280	−	2.39639i	0.168989	−	0.113985i
$443$	4.83653	−	3.02220i	0.229790	−	0.143589i	−0.410138	−	0.912023i	$-0.634520\pi$
$443$	4.83653	−	3.02220i	0.229790	−	0.143589i	0.639928	+	0.768434i	$0.278964\pi$
$444$	−13.3737	−	2.84266i	−0.634686	−	0.134907i
$445$	5.30813	−	11.9223i	0.251630	−	0.565169i
$446$	−16.6218	+	8.10701i	−0.787066	+	0.383878i
$447$	−2.89651	+	0.407077i	−0.137000	+	0.0192541i
$448$	−0.0323920	−	0.152392i	−0.00153038	−	0.00719987i
$449$	−9.25400	−	20.7848i	−0.436723	−	0.980896i	−0.989092	−	0.147297i	$-0.952943\pi$
$449$	−9.25400	−	20.7848i	−0.436723	−	0.980896i	0.552369	−	0.833600i	$-0.313724\pi$
$450$	14.8547	+	12.4646i	0.700257	+	0.587585i
$451$	−2.81804	−	4.20746i	−0.132696	−	0.198122i
$452$	−3.25833	−	8.95219i	−0.153259	−	0.421075i
$453$	3.00962	+	43.0395i	0.141404	+	2.02217i
$454$	2.72770	+	0.383353i	0.128017	+	0.0179916i
$455$	−0.158244	+	0.0514167i	−0.00741861	+	0.00241045i
$456$	−11.7035	+	3.99167i	−0.548066	+	0.186927i
$457$	−15.2281	−	20.9597i	−0.712343	−	0.980456i	−0.999744	−	0.0226453i	$-0.992791\pi$
$457$	−15.2281	−	20.9597i	−0.712343	−	0.980456i	0.287401	−	0.957810i	$-0.407209\pi$
$458$	−16.7810	+	8.92260i	−0.784123	+	0.416926i
$459$	−9.39741	−	23.2594i	−0.438634	−	1.08566i
$460$	8.47201	+	2.42931i	0.395009	+	0.113267i
$461$	−3.25623	+	8.94642i	−0.151658	+	0.416676i	−0.992135	−	0.125170i	$-0.960052\pi$
$461$	−3.25623	+	8.94642i	−0.151658	+	0.416676i	0.840478	+	0.541846i	$0.182275\pi$
$462$	−1.46194	−	0.107023i	−0.0680155	−	0.00497915i
$463$	−0.261483	+	0.452903i	−0.0121522	+	0.0210482i	−0.872038	−	0.489439i	$-0.837202\pi$
$463$	−0.261483	+	0.452903i	−0.0121522	+	0.0210482i	0.859885	+	0.510487i	$0.170535\pi$
$464$	−0.272400	+	2.59172i	−0.0126459	+	0.120317i
$465$	14.6439	+	7.78633i	0.679097	+	0.361082i
$466$	1.97916	+	14.0825i	0.0916830	+	0.652358i
$467$	−11.1920	−	4.98298i	−0.517902	−	0.230585i	0.131103	−	0.991369i	$-0.458148\pi$
$467$	−11.1920	−	4.98298i	−0.517902	−	0.230585i	−0.649005	+	0.760784i	$0.724815\pi$
$468$	0.523567	+	4.98141i	0.0242019	+	0.230266i
$469$	−0.292210	+	0.723246i	−0.0134930	+	0.0333964i
$470$	3.25266	−	4.16322i	0.150034	−	0.192035i
$471$	−8.67125	+	30.2402i	−0.399550	+	1.39340i
$472$	1.64970	+	1.96604i	0.0759337	+	0.0904943i
$473$	1.22779	−	8.53409i	0.0564540	−	0.392398i
$474$			37.0909i			1.70364i
$475$	16.0280	−	4.84916i	0.735417	−	0.222495i
$476$	0.207916	−	0.639900i	0.00952982	−	0.0293298i
$477$	−17.6514	−	33.1975i	−0.808202	−	1.52001i
$478$	−12.7335	−	3.17483i	−0.582419	−	0.145213i
$479$	−24.6425	−	16.6216i	−1.12594	−	0.759458i	−0.152481	−	0.988306i	$-0.548726\pi$
$479$	−24.6425	−	16.6216i	−1.12594	−	0.759458i	−0.973462	+	0.228848i	$0.926504\pi$
$480$	−3.05128	−	0.106553i	−0.139271	−	0.00486346i
$481$	2.53438	+	4.05586i	0.115558	+	0.184931i
$482$	−17.5975	+	7.83493i	−0.801546	+	0.356871i
$483$	−1.80965	−	3.13441i	−0.0823420	−	0.142621i
$484$	−9.67852	−	5.22745i	−0.439933	−	0.237611i
$485$	−0.299991	−	0.0528964i	−0.0136219	−	0.00240190i
$486$	−13.5625	−	1.42548i	−0.615209	−	0.0646610i
$487$	14.1650	−	12.7542i	0.641877	−	0.577949i	−0.282576	−	0.959245i	$-0.591189\pi$
$487$	14.1650	−	12.7542i	0.641877	−	0.577949i	0.924453	+	0.381296i	$0.124522\pi$
$488$	13.4763	+	5.44480i	0.610045	+	0.246474i
$489$	−7.78991	−	27.1666i	−0.352272	−	1.22852i
$490$	4.19821	−	6.22410i	0.189656	−	0.281176i
$491$	−14.8922	+	23.8326i	−0.672077	+	1.07555i	0.319694	+	0.947521i	$0.396420\pi$
$491$	−14.8922	+	23.8326i	−0.672077	+	1.07555i	−0.991771	+	0.128027i	$0.959136\pi$
$492$	−0.602819	+	4.28928i	−0.0271772	+	0.193376i
$493$	−6.61513	+	9.10494i	−0.297930	+	0.410066i
$494$	3.84822	+	1.97493i	0.173139	+	0.0888564i
$495$	−5.62362	+	17.1175i	−0.252763	+	0.769375i
$496$	5.34968	−	0.943293i	0.240208	−	0.0423551i
$497$	0.832978	−	0.0582475i	0.0373642	−	0.00261276i
$498$	0.273292	+	7.82606i	0.0122465	+	0.350694i
$499$	−0.983564	+	28.1656i	−0.0440304	+	1.26086i	0.753444	+	0.657512i	$0.228391\pi$
$499$	−0.983564	+	28.1656i	−0.0440304	+	1.26086i	−0.797475	+	0.603353i	$0.793831\pi$
$500$	9.49268	+	0.663793i	0.424526	+	0.0296857i
$501$	44.2632	−	4.65225i	1.97753	−	0.207847i
$502$	15.0821	−	16.7503i	0.673145	−	0.747603i
$503$	−4.01874	+	7.55816i	−0.179187	+	0.337002i	−0.956314	−	0.292342i	$-0.905565\pi$
$503$	−4.01874	+	7.55816i	−0.179187	+	0.337002i	0.777127	+	0.629344i	$0.216676\pi$
$504$	0.546284	+	0.565693i	0.0243334	+	0.0251980i
$505$	−14.2399	+	8.22138i	−0.633665	+	0.365847i
$506$	−2.75084	−	27.0202i	−0.122290	−	1.20120i
$507$	−21.9097	+	26.1110i	−0.973044	+	1.15963i
$508$	3.78507	+	5.61160i	0.167936	+	0.248975i
$509$	22.0749	−	0.770871i	0.978451	−	0.0341683i	0.458794	−	0.888543i	$-0.348282\pi$
$509$	22.0749	−	0.770871i	0.978451	−	0.0341683i	0.519658	+	0.854375i	$0.326060\pi$
$510$	−11.1819	−	6.98720i	−0.495141	−	0.309399i
$511$	−0.290233	−	0.280275i	−0.0128392	−	0.0123986i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	15.9917	−	19.6307i	0.706052	−	0.866717i
$514$	13.2674	+	4.31085i	0.585201	+	0.190143i
$515$	3.45390	+	1.68458i	0.152197	+	0.0742315i
$516$	−5.64934	+	4.74036i	−0.248698	+	0.208683i
$517$	−15.6355	−	4.53868i	−0.687650	−	0.199611i
$518$	0.705598	+	0.256817i	0.0310022	+	0.0112839i
$519$	−13.0565	+	3.25534i	−0.573115	+	0.142894i
$520$	0.714618	+	0.793663i	0.0313381	+	0.0348044i
$521$	26.0327	+	23.4400i	1.14052	+	1.02692i	0.999317	+	0.0369434i	$0.0117621\pi$
$521$	26.0327	+	23.4400i	1.14052	+	1.02692i	0.141198	+	0.989981i	$0.454905\pi$
$522$	−5.76637	−	11.8228i	−0.252387	−	0.517471i
$523$	−18.8082	−	38.5625i	−0.822424	−	1.68622i	−0.722655	−	0.691209i	$-0.757078\pi$
$523$	−18.8082	−	38.5625i	−0.822424	−	1.68622i	−0.0997698	−	0.995011i	$-0.531811\pi$
$524$	−1.53164	−	1.37910i	−0.0669100	−	0.0602461i
$525$	−1.13612	−	1.26179i	−0.0495846	−	0.0550692i
$526$	−9.32775	+	2.32567i	−0.406709	+	0.101404i
$527$	22.0449	+	8.02370i	0.960292	+	0.349518i
$528$	3.18911	+	8.85175i	0.138788	+	0.385223i
$529$	33.7519	−	28.3212i	1.46747	−	1.23136i
$530$	−7.20536	−	3.51429i	−0.312981	−	0.152651i
$531$	−12.3206	−	4.00321i	−0.534669	−	0.173725i
$532$	0.667002	−	0.127633i	0.0289182	−	0.00553359i
$533$	1.22576	−	0.890566i	0.0530935	−	0.0385747i
$534$	24.7448	+	23.8958i	1.07081	+	1.03407i
$535$	11.4155	+	7.13319i	0.493535	+	0.308395i
$536$	5.00376	−	0.174735i	0.216129	−	0.00754741i
$537$	−6.80265	−	10.0853i	−0.293556	−	0.435215i
$538$	−13.0037	+	15.4972i	−0.560629	+	0.668131i
$539$	−22.6145	−	4.88402i	−0.974075	−	0.210370i
$540$	5.41415	−	3.12586i	0.232988	−	0.134516i
$541$	17.3128	+	17.9280i	0.744336	+	0.770783i	0.979559	−	0.201159i	$-0.0644707\pi$
$541$	17.3128	+	17.9280i	0.744336	+	0.770783i	−0.235222	+	0.971942i	$0.575582\pi$
$542$	5.60380	−	10.5392i	0.240704	−	0.452698i
$543$	−6.55310	+	7.27795i	−0.281220	+	0.312327i
$544$	−4.29498	+	0.451420i	−0.184146	+	0.0193545i
$545$	−15.7521	−	1.10149i	−0.674745	−	0.0471828i
$546$	0.0153060	−	0.438307i	0.000655037	−	0.0187578i
$547$	−0.961215	−	27.5256i	−0.0410986	−	1.17691i	−0.828326	−	0.560246i	$-0.810706\pi$
$547$	−0.961215	−	27.5256i	−0.0410986	−	1.17691i	0.787227	−	0.616663i	$-0.211516\pi$
$548$	17.4820	−	1.22246i	0.746794	−	0.0522209i
$549$	−72.2513	+	12.7398i	−3.08361	+	0.543723i
$550$	−3.89776	−	12.1306i	−0.166201	−	0.517251i
$551$	−11.2705	−	1.41724i	−0.480139	−	0.0603766i
$552$	−13.6548	+	18.7942i	−0.581186	+	0.799934i
$553$	0.283496	−	2.01718i	0.0120555	−	0.0857792i
$554$	−7.34664	+	11.7571i	−0.312129	+	0.499511i
$555$	8.22851	−	12.1993i	0.349281	−	0.517830i
$556$	3.97861	+	13.8750i	0.168730	+	0.588433i
$557$	−13.7229	−	5.54441i	−0.581457	−	0.234924i	0.0649857	−	0.997886i	$-0.479300\pi$
$557$	−13.7229	−	5.54441i	−0.581457	−	0.234924i	−0.646443	+	0.762962i	$0.723744\pi$
$558$	−20.3769	+	18.3474i	−0.862622	+	0.776708i
$559$	2.56551	+	0.269646i	0.108509	+	0.0114048i
$560$	0.165129	+	0.0291167i	0.00697798	+	0.00123041i
$561$	−7.18633	+	39.9923i	−0.303407	+	1.68848i
$562$	−5.15565	−	8.92985i	−0.217478	−	0.376683i
$563$	−22.9292	+	10.2087i	−0.966349	+	0.430247i	−0.828366	−	0.560188i	$-0.810729\pi$
$563$	−22.9292	+	10.2087i	−0.966349	+	0.430247i	−0.137984	+	0.990434i	$0.544062\pi$
$564$	7.37951	+	11.8097i	0.310733	+	0.497277i
$565$	10.2469	+	0.357829i	0.431089	+	0.0150540i
$566$	−3.60209	−	2.42964i	−0.151407	−	0.102126i
$567$	−0.201917	−	0.0503435i	−0.00847971	−	0.00211423i
$568$	−2.51619	−	4.73226i	−0.105577	−	0.198561i
$569$	−10.9771	+	33.7840i	−0.460184	+	1.41630i	0.404756	+	0.914425i	$0.367356\pi$
$569$	−10.9771	+	33.7840i	−0.460184	+	1.41630i	−0.864940	+	0.501875i	$0.832644\pi$
$570$	0.735289	−	13.2880i	0.0307979	−	0.556574i
$571$			28.0582i			1.17420i	0.809514	+	0.587100i	$0.199731\pi$
$571$			28.0582i			1.17420i	−0.809514	+	0.587100i	$0.800269\pi$
$572$	1.45238	−	2.95333i	0.0607272	−	0.123485i
$573$	−43.4965	−	51.8371i	−1.81709	−	2.16552i
$574$	0.0655684	−	0.228664i	0.00273677	−	0.00954426i
$575$	19.3685	−	24.7905i	0.807722	−	1.03384i
$576$	1.89088	−	4.68008i	0.0787865	−	0.195003i
$577$	4.44214	+	42.2641i	0.184929	+	1.75948i	0.556289	+	0.830989i	$0.312225\pi$
$577$	4.44214	+	42.2641i	0.184929	+	1.75948i	−0.371361	+	0.928489i	$0.621109\pi$
$578$	−1.50792	−	0.671367i	−0.0627210	−	0.0279252i
$579$	−9.31611	−	66.2876i	−0.387164	−	2.75482i
$580$	−2.47640	−	1.31673i	−0.102827	−	0.0546741i
$581$	0.0449539	−	0.427708i	0.00186500	−	0.0177443i
$582$	0.401465	−	0.695357i	0.0166412	−	0.0288235i
$583$	−1.80370	+	24.6387i	−0.0747018	+	1.02043i
$584$	−0.885738	+	2.43355i	−0.0366521	+	0.100701i
$585$	−5.18194	−	1.48590i	−0.214247	−	0.0614343i
$586$	−0.0592955	−	0.146762i	−0.00244948	−	0.00606266i
$587$	6.23866	−	3.31715i	0.257497	−	0.136914i	−0.335705	−	0.941967i	$-0.608975\pi$
$587$	6.23866	−	3.31715i	0.257497	−	0.136914i	0.593202	+	0.805054i	$0.297863\pi$
$588$	11.6317	+	16.0096i	0.479682	+	0.660226i
$589$	3.63585	+	23.3976i	0.149813	+	0.964082i
$590$	−2.62698	+	0.853559i	−0.108151	+	0.0351405i
$591$	−29.8956	−	4.20155i	−1.22974	−	0.172829i
$592$	−0.336199	−	4.80787i	−0.0138177	−	0.197602i
$593$	−11.8555	−	32.5727i	−0.486846	−	1.33760i	−0.903521	−	0.428543i	$-0.859027\pi$
$593$	−11.8555	−	32.5727i	−0.486846	−	1.33760i	0.416675	−	0.909055i	$-0.363195\pi$
$594$	−15.1427	−	11.9106i	−0.621313	−	0.488696i
$595$	0.554719	+	0.465464i	0.0227412	+	0.0190822i
$596$	−0.419373	−	0.941928i	−0.0171782	−	0.0385829i
$597$	4.50501	+	21.1944i	0.184378	+	0.867429i
$598$	8.04701	−	1.13093i	0.329067	−	0.0462473i
$599$	38.0600	−	18.5631i	1.55509	−	0.758467i	0.557655	−	0.830073i	$-0.311701\pi$
$599$	38.0600	−	18.5631i	1.55509	−	0.758467i	0.997433	+	0.0716057i	$0.0228123\pi$
$600$	−4.43271	+	9.95603i	−0.180965	+	0.406453i
$601$	−47.3828	−	10.0715i	−1.93279	−	0.410826i	−0.998529	−	0.0542281i	$-0.982730\pi$
$601$	−47.3828	−	10.0715i	−1.93279	−	0.410826i	−0.934258	−	0.356598i	$-0.883936\pi$
$602$	0.343470	−	0.214624i	0.0139988	−	0.00874742i
$603$	−20.9519	+	14.1322i	−0.853226	+	0.575508i
$604$	−14.2915	+	5.20169i	−0.581514	+	0.211654i
$605$	9.11847	−	7.55046i	0.370718	−	0.306970i
$606$	−7.52603	−	42.6823i	−0.305724	−	1.73385i
$607$	20.2505	+	14.7129i	0.821944	+	0.597177i	0.917269	−	0.398269i	$-0.130389\pi$
$607$	20.2505	+	14.7129i	0.821944	+	0.597177i	−0.0953245	+	0.995446i	$0.530389\pi$
$608$	−2.48973	−	3.57788i	−0.100972	−	0.145102i
$609$	0.355917	+	1.09540i	0.0144225	+	0.0443878i
$610$	−10.8665	+	11.2526i	−0.439972	+	0.455605i
$611$	1.17844	−	4.72648i	0.0476747	−	0.191213i
$612$	17.1778	−	13.4207i	0.694370	−	0.542501i
$613$	13.9810	+	10.9231i	0.564687	+	0.441182i	0.857129	−	0.515102i	$-0.172246\pi$
$613$	13.9810	+	10.9231i	0.564687	+	0.441182i	−0.292442	+	0.956283i	$0.594468\pi$
$614$	−3.19158	−	12.8007i	−0.128802	−	0.516596i
$615$	−4.03715	−	2.33085i	−0.162794	−	0.0939890i
$616$	−0.105783	−	0.505776i	−0.00426210	−	0.0203783i
$617$	−7.08491	+	40.1805i	−0.285228	+	1.61761i	0.419242	+	0.907874i	$0.362296\pi$
$617$	−7.08491	+	40.1805i	−0.285228	+	1.61761i	−0.704470	+	0.709733i	$0.748815\pi$
$618$	−7.28626	+	7.03626i	−0.293096	+	0.283040i
$619$	−25.4091	+	5.40087i	−1.02128	+	0.217079i	−0.687970	−	0.725739i	$-0.741498\pi$
$619$	−25.4091	+	5.40087i	−1.02128	+	0.217079i	−0.333308	+	0.942818i	$0.608165\pi$
$620$	−1.21554	+	5.71865i	−0.0488171	+	0.229667i
$621$	3.31820	−	47.4525i	0.133155	−	1.90420i
$622$	−9.28816	+	2.66334i	−0.372421	+	0.106790i
$623$	−1.16310	−	1.48870i	−0.0465986	−	0.0596434i
$624$	−2.61006	+	1.05453i	−0.104486	+	0.0422150i
$625$	3.93087	−	8.05948i	0.157235	−	0.322379i
$626$	−29.0595			−1.16145
$627$	−38.8591	+	13.1121i	−1.55188	+	0.523649i
$628$	−11.0894			−0.442517
$629$	9.12433	−	18.7076i	0.363811	−	0.745923i
$630$	−0.784740	+	0.317056i	−0.0312648	+	0.0126318i
$631$	4.43343	+	5.67453i	0.176492	+	0.225899i	0.868120	−	0.496355i	$-0.165328\pi$
$631$	4.43343	+	5.67453i	0.176492	+	0.225899i	−0.691628	+	0.722254i	$0.743106\pi$
$632$	−12.5682	+	3.60388i	−0.499938	+	0.143355i
$633$	−4.75808	+	68.0437i	−0.189117	+	2.70449i
$634$	−6.52539	+	30.6996i	−0.259156	+	1.21924i
$635$	−7.12574	+	1.51462i	−0.282776	+	0.0601060i
$636$	15.2002	−	14.6787i	0.602729	−	0.582048i
$637$	1.20201	−	6.81696i	0.0476255	−	0.270098i
$638$	−0.931489	+	8.59275i	−0.0368780	+	0.340190i
$639$	23.4289	+	13.5267i	0.926833	+	0.535107i
$640$	−0.260368	−	1.04428i	−0.0102920	−	0.0412788i
$641$	−21.6449	−	16.9108i	−0.854920	−	0.667937i	0.0897478	−	0.995965i	$-0.471394\pi$
$641$	−21.6449	−	16.9108i	−0.854920	−	0.667937i	−0.944668	+	0.328028i	$0.893616\pi$
$642$	−27.9594	+	21.8442i	−1.10347	+	0.862124i
$643$	0.994667	−	3.98939i	0.0392258	−	0.157326i	−0.947489	−	0.319789i	$-0.896388\pi$
$643$	0.994667	−	3.98939i	0.0392258	−	0.157326i	0.986715	+	0.162462i	$0.0519436\pi$
$644$	0.886262	−	0.917751i	0.0349236	−	0.0361645i
$645$	−2.45267	−	7.54854i	−0.0965737	−	0.297223i
$646$	−1.58593	−	18.7576i	−0.0623974	−	0.738007i
$647$	−16.9972	−	12.3492i	−0.668229	−	0.485497i	0.201203	−	0.979550i	$-0.435515\pi$
$647$	−16.9972	−	12.3492i	−0.668229	−	0.485497i	−0.869432	+	0.494053i	$0.835515\pi$
$648$	0.231942	+	1.31541i	0.00911154	+	0.0516741i
$649$	5.45014	+	6.53843i	0.213937	+	0.256656i
$650$	3.58226	−	1.30384i	0.140508	−	0.0511407i
$651$	1.99042	−	1.34255i	0.0780105	−	0.0526188i
$652$	8.44852	−	5.27922i	0.330869	−	0.206750i
$653$	−33.9369	−	7.21352i	−1.32805	−	0.282287i	−0.511365	−	0.859364i	$-0.670860\pi$
$653$	−33.9369	−	7.21352i	−1.32805	−	0.282287i	−0.816690	+	0.577077i	$0.804193\pi$
$654$	16.9290	−	38.0232i	0.661976	−	1.48682i
$655$	1.99369	−	0.972385i	0.0778997	−	0.0379942i
$656$	−1.51199	+	0.212497i	−0.0590335	+	0.00829661i
$657$	−2.71782	−	12.7863i	−0.106032	−	0.498842i
$658$	−0.311069	−	0.698672i	−0.0121267	−	0.0272371i
$659$	−28.8320	−	24.1929i	−1.12314	−	0.942422i	−0.124377	−	0.992235i	$-0.539693\pi$
$659$	−28.8320	−	24.1929i	−1.12314	−	0.942422i	−0.998759	+	0.0498126i	$0.984138\pi$
$660$	−10.1188	−	0.386412i	−0.393872	−	0.0150411i
$661$	9.10494	+	25.0156i	0.354141	+	0.972995i	0.981025	+	0.193882i	$0.0621079\pi$
$661$	9.10494	+	25.0156i	0.354141	+	0.972995i	−0.626884	+	0.779113i	$0.715670\pi$
$662$	1.70621	+	24.3999i	0.0663136	+	0.948329i
$663$	−12.0388	−	1.69194i	−0.467548	−	0.0657096i
$664$	−2.62531	+	0.853014i	−0.101882	+	0.0331034i
$665$	−0.141553	+	0.717046i	−0.00548918	+	0.0278059i
$666$	14.2994	+	19.6815i	0.554092	+	0.762642i
$667$	−18.8425	+	10.0188i	−0.729586	+	0.387928i
$668$	5.87718	+	14.5465i	0.227395	+	0.562823i
$669$	50.4306	+	14.4607i	1.94976	+	0.559085i
$670$	−1.84300	+	5.06360i	−0.0712014	+	0.195624i
$671$	44.6368	+	18.2041i	1.72319	+	0.702760i
$672$	−0.220985	+	0.382758i	−0.00852469	+	0.0147652i
$673$	4.67992	−	44.5264i	0.180398	−	1.71637i	−0.412389	−	0.911008i	$-0.635305\pi$
$673$	4.67992	−	44.5264i	0.180398	−	1.71637i	0.592786	−	0.805360i	$-0.298028\pi$
$674$	23.1890	+	12.3298i	0.893207	+	0.474927i
$675$	−3.10573	−	22.0984i	−0.119540	−	0.850568i
$676$	−10.9765	−	4.88707i	−0.422174	−	0.187964i
$677$	3.82518	+	36.3942i	0.147014	+	1.39874i	0.780582	+	0.625054i	$0.214923\pi$
$677$	3.82518	+	36.3942i	0.147014	+	1.39874i	−0.633568	+	0.773687i	$0.718410\pi$
$678$	−10.1240	+	25.0578i	−0.388810	+	0.962340i
$679$	−0.0271484	+	0.0347484i	−0.00104186	+	0.00133352i
$680$	1.28114	−	4.46788i	0.0491296	−	0.171335i
$681$	−5.02279	−	5.98592i	−0.192474	−	0.229381i
$682$	17.7530	−	3.07064i	0.679797	−	0.117581i
$683$		−	20.5750i		−	0.787282i	−0.919264	−	0.393641i	$-0.871215\pi$
$683$		−	20.5750i		−	0.787282i	0.919264	−	0.393641i	$-0.128785\pi$
$684$	20.2279	+	8.65599i	0.773432	+	0.330970i
$685$	−5.82835	+	17.9378i	−0.222690	+	0.685369i
$686$	−1.02222	−	1.92251i	−0.0390284	−	0.0734018i
$687$	52.3143	+	13.0434i	1.99591	+	0.497637i
$688$	−2.15518	−	1.45369i	−0.0821655	−	0.0554213i
$689$	−7.38699	−	0.257959i	−0.281422	−	0.00982747i
$690$	−13.2492	−	21.2031i	−0.504387	−	0.807188i
$691$	−8.34279	+	3.71445i	−0.317375	+	0.141304i	−0.559241	−	0.829005i	$-0.688907\pi$
$691$	−8.34279	+	3.71445i	−0.317375	+	0.141304i	0.241866	+	0.970310i	$0.422241\pi$
$692$	−2.37169	−	4.10788i	−0.0901581	−	0.156158i
$693$	1.80569	+	1.88209i	0.0685924	+	0.0714948i
$694$	−3.86908	−	0.682224i	−0.146868	−	0.0258969i
$695$	−15.4497	−	1.62383i	−0.586041	−	0.0615954i
$696$	5.49390	−	4.94673i	0.208246	−	0.187505i
$697$	−6.11378	−	2.47013i	−0.231576	−	0.0935628i
$698$	−3.00022	−	10.4630i	−0.113560	−	0.396031i
$699$	22.5591	−	33.4453i	0.853264	−	1.26502i
$700$	0.317169	−	0.507577i	0.0119879	−	0.0191846i
$701$	3.69521	−	26.2928i	0.139566	−	0.993065i	−0.787005	−	0.616946i	$-0.788370\pi$
$701$	3.69521	−	26.2928i	0.139566	−	0.993065i	0.926571	−	0.376119i	$-0.122742\pi$
$702$	3.38809	−	4.66330i	0.127875	−	0.176005i
$703$	20.9825	−	1.03825i	0.791371	−	0.0391584i
$704$	−2.68955	+	1.94070i	−0.101366	+	0.0731428i
$705$	−14.7599	+	2.60256i	−0.555889	+	0.0980182i
$706$	31.9979	−	2.23751i	1.20426	−	0.0842099i
$707$	0.0830692	+	2.37879i	0.00312414	+	0.0894636i
$708$	0.254092	−	7.27625i	0.00954937	−	0.273458i
$709$	−7.27773	−	0.508909i	−0.273321	−	0.0191125i	−0.0675617	−	0.997715i	$-0.521522\pi$
$709$	−7.27773	−	0.508909i	−0.273321	−	0.0191125i	−0.205759	+	0.978603i	$0.565966\pi$
$710$	5.73668	−	0.602950i	0.215294	−	0.0226283i
$711$	44.1602	−	49.0449i	1.65614	−	1.83933i
$712$	−5.69278	+	10.7066i	−0.213346	+	0.401246i
$713$	30.9015	+	31.9994i	1.15727	+	1.19839i
$714$	−1.65299	+	0.954355i	−0.0618616	+	0.0357158i
$715$	2.36152	+	2.64000i	0.0883158	+	0.0987305i
$716$	2.75645	−	3.28501i	0.103013	−	0.122767i
$717$	20.8181	+	30.8641i	0.777466	+	1.15264i
$718$	−20.2290	+	0.706411i	−0.754938	+	0.0263630i
$719$	32.8452	+	20.5240i	1.22492	+	0.765415i	0.978997	−	0.203874i	$-0.0653532\pi$
$719$	32.8452	+	20.5240i	1.22492	+	0.765415i	0.245924	+	0.969289i	$0.420909\pi$
$720$	3.90782	+	3.77374i	0.145636	+	0.140639i
$721$	0.450042	−	0.326975i	0.0167605	−	0.0121772i
$722$	15.8135	−	10.5325i	0.588516	−	0.391981i
$723$	51.9711	+	16.8864i	1.93283	+	0.628014i
$724$	−3.10286	−	1.51337i	−0.115317	−	0.0562438i
$725$	−7.66918	+	6.43521i	−0.284826	+	0.238998i
$726$	10.4812	+	29.3923i	0.388995	+	1.09085i
$727$	19.7985	+	7.20607i	0.734286	+	0.267258i	0.681978	−	0.731373i	$-0.261120\pi$
$727$	19.7985	+	7.20607i	0.734286	+	0.267258i	0.0523080	+	0.998631i	$0.483342\pi$
$728$	0.150008	−	0.0374011i	0.00555965	−	0.00138618i
$729$	28.5676	+	31.7276i	1.05806	+	1.17510i
$730$	−2.07129	−	1.86499i	−0.0766618	−	0.0690266i
$731$	−4.92151	−	10.0906i	−0.182028	−	0.373214i
$732$	−18.0752	−	37.0596i	−0.668077	−	1.36976i
$733$	8.49002	+	7.64445i	0.313586	+	0.282354i	0.810861	−	0.585239i	$-0.198999\pi$
$733$	8.49002	+	7.64445i	0.313586	+	0.282354i	−0.497275	+	0.867593i	$0.665666\pi$
$734$	17.1846	+	19.0855i	0.634297	+	0.704458i
$735$	−20.6653	+	5.15243i	−0.762249	+	0.190050i
$736$	−7.69516	−	2.80081i	−0.283647	−	0.103239i
$737$	16.5974	−	0.525384i	0.611373	−	0.0193528i
$738$	5.90390	−	4.95396i	0.217326	−	0.182358i
$739$	25.2811	+	12.3304i	0.929982	+	0.453582i	0.840138	−	0.542373i	$-0.182474\pi$
$739$	25.2811	+	12.3304i	0.929982	+	0.453582i	0.0898443	+	0.995956i	$0.471363\pi$
$740$	4.93323	+	1.60290i	0.181349	+	0.0589239i
$741$	−4.36389	−	11.4682i	−0.160311	−	0.421296i
$742$	−0.938856	+	0.682119i	−0.0344665	+	0.0250414i
$743$	−1.04594	−	1.01005i	−0.0383717	−	0.0370551i	0.675225	−	0.737611i	$-0.264046\pi$
$743$	−1.04594	−	1.01005i	−0.0383717	−	0.0370551i	−0.713597	+	0.700556i	$0.752935\pi$
$744$	−13.0687	−	8.16620i	−0.479120	−	0.299387i
$745$	1.10901	−	0.0387275i	0.0406310	−	0.00141887i
$746$	−11.4609	−	16.9915i	−0.419614	−	0.622103i
$747$	8.95631	−	10.6737i	0.327694	−	0.390531i
$748$	−14.2496	+	1.45071i	−0.521018	+	0.0530432i
$749$	1.68753	−	0.974294i	0.0616609	−	0.0355999i
$750$	−18.7523	−	19.4185i	−0.684736	−	0.709064i
$751$	−21.4694	+	40.3781i	−0.783429	+	1.47342i	0.0949656	+	0.995481i	$0.469726\pi$
$751$	−21.4694	+	40.3781i	−0.783429	+	1.47342i	−0.878395	+	0.477936i	$0.841385\pi$
$752$	−3.28469	+	3.64802i	−0.119780	+	0.133030i
$753$	−63.5913	+	6.68372i	−2.31740	+	0.243568i
$754$	−2.57967	−	0.180388i	−0.0939459	−	0.00656934i
$755$	0.571248	−	16.3584i	0.0207899	−	0.595344i
$756$	−0.0315838	−	0.904442i	−0.00114869	−	0.0328942i
$757$	1.33256	−	0.0931820i	0.0484329	−	0.00338676i	−0.0455195	−	0.998963i	$-0.514494\pi$
$757$	1.33256	−	0.0931820i	0.0484329	−	0.00338676i	0.0939524	+	0.995577i	$0.470050\pi$
$758$	27.2728	−	4.80892i	0.990591	−	0.174668i
$759$	−45.4909	+	62.1852i	−1.65121	+	2.25718i
$760$	4.57409	−	1.04196i	0.165920	−	0.0377958i
$761$	8.71427	−	11.9942i	0.315892	−	0.434788i	−0.621315	−	0.783561i	$-0.713401\pi$
$761$	8.71427	−	11.9942i	0.315892	−	0.434788i	0.937207	+	0.348772i	$0.113401\pi$
$762$	2.67240	−	19.0151i	0.0968110	−	0.688846i
$763$	−1.21130	+	1.93849i	−0.0438521	+	0.0701781i
$764$	13.3387	−	19.7755i	0.482578	−	0.715451i
$765$	6.46674	+	22.5522i	0.233806	+	0.815377i
$766$	14.0270	+	5.66728i	0.506817	+	0.204767i
$767$	−1.89261	+	1.70412i	−0.0683383	+	0.0615320i
$768$	2.82129	+	0.296530i	0.101805	+	0.0107001i
$769$	−49.2377	−	8.68193i	−1.77556	−	0.313078i	−0.812616	−	0.582799i	$-0.801958\pi$
$769$	−49.2377	−	8.68193i	−1.77556	−	0.313078i	−0.962939	+	0.269721i	$0.913069\pi$
$770$	0.547353	+	0.0983555i	0.0197252	+	0.00354449i
$771$	−19.7872	−	34.2725i	−0.712619	−	1.23429i
$772$	21.5564	−	9.59751i	0.775830	−	0.345422i
$773$	8.00477	+	12.8103i	0.287912	+	0.460755i	0.960113	−	0.279614i	$-0.0902065\pi$
$773$	8.00477	+	12.8103i	0.287912	+	0.460755i	−0.672201	+	0.740369i	$0.734651\pi$
$774$	13.1139	+	0.457948i	0.471370	+	0.0164606i
$775$	17.3010	+	11.6697i	0.621472	+	0.419188i
$776$	0.274630	+	0.0684728i	0.00985863	+	0.00245803i
$777$	−1.00003	−	1.88079i	−0.0358760	−	0.0674730i
$778$	3.94448	−	12.1399i	0.141416	−	0.435235i
$779$	−0.791807	−	6.60813i	−0.0283694	−	0.236761i
$780$		−	3.02968i		−	0.108480i
$781$	−8.29400	−	15.7223i	−0.296783	−	0.562587i
$782$	−22.7324	−	27.0915i	−0.812910	−	0.968788i
$783$	−4.17251	+	14.5513i	−0.149113	+	0.520020i
$784$	−4.29469	+	5.49695i	−0.153382	+	0.196320i
$785$	4.47093	−	11.0659i	0.159574	−	0.394960i
$786$	0.611156	+	5.81476i	0.0217992	+	0.207406i
$787$	−4.37357	−	1.94724i	−0.155901	−	0.0694115i	0.327303	−	0.944920i	$-0.393860\pi$
$787$	−4.37357	−	1.94724i	−0.155901	−	0.0694115i	−0.483204	+	0.875508i	$0.660527\pi$
$788$	−1.48107	−	10.5384i	−0.0527609	−	0.375413i
$789$	24.0792	+	12.8031i	0.857242	+	0.455803i
$790$	1.47089	−	13.9946i	0.0523319	−	0.497905i
$791$	0.742117	−	1.28538i	0.0263866	−	0.0457030i
$792$	6.32194	−	15.5015i	0.224640	−	0.550823i
$793$	−4.93296	+	13.5532i	−0.175175	+	0.481288i
$794$	16.7005	+	4.78880i	0.592680	+	0.169948i
$795$	8.51932	+	21.0860i	0.302149	+	0.747845i
$796$	−6.74400	+	3.58585i	−0.239035	+	0.127097i
$797$	26.1996	+	36.0606i	0.928036	+	1.27733i	0.960621	+	0.277864i	$0.0896263\pi$
$797$	26.1996	+	36.0606i	0.928036	+	1.27733i	−0.0325841	+	0.999469i	$0.510374\pi$
$798$	−1.64843	−	0.997038i	−0.0583539	−	0.0352948i
$799$	−20.1621	+	6.55108i	−0.713285	+	0.231760i
$800$	−3.80430	−	0.534659i	−0.134502	−	0.0189031i
$801$	−4.26961	−	61.0582i	−0.150859	−	2.15739i
$802$	5.25687	+	14.4431i	0.185626	+	0.510004i
$803$	−2.96398	+	8.06153i	−0.104597	+	0.284485i
$804$	−10.8805	−	9.12983i	−0.383726	−	0.321984i
$805$	0.558492	+	1.25439i	0.0196843	+	0.0442116i
$806$	1.12074	+	5.27267i	0.0394764	+	0.185722i
$807$	56.8311	−	7.98708i	2.00055	−	0.281159i
$808$	13.7316	−	6.69736i	0.483077	−	0.235612i
$809$	−14.1274	+	31.7307i	−0.496694	+	1.11559i	0.475137	+	0.879912i	$0.342399\pi$
$809$	−14.1274	+	31.7307i	−0.496694	+	1.11559i	−0.971831	+	0.235681i	$0.924268\pi$
$810$	−1.40613	−	0.298883i	−0.0494065	−	0.0105017i
$811$	−41.4473	+	25.8991i	−1.45541	+	0.909442i	−0.455596	+	0.890186i	$0.650574\pi$
$811$	−41.4473	+	25.8991i	−1.45541	+	0.909442i	−0.999815	+	0.0192553i	$0.993870\pi$
$812$	−0.336594	+	0.227035i	−0.0118121	+	0.00796738i
$813$	−31.8195	+	11.5813i	−1.11596	+	0.406176i
$814$	−1.06302	−	15.9495i	−0.0372587	−	0.559028i
$815$	1.86184	+	10.5590i	0.0652175	+	0.369867i
$816$	9.91148	+	7.20111i	0.346971	+	0.252089i
$817$	6.52653	−	9.26319i	0.228334	−	0.324078i
$818$	−3.42841	−	10.5516i	−0.119872	−	0.368927i
$819$	−0.542086	+	0.561346i	−0.0189420	+	0.0196150i
$820$	0.397544	−	1.59446i	0.0138828	−	0.0556811i
$821$	−23.7042	+	18.5197i	−0.827281	+	0.646343i	−0.937663	−	0.347547i	$-0.887015\pi$
$821$	−23.7042	+	18.5197i	−0.827281	+	0.646343i	0.110382	+	0.993889i	$0.464793\pi$
$822$	−39.1757	−	30.6074i	−1.36641	−	1.06756i
$823$	−8.81720	−	35.3639i	−0.307348	−	1.23271i	−0.903062	−	0.429510i	$-0.858686\pi$
$823$	−8.81720	−	35.3639i	−0.307348	−	1.23271i	0.595714	−	0.803197i	$-0.296869\pi$
$824$	−3.09220	−	1.78528i	−0.107722	−	0.0621932i
$825$	−14.8093	+	32.9723i	−0.515593	+	1.14795i
$826$	−0.0694333	+	0.393776i	−0.00241589	+	0.0137012i
$827$	10.2269	−	9.87599i	0.355624	−	0.343422i	−0.495290	−	0.868728i	$-0.664938\pi$
$827$	10.2269	−	9.87599i	0.355624	−	0.343422i	0.850913	+	0.525306i	$0.176049\pi$
$828$	40.4319	−	8.59406i	1.40510	−	0.298664i
$829$	2.46106	−	11.5784i	0.0854761	−	0.402134i	−0.914521	−	0.404538i	$-0.867432\pi$
$829$	2.46106	−	11.5784i	0.0854761	−	0.402134i	0.999997	+	0.00240494i	$0.000765516\pi$
$830$	0.207239	−	2.96365i	0.00719337	−	0.102870i
$831$	37.8055	−	10.8406i	1.31146	−	0.376055i
$832$	−0.610931	−	0.781955i	−0.0211802	−	0.0271094i
$833$	−27.9320	+	11.2853i	−0.967786	+	0.391011i
$834$	17.9502	−	36.8033i	0.621564	−	1.27439i
$835$	−16.8852			−0.584337
$836$	−8.21874	−	11.8934i	−0.284251	−	0.411341i
$837$	31.5546			1.09069
$838$	−3.74146	+	7.67114i	−0.129247	+	0.264995i
$839$	−15.4152	+	6.22813i	−0.532191	+	0.215019i	−0.624943	−	0.780670i	$-0.714878\pi$
$839$	−15.4152	+	6.22813i	−0.532191	+	0.215019i	0.0927525	+	0.995689i	$0.470433\pi$
$840$	−0.292852	−	0.374833i	−0.0101044	−	0.0129330i
$841$	−21.3485	+	6.12158i	−0.736154	+	0.211089i
$842$	−2.15785	+	30.8586i	−0.0743643	+	1.06346i
$843$	−6.08172	+	28.6123i	−0.209466	+	0.985458i
$844$	−23.5189	+	4.99910i	−0.809554	+	0.172076i
$845$	9.30212	−	8.98296i	0.320003	−	0.309023i
$846$	4.30271	−	24.4019i	0.147930	−	0.838953i
$847$	−0.345367	−	1.67861i	−0.0118669	−	0.0576776i
$848$	6.45079	+	3.72436i	0.221521	+	0.127895i
$849$	2.98188	+	11.9597i	0.102338	+	0.410455i
$850$	−13.0738	−	10.2143i	−0.448426	−	0.350349i
$851$	31.1011	−	24.2989i	1.06613	−	0.832954i
$852$	−3.67826	+	14.7527i	−0.126015	+	0.505419i
$853$	15.4965	−	16.0471i	0.530589	−	0.549441i	−0.399520	−	0.916724i	$-0.630823\pi$
$853$	15.4965	−	16.0471i	0.530589	−	0.549441i	0.930109	+	0.367284i	$0.119712\pi$
$854$	0.699758	+	2.15363i	0.0239452	+	0.0736958i
$855$	−16.7929	+	16.6952i	−0.574306	+	0.570964i
$856$	−10.1186	−	7.35156i	−0.345845	−	0.251271i
$857$	−4.81903	−	27.3301i	−0.164615	−	0.933578i	−0.949461	−	0.313886i	$-0.898369\pi$
$857$	−4.81903	−	27.3301i	−0.164615	−	0.933578i	0.784846	−	0.619691i	$-0.212742\pi$
$858$	−8.66794	+	3.46922i	−0.295919	+	0.118437i
$859$	−17.2376	+	6.27399i	−0.588141	+	0.214066i	−0.618911	−	0.785461i	$-0.712426\pi$
$859$	−17.2376	+	6.27399i	−0.588141	+	0.214066i	0.0307708	+	0.999526i	$0.490204\pi$
$860$	2.31951	−	1.56453i	0.0790947	−	0.0533500i
$861$	−0.572283	+	0.357602i	−0.0195034	+	0.0121871i
$862$	13.1017	+	2.78485i	0.446246	+	0.0948525i
$863$	3.48055	−	7.81745i	0.118479	−	0.266109i	−0.844564	−	0.535454i	$-0.820141\pi$
$863$	3.48055	−	7.81745i	0.118479	−	0.266109i	0.963044	+	0.269345i	$0.0868072\pi$
$864$	−5.22091	+	2.54641i	−0.177619	+	0.0866306i
$865$	5.05537	−	0.710487i	0.171888	−	0.0241573i
$866$	4.28689	+	20.1682i	0.145675	+	0.685345i
$867$	1.90456	+	4.27771i	0.0646822	+	0.145279i
$868$	0.648320	+	0.544005i	0.0220054	+	0.0184647i
$869$	−41.7229	+	11.8167i	−1.41535	+	0.400853i
$870$	2.72127	+	7.47663i	0.0922597	+	0.253481i
$871$	0.346573	+	4.95623i	0.0117432	+	0.167936i
$872$	14.5290	+	2.04192i	0.492015	+	0.0691482i
$873$	−1.35874	+	0.441482i	−0.0459865	+	0.0149419i
$874$	12.8892	−	33.2868i	0.435983	−	1.12594i
$875$	0.871417	+	1.19940i	0.0294593	+	0.0405472i
$876$	6.48668	−	3.44903i	0.219165	−	0.116532i
$877$	−8.68296	−	21.4911i	−0.293203	−	0.725703i	−0.999836	−	0.0181222i	$-0.994231\pi$
$877$	−8.68296	−	21.4911i	−0.293203	−	0.725703i	0.706633	−	0.707580i	$-0.250213\pi$
$878$	3.49194	+	1.00130i	0.117847	+	0.0337922i
$879$	−0.153579	+	0.421955i	−0.00518010	+	0.0142322i
$880$	−0.852240	−	3.46629i	−0.0287290	−	0.116848i
$881$	25.1601	−	43.5785i	0.847664	−	1.46820i	−0.0356236	−	0.999365i	$-0.511342\pi$
$881$	25.1601	−	43.5785i	0.847664	−	1.46820i	0.883288	−	0.468832i	$-0.155325\pi$
$882$	3.68054	−	35.0180i	0.123930	−	1.17912i
$883$	−13.2813	−	7.06181i	−0.446952	−	0.237649i	0.230709	−	0.973023i	$-0.425895\pi$
$883$	−13.2813	−	7.06181i	−0.446952	−	0.237649i	−0.677662	+	0.735374i	$0.737007\pi$
$884$	−0.596419	−	4.24375i	−0.0200598	−	0.142733i
$885$	7.15839	+	3.18712i	0.240627	+	0.107134i
$886$	−0.596139	−	5.67189i	−0.0200277	−	0.190551i
$887$	6.54129	−	16.1903i	0.219635	−	0.543616i	−0.776631	−	0.629956i	$-0.783073\pi$
$887$	6.54129	−	16.1903i	0.219635	−	0.543616i	0.996266	+	0.0863404i	$0.0275173\pi$
$888$	−8.41760	+	10.7740i	−0.282476	+	0.361553i
$889$	−0.290677	+	1.01371i	−0.00974898	+	0.0339987i
$890$	−8.38872	−	9.99729i	−0.281191	−	0.335110i
$891$	0.755027	+	4.36520i	0.0252944	+	0.146240i
$892$			18.4935i			0.619207i
$893$	−15.6064	−	14.6386i	−0.522248	−	0.489862i
$894$	−0.903866	+	2.78181i	−0.0302298	+	0.0930378i
$895$	2.16673	+	4.07503i	0.0724258	+	0.136213i
$896$	−0.151169	−	0.0376907i	−0.00505021	−	0.00125916i
$897$	−19.1113	−	12.8907i	−0.638107	−	0.430409i
$898$	−22.7380	−	0.794027i	−0.758776	−	0.0264970i
$899$	−7.50169	−	12.0052i	−0.250195	−	0.400396i
$900$	17.7149	−	7.88720i	0.590498	−	0.262907i
$901$	16.0842	+	27.8586i	0.535842	+	0.928105i
$902$	−5.01699	+	0.688408i	−0.167047	+	0.0229215i
$903$	−1.13150	−	0.199514i	−0.0376539	−	0.00663940i
$904$	−9.47453	−	0.995813i	−0.315118	−	0.0331203i
$905$	2.76114	−	2.48614i	0.0917834	−	0.0826421i
$906$	40.0030	+	16.1623i	1.32901	+	0.536955i
$907$	10.6228	+	37.0460i	0.352724	+	1.23009i	0.915105	+	0.403216i	$0.132108\pi$
$907$	10.6228	+	37.0460i	0.352724	+	1.23009i	−0.562381	+	0.826878i	$0.690115\pi$
$908$	1.54030	−	2.28359i	0.0511166	−	0.0757835i
$909$	−40.8657	+	65.3988i	−1.35543	+	2.16914i
$910$	−0.0231567	+	0.164769i	−0.000767638	+	0.00546203i
$911$	25.4733	−	35.0609i	0.843967	−	1.16162i	−0.141193	−	0.989982i	$-0.545094\pi$
$911$	25.4733	−	35.0609i	0.843967	−	1.16162i	0.985160	−	0.171639i	$-0.0549062\pi$
$912$	−1.54279	+	12.2689i	−0.0510868	+	0.406262i
$913$	−8.71634	+	2.80070i	−0.288469	+	0.0926898i
$914$	−25.5141	+	4.49882i	−0.843931	+	0.148808i
$915$	44.2684	−	3.09555i	1.46347	−	0.102336i
$916$	0.663287	+	18.9940i	0.0219156	+	0.627581i
$917$	0.0112063	−	0.320906i	0.000370064	−	0.0105972i
$918$	−25.0250	−	1.74992i	−0.825947	−	0.0577559i
$919$	10.7839	−	1.13344i	0.355729	−	0.0373887i	0.0750215	−	0.997182i	$-0.476097\pi$
$919$	10.7839	−	1.13344i	0.355729	−	0.0373887i	0.280708	+	0.959793i	$0.409431\pi$
$920$	5.89733	−	6.54965i	0.194429	−	0.215936i
$921$	−17.5701	+	33.0445i	−0.578954	+	1.08885i
$922$	6.61355	+	6.84853i	0.217806	+	0.225544i
$923$	4.60590	−	2.65922i	0.151605	−	0.0875291i
$924$	−0.737063	+	1.26707i	−0.0242476	+	0.0416834i
$925$	11.9015	−	14.1837i	0.391319	−	0.466356i
$926$	0.292439	+	0.433559i	0.00961015	+	0.0142476i
$927$	18.0119	−	0.628990i	0.591589	−	0.0206587i
$928$	2.21001	+	1.38096i	0.0725470	+	0.0453324i
$929$	−33.0752	−	31.9404i	−1.08516	−	1.04793i	−0.998664	−	0.0516773i	$-0.983543\pi$
$929$	−33.0752	−	31.9404i	−1.08516	−	1.04793i	−0.0864987	−	0.996252i	$-0.527568\pi$
$930$	13.4178	−	9.74859i	0.439987	−	0.319669i
$931$	−23.5743	−	19.2043i	−0.772618	−	0.629396i
$932$	13.5249	+	4.39449i	0.443021	+	0.143946i
$933$	24.6367	+	12.0161i	0.806569	+	0.393390i
$934$	−9.38491	+	7.87488i	−0.307084	+	0.257674i
$935$	4.29739	−	14.8043i	0.140540	−	0.484153i
$936$	4.70678	+	1.71313i	0.153846	+	0.0559953i
$937$	5.43232	−	1.35443i	0.177466	−	0.0442473i	−0.152175	−	0.988354i	$-0.548628\pi$
$937$	5.43232	−	1.35443i	0.177466	−	0.0442473i	0.329641	+	0.944106i	$0.393072\pi$
$938$	0.521952	+	0.579687i	0.0170424	+	0.0189275i
$939$	61.2625	+	55.1610i	1.99923	+	1.80011i
$940$	−2.31600	−	4.74851i	−0.0755396	−	0.154879i
$941$	4.81621	+	9.87469i	0.157004	+	0.321906i	0.962767	−	0.270332i	$-0.0871335\pi$
$941$	4.81621	+	9.87469i	0.157004	+	0.321906i	−0.805763	+	0.592238i	$0.798245\pi$
$942$	23.3785	+	21.0501i	0.761714	+	0.685850i
$943$	−8.36643	−	9.29186i	−0.272448	−	0.302584i
$944$	2.49025	−	0.620888i	0.0810506	−	0.0202082i
$945$	0.915259	+	0.333127i	0.0297734	+	0.0108366i
$946$	−7.13216	−	4.84463i	−0.231886	−	0.157513i
$947$	44.1474	−	37.0441i	1.43460	−	1.20377i	0.491667	−	0.870783i	$-0.336388\pi$
$947$	44.1474	−	37.0441i	1.43460	−	1.20377i	0.942931	−	0.332987i	$-0.108057\pi$
$948$	33.3370	+	16.2596i	1.08274	+	0.528086i
$949$	−2.44405	−	0.794120i	−0.0793372	−	0.0257782i
$950$	2.66784	−	16.5316i	0.0865560	−	0.536357i
$951$	72.0310	−	52.3336i	2.33577	−	1.69703i
$952$	−0.483994	−	0.467387i	−0.0156863	−	0.0151481i
$953$	30.3701	+	18.9773i	0.983783	+	0.614736i	0.923562	−	0.383449i	$-0.125264\pi$
$953$	30.3701	+	18.9773i	0.983783	+	0.614736i	0.0602213	+	0.998185i	$0.480819\pi$
$954$	−37.5756	+	1.31217i	−1.21655	+	0.0424830i
$955$	14.3558	+	21.2833i	0.464542	+	0.688712i
$956$	−8.43553	+	10.0531i	−0.272825	+	0.325140i
$957$	18.2746	−	16.3469i	0.590735	−	0.528420i
$958$	−25.7419	+	14.8621i	−0.831683	+	0.480172i
$959$	1.89662	+	1.96401i	0.0612451	+	0.0634211i
$960$	−1.43336	+	2.69577i	−0.0462616	+	0.0870054i
$961$	0.997769	−	1.10813i	0.0321861	−	0.0357463i
$962$	4.75638	−	0.499916i	0.153352	−	0.0161179i
$963$	62.9781	+	4.40386i	2.02944	+	0.141912i
$964$	−0.672266	+	19.2512i	−0.0216522	+	0.620038i
$965$	0.886293	+	25.3801i	0.0285308	+	0.817015i
$966$	−3.61049	+	0.252470i	−0.116166	+	0.00812308i
$967$	−14.0733	+	2.48151i	−0.452568	+	0.0798000i	−0.395286	−	0.918558i	$-0.629355\pi$
$967$	−14.0733	+	2.48151i	−0.452568	+	0.0798000i	−0.0572820	+	0.998358i	$0.518243\pi$
$968$	−8.94119	+	6.40743i	−0.287381	+	0.205943i
$969$	−32.2625	+	42.5548i	−1.03642	+	1.36706i
$970$	−0.179050	+	0.246442i	−0.00574896	+	0.00791276i
$971$	6.70467	−	47.7062i	0.215163	−	1.53096i	−0.520645	−	0.853773i	$-0.674308\pi$
$971$	6.70467	−	47.7062i	0.215163	−	1.53096i	0.735808	−	0.677191i	$-0.236803\pi$
$972$	−7.22663	+	11.5650i	−0.231794	+	0.370948i
$973$	−1.25752	+	1.86434i	−0.0403141	+	0.0597681i
$974$	−5.25389	−	18.3225i	−0.168346	−	0.587091i
$975$	−10.0270	−	4.05118i	−0.321122	−	0.129742i
$976$	10.8014	−	9.72561i	0.345744	−	0.311309i
$977$	3.61106	+	0.379537i	0.115528	+	0.0121425i	0.162116	−	0.986772i	$-0.448168\pi$
$977$	3.61106	+	0.379537i	0.115528	+	0.0121425i	−0.0465880	+	0.998914i	$0.514835\pi$
$978$	−27.8321	−	4.90755i	−0.889972	−	0.156926i
$979$	−18.9966	+	35.4479i	−0.607133	+	1.13292i
$980$	−3.75381	−	6.50179i	−0.119911	−	0.207692i
$981$	−67.6553	+	30.1221i	−2.16007	+	0.961724i
$982$	14.8922	+	23.8326i	0.475230	+	0.760527i
$983$	−27.9710	−	0.976768i	−0.892135	−	0.0311541i	−0.414837	−	0.909896i	$-0.636162\pi$
$983$	−27.9710	−	0.976768i	−0.892135	−	0.0311541i	−0.477298	+	0.878741i	$0.658384\pi$
$984$	3.59092	+	2.42211i	0.114474	+	0.0772139i
$985$	11.1132	+	2.77082i	0.354094	+	0.0882857i
$986$	5.28359	+	9.93698i	0.168264	+	0.316458i
$987$	−0.670439	+	2.06340i	−0.0213403	+	0.0656787i
$988$	3.46200	−	2.59300i	0.110141	−	0.0824943i
$989$		−	21.2883i		−	0.676929i
$990$	12.9199	+	12.5583i	0.410621	+	0.399129i
$991$	36.5186	+	43.5212i	1.16005	+	1.38250i	0.910178	+	0.414217i	$0.135944\pi$
$991$	36.5186	+	43.5212i	1.16005	+	1.38250i	0.249873	+	0.968279i	$0.419611\pi$
$992$	1.49732	−	5.22177i	0.0475399	−	0.165791i
$993$	42.7192	−	54.6781i	1.35565	−	1.73516i
$994$	0.312801	−	0.774210i	0.00992145	−	0.0245564i
$995$	−0.859271	−	8.17542i	−0.0272407	−	0.259178i
$996$	7.15382	+	3.18509i	0.226677	+	0.100923i
$997$	−5.74635	−	40.8874i	−0.181989	−	1.29492i	−0.840279	−	0.542154i	$-0.817609\pi$
$997$	−5.74635	−	40.8874i	−0.181989	−	1.29492i	0.658291	−	0.752764i	$-0.271280\pi$
$998$	24.8839	+	13.2310i	0.787686	+	0.418820i
$999$	2.92640	−	27.8428i	0.0925871	−	0.880907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.b.29.1	yes	240
11.8	odd	10		418.2.v.a.371.10	yes	240
19.2	odd	18		418.2.v.a.249.10	✓	240
209.173	even	90	inner	418.2.v.b.173.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.249.10	✓	240	19.2	odd	18
418.2.v.a.371.10	yes	240	11.8	odd	10
418.2.v.b.29.1	yes	240	1.1	even	1	trivial
418.2.v.b.173.1	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)

\(f(q)\)	\(=\)	\(q+(0.438371 - 0.898794i) q^{2} +(-2.63027 + 1.06270i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(1.03456 - 0.296655i) q^{5} +(-0.197888 + 2.82992i) q^{6} +(0.0323920 - 0.152392i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(3.63096 - 3.50638i) q^{9} +O(q^{10})\)	\(q+(0.438371 - 0.898794i) q^{2} +(-2.63027 + 1.06270i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(1.03456 - 0.296655i) q^{5} +(-0.197888 + 2.82992i) q^{6} +(0.0323920 - 0.152392i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(3.63096 - 3.50638i) q^{9} +(0.186889 - 1.05990i) q^{10} +(-3.24638 + 0.678977i) q^{11} +(2.45677 + 1.41842i) q^{12} +(-0.240063 - 0.962840i) q^{13} +(-0.122770 - 0.0959182i) q^{14} +(-2.40591 + 1.87970i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-2.99998 + 3.10657i) q^{17} +(-1.55980 - 4.80058i) q^{18} +(-4.20706 - 1.14045i) q^{19} +(-0.870704 - 0.632604i) q^{20} +(0.0767474 + 0.435256i) q^{21} +(-0.812859 + 3.21547i) q^{22} +(-7.69516 + 2.80081i) q^{23} +(2.35184 - 1.58634i) q^{24} +(-3.25794 + 2.03578i) q^{25} +(-0.970631 - 0.206314i) q^{26} +(-2.36265 + 5.30660i) q^{27} +(-0.140029 + 0.0682969i) q^{28} +(2.58063 - 0.362684i) q^{29} +(0.634784 + 2.98642i) q^{30} +(-2.20948 - 4.96257i) q^{31} +(0.766044 + 0.642788i) q^{32} +(7.81730 - 5.23581i) q^{33} +(1.47706 + 4.05819i) q^{34} +(-0.0116965 - 0.167268i) q^{35} +(-4.99851 - 0.702495i) q^{36} +(-4.58373 + 1.48934i) q^{37} +(-2.86928 + 3.28134i) q^{38} +(1.65464 + 2.27741i) q^{39} +(-0.950272 + 0.505269i) q^{40} +(0.571969 + 1.41567i) q^{41} +(0.424849 + 0.121824i) q^{42} +(-0.889121 + 2.44284i) q^{43} +(2.53371 + 2.14016i) q^{44} +(2.71626 - 4.70469i) q^{45} +(-0.855985 + 8.14416i) q^{46} +(4.33430 + 2.30459i) q^{47} +(-0.394811 - 2.80923i) q^{48} +(6.37264 + 2.83728i) q^{49} +(0.401566 + 3.82064i) q^{50} +(4.58940 - 11.3592i) q^{51} +(-0.610931 + 0.781955i) q^{52} +(2.05315 - 7.16018i) q^{53} +(3.73382 + 4.44980i) q^{54} +(-3.15715 + 1.66549i) q^{55} +0.155797i q^{56} +(12.2777 - 1.47115i) q^{57} +(0.805296 - 2.47844i) q^{58} +(-1.20489 - 2.26607i) q^{59} +(2.96245 + 0.738622i) q^{60} +(-12.0498 - 8.12770i) q^{61} +(-5.42890 - 0.189581i) q^{62} +(-0.416732 - 0.666910i) q^{63} +(0.913545 - 0.406737i) q^{64} +(-0.533990 - 0.924897i) q^{65} +(-1.27904 - 9.32138i) q^{66} +(-4.93074 - 0.869423i) q^{67} +(4.29498 + 0.451420i) q^{68} +(17.2639 - 15.5445i) q^{69} +(-0.155467 - 0.0628127i) q^{70} +(1.47731 + 5.15199i) q^{71} +(-2.82260 + 4.18468i) q^{72} +(1.37235 - 2.19621i) q^{73} +(-0.670761 + 4.77271i) q^{74} +(6.40582 - 8.81685i) q^{75} +(1.69144 + 4.01734i) q^{76} +(-0.00168583 + 0.516718i) q^{77} +(2.77227 - 0.488826i) q^{78} +(13.0429 - 0.912047i) q^{79} +(0.0375606 + 1.07559i) q^{80} +(0.0466153 - 1.33489i) q^{81} +(1.52313 + 0.106508i) q^{82} +(2.74529 - 0.288542i) q^{83} +(0.295736 - 0.328448i) q^{84} +(-2.18207 + 4.10388i) q^{85} +(1.80585 + 1.87001i) q^{86} +(-6.40232 + 3.69638i) q^{87} +(3.03427 - 1.33910i) q^{88} +(7.79440 - 9.28901i) q^{89} +(-3.03782 - 4.50376i) q^{90} +(-0.154506 + 0.00539546i) q^{91} +(6.94468 + 4.33952i) q^{92} +(11.0852 + 10.7049i) q^{93} +(3.97138 - 2.88538i) q^{94} +(-4.69077 + 0.0681840i) q^{95} +(-2.69799 - 0.876630i) q^{96} +(-0.254392 - 0.124075i) q^{97} +(5.34372 - 4.48391i) q^{98} +(-9.40674 + 13.8484i) 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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