LMFDB - Embedded newform 289.2.i.a.117.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(2,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(136))

chi = DirichletCharacter(H, H._module([95]))

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

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

chi := DirichletCharacter("289.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.i (of order $136$, degree $64$, 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:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$1600$
Relative dimension:	$25$ over $\Q(\zeta_{136})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{136}]$

Embedding invariants

Embedding label			117.16
Character	$\chi$	$=$	289.117
Dual form			289.2.i.a.42.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540824 + 0.789506i) q^{2} +(1.51234 - 1.73795i) q^{3} +(0.391654 - 1.01098i) q^{4} +(1.21780 - 1.69255i) q^{5} +(2.19003 + 0.254079i) q^{6} +(-2.93846 + 1.72682i) q^{7} +(2.87311 - 0.675749i) q^{8} +(-0.318816 - 2.28551i) q^{9} +O(q^{10})$	\(q+(0.540824 + 0.789506i) q^{2} +(1.51234 - 1.73795i) q^{3} +(0.391654 - 1.01098i) q^{4} +(1.21780 - 1.69255i) q^{5} +(2.19003 + 0.254079i) q^{6} +(-2.93846 + 1.72682i) q^{7} +(2.87311 - 0.675749i) q^{8} +(-0.318816 - 2.28551i) q^{9} +(1.99490 + 0.0460903i) q^{10} +(-3.90405 + 4.08872i) q^{11} +(-1.16471 - 2.20962i) q^{12} +(1.02339 - 1.65283i) q^{13} +(-2.95252 - 1.38602i) q^{14} +(-1.09983 - 4.67620i) q^{15} +(0.484904 + 0.442049i) q^{16} +(3.02196 + 2.80495i) q^{17} +(1.63200 - 1.48777i) q^{18} +(-0.288271 - 0.197470i) q^{19} +(-1.23417 - 1.89407i) q^{20} +(-1.44282 + 7.71843i) q^{21} +(-5.33947 - 0.870995i) q^{22} +(-2.58325 - 4.39581i) q^{23} +(3.17071 - 6.01528i) q^{24} +(0.207269 + 0.618407i) q^{25} +(1.85839 - 0.0859185i) q^{26} +(1.33640 + 0.870797i) q^{27} +(0.594917 + 3.64703i) q^{28} +(4.79053 - 0.110681i) q^{29} +(3.09707 - 3.39733i) q^{30} +(-0.675023 + 4.13810i) q^{31} +(0.728787 - 5.22450i) q^{32} +(1.20172 + 12.9686i) q^{33} +(-0.580171 + 3.90284i) q^{34} +(-0.655727 + 7.07642i) q^{35} +(-2.43547 - 0.572817i) q^{36} +(-2.23354 + 0.691648i) q^{37} -0.334388i q^{38} +(-1.32482 - 4.27823i) q^{39} +(2.35514 - 5.68582i) q^{40} +(0.627845 + 9.04532i) q^{41} +(-6.87406 + 3.03520i) q^{42} +(0.179546 - 3.88353i) q^{43} +(2.60456 + 5.54827i) q^{44} +(-4.25661 - 2.24370i) q^{45} +(2.07343 - 4.41685i) q^{46} +(2.42362 - 1.83023i) q^{47} +(1.50160 - 0.174210i) q^{48} +(2.24638 - 4.03303i) q^{49} +(-0.376140 + 0.498089i) q^{50} +(9.44510 - 1.00998i) q^{51} +(-1.27015 - 1.68196i) q^{52} +(-0.0836135 + 0.0116636i) q^{53} +(0.0352578 + 1.52604i) q^{54} +(2.16600 + 11.5871i) q^{55} +(-7.27561 + 6.94701i) q^{56} +(-0.779158 + 0.202358i) q^{57} +(2.67822 + 3.72230i) q^{58} +(-6.29884 - 11.3086i) q^{59} +(-5.15828 - 0.719550i) q^{60} +(0.0516351 - 0.445069i) q^{61} +(-3.63213 + 1.70505i) q^{62} +(4.88350 + 6.16535i) q^{63} +(5.69365 - 2.83510i) q^{64} +(-1.55121 - 3.74496i) q^{65} +(-9.58886 + 7.96248i) q^{66} +(-6.80847 + 1.27272i) q^{67} +(4.01930 - 1.95657i) q^{68} +(-11.5464 - 2.15840i) q^{69} +(-5.94151 + 3.30940i) q^{70} +(-5.30723 - 1.37836i) q^{71} +(-2.46043 - 6.35110i) q^{72} +(-3.05725 - 1.10387i) q^{73} +(-1.75401 - 1.38933i) q^{74} +(1.38822 + 0.575020i) q^{75} +(-0.312540 + 0.214095i) q^{76} +(4.41140 - 18.7561i) q^{77} +(2.66120 - 3.35972i) q^{78} +(-0.329327 + 1.56118i) q^{79} +(1.33871 - 0.282397i) q^{80} +(10.1931 - 2.90020i) q^{81} +(-6.80178 + 5.38762i) q^{82} +(-10.8113 + 3.62358i) q^{83} +(7.23806 + 4.48162i) q^{84} +(8.42768 - 1.69896i) q^{85} +(3.16317 - 1.95855i) q^{86} +(7.05257 - 8.49308i) q^{87} +(-8.45382 + 14.3855i) q^{88} +(-7.75082 - 12.5180i) q^{89} +(-0.530665 - 4.57407i) q^{90} +(-0.153040 + 6.62397i) q^{91} +(-5.45580 + 0.889971i) q^{92} +(6.17094 + 7.43138i) q^{93} +(2.75573 + 0.923627i) q^{94} +(-0.685287 + 0.247434i) q^{95} +(-7.97774 - 9.16783i) q^{96} +(-3.47443 + 13.3779i) q^{97} +(4.39900 - 0.407627i) q^{98} +(10.5895 + 7.61922i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1600 q - 64 q^{2} - 64 q^{3} - 68 q^{4} - 68 q^{5} - 72 q^{6} - 64 q^{7} - 72 q^{8} - 76 q^{9}+O(q^{10}) $ 1600 * q - 64 * q^2 - 64 * q^3 - 68 * q^4 - 68 * q^5 - 72 * q^6 - 64 * q^7 - 72 * q^8 - 76 * q^9	\( 1600 q - 64 q^{2} - 64 q^{3} - 68 q^{4} - 68 q^{5} - 72 q^{6} - 64 q^{7} - 72 q^{8} - 76 q^{9} - 72 q^{10} - 64 q^{11} - 64 q^{12} - 68 q^{13} - 72 q^{14} - 60 q^{15} + 40 q^{16} - 68 q^{17} - 72 q^{18} - 76 q^{19} - 72 q^{20} - 68 q^{21} - 80 q^{22} - 72 q^{23} + 260 q^{24} - 64 q^{25} - 64 q^{26} - 76 q^{27} - 72 q^{28} - 64 q^{29} - 68 q^{30} - 56 q^{31} - 72 q^{32} - 44 q^{33} - 48 q^{34} - 92 q^{35} - 68 q^{36} - 68 q^{37} + 204 q^{39} - 60 q^{40} - 64 q^{41} - 60 q^{42} - 60 q^{43} - 48 q^{44} - 80 q^{45} - 88 q^{46} - 68 q^{47} - 80 q^{48} - 76 q^{49} - 32 q^{50} - 96 q^{51} - 116 q^{52} - 64 q^{53} + 484 q^{54} - 68 q^{55} - 48 q^{56} - 44 q^{57} - 68 q^{58} - 68 q^{59} - 60 q^{60} - 68 q^{61} + 352 q^{62} - 56 q^{63} - 68 q^{64} - 64 q^{65} - 76 q^{66} - 44 q^{67} - 80 q^{68} - 92 q^{69} - 60 q^{70} - 88 q^{71} - 68 q^{72} - 40 q^{73} - 88 q^{74} - 56 q^{75} + 60 q^{76} + 604 q^{77} - 60 q^{78} - 64 q^{79} - 68 q^{80} - 68 q^{81} - 72 q^{82} - 84 q^{83} - 4 q^{84} + 268 q^{85} - 132 q^{86} - 84 q^{87} - 80 q^{88} - 68 q^{89} - 72 q^{90} - 68 q^{91} + 232 q^{92} - 92 q^{93} - 44 q^{94} - 60 q^{95} - 48 q^{96} - 92 q^{97} - 68 q^{98} - 64 q^{99}+O(q^{100}) \) 1600 * q - 64 * q^2 - 64 * q^3 - 68 * q^4 - 68 * q^5 - 72 * q^6 - 64 * q^7 - 72 * q^8 - 76 * q^9 - 72 * q^10 - 64 * q^11 - 64 * q^12 - 68 * q^13 - 72 * q^14 - 60 * q^15 + 40 * q^16 - 68 * q^17 - 72 * q^18 - 76 * q^19 - 72 * q^20 - 68 * q^21 - 80 * q^22 - 72 * q^23 + 260 * q^24 - 64 * q^25 - 64 * q^26 - 76 * q^27 - 72 * q^28 - 64 * q^29 - 68 * q^30 - 56 * q^31 - 72 * q^32 - 44 * q^33 - 48 * q^34 - 92 * q^35 - 68 * q^36 - 68 * q^37 + 204 * q^39 - 60 * q^40 - 64 * q^41 - 60 * q^42 - 60 * q^43 - 48 * q^44 - 80 * q^45 - 88 * q^46 - 68 * q^47 - 80 * q^48 - 76 * q^49 - 32 * q^50 - 96 * q^51 - 116 * q^52 - 64 * q^53 + 484 * q^54 - 68 * q^55 - 48 * q^56 - 44 * q^57 - 68 * q^58 - 68 * q^59 - 60 * q^60 - 68 * q^61 + 352 * q^62 - 56 * q^63 - 68 * q^64 - 64 * q^65 - 76 * q^66 - 44 * q^67 - 80 * q^68 - 92 * q^69 - 60 * q^70 - 88 * q^71 - 68 * q^72 - 40 * q^73 - 88 * q^74 - 56 * q^75 + 60 * q^76 + 604 * q^77 - 60 * q^78 - 64 * q^79 - 68 * q^80 - 68 * q^81 - 72 * q^82 - 84 * q^83 - 4 * q^84 + 268 * q^85 - 132 * q^86 - 84 * q^87 - 80 * q^88 - 68 * q^89 - 72 * q^90 - 68 * q^91 + 232 * q^92 - 92 * q^93 - 44 * q^94 - 60 * q^95 - 48 * q^96 - 92 * q^97 - 68 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{99}{136}\right)$

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 $

$2$	0.540824	+	0.789506i	0.382420	+	0.558265i	0.967552	−	0.252674i	$-0.0813099\pi$
$2$	0.540824	+	0.789506i	0.382420	+	0.558265i	−0.585131	+	0.810939i	$0.698957\pi$
$3$	1.51234	−	1.73795i	0.873151	−	1.00340i	−0.126783	−	0.991930i	$-0.540465\pi$
$3$	1.51234	−	1.73795i	0.873151	−	1.00340i	0.999934	−	0.0114745i	$-0.00365251\pi$
$4$	0.391654	−	1.01098i	0.195827	−	0.505488i
$5$	1.21780	−	1.69255i	0.544619	−	0.756933i	−0.445785	−	0.895140i	$-0.647075\pi$
$5$	1.21780	−	1.69255i	0.544619	−	0.756933i	0.990403	+	0.138208i	$0.0441341\pi$
$6$	2.19003	+	0.254079i	0.894077	+	0.103727i
$7$	−2.93846	+	1.72682i	−1.11063	+	0.652677i	−0.942874	−	0.333151i	$-0.891888\pi$
$7$	−2.93846	+	1.72682i	−1.11063	+	0.652677i	−0.167759	+	0.985828i	$0.553653\pi$
$8$	2.87311	−	0.675749i	1.01580	−	0.238913i
$9$	−0.318816	−	2.28551i	−0.106272	−	0.761838i
$10$	1.99490	+	0.0460903i	0.630842	+	0.0145750i
$11$	−3.90405	+	4.08872i	−1.17712	+	1.23279i	−0.210211	+	0.977656i	$0.567415\pi$
$11$	−3.90405	+	4.08872i	−1.17712	+	1.23279i	−0.966904	+	0.255139i	$0.917879\pi$
$12$	−1.16471	−	2.20962i	−0.336223	−	0.637862i
$13$	1.02339	−	1.65283i	0.283836	−	0.458412i	−0.676821	−	0.736148i	$-0.736643\pi$
$13$	1.02339	−	1.65283i	0.283836	−	0.458412i	0.960657	+	0.277736i	$0.0895841\pi$
$14$	−2.95252	−	1.38602i	−0.789095	−	0.370430i
$15$	−1.09983	−	4.67620i	−0.283976	−	1.20739i
$16$	0.484904	+	0.442049i	0.121226	+	0.110512i
$17$	3.02196	+	2.80495i	0.732934	+	0.680300i
$17$	3.02196	+	2.80495i	0.732934	+	0.680300i
$18$	1.63200	−	1.48777i	0.384667	−	0.350670i
$19$	−0.288271	−	0.197470i	−0.0661339	−	0.0453028i	0.531615	−	0.846986i	$-0.321585\pi$
$19$	−0.288271	−	0.197470i	−0.0661339	−	0.0453028i	−0.597749	+	0.801683i	$0.703938\pi$
$20$	−1.23417	−	1.89407i	−0.275969	−	0.423526i
$21$	−1.44282	+	7.71843i	−0.314850	+	1.68430i
$22$	−5.33947	−	0.870995i	−1.13838	−	0.185697i
$23$	−2.58325	−	4.39581i	−0.538645	−	0.916589i	−0.999575	−	0.0291521i	$-0.990719\pi$
$23$	−2.58325	−	4.39581i	−0.538645	−	0.916589i	0.460930	−	0.887437i	$-0.347516\pi$
$24$	3.17071	−	6.01528i	0.647218	−	1.22786i
$25$	0.207269	+	0.618407i	0.0414538	+	0.123681i
$26$	1.85839	−	0.0859185i	0.364460	−	0.0168500i
$27$	1.33640	+	0.870797i	0.257190	+	0.167585i
$28$	0.594917	+	3.64703i	0.112429	+	0.689223i
$29$	4.79053	−	0.110681i	0.889580	−	0.0205529i	0.424104	−	0.905614i	$-0.360589\pi$
$29$	4.79053	−	0.110681i	0.889580	−	0.0205529i	0.465476	+	0.885061i	$0.345883\pi$
$30$	3.09707	−	3.39733i	0.565446	−	0.620264i
$31$	−0.675023	+	4.13810i	−0.121238	+	0.743225i	0.853703	+	0.520760i	$0.174351\pi$
$31$	−0.675023	+	4.13810i	−0.121238	+	0.743225i	−0.974941	+	0.222465i	$0.928590\pi$
$32$	0.728787	−	5.22450i	0.128833	−	0.923570i
$33$	1.20172	+	12.9686i	0.209192	+	2.25754i
$34$	−0.580171	+	3.90284i	−0.0994985	+	0.669332i
$35$	−0.655727	+	7.07642i	−0.110838	+	1.19613i
$36$	−2.43547	−	0.572817i	−0.405911	−	0.0954695i
$37$	−2.23354	+	0.691648i	−0.367192	+	0.113706i	−0.473887	−	0.880586i	$-0.657150\pi$
$37$	−2.23354	+	0.691648i	−0.367192	+	0.113706i	0.106695	+	0.994292i	$0.465973\pi$
$38$		−	0.334388i		−	0.0542450i
$39$	−1.32482	−	4.27823i	−0.212140	−	0.685066i
$40$	2.35514	−	5.68582i	0.372381	−	0.899007i
$41$	0.627845	+	9.04532i	0.0980529	+	1.41264i	0.753523	+	0.657421i	$0.228353\pi$
$41$	0.627845	+	9.04532i	0.0980529	+	1.41264i	−0.655471	+	0.755221i	$0.727530\pi$
$42$	−6.87406	+	3.03520i	−1.06069	+	0.468341i
$43$	0.179546	−	3.88353i	0.0273806	−	0.592233i	−0.940344	−	0.340224i	$-0.889497\pi$
$43$	0.179546	−	3.88353i	0.0273806	−	0.592233i	0.967725	−	0.252009i	$-0.0810911\pi$
$44$	2.60456	+	5.54827i	0.392652	+	0.836433i
$45$	−4.25661	−	2.24370i	−0.634538	−	0.334471i
$46$	2.07343	−	4.41685i	0.305711	−	0.651229i
$47$	2.42362	−	1.83023i	0.353521	−	0.266966i	−0.410905	−	0.911678i	$-0.634787\pi$
$47$	2.42362	−	1.83023i	0.353521	−	0.266966i	0.764426	+	0.644712i	$0.223023\pi$
$48$	1.50160	−	0.174210i	0.216737	−	0.0251450i
$49$	2.24638	−	4.03303i	0.320912	−	0.576147i
$50$	−0.376140	+	0.498089i	−0.0531942	+	0.0704405i
$51$	9.44510	−	1.00998i	1.32258	−	0.141425i
$52$	−1.27015	−	1.68196i	−0.176139	−	0.233245i
$53$	−0.0836135	+	0.0116636i	−0.0114852	+	0.00160212i	−0.143897	−	0.989593i	$-0.545963\pi$
$53$	−0.0836135	+	0.0116636i	−0.0114852	+	0.00160212i	0.132411	+	0.991195i	$0.457728\pi$
$54$	0.0352578	+	1.52604i	0.00479798	+	0.207668i
$55$	2.16600	+	11.5871i	0.292063	+	1.56240i
$56$	−7.27561	+	6.94701i	−0.972244	+	0.928333i
$57$	−0.779158	+	0.202358i	−0.103202	+	0.0268029i
$58$	2.67822	+	3.72230i	0.351667	+	0.488761i
$59$	−6.29884	−	11.3086i	−0.820039	−	1.47225i	−0.880482	−	0.474080i	$-0.842781\pi$
$59$	−6.29884	−	11.3086i	−0.820039	−	1.47225i	0.0604431	−	0.998172i	$-0.480749\pi$
$60$	−5.15828	−	0.719550i	−0.665932	−	0.0928935i
$61$	0.0516351	−	0.445069i	0.00661120	−	0.0569852i	−0.989623	−	0.143688i	$-0.954104\pi$
$61$	0.0516351	−	0.445069i	0.00661120	−	0.0569852i	0.996234	+	0.0867031i	$0.0276331\pi$
$62$	−3.63213	+	1.70505i	−0.461280	+	0.216542i
$63$	4.88350	+	6.16535i	0.615264	+	0.776761i
$64$	5.69365	−	2.83510i	0.711707	−	0.354388i
$65$	−1.55121	−	3.74496i	−0.192404	−	0.464505i
$66$	−9.58886	+	7.96248i	−1.18031	+	0.980114i
$67$	−6.80847	+	1.27272i	−0.831788	+	0.155488i	−0.582386	−	0.812912i	$-0.697881\pi$
$67$	−6.80847	+	1.27272i	−0.831788	+	0.155488i	−0.249401	+	0.968400i	$0.580234\pi$
$68$	4.01930	−	1.95657i	0.487412	−	0.237268i
$69$	−11.5464	−	2.15840i	−1.39003	−	0.259841i
$70$	−5.94151	+	3.30940i	−0.710147	+	0.395549i
$71$	−5.30723	−	1.37836i	−0.629852	−	0.163581i	−0.0772308	−	0.997013i	$-0.524608\pi$
$71$	−5.30723	−	1.37836i	−0.629852	−	0.163581i	−0.552622	+	0.833432i	$0.686373\pi$
$72$	−2.46043	−	6.35110i	−0.289964	−	0.748484i
$73$	−3.05725	−	1.10387i	−0.357824	−	0.129198i	0.154495	−	0.987994i	$-0.450625\pi$
$73$	−3.05725	−	1.10387i	−0.357824	−	0.129198i	−0.512319	+	0.858796i	$0.671213\pi$
$74$	−1.75401	−	1.38933i	−0.203900	−	0.161507i
$75$	1.38822	+	0.575020i	0.160298	+	0.0663976i
$76$	−0.312540	+	0.214095i	−0.0358508	+	0.0245584i
$77$	4.41140	−	18.7561i	0.502726	−	2.13746i
$78$	2.66120	−	3.35972i	0.301321	−	0.380414i
$79$	−0.329327	+	1.56118i	−0.0370522	+	0.175646i	−0.993043	−	0.117749i	$-0.962432\pi$
$79$	−0.329327	+	1.56118i	−0.0370522	+	0.175646i	0.955991	+	0.293395i	$0.0947852\pi$
$80$	1.33871	−	0.282397i	0.149672	−	0.0315730i
$81$	10.1931	−	2.90020i	1.13257	−	0.322245i
$82$	−6.80178	+	5.38762i	−0.751131	+	0.594963i
$83$	−10.8113	+	3.62358i	−1.18669	+	0.397740i	−0.841222	−	0.540690i	$-0.818163\pi$
$83$	−10.8113	+	3.62358i	−1.18669	+	0.397740i	−0.345471	+	0.938429i	$0.612281\pi$
$84$	7.23806	+	4.48162i	0.789738	+	0.488985i
$85$	8.42768	−	1.69896i	0.914111	−	0.184278i
$86$	3.16317	−	1.95855i	0.341094	−	0.211196i
$87$	7.05257	−	8.49308i	0.756115	−	0.910554i
$88$	−8.45382	+	14.3855i	−0.901180	+	1.53350i
$89$	−7.75082	−	12.5180i	−0.821586	−	1.32691i	−0.942487	−	0.334242i	$-0.891520\pi$
$89$	−7.75082	−	12.5180i	−0.821586	−	1.32691i	0.120901	−	0.992665i	$-0.461421\pi$
$90$	−0.530665	−	4.57407i	−0.0559370	−	0.482149i
$91$	−0.153040	+	6.62397i	−0.0160430	+	0.694380i
$92$	−5.45580	+	0.889971i	−0.568806	+	0.0927858i
$93$	6.17094	+	7.43138i	0.639897	+	0.770599i
$94$	2.75573	+	0.923627i	0.284232	+	0.0952648i
$95$	−0.685287	+	0.247434i	−0.0703089	+	0.0253862i
$96$	−7.97774	−	9.16783i	−0.814225	−	0.935688i
$97$	−3.47443	+	13.3779i	−0.352775	+	1.35832i	0.513214	+	0.858261i	$0.328455\pi$
$97$	−3.47443	+	13.3779i	−0.352775	+	1.35832i	−0.865989	+	0.500064i	$0.833310\pi$
$98$	4.39900	−	0.407627i	0.444366	−	0.0411765i
$99$	10.5895	+	7.61922i	1.06428	+	0.765761i
$100$	0.706372	+	0.0326576i	0.0706372	+	0.00326576i
$101$	−3.67486	−	12.9158i	−0.365662	−	1.28517i	−0.898508	−	0.438956i	$-0.855348\pi$
$101$	−3.67486	−	12.9158i	−0.365662	−	1.28517i	0.532847	−	0.846212i	$-0.321122\pi$
$102$	5.90552	+	6.91074i	0.584734	+	0.684265i
$103$	−2.50257	+	8.79561i	−0.246585	+	0.866657i	0.735389	+	0.677645i	$0.236999\pi$
$103$	−2.50257	+	8.79561i	−0.246585	+	0.866657i	−0.981975	+	0.189013i	$0.939471\pi$
$104$	1.82341	−	5.44030i	0.178800	−	0.533466i
$105$	11.3068	+	11.8416i	1.10343	+	1.15562i
$106$	−0.0544287	−	0.0597054i	−0.00528658	−	0.00579911i
$107$	10.8942	−	7.09868i	1.05319	−	0.686256i	0.101972	−	0.994787i	$-0.467485\pi$
$107$	10.8942	−	7.09868i	1.05319	−	0.686256i	0.951214	+	0.308532i	$0.0998376\pi$
$108$	1.40376	−	1.01002i	0.135077	−	0.0971890i
$109$	−1.62019	+	1.40987i	−0.155186	+	0.135041i	−0.730558	−	0.682851i	$-0.760740\pi$
$109$	−1.62019	+	1.40987i	−0.155186	+	0.135041i	0.575372	+	0.817892i	$0.304857\pi$
$110$	−7.97664	+	7.97664i	−0.760543	+	0.760543i
$111$	−2.17583	+	4.92779i	−0.206521	+	0.467725i
$112$	−2.18821	−	0.461597i	−0.206766	−	0.0436168i
$113$	−5.01426	+	0.348045i	−0.471702	+	0.0327413i	−0.303132	−	0.952948i	$-0.598032\pi$
$113$	−5.01426	+	0.348045i	−0.471702	+	0.0327413i	−0.168569	+	0.985690i	$0.553915\pi$
$114$	−0.581150	−	0.505710i	−0.0544297	−	0.0473641i
$115$	−10.5860	−	0.980940i	−0.987152	−	0.0914731i
$116$	1.76434	−	4.88646i	0.163815	−	0.453697i
$117$	−4.10383	−	1.81202i	−0.379399	−	0.167521i
$118$	5.52163	−	11.0889i	0.508307	−	1.02082i
$119$	−13.7236	−	3.02382i	−1.25804	−	0.277193i
$120$	−6.31988	−	12.6920i	−0.576923	−	1.15862i
$121$	−0.967970	−	20.9369i	−0.0879972	−	1.90335i
$122$	0.379310	−	0.199938i	0.0343411	−	0.0181015i
$123$	16.6698	+	12.5885i	1.50307	+	1.13506i
$124$	3.91915	+	2.30314i	0.351950	+	0.206828i
$125$	11.2582	+	3.48626i	1.00696	+	0.311821i
$126$	−2.22646	+	7.18993i	−0.198349	+	0.640529i
$127$	16.7102	+	13.8760i	1.48279	+	1.23130i	0.911992	+	0.410209i	$0.134544\pi$
$127$	16.7102	+	13.8760i	1.48279	+	1.23130i	0.570802	+	0.821087i	$0.306632\pi$
$128$	−3.89927	−	2.17188i	−0.344650	−	0.191969i
$129$	−6.47784	−	6.18527i	−0.570342	−	0.544583i
$130$	2.11773	−	3.25005i	0.185737	−	0.285049i
$131$	−13.8814	+	5.74986i	−1.21282	+	0.502367i	−0.895121	−	0.445823i	$-0.852911\pi$
$131$	−13.8814	+	5.74986i	−1.21282	+	0.502367i	−0.317701	+	0.948191i	$0.602911\pi$
$132$	13.5816	+	3.86429i	1.18213	+	0.336344i
$133$	1.18807	+	0.0824650i	0.103019	+	0.00715062i
$134$	−4.68701	−	4.68701i	−0.404896	−	0.404896i
$135$	3.10134	−	1.20147i	0.266921	−	0.103406i
$136$	10.5779	+	6.01683i	0.907045	+	0.515939i
$137$	−19.6727	−	7.62126i	−1.68076	−	0.651128i	−0.683842	−	0.729630i	$-0.739692\pi$
$137$	−19.6727	−	7.62126i	−1.68076	−	0.651128i	−0.996914	+	0.0785014i	$0.974986\pi$
$138$	−4.54052	−	10.2833i	−0.386515	−	0.875373i
$139$	3.20367	+	15.1870i	0.271731	+	1.28815i	0.872457	+	0.488692i	$0.162526\pi$
$139$	3.20367	+	15.1870i	0.271731	+	1.28815i	−0.600725	+	0.799456i	$0.705121\pi$
$140$	6.89728	+	3.43444i	0.582927	+	0.290263i
$141$	0.484492	−	6.98005i	0.0408016	−	0.587827i
$142$	−1.78206	−	4.93554i	−0.149547	−	0.414181i
$143$	2.76258	+	10.6371i	0.231019	+	0.889516i
$144$	0.855713	−	1.24919i	0.0713095	−	0.104099i
$145$	5.64660	−	8.24302i	0.468924	−	0.684545i
$146$	−0.781922	−	3.01071i	−0.0647124	−	0.249168i
$147$	−3.61189	−	10.0034i	−0.297904	−	0.825067i
$148$	−0.175537	+	2.52895i	−0.0144290	+	0.207878i
$149$	8.09366	+	4.03017i	0.663059	+	0.330164i	0.745571	−	0.666426i	$-0.232177\pi$
$149$	8.09366	+	4.03017i	0.663059	+	0.330164i	−0.0825124	+	0.996590i	$0.526294\pi$
$150$	0.296802	+	1.40699i	0.0242338	+	0.114880i
$151$	−2.66051	−	6.02548i	−0.216509	−	0.490346i	0.773073	−	0.634317i	$-0.218719\pi$
$151$	−2.66051	−	6.02548i	−0.216509	−	0.490346i	−0.989582	+	0.143971i	$0.954013\pi$
$152$	−0.961675	−	0.372555i	−0.0780021	−	0.0302182i
$153$	5.44730	−	7.80101i	0.440388	−	0.630674i
$154$	17.1939	−	6.66094i	1.38552	−	0.536754i
$155$	6.18191	+	6.18191i	0.496543	+	0.496543i
$156$	−4.84406	−	0.336231i	−0.387835	−	0.0269200i
$157$	21.1205	+	6.00930i	1.68560	+	0.479594i	0.974666	−	0.223666i	$-0.0718025\pi$
$157$	21.1205	+	6.00930i	1.68560	+	0.479594i	0.710933	+	0.703260i	$0.248273\pi$
$158$	−1.41067	+	0.584318i	−0.112227	+	0.0464858i
$159$	−0.106182	+	0.162955i	−0.00842075	+	0.0129232i
$160$	−7.95523	−	7.59593i	−0.628916	−	0.600511i
$161$	15.1815	+	8.45607i	1.19647	+	0.666431i
$162$	7.80243	+	6.47905i	0.613017	+	0.509043i
$163$	1.60352	−	5.17825i	0.125597	−	0.405592i	−0.870675	−	0.491859i	$-0.836317\pi$
$163$	1.60352	−	5.17825i	0.125597	−	0.405592i	0.996272	+	0.0862673i	$0.0274939\pi$
$164$	9.39050	+	2.90790i	0.733275	+	0.227069i
$165$	23.4135	+	13.7592i	1.82274	+	1.07115i
$166$	−8.70785	−	6.57586i	−0.675860	−	0.510386i
$167$	15.0724	−	7.94482i	1.16634	−	0.614789i	0.232541	−	0.972587i	$-0.425296\pi$
$167$	15.0724	−	7.94482i	1.16634	−	0.614789i	0.933799	+	0.357798i	$0.116472\pi$
$168$	1.07033	+	23.1509i	0.0825778	+	1.78613i
$169$	4.11008	+	8.25416i	0.316160	+	0.634935i
$170$	5.89923	+	5.73487i	0.452451	+	0.439844i
$171$	−0.359416	+	0.721804i	−0.0274852	+	0.0551978i
$172$	−3.85584	−	1.70252i	−0.294005	−	0.129816i
$173$	7.38912	−	20.4647i	0.561784	−	1.55590i	−0.247746	−	0.968825i	$-0.579690\pi$
$173$	7.38912	−	20.4647i	0.561784	−	1.55590i	0.809530	−	0.587078i	$-0.199722\pi$
$174$	10.5195	+	0.974779i	0.797484	+	0.0738978i
$175$	−1.67693	−	1.45924i	−0.126764	−	0.110308i
$176$	−3.70050	+	0.256856i	−0.278936	+	0.0193612i
$177$	−29.1797	−	6.15539i	−2.19328	−	0.462667i
$178$	5.69121	−	12.8894i	0.426574	−	0.966099i
$179$	14.2329	−	14.2329i	1.06382	−	1.06382i	0.0659952	−	0.997820i	$-0.478978\pi$
$179$	14.2329	−	14.2329i	1.06382	−	1.06382i	0.997820	−	0.0659952i	$-0.0210222\pi$
$180$	−3.93545	+	3.42458i	−0.293331	+	0.255253i
$181$	−5.82875	+	4.19383i	−0.433248	+	0.311725i	−0.779484	−	0.626422i	$-0.784519\pi$
$181$	−5.82875	+	4.19383i	−0.433248	+	0.311725i	0.346236	+	0.938148i	$0.387460\pi$
$182$	−5.31243	+	3.46157i	−0.393783	+	0.256589i
$183$	−0.695416	−	0.762835i	−0.0514066	−	0.0563904i
$184$	−10.3924	−	10.8840i	−0.766140	−	0.802379i
$185$	−1.54937	+	4.62268i	−0.113912	+	0.339866i
$186$	−2.52973	+	8.89107i	−0.185489	+	0.651925i
$187$	−23.2665	+	1.40530i	−1.70142	+	0.102766i
$188$	−0.901100	−	3.16704i	−0.0657194	−	0.230980i
$189$	−5.43067	−	0.251075i	−0.395023	−	0.0182630i
$190$	−0.565970	−	0.407220i	−0.0410598	−	0.0295428i
$191$	−16.9438	+	1.57007i	−1.22601	+	0.113607i	−0.685715	−	0.727870i	$-0.740511\pi$
$191$	−16.9438	+	1.57007i	−1.22601	+	0.113607i	−0.540294	+	0.841476i	$0.681687\pi$
$192$	3.68349	−	14.1829i	0.265833	−	1.02356i
$193$	−8.96649	−	10.3041i	−0.645422	−	0.741704i	0.334211	−	0.942498i	$-0.391530\pi$
$193$	−8.96649	−	10.3041i	−0.645422	−	0.741704i	−0.979633	+	0.200794i	$0.935648\pi$
$194$	−12.4410	+	4.49203i	−0.893213	+	0.322509i
$195$	−8.85450	−	2.96773i	−0.634084	−	0.212524i
$196$	−3.19749	−	3.85059i	−0.228392	−	0.275042i
$197$	1.23969	−	0.202222i	0.0883239	−	0.0144077i	−0.116673	−	0.993170i	$-0.537223\pi$
$197$	1.23969	−	0.202222i	0.0883239	−	0.0144077i	0.204997	+	0.978763i	$0.434282\pi$
$198$	−0.288365	+	12.4811i	−0.0204932	+	0.886995i
$199$	−3.20224	−	27.6017i	−0.227001	−	1.95663i	−0.285602	−	0.958348i	$-0.592194\pi$
$199$	−3.20224	−	27.6017i	−0.227001	−	1.95663i	0.0586016	−	0.998281i	$-0.481336\pi$
$200$	1.01339	+	1.63669i	0.0716578	+	0.115731i
$201$	−8.08482	+	13.7576i	−0.570259	+	0.970384i
$202$	8.20963	−	9.88649i	0.577628	−	0.695611i
$203$	−13.8856	+	8.59763i	−0.974581	+	0.603435i
$204$	2.67815	−	9.94434i	0.187508	−	0.696243i
$205$	16.0743	+	9.95277i	1.12268	+	0.695132i
$206$	−8.29764	+	2.78109i	−0.578124	+	0.193768i
$207$	−9.22310	+	7.30551i	−0.641050	+	0.507768i
$208$	1.22687	−	0.349076i	0.0850684	−	0.0242040i
$209$	1.93283	−	0.407725i	0.133696	−	0.0282029i
$210$	−3.23403	+	15.3310i	−0.223170	+	1.05794i
$211$	1.15469	−	1.45777i	0.0794918	−	0.100357i	−0.742531	−	0.669812i	$-0.766375\pi$
$211$	1.15469	−	1.45777i	0.0794918	−	0.100357i	0.822023	+	0.569454i	$0.192845\pi$
$212$	−0.0209560	+	0.0890994i	−0.00143926	+	0.00611937i
$213$	−10.4219	+	7.13914i	−0.714094	+	0.489166i
$214$	11.4963	+	4.76193i	0.785873	+	0.325519i
$215$	−6.35443	−	5.03327i	−0.433368	−	0.343266i
$216$	4.42807	+	1.59882i	0.301292	+	0.108786i
$217$	−5.16224	−	13.3253i	−0.350436	−	0.904579i
$218$	−1.98934	−	0.516657i	−0.134735	−	0.0349924i
$219$	−6.54207	+	3.64391i	−0.442072	+	0.246233i
$220$	12.5626	+	2.34835i	0.846969	+	0.158326i
$221$	7.72873	−	2.12424i	0.519891	−	0.142892i
$222$	−5.06726	+	0.947235i	−0.340092	+	0.0635743i
$223$	−18.0524	+	14.9905i	−1.20888	+	1.00384i	−0.209213	+	0.977870i	$0.567090\pi$
$223$	−18.0524	+	14.9905i	−1.20888	+	1.00384i	−0.999663	+	0.0259680i	$0.991733\pi$
$224$	6.88028	+	16.6105i	0.459708	+	1.10983i
$225$	1.34730	−	0.670874i	0.0898198	−	0.0447249i
$226$	−2.98662	−	3.77056i	−0.198667	−	0.250814i
$227$	13.5413	−	6.35677i	0.898766	−	0.421913i	0.0805013	−	0.996755i	$-0.474348\pi$
$227$	13.5413	−	6.35677i	0.898766	−	0.421913i	0.818265	+	0.574841i	$0.194936\pi$
$228$	−0.100582	+	0.866964i	−0.00666119	+	0.0574161i
$229$	11.4395	+	1.59574i	0.755941	+	0.105449i	0.505671	−	0.862727i	$-0.331245\pi$
$229$	11.4395	+	1.59574i	0.755941	+	0.105449i	0.250271	+	0.968176i	$0.419480\pi$
$230$	−4.95072	−	8.88825i	−0.326441	−	0.586074i
$231$	−25.9256	−	36.0325i	−1.70578	−	2.37076i
$232$	13.6889	−	3.55520i	0.898722	−	0.233410i
$233$	−8.77080	+	8.37467i	−0.574594	+	0.548643i	−0.921061	−	0.389419i	$-0.872676\pi$
$233$	−8.77080	+	8.37467i	−0.574594	+	0.548643i	0.346466	+	0.938063i	$0.387382\pi$
$234$	−0.788852	−	4.21998i	−0.0515688	−	0.275869i
$235$	−0.146271	−	6.33096i	−0.00954166	−	0.412986i
$236$	−13.8997	+	1.93892i	−0.904792	+	0.126213i
$237$	2.21519	+	2.93339i	0.143892	+	0.190544i
$238$	−5.03471	−	12.4702i	−0.326352	−	0.808322i
$239$	−2.20000	+	2.91328i	−0.142306	+	0.188444i	−0.863589	−	0.504197i	$-0.831788\pi$
$239$	−2.20000	+	2.91328i	−0.142306	+	0.188444i	0.721282	+	0.692641i	$0.243553\pi$
$240$	1.53379	−	2.75369i	0.0990060	−	0.177750i
$241$	−8.37490	+	0.971623i	−0.539475	+	0.0625877i	−0.380650	−	0.924719i	$-0.624300\pi$
$241$	−8.37490	+	0.971623i	−0.539475	+	0.0625877i	−0.158824	+	0.987307i	$0.550770\pi$
$242$	16.0063	−	12.0874i	1.02892	−	0.777006i
$243$	8.34169	−	17.7696i	0.535120	−	1.13992i
$244$	−0.429731	−	0.226515i	−0.0275107	−	0.0145011i
$245$	−4.09046	−	8.71355i	−0.261330	−	0.556689i
$246$	−0.923226	+	19.9691i	−0.0588627	+	1.27318i
$247$	−0.621397	+	0.274374i	−0.0395385	+	0.0174580i
$248$	0.856904	+	12.3454i	0.0544135	+	0.783932i
$249$	−10.0528	+	24.2696i	−0.637069	+	1.53802i
$250$	3.33628	+	10.7739i	0.211005	+	0.681399i
$251$			8.97627i			0.566577i	0.959035	+	0.283289i	$0.0914255\pi$
$251$			8.97627i			0.566577i	−0.959035	+	0.283289i	$0.908575\pi$
$252$	8.14567	−	2.52242i	0.513129	−	0.158898i
$253$	28.0584	+	6.59926i	1.76401	+	0.414892i
$254$	−1.91789	+	20.6973i	−0.120339	+	1.29867i
$255$	9.79284	−	17.2163i	0.613252	−	1.07813i
$256$	−1.56785	−	16.9198i	−0.0979905	−	1.05749i
$257$	−4.00179	+	28.6879i	−0.249625	+	1.78950i	0.299845	+	0.953988i	$0.403065\pi$
$257$	−4.00179	+	28.6879i	−0.249625	+	1.78950i	−0.549470	+	0.835514i	$0.685170\pi$
$258$	1.37994	−	8.45943i	0.0859110	−	0.526661i
$259$	5.36881	−	5.88931i	0.333602	−	0.365944i
$260$	−4.39360	+	0.101510i	−0.272480	+	0.00629538i
$261$	−1.78026	−	10.9135i	−0.110195	−	0.675532i
$262$	−12.0469	−	7.84978i	−0.744262	−	0.484961i
$263$	20.2275	−	0.935173i	1.24728	−	0.0576652i	0.587562	−	0.809179i	$-0.300088\pi$
$263$	20.2275	−	0.935173i	1.24728	−	0.0576652i	0.659718	+	0.751514i	$0.270676\pi$
$264$	12.2162	+	36.4481i	0.751853	+	2.24323i
$265$	−0.0820837	+	0.155724i	−0.00504236	+	0.00956607i
$266$	0.577429	+	0.982586i	0.0354045	+	0.0602462i
$267$	−33.4776	−	5.46099i	−2.04879	−	0.334207i
$268$	−1.37987	+	7.38168i	−0.0842892	+	0.450908i
$269$	−9.03846	−	13.8712i	−0.551084	−	0.845741i	0.447743	−	0.894162i	$-0.352228\pi$
$269$	−9.03846	−	13.8712i	−0.551084	−	0.845741i	−0.998827	+	0.0484212i	$0.984581\pi$
$270$	2.62585	+	1.79875i	0.159804	+	0.109468i
$271$	5.42845	−	4.94869i	0.329755	−	0.300612i	−0.491837	−	0.870687i	$-0.663674\pi$
$271$	5.42845	−	4.94869i	0.329755	−	0.300612i	0.821592	+	0.570076i	$0.193086\pi$
$272$	0.225440	+	2.69599i	0.0136693	+	0.163468i
$273$	11.2807	+	10.2837i	0.682737	+	0.622397i
$274$	−4.62247	−	19.6535i	−0.279253	−	1.18731i
$275$	−3.33768	−	1.56683i	−0.201270	−	0.0944832i
$276$	−6.70431	+	10.8278i	−0.403552	+	0.651759i
$277$	6.85969	+	13.0138i	0.412159	+	0.781923i	0.999627	−	0.0273243i	$-0.00869869\pi$
$277$	6.85969	+	13.0138i	0.412159	+	0.781923i	−0.587468	+	0.809247i	$0.699875\pi$
$278$	−10.2576	+	10.7428i	−0.615212	+	0.644312i
$279$	9.67290	+	0.223483i	0.579102	+	0.0133796i
$280$	2.89791	+	20.7745i	0.173183	+	1.24151i
$281$	8.93579	−	2.10168i	0.533065	−	0.125376i	0.0463312	−	0.998926i	$-0.485247\pi$
$281$	8.93579	−	2.10168i	0.533065	−	0.125376i	0.486734	+	0.873550i	$0.338188\pi$
$282$	5.77282	−	3.39247i	0.343766	−	0.202019i
$283$	3.07890	+	0.357202i	0.183022	+	0.0212334i	0.206264	−	0.978496i	$-0.433869\pi$
$283$	3.07890	+	0.357202i	0.183022	+	0.0212334i	−0.0232422	+	0.999730i	$0.507399\pi$
$284$	−3.47209	+	4.82565i	−0.206030	+	0.286349i
$285$	−0.606361	+	1.56520i	−0.0359177	+	0.0927143i
$286$	−6.90395	+	7.93386i	−0.408239	+	0.469139i
$287$	−17.4646	−	25.4951i	−1.03090	−	1.50493i
$288$	−12.1730			−0.717302
$289$	1.26454	+	16.9529i	0.0743848	+	0.997230i
$290$	9.56173			0.561484
$291$	17.9956	+	26.2704i	1.05492	+	1.54000i
$292$	−2.31337	+	2.65847i	−0.135380	+	0.155575i
$293$	9.09546	−	23.4781i	0.531363	−	1.37160i	−0.366125	−	0.930566i	$-0.619316\pi$
$293$	9.09546	−	23.4781i	0.531363	−	1.37160i	0.897488	−	0.441039i	$-0.145390\pi$
$294$	5.94435	−	8.26170i	0.346682	−	0.481832i
$295$	−26.8111	−	3.11052i	−1.56100	−	0.181102i
$296$	−5.94983	+	3.49650i	−0.345827	+	0.203230i
$297$	−8.77782	+	2.06452i	−0.509341	+	0.119796i
$298$	1.19541	+	8.56961i	0.0692482	+	0.496424i
$299$	−9.90917	−	0.228942i	−0.573062	−	0.0132401i
$300$	1.12503	−	1.17825i	0.0649539	−	0.0680262i
$301$	6.17857	+	11.7216i	0.356127	+	0.675623i
$302$	3.31828	−	5.35921i	0.190946	−	0.308388i
$303$	−28.0046	−	13.1464i	−1.60882	−	0.755239i
$304$	−0.0524924	−	0.223184i	−0.00301065	−	0.0128005i
$305$	−0.690421	−	0.629402i	−0.0395334	−	0.0360394i
$306$	9.10497	+	0.0817020i	0.520497	+	0.00467059i
$307$	−1.40802	+	1.28358i	−0.0803601	+	0.0732579i	−0.712879	−	0.701287i	$-0.752609\pi$
$307$	−1.40802	+	1.28358i	−0.0803601	+	0.0732579i	0.632519	+	0.774545i	$0.282021\pi$
$308$	−17.2343	−	11.8057i	−0.982013	−	0.672694i
$309$	11.5016	+	17.6513i	0.654302	+	1.00415i
$310$	−1.53733	+	8.22398i	−0.0873144	+	0.467091i
$311$	6.52200	+	1.06389i	0.369829	+	0.0603278i	0.343059	−	0.939314i	$-0.388537\pi$
$311$	6.52200	+	1.06389i	0.369829	+	0.0603278i	0.0267693	+	0.999642i	$0.491478\pi$
$312$	−6.69735	−	11.3966i	−0.379163	−	0.645205i
$313$	2.17957	−	4.13494i	0.123196	−	0.233721i	−0.815278	−	0.579070i	$-0.803416\pi$
$313$	2.17957	−	4.13494i	0.123196	−	0.233721i	0.938474	+	0.345349i	$0.112239\pi$
$314$	6.67809	+	19.9247i	0.376867	+	1.12442i
$315$	16.3823	−	0.757401i	0.923040	−	0.0426747i
$316$	1.44933	+	0.944384i	0.0815313	+	0.0531257i
$317$	−2.64958	−	16.2428i	−0.148815	−	0.912284i	−0.949630	−	0.313372i	$-0.898541\pi$
$317$	−2.64958	−	16.2428i	−0.148815	−	0.912284i	0.800815	−	0.598912i	$-0.204400\pi$
$318$	−0.186080	+	0.00429920i	−0.0104348	+	0.000241087i
$319$	−18.2499	+	20.0192i	−1.02180	+	1.12086i
$320$	2.13519	−	13.0894i	0.119361	−	0.731720i
$321$	4.13869	−	29.6693i	0.230999	−	1.65598i
$322$	1.53443	+	16.5592i	0.0855106	+	0.922806i
$323$	−0.317251	−	1.40533i	−0.0176523	−	0.0781948i
$324$	1.06016	−	11.4409i	0.0588976	−	0.635606i
$325$	1.23423	+	0.290289i	0.0684630	+	0.0161024i
$326$	4.95548	−	1.53454i	0.274459	−	0.0849901i
$327$			4.94801i			0.273625i
$328$	7.91623	+	25.5639i	0.437101	+	1.41153i
$329$	−3.96121	+	9.56320i	−0.218389	+	0.527237i
$330$	1.79958	+	25.9264i	0.0990634	+	1.42720i
$331$	17.6587	−	7.79708i	0.970610	−	0.428566i	0.142909	−	0.989736i	$-0.454354\pi$
$331$	17.6587	−	7.79708i	0.970610	−	0.428566i	0.827701	+	0.561170i	$0.189648\pi$
$332$	−0.570936	+	12.3492i	−0.0313342	+	0.677748i
$333$	2.29286	+	4.88429i	0.125648	+	0.267657i
$334$	14.4240	+	7.60303i	0.789247	+	0.416019i
$335$	−6.13724	+	13.0736i	−0.335313	+	0.714289i
$336$	−4.11155	+	3.10490i	−0.224304	+	0.169386i
$337$	9.70698	−	1.12617i	0.528773	−	0.0613461i	0.153300	−	0.988180i	$-0.451010\pi$
$337$	9.70698	−	1.12617i	0.528773	−	0.0613461i	0.375473	+	0.926834i	$0.377480\pi$
$338$	−4.29388	+	7.70899i	−0.233556	+	0.419314i
$339$	−6.97839	+	9.24088i	−0.379014	+	0.501896i
$340$	1.58313	−	9.18559i	0.0858574	−	0.498159i
$341$	−14.2842	−	18.9153i	−0.773533	−	1.02432i
$342$	−0.764250	+	0.106608i	−0.0413259	+	0.00576472i
$343$	−0.187644	−	8.12169i	−0.0101318	−	0.438530i
$344$	−2.10844	−	11.2791i	−0.113679	−	0.608130i
$345$	−17.7145	+	16.9145i	−0.953718	+	0.910644i
$346$	20.1532	−	5.23406i	1.08344	−	0.281385i
$347$	12.1548	+	16.8932i	0.652501	+	0.906872i	0.999520	−	0.0309861i	$-0.00986476\pi$
$347$	12.1548	+	16.8932i	0.652501	+	0.906872i	−0.347019	+	0.937858i	$0.612806\pi$
$348$	−5.82414	−	10.4563i	−0.312207	−	0.560518i
$349$	−16.5281	−	2.30557i	−0.884728	−	0.123414i	−0.318754	−	0.947837i	$-0.603264\pi$
$349$	−16.5281	−	2.30557i	−0.884728	−	0.123414i	−0.565974	+	0.824423i	$0.691500\pi$
$350$	0.245158	−	2.11314i	0.0131043	−	0.112952i
$351$	2.80693	−	1.31768i	0.149823	−	0.0703323i
$352$	18.5163	+	23.3765i	0.986922	+	1.24597i
$353$	24.5844	−	12.2416i	1.30850	−	0.651554i	0.350024	−	0.936741i	$-0.386173\pi$
$353$	24.5844	−	12.2416i	1.30850	−	0.651554i	0.958472	+	0.285187i	$0.0920558\pi$
$354$	−10.9214	−	26.3666i	−0.580465	−	1.40137i
$355$	−8.79611	+	7.30420i	−0.466849	+	0.387667i
$356$	−15.6911	+	2.93317i	−0.831625	+	0.155458i
$357$	−26.0100	+	19.2778i	−1.37659	+	1.02029i
$358$	18.9344	+	3.53946i	1.00072	+	0.187066i
$359$	6.06090	−	3.37590i	0.319882	−	0.178173i	−0.318439	−	0.947943i	$-0.603159\pi$
$359$	6.06090	−	3.37590i	0.319882	−	0.178173i	0.638321	+	0.769770i	$0.279629\pi$
$360$	−13.7459	−	3.56999i	−0.724472	−	0.188155i
$361$	−6.81949	−	17.6031i	−0.358920	−	0.926480i
$362$	−6.46339	−	2.33371i	−0.339708	−	0.122657i
$363$	−37.8511	−	29.9814i	−1.98667	−	1.57362i
$364$	6.63673	+	2.74903i	0.347859	+	0.144088i
$365$	−5.59149	+	3.83026i	−0.292672	+	0.200485i
$366$	0.226165	−	0.961595i	0.0118218	−	0.0502634i
$367$	−13.2569	+	16.7367i	−0.692006	+	0.873647i	−0.996895	−	0.0787408i	$-0.974910\pi$
$367$	−13.2569	+	16.7367i	−0.692006	+	0.873647i	0.304889	+	0.952388i	$0.401381\pi$
$368$	0.690530	−	3.27347i	0.0359963	−	0.170641i
$369$	20.4730	−	4.31874i	1.06578	−	0.224825i
$370$	−4.48757	+	1.27682i	−0.233298	+	0.0663789i
$371$	0.225554	−	0.178659i	0.0117102	−	0.00927550i
$372$	9.92983	−	3.32814i	0.514838	−	0.172556i
$373$	−4.48158	−	2.77487i	−0.232047	−	0.143678i	0.405484	−	0.914102i	$-0.367103\pi$
$373$	−4.48158	−	2.77487i	−0.232047	−	0.143678i	−0.637531	+	0.770425i	$0.720044\pi$
$374$	−13.6926	−	17.6091i	−0.708028	−	0.910543i
$375$	23.0852	−	14.2937i	1.19211	−	0.738126i
$376$	5.72654	−	6.89621i	0.295324	−	0.355645i
$377$	4.71963	−	8.03119i	0.243073	−	0.413627i
$378$	−2.73881	−	4.42333i	−0.140869	−	0.227512i
$379$	−2.20187	−	18.9790i	−0.113102	−	0.974886i	−0.922067	−	0.387029i	$-0.873501\pi$
$379$	−2.20187	−	18.9790i	−0.113102	−	0.974886i	0.808965	−	0.587857i	$-0.200028\pi$
$380$	−0.0182457	+	0.789717i	−0.000935983	+	0.0405116i
$381$	49.3874	−	8.05626i	2.53019	−	0.412735i
$382$	−10.4032	−	12.5281i	−0.532274	−	0.640993i
$383$	11.2856	+	3.78254i	0.576666	+	0.193279i	0.591074	−	0.806617i	$-0.298704\pi$
$383$	11.2856	+	3.78254i	0.576666	+	0.193279i	−0.0144083	+	0.999896i	$0.504586\pi$
$384$	−9.67166	+	3.49211i	−0.493555	+	0.178206i
$385$	−26.3735	−	30.3078i	−1.34412	−	1.54463i
$386$	3.28584	−	12.6518i	0.167245	−	0.643960i
$387$	−8.93311	+	0.827774i	−0.454095	+	0.0420781i
$388$	12.1640	+	8.75209i	0.617534	+	0.444320i
$389$	18.9406	+	0.875679i	0.960329	+	0.0443987i	0.520663	−	0.853763i	$-0.325685\pi$
$389$	18.9406	+	0.875679i	0.960329	+	0.0443987i	0.439666	+	0.898161i	$0.355097\pi$
$390$	−2.44569	−	8.59570i	−0.123842	−	0.435260i
$391$	4.52351	−	20.5299i	0.228764	−	1.03824i
$392$	3.72878	−	13.1053i	0.188332	−	0.661918i
$393$	−11.0005	+	32.8209i	−0.554899	+	1.65559i
$394$	0.830108	+	0.869373i	0.0418202	+	0.0437984i
$395$	2.24132	+	2.45861i	0.112773	+	0.123706i
$396$	11.8503	−	7.72163i	0.595499	−	0.388027i
$397$	−3.02619	+	2.17737i	−0.151880	+	0.109279i	−0.657420	−	0.753524i	$-0.728352\pi$
$397$	−3.02619	+	2.17737i	−0.151880	+	0.109279i	0.505540	+	0.862803i	$0.331293\pi$
$398$	20.0598	−	17.4558i	1.00551	−	0.874982i
$399$	1.94009	−	1.94009i	0.0971258	−	0.0971258i
$400$	−0.172860	+	0.391491i	−0.00864301	+	0.0195745i
$401$	−4.01613	−	0.847193i	−0.200556	−	0.0423068i	0.105040	−	0.994468i	$-0.466503\pi$
$401$	−4.01613	−	0.847193i	−0.200556	−	0.0423068i	−0.305596	+	0.952161i	$0.598856\pi$
$402$	−15.2342	+	1.05742i	−0.759810	+	0.0527392i
$403$	6.14876	+	5.35058i	0.306291	+	0.266531i
$404$	−14.4968	−	1.34333i	−0.721244	−	0.0668331i
$405$	7.50452	−	20.7843i	0.372903	−	1.03278i
$406$	−14.2976	−	6.31300i	−0.709577	−	0.313309i
$407$	5.89191	−	11.8326i	0.292051	−	0.586518i
$408$	26.4543	−	9.28430i	1.30968	−	0.459641i
$409$	−2.41891	−	4.85782i	−0.119607	−	0.240204i	0.827266	−	0.561810i	$-0.189895\pi$
$409$	−2.41891	−	4.85782i	−0.119607	−	0.240204i	−0.946873	+	0.321606i	$0.895777\pi$
$410$	0.835585	+	18.0734i	0.0412666	+	0.892583i
$411$	−42.9973	+	22.6643i	−2.12090	+	1.11795i
$412$	7.91202	+	5.97488i	0.389797	+	0.294361i
$413$	38.0368	+	22.3528i	1.87167	+	1.09991i
$414$	−10.7558	−	3.33069i	−0.528620	−	0.163695i
$415$	−7.03294	+	22.7115i	−0.345233	+	1.11486i
$416$	−7.88936	−	6.55124i	−0.386808	−	0.321201i
$417$	31.2393	+	17.4002i	1.52980	+	0.852091i
$418$	1.36722	+	1.30547i	0.0668729	+	0.0638526i
$419$	−21.6865	+	33.2820i	−1.05946	+	1.62593i	−0.327130	+	0.944979i	$0.606081\pi$
$419$	−21.6865	+	33.2820i	−1.05946	+	1.62593i	−0.732327	+	0.680953i	$0.761566\pi$
$420$	16.3999	−	6.79307i	0.800234	−	0.331468i
$421$	20.3629	+	5.79374i	0.992427	+	0.282370i	0.730645	−	0.682757i	$-0.239219\pi$
$421$	20.3629	+	5.79374i	0.992427	+	0.282370i	0.261782	+	0.965127i	$0.415690\pi$
$422$	1.77540	+	0.123232i	0.0864252	+	0.00599886i
$423$	−4.95570	−	4.95570i	−0.240955	−	0.240955i
$424$	−0.232349	+	0.0900126i	−0.0112839	+	0.00437140i
$425$	−1.10824	+	2.45018i	−0.0537574	+	0.118851i
$426$	−11.2728	−	4.36710i	−0.546169	−	0.211587i
$427$	0.616827	+	1.39698i	0.0298503	+	0.0676046i
$428$	−2.90982	−	13.7941i	−0.140652	−	0.666761i
$429$	22.6646	+	11.2856i	1.09426	+	0.544876i
$430$	0.537170	−	7.73897i	0.0259046	−	0.373206i
$431$	5.20568	+	14.4175i	0.250749	+	0.694468i	0.999500	+	0.0316165i	$0.0100655\pi$
$431$	5.20568	+	14.4175i	0.250749	+	0.694468i	−0.748751	+	0.662851i	$0.769346\pi$
$432$	0.263091	+	1.01301i	0.0126580	+	0.0487383i
$433$	−3.63295	+	5.30346i	−0.174589	+	0.254868i	−0.902390	−	0.430920i	$-0.858189\pi$
$433$	−3.63295	+	5.30346i	−0.174589	+	0.254868i	0.727802	+	0.685788i	$0.240542\pi$
$434$	7.72852	−	11.2823i	0.370981	−	0.541565i
$435$	−5.78635	−	22.2798i	−0.277434	−	1.06823i
$436$	0.790791	+	2.19015i	0.0378720	+	0.104889i
$437$	−0.123364	+	1.77730i	−0.00590130	+	0.0850197i
$438$	−6.41500	−	3.19429i	−0.306521	−	0.152629i
$439$	−7.22338	−	34.2425i	−0.344753	−	1.63431i	−0.710575	−	0.703622i	$-0.751565\pi$
$439$	−7.22338	−	34.2425i	−0.344753	−	1.63431i	0.365822	−	0.930685i	$-0.380788\pi$
$440$	14.0531	+	31.8273i	0.669956	+	1.51730i
$441$	−9.93372	−	3.84834i	−0.473034	−	0.183254i
$442$	5.85698	+	4.95304i	0.278588	+	0.235592i
$443$	30.2693	−	11.7264i	1.43814	−	0.557138i	0.489080	−	0.872239i	$-0.337333\pi$
$443$	30.2693	−	11.7264i	1.43814	−	0.557138i	0.949058	+	0.315101i	$0.102039\pi$
$444$	4.12971	+	4.12971i	0.195987	+	0.195987i
$445$	−30.6264	−	2.12581i	−1.45183	−	0.100773i
$446$	−21.5982	−	6.14523i	−1.02271	−	0.290985i
$447$	19.2446	−	7.97138i	0.910239	−	0.377033i
$448$	−11.8348	+	18.1627i	−0.559143	+	0.858109i
$449$	−22.2059	−	21.2030i	−1.04796	−	1.00063i	−0.999998	−	0.00178022i	$-0.999433\pi$
$449$	−22.2059	−	21.2030i	−1.04796	−	1.00063i	−0.0479617	−	0.998849i	$-0.515273\pi$
$450$	1.25831	+	0.700874i	0.0593173	+	0.0330395i
$451$	−39.4349	−	32.7463i	−1.85692	−	1.54196i
$452$	−1.61199	+	5.20561i	−0.0758217	+	0.244851i
$453$	−14.4956	−	4.48876i	−0.681061	−	0.210900i
$454$	12.3422	+	7.25303i	0.579246	+	0.340402i
$455$	11.0250	+	8.32572i	0.516862	+	0.390316i
$456$	−2.10186	+	1.10791i	−0.0984287	+	0.0518827i
$457$	1.15723	+	25.0305i	0.0541330	+	1.17088i	0.836466	+	0.548018i	$0.184618\pi$
$457$	1.15723	+	25.0305i	0.0541330	+	1.17088i	−0.782333	+	0.622860i	$0.785971\pi$
$458$	4.92690	+	9.89454i	0.230219	+	0.462342i
$459$	1.59601	+	6.38005i	0.0744955	+	0.297795i
$460$	−5.13777	+	10.3180i	−0.239550	+	0.481081i
$461$	−7.16409	−	3.16325i	−0.333665	−	0.147327i	0.230315	−	0.973116i	$-0.426024\pi$
$461$	−7.16409	−	3.16325i	−0.333665	−	0.147327i	−0.563980	+	0.825789i	$0.690730\pi$
$462$	14.4266	−	39.9557i	0.671188	−	1.85891i
$463$	32.4641	+	3.00824i	1.50873	+	0.139805i	0.814592	−	0.580034i	$-0.196961\pi$
$463$	32.4641	+	3.00824i	1.50873	+	0.139805i	0.694141	+	0.719839i	$0.255784\pi$
$464$	2.37188	+	2.06398i	0.110112	+	0.0958178i
$465$	20.0930	−	1.39468i	0.931791	−	0.0646765i
$466$	−11.3553	−	2.39538i	−0.526025	−	0.110964i
$467$	1.51270	−	3.42594i	0.0699994	−	0.158534i	−0.876353	−	0.481669i	$-0.840031\pi$
$467$	1.51270	−	3.42594i	0.0699994	−	0.158534i	0.946353	+	0.323135i	$0.104737\pi$
$468$	−3.43919	+	3.43919i	−0.158977	+	0.158977i
$469$	17.8086	−	15.4969i	0.822326	−	0.715579i
$470$	4.91922	−	3.53942i	0.226907	−	0.163261i
$471$	42.3853	−	27.6182i	1.95301	−	1.27258i
$472$	−25.7390	−	28.2344i	−1.18473	−	1.29959i
$473$	15.1777	+	15.8956i	0.697871	+	0.730881i
$474$	−1.11790	+	3.33536i	−0.0513468	+	0.153198i
$475$	0.0623673	−	0.219198i	0.00286161	−	0.0100575i
$476$	−8.43190	+	12.6899i	−0.386476	+	0.581641i
$477$	0.0533146	+	0.187381i	0.00244111	+	0.00857961i
$478$	−3.48987	−	0.161346i	−0.159623	−	0.00737980i
$479$	−4.19648	−	3.01940i	−0.191742	−	0.137960i	0.484083	−	0.875022i	$-0.339153\pi$
$479$	−4.19648	−	3.01940i	−0.191742	−	0.137960i	−0.675824	+	0.737063i	$0.736212\pi$
$480$	−25.2324	+	2.33812i	−1.15169	+	0.106720i
$481$	−1.14260	+	4.39948i	−0.0520982	+	0.200599i
$482$	−5.29645	−	6.08656i	−0.241247	−	0.277235i
$483$	37.6559	−	13.5963i	1.71340	−	0.618652i
$484$	−21.5458	−	7.22142i	−0.979354	−	0.328246i
$485$	18.4117	+	22.1724i	0.836032	+	1.00680i
$486$	18.5406	−	3.02441i	0.841018	−	0.137190i
$487$	−0.285810	+	12.3706i	−0.0129513	+	0.560564i	0.953164	+	0.302454i	$0.0978057\pi$
$487$	−0.285810	+	12.3706i	−0.0129513	+	0.560564i	−0.966115	+	0.258110i	$0.916900\pi$
$488$	−0.152401	−	1.31362i	−0.00689889	−	0.0594649i
$489$	−6.57446	−	10.6181i	−0.297308	−	0.480168i
$490$	4.66719	−	7.94194i	0.210842	−	0.358780i
$491$	−23.5050	+	28.3060i	−1.06077	+	1.27743i	−0.101528	+	0.994833i	$0.532373\pi$
$491$	−23.5050	+	28.3060i	−1.06077	+	1.27743i	−0.959238	+	0.282599i	$0.908803\pi$
$492$	19.2554	−	11.9225i	0.868102	−	0.537506i
$493$	14.7873	+	13.1027i	0.665985	+	0.590117i
$494$	−0.552686	−	0.342209i	−0.0248665	−	0.0153967i
$495$	25.7919	−	8.64456i	1.15926	−	0.388544i
$496$	−2.15656	+	1.70819i	−0.0968326	+	0.0767000i
$497$	17.9752	−	5.11440i	0.806300	−	0.229412i
$498$	−24.5978	+	5.18883i	−1.10225	+	0.232517i
$499$	3.62658	−	17.1918i	0.162348	−	0.769613i	−0.818449	−	0.574580i	$-0.805166\pi$
$499$	3.62658	−	17.1918i	0.162348	−	0.769613i	0.980797	−	0.195033i	$-0.0624815\pi$
$500$	7.93385	−	10.0164i	0.354813	−	0.447945i
$501$	8.98701	−	38.2104i	0.401510	−	1.70712i
$502$	−7.08682	+	4.85459i	−0.316300	+	0.216671i
$503$	6.86871	+	2.84511i	0.306261	+	0.126857i	0.530521	−	0.847672i	$-0.321996\pi$
$503$	6.86871	+	2.84511i	0.306261	+	0.126857i	−0.224260	+	0.974529i	$0.571996\pi$
$504$	18.1971	+	14.4137i	0.810562	+	0.642037i
$505$	−26.3359	−	9.50900i	−1.17193	−	0.423145i
$506$	9.96448	+	25.7213i	0.442975	+	1.14345i
$507$	20.5612	+	5.34000i	0.913153	+	0.237158i
$508$	20.5730	−	11.4591i	0.912777	−	0.508414i
$509$	9.34638	+	1.74714i	0.414271	+	0.0774407i	0.386759	−	0.922181i	$-0.373594\pi$
$509$	9.34638	+	1.74714i	0.414271	+	0.0774407i	0.0275120	+	0.999621i	$0.491242\pi$
$510$	18.8886	−	1.57948i	0.836400	−	0.0699404i
$511$	10.8898	−	2.03565i	0.481735	−	0.0900519i
$512$	5.64273	−	4.68566i	0.249376	−	0.207079i
$513$	−0.213289	−	0.514925i	−0.00941694	−	0.0227345i
$514$	−24.8135	+	12.3557i	−1.09448	+	0.544985i
$515$	11.8394	+	14.9471i	0.521706	+	0.658646i
$516$	−8.79023	+	4.12645i	−0.386968	+	0.181657i
$517$	−1.97863	+	17.0548i	−0.0870201	+	0.750069i
$518$	7.55323	+	1.05363i	0.331870	+	0.0462939i
$519$	−24.3917	−	43.7916i	−1.07068	−	1.92224i
$520$	−6.98745	−	9.71144i	−0.306420	−	0.425875i
$521$	25.0797	−	6.51352i	1.09876	−	0.285362i	0.342424	−	0.939546i	$-0.388752\pi$
$521$	25.0797	−	6.51352i	1.09876	−	0.285362i	0.756336	+	0.654183i	$0.226987\pi$
$522$	7.65350	−	7.30784i	0.334985	−	0.319855i
$523$	4.02679	+	21.5414i	0.176079	+	0.941940i	0.950839	+	0.309685i	$0.100223\pi$
$523$	4.02679	+	21.5414i	0.176079	+	0.941940i	−0.774760	+	0.632255i	$0.782129\pi$
$524$	0.376266	+	16.2857i	0.0164373	+	0.711445i
$525$	−5.07218	+	0.707539i	−0.221368	+	0.0308795i
$526$	11.6778	+	15.4640i	0.509178	+	0.674261i
$527$	−13.6471	+	10.6118i	−0.594475	+	0.462257i
$528$	−5.15002	+	6.81974i	−0.224126	+	0.296791i
$529$	−1.45801	+	2.61763i	−0.0633918	+	0.113810i
$530$	−0.167338	+	0.0194139i	−0.00726870	+	0.000843287i
$531$	−23.8378	+	18.0014i	−1.03447	+	0.781196i
$532$	0.548682	−	1.16881i	0.0237884	−	0.0506744i
$533$	15.5929	+	8.21914i	0.675402	+	0.356011i
$534$	−13.7940	−	29.3842i	−0.596924	−	1.27158i
$535$	1.25216	−	27.0839i	0.0541358	−	1.17094i
$536$	−18.7015	+	8.25750i	−0.807780	+	0.356670i
$537$	−3.21102	−	46.2610i	−0.138566	−	1.99631i
$538$	6.06317	−	14.6378i	0.261402	−	0.631080i
$539$	7.71992	+	24.9300i	0.332520	+	1.07381i
$540$		−	3.60595i		−	0.155175i
$541$	−19.0904	+	5.91163i	−0.820762	+	0.254161i	−0.677499	−	0.735524i	$-0.736936\pi$
$541$	−19.0904	+	5.91163i	−0.820762	+	0.254161i	−0.143263	+	0.989685i	$0.545760\pi$
$542$	6.84286	+	1.60943i	0.293926	+	0.0691308i
$543$	−1.52641	+	16.4726i	−0.0655045	+	0.706906i
$544$	16.8568	−	13.7441i	0.722730	−	0.589271i
$545$	0.413206	+	4.45920i	0.0176998	+	0.191011i
$546$	−2.01817	+	14.4678i	−0.0863699	+	0.619165i
$547$	−4.52632	+	27.7478i	−0.193532	+	1.18641i	0.692024	+	0.721875i	$0.256719\pi$
$547$	−4.52632	+	27.7478i	−0.193532	+	1.18641i	−0.885555	+	0.464534i	$0.846222\pi$
$548$	−15.4098	+	16.9038i	−0.658276	+	0.722094i
$549$	−1.03367	+	0.0238820i	−0.0441161	+	0.00101926i
$550$	−0.568078	−	3.48249i	−0.0242229	−	0.148494i
$551$	−1.40283	−	0.914082i	−0.0597625	−	0.0389412i
$552$	−34.6327	+	1.60117i	−1.47407	+	0.0681502i
$553$	−1.72817	−	5.15614i	−0.0734891	−	0.219262i
$554$	−6.56458	+	12.4539i	−0.278902	+	0.529117i
$555$	5.69081	+	9.68379i	0.241561	+	0.411054i
$556$	16.6085	+	2.70924i	0.704356	+	0.114897i
$557$	−6.03338	+	32.2758i	−0.255643	+	1.36757i	0.578349	+	0.815790i	$0.303697\pi$
$557$	−6.03338	+	32.2758i	−0.255643	+	1.36757i	−0.833991	+	0.551778i	$0.813950\pi$
$558$	5.05490	+	7.75768i	0.213991	+	0.328409i
$559$	−6.23505	−	4.27111i	−0.263715	−	0.180649i
$560$	−3.44609	+	3.14152i	−0.145624	+	0.132754i
$561$	−32.7446	+	42.5613i	−1.38248	+	1.79694i
$562$	6.49198	+	5.91822i	0.273848	+	0.249645i
$563$	−3.88448	−	16.5158i	−0.163711	−	0.696057i	−0.990953	−	0.134211i	$-0.957150\pi$
$563$	−3.88448	−	16.5158i	−0.163711	−	0.696057i	0.827242	−	0.561846i	$-0.189909\pi$
$564$	−6.86692	−	3.22358i	−0.289149	−	0.135737i
$565$	−5.51730	+	8.91075i	−0.232115	+	0.374878i
$566$	1.38313	+	2.62399i	0.0581373	+	0.110295i
$567$	−24.9440	+	26.1239i	−1.04755	+	1.09710i
$568$	−16.1797	−	0.373816i	−0.678884	−	0.0156850i
$569$	0.800846	+	5.74108i	0.0335732	+	0.240679i	0.999859	−	0.0167935i	$-0.00534578\pi$
$569$	0.800846	+	5.74108i	0.0335732	+	0.240679i	−0.966286	+	0.257472i	$0.917110\pi$
$570$	−1.56367	+	0.367771i	−0.0654948	+	0.0154042i
$571$	−22.9665	+	13.4966i	−0.961119	+	0.564814i	−0.901207	−	0.433390i	$-0.857317\pi$
$571$	−22.9665	+	13.4966i	−0.961119	+	0.564814i	−0.0599121	+	0.998204i	$0.519082\pi$
$572$	11.8358	+	1.37314i	0.494879	+	0.0574140i
$573$	−22.8961	+	31.8219i	−0.956499	+	1.32938i
$574$	10.6833	−	27.5767i	0.445912	−	1.15103i
$575$	2.18297	−	2.50861i	0.0910360	−	0.104616i
$576$	−8.29489	−	12.1091i	−0.345621	−	0.504544i
$577$	−24.9619			−1.03918			−0.519589	−	0.854416i	$-0.673915\pi$
$577$	−24.9619			−1.03918			−0.519589	+	0.854416i	$0.673915\pi$
$578$	−12.7005	+	10.1669i	−0.528272	+	0.422887i
$579$	−31.4684			−1.30778
$580$	−6.12198	−	8.93699i	−0.254201	−	0.371088i
$581$	25.5112	−	29.3169i	1.05838	−	1.21627i
$582$	−11.0082	+	28.4153i	−0.456303	+	1.17785i
$583$	0.278742	−	0.387407i	0.0115443	−	0.0160448i
$584$	−9.52975	−	1.10560i	−0.394344	−	0.0457502i
$585$	−8.06460	+	4.73927i	−0.333430	+	0.195945i
$586$	23.4551	−	5.51660i	0.968923	−	0.227889i
$587$	1.06146	+	7.60936i	0.0438112	+	0.314072i	0.999787	+	0.0206273i	$0.00656635\pi$
$587$	1.06146	+	7.60936i	0.0438112	+	0.314072i	−0.955976	+	0.293445i	$0.905198\pi$
$588$	−11.5278	−	0.266340i	−0.475400	−	0.0109837i
$589$	1.01174	−	1.05960i	0.0416881	−	0.0436600i
$590$	−12.0443	−	22.8498i	−0.495857	−	0.940711i
$591$	1.52338	−	2.46034i	0.0626634	−	0.101205i
$592$	−1.38880	−	0.651951i	−0.0570792	−	0.0267950i
$593$	8.27249	+	35.1725i	0.339710	+	1.44436i	0.822571	+	0.568663i	$0.192539\pi$
$593$	8.27249	+	35.1725i	0.339710	+	1.44436i	−0.482860	+	0.875697i	$0.660402\pi$
$594$	−6.37721	−	5.81360i	−0.261660	−	0.238535i
$595$	−21.8306	+	19.5454i	−0.894967	+	0.801284i
$596$	7.24432	−	6.60407i	0.296739	−	0.270513i
$597$	−52.8131	−	36.1778i	−2.16150	−	1.48066i
$598$	−5.17837	−	7.94717i	−0.211759	−	0.324984i
$599$	−4.44675	+	23.7880i	−0.181689	+	0.971952i	0.763593	+	0.645698i	$0.223434\pi$
$599$	−4.44675	+	23.7880i	−0.181689	+	0.971952i	−0.945282	+	0.326254i	$0.894214\pi$
$600$	4.37708	+	0.714006i	0.178693	+	0.0291492i
$601$	2.52043	+	4.28890i	0.102810	+	0.174948i	0.909106	−	0.416565i	$-0.136766\pi$
$601$	2.52043	+	4.28890i	0.102810	+	0.174948i	−0.806296	+	0.591513i	$0.798531\pi$
$602$	−5.91277	+	11.2174i	−0.240987	+	0.457185i
$603$	5.07948	+	15.1551i	0.206852	+	0.617164i
$604$	−7.13361	+	0.329807i	−0.290263	+	0.0134197i
$605$	−36.6155	−	23.8587i	−1.48863	−	0.969993i
$606$	−4.76642	−	29.2197i	−0.193623	−	1.18697i
$607$	−12.5142	+	0.289128i	−0.507935	+	0.0117354i	−0.276308	−	0.961069i	$-0.589111\pi$
$607$	−12.5142	+	0.289128i	−0.507935	+	0.0117354i	−0.231627	+	0.972805i	$0.574405\pi$
$608$	−1.24177	+	1.36216i	−0.0503605	+	0.0552428i
$609$	−6.05762	+	37.1351i	−0.245467	+	1.50479i
$610$	0.123520	−	0.885487i	0.00500118	−	0.0358523i
$611$	−0.544756	−	5.87885i	−0.0220385	−	0.237833i
$612$	−5.75318	−	8.56239i	−0.232558	−	0.346114i
$613$	−2.35246	+	25.3871i	−0.0950150	+	1.02538i	0.806095	+	0.591786i	$0.201577\pi$
$613$	−2.35246	+	25.3871i	−0.0950150	+	1.02538i	−0.901110	+	0.433590i	$0.857247\pi$
$614$	−1.77489	−	0.417450i	−0.0716286	−	0.0168469i
$615$	41.6072	−	12.8843i	1.67776	−	0.519544i
$616$		−	56.8694i		−	2.29133i
$617$	10.2357	+	33.0542i	0.412074	+	1.33071i	0.891456	+	0.453107i	$0.149684\pi$
$617$	10.2357	+	33.0542i	0.412074	+	1.33071i	−0.479382	+	0.877606i	$0.659139\pi$
$618$	−7.71548	+	18.6268i	−0.310362	+	0.749281i
$619$	1.74448	+	25.1326i	0.0701165	+	1.01016i	0.895347	+	0.445369i	$0.146927\pi$
$619$	1.74448	+	25.1326i	0.0701165	+	1.01016i	−0.825231	+	0.564796i	$0.808955\pi$
$620$	8.67094	−	3.82859i	0.348233	−	0.153760i
$621$	0.375597	−	8.12404i	0.0150722	−	0.326007i
$622$	2.68730	+	5.72453i	0.107751	+	0.229533i
$623$	44.3918	+	23.3993i	1.77852	+	0.937475i
$624$	1.24878	−	2.66017i	0.0499911	−	0.106492i
$625$	17.0086	−	12.8443i	0.680342	−	0.513771i
$626$	4.44332	−	0.515497i	0.177591	−	0.0206034i
$627$	2.21449	−	3.97577i	0.0884382	−	0.158777i
$628$	14.3472	−	18.9987i	0.572515	−	0.758133i
$629$	−8.68972	−	4.17483i	−0.346482	−	0.166461i
$630$	9.45793	+	12.5243i	0.376813	+	0.498981i
$631$	−0.298686	+	0.0416650i	−0.0118905	+	0.00165866i	−0.144099	−	0.989563i	$-0.546028\pi$
$631$	−0.298686	+	0.0416650i	−0.0118905	+	0.00165866i	0.132209	+	0.991222i	$0.457793\pi$
$632$	0.108773	+	4.70798i	0.00432677	+	0.187273i
$633$	−0.787253	−	4.21143i	−0.0312905	−	0.167389i
$634$	11.3908	−	10.8763i	0.452386	−	0.431954i
$635$	43.8357	−	11.3847i	1.73957	−	0.451788i
$636$	0.123158	+	0.171169i	0.00488351	+	0.00678730i
$637$	−4.36698	−	7.84022i	−0.173026	−	0.310641i
$638$	−25.6753	−	3.58155i	−1.01650	−	0.141795i
$639$	−1.45823	+	12.5692i	−0.0576866	+	0.497230i
$640$	−8.42458	+	3.95480i	−0.333011	+	0.156327i
$641$	−22.8444	−	28.8406i	−0.902298	−	1.13914i	−0.989728	−	0.142966i	$-0.954336\pi$
$641$	−22.8444	−	28.8406i	−0.902298	−	1.13914i	0.0874300	−	0.996171i	$-0.472135\pi$
$642$	25.6624	−	12.7783i	1.01281	−	0.504321i
$643$	3.17340	+	7.66125i	0.125146	+	0.302130i	0.974019	−	0.226468i	$-0.0727178\pi$
$643$	3.17340	+	7.66125i	0.125146	+	0.302130i	−0.848872	+	0.528598i	$0.822718\pi$
$644$	14.4948	−	12.0363i	0.571175	−	0.474298i
$645$	−18.3576	+	3.43164i	−0.722831	+	0.135121i
$646$	0.937942	−	1.01051i	0.0369028	−	0.0397580i
$647$	−16.9099	−	3.16102i	−0.664799	−	0.124272i	−0.159475	−	0.987202i	$-0.550980\pi$
$647$	−16.9099	−	3.16102i	−0.664799	−	0.124272i	−0.505324	+	0.862930i	$0.668627\pi$
$648$	27.3262	−	15.2206i	1.07348	−	0.597922i
$649$	70.8286	+	18.3951i	2.78026	+	0.722071i
$650$	0.438319	+	1.13143i	0.0171923	+	0.0443784i
$651$	−30.9657	−	11.1807i	−1.21364	−	0.438205i
$652$	−4.60707	−	3.64921i	−0.180427	−	0.142914i
$653$	−7.89816	−	3.27152i	−0.309079	−	0.128025i	0.222752	−	0.974875i	$-0.428496\pi$
$653$	−7.89816	−	3.27152i	−0.309079	−	0.128025i	−0.531831	+	0.846850i	$0.678496\pi$
$654$	−3.90648	+	2.67600i	−0.152756	+	0.104640i
$655$	−7.17287	+	30.4972i	−0.280267	+	1.19162i
$656$	−3.69403	+	4.66365i	−0.144227	+	0.182085i
$657$	−1.54821	+	7.33932i	−0.0604014	+	0.286334i
$658$	−9.69253	+	2.04461i	−0.377854	+	0.0797074i
$659$	4.43222	−	1.26108i	0.172655	−	0.0491246i	−0.186231	−	0.982506i	$-0.559627\pi$
$659$	4.43222	−	1.26108i	0.172655	−	0.0491246i	0.358886	+	0.933381i	$0.383157\pi$
$660$	23.0802	−	18.2816i	0.898397	−	0.711610i
$661$	−17.5793	+	5.89198i	−0.683755	+	0.229171i	−0.638292	−	0.769795i	$-0.720359\pi$
$661$	−17.5793	+	5.89198i	−0.683755	+	0.229171i	−0.0454629	+	0.998966i	$0.514476\pi$
$662$	15.7061	+	9.72480i	0.610435	+	0.377965i
$663$	7.99667	−	16.6447i	0.310565	−	0.646427i
$664$	−28.6134	+	17.7167i	−1.11042	+	0.687540i
$665$	1.58641	−	1.91044i	0.0615184	−	0.0740838i
$666$	−2.61614	+	4.45177i	−0.101373	+	0.172502i
$667$	−12.8617	−	20.7723i	−0.498006	−	0.804308i
$668$	−2.12884	−	18.3495i	−0.0823672	−	0.709964i
$669$	−1.24866	+	54.0449i	−0.0482758	+	2.08949i
$670$	−13.6409	+	2.22515i	−0.526993	+	0.0859651i
$671$	1.61817	+	1.94869i	0.0624689	+	0.0752284i
$672$	39.2735	+	13.1631i	1.51501	+	0.507779i
$673$	29.5152	−	10.6569i	1.13773	−	0.410795i	0.298411	−	0.954438i	$-0.403544\pi$
$673$	29.5152	−	10.6569i	1.13773	−	0.410795i	0.839317	+	0.543643i	$0.182955\pi$
$674$	6.13888	+	7.05466i	0.236461	+	0.271735i
$675$	−0.261512	+	1.00693i	−0.0100656	+	0.0387567i
$676$	9.95450	−	0.922420i	0.382865	−	0.0354777i
$677$	−31.0978	−	22.3751i	−1.19519	−	0.859944i	−0.202335	−	0.979316i	$-0.564853\pi$
$677$	−31.0978	−	22.3751i	−1.19519	−	0.859944i	−0.992850	+	0.119372i	$0.961912\pi$
$678$	−11.0698	−	0.511789i	−0.425134	−	0.0196551i
$679$	−12.8919	−	45.3102i	−0.494745	−	1.73885i
$680$	23.0656	−	10.5763i	0.884525	−	0.405582i
$681$	9.43132	−	33.1477i	0.361409	−	1.27022i
$682$	7.20853	−	21.5073i	0.276029	−	0.823559i
$683$	30.1378	+	31.5633i	1.15319	+	1.20774i	0.974633	+	0.223808i	$0.0718487\pi$
$683$	30.1378	+	31.5633i	1.15319	+	1.20774i	0.178557	+	0.983930i	$0.442857\pi$
$684$	0.588961	+	0.646059i	0.0225195	+	0.0247027i
$685$	−36.8570	+	24.0160i	−1.40823	+	0.917603i
$686$	6.31064	−	4.54056i	0.240942	−	0.173359i
$687$	20.0737	−	17.4679i	0.765859	−	0.666442i
$688$	1.80377	−	1.80377i	0.0687681	−	0.0687681i
$689$	−0.0662911	+	0.150135i	−0.00252549	+	0.00571969i
$690$	−22.9345	−	4.83798i	−0.873102	−	0.184179i
$691$	−7.98114	+	0.553978i	−0.303617	+	0.0210743i	−0.220246	−	0.975444i	$-0.570686\pi$
$691$	−7.98114	+	0.553978i	−0.303617	+	0.0210743i	−0.0833704	+	0.996519i	$0.526568\pi$
$692$	−17.7954	−	15.4853i	−0.676478	−	0.588663i
$693$	−44.2738	−	4.10257i	−1.68182	−	0.155844i
$694$	−6.76367	+	18.7325i	−0.256745	+	0.711075i
$695$	29.6063	+	13.0725i	1.12303	+	0.495867i
$696$	14.5236	−	29.1673i	0.550516	−	1.10558i
$697$	−23.4743	+	29.0957i	−0.889153	+	1.10208i
$698$	−7.11852	−	14.2959i	−0.269440	−	0.541109i
$699$	1.29029	+	27.9086i	0.0488033	+	1.05560i
$700$	−2.13204	+	1.12382i	−0.0805835	+	0.0424763i
$701$	−14.5171	−	10.9628i	−0.548304	−	0.414060i	0.291805	−	0.956478i	$-0.405744\pi$
$701$	−14.5171	−	10.9628i	−0.548304	−	0.414060i	−0.840109	+	0.542418i	$0.817509\pi$
$702$	2.55837	+	1.50346i	0.0965594	+	0.0567444i
$703$	0.780446	+	0.241676i	0.0294351	+	0.00911498i
$704$	−10.6364	+	34.3481i	−0.400874	+	1.29454i
$705$	−11.2241	−	9.32037i	−0.422724	−	0.351025i
$706$	22.9606	+	12.7890i	0.864135	+	0.481320i
$707$	33.1017	+	31.6066i	1.24492	+	1.18869i
$708$	−17.6513	+	27.0892i	−0.663377	+	1.01808i
$709$	−42.0682	+	17.4252i	−1.57990	+	0.654418i	−0.988399	−	0.151882i	$-0.951466\pi$
$709$	−42.0682	+	17.4252i	−1.57990	+	0.654418i	−0.591506	+	0.806300i	$0.701466\pi$
$710$	−10.5239	−	2.99430i	−0.394953	−	0.112374i
$711$	3.67309	+	0.254953i	0.137752	+	0.00956148i
$712$	−30.7280	−	30.7280i	−1.15158	−	1.15158i
$713$	19.9340	−	7.72249i	0.746536	−	0.289210i
$714$	−29.2867	−	10.1091i	−1.09603	−	0.378325i
$715$	21.3681	+	8.27804i	0.799121	+	0.309581i
$716$	−8.81473	−	19.9635i	−0.329422	−	0.746070i
$717$	1.73596	+	8.22937i	0.0648308	+	0.307331i
$718$	5.94318	+	2.95935i	0.221797	+	0.110442i
$719$	1.78127	−	25.6627i	0.0664303	−	0.957057i	−0.842122	−	0.539286i	$-0.818694\pi$
$719$	1.78127	−	25.6627i	0.0664303	−	0.957057i	0.908553	−	0.417770i	$-0.137188\pi$
$720$	−1.07222	−	2.96961i	−0.0399595	−	0.110671i
$721$	−7.83477	−	30.1670i	−0.291782	−	1.12348i
$722$	10.2096	−	14.9042i	0.379963	−	0.554678i
$723$	−10.9771	+	16.0246i	−0.408242	+	0.595960i
$724$	1.95701	+	7.53527i	0.0727316	+	0.280046i
$725$	1.06137	+	2.93956i	0.0394185	+	0.109172i
$726$	3.19973	−	46.0983i	0.118753	−	1.71087i
$727$	19.3508	+	9.63554i	0.717680	+	0.357362i	0.767197	−	0.641411i	$-0.221651\pi$
$727$	19.3508	+	9.63554i	0.717680	+	0.357362i	−0.0495173	+	0.998773i	$0.515768\pi$
$728$	4.03644	+	19.1348i	0.149600	+	0.709183i
$729$	−5.42523	−	12.2870i	−0.200934	−	0.455073i
$730$	−6.04802	−	2.34302i	−0.223847	−	0.0867189i
$731$	11.4357	−	11.2323i	0.422964	−	0.415441i
$732$	−1.04357	+	0.404282i	−0.0385715	+	0.0149427i
$733$	23.1160	+	23.1160i	0.853809	+	0.853809i	0.990600	−	0.136791i	$-0.0436790\pi$
$733$	23.1160	+	23.1160i	0.853809	+	0.853809i	−0.136791	+	0.990600i	$0.543679\pi$
$734$	−20.3834	−	1.41483i	−0.752364	−	0.0522223i
$735$	−21.3299	−	6.06887i	−0.786764	−	0.223854i
$736$	−24.8485	+	10.2926i	−0.915929	+	0.379390i
$737$	21.3768	−	32.8067i	0.787426	−	1.20845i
$738$	14.4820	+	13.8279i	0.533089	+	0.509013i
$739$	−6.72864	−	3.74783i	−0.247517	−	0.137866i	0.357939	−	0.933745i	$-0.383480\pi$
$739$	−6.72864	−	3.74783i	−0.247517	−	0.137866i	−0.605456	+	0.795879i	$0.707009\pi$
$740$	4.06660	+	3.37687i	0.149491	+	0.124136i
$741$	−0.462918	+	1.49490i	−0.0170057	+	0.0549166i
$742$	0.263037	+	0.0814532i	0.00965639	+	0.00299024i
$743$	−15.3102	−	8.99721i	−0.561675	−	0.330076i	0.198183	−	0.980165i	$-0.436496\pi$
$743$	−15.3102	−	8.99721i	−0.561675	−	0.330076i	−0.759858	+	0.650089i	$0.774731\pi$
$744$	22.7515	+	17.1812i	0.834112	+	0.629892i
$745$	16.6778	−	8.79100i	0.611026	−	0.322077i
$746$	−0.232965	−	5.03895i	−0.00852945	−	0.184489i
$747$	11.7286	+	23.5541i	0.429125	+	0.861800i
$748$	−7.69172	+	24.0723i	−0.281237	+	0.880171i
$749$	−19.7541	+	39.6716i	−0.721799	+	1.44957i
$750$	23.7700	+	10.4955i	0.867959	+	0.383241i
$751$	−8.46732	+	23.4509i	−0.308977	+	0.855734i	0.683125	+	0.730301i	$0.260620\pi$
$751$	−8.46732	+	23.4509i	−0.308977	+	0.855734i	−0.992102	+	0.125433i	$0.959968\pi$
$752$	1.98427	+	0.183870i	0.0723589	+	0.00670504i
$753$	15.6003	+	13.5752i	0.568507	+	0.494708i
$754$	8.89316	−	0.617283i	0.323870	−	0.0224801i
$755$	−13.4384	−	2.83480i	−0.489074	−	0.103169i
$756$	−2.38077	+	5.39194i	−0.0865879	+	0.196103i
$757$	27.2335	−	27.2335i	0.989818	−	0.989818i	−0.0101310	−	0.999949i	$-0.503225\pi$
$757$	27.2335	−	27.2335i	0.989818	−	0.989818i	0.999949	+	0.0101310i	$0.00322485\pi$
$758$	13.7932	−	12.0027i	0.500992	−	0.435958i
$759$	53.9030	−	38.7836i	1.95656	−	1.40776i
$760$	−1.80170	+	1.17399i	−0.0653545	+	0.0425850i
$761$	−3.61844	−	3.96924i	−0.131168	−	0.143885i	0.669915	−	0.742438i	$-0.266331\pi$
$761$	−3.61844	−	3.96924i	−0.131168	−	0.143885i	−0.801083	+	0.598553i	$0.795742\pi$
$762$	33.0704	+	34.6346i	1.19801	+	1.25468i
$763$	2.32626	−	6.94061i	0.0842163	−	0.251267i
$764$	−5.04880	+	17.7447i	−0.182659	+	0.641981i
$765$	−6.56987	−	18.7199i	−0.237534	−	0.676821i
$766$	3.11717	+	10.9557i	0.112628	+	0.395846i
$767$	−25.1373	−	1.16217i	−0.907654	−	0.0419634i
$768$	−31.7768	−	22.8636i	−1.14665	−	0.825021i
$769$	−0.457835	+	0.0424246i	−0.0165099	+	0.00152987i	−0.100520	−	0.994935i	$-0.532051\pi$
$769$	−0.457835	+	0.0424246i	−0.0165099	+	0.00152987i	0.0840102	+	0.996465i	$0.473227\pi$
$770$	9.66477	−	37.2132i	0.348294	−	1.34107i
$771$	43.8060	+	50.3408i	1.57763	+	1.81298i
$772$	−13.9290	+	5.02927i	−0.501314	+	0.181008i
$773$	−41.7345	−	13.9880i	−1.50109	−	0.503113i	−0.556351	−	0.830947i	$-0.687799\pi$
$773$	−41.7345	−	13.9880i	−1.50109	−	0.503113i	−0.944735	+	0.327834i	$0.893681\pi$
$774$	−5.48477	−	6.60506i	−0.197146	−	0.237414i
$775$	−2.69894	+	0.440262i	−0.0969488	+	0.0158147i
$776$	−0.942279	+	40.7841i	−0.0338258	+	1.46407i
$777$	−2.11583	−	18.2374i	−0.0759049	−	0.654262i
$778$	9.55220	+	15.4273i	0.342463	+	0.553097i
$779$	1.60519	−	2.73148i	0.0575120	−	0.0978656i
$780$	−6.46821	+	7.78937i	−0.231599	+	0.278904i
$781$	26.3554	−	16.3186i	0.943071	−	0.583925i
$782$	18.6549	−	7.53171i	0.667097	−	0.269333i
$783$	6.49845	+	4.02367i	0.232236	+	0.143794i
$784$	2.87207	−	0.962622i	0.102574	−	0.0343793i
$785$	35.8917	−	28.4294i	1.28103	−	1.01469i
$786$	−31.8616	+	9.06541i	−1.13647	+	0.323352i
$787$	−7.31465	+	1.54301i	−0.260739	+	0.0550023i	−0.334934	−	0.942241i	$-0.608714\pi$
$787$	−7.31465	+	1.54301i	−0.260739	+	0.0550023i	0.0741951	+	0.997244i	$0.476361\pi$
$788$	0.281086	−	1.33249i	0.0100133	−	0.0474681i
$789$	28.9656	−	36.5686i	1.03120	−	1.30188i
$790$	−0.728929	+	3.09921i	−0.0259341	+	0.110265i
$791$	14.1332	−	9.68144i	0.502518	−	0.344233i
$792$	35.5735	+	14.7350i	1.26405	+	0.523586i
$793$	−0.682778	−	0.540821i	−0.0242462	−	0.0192051i
$794$	−3.35568	−	1.21162i	−0.119089	−	0.0429989i
$795$	0.146502	+	0.378166i	0.00519590	+	0.0134122i
$796$	−29.1588	−	7.57292i	−1.03351	−	0.268415i
$797$	−25.5336	+	14.2221i	−0.904447	+	0.503773i	−0.868561	−	0.495582i	$-0.834955\pi$
$797$	−25.5336	+	14.2221i	−0.904447	+	0.503773i	−0.0358857	+	0.999356i	$0.511425\pi$
$798$	2.58095	+	0.482464i	0.0913648	+	0.0170790i
$799$	12.4578	+	1.26722i	0.440725	+	0.0448312i
$800$	3.38192	−	0.632191i	0.119569	−	0.0223513i
$801$	−26.1390	+	21.7056i	−0.923577	+	0.766928i
$802$	−1.50316	−	3.62894i	−0.0530783	−	0.128142i
$803$	16.4491	−	8.19066i	0.580475	−	0.289042i
$804$	10.7421	+	13.5618i	0.378846	+	0.478287i
$805$	32.8005	−	15.3977i	1.15607	−	0.542699i
$806$	−0.898916	+	7.74820i	−0.0316630	+	0.272919i
$807$	−37.7767	−	5.26962i	−1.32980	−	0.185499i
$808$	−19.2861	−	34.6252i	−0.678482	−	1.21811i
$809$	−1.70482	−	2.36943i	−0.0599384	−	0.0833048i	0.780685	−	0.624924i	$-0.214870\pi$
$809$	−1.70482	−	2.36943i	−0.0599384	−	0.0833048i	−0.840624	+	0.541620i	$0.817811\pi$
$810$	20.4680	−	5.31580i	0.719171	−	0.186778i
$811$	25.4345	−	24.2858i	0.893127	−	0.852789i	−0.0966638	−	0.995317i	$-0.530817\pi$
$811$	25.4345	−	24.2858i	0.893127	−	0.852789i	0.989791	+	0.142528i	$0.0455230\pi$
$812$	3.25363	+	17.4054i	0.114180	+	0.610808i
$813$	−0.390886	−	16.9185i	−0.0137090	−	0.593357i
$814$	12.5284	−	1.74763i	0.439119	−	0.0612544i
$815$	−6.81169	−	9.02014i	−0.238603	−	0.315962i
$816$	5.02643	+	3.68545i	0.175960	+	0.129017i
$817$	−0.818640	+	1.08405i	−0.0286406	+	0.0379262i
$818$	2.52707	−	4.53697i	0.0883571	−	0.158631i
$819$	15.1880	−	1.76205i	0.530710	−	0.0615709i
$820$	16.3576	−	12.3527i	0.571231	−	0.431374i
$821$	18.6523	−	39.7335i	0.650971	−	1.38671i	−0.256480	−	0.966550i	$-0.582563\pi$
$821$	18.6523	−	39.7335i	0.650971	−	1.38671i	0.907451	−	0.420159i	$-0.138026\pi$
$822$	−41.1475	−	21.6892i	−1.43519	−	0.756499i
$823$	−18.0417	−	38.4326i	−0.628893	−	1.33968i	−0.923330	−	0.384007i	$-0.874544\pi$
$823$	−18.0417	−	38.4326i	−0.628893	−	1.33968i	0.294437	−	0.955671i	$-0.404868\pi$
$824$	−1.24652	+	26.9619i	−0.0434247	+	0.939261i
$825$	−7.77078	+	3.43113i	−0.270544	+	0.119457i
$826$	2.92353	+	42.1192i	0.101723	+	1.46551i
$827$	6.11926	−	14.7732i	0.212788	−	0.513715i	−0.781062	−	0.624454i	$-0.785322\pi$
$827$	6.11926	−	14.7732i	0.212788	−	0.513715i	0.993850	+	0.110739i	$0.0353217\pi$
$828$	3.77344	+	12.1856i	0.131136	+	0.423478i
$829$		−	27.2504i		−	0.946444i	−0.880943	−	0.473222i	$-0.843091\pi$
$829$		−	27.2504i		−	0.946444i	0.880943	−	0.473222i	$-0.156909\pi$
$830$	−21.7344	+	6.73038i	−0.754414	+	0.233615i
$831$	32.9915	+	7.75953i	1.14446	+	0.269175i
$832$	1.14088	−	12.3120i	0.0395528	−	0.426843i
$833$	18.1009	−	5.88668i	0.627159	−	0.203961i
$834$	3.15743	+	34.0741i	0.109333	+	1.17989i
$835$	4.90826	−	35.1861i	0.169857	−	1.21767i
$836$	0.344799	−	2.11373i	0.0119251	−	0.0731048i
$837$	−4.50555	+	4.94235i	−0.155735	+	0.170833i
$838$	−38.0050	+	0.878069i	−1.31286	+	0.0303324i
$839$	−6.19972	−	38.0062i	−0.214038	−	1.31212i	−0.844356	−	0.535783i	$-0.820017\pi$
$839$	−6.19972	−	38.0062i	−0.214038	−	1.31212i	0.630318	−	0.776337i	$-0.282925\pi$
$840$	40.4876	+	26.3817i	1.39695	+	0.910254i
$841$	−6.03211	+	0.278881i	−0.208004	+	0.00961659i
$842$	6.43855	+	19.2100i	0.221887	+	0.662021i
$843$	9.86137	−	18.7084i	0.339644	−	0.644352i
$844$	−1.02154	−	1.73830i	−0.0351627	−	0.0598348i
$845$	18.9759	+	3.09542i	0.652790	+	0.106486i
$846$	1.23239	−	6.59272i	0.0423706	−	0.226663i
$847$	38.9986	+	59.8505i	1.34001	+	2.05649i
$848$	−0.0457004	−	0.0313055i	−0.00156936	−	0.00107504i
$849$	5.27715	−	4.81076i	0.181111	−	0.165105i
$850$	−2.53379	+	0.450157i	−0.0869084	+	0.0154402i
$851$	8.81015	+	8.03151i	0.302008	+	0.275317i
$852$	3.13574	+	13.3323i	0.107429	+	0.456758i
$853$	10.8572	+	5.09677i	0.371744	+	0.174510i	0.601760	−	0.798677i	$-0.294466\pi$
$853$	10.8572	+	5.09677i	0.371744	+	0.174510i	−0.230016	+	0.973187i	$0.573878\pi$
$854$	−0.769329	+	1.24251i	−0.0263259	+	0.0425178i
$855$	0.783994	+	1.48735i	0.0268120	+	0.0508662i
$856$	26.5034	−	27.7571i	0.905869	−	0.948717i
$857$	−19.0152	−	0.439329i	−0.649548	−	0.0150072i	−0.302929	−	0.953013i	$-0.597964\pi$
$857$	−19.0152	−	0.439329i	−0.649548	−	0.0150072i	−0.346619	+	0.938006i	$0.612670\pi$
$858$	3.34750	+	23.9974i	0.114282	+	0.819258i
$859$	−14.4736	+	3.40416i	−0.493833	+	0.116149i	−0.468379	−	0.883527i	$-0.655162\pi$
$859$	−14.4736	+	3.40416i	−0.493833	+	0.116149i	−0.0254539	+	0.999676i	$0.508103\pi$
$860$	−7.57726	+	4.45287i	−0.258382	+	0.151842i
$861$	−70.7216	−	8.20484i	−2.41018	−	0.279620i
$862$	−8.56736	+	11.9073i	−0.291805	+	0.405563i
$863$	−2.80220	+	7.23331i	−0.0953880	+	0.246225i	−0.972003	−	0.234967i	$-0.924502\pi$
$863$	−2.80220	+	7.23331i	−0.0953880	+	0.246225i	0.876615	+	0.481192i	$0.159796\pi$
$864$	5.52343	−	6.34740i	0.187911	−	0.215943i
$865$	−25.6391	−	37.4285i	−0.871756	−	1.27261i
$866$	−6.15190			−0.209050
$867$	31.3757	+	23.4409i	1.06557	+	0.796094i
$868$	−15.4934			−0.525879
$869$	−5.09751	−	7.44145i	−0.172921	−	0.252434i
$870$	14.4606	−	16.6178i	0.490261	−	0.563396i
$871$	−4.86411	+	12.5557i	−0.164814	+	0.425434i
$872$	−3.70226	+	5.14555i	−0.125374	+	0.174250i
$873$	31.6832	+	3.67576i	1.07231	+	0.124406i
$874$	−1.46991	+	0.863810i	−0.0497203	+	0.0292188i
$875$	−39.1019	+	9.19668i	−1.32188	+	0.310904i
$876$	1.12168	+	8.04103i	0.0378979	+	0.271681i
$877$	5.47713	+	0.126544i	0.184949	+	0.00427308i	0.115474	−	0.993311i	$-0.463161\pi$
$877$	5.47713	+	0.126544i	0.184949	+	0.00427308i	0.0694759	+	0.997584i	$0.477867\pi$
$878$	23.1281	−	24.2221i	0.780536	−	0.817456i
$879$	−27.0483	−	51.3144i	−0.912315	−	1.73079i
$880$	−4.07175	+	6.57610i	−0.137259	+	0.221680i
$881$	−45.8860	−	21.5405i	−1.54594	−	0.725719i	−0.551813	−	0.833968i	$-0.686064\pi$
$881$	−45.8860	−	21.5405i	−1.54594	−	0.725719i	−0.994124	+	0.108249i	$0.965476\pi$
$882$	−2.33411	−	9.92401i	−0.0785934	−	0.334159i
$883$	10.7229	+	9.77524i	0.360855	+	0.328963i	0.833736	−	0.552163i	$-0.186198\pi$
$883$	10.7229	+	9.77524i	0.360855	+	0.328963i	−0.472881	+	0.881127i	$0.656786\pi$
$884$	0.879437	−	8.64553i	0.0295787	−	0.290781i
$885$	−45.9535	+	41.8922i	−1.54471	+	1.40819i
$886$	25.6284	+	17.5559i	0.861004	+	0.589801i
$887$	−3.21028	−	4.92677i	−0.107791	−	0.165425i	0.779843	−	0.625975i	$-0.215299\pi$
$887$	−3.21028	−	4.92677i	−0.107791	−	0.165425i	−0.887633	+	0.460551i	$0.847652\pi$
$888$	−2.92145	+	15.6284i	−0.0980376	+	0.524455i
$889$	−73.0637	−	11.9184i	−2.45048	−	0.399731i
$890$	−14.8852	−	25.3294i	−0.498951	−	0.849044i
$891$	−27.9365	+	52.9994i	−0.935907	+	1.77555i
$892$	8.08475	+	24.1216i	0.270697	+	0.807651i
$893$	−1.06007	+	0.0490102i	−0.0354740	+	0.00164006i
$894$	16.7014	+	10.8826i	0.558578	+	0.363969i
$895$	−6.75704	−	41.4228i	−0.225863	−	1.38461i
$896$	15.2083	−	0.351373i	0.508074	−	0.0117386i
$897$	−15.3839	+	16.8754i	−0.513655	+	0.563453i
$898$	4.73039	−	28.9987i	0.157855	−	0.967701i
$899$	−2.77571	+	19.8984i	−0.0925752	+	0.663650i
$900$	−0.150563	−	1.62484i	−0.00501877	−	0.0541612i
$901$	−0.285393	−	0.199285i	−0.00950782	−	0.00663913i
$902$	4.52607	−	48.8441i	0.150702	−	1.62633i
$903$	29.7157	+	6.98907i	0.988877	+	0.232582i
$904$	−14.1713	+	4.38835i	−0.471331	+	0.145954i
$905$			14.9727i			0.497711i
$906$	−4.29565	−	13.8720i	−0.142713	−	0.460865i
$907$	5.00160	−	12.0749i	0.166075	−	0.400942i	−0.818830	−	0.574037i	$-0.805377\pi$
$907$	5.00160	−	12.0749i	0.166075	−	0.400942i	0.984905	+	0.173095i	$0.0553767\pi$
$908$	−1.12304	−	16.1796i	−0.0372694	−	0.536938i
$909$	−28.3476	+	12.5167i	−0.940231	+	0.415152i
$910$	−0.610601	+	13.2071i	−0.0202412	+	0.437811i
$911$	22.5140	+	47.9597i	0.745923	+	1.58898i	0.806796	+	0.590830i	$0.201200\pi$
$911$	22.5140	+	47.9597i	0.745923	+	1.58898i	−0.0608730	+	0.998146i	$0.519388\pi$
$912$	−0.467269	−	0.246302i	−0.0154728	−	0.00815586i
$913$	27.3921	−	58.3510i	0.906545	−	1.93113i
$914$	−19.1359	+	14.4507i	−0.632959	+	0.477988i
$915$	−2.13802	+	0.248045i	−0.0706808	+	0.00820010i
$916$	6.09357	−	10.9401i	0.201337	−	0.361470i
$917$	30.8609	−	40.8664i	1.01912	−	1.34953i
$918$	−4.17393	+	4.71055i	−0.137760	+	0.155471i
$919$	8.97487	+	11.8846i	0.296054	+	0.392038i	0.921595	−	0.388153i	$-0.126887\pi$
$919$	8.97487	+	11.8846i	0.296054	+	0.392038i	−0.625542	+	0.780191i	$0.715122\pi$
$920$	−31.0777	+	4.33515i	−1.02460	+	0.142926i
$921$	0.101387	+	4.38828i	0.00334082	+	0.144599i
$922$	−1.37710	−	7.36686i	−0.0453525	−	0.242614i
$923$	−7.70954	+	7.36134i	−0.253762	+	0.242301i
$924$	−46.5819	+	12.0979i	−1.53243	+	0.397992i
$925$	−0.890664	−	1.23788i	−0.0292848	−	0.0407012i
$926$	15.1823	+	27.2575i	0.498922	+	0.895737i
$927$	20.9004	+	2.91548i	0.686458	+	0.0957568i
$928$	2.91303	−	25.1088i	0.0956248	−	0.824237i
$929$	42.1456	−	19.7847i	1.38275	−	0.649114i	0.417078	−	0.908871i	$-0.363054\pi$
$929$	42.1456	−	19.7847i	1.38275	−	0.649114i	0.965674	+	0.259757i	$0.0836426\pi$
$930$	11.9679	+	15.1093i	0.392443	+	0.495453i
$931$	−1.44397	+	0.719011i	−0.0473242	+	0.0235646i
$932$	5.03147	+	12.1471i	0.164811	+	0.397890i
$933$	11.7125	−	9.72592i	0.383450	−	0.318412i
$934$	3.52290	−	0.658545i	0.115273	−	0.0215482i
$935$	−25.9556	+	41.0912i	−0.848837	+	1.34383i
$936$	−13.0152	−	2.43297i	−0.425416	−	0.0795240i
$937$	14.1063	−	7.85717i	0.460833	−	0.256682i	−0.238958	−	0.971030i	$-0.576806\pi$
$937$	14.1063	−	7.85717i	0.460833	−	0.256682i	0.699791	+	0.714347i	$0.253276\pi$
$938$	21.8662	+	5.67894i	0.713957	+	0.185424i
$939$	−3.89007	−	10.0414i	−0.126948	−	0.327689i
$940$	−6.45774	−	2.33167i	−0.210628	−	0.0760508i
$941$	9.33471	+	7.39392i	0.304303	+	0.241035i	0.761249	−	0.648459i	$-0.224586\pi$
$941$	9.33471	+	7.39392i	0.304303	+	0.241035i	−0.456946	+	0.889494i	$0.651057\pi$
$942$	44.7277	+	18.5268i	1.45731	+	0.603637i
$943$	38.1396	−	26.1262i	1.24200	−	0.850787i
$944$	1.94461	−	8.26797i	0.0632916	−	0.269099i
$945$	−7.03845	+	8.88593i	−0.228961	+	0.289059i
$946$	−4.34122	+	20.5796i	−0.141145	+	0.669101i
$947$	−22.4270	+	4.73091i	−0.728779	+	0.153734i	−0.555947	−	0.831217i	$-0.687644\pi$
$947$	−22.4270	+	4.73091i	−0.728779	+	0.153734i	−0.172831	+	0.984951i	$0.555291\pi$
$948$	3.83318	−	1.09063i	0.124496	−	0.0354221i
$949$	−4.95325	+	3.92341i	−0.160789	+	0.127359i
$950$	0.206788	−	0.0693084i	0.00670909	−	0.00224866i
$951$	−32.2361	−	19.9598i	−1.04533	−	0.647240i
$952$	−41.4726	+	0.585917i	−1.34414	+	0.0189897i
$953$	−11.2579	+	6.97058i	−0.364678	+	0.225799i	−0.696523	−	0.717535i	$-0.745270\pi$
$953$	−11.2579	+	6.97058i	−0.364678	+	0.225799i	0.331844	+	0.943334i	$0.392329\pi$
$954$	−0.119105	+	0.143433i	−0.00385617	+	0.00464380i
$955$	−17.9768	+	30.5903i	−0.581715	+	0.989879i
$956$	2.08361	+	3.36515i	0.0673889	+	0.108837i
$957$	7.19223	+	61.9934i	0.232492	+	2.00396i
$958$	0.114275	−	4.94611i	0.00369206	−	0.159801i
$959$	70.9681	−	11.5766i	2.29168	−	0.373827i
$960$	−19.5196	−	23.5065i	−0.629991	−	0.758670i
$961$	12.7247	+	4.26490i	0.410476	+	0.137578i
$962$	−4.09136	+	1.47725i	−0.131911	+	0.0476286i
$963$	−19.6974	−	22.6358i	−0.634740	−	0.729428i
$964$	−2.29778	+	8.84737i	−0.0740064	+	0.284954i
$965$	−28.3596	+	2.62791i	−0.912929	+	0.0845953i
$966$	31.0996	+	22.3764i	1.00061	+	0.719948i
$967$	43.6792	+	2.01941i	1.40463	+	0.0649398i	0.735156	−	0.677898i	$-0.237109\pi$
$967$	43.6792	+	2.01941i	1.40463	+	0.0649398i	0.669471	+	0.742838i	$0.266521\pi$
$968$	−16.9292	−	59.4998i	−0.544124	−	1.91240i
$969$	−2.92219	−	1.57398i	−0.0938743	−	0.0505635i
$970$	−7.54773	+	26.5275i	−0.242343	+	0.851747i
$971$	8.93364	−	26.6544i	0.286694	−	0.855379i	−0.702874	−	0.711314i	$-0.748100\pi$
$971$	8.93364	−	26.6544i	0.286694	−	0.855379i	0.989568	−	0.144065i	$-0.0460174\pi$
$972$	−14.6976	−	15.3928i	−0.471425	−	0.493724i
$973$	−35.6391	−	39.0943i	−1.14254	−	1.25330i
$974$	−9.92121	+	6.46465i	−0.317896	+	0.207141i
$975$	2.37109	−	1.70602i	0.0759358	−	0.0546364i
$976$	0.221780	−	0.192990i	0.00709900	−	0.00617747i
$977$	18.7736	−	18.7736i	0.600621	−	0.600621i	−0.339856	−	0.940477i	$-0.610378\pi$
$977$	18.7736	−	18.7736i	0.600621	−	0.600621i	0.940477	+	0.339856i	$0.110378\pi$
$978$	4.82744	−	10.9331i	0.154365	−	0.349603i
$979$	81.4422	+	17.1800i	2.60290	+	0.549076i
$980$	−10.4112	+	0.722655i	−0.332575	+	0.0230844i
$981$	3.73882	+	3.25348i	0.119371	+	0.103875i
$982$	−35.0598	−	3.24877i	−1.11880	−	0.103672i
$983$	−12.2456	+	33.9151i	−0.390574	+	1.08172i	0.574217	+	0.818703i	$0.305307\pi$
$983$	−12.2456	+	33.9151i	−0.390574	+	1.08172i	−0.964790	+	0.263020i	$0.915282\pi$
$984$	56.4008	+	24.9034i	1.79799	+	0.793892i
$985$	1.16742	−	2.34450i	0.0371972	−	0.0747020i
$986$	−2.34736	+	18.7609i	−0.0747551	+	0.597469i
$987$	10.6297	+	21.3472i	0.338346	+	0.679489i
$988$	0.0340124	+	0.735677i	0.00108208	+	0.0234050i
$989$	−17.5351	+	9.24288i	−0.557582	+	0.293907i
$990$	20.7738	+	15.6876i	0.660235	+	0.498586i
$991$	6.67387	+	3.92199i	0.212003	+	0.124586i	0.608811	−	0.793315i	$-0.291647\pi$
$991$	6.67387	+	3.92199i	0.212003	+	0.124586i	−0.396808	+	0.917902i	$0.629882\pi$
$992$	21.1276	+	6.54245i	0.670801	+	0.207723i
$993$	13.1551	−	42.4818i	0.417464	−	1.34812i
$994$	13.7593	+	11.4256i	0.436418	+	0.362397i
$995$	−50.6170	−	28.1935i	−1.60467	−	0.893793i
$996$	20.5987	+	19.6684i	0.652696	+	0.623217i
$997$	−1.96543	+	3.01631i	−0.0622457	+	0.0955275i	−0.867591	−	0.497278i	$-0.834333\pi$
$997$	−1.96543	+	3.01631i	−0.0622457	+	0.0955275i	0.805345	+	0.592806i	$0.201980\pi$
$998$	15.5344	−	6.43456i	0.491733	−	0.203682i
$999$	−3.58719	−	1.02064i	−0.113494	−	0.0322917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.i.a.117.16	yes	1600
289.42	even	136	inner	289.2.i.a.42.16	✓	1600

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.i.a.42.16	✓	1600	289.42	even	136	inner
289.2.i.a.117.16	yes	1600	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.i (of order \(136\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540824 + 0.789506i) q^{2} +(1.51234 - 1.73795i) q^{3} +(0.391654 - 1.01098i) q^{4} +(1.21780 - 1.69255i) q^{5} +(2.19003 + 0.254079i) q^{6} +(-2.93846 + 1.72682i) q^{7} +(2.87311 - 0.675749i) q^{8} +(-0.318816 - 2.28551i) q^{9} +O(q^{10})\)	\(q+(0.540824 + 0.789506i) q^{2} +(1.51234 - 1.73795i) q^{3} +(0.391654 - 1.01098i) q^{4} +(1.21780 - 1.69255i) q^{5} +(2.19003 + 0.254079i) q^{6} +(-2.93846 + 1.72682i) q^{7} +(2.87311 - 0.675749i) q^{8} +(-0.318816 - 2.28551i) q^{9} +(1.99490 + 0.0460903i) q^{10} +(-3.90405 + 4.08872i) q^{11} +(-1.16471 - 2.20962i) q^{12} +(1.02339 - 1.65283i) q^{13} +(-2.95252 - 1.38602i) q^{14} +(-1.09983 - 4.67620i) q^{15} +(0.484904 + 0.442049i) q^{16} +(3.02196 + 2.80495i) q^{17} +(1.63200 - 1.48777i) q^{18} +(-0.288271 - 0.197470i) q^{19} +(-1.23417 - 1.89407i) q^{20} +(-1.44282 + 7.71843i) q^{21} +(-5.33947 - 0.870995i) q^{22} +(-2.58325 - 4.39581i) q^{23} +(3.17071 - 6.01528i) q^{24} +(0.207269 + 0.618407i) q^{25} +(1.85839 - 0.0859185i) q^{26} +(1.33640 + 0.870797i) q^{27} +(0.594917 + 3.64703i) q^{28} +(4.79053 - 0.110681i) q^{29} +(3.09707 - 3.39733i) q^{30} +(-0.675023 + 4.13810i) q^{31} +(0.728787 - 5.22450i) q^{32} +(1.20172 + 12.9686i) q^{33} +(-0.580171 + 3.90284i) q^{34} +(-0.655727 + 7.07642i) q^{35} +(-2.43547 - 0.572817i) q^{36} +(-2.23354 + 0.691648i) q^{37} -0.334388i q^{38} +(-1.32482 - 4.27823i) q^{39} +(2.35514 - 5.68582i) q^{40} +(0.627845 + 9.04532i) q^{41} +(-6.87406 + 3.03520i) q^{42} +(0.179546 - 3.88353i) q^{43} +(2.60456 + 5.54827i) q^{44} +(-4.25661 - 2.24370i) q^{45} +(2.07343 - 4.41685i) q^{46} +(2.42362 - 1.83023i) q^{47} +(1.50160 - 0.174210i) q^{48} +(2.24638 - 4.03303i) q^{49} +(-0.376140 + 0.498089i) q^{50} +(9.44510 - 1.00998i) q^{51} +(-1.27015 - 1.68196i) q^{52} +(-0.0836135 + 0.0116636i) q^{53} +(0.0352578 + 1.52604i) q^{54} +(2.16600 + 11.5871i) q^{55} +(-7.27561 + 6.94701i) q^{56} +(-0.779158 + 0.202358i) q^{57} +(2.67822 + 3.72230i) q^{58} +(-6.29884 - 11.3086i) q^{59} +(-5.15828 - 0.719550i) q^{60} +(0.0516351 - 0.445069i) q^{61} +(-3.63213 + 1.70505i) q^{62} +(4.88350 + 6.16535i) q^{63} +(5.69365 - 2.83510i) q^{64} +(-1.55121 - 3.74496i) q^{65} +(-9.58886 + 7.96248i) q^{66} +(-6.80847 + 1.27272i) q^{67} +(4.01930 - 1.95657i) q^{68} +(-11.5464 - 2.15840i) q^{69} +(-5.94151 + 3.30940i) q^{70} +(-5.30723 - 1.37836i) q^{71} +(-2.46043 - 6.35110i) q^{72} +(-3.05725 - 1.10387i) q^{73} +(-1.75401 - 1.38933i) q^{74} +(1.38822 + 0.575020i) q^{75} +(-0.312540 + 0.214095i) q^{76} +(4.41140 - 18.7561i) q^{77} +(2.66120 - 3.35972i) q^{78} +(-0.329327 + 1.56118i) q^{79} +(1.33871 - 0.282397i) q^{80} +(10.1931 - 2.90020i) q^{81} +(-6.80178 + 5.38762i) q^{82} +(-10.8113 + 3.62358i) q^{83} +(7.23806 + 4.48162i) q^{84} +(8.42768 - 1.69896i) q^{85} +(3.16317 - 1.95855i) q^{86} +(7.05257 - 8.49308i) q^{87} +(-8.45382 + 14.3855i) q^{88} +(-7.75082 - 12.5180i) q^{89} +(-0.530665 - 4.57407i) q^{90} +(-0.153040 + 6.62397i) q^{91} +(-5.45580 + 0.889971i) q^{92} +(6.17094 + 7.43138i) q^{93} +(2.75573 + 0.923627i) q^{94} +(-0.685287 + 0.247434i) q^{95} +(-7.97774 - 9.16783i) q^{96} +(-3.47443 + 13.3779i) q^{97} +(4.39900 - 0.407627i) q^{98} +(10.5895 + 7.61922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1600 q - 64 q^{2} - 64 q^{3} - 68 q^{4} - 68 q^{5} - 72 q^{6} - 64 q^{7} - 72 q^{8} - 76 q^{9}+O(q^{10}) \) 1600 * q - 64 * q^2 - 64 * q^3 - 68 * q^4 - 68 * q^5 - 72 * q^6 - 64 * q^7 - 72 * q^8 - 76 * q^9	\( 1600 q - 64 q^{2} - 64 q^{3} - 68 q^{4} - 68 q^{5} - 72 q^{6} - 64 q^{7} - 72 q^{8} - 76 q^{9} - 72 q^{10} - 64 q^{11} - 64 q^{12} - 68 q^{13} - 72 q^{14} - 60 q^{15} + 40 q^{16} - 68 q^{17} - 72 q^{18} - 76 q^{19} - 72 q^{20} - 68 q^{21} - 80 q^{22} - 72 q^{23} + 260 q^{24} - 64 q^{25} - 64 q^{26} - 76 q^{27} - 72 q^{28} - 64 q^{29} - 68 q^{30} - 56 q^{31} - 72 q^{32} - 44 q^{33} - 48 q^{34} - 92 q^{35} - 68 q^{36} - 68 q^{37} + 204 q^{39} - 60 q^{40} - 64 q^{41} - 60 q^{42} - 60 q^{43} - 48 q^{44} - 80 q^{45} - 88 q^{46} - 68 q^{47} - 80 q^{48} - 76 q^{49} - 32 q^{50} - 96 q^{51} - 116 q^{52} - 64 q^{53} + 484 q^{54} - 68 q^{55} - 48 q^{56} - 44 q^{57} - 68 q^{58} - 68 q^{59} - 60 q^{60} - 68 q^{61} + 352 q^{62} - 56 q^{63} - 68 q^{64} - 64 q^{65} - 76 q^{66} - 44 q^{67} - 80 q^{68} - 92 q^{69} - 60 q^{70} - 88 q^{71} - 68 q^{72} - 40 q^{73} - 88 q^{74} - 56 q^{75} + 60 q^{76} + 604 q^{77} - 60 q^{78} - 64 q^{79} - 68 q^{80} - 68 q^{81} - 72 q^{82} - 84 q^{83} - 4 q^{84} + 268 q^{85} - 132 q^{86} - 84 q^{87} - 80 q^{88} - 68 q^{89} - 72 q^{90} - 68 q^{91} + 232 q^{92} - 92 q^{93} - 44 q^{94} - 60 q^{95} - 48 q^{96} - 92 q^{97} - 68 q^{98} - 64 q^{99}+O(q^{100}) \) 1600 * q - 64 * q^2 - 64 * q^3 - 68 * q^4 - 68 * q^5 - 72 * q^6 - 64 * q^7 - 72 * q^8 - 76 * q^9 - 72 * q^10 - 64 * q^11 - 64 * q^12 - 68 * q^13 - 72 * q^14 - 60 * q^15 + 40 * q^16 - 68 * q^17 - 72 * q^18 - 76 * q^19 - 72 * q^20 - 68 * q^21 - 80 * q^22 - 72 * q^23 + 260 * q^24 - 64 * q^25 - 64 * q^26 - 76 * q^27 - 72 * q^28 - 64 * q^29 - 68 * q^30 - 56 * q^31 - 72 * q^32 - 44 * q^33 - 48 * q^34 - 92 * q^35 - 68 * q^36 - 68 * q^37 + 204 * q^39 - 60 * q^40 - 64 * q^41 - 60 * q^42 - 60 * q^43 - 48 * q^44 - 80 * q^45 - 88 * q^46 - 68 * q^47 - 80 * q^48 - 76 * q^49 - 32 * q^50 - 96 * q^51 - 116 * q^52 - 64 * q^53 + 484 * q^54 - 68 * q^55 - 48 * q^56 - 44 * q^57 - 68 * q^58 - 68 * q^59 - 60 * q^60 - 68 * q^61 + 352 * q^62 - 56 * q^63 - 68 * q^64 - 64 * q^65 - 76 * q^66 - 44 * q^67 - 80 * q^68 - 92 * q^69 - 60 * q^70 - 88 * q^71 - 68 * q^72 - 40 * q^73 - 88 * q^74 - 56 * q^75 + 60 * q^76 + 604 * q^77 - 60 * q^78 - 64 * q^79 - 68 * q^80 - 68 * q^81 - 72 * q^82 - 84 * q^83 - 4 * q^84 + 268 * q^85 - 132 * q^86 - 84 * q^87 - 80 * q^88 - 68 * q^89 - 72 * q^90 - 68 * q^91 + 232 * q^92 - 92 * q^93 - 44 * q^94 - 60 * q^95 - 48 * q^96 - 92 * q^97 - 68 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

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Database

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