LMFDB - Embedded newform 690.2.q.b.251.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 9]))

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

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

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			251.16
Character	$\chi$	$=$	690.251
Dual form			690.2.q.b.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540641 - 0.841254i) q^{2} +(1.64273 - 0.549041i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.426243 - 1.67878i) q^{6} +(0.918508 + 0.795892i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(2.39711 - 1.80385i) q^{9} +O(q^{10})$	\(q+(0.540641 - 0.841254i) q^{2} +(1.64273 - 0.549041i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.426243 - 1.67878i) q^{6} +(0.918508 + 0.795892i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(2.39711 - 1.80385i) q^{9} +(0.755750 - 0.654861i) q^{10} +(3.79809 - 2.44088i) q^{11} +(-1.18184 - 1.26620i) q^{12} +(0.541306 + 0.624700i) q^{13} +(1.16613 - 0.342407i) q^{14} +(1.73087 - 0.0639912i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-2.35358 + 5.15361i) q^{17} +(-0.221521 - 2.99181i) q^{18} +(-5.34856 + 2.44261i) q^{19} +(-0.142315 - 0.989821i) q^{20} +(1.94584 + 0.803135i) q^{21} -4.51480i q^{22} +(-4.39922 - 1.90967i) q^{23} +(-1.70414 + 0.309668i) q^{24} +(0.841254 + 0.540641i) q^{25} +(0.818184 - 0.117637i) q^{26} +(2.94741 - 4.27934i) q^{27} +(0.342407 - 1.16613i) q^{28} +(6.42428 + 2.93387i) q^{29} +(0.881945 - 1.49070i) q^{30} +(0.809818 - 5.63241i) q^{31} +(0.281733 + 0.959493i) q^{32} +(4.89908 - 6.09502i) q^{33} +(3.06306 + 4.76621i) q^{34} +(0.657074 + 1.02243i) q^{35} +(-2.63663 - 1.43114i) q^{36} +(-2.68722 - 9.15183i) q^{37} +(-0.836800 + 5.82007i) q^{38} +(1.23220 + 0.729013i) q^{39} +(-0.909632 - 0.415415i) q^{40} +(0.674489 - 2.29710i) q^{41} +(1.72764 - 1.20273i) q^{42} +(-1.09713 + 0.157743i) q^{43} +(-3.79809 - 2.44088i) q^{44} +(2.80821 - 1.05544i) q^{45} +(-3.98492 + 2.66842i) q^{46} +10.1087i q^{47} +(-0.660820 + 1.60104i) q^{48} +(-0.785990 - 5.46668i) q^{49} +(0.909632 - 0.415415i) q^{50} +(-1.03674 + 9.75820i) q^{51} +(0.343381 - 0.751899i) q^{52} +(-4.13803 + 4.77554i) q^{53} +(-2.00652 - 4.79311i) q^{54} +(4.33192 - 1.27197i) q^{55} +(-0.795892 - 0.918508i) q^{56} +(-7.44514 + 6.94912i) q^{57} +(5.94135 - 3.81828i) q^{58} +(-10.1925 + 8.83189i) q^{59} +(-0.777237 - 1.54787i) q^{60} +(-11.5222 - 1.65664i) q^{61} +(-4.30046 - 3.72637i) q^{62} +(3.63743 + 0.250988i) q^{63} +(0.959493 + 0.281733i) q^{64} +(0.343381 + 0.751899i) q^{65} +(-2.47881 - 7.41658i) q^{66} +(3.39400 - 5.28116i) q^{67} +5.66560 q^{68} +(-8.27521 - 0.721716i) q^{69} +1.21536 q^{70} +(5.79095 - 9.01089i) q^{71} +(-2.62942 + 1.44435i) q^{72} +(3.89553 + 8.53001i) q^{73} +(-9.15183 - 2.68722i) q^{74} +(1.67878 + 0.426243i) q^{75} +(4.44375 + 3.85053i) q^{76} +(5.43126 + 0.780897i) q^{77} +(1.27947 - 0.642462i) q^{78} +(-8.25506 + 7.15305i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(2.49225 - 8.64804i) q^{81} +(-1.56779 - 1.80932i) q^{82} +(4.95270 - 1.45424i) q^{83} +(-0.0777724 - 2.10363i) q^{84} +(-3.71018 + 4.28178i) q^{85} +(-0.460451 + 1.00825i) q^{86} +(12.1641 + 1.29236i) q^{87} +(-4.10681 + 1.87552i) q^{88} +(2.66990 + 18.5696i) q^{89} +(0.630343 - 2.93303i) q^{90} +1.00461i q^{91} +(0.0904052 + 4.79498i) q^{92} +(-1.76211 - 9.69714i) q^{93} +(8.50395 + 5.46516i) q^{94} +(-5.82007 + 0.836800i) q^{95} +(0.989611 + 1.42150i) q^{96} +(-2.65640 + 9.04686i) q^{97} +(-5.02381 - 2.29429i) q^{98} +(4.70144 - 12.7022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9	$ 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9} + 12 q^{11} + 12 q^{14} - 16 q^{16} - 8 q^{18} - 16 q^{20} + 70 q^{21} - 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} + 2 q^{30} - 4 q^{31} - 16 q^{33} + 2 q^{36} - 72 q^{38} + 140 q^{39} - 44 q^{41} + 44 q^{43} - 12 q^{44} + 2 q^{45} + 4 q^{46} + 70 q^{49} + 2 q^{51} + 52 q^{53} - 62 q^{54} + 10 q^{55} + 54 q^{56} - 94 q^{57} - 36 q^{58} - 44 q^{61} + 16 q^{64} - 54 q^{66} - 44 q^{67} - 30 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} + 24 q^{74} + 88 q^{77} - 54 q^{78} - 44 q^{79} + 16 q^{80} - 66 q^{81} - 28 q^{82} - 4 q^{83} - 4 q^{84} - 158 q^{86} + 156 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} + 88 q^{98} - 58 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9 + 12 * q^11 + 12 * q^14 - 16 * q^16 - 8 * q^18 - 16 * q^20 + 70 * q^21 - 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 + 2 * q^30 - 4 * q^31 - 16 * q^33 + 2 * q^36 - 72 * q^38 + 140 * q^39 - 44 * q^41 + 44 * q^43 - 12 * q^44 + 2 * q^45 + 4 * q^46 + 70 * q^49 + 2 * q^51 + 52 * q^53 - 62 * q^54 + 10 * q^55 + 54 * q^56 - 94 * q^57 - 36 * q^58 - 44 * q^61 + 16 * q^64 - 54 * q^66 - 44 * q^67 - 30 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 + 24 * q^74 + 88 * q^77 - 54 * q^78 - 44 * q^79 + 16 * q^80 - 66 * q^81 - 28 * q^82 - 4 * q^83 - 4 * q^84 - 158 * q^86 + 156 * q^87 - 80 * q^89 + 8 * q^90 + 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 + 88 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$3$	1.64273	−	0.549041i	0.948429	−	0.316989i
$3$	1.64273	−	0.549041i	0.948429	−	0.316989i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$6$	0.426243	−	1.67878i	0.174013	−	0.685361i
$7$	0.918508	+	0.795892i	0.347163	+	0.300819i	0.810935	−	0.585136i	$-0.198959\pi$
$7$	0.918508	+	0.795892i	0.347163	+	0.300819i	−0.463772	+	0.885955i	$0.653504\pi$
$8$	−0.989821	−	0.142315i	−0.349955	−	0.0503159i
$9$	2.39711	−	1.80385i	0.799036	−	0.601283i
$10$	0.755750	−	0.654861i	0.238989	−	0.207085i
$11$	3.79809	−	2.44088i	1.14517	−	0.735954i	0.176496	−	0.984301i	$-0.443524\pi$
$11$	3.79809	−	2.44088i	1.14517	−	0.735954i	0.968671	+	0.248347i	$0.0798873\pi$
$12$	−1.18184	−	1.26620i	−0.341168	−	0.365520i
$13$	0.541306	+	0.624700i	0.150131	+	0.173261i	0.825834	−	0.563914i	$-0.190705\pi$
$13$	0.541306	+	0.624700i	0.150131	+	0.173261i	−0.675702	+	0.737175i	$0.736160\pi$
$14$	1.16613	−	0.342407i	0.311661	−	0.0915120i
$15$	1.73087	−	0.0639912i	0.446908	−	0.0165225i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−2.35358	+	5.15361i	−0.570826	+	1.24994i	0.375530	+	0.926810i	$0.377461\pi$
$17$	−2.35358	+	5.15361i	−0.570826	+	1.24994i	−0.946356	+	0.323125i	$0.895267\pi$
$18$	−0.221521	−	2.99181i	−0.0522129	−	0.705176i
$19$	−5.34856	+	2.44261i	−1.22704	+	0.560372i	−0.920223	−	0.391395i	$-0.871993\pi$
$19$	−5.34856	+	2.44261i	−1.22704	+	0.560372i	−0.306822	+	0.951767i	$0.599266\pi$
$20$	−0.142315	−	0.989821i	−0.0318226	−	0.221331i
$21$	1.94584	+	0.803135i	0.424616	+	0.175258i
$22$		−	4.51480i		−	0.962558i
$23$	−4.39922	−	1.90967i	−0.917301	−	0.398194i
$23$	−4.39922	−	1.90967i	−0.917301	−	0.398194i
$24$	−1.70414	+	0.309668i	−0.347857	+	0.0632107i
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	0.818184	−	0.117637i	0.160459	−	0.0230705i
$27$	2.94741	−	4.27934i	0.567229	−	0.823560i
$28$	0.342407	−	1.16613i	0.0647088	−	0.220378i
$29$	6.42428	+	2.93387i	1.19296	+	0.544806i	0.910113	−	0.414360i	$-0.135995\pi$
$29$	6.42428	+	2.93387i	1.19296	+	0.544806i	0.282845	+	0.959166i	$0.408722\pi$
$30$	0.881945	−	1.49070i	0.161020	−	0.272162i
$31$	0.809818	−	5.63241i	0.145448	−	1.01161i	−0.778104	−	0.628136i	$-0.783818\pi$
$31$	0.809818	−	5.63241i	0.145448	−	1.01161i	0.923551	−	0.383475i	$-0.125273\pi$
$32$	0.281733	+	0.959493i	0.0498038	+	0.169616i
$33$	4.89908	−	6.09502i	0.852821	−	1.06101i
$34$	3.06306	+	4.76621i	0.525310	+	0.817398i
$35$	0.657074	+	1.02243i	0.111066	+	0.172822i
$36$	−2.63663	−	1.43114i	−0.439439	−	0.238523i
$37$	−2.68722	−	9.15183i	−0.441776	−	1.50455i	−0.816462	−	0.577400i	$-0.804067\pi$
$37$	−2.68722	−	9.15183i	−0.441776	−	1.50455i	0.374685	−	0.927152i	$-0.377751\pi$
$38$	−0.836800	+	5.82007i	−0.135747	+	0.944140i
$39$	1.23220	+	0.729013i	0.197311	+	0.116736i
$40$	−0.909632	−	0.415415i	−0.143825	−	0.0656829i
$41$	0.674489	−	2.29710i	0.105337	−	0.358746i	−0.889909	−	0.456139i	$-0.849232\pi$
$41$	0.674489	−	2.29710i	0.105337	−	0.358746i	0.995246	+	0.0973925i	$0.0310502\pi$
$42$	1.72764	−	1.20273i	0.266580	−	0.185586i
$43$	−1.09713	+	0.157743i	−0.167311	+	0.0240557i	−0.225461	−	0.974252i	$-0.572389\pi$
$43$	−1.09713	+	0.157743i	−0.167311	+	0.0240557i	0.0581503	+	0.998308i	$0.481480\pi$
$44$	−3.79809	−	2.44088i	−0.572584	−	0.367977i
$45$	2.80821	−	1.05544i	0.418623	−	0.157335i
$46$	−3.98492	+	2.66842i	−0.587544	+	0.393436i
$47$			10.1087i			1.47450i	0.675620	+	0.737250i	$0.263876\pi$
$47$			10.1087i			1.47450i	−0.675620	+	0.737250i	$0.736124\pi$
$48$	−0.660820	+	1.60104i	−0.0953812	+	0.231090i
$49$	−0.785990	−	5.46668i	−0.112284	−	0.780955i
$50$	0.909632	−	0.415415i	0.128641	−	0.0587486i
$51$	−1.03674	+	9.75820i	−0.145173	+	1.36642i
$52$	0.343381	−	0.751899i	0.0476184	−	0.104270i
$53$	−4.13803	+	4.77554i	−0.568402	+	0.655971i	−0.965070	−	0.261991i	$-0.915621\pi$
$53$	−4.13803	+	4.77554i	−0.568402	+	0.655971i	0.396668	+	0.917962i	$0.370166\pi$
$54$	−2.00652	−	4.79311i	−0.273053	−	0.652259i
$55$	4.33192	−	1.27197i	0.584116	−	0.171512i
$56$	−0.795892	−	0.918508i	−0.106356	−	0.122741i
$57$	−7.44514	+	6.94912i	−0.986133	+	0.920433i
$58$	5.94135	−	3.81828i	0.780138	−	0.501364i
$59$	−10.1925	+	8.83189i	−1.32696	+	1.14981i	−0.349910	+	0.936783i	$0.613788\pi$
$59$	−10.1925	+	8.83189i	−1.32696	+	1.14981i	−0.977046	+	0.213030i	$0.931667\pi$
$60$	−0.777237	−	1.54787i	−0.100341	−	0.199829i
$61$	−11.5222	−	1.65664i	−1.47526	−	0.212111i	−0.642732	−	0.766091i	$-0.722199\pi$
$61$	−11.5222	−	1.65664i	−1.47526	−	0.212111i	−0.832530	+	0.553980i	$0.813108\pi$
$62$	−4.30046	−	3.72637i	−0.546160	−	0.473250i
$63$	3.63743	+	0.250988i	0.458273	+	0.0316215i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	0.343381	+	0.751899i	0.0425912	+	0.0932616i
$66$	−2.47881	−	7.41658i	−0.305120	−	0.912918i
$67$	3.39400	−	5.28116i	0.414643	−	0.645197i	−0.569620	−	0.821908i	$-0.692910\pi$
$67$	3.39400	−	5.28116i	0.414643	−	0.645197i	0.984263	+	0.176712i	$0.0565460\pi$
$68$	5.66560			0.687055
$69$	−8.27521	−	0.721716i	−0.996218	−	0.0868843i
$70$	1.21536			0.145263
$71$	5.79095	−	9.01089i	0.687259	−	1.06940i	−0.305836	−	0.952084i	$-0.598936\pi$
$71$	5.79095	−	9.01089i	0.687259	−	1.06940i	0.993095	−	0.117312i	$-0.0374277\pi$
$72$	−2.62942	+	1.44435i	−0.309881	+	0.170218i
$73$	3.89553	+	8.53001i	0.455937	+	0.998362i	0.988395	+	0.151906i	$0.0485411\pi$
$73$	3.89553	+	8.53001i	0.455937	+	0.998362i	−0.532458	+	0.846456i	$0.678732\pi$
$74$	−9.15183	−	2.68722i	−1.06388	−	0.312383i
$75$	1.67878	+	0.426243i	0.193849	+	0.0492183i
$76$	4.44375	+	3.85053i	0.509733	+	0.441686i
$77$	5.43126	+	0.780897i	0.618949	+	0.0889915i
$78$	1.27947	−	0.642462i	0.144871	−	0.0727445i
$79$	−8.25506	+	7.15305i	−0.928767	+	0.804781i	−0.981031	−	0.193852i	$-0.937902\pi$
$79$	−8.25506	+	7.15305i	−0.928767	+	0.804781i	0.0522639	+	0.998633i	$0.483356\pi$
$80$	−0.841254	+	0.540641i	−0.0940550	+	0.0604455i
$81$	2.49225	−	8.64804i	0.276917	−	0.960894i
$82$	−1.56779	−	1.80932i	−0.173133	−	0.199806i
$83$	4.95270	−	1.45424i	0.543630	−	0.159624i	0.00162375	−	0.999999i	$-0.499483\pi$
$83$	4.95270	−	1.45424i	0.543630	−	0.159624i	0.542006	+	0.840375i	$0.317665\pi$
$84$	−0.0777724	−	2.10363i	−0.00848566	−	0.229525i
$85$	−3.71018	+	4.28178i	−0.402426	+	0.464424i
$86$	−0.460451	+	1.00825i	−0.0496517	+	0.108722i
$87$	12.1641	+	1.29236i	1.30413	+	0.138555i
$88$	−4.10681	+	1.87552i	−0.437787	+	0.199931i
$89$	2.66990	+	18.5696i	0.283009	+	1.96837i	0.246982	+	0.969020i	$0.420561\pi$
$89$	2.66990	+	18.5696i	0.283009	+	1.96837i	0.0360269	+	0.999351i	$0.488530\pi$
$90$	0.630343	−	2.93303i	0.0664440	−	0.309169i
$91$			1.00461i			0.105312i
$92$	0.0904052	+	4.79498i	0.00942539	+	0.499911i
$93$	−1.76211	−	9.69714i	−0.182723	−	1.00555i
$94$	8.50395	+	5.46516i	0.877115	+	0.563688i
$95$	−5.82007	+	0.836800i	−0.597127	+	0.0858539i
$96$	0.989611	+	1.42150i	0.101002	+	0.145082i
$97$	−2.65640	+	9.04686i	−0.269716	+	0.918569i	0.707570	+	0.706644i	$0.249792\pi$
$97$	−2.65640	+	9.04686i	−0.269716	+	0.918569i	−0.977286	+	0.211926i	$0.932027\pi$
$98$	−5.02381	−	2.29429i	−0.507481	−	0.231759i
$99$	4.70144	−	12.7022i	0.472513	−	1.27662i
$100$	0.142315	−	0.989821i	0.0142315	−	0.0989821i
$101$	−0.720376	−	2.45338i	−0.0716801	−	0.244120i	0.915857	−	0.401504i	$-0.131512\pi$
$101$	−0.720376	−	2.45338i	−0.0716801	−	0.244120i	−0.987538	+	0.157384i	$0.949694\pi$
$102$	7.64861	+	6.14784i	0.757325	+	0.608727i
$103$	−2.93126	−	4.56113i	−0.288826	−	0.449421i	0.666274	−	0.745707i	$-0.267888\pi$
$103$	−2.93126	−	4.56113i	−0.288826	−	0.449421i	−0.955099	+	0.296286i	$0.904252\pi$
$104$	−0.446892	−	0.695378i	−0.0438214	−	0.0681874i
$105$	1.64075	+	1.31881i	0.160121	+	0.128702i
$106$	1.78025	+	6.06298i	0.172913	+	0.588889i
$107$	−0.0750997	+	0.522330i	−0.00726016	+	0.0504955i	−0.993129	−	0.117021i	$-0.962666\pi$
$107$	−0.0750997	+	0.522330i	−0.00726016	+	0.0504955i	0.985869	+	0.167516i	$0.0535747\pi$
$108$	−5.11703	−	0.903352i	−0.492386	−	0.0869251i
$109$	2.22756	+	1.01729i	0.213361	+	0.0974387i	0.519229	−	0.854635i	$-0.326219\pi$
$109$	2.22756	+	1.01729i	0.213361	+	0.0974387i	−0.305868	+	0.952074i	$0.598947\pi$
$110$	1.27197	−	4.33192i	0.121277	−	0.413032i
$111$	−9.43910	−	13.5586i	−0.895920	−	1.28692i
$112$	−1.20299	+	0.172964i	−0.113672	+	0.0163435i
$113$	12.0956	+	7.77336i	1.13786	+	0.731256i	0.967185	−	0.254072i	$-0.0817699\pi$
$113$	12.0956	+	7.77336i	1.13786	+	0.731256i	0.170672	+	0.985328i	$0.445406\pi$
$114$	1.82082	+	10.0202i	0.170536	+	0.938480i
$115$	−3.68301	−	3.07172i	−0.343442	−	0.286439i
$116$		−	7.06250i		−	0.655737i
$117$	2.42443	+	0.521040i	0.224139	+	0.0481701i
$118$	1.91935	+	13.3494i	0.176691	+	1.22891i
$119$	−6.26350	+	2.86044i	−0.574174	+	0.262217i
$120$	−1.72236	−	0.182988i	−0.157229	−	0.0167045i
$121$	3.89801	−	8.53545i	0.354364	−	0.775950i
$122$	−7.62301	+	8.79742i	−0.690154	+	0.796481i
$123$	−0.153200	−	4.14383i	−0.0138136	−	0.373636i
$124$	−5.45983	+	1.60315i	−0.490307	+	0.143967i
$125$	0.654861	+	0.755750i	0.0585725	+	0.0675963i
$126$	2.17769	−	2.92431i	0.194004	−	0.260518i
$127$	−6.55966	+	4.21564i	−0.582076	+	0.374077i	−0.798294	−	0.602268i	$-0.794264\pi$
$127$	−6.55966	+	4.21564i	−0.582076	+	0.374077i	0.216218	+	0.976345i	$0.430628\pi$
$128$	0.755750	−	0.654861i	0.0667995	−	0.0578821i
$129$	−1.71568	+	0.861499i	−0.151057	+	0.0758508i
$130$	0.818184	+	0.117637i	0.0717594	+	0.0103174i
$131$	5.92912	+	5.13761i	0.518030	+	0.448875i	0.874214	−	0.485540i	$-0.161377\pi$
$131$	5.92912	+	5.13761i	0.518030	+	0.448875i	−0.356185	+	0.934416i	$0.615923\pi$
$132$	−7.57937	−	1.92440i	−0.659700	−	0.167498i
$133$	−6.85675	−	2.01332i	−0.594556	−	0.174577i
$134$	−2.60786	−	5.71042i	−0.225285	−	0.493305i
$135$	4.03365	−	3.27562i	0.347161	−	0.281921i
$136$	3.06306	−	4.76621i	0.262655	−	0.408699i
$137$	−5.17810			−0.442395			−0.221198	−	0.975229i	$-0.570997\pi$
$137$	−5.17810			−0.442395			−0.221198	+	0.975229i	$0.570997\pi$
$138$	−5.08106	+	6.57136i	−0.432529	+	0.559391i
$139$	4.09865			0.347643			0.173821	−	0.984777i	$-0.444388\pi$
$139$	4.09865			0.347643			0.173821	+	0.984777i	$0.444388\pi$
$140$	0.657074	−	1.02243i	0.0555329	−	0.0864108i
$141$	5.55007	+	16.6058i	0.467400	+	1.39846i
$142$	−4.44962	−	9.74331i	−0.373404	−	0.817640i
$143$	3.58075	+	1.05140i	0.299437	+	0.0879227i
$144$	−0.206513	+	2.99288i	−0.0172094	+	0.249407i
$145$	5.33748	+	4.62495i	0.443254	+	0.384081i
$146$	9.28198	+	1.33455i	0.768182	+	0.110448i
$147$	−4.29260	−	8.54873i	−0.354048	−	0.705087i
$148$	−7.20849	+	6.24619i	−0.592534	+	0.513434i
$149$	−4.17612	+	2.68383i	−0.342121	+	0.219868i	−0.700406	−	0.713744i	$-0.746998\pi$
$149$	−4.17612	+	2.68383i	−0.342121	+	0.219868i	0.358285	+	0.933612i	$0.383361\pi$
$150$	1.26620	−	1.18184i	0.103385	−	0.0964968i
$151$	−2.90627	−	3.35401i	−0.236509	−	0.272946i	0.625071	−	0.780568i	$-0.285070\pi$
$151$	−2.90627	−	3.35401i	−0.236509	−	0.272946i	−0.861580	+	0.507622i	$0.830525\pi$
$152$	5.64174	−	1.65656i	0.457606	−	0.134365i
$153$	3.65457	+	16.5993i	0.295454	+	1.34197i
$154$	3.59329	−	4.14688i	0.289556	−	0.334165i
$155$	2.36385	−	5.17611i	0.189869	−	0.415755i
$156$	0.151258	−	1.42370i	0.0121103	−	0.113987i
$157$	−7.02196	+	3.20682i	−0.560414	+	0.255932i	−0.675421	−	0.737432i	$-0.736038\pi$
$157$	−7.02196	+	3.20682i	−0.560414	+	0.255932i	0.115007	+	0.993365i	$0.463311\pi$
$158$	1.55451	+	10.8118i	0.123670	+	0.860143i
$159$	−4.17569	+	10.1169i	−0.331154	+	0.802319i
$160$			1.00000i			0.0790569i
$161$	−2.52083	−	5.25535i	−0.198669	−	0.414180i
$162$	−5.92779	−	6.77210i	−0.465731	−	0.532067i
$163$	9.13396	+	5.87004i	0.715427	+	0.459777i	0.847043	−	0.531524i	$-0.178380\pi$
$163$	9.13396	+	5.87004i	0.715427	+	0.459777i	−0.131616	+	0.991301i	$0.542017\pi$
$164$	−2.36971	+	0.340712i	−0.185043	+	0.0266052i
$165$	6.41780	−	4.46789i	0.499625	−	0.347825i
$166$	1.45424	−	4.95270i	0.112871	−	0.384404i
$167$	8.04012	+	3.67180i	0.622163	+	0.284132i	0.701449	−	0.712720i	$-0.252537\pi$
$167$	8.04012	+	3.67180i	0.622163	+	0.284132i	−0.0792861	+	0.996852i	$0.525264\pi$
$168$	−1.81173	−	1.07188i	−0.139778	−	0.0826975i
$169$	1.75285	−	12.1914i	0.134835	−	0.937798i
$170$	1.59619	+	5.43611i	0.122422	+	0.416930i
$171$	−8.41499	+	15.5032i	−0.643510	+	1.18556i
$172$	0.599253	+	0.932456i	0.0456926	+	0.0710991i
$173$	−5.31578	−	8.27151i	−0.404151	−	0.628871i	0.578205	−	0.815892i	$-0.303753\pi$
$173$	−5.31578	−	8.27151i	−0.404151	−	0.628871i	−0.982356	+	0.187020i	$0.940117\pi$
$174$	7.66363	−	9.53443i	0.580979	−	0.722803i
$175$	0.342407	+	1.16613i	0.0258835	+	0.0881511i
$176$	−0.642523	+	4.46884i	−0.0484320	+	0.336852i
$177$	−11.8945	+	20.1045i	−0.894045	+	1.51115i
$178$	17.0652	+	7.79341i	1.27909	+	0.584140i
$179$	7.40069	−	25.2044i	0.553153	−	1.88387i	0.0938544	−	0.995586i	$-0.470081\pi$
$179$	7.40069	−	25.2044i	0.553153	−	1.88387i	0.459299	−	0.888282i	$-0.348101\pi$
$180$	−2.12663	−	2.11599i	−0.158510	−	0.157717i
$181$	17.9041	−	2.57422i	1.33080	−	0.191340i	0.560041	−	0.828465i	$-0.310785\pi$
$181$	17.9041	−	2.57422i	1.33080	−	0.191340i	0.770761	+	0.637125i	$0.219876\pi$
$182$	0.845135	+	0.543135i	0.0626455	+	0.0402598i
$183$	−19.8373	+	3.60474i	−1.46642	+	0.266470i
$184$	4.08267	+	2.51631i	0.300978	+	0.185505i
$185$		−	9.53820i		−	0.701262i
$186$	−9.11042	−	3.76029i	−0.668009	−	0.275717i
$187$	3.64028	+	25.3187i	0.266204	+	1.85149i
$188$	9.19516	−	4.19929i	0.670626	−	0.306265i
$189$	6.11311	−	1.58480i	0.444664	−	0.115277i
$190$	−2.44261	+	5.34856i	−0.177205	+	0.388026i
$191$	10.4151	−	12.0197i	0.753611	−	0.869713i	−0.241302	−	0.970450i	$-0.577574\pi$
$191$	10.4151	−	12.0197i	0.753611	−	0.869713i	0.994913	+	0.100737i	$0.0321199\pi$
$192$	1.73087	−	0.0639912i	0.124915	−	0.00461817i
$193$	−13.5764	+	3.98640i	−0.977253	+	0.286947i	−0.731090	−	0.682281i	$-0.760988\pi$
$193$	−13.5764	+	3.98640i	−0.977253	+	0.286947i	−0.246163	+	0.969228i	$0.579170\pi$
$194$	6.17454	+	7.12580i	0.443306	+	0.511603i
$195$	0.976905	+	1.04664i	0.0699576	+	0.0749511i
$196$	−4.64616	+	2.98590i	−0.331868	+	0.213279i
$197$	−20.2144	+	17.5159i	−1.44022	+	1.24796i	−0.521380	+	0.853325i	$0.674582\pi$
$197$	−20.2144	+	17.5159i	−1.44022	+	1.24796i	−0.918839	+	0.394632i	$0.870872\pi$
$198$	−8.14402	−	10.8225i	−0.578770	−	0.769119i
$199$	−2.29120	−	0.329425i	−0.162419	−	0.0233523i	0.0606257	−	0.998161i	$-0.480690\pi$
$199$	−2.29120	−	0.329425i	−0.162419	−	0.0233523i	−0.223044	+	0.974808i	$0.571599\pi$
$200$	−0.755750	−	0.654861i	−0.0534396	−	0.0463056i
$201$	2.67584	−	10.5390i	0.188739	−	0.743360i
$202$	−2.45338	−	0.720376i	−0.172619	−	0.0506855i
$203$	3.56571	+	7.80781i	0.250264	+	0.548001i
$204$	9.30704	−	3.11065i	0.651623	−	0.217789i
$205$	1.29433	−	2.01402i	0.0904002	−	0.140666i
$206$	−5.42182			−0.377756
$207$	−13.9902	+	3.35785i	−0.972384	+	0.233387i
$208$	−0.826597			−0.0573142
$209$	−14.3522	+	22.3325i	−0.992763	+	1.54477i
$210$	1.99651	−	0.667283i	0.137772	−	0.0460469i
$211$	0.389953	+	0.853877i	0.0268454	+	0.0587833i	0.922580	−	0.385806i	$-0.126077\pi$
$211$	0.389953	+	0.853877i	0.0268454	+	0.0587833i	−0.895734	+	0.444590i	$0.853349\pi$
$212$	6.06298	+	1.78025i	0.416407	+	0.122268i
$213$	4.56560	−	17.9819i	0.312830	−	1.23210i
$214$	0.398810	+	0.345571i	0.0272621	+	0.0236227i
$215$	−1.09713	−	0.157743i	−0.0748236	−	0.0107580i
$216$	−3.52642	+	3.81633i	−0.239943	+	0.259668i
$217$	5.22661	−	4.52889i	0.354806	−	0.307441i
$218$	2.06011	−	1.32395i	0.139528	−	0.0896692i
$219$	11.0826	+	11.8737i	0.748894	+	0.802349i
$220$	−2.95656	−	3.41206i	−0.199332	−	0.230041i
$221$	−4.49347	+	1.31940i	−0.302264	+	0.0887526i
$222$	−16.5094	+	0.610360i	−1.10804	+	0.0409647i
$223$	12.8486	−	14.8281i	0.860409	−	0.992965i	−0.139587	−	0.990210i	$-0.544578\pi$
$223$	12.8486	−	14.8281i	0.860409	−	0.992965i	0.999996	−	0.00275528i	$-0.000877034\pi$
$224$	−0.504879	+	1.10553i	−0.0337336	+	0.0738664i
$225$	2.99181	−	0.221521i	0.199454	−	0.0147680i
$226$	13.0787	−	5.97286i	0.869985	−	0.397309i
$227$	0.618974	+	4.30506i	0.0410828	+	0.285737i	0.999998	+	0.00204388i	$0.000650586\pi$
$227$	0.618974	+	4.30506i	0.0410828	+	0.285737i	−0.958915	+	0.283693i	$0.908440\pi$
$228$	9.41396	+	3.88557i	0.623455	+	0.257328i
$229$		−	3.54266i		−	0.234105i	−0.993126	−	0.117053i	$-0.962655\pi$
$229$		−	3.54266i		−	0.234105i	0.993126	−	0.117053i	$-0.0373446\pi$
$230$	−4.57528	+	1.43764i	−0.301685	+	0.0947955i
$231$	9.35082	−	1.69918i	0.615239	−	0.111798i
$232$	−5.94135	−	3.81828i	−0.390069	−	0.250682i
$233$	15.9742	−	2.29675i	1.04651	−	0.150465i	0.402450	−	0.915442i	$-0.368159\pi$
$233$	15.9742	−	2.29675i	1.04651	−	0.150465i	0.644057	+	0.764977i	$0.277250\pi$
$234$	1.74907	−	1.75787i	0.114341	−	0.114915i
$235$	−2.84794	+	9.69919i	−0.185779	+	0.632705i
$236$	12.2679	+	5.60256i	0.798572	+	0.364696i
$237$	−9.63350	+	16.2829i	−0.625763	+	1.05769i
$238$	−0.979945	+	6.81566i	−0.0635204	+	0.441794i
$239$	−3.19474	−	10.8803i	−0.206651	−	0.703788i	−0.995960	−	0.0897928i	$-0.971380\pi$
$239$	−3.19474	−	10.8803i	−0.206651	−	0.703788i	0.789310	−	0.613995i	$-0.210439\pi$
$240$	−1.08512	+	1.35001i	−0.0700440	+	0.0871427i
$241$	4.24250	+	6.60147i	0.273284	+	0.425238i	0.950583	−	0.310470i	$-0.100486\pi$
$241$	4.24250	+	6.60147i	0.273284	+	0.425238i	−0.677300	+	0.735707i	$0.736850\pi$
$242$	−5.07305	−	7.89382i	−0.326108	−	0.507434i
$243$	−0.654041	−	15.5747i	−0.0419567	−	0.999119i
$244$	3.27955	+	11.1691i	0.209952	+	0.715030i
$245$	0.785990	−	5.46668i	0.0502151	−	0.349254i
$246$	−3.56884	−	2.11144i	−0.227541	−	0.134621i
$247$	−4.42111	−	2.01905i	−0.281308	−	0.128469i
$248$	−1.60315	+	5.45983i	−0.101800	+	0.346700i
$249$	7.33750	−	5.10817i	0.464995	−	0.323717i
$250$	0.989821	−	0.142315i	0.0626018	−	0.00900078i
$251$	−22.5645	−	14.5013i	−1.42426	−	0.915316i	−0.999952	−	0.00979751i	$-0.996881\pi$
$251$	−22.5645	−	14.5013i	−1.42426	−	0.915316i	−0.424307	−	0.905518i	$-0.639482\pi$
$252$	−1.28274	−	3.41299i	−0.0808049	−	0.214998i
$253$	−21.3699	+	3.48489i	−1.34352	+	0.219093i
$254$			7.79748i			0.489258i
$255$	−3.74395	+	9.07084i	−0.234455	+	0.568038i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−17.5364	+	8.00861i	−1.09389	+	0.499563i	−0.878878	−	0.477048i	$-0.841707\pi$
$257$	−17.5364	+	8.00861i	−1.09389	+	0.499563i	−0.215014	+	0.976611i	$0.568980\pi$
$258$	−0.202827	+	1.90908i	−0.0126274	+	0.118854i
$259$	4.81563	−	10.5448i	0.299229	−	0.655220i
$260$	0.541306	−	0.624700i	0.0335704	−	0.0387423i
$261$	20.6919	−	4.55563i	1.28080	−	0.281986i
$262$	7.52756	−	2.21029i	0.465054	−	0.136552i
$263$	−6.40556	−	7.39241i	−0.394984	−	0.455836i	0.523071	−	0.852289i	$-0.324786\pi$
$263$	−6.40556	−	7.39241i	−0.394984	−	0.455836i	−0.918055	+	0.396453i	$0.870241\pi$
$264$	−5.71663	+	5.33577i	−0.351834	+	0.328394i
$265$	−5.31584	+	3.41628i	−0.326549	+	0.209860i
$266$	−5.40076	+	4.67978i	−0.331142	+	0.286936i
$267$	14.5814	+	29.0389i	0.892366	+	1.77715i
$268$	−6.21383	−	0.893414i	−0.379570	−	0.0545739i
$269$	−5.20011	−	4.50592i	−0.317057	−	0.274731i	0.481763	−	0.876301i	$-0.339997\pi$
$269$	−5.20011	−	4.50592i	−0.317057	−	0.274731i	−0.798820	+	0.601570i	$0.794542\pi$
$270$	−0.574873	−	5.16425i	−0.0349856	−	0.314287i
$271$	−18.0293	−	5.29387i	−1.09520	−	0.321580i	−0.316257	−	0.948674i	$-0.602426\pi$
$271$	−18.0293	−	5.29387i	−1.09520	−	0.321580i	−0.778944	+	0.627094i	$0.784244\pi$
$272$	−2.35358	−	5.15361i	−0.142707	−	0.312484i
$273$	0.551574	+	1.65031i	0.0333828	+	0.0998811i
$274$	−2.79949	+	4.35610i	−0.169124	+	0.263162i
$275$	4.51480			0.272253
$276$	2.78115	+	7.82721i	0.167406	+	0.471143i
$277$	7.95458			0.477944			0.238972	−	0.971026i	$-0.423190\pi$
$277$	7.95458			0.477944			0.238972	+	0.971026i	$0.423190\pi$
$278$	2.21590	−	3.44800i	0.132901	−	0.206797i
$279$	−8.21880	−	14.9623i	−0.492047	−	0.895769i
$280$	−0.504879	−	1.10553i	−0.0301723	−	0.0660681i
$281$	26.1373	+	7.67461i	1.55922	+	0.457829i	0.943841	−	0.330400i	$-0.107184\pi$
$281$	26.1373	+	7.67461i	1.55922	+	0.457829i	0.615382	+	0.788229i	$0.289002\pi$
$282$	16.9703	+	4.30875i	1.01056	+	0.256582i
$283$	−4.81602	−	4.17311i	−0.286283	−	0.248066i	0.499866	−	0.866103i	$-0.333383\pi$
$283$	−4.81602	−	4.17311i	−0.286283	−	0.248066i	−0.786149	+	0.618037i	$0.787928\pi$
$284$	−10.6022	−	1.52437i	−0.629127	−	0.0904548i
$285$	−9.10135	+	4.57009i	−0.539118	+	0.270709i
$286$	2.82040	−	2.44389i	0.166774	−	0.144510i
$287$	2.44777	−	1.57308i	0.144487	−	0.0928562i
$288$	2.40612	+	1.79180i	0.141782	+	0.105583i
$289$	−9.88779	−	11.4111i	−0.581635	−	0.671242i
$290$	6.77642	−	1.98974i	0.397925	−	0.116841i
$291$	0.603360	+	16.3200i	0.0353696	+	0.956695i
$292$	6.14091	−	7.08699i	0.359370	−	0.414735i
$293$	−2.93117	+	6.41837i	−0.171241	+	0.374965i	−0.975722	−	0.219013i	$-0.929716\pi$
$293$	−2.93117	+	6.41837i	−0.171241	+	0.374965i	0.804481	+	0.593978i	$0.202444\pi$
$294$	−9.51241	−	1.01063i	−0.554775	−	0.0589409i
$295$	−12.2679	+	5.60256i	−0.714265	+	0.326194i
$296$	1.35743	+	9.44111i	0.0788988	+	0.548753i
$297$	0.749135	−	23.4476i	0.0434692	−	1.36057i
$298$			4.96416i			0.287566i
$299$	−1.18835	−	3.78191i	−0.0687242	−	0.218714i
$300$	−0.309668	−	1.70414i	−0.0178787	−	0.0983888i
$301$	−1.13327	−	0.728308i	−0.0653206	−	0.0419790i
$302$	−4.39282	+	0.631593i	−0.252779	+	0.0363441i
$303$	−2.53039	−	3.63471i	−0.145367	−	0.208809i
$304$	1.65656	−	5.64174i	0.0950105	−	0.323576i
$305$	−10.5887	−	4.83570i	−0.606308	−	0.276891i
$306$	15.9400	+	5.89982i	0.911229	+	0.337270i
$307$	2.93857	−	20.4382i	0.167713	−	1.16647i	−0.715884	−	0.698220i	$-0.753976\pi$
$307$	2.93857	−	20.4382i	0.167713	−	1.16647i	0.883596	−	0.468249i	$-0.155115\pi$
$308$	−1.54590	−	5.26484i	−0.0880857	−	0.299992i
$309$	−7.31951	−	5.88331i	−0.416392	−	0.334690i
$310$	−3.07642	−	4.78701i	−0.174729	−	0.271884i
$311$	−5.55004	−	8.63602i	−0.314714	−	0.489704i	0.647475	−	0.762086i	$-0.275825\pi$
$311$	−5.55004	−	8.63602i	−0.314714	−	0.489704i	−0.962189	+	0.272382i	$0.912188\pi$
$312$	−1.11591	−	0.896954i	−0.0631761	−	0.0507800i
$313$	4.79668	+	16.3360i	0.271124	+	0.923365i	0.976678	+	0.214708i	$0.0688801\pi$
$313$	4.79668	+	16.3360i	0.271124	+	0.923365i	−0.705554	+	0.708656i	$0.749302\pi$
$314$	−1.09861	+	7.64099i	−0.0619981	+	0.431206i
$315$	3.41938	+	1.26560i	0.192660	+	0.0713087i
$316$	9.93592	+	4.53758i	0.558939	+	0.255259i
$317$	−1.15062	+	3.91864i	−0.0646251	+	0.220093i	−0.985474	−	0.169827i	$-0.945679\pi$
$317$	−1.15062	+	3.91864i	−0.0646251	+	0.220093i	0.920849	+	0.389920i	$0.127497\pi$
$318$	6.25330	+	8.98240i	0.350668	+	0.503708i
$319$	31.5612	−	4.53782i	1.76709	−	0.254069i
$320$	0.841254	+	0.540641i	0.0470275	+	0.0302227i
$321$	0.163412	+	0.899279i	0.00912078	+	0.0501928i
$322$	−5.78395	−	0.720602i	−0.322327	−	0.0401576i
$323$		−	33.3133i		−	1.85360i
$324$	−8.90186	+	1.32550i	−0.494548	+	0.0736386i
$325$	0.117637	+	0.818184i	0.00652533	+	0.0453847i
$326$	9.87638	−	4.51039i	0.547002	−	0.249808i
$327$	4.21780	+	0.448112i	0.233245	+	0.0247806i
$328$	−0.994535	+	2.17773i	−0.0549140	+	0.120245i
$329$	−8.04540	+	9.28489i	−0.443557	+	0.511893i
$330$	−0.288907	−	7.81452i	−0.0159038	−	0.430175i
$331$	16.0827	−	4.72230i	0.883984	−	0.259561i	0.191931	−	0.981408i	$-0.438525\pi$
$331$	16.0827	−	4.72230i	0.883984	−	0.259561i	0.692052	+	0.721847i	$0.256707\pi$
$332$	−3.38026	−	3.90102i	−0.185516	−	0.214096i
$333$	−22.9501	−	17.0906i	−1.25766	−	0.936558i
$334$	7.43573	−	4.77865i	0.406865	−	0.261476i
$335$	4.74439	−	4.11104i	0.259214	−	0.224610i
$336$	−1.88122	+	0.944623i	−0.102629	+	0.0515334i
$337$	22.0624	+	3.17209i	1.20181	+	0.172795i	0.713995	−	0.700151i	$-0.246884\pi$
$337$	22.0624	+	3.17209i	1.20181	+	0.172795i	0.487818	+	0.872945i	$0.337793\pi$
$338$	−9.30837	−	8.06575i	−0.506309	−	0.438719i
$339$	24.1377	+	6.12854i	1.31098	+	0.332857i
$340$	5.43611	+	1.59619i	0.294814	+	0.0865653i
$341$	−10.6723	−	23.3691i	−0.577937	−	1.26551i
$342$	8.49263	+	15.4608i	0.459229	+	0.836024i
$343$	8.22847	−	12.8037i	0.444295	−	0.691337i
$344$	1.10841			0.0597616
$345$	−7.73668	−	3.02388i	−0.416529	−	0.162800i
$346$	−9.83236			−0.528591
$347$	11.4610	−	17.8337i	0.615261	−	0.957364i	−0.384158	−	0.923267i	$-0.625508\pi$
$347$	11.4610	−	17.8337i	0.615261	−	0.957364i	0.999419	−	0.0340970i	$-0.0108555\pi$
$348$	−3.87760	−	11.6018i	−0.207861	−	0.621920i
$349$	−8.89410	−	19.4754i	−0.476090	−	1.04249i	−0.983520	−	0.180799i	$-0.942132\pi$
$349$	−8.89410	−	19.4754i	−0.476090	−	1.04249i	0.507430	−	0.861693i	$-0.330596\pi$
$350$	1.16613	+	0.342407i	0.0623323	+	0.0183024i
$351$	4.26876	−	0.475188i	0.227849	−	0.0253637i
$352$	3.41206	+	2.95656i	0.181863	+	0.157585i
$353$	−7.32358	−	1.05297i	−0.389795	−	0.0560441i	−0.0553688	−	0.998466i	$-0.517633\pi$
$353$	−7.32358	−	1.05297i	−0.389795	−	0.0560441i	−0.334426	+	0.942422i	$0.608543\pi$
$354$	10.4823	+	20.8756i	0.557130	+	1.10953i
$355$	8.09503	−	7.01439i	0.429640	−	0.372285i
$356$	15.7824	−	10.1427i	0.836463	−	0.537562i
$357$	−8.71872	+	8.13785i	−0.461444	+	0.430701i
$358$	−17.2022	−	19.8524i	−0.909165	−	1.04923i
$359$	27.6335	−	8.11392i	1.45844	−	0.428236i	0.546116	−	0.837709i	$-0.316106\pi$
$359$	27.6335	−	8.11392i	1.45844	−	0.428236i	0.912322	+	0.409473i	$0.134288\pi$
$360$	−2.92983	+	0.645045i	−0.154416	+	0.0339969i
$361$	10.1984	−	11.7696i	0.536760	−	0.619454i
$362$	7.51412	−	16.4536i	0.394933	−	0.864783i
$363$	1.71705	−	16.1616i	0.0901220	−	0.848263i
$364$	0.913829	−	0.417332i	0.0478976	−	0.0218741i
$365$	1.33455	+	9.28198i	0.0698534	+	0.485841i
$366$	−7.69238	+	18.6371i	−0.402087	+	0.974177i
$367$		−	7.95265i		−	0.415125i	−0.978222	−	0.207563i	$-0.933447\pi$
$367$		−	7.95265i		−	0.415125i	0.978222	−	0.207563i	$-0.0665531\pi$
$368$	4.32411	−	2.07414i	0.225410	−	0.108122i
$369$	−2.52680	−	6.72307i	−0.131540	−	0.349989i
$370$	−8.02404	−	5.15674i	−0.417150	−	0.268086i
$371$	−7.60163	+	1.09295i	−0.394657	+	0.0567431i
$372$	−8.08882	+	5.63121i	−0.419386	+	0.291965i
$373$	−9.46379	+	32.2307i	−0.490017	+	1.66884i	0.228666	+	0.973505i	$0.426564\pi$
$373$	−9.46379	+	32.2307i	−0.490017	+	1.66884i	−0.718683	+	0.695338i	$0.755255\pi$
$374$	23.2675	+	10.6259i	1.20314	+	0.549454i
$375$	1.49070	+	0.881945i	0.0769792	+	0.0455435i
$376$	1.43861	−	10.0058i	0.0741908	−	0.516008i
$377$	1.64471	+	5.60137i	0.0847069	+	0.288485i
$378$	1.97178	−	5.99948i	0.101418	−	0.308580i
$379$	−17.7025	−	27.5457i	−0.909318	−	1.41493i	−0.909855	−	0.414927i	$-0.863807\pi$
$379$	−17.7025	−	27.5457i	−0.909318	−	1.41493i	0.000536717	−	1.00000i	$-0.499829\pi$
$380$	3.17892	+	4.94650i	0.163075	+	0.253750i
$381$	−8.46118	+	10.5267i	−0.433479	+	0.539298i
$382$	−4.48076	−	15.2601i	−0.229256	−	0.780774i
$383$	−1.04226	+	7.24908i	−0.0532570	+	0.370411i	0.945712	+	0.325007i	$0.105367\pi$
$383$	−1.04226	+	7.24908i	−0.0532570	+	0.370411i	−0.998969	+	0.0454039i	$0.985543\pi$
$384$	0.881945	−	1.49070i	0.0450066	−	0.0760717i
$385$	4.99125	+	2.27943i	0.254378	+	0.116170i
$386$	−3.98640	+	13.5764i	−0.202902	+	0.691022i
$387$	−2.34539	+	2.35719i	−0.119223	+	0.119822i
$388$	9.33282	−	1.34186i	0.473802	−	0.0681225i
$389$	−17.8160	−	11.4496i	−0.903307	−	0.580520i	0.00446260	−	0.999990i	$-0.498580\pi$
$389$	−17.8160	−	11.4496i	−0.903307	−	0.580520i	−0.907769	+	0.419470i	$0.862216\pi$
$390$	1.40864	−	0.255971i	0.0713293	−	0.0129616i
$391$	20.1956	−	18.1773i	1.02134	−	0.919268i
$392$			5.52290i			0.278949i
$393$	12.5607	+	5.18437i	0.633603	+	0.261517i
$394$	3.80657	+	26.4753i	0.191772	+	1.33381i
$395$	−9.93592	+	4.53758i	−0.499930	+	0.228311i
$396$	−13.5074	+	1.00012i	−0.678773	+	0.0502580i
$397$	4.88973	−	10.7070i	0.245409	−	0.537370i	−0.746340	−	0.665564i	$-0.768191\pi$
$397$	4.88973	−	10.7070i	0.245409	−	0.537370i	0.991749	+	0.128195i	$0.0409182\pi$
$398$	−1.51584	+	1.74938i	−0.0759824	+	0.0876884i
$399$	−12.3692	+	0.457295i	−0.619233	+	0.0228934i
$400$	−0.959493	+	0.281733i	−0.0479746	+	0.0140866i
$401$	15.2324	+	17.5791i	0.760670	+	0.877860i	0.995557	−	0.0941628i	$-0.0300174\pi$
$401$	15.2324	+	17.5791i	0.760670	+	0.877860i	−0.234887	+	0.972023i	$0.575472\pi$
$402$	−7.41926	−	7.94885i	−0.370039	−	0.396452i
$403$	3.95693	−	2.54296i	0.197109	−	0.126674i
$404$	−1.93241	+	1.67445i	−0.0961412	+	0.0833068i
$405$	4.82773	−	7.59559i	0.239892	−	0.377428i
$406$	8.49612	+	1.22156i	0.421655	+	0.0606249i
$407$	−32.5449	−	28.2003i	−1.61319	−	1.39784i
$408$	2.41492	−	9.51133i	0.119557	−	0.470881i
$409$	−23.7035	−	6.95998i	−1.17206	−	0.344149i	−0.362954	−	0.931807i	$-0.618232\pi$
$409$	−23.7035	−	6.95998i	−1.17206	−	0.344149i	−0.809110	+	0.587658i	$0.800050\pi$
$410$	−0.994535	−	2.17773i	−0.0491166	−	0.107550i
$411$	−8.50622	+	2.84299i	−0.419581	+	0.140234i
$412$	−2.93126	+	4.56113i	−0.144413	+	0.224711i
$413$	−16.3912			−0.806556
$414$	−4.73885	+	13.5847i	−0.232902	+	0.667650i
$415$	5.16179			0.253382
$416$	−0.446892	+	0.695378i	−0.0219107	+	0.0340937i
$417$	6.73296	−	2.25033i	0.329715	−	0.110199i
$418$	11.0279	+	24.1477i	0.539391	+	1.18110i
$419$	26.3646	+	7.74134i	1.28799	+	0.378189i	0.852842	−	0.522168i	$-0.174877\pi$
$419$	26.3646	+	7.74134i	1.28799	+	0.378189i	0.435151	+	0.900357i	$0.356695\pi$
$420$	0.518039	−	2.04033i	0.0252777	−	0.0995578i
$421$	−7.88516	−	6.83253i	−0.384299	−	0.332997i	0.441191	−	0.897413i	$-0.354556\pi$
$421$	−7.88516	−	6.83253i	−0.384299	−	0.332997i	−0.825491	+	0.564416i	$0.809101\pi$
$422$	0.929152	+	0.133592i	0.0452304	+	0.00650315i
$423$	18.2345	+	24.2316i	0.886592	+	1.17818i
$424$	4.77554	−	4.13803i	0.231921	−	0.200960i
$425$	−4.76621	+	3.06306i	−0.231195	+	0.148580i
$426$	−12.6590	−	13.5626i	−0.613330	−	0.657109i
$427$	−9.26470	−	10.6920i	−0.448350	−	0.517424i
$428$	0.506326	−	0.148671i	0.0244742	−	0.00718627i
$429$	6.45946	−	0.238810i	0.311866	−	0.0115299i
$430$	−0.725856	+	0.837682i	−0.0350039	+	0.0403966i
$431$	−8.67898	+	19.0043i	−0.418052	+	0.915406i	0.577065	+	0.816699i	$0.304198\pi$
$431$	−8.67898	+	19.0043i	−0.418052	+	0.915406i	−0.995116	+	0.0987075i	$0.968529\pi$
$432$	1.30397	+	5.02988i	0.0627373	+	0.242000i
$433$	−20.6247	+	9.41898i	−0.991159	+	0.452647i	−0.843929	−	0.536455i	$-0.819763\pi$
$433$	−20.6247	+	9.41898i	−0.991159	+	0.452647i	−0.147230	+	0.989102i	$0.547036\pi$
$434$	−0.984221	−	6.84541i	−0.0472441	−	0.328590i
$435$	11.3073	+	4.66704i	0.542144	+	0.223768i
$436$		−	2.44885i		−	0.117279i
$437$	28.1941	−	0.531575i	1.34871	−	0.0254287i
$438$	15.9805	−	2.90389i	0.763577	−	0.138753i
$439$	−10.2276	−	6.57288i	−0.488137	−	0.313707i	0.273319	−	0.961924i	$-0.411879\pi$
$439$	−10.2276	−	6.57288i	−0.488137	−	0.313707i	−0.761456	+	0.648217i	$0.775515\pi$
$440$	−4.46884	+	0.642523i	−0.213044	+	0.0306311i
$441$	−11.7452	−	11.6864i	−0.559294	−	0.556496i
$442$	−1.31940	+	4.49347i	−0.0627576	+	0.213733i
$443$	33.2316	+	15.1764i	1.57888	+	0.721050i	0.995816	−	0.0913761i	$-0.0291265\pi$
$443$	33.2316	+	15.1764i	1.57888	+	0.721050i	0.583064	+	0.812426i	$0.301854\pi$
$444$	−8.41217	+	14.2185i	−0.399224	+	0.674782i
$445$	−2.66990	+	18.5696i	−0.126565	+	0.880282i
$446$	−5.52771	−	18.8257i	−0.261745	−	0.891421i
$447$	−5.38669	+	6.70166i	−0.254782	+	0.316977i
$448$	0.657074	+	1.02243i	0.0310438	+	0.0483051i
$449$	−12.8166	−	19.9430i	−0.604851	−	0.941167i	−0.999748	−	0.0224414i	$-0.992856\pi$
$449$	−12.8166	−	19.9430i	−0.604851	−	0.941167i	0.394897	−	0.918725i	$-0.370780\pi$
$450$	1.43114	−	2.63663i	0.0674646	−	0.124292i
$451$	−3.04518	−	10.3709i	−0.143392	−	0.488348i
$452$	2.04621	−	14.2317i	0.0962456	−	0.669403i
$453$	−6.61570	−	3.91407i	−0.310833	−	0.183899i
$454$	3.95629	+	1.80678i	0.185678	+	0.0847963i
$455$	−0.283032	+	0.963920i	−0.0132688	+	0.0451892i
$456$	8.35832	−	5.81883i	0.391414	−	0.272492i
$457$	−18.5992	+	2.67415i	−0.870032	+	0.125092i	−0.562850	−	0.826559i	$-0.690295\pi$
$457$	−18.5992	+	2.67415i	−0.870032	+	0.125092i	−0.307182	+	0.951651i	$0.599386\pi$
$458$	−2.98027	−	1.91531i	−0.139259	−	0.0894963i
$459$	15.1171	+	25.2616i	0.705608	+	1.17911i
$460$	−1.26416	+	4.62622i	−0.0589417	+	0.215699i
$461$		−	31.8379i		−	1.48284i	−0.671043	−	0.741418i	$-0.734153\pi$
$461$		−	31.8379i		−	1.48284i	0.671043	−	0.741418i	$-0.265847\pi$
$462$	3.62599	−	8.78506i	0.168696	−	0.408718i
$463$	−3.75393	−	26.1092i	−0.174460	−	1.21340i	−0.869320	−	0.494250i	$-0.835443\pi$
$463$	−3.75393	−	26.1092i	−0.174460	−	1.21340i	0.694860	−	0.719145i	$-0.255466\pi$
$464$	−6.42428	+	2.93387i	−0.298239	+	0.136201i
$465$	1.04126	−	9.80078i	0.0482875	−	0.454500i
$466$	6.70418	−	14.6801i	0.310565	−	0.680043i
$467$	8.91992	−	10.2941i	0.412765	−	0.476356i	−0.510855	−	0.859667i	$-0.670671\pi$
$467$	8.91992	−	10.2941i	0.412765	−	0.476356i	0.923619	+	0.383311i	$0.125216\pi$
$468$	−0.533192	−	2.42179i	−0.0246468	−	0.111947i
$469$	7.32065	−	2.14954i	0.338036	−	0.0992563i
$470$	6.61977	+	7.63962i	0.305347	+	0.352389i
$471$	−9.77450	+	9.12328i	−0.450385	+	0.420379i
$472$	11.3457	−	7.29144i	0.522228	−	0.335616i
$473$	−3.78197	+	3.27709i	−0.173895	+	0.150681i
$474$	8.48977	+	16.9074i	0.389948	+	0.776583i
$475$	−5.82007	−	0.836800i	−0.267043	−	0.0383950i
$476$	5.20390	+	4.50921i	0.238521	+	0.206679i
$477$	−1.30495	+	18.9119i	−0.0597493	+	0.865915i
$478$	−10.8803	−	3.19474i	−0.497653	−	0.146124i
$479$	−0.334010	−	0.731380i	−0.0152613	−	0.0334176i	0.901848	−	0.432054i	$-0.142211\pi$
$479$	−0.334010	−	0.731380i	−0.0152613	−	0.0334176i	−0.917109	+	0.398636i	$0.869484\pi$
$480$	0.549041	+	1.64273i	0.0250602	+	0.0749799i
$481$	4.26254	−	6.63265i	0.194355	−	0.302423i
$482$	7.84718			0.357429
$483$	−7.02644	−	7.24908i	−0.319714	−	0.329844i
$484$	−9.38341			−0.426518
$485$	−5.09759	+	7.93200i	−0.231470	+	0.360174i
$486$	−13.4559	−	7.87012i	−0.610372	−	0.356996i
$487$	6.33462	+	13.8709i	0.287049	+	0.628550i	0.997141	−	0.0755587i	$-0.0240740\pi$
$487$	6.33462	+	13.8709i	0.287049	+	0.628550i	−0.710092	+	0.704109i	$0.751347\pi$
$488$	11.1691	+	3.27955i	0.505602	+	0.148458i
$489$	18.2275	+	4.62796i	0.824276	+	0.209283i
$490$	−4.17393	−	3.61673i	−0.188559	−	0.163387i
$491$	30.6673	+	4.40929i	1.38399	+	0.198988i	0.793754	−	0.608239i	$-0.208124\pi$
$491$	30.6673	+	4.40929i	1.38399	+	0.198988i	0.590240	+	0.807228i	$0.299033\pi$
$492$	−3.70572	+	1.86076i	−0.167067	+	0.0838897i
$493$	−30.2401	+	26.2032i	−1.36194	+	1.18013i
$494$	−4.08877	+	2.62769i	−0.183962	+	0.118225i
$495$	8.08964	−	10.8632i	0.363602	−	0.488263i
$496$	3.72637	+	4.30046i	0.167319	+	0.193097i
$497$	12.4907	−	3.66761i	0.560286	−	0.164515i
$498$	−0.330309	−	8.93438i	−0.0148015	−	0.400359i
$499$	−10.7267	+	12.3793i	−0.480194	+	0.554173i	−0.943219	−	0.332172i	$-0.892219\pi$
$499$	−10.7267	+	12.3793i	−0.480194	+	0.554173i	0.463025	+	0.886345i	$0.346764\pi$
$500$	0.415415	−	0.909632i	0.0185779	−	0.0406800i
$501$	15.2237	+	1.61741i	0.680144	+	0.0722606i
$502$	−24.3986	+	11.1425i	−1.08896	+	0.497312i
$503$	−0.634724	−	4.41460i	−0.0283009	−	0.196837i	0.970766	−	0.240028i	$-0.0771567\pi$
$503$	−0.634724	−	4.41460i	−0.0283009	−	0.196837i	−0.999067	+	0.0431909i	$0.986248\pi$
$504$	−3.56469	−	0.766094i	−0.158784	−	0.0341245i
$505$		−	2.55695i		−	0.113783i
$506$	−8.62178	+	19.8616i	−0.383285	+	0.882956i
$507$	−3.81410	−	20.9895i	−0.169390	−	0.932176i
$508$	6.55966	+	4.21564i	0.291038	+	0.187039i
$509$	−8.96788	+	1.28939i	−0.397494	+	0.0571511i	−0.338164	−	0.941087i	$-0.609806\pi$
$509$	−8.96788	+	1.28939i	−0.397494	+	0.0571511i	−0.0593308	+	0.998238i	$0.518897\pi$
$510$	5.60674	+	8.05367i	0.248271	+	0.356623i
$511$	−3.21089	+	10.9353i	−0.142042	+	0.483749i
$512$	−0.909632	−	0.415415i	−0.0402004	−	0.0183589i
$513$	−5.31164	+	30.0877i	−0.234515	+	1.32840i
$514$	−2.74363	+	19.0824i	−0.121016	+	0.841686i
$515$	−1.52750	−	5.20220i	−0.0673099	−	0.229236i
$516$	1.49637	+	1.20276i	0.0658738	+	0.0529484i
$517$	24.6741	+	38.3936i	1.08516	+	1.68855i
$518$	−6.26730	−	9.75210i	−0.275369	−	0.428483i
$519$	−13.2738	−	10.6693i	−0.582654	−	0.468328i
$520$	−0.232879	−	0.793114i	−0.0102124	−	0.0347804i
$521$	0.167605	−	1.16572i	0.00734292	−	0.0510711i	−0.985821	−	0.167803i	$-0.946333\pi$
$521$	0.167605	−	1.16572i	0.00734292	−	0.0510711i	0.993163	+	0.116732i	$0.0372418\pi$
$522$	7.35447	−	19.8701i	0.321896	−	0.869692i
$523$	−11.9592	−	5.46159i	−0.522940	−	0.238819i	0.136413	−	0.990652i	$-0.456443\pi$
$523$	−11.9592	−	5.46159i	−0.522940	−	0.238819i	−0.659353	+	0.751833i	$0.729170\pi$
$524$	2.21029	−	7.52756i	0.0965570	−	0.328843i
$525$	1.20273	+	1.72764i	0.0524916	+	0.0754003i
$526$	−9.68200	+	1.39206i	−0.422155	+	0.0606968i
$527$	27.1213	+	17.4298i	1.18142	+	0.759254i
$528$	1.39809	+	7.69387i	0.0608440	+	0.334833i
$529$	15.7063	+	16.8021i	0.682883	+	0.730528i
$530$			6.31895i			0.274477i
$531$	−8.50122	+	39.5568i	−0.368922	+	1.71662i
$532$	1.01701	+	7.07348i	0.0440931	+	0.306674i
$533$	1.80010	−	0.822079i	0.0779711	−	0.0356082i
$534$	32.3123	+	3.43296i	1.39829	+	0.148559i
$535$	−0.219215	+	0.480014i	−0.00947749	+	0.0207528i
$536$	−4.11104	+	4.74439i	−0.177570	+	0.204926i
$537$	−1.68095	−	45.4673i	−0.0725384	−	1.96206i
$538$	−6.60202	+	1.93853i	−0.284633	+	0.0835759i
$539$	−16.3288	−	18.8444i	−0.703331	−	0.811688i
$540$	−4.65525	−	2.30839i	−0.200330	−	0.0993374i
$541$	−6.96297	+	4.47483i	−0.299361	+	0.192388i	−0.681695	−	0.731637i	$-0.738757\pi$
$541$	−6.96297	+	4.47483i	−0.299361	+	0.192388i	0.382334	+	0.924024i	$0.375121\pi$
$542$	−14.2008	+	12.3051i	−0.609979	+	0.528550i
$543$	27.9982	−	14.0588i	1.20152	−	0.603322i
$544$	−5.60794	−	0.806300i	−0.240438	−	0.0345698i
$545$	1.85072	+	1.60366i	0.0792761	+	0.0686931i
$546$	1.68653	+	0.428209i	0.0721768	+	0.0183257i
$547$	20.4811	+	6.01378i	0.875707	+	0.257131i	0.688541	−	0.725198i	$-0.258252\pi$
$547$	20.4811	+	6.01378i	0.875707	+	0.257131i	0.187166	+	0.982328i	$0.440070\pi$
$548$	2.15106	+	4.71017i	0.0918888	+	0.201208i
$549$	−30.6082	+	16.8131i	−1.30633	+	0.717566i
$550$	2.44088	−	3.79809i	0.104080	−	0.161951i
$551$	−41.5269			−1.76911
$552$	8.08827	+	1.89205i	0.344260	+	0.0805312i
$553$	−13.2754			−0.564527
$554$	4.30057	−	6.69182i	0.182714	−	0.284308i
$555$	−5.23686	−	15.6687i	−0.222292	−	0.665097i
$556$	−1.70264	−	3.72826i	−0.0722080	−	0.158113i
$557$	34.9105	+	10.2507i	1.47921	+	0.434334i	0.919079	−	0.394072i	$-0.128934\pi$
$557$	34.9105	+	10.2507i	1.47921	+	0.434334i	0.560127	+	0.828407i	$0.310752\pi$
$558$	−17.0305	−	1.17513i	−0.720958	−	0.0497471i
$559$	−0.692425	−	0.599990i	−0.0292865	−	0.0253769i
$560$	−1.20299	−	0.172964i	−0.0508356	−	0.00730906i
$561$	19.8810	+	39.5931i	0.839376	+	1.67162i
$562$	20.5872	−	17.8389i	0.868419	−	0.752489i
$563$	−7.32923	+	4.71021i	−0.308890	+	0.198512i	−0.685897	−	0.727699i	$-0.740590\pi$
$563$	−7.32923	+	4.71021i	−0.308890	+	0.198512i	0.377006	+	0.926211i	$0.376953\pi$
$564$	12.7996	−	11.9468i	0.538959	−	0.503052i
$565$	9.41562	+	10.8662i	0.396118	+	0.457145i
$566$	−6.11438	+	1.79534i	−0.257007	+	0.0754640i
$567$	9.17206	−	5.95974i	0.385190	−	0.250285i
$568$	−7.01439	+	8.09503i	−0.294317	+	0.339660i
$569$	11.2547	−	24.6443i	0.471821	−	1.03314i	−0.512811	−	0.858501i	$-0.671396\pi$
$569$	11.2547	−	24.6443i	0.471821	−	1.03314i	0.984632	−	0.174642i	$-0.0558768\pi$
$570$	−1.07596	+	10.1273i	−0.0450669	+	0.424187i
$571$	18.0331	−	8.23544i	0.754661	−	0.344642i	−0.000657473	−	1.00000i	$-0.500209\pi$
$571$	18.0331	−	8.23544i	0.754661	−	0.344642i	0.755319	+	0.655357i	$0.227482\pi$
$572$	−0.531107	−	3.69393i	−0.0222067	−	0.154451i
$573$	10.5099	−	25.4634i	0.439057	−	1.06375i
$574$		−	2.90966i		−	0.121447i
$575$	−2.66842	−	3.98492i	−0.111281	−	0.166183i
$576$	2.80821	−	1.05544i	0.117009	−	0.0439766i
$577$	−8.40219	−	5.39976i	−0.349788	−	0.224795i	0.353934	−	0.935270i	$-0.384844\pi$
$577$	−8.40219	−	5.39976i	−0.349788	−	0.224795i	−0.703722	+	0.710475i	$0.748480\pi$
$578$	−14.9454	+	2.14882i	−0.621646	+	0.0893792i
$579$	−20.1137	+	14.0026i	−0.835896	+	0.581928i
$580$	1.98974	−	6.77642i	0.0826193	−	0.281375i
$581$	5.70652	+	2.60608i	0.236746	+	0.108118i
$582$	14.0555	+	8.31568i	0.582617	+	0.344696i
$583$	−4.06007	+	28.2384i	−0.168151	+	1.16951i
$584$	−2.64193	−	8.99758i	−0.109324	−	0.372322i
$585$	2.17943	+	1.18298i	0.0901085	+	0.0489100i
$586$	3.81477	+	5.93589i	0.157587	+	0.245209i
$587$	8.78766	+	13.6739i	0.362706	+	0.564381i	0.973865	−	0.227126i	$-0.0729331\pi$
$587$	8.78766	+	13.6739i	0.362706	+	0.564381i	−0.611160	+	0.791507i	$0.709297\pi$
$588$	−5.99299	+	7.45596i	−0.247147	+	0.307479i
$589$	9.42640	+	32.1034i	0.388408	+	1.32280i
$590$	−1.91935	+	13.3494i	−0.0790185	+	0.549586i
$591$	−23.5899	+	39.8724i	−0.970357	+	1.64013i
$592$	8.67625	+	3.96231i	0.356592	+	0.162850i
$593$	9.85283	−	33.5556i	0.404607	−	1.37797i	−0.465476	−	0.885060i	$-0.654117\pi$
$593$	9.85283	−	33.5556i	0.404607	−	1.37797i	0.870083	−	0.492905i	$-0.164065\pi$
$594$	−19.3204	−	13.3070i	−0.792725	−	0.545991i
$595$	−6.81566	+	0.979945i	−0.279415	+	0.0401738i
$596$	4.17612	+	2.68383i	0.171060	+	0.109934i
$597$	−3.94468	+	0.716807i	−0.161445	+	0.0293370i
$598$	−3.82402	−	1.04495i	−0.156376	−	0.0427312i
$599$			19.8338i			0.810387i	0.914231	+	0.405194i	$0.132796\pi$
$599$			19.8338i			0.810387i	−0.914231	+	0.405194i	$0.867204\pi$
$600$	−1.60104	−	0.660820i	−0.0653620	−	0.0269779i
$601$	3.02790	+	21.0595i	0.123510	+	0.859034i	0.953530	+	0.301299i	$0.0974203\pi$
$601$	3.02790	+	21.0595i	0.123510	+	0.859034i	−0.830019	+	0.557735i	$0.811671\pi$
$602$	−1.22538	+	0.559614i	−0.0499429	+	0.0228082i
$603$	−1.39065	−	18.7818i	−0.0566315	−	0.764853i
$604$	−1.84361	+	4.03694i	−0.0750154	+	0.164261i
$605$	6.14482	−	7.09150i	0.249823	−	0.288311i
$606$	−4.42574	+	0.163622i	−0.179784	+	0.00664670i
$607$	27.1785	−	7.98032i	1.10314	−	0.323911i	0.321041	−	0.947065i	$-0.395967\pi$
$607$	27.1785	−	7.98032i	1.10314	−	0.323911i	0.782099	+	0.623154i	$0.214149\pi$
$608$	−3.85053	−	4.44375i	−0.156160	−	0.180218i
$609$	10.1443	+	10.8684i	0.411068	+	0.440409i
$610$	−9.79274	+	6.29341i	−0.396496	+	0.254813i
$611$	−6.31489	+	5.47188i	−0.255473	+	0.221369i
$612$	13.5811	−	10.2199i	0.548982	−	0.413115i
$613$	−10.1909	−	1.46523i	−0.411605	−	0.0591799i	−0.0665980	−	0.997780i	$-0.521214\pi$
$613$	−10.1909	−	1.46523i	−0.411605	−	0.0591799i	−0.345007	+	0.938600i	$0.612124\pi$
$614$	−15.6050	−	13.5218i	−0.629766	−	0.545695i
$615$	1.02046	−	4.01914i	0.0411488	−	0.162067i
$616$	−5.26484	−	1.54590i	−0.212127	−	0.0622860i
$617$	−11.0026	−	24.0924i	−0.442948	−	0.969922i	−0.991048	−	0.133509i	$-0.957376\pi$
$617$	−11.0026	−	24.0924i	−0.442948	−	0.969922i	0.548099	−	0.836413i	$-0.315352\pi$
$618$	−8.90658	+	2.97680i	−0.358275	+	0.119745i
$619$	13.6687	−	21.2689i	0.549390	−	0.854868i	−0.449879	−	0.893089i	$-0.648533\pi$
$619$	13.6687	−	21.2689i	0.549390	−	0.854868i	0.999269	+	0.0382218i	$0.0121693\pi$
$620$	−5.69033			−0.228529
$621$	−21.1384	+	13.1972i	−0.848256	+	0.529586i
$622$	−10.2657			−0.411615
$623$	−12.3270	+	19.1813i	−0.493873	+	0.768481i
$624$	−1.35787	+	0.453836i	−0.0543585	+	0.0181680i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	16.3360	+	4.79668i	0.652918	+	0.191714i
$627$	−11.3153	+	44.5661i	−0.451890	+	1.77980i
$628$	5.83406	+	5.05524i	0.232804	+	0.201726i
$629$	53.4896	+	7.69064i	2.13277	+	0.306646i
$630$	2.91335	−	2.19233i	0.116071	−	0.0873444i
$631$	−15.2886	+	13.2477i	−0.608631	+	0.527382i	−0.903740	−	0.428082i	$-0.859190\pi$
$631$	−15.2886	+	13.2477i	−0.608631	+	0.527382i	0.295109	+	0.955464i	$0.404644\pi$
$632$	9.18902	−	5.90543i	0.365520	−	0.234905i
$633$	1.10940	+	1.18859i	0.0440947	+	0.0472421i
$634$	2.67450	+	3.08654i	0.106218	+	0.122582i
$635$	−7.48163	+	2.19681i	−0.296899	+	0.0871775i
$636$	10.9373	−	0.404357i	0.433691	−	0.0160338i
$637$	2.98958	−	3.45016i	0.118451	−	0.136700i
$638$	13.2458	−	29.0043i	0.524407	−	1.14829i
$639$	−2.37277	−	32.0461i	−0.0938652	−	1.26772i
$640$	0.909632	−	0.415415i	0.0359564	−	0.0164207i
$641$	−4.53648	−	31.5519i	−0.179180	−	1.24622i	−0.858666	−	0.512536i	$-0.828706\pi$
$641$	−4.53648	−	31.5519i	−0.179180	−	1.24622i	0.679486	−	0.733689i	$-0.262203\pi$
$642$	0.844869	+	0.348716i	0.0333443	+	0.0137627i
$643$		−	2.72511i		−	0.107468i	−0.998555	−	0.0537339i	$-0.982888\pi$
$643$		−	2.72511i		−	0.107468i	0.998555	−	0.0537339i	$-0.0171123\pi$
$644$	−3.73325	+	4.47618i	−0.147111	+	0.176386i
$645$	−1.88889	+	0.343240i	−0.0743751	+	0.0135151i
$646$	−28.0249	−	18.0105i	−1.10263	−	0.708615i
$647$	3.54478	−	0.509662i	0.139360	−	0.0200369i	−0.0722820	−	0.997384i	$-0.523028\pi$
$647$	3.54478	−	0.509662i	0.139360	−	0.0200369i	0.211642	+	0.977347i	$0.432119\pi$
$648$	−3.69763	+	8.20534i	−0.145257	+	0.322336i
$649$	−17.1546	+	58.4231i	−0.673376	+	2.29331i
$650$	0.751899	+	0.343381i	0.0294919	+	0.0134685i
$651$	6.09936	−	10.3094i	0.239053	−	0.404055i
$652$	1.54519	−	10.7470i	0.0605144	−	0.420887i
$653$	5.31800	+	18.1114i	0.208109	+	0.708755i	0.995707	+	0.0925650i	$0.0295066\pi$
$653$	5.31800	+	18.1114i	0.208109	+	0.708755i	−0.787597	+	0.616190i	$0.788675\pi$
$654$	2.65729	−	3.30597i	0.103908	−	0.129274i
$655$	4.24152	+	6.59993i	0.165730	+	0.257881i
$656$	1.29433	+	2.01402i	0.0505353	+	0.0786344i
$657$	24.7249	+	13.4204i	0.964608	+	0.523580i
$658$	3.46127	+	11.7880i	0.134934	+	0.459545i
$659$	−1.29883	+	9.03358i	−0.0505954	+	0.351899i	0.948760	+	0.315998i	$0.102339\pi$
$659$	−1.29883	+	9.03358i	−0.0505954	+	0.351899i	−0.999355	+	0.0359009i	$0.988570\pi$
$660$	−6.73019	−	3.98181i	−0.261972	−	0.154992i
$661$	12.9016	+	5.89198i	0.501815	+	0.229171i	0.650207	−	0.759757i	$-0.274682\pi$
$661$	12.9016	+	5.89198i	0.501815	+	0.229171i	−0.148392	+	0.988929i	$0.547410\pi$
$662$	4.72230	−	16.0827i	0.183537	−	0.625071i
$663$	−6.65714	+	4.63452i	−0.258542	+	0.179990i
$664$	−5.10925	+	0.734600i	−0.198277	+	0.0285080i
$665$	−6.01179	−	3.86354i	−0.233127	−	0.149822i
$666$	−26.7853	+	10.0670i	−1.03791	+	0.390087i
$667$	−22.6591	−	25.1750i	−0.877364	−	0.974780i
$668$		−	8.83887i		−	0.341986i
$669$	12.9656	−	31.4130i	0.501278	−	1.21450i
$670$	−0.893414	−	6.21383i	−0.0345156	−	0.240061i
$671$	−47.8059	+	21.8322i	−1.84553	+	0.842823i
$672$	−0.222397	+	2.09329i	−0.00857915	+	0.0807502i
$673$	−6.95234	+	15.2235i	−0.267993	+	0.586823i	−0.995008	−	0.0997991i	$-0.968180\pi$
$673$	−6.95234	+	15.2235i	−0.267993	+	0.586823i	0.727015	+	0.686622i	$0.240907\pi$
$674$	14.5963	−	16.8451i	0.562230	−	0.648848i
$675$	4.79311	−	2.00652i	0.184487	−	0.0772312i
$676$	−11.8178	+	3.47003i	−0.454532	+	0.133463i
$677$	−13.9117	−	16.0549i	−0.534669	−	0.617040i	0.422573	−	0.906329i	$-0.361127\pi$
$677$	−13.9117	−	16.0549i	−0.534669	−	0.617040i	−0.957242	+	0.289288i	$0.906581\pi$
$678$	18.2055	−	16.9925i	0.699176	−	0.652595i
$679$	−9.64024	+	6.19541i	−0.369959	+	0.237758i
$680$	4.28178	−	3.71018i	0.164199	−	0.142279i
$681$	3.38046	+	6.73220i	0.129540	+	0.257978i
$682$	−25.4292	−	3.65617i	−0.973734	−	0.140002i
$683$	−2.18782	−	1.89576i	−0.0837146	−	0.0725391i	0.611998	−	0.790859i	$-0.290366\pi$
$683$	−2.18782	−	1.89576i	−0.0837146	−	0.0725391i	−0.695713	+	0.718320i	$0.744911\pi$
$684$	17.5979	+	1.21428i	0.672873	+	0.0464292i
$685$	−4.96836	−	1.45884i	−0.189831	−	0.0557394i
$686$	−6.32255	−	13.8445i	−0.241396	−	0.528584i
$687$	−1.94506	−	5.81962i	−0.0742088	−	0.222032i
$688$	0.599253	−	0.932456i	0.0228463	−	0.0355495i
$689$	−5.22322			−0.198989
$690$	−6.72661	+	4.87367i	−0.256078	+	0.185538i
$691$	−5.21430			−0.198361			−0.0991807	−	0.995069i	$-0.531622\pi$
$691$	−5.21430			−0.198361			−0.0991807	+	0.995069i	$0.531622\pi$
$692$	−5.31578	+	8.27151i	−0.202076	+	0.314436i
$693$	14.4279	−	7.92528i	0.548072	−	0.301056i
$694$	−8.80638	−	19.2833i	−0.334286	−	0.731983i
$695$	3.93262	+	1.15472i	0.149173	+	0.0438011i
$696$	−11.8564	−	3.01034i	−0.449416	−	0.114107i
$697$	10.2509	+	8.88245i	0.388280	+	0.336447i
$698$	−21.1922	−	3.04698i	−0.802138	−	0.115330i
$699$	24.9803	−	12.5434i	0.944842	−	0.474437i
$700$	0.918508	−	0.795892i	0.0347163	−	0.0300819i
$701$	−14.7430	+	9.47478i	−0.556837	+	0.357857i	−0.788592	−	0.614917i	$-0.789190\pi$
$701$	−14.7430	+	9.47478i	−0.556837	+	0.357857i	0.231755	+	0.972774i	$0.425553\pi$
$702$	1.90811	−	3.84801i	0.0720170	−	0.145234i
$703$	36.7271	+	42.3853i	1.38519	+	1.59859i
$704$	4.33192	−	1.27197i	0.163265	−	0.0479390i
$705$	0.646865	+	17.4968i	0.0243624	+	0.658966i
$706$	−4.84525	+	5.59171i	−0.182353	+	0.210447i
$707$	1.29095	−	2.82679i	0.0485512	−	0.106312i
$708$	23.2289	+	2.46790i	0.872994	+	0.0927495i
$709$	11.0655	−	5.05344i	0.415573	−	0.189786i	−0.196645	−	0.980475i	$-0.563005\pi$
$709$	11.0655	−	5.05344i	0.415573	−	0.189786i	0.612218	+	0.790689i	$0.290277\pi$
$710$	−1.52437	−	10.6022i	−0.0572087	−	0.397895i
$711$	−6.88524	+	32.0375i	−0.258217	+	1.20150i
$712$		−	18.7605i		−	0.703081i
$713$	−14.3186	+	23.2317i	−0.536237	+	0.870035i
$714$	2.13230	+	11.7343i	0.0797992	+	0.439146i
$715$	3.13949	+	2.01763i	0.117410	+	0.0754550i
$716$	−26.0011	+	3.73840i	−0.971707	+	0.139710i
$717$	−11.2218	−	16.1193i	−0.419087	−	0.601987i
$718$	8.11392	−	27.6335i	0.302809	−	1.03127i
$719$	−10.5859	−	4.83442i	−0.394788	−	0.180294i	0.208122	−	0.978103i	$-0.433265\pi$
$719$	−10.5859	−	4.83442i	−0.394788	−	0.180294i	−0.602910	+	0.797809i	$0.705992\pi$
$720$	−1.04134	+	2.81347i	−0.0388085	+	0.104852i
$721$	0.937779	−	6.52240i	0.0349247	−	0.242907i
$722$	−4.38755	−	14.9426i	−0.163288	−	0.556107i
$723$	10.5938	+	8.51510i	0.393986	+	0.316680i
$724$	−9.77923	−	15.2168i	−0.363442	−	0.565527i
$725$	3.81828	+	5.94135i	0.141807	+	0.220656i
$726$	−12.6677	−	10.1821i	−0.470142	−	0.377893i
$727$	9.91381	+	33.7633i	0.367683	+	1.25221i	0.910902	+	0.412622i	$0.135387\pi$
$727$	9.91381	+	33.7633i	0.367683	+	1.25221i	−0.543219	+	0.839591i	$0.682795\pi$
$728$	0.142971	−	0.994388i	0.00529887	−	0.0368545i
$729$	−9.62558	−	25.2259i	−0.356503	−	0.934294i
$730$	8.53001	+	3.89553i	0.315710	+	0.144180i
$731$	1.76923	−	6.02545i	0.0654374	−	0.222859i
$732$	11.5197	+	16.5472i	0.425781	+	0.611603i
$733$	6.72325	−	0.966658i	0.248329	−	0.0357043i	−0.0170262	−	0.999855i	$-0.505420\pi$
$733$	6.72325	−	0.966658i	0.248329	−	0.0357043i	0.265355	+	0.964151i	$0.414511\pi$
$734$	−6.69020	−	4.29953i	−0.246940	−	0.158698i
$735$	−1.71027	−	9.41181i	−0.0630841	−	0.347160i
$736$	0.592912	−	4.75904i	0.0218550	−	0.175421i
$737$		−	28.3427i		−	1.04402i
$738$	−7.02189	−	1.50909i	−0.258479	−	0.0555503i
$739$	2.45064	+	17.0446i	0.0901483	+	0.626995i	0.983938	+	0.178509i	$0.0571275\pi$
$739$	2.45064	+	17.0446i	0.0901483	+	0.626995i	−0.893790	+	0.448486i	$0.851963\pi$
$740$	−8.67625	+	3.96231i	−0.318945	+	0.145657i
$741$	−8.37122	−	0.889383i	−0.307524	−	0.0326723i
$742$	−3.19030	+	6.98579i	−0.117120	+	0.256456i
$743$	13.5864	−	15.6795i	0.498436	−	0.575226i	−0.449664	−	0.893198i	$-0.648456\pi$
$743$	13.5864	−	15.6795i	0.498436	−	0.575226i	0.948100	+	0.317972i	$0.103002\pi$
$744$	0.364131	+	9.84921i	0.0133497	+	0.361090i
$745$	−4.76308	+	1.39857i	−0.174506	+	0.0512395i
$746$	21.9977	+	25.3867i	0.805393	+	0.929473i
$747$	9.24893	−	12.4199i	0.338400	−	0.454421i
$748$	21.5185	−	13.8291i	0.786793	−	0.505641i
$749$	−0.484698	+	0.419993i	−0.0177105	+	0.0153462i
$750$	1.54787	−	0.777237i	0.0565202	−	0.0283807i
$751$	−52.7729	−	7.58760i	−1.92571	−	0.276875i	−0.929863	−	0.367907i	$-0.880075\pi$
$751$	−52.7729	−	7.58760i	−1.92571	−	0.276875i	−0.995848	+	0.0910312i	$0.970984\pi$
$752$	−7.63962	−	6.61977i	−0.278588	−	0.241398i
$753$	−45.0292	−	11.4329i	−1.64095	−	0.416638i
$754$	5.60137	+	1.64471i	0.203990	+	0.0598968i
$755$	−1.84361	−	4.03694i	−0.0670959	−	0.146919i
$756$	−3.98106	−	4.90234i	−0.144790	−	0.178296i
$757$	2.67101	−	4.15617i	0.0970794	−	0.151059i	−0.789316	−	0.613987i	$-0.789565\pi$
$757$	2.67101	−	4.15617i	0.0970794	−	0.151059i	0.886396	+	0.462928i	$0.153201\pi$
$758$	−32.7436			−1.18930
$759$	−33.1916	+	17.4577i	−1.20478	+	0.633674i
$760$	5.87992			0.213287
$761$	−20.1417	+	31.3410i	−0.730135	+	1.13611i	0.255432	+	0.966827i	$0.417782\pi$
$761$	−20.1417	+	31.3410i	−0.730135	+	1.13611i	−0.985567	+	0.169285i	$0.945854\pi$
$762$	4.28114	+	12.8091i	0.155089	+	0.464026i
$763$	1.23637	+	2.70728i	0.0447598	+	0.0980102i
$764$	−15.2601	−	4.48076i	−0.552090	−	0.162108i
$765$	−1.17002	+	16.9565i	−0.0423022	+	0.613063i
$766$	5.53482	+	4.79595i	0.199981	+	0.173285i
$767$	−11.0346	−	1.58653i	−0.398435	−	0.0572863i
$768$	−0.777237	−	1.54787i	−0.0280461	−	0.0558540i
$769$	23.1579	−	20.0664i	0.835095	−	0.723614i	−0.128290	−	0.991737i	$-0.540949\pi$
$769$	23.1579	−	20.0664i	0.835095	−	0.723614i	0.963385	+	0.268123i	$0.0864034\pi$
$770$	4.61605	−	2.96655i	0.166351	−	0.106907i
$771$	−24.4105	+	22.7842i	−0.879122	+	0.820552i
$772$	9.26601	+	10.6935i	0.333491	+	0.384869i
$773$	−3.16327	+	0.928819i	−0.113775	+	0.0334073i	−0.338124	−	0.941101i	$-0.609792\pi$
$773$	−3.16327	+	0.928819i	−0.113775	+	0.0334073i	0.224350	+	0.974509i	$0.427974\pi$
$774$	0.714976	+	3.24746i	0.0256993	+	0.116728i
$775$	3.72637	−	4.30046i	0.133855	−	0.154477i
$776$	3.91686	−	8.57673i	0.140607	−	0.307887i
$777$	2.12126	−	19.9662i	0.0761000	−	0.716282i
$778$	−19.2641	+	8.79762i	−0.690652	+	0.315410i
$779$	2.00336	+	13.9337i	0.0717779	+	0.499226i
$780$	0.546232	−	1.32341i	0.0195582	−	0.0473857i
$781$		−	48.3592i		−	1.73043i
$782$	−4.37318	−	26.8170i	−0.156384	−	0.958976i
$783$	31.4900	−	18.8444i	1.12536	−	0.673443i
$784$	4.64616	+	2.98590i	0.165934	+	0.106639i
$785$	−7.64099	+	1.09861i	−0.272719	+	0.0392110i
$786$	11.1522	−	7.76384i	0.397785	−	0.276927i
$787$	1.34251	−	4.57216i	0.0478552	−	0.162980i	−0.932099	−	0.362205i	$-0.882024\pi$
$787$	1.34251	−	4.57216i	0.0478552	−	0.162980i	0.979954	+	0.199225i	$0.0638423\pi$
$788$	24.3304	+	11.1113i	0.866735	+	0.395825i
$789$	−14.5813	−	8.62680i	−0.519109	−	0.307122i
$790$	−1.55451	+	10.8118i	−0.0553069	+	0.384668i
$791$	4.92314	+	16.7667i	0.175047	+	0.596154i
$792$	−6.46131	+	11.9039i	−0.229593	+	0.422986i
$793$	−5.20212	−	8.09465i	−0.184733	−	0.287449i
$794$	−6.36373	−	9.90215i	−0.225840	−	0.351414i
$795$	−6.85679	+	8.53063i	−0.243185	+	0.302550i
$796$	0.652143	+	2.22099i	0.0231146	+	0.0787211i
$797$	−4.94779	+	34.4126i	−0.175260	+	1.21896i	0.692295	+	0.721615i	$0.256600\pi$
$797$	−4.94779	+	34.4126i	−0.175260	+	1.21896i	−0.867554	+	0.497342i	$0.834309\pi$
$798$	−6.30258	+	10.6528i	−0.223109	+	0.377106i
$799$	−52.0962	−	23.7915i	−1.84303	−	0.841683i
$800$	−0.281733	+	0.959493i	−0.00996075	+	0.0339232i
$801$	39.8968	+	39.6972i	1.40968	+	1.40263i
$802$	23.0238	−	3.31032i	0.812997	−	0.116891i
$803$	35.6163	+	22.8892i	1.25687	+	0.807743i
$804$	−10.6982	+	1.94401i	−0.377295	+	0.0685600i
$805$	−0.938115	−	5.75268i	−0.0330642	−	0.202755i
$806$		−	4.70361i		−	0.165678i
$807$	−11.0163	−	4.54693i	−0.387792	−	0.160060i
$808$	0.363892	+	2.53092i	0.0128017	+	0.0890376i
$809$	−10.9037	+	4.97954i	−0.383352	+	0.175071i	−0.597764	−	0.801672i	$-0.703944\pi$
$809$	−10.9037	+	4.97954i	−0.383352	+	0.175071i	0.214411	+	0.976743i	$0.431217\pi$
$810$	−3.77975	−	8.16783i	−0.132807	−	0.286988i
$811$	−2.36443	+	5.17739i	−0.0830265	+	0.181803i	−0.946592	−	0.322434i	$-0.895499\pi$
$811$	−2.36443	+	5.17739i	−0.0830265	+	0.181803i	0.863565	+	0.504237i	$0.168226\pi$
$812$	5.62099	−	6.48696i	0.197258	−	0.227648i
$813$	−32.5237	+	1.20242i	−1.14066	+	0.0421708i
$814$	−41.3187	+	12.1323i	−1.44822	+	0.425235i
$815$	7.11019	+	8.20560i	0.249059	+	0.287429i
$816$	−6.69583	−	7.17377i	−0.234401	−	0.251132i
$817$	5.48276	−	3.52356i	0.191818	−	0.123274i
$818$	−18.6702	+	16.1778i	−0.652788	+	0.565644i
$819$	1.81217	+	2.40817i	0.0633224	+	0.0841482i
$820$	−2.36971	−	0.340712i	−0.0827537	−	0.0118982i
$821$	22.8837	+	19.8289i	0.798648	+	0.692033i	0.955305	−	0.295620i	$-0.0955263\pi$
$821$	22.8837	+	19.8289i	0.798648	+	0.692033i	−0.156657	+	0.987653i	$0.550072\pi$
$822$	−2.20713	+	8.69292i	−0.0769825	+	0.303200i
$823$	19.6742	+	5.77686i	0.685798	+	0.201369i	0.606026	−	0.795445i	$-0.292763\pi$
$823$	19.6742	+	5.77686i	0.685798	+	0.201369i	0.0797720	+	0.996813i	$0.474581\pi$
$824$	2.25231	+	4.93186i	0.0784628	+	0.171810i
$825$	7.41658	−	2.47881i	0.258212	−	0.0863011i
$826$	−8.86173	+	13.7891i	−0.308339	+	0.479785i
$827$	19.9946			0.695281			0.347640	−	0.937628i	$-0.386983\pi$
$827$	19.9946			0.695281			0.347640	+	0.937628i	$0.386983\pi$
$828$	8.86613	+	11.3310i	0.308119	+	0.393780i
$829$	40.4650			1.40541			0.702704	−	0.711483i	$-0.251976\pi$
$829$	40.4650			1.40541			0.702704	+	0.711483i	$0.251976\pi$
$830$	2.79068	−	4.34238i	0.0968658	−	0.150726i
$831$	13.0672	−	4.36739i	0.453296	−	0.151503i
$832$	0.343381	+	0.751899i	0.0119046	+	0.0260674i
$833$	30.0231	+	8.81557i	1.04024	+	0.305441i
$834$	1.74702	−	6.88075i	0.0604943	−	0.238261i
$835$	6.67997	+	5.78823i	0.231170	+	0.200310i
$836$	26.2764	+	3.77798i	0.908790	+	0.130664i
$837$	−21.7162	−	20.0665i	−0.750620	−	0.693600i
$838$	20.7662	−	17.9940i	0.717356	−	0.621593i
$839$	15.3339	−	9.85452i	0.529386	−	0.340216i	−0.248489	−	0.968635i	$-0.579934\pi$
$839$	15.3339	−	9.85452i	0.529386	−	0.340216i	0.777875	+	0.628419i	$0.216298\pi$
$840$	−1.43636	−	1.53889i	−0.0495591	−	0.0530966i
$841$	13.6728	+	15.7792i	0.471475	+	0.544111i
$842$	−10.0109	+	2.93947i	−0.344999	+	0.101301i
$843$	47.1502	−	1.74317i	1.62394	−	0.0600380i
$844$	0.614722	−	0.709427i	0.0211596	−	0.0244195i
$845$	5.11656	−	11.2037i	0.176015	−	0.385419i
$846$	30.2432	−	2.23928i	1.03978	−	0.0769879i
$847$	10.3736	−	4.73748i	0.356443	−	0.162782i
$848$	−0.899280	−	6.25463i	−0.0308814	−	0.214785i
$849$	−10.2026	−	4.21109i	−0.350153	−	0.144524i
$850$			5.66560i			0.194329i
$851$	−5.65531	+	45.3926i	−0.193861	+	1.55604i
$852$	−18.2535	+	3.31694i	−0.625356	+	0.113636i
$853$	47.8655	+	30.7613i	1.63888	+	1.05325i	0.941755	+	0.336300i	$0.109176\pi$
$853$	47.8655	+	30.7613i	1.63888	+	1.05325i	0.697128	+	0.716946i	$0.254461\pi$
$854$	−14.0036	+	2.01341i	−0.479193	+	0.0688975i
$855$	−12.4419	+	12.5044i	−0.425503	+	0.427643i
$856$	0.148671	−	0.506326i	0.00508146	−	0.0173059i
$857$	32.7379	+	14.9509i	1.11831	+	0.510713i	0.886815	−	0.462124i	$-0.152913\pi$
$857$	32.7379	+	14.9509i	1.11831	+	0.510713i	0.231490	+	0.972837i	$0.425640\pi$
$858$	3.29135	−	5.56315i	0.112365	−	0.189923i
$859$	−1.58754	+	11.0416i	−0.0541661	+	0.376734i	0.944650	+	0.328081i	$0.106402\pi$
$859$	−1.58754	+	11.0416i	−0.0541661	+	0.376734i	−0.998816	+	0.0486529i	$0.984507\pi$
$860$	0.312276	+	1.06351i	0.0106485	+	0.0362655i
$861$	3.15732	−	3.92807i	0.107601	−	0.133868i
$862$	11.2952	+	17.5757i	0.384717	+	0.598632i
$863$	−1.19364	−	1.85735i	−0.0406321	−	0.0632248i	0.820343	−	0.571871i	$-0.193782\pi$
$863$	−1.19364	−	1.85735i	−0.0406321	−	0.0632248i	−0.860975	+	0.508647i	$0.830146\pi$
$864$	4.93638	+	1.62239i	0.167939	+	0.0551947i
$865$	−2.77010	−	9.43408i	−0.0941861	−	0.320768i
$866$	−3.22680	+	22.4429i	−0.109651	+	0.762640i
$867$	−22.5081	−	13.3166i	−0.764416	−	0.452254i
$868$	−6.29084	−	2.87293i	−0.213525	−	0.0975135i
$869$	−13.8937	+	47.3176i	−0.471311	+	1.60514i
$870$	10.0394	−	6.98913i	0.340366	−	0.236954i
$871$	5.13633	−	0.738493i	0.174038	−	0.0250229i
$872$	−2.06011	−	1.32395i	−0.0697640	−	0.0448346i
$873$	9.95150	+	26.4780i	0.336807	+	0.896146i
$874$	14.7957	−	24.0058i	0.500472	−	0.812007i
$875$			1.21536i			0.0410867i
$876$	6.19680	−	15.0136i	0.209370	−	0.507263i
$877$	−4.52580	−	31.4776i	−0.152825	−	1.06292i	−0.911454	−	0.411401i	$-0.865040\pi$
$877$	−4.52580	−	31.4776i	−0.152825	−	1.06292i	0.758629	−	0.651523i	$-0.225869\pi$
$878$	−11.0589	+	5.05044i	−0.373221	+	0.170444i
$879$	−1.29117	+	12.1530i	−0.0435500	+	0.409910i
$880$	−1.87552	+	4.10681i	−0.0632236	+	0.138440i
$881$	8.94839	−	10.3270i	0.301479	−	0.347925i	−0.584716	−	0.811238i	$-0.698794\pi$
$881$	8.94839	−	10.3270i	0.301479	−	0.347925i	0.886195	+	0.463313i	$0.153339\pi$
$882$	−16.1812	+	3.56252i	−0.544848	+	0.119956i
$883$	0.481261	−	0.141311i	0.0161957	−	0.00475549i	−0.273625	−	0.961837i	$-0.588223\pi$
$883$	0.481261	−	0.141311i	0.0161957	−	0.00475549i	0.289820	+	0.957081i	$0.406404\pi$
$884$	3.06683	+	3.53931i	0.103148	+	0.119040i
$885$	−17.0768	+	15.9391i	−0.574030	+	0.535786i
$886$	30.7335	−	19.7512i	1.03251	−	0.663556i
$887$	−25.8267	+	22.3790i	−0.867177	+	0.751413i	−0.969953	−	0.243292i	$-0.921773\pi$
$887$	−25.8267	+	22.3790i	−0.867177	+	0.751413i	0.102777	+	0.994704i	$0.467227\pi$
$888$	7.41344	+	14.7639i	0.248779	+	0.495444i
$889$	−9.38029	−	1.34868i	−0.314605	−	0.0452334i
$890$	14.1783	+	12.2855i	0.475256	+	0.411812i
$891$	−11.6431	−	38.9294i	−0.390058	−	1.30418i
$892$	−18.8257	−	5.52771i	−0.630330	−	0.185082i
$893$	−24.6915	−	54.0668i	−0.826269	−	1.80928i
$894$	2.72553	+	8.15476i	0.0911553	+	0.272736i
$895$	14.2018	−	22.0985i	0.474714	−	0.738670i
$896$	1.21536			0.0406023
$897$	−4.02857	−	5.56020i	−0.134510	−	0.185650i
$898$	−23.7063			−0.791088
$899$	21.7272	−	33.8083i	0.724644	−	1.12757i
$900$	−1.44435	−	2.62942i	−0.0481448	−	0.0876474i
$901$	−14.8721	−	32.5654i	−0.495462	−	1.08491i
$902$	−10.3709	−	3.04518i	−0.345314	−	0.101393i
$903$	−2.26152	−	0.574200i	−0.0752588	−	0.0191082i
$904$	−10.8662	−	9.41562i	−0.361405	−	0.313159i
$905$	17.9041	+	2.57422i	0.595153	+	0.0855700i
$906$	−6.86944	+	3.44938i	−0.228222	+	0.114598i
$907$	−16.5833	+	14.3695i	−0.550641	+	0.477133i	−0.885180	−	0.465249i	$-0.845965\pi$
$907$	−16.5833	+	14.3695i	−0.550641	+	0.477133i	0.334539	+	0.942382i	$0.391419\pi$
$908$	3.65889	−	2.35143i	0.121425	−	0.0780348i
$909$	−6.15234	−	4.58156i	−0.204060	−	0.151961i
$910$	0.657882	+	0.759236i	0.0218086	+	0.0251684i
$911$	−50.5793	+	14.8514i	−1.67577	+	0.492049i	−0.975161	−	0.221499i	$-0.928905\pi$
$911$	−50.5793	+	14.8514i	−1.67577	+	0.492049i	−0.700606	+	0.713548i	$0.747087\pi$
$912$	−0.376263	−	10.1774i	−0.0124593	−	0.337006i
$913$	15.2612	−	17.6123i	0.505071	−	0.582883i
$914$	−7.80582	+	17.0924i	−0.258194	+	0.565365i
$915$	−20.0494	−	2.13010i	−0.662811	−	0.0704191i
$916$	−3.22251	+	1.47167i	−0.106475	+	0.0486254i
$917$	1.35696	+	9.43788i	0.0448108	+	0.311666i
$918$	29.4243	+	0.940087i	0.971148	+	0.0310275i
$919$		−	29.2165i		−	0.963762i	−0.876237	−	0.481881i	$-0.839954\pi$
$919$		−	29.2165i		−	0.963762i	0.876237	−	0.481881i	$-0.160046\pi$
$920$	3.20837	+	3.56460i	0.105777	+	0.117521i
$921$	−6.39414	−	35.1878i	−0.210694	−	1.15948i
$922$	−26.7837	−	17.2128i	−0.882074	−	0.566875i
$923$	8.76378	−	1.26004i	0.288463	−	0.0414748i
$924$	−5.43010	−	7.79994i	−0.178637	−	0.256599i
$925$	2.68722	−	9.15183i	0.0883553	−	0.300910i
$926$	−23.9939	−	10.9577i	−0.788490	−	0.360091i
$927$	−15.2541	−	5.64597i	−0.501012	−	0.185438i
$928$	−1.00510	+	6.99061i	−0.0329940	+	0.229478i
$929$	−0.417549	−	1.42204i	−0.0136993	−	0.0466557i	0.952360	−	0.304977i	$-0.0986488\pi$
$929$	−0.417549	−	1.42204i	−0.0136993	−	0.0466557i	−0.966059	+	0.258321i	$0.916831\pi$
$930$	−7.68199	−	6.17467i	−0.251902	−	0.202475i
$931$	17.5569	+	27.3190i	0.575403	+	0.895345i
$932$	−8.72513	−	13.5766i	−0.285801	−	0.444715i
$933$	−13.8587	−	11.1394i	−0.453714	−	0.364689i
$934$	−3.83750	−	13.0693i	−0.125567	−	0.427642i
$935$	−3.64028	+	25.3187i	−0.119050	+	0.828010i
$936$	−2.32561	−	0.860769i	−0.0760148	−	0.0281351i
$937$	−9.83961	−	4.49360i	−0.321446	−	0.146800i	0.248156	−	0.968720i	$-0.420175\pi$
$937$	−9.83961	−	4.49360i	−0.321446	−	0.146800i	−0.569602	+	0.821921i	$0.692903\pi$
$938$	2.14954	−	7.32065i	0.0701848	−	0.239028i
$939$	16.8488	+	24.2020i	0.549839	+	0.789803i
$940$	10.0058	−	1.43861i	0.326352	−	0.0469224i
$941$	15.5870	+	10.0172i	0.508122	+	0.326550i	0.769458	−	0.638698i	$-0.220526\pi$
$941$	15.5870	+	10.0172i	0.508122	+	0.326550i	−0.261335	+	0.965248i	$0.584163\pi$
$942$	2.39050	+	13.1552i	0.0778868	+	0.428621i
$943$	−7.35393	+	8.81739i	−0.239477	+	0.287134i
$944$		−	13.4867i		−	0.438954i
$945$	6.31198	+	0.201663i	0.205329	+	0.00656011i
$946$	0.712180	+	4.95332i	0.0231550	+	0.161046i
$947$	3.66173	−	1.67226i	0.118990	−	0.0543411i	−0.355030	−	0.934855i	$-0.615529\pi$
$947$	3.66173	−	1.67226i	0.118990	−	0.0543411i	0.474021	+	0.880514i	$0.342802\pi$
$948$	18.8133	+	1.99878i	0.611028	+	0.0649175i
$949$	−3.22003	+	7.05088i	−0.104527	+	0.228881i
$950$	−3.85053	+	4.44375i	−0.124928	+	0.144174i
$951$	0.261345	+	7.06900i	0.00847469	+	0.229228i
$952$	6.60683	−	1.93994i	0.214129	−	0.0628738i
$953$	14.5252	+	16.7630i	0.470517	+	0.543006i	0.940555	−	0.339640i	$-0.110305\pi$
$953$	14.5252	+	16.7630i	0.470517	+	0.543006i	−0.470038	+	0.882646i	$0.655760\pi$
$954$	15.2042	+	11.3223i	0.492253	+	0.366574i
$955$	13.3796	−	8.59852i	0.432952	−	0.278242i
$956$	−8.56993	+	7.42588i	−0.277171	+	0.240170i
$957$	49.3550	−	24.7828i	1.59542	−	0.801114i
$958$	−0.795856	−	0.114427i	−0.0257129	−	0.00369696i
$959$	−4.75613	−	4.12121i	−0.153584	−	0.133081i
$960$	1.67878	+	0.426243i	0.0541825	+	0.0137569i
$961$	−1.32396	−	0.388750i	−0.0427084	−	0.0125403i
$962$	−3.27523	−	7.17176i	−0.105598	−	0.231227i
$963$	0.762183	+	1.38755i	0.0245610	+	0.0447132i
$964$	4.24250	−	6.60147i	0.136642	−	0.212619i
$965$	−14.1496			−0.455491
$966$	−9.89709	+	1.99187i	−0.318434	+	0.0640875i
$967$	−6.64612			−0.213725			−0.106862	−	0.994274i	$-0.534080\pi$
$967$	−6.64612			−0.213725			−0.106862	+	0.994274i	$0.534080\pi$
$968$	−5.07305	+	7.89382i	−0.163054	+	0.253717i
$969$	−18.2904	−	54.7247i	−0.587571	−	1.75801i
$970$	3.91686	+	8.57673i	0.125763	+	0.275382i
$971$	−3.41705	−	1.00334i	−0.109658	−	0.0321986i	0.226443	−	0.974024i	$-0.427290\pi$
$971$	−3.41705	−	1.00334i	−0.109658	−	0.0321986i	−0.336101	+	0.941826i	$0.609108\pi$
$972$	−13.8956	+	7.06491i	−0.445701	+	0.226607i
$973$	3.76464	+	3.26208i	0.120689	+	0.104578i
$974$	15.0937	+	2.17015i	0.483633	+	0.0695359i
$975$	0.642462	+	1.27947i	0.0205752	+	0.0409757i
$976$	8.79742	−	7.62301i	0.281598	−	0.244006i
$977$	−39.1841	+	25.1821i	−1.25361	+	0.805647i	−0.987396	−	0.158267i	$-0.949409\pi$
$977$	−39.1841	+	25.1821i	−1.25361	+	0.805647i	−0.266215	+	0.963914i	$0.585773\pi$
$978$	13.7478	−	12.8319i	0.439607	−	0.410318i
$979$	55.4667	+	64.0120i	1.77272	+	2.04583i
$980$	−5.29918	+	1.55598i	−0.169276	+	0.0497040i
$981$	7.17473	−	1.57962i	0.229071	−	0.0504334i
$982$	20.2893	−	23.4151i	0.647457	−	0.747206i
$983$	−21.2803	+	46.5973i	−0.678735	+	1.48622i	0.185242	+	0.982693i	$0.440693\pi$
$983$	−21.2803	+	46.5973i	−0.678735	+	1.48622i	−0.863978	+	0.503530i	$0.832034\pi$
$984$	−0.438088	+	4.12345i	−0.0139657	+	0.131451i
$985$	−24.3304	+	11.1113i	−0.775231	+	0.354036i
$986$	5.69449	+	39.6060i	0.181349	+	1.26131i
$987$	−8.11862	+	19.6698i	−0.258419	+	0.626097i
$988$			4.86032i			0.154628i
$989$	5.12776	+	1.40121i	0.163053	+	0.0445558i
$990$	−4.76509	−	12.6785i	−0.151444	−	0.402949i
$991$	−34.5184	−	22.1836i	−1.09651	−	0.704686i	−0.138199	−	0.990405i	$-0.544131\pi$
$991$	−34.5184	−	22.1836i	−1.09651	−	0.704686i	−0.958313	+	0.285719i	$0.907768\pi$
$992$	5.63241	−	0.809818i	0.178829	−	0.0257118i
$993$	23.8267	−	16.5875i	0.756118	−	0.526388i
$994$	3.66761	−	12.4907i	0.116329	−	0.396182i
$995$	−2.10558	−	0.961586i	−0.0667513	−	0.0304843i
$996$	−7.69466	−	4.55242i	−0.243815	−	0.144249i
$997$	−2.15501	+	14.9884i	−0.0682497	+	0.474687i	0.926820	+	0.375507i	$0.122531\pi$
$997$	−2.15501	+	14.9884i	−0.0682497	+	0.474687i	−0.995069	+	0.0991806i	$0.968378\pi$
$998$	4.61482	+	15.7166i	0.146080	+	0.497502i
$999$	−47.0842	−	15.4746i	−1.48968	−	0.489596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.b.251.16	yes	160
3.2	odd	2		690.2.q.a.251.1	yes	160
23.11	odd	22		690.2.q.a.11.1	✓	160
69.11	even	22	inner	690.2.q.b.11.16	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.11.1	✓	160	23.11	odd	22
690.2.q.a.251.1	yes	160	3.2	odd	2
690.2.q.b.11.16	yes	160	69.11	even	22	inner
690.2.q.b.251.16	yes	160	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 - 0.841254i) q^{2} +(1.64273 - 0.549041i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.426243 - 1.67878i) q^{6} +(0.918508 + 0.795892i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(2.39711 - 1.80385i) q^{9} +O(q^{10})\)	\(q+(0.540641 - 0.841254i) q^{2} +(1.64273 - 0.549041i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.426243 - 1.67878i) q^{6} +(0.918508 + 0.795892i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(2.39711 - 1.80385i) q^{9} +(0.755750 - 0.654861i) q^{10} +(3.79809 - 2.44088i) q^{11} +(-1.18184 - 1.26620i) q^{12} +(0.541306 + 0.624700i) q^{13} +(1.16613 - 0.342407i) q^{14} +(1.73087 - 0.0639912i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-2.35358 + 5.15361i) q^{17} +(-0.221521 - 2.99181i) q^{18} +(-5.34856 + 2.44261i) q^{19} +(-0.142315 - 0.989821i) q^{20} +(1.94584 + 0.803135i) q^{21} -4.51480i q^{22} +(-4.39922 - 1.90967i) q^{23} +(-1.70414 + 0.309668i) q^{24} +(0.841254 + 0.540641i) q^{25} +(0.818184 - 0.117637i) q^{26} +(2.94741 - 4.27934i) q^{27} +(0.342407 - 1.16613i) q^{28} +(6.42428 + 2.93387i) q^{29} +(0.881945 - 1.49070i) q^{30} +(0.809818 - 5.63241i) q^{31} +(0.281733 + 0.959493i) q^{32} +(4.89908 - 6.09502i) q^{33} +(3.06306 + 4.76621i) q^{34} +(0.657074 + 1.02243i) q^{35} +(-2.63663 - 1.43114i) q^{36} +(-2.68722 - 9.15183i) q^{37} +(-0.836800 + 5.82007i) q^{38} +(1.23220 + 0.729013i) q^{39} +(-0.909632 - 0.415415i) q^{40} +(0.674489 - 2.29710i) q^{41} +(1.72764 - 1.20273i) q^{42} +(-1.09713 + 0.157743i) q^{43} +(-3.79809 - 2.44088i) q^{44} +(2.80821 - 1.05544i) q^{45} +(-3.98492 + 2.66842i) q^{46} +10.1087i q^{47} +(-0.660820 + 1.60104i) q^{48} +(-0.785990 - 5.46668i) q^{49} +(0.909632 - 0.415415i) q^{50} +(-1.03674 + 9.75820i) q^{51} +(0.343381 - 0.751899i) q^{52} +(-4.13803 + 4.77554i) q^{53} +(-2.00652 - 4.79311i) q^{54} +(4.33192 - 1.27197i) q^{55} +(-0.795892 - 0.918508i) q^{56} +(-7.44514 + 6.94912i) q^{57} +(5.94135 - 3.81828i) q^{58} +(-10.1925 + 8.83189i) q^{59} +(-0.777237 - 1.54787i) q^{60} +(-11.5222 - 1.65664i) q^{61} +(-4.30046 - 3.72637i) q^{62} +(3.63743 + 0.250988i) q^{63} +(0.959493 + 0.281733i) q^{64} +(0.343381 + 0.751899i) q^{65} +(-2.47881 - 7.41658i) q^{66} +(3.39400 - 5.28116i) q^{67} +5.66560 q^{68} +(-8.27521 - 0.721716i) q^{69} +1.21536 q^{70} +(5.79095 - 9.01089i) q^{71} +(-2.62942 + 1.44435i) q^{72} +(3.89553 + 8.53001i) q^{73} +(-9.15183 - 2.68722i) q^{74} +(1.67878 + 0.426243i) q^{75} +(4.44375 + 3.85053i) q^{76} +(5.43126 + 0.780897i) q^{77} +(1.27947 - 0.642462i) q^{78} +(-8.25506 + 7.15305i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(2.49225 - 8.64804i) q^{81} +(-1.56779 - 1.80932i) q^{82} +(4.95270 - 1.45424i) q^{83} +(-0.0777724 - 2.10363i) q^{84} +(-3.71018 + 4.28178i) q^{85} +(-0.460451 + 1.00825i) q^{86} +(12.1641 + 1.29236i) q^{87} +(-4.10681 + 1.87552i) q^{88} +(2.66990 + 18.5696i) q^{89} +(0.630343 - 2.93303i) q^{90} +1.00461i q^{91} +(0.0904052 + 4.79498i) q^{92} +(-1.76211 - 9.69714i) q^{93} +(8.50395 + 5.46516i) q^{94} +(-5.82007 + 0.836800i) q^{95} +(0.989611 + 1.42150i) q^{96} +(-2.65640 + 9.04686i) q^{97} +(-5.02381 - 2.29429i) q^{98} +(4.70144 - 12.7022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9	\( 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9} + 12 q^{11} + 12 q^{14} - 16 q^{16} - 8 q^{18} - 16 q^{20} + 70 q^{21} - 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} + 2 q^{30} - 4 q^{31} - 16 q^{33} + 2 q^{36} - 72 q^{38} + 140 q^{39} - 44 q^{41} + 44 q^{43} - 12 q^{44} + 2 q^{45} + 4 q^{46} + 70 q^{49} + 2 q^{51} + 52 q^{53} - 62 q^{54} + 10 q^{55} + 54 q^{56} - 94 q^{57} - 36 q^{58} - 44 q^{61} + 16 q^{64} - 54 q^{66} - 44 q^{67} - 30 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} + 24 q^{74} + 88 q^{77} - 54 q^{78} - 44 q^{79} + 16 q^{80} - 66 q^{81} - 28 q^{82} - 4 q^{83} - 4 q^{84} - 158 q^{86} + 156 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} + 88 q^{98} - 58 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9 + 12 * q^11 + 12 * q^14 - 16 * q^16 - 8 * q^18 - 16 * q^20 + 70 * q^21 - 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 + 2 * q^30 - 4 * q^31 - 16 * q^33 + 2 * q^36 - 72 * q^38 + 140 * q^39 - 44 * q^41 + 44 * q^43 - 12 * q^44 + 2 * q^45 + 4 * q^46 + 70 * q^49 + 2 * q^51 + 52 * q^53 - 62 * q^54 + 10 * q^55 + 54 * q^56 - 94 * q^57 - 36 * q^58 - 44 * q^61 + 16 * q^64 - 54 * q^66 - 44 * q^67 - 30 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 + 24 * q^74 + 88 * q^77 - 54 * q^78 - 44 * q^79 + 16 * q^80 - 66 * q^81 - 28 * q^82 - 4 * q^83 - 4 * q^84 - 158 * q^86 + 156 * q^87 - 80 * q^89 + 8 * q^90 + 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 + 88 * q^98 - 58 * q^99

Introduction

L-functions

Modular forms

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