LMFDB - Embedded newform 192.2.s.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(11,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8]))

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

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

chi := DirichletCharacter("192.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	192.11
Dual form			192.2.s.a.35.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14703 - 0.827236i) q^{2} +(1.31348 - 1.12905i) q^{3} +(0.631361 + 1.89773i) q^{4} +(-2.57009 + 1.71728i) q^{5} +(-2.44060 + 0.208501i) q^{6} +(1.31022 - 3.16314i) q^{7} +(0.845681 - 2.69904i) q^{8} +(0.450472 - 2.96599i) q^{9} +O(q^{10})$	\(q+(-1.14703 - 0.827236i) q^{2} +(1.31348 - 1.12905i) q^{3} +(0.631361 + 1.89773i) q^{4} +(-2.57009 + 1.71728i) q^{5} +(-2.44060 + 0.208501i) q^{6} +(1.31022 - 3.16314i) q^{7} +(0.845681 - 2.69904i) q^{8} +(0.450472 - 2.96599i) q^{9} +(4.36857 + 0.156298i) q^{10} +(1.15458 - 5.80445i) q^{11} +(2.97192 + 1.77980i) q^{12} +(0.813910 - 1.21810i) q^{13} +(-4.11952 + 2.54436i) q^{14} +(-1.43687 + 5.15739i) q^{15} +(-3.20277 + 2.39631i) q^{16} +(1.22808 + 1.22808i) q^{17} +(-2.97028 + 3.02943i) q^{18} +(-0.547947 + 0.820061i) q^{19} +(-4.88159 - 3.79312i) q^{20} +(-1.85041 - 5.63403i) q^{21} +(-6.12599 + 5.70278i) q^{22} +(3.01135 + 7.27003i) q^{23} +(-1.93658 - 4.49996i) q^{24} +(1.74290 - 4.20772i) q^{25} +(-1.94124 + 0.723906i) q^{26} +(-2.75707 - 4.40438i) q^{27} +(6.83001 + 0.489354i) q^{28} +(-0.732439 + 0.145691i) q^{29} +(5.91451 - 4.72706i) q^{30} +1.03663 q^{31} +(5.65598 - 0.0991941i) q^{32} +(-5.03703 - 8.92763i) q^{33} +(-0.392734 - 2.42456i) q^{34} +(2.06462 + 10.3796i) q^{35} +(5.91306 - 1.01773i) q^{36} +(-6.90324 + 4.61260i) q^{37} +(1.30690 - 0.487354i) q^{38} +(-0.306248 - 2.51891i) q^{39} +(2.46153 + 8.38905i) q^{40} +(6.10375 - 2.52826i) q^{41} +(-2.53820 + 7.99314i) q^{42} +(-1.58742 + 7.98050i) q^{43} +(11.7442 - 1.47363i) q^{44} +(3.93567 + 8.39644i) q^{45} +(2.55993 - 10.8301i) q^{46} +(0.578413 - 0.578413i) q^{47} +(-1.50122 + 6.76360i) q^{48} +(-3.33904 - 3.33904i) q^{49} +(-5.47994 + 3.38460i) q^{50} +(2.99963 + 0.226493i) q^{51} +(2.82550 + 0.775520i) q^{52} +(0.204871 + 0.0407514i) q^{53} +(-0.481012 + 7.33271i) q^{54} +(7.00050 + 16.9007i) q^{55} +(-7.42942 - 6.21133i) q^{56} +(0.206175 + 1.69580i) q^{57} +(0.960652 + 0.438788i) q^{58} +(0.283996 + 0.425031i) q^{59} +(-10.6945 + 0.529387i) q^{60} +(-2.27628 + 0.452780i) q^{61} +(-1.18904 - 0.857535i) q^{62} +(-8.79161 - 5.31099i) q^{63} +(-6.56965 - 4.56506i) q^{64} +4.52834i q^{65} +(-1.60763 + 14.4071i) q^{66} +(-0.0197253 - 0.0991660i) q^{67} +(-1.55521 + 3.10593i) q^{68} +(12.1636 + 6.14909i) q^{69} +(6.21816 - 13.6136i) q^{70} +(-3.96205 - 1.64114i) q^{71} +(-7.62436 - 3.72412i) q^{72} +(8.68148 - 3.59599i) q^{73} +(11.7339 + 0.419816i) q^{74} +(-2.46148 - 7.49459i) q^{75} +(-1.90221 - 0.522102i) q^{76} +(-16.8476 - 11.2572i) q^{77} +(-1.73245 + 3.14260i) q^{78} +(10.1185 - 10.1185i) q^{79} +(4.11627 - 11.6588i) q^{80} +(-8.59415 - 2.67219i) q^{81} +(-9.09266 - 2.14925i) q^{82} +(9.61018 + 6.42132i) q^{83} +(9.52360 - 7.06869i) q^{84} +(-5.26524 - 1.04732i) q^{85} +(8.42258 - 7.84071i) q^{86} +(-0.797553 + 1.01833i) q^{87} +(-14.6901 - 8.02497i) q^{88} +(4.96427 + 2.05627i) q^{89} +(2.43150 - 12.8867i) q^{90} +(-2.78663 - 4.17049i) q^{91} +(-11.8953 + 10.3047i) q^{92} +(1.36159 - 1.17041i) q^{93} +(-1.14194 + 0.184974i) q^{94} -3.04861i q^{95} +(7.31704 - 6.51620i) q^{96} +8.36948i q^{97} +(1.06781 + 6.59216i) q^{98} +(-16.6958 - 6.03921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{16}\right)$

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 $

$2$	−1.14703	−	0.827236i	−0.811074	−	0.584944i
$2$	−1.14703	−	0.827236i	−0.811074	−	0.584944i
$3$	1.31348	−	1.12905i	0.758339	−	0.651860i
$3$	1.31348	−	1.12905i	0.758339	−	0.651860i
$4$	0.631361	+	1.89773i	0.315680	+	0.948866i
$5$	−2.57009	+	1.71728i	−1.14938	+	0.767990i	−0.976194	−	0.216899i	$-0.930406\pi$
$5$	−2.57009	+	1.71728i	−1.14938	+	0.767990i	−0.173185	+	0.984889i	$0.555406\pi$
$6$	−2.44060	+	0.208501i	−0.996371	+	0.0851200i
$7$	1.31022	−	3.16314i	0.495215	−	1.19555i	−0.456818	−	0.889560i	$-0.651011\pi$
$7$	1.31022	−	3.16314i	0.495215	−	1.19555i	0.952033	−	0.305994i	$-0.0989889\pi$
$8$	0.845681	−	2.69904i	0.298993	−	0.954255i
$9$	0.450472	−	2.96599i	0.150157	−	0.988662i
$10$	4.36857	+	0.156298i	1.38146	+	0.0494259i
$11$	1.15458	−	5.80445i	0.348118	−	1.75011i	−0.268908	−	0.963166i	$-0.586663\pi$
$11$	1.15458	−	5.80445i	0.348118	−	1.75011i	0.617026	−	0.786943i	$-0.288337\pi$
$12$	2.97192	+	1.77980i	0.857920	+	0.513783i
$13$	0.813910	−	1.21810i	0.225738	−	0.337841i	−0.701261	−	0.712905i	$-0.747379\pi$
$13$	0.813910	−	1.21810i	0.225738	−	0.337841i	0.926999	+	0.375064i	$0.122379\pi$
$14$	−4.11952	+	2.54436i	−1.10099	+	0.680009i
$15$	−1.43687	+	5.15739i	−0.370997	+	1.33163i
$16$	−3.20277	+	2.39631i	−0.800692	+	0.599077i
$17$	1.22808	+	1.22808i	0.297854	+	0.297854i	0.840173	−	0.542319i	$-0.182454\pi$
$17$	1.22808	+	1.22808i	0.297854	+	0.297854i	−0.542319	+	0.840173i	$0.682454\pi$
$18$	−2.97028	+	3.02943i	−0.700101	+	0.714044i
$19$	−0.547947	+	0.820061i	−0.125708	+	0.188135i	−0.888985	−	0.457936i	$-0.848589\pi$
$19$	−0.547947	+	0.820061i	−0.125708	+	0.188135i	0.763277	+	0.646071i	$0.223589\pi$
$20$	−4.88159	−	3.79312i	−1.09156	−	0.848166i
$21$	−1.85041	−	5.63403i	−0.403793	−	1.22945i
$22$	−6.12599	+	5.70278i	−1.30607	+	1.21584i
$23$	3.01135	+	7.27003i	0.627909	+	1.51591i	0.842216	+	0.539141i	$0.181251\pi$
$23$	3.01135	+	7.27003i	0.627909	+	1.51591i	−0.214307	+	0.976766i	$0.568749\pi$
$24$	−1.93658	−	4.49996i	−0.395302	−	0.918551i
$25$	1.74290	−	4.20772i	0.348579	−	0.841544i
$26$	−1.94124	+	0.723906i	−0.380708	+	0.141970i
$27$	−2.75707	−	4.40438i	−0.530599	−	0.847623i
$28$	6.83001	+	0.489354i	1.29075	+	0.0924791i
$29$	−0.732439	+	0.145691i	−0.136011	+	0.0270542i	−0.262626	−	0.964898i	$-0.584589\pi$
$29$	−0.732439	+	0.145691i	−0.136011	+	0.0270542i	0.126616	+	0.991952i	$0.459589\pi$
$30$	5.91451	−	4.72706i	1.07984	−	0.863038i
$31$	1.03663			0.186184			0.0930918	−	0.995658i	$-0.470325\pi$
$31$	1.03663			0.186184			0.0930918	+	0.995658i	$0.470325\pi$
$32$	5.65598	−	0.0991941i	0.999846	−	0.0175352i
$33$	−5.03703	−	8.92763i	−0.876834	−	1.55410i
$34$	−0.392734	−	2.42456i	−0.0673534	−	0.415809i
$35$	2.06462	+	10.3796i	0.348985	+	1.75447i
$36$	5.91306	−	1.01773i	0.985509	−	0.169622i
$37$	−6.90324	+	4.61260i	−1.13489	+	0.758307i	−0.973523	−	0.228589i	$-0.926589\pi$
$37$	−6.90324	+	4.61260i	−1.13489	+	0.758307i	−0.161363	+	0.986895i	$0.551589\pi$
$38$	1.30690	−	0.487354i	0.212007	−	0.0790593i
$39$	−0.306248	−	2.51891i	−0.0490389	−	0.403348i
$40$	2.46153	+	8.38905i	0.389202	+	1.32642i
$41$	6.10375	−	2.52826i	0.953246	−	0.394847i	0.148796	−	0.988868i	$-0.452460\pi$
$41$	6.10375	−	2.52826i	0.953246	−	0.394847i	0.804450	+	0.594020i	$0.202460\pi$
$42$	−2.53820	+	7.99314i	−0.391652	+	1.23337i
$43$	−1.58742	+	7.98050i	−0.242079	+	1.21702i	0.648153	+	0.761510i	$0.275542\pi$
$43$	−1.58742	+	7.98050i	−0.242079	+	1.21702i	−0.890233	+	0.455506i	$0.849458\pi$
$44$	11.7442	−	1.47363i	1.77051	−	0.222158i
$45$	3.93567	+	8.39644i	0.586695	+	1.25167i
$46$	2.55993	−	10.8301i	0.377441	−	1.59680i
$47$	0.578413	−	0.578413i	0.0843702	−	0.0843702i	−0.663662	−	0.748032i	$-0.730999\pi$
$47$	0.578413	−	0.578413i	0.0843702	−	0.0843702i	0.748032	+	0.663662i	$0.230999\pi$
$48$	−1.50122	+	6.76360i	−0.216682	+	0.976242i
$49$	−3.33904	−	3.33904i	−0.477006	−	0.477006i
$50$	−5.47994	+	3.38460i	−0.774980	+	0.478655i
$51$	2.99963	+	0.226493i	0.420033	+	0.0317153i
$52$	2.82550	+	0.775520i	0.391827	+	0.107545i
$53$	0.204871	+	0.0407514i	0.0281412	+	0.00559764i	0.209141	−	0.977886i	$-0.432933\pi$
$53$	0.204871	+	0.0407514i	0.0281412	+	0.00559764i	−0.181000	+	0.983483i	$0.557933\pi$
$54$	−0.481012	+	7.33271i	−0.0654575	+	0.997855i
$55$	7.00050	+	16.9007i	0.943947	+	2.27889i
$56$	−7.42942	−	6.21133i	−0.992798	−	0.830024i
$57$	0.206175	+	1.69580i	0.0273085	+	0.224614i
$58$	0.960652	+	0.438788i	0.126140	+	0.0576157i
$59$	0.283996	+	0.425031i	0.0369732	+	0.0553343i	0.849496	−	0.527595i	$-0.176906\pi$
$59$	0.283996	+	0.425031i	0.0369732	+	0.0553343i	−0.812523	+	0.582930i	$0.801906\pi$
$60$	−10.6945	+	0.529387i	−1.38066	+	0.0683436i
$61$	−2.27628	+	0.452780i	−0.291448	+	0.0579726i	−0.338649	−	0.940913i	$-0.609970\pi$
$61$	−2.27628	+	0.452780i	−0.291448	+	0.0579726i	0.0472010	+	0.998885i	$0.484970\pi$
$62$	−1.18904	−	0.857535i	−0.151009	−	0.108907i
$63$	−8.79161	−	5.31099i	−1.10764	−	0.669121i
$64$	−6.56965	−	4.56506i	−0.821206	−	0.570632i
$65$			4.52834i			0.561672i
$66$	−1.60763	+	14.4071i	−0.197886	+	1.77339i
$67$	−0.0197253	−	0.0991660i	−0.00240983	−	0.0121151i	0.979562	−	0.201144i	$-0.0644660\pi$
$67$	−0.0197253	−	0.0991660i	−0.00240983	−	0.0121151i	−0.981971	+	0.189029i	$0.939466\pi$
$68$	−1.55521	+	3.10593i	−0.188596	+	0.376650i
$69$	12.1636	+	6.14909i	1.46433	+	0.740263i
$70$	6.21816	−	13.6136i	0.743212	−	1.62714i
$71$	−3.96205	−	1.64114i	−0.470209	−	0.194767i	0.134981	−	0.990848i	$-0.456903\pi$
$71$	−3.96205	−	1.64114i	−0.470209	−	0.194767i	−0.605190	+	0.796081i	$0.706903\pi$
$72$	−7.62436	−	3.72412i	−0.898540	−	0.438892i
$73$	8.68148	−	3.59599i	1.01609	−	0.420878i	0.188417	−	0.982089i	$-0.439664\pi$
$73$	8.68148	−	3.59599i	1.01609	−	0.420878i	0.827673	+	0.561211i	$0.189664\pi$
$74$	11.7339	+	0.419816i	1.36404	+	0.0488027i
$75$	−2.46148	−	7.49459i	−0.284228	−	0.865401i
$76$	−1.90221	−	0.522102i	−0.218198	−	0.0598892i
$77$	−16.8476	−	11.2572i	−1.91996	−	1.28287i
$78$	−1.73245	+	3.14260i	−0.196162	+	0.355830i
$79$	10.1185	−	10.1185i	1.13842	−	1.13842i	0.149682	−	0.988734i	$-0.452175\pi$
$79$	10.1185	−	10.1185i	1.13842	−	1.13842i	0.988734	−	0.149682i	$-0.0478249\pi$
$80$	4.11627	−	11.6588i	0.460213	−	1.30349i
$81$	−8.59415	−	2.67219i	−0.954906	−	0.296910i
$82$	−9.09266	−	2.14925i	−1.00412	−	0.237345i
$83$	9.61018	+	6.42132i	1.05485	+	0.704831i	0.956917	−	0.290362i	$-0.0937756\pi$
$83$	9.61018	+	6.42132i	1.05485	+	0.704831i	0.0979371	+	0.995193i	$0.468776\pi$
$84$	9.52360	−	7.06869i	1.03911	−	0.771258i
$85$	−5.26524	−	1.04732i	−0.571095	−	0.113598i
$86$	8.42258	−	7.84071i	0.908230	−	0.845486i
$87$	−0.797553	+	1.01833i	−0.0855066	+	0.109176i
$88$	−14.6901	−	8.02497i	−1.56597	−	0.855465i
$89$	4.96427	+	2.05627i	0.526212	+	0.217964i	0.629943	−	0.776641i	$-0.283078\pi$
$89$	4.96427	+	2.05627i	0.526212	+	0.217964i	−0.103731	+	0.994605i	$0.533078\pi$
$90$	2.43150	−	12.8867i	0.256302	−	1.35838i
$91$	−2.78663	−	4.17049i	−0.292118	−	0.437186i
$92$	−11.8953	+	10.3047i	−1.24017	+	1.07434i
$93$	1.36159	−	1.17041i	0.141190	−	0.121366i
$94$	−1.14194	+	0.184974i	−0.117782	+	0.0190786i
$95$		−	3.04861i		−	0.312781i
$96$	7.31704	−	6.51620i	0.746792	−	0.665057i
$97$			8.36948i			0.849792i	0.905242	+	0.424896i	$0.139689\pi$
$97$			8.36948i			0.849792i	−0.905242	+	0.424896i	$0.860311\pi$
$98$	1.06781	+	6.59216i	0.107865	+	0.665909i
$99$	−16.6958	−	6.03921i	−1.67799	−	0.606963i
$100$	9.08552	+	0.650956i	0.908552	+	0.0650956i
$101$	3.35535	+	5.02163i	0.333869	+	0.499671i	0.959982	−	0.280062i	$-0.0903550\pi$
$101$	3.35535	+	5.02163i	0.333869	+	0.499671i	−0.626113	+	0.779733i	$0.715355\pi$
$102$	−3.25331	−	2.74120i	−0.322126	−	0.271419i
$103$	8.42771	+	3.49087i	0.830407	+	0.343966i	0.757064	−	0.653341i	$-0.226633\pi$
$103$	8.42771	+	3.49087i	0.830407	+	0.343966i	0.0733432	+	0.997307i	$0.476633\pi$
$104$	−2.59940	−	3.22690i	−0.254892	−	0.316424i
$105$	14.4309	+	11.3023i	1.40831	+	1.10299i
$106$	−0.201283	−	0.216220i	−0.0195503	−	0.0210012i
$107$	−9.70142	−	1.92973i	−0.937871	−	0.186554i	−0.297589	−	0.954694i	$-0.596183\pi$
$107$	−9.70142	−	1.92973i	−0.937871	−	0.186554i	−0.640282	+	0.768140i	$0.721183\pi$
$108$	6.61762	−	8.01294i	0.636781	−	0.771045i
$109$	−0.338939	−	0.226472i	−0.0324645	−	0.0216921i	0.539232	−	0.842157i	$-0.318715\pi$
$109$	−0.338939	−	0.226472i	−0.0324645	−	0.0216921i	−0.571697	+	0.820465i	$0.693715\pi$
$110$	5.95108	−	25.1767i	0.567413	−	2.40050i
$111$	−3.85941	+	13.8527i	−0.366319	+	1.31484i
$112$	3.38354	+	13.2705i	0.319714	+	1.25394i
$113$	−9.15826	+	9.15826i	−0.861537	+	0.861537i	−0.991517	−	0.129980i	$-0.958509\pi$
$113$	−9.15826	+	9.15826i	−0.861537	+	0.861537i	0.129980	+	0.991517i	$0.458509\pi$
$114$	1.16634	−	2.11569i	0.109237	−	0.198152i
$115$	−20.2241	−	13.5133i	−1.88591	−	1.26012i
$116$	−0.738916	−	1.29799i	−0.0686067	−	0.120515i
$117$	−3.24623	−	2.96277i	−0.300114	−	0.273908i
$118$	0.0258480	−	0.722455i	0.00237950	−	0.0665074i
$119$	5.49365	−	2.27554i	0.503602	−	0.208599i
$120$	12.7049	+	8.23966i	1.15979	+	0.752175i
$121$	−22.1960	−	9.19387i	−2.01781	−	0.835806i
$122$	2.98552	+	1.36367i	0.270296	+	0.123461i
$123$	5.16263	−	10.2123i	0.465499	−	0.920811i
$124$	0.654486	+	1.96724i	0.0587745	+	0.176663i
$125$	−0.268706	−	1.35088i	−0.0240338	−	0.120826i
$126$	5.69081	+	13.3646i	0.506978	+	1.19061i
$127$			7.30191i			0.647940i	0.946067	+	0.323970i	$0.105018\pi$
$127$			7.30191i			0.647940i	−0.946067	+	0.323970i	$0.894982\pi$
$128$	3.75921	+	10.6709i	0.332270	+	0.943184i
$129$	6.92537	+	12.2745i	0.609745	+	1.08071i
$130$	3.74601	−	5.19415i	0.328547	−	0.455557i
$131$	−12.9060	+	2.56717i	−1.12761	+	0.224295i	−0.723438	−	0.690390i	$-0.757439\pi$
$131$	−12.9060	+	2.56717i	−1.12761	+	0.224295i	−0.404169	+	0.914685i	$0.632439\pi$
$132$	13.7621	−	15.1955i	1.19783	−	1.32260i
$133$	1.87604	+	2.80769i	0.162673	+	0.243458i
$134$	−0.0594081	+	0.130064i	−0.00513208	+	0.0112358i
$135$	14.6495	+	6.58498i	1.26083	+	0.566745i
$136$	4.35321	−	2.27608i	0.373285	−	0.195172i
$137$	0.467326	+	1.12823i	0.0399264	+	0.0963908i	0.942585	−	0.333967i	$-0.108387\pi$
$137$	0.467326	+	1.12823i	0.0399264	+	0.0963908i	−0.902658	+	0.430358i	$0.858387\pi$
$138$	−8.86530	−	17.1154i	−0.754664	−	1.45696i
$139$	12.8230	+	2.55065i	1.08763	+	0.216343i	0.706171	−	0.708042i	$-0.250421\pi$
$139$	12.8230	+	2.55065i	1.08763	+	0.216343i	0.381461	+	0.924385i	$0.375421\pi$
$140$	−18.3941	+	10.4713i	−1.55458	+	0.884990i
$141$	0.106675	−	1.41279i	0.00898370	−	0.118979i
$142$	3.18699	+	5.15999i	0.267446	+	0.433017i
$143$	−6.13070	−	6.13070i	−0.512675	−	0.512675i
$144$	5.66466	+	10.5788i	0.472055	+	0.881569i
$145$	1.63224	−	1.63224i	0.135550	−	0.135550i
$146$	−12.9327	−	3.05692i	−1.07031	−	0.252993i
$147$	−8.15573	−	0.615813i	−0.672673	−	0.0507914i
$148$	−13.1119	−	10.1883i	−1.07779	−	0.837472i
$149$	−1.28908	+	6.48064i	−0.105606	+	0.530915i	0.891375	+	0.453266i	$0.149741\pi$
$149$	−1.28908	+	6.48064i	−0.105606	+	0.530915i	−0.996981	+	0.0776488i	$0.975259\pi$
$150$	−3.37640	+	10.6328i	−0.275682	+	0.868161i
$151$	−6.13029	+	2.53925i	−0.498876	+	0.206641i	−0.617910	−	0.786249i	$-0.712020\pi$
$151$	−6.13029	+	2.53925i	−0.498876	+	0.206641i	0.119034	+	0.992890i	$0.462020\pi$
$152$	1.74999	+	2.17244i	0.141943	+	0.176208i
$153$	4.19569	−	3.08926i	0.339201	−	0.249752i
$154$	10.0123	+	26.8492i	0.806816	+	2.16357i
$155$	−2.66422	+	1.78018i	−0.213996	+	0.142987i
$156$	4.58685	−	2.17151i	0.367242	−	0.173860i
$157$	−3.06258	−	15.3966i	−0.244420	−	1.22878i	−0.886711	−	0.462323i	$-0.847016\pi$
$157$	−3.06258	−	15.3966i	−0.244420	−	1.22878i	0.642291	−	0.766461i	$-0.277984\pi$
$158$	−19.9765	+	3.23583i	−1.58925	+	0.257429i
$159$	0.315105	−	0.177785i	0.0249895	−	0.0140992i
$160$	−14.3660	+	9.96784i	−1.13574	+	0.788027i
$161$	26.9416			2.12330
$162$	7.64723	+	10.1745i	0.600823	+	0.799382i
$163$	17.3236	−	3.44588i	1.35689	−	0.269902i	0.537561	−	0.843225i	$-0.319346\pi$
$163$	17.3236	−	3.44588i	1.35689	−	0.269902i	0.819330	+	0.573322i	$0.194346\pi$
$164$	8.65162	+	9.98704i	0.675578	+	0.779857i
$165$	28.2768	+	14.2948i	2.20135	+	1.11285i
$166$	−5.71123	−	15.3153i	−0.443277	−	1.18870i
$167$	6.20048	−	14.9693i	0.479808	−	1.15836i	−0.479891	−	0.877328i	$-0.659324\pi$
$167$	6.20048	−	14.9693i	0.479808	−	1.15836i	0.959699	−	0.281030i	$-0.0906761\pi$
$168$	−16.7713	+	0.229744i	−1.29394	+	0.0177251i
$169$	4.15356	+	10.0276i	0.319505	+	0.771352i
$170$	5.17301	+	5.55690i	0.396752	+	0.426195i
$171$	2.18546	+	1.99462i	0.167126	+	0.152532i
$172$	−16.1471	+	2.02608i	−1.23120	+	0.154487i
$173$	0.406281	−	0.608043i	0.0308890	−	0.0462286i	−0.815704	−	0.578470i	$-0.803650\pi$
$173$	0.406281	−	0.608043i	0.0308890	−	0.0462286i	0.846593	+	0.532241i	$0.178650\pi$
$174$	1.75721	−	0.508288i	0.133214	−	0.0385332i
$175$	−11.0260	−	11.0260i	−0.833491	−	0.833491i
$176$	10.2114	+	21.3570i	0.769714	+	1.60985i
$177$	0.852907	+	0.237623i	0.0641084	+	0.0178608i
$178$	−3.99316	−	6.46523i	−0.299300	−	0.484590i
$179$	6.10014	−	9.12950i	0.455946	−	0.682371i	−0.530271	−	0.847828i	$-0.677910\pi$
$179$	6.10014	−	9.12950i	0.455946	−	0.682371i	0.986217	+	0.165457i	$0.0529099\pi$
$180$	−13.4493	+	12.7700i	−1.00246	+	0.951822i
$181$	−2.58486	+	12.9950i	−0.192131	+	0.965910i	0.757570	+	0.652754i	$0.226386\pi$
$181$	−2.58486	+	12.9950i	−0.192131	+	0.965910i	−0.949702	+	0.313156i	$0.898614\pi$
$182$	−0.253626	+	7.08888i	−0.0188000	+	0.525463i
$183$	−2.47864	+	3.16476i	−0.183226	+	0.233946i
$184$	22.1688	−	1.97962i	1.63430	−	0.145939i
$185$	9.82083	−	23.7096i	0.722042	−	1.74316i
$186$	−2.52999	+	0.216137i	−0.185508	+	0.0158480i
$187$	8.54626	−	5.71043i	0.624964	−	0.417588i
$188$	1.46286	+	0.732485i	0.106690	+	0.0534219i
$189$	−17.5440	+	2.95032i	−1.27614	+	0.214604i
$190$	−2.52192	+	3.49685i	−0.182959	+	0.253688i
$191$	−1.56908			−0.113535			−0.0567675	−	0.998387i	$-0.518079\pi$
$191$	−1.56908			−0.113535			−0.0567675	+	0.998387i	$0.518079\pi$
$192$	−13.7833	+	1.42137i	−0.994725	+	0.102578i
$193$	−11.6228			−0.836627			−0.418313	−	0.908303i	$-0.637379\pi$
$193$	−11.6228			−0.836627			−0.418313	+	0.908303i	$0.637379\pi$
$194$	6.92354	−	9.60006i	0.497081	−	0.689244i
$195$	5.11275	+	5.94790i	0.366131	+	0.425938i
$196$	4.22846	−	8.44474i	0.302033	−	0.603196i
$197$	0.0214754	−	0.0143494i	0.00153006	−	0.00102235i	−0.554805	−	0.831980i	$-0.687207\pi$
$197$	0.0214754	−	0.0143494i	0.00153006	−	0.00102235i	0.556335	+	0.830958i	$0.312207\pi$
$198$	14.1548	+	20.7385i	1.00594	+	1.47382i
$199$	6.01457	−	14.5204i	0.426361	−	1.02933i	−0.554071	−	0.832470i	$-0.686926\pi$
$199$	6.01457	−	14.5204i	0.426361	−	1.02933i	0.980432	−	0.196858i	$-0.0630737\pi$
$200$	−9.88288	−	8.26254i	−0.698825	−	0.584250i
$201$	−0.137873	−	0.107982i	−0.00972479	−	0.00761645i
$202$	0.305387	−	8.53563i	0.0214870	−	0.600565i
$203$	−0.498811	+	2.50769i	−0.0350097	+	0.176006i
$204$	1.46403	+	5.83550i	0.102503	+	0.408567i
$205$	−11.3455	+	16.9797i	−0.792402	+	1.18591i
$206$	−6.77907	−	10.9758i	−0.472320	−	0.764723i
$207$	22.9194	−	5.65667i	1.59300	−	0.393165i
$208$	0.312183	+	5.85168i	0.0216460	+	0.405741i
$209$	4.12736	+	4.12736i	0.285495	+	0.285495i
$210$	−7.20306	−	24.9019i	−0.497058	−	1.71839i
$211$	6.61703	−	9.90309i	0.455535	−	0.681757i	−0.530615	−	0.847613i	$-0.678039\pi$
$211$	6.61703	−	9.90309i	0.455535	−	0.681757i	0.986150	+	0.165856i	$0.0530388\pi$
$212$	0.0520125	+	0.414519i	0.00357223	+	0.0284693i
$213$	−7.05702	+	2.31777i	−0.483539	+	0.158811i
$214$	9.53148	+	10.2388i	0.651559	+	0.699912i
$215$	−9.62494	−	23.2367i	−0.656415	−	1.58473i
$216$	−14.2192	+	3.71675i	−0.967494	+	0.252893i
$217$	1.35820	−	3.27899i	0.0922009	−	0.222593i
$218$	0.201428	+	0.540153i	0.0136424	+	0.0365838i
$219$	7.34291	−	14.5251i	0.496188	−	0.981517i
$220$	−27.6531	+	23.9555i	−1.86437	+	1.61508i
$221$	2.49548	−	0.496381i	0.167864	−	0.0333902i
$222$	15.8863	−	12.6968i	1.06622	−	0.852156i
$223$	−19.3569			−1.29624			−0.648118	−	0.761540i	$-0.724444\pi$
$223$	−19.3569			−1.29624			−0.648118	+	0.761540i	$0.724444\pi$
$224$	7.09679	−	18.0206i	0.474174	−	1.20405i
$225$	−11.6949	−	7.06487i	−0.779661	−	0.470991i
$226$	18.0809	−	2.92877i	1.20272	−	0.194819i
$227$	5.20551	+	26.1699i	0.345502	+	1.73696i	0.628477	+	0.777828i	$0.283679\pi$
$227$	5.20551	+	26.1699i	0.345502	+	1.73696i	−0.282975	+	0.959127i	$0.591321\pi$
$228$	−3.08800	+	1.46192i	−0.204508	+	0.0968183i
$229$	8.34090	−	5.57321i	0.551182	−	0.368288i	−0.248574	−	0.968613i	$-0.579962\pi$
$229$	8.34090	−	5.57321i	0.551182	−	0.368288i	0.799756	+	0.600325i	$0.204962\pi$
$230$	12.0190	+	32.2303i	0.792508	+	2.12520i
$231$	−34.8389	+	4.23570i	−2.29223	+	0.278689i
$232$	−0.226183	+	2.10009i	−0.0148497	+	0.137878i
$233$	−21.7138	+	8.99414i	−1.42252	+	0.589225i	−0.955491	−	0.295019i	$-0.904674\pi$
$233$	−21.7138	+	8.99414i	−1.42252	+	0.589225i	−0.467025	+	0.884244i	$0.654674\pi$
$234$	1.27262	+	6.08379i	0.0831938	+	0.397710i
$235$	−0.493276	+	2.47987i	−0.0321778	+	0.161769i
$236$	−0.627290	+	0.807297i	−0.0408331	+	0.0525505i
$237$	1.86613	−	24.7147i	0.121218	−	1.60539i
$238$	−8.18379	−	1.93442i	−0.530477	−	0.125390i
$239$	−14.5937	+	14.5937i	−0.943988	+	0.943988i	−0.998512	−	0.0545240i	$-0.982636\pi$
$239$	−14.5937	+	14.5937i	−0.943988	+	0.943988i	0.0545240	+	0.998512i	$0.482636\pi$
$240$	−7.75673	−	19.9611i	−0.500695	−	1.28848i
$241$	−3.87352	−	3.87352i	−0.249515	−	0.249515i	0.571256	−	0.820772i	$-0.306456\pi$
$241$	−3.87352	−	3.87352i	−0.249515	−	0.249515i	−0.820772	+	0.571256i	$0.806456\pi$
$242$	17.8540	+	28.9069i	1.14770	+	1.85821i
$243$	−14.3053	+	6.19339i	−0.917686	+	0.397306i
$244$	−2.29641	−	4.03390i	−0.147013	−	0.258244i
$245$	14.3157	+	2.84757i	0.914596	+	0.181925i
$246$	−14.3697	+	7.44310i	−0.916177	+	0.474555i
$247$	0.552939	+	1.33491i	0.0351827	+	0.0849385i
$248$	0.876655	−	2.79790i	0.0556677	−	0.177667i
$249$	19.8728	−	2.41613i	1.25939	−	0.153116i
$250$	−0.809279	+	1.77178i	−0.0511833	+	0.112057i
$251$	−3.73614	−	5.59153i	−0.235823	−	0.352934i	0.694616	−	0.719381i	$-0.255574\pi$
$251$	−3.73614	−	5.59153i	−0.235823	−	0.352934i	−0.930439	+	0.366447i	$0.880574\pi$
$252$	4.52814	−	20.0373i	0.285246	−	1.26223i
$253$	45.6754	−	9.08540i	2.87159	−	0.571194i
$254$	6.04040	−	8.37552i	0.379009	−	0.525527i
$255$	−8.09828	+	4.56910i	−0.507134	+	0.286128i
$256$	4.51543	−	15.3496i	0.282214	−	0.959351i
$257$			0.727765i			0.0453967i	0.999742	+	0.0226984i	$0.00722574\pi$
$257$			0.727765i			0.0453967i	−0.999742	+	0.0226984i	$0.992774\pi$
$258$	2.21032	−	19.8082i	0.137608	−	1.23320i
$259$	5.54556	+	27.8794i	0.344584	+	1.73234i
$260$	−8.59358	+	2.85902i	−0.532951	+	0.177309i
$261$	0.102175	+	2.23803i	0.00632446	+	0.138531i
$262$	16.9273	+	7.73172i	1.04577	+	0.477667i
$263$	11.2076	+	4.64236i	0.691093	+	0.286260i	0.700455	−	0.713696i	$-0.252980\pi$
$263$	11.2076	+	4.64236i	0.691093	+	0.286260i	−0.00936254	+	0.999956i	$0.502980\pi$
$264$	−28.3558	+	6.04522i	−1.74518	+	0.372057i
$265$	−0.596519	+	0.247086i	−0.0366439	+	0.0151784i
$266$	0.170748	−	4.77244i	0.0104692	−	0.292617i
$267$	8.84213	−	2.90406i	0.541129	−	0.177726i
$268$	0.175737	−	0.100043i	0.0107348	−	0.00611110i
$269$	1.02451	+	0.684556i	0.0624655	+	0.0417381i	0.586411	−	0.810014i	$-0.300540\pi$
$269$	1.02451	+	0.684556i	0.0624655	+	0.0417381i	−0.523945	+	0.851752i	$0.675540\pi$
$270$	−11.3561	−	19.6718i	−0.691108	−	1.19718i
$271$	−4.94217	+	4.94217i	−0.300216	+	0.300216i	−0.841098	−	0.540883i	$-0.818090\pi$
$271$	−4.94217	+	4.94217i	−0.300216	+	0.300216i	0.540883	+	0.841098i	$0.318090\pi$
$272$	−6.87612	−	0.990399i	−0.416926	−	0.0600518i
$273$	−8.36890	−	2.33161i	−0.506509	−	0.141115i
$274$	0.397271	−	1.68070i	0.0240000	−	0.101535i
$275$	−22.4112	−	14.9747i	−1.35145	−	0.903008i
$276$	−3.98968	+	26.9656i	−0.240151	+	1.62314i
$277$	−28.3917	−	5.64746i	−1.70589	−	0.339323i	−0.756637	−	0.653835i	$-0.773159\pi$
$277$	−28.3917	−	5.64746i	−1.70589	−	0.339323i	−0.949254	+	0.314512i	$0.898159\pi$
$278$	−12.5984	−	13.5333i	−0.755600	−	0.811674i
$279$	0.466971	−	3.07462i	0.0279568	−	0.184073i
$280$	29.7609	+	3.20529i	1.77855	+	0.191553i
$281$	8.53529	+	3.53543i	0.509172	+	0.210906i	0.622453	−	0.782657i	$-0.286136\pi$
$281$	8.53529	+	3.53543i	0.509172	+	0.210906i	−0.113281	+	0.993563i	$0.536136\pi$
$282$	−1.29107	+	1.53227i	−0.0768824	+	0.0912456i
$283$	9.37337	+	14.0282i	0.557189	+	0.833892i	0.997968	−	0.0637235i	$-0.0202976\pi$
$283$	9.37337	+	14.0282i	0.557189	+	0.833892i	−0.440778	+	0.897616i	$0.645298\pi$
$284$	0.612950	−	8.55506i	0.0363719	−	0.507650i
$285$	−3.44205	−	4.00430i	−0.203889	−	0.237194i
$286$	1.96057	+	12.1036i	0.115931	+	0.715703i
$287$		−	22.6196i		−	1.33519i
$288$	2.25366	−	16.8203i	0.132798	−	0.991143i
$289$		−	13.9836i		−	0.822567i
$290$	−3.22248	+	0.521983i	−0.189231	+	0.0306519i
$291$	9.44960	+	10.9932i	0.553945	+	0.644431i
$292$	12.3054	+	14.2048i	0.720117	+	0.831270i
$293$	−10.7542	−	16.0948i	−0.628269	−	0.940270i	−0.999929	−	0.0119017i	$-0.996211\pi$
$293$	−10.7542	−	16.0948i	−0.628269	−	0.940270i	0.371661	−	0.928369i	$-0.378789\pi$
$294$	8.84546	+	7.45307i	0.515877	+	0.434672i
$295$	−1.45979	−	0.604666i	−0.0849924	−	0.0352050i
$296$	6.61165	+	22.5329i	0.384295	+	1.30970i
$297$	−28.7483	+	10.9181i	−1.66814	+	0.633533i
$298$	6.83964	−	6.36713i	0.396210	−	0.368838i
$299$	11.3066	+	2.24903i	0.653878	+	0.130065i
$300$	12.6686	−	9.40303i	0.731424	−	0.542884i
$301$	23.1636	+	15.4774i	1.33513	+	0.892103i
$302$	9.13220	+	2.15860i	0.525499	+	0.124213i
$303$	10.0769	+	2.80745i	0.578902	+	0.161284i
$304$	−0.210170	−	3.93952i	−0.0120541	−	0.225947i
$305$	5.07270	−	5.07270i	0.290462	−	0.290462i
$306$	−7.36813	+	0.0726477i	−0.421208	+	0.00415299i
$307$	8.50943	+	5.68582i	0.485659	+	0.324507i	0.774179	−	0.632967i	$-0.218163\pi$
$307$	8.50943	+	5.68582i	0.485659	+	0.324507i	−0.288520	+	0.957474i	$0.593163\pi$
$308$	10.7262	−	39.0795i	0.611182	−	2.22676i
$309$	15.0110	−	4.93015i	0.853948	−	0.280466i
$310$	4.52857	+	0.162023i	0.257206	+	0.00920229i
$311$	4.51405	−	1.86978i	0.255968	−	0.106026i	−0.251010	−	0.967985i	$-0.580763\pi$
$311$	4.51405	−	1.86978i	0.255968	−	0.106026i	0.506978	+	0.861959i	$0.330763\pi$
$312$	−7.05762	−	1.30362i	−0.399559	−	0.0738027i
$313$	4.15551	+	1.72127i	0.234883	+	0.0972918i	0.497021	−	0.867739i	$-0.334427\pi$
$313$	4.15551	+	1.72127i	0.234883	+	0.0972918i	−0.262137	+	0.965031i	$0.584427\pi$
$314$	−9.22377	+	20.1939i	−0.520527	+	1.13961i
$315$	31.7157	−	1.44794i	1.78698	−	0.0815822i
$316$	25.5905	+	12.8137i	1.43958	+	0.720828i
$317$	−2.73984	−	13.7741i	−0.153885	−	0.773630i	−0.978227	−	0.207538i	$-0.933455\pi$
$317$	−2.73984	−	13.7741i	−0.153885	−	0.773630i	0.824342	−	0.566092i	$-0.191545\pi$
$318$	−0.508506	−	0.0567422i	−0.0285156	−	0.00318194i
$319$			4.41962i			0.247451i
$320$	24.7241	+	0.450685i	1.38212	+	0.0251941i
$321$	−14.9214	+	8.41876i	−0.832832	+	0.469889i
$322$	−30.9029	−	22.2871i	−1.72215	−	1.24201i
$323$	−1.68003	+	0.334178i	−0.0934792	+	0.0185942i
$324$	−0.354915	−	17.9965i	−0.0197175	−	0.999806i
$325$	−3.70688	−	5.54773i	−0.205621	−	0.307733i
$326$	−22.7213	−	10.3782i	−1.25842	−	0.574795i
$327$	−0.700889	+	0.0852138i	−0.0387593	+	0.00471234i
$328$	−1.66204	−	18.6124i	−0.0917710	−	1.02770i
$329$	−1.07176	−	2.58745i	−0.0590878	−	0.142650i
$330$	−20.6092	−	39.7882i	−1.13450	−	2.19027i
$331$	−23.0883	−	4.59255i	−1.26905	−	0.252429i	−0.485762	−	0.874091i	$-0.661458\pi$
$331$	−23.0883	−	4.59255i	−1.26905	−	0.252429i	−0.783286	+	0.621662i	$0.786458\pi$
$332$	−6.11844	+	22.2917i	−0.335793	+	1.22342i
$333$	10.5712	+	22.5528i	0.579297	+	1.23588i
$334$	−19.4953	+	12.0410i	−1.06673	+	0.658853i
$335$	0.220992	+	0.220992i	0.0120741	+	0.0120741i
$336$	19.4273	+	13.6103i	1.05985	+	0.742505i
$337$	−23.1601	+	23.1601i	−1.26161	+	1.26161i	−0.311300	+	0.950312i	$0.600765\pi$
$337$	−23.1601	+	23.1601i	−1.26161	+	1.26161i	−0.950312	+	0.311300i	$0.899235\pi$
$338$	3.53091	−	14.9379i	0.192056	−	0.812516i
$339$	−1.68904	+	22.3694i	−0.0917361	+	1.21494i
$340$	−1.33673	−	10.6532i	−0.0724945	−	0.577753i
$341$	1.19687	−	6.01705i	0.0648139	−	0.325842i
$342$	−0.856765	−	4.09578i	−0.0463285	−	0.221474i
$343$	7.20526	−	2.98452i	0.389048	−	0.161149i
$344$	20.1973	+	11.0335i	1.08896	+	0.594885i
$345$	−41.8213	+	5.08461i	−2.25158	+	0.273746i
$346$	−0.969012	+	0.361354i	−0.0520944	+	0.0194265i
$347$	12.9767	−	8.67074i	0.696625	−	0.465470i	−0.156160	−	0.987732i	$-0.549912\pi$
$347$	12.9767	−	8.67074i	0.696625	−	0.465470i	0.852785	+	0.522262i	$0.174912\pi$
$348$	−2.43605	−	0.870609i	−0.130586	−	0.0466695i
$349$	−7.17861	−	36.0893i	−0.384262	−	1.93182i	−0.362309	−	0.932058i	$-0.618011\pi$
$349$	−7.17861	−	36.0893i	−0.384262	−	1.93182i	−0.0219536	−	0.999759i	$-0.506989\pi$
$350$	3.52607	+	21.7684i	0.188477	+	1.16357i
$351$	−7.60900	−	0.226371i	−0.406138	−	0.0120828i
$352$	5.95451	−	32.9444i	0.317376	−	1.75594i
$353$	−26.2610			−1.39773			−0.698867	−	0.715251i	$-0.746312\pi$
$353$	−26.2610			−1.39773			−0.698867	+	0.715251i	$0.746312\pi$
$354$	−0.781741	−	0.978116i	−0.0415490	−	0.0519863i
$355$	13.0011	−	2.58608i	0.690028	−	0.137255i
$356$	−0.767998	+	10.7191i	−0.0407038	+	0.568111i
$357$	4.64660	−	9.19151i	0.245924	−	0.486466i
$358$	−14.5493	+	5.42557i	−0.768955	+	0.286750i
$359$	9.81229	−	23.6890i	0.517873	−	1.25026i	−0.421334	−	0.906905i	$-0.638438\pi$
$359$	9.81229	−	23.6890i	0.517873	−	1.25026i	0.939207	−	0.343351i	$-0.111562\pi$
$360$	25.9907	−	3.52183i	1.36983	−	0.185617i
$361$	6.89873	+	16.6550i	0.363091	+	0.876579i
$362$	13.7148	−	12.7674i	0.720836	−	0.671038i
$363$	−39.5344	+	12.9845i	−2.07502	+	0.681507i
$364$	6.15510	−	7.92136i	0.322615	−	0.415192i
$365$	−16.1369	+	24.1505i	−0.844642	+	1.26410i
$366$	5.46109	−	1.57966i	0.285456	−	0.0825702i
$367$	−0.334544	−	0.334544i	−0.0174631	−	0.0174631i	0.698321	−	0.715784i	$-0.253931\pi$
$367$	−0.334544	−	0.334544i	−0.0174631	−	0.0174631i	−0.715784	+	0.698321i	$0.753931\pi$
$368$	−27.0659	−	16.0681i	−1.41091	−	0.837608i
$369$	−4.74921	−	19.2426i	−0.247234	−	1.00173i
$370$	−30.8782	+	19.0715i	−1.60528	+	0.991479i
$371$	0.397328	−	0.594643i	0.0206282	−	0.0308723i
$372$	3.08077	+	1.84498i	0.159731	+	0.0956579i
$373$	−3.40785	+	17.1324i	−0.176452	+	0.887082i	0.786538	+	0.617542i	$0.211872\pi$
$373$	−3.40785	+	17.1324i	−0.176452	+	0.887082i	−0.962989	+	0.269540i	$0.913128\pi$
$374$	−14.5267	−	0.519735i	−0.751158	−	0.0268749i
$375$	−1.87815	−	1.47097i	−0.0969874	−	0.0759605i
$376$	−1.07201	−	2.05031i	−0.0552845	−	0.105737i
$377$	−0.418673	+	1.01077i	−0.0215628	+	0.0520571i
$378$	22.5642	+	11.1289i	1.16057	+	0.572411i
$379$	−14.4857	+	9.67906i	−0.744082	+	0.497180i	−0.868893	−	0.495001i	$-0.835168\pi$
$379$	−14.4857	+	9.67906i	−0.744082	+	0.497180i	0.124810	+	0.992181i	$0.460168\pi$
$380$	5.78544	−	1.92477i	0.296787	−	0.0987388i
$381$	8.24426	+	9.59093i	0.422366	+	0.491358i
$382$	1.79979	+	1.29800i	0.0920852	+	0.0664116i
$383$	7.87812			0.402553			0.201277	−	0.979534i	$-0.435491\pi$
$383$	7.87812			0.402553			0.201277	+	0.979534i	$0.435491\pi$
$384$	16.9857	+	9.77170i	0.866798	+	0.498660i
$385$	62.6314			3.19199
$386$	13.3317	+	9.61479i	0.678566	+	0.489380i
$387$	22.9550	+	8.30326i	1.16687	+	0.422079i
$388$	−15.8830	+	5.28416i	−0.806338	+	0.268263i
$389$	−17.6512	+	11.7942i	−0.894953	+	0.597988i	−0.915729	−	0.401796i	$-0.868386\pi$
$389$	−17.6512	+	11.7942i	−0.894953	+	0.597988i	0.0207767	+	0.999784i	$0.493386\pi$
$390$	−0.944162	−	11.0519i	−0.0478095	−	0.559633i
$391$	−5.23002	+	12.6264i	−0.264493	+	0.638543i
$392$	−11.8360	+	6.18845i	−0.597807	+	0.312564i
$393$	−14.0534	+	17.9436i	−0.708900	+	0.905133i
$394$	−0.0365033	−	0.00130601i	−0.00183901	−	6.57959e-5i
$395$	−8.62913	+	43.3816i	−0.434179	+	2.18276i
$396$	0.919698	−	35.4971i	0.0462165	−	1.78380i
$397$	11.9603	−	17.8998i	0.600268	−	0.898364i	−0.399564	−	0.916705i	$-0.630838\pi$
$397$	11.9603	−	17.8998i	0.600268	−	0.898364i	0.999832	+	0.0183409i	$0.00583842\pi$
$398$	−18.9107	+	11.6799i	−0.947909	+	0.585462i
$399$	5.63418	+	1.56970i	0.282062	+	0.0785834i
$400$	4.50090	+	17.6529i	0.225045	+	0.882643i
$401$	−25.1649	−	25.1649i	−1.25668	−	1.25668i	−0.952670	−	0.304006i	$-0.901676\pi$
$401$	−25.1649	−	25.1649i	−1.25668	−	1.25668i	−0.304006	−	0.952670i	$-0.598324\pi$
$402$	0.0688178	+	0.237912i	0.00343232	+	0.0118660i
$403$	0.843721	−	1.26272i	0.0420287	−	0.0629005i
$404$	−7.41127	+	9.53800i	−0.368724	+	0.474533i
$405$	26.6766	−	7.89079i	1.32557	−	0.392096i
$406$	2.64661	−	2.46377i	0.131349	−	0.122275i
$407$	18.8033	+	45.3952i	0.932044	+	2.25015i
$408$	3.14805	−	7.90460i	0.155852	−	0.391336i
$409$	−2.74245	+	6.62085i	−0.135605	+	0.327380i	−0.977066	−	0.212939i	$-0.931696\pi$
$409$	−2.74245	+	6.62085i	−0.135605	+	0.327380i	0.841460	+	0.540319i	$0.181696\pi$
$410$	27.0598	−	10.0909i	1.33639	−	0.498352i
$411$	1.88765	+	0.954267i	0.0931110	+	0.0470705i
$412$	−1.30381	+	18.1975i	−0.0642341	+	0.896528i
$413$	1.71653	−	0.341439i	0.0844648	−	0.0168011i
$414$	−30.9686	−	12.4713i	−1.52202	−	0.612933i
$415$	−35.7262			−1.75373
$416$	4.48264	−	6.97031i	0.219779	−	0.341747i
$417$	19.7226	−	11.1276i	0.965819	−	0.544922i
$418$	−1.31991	−	8.14851i	−0.0645589	−	0.398557i
$419$	−3.42350	−	17.2111i	−0.167249	−	0.840816i	−0.969738	−	0.244149i	$-0.921491\pi$
$419$	−3.42350	−	17.2111i	−0.167249	−	0.840816i	0.802489	−	0.596667i	$-0.203509\pi$
$420$	−12.3376	+	34.5219i	−0.602013	+	1.68449i
$421$	7.96259	−	5.32043i	0.388073	−	0.259302i	−0.346194	−	0.938163i	$-0.612526\pi$
$421$	7.96259	−	5.32043i	0.388073	−	0.259302i	0.734267	+	0.678861i	$0.237526\pi$
$422$	−15.7821	+	5.88530i	−0.768262	+	0.286492i
$423$	−1.45501	−	1.97612i	−0.0707448	−	0.0960824i
$424$	0.283246	−	0.518493i	0.0137556	−	0.0251803i
$425$	7.30784	−	3.02701i	0.354483	−	0.146831i
$426$	10.0120	+	3.17927i	0.485081	+	0.154036i
$427$	−1.55021	+	7.79344i	−0.0750200	+	0.377151i
$428$	−2.46298	−	19.6290i	−0.119053	−	0.948805i
$429$	−14.9745	−	1.13067i	−0.722974	−	0.0545894i
$430$	−8.18209	+	34.6153i	−0.394576	+	1.66930i
$431$	3.22023	−	3.22023i	0.155113	−	0.155113i	−0.625284	−	0.780397i	$-0.715017\pi$
$431$	3.22023	−	3.22023i	0.155113	−	0.155113i	0.780397	+	0.625284i	$0.215017\pi$
$432$	19.3845	+	7.49941i	0.932637	+	0.360815i
$433$	25.3579	+	25.3579i	1.21862	+	1.21862i	0.968114	+	0.250511i	$0.0805987\pi$
$433$	25.3579	+	25.3579i	1.21862	+	1.21862i	0.250511	+	0.968114i	$0.419401\pi$
$434$	−4.27041	+	2.63755i	−0.204986	+	0.126607i
$435$	0.301031	−	3.98681i	0.0144333	−	0.191153i
$436$	0.215790	−	0.786200i	0.0103345	−	0.0376522i
$437$	−7.61193	−	1.51411i	−0.364128	−	0.0724296i
$438$	−20.4383	+	10.5865i	−0.976578	+	0.505841i
$439$	1.75719	+	4.24223i	0.0838661	+	0.202471i	0.960249	−	0.279144i	$-0.0900506\pi$
$439$	1.75719	+	4.24223i	0.0838661	+	0.202471i	−0.876383	+	0.481614i	$0.840051\pi$
$440$	51.5359	−	4.60203i	2.45688	−	0.219393i
$441$	−11.4077	+	8.39941i	−0.543224	+	0.399972i
$442$	−3.27302	−	1.49498i	−0.155681	−	0.0711092i
$443$	9.26880	+	13.8717i	0.440374	+	0.659066i	0.983567	−	0.180541i	$-0.0577850\pi$
$443$	9.26880	+	13.8717i	0.440374	+	0.659066i	−0.543193	+	0.839608i	$0.682785\pi$
$444$	−28.7254	+	1.42193i	−1.36325	+	0.0674818i
$445$	−16.2898	+	3.24025i	−0.772211	+	0.153602i
$446$	22.2030	+	16.0128i	1.05134	+	0.758226i
$447$	5.62382	+	9.96765i	0.265997	+	0.471454i
$448$	−23.0476	+	14.7995i	−1.08889	+	0.699211i
$449$		−	17.8223i		−	0.841087i	−0.907272	−	0.420544i	$-0.861839\pi$
$449$		−	17.8223i		−	0.841087i	0.907272	−	0.420544i	$-0.138161\pi$
$450$	7.57013	+	17.7781i	0.356859	+	0.838067i
$451$	−7.62789	−	38.3480i	−0.359184	−	1.80574i
$452$	−23.1621	−	11.5978i	−1.08945	−	0.545512i
$453$	−5.18508	+	10.2567i	−0.243616	+	0.481902i
$454$	15.6778	−	34.3238i	0.735795	−	1.61090i
$455$	14.3238	+	5.93311i	0.671509	+	0.278148i
$456$	4.75139	+	0.877631i	0.222504	+	0.0410988i
$457$	1.36147	−	0.563939i	0.0636869	−	0.0263800i	−0.350613	−	0.936521i	$-0.614027\pi$
$457$	1.36147	−	0.563939i	0.0636869	−	0.0263800i	0.414299	+	0.910141i	$0.364027\pi$
$458$	−14.1776	−	0.507247i	−0.662477	−	0.0237021i
$459$	2.02303	−	8.79485i	0.0944268	−	0.410508i
$460$	12.8759	−	46.9117i	0.600343	−	2.18727i
$461$	−9.13584	−	6.10437i	−0.425498	−	0.284309i	0.324327	−	0.945945i	$-0.394862\pi$
$461$	−9.13584	−	6.10437i	−0.425498	−	0.284309i	−0.749825	+	0.661636i	$0.769862\pi$
$462$	43.4653	+	23.9615i	2.02219	+	1.11479i
$463$	−5.48231	+	5.48231i	−0.254785	+	0.254785i	−0.822929	−	0.568144i	$-0.807662\pi$
$463$	−5.48231	+	5.48231i	−0.254785	+	0.254785i	0.568144	+	0.822929i	$0.307662\pi$
$464$	1.99671	−	2.22176i	0.0926950	−	0.103143i
$465$	−1.48949	+	5.34628i	−0.0690736	+	0.247928i
$466$	32.3466	+	7.64586i	1.49843	+	0.354187i
$467$	22.7550	+	15.2044i	1.05298	+	0.703577i	0.956492	−	0.291757i	$-0.0942400\pi$
$467$	22.7550	+	15.2044i	1.05298	+	0.703577i	0.0964850	+	0.995334i	$0.469240\pi$
$468$	3.57299	−	8.03105i	0.165162	−	0.371236i
$469$	−0.339520	−	0.0675348i	−0.0156776	−	0.00311847i
$470$	2.61724	−	2.43643i	0.120724	−	0.112384i
$471$	−21.4063	−	16.7654i	−0.986349	−	0.772508i
$472$	1.38735	−	0.407078i	0.0638578	−	0.0187373i
$473$	44.4897	+	18.4282i	2.04564	+	0.847330i
$474$	−22.5854	+	26.8048i	−1.03738	+	1.23119i
$475$	2.49558	+	3.73489i	0.114505	+	0.171369i
$476$	7.78684	+	8.98877i	0.356909	+	0.412000i
$477$	0.213157	−	0.589288i	0.00975979	−	0.0269816i
$478$	28.8119	−	4.66700i	1.31782	−	0.213463i
$479$			4.77550i			0.218198i	0.994031	+	0.109099i	$0.0347966\pi$
$479$			4.77550i			0.218198i	−0.994031	+	0.109099i	$0.965203\pi$
$480$	−7.61531	+	29.3126i	−0.347590	+	1.33793i
$481$			12.1631i			0.554590i
$482$	1.23873	+	7.64737i	0.0564228	+	0.348328i
$483$	35.3874	−	30.4186i	1.61018	−	1.38409i
$484$	3.43383	−	47.9266i	0.156083	−	2.17848i
$485$	−14.3727	−	21.5103i	−0.652632	−	0.976733i
$486$	21.5320	+	4.72986i	0.976713	+	0.214551i
$487$	−17.7784	−	7.36404i	−0.805615	−	0.333697i	−0.0584121	−	0.998293i	$-0.518604\pi$
$487$	−17.7784	−	7.36404i	−0.805615	−	0.333697i	−0.747203	+	0.664596i	$0.768604\pi$
$488$	−0.702935	+	6.52668i	−0.0318204	+	0.295449i
$489$	18.8637	−	24.0854i	0.853045	−	1.08918i
$490$	−14.0649	−	15.1087i	−0.635389	−	0.682542i
$491$	12.2480	+	2.43628i	0.552745	+	0.109948i	0.463557	−	0.886067i	$-0.346573\pi$
$491$	12.2480	+	2.43628i	0.552745	+	0.109948i	0.0891876	+	0.996015i	$0.471573\pi$
$492$	22.6397	+	3.34965i	1.02067	+	0.151014i
$493$	−1.07842	−	0.720574i	−0.0485694	−	0.0324530i
$494$	0.470050	−	1.98860i	0.0211485	−	0.0894712i
$495$	53.2808	−	13.1501i	2.39479	−	0.591052i
$496$	−3.32007	+	2.48408i	−0.149076	+	0.111538i
$497$	−10.3823	+	10.3823i	−0.465709	+	0.465709i
$498$	−24.7934	−	13.6681i	−1.11102	−	0.612484i
$499$	−6.01358	−	4.01814i	−0.269205	−	0.179877i	0.413640	−	0.910441i	$-0.364257\pi$
$499$	−6.01358	−	4.01814i	−0.269205	−	0.179877i	−0.682844	+	0.730564i	$0.739257\pi$
$500$	2.39395	−	1.36282i	0.107061	−	0.0609472i
$501$	−8.75692	−	26.6626i	−0.391230	−	1.19120i
$502$	−0.340045	+	9.50432i	−0.0151770	+	0.424199i
$503$	−38.9949	+	16.1522i	−1.73870	+	0.720191i	−0.739818	+	0.672807i	$0.765089\pi$
$503$	−38.9949	+	16.1522i	−1.73870	+	0.720191i	−0.998877	+	0.0473844i	$0.984911\pi$
$504$	−21.7695	+	19.2375i	−0.969689	+	0.856908i
$505$	−17.2471	−	7.14397i	−0.767485	−	0.317903i
$506$	−59.9069	−	27.3631i	−2.66319	−	1.21644i
$507$	16.7773	+	8.48146i	0.745107	+	0.376675i
$508$	−13.8571	+	4.61014i	−0.614808	+	0.204542i
$509$	3.24419	+	16.3096i	0.143796	+	0.722912i	0.983649	+	0.180097i	$0.0576413\pi$
$509$	3.24419	+	16.3096i	0.143796	+	0.722912i	−0.839853	+	0.542814i	$0.817359\pi$
$510$	13.0687	+	1.45829i	0.578692	+	0.0645740i
$511$		−	32.1723i		−	1.42322i
$512$	−17.8771	+	13.8712i	−0.790064	+	0.613025i
$513$	5.12259	+	0.152399i	0.226168	+	0.00672859i
$514$	0.602034	−	0.834769i	0.0265546	−	0.0368201i
$515$	−27.6548	+	5.50088i	−1.21861	+	0.242398i
$516$	−18.9214	+	20.8922i	−0.832966	+	0.919726i
$517$	−2.68955	−	4.02519i	−0.118286	−	0.177028i
$518$	16.7019	−	36.5660i	0.733841	−	1.60662i
$519$	−0.152870	−	1.25737i	−0.00671026	−	0.0551923i
$520$	12.2222	+	3.82953i	0.535978	+	0.167936i
$521$	−3.65660	−	8.82782i	−0.160199	−	0.386754i	0.823316	−	0.567584i	$-0.192122\pi$
$521$	−3.65660	−	8.82782i	−0.160199	−	0.386754i	−0.983514	+	0.180830i	$0.942122\pi$
$522$	1.73419	−	2.65162i	0.0759032	−	0.116058i
$523$	−31.5452	−	6.27473i	−1.37937	−	0.274375i	−0.550979	−	0.834519i	$-0.685746\pi$
$523$	−31.5452	−	6.27473i	−1.37937	−	0.274375i	−0.828395	+	0.560144i	$0.810746\pi$
$524$	−13.0202	−	22.8714i	−0.568789	−	0.999141i
$525$	−26.9315	−	2.03351i	−1.17539	−	0.0887497i
$526$	−9.01519	−	14.5963i	−0.393081	−	0.636429i
$527$	1.27306	+	1.27306i	0.0554555	+	0.0554555i
$528$	37.5258	+	16.5229i	1.63310	+	0.719065i
$529$	−27.5217	+	27.5217i	−1.19660	+	1.19660i
$530$	0.888625	+	0.210046i	0.0385994	+	0.00912383i
$531$	1.38857	−	0.650865i	0.0602587	−	0.0282451i
$532$	−4.14379	+	5.33289i	−0.179656	+	0.231210i
$533$	1.88823	−	9.49277i	0.0817883	−	0.411178i
$534$	−12.5445	−	3.98348i	−0.542855	−	0.172382i
$535$	28.2474	−	11.7005i	1.22124	−	0.505855i
$536$	−0.284334	−	0.0306233i	−0.0122814	−	0.00132272i
$537$	−2.29528	−	18.8788i	−0.0990487	−	0.814682i
$538$	−0.608856	−	1.63272i	−0.0262497	−	0.0703916i
$539$	−23.2365	+	15.5261i	−1.00087	+	0.668758i
$540$	−3.24743	+	31.9583i	−0.139747	+	1.37526i
$541$	5.80866	+	29.2021i	0.249734	+	1.25550i	0.878440	+	0.477853i	$0.158585\pi$
$541$	5.80866	+	29.2021i	0.249734	+	1.25550i	−0.628706	+	0.777643i	$0.716415\pi$
$542$	9.75717	−	1.58048i	0.419106	−	0.0678875i
$543$	11.2769	+	19.9871i	0.483937	+	0.857730i
$544$	7.06783	+	6.82419i	0.303031	+	0.292585i
$545$	1.26002			0.0539733
$546$	7.67060	+	9.59748i	0.328271	+	0.410734i
$547$	−0.203515	+	0.0404817i	−0.00870169	+	0.00173087i	−0.199439	−	0.979910i	$-0.563912\pi$
$547$	−0.203515	+	0.0404817i	−0.00870169	+	0.00173087i	0.190738	+	0.981641i	$0.438912\pi$
$548$	−1.84602	+	1.59918i	−0.0788579	+	0.0683135i
$549$	0.317539	+	6.95538i	0.0135523	+	0.296849i
$550$	13.3188	+	35.7158i	0.567914	+	1.52293i
$551$	0.281863	−	0.680476i	0.0120077	−	0.0289893i
$552$	26.8832	−	27.6299i	1.14422	−	1.17601i
$553$	−18.7487	−	45.2635i	−0.797278	−	1.92480i
$554$	27.8944	+	29.9644i	1.18512	+	1.27307i
$555$	−13.8699	−	42.2304i	−0.588745	−	1.79258i
$556$	3.25548	+	25.9450i	0.138063	+	1.10031i
$557$	−14.7746	+	22.1117i	−0.626020	+	0.936905i	0.373936	+	0.927455i	$0.378008\pi$
$557$	−14.7746	+	22.1117i	−0.626020	+	0.936905i	−0.999955	+	0.00945012i	$0.996992\pi$
$558$	−3.07907	+	3.14039i	−0.130347	+	0.132943i
$559$	8.42906	+	8.42906i	0.356511	+	0.356511i
$560$	−31.4851	−	28.2958i	−1.33049	−	1.19572i
$561$	4.77798	−	17.1497i	0.201726	−	0.724062i
$562$	−6.86560	−	11.1159i	−0.289608	−	0.468898i
$563$	9.50695	−	14.2282i	0.400670	−	0.599645i	−0.575196	−	0.818016i	$-0.695074\pi$
$563$	9.50695	−	14.2282i	0.400670	−	0.599645i	0.975866	+	0.218370i	$0.0700741\pi$
$564$	2.74845	−	0.689542i	0.115731	−	0.0290349i
$565$	7.81026	−	39.2648i	0.328580	−	1.65188i
$566$	0.853119	−	23.8448i	0.0358593	−	1.00227i
$567$	−19.7127	+	23.6834i	−0.827855	+	0.994607i
$568$	−7.78013	+	9.30587i	−0.326447	+	0.390466i
$569$	−10.2390	+	24.7192i	−0.429242	+	1.03628i	0.550286	+	0.834976i	$0.314519\pi$
$569$	−10.2390	+	24.7192i	−0.429242	+	1.03628i	−0.979528	+	0.201306i	$0.935481\pi$
$570$	0.635637	+	7.44044i	0.0266239	+	0.311646i
$571$	−3.09583	+	2.06856i	−0.129556	+	0.0865667i	−0.618660	−	0.785659i	$-0.712324\pi$
$571$	−3.09583	+	2.06856i	−0.129556	+	0.0865667i	0.489103	+	0.872226i	$0.337324\pi$
$572$	7.76373	−	15.5051i	0.324618	−	0.648301i
$573$	−2.06096	+	1.77158i	−0.0860980	+	0.0740089i
$574$	−18.7117	+	25.9454i	−0.781013	+	1.08294i
$575$	35.8387			1.49458
$576$	−16.4993	+	17.4291i	−0.687472	+	0.726211i
$577$	−13.7169			−0.571043			−0.285522	−	0.958372i	$-0.592167\pi$
$577$	−13.7169			−0.571043			−0.285522	+	0.958372i	$0.592167\pi$
$578$	−11.5678	+	16.0397i	−0.481156	+	0.667162i
$579$	−15.2663	+	13.1228i	−0.634447	+	0.545364i
$580$	4.12809	+	2.06702i	0.171410	+	0.0858284i
$581$	32.9029	−	21.9850i	1.36504	−	0.912093i
$582$	−1.74504	−	20.4266i	−0.0723343	−	0.846708i
$583$	0.473080	−	1.14212i	0.0195930	−	0.0473016i
$584$	−2.36395	−	26.4727i	−0.0978211	−	1.09545i
$585$	13.4310	+	2.03989i	0.555304	+	0.0843392i
$586$	−0.978797	+	27.3576i	−0.0404337	+	1.13013i
$587$	5.12154	−	25.7477i	0.211388	−	1.06272i	−0.718682	−	0.695339i	$-0.755254\pi$
$587$	5.12154	−	25.7477i	0.211388	−	1.06272i	0.930070	−	0.367382i	$-0.119746\pi$
$588$	−3.98056	−	15.8662i	−0.164156	−	0.654310i
$589$	−0.568017	+	0.850097i	−0.0234047	+	0.0350277i
$590$	1.17423	+	1.90116i	0.0483421	+	0.0782697i
$591$	0.0120063	−	0.0430945i	0.000493873	−	0.00177267i
$592$	11.0563	−	31.3154i	0.454410	−	1.28705i
$593$	29.8912	+	29.8912i	1.22748	+	1.22748i	0.964913	+	0.262571i	$0.0845704\pi$
$593$	29.8912	+	29.8912i	1.22748	+	1.22748i	0.262571	+	0.964913i	$0.415430\pi$
$594$	42.0070	+	11.2582i	1.72357	+	0.461929i
$595$	−10.2114	+	15.2825i	−0.418627	+	0.626520i
$596$	−13.1124	+	1.64530i	−0.537105	+	0.0673940i
$597$	−8.49435	−	25.8631i	−0.347651	−	1.05851i
$598$	−11.1086	−	11.9329i	−0.454263	−	0.487974i
$599$	−11.8306	−	28.5615i	−0.483384	−	1.16699i	−0.957992	−	0.286796i	$-0.907410\pi$
$599$	−11.8306	−	28.5615i	−0.483384	−	1.16699i	0.474607	−	0.880198i	$-0.342590\pi$
$600$	−22.3098	+	0.305614i	−0.910796	+	0.0124766i
$601$	16.8090	−	40.5806i	0.685654	−	1.65532i	−0.0677046	−	0.997705i	$-0.521568\pi$
$601$	16.8090	−	40.5806i	0.685654	−	1.65532i	0.753359	−	0.657610i	$-0.228432\pi$
$602$	−13.7659	−	36.9148i	−0.561055	−	1.50454i
$603$	−0.303011	+	0.0138336i	−0.0123396	+	0.000563347i
$604$	−8.68924	−	10.0305i	−0.353560	−	0.408134i
$605$	72.8340	−	14.4876i	2.96112	−	0.589004i
$606$	−9.23607	−	11.5562i	−0.375190	−	0.469438i
$607$	3.32089			0.134791			0.0673953	−	0.997726i	$-0.478531\pi$
$607$	3.32089			0.134791			0.0673953	+	0.997726i	$0.478531\pi$
$608$	−3.01784	+	4.69261i	−0.122389	+	0.190310i
$609$	2.17614	+	3.85700i	0.0881818	+	0.156293i
$610$	−10.0149	+	1.62222i	−0.405490	+	0.0656819i
$611$	−0.233790	−	1.17534i	−0.00945814	−	0.0475493i
$612$	8.51157	+	6.01186i	0.344060	+	0.243015i
$613$	18.6015	−	12.4291i	0.751306	−	0.502007i	−0.119983	−	0.992776i	$-0.538284\pi$
$613$	18.6015	−	12.4291i	0.751306	−	0.502007i	0.871290	+	0.490769i	$0.163284\pi$
$614$	−5.05706	−	13.5611i	−0.204087	−	0.547282i
$615$	4.26892	+	35.1122i	0.172140	+	1.41586i
$616$	−44.6312	+	35.9523i	−1.79824	+	1.44856i
$617$	−26.6248	+	11.0284i	−1.07187	+	0.443985i	−0.847652	−	0.530553i	$-0.821984\pi$
$617$	−26.6248	+	11.0284i	−1.07187	+	0.443985i	−0.224222	+	0.974538i	$0.571984\pi$
$618$	−21.2965	−	6.76264i	−0.856672	−	0.272033i
$619$	−7.51227	+	37.7668i	−0.301944	+	1.51797i	0.470219	+	0.882550i	$0.344175\pi$
$619$	−7.51227	+	37.7668i	−0.301944	+	1.51797i	−0.772163	+	0.635424i	$0.780825\pi$
$620$	−5.06038	−	3.93204i	−0.203230	−	0.157915i
$621$	23.7175	−	33.3071i	0.951750	−	1.33657i
$622$	−6.72450	−	1.58949i	−0.269628	−	0.0637327i
$623$	13.0085	−	13.0085i	0.521176	−	0.521176i
$624$	7.01691	+	7.33360i	0.280901	+	0.293579i
$625$	19.1127	+	19.1127i	0.764507	+	0.764507i
$626$	−3.34260	−	5.41193i	−0.133597	−	0.216304i
$627$	10.0812	+	0.761201i	0.402606	+	0.0303994i
$628$	27.2851	−	15.5328i	1.08879	−	0.619825i
$629$	−14.1424	−	2.81310i	−0.563894	−	0.112166i
$630$	−37.5767	−	24.5755i	−1.49709	−	0.979112i
$631$	−5.09145	−	12.2919i	−0.202688	−	0.489331i	0.789550	−	0.613686i	$-0.210314\pi$
$631$	−5.09145	−	12.2919i	−0.202688	−	0.489331i	−0.992238	+	0.124355i	$0.960314\pi$
$632$	−18.7532	−	35.8671i	−0.745961	−	1.42672i
$633$	−2.48977	−	20.4785i	−0.0989595	−	0.813948i
$634$	−8.25175	+	18.0658i	−0.327719	+	0.717485i
$635$	−12.5394	−	18.7666i	−0.497612	−	0.744728i
$636$	0.536332	+	0.485739i	0.0212670	+	0.0192608i
$637$	−6.78498	+	1.34962i	−0.268831	+	0.0534737i
$638$	3.65607	−	5.06944i	0.144745	−	0.200701i
$639$	−6.65238	+	11.0121i	−0.263164	+	0.435632i
$640$	−27.9864	−	20.9696i	−1.10626	−	0.828895i
$641$		−	26.7664i		−	1.05721i	−0.848868	−	0.528605i	$-0.822715\pi$
$641$		−	26.7664i		−	1.05721i	0.848868	−	0.528605i	$-0.177285\pi$
$642$	24.0796	+	2.68695i	0.950347	+	0.106046i
$643$	−8.55540	−	43.0109i	−0.337392	−	1.69618i	−0.661321	−	0.750103i	$-0.730004\pi$
$643$	−8.55540	−	43.0109i	−0.337392	−	1.69618i	0.323928	−	0.946082i	$-0.394996\pi$
$644$	17.0099	+	51.1280i	0.670284	+	2.01473i
$645$	−38.8776	−	19.6539i	−1.53081	−	0.773870i
$646$	2.20349	+	1.00647i	0.0866950	+	0.0395989i
$647$	−39.3551	−	16.3014i	−1.54721	−	0.640875i	−0.564400	−	0.825501i	$-0.690892\pi$
$647$	−39.3551	−	16.3014i	−1.54721	−	0.640875i	−0.982809	+	0.184627i	$0.940892\pi$
$648$	−14.4803	+	20.9361i	−0.568838	+	0.822449i
$649$	2.79497	−	1.15771i	0.109712	−	0.0454442i
$650$	−0.337382	+	9.42989i	−0.0132332	+	0.369871i
$651$	−1.91819	−	5.84039i	−0.0751797	−	0.228903i
$652$	17.4768	+	30.7000i	0.684445	+	1.20230i
$653$	41.4630	+	27.7047i	1.62257	+	1.08417i	0.932954	+	0.359995i	$0.117222\pi$
$653$	41.4630	+	27.7047i	1.62257	+	1.08417i	0.689618	+	0.724173i	$0.257778\pi$
$654$	0.874434	+	0.482058i	0.0341931	+	0.0188500i
$655$	28.7611	−	28.7611i	1.12379	−	1.12379i
$656$	−13.4904	+	22.7239i	−0.526712	+	0.887218i
$657$	−6.75488	−	27.3690i	−0.263533	−	1.06777i
$658$	−0.911092	+	3.85448i	−0.0355181	+	0.150263i
$659$	11.5398	+	7.71062i	0.449525	+	0.300363i	0.759649	−	0.650333i	$-0.225371\pi$
$659$	11.5398	+	7.71062i	0.449525	+	0.300363i	−0.310124	+	0.950696i	$0.600371\pi$
$660$	−9.27484	+	62.6870i	−0.361023	+	2.44009i
$661$	−2.41656	−	0.480684i	−0.0939933	−	0.0186964i	0.147870	−	0.989007i	$-0.452758\pi$
$661$	−2.41656	−	0.480684i	−0.0939933	−	0.0186964i	−0.241863	+	0.970310i	$0.577758\pi$
$662$	22.6839	+	24.3673i	0.881634	+	0.947061i
$663$	2.71732	−	3.46952i	0.105532	−	0.134745i
$664$	25.4585	−	20.5079i	0.987983	−	0.795860i
$665$	−9.64318	−	3.99434i	−0.373946	−	0.154894i
$666$	6.53098	−	34.6136i	0.253070	−	1.34125i
$667$	−3.26481	−	4.88613i	−0.126414	−	0.189192i
$668$	32.3224	+	2.31582i	1.25059	+	0.0896019i
$669$	−25.4250	+	21.8550i	−0.982987	+	0.844964i
$670$	−0.0706720	−	0.436296i	−0.00273030	−	0.0168556i
$671$			13.7353i			0.530247i
$672$	−11.0248	−	31.6825i	−0.425290	−	1.22218i
$673$		−	2.03408i		−	0.0784081i	−0.999231	−	0.0392041i	$-0.987518\pi$
$673$		−	2.03408i		−	0.0784081i	0.999231	−	0.0392041i	$-0.0124822\pi$
$674$	45.7243	−	7.40649i	1.76123	−	0.285287i
$675$	−23.3377	+	3.92462i	−0.898268	+	0.151059i
$676$	−16.4073	+	14.2134i	−0.631048	+	0.546668i
$677$	27.9479	+	41.8269i	1.07412	+	1.60754i	0.749890	+	0.661562i	$0.230106\pi$
$677$	27.9479	+	41.8269i	1.07412	+	1.60754i	0.324233	+	0.945977i	$0.394894\pi$
$678$	20.4422	−	24.2612i	0.785076	−	0.931744i
$679$	26.4738	+	10.9658i	1.01597	+	0.420830i
$680$	−7.27947	+	13.3254i	−0.279155	+	0.511006i
$681$	36.3846	+	28.4964i	1.39426	+	1.09198i
$682$	−6.35036	+	5.91165i	−0.243168	+	0.226369i
$683$	25.4489	+	5.06210i	0.973775	+	0.193696i	0.656241	−	0.754551i	$-0.272145\pi$
$683$	25.4489	+	5.06210i	0.973775	+	0.193696i	0.317533	+	0.948247i	$0.397145\pi$
$684$	−2.40544	+	5.40673i	−0.0919743	+	0.206732i
$685$	−3.13855	−	2.09711i	−0.119918	−	0.0801265i
$686$	−10.7336	−	2.53712i	−0.409809	−	0.0968676i
$687$	4.66317	−	16.7376i	0.177911	−	0.638581i
$688$	−14.0396	−	29.3636i	−0.535255	−	1.11948i
$689$	0.216386	−	0.216386i	0.00824366	−	0.00824366i
$690$	52.1765	+	28.7639i	1.98632	+	1.09502i
$691$	−14.8014	−	9.88998i	−0.563072	−	0.376233i	0.241217	−	0.970471i	$-0.422454\pi$
$691$	−14.8014	−	9.88998i	−0.563072	−	0.376233i	−0.804289	+	0.594239i	$0.797454\pi$
$692$	1.41041	+	0.387118i	0.0536158	+	0.0147160i
$693$	−40.9780	+	44.8986i	−1.55662	+	1.70556i
$694$	−22.0574	−	0.789169i	−0.837288	−	0.0299564i
$695$	−37.3364	+	15.4652i	−1.41625	+	0.586630i
$696$	2.07403	+	3.01381i	0.0786159	+	0.114238i
$697$	10.6008	+	4.39100i	0.401534	+	0.166321i
$698$	−21.6203	+	47.3340i	−0.818340	+	1.79162i
$699$	−18.3658	+	36.3297i	−0.694658	+	1.37411i
$700$	13.9631	−	27.8859i	0.527754	−	1.05399i
$701$	−1.80129	−	9.05570i	−0.0680338	−	0.342029i	0.931744	−	0.363116i	$-0.118287\pi$
$701$	−1.80129	−	9.05570i	−0.0680338	−	0.342029i	−0.999778	+	0.0210872i	$0.993287\pi$
$702$	8.54049	+	6.55409i	0.322340	+	0.247368i
$703$		−	8.18854i		−	0.308837i
$704$	−34.0828	+	32.8625i	−1.28454	+	1.23855i
$705$	2.15200	+	3.81420i	0.0810489	+	0.143651i
$706$	30.1222	+	21.7241i	1.13367	+	0.817597i
$707$	20.2803	−	4.03401i	0.762721	−	0.151715i
$708$	0.0875478	+	1.76861i	0.00329025	+	0.0664686i
$709$	20.1678	+	30.1833i	0.757418	+	1.13356i	0.987071	+	0.160284i	$0.0512409\pi$
$709$	20.1678	+	30.1833i	0.757418	+	1.13356i	−0.229653	+	0.973273i	$0.573759\pi$
$710$	−17.0520	−	7.78868i	−0.639950	−	0.292304i
$711$	−25.4531	−	34.5693i	−0.954567	−	1.29645i
$712$	9.74815	−	11.6598i	0.365327	−	0.436971i
$713$	3.12164	+	7.53631i	0.116906	+	0.282237i
$714$	−12.9333	+	6.69912i	−0.484018	+	0.250708i
$715$	26.2846	+	5.22832i	0.982987	+	0.195528i
$716$	21.1767	+	5.81241i	0.791412	+	0.217220i
$717$	−2.69149	+	35.6457i	−0.100515	+	1.33121i
$718$	−30.8514	+	19.0549i	−1.15136	+	0.711123i
$719$	3.33500	+	3.33500i	0.124374	+	0.124374i	0.766554	−	0.642180i	$-0.221970\pi$
$719$	3.33500	+	3.33500i	0.124374	+	0.124374i	−0.642180	+	0.766554i	$0.721970\pi$
$720$	−32.7255	−	17.4608i	−1.21961	−	0.650724i
$721$	22.0842	−	22.0842i	0.822460	−	0.822460i
$722$	5.86457	−	24.8107i	0.218257	−	0.923358i
$723$	−9.46122	−	0.714386i	−0.351867	−	0.0265683i
$724$	−26.2930	+	3.29915i	−0.977171	+	0.122612i
$725$	−0.663537	+	3.33583i	−0.0246431	+	0.123889i
$726$	56.0884	+	17.8107i	2.08163	+	0.661016i
$727$	−34.6479	+	14.3516i	−1.28502	+	0.532272i	−0.917497	−	0.397743i	$-0.869794\pi$
$727$	−34.6479	+	14.3516i	−1.28502	+	0.532272i	−0.367521	+	0.930015i	$0.619794\pi$
$728$	−13.6129	+	3.99433i	−0.504529	+	0.148040i
$729$	−11.7971	+	24.2864i	−0.436930	+	0.899496i
$730$	38.4877	−	14.3524i	1.42449	−	0.531207i
$731$	−11.7502	+	7.85123i	−0.434597	+	0.290388i
$732$	−7.57079	−	2.70569i	−0.279824	−	0.100005i
$733$	7.64916	+	38.4549i	0.282528	+	1.42037i	0.817711	+	0.575629i	$0.195243\pi$
$733$	7.64916	+	38.4549i	0.282528	+	1.42037i	−0.535183	+	0.844736i	$0.679757\pi$
$734$	0.106986	+	0.660480i	0.00394891	+	0.0243788i
$735$	22.0185	−	12.4230i	0.812164	−	0.458228i
$736$	17.7533	+	40.8205i	0.654394	+	1.50466i
$737$	−0.598379			−0.0220416
$738$	−10.4707	+	26.0005i	−0.385430	+	0.957093i
$739$	−4.81148	+	0.957063i	−0.176993	+	0.0352061i	−0.282791	−	0.959182i	$-0.591260\pi$
$739$	−4.81148	+	0.957063i	−0.176993	+	0.0352061i	0.105798	+	0.994388i	$0.466260\pi$
$740$	51.1949	+	3.66799i	1.88196	+	0.134838i
$741$	2.23346	+	1.12909i	0.0820484	+	0.0414780i
$742$	−0.947658	+	0.353390i	−0.0347896	+	0.0129734i
$743$	−3.62259	+	8.74570i	−0.132900	+	0.320849i	−0.976295	−	0.216446i	$-0.930554\pi$
$743$	−3.62259	+	8.74570i	−0.132900	+	0.320849i	0.843395	+	0.537294i	$0.180554\pi$
$744$	−2.00751	−	4.66478i	−0.0735988	−	0.171019i
$745$	−7.81602	−	18.8695i	−0.286357	−	0.691327i
$746$	18.0814	−	16.8323i	0.662009	−	0.616274i
$747$	23.3747	−	25.6110i	0.855234	−	0.937059i
$748$	16.2326	+	12.6132i	0.593524	+	0.461183i
$749$	−18.8150	+	28.1586i	−0.687484	+	1.02889i
$750$	0.937462	+	3.24092i	0.0342313	+	0.118342i
$751$	2.62749	+	2.62749i	0.0958786	+	0.0958786i	0.753419	−	0.657541i	$-0.228403\pi$
$751$	2.62749	+	2.62749i	0.0958786	+	0.0958786i	−0.657541	+	0.753419i	$0.728403\pi$
$752$	−0.466467	+	3.23858i	−0.0170103	+	0.118099i
$753$	−11.2205	−	3.12607i	−0.408897	−	0.113920i
$754$	1.31637	−	0.813039i	0.0479395	−	0.0296091i
$755$	11.3948	−	17.0535i	0.414699	−	0.620641i
$756$	−16.6755	−	31.4311i	−0.606483	−	1.14314i
$757$	−6.61662	+	33.2640i	−0.240485	+	1.20900i	0.652104	+	0.758130i	$0.273887\pi$
$757$	−6.61662	+	33.2640i	−0.240485	+	1.20900i	−0.892589	+	0.450871i	$0.851113\pi$
$758$	24.6225	+	0.880941i	0.894328	+	0.0319972i
$759$	49.7359	−	63.5035i	1.80530	−	2.30503i
$760$	−8.22832	−	2.57815i	−0.298473	−	0.0935194i
$761$	−10.5642	+	25.5043i	−0.382953	+	0.924531i	0.608438	+	0.793601i	$0.291796\pi$
$761$	−10.5642	+	25.5043i	−0.382953	+	0.924531i	−0.991392	+	0.130930i	$0.958204\pi$
$762$	−1.52245	−	17.8210i	−0.0551526	−	0.645588i
$763$	−1.16044	+	0.775384i	−0.0420109	+	0.0280708i
$764$	−0.990658	−	2.97770i	−0.0358408	−	0.107729i
$765$	−5.47818	+	15.1448i	−0.198064	+	0.547563i
$766$	−9.03645	−	6.51707i	−0.326500	−	0.235471i
$767$	0.748879			0.0270404
$768$	−11.3996	−	25.2596i	−0.411348	−	0.911478i
$769$	−2.19548			−0.0791710			−0.0395855	−	0.999216i	$-0.512604\pi$
$769$	−2.19548			−0.0791710			−0.0395855	+	0.999216i	$0.512604\pi$
$770$	−71.8402	−	51.8110i	−2.58894	−	1.86714i
$771$	0.821687	+	0.955907i	0.0295923	+	0.0344261i
$772$	−7.33818	−	22.0569i	−0.264107	−	0.793846i
$773$	−31.2396	+	20.8736i	−1.12361	+	0.750772i	−0.971370	−	0.237572i	$-0.923649\pi$
$773$	−31.2396	+	20.8736i	−1.12361	+	0.750772i	−0.152240	+	0.988344i	$0.548649\pi$
$774$	−19.4613	−	28.5133i	−0.699522	−	1.02489i
$775$	1.80673	−	4.36184i	0.0648997	−	0.156682i
$776$	22.5896	+	7.07791i	0.810918	+	0.254082i
$777$	38.7614	+	30.3579i	1.39056	+	1.08908i
$778$	30.0031	+	1.07345i	1.07566	+	0.0384850i
$779$	−1.27121	+	6.39080i	−0.0455458	+	0.228974i
$780$	−8.05953	+	13.4579i	−0.288577	+	0.481870i
$781$	−14.1004	+	21.1027i	−0.504552	+	0.755115i
$782$	16.4440	−	10.1564i	0.588036	−	0.363192i
$783$	2.66107	+	2.82426i	0.0950988	+	0.100931i
$784$	18.6955	+	2.69280i	0.667698	+	0.0961716i
$785$	34.3114	+	34.3114i	1.22463	+	1.22463i
$786$	30.9632	−	8.95636i	1.10442	−	0.319463i
$787$	21.7175	−	32.5026i	0.774147	−	1.15859i	−0.209381	−	0.977834i	$-0.567145\pi$
$787$	21.7175	−	32.5026i	0.774147	−	1.15859i	0.983528	−	0.180758i	$-0.0578552\pi$
$788$	0.0407900	+	0.0316948i	0.00145308	+	0.00112908i
$789$	19.9625	−	6.55638i	0.710684	−	0.233413i
$790$	45.7847	−	42.6217i	1.62895	−	1.51641i
$791$	16.9696	+	40.9682i	0.603368	+	1.45666i
$792$	−30.4194	+	39.9555i	−1.08091	+	1.41976i
$793$	−1.30116	+	3.14127i	−0.0462054	+	0.111550i
$794$	−28.5261	+	10.6377i	−1.01235	+	0.377516i
$795$	−0.504543	+	0.998046i	−0.0178943	+	0.0353970i
$796$	31.3533	+	2.24639i	1.11129	+	0.0796210i
$797$	19.8433	−	3.94707i	0.702885	−	0.139812i	0.169307	−	0.985563i	$-0.445847\pi$
$797$	19.8433	−	3.94707i	0.702885	−	0.139812i	0.533578	+	0.845751i	$0.320847\pi$
$798$	−5.16407	−	6.46130i	−0.182806	−	0.228727i
$799$	1.42068			0.0502599
$800$	9.44041	−	23.9717i	0.333769	−	0.847527i
$801$	8.33513	−	13.7977i	0.294507	−	0.487517i
$802$	8.04762	+	49.6823i	0.284171	+	1.75434i
$803$	−10.8493	−	54.5431i	−0.382863	−	1.92478i
$804$	0.117873	−	0.329821i	0.00415706	−	0.0116319i
$805$	−69.2424	+	46.2663i	−2.44048	+	1.63067i
$806$	−2.01234	+	0.750420i	−0.0708817	+	0.0264324i
$807$	2.11858	−	0.257576i	0.0745775	−	0.00906710i
$808$	16.3911	−	4.80952i	0.576638	−	0.169198i
$809$	−24.0328	+	9.95470i	−0.844947	+	0.349989i	−0.762802	−	0.646632i	$-0.776177\pi$
$809$	−24.0328	+	9.95470i	−0.844947	+	0.349989i	−0.0821450	+	0.996620i	$0.526177\pi$
$810$	−37.1265	−	13.0169i	−1.30449	−	0.457367i
$811$	−0.113676	+	0.571490i	−0.00399172	+	0.0200677i	−0.982730	−	0.185046i	$-0.940757\pi$
$811$	−0.113676	+	0.571490i	−0.00399172	+	0.0200677i	0.978738	+	0.205114i	$0.0657565\pi$
$812$	−5.07386	+	0.636650i	−0.178058	+	0.0223420i
$813$	−0.911475	+	12.0714i	−0.0319668	+	0.423364i
$814$	15.9846	−	67.6244i	0.560258	−	2.37023i
$815$	−38.6057	+	38.6057i	−1.35230	+	1.35230i
$816$	−10.1499	+	6.46264i	−0.355317	+	0.226238i
$817$	−5.67468	−	5.67468i	−0.198532	−	0.198532i
$818$	8.62268	−	5.32567i	0.301485	−	0.186208i
$819$	−13.6249	+	6.38642i	−0.476093	+	0.223160i
$820$	−39.3860	−	10.8103i	−1.37542	−	0.377513i
$821$	14.1155	+	2.80775i	0.492634	+	0.0979910i	0.435155	−	0.900356i	$-0.356694\pi$
$821$	14.1155	+	2.80775i	0.492634	+	0.0979910i	0.0574793	+	0.998347i	$0.481694\pi$
$822$	−1.37579	−	2.65611i	−0.0479863	−	0.0926424i
$823$	7.96110	+	19.2198i	0.277506	+	0.669960i	0.999765	−	0.0216629i	$-0.00689607\pi$
$823$	7.96110	+	19.2198i	0.277506	+	0.669960i	−0.722259	+	0.691623i	$0.756896\pi$
$824$	16.5492	−	19.7946i	0.576517	−	0.689577i
$825$	−46.3440	+	5.63448i	−1.61349	+	0.196168i
$826$	−2.25136	−	1.02833i	−0.0783349	−	0.0357803i
$827$	−8.62385	−	12.9065i	−0.299881	−	0.448803i	0.650676	−	0.759356i	$-0.274486\pi$
$827$	−8.62385	−	12.9065i	−0.299881	−	0.448803i	−0.950556	+	0.310553i	$0.899486\pi$
$828$	25.2052	+	39.9234i	0.875942	+	1.38743i
$829$	8.00756	−	1.59280i	0.278114	−	0.0553203i	−0.0540625	−	0.998538i	$-0.517217\pi$
$829$	8.00756	−	1.59280i	0.278114	−	0.0553203i	0.332177	+	0.943217i	$0.392217\pi$
$830$	40.9791	+	29.5540i	1.42240	+	1.02583i
$831$	−43.6683	+	24.6379i	−1.51484	+	0.854680i
$832$	−10.9078	+	4.28696i	−0.378160	+	0.148624i
$833$		−	8.20123i		−	0.284156i
$834$	−31.8276	−	3.55152i	−1.10210	−	0.122979i
$835$	9.77065	+	49.1204i	0.338127	+	1.69988i
$836$	−5.22677	+	10.4385i	−0.180771	+	0.361022i
$837$	−2.85806	−	4.56570i	−0.0987888	−	0.157814i
$838$	−10.3108	+	22.5737i	−0.356180	+	0.779795i
$839$	−25.0437	−	10.3734i	−0.864604	−	0.358131i	−0.0940975	−	0.995563i	$-0.529997\pi$
$839$	−25.0437	−	10.3734i	−0.864604	−	0.358131i	−0.770506	+	0.637432i	$0.779997\pi$
$840$	42.7093	−	29.3915i	1.47361	−	1.01410i
$841$	−26.2773	+	10.8844i	−0.906113	+	0.375324i
$842$	−13.5346	−	0.484240i	−0.466433	−	0.0166880i
$843$	15.2026	−	4.99308i	0.523607	−	0.171971i
$844$	22.9711	+	6.30493i	0.790699	+	0.217024i
$845$	−27.8952	−	18.6390i	−0.959623	−	0.641200i
$846$	0.0342162	+	3.47031i	0.00117638	+	0.119312i
$847$	−58.1630	+	58.1630i	−1.99850	+	1.99850i
$848$	−0.753808	+	0.360417i	−0.0258859	+	0.0123768i
$849$	28.1504	+	7.84280i	0.966120	+	0.269164i
$850$	−10.8864	−	2.57324i	−0.373400	−	0.0882614i
$851$	−54.3218	−	36.2967i	−1.86213	−	1.24423i
$852$	−8.85403	−	11.9290i	−0.303334	−	0.408680i
$853$	37.3136	+	7.42214i	1.27759	+	0.254129i	0.786834	−	0.617165i	$-0.211719\pi$
$853$	37.3136	+	7.42214i	1.27759	+	0.254129i	0.490761	+	0.871294i	$0.336719\pi$
$854$	8.22515	−	7.65692i	0.281459	−	0.262015i
$855$	−9.04213	−	1.37331i	−0.309234	−	0.0469663i
$856$	−13.4127	+	24.5526i	−0.458438	+	0.839190i
$857$	−19.0695	−	7.89884i	−0.651402	−	0.269819i	0.0324137	−	0.999475i	$-0.489681\pi$
$857$	−19.0695	−	7.89884i	−0.651402	−	0.269819i	−0.683815	+	0.729655i	$0.739681\pi$
$858$	16.2408	+	13.6843i	0.554453	+	0.467175i
$859$	−28.7274	−	42.9936i	−0.980165	−	1.46692i	−0.881717	−	0.471779i	$-0.843612\pi$
$859$	−28.7274	−	42.9936i	−0.980165	−	1.46692i	−0.0984485	−	0.995142i	$-0.531388\pi$
$860$	38.0201	−	32.9363i	1.29647	−	1.12312i
$861$	−25.5387	−	29.7104i	−0.870358	−	1.01253i
$862$	−6.35760	+	1.02981i	−0.216541	+	0.0350756i
$863$		−	15.3678i		−	0.523125i	−0.965187	−	0.261562i	$-0.915762\pi$
$863$		−	15.3678i		−	0.523125i	0.965187	−	0.261562i	$-0.0842377\pi$
$864$	−16.0308	−	24.6376i	−0.545381	−	0.838189i
$865$			2.26042i			0.0768567i
$866$	−8.10934	−	50.0634i	−0.275567	−	1.70122i
$867$	−15.7883	−	18.3673i	−0.536198	−	0.623785i
$868$	7.08017	+	0.507277i	0.240317	+	0.0172181i
$869$	−47.0496	−	70.4147i	−1.59605	−	2.38865i
$870$	−3.64333	+	4.32397i	−0.123520	+	0.146596i
$871$	−0.136849	−	0.0566847i	−0.00463695	−	0.00192069i
$872$	−0.897891	+	0.723287i	−0.0304064	+	0.0244936i
$873$	24.8238	+	3.77022i	0.840157	+	0.127603i
$874$	7.47860	+	8.03360i	0.252967	+	0.271740i
$875$	−4.62507	−	0.919984i	−0.156356	−	0.0311011i
$876$	32.2008	+	4.76426i	1.08796	+	0.160970i
$877$	−25.6500	−	17.1388i	−0.866138	−	0.578735i	0.0411930	−	0.999151i	$-0.486884\pi$
$877$	−25.6500	−	17.1388i	−0.866138	−	0.578735i	−0.907331	+	0.420416i	$0.861884\pi$
$878$	1.49378	−	6.31958i	0.0504125	−	0.213276i
$879$	−32.2974	−	8.99818i	−1.08937	−	0.303501i
$880$	−62.9202	−	37.3536i	−2.12104	−	1.25919i
$881$	20.7646	−	20.7646i	0.699577	−	0.699577i	−0.264743	−	0.964319i	$-0.585287\pi$
$881$	20.7646	−	20.7646i	0.699577	−	0.699577i	0.964319	+	0.264743i	$0.0852870\pi$
$882$	20.0333	−	0.197522i	0.674555	−	0.00665092i
$883$	26.4159	+	17.6506i	0.888967	+	0.593989i	0.914007	−	0.405698i	$-0.132971\pi$
$883$	26.4159	+	17.6506i	0.888967	+	0.593989i	−0.0250402	+	0.999686i	$0.507971\pi$
$884$	2.51755	+	4.42235i	0.0846742	+	0.148740i
$885$	−2.60011	+	0.853967i	−0.0874018	+	0.0287058i
$886$	0.843601	−	23.5788i	0.0283413	−	0.792145i
$887$	31.0310	−	12.8535i	1.04192	−	0.431578i	0.204919	−	0.978779i	$-0.434307\pi$
$887$	31.0310	−	12.8535i	1.04192	−	0.431578i	0.837001	+	0.547201i	$0.184307\pi$
$888$	34.1252	+	22.1317i	1.14517	+	0.742691i
$889$	23.0970	+	9.56708i	0.774647	+	0.320869i
$890$	21.3654	+	9.75886i	0.716169	+	0.327118i
$891$	−25.4332	+	46.7991i	−0.852044	+	1.56783i
$892$	−12.2212	−	36.7343i	−0.409196	−	1.22995i
$893$	0.157394	+	0.791274i	0.00526699	+	0.0264790i
$894$	1.79491	−	16.0854i	0.0600308	−	0.537977i
$895$			33.9393i			1.13446i
$896$	38.6790	+	2.09028i	1.29217	+	0.0698314i
$897$	17.3903	−	9.81173i	0.580646	−	0.327604i
$898$	−14.7433	+	20.4428i	−0.491989	+	0.682183i
$899$	−0.759266	+	0.151027i	−0.0253229	+	0.00503705i
$900$	6.02350	−	26.6543i	0.200783	−	0.888476i
$901$	0.201553	+	0.301645i	0.00671469	+	0.0100492i
$902$	−22.9734	+	50.2964i	−0.764932	+	1.67469i
$903$	47.8998	−	5.82364i	1.59401	−	0.193799i
$904$	16.9736	+	32.4635i	0.564532	+	1.07972i
$905$	−15.6727	−	37.8372i	−0.520978	−	1.25775i
$906$	14.4322	−	7.47546i	0.479476	−	0.248356i
$907$	25.2579	+	5.02410i	0.838673	+	0.166822i	0.595696	−	0.803210i	$-0.296876\pi$
$907$	25.2579	+	5.02410i	0.838673	+	0.166822i	0.242977	+	0.970032i	$0.421876\pi$
$908$	−46.3768	+	26.4013i	−1.53907	+	0.876158i
$909$	16.4056	−	7.68980i	0.544139	−	0.255055i
$910$	−11.5217	−	18.6546i	−0.381942	−	0.618394i
$911$	21.2408	+	21.2408i	0.703738	+	0.703738i	0.965211	−	0.261472i	$-0.0842081\pi$
$911$	21.2408	+	21.2408i	0.703738	+	0.703738i	−0.261472	+	0.965211i	$0.584208\pi$
$912$	−4.72398	−	4.93719i	−0.156427	−	0.163487i
$913$	48.3679	−	48.3679i	1.60074	−	1.60074i
$914$	−2.02816	−	0.479401i	−0.0670856	−	0.0158572i
$915$	0.935547	−	12.3902i	0.0309282	−	0.409609i
$916$	15.8426	+	12.3101i	0.523453	+	0.406736i
$917$	−8.78937	+	44.1872i	−0.290251	+	1.45919i
$918$	−9.59589	+	8.41444i	−0.316712	+	0.277718i
$919$	36.7276	−	15.2131i	1.21153	−	0.501833i	0.316823	−	0.948485i	$-0.397384\pi$
$919$	36.7276	−	15.2131i	1.21153	−	0.501833i	0.894708	+	0.446652i	$0.147384\pi$
$920$	−53.5761	+	43.1577i	−1.76635	+	1.42287i
$921$	17.5966	−	2.13939i	0.579827	−	0.0704951i
$922$	5.42934	+	14.5594i	0.178806	+	0.479488i
$923$	−5.22383	+	3.49045i	−0.171944	+	0.114890i
$924$	−30.0342	−	63.4407i	−0.988051	−	2.08704i
$925$	7.37690	+	37.0862i	0.242551	+	1.21939i
$926$	10.8235	−	1.75322i	0.355684	−	0.0576143i
$927$	14.1503	−	23.4239i	0.464758	−	0.769343i
$928$	−4.12821	+	0.896681i	−0.135515	+	0.0294350i
$929$	31.1181			1.02095			0.510475	−	0.859892i	$-0.329470\pi$
$929$	31.1181			1.02095			0.510475	+	0.859892i	$0.329470\pi$
$930$	6.13113	−	4.90019i	0.201048	−	0.160684i
$931$	4.56784	−	0.908599i	0.149705	−	0.0297781i
$932$	−30.7777	−	35.5283i	−1.00816	−	1.16377i
$933$	3.81804	−	7.55253i	0.124997	−	0.247259i
$934$	−13.5231	−	36.2637i	−0.442489	−	1.18659i
$935$	−12.1583	+	29.3526i	−0.397617	+	0.959933i
$936$	−10.7419	+	6.25616i	−0.351110	+	0.204489i
$937$	5.39785	+	13.0316i	0.176340	+	0.425723i	0.987194	−	0.159527i	$-0.0509968\pi$
$937$	5.39785	+	13.0316i	0.176340	+	0.425723i	−0.810854	+	0.585249i	$0.800997\pi$
$938$	0.333573	+	0.358328i	0.0108916	+	0.0116998i
$939$	7.40159	−	2.43094i	0.241542	−	0.0793307i
$940$	−5.01756	+	0.629586i	−0.163655	+	0.0205348i
$941$	32.0205	−	47.9221i	1.04384	−	1.56221i	0.236940	−	0.971524i	$-0.423856\pi$
$941$	32.0205	−	47.9221i	1.04384	−	1.56221i	0.806898	−	0.590690i	$-0.201144\pi$
$942$	10.6847	+	36.9384i	0.348127	+	1.20352i
$943$	36.7610	+	36.7610i	1.19710	+	1.19710i
$944$	−1.92808	−	0.680732i	−0.0627536	−	0.0221559i
$945$	40.0232	−	37.7106i	1.30195	−	1.22672i
$946$	−35.7865	−	57.9412i	−1.16352	−	1.88383i
$947$	27.4825	−	41.1305i	0.893062	−	1.33656i	−0.0481837	−	0.998838i	$-0.515343\pi$
$947$	27.4825	−	41.1305i	0.893062	−	1.33656i	0.941246	−	0.337723i	$-0.109657\pi$
$948$	48.0801	−	12.0625i	1.56157	−	0.391772i
$949$	2.68566	−	13.5017i	0.0871804	−	0.438285i
$950$	0.227135	−	6.34847i	0.00736924	−	0.205971i
$951$	−19.1504	−	14.9986i	−0.620995	−	0.486363i
$952$	−1.49591	−	16.7520i	−0.0484828	−	0.542934i
$953$	12.4807	−	30.1312i	0.404291	−	0.976045i	−0.582321	−	0.812959i	$-0.697855\pi$
$953$	12.4807	−	30.1312i	0.404291	−	0.976045i	0.986612	−	0.163086i	$-0.0521448\pi$
$954$	−0.731978	+	0.499601i	−0.0236987	+	0.0161752i
$955$	4.03269	−	2.69455i	0.130495	−	0.0871937i
$956$	−36.9088	−	18.4810i	−1.19372	−	0.597719i
$957$	4.98999	+	5.80509i	0.161304	+	0.187652i
$958$	3.95047	−	5.47765i	0.127634	−	0.176975i
$959$	4.18103			0.135013
$960$	32.9835	−	27.3228i	1.06454	−	0.881841i
$961$	−29.9254			−0.965336
$962$	10.0618	−	13.9515i	0.324404	−	0.449813i
$963$	−10.0938	+	27.9050i	−0.325267	+	0.899225i
$964$	4.90531	−	9.79649i	0.157989	−	0.315524i
$965$	29.8716	−	19.9596i	0.961601	−	0.642521i
$966$	−65.7538	+	5.61735i	−2.11559	+	0.180735i
$967$	−4.31230	+	10.4108i	−0.138674	+	0.334789i	−0.977925	−	0.208955i	$-0.932994\pi$
$967$	−4.31230	+	10.4108i	−0.138674	+	0.334789i	0.839251	+	0.543744i	$0.182994\pi$
$968$	−43.5853	+	52.1327i	−1.40089	+	1.67561i
$969$	−1.82938	+	2.33578i	−0.0587682	+	0.0750360i
$970$	−1.30814	+	36.5626i	−0.0420017	+	1.17396i
$971$	−1.02982	+	5.17724i	−0.0330484	+	0.166146i	−0.993785	−	0.111316i	$-0.964493\pi$
$971$	−1.02982	+	5.17724i	−0.0330484	+	0.166146i	0.960737	+	0.277462i	$0.0894933\pi$
$972$	−20.7852	−	23.2374i	−0.666686	−	0.745339i
$973$	24.8689	−	37.2190i	0.797262	−	1.19319i
$974$	14.3005	+	23.1537i	0.458219	+	0.741892i
$975$	−11.1326	−	3.10158i	−0.356529	−	0.0993302i
$976$	6.20540	−	6.90482i	0.198630	−	0.221018i
$977$	−16.9920	−	16.9920i	−0.543623	−	0.543623i	0.380966	−	0.924589i	$-0.375591\pi$
$977$	−16.9920	−	16.9920i	−0.543623	−	0.543623i	−0.924589	+	0.380966i	$0.875591\pi$
$978$	−41.5616	+	12.0220i	−1.32899	+	0.384421i
$979$	17.6672	−	26.4408i	0.564645	−	0.845051i
$980$	3.63445	+	28.9652i	0.116098	+	0.925259i
$981$	−0.824395	+	0.903269i	−0.0263209	+	0.0288392i
$982$	−12.0335	−	12.9265i	−0.384003	−	0.412500i
$983$	15.5086	+	37.4410i	0.494647	+	1.19418i	0.952331	+	0.305068i	$0.0986791\pi$
$983$	15.5086	+	37.4410i	0.494647	+	1.19418i	−0.457684	+	0.889115i	$0.651321\pi$
$984$	−23.1975	−	22.5705i	−0.739508	−	0.719521i
$985$	−0.0305517	+	0.0737584i	−0.000973459	+	0.00235014i
$986$	0.640891	+	1.71863i	0.0204101	+	0.0547322i
$987$	−4.32910	−	2.18849i	−0.137797	−	0.0696605i
$988$	−2.18420	+	1.89214i	−0.0694887	+	0.0601970i
$989$	−62.7988	+	12.4915i	−1.99689	+	0.397205i
$990$	−71.9929	−	28.9922i	−2.28809	−	0.921433i
$991$	49.7500			1.58036			0.790180	−	0.612875i	$-0.209987\pi$
$991$	49.7500			1.58036			0.790180	+	0.612875i	$0.209987\pi$
$992$	5.86314	−	0.102827i	0.186155	−	0.00326477i
$993$	−35.5113	+	20.0357i	−1.12692	+	0.635814i
$994$	20.4974	−	3.32021i	0.650139	−	0.105311i
$995$	9.47768	+	47.6475i	0.300463	+	1.51053i
$996$	17.1321	+	36.1878i	0.542851	+	1.14665i
$997$	21.3541	−	14.2684i	0.676291	−	0.451883i	−0.169406	−	0.985546i	$-0.554185\pi$
$997$	21.3541	−	14.2684i	0.676291	−	0.451883i	0.845697	+	0.533663i	$0.179185\pi$
$998$	3.57381	+	9.58359i	0.113127	+	0.303363i
$999$	39.3484	+	17.6872i	1.24493	+	0.559599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.11.6	✓	240
3.2	odd	2	inner	192.2.s.a.11.25	yes	240
4.3	odd	2		768.2.s.a.719.7		240
12.11	even	2		768.2.s.a.719.28		240
64.29	even	16		768.2.s.a.47.28		240
64.35	odd	16	inner	192.2.s.a.35.25	yes	240
192.29	odd	16		768.2.s.a.47.7		240
192.35	even	16	inner	192.2.s.a.35.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.11.6	✓	240	1.1	even	1	trivial
192.2.s.a.11.25	yes	240	3.2	odd	2	inner
192.2.s.a.35.6	yes	240	192.35	even	16	inner
192.2.s.a.35.25	yes	240	64.35	odd	16	inner
768.2.s.a.47.7		240	192.29	odd	16
768.2.s.a.47.28		240	64.29	even	16
768.2.s.a.719.7		240	4.3	odd	2
768.2.s.a.719.28		240	12.11	even	2

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14703 - 0.827236i) q^{2} +(1.31348 - 1.12905i) q^{3} +(0.631361 + 1.89773i) q^{4} +(-2.57009 + 1.71728i) q^{5} +(-2.44060 + 0.208501i) q^{6} +(1.31022 - 3.16314i) q^{7} +(0.845681 - 2.69904i) q^{8} +(0.450472 - 2.96599i) q^{9} +O(q^{10})\)	\(q+(-1.14703 - 0.827236i) q^{2} +(1.31348 - 1.12905i) q^{3} +(0.631361 + 1.89773i) q^{4} +(-2.57009 + 1.71728i) q^{5} +(-2.44060 + 0.208501i) q^{6} +(1.31022 - 3.16314i) q^{7} +(0.845681 - 2.69904i) q^{8} +(0.450472 - 2.96599i) q^{9} +(4.36857 + 0.156298i) q^{10} +(1.15458 - 5.80445i) q^{11} +(2.97192 + 1.77980i) q^{12} +(0.813910 - 1.21810i) q^{13} +(-4.11952 + 2.54436i) q^{14} +(-1.43687 + 5.15739i) q^{15} +(-3.20277 + 2.39631i) q^{16} +(1.22808 + 1.22808i) q^{17} +(-2.97028 + 3.02943i) q^{18} +(-0.547947 + 0.820061i) q^{19} +(-4.88159 - 3.79312i) q^{20} +(-1.85041 - 5.63403i) q^{21} +(-6.12599 + 5.70278i) q^{22} +(3.01135 + 7.27003i) q^{23} +(-1.93658 - 4.49996i) q^{24} +(1.74290 - 4.20772i) q^{25} +(-1.94124 + 0.723906i) q^{26} +(-2.75707 - 4.40438i) q^{27} +(6.83001 + 0.489354i) q^{28} +(-0.732439 + 0.145691i) q^{29} +(5.91451 - 4.72706i) q^{30} +1.03663 q^{31} +(5.65598 - 0.0991941i) q^{32} +(-5.03703 - 8.92763i) q^{33} +(-0.392734 - 2.42456i) q^{34} +(2.06462 + 10.3796i) q^{35} +(5.91306 - 1.01773i) q^{36} +(-6.90324 + 4.61260i) q^{37} +(1.30690 - 0.487354i) q^{38} +(-0.306248 - 2.51891i) q^{39} +(2.46153 + 8.38905i) q^{40} +(6.10375 - 2.52826i) q^{41} +(-2.53820 + 7.99314i) q^{42} +(-1.58742 + 7.98050i) q^{43} +(11.7442 - 1.47363i) q^{44} +(3.93567 + 8.39644i) q^{45} +(2.55993 - 10.8301i) q^{46} +(0.578413 - 0.578413i) q^{47} +(-1.50122 + 6.76360i) q^{48} +(-3.33904 - 3.33904i) q^{49} +(-5.47994 + 3.38460i) q^{50} +(2.99963 + 0.226493i) q^{51} +(2.82550 + 0.775520i) q^{52} +(0.204871 + 0.0407514i) q^{53} +(-0.481012 + 7.33271i) q^{54} +(7.00050 + 16.9007i) q^{55} +(-7.42942 - 6.21133i) q^{56} +(0.206175 + 1.69580i) q^{57} +(0.960652 + 0.438788i) q^{58} +(0.283996 + 0.425031i) q^{59} +(-10.6945 + 0.529387i) q^{60} +(-2.27628 + 0.452780i) q^{61} +(-1.18904 - 0.857535i) q^{62} +(-8.79161 - 5.31099i) q^{63} +(-6.56965 - 4.56506i) q^{64} +4.52834i q^{65} +(-1.60763 + 14.4071i) q^{66} +(-0.0197253 - 0.0991660i) q^{67} +(-1.55521 + 3.10593i) q^{68} +(12.1636 + 6.14909i) q^{69} +(6.21816 - 13.6136i) q^{70} +(-3.96205 - 1.64114i) q^{71} +(-7.62436 - 3.72412i) q^{72} +(8.68148 - 3.59599i) q^{73} +(11.7339 + 0.419816i) q^{74} +(-2.46148 - 7.49459i) q^{75} +(-1.90221 - 0.522102i) q^{76} +(-16.8476 - 11.2572i) q^{77} +(-1.73245 + 3.14260i) q^{78} +(10.1185 - 10.1185i) q^{79} +(4.11627 - 11.6588i) q^{80} +(-8.59415 - 2.67219i) q^{81} +(-9.09266 - 2.14925i) q^{82} +(9.61018 + 6.42132i) q^{83} +(9.52360 - 7.06869i) q^{84} +(-5.26524 - 1.04732i) q^{85} +(8.42258 - 7.84071i) q^{86} +(-0.797553 + 1.01833i) q^{87} +(-14.6901 - 8.02497i) q^{88} +(4.96427 + 2.05627i) q^{89} +(2.43150 - 12.8867i) q^{90} +(-2.78663 - 4.17049i) q^{91} +(-11.8953 + 10.3047i) q^{92} +(1.36159 - 1.17041i) q^{93} +(-1.14194 + 0.184974i) q^{94} -3.04861i q^{95} +(7.31704 - 6.51620i) q^{96} +8.36948i q^{97} +(1.06781 + 6.59216i) q^{98} +(-16.6958 - 6.03921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more