LMFDB - Embedded newform 804.2.u.a.43.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(43,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 3]))

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

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

chi := DirichletCharacter("804.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.u (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$340$
Relative dimension:	$34$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			43.18
Character	$\chi$	$=$	804.43
Dual form			804.2.u.a.187.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.141967 - 1.40707i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-1.95969 - 0.399514i) q^{4} +(0.394110 + 0.0566645i) q^{5} +(-0.641289 - 1.26046i) q^{6} +(-1.35700 + 2.97142i) q^{7} +(-0.840356 + 2.70070i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.141967 - 1.40707i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-1.95969 - 0.399514i) q^{4} +(0.394110 + 0.0566645i) q^{5} +(-0.641289 - 1.26046i) q^{6} +(-1.35700 + 2.97142i) q^{7} +(-0.840356 + 2.70070i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.135682 - 0.546496i) q^{10} +(-0.554357 + 3.85564i) q^{11} +(-1.86459 + 0.723396i) q^{12} +(-1.49755 + 5.10019i) q^{13} +(3.98835 + 2.33124i) q^{14} +(0.362182 - 0.165403i) q^{15} +(3.68078 + 1.56585i) q^{16} +(3.41778 - 3.94432i) q^{17} +(-1.22094 - 0.713655i) q^{18} +(7.57893 - 3.46118i) q^{19} +(-0.749696 - 0.268498i) q^{20} +(0.464889 + 3.23337i) q^{21} +(5.34645 + 1.32739i) q^{22} +(4.51663 + 7.02801i) q^{23} +(0.753159 + 2.72631i) q^{24} +(-4.64535 - 1.36400i) q^{25} +(6.96372 + 2.83122i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(3.84643 - 5.28093i) q^{28} -0.788224 q^{29} +(-0.181316 - 0.533097i) q^{30} +(-1.41693 + 0.416049i) q^{31} +(2.72581 - 4.95681i) q^{32} +(1.61816 + 3.54328i) q^{33} +(-5.06473 - 5.36901i) q^{34} +(-0.703183 + 1.09417i) q^{35} +(-1.17750 + 1.61663i) q^{36} -7.45763 q^{37} +(-3.79417 - 11.1555i) q^{38} +(1.49755 + 5.10019i) q^{39} +(-0.484227 + 1.01676i) q^{40} +(2.20772 + 1.91300i) q^{41} +(4.61558 - 0.195099i) q^{42} +(-4.15189 + 4.79154i) q^{43} +(2.62675 - 7.33439i) q^{44} +(0.215263 - 0.334956i) q^{45} +(10.5301 - 5.35747i) q^{46} +(-0.0719417 - 0.111943i) q^{47} +(3.94303 - 0.672702i) q^{48} +(-2.40387 - 2.77421i) q^{49} +(-2.57873 + 6.34269i) q^{50} +(0.742754 - 5.16597i) q^{51} +(4.97234 - 9.39651i) q^{52} +(-4.19901 + 3.63846i) q^{53} +(-1.41295 + 0.0597251i) q^{54} +(-0.436956 + 1.48813i) q^{55} +(-6.88457 - 6.16192i) q^{56} +(4.50455 - 7.00921i) q^{57} +(-0.111902 + 1.10909i) q^{58} +(0.471937 + 1.60727i) q^{59} +(-0.775845 + 0.179442i) q^{60} +(7.27409 - 1.04586i) q^{61} +(0.384253 + 2.05279i) q^{62} +(2.13918 + 2.46875i) q^{63} +(-6.58760 - 4.53910i) q^{64} +(-0.879201 + 1.92518i) q^{65} +(5.21536 - 1.77384i) q^{66} +(6.87996 + 4.43466i) q^{67} +(-8.27360 + 6.36420i) q^{68} +(7.59926 + 3.47046i) q^{69} +(1.43975 + 1.14476i) q^{70} +(-7.54441 + 6.53727i) q^{71} +(2.10755 + 1.88633i) q^{72} +(-2.05323 - 14.2805i) q^{73} +(-1.05874 + 10.4934i) q^{74} +(-4.64535 + 1.36400i) q^{75} +(-16.2352 + 3.75495i) q^{76} +(-10.7045 - 6.87934i) q^{77} +(7.38893 - 1.38310i) q^{78} +(8.61277 + 2.52894i) q^{79} +(1.36190 + 0.825687i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(3.00515 - 2.83483i) q^{82} +(8.55062 + 1.22939i) q^{83} +(0.380741 - 6.52214i) q^{84} +(1.57048 - 1.36083i) q^{85} +(6.15260 + 6.52224i) q^{86} +(-0.663096 + 0.426146i) q^{87} +(-9.94708 - 4.73726i) q^{88} +(11.1650 + 7.17534i) q^{89} +(-0.440746 - 0.350443i) q^{90} +(-13.1226 - 11.3708i) q^{91} +(-6.04340 - 15.5772i) q^{92} +(-0.967068 + 1.11606i) q^{93} +(-0.167726 + 0.0853347i) q^{94} +(3.18306 - 0.934631i) q^{95} +(-0.386759 - 5.64362i) q^{96} -8.01040i q^{97} +(-4.24478 + 2.98857i) q^{98} +(3.27692 + 2.10595i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 340 q - 34 q^{3} - 2 q^{4} + 11 q^{6} - 4 q^{7} + 39 q^{8} - 34 q^{9}+O(q^{10}) $ 340 * q - 34 * q^3 - 2 * q^4 + 11 * q^6 - 4 * q^7 + 39 * q^8 - 34 * q^9	$ 340 q - 34 q^{3} - 2 q^{4} + 11 q^{6} - 4 q^{7} + 39 q^{8} - 34 q^{9} - 27 q^{10} + 9 q^{12} + 4 q^{14} - 2 q^{16} + 12 q^{20} - 4 q^{21} - 3 q^{22} + 6 q^{24} + 34 q^{25} - 10 q^{26} - 34 q^{27} - 25 q^{28} + 16 q^{29} + 6 q^{30} + 4 q^{31} - 55 q^{32} + 9 q^{36} - 12 q^{37} - 26 q^{38} - 37 q^{40} + 4 q^{42} + 4 q^{43} + 51 q^{44} + 81 q^{46} - 2 q^{48} - 46 q^{49} - 15 q^{50} - 32 q^{52} - 14 q^{56} + 66 q^{57} - 92 q^{58} - 43 q^{60} + 2 q^{62} + 18 q^{63} + 7 q^{64} + 8 q^{66} + 18 q^{67} - 208 q^{68} - 56 q^{70} + 6 q^{72} + 54 q^{73} - 22 q^{74} + 34 q^{75} + 120 q^{76} + 8 q^{77} - 10 q^{78} - 10 q^{79} + 68 q^{80} - 34 q^{81} + 84 q^{82} + 8 q^{84} + 104 q^{86} + 16 q^{87} + 138 q^{88} - 27 q^{90} - 42 q^{92} + 4 q^{93} - 32 q^{94} + 40 q^{95} + 7 q^{98}+O(q^{100}) $ 340 * q - 34 * q^3 - 2 * q^4 + 11 * q^6 - 4 * q^7 + 39 * q^8 - 34 * q^9 - 27 * q^10 + 9 * q^12 + 4 * q^14 - 2 * q^16 + 12 * q^20 - 4 * q^21 - 3 * q^22 + 6 * q^24 + 34 * q^25 - 10 * q^26 - 34 * q^27 - 25 * q^28 + 16 * q^29 + 6 * q^30 + 4 * q^31 - 55 * q^32 + 9 * q^36 - 12 * q^37 - 26 * q^38 - 37 * q^40 + 4 * q^42 + 4 * q^43 + 51 * q^44 + 81 * q^46 - 2 * q^48 - 46 * q^49 - 15 * q^50 - 32 * q^52 - 14 * q^56 + 66 * q^57 - 92 * q^58 - 43 * q^60 + 2 * q^62 + 18 * q^63 + 7 * q^64 + 8 * q^66 + 18 * q^67 - 208 * q^68 - 56 * q^70 + 6 * q^72 + 54 * q^73 - 22 * q^74 + 34 * q^75 + 120 * q^76 + 8 * q^77 - 10 * q^78 - 10 * q^79 + 68 * q^80 - 34 * q^81 + 84 * q^82 + 8 * q^84 + 104 * q^86 + 16 * q^87 + 138 * q^88 - 27 * q^90 - 42 * q^92 + 4 * q^93 - 32 * q^94 + 40 * q^95 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$-1$

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 $

$2$	0.141967	−	1.40707i	0.100386	−	0.994949i
$2$	0.141967	−	1.40707i	0.100386	−	0.994949i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	−1.95969	−	0.399514i	−0.979845	−	0.199757i
$5$	0.394110	+	0.0566645i	0.176252	+	0.0253411i	0.229875	−	0.973220i	$-0.426168\pi$
$5$	0.394110	+	0.0566645i	0.176252	+	0.0253411i	−0.0536239	+	0.998561i	$0.517077\pi$
$6$	−0.641289	−	1.26046i	−0.261805	−	0.514579i
$7$	−1.35700	+	2.97142i	−0.512899	+	1.12309i	0.459160	+	0.888354i	$0.348151\pi$
$7$	−1.35700	+	2.97142i	−0.512899	+	1.12309i	−0.972059	+	0.234738i	$0.924577\pi$
$8$	−0.840356	+	2.70070i	−0.297111	+	0.954843i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	0.135682	−	0.546496i	0.0429063	−	0.172817i
$11$	−0.554357	+	3.85564i	−0.167145	+	1.16252i	0.717604	+	0.696451i	$0.245239\pi$
$11$	−0.554357	+	3.85564i	−0.167145	+	1.16252i	−0.884749	+	0.466068i	$0.845670\pi$
$12$	−1.86459	+	0.723396i	−0.538261	+	0.208826i
$13$	−1.49755	+	5.10019i	−0.415346	+	1.41454i	0.440707	+	0.897651i	$0.354728\pi$
$13$	−1.49755	+	5.10019i	−0.415346	+	1.41454i	−0.856053	+	0.516888i	$0.827090\pi$
$14$	3.98835	+	2.33124i	1.06593	+	0.623051i
$15$	0.362182	−	0.165403i	0.0935150	−	0.0427068i
$16$	3.68078	+	1.56585i	0.920194	+	0.391462i
$17$	3.41778	−	3.94432i	0.828932	−	0.956639i	−0.170656	−	0.985331i	$-0.554589\pi$
$17$	3.41778	−	3.94432i	0.828932	−	0.956639i	0.999588	+	0.0286917i	$0.00913411\pi$
$18$	−1.22094	−	0.713655i	−0.287778	−	0.168210i
$19$	7.57893	−	3.46118i	1.73873	−	0.794049i	0.747129	−	0.664679i	$-0.231432\pi$
$19$	7.57893	−	3.46118i	1.73873	−	0.794049i	0.991596	−	0.129371i	$-0.0412957\pi$
$20$	−0.749696	−	0.268498i	−0.167637	−	0.0600379i
$21$	0.464889	+	3.23337i	0.101447	+	0.705579i
$22$	5.34645	+	1.32739i	1.13987	+	0.283001i
$23$	4.51663	+	7.02801i	0.941782	+	1.46544i	0.884204	+	0.467100i	$0.154701\pi$
$23$	4.51663	+	7.02801i	0.941782	+	1.46544i	0.0575775	+	0.998341i	$0.481662\pi$
$24$	0.753159	+	2.72631i	0.153738	+	0.556505i
$25$	−4.64535	−	1.36400i	−0.929071	−	0.272800i
$26$	6.96372	+	2.83122i	1.36570	+	0.555247i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	3.84643	−	5.28093i	0.726908	−	0.998002i
$29$	−0.788224			−0.146369			−0.0731847	−	0.997318i	$-0.523316\pi$
$29$	−0.788224			−0.146369			−0.0731847	+	0.997318i	$0.523316\pi$
$30$	−0.181316	−	0.533097i	−0.0331036	−	0.0973297i
$31$	−1.41693	+	0.416049i	−0.254489	+	0.0747247i	−0.406489	−	0.913656i	$-0.633247\pi$
$31$	−1.41693	+	0.416049i	−0.254489	+	0.0747247i	0.152000	+	0.988381i	$0.451429\pi$
$32$	2.72581	−	4.95681i	0.481859	−	0.876249i
$33$	1.61816	+	3.54328i	0.281686	+	0.616806i
$34$	−5.06473	−	5.36901i	−0.868594	−	0.920778i
$35$	−0.703183	+	1.09417i	−0.118860	+	0.184949i
$36$	−1.17750	+	1.61663i	−0.196249	+	0.269439i
$37$	−7.45763			−1.22603			−0.613013	−	0.790073i	$-0.710043\pi$
$37$	−7.45763			−1.22603			−0.613013	+	0.790073i	$0.710043\pi$
$38$	−3.79417	−	11.1555i	−0.615495	−	1.80965i
$39$	1.49755	+	5.10019i	0.239800	+	0.816684i
$40$	−0.484227	+	1.01676i	−0.0765630	+	0.160763i
$41$	2.20772	+	1.91300i	0.344788	+	0.298761i	0.809990	−	0.586444i	$-0.199473\pi$
$41$	2.20772	+	1.91300i	0.344788	+	0.298761i	−0.465202	+	0.885205i	$0.654018\pi$
$42$	4.61558	−	0.195099i	0.712199	−	0.0301045i
$43$	−4.15189	+	4.79154i	−0.633157	+	0.730702i	−0.978149	−	0.207903i	$-0.933336\pi$
$43$	−4.15189	+	4.79154i	−0.633157	+	0.730702i	0.344992	+	0.938606i	$0.387882\pi$
$44$	2.62675	−	7.33439i	0.395998	−	1.10570i
$45$	0.215263	−	0.334956i	0.0320895	−	0.0499323i
$46$	10.5301	−	5.35747i	1.55258	−	0.789915i
$47$	−0.0719417	−	0.111943i	−0.0104938	−	0.0163286i	0.835967	−	0.548780i	$-0.184907\pi$
$47$	−0.0719417	−	0.111943i	−0.0104938	−	0.0163286i	−0.846461	+	0.532451i	$0.821271\pi$
$48$	3.94303	−	0.672702i	0.569127	−	0.0970961i
$49$	−2.40387	−	2.77421i	−0.343410	−	0.396316i
$50$	−2.57873	+	6.34269i	−0.364687	+	0.896992i
$51$	0.742754	−	5.16597i	0.104006	−	0.723380i
$52$	4.97234	−	9.39651i	0.689539	−	1.30306i
$53$	−4.19901	+	3.63846i	−0.576778	+	0.499781i	−0.893697	−	0.448672i	$-0.851897\pi$
$53$	−4.19901	+	3.63846i	−0.576778	+	0.499781i	0.316918	+	0.948453i	$0.397352\pi$
$54$	−1.41295	+	0.0597251i	−0.192278	+	0.00812756i
$55$	−0.436956	+	1.48813i	−0.0589191	+	0.200660i
$56$	−6.88457	−	6.16192i	−0.919989	−	0.823421i
$57$	4.50455	−	7.00921i	0.596642	−	0.928392i
$58$	−0.111902	+	1.10909i	−0.0146934	+	0.145630i
$59$	0.471937	+	1.60727i	0.0614410	+	0.209249i	0.984492	−	0.175428i	$-0.0561310\pi$
$59$	0.471937	+	1.60727i	0.0614410	+	0.209249i	−0.923051	+	0.384677i	$0.874313\pi$
$60$	−0.775845	+	0.179442i	−0.100161	+	0.0231658i
$61$	7.27409	−	1.04586i	0.931352	−	0.133908i	0.340095	−	0.940391i	$-0.389541\pi$
$61$	7.27409	−	1.04586i	0.931352	−	0.133908i	0.591257	+	0.806483i	$0.298632\pi$
$62$	0.384253	+	2.05279i	0.0488002	+	0.260705i
$63$	2.13918	+	2.46875i	0.269512	+	0.311033i
$64$	−6.58760	−	4.53910i	−0.823451	−	0.567388i
$65$	−0.879201	+	1.92518i	−0.109051	+	0.238789i
$66$	5.21536	−	1.77384i	0.641967	−	0.218344i
$67$	6.87996	+	4.43466i	0.840520	+	0.541780i
$67$	6.87996	+	4.43466i	0.840520	+	0.541780i
$68$	−8.27360	+	6.36420i	−1.00332	+	0.771773i
$69$	7.59926	+	3.47046i	0.914843	+	0.417795i
$70$	1.43975	+	1.14476i	0.172083	+	0.136826i
$71$	−7.54441	+	6.53727i	−0.895356	+	0.775831i	−0.975281	−	0.220970i	$-0.929078\pi$
$71$	−7.54441	+	6.53727i	−0.895356	+	0.775831i	0.0799241	+	0.996801i	$0.474532\pi$
$72$	2.10755	+	1.88633i	0.248377	+	0.222306i
$73$	−2.05323	−	14.2805i	−0.240312	−	1.67141i	−0.650576	−	0.759441i	$-0.725472\pi$
$73$	−2.05323	−	14.2805i	−0.240312	−	1.67141i	0.410263	−	0.911967i	$-0.365437\pi$
$74$	−1.05874	+	10.4934i	−0.123075	+	1.21983i
$75$	−4.64535	+	1.36400i	−0.536399	+	0.157501i
$76$	−16.2352	+	3.75495i	−1.86230	+	0.430723i
$77$	−10.7045	−	6.87934i	−1.21989	−	0.783974i
$78$	7.38893	−	1.38310i	0.836632	−	0.156605i
$79$	8.61277	+	2.52894i	0.969013	+	0.284528i	0.727682	−	0.685915i	$-0.240598\pi$
$79$	8.61277	+	2.52894i	0.969013	+	0.284528i	0.241331	+	0.970443i	$0.422416\pi$
$80$	1.36190	+	0.825687i	0.152265	+	0.0923146i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	3.00515	−	2.83483i	0.331863	−	0.313055i
$83$	8.55062	+	1.22939i	0.938552	+	0.134943i	0.594580	−	0.804036i	$-0.297318\pi$
$83$	8.55062	+	1.22939i	0.938552	+	0.134943i	0.343972	+	0.938980i	$0.388227\pi$
$84$	0.380741	−	6.52214i	0.0415422	−	0.711624i
$85$	1.57048	−	1.36083i	0.170343	−	0.147603i
$86$	6.15260	+	6.52224i	0.663451	+	0.703311i
$87$	−0.663096	+	0.426146i	−0.0710913	+	0.0456876i
$88$	−9.94708	−	4.73726i	−1.06036	−	0.504994i
$89$	11.1650	+	7.17534i	1.18349	+	0.760584i	0.976025	−	0.217658i	$-0.0698417\pi$
$89$	11.1650	+	7.17534i	1.18349	+	0.760584i	0.207467	+	0.978242i	$0.433478\pi$
$90$	−0.440746	−	0.350443i	−0.0464587	−	0.0369399i
$91$	−13.1226	−	11.3708i	−1.37563	−	1.19199i
$92$	−6.04340	−	15.5772i	−0.630068	−	1.62403i
$93$	−0.967068	+	1.11606i	−0.100280	+	0.115730i
$94$	−0.167726	+	0.0853347i	−0.0172996	+	0.00880161i
$95$	3.18306	−	0.934631i	0.326575	−	0.0958911i
$96$	−0.386759	−	5.64362i	−0.0394734	−	0.575999i
$97$		−	8.01040i		−	0.813333i	−0.913577	−	0.406666i	$-0.866691\pi$
$97$		−	8.01040i		−	0.813333i	0.913577	−	0.406666i	$-0.133309\pi$
$98$	−4.24478	+	2.98857i	−0.428788	+	0.301891i
$99$	3.27692	+	2.10595i	0.329343	+	0.211656i
$100$	8.55852	+	4.52890i	0.855852	+	0.452890i
$101$	2.90292	−	1.32572i	0.288851	−	0.131914i	−0.265720	−	0.964050i	$-0.585610\pi$
$101$	2.90292	−	1.32572i	0.288851	−	0.131914i	0.554571	+	0.832136i	$0.312882\pi$
$102$	−7.16343	−	1.77850i	−0.709285	−	0.176098i
$103$	−2.36835	−	8.06586i	−0.233361	−	0.794753i	−0.990018	−	0.140941i	$-0.954987\pi$
$103$	−2.36835	−	8.06586i	−0.233361	−	0.794753i	0.756657	−	0.653812i	$-0.226831\pi$
$104$	−12.5156	−	8.33042i	−1.22726	−	0.816865i
$105$			1.30065i			0.126930i
$106$	4.52345	+	6.42484i	0.439356	+	0.624036i
$107$	−18.1066	+	2.60333i	−1.75043	+	0.251673i	−0.941686	−	0.336492i	$-0.890759\pi$
$107$	−18.1066	+	2.60333i	−1.75043	+	0.251673i	−0.808741	+	0.588165i	$0.799850\pi$
$108$	−0.116555	+	1.99660i	−0.0112155	+	0.192123i
$109$	3.03281	−	10.3288i	0.290491	−	0.989320i	−0.676909	−	0.736066i	$-0.736681\pi$
$109$	3.03281	−	10.3288i	0.290491	−	0.989320i	0.967400	−	0.253254i	$-0.0815008\pi$
$110$	2.03188	+	0.826093i	0.193732	+	0.0787649i
$111$	−6.27375	+	4.03190i	−0.595478	+	0.382691i
$112$	−9.64763	+	8.81228i	−0.911615	+	0.832682i
$113$	−9.02815	+	1.29805i	−0.849297	+	0.122111i	−0.553201	−	0.833048i	$-0.686594\pi$
$113$	−9.02815	+	1.29805i	−0.849297	+	0.122111i	−0.296096	+	0.955158i	$0.595685\pi$
$114$	−9.22295	−	7.33328i	−0.863808	−	0.686825i
$115$	1.38181	+	3.02574i	0.128855	+	0.282152i
$116$	1.54467	+	0.314907i	0.143419	+	0.0292384i
$117$	4.01719	+	3.48092i	0.371390	+	0.321811i
$118$	2.32854	−	0.435870i	0.214360	−	0.0401251i
$119$	7.08232	+	15.5081i	0.649235	+	1.42163i
$120$	0.142343	+	1.11714i	0.0129941	+	0.101981i
$121$	−4.00422	−	1.17574i	−0.364020	−	0.106886i
$122$	−0.438914	−	10.3836i	−0.0397374	−	0.940090i
$123$	2.89150	+	0.415735i	0.260718	+	0.0374855i
$124$	2.94297	−	0.249243i	0.264287	−	0.0223826i
$125$	−3.56440	−	1.62781i	−0.318810	−	0.145596i
$126$	3.77739	−	2.65950i	0.336517	−	0.236927i
$127$	7.57922	+	3.46131i	0.672547	+	0.307142i	0.722260	−	0.691622i	$-0.243103\pi$
$127$	7.57922	+	3.46131i	0.672547	+	0.307142i	−0.0497133	+	0.998764i	$0.515831\pi$
$128$	−7.32206	+	8.62482i	−0.647185	+	0.762333i
$129$	−0.902292	+	6.27558i	−0.0794424	+	0.552534i
$130$	2.58405	+	1.51041i	0.226636	+	0.132472i
$131$	10.1077	+	15.7279i	0.883117	+	1.37416i	0.926977	+	0.375119i	$0.122398\pi$
$131$	10.1077	+	15.7279i	0.883117	+	1.37416i	−0.0438602	+	0.999038i	$0.513966\pi$
$132$	−1.75550	−	7.59021i	−0.152797	−	0.660643i
$133$			27.2170i			2.36002i
$134$	7.21660	−	9.05100i	0.623419	−	0.781888i
$135$		−	0.398163i		−	0.0342684i
$136$	7.78030	+	12.5450i	0.667155	+	1.07573i
$137$	3.46854	+	5.39715i	0.296337	+	0.461110i	0.957213	−	0.289386i	$-0.0934511\pi$
$137$	3.46854	+	5.39715i	0.296337	+	0.461110i	−0.660875	+	0.750496i	$0.729815\pi$
$138$	5.96203	−	10.2000i	0.507522	−	0.868281i
$139$	1.49527	−	10.3998i	0.126827	−	0.882102i	−0.822713	−	0.568457i	$-0.807541\pi$
$139$	1.49527	−	10.3998i	0.126827	−	0.882102i	0.949540	−	0.313645i	$-0.101550\pi$
$140$	1.81516	−	1.86331i	0.153409	−	0.157479i
$141$	−0.121042	−	0.0552782i	−0.0101936	−	0.00465527i
$142$	8.12733	+	11.5436i	0.682031	+	0.968716i
$143$	−18.8343	−	8.60135i	−1.57501	−	0.719281i
$144$	2.95340	−	2.69767i	0.246116	−	0.224806i
$145$	−0.310647	−	0.0446643i	−0.0257978	−	0.00370917i
$146$	−20.3852	+	0.861676i	−1.68709	+	0.0713128i
$147$	−3.52212	−	1.03419i	−0.290499	−	0.0852983i
$148$	14.6146	+	2.97943i	1.20132	+	0.244908i
$149$	−5.22446	−	11.4400i	−0.428004	−	0.937199i	−0.993646	−	0.112548i	$-0.964099\pi$
$149$	−5.22446	−	11.4400i	−0.428004	−	0.937199i	0.565642	−	0.824651i	$-0.308628\pi$
$150$	1.25976	+	6.72998i	0.102859	+	0.549500i
$151$	1.32875	+	1.15137i	0.108132	+	0.0936971i	0.707249	−	0.706965i	$-0.249936\pi$
$151$	1.32875	+	1.15137i	0.108132	+	0.0936971i	−0.599117	+	0.800662i	$0.704481\pi$
$152$	2.97863	+	23.3771i	0.241599	+	1.89613i
$153$	−2.16809	−	4.74745i	−0.175279	−	0.383809i
$154$	−11.1994	+	14.0853i	−0.902473	+	1.13503i
$155$	−0.582004	+	0.0836795i	−0.0467477	+	0.00672130i
$156$	−0.897138	−	10.5931i	−0.0718285	−	0.848126i
$157$	−1.78077	+	1.14443i	−0.142121	+	0.0913354i	−0.609769	−	0.792579i	$-0.708738\pi$
$157$	−1.78077	+	1.14443i	−0.142121	+	0.0913354i	0.467648	+	0.883915i	$0.345101\pi$
$158$	4.78112	−	11.7597i	0.380366	−	0.935555i
$159$	−1.56533	+	5.33103i	−0.124139	+	0.422778i
$160$	1.35514	−	1.79907i	0.107134	−	0.142229i
$161$	−27.0123	+	3.88378i	−2.12886	+	0.306085i
$162$	−1.15636	+	0.814143i	−0.0908523	+	0.0639651i
$163$		−	19.4963i		−	1.52707i	−0.645766	−	0.763536i	$-0.723462\pi$
$163$		−	19.4963i		−	1.52707i	0.645766	−	0.763536i	$-0.276538\pi$
$164$	−3.56218	−	4.63091i	−0.278159	−	0.361613i
$165$	0.436956	+	1.48813i	0.0340170	+	0.115851i
$166$	2.94375	−	11.8568i	0.228479	−	0.920265i
$167$	8.49559	−	3.87981i	0.657409	−	0.300228i	−0.0586396	−	0.998279i	$-0.518676\pi$
$167$	8.49559	−	3.87981i	0.657409	−	0.300228i	0.716048	+	0.698051i	$0.245949\pi$
$168$	−9.12305	−	1.46166i	−0.703859	−	0.112769i
$169$	−12.8330	−	8.24727i	−0.987154	−	0.634406i
$170$	−1.69183	−	2.40297i	−0.129757	−	0.184300i
$171$		−	8.33186i		−	0.637154i
$172$	10.0507	−	7.73119i	0.766359	−	0.589498i
$173$	11.4342	−	3.35738i	0.869325	−	0.255257i	0.183497	−	0.983020i	$-0.441258\pi$
$173$	11.4342	−	3.35738i	0.869325	−	0.255257i	0.685828	+	0.727764i	$0.259440\pi$
$174$	0.505479	+	0.993521i	0.0383203	+	0.0753186i
$175$	10.3568	−	11.9524i	0.782899	−	0.903513i
$176$	−8.07782	+	13.3237i	−0.608888	+	1.00431i
$177$	1.26598	+	1.09697i	0.0951565	+	0.0824536i
$178$	11.6813	−	14.6913i	0.875548	−	1.10116i
$179$	10.0084	+	6.43201i	0.748064	+	0.480751i	0.858296	−	0.513155i	$-0.171523\pi$
$179$	10.0084	+	6.43201i	0.748064	+	0.480751i	−0.110233	+	0.993906i	$0.535160\pi$
$180$	−0.555669	+	0.570410i	−0.0414171	+	0.0425158i
$181$	7.67268	−	4.93093i	0.570306	−	0.366513i	−0.223482	−	0.974708i	$-0.571742\pi$
$181$	7.67268	−	4.93093i	0.570306	−	0.366513i	0.793788	+	0.608195i	$0.208106\pi$
$182$	−17.8625	+	16.8502i	−1.32406	+	1.24902i
$183$	5.55392	−	4.81250i	0.410558	−	0.355750i
$184$	−22.7761	+	6.29205i	−1.67908	+	0.463856i
$185$	−2.93913	−	0.422583i	−0.216089	−	0.0310689i
$186$	1.43308	+	1.51917i	0.105078	+	0.111391i
$187$	13.3132	+	15.3643i	0.973559	+	1.12355i
$188$	0.0962605	+	0.248116i	0.00702052	+	0.0180957i
$189$	3.13430	+	0.920313i	0.227987	+	0.0669430i
$190$	−0.863202	−	4.61147i	−0.0626233	−	0.334552i
$191$	−1.54101	−	0.990345i	−0.111503	−	0.0716588i	0.483701	−	0.875234i	$-0.339292\pi$
$191$	−1.54101	−	0.990345i	−0.111503	−	0.0716588i	−0.595204	+	0.803575i	$0.702929\pi$
$192$	−7.99587	−	0.257010i	−0.577052	−	0.0185481i
$193$	−22.4945	+	6.60499i	−1.61919	+	0.475438i	−0.960801	−	0.277238i	$-0.910581\pi$
$193$	−22.4945	+	6.60499i	−1.61919	+	0.475438i	−0.658391	+	0.752676i	$0.728763\pi$
$194$	−11.2712	−	1.13721i	−0.809224	−	0.0816470i
$195$	0.301201	+	2.09490i	0.0215694	+	0.150019i
$196$	3.60250	+	6.39698i	0.257322	+	0.456927i
$197$	10.4987	−	9.09716i	0.748000	−	0.648146i	−0.195051	−	0.980793i	$-0.562487\pi$
$197$	10.4987	−	9.09716i	0.748000	−	0.648146i	0.943051	+	0.332647i	$0.107942\pi$
$198$	3.42844	−	4.31189i	0.243648	−	0.306432i
$199$	−23.5339	−	10.7476i	−1.66827	−	0.761875i	−0.999836	−	0.0181074i	$-0.994236\pi$
$199$	−23.5339	−	10.7476i	−1.66827	−	0.761875i	−0.668438	−	0.743768i	$-0.733037\pi$
$200$	7.58751	−	11.3995i	0.536518	−	0.806065i
$201$	8.18535	+	0.0110887i	0.577350	+	0.000782134i
$202$	−1.45326	−	4.27282i	−0.102251	−	0.300634i
$203$	1.06962	−	2.34215i	0.0750727	−	0.164386i
$204$	−3.51945	+	9.82695i	−0.246410	+	0.688024i
$205$	0.761686	+	0.879033i	0.0531985	+	0.0613943i
$206$	−11.6855	+	2.18735i	−0.814164	+	0.152400i
$207$	8.26918	−	1.18893i	0.574748	−	0.0826362i
$208$	−13.4983	+	16.4277i	−0.935938	+	1.13906i
$209$	9.14363	+	31.1403i	0.632478	+	2.15402i
$210$	1.83010	+	0.184649i	0.126289	+	0.0127420i
$211$	1.45400	−	2.26247i	0.100098	−	0.155755i	−0.787592	−	0.616197i	$-0.788673\pi$
$211$	1.45400	−	2.26247i	0.100098	−	0.155755i	0.887690	+	0.460442i	$0.152309\pi$
$212$	9.68238	−	5.45270i	0.664989	−	0.374493i
$213$	−2.81245	+	9.57831i	−0.192706	+	0.656295i
$214$	1.09254	+	25.8468i	0.0746843	+	1.76685i
$215$	−1.90781	+	1.65313i	−0.130112	+	0.112742i
$216$	2.79281	+	0.447452i	0.190027	+	0.0304452i
$217$	0.686526	−	4.77489i	0.0466044	−	0.324141i
$218$	−14.1028	−	5.73372i	−0.955162	−	0.388337i
$219$	−9.44792	−	10.9035i	−0.638431	−	0.736789i
$220$	1.45083	−	2.74171i	0.0978149	−	0.184846i
$221$	14.9985	+	23.3381i	1.00891	+	1.56989i
$222$	4.78250	+	9.40001i	0.320980	+	0.630887i
$223$	7.66560	−	11.9279i	0.513327	−	0.798752i	−0.483746	−	0.875208i	$-0.660724\pi$
$223$	7.66560	−	11.9279i	0.513327	−	0.798752i	0.997073	+	0.0764563i	$0.0243606\pi$
$224$	11.0299	+	14.8259i	0.736963	+	0.990600i
$225$	−3.17049	+	3.65894i	−0.211366	+	0.243929i
$226$	0.544752	+	12.8875i	0.0362364	+	0.857265i
$227$	−5.95177	−	5.15724i	−0.395033	−	0.342298i	0.434584	−	0.900631i	$-0.356896\pi$
$227$	−5.95177	−	5.15724i	−0.395033	−	0.342298i	−0.829617	+	0.558333i	$0.811441\pi$
$228$	−11.6278	+	11.9363i	−0.770070	+	0.790498i
$229$	0.497563	+	1.69454i	0.0328799	+	0.111979i	0.974298	−	0.225263i	$-0.0723242\pi$
$229$	0.497563	+	1.69454i	0.0328799	+	0.111979i	−0.941418	+	0.337242i	$0.890506\pi$
$230$	4.45360	−	1.51475i	0.293662	−	0.0998796i
$231$	−12.7244			−0.837206
$232$	0.662388	−	2.12876i	0.0434879	−	0.139760i
$233$	−11.7432	+	18.2727i	−0.769320	+	1.19709i	0.206486	+	0.978449i	$0.433797\pi$
$233$	−11.7432	+	18.2727i	−0.769320	+	1.19709i	−0.975807	+	0.218636i	$0.929839\pi$
$234$	5.46820	−	5.15830i	0.357468	−	0.337208i
$235$	−0.0220097	−	0.0481946i	−0.00143576	−	0.00314387i
$236$	−0.282723	−	3.33830i	−0.0184037	−	0.217305i
$237$	8.61277	−	2.52894i	0.559460	−	0.164272i
$238$	22.8265	−	7.76368i	1.47962	−	0.503245i
$239$	−19.5666			−1.26566			−0.632829	−	0.774291i	$-0.718106\pi$
$239$	−19.5666			−1.26566			−0.632829	+	0.774291i	$0.718106\pi$
$240$	1.59211	−	0.0416889i	0.102770	−	0.00269100i
$241$	0.784797	+	5.45838i	0.0505532	+	0.351605i	0.999361	+	0.0357504i	$0.0113821\pi$
$241$	0.784797	+	5.45838i	0.0505532	+	0.351605i	−0.948808	+	0.315855i	$0.897709\pi$
$242$	−2.22282	+	5.46730i	−0.142888	+	0.351451i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	−14.6728	−	0.856549i	−0.939330	−	0.0548350i
$245$	−0.790191	−	1.22956i	−0.0504834	−	0.0785538i
$246$	0.995465	−	4.00952i	0.0634685	−	0.255638i
$247$	6.30285	+	43.8373i	0.401041	+	2.78930i
$248$	0.0671024	−	4.17635i	0.00426101	−	0.265198i
$249$	7.85790	−	3.58858i	0.497974	−	0.227417i
$250$	−2.79646	+	4.78427i	−0.176864	+	0.302584i
$251$	2.46114	−	2.84031i	0.155346	−	0.179279i	−0.672742	−	0.739877i	$-0.734883\pi$
$251$	2.46114	−	2.84031i	0.155346	−	0.179279i	0.828088	+	0.560599i	$0.189429\pi$
$252$	−3.20583	−	5.69262i	−0.201949	−	0.358601i
$253$	−29.6013	+	13.5185i	−1.86102	+	0.849898i
$254$	5.94630	−	10.1731i	0.373104	−	0.638317i
$255$	0.585454	−	1.99387i	0.0366625	−	0.124861i
$256$	11.0962	+	11.5271i	0.693514	+	0.720443i
$257$	2.98994	−	20.7955i	0.186508	−	1.29719i	−0.654457	−	0.756099i	$-0.727103\pi$
$257$	2.98994	−	20.7955i	0.186508	−	1.29719i	0.840965	−	0.541090i	$-0.181988\pi$
$258$	8.70208	+	2.16051i	0.541768	+	0.134508i
$259$	10.1200	−	22.1598i	0.628828	−	1.37694i
$260$	2.49210	−	3.42151i	0.154553	−	0.212193i
$261$	−0.327440	+	0.716993i	−0.0202680	+	0.0443808i
$262$	23.5653	−	11.9894i	1.45587	−	0.740710i
$263$	−7.47289	−	1.07444i	−0.460798	−	0.0662528i	−0.0919934	−	0.995760i	$-0.529324\pi$
$263$	−7.47289	−	1.07444i	−0.460798	−	0.0662528i	−0.368805	+	0.929507i	$0.620233\pi$
$264$	−10.9292	+	1.39256i	−0.672644	+	0.0857061i
$265$	−1.86104	+	1.19602i	−0.114323	+	0.0734710i
$266$	38.2963	+	3.86392i	2.34810	+	0.236912i
$267$	13.2719			0.812228
$268$	−11.7109	−	11.4392i	−0.715356	−	0.698761i
$269$	7.05814			0.430342			0.215171	−	0.976576i	$-0.430969\pi$
$269$	7.05814			0.430342			0.215171	+	0.976576i	$0.430969\pi$
$270$	−0.560243	−	0.0565259i	−0.0340953	−	0.00344006i
$271$	−14.2855	+	9.18073i	−0.867782	+	0.557690i	−0.897074	−	0.441881i	$-0.854311\pi$
$271$	−14.2855	+	9.18073i	−0.867782	+	0.557690i	0.0292913	+	0.999571i	$0.490675\pi$
$272$	18.7563	−	9.16645i	1.13727	−	0.555798i
$273$	−17.1870	−	2.47112i	−1.04021	−	0.149559i
$274$	8.08659	−	4.11426i	0.488529	−	0.248552i
$275$	7.83427	−	17.1547i	0.472424	−	1.03446i
$276$	−13.5057	−	9.83705i	−0.812947	−	0.592121i
$277$	−2.31289	+	5.06452i	−0.138968	+	0.304297i	−0.966301	−	0.257414i	$-0.917130\pi$
$277$	−2.31289	+	5.06452i	−0.138968	+	0.304297i	0.827333	+	0.561711i	$0.189857\pi$
$278$	−14.4210	−	3.58038i	−0.864914	−	0.214737i
$279$	−0.210164	+	1.46172i	−0.0125822	+	0.0875110i
$280$	−2.36412	−	2.81859i	−0.141283	−	0.168443i
$281$	2.92275	−	9.95398i	0.174357	−	0.593805i	−0.825223	−	0.564808i	$-0.808950\pi$
$281$	2.92275	−	9.95398i	0.174357	−	0.593805i	0.999579	−	0.0289973i	$-0.00923143\pi$
$282$	−0.0949643	+	0.162467i	−0.00565504	+	0.00967480i
$283$	−20.3987	+	9.31578i	−1.21258	+	0.553766i	−0.915975	−	0.401235i	$-0.868581\pi$
$283$	−20.3987	+	9.31578i	−1.21258	+	0.553766i	−0.296603	+	0.955001i	$0.595854\pi$
$284$	17.3964	−	9.79692i	1.03229	−	0.581340i
$285$	2.17246	−	2.50715i	0.128686	−	0.148511i
$286$	−14.7765	+	25.2801i	−0.873755	+	1.49484i
$287$	−8.68022	+	3.96412i	−0.512377	+	0.233995i
$288$	−3.37653	−	4.53862i	−0.198964	−	0.267440i
$289$	−1.45714	−	10.1347i	−0.0857144	−	0.596157i
$290$	−0.106947	+	0.430761i	−0.00628017	+	0.0252952i
$291$	−4.33075	−	6.73878i	−0.253873	−	0.395034i
$292$	−1.68158	+	28.8057i	−0.0984070	+	1.68573i
$293$	−9.35400	−	2.74658i	−0.546467	−	0.160457i	−0.00316552	−	0.999995i	$-0.501008\pi$
$293$	−9.35400	−	2.74658i	−0.546467	−	0.160457i	−0.543301	+	0.839538i	$0.682826\pi$
$294$	−1.95520	+	4.80905i	−0.114029	+	0.280469i
$295$	0.0949202	+	0.660184i	0.00552647	+	0.0384374i
$296$	6.26706	−	20.1408i	0.364265	−	1.17066i
$297$	3.89529			0.226028
$298$	−16.8385	+	5.72708i	−0.975430	+	0.331761i
$299$	−42.6081	+	12.5109i	−2.46409	+	0.723522i
$300$	9.64839	−	0.817130i	0.557050	−	0.0471770i
$301$	−8.60355	−	18.8392i	−0.495901	−	1.08587i
$302$	1.80870	−	1.70619i	0.104079	−	0.0981801i
$303$	1.72535	−	2.68470i	0.0991190	−	0.154232i
$304$	33.3160	−	0.872371i	1.91081	−	0.0500339i
$305$	2.92606			0.167546
$306$	−6.98779	+	2.37667i	−0.399465	+	0.135865i
$307$	0.334328	+	1.13862i	0.0190811	+	0.0649843i	0.968483	−	0.249079i	$-0.0801278\pi$
$307$	0.334328	+	1.13862i	0.0190811	+	0.0649843i	−0.949402	+	0.314063i	$0.898310\pi$
$308$	18.2291	+	17.7580i	1.03870	+	1.01185i
$309$	−6.35312	−	5.50501i	−0.361416	−	0.313169i
$310$	0.0351177	+	0.830799i	0.00199455	+	0.0471862i
$311$	19.9196	−	22.9885i	1.12954	−	1.30356i	0.182224	−	0.983257i	$-0.441670\pi$
$311$	19.9196	−	22.9885i	1.12954	−	1.30356i	0.947316	−	0.320301i	$-0.103784\pi$
$312$	−15.0326	−	0.241532i	−0.851053	−	0.0136741i
$313$	15.6200	−	24.3053i	0.882897	−	1.37382i	−0.0442111	−	0.999022i	$-0.514077\pi$
$313$	15.6200	−	24.3053i	0.882897	−	1.37382i	0.927109	−	0.374793i	$-0.122286\pi$
$314$	1.35748	+	2.66813i	0.0766071	+	0.150571i
$315$	0.703183	+	1.09417i	0.0396199	+	0.0616498i
$316$	−15.8680	−	8.39686i	−0.892646	−	0.472360i
$317$	7.52637	+	8.68589i	0.422723	+	0.487848i	0.926664	−	0.375889i	$-0.122663\pi$
$317$	7.52637	+	8.68589i	0.422723	+	0.487848i	−0.503942	+	0.863738i	$0.668117\pi$
$318$	7.27890	+	2.95936i	0.408180	+	0.165953i
$319$	0.436957	−	3.03911i	0.0244649	−	0.170157i
$320$	−2.33904	−	2.16219i	−0.130756	−	0.120870i
$321$	−13.8247	+	11.9792i	−0.771622	+	0.668614i
$322$	1.62990	+	38.5595i	0.0908308	+	2.14884i
$323$	12.2511	−	41.7233i	0.681667	−	2.32155i
$324$	0.981392	+	1.74266i	0.0545218	+	0.0968145i
$325$	13.9133	−	21.6495i	0.771772	−	1.20090i
$326$	−27.4327	−	2.76783i	−1.51936	−	0.153296i
$327$	−3.03281	−	10.3288i	−0.167715	−	0.571184i
$328$	−7.02172	+	4.35480i	−0.387710	+	0.240454i
$329$	0.430257	−	0.0618615i	0.0237208	−	0.00341054i
$330$	2.15594	−	0.403562i	0.118681	−	0.0222153i
$331$	−8.09173	−	9.33835i	−0.444762	−	0.513282i	0.488459	−	0.872587i	$-0.337559\pi$
$331$	−8.09173	−	9.33835i	−0.444762	−	0.513282i	−0.933220	+	0.359305i	$0.883014\pi$
$332$	−16.2654	−	5.82533i	−0.892680	−	0.319706i
$333$	−3.09801	+	6.78370i	−0.169770	+	0.371744i
$334$	−4.25307	−	12.5047i	−0.232717	−	0.684226i
$335$	2.46017	+	2.13759i	0.134414	+	0.116789i
$336$	−3.35182	+	12.6293i	−0.182857	+	0.688983i
$337$	29.3782	+	13.4166i	1.60033	+	0.730846i	0.997739	−	0.0672044i	$-0.0214079\pi$
$337$	29.3782	+	13.4166i	1.60033	+	0.730846i	0.602591	+	0.798051i	$0.294135\pi$
$338$	−13.4264	+	16.8861i	−0.730297	+	0.918483i
$339$	−6.89319	+	5.97298i	−0.374387	+	0.324408i
$340$	−3.62134	+	2.03938i	−0.196394	+	0.110601i
$341$	−0.818649	−	5.69383i	−0.0443323	−	0.308338i
$342$	−11.7235	−	1.18285i	−0.633935	−	0.0639611i
$343$	−10.4347	+	3.06390i	−0.563419	+	0.165435i
$344$	−9.45146	−	15.2396i	−0.509588	−	0.821665i
$345$	2.79829	+	1.79835i	0.150655	+	0.0968201i
$346$	−3.10079	−	16.5653i	−0.166700	−	0.890557i
$347$	27.3795	+	8.03936i	1.46981	+	0.431575i	0.916038	−	0.401092i	$-0.131369\pi$
$347$	27.3795	+	8.03936i	1.46981	+	0.431575i	0.553773	+	0.832667i	$0.313187\pi$
$348$	1.46971	−	0.570198i	0.0787850	−	0.0305658i
$349$	5.60117	+	6.46410i	0.299824	+	0.346015i	0.885592	−	0.464463i	$-0.153753\pi$
$349$	5.60117	+	6.46410i	0.299824	+	0.346015i	−0.585769	+	0.810478i	$0.699207\pi$
$350$	−15.3475	−	16.2695i	−0.820357	−	0.869644i
$351$	5.26140	+	0.756476i	0.280833	+	0.0403777i
$352$	17.6006	+	13.2576i	0.938115	+	0.706631i
$353$	14.5304	−	12.5907i	0.773376	−	0.670134i	−0.175960	−	0.984397i	$-0.556303\pi$
$353$	14.5304	−	12.5907i	0.773376	−	0.670134i	0.949336	+	0.314263i	$0.101757\pi$
$354$	1.72325	−	1.62558i	0.0915894	−	0.0863987i
$355$	−3.34376	+	2.14890i	−0.177468	+	0.114052i
$356$	−19.0134	−	18.5220i	−1.00771	−	0.981666i
$357$	14.3423	+	9.21727i	0.759078	+	0.487830i
$358$	10.4712	−	13.1694i	0.553418	−	0.696024i
$359$	−25.8786	−	22.4239i	−1.36582	−	1.18349i	−0.963410	−	0.268031i	$-0.913627\pi$
$359$	−25.8786	−	22.4239i	−1.36582	−	1.18349i	−0.402410	−	0.915459i	$-0.631827\pi$
$360$	0.723720	+	0.862844i	0.0381434	+	0.0454759i
$361$	33.0180	−	38.1049i	1.73779	−	2.00552i
$362$	−5.84890	−	11.4960i	−0.307411	−	0.604218i
$363$	−4.00422	+	1.17574i	−0.210167	+	0.0617106i
$364$	21.1735	+	27.5260i	1.10979	+	1.44276i
$365$		−	5.74445i		−	0.300678i
$366$	−5.98305	−	8.49798i	−0.312739	−	0.444196i
$367$	−3.14390	−	2.02046i	−0.164110	−	0.105467i	0.456008	−	0.889976i	$-0.349279\pi$
$367$	−3.14390	−	2.02046i	−0.164110	−	0.105467i	−0.620118	+	0.784509i	$0.712915\pi$
$368$	5.61989	+	32.9409i	0.292957	+	1.71716i
$369$	2.65725	−	1.21352i	0.138331	−	0.0631735i
$370$	−1.01186	+	4.07557i	−0.0526042	+	0.211879i
$371$	−5.11334	−	17.4144i	−0.265471	−	0.904113i
$372$	2.34103	−	1.80077i	0.121377	−	0.0933654i
$373$			6.03507i			0.312484i	0.987719	+	0.156242i	$0.0499380\pi$
$373$			6.03507i			0.312484i	−0.987719	+	0.156242i	$0.950062\pi$
$374$	23.5086	−	16.5514i	1.21560	−	0.855853i
$375$	−3.87862	+	0.557662i	−0.200291	+	0.0287975i
$376$	0.362783	−	0.100221i	0.0187091	−	0.00516850i
$377$	1.18041	−	4.02009i	0.0607940	−	0.207045i
$378$	1.73991	−	4.27952i	0.0894914	−	0.220115i
$379$	10.1738	−	6.53832i	0.522594	−	0.335851i	−0.252603	−	0.967570i	$-0.581287\pi$
$379$	10.1738	−	6.53832i	0.522594	−	0.335851i	0.775198	+	0.631719i	$0.217650\pi$
$380$	−6.61121	+	0.559909i	−0.339148	+	0.0287227i
$381$	8.24737	−	1.18579i	0.422525	−	0.0607500i
$382$	−1.61226	+	2.02771i	−0.0824902	+	0.103747i
$383$	3.62672	+	7.94142i	0.185317	+	0.405787i	0.979374	−	0.202056i	$-0.0647622\pi$
$383$	3.62672	+	7.94142i	0.185317	+	0.405787i	−0.794057	+	0.607843i	$0.792035\pi$
$384$	−1.49678	+	11.2143i	−0.0763822	+	0.572275i
$385$	−3.82893	−	3.31778i	−0.195140	−	0.169090i
$386$	6.10021	+	32.5891i	0.310492	+	1.65874i
$387$	2.63378	+	5.76717i	0.133882	+	0.293162i
$388$	−3.20027	+	15.6979i	−0.162469	+	0.796941i
$389$	30.3924	+	8.92401i	1.54096	+	0.452465i	0.938382	−	0.345598i	$-0.112324\pi$
$389$	30.3924	+	8.92401i	1.54096	+	0.452465i	0.602573	+	0.798064i	$0.294142\pi$
$390$	2.99043	−	0.126405i	0.151426	−	0.00640074i
$391$	43.1576	+	6.20512i	2.18257	+	0.313806i
$392$	9.51244	−	4.16082i	0.480451	−	0.210153i
$393$	17.0063	+	7.76653i	0.857856	+	0.391770i
$394$	−11.3099	−	16.0639i	−0.569783	−	0.809286i
$395$	3.25108	+	1.48472i	0.163580	+	0.0747043i
$396$	−5.58040	−	5.43619i	−0.280426	−	0.273179i
$397$	−2.86622	+	19.9350i	−0.143851	+	1.00051i	0.782178	+	0.623055i	$0.214109\pi$
$397$	−2.86622	+	19.9350i	−0.143851	+	1.00051i	−0.926029	+	0.377452i	$0.876800\pi$
$398$	−18.4636	+	31.5880i	−0.925498	+	1.58337i
$399$	14.7146	+	22.8964i	0.736653	+	1.14626i
$400$	−14.9627	−	12.2945i	−0.748134	−	0.614725i
$401$		−	17.8460i		−	0.891188i	−0.895235	−	0.445594i	$-0.852992\pi$
$401$		−	17.8460i		−	0.891188i	0.895235	−	0.445594i	$-0.147008\pi$
$402$	1.17765	−	11.5158i	0.0587358	−	0.574355i
$403$		−	7.84969i		−	0.391021i
$404$	−6.21847	+	1.43824i	−0.309380	+	0.0715552i
$405$	−0.215263	−	0.334956i	−0.0106965	−	0.0166441i
$406$	−3.14371	−	1.83754i	−0.156020	−	0.0911956i
$407$	4.13419	−	28.7539i	0.204924	−	1.42528i
$408$	13.3276	+	6.34721i	0.659813	+	0.314234i
$409$	−25.9278	−	11.8408i	−1.28205	−	0.585491i	−0.346286	−	0.938129i	$-0.612557\pi$
$409$	−25.9278	−	11.8408i	−1.28205	−	0.585491i	−0.935760	+	0.352638i	$0.885285\pi$
$410$	1.34499	−	0.946952i	0.0664246	−	0.0467666i
$411$	5.83584	+	2.66514i	0.287861	+	0.131462i
$412$	1.41881	+	16.7528i	0.0698996	+	0.825350i
$413$	−5.41630	−	0.778747i	−0.266519	−	0.0383196i
$414$	−0.498956	−	11.8041i	−0.0245224	−	0.580140i
$415$	3.30022	+	0.969033i	0.162002	+	0.0475680i
$416$	21.1987	+	21.3252i	1.03935	+	1.04556i
$417$	−4.36467	−	9.55729i	−0.213739	−	0.468023i
$418$	45.1147	−	8.44483i	2.20663	−	0.413050i
$419$	22.6804	+	19.6527i	1.10801	+	0.960098i	0.999422	−	0.0339888i	$-0.0108210\pi$
$419$	22.6804	+	19.6527i	1.10801	+	0.960098i	0.108590	+	0.994087i	$0.465367\pi$
$420$	0.519628	−	2.54887i	0.0253552	−	0.124372i
$421$	−1.28307	−	2.80952i	−0.0625328	−	0.136928i	0.875785	−	0.482701i	$-0.160344\pi$
$421$	−1.28307	−	2.80952i	−0.0625328	−	0.136928i	−0.938318	+	0.345773i	$0.887617\pi$
$422$	−2.97703	−	2.36708i	−0.144920	−	0.115227i
$423$	−0.131713	+	0.0189375i	−0.00640411	+	0.000920772i
$424$	−6.29775	−	14.3979i	−0.305846	−	0.699223i
$425$	−21.2568	+	13.6609i	−1.03111	+	0.662653i
$426$	13.0781	+	5.31711i	0.633635	+	0.257615i
$427$	−6.76329	+	23.0336i	−0.327298	+	1.11468i
$428$	36.5233	+	2.13211i	1.76542	+	0.103059i
$429$	−20.4947	+	2.94669i	−0.989493	+	0.142268i
$430$	2.05522	+	2.91912i	0.0991116	+	0.140772i
$431$		−	0.857885i		−	0.0413228i	−0.999787	−	0.0206614i	$-0.993423\pi$
$431$		−	0.857885i		−	0.0413228i	0.999787	−	0.0206614i	$-0.00657720\pi$
$432$	1.02608	−	3.86616i	0.0493674	−	0.186010i
$433$	−3.07831	−	10.4838i	−0.147934	−	0.503817i	0.851867	−	0.523758i	$-0.175470\pi$
$433$	−3.07831	−	10.4838i	−0.147934	−	0.503817i	−0.999801	+	0.0199409i	$0.993652\pi$
$434$	−6.62114	−	1.64387i	−0.317825	−	0.0789081i
$435$	−0.285480	+	0.130374i	−0.0136877	+	0.00625098i
$436$	−10.0699	+	19.0296i	−0.482260	+	0.911353i
$437$	58.5564	+	37.6319i	2.80113	+	1.80018i
$438$	−16.6832	+	11.7459i	−0.797156	+	0.561243i
$439$		−	35.5703i		−	1.69768i	−0.528652	−	0.848838i	$-0.677302\pi$
$439$		−	35.5703i		−	1.69768i	0.528652	−	0.848838i	$-0.322698\pi$
$440$	−3.65181	−	2.43065i	−0.174093	−	0.115877i
$441$	−3.52212	+	1.03419i	−0.167720	+	0.0492470i
$442$	34.9677	−	17.7907i	1.66324	−	0.846218i
$443$	7.38173	−	8.51897i	0.350717	−	0.404749i	−0.552791	−	0.833320i	$-0.686437\pi$
$443$	7.38173	−	8.51897i	0.350717	−	0.404749i	0.903508	+	0.428571i	$0.140983\pi$
$444$	13.9054	−	5.39482i	0.659922	−	0.256027i
$445$	3.99367	+	3.46054i	0.189318	+	0.164045i
$446$	−15.6951	−	12.4794i	−0.743187	−	0.590917i
$447$	−10.5800	−	6.79936i	−0.500417	−	0.321599i
$448$	22.4270	−	13.4150i	1.05958	−	0.633798i
$449$	28.0328	−	18.0156i	1.32295	−	0.850207i	0.327439	−	0.944872i	$-0.393814\pi$
$449$	28.0328	−	18.0156i	1.32295	−	0.850207i	0.995509	+	0.0946647i	$0.0301779\pi$
$450$	4.69827	+	4.98054i	0.221479	+	0.234785i
$451$	−8.59971	+	7.45169i	−0.404944	+	0.350886i
$452$	18.2110	+	1.06310i	0.856573	+	0.0500038i
$453$	1.74029	+	0.250216i	0.0817661	+	0.0117562i
$454$	−8.10155	+	7.64240i	−0.380225	+	0.358676i
$455$	−4.52745	−	5.22495i	−0.212250	−	0.244950i
$456$	15.1444	+	18.0557i	0.709201	+	0.845534i
$457$	−28.4776	−	8.36177i	−1.33212	−	0.391147i	−0.463271	−	0.886217i	$-0.653324\pi$
$457$	−28.4776	−	8.36177i	−1.33212	−	0.391147i	−0.868853	+	0.495070i	$0.835143\pi$
$458$	2.45498	−	0.459537i	0.114714	−	0.0214728i
$459$	−4.39058	−	2.82165i	−0.204935	−	0.131703i
$460$	−1.49909	−	6.48158i	−0.0698956	−	0.302205i
$461$	6.42584	−	1.88680i	0.299281	−	0.0878769i	−0.128645	−	0.991691i	$-0.541063\pi$
$461$	6.42584	−	1.88680i	0.299281	−	0.0878769i	0.427926	+	0.903814i	$0.359244\pi$
$462$	−1.80645	+	17.9042i	−0.0840435	+	0.832977i
$463$	3.53580	+	24.5921i	0.164323	+	1.14289i	0.890368	+	0.455242i	$0.150447\pi$
$463$	3.53580	+	24.5921i	0.164323	+	1.14289i	−0.726045	+	0.687647i	$0.758644\pi$
$464$	−2.90127	−	1.23424i	−0.134688	−	0.0572981i
$465$	−0.444372	+	0.385051i	−0.0206073	+	0.0178563i
$466$	24.0438	+	19.1176i	1.11381	+	0.885604i
$467$	14.5545	+	6.64681i	0.673501	+	0.307578i	0.722650	−	0.691214i	$-0.242924\pi$
$467$	14.5545	+	6.64681i	0.673501	+	0.307578i	−0.0491490	+	0.998791i	$0.515651\pi$
$468$	−6.48178	−	8.42645i	−0.299620	−	0.389513i
$469$	−22.5134	+	14.4254i	−1.03957	+	0.666103i
$470$	−0.0709378	+	0.0241272i	−0.00327212	+	0.00111291i
$471$	−0.879351	+	1.92551i	−0.0405183	+	0.0887228i
$472$	−4.73736	−	0.0761163i	−0.218055	−	0.00350354i
$473$	−16.1728	−	18.6644i	−0.743626	−	0.858191i
$474$	−2.33566	−	12.4778i	−0.107281	−	0.573124i
$475$	−39.9278	+	5.74076i	−1.83202	+	0.263404i
$476$	−7.68344	−	33.2206i	−0.352170	−	1.52266i
$477$	1.56533	+	5.33103i	0.0716716	+	0.244091i
$478$	−2.77781	+	27.5316i	−0.127054	+	1.25927i
$479$	11.0965	−	17.2666i	0.507014	−	0.788930i	−0.489531	−	0.871986i	$-0.662832\pi$
$479$	11.0965	−	17.2666i	0.507014	−	0.788930i	0.996545	+	0.0830565i	$0.0264682\pi$
$480$	0.167367	−	2.24612i	0.00763923	−	0.102521i
$481$	11.1682	−	38.0353i	0.509225	−	1.73426i
$482$	7.79174	−	0.329355i	0.354904	−	0.0150017i
$483$	−20.6244	+	17.8712i	−0.938444	+	0.813167i
$484$	7.37730	+	3.90384i	0.335332	+	0.177447i
$485$	0.453905	−	3.15698i	0.0206108	−	0.143351i
$486$	−0.532634	+	1.31008i	−0.0241607	+	0.0594263i
$487$	1.34987	+	1.55783i	0.0611683	+	0.0705920i	0.785509	−	0.618850i	$-0.212401\pi$
$487$	1.34987	+	1.55783i	0.0611683	+	0.0705920i	−0.724341	+	0.689442i	$0.757856\pi$
$488$	−3.28828	+	20.5241i	−0.148853	+	0.929081i
$489$	−10.5405	−	16.4014i	−0.476659	−	0.741695i
$490$	−1.84226	+	0.937297i	−0.0832248	+	0.0423427i
$491$	−6.93054	+	10.7841i	−0.312771	+	0.486681i	−0.961676	−	0.274188i	$-0.911591\pi$
$491$	−6.93054	+	10.7841i	−0.312771	+	0.486681i	0.648905	+	0.760869i	$0.275227\pi$
$492$	−5.50035	−	1.96991i	−0.247975	−	0.0888103i
$493$	−2.69397	+	3.10901i	−0.121330	+	0.140023i
$494$	62.5769	−	2.64511i	2.81547	−	0.119009i
$495$	1.17214	+	1.01566i	0.0526836	+	0.0456506i
$496$	−5.86689	−	0.687321i	−0.263431	−	0.0308616i
$497$	−9.18720	−	31.2887i	−0.412102	−	1.40349i
$498$	−3.93382	−	11.5661i	−0.176279	−	0.518288i
$499$	−11.2388			−0.503116			−0.251558	−	0.967842i	$-0.580943\pi$
$499$	−11.2388			−0.503116			−0.251558	+	0.967842i	$0.580943\pi$
$500$	6.33479	+	4.61403i	0.283300	+	0.206346i
$501$	5.04936	−	7.85697i	0.225589	−	0.351023i
$502$	−3.64711	−	3.86623i	−0.162779	−	0.172558i
$503$	9.94868	+	21.7846i	0.443590	+	0.971326i	0.990925	+	0.134413i	$0.0429148\pi$
$503$	9.94868	+	21.7846i	0.443590	+	0.971326i	−0.547336	+	0.836913i	$0.684358\pi$
$504$	−8.46503	+	3.70267i	−0.377062	+	0.164930i
$505$	1.21919	−	0.357987i	0.0542533	−	0.0159302i
$506$	14.8190	+	43.5703i	0.658785	+	1.93693i
$507$	−15.2546			−0.677482
$508$	−13.4701	−	9.81111i	−0.597638	−	0.435297i
$509$	0.489698	+	3.40593i	0.0217055	+	0.150965i	0.997792	−	0.0664179i	$-0.0211571\pi$
$509$	0.489698	+	3.40593i	0.0217055	+	0.150965i	−0.976086	+	0.217383i	$0.930248\pi$
$510$	−2.72240	−	1.10684i	−0.120550	−	0.0490116i
$511$	45.2197	+	13.2777i	2.00040	+	0.587371i
$512$	17.7947	−	13.9767i	0.786422	−	0.617689i
$513$	−4.50455	−	7.00921i	−0.198881	−	0.309464i
$514$	−28.8363	−	7.15933i	−1.27191	−	0.315785i
$515$	−0.476343	−	3.31304i	−0.0209902	−	0.145990i
$516$	4.27540	−	11.9377i	0.188214	−	0.525529i
$517$	0.471495	−	0.215325i	0.0207363	−	0.00946996i
$518$	−29.7436	−	17.3855i	−1.30686	−	0.763876i
$519$	7.80391	−	9.00619i	0.342554	−	0.395328i
$520$	−4.46050	−	3.99230i	−0.195606	−	0.175074i
$521$	14.2948	−	6.52824i	0.626268	−	0.286007i	−0.0768909	−	0.997040i	$-0.524499\pi$
$521$	14.2948	−	6.52824i	0.626268	−	0.286007i	0.703159	+	0.711032i	$0.251772\pi$
$522$	0.962374	+	0.562520i	0.0421220	+	0.0246208i
$523$	3.27394	−	11.1500i	0.143159	−	0.487556i	−0.856428	−	0.516266i	$-0.827322\pi$
$523$	3.27394	−	11.1500i	0.143159	−	0.487556i	0.999588	+	0.0287098i	$0.00913986\pi$
$524$	−13.5245	−	34.8601i	−0.590820	−	1.52287i
$525$	2.25074	−	15.6543i	0.0982305	−	0.683208i
$526$	−2.57271	+	10.3623i	−0.112176	+	0.451820i
$527$	−3.20173	+	7.01081i	−0.139470	+	0.305396i
$528$	0.407848	+	15.5758i	0.0177493	+	0.677850i
$529$	−19.4384	+	42.5643i	−0.845150	+	1.85062i
$530$	1.41868	+	2.78842i	0.0616235	+	0.121121i
$531$	1.65807	+	0.238395i	0.0719543	+	0.0103455i
$532$	10.8736	−	53.3370i	0.471430	−	2.31245i
$533$	−13.0628	+	8.39498i	−0.565815	+	0.363627i
$534$	1.88417	−	18.6745i	0.0815360	−	0.808125i
$535$	−7.28350			−0.314893
$536$	−17.7583	+	14.8540i	−0.767042	+	0.641596i
$537$	11.8970			0.513394
$538$	1.00202	−	9.93129i	0.0432002	−	0.428168i
$539$	12.0290	−	7.73055i	0.518125	−	0.332978i
$540$	−0.159072	+	0.780277i	−0.00684536	+	0.0335778i
$541$	36.0016	+	5.17625i	1.54783	+	0.222544i	0.862639	−	0.505820i	$-0.168810\pi$
$541$	36.0016	+	5.17625i	1.54783	+	0.222544i	0.685190	+	0.728365i	$0.259719\pi$
$542$	10.8899	+	21.4041i	0.467760	+	0.919383i
$543$	3.78881	−	8.29633i	0.162593	−	0.356030i
$544$	−10.2351	−	27.6927i	−0.438825	−	1.18732i
$545$	1.78054	−	3.89884i	0.0762699	−	0.167008i
$546$	−5.91702	+	23.8325i	−0.253225	+	1.01994i
$547$	−2.77012	+	19.2666i	−0.118442	+	0.823781i	0.840830	+	0.541299i	$0.182067\pi$
$547$	−2.77012	+	19.2666i	−0.118442	+	0.823781i	−0.959272	+	0.282483i	$0.908842\pi$
$548$	−4.64102	−	11.9625i	−0.198255	−	0.511012i
$549$	2.07042	−	7.05121i	0.0883635	−	0.300938i
$550$	−23.0256	−	13.4588i	−0.981815	−	0.573883i
$551$	−5.97389	+	2.72818i	−0.254496	+	0.116225i
$552$	−15.7588	+	17.6069i	−0.670738	+	0.749400i
$553$	−19.2021	+	22.1604i	−0.816557	+	0.942357i
$554$	6.79777	+	3.97339i	0.288810	+	0.168813i
$555$	−2.70102	+	1.23351i	−0.114652	+	0.0523597i
$556$	−7.08515	+	19.7831i	−0.300477	+	0.838989i
$557$	−0.168683	−	1.17321i	−0.00714731	−	0.0497106i	0.985936	−	0.167125i	$-0.0534484\pi$
$557$	−0.168683	−	1.17321i	−0.00714731	−	0.0497106i	−0.993083	+	0.117415i	$0.962539\pi$
$558$	2.02691	+	0.503231i	0.0858059	+	0.0213035i
$559$	−18.2201	−	28.3510i	−0.770628	−	1.19912i
$560$	−4.30157	+	2.92633i	−0.181775	+	0.123660i
$561$	19.5063	+	5.72758i	0.823559	+	0.241819i
$562$	−13.5910	−	5.52565i	−0.573302	−	0.233086i
$563$	2.39914	+	16.6864i	0.101112	+	0.703247i	0.975817	+	0.218591i	$0.0701460\pi$
$563$	2.39914	+	16.6864i	0.101112	+	0.703247i	−0.874705	+	0.484656i	$0.838945\pi$
$564$	0.215121	+	0.156686i	0.00905824	+	0.00659769i
$565$	−3.63164			−0.152784
$566$	10.2120	+	30.0250i	0.429243	+	1.26204i
$567$	3.13430	−	0.920313i	0.131628	−	0.0386495i
$568$	−11.3152	−	25.8688i	−0.474777	−	1.08543i
$569$	0.657160	+	1.43898i	0.0275496	+	0.0603252i	0.922907	−	0.385024i	$-0.125807\pi$
$569$	0.657160	+	1.43898i	0.0275496	+	0.0603252i	−0.895357	+	0.445349i	$0.853080\pi$
$570$	−3.21932	−	3.41274i	−0.134843	−	0.142944i
$571$	9.91009	−	15.4204i	0.414725	−	0.645324i	−0.569553	−	0.821955i	$-0.692884\pi$
$571$	9.91009	−	15.4204i	0.414725	−	0.645324i	0.984277	+	0.176631i	$0.0565199\pi$
$572$	33.4731	+	24.3806i	1.39958	+	1.01940i
$573$	−1.83180			−0.0765245
$574$	4.34549	+	12.7764i	0.181377	+	0.533279i
$575$	−11.3951	−	38.8083i	−0.475210	−	1.61842i
$576$	−6.86550	+	4.10668i	−0.286063	+	0.171112i
$577$	−16.8795	−	14.6262i	−0.702704	−	0.608897i	0.228436	−	0.973559i	$-0.426639\pi$
$577$	−16.8795	−	14.6262i	−0.702704	−	0.608897i	−0.931140	+	0.364662i	$0.881184\pi$
$578$	−14.4670	+	0.611518i	−0.601750	+	0.0254358i
$579$	−15.3527	+	17.7179i	−0.638036	+	0.736333i
$580$	0.590928	+	0.211636i	0.0245370	+	0.00878771i
$581$	−15.2563	+	23.7392i	−0.632937	+	0.984869i
$582$	−10.0968	+	5.13698i	−0.418524	+	0.212935i
$583$	−11.7008	−	18.2069i	−0.484600	−	0.754052i
$584$	40.2929	+	6.45555i	1.66733	+	0.267133i
$585$	1.38597	+	1.59950i	0.0573029	+	0.0661311i
$586$	−5.19259	+	12.7718i	−0.214504	+	0.527599i
$587$	−2.22070	+	15.4453i	−0.0916579	+	0.637495i	0.891266	+	0.453481i	$0.149818\pi$
$587$	−2.22070	+	15.4453i	−0.0916579	+	0.637495i	−0.982924	+	0.184014i	$0.941091\pi$
$588$	6.48909	+	3.43382i	0.267606	+	0.141609i
$589$	−9.29882	+	8.05747i	−0.383151	+	0.332002i
$590$	0.942401	−	0.0398350i	0.0387980	−	0.00163998i
$591$	3.91376	−	13.3290i	0.160990	−	0.548283i
$592$	−27.4499	−	11.6775i	−1.12818	−	0.479943i
$593$	−14.0529	+	21.8667i	−0.577082	+	0.897957i	−0.999966	−	0.00822670i	$-0.997381\pi$
$593$	−14.0529	+	21.8667i	−0.577082	+	0.897957i	0.422884	+	0.906184i	$0.361018\pi$
$594$	0.553002	−	5.48094i	0.0226899	−	0.224886i
$595$	1.91246	+	6.51323i	0.0784030	+	0.267016i
$596$	5.66789	+	24.5061i	0.232166	+	1.00381i
$597$	−25.6086	+	3.68195i	−1.04809	+	0.150692i
$598$	11.5547	+	61.7287i	0.472508	+	2.52427i
$599$	5.52075	+	6.37129i	0.225572	+	0.260324i	0.857242	−	0.514913i	$-0.172176\pi$
$599$	5.52075	+	6.37129i	0.225572	+	0.260324i	−0.631670	+	0.775237i	$0.717630\pi$
$600$	0.219992	−	13.6920i	0.00898114	−	0.558972i
$601$	−11.2032	+	24.5315i	−0.456986	+	1.00066i	0.531178	+	0.847260i	$0.321750\pi$
$601$	−11.2032	+	24.5315i	−0.456986	+	1.00066i	−0.988164	+	0.153400i	$0.950978\pi$
$602$	−27.7294	+	9.43126i	−1.13017	+	0.384390i
$603$	6.89195	−	4.41600i	0.280662	−	0.179834i
$604$	−2.14395	−	2.78718i	−0.0872362	−	0.113409i
$605$	−1.51148	−	0.690270i	−0.0614504	−	0.0280635i
$606$	−3.53262	−	2.80883i	−0.143503	−	0.114101i
$607$	28.3078	−	24.5288i	1.14898	−	0.995594i	0.148999	−	0.988837i	$-0.452395\pi$
$607$	28.3078	−	24.5288i	1.14898	−	0.995594i	0.999977	−	0.00675629i	$-0.00215061\pi$
$608$	3.50228	−	47.0018i	0.142036	−	1.90618i
$609$	−0.366436	−	2.54862i	−0.0148487	−	0.103275i
$610$	0.415403	−	4.11717i	0.0168192	−	0.166699i
$611$	0.678670	−	0.199275i	0.0274560	−	0.00806182i
$612$	2.35211	+	10.1697i	0.0950783	+	0.411086i
$613$	11.9271	+	7.66506i	0.481729	+	0.309589i	0.758872	−	0.651240i	$-0.225751\pi$
$613$	11.9271	+	7.66506i	0.481729	+	0.309589i	−0.277142	+	0.960829i	$0.589387\pi$
$614$	1.64958	−	0.308777i	0.0665715	−	0.0124612i
$615$	1.11601	+	0.327691i	0.0450020	+	0.0132138i
$616$	27.5746	−	23.1285i	1.11101	−	0.931874i
$617$	−14.3695	−	16.5833i	−0.578495	−	0.667619i	0.388786	−	0.921328i	$-0.372895\pi$
$617$	−14.3695	−	16.5833i	−0.578495	−	0.667619i	−0.967280	+	0.253710i	$0.918349\pi$
$618$	−8.64786	+	8.15775i	−0.347868	+	0.328153i
$619$	−19.2280	−	2.76457i	−0.772839	−	0.111117i	−0.255398	−	0.966836i	$-0.582206\pi$
$619$	−19.2280	−	2.76457i	−0.772839	−	0.111117i	−0.517441	+	0.855719i	$0.673115\pi$
$620$	1.17398	+	0.0685329i	0.0471481	+	0.00275235i
$621$	6.31369	−	5.47084i	0.253360	−	0.219537i
$622$	−29.5185	−	31.2919i	−1.18358	−	1.25469i
$623$	−36.4720	+	23.4391i	−1.46122	+	0.939068i
$624$	−2.47398	+	21.1176i	−0.0990385	+	0.845381i
$625$	19.0520	+	12.2440i	0.762079	+	0.489758i
$626$	−31.9817	−	25.4290i	−1.27825	−	1.01635i
$627$	24.5279	+	21.2535i	0.979548	+	0.848783i
$628$	3.94697	−	1.53128i	0.157501	−	0.0611049i
$629$	−25.4885	+	29.4153i	−1.01629	+	1.17286i
$630$	1.63941	−	0.834091i	0.0653156	−	0.0332310i
$631$	17.2118	−	5.05384i	0.685191	−	0.201190i	0.0794344	−	0.996840i	$-0.474689\pi$
$631$	17.2118	−	5.05384i	0.685191	−	0.201190i	0.605757	+	0.795650i	$0.292870\pi$
$632$	−14.0677	+	21.1353i	−0.559583	+	0.840719i
$633$		−	2.68940i		−	0.106894i
$634$	13.2901	−	9.35702i	0.527819	−	0.371615i
$635$	2.79091	+	1.79361i	0.110754	+	0.0711773i
$636$	5.19739	−	9.82179i	0.206090	−	0.389459i
$637$	17.7489	−	8.10567i	0.703239	−	0.321158i
$638$	−4.21420	−	1.04628i	−0.166842	−	0.0414227i
$639$	2.81245	+	9.57831i	0.111259	+	0.378912i
$640$	−3.37442	+	2.98423i	−0.133386	+	0.117962i
$641$			5.95345i			0.235147i	0.993064	+	0.117574i	$0.0375116\pi$
$641$			5.95345i			0.235147i	−0.993064	+	0.117574i	$0.962488\pi$
$642$	14.8929	+	21.1530i	0.587777	+	0.834843i
$643$	−10.5079	+	1.51081i	−0.414393	+	0.0595807i	−0.346358	−	0.938102i	$-0.612582\pi$
$643$	−10.5079	+	1.51081i	−0.414393	+	0.0595807i	−0.0680345	+	0.997683i	$0.521673\pi$
$644$	54.4873	+	3.18079i	2.14710	+	0.125341i
$645$	−0.711205	+	2.42214i	−0.0280037	+	0.0953718i
$646$	−56.9683	−	23.1614i	−2.24139	−	0.911274i
$647$	8.96081	−	5.75876i	0.352286	−	0.226400i	−0.352514	−	0.935806i	$-0.614673\pi$
$647$	8.96081	−	5.75876i	0.352286	−	0.226400i	0.704800	+	0.709406i	$0.251037\pi$
$648$	2.59137	−	1.13349i	0.101799	−	0.0445276i
$649$	−6.45868	+	0.928618i	−0.253525	+	0.0364514i
$650$	−28.4872	−	22.6505i	−1.11736	−	0.888426i
$651$	−2.00396	−	4.38806i	−0.0785413	−	0.171982i
$652$	−7.78907	+	38.2068i	−0.305044	+	1.49629i
$653$	31.5449	+	27.3338i	1.23445	+	1.06965i	0.995116	+	0.0987168i	$0.0314738\pi$
$653$	31.5449	+	27.3338i	1.23445	+	1.06965i	0.239332	+	0.970938i	$0.423072\pi$
$654$	−14.9639	+	2.80103i	−0.585135	+	0.109529i
$655$	3.09235	+	6.77129i	0.120828	+	0.264576i
$656$	5.13065	+	10.4983i	0.200318	+	0.409889i
$657$	−13.8430	−	4.06466i	−0.540065	−	0.158577i
$658$	−0.0259614	−	0.614183i	−0.00101208	−	0.0239434i
$659$	−35.3731	−	5.08588i	−1.37794	−	0.198118i	−0.586789	−	0.809740i	$-0.699608\pi$
$659$	−35.3731	−	5.08588i	−1.37794	−	0.198118i	−0.791150	+	0.611622i	$0.790517\pi$
$660$	−0.261767	−	3.09085i	−0.0101893	−	0.120311i
$661$	5.57327	+	2.54522i	0.216775	+	0.0989978i	0.520843	−	0.853653i	$-0.325618\pi$
$661$	5.57327	+	2.54522i	0.216775	+	0.0989978i	−0.304068	+	0.952650i	$0.598345\pi$
$662$	−14.2885	+	10.0599i	−0.555337	+	0.390989i
$663$	25.2351	+	11.5245i	0.980050	+	0.447574i
$664$	−10.5058	+	22.0596i	−0.407704	+	0.856077i
$665$	−1.54224	+	10.7265i	−0.0598055	+	0.415956i
$666$	9.10532	+	5.32218i	0.352824	+	0.206230i
$667$	−3.56011	−	5.53964i	−0.137848	−	0.214496i
$668$	−18.1988	+	4.20911i	−0.704132	+	0.162855i
$669$		−	14.1787i		−	0.548182i
$670$	3.35701	−	3.15817i	0.129693	−	0.122011i
$671$			28.6261i			1.10510i
$672$	17.2944	+	6.50918i	0.667146	+	0.251097i
$673$	−2.86220	−	4.45367i	−0.110330	−	0.171677i	0.781698	−	0.623657i	$-0.214354\pi$
$673$	−2.86220	−	4.45367i	−0.110330	−	0.171677i	−0.892028	+	0.451981i	$0.850718\pi$
$674$	23.0487	−	39.4324i	0.887805	−	1.51888i
$675$	−0.689012	+	4.79219i	−0.0265201	+	0.184451i
$676$	21.8538	+	21.2891i	0.840532	+	0.818811i
$677$	−17.2058	−	7.85761i	−0.661271	−	0.301992i	0.0563655	−	0.998410i	$-0.482049\pi$
$677$	−17.2058	−	7.85761i	−0.661271	−	0.301992i	−0.717637	+	0.696418i	$0.754776\pi$
$678$	7.42580	+	10.5472i	0.285186	+	0.405061i
$679$	23.8023	+	10.8701i	0.913448	+	0.417158i
$680$	2.35544	+	5.38500i	0.0903270	+	0.206505i
$681$	−7.79516	−	1.12078i	−0.298711	−	0.0429482i
$682$	−8.12783	+	0.343561i	−0.311231	+	0.0131556i
$683$	19.2718	+	5.65871i	0.737415	+	0.216525i	0.628808	−	0.777560i	$-0.283543\pi$
$683$	19.2718	+	5.65871i	0.737415	+	0.216525i	0.108606	+	0.994085i	$0.465361\pi$
$684$	−3.32870	+	16.3279i	−0.127276	+	0.624312i
$685$	1.06116	+	2.32362i	0.0405449	+	0.0887808i
$686$	2.82974	+	15.1173i	0.108040	+	0.577181i
$687$	1.33472	+	1.15654i	0.0509226	+	0.0441247i
$688$	−22.7850	+	11.1353i	−0.868670	+	0.424531i
$689$	−12.2686	−	26.8645i	−0.467397	−	1.02346i
$690$	2.92767	−	3.68209i	0.111455	−	0.140175i
$691$	7.81825	−	1.12409i	0.297420	−	0.0427626i	0.00801064	−	0.999968i	$-0.497450\pi$
$691$	7.81825	−	1.12409i	0.297420	−	0.0427626i	0.289410	+	0.957205i	$0.406541\pi$
$692$	−23.7488	+	2.01130i	−0.902793	+	0.0764583i
$693$	−10.7045	+	6.87934i	−0.406629	+	0.261325i
$694$	15.1989	−	37.3836i	0.576943	−	1.41906i
$695$	1.17860	−	4.01395i	0.0447069	−	0.152258i
$696$	−0.593657	−	2.14894i	−0.0225025	−	0.0814553i
$697$	15.0910	−	2.16976i	0.571612	−	0.0821854i
$698$	9.89062	−	6.96355i	0.374365	−	0.263574i
$699$			21.7208i			0.821557i
$700$	−25.0712	+	19.2852i	−0.947603	+	0.728914i
$701$	2.82029	+	9.60503i	0.106521	+	0.362777i	0.995452	−	0.0952639i	$-0.0303695\pi$
$701$	2.82029	+	9.60503i	0.106521	+	0.362777i	−0.888931	+	0.458041i	$0.848551\pi$
$702$	1.81136	−	7.29577i	0.0683653	−	0.275361i
$703$	−56.5208	+	25.8122i	−2.13172	+	0.973525i
$704$	21.1530	−	22.8831i	0.797235	−	0.862441i
$705$	−0.0445718	−	0.0286445i	−0.00167867	−	0.00107882i
$706$	−15.6531	−	22.2328i	−0.589113	−	0.836741i
$707$			10.4248i			0.392065i
$708$	−2.04266	−	2.65550i	−0.0767680	−	0.0998000i
$709$	39.6147	−	11.6319i	1.48776	−	0.436847i	0.565936	−	0.824449i	$-0.308515\pi$
$709$	39.6147	−	11.6319i	1.48776	−	0.436847i	0.921827	+	0.387602i	$0.126697\pi$
$710$	2.54896	+	5.00998i	0.0956606	+	0.188021i
$711$	5.87828	−	6.78389i	0.220453	−	0.254416i
$712$	−28.7611	+	24.1236i	−1.07787	+	0.904071i
$713$	−9.32376	−	8.07909i	−0.349178	−	0.302564i
$714$	15.0055	−	18.8721i	0.561566	−	0.706272i
$715$	−6.93541	−	4.45712i	−0.259370	−	0.166687i
$716$	−17.0437	−	16.6033i	−0.636953	−	0.620493i
$717$	−16.4605	+	10.5785i	−0.614728	+	0.395062i
$718$	−35.2260	+	33.2295i	−1.31462	+	1.24012i
$719$	13.8348	−	11.9879i	0.515949	−	0.447073i	−0.357553	−	0.933893i	$-0.616389\pi$
$719$	13.8348	−	11.9879i	0.515949	−	0.447073i	0.873502	+	0.486820i	$0.161843\pi$
$720$	1.31683	−	0.895829i	0.0490752	−	0.0333856i
$721$	27.1809	+	3.90803i	1.01227	+	0.145543i
$722$	−48.9287	−	51.8683i	−1.82094	−	1.93034i
$723$	3.61124	+	4.16759i	0.134303	+	0.154994i
$724$	−17.0061	+	6.59776i	−0.632026	+	0.245204i
$725$	3.66158	+	1.07514i	0.135988	+	0.0399295i
$726$	1.08589	+	5.80113i	0.0403011	+	0.215300i
$727$	−23.8616	−	15.3349i	−0.884977	−	0.568740i	0.0173223	−	0.999850i	$-0.494486\pi$
$727$	−23.8616	−	15.3349i	−0.884977	−	0.568740i	−0.902300	+	0.431110i	$0.858122\pi$
$728$	41.7370	−	25.8848i	1.54687	−	0.959356i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−8.08284	−	0.815521i	−0.299159	−	0.0301838i
$731$	4.70914	+	32.7528i	0.174174	+	1.21141i
$732$	−12.8066	+	7.21215i	−0.473347	+	0.266569i
$733$	−32.9906	+	28.5865i	−1.21853	+	1.05587i	−0.221803	+	0.975092i	$0.571194\pi$
$733$	−32.9906	+	28.5865i	−1.21853	+	1.05587i	−0.996732	+	0.0807750i	$0.974260\pi$
$734$	−3.28926	+	4.13685i	−0.121409	+	0.152694i
$735$	−1.32950	−	0.607163i	−0.0490394	−	0.0223955i
$736$	47.1480	−	3.23107i	1.73790	−	0.119099i
$737$	−20.9124	+	24.0682i	−0.770318	+	0.886565i
$738$	−1.33027	−	3.91121i	−0.0489680	−	0.143974i
$739$	−2.06135	+	4.51372i	−0.0758279	+	0.166040i	−0.943749	−	0.330661i	$-0.892728\pi$
$739$	−2.06135	+	4.51372i	−0.0758279	+	0.166040i	0.867922	+	0.496701i	$0.165456\pi$
$740$	5.59095	+	2.00236i	0.205528	+	0.0736081i
$741$	29.0025	+	33.4707i	1.06543	+	1.22958i
$742$	−25.2293	+	4.72256i	−0.926195	+	0.173370i
$743$	−16.1700	+	2.32490i	−0.593220	+	0.0852922i	−0.432385	−	0.901689i	$-0.642328\pi$
$743$	−16.1700	+	2.32490i	−0.593220	+	0.0852922i	−0.160835	+	0.986981i	$0.551419\pi$
$744$	−2.20145	−	3.54965i	−0.0807092	−	0.130136i
$745$	−1.41077	−	4.80465i	−0.0516867	−	0.176029i
$746$	8.49177	+	0.856780i	0.310906	+	0.0313689i
$747$	4.67035	−	7.26721i	0.170879	−	0.265893i
$748$	−19.9515	−	35.4281i	−0.729501	−	1.29538i
$749$	16.8351	−	57.3350i	0.615140	−	2.09497i
$750$	0.234033	+	5.53666i	0.00854569	+	0.202170i
$751$	11.0292	−	9.55686i	0.402461	−	0.348735i	−0.429989	−	0.902834i	$-0.641483\pi$
$751$	11.0292	−	9.55686i	0.402461	−	0.348735i	0.832451	+	0.554099i	$0.186937\pi$
$752$	−0.0895147	−	0.524689i	−0.00326426	−	0.0191334i
$753$	0.534857	−	3.72001i	0.0194913	−	0.135565i
$754$	−5.48897	−	2.23163i	−0.199897	−	0.0812713i
$755$	0.458433	+	0.529059i	0.0166841	+	0.0192544i
$756$	−5.77458	−	3.05573i	−0.210019	−	0.111136i
$757$	−5.01047	−	7.79644i	−0.182109	−	0.283366i	0.738182	−	0.674601i	$-0.235684\pi$
$757$	−5.01047	−	7.79644i	−0.182109	−	0.283366i	−0.920291	+	0.391235i	$0.872048\pi$
$758$	−7.75553	−	15.2435i	−0.281694	−	0.553669i
$759$	−17.5936	+	27.3761i	−0.638606	+	0.993690i
$760$	−0.150742	+	9.38193i	−0.00546798	+	0.340318i
$761$	−2.08659	+	2.40805i	−0.0756388	+	0.0872918i	−0.792308	−	0.610122i	$-0.791120\pi$
$761$	−2.08659	+	2.40805i	−0.0756388	+	0.0872918i	0.716669	+	0.697414i	$0.245666\pi$
$762$	−0.497640	−	11.7730i	−0.0180276	−	0.426490i
$763$	26.5757	+	23.0280i	0.962106	+	0.833669i
$764$	2.62424	+	2.55642i	0.0949417	+	0.0924882i
$765$	−0.585454	−	1.99387i	−0.0211671	−	0.0720886i
$766$	11.6890	−	3.97563i	0.422341	−	0.143646i
$767$	−8.90414			−0.321510
$768$	15.5668	+	3.69812i	0.561717	+	0.133445i
$769$	15.2961	−	23.8011i	0.551590	−	0.858291i	−0.447767	−	0.894150i	$-0.647780\pi$
$769$	15.2961	−	23.8011i	0.551590	−	0.858291i	0.999357	+	0.0358593i	$0.0114168\pi$
$770$	−5.21193	+	4.91655i	−0.187825	+	0.177180i
$771$	−8.72761	−	19.1108i	−0.314317	−	0.688258i
$772$	46.7211	−	3.95685i	1.68153	−	0.142410i
$773$	−14.6433	+	4.29967i	−0.526684	+	0.154649i	−0.534256	−	0.845323i	$-0.679408\pi$
$773$	−14.6433	+	4.29967i	−0.526684	+	0.154649i	0.00757140	+	0.999971i	$0.497590\pi$
$774$	8.48872	−	2.88716i	0.305121	−	0.103777i
$775$	7.14965			0.256823
$776$	21.6337	+	6.73159i	0.776605	+	0.241650i
$777$	−3.46697	−	24.1133i	−0.124377	−	0.865059i
$778$	16.8714	−	41.4973i	0.604870	−	1.48775i
$779$	23.3534	+	6.85718i	0.836722	+	0.245684i
$780$	0.246681	−	4.22568i	0.00883260	−	0.151304i
$781$	−21.0230	−	32.7125i	−0.752264	−	1.17055i
$782$	14.8580	−	59.8448i	0.531320	−	2.14005i
$783$	0.112176	+	0.780201i	0.00400884	+	0.0278821i
$784$	−4.50411	−	13.9754i	−0.160861	−	0.499120i
$785$	−0.766667	+	0.350125i	−0.0273635	+	0.0124965i
$786$	13.3424	−	22.8265i	0.475907	−	0.814194i
$787$	8.15711	−	9.41380i	0.290769	−	0.335566i	−0.591505	−	0.806301i	$-0.701466\pi$
$787$	8.15711	−	9.41380i	0.290769	−	0.335566i	0.882274	+	0.470736i	$0.156011\pi$
$788$	−24.2086	+	13.6332i	−0.862396	+	0.485664i
$789$	−6.86748	+	3.13627i	−0.244489	+	0.111654i
$790$	2.55065	−	4.36372i	0.0907480	−	0.155254i
$791$	8.39417	−	28.5879i	0.298462	−	1.01647i
$792$	−8.44133	+	7.08025i	−0.299950	+	0.251586i
$793$	−5.55926	+	38.6655i	−0.197415	+	1.37305i
$794$	27.6430	+	6.86307i	0.981013	+	0.243561i
$795$	−0.918993	+	2.01231i	−0.0325933	+	0.0713694i
$796$	41.8254	+	30.4641i	1.48246	+	1.07977i
$797$	4.76013	−	10.4232i	0.168613	−	0.369210i	−0.806396	−	0.591375i	$-0.798585\pi$
$797$	4.76013	−	10.4232i	0.168613	−	0.369210i	0.975009	+	0.222165i	$0.0713125\pi$
$798$	34.3059	−	17.4540i	1.21441	−	0.617865i
$799$	−0.687422	−	0.0988363i	−0.0243192	−	0.00349658i
$800$	−19.4234	+	19.3081i	−0.686722	+	0.682646i
$801$	11.1650	−	7.17534i	0.394497	−	0.253528i
$802$	−25.1106	−	2.53354i	−0.886686	−	0.0894625i
$803$	56.1988			1.98321
$804$	−16.0363	−	3.29189i	−0.565557	−	0.116096i
$805$	−10.8659			−0.382972
$806$	−11.0451	−	1.11440i	−0.389046	−	0.0392529i
$807$	5.93768	−	3.81592i	0.209016	−	0.134327i
$808$	1.14089	+	8.95400i	0.0401364	+	0.315001i
$809$	18.2815	+	2.62848i	0.642742	+	0.0924123i	0.455976	−	0.889992i	$-0.349290\pi$
$809$	18.2815	+	2.62848i	0.642742	+	0.0924123i	0.186766	+	0.982404i	$0.440199\pi$
$810$	−0.501867	+	0.255338i	−0.0176338	+	0.00897165i
$811$	9.57225	−	20.9603i	0.336127	−	0.736016i	−0.663802	−	0.747908i	$-0.731058\pi$
$811$	9.57225	−	20.9603i	0.336127	−	0.736016i	0.999929	+	0.0118923i	$0.00378551\pi$
$812$	−3.03185	+	4.16255i	−0.106397	+	0.146077i
$813$	−7.05425	+	15.4466i	−0.247403	+	0.541738i
$814$	−39.8719	−	9.89919i	−1.39751	−	0.346967i
$815$	1.10475	−	7.68371i	0.0386977	−	0.269149i
$816$	10.8230	−	17.8517i	0.378882	−	0.624935i
$817$	−14.8825	+	50.6852i	−0.520673	+	1.77325i
$818$	−20.3417	+	34.8012i	−0.711232	+	1.21680i
$819$	−15.7946	+	7.21316i	−0.551909	+	0.252048i
$820$	−1.14148	−	2.02694i	−0.0398623	−	0.0707837i
$821$	−6.10963	+	7.05089i	−0.213228	+	0.246078i	−0.852280	−	0.523085i	$-0.824781\pi$
$821$	−6.10963	+	7.05089i	−0.213228	+	0.246078i	0.639053	+	0.769163i	$0.279326\pi$
$822$	4.57853	−	7.83308i	0.159695	−	0.273210i
$823$	−24.1743	+	11.0400i	−0.842664	+	0.384832i	−0.789497	−	0.613754i	$-0.789659\pi$
$823$	−24.1743	+	11.0400i	−0.842664	+	0.384832i	−0.0531666	+	0.998586i	$0.516931\pi$
$824$	23.7738	+	0.381979i	0.828198	+	0.0133069i
$825$	−2.68390	−	18.6669i	−0.0934415	−	0.649900i
$826$	−1.86469	+	7.51056i	−0.0648807	+	0.261326i
$827$	15.9423	+	24.8068i	0.554370	+	0.862616i	0.999460	−	0.0328697i	$-0.0104646\pi$
$827$	15.9423	+	24.8068i	0.554370	+	0.862616i	−0.445090	+	0.895486i	$0.646828\pi$
$828$	−16.6800	−	0.973724i	−0.579671	−	0.0338392i
$829$	7.46935	+	2.19320i	0.259421	+	0.0761729i	0.408857	−	0.912599i	$-0.365928\pi$
$829$	7.46935	+	2.19320i	0.259421	+	0.0761729i	−0.149436	+	0.988771i	$0.547746\pi$
$830$	1.83202	−	4.50608i	0.0635903	−	0.156408i
$831$	0.792360	+	5.51098i	0.0274867	+	0.191174i
$832$	33.0156	−	26.8005i	1.14461	−	0.929140i
$833$	−19.1583			−0.663795
$834$	−14.0674	+	4.78458i	−0.487115	+	0.165676i
$835$	3.56805	−	1.04767i	0.123477	−	0.0362562i
$836$	−5.47767	−	64.6785i	−0.189449	−	2.23695i
$837$	0.613465	+	1.34330i	0.0212045	+	0.0464313i
$838$	30.8726	−	29.1229i	1.06648	−	1.00603i
$839$	−24.4308	+	38.0151i	−0.843446	+	1.31243i	0.104672	+	0.994507i	$0.466621\pi$
$839$	−24.4308	+	38.0151i	−0.843446	+	1.31243i	−0.948117	+	0.317920i	$0.897016\pi$
$840$	−3.51266	−	1.09301i	−0.121198	−	0.0377123i
$841$	−28.3787			−0.978576
$842$	−4.13535	+	1.40650i	−0.142513	+	0.0484713i
$843$	−2.92275	−	9.95398i	−0.100665	−	0.342833i
$844$	−3.75328	+	3.85285i	−0.129193	+	0.132620i
$845$	−4.59029	−	3.97751i	−0.157911	−	0.136831i
$846$	0.00794747	+	0.188018i	0.000273240	+	0.00646419i
$847$	8.92737	−	10.3027i	0.306748	−	0.354006i
$848$	−21.1529	+	6.81735i	−0.726394	+	0.234109i
$849$	−12.1240	+	18.8653i	−0.416095	+	0.647456i
$850$	16.2041	+	31.8492i	0.555797	+	1.09242i
$851$	−33.6833	−	52.4123i	−1.15465	−	1.79667i
$852$	9.33820	−	17.6469i	0.319921	−	0.604574i
$853$	−22.9592	−	26.4963i	−0.786108	−	0.907217i	0.211426	−	0.977394i	$-0.432189\pi$
$853$	−22.9592	−	26.4963i	−0.786108	−	0.907217i	−0.997535	+	0.0701767i	$0.977644\pi$
$854$	31.4498	+	12.7864i	1.07619	+	0.437543i
$855$	0.472121	−	3.28367i	0.0161462	−	0.112299i
$856$	8.18513	−	51.0882i	0.279762	−	1.74616i
$857$	8.62572	−	7.47423i	0.294649	−	0.255315i	−0.494973	−	0.868908i	$-0.664822\pi$
$857$	8.62572	−	7.47423i	0.294649	−	0.255315i	0.789622	+	0.613593i	$0.210277\pi$
$858$	1.23663	+	29.2558i	0.0422180	+	0.998776i
$859$	0.102614	−	0.349471i	0.00350114	−	0.0119238i	−0.957724	−	0.287689i	$-0.907113\pi$
$859$	0.102614	−	0.349471i	0.00350114	−	0.0119238i	0.961225	+	0.275765i	$0.0889312\pi$
$860$	4.39917	−	2.47742i	0.150011	−	0.0844794i
$861$	−5.15910	+	8.02771i	−0.175822	+	0.273584i
$862$	−1.20710	−	0.121791i	−0.0411141	−	0.00414822i
$863$	−6.96996	−	23.7375i	−0.237260	−	0.808034i	−0.988916	−	0.148478i	$-0.952562\pi$
$863$	−6.96996	−	23.7375i	−0.237260	−	0.808034i	0.751655	−	0.659556i	$-0.229256\pi$
$864$	−5.29428	−	1.99264i	−0.180115	−	0.0677908i
$865$	4.69657	−	0.675265i	0.159688	−	0.0229597i
$866$	−15.1884	+	2.84305i	−0.516123	+	0.0966108i
$867$	−6.70504	−	7.73803i	−0.227715	−	0.262797i
$868$	−3.25302	+	9.08303i	−0.110415	+	0.308298i
$869$	−14.5252	+	31.8058i	−0.492735	+	1.07894i
$870$	0.142917	+	0.420200i	0.00484535	+	0.0142461i
$871$	−32.9207	+	28.4480i	−1.11548	+	0.963923i
$872$	25.3464	+	16.8706i	0.858338	+	0.571310i
$873$	−7.28652	−	3.32764i	−0.246611	−	0.112624i
$874$	61.2638	−	77.0505i	2.07228	−	2.60627i
$875$	9.67381	−	8.38240i	0.327034	−	0.283377i
$876$	14.1589	+	25.1420i	0.478385	+	0.849470i
$877$	−0.256037	−	1.78077i	−0.00864575	−	0.0601325i	0.985042	−	0.172315i	$-0.0551248\pi$
$877$	−0.256037	−	1.78077i	−0.00864575	−	0.0601325i	−0.993688	+	0.112183i	$0.964216\pi$
$878$	−50.0499	−	5.04980i	−1.68910	−	0.170422i
$879$	−9.35400	+	2.74658i	−0.315503	+	0.0926399i
$880$	−3.93853	+	4.79328i	−0.132768	+	0.161582i
$881$	−10.8892	−	6.99804i	−0.366865	−	0.235770i	0.344200	−	0.938897i	$-0.388150\pi$
$881$	−10.8892	−	6.99804i	−0.366865	−	0.235770i	−0.711065	+	0.703127i	$0.751787\pi$
$882$	0.955150	+	5.10269i	0.0321616	+	0.171816i
$883$	25.1671	+	7.38973i	0.846941	+	0.248684i	0.676279	−	0.736645i	$-0.263591\pi$
$883$	25.1671	+	7.38973i	0.846941	+	0.248684i	0.170662	+	0.985330i	$0.445410\pi$
$884$	−20.0685	−	51.7277i	−0.674978	−	1.73979i
$885$	0.436774	+	0.504065i	0.0146820	+	0.0169439i
$886$	−10.9388	−	11.5960i	−0.367497	−	0.389576i
$887$	−4.44474	−	0.639058i	−0.149240	−	0.0214575i	0.0672899	−	0.997733i	$-0.478565\pi$
$887$	−4.44474	−	0.639058i	−0.149240	−	0.0214575i	−0.216530	+	0.976276i	$0.569474\pi$
$888$	−5.61678	−	20.3318i	−0.188487	−	0.682290i
$889$	−20.5700	+	17.8240i	−0.689897	+	0.597799i
$890$	5.43618	−	5.12809i	0.182221	−	0.171894i
$891$	3.27692	−	2.10595i	0.109781	−	0.0705520i
$892$	−19.7876	+	20.3125i	−0.662537	+	0.680113i
$893$	−0.932698	−	0.599408i	−0.0312115	−	0.0200584i
$894$	−11.0692	+	13.9215i	−0.370209	+	0.465606i
$895$	3.57995	+	3.10204i	0.119665	+	0.103690i
$896$	−15.6919	−	33.4608i	−0.524230	−	1.11785i
$897$	−29.0803	+	33.5605i	−0.970964	+	1.12055i
$898$	−21.3694	−	42.0017i	−0.713108	−	1.40161i
$899$	1.11686	−	0.327940i	0.0372494	−	0.0109374i
$900$	7.67497	−	5.90373i	0.255832	−	0.196791i
$901$			28.9977i			0.966054i
$902$	9.26417	+	13.1583i	0.308463	+	0.438123i
$903$	−17.4230	−	11.1971i	−0.579801	−	0.372615i
$904$	4.08121	−	25.4732i	0.135739	−	0.847226i
$905$	3.30329	−	1.50856i	0.109805	−	0.0501463i
$906$	0.599136	−	2.41319i	0.0199050	−	0.0801729i
$907$	12.5605	+	42.7771i	0.417064	+	1.42039i	0.853706	+	0.520755i	$0.174349\pi$
$907$	12.5605	+	42.7771i	0.417064	+	1.42039i	−0.436642	+	0.899635i	$0.643832\pi$
$908$	9.60324	+	12.4844i	0.318695	+	0.414310i
$909$		−	3.19131i		−	0.105849i
$910$	−7.99462	+	5.62866i	−0.265019	+	0.186588i
$911$	9.81740	−	1.41153i	0.325265	−	0.0467660i	0.0222517	−	0.999752i	$-0.492916\pi$
$911$	9.81740	−	1.41153i	0.325265	−	0.0467660i	0.303013	+	0.952986i	$0.402007\pi$
$912$	27.5556	−	18.7459i	0.912457	−	0.620739i
$913$	−9.48019	+	32.2866i	−0.313749	+	1.06853i
$914$	−15.8085	+	38.8828i	−0.522897	+	1.28613i
$915$	2.46156	−	1.58195i	0.0813766	−	0.0522975i
$916$	−0.298075	−	3.51957i	−0.00984867	−	0.116290i
$917$	−60.4506	+	8.69148i	−1.99625	+	0.287018i
$918$	−4.59358	+	5.77727i	−0.151611	+	0.190678i
$919$	21.0946	+	46.1907i	0.695846	+	1.52369i	0.844936	+	0.534867i	$0.179638\pi$
$919$	21.0946	+	46.1907i	0.695846	+	1.52369i	−0.149090	+	0.988824i	$0.547635\pi$
$920$	−9.33285	+	1.18916i	−0.307695	+	0.0392055i
$921$	0.896837	+	0.777114i	0.0295518	+	0.0256068i
$922$	−1.74260	−	9.30947i	−0.0573894	−	0.306591i
$923$	−22.0432	−	48.2678i	−0.725560	−	1.58875i
$924$	24.9359	+	5.08359i	0.820332	+	0.167238i
$925$	34.6433	+	10.1722i	1.13906	+	0.334460i
$926$	35.1047	−	1.48387i	1.15361	−	0.0487629i
$927$	−8.32081	−	1.19635i	−0.273291	−	0.0392934i
$928$	−2.14855	+	3.90707i	−0.0705295	+	0.128256i
$929$	29.2237	+	13.3460i	0.958799	+	0.437869i	0.832440	−	0.554116i	$-0.186943\pi$
$929$	29.2237	+	13.3460i	0.958799	+	0.437869i	0.126359	+	0.991985i	$0.459671\pi$
$930$	0.478707	+	0.679927i	0.0156974	+	0.0222957i
$931$	−27.8208	−	12.7053i	−0.911791	−	0.416401i
$932$	30.3132	−	31.1173i	0.992941	−	1.01928i
$933$	4.32895	−	30.1085i	0.141724	−	0.985709i
$934$	11.4188	−	19.5356i	0.373634	−	0.639223i
$935$	4.37627	+	6.80961i	0.143119	+	0.222698i
$936$	−12.7768	+	7.92404i	−0.417623	+	0.259005i
$937$		−	1.61786i		−	0.0528531i	−0.999651	−	0.0264265i	$-0.991587\pi$
$937$		−	1.61786i		−	0.0528531i	0.999651	−	0.0264265i	$-0.00841281\pi$
$938$	17.1014	+	33.7258i	0.558381	+	1.10119i
$939$		−	28.8917i		−	0.942846i
$940$	0.0238779	+	0.103240i	0.000778810	+	0.00336731i
$941$	21.0964	+	32.8267i	0.687724	+	1.07012i	0.993030	+	0.117865i	$0.0376051\pi$
$941$	21.0964	+	32.8267i	0.687724	+	1.07012i	−0.305305	+	0.952255i	$0.598758\pi$
$942$	2.58449	+	1.51067i	0.0842072	+	0.0492202i
$943$	−3.47314	+	24.1562i	−0.113101	+	0.786634i
$944$	−0.779649	+	6.65499i	−0.0253754	+	0.216601i
$945$	1.18311	+	0.540309i	0.0384866	+	0.0175762i
$946$	−28.5581	+	20.1065i	−0.928505	+	0.653720i
$947$	5.03076	+	2.29747i	0.163478	+	0.0746578i	0.495473	−	0.868623i	$-0.334995\pi$
$947$	5.03076	+	2.29747i	0.163478	+	0.0746578i	−0.331996	+	0.943281i	$0.607722\pi$
$948$	−17.8887	+	1.51501i	−0.580999	+	0.0492052i
$949$	75.9082	+	10.9140i	2.46409	+	0.354282i
$950$	2.40922	+	56.9963i	0.0781653	+	1.84920i
$951$	11.0275	+	3.23798i	0.357592	+	0.104999i
$952$	−47.8345	+	6.09491i	−1.55033	+	0.197537i
$953$	−3.81068	−	8.34422i	−0.123440	−	0.270296i	0.837816	−	0.545952i	$-0.183832\pi$
$953$	−3.81068	−	8.34422i	−0.123440	−	0.270296i	−0.961256	+	0.275657i	$0.911105\pi$
$954$	7.72335	−	1.44570i	0.250053	−	0.0468063i
$955$	−0.551209	−	0.477626i	−0.0178367	−	0.0154556i
$956$	38.3445	+	7.81714i	1.24015	+	0.252824i
$957$	−1.27547	−	2.79290i	−0.0412302	−	0.0902815i
$958$	−22.7199	−	18.0649i	−0.734047	−	0.583650i
$959$	−20.7440	+	2.98254i	−0.669860	+	0.0963113i
$960$	−3.13669	−	0.554372i	−0.101236	−	0.0178923i
$961$	−24.2443	+	15.5808i	−0.782073	+	0.502608i
$962$	−51.9329	−	21.1142i	−1.67438	−	0.680748i
$963$	−5.15366	+	17.5518i	−0.166074	+	0.565598i
$964$	0.642743	−	11.0103i	0.0207014	−	0.354617i
$965$	−9.23960	+	1.32845i	−0.297433	+	0.0427645i
$966$	22.2180	+	31.5571i	0.714853	+	1.01533i
$967$		−	4.43574i		−	0.142644i	−0.997453	−	0.0713218i	$-0.977278\pi$
$967$		−	4.43574i		−	0.142644i	0.997453	−	0.0713218i	$-0.0227217\pi$
$968$	6.54031	−	9.82616i	0.210213	−	0.315825i
$969$	−12.2511	−	41.7233i	−0.393561	−	1.34035i
$970$	−4.37765	−	1.08686i	−0.140558	−	0.0348971i
$971$	−50.6027	+	23.1095i	−1.62392	+	0.741618i	−0.999229	−	0.0392568i	$-0.987501\pi$
$971$	−50.6027	+	23.1095i	−1.62392	+	0.741618i	−0.624688	+	0.780875i	$0.714774\pi$
$972$	1.76775	+	0.935440i	0.0567007	+	0.0300043i
$973$	28.8732	+	18.5557i	0.925632	+	0.594868i
$974$	2.38361	−	1.67820i	0.0763758	−	0.0537729i
$975$		−	25.7349i		−	0.824175i
$976$	28.4120	+	7.54057i	0.909445	+	0.241368i
$977$	40.4643	−	11.8814i	1.29457	−	0.380119i	0.439316	−	0.898333i	$-0.355221\pi$
$977$	40.4643	−	11.8814i	1.29457	−	0.380119i	0.855251	+	0.518214i	$0.173403\pi$
$978$	−24.5743	+	12.5028i	−0.785799	+	0.399795i
$979$	−33.8549	+	39.0707i	−1.08201	+	1.24870i
$980$	1.05730	+	2.72525i	0.0337743	+	0.0870550i
$981$	−8.13554	−	7.04948i	−0.259748	−	0.225073i
$982$	14.1901	+	11.2827i	0.452825	+	0.360047i
$983$	34.4825	+	22.1606i	1.09982	+	0.706812i	0.959052	−	0.283230i	$-0.0914060\pi$
$983$	34.4825	+	22.1606i	1.09982	+	0.706812i	0.140769	+	0.990042i	$0.455042\pi$
$984$	−3.55266	+	7.45972i	−0.113255	+	0.237807i
$985$	4.65312	−	2.99038i	0.148261	−	0.0952815i
$986$	3.99214	+	4.23198i	0.127136	+	0.134774i
$987$	0.328510	−	0.284655i	0.0104566	−	0.00906068i
$988$	5.16199	−	88.4256i	0.164225	−	2.81319i
$989$	−52.4275	−	7.53794i	−1.66710	−	0.239692i
$990$	1.59551	−	1.50509i	0.0507087	−	0.0478348i
$991$	−16.7417	−	19.3210i	−0.531818	−	0.613751i	0.424732	−	0.905319i	$-0.360368\pi$
$991$	−16.7417	−	19.3210i	−0.531818	−	0.613751i	−0.956550	+	0.291568i	$0.905823\pi$
$992$	−1.80001	+	8.15755i	−0.0571504	+	0.259002i
$993$	−11.8559	−	3.48120i	−0.376235	−	0.110473i
$994$	−45.3297	+	8.48507i	−1.43777	+	0.269130i
$995$	−8.66595	−	5.56927i	−0.274729	−	0.176558i
$996$	−16.8327	+	3.89317i	−0.533366	+	0.123360i
$997$	20.7806	−	6.10173i	0.658128	−	0.193244i	0.0644181	−	0.997923i	$-0.479481\pi$
$997$	20.7806	−	6.10173i	0.658128	−	0.193244i	0.593710	+	0.804679i	$0.297663\pi$
$998$	−1.59553	+	15.8137i	−0.0505057	+	0.500575i
$999$	1.06133	+	7.38172i	0.0335790	+	0.233547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.u.a.43.18	✓	340
4.3	odd	2		804.2.u.b.43.10	yes	340
67.53	odd	22		804.2.u.b.187.10	yes	340
268.187	even	22	inner	804.2.u.a.187.18	yes	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.u.a.43.18	✓	340	1.1	even	1	trivial
804.2.u.a.187.18	yes	340	268.187	even	22	inner
804.2.u.b.43.10	yes	340	4.3	odd	2
804.2.u.b.187.10	yes	340	67.53	odd	22

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.141967 - 1.40707i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-1.95969 - 0.399514i) q^{4} +(0.394110 + 0.0566645i) q^{5} +(-0.641289 - 1.26046i) q^{6} +(-1.35700 + 2.97142i) q^{7} +(-0.840356 + 2.70070i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.141967 - 1.40707i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-1.95969 - 0.399514i) q^{4} +(0.394110 + 0.0566645i) q^{5} +(-0.641289 - 1.26046i) q^{6} +(-1.35700 + 2.97142i) q^{7} +(-0.840356 + 2.70070i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.135682 - 0.546496i) q^{10} +(-0.554357 + 3.85564i) q^{11} +(-1.86459 + 0.723396i) q^{12} +(-1.49755 + 5.10019i) q^{13} +(3.98835 + 2.33124i) q^{14} +(0.362182 - 0.165403i) q^{15} +(3.68078 + 1.56585i) q^{16} +(3.41778 - 3.94432i) q^{17} +(-1.22094 - 0.713655i) q^{18} +(7.57893 - 3.46118i) q^{19} +(-0.749696 - 0.268498i) q^{20} +(0.464889 + 3.23337i) q^{21} +(5.34645 + 1.32739i) q^{22} +(4.51663 + 7.02801i) q^{23} +(0.753159 + 2.72631i) q^{24} +(-4.64535 - 1.36400i) q^{25} +(6.96372 + 2.83122i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(3.84643 - 5.28093i) q^{28} -0.788224 q^{29} +(-0.181316 - 0.533097i) q^{30} +(-1.41693 + 0.416049i) q^{31} +(2.72581 - 4.95681i) q^{32} +(1.61816 + 3.54328i) q^{33} +(-5.06473 - 5.36901i) q^{34} +(-0.703183 + 1.09417i) q^{35} +(-1.17750 + 1.61663i) q^{36} -7.45763 q^{37} +(-3.79417 - 11.1555i) q^{38} +(1.49755 + 5.10019i) q^{39} +(-0.484227 + 1.01676i) q^{40} +(2.20772 + 1.91300i) q^{41} +(4.61558 - 0.195099i) q^{42} +(-4.15189 + 4.79154i) q^{43} +(2.62675 - 7.33439i) q^{44} +(0.215263 - 0.334956i) q^{45} +(10.5301 - 5.35747i) q^{46} +(-0.0719417 - 0.111943i) q^{47} +(3.94303 - 0.672702i) q^{48} +(-2.40387 - 2.77421i) q^{49} +(-2.57873 + 6.34269i) q^{50} +(0.742754 - 5.16597i) q^{51} +(4.97234 - 9.39651i) q^{52} +(-4.19901 + 3.63846i) q^{53} +(-1.41295 + 0.0597251i) q^{54} +(-0.436956 + 1.48813i) q^{55} +(-6.88457 - 6.16192i) q^{56} +(4.50455 - 7.00921i) q^{57} +(-0.111902 + 1.10909i) q^{58} +(0.471937 + 1.60727i) q^{59} +(-0.775845 + 0.179442i) q^{60} +(7.27409 - 1.04586i) q^{61} +(0.384253 + 2.05279i) q^{62} +(2.13918 + 2.46875i) q^{63} +(-6.58760 - 4.53910i) q^{64} +(-0.879201 + 1.92518i) q^{65} +(5.21536 - 1.77384i) q^{66} +(6.87996 + 4.43466i) q^{67} +(-8.27360 + 6.36420i) q^{68} +(7.59926 + 3.47046i) q^{69} +(1.43975 + 1.14476i) q^{70} +(-7.54441 + 6.53727i) q^{71} +(2.10755 + 1.88633i) q^{72} +(-2.05323 - 14.2805i) q^{73} +(-1.05874 + 10.4934i) q^{74} +(-4.64535 + 1.36400i) q^{75} +(-16.2352 + 3.75495i) q^{76} +(-10.7045 - 6.87934i) q^{77} +(7.38893 - 1.38310i) q^{78} +(8.61277 + 2.52894i) q^{79} +(1.36190 + 0.825687i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(3.00515 - 2.83483i) q^{82} +(8.55062 + 1.22939i) q^{83} +(0.380741 - 6.52214i) q^{84} +(1.57048 - 1.36083i) q^{85} +(6.15260 + 6.52224i) q^{86} +(-0.663096 + 0.426146i) q^{87} +(-9.94708 - 4.73726i) q^{88} +(11.1650 + 7.17534i) q^{89} +(-0.440746 - 0.350443i) q^{90} +(-13.1226 - 11.3708i) q^{91} +(-6.04340 - 15.5772i) q^{92} +(-0.967068 + 1.11606i) q^{93} +(-0.167726 + 0.0853347i) q^{94} +(3.18306 - 0.934631i) q^{95} +(-0.386759 - 5.64362i) q^{96} -8.01040i q^{97} +(-4.24478 + 2.98857i) q^{98} +(3.27692 + 2.10595i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q - 34 q^{3} - 2 q^{4} + 11 q^{6} - 4 q^{7} + 39 q^{8} - 34 q^{9}+O(q^{10}) \) 340 * q - 34 * q^3 - 2 * q^4 + 11 * q^6 - 4 * q^7 + 39 * q^8 - 34 * q^9	\( 340 q - 34 q^{3} - 2 q^{4} + 11 q^{6} - 4 q^{7} + 39 q^{8} - 34 q^{9} - 27 q^{10} + 9 q^{12} + 4 q^{14} - 2 q^{16} + 12 q^{20} - 4 q^{21} - 3 q^{22} + 6 q^{24} + 34 q^{25} - 10 q^{26} - 34 q^{27} - 25 q^{28} + 16 q^{29} + 6 q^{30} + 4 q^{31} - 55 q^{32} + 9 q^{36} - 12 q^{37} - 26 q^{38} - 37 q^{40} + 4 q^{42} + 4 q^{43} + 51 q^{44} + 81 q^{46} - 2 q^{48} - 46 q^{49} - 15 q^{50} - 32 q^{52} - 14 q^{56} + 66 q^{57} - 92 q^{58} - 43 q^{60} + 2 q^{62} + 18 q^{63} + 7 q^{64} + 8 q^{66} + 18 q^{67} - 208 q^{68} - 56 q^{70} + 6 q^{72} + 54 q^{73} - 22 q^{74} + 34 q^{75} + 120 q^{76} + 8 q^{77} - 10 q^{78} - 10 q^{79} + 68 q^{80} - 34 q^{81} + 84 q^{82} + 8 q^{84} + 104 q^{86} + 16 q^{87} + 138 q^{88} - 27 q^{90} - 42 q^{92} + 4 q^{93} - 32 q^{94} + 40 q^{95} + 7 q^{98}+O(q^{100}) \) 340 * q - 34 * q^3 - 2 * q^4 + 11 * q^6 - 4 * q^7 + 39 * q^8 - 34 * q^9 - 27 * q^10 + 9 * q^12 + 4 * q^14 - 2 * q^16 + 12 * q^20 - 4 * q^21 - 3 * q^22 + 6 * q^24 + 34 * q^25 - 10 * q^26 - 34 * q^27 - 25 * q^28 + 16 * q^29 + 6 * q^30 + 4 * q^31 - 55 * q^32 + 9 * q^36 - 12 * q^37 - 26 * q^38 - 37 * q^40 + 4 * q^42 + 4 * q^43 + 51 * q^44 + 81 * q^46 - 2 * q^48 - 46 * q^49 - 15 * q^50 - 32 * q^52 - 14 * q^56 + 66 * q^57 - 92 * q^58 - 43 * q^60 + 2 * q^62 + 18 * q^63 + 7 * q^64 + 8 * q^66 + 18 * q^67 - 208 * q^68 - 56 * q^70 + 6 * q^72 + 54 * q^73 - 22 * q^74 + 34 * q^75 + 120 * q^76 + 8 * q^77 - 10 * q^78 - 10 * q^79 + 68 * q^80 - 34 * q^81 + 84 * q^82 + 8 * q^84 + 104 * q^86 + 16 * q^87 + 138 * q^88 - 27 * q^90 - 42 * q^92 + 4 * q^93 - 32 * q^94 + 40 * q^95 + 7 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more