LMFDB - Embedded newform 225.2.w.a.92.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(2,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.w (of order $60$, degree $16$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$448$
Relative dimension:	$28$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			92.4
Character	$\chi$	$=$	225.92
Dual form			225.2.w.a.203.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75192 + 1.13771i) q^{2} +(1.04649 - 1.38017i) q^{3} +(0.961361 - 2.15925i) q^{4} +(1.16649 + 1.90770i) q^{5} +(-0.263140 + 3.60854i) q^{6} +(1.54129 - 0.412989i) q^{7} +(0.118816 + 0.750173i) q^{8} +(-0.809713 - 2.88866i) q^{9} +O(q^{10})$	\(q+(-1.75192 + 1.13771i) q^{2} +(1.04649 - 1.38017i) q^{3} +(0.961361 - 2.15925i) q^{4} +(1.16649 + 1.90770i) q^{5} +(-0.263140 + 3.60854i) q^{6} +(1.54129 - 0.412989i) q^{7} +(0.118816 + 0.750173i) q^{8} +(-0.809713 - 2.88866i) q^{9} +(-4.21399 - 2.01500i) q^{10} +(-0.630567 + 2.96658i) q^{11} +(-1.97407 - 3.58648i) q^{12} +(1.75498 - 2.70244i) q^{13} +(-2.23036 + 2.47707i) q^{14} +(3.85366 + 0.386441i) q^{15} +(2.10148 + 2.33393i) q^{16} +(2.81003 - 0.445065i) q^{17} +(4.70501 + 4.13948i) q^{18} +(0.869489 - 1.19675i) q^{19} +(5.24061 - 0.684756i) q^{20} +(1.04296 - 2.55943i) q^{21} +(-2.27041 - 5.91461i) q^{22} +(5.04636 - 0.264469i) q^{23} +(1.15970 + 0.621064i) q^{24} +(-2.27861 + 4.45061i) q^{25} +6.73110i q^{26} +(-4.83419 - 1.90542i) q^{27} +(0.589994 - 3.72508i) q^{28} +(0.977494 + 9.30024i) q^{29} +(-7.19095 + 3.70732i) q^{30} +(-0.294781 + 2.80465i) q^{31} +(-7.80423 - 2.09114i) q^{32} +(3.43449 + 3.97479i) q^{33} +(-4.41659 + 3.97671i) q^{34} +(2.58576 + 2.45858i) q^{35} +(-7.01578 - 1.02867i) q^{36} +(5.15475 - 2.62648i) q^{37} +(-0.161722 + 3.08583i) q^{38} +(-1.89323 - 5.25024i) q^{39} +(-1.29250 + 1.10173i) q^{40} +(-2.32843 - 10.9544i) q^{41} +(1.08471 + 5.67049i) q^{42} +(0.0709590 + 0.264823i) q^{43} +(5.79940 + 4.21351i) q^{44} +(4.56617 - 4.91427i) q^{45} +(-8.53992 + 6.20461i) q^{46} +(-9.28216 - 7.51654i) q^{47} +(5.42038 - 0.457952i) q^{48} +(-3.85715 + 2.22693i) q^{49} +(-1.07155 - 10.3895i) q^{50} +(2.32641 - 4.34406i) q^{51} +(-4.14807 - 6.38747i) q^{52} +(-1.02987 - 0.163115i) q^{53} +(10.6369 - 2.16176i) q^{54} +(-6.39489 + 2.25755i) q^{55} +(0.492943 + 1.10717i) q^{56} +(-0.741799 - 2.45243i) q^{57} +(-12.2934 - 15.1811i) q^{58} +(-6.16692 + 1.31082i) q^{59} +(4.53918 - 7.94951i) q^{60} +(6.60922 + 1.40483i) q^{61} +(-2.67444 - 5.24889i) q^{62} +(-2.44099 - 4.11788i) q^{63} +(10.0777 - 3.27444i) q^{64} +(7.20259 + 0.195616i) q^{65} +(-10.5391 - 3.05605i) q^{66} +(-4.46196 + 3.61322i) q^{67} +(1.74045 - 6.49543i) q^{68} +(4.91596 - 7.24158i) q^{69} +(-7.32718 - 1.36538i) q^{70} +(-4.15713 - 5.72180i) q^{71} +(2.07079 - 0.950643i) q^{72} +(2.32334 + 1.18380i) q^{73} +(-6.04254 + 10.4660i) q^{74} +(3.75803 + 7.80239i) q^{75} +(-1.74819 - 3.02796i) q^{76} +(0.253276 + 4.83279i) q^{77} +(9.29003 + 7.04404i) q^{78} +(-8.00246 + 0.841093i) q^{79} +(-2.00108 + 6.73147i) q^{80} +(-7.68873 + 4.67797i) q^{81} +(16.5421 + 16.5421i) q^{82} +(-16.7948 - 6.44693i) q^{83} +(-4.52380 - 4.71255i) q^{84} +(4.12692 + 4.84152i) q^{85} +(-0.425605 - 0.383217i) q^{86} +(13.8588 + 8.38351i) q^{87} +(-2.30037 - 0.120557i) q^{88} +(1.02996 + 3.16988i) q^{89} +(-2.40854 + 13.8044i) q^{90} +(1.58887 - 4.89004i) q^{91} +(4.28032 - 11.1506i) q^{92} +(3.56240 + 3.34189i) q^{93} +(24.8132 + 2.60797i) q^{94} +(3.29728 + 0.262728i) q^{95} +(-11.0532 + 8.58277i) q^{96} +(-5.18249 + 6.39984i) q^{97} +(4.22381 - 8.28970i) q^{98} +(9.08003 - 0.580587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−1.75192	+	1.13771i	−1.23879	+	0.804481i	−0.986594	−	0.163194i	$-0.947820\pi$
$2$	−1.75192	+	1.13771i	−1.23879	+	0.804481i	−0.252199	+	0.967675i	$0.581154\pi$
$3$	1.04649	−	1.38017i	0.604192	−	0.796839i
$3$	1.04649	−	1.38017i	0.604192	−	0.796839i
$4$	0.961361	−	2.15925i	0.480681	−	1.07963i
$5$	1.16649	+	1.90770i	0.521669	+	0.853148i
$5$	1.16649	+	1.90770i	0.521669	+	0.853148i
$6$	−0.263140	+	3.60854i	−0.107426	+	1.47318i
$7$	1.54129	−	0.412989i	0.582555	−	0.156095i	0.0445064	−	0.999009i	$-0.485828\pi$
$7$	1.54129	−	0.412989i	0.582555	−	0.156095i	0.538048	+	0.842914i	$0.319162\pi$
$8$	0.118816	+	0.750173i	0.0420077	+	0.265226i
$9$	−0.809713	−	2.88866i	−0.269904	−	0.962887i
$10$	−4.21399	−	2.01500i	−1.33258	−	0.637200i
$11$	−0.630567	+	2.96658i	−0.190123	+	0.894458i	0.774857	+	0.632136i	$0.217822\pi$
$11$	−0.630567	+	2.96658i	−0.190123	+	0.894458i	−0.964980	+	0.262322i	$0.915512\pi$
$12$	−1.97407	−	3.58648i	−0.569865	−	1.03533i
$13$	1.75498	−	2.70244i	0.486744	−	0.749521i	−0.506910	−	0.861999i	$-0.669212\pi$
$13$	1.75498	−	2.70244i	0.486744	−	0.749521i	0.993654	+	0.112478i	$0.0358789\pi$
$14$	−2.23036	+	2.47707i	−0.596089	+	0.662024i
$15$	3.85366	+	0.386441i	0.995010	+	0.0997788i
$16$	2.10148	+	2.33393i	0.525369	+	0.583481i
$17$	2.81003	−	0.445065i	0.681533	−	0.107944i	0.193937	−	0.981014i	$-0.437874\pi$
$17$	2.81003	−	0.445065i	0.681533	−	0.107944i	0.487595	+	0.873070i	$0.337874\pi$
$18$	4.70501	+	4.13948i	1.10898	+	0.975685i
$19$	0.869489	−	1.19675i	0.199475	−	0.274553i	−0.697548	−	0.716538i	$-0.745726\pi$
$19$	0.869489	−	1.19675i	0.199475	−	0.274553i	0.897022	+	0.441985i	$0.145726\pi$
$20$	5.24061	−	0.684756i	1.17184	−	0.153116i
$21$	1.04296	−	2.55943i	0.227592	−	0.558514i
$22$	−2.27041	−	5.91461i	−0.484052	−	1.26100i
$23$	5.04636	−	0.264469i	1.05224	−	0.0551455i	0.481636	−	0.876372i	$-0.340043\pi$
$23$	5.04636	−	0.264469i	1.05224	−	0.0551455i	0.570603	+	0.821226i	$0.306710\pi$
$24$	1.15970	+	0.621064i	0.236723	+	0.126774i
$25$	−2.27861	+	4.45061i	−0.455723	+	0.890122i
$26$			6.73110i			1.32008i
$27$	−4.83419	−	1.90542i	−0.930340	−	0.366698i
$28$	0.589994	−	3.72508i	0.111498	−	0.703973i
$29$	0.977494	+	9.30024i	0.181516	+	1.72701i	0.584147	+	0.811648i	$0.301429\pi$
$29$	0.977494	+	9.30024i	0.181516	+	1.72701i	−0.402631	+	0.915363i	$0.631904\pi$
$30$	−7.19095	+	3.70732i	−1.31288	+	0.676862i
$31$	−0.294781	+	2.80465i	−0.0529442	+	0.503730i	0.935629	+	0.352986i	$0.114834\pi$
$31$	−0.294781	+	2.80465i	−0.0529442	+	0.503730i	−0.988573	+	0.150744i	$0.951833\pi$
$32$	−7.80423	−	2.09114i	−1.37961	−	0.369664i
$33$	3.43449	+	3.97479i	0.597868	+	0.691922i
$34$	−4.41659	+	3.97671i	−0.757439	+	0.682001i
$35$	2.58576	+	2.45858i	0.437073	+	0.415575i
$36$	−7.01578	−	1.02867i	−1.16930	−	0.171445i
$37$	5.15475	−	2.62648i	0.847436	−	0.431790i	0.0243478	−	0.999704i	$-0.492249\pi$
$37$	5.15475	−	2.62648i	0.847436	−	0.431790i	0.823088	+	0.567913i	$0.192249\pi$
$38$	−0.161722	+	3.08583i	−0.0262347	+	0.500588i
$39$	−1.89323	−	5.25024i	−0.303160	−	0.840711i
$40$	−1.29250	+	1.10173i	−0.204363	+	0.174199i
$41$	−2.32843	−	10.9544i	−0.363639	−	1.71079i	−0.656240	−	0.754553i	$-0.727854\pi$
$41$	−2.32843	−	10.9544i	−0.363639	−	1.71079i	0.292600	−	0.956235i	$-0.405479\pi$
$42$	1.08471	+	5.67049i	0.167374	+	0.874976i
$43$	0.0709590	+	0.264823i	0.0108211	+	0.0403851i	0.971125	−	0.238570i	$-0.0766786\pi$
$43$	0.0709590	+	0.264823i	0.0108211	+	0.0403851i	−0.960304	+	0.278955i	$0.910012\pi$
$44$	5.79940	+	4.21351i	0.874292	+	0.635210i
$45$	4.56617	−	4.91427i	0.680684	−	0.732577i
$46$	−8.53992	+	6.20461i	−1.25914	+	0.914820i
$47$	−9.28216	−	7.51654i	−1.35394	−	1.09640i	−0.986035	−	0.166537i	$-0.946741\pi$
$47$	−9.28216	−	7.51654i	−1.35394	−	1.09640i	−0.367906	−	0.929863i	$-0.619925\pi$
$48$	5.42038	−	0.457952i	0.782364	−	0.0660997i
$49$	−3.85715	+	2.22693i	−0.551021	+	0.318132i
$50$	−1.07155	−	10.3895i	−0.151541	−	1.46930i
$51$	2.32641	−	4.34406i	0.325762	−	0.608291i
$52$	−4.14807	−	6.38747i	−0.575234	−	0.885782i
$53$	−1.02987	−	0.163115i	−0.141463	−	0.0224056i	0.0853012	−	0.996355i	$-0.472815\pi$
$53$	−1.02987	−	0.163115i	−0.141463	−	0.0224056i	−0.226764	+	0.973950i	$0.572815\pi$
$54$	10.6369	−	2.16176i	1.44750	−	0.294178i
$55$	−6.39489	+	2.25755i	−0.862286	+	0.304408i
$56$	0.492943	+	1.10717i	0.0658722	+	0.147951i
$57$	−0.741799	−	2.45243i	−0.0982537	−	0.324832i
$58$	−12.2934	−	15.1811i	−1.61421	−	1.99338i
$59$	−6.16692	+	1.31082i	−0.802865	+	0.170654i	−0.591028	−	0.806651i	$-0.701278\pi$
$59$	−6.16692	+	1.31082i	−0.802865	+	0.170654i	−0.211837	+	0.977305i	$0.567944\pi$
$60$	4.53918	−	7.94951i	0.586006	−	1.02628i
$61$	6.60922	+	1.40483i	0.846223	+	0.179870i	0.610566	−	0.791966i	$-0.290942\pi$
$61$	6.60922	+	1.40483i	0.846223	+	0.179870i	0.235658	+	0.971836i	$0.424276\pi$
$62$	−2.67444	−	5.24889i	−0.339655	−	0.666610i
$63$	−2.44099	−	4.11788i	−0.307536	−	0.518804i
$64$	10.0777	−	3.27444i	1.25971	−	0.409304i
$65$	7.20259	+	0.195616i	0.893372	+	0.0242631i
$66$	−10.5391	−	3.05605i	−1.29727	−	0.376174i
$67$	−4.46196	+	3.61322i	−0.545115	+	0.441425i	−0.861905	−	0.507071i	$-0.830728\pi$
$67$	−4.46196	+	3.61322i	−0.545115	+	0.441425i	0.316790	+	0.948496i	$0.397395\pi$
$68$	1.74045	−	6.49543i	0.211060	−	0.787687i
$69$	4.91596	−	7.24158i	0.591812	−	0.871783i
$70$	−7.32718	−	1.36538i	−0.875765	−	0.163195i
$71$	−4.15713	−	5.72180i	−0.493360	−	0.679052i	0.487643	−	0.873043i	$-0.337857\pi$
$71$	−4.15713	−	5.72180i	−0.493360	−	0.679052i	−0.981003	+	0.193991i	$0.937857\pi$
$72$	2.07079	−	0.950643i	0.244045	−	0.112034i
$73$	2.32334	+	1.18380i	0.271926	+	0.138553i	0.584637	−	0.811295i	$-0.301237\pi$
$73$	2.32334	+	1.18380i	0.271926	+	0.138553i	−0.312711	+	0.949848i	$0.601237\pi$
$74$	−6.04254	+	10.4660i	−0.702431	+	1.21665i
$75$	3.75803	+	7.80239i	0.433940	+	0.900942i
$76$	−1.74819	−	3.02796i	−0.200531	−	0.347330i
$77$	0.253276	+	4.83279i	0.0288635	+	0.550748i
$78$	9.29003	+	7.04404i	1.05189	+	0.797580i
$79$	−8.00246	+	0.841093i	−0.900347	+	0.0946303i	−0.543380	−	0.839487i	$-0.682856\pi$
$79$	−8.00246	+	0.841093i	−0.900347	+	0.0946303i	−0.356967	+	0.934117i	$0.616189\pi$
$80$	−2.00108	+	6.73147i	−0.223727	+	0.752602i
$81$	−7.68873	+	4.67797i	−0.854303	+	0.519775i
$82$	16.5421	+	16.5421i	1.82677	+	1.82677i
$83$	−16.7948	−	6.44693i	−1.84347	−	0.707643i	−0.978640	−	0.205582i	$-0.934091\pi$
$83$	−16.7948	−	6.44693i	−1.84347	−	0.707643i	−0.864832	−	0.502061i	$-0.832575\pi$
$84$	−4.52380	−	4.71255i	−0.493587	−	0.514181i
$85$	4.12692	+	4.84152i	0.447627	+	0.525137i
$86$	−0.425605	−	0.383217i	−0.0458942	−	0.0413233i
$87$	13.8588	+	8.38351i	1.48582	+	0.898807i
$88$	−2.30037	−	0.120557i	−0.245220	−	0.0128514i
$89$	1.02996	+	3.16988i	0.109175	+	0.336007i	0.990688	−	0.136154i	$-0.0434742\pi$
$89$	1.02996	+	3.16988i	0.109175	+	0.336007i	−0.881513	+	0.472161i	$0.843474\pi$
$90$	−2.40854	+	13.8044i	−0.253882	+	1.45511i
$91$	1.58887	−	4.89004i	0.166559	−	0.512615i
$92$	4.28032	−	11.1506i	0.446254	−	1.16253i
$93$	3.56240	+	3.34189i	0.369403	+	0.346538i
$94$	24.8132	+	2.60797i	2.55929	+	0.268992i
$95$	3.29728	+	0.262728i	0.338294	+	0.0269554i
$96$	−11.0532	+	8.58277i	−1.12811	+	0.875975i
$97$	−5.18249	+	6.39984i	−0.526202	+	0.649805i	−0.969071	−	0.246781i	$-0.920627\pi$
$97$	−5.18249	+	6.39984i	−0.526202	+	0.649805i	0.442870	+	0.896586i	$0.353960\pi$
$98$	4.22381	−	8.28970i	0.426670	−	0.837386i
$99$	9.08003	−	0.580587i	0.912577	−	0.0583512i
$100$	7.41942	+	9.19874i	0.741942	+	0.919874i
$101$	−3.92938	−	2.26863i	−0.390988	−	0.225737i	0.291600	−	0.956540i	$-0.405812\pi$
$101$	−3.92938	−	2.26863i	−0.390988	−	0.225737i	−0.682588	+	0.730803i	$0.739146\pi$
$102$	0.866603	+	10.2572i	0.0858065	+	1.01562i
$103$	−11.5778	+	4.44429i	−1.14079	+	0.437909i	−0.854098	−	0.520113i	$-0.825890\pi$
$103$	−11.5778	+	4.44429i	−1.14079	+	0.437909i	−0.286695	+	0.958022i	$0.592557\pi$
$104$	2.23581	+	0.995448i	0.219239	+	0.0976117i
$105$	6.09922	−	0.995896i	0.595222	−	0.0971895i
$106$	1.98982	−	0.885925i	0.193269	−	0.0860487i
$107$	−2.13317	+	2.13317i	−0.206221	+	0.206221i	−0.802659	−	0.596438i	$-0.796582\pi$
$107$	−2.13317	+	2.13317i	−0.206221	+	0.206221i	0.596438	+	0.802659i	$0.296582\pi$
$108$	−8.76168	+	8.60643i	−0.843093	+	0.828155i
$109$	−8.66496	−	2.81542i	−0.829953	−	0.269668i	−0.136927	−	0.990581i	$-0.543723\pi$
$109$	−8.66496	−	2.81542i	−0.829953	−	0.269668i	−0.693026	+	0.720913i	$0.743723\pi$
$110$	8.63488	−	11.2306i	0.823303	−	1.07079i
$111$	1.76943	−	9.86300i	0.167947	−	0.936154i
$112$	4.20288	+	2.72938i	0.397135	+	0.257902i
$113$	5.00872	+	3.25270i	0.471181	+	0.305988i	0.758299	−	0.651907i	$-0.226031\pi$
$113$	5.00872	+	3.25270i	0.471181	+	0.305988i	−0.287118	+	0.957895i	$0.592697\pi$
$114$	4.08972	+	3.45250i	0.383037	+	0.323356i
$115$	6.39104	+	9.31842i	0.595968	+	0.868948i
$116$	21.0213	+	6.83023i	1.95178	+	0.634171i
$117$	−9.22745	−	2.88135i	−0.853078	−	0.266381i
$118$	9.31261	−	9.31261i	0.857295	−	0.857295i
$119$	4.14728	−	1.84649i	0.380180	−	0.169267i
$120$	0.167977	+	2.93682i	0.0153341	+	0.268094i
$121$	1.64600	+	0.732848i	0.149637	+	0.0666226i
$122$	−13.1771	+	5.05821i	−1.19300	+	0.457949i
$123$	−17.5555	−	8.25005i	−1.58293	−	0.743882i
$124$	5.77256	+	3.33279i	0.518391	+	0.299293i
$125$	−11.1484	+	0.844679i	−0.997142	+	0.0755504i
$126$	8.96136	+	4.43704i	0.798341	+	0.395283i
$127$	5.28956	−	10.3813i	0.469372	−	0.921195i	−0.528034	−	0.849223i	$-0.677071\pi$
$127$	5.28956	−	10.3813i	0.469372	−	0.921195i	0.997407	−	0.0719719i	$-0.0229292\pi$
$128$	−3.76068	+	4.64405i	−0.332400	+	0.410480i
$129$	0.439757	+	0.179199i	0.0387184	+	0.0157776i
$130$	−12.8409	+	7.85175i	−1.12622	+	0.688644i
$131$	20.7466	+	2.18056i	1.81264	+	0.190516i	0.949356	−	0.314201i	$-0.101737\pi$
$131$	20.7466	+	2.18056i	1.81264	+	0.190516i	0.863285	+	0.504717i	$0.168403\pi$
$132$	11.8844	−	3.59473i	1.03440	−	0.312881i
$133$	0.845895	−	2.20363i	0.0733484	−	0.191079i
$134$	3.70619	−	11.4065i	0.320166	−	0.985369i
$135$	−2.00406	−	11.4448i	−0.172482	−	0.985013i
$136$	0.667751	+	2.05513i	0.0572592	+	0.176226i
$137$	8.85612	+	0.464129i	0.756629	+	0.0396533i	0.426750	−	0.904370i	$-0.359659\pi$
$137$	8.85612	+	0.464129i	0.756629	+	0.0396533i	0.329880	+	0.944023i	$0.392992\pi$
$138$	−0.373555	+	18.2796i	−0.0317991	+	1.55606i
$139$	−1.62373	−	1.46201i	−0.137723	−	0.124006i	0.597390	−	0.801951i	$-0.296204\pi$
$139$	−1.62373	−	1.46201i	−0.137723	−	0.124006i	−0.735113	+	0.677944i	$0.762871\pi$
$140$	7.79453	−	3.21973i	0.658758	−	0.272116i
$141$	−20.0878	+	4.94492i	−1.69169	+	0.416437i
$142$	13.7927	+	5.29452i	1.15746	+	0.444306i
$143$	6.91036	+	6.91036i	0.577874	+	0.577874i
$144$	5.04033	−	7.96026i	0.420027	−	0.663355i
$145$	−16.6018	+	12.7134i	−1.37870	+	1.05579i
$146$	−5.41712	+	0.569362i	−0.448324	+	0.0471207i
$147$	−0.962945	+	7.65396i	−0.0794224	+	0.631288i
$148$	−0.715650	−	13.6554i	−0.0588260	−	1.12247i
$149$	4.62773	+	8.01546i	0.379118	+	0.656652i	0.990934	−	0.134348i	$-0.0428940\pi$
$149$	4.62773	+	8.01546i	0.379118	+	0.656652i	−0.611816	+	0.791000i	$0.709561\pi$
$150$	−15.4606	−	9.39359i	−1.26235	−	0.766984i
$151$	11.9043	−	20.6188i	0.968758	−	1.67794i	0.269597	−	0.962973i	$-0.413110\pi$
$151$	11.9043	−	20.6188i	0.968758	−	1.67794i	0.699161	−	0.714964i	$-0.253557\pi$
$152$	1.00108	+	0.510075i	0.0811981	+	0.0413725i
$153$	−3.56096	−	7.75685i	−0.287887	−	0.627104i
$154$	−5.94203	−	8.17850i	−0.478822	−	0.659043i
$155$	−5.69428	+	2.70924i	−0.457376	+	0.217611i
$156$	−13.1567	−	0.959405i	−1.05338	−	0.0768138i
$157$	−5.36818	+	20.0343i	−0.428428	+	1.59891i	0.327895	+	0.944714i	$0.393661\pi$
$157$	−5.36818	+	20.0343i	−0.428428	+	1.59891i	−0.756322	+	0.654199i	$0.773006\pi$
$158$	13.0627	−	10.5780i	1.03922	−	0.841540i
$159$	−1.30287	+	1.25069i	−0.103325	+	0.0991861i
$160$	−5.11428	−	17.3274i	−0.404319	−	1.36985i
$161$	7.66871	−	2.49171i	0.604379	−	0.196375i
$162$	8.14785	−	16.9430i	0.640156	−	1.33116i
$163$	1.69900	+	3.33448i	0.133076	+	0.261176i	0.947923	−	0.318500i	$-0.103179\pi$
$163$	1.69900	+	3.33448i	0.133076	+	0.261176i	−0.814847	+	0.579676i	$0.803179\pi$
$164$	−25.8917	−	5.50346i	−2.02181	−	0.429748i
$165$	−3.57640	+	11.1885i	−0.278422	+	0.871024i
$166$	36.7579	−	7.81313i	2.85297	−	0.606417i
$167$	−7.83279	−	9.67269i	−0.606119	−	0.748495i	0.378038	−	0.925790i	$-0.376599\pi$
$167$	−7.83279	−	9.67269i	−0.606119	−	0.748495i	−0.984158	+	0.177295i	$0.943265\pi$
$168$	2.04393	+	0.478298i	0.157693	+	0.0369015i
$169$	1.06438	+	2.39064i	0.0818755	+	0.183895i
$170$	−12.7383	−	3.78672i	−0.976980	−	0.290428i
$171$	−4.16104	−	1.54264i	−0.318203	−	0.117968i
$172$	0.640036	+	0.101372i	0.0488023	+	0.00772952i
$173$	4.00328	+	6.16451i	0.304364	+	0.468679i	0.957448	−	0.288606i	$-0.0931918\pi$
$173$	4.00328	+	6.16451i	0.304364	+	0.468679i	−0.653084	+	0.757285i	$0.726525\pi$
$174$	−33.8175	+	1.08006i	−2.56370	+	0.0818792i
$175$	−1.67396	+	7.80074i	−0.126540	+	0.589681i
$176$	−8.24890	+	4.76251i	−0.621784	+	0.358987i
$177$	−4.64448	+	9.88313i	−0.349100	+	0.742862i
$178$	−5.41080	−	4.38158i	−0.405556	−	0.328413i
$179$	13.0654	−	9.49258i	0.976555	−	0.709509i	0.0196191	−	0.999808i	$-0.493755\pi$
$179$	13.0654	−	9.49258i	0.976555	−	0.709509i	0.956936	+	0.290299i	$0.0937546\pi$
$180$	−6.22142	−	14.5839i	−0.463717	−	1.08702i
$181$	−15.7593	−	11.4498i	−1.17138	−	0.851059i	−0.180209	−	0.983628i	$-0.557677\pi$
$181$	−15.7593	−	11.4498i	−1.17138	−	0.851059i	−0.991174	+	0.132569i	$0.957677\pi$
$182$	2.77987	+	10.3746i	0.206058	+	0.769017i
$183$	8.85539	−	7.65167i	0.654609	−	0.565628i
$184$	0.797984	+	3.75422i	0.0588281	+	0.276765i
$185$	11.0235	+	6.76995i	0.810462	+	0.497737i
$186$	−10.0431	−	1.80174i	−0.736397	−	0.132110i
$187$	−0.451589	+	8.61683i	−0.0330235	+	0.630125i
$188$	−25.1536	+	12.8164i	−1.83452	+	0.934732i
$189$	−8.23783	−	0.940349i	−0.599214	−	0.0684004i
$190$	−6.07548	+	3.29107i	−0.440761	+	0.238759i
$191$	−9.70885	+	8.74189i	−0.702508	+	0.632541i	−0.940922	−	0.338623i	$-0.890039\pi$
$191$	−9.70885	+	8.74189i	−0.702508	+	0.632541i	0.238415	+	0.971163i	$0.423372\pi$
$192$	6.02693	−	17.3355i	0.434957	−	1.25108i
$193$	12.6500	+	3.38956i	0.910568	+	0.243986i	0.683549	−	0.729905i	$-0.260436\pi$
$193$	12.6500	+	3.38956i	0.910568	+	0.243986i	0.227019	+	0.973890i	$0.427102\pi$
$194$	1.79814	−	17.1081i	0.129099	−	1.22829i
$195$	7.80743	−	9.73606i	0.559102	−	0.697214i
$196$	1.10038	+	10.4694i	0.0785987	+	0.747817i
$197$	3.82572	−	24.1546i	0.272571	−	1.72095i	−0.348600	−	0.937272i	$-0.613343\pi$
$197$	3.82572	−	24.1546i	0.272571	−	1.72095i	0.621171	−	0.783675i	$-0.286657\pi$
$198$	−15.2469	+	11.3476i	−1.08355	+	0.806437i
$199$			3.87326i			0.274568i	0.990532	+	0.137284i	$0.0438374\pi$
$199$			3.87326i			0.274568i	−0.990532	+	0.137284i	$0.956163\pi$
$200$	−3.60946	−	1.18055i	−0.255227	−	0.0834776i
$201$	0.317445	+	9.93944i	0.0223909	+	0.701074i
$202$	9.46498	−	0.496039i	0.665954	−	0.0349012i
$203$	5.34750	+	13.9307i	0.375321	+	0.977744i
$204$	−7.14341	−	9.19952i	−0.500139	−	0.644095i
$205$	18.1816	−	17.2201i	1.26986	−	1.20270i
$206$	15.2270	−	20.9582i	1.06092	−	1.46022i
$207$	−4.85006	−	14.3631i	−0.337103	−	0.998303i
$208$	9.99533	−	1.58311i	0.693052	−	0.109769i
$209$	3.00198	+	3.33404i	0.207652	+	0.230620i
$210$	−9.55228	+	8.68386i	−0.659170	+	0.599243i
$211$	4.07714	−	4.52812i	0.280682	−	0.311729i	−0.586275	−	0.810112i	$-0.699406\pi$
$211$	4.07714	−	4.52812i	0.280682	−	0.311729i	0.866957	+	0.498384i	$0.166073\pi$
$212$	−1.34228	+	2.06693i	−0.0921883	+	0.141957i
$213$	−12.2474	−	0.250284i	−0.839180	−	0.0171492i
$214$	1.31021	−	6.16407i	0.0895643	−	0.421367i
$215$	−0.422428	+	0.444281i	−0.0288094	+	0.0302997i
$216$	0.855017	−	3.85287i	0.0581765	−	0.262155i
$217$	0.703945	+	4.44453i	0.0477869	+	0.301715i
$218$	18.3834	−	4.92582i	1.24508	−	0.333619i
$219$	4.06519	−	1.96776i	0.274700	−	0.132969i
$220$	−1.27317	+	15.9785i	−0.0858372	+	1.07727i
$221$	3.72879	−	8.37501i	0.250826	−	0.563364i
$222$	8.12132	+	19.2923i	0.545068	+	1.29481i
$223$	−6.44476	+	4.18528i	−0.431573	+	0.280267i	−0.742089	−	0.670301i	$-0.766165\pi$
$223$	−6.44476	+	4.18528i	−0.431573	+	0.280267i	0.310516	+	0.950568i	$0.399498\pi$
$224$	−12.8922			−0.861398
$225$	14.7013	+	2.97842i	0.980088	+	0.198562i
$226$	−12.4755			−0.829857
$227$	−3.53215	+	2.29380i	−0.234437	+	0.152245i	−0.656512	−	0.754316i	$-0.727969\pi$
$227$	−3.53215	+	2.29380i	−0.234437	+	0.152245i	0.422075	+	0.906561i	$0.361302\pi$
$228$	−6.00855	−	0.755936i	−0.397926	−	0.0500631i
$229$	−3.98660	+	8.95405i	−0.263442	+	0.591700i	−0.996035	−	0.0889670i	$-0.971643\pi$
$229$	−3.98660	+	8.95405i	−0.263442	+	0.591700i	0.732593	+	0.680667i	$0.238310\pi$
$230$	−21.7982	−	9.05397i	−1.43733	−	0.597001i
$231$	6.93511	+	4.70791i	0.456297	+	0.309758i
$232$	−6.86064	+	1.83830i	−0.450423	+	0.120691i
$233$	3.75549	+	23.7113i	0.246031	+	1.55338i	0.733166	+	0.680050i	$0.238042\pi$
$233$	3.75549	+	23.7113i	0.246031	+	1.55338i	−0.487136	+	0.873326i	$0.661958\pi$
$234$	19.4439	−	5.45026i	1.27109	−	0.356295i
$235$	3.51176	−	26.4755i	0.229082	−	1.72707i
$236$	−3.09825	+	14.5761i	−0.201679	+	0.948824i
$237$	−7.21366	+	11.9249i	−0.468577	+	0.774607i
$238$	−5.16493	+	7.95329i	−0.334792	+	0.515535i
$239$	−10.6565	+	11.8352i	−0.689310	+	0.765556i	−0.981636	−	0.190763i	$-0.938904\pi$
$239$	−10.6565	+	11.8352i	−0.689310	+	0.765556i	0.292327	+	0.956319i	$0.405571\pi$
$240$	7.19644	+	9.80624i	0.464528	+	0.632990i
$241$	−10.1394	−	11.2609i	−0.653136	−	0.725381i	0.322061	−	0.946719i	$-0.395624\pi$
$241$	−10.1394	−	11.2609i	−0.653136	−	0.725381i	−0.975197	+	0.221338i	$0.928958\pi$
$242$	−3.71743	+	0.588783i	−0.238966	+	0.0378484i
$243$	−1.58981	+	15.5072i	−0.101986	+	0.994786i
$244$	9.38723	−	12.9204i	0.600956	−	0.827145i
$245$	−8.74761	−	4.76059i	−0.558865	−	0.304143i
$246$	40.1420	−	5.51968i	2.55936	−	0.351922i
$247$	−1.70820	−	4.45001i	−0.108690	−	0.283148i
$248$	−2.13900	+	0.112100i	−0.135826	+	0.00711836i
$249$	−26.4735	+	16.4330i	−1.67769	+	1.04140i
$250$	18.5701	−	14.1634i	1.17447	−	0.895773i
$251$			28.4114i			1.79331i	0.442728	+	0.896656i	$0.354011\pi$
$251$			28.4114i			1.79331i	−0.442728	+	0.896656i	$0.645989\pi$
$252$	−11.2382	+	1.31195i	−0.707941	+	0.0826450i
$253$	−2.39750	+	15.1372i	−0.150729	+	0.951668i
$254$	2.54407	+	24.2052i	0.159629	+	1.51877i
$255$	11.0009	−	0.629215i	0.688902	−	0.0394030i
$256$	−0.910407	+	8.66194i	−0.0569004	+	0.541371i
$257$	−20.8946	−	5.59869i	−1.30337	−	0.349236i	−0.460645	−	0.887584i	$-0.652382\pi$
$257$	−20.8946	−	5.59869i	−1.30337	−	0.349236i	−0.842723	+	0.538348i	$0.819049\pi$
$258$	−0.974295	+	0.186373i	−0.0606569	+	0.0116031i
$259$	6.86029	−	6.17703i	0.426278	−	0.383822i
$260$	7.34668	−	15.3642i	0.455621	−	0.952845i
$261$	26.0737	−	10.3542i	1.61392	−	0.640907i
$262$	−38.8272	+	19.7835i	−2.39875	+	1.22223i
$263$	0.314897	−	6.00858i	0.0194174	−	0.370505i	−0.971588	−	0.236680i	$-0.923941\pi$
$263$	0.314897	−	6.00858i	0.0194174	−	0.370505i	0.991005	−	0.133825i	$-0.0427260\pi$
$264$	−2.57371	+	3.04873i	−0.158401	+	0.187636i
$265$	−0.890154	−	2.15495i	−0.0546817	−	0.132377i
$266$	1.02515	+	4.82297i	0.0628562	+	0.295715i
$267$	5.45280	+	1.89574i	0.333706	+	0.116017i
$268$	3.51230	+	13.1081i	0.214548	+	0.800705i
$269$	14.3247	+	10.4075i	0.873390	+	0.634555i	0.931494	−	0.363756i	$-0.118506\pi$
$269$	14.3247	+	10.4075i	0.873390	+	0.634555i	−0.0581044	+	0.998311i	$0.518506\pi$
$270$	16.5318	+	17.7703i	1.00609	+	1.08147i
$271$	16.3701	−	11.8936i	0.994414	−	0.722484i	0.0335307	−	0.999438i	$-0.489325\pi$
$271$	16.3701	−	11.8936i	0.994414	−	0.722484i	0.960883	+	0.276954i	$0.0893249\pi$
$272$	6.94396	+	5.62311i	0.421039	+	0.340951i
$273$	−5.08632	−	7.31028i	−0.307838	−	0.442438i
$274$	−16.0432	+	9.26256i	−0.969207	+	0.559572i
$275$	−11.7663	−	9.56610i	−0.709533	−	0.576857i
$276$	−10.9104	−	17.5766i	−0.656727	−	1.05798i
$277$	−7.78980	−	11.9952i	−0.468044	−	0.720724i	0.523281	−	0.852160i	$-0.324708\pi$
$277$	−7.78980	−	11.9952i	−0.468044	−	0.720724i	−0.991325	+	0.131436i	$0.958041\pi$
$278$	4.50799	+	0.713995i	0.270371	+	0.0428226i
$279$	8.34037	−	1.41944i	0.499325	−	0.0849797i
$280$	−1.53713	+	2.23188i	−0.0918610	+	0.133380i
$281$	6.11702	+	13.7391i	0.364911	+	0.819603i	0.998928	+	0.0462845i	$0.0147381\pi$
$281$	6.11702	+	13.7391i	0.364911	+	0.819603i	−0.634017	+	0.773319i	$0.718595\pi$
$282$	29.5662	−	31.5171i	1.76064	−	1.87682i
$283$	−7.69676	−	9.50471i	−0.457525	−	0.564997i	0.495220	−	0.868768i	$-0.335088\pi$
$283$	−7.69676	−	9.50471i	−0.457525	−	0.564997i	−0.952745	+	0.303771i	$0.901754\pi$
$284$	−16.3513	+	3.47558i	−0.970271	+	0.206238i
$285$	3.81319	−	4.27585i	0.225874	−	0.253280i
$286$	−19.9684	−	4.24441i	−1.18075	−	0.250977i
$287$	−8.11283	−	15.9223i	−0.478885	−	0.939865i
$288$	0.278599	+	24.2370i	0.0164166	+	1.42818i
$289$	−8.46977	+	2.75200i	−0.498222	+	0.161882i
$290$	14.6209	−	41.1608i	0.858567	−	2.41704i
$291$	3.40941	+	13.8501i	0.199863	+	0.811905i
$292$	4.78969	−	3.87861i	0.280295	−	0.226979i
$293$	7.87126	−	29.3759i	0.459844	−	1.71616i	−0.213599	−	0.976921i	$-0.568519\pi$
$293$	7.87126	−	29.3759i	0.459844	−	1.71616i	0.673443	−	0.739239i	$-0.264815\pi$
$294$	−7.02097	−	14.5047i	−0.409472	−	0.845929i
$295$	−9.69428	−	10.2356i	−0.564423	−	0.595937i
$296$	2.58278	+	3.55489i	0.150121	+	0.206624i
$297$	8.70086	−	13.1395i	0.504875	−	0.762432i
$298$	−17.2267	−	8.77742i	−0.997913	−	0.508462i
$299$	8.14156	−	14.1016i	0.470839	−	0.815517i
$300$	20.4601	−	0.613623i	1.18127	−	0.0354276i
$301$	0.218738	+	0.378864i	0.0126078	+	0.0218374i
$302$	2.60289	+	49.6661i	0.149780	+	2.85796i
$303$	−7.24314	+	3.04909i	−0.416108	+	0.175166i
$304$	4.62033	−	0.485617i	0.264994	−	0.0278520i
$305$	5.02958	+	14.2471i	0.287993	+	0.815787i
$306$	15.0635	+	9.53803i	0.861126	+	0.545253i
$307$	1.74489	+	1.74489i	0.0995862	+	0.0995862i	0.755145	−	0.655558i	$-0.227567\pi$
$307$	1.74489	+	1.74489i	0.0995862	+	0.0995862i	−0.655558	+	0.755145i	$0.727567\pi$
$308$	10.6787	+	4.09917i	0.608476	+	0.233572i
$309$	−5.98218	+	20.6302i	−0.340314	+	1.17361i
$310$	6.89359	−	11.2248i	0.391529	−	0.637526i
$311$	1.64232	+	1.47876i	0.0931277	+	0.0838526i	0.714380	−	0.699758i	$-0.246709\pi$
$311$	1.64232	+	1.47876i	0.0931277	+	0.0838526i	−0.621252	+	0.783611i	$0.713376\pi$
$312$	3.71364	−	2.04406i	0.210243	−	0.115722i
$313$	5.37176	+	0.281522i	0.303630	+	0.0159126i	0.203543	−	0.979066i	$-0.434754\pi$
$313$	5.37176	+	0.281522i	0.303630	+	0.0159126i	0.100087	+	0.994979i	$0.468088\pi$
$314$	−13.3886	−	41.2059i	−0.755563	−	2.32538i
$315$	5.00827	−	9.46012i	0.282184	−	0.533018i
$316$	−5.87712	+	18.0879i	−0.330614	+	1.01753i
$317$	4.25766	−	11.0916i	0.239134	−	0.622965i	−0.760519	−	0.649316i	$-0.775055\pi$
$317$	4.25766	−	11.0916i	0.239134	−	0.622965i	0.999653	+	0.0263506i	$0.00838863\pi$
$318$	0.859606	−	3.67340i	0.0482043	−	0.205994i
$319$	−28.2063	−	2.96460i	−1.57925	−	0.165986i
$320$	18.0021	+	15.4056i	1.00635	+	0.861197i
$321$	0.711784	+	5.17647i	0.0397279	+	0.288922i
$322$	−10.6001	+	13.0900i	−0.590720	+	0.729479i
$323$	1.91066	−	3.74988i	0.106312	−	0.208649i
$324$	2.70928	+	21.0991i	0.150516	+	1.17217i
$325$	8.02856	+	13.9685i	0.445344	+	0.774835i
$326$	−6.77017	−	3.90876i	−0.374965	−	0.216486i
$327$	−12.9535	+	9.01277i	−0.716333	+	0.498407i
$328$	7.94103	−	3.04827i	0.438470	−	0.168313i
$329$	−17.4108	−	7.75178i	−0.959888	−	0.427370i
$330$	−6.46371	−	23.6702i	−0.355816	−	1.30300i
$331$	−1.44620	+	0.643889i	−0.0794902	+	0.0353913i	−0.446097	−	0.894985i	$-0.647186\pi$
$331$	−1.44620	+	0.643889i	−0.0794902	+	0.0353913i	0.366606	+	0.930376i	$0.380520\pi$
$332$	−30.0665	+	30.0665i	−1.65011	+	1.65011i
$333$	−11.7609	−	12.7636i	−0.644492	−	0.699443i
$334$	24.7271	+	8.03432i	1.35301	+	0.439619i
$335$	−12.0977	−	4.29728i	−0.660970	−	0.234786i
$336$	8.16527	−	2.94439i	0.445452	−	0.160630i
$337$	4.96824	+	3.22642i	0.270638	+	0.175754i	0.672822	−	0.739805i	$-0.265082\pi$
$337$	4.96824	+	3.22642i	0.270638	+	0.175754i	−0.402184	+	0.915559i	$0.631749\pi$
$338$	−4.58456	−	2.97725i	−0.249367	−	0.161941i
$339$	9.73084	−	3.50894i	0.528507	−	0.190579i
$340$	14.4215	−	4.25660i	0.782117	−	0.230847i
$341$	−8.13435	−	2.64301i	−0.440500	−	0.143127i
$342$	9.04487	−	2.03148i	0.489091	−	0.109850i
$343$	−12.9234	+	12.9234i	−0.697801	+	0.697801i
$344$	−0.190232	+	0.0846966i	−0.0102566	+	0.00456653i
$345$	19.5491	+	0.930952i	1.05249	+	0.0501208i
$346$	−14.0268	−	6.24515i	−0.754087	−	0.335741i
$347$	24.5366	−	9.41871i	1.31719	−	0.505623i	0.404601	−	0.914493i	$-0.367411\pi$
$347$	24.5366	−	9.41871i	1.31719	−	0.505623i	0.912592	+	0.408870i	$0.134077\pi$
$348$	31.4254	−	21.8651i	1.68458	−	1.17209i
$349$	19.1445	+	11.0531i	1.02478	+	0.591659i	0.915486	−	0.402350i	$-0.131807\pi$
$349$	19.1445	+	11.0531i	1.02478	+	0.591659i	0.109297	+	0.994009i	$0.465140\pi$
$350$	−5.94233	−	15.5707i	−0.317631	−	0.832291i
$351$	−13.6332	+	9.72010i	−0.727686	+	0.518821i
$352$	11.1246	−	21.8333i	0.592944	−	1.16372i
$353$	18.3429	−	22.6516i	0.976293	−	1.20562i	−0.00233822	−	0.999997i	$-0.500744\pi$
$353$	18.3429	−	22.6516i	0.976293	−	1.20562i	0.978631	−	0.205624i	$-0.0659224\pi$
$354$	−3.10738	−	22.5985i	−0.165155	−	1.20110i
$355$	6.06621	−	14.6049i	0.321961	−	0.775150i
$356$	7.83473	+	0.823463i	0.415240	+	0.0436435i
$357$	1.79163	−	7.65626i	0.0948232	−	0.405212i
$358$	−12.0897	+	31.4949i	−0.638963	+	1.66456i
$359$	−8.63386	+	26.5723i	−0.455678	+	1.40243i	0.414660	+	0.909976i	$0.363901\pi$
$359$	−8.63386	+	26.5723i	−0.455678	+	1.40243i	−0.870338	+	0.492455i	$0.836099\pi$
$360$	4.22909	+	2.84152i	0.222892	+	0.149761i
$361$	5.19513	+	15.9890i	0.273428	+	0.841524i
$362$	40.6356	+	2.12962i	2.13576	+	0.111931i
$363$	2.73398	−	1.50484i	0.143497	−	0.0789836i
$364$	−9.03135	−	8.13186i	−0.473371	−	0.426225i
$365$	0.451814	+	5.81311i	0.0236490	+	0.304272i
$366$	−6.80854	+	23.4799i	−0.355888	+	1.22732i
$367$	−31.4107	−	12.0575i	−1.63963	−	0.629394i	−0.648369	−	0.761326i	$-0.724548\pi$
$367$	−31.4107	−	12.0575i	−1.63963	−	0.629394i	−0.991259	+	0.131933i	$0.957882\pi$
$368$	11.2221	+	11.2221i	0.584990	+	0.584990i
$369$	−29.7582	+	15.5959i	−1.54915	+	0.811892i
$370$	−27.0145	+	0.681111i	−1.40441	+	0.0354093i
$371$	−1.65469	+	0.173915i	−0.0859075	+	0.00902924i
$372$	10.6407	−	4.47935i	0.551696	−	0.232244i
$373$	0.163329	+	3.11650i	0.00845685	+	0.161366i	0.999593	+	0.0285183i	$0.00907888\pi$
$373$	0.163329	+	3.11650i	0.00845685	+	0.161366i	−0.991136	+	0.132848i	$0.957588\pi$
$374$	−9.01229	−	15.6098i	−0.466015	−	0.807161i
$375$	−10.5009	+	16.2706i	−0.542264	+	0.840208i
$376$	4.53584	−	7.85630i	0.233918	−	0.405158i
$377$	26.8488	+	13.6801i	1.38278	+	0.704563i
$378$	15.5018	−	7.72483i	0.797328	−	0.397322i
$379$	−4.85248	−	6.67886i	−0.249255	−	0.343070i	0.665995	−	0.745956i	$-0.268007\pi$
$379$	−4.85248	−	6.67886i	−0.249255	−	0.343070i	−0.915250	+	0.402886i	$0.868007\pi$
$380$	3.73718	−	6.86709i	0.191713	−	0.352274i
$381$	−8.79249	−	18.1644i	−0.450453	−	0.930593i
$382$	7.06338	−	26.3609i	0.361394	−	1.34874i
$383$	6.62260	−	5.36288i	0.338399	−	0.274030i	−0.445024	−	0.895518i	$-0.646805\pi$
$383$	6.62260	−	5.36288i	0.338399	−	0.274030i	0.783423	+	0.621488i	$0.213472\pi$
$384$	2.47404	+	10.0503i	0.126253	+	0.512878i
$385$	−8.92406	+	6.12057i	−0.454812	+	0.311933i
$386$	−26.0181	+	8.45380i	−1.32429	+	0.430287i
$387$	0.707527	−	0.419407i	0.0359656	−	0.0213197i
$388$	8.83662	+	17.3428i	0.448611	+	0.880450i
$389$	11.9071	+	2.53094i	0.603715	+	0.128324i	0.499622	−	0.866244i	$-0.333472\pi$
$389$	11.9071	+	2.53094i	0.603715	+	0.128324i	0.104094	+	0.994567i	$0.466806\pi$
$390$	−2.60118	+	25.9394i	−0.131716	+	1.31349i
$391$	14.0627	−	2.98912i	0.711182	−	0.151166i
$392$	−2.12887	−	2.62893i	−0.107524	−	0.132781i
$393$	24.7207	−	26.3518i	1.24699	−	1.32927i
$394$	20.7786	+	46.6695i	1.04681	+	2.35118i
$395$	−10.9393	−	14.2851i	−0.550417	−	0.718764i
$396$	7.47555	−	20.1642i	0.375661	−	1.01329i
$397$	11.1505	+	1.76607i	0.559629	+	0.0886365i	0.429840	−	0.902905i	$-0.358570\pi$
$397$	11.1505	+	1.76607i	0.559629	+	0.0886365i	0.129789	+	0.991542i	$0.458570\pi$
$398$	−4.40664	−	6.78564i	−0.220885	−	0.340133i
$399$	−2.15616	−	3.47356i	−0.107943	−	0.173895i
$400$	−15.1758	+	4.03474i	−0.758792	+	0.201737i
$401$	−7.16477	+	4.13658i	−0.357791	+	0.206571i	−0.668112	−	0.744061i	$-0.732897\pi$
$401$	−7.16477	+	4.13658i	−0.357791	+	0.206571i	0.310320	+	0.950632i	$0.399564\pi$
$402$	−11.8643	−	17.0519i	−0.591739	−	0.850472i
$403$	7.06205	+	5.71874i	0.351786	+	0.284871i
$404$	−8.67609	+	6.30355i	−0.431652	+	0.313613i
$405$	−17.8930	−	9.21096i	−0.889108	−	0.457697i
$406$	−25.2175	−	18.3216i	−1.25152	−	0.909284i
$407$	4.54125	+	16.9482i	0.225101	+	0.840090i
$408$	3.53521	+	1.22906i	0.175019	+	0.0608478i
$409$	1.36453	+	6.41962i	0.0674718	+	0.317430i	0.998921	−	0.0464416i	$-0.0147881\pi$
$409$	1.36453	+	6.41962i	0.0674718	+	0.317430i	−0.931449	+	0.363871i	$0.881455\pi$
$410$	−12.2612	+	50.8535i	−0.605535	+	2.51147i
$411$	9.90842	−	11.7372i	0.488746	−	0.578953i
$412$	−1.53408	+	29.2719i	−0.0755785	+	1.44212i
$413$	−8.96369	+	4.56723i	−0.441074	+	0.224739i
$414$	24.8379	+	19.6450i	1.22072	+	0.965498i
$415$	−7.29217	−	39.5597i	−0.357959	−	1.94191i
$416$	−19.3474	+	17.4205i	−0.948586	+	0.854111i
$417$	−3.71704	+	0.711033i	−0.182024	+	0.0348194i
$418$	−9.05240	−	2.42558i	−0.442767	−	0.118639i
$419$	−0.220607	+	2.09894i	−0.0107774	+	0.102540i	−0.998588	−	0.0531196i	$-0.983084\pi$
$419$	−0.220607	+	2.09894i	−0.0107774	+	0.102540i	0.987811	+	0.155659i	$0.0497502\pi$
$420$	3.71316	−	14.1272i	0.181184	−	0.689335i
$421$	1.40796	+	13.3959i	0.0686199	+	0.652875i	0.973731	+	0.227700i	$0.0731207\pi$
$421$	1.40796	+	13.3959i	0.0686199	+	0.652875i	−0.905111	+	0.425175i	$0.860213\pi$
$422$	−1.99113	+	12.5715i	−0.0969266	+	0.611970i
$423$	−14.1969	+	32.8992i	−0.690275	+	1.59962i
$424$		−	0.791959i		−	0.0384609i
$425$	−4.42216	+	13.5205i	−0.214506	+	0.655840i
$426$	21.7412	−	13.4955i	1.05337	−	0.653860i
$427$	10.7669	−	0.564271i	0.521048	−	0.0273070i
$428$	2.55531	+	6.65680i	0.123515	+	0.321769i
$429$	16.7691	−	2.30581i	0.809619	−	0.111326i
$430$	0.234598	−	1.25894i	0.0113133	−	0.0607116i
$431$	−11.5429	+	15.8874i	−0.556000	+	0.765269i	−0.990811	−	0.135253i	$-0.956815\pi$
$431$	−11.5429	+	15.8874i	−0.556000	+	0.765269i	0.434811	+	0.900522i	$0.356815\pi$
$432$	−5.71182	−	15.2868i	−0.274810	−	0.735488i
$433$	−3.82567	+	0.605926i	−0.183850	+	0.0291190i	−0.247680	−	0.968842i	$-0.579668\pi$
$433$	−3.82567	+	0.605926i	−0.183850	+	0.0291190i	0.0638305	+	0.997961i	$0.479668\pi$
$434$	−6.28984	−	6.98557i	−0.301922	−	0.335318i
$435$	0.172929	+	36.2177i	0.00829132	+	1.73650i
$436$	−14.4094	+	16.0032i	−0.690083	+	0.766415i
$437$	4.07125	−	6.26918i	0.194754	−	0.299896i
$438$	−4.88315	+	8.07235i	−0.233326	+	0.385712i
$439$	6.23430	−	29.3301i	0.297547	−	1.39985i	−0.534512	−	0.845161i	$-0.679504\pi$
$439$	6.23430	−	29.3301i	0.297547	−	1.39985i	0.832059	−	0.554688i	$-0.187162\pi$
$440$	−2.45337	−	4.52904i	−0.116960	−	0.215913i
$441$	9.55602	+	9.33882i	0.455048	+	0.444706i
$442$	2.99578	+	18.9146i	0.142495	+	0.899676i
$443$	−10.9540	+	2.93511i	−0.520439	+	0.139451i	−0.509470	−	0.860489i	$-0.670158\pi$
$443$	−10.9540	+	2.93511i	−0.520439	+	0.139451i	−0.0109695	+	0.999940i	$0.503492\pi$
$444$	−19.5956	−	13.3025i	−0.929968	−	0.631311i
$445$	−4.84574	+	5.66247i	−0.229710	+	0.268427i
$446$	6.52906	−	14.6645i	0.309160	−	0.694385i
$447$	15.9055	+	2.00108i	0.752306	+	0.0946477i
$448$	14.1804	−	9.20884i	0.669959	−	0.435077i
$449$	26.3618			1.24409			0.622044	−	0.782982i	$-0.286302\pi$
$449$	26.3618			1.24409			0.622044	+	0.782982i	$0.286302\pi$
$450$	−29.1441	+	11.5079i	−1.37387	+	0.542486i
$451$	33.9653			1.59936
$452$	11.8386	−	7.68807i	0.556840	−	0.361616i
$453$	−15.9997	−	38.0073i	−0.751730	−	1.78574i
$454$	3.57835	−	8.03711i	0.167940	−	0.377200i
$455$	11.1821	−	2.67309i	0.524225	−	0.125316i
$456$	1.75161	−	0.847864i	0.0820265	−	0.0397049i
$457$	−11.1972	+	3.00027i	−0.523782	+	0.140347i	−0.511015	−	0.859572i	$-0.670730\pi$
$457$	−11.1972	+	3.00027i	−0.523782	+	0.140347i	−0.0127665	+	0.999919i	$0.504064\pi$
$458$	−3.20291	−	20.2223i	−0.149662	−	0.944928i
$459$	−14.4323	−	3.20276i	−0.673640	−	0.149492i
$460$	26.2649	−	4.84150i	1.22461	−	0.225736i
$461$	1.18343	−	5.56760i	0.0551178	−	0.259309i	−0.941958	−	0.335732i	$-0.891016\pi$
$461$	1.18343	−	5.56760i	0.0551178	−	0.259309i	0.997076	+	0.0764227i	$0.0243498\pi$
$462$	−17.5060	−	0.357746i	−0.814451	−	0.0166438i
$463$	6.46171	−	9.95016i	0.300301	−	0.462423i	−0.656019	−	0.754744i	$-0.727761\pi$
$463$	6.46171	−	9.95016i	0.300301	−	0.462423i	0.956320	+	0.292321i	$0.0944276\pi$
$464$	−19.6519	+	21.8256i	−0.912315	+	1.01323i
$465$	−2.21982	+	10.6942i	−0.102942	+	0.495934i
$466$	−33.5558	−	37.2675i	−1.55444	−	1.72638i
$467$	11.4153	−	1.80800i	0.528236	−	0.0836644i	0.113381	−	0.993552i	$-0.463832\pi$
$467$	11.4153	−	1.80800i	0.528236	−	0.0836644i	0.414856	+	0.909887i	$0.363832\pi$
$468$	−15.0925	+	17.1544i	−0.697650	+	0.792961i
$469$	−5.38497	+	7.41178i	−0.248655	+	0.342244i
$470$	23.9691	+	50.3782i	1.10561	+	2.32377i
$471$	22.0329	+	28.3747i	1.01522	+	1.30744i
$472$	−1.71607	−	4.47051i	−0.0789884	−	0.205772i
$473$	−0.830363	+	0.0435175i	−0.0381801	+	0.00200093i
$474$	−0.929346	−	29.0985i	−0.0426863	−	1.33654i
$475$	3.34503	+	6.59669i	0.153481	+	0.302677i
$476$		−	10.7302i		−	0.491816i
$477$	0.362713	+	3.10702i	0.0166075	+	0.142260i
$478$	5.20424	−	32.8583i	0.238036	−	1.50290i
$479$	−1.13011	−	10.7523i	−0.0516360	−	0.491284i	−0.989526	−	0.144352i	$-0.953890\pi$
$479$	−1.13011	−	10.7523i	−0.0516360	−	0.491284i	0.937890	−	0.346932i	$-0.112776\pi$
$480$	−29.2667	−	11.0744i	−1.33584	−	0.505475i
$481$	1.94861	−	18.5398i	0.0888491	−	0.845343i
$482$	30.5751	+	8.19256i	1.39266	+	0.373161i
$483$	4.58625	−	13.1916i	0.208682	−	0.600240i
$484$	3.16481	−	2.84961i	0.143855	−	0.129528i
$485$	−18.2543	−	2.42128i	−0.828883	−	0.109945i
$486$	−14.8574	−	28.9760i	−0.673947	−	1.31438i
$487$	−8.43211	+	4.29637i	−0.382095	+	0.194687i	−0.634479	−	0.772940i	$-0.718785\pi$
$487$	−8.43211	+	4.29637i	−0.382095	+	0.194687i	0.252384	+	0.967627i	$0.418785\pi$
$488$	−0.268588	+	5.12497i	−0.0121584	+	0.231996i
$489$	6.38012	+	1.14460i	0.288519	+	0.0517605i
$490$	20.7413	−	1.61208i	0.936995	−	0.0728263i
$491$	2.04717	+	9.63119i	0.0923876	+	0.434650i	0.999893	+	0.0146097i	$0.00465057\pi$
$491$	2.04717	+	9.63119i	0.0923876	+	0.434650i	−0.907506	+	0.420040i	$0.862016\pi$
$492$	−34.6912	+	29.9756i	−1.56400	+	1.35140i
$493$	6.88600	+	25.6989i	0.310130	+	1.15742i
$494$	8.05544	+	5.85262i	0.362432	+	0.263322i
$495$	11.6993	+	16.6447i	0.525846	+	0.748123i
$496$	−7.16532	+	5.20591i	−0.321732	+	0.233752i
$497$	−8.77040	−	7.10213i	−0.393406	−	0.318574i
$498$	27.6834	−	58.9083i	1.24052	−	2.63975i
$499$	19.6274	−	11.3319i	0.878645	−	0.507286i	0.00843381	−	0.999964i	$-0.497315\pi$
$499$	19.6274	−	11.3319i	0.878645	−	0.507286i	0.870212	+	0.492678i	$0.163982\pi$
$500$	−8.89375	+	24.8842i	−0.397741	+	1.11286i
$501$	−21.5469	+	0.688162i	−0.962642	+	0.0307448i
$502$	−32.3239	−	49.7744i	−1.44269	−	2.22154i
$503$	−35.9519	−	5.69422i	−1.60302	−	0.253893i	−0.710095	−	0.704106i	$-0.751348\pi$
$503$	−35.9519	−	5.69422i	−1.60302	−	0.253893i	−0.892921	+	0.450214i	$0.851348\pi$
$504$	2.79909	−	2.32043i	0.124681	−	0.103360i
$505$	−0.255718	−	10.1424i	−0.0113793	−	0.451330i
$506$	−13.0215	−	29.2468i	−0.578877	−	1.30018i
$507$	4.41334	+	1.03276i	0.196003	+	0.0458665i
$508$	−17.3308	−	21.4017i	−0.768928	−	0.949547i
$509$	19.8906	−	4.22787i	0.881634	−	0.187397i	0.255215	−	0.966884i	$-0.417854\pi$
$509$	19.8906	−	4.22787i	0.881634	−	0.187397i	0.626418	+	0.779487i	$0.284520\pi$
$510$	−18.5568	+	13.6181i	−0.821708	+	0.603021i
$511$	4.06985	+	0.865072i	0.180039	+	0.0382685i
$512$	−13.6857	−	26.8597i	−0.604828	−	1.18704i
$513$	−6.48359	+	4.12857i	−0.286257	+	0.182281i
$514$	42.9753	−	13.9635i	1.89556	−	0.615904i
$515$	−21.9837	−	16.9027i	−0.968717	−	0.744821i
$516$	0.809702	−	0.777271i	0.0356451	−	0.0342175i
$517$	28.1515	−	22.7966i	1.23810	−	1.00259i
$518$	−4.99100	+	18.6267i	−0.219292	+	0.818408i
$519$	12.6974	+	0.925917i	0.557356	+	0.0406432i
$520$	0.709035	+	5.42643i	0.0310933	+	0.237965i
$521$	−18.0241	−	24.8080i	−0.789650	−	1.08686i	−0.994152	−	0.107994i	$-0.965557\pi$
$521$	−18.0241	−	24.8080i	−0.789650	−	1.08686i	0.204502	−	0.978866i	$-0.434443\pi$
$522$	−33.8990	+	47.8040i	−1.48372	+	2.09232i
$523$	−2.88579	−	1.47038i	−0.126187	−	0.0642954i	0.389757	−	0.920918i	$-0.372559\pi$
$523$	−2.88579	−	1.47038i	−0.126187	−	0.0642954i	−0.515944	+	0.856622i	$0.672559\pi$
$524$	24.6534	−	42.7009i	1.07699	−	1.86540i
$525$	9.01453	+	10.4738i	0.393426	+	0.457112i
$526$	6.28435	+	10.8848i	0.274010	+	0.474600i
$527$	0.419910	+	8.01235i	0.0182915	+	0.349023i
$528$	−2.05936	+	16.3688i	−0.0896220	+	0.712359i
$529$	2.52180	−	0.265052i	0.109643	−	0.0115240i
$530$	4.01118	+	2.76255i	0.174234	+	0.119998i
$531$	8.77995	+	16.7528i	0.381017	+	0.727008i
$532$	−3.94499	−	3.94499i	−0.171037	−	0.171037i
$533$	−33.6899	−	12.9323i	−1.45927	−	0.560161i
$534$	−11.7097	+	2.88251i	−0.506726	+	0.124739i
$535$	−6.55776	−	1.58113i	−0.283517	−	0.0683580i
$536$	−3.24069	−	2.91793i	−0.139976	−	0.126035i
$537$	0.571510	−	27.9663i	0.0246625	−	1.20684i
$538$	−36.9363	−	1.93575i	−1.59244	−	0.0834561i
$539$	−4.17417	−	12.8468i	−0.179794	−	0.553350i
$540$	−26.6389	−	6.67533i	−1.14635	−	0.287261i
$541$	1.37925	−	4.24488i	0.0592984	−	0.182502i	−0.917020	−	0.398842i	$-0.869412\pi$
$541$	1.37925	−	4.24488i	0.0592984	−	0.182502i	0.976318	+	0.216340i	$0.0694121\pi$
$542$	−15.1477	+	39.4610i	−0.650648	+	1.69500i
$543$	−32.2947	+	9.76835i	−1.38590	+	0.419200i
$544$	−22.8608	−	2.40277i	−0.980149	−	0.103018i
$545$	−4.73661	−	19.8143i	−0.202894	−	0.848750i
$546$	17.2278	+	7.02026i	0.737281	+	0.300439i
$547$	8.65778	−	10.6915i	0.370180	−	0.457134i	−0.557684	−	0.830053i	$-0.688310\pi$
$547$	8.65778	−	10.6915i	0.370180	−	0.457134i	0.927864	+	0.372919i	$0.121643\pi$
$548$	9.51610	−	18.6764i	0.406508	−	0.797816i
$549$	−1.29348	−	20.2293i	−0.0552045	−	0.863365i
$550$	31.4970	+	3.37242i	1.34304	+	0.143800i
$551$	11.9800	+	6.91664i	0.510364	+	0.294659i
$552$	6.01652	+	2.82741i	0.256080	+	0.120342i
$553$	−11.9868	+	4.60130i	−0.509730	+	0.195667i
$554$	27.2942	+	12.1522i	1.15962	+	0.516295i
$555$	20.8796	−	8.12953i	0.886291	−	0.345079i
$556$	−4.71785	+	2.10052i	−0.200081	+	0.0890819i
$557$	−5.62408	+	5.62408i	−0.238300	+	0.238300i	−0.816146	−	0.577846i	$-0.803893\pi$
$557$	−5.62408	+	5.62408i	−0.238300	+	0.238300i	0.577846	+	0.816146i	$0.303893\pi$
$558$	−12.9967	+	11.9757i	−0.550196	+	0.506970i
$559$	0.840198	+	0.272997i	0.0355366	+	0.0115465i
$560$	−0.304225	+	11.2016i	−0.0128559	+	0.473354i
$561$	11.4201	+	9.64070i	0.482156	+	0.407031i
$562$	−26.3476	−	17.1103i	−1.11140	−	0.721755i
$563$	22.7496	+	14.7738i	0.958781	+	0.622640i	0.926282	−	0.376832i	$-0.122987\pi$
$563$	22.7496	+	14.7738i	0.958781	+	0.622640i	0.0324997	+	0.999472i	$0.489653\pi$
$564$	−8.63427	+	48.1284i	−0.363568	+	2.02657i
$565$	−0.362556	+	13.3493i	−0.0152528	+	0.561611i
$566$	24.2977	+	7.89480i	1.02131	+	0.331843i
$567$	−9.91865	+	10.3855i	−0.416544	+	0.436150i
$568$	3.79840	−	3.79840i	0.159377	−	0.159377i
$569$	26.1058	−	11.6231i	1.09441	−	0.487264i	0.221510	−	0.975158i	$-0.428902\pi$
$569$	26.1058	−	11.6231i	1.09441	−	0.487264i	0.872903	+	0.487894i	$0.162235\pi$
$570$	−1.81571	+	11.8292i	−0.0760518	+	0.495472i
$571$	−23.1473	−	10.3058i	−0.968684	−	0.431286i	−0.139476	−	0.990226i	$-0.544542\pi$
$571$	−23.1473	−	10.3058i	−0.968684	−	0.431286i	−0.829208	+	0.558940i	$0.811208\pi$
$572$	21.5646	−	8.27786i	0.901660	−	0.346115i
$573$	1.90503	+	22.5481i	0.0795836	+	0.941961i
$574$	32.3280	+	18.6646i	1.34934	+	0.779044i
$575$	−10.3217	+	23.0620i	−0.430443	+	0.961752i
$576$	−17.6188	−	26.4596i	−0.734115	−	1.10249i
$577$	7.34285	−	14.4112i	0.305687	−	0.599944i	−0.686150	−	0.727460i	$-0.740700\pi$
$577$	7.34285	−	14.4112i	0.305687	−	0.599944i	0.991836	+	0.127516i	$0.0407005\pi$
$578$	11.7074	−	14.4574i	0.486963	−	0.601349i
$579$	17.9163	−	13.9120i	0.744575	−	0.578161i
$580$	11.4911	+	48.0696i	0.477140	+	1.99598i
$581$	−28.5483	−	3.00055i	−1.18438	−	0.124484i
$582$	−21.7303	−	20.3852i	−0.900751	−	0.844996i
$583$	1.13329	−	2.95233i	0.0469363	−	0.122273i
$584$	−0.612005	+	1.88356i	−0.0253250	+	0.0779422i
$585$	−5.26696	−	20.9642i	−0.217762	−	0.866765i
$586$	19.6315	+	60.4194i	0.810968	+	2.49590i
$587$	−22.7736	−	1.19351i	−0.939966	−	0.0492615i	−0.423805	−	0.905753i	$-0.639306\pi$
$587$	−22.7736	−	1.19351i	−0.939966	−	0.0492615i	−0.516161	+	0.856492i	$0.672639\pi$
$588$	15.6011	+	9.43746i	0.643378	+	0.389194i
$589$	3.10016	+	2.79139i	0.127740	+	0.115017i
$590$	28.6287	+	6.90259i	1.17862	+	0.284175i
$591$	−29.3338	−	30.5577i	−1.20663	−	1.25698i
$592$	16.9626	+	6.51133i	0.697158	+	0.267614i
$593$	−2.02984	−	2.02984i	−0.0833555	−	0.0833555i	0.664200	−	0.747555i	$-0.268772\pi$
$593$	−2.02984	−	2.02984i	−0.0833555	−	0.0833555i	−0.747555	+	0.664200i	$0.768772\pi$
$594$	−0.294249	+	32.9184i	−0.0120732	+	1.35066i
$595$	8.36029	+	5.75784i	0.342738	+	0.236049i
$596$	21.7563	−	2.28668i	0.891173	−	0.0936661i
$597$	5.34574	+	4.05334i	0.218787	+	0.165892i
$598$	1.78016	+	33.9676i	0.0727963	+	1.38904i
$599$	−4.62678	−	8.01382i	−0.189045	−	0.327436i	0.755887	−	0.654702i	$-0.227206\pi$
$599$	−4.62678	−	8.01382i	−0.189045	−	0.327436i	−0.944932	+	0.327266i	$0.893873\pi$
$600$	−5.40662	+	3.74622i	−0.220724	+	0.152939i
$601$	−12.1530	+	21.0496i	−0.495730	+	0.858629i	−0.999988	−	0.00492383i	$-0.998433\pi$
$601$	−12.1530	+	21.0496i	−0.495730	+	0.858629i	0.504258	+	0.863553i	$0.331766\pi$
$602$	−0.814247	−	0.414880i	−0.0331862	−	0.0169092i
$603$	14.0503	+	9.96341i	0.572171	+	0.405741i
$604$	−33.0770	−	45.5265i	−1.34588	−	1.85245i
$605$	0.521991	+	3.99493i	0.0212220	+	0.162417i
$606$	9.22041	−	13.5823i	0.374553	−	0.551745i
$607$	−2.97253	+	11.0936i	−0.120651	+	0.450276i	−0.999647	−	0.0265523i	$-0.991547\pi$
$607$	−2.97253	+	11.0936i	−0.120651	+	0.450276i	0.878996	+	0.476829i	$0.158214\pi$
$608$	−9.28826	+	7.52148i	−0.376689	+	0.305036i
$609$	24.8228	+	7.19793i	1.00587	+	0.291675i
$610$	−25.0204	−	19.2376i	−1.01305	−	0.778906i
$611$	−36.6030	+	11.8930i	−1.48080	+	0.481141i
$612$	−20.1724	+	0.231877i	−0.815420	+	0.00937309i
$613$	10.0629	+	19.7496i	0.406438	+	0.797679i	0.999975	−	0.00712782i	$-0.00226888\pi$
$613$	10.0629	+	19.7496i	0.406438	+	0.797679i	−0.593537	+	0.804807i	$0.702269\pi$
$614$	−5.04208	−	1.07173i	−0.203482	−	0.0432514i
$615$	−4.73973	−	43.1142i	−0.191124	−	1.73853i
$616$	−3.59534	+	0.764212i	−0.144860	+	0.0307910i
$617$	−5.26755	−	6.50488i	−0.212063	−	0.261876i	0.660004	−	0.751262i	$-0.270554\pi$
$617$	−5.26755	−	6.50488i	−0.212063	−	0.261876i	−0.872068	+	0.489385i	$0.837221\pi$
$618$	−12.9908	−	42.9483i	−0.522567	−	1.72763i
$619$	6.00000	+	13.4762i	0.241160	+	0.541655i	0.993058	−	0.117625i	$-0.0375280\pi$
$619$	6.00000	+	13.4762i	0.241160	+	0.541655i	−0.751898	+	0.659280i	$0.770861\pi$
$620$	0.375670	+	14.8999i	0.0150873	+	0.598396i
$621$	−24.8990	−	8.33695i	−0.999161	−	0.334550i
$622$	−4.55961	−	0.722171i	−0.182824	−	0.0289564i
$623$	2.89659	+	4.46036i	0.116049	+	0.178700i
$624$	8.27508	−	15.4519i	0.331268	−	0.618572i
$625$	−14.6158	−	20.2824i	−0.584634	−	0.811297i
$626$	−9.73117	+	5.61829i	−0.388936	+	0.224552i
$627$	7.74308	−	0.654191i	0.309229	−	0.0261259i
$628$	38.0984	+	30.8515i	1.52029	+	1.23111i
$629$	13.3161	−	9.67468i	0.530946	−	0.385755i
$630$	1.98878	+	22.2713i	0.0792349	+	0.887310i
$631$	−1.84483	−	1.34035i	−0.0734415	−	0.0533584i	0.550459	−	0.834862i	$-0.314453\pi$
$631$	−1.84483	−	1.34035i	−0.0734415	−	0.0533584i	−0.623900	+	0.781504i	$0.714453\pi$
$632$	−1.58178	−	5.90329i	−0.0629199	−	0.234820i
$633$	−1.98287	−	10.3658i	−0.0788119	−	0.412002i
$634$	5.15992	+	24.2755i	0.204927	+	0.964104i
$635$	25.9746	−	2.01884i	1.03077	−	0.0801150i
$636$	1.44802	+	4.01560i	0.0574178	+	0.159229i
$637$	−0.751103	+	14.3319i	−0.0297598	+	0.567851i
$638$	52.7879	−	26.8968i	2.08989	−	1.06485i
$639$	−13.1623	+	16.6416i	−0.520691	+	0.658330i
$640$	−13.2462	−	1.75701i	−0.523603	−	0.0694517i
$641$	23.3899	−	21.0604i	0.923845	−	0.831834i	−0.0622423	−	0.998061i	$-0.519825\pi$
$641$	23.3899	−	21.0604i	0.923845	−	0.831834i	0.986087	+	0.166227i	$0.0531585\pi$
$642$	−7.13630	−	8.25895i	−0.281647	−	0.325955i
$643$	27.6088	+	7.39776i	1.08879	+	0.291739i	0.758190	−	0.652033i	$-0.226084\pi$
$643$	27.6088	+	7.39776i	1.08879	+	0.291739i	0.330595	+	0.943773i	$0.392750\pi$
$644$	1.99216	−	18.9541i	0.0785020	−	0.746896i
$645$	0.171113	+	1.04796i	0.00673757	+	0.0412633i
$646$	0.918954	+	8.74326i	0.0361557	+	0.343999i
$647$	4.65681	−	29.4019i	0.183078	−	1.15591i	−0.709396	−	0.704810i	$-0.751032\pi$
$647$	4.65681	−	29.4019i	0.183078	−	1.15591i	0.892474	−	0.451099i	$-0.148968\pi$
$648$	−4.42283	−	5.21206i	−0.173745	−	0.204749i
$649$		−	19.1212i		−	0.750574i
$650$	−29.9575	−	15.3376i	−1.17503	−	0.601589i
$651$	6.87087	+	3.67960i	0.269290	+	0.144215i
$652$	8.83333	−	0.462935i	0.345940	−	0.0181299i
$653$	−7.70311	−	20.0673i	−0.301446	−	0.785293i	−0.997718	−	0.0675156i	$-0.978493\pi$
$653$	−7.70311	−	20.0673i	−0.301446	−	0.785293i	0.696272	−	0.717778i	$-0.254841\pi$
$654$	12.4396	−	30.5270i	0.486428	−	1.19370i
$655$	20.0408	+	42.1219i	0.783060	+	1.64584i
$656$	20.6736	−	28.4547i	0.807168	−	1.11097i
$657$	1.53836	−	7.66988i	0.0600171	−	0.299230i
$658$	39.3215	−	6.22792i	1.53291	−	0.242790i
$659$	21.9155	+	24.3396i	0.853706	+	0.948137i	0.999150	−	0.0412298i	$-0.0131276\pi$
$659$	21.9155	+	24.3396i	0.853706	+	0.948137i	−0.145444	+	0.989367i	$0.546461\pi$
$660$	20.7206	+	18.4785i	0.806549	+	0.719276i
$661$	32.4872	−	36.0807i	1.26361	−	1.40338i	0.387061	−	0.922054i	$-0.373490\pi$
$661$	32.4872	−	36.0807i	1.26361	−	1.40338i	0.876544	−	0.481322i	$-0.159843\pi$
$662$	1.80106	−	2.77339i	0.0700002	−	0.107791i
$663$	−7.65675	−	13.9107i	−0.297363	−	0.540248i
$664$	2.84082	−	13.3650i	0.110245	−	0.518663i
$665$	5.19059	−	0.956799i	0.201282	−	0.0371031i
$666$	35.1254	+	8.98040i	1.36108	+	0.347983i
$667$	7.39241	+	46.6738i	0.286235	+	1.80722i
$668$	−28.4159	+	7.61402i	−1.09944	+	0.294595i
$669$	−0.968010	+	13.2747i	−0.0374254	+	0.513229i
$670$	26.0833	−	6.23523i	1.00769	−	0.240888i
$671$	−8.33510	+	18.7209i	−0.321773	+	0.722714i
$672$	−13.4916	+	17.7934i	−0.520450	+	0.686396i
$673$	24.8577	−	16.1428i	0.958196	−	0.622260i	0.0320744	−	0.999485i	$-0.489789\pi$
$673$	24.8577	−	16.1428i	0.958196	−	0.622260i	0.926121	+	0.377226i	$0.123122\pi$
$674$	−12.3747			−0.476655
$675$	19.4955	−	17.1734i	0.750383	−	0.661003i
$676$	6.18525			0.237894
$677$	6.84878	−	4.44765i	0.263220	−	0.170937i	−0.406281	−	0.913748i	$-0.633175\pi$
$677$	6.84878	−	4.44765i	0.263220	−	0.170937i	0.669501	+	0.742811i	$0.266508\pi$
$678$	−13.0555	+	17.2182i	−0.501393	+	0.661262i
$679$	−5.34468	+	12.0043i	−0.205110	+	0.460684i
$680$	−3.14164	+	3.67115i	−0.120476	+	0.140782i
$681$	−0.530533	+	7.27540i	−0.0203301	+	0.278794i
$682$	17.2577	−	4.62418i	0.660831	−	0.177069i
$683$	2.89318	+	18.2668i	0.110704	+	0.698960i	0.979144	+	0.203166i	$0.0651230\pi$
$683$	2.89318	+	18.2668i	0.110704	+	0.698960i	−0.868440	+	0.495794i	$0.834877\pi$
$684$	−7.33120	+	7.50171i	−0.280316	+	0.286835i
$685$	9.44513	+	17.4362i	0.360880	+	0.666202i
$686$	7.93770	−	37.3439i	0.303063	−	1.42580i
$687$	8.18613	+	14.8725i	0.312320	+	0.567421i
$688$	−0.468958	+	0.722131i	−0.0178788	+	0.0275310i
$689$	−2.24821	+	2.49689i	−0.0856499	+	0.0951238i
$690$	−35.3076	+	20.6103i	−1.34414	+	0.784619i
$691$	−13.6930	−	15.2076i	−0.520905	−	0.578524i	0.424085	−	0.905622i	$-0.360596\pi$
$691$	−13.6930	−	15.2076i	−0.520905	−	0.578524i	−0.944990	+	0.327098i	$0.893929\pi$
$692$	17.1593	−	2.71777i	0.652300	−	0.103314i
$693$	13.7552	−	4.64481i	0.522518	−	0.176442i
$694$	−32.2703	+	44.4163i	−1.22497	+	1.68602i
$695$	0.895017	−	4.80301i	0.0339499	−	0.182188i
$696$	−4.64244	+	11.3926i	−0.175971	+	0.431835i
$697$	−11.4184	−	29.7459i	−0.432501	−	1.12670i
$698$	−46.1148	+	2.41678i	−1.74547	+	0.0914763i
$699$	36.6555	+	19.6304i	1.38644	+	0.742490i
$700$	15.2345	+	11.1138i	0.575810	+	0.420064i
$701$		−	19.1636i		−	0.723800i	−0.932217	−	0.361900i	$-0.882128\pi$
$701$		−	19.1636i		−	0.723800i	0.932217	−	0.361900i	$-0.117872\pi$
$702$	12.8256	−	32.5394i	0.484070	−	1.22812i
$703$	1.33877	−	8.45264i	0.0504926	−	0.318797i
$704$	3.35924	+	31.9610i	0.126606	+	1.20458i
$705$	−32.8655	−	32.5532i	−1.23779	−	1.22602i
$706$	−6.36433	+	60.5525i	−0.239525	+	2.27892i
$707$	−6.99325	−	1.87384i	−0.263008	−	0.0704728i
$708$	16.8752	+	19.5299i	0.634207	+	0.733977i
$709$	6.31930	−	5.68992i	0.237326	−	0.213690i	−0.541882	−	0.840455i	$-0.682288\pi$
$709$	6.31930	−	5.68992i	0.237326	−	0.213690i	0.779208	+	0.626765i	$0.215621\pi$
$710$	5.98867	+	32.4882i	0.224751	+	1.21926i
$711$	8.90933	+	22.4354i	0.334126	+	0.841392i
$712$	−2.25558	+	1.14928i	−0.0845315	+	0.0430710i
$713$	−0.745828	+	14.2312i	−0.0279315	+	0.532964i
$714$	5.57180	+	15.4515i	0.208520	+	0.578258i
$715$	−5.12202	+	21.2437i	−0.191553	+	0.794471i
$716$	−7.93630	−	37.3373i	−0.296593	−	1.39536i
$717$	5.18264	+	27.0931i	0.193549	+	1.01181i
$718$	−15.1057	−	56.3753i	−0.563740	−	2.10391i
$719$	−10.3638	−	7.52971i	−0.386503	−	0.280811i	0.377518	−	0.926002i	$-0.376778\pi$
$719$	−10.3638	−	7.52971i	−0.386503	−	0.280811i	−0.764021	+	0.645191i	$0.776778\pi$
$720$	21.0652	+	0.329869i	0.785055	+	0.0122935i
$721$	−16.0093	+	11.6315i	−0.596218	+	0.433178i
$722$	−27.2922	−	22.1008i	−1.01571	−	0.822506i
$723$	−26.1528	+	2.20957i	−0.972631	+	0.0821748i
$724$	−39.8735	+	23.0210i	−1.48189	+	0.855568i
$725$	−43.6190	−	16.8412i	−1.61997	−	0.625466i
$726$	−3.07764	+	5.74683i	−0.114222	+	0.213285i
$727$	8.92134	+	13.7377i	0.330874	+	0.509501i	0.964480	−	0.264154i	$-0.0850928\pi$
$727$	8.92134	+	13.7377i	0.330874	+	0.509501i	−0.633606	+	0.773656i	$0.718426\pi$
$728$	3.85715	+	0.610913i	0.142956	+	0.0226420i
$729$	19.7387	+	18.4223i	0.731065	+	0.682308i
$730$	−7.40517	−	9.67006i	−0.274078	−	0.357905i
$731$	0.317260	+	0.712578i	0.0117343	+	0.0263557i
$732$	−8.00866	−	26.4770i	−0.296008	−	0.978619i
$733$	23.9350	+	29.5572i	0.884058	+	1.09172i	0.995195	+	0.0979158i	$0.0312176\pi$
$733$	23.9350	+	29.5572i	0.884058	+	1.09172i	−0.111137	+	0.993805i	$0.535449\pi$
$734$	68.7469	−	14.6126i	2.53749	−	0.539361i
$735$	−15.7247	+	7.09124i	−0.580014	+	0.261564i
$736$	−39.9360	−	8.48865i	−1.47206	−	0.312896i
$737$	−7.90536	−	15.5151i	−0.291198	−	0.571507i
$738$	34.3902	−	61.1789i	1.26592	−	2.25203i
$739$	−4.42835	+	1.43886i	−0.162899	+	0.0529292i	−0.389331	−	0.921098i	$-0.627294\pi$
$739$	−4.42835	+	1.43886i	−0.162899	+	0.0529292i	0.226432	+	0.974027i	$0.427294\pi$
$740$	25.2156	−	17.2941i	0.926943	−	0.635744i
$741$	−7.92937	−	2.29930i	−0.291293	−	0.0844669i
$742$	2.70102	−	2.18725i	0.0991577	−	0.0802963i
$743$	−11.9547	+	44.6154i	−0.438574	+	1.63678i	0.293791	+	0.955870i	$0.405083\pi$
$743$	−11.9547	+	44.6154i	−0.438574	+	1.63678i	−0.732365	+	0.680912i	$0.761584\pi$
$744$	−2.08372	+	3.06948i	−0.0763930	+	0.112533i
$745$	−9.89288	+	18.1782i	−0.362447	+	0.665999i
$746$	−3.83181	−	5.27403i	−0.140292	−	0.193096i
$747$	−5.02401	+	53.7347i	−0.183819	+	1.96605i
$748$	18.1718	+	9.25898i	0.664426	+	0.338542i
$749$	−2.40687	+	4.16882i	−0.0879451	+	0.152325i
$750$	−0.114469	−	40.4516i	−0.00417981	−	1.47709i
$751$	23.6198	+	40.9107i	0.861899	+	1.49285i	0.870094	+	0.492886i	$0.164058\pi$
$751$	23.6198	+	40.9107i	0.861899	+	1.49285i	−0.00819555	+	0.999966i	$0.502609\pi$
$752$	−1.96318	−	37.4597i	−0.0715898	−	1.36601i
$753$	39.2124	+	29.7323i	1.42898	+	1.08350i
$754$	−62.6008	+	6.57961i	−2.27979	+	0.239615i
$755$	53.2207	−	1.34184i	1.93690	−	0.0488347i
$756$	−9.94998	+	16.8835i	−0.361877	+	0.614048i
$757$	10.8422	+	10.8422i	0.394066	+	0.394066i	0.876134	−	0.482068i	$-0.160114\pi$
$757$	10.8422	+	10.8422i	0.394066	+	0.394066i	−0.482068	+	0.876134i	$0.660114\pi$
$758$	16.0997	+	6.18011i	0.584769	+	0.224472i
$759$	18.3829	+	19.1499i	0.667257	+	0.695097i
$760$	0.194677	+	2.50475i	0.00706169	+	0.0908568i
$761$	2.90552	+	2.61614i	0.105325	+	0.0948351i	0.720111	−	0.693859i	$-0.244091\pi$
$761$	2.90552	+	2.61614i	0.105325	+	0.0948351i	−0.614786	+	0.788694i	$0.710758\pi$
$762$	36.0696	+	21.8193i	1.30666	+	0.790430i
$763$	−14.5180	−	0.760856i	−0.525587	−	0.0275448i
$764$	9.54223	+	29.3680i	0.345226	+	1.06250i
$765$	10.6439	−	15.8415i	0.384831	−	0.572751i
$766$	−5.50086	+	16.9299i	−0.198754	+	0.611702i
$767$	−7.28043	+	18.9662i	−0.262881	+	0.684829i
$768$	11.0022	+	10.3212i	0.397007	+	0.372433i
$769$	−28.9215	−	3.03977i	−1.04294	−	0.109617i	−0.432461	−	0.901653i	$-0.642355\pi$
$769$	−28.9215	−	3.03977i	−1.04294	−	0.109617i	−0.610474	+	0.792036i	$0.709021\pi$
$770$	8.67080	−	20.8757i	0.312474	−	0.752309i
$771$	−29.5931	+	22.9790i	−1.06577	+	0.827568i
$772$	19.4801	−	24.0560i	0.701106	−	0.865793i
$773$	1.50505	−	2.95383i	0.0541329	−	0.106242i	−0.862355	−	0.506304i	$-0.831011\pi$
$773$	1.50505	−	2.95383i	0.0541329	−	0.106242i	0.916488	+	0.400062i	$0.131011\pi$
$774$	−0.762365	+	1.53973i	−0.0274027	+	0.0553443i
$775$	−11.8107	−	7.70267i	−0.424253	−	0.276688i
$776$	−5.41674	−	3.12736i	−0.194450	−	0.112266i
$777$	−1.34609	−	15.9325i	−0.0482909	−	0.571577i
$778$	−23.7398	+	9.11285i	−0.851112	+	0.326711i
$779$	−15.1342	−	6.73818i	−0.542239	−	0.241420i
$780$	−13.5168	−	26.2181i	−0.483981	−	0.938758i
$781$	19.5955	−	8.72449i	0.701183	−	0.312187i
$782$	−21.2360	+	21.2360i	−0.759397	+	0.759397i
$783$	12.9955	−	46.8216i	0.464420	−	1.67327i
$784$	−13.3032	−	4.32247i	−0.475114	−	0.154374i
$785$	−44.4813	+	13.1289i	−1.58761	+	0.468592i
$786$	−13.3279	+	74.2912i	−0.475390	+	2.64988i
$787$	−18.0119	−	11.6970i	−0.642054	−	0.416955i	0.182132	−	0.983274i	$-0.441700\pi$
$787$	−18.0119	−	11.6970i	−0.642054	−	0.416955i	−0.824186	+	0.566319i	$0.808367\pi$
$788$	−48.4781	−	31.4820i	−1.72696	−	1.12150i
$789$	−7.96330	−	6.72254i	−0.283501	−	0.239329i
$790$	35.4171	+	12.5806i	1.26008	+	0.447599i
$791$	9.06324	+	2.94483i	0.322252	+	0.104706i
$792$	1.51439	+	6.74261i	0.0538115	+	0.239588i
$793$	15.3955	−	15.3955i	0.546711	−	0.546711i
$794$	−21.5441	+	9.59204i	−0.764571	+	0.340409i
$795$	−3.90572	−	1.02657i	−0.138522	−	0.0364088i
$796$	8.36335	+	3.72360i	0.296431	+	0.131980i
$797$	−3.62473	+	1.39140i	−0.128394	+	0.0492860i	−0.421717	−	0.906728i	$-0.638572\pi$
$797$	−3.62473	+	1.39140i	−0.128394	+	0.0492860i	0.293322	+	0.956014i	$0.405239\pi$
$798$	7.72930	+	3.63231i	0.273614	+	0.128582i
$799$	−29.4285	−	16.9905i	−1.04111	−	0.601082i
$800$	27.0896	−	29.9687i	0.957763	−	1.05955i
$801$	8.32274	−	5.54189i	0.294070	−	0.195813i
$802$	7.84586	−	15.3984i	0.277047	−	0.543735i
$803$	−4.97686	+	6.14591i	−0.175630	+	0.216884i
$804$	21.7669	+	8.86995i	0.767661	+	0.312819i
$805$	13.6989	+	11.7230i	0.482822	+	0.413182i
$806$	−18.8784	−	1.98420i	−0.664963	−	0.0698904i
$807$	29.3547	−	8.87907i	1.03333	−	0.312558i
$808$	1.23499	−	3.21726i	0.0434468	−	0.113183i
$809$	5.61539	−	17.2824i	0.197427	−	0.607617i	−0.802513	−	0.596635i	$-0.796504\pi$
$809$	5.61539	−	17.2824i	0.197427	−	0.607617i	0.999940	−	0.0109822i	$-0.00349580\pi$
$810$	41.8264	−	4.22013i	1.46963	−	0.148280i
$811$	5.45388	+	16.7853i	0.191512	+	0.589413i	1.00000		0.000899698i	$0.000286383\pi$
$811$	5.45388	+	16.7853i	0.191512	+	0.589413i	−0.808488	+	0.588513i	$0.799714\pi$
$812$	35.2208	+	1.84584i	1.23601	+	0.0647764i
$813$	0.716065	−	35.0400i	0.0251135	−	1.22891i
$814$	−27.2380	−	24.5252i	−0.954690	−	0.859607i
$815$	−4.37931	+	7.13080i	−0.153400	+	0.249781i
$816$	15.0276	−	3.69928i	0.526072	−	0.129501i
$817$	0.378624	+	0.145340i	0.0132464	+	0.00508481i
$818$	−9.69420	−	9.69420i	−0.338950	−	0.338950i
$819$	−15.4122	−	0.630179i	−0.538546	−	0.0220202i
$820$	−19.7035	−	55.8133i	−0.688075	−	1.94908i
$821$	5.43121	−	0.570843i	0.189550	−	0.0199226i	−0.00927751	−	0.999957i	$-0.502953\pi$
$821$	5.43121	−	0.570843i	0.189550	−	0.0199226i	0.198828	+	0.980034i	$0.436286\pi$
$822$	−4.00523	+	31.8355i	−0.139698	+	1.11039i
$823$	−0.495459	−	9.45391i	−0.0172706	−	0.329543i	−0.993578	−	0.113153i	$-0.963905\pi$
$823$	−0.495459	−	9.45391i	−0.0172706	−	0.329543i	0.976307	−	0.216390i	$-0.0694283\pi$
$824$	−4.70961	−	8.15728i	−0.164067	−	0.284172i
$825$	−25.5161	+	6.22858i	−0.888357	+	0.216851i
$826$	10.5075	−	18.1995i	0.365602	−	0.633241i
$827$	3.94095	+	2.00801i	0.137040	+	0.0698254i	0.521166	−	0.853455i	$-0.325497\pi$
$827$	3.94095	+	2.00801i	0.137040	+	0.0698254i	−0.384126	+	0.923281i	$0.625497\pi$
$828$	−35.6762	−	3.33560i	−1.23983	−	0.115920i
$829$	−14.1718	−	19.5058i	−0.492206	−	0.677464i	0.488587	−	0.872515i	$-0.337513\pi$
$829$	−14.1718	−	19.5058i	−0.492206	−	0.677464i	−0.980793	+	0.195052i	$0.937513\pi$
$830$	57.7827	+	61.0090i	2.00567	+	2.11765i
$831$	−24.7074	−	1.80170i	−0.857089	−	0.0625002i
$832$	8.83719	−	32.9808i	0.306374	−	1.14341i
$833$	−9.84758	+	7.97441i	−0.341198	+	0.276297i
$834$	5.70300	−	5.47458i	0.197479	−	0.189569i
$835$	9.31570	−	26.2257i	0.322383	−	0.907576i
$836$	10.0850	−	3.27682i	0.348798	−	0.113331i
$837$	6.76906	−	12.9965i	0.233973	−	0.449226i
$838$	−2.00149	−	3.92815i	−0.0691404	−	0.135696i
$839$	−36.2974	−	7.71524i	−1.25312	−	0.266360i	−0.466905	−	0.884307i	$-0.654631\pi$
$839$	−36.2974	−	7.71524i	−1.25312	−	0.266360i	−0.786219	+	0.617948i	$0.787964\pi$
$840$	1.47178	+	4.45714i	0.0507811	+	0.153786i
$841$	−57.1726	+	12.1524i	−1.97147	+	0.419049i
$842$	−17.7072	−	21.8666i	−0.610232	−	0.753573i
$843$	25.3636	+	5.93530i	0.873568	+	0.204422i
$844$	−5.85775	−	13.1567i	−0.201632	−	0.452873i
$845$	−3.31903	+	4.81917i	−0.114178	+	0.165784i
$846$	−12.5580	−	73.7887i	−0.431754	−	2.53691i
$847$	2.83964	+	0.449754i	0.0975710	+	0.0154537i
$848$	−1.78354	−	2.74642i	−0.0612472	−	0.0943123i
$849$	−21.1727	+	0.676212i	−0.726644	+	0.0232075i
$850$	−7.63510	−	28.7179i	−0.261882	−	0.985016i
$851$	25.3181	−	14.6174i	0.867894	−	0.501079i
$852$	−12.3146	+	26.2047i	−0.421892	+	0.897757i
$853$	2.83001	+	2.29170i	0.0968977	+	0.0784662i	0.676545	−	0.736401i	$-0.263476\pi$
$853$	2.83001	+	2.29170i	0.0968977	+	0.0784662i	−0.579647	+	0.814867i	$0.696810\pi$
$854$	−18.2208	+	13.2382i	−0.623503	+	0.453001i
$855$	−1.91092	−	9.73747i	−0.0653521	−	0.333014i
$856$	−1.85370	−	1.34679i	−0.0633582	−	0.0460324i
$857$	−10.2423	−	38.2248i	−0.349871	−	1.30573i	−0.886818	−	0.462119i	$-0.847089\pi$
$857$	−10.2423	−	38.2248i	−0.349871	−	1.30573i	0.536947	−	0.843616i	$-0.319577\pi$
$858$	−26.7547	+	23.1179i	−0.913390	+	0.789233i
$859$	−4.38770	−	20.6425i	−0.149706	−	0.704313i	−0.987409	−	0.158187i	$-0.949435\pi$
$859$	−4.38770	−	20.6425i	−0.149706	−	0.704313i	0.837703	−	0.546126i	$-0.183898\pi$
$860$	0.553208	+	1.33924i	0.0188642	+	0.0456678i
$861$	−30.4654	−	5.46552i	−1.03826	−	0.186265i
$862$	2.14693	−	40.9658i	0.0731247	−	1.39530i
$863$	−15.3604	+	7.82654i	−0.522876	+	0.266418i	−0.695445	−	0.718579i	$-0.744793\pi$
$863$	−15.3604	+	7.82654i	−0.522876	+	0.266418i	0.172570	+	0.984997i	$0.444793\pi$
$864$	33.7426	+	24.9793i	1.14795	+	0.849812i
$865$	−7.09024	+	14.8279i	−0.241075	+	0.504163i
$866$	6.01289	−	5.41403i	0.204326	−	0.183976i
$867$	−5.06533	+	14.5696i	−0.172028	+	0.494810i
$868$	10.2736	+	2.75281i	0.348709	+	0.0934364i
$869$	2.55091	−	24.2703i	0.0865338	−	0.823314i
$870$	−41.5081	−	63.2536i	−1.40726	−	2.14450i
$871$	1.93384	+	18.3993i	0.0655258	+	0.623436i
$872$	1.08252	−	6.83473i	0.0366586	−	0.231453i
$873$	22.6833	+	9.78841i	0.767713	+	0.331288i
$874$			15.6150i			0.528185i
$875$	−16.8341	+	5.90606i	−0.569097	+	0.199661i
$876$	−0.340762	−	10.6695i	−0.0115133	−	0.360489i
$877$	17.2823	−	0.905727i	0.583582	−	0.0305842i	0.241739	−	0.970341i	$-0.422282\pi$
$877$	17.2823	−	0.905727i	0.583582	−	0.0305842i	0.341843	+	0.939757i	$0.388949\pi$
$878$	22.4471	+	58.4767i	0.757553	+	1.97349i
$879$	−32.3065	−	41.6053i	−1.08967	−	1.40331i
$880$	−18.7077	−	10.1810i	−0.630635	−	0.343201i
$881$	−18.1001	+	24.9127i	−0.609809	+	0.839330i	−0.996562	−	0.0828534i	$-0.973597\pi$
$881$	−18.1001	+	24.9127i	−0.609809	+	0.839330i	0.386753	+	0.922183i	$0.373597\pi$
$882$	−27.3662	−	5.48889i	−0.921468	−	0.184820i
$883$	38.5627	−	6.10772i	1.29774	−	0.205541i	0.530928	−	0.847417i	$-0.321843\pi$
$883$	38.5627	−	6.10772i	1.29774	−	0.205541i	0.766809	+	0.641876i	$0.221843\pi$
$884$	−14.4990	−	16.1028i	−0.487655	−	0.541596i
$885$	−24.2717	+	2.66829i	−0.815886	+	0.0896937i
$886$	15.8512	−	17.6045i	0.532531	−	0.591435i
$887$	1.22475	−	1.88594i	0.0411229	−	0.0633237i	−0.817511	−	0.575913i	$-0.804647\pi$
$887$	1.22475	−	1.88594i	0.0411229	−	0.0633237i	0.858634	+	0.512589i	$0.171313\pi$
$888$	7.60919	+	0.155499i	0.255348	+	0.00521819i
$889$	3.86539	−	18.1852i	0.129641	−	0.609913i
$890$	2.04709	−	15.4332i	0.0686187	−	0.517323i
$891$	−9.02934	−	25.7590i	−0.302494	−	0.862960i
$892$	2.84133	+	17.9394i	0.0951346	+	0.600656i
$893$	−17.0662	+	4.57286i	−0.571097	+	0.153025i
$894$	−30.1418	+	14.5901i	−1.00809	+	0.487967i
$895$	33.3496	+	13.8519i	1.11475	+	0.463017i
$896$	−3.87837	+	8.71097i	−0.129567	+	0.291013i
$897$	−10.9425	−	25.9939i	−0.365358	−	0.867911i
$898$	−46.1836	+	29.9920i	−1.54117	+	1.00085i
$899$	−26.3721			−0.879558
$900$	20.5645	−	28.8805i	0.685482	−	0.962684i
$901$	−2.96656			−0.0988303
$902$	−59.5044	+	38.6426i	−1.98128	+	1.28666i
$903$	0.751802	+	0.0945843i	0.0250184	+	0.00314757i
$904$	−1.84497	+	4.14388i	−0.0613629	+	0.137823i
$905$	3.45973	−	43.4201i	0.115005	−	1.44333i
$906$	71.2714	+	48.3827i	2.36783	+	1.60741i
$907$	−13.7576	+	3.68635i	−0.456815	+	0.122403i	−0.479887	−	0.877331i	$-0.659322\pi$
$907$	−13.7576	+	3.68635i	−0.456815	+	0.122403i	0.0230714	+	0.999734i	$0.492656\pi$
$908$	1.55723	+	9.83198i	0.0516786	+	0.326286i
$909$	−3.37163	+	13.1876i	−0.111830	+	0.437404i
$910$	−16.5489	+	17.4050i	−0.548592	+	0.576970i
$911$	7.71216	−	36.2829i	0.255515	−	1.20211i	−0.643934	−	0.765081i	$-0.722699\pi$
$911$	7.71216	−	36.2829i	0.255515	−	1.20211i	0.899450	−	0.437024i	$-0.143968\pi$
$912$	4.16491	−	6.88502i	0.137914	−	0.227986i
$913$	29.7156	−	45.7580i	0.983443	−	1.51437i
$914$	16.2031	−	17.9954i	0.535951	−	0.595234i
$915$	24.9268	+	7.96782i	0.824053	+	0.263408i
$916$	15.5015	+	17.2162i	0.512184	+	0.568838i
$917$	32.8772	−	5.20724i	1.08570	−	0.171958i
$918$	28.9279	−	10.8087i	0.954764	−	0.356741i
$919$	7.41475	−	10.2055i	0.244590	−	0.336649i	−0.669017	−	0.743247i	$-0.733285\pi$
$919$	7.41475	−	10.2055i	0.244590	−	0.336649i	0.913607	+	0.406598i	$0.133285\pi$
$920$	−6.23107	+	5.90156i	−0.205432	+	0.194569i
$921$	4.23425	−	0.582225i	0.139523	−	0.0191850i
$922$	4.26103	+	11.1004i	0.140330	+	0.365571i
$923$	−22.7585	+	1.19272i	−0.749104	+	0.0392589i
$924$	16.8327	−	10.4486i	0.553756	−	0.343735i
$925$	−0.0562600	+	28.9265i	−0.00184982	+	0.951098i
$926$			24.7834i			0.814433i
$927$	22.2127	+	29.8457i	0.729562	+	0.980261i
$928$	11.8195	−	74.6252i	0.387993	−	2.44969i
$929$	4.36016	+	41.4842i	0.143052	+	1.36105i	0.796756	+	0.604301i	$0.206547\pi$
$929$	4.36016	+	41.4842i	0.143052	+	1.36105i	−0.653704	+	0.756750i	$0.726786\pi$
$930$	−8.27800	−	21.2609i	−0.271446	−	0.697174i
$931$	−0.688677	+	6.55233i	−0.0225705	+	0.214744i
$932$	54.8090	+	14.6860i	1.79533	+	0.481057i
$933$	3.75961	−	0.719175i	0.123084	−	0.0235447i
$934$	−17.9417	+	16.1547i	−0.587069	+	0.528599i
$935$	−16.9651	+	9.18993i	−0.554817	+	0.300543i
$936$	1.06515	−	7.26453i	0.0348154	−	0.237449i
$937$	−27.7649	+	14.1469i	−0.907039	+	0.462159i	−0.844300	−	0.535871i	$-0.819983\pi$
$937$	−27.7649	+	14.1469i	−0.907039	+	0.462159i	−0.0627385	+	0.998030i	$0.519983\pi$
$938$	1.00158	−	19.1113i	0.0327029	−	0.624008i
$939$	6.01004	−	7.11931i	0.196130	−	0.232330i
$940$	−53.7912	−	33.0353i	−1.75448	−	1.07749i
$941$	9.18025	+	43.1897i	0.299268	+	1.40794i	0.828748	+	0.559622i	$0.189054\pi$
$941$	9.18025	+	43.1897i	0.299268	+	1.40794i	−0.529480	+	0.848322i	$0.677613\pi$
$942$	−70.8820	−	24.6431i	−2.30946	−	0.802916i
$943$	−14.6472	−	54.6640i	−0.476977	−	1.78010i
$944$	−16.0190	−	11.6385i	−0.521374	−	0.378800i
$945$	−7.81542	−	16.8122i	−0.254236	−	0.546900i
$946$	1.40522	−	1.02095i	0.0456875	−	0.0331939i
$947$	2.39415	+	1.93875i	0.0777995	+	0.0630008i	0.667431	−	0.744671i	$-0.267394\pi$
$947$	2.39415	+	1.93875i	0.0777995	+	0.0630008i	−0.589632	+	0.807672i	$0.700727\pi$
$948$	18.8140	+	27.0403i	0.611049	+	0.878227i
$949$	7.27656	−	4.20112i	0.236207	−	0.136374i
$950$	−13.3653	−	7.75118i	−0.433629	−	0.251481i
$951$	−10.8526	−	17.4835i	−0.351920	−	0.566942i
$952$	1.87795	+	2.89178i	0.0608646	+	0.0937232i
$953$	−14.9085	−	2.36127i	−0.482933	−	0.0764891i	−0.0897792	−	0.995962i	$-0.528616\pi$
$953$	−14.9085	−	2.36127i	−0.482933	−	0.0764891i	−0.393154	+	0.919473i	$0.628616\pi$
$954$	−4.17032	−	5.03057i	−0.135019	−	0.162871i
$955$	−28.0021	−	8.32424i	−0.906127	−	0.269366i
$956$	15.3105	+	34.3879i	0.495176	+	1.11218i
$957$	−33.6093	+	35.8269i	−1.08643	+	1.15812i
$958$	14.2128	+	17.5514i	0.459195	+	0.567059i
$959$	13.8416	−	2.94212i	0.446968	−	0.0950059i
$960$	40.1013	−	8.72411i	1.29426	−	0.281570i
$961$	22.5434	+	4.79175i	0.727207	+	0.154573i
$962$	17.6791	+	34.6972i	0.569997	+	1.11868i
$963$	7.88926	+	4.43475i	0.254228	+	0.142908i
$964$	−34.0628	+	11.0677i	−1.09709	+	0.356466i
$965$	8.28983	+	28.0863i	0.266859	+	0.904129i
$966$	6.97350	+	28.3285i	0.224369	+	0.911454i
$967$	−2.16166	+	1.75048i	−0.0695144	+	0.0562917i	−0.663448	−	0.748222i	$-0.730908\pi$
$967$	−2.16166	+	1.75048i	−0.0695144	+	0.0562917i	0.593933	+	0.804514i	$0.297574\pi$
$968$	−0.354192	+	1.32186i	−0.0113841	+	0.0424862i
$969$	−3.17597	−	6.56124i	−0.102027	−	0.210778i
$970$	34.7347	−	16.5261i	1.11526	−	0.530622i
$971$	11.7385	+	16.1566i	0.376705	+	0.518490i	0.954708	−	0.297544i	$-0.0961677\pi$
$971$	11.7385	+	16.1566i	0.376705	+	0.518490i	−0.578003	+	0.816035i	$0.696168\pi$
$972$	31.9555	+	18.3408i	1.02497	+	0.588281i
$973$	−3.10644	−	1.58281i	−0.0995880	−	0.0507426i
$974$	9.88434	−	17.1202i	0.316715	−	0.548566i
$975$	27.6807	+	3.53722i	0.886492	+	0.113282i
$976$	10.6103	+	18.3776i	0.339629	+	0.588254i
$977$	1.23296	+	23.5263i	0.0394459	+	0.752673i	0.944727	+	0.327859i	$0.106327\pi$
$977$	1.23296	+	23.5263i	0.0394459	+	0.752673i	−0.905281	+	0.424814i	$0.860339\pi$
$978$	−12.4797	+	5.25347i	−0.399056	+	0.167988i
$979$	−10.0532	+	1.05663i	−0.321301	+	0.0337700i
$980$	−18.6889	+	14.3117i	−0.596996	+	0.457169i
$981$	−1.11665	+	27.3098i	−0.0356520	+	0.871936i
$982$	−14.5440	−	14.5440i	−0.464117	−	0.464117i
$983$	−13.4276	−	5.15438i	−0.428275	−	0.164399i	0.134676	−	0.990890i	$-0.457001\pi$
$983$	−13.4276	−	5.15438i	−0.428275	−	0.164399i	−0.562951	+	0.826490i	$0.690334\pi$
$984$	4.10309	−	14.1499i	0.130802	−	0.451083i
$985$	50.5424	−	20.8778i	1.61041	−	0.665221i
$986$	−41.3016	−	37.1881i	−1.31531	−	1.18431i
$987$	−28.9190	+	15.9176i	−0.920501	+	0.506663i
$988$	−11.2509	−	0.589635i	−0.357939	−	0.0187588i
$989$	0.428122	+	1.31762i	0.0136135	+	0.0418980i
$990$	−39.4331	−	15.8497i	−1.25327	−	0.503737i
$991$	−9.97763	+	30.7080i	−0.316950	+	0.975472i	0.657994	+	0.753023i	$0.271405\pi$
$991$	−9.97763	+	30.7080i	−0.316950	+	0.975472i	−0.974944	+	0.222449i	$0.928595\pi$
$992$	8.16544	−	21.2717i	0.259253	−	0.675377i
$993$	−0.624760	+	2.66982i	−0.0198262	+	0.0847240i
$994$	23.4452	+	2.46419i	0.743635	+	0.0781592i
$995$	−7.38901	+	4.51811i	−0.234247	+	0.143234i
$996$	10.0324	+	72.9609i	0.317889	+	2.31186i
$997$	−8.79803	+	10.8647i	−0.278637	+	0.344087i	−0.897182	−	0.441662i	$-0.854389\pi$
$997$	−8.79803	+	10.8647i	−0.278637	+	0.344087i	0.618545	+	0.785749i	$0.287722\pi$
$998$	−21.4933	+	42.1829i	−0.680357	+	1.33528i
$999$	−29.9236	+	2.87492i	−0.946740	+	0.0909583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.w.a.92.4	✓	448
3.2	odd	2		675.2.bd.a.467.25		448
9.4	even	3		675.2.bd.a.17.4		448
9.5	odd	6	inner	225.2.w.a.167.25	yes	448
25.3	odd	20	inner	225.2.w.a.128.25	yes	448
75.53	even	20		675.2.bd.a.278.4		448
225.103	odd	60		675.2.bd.a.503.25		448
225.203	even	60	inner	225.2.w.a.203.4	yes	448

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.w.a.92.4	✓	448	1.1	even	1	trivial
225.2.w.a.128.25	yes	448	25.3	odd	20	inner
225.2.w.a.167.25	yes	448	9.5	odd	6	inner
225.2.w.a.203.4	yes	448	225.203	even	60	inner
675.2.bd.a.17.4		448	9.4	even	3
675.2.bd.a.278.4		448	75.53	even	20
675.2.bd.a.467.25		448	3.2	odd	2
675.2.bd.a.503.25		448	225.103	odd	60

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.w (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75192 + 1.13771i) q^{2} +(1.04649 - 1.38017i) q^{3} +(0.961361 - 2.15925i) q^{4} +(1.16649 + 1.90770i) q^{5} +(-0.263140 + 3.60854i) q^{6} +(1.54129 - 0.412989i) q^{7} +(0.118816 + 0.750173i) q^{8} +(-0.809713 - 2.88866i) q^{9} +O(q^{10})\)	\(q+(-1.75192 + 1.13771i) q^{2} +(1.04649 - 1.38017i) q^{3} +(0.961361 - 2.15925i) q^{4} +(1.16649 + 1.90770i) q^{5} +(-0.263140 + 3.60854i) q^{6} +(1.54129 - 0.412989i) q^{7} +(0.118816 + 0.750173i) q^{8} +(-0.809713 - 2.88866i) q^{9} +(-4.21399 - 2.01500i) q^{10} +(-0.630567 + 2.96658i) q^{11} +(-1.97407 - 3.58648i) q^{12} +(1.75498 - 2.70244i) q^{13} +(-2.23036 + 2.47707i) q^{14} +(3.85366 + 0.386441i) q^{15} +(2.10148 + 2.33393i) q^{16} +(2.81003 - 0.445065i) q^{17} +(4.70501 + 4.13948i) q^{18} +(0.869489 - 1.19675i) q^{19} +(5.24061 - 0.684756i) q^{20} +(1.04296 - 2.55943i) q^{21} +(-2.27041 - 5.91461i) q^{22} +(5.04636 - 0.264469i) q^{23} +(1.15970 + 0.621064i) q^{24} +(-2.27861 + 4.45061i) q^{25} +6.73110i q^{26} +(-4.83419 - 1.90542i) q^{27} +(0.589994 - 3.72508i) q^{28} +(0.977494 + 9.30024i) q^{29} +(-7.19095 + 3.70732i) q^{30} +(-0.294781 + 2.80465i) q^{31} +(-7.80423 - 2.09114i) q^{32} +(3.43449 + 3.97479i) q^{33} +(-4.41659 + 3.97671i) q^{34} +(2.58576 + 2.45858i) q^{35} +(-7.01578 - 1.02867i) q^{36} +(5.15475 - 2.62648i) q^{37} +(-0.161722 + 3.08583i) q^{38} +(-1.89323 - 5.25024i) q^{39} +(-1.29250 + 1.10173i) q^{40} +(-2.32843 - 10.9544i) q^{41} +(1.08471 + 5.67049i) q^{42} +(0.0709590 + 0.264823i) q^{43} +(5.79940 + 4.21351i) q^{44} +(4.56617 - 4.91427i) q^{45} +(-8.53992 + 6.20461i) q^{46} +(-9.28216 - 7.51654i) q^{47} +(5.42038 - 0.457952i) q^{48} +(-3.85715 + 2.22693i) q^{49} +(-1.07155 - 10.3895i) q^{50} +(2.32641 - 4.34406i) q^{51} +(-4.14807 - 6.38747i) q^{52} +(-1.02987 - 0.163115i) q^{53} +(10.6369 - 2.16176i) q^{54} +(-6.39489 + 2.25755i) q^{55} +(0.492943 + 1.10717i) q^{56} +(-0.741799 - 2.45243i) q^{57} +(-12.2934 - 15.1811i) q^{58} +(-6.16692 + 1.31082i) q^{59} +(4.53918 - 7.94951i) q^{60} +(6.60922 + 1.40483i) q^{61} +(-2.67444 - 5.24889i) q^{62} +(-2.44099 - 4.11788i) q^{63} +(10.0777 - 3.27444i) q^{64} +(7.20259 + 0.195616i) q^{65} +(-10.5391 - 3.05605i) q^{66} +(-4.46196 + 3.61322i) q^{67} +(1.74045 - 6.49543i) q^{68} +(4.91596 - 7.24158i) q^{69} +(-7.32718 - 1.36538i) q^{70} +(-4.15713 - 5.72180i) q^{71} +(2.07079 - 0.950643i) q^{72} +(2.32334 + 1.18380i) q^{73} +(-6.04254 + 10.4660i) q^{74} +(3.75803 + 7.80239i) q^{75} +(-1.74819 - 3.02796i) q^{76} +(0.253276 + 4.83279i) q^{77} +(9.29003 + 7.04404i) q^{78} +(-8.00246 + 0.841093i) q^{79} +(-2.00108 + 6.73147i) q^{80} +(-7.68873 + 4.67797i) q^{81} +(16.5421 + 16.5421i) q^{82} +(-16.7948 - 6.44693i) q^{83} +(-4.52380 - 4.71255i) q^{84} +(4.12692 + 4.84152i) q^{85} +(-0.425605 - 0.383217i) q^{86} +(13.8588 + 8.38351i) q^{87} +(-2.30037 - 0.120557i) q^{88} +(1.02996 + 3.16988i) q^{89} +(-2.40854 + 13.8044i) q^{90} +(1.58887 - 4.89004i) q^{91} +(4.28032 - 11.1506i) q^{92} +(3.56240 + 3.34189i) q^{93} +(24.8132 + 2.60797i) q^{94} +(3.29728 + 0.262728i) q^{95} +(-11.0532 + 8.58277i) q^{96} +(-5.18249 + 6.39984i) q^{97} +(4.22381 - 8.28970i) q^{98} +(9.08003 - 0.580587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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