LMFDB - Embedded newform 552.2.j.d.323.30

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(323,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.323"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [42,0,2,4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.30
Character	$\chi$	$=$	552.323
Dual form			552.2.j.d.323.29

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866210 + 1.11789i) q^{2} +(-1.39323 - 1.02904i) q^{3} +(-0.499360 + 1.93666i) q^{4} +3.31842 q^{5} +(-0.0564720 - 2.44884i) q^{6} -4.93974i q^{7} +(-2.59752 + 1.11932i) q^{8} +(0.882155 + 2.86737i) q^{9} +(2.87445 + 3.70963i) q^{10} -2.29922i q^{11} +(2.68862 - 2.18434i) q^{12} -1.77644i q^{13} +(5.52209 - 4.27885i) q^{14} +(-4.62331 - 3.41479i) q^{15} +(-3.50128 - 1.93418i) q^{16} -3.10776i q^{17} +(-2.44127 + 3.46990i) q^{18} -0.712730 q^{19} +(-1.65709 + 6.42664i) q^{20} +(-5.08319 + 6.88217i) q^{21} +(2.57028 - 1.99161i) q^{22} +1.00000 q^{23} +(4.77076 + 1.11349i) q^{24} +6.01192 q^{25} +(1.98587 - 1.53877i) q^{26} +(1.72160 - 4.90266i) q^{27} +(9.56658 + 2.46671i) q^{28} +7.87082 q^{29} +(-0.187398 - 8.12628i) q^{30} +8.99561i q^{31} +(-0.870642 - 5.58945i) q^{32} +(-2.36599 + 3.20334i) q^{33} +(3.47413 - 2.69197i) q^{34} -16.3921i q^{35} +(-5.99362 + 0.276581i) q^{36} +5.63769i q^{37} +(-0.617374 - 0.796754i) q^{38} +(-1.82803 + 2.47498i) q^{39} +(-8.61967 + 3.71438i) q^{40} -4.43652i q^{41} +(-12.0966 + 0.278957i) q^{42} +11.4065 q^{43} +(4.45281 + 1.14814i) q^{44} +(2.92736 + 9.51514i) q^{45} +(0.866210 + 1.11789i) q^{46} -5.16171 q^{47} +(2.88772 + 6.29770i) q^{48} -17.4011 q^{49} +(5.20758 + 6.72067i) q^{50} +(-3.19801 + 4.32981i) q^{51} +(3.44036 + 0.887084i) q^{52} +1.07460 q^{53} +(6.97191 - 2.32218i) q^{54} -7.62979i q^{55} +(5.52916 + 12.8311i) q^{56} +(0.992994 + 0.733427i) q^{57} +(6.81778 + 8.79872i) q^{58} +11.0580i q^{59} +(8.92197 - 7.24855i) q^{60} +2.25214i q^{61} +(-10.0561 + 7.79208i) q^{62} +(14.1641 - 4.35762i) q^{63} +(5.49424 - 5.81492i) q^{64} -5.89498i q^{65} +(-5.63043 + 0.129842i) q^{66} +6.72040 q^{67} +(6.01866 + 1.55189i) q^{68} +(-1.39323 - 1.02904i) q^{69} +(18.3246 - 14.1990i) q^{70} -11.8882 q^{71} +(-5.50092 - 6.46064i) q^{72} -9.31327 q^{73} +(-6.30232 + 4.88342i) q^{74} +(-8.37596 - 6.18650i) q^{75} +(0.355909 - 1.38031i) q^{76} -11.3576 q^{77} +(-4.35022 + 0.100319i) q^{78} +2.14336i q^{79} +(-11.6187 - 6.41842i) q^{80} +(-7.44361 + 5.05893i) q^{81} +(4.95955 - 3.84296i) q^{82} -10.3856i q^{83} +(-10.7901 - 13.2811i) q^{84} -10.3128i q^{85} +(9.88046 + 12.7513i) q^{86} +(-10.9658 - 8.09939i) q^{87} +(2.57357 + 5.97228i) q^{88} -4.78521i q^{89} +(-8.10117 + 11.5146i) q^{90} -8.77516 q^{91} +(-0.499360 + 1.93666i) q^{92} +(9.25683 - 12.5329i) q^{93} +(-4.47112 - 5.77022i) q^{94} -2.36514 q^{95} +(-4.53877 + 8.68329i) q^{96} -4.06810 q^{97} +(-15.0730 - 19.4525i) q^{98} +(6.59272 - 2.02827i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24}+ \cdots + 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	0.866210	+	1.11789i	0.612503	+	0.790468i
$2$	0.866210	+	1.11789i	0.612503	+	0.790468i
$3$	−1.39323	−	1.02904i	−0.804379	−	0.594116i
$3$	−1.39323	−	1.02904i	−0.804379	−	0.594116i
$4$	−0.499360	+	1.93666i	−0.249680	+	0.968328i
$5$	3.31842			1.48404			0.742022	−	0.670376i	$-0.233867\pi$
$5$	3.31842			1.48404			0.742022	+	0.670376i	$0.233867\pi$
$6$	−0.0564720	−	2.44884i	−0.0230546	−	0.999734i
$7$		−	4.93974i		−	1.86705i	−0.358516	−	0.933524i	$-0.616717\pi$
$7$		−	4.93974i		−	1.86705i	0.358516	−	0.933524i	$-0.383283\pi$
$8$	−2.59752	+	1.11932i	−0.918363	+	0.395740i
$9$	0.882155	+	2.86737i	0.294052	+	0.955790i
$10$	2.87445	+	3.70963i	0.908981	+	1.17309i
$11$		−	2.29922i		−	0.693242i	−0.938005	−	0.346621i	$-0.887329\pi$
$11$		−	2.29922i		−	0.693242i	0.938005	−	0.346621i	$-0.112671\pi$
$12$	2.68862	−	2.18434i	0.776137	−	0.630564i
$13$		−	1.77644i		−	0.492696i	−0.969181	−	0.246348i	$-0.920769\pi$
$13$		−	1.77644i		−	0.492696i	0.969181	−	0.246348i	$-0.0792306\pi$
$14$	5.52209	−	4.27885i	1.47584	−	1.14357i
$15$	−4.62331	−	3.41479i	−1.19373	−	0.881694i
$16$	−3.50128	−	1.93418i	−0.875320	−	0.483545i
$17$		−	3.10776i		−	0.753742i	−0.926266	−	0.376871i	$-0.877000\pi$
$17$		−	3.10776i		−	0.753742i	0.926266	−	0.376871i	$-0.123000\pi$
$18$	−2.44127	+	3.46990i	−0.575414	+	0.817862i
$19$	−0.712730			−0.163511			−0.0817557	−	0.996652i	$-0.526053\pi$
$19$	−0.712730			−0.163511			−0.0817557	+	0.996652i	$0.526053\pi$
$20$	−1.65709	+	6.42664i	−0.370536	+	1.43704i
$21$	−5.08319	+	6.88217i	−1.10924	+	1.50181i
$22$	2.57028	−	1.99161i	0.547986	−	0.424613i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	4.77076	+	1.11349i	0.973827	+	0.227289i
$25$	6.01192			1.20238
$26$	1.98587	−	1.53877i	0.389460	−	0.301778i
$27$	1.72160	−	4.90266i	0.331321	−	0.943518i
$28$	9.56658	+	2.46671i	1.80791	+	0.466164i
$29$	7.87082			1.46157			0.730787	−	0.682605i	$-0.239153\pi$
$29$	7.87082			1.46157			0.730787	+	0.682605i	$0.239153\pi$
$30$	−0.187398	−	8.12628i	−0.0342140	−	1.48365i
$31$			8.99561i			1.61566i	0.589417	+	0.807829i	$0.299358\pi$
$31$			8.99561i			1.61566i	−0.589417	+	0.807829i	$0.700642\pi$
$32$	−0.870642	−	5.58945i	−0.153909	−	0.988085i
$33$	−2.36599	+	3.20334i	−0.411866	+	0.557629i
$34$	3.47413	−	2.69197i	0.595809	−	0.461669i
$35$		−	16.3921i		−	2.77078i
$36$	−5.99362	+	0.276581i	−0.998937	+	0.0460969i
$37$			5.63769i			0.926830i	0.886141	+	0.463415i	$0.153376\pi$
$37$			5.63769i			0.926830i	−0.886141	+	0.463415i	$0.846624\pi$
$38$	−0.617374	−	0.796754i	−0.100151	−	0.129251i
$39$	−1.82803	+	2.47498i	−0.292719	+	0.396314i
$40$	−8.61967	+	3.71438i	−1.36289	+	0.587295i
$41$		−	4.43652i		−	0.692868i	−0.938074	−	0.346434i	$-0.887392\pi$
$41$		−	4.43652i		−	0.692868i	0.938074	−	0.346434i	$-0.112608\pi$
$42$	−12.0966	+	0.278957i	−1.86655	+	0.0430440i
$43$	11.4065			1.73948			0.869740	−	0.493510i	$-0.164286\pi$
$43$	11.4065			1.73948			0.869740	+	0.493510i	$0.164286\pi$
$44$	4.45281	+	1.14814i	0.671286	+	0.173089i
$45$	2.92736	+	9.51514i	0.436385	+	1.41843i
$46$	0.866210	+	1.11789i	0.127716	+	0.164824i
$47$	−5.16171			−0.752912			−0.376456	−	0.926434i	$-0.622857\pi$
$47$	−5.16171			−0.752912			−0.376456	+	0.926434i	$0.622857\pi$
$48$	2.88772	+	6.29770i	0.416807	+	0.908995i
$49$	−17.4011			−2.48586
$50$	5.20758	+	6.72067i	0.736464	+	0.950446i
$51$	−3.19801	+	4.32981i	−0.447810	+	0.606294i
$52$	3.44036	+	0.887084i	0.477091	+	0.123016i
$53$	1.07460			0.147607			0.0738036	−	0.997273i	$-0.476486\pi$
$53$	1.07460			0.147607			0.0738036	+	0.997273i	$0.476486\pi$
$54$	6.97191	−	2.32218i	0.948756	−	0.316009i
$55$		−	7.62979i		−	1.02880i
$56$	5.52916	+	12.8311i	0.738865	+	1.71463i
$57$	0.992994	+	0.733427i	0.131525	+	0.0971448i
$58$	6.81778	+	8.79872i	0.895219	+	1.15533i
$59$			11.0580i			1.43963i	0.694164	+	0.719817i	$0.255774\pi$
$59$			11.0580i			1.43963i	−0.694164	+	0.719817i	$0.744226\pi$
$60$	8.92197	−	7.24855i	1.15182	−	0.935784i
$61$			2.25214i			0.288357i	0.989552	+	0.144178i	$0.0460539\pi$
$61$			2.25214i			0.288357i	−0.989552	+	0.144178i	$0.953946\pi$
$62$	−10.0561	+	7.79208i	−1.27713	+	0.989596i
$63$	14.1641	−	4.35762i	1.78450	−	0.549008i
$64$	5.49424	−	5.81492i	0.686780	−	0.726865i
$65$		−	5.89498i		−	0.731182i
$66$	−5.63043	+	0.129842i	−0.693058	+	0.0159824i
$67$	6.72040			0.821027			0.410514	−	0.911855i	$-0.365349\pi$
$67$	6.72040			0.821027			0.410514	+	0.911855i	$0.365349\pi$
$68$	6.01866	+	1.55189i	0.729870	+	0.188194i
$69$	−1.39323	−	1.02904i	−0.167725	−	0.123882i
$70$	18.3246	−	14.1990i	2.19021	−	1.69711i
$71$	−11.8882			−1.41087			−0.705433	−	0.708777i	$-0.749247\pi$
$71$	−11.8882			−1.41087			−0.705433	+	0.708777i	$0.749247\pi$
$72$	−5.50092	−	6.46064i	−0.648290	−	0.761393i
$73$	−9.31327			−1.09004			−0.545018	−	0.838424i	$-0.683477\pi$
$73$	−9.31327			−1.09004			−0.545018	+	0.838424i	$0.683477\pi$
$74$	−6.30232	+	4.88342i	−0.732630	+	0.567686i
$75$	−8.37596	−	6.18650i	−0.967172	−	0.714356i
$76$	0.355909	−	1.38031i	0.0408256	−	0.158333i
$77$	−11.3576			−1.29432
$78$	−4.35022	+	0.100319i	−0.492565	+	0.0113589i
$79$			2.14336i			0.241146i	0.992704	+	0.120573i	$0.0384732\pi$
$79$			2.14336i			0.241146i	−0.992704	+	0.120573i	$0.961527\pi$
$80$	−11.6187	−	6.41842i	−1.29901	−	0.717601i
$81$	−7.44361	+	5.05893i	−0.827067	+	0.562103i
$82$	4.95955	−	3.84296i	0.547690	−	0.424384i
$83$		−	10.3856i		−	1.13997i	−0.821656	−	0.569984i	$-0.806949\pi$
$83$		−	10.3856i		−	1.13997i	0.821656	−	0.569984i	$-0.193051\pi$
$84$	−10.7901	−	13.2811i	−1.17729	−	1.44908i
$85$		−	10.3128i		−	1.11859i
$86$	9.88046	+	12.7513i	1.06544	+	1.37500i
$87$	−10.9658	−	8.09939i	−1.17566	−	0.868345i
$88$	2.57357	+	5.97228i	0.274343	+	0.636648i
$89$		−	4.78521i		−	0.507231i	−0.967305	−	0.253616i	$-0.918380\pi$
$89$		−	4.78521i		−	0.507231i	0.967305	−	0.253616i	$-0.0816199\pi$
$90$	−8.10117	+	11.5146i	−0.853939	+	1.21374i
$91$	−8.77516			−0.919886
$92$	−0.499360	+	1.93666i	−0.0520619	+	0.201910i
$93$	9.25683	−	12.5329i	0.959889	−	1.29960i
$94$	−4.47112	−	5.77022i	−0.461161	−	0.595153i
$95$	−2.36514			−0.242658
$96$	−4.53877	+	8.68329i	−0.463236	+	0.886235i
$97$	−4.06810			−0.413053			−0.206526	−	0.978441i	$-0.566216\pi$
$97$	−4.06810			−0.413053			−0.206526	+	0.978441i	$0.566216\pi$
$98$	−15.0730	−	19.4525i	−1.52260	−	1.96500i
$99$	6.59272	−	2.02827i	0.662593	−	0.203849i
$100$	−3.00211	+	11.6430i	−0.300211	+	1.16430i
$101$	1.88761			0.187824			0.0939122	−	0.995580i	$-0.470063\pi$
$101$	1.88761			0.187824			0.0939122	+	0.995580i	$0.470063\pi$
$102$	−7.61040	+	0.175501i	−0.753542	+	0.0173772i
$103$			14.8765i			1.46583i	0.680320	+	0.732915i	$0.261841\pi$
$103$			14.8765i			1.46583i	−0.680320	+	0.732915i	$0.738159\pi$
$104$	1.98841	+	4.61434i	0.194979	+	0.452474i
$105$	−16.8682	+	22.8380i	−1.64616	+	2.22876i
$106$	0.930826	+	1.20128i	0.0904098	+	0.116679i
$107$			4.74136i			0.458365i	0.973383	+	0.229182i	$0.0736052\pi$
$107$			4.74136i			0.458365i	−0.973383	+	0.229182i	$0.926395\pi$
$108$	8.63508	+	5.78233i	0.830911	+	0.556405i
$109$			8.20089i			0.785503i	0.919645	+	0.392751i	$0.128477\pi$
$109$			8.20089i			0.785503i	−0.919645	+	0.392751i	$0.871523\pi$
$110$	8.52928	−	6.60900i	0.813234	−	0.630144i
$111$	5.80140	−	7.85457i	0.550645	−	0.745523i
$112$	−9.55434	+	17.2954i	−0.902801	+	1.63426i
$113$			0.839993i			0.0790199i	0.999219	+	0.0395100i	$0.0125797\pi$
$113$			0.839993i			0.0790199i	−0.999219	+	0.0395100i	$0.987420\pi$
$114$	0.0402493	+	1.74536i	0.00376969	+	0.163468i
$115$	3.31842			0.309444
$116$	−3.93037	+	15.2431i	−0.364926	+	1.41528i
$117$	5.09371	−	1.56710i	0.470914	−	0.144878i
$118$	−12.3617	+	9.57859i	−1.13799	+	0.881781i
$119$	−15.3515			−1.40727
$120$	15.8314	+	3.69501i	1.44520	+	0.337307i
$121$	5.71357			0.519416
$122$	−2.51765	+	1.95083i	−0.227937	+	0.176619i
$123$	−4.56535	+	6.18107i	−0.411644	+	0.557329i
$124$	−17.4214	−	4.49205i	−1.56449	−	0.403398i
$125$	3.35797			0.300346
$126$	17.1404	+	12.0593i	1.52699	+	1.07432i
$127$			5.09595i			0.452192i	0.974105	+	0.226096i	$0.0725964\pi$
$127$			5.09595i			0.452192i	−0.974105	+	0.226096i	$0.927404\pi$
$128$	11.2596	+	1.10501i	0.995219	+	0.0976704i
$129$	−15.8919	−	11.7378i	−1.39920	−	1.03345i
$130$	6.58994	−	5.10629i	0.577976	−	0.447851i
$131$		−	8.13477i		−	0.710738i	−0.934726	−	0.355369i	$-0.884355\pi$
$131$		−	8.13477i		−	0.710738i	0.934726	−	0.355369i	$-0.115645\pi$
$132$	−5.02228	−	6.18173i	−0.437134	−	0.538051i
$133$			3.52070i			0.305284i
$134$	5.82127	+	7.51267i	0.502882	+	0.648996i
$135$	5.71298	−	16.2691i	0.491695	−	1.40022i
$136$	3.47858	+	8.07247i	0.298286	+	0.692208i
$137$		−	2.73334i		−	0.233525i	−0.993160	−	0.116762i	$-0.962748\pi$
$137$		−	2.73334i		−	0.233525i	0.993160	−	0.116762i	$-0.0372516\pi$
$138$	−0.0564720	−	2.44884i	−0.00480721	−	0.208459i
$139$	−22.8692			−1.93974			−0.969872	−	0.243615i	$-0.921667\pi$
$139$	−22.8692			−1.93974			−0.969872	+	0.243615i	$0.921667\pi$
$140$	31.7460	+	8.18558i	2.68302	+	0.691808i
$141$	7.19142	+	5.31160i	0.605627	+	0.447317i
$142$	−10.2976	−	13.2897i	−0.864159	−	1.11524i
$143$	−4.08443			−0.341558
$144$	2.45733	−	11.7457i	0.204778	−	0.978808i
$145$	26.1187			2.16904
$146$	−8.06725	−	10.4112i	−0.667650	−	0.861639i
$147$	24.2436	+	17.9064i	1.99958	+	1.47689i
$148$	−10.9183	−	2.81524i	−0.897476	−	0.231411i
$149$	−2.84641			−0.233187			−0.116594	−	0.993180i	$-0.537197\pi$
$149$	−2.84641			−0.233187			−0.116594	+	0.993180i	$0.537197\pi$
$150$	−0.339505	−	14.7222i	−0.0277205	−	1.20206i
$151$			4.43176i			0.360652i	0.983607	+	0.180326i	$0.0577152\pi$
$151$			4.43176i			0.360652i	−0.983607	+	0.180326i	$0.942285\pi$
$152$	1.85133	−	0.797774i	0.150163	−	0.0647080i
$153$	8.91109	−	2.74152i	0.720419	−	0.221639i
$154$	−9.83804	−	12.6965i	−0.792772	−	1.02312i
$155$			29.8512i			2.39771i
$156$	−3.88035	−	4.77617i	−0.310676	−	0.382400i
$157$		−	8.05473i		−	0.642837i	−0.946937	−	0.321419i	$-0.895840\pi$
$157$		−	8.05473i		−	0.642837i	0.946937	−	0.321419i	$-0.104160\pi$
$158$	−2.39604	+	1.85660i	−0.190619	+	0.147703i
$159$	−1.49716	−	1.10580i	−0.118732	−	0.0876958i
$160$	−2.88916	−	18.5482i	−0.228408	−	1.46636i
$161$		−	4.93974i		−	0.389306i
$162$	−12.1031	−	3.93905i	−0.950906	−	0.309481i
$163$	14.0874			1.10341			0.551706	−	0.834039i	$-0.313977\pi$
$163$	14.0874			1.10341			0.551706	+	0.834039i	$0.313977\pi$
$164$	8.59202	+	2.21542i	0.670924	+	0.172995i
$165$	−7.85136	+	10.6300i	−0.611227	+	0.827546i
$166$	11.6100	−	8.99612i	0.901109	−	0.698234i
$167$	−8.97815			−0.694750			−0.347375	−	0.937726i	$-0.612927\pi$
$167$	−8.97815			−0.694750			−0.347375	+	0.937726i	$0.612927\pi$
$168$	5.50033	−	23.5663i	0.424360	−	1.81818i
$169$	9.84426			0.757251
$170$	11.5286	−	8.93309i	0.884206	−	0.685137i
$171$	−0.628738	−	2.04366i	−0.0480808	−	0.156283i
$172$	−5.69597	+	22.0905i	−0.434314	+	1.68439i
$173$	14.8819			1.13145			0.565726	−	0.824593i	$-0.308596\pi$
$173$	14.8819			1.13145			0.565726	+	0.824593i	$0.308596\pi$
$174$	−0.444481	−	19.2744i	−0.0336960	−	1.46119i
$175$		−	29.6973i		−	2.24491i
$176$	−4.44711	+	8.05022i	−0.335213	+	0.606808i
$177$	11.3792	−	15.4063i	0.855310	−	1.15801i
$178$	5.34934	−	4.14500i	0.400950	−	0.310681i
$179$			2.46848i			0.184503i	0.995736	+	0.0922516i	$0.0294064\pi$
$179$			2.46848i			0.184503i	−0.995736	+	0.0922516i	$0.970594\pi$
$180$	−19.8894	+	0.917814i	−1.48247	+	0.0684098i
$181$			17.1268i			1.27302i	0.771267	+	0.636512i	$0.219623\pi$
$181$			17.1268i			1.27302i	−0.771267	+	0.636512i	$0.780377\pi$
$182$	−7.60113	−	9.80967i	−0.563433	−	0.727141i
$183$	2.31754	−	3.13774i	0.171317	−	0.231948i
$184$	−2.59752	+	1.11932i	−0.191492	+	0.0825175i
$185$			18.7082i			1.37546i
$186$	22.0288	−	0.507999i	1.61523	−	0.0372483i
$187$	−7.14543			−0.522526
$188$	2.57755	−	9.99645i	0.187987	−	0.729066i
$189$	−24.2179	−	8.50424i	−1.76159	−	0.618592i
$190$	−2.04871	−	2.64397i	−0.148629	−	0.191813i
$191$	19.5086			1.41159			0.705797	−	0.708414i	$-0.250589\pi$
$191$	19.5086			1.41159			0.705797	+	0.708414i	$0.250589\pi$
$192$	−13.6385	+	2.44771i	−0.984274	+	0.176648i
$193$	−11.1672			−0.803835			−0.401918	−	0.915676i	$-0.631656\pi$
$193$	−11.1672			−0.803835			−0.401918	+	0.915676i	$0.631656\pi$
$194$	−3.52383	−	4.54769i	−0.252996	−	0.326505i
$195$	−6.06617	+	8.21303i	−0.434407	+	0.588148i
$196$	8.68939	−	33.6999i	0.620671	−	2.40713i
$197$	6.10448			0.434926			0.217463	−	0.976069i	$-0.430222\pi$
$197$	6.10448			0.434926			0.217463	+	0.976069i	$0.430222\pi$
$198$	7.97807	+	5.61303i	0.566977	+	0.398901i
$199$			0.550823i			0.0390468i	0.999809	+	0.0195234i	$0.00621489\pi$
$199$			0.550823i			0.0390468i	−0.999809	+	0.0195234i	$0.993785\pi$
$200$	−15.6161	+	6.72927i	−1.10422	+	0.475831i
$201$	−9.36303	−	6.91555i	−0.660417	−	0.487786i
$202$	1.63507	+	2.11014i	0.115043	+	0.148469i
$203$		−	38.8798i		−	2.72883i
$204$	−6.78839	−	8.35557i	−0.475283	−	0.585007i
$205$		−	14.7222i		−	1.02825i
$206$	−16.6304	+	12.8862i	−1.15869	+	0.897825i
$207$	0.882155	+	2.86737i	0.0613140	+	0.199296i
$208$	−3.43595	+	6.21981i	−0.238240	+	0.431266i
$209$			1.63873i			0.113353i
$210$	−40.1417	+	0.925697i	−2.77004	+	0.0638791i
$211$	−3.42516			−0.235797			−0.117899	−	0.993026i	$-0.537616\pi$
$211$	−3.42516			−0.235797			−0.117899	+	0.993026i	$0.537616\pi$
$212$	−0.536611	+	2.08112i	−0.0368546	+	0.142932i
$213$	16.5629	+	12.2334i	1.13487	+	0.838218i
$214$	−5.30033	+	4.10702i	−0.362323	+	0.280750i
$215$	37.8517			2.58146
$216$	1.01577	+	14.6618i	0.0691147	+	0.997609i
$217$	44.4360			3.01651
$218$	−9.16770	+	7.10369i	−0.620915	+	0.481123i
$219$	12.9755	+	9.58373i	0.876802	+	0.647608i
$220$	14.7763	+	3.81001i	0.996217	+	0.256871i
$221$	−5.52075			−0.371366
$222$	13.8058	−	0.318371i	0.926584	−	0.0213677i
$223$			1.11567i			0.0747110i	0.999302	+	0.0373555i	$0.0118934\pi$
$223$			1.11567i			0.0747110i	−0.999302	+	0.0373555i	$0.988107\pi$
$224$	−27.6105	+	4.30075i	−1.84480	+	0.287356i
$225$	5.30344	+	17.2384i	0.353563	+	1.14923i
$226$	−0.939021	+	0.727611i	−0.0624628	+	0.0484000i
$227$		−	6.31376i		−	0.419059i	−0.977802	−	0.209529i	$-0.932807\pi$
$227$		−	6.31376i		−	0.419059i	0.977802	−	0.209529i	$-0.0671932\pi$
$228$	−1.91626	+	1.55684i	−0.126907	+	0.103104i
$229$			15.3934i			1.01722i	0.860996	+	0.508612i	$0.169841\pi$
$229$			15.3934i			1.01722i	−0.860996	+	0.508612i	$0.830159\pi$
$230$	2.87445	+	3.70963i	0.189536	+	0.244606i
$231$	15.8237	+	11.6874i	1.04112	+	0.768974i
$232$	−20.4446	+	8.80998i	−1.34226	+	0.578403i
$233$			23.7149i			1.55362i	0.629737	+	0.776808i	$0.283163\pi$
$233$			23.7149i			1.55362i	−0.629737	+	0.776808i	$0.716837\pi$
$234$	6.16406	+	4.33678i	0.402957	+	0.283504i
$235$	−17.1287			−1.11735
$236$	−21.4156	−	5.52195i	−1.39404	−	0.359448i
$237$	2.20560	−	2.98618i	0.143269	−	0.193973i
$238$	−13.2976	−	17.1613i	−0.861958	−	1.11240i
$239$	28.6833			1.85537			0.927683	−	0.373369i	$-0.121797\pi$
$239$	28.6833			1.85537			0.927683	+	0.373369i	$0.121797\pi$
$240$	9.58269	+	20.8984i	0.618560	+	1.34899i
$241$	−0.646602			−0.0416513			−0.0208256	−	0.999783i	$-0.506629\pi$
$241$	−0.646602			−0.0416513			−0.0208256	+	0.999783i	$0.506629\pi$
$242$	4.94915	+	6.38715i	0.318144	+	0.410581i
$243$	15.5765	+	0.611540i	0.999230	+	0.0392303i
$244$	−4.36162	−	1.12463i	−0.279224	−	0.0719970i
$245$	−57.7440			−3.68913
$246$	−10.8643	+	0.250539i	−0.692684	+	0.0159738i
$247$			1.26612i			0.0805614i
$248$	−10.0690	−	23.3663i	−0.639380	−	1.48376i
$249$	−10.6872	+	14.4695i	−0.677274	+	0.916967i
$250$	2.90871	+	3.75385i	0.183963	+	0.237414i
$251$			16.0797i			1.01494i	0.861668	+	0.507472i	$0.169420\pi$
$251$			16.0797i			1.01494i	−0.861668	+	0.507472i	$0.830580\pi$
$252$	1.36624	+	29.6069i	0.0860651	+	1.86506i
$253$		−	2.29922i		−	0.144551i
$254$	−5.69671	+	4.41416i	−0.357444	+	0.276969i
$255$	−10.6123	+	14.3681i	−0.664570	+	0.899767i
$256$	8.51791	+	13.5442i	0.532369	+	0.846512i
$257$		−	5.95973i		−	0.371758i	−0.982573	−	0.185879i	$-0.940487\pi$
$257$		−	5.95973i		−	0.371758i	0.982573	−	0.185879i	$-0.0595132\pi$
$258$	−0.644149	−	27.9328i	−0.0401030	−	1.73902i
$259$	27.8487			1.73044
$260$	11.4165	+	2.94372i	0.708024	+	0.182562i
$261$	6.94328	+	22.5685i	0.429778	+	1.39696i
$262$	9.09379	−	7.04642i	0.561816	−	0.435329i
$263$	−9.88085			−0.609279			−0.304640	−	0.952468i	$-0.598536\pi$
$263$	−9.88085			−0.609279			−0.304640	+	0.952468i	$0.598536\pi$
$264$	2.56015	−	10.9690i	0.157567	−	0.675098i
$265$	3.56596			0.219055
$266$	−3.93576	+	3.04967i	−0.241317	+	0.186987i
$267$	−4.92417	+	6.66688i	−0.301354	+	0.408006i
$268$	−3.35590	+	13.0151i	−0.204994	+	0.795024i
$269$	13.7330			0.837316			0.418658	−	0.908144i	$-0.362501\pi$
$269$	13.7330			0.837316			0.418658	+	0.908144i	$0.362501\pi$
$270$	23.1357	−	7.70597i	1.40800	−	0.468971i
$271$		−	23.1515i		−	1.40635i	−0.711016	−	0.703175i	$-0.751765\pi$
$271$		−	23.1515i		−	1.40635i	0.711016	−	0.703175i	$-0.248235\pi$
$272$	−6.01096	+	10.8811i	−0.364468	+	0.659765i
$273$	12.2258	+	9.02998i	0.739937	+	0.546520i
$274$	3.05558	−	2.36765i	0.184594	−	0.143035i
$275$		−	13.8227i		−	0.833543i
$276$	2.68862	−	2.18434i	0.161836	−	0.131482i
$277$		−	2.28715i		−	0.137422i	−0.997637	−	0.0687109i	$-0.978111\pi$
$277$		−	2.28715i		−	0.137422i	0.997637	−	0.0687109i	$-0.0218886\pi$
$278$	−19.8096	−	25.5653i	−1.18810	−	1.53331i
$279$	−25.7937	+	7.93552i	−1.54423	+	0.475087i
$280$	18.3481	+	42.5790i	1.09651	+	2.54458i
$281$		−	10.7228i		−	0.639668i	−0.947474	−	0.319834i	$-0.896373\pi$
$281$		−	10.7228i		−	0.639668i	0.947474	−	0.319834i	$-0.103627\pi$
$282$	0.291492	+	12.6402i	0.0173581	+	0.752712i
$283$	21.8617			1.29954			0.649770	−	0.760130i	$-0.274865\pi$
$283$	21.8617			1.29954			0.649770	+	0.760130i	$0.274865\pi$
$284$	5.93647	−	23.0233i	0.352265	−	1.36618i
$285$	3.29517	+	2.43382i	0.195189	+	0.144167i
$286$	−3.53798	−	4.56595i	−0.209205	−	0.269990i
$287$	−21.9153			−1.29362
$288$	15.2590	−	7.42722i	0.899144	−	0.437653i
$289$	7.34184			0.431873
$290$	22.6243	+	29.1979i	1.32854	+	1.71456i
$291$	5.66778	+	4.18623i	0.332251	+	0.245401i
$292$	4.65068	−	18.0366i	0.272160	−	1.05551i
$293$	8.90093			0.519998			0.259999	−	0.965609i	$-0.416278\pi$
$293$	8.90093			0.519998			0.259999	+	0.965609i	$0.416278\pi$
$294$	0.982672	+	42.6124i	0.0573106	+	2.48520i
$295$			36.6952i			2.13648i
$296$	−6.31038	−	14.6440i	−0.366784	−	0.851166i
$297$	−11.2723	−	3.95833i	−0.654086	−	0.229686i
$298$	−2.46559	−	3.18198i	−0.142828	−	0.184327i
$299$		−	1.77644i		−	0.102734i
$300$	16.1638	−	13.1321i	0.933215	−	0.758180i
$301$		−	56.3453i		−	3.24769i
$302$	−4.95423	+	3.83884i	−0.285084	+	0.220900i
$303$	−2.62987	−	1.94243i	−0.151082	−	0.111590i
$304$	2.49547	+	1.37855i	0.143125	+	0.0790651i
$305$			7.47354i			0.427934i
$306$	10.7836	+	7.58689i	0.616457	+	0.433713i
$307$	−31.5028			−1.79796			−0.898979	−	0.437992i	$-0.855690\pi$
$307$	−31.5028			−1.79796			−0.898979	+	0.437992i	$0.855690\pi$
$308$	5.67152	−	21.9957i	0.323165	−	1.25332i
$309$	15.3086	−	20.7264i	0.870873	−	1.17908i
$310$	−33.3704	+	25.8574i	−1.89531	+	1.46860i
$311$	−18.9616			−1.07522			−0.537608	−	0.843195i	$-0.680672\pi$
$311$	−18.9616			−1.07522			−0.537608	+	0.843195i	$0.680672\pi$
$312$	1.97804	−	8.47497i	0.111985	−	0.479801i
$313$	0.511780			0.0289275			0.0144638	−	0.999895i	$-0.495396\pi$
$313$	0.511780			0.0289275			0.0144638	+	0.999895i	$0.495396\pi$
$314$	9.00431	−	6.97709i	0.508143	−	0.393740i
$315$	47.0023	−	14.4604i	2.64828	−	0.814752i
$316$	−4.15094	−	1.07031i	−0.233509	−	0.0602094i
$317$	−8.11974			−0.456050			−0.228025	−	0.973655i	$-0.573227\pi$
$317$	−8.11974			−0.456050			−0.228025	+	0.973655i	$0.573227\pi$
$318$	−0.0606846	−	2.63151i	−0.00340302	−	0.147568i
$319$		−	18.0968i		−	1.01322i
$320$	18.2322	−	19.2964i	1.01921	−	1.07870i
$321$	4.87905	−	6.60579i	0.272322	−	0.368699i
$322$	5.52209	−	4.27885i	0.307734	−	0.238451i
$323$			2.21499i			0.123245i
$324$	−6.08036	−	16.9419i	−0.337798	−	0.941219i
$325$		−	10.6798i		−	0.592410i
$326$	12.2027	+	15.7482i	0.675843	+	0.872211i
$327$	8.43904	−	11.4257i	0.466680	−	0.631842i
$328$	4.96589	+	11.5240i	0.274195	+	0.636304i
$329$			25.4975i			1.40572i
$330$	−18.6841	+	0.430869i	−1.02853	+	0.0237186i
$331$	−16.6391			−0.914567			−0.457284	−	0.889321i	$-0.651178\pi$
$331$	−16.6391			−0.914567			−0.457284	+	0.889321i	$0.651178\pi$
$332$	20.1134	+	5.18616i	1.10386	+	0.284627i
$333$	−16.1653	+	4.97331i	−0.885854	+	0.272536i
$334$	−7.77696	−	10.0366i	−0.425536	−	0.549178i
$335$	22.3011			1.21844
$336$	31.1090	−	14.2646i	1.69714	−	0.778199i
$337$	−14.7150			−0.801577			−0.400788	−	0.916171i	$-0.631264\pi$
$337$	−14.7150			−0.801577			−0.400788	+	0.916171i	$0.631264\pi$
$338$	8.52720	+	11.0048i	0.463818	+	0.598583i
$339$	0.864387	−	1.17030i	0.0469470	−	0.0635620i
$340$	19.9724	+	5.14983i	1.08316	+	0.279289i
$341$	20.6829			1.12004
$342$	1.73997	−	2.47310i	0.0940867	−	0.133730i
$343$			51.3785i			2.77418i
$344$	−29.6287	+	12.7676i	−1.59747	+	0.688382i
$345$	−4.62331	−	3.41479i	−0.248911	−	0.183846i
$346$	12.8909	+	16.6364i	0.693017	+	0.894377i
$347$			2.14159i			0.114966i	0.998346	+	0.0574832i	$0.0183076\pi$
$347$			2.14159i			0.114966i	−0.998346	+	0.0574832i	$0.981692\pi$
$348$	21.1616	−	17.1925i	1.13438	−	0.921617i
$349$			16.8713i			0.903098i	0.892246	+	0.451549i	$0.149128\pi$
$349$			16.8713i			0.903098i	−0.892246	+	0.451549i	$0.850872\pi$
$350$	33.1984	−	25.7241i	1.77453	−	1.37501i
$351$	−8.70929	−	3.05831i	−0.464867	−	0.163241i
$352$	−12.8514	+	2.00180i	−0.684982	+	0.106696i
$353$		−	22.4447i		−	1.19461i	−0.802014	−	0.597306i	$-0.796238\pi$
$353$		−	22.4447i		−	1.19461i	0.802014	−	0.597306i	$-0.203762\pi$
$354$	27.0794	−	0.624469i	1.43925	−	0.0331902i
$355$	−39.4499			−2.09378
$356$	9.26731	+	2.38954i	0.491167	+	0.126646i
$357$	21.3881	+	15.7973i	1.13198	+	0.836083i
$358$	−2.75950	+	2.13823i	−0.145844	+	0.113009i
$359$	−14.1639			−0.747543			−0.373771	−	0.927521i	$-0.621936\pi$
$359$	−14.1639			−0.747543			−0.373771	+	0.927521i	$0.621936\pi$
$360$	−18.2544	−	21.4391i	−0.962090	−	1.12994i
$361$	−18.4920			−0.973264
$362$	−19.1459	+	14.8354i	−1.00629	+	0.779731i
$363$	−7.96029	−	5.87949i	−0.417807	−	0.308593i
$364$	4.38196	−	16.9945i	0.229677	−	0.890752i
$365$	−30.9054			−1.61766
$366$	5.51512	−	0.127183i	0.288280	−	0.00664795i
$367$			26.8266i			1.40034i	0.713977	+	0.700169i	$0.246892\pi$
$367$			26.8266i			1.40034i	−0.713977	+	0.700169i	$0.753108\pi$
$368$	−3.50128	−	1.93418i	−0.182517	−	0.100826i
$369$	12.7211	−	3.91370i	0.662236	−	0.203739i
$370$	−20.9137	+	16.2052i	−1.08725	+	0.842471i
$371$		−	5.30823i		−	0.275590i
$372$	19.6494	+	24.1857i	1.01878	+	1.25397i
$373$		−	33.0544i		−	1.71149i	−0.517395	−	0.855747i	$-0.673098\pi$
$373$		−	33.0544i		−	1.71149i	0.517395	−	0.855747i	$-0.326902\pi$
$374$	−6.18944	−	7.98781i	−0.320048	−	0.413040i
$375$	−4.67841	−	3.45549i	−0.241592	−	0.178441i
$376$	13.4076	−	5.77761i	0.691446	−	0.297957i
$377$		−	13.9820i		−	0.720112i
$378$	−11.4710	−	34.4394i	−0.590003	−	1.77137i
$379$	−16.1853			−0.831385			−0.415693	−	0.909505i	$-0.636461\pi$
$379$	−16.1853			−0.831385			−0.415693	+	0.909505i	$0.636461\pi$
$380$	1.18106	−	4.58046i	0.0605869	−	0.234973i
$381$	5.24393	−	7.09981i	0.268655	−	0.363734i
$382$	16.8986	+	21.8085i	0.864605	+	1.11582i
$383$	9.98774			0.510350			0.255175	−	0.966895i	$-0.417867\pi$
$383$	9.98774			0.510350			0.255175	+	0.966895i	$0.417867\pi$
$384$	−14.5501	−	13.1261i	−0.742506	−	0.669840i
$385$	−37.6892			−1.92082
$386$	−9.67317	−	12.4838i	−0.492352	−	0.635406i
$387$	10.0623	+	32.7067i	0.511497	+	1.66258i
$388$	2.03145	−	7.87851i	0.103131	−	0.399971i
$389$	−9.55537			−0.484477			−0.242238	−	0.970217i	$-0.577882\pi$
$389$	−9.55537			−0.484477			−0.242238	+	0.970217i	$0.577882\pi$
$390$	−14.4358	+	0.332901i	−0.730988	+	0.0168571i
$391$		−	3.10776i		−	0.157166i
$392$	45.1996	−	19.4774i	2.28293	−	0.983756i
$393$	−8.37100	+	11.3336i	−0.422261	+	0.571703i
$394$	5.28776	+	6.82414i	0.266394	+	0.343795i
$395$			7.11256i			0.357872i
$396$	0.635923	+	13.7807i	0.0319563	+	0.692505i
$397$			10.5693i			0.530457i	0.964186	+	0.265228i	$0.0854474\pi$
$397$			10.5693i			0.530457i	−0.964186	+	0.265228i	$0.914553\pi$
$398$	−0.615760	+	0.477128i	−0.0308653	+	0.0239163i
$399$	3.62294	−	4.90513i	0.181374	−	0.245564i
$400$	−21.0494	−	11.6281i	−1.05247	−	0.581406i
$401$		−	3.86700i		−	0.193109i	−0.995328	−	0.0965543i	$-0.969218\pi$
$401$		−	3.86700i		−	0.193109i	0.995328	−	0.0965543i	$-0.0307821\pi$
$402$	−0.379514	−	16.4572i	−0.0189284	−	0.820809i
$403$	15.9802			0.796028
$404$	−0.942598	+	3.65566i	−0.0468960	+	0.181876i
$405$	−24.7010	+	16.7876i	−1.22740	+	0.834185i
$406$	43.4634	−	33.6781i	2.15705	−	1.67142i
$407$	12.9623			0.642517
$408$	3.46044	−	14.8264i	0.171317	−	0.734014i
$409$	20.9872			1.03775			0.518876	−	0.854849i	$-0.326351\pi$
$409$	20.9872			1.03775			0.518876	+	0.854849i	$0.326351\pi$
$410$	16.4579	−	12.7526i	0.812796	−	0.629804i
$411$	−2.81272	+	3.80816i	−0.138741	+	0.187843i
$412$	−28.8108	−	7.42875i	−1.41940	−	0.365988i
$413$	54.6239			2.68787
$414$	−2.44127	+	3.46990i	−0.119982	+	0.170536i
$415$		−	34.4638i		−	1.69176i
$416$	−9.92933	+	1.54664i	−0.486825	+	0.0758305i
$417$	31.8620	+	23.5334i	1.56029	+	1.15243i
$418$	−1.83192	+	1.41948i	−0.0896020	+	0.0694291i
$419$		−	27.7366i		−	1.35502i	−0.735514	−	0.677510i	$-0.763059\pi$
$419$		−	27.7366i		−	1.35502i	0.735514	−	0.677510i	$-0.236941\pi$
$420$	−35.8060	−	44.0722i	−1.74715	−	2.15050i
$421$			12.8814i			0.627801i	0.949456	+	0.313900i	$0.101636\pi$
$421$			12.8814i			0.627801i	−0.949456	+	0.313900i	$0.898364\pi$
$422$	−2.96690	−	3.82895i	−0.144427	−	0.186390i
$423$	−4.55342	−	14.8005i	−0.221395	−	0.719625i
$424$	−2.79129	+	1.20282i	−0.135557	+	0.0584140i
$425$		−	18.6836i		−	0.906287i
$426$	0.671348	+	29.1122i	0.0325269	+	1.41049i
$427$	11.1250			0.538376
$428$	−9.18239	−	2.36765i	−0.443848	−	0.114445i
$429$	5.69054	+	4.20304i	0.274742	+	0.202925i
$430$	32.7875	+	42.3141i	1.58115	+	2.04057i
$431$	3.99768			0.192561			0.0962807	−	0.995354i	$-0.469305\pi$
$431$	3.99768			0.192561			0.0962807	+	0.995354i	$0.469305\pi$
$432$	−15.5104	+	13.8357i	−0.746245	+	0.665671i
$433$	7.04364			0.338496			0.169248	−	0.985574i	$-0.445866\pi$
$433$	7.04364			0.338496			0.169248	+	0.985574i	$0.445866\pi$
$434$	38.4909	+	49.6746i	1.84762	+	2.38446i
$435$	−36.3892	−	26.8772i	−1.74473	−	1.28866i
$436$	−15.8823	−	4.09520i	−0.760625	−	0.196124i
$437$	−0.712730			−0.0340945
$438$	0.525939	+	22.8067i	0.0251303	+	1.08975i
$439$		−	4.65073i		−	0.221967i	−0.993822	−	0.110984i	$-0.964600\pi$
$439$		−	4.65073i		−	0.221967i	0.993822	−	0.110984i	$-0.0354001\pi$
$440$	8.54019	+	19.8186i	0.407138	+	0.944812i
$441$	−15.3504	−	49.8952i	−0.730973	−	2.37596i
$442$	−4.78213	−	6.17159i	−0.227463	−	0.293553i
$443$			1.08991i			0.0517832i	0.999665	+	0.0258916i	$0.00824248\pi$
$443$			1.08991i			0.0517832i	−0.999665	+	0.0258916i	$0.991758\pi$
$444$	12.3146	+	15.1576i	0.584426	+	0.719347i
$445$		−	15.8793i		−	0.752753i
$446$	−1.24720	+	0.966408i	−0.0590567	+	0.0457607i
$447$	3.96569	+	2.92907i	0.187571	+	0.138540i
$448$	−28.7242	−	27.1401i	−1.35709	−	1.28225i
$449$			1.25542i			0.0592467i	0.999561	+	0.0296234i	$0.00943079\pi$
$449$			1.25542i			0.0592467i	−0.999561	+	0.0296234i	$0.990569\pi$
$450$	−14.6767	+	20.8607i	−0.691868	+	0.983385i
$451$	−10.2006			−0.480325
$452$	−1.62678	−	0.419459i	−0.0765172	−	0.0197297i
$453$	4.56046	−	6.17444i	0.214269	−	0.290101i
$454$	7.05809	−	5.46904i	0.331253	−	0.256675i
$455$	−29.1197			−1.36515
$456$	−3.40026	−	0.793615i	−0.159232	−	0.0371644i
$457$	−9.91097			−0.463616			−0.231808	−	0.972762i	$-0.574464\pi$
$457$	−9.91097			−0.463616			−0.231808	+	0.972762i	$0.574464\pi$
$458$	−17.2081	+	13.3339i	−0.804083	+	0.623052i
$459$	−15.2363	−	5.35030i	−0.711169	−	0.249731i
$460$	−1.65709	+	6.42664i	−0.0772621	+	0.299644i
$461$	15.4904			0.721462			0.360731	−	0.932670i	$-0.382527\pi$
$461$	15.4904			0.721462			0.360731	+	0.932670i	$0.382527\pi$
$462$	0.641384	+	27.8129i	0.0298399	+	1.29397i
$463$			14.5872i			0.677927i	0.940800	+	0.338963i	$0.110076\pi$
$463$			14.5872i			0.677927i	−0.940800	+	0.338963i	$0.889924\pi$
$464$	−27.5579	−	15.2236i	−1.27935	−	0.706737i
$465$	30.7181	−	41.5895i	1.42452	−	1.92867i
$466$	−26.5107	+	20.5421i	−1.22808	+	0.951595i
$467$			22.9252i			1.06085i	0.847732	+	0.530425i	$0.177968\pi$
$467$			22.9252i			1.06085i	−0.847732	+	0.530425i	$0.822032\pi$
$468$	0.491330	+	10.6473i	0.0227118	+	0.492172i
$469$		−	33.1970i		−	1.53290i
$470$	−14.8371	−	19.1480i	−0.684383	−	0.883233i
$471$	−8.28864	+	11.2221i	−0.381920	+	0.517085i
$472$	−12.3775	−	28.7235i	−0.569721	−	1.32211i
$473$		−	26.2262i		−	1.20588i
$474$	5.24873	−	0.121039i	0.241082	−	0.00555953i
$475$	−4.28487			−0.196604
$476$	7.66594	−	29.7306i	0.351368	−	1.36270i
$477$	0.947960	+	3.08126i	0.0434041	+	0.141081i
$478$	24.8457	+	32.0648i	1.13642	+	1.46661i
$479$	−2.30001			−0.105090			−0.0525451	−	0.998619i	$-0.516733\pi$
$479$	−2.30001			−0.105090			−0.0525451	+	0.998619i	$0.516733\pi$
$480$	−15.0615	+	28.8148i	−0.687462	+	1.31521i
$481$	10.0150			0.456645
$482$	−0.560093	−	0.722830i	−0.0255115	−	0.0329240i
$483$	−5.08319	+	6.88217i	−0.231293	+	0.313150i
$484$	−2.85313	+	11.0652i	−0.129688	+	0.502965i
$485$	−13.4997			−0.612988
$486$	12.8088	+	17.9425i	0.581021	+	0.813888i
$487$			2.80584i			0.127145i	0.997977	+	0.0635725i	$0.0202494\pi$
$487$			2.80584i			0.127145i	−0.997977	+	0.0635725i	$0.979751\pi$
$488$	−2.52087	−	5.84998i	−0.114114	−	0.264816i
$489$	−19.6269	−	14.4965i	−0.887561	−	0.655555i
$490$	−50.0184	−	64.5515i	−2.25960	−	2.91614i
$491$			11.3259i			0.511129i	0.966792	+	0.255565i	$0.0822613\pi$
$491$			11.3259i			0.511129i	−0.966792	+	0.255565i	$0.917739\pi$
$492$	−9.69086	−	11.9281i	−0.436898	−	0.537761i
$493$		−	24.4606i		−	1.10165i
$494$	−1.41539	+	1.09673i	−0.0636813	+	0.0493441i
$495$	21.8774	−	6.73066i	0.983317	−	0.302521i
$496$	17.3991	−	31.4961i	0.781243	−	1.41422i
$497$			58.7244i			2.63415i
$498$	−25.4327	+	0.586496i	−1.13967	+	0.0262815i
$499$	−16.3916			−0.733791			−0.366895	−	0.930262i	$-0.619579\pi$
$499$	−16.3916			−0.733791			−0.366895	+	0.930262i	$0.619579\pi$
$500$	−1.67684	+	6.50324i	−0.0749905	+	0.290834i
$501$	12.5086	+	9.23887i	0.558842	+	0.412762i
$502$	−17.9754	+	13.9284i	−0.802281	+	0.621657i
$503$	4.17583			0.186191			0.0930955	−	0.995657i	$-0.470324\pi$
$503$	4.17583			0.186191			0.0930955	+	0.995657i	$0.470324\pi$
$504$	−31.9139	+	27.1731i	−1.42156	+	1.21039i
$505$	6.26389			0.278739
$506$	2.57028	−	1.99161i	0.114263	−	0.0885379i
$507$	−13.7153	−	10.1301i	−0.609117	−	0.449895i
$508$	−9.86910	−	2.54471i	−0.437871	−	0.112903i
$509$	16.5267			0.732535			0.366267	−	0.930510i	$-0.380636\pi$
$509$	16.5267			0.732535			0.366267	+	0.930510i	$0.380636\pi$
$510$	−25.2545	+	0.582387i	−1.11829	+	0.0257885i
$511$			46.0052i			2.03515i
$512$	−7.76264	+	21.2542i	−0.343063	+	0.939312i
$513$	−1.22703	+	3.49428i	−0.0541748	+	0.154276i
$514$	6.66233	−	5.16238i	0.293863	−	0.227703i
$515$			49.3666i			2.17535i
$516$	30.6678	−	24.9157i	1.35008	−	1.09685i
$517$			11.8679i			0.521950i
$518$	24.1228	+	31.1318i	1.05990	+	1.36785i
$519$	−20.7339	−	15.3141i	−0.910116	−	0.672214i
$520$	6.59837	+	15.3123i	0.289358	+	0.671490i
$521$		−	39.2764i		−	1.72073i	−0.509678	−	0.860365i	$-0.670235\pi$
$521$		−	39.2764i		−	1.72073i	0.509678	−	0.860365i	$-0.329765\pi$
$522$	−19.2148	+	27.3109i	−0.841010	+	1.19537i
$523$	42.6690			1.86579			0.932893	−	0.360153i	$-0.117275\pi$
$523$	42.6690			1.86579			0.932893	+	0.360153i	$0.117275\pi$
$524$	15.7543	+	4.06218i	0.688228	+	0.177457i
$525$	−30.5597	+	41.3751i	−1.33374	+	1.80576i
$526$	−8.55889	−	11.0457i	−0.373185	−	0.481616i
$527$	27.9562			1.21779
$528$	14.4798	−	6.63952i	0.630153	−	0.288948i
$529$	1.00000			0.0434783
$530$	3.08887	+	3.98636i	0.134172	+	0.173156i
$531$	−31.7075	+	9.75491i	−1.37599	+	0.423327i
$532$	−6.81839	−	1.75810i	−0.295615	−	0.0762232i
$533$	−7.88121			−0.341373
$534$	−11.7182	+	0.270230i	−0.507097	+	0.0116940i
$535$			15.7338i			0.680233i
$536$	−17.4564	+	7.52228i	−0.754001	+	0.324913i
$537$	2.54017	−	3.43916i	0.109616	−	0.148411i
$538$	11.8957	+	15.3520i	0.512859	+	0.661872i
$539$			40.0089i			1.72331i
$540$	28.6548	+	19.1882i	1.23311	+	0.825729i
$541$		−	28.5798i		−	1.22874i	−0.789018	−	0.614370i	$-0.789410\pi$
$541$		−	28.5798i		−	1.22874i	0.789018	−	0.614370i	$-0.210590\pi$
$542$	25.8808	−	20.0540i	1.11168	−	0.861394i
$543$	17.6241	−	23.8615i	0.756324	−	1.02399i
$544$	−17.3707	+	2.70574i	−0.744761	+	0.116008i
$545$			27.2140i			1.16572i
$546$	0.495550	+	21.4889i	0.0212076	+	0.919642i
$547$	15.0482			0.643416			0.321708	−	0.946839i	$-0.395743\pi$
$547$	15.0482			0.643416			0.321708	+	0.946839i	$0.395743\pi$
$548$	5.29354	+	1.36492i	0.226129	+	0.0583065i
$549$	−6.45771	+	1.98674i	−0.275608	+	0.0847918i
$550$	15.4523	−	11.9734i	0.658889	−	0.510548i
$551$	−5.60977			−0.238984
$552$	4.77076	+	1.11349i	0.203057	+	0.0473931i
$553$	10.5876			0.450231
$554$	2.55679	−	1.98116i	0.108628	−	0.0841712i
$555$	19.2515	−	26.0648i	0.817181	−	1.10639i
$556$	11.4200	−	44.2899i	0.484315	−	1.87831i
$557$	−19.5109			−0.826702			−0.413351	−	0.910572i	$-0.635642\pi$
$557$	−19.5109			−0.826702			−0.413351	+	0.910572i	$0.635642\pi$
$558$	−31.2138	−	21.9607i	−1.32139	−	0.929672i
$559$		−	20.2630i		−	0.857035i
$560$	−31.7053	+	57.3935i	−1.33979	+	2.42532i
$561$	9.95519	+	7.35293i	0.420309	+	0.310441i
$562$	11.9869	−	9.28818i	0.505637	−	0.391798i
$563$		−	21.9485i		−	0.925019i	−0.886614	−	0.462509i	$-0.846949\pi$
$563$		−	21.9485i		−	0.925019i	0.886614	−	0.462509i	$-0.153051\pi$
$564$	−13.8779	+	11.2749i	−0.584363	+	0.474759i
$565$			2.78745i			0.117269i
$566$	18.9368	+	24.4390i	0.795973	+	1.02725i
$567$	24.9898	+	36.7695i	1.04947	+	1.54417i
$568$	30.8798	−	13.3067i	1.29569	−	0.558336i
$569$		−	21.5311i		−	0.902631i	−0.892365	−	0.451315i	$-0.850955\pi$
$569$		−	21.5311i		−	0.902631i	0.892365	−	0.451315i	$-0.149045\pi$
$570$	0.133564	+	5.79184i	0.00559438	+	0.242594i
$571$	−30.2328			−1.26520			−0.632602	−	0.774477i	$-0.718013\pi$
$571$	−30.2328			−1.26520			−0.632602	+	0.774477i	$0.718013\pi$
$572$	2.03960	−	7.91015i	0.0852801	−	0.330740i
$573$	−27.1799	−	20.0751i	−1.13546	−	0.838651i
$574$	−18.9832	−	24.4989i	−0.792344	−	1.02256i
$575$	6.01192			0.250714
$576$	21.5203	+	10.6243i	0.896679	+	0.442681i
$577$	−11.6398			−0.484570			−0.242285	−	0.970205i	$-0.577897\pi$
$577$	−11.6398			−0.484570			−0.242285	+	0.970205i	$0.577897\pi$
$578$	6.35958	+	8.20738i	0.264524	+	0.341382i
$579$	15.5585	+	11.4915i	0.646588	+	0.477572i
$580$	−13.0426	+	50.5830i	−0.541566	+	2.10034i
$581$	−51.3022			−2.12837
$582$	0.229733	+	9.96212i	0.00952276	+	0.412943i
$583$		−	2.47074i		−	0.102327i
$584$	24.1914	−	10.4245i	1.00105	−	0.431371i
$585$	16.9031	−	5.20028i	0.698856	−	0.215005i
$586$	7.71007	+	9.95027i	0.318500	+	0.411042i
$587$		−	24.8562i		−	1.02593i	−0.858411	−	0.512963i	$-0.828548\pi$
$587$		−	24.8562i		−	1.02593i	0.858411	−	0.512963i	$-0.171452\pi$
$588$	−46.7848	+	38.0098i	−1.92937	+	1.56750i
$589$		−	6.41144i		−	0.264179i
$590$	−41.0213	+	31.7858i	−1.68882	+	1.30860i
$591$	−8.50492	−	6.28175i	−0.349846	−	0.258397i
$592$	10.9043	−	19.7391i	0.448164	−	0.811272i
$593$			22.4837i			0.923293i	0.887064	+	0.461646i	$0.152741\pi$
$593$			22.4837i			0.923293i	−0.887064	+	0.461646i	$0.847259\pi$
$594$	−5.33921	−	16.0300i	−0.219071	−	0.657718i
$595$	−50.9428			−2.08845
$596$	1.42138	−	5.51252i	0.0582222	−	0.225802i
$597$	0.566819	−	0.767421i	0.0231983	−	0.0314084i
$598$	1.98587	−	1.53877i	0.0812081	−	0.0629250i
$599$	36.1704			1.47788			0.738941	−	0.673770i	$-0.235326\pi$
$599$	36.1704			1.47788			0.738941	+	0.673770i	$0.235326\pi$
$600$	28.6814	+	6.69419i	1.17091	+	0.273289i
$601$	−24.8155			−1.01224			−0.506122	−	0.862462i	$-0.668922\pi$
$601$	−24.8155			−1.01224			−0.506122	+	0.862462i	$0.668922\pi$
$602$	62.9879	−	48.8069i	2.56720	−	1.98922i
$603$	5.92843	+	19.2699i	0.241424	+	0.784729i
$604$	−8.58280	−	2.21305i	−0.349229	−	0.0900475i
$605$	18.9600			0.770835
$606$	−0.106597	−	4.62246i	−0.00433021	−	0.187774i
$607$			33.4349i			1.35708i	0.734564	+	0.678540i	$0.237387\pi$
$607$			33.4349i			1.35708i	−0.734564	+	0.678540i	$0.762613\pi$
$608$	0.620533	+	3.98377i	0.0251659	+	0.161563i
$609$	−40.0089	+	54.1684i	−1.62124	+	2.19501i
$610$	−8.35461	+	6.47366i	−0.338268	+	0.262111i
$611$			9.16946i			0.370957i
$612$	0.859548	+	18.6267i	0.0347452	+	0.752941i
$613$			5.29916i			0.214031i	0.994257	+	0.107016i	$0.0341295\pi$
$613$			5.29916i			0.214031i	−0.994257	+	0.107016i	$0.965871\pi$
$614$	−27.2880	−	35.2167i	−1.10125	−	1.42123i
$615$	−15.1498	+	20.5114i	−0.610898	+	0.827100i
$616$	29.5015	−	12.7128i	1.18865	−	0.512212i
$617$		−	11.3569i		−	0.457211i	−0.973519	−	0.228606i	$-0.926583\pi$
$617$		−	11.3569i		−	0.457211i	0.973519	−	0.228606i	$-0.0734166\pi$
$618$	36.4303	−	0.840108i	1.46544	−	0.0337941i
$619$	−0.235751			−0.00947565			−0.00473782	−	0.999989i	$-0.501508\pi$
$619$	−0.235751			−0.00947565			−0.00473782	+	0.999989i	$0.501508\pi$
$620$	−57.8115	−	14.9065i	−2.32177	−	0.598660i
$621$	1.72160	−	4.90266i	0.0690852	−	0.196737i
$622$	−16.4248	−	21.1970i	−0.658572	−	0.849923i
$623$	−23.6377			−0.947025
$624$	11.1875	−	5.12987i	0.447858	−	0.205359i
$625$	−18.9164			−0.756657
$626$	0.443309	+	0.572115i	0.0177182	+	0.0228663i
$627$	1.68631	−	2.28311i	0.0673449	−	0.0911788i
$628$	15.5992	+	4.02221i	0.622478	+	0.160504i
$629$	17.5206			0.698591
$630$	56.8790	+	40.0177i	2.26612	+	1.59434i
$631$			30.3514i			1.20827i	0.796883	+	0.604134i	$0.206481\pi$
$631$			30.3514i			1.20827i	−0.796883	+	0.604134i	$0.793519\pi$
$632$	−2.39910	−	5.56741i	−0.0954312	−	0.221460i
$633$	4.77201	+	3.52462i	0.189671	+	0.140091i
$634$	−7.03340	−	9.07698i	−0.279332	−	0.360493i
$635$			16.9105i			0.671073i
$636$	2.88918	−	2.34728i	0.114563	−	0.0930758i
$637$			30.9119i			1.22478i
$638$	20.2302	−	15.6756i	0.800922	−	0.620603i
$639$	−10.4872	−	34.0877i	−0.414867	−	1.34849i
$640$	37.3641	+	3.66691i	1.47695	+	0.144947i
$641$		−	14.8548i		−	0.586728i	−0.956001	−	0.293364i	$-0.905225\pi$
$641$		−	14.8548i		−	0.586728i	0.956001	−	0.293364i	$-0.0947747\pi$
$642$	11.6108	−	0.267754i	0.458243	−	0.0105674i
$643$	−3.57141			−0.140843			−0.0704214	−	0.997517i	$-0.522434\pi$
$643$	−3.57141			−0.140843			−0.0704214	+	0.997517i	$0.522434\pi$
$644$	9.56658	+	2.46671i	0.376976	+	0.0972020i
$645$	−52.7359	−	38.9509i	−2.07648	−	1.53369i
$646$	−2.47612	+	1.91865i	−0.0974216	+	0.0754882i
$647$	−22.3405			−0.878296			−0.439148	−	0.898415i	$-0.644720\pi$
$647$	−22.3405			−0.878296			−0.439148	+	0.898415i	$0.644720\pi$
$648$	13.6724	−	21.4725i	0.537101	−	0.843518i
$649$	25.4249			0.998015
$650$	11.9389	−	9.25096i	0.468281	−	0.362853i
$651$	−61.9093	−	45.7264i	−2.42642	−	1.79216i
$652$	−7.03469	+	27.2825i	−0.275500	+	1.06846i
$653$	−37.1894			−1.45533			−0.727667	−	0.685931i	$-0.759395\pi$
$653$	−37.1894			−1.45533			−0.727667	+	0.685931i	$0.759395\pi$
$654$	20.0827	−	0.463120i	0.785294	−	0.0181094i
$655$		−	26.9946i		−	1.05477i
$656$	−8.58102	+	15.5335i	−0.335033	+	0.606481i
$657$	−8.21575	−	26.7046i	−0.320527	−	1.04184i
$658$	−28.5034	+	22.0862i	−1.11118	+	0.861009i
$659$		−	25.7209i		−	1.00195i	−0.865463	−	0.500973i	$-0.832976\pi$
$659$		−	25.7209i		−	1.00195i	0.865463	−	0.500973i	$-0.167024\pi$
$660$	−16.6660	−	20.5136i	−0.648725	−	0.798491i
$661$			8.78002i			0.341503i	0.985314	+	0.170752i	$0.0546196\pi$
$661$			8.78002i			0.341503i	−0.985314	+	0.170752i	$0.945380\pi$
$662$	−14.4130	−	18.6007i	−0.560175	−	0.722936i
$663$	7.69164	+	5.68107i	0.298719	+	0.220634i
$664$	11.6248	+	26.9768i	0.451131	+	1.04690i
$665$			11.6832i			0.453054i
$666$	−19.5622	−	13.7631i	−0.758019	−	0.533311i
$667$	7.87082			0.304759
$668$	4.48333	−	17.3876i	0.173465	−	0.672746i
$669$	1.14807	−	1.55439i	0.0443871	−	0.0600960i
$670$	19.3174	+	24.9302i	0.746298	+	0.963138i
$671$	5.17817			0.199901
$672$	42.8932	+	22.4203i	1.65464	+	0.864883i
$673$	27.0333			1.04206			0.521029	−	0.853539i	$-0.325548\pi$
$673$	27.0333			1.04206			0.521029	+	0.853539i	$0.325548\pi$
$674$	−12.7463	−	16.4498i	−0.490968	−	0.633621i
$675$	10.3501	−	29.4744i	0.398375	−	1.13447i
$676$	−4.91583	+	19.0650i	−0.189070	+	0.733267i
$677$	−22.1004			−0.849385			−0.424693	−	0.905338i	$-0.639618\pi$
$677$	−22.1004			−0.849385			−0.424693	+	0.905338i	$0.639618\pi$
$678$	2.05701	−	0.0474361i	0.0789989	−	0.00182177i
$679$			20.0954i			0.771189i
$680$	11.5434	+	26.7878i	0.442669	+	1.02727i
$681$	−6.49711	+	8.79649i	−0.248970	+	0.337082i
$682$	17.9157	+	23.1212i	0.686029	+	0.885358i
$683$			20.9109i			0.800132i	0.916486	+	0.400066i	$0.131013\pi$
$683$			20.9109i			0.800132i	−0.916486	+	0.400066i	$0.868987\pi$
$684$	4.27183	−	0.197128i	0.163338	−	0.00753737i
$685$		−	9.07037i		−	0.346561i
$686$	−57.4356	+	44.5046i	−2.19290	+	1.69919i
$687$	15.8404	−	21.4465i	0.604349	−	0.818233i
$688$	−39.9375	−	22.0623i	−1.52260	−	0.841116i
$689$		−	1.90896i		−	0.0727254i
$690$	−0.187398	−	8.12628i	−0.00713411	−	0.309362i
$691$	26.5524			1.01010			0.505051	−	0.863089i	$-0.331474\pi$
$691$	26.5524			1.01010			0.505051	+	0.863089i	$0.331474\pi$
$692$	−7.43144	+	28.8212i	−0.282501	+	1.09562i
$693$	−10.0191	−	32.5663i	−0.380596	−	1.23709i
$694$	−2.39406	+	1.85506i	−0.0908772	+	0.0704172i
$695$	−75.8898			−2.87866
$696$	37.5498	+	8.76405i	1.42332	+	0.332200i
$697$	−13.7876			−0.522244
$698$	−18.8602	+	14.6141i	−0.713870	+	0.553150i
$699$	24.4036	−	33.0402i	0.923029	−	1.24970i
$700$	57.5135	+	14.8297i	2.17381	+	0.560509i
$701$	−45.4259			−1.71571			−0.857856	−	0.513891i	$-0.828204\pi$
$701$	−45.4259			−1.71571			−0.857856	+	0.513891i	$0.828204\pi$
$702$	−4.12522	−	12.3852i	−0.155696	−	0.467448i
$703$		−	4.01815i		−	0.151547i
$704$	−13.3698	−	12.6325i	−0.503894	−	0.476105i
$705$	23.8642	+	17.6261i	0.898776	+	0.663838i
$706$	25.0907	−	19.4418i	0.944302	−	0.731703i
$707$		−	9.32431i		−	0.350677i
$708$	24.1545	+	29.7309i	0.907782	+	1.11735i
$709$			37.5812i			1.41139i	0.708515	+	0.705696i	$0.249365\pi$
$709$			37.5812i			1.41139i	−0.708515	+	0.705696i	$0.750635\pi$
$710$	−34.1719	−	44.1007i	−1.28245	−	1.65507i
$711$	−6.14579	+	1.89077i	−0.230485	+	0.0709095i
$712$	5.35619	+	12.4297i	0.200732	+	0.465822i
$713$			8.99561i			0.336888i
$714$	0.866930	+	37.5934i	0.0324441	+	1.40690i
$715$	−13.5539			−0.506886
$716$	−4.78061	−	1.23266i	−0.178660	−	0.0460668i
$717$	−39.9623	−	29.5162i	−1.49242	−	1.10230i
$718$	−12.2689	−	15.8337i	−0.457872	−	0.590909i
$719$	22.4630			0.837730			0.418865	−	0.908049i	$-0.362428\pi$
$719$	22.4630			0.837730			0.418865	+	0.908049i	$0.362428\pi$
$720$	8.15447	−	38.9772i	0.303899	−	1.45259i
$721$	73.4863			2.73677
$722$	−16.0180	−	20.6721i	−0.596127	−	0.769334i
$723$	0.900862	+	0.665379i	0.0335034	+	0.0247457i
$724$	−33.1687	−	8.55244i	−1.23271	−	0.317849i
$725$	47.3187			1.75737
$726$	−0.322657	−	13.9916i	−0.0119749	−	0.519277i
$727$		−	52.5610i		−	1.94938i	−0.223562	−	0.974690i	$-0.571769\pi$
$727$		−	52.5610i		−	1.94938i	0.223562	−	0.974690i	$-0.428231\pi$
$728$	22.7937	−	9.82222i	0.844789	−	0.364036i
$729$	−21.0722	−	16.8808i	−0.780453	−	0.625215i
$730$	−26.7705	−	34.5488i	−0.990822	−	1.27871i
$731$		−	35.4487i		−	1.31112i
$732$	4.91943	+	6.05514i	0.181827	+	0.223804i
$733$		−	1.78537i		−	0.0659443i	−0.999456	−	0.0329721i	$-0.989503\pi$
$733$		−	1.78537i		−	0.0659443i	0.999456	−	0.0329721i	$-0.0104973\pi$
$734$	−29.9892	+	23.2375i	−1.10692	+	0.857712i
$735$	80.4504	+	59.4209i	2.96746	+	2.19177i
$736$	−0.870642	−	5.58945i	−0.0320923	−	0.206030i
$737$		−	15.4517i		−	0.569170i
$738$	15.3943	+	10.8308i	0.566671	+	0.398686i
$739$	−6.12718			−0.225392			−0.112696	−	0.993630i	$-0.535949\pi$
$739$	−6.12718			−0.225392			−0.112696	+	0.993630i	$0.535949\pi$
$740$	−36.2314	−	9.34214i	−1.33189	−	0.343424i
$741$	1.30289	−	1.76399i	0.0478629	−	0.0648019i
$742$	5.93402	−	4.59804i	0.217845	−	0.168799i
$743$	47.9551			1.75930			0.879651	−	0.475621i	$-0.157776\pi$
$743$	47.9551			1.75930			0.879651	+	0.475621i	$0.157776\pi$
$744$	−10.0165	+	42.9159i	−0.367222	+	1.57337i
$745$	−9.44559			−0.346060
$746$	36.9512	−	28.6321i	1.35288	−	1.04829i
$747$	29.7794	−	9.16172i	1.08957	−	0.335210i
$748$	3.56814	−	13.8382i	0.130464	−	0.505976i
$749$	23.4211			0.855789
$750$	−0.189631	−	8.22313i	−0.00692436	−	0.300266i
$751$		−	23.3449i		−	0.851869i	−0.904754	−	0.425935i	$-0.859945\pi$
$751$		−	23.3449i		−	0.851869i	0.904754	−	0.425935i	$-0.140055\pi$
$752$	18.0726	+	9.98366i	0.659039	+	0.364067i
$753$	16.5467	−	22.4027i	0.602995	−	0.816400i
$754$	15.6304	−	12.1114i	0.569226	−	0.441071i
$755$			14.7065i			0.535223i
$756$	28.5632	−	42.6551i	1.03883	−	1.55135i
$757$			11.8751i			0.431608i	0.976437	+	0.215804i	$0.0692371\pi$
$757$			11.8751i			0.431608i	−0.976437	+	0.215804i	$0.930763\pi$
$758$	−14.0199	−	18.0934i	−0.509226	−	0.657184i
$759$	−2.36599	+	3.20334i	−0.0858801	+	0.116274i
$760$	6.14350	−	2.64735i	0.222848	−	0.0960295i
$761$		−	46.9872i		−	1.70328i	−0.524124	−	0.851642i	$-0.675607\pi$
$761$		−	46.9872i		−	1.70328i	0.524124	−	0.851642i	$-0.324393\pi$
$762$	12.4792	−	0.287778i	0.452072	−	0.0104251i
$763$	40.5103			1.46657
$764$	−9.74182	+	37.7815i	−0.352447	+	1.36689i
$765$	29.5707	−	9.09753i	1.06913	−	0.328922i
$766$	8.65148	+	11.1652i	0.312591	+	0.403415i
$767$	19.6440			0.709302
$768$	2.07015	−	27.6354i	0.0747001	−	0.997206i
$769$	−45.2352			−1.63122			−0.815612	−	0.578600i	$-0.803599\pi$
$769$	−45.2352			−1.63122			−0.815612	+	0.578600i	$0.803599\pi$
$770$	−32.6468	−	42.1324i	−1.17651	−	1.51835i
$771$	−6.13280	+	8.30324i	−0.220867	+	0.299034i
$772$	5.57647	−	21.6271i	0.200702	−	0.778377i
$773$	14.5303			0.522618			0.261309	−	0.965255i	$-0.415846\pi$
$773$	14.5303			0.522618			0.261309	+	0.965255i	$0.415846\pi$
$774$	−27.8465	+	39.5795i	−1.00092	+	1.42266i
$775$			54.0808i			1.94264i
$776$	10.5670	−	4.55351i	0.379332	−	0.163461i
$777$	−38.7995	−	28.6574i	−1.39193	−	1.02808i
$778$	−8.27696	−	10.6819i	−0.296743	−	0.382963i
$779$			3.16204i			0.113292i
$780$	−12.8766	−	15.8493i	−0.461057	−	0.567497i
$781$			27.3335i			0.978071i
$782$	3.47413	−	2.69197i	0.124235	−	0.0962647i
$783$	13.5504	−	38.5880i	0.484251	−	1.37902i
$784$	60.9259	+	33.6567i	2.17593	+	1.20203i
$785$		−	26.7290i		−	0.953998i
$786$	−19.9207	+	0.459387i	−0.710550	+	0.0163858i
$787$	−32.3375			−1.15271			−0.576353	−	0.817201i	$-0.695525\pi$
$787$	−32.3375			−1.15271			−0.576353	+	0.817201i	$0.695525\pi$
$788$	−3.04833	+	11.8223i	−0.108592	+	0.421151i
$789$	13.7662	+	10.1678i	0.490091	+	0.361983i
$790$	−7.95106	+	6.16097i	−0.282886	+	0.219197i
$791$	4.14935			0.147534
$792$	−14.8545	+	12.6479i	−0.527830	+	0.449422i
$793$	4.00079			0.142072
$794$	−11.8153	+	9.15521i	−0.419309	+	0.324906i
$795$	−4.96819	−	3.66952i	−0.176204	−	0.130144i
$796$	−1.06675	−	0.275059i	−0.0378101	−	0.00974921i
$797$	20.7479			0.734930			0.367465	−	0.930037i	$-0.380226\pi$
$797$	20.7479			0.734930			0.367465	+	0.930037i	$0.380226\pi$
$798$	8.62163	−	0.198821i	0.305202	−	0.00703819i
$799$			16.0413i			0.567501i
$800$	−5.23423	−	33.6033i	−0.185058	−	1.18806i
$801$	13.7210	−	4.22130i	0.484806	−	0.149152i
$802$	4.32288	−	3.34963i	0.152646	−	0.118280i
$803$			21.4133i			0.755659i
$804$	18.0686	−	14.6796i	0.637230	−	0.517710i
$805$		−	16.3921i		−	0.577747i
$806$	13.8422	+	17.8641i	0.487570	+	0.629235i
$807$	−19.1332	−	14.1318i	−0.673520	−	0.497463i
$808$	−4.90311	+	2.11284i	−0.172491	+	0.0743296i
$809$			53.1941i			1.87021i	0.354376	+	0.935103i	$0.384693\pi$
$809$			53.1941i			1.87021i	−0.354376	+	0.935103i	$0.615307\pi$
$810$	−40.1630	−	13.0714i	−1.41119	−	0.459283i
$811$	−9.96629			−0.349964			−0.174982	−	0.984572i	$-0.555987\pi$
$811$	−9.96629			−0.349964			−0.174982	+	0.984572i	$0.555987\pi$
$812$	75.2969	+	19.4150i	2.64240	+	0.681334i
$813$	−23.8238	+	32.2552i	−0.835536	+	1.13124i
$814$	11.2281	+	14.4904i	0.393544	+	0.507890i
$815$	46.7480			1.63751
$816$	19.5717	−	8.97435i	0.685148	−	0.314165i
$817$	−8.12978			−0.284425
$818$	18.1794	+	23.4615i	0.635627	+	0.820311i
$819$	−7.74105	−	25.1616i	−0.270494	−	0.879218i
$820$	28.5119	+	7.35170i	0.995680	+	0.256733i
$821$	39.5328			1.37971			0.689853	−	0.723950i	$-0.257675\pi$
$821$	39.5328			1.37971			0.689853	+	0.723950i	$0.257675\pi$
$822$	−6.69351	+	0.154357i	−0.233463	+	0.00538382i
$823$		−	0.0765522i		−	0.00266844i	−0.999999	−	0.00133422i	$-0.999575\pi$
$823$		−	0.0765522i		−	0.00266844i	0.999999	−	0.00133422i	$-0.000424696\pi$
$824$	−16.6516	−	38.6422i	−0.580087	−	1.34616i
$825$	−14.2242	+	19.2582i	−0.495221	+	0.670485i
$826$	47.3158	+	61.0635i	1.64633	+	2.12467i
$827$			1.87240i			0.0651099i	0.999470	+	0.0325549i	$0.0103644\pi$
$827$			1.87240i			0.0651099i	−0.999470	+	0.0325549i	$0.989636\pi$
$828$	−5.99362	+	0.276581i	−0.208293	+	0.00961187i
$829$		−	19.8929i		−	0.690909i	−0.938436	−	0.345454i	$-0.887725\pi$
$829$		−	19.8929i		−	0.690909i	0.938436	−	0.345454i	$-0.112275\pi$
$830$	38.5268	−	29.8529i	1.33728	−	1.03621i
$831$	−2.35357	+	3.18652i	−0.0816445	+	0.110539i
$832$	−10.3299	−	9.76019i	−0.358124	−	0.338374i
$833$			54.0782i			1.87370i
$834$	1.29147	+	56.0031i	0.0447200	+	1.93923i
$835$	−29.7933			−1.03104
$836$	−3.17365	−	0.818314i	−0.109763	−	0.0283020i
$837$	44.1024	+	15.4868i	1.52440	+	0.535302i
$838$	31.0064	−	24.0257i	1.07110	−	0.829953i
$839$	−8.85955			−0.305866			−0.152933	−	0.988237i	$-0.548872\pi$
$839$	−8.85955			−0.305866			−0.152933	+	0.988237i	$0.548872\pi$
$840$	18.2524	−	78.2030i	0.629768	−	2.69826i
$841$	32.9498			1.13620
$842$	−14.4000	+	11.1580i	−0.496256	+	0.384530i
$843$	−11.0342	+	14.9393i	−0.380037	+	0.514535i
$844$	1.71039	−	6.63335i	0.0588739	−	0.228329i
$845$	32.6674			1.12379
$846$	12.6011	−	17.9106i	0.433236	−	0.615779i
$847$		−	28.2236i		−	0.969773i
$848$	−3.76246	−	2.07846i	−0.129203	−	0.0713747i
$849$	−30.4582	−	22.4965i	−1.04532	−	0.772078i
$850$	20.8862	−	16.1839i	0.716391	−	0.555104i
$851$			5.63769i			0.193257i
$852$	−31.9627	+	25.9678i	−1.09502	+	0.889641i
$853$		−	5.57444i		−	0.190865i	−0.995436	−	0.0954327i	$-0.969577\pi$
$853$		−	5.57444i		−	0.190865i	0.995436	−	0.0954327i	$-0.0304235\pi$
$854$	9.63657	+	12.4365i	0.329757	+	0.425569i
$855$	−2.08642	−	6.78172i	−0.0713540	−	0.231930i
$856$	−5.30711	−	12.3158i	−0.181393	−	0.420945i
$857$		−	46.2450i		−	1.57970i	−0.613300	−	0.789850i	$-0.710158\pi$
$857$		−	46.2450i		−	1.57970i	0.613300	−	0.789850i	$-0.289842\pi$
$858$	0.230656	+	10.0021i	0.00787447	+	0.341467i
$859$	1.14194			0.0389623			0.0194812	−	0.999810i	$-0.493799\pi$
$859$	1.14194			0.0389623			0.0194812	+	0.999810i	$0.493799\pi$
$860$	−18.9016	+	73.3057i	−0.644540	+	2.49970i
$861$	30.5329	+	22.5517i	1.04056	+	0.768559i
$862$	3.46283	+	4.46897i	0.117944	+	0.152214i
$863$	31.8575			1.08444			0.542222	−	0.840235i	$-0.317583\pi$
$863$	31.8575			1.08444			0.542222	+	0.840235i	$0.317583\pi$
$864$	−28.9021	−	5.35431i	−0.983269	−	0.182157i
$865$	49.3845			1.67912
$866$	6.10127	+	7.87402i	0.207330	+	0.267570i
$867$	−10.2288	−	7.55505i	−0.347390	−	0.256583i
$868$	−22.1896	+	86.0572i	−0.753163	+	2.92097i
$869$	4.92805			0.167173
$870$	−1.47497	−	63.9605i	−0.0500063	−	2.16846i
$871$		−	11.9384i		−	0.404517i
$872$	−9.17943	−	21.3020i	−0.310855	−	0.721376i
$873$	−3.58869	−	11.6647i	−0.121459	−	0.394791i
$874$	−0.617374	−	0.796754i	−0.0208830	−	0.0269506i
$875$		−	16.5875i		−	0.560761i
$876$	−25.0398	+	20.3433i	−0.846017	+	0.687338i
$877$			6.78039i			0.228958i	0.993426	+	0.114479i	$0.0365198\pi$
$877$			6.78039i			0.228958i	−0.993426	+	0.114479i	$0.963480\pi$
$878$	5.19900	−	4.02851i	0.175458	−	0.135955i
$879$	−12.4010	−	9.15941i	−0.418275	−	0.308939i
$880$	−14.7574	+	26.7140i	−0.497471	+	0.900530i
$881$		−	0.290005i		−	0.00977053i	−0.999988	−	0.00488526i	$-0.998445\pi$
$881$		−	0.290005i		−	0.00977053i	0.999988	−	0.00488526i	$-0.00155503\pi$
$882$	42.4807	−	60.3798i	1.43040	−	2.03310i
$883$	54.1672			1.82287			0.911437	−	0.411441i	$-0.134974\pi$
$883$	54.1672			1.82287			0.911437	+	0.411441i	$0.134974\pi$
$884$	2.75684	−	10.6918i	0.0927226	−	0.359604i
$885$	37.7609	−	51.1248i	1.26932	−	1.71854i
$886$	−1.21840	+	0.944092i	−0.0409330	+	0.0317174i
$887$	3.48451			0.116998			0.0584992	−	0.998287i	$-0.481369\pi$
$887$	3.48451			0.116998			0.0584992	+	0.998287i	$0.481369\pi$
$888$	−6.27748	+	26.8960i	−0.210659	+	0.902572i
$889$	25.1727			0.844264
$890$	17.7514	−	13.7549i	0.595028	−	0.461064i
$891$	11.6316	+	17.1145i	0.389673	+	0.573358i
$892$	−2.16068	−	0.557123i	−0.0723448	−	0.0186539i
$893$	3.67890			0.123110
$894$	0.160742	+	6.97040i	0.00537603	+	0.233125i
$895$			8.19147i			0.273811i
$896$	5.45849	−	55.6196i	0.182355	−	1.85812i
$897$	−1.82803	+	2.47498i	−0.0610361	+	0.0826372i
$898$	−1.40342	+	1.08745i	−0.0468327	+	0.0362888i
$899$			70.8028i			2.36141i
$900$	−36.0332	+	1.66279i	−1.20111	+	0.0554262i
$901$		−	3.33958i		−	0.111258i
$902$	−8.83582	−	11.4031i	−0.294201	−	0.379682i
$903$	−57.9816	+	78.5018i	−1.92951	+	2.61238i
$904$	−0.940223	−	2.18190i	−0.0312713	−	0.0725690i
$905$			56.8339i			1.88922i
$906$	10.8527	−	0.250270i	0.360556	−	0.00831467i
$907$	36.5392			1.21326			0.606632	−	0.794983i	$-0.292520\pi$
$907$	36.5392			1.21326			0.606632	+	0.794983i	$0.292520\pi$
$908$	12.2276	+	3.15284i	0.405787	+	0.104631i
$909$	1.66517	+	5.41248i	0.0552301	+	0.179521i
$910$	−25.2237	−	32.5526i	−0.836159	−	1.07911i
$911$	−50.4551			−1.67165			−0.835827	−	0.548994i	$-0.815011\pi$
$911$	−50.4551			−1.67165			−0.835827	+	0.548994i	$0.815011\pi$
$912$	−2.05817	−	4.48856i	−0.0681527	−	0.148631i
$913$	−23.8788			−0.790274
$914$	−8.58498	−	11.0794i	−0.283966	−	0.366473i
$915$	7.69057	−	10.4123i	0.254243	−	0.344221i
$916$	−29.8117	−	7.68684i	−0.985006	−	0.253980i
$917$	−40.1837			−1.32698
$918$	−7.21677	−	21.6670i	−0.238189	−	0.715117i
$919$		−	46.1632i		−	1.52278i	−0.648292	−	0.761391i	$-0.724517\pi$
$919$		−	46.1632i		−	1.52278i	0.648292	−	0.761391i	$-0.275483\pi$
$920$	−8.61967	+	3.71438i	−0.284182	+	0.122459i
$921$	43.8905	+	32.4176i	1.44624	+	1.06820i
$922$	13.4180	+	17.3166i	0.441898	+	0.570293i
$923$			21.1186i			0.695128i
$924$	−30.5362	+	24.8088i	−1.00457	+	0.816149i
$925$			33.8933i			1.11441i
$926$	−16.3069	+	12.6356i	−0.535879	+	0.415232i
$927$	−42.6565	+	13.1234i	−1.40102	+	0.431030i
$928$	−6.85267	−	43.9936i	−0.224950	−	1.44416i
$929$		−	39.3991i		−	1.29264i	−0.763065	−	0.646322i	$-0.776306\pi$
$929$		−	39.3991i		−	1.29264i	0.763065	−	0.646322i	$-0.223694\pi$
$930$	73.1008	−	1.68576i	2.39707	−	0.0552781i
$931$	12.4023			0.406467
$932$	−45.9277	−	11.8423i	−1.50441	−	0.387907i
$933$	26.4178	+	19.5123i	0.864881	+	0.638803i
$934$	−25.6278	+	19.8580i	−0.838569	+	0.649774i
$935$	−23.7115			−0.775450
$936$	−11.4769	+	9.77206i	−0.375135	+	0.319410i
$937$	−43.9128			−1.43457			−0.717284	−	0.696781i	$-0.754615\pi$
$937$	−43.9128			−1.43457			−0.717284	+	0.696781i	$0.754615\pi$
$938$	37.1106	−	28.7556i	1.21171	−	0.938903i
$939$	−0.713026	−	0.526642i	−0.0232687	−	0.0171863i
$940$	8.55340	−	33.1724i	0.278981	−	1.08197i
$941$	−14.8447			−0.483924			−0.241962	−	0.970286i	$-0.577791\pi$
$941$	−14.8447			−0.483924			−0.241962	+	0.970286i	$0.577791\pi$
$942$	−19.7247	+	0.454866i	−0.642667	+	0.0148203i
$943$		−	4.43652i		−	0.144473i
$944$	21.3882	−	38.7173i	0.696128	−	1.26014i
$945$	−80.3652	−	28.2206i	−2.61428	−	0.918017i
$946$	29.3180	−	22.7174i	0.953211	−	0.738606i
$947$			40.2548i			1.30811i	0.756448	+	0.654053i	$0.226933\pi$
$947$			40.2548i			1.30811i	−0.756448	+	0.654053i	$0.773067\pi$
$948$	4.68181	+	5.76266i	0.152058	+	0.187163i
$949$			16.5445i			0.537056i
$950$	−3.71160	−	4.79002i	−0.120420	−	0.155409i
$951$	11.3126	+	8.35553i	0.366837	+	0.270947i
$952$	39.8759	−	17.1833i	1.29239	−	0.556913i
$953$			45.9272i			1.48773i	0.668331	+	0.743864i	$0.267009\pi$
$953$			45.9272i			1.48773i	−0.668331	+	0.743864i	$0.732991\pi$
$954$	−2.62338	+	3.72874i	−0.0849352	+	0.120722i
$955$	64.7378			2.09487
$956$	−14.3233	+	55.5496i	−0.463248	+	1.79660i
$957$	−18.6223	+	25.2129i	−0.601973	+	0.815017i
$958$	−1.99229	−	2.57116i	−0.0643681	−	0.0830705i
$959$	−13.5020			−0.436002
$960$	−45.2583	+	8.12253i	−1.46071	+	0.262154i
$961$	−49.9209			−1.61035
$962$	8.67511	+	11.1957i	0.279697	+	0.360964i
$963$	−13.5952	+	4.18262i	−0.438100	+	0.134783i
$964$	0.322887	−	1.25225i	0.0103995	−	0.0403321i
$965$	−37.0576			−1.19293
$966$	−12.0966	+	0.278957i	−0.389203	+	0.00897529i
$967$			12.3610i			0.397504i	0.980050	+	0.198752i	$0.0636889\pi$
$967$			12.3610i			0.397504i	−0.980050	+	0.198752i	$0.936311\pi$
$968$	−14.8411	+	6.39532i	−0.477012	+	0.205553i
$969$	2.27931	−	3.08598i	0.0732221	−	0.0991361i
$970$	−11.6935	−	15.0911i	−0.375457	−	0.484548i
$971$			28.1907i			0.904683i	0.891845	+	0.452342i	$0.149411\pi$
$971$			28.1907i			0.904683i	−0.891845	+	0.452342i	$0.850589\pi$
$972$	−8.96260	+	29.8609i	−0.287476	+	0.957788i
$973$			112.968i			3.62159i
$974$	−3.13663	+	2.43045i	−0.100504	+	0.0778766i
$975$	−10.9900	+	14.8794i	−0.351960	+	0.476522i
$976$	4.35604	−	7.88536i	0.139433	−	0.252404i
$977$		−	46.0765i		−	1.47412i	−0.675828	−	0.737060i	$-0.736214\pi$
$977$		−	46.0765i		−	1.47412i	0.675828	−	0.737060i	$-0.263786\pi$
$978$	−0.795544	−	34.4978i	−0.0254387	−	1.10312i
$979$	−11.0023			−0.351634
$980$	28.8351	−	111.830i	0.921102	−	3.57229i
$981$	−23.5150	+	7.23445i	−0.750775	+	0.230978i
$982$	−12.6611	+	9.81058i	−0.404031	+	0.313068i
$983$	−43.4132			−1.38466			−0.692332	−	0.721579i	$-0.743417\pi$
$983$	−43.4132			−1.38466			−0.692332	+	0.721579i	$0.743417\pi$
$984$	4.94000	−	21.1656i	0.157482	−	0.674734i
$985$	20.2572			0.645449
$986$	27.3443	−	21.1880i	0.870819	−	0.674764i
$987$	26.2379	−	35.5238i	0.835162	−	1.13073i
$988$	−2.45204	−	0.632251i	−0.0780099	−	0.0201146i
$989$	11.4065			0.362707
$990$	26.4746	+	18.6264i	0.841418	+	0.591986i
$991$			41.8722i			1.33011i	0.746792	+	0.665057i	$0.231593\pi$
$991$			41.8722i			1.33011i	−0.746792	+	0.665057i	$0.768407\pi$
$992$	50.2805	−	7.83195i	1.59641	−	0.248665i
$993$	23.1820	+	17.1223i	0.735659	+	0.543359i
$994$	−65.6475	+	50.8677i	−2.08221	+	1.61343i
$995$			1.82786i			0.0579471i
$996$	−22.6857	−	27.9229i	−0.718823	−	0.884772i
$997$		−	37.7746i		−	1.19633i	−0.801372	−	0.598167i	$-0.795896\pi$
$997$		−	37.7746i		−	1.19633i	0.801372	−	0.598167i	$-0.204104\pi$
$998$	−14.1986	−	18.3241i	−0.449449	−	0.580038i
$999$	27.6397	+	9.70581i	0.874481	+	0.307078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.d.323.30	yes	42
3.2	odd	2		552.2.j.c.323.13	✓	42
4.3	odd	2		2208.2.j.d.47.34		42
8.3	odd	2		552.2.j.c.323.14	yes	42
8.5	even	2		2208.2.j.c.47.34		42
12.11	even	2		2208.2.j.c.47.33		42
24.5	odd	2		2208.2.j.d.47.33		42
24.11	even	2	inner	552.2.j.d.323.29	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.13	✓	42	3.2	odd	2
552.2.j.c.323.14	yes	42	8.3	odd	2
552.2.j.d.323.29	yes	42	24.11	even	2	inner
552.2.j.d.323.30	yes	42	1.1	even	1	trivial
2208.2.j.c.47.33		42	12.11	even	2
2208.2.j.c.47.34		42	8.5	even	2
2208.2.j.d.47.33		42	24.5	odd	2
2208.2.j.d.47.34		42	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866210 + 1.11789i) q^{2} +(-1.39323 - 1.02904i) q^{3} +(-0.499360 + 1.93666i) q^{4} +3.31842 q^{5} +(-0.0564720 - 2.44884i) q^{6} -4.93974i q^{7} +(-2.59752 + 1.11932i) q^{8} +(0.882155 + 2.86737i) q^{9} +(2.87445 + 3.70963i) q^{10} -2.29922i q^{11} +(2.68862 - 2.18434i) q^{12} -1.77644i q^{13} +(5.52209 - 4.27885i) q^{14} +(-4.62331 - 3.41479i) q^{15} +(-3.50128 - 1.93418i) q^{16} -3.10776i q^{17} +(-2.44127 + 3.46990i) q^{18} -0.712730 q^{19} +(-1.65709 + 6.42664i) q^{20} +(-5.08319 + 6.88217i) q^{21} +(2.57028 - 1.99161i) q^{22} +1.00000 q^{23} +(4.77076 + 1.11349i) q^{24} +6.01192 q^{25} +(1.98587 - 1.53877i) q^{26} +(1.72160 - 4.90266i) q^{27} +(9.56658 + 2.46671i) q^{28} +7.87082 q^{29} +(-0.187398 - 8.12628i) q^{30} +8.99561i q^{31} +(-0.870642 - 5.58945i) q^{32} +(-2.36599 + 3.20334i) q^{33} +(3.47413 - 2.69197i) q^{34} -16.3921i q^{35} +(-5.99362 + 0.276581i) q^{36} +5.63769i q^{37} +(-0.617374 - 0.796754i) q^{38} +(-1.82803 + 2.47498i) q^{39} +(-8.61967 + 3.71438i) q^{40} -4.43652i q^{41} +(-12.0966 + 0.278957i) q^{42} +11.4065 q^{43} +(4.45281 + 1.14814i) q^{44} +(2.92736 + 9.51514i) q^{45} +(0.866210 + 1.11789i) q^{46} -5.16171 q^{47} +(2.88772 + 6.29770i) q^{48} -17.4011 q^{49} +(5.20758 + 6.72067i) q^{50} +(-3.19801 + 4.32981i) q^{51} +(3.44036 + 0.887084i) q^{52} +1.07460 q^{53} +(6.97191 - 2.32218i) q^{54} -7.62979i q^{55} +(5.52916 + 12.8311i) q^{56} +(0.992994 + 0.733427i) q^{57} +(6.81778 + 8.79872i) q^{58} +11.0580i q^{59} +(8.92197 - 7.24855i) q^{60} +2.25214i q^{61} +(-10.0561 + 7.79208i) q^{62} +(14.1641 - 4.35762i) q^{63} +(5.49424 - 5.81492i) q^{64} -5.89498i q^{65} +(-5.63043 + 0.129842i) q^{66} +6.72040 q^{67} +(6.01866 + 1.55189i) q^{68} +(-1.39323 - 1.02904i) q^{69} +(18.3246 - 14.1990i) q^{70} -11.8882 q^{71} +(-5.50092 - 6.46064i) q^{72} -9.31327 q^{73} +(-6.30232 + 4.88342i) q^{74} +(-8.37596 - 6.18650i) q^{75} +(0.355909 - 1.38031i) q^{76} -11.3576 q^{77} +(-4.35022 + 0.100319i) q^{78} +2.14336i q^{79} +(-11.6187 - 6.41842i) q^{80} +(-7.44361 + 5.05893i) q^{81} +(4.95955 - 3.84296i) q^{82} -10.3856i q^{83} +(-10.7901 - 13.2811i) q^{84} -10.3128i q^{85} +(9.88046 + 12.7513i) q^{86} +(-10.9658 - 8.09939i) q^{87} +(2.57357 + 5.97228i) q^{88} -4.78521i q^{89} +(-8.10117 + 11.5146i) q^{90} -8.77516 q^{91} +(-0.499360 + 1.93666i) q^{92} +(9.25683 - 12.5329i) q^{93} +(-4.47112 - 5.77022i) q^{94} -2.36514 q^{95} +(-4.53877 + 8.68329i) q^{96} -4.06810 q^{97} +(-15.0730 - 19.4525i) q^{98} +(6.59272 - 2.02827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24}+ \cdots + 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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