LMFDB - Embedded newform 552.2.j.c.323.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(323,552)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			323.14
Character	$\chi$	$=$	552.323
Dual form			552.2.j.c.323.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866210 + 1.11789i) q^{2} +(-1.39323 - 1.02904i) q^{3} +(-0.499360 - 1.93666i) q^{4} -3.31842 q^{5} +(2.35718 - 0.666110i) q^{6} +4.93974i q^{7} +(2.59752 + 1.11932i) q^{8} +(0.882155 + 2.86737i) q^{9} +O(q^{10})$	\(q+(-0.866210 + 1.11789i) q^{2} +(-1.39323 - 1.02904i) q^{3} +(-0.499360 - 1.93666i) q^{4} -3.31842 q^{5} +(2.35718 - 0.666110i) 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} +(-1.29718 + 3.21206i) 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} +(-3.96954 - 1.49759i) 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} +(-2.46711 - 4.23242i) 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} +(-7.82212 + 2.21043i) 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} +(5.11260 - 3.14028i) 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} +(3.29041 + 11.6439i) 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} +(6.86842 + 0.908208i) 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} +(3.98938 + 6.17129i) 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} +(4.30457 - 10.6590i) 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} +(-1.53154 - 5.41968i) 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} +(-0.918090 + 8.43547i) 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} +(1.18330 + 4.18739i) 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} +(-15.8668 - 6.40771i) 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} +(13.1726 + 4.96964i) 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} +(-6.96477 + 6.89144i) 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} + q^{6} + 9 q^{8} + 2 q^{9}+O(q^{10}) $ 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9	$ 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{14} + 8 q^{15} - 12 q^{16} + 16 q^{18} + 4 q^{19} + 2 q^{20} - 8 q^{21} + 18 q^{22} - 42 q^{23} - 24 q^{24} + 22 q^{25} - 11 q^{26} - 16 q^{27} + 6 q^{28} - 24 q^{30} + 20 q^{32} + 12 q^{33} + 14 q^{34} + 15 q^{36} + 22 q^{38} - 8 q^{39} + 4 q^{40} + 36 q^{42} + 28 q^{43} - 56 q^{44} + 8 q^{45} - 9 q^{48} - 50 q^{49} - 20 q^{50} + 28 q^{51} - q^{52} - 24 q^{53} - 24 q^{54} + 34 q^{56} - 8 q^{57} - 21 q^{58} + 18 q^{60} + 79 q^{62} + 16 q^{63} + 7 q^{64} + 16 q^{66} - 4 q^{67} - 20 q^{68} - 2 q^{69} - 8 q^{70} - 62 q^{72} + 4 q^{73} - 36 q^{74} - 6 q^{75} + 14 q^{76} - 32 q^{77} - 62 q^{78} + 52 q^{80} + 18 q^{81} + 11 q^{82} + 66 q^{84} + 28 q^{86} + 48 q^{87} - 38 q^{88} - 8 q^{91} - 4 q^{92} + 22 q^{93} + q^{94} + 16 q^{95} - 54 q^{96} + 20 q^{97} - 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^14 + 8 * q^15 - 12 * q^16 + 16 * q^18 + 4 * q^19 + 2 * q^20 - 8 * q^21 + 18 * q^22 - 42 * q^23 - 24 * q^24 + 22 * q^25 - 11 * q^26 - 16 * q^27 + 6 * q^28 - 24 * q^30 + 20 * q^32 + 12 * q^33 + 14 * q^34 + 15 * q^36 + 22 * q^38 - 8 * q^39 + 4 * q^40 + 36 * q^42 + 28 * q^43 - 56 * q^44 + 8 * q^45 - 9 * q^48 - 50 * q^49 - 20 * q^50 + 28 * q^51 - q^52 - 24 * q^53 - 24 * q^54 + 34 * q^56 - 8 * q^57 - 21 * q^58 + 18 * q^60 + 79 * q^62 + 16 * q^63 + 7 * q^64 + 16 * q^66 - 4 * q^67 - 20 * q^68 - 2 * q^69 - 8 * q^70 - 62 * q^72 + 4 * q^73 - 36 * q^74 - 6 * q^75 + 14 * q^76 - 32 * q^77 - 62 * q^78 + 52 * q^80 + 18 * q^81 + 11 * q^82 + 66 * q^84 + 28 * q^86 + 48 * q^87 - 38 * q^88 - 8 * q^91 - 4 * q^92 + 22 * q^93 + q^94 + 16 * q^95 - 54 * q^96 + 20 * q^97 - 64 * q^98

Display 100 coefficients 10 coefficients

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	$-0.766133\pi$
$5$	−3.31842			−1.48404			−0.742022	+	0.670376i	$0.766133\pi$
$6$	2.35718	−	0.666110i	0.962315	−	0.271938i
$7$			4.93974i			1.86705i	0.358516	+	0.933524i	$0.383283\pi$
$7$			4.93974i			1.86705i	−0.358516	+	0.933524i	$0.616717\pi$
$8$	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	$-0.112671\pi$
$12$	−1.29718	+	3.21206i	−0.374462	+	0.927242i
$13$			1.77644i			0.492696i	0.969181	+	0.246348i	$0.0792306\pi$
$13$			1.77644i			0.492696i	−0.969181	+	0.246348i	$0.920769\pi$
$14$	−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	$-0.123000\pi$
$18$	−3.96954	−	1.49759i	−0.935629	−	0.352986i
$19$	−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
$24$	−2.46711	−	4.23242i	−0.503596	−	0.863939i
$25$	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	$-0.760847\pi$
$29$	−7.87082			−1.46157			−0.730787	+	0.682605i	$0.760847\pi$
$30$	−7.82212	+	2.21043i	−1.42812	+	0.403568i
$31$		−	8.99561i		−	1.61566i	−0.589417	−	0.807829i	$-0.700642\pi$
$31$		−	8.99561i		−	1.61566i	0.589417	−	0.807829i	$-0.299358\pi$
$32$	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
$36$	5.11260	−	3.14028i	0.852099	−	0.523380i
$37$		−	5.63769i		−	0.926830i	−0.886141	−	0.463415i	$-0.846624\pi$
$37$		−	5.63769i		−	0.926830i	0.886141	−	0.463415i	$-0.153376\pi$
$38$	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	$-0.112608\pi$
$42$	3.29041	+	11.6439i	0.507721	+	1.79669i
$43$	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	$-0.377143\pi$
$47$	5.16171			0.752912			0.376456	+	0.926434i	$0.377143\pi$
$48$	6.86842	+	0.908208i	0.991371	+	0.131088i
$49$	−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	$-0.523514\pi$
$53$	−1.07460			−0.147607			−0.0738036	+	0.997273i	$0.523514\pi$
$54$	3.98938	+	6.17129i	0.542886	+	0.839807i
$55$			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	$0.744226\pi$
$60$	4.30457	−	10.6590i	0.555718	−	1.37607i
$61$		−	2.25214i		−	0.288357i	−0.989552	−	0.144178i	$-0.953946\pi$
$61$		−	2.25214i		−	0.288357i	0.989552	−	0.144178i	$-0.0460539\pi$
$62$	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
$66$	−1.53154	−	5.41968i	−0.188519	−	0.667117i
$67$	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	$-0.250753\pi$
$71$	11.8882			1.41087			0.705433	+	0.708777i	$0.250753\pi$
$72$	−0.918090	+	8.43547i	−0.108198	+	0.994129i
$73$	−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
$78$	1.18330	+	4.18739i	0.133983	+	0.474129i
$79$		−	2.14336i		−	0.241146i	−0.992704	−	0.120573i	$-0.961527\pi$
$79$		−	2.14336i		−	0.241146i	0.992704	−	0.120573i	$-0.0384732\pi$
$80$	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	$-0.193051\pi$
$84$	−15.8668	−	6.40771i	−1.73120	−	0.699139i
$85$			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	$-0.0816199\pi$
$90$	13.1726	+	4.96964i	1.38851	+	0.523846i
$91$	−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
$96$	−6.96477	+	6.89144i	−0.710839	+	0.703355i
$97$	−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	$-0.529937\pi$
$101$	−1.88761			−0.187824			−0.0939122	+	0.995580i	$0.529937\pi$
$102$	−2.07011	−	7.32554i	−0.204971	−	0.725337i
$103$		−	14.8765i		−	1.46583i	−0.680320	−	0.732915i	$-0.738159\pi$
$103$		−	14.8765i		−	1.46583i	0.680320	−	0.732915i	$-0.261841\pi$
$104$	−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	$0.926395\pi$
$108$	−10.3545	−	0.885944i	−0.996360	−	0.0852500i
$109$		−	8.20089i		−	0.785503i	−0.919645	−	0.392751i	$-0.871523\pi$
$109$		−	8.20089i		−	0.785503i	0.919645	−	0.392751i	$-0.128477\pi$
$110$	−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	$0.987420\pi$
$114$	−1.68003	+	0.474756i	−0.157349	+	0.0444650i
$115$	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
$120$	8.18690	+	14.0450i	0.747359	+	1.28212i
$121$	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
$126$	7.39771	−	19.6085i	0.659041	−	1.74686i
$127$		−	5.09595i		−	0.452192i	−0.974105	−	0.226096i	$-0.927404\pi$
$127$		−	5.09595i		−	0.452192i	0.974105	−	0.226096i	$-0.0725964\pi$
$128$	−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	$-0.115645\pi$
$132$	7.38525	+	2.98250i	0.642803	+	0.259593i
$133$		−	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	$-0.0372516\pi$
$138$	−2.35718	+	0.666110i	−0.200656	+	0.0567030i
$139$	−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
$144$	−8.63467	−	8.33321i	−0.719556	−	0.694434i
$145$	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	$-0.462803\pi$
$149$	2.84641			0.233187			0.116594	+	0.993180i	$0.462803\pi$
$150$	14.1712	−	4.00460i	1.15707	−	0.326974i
$151$		−	4.43176i		−	0.360652i	−0.983607	−	0.180326i	$-0.942285\pi$
$151$		−	4.43176i		−	0.360652i	0.983607	−	0.180326i	$-0.0577152\pi$
$152$	−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
$156$	−5.70604	−	2.30435i	−0.456848	−	0.184496i
$157$			8.05473i			0.642837i	0.946937	+	0.321419i	$0.104160\pi$
$157$			8.05473i			0.642837i	−0.946937	+	0.321419i	$0.895840\pi$
$158$	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
$162$	0.792398	−	12.7032i	0.0622567	−	0.998060i
$163$	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	$-0.387073\pi$
$167$	8.97815			0.694750			0.347375	+	0.937726i	$0.387073\pi$
$168$	20.9071	−	12.1869i	1.61301	−	0.940238i
$169$	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	$-0.691404\pi$
$173$	−14.8819			−1.13145			−0.565726	+	0.824593i	$0.691404\pi$
$174$	−18.5529	+	5.24283i	−1.40649	+	0.397458i
$175$			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	$0.970594\pi$
$180$	−16.9657	+	10.4208i	−1.26455	+	0.776719i
$181$		−	17.1268i		−	1.27302i	−0.771267	−	0.636512i	$-0.780377\pi$
$181$		−	17.1268i		−	1.27302i	0.771267	−	0.636512i	$-0.219623\pi$
$182$	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
$186$	−5.99206	−	21.2043i	−0.439359	−	1.55477i
$187$	−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	$-0.749411\pi$
$191$	−19.5086			−1.41159			−0.705797	+	0.708414i	$0.749411\pi$
$192$	−1.67093	−	13.7553i	−0.120589	−	0.992703i
$193$	−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	$-0.569778\pi$
$197$	−6.10448			−0.434926			−0.217463	+	0.976069i	$0.569778\pi$
$198$	−3.44330	+	9.12685i	−0.244704	+	0.648617i
$199$		−	0.550823i		−	0.0390468i	−0.999809	−	0.0195234i	$-0.993785\pi$
$199$		−	0.550823i		−	0.0390468i	0.999809	−	0.0195234i	$-0.00621489\pi$
$200$	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
$204$	9.98231	+	4.03131i	0.698901	+	0.282248i
$205$			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
$210$	−10.9190	−	38.6392i	−0.753480	−	2.66636i
$211$	−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
$216$	9.95954	−	10.8078i	0.677661	−	0.735375i
$217$	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
$222$	−3.75532	−	13.2890i	−0.252040	−	0.891902i
$223$		−	1.11567i		−	0.0747110i	−0.999302	−	0.0373555i	$-0.988107\pi$
$223$		−	1.11567i		−	0.0747110i	0.999302	−	0.0373555i	$-0.0118934\pi$
$224$	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	$-0.0671932\pi$
$228$	0.924536	−	2.28933i	0.0612289	−	0.151615i
$229$		−	15.3934i		−	1.01722i	−0.860996	−	0.508612i	$-0.830159\pi$
$229$		−	15.3934i		−	1.01722i	0.860996	−	0.508612i	$-0.169841\pi$
$230$	−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	$0.716837\pi$
$234$	2.66038	−	7.05165i	0.173915	−	0.460980i
$235$	−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	$-0.878203\pi$
$239$	−28.6833			−1.85537			−0.927683	+	0.373369i	$0.878203\pi$
$240$	−22.7923	−	3.01382i	−1.47124	−	0.194541i
$241$	−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
$246$	−2.95521	−	10.4577i	−0.188417	−	0.666757i
$247$		−	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	$0.830580\pi$
$252$	15.5122	+	25.2549i	0.977175	+	1.59091i
$253$			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	$-0.0595132\pi$
$258$	26.8873	−	7.59800i	1.67393	−	0.473031i
$259$	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	$-0.401464\pi$
$263$	9.88085			0.609279			0.304640	+	0.952468i	$0.401464\pi$
$264$	−9.73128	+	5.67243i	−0.598919	+	0.349114i
$265$	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	$-0.637499\pi$
$269$	−13.7330			−0.837316			−0.418658	+	0.908144i	$0.637499\pi$
$270$	−13.2384	−	20.4789i	−0.805666	−	1.24631i
$271$			23.1515i			1.40635i	0.711016	+	0.703175i	$0.248235\pi$
$271$			23.1515i			1.40635i	−0.711016	+	0.703175i	$0.751765\pi$
$272$	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
$276$	1.29718	−	3.21206i	0.0780808	−	0.193343i
$277$			2.28715i			0.137422i	0.997637	+	0.0687109i	$0.0218886\pi$
$277$			2.28715i			0.137422i	−0.997637	+	0.0687109i	$0.978111\pi$
$278$	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	$-0.103627\pi$
$282$	12.1671	−	3.43826i	0.724538	−	0.204746i
$283$	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
$288$	16.7951	−	2.43431i	0.989659	−	0.143443i
$289$	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	$-0.583722\pi$
$293$	−8.90093			−0.519998			−0.259999	+	0.965609i	$0.583722\pi$
$294$	−41.0174	+	11.5910i	−2.39218	+	0.676001i
$295$		−	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
$300$	−7.79851	+	19.3107i	−0.450247	+	1.11490i
$301$			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
$306$	−4.65415	+	12.3364i	−0.266060	+	0.705223i
$307$	−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	$-0.319328\pi$
$311$	18.9616			1.07522			0.537608	+	0.843195i	$0.319328\pi$
$312$	7.51864	−	4.38267i	0.425659	−	0.248120i
$313$	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	$-0.426773\pi$
$317$	8.11974			0.456050			0.228025	+	0.973655i	$0.426773\pi$
$318$	−2.53302	+	0.715799i	−0.142045	+	0.0401400i
$319$			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
$324$	13.5144	+	11.8895i	0.750802	+	0.660527i
$325$			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
$330$	5.08228	+	17.9848i	0.279770	+	0.990030i
$331$	−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
$336$	−4.48631	+	33.9282i	−0.244748	+	1.85094i
$337$	−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
$342$	2.82921	+	1.06738i	0.152986	+	0.0577172i
$343$		−	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	$0.981692\pi$
$348$	10.2098	−	25.2816i	0.547305	−	1.35523i
$349$		−	16.8713i		−	0.903098i	−0.892246	−	0.451549i	$-0.850872\pi$
$349$		−	16.8713i		−	0.903098i	0.892246	−	0.451549i	$-0.149128\pi$
$350$	−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	$-0.203762\pi$
$354$	7.36587	+	26.0658i	0.391492	+	1.38538i
$355$	−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	$-0.378064\pi$
$359$	14.1639			0.747543			0.373771	+	0.927521i	$0.378064\pi$
$360$	3.04661	−	27.9924i	0.160570	−	1.47533i
$361$	−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
$366$	−1.50017	−	5.30870i	−0.0784152	−	0.277490i
$367$		−	26.8266i		−	1.40034i	−0.713977	−	0.700169i	$-0.753108\pi$
$367$		−	26.8266i		−	1.40034i	0.713977	−	0.700169i	$-0.246892\pi$
$368$	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
$372$	28.8944	+	11.6689i	1.49811	+	0.605003i
$373$			33.0544i			1.71149i	0.517395	+	0.855747i	$0.326902\pi$
$373$			33.0544i			1.71149i	−0.517395	+	0.855747i	$0.673098\pi$
$374$	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
$378$	−30.4846	+	19.7065i	−1.56796	+	1.01359i
$379$	−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	$-0.582133\pi$
$383$	−9.98774			−0.510350			−0.255175	+	0.966895i	$0.582133\pi$
$384$	16.8243	+	10.0471i	0.858561	+	0.512712i
$385$	−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	$-0.422118\pi$
$389$	9.55537			0.484477			0.242238	+	0.970217i	$0.422118\pi$
$390$	−3.92670	−	13.8955i	−0.198836	−	0.703627i
$391$			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
$396$	−7.22021	−	11.7550i	−0.362829	−	0.590711i
$397$		−	10.5693i		−	0.530457i	−0.964186	−	0.265228i	$-0.914553\pi$
$397$		−	10.5693i		−	0.530457i	0.964186	−	0.265228i	$-0.0854474\pi$
$398$	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	$-0.0307821\pi$
$402$	15.8412	−	4.47652i	0.790086	−	0.223269i
$403$	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
$408$	−13.1533	+	7.66717i	−0.651187	+	0.379582i
$409$	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
$414$	3.96954	+	1.49759i	0.195092	+	0.0736026i
$415$			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	$-0.236941\pi$
$420$	52.6526	+	21.2635i	2.56918	+	1.03755i
$421$		−	12.8814i		−	0.627801i	−0.949456	−	0.313900i	$-0.898364\pi$
$421$		−	12.8814i		−	0.627801i	0.949456	−	0.313900i	$-0.101636\pi$
$422$	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
$426$	28.0225	−	7.91882i	1.35770	−	0.383668i
$427$	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	$-0.530695\pi$
$431$	−3.99768			−0.192561			−0.0962807	+	0.995354i	$0.530695\pi$
$432$	3.45484	+	20.4955i	0.166221	+	0.986088i
$433$	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
$438$	−21.9531	+	6.20366i	−1.04896	+	0.296422i
$439$			4.65073i			0.221967i	0.993822	+	0.110984i	$0.0354001\pi$
$439$			4.65073i			0.221967i	−0.993822	+	0.110984i	$0.964600\pi$
$440$	−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	$0.991758\pi$
$444$	18.1086	+	7.31307i	0.859396	+	0.347063i
$445$			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	$0.990569\pi$
$450$	−23.8645	−	9.00339i	−1.12498	−	0.424424i
$451$	−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
$456$	1.75838	+	3.01657i	0.0823438	+	0.141264i
$457$	−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	$-0.617473\pi$
$461$	−15.4904			−0.721462			−0.360731	+	0.932670i	$0.617473\pi$
$462$	26.7718	−	7.56539i	1.24554	−	0.351974i
$463$		−	14.5872i		−	0.677927i	−0.940800	−	0.338963i	$-0.889924\pi$
$463$		−	14.5872i		−	0.677927i	0.940800	−	0.338963i	$-0.110076\pi$
$464$	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	$0.822032\pi$
$468$	5.57852	+	9.08222i	0.257867	+	0.419826i
$469$			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
$474$	−1.42771	−	5.05227i	−0.0655769	−	0.232059i
$475$	−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	$-0.483267\pi$
$479$	2.30001			0.105090			0.0525451	+	0.998619i	$0.483267\pi$
$480$	23.1120	−	22.8687i	1.05492	−	1.04381i
$481$	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
$486$	−14.1761	+	16.8831i	−0.643042	+	0.765831i
$487$		−	2.80584i		−	0.127145i	−0.997977	−	0.0635725i	$-0.979751\pi$
$487$		−	2.80584i		−	0.127145i	0.997977	−	0.0635725i	$-0.0202494\pi$
$488$	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	$0.917739\pi$
$492$	14.2504	+	5.75494i	0.642456	+	0.259453i
$493$			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
$498$	−6.91795	−	24.4807i	−0.310001	−	1.09701i
$499$	−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	$-0.529676\pi$
$503$	−4.17583			−0.186191			−0.0930955	+	0.995657i	$0.529676\pi$
$504$	−41.6690	−	4.53513i	−1.85609	−	0.202011i
$505$	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	$-0.619364\pi$
$509$	−16.5267			−0.732535			−0.366267	+	0.930510i	$0.619364\pi$
$510$	6.86949	+	24.3092i	0.304186	+	1.07643i
$511$		−	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
$516$	−14.7963	+	36.6385i	−0.651370	+	1.61292i
$517$		−	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	$-0.329765\pi$
$522$	31.2435	+	11.7873i	1.36749	+	0.515915i
$523$	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
$528$	2.08817	−	15.7920i	0.0908760	−	0.687260i
$529$	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
$534$	−3.18748	−	11.2796i	−0.137936	−	0.488116i
$535$		−	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
$540$	34.3605	+	2.93994i	1.47864	+	0.126515i
$541$			28.5798i			1.22874i	0.789018	+	0.614370i	$0.210590\pi$
$541$			28.5798i			1.22874i	−0.789018	+	0.614370i	$0.789410\pi$
$542$	−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
$546$	−20.6846	+	5.84522i	−0.885220	+	0.250152i
$547$	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
$552$	2.46711	+	4.23242i	0.105007	+	0.180144i
$553$	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	$-0.364358\pi$
$557$	19.5109			0.826702			0.413351	+	0.910572i	$0.364358\pi$
$558$	−13.4717	+	35.7084i	−0.570304	+	1.51166i
$559$			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	$-0.153051\pi$
$564$	−6.69564	+	16.5797i	−0.281937	+	0.698132i
$565$		−	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	$-0.149045\pi$
$570$	5.57506	−	1.57544i	0.233513	−	0.0659880i
$571$	−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
$576$	−11.8268	+	20.8837i	−0.492782	+	0.870153i
$577$	−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
$582$	−9.58924	+	2.70980i	−0.397487	+	0.112325i
$583$			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	$-0.171452\pi$
$588$	22.5722	−	55.8932i	0.930862	−	2.30500i
$589$			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	$0.847259\pi$
$594$	14.1892	−	9.17248i	0.582189	−	0.376351i
$595$	−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	$-0.764674\pi$
$599$	−36.1704			−1.47788			−0.738941	+	0.673770i	$0.764674\pi$
$600$	−14.8321	−	25.4450i	−0.605516	−	1.03879i
$601$	−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
$606$	−4.44944	+	1.25736i	−0.180746	+	0.0510766i
$607$		−	33.4349i		−	1.35708i	−0.734564	−	0.678540i	$-0.762613\pi$
$607$		−	33.4349i		−	1.35708i	0.734564	−	0.678540i	$-0.237387\pi$
$608$	−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
$612$	−9.75923	−	15.8887i	−0.394494	−	0.642263i
$613$		−	5.29916i		−	0.214031i	−0.994257	−	0.107016i	$-0.965871\pi$
$613$		−	5.29916i		−	0.214031i	0.994257	−	0.107016i	$-0.0341295\pi$
$614$	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	$-0.0734166\pi$
$618$	−9.90941	−	35.0667i	−0.398615	−	1.41059i
$619$	−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
$624$	−1.61338	+	12.2013i	−0.0645868	+	0.488444i
$625$	−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
$630$	−24.5487	+	65.0692i	−0.978045	+	2.59242i
$631$		−	30.3514i		−	1.20827i	−0.796883	−	0.604134i	$-0.793519\pi$
$631$		−	30.3514i		−	1.20827i	0.796883	−	0.604134i	$-0.206481\pi$
$632$	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
$636$	1.39394	−	3.45167i	0.0552733	−	0.136868i
$637$		−	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	$-0.0947747\pi$
$642$	3.15827	+	11.1762i	0.124647	+	0.441091i
$643$	−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	$-0.355280\pi$
$647$	22.3405			0.878296			0.439148	+	0.898415i	$0.355280\pi$
$648$	−24.9975	+	4.80889i	−0.981994	+	0.188911i
$649$	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	$-0.240605\pi$
$653$	37.1894			1.45533			0.727667	+	0.685931i	$0.240605\pi$
$654$	−5.46269	−	19.3310i	−0.213608	−	0.755901i
$655$			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	$-0.167024\pi$
$660$	−24.5074	−	9.89718i	−0.953948	−	0.385247i
$661$		−	8.78002i		−	0.341503i	−0.985314	−	0.170752i	$-0.945380\pi$
$661$		−	8.78002i		−	0.341503i	0.985314	−	0.170752i	$-0.0546196\pi$
$662$	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
$666$	−8.44295	+	22.3790i	−0.327158	+	0.867169i
$667$	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
$672$	−34.0420	−	34.4042i	−1.31320	−	1.32717i
$673$	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	$-0.360382\pi$
$677$	22.1004			0.849385			0.424693	+	0.905338i	$0.360382\pi$
$678$	0.559528	+	1.98002i	0.0214885	+	0.0760421i
$679$		−	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	$0.868987\pi$
$684$	−3.64390	+	2.23817i	−0.139328	+	0.0855787i
$685$			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
$690$	7.82212	−	2.21043i	0.297783	−	0.0841497i
$691$	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
$696$	19.4182	+	33.3126i	0.736044	+	1.26271i
$697$	−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	$-0.171796\pi$
$701$	45.4259			1.71571			0.857856	+	0.513891i	$0.171796\pi$
$702$	−10.9629	+	7.08690i	−0.413769	+	0.267478i
$703$			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
$708$	−35.5191	−	14.3442i	−1.33489	−	0.539089i
$709$		−	37.5812i		−	1.41139i	−0.708515	−	0.705696i	$-0.750635\pi$
$709$		−	37.5812i		−	1.41139i	0.708515	−	0.705696i	$-0.249365\pi$
$710$	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
$714$	36.1863	−	10.2258i	1.35424	−	0.382691i
$715$	−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	$-0.637572\pi$
$719$	−22.4630			−0.837730			−0.418865	+	0.908049i	$0.637572\pi$
$720$	28.6535	+	27.6531i	1.06785	+	1.03057i
$721$	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
$726$	13.4679	−	3.80586i	0.499841	−	0.141249i
$727$			52.5610i			1.94938i	0.223562	+	0.974690i	$0.428231\pi$
$727$			52.5610i			1.94938i	−0.223562	+	0.974690i	$0.571769\pi$
$728$	−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
$732$	7.23401	+	2.92142i	0.267377	+	0.107979i
$733$			1.78537i			0.0659443i	0.999456	+	0.0329721i	$0.0104973\pi$
$733$			1.78537i			0.0659443i	−0.999456	+	0.0329721i	$0.989503\pi$
$734$	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
$738$	−6.64409	+	17.6109i	−0.244572	+	0.648267i
$739$	−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	$-0.842224\pi$
$743$	−47.9551			−1.75930			−0.879651	+	0.475621i	$0.842224\pi$
$744$	−38.0732	+	22.1931i	−1.39583	+	0.813640i
$745$	−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
$750$	−7.91535	+	2.23678i	−0.289028	+	0.0816756i
$751$			23.3449i			0.851869i	0.904754	+	0.425935i	$0.140055\pi$
$751$			23.3449i			0.851869i	−0.904754	+	0.425935i	$0.859945\pi$
$752$	−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
$756$	4.37633	−	51.1484i	0.159166	−	1.86025i
$757$		−	11.8751i		−	0.431608i	−0.976437	−	0.215804i	$-0.930763\pi$
$757$		−	11.8751i		−	0.431608i	0.976437	−	0.215804i	$-0.0692371\pi$
$758$	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	$-0.324393\pi$
$762$	−3.39446	−	12.0121i	−0.122968	−	0.435151i
$763$	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
$768$	−25.8049	+	10.1049i	−0.931153	+	0.364628i
$769$	−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	$-0.584154\pi$
$773$	−14.5303			−0.522618			−0.261309	+	0.965255i	$0.584154\pi$
$774$	−45.2787	−	17.0823i	−1.62751	−	0.614011i
$775$		−	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
$780$	18.9350	+	7.64682i	0.677983	+	0.273800i
$781$		−	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
$786$	−5.41865	−	19.1751i	−0.193277	−	0.683954i
$787$	−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
$792$	19.3950	+	2.11090i	0.689172	+	0.0750074i
$793$	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	$-0.619774\pi$
$797$	−20.7479			−0.734930			−0.367465	+	0.930037i	$0.619774\pi$
$798$	−2.34517	−	8.29893i	−0.0830183	−	0.293779i
$799$		−	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
$804$	−8.71753	+	21.5863i	−0.307444	+	0.761291i
$805$			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	$0.615307\pi$
$810$	−2.62951	+	42.1547i	−0.0923916	+	1.48116i
$811$	−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
$816$	2.82249	−	21.3454i	0.0988069	−	0.747238i
$817$	−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	$-0.742325\pi$
$821$	−39.5328			−1.37971			−0.689853	+	0.723950i	$0.742325\pi$
$822$	−1.82070	−	6.44297i	−0.0635044	−	0.224725i
$823$			0.0765522i			0.00266844i	0.999999	+	0.00133422i	$0.000424696\pi$
$823$			0.0765522i			0.00266844i	−0.999999	+	0.00133422i	$0.999575\pi$
$824$	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	$0.989636\pi$
$828$	−5.11260	+	3.14028i	−0.177675	+	0.109132i
$829$			19.8929i			0.690909i	0.938436	+	0.345454i	$0.112275\pi$
$829$			19.8929i			0.690909i	−0.938436	+	0.345454i	$0.887725\pi$
$830$	−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
$834$	−53.9069	+	15.2334i	−1.86664	+	0.527490i
$835$	−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	$-0.451128\pi$
$839$	8.85955			0.305866			0.152933	+	0.988237i	$0.451128\pi$
$840$	−69.3784	+	40.4412i	−2.39378	+	1.39535i
$841$	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
$846$	−20.4896	−	7.73012i	−0.704446	−	0.265767i
$847$			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
$852$	−15.4210	+	38.1855i	−0.528316	+	1.30821i
$853$			5.57444i			0.190865i	0.995436	+	0.0954327i	$0.0304235\pi$
$853$			5.57444i			0.190865i	−0.995436	+	0.0954327i	$0.969577\pi$
$854$	−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	$-0.289842\pi$
$858$	9.62775	−	2.72068i	0.328686	−	0.0928825i
$859$	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	$-0.682417\pi$
$863$	−31.8575			−1.08444			−0.542222	+	0.840235i	$0.682417\pi$
$864$	−25.9043	−	13.8912i	−0.881283	−	0.472590i
$865$	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
$870$	61.5665	−	17.3979i	2.08730	−	0.589845i
$871$			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
$876$	12.0809	−	29.9148i	0.408177	−	1.01073i
$877$		−	6.78039i		−	0.228958i	−0.993426	−	0.114479i	$-0.963480\pi$
$877$		−	6.78039i		−	0.228958i	0.993426	−	0.114479i	$-0.0365198\pi$
$878$	−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	$-0.00155503\pi$
$882$	69.0741	+	26.0597i	2.32585	+	0.877474i
$883$	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	$-0.518631\pi$
$887$	−3.48451			−0.116998			−0.0584992	+	0.998287i	$0.518631\pi$
$888$	−23.8611	+	13.9088i	−0.800725	+	0.466748i
$889$	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
$894$	6.70951	−	1.89602i	0.224399	−	0.0634125i
$895$		−	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
$900$	30.7365	−	18.8791i	1.02455	−	0.629304i
$901$			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
$906$	−2.95204	−	10.4465i	−0.0980749	−	0.347060i
$907$	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	$-0.184989\pi$
$911$	50.4551			1.67165			0.835827	+	0.548994i	$0.184989\pi$
$912$	−4.89533	−	0.647307i	−0.162100	−	0.0214345i
$913$	−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
$918$	19.1789	−	12.3980i	0.632997	−	0.409196i
$919$			46.1632i			1.52278i	0.648292	+	0.761391i	$0.275483\pi$
$919$			46.1632i			1.52278i	−0.648292	+	0.761391i	$0.724517\pi$
$920$	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
$924$	−14.7328	+	36.4812i	−0.484672	+	1.20014i
$925$		−	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	$-0.223694\pi$
$930$	19.8842	+	70.3647i	0.652028	+	2.30735i
$931$	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
$936$	−14.9851	−	1.63093i	−0.489803	−	0.0533087i
$937$	−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	$-0.422209\pi$
$941$	14.8447			0.483924			0.241962	+	0.970286i	$0.422209\pi$
$942$	5.36533	+	18.9864i	0.174812	+	0.618612i
$943$			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	$0.773067\pi$
$948$	6.88459	+	2.78031i	0.223601	+	0.0903002i
$949$		−	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	$0.732991\pi$
$954$	4.26565	+	1.60931i	0.138106	+	0.0521032i
$955$	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
$960$	5.54484	+	45.6458i	0.178959	+	1.47321i
$961$	−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
$966$	−3.29041	−	11.6439i	−0.105867	−	0.374635i
$967$		−	12.3610i		−	0.397504i	−0.980050	−	0.198752i	$-0.936311\pi$
$967$		−	12.3610i		−	0.397504i	0.980050	−	0.198752i	$-0.0636889\pi$
$968$	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	$0.850589\pi$
$972$	−6.59392	−	30.4716i	−0.211500	−	0.977378i
$973$		−	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	$-0.263786\pi$
$978$	33.2066	−	9.38376i	1.06183	−	0.300060i
$979$	−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	$-0.256583\pi$
$983$	43.4132			1.38466			0.692332	+	0.721579i	$0.256583\pi$
$984$	−18.7772	+	10.9454i	−0.598596	+	0.348926i
$985$	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
$990$	11.4263	−	30.2867i	0.363152	−	0.962576i
$991$		−	41.8722i		−	1.33011i	−0.746792	−	0.665057i	$-0.768407\pi$
$991$		−	41.8722i		−	1.33011i	0.746792	−	0.665057i	$-0.231593\pi$
$992$	−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
$996$	33.3592	+	13.4720i	1.05703	+	0.426875i
$997$			37.7746i			1.19633i	0.801372	+	0.598167i	$0.204104\pi$
$997$			37.7746i			1.19633i	−0.801372	+	0.598167i	$0.795896\pi$
$998$	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.c.323.14	yes	42
3.2	odd	2		552.2.j.d.323.29	yes	42
4.3	odd	2		2208.2.j.c.47.34		42
8.3	odd	2		552.2.j.d.323.30	yes	42
8.5	even	2		2208.2.j.d.47.34		42
12.11	even	2		2208.2.j.d.47.33		42
24.5	odd	2		2208.2.j.c.47.33		42
24.11	even	2	inner	552.2.j.c.323.13	✓	42

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866210 + 1.11789i) q^{2} +(-1.39323 - 1.02904i) q^{3} +(-0.499360 - 1.93666i) q^{4} -3.31842 q^{5} +(2.35718 - 0.666110i) q^{6} +4.93974i q^{7} +(2.59752 + 1.11932i) q^{8} +(0.882155 + 2.86737i) q^{9} +O(q^{10})\)	\(q+(-0.866210 + 1.11789i) q^{2} +(-1.39323 - 1.02904i) q^{3} +(-0.499360 - 1.93666i) q^{4} -3.31842 q^{5} +(2.35718 - 0.666110i) 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} +(-1.29718 + 3.21206i) 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} +(-3.96954 - 1.49759i) 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} +(-2.46711 - 4.23242i) 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} +(-7.82212 + 2.21043i) 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} +(5.11260 - 3.14028i) 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} +(3.29041 + 11.6439i) 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} +(6.86842 + 0.908208i) 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} +(3.98938 + 6.17129i) 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} +(4.30457 - 10.6590i) 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} +(-1.53154 - 5.41968i) 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} +(-0.918090 + 8.43547i) 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} +(1.18330 + 4.18739i) 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} +(-15.8668 - 6.40771i) 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} +(13.1726 + 4.96964i) 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} +(-6.96477 + 6.89144i) q^{96} -4.06810 q^{97} +(15.0730 - 19.4525i) q^{98} +(6.59272 - 2.02827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9}+O(q^{10}) \) 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9	\( 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{14} + 8 q^{15} - 12 q^{16} + 16 q^{18} + 4 q^{19} + 2 q^{20} - 8 q^{21} + 18 q^{22} - 42 q^{23} - 24 q^{24} + 22 q^{25} - 11 q^{26} - 16 q^{27} + 6 q^{28} - 24 q^{30} + 20 q^{32} + 12 q^{33} + 14 q^{34} + 15 q^{36} + 22 q^{38} - 8 q^{39} + 4 q^{40} + 36 q^{42} + 28 q^{43} - 56 q^{44} + 8 q^{45} - 9 q^{48} - 50 q^{49} - 20 q^{50} + 28 q^{51} - q^{52} - 24 q^{53} - 24 q^{54} + 34 q^{56} - 8 q^{57} - 21 q^{58} + 18 q^{60} + 79 q^{62} + 16 q^{63} + 7 q^{64} + 16 q^{66} - 4 q^{67} - 20 q^{68} - 2 q^{69} - 8 q^{70} - 62 q^{72} + 4 q^{73} - 36 q^{74} - 6 q^{75} + 14 q^{76} - 32 q^{77} - 62 q^{78} + 52 q^{80} + 18 q^{81} + 11 q^{82} + 66 q^{84} + 28 q^{86} + 48 q^{87} - 38 q^{88} - 8 q^{91} - 4 q^{92} + 22 q^{93} + q^{94} + 16 q^{95} - 54 q^{96} + 20 q^{97} - 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^14 + 8 * q^15 - 12 * q^16 + 16 * q^18 + 4 * q^19 + 2 * q^20 - 8 * q^21 + 18 * q^22 - 42 * q^23 - 24 * q^24 + 22 * q^25 - 11 * q^26 - 16 * q^27 + 6 * q^28 - 24 * q^30 + 20 * q^32 + 12 * q^33 + 14 * q^34 + 15 * q^36 + 22 * q^38 - 8 * q^39 + 4 * q^40 + 36 * q^42 + 28 * q^43 - 56 * q^44 + 8 * q^45 - 9 * q^48 - 50 * q^49 - 20 * q^50 + 28 * q^51 - q^52 - 24 * q^53 - 24 * q^54 + 34 * q^56 - 8 * q^57 - 21 * q^58 + 18 * q^60 + 79 * q^62 + 16 * q^63 + 7 * q^64 + 16 * q^66 - 4 * q^67 - 20 * q^68 - 2 * q^69 - 8 * q^70 - 62 * q^72 + 4 * q^73 - 36 * q^74 - 6 * q^75 + 14 * q^76 - 32 * q^77 - 62 * q^78 + 52 * q^80 + 18 * q^81 + 11 * q^82 + 66 * q^84 + 28 * q^86 + 48 * q^87 - 38 * q^88 - 8 * q^91 - 4 * q^92 + 22 * q^93 + q^94 + 16 * q^95 - 54 * q^96 + 20 * q^97 - 64 * q^98

Introduction

L-functions

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