LMFDB - Embedded newform 230.2.j.a.209.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(9,230)] 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("230.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.j (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			209.9
Character	$\chi$	$=$	230.209
Dual form			230.2.j.a.219.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.540641 - 0.841254i) q^{2} +(-0.665993 + 0.0957553i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.06117 - 1.96823i) q^{5} +(-0.279508 + 0.612038i) q^{6} +(-1.62329 - 1.40659i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-2.44410 + 0.717653i) q^{9} +(-1.08207 - 1.95681i) q^{10} +(3.00982 - 1.93430i) q^{11} +(0.363766 + 0.566030i) q^{12} +(3.40020 - 2.94629i) q^{13} +(-2.06092 + 0.605141i) q^{14} +(-0.518260 + 1.41244i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-5.12683 - 2.34135i) q^{17} +(-0.717653 + 2.44410i) q^{18} +(2.28599 + 5.00562i) q^{19} +(-2.23119 - 0.147638i) q^{20} +(1.21579 + 0.781342i) q^{21} -3.57778i q^{22} +(2.94656 + 3.78388i) q^{23} +0.672842 q^{24} +(-2.74786 - 4.17724i) q^{25} +(-0.640289 - 4.45331i) q^{26} +(3.39515 - 1.55051i) q^{27} +(-0.605141 + 2.06092i) q^{28} +(3.52252 - 7.71324i) q^{29} +(0.908027 + 1.19961i) q^{30} +(-0.681945 + 4.74303i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-1.81930 + 1.57643i) q^{33} +(-4.74144 + 3.04714i) q^{34} +(-4.49108 + 1.70239i) q^{35} +(1.66812 + 1.92511i) q^{36} +(2.34825 + 7.99739i) q^{37} +(5.44690 + 0.783146i) q^{38} +(-1.98238 + 2.28779i) q^{39} +(-1.33047 + 1.79718i) q^{40} +(9.99296 + 2.93420i) q^{41} +(1.31461 - 0.600364i) q^{42} +(-3.35224 + 0.481980i) q^{43} +(-3.00982 - 1.93430i) q^{44} +(-1.18109 + 5.57210i) q^{45} +(4.77624 - 0.433085i) q^{46} +10.7053i q^{47} +(0.363766 - 0.566030i) q^{48} +(-0.339622 - 2.36212i) q^{49} +(-4.99972 + 0.0532591i) q^{50} +(3.63863 + 1.06840i) q^{51} +(-4.09253 - 1.86900i) q^{52} +(4.00429 + 3.46974i) q^{53} +(0.531182 - 3.69445i) q^{54} +(-0.613217 - 7.97663i) q^{55} +(1.40659 + 1.62329i) q^{56} +(-2.00177 - 3.11481i) q^{57} +(-4.58437 - 7.13343i) q^{58} +(1.25908 + 1.45305i) q^{59} +(1.50009 - 0.115322i) q^{60} +(0.973399 - 6.77014i) q^{61} +(3.62141 + 3.13797i) q^{62} +(4.97694 + 2.27289i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-2.19080 - 9.81887i) q^{65} +(0.342592 + 2.38278i) q^{66} +(0.464748 - 0.723162i) q^{67} +5.63616i q^{68} +(-2.32472 - 2.23789i) q^{69} +(-0.995922 + 4.69852i) q^{70} +(7.34689 + 4.72156i) q^{71} +(2.52136 - 0.362516i) q^{72} +(-5.78187 + 2.64049i) q^{73} +(7.99739 + 2.34825i) q^{74} +(2.23004 + 2.51889i) q^{75} +(3.60364 - 4.15882i) q^{76} +(-7.60660 - 1.09366i) q^{77} +(0.852857 + 2.90456i) q^{78} +(-9.61636 - 11.0979i) q^{79} +(0.792573 + 2.09089i) q^{80} +(4.31606 - 2.77376i) q^{81} +(7.87101 - 6.82027i) q^{82} +(-1.86485 - 6.35109i) q^{83} +(0.205675 - 1.43050i) q^{84} +(-10.0487 + 7.60623i) q^{85} +(-1.40689 + 3.08066i) q^{86} +(-1.60739 + 5.47427i) q^{87} +(-3.25447 + 1.48626i) q^{88} +(-0.622136 - 4.32705i) q^{89} +(4.04900 + 4.00610i) q^{90} -9.66375 q^{91} +(2.21789 - 4.25217i) q^{92} -3.22413i q^{93} +(9.00583 + 5.78770i) q^{94} +(12.2780 + 0.812439i) q^{95} +(-0.279508 - 0.612038i) q^{96} +(1.51710 - 5.16676i) q^{97} +(-2.17076 - 0.991351i) q^{98} +(-5.96816 + 6.88762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41}+ \cdots + 188 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{1}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$3$	−0.665993	+	0.0957553i	−0.384511	+	0.0552844i	−0.331860	−	0.943329i	$-0.607676\pi$
$3$	−0.665993	+	0.0957553i	−0.384511	+	0.0552844i	−0.0526511	+	0.998613i	$0.516767\pi$
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	1.06117	−	1.96823i	0.474568	−	0.880219i
$5$	1.06117	−	1.96823i	0.474568	−	0.880219i
$6$	−0.279508	+	0.612038i	−0.114109	+	0.249864i
$7$	−1.62329	−	1.40659i	−0.613548	−	0.531642i	0.291709	−	0.956507i	$-0.405776\pi$
$7$	−1.62329	−	1.40659i	−0.613548	−	0.531642i	−0.905257	+	0.424865i	$0.860322\pi$
$8$	−0.989821	−	0.142315i	−0.349955	−	0.0503159i
$9$	−2.44410	+	0.717653i	−0.814700	+	0.239218i
$10$	−1.08207	−	1.95681i	−0.342181	−	0.618799i
$11$	3.00982	−	1.93430i	0.907496	−	0.583212i	−0.00150867	−	0.999999i	$-0.500480\pi$
$11$	3.00982	−	1.93430i	0.907496	−	0.583212i	0.909004	+	0.416787i	$0.136844\pi$
$12$	0.363766	+	0.566030i	0.105010	+	0.163399i
$13$	3.40020	−	2.94629i	0.943045	−	0.817153i	−0.0402468	−	0.999190i	$-0.512814\pi$
$13$	3.40020	−	2.94629i	0.943045	−	0.817153i	0.983292	+	0.182037i	$0.0582690\pi$
$14$	−2.06092	+	0.605141i	−0.550804	+	0.161731i
$15$	−0.518260	+	1.41244i	−0.133814	+	0.364690i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−5.12683	−	2.34135i	−1.24344	−	0.567860i	−0.318482	−	0.947929i	$-0.603173\pi$
$17$	−5.12683	−	2.34135i	−1.24344	−	0.567860i	−0.924958	+	0.380069i	$0.875900\pi$
$18$	−0.717653	+	2.44410i	−0.169152	+	0.576080i
$19$	2.28599	+	5.00562i	0.524442	+	1.14837i	0.967730	+	0.251989i	$0.0810848\pi$
$19$	2.28599	+	5.00562i	0.524442	+	1.14837i	−0.443288	+	0.896379i	$0.646188\pi$
$20$	−2.23119	−	0.147638i	−0.498909	−	0.0330129i
$21$	1.21579	+	0.781342i	0.265308	+	0.170503i
$22$		−	3.57778i		−	0.762786i
$23$	2.94656	+	3.78388i	0.614401	+	0.788994i
$23$	2.94656	+	3.78388i	0.614401	+	0.788994i
$24$	0.672842			0.137343
$25$	−2.74786	−	4.17724i	−0.549571	−	0.835447i
$26$	−0.640289	−	4.45331i	−0.125571	−	0.873366i
$27$	3.39515	−	1.55051i	0.653397	−	0.298396i
$28$	−0.605141	+	2.06092i	−0.114361	+	0.389477i
$29$	3.52252	−	7.71324i	0.654115	−	1.43231i	−0.233790	−	0.972287i	$-0.575113\pi$
$29$	3.52252	−	7.71324i	0.654115	−	1.43231i	0.887905	−	0.460026i	$-0.152160\pi$
$30$	0.908027	+	1.19961i	0.165782	+	0.219018i
$31$	−0.681945	+	4.74303i	−0.122481	+	0.851874i	0.832249	+	0.554401i	$0.187053\pi$
$31$	−0.681945	+	4.74303i	−0.122481	+	0.851874i	−0.954730	+	0.297472i	$0.903856\pi$
$32$	0.281733	+	0.959493i	0.0498038	+	0.169616i
$33$	−1.81930	+	1.57643i	−0.316700	+	0.274422i
$34$	−4.74144	+	3.04714i	−0.813151	+	0.522580i
$35$	−4.49108	+	1.70239i	−0.759131	+	0.287756i
$36$	1.66812	+	1.92511i	0.278019	+	0.320851i
$37$	2.34825	+	7.99739i	0.386049	+	1.31476i	0.891936	+	0.452163i	$0.149347\pi$
$37$	2.34825	+	7.99739i	0.386049	+	1.31476i	−0.505886	+	0.862600i	$0.668835\pi$
$38$	5.44690	+	0.783146i	0.883604	+	0.127043i
$39$	−1.98238	+	2.28779i	−0.317436	+	0.366340i
$40$	−1.33047	+	1.79718i	−0.210366	+	0.284159i
$41$	9.99296	+	2.93420i	1.56064	+	0.458245i	0.944259	−	0.329204i	$-0.106780\pi$
$41$	9.99296	+	2.93420i	1.56064	+	0.458245i	0.616380	+	0.787449i	$0.288599\pi$
$42$	1.31461	−	0.600364i	0.202849	−	0.0926381i
$43$	−3.35224	+	0.481980i	−0.511212	+	0.0735012i	−0.393094	−	0.919498i	$-0.628595\pi$
$43$	−3.35224	+	0.481980i	−0.511212	+	0.0735012i	−0.118118	+	0.993000i	$0.537686\pi$
$44$	−3.00982	−	1.93430i	−0.453748	−	0.291606i
$45$	−1.18109	+	5.57210i	−0.176067	+	0.830640i
$46$	4.77624	−	0.433085i	0.704218	−	0.0638549i
$47$			10.7053i			1.56152i	0.624830	+	0.780761i	$0.285168\pi$
$47$			10.7053i			1.56152i	−0.624830	+	0.780761i	$0.714832\pi$
$48$	0.363766	−	0.566030i	0.0525050	−	0.0816994i
$49$	−0.339622	−	2.36212i	−0.0485174	−	0.337446i
$50$	−4.99972	+	0.0532591i	−0.707067	+	0.00753197i
$51$	3.63863	+	1.06840i	0.509510	+	0.149606i
$52$	−4.09253	−	1.86900i	−0.567532	−	0.259183i
$53$	4.00429	+	3.46974i	0.550031	+	0.476605i	0.884978	−	0.465632i	$-0.154173\pi$
$53$	4.00429	+	3.46974i	0.550031	+	0.476605i	−0.334947	+	0.942237i	$0.608718\pi$
$54$	0.531182	−	3.69445i	0.0722847	−	0.502751i
$55$	−0.613217	−	7.97663i	−0.0826862	−	1.07557i
$56$	1.40659	+	1.62329i	0.187964	+	0.216922i
$57$	−2.00177	−	3.11481i	−0.265141	−	0.412567i
$58$	−4.58437	−	7.13343i	−0.601958	−	0.936665i
$59$	1.25908	+	1.45305i	0.163918	+	0.189171i	0.831766	−	0.555126i	$-0.187330\pi$
$59$	1.25908	+	1.45305i	0.163918	+	0.189171i	−0.667848	+	0.744297i	$0.732785\pi$
$60$	1.50009	−	0.115322i	0.193661	−	0.0148880i
$61$	0.973399	−	6.77014i	0.124631	−	0.866828i	−0.827572	−	0.561360i	$-0.810278\pi$
$61$	0.973399	−	6.77014i	0.124631	−	0.866828i	0.952203	−	0.305467i	$-0.0988127\pi$
$62$	3.62141	+	3.13797i	0.459919	+	0.398522i
$63$	4.97694	+	2.27289i	0.627036	+	0.286358i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−2.19080	−	9.81887i	−0.271735	−	1.21788i
$66$	0.342592	+	2.38278i	0.0421701	+	0.293300i
$67$	0.464748	−	0.723162i	0.0567780	−	0.0883483i	−0.811704	−	0.584069i	$-0.801460\pi$
$67$	0.464748	−	0.723162i	0.0567780	−	0.0883483i	0.868482	+	0.495721i	$0.165096\pi$
$68$			5.63616i			0.683485i
$69$	−2.32472	−	2.23789i	−0.279863	−	0.269410i
$70$	−0.995922	+	4.69852i	−0.119035	+	0.561581i
$71$	7.34689	+	4.72156i	0.871916	+	0.560346i	0.898338	−	0.439305i	$-0.144775\pi$
$71$	7.34689	+	4.72156i	0.871916	+	0.560346i	−0.0264224	+	0.999651i	$0.508411\pi$
$72$	2.52136	−	0.362516i	0.297145	−	0.0427230i
$73$	−5.78187	+	2.64049i	−0.676717	+	0.309046i	−0.723965	−	0.689837i	$-0.757682\pi$
$73$	−5.78187	+	2.64049i	−0.676717	+	0.309046i	0.0472479	+	0.998883i	$0.484955\pi$
$74$	7.99739	+	2.34825i	0.929678	+	0.272978i
$75$	2.23004	+	2.51889i	0.257503	+	0.290856i
$76$	3.60364	−	4.15882i	0.413366	−	0.477050i
$77$	−7.60660	−	1.09366i	−0.866852	−	0.124634i
$78$	0.852857	+	2.90456i	0.0965670	+	0.328877i
$79$	−9.61636	−	11.0979i	−1.08192	−	1.24861i	−0.966876	−	0.255248i	$-0.917843\pi$
$79$	−9.61636	−	11.0979i	−1.08192	−	1.24861i	−0.115049	−	0.993360i	$-0.536703\pi$
$80$	0.792573	+	2.09089i	0.0886124	+	0.233769i
$81$	4.31606	−	2.77376i	0.479562	−	0.308196i
$82$	7.87101	−	6.82027i	0.869208	−	0.753173i
$83$	−1.86485	−	6.35109i	−0.204694	−	0.697123i	−0.996289	−	0.0860767i	$-0.972567\pi$
$83$	−1.86485	−	6.35109i	−0.204694	−	0.697123i	0.791595	−	0.611047i	$-0.209251\pi$
$84$	0.205675	−	1.43050i	0.0224410	−	0.156081i
$85$	−10.0487	+	7.60623i	−1.08994	+	0.825011i
$86$	−1.40689	+	3.08066i	−0.151709	+	0.332196i
$87$	−1.60739	+	5.47427i	−0.172330	+	0.586903i
$88$	−3.25447	+	1.48626i	−0.346927	+	0.158436i
$89$	−0.622136	−	4.32705i	−0.0659463	−	0.458667i	−0.995861	−	0.0908909i	$-0.971029\pi$
$89$	−0.622136	−	4.32705i	−0.0659463	−	0.458667i	0.929915	−	0.367776i	$-0.119881\pi$
$90$	4.04900	+	4.00610i	0.426802	+	0.422280i
$91$	−9.66375			−1.01304
$92$	2.21789	−	4.25217i	0.231231	−	0.443319i
$93$		−	3.22413i		−	0.334326i
$94$	9.00583	+	5.78770i	0.928881	+	0.596955i
$95$	12.2780	+	0.812439i	1.25970	+	0.0833545i
$96$	−0.279508	−	0.612038i	−0.0285272	−	0.0624659i
$97$	1.51710	−	5.16676i	0.154038	−	0.524605i	−0.845924	−	0.533303i	$-0.820951\pi$
$97$	1.51710	−	5.16676i	0.154038	−	0.524605i	0.999962	+	0.00869816i	$0.00276875\pi$
$98$	−2.17076	−	0.991351i	−0.219279	−	0.100142i
$99$	−5.96816	+	6.88762i	−0.599822	+	0.692232i
$100$	−2.65825	+	4.23482i	−0.265825	+	0.423482i
$101$	−12.2869	+	3.60777i	−1.22260	+	0.358987i	−0.828451	−	0.560061i	$-0.810778\pi$
$101$	−12.2869	+	3.60777i	−1.22260	+	0.358987i	−0.394146	+	0.919048i	$0.628959\pi$
$102$	2.86599	−	2.48339i	0.283775	−	0.245892i
$103$	−7.70414	−	11.9879i	−0.759112	−	1.18120i	−0.978637	−	0.205594i	$-0.934087\pi$
$103$	−7.70414	−	11.9879i	−0.759112	−	1.18120i	0.219526	−	0.975607i	$-0.429549\pi$
$104$	−3.78489	+	2.43240i	−0.371139	+	0.238516i
$105$	2.82802	−	1.56382i	0.275986	−	0.152614i
$106$	5.08381	−	1.49274i	0.493783	−	0.144988i
$107$	3.89393	+	0.559862i	0.376440	+	0.0541239i	0.327938	−	0.944699i	$-0.393646\pi$
$107$	3.89393	+	0.559862i	0.376440	+	0.0541239i	0.0485019	+	0.998823i	$0.484555\pi$
$108$	−2.82079	−	2.44423i	−0.271431	−	0.235196i
$109$	−4.07802	+	8.92962i	−0.390604	+	0.855303i	0.607534	+	0.794294i	$0.292159\pi$
$109$	−4.07802	+	8.92962i	−0.390604	+	0.855303i	−0.998137	+	0.0610086i	$0.980568\pi$
$110$	−7.04190	−	3.79662i	−0.671419	−	0.361994i
$111$	−2.32971	−	5.10135i	−0.221126	−	0.484199i
$112$	2.12606	−	0.305682i	0.200894	−	0.0288842i
$113$	2.59243	−	4.03389i	0.243875	−	0.379477i	−0.697640	−	0.716449i	$-0.745766\pi$
$113$	2.59243	−	4.03389i	0.243875	−	0.379477i	0.941515	+	0.336972i	$0.109403\pi$
$114$	−3.70259			−0.346779
$115$	10.5743	−	1.78419i	0.986062	−	0.166376i
$116$	−8.47952			−0.787304
$117$	−6.19601	+	9.64119i	−0.572822	+	0.891328i
$118$	1.90309	−	0.273624i	0.175194	−	0.0251891i
$119$	5.02904	+	11.0121i	0.461011	+	1.00947i
$120$	0.713996	−	1.32431i	0.0651786	−	0.120892i
$121$	0.747967	−	1.63782i	0.0679970	−	0.148893i
$122$	−5.16914	−	4.47909i	−0.467992	−	0.405518i
$123$	−6.93621	−	0.997276i	−0.625417	−	0.0899214i
$124$	4.59770	−	1.35001i	0.412886	−	0.121234i
$125$	−11.1377	+	0.975672i	−0.996185	+	0.0872667i
$126$	4.60282	−	2.95805i	0.410052	−	0.263524i
$127$	−1.14551	−	1.78245i	−0.101648	−	0.158167i	0.786704	−	0.617330i	$-0.211786\pi$
$127$	−1.14551	−	1.78245i	−0.101648	−	0.158167i	−0.888352	+	0.459163i	$0.848149\pi$
$128$	0.755750	−	0.654861i	0.0667995	−	0.0578821i
$129$	2.18642	−	0.641990i	0.192503	−	0.0565241i
$130$	−9.44459	−	3.46546i	−0.828345	−	0.303941i
$131$	−4.29884	+	4.96113i	−0.375591	+	0.433456i	−0.911803	−	0.410628i	$-0.865309\pi$
$131$	−4.29884	+	4.96113i	−0.375591	+	0.433456i	0.536212	+	0.844084i	$0.319855\pi$
$132$	2.18974	+	1.00002i	0.190592	+	0.0870406i
$133$	3.33004	−	11.3411i	0.288751	−	0.983395i
$134$	−0.357101	−	0.781941i	−0.0308488	−	0.0675494i
$135$	0.551051	−	8.32779i	0.0474269	−	0.716742i
$136$	4.74144	+	3.04714i	0.406575	+	0.261290i
$137$			6.32163i			0.540093i	0.962847	+	0.270047i	$0.0870391\pi$
$137$			6.32163i			0.540093i	−0.962847	+	0.270047i	$0.912961\pi$
$138$	−3.13947	+	0.745782i	−0.267249	+	0.0634852i
$139$	−11.5195			−0.977069			−0.488534	−	0.872545i	$-0.662468\pi$
$139$	−11.5195			−0.977069			−0.488534	+	0.872545i	$0.662468\pi$
$140$	3.41421	+	3.37803i	0.288553	+	0.285496i
$141$	−1.02509	−	7.12962i	−0.0863277	−	0.600423i
$142$	7.94406	−	3.62793i	0.666651	−	0.304449i
$143$	4.53500	−	15.4448i	0.379236	−	1.29156i
$144$	1.05818	−	2.31709i	0.0881817	−	0.193091i
$145$	−11.4435	−	15.1182i	−0.950327	−	1.25549i
$146$	−0.904592	+	6.29158i	−0.0748646	+	0.520695i
$147$	0.452371	+	1.54063i	0.0373109	+	0.127069i
$148$	6.29918	−	5.45827i	0.517790	−	0.448667i
$149$	11.1553	−	7.16911i	0.913882	−	0.587316i	0.00300539	−	0.999995i	$-0.499043\pi$
$149$	11.1553	−	7.16911i	0.913882	−	0.587316i	0.910876	+	0.412679i	$0.135407\pi$
$150$	3.32468	−	0.514220i	0.271459	−	0.0419859i
$151$	11.3340	+	13.0801i	0.922344	+	1.06444i	0.997734	+	0.0672881i	$0.0214346\pi$
$151$	11.3340	+	13.0801i	0.922344	+	1.06444i	−0.0753891	+	0.997154i	$0.524020\pi$
$152$	−1.55035	−	5.28000i	−0.125750	−	0.428265i
$153$	14.2108	+	2.04320i	1.14887	+	0.165183i
$154$	−5.03248	+	5.80780i	−0.405529	+	0.468006i
$155$	8.61172	+	6.37537i	0.691710	+	0.512082i
$156$	2.90456	+	0.852857i	0.232551	+	0.0682832i
$157$	−2.37044	+	1.08254i	−0.189182	+	0.0863965i	−0.507754	−	0.861502i	$-0.669524\pi$
$157$	−2.37044	+	1.08254i	−0.189182	+	0.0863965i	0.318572	+	0.947899i	$0.396797\pi$
$158$	−14.5351	+	2.08983i	−1.15635	+	0.166258i
$159$	−2.99907	−	1.92739i	−0.237842	−	0.152852i
$160$	2.18747	+	0.463667i	0.172934	+	0.0366561i
$161$	0.539242	−	10.2870i	0.0424982	−	0.810727i
$162$		−	5.13051i		−	0.403091i
$163$	−0.103171	+	0.160537i	−0.00808097	+	0.0125742i	−0.845271	−	0.534339i	$-0.820561\pi$
$163$	−0.103171	+	0.160537i	−0.00808097	+	0.0125742i	0.837190	+	0.546913i	$0.184197\pi$
$164$	−1.48219	−	10.3088i	−0.115739	−	0.804984i
$165$	1.17220	+	5.25366i	0.0912559	+	0.408997i
$166$	−6.35109	−	1.86485i	−0.492941	−	0.144740i
$167$	3.82072	+	1.74487i	0.295657	+	0.135022i	0.557721	−	0.830029i	$-0.311676\pi$
$167$	3.82072	+	1.74487i	0.295657	+	0.135022i	−0.262064	+	0.965050i	$0.584403\pi$
$168$	−1.09222	−	0.946414i	−0.0842666	−	0.0730174i
$169$	1.03064	−	7.16823i	0.0792797	−	0.551403i
$170$	0.966015	+	12.5658i	0.0740900	+	0.963750i
$171$	−9.17950	−	10.5937i	−0.701974	−	0.810121i
$172$	1.83100	+	2.84909i	0.139612	+	0.217241i
$173$	6.93676	+	10.7938i	0.527392	+	0.820638i	0.998098	−	0.0616525i	$-0.0196371\pi$
$173$	6.93676	+	10.7938i	0.527392	+	0.820638i	−0.470706	+	0.882290i	$0.656001\pi$
$174$	3.73622	+	4.31183i	0.283242	+	0.326879i
$175$	−1.41509	+	10.6460i	−0.106971	+	0.804762i
$176$	−0.509172	+	3.54137i	−0.0383803	+	0.266941i
$177$	−0.977674	−	0.847159i	−0.0734865	−	0.0636764i
$178$	−3.97650	−	1.81601i	−0.298051	−	0.136115i
$179$	18.1063	+	5.31648i	1.35332	+	0.397372i	0.876405	−	0.481575i	$-0.159935\pi$
$179$	18.1063	+	5.31648i	1.35332	+	0.397372i	0.476920	+	0.878947i	$0.341753\pi$
$180$	5.55920	−	1.24038i	0.414359	−	0.0924522i
$181$	−0.448621	−	3.12022i	−0.0333457	−	0.231924i	0.966332	−	0.257297i	$-0.0828319\pi$
$181$	−0.448621	−	3.12022i	−0.0333457	−	0.231924i	−0.999678	+	0.0253726i	$0.991923\pi$
$182$	−5.22462	+	8.12966i	−0.387274	+	0.602611i
$183$			4.60207i			0.340195i
$184$	−2.37807	−	4.16471i	−0.175314	−	0.307026i
$185$	18.2326	+	3.86467i	1.34049	+	0.284136i
$186$	−2.71231	−	1.74309i	−0.198876	−	0.127810i
$187$	−19.9597	+	2.86977i	−1.45960	+	0.209859i
$188$	9.73784	−	4.44712i	0.710205	−	0.324340i
$189$	−7.69227	−	2.25865i	−0.559530	−	0.164293i
$190$	7.32147	−	9.88970i	0.531155	−	0.717474i
$191$	0.0925216	−	0.106776i	0.00669462	−	0.00772601i	−0.752392	−	0.658715i	$-0.771100\pi$
$191$	0.0925216	−	0.106776i	0.00669462	−	0.00772601i	0.759087	+	0.650989i	$0.225646\pi$
$192$	−0.665993	−	0.0957553i	−0.0480639	−	0.00691055i
$193$	4.15927	+	14.1652i	0.299391	+	1.01963i	0.962539	+	0.271144i	$0.0874019\pi$
$193$	4.15927	+	14.1652i	0.299391	+	1.01963i	−0.663148	+	0.748489i	$0.730780\pi$
$194$	−3.52635	−	4.06962i	−0.253177	−	0.292182i
$195$	2.39926	+	6.32952i	0.171815	+	0.453266i
$196$	−2.00758	+	1.29019i	−0.143398	+	0.0921565i
$197$	1.53751	−	1.33226i	0.109543	−	0.0949194i	−0.598367	−	0.801222i	$-0.704184\pi$
$197$	1.53751	−	1.33226i	0.109543	−	0.0949194i	0.707910	+	0.706303i	$0.249638\pi$
$198$	2.56761	+	8.74446i	0.182472	+	0.621442i
$199$	−1.74376	+	12.1281i	−0.123612	+	0.859740i	0.829798	+	0.558063i	$0.188455\pi$
$199$	−1.74376	+	12.1281i	−0.123612	+	0.859740i	−0.953410	+	0.301677i	$0.902454\pi$
$200$	2.12540	+	4.52578i	0.150289	+	0.320021i
$201$	−0.240272	+	0.526123i	−0.0169475	+	0.0371098i
$202$	−3.60777	+	12.2869i	−0.253842	+	0.864507i
$203$	−16.5675	+	7.56611i	−1.16281	+	0.531037i
$204$	−0.539693	−	3.75365i	−0.0377860	−	0.262808i
$205$	16.3794	−	16.5548i	1.14398	−	1.15624i
$206$	−14.2500			−0.992846
$207$	−9.91721	−	7.13358i	−0.689294	−	0.495818i
$208$			4.49911i			0.311957i
$209$	16.5628	+	10.6443i	1.14567	+	0.736278i
$210$	0.213369	−	3.22455i	0.0147238	−	0.222515i
$211$	0.488377	+	1.06940i	0.0336212	+	0.0736202i	0.925698	−	0.378265i	$-0.123479\pi$
$211$	0.488377	+	1.06940i	0.0336212	+	0.0736202i	−0.892076	+	0.451885i	$0.850752\pi$
$212$	1.49274	−	5.08381i	0.102522	−	0.349158i
$213$	−5.34509	−	2.44102i	−0.366240	−	0.167256i
$214$	2.57620	−	2.97310i	0.176106	−	0.203237i
$215$	−2.60864	+	7.10944i	−0.177908	+	0.484860i
$216$	−3.58125	+	1.05155i	−0.243673	+	0.0715490i
$217$	7.77851	−	6.74012i	0.528040	−	0.457549i
$218$	5.30733	+	8.25837i	0.359458	+	0.559327i
$219$	3.59784	−	2.31219i	0.243120	−	0.156244i
$220$	−7.00106	+	3.87141i	−0.472011	+	0.261011i
$221$	−24.3305	+	7.14409i	−1.63665	+	0.480563i
$222$	−5.55106	−	0.798122i	−0.372563	−	0.0535665i
$223$	−4.77158	−	4.13460i	−0.319529	−	0.276873i	0.480296	−	0.877106i	$-0.340529\pi$
$223$	−4.77158	−	4.13460i	−0.319529	−	0.276873i	−0.799825	+	0.600233i	$0.795075\pi$
$224$	0.892281	−	1.95382i	0.0596180	−	0.130545i
$225$	9.71384	+	8.23758i	0.647589	+	0.549172i
$226$	−1.99196	−	4.36178i	−0.132503	−	0.290141i
$227$	14.0217	−	2.01602i	0.930653	−	0.133808i	0.339718	−	0.940527i	$-0.389668\pi$
$227$	14.0217	−	2.01602i	0.930653	−	0.133808i	0.590934	+	0.806720i	$0.298759\pi$
$228$	−2.00177	+	3.11481i	−0.132570	+	0.206284i
$229$	−19.7975			−1.30826			−0.654129	−	0.756383i	$-0.726964\pi$
$229$	−19.7975			−1.30826			−0.654129	+	0.756383i	$0.726964\pi$
$230$	4.21597	−	9.86031i	0.277993	−	0.650169i
$231$	5.17066			0.340205
$232$	−4.58437	+	7.13343i	−0.300979	+	0.468332i
$233$	3.18877	−	0.458476i	0.208903	−	0.0300358i	−0.0370686	−	0.999313i	$-0.511802\pi$
$233$	3.18877	−	0.458476i	0.208903	−	0.0300358i	0.245972	+	0.969277i	$0.420893\pi$
$234$	4.76086	+	10.4248i	0.311227	+	0.681493i
$235$	21.0704	+	11.3600i	1.37448	+	0.741048i
$236$	0.798703	−	1.74892i	0.0519912	−	0.113845i
$237$	7.46711	+	6.47029i	0.485041	+	0.420290i
$238$	11.9828	+	1.72287i	0.776732	+	0.111677i
$239$	24.3595	−	7.15258i	1.57568	−	0.462662i	0.627033	−	0.778993i	$-0.284269\pi$
$239$	24.3595	−	7.15258i	1.57568	−	0.462662i	0.948649	+	0.316331i	$0.102451\pi$
$240$	−0.728062	−	1.31663i	−0.0469962	−	0.0849879i
$241$	7.58766	−	4.87629i	0.488764	−	0.314110i	−0.272944	−	0.962030i	$-0.587997\pi$
$241$	7.58766	−	4.87629i	0.488764	−	0.314110i	0.761708	+	0.647920i	$0.224361\pi$
$242$	−0.973439	−	1.51470i	−0.0625751	−	0.0973687i
$243$	−11.0712	+	9.59328i	−0.710220	+	0.615409i
$244$	−6.56270	+	1.92698i	−0.420134	+	0.123362i
$245$	−5.00959	−	1.83815i	−0.320051	−	0.117435i
$246$	−4.58896	+	5.29594i	−0.292581	+	0.337657i
$247$	22.5208	+	10.2849i	1.43297	+	0.654414i
$248$	1.35001	−	4.59770i	0.0857256	−	0.291955i
$249$	1.85013	+	4.05122i	0.117247	+	0.256735i
$250$	−5.20070	+	9.89711i	−0.328921	+	0.625948i
$251$	−10.3132	−	6.62787i	−0.650961	−	0.418347i	0.173056	−	0.984912i	$-0.444636\pi$
$251$	−10.3132	−	6.62787i	−0.650961	−	0.418347i	−0.824017	+	0.566565i	$0.808272\pi$
$252$		−	5.47138i		−	0.344665i
$253$	16.1878	+	5.68929i	1.01772	+	0.357683i
$254$	−2.11881			−0.132946
$255$	5.96405	−	6.02792i	0.373483	−	0.377483i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−22.2902	+	10.1796i	−1.39043	+	0.634986i	−0.963108	−	0.269115i	$-0.913269\pi$
$257$	−22.2902	+	10.1796i	−1.39043	+	0.634986i	−0.427318	+	0.904101i	$0.640542\pi$
$258$	0.641990	−	2.18642i	0.0399686	−	0.136120i
$259$	7.43718	−	16.2851i	0.462124	−	1.01191i
$260$	−8.02146	+	6.07172i	−0.497470	+	0.376552i
$261$	−3.07396	+	21.3799i	−0.190274	+	1.32338i
$262$	1.84944	+	6.29860i	0.114259	+	0.389129i
$263$	−12.8796	+	11.1602i	−0.794191	+	0.688170i	−0.954274	−	0.298933i	$-0.903369\pi$
$263$	−12.8796	+	11.1602i	−0.794191	+	0.688170i	0.160083	+	0.987103i	$0.448824\pi$
$264$	2.02513	−	1.30147i	0.124638	−	0.0801002i
$265$	11.0785	−	4.19940i	0.680544	−	0.257967i
$266$	−7.74036	−	8.93285i	−0.474592	−	0.547708i
$267$	0.828676	+	2.82221i	0.0507142	+	0.172717i
$268$	−0.850874	−	0.122337i	−0.0519754	−	0.00747294i
$269$	−18.8639	+	21.7701i	−1.15015	+	1.32735i	−0.213558	+	0.976930i	$0.568505\pi$
$269$	−18.8639	+	21.7701i	−1.15015	+	1.32735i	−0.936594	+	0.350416i	$0.886040\pi$
$270$	−6.70786	−	4.96591i	−0.408227	−	0.302216i
$271$	−30.8450	−	9.05690i	−1.87370	−	0.550168i	−0.997695	−	0.0678644i	$-0.978381\pi$
$271$	−30.8450	−	9.05690i	−1.87370	−	0.550168i	−0.876004	−	0.482303i	$-0.839800\pi$
$272$	5.12683	−	2.34135i	0.310860	−	0.141965i
$273$	6.43599	−	0.925356i	0.389524	−	0.0560051i
$274$	5.31809	+	3.41773i	0.321278	+	0.206473i
$275$	−16.3506	−	7.25757i	−0.985976	−	0.437648i
$276$	−1.06993	+	3.04429i	−0.0644025	+	0.183245i
$277$			5.64509i			0.339180i	0.985515	+	0.169590i	$0.0542444\pi$
$277$			5.64509i			0.339180i	−0.985515	+	0.169590i	$0.945756\pi$
$278$	−6.22790	+	9.69079i	−0.373524	+	0.581215i
$279$	−1.73711	−	12.0819i	−0.103998	−	0.723322i
$280$	4.68764	−	1.04591i	0.280140	−	0.0625053i
$281$	10.5515	+	3.09821i	0.629451	+	0.184824i	0.580871	−	0.813996i	$-0.302712\pi$
$281$	10.5515	+	3.09821i	0.629451	+	0.184824i	0.0485803	+	0.998819i	$0.484530\pi$
$282$	−6.55202	−	2.99221i	−0.390167	−	0.178183i
$283$	3.92812	+	3.40373i	0.233502	+	0.202331i	0.763751	−	0.645512i	$-0.223356\pi$
$283$	3.92812	+	3.40373i	0.233502	+	0.202331i	−0.530248	+	0.847843i	$0.677901\pi$
$284$	1.24287	−	8.64438i	0.0737510	−	0.512949i
$285$	−8.25488	+	0.634608i	−0.488977	+	0.0375910i
$286$	−10.5412	−	12.1652i	−0.623313	−	0.719341i
$287$	−12.0943	−	18.8191i	−0.713904	−	1.11086i
$288$	−1.37717	−	2.14291i	−0.0811503	−	0.126272i
$289$	9.66989	+	11.1597i	0.568817	+	0.656450i
$290$	−18.9050	+	1.45335i	−1.11014	+	0.0853439i
$291$	−0.515631	+	3.58630i	−0.0302268	+	0.210232i
$292$	4.80375	+	4.16247i	0.281118	+	0.243590i
$293$	9.44334	+	4.31263i	0.551686	+	0.251947i	0.671697	−	0.740826i	$-0.265566\pi$
$293$	9.44334	+	4.31263i	0.551686	+	0.251947i	−0.120011	+	0.992773i	$0.538293\pi$
$294$	1.54063	+	0.452371i	0.0898516	+	0.0263828i
$295$	4.19603	−	0.936223i	0.244302	−	0.0545090i
$296$	−1.18620	−	8.25018i	−0.0689463	−	0.479532i
$297$	7.21965	−	11.2340i	0.418926	−	0.651862i
$298$		−	13.2604i		−	0.768154i
$299$	21.1673	+	4.18452i	1.22414	+	0.241997i
$300$	1.36487	−	3.07490i	0.0788006	−	0.177530i
$301$	6.11963	+	3.93285i	0.352729	+	0.226685i
$302$	17.1313	−	2.46310i	0.985794	−	0.141736i
$303$	7.83756	−	3.57929i	0.450256	−	0.205625i
$304$	−5.28000	−	1.55035i	−0.302829	−	0.0889186i
$305$	−12.2923	−	9.10011i	−0.703852	−	0.521071i
$306$	9.40178	−	10.8502i	0.537464	−	0.620266i
$307$	−0.941037	−	0.135301i	−0.0537078	−	0.00772202i	0.115409	−	0.993318i	$-0.463182\pi$
$307$	−0.941037	−	0.135301i	−0.0537078	−	0.00772202i	−0.169116	+	0.985596i	$0.554091\pi$
$308$	2.16506	+	7.37353i	0.123366	+	0.420146i
$309$	6.27881	+	7.24613i	0.357189	+	0.412218i
$310$	10.0191	−	3.79786i	0.569049	−	0.215704i
$311$	−3.48282	+	2.23827i	−0.197492	+	0.126921i	−0.635650	−	0.771978i	$-0.719268\pi$
$311$	−3.48282	+	2.23827i	−0.197492	+	0.126921i	0.438157	+	0.898898i	$0.355631\pi$
$312$	2.28779	−	1.98238i	0.129521	−	0.112230i
$313$	2.67304	+	9.10353i	0.151089	+	0.514562i	0.999900	−	0.0141343i	$-0.00449923\pi$
$313$	2.67304	+	9.10353i	0.151089	+	0.514562i	−0.848811	+	0.528696i	$0.822681\pi$
$314$	−0.370863	+	2.57941i	−0.0209290	+	0.145565i
$315$	9.75494	−	7.38385i	0.549628	−	0.416033i
$316$	−6.10020	+	13.3576i	−0.343163	+	0.751422i
$317$	4.00899	−	13.6534i	0.225167	−	0.766850i	−0.766969	−	0.641685i	$-0.778236\pi$
$317$	4.00899	−	13.6534i	0.225167	−	0.766850i	0.992136	−	0.125165i	$-0.0399460\pi$
$318$	−3.24284	+	1.48096i	−0.181850	+	0.0830480i
$319$	−4.31753	−	30.0291i	−0.241735	−	1.68131i
$320$	1.57270	−	1.58954i	0.0879163	−	0.0888578i
$321$	−2.64694			−0.147738
$322$	−8.36242	−	6.01520i	−0.466019	−	0.335214i
$323$		−	31.0153i		−	1.72574i
$324$	−4.31606	−	2.77376i	−0.239781	−	0.154098i
$325$	−21.6506	−	6.10745i	−1.20096	−	0.338780i
$326$	0.0792739	+	0.173586i	0.00439058	+	0.00961402i
$327$	1.86087	−	6.33756i	0.102907	−	0.350468i
$328$	−9.47367	−	4.32648i	−0.523096	−	0.238890i
$329$	15.0579	−	17.3778i	0.830171	−	0.958068i
$330$	5.05340	+	1.85422i	0.278181	+	0.102072i
$331$	−8.51959	+	2.50158i	−0.468279	+	0.137499i	−0.507355	−	0.861737i	$-0.669377\pi$
$331$	−8.51959	+	2.50158i	−0.468279	+	0.137499i	0.0390760	+	0.999236i	$0.487559\pi$
$332$	−5.00247	+	4.33467i	−0.274546	+	0.237896i
$333$	−11.4787	−	17.8612i	−0.629029	−	0.978788i
$334$	3.53351	−	2.27085i	0.193345	−	0.124255i
$335$	−0.930174	−	1.68212i	−0.0508208	−	0.0919043i
$336$	−1.38667	+	0.407164i	−0.0756492	+	0.0222126i
$337$	−13.2132	−	1.89977i	−0.719769	−	0.103487i	−0.227310	−	0.973823i	$-0.572993\pi$
$337$	−13.2132	−	1.89977i	−0.719769	−	0.103487i	−0.492459	+	0.870335i	$0.663902\pi$
$338$	−5.47310	−	4.74247i	−0.297697	−	0.257956i
$339$	−1.34027	+	2.93478i	−0.0727935	+	0.159396i
$340$	11.0933	+	5.98090i	0.601617	+	0.324360i
$341$	7.12189	+	15.5948i	0.385672	+	0.844504i
$342$	−13.8748	+	1.99490i	−0.750263	+	0.107872i
$343$	−10.9000	+	16.9608i	−0.588547	+	0.915796i
$344$	3.38671			0.182599
$345$	−6.87159	+	2.20081i	−0.369954	+	0.118487i
$346$	12.8306			0.689778
$347$	11.7438	−	18.2737i	0.630441	−	0.980985i	−0.368245	−	0.929729i	$-0.620041\pi$
$347$	11.7438	−	18.2737i	0.630441	−	0.980985i	0.998686	−	0.0512563i	$-0.0163225\pi$
$348$	5.64730	−	0.811959i	0.302727	−	0.0435256i
$349$	1.38811	+	3.03954i	0.0743040	+	0.162703i	0.943139	−	0.332399i	$-0.107858\pi$
$349$	1.38811	+	3.03954i	0.0743040	+	0.162703i	−0.868835	+	0.495102i	$0.835131\pi$
$350$	8.19093	+	6.94611i	0.437823	+	0.371285i
$351$	6.97592	−	15.2751i	0.372347	−	0.815326i
$352$	2.70391	+	2.34295i	0.144119	+	0.124880i
$353$	18.8209	+	2.70604i	1.00174	+	0.144028i	0.623618	−	0.781729i	$-0.285662\pi$
$353$	18.8209	+	2.70604i	1.00174	+	0.144028i	0.378118	+	0.925757i	$0.376571\pi$
$354$	−1.24125	+	0.364463i	−0.0659715	+	0.0193710i
$355$	17.0894	−	9.45001i	0.907011	−	0.501555i
$356$	−3.67758	+	2.36344i	−0.194911	+	0.125262i
$357$	−4.40377	−	6.85240i	−0.233072	−	0.362668i
$358$	14.2615	−	12.3576i	0.753743	−	0.653122i
$359$	−2.06521	+	0.606402i	−0.108998	+	0.0320047i	−0.335777	−	0.941942i	$-0.608999\pi$
$359$	−2.06521	+	0.606402i	−0.108998	+	0.0320047i	0.226779	+	0.973946i	$0.427181\pi$
$360$	1.96206	−	5.34730i	0.103410	−	0.281827i
$361$	−7.38816	+	8.52639i	−0.388850	+	0.448757i
$362$	−2.86744	−	1.30952i	−0.150709	−	0.0688267i
$363$	−0.341311	+	1.16240i	−0.0179142	+	0.0610100i
$364$	4.01447	+	8.79046i	0.210415	+	0.460745i
$365$	−0.938428	+	14.1820i	−0.0491196	+	0.742322i
$366$	3.87151	+	2.48807i	0.202367	+	0.130053i
$367$			11.6141i			0.606252i	0.952951	+	0.303126i	$0.0980303\pi$
$367$			11.6141i			0.606252i	−0.952951	+	0.303126i	$0.901970\pi$
$368$	−4.78926	−	0.251052i	−0.249657	−	0.0130870i
$369$	−26.5296			−1.38107
$370$	13.1084	−	13.2488i	0.681475	−	0.688773i
$371$	−1.61964	−	11.2648i	−0.0840873	−	0.584840i
$372$	−2.93277	+	1.33935i	−0.152057	+	0.0694421i
$373$	−0.666115	+	2.26858i	−0.0344901	+	0.117463i	−0.974939	−	0.222473i	$-0.928587\pi$
$373$	−0.666115	+	2.26858i	−0.0344901	+	0.117463i	0.940449	+	0.339936i	$0.110405\pi$
$374$	−8.37683	+	18.3427i	−0.433156	+	0.948478i
$375$	7.32420	−	1.71628i	0.378220	−	0.0886285i
$376$	1.52352	−	10.5963i	0.0785693	−	0.546462i
$377$	−10.7482	−	36.6049i	−0.553559	−	1.88525i
$378$	−6.05886	+	5.25003i	−0.311634	+	0.270032i
$379$	−12.2007	+	7.84092i	−0.626708	+	0.402761i	−0.815090	−	0.579335i	$-0.803312\pi$
$379$	−12.2007	+	7.84092i	−0.626708	+	0.402761i	0.188381	+	0.982096i	$0.439676\pi$
$380$	−4.36146	−	11.5060i	−0.223738	−	0.590245i
$381$	0.933584	+	1.07741i	0.0478289	+	0.0551975i
$382$	−0.0398044	−	0.135561i	−0.00203657	−	0.00693592i
$383$	−16.3972	−	2.35757i	−0.837860	−	0.120466i	−0.289990	−	0.957030i	$-0.593652\pi$
$383$	−16.3972	−	2.35757i	−0.837860	−	0.120466i	−0.547870	+	0.836564i	$0.684561\pi$
$384$	−0.440618	+	0.508500i	−0.0224852	+	0.0259493i
$385$	−10.2244	+	13.8110i	−0.521086	+	0.703872i
$386$	14.1652	+	4.15927i	0.720989	+	0.211701i
$387$	7.84733	−	3.58375i	0.398902	−	0.182172i
$388$	−5.33007	+	0.766349i	−0.270593	+	0.0389055i
$389$	−13.0419	−	8.38153i	−0.661251	−	0.424960i	0.166511	−	0.986040i	$-0.446750\pi$
$389$	−13.0419	−	8.38153i	−0.661251	−	0.424960i	−0.827762	+	0.561079i	$0.810386\pi$
$390$	6.62187	+	1.40360i	0.335311	+	0.0710743i
$391$	−6.24716	−	26.2983i	−0.315932	−	1.32996i
$392$			2.38641i			0.120532i
$393$	2.38794	−	3.71571i	0.120456	−	0.187433i
$394$	−0.289527	−	2.01371i	−0.0145862	−	0.101449i
$395$	−32.0477	+	7.15052i	−1.61249	+	0.359782i
$396$	8.74446	+	2.56761i	0.439426	+	0.129027i
$397$	20.7499	+	9.47616i	1.04141	+	0.475595i	0.861324	−	0.508056i	$-0.169636\pi$
$397$	20.7499	+	9.47616i	1.04141	+	0.475595i	0.180084	+	0.983651i	$0.442363\pi$
$398$	9.26008	+	8.02391i	0.464166	+	0.402202i
$399$	−1.13181	+	7.87194i	−0.0566616	+	0.394090i
$400$	4.95641	+	0.658817i	0.247820	+	0.0329408i
$401$	−15.8763	−	18.3222i	−0.792824	−	0.914967i	0.205141	−	0.978732i	$-0.434235\pi$
$401$	−15.8763	−	18.3222i	−0.792824	−	0.914967i	−0.997965	+	0.0637652i	$0.979689\pi$
$402$	0.312702	+	0.486573i	0.0155961	+	0.0242681i
$403$	11.6556	+	18.1364i	0.580606	+	0.903441i
$404$	8.38593	+	9.67788i	0.417215	+	0.481492i
$405$	−0.879348	−	11.4384i	−0.0436952	−	0.568380i
$406$	−2.59204	+	18.0280i	−0.128641	+	0.894715i
$407$	22.5371	+	19.5285i	1.11712	+	0.967993i
$408$	−3.44955	−	1.57536i	−0.170778	−	0.0779917i
$409$	8.25387	+	2.42355i	0.408128	+	0.119837i	0.479351	−	0.877623i	$-0.340872\pi$
$409$	8.25387	+	2.42355i	0.408128	+	0.119837i	−0.0712233	+	0.997460i	$0.522690\pi$
$410$	−5.07141	−	22.7294i	−0.250459	−	1.12252i
$411$	−0.605330	−	4.21016i	−0.0298587	−	0.207672i
$412$	−7.70414	+	11.9879i	−0.379556	+	0.590600i
$413$		−	4.12974i		−	0.203211i
$414$	−11.3628	+	4.48618i	−0.558451	+	0.220484i
$415$	−14.4793	−	3.06911i	−0.710762	−	0.150657i
$416$	3.78489	+	2.43240i	0.185569	+	0.119258i
$417$	7.67189	−	1.10305i	0.375694	−	0.0540166i
$418$	17.9090	−	8.17878i	0.875959	−	0.400037i
$419$	−11.4519	−	3.36258i	−0.559462	−	0.164273i	−0.0102374	−	0.999948i	$-0.503259\pi$
$419$	−11.4519	−	3.36258i	−0.559462	−	0.164273i	−0.549225	+	0.835675i	$0.685077\pi$
$420$	−2.59731	−	1.92282i	−0.126736	−	0.0938239i
$421$	−4.03795	+	4.66005i	−0.196798	+	0.227117i	−0.845568	−	0.533867i	$-0.820738\pi$
$421$	−4.03795	+	4.66005i	−0.196798	+	0.227117i	0.648770	+	0.760984i	$0.275284\pi$
$422$	1.16367	+	0.167310i	0.0566465	+	0.00814454i
$423$	−7.68266	−	26.1647i	−0.373543	−	1.27217i
$424$	−3.46974	−	4.00429i	−0.168505	−	0.194465i
$425$	4.30744	+	27.8497i	0.208942	+	1.35091i
$426$	−4.94330	+	3.17686i	−0.239503	+	0.153920i
$427$	−11.1029	+	9.62076i	−0.537309	+	0.465581i
$428$	−1.10833	−	3.77462i	−0.0535730	−	0.182453i
$429$	−1.54136	+	10.7204i	−0.0744174	+	0.517584i
$430$	4.57051	+	6.03818i	0.220409	+	0.291187i
$431$	−15.2065	+	33.2976i	−0.732472	+	1.60389i	0.0630819	+	0.998008i	$0.479907\pi$
$431$	−15.2065	+	33.2976i	−0.732472	+	1.60389i	−0.795554	+	0.605882i	$0.792820\pi$
$432$	−1.05155	+	3.58125i	−0.0505928	+	0.172303i
$433$	4.22009	−	1.92725i	0.202804	−	0.0926177i	−0.311424	−	0.950271i	$-0.600806\pi$
$433$	4.22009	−	1.92725i	0.202804	−	0.0926177i	0.514228	+	0.857654i	$0.328079\pi$
$434$	−1.46477	−	10.1877i	−0.0703111	−	0.489025i
$435$	9.06890	+	8.97281i	0.434821	+	0.430213i
$436$	9.81674			0.470137
$437$	−12.2049	+	23.3993i	−0.583838	+	1.11934i
$438$		−	4.27677i		−	0.204352i
$439$	11.1991	+	7.19721i	0.534502	+	0.343504i	0.779885	−	0.625922i	$-0.215277\pi$
$439$	11.1991	+	7.19721i	0.534502	+	0.343504i	−0.245383	+	0.969426i	$0.578914\pi$
$440$	−0.528217	+	7.98271i	−0.0251818	+	0.380561i
$441$	2.52525	+	5.52953i	0.120250	+	0.263311i
$442$	−7.14409	+	24.3305i	−0.339810	+	1.15729i
$443$	36.2064	+	16.5349i	1.72022	+	0.785598i	0.995308	+	0.0967560i	$0.0308466\pi$
$443$	36.2064	+	16.5349i	1.72022	+	0.785598i	0.724911	+	0.688842i	$0.241881\pi$
$444$	−3.67255	+	4.23835i	−0.174292	+	0.201143i
$445$	−9.17682	−	3.36721i	−0.435023	−	0.159621i
$446$	−6.05796	+	1.77878i	−0.286853	+	0.0842276i
$447$	−6.74290	+	5.84276i	−0.318928	+	0.276353i
$448$	−1.16126	−	1.80695i	−0.0548642	−	0.0853704i
$449$	15.3063	−	9.83679i	0.722351	−	0.464227i	−0.127103	−	0.991890i	$-0.540568\pi$
$449$	15.3063	−	9.83679i	0.722351	−	0.464227i	0.849454	+	0.527663i	$0.176932\pi$
$450$	12.1816	−	3.71823i	0.574246	−	0.175279i
$451$	35.7527	−	10.4979i	1.68353	−	0.494328i
$452$	−4.74629	−	0.682414i	−0.223247	−	0.0320980i
$453$	−8.80083	−	7.62596i	−0.413499	−	0.358299i
$454$	5.88472	−	12.8857i	0.276184	−	0.604758i
$455$	−10.2548	+	19.0205i	−0.480754	+	0.891694i
$456$	1.53811	+	3.36799i	0.0720286	+	0.157721i
$457$	35.7105	−	5.13439i	1.67046	−	0.240177i	0.758863	−	0.651251i	$-0.225755\pi$
$457$	35.7105	−	5.13439i	1.67046	−	0.240177i	0.911602	+	0.411074i	$0.134846\pi$
$458$	−10.7033	+	16.6547i	−0.500135	+	0.778225i
$459$	−21.0367			−0.981907
$460$	−6.01569	−	8.87758i	−0.280483	−	0.413919i
$461$	−7.33582			−0.341663			−0.170832	−	0.985300i	$-0.554645\pi$
$461$	−7.33582			−0.341663			−0.170832	+	0.985300i	$0.554645\pi$
$462$	2.79547	−	4.34984i	0.130057	−	0.202373i
$463$	−31.2533	+	4.49355i	−1.45247	+	0.208833i	−0.822932	−	0.568140i	$-0.807663\pi$
$463$	−31.2533	+	4.49355i	−1.45247	+	0.208833i	−0.629534	+	0.776973i	$0.716754\pi$
$464$	3.52252	+	7.71324i	0.163529	+	0.358078i
$465$	−6.34582	−	3.42133i	−0.294280	−	0.158660i
$466$	1.33828	−	2.93043i	0.0619948	−	0.135750i
$467$	−4.83467	−	4.18927i	−0.223722	−	0.193856i	0.535787	−	0.844353i	$-0.320015\pi$
$467$	−4.83467	−	4.18927i	−0.223722	−	0.193856i	−0.759509	+	0.650497i	$0.774561\pi$
$468$	11.3438	+	1.63100i	0.524370	+	0.0753930i
$469$	−1.77162	+	0.520194i	−0.0818057	+	0.0240203i
$470$	20.9482	−	11.5838i	0.966268	−	0.534323i
$471$	1.47504	−	0.947950i	0.0679662	−	0.0436792i
$472$	−1.03947	−	1.61745i	−0.0478455	−	0.0744491i
$473$	−9.15736	+	7.93490i	−0.421056	+	0.364847i
$474$	9.48017	−	2.78363i	0.435439	−	0.127856i
$475$	14.6281	−	23.3039i	0.671183	−	1.06925i
$476$	7.92779	−	9.14915i	0.363370	−	0.419351i
$477$	−12.2770	−	5.60670i	−0.562123	−	0.256713i
$478$	7.15258	−	24.3595i	0.327151	−	1.11418i
$479$	−7.91448	−	17.3303i	−0.361622	−	0.791842i	−0.999760	−	0.0219195i	$-0.993022\pi$
$479$	−7.91448	−	17.3303i	−0.361622	−	0.791842i	0.638138	−	0.769922i	$-0.279705\pi$
$480$	−1.50124	−	0.0993370i	−0.0685218	−	0.00453409i
$481$	31.5471	+	20.2741i	1.43842	+	0.924419i
$482$		−	9.01947i		−	0.410826i
$483$	0.625901	+	6.90269i	0.0284795	+	0.314083i
$484$	−1.80053			−0.0818422
$485$	−8.55948	−	8.46878i	−0.388666	−	0.384548i
$486$	2.08482	+	14.5002i	0.0945694	+	0.657744i
$487$	11.3435	−	5.18039i	0.514022	−	0.234746i	−0.141478	−	0.989941i	$-0.545185\pi$
$487$	11.3435	−	5.18039i	0.514022	−	0.234746i	0.655500	+	0.755195i	$0.272458\pi$
$488$	−1.92698	+	6.56270i	−0.0872304	+	0.297079i
$489$	0.0533388	−	0.116796i	0.00241206	−	0.00528168i
$490$	−4.25474	+	3.22056i	−0.192209	+	0.145490i
$491$	1.90943	−	13.2804i	0.0861715	−	0.599336i	−0.900284	−	0.435304i	$-0.856641\pi$
$491$	1.90943	−	13.2804i	0.0861715	−	0.599336i	0.986455	−	0.164032i	$-0.0524500\pi$
$492$	1.97425	+	6.72368i	0.0890061	+	0.303127i
$493$	−36.1187	+	31.2971i	−1.62671	+	1.40955i
$494$	20.8279	−	13.3853i	0.937092	−	0.602232i
$495$	7.22322	+	19.0556i	0.324659	+	0.856486i
$496$	−3.13797	−	3.62141i	−0.140899	−	0.162606i
$497$	−5.28486	−	17.9986i	−0.237058	−	0.807346i
$498$	4.40835	+	0.633826i	0.197543	+	0.0284024i
$499$	2.03359	−	2.34689i	0.0910360	−	0.105061i	−0.708404	−	0.705807i	$-0.750584\pi$
$499$	2.03359	−	2.34689i	0.0910360	−	0.105061i	0.799440	+	0.600746i	$0.205130\pi$
$500$	5.51426	+	9.72589i	0.246605	+	0.434955i
$501$	−2.71166	−	0.796214i	−0.121148	−	0.0355722i
$502$	−11.1514	+	5.09269i	−0.497713	+	0.227298i
$503$	−29.2657	+	4.20777i	−1.30489	+	0.187615i	−0.759468	−	0.650544i	$-0.774541\pi$
$503$	−29.2657	+	4.20777i	−1.30489	+	0.187615i	−0.545425	+	0.838160i	$0.683632\pi$
$504$	−4.60282	−	2.95805i	−0.205026	−	0.131762i
$505$	−5.93756	+	28.0120i	−0.264218	+	1.24652i
$506$	13.5379	−	10.5422i	0.601833	−	0.468656i
$507$			4.87268i			0.216403i
$508$	−1.14551	+	1.78245i	−0.0508240	+	0.0790836i
$509$	2.13588	+	14.8554i	0.0946713	+	0.658453i	0.980800	+	0.195015i	$0.0624755\pi$
$509$	2.13588	+	14.8554i	0.0946713	+	0.658453i	−0.886129	+	0.463439i	$0.846615\pi$
$510$	−1.84660	−	8.27621i	−0.0817688	−	0.366477i
$511$	13.0998	+	3.84644i	0.579500	+	0.170157i
$512$	−0.909632	−	0.415415i	−0.0402004	−	0.0183589i
$513$	15.5226	+	13.4504i	0.685338	+	0.593849i
$514$	−3.48738	+	24.2552i	−0.153822	+	1.06985i
$515$	−31.7703	+	2.44239i	−1.39997	+	0.107625i
$516$	−1.49225	−	1.72214i	−0.0656924	−	0.0758131i
$517$	20.7071	+	32.2209i	0.910698	+	1.41707i
$518$	−9.67909	−	15.0610i	−0.425275	−	0.661741i
$519$	−5.65340	−	6.52437i	−0.248157	−	0.286388i
$520$	0.771128	+	10.0307i	0.0338162	+	0.439876i
$521$	3.40203	−	23.6616i	0.149045	−	1.03663i	−0.768741	−	0.639560i	$-0.779117\pi$
$521$	3.40203	−	23.6616i	0.149045	−	1.03663i	0.917787	−	0.397074i	$-0.129974\pi$
$522$	16.3240	+	14.1448i	0.714482	+	0.619102i
$523$	−29.5151	−	13.4791i	−1.29060	−	0.589399i	−0.352518	−	0.935805i	$-0.614675\pi$
$523$	−29.5151	−	13.4791i	−1.29060	−	0.589399i	−0.938085	+	0.346406i	$0.887402\pi$
$524$	6.29860	+	1.84944i	0.275156	+	0.0807930i
$525$	−0.0769708	−	7.22566i	−0.00335928	−	0.315354i
$526$	2.42535	+	16.8687i	0.105750	+	0.735510i
$527$	14.6013	−	22.7201i	0.636043	−	0.989702i
$528$		−	2.40728i		−	0.104763i
$529$	−5.63553	+	22.2989i	−0.245023	+	0.969517i
$530$	2.45671	−	11.5902i	0.106713	−	0.503444i
$531$	−4.12010	−	2.64783i	−0.178797	−	0.114906i
$532$	−11.6995	+	1.68214i	−0.507239	+	0.0729300i
$533$	42.6230	−	19.4653i	1.84621	−	0.843135i
$534$	2.82221	+	0.828676i	0.122129	+	0.0358603i
$535$	5.23404	−	7.07003i	0.226287	−	0.305664i
$536$	−0.562934	+	0.649660i	−0.0243150	+	0.0280611i
$537$	−12.5677	−	1.80697i	−0.542337	−	0.0779763i
$538$	8.11558	+	27.6391i	0.349887	+	1.19161i
$539$	−5.59124	−	6.45263i	−0.240832	−	0.277935i
$540$	−7.80413	+	2.95823i	−0.335836	+	0.127302i
$541$	−4.61180	+	2.96382i	−0.198277	+	0.127425i	−0.636012	−	0.771679i	$-0.719417\pi$
$541$	−4.61180	+	2.96382i	−0.198277	+	0.127425i	0.437735	+	0.899104i	$0.355781\pi$
$542$	−24.2952	+	21.0519i	−1.04357	+	0.904257i
$543$	0.597556	+	2.03509i	0.0256436	+	0.0873341i
$544$	0.802110	−	5.57880i	0.0343902	−	0.239189i
$545$	13.2481	+	17.5023i	0.567486	+	0.749716i
$546$	2.70110	−	5.91458i	0.115596	−	0.253121i
$547$	2.66577	−	9.07877i	0.113980	−	0.388180i	−0.882667	−	0.469998i	$-0.844254\pi$
$547$	2.66577	−	9.07877i	0.113980	−	0.388180i	0.996647	+	0.0818182i	$0.0260727\pi$
$548$	5.75036	−	2.62610i	0.245643	−	0.112181i
$549$	2.47952	+	17.2455i	0.105824	+	0.736019i
$550$	−14.9452	+	9.83123i	−0.637267	+	0.419205i
$551$	46.6620			1.98787
$552$	1.98257	+	2.54595i	0.0843838	+	0.108363i
$553$			31.5414i			1.34128i
$554$	4.74895	+	3.05196i	0.201763	+	0.129666i
$555$	−12.5128	−	0.827976i	−0.531140	−	0.0351456i
$556$	4.78536	+	10.4785i	0.202945	+	0.444386i
$557$	−2.65307	+	9.03551i	−0.112414	+	0.382847i	−0.996411	−	0.0846454i	$-0.973024\pi$
$557$	−2.65307	+	9.03551i	−0.112414	+	0.382847i	0.883997	+	0.467492i	$0.154842\pi$
$558$	−11.1031	−	5.07059i	−0.470030	−	0.214655i
$559$	−9.97823	+	11.5155i	−0.422034	+	0.487053i
$560$	1.65445	−	4.50896i	0.0699134	−	0.190538i
$561$	13.0182	−	3.82250i	0.549630	−	0.161386i
$562$	8.31096	−	7.20149i	0.350577	−	0.303777i
$563$	−20.3569	−	31.6759i	−0.857939	−	1.33498i	−0.940990	−	0.338434i	$-0.890103\pi$
$563$	−20.3569	−	31.6759i	−0.857939	−	1.33498i	0.0830510	−	0.996545i	$-0.473534\pi$
$564$	−6.05950	+	3.89420i	−0.255151	+	0.163976i
$565$	−5.18864	−	9.38312i	−0.218288	−	0.394751i
$566$	4.98710	−	1.46435i	0.209624	−	0.0615511i
$567$	−10.9078	−	1.56830i	−0.458084	−	0.0658626i
$568$	−6.60016	−	5.71907i	−0.276937	−	0.239967i
$569$	13.1920	−	28.8864i	0.553037	−	1.21098i	−0.402313	−	0.915502i	$-0.631794\pi$
$569$	13.1920	−	28.8864i	0.553037	−	1.21098i	0.955349	−	0.295479i	$-0.0954792\pi$
$570$	−3.92906	+	7.28754i	−0.164570	+	0.305242i
$571$	−9.00512	−	19.7185i	−0.376853	−	0.825192i	−0.999102	−	0.0423730i	$-0.986508\pi$
$571$	−9.00512	−	19.7185i	−0.376853	−	0.825192i	0.622249	−	0.782819i	$-0.286219\pi$
$572$	−15.9330	+	2.29082i	−0.666191	+	0.0957838i
$573$	−0.0513944	+	0.0799712i	−0.00214703	+	0.00334085i
$574$	−22.3703			−0.933719
$575$	7.70944	−	22.7060i	0.321506	−	0.946908i
$576$	−2.54728			−0.106137
$577$	12.5493	−	19.5270i	0.522433	−	0.812921i	−0.475328	−	0.879809i	$-0.657670\pi$
$577$	12.5493	−	19.5270i	0.522433	−	0.812921i	0.997761	+	0.0668874i	$0.0213068\pi$
$578$	14.6160	−	2.10147i	0.607947	−	0.0874096i
$579$	−4.12644	−	9.03564i	−0.171489	−	0.375508i
$580$	−8.99817	+	16.6896i	−0.373629	+	0.693000i
$581$	−5.90620	+	12.9328i	−0.245031	+	0.536542i
$582$	2.73821	+	2.37267i	0.113503	+	0.0983505i
$583$	18.7637	+	2.69781i	0.777113	+	0.111732i
$584$	6.09880	−	1.79077i	0.252370	−	0.0741026i
$585$	12.4011	+	22.4261i	0.512721	+	0.927204i
$586$	8.73347	−	5.61266i	0.360776	−	0.231857i
$587$	9.48409	+	14.7575i	0.391450	+	0.609109i	0.979915	−	0.199414i	$-0.0639039\pi$
$587$	9.48409	+	14.7575i	0.391450	+	0.609109i	−0.588465	+	0.808523i	$0.700268\pi$
$588$	1.21349	−	1.05149i	0.0500434	−	0.0433629i
$589$	−25.3008	+	7.42897i	−1.04250	+	0.306105i
$590$	1.48094	−	4.03608i	0.0609695	−	0.166163i
$591$	−0.896398	+	1.03450i	−0.0368729	+	0.0425536i
$592$	−7.58180	−	3.46249i	−0.311610	−	0.142307i
$593$	8.88549	−	30.2612i	0.364883	−	1.24268i	−0.548698	−	0.836021i	$-0.684876\pi$
$593$	8.88549	−	30.2612i	0.364883	−	1.24268i	0.913581	−	0.406657i	$-0.133306\pi$
$594$	−5.54740	−	12.1471i	−0.227613	−	0.498402i
$595$	27.0109	+	1.78732i	1.10734	+	0.0732728i
$596$	−11.1553	−	7.16911i	−0.456941	−	0.293658i
$597$		−	8.24422i		−	0.337414i
$598$	14.9642	−	15.5447i	0.611930	−	0.635672i
$599$	27.0065			1.10345			0.551727	−	0.834025i	$-0.313969\pi$
$599$	27.0065			1.10345			0.551727	+	0.834025i	$0.313969\pi$
$600$	−1.84887	−	2.81062i	−0.0754798	−	0.114743i
$601$	1.94657	+	13.5387i	0.0794022	+	0.552254i	0.990227	+	0.139462i	$0.0445373\pi$
$601$	1.94657	+	13.5387i	0.0794022	+	0.552254i	−0.910825	+	0.412792i	$0.864554\pi$
$602$	6.61704	−	3.02190i	0.269690	−	0.123163i
$603$	−0.616912	+	2.10101i	−0.0251226	+	0.0855597i
$604$	7.18977	−	15.7434i	0.292547	−	0.640590i
$605$	−2.42989	−	3.21017i	−0.0987889	−	0.130512i
$606$	1.22621	−	8.52848i	0.0498114	−	0.346446i
$607$	0.196632	+	0.669666i	0.00798103	+	0.0271809i	0.963387	−	0.268114i	$-0.0864003\pi$
$607$	0.196632	+	0.669666i	0.00798103	+	0.0271809i	−0.955406	+	0.295295i	$0.904582\pi$
$608$	−4.15882	+	3.60364i	−0.168663	+	0.146147i
$609$	10.3093	−	6.62540i	0.417755	−	0.268475i
$610$	−14.3012	+	5.42101i	−0.579038	+	0.219490i
$611$	31.5407	+	36.4000i	1.27600	+	1.47258i
$612$	−4.04481	−	13.7754i	−0.163502	−	0.556836i
$613$	38.6183	+	5.55248i	1.55978	+	0.224262i	0.867526	−	0.497392i	$-0.165709\pi$
$613$	38.6183	+	5.55248i	1.55978	+	0.224262i	0.692254	+	0.721654i	$0.256618\pi$
$614$	−0.622585	+	0.718502i	−0.0251255	+	0.0289964i
$615$	−9.32334	+	12.5938i	−0.375953	+	0.507830i
$616$	7.37353	+	2.16506i	0.297088	+	0.0872329i
$617$	−17.4707	+	7.97858i	−0.703342	+	0.321206i	−0.734785	−	0.678300i	$-0.762717\pi$
$617$	−17.4707	+	7.97858i	−0.703342	+	0.321206i	0.0314429	+	0.999506i	$0.489990\pi$
$618$	9.49041	−	1.36452i	0.381760	−	0.0548888i
$619$	−12.2502	−	7.87271i	−0.492376	−	0.316431i	0.270784	−	0.962640i	$-0.412717\pi$
$619$	−12.2502	−	7.87271i	−0.492376	−	0.316431i	−0.763160	+	0.646209i	$0.776353\pi$
$620$	2.22180	−	10.4819i	0.0892297	−	0.420964i
$621$	15.8710	+	8.27816i	0.636881	+	0.332191i
$622$			4.14003i			0.166000i
$623$	−5.07649	+	7.89917i	−0.203385	+	0.316474i
$624$	−0.430813	−	2.99637i	−0.0172463	−	0.119951i
$625$	−9.89858	+	22.9569i	−0.395943	+	0.918275i
$626$	9.10353	+	2.67304i	0.363850	+	0.106836i
$627$	−12.0499	−	5.50302i	−0.481228	−	0.219770i
$628$	1.96943	+	1.70652i	0.0785890	+	0.0680978i
$629$	6.68560	−	46.4993i	0.266572	−	1.85405i
$630$	−0.937772	−	12.1984i	−0.0373617	−	0.485995i
$631$	24.8801	+	28.7132i	0.990463	+	1.14306i	0.989715	+	0.143056i	$0.0456928\pi$
$631$	24.8801	+	28.7132i	0.990463	+	1.14306i	0.000748389		1.00000i	$0.499762\pi$
$632$	7.93909	+	12.3535i	0.315800	+	0.491394i
$633$	−0.427656	−	0.665445i	−0.0169978	−	0.0264491i
$634$	−9.31852	−	10.7541i	−0.370086	−	0.427102i
$635$	−4.72386	+	0.363155i	−0.187461	+	0.0144114i
$636$	−0.507353	+	3.52872i	−0.0201179	+	0.139923i
$637$	−8.11426	−	7.03105i	−0.321499	−	0.278580i
$638$	−27.5963	−	12.6028i	−1.09255	−	0.498950i
$639$	−21.3450	−	6.26746i	−0.844395	−	0.247937i
$640$	−0.486941	−	2.18240i	−0.0192480	−	0.0862671i
$641$	−4.44860	−	30.9407i	−0.175709	−	1.22208i	−0.866555	−	0.499082i	$-0.833671\pi$
$641$	−4.44860	−	30.9407i	−0.175709	−	1.22208i	0.690845	−	0.723002i	$-0.257238\pi$
$642$	−1.43104	+	2.22675i	−0.0564787	+	0.0878826i
$643$		−	16.3114i		−	0.643260i	−0.946865	−	0.321630i	$-0.895769\pi$
$643$		−	16.3114i		−	0.643260i	0.946865	−	0.321630i	$-0.104231\pi$
$644$	−9.58137	+	3.78285i	−0.377559	+	0.149065i
$645$	1.05657	−	4.98463i	0.0416023	−	0.196270i
$646$	−26.0917	−	16.7681i	−1.02657	−	0.659734i
$647$	−24.3191	+	3.49656i	−0.956084	+	0.137464i	−0.602659	−	0.797999i	$-0.705892\pi$
$647$	−24.3191	+	3.49656i	−0.956084	+	0.137464i	−0.353425	+	0.935463i	$0.614983\pi$
$648$	−4.66688	+	2.13129i	−0.183332	+	0.0837250i
$649$	6.60023	+	1.93800i	0.259082	+	0.0760732i
$650$	−16.8431	+	14.9117i	−0.660641	+	0.584885i
$651$	−4.53503	+	5.23371i	−0.177742	+	0.205125i
$652$	0.188888	+	0.0271580i	0.00739744	+	0.00106359i
$653$	−7.71063	−	26.2600i	−0.301740	−	1.02763i	−0.961191	−	0.275885i	$-0.911029\pi$
$653$	−7.71063	−	26.2600i	−0.301740	−	1.02763i	0.659450	−	0.751748i	$-0.270789\pi$
$654$	−4.32543	−	4.99181i	−0.169138	−	0.195195i
$655$	5.20285	+	13.7257i	0.203292	+	0.536307i
$656$	−8.76152	+	5.63069i	−0.342080	+	0.219841i
$657$	12.2365	−	10.6030i	0.477392	−	0.413663i
$658$	−6.47819	−	22.0627i	−0.252546	−	0.860093i
$659$	−2.08830	+	14.5244i	−0.0813486	+	0.565792i	0.907859	+	0.419275i	$0.137716\pi$
$659$	−2.08830	+	14.5244i	−0.0813486	+	0.565792i	−0.989208	+	0.146517i	$0.953194\pi$
$660$	4.29195	−	3.24872i	0.167064	−	0.126456i
$661$	13.4754	−	29.5070i	0.524133	−	1.14769i	−0.443718	−	0.896166i	$-0.646341\pi$
$661$	13.4754	−	29.5070i	0.524133	−	1.14769i	0.967851	−	0.251525i	$-0.0809319\pi$
$662$	−2.50158	+	8.51959i	−0.0972266	+	0.331123i
$663$	15.5199	−	7.08769i	0.602742	−	0.275263i
$664$	0.942013	+	6.55185i	0.0365572	+	0.254261i
$665$	−18.7881	−	18.5890i	−0.728571	−	0.720851i
$666$	−21.2317			−0.822710
$667$	39.5653	−	9.39875i	1.53198	−	0.363921i
$668$		−	4.20030i		−	0.162514i
$669$	3.57375	+	2.29671i	0.138169	+	0.0887960i
$670$	−1.91798	−	0.126913i	−0.0740982	−	0.00490309i
$671$	−10.1657	−	22.2598i	−0.392442	−	0.859328i
$672$	−0.407164	+	1.38667i	−0.0157067	+	0.0534921i
$673$	−15.7371	−	7.18690i	−0.606621	−	0.277035i	0.0883303	−	0.996091i	$-0.471847\pi$
$673$	−15.7371	−	7.18690i	−0.606621	−	0.277035i	−0.694951	+	0.719057i	$0.744574\pi$
$674$	−8.74179	+	10.0886i	−0.336721	+	0.388597i
$675$	−15.8062	−	9.92175i	−0.608382	−	0.381888i
$676$	−6.94860	+	2.04029i	−0.267254	+	0.0784728i
$677$	−1.93111	+	1.67332i	−0.0742186	+	0.0643108i	−0.691180	−	0.722683i	$-0.742909\pi$
$677$	−1.93111	+	1.67332i	−0.0742186	+	0.0643108i	0.616961	+	0.786993i	$0.288363\pi$
$678$	1.74429	+	2.71417i	0.0669891	+	0.104237i
$679$	−9.73022	+	6.25323i	−0.373412	+	0.239977i
$680$	11.0289	−	6.09873i	0.422940	−	0.233875i
$681$	−9.14531	+	2.68530i	−0.350449	+	0.102901i
$682$	16.9695	+	2.43985i	0.649797	+	0.0934267i
$683$	−26.9619	−	23.3626i	−1.03167	−	0.893946i	−0.0372347	−	0.999307i	$-0.511855\pi$
$683$	−26.9619	−	23.3626i	−1.03167	−	0.893946i	−0.994434	+	0.105360i	$0.966400\pi$
$684$	−5.82307	+	12.7507i	−0.222651	+	0.487537i
$685$	12.4424	+	6.70830i	0.475400	+	0.256311i
$686$	8.37532	+	18.3394i	0.319771	+	0.700201i
$687$	13.1850	−	1.89572i	0.503040	−	0.0723262i
$688$	1.83100	−	2.84909i	0.0698061	−	0.108620i
$689$	23.8382			0.908164
$690$	−1.86363	+	6.97060i	−0.0709471	+	0.265366i
$691$	−5.18589			−0.197281			−0.0986404	−	0.995123i	$-0.531449\pi$
$691$	−5.18589			−0.197281			−0.0986404	+	0.995123i	$0.531449\pi$
$692$	6.93676	−	10.7938i	0.263696	−	0.410319i
$693$	19.3762	−	2.78587i	0.736039	−	0.105826i
$694$	−9.02366	−	19.7590i	−0.342533	−	0.750043i
$695$	−12.2241	+	22.6730i	−0.463685	+	0.860034i
$696$	2.37010	−	5.18979i	0.0898383	−	0.196718i
$697$	−44.3623	−	38.4401i	−1.68034	−	1.45602i
$698$	3.30750	+	0.475546i	0.125191	+	0.0179997i
$699$	−2.07980	+	0.610684i	−0.0786652	+	0.0230982i
$700$	10.2718	−	3.13530i	0.388237	−	0.118503i
$701$	−16.0200	+	10.2954i	−0.605067	+	0.388853i	−0.807004	−	0.590545i	$-0.798913\pi$
$701$	−16.0200	+	10.2954i	−0.605067	+	0.388853i	0.201937	+	0.979398i	$0.435276\pi$
$702$	−9.07879	−	14.1269i	−0.342657	−	0.533185i
$703$	−34.6638	+	30.0364i	−1.30737	+	1.13284i
$704$	3.43286	−	1.00798i	0.129381	−	0.0379896i
$705$	−15.1205	−	5.54811i	−0.569472	−	0.208954i
$706$	12.4518	−	14.3702i	0.468630	−	0.540828i
$707$	25.0200	+	11.4263i	0.940974	+	0.429728i
$708$	−0.364463	+	1.24125i	−0.0136973	+	0.0466489i
$709$	17.7445	+	38.8550i	0.666409	+	1.45923i	0.876427	+	0.481535i	$0.159920\pi$
$709$	17.7445	+	38.8550i	0.666409	+	1.45923i	−0.210018	+	0.977697i	$0.567352\pi$
$710$	1.28936	−	19.4856i	0.0483889	−	0.731280i
$711$	31.4678	+	20.2231i	1.18013	+	0.758426i
$712$			4.37155i			0.163831i
$713$	−19.9565	+	11.3952i	−0.747376	+	0.426755i
$714$	−8.14546			−0.304836
$715$	−25.5865	−	25.3154i	−0.956881	−	0.946742i
$716$	−2.68557	−	18.6786i	−0.100365	−	0.698051i
$717$	−15.5383	+	7.09612i	−0.580289	+	0.265009i
$718$	−0.606402	+	2.06521i	−0.0226307	+	0.0770731i
$719$	−13.0242	+	28.5190i	−0.485720	+	1.06358i	0.495131	+	0.868819i	$0.335120\pi$
$719$	−13.0242	+	28.5190i	−0.485720	+	1.06358i	−0.980851	+	0.194760i	$0.937607\pi$
$720$	−3.43766	−	4.54156i	−0.128114	−	0.169254i
$721$	−4.35597	+	30.2964i	−0.162225	+	1.12830i
$722$	3.17851	+	10.8250i	0.118292	+	0.402866i
$723$	−4.58640	+	3.97414i	−0.170570	+	0.147800i
$724$	−2.65189	+	1.70427i	−0.0985568	+	0.0633386i
$725$	−41.8994	+	6.48048i	−1.55610	+	0.240679i
$726$	0.793345	+	0.915568i	0.0294438	+	0.0339799i
$727$	−10.0017	−	34.0626i	−0.370942	−	1.26331i	−0.907716	−	0.419585i	$-0.862176\pi$
$727$	−10.0017	−	34.0626i	−0.370942	−	1.26331i	0.536775	−	0.843726i	$-0.319643\pi$
$728$	9.56539	+	1.37529i	0.354517	+	0.0509718i
$729$	−3.62455	+	4.18295i	−0.134242	+	0.154924i
$730$	11.4233	+	8.45685i	0.422797	+	0.313002i
$731$	18.3149	+	5.37773i	0.677400	+	0.198903i
$732$	4.18619	−	1.91177i	0.154726	−	0.0706611i
$733$	32.1240	−	4.61874i	1.18653	−	0.170597i	0.479344	−	0.877627i	$-0.340874\pi$
$733$	32.1240	−	4.61874i	1.18653	−	0.170597i	0.707184	+	0.707030i	$0.249965\pi$
$734$	9.77041	+	6.27906i	0.360632	+	0.231764i
$735$	3.51236	+	0.744498i	0.129555	+	0.0274612i
$736$	−2.80047	+	3.89325i	−0.103227	+	0.143507i
$737$		−	3.07555i		−	0.113289i
$738$	−14.3430	+	22.3181i	−0.527972	+	0.821540i
$739$	1.23645	+	8.59969i	0.0454835	+	0.316345i	0.999844	+	0.0176862i	$0.00563000\pi$
$739$	1.23645	+	8.59969i	0.0454835	+	0.316345i	−0.954360	+	0.298658i	$0.903461\pi$
$740$	−4.05866	−	18.1904i	−0.149199	−	0.668691i
$741$	−15.9835	−	4.69319i	−0.587170	−	0.172409i
$742$	−10.3522	−	4.72769i	−0.380041	−	0.173559i
$743$	13.4558	+	11.6596i	0.493647	+	0.427748i	0.865775	−	0.500434i	$-0.166826\pi$
$743$	13.4558	+	11.6596i	0.493647	+	0.427748i	−0.372128	+	0.928182i	$0.621372\pi$
$744$	−0.458841	+	3.19131i	−0.0168219	+	0.116999i
$745$	−2.27278	−	29.5639i	−0.0832681	−	1.08314i
$746$	1.54832	+	1.78686i	0.0566881	+	0.0654216i
$747$	9.11576	+	14.1844i	0.333528	+	0.518980i
$748$	10.9020	+	16.9638i	0.398617	+	0.620260i
$749$	−5.53349	−	6.38599i	−0.202189	−	0.233339i
$750$	2.51593	−	7.08940i	0.0918688	−	0.258868i
$751$	−1.15010	+	7.99912i	−0.0419678	+	0.291892i	0.958019	+	0.286705i	$0.0925601\pi$
$751$	−1.15010	+	7.99912i	−0.0419678	+	0.291892i	−0.999987	+	0.00518675i	$0.998349\pi$
$752$	−8.09049	−	7.01045i	−0.295030	−	0.255645i
$753$	7.50315	+	3.42657i	0.273430	+	0.124871i
$754$	−36.6049	−	10.7482i	−1.33307	−	0.391425i
$755$	37.7718	−	8.42770i	1.37466	−	0.306715i
$756$	1.14094	+	7.93541i	0.0414956	+	0.288608i
$757$	−5.46238	+	8.49962i	−0.198533	+	0.308924i	−0.926218	−	0.376988i	$-0.876960\pi$
$757$	−5.46238	+	8.49962i	−0.198533	+	0.308924i	0.727685	+	0.685912i	$0.240596\pi$
$758$			14.5030i			0.526773i
$759$	−11.3257	−	2.23896i	−0.411098	−	0.0812692i
$760$	−12.0374	−	2.55152i	−0.436644	−	0.0925532i
$761$	−4.92933	−	3.16789i	−0.178688	−	0.114836i	0.448239	−	0.893914i	$-0.352051\pi$
$761$	−4.92933	−	3.16789i	−0.178688	−	0.114836i	−0.626927	+	0.779078i	$0.715688\pi$
$762$	1.41111	−	0.202887i	0.0511192	−	0.00734982i
$763$	19.1802	−	8.75929i	0.694369	−	0.317108i
$764$	−0.135561	−	0.0398044i	−0.00490444	−	0.00144007i
$765$	19.1015	−	25.8019i	0.690615	−	0.932870i
$766$	−10.8483	+	12.5196i	−0.391966	+	0.452353i
$767$	8.56222	+	1.23106i	0.309164	+	0.0444510i
$768$	0.189561	+	0.645587i	0.00684021	+	0.0232956i
$769$	−16.8713	−	19.4705i	−0.608394	−	0.702124i	0.365066	−	0.930982i	$-0.381047\pi$
$769$	−16.8713	−	19.4705i	−0.608394	−	0.702124i	−0.973460	+	0.228857i	$0.926501\pi$
$770$	6.09078	+	16.0681i	0.219496	+	0.579055i
$771$	13.8704	−	8.91395i	0.499530	−	0.321028i
$772$	11.1573	−	9.66784i	0.401559	−	0.347953i
$773$	9.97008	+	33.9550i	0.358599	+	1.22128i	0.919400	+	0.393325i	$0.128675\pi$
$773$	9.97008	+	33.9550i	0.358599	+	1.22128i	−0.560801	+	0.827951i	$0.689507\pi$
$774$	1.22774	−	8.53911i	0.0441302	−	0.306932i
$775$	21.6866	−	10.1845i	0.779007	−	0.365839i
$776$	−2.23696	+	4.89826i	−0.0803022	+	0.175837i
$777$	−3.39372	+	11.5579i	−0.121749	+	0.414639i
$778$	−14.1020	+	6.44016i	−0.505580	+	0.230891i
$779$	8.15634	+	56.7286i	0.292231	+	2.03251i
$780$	4.76084	−	4.81182i	0.170465	−	0.172291i
$781$	31.2457			1.11806
$782$	−25.5010	−	8.96247i	−0.911913	−	0.320497i
$783$		−	31.6493i		−	1.13105i
$784$	2.00758	+	1.29019i	0.0716991	+	0.0460782i
$785$	−0.384735	+	5.81433i	−0.0137318	+	0.207522i
$786$	−1.83484	−	4.01773i	−0.0654464	−	0.143308i
$787$	−0.938143	+	3.19502i	−0.0334412	+	0.113890i	−0.974522	−	0.224291i	$-0.927993\pi$
$787$	−0.938143	+	3.19502i	−0.0334412	+	0.113890i	0.941081	+	0.338181i	$0.109812\pi$
$788$	−1.85057	−	0.845126i	−0.0659237	−	0.0301064i
$789$	7.50907	−	8.66593i	0.267330	−	0.308515i
$790$	−11.3109	+	30.8261i	−0.402423	+	1.09674i
$791$	−9.88232	+	2.90171i	−0.351375	+	0.103173i
$792$	6.88762	−	5.96816i	0.244741	−	0.212069i
$793$	−16.6370	−	25.8877i	−0.590798	−	0.919300i
$794$	19.1901	−	12.3327i	0.681031	−	0.437672i
$795$	−6.97606	+	3.85759i	−0.247415	+	0.136815i
$796$	11.7565	−	3.45202i	0.416699	−	0.122354i
$797$	23.7722	+	3.41793i	0.842056	+	0.121069i	0.549827	−	0.835279i	$-0.314694\pi$
$797$	23.7722	+	3.41793i	0.842056	+	0.121069i	0.292230	+	0.956348i	$0.405603\pi$
$798$	6.01039	+	5.20803i	0.212766	+	0.184362i
$799$	25.0647	−	54.8841i	0.886726	−	1.94166i
$800$	3.23387	−	3.81341i	0.114334	−	0.134824i
$801$	4.62588	+	10.1293i	0.163448	+	0.357900i
$802$	−23.9970	+	3.45025i	−0.847363	+	0.121832i
$803$	−12.2949	+	19.1313i	−0.433878	+	0.675127i
$804$	0.578391			0.0203983
$805$	−19.6749	−	11.9775i	−0.693449	−	0.422153i
$806$	21.5588			0.759378
$807$	10.4786	−	16.3051i	0.368865	−	0.573965i
$808$	12.6753	−	1.82244i	0.445916	−	0.0641131i
$809$	−2.42142	−	5.30216i	−0.0851325	−	0.186414i	0.862278	−	0.506436i	$-0.169037\pi$
$809$	−2.42142	−	5.30216i	−0.0851325	−	0.186414i	−0.947410	+	0.320021i	$0.896310\pi$
$810$	−10.0980	−	5.44432i	−0.354808	−	0.191294i
$811$	−11.1709	+	24.4608i	−0.392262	+	0.858935i	0.605734	+	0.795667i	$0.292879\pi$
$811$	−11.1709	+	24.4608i	−0.392262	+	0.858935i	−0.997997	+	0.0632676i	$0.979848\pi$
$812$	13.7648	+	11.9272i	0.483048	+	0.418564i
$813$	21.4098	+	3.07826i	0.750874	+	0.107959i
$814$	28.6129	−	8.40151i	1.00288	−	0.294473i
$815$	0.206492	+	0.373420i	0.00723311	+	0.0130803i
$816$	−3.19024	+	2.05024i	−0.111681	+	0.0717728i
$817$	−10.0758	−	15.6783i	−0.352508	−	0.548513i
$818$	6.50120	−	5.63332i	0.227309	−	0.196965i
$819$	23.6192	−	6.93522i	0.825321	−	0.242336i
$820$	−21.8630	−	8.02209i	−0.763489	−	0.280144i
$821$	20.3274	−	23.4591i	0.709432	−	0.818728i	−0.280563	−	0.959836i	$-0.590521\pi$
$821$	20.3274	−	23.4591i	0.709432	−	0.818728i	0.989994	+	0.141108i	$0.0450665\pi$
$822$	−3.86908	−	1.76695i	−0.134950	−	0.0616294i
$823$	12.2434	−	41.6971i	0.426777	−	1.45347i	−0.413096	−	0.910687i	$-0.635553\pi$
$823$	12.2434	−	41.6971i	0.426777	−	1.45347i	0.839874	−	0.542782i	$-0.182629\pi$
$824$	5.91967	+	12.9623i	0.206222	+	0.451562i
$825$	11.5843	+	3.26784i	0.403314	+	0.113772i
$826$	−3.47416	−	2.23271i	−0.120881	−	0.0776858i
$827$			18.6806i			0.649590i	0.945785	+	0.324795i	$0.105295\pi$
$827$			18.6806i			0.649590i	−0.945785	+	0.324795i	$0.894705\pi$
$828$	−2.36918	+	11.9844i	−0.0823345	+	0.416487i
$829$	9.03092			0.313657			0.156828	−	0.987626i	$-0.449873\pi$
$829$	9.03092			0.313657			0.156828	+	0.987626i	$0.449873\pi$
$830$	−10.4100	+	10.5215i	−0.361337	+	0.365207i
$831$	−0.540547	−	3.75959i	−0.0187514	−	0.130419i
$832$	4.09253	−	1.86900i	0.141883	−	0.0647958i
$833$	−3.78936	+	12.9054i	−0.131293	+	0.447145i
$834$	3.21979	−	7.05036i	0.111492	−	0.244134i
$835$	7.48872	−	5.66847i	0.259158	−	0.196166i
$836$	2.80193	−	19.4878i	0.0969066	−	0.674000i
$837$	5.03883	+	17.1607i	0.174167	+	0.593160i
$838$	−9.02015	+	7.81601i	−0.311596	+	0.269999i
$839$	−18.0277	+	11.5857i	−0.622385	+	0.399983i	−0.813483	−	0.581588i	$-0.802432\pi$
$839$	−18.0277	+	11.5857i	−0.622385	+	0.399983i	0.191098	+	0.981571i	$0.438795\pi$
$840$	−3.02179	+	1.14544i	−0.104262	+	0.0395214i
$841$	−28.0950	−	32.4233i	−0.968793	−	1.11805i
$842$	1.73720	+	5.91636i	0.0598678	+	0.203891i
$843$	−7.32391	−	1.05302i	−0.252249	−	0.0362679i
$844$	0.769877	−	0.888486i	0.0265003	−	0.0305829i
$845$	−13.0151	−	9.63521i	−0.447732	−	0.331461i
$846$	−26.1647	−	7.68266i	−0.899562	−	0.264135i
$847$	−3.51791	+	1.60658i	−0.120877	+	0.0552027i
$848$	−5.24450	+	0.754046i	−0.180097	+	0.0258940i
$849$	−2.94203	−	1.89072i	−0.100970	−	0.0648895i
$850$	25.7574	+	11.4330i	0.883472	+	0.392149i
$851$	−23.3419	+	32.4503i	−0.800151	+	1.11238i
$852$			5.87611i			0.201312i
$853$	−30.2776	+	47.1128i	−1.03668	+	1.61311i	−0.279230	+	0.960224i	$0.590079\pi$
$853$	−30.2776	+	47.1128i	−1.03668	+	1.61311i	−0.757455	+	0.652888i	$0.773557\pi$
$854$	2.09079	+	14.5418i	0.0715454	+	0.497609i
$855$	−30.5918	+	6.82568i	−1.04622	+	0.233433i
$856$	−3.77462	−	1.10833i	−0.129014	−	0.0378818i
$857$	28.9414	+	13.2171i	0.988618	+	0.451487i	0.843035	−	0.537859i	$-0.180767\pi$
$857$	28.9414	+	13.2171i	0.988618	+	0.451487i	0.145583	+	0.989346i	$0.453494\pi$
$858$	8.18523	+	7.09254i	0.279439	+	0.242135i
$859$	0.267029	−	1.85723i	0.00911090	−	0.0633677i	−0.984759	−	0.173926i	$-0.944355\pi$
$859$	0.267029	−	1.85723i	0.00911090	−	0.0633677i	0.993870	+	0.110558i	$0.0352638\pi$
$860$	7.55064	−	0.580469i	0.257475	−	0.0197938i
$861$	9.85675	+	11.3753i	0.335917	+	0.387669i
$862$	19.7905	+	30.7946i	0.674067	+	1.04887i
$863$	19.3769	+	30.1510i	0.659597	+	1.02635i	0.996400	+	0.0847780i	$0.0270181\pi$
$863$	19.3769	+	30.1510i	0.659597	+	1.02635i	−0.336803	+	0.941575i	$0.609346\pi$
$864$	2.44423	+	2.82079i	0.0831544	+	0.0959653i
$865$	28.6057	−	2.19912i	0.972624	−	0.0747722i
$866$	0.660246	−	4.59211i	0.0224361	−	0.156046i
$867$	−7.50868	−	6.50631i	−0.255008	−	0.220966i
$868$	−9.36234	−	4.27564i	−0.317779	−	0.145125i
$869$	−50.4101	−	14.8017i	−1.71004	−	0.502115i
$870$	12.4514	−	2.77818i	0.422143	−	0.0941891i
$871$	−0.550408	−	3.82817i	−0.0186499	−	0.129713i
$872$	5.30733	−	8.25837i	0.179729	−	0.279664i
$873$			13.7168i			0.464244i
$874$	13.0863	+	22.9180i	0.442651	+	0.775213i
$875$	19.4521	+	14.0824i	0.657602	+	0.476072i
$876$	−3.59784	−	2.31219i	−0.121560	−	0.0781218i
$877$	−5.37700	+	0.773096i	−0.181568	+	0.0261056i	−0.232499	−	0.972597i	$-0.574690\pi$
$877$	−5.37700	+	0.773096i	−0.181568	+	0.0261056i	0.0509308	+	0.998702i	$0.483781\pi$
$878$	12.1093	−	5.53015i	0.408671	−	0.186634i
$879$	−6.70216	−	1.96793i	−0.226058	−	0.0663767i
$880$	6.42991	+	4.76014i	0.216752	+	0.160464i
$881$	15.7210	−	18.1430i	0.529655	−	0.611254i	−0.426367	−	0.904550i	$-0.640207\pi$
$881$	15.7210	−	18.1430i	0.529655	−	0.611254i	0.956022	+	0.293296i	$0.0947522\pi$
$882$	6.01699	+	0.865113i	0.202603	+	0.0291299i
$883$	14.1070	+	48.0442i	0.474740	+	1.61681i	0.754191	+	0.656655i	$0.228029\pi$
$883$	14.1070	+	48.0442i	0.474740	+	1.61681i	−0.279452	+	0.960160i	$0.590153\pi$
$884$	16.6058	+	19.1641i	0.558512	+	0.644557i
$885$	−2.70488	+	1.02531i	−0.0909235	+	0.0344654i
$886$	33.4847	−	21.5193i	1.12494	−	0.722956i
$887$	−0.904125	+	0.783429i	−0.0303576	+	0.0263050i	−0.669907	−	0.742445i	$-0.733666\pi$
$887$	−0.904125	+	0.783429i	−0.0303576	+	0.0263050i	0.639550	+	0.768750i	$0.279121\pi$
$888$	1.58000	+	5.38098i	0.0530212	+	0.180574i
$889$	−0.647681	+	4.50472i	−0.0217225	+	0.151083i
$890$	−7.79404	+	5.89958i	−0.261257	+	0.197754i
$891$	7.62529	−	16.6971i	0.255457	−	0.559373i
$892$	−1.77878	+	6.05796i	−0.0595579	+	0.202836i
$893$	−53.5865	+	24.4721i	−1.79320	+	0.818928i
$894$	1.26975	+	8.83133i	0.0424669	+	0.295364i
$895$	29.6778	−	29.9956i	0.992019	−	1.00264i
$896$	−2.14793			−0.0717572
$897$	−14.4980	−	0.759981i	−0.484073	−	0.0253750i
$898$		−	18.1947i		−	0.607164i
$899$	34.1820	+	21.9674i	1.14003	+	0.732655i
$900$	3.45789	−	12.2580i	0.115263	−	0.408601i
$901$	−12.4055	−	27.1642i	−0.413286	−	0.904971i
$902$	10.4979	−	35.7527i	0.349543	−	1.19043i
$903$	−4.45222	−	2.03326i	−0.148161	−	0.0676627i
$904$	−3.14012	+	3.62389i	−0.104439	+	0.120529i
$905$	−6.61738	−	2.42809i	−0.219969	−	0.0807123i
$906$	−11.1734	+	3.28082i	−0.371213	+	0.108998i
$907$	1.47406	−	1.27728i	0.0489455	−	0.0424115i	−0.630045	−	0.776559i	$-0.716963\pi$
$907$	1.47406	−	1.27728i	0.0489455	−	0.0424115i	0.678990	+	0.734147i	$0.262418\pi$
$908$	−7.65865	−	11.9171i	−0.254161	−	0.395483i
$909$	27.4414	−	17.6355i	0.910174	−	0.584933i
$910$	10.4569	+	18.9102i	0.346641	+	0.626866i
$911$	−37.6676	+	11.0602i	−1.24798	+	0.366441i	−0.838009	−	0.545656i	$-0.816280\pi$
$911$	−37.6676	+	11.0602i	−1.24798	+	0.366441i	−0.409974	+	0.912097i	$0.634462\pi$
$912$	3.66490	+	0.526933i	0.121357	+	0.0174485i
$913$	−17.8978	−	15.5085i	−0.592329	−	0.513256i
$914$	14.9872	−	32.8174i	0.495733	−	1.08550i
$915$	9.05794	+	4.88356i	0.299446	+	0.161446i
$916$	8.22419	+	18.0085i	0.271735	+	0.595016i
$917$	13.9566	−	2.00665i	0.460887	−	0.0662655i
$918$	−11.3733	+	17.6972i	−0.375374	+	0.584093i
$919$	−16.8622			−0.556233			−0.278116	−	0.960547i	$-0.589710\pi$
$919$	−16.8622			−0.556233			−0.278116	+	0.960547i	$0.589710\pi$
$920$	−10.7206	+	0.261141i	−0.353449	+	0.00860955i
$921$	0.639680			0.0210782
$922$	−3.96605	+	6.17129i	−0.130615	+	0.203241i
$923$	38.8920	−	5.59182i	1.28014	−	0.184057i
$924$	−2.14797	−	4.70340i	−0.0706631	−	0.154731i
$925$	26.9543	−	31.7848i	0.886253	−	1.04508i
$926$	−13.1166	+	28.7214i	−0.431039	+	0.943843i
$927$	27.4328	+	23.7707i	0.901013	+	0.780732i
$928$	8.39321	+	1.20676i	0.275521	+	0.0396139i
$929$	−34.6187	+	10.1650i	−1.13580	+	0.333502i	−0.794986	−	0.606628i	$-0.792522\pi$
$929$	−34.6187	+	10.1650i	−1.13580	+	0.333502i	−0.340817	+	0.940130i	$0.610704\pi$
$930$	−6.30902	+	3.48873i	−0.206881	+	0.114400i
$931$	11.0475	−	7.09980i	0.362068	−	0.232687i
$932$	−1.74171	−	2.71015i	−0.0570515	−	0.0887739i
$933$	2.10520	−	1.82417i	0.0689213	−	0.0597206i
$934$	−6.13806	+	1.80230i	−0.200843	+	0.0589730i
$935$	−15.5322	+	42.3306i	−0.507957	+	1.38436i
$936$	7.50503	−	8.66127i	0.245310	−	0.283102i
$937$	−8.47312	−	3.86954i	−0.276805	−	0.126412i	0.272176	−	0.962247i	$-0.412257\pi$
$937$	−8.47312	−	3.86954i	−0.276805	−	0.126412i	−0.548981	+	0.835835i	$0.684984\pi$
$938$	−0.520194	+	1.77162i	−0.0169849	+	0.0578453i
$939$	−2.65194	−	5.80693i	−0.0865427	−	0.189502i
$940$	1.58050	−	23.8854i	0.0515503	−	0.779057i
$941$	−48.2646	−	31.0178i	−1.57338	−	1.01115i	−0.978227	−	0.207538i	$-0.933455\pi$
$941$	−48.2646	−	31.0178i	−1.57338	−	1.01115i	−0.595153	−	0.803612i	$-0.702909\pi$
$942$		−	1.75338i		−	0.0571283i
$943$	18.3422	+	46.4580i	0.597305	+	1.51288i
$944$	−1.92266			−0.0625774
$945$	−12.6083	+	12.7433i	−0.410149	+	0.414541i
$946$	1.72442	+	11.9936i	0.0560657	+	0.389945i
$947$	−50.7170	+	23.1617i	−1.64808	+	0.752653i	−0.999961	−	0.00888487i	$-0.997172\pi$
$947$	−50.7170	+	23.1617i	−1.64808	+	0.752653i	−0.648120	+	0.761538i	$0.724445\pi$
$948$	2.78363	−	9.48017i	0.0904081	−	0.307902i
$949$	−11.8799	+	26.0132i	−0.385636	+	0.844426i
$950$	−11.6959	−	24.9049i	−0.379465	−	0.808023i
$951$	−1.36258	+	9.47693i	−0.0441846	+	0.307310i
$952$	−3.41067	−	11.6157i	−0.110541	−	0.376467i
$953$	9.78866	−	8.48192i	0.317086	−	0.274756i	−0.481746	−	0.876311i	$-0.659997\pi$
$953$	9.78866	−	8.48192i	0.317086	−	0.274756i	0.798832	+	0.601555i	$0.205452\pi$
$954$	−11.3541	+	7.29682i	−0.367602	+	0.236243i
$955$	−0.111978	−	0.295410i	−0.00362353	−	0.00955925i
$956$	−16.6255	−	19.1868i	−0.537707	−	0.620547i
$957$	5.75089	+	19.5857i	0.185900	+	0.633117i
$958$	−18.8581	−	2.71138i	−0.609277	−	0.0876007i
$959$	8.89196	−	10.2619i	0.287136	−	0.331373i
$960$	−0.895197	+	1.20921i	−0.0288924	+	0.0390272i
$961$	7.71298	+	2.26473i	0.248806	+	0.0730559i
$962$	34.1113	−	15.5781i	1.09979	−	0.502258i
$963$	−9.91894	+	1.42613i	−0.319633	+	0.0459563i
$964$	−7.58766	−	4.87629i	−0.244382	−	0.157055i
$965$	32.2940	+	6.84520i	1.03958	+	0.220355i
$966$	6.14530	+	3.20533i	0.197722	+	0.103130i
$967$		−	13.4094i		−	0.431218i	−0.976480	−	0.215609i	$-0.930826\pi$
$967$		−	13.4094i		−	0.431218i	0.976480	−	0.215609i	$-0.0691737\pi$
$968$	−0.973439	+	1.51470i	−0.0312875	+	0.0486843i
$969$	2.96988	+	20.6560i	0.0954063	+	0.663566i
$970$	−11.7520	+	2.62212i	−0.377334	+	0.0841912i
$971$	−50.8163	−	14.9210i	−1.63077	−	0.478838i	−0.666889	−	0.745157i	$-0.732374\pi$
$971$	−50.8163	−	14.9210i	−1.63077	−	0.478838i	−0.963885	+	0.266319i	$0.914192\pi$
$972$	13.3255	+	6.08556i	0.427416	+	0.195194i
$973$	18.6995	+	16.2032i	0.599478	+	0.519451i
$974$	1.77472	−	12.3435i	0.0568658	−	0.395510i
$975$	15.0040	+	1.99436i	0.480511	+	0.0638707i
$976$	4.47909	+	5.16914i	0.143372	+	0.165460i
$977$	21.8050	+	33.9293i	0.697605	+	1.08549i	0.991557	+	0.129674i	$0.0413930\pi$
$977$	21.8050	+	33.9293i	0.697605	+	1.08549i	−0.293952	+	0.955820i	$0.594971\pi$
$978$	−0.0694177	−	0.108016i	−0.00221973	−	0.00345397i
$979$	−10.2423	−	11.8203i	−0.327346	−	0.377777i
$980$	0.409021	+	5.32048i	0.0130657	+	0.169956i
$981$	3.55873	−	24.7515i	0.113621	−	0.790255i
$982$	−10.1399	−	8.78624i	−0.323576	−	0.280380i
$983$	18.0252	+	8.23184i	0.574915	+	0.262555i	0.681584	−	0.731740i	$-0.261291\pi$
$983$	18.0252	+	8.23184i	0.574915	+	0.262555i	−0.106669	+	0.994295i	$0.534019\pi$
$984$	6.72368	+	1.97425i	0.214343	+	0.0629368i
$985$	−0.990639	−	4.43991i	−0.0315644	−	0.141467i
$986$	6.80150	+	47.3055i	0.216604	+	1.50651i
$987$	−8.36446	+	13.0154i	−0.266244	+	0.414283i
$988$		−	24.7582i		−	0.787662i
$989$	−11.7013	−	11.2643i	−0.372081	−	0.358184i
$990$	19.9358	+	4.22569i	0.633600	+	0.134301i
$991$	−36.7271	−	23.6031i	−1.16668	−	0.749777i	−0.193786	−	0.981044i	$-0.562077\pi$
$991$	−36.7271	−	23.6031i	−1.16668	−	0.749777i	−0.972890	+	0.231267i	$0.925713\pi$
$992$	−4.74303	+	0.681945i	−0.150591	+	0.0216518i
$993$	5.43445	−	2.48183i	0.172457	−	0.0787585i
$994$	−17.9986	−	5.28486i	−0.570880	−	0.167626i
$995$	22.0205	+	16.3021i	0.698097	+	0.516810i
$996$	2.91654	−	3.36587i	0.0924142	−	0.106652i
$997$	9.25208	+	1.33025i	0.293016	+	0.0421294i	0.287255	−	0.957854i	$-0.407257\pi$
$997$	9.25208	+	1.33025i	0.293016	+	0.0421294i	0.00576084	+	0.999983i	$0.498166\pi$
$998$	−0.874886	−	2.97959i	−0.0276940	−	0.0943172i
$999$	20.3727	+	23.5113i	0.644564	+	0.743866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.j.a.209.9	yes	120
5.4	even	2	inner	230.2.j.a.209.4	✓	120
23.12	even	11	inner	230.2.j.a.219.4	yes	120
115.104	even	22	inner	230.2.j.a.219.9	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.j.a.209.4	✓	120	5.4	even	2	inner
230.2.j.a.209.9	yes	120	1.1	even	1	trivial
230.2.j.a.219.4	yes	120	23.12	even	11	inner
230.2.j.a.219.9	yes	120	115.104	even	22	inner

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 - 0.841254i) q^{2} +(-0.665993 + 0.0957553i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.06117 - 1.96823i) q^{5} +(-0.279508 + 0.612038i) q^{6} +(-1.62329 - 1.40659i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-2.44410 + 0.717653i) q^{9} +(-1.08207 - 1.95681i) q^{10} +(3.00982 - 1.93430i) q^{11} +(0.363766 + 0.566030i) q^{12} +(3.40020 - 2.94629i) q^{13} +(-2.06092 + 0.605141i) q^{14} +(-0.518260 + 1.41244i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-5.12683 - 2.34135i) q^{17} +(-0.717653 + 2.44410i) q^{18} +(2.28599 + 5.00562i) q^{19} +(-2.23119 - 0.147638i) q^{20} +(1.21579 + 0.781342i) q^{21} -3.57778i q^{22} +(2.94656 + 3.78388i) q^{23} +0.672842 q^{24} +(-2.74786 - 4.17724i) q^{25} +(-0.640289 - 4.45331i) q^{26} +(3.39515 - 1.55051i) q^{27} +(-0.605141 + 2.06092i) q^{28} +(3.52252 - 7.71324i) q^{29} +(0.908027 + 1.19961i) q^{30} +(-0.681945 + 4.74303i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-1.81930 + 1.57643i) q^{33} +(-4.74144 + 3.04714i) q^{34} +(-4.49108 + 1.70239i) q^{35} +(1.66812 + 1.92511i) q^{36} +(2.34825 + 7.99739i) q^{37} +(5.44690 + 0.783146i) q^{38} +(-1.98238 + 2.28779i) q^{39} +(-1.33047 + 1.79718i) q^{40} +(9.99296 + 2.93420i) q^{41} +(1.31461 - 0.600364i) q^{42} +(-3.35224 + 0.481980i) q^{43} +(-3.00982 - 1.93430i) q^{44} +(-1.18109 + 5.57210i) q^{45} +(4.77624 - 0.433085i) q^{46} +10.7053i q^{47} +(0.363766 - 0.566030i) q^{48} +(-0.339622 - 2.36212i) q^{49} +(-4.99972 + 0.0532591i) q^{50} +(3.63863 + 1.06840i) q^{51} +(-4.09253 - 1.86900i) q^{52} +(4.00429 + 3.46974i) q^{53} +(0.531182 - 3.69445i) q^{54} +(-0.613217 - 7.97663i) q^{55} +(1.40659 + 1.62329i) q^{56} +(-2.00177 - 3.11481i) q^{57} +(-4.58437 - 7.13343i) q^{58} +(1.25908 + 1.45305i) q^{59} +(1.50009 - 0.115322i) q^{60} +(0.973399 - 6.77014i) q^{61} +(3.62141 + 3.13797i) q^{62} +(4.97694 + 2.27289i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-2.19080 - 9.81887i) q^{65} +(0.342592 + 2.38278i) q^{66} +(0.464748 - 0.723162i) q^{67} +5.63616i q^{68} +(-2.32472 - 2.23789i) q^{69} +(-0.995922 + 4.69852i) q^{70} +(7.34689 + 4.72156i) q^{71} +(2.52136 - 0.362516i) q^{72} +(-5.78187 + 2.64049i) q^{73} +(7.99739 + 2.34825i) q^{74} +(2.23004 + 2.51889i) q^{75} +(3.60364 - 4.15882i) q^{76} +(-7.60660 - 1.09366i) q^{77} +(0.852857 + 2.90456i) q^{78} +(-9.61636 - 11.0979i) q^{79} +(0.792573 + 2.09089i) q^{80} +(4.31606 - 2.77376i) q^{81} +(7.87101 - 6.82027i) q^{82} +(-1.86485 - 6.35109i) q^{83} +(0.205675 - 1.43050i) q^{84} +(-10.0487 + 7.60623i) q^{85} +(-1.40689 + 3.08066i) q^{86} +(-1.60739 + 5.47427i) q^{87} +(-3.25447 + 1.48626i) q^{88} +(-0.622136 - 4.32705i) q^{89} +(4.04900 + 4.00610i) q^{90} -9.66375 q^{91} +(2.21789 - 4.25217i) q^{92} -3.22413i q^{93} +(9.00583 + 5.78770i) q^{94} +(12.2780 + 0.812439i) q^{95} +(-0.279508 - 0.612038i) q^{96} +(1.51710 - 5.16676i) q^{97} +(-2.17076 - 0.991351i) q^{98} +(-5.96816 + 6.88762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41}+ \cdots + 188 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more