LMFDB - Embedded newform 230.2.l.a.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] 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("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	230.67
Dual form			230.2.l.a.103.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.212565 - 0.977147i) q^{2} +(-1.52800 - 1.14385i) q^{3} +(-0.909632 + 0.415415i) q^{4} +(-0.841561 + 2.07166i) q^{5} +(-0.792907 + 1.73622i) q^{6} +(0.194262 + 2.71614i) q^{7} +(0.599278 + 0.800541i) q^{8} +(0.181204 + 0.617123i) q^{9} +(2.20320 + 0.381966i) q^{10} +(1.89773 + 2.95293i) q^{11} +(1.86509 + 0.405726i) q^{12} +(-2.60053 - 0.185993i) q^{13} +(2.61278 - 0.767180i) q^{14} +(3.65557 - 2.20288i) q^{15} +(0.654861 - 0.755750i) q^{16} +(0.176913 + 0.474323i) q^{17} +(0.564502 - 0.308241i) q^{18} +(3.08215 + 6.74897i) q^{19} +(-0.0950878 - 2.23405i) q^{20} +(2.81002 - 4.37247i) q^{21} +(2.48205 - 2.48205i) q^{22} +(-1.67732 - 4.49295i) q^{23} -1.90871i q^{24} +(-3.58355 - 3.48686i) q^{25} +(0.371039 + 2.58063i) q^{26} +(-1.57206 + 4.21486i) q^{27} +(-1.30503 - 2.38999i) q^{28} +(1.51901 + 0.693708i) q^{29} +(-2.92959 - 3.10377i) q^{30} +(-1.51827 + 10.5598i) q^{31} +(-0.877679 - 0.479249i) q^{32} +(0.477963 - 6.68280i) q^{33} +(0.425877 - 0.273695i) q^{34} +(-5.79040 - 1.88335i) q^{35} +(-0.421191 - 0.486080i) q^{36} +(-0.403846 + 0.739590i) q^{37} +(5.93958 - 4.44631i) q^{38} +(3.76086 + 3.25881i) q^{39} +(-2.16278 + 0.567795i) q^{40} +(-6.80249 - 1.99739i) q^{41} +(-4.86986 - 1.81636i) q^{42} +(-2.05606 + 2.74658i) q^{43} +(-2.95293 - 1.89773i) q^{44} +(-1.43096 - 0.143954i) q^{45} +(-4.03373 + 2.59403i) q^{46} +(-0.775455 - 0.775455i) q^{47} +(-1.86509 + 0.405726i) q^{48} +(-0.410934 + 0.0590834i) q^{49} +(-2.64543 + 4.24284i) q^{50} +(0.272229 - 0.927127i) q^{51} +(2.44279 - 0.911113i) q^{52} +(-6.99930 + 0.500600i) q^{53} +(4.45271 + 0.640203i) q^{54} +(-7.71453 + 1.44639i) q^{55} +(-2.05797 + 1.78324i) q^{56} +(3.01026 - 13.8379i) q^{57} +(0.354966 - 1.63175i) q^{58} +(10.1487 - 8.79387i) q^{59} +(-2.41011 + 3.52239i) q^{60} +(3.87817 + 0.557596i) q^{61} +(10.6412 - 0.761072i) q^{62} +(-1.64099 + 0.612058i) q^{63} +(-0.281733 + 0.959493i) q^{64} +(2.57382 - 5.23089i) q^{65} +(-6.63168 + 0.953491i) q^{66} +(6.64026 - 1.44450i) q^{67} +(-0.357967 - 0.357967i) q^{68} +(-2.57630 + 8.78383i) q^{69} +(-0.609474 + 6.05841i) q^{70} +(-12.1107 - 7.78309i) q^{71} +(-0.385441 + 0.514889i) q^{72} +(4.78023 + 1.78293i) q^{73} +(0.808531 + 0.237406i) q^{74} +(1.48724 + 9.42696i) q^{75} +(-5.60725 - 4.85871i) q^{76} +(-7.65192 + 5.72815i) q^{77} +(2.38490 - 4.36762i) q^{78} +(-0.340883 - 0.393400i) q^{79} +(1.01455 + 1.99266i) q^{80} +(8.84650 - 5.68530i) q^{81} +(-0.505771 + 7.07160i) q^{82} +(10.0407 + 5.48264i) q^{83} +(-0.739691 + 5.14467i) q^{84} +(-1.13152 - 0.0326675i) q^{85} +(3.12086 + 1.42525i) q^{86} +(-1.52755 - 2.79750i) q^{87} +(-1.22667 + 3.28884i) q^{88} +(-1.60459 - 11.1602i) q^{89} +(0.163508 + 1.42886i) q^{90} -7.09953i q^{91} +(3.39218 + 3.39015i) q^{92} +(14.3987 - 14.3987i) q^{93} +(-0.592898 + 0.922568i) q^{94} +(-16.5754 + 0.705499i) q^{95} +(0.792907 + 1.73622i) q^{96} +(-0.972389 + 0.530964i) q^{97} +(0.145083 + 0.388984i) q^{98} +(-1.47844 + 1.70622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

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

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.212565	−	0.977147i	−0.150306	−	0.690947i
$2$	−0.212565	−	0.977147i	−0.150306	−	0.690947i
$3$	−1.52800	−	1.14385i	−0.882192	−	0.660401i	0.0590054	−	0.998258i	$-0.481207\pi$
$3$	−1.52800	−	1.14385i	−0.882192	−	0.660401i	−0.941197	+	0.337857i	$0.890298\pi$
$4$	−0.909632	+	0.415415i	−0.454816	+	0.207708i
$5$	−0.841561	+	2.07166i	−0.376358	+	0.926475i
$5$	−0.841561	+	2.07166i	−0.376358	+	0.926475i
$6$	−0.792907	+	1.73622i	−0.323703	+	0.708811i
$7$	0.194262	+	2.71614i	0.0734242	+	1.02660i	0.891950	+	0.452135i	$0.149337\pi$
$7$	0.194262	+	2.71614i	0.0734242	+	1.02660i	−0.818526	+	0.574470i	$0.805208\pi$
$8$	0.599278	+	0.800541i	0.211877	+	0.283034i
$9$	0.181204	+	0.617123i	0.0604012	+	0.205708i
$10$	2.20320	+	0.381966i	0.696714	+	0.120788i
$11$	1.89773	+	2.95293i	0.572188	+	0.890342i	0.999908	−	0.0135693i	$-0.00431938\pi$
$11$	1.89773	+	2.95293i	0.572188	+	0.890342i	−0.427720	+	0.903911i	$0.640683\pi$
$12$	1.86509	+	0.405726i	0.538405	+	0.117123i
$13$	−2.60053	−	0.185993i	−0.721257	−	0.0515853i	−0.294115	−	0.955770i	$-0.595025\pi$
$13$	−2.60053	−	0.185993i	−0.721257	−	0.0515853i	−0.427142	+	0.904185i	$0.640479\pi$
$14$	2.61278	−	0.767180i	0.698294	−	0.205037i
$15$	3.65557	−	2.20288i	0.943864	−	0.568782i
$16$	0.654861	−	0.755750i	0.163715	−	0.188937i
$17$	0.176913	+	0.474323i	0.0429077	+	0.115040i	0.956636	−	0.291285i	$-0.0940828\pi$
$17$	0.176913	+	0.474323i	0.0429077	+	0.115040i	−0.913729	+	0.406325i	$0.866810\pi$
$18$	0.564502	−	0.308241i	0.133054	−	0.0726532i
$19$	3.08215	+	6.74897i	0.707094	+	1.54832i	0.831152	+	0.556045i	$0.187682\pi$
$19$	3.08215	+	6.74897i	0.707094	+	1.54832i	−0.124058	+	0.992275i	$0.539591\pi$
$20$	−0.0950878	−	2.23405i	−0.0212623	−	0.499548i
$21$	2.81002	−	4.37247i	0.613196	−	0.954152i
$22$	2.48205	−	2.48205i	0.529176	−	0.529176i
$23$	−1.67732	−	4.49295i	−0.349746	−	0.936845i
$23$	−1.67732	−	4.49295i	−0.349746	−	0.936845i
$24$		−	1.90871i		−	0.389614i
$25$	−3.58355	−	3.48686i	−0.716710	−	0.697371i
$26$	0.371039	+	2.58063i	0.0727668	+	0.506104i
$27$	−1.57206	+	4.21486i	−0.302544	+	0.811151i
$28$	−1.30503	−	2.38999i	−0.246628	−	0.451666i
$29$	1.51901	+	0.693708i	0.282073	+	0.128818i	0.551428	−	0.834223i	$-0.314083\pi$
$29$	1.51901	+	0.693708i	0.282073	+	0.128818i	−0.269355	+	0.963041i	$0.586810\pi$
$30$	−2.92959	−	3.10377i	−0.534867	−	0.566669i
$31$	−1.51827	+	10.5598i	−0.272689	+	1.89659i	0.147349	+	0.989085i	$0.452926\pi$
$31$	−1.51827	+	10.5598i	−0.272689	+	1.89659i	−0.420038	+	0.907507i	$0.637983\pi$
$32$	−0.877679	−	0.479249i	−0.155153	−	0.0847201i
$33$	0.477963	−	6.68280i	0.0832027	−	1.16333i
$34$	0.425877	−	0.273695i	0.0730373	−	0.0469382i
$35$	−5.79040	−	1.88335i	−0.978757	−	0.318345i
$36$	−0.421191	−	0.486080i	−0.0701984	−	0.0810133i
$37$	−0.403846	+	0.739590i	−0.0663919	+	0.121588i	−0.908767	−	0.417304i	$-0.862975\pi$
$37$	−0.403846	+	0.739590i	−0.0663919	+	0.121588i	0.842375	+	0.538892i	$0.181157\pi$
$38$	5.93958	−	4.44631i	0.963526	−	0.721287i
$39$	3.76086	+	3.25881i	0.602220	+	0.521827i
$40$	−2.16278	+	0.567795i	−0.341965	+	0.0897763i
$41$	−6.80249	−	1.99739i	−1.06237	−	0.311940i	−0.296565	−	0.955013i	$-0.595841\pi$
$41$	−6.80249	−	1.99739i	−1.06237	−	0.311940i	−0.765805	+	0.643073i	$0.777659\pi$
$42$	−4.86986	−	1.81636i	−0.751436	−	0.280271i
$43$	−2.05606	+	2.74658i	−0.313546	+	0.418849i	−0.929436	−	0.368984i	$-0.879706\pi$
$43$	−2.05606	+	2.74658i	−0.313546	+	0.418849i	0.615890	+	0.787833i	$0.288797\pi$
$44$	−2.95293	−	1.89773i	−0.445171	−	0.286094i
$45$	−1.43096	−	0.143954i	−0.213315	−	0.0214594i
$46$	−4.03373	+	2.59403i	−0.594741	+	0.382469i
$47$	−0.775455	−	0.775455i	−0.113112	−	0.113112i	0.648286	−	0.761397i	$-0.275486\pi$
$47$	−0.775455	−	0.775455i	−0.113112	−	0.113112i	−0.761397	+	0.648286i	$0.775486\pi$
$48$	−1.86509	+	0.405726i	−0.269203	+	0.0585614i
$49$	−0.410934	+	0.0590834i	−0.0587048	+	0.00844048i
$50$	−2.64543	+	4.24284i	−0.374121	+	0.600028i
$51$	0.272229	−	0.927127i	0.0381197	−	0.129824i
$52$	2.44279	−	0.911113i	0.338754	−	0.126349i
$53$	−6.99930	+	0.500600i	−0.961428	+	0.0687627i	−0.543221	−	0.839589i	$-0.682796\pi$
$53$	−6.99930	+	0.500600i	−0.961428	+	0.0687627i	−0.418206	+	0.908352i	$0.637341\pi$
$54$	4.45271	+	0.640203i	0.605937	+	0.0871205i
$55$	−7.71453	+	1.44639i	−1.04023	+	0.195031i
$56$	−2.05797	+	1.78324i	−0.275007	+	0.238295i
$57$	3.01026	−	13.8379i	0.398719	−	1.83288i
$58$	0.354966	−	1.63175i	0.0466094	−	0.214260i
$59$	10.1487	−	8.79387i	1.32124	−	1.14486i	0.342560	−	0.939496i	$-0.388706\pi$
$59$	10.1487	−	8.79387i	1.32124	−	1.14486i	0.978685	−	0.205369i	$-0.0658394\pi$
$60$	−2.41011	+	3.52239i	−0.311144	+	0.454739i
$61$	3.87817	+	0.557596i	0.496548	+	0.0713929i	0.386039	−	0.922482i	$-0.373843\pi$
$61$	3.87817	+	0.557596i	0.496548	+	0.0713929i	0.110509	+	0.993875i	$0.464752\pi$
$62$	10.6412	−	0.761072i	1.35143	−	0.0966563i
$63$	−1.64099	+	0.612058i	−0.206745	+	0.0771121i
$64$	−0.281733	+	0.959493i	−0.0352166	+	0.119937i
$65$	2.57382	−	5.23089i	0.319243	−	0.648812i
$66$	−6.63168	+	0.953491i	−0.816303	+	0.117367i
$67$	6.64026	−	1.44450i	0.811237	−	0.176474i	0.212232	−	0.977219i	$-0.431927\pi$
$67$	6.64026	−	1.44450i	0.811237	−	0.176474i	0.599005	+	0.800746i	$0.295563\pi$
$68$	−0.357967	−	0.357967i	−0.0434098	−	0.0434098i
$69$	−2.57630	+	8.78383i	−0.310150	+	1.05745i
$70$	−0.609474	+	6.05841i	−0.0728460	+	0.724119i
$71$	−12.1107	−	7.78309i	−1.43728	−	0.923683i	−0.999700	−	0.0245031i	$-0.992200\pi$
$71$	−12.1107	−	7.78309i	−1.43728	−	0.923683i	−0.437579	−	0.899180i	$-0.644164\pi$
$72$	−0.385441	+	0.514889i	−0.0454246	+	0.0606802i
$73$	4.78023	+	1.78293i	0.559484	+	0.208677i	0.613266	−	0.789876i	$-0.289855\pi$
$73$	4.78023	+	1.78293i	0.559484	+	0.208677i	−0.0537829	+	0.998553i	$0.517128\pi$
$74$	0.808531	+	0.237406i	0.0939899	+	0.0275979i
$75$	1.48724	+	9.42696i	0.171731	+	1.08853i
$76$	−5.60725	−	4.85871i	−0.643195	−	0.557332i
$77$	−7.65192	+	5.72815i	−0.872017	+	0.652784i
$78$	2.38490	−	4.36762i	0.270037	−	0.494536i
$79$	−0.340883	−	0.393400i	−0.0383524	−	0.0442610i	0.736249	−	0.676710i	$-0.236595\pi$
$79$	−0.340883	−	0.393400i	−0.0383524	−	0.0442610i	−0.774602	+	0.632449i	$0.782050\pi$
$80$	1.01455	+	1.99266i	0.113430	+	0.222786i
$81$	8.84650	−	5.68530i	0.982944	−	0.631700i
$82$	−0.505771	+	7.07160i	−0.0558531	+	0.780928i
$83$	10.0407	+	5.48264i	1.10211	+	0.601798i	0.924069	−	0.382225i	$-0.124842\pi$
$83$	10.0407	+	5.48264i	1.10211	+	0.601798i	0.178041	+	0.984023i	$0.443024\pi$
$84$	−0.739691	+	5.14467i	−0.0807069	+	0.561329i
$85$	−1.13152	−	0.0326675i	−0.122730	−	0.00354328i
$86$	3.12086	+	1.42525i	0.336531	+	0.153688i
$87$	−1.52755	−	2.79750i	−0.163771	−	0.299924i
$88$	−1.22667	+	3.28884i	−0.130764	+	0.350591i
$89$	−1.60459	−	11.1602i	−0.170086	−	1.18298i	−0.878698	−	0.477378i	$-0.841587\pi$
$89$	−1.60459	−	11.1602i	−0.170086	−	1.18298i	0.708612	−	0.705599i	$-0.249322\pi$
$90$	0.163508	+	1.42886i	0.0172353	+	0.150615i
$91$		−	7.09953i		−	0.744233i
$92$	3.39218	+	3.39015i	0.353660	+	0.353447i
$93$	14.3987	−	14.3987i	1.49307	−	1.49307i
$94$	−0.592898	+	0.922568i	−0.0611528	+	0.0951556i
$95$	−16.5754	+	0.705499i	−1.70060	+	0.0723827i
$96$	0.792907	+	1.73622i	0.0809257	+	0.177203i
$97$	−0.972389	+	0.530964i	−0.0987311	+	0.0539113i	−0.527856	−	0.849334i	$-0.677004\pi$
$97$	−0.972389	+	0.530964i	−0.0987311	+	0.0539113i	0.429125	+	0.903245i	$0.358822\pi$
$98$	0.145083	+	0.388984i	0.0146556	+	0.0392933i
$99$	−1.47844	+	1.70622i	−0.148589	+	0.171481i
$100$	4.70820	+	1.68310i	0.470820	+	0.168310i
$101$	12.6947	−	3.72749i	1.26317	−	0.370900i	0.419495	−	0.907757i	$-0.362207\pi$
$101$	12.6947	−	3.72749i	1.26317	−	0.370900i	0.843673	+	0.536858i	$0.180389\pi$
$102$	−0.963806	−	0.0689328i	−0.0954310	−	0.00682536i
$103$	−3.96955	−	0.863523i	−0.391131	−	0.0850854i	0.0126988	−	0.999919i	$-0.495958\pi$
$103$	−3.96955	−	0.863523i	−0.391131	−	0.0850854i	−0.403830	+	0.914834i	$0.632321\pi$
$104$	−1.40954	−	2.19329i	−0.138217	−	0.215070i
$105$	6.69348	+	9.50111i	0.653216	+	0.927213i
$106$	1.97697	+	6.73293i	0.192020	+	0.653960i
$107$	3.58645	+	4.79094i	0.346715	+	0.463158i	0.939672	−	0.342077i	$-0.111130\pi$
$107$	3.58645	+	4.79094i	0.346715	+	0.463158i	−0.592957	+	0.805234i	$0.702039\pi$
$108$	−0.320919	−	4.48703i	−0.0308804	−	0.431765i
$109$	−2.62843	+	5.75546i	−0.251758	+	0.551274i	−0.992744	−	0.120247i	$-0.961631\pi$
$109$	−2.62843	+	5.75546i	−0.251758	+	0.551274i	0.740986	+	0.671521i	$0.234359\pi$
$110$	3.05317	+	7.23077i	0.291109	+	0.689427i
$111$	1.46306	−	0.668155i	0.138867	−	0.0634185i
$112$	2.17994	+	1.63188i	0.205985	+	0.154198i
$113$	2.28880	+	10.5214i	0.215312	+	0.989774i	0.950213	+	0.311600i	$0.100865\pi$
$113$	2.28880	+	10.5214i	0.215312	+	0.989774i	−0.734901	+	0.678174i	$0.762771\pi$
$114$	−14.1616			−1.32635
$115$	10.7194	+	0.306252i	0.999592	+	0.0285581i
$116$	−1.66992			−0.155048
$117$	−0.356444	−	1.63855i	−0.0329533	−	0.151484i
$118$	−10.7502	−	8.04747i	−0.989633	−	0.740830i
$119$	−1.25396	+	0.572664i	−0.114950	+	0.0524960i
$120$	3.95420	+	1.60630i	0.360967	+	0.146634i
$121$	−0.548842	+	1.20180i	−0.0498947	+	0.109254i
$122$	−0.279510	−	3.90806i	−0.0253057	−	0.353820i
$123$	8.10950	+	10.8330i	0.731209	+	0.976781i
$124$	−3.00562	−	10.2362i	−0.269913	−	0.919240i
$125$	10.2394	−	4.48949i	0.915836	−	0.401553i
$126$	0.946888	+	1.47339i	0.0843555	+	0.131260i
$127$	0.632702	+	0.137636i	0.0561432	+	0.0122132i	0.240549	−	0.970637i	$-0.422672\pi$
$127$	0.632702	+	0.137636i	0.0561432	+	0.0122132i	−0.184406	+	0.982850i	$0.559036\pi$
$128$	0.997452	+	0.0713392i	0.0881631	+	0.00630555i
$129$	6.28333	−	1.84495i	0.553216	−	0.162439i
$130$	−5.65845	−	1.40309i	−0.496279	−	0.123059i
$131$	−1.91866	+	2.21425i	−0.167634	+	0.193460i	−0.833351	−	0.552745i	$-0.813580\pi$
$131$	−1.91866	+	2.21425i	−0.167634	+	0.193460i	0.665717	+	0.746205i	$0.268126\pi$
$132$	2.34136	+	6.27744i	0.203790	+	0.546381i
$133$	−17.7324	+	9.68263i	−1.53759	+	0.839590i
$134$	−2.82298	−	6.18146i	−0.243868	−	0.533997i
$135$	−7.40878	−	6.80384i	−0.637646	−	0.585582i
$136$	−0.273695	+	0.425877i	−0.0234691	+	0.0365187i
$137$	13.5632	−	13.5632i	1.15878	−	1.15878i	0.174044	−	0.984738i	$-0.444316\pi$
$137$	13.5632	−	13.5632i	1.15878	−	1.15878i	0.984738	−	0.174044i	$-0.0556835\pi$
$138$	9.13073	+	0.650285i	0.777259	+	0.0553560i
$139$			6.14198i			0.520956i	0.965480	+	0.260478i	$0.0838801\pi$
$139$			6.14198i			0.520956i	−0.965480	+	0.260478i	$0.916120\pi$
$140$	6.04951	−	0.692263i	0.511277	−	0.0585069i
$141$	0.297894	+	2.07190i	0.0250872	+	0.174485i
$142$	−5.03090	+	13.4884i	−0.422184	+	1.13192i
$143$	−4.38588	−	8.03215i	−0.366766	−	0.671682i
$144$	0.585053	+	0.267185i	0.0487544	+	0.0222654i
$145$	−2.71547	+	2.56307i	−0.225507	+	0.212852i
$146$	0.726077	−	5.04998i	0.0600906	−	0.417939i
$147$	0.695490	+	0.379766i	0.0573630	+	0.0313226i
$148$	0.0601150	−	0.840518i	0.00494143	−	0.0690902i
$149$	−9.71839	+	6.24563i	−0.796161	+	0.511662i	−0.874361	−	0.485276i	$-0.838719\pi$
$149$	−9.71839	+	6.24563i	−0.796161	+	0.511662i	0.0781999	+	0.996938i	$0.475083\pi$
$150$	8.89539	−	3.45709i	0.726305	−	0.282270i
$151$	13.4841	+	15.5614i	1.09732	+	1.26637i	0.961252	+	0.275671i	$0.0889000\pi$
$151$	13.4841	+	15.5614i	1.09732	+	1.26637i	0.136065	+	0.990700i	$0.456555\pi$
$152$	−3.55576	+	6.51190i	−0.288411	+	0.528184i
$153$	−0.260658	+	0.195126i	−0.0210729	+	0.0157750i
$154$	7.22378	+	6.25944i	0.582109	+	0.504400i
$155$	−20.5985	−	12.0320i	−1.65451	−	0.966435i
$156$	−4.77476	−	1.40200i	−0.382287	−	0.112249i
$157$	14.1577	+	5.28055i	1.12991	+	0.421434i	0.843744	−	0.536747i	$-0.180347\pi$
$157$	14.1577	+	5.28055i	1.12991	+	0.421434i	0.286165	+	0.958180i	$0.407620\pi$
$158$	−0.311950	+	0.416716i	−0.0248174	+	0.0331522i
$159$	11.2675	+	7.24121i	0.893575	+	0.574266i
$160$	1.73146	−	1.41494i	0.136884	−	0.111860i
$161$	11.8776	−	5.42865i	0.936089	−	0.427838i
$162$	−7.43583	−	7.43583i	−0.584214	−	0.584214i
$163$	−3.87801	+	0.843608i	−0.303749	+	0.0660765i	−0.361857	−	0.932234i	$-0.617857\pi$
$163$	−3.87801	+	0.843608i	−0.303749	+	0.0660765i	0.0581077	+	0.998310i	$0.481493\pi$
$164$	7.01751	−	1.00897i	0.547975	−	0.0787869i
$165$	13.4423	+	6.61416i	1.04648	+	0.514912i
$166$	3.22304	−	10.9767i	0.250156	−	0.851954i
$167$	−3.83606	+	1.43078i	−0.296843	+	0.110717i	−0.493473	−	0.869761i	$-0.664273\pi$
$167$	−3.83606	+	1.43078i	−0.296843	+	0.110717i	0.196630	+	0.980478i	$0.437000\pi$
$168$	5.18433	−	0.370790i	0.399979	−	0.0286071i
$169$	−6.13952	−	0.882730i	−0.472271	−	0.0679023i
$170$	0.208601	+	1.11260i	0.0159989	+	0.0853328i
$171$	−3.60644	+	3.12500i	−0.275792	+	0.238975i
$172$	0.729290	−	3.35249i	0.0556078	−	0.255625i
$173$	−2.66036	+	12.2295i	−0.202263	+	0.929789i	0.758339	+	0.651861i	$0.226011\pi$
$173$	−2.66036	+	12.2295i	−0.202263	+	0.929789i	−0.960602	+	0.277928i	$0.910352\pi$
$174$	−2.40887	+	2.08729i	−0.182616	+	0.158237i
$175$	8.77465	−	10.4108i	0.663301	−	0.786982i
$176$	3.47443	+	0.499547i	0.261895	+	0.0376548i
$177$	−25.5660	+	1.82852i	−1.92166	+	0.137440i
$178$	−10.5641	+	3.94019i	−0.791809	+	0.295330i
$179$	3.94983	−	13.4519i	0.295224	−	1.00544i	−0.669639	−	0.742687i	$-0.733551\pi$
$179$	3.94983	−	13.4519i	0.295224	−	1.00544i	0.964863	−	0.262754i	$-0.0846307\pi$
$180$	1.36145	−	0.463498i	0.101476	−	0.0345471i
$181$	−14.0538	+	2.02063i	−1.04461	+	0.150192i	−0.643194	−	0.765703i	$-0.722391\pi$
$181$	−14.0538	+	2.02063i	−1.04461	+	0.150192i	−0.401417	+	0.915896i	$0.631482\pi$
$182$	−6.93729	+	1.50911i	−0.514226	+	0.111863i
$183$	−5.28804	−	5.28804i	−0.390903	−	0.390903i
$184$	2.59161	−	4.03529i	0.191056	−	0.297485i
$185$	−1.19232	−	1.45904i	−0.0876609	−	0.107271i
$186$	−17.1303	−	11.0090i	−1.25605	−	0.807217i
$187$	−1.06491	+	1.42255i	−0.0778737	+	0.104027i
$188$	1.02751	+	0.383243i	0.0749392	+	0.0279509i
$189$	−11.7536	−	3.45116i	−0.854945	−	0.251035i
$190$	4.21273	+	16.0466i	0.305623	+	1.16414i
$191$	13.4768	+	11.6778i	0.975150	+	0.844972i	0.987923	−	0.154946i	$-0.0495203\pi$
$191$	13.4768	+	11.6778i	0.975150	+	0.844972i	−0.0127727	+	0.999918i	$0.504066\pi$
$192$	1.52800	−	1.14385i	0.110274	−	0.0825501i
$193$	1.58940	−	2.91077i	0.114407	−	0.209522i	−0.814201	−	0.580584i	$-0.802824\pi$
$193$	1.58940	−	2.91077i	0.114407	−	0.209522i	0.928608	+	0.371062i	$0.121006\pi$
$194$	0.725526	+	0.837302i	0.0520898	+	0.0601148i
$195$	−9.91613	+	5.04874i	−0.710109	+	0.361548i
$196$	0.349254	−	0.224452i	0.0249467	−	0.0160323i
$197$	1.16935	−	16.3497i	0.0833130	−	1.16487i	−0.768085	−	0.640348i	$-0.778790\pi$
$197$	1.16935	−	16.3497i	0.0833130	−	1.16487i	0.851398	−	0.524520i	$-0.175755\pi$
$198$	1.98149	+	1.08197i	0.140818	+	0.0768926i
$199$	−0.227833	+	1.58462i	−0.0161507	+	0.112330i	−0.996302	−	0.0859203i	$-0.972617\pi$
$199$	−0.227833	+	1.58462i	−0.0161507	+	0.112330i	0.980151	+	0.198251i	$0.0635260\pi$
$200$	0.643831	−	4.95837i	0.0455257	−	0.350610i
$201$	−11.7986	−	5.38825i	−0.832210	−	0.380058i
$202$	−6.34076	−	11.6122i	−0.446134	−	0.817034i
$203$	−1.58912	+	4.26061i	−0.111535	+	0.299036i
$204$	0.137514	+	0.956433i	0.00962792	+	0.0669637i
$205$	9.86262	−	12.4115i	0.688835	−	0.866858i
$206$			4.06239i			0.283040i
$207$	2.46876	−	1.84925i	0.171591	−	0.128532i
$208$	−1.84355	+	1.84355i	−0.127827	+	0.127827i
$209$	−14.0801	+	21.9091i	−0.973943	+	1.51549i
$210$	7.86118	−	8.56012i	0.542473	−	0.590704i
$211$	−7.91762	−	17.3372i	−0.545072	−	1.19354i	−0.959046	−	0.283252i	$-0.908587\pi$
$211$	−7.91762	−	17.3372i	−0.545072	−	1.19354i	0.413974	−	0.910289i	$-0.364140\pi$
$212$	6.15883	−	3.36298i	0.422990	−	0.230970i
$213$	9.60254	+	25.7454i	0.657955	+	1.76405i
$214$	3.91910	−	4.52288i	0.267904	−	0.309178i
$215$	−3.95967	−	6.57087i	−0.270047	−	0.448130i
$216$	−4.31627	+	1.26737i	−0.293685	+	0.0862338i
$217$	−28.9768	−	2.07246i	−1.96707	−	0.140688i
$218$	6.18265	+	1.34495i	0.418742	+	0.0910917i
$219$	−5.26479	−	8.19218i	−0.355762	−	0.553576i
$220$	6.41653	−	4.52041i	0.432602	−	0.304766i
$221$	−0.371847	−	1.26639i	−0.0250131	−	0.0851869i
$222$	−0.963881	−	1.28759i	−0.0646914	−	0.0864176i
$223$	−1.11200	−	15.5478i	−0.0744649	−	1.04116i	−0.888061	−	0.459725i	$-0.847948\pi$
$223$	−1.11200	−	15.5478i	−0.0744649	−	1.04116i	0.813596	−	0.581430i	$-0.197507\pi$
$224$	1.13121	−	2.47700i	0.0755820	−	0.165502i
$225$	1.50247	−	2.84332i	0.100164	−	0.189555i
$226$	9.79448	−	4.47299i	0.651519	−	0.297539i
$227$	14.0952	+	10.5515i	0.935531	+	0.700330i	0.954097	−	0.299498i	$-0.0968192\pi$
$227$	14.0952	+	10.5515i	0.935531	+	0.700330i	−0.0185662	+	0.999828i	$0.505910\pi$
$228$	3.01026	+	13.8379i	0.199359	+	0.916440i
$229$	−20.4427			−1.35089			−0.675446	−	0.737409i	$-0.736049\pi$
$229$	−20.4427			−1.35089			−0.675446	+	0.737409i	$0.736049\pi$
$230$	−1.97933	−	10.5396i	−0.130513	−	0.694958i
$231$	18.2443			1.20039
$232$	0.354966	+	1.63175i	0.0233047	+	0.107130i
$233$	4.57262	+	3.42302i	0.299562	+	0.224250i	0.738476	−	0.674280i	$-0.235546\pi$
$233$	4.57262	+	3.42302i	0.299562	+	0.224250i	−0.438914	+	0.898529i	$0.644637\pi$
$234$	−1.52533	+	0.696597i	−0.0997142	+	0.0455380i
$235$	2.25907	−	0.953886i	0.147366	−	0.0622247i
$236$	−5.57845	+	12.2151i	−0.363126	+	0.795135i
$237$	0.0708802	+	0.991035i	0.00460416	+	0.0643746i
$238$	0.826125	+	1.10357i	0.0535497	+	0.0715341i
$239$	−3.98993	−	13.5885i	−0.258087	−	0.878964i	−0.981969	−	0.189041i	$-0.939462\pi$
$239$	−3.98993	−	13.5885i	−0.258087	−	0.878964i	0.723882	−	0.689924i	$-0.242356\pi$
$240$	0.729062	−	4.20528i	0.0470608	−	0.271449i
$241$	−2.55334	−	3.97307i	−0.164475	−	0.255928i	0.749227	−	0.662314i	$-0.230425\pi$
$241$	−2.55334	−	3.97307i	−0.164475	−	0.255928i	−0.913702	+	0.406386i	$0.866789\pi$
$242$	1.29100	+	0.280839i	0.0829884	+	0.0180530i
$243$	−6.55948	−	0.469143i	−0.420791	−	0.0300955i
$244$	−3.75934	+	1.10384i	−0.240667	+	0.0706662i
$245$	0.223425	−	0.901037i	0.0142741	−	0.0575652i
$246$	8.86166	−	10.2269i	0.564999	−	0.652043i
$247$	−6.75996	−	18.1241i	−0.430126	−	1.15321i
$248$	−9.36340	+	5.11280i	−0.594576	+	0.324663i
$249$	−9.07090	−	19.8625i	−0.574845	−	1.25874i
$250$	−6.56343	−	9.05105i	−0.415108	−	0.572438i
$251$	−14.1240	+	21.9773i	−0.891497	+	1.38720i	0.0303076	+	0.999541i	$0.490351\pi$
$251$	−14.1240	+	21.9773i	−0.891497	+	1.38720i	−0.921804	+	0.387655i	$0.873285\pi$
$252$	1.23844	−	1.23844i	0.0780144	−	0.0780144i
$253$	10.0843	−	13.4794i	0.633992	−	0.847445i
$254$		−	0.647500i		−	0.0406277i
$255$	1.69159	+	1.34420i	0.105932	+	0.0841771i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	2.14373	−	5.74757i	0.133722	−	0.358523i	−0.852780	−	0.522270i	$-0.825085\pi$
$257$	2.14373	−	5.74757i	0.133722	−	0.358523i	0.986502	+	0.163747i	$0.0523580\pi$
$258$	−3.13841	−	5.74756i	−0.195389	−	0.357828i
$259$	−2.08728	−	0.953230i	−0.129697	−	0.0592308i
$260$	−0.168239	+	5.82738i	−0.0104338	+	0.361399i
$261$	−0.152853	+	1.06312i	−0.00946138	+	0.0658053i
$262$	2.57149	+	1.40414i	0.158867	+	0.0867480i
$263$	−1.07656	+	15.0523i	−0.0663838	+	0.928167i	0.849722	+	0.527231i	$0.176770\pi$
$263$	−1.07656	+	15.0523i	−0.0663838	+	0.928167i	−0.916106	+	0.400936i	$0.868685\pi$
$264$	5.63629	−	3.62222i	0.346890	−	0.222932i
$265$	4.85326	−	14.9215i	0.298134	−	0.916618i
$266$	13.2306	+	15.2690i	0.811223	+	0.936201i
$267$	−10.3137	+	18.8882i	−0.631190	+	1.15594i
$268$	−5.44012	+	4.07243i	−0.332308	+	0.248763i
$269$	18.8247	+	16.3117i	1.14776	+	0.994542i	0.999985	+	0.00552156i	$0.00175758\pi$
$269$	18.8247	+	16.3117i	1.14776	+	0.994542i	0.147778	+	0.989021i	$0.452788\pi$
$270$	−5.07351	+	8.68573i	−0.308764	+	0.528596i
$271$	25.5606	+	7.50528i	1.55270	+	0.455913i	0.941906	−	0.335877i	$-0.109033\pi$
$271$	25.5606	+	7.50528i	1.55270	+	0.455913i	0.610793	+	0.791790i	$0.290851\pi$
$272$	0.474323	+	0.176913i	0.0287600	+	0.0107269i
$273$	−8.12078	+	10.8481i	−0.491492	+	0.656557i
$274$	−16.1363	−	10.3702i	−0.974829	−	0.626485i
$275$	3.49582	−	17.1991i	0.210806	−	1.03714i
$276$	−1.30545	−	9.06029i	−0.0785789	−	0.545365i
$277$	3.22806	+	3.22806i	0.193955	+	0.193955i	0.797403	−	0.603447i	$-0.206207\pi$
$277$	3.22806	+	3.22806i	0.193955	+	0.193955i	−0.603447	+	0.797403i	$0.706207\pi$
$278$	6.00161	−	1.30557i	0.359953	−	0.0783030i
$279$	−6.79179	+	0.976512i	−0.406614	+	0.0584622i
$280$	−1.96236	−	5.76411i	−0.117273	−	0.344471i
$281$	4.45264	−	15.1643i	0.265622	−	0.904626i	−0.713380	−	0.700777i	$-0.752837\pi$
$281$	4.45264	−	15.1643i	0.265622	−	0.904626i	0.979002	−	0.203849i	$-0.0653451\pi$
$282$	1.96123	−	0.731500i	0.116789	−	0.0435602i
$283$	13.7320	−	0.982129i	0.816280	−	0.0583815i	0.343047	−	0.939318i	$-0.388541\pi$
$283$	13.7320	−	0.982129i	0.816280	−	0.0583815i	0.473234	+	0.880937i	$0.343087\pi$
$284$	14.2495	+	2.04877i	0.845553	+	0.121572i
$285$	26.1342	+	17.8817i	1.54806	+	1.05922i
$286$	−6.91630	+	5.99301i	−0.408969	+	0.354374i
$287$	4.10373	−	18.8645i	0.242235	−	1.11354i
$288$	0.136717	−	0.628477i	0.00805612	−	0.0370334i
$289$	12.6541	−	10.9648i	0.744356	−	0.644989i
$290$	3.08171	+	2.10859i	0.180964	+	0.123821i
$291$	2.09315	+	0.300950i	0.122703	+	0.0176420i
$292$	−5.08891	+	0.363966i	−0.297806	+	0.0212995i
$293$	−19.4179	+	7.24251i	−1.13441	+	0.423112i	−0.845357	−	0.534202i	$-0.820612\pi$
$293$	−19.4179	+	7.24251i	−1.13441	+	0.423112i	−0.289050	+	0.957314i	$0.593339\pi$
$294$	0.223250	−	0.760321i	0.0130202	−	0.0443428i
$295$	9.67719	+	28.4252i	0.563428	+	1.65498i
$296$	−0.834088	+	0.119924i	−0.0484804	+	0.00697043i
$297$	−15.4296	+	3.35649i	−0.895314	+	0.194764i
$298$	8.16869	+	8.16869i	0.473199	+	0.473199i
$299$	3.52626	+	11.9960i	0.203929	+	0.693747i
$300$	−5.26894	−	7.95724i	−0.304202	−	0.459412i
$301$	−7.85950	−	5.05100i	−0.453014	−	0.291135i
$302$	12.3396	−	16.4837i	0.710062	−	0.948531i
$303$	−23.6612	−	8.82516i	−1.35930	−	0.506992i
$304$	7.11891	+	2.09030i	0.408297	+	0.119887i
$305$	−4.41886	+	7.56499i	−0.253023	+	0.433170i
$306$	0.246074	+	0.213224i	0.0140671	+	0.0121892i
$307$	−26.7894	+	20.0543i	−1.52895	+	1.14456i	−0.586625	+	0.809858i	$0.699544\pi$
$307$	−26.7894	+	20.0543i	−1.52895	+	1.14456i	−0.942325	+	0.334699i	$0.891365\pi$
$308$	4.58087	−	8.38923i	0.261019	−	0.478021i
$309$	5.07774	+	5.86002i	0.288863	+	0.333365i
$310$	−7.37852	+	22.6854i	−0.419072	+	1.28844i
$311$	3.65807	−	2.35090i	0.207430	−	0.133307i	−0.432801	−	0.901489i	$-0.642475\pi$
$311$	3.65807	−	2.35090i	0.207430	−	0.133307i	0.640231	+	0.768182i	$0.278838\pi$
$312$	−0.355008	+	4.96366i	−0.0200984	+	0.281012i
$313$	26.2858	+	14.3531i	1.48576	+	0.811287i	0.998092	−	0.0617418i	$-0.0196655\pi$
$313$	26.2858	+	14.3531i	1.48576	+	0.811287i	0.487669	+	0.873029i	$0.337847\pi$
$314$	2.15044	−	14.9566i	0.121356	−	0.844051i
$315$	0.113018	−	3.91466i	0.00636785	−	0.220566i
$316$	0.473503	+	0.216241i	0.0266366	+	0.0121645i
$317$	14.0964	+	25.8156i	0.791732	+	1.44995i	0.890570	+	0.454846i	$0.150306\pi$
$317$	14.0964	+	25.8156i	0.791732	+	1.44995i	−0.0988381	+	0.995104i	$0.531513\pi$
$318$	4.68064	−	12.5493i	0.262477	−	0.703729i
$319$	0.834202	+	5.80200i	0.0467064	+	0.324850i
$320$	−1.75065	−	1.39113i	−0.0978642	−	0.0777663i
$321$		−	11.4229i		−	0.637565i
$322$	−7.82936	−	10.4523i	−0.436313	−	0.582482i
$323$	−2.65592	+	2.65592i	−0.147779	+	0.147779i
$324$	−5.68530	+	8.84650i	−0.315850	+	0.491472i
$325$	8.67059	+	9.73419i	0.480958	+	0.539956i
$326$	1.64866	+	3.61006i	0.0913108	+	0.199943i
$327$	10.5996	−	5.78783i	0.586160	−	0.320068i
$328$	−2.47759	−	6.64266i	−0.136802	−	0.366780i
$329$	1.95560	−	2.25689i	0.107816	−	0.124426i
$330$	3.60565	−	14.5410i	0.198485	−	0.800456i
$331$	22.0320	−	6.46919i	1.21099	−	0.355579i	0.386945	−	0.922103i	$-0.373530\pi$
$331$	22.0320	−	6.46919i	1.21099	−	0.355579i	0.824045	+	0.566524i	$0.191712\pi$
$332$	−11.4109	−	0.816125i	−0.626255	−	0.0447907i
$333$	−0.529596	−	0.115207i	−0.0290217	−	0.00631328i
$334$	2.21349	+	3.44426i	0.121117	+	0.188462i
$335$	−2.59567	+	14.9720i	−0.141817	+	0.818007i
$336$	−1.46432	−	4.98703i	−0.0798855	−	0.272065i
$337$	6.00418	+	8.02064i	0.327068	+	0.436912i	0.933692	−	0.358077i	$-0.116567\pi$
$337$	6.00418	+	8.02064i	0.327068	+	0.436912i	−0.606624	+	0.794989i	$0.707477\pi$
$338$	0.442493	+	6.18686i	0.0240684	+	0.336521i
$339$	8.53764	−	18.6948i	0.463701	−	1.01536i
$340$	1.04284	−	0.440334i	0.0565557	−	0.0238805i
$341$	−34.0635	+	15.5563i	−1.84464	+	0.842421i
$342$	3.82019	+	2.85976i	0.206572	+	0.154638i
$343$	3.81152	+	17.5213i	0.205803	+	0.946059i
$344$	−3.43090			−0.184982
$345$	−16.0290	−	12.7293i	−0.862972	−	0.685325i
$346$	12.5155			0.672836
$347$	5.35330	+	24.6087i	0.287380	+	1.32106i	0.863768	+	0.503889i	$0.168098\pi$
$347$	5.35330	+	24.6087i	0.287380	+	1.32106i	−0.576388	+	0.817176i	$0.695538\pi$
$348$	2.55164	+	1.91013i	0.136782	+	0.102394i
$349$	26.8981	−	12.2840i	1.43982	−	0.657546i	0.465987	−	0.884792i	$-0.345699\pi$
$349$	26.8981	−	12.2840i	1.43982	−	0.657546i	0.973837	+	0.227246i	$0.0729722\pi$
$350$	−12.0381	−	6.36114i	−0.643461	−	0.340017i
$351$	4.87213	−	10.6685i	0.260055	−	0.569441i
$352$	−0.250412	−	3.50121i	−0.0133470	−	0.186615i
$353$	7.45571	+	9.95966i	0.396827	+	0.530099i	0.953804	−	0.300429i	$-0.0971297\pi$
$353$	7.45571	+	9.95966i	0.396827	+	0.530099i	−0.556977	+	0.830528i	$0.688039\pi$
$354$	7.22118	+	24.5931i	0.383802	+	1.30711i
$355$	26.3158	−	18.5394i	1.39670	−	0.983967i
$356$	6.09569	+	9.48508i	0.323071	+	0.502708i
$357$	2.57109	+	0.559307i	0.136077	+	0.0296017i
$358$	−13.9841	−	1.00016i	−0.739080	−	0.0528601i
$359$	−22.4059	+	6.57897i	−1.18254	+	0.347225i	−0.813152	−	0.582051i	$-0.802250\pi$
$359$	−22.4059	+	6.57897i	−1.18254	+	0.347225i	−0.369387	+	0.929276i	$0.620432\pi$
$360$	−0.742302	−	1.23181i	−0.0391228	−	0.0649222i
$361$	−23.6066	+	27.2434i	−1.24245	+	1.43387i
$362$	4.96180	+	13.3031i	0.260787	+	0.699196i
$363$	2.21330	−	1.20855i	0.116168	−	0.0634327i
$364$	2.94925	+	6.45796i	0.154583	+	0.338489i
$365$	−7.71649	+	8.40256i	−0.403899	+	0.439810i
$366$	−4.04314	+	6.29125i	−0.211338	+	0.328849i
$367$	−17.3758	+	17.3758i	−0.907007	+	0.907007i	−0.996030	−	0.0890223i	$-0.971626\pi$
$367$	−17.3758	+	17.3758i	−0.907007	+	0.907007i	0.0890223	+	0.996030i	$0.471626\pi$
$368$	−4.49396	−	1.67462i	−0.234264	−	0.0872957i
$369$		−	4.55990i		−	0.237379i
$370$	−1.17225	+	1.47521i	−0.0609426	+	0.0766925i
$371$	−2.71940	−	18.9138i	−0.141184	−	0.981957i
$372$	−7.11607	+	19.0789i	−0.368951	+	0.989197i
$373$	−13.4528	−	24.6369i	−0.696558	−	1.27565i	−0.951188	−	0.308612i	$-0.900135\pi$
$373$	−13.4528	−	24.6369i	−0.696558	−	1.27565i	0.254630	−	0.967039i	$-0.418046\pi$
$374$	1.61640	+	0.738186i	0.0835822	+	0.0381707i
$375$	−20.7811	−	4.85231i	−1.07313	−	0.250572i
$376$	0.156071	−	1.08550i	0.00804874	−	0.0559802i
$377$	−3.82120	−	2.08653i	−0.196802	−	0.107462i
$378$	−0.873888	+	12.2185i	−0.0449479	+	0.628454i
$379$	19.5801	−	12.5833i	1.00576	−	0.646363i	0.0694676	−	0.997584i	$-0.477870\pi$
$379$	19.5801	−	12.5833i	1.00576	−	0.646363i	0.936292	+	0.351222i	$0.114234\pi$
$380$	14.7844	−	7.52741i	0.758425	−	0.386148i
$381$	−0.809335	−	0.934023i	−0.0414635	−	0.0478514i
$382$	8.54617	−	15.6511i	0.437260	−	0.800782i
$383$	16.1039	−	12.0552i	0.822871	−	0.615994i	−0.102638	−	0.994719i	$-0.532728\pi$
$383$	16.1039	−	12.0552i	0.822871	−	0.615994i	0.925509	+	0.378725i	$0.123637\pi$
$384$	−1.44251	−	1.24994i	−0.0736126	−	0.0637857i
$385$	−5.42723	−	20.6728i	−0.276597	−	1.05358i
$386$	−3.18210	−	0.934348i	−0.161965	−	0.0475571i
$387$	−2.06754	−	0.771153i	−0.105099	−	0.0391999i
$388$	0.663945	−	0.886927i	0.0337067	−	0.0450269i
$389$	−19.8783	−	12.7750i	−1.00787	−	0.647720i	−0.0710303	−	0.997474i	$-0.522629\pi$
$389$	−19.8783	−	12.7750i	−1.00787	−	0.647720i	−0.936841	+	0.349754i	$0.886265\pi$
$390$	7.04119	+	8.61633i	0.356545	+	0.436305i
$391$	1.83437	−	1.59045i	0.0927679	−	0.0804327i
$392$	−0.293562	−	0.293562i	−0.0148271	−	0.0148271i
$393$	5.46448	−	1.18872i	0.275647	−	0.0599632i
$394$	−16.2246	+	2.33275i	−0.817384	+	0.117522i
$395$	1.10187	−	0.375124i	0.0554409	−	0.0188745i
$396$	0.636053	−	2.16620i	0.0319628	−	0.108855i
$397$	−9.19072	+	3.42796i	−0.461269	+	0.172044i	−0.569346	−	0.822098i	$-0.692803\pi$
$397$	−9.19072	+	3.42796i	−0.461269	+	0.172044i	0.108077	+	0.994143i	$0.465531\pi$
$398$	1.59683	−	0.114208i	0.0800419	−	0.00572471i
$399$	38.1706	+	5.48810i	1.91092	+	0.274749i
$400$	−4.98192	+	0.424861i	−0.249096	+	0.0212430i
$401$	2.67939	−	2.32171i	0.133803	−	0.115941i	−0.585389	−	0.810753i	$-0.699058\pi$
$401$	2.67939	−	2.32171i	0.133803	−	0.115941i	0.719191	+	0.694812i	$0.244513\pi$
$402$	−2.75713	+	12.6743i	−0.137513	+	0.632138i
$403$	5.91234	−	27.1786i	0.294515	−	1.35386i
$404$	−9.99903	+	8.66421i	−0.497470	+	0.431061i
$405$	4.33314	+	23.1115i	0.215315	+	1.14842i
$406$	4.50103	+	0.647150i	0.223382	+	0.0321175i
$407$	−2.95035	+	0.211013i	−0.146243	+	0.0104595i
$408$	0.905344	−	0.337676i	0.0448212	−	0.0167175i
$409$	−2.18210	+	7.43155i	−0.107898	+	0.367466i	−0.995686	−	0.0927859i	$-0.970423\pi$
$409$	−2.18210	+	7.43155i	−0.107898	+	0.367466i	0.887788	+	0.460252i	$0.152241\pi$
$410$	−14.2243	−	6.99897i	−0.702489	−	0.345655i
$411$	−36.2388	+	5.21035i	−1.78753	+	0.257008i
$412$	3.96955	−	0.863523i	0.195566	−	0.0425427i
$413$	25.8569	+	25.8569i	1.27234	+	1.27234i
$414$	−2.33176	−	2.01926i	−0.114600	−	0.0992411i
$415$	−19.8080	+	16.1869i	−0.972338	+	0.794586i
$416$	2.19329	+	1.40954i	0.107535	+	0.0691085i
$417$	7.02549	−	9.38495i	0.344040	−	0.459583i
$418$	24.4014	+	9.10124i	1.19351	+	0.445156i
$419$	−30.0589	−	8.82609i	−1.46847	−	0.431182i	−0.552870	−	0.833267i	$-0.686467\pi$
$419$	−30.0589	−	8.82609i	−1.46847	−	0.431182i	−0.915602	+	0.402085i	$0.868286\pi$
$420$	−10.0355	−	5.86194i	−0.489682	−	0.286033i
$421$	6.26018	+	5.42448i	0.305102	+	0.264373i	0.793932	−	0.608007i	$-0.208031\pi$
$421$	6.26018	+	5.42448i	0.305102	+	0.264373i	−0.488830	+	0.872379i	$0.662576\pi$
$422$	−15.2580	+	11.4220i	−0.742746	+	0.556012i
$423$	0.338035	−	0.619066i	0.0164358	−	0.0301000i
$424$	−4.59527	−	5.30323i	−0.223166	−	0.257548i
$425$	1.01992	−	2.31663i	0.0494733	−	0.112373i
$426$	23.1159	−	14.8557i	1.11997	−	0.719760i
$427$	−0.761129	+	10.6420i	−0.0368336	+	0.515001i
$428$	−5.25258	−	2.86813i	−0.253893	−	0.138636i
$429$	−2.48591	+	17.2899i	−0.120021	+	0.834765i
$430$	−5.57902	+	5.26592i	−0.269044	+	0.253945i
$431$	−6.24076	−	2.85006i	−0.300607	−	0.137282i	0.259401	−	0.965770i	$-0.416475\pi$
$431$	−6.24076	−	2.85006i	−0.300607	−	0.137282i	−0.560008	+	0.828487i	$0.689202\pi$
$432$	2.15590	+	3.94823i	0.103726	+	0.189960i
$433$	11.8846	−	31.8638i	0.571136	−	1.53127i	−0.254501	−	0.967073i	$-0.581911\pi$
$433$	11.8846	−	31.8638i	0.571136	−	1.53127i	0.825637	−	0.564202i	$-0.190816\pi$
$434$	4.13436	+	28.7551i	0.198456	+	1.38029i
$435$	7.08100	−	0.810299i	0.339508	−	0.0388509i
$436$		−	6.32725i		−	0.303020i
$437$	25.1530	−	25.1681i	1.20323	−	1.20396i
$438$	−6.88585	+	6.88585i	−0.329019	+	0.329019i
$439$	13.2135	−	20.5606i	0.630645	−	0.981303i	−0.368029	−	0.929814i	$-0.619967\pi$
$439$	13.2135	−	20.5606i	0.630645	−	0.981303i	0.998674	−	0.0514883i	$-0.0163965\pi$
$440$	−5.78104	−	5.30901i	−0.275600	−	0.253097i
$441$	−0.110924	−	0.242890i	−0.00528211	−	0.0115662i
$442$	−1.15841	+	0.632540i	−0.0551000	+	0.0300869i
$443$	−11.2819	−	30.2479i	−0.536019	−	1.43712i	−0.869295	−	0.494293i	$-0.835427\pi$
$443$	−11.2819	−	30.2479i	−0.536019	−	1.43712i	0.333276	−	0.942829i	$-0.391846\pi$
$444$	−1.05328	+	1.21555i	−0.0499865	+	0.0576875i
$445$	24.4705	+	6.06780i	1.16001	+	0.287641i
$446$	−14.9561	+	4.39150i	−0.708191	+	0.207944i
$447$	21.9938	+	1.57302i	1.04027	+	0.0744015i
$448$	−2.66085	−	0.578832i	−0.125713	−	0.0273472i
$449$	−2.98949	−	4.65174i	−0.141083	−	0.219529i	0.763521	−	0.645784i	$-0.223469\pi$
$449$	−2.98949	−	4.65174i	−0.141083	−	0.219529i	−0.904603	+	0.426255i	$0.859833\pi$
$450$	−3.09771	−	0.863739i	−0.146028	−	0.0407170i
$451$	−7.01115	−	23.8778i	−0.330142	−	1.12436i
$452$	−6.45273	−	8.61984i	−0.303511	−	0.405443i
$453$	−2.80375	−	39.2016i	−0.131732	−	1.84185i
$454$	7.31424	−	16.0160i	0.343274	−	0.751666i
$455$	14.7078	+	5.97469i	0.689513	+	0.280098i
$456$	12.8818	−	5.88293i	0.603247	−	0.275494i
$457$	8.76528	+	6.56161i	0.410023	+	0.306939i	0.784305	−	0.620376i	$-0.213020\pi$
$457$	8.76528	+	6.56161i	0.410023	+	0.306939i	−0.374282	+	0.927315i	$0.622111\pi$
$458$	4.34541	+	19.9755i	0.203048	+	0.933395i
$459$	−2.27732			−0.106296
$460$	−9.87796	+	4.17444i	−0.460562	+	0.194634i
$461$	7.32613			0.341212			0.170606	−	0.985339i	$-0.445428\pi$
$461$	7.32613			0.341212			0.170606	+	0.985339i	$0.445428\pi$
$462$	−3.87810	−	17.8273i	−0.180426	−	0.829403i
$463$	19.9674	+	14.9474i	0.927966	+	0.694666i	0.952341	−	0.305036i	$-0.0986686\pi$
$463$	19.9674	+	14.9474i	0.927966	+	0.694666i	−0.0243749	+	0.999703i	$0.507760\pi$
$464$	1.51901	−	0.693708i	0.0705183	−	0.0322046i
$465$	17.7118	+	41.9465i	0.821365	+	1.94522i
$466$	2.37281	−	5.19574i	0.109918	−	0.240688i
$467$	−0.535220	−	7.48336i	−0.0247670	−	0.346288i	−0.994693	−	0.102888i	$-0.967192\pi$
$467$	−0.535220	−	7.48336i	−0.0247670	−	0.346288i	0.969926	−	0.243400i	$-0.0782629\pi$
$468$	1.00491	+	1.34240i	0.0464520	+	0.0620526i
$469$	5.21342	+	17.7553i	0.240733	+	0.819862i
$470$	−1.41229	−	2.00468i	−0.0651439	−	0.0924690i
$471$	−15.5929	−	24.2630i	−0.718481	−	1.11798i
$472$	13.1217	+	2.85446i	0.603977	+	0.131387i
$473$	−12.0123	−	0.859137i	−0.552326	−	0.0395032i
$474$	0.953320	−	0.279920i	0.0437874	−	0.0128571i
$475$	12.4876	−	34.9323i	0.572972	−	1.60280i
$476$	0.902748	−	1.04183i	0.0413774	−	0.0477521i
$477$	−1.57723	−	4.22872i	−0.0722164	−	0.193620i
$478$	−12.4298	+	6.78718i	−0.568526	+	0.310439i
$479$	−10.3005	−	22.5550i	−0.470642	−	1.03056i	−0.984931	−	0.172946i	$-0.944671\pi$
$479$	−10.3005	−	22.5550i	−0.470642	−	1.03056i	0.514289	−	0.857617i	$-0.328056\pi$
$480$	−4.26415	+	0.181495i	−0.194631	+	0.00828408i
$481$	1.18777	−	1.84821i	0.0541578	−	0.0842712i
$482$	−3.33952	+	3.33952i	−0.152111	+	0.152111i
$483$	−24.3586	−	5.29123i	−1.10835	−	0.240759i
$484$		−	1.32119i		−	0.0600541i
$485$	−0.281653	−	2.46130i	−0.0127892	−	0.111762i
$486$	0.935895	+	6.50930i	0.0424531	+	0.295268i
$487$	13.0803	−	35.0697i	0.592725	−	1.58916i	−0.200144	−	0.979767i	$-0.564141\pi$
$487$	13.0803	−	35.0697i	0.592725	−	1.58916i	0.792869	−	0.609392i	$-0.208586\pi$
$488$	1.87772	+	3.43879i	0.0850004	+	0.155667i
$489$	6.89056	+	3.14681i	0.311602	+	0.142304i
$490$	−0.927938	−	0.0267900i	−0.0419200	−	0.00121025i
$491$	−1.29544	+	9.00995i	−0.0584622	+	0.406613i	0.939486	+	0.342587i	$0.111303\pi$
$491$	−1.29544	+	9.00995i	−0.0584622	+	0.406613i	−0.997948	+	0.0640261i	$0.979606\pi$
$492$	−11.8769	−	6.48526i	−0.535450	−	0.292378i
$493$	−0.0603088	+	0.843227i	−0.00271617	+	0.0379770i
$494$	−16.2730	+	10.4580i	−0.732158	+	0.470529i
$495$	−2.29050	−	4.49872i	−0.102950	−	0.202202i
$496$	6.98629	+	8.06261i	0.313694	+	0.362022i
$497$	18.7873	−	34.4064i	0.842726	−	1.54334i
$498$	−17.4804	+	13.0857i	−0.783317	+	0.586384i
$499$	5.46203	+	4.73288i	0.244514	+	0.211873i	0.768492	−	0.639859i	$-0.221007\pi$
$499$	5.46203	+	4.73288i	0.244514	+	0.211873i	−0.523978	+	0.851732i	$0.675553\pi$
$500$	−7.44904	+	8.33737i	−0.333131	+	0.372859i
$501$	7.49809	+	2.20164i	0.334990	+	0.0983620i
$502$	24.4773	+	9.12957i	1.09248	+	0.407473i
$503$	−0.559754	+	0.747744i	−0.0249582	+	0.0333403i	−0.812847	−	0.582478i	$-0.802083\pi$
$503$	−0.559754	+	0.747744i	−0.0249582	+	0.0333403i	0.787889	+	0.615818i	$0.211174\pi$
$504$	−1.47339	−	0.946888i	−0.0656299	−	0.0421778i
$505$	−2.96125	+	29.4360i	−0.131774	+	1.30988i
$506$	−15.3149	−	6.98854i	−0.680832	−	0.310679i
$507$	8.37149	+	8.37149i	0.371791	+	0.371791i
$508$	−0.632702	+	0.137636i	−0.0280716	+	0.00610661i
$509$	7.45859	−	1.07238i	0.330596	−	0.0475325i	0.0249817	−	0.999688i	$-0.492047\pi$
$509$	7.45859	−	1.07238i	0.330596	−	0.0475325i	0.305614	+	0.952155i	$0.401138\pi$
$510$	0.953907	−	1.93867i	0.0422397	−	0.0858456i
$511$	−3.91408	+	13.3301i	−0.173149	+	0.589690i
$512$	−0.936950	+	0.349464i	−0.0414077	+	0.0154443i
$513$	−33.2913	+	2.38104i	−1.46985	+	0.105126i
$514$	−6.07190	−	0.873008i	−0.267820	−	0.0385067i
$515$	5.12954	−	7.49685i	0.226035	−	0.330351i
$516$	−4.94910	+	4.28842i	−0.217872	+	0.188787i
$517$	0.818258	−	3.76147i	0.0359869	−	0.165429i
$518$	−0.487762	+	2.24220i	−0.0214310	+	0.0985168i
$519$	18.0537	−	15.6436i	0.792468	−	0.686677i
$520$	5.72997	−	1.07431i	0.251276	−	0.0471114i
$521$	−33.0477	−	4.75155i	−1.44785	−	0.208169i	−0.626867	−	0.779126i	$-0.715663\pi$
$521$	−33.0477	−	4.75155i	−1.44785	−	0.208169i	−0.820980	+	0.570957i	$0.806572\pi$
$522$	1.07131	−	0.0766218i	0.0468901	−	0.00335365i
$523$	−33.0261	+	12.3181i	−1.44413	+	0.538632i	−0.944762	−	0.327758i	$-0.893707\pi$
$523$	−33.0261	+	12.3181i	−1.44413	+	0.538632i	−0.499367	+	0.866391i	$0.666434\pi$
$524$	0.825441	−	2.81119i	0.0360596	−	0.122808i
$525$	−25.3160	+	5.87085i	−1.10488	+	0.256225i
$526$	14.9372	−	2.14764i	0.651292	−	0.0936417i
$527$	−5.27734	+	1.14801i	−0.229885	+	0.0500083i
$528$	−4.73752	−	4.73752i	−0.206174	−	0.206174i
$529$	−17.3732	+	15.0722i	−0.755356	+	0.655315i
$530$	−15.6121	−	1.57057i	−0.678146	−	0.0682212i
$531$	7.26587	+	4.66949i	0.315312	+	0.202639i
$532$	12.1077	−	16.1739i	0.524933	−	0.701229i
$533$	17.3186	+	6.45949i	0.750150	+	0.279792i
$534$	20.6489	+	6.06305i	0.893564	+	0.262374i
$535$	−12.9434	+	3.39804i	−0.559593	+	0.146910i
$536$	5.13574	+	4.45014i	0.221830	+	0.192217i
$537$	−21.4222	+	16.0365i	−0.924438	+	0.692026i
$538$	11.9375	−	21.8618i	0.514660	−	0.942529i
$539$	−0.954312	−	1.10133i	−0.0411051	−	0.0474378i
$540$	9.56568	+	3.11128i	0.411641	+	0.133888i
$541$	−26.3540	+	16.9367i	−1.13305	+	0.728164i	−0.966194	−	0.257818i	$-0.916997\pi$
$541$	−26.3540	+	16.9367i	−1.13305	+	0.728164i	−0.166852	+	0.985982i	$0.553360\pi$
$542$	1.90046	−	26.5719i	0.0816316	−	1.14136i
$543$	23.7855	+	12.9879i	1.02073	+	0.557363i
$544$	0.0720456	−	0.501088i	0.00308893	−	0.0214840i
$545$	−9.71138	−	10.2888i	−0.415990	−	0.440723i
$546$	12.3264	+	5.62927i	0.527520	+	0.240910i
$547$	−14.6784	−	26.8815i	−0.627604	−	1.14937i	−0.977170	−	0.212459i	$-0.931853\pi$
$547$	−14.6784	−	26.8815i	−0.627604	−	1.14937i	0.349566	−	0.936912i	$-0.386329\pi$
$548$	−6.70316	+	17.9719i	−0.286345	+	0.767720i
$549$	0.358632	+	2.49434i	0.0153061	+	0.106456i
$550$	−17.5491	+	0.239998i	−0.748298	+	0.0102336i
$551$			12.3899i			0.527826i
$552$	−8.57574	+	3.20152i	−0.365008	+	0.136266i
$553$	1.00231	−	1.00231i	0.0426225	−	0.0426225i
$554$	2.46812	−	3.84046i	0.104860	−	0.163166i
$555$	0.152940	+	3.59325i	0.00649192	+	0.152525i
$556$	−2.55147	−	5.58694i	−0.108206	−	0.236939i
$557$	8.09607	−	4.42079i	0.343041	−	0.187315i	−0.298488	−	0.954413i	$-0.596482\pi$
$557$	8.09607	−	4.42079i	0.343041	−	0.187315i	0.641529	+	0.767099i	$0.278300\pi$
$558$	2.39789	+	6.42900i	0.101511	+	0.272161i
$559$	5.85769	−	6.76014i	0.247754	−	0.285923i
$560$	−5.21525	+	3.14276i	−0.220385	+	0.132806i
$561$	3.25436	−	0.955566i	0.137399	−	0.0403440i
$562$	−15.7642	−	1.12748i	−0.664974	−	0.0475598i
$563$	−23.3896	−	5.08810i	−0.985755	−	0.214438i	−0.309334	−	0.950953i	$-0.600106\pi$
$563$	−23.3896	−	5.08810i	−0.985755	−	0.214438i	−0.676421	+	0.736516i	$0.736470\pi$
$564$	−1.13167	−	1.76091i	−0.0476520	−	0.0741479i
$565$	−23.7230	−	4.11282i	−0.998035	−	0.173028i
$566$	−3.87862	−	13.2094i	−0.163031	−	0.555231i
$567$	17.1606	+	22.9239i	0.720678	+	0.962713i
$568$	−1.02700	−	14.3594i	−0.0430921	−	0.602506i
$569$	−3.29043	+	7.20503i	−0.137942	+	0.302051i	−0.965978	−	0.258624i	$-0.916731\pi$
$569$	−3.29043	+	7.20503i	−0.137942	+	0.302051i	0.828036	+	0.560675i	$0.189458\pi$
$570$	11.9178	−	29.3380i	0.499183	−	1.22883i
$571$	26.7887	−	12.2340i	1.12107	−	0.511976i	0.233366	−	0.972389i	$-0.425026\pi$
$571$	26.7887	−	12.2340i	1.12107	−	0.511976i	0.887705	+	0.460413i	$0.152299\pi$
$572$	7.32621	+	5.48433i	0.306324	+	0.229312i
$573$	−7.23507	−	33.2591i	−0.302249	−	1.38942i
$574$	−19.3057			−0.805806
$575$	−9.65551	+	21.9493i	−0.402662	+	0.915349i
$576$	−0.643176			−0.0267990
$577$	−0.294530	−	1.35393i	−0.0122615	−	0.0563650i	0.970610	−	0.240659i	$-0.0773637\pi$
$577$	−0.294530	−	1.35393i	−0.0122615	−	0.0563650i	−0.982871	+	0.184294i	$0.941000\pi$
$578$	−13.4040	−	10.0341i	−0.557534	−	0.417365i
$579$	−5.75808	+	2.62963i	−0.239298	+	0.109284i
$580$	1.40534	−	3.45950i	0.0583534	−	0.143648i
$581$	−12.9411	+	28.3370i	−0.536887	+	1.17562i
$582$	−0.150859	−	2.10929i	−0.00625332	−	0.0874329i
$583$	−14.7610	−	19.7184i	−0.611340	−	0.816654i
$584$	1.43737	+	4.89524i	0.0594789	+	0.202567i
$585$	3.69448	+	0.640507i	0.152748	+	0.0264817i
$586$	11.2046	+	17.4347i	0.462857	+	0.720219i
$587$	14.0867	+	3.06438i	0.581421	+	0.126480i	0.493651	−	0.869660i	$-0.335662\pi$
$587$	14.0867	+	3.06438i	0.581421	+	0.126480i	0.0877705	+	0.996141i	$0.472026\pi$
$588$	−0.790400	−	0.0565306i	−0.0325956	−	0.00233128i
$589$	−75.9471	+	22.3001i	−3.12935	+	0.918859i
$590$	25.7185	−	15.4982i	1.05882	−	0.638053i
$591$	−20.4883	+	23.6448i	−0.842777	+	0.972617i
$592$	0.294481	+	0.789535i	0.0121031	+	0.0324497i
$593$	12.9385	−	7.06496i	0.531321	−	0.290123i	−0.191107	−	0.981569i	$-0.561208\pi$
$593$	12.9385	−	7.06496i	0.531321	−	0.290123i	0.722428	+	0.691446i	$0.243026\pi$
$594$	6.55958	+	14.3635i	0.269143	+	0.589340i
$595$	−0.131082	−	3.07971i	−0.00537383	−	0.126256i
$596$	6.24563	−	9.71839i	0.255831	−	0.398081i
$597$	2.16069	−	2.16069i	0.0884311	−	0.0884311i
$598$	10.9723	−	5.99561i	0.448691	−	0.245179i
$599$			3.85951i			0.157695i	0.996887	+	0.0788477i	$0.0251241\pi$
$599$			3.85951i			0.157695i	−0.996887	+	0.0788477i	$0.974876\pi$
$600$	−6.65540	+	6.83996i	−0.271706	+	0.279240i
$601$	1.23220	+	8.57017i	0.0502627	+	0.349584i	0.999397	+	0.0347139i	$0.0110520\pi$
$601$	1.23220	+	8.57017i	0.0502627	+	0.349584i	−0.949135	+	0.314871i	$0.898039\pi$
$602$	−3.26491	+	8.75356i	−0.133068	+	0.356768i
$603$	2.09467	+	3.83610i	0.0853016	+	0.156218i
$604$	−18.7300	−	8.55369i	−0.762112	−	0.348045i
$605$	−2.02783	−	2.14840i	−0.0824430	−	0.0873448i
$606$	−3.59394	+	24.9964i	−0.145994	+	1.01541i
$607$	−22.4617	−	12.2650i	−0.911691	−	0.497821i	−0.0463052	−	0.998927i	$-0.514745\pi$
$607$	−22.4617	−	12.2650i	−0.911691	−	0.497821i	−0.865386	+	0.501106i	$0.832926\pi$
$608$	0.529297	−	7.40055i	0.0214658	−	0.300132i
$609$	7.30167	−	4.69250i	0.295878	−	0.190150i
$610$	8.33141	+	2.70982i	0.337329	+	0.109718i
$611$	1.87236	+	2.16082i	0.0757477	+	0.0874175i
$612$	0.156044	−	0.285774i	0.00630772	−	0.0115517i
$613$	18.7037	−	14.0014i	0.755436	−	0.565512i	−0.150659	−	0.988586i	$-0.548140\pi$
$613$	18.7037	−	14.0014i	0.755436	−	0.565512i	0.906095	+	0.423073i	$0.139049\pi$
$614$	25.2905	+	21.9143i	1.02064	+	0.884390i
$615$	−29.2670	+	7.68348i	−1.18016	+	0.309828i
$616$	−9.17125	−	2.69292i	−0.369520	−	0.108501i
$617$	−16.2954	−	6.07786i	−0.656027	−	0.244686i	−0.000664471	−	1.00000i	$-0.500212\pi$
$617$	−16.2954	−	6.07786i	−0.656027	−	0.244686i	−0.655363	+	0.755314i	$0.727484\pi$
$618$	4.64675	−	6.20734i	0.186920	−	0.249696i
$619$	21.8424	+	14.0373i	0.877920	+	0.564205i	0.900166	−	0.435547i	$-0.143445\pi$
$619$	21.8424	+	14.0373i	0.877920	+	0.564205i	−0.0222455	+	0.999753i	$0.507082\pi$
$620$	23.7354	+	2.38777i	0.953236	+	0.0958951i
$621$	21.5740	−	0.00648145i	0.865736	−	0.000260092i
$622$	−3.07475	−	3.07475i	−0.123286	−	0.123286i
$623$	30.0009	−	6.52630i	1.20196	−	0.261471i
$624$	4.92568	−	0.708206i	0.197185	−	0.0283509i
$625$	0.683662	+	24.9907i	0.0273465	+	0.999626i
$626$	8.43767	−	28.7361i	0.337237	−	1.14852i
$627$	46.5752	−	17.3716i	1.86003	−	0.693756i
$628$	−15.0719	+	1.07797i	−0.601435	+	0.0430155i
$629$	−0.422250	−	0.0607103i	−0.0168362	−	0.00242068i
$630$	−3.84922	+	0.721686i	−0.153357	+	0.0287526i
$631$	3.90881	−	3.38700i	0.155607	−	0.134834i	−0.573578	−	0.819151i	$-0.694445\pi$
$631$	3.90881	−	3.38700i	0.155607	−	0.134834i	0.729185	+	0.684317i	$0.239899\pi$
$632$	0.110649	−	0.508647i	0.00440140	−	0.0202329i
$633$	−7.73295	+	35.5478i	−0.307357	+	1.41290i
$634$	22.2292	−	19.2617i	0.882836	−	0.764982i
$635$	−0.817592	+	1.19491i	−0.0324452	+	0.0474187i
$636$	−13.2574	−	1.90613i	−0.525691	−	0.0755830i
$637$	1.07963	−	0.0772170i	0.0427767	−	0.00305945i
$638$	5.49209	−	2.04844i	0.217434	−	0.0810986i
$639$	2.60862	−	8.88413i	0.103195	−	0.351451i
$640$	−0.987207	+	2.00635i	−0.0390228	+	0.0793078i
$641$	29.4952	−	4.24077i	1.16499	−	0.167501i	0.467433	−	0.884028i	$-0.345179\pi$
$641$	29.4952	−	4.24077i	1.16499	−	0.167501i	0.697558	+	0.716528i	$0.254270\pi$
$642$	−11.1619	+	2.42812i	−0.440524	+	0.0958301i
$643$	−9.46253	−	9.46253i	−0.373166	−	0.373166i	0.495463	−	0.868629i	$-0.334998\pi$
$643$	−9.46253	−	9.46253i	−0.373166	−	0.373166i	−0.868629	+	0.495463i	$0.834998\pi$
$644$	−8.54914	+	9.87223i	−0.336883	+	0.389020i
$645$	−1.46569	+	14.5696i	−0.0577116	+	0.573676i
$646$	3.15977	+	2.03066i	0.124320	+	0.0798954i
$647$	−12.9360	+	17.2804i	−0.508565	+	0.679363i	−0.979184	−	0.202973i	$-0.934940\pi$
$647$	−12.9360	+	17.2804i	−0.508565	+	0.679363i	0.470619	+	0.882336i	$0.344031\pi$
$648$	9.85282	+	3.67491i	0.387056	+	0.144364i
$649$	45.2272	+	13.2799i	1.77532	+	0.521281i
$650$	7.66866	−	10.5416i	0.300790	−	0.413475i
$651$	41.9060	+	36.3117i	1.64242	+	1.42317i
$652$	3.17711	−	2.37835i	0.124425	−	0.0931436i
$653$	−9.83948	+	18.0197i	−0.385049	+	0.705164i	−0.996270	−	0.0862963i	$-0.972497\pi$
$653$	−9.83948	+	18.0197i	−0.385049	+	0.705164i	0.611221	+	0.791460i	$0.290679\pi$
$654$	−7.90867	−	9.12710i	−0.309254	−	0.356898i
$655$	−2.97251	−	5.83824i	−0.116145	−	0.228119i
$656$	−5.96421	+	3.83296i	−0.232863	+	0.149652i
$657$	−0.234094	+	3.27306i	−0.00913288	+	0.127694i
$658$	−2.62100	−	1.43118i	−0.102177	−	0.0557930i
$659$	−3.24669	+	22.5812i	−0.126473	+	0.879640i	0.823502	+	0.567314i	$0.192017\pi$
$659$	−3.24669	+	22.5812i	−0.126473	+	0.879640i	−0.949975	+	0.312326i	$0.898892\pi$
$660$	−14.9751	−	0.432339i	−0.582906	−	0.0168288i
$661$	12.5052	+	5.71093i	0.486395	+	0.222129i	0.643490	−	0.765454i	$-0.277486\pi$
$661$	12.5052	+	5.71093i	0.486395	+	0.222129i	−0.157095	+	0.987583i	$0.550213\pi$
$662$	−11.0046	−	20.1534i	−0.427705	−	0.783284i
$663$	−0.880379	+	2.36039i	−0.0341911	+	0.0916699i
$664$	1.62809	+	11.3236i	0.0631822	+	0.439442i
$665$	−5.13621	−	44.8840i	−0.199174	−	1.74053i
$666$			0.541982i			0.0210014i
$667$	0.568930	−	7.98841i	0.0220291	−	0.309312i
$668$	2.89504	−	2.89504i	0.112012	−	0.112012i
$669$	−16.0851	+	25.0290i	−0.621887	+	0.967676i
$670$	15.1816	−	0.646175i	0.586516	−	0.0249639i
$671$	5.71318	+	12.5101i	0.220555	+	0.482948i
$672$	−4.56180	+	2.49093i	−0.175975	+	0.0960897i
$673$	−9.93453	−	26.6355i	−0.382948	−	1.02672i	−0.975269	−	0.221021i	$-0.929061\pi$
$673$	−9.93453	−	26.6355i	−0.382948	−	1.02672i	0.592321	−	0.805702i	$-0.298212\pi$
$674$	6.56106	−	7.57187i	0.252723	−	0.291658i
$675$	20.3302	−	9.62262i	0.782509	−	0.370375i
$676$	5.95141	−	1.74749i	0.228900	−	0.0672112i
$677$	47.6127	+	3.40533i	1.82990	+	0.130877i	0.943361	−	0.331769i	$-0.107645\pi$
$677$	47.6127	+	3.40533i	1.82990	+	0.130877i	0.886543	+	0.462646i	$0.153100\pi$
$678$	−20.0824	−	4.36866i	−0.771260	−	0.167777i
$679$	−1.63107	−	2.53800i	−0.0625948	−	0.0973995i
$680$	−0.651942	−	0.925404i	−0.0250008	−	0.0354876i
$681$	−9.46813	−	32.2455i	−0.362820	−	1.23565i
$682$	22.4415	+	29.9784i	0.859330	+	1.14793i
$683$	0.681711	+	9.53157i	0.0260849	+	0.364715i	0.993683	+	0.112221i	$0.0357964\pi$
$683$	0.681711	+	9.53157i	0.0260849	+	0.364715i	−0.967598	+	0.252494i	$0.918749\pi$
$684$	1.98236	−	4.34077i	0.0757976	−	0.165974i
$685$	16.6841	+	39.5126i	0.637466	+	1.50970i
$686$	16.3106	−	7.44882i	0.622743	−	0.284397i
$687$	31.2365	+	23.3833i	1.19175	+	0.892130i
$688$	0.729290	+	3.35249i	0.0278039	+	0.127813i
$689$	18.2950			0.696983
$690$	−9.03123	+	18.3685i	−0.343813	+	0.699277i
$691$	−34.6221			−1.31709			−0.658543	−	0.752544i	$-0.728827\pi$
$691$	−34.6221			−1.31709			−0.658543	+	0.752544i	$0.728827\pi$
$692$	−2.66036	−	12.2295i	−0.101132	−	0.464894i
$693$	−4.92153	−	3.68421i	−0.186953	−	0.139952i
$694$	22.9084	−	10.4619i	0.869591	−	0.397129i
$695$	−12.7241	−	5.16885i	−0.482652	−	0.196066i
$696$	1.32409	−	2.89935i	0.0501894	−	0.109900i
$697$	−0.256042	−	3.57994i	−0.00969829	−	0.135600i
$698$	−17.7208	−	23.6723i	−0.670744	−	0.896009i
$699$	−3.07156	−	10.4608i	−0.116177	−	0.395662i
$700$	−3.65690	+	13.1151i	−0.138218	+	0.495705i
$701$	9.66538	+	15.0396i	0.365056	+	0.568039i	0.974387	−	0.224877i	$-0.0721982\pi$
$701$	9.66538	+	15.0396i	0.365056	+	0.568039i	−0.609331	+	0.792916i	$0.708562\pi$
$702$	−11.4603	−	2.49304i	−0.432542	−	0.0940937i
$703$	−6.23618	−	0.446021i	−0.235202	−	0.0168220i
$704$	−3.36797	+	0.988925i	−0.126935	+	0.0372715i
$705$	−4.54296	−	1.12649i	−0.171098	−	0.0424262i
$706$	8.14723	−	9.40240i	0.306625	−	0.353864i
$707$	12.5905	+	33.7564i	0.473514	+	1.26954i
$708$	22.4961	−	12.2838i	0.845455	−	0.461653i
$709$	1.16284	+	2.54627i	0.0436714	+	0.0956271i	0.930210	−	0.367027i	$-0.119624\pi$
$709$	1.16284	+	2.54627i	0.0436714	+	0.0956271i	−0.886539	+	0.462654i	$0.846897\pi$
$710$	−23.7095	−	21.7736i	−0.889802	−	0.817149i
$711$	0.181007	−	0.281652i	0.00678829	−	0.0105628i
$712$	7.97259	−	7.97259i	0.298785	−	0.298785i
$713$	49.9911	−	10.8906i	1.87218	−	0.407858i
$714$		−	2.63122i		−	0.0984711i
$715$	20.3309	−	2.32652i	0.760331	−	0.0870068i
$716$	1.99522	+	13.8771i	0.0745650	+	0.518611i
$717$	−9.44651	+	25.3271i	−0.352786	+	0.945856i
$718$	11.1913	+	20.4954i	0.417657	+	0.764882i
$719$	−14.2897	−	6.52587i	−0.532915	−	0.243374i	0.130735	−	0.991417i	$-0.458266\pi$
$719$	−14.2897	−	6.52587i	−0.532915	−	0.243374i	−0.663650	+	0.748043i	$0.730994\pi$
$720$	−1.04587	+	0.987179i	−0.0389774	+	0.0367900i
$721$	1.57432	−	10.9496i	0.0586306	−	0.407785i
$722$	31.6388	+	17.2761i	1.17747	+	0.642949i
$723$	−0.643084	+	8.99149i	−0.0239165	+	0.334397i
$724$	11.9444	−	7.67619i	0.443910	−	0.285283i
$725$	−3.02459	−	7.78251i	−0.112330	−	0.289035i
$726$	−1.65141	−	1.90582i	−0.0612895	−	0.0707318i
$727$	−6.35042	+	11.6299i	−0.235524	+	0.431330i	−0.968532	−	0.248890i	$-0.919934\pi$
$727$	−6.35042	+	11.6299i	−0.235524	+	0.431330i	0.733008	+	0.680220i	$0.238116\pi$
$728$	5.68347	−	4.25459i	0.210643	−	0.157686i
$729$	−14.3558	−	12.4394i	−0.531696	−	0.460717i
$730$	9.85080	+	5.75405i	0.364594	+	0.212967i
$731$	−1.66651	−	0.489331i	−0.0616380	−	0.0180985i
$732$	7.00690	+	2.61344i	0.258983	+	0.0965955i
$733$	11.4284	−	15.2666i	0.422118	−	0.563884i	−0.538190	−	0.842823i	$-0.680892\pi$
$733$	11.4284	−	15.2666i	0.422118	−	0.563884i	0.960309	+	0.278939i	$0.0899828\pi$
$734$	20.6722	+	13.2852i	0.763023	+	0.490365i
$735$	−1.37204	+	1.12122i	−0.0506086	+	0.0413569i
$736$	−0.681092	+	4.74722i	−0.0251054	+	0.174985i
$737$	16.8669	+	16.8669i	0.621302	+	0.621302i
$738$	−4.45570	+	0.969277i	−0.164016	+	0.0356796i
$739$	−19.2249	+	2.76412i	−0.707200	+	0.101680i	−0.486524	−	0.873667i	$-0.661735\pi$
$739$	−19.2249	+	2.76412i	−0.707200	+	0.101680i	−0.220676	+	0.975347i	$0.570826\pi$
$740$	1.69068	+	0.831885i	0.0621505	+	0.0305807i
$741$	−10.4020	+	35.4261i	−0.382128	+	1.30141i
$742$	−17.9035	+	6.67768i	−0.657260	+	0.245145i
$743$	23.0742	−	1.65030i	0.846510	−	0.0605436i	0.358657	−	0.933469i	$-0.383235\pi$
$743$	23.0742	−	1.65030i	0.846510	−	0.0605436i	0.487853	+	0.872926i	$0.337780\pi$
$744$	20.1555	+	2.89793i	0.738938	+	0.106243i
$745$	−4.76020	−	25.3893i	−0.174400	−	0.930191i
$746$	−21.2143	+	18.3823i	−0.776710	+	0.673023i
$747$	−1.56405	+	7.18982i	−0.0572256	+	0.263062i
$748$	0.377725	−	1.73638i	0.0138110	−	0.0634882i
$749$	−12.3162	+	10.6720i	−0.450023	+	0.389947i
$750$	−0.324090	+	21.3376i	−0.0118341	+	0.779138i
$751$	3.38947	+	0.487332i	0.123684	+	0.0177830i	0.203879	−	0.978996i	$-0.434645\pi$
$751$	3.38947	+	0.487332i	0.123684	+	0.0177830i	−0.0801950	+	0.996779i	$0.525554\pi$
$752$	−1.09386	+	0.0782347i	−0.0398891	+	0.00285293i
$753$	46.7201	−	17.4257i	1.70258	−	0.635028i
$754$	−1.22660	+	4.17740i	−0.0446700	+	0.152132i
$755$	−43.5856	+	14.8385i	−1.58624	+	0.540028i
$756$	12.1251	−	1.74332i	0.440985	−	0.0634040i
$757$	24.9505	−	5.42765i	0.906842	−	0.197271i	0.265126	−	0.964214i	$-0.414586\pi$
$757$	24.9505	−	5.42765i	0.906842	−	0.197271i	0.641716	+	0.766942i	$0.278223\pi$
$758$	−16.4578	−	16.4578i	−0.597775	−	0.597775i
$759$	−30.8272	+	9.06174i	−1.11896	+	0.328920i
$760$	−10.4980	−	12.8465i	−0.380804	−	0.465991i
$761$	−18.7361	−	12.0410i	−0.679184	−	0.436485i	0.155042	−	0.987908i	$-0.450449\pi$
$761$	−18.7361	−	12.0410i	−0.679184	−	0.436485i	−0.834226	+	0.551423i	$0.814085\pi$
$762$	−0.740641	+	0.989380i	−0.0268306	+	0.0358415i
$763$	−16.1433	−	6.02112i	−0.584425	−	0.217979i
$764$	−17.1101	−	5.02397i	−0.619021	−	0.181761i
$765$	−0.184875	−	0.704205i	−0.00668418	−	0.0254606i
$766$	−15.2029	−	13.1734i	−0.549302	−	0.475973i
$767$	−28.0275	+	20.9811i	−1.01201	+	0.757585i
$768$	−0.914748	+	1.67524i	−0.0330081	+	0.0604498i
$769$	30.0590	+	34.6899i	1.08395	+	1.25095i	0.966169	+	0.257911i	$0.0830340\pi$
$769$	30.0590	+	34.6899i	1.08395	+	1.25095i	0.117785	+	0.993039i	$0.462421\pi$
$770$	−19.0467	+	9.69751i	−0.686395	+	0.349474i
$771$	−9.84997	+	6.33019i	−0.354738	+	0.227976i
$772$	−0.236592	+	3.30799i	−0.00851513	+	0.119057i
$773$	−4.62232	−	2.52398i	−0.166253	−	0.0907812i	0.393968	−	0.919124i	$-0.371102\pi$
$773$	−4.62232	−	2.52398i	−0.166253	−	0.0907812i	−0.560221	+	0.828343i	$0.689284\pi$
$774$	−0.314042	+	2.18421i	−0.0112880	+	0.0785098i
$775$	42.2612	−	32.5475i	1.51807	−	1.16914i
$776$	−1.00779	−	0.460242i	−0.0361775	−	0.0165217i
$777$	2.09902	+	3.84407i	0.0753019	+	0.137905i
$778$	−8.25764	+	22.1396i	−0.296051	+	0.793743i
$779$	−7.48597	−	52.0660i	−0.268213	−	1.86546i
$780$	6.92271	−	8.71181i	0.247873	−	0.311933i
$781$		−	50.5324i		−	1.80819i
$782$	−1.94403	−	1.45437i	−0.0695183	−	0.0520082i
$783$	−5.31187	+	5.31187i	−0.189831	+	0.189831i
$784$	−0.224452	+	0.349254i	−0.00801615	+	0.0124734i
$785$	−22.8541	+	24.8860i	−0.815697	+	0.888221i
$786$	−2.32312	−	5.08692i	−0.0828629	−	0.181444i
$787$	−33.8934	+	18.5072i	−1.20817	+	0.659711i	−0.951756	−	0.306856i	$-0.900723\pi$
$787$	−33.8934	+	18.5072i	−1.20817	+	0.659711i	−0.256414	+	0.966567i	$0.582541\pi$
$788$	5.72823	+	15.3580i	0.204060	+	0.547105i
$789$	18.8626	−	21.7686i	0.671526	−	0.774982i
$790$	−0.600770	−	0.996946i	−0.0213744	−	0.0354698i
$791$	−28.1331	+	8.26062i	−1.00030	+	0.293714i
$792$	−2.25189	−	0.161059i	−0.0800176	−	0.00572297i
$793$	−9.98157	−	2.17136i	−0.354456	−	0.0771072i
$794$	5.30325	+	8.25201i	0.188205	+	0.292853i
$795$	−24.4837	+	17.2486i	−0.868346	+	0.611745i
$796$	−0.451029	−	1.53606i	−0.0159863	−	0.0544443i
$797$	−23.8793	−	31.8991i	−0.845850	−	1.12992i	−0.990097	−	0.140381i	$-0.955167\pi$
$797$	−23.8793	−	31.8991i	−0.845850	−	1.12992i	0.144248	−	0.989542i	$-0.453924\pi$
$798$	−2.75106	−	38.4649i	−0.0973865	−	1.36164i
$799$	0.230627	−	0.505004i	0.00815901	−	0.0178657i
$800$	1.47413	+	4.77775i	0.0521185	+	0.168919i
$801$	6.59644	−	3.01249i	0.233074	−	0.106441i
$802$	−2.83820	−	2.12465i	−0.100220	−	0.0750239i
$803$	3.80672	+	17.4992i	0.134336	+	0.617534i
$804$	12.9708			0.457443
$805$	1.25056	+	29.1750i	0.0440764	+	1.02828i
$806$	−27.8142			−0.979715
$807$	−10.1061	−	46.4569i	−0.355751	−	1.63536i
$808$	10.5917	+	7.92881i	0.372613	+	0.278935i
$809$	24.6869	−	11.2741i	0.867945	−	0.396377i	0.0688821	−	0.997625i	$-0.478057\pi$
$809$	24.6869	−	11.2741i	0.867945	−	0.396377i	0.799063	+	0.601248i	$0.205329\pi$
$810$	21.6622	−	9.14681i	0.761133	−	0.321386i
$811$	0.0399424	−	0.0874616i	0.00140257	−	0.00307119i	−0.908929	−	0.416950i	$-0.863099\pi$
$811$	0.0399424	−	0.0874616i	0.00140257	−	0.00307119i	0.910332	+	0.413879i	$0.135826\pi$
$812$	−0.324402	−	4.53573i	−0.0113843	−	0.159173i
$813$	−30.4718	−	40.7056i	−1.06869	−	1.42761i
$814$	0.833333	+	2.83807i	0.0292083	+	0.0994743i
$815$	1.51591	−	8.74386i	0.0531000	−	0.306284i
$816$	−0.522404	−	0.812876i	−0.0182878	−	0.0284564i
$817$	−24.8736	−	5.41093i	−0.870219	−	0.189305i
$818$	7.72555	+	0.552542i	0.270118	+	0.0193192i
$819$	4.38128	−	1.28646i	0.153094	−	0.0449526i
$820$	−3.81543	+	15.3870i	−0.133240	+	0.537337i
$821$	4.51461	−	5.21014i	0.157561	−	0.181835i	−0.671480	−	0.741022i	$-0.734341\pi$
$821$	4.51461	−	5.21014i	0.157561	−	0.181835i	0.829041	+	0.559187i	$0.188887\pi$
$822$	12.7944	+	34.3031i	0.446256	+	1.19646i
$823$	−9.76656	+	5.33294i	−0.340441	+	0.185895i	−0.640370	−	0.768067i	$-0.721219\pi$
$823$	−9.76656	+	5.33294i	−0.340441	+	0.185895i	0.299929	+	0.953962i	$0.403037\pi$
$824$	−1.68758	−	3.69528i	−0.0587895	−	0.128731i
$825$	−25.0148	+	22.2816i	−0.870902	+	0.775744i
$826$	19.7697	−	30.7623i	0.687876	−	1.07036i
$827$	17.8222	−	17.8222i	0.619738	−	0.619738i	−0.325726	−	0.945464i	$-0.605609\pi$
$827$	17.8222	−	17.8222i	0.619738	−	0.619738i	0.945464	+	0.325726i	$0.105609\pi$
$828$	−1.47746	+	2.70770i	−0.0513453	+	0.0940991i
$829$		−	21.3229i		−	0.740573i	−0.928918	−	0.370287i	$-0.879259\pi$
$829$		−	21.3229i		−	0.740573i	0.928918	−	0.370287i	$-0.120741\pi$
$830$	20.0275	+	15.9146i	0.695165	+	0.552403i
$831$	−1.24007	−	8.62489i	−0.0430176	−	0.299194i
$832$	0.911113	−	2.44279i	0.0315872	−	0.0846884i
$833$	−0.100724	−	0.184463i	−0.00348989	−	0.00639125i
$834$	−10.6638	−	4.87002i	−0.369259	−	0.168635i
$835$	0.264196	−	9.15110i	0.00914289	−	0.316687i
$836$	3.70637	−	25.7783i	0.128187	−	0.891562i
$837$	−42.1212	−	22.9999i	−1.45592	−	0.794993i
$838$	−2.23491	+	31.2481i	−0.0772035	+	1.07945i
$839$	−16.5502	+	10.6362i	−0.571377	+	0.367202i	−0.794199	−	0.607657i	$-0.792109\pi$
$839$	−16.5502	+	10.6362i	−0.571377	+	0.367202i	0.222822	+	0.974859i	$0.428473\pi$
$840$	−3.59478	+	11.0522i	−0.124032	+	0.381337i
$841$	−17.1648	−	19.8092i	−0.591890	−	0.683077i
$842$	3.96981	−	7.27017i	0.136809	−	0.250547i
$843$	−24.1493	+	18.0779i	−0.831746	+	0.622637i
$844$	14.4042	+	12.4813i	0.495815	+	0.429626i
$845$	6.99550	−	11.9761i	0.240653	−	0.411992i
$846$	−0.676773	−	0.198718i	−0.0232679	−	0.00683208i
$847$	−3.37087	−	1.25727i	−0.115824	−	0.0432002i
$848$	−4.20524	+	5.61754i	−0.144408	+	0.192907i
$849$	−22.1059	−	14.2066i	−0.758671	−	0.487568i
$850$	−2.48049	−	0.504174i	−0.0850800	−	0.0172930i
$851$	4.00032	+	0.573932i	0.137129	+	0.0196741i
$852$	−19.4298	−	19.4298i	−0.665654	−	0.665654i
$853$	7.55686	−	1.64389i	0.258742	−	0.0562859i	−0.0813231	−	0.996688i	$-0.525915\pi$
$853$	7.55686	−	1.64389i	0.258742	−	0.0562859i	0.340065	+	0.940402i	$0.389551\pi$
$854$	10.5606	−	1.51838i	0.361375	−	0.0519578i
$855$	−3.43890	−	10.1012i	−0.117608	−	0.345454i
$856$	−1.68606	+	5.74221i	−0.0576285	+	0.196265i
$857$	44.0200	−	16.4186i	1.50369	−	0.560849i	0.543310	−	0.839532i	$-0.317171\pi$
$857$	44.0200	−	16.4186i	1.50369	−	0.560849i	0.960383	+	0.278683i	$0.0898979\pi$
$858$	17.4232	−	1.24613i	0.594818	−	0.0425422i
$859$	28.4060	+	4.08417i	0.969200	+	0.139350i	0.608692	−	0.793406i	$-0.291694\pi$
$859$	28.4060	+	4.08417i	0.969200	+	0.139350i	0.360508	+	0.932756i	$0.382603\pi$
$860$	6.33148	+	4.33217i	0.215902	+	0.147726i
$861$	−27.8487	+	24.1310i	−0.949079	+	0.822382i
$862$	−1.45836	+	6.70396i	−0.0496718	+	0.228338i
$863$	−4.45934	+	20.4993i	−0.151798	+	0.697803i	0.836835	+	0.547455i	$0.184403\pi$
$863$	−4.45934	+	20.4993i	−0.151798	+	0.697803i	−0.988633	+	0.150348i	$0.951961\pi$
$864$	3.39974	−	2.94589i	0.115661	−	0.100221i
$865$	−23.0964	−	15.8032i	−0.785302	−	0.537325i
$866$	−33.6618	−	4.83984i	−1.14388	−	0.164464i
$867$	−31.8775	+	2.27992i	−1.08262	+	0.0774302i
$868$	27.2191	−	10.1522i	0.923878	−	0.344588i
$869$	0.514778	−	1.75317i	0.0174627	−	0.0594723i
$870$	−2.29696	−	6.74694i	−0.0778741	−	0.228743i
$871$	−17.5368	+	2.52142i	−0.594213	+	0.0854350i
$872$	−6.18265	+	1.34495i	−0.209371	+	0.0455458i
$873$	−0.503871	−	0.503871i	−0.0170534	−	0.0170534i
$874$	−29.9396	−	19.2283i	−1.01272	−	0.650408i
$875$	14.1832	+	26.9394i	0.479480	+	0.910718i
$876$	8.19218	+	5.26479i	0.276788	+	0.177881i
$877$	−8.27657	+	11.0562i	−0.279480	+	0.373342i	−0.918213	−	0.396087i	$-0.870368\pi$
$877$	−8.27657	+	11.0562i	−0.279480	+	0.373342i	0.638733	+	0.769428i	$0.279459\pi$
$878$	−22.8994	−	8.54105i	−0.772818	−	0.288246i
$879$	37.9549	+	11.1446i	1.28019	+	0.375897i
$880$	−3.95883	+	6.77743i	−0.133452	+	0.228467i
$881$	−1.48600	−	1.28763i	−0.0500646	−	0.0433812i	0.629469	−	0.777026i	$-0.283272\pi$
$881$	−1.48600	−	1.28763i	−0.0500646	−	0.0433812i	−0.679534	+	0.733644i	$0.737818\pi$
$882$	−0.213761	+	0.160019i	−0.00719771	+	0.00538814i
$883$	−12.9447	+	23.7064i	−0.435623	+	0.797785i	−0.999608	−	0.0280007i	$-0.991086\pi$
$883$	−12.9447	+	23.7064i	−0.435623	+	0.797785i	0.563984	+	0.825785i	$0.309268\pi$
$884$	0.864323	+	0.997482i	0.0290703	+	0.0335489i
$885$	17.7273	−	54.5029i	0.595897	−	1.83210i
$886$	−27.1585	+	17.4537i	−0.912409	+	0.586369i
$887$	−1.03645	+	14.4915i	−0.0348007	+	0.486577i	0.949927	+	0.312473i	$0.101157\pi$
$887$	−1.03645	+	14.4915i	−0.0348007	+	0.486577i	−0.984727	+	0.174104i	$0.944297\pi$
$888$	1.41166	+	0.770826i	0.0473723	+	0.0258672i
$889$	−0.250928	+	1.74525i	−0.00841587	+	0.0585337i
$890$	0.727566	−	25.2010i	0.0243881	−	0.844741i
$891$	33.5766	+	15.3339i	1.12486	+	0.513705i
$892$	7.47029	+	13.6808i	0.250124	+	0.458067i
$893$	2.84345	−	7.62359i	0.0951525	−	0.255114i
$894$	−3.13803	−	21.8255i	−0.104952	−	0.729954i
$895$	24.5437	+	19.5033i	0.820405	+	0.651923i
$896$			2.72308i			0.0909717i
$897$	8.33348	−	22.3634i	0.278247	−	0.746693i
$898$	−3.90997	+	3.90997i	−0.130477	+	0.130477i
$899$	−9.63166	+	14.9872i	−0.321234	+	0.499850i
$900$	−0.185533	+	3.21052i	−0.00618444	+	0.107017i
$901$	−1.47571	−	3.23136i	−0.0491632	−	0.107652i
$902$	−21.8418	+	11.9265i	−0.727252	+	0.397109i
$903$	6.23176	+	16.7080i	0.207380	+	0.556008i
$904$	−7.05122	+	8.13755i	−0.234520	+	0.270651i
$905$	7.64107	−	30.8152i	0.253998	−	1.02433i
$906$	−37.7097	+	11.0726i	−1.25282	+	0.367862i
$907$	−7.94060	−	0.567923i	−0.263663	−	0.0188576i	−0.0611184	−	0.998131i	$-0.519467\pi$
$907$	−7.94060	−	0.567923i	−0.263663	−	0.0188576i	−0.202545	+	0.979273i	$0.564921\pi$
$908$	−17.2047	−	3.74265i	−0.570958	−	0.124204i
$909$	4.60064	+	7.15874i	0.152594	+	0.237440i
$910$	2.71178	−	15.6417i	0.0898946	−	0.518518i
$911$	2.44951	+	8.34228i	0.0811560	+	0.276392i	0.990067	−	0.140599i	$-0.0449028\pi$
$911$	2.44951	+	8.34228i	0.0811560	+	0.276392i	−0.908911	+	0.416991i	$0.863085\pi$
$912$	−8.48672	−	11.3369i	−0.281023	−	0.375403i
$913$	2.86472	+	40.0541i	0.0948085	+	1.32560i
$914$	4.54846	−	9.95974i	0.150450	−	0.329439i
$915$	15.4052	−	6.50481i	0.509281	−	0.215042i
$916$	18.5953	−	8.49221i	0.614407	−	0.280590i
$917$	−6.38694	−	4.78120i	−0.210915	−	0.157889i
$918$	0.484080	+	2.22528i	0.0159770	+	0.0734452i
$919$	34.6202			1.14201			0.571007	−	0.820945i	$-0.306553\pi$
$919$	34.6202			1.14201			0.571007	+	0.820945i	$0.306553\pi$
$920$	6.17875	+	8.76488i	0.203707	+	0.288969i
$921$	63.8732			2.10469
$922$	−1.55728	−	7.15870i	−0.0512863	−	0.235759i
$923$	30.0467	+	22.4927i	0.988999	+	0.740355i
$924$	−16.5956	+	7.57895i	−0.545954	+	0.249329i
$925$	4.02605	−	1.24220i	0.132376	−	0.0408433i
$926$	10.3615	−	22.6884i	0.340499	−	0.745588i
$927$	−0.186397	−	2.60617i	−0.00612209	−	0.0855980i
$928$	−1.00074	−	1.33684i	−0.0328510	−	0.0438838i
$929$	5.10064	+	17.3712i	0.167347	+	0.569931i	0.999873	+	0.0159449i	$0.00507562\pi$
$929$	5.10064	+	17.3712i	0.167347	+	0.569931i	−0.832526	+	0.553986i	$0.813106\pi$
$930$	37.2230	−	26.2234i	1.22059	−	0.859900i
$931$	−1.66531	−	2.59128i	−0.0545784	−	0.0849256i
$932$	−5.58138	−	1.21415i	−0.182824	−	0.0397709i
$933$	−8.27861	−	0.592098i	−0.271029	−	0.0193844i
$934$	−7.19857	+	2.11369i	−0.235544	+	0.0691621i
$935$	−2.05085	−	3.40329i	−0.0670701	−	0.111299i
$936$	1.09812	−	1.26729i	0.0358930	−	0.0414228i
$937$	3.57013	+	9.57190i	0.116631	+	0.312700i	0.982128	−	0.188214i	$-0.0602699\pi$
$937$	3.57013	+	9.57190i	0.116631	+	0.312700i	−0.865497	+	0.500914i	$0.832997\pi$
$938$	16.2413	−	8.86843i	0.530298	−	0.289564i
$939$	−23.7469	−	51.9985i	−0.774952	−	1.69691i
$940$	−1.65866	+	1.80614i	−0.0540997	+	0.0589097i
$941$	1.68791	−	2.62644i	0.0550242	−	0.0856194i	−0.812651	−	0.582750i	$-0.801977\pi$
$941$	1.68791	−	2.62644i	0.0550242	−	0.0856194i	0.867676	+	0.497131i	$0.165613\pi$
$942$	−20.3940	+	20.3940i	−0.664471	+	0.664471i
$943$	2.43578	+	33.9135i	0.0793200	+	1.10438i
$944$		−	13.4286i		−	0.437064i
$945$	17.0410	−	21.4450i	0.554342	−	0.697606i
$946$	1.71390	+	11.9204i	0.0557236	+	0.387566i
$947$	−11.9245	+	31.9709i	−0.387495	+	1.03891i	0.586021	+	0.810296i	$0.300693\pi$
$947$	−11.9245	+	31.9709i	−0.387495	+	1.03891i	−0.973516	+	0.228618i	$0.926579\pi$
$948$	−0.476166	−	0.872032i	−0.0154651	−	0.0283223i
$949$	−12.0995	−	5.52566i	−0.392767	−	0.179371i
$950$	−36.7884	−	4.77687i	−1.19357	−	0.154982i
$951$	7.98982	−	55.5704i	0.259088	−	1.80199i
$952$	−1.20991	−	0.660661i	−0.0392134	−	0.0214122i
$953$	0.566486	−	7.92051i	0.0183503	−	0.256571i	−0.979993	−	0.199032i	$-0.936220\pi$
$953$	0.566486	−	7.92051i	0.0183503	−	0.256571i	0.998343	−	0.0575385i	$-0.0183252\pi$
$954$	−3.79681	+	2.44006i	−0.122926	+	0.0790000i
$955$	−35.5339	+	18.0919i	−1.14985	+	0.585440i
$956$	9.27422	+	10.7030i	0.299950	+	0.346160i
$957$	5.36195	−	9.81967i	0.173327	−	0.317425i
$958$	−19.8500	+	14.8595i	−0.641324	+	0.480089i
$959$	39.4744	+	34.2047i	1.27469	+	1.10453i
$960$	1.08376	+	4.12812i	0.0349781	+	0.133234i
$961$	−79.4594	−	23.3314i	−2.56321	−	0.752625i
$962$	−2.05845	−	0.767763i	−0.0663672	−	0.0247537i
$963$	−2.30672	+	3.08142i	−0.0743330	+	0.0992973i
$964$	3.97307	+	2.55334i	0.127964	+	0.0822375i
$965$	4.69254	+	5.74228i	0.151058	+	0.184851i
$966$	0.00748868	+	24.9267i	0.000240944	+	0.802002i
$967$	25.5319	+	25.5319i	0.821052	+	0.821052i	0.986259	−	0.165207i	$-0.0528293\pi$
$967$	25.5319	+	25.5319i	0.821052	+	0.821052i	−0.165207	+	0.986259i	$0.552829\pi$
$968$	−1.29100	+	0.280839i	−0.0414942	+	0.00902651i
$969$	7.09620	−	1.02028i	0.227963	−	0.0327761i
$970$	−2.34518	+	0.798403i	−0.0752992	+	0.0256352i
$971$	−7.09037	+	24.1476i	−0.227541	+	0.774933i	0.764009	+	0.645206i	$0.223228\pi$
$971$	−7.09037	+	24.1476i	−0.227541	+	0.774933i	−0.991550	+	0.129727i	$0.958590\pi$
$972$	6.16160	−	2.29816i	0.197633	−	0.0737134i
$973$	−16.6825	+	1.19315i	−0.534816	+	0.0382508i
$974$	−37.0486	−	5.32679i	−1.18711	−	0.170681i
$975$	−2.11425	−	24.7917i	−0.0677102	−	0.793969i
$976$	2.96106	−	2.56578i	0.0947813	−	0.0821285i
$977$	0.574442	−	2.64067i	0.0183780	−	0.0844824i	−0.967044	−	0.254608i	$-0.918054\pi$
$977$	0.574442	−	2.64067i	0.0183780	−	0.0844824i	0.985422	+	0.170125i	$0.0544173\pi$
$978$	1.61020	−	7.40199i	0.0514887	−	0.236690i
$979$	29.9101	−	25.9173i	0.955932	−	0.828320i
$980$	0.171070	+	0.912427i	0.00546462	+	0.0291464i
$981$	−4.02811	−	0.579155i	−0.128608	−	0.0184910i
$982$	9.07941	−	0.649372i	0.289736	−	0.0207223i
$983$	−10.4008	+	3.87930i	−0.331734	+	0.123731i	−0.509812	−	0.860286i	$-0.670285\pi$
$983$	−10.4008	+	3.87930i	−0.331734	+	0.123731i	0.178077	+	0.984016i	$0.443012\pi$
$984$	−3.81244	+	12.9840i	−0.121536	+	0.413914i
$985$	32.8869	+	16.1818i	1.04786	+	0.515594i
$986$	0.836776	−	0.120310i	0.0266484	−	0.00383146i
$987$	−5.56970	+	1.21161i	−0.177285	+	0.0385661i
$988$	13.6781	+	13.6781i	0.435159	+	0.435159i
$989$	15.7889	+	4.63089i	0.502058	+	0.147254i
$990$	−3.90903	+	3.19442i	−0.124237	+	0.101525i
$991$	13.6616	+	8.77980i	0.433976	+	0.278900i	0.739335	−	0.673338i	$-0.235140\pi$
$991$	13.6616	+	8.77980i	0.433976	+	0.278900i	−0.305359	+	0.952237i	$0.598776\pi$
$992$	6.39331	−	8.54046i	0.202988	−	0.271160i
$993$	−41.0647	−	15.3164i	−1.30315	−	0.486050i
$994$	−37.6136	−	11.0444i	−1.19303	−	0.350306i
$995$	−3.09105	−	1.80554i	−0.0979929	−	0.0572396i
$996$	16.5024	+	14.2994i	0.522898	+	0.453093i
$997$	3.99753	−	2.99251i	0.126603	−	0.0947739i	−0.534100	−	0.845422i	$-0.679349\pi$
$997$	3.99753	−	2.99251i	0.126603	−	0.0947739i	0.660703	+	0.750648i	$0.270258\pi$
$998$	3.46368	−	6.34325i	0.109641	−	0.200792i
$999$	−2.48240	−	2.86484i	−0.0785396	−	0.0906395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.67.1	yes	240
5.3	odd	4	inner	230.2.l.a.113.6	yes	240
23.11	odd	22	inner	230.2.l.a.57.6	✓	240
115.103	even	44	inner	230.2.l.a.103.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.6	✓	240	23.11	odd	22	inner
230.2.l.a.67.1	yes	240	1.1	even	1	trivial
230.2.l.a.103.1	yes	240	115.103	even	44	inner
230.2.l.a.113.6	yes	240	5.3	odd	4	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.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.212565 - 0.977147i) q^{2} +(-1.52800 - 1.14385i) q^{3} +(-0.909632 + 0.415415i) q^{4} +(-0.841561 + 2.07166i) q^{5} +(-0.792907 + 1.73622i) q^{6} +(0.194262 + 2.71614i) q^{7} +(0.599278 + 0.800541i) q^{8} +(0.181204 + 0.617123i) q^{9} +(2.20320 + 0.381966i) q^{10} +(1.89773 + 2.95293i) q^{11} +(1.86509 + 0.405726i) q^{12} +(-2.60053 - 0.185993i) q^{13} +(2.61278 - 0.767180i) q^{14} +(3.65557 - 2.20288i) q^{15} +(0.654861 - 0.755750i) q^{16} +(0.176913 + 0.474323i) q^{17} +(0.564502 - 0.308241i) q^{18} +(3.08215 + 6.74897i) q^{19} +(-0.0950878 - 2.23405i) q^{20} +(2.81002 - 4.37247i) q^{21} +(2.48205 - 2.48205i) q^{22} +(-1.67732 - 4.49295i) q^{23} -1.90871i q^{24} +(-3.58355 - 3.48686i) q^{25} +(0.371039 + 2.58063i) q^{26} +(-1.57206 + 4.21486i) q^{27} +(-1.30503 - 2.38999i) q^{28} +(1.51901 + 0.693708i) q^{29} +(-2.92959 - 3.10377i) q^{30} +(-1.51827 + 10.5598i) q^{31} +(-0.877679 - 0.479249i) q^{32} +(0.477963 - 6.68280i) q^{33} +(0.425877 - 0.273695i) q^{34} +(-5.79040 - 1.88335i) q^{35} +(-0.421191 - 0.486080i) q^{36} +(-0.403846 + 0.739590i) q^{37} +(5.93958 - 4.44631i) q^{38} +(3.76086 + 3.25881i) q^{39} +(-2.16278 + 0.567795i) q^{40} +(-6.80249 - 1.99739i) q^{41} +(-4.86986 - 1.81636i) q^{42} +(-2.05606 + 2.74658i) q^{43} +(-2.95293 - 1.89773i) q^{44} +(-1.43096 - 0.143954i) q^{45} +(-4.03373 + 2.59403i) q^{46} +(-0.775455 - 0.775455i) q^{47} +(-1.86509 + 0.405726i) q^{48} +(-0.410934 + 0.0590834i) q^{49} +(-2.64543 + 4.24284i) q^{50} +(0.272229 - 0.927127i) q^{51} +(2.44279 - 0.911113i) q^{52} +(-6.99930 + 0.500600i) q^{53} +(4.45271 + 0.640203i) q^{54} +(-7.71453 + 1.44639i) q^{55} +(-2.05797 + 1.78324i) q^{56} +(3.01026 - 13.8379i) q^{57} +(0.354966 - 1.63175i) q^{58} +(10.1487 - 8.79387i) q^{59} +(-2.41011 + 3.52239i) q^{60} +(3.87817 + 0.557596i) q^{61} +(10.6412 - 0.761072i) q^{62} +(-1.64099 + 0.612058i) q^{63} +(-0.281733 + 0.959493i) q^{64} +(2.57382 - 5.23089i) q^{65} +(-6.63168 + 0.953491i) q^{66} +(6.64026 - 1.44450i) q^{67} +(-0.357967 - 0.357967i) q^{68} +(-2.57630 + 8.78383i) q^{69} +(-0.609474 + 6.05841i) q^{70} +(-12.1107 - 7.78309i) q^{71} +(-0.385441 + 0.514889i) q^{72} +(4.78023 + 1.78293i) q^{73} +(0.808531 + 0.237406i) q^{74} +(1.48724 + 9.42696i) q^{75} +(-5.60725 - 4.85871i) q^{76} +(-7.65192 + 5.72815i) q^{77} +(2.38490 - 4.36762i) q^{78} +(-0.340883 - 0.393400i) q^{79} +(1.01455 + 1.99266i) q^{80} +(8.84650 - 5.68530i) q^{81} +(-0.505771 + 7.07160i) q^{82} +(10.0407 + 5.48264i) q^{83} +(-0.739691 + 5.14467i) q^{84} +(-1.13152 - 0.0326675i) q^{85} +(3.12086 + 1.42525i) q^{86} +(-1.52755 - 2.79750i) q^{87} +(-1.22667 + 3.28884i) q^{88} +(-1.60459 - 11.1602i) q^{89} +(0.163508 + 1.42886i) q^{90} -7.09953i q^{91} +(3.39218 + 3.39015i) q^{92} +(14.3987 - 14.3987i) q^{93} +(-0.592898 + 0.922568i) q^{94} +(-16.5754 + 0.705499i) q^{95} +(0.792907 + 1.73622i) q^{96} +(-0.972389 + 0.530964i) q^{97} +(0.145083 + 0.388984i) q^{98} +(-1.47844 + 1.70622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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