LMFDB - Embedded newform 230.2.l.a.113.6

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			113.6
Character	$\chi$	$=$	230.113
Dual form			230.2.l.a.57.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.977147 + 0.212565i) q^{2} +(1.14385 - 1.52800i) q^{3} +(0.909632 - 0.415415i) q^{4} +(-0.412058 + 2.19777i) q^{5} +(-0.792907 + 1.73622i) q^{6} +(2.71614 - 0.194262i) q^{7} +(-0.800541 + 0.599278i) q^{8} +(-0.181204 - 0.617123i) q^{9} +(-0.0645294 - 2.23514i) q^{10} +(1.89773 + 2.95293i) q^{11} +(0.405726 - 1.86509i) q^{12} +(0.185993 - 2.60053i) q^{13} +(-2.61278 + 0.767180i) q^{14} +(2.88687 + 3.14354i) q^{15} +(0.654861 - 0.755750i) q^{16} +(0.474323 - 0.176913i) q^{17} +(0.308241 + 0.564502i) q^{18} +(-3.08215 - 6.74897i) q^{19} +(0.538167 + 2.17034i) q^{20} +(2.81002 - 4.37247i) q^{21} +(-2.48205 - 2.48205i) q^{22} +(4.49295 - 1.67732i) q^{23} +1.90871i q^{24} +(-4.66042 - 1.81122i) q^{25} +(0.371039 + 2.58063i) q^{26} +(4.21486 + 1.57206i) q^{27} +(2.38999 - 1.30503i) q^{28} +(-1.51901 - 0.693708i) q^{29} +(-3.48910 - 2.45805i) q^{30} +(-1.51827 + 10.5598i) q^{31} +(-0.479249 + 0.877679i) q^{32} +(6.68280 + 0.477963i) q^{33} +(-0.425877 + 0.273695i) q^{34} +(-0.692263 + 6.04951i) q^{35} +(-0.421191 - 0.486080i) q^{36} +(0.739590 + 0.403846i) q^{37} +(4.44631 + 5.93958i) q^{38} +(-3.76086 - 3.25881i) q^{39} +(-0.987207 - 2.00635i) q^{40} +(-6.80249 - 1.99739i) q^{41} +(-1.81636 + 4.86986i) q^{42} +(-2.74658 - 2.05606i) 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} +(-0.405726 - 1.86509i) q^{48} +(0.410934 - 0.0590834i) q^{49} +(4.93891 + 0.779184i) q^{50} +(0.272229 - 0.927127i) q^{51} +(-0.911113 - 2.44279i) q^{52} +(-0.500600 - 6.99930i) q^{53} +(-4.45271 - 0.640203i) q^{54} +(-7.27185 + 2.95401i) q^{55} +(-2.05797 + 1.78324i) q^{56} +(-13.8379 - 3.01026i) q^{57} +(1.63175 + 0.354966i) q^{58} +(-10.1487 + 8.79387i) q^{59} +(3.93186 + 1.66022i) q^{60} +(3.87817 + 0.557596i) q^{61} +(-0.761072 - 10.6412i) q^{62} +(-0.612058 - 1.64099i) q^{63} +(0.281733 - 0.959493i) q^{64} +(5.63873 + 1.48034i) q^{65} +(-6.63168 + 0.953491i) q^{66} +(-1.44450 - 6.64026i) 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} +(0.514889 + 0.385441i) q^{72} +(-1.78293 + 4.78023i) q^{73} +(-0.808531 - 0.237406i) q^{74} +(-8.09835 + 5.04937i) q^{75} +(-5.60725 - 4.85871i) q^{76} +(5.72815 + 7.65192i) q^{77} +(4.36762 + 2.38490i) q^{78} +(0.340883 + 0.393400i) q^{79} +(1.39113 + 1.75065i) q^{80} +(8.84650 - 5.68530i) q^{81} +(7.07160 + 0.505771i) q^{82} +(-5.48264 + 10.0407i) q^{83} +(0.739691 - 5.14467i) q^{84} +(0.193367 + 1.11535i) q^{85} +(3.12086 + 1.42525i) q^{86} +(-2.79750 + 1.52755i) q^{87} +(-3.28884 - 1.22667i) q^{88} +(1.60459 + 11.1602i) q^{89} +(-1.36766 + 0.444837i) q^{90} -7.09953i q^{91} +(3.39015 - 3.39218i) q^{92} +(14.3987 + 14.3987i) q^{93} +(0.592898 - 0.922568i) q^{94} +(16.1027 - 3.99290i) q^{95} +(0.792907 + 1.73622i) q^{96} +(0.530964 + 0.972389i) q^{97} +(-0.388984 + 0.145083i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.977147	+	0.212565i	−0.690947	+	0.150306i
$2$	−0.977147	+	0.212565i	−0.690947	+	0.150306i
$3$	1.14385	−	1.52800i	0.660401	−	0.882192i	−0.337857	−	0.941197i	$-0.609702\pi$
$3$	1.14385	−	1.52800i	0.660401	−	0.882192i	0.998258	+	0.0590054i	$0.0187929\pi$
$4$	0.909632	−	0.415415i	0.454816	−	0.207708i
$5$	−0.412058	+	2.19777i	−0.184278	+	0.982874i
$5$	−0.412058	+	2.19777i	−0.184278	+	0.982874i
$6$	−0.792907	+	1.73622i	−0.323703	+	0.708811i
$7$	2.71614	−	0.194262i	1.02660	−	0.0734242i	0.452135	−	0.891950i	$-0.350663\pi$
$7$	2.71614	−	0.194262i	1.02660	−	0.0734242i	0.574470	+	0.818526i	$0.305208\pi$
$8$	−0.800541	+	0.599278i	−0.283034	+	0.211877i
$9$	−0.181204	−	0.617123i	−0.0604012	−	0.205708i
$10$	−0.0645294	−	2.23514i	−0.0204060	−	0.706812i
$11$	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	$0.640683\pi$
$12$	0.405726	−	1.86509i	0.117123	−	0.538405i
$13$	0.185993	−	2.60053i	0.0515853	−	0.721257i	−0.904185	−	0.427142i	$-0.859521\pi$
$13$	0.185993	−	2.60053i	0.0515853	−	0.721257i	0.955770	−	0.294115i	$-0.0950249\pi$
$14$	−2.61278	+	0.767180i	−0.698294	+	0.205037i
$15$	2.88687	+	3.14354i	0.745387	+	0.811659i
$16$	0.654861	−	0.755750i	0.163715	−	0.188937i
$17$	0.474323	−	0.176913i	0.115040	−	0.0429077i	−0.291285	−	0.956636i	$-0.594083\pi$
$17$	0.474323	−	0.176913i	0.115040	−	0.0429077i	0.406325	+	0.913729i	$0.366810\pi$
$18$	0.308241	+	0.564502i	0.0726532	+	0.133054i
$19$	−3.08215	−	6.74897i	−0.707094	−	1.54832i	−0.831152	−	0.556045i	$-0.812318\pi$
$19$	−3.08215	−	6.74897i	−0.707094	−	1.54832i	0.124058	−	0.992275i	$-0.460409\pi$
$20$	0.538167	+	2.17034i	0.120338	+	0.485303i
$21$	2.81002	−	4.37247i	0.613196	−	0.954152i
$22$	−2.48205	−	2.48205i	−0.529176	−	0.529176i
$23$	4.49295	−	1.67732i	0.936845	−	0.349746i
$23$	4.49295	−	1.67732i	0.936845	−	0.349746i
$24$			1.90871i			0.389614i
$25$	−4.66042	−	1.81122i	−0.932083	−	0.362244i
$26$	0.371039	+	2.58063i	0.0727668	+	0.506104i
$27$	4.21486	+	1.57206i	0.811151	+	0.302544i
$28$	2.38999	−	1.30503i	0.451666	−	0.246628i
$29$	−1.51901	−	0.693708i	−0.282073	−	0.128818i	0.269355	−	0.963041i	$-0.413190\pi$
$29$	−1.51901	−	0.693708i	−0.282073	−	0.128818i	−0.551428	+	0.834223i	$0.685917\pi$
$30$	−3.48910	−	2.45805i	−0.637020	−	0.448777i
$31$	−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	$0.637983\pi$
$32$	−0.479249	+	0.877679i	−0.0847201	+	0.155153i
$33$	6.68280	+	0.477963i	1.16333	+	0.0832027i
$34$	−0.425877	+	0.273695i	−0.0730373	+	0.0469382i
$35$	−0.692263	+	6.04951i	−0.117014	+	1.02255i
$36$	−0.421191	−	0.486080i	−0.0701984	−	0.0810133i
$37$	0.739590	+	0.403846i	0.121588	+	0.0663919i	0.538892	−	0.842375i	$-0.318843\pi$
$37$	0.739590	+	0.403846i	0.121588	+	0.0663919i	−0.417304	+	0.908767i	$0.637025\pi$
$38$	4.44631	+	5.93958i	0.721287	+	0.963526i
$39$	−3.76086	−	3.25881i	−0.602220	−	0.521827i
$40$	−0.987207	−	2.00635i	−0.156091	−	0.317231i
$41$	−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	$0.777659\pi$
$42$	−1.81636	+	4.86986i	−0.280271	+	0.751436i
$43$	−2.74658	−	2.05606i	−0.418849	−	0.313546i	0.368984	−	0.929436i	$-0.379706\pi$
$43$	−2.74658	−	2.05606i	−0.418849	−	0.313546i	−0.787833	+	0.615890i	$0.788797\pi$
$44$	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	−0.761397	−	0.648286i	$-0.775486\pi$
$47$	−0.775455	+	0.775455i	−0.113112	+	0.113112i	0.648286	+	0.761397i	$0.275486\pi$
$48$	−0.405726	−	1.86509i	−0.0585614	−	0.269203i
$49$	0.410934	−	0.0590834i	0.0587048	−	0.00844048i
$50$	4.93891	+	0.779184i	0.698468	+	0.110193i
$51$	0.272229	−	0.927127i	0.0381197	−	0.129824i
$52$	−0.911113	−	2.44279i	−0.126349	−	0.338754i
$53$	−0.500600	−	6.99930i	−0.0687627	−	0.961428i	−0.908352	−	0.418206i	$-0.862659\pi$
$53$	−0.500600	−	6.99930i	−0.0687627	−	0.961428i	0.839589	−	0.543221i	$-0.182796\pi$
$54$	−4.45271	−	0.640203i	−0.605937	−	0.0871205i
$55$	−7.27185	+	2.95401i	−0.980536	+	0.398319i
$56$	−2.05797	+	1.78324i	−0.275007	+	0.238295i
$57$	−13.8379	−	3.01026i	−1.83288	−	0.398719i
$58$	1.63175	+	0.354966i	0.214260	+	0.0466094i
$59$	−10.1487	+	8.79387i	−1.32124	+	1.14486i	−0.342560	+	0.939496i	$0.611294\pi$
$59$	−10.1487	+	8.79387i	−1.32124	+	1.14486i	−0.978685	+	0.205369i	$0.934161\pi$
$60$	3.93186	+	1.66022i	0.507601	+	0.214333i
$61$	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	$0.464752\pi$
$62$	−0.761072	−	10.6412i	−0.0966563	−	1.35143i
$63$	−0.612058	−	1.64099i	−0.0771121	−	0.206745i
$64$	0.281733	−	0.959493i	0.0352166	−	0.119937i
$65$	5.63873	+	1.48034i	0.699399	+	0.183613i
$66$	−6.63168	+	0.953491i	−0.816303	+	0.117367i
$67$	−1.44450	−	6.64026i	−0.176474	−	0.811237i	−0.977219	−	0.212232i	$-0.931927\pi$
$67$	−1.44450	−	6.64026i	−0.176474	−	0.811237i	0.800746	−	0.599005i	$-0.204437\pi$
$68$	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	$-0.644164\pi$
$72$	0.514889	+	0.385441i	0.0606802	+	0.0454246i
$73$	−1.78293	+	4.78023i	−0.208677	+	0.559484i	−0.998553	−	0.0537829i	$-0.982872\pi$
$73$	−1.78293	+	4.78023i	−0.208677	+	0.559484i	0.789876	+	0.613266i	$0.210145\pi$
$74$	−0.808531	−	0.237406i	−0.0939899	−	0.0275979i
$75$	−8.09835	+	5.04937i	−0.935117	+	0.583050i
$76$	−5.60725	−	4.85871i	−0.643195	−	0.557332i
$77$	5.72815	+	7.65192i	0.652784	+	0.872017i
$78$	4.36762	+	2.38490i	0.494536	+	0.270037i
$79$	0.340883	+	0.393400i	0.0383524	+	0.0442610i	0.774602	−	0.632449i	$-0.217950\pi$
$79$	0.340883	+	0.393400i	0.0383524	+	0.0442610i	−0.736249	+	0.676710i	$0.763405\pi$
$80$	1.39113	+	1.75065i	0.155533	+	0.195728i
$81$	8.84650	−	5.68530i	0.982944	−	0.631700i
$82$	7.07160	+	0.505771i	0.780928	+	0.0558531i
$83$	−5.48264	+	10.0407i	−0.601798	+	1.10211i	0.382225	+	0.924069i	$0.375158\pi$
$83$	−5.48264	+	10.0407i	−0.601798	+	1.10211i	−0.984023	+	0.178041i	$0.943024\pi$
$84$	0.739691	−	5.14467i	0.0807069	−	0.561329i
$85$	0.193367	+	1.11535i	0.0209736	+	0.120977i
$86$	3.12086	+	1.42525i	0.336531	+	0.153688i
$87$	−2.79750	+	1.52755i	−0.299924	+	0.163771i
$88$	−3.28884	−	1.22667i	−0.350591	−	0.130764i
$89$	1.60459	+	11.1602i	0.170086	+	1.18298i	0.878698	+	0.477378i	$0.158413\pi$
$89$	1.60459	+	11.1602i	0.170086	+	1.18298i	−0.708612	+	0.705599i	$0.750678\pi$
$90$	−1.36766	+	0.444837i	−0.144164	+	0.0468900i
$91$		−	7.09953i		−	0.744233i
$92$	3.39015	−	3.39218i	0.353447	−	0.353660i
$93$	14.3987	+	14.3987i	1.49307	+	1.49307i
$94$	0.592898	−	0.922568i	0.0611528	−	0.0951556i
$95$	16.1027	−	3.99290i	1.65211	−	0.409663i
$96$	0.792907	+	1.73622i	0.0809257	+	0.177203i
$97$	0.530964	+	0.972389i	0.0539113	+	0.0987311i	0.903245	−	0.429125i	$-0.141178\pi$
$97$	0.530964	+	0.972389i	0.0539113	+	0.0987311i	−0.849334	+	0.527856i	$0.822996\pi$
$98$	−0.388984	+	0.145083i	−0.0392933	+	0.0146556i
$99$	1.47844	−	1.70622i	0.148589	−	0.171481i
$100$	−4.99167	+	0.288464i	−0.499167	+	0.0288464i
$101$	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	$0.180389\pi$
$102$	−0.0689328	+	0.963806i	−0.00682536	+	0.0954310i
$103$	0.863523	−	3.96955i	0.0850854	−	0.391131i	−0.914834	−	0.403830i	$-0.867679\pi$
$103$	0.863523	−	3.96955i	0.0850854	−	0.391131i	0.999919	+	0.0126988i	$0.00404227\pi$
$104$	1.40954	+	2.19329i	0.138217	+	0.215070i
$105$	8.45182	+	7.97750i	0.824813	+	0.778524i
$106$	1.97697	+	6.73293i	0.192020	+	0.653960i
$107$	4.79094	−	3.58645i	0.463158	−	0.346715i	−0.342077	−	0.939672i	$-0.611130\pi$
$107$	4.79094	−	3.58645i	0.463158	−	0.346715i	0.805234	+	0.592957i	$0.202039\pi$
$108$	4.48703	−	0.320919i	0.431765	−	0.0308804i
$109$	2.62843	−	5.75546i	0.251758	−	0.551274i	−0.740986	−	0.671521i	$-0.765641\pi$
$109$	2.62843	−	5.75546i	0.251758	−	0.551274i	0.992744	+	0.120247i	$0.0383687\pi$
$110$	6.47774	−	4.43224i	0.617629	−	0.422598i
$111$	1.46306	−	0.668155i	0.138867	−	0.0634185i
$112$	1.63188	−	2.17994i	0.154198	−	0.205985i
$113$	−10.5214	+	2.28880i	−0.989774	+	0.215312i	−0.678174	−	0.734901i	$-0.737229\pi$
$113$	−10.5214	+	2.28880i	−0.989774	+	0.215312i	−0.311600	+	0.950213i	$0.600865\pi$
$114$	14.1616			1.32635
$115$	1.83502	+	10.5656i	0.171116	+	0.985251i
$116$	−1.66992			−0.155048
$117$	−1.63855	+	0.356444i	−0.151484	+	0.0329533i
$118$	8.04747	−	10.7502i	0.740830	−	0.989633i
$119$	1.25396	−	0.572664i	0.114950	−	0.0524960i
$120$	−4.19491	−	0.786499i	−0.382941	−	0.0717972i
$121$	−0.548842	+	1.20180i	−0.0498947	+	0.109254i
$122$	−3.90806	+	0.279510i	−0.353820	+	0.0253057i
$123$	−10.8330	+	8.10950i	−0.976781	+	0.731209i
$124$	3.00562	+	10.2362i	0.269913	+	0.919240i
$125$	5.90101	−	9.49621i	0.527802	−	0.849367i
$126$	0.946888	+	1.47339i	0.0843555	+	0.131260i
$127$	0.137636	−	0.632702i	0.0122132	−	0.0561432i	−0.970637	−	0.240549i	$-0.922672\pi$
$127$	0.137636	−	0.632702i	0.0122132	−	0.0561432i	0.982850	+	0.184406i	$0.0590361\pi$
$128$	−0.0713392	+	0.997452i	−0.00630555	+	0.0881631i
$129$	−6.28333	+	1.84495i	−0.553216	+	0.162439i
$130$	−5.82454	−	0.247910i	−0.510846	−	0.0217432i
$131$	−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	$0.268126\pi$
$132$	6.27744	−	2.34136i	0.546381	−	0.203790i
$133$	−9.68263	−	17.7324i	−0.839590	−	1.53759i
$134$	2.82298	+	6.18146i	0.243868	+	0.533997i
$135$	−5.19181	+	8.61554i	−0.446839	+	0.741507i
$136$	−0.273695	+	0.425877i	−0.0234691	+	0.0365187i
$137$	−13.5632	−	13.5632i	−1.15878	−	1.15878i	−0.984738	−	0.174044i	$-0.944316\pi$
$137$	−13.5632	−	13.5632i	−1.15878	−	1.15878i	−0.174044	−	0.984738i	$-0.555684\pi$
$138$	−0.650285	+	9.13073i	−0.0553560	+	0.777259i
$139$		−	6.14198i		−	0.520956i	−0.965480	−	0.260478i	$-0.916120\pi$
$139$		−	6.14198i		−	0.520956i	0.965480	−	0.260478i	$-0.0838801\pi$
$140$	1.88335	+	5.79040i	0.159172	+	0.489378i
$141$	0.297894	+	2.07190i	0.0250872	+	0.174485i
$142$	13.4884	+	5.03090i	1.13192	+	0.422184i
$143$	8.03215	−	4.38588i	0.671682	−	0.366766i
$144$	−0.585053	−	0.267185i	−0.0487544	−	0.0222654i
$145$	2.15053	−	3.05259i	0.178592	−	0.253504i
$146$	0.726077	−	5.04998i	0.0600906	−	0.417939i
$147$	0.379766	−	0.695490i	0.0313226	−	0.0573630i
$148$	0.840518	+	0.0601150i	0.0690902	+	0.00494143i
$149$	9.71839	−	6.24563i	0.796161	−	0.511662i	−0.0781999	−	0.996938i	$-0.524917\pi$
$149$	9.71839	−	6.24563i	0.796161	−	0.511662i	0.874361	+	0.485276i	$0.161281\pi$
$150$	6.83996	−	6.65540i	0.558480	−	0.543411i
$151$	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	$0.456555\pi$
$152$	6.51190	+	3.55576i	0.528184	+	0.288411i
$153$	−0.195126	−	0.260658i	−0.0157750	−	0.0210729i
$154$	−7.22378	−	6.25944i	−0.582109	−	0.504400i
$155$	−22.5824	−	7.68804i	−1.81386	−	0.617518i
$156$	−4.77476	−	1.40200i	−0.382287	−	0.112249i
$157$	5.28055	−	14.1577i	0.421434	−	1.12991i	−0.536747	−	0.843744i	$-0.680347\pi$
$157$	5.28055	−	14.1577i	0.421434	−	1.12991i	0.958180	−	0.286165i	$-0.0923804\pi$
$158$	−0.416716	−	0.311950i	−0.0331522	−	0.0248174i
$159$	−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
$163$	−0.843608	−	3.87801i	−0.0660765	−	0.303749i	0.932234	−	0.361857i	$-0.117857\pi$
$163$	−0.843608	−	3.87801i	−0.0660765	−	0.303749i	−0.998310	+	0.0581077i	$0.981493\pi$
$164$	−7.01751	+	1.00897i	−0.547975	+	0.0787869i
$165$	−3.80415	+	14.4903i	−0.296153	+	1.12807i
$166$	3.22304	−	10.9767i	0.250156	−	0.851954i
$167$	1.43078	+	3.83606i	0.110717	+	0.296843i	0.980478	−	0.196630i	$-0.0629998\pi$
$167$	1.43078	+	3.83606i	0.110717	+	0.296843i	−0.869761	+	0.493473i	$0.835727\pi$
$168$	0.370790	+	5.18433i	0.0286071	+	0.399979i
$169$	6.13952	+	0.882730i	0.472271	+	0.0679023i
$170$	−0.426033	−	1.04876i	−0.0326752	−	0.0804362i
$171$	−3.60644	+	3.12500i	−0.275792	+	0.238975i
$172$	−3.35249	−	0.729290i	−0.255625	−	0.0556078i
$173$	−12.2295	−	2.66036i	−0.929789	−	0.202263i	−0.277928	−	0.960602i	$-0.589648\pi$
$173$	−12.2295	−	2.66036i	−0.929789	−	0.202263i	−0.651861	+	0.758339i	$0.726011\pi$
$174$	2.40887	−	2.08729i	0.182616	−	0.158237i
$175$	−13.0102	−	4.01418i	−0.983479	−	0.303444i
$176$	3.47443	+	0.499547i	0.261895	+	0.0376548i
$177$	1.82852	+	25.5660i	0.137440	+	1.92166i
$178$	−3.94019	−	10.5641i	−0.295330	−	0.791809i
$179$	−3.94983	+	13.4519i	−0.295224	+	1.00544i	0.669639	+	0.742687i	$0.266449\pi$
$179$	−3.94983	+	13.4519i	−0.295224	+	1.00544i	−0.964863	+	0.262754i	$0.915369\pi$
$180$	1.24185	−	0.725389i	0.0925619	−	0.0540673i
$181$	−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	$0.631482\pi$
$182$	1.50911	+	6.93729i	0.111863	+	0.514226i
$183$	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
$187$	1.42255	+	1.06491i	0.104027	+	0.0778737i
$188$	−0.383243	+	1.02751i	−0.0279509	+	0.0749392i
$189$	11.7536	+	3.45116i	0.854945	+	0.251035i
$190$	−14.8860	+	7.32454i	−1.07994	+	0.531378i
$191$	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	$0.504066\pi$
$192$	−1.14385	−	1.52800i	−0.0825501	−	0.110274i
$193$	2.91077	+	1.58940i	0.209522	+	0.114407i	0.580584	−	0.814201i	$-0.302824\pi$
$193$	2.91077	+	1.58940i	0.209522	+	0.114407i	−0.371062	+	0.928608i	$0.621006\pi$
$194$	−0.725526	−	0.837302i	−0.0520898	−	0.0601148i
$195$	8.71181	−	6.92271i	0.623866	−	0.495745i
$196$	0.349254	−	0.224452i	0.0249467	−	0.0160323i
$197$	−16.3497	−	1.16935i	−1.16487	−	0.0833130i	−0.524520	−	0.851398i	$-0.675755\pi$
$197$	−16.3497	−	1.16935i	−1.16487	−	0.0833130i	−0.640348	+	0.768085i	$0.721210\pi$
$198$	−1.08197	+	1.98149i	−0.0768926	+	0.140818i
$199$	0.227833	−	1.58462i	0.0161507	−	0.112330i	−0.980151	−	0.198251i	$-0.936474\pi$
$199$	0.227833	−	1.58462i	0.0161507	−	0.112330i	0.996302	+	0.0859203i	$0.0273831\pi$
$200$	4.81628	−	1.34293i	0.340562	−	0.0949594i
$201$	−11.7986	−	5.38825i	−0.832210	−	0.380058i
$202$	−11.6122	+	6.34076i	−0.817034	+	0.446134i
$203$	−4.26061	−	1.58912i	−0.299036	−	0.111535i
$204$	−0.137514	−	0.956433i	−0.00962792	−	0.0669637i
$205$	7.19283	−	14.1273i	0.502369	−	0.986692i
$206$			4.06239i			0.283040i
$207$	−1.84925	−	2.46876i	−0.128532	−	0.171591i
$208$	−1.84355	−	1.84355i	−0.127827	−	0.127827i
$209$	14.0801	−	21.9091i	0.973943	−	1.51549i
$210$	−9.95441	−	5.99862i	−0.686919	−	0.413944i
$211$	−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	$-0.364140\pi$
$212$	−3.36298	−	6.15883i	−0.230970	−	0.422990i
$213$	−25.7454	+	9.60254i	−1.76405	+	0.657955i
$214$	−3.91910	+	4.52288i	−0.267904	+	0.309178i
$215$	5.65050	−	5.18914i	0.385361	−	0.353896i
$216$	−4.31627	+	1.26737i	−0.293685	+	0.0862338i
$217$	−2.07246	+	28.9768i	−0.140688	+	1.96707i
$218$	−1.34495	+	6.18265i	−0.0910917	+	0.418742i
$219$	5.26479	+	8.19218i	0.355762	+	0.553576i
$220$	−5.38757	+	5.70790i	−0.363230	+	0.384826i
$221$	−0.371847	−	1.26639i	−0.0250131	−	0.0851869i
$222$	−1.28759	+	0.963881i	−0.0864176	+	0.0646914i
$223$	15.5478	−	1.11200i	1.04116	−	0.0744649i	0.459725	−	0.888061i	$-0.347948\pi$
$223$	15.5478	−	1.11200i	1.04116	−	0.0744649i	0.581430	+	0.813596i	$0.302493\pi$
$224$	−1.13121	+	2.47700i	−0.0755820	+	0.165502i
$225$	−0.273260	+	3.20425i	−0.0182174	+	0.213617i
$226$	9.79448	−	4.47299i	0.651519	−	0.297539i
$227$	10.5515	−	14.0952i	0.700330	−	0.935531i	−0.299498	−	0.954097i	$-0.596819\pi$
$227$	10.5515	−	14.0952i	0.700330	−	0.935531i	0.999828	+	0.0185662i	$0.00591014\pi$
$228$	−13.8379	+	3.01026i	−0.916440	+	0.199359i
$229$	20.4427			1.35089			0.675446	−	0.737409i	$-0.263951\pi$
$229$	20.4427			1.35089			0.675446	+	0.737409i	$0.263951\pi$
$230$	−4.03897	−	9.93412i	−0.266322	−	0.655036i
$231$	18.2443			1.20039
$232$	1.63175	−	0.354966i	0.107130	−	0.0233047i
$233$	−3.42302	+	4.57262i	−0.224250	+	0.299562i	−0.898529	−	0.438914i	$-0.855363\pi$
$233$	−3.42302	+	4.57262i	−0.224250	+	0.299562i	0.674280	+	0.738476i	$0.264454\pi$
$234$	1.52533	−	0.696597i	0.0997142	−	0.0455380i
$235$	−1.38474	−	2.02381i	−0.0903306	−	0.132019i
$236$	−5.57845	+	12.2151i	−0.363126	+	0.795135i
$237$	0.991035	−	0.0708802i	0.0643746	−	0.00460416i
$238$	−1.10357	+	0.826125i	−0.0715341	+	0.0535497i
$239$	3.98993	+	13.5885i	0.258087	+	0.878964i	0.981969	+	0.189041i	$0.0605378\pi$
$239$	3.98993	+	13.5885i	0.258087	+	0.878964i	−0.723882	+	0.689924i	$0.757644\pi$
$240$	4.26623	−	0.123168i	0.275384	−	0.00795046i
$241$	−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	$0.866789\pi$
$242$	0.280839	−	1.29100i	0.0180530	−	0.0829884i
$243$	0.469143	−	6.55948i	0.0300955	−	0.420791i
$244$	3.75934	−	1.10384i	0.240667	−	0.0706662i
$245$	−0.0394766	+	0.927485i	−0.00252207	+	0.0592549i
$246$	8.86166	−	10.2269i	0.564999	−	0.652043i
$247$	−18.1241	+	6.75996i	−1.15321	+	0.430126i
$248$	−5.11280	−	9.36340i	−0.324663	−	0.594576i
$249$	9.07090	+	19.8625i	0.574845	+	1.25874i
$250$	−3.74759	+	10.5335i	−0.237018	+	0.666200i
$251$	−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
$253$	13.4794	+	10.0843i	0.847445	+	0.633992i
$254$			0.647500i			0.0406277i
$255$	1.92544	+	0.980328i	0.120576	+	0.0613905i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−5.74757	−	2.14373i	−0.358523	−	0.133722i	0.163747	−	0.986502i	$-0.447642\pi$
$257$	−5.74757	−	2.14373i	−0.358523	−	0.133722i	−0.522270	+	0.852780i	$0.674915\pi$
$258$	5.74756	−	3.13841i	0.357828	−	0.195389i
$259$	2.08728	+	0.953230i	0.129697	+	0.0592308i
$260$	5.74413	−	0.995850i	0.356236	−	0.0617600i
$261$	−0.152853	+	1.06312i	−0.00946138	+	0.0658053i
$262$	1.40414	−	2.57149i	0.0867480	−	0.158867i
$263$	−15.0523	−	1.07656i	−0.928167	−	0.0663838i	−0.400936	−	0.916106i	$-0.631315\pi$
$263$	−15.0523	−	1.07656i	−0.928167	−	0.0663838i	−0.527231	+	0.849722i	$0.676770\pi$
$264$	−5.63629	+	3.62222i	−0.346890	+	0.222932i
$265$	15.5891	+	1.78391i	0.957634	+	0.109585i
$266$	13.2306	+	15.2690i	0.811223	+	0.936201i
$267$	18.8882	+	10.3137i	1.15594	+	0.631190i
$268$	−4.07243	−	5.44012i	−0.248763	−	0.332308i
$269$	−18.8247	−	16.3117i	−1.14776	−	0.994542i	−0.999985	−	0.00552156i	$-0.998242\pi$
$269$	−18.8247	−	16.3117i	−1.14776	−	0.994542i	−0.147778	−	0.989021i	$-0.547212\pi$
$270$	3.24179	−	9.52224i	0.197289	−	0.579505i
$271$	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	$0.290851\pi$
$272$	0.176913	−	0.474323i	0.0107269	−	0.0287600i
$273$	−10.8481	−	8.12078i	−0.656557	−	0.491492i
$274$	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	−0.603447	−	0.797403i	$-0.706207\pi$
$277$	3.22806	−	3.22806i	0.193955	−	0.193955i	0.797403	+	0.603447i	$0.206207\pi$
$278$	1.30557	+	6.00161i	0.0783030	+	0.359953i
$279$	6.79179	−	0.976512i	0.406614	−	0.0584622i
$280$	−3.07115	−	5.25774i	−0.183536	−	0.314210i
$281$	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	$-0.0653451\pi$
$282$	−0.731500	−	1.96123i	−0.0435602	−	0.116789i
$283$	0.982129	+	13.7320i	0.0583815	+	0.816280i	0.939318	+	0.343047i	$0.111459\pi$
$283$	0.982129	+	13.7320i	0.0583815	+	0.816280i	−0.880937	+	0.473234i	$0.843087\pi$
$284$	−14.2495	−	2.04877i	−0.845553	−	0.121572i
$285$	12.3179	−	29.1723i	0.729650	−	1.72802i
$286$	−6.91630	+	5.99301i	−0.408969	+	0.354374i
$287$	−18.8645	−	4.10373i	−1.11354	−	0.242235i
$288$	0.628477	+	0.136717i	0.0370334	+	0.00805612i
$289$	−12.6541	+	10.9648i	−0.744356	+	0.644989i
$290$	−1.45251	+	3.43996i	−0.0852945	+	0.202001i
$291$	2.09315	+	0.300950i	0.122703	+	0.0176420i
$292$	0.363966	+	5.08891i	0.0212995	+	0.297806i
$293$	−7.24251	−	19.4179i	−0.423112	−	1.13441i	−0.957314	−	0.289050i	$-0.906661\pi$
$293$	−7.24251	−	19.4179i	−0.423112	−	1.13441i	0.534202	−	0.845357i	$-0.320612\pi$
$294$	−0.223250	+	0.760321i	−0.0130202	+	0.0443428i
$295$	−15.1451	−	25.9281i	−0.881782	−	1.50959i
$296$	−0.834088	+	0.119924i	−0.0484804	+	0.00697043i
$297$	3.35649	+	15.4296i	0.194764	+	0.895314i
$298$	−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
$302$	−16.4837	−	12.3396i	−0.948531	−	0.710062i
$303$	8.82516	−	23.6612i	0.506992	−	1.35930i
$304$	−7.11891	−	2.09030i	−0.408297	−	0.119887i
$305$	−2.82350	+	8.29357i	−0.161673	+	0.474888i
$306$	0.246074	+	0.213224i	0.0140671	+	0.0121892i
$307$	20.0543	+	26.7894i	1.14456	+	1.52895i	0.809858	+	0.586625i	$0.199544\pi$
$307$	20.0543	+	26.7894i	1.14456	+	1.52895i	0.334699	+	0.942325i	$0.391365\pi$
$308$	8.38923	+	4.58087i	0.478021	+	0.261019i
$309$	−5.07774	−	5.86002i	−0.288863	−	0.333365i
$310$	23.7005	+	2.71212i	1.34610	+	0.154038i
$311$	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	$0.278838\pi$
$312$	4.96366	+	0.355008i	0.281012	+	0.0200984i
$313$	−14.3531	+	26.2858i	−0.811287	+	1.48576i	0.0617418	+	0.998092i	$0.480334\pi$
$313$	−14.3531	+	26.2858i	−0.811287	+	1.48576i	−0.873029	+	0.487669i	$0.837847\pi$
$314$	−2.15044	+	14.9566i	−0.121356	+	0.844051i
$315$	3.85873	−	0.668982i	0.217415	−	0.0376929i
$316$	0.473503	+	0.216241i	0.0266366	+	0.0121645i
$317$	25.8156	−	14.0964i	1.44995	−	0.791732i	0.454846	−	0.890570i	$-0.349694\pi$
$317$	25.8156	−	14.0964i	1.44995	−	0.791732i	0.995104	+	0.0988381i	$0.0315126\pi$
$318$	12.5493	+	4.68064i	0.703729	+	0.262477i
$319$	−0.834202	−	5.80200i	−0.0467064	−	0.324850i
$320$	1.99266	+	1.01455i	0.111393	+	0.0567151i
$321$		−	11.4229i		−	0.637565i
$322$	−10.4523	+	7.82936i	−0.582482	+	0.436313i
$323$	−2.65592	−	2.65592i	−0.147779	−	0.147779i
$324$	5.68530	−	8.84650i	0.315850	−	0.491472i
$325$	−5.57693	+	11.7827i	−0.309353	+	0.653585i
$326$	1.64866	+	3.61006i	0.0913108	+	0.199943i
$327$	−5.78783	−	10.5996i	−0.320068	−	0.586160i
$328$	6.64266	−	2.47759i	0.366780	−	0.136802i
$329$	−1.95560	+	2.25689i	−0.107816	+	0.124426i
$330$	0.637076	−	14.9678i	0.0350699	−	0.823951i
$331$	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	$0.191712\pi$
$332$	−0.816125	+	11.4109i	−0.0447907	+	0.626255i
$333$	0.115207	−	0.529596i	0.00631328	−	0.0290217i
$334$	−2.21349	−	3.44426i	−0.121117	−	0.188462i
$335$	15.1890	−	0.438513i	0.829864	−	0.0239586i
$336$	−1.46432	−	4.98703i	−0.0798855	−	0.272065i
$337$	8.02064	−	6.00418i	0.436912	−	0.327068i	−0.358077	−	0.933692i	$-0.616567\pi$
$337$	8.02064	−	6.00418i	0.436912	−	0.327068i	0.794989	+	0.606624i	$0.207477\pi$
$338$	−6.18686	+	0.442493i	−0.336521	+	0.0240684i
$339$	−8.53764	+	18.6948i	−0.463701	+	1.01536i
$340$	0.639227	+	0.934232i	0.0346669	+	0.0506659i
$341$	−34.0635	+	15.5563i	−1.84464	+	0.842421i
$342$	2.85976	−	3.82019i	0.154638	−	0.206572i
$343$	−17.5213	+	3.81152i	−0.946059	+	0.205803i
$344$	3.43090			0.184982
$345$	18.2433	+	9.28157i	0.982186	+	0.499703i
$346$	12.5155			0.672836
$347$	24.6087	−	5.35330i	1.32106	−	0.287380i	0.503889	−	0.863768i	$-0.331902\pi$
$347$	24.6087	−	5.35330i	1.32106	−	0.287380i	0.817176	+	0.576388i	$0.195538\pi$
$348$	−1.91013	+	2.55164i	−0.102394	+	0.136782i
$349$	−26.8981	+	12.2840i	−1.43982	+	0.657546i	−0.973837	−	0.227246i	$-0.927028\pi$
$349$	−26.8981	+	12.2840i	−1.43982	+	0.657546i	−0.465987	+	0.884792i	$0.654301\pi$
$350$	13.5662	+	1.15693i	0.725141	+	0.0618405i
$351$	4.87213	−	10.6685i	0.260055	−	0.569441i
$352$	−3.50121	+	0.250412i	−0.186615	+	0.0133470i
$353$	−9.95966	+	7.45571i	−0.530099	+	0.396827i	−0.830528	−	0.556977i	$-0.811961\pi$
$353$	−9.95966	+	7.45571i	−0.530099	+	0.396827i	0.300429	+	0.953804i	$0.402870\pi$
$354$	−7.22118	−	24.5931i	−0.383802	−	1.30711i
$355$	22.0958	−	23.4096i	1.17272	−	1.24245i
$356$	6.09569	+	9.48508i	0.323071	+	0.502708i
$357$	0.559307	−	2.57109i	0.0296017	−	0.136077i
$358$	1.00016	−	13.9841i	0.0528601	−	0.739080i
$359$	22.4059	−	6.57897i	1.18254	−	0.347225i	0.369387	−	0.929276i	$-0.379568\pi$
$359$	22.4059	−	6.57897i	1.18254	−	0.347225i	0.813152	+	0.582051i	$0.197750\pi$
$360$	−1.05928	+	0.972785i	−0.0558287	+	0.0512703i
$361$	−23.6066	+	27.2434i	−1.24245	+	1.43387i
$362$	13.3031	−	4.96180i	0.699196	−	0.260787i
$363$	1.20855	+	2.21330i	0.0634327	+	0.116168i
$364$	−2.94925	−	6.45796i	−0.154583	−	0.338489i
$365$	−9.77119	−	5.88821i	−0.511447	−	0.308203i
$366$	−4.04314	+	6.29125i	−0.211338	+	0.328849i
$367$	17.3758	+	17.3758i	0.907007	+	0.907007i	0.996030	−	0.0890223i	$-0.0283742\pi$
$367$	17.3758	+	17.3758i	0.907007	+	0.907007i	−0.0890223	+	0.996030i	$0.528374\pi$
$368$	1.67462	−	4.49396i	0.0872957	−	0.234264i
$369$			4.55990i			0.237379i
$370$	0.854927	−	1.67914i	0.0444455	−	0.0872945i
$371$	−2.71940	−	18.9138i	−0.141184	−	0.981957i
$372$	19.0789	+	7.11607i	0.989197	+	0.368951i
$373$	24.6369	−	13.4528i	1.27565	−	0.696558i	0.308612	−	0.951188i	$-0.400135\pi$
$373$	24.6369	−	13.4528i	1.27565	−	0.696558i	0.967039	+	0.254630i	$0.0819537\pi$
$374$	−1.61640	−	0.738186i	−0.0835822	−	0.0381707i
$375$	−7.76037	−	19.8790i	−0.400744	−	1.02655i
$376$	0.156071	−	1.08550i	0.00804874	−	0.0559802i
$377$	−2.08653	+	3.82120i	−0.107462	+	0.196802i
$378$	−12.2185	−	0.873888i	−0.628454	−	0.0449479i
$379$	−19.5801	+	12.5833i	−1.00576	+	0.646363i	−0.936292	−	0.351222i	$-0.885766\pi$
$379$	−19.5801	+	12.5833i	−1.00576	+	0.646363i	−0.0694676	+	0.997584i	$0.522130\pi$
$380$	12.9888	−	10.3214i	0.666314	−	0.529476i
$381$	−0.809335	−	0.934023i	−0.0414635	−	0.0478514i
$382$	−15.6511	−	8.54617i	−0.800782	−	0.437260i
$383$	12.0552	+	16.1039i	0.615994	+	0.822871i	0.994719	−	0.102638i	$-0.0327283\pi$
$383$	12.0552	+	16.1039i	0.615994	+	0.822871i	−0.378725	+	0.925509i	$0.623637\pi$
$384$	1.44251	+	1.24994i	0.0736126	+	0.0637857i
$385$	−19.1775	+	9.43615i	−0.977376	+	0.480911i
$386$	−3.18210	−	0.934348i	−0.161965	−	0.0475571i
$387$	−0.771153	+	2.06754i	−0.0391999	+	0.105099i
$388$	0.886927	+	0.663945i	0.0450269	+	0.0337067i
$389$	19.8783	+	12.7750i	1.00787	+	0.647720i	0.936841	−	0.349754i	$-0.113735\pi$
$389$	19.8783	+	12.7750i	1.00787	+	0.647720i	0.0710303	+	0.997474i	$0.477371\pi$
$390$	−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
$393$	1.18872	+	5.46448i	0.0599632	+	0.275647i
$394$	16.2246	−	2.33275i	0.817384	−	0.117522i
$395$	−1.00507	+	0.587081i	−0.0505705	+	0.0295392i
$396$	0.636053	−	2.16620i	0.0319628	−	0.108855i
$397$	3.42796	+	9.19072i	0.172044	+	0.461269i	0.994143	−	0.108077i	$-0.0344693\pi$
$397$	3.42796	+	9.19072i	0.172044	+	0.461269i	−0.822098	+	0.569346i	$0.807197\pi$
$398$	0.114208	+	1.59683i	0.00572471	+	0.0800419i
$399$	−38.1706	−	5.48810i	−1.91092	−	0.274749i
$400$	−4.42075	+	2.33601i	−0.221038	+	0.116801i
$401$	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	$0.244513\pi$
$402$	12.6743	+	2.75713i	0.632138	+	0.137513i
$403$	27.1786	+	5.91234i	1.35386	+	0.294515i
$404$	9.99903	−	8.66421i	0.497470	−	0.431061i
$405$	8.84973	+	21.7853i	0.439747	+	1.08252i
$406$	4.50103	+	0.647150i	0.223382	+	0.0321175i
$407$	0.211013	+	2.95035i	0.0104595	+	0.146243i
$408$	0.337676	+	0.905344i	0.0167175	+	0.0448212i
$409$	2.18210	−	7.43155i	0.107898	−	0.367466i	−0.887788	−	0.460252i	$-0.847759\pi$
$409$	2.18210	−	7.43155i	0.107898	−	0.367466i	0.995686	+	0.0927859i	$0.0295772\pi$
$410$	−4.02548	+	15.3334i	−0.198804	+	0.757262i
$411$	−36.2388	+	5.21035i	−1.78753	+	0.257008i
$412$	−0.863523	−	3.96955i	−0.0425427	−	0.195566i
$413$	−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
$417$	−9.38495	−	7.02549i	−0.459583	−	0.344040i
$418$	−9.10124	+	24.4014i	−0.445156	+	1.19351i
$419$	30.0589	+	8.82609i	1.46847	+	0.431182i	0.915602	−	0.402085i	$-0.131714\pi$
$419$	30.0589	+	8.82609i	1.46847	+	0.431182i	0.552870	+	0.833267i	$0.313533\pi$
$420$	11.0020	+	3.74557i	0.536843	+	0.182765i
$421$	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	$0.662576\pi$
$422$	11.4220	+	15.2580i	0.556012	+	0.742746i
$423$	0.619066	+	0.338035i	0.0301000	+	0.0164358i
$424$	4.59527	+	5.30323i	0.223166	+	0.257548i
$425$	−2.53097	−	0.0346130i	−0.122770	−	0.00167898i
$426$	23.1159	−	14.8557i	1.11997	−	0.719760i
$427$	10.6420	+	0.761129i	0.515001	+	0.0368336i
$428$	2.86813	−	5.25258i	0.138636	−	0.253893i
$429$	2.48591	−	17.2899i	0.120021	−	0.834765i
$430$	−4.41834	+	6.27165i	−0.213071	+	0.302446i
$431$	−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	$0.689202\pi$
$432$	3.94823	−	2.15590i	0.189960	−	0.103726i
$433$	31.8638	+	11.8846i	1.53127	+	0.571136i	0.967073	−	0.254501i	$-0.0819111\pi$
$433$	31.8638	+	11.8846i	1.53127	+	0.571136i	0.564202	+	0.825637i	$0.309184\pi$
$434$	−4.13436	−	28.7551i	−0.198456	−	1.38029i
$435$	−2.20448	−	6.77772i	−0.105697	−	0.324967i
$436$		−	6.32725i		−	0.303020i
$437$	−25.1681	−	25.1530i	−1.20396	−	1.20323i
$438$	−6.88585	−	6.88585i	−0.329019	−	0.329019i
$439$	−13.2135	+	20.5606i	−0.630645	+	0.981303i	0.368029	+	0.929814i	$0.380033\pi$
$439$	−13.2135	+	20.5606i	−0.630645	+	0.981303i	−0.998674	+	0.0514883i	$0.983604\pi$
$440$	4.05114	−	6.72266i	0.193131	−	0.320490i
$441$	−0.110924	−	0.242890i	−0.00528211	−	0.0115662i
$442$	0.632540	+	1.15841i	0.0300869	+	0.0551000i
$443$	30.2479	−	11.2819i	1.43712	−	0.536019i	0.494293	−	0.869295i	$-0.335427\pi$
$443$	30.2479	−	11.2819i	1.43712	−	0.536019i	0.942829	+	0.333276i	$0.108154\pi$
$444$	1.05328	−	1.21555i	0.0499865	−	0.0576875i
$445$	−25.1887	−	1.07211i	−1.19406	−	0.0508229i
$446$	−14.9561	+	4.39150i	−0.708191	+	0.207944i
$447$	1.57302	−	21.9938i	0.0744015	−	1.04027i
$448$	0.578832	−	2.66085i	0.0273472	−	0.125713i
$449$	2.98949	+	4.65174i	0.141083	+	0.219529i	0.904603	−	0.426255i	$-0.140167\pi$
$449$	2.98949	+	4.65174i	0.141083	+	0.219529i	−0.763521	+	0.645784i	$0.776531\pi$
$450$	−0.414097	−	3.18911i	−0.0195207	−	0.150336i
$451$	−7.01115	−	23.8778i	−0.330142	−	1.12436i
$452$	−8.61984	+	6.45273i	−0.405443	+	0.303511i
$453$	39.2016	−	2.80375i	1.84185	−	0.131732i
$454$	−7.31424	+	16.0160i	−0.343274	+	0.751666i
$455$	15.6032	+	2.92542i	0.731488	+	0.137146i
$456$	12.8818	−	5.88293i	0.603247	−	0.275494i
$457$	6.56161	−	8.76528i	0.306939	−	0.410023i	−0.620376	−	0.784305i	$-0.713020\pi$
$457$	6.56161	−	8.76528i	0.306939	−	0.410023i	0.927315	+	0.374282i	$0.122111\pi$
$458$	−19.9755	+	4.34541i	−0.933395	+	0.203048i
$459$	2.27732			0.106296
$460$	6.05832	+	8.84855i	0.282470	+	0.412566i
$461$	7.32613			0.341212			0.170606	−	0.985339i	$-0.445428\pi$
$461$	7.32613			0.341212			0.170606	+	0.985339i	$0.445428\pi$
$462$	−17.8273	+	3.87810i	−0.829403	+	0.180426i
$463$	−14.9474	+	19.9674i	−0.694666	+	0.927966i	−0.999703	−	0.0243749i	$-0.992240\pi$
$463$	−14.9474	+	19.9674i	−0.694666	+	0.927966i	0.305036	+	0.952341i	$0.401331\pi$
$464$	−1.51901	+	0.693708i	−0.0705183	+	0.0322046i
$465$	−37.5781	+	25.7120i	−1.74264	+	1.19236i
$466$	2.37281	−	5.19574i	0.109918	−	0.240688i
$467$	−7.48336	+	0.535220i	−0.346288	+	0.0247670i	−0.243400	−	0.969926i	$-0.578263\pi$
$467$	−7.48336	+	0.535220i	−0.346288	+	0.0247670i	−0.102888	+	0.994693i	$0.532808\pi$
$468$	−1.34240	+	1.00491i	−0.0620526	+	0.0464520i
$469$	−5.21342	−	17.7553i	−0.240733	−	0.819862i
$470$	1.78329	+	1.68321i	0.0822569	+	0.0776406i
$471$	−15.5929	−	24.2630i	−0.718481	−	1.11798i
$472$	2.85446	−	13.1217i	0.131387	−	0.603977i
$473$	0.859137	−	12.0123i	0.0395032	−	0.552326i
$474$	−0.953320	+	0.279920i	−0.0437874	+	0.0128571i
$475$	2.14025	+	37.0355i	0.0982012	+	1.69930i
$476$	0.902748	−	1.04183i	0.0413774	−	0.0477521i
$477$	−4.22872	+	1.57723i	−0.193620	+	0.0722164i
$478$	−6.78718	−	12.4298i	−0.310439	−	0.568526i
$479$	10.3005	+	22.5550i	0.470642	+	1.03056i	0.984931	+	0.172946i	$0.0553286\pi$
$479$	10.3005	+	22.5550i	0.470642	+	1.03056i	−0.514289	+	0.857617i	$0.671944\pi$
$480$	−4.14255	+	1.02721i	−0.189081	+	0.0468853i
$481$	1.18777	−	1.84821i	0.0541578	−	0.0842712i
$482$	3.33952	+	3.33952i	0.152111	+	0.152111i
$483$	5.29123	−	24.3586i	0.240759	−	1.10835i
$484$			1.32119i			0.0600541i
$485$	−2.35588	+	0.766259i	−0.106975	+	0.0347940i
$486$	0.935895	+	6.50930i	0.0424531	+	0.295268i
$487$	−35.0697	−	13.0803i	−1.58916	−	0.592725i	−0.609392	−	0.792869i	$-0.708586\pi$
$487$	−35.0697	−	13.0803i	−1.58916	−	0.592725i	−0.979767	+	0.200144i	$0.935859\pi$
$488$	−3.43879	+	1.87772i	−0.155667	+	0.0850004i
$489$	−6.89056	−	3.14681i	−0.311602	−	0.142304i
$490$	−0.158577	−	0.914681i	−0.00716377	−	0.0413211i
$491$	−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	$0.979606\pi$
$492$	−6.48526	+	11.8769i	−0.292378	+	0.535450i
$493$	−0.843227	−	0.0603088i	−0.0379770	−	0.00271617i
$494$	16.2730	−	10.4580i	0.732158	−	0.470529i
$495$	3.14067	+	3.95234i	0.141163	+	0.177645i
$496$	6.98629	+	8.06261i	0.313694	+	0.362022i
$497$	−34.4064	−	18.7873i	−1.54334	−	0.842726i
$498$	−13.0857	−	17.4804i	−0.586384	−	0.783317i
$499$	−5.46203	−	4.73288i	−0.244514	−	0.211873i	0.523978	−	0.851732i	$-0.324447\pi$
$499$	−5.46203	−	4.73288i	−0.244514	−	0.211873i	−0.768492	+	0.639859i	$0.778993\pi$
$500$	1.42288	−	11.0894i	0.0636330	−	0.495934i
$501$	7.49809	+	2.20164i	0.334990	+	0.0983620i
$502$	9.12957	−	24.4773i	0.407473	−	1.09248i
$503$	−0.747744	−	0.559754i	−0.0333403	−	0.0249582i	0.582478	−	0.812847i	$-0.302083\pi$
$503$	−0.747744	−	0.559754i	−0.0333403	−	0.0249582i	−0.615818	+	0.787889i	$0.711174\pi$
$504$	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
$508$	−0.137636	−	0.632702i	−0.00610661	−	0.0280716i
$509$	−7.45859	+	1.07238i	−0.330596	+	0.0475325i	−0.305614	−	0.952155i	$-0.598862\pi$
$509$	−7.45859	+	1.07238i	−0.330596	+	0.0475325i	−0.0249817	+	0.999688i	$0.507953\pi$
$510$	−2.08982	−	0.548642i	−0.0925389	−	0.0242943i
$511$	−3.91408	+	13.3301i	−0.173149	+	0.589690i
$512$	0.349464	+	0.936950i	0.0154443	+	0.0414077i
$513$	−2.38104	−	33.2913i	−0.105126	−	1.46985i
$514$	6.07190	+	0.873008i	0.267820	+	0.0385067i
$515$	8.36835	+	3.53351i	0.368754	+	0.155705i
$516$	−4.94910	+	4.28842i	−0.217872	+	0.188787i
$517$	−3.76147	−	0.818258i	−0.165429	−	0.0359869i
$518$	−2.24220	−	0.487762i	−0.0985168	−	0.0214310i
$519$	−18.0537	+	15.6436i	−0.792468	+	0.686677i
$520$	−5.40117	+	2.19409i	−0.236857	+	0.0962174i
$521$	−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	$0.806572\pi$
$522$	−0.0766218	−	1.07131i	−0.00335365	−	0.0468901i
$523$	−12.3181	−	33.0261i	−0.538632	−	1.44413i	−0.866391	−	0.499367i	$-0.833566\pi$
$523$	−12.3181	−	33.0261i	−0.538632	−	1.44413i	0.327758	−	0.944762i	$-0.393707\pi$
$524$	−0.825441	+	2.81119i	−0.0360596	+	0.122808i
$525$	−21.0154	+	15.2880i	−0.917186	+	0.667223i
$526$	14.9372	−	2.14764i	0.651292	−	0.0936417i
$527$	1.14801	+	5.27734i	0.0500083	+	0.229885i
$528$	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
$532$	−16.1739	−	12.1077i	−0.701229	−	0.524933i
$533$	−6.45949	+	17.3186i	−0.279792	+	0.750150i
$534$	−20.6489	−	6.06305i	−0.893564	−	0.262374i
$535$	5.90807	+	12.0072i	0.255428	+	0.519118i
$536$	5.13574	+	4.45014i	0.221830	+	0.192217i
$537$	16.0365	+	21.4222i	0.692026	+	0.924438i
$538$	21.8618	+	11.9375i	0.942529	+	0.514660i
$539$	0.954312	+	1.10133i	0.0411051	+	0.0474378i
$540$	−1.14361	+	9.99372i	−0.0492131	+	0.430061i
$541$	−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	$0.553360\pi$
$542$	−26.5719	−	1.90046i	−1.14136	−	0.0816316i
$543$	−12.9879	+	23.7855i	−0.557363	+	1.02073i
$544$	−0.0720456	+	0.501088i	−0.00308893	+	0.0214840i
$545$	11.5661	+	8.14828i	0.495439	+	0.349034i
$546$	12.3264	+	5.62927i	0.527520	+	0.240910i
$547$	−26.8815	+	14.6784i	−1.14937	+	0.627604i	−0.936912	−	0.349566i	$-0.886329\pi$
$547$	−26.8815	+	14.6784i	−1.14937	+	0.627604i	−0.212459	+	0.977170i	$0.568147\pi$
$548$	−17.9719	−	6.70316i	−0.767720	−	0.286345i
$549$	−0.358632	−	2.49434i	−0.0153061	−	0.106456i
$550$	7.07186	+	16.0630i	0.301545	+	0.684927i
$551$			12.3899i			0.527826i
$552$	3.20152	+	8.57574i	0.136266	+	0.365008i
$553$	1.00231	+	1.00231i	0.0426225	+	0.0426225i
$554$	−2.46812	+	3.84046i	−0.104860	+	0.163166i
$555$	0.865590	+	3.49078i	0.0367423	+	0.148176i
$556$	−2.55147	−	5.58694i	−0.108206	−	0.236939i
$557$	−4.42079	−	8.09607i	−0.187315	−	0.343041i	0.767099	−	0.641529i	$-0.221700\pi$
$557$	−4.42079	−	8.09607i	−0.187315	−	0.343041i	−0.954413	+	0.298488i	$0.903518\pi$
$558$	−6.42900	+	2.39789i	−0.272161	+	0.101511i
$559$	−5.85769	+	6.76014i	−0.247754	+	0.285923i
$560$	4.11858	+	4.48476i	0.174042	+	0.189516i
$561$	3.25436	−	0.955566i	0.137399	−	0.0403440i
$562$	−1.12748	+	15.7642i	−0.0475598	+	0.664974i
$563$	5.08810	−	23.3896i	0.214438	−	0.985755i	−0.736516	−	0.676421i	$-0.763530\pi$
$563$	5.08810	−	23.3896i	0.214438	−	0.985755i	0.950953	−	0.309334i	$-0.100106\pi$
$564$	1.13167	+	1.76091i	0.0476520	+	0.0741479i
$565$	−0.694822	−	24.0669i	−0.0292314	−	1.01250i
$566$	−3.87862	−	13.2094i	−0.163031	−	0.555231i
$567$	22.9239	−	17.1606i	0.962713	−	0.720678i
$568$	14.3594	−	1.02700i	0.602506	−	0.0430921i
$569$	3.29043	−	7.20503i	0.137942	−	0.302051i	−0.828036	−	0.560675i	$-0.810542\pi$
$569$	3.29043	−	7.20503i	0.137942	−	0.302051i	0.965978	+	0.258624i	$0.0832691\pi$
$570$	−5.83539	+	31.1239i	−0.244418	+	1.30364i
$571$	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	$0.152299\pi$
$572$	5.48433	−	7.32621i	0.229312	−	0.306324i
$573$	33.2591	−	7.23507i	1.38942	−	0.302249i
$574$	19.3057			0.805806
$575$	−23.9770	−	0.320700i	−0.999911	−	0.0133741i
$576$	−0.643176			−0.0267990
$577$	−1.35393	+	0.294530i	−0.0563650	+	0.0122615i	−0.240659	−	0.970610i	$-0.577364\pi$
$577$	−1.35393	+	0.294530i	−0.0563650	+	0.0122615i	0.184294	+	0.982871i	$0.441000\pi$
$578$	10.0341	−	13.4040i	0.417365	−	0.557534i
$579$	5.75808	−	2.62963i	0.239298	−	0.109284i
$580$	0.688102	−	3.67010i	0.0285719	−	0.152393i
$581$	−12.9411	+	28.3370i	−0.536887	+	1.17562i
$582$	−2.10929	+	0.150859i	−0.0874329	+	0.00625332i
$583$	19.7184	−	14.7610i	0.816654	−	0.611340i
$584$	−1.43737	−	4.89524i	−0.0594789	−	0.202567i
$585$	−0.108207	−	3.74803i	−0.00447383	−	0.154962i
$586$	11.2046	+	17.4347i	0.462857	+	0.720219i
$587$	3.06438	−	14.0867i	0.126480	−	0.581421i	−0.869660	−	0.493651i	$-0.835662\pi$
$587$	3.06438	−	14.0867i	0.126480	−	0.581421i	0.996141	−	0.0877705i	$-0.0279742\pi$
$588$	0.0565306	−	0.790400i	0.00233128	−	0.0325956i
$589$	75.9471	−	22.3001i	3.12935	−	0.918859i
$590$	20.3104	+	22.1162i	0.836166	+	0.910510i
$591$	−20.4883	+	23.6448i	−0.842777	+	0.972617i
$592$	0.789535	−	0.294481i	0.0324497	−	0.0121031i
$593$	7.06496	+	12.9385i	0.290123	+	0.531321i	0.981569	−	0.191107i	$-0.0612078\pi$
$593$	7.06496	+	12.9385i	0.290123	+	0.531321i	−0.691446	+	0.722428i	$0.743026\pi$
$594$	−6.55958	−	14.3635i	−0.269143	−	0.589340i
$595$	0.741882	+	2.99189i	0.0304142	+	0.122655i
$596$	6.24563	−	9.71839i	0.255831	−	0.398081i
$597$	−2.16069	−	2.16069i	−0.0884311	−	0.0884311i
$598$	5.99561	+	10.9723i	0.245179	+	0.448691i
$599$		−	3.85951i		−	0.157695i	−0.996887	−	0.0788477i	$-0.974876\pi$
$599$		−	3.85951i		−	0.157695i	0.996887	−	0.0788477i	$-0.0251241\pi$
$600$	3.45709	−	8.89539i	0.141135	−	0.363153i
$601$	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	$0.898039\pi$
$602$	8.75356	+	3.26491i	0.356768	+	0.133068i
$603$	−3.83610	+	2.09467i	−0.156218	+	0.0853016i
$604$	18.7300	+	8.55369i	0.762112	+	0.348045i
$605$	−2.41512	−	1.70144i	−0.0981886	−	0.0691734i
$606$	−3.59394	+	24.9964i	−0.145994	+	1.01541i
$607$	−12.2650	+	22.4617i	−0.497821	+	0.911691i	0.501106	+	0.865386i	$0.332926\pi$
$607$	−12.2650	+	22.4617i	−0.497821	+	0.911691i	−0.998927	+	0.0463052i	$0.985255\pi$
$608$	7.40055	+	0.529297i	0.300132	+	0.0214658i
$609$	−7.30167	+	4.69250i	−0.295878	+	0.190150i
$610$	0.996048	−	8.70421i	0.0403288	−	0.352423i
$611$	1.87236	+	2.16082i	0.0757477	+	0.0874175i
$612$	−0.285774	−	0.156044i	−0.0115517	−	0.00630772i
$613$	14.0014	+	18.7037i	0.565512	+	0.755436i	0.988586	−	0.150659i	$-0.0481397\pi$
$613$	14.0014	+	18.7037i	0.565512	+	0.755436i	−0.423073	+	0.906095i	$0.639049\pi$
$614$	−25.2905	−	21.9143i	−1.02064	−	0.884390i
$615$	−13.3590	−	27.1501i	−0.538687	−	1.09480i
$616$	−9.17125	−	2.69292i	−0.369520	−	0.108501i
$617$	−6.07786	+	16.2954i	−0.244686	+	0.656027i	0.755314	+	0.655363i	$0.227484\pi$
$617$	−6.07786	+	16.2954i	−0.244686	+	0.656027i	−1.00000		0.000664471i	$0.999788\pi$
$618$	6.20734	+	4.64675i	0.249696	+	0.186920i
$619$	−21.8424	−	14.0373i	−0.877920	−	0.564205i	0.0222455	−	0.999753i	$-0.492918\pi$
$619$	−21.8424	−	14.0373i	−0.877920	−	0.564205i	−0.900166	+	0.435547i	$0.856555\pi$
$620$	−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
$623$	6.52630	+	30.0009i	0.261471	+	1.20196i
$624$	−4.92568	+	0.708206i	−0.197185	+	0.0283509i
$625$	18.4390	+	16.8821i	0.737559	+	0.675283i
$626$	8.43767	−	28.7361i	0.337237	−	1.14852i
$627$	−17.3716	−	46.5752i	−0.693756	−	1.86003i
$628$	−1.07797	−	15.0719i	−0.0430155	−	0.601435i
$629$	0.422250	+	0.0607103i	0.0168362	+	0.00242068i
$630$	−3.62834	+	1.47393i	−0.144557	+	0.0587226i
$631$	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	$0.239899\pi$
$632$	−0.508647	−	0.110649i	−0.0202329	−	0.00440140i
$633$	−35.5478	−	7.73295i	−1.41290	−	0.307357i
$634$	−22.2292	+	19.2617i	−0.882836	+	0.764982i
$635$	1.33382	+	0.563202i	0.0529311	+	0.0223500i
$636$	−13.2574	−	1.90613i	−0.525691	−	0.0755830i
$637$	−0.0772170	−	1.07963i	−0.00305945	−	0.0427767i
$638$	2.04844	+	5.49209i	0.0810986	+	0.217434i
$639$	−2.60862	+	8.88413i	−0.103195	+	0.351451i
$640$	−2.16278	−	0.567795i	−0.0854913	−	0.0224441i
$641$	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	$0.254270\pi$
$642$	2.42812	+	11.1619i	0.0958301	+	0.440524i
$643$	9.46253	−	9.46253i	0.373166	−	0.373166i	−0.495463	−	0.868629i	$-0.665002\pi$
$643$	9.46253	−	9.46253i	0.373166	−	0.373166i	0.868629	+	0.495463i	$0.165002\pi$
$644$	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
$647$	17.2804	+	12.9360i	0.679363	+	0.508565i	0.882336	−	0.470619i	$-0.155969\pi$
$647$	17.2804	+	12.9360i	0.679363	+	0.508565i	−0.202973	+	0.979184i	$0.565060\pi$
$648$	−3.67491	+	9.85282i	−0.144364	+	0.387056i
$649$	−45.2272	−	13.2799i	−1.77532	−	0.521281i
$650$	2.94490	−	12.6989i	0.115508	−	0.498090i
$651$	41.9060	+	36.3117i	1.64242	+	1.42317i
$652$	−2.37835	−	3.17711i	−0.0931436	−	0.124425i
$653$	−18.0197	−	9.83948i	−0.705164	−	0.385049i	0.0862963	−	0.996270i	$-0.472497\pi$
$653$	−18.0197	−	9.83948i	−0.705164	−	0.385049i	−0.791460	+	0.611221i	$0.790679\pi$
$654$	7.90867	+	9.12710i	0.309254	+	0.356898i
$655$	−4.07582	−	5.12918i	−0.159256	−	0.200414i
$656$	−5.96421	+	3.83296i	−0.232863	+	0.149652i
$657$	3.27306	+	0.234094i	0.127694	+	0.00913288i
$658$	1.43118	−	2.62100i	0.0557930	−	0.102177i
$659$	3.24669	−	22.5812i	0.126473	−	0.879640i	−0.823502	−	0.567314i	$-0.807983\pi$
$659$	3.24669	−	22.5812i	0.126473	−	0.879640i	0.949975	−	0.312326i	$-0.101108\pi$
$660$	2.55912	+	14.7612i	0.0996136	+	0.574578i
$661$	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	$0.550213\pi$
$662$	−20.1534	+	11.0046i	−0.783284	+	0.427705i
$663$	−2.36039	−	0.880379i	−0.0916699	−	0.0341911i
$664$	−1.62809	−	11.3236i	−0.0631822	−	0.439442i
$665$	42.9616	−	13.9734i	1.66598	−	0.541867i
$666$			0.541982i			0.0210014i
$667$	−7.98841	−	0.568930i	−0.309312	−	0.0220291i
$668$	2.89504	+	2.89504i	0.112012	+	0.112012i
$669$	16.0851	−	25.0290i	0.621887	−	0.967676i
$670$	−14.7487	+	3.65715i	−0.569791	+	0.141288i
$671$	5.71318	+	12.5101i	0.220555	+	0.482948i
$672$	2.49093	+	4.56180i	0.0960897	+	0.175975i
$673$	26.6355	−	9.93453i	1.02672	−	0.382948i	0.221021	−	0.975269i	$-0.429061\pi$
$673$	26.6355	−	9.93453i	1.02672	−	0.382948i	0.805702	+	0.592321i	$0.201788\pi$
$674$	−6.56106	+	7.57187i	−0.252723	+	0.291658i
$675$	−16.7957	−	14.9605i	−0.646466	−	0.575830i
$676$	5.95141	−	1.74749i	0.228900	−	0.0672112i
$677$	3.40533	−	47.6127i	0.130877	−	1.82990i	−0.331769	−	0.943361i	$-0.607645\pi$
$677$	3.40533	−	47.6127i	0.130877	−	1.82990i	0.462646	−	0.886543i	$-0.346900\pi$
$678$	4.36866	−	20.0824i	0.167777	−	0.771260i
$679$	1.63107	+	2.53800i	0.0625948	+	0.0973995i
$680$	−0.823204	−	0.777005i	−0.0315684	−	0.0297968i
$681$	−9.46813	−	32.2455i	−0.362820	−	1.23565i
$682$	29.9784	−	22.4415i	1.14793	−	0.859330i
$683$	−9.53157	+	0.681711i	−0.364715	+	0.0260849i	−0.252494	−	0.967598i	$-0.581251\pi$
$683$	−9.53157	+	0.681711i	−0.364715	+	0.0260849i	−0.112221	+	0.993683i	$0.535796\pi$
$684$	−1.98236	+	4.34077i	−0.0757976	+	0.165974i
$685$	35.3977	−	24.2200i	1.35247	−	0.925399i
$686$	16.3106	−	7.44882i	0.622743	−	0.284397i
$687$	23.3833	−	31.2365i	0.892130	−	1.19175i
$688$	−3.35249	+	0.729290i	−0.127813	+	0.0278039i
$689$	−18.2950			−0.696983
$690$	−19.7993	−	5.19157i	−0.753747	−	0.197640i
$691$	−34.6221			−1.31709			−0.658543	−	0.752544i	$-0.728827\pi$
$691$	−34.6221			−1.31709			−0.658543	+	0.752544i	$0.728827\pi$
$692$	−12.2295	+	2.66036i	−0.464894	+	0.101132i
$693$	3.68421	−	4.92153i	0.139952	−	0.186953i
$694$	−22.9084	+	10.4619i	−0.869591	+	0.397129i
$695$	13.4987	+	2.53085i	0.512034	+	0.0960006i
$696$	1.32409	−	2.89935i	0.0501894	−	0.109900i
$697$	−3.57994	+	0.256042i	−0.135600	+	0.00969829i
$698$	23.6723	−	17.7208i	0.896009	−	0.670744i
$699$	3.07156	+	10.4608i	0.116177	+	0.395662i
$700$	−13.5020	+	1.75320i	−0.510329	+	0.0662648i
$701$	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	$0.708562\pi$
$702$	−2.49304	+	11.4603i	−0.0940937	+	0.432542i
$703$	0.446021	−	6.23618i	0.0168220	−	0.235202i
$704$	3.36797	−	0.988925i	0.126935	−	0.0372715i
$705$	−4.67631	−	0.199038i	−0.176120	−	0.00749621i
$706$	8.14723	−	9.40240i	0.306625	−	0.353864i
$707$	33.7564	−	12.5905i	1.26954	−	0.473514i
$708$	12.2838	+	22.4961i	0.461653	+	0.845455i
$709$	−1.16284	−	2.54627i	−0.0436714	−	0.0956271i	0.886539	−	0.462654i	$-0.153103\pi$
$709$	−1.16284	−	2.54627i	−0.0436714	−	0.0956271i	−0.930210	+	0.367027i	$0.880376\pi$
$710$	−16.6148	+	27.5714i	−0.623541	+	1.03474i
$711$	0.181007	−	0.281652i	0.00678829	−	0.0105628i
$712$	−7.97259	−	7.97259i	−0.298785	−	0.298785i
$713$	10.8906	+	49.9911i	0.407858	+	1.87218i
$714$			2.63122i			0.0984711i
$715$	6.32947	+	19.4601i	0.236709	+	0.727765i
$716$	1.99522	+	13.8771i	0.0745650	+	0.518611i
$717$	25.3271	+	9.44651i	0.945856	+	0.352786i
$718$	−20.4954	+	11.1913i	−0.764882	+	0.417657i
$719$	14.2897	+	6.52587i	0.532915	+	0.243374i	0.663650	−	0.748043i	$-0.269006\pi$
$719$	14.2897	+	6.52587i	0.532915	+	0.243374i	−0.130735	+	0.991417i	$0.541734\pi$
$720$	0.828288	−	1.17572i	0.0308685	−	0.0438165i
$721$	1.57432	−	10.9496i	0.0586306	−	0.407785i
$722$	17.2761	−	31.6388i	0.642949	−	1.17747i
$723$	−8.99149	−	0.643084i	−0.334397	−	0.0239165i
$724$	−11.9444	+	7.67619i	−0.443910	+	0.285283i
$725$	5.82276	+	5.98423i	0.216252	+	0.222249i
$726$	−1.65141	−	1.90582i	−0.0612895	−	0.0707318i
$727$	11.6299	+	6.35042i	0.431330	+	0.235524i	0.680220	−	0.733008i	$-0.261884\pi$
$727$	11.6299	+	6.35042i	0.431330	+	0.235524i	−0.248890	+	0.968532i	$0.580066\pi$
$728$	4.25459	+	5.68347i	0.157686	+	0.210643i
$729$	14.3558	+	12.4394i	0.531696	+	0.460717i
$730$	10.7995	+	3.67663i	0.399708	+	0.136078i
$731$	−1.66651	−	0.489331i	−0.0616380	−	0.0180985i
$732$	2.61344	−	7.00690i	0.0965955	−	0.258983i
$733$	15.2666	+	11.4284i	0.563884	+	0.422118i	0.842823	−	0.538190i	$-0.180892\pi$
$733$	15.2666	+	11.4284i	0.563884	+	0.422118i	−0.278939	+	0.960309i	$0.589983\pi$
$734$	−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
$738$	−0.969277	−	4.45570i	−0.0356796	−	0.164016i
$739$	19.2249	−	2.76412i	0.707200	−	0.101680i	0.220676	−	0.975347i	$-0.429174\pi$
$739$	19.2249	−	2.76412i	0.707200	−	0.101680i	0.486524	+	0.873667i	$0.338265\pi$
$740$	−0.478461	+	1.82250i	−0.0175886	+	0.0669963i
$741$	−10.4020	+	35.4261i	−0.382128	+	1.30141i
$742$	6.67768	+	17.9035i	0.245145	+	0.657260i
$743$	1.65030	+	23.0742i	0.0605436	+	0.846510i	0.933469	+	0.358657i	$0.116765\pi$
$743$	1.65030	+	23.0742i	0.0605436	+	0.846510i	−0.872926	+	0.487853i	$0.837780\pi$
$744$	−20.1555	−	2.89793i	−0.738938	−	0.106243i
$745$	9.72194	+	23.9324i	0.356184	+	0.876814i
$746$	−21.2143	+	18.3823i	−0.776710	+	0.673023i
$747$	7.18982	+	1.56405i	0.263062	+	0.0572256i
$748$	1.73638	+	0.377725i	0.0634882	+	0.0138110i
$749$	12.3162	−	10.6720i	0.450023	−	0.389947i
$750$	11.8086	+	17.7751i	0.431189	+	0.649055i
$751$	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	$0.525554\pi$
$752$	0.0782347	+	1.09386i	0.00285293	+	0.0398891i
$753$	17.4257	+	46.7201i	0.635028	+	1.70258i
$754$	1.22660	−	4.17740i	0.0446700	−	0.152132i
$755$	−39.7567	+	23.2227i	−1.44689	+	0.845160i
$756$	12.1251	−	1.74332i	0.440985	−	0.0634040i
$757$	−5.42765	−	24.9505i	−0.197271	−	0.906842i	−0.964214	−	0.265126i	$-0.914586\pi$
$757$	−5.42765	−	24.9505i	−0.197271	−	0.906842i	0.766942	−	0.641716i	$-0.221777\pi$
$758$	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	$0.814085\pi$
$762$	0.989380	+	0.740641i	0.0358415	+	0.0268306i
$763$	6.02112	−	16.1433i	0.217979	−	0.584425i
$764$	17.1101	+	5.02397i	0.619021	+	0.181761i
$765$	0.653270	−	0.321437i	0.0236190	−	0.0116216i
$766$	−15.2029	−	13.1734i	−0.549302	−	0.475973i
$767$	20.9811	+	28.0275i	0.757585	+	1.01201i
$768$	−1.67524	−	0.914748i	−0.0604498	−	0.0330081i
$769$	−30.0590	−	34.6899i	−1.08395	−	1.25095i	−0.966169	−	0.257911i	$-0.916966\pi$
$769$	−30.0590	−	34.6899i	−1.08395	−	1.25095i	−0.117785	−	0.993039i	$-0.537579\pi$
$770$	16.7334	−	13.2970i	0.603032	−	0.479190i
$771$	−9.84997	+	6.33019i	−0.354738	+	0.227976i
$772$	3.30799	+	0.236592i	0.119057	+	0.00851513i
$773$	2.52398	−	4.62232i	0.0907812	−	0.166253i	−0.828343	−	0.560221i	$-0.810716\pi$
$773$	2.52398	−	4.62232i	0.0907812	−	0.166253i	0.919124	+	0.393968i	$0.128898\pi$
$774$	0.314042	−	2.18421i	0.0112880	−	0.0785098i
$775$	26.2018	−	46.4630i	0.941197	−	1.66900i
$776$	−1.00779	−	0.460242i	−0.0361775	−	0.0165217i
$777$	3.84407	−	2.09902i	0.137905	−	0.0753019i
$778$	−22.1396	−	8.25764i	−0.793743	−	0.296051i
$779$	7.48597	+	52.0660i	0.268213	+	1.86546i
$780$	5.04874	−	9.91613i	0.180774	−	0.355055i
$781$		−	50.5324i		−	1.80819i
$782$	−1.45437	+	1.94403i	−0.0520082	+	0.0695183i
$783$	−5.31187	−	5.31187i	−0.189831	−	0.189831i
$784$	0.224452	−	0.349254i	0.00801615	−	0.0124734i
$785$	28.9395	+	17.4392i	1.03290	+	0.622434i
$786$	−2.32312	−	5.08692i	−0.0828629	−	0.181444i
$787$	18.5072	+	33.8934i	0.659711	+	1.20817i	0.966567	+	0.256414i	$0.0825411\pi$
$787$	18.5072	+	33.8934i	0.659711	+	1.20817i	−0.306856	+	0.951756i	$0.599277\pi$
$788$	−15.3580	+	5.72823i	−0.547105	+	0.204060i
$789$	−18.8626	+	21.7686i	−0.671526	+	0.774982i
$790$	0.857306	−	0.787307i	0.0305016	−	0.0280111i
$791$	−28.1331	+	8.26062i	−1.00030	+	0.293714i
$792$	−0.161059	+	2.25189i	−0.00572297	+	0.0800176i
$793$	2.17136	−	9.98157i	0.0771072	−	0.354456i
$794$	−5.30325	−	8.25201i	−0.188205	−	0.292853i
$795$	20.5574	−	21.7797i	0.729097	−	0.772447i
$796$	−0.451029	−	1.53606i	−0.0159863	−	0.0544443i
$797$	−31.8991	+	23.8793i	−1.12992	+	0.845850i	−0.989542	−	0.144248i	$-0.953924\pi$
$797$	−31.8991	+	23.8793i	−1.12992	+	0.845850i	−0.140381	+	0.990097i	$0.544833\pi$
$798$	38.4649	−	2.75106i	1.36164	−	0.0973865i
$799$	−0.230627	+	0.505004i	−0.00815901	+	0.0178657i
$800$	3.82317	−	3.22232i	0.135169	−	0.113926i
$801$	6.59644	−	3.01249i	0.233074	−	0.106441i
$802$	−2.12465	+	2.83820i	−0.0750239	+	0.100220i
$803$	−17.4992	+	3.80672i	−0.617534	+	0.134336i
$804$	−12.9708			−0.457443
$805$	7.03667	+	28.3413i	0.248010	+	0.998899i
$806$	−27.8142			−0.979715
$807$	−46.4569	+	10.1061i	−1.63536	+	0.355751i
$808$	−7.92881	+	10.5917i	−0.278935	+	0.372613i
$809$	−24.6869	+	11.2741i	−0.867945	+	0.396377i	−0.799063	−	0.601248i	$-0.794671\pi$
$809$	−24.6869	+	11.2741i	−0.867945	+	0.396377i	−0.0688821	+	0.997625i	$0.521943\pi$
$810$	−13.2783	−	19.4063i	−0.466551	−	0.681867i
$811$	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	$0.135826\pi$
$812$	−4.53573	+	0.324402i	−0.159173	+	0.0113843i
$813$	40.7056	−	30.4718i	1.42761	−	1.06869i
$814$	−0.833333	−	2.83807i	−0.0292083	−	0.0994743i
$815$	8.87059	−	0.256098i	0.310723	−	0.00897073i
$816$	−0.522404	−	0.812876i	−0.0182878	−	0.0284564i
$817$	−5.41093	+	24.8736i	−0.189305	+	0.870219i
$818$	−0.552542	+	7.72555i	−0.0193192	+	0.270118i
$819$	−4.38128	+	1.28646i	−0.153094	+	0.0449526i
$820$	0.674141	−	15.8386i	0.0235420	−	0.553109i
$821$	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	$0.188887\pi$
$822$	34.3031	−	12.7944i	1.19646	−	0.446256i
$823$	−5.33294	−	9.76656i	−0.185895	−	0.340441i	0.768067	−	0.640370i	$-0.221219\pi$
$823$	−5.33294	−	9.76656i	−0.185895	−	0.340441i	−0.953962	+	0.299929i	$0.903037\pi$
$824$	1.68758	+	3.69528i	0.0587895	+	0.128731i
$825$	−30.2789	−	14.3315i	−1.05418	−	0.498960i
$826$	19.7697	−	30.7623i	0.687876	−	1.07036i
$827$	−17.8222	−	17.8222i	−0.619738	−	0.619738i	0.325726	−	0.945464i	$-0.394391\pi$
$827$	−17.8222	−	17.8222i	−0.619738	−	0.619738i	−0.945464	+	0.325726i	$0.894391\pi$
$828$	−2.70770	−	1.47746i	−0.0940991	−	0.0513453i
$829$			21.3229i			0.740573i	0.928918	+	0.370287i	$0.120741\pi$
$829$			21.3229i			0.740573i	−0.928918	+	0.370287i	$0.879259\pi$
$830$	22.7961	+	11.6065i	0.791265	+	0.402868i
$831$	−1.24007	−	8.62489i	−0.0430176	−	0.299194i
$832$	−2.44279	−	0.911113i	−0.0846884	−	0.0315872i
$833$	0.184463	−	0.100724i	0.00639125	−	0.00348989i
$834$	10.6638	+	4.87002i	0.369259	+	0.168635i
$835$	−9.02035	+	1.56384i	−0.312162	+	0.0541191i
$836$	3.70637	−	25.7783i	0.128187	−	0.891562i
$837$	−22.9999	+	42.1212i	−0.794993	+	1.45592i
$838$	−31.2481	−	2.23491i	−1.07945	−	0.0772035i
$839$	16.5502	−	10.6362i	0.571377	−	0.367202i	−0.222822	−	0.974859i	$-0.571527\pi$
$839$	16.5502	−	10.6362i	0.571377	−	0.367202i	0.794199	+	0.607657i	$0.207891\pi$
$840$	−11.5468	−	1.32133i	−0.398401	−	0.0455902i
$841$	−17.1648	−	19.8092i	−0.591890	−	0.683077i
$842$	−7.27017	−	3.96981i	−0.250547	−	0.136809i
$843$	−18.0779	−	24.1493i	−0.622637	−	0.831746i
$844$	−14.4042	−	12.4813i	−0.495815	−	0.429626i
$845$	−4.46988	+	13.1295i	−0.153769	+	0.451670i
$846$	−0.676773	−	0.198718i	−0.0232679	−	0.00683208i
$847$	−1.25727	+	3.37087i	−0.0432002	+	0.115824i
$848$	−5.61754	−	4.20524i	−0.192907	−	0.144408i
$849$	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
$853$	1.64389	+	7.55686i	0.0562859	+	0.258742i	0.996688	−	0.0813231i	$-0.0259146\pi$
$853$	1.64389	+	7.55686i	0.0562859	+	0.258742i	−0.940402	+	0.340065i	$0.889551\pi$
$854$	−10.5606	+	1.51838i	−0.361375	+	0.0519578i
$855$	−5.38198	−	9.21383i	−0.184060	−	0.315106i
$856$	−1.68606	+	5.74221i	−0.0576285	+	0.196265i
$857$	−16.4186	−	44.0200i	−0.560849	−	1.50369i	−0.839532	−	0.543310i	$-0.817171\pi$
$857$	−16.4186	−	44.0200i	−0.560849	−	1.50369i	0.278683	−	0.960383i	$-0.410102\pi$
$858$	1.24613	+	17.4232i	0.0425422	+	0.594818i
$859$	−28.4060	−	4.08417i	−0.969200	−	0.139350i	−0.360508	−	0.932756i	$-0.617397\pi$
$859$	−28.4060	−	4.08417i	−0.969200	−	0.139350i	−0.608692	+	0.793406i	$0.708306\pi$
$860$	2.98423	−	7.06751i	0.101762	−	0.241000i
$861$	−27.8487	+	24.1310i	−0.949079	+	0.822382i
$862$	6.70396	+	1.45836i	0.228338	+	0.0496718i
$863$	−20.4993	−	4.45934i	−0.697803	−	0.151798i	−0.150348	−	0.988633i	$-0.548039\pi$
$863$	−20.4993	−	4.45934i	−0.697803	−	0.151798i	−0.547455	+	0.836835i	$0.684403\pi$
$864$	−3.39974	+	2.94589i	−0.115661	+	0.100221i
$865$	10.8861	−	25.7814i	0.370139	−	0.876593i
$866$	−33.6618	−	4.83984i	−1.14388	−	0.164464i
$867$	2.27992	+	31.8775i	0.0774302	+	1.08262i
$868$	10.1522	+	27.2191i	0.344588	+	0.923878i
$869$	−0.514778	+	1.75317i	−0.0174627	+	0.0594723i
$870$	3.59481	+	6.15423i	0.121875	+	0.208648i
$871$	−17.5368	+	2.52142i	−0.594213	+	0.0854350i
$872$	1.34495	+	6.18265i	0.0455458	+	0.209371i
$873$	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
$877$	11.0562	+	8.27657i	0.373342	+	0.279480i	0.769428	−	0.638733i	$-0.220541\pi$
$877$	11.0562	+	8.27657i	0.373342	+	0.279480i	−0.396087	+	0.918213i	$0.629632\pi$
$878$	8.54105	−	22.8994i	0.288246	−	0.772818i
$879$	−37.9549	−	11.1446i	−1.28019	−	0.375897i
$880$	−2.52956	+	7.43016i	−0.0852713	+	0.250471i
$881$	−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	$0.737818\pi$
$882$	0.160019	+	0.213761i	0.00538814	+	0.00719771i
$883$	−23.7064	−	12.9447i	−0.797785	−	0.435623i	0.0280007	−	0.999608i	$-0.491086\pi$
$883$	−23.7064	−	12.9447i	−0.797785	−	0.435623i	−0.825785	+	0.563984i	$0.809268\pi$
$884$	−0.864323	−	0.997482i	−0.0290703	−	0.0335489i
$885$	−56.9418	−	6.51601i	−1.91408	−	0.219033i
$886$	−27.1585	+	17.4537i	−0.912409	+	0.586369i
$887$	14.4915	+	1.03645i	0.486577	+	0.0348007i	0.312473	−	0.949927i	$-0.398843\pi$
$887$	14.4915	+	1.03645i	0.486577	+	0.0348007i	0.174104	+	0.984727i	$0.444297\pi$
$888$	−0.770826	+	1.41166i	−0.0258672	+	0.0473723i
$889$	0.250928	−	1.74525i	0.00841587	−	0.0585337i
$890$	24.8410	−	4.30664i	0.832672	−	0.144359i
$891$	33.5766	+	15.3339i	1.12486	+	0.513705i
$892$	13.6808	−	7.47029i	0.458067	−	0.250124i
$893$	7.62359	+	2.84345i	0.255114	+	0.0951525i
$894$	3.13803	+	21.8255i	0.104952	+	0.729954i
$895$	−27.9366	−	14.2238i	−0.933818	−	0.475448i
$896$			2.72308i			0.0909717i
$897$	−22.3634	−	8.33348i	−0.746693	−	0.278247i
$898$	−3.90997	−	3.90997i	−0.130477	−	0.130477i
$899$	9.63166	−	14.9872i	0.321234	−	0.499850i
$900$	1.08253	+	3.02820i	0.0360842	+	0.100940i
$901$	−1.47571	−	3.23136i	−0.0491632	−	0.107652i
$902$	11.9265	+	21.8418i	0.397109	+	0.727252i
$903$	−16.7080	+	6.23176i	−0.556008	+	0.207380i
$904$	7.05122	−	8.13755i	0.234520	−	0.270651i
$905$	1.35009	−	31.7197i	0.0448784	−	1.05440i
$906$	−37.7097	+	11.0726i	−1.25282	+	0.367862i
$907$	−0.567923	+	7.94060i	−0.0188576	+	0.263663i	0.979273	+	0.202545i	$0.0649213\pi$
$907$	−0.567923	+	7.94060i	−0.0188576	+	0.263663i	−0.998131	+	0.0611184i	$0.980533\pi$
$908$	3.74265	−	17.2047i	0.124204	−	0.570958i
$909$	−4.60064	−	7.15874i	−0.152594	−	0.237440i
$910$	−15.8684	+	0.458129i	−0.526033	+	0.0151868i
$911$	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	$0.863085\pi$
$912$	−11.3369	+	8.48672i	−0.375403	+	0.281023i
$913$	−40.0541	+	2.86472i	−1.32560	+	0.0948085i
$914$	−4.54846	+	9.95974i	−0.150450	+	0.329439i
$915$	9.44294	+	13.8009i	0.312174	+	0.456243i
$916$	18.5953	−	8.49221i	0.614407	−	0.280590i
$917$	−4.78120	+	6.38694i	−0.157889	+	0.210915i
$918$	−2.22528	+	0.484080i	−0.0734452	+	0.0159770i
$919$	−34.6202			−1.14201			−0.571007	−	0.820945i	$-0.693447\pi$
$919$	−34.6202			−1.14201			−0.571007	+	0.820945i	$0.693447\pi$
$920$	−7.80076	−	7.35854i	−0.257183	−	0.242604i
$921$	63.8732			2.10469
$922$	−7.15870	+	1.55728i	−0.235759	+	0.0512863i
$923$	−22.4927	+	30.0467i	−0.740355	+	0.988999i
$924$	16.5956	−	7.57895i	0.545954	−	0.249329i
$925$	−2.71534	−	3.22165i	−0.0892799	−	0.105927i
$926$	10.3615	−	22.6884i	0.340499	−	0.745588i
$927$	−2.60617	+	0.186397i	−0.0855980	+	0.00612209i
$928$	1.33684	−	1.00074i	0.0438838	−	0.0328510i
$929$	−5.10064	−	17.3712i	−0.167347	−	0.569931i	−0.999873	−	0.0159449i	$-0.994924\pi$
$929$	−5.10064	−	17.3712i	−0.167347	−	0.569931i	0.832526	−	0.553986i	$-0.186894\pi$
$930$	31.2539	−	33.1122i	1.02486	−	1.08579i
$931$	−1.66531	−	2.59128i	−0.0545784	−	0.0849256i
$932$	−1.21415	+	5.58138i	−0.0397709	+	0.182824i
$933$	0.592098	−	8.27861i	0.0193844	−	0.271029i
$934$	7.19857	−	2.11369i	0.235544	−	0.0691621i
$935$	−2.92660	+	2.68764i	−0.0957100	+	0.0878952i
$936$	1.09812	−	1.26729i	0.0358930	−	0.0414228i
$937$	9.57190	−	3.57013i	0.312700	−	0.116631i	−0.188214	−	0.982128i	$-0.560270\pi$
$937$	9.57190	−	3.57013i	0.312700	−	0.116631i	0.500914	+	0.865497i	$0.332997\pi$
$938$	8.86843	+	16.2413i	0.289564	+	0.530298i
$939$	23.7469	+	51.9985i	0.774952	+	1.69691i
$940$	−2.10032	−	1.26568i	−0.0685050	−	0.0412818i
$941$	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
$943$	−33.9135	+	2.43578i	−1.10438	+	0.0793200i
$944$			13.4286i			0.437064i
$945$	−12.4280	+	24.4096i	−0.404283	+	0.794044i
$946$	1.71390	+	11.9204i	0.0557236	+	0.387566i
$947$	31.9709	+	11.9245i	1.03891	+	0.387495i	0.810296	−	0.586021i	$-0.199307\pi$
$947$	31.9709	+	11.9245i	1.03891	+	0.387495i	0.228618	+	0.973516i	$0.426579\pi$
$948$	0.872032	−	0.476166i	0.0283223	−	0.0154651i
$949$	12.0995	+	5.52566i	0.392767	+	0.179371i
$950$	−9.96379	−	35.7341i	−0.323268	−	1.15937i
$951$	7.98982	−	55.5704i	0.259088	−	1.80199i
$952$	−0.660661	+	1.20991i	−0.0214122	+	0.0392134i
$953$	7.92051	+	0.566486i	0.256571	+	0.0183503i	0.199032	−	0.979993i	$-0.436220\pi$
$953$	7.92051	+	0.566486i	0.256571	+	0.0183503i	0.0575385	+	0.998343i	$0.481675\pi$
$954$	3.79681	−	2.44006i	0.122926	−	0.0790000i
$955$	−31.2183	+	24.8071i	−1.01020	+	0.802740i
$956$	9.27422	+	10.7030i	0.299950	+	0.346160i
$957$	−9.81967	−	5.36195i	−0.317425	−	0.173327i
$958$	−14.8595	−	19.8500i	−0.480089	−	0.641324i
$959$	−39.4744	−	34.2047i	−1.27469	−	1.10453i
$960$	3.82953	−	1.88429i	0.123598	−	0.0608153i
$961$	−79.4594	−	23.3314i	−2.56321	−	0.752625i
$962$	−0.767763	+	2.05845i	−0.0247537	+	0.0663672i
$963$	−3.08142	−	2.30672i	−0.0992973	−	0.0743330i
$964$	−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	−0.165207	−	0.986259i	$-0.552829\pi$
$967$	25.5319	−	25.5319i	0.821052	−	0.821052i	0.986259	+	0.165207i	$0.0528293\pi$
$968$	−0.280839	−	1.29100i	−0.00902651	−	0.0414942i
$969$	−7.09620	+	1.02028i	−0.227963	+	0.0327761i
$970$	2.13916	−	1.24953i	0.0686843	−	0.0401199i
$971$	−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	$0.958590\pi$
$972$	−2.29816	−	6.16160i	−0.0737134	−	0.197633i
$973$	−1.19315	−	16.6825i	−0.0382508	−	0.534816i
$974$	37.0486	+	5.32679i	1.18711	+	0.170681i
$975$	11.6248	+	21.9991i	0.372291	+	0.704536i
$976$	2.96106	−	2.56578i	0.0947813	−	0.0821285i
$977$	−2.64067	−	0.574442i	−0.0844824	−	0.0183780i	0.170125	−	0.985422i	$-0.445583\pi$
$977$	−2.64067	−	0.574442i	−0.0844824	−	0.0183780i	−0.254608	+	0.967044i	$0.581946\pi$
$978$	7.40199	+	1.61020i	0.236690	+	0.0514887i
$979$	−29.9101	+	25.9173i	−0.955932	+	0.828320i
$980$	0.349382	+	0.860069i	0.0111606	+	0.0274739i
$981$	−4.02811	−	0.579155i	−0.128608	−	0.0184910i
$982$	−0.649372	−	9.07941i	−0.0207223	−	0.289736i
$983$	−3.87930	−	10.4008i	−0.123731	−	0.331734i	0.860286	−	0.509812i	$-0.170285\pi$
$983$	−3.87930	−	10.4008i	−0.123731	−	0.331734i	−0.984016	+	0.178077i	$0.943012\pi$
$984$	3.81244	−	12.9840i	0.121536	−	0.413914i
$985$	9.30699	−	35.4511i	0.296545	−	1.12957i
$986$	0.836776	−	0.120310i	0.0266484	−	0.00383146i
$987$	1.21161	+	5.56970i	0.0385661	+	0.177285i
$988$	−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	$0.598776\pi$
$992$	−8.54046	−	6.39331i	−0.271160	−	0.202988i
$993$	15.3164	−	41.0647i	0.486050	−	1.30315i
$994$	37.6136	+	11.0444i	1.19303	+	0.350306i
$995$	3.38875	+	1.15368i	0.107430	+	0.0365741i
$996$	16.5024	+	14.2994i	0.522898	+	0.453093i
$997$	−2.99251	−	3.99753i	−0.0947739	−	0.126603i	0.750648	−	0.660703i	$-0.229742\pi$
$997$	−2.99251	−	3.99753i	−0.0947739	−	0.126603i	−0.845422	+	0.534100i	$0.820651\pi$
$998$	6.34325	+	3.46368i	0.200792	+	0.109641i
$999$	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.113.6	yes	240
5.2	odd	4	inner	230.2.l.a.67.1	yes	240
23.11	odd	22	inner	230.2.l.a.103.1	yes	240
115.57	even	44	inner	230.2.l.a.57.6	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.6	✓	240	115.57	even	44	inner
230.2.l.a.67.1	yes	240	5.2	odd	4	inner
230.2.l.a.103.1	yes	240	23.11	odd	22	inner
230.2.l.a.113.6	yes	240	1.1	even	1	trivial

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+(-0.977147 + 0.212565i) q^{2} +(1.14385 - 1.52800i) q^{3} +(0.909632 - 0.415415i) q^{4} +(-0.412058 + 2.19777i) q^{5} +(-0.792907 + 1.73622i) q^{6} +(2.71614 - 0.194262i) q^{7} +(-0.800541 + 0.599278i) q^{8} +(-0.181204 - 0.617123i) q^{9} +(-0.0645294 - 2.23514i) q^{10} +(1.89773 + 2.95293i) q^{11} +(0.405726 - 1.86509i) q^{12} +(0.185993 - 2.60053i) q^{13} +(-2.61278 + 0.767180i) q^{14} +(2.88687 + 3.14354i) q^{15} +(0.654861 - 0.755750i) q^{16} +(0.474323 - 0.176913i) q^{17} +(0.308241 + 0.564502i) q^{18} +(-3.08215 - 6.74897i) q^{19} +(0.538167 + 2.17034i) q^{20} +(2.81002 - 4.37247i) q^{21} +(-2.48205 - 2.48205i) q^{22} +(4.49295 - 1.67732i) q^{23} +1.90871i q^{24} +(-4.66042 - 1.81122i) q^{25} +(0.371039 + 2.58063i) q^{26} +(4.21486 + 1.57206i) q^{27} +(2.38999 - 1.30503i) q^{28} +(-1.51901 - 0.693708i) q^{29} +(-3.48910 - 2.45805i) q^{30} +(-1.51827 + 10.5598i) q^{31} +(-0.479249 + 0.877679i) q^{32} +(6.68280 + 0.477963i) q^{33} +(-0.425877 + 0.273695i) q^{34} +(-0.692263 + 6.04951i) q^{35} +(-0.421191 - 0.486080i) q^{36} +(0.739590 + 0.403846i) q^{37} +(4.44631 + 5.93958i) q^{38} +(-3.76086 - 3.25881i) q^{39} +(-0.987207 - 2.00635i) q^{40} +(-6.80249 - 1.99739i) q^{41} +(-1.81636 + 4.86986i) q^{42} +(-2.74658 - 2.05606i) 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} +(-0.405726 - 1.86509i) q^{48} +(0.410934 - 0.0590834i) q^{49} +(4.93891 + 0.779184i) q^{50} +(0.272229 - 0.927127i) q^{51} +(-0.911113 - 2.44279i) q^{52} +(-0.500600 - 6.99930i) q^{53} +(-4.45271 - 0.640203i) q^{54} +(-7.27185 + 2.95401i) q^{55} +(-2.05797 + 1.78324i) q^{56} +(-13.8379 - 3.01026i) q^{57} +(1.63175 + 0.354966i) q^{58} +(-10.1487 + 8.79387i) q^{59} +(3.93186 + 1.66022i) q^{60} +(3.87817 + 0.557596i) q^{61} +(-0.761072 - 10.6412i) q^{62} +(-0.612058 - 1.64099i) q^{63} +(0.281733 - 0.959493i) q^{64} +(5.63873 + 1.48034i) q^{65} +(-6.63168 + 0.953491i) q^{66} +(-1.44450 - 6.64026i) 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} +(0.514889 + 0.385441i) q^{72} +(-1.78293 + 4.78023i) q^{73} +(-0.808531 - 0.237406i) q^{74} +(-8.09835 + 5.04937i) q^{75} +(-5.60725 - 4.85871i) q^{76} +(5.72815 + 7.65192i) q^{77} +(4.36762 + 2.38490i) q^{78} +(0.340883 + 0.393400i) q^{79} +(1.39113 + 1.75065i) q^{80} +(8.84650 - 5.68530i) q^{81} +(7.07160 + 0.505771i) q^{82} +(-5.48264 + 10.0407i) q^{83} +(0.739691 - 5.14467i) q^{84} +(0.193367 + 1.11535i) q^{85} +(3.12086 + 1.42525i) q^{86} +(-2.79750 + 1.52755i) q^{87} +(-3.28884 - 1.22667i) q^{88} +(1.60459 + 11.1602i) q^{89} +(-1.36766 + 0.444837i) q^{90} -7.09953i q^{91} +(3.39015 - 3.39218i) q^{92} +(14.3987 + 14.3987i) q^{93} +(0.592898 - 0.922568i) q^{94} +(16.1027 - 3.99290i) q^{95} +(0.792907 + 1.73622i) q^{96} +(0.530964 + 0.972389i) q^{97} +(-0.388984 + 0.145083i) 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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