LMFDB - Embedded newform 684.2.o.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(11,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("684.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$232$
Relative dimension:	$116$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	684.11
Dual form			684.2.o.a.311.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41338 - 0.0484033i) q^{2} +(-1.15926 + 1.28691i) q^{3} +(1.99531 + 0.136825i) q^{4} -0.365397i q^{5} +(1.70076 - 1.76278i) q^{6} +(-3.58119 - 2.06760i) q^{7} +(-2.81352 - 0.289966i) q^{8} +(-0.312254 - 2.98371i) q^{9} +(-0.0176864 + 0.516447i) q^{10} +(2.42667 - 4.20311i) q^{11} +(-2.48916 + 2.40917i) q^{12} +(-2.26421 + 3.92173i) q^{13} +(4.96153 + 3.09566i) q^{14} +(0.470232 + 0.423589i) q^{15} +(3.96256 + 0.546017i) q^{16} +(4.86446 + 2.80849i) q^{17} +(0.296914 + 4.23224i) q^{18} +(-2.00062 + 3.87266i) q^{19} +(0.0499955 - 0.729082i) q^{20} +(6.81233 - 2.21178i) q^{21} +(-3.63326 + 5.82315i) q^{22} +(-0.520572 + 0.901657i) q^{23} +(3.63475 - 3.28460i) q^{24} +4.86648 q^{25} +(3.39003 - 5.43332i) q^{26} +(4.20173 + 3.05703i) q^{27} +(-6.86271 - 4.61551i) q^{28} +0.317438i q^{29} +(-0.644116 - 0.621455i) q^{30} +(-6.35356 + 3.66823i) q^{31} +(-5.57419 - 0.963533i) q^{32} +(2.59588 + 7.99536i) q^{33} +(-6.73941 - 4.20494i) q^{34} +(-0.755496 + 1.30856i) q^{35} +(-0.214800 - 5.99615i) q^{36} -0.486469 q^{37} +(3.01510 - 5.37672i) q^{38} +(-2.42210 - 7.46011i) q^{39} +(-0.105953 + 1.02805i) q^{40} +1.31049i q^{41} +(-9.73550 + 2.79636i) q^{42} +(-8.54619 + 4.93414i) q^{43} +(5.41705 - 8.05449i) q^{44} +(-1.09024 + 0.114097i) q^{45} +(0.779412 - 1.24919i) q^{46} +10.6956 q^{47} +(-5.29629 + 4.46647i) q^{48} +(5.04996 + 8.74679i) q^{49} +(-6.87822 - 0.235554i) q^{50} +(-9.25342 + 3.00433i) q^{51} +(-5.05440 + 7.51528i) q^{52} +(-6.32685 + 3.65281i) q^{53} +(-5.79069 - 4.52414i) q^{54} +(-1.53580 - 0.886697i) q^{55} +(9.47624 + 6.85568i) q^{56} +(-2.66452 - 7.06402i) q^{57} +(0.0153650 - 0.448662i) q^{58} -2.67518 q^{59} +(0.880303 + 0.909532i) q^{60} +5.89625 q^{61} +(9.15759 - 4.87709i) q^{62} +(-5.05088 + 11.3308i) q^{63} +(7.83184 + 1.63165i) q^{64} +(1.43299 + 0.827336i) q^{65} +(-3.28198 - 11.4262i) q^{66} +(13.7059 + 7.91310i) q^{67} +(9.32185 + 6.26941i) q^{68} +(-0.556872 - 1.71518i) q^{69} +(1.13115 - 1.81293i) q^{70} +(3.69330 - 6.39698i) q^{71} +(0.0133612 + 8.48527i) q^{72} +(-3.25587 + 5.63934i) q^{73} +(0.687568 + 0.0235467i) q^{74} +(-5.64150 + 6.26271i) q^{75} +(-4.52175 + 7.45344i) q^{76} +(-17.3807 + 10.0348i) q^{77} +(3.06226 + 10.6612i) q^{78} +(-4.27446 + 2.46786i) q^{79} +(0.199513 - 1.44791i) q^{80} +(-8.80499 + 1.86335i) q^{81} +(0.0634320 - 1.85223i) q^{82} +(-7.89843 + 13.6805i) q^{83} +(13.8954 - 3.48110i) q^{84} +(1.02622 - 1.77746i) q^{85} +(12.3179 - 6.56018i) q^{86} +(-0.408512 - 0.367991i) q^{87} +(-8.04624 + 11.1219i) q^{88} +(2.37814 - 1.37302i) q^{89} +(1.54645 - 0.108492i) q^{90} +(16.2172 - 9.36298i) q^{91} +(-1.16207 + 1.72786i) q^{92} +(2.64473 - 12.4289i) q^{93} +(-15.1170 - 0.517701i) q^{94} +(1.41506 + 0.731023i) q^{95} +(7.70189 - 6.05648i) q^{96} +(-0.673718 - 1.16691i) q^{97} +(-6.71417 - 12.6070i) q^{98} +(-13.2986 - 5.92802i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 232 q - 3 q^{2} + q^{4} + 3 q^{6} + 2 q^{10} - q^{12} + 2 q^{13} + q^{16} - 12 q^{17} - 16 q^{18} - 27 q^{20} - 14 q^{21} + 6 q^{22} - 10 q^{24} - 204 q^{25} - 6 q^{28} - 9 q^{30} - 3 q^{32} - 12 q^{33}+ \cdots - 162 q^{98}+O(q^{100}) $ 232 * q - 3 * q^2 + q^4 + 3 * q^6 + 2 * q^10 - q^12 + 2 * q^13 + q^16 - 12 * q^17 - 16 * q^18 - 27 * q^20 - 14 * q^21 + 6 * q^22 - 10 * q^24 - 204 * q^25 - 6 * q^28 - 9 * q^30 - 3 * q^32 - 12 * q^33 + 2 * q^34 + 13 * q^36 - 16 * q^37 - 3 * q^38 - 16 * q^40 - 43 * q^42 + 21 * q^44 + 2 * q^45 - 24 * q^46 + 58 * q^48 + 88 * q^49 + 9 * q^50 + 17 * q^52 + 41 * q^54 - 48 * q^56 - 12 * q^57 + 2 * q^58 + 16 * q^60 - 4 * q^61 + 6 * q^62 + 16 * q^64 + 12 * q^65 - 27 * q^66 - 18 * q^68 - 14 * q^69 + 60 * q^70 + 15 * q^72 + 2 * q^73 - 30 * q^74 + 3 * q^76 - 12 * q^77 - 64 * q^78 + 54 * q^80 + 4 * q^81 + 2 * q^82 - 10 * q^84 + 22 * q^85 + 51 * q^86 - 18 * q^88 + 14 * q^90 + 57 * q^92 + 4 * q^93 - 6 * q^94 - 17 * q^96 - 4 * q^97 - 162 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.41338	−	0.0484033i	−0.999414	−	0.0342263i
$2$	−1.41338	−	0.0484033i	−0.999414	−	0.0342263i
$3$	−1.15926	+	1.28691i	−0.669296	+	0.742996i
$3$	−1.15926	+	1.28691i	−0.669296	+	0.742996i
$4$	1.99531	+	0.136825i	0.997657	+	0.0684125i
$5$		−	0.365397i		−	0.163411i	−0.996657	−	0.0817053i	$-0.973963\pi$
$5$		−	0.365397i		−	0.163411i	0.996657	−	0.0817053i	$-0.0260366\pi$
$6$	1.70076	−	1.76278i	0.694334	−	0.719653i
$7$	−3.58119	−	2.06760i	−1.35356	−	0.781480i	−0.364817	−	0.931079i	$-0.618868\pi$
$7$	−3.58119	−	2.06760i	−1.35356	−	0.781480i	−0.988747	+	0.149599i	$0.952202\pi$
$8$	−2.81352	−	0.289966i	−0.994731	−	0.102518i
$9$	−0.312254	−	2.98371i	−0.104085	−	0.994568i
$10$	−0.0176864	+	0.516447i	−0.00559294	+	0.163315i
$11$	2.42667	−	4.20311i	0.731667	−	1.26728i	−0.224503	−	0.974473i	$-0.572076\pi$
$11$	2.42667	−	4.20311i	0.731667	−	1.26728i	0.956170	−	0.292811i	$-0.0945908\pi$
$12$	−2.48916	+	2.40917i	−0.718558	+	0.695467i
$13$	−2.26421	+	3.92173i	−0.627979	+	1.08769i	0.359978	+	0.932961i	$0.382784\pi$
$13$	−2.26421	+	3.92173i	−0.627979	+	1.08769i	−0.987957	+	0.154731i	$0.950549\pi$
$14$	4.96153	+	3.09566i	1.32602	+	0.827350i
$15$	0.470232	+	0.423589i	0.121413	+	0.109370i
$16$	3.96256	+	0.546017i	0.990639	+	0.136504i
$17$	4.86446	+	2.80849i	1.17980	+	0.681160i	0.955969	−	0.293467i	$-0.0948091\pi$
$17$	4.86446	+	2.80849i	1.17980	+	0.681160i	0.223835	+	0.974627i	$0.428142\pi$
$18$	0.296914	+	4.23224i	0.0699833	+	0.997548i
$19$	−2.00062	+	3.87266i	−0.458975	+	0.888449i
$19$	−2.00062	+	3.87266i	−0.458975	+	0.888449i
$20$	0.0499955	−	0.729082i	0.0111793	−	0.163028i
$21$	6.81233	−	2.21178i	1.48657	−	0.482650i
$22$	−3.63326	+	5.82315i	−0.774613	+	1.24150i
$23$	−0.520572	+	0.901657i	−0.108547	+	0.188008i	−0.915182	−	0.403041i	$-0.867953\pi$
$23$	−0.520572	+	0.901657i	−0.108547	+	0.188008i	0.806635	+	0.591050i	$0.201286\pi$
$24$	3.63475	−	3.28460i	0.741941	−	0.670466i
$25$	4.86648			0.973297
$26$	3.39003	−	5.43332i	0.664839	−	1.06556i
$27$	4.20173	+	3.05703i	0.808623	+	0.588327i
$28$	−6.86271	−	4.61551i	−1.29693	−	0.872250i
$29$			0.317438i			0.0589467i	0.999566	+	0.0294734i	$0.00938302\pi$
$29$			0.317438i			0.0589467i	−0.999566	+	0.0294734i	$0.990617\pi$
$30$	−0.644116	−	0.621455i	−0.117599	−	0.113462i
$31$	−6.35356	+	3.66823i	−1.14113	+	0.658834i	−0.946711	−	0.322084i	$-0.895617\pi$
$31$	−6.35356	+	3.66823i	−1.14113	+	0.658834i	−0.194423	+	0.980918i	$0.562283\pi$
$32$	−5.57419	−	0.963533i	−0.985387	−	0.170330i
$33$	2.59588	+	7.99536i	0.451885	+	1.39181i
$34$	−6.73941	−	4.20494i	−1.15580	−	0.721141i
$35$	−0.755496	+	1.30856i	−0.127702	+	0.221187i
$36$	−0.214800	−	5.99615i	−0.0357999	−	0.999359i
$37$	−0.486469			−0.0799751			−0.0399875	−	0.999200i	$-0.512732\pi$
$37$	−0.486469			−0.0799751			−0.0399875	+	0.999200i	$0.512732\pi$
$38$	3.01510	−	5.37672i	0.489114	−	0.872220i
$39$	−2.42210	−	7.46011i	−0.387846	−	1.19457i
$40$	−0.105953	+	1.02805i	−0.0167526	+	0.162550i
$41$			1.31049i			0.204664i	0.994750	+	0.102332i	$0.0326304\pi$
$41$			1.31049i			0.204664i	−0.994750	+	0.102332i	$0.967370\pi$
$42$	−9.73550	+	2.79636i	−1.50222	+	0.431487i
$43$	−8.54619	+	4.93414i	−1.30328	+	0.752450i	−0.980965	−	0.194182i	$-0.937795\pi$
$43$	−8.54619	+	4.93414i	−1.30328	+	0.752450i	−0.322316	+	0.946632i	$0.604461\pi$
$44$	5.41705	−	8.05449i	0.816651	−	1.21426i
$45$	−1.09024	+	0.114097i	−0.162523	+	0.0170085i
$46$	0.779412	−	1.24919i	0.114918	−	0.184183i
$47$	10.6956			1.56011			0.780056	−	0.625710i	$-0.215191\pi$
$47$	10.6956			1.56011			0.780056	+	0.625710i	$0.215191\pi$
$48$	−5.29629	+	4.46647i	−0.764454	+	0.644679i
$49$	5.04996	+	8.74679i	0.721423	+	1.24954i
$50$	−6.87822	−	0.235554i	−0.972727	−	0.0333123i
$51$	−9.25342	+	3.00433i	−1.29574	+	0.420691i
$52$	−5.05440	+	7.51528i	−0.700919	+	1.04218i
$53$	−6.32685	+	3.65281i	−0.869060	+	0.501752i	−0.867036	−	0.498246i	$-0.833978\pi$
$53$	−6.32685	+	3.65281i	−0.869060	+	0.501752i	−0.00202431	+	0.999998i	$0.500644\pi$
$54$	−5.79069	−	4.52414i	−0.788013	−	0.615658i
$55$	−1.53580	−	0.886697i	−0.207088	−	0.119562i
$56$	9.47624	+	6.85568i	1.26632	+	0.916128i
$57$	−2.66452	−	7.06402i	−0.352924	−	0.935652i
$58$	0.0153650	−	0.448662i	0.00201753	−	0.0589122i
$59$	−2.67518			−0.348279			−0.174139	−	0.984721i	$-0.555714\pi$
$59$	−2.67518			−0.348279			−0.174139	+	0.984721i	$0.555714\pi$
$60$	0.880303	+	0.909532i	0.113647	+	0.117420i
$61$	5.89625			0.754937			0.377469	−	0.926022i	$-0.376795\pi$
$61$	5.89625			0.754937			0.377469	+	0.926022i	$0.376795\pi$
$62$	9.15759	−	4.87709i	1.16301	−	0.619391i
$63$	−5.05088	+	11.3308i	−0.636351	+	1.42755i
$64$	7.83184	+	1.63165i	0.978980	+	0.203957i
$65$	1.43299	+	0.827336i	0.177740	+	0.102618i
$66$	−3.28198	−	11.4262i	−0.403983	−	1.40647i
$67$	13.7059	+	7.91310i	1.67444	+	0.966739i	0.965103	+	0.261872i	$0.0843398\pi$
$67$	13.7059	+	7.91310i	1.67444	+	0.966739i	0.709339	+	0.704867i	$0.248994\pi$
$68$	9.32185	+	6.26941i	1.13044	+	0.760277i
$69$	−0.556872	−	1.71518i	−0.0670395	−	0.206483i
$70$	1.13115	−	1.81293i	0.135198	−	0.216686i
$71$	3.69330	−	6.39698i	0.438314	−	0.759181i	−0.559246	−	0.829002i	$-0.688909\pi$
$71$	3.69330	−	6.39698i	0.438314	−	0.759181i	0.997560	+	0.0698204i	$0.0222426\pi$
$72$	0.0133612	+	8.48527i	0.00157463	+	0.999999i
$73$	−3.25587	+	5.63934i	−0.381071	+	0.660035i	−0.991216	−	0.132256i	$-0.957778\pi$
$73$	−3.25587	+	5.63934i	−0.381071	+	0.660035i	0.610144	+	0.792290i	$0.291111\pi$
$74$	0.687568	+	0.0235467i	0.0799282	+	0.00273725i
$75$	−5.64150	+	6.26271i	−0.651424	+	0.723155i
$76$	−4.52175	+	7.45344i	−0.518680	+	0.854968i
$77$	−17.3807	+	10.0348i	−1.98072	+	1.14357i
$78$	3.06226	+	10.6612i	0.346733	+	1.20715i
$79$	−4.27446	+	2.46786i	−0.480914	+	0.277656i	−0.720797	−	0.693146i	$-0.756224\pi$
$79$	−4.27446	+	2.46786i	−0.480914	+	0.277656i	0.239883	+	0.970802i	$0.422891\pi$
$80$	0.199513	−	1.44791i	0.0223063	−	0.161881i
$81$	−8.80499	+	1.86335i	−0.978333	+	0.207039i
$82$	0.0634320	−	1.85223i	0.00700490	−	0.204544i
$83$	−7.89843	+	13.6805i	−0.866966	+	1.50163i	−0.00188395	+	0.999998i	$0.500600\pi$
$83$	−7.89843	+	13.6805i	−0.866966	+	1.50163i	−0.865082	+	0.501631i	$0.832734\pi$
$84$	13.8954	−	3.48110i	1.51611	−	0.379819i
$85$	1.02622	−	1.77746i	0.111309	−	0.192792i
$86$	12.3179	−	6.56018i	1.32827	−	0.707402i
$87$	−0.408512	−	0.367991i	−0.0437971	−	0.0394528i
$88$	−8.04624	+	11.1219i	−0.857732	+	1.18560i
$89$	2.37814	−	1.37302i	0.252082	−	0.145539i	−0.368635	−	0.929574i	$-0.620175\pi$
$89$	2.37814	−	1.37302i	0.252082	−	0.145539i	0.620717	+	0.784035i	$0.286842\pi$
$90$	1.54645	−	0.108492i	0.163010	−	0.0114360i
$91$	16.2172	−	9.36298i	1.70002	−	0.981507i
$92$	−1.16207	+	1.72786i	−0.121155	+	0.180142i
$93$	2.64473	−	12.4289i	0.274246	−	1.28881i
$94$	−15.1170	−	0.517701i	−1.55920	−	0.0533968i
$95$	1.41506	+	0.731023i	0.145182	+	0.0750014i
$96$	7.70189	−	6.05648i	0.786071	−	0.618137i
$97$	−0.673718	−	1.16691i	−0.0684057	−	0.118482i	0.829794	−	0.558070i	$-0.188458\pi$
$97$	−0.673718	−	1.16691i	−0.0684057	−	0.118482i	−0.898200	+	0.439588i	$0.855125\pi$
$98$	−6.71417	−	12.6070i	−0.678233	−	1.27350i
$99$	−13.2986	−	5.92802i	−1.33656	−	0.595788i
$100$	9.71017	+	0.665856i	0.971017	+	0.0665856i
$101$			16.8767i			1.67929i	0.543134	+	0.839646i	$0.317237\pi$
$101$			16.8767i			1.67929i	−0.543134	+	0.839646i	$0.682763\pi$
$102$	13.2241	−	3.79839i	1.30938	−	0.376096i
$103$	−4.05841	+	2.34312i	−0.399887	+	0.230875i	−0.686435	−	0.727191i	$-0.740825\pi$
$103$	−4.05841	+	2.34312i	−0.399887	+	0.230875i	0.286548	+	0.958066i	$0.407492\pi$
$104$	7.50758	−	10.3773i	0.736179	−	1.01758i
$105$	−0.808178	−	2.48921i	−0.0788701	−	0.242922i
$106$	9.11909	−	4.85659i	0.885724	−	0.471713i
$107$	2.04959			0.198141			0.0990705	−	0.995080i	$-0.468413\pi$
$107$	2.04959			0.198141			0.0990705	+	0.995080i	$0.468413\pi$
$108$	7.96549	+	6.67465i	0.766480	+	0.642268i
$109$	−2.24118	+	3.88183i	−0.214666	+	0.371812i	−0.953169	−	0.302438i	$-0.902200\pi$
$109$	−2.24118	+	3.88183i	−0.214666	+	0.371812i	0.738503	+	0.674250i	$0.235533\pi$
$110$	2.12776	+	1.32758i	0.202874	+	0.126580i
$111$	0.563942	−	0.626040i	0.0535270	−	0.0594211i
$112$	−13.0617	−	10.1484i	−1.23422	−	0.958933i
$113$	6.82561	−	3.94077i	0.642099	−	0.370716i	−0.143323	−	0.989676i	$-0.545779\pi$
$113$	6.82561	−	3.94077i	0.642099	−	0.370716i	0.785423	+	0.618960i	$0.212446\pi$
$114$	3.42407	+	10.1131i	0.320693	+	0.947183i
$115$	0.329463	+	0.190216i	0.0307226	+	0.0177377i
$116$	−0.0434334	+	0.633388i	−0.00403269	+	0.0588086i
$117$	12.4083	+	5.53116i	1.14715	+	0.511356i
$118$	3.78106	+	0.129487i	0.348074	+	0.0119203i
$119$	−11.6137	−	20.1155i	−1.06463	−	1.84399i
$120$	−1.20018	−	1.32813i	−0.109561	−	0.121241i
$121$	−6.27741	−	10.8728i	−0.570673	−	0.988435i
$122$	−8.33367	−	0.285398i	−0.754495	−	0.0258387i
$123$	−1.68648	−	1.51919i	−0.152065	−	0.136981i
$124$	−13.1793	+	6.44995i	−1.18353	+	0.579223i
$125$		−	3.60519i		−	0.322458i
$126$	7.68728	−	15.7704i	0.684837	−	1.40494i
$127$	7.12198	−	4.11188i	0.631974	−	0.364870i	−0.149542	−	0.988755i	$-0.547780\pi$
$127$	7.12198	−	4.11188i	0.631974	−	0.364870i	0.781516	+	0.623885i	$0.214447\pi$
$128$	−10.9904	−	2.68524i	−0.971426	−	0.237344i
$129$	3.55743	−	16.7181i	0.313215	−	1.47194i
$130$	−1.98532	−	1.23871i	−0.174124	−	0.108642i
$131$	15.4520			1.35004			0.675022	−	0.737797i	$-0.264134\pi$
$131$	15.4520			1.35004			0.675022	+	0.737797i	$0.264134\pi$
$132$	4.08563	+	16.3084i	0.355608	+	1.41947i
$133$	15.1717	−	9.73225i	1.31556	−	0.843893i
$134$	−18.9887	−	11.8477i	−1.64037	−	1.02348i
$135$	1.11703	−	1.53530i	0.0961388	−	0.132138i
$136$	−12.8719	−	9.31230i	−1.10376	−	0.798523i
$137$		−	2.37698i		−	0.203079i	−0.994831	−	0.101540i	$-0.967623\pi$
$137$		−	2.37698i		−	0.203079i	0.994831	−	0.101540i	$-0.0323769\pi$
$138$	0.704054	+	2.45116i	0.0599331	+	0.208657i
$139$	12.9092	+	7.45314i	1.09495	+	0.632167i	0.934889	−	0.354941i	$-0.115499\pi$
$139$	12.9092	+	7.45314i	1.09495	+	0.632167i	0.160056	+	0.987108i	$0.448832\pi$
$140$	−1.68650	+	2.50761i	−0.142535	+	0.211932i
$141$	−12.3989	+	13.7642i	−1.04418	+	1.15916i
$142$	−5.52968	+	8.86262i	−0.464041	+	0.743735i
$143$	10.9890	+	19.0334i	0.918943	+	1.59166i
$144$	0.391830	−	11.9936i	0.0326525	−	0.999467i
$145$	0.115991			0.00963252
$146$	4.87477	−	7.81296i	0.403438	−	0.646605i
$147$	−17.1105	−	3.64094i	−1.41125	−	0.300300i
$148$	−0.970659	−	0.0665611i	−0.0797877	−	0.00547129i
$149$		−	9.90011i		−	0.811049i	−0.914084	−	0.405524i	$-0.867089\pi$
$149$		−	9.90011i		−	0.811049i	0.914084	−	0.405524i	$-0.132911\pi$
$150$	8.27675	−	8.57855i	0.675793	−	0.700436i
$151$	5.68293	+	3.28104i	0.462470	+	0.267007i	0.713082	−	0.701080i	$-0.247299\pi$
$151$	5.68293	+	3.28104i	0.462470	+	0.267007i	−0.250612	+	0.968088i	$0.580632\pi$
$152$	6.75175	−	10.3157i	0.547639	−	0.836715i
$153$	6.86078	−	15.3911i	0.554661	−	1.24429i
$154$	25.0514	−	13.3417i	2.01870	−	1.07510i
$155$	1.34036	+	2.32158i	0.107660	+	0.186473i
$156$	−3.81212	−	15.2167i	−0.305213	−	1.21831i
$157$	−16.2493			−1.29683			−0.648416	−	0.761286i	$-0.724568\pi$
$157$	−16.2493			−1.29683			−0.648416	+	0.761286i	$0.724568\pi$
$158$	6.16090	−	3.28114i	0.490135	−	0.261033i
$159$	2.63361	−	12.3766i	0.208859	−	0.981529i
$160$	−0.352073	+	2.03679i	−0.0278338	+	0.161023i
$161$	3.72854	−	2.15267i	0.293850	−	0.169654i
$162$	12.5350	−	2.20744i	0.984846	−	0.173433i
$163$		−	17.3365i		−	1.35790i	−0.734186	−	0.678949i	$-0.762436\pi$
$163$		−	17.3365i		−	1.35790i	0.734186	−	0.678949i	$-0.237564\pi$
$164$	−0.179308	+	2.61484i	−0.0140016	+	0.204185i
$165$	2.92148	−	0.948527i	0.227437	−	0.0738428i
$166$	11.8257	−	18.9535i	0.917853	−	1.47108i
$167$	−3.64106	+	6.30650i	−0.281754	+	0.488011i	−0.971817	−	0.235738i	$-0.924249\pi$
$167$	−3.64106	+	6.30650i	−0.281754	+	0.488011i	0.690063	+	0.723749i	$0.257583\pi$
$168$	−19.8080	+	4.24755i	−1.52822	+	0.327706i
$169$	−3.75330	−	6.50091i	−0.288715	−	0.500070i
$170$	−1.53647	+	2.46256i	−0.117842	+	0.188870i
$171$	12.1796	+	4.76002i	0.931396	+	0.364008i
$172$	−17.7274	+	8.67584i	−1.35170	+	0.661526i
$173$	0.889494	−	0.513550i	0.0676270	−	0.0390445i	−0.465805	−	0.884887i	$-0.654235\pi$
$173$	0.889494	−	0.513550i	0.0676270	−	0.0390445i	0.533432	+	0.845843i	$0.320902\pi$
$174$	0.559573	+	0.539887i	0.0424212	+	0.0409287i
$175$	−17.4278	−	10.0620i	−1.31742	−	0.760613i
$176$	11.9108	−	15.3301i	0.897808	−	1.15555i
$177$	3.10121	−	3.44270i	0.233102	−	0.258769i
$178$	−3.42768	+	1.82549i	−0.256915	+	0.136826i
$179$	4.04846			0.302596			0.151298	−	0.988488i	$-0.451655\pi$
$179$	4.04846			0.302596			0.151298	+	0.988488i	$0.451655\pi$
$180$	−2.19098	+	0.0784872i	−0.163306	+	0.00585009i
$181$	−4.25940	−	7.37749i	−0.316598	−	0.548365i	0.663178	−	0.748462i	$-0.269207\pi$
$181$	−4.25940	−	7.37749i	−0.316598	−	0.548365i	−0.979776	+	0.200098i	$0.935874\pi$
$182$	−23.3743	+	12.4485i	−1.73262	+	0.922746i
$183$	−6.83526	+	7.58792i	−0.505277	+	0.560915i
$184$	1.72609	−	2.38589i	0.127249	−	0.175890i
$185$			0.177755i			0.0130688i
$186$	−4.33962	+	17.4387i	−0.318197	+	1.27867i
$187$	23.6088	−	13.6306i	1.72645	−	0.996765i
$188$	21.3411	+	1.46342i	1.55646	+	0.106731i
$189$	−8.72647	−	19.6353i	−0.634758	−	1.42826i
$190$	−1.96464	−	1.10171i	−0.142530	−	0.0799265i
$191$	−11.0680	+	19.1704i	−0.800856	+	1.38712i	0.118198	+	0.992990i	$0.462288\pi$
$191$	−11.0680	+	19.1704i	−0.800856	+	1.38712i	−0.919054	+	0.394133i	$0.871045\pi$
$192$	−11.1789	+	8.18734i	−0.806767	+	0.590870i
$193$	−6.34807			−0.456944			−0.228472	−	0.973551i	$-0.573373\pi$
$193$	−6.34807			−0.456944			−0.228472	+	0.973551i	$0.573373\pi$
$194$	0.895740	+	1.68191i	0.0643104	+	0.120754i
$195$	−2.72590	+	0.885028i	−0.195206	+	0.0633781i
$196$	8.87948	+	18.1436i	0.634249	+	1.29597i
$197$			6.47310i			0.461189i	0.973050	+	0.230595i	$0.0740671\pi$
$197$			6.47310i			0.461189i	−0.973050	+	0.230595i	$0.925933\pi$
$198$	18.5091	+	9.02226i	1.31538	+	0.641184i
$199$	−13.8836	+	8.01570i	−0.984182	+	0.568218i	−0.903530	−	0.428525i	$-0.859034\pi$
$199$	−13.8836	+	8.01570i	−0.984182	+	0.568218i	−0.0806519	+	0.996742i	$0.525700\pi$
$200$	−13.6920	−	1.41112i	−0.968169	−	0.0997809i
$201$	−26.0721	+	8.46489i	−1.83898	+	0.597067i
$202$	0.816886	−	23.8532i	0.0574759	−	1.67831i
$203$	0.656335	−	1.13681i	0.0460657	−	0.0797881i
$204$	−18.8745	+	4.72849i	−1.32148	+	0.331061i
$205$	0.478850			0.0334443
$206$	5.84951	−	3.11529i	0.407555	−	0.217053i
$207$	2.85283	+	1.27169i	0.198285	+	0.0883884i
$208$	−11.1134	+	14.3038i	−0.770575	+	0.991788i
$209$	11.4224	+	17.8065i	0.790101	+	1.23170i
$210$	1.02178	+	3.55733i	0.0705096	+	0.245479i
$211$			22.2739i			1.53340i	0.642007	+	0.766699i	$0.278102\pi$
$211$			22.2739i			1.53340i	−0.642007	+	0.766699i	$0.721898\pi$
$212$	−13.1239	+	6.42283i	−0.901350	+	0.441122i
$213$	3.95083	+	12.1687i	0.270707	+	0.833782i
$214$	−2.89685	−	0.0992066i	−0.198025	−	0.00678163i
$215$	1.80292	+	3.12275i	0.122958	+	0.212970i
$216$	−10.9352	−	9.81940i	−0.744048	−	0.668126i
$217$	30.3378			2.05946
$218$	3.35554	−	5.37804i	0.227266	−	0.364247i
$219$	−3.48291	−	10.7274i	−0.235353	−	0.724893i
$220$	−2.94309	−	1.97938i	−0.198423	−	0.133449i
$221$	−22.0283	+	12.7180i	−1.48178	+	0.855509i
$222$	−0.827370	+	0.857539i	−0.0555294	+	0.0575543i
$223$	17.5229	−	10.1169i	1.17342	−	0.677475i	0.218937	−	0.975739i	$-0.429741\pi$
$223$	17.5229	−	10.1169i	1.17342	−	0.677475i	0.954483	+	0.298264i	$0.0964077\pi$
$224$	17.9700	+	14.9758i	1.20067	+	1.00061i
$225$	−1.51958	−	14.5202i	−0.101305	−	0.968010i
$226$	−9.83796	+	5.23944i	−0.654411	+	0.348522i
$227$	4.09916	−	7.09996i	0.272071	−	0.471241i	−0.697321	−	0.716759i	$-0.745625\pi$
$227$	4.09916	−	7.09996i	0.272071	−	0.471241i	0.969392	+	0.245518i	$0.0789582\pi$
$228$	−4.35001	−	14.4595i	−0.288087	−	0.957604i
$229$	12.7921	+	22.1566i	0.845328	+	1.46415i	0.885336	+	0.464952i	$0.153928\pi$
$229$	12.7921	+	22.1566i	0.845328	+	1.46415i	−0.0400079	+	0.999199i	$0.512738\pi$
$230$	−0.456451	−	0.284795i	−0.0300975	−	0.0187788i
$231$	7.23489	−	34.0002i	0.476021	−	2.23705i
$232$	0.0920461	−	0.893119i	0.00604312	−	0.0586361i
$233$	−13.6560	−	7.88429i	−0.894633	−	0.516517i	−0.0191782	−	0.999816i	$-0.506105\pi$
$233$	−13.6560	−	7.88429i	−0.894633	−	0.516517i	−0.875455	+	0.483299i	$0.839438\pi$
$234$	−17.2700	−	8.41826i	−1.12897	−	0.550319i
$235$		−	3.90814i		−	0.254939i
$236$	−5.33782	−	0.366031i	−0.347463	−	0.0238266i
$237$	1.77928	−	8.36170i	0.115577	−	0.543151i
$238$	15.4410	+	28.9931i	1.00089	+	1.87934i
$239$	0.177886	+	0.308108i	0.0115065	+	0.0199299i	0.871721	−	0.490002i	$-0.163004\pi$
$239$	0.177886	+	0.308108i	0.0115065	+	0.0199299i	−0.860215	+	0.509932i	$0.829671\pi$
$240$	1.63203	+	1.93525i	0.105347	+	0.124920i
$241$	17.9658			1.15728			0.578641	−	0.815582i	$-0.303583\pi$
$241$	17.9658			1.15728			0.578641	+	0.815582i	$0.303583\pi$
$242$	8.34612	+	15.6713i	0.536509	+	1.00739i
$243$	7.80928	−	13.4913i	0.500966	−	0.865467i
$244$	11.7649	+	0.806754i	0.753169	+	0.0516471i
$245$	3.19605	−	1.84524i	0.204188	−	0.117888i
$246$	2.31011	+	2.22884i	0.147287	+	0.142105i
$247$	−10.6577	−	16.6144i	−0.678132	−	1.05715i
$248$	18.9396	−	8.47834i	1.20266	−	0.538375i
$249$	−8.44920	−	26.0237i	−0.535446	−	1.64919i
$250$	−0.174503	+	5.09552i	−0.0110365	+	0.322269i
$251$	2.67505	+	4.63332i	0.168848	+	0.292452i	0.938015	−	0.346595i	$-0.112662\pi$
$251$	2.67505	+	4.63332i	0.168848	+	0.292452i	−0.769167	+	0.639047i	$0.779329\pi$
$252$	−11.6284	+	21.9175i	−0.732522	+	1.38067i
$253$	2.52651	+	4.37604i	0.158840	+	0.275119i
$254$	−10.2651	+	5.46694i	−0.644092	+	0.343026i
$255$	1.09778	+	3.38117i	0.0687454	+	0.211737i
$256$	15.4037	+	4.32725i	0.962733	+	0.270453i
$257$	−14.8783	−	8.59001i	−0.928085	−	0.535830i	−0.0418797	−	0.999123i	$-0.513335\pi$
$257$	−14.8783	−	8.59001i	−0.928085	−	0.535830i	−0.886205	+	0.463292i	$0.846668\pi$
$258$	−5.83723	+	23.4569i	−0.363410	+	1.46036i
$259$	1.74214	+	1.00583i	0.108251	+	0.0624989i
$260$	2.74606	+	1.84686i	0.170304	+	0.114538i
$261$	0.947141	−	0.0991212i	0.0586265	−	0.00613545i
$262$	−21.8396	−	0.747926i	−1.34925	−	0.0462070i
$263$	5.62303	+	9.73938i	0.346731	+	0.600556i	0.985667	−	0.168704i	$-0.0539583\pi$
$263$	5.62303	+	9.73938i	0.346731	+	0.600556i	−0.638936	+	0.769260i	$0.720625\pi$
$264$	−4.98519	−	23.2479i	−0.306817	−	1.43081i
$265$	1.33473	+	2.31182i	0.0819916	+	0.142014i
$266$	−21.9146	+	13.0211i	−1.34367	+	0.798372i
$267$	−0.989922	+	4.65211i	−0.0605823	+	0.284705i
$268$	26.2649	+	17.6644i	1.60438	+	1.07903i
$269$	−8.44582	−	4.87619i	−0.514951	−	0.297307i	0.219916	−	0.975519i	$-0.429422\pi$
$269$	−8.44582	−	4.87619i	−0.514951	−	0.297307i	−0.734866	+	0.678212i	$0.762755\pi$
$270$	−1.65311	+	2.11590i	−0.100605	+	0.128770i
$271$	−16.5141	−	9.53440i	−1.00316	−	0.579174i	−0.0939772	−	0.995574i	$-0.529958\pi$
$271$	−16.5141	−	9.53440i	−1.00316	−	0.579174i	−0.909181	+	0.416401i	$0.863291\pi$
$272$	17.7422	+	13.7849i	1.07578	+	0.835832i
$273$	−6.75055	+	31.7240i	−0.408562	+	1.92003i
$274$	−0.115054	+	3.35959i	−0.00695065	+	0.202960i
$275$	11.8093	−	20.4544i	0.712129	−	1.23344i
$276$	−0.876455	−	3.49851i	−0.0527564	−	0.210586i
$277$	−2.06828	+	3.58236i	−0.124271	+	0.215243i	−0.921448	−	0.388503i	$-0.872992\pi$
$277$	−2.06828	+	3.58236i	−0.124271	+	0.215243i	0.797177	+	0.603746i	$0.206326\pi$
$278$	−17.8849	−	11.1590i	−1.07267	−	0.669272i
$279$	12.9288	+	17.8117i	0.774030	+	1.06636i
$280$	2.50505	−	3.46259i	0.149705	−	0.206929i
$281$		−	10.5703i		−	0.630572i	−0.948997	−	0.315286i	$-0.897900\pi$
$281$		−	10.5703i		−	0.630572i	0.948997	−	0.315286i	$-0.102100\pi$
$282$	18.1907	−	18.8540i	1.08324	−	1.12274i
$283$		−	7.03313i		−	0.418076i	−0.977907	−	0.209038i	$-0.932967\pi$
$283$		−	7.03313i		−	0.418076i	0.977907	−	0.209038i	$-0.0670333\pi$
$284$	8.24455	−	12.2586i	0.489224	−	0.727417i
$285$	−2.58117	+	0.973607i	−0.152896	+	0.0576715i
$286$	−14.6104	−	27.4335i	−0.863928	−	1.62218i
$287$	2.70957	−	4.69312i	0.159941	−	0.277026i
$288$	−1.13434	+	16.9326i	−0.0668414	+	0.997764i
$289$	7.27529	+	12.6012i	0.427958	+	0.741245i
$290$	−0.163940	−	0.00561434i	−0.00962687	−	0.000329685i
$291$	2.28272	+	0.485739i	0.133815	+	0.0284745i
$292$	−7.26809	+	10.8068i	−0.425333	+	0.632418i
$293$	26.0932	−	15.0649i	1.52438	−	0.880101i	0.524796	−	0.851228i	$-0.324141\pi$
$293$	26.0932	−	15.0649i	1.52438	−	0.880101i	0.999583	−	0.0288731i	$-0.00919187\pi$
$294$	24.0075	+	5.97425i	1.40014	+	0.348425i
$295$			0.977503i			0.0569124i
$296$	1.36869	+	0.141060i	0.0795537	+	0.00819892i
$297$	23.0452	−	10.2419i	1.33722	−	0.594297i
$298$	−0.479198	+	13.9927i	−0.0277592	+	0.810574i
$299$	−2.35737	−	4.08308i	−0.136330	−	0.236131i
$300$	−12.1135	+	11.7242i	−0.699371	+	0.676895i
$301$	40.8074			2.35210
$302$	−7.87335	−	4.91244i	−0.453060	−	0.282679i
$303$	−21.7187	−	19.5644i	−1.24771	−	1.12394i
$304$	−10.0421	+	14.2533i	−0.575956	+	0.817481i
$305$		−	2.15447i		−	0.123365i
$306$	−10.4419	+	21.4214i	−0.596923	+	1.22458i
$307$	7.54573	+	4.35653i	0.430658	+	0.248640i	0.699627	−	0.714509i	$-0.253350\pi$
$307$	7.54573	+	4.35653i	0.430658	+	0.248640i	−0.268969	+	0.963149i	$0.586683\pi$
$308$	−36.0530	+	17.6444i	−2.05431	+	1.00538i
$309$	1.68935	−	7.93907i	0.0961039	−	0.451638i
$310$	−1.78208	−	3.34616i	−0.101215	−	0.190049i
$311$	−0.123405	−	0.213743i	−0.00699764	−	0.0121203i	0.862505	−	0.506048i	$-0.168894\pi$
$311$	−0.123405	−	0.213743i	−0.00699764	−	0.0121203i	−0.869503	+	0.493928i	$0.835561\pi$
$312$	4.65145	+	21.6915i	0.263337	+	1.22804i
$313$	−8.24483			−0.466025			−0.233013	−	0.972474i	$-0.574858\pi$
$313$	−8.24483			−0.466025			−0.233013	+	0.972474i	$0.574858\pi$
$314$	22.9665	+	0.786517i	1.29607	+	0.0443857i
$315$	4.14026	+	1.84558i	0.233277	+	0.103986i
$316$	−8.86655	+	4.33930i	−0.498782	+	0.244105i
$317$			6.58752i			0.369992i	0.982739	+	0.184996i	$0.0592272\pi$
$317$			6.58752i			0.369992i	−0.982739	+	0.184996i	$0.940773\pi$
$318$	−4.32138	+	17.3654i	−0.242331	+	0.973805i
$319$	1.33422	+	0.770315i	0.0747022	+	0.0431294i
$320$	0.596202	−	2.86173i	0.0333287	−	0.159976i
$321$	−2.37599	+	2.63762i	−0.132615	+	0.147218i
$322$	−5.37405	+	2.86208i	−0.299484	+	0.159498i
$323$	−20.6083	+	13.2196i	−1.14668	+	0.735561i
$324$	−17.8237	+	2.51322i	−0.990205	+	0.139623i
$325$	−11.0187	+	19.0850i	−0.611210	+	1.05865i
$326$	−0.839142	+	24.5031i	−0.0464758	+	1.35710i
$327$	−2.39746	−	7.38422i	−0.132580	−	0.408348i
$328$	0.379998	−	3.68710i	0.0209819	−	0.203586i
$329$	−38.3030	−	22.1142i	−2.11171	−	1.21920i
$330$	−4.17509	+	1.19922i	−0.229831	+	0.0660152i
$331$	17.1904	+	9.92488i	0.944870	+	0.545521i	0.891483	−	0.453053i	$-0.149665\pi$
$331$	17.1904	+	9.92488i	0.944870	+	0.545521i	0.0533862	+	0.998574i	$0.482999\pi$
$332$	−17.6317	+	26.2162i	−0.967665	+	1.43880i
$333$	0.151902	+	1.45148i	0.00832418	+	0.0795407i
$334$	5.45147	−	8.73727i	0.298291	−	0.478082i
$335$	2.89143	−	5.00810i	0.157976	−	0.273622i
$336$	28.2019	−	5.04465i	1.53854	−	0.275208i
$337$	−27.2098			−1.48221			−0.741105	−	0.671389i	$-0.765698\pi$
$337$	−27.2098			−1.48221			−0.741105	+	0.671389i	$0.765698\pi$
$338$	4.99019	+	9.36996i	0.271431	+	0.509658i
$339$	−2.84123	+	13.3523i	−0.154314	+	0.725196i
$340$	2.29082	−	3.40618i	0.124237	−	0.184726i
$341$			35.6063i			1.92819i
$342$	−16.9840	−	7.31727i	−0.918392	−	0.395673i
$343$		−	12.8188i		−	0.692152i
$344$	25.4756	−	11.4042i	1.37355	−	0.614875i
$345$	−0.626721	+	0.203480i	−0.0337415	+	0.0109550i
$346$	−1.28206	+	0.682789i	−0.0689237	+	0.0367070i
$347$	−3.58049			−0.192211			−0.0961054	−	0.995371i	$-0.530639\pi$
$347$	−3.58049			−0.192211			−0.0961054	+	0.995371i	$0.530639\pi$
$348$	−0.764760	−	0.790153i	−0.0409955	−	0.0423567i
$349$	−4.93707	+	8.55126i	−0.264275	+	0.457738i	−0.967374	−	0.253354i	$-0.918466\pi$
$349$	−4.93707	+	8.55126i	−0.264275	+	0.457738i	0.703098	+	0.711093i	$0.251799\pi$
$350$	24.1452	+	15.0650i	1.29061	+	0.805257i
$351$	−21.5025	+	9.55627i	−1.14772	+	0.510076i
$352$	−17.5765	+	21.0907i	−0.936832	+	1.12414i
$353$	−17.8887	−	10.3281i	−0.952121	−	0.549707i	−0.0583817	−	0.998294i	$-0.518594\pi$
$353$	−17.8887	−	10.3281i	−0.952121	−	0.549707i	−0.893739	+	0.448587i	$0.851927\pi$
$354$	−4.54985	+	4.71576i	−0.241822	+	0.250640i
$355$	−2.33744	−	1.34952i	−0.124058	−	0.0716251i
$356$	4.93299	−	2.41421i	0.261448	−	0.127953i
$357$	39.3500	+	8.37329i	2.08262	+	0.443161i
$358$	−5.72204	−	0.195959i	−0.302419	−	0.0103567i
$359$	12.3428	−	21.3783i	0.651427	−	1.12830i	−0.331350	−	0.943508i	$-0.607504\pi$
$359$	12.3428	−	21.3783i	0.651427	−	1.12830i	0.982777	−	0.184797i	$-0.0591627\pi$
$360$	3.10050	−	0.00488214i	0.163410	−	0.000257311i
$361$	−10.9950	−	15.4955i	−0.578684	−	0.815552i
$362$	5.66307	+	10.6334i	0.297644	+	0.558879i
$363$	21.2694	+	4.52591i	1.11635	+	0.237548i
$364$	33.6394	−	16.4632i	1.76318	−	0.862905i
$365$	2.06060	+	1.18969i	0.107857	+	0.0622711i
$366$	10.0281	−	10.3938i	0.524179	−	0.543293i
$367$		−	11.5149i		−	0.601070i	−0.953771	−	0.300535i	$-0.902835\pi$
$367$		−	11.5149i		−	0.601070i	0.953771	−	0.300535i	$-0.0971653\pi$
$368$	−2.55512	+	3.28863i	−0.133195	+	0.171431i
$369$	3.91012	−	0.409206i	0.203553	−	0.0213024i
$370$	0.00860390	−	0.251236i	0.000447296	−	0.0130611i
$371$	30.2102			1.56844
$372$	6.97765	−	24.4376i	0.361774	−	1.26703i
$373$	−0.470209	−	0.814427i	−0.0243465	−	0.0421694i	0.853595	−	0.520936i	$-0.174417\pi$
$373$	−0.470209	−	0.814427i	−0.0243465	−	0.0421694i	−0.877942	+	0.478767i	$0.841084\pi$
$374$	−34.0281	+	18.1225i	−1.75955	+	0.937091i
$375$	4.63954	+	4.17933i	0.239585	+	0.215820i
$376$	−30.0923	−	3.10136i	−1.55189	−	0.159940i
$377$	−1.24490	−	0.718746i	−0.0641158	−	0.0370173i
$378$	11.3835	+	28.1747i	0.585502	+	1.44915i
$379$			5.32197i			0.273371i	0.990614	+	0.136686i	$0.0436450\pi$
$379$			5.32197i			0.273371i	−0.990614	+	0.136686i	$0.956355\pi$
$380$	2.72347	+	1.65224i	0.139711	+	0.0847579i
$381$	−2.96460	+	13.9320i	−0.151881	+	0.713760i
$382$	16.5713	−	26.5594i	0.847862	−	1.35890i
$383$	−22.6689			−1.15833			−0.579163	−	0.815212i	$-0.696620\pi$
$383$	−22.6689			−1.15833			−0.579163	+	0.815212i	$0.696620\pi$
$384$	16.1964	−	11.0308i	0.826517	−	0.562911i
$385$	3.66667	+	6.35087i	0.186871	+	0.323670i
$386$	8.97226	+	0.307267i	0.456676	+	0.0156395i
$387$	17.3906	+	23.9586i	0.884014	+	1.21788i
$388$	−1.18462	−	2.42054i	−0.0601398	−	0.122884i
$389$			17.3620i			0.880288i	0.897927	+	0.440144i	$0.145073\pi$
$389$			17.3620i			0.880288i	−0.897927	+	0.440144i	$0.854927\pi$
$390$	3.89559	−	1.11894i	0.197261	−	0.0566598i
$391$	−5.06460	+	2.92405i	−0.256128	+	0.147875i
$392$	−11.6719	−	26.0736i	−0.589521	−	1.31692i
$393$	−17.9128	+	19.8852i	−0.903580	+	1.00308i
$394$	0.313319	−	9.14898i	0.0157848	−	0.460919i
$395$	0.901749	+	1.56187i	0.0453719	+	0.0785864i
$396$	−25.7237	−	13.6478i	−1.29267	−	0.685829i
$397$	−0.632206	+	1.09501i	−0.0317295	+	0.0549572i	−0.881454	−	0.472270i	$-0.843435\pi$
$397$	−0.632206	+	1.09501i	−0.0317295	+	0.0549572i	0.849725	+	0.527227i	$0.176768\pi$
$398$	20.0109	−	10.6573i	1.00305	−	0.534200i
$399$	−5.06344	+	30.8068i	−0.253489	+	1.54227i
$400$	19.2837	+	2.65719i	0.964186	+	0.132859i
$401$		−	3.85152i		−	0.192336i	−0.995365	−	0.0961678i	$-0.969341\pi$
$401$		−	3.85152i		−	0.192336i	0.995365	−	0.0961678i	$-0.0306585\pi$
$402$	37.2596	−	10.7022i	1.85834	−	0.533776i
$403$		−	33.2226i		−	1.65494i
$404$	−2.30915	+	33.6743i	−0.114884	+	1.67536i
$405$	0.680862	+	3.21732i	0.0338323	+	0.159870i
$406$	−0.982679	+	1.57498i	−0.0487696	+	0.0781647i
$407$	−1.18050	+	2.04468i	−0.0585151	+	0.101351i
$408$	26.9059	−	5.76959i	1.33204	−	0.285637i
$409$	−8.77657	+	15.2015i	−0.433973	+	0.751664i	−0.997211	−	0.0746309i	$-0.976222\pi$
$409$	−8.77657	+	15.2015i	−0.433973	+	0.751664i	0.563238	+	0.826295i	$0.309555\pi$
$410$	−0.676799	−	0.0231779i	−0.0334247	−	0.00114467i
$411$	3.05895	+	2.75553i	0.150887	+	0.135920i
$412$	−8.41840	+	4.11998i	−0.414745	+	0.202977i
$413$	9.58033	+	5.53121i	0.471417	+	0.272173i
$414$	−3.97059	−	1.93547i	−0.195144	−	0.0951231i
$415$	4.99881	+	2.88607i	0.245382	+	0.141671i
$416$	16.3999	−	19.6788i	0.804069	−	0.964833i
$417$	−24.5566	+	7.97285i	−1.20254	+	0.390432i
$418$	−15.2823	−	25.7203i	−0.747482	−	1.25802i
$419$	8.45672	+	14.6475i	0.413138	+	0.715576i	0.995231	−	0.0975464i	$-0.0310994\pi$
$419$	8.45672	+	14.6475i	0.413138	+	0.715576i	−0.582093	+	0.813122i	$0.697766\pi$
$420$	−1.27198	−	5.07733i	−0.0620665	−	0.247748i
$421$	−12.8876	−	22.3220i	−0.628103	−	1.08791i	−0.987932	−	0.154888i	$-0.950498\pi$
$421$	−12.8876	−	22.3220i	−0.628103	−	1.08791i	0.359829	−	0.933018i	$-0.382835\pi$
$422$	1.07813	−	31.4816i	0.0524825	−	1.53250i
$423$	−3.33974	−	31.9125i	−0.162384	−	1.55164i
$424$	18.8599	−	8.44270i	0.915920	−	0.410014i
$425$	23.6728	+	13.6675i	1.14830	+	0.662971i
$426$	−4.99505	−	17.3902i	−0.242011	−	0.842559i
$427$	−21.1156	−	12.1911i	−1.02186	−	0.589969i
$428$	4.08957	+	0.280434i	0.197677	+	0.0135553i
$429$	−37.2333	−	7.92286i	−1.79764	−	0.382519i
$430$	−2.39707	−	4.50092i	−0.115597	−	0.217054i
$431$	−7.68224	−	13.3060i	−0.370040	−	0.640929i	0.619531	−	0.784972i	$-0.287323\pi$
$431$	−7.68224	−	13.3060i	−0.370040	−	0.640929i	−0.989571	+	0.144043i	$0.953990\pi$
$432$	14.9804	+	14.4079i	0.720745	+	0.693200i
$433$	12.9872	+	22.4945i	0.624126	+	1.08102i	0.988709	+	0.149848i	$0.0478783\pi$
$433$	12.9872	+	22.4945i	0.624126	+	1.08102i	−0.364583	+	0.931171i	$0.618788\pi$
$434$	−42.8790	−	1.46845i	−2.05826	−	0.0704878i
$435$	−0.134463	+	0.149269i	−0.00644701	+	0.00715692i
$436$	−5.00298	+	7.43883i	−0.239599	+	0.356255i
$437$	−2.45034	−	3.81987i	−0.117216	−	0.182729i
$438$	4.40345	+	15.3306i	0.210405	+	0.732524i
$439$	−1.78069	+	1.02808i	−0.0849877	+	0.0490677i	−0.541892	−	0.840448i	$-0.682292\pi$
$439$	−1.78069	+	1.02808i	−0.0849877	+	0.0490677i	0.456904	+	0.889516i	$0.348958\pi$
$440$	4.06391	+	2.94007i	0.193739	+	0.140163i
$441$	24.5210	−	17.7988i	1.16767	−	0.847563i
$442$	31.7501	−	16.9093i	1.51020	−	0.804291i
$443$	−9.14330			−0.434412			−0.217206	−	0.976126i	$-0.569694\pi$
$443$	−9.14330			−0.434412			−0.217206	+	0.976126i	$0.569694\pi$
$444$	1.21090	−	1.17199i	0.0574667	−	0.0556200i
$445$	−0.501697	−	0.868964i	−0.0237827	−	0.0411929i
$446$	−25.2563	+	13.4508i	−1.19592	+	0.636916i
$447$	12.7405	+	11.4768i	0.602606	+	0.542832i
$448$	−24.6737	−	22.0364i	−1.16572	−	1.04112i
$449$		−	18.2332i		−	0.860476i	−0.902716	−	0.430238i	$-0.858430\pi$
$449$		−	18.2332i		−	0.860476i	0.902716	−	0.430238i	$-0.141570\pi$
$450$	1.44493	+	20.5961i	0.0681145	+	0.970911i
$451$	5.50813	+	3.18012i	0.259368	+	0.149746i
$452$	14.1584	−	6.92916i	0.665957	−	0.325920i
$453$	−10.8104	+	3.50983i	−0.507915	+	0.164906i
$454$	−6.13735	+	9.83656i	−0.288040	+	0.461652i
$455$	−3.42121	−	5.92570i	−0.160389	−	0.277801i
$456$	5.44836	+	20.6474i	0.255143	+	0.966903i
$457$	10.1417	−	17.5659i	0.474407	−	0.821696i	−0.525164	−	0.851001i	$-0.675996\pi$
$457$	10.1417	−	17.5659i	0.474407	−	0.821696i	0.999571	+	0.0293049i	$0.00932936\pi$
$458$	−17.0078	−	31.9350i	−0.794720	−	1.49223i
$459$	11.8535	+	26.6713i	0.553272	+	1.24491i
$460$	0.631356	+	0.424619i	0.0294371	+	0.0197979i
$461$	4.90265	−	2.83055i	0.228339	−	0.131832i	−0.381467	−	0.924383i	$-0.624581\pi$
$461$	4.90265	−	2.83055i	0.228339	−	0.131832i	0.609806	+	0.792551i	$0.291248\pi$
$462$	−11.8714	+	47.7052i	−0.552308	+	2.21945i
$463$	−4.69631	+	2.71141i	−0.218256	+	0.126010i	−0.605142	−	0.796117i	$-0.706884\pi$
$463$	−4.69631	+	2.71141i	−0.218256	+	0.126010i	0.386887	+	0.922127i	$0.373551\pi$
$464$	−0.173326	+	1.25787i	−0.00804648	+	0.0583949i
$465$	−4.54147	−	0.966379i	−0.210606	−	0.0448147i
$466$	18.9195	+	11.8045i	0.876431	+	0.546834i
$467$	−24.1477			−1.11742			−0.558711	−	0.829363i	$-0.688704\pi$
$467$	−24.1477			−1.11742			−0.558711	+	0.829363i	$0.688704\pi$
$468$	24.0016	+	12.7342i	1.10948	+	0.588637i
$469$	−32.7223	−	56.6767i	−1.51098	−	2.61709i
$470$	−0.189167	+	5.52370i	−0.00872561	+	0.254789i
$471$	18.8370	−	20.9113i	0.867965	−	0.963540i
$472$	7.52668	+	0.775711i	0.346443	+	0.0357050i
$473$			47.8941i			2.20217i
$474$	−2.91955	+	11.7322i	−0.134099	+	0.538877i
$475$	−9.73601	+	18.8462i	−0.446719	+	0.864725i
$476$	−20.4207	−	41.7258i	−0.935980	−	1.91250i
$477$	12.8745	+	17.7369i	0.589483	+	0.812115i
$478$	−0.236509	−	0.444086i	−0.0108177	−	0.0203120i
$479$	−34.9398			−1.59644			−0.798220	−	0.602366i	$-0.794225\pi$
$479$	−34.9398			−1.59644			−0.798220	+	0.602366i	$0.794225\pi$
$480$	−2.21302	−	2.81425i	−0.101010	−	0.128452i
$481$	1.10147	−	1.90780i	0.0502227	−	0.0869882i
$482$	−25.3927	−	0.869605i	−1.15660	−	0.0396094i
$483$	−1.55204	+	7.29377i	−0.0706203	+	0.331878i
$484$	−11.0377	−	22.5535i	−0.501715	−	1.02516i
$485$	−0.426387	+	0.246175i	−0.0193612	+	0.0111782i
$486$	−11.6905	+	18.6904i	−0.530294	+	0.847814i
$487$		−	34.8737i		−	1.58028i	−0.612929	−	0.790138i	$-0.710009\pi$
$487$		−	34.8737i		−	1.58028i	0.612929	−	0.790138i	$-0.289991\pi$
$488$	−16.5892	−	1.70971i	−0.750960	−	0.0773950i
$489$	22.3104	+	20.0974i	1.00891	+	0.908836i
$490$	−4.60657	+	2.45334i	−0.208104	+	0.110831i
$491$	−14.0527			−0.634189			−0.317095	−	0.948394i	$-0.602707\pi$
$491$	−14.0527			−0.634189			−0.317095	+	0.948394i	$0.602707\pi$
$492$	−3.15719	−	3.26202i	−0.142337	−	0.147063i
$493$	−0.891522	+	1.54416i	−0.0401521	+	0.0695455i
$494$	14.2592	+	23.9984i	0.641553	+	1.07974i
$495$	−2.16608	+	4.85926i	−0.0973581	+	0.218408i
$496$	−27.1793	+	11.0664i	−1.22039	+	0.496897i
$497$	−26.4528	+	15.2725i	−1.18657	+	0.685067i
$498$	10.6823	+	37.1905i	0.478687	+	1.66655i
$499$			15.0775i			0.674962i	0.941332	+	0.337481i	$0.109575\pi$
$499$			15.0775i			0.674962i	−0.941332	+	0.337481i	$0.890425\pi$
$500$	0.493279	−	7.19348i	0.0220601	−	0.321702i
$501$	−3.89495	−	11.9965i	−0.174014	−	0.535966i
$502$	−3.55660	−	6.67814i	−0.158739	−	0.298060i
$503$	12.0943	+	20.9480i	0.539259	+	0.934024i	0.998944	+	0.0459420i	$0.0146289\pi$
$503$	12.0943	+	20.9480i	0.539259	+	0.934024i	−0.459685	+	0.888082i	$0.652038\pi$
$504$	17.4963	−	30.4150i	0.779348	−	1.35479i
$505$	6.16669			0.274414
$506$	−3.35911	−	6.30732i	−0.149331	−	0.280395i
$507$	12.7171	+	2.70607i	0.564786	+	0.120181i
$508$	14.7732	−	7.23002i	0.655455	−	0.320780i
$509$	−21.0928	−	12.1779i	−0.934922	−	0.539777i	−0.0465570	−	0.998916i	$-0.514825\pi$
$509$	−21.0928	−	12.1779i	−0.934922	−	0.539777i	−0.888365	+	0.459138i	$0.848158\pi$
$510$	−1.38792	−	4.83204i	−0.0614581	−	0.213966i
$511$	23.3198	−	13.4637i	1.03161	−	0.595599i
$512$	−21.5619	−	6.86166i	−0.952912	−	0.303245i
$513$	−20.2449	+	10.1559i	−0.893836	+	0.448394i
$514$	20.6130	+	12.8612i	0.909202	+	0.567281i
$515$	0.856171	+	1.48293i	0.0377274	+	0.0653458i
$516$	9.38565	−	32.8711i	0.413180	−	1.44707i
$517$	25.9546	−	44.9547i	1.14148	−	1.97711i
$518$	−2.41363	−	1.50594i	−0.106049	−	0.0661674i
$519$	−0.370261	+	1.74003i	−0.0162526	+	0.0763789i
$520$	−3.79185	−	2.74325i	−0.166284	−	0.120299i
$521$		−	33.6212i		−	1.47297i	−0.676452	−	0.736486i	$-0.736484\pi$
$521$		−	33.6212i		−	1.47297i	0.676452	−	0.736486i	$-0.263516\pi$
$522$	−1.34347	+	0.0942517i	−0.0588022	+	0.00412529i
$523$	−9.38312	+	5.41735i	−0.410295	+	0.236884i	−0.690917	−	0.722934i	$-0.742793\pi$
$523$	−9.38312	+	5.41735i	−0.410295	+	0.236884i	0.280621	+	0.959819i	$0.409460\pi$
$524$	30.8315	+	2.11421i	1.34688	+	0.0923598i
$525$	33.1521	−	10.7636i	1.44688	−	0.469762i
$526$	−7.47610	−	14.0377i	−0.325973	−	0.612071i
$527$	−41.2088			−1.79509
$528$	5.92071	+	33.0995i	0.257666	+	1.44047i
$529$	10.9580	+	18.9798i	0.476435	+	0.825210i
$530$	−1.77458	−	3.33209i	−0.0770830	−	0.144737i
$531$	0.835335	+	7.98194i	0.0362505	+	0.346387i
$532$	31.6040	−	17.3430i	1.37021	−	0.751915i
$533$	−5.13939	−	2.96723i	−0.222612	−	0.128525i
$534$	1.62432	−	6.52731i	0.0702911	−	0.282464i
$535$		−	0.748913i		−	0.0323783i
$536$	−36.2673	−	26.2380i	−1.56651	−	1.13331i
$537$	−4.69320	+	5.20999i	−0.202527	+	0.224828i
$538$	11.7012	+	7.30075i	0.504473	+	0.314758i
$539$	49.0183			2.11137
$540$	2.43890	−	2.91057i	0.104953	−	0.125251i
$541$	−1.08440	−	1.87823i	−0.0466218	−	0.0807514i	0.841773	−	0.539832i	$-0.181512\pi$
$541$	−1.08440	−	1.87823i	−0.0466218	−	0.0807514i	−0.888395	+	0.459081i	$0.848179\pi$
$542$	22.8792	+	14.2751i	0.982748	+	0.613169i
$543$	14.4319	+	3.07095i	0.619331	+	0.131787i
$544$	−24.4093	−	20.3422i	−1.04654	−	0.872163i
$545$	1.41841	+	0.818920i	0.0607581	+	0.0350787i
$546$	11.0767	−	44.5115i	0.474038	−	1.90492i
$547$			38.5069i			1.64644i	0.567725	+	0.823218i	$0.307824\pi$
$547$			38.5069i			1.64644i	−0.567725	+	0.823218i	$0.692176\pi$
$548$	0.325230	−	4.74282i	0.0138931	−	0.202603i
$549$	−1.84113	−	17.5927i	−0.0785774	−	0.750837i
$550$	−17.6812	+	28.3383i	−0.753928	+	1.20835i
$551$	−1.22933	−	0.635074i	−0.0523712	−	0.0270550i
$552$	1.06943	+	4.98717i	0.0455179	+	0.212268i
$553$	20.4102			0.867930
$554$	3.09667	−	4.96314i	0.131565	−	0.210864i
$555$	−0.228753	−	0.206063i	−0.00971004	−	0.00874688i
$556$	24.7382	+	16.6377i	1.04913	+	0.705594i
$557$	2.61996	−	1.51264i	0.111011	−	0.0640925i	−0.443466	−	0.896291i	$-0.646251\pi$
$557$	2.61996	−	1.51264i	0.111011	−	0.0640925i	0.554478	+	0.832199i	$0.312918\pi$
$558$	−17.4113	−	25.8006i	−0.737079	−	1.09223i
$559$		−	44.6878i		−	1.89009i
$560$	−3.70819	+	4.77272i	−0.156700	+	0.201684i
$561$	−9.82740	+	46.1836i	−0.414913	+	1.94987i
$562$	−0.511638	+	14.9399i	−0.0215821	+	0.630203i
$563$	10.7802	+	18.6719i	0.454333	+	0.786928i	0.998650	−	0.0519520i	$-0.0165443\pi$
$563$	10.7802	+	18.6719i	0.454333	+	0.786928i	−0.544317	+	0.838880i	$0.683211\pi$
$564$	−26.6230	+	25.7675i	−1.12103	+	1.08501i
$565$	−1.43995	−	2.49406i	−0.0605790	−	0.104926i
$566$	−0.340427	+	9.94053i	−0.0143092	+	0.417831i
$567$	35.3851	+	11.5322i	1.48603	+	0.484308i
$568$	−12.2461	+	16.9271i	−0.513834	+	0.710246i
$569$	−7.53539	−	4.35056i	−0.315900	−	0.182385i	0.333663	−	0.942692i	$-0.391715\pi$
$569$	−7.53539	−	4.35056i	−0.315900	−	0.182385i	−0.649564	+	0.760307i	$0.725048\pi$
$570$	3.69532	−	1.25114i	0.154780	−	0.0524047i
$571$	−31.5569	+	18.2194i	−1.32061	+	0.762456i	−0.983826	−	0.179124i	$-0.942674\pi$
$571$	−31.5569	+	18.2194i	−1.32061	+	0.762456i	−0.336787	+	0.941581i	$0.609340\pi$
$572$	19.3222	+	39.4813i	0.807901	+	1.65079i
$573$	−11.8398	−	36.4669i	−0.494616	−	1.52343i
$574$	−4.05683	+	6.50203i	−0.169329	+	0.271390i
$575$	−2.53335	+	4.38790i	−0.105648	+	0.182988i
$576$	2.42285	−	23.8774i	0.100952	−	0.994891i
$577$	−10.8977			−0.453679			−0.226839	−	0.973932i	$-0.572839\pi$
$577$	−10.8977			−0.453679			−0.226839	+	0.973932i	$0.572839\pi$
$578$	−9.67284	−	18.1624i	−0.402337	−	0.755458i
$579$	7.35903	−	8.16936i	0.305831	−	0.339507i
$580$	0.231438	+	0.0158704i	0.00960995	+	0.000658984i
$581$	56.5716	−	32.6617i	2.34699	−	1.35503i
$582$	−3.20285	−	0.797028i	−0.132762	−	0.0330379i
$583$			35.4566i			1.46846i
$584$	10.7957	−	14.9223i	0.446729	−	0.617490i
$585$	2.02107	−	4.53396i	0.0835610	−	0.187456i
$586$	−37.6089	+	20.0295i	−1.55361	+	0.827411i
$587$	−12.2112	−	21.1503i	−0.504008	−	0.872968i	−0.999989	−	0.00463456i	$-0.998525\pi$
$587$	−12.2112	−	21.1503i	−0.504008	−	0.872968i	0.495981	−	0.868333i	$-0.334809\pi$
$588$	−33.6426	−	9.60596i	−1.38740	−	0.396143i
$589$	−1.49472	−	31.9440i	−0.0615890	−	1.31623i
$590$	0.0473143	−	1.38159i	0.00194790	−	0.0568791i
$591$	−8.33027	−	7.50397i	−0.342662	−	0.308672i
$592$	−1.92766	−	0.265621i	−0.0792264	−	0.0109169i
$593$	13.1016	−	7.56424i	0.538020	−	0.310626i	−0.206256	−	0.978498i	$-0.566128\pi$
$593$	13.1016	−	7.56424i	0.538020	−	0.310626i	0.744276	+	0.667872i	$0.232795\pi$
$594$	−33.0675	+	13.3603i	−1.35678	+	0.548180i
$595$	−7.35016	+	4.24362i	−0.301327	+	0.173971i
$596$	1.35458	−	19.7538i	0.0554858	−	0.809149i
$597$	5.77918	−	27.1591i	0.236526	−	1.11155i
$598$	3.13424	+	5.88507i	0.128168	+	0.240658i
$599$	−18.4482	+	31.9532i	−0.753772	+	1.30557i	0.192210	+	0.981354i	$0.438434\pi$
$599$	−18.4482	+	31.9532i	−0.753772	+	1.30557i	−0.945982	+	0.324218i	$0.894899\pi$
$600$	17.6885	−	15.9844i	0.722129	−	0.652562i
$601$	−10.8058	+	18.7161i	−0.440776	+	0.763446i	−0.997747	−	0.0670854i	$-0.978630\pi$
$601$	−10.8058	+	18.7161i	−0.440776	+	0.763446i	0.556971	+	0.830532i	$0.311963\pi$
$602$	−57.6766	−	1.97521i	−2.35072	−	0.0805036i
$603$	19.3306	−	43.3653i	0.787205	−	1.76597i
$604$	10.8903	+	7.32427i	0.443120	+	0.298020i
$605$	−3.97289	+	2.29375i	−0.161521	+	0.0932541i
$606$	29.7499	+	28.7032i	1.20851	+	1.16599i
$607$	−2.86383	+	1.65343i	−0.116239	+	0.0671107i	−0.556992	−	0.830518i	$-0.688045\pi$
$607$	−2.86383	+	1.65343i	−0.116239	+	0.0671107i	0.440753	+	0.897628i	$0.354711\pi$
$608$	14.8833	−	19.6593i	0.603598	−	0.797289i
$609$	0.702102	+	2.16249i	0.0284506	+	0.0876285i
$610$	−0.104284	+	3.04510i	−0.00422232	+	0.123293i
$611$	−24.2171	+	41.9452i	−0.979717	+	1.69692i
$612$	15.7953	−	29.7713i	0.638487	−	1.20343i
$613$	−1.82976	+	3.16924i	−0.0739034	+	0.128004i	−0.900609	−	0.434630i	$-0.856879\pi$
$613$	−1.82976	+	3.16924i	−0.0739034	+	0.128004i	0.826705	+	0.562635i	$0.190212\pi$
$614$	−10.4542	−	6.52269i	−0.421895	−	0.263234i
$615$	−0.555109	+	0.616235i	−0.0223842	+	0.0248490i
$616$	51.8108	−	23.1932i	2.08752	−	0.934482i
$617$	26.7111	+	15.4217i	1.07535	+	0.620853i	0.929638	−	0.368474i	$-0.120120\pi$
$617$	26.7111	+	15.4217i	1.07535	+	0.620853i	0.145712	+	0.989327i	$0.453453\pi$
$618$	−2.77198	+	11.1392i	−0.111505	+	0.448084i
$619$	−1.40642	−	0.811997i	−0.0565288	−	0.0326369i	0.471469	−	0.881882i	$-0.343724\pi$
$619$	−1.40642	−	0.811997i	−0.0565288	−	0.0326369i	−0.527998	+	0.849246i	$0.677057\pi$
$620$	2.35679	+	4.81567i	0.0946511	+	0.193402i
$621$	−4.94370	+	2.19711i	−0.198384	+	0.0881671i
$622$	0.164073	+	0.308075i	0.00657871	+	0.0123527i
$623$	−11.3554			−0.454945
$624$	−5.52435	−	30.8836i	−0.221151	−	1.23633i
$625$	23.0151			0.920604
$626$	11.6531	+	0.399077i	0.465752	+	0.0159503i
$627$	−36.1567	−	5.94276i	−1.44396	−	0.237331i
$628$	−32.4224	−	2.22330i	−1.29379	−	0.0887194i
$629$	−2.36641	−	1.36625i	−0.0943549	−	0.0544758i
$630$	−5.76245	−	2.80891i	−0.229581	−	0.111910i
$631$	−3.76686	+	2.17480i	−0.149956	+	0.0865773i	−0.573101	−	0.819485i	$-0.694260\pi$
$631$	−3.76686	+	2.17480i	−0.149956	+	0.0865773i	0.423144	+	0.906062i	$0.360926\pi$
$632$	12.7419	−	5.70393i	0.506845	−	0.226890i
$633$	−28.6644	−	25.8211i	−1.13931	−	1.02630i
$634$	0.318857	−	9.31070i	0.0126634	−	0.369775i
$635$	−1.50247	−	2.60235i	−0.0596237	−	0.103271i
$636$	6.94832	−	24.3349i	0.275519	−	0.964940i
$637$	−45.7367			−1.81215
$638$	−1.84849	−	1.15333i	−0.0731823	−	0.0456609i
$639$	−20.2399	−	9.02223i	−0.800680	−	0.356914i
$640$	−0.981180	+	4.01587i	−0.0387845	+	0.158741i
$641$	38.7414	−	22.3674i	1.53019	−	0.883458i	0.530842	−	0.847471i	$-0.321876\pi$
$641$	38.7414	−	22.3674i	1.53019	−	0.883458i	0.999352	−	0.0359876i	$-0.0114577\pi$
$642$	3.48586	−	3.61297i	0.137576	−	0.142593i
$643$		−	12.6406i		−	0.498497i	−0.968440	−	0.249249i	$-0.919816\pi$
$643$		−	12.6406i		−	0.498497i	0.968440	−	0.249249i	$-0.0801837\pi$
$644$	7.73414	−	3.78510i	0.304768	−	0.149154i
$645$	−6.10874	−	1.29988i	−0.240531	−	0.0511826i
$646$	29.7673	−	17.6869i	1.17118	−	0.695883i
$647$	26.5604			1.04420			0.522099	−	0.852885i	$-0.325149\pi$
$647$	26.5604			1.04420			0.522099	+	0.852885i	$0.325149\pi$
$648$	25.3134	−	2.68943i	0.994403	−	0.105651i
$649$	−6.49176	+	11.2441i	−0.254824	+	0.441368i
$650$	16.4975	−	26.4412i	0.647086	−	1.03711i
$651$	−35.1692	+	39.0419i	−1.37839	+	1.53017i
$652$	2.37206	−	34.5917i	0.0928971	−	1.35472i
$653$	10.6669	−	6.15853i	0.417428	−	0.241002i	−0.276548	−	0.961000i	$-0.589191\pi$
$653$	10.6669	−	6.15853i	0.417428	−	0.241002i	0.693976	+	0.719998i	$0.255857\pi$
$654$	3.03111	+	10.5528i	0.118526	+	0.412647i
$655$		−	5.64611i		−	0.220612i
$656$	−0.715551	+	5.19290i	−0.0279376	+	0.202748i
$657$	17.8428	+	7.95366i	0.696113	+	0.310302i
$658$	53.0664	+	33.1099i	2.06874	+	1.29076i
$659$	50.3285			1.96052			0.980261	−	0.197709i	$-0.0633501\pi$
$659$	50.3285			1.96052			0.980261	+	0.197709i	$0.0633501\pi$
$660$	5.95906	−	1.49288i	0.231956	−	0.0581102i
$661$	−22.4069	+	38.8100i	−0.871529	+	1.50953i	−0.0111137	+	0.999938i	$0.503538\pi$
$661$	−22.4069	+	38.8100i	−0.871529	+	1.50953i	−0.860415	+	0.509594i	$0.829796\pi$
$662$	−23.8163	−	14.8597i	−0.925645	−	0.577540i
$663$	9.16950	−	43.0918i	0.356114	−	1.67355i
$664$	26.1893	−	36.2001i	1.01634	−	1.40484i
$665$	−3.55614	−	5.54372i	−0.137901	−	0.214976i
$666$	−0.144440	−	2.05885i	−0.00559692	−	0.0797790i
$667$	−0.286220	−	0.165249i	−0.0110825	−	0.00639847i
$668$	−8.12794	+	12.0853i	−0.314479	+	0.467593i
$669$	−7.29408	+	34.2783i	−0.282005	+	1.32528i
$670$	−4.32911	+	6.93842i	−0.167248	+	0.268054i
$671$	14.3082	−	24.7826i	0.552363	−	0.956721i
$672$	−40.1043	+	5.76497i	−1.54706	+	0.222389i
$673$	0.427418	−	0.740310i	0.0164758	−	0.0285369i	−0.857670	−	0.514201i	$-0.828089\pi$
$673$	0.427418	−	0.740310i	0.0164758	−	0.0285369i	0.874146	+	0.485664i	$0.161422\pi$
$674$	38.4579	+	1.31704i	1.48134	+	0.0507305i
$675$	20.4477	+	14.8770i	0.787031	+	0.572617i
$676$	−6.59953	−	13.4849i	−0.253828	−	0.518650i
$677$	−28.1281	−	16.2398i	−1.08105	−	0.624145i	−0.149872	−	0.988705i	$-0.547886\pi$
$677$	−28.1281	−	16.2398i	−1.08105	−	0.624145i	−0.931180	+	0.364560i	$0.881219\pi$
$678$	4.66204	−	18.7344i	0.179045	−	0.719489i
$679$			5.57192i			0.213831i
$680$	−3.40269	+	4.70336i	−0.130487	+	0.180365i
$681$	4.38500	+	13.5059i	0.168034	+	0.517547i
$682$	1.72346	−	50.3254i	0.0659947	−	1.92706i
$683$	−21.3840			−0.818237			−0.409118	−	0.912481i	$-0.634164\pi$
$683$	−21.3840			−0.818237			−0.409118	+	0.912481i	$0.634164\pi$
$684$	23.6508	+	11.1642i	0.904311	+	0.426874i
$685$	−0.868543			−0.0331853
$686$	−0.620473	+	18.1179i	−0.0236898	+	0.691746i
$687$	−43.3428	−	9.22291i	−1.65363	−	0.351876i
$688$	−36.5589	+	14.8855i	−1.39379	+	0.567503i
$689$		−	33.0829i		−	1.26036i
$690$	0.895648	−	0.257260i	0.0340967	−	0.00979370i
$691$	−7.97790	−	4.60604i	−0.303494	−	0.175222i	0.340518	−	0.940238i	$-0.389398\pi$
$691$	−7.97790	−	4.60604i	−0.303494	−	0.175222i	−0.644011	+	0.765016i	$0.722731\pi$
$692$	1.84509	−	0.902988i	0.0701397	−	0.0343265i
$693$	35.3680	+	48.7255i	1.34352	+	1.85093i
$694$	5.06061	+	0.173308i	0.192098	+	0.00657866i
$695$	2.72336	−	4.71699i	0.103303	−	0.178926i
$696$	1.04265	+	1.15381i	0.0395217	+	0.0437350i
$697$	−3.68051	+	6.37482i	−0.139409	+	0.241464i
$698$	7.39189	−	11.8473i	0.279787	−	0.448425i
$699$	25.9771	−	8.43407i	0.982545	−	0.319006i
$700$	−33.3973	−	22.4613i	−1.26230	−	0.848958i
$701$	36.1655	+	20.8802i	1.36595	+	0.788634i	0.990408	−	0.138171i	$-0.0441222\pi$
$701$	36.1655	+	20.8802i	1.36595	+	0.788634i	0.375545	+	0.926804i	$0.377456\pi$
$702$	30.8538	−	12.4659i	1.16450	−	0.470495i
$703$	0.973242	−	1.88393i	0.0367065	−	0.0710538i
$704$	25.8633	−	28.9586i	0.974758	−	1.09142i
$705$	5.02941	+	4.53053i	0.189418	+	0.170630i
$706$	24.7837	+	15.4634i	0.932749	+	0.581973i
$707$	34.8943	−	60.4386i	1.31233	−	2.27303i
$708$	6.65895	−	6.44495i	0.250258	−	0.242216i
$709$	46.0033			1.72769			0.863844	−	0.503759i	$-0.168050\pi$
$709$	46.0033			1.72769			0.863844	+	0.503759i	$0.168050\pi$
$710$	3.23838	+	2.02053i	0.121534	+	0.0758292i
$711$	8.69808	+	11.9831i	0.326203	+	0.449402i
$712$	−7.08907	+	3.17344i	−0.265674	+	0.118930i
$713$		−	7.63831i		−	0.286057i
$714$	−55.2115	−	13.7393i	−2.06624	−	0.514182i
$715$	6.95477	−	4.01534i	0.260094	−	0.150165i
$716$	8.07796	+	0.553931i	0.301887	+	0.0207014i
$717$	−0.602722	−	0.128253i	−0.0225091	−	0.00478970i
$718$	−18.4799	+	29.6184i	−0.689663	+	1.10535i
$719$	11.4754	−	19.8760i	0.427961	−	0.741250i	−0.568731	−	0.822524i	$-0.692565\pi$
$719$	11.4754	−	19.8760i	0.427961	−	0.741250i	0.996692	+	0.0812735i	$0.0258987\pi$
$720$	−4.38243	−	0.143174i	−0.163324	−	0.00533577i
$721$	19.3786			0.721696
$722$	14.7901	+	22.4333i	0.550432	+	0.834880i
$723$	−20.8270	+	23.1203i	−0.774564	+	0.859855i
$724$	−7.48941	−	15.3032i	−0.278342	−	0.568739i
$725$			1.54481i			0.0573726i
$726$	−29.8428	−	7.42635i	−1.10757	−	0.275618i
$727$	−4.13454	+	2.38708i	−0.153342	+	0.0885319i	−0.574708	−	0.818359i	$-0.694884\pi$
$727$	−4.13454	+	2.38708i	−0.153342	+	0.0885319i	0.421366	+	0.906891i	$0.361551\pi$
$728$	−48.3423	+	21.6405i	−1.79168	+	0.802052i
$729$	8.30908	+	25.6897i	0.307744	+	0.951469i
$730$	−2.85484	−	1.78123i	−0.105662	−	0.0659261i
$731$	−55.4301			−2.05015
$732$	−14.6767	+	14.2050i	−0.542467	+	0.525034i
$733$	12.9968	+	22.5111i	0.480047	+	0.831465i	0.999738	−	0.0228887i	$-0.00728634\pi$
$733$	12.9968	+	22.5111i	0.480047	+	0.831465i	−0.519691	+	0.854354i	$0.673953\pi$
$734$	−0.557356	+	16.2749i	−0.0205724	+	0.600718i
$735$	−1.33039	+	6.25213i	−0.0490721	+	0.230613i
$736$	3.77054	−	4.52442i	0.138984	−	0.166772i
$737$	66.5192	−	38.4049i	2.45027	−	1.41466i
$738$	−5.54631	+	0.389103i	−0.204162	+	0.0143231i
$739$	−16.0190	−	9.24858i	−0.589269	−	0.340215i	0.175539	−	0.984472i	$-0.443833\pi$
$739$	−16.0190	−	9.24858i	−0.589269	−	0.340215i	−0.764808	+	0.644258i	$0.777166\pi$
$740$	−0.0243212	+	0.354676i	−0.000894067	+	0.0130382i
$741$	33.7362	+	5.54492i	1.23933	+	0.203698i
$742$	−42.6987	−	1.46227i	−1.56752	−	0.0536818i
$743$	−2.91470			−0.106930			−0.0534649	−	0.998570i	$-0.517027\pi$
$743$	−2.91470			−0.106930			−0.0534649	+	0.998570i	$0.517027\pi$
$744$	−11.0450	+	34.2020i	−0.404928	+	1.25391i
$745$	−3.61748			−0.132534
$746$	0.625166	+	1.17386i	0.0228890	+	0.0429780i
$747$	43.2849	+	19.2948i	1.58371	+	0.705960i
$748$	48.9720	−	23.9670i	1.79059	−	0.876319i
$749$	−7.33996	−	4.23773i	−0.268196	−	0.154843i
$750$	−6.35516	−	6.13157i	−0.232058	−	0.223893i
$751$	11.9887	+	6.92165i	0.437472	+	0.252575i	0.702525	−	0.711659i	$-0.252056\pi$
$751$	11.9887	+	6.92165i	0.437472	+	0.252575i	−0.265053	+	0.964234i	$0.585389\pi$
$752$	42.3819	+	5.83998i	1.54551	+	0.212962i
$753$	−9.06371	−	1.92866i	−0.330300	−	0.0702844i
$754$	1.72474	+	1.07612i	0.0628113	+	0.0391901i
$755$	1.19888	−	2.07653i	0.0436318	−	0.0755725i
$756$	−14.7255	−	40.3727i	−0.535560	−	1.46834i
$757$	−24.7846	+	42.9282i	−0.900812	+	1.56025i	−0.0743695	+	0.997231i	$0.523694\pi$
$757$	−24.7846	+	42.9282i	−0.900812	+	1.56025i	−0.826442	+	0.563021i	$0.809639\pi$
$758$	0.257601	−	7.52199i	0.00935647	−	0.273211i
$759$	−8.56042	−	1.82157i	−0.310723	−	0.0661188i
$760$	−3.76933	−	2.46707i	−0.136728	−	0.0894900i
$761$	−31.9767	+	18.4618i	−1.15916	+	0.669239i	−0.951102	−	0.308878i	$-0.900046\pi$
$761$	−31.9767	+	18.4618i	−1.15916	+	0.669239i	−0.208054	+	0.978117i	$0.566713\pi$
$762$	4.86447	−	19.5478i	0.176221	−	0.708143i
$763$	16.0522	−	9.26773i	0.581128	−	0.335514i
$764$	−24.7072	+	36.7366i	−0.893876	+	1.32908i
$765$	−5.62385	−	2.50691i	−0.203331	−	0.0906375i
$766$	32.0398	+	1.09725i	1.15765	+	0.0396452i
$767$	6.05717	−	10.4913i	0.218712	−	0.378820i
$768$	−23.4256	+	14.8068i	−0.845299	+	0.534293i
$769$	0.623376	−	1.07972i	0.0224795	−	0.0389356i	−0.854567	−	0.519341i	$-0.826177\pi$
$769$	0.623376	−	1.07972i	0.0224795	−	0.0389356i	0.877046	+	0.480406i	$0.159511\pi$
$770$	−4.87502	−	9.15370i	−0.175684	−	0.329876i
$771$	28.3023	−	9.18900i	1.01928	−	0.330934i
$772$	−12.6664	−	0.868573i	−0.455873	−	0.0312606i
$773$	−41.4815	+	23.9494i	−1.49199	+	0.861399i	−0.999958	−	0.00917936i	$-0.997078\pi$
$773$	−41.4815	+	23.9494i	−1.49199	+	0.861399i	−0.492029	+	0.870579i	$0.663745\pi$
$774$	−23.4200	−	34.7045i	−0.841813	−	1.24743i
$775$	−30.9195	+	17.8514i	−1.11066	+	0.641241i
$776$	1.55716	+	3.47850i	0.0558987	+	0.124871i
$777$	−3.31399	+	1.07596i	−0.118889	+	0.0385999i
$778$	0.840377	−	24.5392i	0.0301290	−	0.879772i
$779$	−5.07509	−	2.62180i	−0.181834	−	0.0939357i
$780$	−5.56013	+	1.39294i	−0.199085	+	0.0498751i
$781$	−17.9248	−	31.0466i	−0.641399	−	1.11094i
$782$	7.29976	−	3.88766i	0.261039	−	0.139022i
$783$	−0.970418	+	1.33379i	−0.0346799	+	0.0476657i
$784$	15.2349	+	37.4170i	0.544102	+	1.33632i
$785$			5.93743i			0.211916i
$786$	26.2802	−	27.2384i	0.937382	−	0.971563i
$787$	−16.6941	+	9.63833i	−0.595079	+	0.343569i	−0.767103	−	0.641524i	$-0.778303\pi$
$787$	−16.6941	+	9.63833i	−0.595079	+	0.343569i	0.172024	+	0.985093i	$0.444969\pi$
$788$	−0.885681	+	12.9159i	−0.0315511	+	0.460109i
$789$	−19.0522	−	4.05411i	−0.678276	−	0.144330i
$790$	−1.19892	−	2.25118i	−0.0426556	−	0.0800933i
$791$	−32.5918			−1.15883
$792$	35.6969	+	20.5348i	1.26844	+	0.729671i
$793$	−13.3504	+	23.1235i	−0.474085	+	0.821139i
$794$	0.946553	−	1.51707i	0.0335919	−	0.0538390i
$795$	−4.52238	−	0.962316i	−0.160392	−	0.0341298i
$796$	−28.7989	+	14.0942i	−1.02075	+	0.499556i
$797$	10.9815	−	6.34018i	0.388985	−	0.224581i	−0.292735	−	0.956194i	$-0.594565\pi$
$797$	10.9815	−	6.34018i	0.388985	−	0.224581i	0.681720	+	0.731613i	$0.261232\pi$
$798$	8.64774	−	43.2967i	0.306127	−	1.53269i
$799$	52.0282	+	30.0385i	1.84063	+	1.06269i
$800$	−27.1267	−	4.68902i	−0.959074	−	0.165782i
$801$	−4.83926	−	6.66692i	−0.170987	−	0.235564i
$802$	−0.186426	+	5.44367i	−0.00658293	+	0.192223i
$803$	15.8018	+	27.3696i	0.557635	+	0.965851i
$804$	−53.1801	+	13.3228i	−1.87552	+	0.469859i
$805$	−0.786580	−	1.36240i	−0.0277233	−	0.0480182i
$806$	−1.60808	+	46.9563i	−0.0566423	+	1.65397i
$807$	16.0661	−	5.21622i	0.565552	−	0.183620i
$808$	4.89366	−	47.4829i	0.172158	−	1.67044i
$809$			23.4992i			0.826189i	0.910688	+	0.413095i	$0.135552\pi$
$809$			23.4992i			0.826189i	−0.910688	+	0.413095i	$0.864448\pi$
$810$	−0.806592	−	4.58027i	−0.0283407	−	0.160934i
$811$	12.8736	−	7.43259i	0.452054	−	0.260993i	−0.256643	−	0.966506i	$-0.582617\pi$
$811$	12.8736	−	7.43259i	0.452054	−	0.260993i	0.708697	+	0.705513i	$0.249283\pi$
$812$	1.46514	−	2.17848i	0.0514163	−	0.0764497i
$813$	31.4139	−	10.1992i	1.10173	−	0.357703i
$814$	1.76747	−	2.83278i	0.0619497	−	0.0992890i
$815$	−6.33470			−0.221895
$816$	−38.3076	+	6.85232i	−1.34103	+	0.239879i
$817$	−2.01055	−	42.9678i	−0.0703404	−	1.50325i
$818$	13.1405	−	21.0607i	0.459446	−	0.736370i
$819$	−33.0002	−	45.4636i	−1.15312	−	1.58863i
$820$	0.955456	+	0.0655186i	0.0333660	+	0.00228801i
$821$		−	12.4019i		−	0.432830i	−0.976301	−	0.216415i	$-0.930564\pi$
$821$		−	12.4019i		−	0.432830i	0.976301	−	0.216415i	$-0.0694364\pi$
$822$	−4.19010	−	4.04269i	−0.146147	−	0.141005i
$823$	26.8916	+	15.5258i	0.937381	+	0.541197i	0.889138	−	0.457639i	$-0.151305\pi$
$823$	26.8916	+	15.5258i	0.937381	+	0.541197i	0.0482425	+	0.998836i	$0.484638\pi$
$824$	12.0979	−	5.41563i	0.421449	−	0.188663i
$825$	12.6328	+	38.9093i	0.439818	+	1.35465i
$826$	−13.2730	−	8.28144i	−0.461826	−	0.288148i
$827$	−11.3897	−	19.7276i	−0.396059	−	0.685995i	0.597176	−	0.802110i	$-0.296289\pi$
$827$	−11.3897	−	19.7276i	−0.396059	−	0.685995i	−0.993236	+	0.116115i	$0.962956\pi$
$828$	5.51829	+	2.92775i	0.191774	+	0.101746i
$829$	−33.6504			−1.16873			−0.584363	−	0.811492i	$-0.698656\pi$
$829$	−33.6504			−1.16873			−0.584363	+	0.811492i	$0.698656\pi$
$830$	−6.92555	−	4.32108i	−0.240389	−	0.149987i
$831$	−2.21250	−	6.81454i	−0.0767507	−	0.236394i
$832$	−24.1318	+	27.0199i	−0.836621	+	0.936748i
$833$			56.7312i			1.96562i
$834$	35.0938	−	10.0801i	1.21520	−	0.349045i
$835$	2.30438	+	1.33043i	0.0797463	+	0.0460415i
$836$	20.3548	+	37.0924i	0.703987	+	1.28287i
$837$	−37.9099	−	4.01015i	−1.31036	−	0.138611i
$838$	−11.2436	−	21.1118i	−0.388404	−	0.729297i
$839$	8.13593	+	14.0918i	0.280883	+	0.486504i	0.971603	−	0.236619i	$-0.0760393\pi$
$839$	8.13593	+	14.0918i	0.280883	+	0.486504i	−0.690719	+	0.723123i	$0.742706\pi$
$840$	1.55204	+	7.23779i	0.0535506	+	0.249727i
$841$	28.8992			0.996525
$842$	17.1347	+	32.1733i	0.590500	+	1.10877i
$843$	13.6030	+	12.2537i	0.468512	+	0.422040i
$844$	−3.04762	+	44.4434i	−0.104904	+	1.52981i
$845$	−2.37541	+	1.37145i	−0.0817167	+	0.0471792i
$846$	3.17567	+	45.2663i	0.109182	+	1.55629i
$847$			51.9167i			1.78388i
$848$	−27.0650	+	11.0199i	−0.929417	+	0.378425i
$849$	9.05098	+	8.15320i	0.310629	+	0.279817i
$850$	−32.7972	−	20.4633i	−1.12494	−	0.701885i
$851$	0.253242	−	0.438628i	0.00868103	−	0.0150360i
$852$	6.21818	+	24.8209i	0.213031	+	0.850349i
$853$	−13.0189	−	22.5494i	−0.445758	−	0.772075i	0.552347	−	0.833614i	$-0.313732\pi$
$853$	−13.0189	−	22.5494i	−0.445758	−	0.772075i	−0.998105	+	0.0615391i	$0.980399\pi$
$854$	29.2544	+	18.2528i	1.00106	+	0.624597i
$855$	1.73930	−	4.45039i	0.0594828	−	0.152200i
$856$	−5.76656	−	0.594310i	−0.197097	−	0.0203131i
$857$	11.6293	−	6.71419i	0.397250	−	0.229353i	−0.288047	−	0.957616i	$-0.593006\pi$
$857$	11.6293	−	6.71419i	0.397250	−	0.229353i	0.685297	+	0.728264i	$0.259672\pi$
$858$	52.2414	+	13.0003i	1.78349	+	0.443822i
$859$	34.9146	+	20.1580i	1.19127	+	0.687781i	0.958595	−	0.284773i	$-0.0919184\pi$
$859$	34.9146	+	20.1580i	1.19127	+	0.687781i	0.232676	+	0.972554i	$0.425252\pi$
$860$	3.17013	+	6.47756i	0.108100	+	0.220883i
$861$	2.89852	+	8.92749i	0.0987812	+	0.304248i
$862$	10.2139	+	19.1784i	0.347887	+	0.653218i
$863$	−20.1375			−0.685489			−0.342744	−	0.939429i	$-0.611356\pi$
$863$	−20.1375			−0.685489			−0.342744	+	0.939429i	$0.611356\pi$
$864$	−20.4757	−	21.0890i	−0.696597	−	0.717462i
$865$	−0.187650	−	0.325019i	−0.00638028	−	0.0110510i
$866$	−17.2671	−	32.4221i	−0.586762	−	1.10175i
$867$	−24.6504	−	5.24536i	−0.837173	−	0.178142i
$868$	60.5334	+	4.15096i	2.05464	+	0.140893i
$869$			23.9547i			0.812606i
$870$	0.197273	−	0.204467i	0.00668819	−	0.00693207i
$871$	−62.0661	+	35.8339i	−2.10303	+	1.21418i
$872$	7.43121	−	10.2718i	0.251652	−	0.347846i
$873$	−3.27136	+	2.37455i	−0.110719	+	0.0803663i
$874$	3.27838	+	5.51756i	0.110893	+	0.186634i
$875$	−7.45409	+	12.9109i	−0.251994	+	0.436467i
$876$	−5.48172	−	21.8812i	−0.185210	−	0.739296i
$877$	17.0301			0.575064			0.287532	−	0.957771i	$-0.407165\pi$
$877$	17.0301			0.575064			0.287532	+	0.957771i	$0.407165\pi$
$878$	2.56656	−	1.36688i	0.0866173	−	0.0461301i
$879$	−10.8615	+	51.0435i	−0.366351	+	1.72166i
$880$	−5.60156	−	4.35216i	−0.188829	−	0.146711i
$881$		−	41.5500i		−	1.39985i	−0.714214	−	0.699927i	$-0.753216\pi$
$881$		−	41.5500i		−	1.39985i	0.714214	−	0.699927i	$-0.246784\pi$
$882$	−35.5191	+	23.9697i	−1.19599	+	0.807101i
$883$	−32.2711	+	18.6317i	−1.08601	+	0.627007i	−0.932511	−	0.361142i	$-0.882387\pi$
$883$	−32.2711	+	18.6317i	−1.08601	+	0.627007i	−0.153497	+	0.988149i	$0.549054\pi$
$884$	−45.6935	+	22.3625i	−1.53684	+	0.752132i
$885$	−1.25795	−	1.13318i	−0.0422857	−	0.0380913i
$886$	12.9230	+	0.442566i	0.434157	+	0.0148683i
$887$	20.5942	−	35.6701i	0.691485	−	1.19769i	−0.279867	−	0.960039i	$-0.590290\pi$
$887$	20.5942	−	35.6701i	0.691485	−	1.19769i	0.971351	−	0.237648i	$-0.0763763\pi$
$888$	−1.76820	+	1.59786i	−0.0593367	+	0.0536205i
$889$	−34.0069			−1.14056
$890$	0.667030	+	1.25246i	0.0223589	+	0.0419827i
$891$	−13.5349	+	41.5301i	−0.453437	+	1.39131i
$892$	36.3479	−	17.7887i	1.21702	−	0.595611i
$893$	−21.3979	+	41.4204i	−0.716052	+	1.38608i
$894$	−17.4517	−	16.8378i	−0.583674	−	0.563139i
$895$		−	1.47930i		−	0.0494475i
$896$	33.8068	+	32.3402i	1.12941	+	1.08041i
$897$	7.98734	+	1.69962i	0.266689	+	0.0567488i
$898$	−0.882544	+	25.7705i	−0.0294509	+	0.859972i
$899$	−1.16444	−	2.01686i	−0.0388361	−	0.0672661i
$900$	−1.04532	−	29.1802i	−0.0348440	−	0.972673i
$901$	−41.0356			−1.36709
$902$	−7.63118	−	4.76135i	−0.254091	−	0.158536i
$903$	−47.3062	+	52.5153i	−1.57425	+	1.74760i
$904$	−20.3467	+	9.10825i	−0.676721	+	0.302936i
$905$	−2.69572	+	1.55637i	−0.0896086	+	0.0517356i
$906$	15.4491	−	4.43748i	0.513261	−	0.147426i
$907$	−3.46054	+	1.99794i	−0.114905	+	0.0663406i	−0.556351	−	0.830947i	$-0.687799\pi$
$907$	−3.46054	+	1.99794i	−0.114905	+	0.0663406i	0.441446	+	0.897288i	$0.354466\pi$
$908$	9.15056	−	13.6058i	0.303672	−	0.451523i
$909$	50.3550	−	5.26981i	1.67017	−	0.174788i
$910$	4.54866	+	8.54090i	0.150787	+	0.283128i
$911$	5.42069	−	9.38891i	0.179595	−	0.311068i	−0.762147	−	0.647404i	$-0.775854\pi$
$911$	5.42069	−	9.38891i	0.179595	−	0.311068i	0.941742	+	0.336336i	$0.109188\pi$
$912$	−6.70122	−	29.4465i	−0.221900	−	0.975070i
$913$	38.3337	+	66.3959i	1.26866	+	2.19738i
$914$	−15.1843	+	24.3364i	−0.502252	+	0.804978i
$915$	2.77261	+	2.49759i	0.0916595	+	0.0825676i
$916$	22.4928	+	45.9597i	0.743181	+	1.51855i
$917$	−55.3365	−	31.9485i	−1.82737	−	1.05503i
$918$	−15.4625	−	38.2706i	−0.510339	−	1.26312i
$919$			37.8563i			1.24876i	0.781119	+	0.624382i	$0.214649\pi$
$919$			37.8563i			1.24876i	−0.781119	+	0.624382i	$0.785351\pi$
$920$	−0.871796	−	0.630709i	−0.0287423	−	0.0207939i
$921$	−14.3539	+	4.66031i	−0.472976	+	0.153563i
$922$	−7.06634	+	3.76335i	−0.232717	+	0.123939i
$923$	16.7248	+	28.9682i	0.550504	+	0.953500i
$924$	19.0880	−	66.8512i	0.627948	−	2.19924i
$925$	−2.36740			−0.0778395
$926$	6.76893	−	3.60496i	0.222441	−	0.118466i
$927$	8.25844	+	11.3774i	0.271243	+	0.373684i
$928$	0.305862	−	1.76946i	0.0100404	−	0.0580853i
$929$	32.0913	−	18.5279i	1.05288	−	0.607882i	0.129427	−	0.991589i	$-0.458686\pi$
$929$	32.0913	−	18.5279i	1.05288	−	0.607882i	0.923455	+	0.383707i	$0.125353\pi$
$930$	6.37207	+	1.58569i	0.208948	+	0.0519967i
$931$	−43.9764	+	2.05775i	−1.44127	+	0.0674399i
$932$	−26.1692	−	17.6001i	−0.857201	−	0.576511i
$933$	0.418125	+	0.0889728i	0.0136888	+	0.00291284i
$934$	34.1300	+	1.16883i	1.11677	+	0.0382452i
$935$	−4.98057	−	8.62660i	−0.162882	−	0.282120i
$936$	−33.3072	−	19.1600i	−1.08868	−	0.626266i
$937$	−16.3433	−	28.3074i	−0.533912	−	0.924763i	−0.999215	−	0.0396117i	$-0.987388\pi$
$937$	−16.3433	−	28.3074i	−0.533912	−	0.924763i	0.465303	−	0.885152i	$-0.345945\pi$
$938$	43.5059	+	81.6899i	1.42052	+	2.66727i
$939$	9.55786	−	10.6103i	0.311909	−	0.346255i
$940$	0.534731	−	7.79796i	0.0174410	−	0.254342i
$941$	13.8278	+	7.98349i	0.450774	+	0.260254i	0.708157	−	0.706055i	$-0.249527\pi$
$941$	13.8278	+	7.98349i	0.450774	+	0.260254i	−0.257383	+	0.966309i	$0.582860\pi$
$942$	−27.6362	+	28.6439i	−0.900435	+	0.933268i
$943$	−1.18161	−	0.682205i	−0.0384786	−	0.0222156i
$944$	−10.6005	−	1.46069i	−0.345018	−	0.0475415i
$945$	−7.17470	+	3.18863i	−0.233393	+	0.103726i
$946$	2.31823	−	67.6927i	0.0753721	−	2.20088i
$947$	−11.9457	−	20.6905i	−0.388182	−	0.672351i	0.604023	−	0.796967i	$-0.293564\pi$
$947$	−11.9457	−	20.6905i	−0.388182	−	0.672351i	−0.992205	+	0.124616i	$0.960230\pi$
$948$	4.69432	−	16.4408i	0.152464	−	0.533971i
$949$	−14.7440	−	25.5373i	−0.478609	−	0.828976i
$950$	14.6729	−	26.1657i	0.476053	−	0.848929i
$951$	−8.47752	−	7.63662i	−0.274902	−	0.247634i
$952$	26.8426	+	59.9631i	0.869974	+	1.94342i
$953$	29.2436	+	16.8838i	0.947294	+	0.546920i	0.892239	−	0.451563i	$-0.149133\pi$
$953$	29.2436	+	16.8838i	0.947294	+	0.546920i	0.0550545	+	0.998483i	$0.482467\pi$
$954$	−17.3381	−	25.6922i	−0.561342	−	0.831815i
$955$	7.00482	+	4.04423i	0.226671	+	0.130868i
$956$	0.312782	+	0.639112i	0.0101161	+	0.0206704i
$957$	−2.53803	+	0.824030i	−0.0820429	+	0.0266371i
$958$	49.3834	+	1.69120i	1.59550	+	0.0546402i
$959$	−4.91465	+	8.51243i	−0.158702	+	0.274881i
$960$	2.99163	+	4.08473i	0.0965545	+	0.131834i
$961$	11.4118	−	19.7659i	0.368124	−	0.637610i
$962$	−1.64914	+	2.64314i	−0.0531705	+	0.0852183i
$963$	−0.639991	−	6.11536i	−0.0206234	−	0.197065i
$964$	35.8475	+	2.45817i	1.15457	+	0.0791725i
$965$			2.31957i			0.0746695i
$966$	2.54667	−	10.2338i	0.0819378	−	0.329267i
$967$		−	38.7485i		−	1.24607i	−0.782195	−	0.623034i	$-0.785900\pi$
$967$		−	38.7485i		−	1.24607i	0.782195	−	0.623034i	$-0.214100\pi$
$968$	14.5089	+	32.4111i	0.466334	+	1.04173i
$969$	6.87784	−	41.8459i	0.220948	−	1.34428i
$970$	0.614565	−	0.327301i	0.0197325	−	0.0105090i
$971$	1.25883	−	2.18036i	0.0403979	−	0.0699711i	−0.845120	−	0.534577i	$-0.820471\pi$
$971$	1.25883	−	2.18036i	0.0403979	−	0.0699711i	0.885517	+	0.464606i	$0.153804\pi$
$972$	17.4279	−	25.8509i	0.559001	−	0.829167i
$973$	−30.8203	−	53.3823i	−0.988052	−	1.71136i
$974$	−1.68800	+	49.2899i	−0.0540870	+	1.57935i
$975$	−11.7871	−	36.3045i	−0.377489	−	1.16267i
$976$	23.3642	+	3.21945i	0.747871	+	0.103052i
$977$	−17.7846	+	10.2680i	−0.568980	+	0.328501i	−0.756742	−	0.653714i	$-0.773210\pi$
$977$	−17.7846	+	10.2680i	−0.568980	+	0.328501i	0.187762	+	0.982215i	$0.439877\pi$
$978$	−30.5604	−	29.4853i	−0.977214	−	0.942835i
$979$		−	13.3274i		−	0.425946i
$980$	6.62961	−	3.24454i	0.211775	−	0.103643i
$981$	12.2821	+	5.47489i	0.392136	+	0.174800i
$982$	19.8619	+	0.680196i	0.633818	+	0.0217059i
$983$	13.3831	+	23.1802i	0.426854	+	0.739333i	0.996592	−	0.0824937i	$-0.0262884\pi$
$983$	13.3831	+	23.1802i	0.426854	+	0.739333i	−0.569737	+	0.821827i	$0.692955\pi$
$984$	4.30443	+	4.76331i	0.137220	+	0.151849i
$985$	2.36525			0.0753632
$986$	1.33481	−	2.13934i	0.0425089	−	0.0681305i
$987$	72.8618	−	23.6563i	2.31922	−	0.752988i
$988$	−18.9922	−	34.6092i	−0.604221	−	1.10107i
$989$		−	10.2743i		−	0.326704i
$990$	3.29671	−	6.76316i	0.104776	−	0.214947i
$991$	−10.6492	−	6.14834i	−0.338284	−	0.195308i	0.321229	−	0.947002i	$-0.395904\pi$
$991$	−10.6492	−	6.14834i	−0.338284	−	0.195308i	−0.659513	+	0.751693i	$0.729237\pi$
$992$	38.9504	−	14.3256i	1.23668	−	0.454837i
$993$	−32.7004	+	10.6170i	−1.03772	+	0.336919i
$994$	38.1272	−	20.3056i	1.20932	−	0.644054i
$995$	2.92891	+	5.07303i	0.0928528	+	0.160826i
$996$	−13.2981	−	53.0816i	−0.421367	−	1.68195i
$997$	10.6087			0.335982			0.167991	−	0.985789i	$-0.446272\pi$
$997$	10.6087			0.335982			0.167991	+	0.985789i	$0.446272\pi$
$998$	0.729801	−	21.3103i	0.0231014	−	0.674566i
$999$	−2.04401	−	1.48715i	−0.0646697	−	0.0470515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.o.a.11.3	✓	232
4.3	odd	2	inner	684.2.o.a.11.40	yes	232
9.5	odd	6		684.2.bi.a.239.38	yes	232
19.7	even	3		684.2.bi.a.83.79	yes	232
36.23	even	6		684.2.bi.a.239.79	yes	232
76.7	odd	6		684.2.bi.a.83.38	yes	232
171.140	odd	6	inner	684.2.o.a.311.40	yes	232
684.311	even	6	inner	684.2.o.a.311.3	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.o.a.11.3	✓	232	1.1	even	1	trivial
684.2.o.a.11.40	yes	232	4.3	odd	2	inner
684.2.o.a.311.3	yes	232	684.311	even	6	inner
684.2.o.a.311.40	yes	232	171.140	odd	6	inner
684.2.bi.a.83.38	yes	232	76.7	odd	6
684.2.bi.a.83.79	yes	232	19.7	even	3
684.2.bi.a.239.38	yes	232	9.5	odd	6
684.2.bi.a.239.79	yes	232	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41338 - 0.0484033i) q^{2} +(-1.15926 + 1.28691i) q^{3} +(1.99531 + 0.136825i) q^{4} -0.365397i q^{5} +(1.70076 - 1.76278i) q^{6} +(-3.58119 - 2.06760i) q^{7} +(-2.81352 - 0.289966i) q^{8} +(-0.312254 - 2.98371i) q^{9} +(-0.0176864 + 0.516447i) q^{10} +(2.42667 - 4.20311i) q^{11} +(-2.48916 + 2.40917i) q^{12} +(-2.26421 + 3.92173i) q^{13} +(4.96153 + 3.09566i) q^{14} +(0.470232 + 0.423589i) q^{15} +(3.96256 + 0.546017i) q^{16} +(4.86446 + 2.80849i) q^{17} +(0.296914 + 4.23224i) q^{18} +(-2.00062 + 3.87266i) q^{19} +(0.0499955 - 0.729082i) q^{20} +(6.81233 - 2.21178i) q^{21} +(-3.63326 + 5.82315i) q^{22} +(-0.520572 + 0.901657i) q^{23} +(3.63475 - 3.28460i) q^{24} +4.86648 q^{25} +(3.39003 - 5.43332i) q^{26} +(4.20173 + 3.05703i) q^{27} +(-6.86271 - 4.61551i) q^{28} +0.317438i q^{29} +(-0.644116 - 0.621455i) q^{30} +(-6.35356 + 3.66823i) q^{31} +(-5.57419 - 0.963533i) q^{32} +(2.59588 + 7.99536i) q^{33} +(-6.73941 - 4.20494i) q^{34} +(-0.755496 + 1.30856i) q^{35} +(-0.214800 - 5.99615i) q^{36} -0.486469 q^{37} +(3.01510 - 5.37672i) q^{38} +(-2.42210 - 7.46011i) q^{39} +(-0.105953 + 1.02805i) q^{40} +1.31049i q^{41} +(-9.73550 + 2.79636i) q^{42} +(-8.54619 + 4.93414i) q^{43} +(5.41705 - 8.05449i) q^{44} +(-1.09024 + 0.114097i) q^{45} +(0.779412 - 1.24919i) q^{46} +10.6956 q^{47} +(-5.29629 + 4.46647i) q^{48} +(5.04996 + 8.74679i) q^{49} +(-6.87822 - 0.235554i) q^{50} +(-9.25342 + 3.00433i) q^{51} +(-5.05440 + 7.51528i) q^{52} +(-6.32685 + 3.65281i) q^{53} +(-5.79069 - 4.52414i) q^{54} +(-1.53580 - 0.886697i) q^{55} +(9.47624 + 6.85568i) q^{56} +(-2.66452 - 7.06402i) q^{57} +(0.0153650 - 0.448662i) q^{58} -2.67518 q^{59} +(0.880303 + 0.909532i) q^{60} +5.89625 q^{61} +(9.15759 - 4.87709i) q^{62} +(-5.05088 + 11.3308i) q^{63} +(7.83184 + 1.63165i) q^{64} +(1.43299 + 0.827336i) q^{65} +(-3.28198 - 11.4262i) q^{66} +(13.7059 + 7.91310i) q^{67} +(9.32185 + 6.26941i) q^{68} +(-0.556872 - 1.71518i) q^{69} +(1.13115 - 1.81293i) q^{70} +(3.69330 - 6.39698i) q^{71} +(0.0133612 + 8.48527i) q^{72} +(-3.25587 + 5.63934i) q^{73} +(0.687568 + 0.0235467i) q^{74} +(-5.64150 + 6.26271i) q^{75} +(-4.52175 + 7.45344i) q^{76} +(-17.3807 + 10.0348i) q^{77} +(3.06226 + 10.6612i) q^{78} +(-4.27446 + 2.46786i) q^{79} +(0.199513 - 1.44791i) q^{80} +(-8.80499 + 1.86335i) q^{81} +(0.0634320 - 1.85223i) q^{82} +(-7.89843 + 13.6805i) q^{83} +(13.8954 - 3.48110i) q^{84} +(1.02622 - 1.77746i) q^{85} +(12.3179 - 6.56018i) q^{86} +(-0.408512 - 0.367991i) q^{87} +(-8.04624 + 11.1219i) q^{88} +(2.37814 - 1.37302i) q^{89} +(1.54645 - 0.108492i) q^{90} +(16.2172 - 9.36298i) q^{91} +(-1.16207 + 1.72786i) q^{92} +(2.64473 - 12.4289i) q^{93} +(-15.1170 - 0.517701i) q^{94} +(1.41506 + 0.731023i) q^{95} +(7.70189 - 6.05648i) q^{96} +(-0.673718 - 1.16691i) q^{97} +(-6.71417 - 12.6070i) q^{98} +(-13.2986 - 5.92802i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - 3 q^{2} + q^{4} + 3 q^{6} + 2 q^{10} - q^{12} + 2 q^{13} + q^{16} - 12 q^{17} - 16 q^{18} - 27 q^{20} - 14 q^{21} + 6 q^{22} - 10 q^{24} - 204 q^{25} - 6 q^{28} - 9 q^{30} - 3 q^{32} - 12 q^{33}+ \cdots - 162 q^{98}+O(q^{100}) \) 232 * q - 3 * q^2 + q^4 + 3 * q^6 + 2 * q^10 - q^12 + 2 * q^13 + q^16 - 12 * q^17 - 16 * q^18 - 27 * q^20 - 14 * q^21 + 6 * q^22 - 10 * q^24 - 204 * q^25 - 6 * q^28 - 9 * q^30 - 3 * q^32 - 12 * q^33 + 2 * q^34 + 13 * q^36 - 16 * q^37 - 3 * q^38 - 16 * q^40 - 43 * q^42 + 21 * q^44 + 2 * q^45 - 24 * q^46 + 58 * q^48 + 88 * q^49 + 9 * q^50 + 17 * q^52 + 41 * q^54 - 48 * q^56 - 12 * q^57 + 2 * q^58 + 16 * q^60 - 4 * q^61 + 6 * q^62 + 16 * q^64 + 12 * q^65 - 27 * q^66 - 18 * q^68 - 14 * q^69 + 60 * q^70 + 15 * q^72 + 2 * q^73 - 30 * q^74 + 3 * q^76 - 12 * q^77 - 64 * q^78 + 54 * q^80 + 4 * q^81 + 2 * q^82 - 10 * q^84 + 22 * q^85 + 51 * q^86 - 18 * q^88 + 14 * q^90 + 57 * q^92 + 4 * q^93 - 6 * q^94 - 17 * q^96 - 4 * q^97 - 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more