LMFDB - Embedded newform 340.2.i.c.47.39

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [340,2,Mod(47,340)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(340, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("340.47"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 340 = 2^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	340.i (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,-4,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.71491366872$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.39
Character	$\chi$	$=$	340.47
Dual form			340.2.i.c.123.39

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17399 - 0.788511i) q^{2} -2.30159i q^{3} +(0.756500 - 1.85141i) q^{4} +(-0.651458 - 2.13907i) q^{5} +(-1.81483 - 2.70204i) q^{6} +3.97452i q^{7} +(-0.571733 - 2.77004i) q^{8} -2.29731 q^{9} +(-2.45148 - 1.99756i) q^{10} +(0.316459 + 0.316459i) q^{11} +(-4.26118 - 1.74115i) q^{12} +(1.77966 - 1.77966i) q^{13} +(3.13395 + 4.66604i) q^{14} +(-4.92325 + 1.49939i) q^{15} +(-2.85542 - 2.80118i) q^{16} +(3.27595 + 2.50362i) q^{17} +(-2.69702 + 1.81145i) q^{18} +2.82964i q^{19} +(-4.45311 - 0.412089i) q^{20} +9.14770 q^{21} +(0.621051 + 0.121988i) q^{22} -0.996717 q^{23} +(-6.37549 + 1.31589i) q^{24} +(-4.15120 + 2.78702i) q^{25} +(0.686018 - 3.49258i) q^{26} -1.61730i q^{27} +(7.35845 + 3.00672i) q^{28} +(0.0246430 - 0.0246430i) q^{29} +(-4.59755 + 5.64230i) q^{30} +(-3.68484 + 3.68484i) q^{31} +(-5.56099 - 1.03702i) q^{32} +(0.728359 - 0.728359i) q^{33} +(5.82007 + 0.356101i) q^{34} +(8.50175 - 2.58923i) q^{35} +(-1.73791 + 4.25325i) q^{36} -1.58941i q^{37} +(2.23120 + 3.32196i) q^{38} +(-4.09604 - 4.09604i) q^{39} +(-5.55284 + 3.02754i) q^{40} +(6.11435 - 6.11435i) q^{41} +(10.7393 - 7.21307i) q^{42} +(4.17559 - 4.17559i) q^{43} +(0.825296 - 0.346494i) q^{44} +(1.49660 + 4.91410i) q^{45} +(-1.17013 + 0.785922i) q^{46} +(6.91175 - 6.91175i) q^{47} +(-6.44716 + 6.57199i) q^{48} -8.79678 q^{49} +(-2.67587 + 6.54521i) q^{50} +(5.76231 - 7.53989i) q^{51} +(-1.94856 - 4.64118i) q^{52} +(9.08331 + 9.08331i) q^{53} +(-1.27526 - 1.89870i) q^{54} +(0.470767 - 0.883087i) q^{55} +(11.0096 - 2.27236i) q^{56} +6.51266 q^{57} +(0.00949931 - 0.0483618i) q^{58} -4.28205i q^{59} +(-0.948458 + 10.2492i) q^{60} +(-9.74339 + 9.74339i) q^{61} +(-1.42042 + 7.23150i) q^{62} -9.13069i q^{63} +(-7.34624 + 3.16745i) q^{64} +(-4.96617 - 2.64743i) q^{65} +(0.280766 - 1.42940i) q^{66} +(5.61205 - 5.61205i) q^{67} +(7.11349 - 4.17113i) q^{68} +2.29403i q^{69} +(7.93932 - 9.74346i) q^{70} +(-10.5354 + 10.5354i) q^{71} +(1.31345 + 6.36364i) q^{72} +6.55715 q^{73} +(-1.25327 - 1.86595i) q^{74} +(6.41458 + 9.55436i) q^{75} +(5.23881 + 2.14062i) q^{76} +(-1.25777 + 1.25777i) q^{77} +(-8.03847 - 1.57893i) q^{78} +(-9.90208 + 9.90208i) q^{79} +(-4.13172 + 7.93277i) q^{80} -10.6143 q^{81} +(2.35694 - 11.9994i) q^{82} +(-5.59012 + 5.59012i) q^{83} +(6.92024 - 16.9361i) q^{84} +(3.22127 - 8.63848i) q^{85} +(1.60960 - 8.19460i) q^{86} +(-0.0567180 - 0.0567180i) q^{87} +(0.695675 - 1.05754i) q^{88} -2.62516i q^{89} +(5.63181 + 4.58901i) q^{90} +(7.07327 + 7.07327i) q^{91} +(-0.754016 + 1.84533i) q^{92} +(8.48099 + 8.48099i) q^{93} +(2.66433 - 13.5643i) q^{94} +(6.05278 - 1.84339i) q^{95} +(-2.38680 + 12.7991i) q^{96} +11.6243i q^{97} +(-10.3273 + 6.93636i) q^{98} +(-0.727005 - 0.727005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 4 q^{2} - 8 q^{5} + 8 q^{8} - 96 q^{9} - 6 q^{10} - 8 q^{13} + 16 q^{14} - 8 q^{17} - 24 q^{18} + 2 q^{20} - 16 q^{21} + 8 q^{24} + 8 q^{29} - 24 q^{30} + 36 q^{32} - 8 q^{33} + 16 q^{34} + 4 q^{38}+ \cdots - 12 q^{98}+O(q^{100}) $ 96 * q - 4 * q^2 - 8 * q^5 + 8 * q^8 - 96 * q^9 - 6 * q^10 - 8 * q^13 + 16 * q^14 - 8 * q^17 - 24 * q^18 + 2 * q^20 - 16 * q^21 + 8 * q^24 + 8 * q^29 - 24 * q^30 + 36 * q^32 - 8 * q^33 + 16 * q^34 + 4 * q^38 - 2 * q^40 + 8 * q^41 + 16 * q^42 - 8 * q^44 - 40 * q^45 - 24 * q^46 + 92 * q^48 - 80 * q^49 - 24 * q^50 + 12 * q^52 + 4 * q^54 - 12 * q^56 + 16 * q^57 + 32 * q^60 + 48 * q^61 + 48 * q^62 - 8 * q^65 + 80 * q^68 + 28 * q^70 + 8 * q^72 - 16 * q^73 - 20 * q^74 + 56 * q^77 - 34 * q^80 - 16 * q^81 + 32 * q^85 + 8 * q^86 - 80 * q^88 - 82 * q^90 - 136 * q^92 + 24 * q^93 - 112 * q^94 + 40 * q^96 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/340\mathbb{Z}\right)^\times$.

$n$	$137$	$171$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.17399	−	0.788511i	0.830136	−	0.557562i
$2$	1.17399	−	0.788511i	0.830136	−	0.557562i
$3$		−	2.30159i		−	1.32882i	−0.747367	−	0.664411i	$-0.768682\pi$
$3$		−	2.30159i		−	1.32882i	0.747367	−	0.664411i	$-0.231318\pi$
$4$	0.756500	−	1.85141i	0.378250	−	0.925704i
$5$	−0.651458	−	2.13907i	−0.291341	−	0.956619i
$5$	−0.651458	−	2.13907i	−0.291341	−	0.956619i
$6$	−1.81483	−	2.70204i	−0.740901	−	1.10310i
$7$			3.97452i			1.50223i	0.660174	+	0.751113i	$0.270483\pi$
$7$			3.97452i			1.50223i	−0.660174	+	0.751113i	$0.729517\pi$
$8$	−0.571733	−	2.77004i	−0.202138	−	0.979357i
$9$	−2.29731			−0.765770
$10$	−2.45148	−	1.99756i	−0.775227	−	0.631683i
$11$	0.316459	+	0.316459i	0.0954161	+	0.0954161i	0.753204	−	0.657787i	$-0.228508\pi$
$11$	0.316459	+	0.316459i	0.0954161	+	0.0954161i	−0.657787	+	0.753204i	$0.728508\pi$
$12$	−4.26118	−	1.74115i	−1.23010	−	0.502627i
$13$	1.77966	−	1.77966i	0.493588	−	0.493588i	−0.415847	−	0.909435i	$-0.636515\pi$
$13$	1.77966	−	1.77966i	0.493588	−	0.493588i	0.909435	+	0.415847i	$0.136515\pi$
$14$	3.13395	+	4.66604i	0.837584	+	1.24705i
$15$	−4.92325	+	1.49939i	−1.27118	+	0.387141i
$16$	−2.85542	−	2.80118i	−0.713854	−	0.700295i
$17$	3.27595	+	2.50362i	0.794535	+	0.607218i
$17$	3.27595	+	2.50362i	0.794535	+	0.607218i
$18$	−2.69702	+	1.81145i	−0.635693	+	0.426964i
$19$			2.82964i			0.649163i	0.945858	+	0.324582i	$0.105223\pi$
$19$			2.82964i			0.649163i	−0.945858	+	0.324582i	$0.894777\pi$
$20$	−4.45311	−	0.412089i	−0.995746	−	0.0921458i
$21$	9.14770			1.99619
$22$	0.621051	+	0.121988i	0.132409	+	0.0260079i
$23$	−0.996717			−0.207830			−0.103915	−	0.994586i	$-0.533137\pi$
$23$	−0.996717			−0.207830			−0.103915	+	0.994586i	$0.533137\pi$
$24$	−6.37549	+	1.31589i	−1.30139	+	0.268606i
$25$	−4.15120	+	2.78702i	−0.830241	+	0.557405i
$26$	0.686018	−	3.49258i	0.134539	−	0.684950i
$27$		−	1.61730i		−	0.311250i
$28$	7.35845	+	3.00672i	1.39062	+	0.568217i
$29$	0.0246430	−	0.0246430i	0.00457608	−	0.00457608i	−0.704815	−	0.709391i	$-0.748970\pi$
$29$	0.0246430	−	0.0246430i	0.00457608	−	0.00457608i	0.709391	+	0.704815i	$0.248970\pi$
$30$	−4.59755	+	5.64230i	−0.839395	+	1.03014i
$31$	−3.68484	+	3.68484i	−0.661817	+	0.661817i	−0.955808	−	0.293991i	$-0.905016\pi$
$31$	−3.68484	+	3.68484i	−0.661817	+	0.661817i	0.293991	+	0.955808i	$0.405016\pi$
$32$	−5.56099	−	1.03702i	−0.983053	−	0.183322i
$33$	0.728359	−	0.728359i	0.126791	−	0.126791i
$34$	5.82007	+	0.356101i	0.998133	+	0.0610709i
$35$	8.50175	−	2.58923i	1.43706	−	0.437660i
$36$	−1.73791	+	4.25325i	−0.289652	+	0.708876i
$37$		−	1.58941i		−	0.261298i	−0.991429	−	0.130649i	$-0.958294\pi$
$37$		−	1.58941i		−	0.261298i	0.991429	−	0.130649i	$-0.0417060\pi$
$38$	2.23120	+	3.32196i	0.361948	+	0.538893i
$39$	−4.09604	−	4.09604i	−0.655891	−	0.655891i
$40$	−5.55284	+	3.02754i	−0.877981	+	0.478696i
$41$	6.11435	−	6.11435i	0.954901	−	0.954901i	−0.0441253	−	0.999026i	$-0.514050\pi$
$41$	6.11435	−	6.11435i	0.954901	−	0.954901i	0.999026	+	0.0441253i	$0.0140501\pi$
$42$	10.7393	−	7.21307i	1.65711	−	1.11300i
$43$	4.17559	−	4.17559i	0.636772	−	0.636772i	−0.312986	−	0.949758i	$-0.601329\pi$
$43$	4.17559	−	4.17559i	0.636772	−	0.636772i	0.949758	+	0.312986i	$0.101329\pi$
$44$	0.825296	−	0.346494i	0.124418	−	0.0522359i
$45$	1.49660	+	4.91410i	0.223100	+	0.732550i
$46$	−1.17013	+	0.785922i	−0.172527	+	0.115878i
$47$	6.91175	−	6.91175i	1.00818	−	1.00818i	0.00821671	−	0.999966i	$-0.497385\pi$
$47$	6.91175	−	6.91175i	1.00818	−	1.00818i	0.999966	−	0.00821671i	$-0.00261549\pi$
$48$	−6.44716	+	6.57199i	−0.930567	+	0.948585i
$49$	−8.79678			−1.25668
$50$	−2.67587	+	6.54521i	−0.378425	+	0.925632i
$51$	5.76231	−	7.53989i	0.806885	−	1.05580i
$52$	−1.94856	−	4.64118i	−0.270216	−	0.643616i
$53$	9.08331	+	9.08331i	1.24769	+	1.24769i	0.956738	+	0.290950i	$0.0939713\pi$
$53$	9.08331	+	9.08331i	1.24769	+	1.24769i	0.290950	+	0.956738i	$0.406029\pi$
$54$	−1.27526	−	1.89870i	−0.173541	−	0.258380i
$55$	0.470767	−	0.883087i	0.0634782	−	0.119075i
$56$	11.0096	−	2.27236i	1.47122	−	0.303657i
$57$	6.51266			0.862623
$58$	0.00949931	−	0.0483618i	0.00124732	−	0.00635022i
$59$		−	4.28205i		−	0.557475i	−0.960367	−	0.278738i	$-0.910084\pi$
$59$		−	4.28205i		−	0.557475i	0.960367	−	0.278738i	$-0.0899159\pi$
$60$	−0.948458	+	10.2492i	−0.122445	+	1.32317i
$61$	−9.74339	+	9.74339i	−1.24751	+	1.24751i	−0.290699	+	0.956815i	$0.593888\pi$
$61$	−9.74339	+	9.74339i	−1.24751	+	1.24751i	−0.956815	+	0.290699i	$0.906112\pi$
$62$	−1.42042	+	7.23150i	−0.180394	+	0.918402i
$63$		−	9.13069i		−	1.15036i
$64$	−7.34624	+	3.16745i	−0.918280	+	0.395931i
$65$	−4.96617	−	2.64743i	−0.615978	−	0.328373i
$66$	0.280766	−	1.42940i	0.0345599	−	0.175948i
$67$	5.61205	−	5.61205i	0.685621	−	0.685621i	−0.275640	−	0.961261i	$-0.588890\pi$
$67$	5.61205	−	5.61205i	0.685621	−	0.685621i	0.961261	+	0.275640i	$0.0888898\pi$
$68$	7.11349	−	4.17113i	0.862637	−	0.505824i
$69$			2.29403i			0.276169i
$70$	7.93932	−	9.74346i	0.948931	−	1.16457i
$71$	−10.5354	+	10.5354i	−1.25032	+	1.25032i	−0.294749	+	0.955575i	$0.595236\pi$
$71$	−10.5354	+	10.5354i	−1.25032	+	1.25032i	−0.955575	+	0.294749i	$0.904764\pi$
$72$	1.31345	+	6.36364i	0.154791	+	0.749962i
$73$	6.55715			0.767456			0.383728	−	0.923446i	$-0.374640\pi$
$73$	6.55715			0.767456			0.383728	+	0.923446i	$0.374640\pi$
$74$	−1.25327	−	1.86595i	−0.145690	−	0.216913i
$75$	6.41458	+	9.55436i	0.740692	+	1.10324i
$76$	5.23881	+	2.14062i	0.600932	+	0.245546i
$77$	−1.25777	+	1.25777i	−0.143337	+	0.143337i
$78$	−8.03847	−	1.57893i	−0.910178	−	0.178779i
$79$	−9.90208	+	9.90208i	−1.11407	+	1.11407i	−0.121477	+	0.992594i	$0.538763\pi$
$79$	−9.90208	+	9.90208i	−1.11407	+	1.11407i	−0.992594	+	0.121477i	$0.961237\pi$
$80$	−4.13172	+	7.93277i	−0.461940	+	0.886911i
$81$	−10.6143			−1.17937
$82$	2.35694	−	11.9994i	0.260281	−	1.32511i
$83$	−5.59012	+	5.59012i	−0.613596	+	0.613596i	−0.943881	−	0.330285i	$-0.892855\pi$
$83$	−5.59012	+	5.59012i	−0.613596	+	0.613596i	0.330285	+	0.943881i	$0.392855\pi$
$84$	6.92024	−	16.9361i	0.755060	−	1.84788i
$85$	3.22127	−	8.63848i	0.349396	−	0.936975i
$86$	1.60960	−	8.19460i	0.173567	−	0.883647i
$87$	−0.0567180	−	0.0567180i	−0.00608081	−	0.00608081i
$88$	0.695675	−	1.05754i	0.0741592	−	0.112734i
$89$		−	2.62516i		−	0.278267i	−0.990274	−	0.139133i	$-0.955568\pi$
$89$		−	2.62516i		−	0.278267i	0.990274	−	0.139133i	$-0.0444317\pi$
$90$	5.63181	+	4.58901i	0.593645	+	0.483724i
$91$	7.07327	+	7.07327i	0.741481	+	0.741481i
$92$	−0.754016	+	1.84533i	−0.0786116	+	0.192389i
$93$	8.48099	+	8.48099i	0.879437	+	0.879437i
$94$	2.66433	−	13.5643i	0.274804	−	1.39905i
$95$	6.05278	−	1.84339i	0.621002	−	0.189128i
$96$	−2.38680	+	12.7991i	−0.243602	+	1.30630i
$97$			11.6243i			1.18027i	0.807304	+	0.590136i	$0.200926\pi$
$97$			11.6243i			1.18027i	−0.807304	+	0.590136i	$0.799074\pi$
$98$	−10.3273	+	6.93636i	−1.04322	+	0.700679i
$99$	−0.727005	−	0.727005i	−0.0730667	−	0.0730667i
$100$	2.01953	+	9.79395i	0.201953	+	0.979395i
$101$	11.0756			1.10206			0.551030	−	0.834485i	$-0.314235\pi$
$101$	11.0756			1.10206			0.551030	+	0.834485i	$0.314235\pi$
$102$	0.819599	−	13.3954i	0.0811524	−	1.32634i
$103$	8.32250	+	8.32250i	0.820041	+	0.820041i	0.986113	−	0.166073i	$-0.0531087\pi$
$103$	8.32250	+	8.32250i	0.820041	+	0.820041i	−0.166073	+	0.986113i	$0.553109\pi$
$104$	−5.94721	−	3.91223i	−0.583172	−	0.383626i
$105$	−5.95935	−	19.5675i	−0.581573	−	1.90960i
$106$	17.8260	+	3.50141i	1.73141	+	0.340087i
$107$	−14.1163			−1.36468			−0.682338	−	0.731037i	$-0.739037\pi$
$107$	−14.1163			−1.36468			−0.682338	+	0.731037i	$0.739037\pi$
$108$	−2.99429	−	1.22349i	−0.288126	−	0.117730i
$109$	−7.15593	−	7.15593i	−0.685414	−	0.685414i	0.275801	−	0.961215i	$-0.411057\pi$
$109$	−7.15593	−	7.15593i	−0.685414	−	0.685414i	−0.961215	+	0.275801i	$0.911057\pi$
$110$	−0.143649	−	1.40794i	−0.0136964	−	0.134242i
$111$	−3.65817			−0.347218
$112$	11.1333	−	11.3489i	1.05200	−	1.07237i
$113$			5.59353i			0.526195i	0.964769	+	0.263097i	$0.0847441\pi$
$113$			5.59353i			0.526195i	−0.964769	+	0.263097i	$0.915256\pi$
$114$	7.64579	−	5.13530i	0.716094	−	0.480965i
$115$	0.649319	+	2.13204i	0.0605493	+	0.198814i
$116$	−0.0269818	−	0.0642666i	−0.00250519	−	0.00596700i
$117$	−4.08842	+	4.08842i	−0.377975	+	0.377975i
$118$	−3.37644	−	5.02708i	−0.310827	−	0.462780i
$119$	−9.95070	+	13.0203i	−0.912179	+	1.19357i
$120$	6.96815	+	12.7803i	0.636102	+	1.16668i
$121$		−	10.7997i		−	0.981792i
$122$	−3.75586	+	19.1214i	−0.340040	+	1.73117i
$123$	−14.0727	−	14.0727i	−1.26889	−	1.26889i
$124$	4.03456	+	9.60972i	0.362314	+	0.862979i
$125$	8.66596	+	7.06407i	0.775107	+	0.631830i
$126$	−7.19966	−	10.7193i	−0.641396	−	0.954954i
$127$	−10.7367	−	10.7367i	−0.952732	−	0.952732i	0.0462005	−	0.998932i	$-0.485289\pi$
$127$	−10.7367	−	10.7367i	−0.952732	−	0.952732i	−0.998932	+	0.0462005i	$0.985289\pi$
$128$	−6.12684	+	9.51114i	−0.541541	+	0.840674i
$129$	−9.61050	−	9.61050i	−0.846157	−	0.846157i
$130$	−7.91776	+	0.807831i	−0.694434	+	0.0708514i
$131$	2.47151	−	2.47151i	0.215937	−	0.215937i	−0.590847	−	0.806784i	$-0.701206\pi$
$131$	2.47151	−	2.47151i	0.215937	−	0.215937i	0.806784	+	0.590847i	$0.201206\pi$
$132$	−0.797486	−	1.89949i	−0.0694122	−	0.165330i
$133$	−11.2464			−0.975190
$134$	2.16332	−	11.0136i	0.186882	−	0.951434i
$135$	−3.45952	+	1.05361i	−0.297748	+	0.0906800i
$136$	5.06217	−	10.5059i	0.434077	−	0.900876i
$137$	1.31722	+	1.31722i	0.112538	+	0.112538i	0.761133	−	0.648595i	$-0.224643\pi$
$137$	1.31722	+	1.31722i	0.112538	+	0.112538i	−0.648595	+	0.761133i	$0.724643\pi$
$138$	1.80887	+	2.69317i	0.153981	+	0.229258i
$139$	9.02417	+	9.02417i	0.765420	+	0.765420i	0.977296	−	0.211876i	$-0.0679574\pi$
$139$	9.02417	+	9.02417i	0.765420	+	0.765420i	−0.211876	+	0.977296i	$0.567957\pi$
$140$	1.63785	−	17.6990i	0.138424	−	1.49584i
$141$	−15.9080	−	15.9080i	−1.33970	−	1.33970i
$142$	−4.06117	+	20.6757i	−0.340805	+	1.73507i
$143$	1.12638			0.0941924
$144$	6.55977	+	6.43517i	0.546648	+	0.536264i
$145$	−0.0687668	−	0.0366591i	−0.00571077	−	0.00304437i
$146$	7.69802	−	5.17038i	0.637092	−	0.427904i
$147$			20.2466i			1.66991i
$148$	−2.94265	−	1.20239i	−0.241884	−	0.0988358i
$149$			10.2039i			0.835935i	0.908462	+	0.417968i	$0.137257\pi$
$149$			10.2039i			0.835935i	−0.908462	+	0.417968i	$0.862743\pi$
$150$	15.0644	+	6.15875i	1.23000	+	0.502860i
$151$	−0.607245			−0.0494169			−0.0247084	−	0.999695i	$-0.507866\pi$
$151$	−0.607245			−0.0494169			−0.0247084	+	0.999695i	$0.507866\pi$
$152$	7.83820	−	1.61780i	0.635762	−	0.131221i
$153$	−7.52588	−	5.75160i	−0.608431	−	0.464989i
$154$	−0.484843	+	2.46838i	−0.0390698	+	0.198908i
$155$	10.2826	+	5.48160i	0.825921	+	0.440292i
$156$	−10.6821	+	4.48478i	−0.855251	+	0.359070i
$157$	1.53399	+	1.53399i	0.122425	+	0.122425i	0.765665	−	0.643240i	$-0.222410\pi$
$157$	1.53399	+	1.53399i	0.122425	+	0.122425i	−0.643240	+	0.765665i	$0.722410\pi$
$158$	−3.81703	+	19.4328i	−0.303667	+	1.54599i
$159$	20.9060	−	20.9060i	1.65796	−	1.65796i
$160$	1.40449	+	12.5709i	0.111034	+	0.993817i
$161$		−	3.96147i		−	0.312207i
$162$	−12.4611	+	8.36949i	−0.979034	+	0.657570i
$163$	−9.03099			−0.707362			−0.353681	−	0.935366i	$-0.615070\pi$
$163$	−9.03099			−0.707362			−0.353681	+	0.935366i	$0.615070\pi$
$164$	−6.69464	−	15.9456i	−0.522764	−	1.24515i
$165$	−2.03250	−	1.08351i	−0.158230	−	0.0843513i
$166$	−2.15487	+	10.9706i	−0.167250	+	0.851485i
$167$	16.9125			1.30873			0.654363	−	0.756181i	$-0.272937\pi$
$167$	16.9125			1.30873			0.654363	+	0.756181i	$0.272937\pi$
$168$	−5.23004	−	25.3395i	−0.403507	−	1.95498i
$169$			6.66565i			0.512742i
$170$	−3.02981	−	12.6815i	−0.232376	−	0.972626i
$171$		−	6.50055i		−	0.497109i
$172$	−4.57189	−	10.8896i	−0.348603	−	0.830321i
$173$	−8.41677			−0.639915			−0.319958	−	0.947432i	$-0.603669\pi$
$173$	−8.41677			−0.639915			−0.319958	+	0.947432i	$0.603669\pi$
$174$	−0.111309	−	0.0218635i	−0.00843832	−	0.00165747i
$175$	−11.0771	−	16.4990i	−0.837348	−	1.24721i
$176$	−0.0171640	−	1.79008i	−0.00129379	−	0.134933i
$177$	−9.85551			−0.740786
$178$	−2.06997	−	3.08191i	−0.155151	−	0.230999i
$179$		−	7.70745i		−	0.576082i	−0.957618	−	0.288041i	$-0.906996\pi$
$179$		−	7.70745i		−	0.576082i	0.957618	−	0.288041i	$-0.0930039\pi$
$180$	10.2302	+	0.946695i	0.762512	+	0.0705625i
$181$	−4.24380	+	4.24380i	−0.315440	+	0.315440i	−0.847012	−	0.531573i	$-0.821601\pi$
$181$	−4.24380	+	4.24380i	−0.315440	+	0.315440i	0.531573	+	0.847012i	$0.321601\pi$
$182$	13.8813	+	2.72659i	1.02895	+	0.202108i
$183$	22.4253	+	22.4253i	1.65772	+	1.65772i
$184$	0.569856	+	2.76095i	0.0420103	+	0.203540i
$185$	−3.39986	+	1.03544i	−0.249962	+	0.0761267i
$186$	16.6439	+	3.26923i	1.22039	+	0.239712i
$187$	0.244411	+	1.82900i	0.0178731	+	0.133750i
$188$	−7.56773	−	18.0252i	−0.551933	−	1.31462i
$189$	6.42801			0.467569
$190$	5.65236	−	6.93680i	0.410065	−	0.503249i
$191$		−	2.55682i		−	0.185005i	−0.995712	−	0.0925025i	$-0.970513\pi$
$191$		−	2.55682i		−	0.185005i	0.995712	−	0.0925025i	$-0.0294866\pi$
$192$	7.29016	+	16.9080i	0.526122	+	1.22023i
$193$		−	17.2114i		−	1.23891i	−0.785034	−	0.619453i	$-0.787355\pi$
$193$		−	17.2114i		−	1.23891i	0.785034	−	0.619453i	$-0.212645\pi$
$194$	9.16592	+	13.6468i	0.658075	+	0.979786i
$195$	−6.09329	+	11.4301i	−0.436350	+	0.818526i
$196$	−6.65477	+	16.2864i	−0.475340	+	1.16332i
$197$	−8.59946			−0.612686			−0.306343	−	0.951921i	$-0.599105\pi$
$197$	−8.59946			−0.612686			−0.306343	+	0.951921i	$0.599105\pi$
$198$	−1.42675	−	0.280244i	−0.101395	−	0.0199161i
$199$	13.0434	+	13.0434i	0.924622	+	0.924622i	0.997352	−	0.0727295i	$-0.0231710\pi$
$199$	13.0434	+	13.0434i	0.924622	+	0.924622i	−0.0727295	+	0.997352i	$0.523171\pi$
$200$	10.0935	+	9.90557i	0.713722	+	0.700429i
$201$	−12.9166	−	12.9166i	−0.911068	−	0.911068i
$202$	13.0026	−	8.73321i	0.914859	−	0.614466i
$203$	0.0979439	+	0.0979439i	0.00687431	+	0.00687431i
$204$	−9.60023	−	16.3723i	−0.672150	−	1.14629i
$205$	−17.0622	−	9.09575i	−1.19168	−	0.635275i
$206$	16.3329	+	3.20814i	1.13797	+	0.223522i
$207$	2.28977			0.159150
$208$	−10.0668	+	0.0965244i	−0.698006	+	0.00669276i
$209$	−0.895465	+	0.895465i	−0.0619406	+	0.0619406i
$210$	−22.4254	−	18.2731i	−1.54750	−	1.26096i
$211$	−19.7527	−	19.7527i	−1.35984	−	1.35984i	−0.874113	−	0.485722i	$-0.838557\pi$
$211$	−19.7527	−	19.7527i	−1.35984	−	1.35984i	−0.485722	−	0.874113i	$-0.661443\pi$
$212$	23.6884	−	9.94538i	1.62693	−	0.683051i
$213$	24.2482	+	24.2482i	1.66146	+	1.66146i
$214$	−16.5724	+	11.1309i	−1.13287	+	0.760891i
$215$	−11.6521	−	6.21164i	−0.794666	−	0.423631i
$216$	−4.48000	+	0.924666i	−0.304825	+	0.0629156i
$217$	−14.6455	−	14.6455i	−0.994199	−	0.994199i
$218$	−14.0435	−	2.75845i	−0.951147	−	0.186826i
$219$		−	15.0919i		−	1.01981i
$220$	−1.27882	−	1.53964i	−0.0862179	−	0.103802i
$221$	10.2857	−	1.37448i	0.691888	−	0.0924575i
$222$	−4.29465	+	2.88451i	−0.288238	+	0.193596i
$223$	−12.5309	+	12.5309i	−0.839133	+	0.839133i	−0.988745	−	0.149612i	$-0.952198\pi$
$223$	−12.5309	+	12.5309i	−0.839133	+	0.839133i	0.149612	+	0.988745i	$0.452198\pi$
$224$	4.12167	−	22.1022i	0.275391	−	1.47677i
$225$	9.53660	−	6.40266i	0.635773	−	0.426844i
$226$	4.41056	+	6.56674i	0.293386	+	0.436813i
$227$		−	9.38343i		−	0.622800i	−0.950279	−	0.311400i	$-0.899202\pi$
$227$		−	9.38343i		−	0.622800i	0.950279	−	0.311400i	$-0.100798\pi$
$228$	4.92682	−	12.0576i	0.326287	−	0.798533i
$229$	−25.8056			−1.70528			−0.852641	−	0.522497i	$-0.825001\pi$
$229$	−25.8056			−1.70528			−0.852641	+	0.522497i	$0.825001\pi$
$230$	2.44343	+	1.99100i	0.161115	+	0.131283i
$231$	2.89488	+	2.89488i	0.190469	+	0.190469i
$232$	−0.0823512	−	0.0541728i	−0.00540662	−	0.00355662i
$233$	15.4422			1.01165			0.505825	−	0.862636i	$-0.331188\pi$
$233$	15.4422			1.01165			0.505825	+	0.862636i	$0.331188\pi$
$234$	−1.57599	+	8.02353i	−0.103026	+	0.524514i
$235$	−19.2874	−	10.2820i	−1.25817	−	0.670722i
$236$	−7.92781	−	3.23937i	−0.516057	−	0.210865i
$237$	22.7905	+	22.7905i	1.48040	+	1.48040i
$238$	−1.41533	+	23.1320i	−0.0917423	+	1.49942i
$239$	−18.3551			−1.18729			−0.593647	−	0.804725i	$-0.702313\pi$
$239$	−18.3551			−1.18729			−0.593647	+	0.804725i	$0.702313\pi$
$240$	18.2580	+	9.50952i	1.17855	+	0.613837i
$241$	−7.57434	−	7.57434i	−0.487906	−	0.487906i	0.419739	−	0.907645i	$-0.362122\pi$
$241$	−7.57434	−	7.57434i	−0.487906	−	0.487906i	−0.907645	+	0.419739i	$0.862122\pi$
$242$	−8.51569	−	12.6787i	−0.547409	−	0.815020i
$243$			19.5778i			1.25592i
$244$	10.6681	+	25.4099i	0.682956	+	1.62670i
$245$	5.73074	+	18.8169i	0.366123	+	1.20217i
$246$	−27.6177	−	5.42472i	−1.76084	−	0.345867i
$247$	5.03578	+	5.03578i	0.320419	+	0.320419i
$248$	12.3139	+	8.10041i	0.781934	+	0.514377i
$249$	12.8662	+	12.8662i	0.815360	+	0.815360i
$250$	15.7438	+	1.45993i	0.995728	+	0.0923340i
$251$			4.50448i			0.284320i	0.989844	+	0.142160i	$0.0454048\pi$
$251$			4.50448i			0.284320i	−0.989844	+	0.142160i	$0.954595\pi$
$252$	−16.9046	−	6.90737i	−1.06489	−	0.435123i
$253$	−0.315420	−	0.315420i	−0.0198303	−	0.0198303i
$254$	−21.0709	−	4.13877i	−1.32210	−	0.259690i
$255$	−19.8822	−	7.41404i	−1.24507	−	0.464285i
$256$	0.306800	+	15.9971i	0.0191750	+	0.999816i
$257$	−16.6800	+	16.6800i	−1.04047	+	1.04047i	−0.0413246	+	0.999146i	$0.513158\pi$
$257$	−16.6800	+	16.6800i	−1.04047	+	1.04047i	−0.999146	+	0.0413246i	$0.986842\pi$
$258$	−18.8606	−	3.70463i	−1.17421	−	0.230640i
$259$	6.31714			0.392528
$260$	−8.65838	+	7.19163i	−0.536970	+	0.446006i
$261$	−0.0566125	+	0.0566125i	−0.00350423	+	0.00350423i
$262$	0.952712	−	4.85034i	0.0588588	−	0.299655i
$263$	19.8644	−	19.8644i	1.22489	−	1.22489i	0.259020	−	0.965872i	$-0.416600\pi$
$263$	19.8644	−	19.8644i	1.22489	−	1.22489i	0.965872	−	0.259020i	$-0.0833996\pi$
$264$	−2.43401	−	1.60116i	−0.149803	−	0.0985444i
$265$	13.5124	−	25.3472i	0.830060	−	1.55707i
$266$	−13.2032	+	8.86794i	−0.809540	+	0.543728i
$267$	−6.04205			−0.369767
$268$	−6.14467	−	14.6357i	−0.375345	−	0.894017i
$269$	4.03411	−	4.03411i	0.245964	−	0.245964i	−0.573348	−	0.819312i	$-0.694356\pi$
$269$	4.03411	−	4.03411i	0.245964	−	0.245964i	0.819312	+	0.573348i	$0.194356\pi$
$270$	−3.23066	+	3.96479i	−0.196612	+	0.241290i
$271$		−	9.49507i		−	0.576785i	−0.957512	−	0.288392i	$-0.906879\pi$
$271$		−	9.49507i		−	0.576785i	0.957512	−	0.288392i	$-0.0931207\pi$
$272$	−2.34111	−	16.3254i	−0.141951	−	0.989874i
$273$	16.2798	−	16.2798i	0.985296	−	0.985296i
$274$	2.58505	+	0.507760i	0.156169	+	0.0306749i
$275$	−2.19567	−	0.431708i	−0.132404	−	0.0260329i
$276$	4.24719	+	1.73543i	0.255651	+	0.104461i
$277$		−	13.4769i		−	0.809749i	−0.914372	−	0.404875i	$-0.867315\pi$
$277$		−	13.4769i		−	0.809749i	0.914372	−	0.404875i	$-0.132685\pi$
$278$	17.7099	+	3.47862i	1.06217	+	0.208633i
$279$	8.46522	−	8.46522i	0.506799	−	0.506799i
$280$	−12.0330	−	22.0698i	−0.719110	−	1.31893i
$281$		−	5.47956i		−	0.326883i	−0.986553	−	0.163442i	$-0.947740\pi$
$281$		−	5.47956i		−	0.326883i	0.986553	−	0.163442i	$-0.0522596\pi$
$282$	−31.2195	−	6.13218i	−1.85909	−	0.365166i
$283$	17.6570			1.04960			0.524800	−	0.851226i	$-0.324140\pi$
$283$	17.6570			1.04960			0.524800	+	0.851226i	$0.324140\pi$
$284$	11.5353	+	27.4754i	0.684494	+	1.63036i
$285$	−4.24272	−	13.9310i	−0.251317	−	0.825201i
$286$	1.32235	−	0.888161i	0.0781925	−	0.0525181i
$287$	24.3016	+	24.3016i	1.43448	+	1.43448i
$288$	12.7753	+	2.38237i	0.752792	+	0.140382i
$289$	4.46373	+	16.4035i	0.262572	+	0.964912i
$290$	−0.109638	+	0.0111861i	−0.00643814	+	0.000656868i
$291$	26.7544			1.56837
$292$	4.96048	−	12.1399i	0.290290	−	0.710437i
$293$	−0.172396	+	0.172396i	−0.0100715	+	0.0100715i	−0.712125	−	0.702053i	$-0.752267\pi$
$293$	−0.172396	+	0.172396i	−0.0100715	+	0.0100715i	0.702053	+	0.712125i	$0.252267\pi$
$294$	15.9647	+	23.7693i	0.931078	+	1.38625i
$295$	−9.15958	+	2.78957i	−0.533291	+	0.162415i
$296$	−4.40273	+	0.908719i	−0.255904	+	0.0528182i
$297$	0.511811	−	0.511811i	0.0296983	−	0.0296983i
$298$	8.04588	+	11.9793i	0.466085	+	0.693939i
$299$	−1.77381	+	1.77381i	−0.102582	+	0.102582i
$300$	22.5416	−	4.64813i	1.30144	−	0.268360i
$301$	16.5960	+	16.5960i	0.956576	+	0.956576i
$302$	−0.712899	+	0.478819i	−0.0410227	+	0.0275530i
$303$		−	25.4914i		−	1.46444i
$304$	7.92632	−	8.07979i	0.454605	−	0.463408i
$305$	27.1892	+	14.4943i	1.55685	+	0.829944i
$306$	−13.3705	−	0.818075i	−0.764340	−	0.0467662i
$307$	−6.07697	+	6.07697i	−0.346831	+	0.346831i	−0.858928	−	0.512097i	$-0.828869\pi$
$307$	−6.07697	+	6.07697i	−0.346831	+	0.346831i	0.512097	+	0.858928i	$0.328869\pi$
$308$	1.37714	+	3.28015i	0.0784701	+	0.186904i
$309$	19.1550	−	19.1550i	1.08969	−	1.08969i
$310$	16.3940	−	1.67264i	0.931117	−	0.0949997i
$311$	16.1494	−	16.1494i	0.915747	−	0.915747i	−0.0809696	−	0.996717i	$-0.525802\pi$
$311$	16.1494	−	16.1494i	0.915747	−	0.915747i	0.996717	+	0.0809696i	$0.0258017\pi$
$312$	−9.00434	+	13.6880i	−0.509771	+	0.774932i
$313$		−	13.3779i		−	0.756162i	−0.925773	−	0.378081i	$-0.876584\pi$
$313$		−	13.3779i		−	0.756162i	0.925773	−	0.378081i	$-0.123416\pi$
$314$	3.01045	+	0.591317i	0.169889	+	0.0333699i
$315$	−19.5312	+	5.94827i	−1.10046	+	0.335147i
$316$	10.8419	+	25.8237i	0.609902	+	1.45270i
$317$	−8.53329			−0.479277			−0.239639	−	0.970862i	$-0.577029\pi$
$317$	−8.53329			−0.479277			−0.239639	+	0.970862i	$0.577029\pi$
$318$	8.05881	−	41.0281i	0.451916	−	2.30074i
$319$	0.0155970			0.000873264
$320$	11.5611	+	13.6506i	0.646288	+	0.763094i
$321$			32.4899i			1.81341i
$322$	−3.12366	−	4.65072i	−0.174075	−	0.259174i
$323$	−7.08435	+	9.26975i	−0.394184	+	0.515783i
$324$	−8.02971	+	19.6514i	−0.446095	+	1.09174i
$325$	−2.42777	+	12.3477i	−0.134669	+	0.684925i
$326$	−10.6023	+	7.12104i	−0.587206	+	0.394398i
$327$	−16.4700	+	16.4700i	−0.910794	+	0.910794i
$328$	−20.4328	−	13.4412i	−1.12821	−	0.742167i
$329$	27.4709	+	27.4709i	1.51452	+	1.51452i
$330$	−3.24050	+	0.330620i	−0.178384	+	0.0182001i
$331$	18.7828			1.03240			0.516198	−	0.856470i	$-0.327347\pi$
$331$	18.7828			1.03240			0.516198	+	0.856470i	$0.327347\pi$
$332$	6.12067	+	14.5785i	0.335915	+	0.800100i
$333$			3.65137i			0.200094i
$334$	19.8550	−	13.3357i	1.08642	−	0.729695i
$335$	−15.6606	−	8.34852i	−0.855627	−	0.456129i
$336$	−26.1205	−	25.6243i	−1.42499	−	1.39792i
$337$		−	5.01734i		−	0.273312i	−0.990619	−	0.136656i	$-0.956364\pi$
$337$		−	5.01734i		−	0.273312i	0.990619	−	0.136656i	$-0.0436355\pi$
$338$	5.25594	+	7.82540i	0.285885	+	0.425645i
$339$	12.8740			0.699220
$340$	−13.5565	−	12.4989i	−0.735202	−	0.677848i
$341$	−2.33220			−0.126296
$342$	−5.12576	−	7.63157i	−0.277169	−	0.412668i
$343$		−	7.14135i		−	0.385597i
$344$	−13.9539	−	9.17924i	−0.752343	−	0.494911i
$345$	4.90708	−	1.49447i	0.264189	−	0.0804593i
$346$	−9.88120	+	6.63672i	−0.531216	+	0.356792i
$347$		−	14.4698i		−	0.776779i	−0.921495	−	0.388390i	$-0.873031\pi$
$347$		−	14.4698i		−	0.776779i	0.921495	−	0.388390i	$-0.126969\pi$
$348$	−0.147915	+	0.0621009i	−0.00792909	+	0.00332896i
$349$	−17.7868			−0.952107			−0.476053	−	0.879416i	$-0.657933\pi$
$349$	−17.7868			−0.952107			−0.476053	+	0.879416i	$0.657933\pi$
$350$	−26.0140	−	10.6353i	−1.39051	−	0.568480i
$351$	−2.87825	−	2.87825i	−0.153629	−	0.153629i
$352$	−1.43165	−	2.08800i	−0.0763072	−	0.111291i
$353$	−6.06103	+	6.06103i	−0.322596	+	0.322596i	−0.849762	−	0.527166i	$-0.823255\pi$
$353$	−6.06103	+	6.06103i	−0.322596	+	0.322596i	0.527166	+	0.849762i	$0.323255\pi$
$354$	−11.5703	+	7.77118i	−0.614952	+	0.413034i
$355$	29.3993	+	15.6726i	1.56035	+	0.831813i
$356$	−4.86025	−	1.98594i	−0.257593	−	0.105254i
$357$	29.9674	+	22.9024i	1.58605	+	1.21212i
$358$	−6.07741	−	9.04846i	−0.321201	−	0.478226i
$359$			35.1275i			1.85396i	0.375115	+	0.926978i	$0.377603\pi$
$359$			35.1275i			1.85396i	−0.375115	+	0.926978i	$0.622397\pi$
$360$	12.7566	−	6.95520i	0.672331	−	0.366571i
$361$	10.9932			0.578587
$362$	−1.63589	+	8.32847i	−0.0859806	+	0.437735i
$363$	−24.8565			−1.30463
$364$	18.4464	−	7.74458i	0.966856	−	0.405926i
$365$	−4.27171	−	14.0262i	−0.223591	−	0.734163i
$366$	44.0096	+	8.64444i	2.30042	+	0.451852i
$367$			11.5170i			0.601184i	0.953753	+	0.300592i	$0.0971842\pi$
$367$			11.5170i			0.601184i	−0.953753	+	0.300592i	$0.902816\pi$
$368$	2.84604	+	2.79198i	0.148360	+	0.145542i
$369$	−14.0465	+	14.0465i	−0.731234	+	0.731234i
$370$	−3.17494	+	3.89642i	−0.165057	+	0.202565i
$371$	−36.1018	+	36.1018i	−1.87431	+	1.87431i
$372$	22.1176	−	9.28589i	1.14675	−	0.481451i
$373$	−1.33651	+	1.33651i	−0.0692020	+	0.0692020i	−0.740861	−	0.671659i	$-0.765582\pi$
$373$	−1.33651	+	1.33651i	−0.0692020	+	0.0692020i	0.671659	+	0.740861i	$0.265582\pi$
$374$	1.72912	+	1.95451i	0.0894108	+	0.101065i
$375$	16.2586	−	19.9455i	0.839589	−	1.02998i
$376$	−23.0975	−	15.1942i	−1.19116	−	0.783579i
$377$		−	0.0877120i		−	0.00451740i
$378$	7.54641	−	5.06855i	0.388145	−	0.260698i
$379$	−2.52004	−	2.52004i	−0.129446	−	0.129446i	0.639416	−	0.768861i	$-0.279176\pi$
$379$	−2.52004	−	2.52004i	−0.129446	−	0.129446i	−0.768861	+	0.639416i	$0.779176\pi$
$380$	1.16606	−	12.6007i	0.0598176	−	0.646401i
$381$	−24.7116	+	24.7116i	−1.26601	+	1.26601i
$382$	−2.01608	−	3.00168i	−0.103152	−	0.153579i
$383$	25.2816	−	25.2816i	1.29183	−	1.29183i	0.358174	−	0.933655i	$-0.383399\pi$
$383$	25.2816	−	25.2816i	1.29183	−	1.29183i	0.933655	−	0.358174i	$-0.116601\pi$
$384$	21.8907	+	14.1015i	1.11711	+	0.719612i
$385$	3.50985	+	1.87107i	0.178878	+	0.0953587i
$386$	−13.5714	−	20.2060i	−0.690766	−	1.02846i
$387$	−9.59263	+	9.59263i	−0.487621	+	0.487621i
$388$	21.5214	+	8.79381i	1.09258	+	0.446438i
$389$	8.35286			0.423507			0.211753	−	0.977323i	$-0.432083\pi$
$389$	8.35286			0.423507			0.211753	+	0.977323i	$0.432083\pi$
$390$	1.85929	+	18.2234i	0.0941490	+	0.922779i
$391$	−3.26520	−	2.49540i	−0.165128	−	0.126198i
$392$	5.02941	+	24.3674i	0.254024	+	1.23074i
$393$	−5.68840	−	5.68840i	−0.286942	−	0.286942i
$394$	−10.0957	+	6.78077i	−0.508613	+	0.341610i
$395$	27.6320	+	14.7304i	1.39032	+	0.741167i
$396$	−1.89596	+	0.796003i	−0.0952756	+	0.0400007i
$397$	12.0104			0.602785			0.301393	−	0.953500i	$-0.402549\pi$
$397$	12.0104			0.602785			0.301393	+	0.953500i	$0.402549\pi$
$398$	25.5977	+	5.02794i	1.28310	+	0.252028i
$399$			25.8847i			1.29585i
$400$	19.6604	+	3.67015i	0.983018	+	0.183508i
$401$	−9.82899	+	9.82899i	−0.490836	+	0.490836i	−0.908570	−	0.417733i	$-0.862825\pi$
$401$	−9.82899	+	9.82899i	−0.490836	+	0.490836i	0.417733	+	0.908570i	$0.362825\pi$
$402$	−25.3489	−	4.97907i	−1.26429	−	0.248333i
$403$			13.1155i			0.653330i
$404$	8.37866	−	20.5054i	0.416854	−	1.02018i
$405$	6.91477	+	22.7047i	0.343598	+	1.12820i
$406$	0.192215	+	0.0377552i	0.00953947	+	0.00187376i
$407$	0.502984	−	0.502984i	0.0249320	−	0.0249320i
$408$	−24.1803	−	11.6510i	−1.19710	−	0.576812i
$409$		−	14.1372i		−	0.699041i	−0.936929	−	0.349521i	$-0.886344\pi$
$409$		−	14.1372i		−	0.699041i	0.936929	−	0.349521i	$-0.113656\pi$
$410$	−27.2030	+	2.77546i	−1.34346	+	0.137070i
$411$	3.03170	−	3.03170i	0.149543	−	0.149543i
$412$	21.7043	−	9.11237i	1.06929	−	0.448934i
$413$	17.0191			0.837454
$414$	2.68816	−	1.80551i	0.132116	−	0.0887358i
$415$	15.5994	+	8.31591i	0.765743	+	0.408212i
$416$	−11.7422	+	8.05110i	−0.575708	+	0.394738i
$417$	20.7699	−	20.7699i	1.01711	−	1.01711i
$418$	−0.345182	+	1.75735i	−0.0168834	+	0.0859548i
$419$	18.4011	−	18.4011i	0.898952	−	0.898952i	−0.0963919	−	0.995343i	$-0.530730\pi$
$419$	18.4011	−	18.4011i	0.898952	−	0.898952i	0.995343	+	0.0963919i	$0.0307302\pi$
$420$	−40.7357	−	3.76966i	−1.98770	−	0.183941i
$421$	8.02236			0.390986			0.195493	−	0.980705i	$-0.437369\pi$
$421$	8.02236			0.390986			0.195493	+	0.980705i	$0.437369\pi$
$422$	−38.7648	−	7.61424i	−1.88704	−	0.370656i
$423$	−15.8784	+	15.8784i	−0.772036	+	0.772036i
$424$	19.9679	−	30.3544i	0.969727	−	1.47414i
$425$	−20.5768	−	1.26290i	−0.998122	−	0.0612595i
$426$	47.5871	+	9.34713i	2.30560	+	0.452870i
$427$	−38.7253	−	38.7253i	−1.87405	−	1.87405i
$428$	−10.6790	+	26.1350i	−0.516188	+	1.26329i
$429$		−	2.59246i		−	0.125165i
$430$	−18.5774	+	1.89541i	−0.895881	+	0.0914046i
$431$	−4.01207	−	4.01207i	−0.193254	−	0.193254i	0.603846	−	0.797101i	$-0.293634\pi$
$431$	−4.01207	−	4.01207i	−0.193254	−	0.193254i	−0.797101	+	0.603846i	$0.793634\pi$
$432$	−4.53036	+	4.61808i	−0.217967	+	0.222187i
$433$	−5.90934	−	5.90934i	−0.283985	−	0.283985i	0.550711	−	0.834696i	$-0.314357\pi$
$433$	−5.90934	−	5.90934i	−0.283985	−	0.283985i	−0.834696	+	0.550711i	$0.814357\pi$
$434$	−28.7417	−	5.64550i	−1.37965	−	0.270993i
$435$	−0.0843741	+	0.158273i	−0.00404543	+	0.00758860i
$436$	−18.6620	+	7.83508i	−0.893748	+	0.375232i
$437$		−	2.82035i		−	0.134915i
$438$	−11.9001	−	17.7177i	−0.568609	−	0.846583i
$439$	−11.3464	−	11.3464i	−0.541535	−	0.541535i	0.382444	−	0.923979i	$-0.375082\pi$
$439$	−11.3464	−	11.3464i	−0.541535	−	0.541535i	−0.923979	+	0.382444i	$0.875082\pi$
$440$	−2.71534	−	0.799154i	−0.129449	−	0.0380982i
$441$	20.2089			0.962330
$442$	10.9915	−	9.72398i	0.522810	−	0.462523i
$443$	2.38905	+	2.38905i	0.113507	+	0.113507i	0.761579	−	0.648072i	$-0.224424\pi$
$443$	2.38905	+	2.38905i	0.113507	+	0.113507i	−0.648072	+	0.761579i	$0.724424\pi$
$444$	−2.76741	+	6.77277i	−0.131335	+	0.321421i
$445$	−5.61540	+	1.71019i	−0.266195	+	0.0810706i
$446$	−4.83039	+	24.5919i	−0.228726	+	1.16446i
$447$	23.4852			1.11081
$448$	−12.5891	−	29.1978i	−0.594778	−	1.37946i
$449$	−22.7355	−	22.7355i	−1.07295	−	1.07295i	−0.997121	−	0.0758322i	$-0.975839\pi$
$449$	−22.7355	−	22.7355i	−1.07295	−	1.07295i	−0.0758322	−	0.997121i	$-0.524161\pi$
$450$	6.14730	−	15.0364i	0.289786	−	0.708821i
$451$	3.86988			0.182226
$452$	10.3559	+	4.23150i	0.487100	+	0.199033i
$453$			1.39763i			0.0656663i
$454$	−7.39894	−	11.0160i	−0.347249	−	0.517008i
$455$	10.5223	−	19.7381i	0.493291	−	0.925338i
$456$	−3.72350	−	18.0403i	−0.174369	−	0.844815i
$457$	−15.5850	+	15.5850i	−0.729037	+	0.729037i	−0.970428	−	0.241391i	$-0.922396\pi$
$457$	−15.5850	+	15.5850i	−0.729037	+	0.729037i	0.241391	+	0.970428i	$0.422396\pi$
$458$	−30.2955	+	20.3480i	−1.41562	+	0.950800i
$459$	4.04912	−	5.29821i	0.188997	−	0.247299i
$460$	4.43849	+	0.410736i	0.206946	+	0.0191506i
$461$			4.68028i			0.217982i	0.994043	+	0.108991i	$0.0347620\pi$
$461$			4.68028i			0.217982i	−0.994043	+	0.108991i	$0.965238\pi$
$462$	5.68119	+	1.11591i	0.264313	+	0.0519168i
$463$	−17.3925	−	17.3925i	−0.808299	−	0.808299i	0.176077	−	0.984376i	$-0.443659\pi$
$463$	−17.3925	−	17.3925i	−0.808299	−	0.808299i	−0.984376	+	0.176077i	$0.943659\pi$
$464$	−0.139395	+	0.00133658i	−0.00647126	+	6.20490e-5i
$465$	12.6164	−	23.6664i	0.585071	−	1.09750i
$466$	18.1289	−	12.1763i	0.839806	−	0.564057i
$467$	−20.1704	−	20.1704i	−0.933373	−	0.933373i	0.0645420	−	0.997915i	$-0.479441\pi$
$467$	−20.1704	−	20.1704i	−0.933373	−	0.933373i	−0.997915	+	0.0645420i	$0.979441\pi$
$468$	4.47644	+	10.6622i	0.206924	+	0.492861i
$469$	22.3052	+	22.3052i	1.02996	+	1.02996i
$470$	−30.7507	+	3.13742i	−1.41842	+	0.144718i
$471$	3.53060	−	3.53060i	0.162682	−	0.162682i
$472$	−11.8614	+	2.44819i	−0.545967	+	0.112687i
$473$	2.64281			0.121517
$474$	44.7264	+	8.78523i	2.05435	+	0.403519i
$475$	−7.88626	−	11.7464i	−0.361847	−	0.538962i
$476$	16.5782	+	28.2727i	0.759862	+	1.29588i
$477$	−20.8672	−	20.8672i	−0.955442	−	0.955442i
$478$	−21.5487	+	14.4732i	−0.985615	+	0.661990i
$479$	−16.3879	−	16.3879i	−0.748780	−	0.748780i	0.225470	−	0.974250i	$-0.427608\pi$
$479$	−16.3879	−	16.3879i	−0.748780	−	0.748780i	−0.974250	+	0.225470i	$0.927608\pi$
$480$	28.9330	−	3.23255i	1.32061	−	0.147545i
$481$	−2.82861	−	2.82861i	−0.128973	−	0.128973i
$482$	−14.8647	−	2.91974i	−0.677066	−	0.132991i
$483$	−9.11767			−0.414868
$484$	−19.9947	−	8.16998i	−0.908848	−	0.371363i
$485$	24.8652	−	7.57277i	1.12907	−	0.343862i
$486$	15.4373	+	22.9842i	0.700252	+	1.04258i
$487$		−	15.3999i		−	0.697836i	−0.937153	−	0.348918i	$-0.886549\pi$
$487$		−	15.3999i		−	0.697836i	0.937153	−	0.348918i	$-0.113451\pi$
$488$	32.5602	+	21.4190i	1.47393	+	0.969591i
$489$			20.7856i			0.939959i
$490$	21.5652	+	17.5721i	0.974215	+	0.793826i
$491$	−8.21180			−0.370593			−0.185297	−	0.982683i	$-0.559325\pi$
$491$	−8.21180			−0.370593			−0.185297	+	0.982683i	$0.559325\pi$
$492$	−36.7003	+	15.4083i	−1.65458	+	0.694660i
$493$	0.142426	−	0.0190325i	0.00641454	−	0.000857179i
$494$	9.88272	+	1.94118i	0.444644	+	0.0873378i
$495$	−1.08150	+	2.02872i	−0.0486097	+	0.0911844i
$496$	20.8436	−	0.199857i	0.935908	−	0.00897385i
$497$	−41.8732	−	41.8732i	−1.87827	−	1.87827i
$498$	25.2498	+	4.95962i	1.13147	+	0.222246i
$499$	−5.92297	+	5.92297i	−0.265149	+	0.265149i	−0.827142	−	0.561993i	$-0.810035\pi$
$499$	−5.92297	+	5.92297i	−0.265149	+	0.265149i	0.561993	+	0.827142i	$0.310035\pi$
$500$	19.6343	−	10.7003i	0.878071	−	0.478530i
$501$		−	38.9255i		−	1.73906i
$502$	3.55183	+	5.28821i	0.158526	+	0.236024i
$503$	−0.409587			−0.0182626			−0.00913129	−	0.999958i	$-0.502907\pi$
$503$	−0.409587			−0.0182626			−0.00913129	+	0.999958i	$0.502907\pi$
$504$	−25.2924	+	5.22032i	−1.12661	+	0.232531i
$505$	−7.21527	−	23.6914i	−0.321075	−	1.05425i
$506$	−0.619012	−	0.121587i	−0.0275185	−	0.00540522i
$507$	15.3416			0.681343
$508$	−28.0004	+	11.7557i	−1.24232	+	0.521576i
$509$		−	3.63324i		−	0.161041i	−0.996753	−	0.0805203i	$-0.974342\pi$
$509$		−	3.63324i		−	0.161041i	0.996753	−	0.0805203i	$-0.0256582\pi$
$510$	−29.1876	+	6.97337i	−1.29245	+	0.308786i
$511$			26.0615i			1.15289i
$512$	12.9740	+	18.5385i	0.573377	+	0.819292i
$513$	4.57638			0.202052
$514$	−6.42977	+	32.7345i	−0.283605	+	1.44386i
$515$	12.3806	−	23.2241i	0.545555	−	1.02338i
$516$	−25.0633	+	10.5226i	−1.10335	+	0.463232i
$517$	4.37458			0.192394
$518$	7.41626	−	4.98114i	0.325852	−	0.218859i
$519$			19.3719i			0.850334i
$520$	−4.49416	+	15.2701i	−0.197082	+	0.669639i
$521$	4.82550	−	4.82550i	0.211409	−	0.211409i	−0.593457	−	0.804866i	$-0.702237\pi$
$521$	4.82550	−	4.82550i	0.211409	−	0.211409i	0.804866	+	0.593457i	$0.202237\pi$
$522$	−0.0218229	+	0.111102i	−0.000955161	+	0.00486281i
$523$	−16.2040	−	16.2040i	−0.708552	−	0.708552i	0.257679	−	0.966231i	$-0.417042\pi$
$523$	−16.2040	−	16.2040i	−0.708552	−	0.708552i	−0.966231	+	0.257679i	$0.917042\pi$
$524$	−2.70608	−	6.44547i	−0.118215	−	0.281572i
$525$	−37.9740	+	25.4949i	−1.65732	+	1.11269i
$526$	7.65729	−	38.9839i	0.333874	−	1.69978i
$527$	−21.2968	+	2.84591i	−0.927704	+	0.123970i
$528$	−4.12003	+	0.0395045i	−0.179301	+	0.00171921i
$529$	−22.0066			−0.956807
$530$	−4.12314	−	40.4120i	−0.179098	−	1.75538i
$531$			9.83719i			0.426898i
$532$	−8.50793	+	20.8217i	−0.368865	+	0.902737i
$533$		−	21.7629i		−	0.942655i
$534$	−7.09330	+	4.76422i	−0.306957	+	0.206168i
$535$	9.19619	+	30.1957i	0.397586	+	1.30548i
$536$	−18.7542	−	12.3370i	−0.810057	−	0.532877i
$537$	−17.7394			−0.765511
$538$	1.55506	−	7.91694i	0.0670433	−	0.341323i
$539$	−2.78382	−	2.78382i	−0.119908	−	0.119908i
$540$	−0.666473	+	7.20204i	−0.0286804	+	0.309926i
$541$	28.1030	+	28.1030i	1.20824	+	1.20824i	0.971596	+	0.236646i	$0.0760482\pi$
$541$	28.1030	+	28.1030i	1.20824	+	1.20824i	0.236646	+	0.971596i	$0.423952\pi$
$542$	−7.48697	−	11.1471i	−0.321593	−	0.478809i
$543$	9.76749	+	9.76749i	0.419163	+	0.419163i
$544$	−15.6212	−	17.3199i	−0.669754	−	0.742583i
$545$	−10.6452	+	19.9688i	−0.455991	+	0.855369i
$546$	6.27548	−	31.9490i	0.268566	−	1.36729i
$547$	41.6594			1.78123			0.890615	−	0.454759i	$-0.150274\pi$
$547$	41.6594			1.78123			0.890615	+	0.454759i	$0.150274\pi$
$548$	3.43519	−	1.44224i	0.146744	−	0.0616093i
$549$	22.3836	−	22.3836i	0.955308	−	0.955308i
$550$	−2.91809	+	1.22449i	−0.124428	+	0.0522124i
$551$	0.0697306	+	0.0697306i	0.00297063	+	0.00297063i
$552$	6.35456	−	1.31157i	0.270468	−	0.0558243i
$553$	−39.3560	−	39.3560i	−1.67359	−	1.67359i
$554$	−10.6267	−	15.8217i	−0.451485	−	0.672202i
$555$	2.38315	+	7.82507i	0.101159	+	0.332156i
$556$	23.5342	−	9.88063i	0.998072	−	0.419032i
$557$	−9.76367	−	9.76367i	−0.413700	−	0.413700i	0.469325	−	0.883025i	$-0.344497\pi$
$557$	−9.76367	−	9.76367i	−0.413700	−	0.413700i	−0.883025	+	0.469325i	$0.844497\pi$
$558$	3.26315	−	16.6130i	0.138140	−	0.703284i
$559$		−	14.8622i		−	0.628606i
$560$	−31.5289	−	16.4216i	−1.33234	−	0.693939i
$561$	4.20961	−	0.562532i	0.177730	−	0.0237501i
$562$	−4.32070	−	6.43295i	−0.182258	−	0.271357i
$563$	−0.0733436	+	0.0733436i	−0.00309107	+	0.00309107i	−0.708651	−	0.705560i	$-0.750696\pi$
$563$	−0.0733436	+	0.0733436i	−0.00309107	+	0.00309107i	0.705560	+	0.708651i	$0.250696\pi$
$564$	−41.4866	+	17.4178i	−1.74690	+	0.733422i
$565$	11.9649	−	3.64395i	0.503368	−	0.153302i
$566$	20.7291	−	13.9227i	0.871310	−	0.585217i
$567$		−	42.1867i		−	1.77168i
$568$	35.2070	+	23.1601i	1.47725	+	0.971775i
$569$	16.9947			0.712455			0.356227	−	0.934399i	$-0.384063\pi$
$569$	16.9947			0.712455			0.356227	+	0.934399i	$0.384063\pi$
$570$	−15.9657	−	13.0094i	−0.668728	−	0.544904i
$571$	8.53314	+	8.53314i	0.357101	+	0.357101i	0.862743	−	0.505642i	$-0.168744\pi$
$571$	8.53314	+	8.53314i	0.357101	+	0.357101i	−0.505642	+	0.862743i	$0.668744\pi$
$572$	0.852104	−	2.08538i	0.0356283	−	0.0871943i
$573$	−5.88475			−0.245839
$574$	47.6919	+	9.36771i	1.99062	+	0.391001i
$575$	4.13758	−	2.77787i	0.172549	−	0.115845i
$576$	16.8766	−	7.27660i	0.703191	−	0.303192i
$577$	15.1656	+	15.1656i	0.631352	+	0.631352i	0.948407	−	0.317055i	$-0.102694\pi$
$577$	15.1656	+	15.1656i	0.631352	+	0.631352i	−0.317055	+	0.948407i	$0.602694\pi$
$578$	18.1747	+	15.7378i	0.755969	+	0.654608i
$579$	−39.6136			−1.64629
$580$	−0.119893	+	0.0995828i	−0.00497828	+	0.00413495i
$581$	−22.2180	−	22.2180i	−0.921760	−	0.921760i
$582$	31.4094	−	21.0962i	1.30196	−	0.874465i
$583$			5.74899i			0.238099i
$584$	−3.74894	−	18.1636i	−0.155132	−	0.751613i
$585$	11.4088	+	6.08196i	0.471697	+	0.251458i
$586$	−0.0664549	+	0.338328i	−0.00274523	+	0.0139762i
$587$	7.76411	+	7.76411i	0.320459	+	0.320459i	0.848943	−	0.528484i	$-0.177239\pi$
$587$	7.76411	+	7.76411i	0.320459	+	0.320459i	−0.528484	+	0.848943i	$0.677239\pi$
$588$	37.4847	+	15.3165i	1.54584	+	0.631643i
$589$	−10.4268	−	10.4268i	−0.429627	−	0.429627i
$590$	−8.55363	+	10.4974i	−0.352148	+	0.432170i
$591$			19.7924i			0.814151i
$592$	−4.45223	+	4.53843i	−0.182985	+	0.186528i
$593$	−11.9777	−	11.9777i	−0.491864	−	0.491864i	0.417029	−	0.908893i	$-0.363071\pi$
$593$	−11.9777	−	11.9777i	−0.491864	−	0.491864i	−0.908893	+	0.417029i	$0.863071\pi$
$594$	0.197292	−	1.00443i	0.00809498	−	0.0412122i
$595$	34.3338	+	12.8030i	1.40755	+	0.524872i
$596$	18.8916	+	7.71924i	0.773828	+	0.316192i
$597$	30.0205	−	30.0205i	1.22866	−	1.22866i
$598$	−0.683765	+	3.48111i	−0.0279612	+	0.142353i
$599$	17.4230			0.711885			0.355943	−	0.934508i	$-0.384160\pi$
$599$	17.4230			0.711885			0.355943	+	0.934508i	$0.384160\pi$
$600$	22.7985	−	23.2312i	0.930747	−	0.948410i
$601$	−8.15209	+	8.15209i	−0.332531	+	0.332531i	−0.853547	−	0.521016i	$-0.825553\pi$
$601$	−8.15209	+	8.15209i	−0.332531	+	0.332531i	0.521016	+	0.853547i	$0.325553\pi$
$602$	32.5696	+	6.39737i	1.32744	+	0.260737i
$603$	−12.8926	+	12.8926i	−0.525028	+	0.525028i
$604$	−0.459381	+	1.12426i	−0.0186919	+	0.0457454i
$605$	−23.1013	+	7.03556i	−0.939201	+	0.286036i
$606$	−20.1003	−	29.9266i	−0.816517	−	1.21569i
$607$	6.35652			0.258003			0.129002	−	0.991644i	$-0.458823\pi$
$607$	6.35652			0.258003			0.129002	+	0.991644i	$0.458823\pi$
$608$	2.93440	−	15.7356i	0.119006	−	0.638162i
$609$	0.225427	−	0.225427i	0.00913474	−	0.00913474i
$610$	43.3487	−	4.42277i	1.75514	−	0.179073i
$611$		−	24.6011i		−	0.995254i
$612$	−16.3419	+	9.58238i	−0.660581	+	0.387345i
$613$	−25.2273	+	25.2273i	−1.01892	+	1.01892i	−0.0191017	+	0.999818i	$0.506081\pi$
$613$	−25.2273	+	25.2273i	−1.01892	+	1.01892i	−0.999818	+	0.0191017i	$0.993919\pi$
$614$	−2.34254	+	11.9261i	−0.0945371	+	0.481297i
$615$	−20.9347	+	39.2702i	−0.844167	+	1.58353i
$616$	4.20319	+	2.76497i	0.169351	+	0.111404i
$617$		−	14.4676i		−	0.582442i	−0.956656	−	0.291221i	$-0.905938\pi$
$617$		−	14.4676i		−	0.582442i	0.956656	−	0.291221i	$-0.0940616\pi$
$618$	7.38381	−	37.5916i	0.297021	−	1.51216i
$619$	6.30612	−	6.30612i	0.253464	−	0.253464i	−0.568925	−	0.822389i	$-0.692641\pi$
$619$	6.30612	−	6.30612i	0.253464	−	0.253464i	0.822389	+	0.568925i	$0.192641\pi$
$620$	17.9275	−	14.8905i	0.719985	−	0.598018i
$621$			1.61199i			0.0646871i
$622$	6.22522	−	31.6932i	0.249609	−	1.27078i
$623$	10.4338			0.418020
$624$	0.222159	+	23.1696i	0.00889349	+	0.927527i
$625$	9.46499	−	23.1390i	0.378600	−	0.925560i
$626$	−10.5486	−	15.7055i	−0.421607	−	0.627717i
$627$	2.06099	+	2.06099i	0.0823081	+	0.0823081i
$628$	4.00049	−	1.67957i	0.159637	−	0.0670222i
$629$	3.97929	−	5.20684i	0.158665	−	0.207610i
$630$	−18.2391	+	22.3837i	−0.726663	+	0.891789i
$631$	10.4038			0.414169			0.207084	−	0.978323i	$-0.433603\pi$
$631$	10.4038			0.414169			0.207084	+	0.978323i	$0.433603\pi$
$632$	33.0905	+	21.7678i	1.31627	+	0.865877i
$633$	−45.4627	+	45.4627i	−1.80698	+	1.80698i
$634$	−10.0180	+	6.72860i	−0.397865	+	0.267227i
$635$	−15.9721	+	29.9611i	−0.633832	+	1.18897i
$636$	−22.8902	−	54.5210i	−0.907654	−	2.16190i
$637$	−15.6553	+	15.6553i	−0.620284	+	0.620284i
$638$	0.0183107	−	0.0122984i	0.000724927	−	0.000486899i
$639$	24.2031	−	24.2031i	0.957460	−	0.957460i
$640$	24.3363	+	6.90960i	0.961978	+	0.273126i
$641$	−7.19778	−	7.19778i	−0.284295	−	0.284295i	0.550524	−	0.834819i	$-0.314428\pi$
$641$	−7.19778	−	7.19778i	−0.284295	−	0.284295i	−0.834819	+	0.550524i	$0.814428\pi$
$642$	25.6187	+	38.1428i	1.01109	+	1.50538i
$643$			33.2263i			1.31032i	0.755491	+	0.655159i	$0.227398\pi$
$643$			33.2263i			1.31032i	−0.755491	+	0.655159i	$0.772602\pi$
$644$	−7.33429	−	2.99685i	−0.289011	−	0.118092i
$645$	−14.2966	+	26.8183i	−0.562930	+	1.05597i
$646$	−1.00764	+	16.4687i	−0.0396450	+	0.647951i
$647$	−16.9696	+	16.9696i	−0.667142	+	0.667142i	−0.957054	−	0.289911i	$-0.906374\pi$
$647$	−16.9696	+	16.9696i	−0.667142	+	0.667142i	0.289911	+	0.957054i	$0.406374\pi$
$648$	6.06854	+	29.4020i	0.238395	+	1.15502i
$649$	1.35509	−	1.35509i	0.0531921	−	0.0531921i
$650$	6.88609	+	16.4103i	0.270095	+	0.643667i
$651$	−33.7078	+	33.7078i	−1.32111	+	1.32111i
$652$	−6.83194	+	16.7200i	−0.267560	+	0.654807i
$653$			22.0075i			0.861221i	0.902538	+	0.430611i	$0.141702\pi$
$653$			22.0075i			0.861221i	−0.902538	+	0.430611i	$0.858298\pi$
$654$	−6.34882	+	32.3224i	−0.248259	+	1.26391i
$655$	−6.89681	−	3.67664i	−0.269481	−	0.143658i
$656$	−34.5864	+	0.331628i	−1.35037	+	0.0129479i
$657$	−15.0638			−0.587695
$658$	53.9116	+	10.5894i	2.10169	+	0.412818i
$659$	−24.7282			−0.963275			−0.481637	−	0.876371i	$-0.659958\pi$
$659$	−24.7282			−0.963275			−0.481637	+	0.876371i	$0.659958\pi$
$660$	−3.54361	+	2.94331i	−0.137935	+	0.114568i
$661$			3.67431i			0.142914i	0.997444	+	0.0714571i	$0.0227649\pi$
$661$			3.67431i			0.142914i	−0.997444	+	0.0714571i	$0.977235\pi$
$662$	22.0508	−	14.8104i	0.857028	−	0.575624i
$663$	−3.16348	−	23.6734i	−0.122860	−	0.919397i
$664$	18.6809	+	12.2888i	0.724960	+	0.476898i
$665$	7.32658	+	24.0569i	0.284113	+	0.932885i
$666$	2.87915	+	4.28667i	0.111565	+	0.166105i
$667$	−0.0245621	+	0.0245621i	−0.000951047	+	0.000951047i
$668$	12.7943	−	31.3119i	0.495025	−	1.21149i
$669$	28.8410	+	28.8410i	1.11506	+	1.11506i
$670$	−24.9682	+	2.54745i	−0.964606	+	0.0984165i
$671$	−6.16677			−0.238066
$672$	−50.8703	−	9.48639i	−1.96236	−	0.365945i
$673$			44.3027i			1.70775i	0.520482	+	0.853873i	$0.325752\pi$
$673$			44.3027i			1.70775i	−0.520482	+	0.853873i	$0.674248\pi$
$674$	−3.95623	−	5.89031i	−0.152388	−	0.226886i
$675$	4.50747	+	6.71376i	0.173493	+	0.258413i
$676$	12.3408	+	5.04256i	0.474647	+	0.193945i
$677$		−	40.3377i		−	1.55030i	−0.631774	−	0.775152i	$-0.717673\pi$
$677$		−	40.3377i		−	1.55030i	0.631774	−	0.775152i	$-0.282327\pi$
$678$	15.1139	−	10.1513i	0.580447	−	0.389858i
$679$	−46.2011			−1.77304
$680$	−25.7707	−	3.98414i	−0.988259	−	0.152785i
$681$	−21.5968			−0.827591
$682$	−2.73798	+	1.83897i	−0.104843	+	0.0704178i
$683$		−	23.5865i		−	0.902513i	−0.892394	−	0.451256i	$-0.850976\pi$
$683$		−	23.5865i		−	0.902513i	0.892394	−	0.451256i	$-0.149024\pi$
$684$	−12.0352	−	4.91766i	−0.460176	−	0.188032i
$685$	1.95951	−	3.67574i	0.0748690	−	0.140443i
$686$	−5.63104	−	8.38387i	−0.214994	−	0.320097i
$687$			59.3939i			2.26602i
$688$	−23.6196	+	0.226474i	−0.900490	+	0.00863426i
$689$	32.3303			1.23169
$690$	4.58246	−	5.62378i	0.174451	−	0.214094i
$691$	−8.90330	−	8.90330i	−0.338697	−	0.338697i	0.517180	−	0.855877i	$-0.326982\pi$
$691$	−8.90330	−	8.90330i	−0.338697	−	0.338697i	−0.855877	+	0.517180i	$0.826982\pi$
$692$	−6.36729	+	15.5829i	−0.242048	+	0.592372i
$693$	2.88949	−	2.88949i	0.109763	−	0.109763i
$694$	−11.4096	−	16.9874i	−0.433102	−	0.644832i
$695$	13.4244	−	25.1822i	0.509217	−	0.955214i
$696$	−0.124684	+	0.189539i	−0.00472612	+	0.00718444i
$697$	35.3383	−	4.72228i	1.33854	−	0.178869i
$698$	−20.8815	+	14.0251i	−0.790377	+	0.530858i
$699$		−	35.5415i		−	1.34430i
$700$	−38.9262	+	8.02666i	−1.47127	+	0.303379i
$701$	18.0112			0.680275			0.340137	−	0.940376i	$-0.389526\pi$
$701$	18.0112			0.680275			0.340137	+	0.940376i	$0.389526\pi$
$702$	−5.64856	−	1.10950i	−0.213191	−	0.0418754i
$703$	4.49746			0.169625
$704$	−3.32715	−	1.32242i	−0.125397	−	0.0498405i
$705$	−23.6649	+	44.3917i	−0.891271	+	1.67189i
$706$	−2.33639	+	11.8948i	−0.0879312	+	0.447665i
$707$			44.0200i			1.65554i
$708$	−7.45569	+	18.2466i	−0.280202	+	0.685748i
$709$	−14.3956	+	14.3956i	−0.540637	+	0.540637i	−0.923716	−	0.383079i	$-0.874864\pi$
$709$	−14.3956	+	14.3956i	−0.540637	+	0.540637i	0.383079	+	0.923716i	$0.374864\pi$
$710$	46.8725	−	4.78229i	1.75909	−	0.179476i
$711$	22.7481	−	22.7481i	0.853122	−	0.853122i
$712$	−7.27181	+	1.50089i	−0.272523	+	0.0562483i
$713$	3.67274	−	3.67274i	0.137545	−	0.137545i
$714$	53.2402	+	3.25751i	1.99247	+	0.121909i
$715$	−0.733788	−	2.40940i	−0.0274421	−	0.0901063i
$716$	−14.2696	−	5.83068i	−0.533281	−	0.217903i
$717$			42.2460i			1.57770i
$718$	27.6984	+	41.2392i	1.03370	+	1.53904i
$719$	6.05351	+	6.05351i	0.225758	+	0.225758i	0.810918	−	0.585160i	$-0.198968\pi$
$719$	6.05351	+	6.05351i	0.225758	+	0.225758i	−0.585160	+	0.810918i	$0.698968\pi$
$720$	9.49184	−	18.2240i	0.353740	−	0.679170i
$721$	−33.0779	+	33.0779i	−1.23189	+	1.23189i
$722$	12.9058	−	8.66823i	0.480306	−	0.322598i
$723$	−17.4330	+	17.4330i	−0.648341	+	0.648341i
$724$	4.64657	+	11.0674i	0.172688	+	0.411318i
$725$	−0.0336175	+	0.170979i	−0.00124852	+	0.00634998i
$726$	−29.1812	+	19.5996i	−1.08302	+	0.727410i
$727$	−1.28879	+	1.28879i	−0.0477986	+	0.0477986i	−0.730602	−	0.682803i	$-0.760761\pi$
$727$	−1.28879	+	1.28879i	−0.0477986	+	0.0477986i	0.682803	+	0.730602i	$0.260761\pi$
$728$	15.5492	−	23.6373i	0.576293	−	0.876056i
$729$	13.2172			0.489526
$730$	−16.0747	−	13.0983i	−0.594952	−	0.484789i
$731$	24.1332	−	3.22493i	0.892597	−	0.119278i
$732$	58.4830	−	24.5536i	2.16160	−	0.907527i
$733$	−29.5695	−	29.5695i	−1.09217	−	1.09217i	−0.995296	−	0.0968766i	$-0.969115\pi$
$733$	−29.5695	−	29.5695i	−1.09217	−	1.09217i	−0.0968766	−	0.995296i	$-0.530885\pi$
$734$	9.08131	+	13.5209i	0.335197	+	0.499064i
$735$	43.3088	−	13.1898i	1.59747	−	0.486513i
$736$	5.54273	+	1.03362i	0.204308	+	0.0380997i
$737$	3.55197			0.130838
$738$	−5.41463	+	27.5664i	−0.199315	+	1.01473i
$739$		−	1.53273i		−	0.0563824i	−0.999603	−	0.0281912i	$-0.991025\pi$
$739$		−	1.53273i		−	0.0563824i	0.999603	−	0.0281912i	$-0.00897472\pi$
$740$	−0.654978	+	7.07783i	−0.0240775	+	0.260186i
$741$	11.5903	−	11.5903i	0.425780	−	0.425780i
$742$	−13.9164	+	70.8497i	−0.510888	+	2.60097i
$743$			14.6366i			0.536964i	0.963285	+	0.268482i	$0.0865220\pi$
$743$			14.6366i			0.536964i	−0.963285	+	0.268482i	$0.913478\pi$
$744$	18.6438	−	28.3415i	0.683515	−	1.03905i
$745$	21.8268	−	6.64741i	0.799672	−	0.243542i
$746$	−0.515195	+	2.62290i	−0.0188626	+	0.0960314i
$747$	12.8422	−	12.8422i	0.469873	−	0.469873i
$748$	3.57112	+	0.931136i	0.130573	+	0.0340457i
$749$		−	56.1055i		−	2.05005i
$750$	3.36015	−	36.2358i	0.122695	−	1.32315i
$751$	−13.3849	+	13.3849i	−0.488421	+	0.488421i	−0.907808	−	0.419387i	$-0.862245\pi$
$751$	−13.3849	+	13.3849i	−0.488421	+	0.488421i	0.419387	+	0.907808i	$0.362245\pi$
$752$	−39.0970	+	0.374877i	−1.42572	+	0.0136704i
$753$	10.3675			0.377811
$754$	−0.0691619	−	0.102973i	−0.00251873	−	0.00375005i
$755$	0.395595	+	1.29894i	0.0143972	+	0.0472731i
$756$	4.86279	−	11.9009i	0.176858	−	0.432830i
$757$	11.4594	−	11.4594i	0.416498	−	0.416498i	−0.467497	−	0.883995i	$-0.654844\pi$
$757$	11.4594	−	11.4594i	0.416498	−	0.416498i	0.883995	+	0.467497i	$0.154844\pi$
$758$	−4.94558	−	0.971419i	−0.179631	−	0.0352835i
$759$	−0.725968	+	0.725968i	−0.0263510	+	0.0263510i
$760$	−8.56684	−	15.7125i	−0.310752	−	0.569953i
$761$	34.4793			1.24987			0.624937	−	0.780675i	$-0.285125\pi$
$761$	34.4793			1.24987			0.624937	+	0.780675i	$0.285125\pi$
$762$	−9.52575	+	48.4964i	−0.345082	+	1.75684i
$763$	28.4414	−	28.4414i	1.02965	−	1.02965i
$764$	−4.73371	−	1.93423i	−0.171260	−	0.0699781i
$765$	−7.40025	+	19.8453i	−0.267557	+	0.717507i
$766$	9.74549	−	49.6151i	0.352119	−	1.79267i
$767$	−7.62057	−	7.62057i	−0.275163	−	0.275163i
$768$	36.8186	−	0.706128i	1.32858	−	0.0254802i
$769$			10.3466i			0.373108i	0.982445	+	0.186554i	$0.0597319\pi$
$769$			10.3466i			0.373108i	−0.982445	+	0.186554i	$0.940268\pi$
$770$	5.59588	−	0.570935i	0.201662	−	0.0205751i
$771$	38.3905	+	38.3905i	1.38260	+	1.38260i
$772$	−31.8654	−	13.0204i	−1.14686	−	0.468616i
$773$	−12.7316	−	12.7316i	−0.457923	−	0.457923i	0.440050	−	0.897973i	$-0.354961\pi$
$773$	−12.7316	−	12.7316i	−0.457923	−	0.457923i	−0.897973	+	0.440050i	$0.854961\pi$
$774$	−3.69774	+	18.8255i	−0.132913	+	0.676670i
$775$	5.02679	−	25.5663i	0.180568	−	0.918367i
$776$	32.1999	−	6.64602i	1.15591	−	0.238578i
$777$		−	14.5395i		−	0.521600i
$778$	9.80617	−	6.58632i	0.351568	−	0.236131i
$779$	17.3014	+	17.3014i	0.619886	+	0.619886i
$780$	16.5522	+	19.9280i	0.592663	+	0.713538i
$781$	−6.66806			−0.238602
$782$	−5.80096	−	0.354932i	−0.207442	−	0.0126924i
$783$	−0.0398552	−	0.0398552i	−0.00142431	−	0.00142431i
$784$	25.1185	+	24.6414i	0.897089	+	0.880049i
$785$	2.28197	−	4.28062i	0.0814469	−	0.152782i
$786$	−11.1635	−	2.19275i	−0.398188	−	0.0782128i
$787$	−2.64490			−0.0942805			−0.0471402	−	0.998888i	$-0.515011\pi$
$787$	−2.64490			−0.0942805			−0.0471402	+	0.998888i	$0.515011\pi$
$788$	−6.50549	+	15.9211i	−0.231749	+	0.567166i
$789$	−45.7197	−	45.7197i	−1.62766	−	1.62766i
$790$	44.0548	−	4.49480i	1.56740	−	0.159918i
$791$	−22.2316			−0.790464
$792$	−1.59818	+	2.42949i	−0.0567889	+	0.0863280i
$793$			34.6798i			1.23152i
$794$	14.1001	−	9.47034i	0.500393	−	0.336090i
$795$	−58.3388	−	31.1000i	−2.06906	−	1.10300i
$796$	34.0160	−	14.2813i	1.20566	−	0.506188i
$797$	−11.6990	+	11.6990i	−0.414401	+	0.414401i	−0.883269	−	0.468867i	$-0.844662\pi$
$797$	−11.6990	+	11.6990i	−0.414401	+	0.414401i	0.468867	+	0.883269i	$0.344662\pi$
$798$	20.4104	+	30.3883i	0.722519	+	1.07573i
$799$	39.9470	−	5.33814i	1.41322	−	0.188850i
$800$	25.9750	−	11.1937i	0.918355	−	0.395757i
$801$			6.03082i			0.213088i
$802$	−3.78885	+	19.2894i	−0.133789	+	0.681132i
$803$	2.07507	+	2.07507i	0.0732276	+	0.0732276i
$804$	−33.6853	+	14.1425i	−1.18799	+	0.498768i
$805$	−8.47384	+	2.58073i	−0.298664	+	0.0909588i
$806$	10.3417	+	15.3975i	0.364272	+	0.542352i
$807$	−9.28486	−	9.28486i	−0.326842	−	0.326842i
$808$	−6.33227	−	30.6798i	−0.222768	−	1.07931i
$809$	9.42441	+	9.42441i	0.331345	+	0.331345i	0.853097	−	0.521752i	$-0.174722\pi$
$809$	9.42441	+	9.42441i	0.331345	+	0.331345i	−0.521752	+	0.853097i	$0.674722\pi$
$810$	26.0208	+	21.2027i	0.914276	+	0.744986i
$811$	21.2640	−	21.2640i	0.746680	−	0.746680i	−0.227174	−	0.973854i	$-0.572949\pi$
$811$	21.2640	−	21.2640i	0.746680	−	0.746680i	0.973854	+	0.227174i	$0.0729486\pi$
$812$	0.255429	−	0.107239i	0.00896379	−	0.00376337i
$813$	−21.8537			−0.766444
$814$	0.193889	−	0.987107i	0.00679581	−	0.0345981i
$815$	5.88331	+	19.3179i	0.206084	+	0.676676i
$816$	−37.5744	+	5.38827i	−1.31537	+	0.188627i
$817$	11.8154	+	11.8154i	0.413369	+	0.413369i
$818$	−11.1474	−	16.5970i	−0.389759	−	0.580299i
$819$	−16.2495	−	16.2495i	−0.567803	−	0.567803i
$820$	−29.7475	+	24.7082i	−1.03883	+	0.862848i
$821$	−35.8809	−	35.8809i	−1.25225	−	1.25225i	−0.954707	−	0.297546i	$-0.903832\pi$
$821$	−35.8809	−	35.8809i	−1.25225	−	1.25225i	−0.297546	−	0.954707i	$-0.596168\pi$
$822$	1.16865	−	5.94972i	0.0407615	−	0.207520i
$823$	−10.3418			−0.360492			−0.180246	−	0.983622i	$-0.557689\pi$
$823$	−10.3418			−0.360492			−0.180246	+	0.983622i	$0.557689\pi$
$824$	18.2954	−	27.8119i	0.637351	−	0.968874i
$825$	−0.993613	+	5.05352i	−0.0345932	+	0.175941i
$826$	19.9802	−	13.4197i	0.695200	−	0.466932i
$827$		−	25.7269i		−	0.894611i	−0.894381	−	0.447305i	$-0.852384\pi$
$827$		−	25.7269i		−	0.894611i	0.894381	−	0.447305i	$-0.147616\pi$
$828$	1.73221	−	4.23929i	0.0601984	−	0.147326i
$829$		−	20.4977i		−	0.711914i	−0.934502	−	0.355957i	$-0.884155\pi$
$829$		−	20.4977i		−	0.711914i	0.934502	−	0.355957i	$-0.115845\pi$
$830$	24.8707	−	2.53750i	0.863274	−	0.0880778i
$831$	−31.0183			−1.07601
$832$	−7.43682	+	18.7108i	−0.257825	+	0.648679i
$833$	−28.8178	−	22.0238i	−0.998479	−	0.763081i
$834$	8.00634	−	40.7610i	0.277237	−	1.41144i
$835$	−11.0178	−	36.1769i	−0.381286	−	1.25195i
$836$	0.980451	+	2.33529i	0.0339096	+	0.0807676i
$837$	5.95951	+	5.95951i	0.205991	+	0.205991i
$838$	7.09320	−	36.1121i	0.245031	−	1.24747i
$839$	−10.8730	+	10.8730i	−0.375377	+	0.375377i	−0.869431	−	0.494054i	$-0.835515\pi$
$839$	−10.8730	+	10.8730i	−0.375377	+	0.375377i	0.494054	+	0.869431i	$0.335515\pi$
$840$	−50.7957	+	27.6950i	−1.75262	+	0.955569i
$841$			28.9988i			0.999958i
$842$	9.41816	−	6.32572i	0.324571	−	0.217999i
$843$	−12.6117			−0.434370
$844$	−51.5133	+	21.6274i	−1.77316	+	0.744447i
$845$	14.2583	−	4.34239i	0.490499	−	0.149383i
$846$	−6.12078	+	31.1614i	−0.210437	+	1.07135i
$847$	42.9236			1.47487
$848$	−0.492657	−	51.3806i	−0.0169179	−	1.76442i
$849$		−	40.6392i		−	1.39473i
$850$	−25.1528	+	14.7424i	−0.862732	+	0.505661i
$851$			1.58419i			0.0543055i
$852$	63.2370	−	26.5495i	2.16646	−	0.909571i
$853$	21.9353			0.751049			0.375524	−	0.926812i	$-0.377463\pi$
$853$	21.9353			0.751049			0.375524	+	0.926812i	$0.377463\pi$
$854$	−75.9984	−	14.9277i	−2.60061	−	0.510816i
$855$	−13.9051	+	4.23484i	−0.475544	+	0.144828i
$856$	8.07076	+	39.1028i	0.275853	+	1.33650i
$857$	36.7404			1.25503			0.627514	−	0.778605i	$-0.284072\pi$
$857$	36.7404			1.25503			0.627514	+	0.778605i	$0.284072\pi$
$858$	−2.04418	−	3.04352i	−0.0697872	−	0.103904i
$859$			40.8467i			1.39367i	0.717230	+	0.696837i	$0.245410\pi$
$859$			40.8467i			1.39367i	−0.717230	+	0.696837i	$0.754590\pi$
$860$	−20.3151	+	16.8737i	−0.692739	+	0.575387i
$861$	55.9322	−	55.9322i	1.90617	−	1.90617i
$862$	−7.87368	−	1.54656i	−0.268179	−	0.0526761i
$863$	−12.7024	−	12.7024i	−0.432396	−	0.432396i	0.457047	−	0.889443i	$-0.348907\pi$
$863$	−12.7024	−	12.7024i	−0.432396	−	0.432396i	−0.889443	+	0.457047i	$0.848907\pi$
$864$	−1.67718	+	8.99381i	−0.0570590	+	0.305976i
$865$	5.48317	+	18.0040i	0.186434	+	0.612155i
$866$	−11.5971	−	2.27792i	−0.394085	−	0.0774068i
$867$	37.7541	−	10.2737i	1.28220	−	0.348912i
$868$	−38.1940	+	16.0354i	−1.29639	+	0.544278i
$869$	−6.26721			−0.212601
$870$	0.0257457	+	0.252341i	0.000872861	+	0.00855514i
$871$		−	19.9750i		−	0.676828i
$872$	−15.7309	+	23.9135i	−0.532717	+	0.809813i
$873$		−	26.7047i		−	0.903817i
$874$	−2.22387	−	3.31105i	−0.0752237	−	0.111998i
$875$	−28.0763	+	34.4430i	−0.949151	+	1.16439i
$876$	−27.9412	−	11.4170i	−0.944044	−	0.385744i
$877$	24.5364			0.828536			0.414268	−	0.910155i	$-0.364038\pi$
$877$	24.5364			0.828536			0.414268	+	0.910155i	$0.364038\pi$
$878$	−22.2673	−	4.37379i	−0.751486	−	0.147608i
$879$	0.396786	+	0.396786i	0.0133832	+	0.0133832i
$880$	−3.81792	+	1.20288i	−0.128702	+	0.0405490i
$881$	5.25903	+	5.25903i	0.177181	+	0.177181i	0.790126	−	0.612945i	$-0.210015\pi$
$881$	5.25903	+	5.25903i	0.177181	+	0.177181i	−0.612945	+	0.790126i	$0.710015\pi$
$882$	23.7251	−	15.9350i	0.798864	−	0.536558i
$883$	35.0208	+	35.0208i	1.17854	+	1.17854i	0.980116	+	0.198428i	$0.0635835\pi$
$883$	35.0208	+	35.0208i	1.17854	+	1.17854i	0.198428	+	0.980116i	$0.436417\pi$
$884$	5.23638	−	20.0827i	0.176119	−	0.675455i
$885$	6.42045	+	21.0816i	0.215821	+	0.708650i
$886$	4.68850	+	0.920924i	0.157513	+	0.0309390i
$887$	−24.6007			−0.826012			−0.413006	−	0.910728i	$-0.635521\pi$
$887$	−24.6007			−0.826012			−0.413006	+	0.910728i	$0.635521\pi$
$888$	2.09150	+	10.1333i	0.0701861	+	0.340051i
$889$	42.6734	−	42.6734i	1.43122	−	1.43122i
$890$	−5.24392	+	6.43554i	−0.175776	+	0.215720i
$891$	−3.35899	−	3.35899i	−0.112531	−	0.112531i
$892$	13.7202	+	32.6795i	0.459386	+	1.09419i
$893$	19.5577	+	19.5577i	0.654475	+	0.654475i
$894$	27.5713	−	18.5183i	0.922122	−	0.619345i
$895$	−16.4867	+	5.02108i	−0.551091	+	0.167836i
$896$	−37.8022	−	24.3512i	−1.26288	−	0.813518i
$897$	4.08259	+	4.08259i	0.136314	+	0.136314i
$898$	−44.6183	−	8.76401i	−1.48893	−	0.292459i
$899$			0.181611i			0.00605706i
$900$	−4.63949	−	22.4997i	−0.154650	−	0.749991i
$901$	7.01530	+	52.4977i	0.233713	+	1.74895i
$902$	4.54320	−	3.05145i	0.151272	−	0.101602i
$903$	38.1971	−	38.1971i	1.27112	−	1.27112i
$904$	15.4943	−	3.19800i	0.515333	−	0.106364i
$905$	11.8424	+	6.31312i	0.393656	+	0.209855i
$906$	1.10205	+	1.64080i	0.0366130	+	0.0545119i
$907$			3.78494i			0.125677i	0.998024	+	0.0628384i	$0.0200153\pi$
$907$			3.78494i			0.125677i	−0.998024	+	0.0628384i	$0.979985\pi$
$908$	−17.3725	−	7.09856i	−0.576528	−	0.235574i
$909$	−25.4440			−0.843924
$910$	−3.21074	−	31.4693i	−0.106435	−	1.04320i
$911$	−38.1615	−	38.1615i	−1.26435	−	1.26435i	−0.948965	−	0.315381i	$-0.897868\pi$
$911$	−38.1615	−	38.1615i	−1.26435	−	1.26435i	−0.315381	−	0.948965i	$-0.602132\pi$
$912$	−18.5963	−	18.2431i	−0.615787	−	0.604090i
$913$	−3.53809			−0.117094
$914$	−6.00768	+	30.5856i	−0.198716	+	1.01168i
$915$	33.3600	−	62.5783i	1.10285	−	2.06877i
$916$	−19.5219	+	47.7767i	−0.645023	+	1.57859i
$917$	9.82306	+	9.82306i	0.324386	+	0.324386i
$918$	0.575925	−	9.41282i	0.0190083	−	0.310669i
$919$	9.18519			0.302991			0.151496	−	0.988458i	$-0.451591\pi$
$919$	9.18519			0.302991			0.151496	+	0.988458i	$0.451591\pi$
$920$	5.53461	−	3.01760i	0.182471	−	0.0994873i
$921$	13.9867	+	13.9867i	0.460877	+	0.460877i
$922$	3.69045	+	5.49459i	0.121538	+	0.180955i
$923$			37.4988i			1.23429i
$924$	7.54957	−	3.16962i	0.248362	−	0.104273i
$925$	4.42973	+	6.59797i	0.145649	+	0.216940i
$926$	−34.1328	−	6.70443i	−1.12167	−	0.220321i
$927$	−19.1194	−	19.1194i	−0.627962	−	0.627962i
$928$	−0.162595	+	0.111484i	−0.00533743	+	0.00365964i
$929$	13.9836	+	13.9836i	0.458785	+	0.458785i	0.898257	−	0.439471i	$-0.144834\pi$
$929$	13.9836	+	13.9836i	0.458785	+	0.458785i	−0.439471	+	0.898257i	$0.644834\pi$
$930$	−3.84973	−	37.7322i	−0.126238	−	1.23729i
$931$		−	24.8917i		−	0.815792i
$932$	11.6820	−	28.5897i	0.382656	−	0.936487i
$933$	−37.1692	−	37.1692i	−1.21687	−	1.21687i
$934$	−39.5843	−	7.77522i	−1.29524	−	0.254413i
$935$	3.75313	−	1.71433i	0.122740	−	0.0560645i
$936$	13.6626	+	8.98760i	0.446575	+	0.293769i
$937$	15.8283	−	15.8283i	0.517089	−	0.517089i	−0.399600	−	0.916689i	$-0.630851\pi$
$937$	15.8283	−	15.8283i	0.517089	−	0.517089i	0.916689	+	0.399600i	$0.130851\pi$
$938$	43.7739	+	8.59814i	1.42927	+	0.280739i
$939$	−30.7904			−1.00481
$940$	−33.6271	+	27.9305i	−1.09679	+	0.910994i
$941$	6.43964	−	6.43964i	0.209926	−	0.209926i	−0.594310	−	0.804236i	$-0.702575\pi$
$941$	6.43964	−	6.43964i	0.209926	−	0.209926i	0.804236	+	0.594310i	$0.202575\pi$
$942$	1.36097	−	6.92881i	0.0443427	−	0.225753i
$943$	−6.09427	+	6.09427i	−0.198457	+	0.198457i
$944$	−11.9948	+	12.2270i	−0.390397	+	0.397956i
$945$	−4.18758	−	13.7499i	−0.136222	−	0.447285i
$946$	3.10263	−	2.08389i	0.100875	−	0.0677530i
$947$	−10.0320			−0.325995			−0.162998	−	0.986626i	$-0.552116\pi$
$947$	−10.0320			−0.325995			−0.162998	+	0.986626i	$0.552116\pi$
$948$	59.4356	−	24.9535i	1.93038	−	0.810452i
$949$	11.6695	−	11.6695i	0.378807	−	0.378807i
$950$	−18.5206	−	7.57173i	−0.600886	−	0.245659i
$951$			19.6401i			0.636875i
$952$	41.7560	+	20.1197i	1.35332	+	0.652082i
$953$	22.3729	−	22.3729i	0.724730	−	0.724730i	−0.244835	−	0.969565i	$-0.578734\pi$
$953$	22.3729	−	22.3729i	0.724730	−	0.724730i	0.969565	+	0.244835i	$0.0787338\pi$
$954$	−40.9518	−	8.04383i	−1.32586	−	0.260428i
$955$	−5.46921	+	1.66566i	−0.176979	+	0.0538995i
$956$	−13.8857	+	33.9828i	−0.449094	+	1.09908i
$957$		−	0.0358979i		−	0.00116041i
$958$	−32.1612	−	6.31715i	−1.03908	−	0.204098i
$959$	−5.23532	+	5.23532i	−0.169057	+	0.169057i
$960$	31.4181	−	26.6090i	1.01402	−	0.858802i
$961$			3.84389i			0.123997i
$962$	−5.55114	−	1.09036i	−0.178976	−	0.0351548i
$963$	32.4295			1.04503
$964$	−19.7532	+	8.29320i	−0.636207	+	0.267106i
$965$	−36.8164	+	11.2125i	−1.18516	+	0.360944i
$966$	−10.7040	+	7.18938i	−0.344397	+	0.231315i
$967$	−34.4166	−	34.4166i	−1.10676	−	1.10676i	−0.993573	−	0.113189i	$-0.963893\pi$
$967$	−34.4166	−	34.4166i	−1.10676	−	1.10676i	−0.113189	−	0.993573i	$-0.536107\pi$
$968$	−29.9156	+	6.17455i	−0.961524	+	0.198457i
$969$	21.3352	+	16.3052i	0.685384	+	0.523800i
$970$	23.2203	−	28.4969i	0.745558	−	0.914979i
$971$	13.1804			0.422980			0.211490	−	0.977380i	$-0.432168\pi$
$971$	13.1804			0.422980			0.211490	+	0.977380i	$0.432168\pi$
$972$	36.2465	+	14.8106i	1.16261	+	0.475051i
$973$	−35.8667	+	35.8667i	−1.14983	+	1.14983i
$974$	−12.1430	−	18.0793i	−0.389086	−	0.579298i
$975$	28.4192	+	5.58773i	0.910144	+	0.178951i
$976$	55.1144	−	0.528459i	1.76417	−	0.0169156i
$977$	−39.7241	+	39.7241i	−1.27089	+	1.27089i	−0.325263	+	0.945623i	$0.605453\pi$
$977$	−39.7241	+	39.7241i	−1.27089	+	1.27089i	−0.945623	+	0.325263i	$0.894547\pi$
$978$	16.3897	+	24.4021i	0.524085	+	0.780293i
$979$	0.830758	−	0.830758i	0.0265511	−	0.0265511i
$980$	39.1730	+	3.62505i	1.25134	+	0.115798i
$981$	16.4394	+	16.4394i	0.524869	+	0.524869i
$982$	−9.64057	+	6.47510i	−0.307643	+	0.206629i
$983$			50.7915i			1.62000i	0.586432	+	0.809999i	$0.300532\pi$
$983$			50.7915i			1.62000i	−0.586432	+	0.809999i	$0.699468\pi$
$984$	−30.9361	+	47.0278i	−0.986208	+	1.49919i
$985$	5.60219	+	18.3948i	0.178501	+	0.586107i
$986$	0.152199	−	0.134648i	0.00484701	−	0.00428808i
$987$	63.2267	−	63.2267i	2.01253	−	2.01253i
$988$	13.1328	−	5.51371i	0.417811	−	0.175415i
$989$	−4.16188	+	4.16188i	−0.132340	+	0.132340i
$990$	0.330006	+	3.23447i	0.0104883	+	0.102798i
$991$	−3.49531	+	3.49531i	−0.111032	+	0.111032i	−0.760440	−	0.649408i	$-0.775017\pi$
$991$	−3.49531	+	3.49531i	−0.111032	+	0.111032i	0.649408	+	0.760440i	$0.275017\pi$
$992$	24.3126	−	16.6701i	0.771927	−	0.529276i
$993$		−	43.2302i		−	1.37187i
$994$	−82.1761	−	16.1412i	−2.60647	−	0.511967i
$995$	19.4035	−	36.3979i	0.615131	−	1.15389i
$996$	33.5538	−	14.0873i	1.06319	−	0.446372i
$997$	29.5083			0.934537			0.467269	−	0.884115i	$-0.345238\pi$
$997$	29.5083			0.934537			0.467269	+	0.884115i	$0.345238\pi$
$998$	−2.28317	+	11.6238i	−0.0722725	+	0.367946i
$999$	−2.57056			−0.0813290

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	340.2.i.c.47.39	yes	96
4.3	odd	2	inner	340.2.i.c.47.34	✓	96
5.3	odd	4		340.2.s.c.183.15	yes	96
17.4	even	4		340.2.s.c.327.10	yes	96
20.3	even	4		340.2.s.c.183.10	yes	96
68.55	odd	4		340.2.s.c.327.15	yes	96
85.38	odd	4	inner	340.2.i.c.123.34	yes	96
340.123	even	4	inner	340.2.i.c.123.39	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
340.2.i.c.47.34	✓	96	4.3	odd	2	inner
340.2.i.c.47.39	yes	96	1.1	even	1	trivial
340.2.i.c.123.34	yes	96	85.38	odd	4	inner
340.2.i.c.123.39	yes	96	340.123	even	4	inner
340.2.s.c.183.10	yes	96	20.3	even	4
340.2.s.c.183.15	yes	96	5.3	odd	4
340.2.s.c.327.10	yes	96	17.4	even	4
340.2.s.c.327.15	yes	96	68.55	odd	4

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:	\( N \)	\(=\)	\( 340 = 2^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	340.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17399 - 0.788511i) q^{2} -2.30159i q^{3} +(0.756500 - 1.85141i) q^{4} +(-0.651458 - 2.13907i) q^{5} +(-1.81483 - 2.70204i) q^{6} +3.97452i q^{7} +(-0.571733 - 2.77004i) q^{8} -2.29731 q^{9} +(-2.45148 - 1.99756i) q^{10} +(0.316459 + 0.316459i) q^{11} +(-4.26118 - 1.74115i) q^{12} +(1.77966 - 1.77966i) q^{13} +(3.13395 + 4.66604i) q^{14} +(-4.92325 + 1.49939i) q^{15} +(-2.85542 - 2.80118i) q^{16} +(3.27595 + 2.50362i) q^{17} +(-2.69702 + 1.81145i) q^{18} +2.82964i q^{19} +(-4.45311 - 0.412089i) q^{20} +9.14770 q^{21} +(0.621051 + 0.121988i) q^{22} -0.996717 q^{23} +(-6.37549 + 1.31589i) q^{24} +(-4.15120 + 2.78702i) q^{25} +(0.686018 - 3.49258i) q^{26} -1.61730i q^{27} +(7.35845 + 3.00672i) q^{28} +(0.0246430 - 0.0246430i) q^{29} +(-4.59755 + 5.64230i) q^{30} +(-3.68484 + 3.68484i) q^{31} +(-5.56099 - 1.03702i) q^{32} +(0.728359 - 0.728359i) q^{33} +(5.82007 + 0.356101i) q^{34} +(8.50175 - 2.58923i) q^{35} +(-1.73791 + 4.25325i) q^{36} -1.58941i q^{37} +(2.23120 + 3.32196i) q^{38} +(-4.09604 - 4.09604i) q^{39} +(-5.55284 + 3.02754i) q^{40} +(6.11435 - 6.11435i) q^{41} +(10.7393 - 7.21307i) q^{42} +(4.17559 - 4.17559i) q^{43} +(0.825296 - 0.346494i) q^{44} +(1.49660 + 4.91410i) q^{45} +(-1.17013 + 0.785922i) q^{46} +(6.91175 - 6.91175i) q^{47} +(-6.44716 + 6.57199i) q^{48} -8.79678 q^{49} +(-2.67587 + 6.54521i) q^{50} +(5.76231 - 7.53989i) q^{51} +(-1.94856 - 4.64118i) q^{52} +(9.08331 + 9.08331i) q^{53} +(-1.27526 - 1.89870i) q^{54} +(0.470767 - 0.883087i) q^{55} +(11.0096 - 2.27236i) q^{56} +6.51266 q^{57} +(0.00949931 - 0.0483618i) q^{58} -4.28205i q^{59} +(-0.948458 + 10.2492i) q^{60} +(-9.74339 + 9.74339i) q^{61} +(-1.42042 + 7.23150i) q^{62} -9.13069i q^{63} +(-7.34624 + 3.16745i) q^{64} +(-4.96617 - 2.64743i) q^{65} +(0.280766 - 1.42940i) q^{66} +(5.61205 - 5.61205i) q^{67} +(7.11349 - 4.17113i) q^{68} +2.29403i q^{69} +(7.93932 - 9.74346i) q^{70} +(-10.5354 + 10.5354i) q^{71} +(1.31345 + 6.36364i) q^{72} +6.55715 q^{73} +(-1.25327 - 1.86595i) q^{74} +(6.41458 + 9.55436i) q^{75} +(5.23881 + 2.14062i) q^{76} +(-1.25777 + 1.25777i) q^{77} +(-8.03847 - 1.57893i) q^{78} +(-9.90208 + 9.90208i) q^{79} +(-4.13172 + 7.93277i) q^{80} -10.6143 q^{81} +(2.35694 - 11.9994i) q^{82} +(-5.59012 + 5.59012i) q^{83} +(6.92024 - 16.9361i) q^{84} +(3.22127 - 8.63848i) q^{85} +(1.60960 - 8.19460i) q^{86} +(-0.0567180 - 0.0567180i) q^{87} +(0.695675 - 1.05754i) q^{88} -2.62516i q^{89} +(5.63181 + 4.58901i) q^{90} +(7.07327 + 7.07327i) q^{91} +(-0.754016 + 1.84533i) q^{92} +(8.48099 + 8.48099i) q^{93} +(2.66433 - 13.5643i) q^{94} +(6.05278 - 1.84339i) q^{95} +(-2.38680 + 12.7991i) q^{96} +11.6243i q^{97} +(-10.3273 + 6.93636i) q^{98} +(-0.727005 - 0.727005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 4 q^{2} - 8 q^{5} + 8 q^{8} - 96 q^{9} - 6 q^{10} - 8 q^{13} + 16 q^{14} - 8 q^{17} - 24 q^{18} + 2 q^{20} - 16 q^{21} + 8 q^{24} + 8 q^{29} - 24 q^{30} + 36 q^{32} - 8 q^{33} + 16 q^{34} + 4 q^{38}+ \cdots - 12 q^{98}+O(q^{100}) \) 96 * q - 4 * q^2 - 8 * q^5 + 8 * q^8 - 96 * q^9 - 6 * q^10 - 8 * q^13 + 16 * q^14 - 8 * q^17 - 24 * q^18 + 2 * q^20 - 16 * q^21 + 8 * q^24 + 8 * q^29 - 24 * q^30 + 36 * q^32 - 8 * q^33 + 16 * q^34 + 4 * q^38 - 2 * q^40 + 8 * q^41 + 16 * q^42 - 8 * q^44 - 40 * q^45 - 24 * q^46 + 92 * q^48 - 80 * q^49 - 24 * q^50 + 12 * q^52 + 4 * q^54 - 12 * q^56 + 16 * q^57 + 32 * q^60 + 48 * q^61 + 48 * q^62 - 8 * q^65 + 80 * q^68 + 28 * q^70 + 8 * q^72 - 16 * q^73 - 20 * q^74 + 56 * q^77 - 34 * q^80 - 16 * q^81 + 32 * q^85 + 8 * q^86 - 80 * q^88 - 82 * q^90 - 136 * q^92 + 24 * q^93 - 112 * q^94 + 40 * q^96 - 12 * q^98

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