LMFDB - Embedded newform 209.2.f.b.58.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [209,2,Mod(20,209)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("209.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(209, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			58.3
Character	$\chi$	$=$	209.58
Dual form			209.2.f.b.191.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.732184 + 0.531963i) q^{2} +(-0.173387 - 0.533629i) q^{3} +(-0.364925 + 1.12312i) q^{4} +(-2.22723 - 1.61818i) q^{5} +(0.410822 + 0.298480i) q^{6} +(0.170311 - 0.524163i) q^{7} +(-0.889607 - 2.73793i) q^{8} +(2.17235 - 1.57831i) q^{9} +2.49156 q^{10} +(0.885404 - 3.19626i) q^{11} +0.662605 q^{12} +(1.24882 - 0.907320i) q^{13} +(0.154136 + 0.474383i) q^{14} +(-0.477336 + 1.46909i) q^{15} +(0.197059 + 0.143172i) q^{16} +(-1.58913 - 1.15457i) q^{17} +(-0.750962 + 2.31122i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(2.63019 - 1.91094i) q^{20} -0.309239 q^{21} +(1.05201 + 2.81125i) q^{22} -3.43489 q^{23} +(-1.30679 + 0.949441i) q^{24} +(0.796977 + 2.45284i) q^{25} +(-0.431705 + 1.32865i) q^{26} +(-2.58069 - 1.87498i) q^{27} +(0.526549 + 0.382561i) q^{28} +(0.396594 - 1.22059i) q^{29} +(-0.432003 - 1.32957i) q^{30} +(3.51066 - 2.55065i) q^{31} +5.53721 q^{32} +(-1.85913 + 0.0817108i) q^{33} +1.77773 q^{34} +(-1.22751 + 0.891840i) q^{35} +(0.979888 + 3.01579i) q^{36} +(-2.30102 + 7.08181i) q^{37} +(0.732184 + 0.531963i) q^{38} +(-0.700701 - 0.509089i) q^{39} +(-2.44910 + 7.53755i) q^{40} +(-2.17638 - 6.69822i) q^{41} +(0.226420 - 0.164503i) q^{42} -7.87829 q^{43} +(3.26669 + 2.16081i) q^{44} -7.39232 q^{45} +(2.51497 - 1.82723i) q^{46} +(1.91960 + 5.90791i) q^{47} +(0.0422332 - 0.129980i) q^{48} +(5.41738 + 3.93596i) q^{49} +(-1.88835 - 1.37197i) q^{50} +(-0.340580 + 1.04820i) q^{51} +(0.563307 + 1.73368i) q^{52} +(3.22601 - 2.34383i) q^{53} +2.88695 q^{54} +(-7.14412 + 5.68607i) q^{55} -1.58663 q^{56} +(-0.453932 + 0.329801i) q^{57} +(0.358929 + 1.10467i) q^{58} +(-0.728326 + 2.24156i) q^{59} +(-1.47578 - 1.07221i) q^{60} +(-1.84007 - 1.33689i) q^{61} +(-1.21360 + 3.73508i) q^{62} +(-0.457315 - 1.40747i) q^{63} +(-4.44837 + 3.23193i) q^{64} -4.24962 q^{65} +(1.31776 - 1.04882i) q^{66} +2.61490 q^{67} +(1.87664 - 1.36346i) q^{68} +(0.595564 + 1.83296i) q^{69} +(0.424339 - 1.30598i) q^{70} +(9.70010 + 7.04754i) q^{71} +(-6.25383 - 4.54367i) q^{72} +(-0.0934697 + 0.287670i) q^{73} +(-2.08249 - 6.40924i) q^{74} +(1.17072 - 0.850581i) q^{75} +1.18092 q^{76} +(-1.52457 - 1.00845i) q^{77} +0.783859 q^{78} +(-1.46269 + 1.06271i) q^{79} +(-0.207219 - 0.637753i) q^{80} +(1.93621 - 5.95904i) q^{81} +(5.15672 + 3.74658i) q^{82} +(-8.64470 - 6.28074i) q^{83} +(0.112849 - 0.347313i) q^{84} +(1.67107 + 5.14301i) q^{85} +(5.76836 - 4.19096i) q^{86} -0.720107 q^{87} +(-9.53878 + 0.419239i) q^{88} +11.4054 q^{89} +(5.41254 - 3.93244i) q^{90} +(-0.262896 - 0.809111i) q^{91} +(1.25348 - 3.85781i) q^{92} +(-1.96980 - 1.43114i) q^{93} +(-4.54829 - 3.30453i) q^{94} +(-0.850727 + 2.61827i) q^{95} +(-0.960079 - 2.95482i) q^{96} +(15.5584 - 11.3038i) q^{97} -6.06030 q^{98} +(-3.12126 - 8.34084i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + q^{3} - 6 q^{4} + 7 q^{5} - 14 q^{6} - 12 q^{7} + 4 q^{8} + 6 q^{9} - 12 q^{10} + 2 q^{11} - 16 q^{12} + 5 q^{13} + 23 q^{14} + 15 q^{15} + 30 q^{16} - 15 q^{17} - 38 q^{18} + 7 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + q^3 - 6 * q^4 + 7 * q^5 - 14 * q^6 - 12 * q^7 + 4 * q^8 + 6 * q^9 - 12 * q^10 + 2 * q^11 - 16 * q^12 + 5 * q^13 + 23 * q^14 + 15 * q^15 + 30 * q^16 - 15 * q^17 - 38 * q^18 + 7 * q^19 + 8 * q^20 - 18 * q^21 + 18 * q^22 - 42 * q^23 - 4 * q^24 + 2 * q^25 + 14 * q^26 + 28 * q^27 - 15 * q^28 - 21 * q^29 + 10 * q^30 + 19 * q^31 - 4 * q^32 - 28 * q^33 - 20 * q^34 - 16 * q^35 + 46 * q^36 + 23 * q^37 + 2 * q^38 - 4 * q^39 - 84 * q^40 + 5 * q^41 + 34 * q^42 - 12 * q^43 - 11 * q^44 - 22 * q^45 + 19 * q^46 + 43 * q^47 + 28 * q^48 - q^49 - 43 * q^50 - 6 * q^51 - 21 * q^52 + 46 * q^53 + 60 * q^54 - 92 * q^55 - 60 * q^56 - q^57 + 63 * q^58 + 3 * q^59 + 40 * q^60 - 12 * q^61 - 25 * q^62 + 9 * q^63 + 44 * q^64 + 26 * q^65 + 13 * q^66 + 24 * q^67 - 19 * q^68 - q^69 - 14 * q^70 + 14 * q^71 - 7 * q^72 + 7 * q^73 - 58 * q^74 + 50 * q^75 - 14 * q^76 - 60 * q^77 + 6 * q^78 - 62 * q^79 + 85 * q^80 + 31 * q^81 + 36 * q^82 + 5 * q^83 - 59 * q^84 - 9 * q^85 + 34 * q^86 - 34 * q^87 - 16 * q^88 - 108 * q^89 - 28 * q^90 + 45 * q^91 + 62 * q^92 + 13 * q^93 - 80 * q^94 - 7 * q^95 - 40 * q^96 + 38 * q^97 + 84 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.732184	+	0.531963i	−0.517732	+	0.376154i	−0.815749	−	0.578406i	$-0.803675\pi$
$2$	−0.732184	+	0.531963i	−0.517732	+	0.376154i	0.298017	+	0.954561i	$0.403675\pi$
$3$	−0.173387	−	0.533629i	−0.100105	−	0.308091i	0.888446	−	0.458982i	$-0.151786\pi$
$3$	−0.173387	−	0.533629i	−0.100105	−	0.308091i	−0.988550	+	0.150891i	$0.951786\pi$
$4$	−0.364925	+	1.12312i	−0.182463	+	0.561562i
$5$	−2.22723	−	1.61818i	−0.996049	−	0.723672i	−0.0348115	−	0.999394i	$-0.511083\pi$
$5$	−2.22723	−	1.61818i	−0.996049	−	0.723672i	−0.961237	+	0.275722i	$0.911083\pi$
$6$	0.410822	+	0.298480i	0.167717	+	0.121854i
$7$	0.170311	−	0.524163i	0.0643715	−	0.198115i	−0.913698	−	0.406394i	$-0.866786\pi$
$7$	0.170311	−	0.524163i	0.0643715	−	0.198115i	0.978070	+	0.208279i	$0.0667861\pi$
$8$	−0.889607	−	2.73793i	−0.314523	−	0.968004i
$9$	2.17235	−	1.57831i	0.724118	−	0.526102i
$10$	2.49156			0.787899
$11$	0.885404	−	3.19626i	0.266959	−	0.963708i
$11$	0.885404	−	3.19626i	0.266959	−	0.963708i
$12$	0.662605			0.191278
$13$	1.24882	−	0.907320i	0.346360	−	0.251645i	−0.400980	−	0.916087i	$-0.631330\pi$
$13$	1.24882	−	0.907320i	0.346360	−	0.251645i	0.747340	+	0.664441i	$0.231330\pi$
$14$	0.154136	+	0.474383i	0.0411947	+	0.126784i
$15$	−0.477336	+	1.46909i	−0.123248	+	0.379317i
$16$	0.197059	+	0.143172i	0.0492647	+	0.0357929i
$17$	−1.58913	−	1.15457i	−0.385422	−	0.280025i	0.378155	−	0.925742i	$-0.376559\pi$
$17$	−1.58913	−	1.15457i	−0.385422	−	0.280025i	−0.763577	+	0.645717i	$0.776559\pi$
$18$	−0.750962	+	2.31122i	−0.177003	+	0.544760i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	2.63019	−	1.91094i	0.588128	−	0.427300i
$21$	−0.309239			−0.0674814
$22$	1.05201	+	2.81125i	0.224290	+	0.599361i
$23$	−3.43489			−0.716224			−0.358112	−	0.933679i	$-0.616579\pi$
$23$	−3.43489			−0.716224			−0.358112	+	0.933679i	$0.616579\pi$
$24$	−1.30679	+	0.949441i	−0.266748	+	0.193804i
$25$	0.796977	+	2.45284i	0.159395	+	0.490569i
$26$	−0.431705	+	1.32865i	−0.0846642	+	0.260570i
$27$	−2.58069	−	1.87498i	−0.496653	−	0.360840i
$28$	0.526549	+	0.382561i	0.0995085	+	0.0722971i
$29$	0.396594	−	1.22059i	0.0736456	−	0.226658i	−0.907457	−	0.420144i	$-0.861979\pi$
$29$	0.396594	−	1.22059i	0.0736456	−	0.226658i	0.981103	+	0.193486i	$0.0619795\pi$
$30$	−0.432003	−	1.32957i	−0.0788725	−	0.242745i
$31$	3.51066	−	2.55065i	0.630534	−	0.458110i	−0.226051	−	0.974115i	$-0.572582\pi$
$31$	3.51066	−	2.55065i	0.630534	−	0.458110i	0.856585	+	0.516006i	$0.172582\pi$
$32$	5.53721			0.978850
$33$	−1.85913	+	0.0817108i	−0.323634	+	0.0142240i
$34$	1.77773			0.304878
$35$	−1.22751	+	0.891840i	−0.207487	+	0.150748i
$36$	0.979888	+	3.01579i	0.163315	+	0.502631i
$37$	−2.30102	+	7.08181i	−0.378285	+	1.16424i	0.562950	+	0.826491i	$0.309666\pi$
$37$	−2.30102	+	7.08181i	−0.378285	+	1.16424i	−0.941235	+	0.337751i	$0.890334\pi$
$38$	0.732184	+	0.531963i	0.118776	+	0.0862958i
$39$	−0.700701	−	0.509089i	−0.112202	−	0.0815195i
$40$	−2.44910	+	7.53755i	−0.387236	+	1.19179i
$41$	−2.17638	−	6.69822i	−0.339894	−	1.04609i	−0.964261	−	0.264955i	$-0.914643\pi$
$41$	−2.17638	−	6.69822i	−0.339894	−	1.04609i	0.624366	−	0.781132i	$-0.285357\pi$
$42$	0.226420	−	0.164503i	0.0349373	−	0.0253834i
$43$	−7.87829			−1.20143			−0.600714	−	0.799464i	$-0.705117\pi$
$43$	−7.87829			−1.20143			−0.600714	+	0.799464i	$0.705117\pi$
$44$	3.26669	+	2.16081i	0.492471	+	0.325755i
$45$	−7.39232			−1.10198
$46$	2.51497	−	1.82723i	0.370812	−	0.269411i
$47$	1.91960	+	5.90791i	0.280002	+	0.861758i	0.987852	+	0.155395i	$0.0496651\pi$
$47$	1.91960	+	5.90791i	0.280002	+	0.861758i	−0.707850	+	0.706362i	$0.750335\pi$
$48$	0.0422332	−	0.129980i	0.00609584	−	0.0187611i
$49$	5.41738	+	3.93596i	0.773911	+	0.562279i
$50$	−1.88835	−	1.37197i	−0.267054	−	0.194026i
$51$	−0.340580	+	1.04820i	−0.0476907	+	0.146777i
$52$	0.563307	+	1.73368i	0.0781167	+	0.240418i
$53$	3.22601	−	2.34383i	0.443126	−	0.321950i	−0.343750	−	0.939061i	$-0.611697\pi$
$53$	3.22601	−	2.34383i	0.443126	−	0.321950i	0.786876	+	0.617111i	$0.211697\pi$
$54$	2.88695			0.392865
$55$	−7.14412	+	5.68607i	−0.963313	+	0.766709i
$56$	−1.58663			−0.212022
$57$	−0.453932	+	0.329801i	−0.0601248	+	0.0436832i
$58$	0.358929	+	1.10467i	0.0471297	+	0.145050i
$59$	−0.728326	+	2.24156i	−0.0948200	+	0.291826i	−0.987207	−	0.159446i	$-0.949029\pi$
$59$	−0.728326	+	2.24156i	−0.0948200	+	0.291826i	0.892387	+	0.451271i	$0.149029\pi$
$60$	−1.47578	−	1.07221i	−0.190522	−	0.138422i
$61$	−1.84007	−	1.33689i	−0.235597	−	0.171171i	0.463722	−	0.885981i	$-0.346514\pi$
$61$	−1.84007	−	1.33689i	−0.235597	−	0.171171i	−0.699319	+	0.714809i	$0.746514\pi$
$62$	−1.21360	+	3.73508i	−0.154128	+	0.474356i
$63$	−0.457315	−	1.40747i	−0.0576163	−	0.177325i
$64$	−4.44837	+	3.23193i	−0.556047	+	0.403992i
$65$	−4.24962			−0.527100
$66$	1.31776	−	1.04882i	0.162205	−	0.129101i
$67$	2.61490			0.319461			0.159730	−	0.987161i	$-0.448937\pi$
$67$	2.61490			0.319461			0.159730	+	0.987161i	$0.448937\pi$
$68$	1.87664	−	1.36346i	0.227577	−	0.165344i
$69$	0.595564	+	1.83296i	0.0716975	+	0.220662i
$70$	0.424339	−	1.30598i	0.0507182	−	0.156095i
$71$	9.70010	+	7.04754i	1.15119	+	0.836389i	0.988639	−	0.150311i	$-0.0480276\pi$
$71$	9.70010	+	7.04754i	1.15119	+	0.836389i	0.162552	+	0.986700i	$0.448028\pi$
$72$	−6.25383	−	4.54367i	−0.737021	−	0.535477i
$73$	−0.0934697	+	0.287670i	−0.0109398	+	0.0336692i	−0.956377	−	0.292134i	$-0.905635\pi$
$73$	−0.0934697	+	0.287670i	−0.0109398	+	0.0336692i	0.945438	+	0.325803i	$0.105635\pi$
$74$	−2.08249	−	6.40924i	−0.242085	−	0.745060i
$75$	1.17072	−	0.850581i	0.135184	−	0.0982166i
$76$	1.18092			0.135461
$77$	−1.52457	−	1.00845i	−0.173740	−	0.114924i
$78$	0.783859			0.0887545
$79$	−1.46269	+	1.06271i	−0.164566	+	0.119564i	−0.667020	−	0.745040i	$-0.732430\pi$
$79$	−1.46269	+	1.06271i	−0.164566	+	0.119564i	0.502454	+	0.864604i	$0.332430\pi$
$80$	−0.207219	−	0.637753i	−0.0231677	−	0.0713030i
$81$	1.93621	−	5.95904i	0.215134	−	0.662115i
$82$	5.15672	+	3.74658i	0.569464	+	0.413740i
$83$	−8.64470	−	6.28074i	−0.948879	−	0.689401i	0.00166243	−	0.999999i	$-0.499471\pi$
$83$	−8.64470	−	6.28074i	−0.948879	−	0.689401i	−0.950541	+	0.310598i	$0.899471\pi$
$84$	0.112849	−	0.347313i	0.0123128	−	0.0378950i
$85$	1.67107	+	5.14301i	0.181252	+	0.557838i
$86$	5.76836	−	4.19096i	0.622018	−	0.451923i
$87$	−0.720107			−0.0772036
$88$	−9.53878	+	0.419239i	−1.01684	+	0.0446910i
$89$	11.4054			1.20897			0.604483	−	0.796618i	$-0.293380\pi$
$89$	11.4054			1.20897			0.604483	+	0.796618i	$0.293380\pi$
$90$	5.41254	−	3.93244i	0.570532	−	0.414516i
$91$	−0.262896	−	0.809111i	−0.0275590	−	0.0848179i
$92$	1.25348	−	3.85781i	0.130684	−	0.402204i
$93$	−1.96980	−	1.43114i	−0.204259	−	0.148403i
$94$	−4.54829	−	3.30453i	−0.469120	−	0.340836i
$95$	−0.850727	+	2.61827i	−0.0872828	+	0.268629i
$96$	−0.960079	−	2.95482i	−0.0979876	−	0.301575i
$97$	15.5584	−	11.3038i	1.57972	−	1.14773i	0.662698	−	0.748886i	$-0.269411\pi$
$97$	15.5584	−	11.3038i	1.57972	−	1.14773i	0.917018	−	0.398845i	$-0.130589\pi$
$98$	−6.06030			−0.612183
$99$	−3.12126	−	8.34084i	−0.313699	−	0.838286i
$100$	−3.04568			−0.304568
$101$	10.6156	−	7.71270i	1.05629	−	0.767442i	0.0828947	−	0.996558i	$-0.473583\pi$
$101$	10.6156	−	7.71270i	1.05629	−	0.767442i	0.973399	+	0.229116i	$0.0735835\pi$
$102$	−0.308235	−	0.948649i	−0.0305198	−	0.0939302i
$103$	−1.74514	+	5.37098i	−0.171953	+	0.529218i	−0.999481	−	0.0322066i	$-0.989747\pi$
$103$	−1.74514	+	5.37098i	−0.171953	+	0.529218i	0.827528	+	0.561425i	$0.189747\pi$
$104$	−3.59513	−	2.61202i	−0.352532	−	0.256129i
$105$	0.688746	+	0.500403i	0.0672148	+	0.0488344i
$106$	−1.11520	+	3.43223i	−0.108318	+	0.333368i
$107$	−1.15739	−	3.56207i	−0.111889	−	0.344358i	0.879397	−	0.476090i	$-0.157946\pi$
$107$	−1.15739	−	3.56207i	−0.111889	−	0.344358i	−0.991285	+	0.131732i	$0.957946\pi$
$108$	3.04759	−	2.21420i	0.293254	−	0.213062i
$109$	11.2982			1.08217			0.541084	−	0.840968i	$-0.318014\pi$
$109$	11.2982			1.08217			0.541084	+	0.840968i	$0.318014\pi$
$110$	2.20603	−	7.96365i	0.210337	−	0.759304i
$111$	4.17803			0.396561
$112$	0.108607	−	0.0789073i	0.0102624	−	0.00745604i
$113$	−0.902876	−	2.77877i	−0.0849355	−	0.261405i	0.899565	−	0.436787i	$-0.143884\pi$
$113$	−0.902876	−	2.77877i	−0.0849355	−	0.261405i	−0.984500	+	0.175383i	$0.943884\pi$
$114$	0.156920	−	0.482950i	0.0146969	−	0.0452324i
$115$	7.65030	+	5.55827i	0.713394	+	0.518311i
$116$	1.22615	+	0.890848i	0.113845	+	0.0827131i
$117$	1.28085	−	3.94204i	0.118414	−	0.364442i
$118$	−0.659156	−	2.02867i	−0.0606802	−	0.186755i
$119$	−0.875832	+	0.636329i	−0.0802874	+	0.0583322i
$120$	4.44690			0.405944
$121$	−9.43212	−	5.65996i	−0.857465	−	0.514542i
$122$	2.05845			0.186363
$123$	−3.19701	+	2.32277i	−0.288265	+	0.209437i
$124$	1.58356	+	4.87370i	0.142208	+	0.437671i
$125$	−2.05955	+	6.33864i	−0.184212	+	0.566945i
$126$	1.08356	+	0.787253i	0.0965313	+	0.0701341i
$127$	12.3504	+	8.97309i	1.09592	+	0.796233i	0.980389	−	0.197071i	$-0.0631428\pi$
$127$	12.3504	+	8.97309i	1.09592	+	0.796233i	0.115532	+	0.993304i	$0.463143\pi$
$128$	−1.88442	+	5.79966i	−0.166561	+	0.512622i
$129$	1.36599	+	4.20409i	0.120269	+	0.370150i
$130$	3.11150	−	2.26064i	0.272897	−	0.198271i
$131$	−14.1608			−1.23724			−0.618618	−	0.785692i	$-0.712307\pi$
$131$	−14.1608			−1.23724			−0.618618	+	0.785692i	$0.712307\pi$
$132$	0.586673	−	2.11786i	0.0510634	−	0.184336i
$133$	−0.551138			−0.0477897
$134$	−1.91459	+	1.39103i	−0.165395	+	0.120167i
$135$	2.71374	+	8.35202i	0.233561	+	0.718828i
$136$	−1.74744	+	5.37805i	−0.149841	+	0.461164i
$137$	8.65184	+	6.28593i	0.739176	+	0.537043i	0.892453	−	0.451140i	$-0.148983\pi$
$137$	8.65184	+	6.28593i	0.739176	+	0.537043i	−0.153277	+	0.988183i	$0.548983\pi$
$138$	−1.41113	−	1.02524i	−0.120123	−	0.0872746i
$139$	3.55666	−	10.9463i	0.301672	−	0.928450i	−0.679226	−	0.733929i	$-0.737685\pi$
$139$	3.55666	−	10.9463i	0.301672	−	0.928450i	0.980898	−	0.194522i	$-0.0623154\pi$
$140$	−0.553697	−	1.70410i	−0.0467959	−	0.144023i
$141$	2.81980	−	2.04871i	0.237470	−	0.172532i
$142$	−10.8513			−0.910620
$143$	−1.79432	−	4.79489i	−0.150048	−	0.400969i
$144$	0.654050			0.0545042
$145$	−2.85844	+	2.07678i	−0.237381	+	0.172467i
$146$	−0.0845928	−	0.260350i	−0.00700095	−	0.0215467i
$147$	1.16104	−	3.57331i	0.0957610	−	0.294722i
$148$	−7.11405	−	5.16866i	−0.584771	−	0.424861i
$149$	−7.89912	−	5.73905i	−0.647121	−	0.470161i	0.215168	−	0.976577i	$-0.430970\pi$
$149$	−7.89912	−	5.73905i	−0.647121	−	0.470161i	−0.862289	+	0.506416i	$0.830970\pi$
$150$	−0.404708	+	1.24556i	−0.0330443	+	0.101700i
$151$	3.93261	+	12.1033i	0.320031	+	0.984954i	0.973634	+	0.228117i	$0.0732567\pi$
$151$	3.93261	+	12.1033i	0.320031	+	0.984954i	−0.653603	+	0.756838i	$0.726743\pi$
$152$	−2.32902	+	1.69213i	−0.188908	+	0.137250i
$153$	−5.27444			−0.426413
$154$	1.65272	−	0.0726388i	0.133180	−	0.00585340i
$155$	−11.9465			−0.959563
$156$	0.827474	−	0.601195i	0.0662509	−	0.0481341i
$157$	−5.59597	−	17.2226i	−0.446607	−	1.37452i	−0.880712	−	0.473653i	$-0.842935\pi$
$157$	−5.59597	−	17.2226i	−0.446607	−	1.37452i	0.434104	−	0.900863i	$-0.357065\pi$
$158$	0.505638	−	1.55619i	0.0402264	−	0.123804i
$159$	−1.81009	−	1.31510i	−0.143549	−	0.104295i
$160$	−12.3327	−	8.96020i	−0.974982	−	0.708366i
$161$	−0.584999	+	1.80044i	−0.0461044	+	0.141895i
$162$	1.75233	+	5.39310i	0.137676	+	0.423722i
$163$	−7.63132	+	5.54448i	−0.597731	+	0.434277i	−0.845073	−	0.534651i	$-0.820443\pi$
$163$	−7.63132	+	5.54448i	−0.597731	+	0.434277i	0.247342	+	0.968928i	$0.420443\pi$
$164$	8.31715			0.649460
$165$	4.27295	+	2.82642i	0.332649	+	0.220037i
$166$	9.67063			0.750587
$167$	−20.2836	+	14.7369i	−1.56959	+	1.14038i	−0.642050	+	0.766663i	$0.721916\pi$
$167$	−20.2836	+	14.7369i	−1.56959	+	1.14038i	−0.927544	+	0.373714i	$0.878084\pi$
$168$	0.275101	+	0.846673i	0.0212245	+	0.0653222i
$169$	−3.28090	+	10.0976i	−0.252377	+	0.776737i
$170$	−3.95942	−	2.87669i	−0.303673	−	0.220632i
$171$	−2.17235	−	1.57831i	−0.166124	−	0.120696i
$172$	2.87499	−	8.84830i	0.219216	−	0.674677i
$173$	−4.72703	−	14.5483i	−0.359389	−	1.10609i	−0.953421	−	0.301644i	$-0.902465\pi$
$173$	−4.72703	−	14.5483i	−0.359389	−	1.10609i	0.594031	−	0.804442i	$-0.297535\pi$
$174$	0.527251	−	0.383070i	0.0399708	−	0.0290405i
$175$	1.42142			0.107450
$176$	0.632090	−	0.503086i	0.0476456	−	0.0379215i
$177$	1.32244			0.0994009
$178$	−8.35082	+	6.06723i	−0.625921	+	0.454758i
$179$	4.34889	+	13.3845i	0.325052	+	1.00041i	0.971417	+	0.237378i	$0.0762881\pi$
$179$	4.34889	+	13.3845i	0.325052	+	1.00041i	−0.646366	+	0.763028i	$0.723712\pi$
$180$	2.69764	−	8.30249i	0.201070	−	0.618831i
$181$	11.2578	+	8.17925i	0.836783	+	0.607959i	0.921470	−	0.388449i	$-0.126989\pi$
$181$	11.2578	+	8.17925i	0.836783	+	0.607959i	−0.0846868	+	0.996408i	$0.526989\pi$
$182$	0.622905	+	0.452567i	0.0461728	+	0.0335465i
$183$	−0.394360	+	1.21372i	−0.0291519	+	0.0897205i
$184$	3.05570	+	9.40448i	0.225269	+	0.693307i
$185$	16.5845	−	12.0494i	1.21932	−	0.885888i
$186$	2.20357			0.161574
$187$	−5.09734	+	4.05702i	−0.372755	+	0.296679i
$188$	−7.33583			−0.535020
$189$	−1.42231	+	1.03337i	−0.103458	+	0.0751667i
$190$	−0.769933	−	2.36961i	−0.0558568	−	0.171910i
$191$	−7.53589	+	23.1931i	−0.545278	+	1.67819i	0.175050	+	0.984560i	$0.443991\pi$
$191$	−7.53589	+	23.1931i	−0.545278	+	1.67819i	−0.720328	+	0.693633i	$0.756009\pi$
$192$	2.49594	+	1.81341i	0.180129	+	0.130872i
$193$	4.25845	+	3.09394i	0.306530	+	0.222707i	0.730406	−	0.683013i	$-0.239331\pi$
$193$	4.25845	+	3.09394i	0.306530	+	0.222707i	−0.423876	+	0.905720i	$0.639331\pi$
$194$	−5.37839	+	16.5530i	−0.386146	+	1.18844i
$195$	0.736827	+	2.26772i	0.0527653	+	0.162395i
$196$	−6.39750	+	4.64806i	−0.456964	+	0.332004i
$197$	27.0775			1.92919			0.964596	−	0.263731i	$-0.0849531\pi$
$197$	27.0775			1.92919			0.964596	+	0.263731i	$0.0849531\pi$
$198$	6.72236	+	4.44663i	0.477737	+	0.316008i
$199$	1.64293			0.116465			0.0582323	−	0.998303i	$-0.481454\pi$
$199$	1.64293			0.116465			0.0582323	+	0.998303i	$0.481454\pi$
$200$	6.00671	−	4.36413i	0.424739	−	0.308591i
$201$	−0.453389	−	1.39539i	−0.0319796	−	0.0984231i
$202$	−3.66972	+	11.2942i	−0.258200	+	0.794659i
$203$	−0.572244	−	0.415760i	−0.0401637	−	0.0291806i
$204$	−1.05297	−	0.765027i	−0.0737226	−	0.0535626i
$205$	−5.99161	+	18.4403i	−0.418472	+	1.28793i
$206$	−1.57940	−	4.86089i	−0.110042	−	0.338674i
$207$	−7.46179	+	5.42131i	−0.518630	+	0.376807i
$208$	0.375993			0.0260704
$209$	−3.31343	+	0.145628i	−0.229194	+	0.0100733i
$210$	−0.770485			−0.0531685
$211$	13.2736	−	9.64380i	0.913789	−	0.663907i	−0.0281812	−	0.999603i	$-0.508972\pi$
$211$	13.2736	−	9.64380i	0.913789	−	0.663907i	0.941970	+	0.335696i	$0.108972\pi$
$212$	1.45516	+	4.47853i	0.0999410	+	0.307587i
$213$	2.07890	−	6.39821i	0.142444	−	0.438398i
$214$	2.74231	+	1.99240i	0.187460	+	0.136198i
$215$	17.5468	+	12.7485i	1.19668	+	0.869440i
$216$	−2.83776	+	8.73372i	−0.193085	+	0.594255i
$217$	−0.739050	−	2.27456i	−0.0501700	−	0.154407i
$218$	−8.27234	+	6.01021i	−0.560274	+	0.407063i
$219$	0.169716			0.0114683
$220$	−3.77909	−	10.0987i	−0.254786	−	0.680855i
$221$	−3.03211			−0.203962
$222$	−3.05909	+	2.22256i	−0.205312	+	0.149168i
$223$	−4.29072	−	13.2055i	−0.287328	−	0.884304i	−0.985691	−	0.168561i	$-0.946088\pi$
$223$	−4.29072	−	13.2055i	−0.287328	−	0.884304i	0.698364	−	0.715743i	$-0.253912\pi$
$224$	0.943047	−	2.90240i	0.0630100	−	0.193925i
$225$	5.60266	+	4.07057i	0.373510	+	0.271371i
$226$	2.13927	+	1.55427i	0.142302	+	0.103389i
$227$	5.88748	−	18.1198i	0.390766	−	1.20265i	−0.541444	−	0.840737i	$-0.682122\pi$
$227$	5.88748	−	18.1198i	0.390766	−	1.20265i	0.932210	−	0.361917i	$-0.117878\pi$
$228$	−0.204756	−	0.630175i	−0.0135603	−	0.0417344i
$229$	18.4341	−	13.3931i	1.21816	−	0.885044i	0.222212	−	0.974998i	$-0.428672\pi$
$229$	18.4341	−	13.3931i	1.21816	−	0.885044i	0.995946	+	0.0899548i	$0.0286723\pi$
$230$	−8.55822			−0.564312
$231$	−0.273801	+	0.988406i	−0.0180148	+	0.0650323i
$232$	−3.69470			−0.242569
$233$	−21.3370	+	15.5023i	−1.39783	+	1.01559i	−0.402881	+	0.915252i	$0.631991\pi$
$233$	−21.3370	+	15.5023i	−1.39783	+	1.01559i	−0.994954	+	0.100334i	$0.968009\pi$
$234$	1.15920	+	3.56766i	0.0757795	+	0.233225i
$235$	5.28467	−	16.2646i	0.344734	−	1.06098i
$236$	−2.25176	−	1.63600i	−0.146577	−	0.106495i
$237$	0.820703	+	0.596275i	0.0533104	+	0.0387322i
$238$	0.302767	−	0.931820i	0.0196255	−	0.0604009i
$239$	1.64378	+	5.05903i	0.106327	+	0.327242i	0.990040	−	0.140789i	$-0.0449638\pi$
$239$	1.64378	+	5.05903i	0.106327	+	0.327242i	−0.883712	+	0.468030i	$0.844964\pi$
$240$	−0.304395	+	0.221156i	−0.0196486	+	0.0142756i
$241$	25.9984			1.67470			0.837351	−	0.546666i	$-0.184103\pi$
$241$	25.9984			1.67470			0.837351	+	0.546666i	$0.184103\pi$
$242$	9.91693	−	0.873405i	0.637485	−	0.0561446i
$243$	−13.0853			−0.839425
$244$	2.17298	−	1.57876i	0.139111	−	0.101070i
$245$	−5.69668	−	17.5326i	−0.363948	−	1.12012i
$246$	1.10518	−	3.40138i	0.0704635	−	0.216864i
$247$	−1.24882	−	0.907320i	−0.0794604	−	0.0577314i
$248$	−10.1066	−	7.34287i	−0.641769	−	0.466273i
$249$	−1.85271	+	5.70206i	−0.117411	+	0.361354i
$250$	−1.86395	−	5.73666i	−0.117887	−	0.362818i
$251$	−21.9375	+	15.9385i	−1.38468	+	1.00603i	−0.388259	+	0.921550i	$0.626923\pi$
$251$	−21.9375	+	15.9385i	−1.38468	+	1.00603i	−0.996425	+	0.0844818i	$0.973077\pi$
$252$	1.74765			0.110092
$253$	−3.04126	+	10.9788i	−0.191203	+	0.690230i
$254$	−13.8161			−0.866900
$255$	2.45472	−	1.78346i	0.153721	−	0.111685i
$256$	−5.10371	−	15.7076i	−0.318982	−	0.981726i
$257$	1.79967	−	5.53883i	0.112261	−	0.345502i	−0.879105	−	0.476628i	$-0.841859\pi$
$257$	1.79967	−	5.53883i	0.112261	−	0.345502i	0.991366	+	0.131125i	$0.0418590\pi$
$258$	−3.23658	−	2.35151i	−0.201500	−	0.146399i
$259$	3.32014	+	2.41222i	0.206303	+	0.149888i
$260$	1.55079	−	4.77285i	0.0961760	−	0.295999i
$261$	−1.06492	−	3.27750i	−0.0659172	−	0.202872i
$262$	10.3683	−	7.53303i	0.640557	−	0.465392i
$263$	22.8835			1.41106			0.705529	−	0.708681i	$-0.250709\pi$
$263$	22.8835			1.41106			0.705529	+	0.708681i	$0.250709\pi$
$264$	1.87762	+	5.01748i	0.115559	+	0.308805i
$265$	−10.9778			−0.674362
$266$	0.403534	−	0.293185i	0.0247423	−	0.0179763i
$267$	−1.97754	−	6.08624i	−0.121023	−	0.372472i
$268$	−0.954243	+	2.93686i	−0.0582896	+	0.179397i
$269$	1.00015	+	0.726655i	0.0609805	+	0.0443049i	0.617858	−	0.786290i	$-0.288001\pi$
$269$	1.00015	+	0.726655i	0.0609805	+	0.0443049i	−0.556877	+	0.830595i	$0.688001\pi$
$270$	−6.42992	−	4.67161i	−0.391313	−	0.284305i
$271$	2.74002	−	8.43293i	0.166445	−	0.512264i	−0.832695	−	0.553732i	$-0.813203\pi$
$271$	2.74002	−	8.43293i	0.166445	−	0.512264i	0.999140	+	0.0414678i	$0.0132034\pi$
$272$	−0.147851	−	0.455038i	−0.00896477	−	0.0275907i
$273$	−0.386183	+	0.280578i	−0.0233729	+	0.0169814i
$274$	−9.67861			−0.584706
$275$	8.54556	−	0.375586i	0.515317	−	0.0226487i
$276$	−2.27597			−0.136998
$277$	−7.74900	+	5.62998i	−0.465592	+	0.338272i	−0.795721	−	0.605663i	$-0.792908\pi$
$277$	−7.74900	+	5.62998i	−0.465592	+	0.338272i	0.330129	+	0.943936i	$0.392908\pi$
$278$	3.21888	+	9.90669i	0.193056	+	0.594164i
$279$	3.60070	−	11.0818i	0.215568	−	0.663451i
$280$	3.53380	+	2.56745i	0.211185	+	0.153435i
$281$	12.5956	+	9.15125i	0.751392	+	0.545918i	0.896258	−	0.443533i	$-0.146275\pi$
$281$	12.5956	+	9.15125i	0.751392	+	0.545918i	−0.144866	+	0.989451i	$0.546275\pi$
$282$	−0.974779	+	3.00006i	−0.0580472	+	0.178651i
$283$	−3.60559	−	11.0969i	−0.214330	−	0.659640i	−0.999200	−	0.0399802i	$-0.987271\pi$
$283$	−3.60559	−	11.0969i	−0.214330	−	0.659640i	0.784870	−	0.619660i	$-0.212729\pi$
$284$	−11.4551	+	8.32259i	−0.679733	+	0.493855i
$285$	1.54469			0.0914996
$286$	3.86447	+	2.55623i	0.228511	+	0.151153i
$287$	−3.88162			−0.229125
$288$	12.0288	−	8.73942i	0.708802	−	0.514975i
$289$	−4.06098	−	12.4984i	−0.238881	−	0.735201i
$290$	0.988135	−	3.04117i	0.0580253	−	0.178584i
$291$	−8.72968	−	6.34249i	−0.511743	−	0.371803i
$292$	−0.288980	−	0.209956i	−0.0169113	−	0.0122867i
$293$	−0.293977	+	0.904768i	−0.0171743	+	0.0528571i	−0.959276	−	0.282469i	$-0.908847\pi$
$293$	−0.293977	+	0.904768i	−0.0171743	+	0.0528571i	0.942102	+	0.335326i	$0.108847\pi$
$294$	1.05078	+	3.23395i	0.0612825	+	0.188608i
$295$	5.24939	−	3.81391i	0.305631	−	0.222054i
$296$	21.4365			1.24597
$297$	−8.27786	+	6.58842i	−0.480330	+	0.382299i
$298$	8.83657			0.511889
$299$	−4.28955	+	3.11654i	−0.248071	+	0.180234i
$300$	0.528081	+	1.62527i	0.0304888	+	0.0938348i
$301$	−1.34176	+	4.12951i	−0.0773378	+	0.238021i
$302$	−9.31791	−	6.76986i	−0.536185	−	0.389561i
$303$	−5.95633	−	4.32753i	−0.342182	−	0.248610i
$304$	0.0752698	−	0.231657i	0.00431702	−	0.0132864i
$305$	1.93494	+	5.95513i	0.110794	+	0.340990i
$306$	3.86186	−	2.80580i	0.220768	−	0.160397i
$307$	−13.7503			−0.784772			−0.392386	−	0.919801i	$-0.628350\pi$
$307$	−13.7503			−0.784772			−0.392386	+	0.919801i	$0.628350\pi$
$308$	1.68897	−	1.34427i	0.0962380	−	0.0765967i
$309$	3.16870			0.180261
$310$	8.74701	−	6.35508i	0.496797	−	0.360944i
$311$	−1.93242	−	5.94739i	−0.109578	−	0.337246i	0.881200	−	0.472744i	$-0.156736\pi$
$311$	−1.93242	−	5.94739i	−0.109578	−	0.337246i	−0.990778	+	0.135498i	$0.956736\pi$
$312$	−0.770501	+	2.37136i	−0.0436210	+	0.134252i
$313$	−17.1274	−	12.4438i	−0.968097	−	0.703364i	−0.0130801	−	0.999914i	$-0.504164\pi$
$313$	−17.1274	−	12.4438i	−0.968097	−	0.703364i	−0.955017	+	0.296551i	$0.904164\pi$
$314$	13.2591	+	9.63329i	0.748253	+	0.543638i
$315$	−1.25899	+	3.87478i	−0.0709362	+	0.218319i
$316$	−0.659779	−	2.03059i	−0.0371155	−	0.114230i
$317$	−14.1825	+	10.3042i	−0.796567	+	0.578740i	−0.909905	−	0.414817i	$-0.863846\pi$
$317$	−14.1825	+	10.3042i	−0.796567	+	0.578740i	0.113338	+	0.993556i	$0.463846\pi$
$318$	2.02490			0.113551
$319$	−3.55017	−	2.34833i	−0.198772	−	0.131481i
$320$	15.1374			0.846207
$321$	−1.70015	+	1.23523i	−0.0948930	+	0.0689438i
$322$	−0.529441	−	1.62945i	−0.0295046	−	0.0908059i
$323$	−0.606995	+	1.86814i	−0.0337741	+	0.103946i
$324$	5.98617	+	4.34920i	0.332565	+	0.241622i
$325$	3.22079	+	2.34004i	0.178657	+	0.129802i
$326$	2.63807	−	8.11916i	0.146109	−	0.449678i
$327$	−1.95895	−	6.02904i	−0.108330	−	0.333407i
$328$	−16.4031	+	11.9176i	−0.905711	+	0.658038i
$329$	3.42364			0.188751
$330$	−4.63214	+	0.203587i	−0.254991	+	0.0112071i
$331$	25.1460			1.38215			0.691074	−	0.722784i	$-0.257138\pi$
$331$	25.1460			1.38215			0.691074	+	0.722784i	$0.257138\pi$
$332$	10.2087	−	7.41707i	0.560276	−	0.407064i
$333$	6.17864	+	19.0159i	0.338588	+	1.04207i
$334$	7.01185	−	21.5803i	0.383672	−	1.18082i
$335$	−5.82399	−	4.23138i	−0.318199	−	0.231185i
$336$	−0.0609382	−	0.0442742i	−0.00332445	−	0.00241536i
$337$	0.360473	−	1.10942i	0.0196362	−	0.0604341i	−0.940758	−	0.339078i	$-0.889885\pi$
$337$	0.360473	−	1.10942i	0.0196362	−	0.0604341i	0.960394	+	0.278644i	$0.0898849\pi$
$338$	−2.96931	−	9.13860i	−0.161509	−	0.497074i
$339$	−1.32629	+	0.963603i	−0.0720339	+	0.0523357i
$340$	−6.38605			−0.346332
$341$	−5.04416	−	13.4793i	−0.273157	−	0.729947i
$342$	2.43016			0.131408
$343$	6.10688	−	4.43691i	0.329741	−	0.239571i
$344$	7.00858	+	21.5702i	0.377877	+	1.16299i
$345$	1.63959	−	5.04615i	0.0882728	−	0.271676i
$346$	11.2002	+	8.13742i	0.602127	+	0.437471i
$347$	19.5496	+	14.2036i	1.04948	+	0.762491i	0.972113	−	0.234512i	$-0.0753493\pi$
$347$	19.5496	+	14.2036i	1.04948	+	0.762491i	0.0773650	+	0.997003i	$0.475349\pi$
$348$	0.262785	−	0.808769i	0.0140868	−	0.0433546i
$349$	4.72261	+	14.5347i	0.252796	+	0.778025i	0.994256	+	0.107028i	$0.0341336\pi$
$349$	4.72261	+	14.5347i	0.252796	+	0.778025i	−0.741460	+	0.670997i	$0.765866\pi$
$350$	−1.04074	+	0.756145i	−0.0556301	+	0.0404176i
$351$	−4.92401			−0.262824
$352$	4.90267	−	17.6983i	0.261313	−	0.943325i
$353$	7.24054			0.385375			0.192688	−	0.981260i	$-0.438280\pi$
$353$	7.24054			0.385375			0.192688	+	0.981260i	$0.438280\pi$
$354$	−0.968271	+	0.703490i	−0.0514630	+	0.0373901i
$355$	−10.2002	−	31.3930i	−0.541371	−	1.66617i
$356$	−4.16210	+	12.8096i	−0.220591	+	0.678909i
$357$	0.491422	+	0.357039i	0.0260088	+	0.0188965i
$358$	−10.3043	−	7.48648i	−0.544597	−	0.395673i
$359$	4.32844	−	13.3216i	0.228446	−	0.703085i	−0.769477	−	0.638674i	$-0.779483\pi$
$359$	4.32844	−	13.3216i	0.228446	−	0.703085i	0.997923	−	0.0644107i	$-0.0205168\pi$
$360$	6.57626	+	20.2396i	0.346599	+	1.06672i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−12.5938			−0.661916
$363$	−1.38492	+	6.01462i	−0.0726893	+	0.315686i
$364$	1.00467			0.0526590
$365$	0.673681	−	0.489458i	0.0352621	−	0.0256194i
$366$	−0.356907	−	1.09845i	−0.0186559	−	0.0574168i
$367$	4.39294	−	13.5201i	0.229310	−	0.705743i	−0.768516	−	0.639831i	$-0.779004\pi$
$367$	4.39294	−	13.5201i	0.229310	−	0.705743i	0.997825	−	0.0659120i	$-0.0209957\pi$
$368$	−0.676875	−	0.491779i	−0.0352846	−	0.0256357i
$369$	−15.2997	−	11.1159i	−0.796472	−	0.578671i
$370$	−5.73312	+	17.6447i	−0.298051	+	0.917305i
$371$	−0.679126	−	2.09014i	−0.0352585	−	0.108514i
$372$	2.32618	−	1.69007i	0.120607	−	0.0876261i
$373$	−22.1851			−1.14870			−0.574351	−	0.818609i	$-0.694746\pi$
$373$	−22.1851			−1.14870			−0.574351	+	0.818609i	$0.694746\pi$
$374$	1.57401	−	5.68208i	0.0813901	−	0.293813i
$375$	3.73959			0.193111
$376$	14.4678	−	10.5114i	0.746117	−	0.542086i
$377$	−0.612192	−	1.88413i	−0.0315295	−	0.0970378i
$378$	0.491680	−	1.51324i	0.0252893	−	0.0778324i
$379$	−23.4950	−	17.0701i	−1.20686	−	0.876834i	−0.211916	−	0.977288i	$-0.567970\pi$
$379$	−23.4950	−	17.0701i	−1.20686	−	0.876834i	−0.994942	+	0.100454i	$0.967970\pi$
$380$	−2.63019	−	1.91094i	−0.134926	−	0.0980294i
$381$	2.64691	−	8.14635i	0.135605	−	0.417350i
$382$	−6.82020	−	20.9904i	−0.348952	−	1.07396i
$383$	−5.19485	+	3.77428i	−0.265445	+	0.192857i	−0.712544	−	0.701628i	$-0.752457\pi$
$383$	−5.19485	+	3.77428i	−0.265445	+	0.192857i	0.447099	+	0.894484i	$0.352457\pi$
$384$	3.42160			0.174608
$385$	1.76371	+	4.71308i	0.0898867	+	0.240201i
$386$	−4.76383			−0.242472
$387$	−17.1144	+	12.4344i	−0.869976	+	0.632075i
$388$	7.01796	+	21.5991i	0.356283	+	1.09653i
$389$	0.650791	−	2.00293i	0.0329964	−	0.101552i	−0.933202	−	0.359353i	$-0.882998\pi$
$389$	0.650791	−	2.00293i	0.0329964	−	0.101552i	0.966198	+	0.257800i	$0.0829976\pi$
$390$	−1.74584	−	1.26842i	−0.0884038	−	0.0642291i
$391$	5.45850	+	3.96583i	0.276048	+	0.200561i
$392$	5.95703	−	18.3338i	0.300875	−	0.925999i
$393$	2.45530	+	7.55663i	0.123853	+	0.381182i
$394$	−19.8257	+	14.4042i	−0.998805	+	0.725674i
$395$	4.97740			0.250440
$396$	10.5068	−	0.461785i	0.527988	−	0.0232056i
$397$	10.9754			0.550839			0.275420	−	0.961324i	$-0.411183\pi$
$397$	10.9754			0.550839			0.275420	+	0.961324i	$0.411183\pi$
$398$	−1.20293	+	0.873980i	−0.0602975	+	0.0438087i
$399$	0.0955600	+	0.294103i	0.00478398	+	0.0147236i
$400$	−0.194126	+	0.597459i	−0.00970631	+	0.0298729i
$401$	−8.68093	−	6.30706i	−0.433505	−	0.314960i	0.349544	−	0.936920i	$-0.386337\pi$
$401$	−8.68093	−	6.30706i	−0.433505	−	0.314960i	−0.783049	+	0.621960i	$0.786337\pi$
$402$	1.07426	+	0.780494i	0.0535791	+	0.0389275i
$403$	2.06993	−	6.37059i	0.103111	−	0.317342i
$404$	4.78841	+	14.7372i	0.238232	+	0.733204i
$405$	−13.9552	+	10.1390i	−0.693439	+	0.503813i
$406$	0.640157			0.0317704
$407$	20.5980	+	13.6249i	1.02100	+	0.675362i
$408$	3.17287			0.157080
$409$	−2.71253	+	1.97077i	−0.134126	+	0.0974483i	−0.652825	−	0.757508i	$-0.726416\pi$
$409$	−2.71253	+	1.97077i	−0.134126	+	0.0974483i	0.518699	+	0.854957i	$0.326416\pi$
$410$	−5.42258	−	16.6890i	−0.267802	−	0.824211i
$411$	1.85424	−	5.70677i	0.0914630	−	0.281494i
$412$	−5.39543	−	3.92001i	−0.265814	−	0.193125i
$413$	1.05090	+	0.763523i	0.0517114	+	0.0375705i
$414$	2.57947	−	7.93879i	0.126774	−	0.390170i
$415$	9.09039	+	27.9774i	0.446230	+	1.37335i
$416$	6.91497	−	5.02402i	0.339034	−	0.246323i
$417$	−6.45793			−0.316246
$418$	2.34857	−	1.86925i	0.114872	−	0.0914278i
$419$	22.8926			1.11838			0.559189	−	0.829040i	$-0.311113\pi$
$419$	22.8926			1.11838			0.559189	+	0.829040i	$0.311113\pi$
$420$	−0.813356	+	0.590938i	−0.0396877	+	0.0288348i
$421$	9.21319	+	28.3553i	0.449024	+	1.38195i	0.878010	+	0.478642i	$0.158871\pi$
$421$	9.21319	+	28.3553i	0.449024	+	1.38195i	−0.428987	+	0.903311i	$0.641129\pi$
$422$	−4.58854	+	14.1221i	−0.223367	+	0.687452i
$423$	13.4945	+	9.80436i	0.656127	+	0.476704i
$424$	−9.28712	−	6.74749i	−0.451023	−	0.327687i
$425$	1.56548	−	4.81807i	0.0759372	−	0.233711i
$426$	1.88147	+	5.79057i	0.0911575	+	0.280554i
$427$	−1.01413	+	0.736811i	−0.0490773	+	0.0356568i
$428$	4.42300			0.213794
$429$	−2.24758	+	1.78887i	−0.108514	+	0.0863675i
$430$	−19.6292			−0.946605
$431$	−11.1503	+	8.10116i	−0.537091	+	0.390219i	−0.823003	−	0.568036i	$-0.807703\pi$
$431$	−11.1503	+	8.10116i	−0.537091	+	0.390219i	0.285913	+	0.958256i	$0.407703\pi$
$432$	−0.240103	−	0.738962i	−0.0115520	−	0.0355533i
$433$	4.88997	−	15.0498i	0.234997	−	0.723246i	−0.762125	−	0.647430i	$-0.775844\pi$
$433$	4.88997	−	15.0498i	0.234997	−	0.723246i	0.997122	−	0.0758158i	$-0.0241561\pi$
$434$	1.75110	+	1.27225i	0.0840557	+	0.0610700i
$435$	1.60385	+	1.16526i	0.0768985	+	0.0558701i
$436$	−4.12299	+	12.6892i	−0.197455	+	0.607705i
$437$	1.06144	+	3.26677i	0.0507755	+	0.156271i
$438$	−0.124263	+	0.0902824i	−0.00593752	+	0.00431386i
$439$	−31.9164			−1.52329			−0.761644	−	0.647995i	$-0.775608\pi$
$439$	−31.9164			−1.52329			−0.761644	+	0.647995i	$0.775608\pi$
$440$	21.9235	+	14.5017i	1.04516	+	0.691342i
$441$	17.9806			0.856219
$442$	2.22006	−	1.61297i	0.105598	−	0.0767211i
$443$	0.416593	+	1.28214i	0.0197929	+	0.0609163i	0.960465	−	0.278400i	$-0.0898042\pi$
$443$	0.416593	+	1.28214i	0.0197929	+	0.0609163i	−0.940672	+	0.339317i	$0.889804\pi$
$444$	−1.52467	+	4.69244i	−0.0723575	+	0.222693i
$445$	−25.4024	−	18.4559i	−1.20419	−	0.874895i
$446$	10.1664	+	7.38633i	0.481394	+	0.349753i
$447$	−1.69292	+	5.21028i	−0.0800725	+	0.246438i
$448$	0.936453	+	2.88211i	0.0442433	+	0.136167i
$449$	19.4161	−	14.1066i	0.916301	−	0.665731i	−0.0262998	−	0.999654i	$-0.508372\pi$
$449$	19.4161	−	14.1066i	0.916301	−	0.665731i	0.942600	+	0.333923i	$0.108372\pi$
$450$	−6.26756			−0.295456
$451$	−23.3362	+	1.02565i	−1.09886	+	0.0482960i
$452$	3.45038			0.162292
$453$	5.77683	−	4.19711i	0.271419	−	0.197197i
$454$	5.32834	+	16.3990i	0.250072	+	0.769641i
$455$	−0.723756	+	2.22749i	−0.0339302	+	0.104426i
$456$	1.30679	+	0.949441i	0.0611962	+	0.0444616i
$457$	4.14622	+	3.01240i	0.193952	+	0.140914i	0.680523	−	0.732727i	$-0.261753\pi$
$457$	4.14622	+	3.01240i	0.193952	+	0.140914i	−0.486571	+	0.873641i	$0.661753\pi$
$458$	−6.37248	+	19.6125i	−0.297767	+	0.916431i
$459$	1.93626	+	5.95918i	0.0903767	+	0.278151i
$460$	−9.03441	+	6.56388i	−0.421231	+	0.306043i
$461$	−22.3578			−1.04131			−0.520653	−	0.853768i	$-0.674312\pi$
$461$	−22.3578			−1.04131			−0.520653	+	0.853768i	$0.674312\pi$
$462$	−0.325322	−	0.869347i	−0.0151354	−	0.0404457i
$463$	7.90078			0.367181			0.183590	−	0.983003i	$-0.441228\pi$
$463$	7.90078			0.367181			0.183590	+	0.983003i	$0.441228\pi$
$464$	0.252906	−	0.183747i	0.0117409	−	0.00853025i
$465$	2.07136	+	6.37499i	0.0960570	+	0.295633i
$466$	7.37600	−	22.7010i	0.341687	−	1.05160i
$467$	20.5641	+	14.9407i	0.951591	+	0.691371i	0.951183	−	0.308629i	$-0.0998701\pi$
$467$	20.5641	+	14.9407i	0.951591	+	0.691371i	0.000408194		1.00000i	$0.499870\pi$
$468$	3.95999	+	2.87710i	0.183050	+	0.132994i
$469$	0.445346	−	1.37063i	0.0205642	−	0.0632900i
$470$	4.78278	+	14.7199i	0.220613	+	0.678978i
$471$	−8.22024	+	5.97235i	−0.378768	+	0.275191i
$472$	6.78514			0.312312
$473$	−6.97547	+	25.1811i	−0.320733	+	1.15783i
$474$	−0.918102			−0.0421698
$475$	2.08651	−	1.51594i	0.0957358	−	0.0695561i
$476$	−0.395064	−	1.21588i	−0.0181077	−	0.0557298i
$477$	3.30874	−	10.1833i	0.151497	−	0.466260i
$478$	−3.89477	−	2.82971i	−0.178142	−	0.129428i
$479$	−13.6968	−	9.95133i	−0.625824	−	0.454688i	0.229127	−	0.973397i	$-0.426413\pi$
$479$	−13.6968	−	9.95133i	−0.625824	−	0.454688i	−0.854951	+	0.518709i	$0.826413\pi$
$480$	−2.64311	+	8.13465i	−0.120641	+	0.371294i
$481$	3.55191	+	10.9317i	0.161953	+	0.498441i
$482$	−19.0356	+	13.8302i	−0.867047	+	0.629947i
$483$	1.06220			0.0483318
$484$	9.79885	−	8.52798i	0.445402	−	0.387635i
$485$	−52.9438			−2.40406
$486$	9.58088	−	6.96091i	0.434597	−	0.315753i
$487$	−1.82207	−	5.60776i	−0.0825659	−	0.254112i	0.901248	−	0.433303i	$-0.142652\pi$
$487$	−1.82207	−	5.60776i	−0.0825659	−	0.254112i	−0.983814	+	0.179191i	$0.942652\pi$
$488$	−2.02337	+	6.22729i	−0.0915936	+	0.281896i
$489$	4.28187	+	3.11096i	0.193633	+	0.140682i
$490$	13.4977	+	9.80665i	0.609764	+	0.443019i
$491$	9.26801	−	28.5240i	0.418260	−	1.28727i	−0.491043	−	0.871135i	$-0.663384\pi$
$491$	9.26801	−	28.5240i	0.418260	−	1.28727i	0.909303	−	0.416135i	$-0.136616\pi$
$492$	−1.44208	−	4.43828i	−0.0650142	−	0.200093i
$493$	−2.03950	+	1.48179i	−0.0918546	+	0.0667363i
$494$	1.39703			0.0628551
$495$	−6.54519	+	23.6278i	−0.294185	+	1.06199i
$496$	1.05699			0.0474601
$497$	5.34609	−	3.88416i	0.239805	−	0.174229i
$498$	−1.67676	−	5.16053i	−0.0751374	−	0.231249i
$499$	11.0259	−	33.9341i	0.493586	−	1.51910i	−0.325563	−	0.945520i	$-0.605554\pi$
$499$	11.0259	−	33.9341i	0.493586	−	1.51910i	0.819149	−	0.573581i	$-0.194446\pi$
$500$	−6.36750	−	4.62626i	−0.284763	−	0.206893i
$501$	11.3810	+	8.26875i	0.508464	+	0.369421i
$502$	7.58359	−	23.3399i	0.338472	−	1.04171i
$503$	−0.0456724	−	0.140565i	−0.00203643	−	0.00626749i	0.950033	−	0.312149i	$-0.101049\pi$
$503$	−0.0456724	−	0.140565i	−0.00203643	−	0.00626749i	−0.952070	+	0.305882i	$0.901049\pi$
$504$	−3.44672	+	2.50419i	−0.153529	+	0.111546i
$505$	−36.1240			−1.60750
$506$	−3.61354	−	9.65633i	−0.160642	−	0.429276i
$507$	5.95723			0.264570
$508$	−14.5849	+	10.5965i	−0.647099	+	0.470145i
$509$	−4.55678	−	14.0243i	−0.201976	−	0.621617i	−0.999824	−	0.0187592i	$-0.994028\pi$
$509$	−4.55678	−	14.0243i	−0.201976	−	0.621617i	0.797848	−	0.602858i	$-0.205972\pi$
$510$	−0.848574	+	2.61164i	−0.0375755	+	0.115645i
$511$	0.134867	+	0.0979867i	0.00596617	+	0.00433468i
$512$	2.22575	+	1.61710i	0.0983653	+	0.0714666i
$513$	−0.985734	+	3.03378i	−0.0435212	+	0.133945i
$514$	1.62876	+	5.01280i	0.0718414	+	0.221105i
$515$	12.5780	−	9.13847i	0.554254	−	0.402689i
$516$	−5.22020			−0.229806
$517$	20.5828	−	0.904636i	0.905232	−	0.0397858i
$518$	−3.71416			−0.163191
$519$	−6.94379	+	5.04496i	−0.304799	+	0.221449i
$520$	3.78049	+	11.6351i	0.165785	+	0.510235i
$521$	−6.65051	+	20.4682i	−0.291364	+	0.896727i	0.693054	+	0.720886i	$0.256265\pi$
$521$	−6.65051	+	20.4682i	−0.291364	+	0.896727i	−0.984418	+	0.175842i	$0.943735\pi$
$522$	2.52323	+	1.83323i	0.110439	+	0.0802384i
$523$	20.4668	+	14.8700i	0.894949	+	0.650219i	0.937164	−	0.348890i	$-0.113441\pi$
$523$	20.4668	+	14.8700i	0.894949	+	0.650219i	−0.0422146	+	0.999109i	$0.513441\pi$
$524$	5.16764	−	15.9044i	0.225749	−	0.694785i
$525$	−0.246456	−	0.758514i	−0.0107562	−	0.0331042i
$526$	−16.7550	+	12.1732i	−0.730551	+	0.530776i
$527$	−8.52383			−0.371304
$528$	−0.378058	−	0.250073i	−0.0164528	−	0.0108831i
$529$	−11.2015			−0.487023
$530$	8.03778	−	5.83979i	0.349139	−	0.253664i
$531$	1.95568	+	6.01898i	0.0848694	+	0.261201i
$532$	0.201124	−	0.618996i	0.00871983	−	0.0268369i
$533$	−8.79534	−	6.39019i	−0.380969	−	0.276790i
$534$	4.68557	+	3.40427i	0.202765	+	0.147317i
$535$	−3.18630	+	9.80641i	−0.137756	+	0.423968i
$536$	−2.32623	−	7.15941i	−0.100478	−	0.309239i
$537$	6.38833	−	4.64140i	0.275677	−	0.200291i
$538$	−1.11885			−0.0482371
$539$	17.3769	−	13.8304i	0.748476	−	0.595718i
$540$	−10.3707			−0.446282
$541$	6.84669	−	4.97441i	0.294362	−	0.213867i	−0.430795	−	0.902450i	$-0.641767\pi$
$541$	6.84669	−	4.97441i	0.294362	−	0.213867i	0.725158	+	0.688583i	$0.241767\pi$
$542$	2.47980	+	7.63204i	0.106517	+	0.327824i
$543$	2.41274	−	7.42565i	0.103541	−	0.318665i
$544$	−8.79937	−	6.39312i	−0.377270	−	0.274103i
$545$	−25.1637	−	18.2825i	−1.07789	−	0.783135i
$546$	0.133500	−	0.410870i	0.00571326	−	0.0175836i
$547$	8.35770	+	25.7224i	0.357349	+	1.09981i	0.954635	+	0.297779i	$0.0962460\pi$
$547$	8.35770	+	25.7224i	0.357349	+	1.09981i	−0.597285	+	0.802029i	$0.703754\pi$
$548$	−10.2171	+	7.42319i	−0.436455	+	0.317103i
$549$	−6.10731			−0.260654
$550$	−6.05713	+	4.82092i	−0.258277	+	0.205565i
$551$	−1.28340			−0.0546749
$552$	4.48869	−	3.26122i	0.191051	−	0.138807i
$553$	0.307920	+	0.947679i	0.0130941	+	0.0402994i
$554$	2.67875	−	8.24436i	0.113809	−	0.350269i
$555$	−9.30544	−	6.76080i	−0.394994	−	0.286980i
$556$	10.9961	+	7.98913i	0.466339	+	0.338815i
$557$	5.22623	−	16.0847i	0.221443	−	0.681530i	−0.777191	−	0.629265i	$-0.783356\pi$
$557$	5.22623	−	16.0847i	0.221443	−	0.681530i	0.998633	−	0.0522651i	$-0.0166441\pi$
$558$	3.25874	+	10.0294i	0.137953	+	0.424577i
$559$	−9.83856	+	7.14813i	−0.416127	+	0.302334i
$560$	−0.369578			−0.0156175
$561$	3.04876	+	2.01666i	0.128719	+	0.0851434i
$562$	−14.0904			−0.594369
$563$	4.03617	−	2.93245i	0.170104	−	0.123588i	−0.499476	−	0.866328i	$-0.666474\pi$
$563$	4.03617	−	2.93245i	0.170104	−	0.123588i	0.669580	+	0.742740i	$0.266474\pi$
$564$	1.27194	+	3.91461i	0.0535581	+	0.164835i
$565$	−2.48563	+	7.64998i	−0.104571	+	0.321837i
$566$	8.54308	+	6.20691i	0.359092	+	0.260896i
$567$	−2.79375	−	2.02978i	−0.117327	−	0.0852427i
$568$	10.6664	−	32.8277i	0.447551	−	1.37742i
$569$	−6.61622	−	20.3626i	−0.277366	−	0.853646i	−0.988584	−	0.150674i	$-0.951856\pi$
$569$	−6.61622	−	20.3626i	−0.277366	−	0.853646i	0.711217	−	0.702972i	$-0.248144\pi$
$570$	−1.13100	+	0.821718i	−0.0473723	+	0.0344180i
$571$	−8.72809			−0.365259			−0.182630	−	0.983182i	$-0.558461\pi$
$571$	−8.72809			−0.365259			−0.182630	+	0.983182i	$0.558461\pi$
$572$	6.04005	−	0.265466i	0.252547	−	0.0110997i
$573$	13.6831			0.571621
$574$	2.84206	−	2.06488i	0.118625	−	0.0861864i
$575$	−2.73753	−	8.42524i	−0.114163	−	0.351357i
$576$	−4.56246	+	14.0418i	−0.190102	+	0.585075i
$577$	28.3974	+	20.6319i	1.18220	+	0.858917i	0.992418	−	0.122910i	$-0.0392226\pi$
$577$	28.3974	+	20.6319i	1.18220	+	0.858917i	0.189780	+	0.981827i	$0.439223\pi$
$578$	9.62208	+	6.99085i	0.400226	+	0.290781i
$579$	0.912661	−	2.80888i	0.0379289	−	0.116733i
$580$	−1.28936	−	3.96825i	−0.0535379	−	0.164773i
$581$	−4.76442	+	3.46155i	−0.197661	+	0.143609i
$582$	9.76570			0.404801
$583$	−4.63517	−	12.3864i	−0.191969	−	0.512992i
$584$	0.870771			0.0360328
$585$	−9.23167	+	6.70720i	−0.381683	+	0.277309i
$586$	−0.266058	−	0.818842i	−0.0109907	−	0.0338260i
$587$	−9.69032	+	29.8237i	−0.399962	+	1.23096i	0.525067	+	0.851061i	$0.324040\pi$
$587$	−9.69032	+	29.8237i	−0.399962	+	1.23096i	−0.925029	+	0.379897i	$0.875960\pi$
$588$	3.58958	+	2.60798i	0.148032	+	0.107551i
$589$	−3.51066	−	2.55065i	−0.144654	−	0.105098i
$590$	−1.81466	+	5.58496i	−0.0747085	+	0.229929i
$591$	−4.69488	−	14.4494i	−0.193122	−	0.594367i
$592$	−1.46735	+	1.06609i	−0.0603077	+	0.0438161i
$593$	31.2636			1.28384			0.641920	−	0.766771i	$-0.278138\pi$
$593$	31.2636			1.28384			0.641920	+	0.766771i	$0.278138\pi$
$594$	2.55612	−	9.22745i	0.104879	−	0.378607i
$595$	2.98038			0.122184
$596$	9.32825	−	6.77737i	0.382100	−	0.277612i
$597$	−0.284863	−	0.876718i	−0.0116587	−	0.0358817i
$598$	1.48286	−	4.56377i	0.0606385	−	0.186626i
$599$	−27.7566	−	20.1663i	−1.13410	−	0.823974i	−0.147816	−	0.989015i	$-0.547224\pi$
$599$	−27.7566	−	20.1663i	−1.13410	−	0.823974i	−0.986287	+	0.165041i	$0.947224\pi$
$600$	−3.37031	−	2.44867i	−0.137592	−	0.0999667i
$601$	−0.230283	+	0.708737i	−0.00939343	+	0.0289100i	−0.955643	−	0.294526i	$-0.904838\pi$
$601$	−0.230283	+	0.708737i	−0.00939343	+	0.0289100i	0.946250	+	0.323436i	$0.104838\pi$
$602$	−1.21433	−	3.73733i	−0.0494925	−	0.152322i
$603$	5.68049	−	4.12712i	0.231327	−	0.168069i
$604$	−15.0286			−0.611506
$605$	11.8487	+	27.8689i	0.481718	+	1.13303i
$606$	6.66322			0.270675
$607$	28.7185	−	20.8652i	1.16565	−	0.846893i	0.175166	−	0.984539i	$-0.443954\pi$
$607$	28.7185	−	20.8652i	1.16565	−	0.846893i	0.990481	+	0.137646i	$0.0439537\pi$
$608$	−1.71109	−	5.26620i	−0.0693939	−	0.213573i
$609$	−0.122642	+	0.377454i	−0.00496971	+	0.0152952i
$610$	−4.58464	−	3.33094i	−0.185627	−	0.134866i
$611$	7.75760	+	5.63622i	0.313839	+	0.228017i
$612$	1.92477	−	5.92384i	0.0778044	−	0.239457i
$613$	−3.76697	−	11.5935i	−0.152146	−	0.468258i	0.845714	−	0.533636i	$-0.179175\pi$
$613$	−3.76697	−	11.5935i	−0.152146	−	0.468258i	−0.997861	+	0.0653777i	$0.979175\pi$
$614$	10.0678	−	7.31465i	0.406302	−	0.295195i
$615$	10.8791			0.438690
$616$	−1.40481	+	5.07128i	−0.0566014	+	0.204328i
$617$	−41.4169			−1.66738			−0.833691	−	0.552232i	$-0.813776\pi$
$617$	−41.4169			−1.66738			−0.833691	+	0.552232i	$0.813776\pi$
$618$	−2.32007	+	1.68563i	−0.0933268	+	0.0678059i
$619$	−1.33329	−	4.10346i	−0.0535896	−	0.164932i	0.920680	−	0.390319i	$-0.127635\pi$
$619$	−1.33329	−	4.10346i	−0.0535896	−	0.164932i	−0.974269	+	0.225387i	$0.927635\pi$
$620$	4.35956	−	13.4174i	0.175084	−	0.538854i
$621$	8.86437	+	6.44034i	0.355715	+	0.258442i
$622$	4.57868	+	3.32661i	0.183588	+	0.133385i
$623$	1.94246	−	5.97827i	0.0778229	−	0.239514i
$624$	−0.0651922	−	0.200641i	−0.00260978	−	0.00803207i
$625$	25.2767	−	18.3646i	1.01107	−	0.734585i
$626$	19.1600			0.765789
$627$	0.652216	+	1.74289i	0.0260470	+	0.0696044i
$628$	21.3853			0.853365
$629$	11.8331	−	8.59725i	0.471817	−	0.342795i
$630$	−1.13943	−	3.50679i	−0.0453958	−	0.139714i
$631$	0.988346	−	3.04182i	0.0393454	−	0.121093i	−0.929455	−	0.368937i	$-0.879722\pi$
$631$	0.988346	−	3.04182i	0.0393454	−	0.121093i	0.968800	+	0.247844i	$0.0797220\pi$
$632$	4.21083	+	3.05935i	0.167498	+	0.121694i
$633$	−7.44767	−	5.41105i	−0.296018	−	0.215070i
$634$	4.90274	−	15.0891i	0.194713	−	0.599264i
$635$	−12.9871	−	39.9703i	−0.515379	−	1.58617i
$636$	2.13757	−	1.55304i	0.0847602	−	0.0615819i
$637$	10.3365			0.409547
$638$	3.84861	−	0.169150i	0.152368	−	0.00669672i
$639$	32.1952			1.27362
$640$	13.5819	−	9.86786i	0.536873	−	0.390061i
$641$	−12.5238	−	38.5444i	−0.494662	−	1.52241i	−0.817482	−	0.575954i	$-0.804631\pi$
$641$	−12.5238	−	38.5444i	−0.494662	−	1.52241i	0.322820	−	0.946460i	$-0.395369\pi$
$642$	0.587725	−	1.80883i	0.0231957	−	0.0713889i
$643$	−9.38035	−	6.81522i	−0.369925	−	0.268766i	0.387255	−	0.921973i	$-0.373423\pi$
$643$	−9.38035	−	6.81522i	−0.369925	−	0.268766i	−0.757180	+	0.653207i	$0.773423\pi$
$644$	−1.80864	−	1.31405i	−0.0712704	−	0.0517809i
$645$	3.76059	−	11.5739i	0.148073	−	0.455722i
$646$	−0.549349	−	1.69072i	−0.0216138	−	0.0665205i
$647$	−9.76819	+	7.09701i	−0.384027	+	0.279012i	−0.763004	−	0.646394i	$-0.776276\pi$
$647$	−9.76819	+	7.09701i	−0.384027	+	0.279012i	0.378976	+	0.925406i	$0.376276\pi$
$648$	−18.0379			−0.708595
$649$	6.51973	+	4.31260i	0.255922	+	0.169284i
$650$	−3.60303			−0.141322
$651$	−1.08563	+	0.788758i	−0.0425493	+	0.0309139i
$652$	−3.44228	−	10.5942i	−0.134810	−	0.414902i
$653$	6.87872	−	21.1705i	0.269185	−	0.828466i	−0.721515	−	0.692399i	$-0.756554\pi$
$653$	6.87872	−	21.1705i	0.269185	−	0.828466i	0.990700	−	0.136067i	$-0.0434463\pi$
$654$	4.64154	+	3.37227i	0.181498	+	0.131866i
$655$	31.5394	+	22.9147i	1.23235	+	0.895353i
$656$	0.530120	−	1.63154i	0.0206977	−	0.0637010i
$657$	0.250983	+	0.772445i	0.00979176	+	0.0301359i
$658$	−2.50673	+	1.82125i	−0.0977227	+	0.0709997i
$659$	−27.6140			−1.07569			−0.537845	−	0.843044i	$-0.680762\pi$
$659$	−27.6140			−1.07569			−0.537845	+	0.843044i	$0.680762\pi$
$660$	−4.73373	+	3.76762i	−0.184260	+	0.146654i
$661$	−31.0090			−1.20611			−0.603056	−	0.797699i	$-0.706050\pi$
$661$	−31.0090			−1.20611			−0.603056	+	0.797699i	$0.706050\pi$
$662$	−18.4115	+	13.3767i	−0.715583	+	0.519901i
$663$	0.525727	+	1.61802i	0.0204176	+	0.0628388i
$664$	−9.50583	+	29.2560i	−0.368898	+	1.13535i
$665$	1.22751	+	0.891840i	0.0476009	+	0.0345841i
$666$	−14.6397	−	10.6363i	−0.567275	−	0.412150i
$667$	−1.36226	+	4.19259i	−0.0527467	+	0.162338i
$668$	−9.14938	−	28.1589i	−0.354000	−	1.08950i
$669$	−6.30288	+	4.57931i	−0.243683	+	0.177046i
$670$	6.51517			0.251703
$671$	−5.90225	+	4.69766i	−0.227854	+	0.181351i
$672$	−1.71232			−0.0660541
$673$	37.9229	−	27.5526i	1.46182	−	1.06207i	0.478935	−	0.877851i	$-0.341023\pi$
$673$	37.9229	−	27.5526i	1.46182	−	1.06207i	0.982884	−	0.184223i	$-0.0589769\pi$
$674$	0.326239	+	1.00406i	0.0125662	+	0.0386749i
$675$	2.54228	−	7.82433i	0.0978524	−	0.301159i
$676$	−10.1435	−	7.36972i	−0.390136	−	0.283451i
$677$	15.2435	+	11.0750i	0.585855	+	0.425649i	0.840830	−	0.541299i	$-0.182067\pi$
$677$	15.2435	+	11.0750i	0.585855	+	0.425649i	−0.254975	+	0.966948i	$0.582067\pi$
$678$	0.458484	−	1.41107i	0.0176080	−	0.0541918i
$679$	−3.27529	−	10.0803i	−0.125694	−	0.386847i
$680$	12.5946	−	9.15051i	0.482981	−	0.350906i
$681$	−10.6901			−0.409645
$682$	10.8638	+	7.18604i	0.415995	+	0.275168i
$683$	28.5334			1.09180			0.545899	−	0.837851i	$-0.316188\pi$
$683$	28.5334			1.09180			0.545899	+	0.837851i	$0.316188\pi$
$684$	2.56538	−	1.86386i	0.0980898	−	0.0712664i
$685$	−9.09790	−	28.0004i	−0.347613	−	1.06984i
$686$	−2.11109	+	6.49727i	−0.0806018	+	0.248067i
$687$	−10.3432	−	7.51477i	−0.394618	−	0.286706i
$688$	−1.55249	−	1.12795i	−0.0591881	−	0.0430026i
$689$	1.90209	−	5.85405i	0.0724640	−	0.223021i
$690$	1.48388	+	4.56692i	0.0564904	+	0.173860i
$691$	14.2085	−	10.3231i	0.540517	−	0.392709i	−0.283760	−	0.958895i	$-0.591582\pi$
$691$	14.2085	−	10.3231i	0.540517	−	0.392709i	0.824277	+	0.566187i	$0.191582\pi$
$692$	18.0645			0.686711
$693$	−4.90355	+	0.215516i	−0.186270	+	0.00818677i
$694$	−21.8697			−0.830163
$695$	−25.6345	+	18.6246i	−0.972373	+	0.706471i
$696$	0.640612	+	1.97160i	0.0242823	+	0.0747333i
$697$	−4.27503	+	13.1572i	−0.161928	+	0.498364i
$698$	−11.1897	−	8.12983i	−0.423538	−	0.307719i
$699$	11.9720	+	8.69818i	0.452823	+	0.328995i
$700$	−0.518713	+	1.59643i	−0.0196055	+	0.0603396i
$701$	11.4346	+	35.1921i	0.431879	+	1.32919i	0.896251	+	0.443547i	$0.146280\pi$
$701$	11.4346	+	35.1921i	0.431879	+	1.32919i	−0.464372	+	0.885640i	$0.653720\pi$
$702$	3.60528	−	2.61939i	0.136073	−	0.0988626i
$703$	7.44626			0.280841
$704$	6.39148	+	17.0797i	0.240888	+	0.643716i
$705$	−9.59554			−0.361389
$706$	−5.30141	+	3.85170i	−0.199521	+	0.144961i
$707$	−2.23476	−	6.87788i	−0.0840467	−	0.258669i
$708$	−0.482592	+	1.48527i	−0.0181369	+	0.0558197i
$709$	−9.11512	−	6.62252i	−0.342325	−	0.248714i	0.403317	−	0.915060i	$-0.367857\pi$
$709$	−9.11512	−	6.62252i	−0.342325	−	0.248714i	−0.745642	+	0.666346i	$0.767857\pi$
$710$	24.1683	+	17.5593i	0.907022	+	0.658990i
$711$	−1.50020	+	4.61715i	−0.0562620	+	0.173157i
$712$	−10.1463	−	31.2271i	−0.380248	−	1.17028i
$713$	−12.0587	+	8.76119i	−0.451603	+	0.328109i
$714$	−0.549742			−0.0205736
$715$	−3.76263	+	13.5829i	−0.140714	+	0.507970i
$716$	−16.6195			−0.621100
$717$	2.41464	−	1.75434i	0.0901764	−	0.0655170i
$718$	3.91736	+	12.0564i	0.146195	+	0.449941i
$719$	−10.3533	+	31.8641i	−0.386112	+	1.18833i	0.549558	+	0.835456i	$0.314796\pi$
$719$	−10.3533	+	31.8641i	−0.386112	+	1.18833i	−0.935670	+	0.352876i	$0.885204\pi$
$720$	−1.45672	−	1.05837i	−0.0542888	−	0.0394432i
$721$	2.51805	+	1.82947i	0.0937772	+	0.0681331i
$722$	0.279669	−	0.860734i	0.0104082	−	0.0320332i
$723$	−4.50777	−	13.8735i	−0.167646	−	0.515961i
$724$	−13.2946	+	9.65906i	−0.494088	+	0.358976i
$725$	3.30999			0.122930
$726$	−2.18554	−	5.14053i	−0.0811130	−	0.190783i
$727$	35.6062			1.32056			0.660280	−	0.751019i	$-0.270438\pi$
$727$	35.6062			1.32056			0.660280	+	0.751019i	$0.270438\pi$
$728$	−1.98141	+	1.43958i	−0.0734361	+	0.0533544i
$729$	−3.53980	−	10.8944i	−0.131104	−	0.403496i
$730$	−0.232885	+	0.716746i	−0.00861946	+	0.0265280i
$731$	12.5197	+	9.09607i	0.463057	+	0.336430i
$732$	−1.21924	−	0.885831i	−0.0450645	−	0.0327412i
$733$	−14.6182	+	44.9901i	−0.539934	+	1.66175i	0.192804	+	0.981237i	$0.438242\pi$
$733$	−14.6182	+	44.9901i	−0.539934	+	1.66175i	−0.732739	+	0.680510i	$0.761758\pi$
$734$	3.97574	+	12.2361i	0.146747	+	0.451642i
$735$	−8.36817	+	6.07983i	−0.308665	+	0.224258i
$736$	−19.0197			−0.701075
$737$	2.31524	−	8.35789i	0.0852831	−	0.307867i
$738$	17.1155			0.630029
$739$	0.862662	−	0.626761i	0.0317335	−	0.0230558i	−0.571805	−	0.820389i	$-0.693757\pi$
$739$	0.862662	−	0.626761i	0.0317335	−	0.0230558i	0.603539	+	0.797334i	$0.293757\pi$
$740$	7.48083	+	23.0236i	0.275001	+	0.846365i
$741$	−0.267644	+	0.823724i	−0.00983215	+	0.0302602i
$742$	1.60912	+	1.16909i	0.0590726	+	0.0429188i
$743$	32.6508	+	23.7222i	1.19784	+	0.870284i	0.994071	−	0.108735i	$-0.0346799\pi$
$743$	32.6508	+	23.7222i	1.19784	+	0.870284i	0.203772	+	0.979018i	$0.434680\pi$
$744$	−2.16602	+	6.66633i	−0.0794102	+	0.244400i
$745$	8.30637	+	25.5644i	0.304322	+	0.936607i
$746$	16.2436	−	11.8017i	0.594720	−	0.432089i
$747$	−28.6923			−1.04980
$748$	−2.69639	−	7.20545i	−0.0985897	−	0.263457i
$749$	−2.06422			−0.0754250
$750$	−2.73806	+	1.98932i	−0.0999800	+	0.0726397i
$751$	12.6782	+	39.0194i	0.462633	+	1.42384i	0.861935	+	0.507019i	$0.169253\pi$
$751$	12.6782	+	39.0194i	0.462633	+	1.42384i	−0.399302	+	0.916820i	$0.630747\pi$
$752$	−0.467572	+	1.43904i	−0.0170506	+	0.0524763i
$753$	12.3090	+	8.94298i	0.448563	+	0.325900i
$754$	1.45053	+	1.05387i	0.0528250	+	0.0383796i
$755$	10.8265	−	33.3206i	0.394017	−	1.21266i
$756$	−0.641566	−	1.97454i	−0.0233335	−	0.0718132i
$757$	−39.1685	+	28.4576i	−1.42360	+	1.03431i	−0.432439	+	0.901663i	$0.642347\pi$
$757$	−39.1685	+	28.4576i	−1.42360	+	1.03431i	−0.991164	+	0.132645i	$0.957653\pi$
$758$	26.2833			0.954654
$759$	6.38592	−	0.280668i	0.231794	−	0.0101876i
$760$	7.92544			0.287486
$761$	−40.5659	+	29.4728i	−1.47051	+	1.06839i	−0.490046	+	0.871696i	$0.663020\pi$
$761$	−40.5659	+	29.4728i	−1.47051	+	1.06839i	−0.980465	+	0.196693i	$0.936980\pi$
$762$	2.39553	+	7.37269i	0.0867809	+	0.267084i
$763$	1.92420	−	5.92209i	0.0696608	−	0.214394i
$764$	−23.2987	−	16.9275i	−0.842916	−	0.612415i
$765$	11.7474	+	8.53498i	0.424728	+	0.308583i
$766$	1.79581	−	5.52694i	0.0648853	−	0.199696i
$767$	1.12426	+	3.46012i	0.0405947	+	0.124938i
$768$	−7.49713	+	5.44698i	−0.270529	+	0.196551i
$769$	−20.5948			−0.742667			−0.371333	−	0.928500i	$-0.621099\pi$
$769$	−20.5948			−0.742667			−0.371333	+	0.928500i	$0.621099\pi$
$770$	−3.79854	−	2.51262i	−0.136890	−	0.0905485i
$771$	−3.26772			−0.117684
$772$	−5.02889	+	3.65371i	−0.180994	+	0.131500i
$773$	−4.80049	−	14.7744i	−0.172662	−	0.531398i	0.826857	−	0.562412i	$-0.190126\pi$
$773$	−4.80049	−	14.7744i	−0.172662	−	0.531398i	−0.999519	+	0.0310140i	$0.990126\pi$
$774$	5.91630	−	18.2085i	0.212657	−	0.654491i
$775$	9.05425	+	6.57830i	0.325238	+	0.236299i
$776$	−44.7900	−	32.5418i	−1.60787	−	1.16818i
$777$	0.711564	−	2.18997i	0.0255272	−	0.0785647i
$778$	0.588985	+	1.81271i	0.0211161	+	0.0649887i
$779$	−5.69785	+	4.13973i	−0.204147	+	0.148321i
$780$	−2.81582			−0.100822
$781$	31.1143	−	24.7641i	1.11336	−	0.886129i
$782$	−6.10630			−0.218361
$783$	−3.31206	+	2.40635i	−0.118363	+	0.0859961i
$784$	0.504025	+	1.55123i	0.0180009	+	0.0554011i
$785$	−15.4058	+	47.4141i	−0.549856	+	1.69228i
$786$	−5.81758	−	4.22672i	−0.207506	−	0.150762i
$787$	−27.4726	−	19.9600i	−0.979294	−	0.711499i	−0.0217433	−	0.999764i	$-0.506922\pi$
$787$	−27.4726	−	19.9600i	−0.979294	−	0.711499i	−0.957551	+	0.288265i	$0.906922\pi$
$788$	−9.88126	+	30.4114i	−0.352005	+	1.08336i
$789$	−3.96770	−	12.2113i	−0.141254	−	0.434735i
$790$	−3.64437	+	2.64779i	−0.129661	+	0.0942042i
$791$	−1.61030			−0.0572556
$792$	−20.0599	+	15.9659i	−0.712798	+	0.567322i
$793$	−3.51090			−0.124676
$794$	−8.03601	+	5.83850i	−0.285187	+	0.207201i
$795$	1.90341	+	5.85809i	0.0675069	+	0.207765i
$796$	−0.599548	+	1.84522i	−0.0212504	+	0.0654021i
$797$	3.83329	+	2.78504i	0.135782	+	0.0986513i	0.653603	−	0.756838i	$-0.273257\pi$
$797$	3.83329	+	2.78504i	0.135782	+	0.0986513i	−0.517821	+	0.855489i	$0.673257\pi$
$798$	−0.226420	−	0.164503i	−0.00801516	−	0.00582336i
$799$	3.77062	−	11.6048i	0.133395	−	0.410548i
$800$	4.41303	+	13.5819i	0.156024	+	0.480193i
$801$	24.7765	−	18.0012i	0.875434	−	0.636040i
$802$	9.71116			0.342913
$803$	0.836709	+	0.553457i	0.0295268	+	0.0195311i
$804$	1.73265			0.0611057
$805$	4.21637	−	3.06337i	0.148607	−	0.107970i
$806$	1.87335	+	5.76557i	0.0659858	+	0.203083i
$807$	0.214351	−	0.659704i	0.00754551	−	0.0232227i
$808$	−30.5605	−	22.2035i	−1.07512	−	0.781118i
$809$	19.3053	+	14.0261i	0.678739	+	0.493133i	0.872939	−	0.487829i	$-0.162211\pi$
$809$	19.3053	+	14.0261i	0.678739	+	0.493133i	−0.194200	+	0.980962i	$0.562211\pi$
$810$	4.82417	−	14.8473i	0.169504	−	0.521680i
$811$	−3.05905	−	9.41477i	−0.107418	−	0.330597i	0.882873	−	0.469612i	$-0.155606\pi$
$811$	−3.05905	−	9.41477i	−0.107418	−	0.330597i	−0.990290	+	0.139015i	$0.955606\pi$
$812$	0.675776	−	0.490980i	0.0237151	−	0.0172300i
$813$	−4.97514			−0.174486
$814$	−22.3294	+	0.981401i	−0.782646	+	0.0343981i
$815$	25.9687			0.909643
$816$	−0.217186	+	0.157795i	−0.00760304	+	0.00552393i
$817$	2.43453	+	7.49270i	0.0851733	+	0.262137i
$818$	0.937696	−	2.88593i	0.0327858	−	0.100904i
$819$	−1.84813	−	1.34274i	−0.0645789	−	0.0469193i
$820$	−18.5242	−	13.4586i	−0.646894	−	0.469996i
$821$	−10.9411	+	33.6732i	−0.381846	+	1.17520i	0.556897	+	0.830582i	$0.311992\pi$
$821$	−10.9411	+	33.6732i	−0.381846	+	1.17520i	−0.938743	+	0.344619i	$0.888008\pi$
$822$	1.67814	+	5.16479i	0.0585320	+	0.180143i
$823$	11.5410	−	8.38505i	0.402295	−	0.292285i	−0.368180	−	0.929755i	$-0.620019\pi$
$823$	11.5410	−	8.38505i	0.402295	−	0.292285i	0.770475	+	0.637470i	$0.220019\pi$
$824$	16.2578			0.566368
$825$	−1.68211	−	4.49504i	−0.0585636	−	0.156497i
$826$	−1.17562			−0.0409050
$827$	−20.0565	+	14.5719i	−0.697433	+	0.506715i	−0.879095	−	0.476646i	$-0.841852\pi$
$827$	−20.0565	+	14.5719i	−0.697433	+	0.506715i	0.181662	+	0.983361i	$0.441852\pi$
$828$	−3.36581	−	10.3589i	−0.116970	−	0.359996i
$829$	−14.2836	+	43.9604i	−0.496090	+	1.52681i	0.319160	+	0.947701i	$0.396599\pi$
$829$	−14.2836	+	43.9604i	−0.496090	+	1.52681i	−0.815251	+	0.579108i	$0.803401\pi$
$830$	−21.5387	−	15.6488i	−0.747621	−	0.543178i
$831$	4.34789	+	3.15893i	0.150827	+	0.109582i
$832$	−2.62282	+	8.07220i	−0.0909298	+	0.279853i
$833$	−4.06459	−	12.5095i	−0.140830	−	0.433429i
$834$	4.72839	−	3.43538i	0.163731	−	0.118957i
$835$	69.0233			2.38865
$836$	1.04559	−	3.77453i	0.0361626	−	0.130545i
$837$	−13.8423			−0.478461
$838$	−16.7616	+	12.1780i	−0.579020	+	0.420683i
$839$	1.96818	+	6.05743i	0.0679491	+	0.209126i	0.979266	−	0.202581i	$-0.0649329\pi$
$839$	1.96818	+	6.05743i	0.0679491	+	0.209126i	−0.911316	+	0.411707i	$0.864933\pi$
$840$	0.757355	−	2.33090i	0.0261312	−	0.0804237i
$841$	22.1289	+	16.0776i	0.763067	+	0.554401i
$842$	−21.8297	−	15.8602i	−0.752302	−	0.546579i
$843$	2.69947	−	8.30810i	0.0929745	−	0.286146i
$844$	5.98733	+	18.4271i	0.206092	+	0.634287i
$845$	23.6470	−	17.1806i	0.813482	−	0.591030i
$846$	−15.0960			−0.519013
$847$	−4.57313	+	3.98002i	−0.157135	+	0.136755i
$848$	0.971284			0.0333540
$849$	−5.29645	+	3.84810i	−0.181774	+	0.132066i
$850$	1.41681	+	4.36049i	0.0485962	+	0.149564i
$851$	7.90375	−	24.3252i	0.270937	−	0.833858i
$852$	6.42734	+	4.66973i	0.220197	+	0.159982i
$853$	13.3316	+	9.68595i	0.456464	+	0.331641i	0.792143	−	0.610336i	$-0.208966\pi$
$853$	13.3316	+	9.68595i	0.456464	+	0.331641i	−0.335678	+	0.941977i	$0.608966\pi$
$854$	0.350576	−	1.07896i	0.0119965	−	0.0369213i
$855$	2.28435	+	7.03052i	0.0781232	+	0.240439i
$856$	−8.72306	+	6.33768i	−0.298148	+	0.216617i
$857$	−32.9876			−1.12683			−0.563417	−	0.826173i	$-0.690513\pi$
$857$	−32.9876			−1.12683			−0.563417	+	0.826173i	$0.690513\pi$
$858$	0.694032	−	2.50541i	0.0236939	−	0.0855334i
$859$	37.8381			1.29102			0.645509	−	0.763752i	$-0.276645\pi$
$859$	37.8381			1.29102			0.645509	+	0.763752i	$0.276645\pi$
$860$	−20.7214	+	15.0550i	−0.706594	+	0.513371i
$861$	0.673022	+	2.07135i	0.0229365	+	0.0705914i
$862$	3.85455	−	11.8631i	0.131286	−	0.404058i
$863$	36.1286	+	26.2490i	1.22983	+	0.893526i	0.996878	−	0.0789609i	$-0.0251602\pi$
$863$	36.1286	+	26.2490i	1.22983	+	0.893526i	0.232956	+	0.972487i	$0.425160\pi$
$864$	−14.2898	−	10.3821i	−0.486149	−	0.353208i
$865$	−13.0136	+	40.0516i	−0.442474	+	1.36180i
$866$	4.42556	+	13.6205i	0.150387	+	0.462843i
$867$	−5.96540	+	4.33412i	−0.202596	+	0.147194i
$868$	2.82431			0.0958635
$869$	2.10161	+	5.61606i	0.0712923	+	0.190512i
$870$	−1.79419			−0.0608286
$871$	3.26554	−	2.37255i	0.110648	−	0.0803908i
$872$	−10.0509	−	30.9336i	−0.340367	−	1.04754i
$873$	15.9574	−	49.1119i	0.540077	−	1.66219i
$874$	−2.51497	−	1.82723i	−0.0850701	−	0.0618071i
$875$	2.97172	+	2.15908i	0.100462	+	0.0729902i
$876$	−0.0619335	+	0.190612i	−0.00209254	+	0.00644017i
$877$	6.37912	+	19.6329i	0.215408	+	0.662956i	0.999124	+	0.0418381i	$0.0133214\pi$
$877$	6.37912	+	19.6329i	0.215408	+	0.662956i	−0.783717	+	0.621118i	$0.786679\pi$
$878$	23.3687	−	16.9784i	0.788656	−	0.572992i
$879$	0.533783			0.0180040
$880$	−2.22190	+	0.0976545i	−0.0749001	+	0.00329193i
$881$	−17.2069			−0.579714			−0.289857	−	0.957070i	$-0.593608\pi$
$881$	−17.2069			−0.579714			−0.289857	+	0.957070i	$0.593608\pi$
$882$	−13.1651	+	9.56501i	−0.443292	+	0.322071i
$883$	9.59142	+	29.5194i	0.322777	+	0.993406i	0.972434	+	0.233178i	$0.0749126\pi$
$883$	9.59142	+	29.5194i	0.322777	+	0.993406i	−0.649657	+	0.760228i	$0.725087\pi$
$884$	1.10649	−	3.40543i	0.0372154	−	0.114537i
$885$	−2.94539	−	2.13995i	−0.0990081	−	0.0719336i
$886$	−0.987073	−	0.717151i	−0.0331614	−	0.0240931i
$887$	−11.2063	+	34.4895i	−0.376271	+	1.15804i	0.566346	+	0.824167i	$0.308356\pi$
$887$	−11.2063	+	34.4895i	−0.376271	+	1.15804i	−0.942617	+	0.333875i	$0.891644\pi$
$888$	−3.71680	−	11.4391i	−0.124728	−	0.383872i
$889$	6.80677	−	4.94541i	0.228292	−	0.165864i
$890$	28.4171			0.952543
$891$	−17.3323	−	11.4648i	−0.580654	−	0.384085i
$892$	16.3972			0.549018
$893$	5.02557	−	3.65129i	0.168174	−	0.122186i
$894$	−1.53214	−	4.71545i	−0.0512426	−	0.157708i
$895$	11.9726	−	36.8477i	0.400198	−	1.23168i
$896$	2.71903	+	1.97549i	0.0908364	+	0.0659965i
$897$	2.40683	+	1.74866i	0.0803617	+	0.0583862i
$898$	−6.71195	+	20.6572i	−0.223981	+	0.689341i
$899$	−1.72099	−	5.29665i	−0.0573981	−	0.176653i
$900$	−6.61630	+	4.80702i	−0.220543	+	0.160234i
$901$	−7.83269			−0.260945
$902$	16.5408	−	13.1650i	0.550749	−	0.438346i
$903$	2.43627			0.0810741
$904$	−6.80486	+	4.94402i	−0.226326	+	0.164436i
$905$	−11.8382	−	36.4342i	−0.393515	−	1.21111i
$906$	−1.99699	+	6.14611i	−0.0663457	+	0.204191i
$907$	−13.2203	−	9.60508i	−0.438972	−	0.318932i	0.346255	−	0.938141i	$-0.387453\pi$
$907$	−13.2203	−	9.60508i	−0.438972	−	0.318932i	−0.785226	+	0.619209i	$0.787453\pi$
$908$	18.2023	+	13.2247i	0.604065	+	0.438879i
$909$	10.8879	−	33.5094i	0.361128	−	1.11144i
$910$	−0.655020	−	2.01595i	−0.0217137	−	0.0668279i
$911$	−13.4856	+	9.79790i	−0.446799	+	0.324619i	−0.788331	−	0.615252i	$-0.789054\pi$
$911$	−13.4856	+	9.79790i	−0.446799	+	0.324619i	0.341531	+	0.939870i	$0.389054\pi$
$912$	−0.136670			−0.00452558
$913$	−27.7289	+	22.0697i	−0.917693	+	0.730400i
$914$	−4.63828			−0.153421
$915$	2.84234	−	2.06508i	0.0939649	−	0.0682695i
$916$	8.31510	+	25.5912i	0.274739	+	0.845558i
$917$	−2.41174	+	7.42258i	−0.0796428	+	0.245115i
$918$	−4.58776	−	3.33320i	−0.151419	−	0.110012i
$919$	−39.0796	−	28.3930i	−1.28912	−	0.936598i	−0.289329	−	0.957230i	$-0.593432\pi$
$919$	−39.0796	−	28.3930i	−1.28912	−	0.936598i	−0.999787	+	0.0206316i	$0.993432\pi$
$920$	8.41238	−	25.8906i	0.277348	−	0.853589i
$921$	2.38412	+	7.33757i	0.0785595	+	0.241781i
$922$	16.3700	−	11.8935i	0.539118	−	0.391692i
$923$	18.5080			0.609200
$924$	−1.01019	−	0.668207i	−0.0332327	−	0.0219824i
$925$	−19.2044			−0.631438
$926$	−5.78483	+	4.20292i	−0.190101	+	0.138117i
$927$	4.68600	+	14.4220i	0.153908	+	0.473681i
$928$	2.19602	−	6.75866i	0.0720880	−	0.221864i
$929$	46.7813	+	33.9886i	1.53484	+	1.11513i	0.953468	+	0.301494i	$0.0974852\pi$
$929$	46.7813	+	33.9886i	1.53484	+	1.11513i	0.581375	+	0.813635i	$0.302515\pi$
$930$	−4.90787	−	3.56578i	−0.160935	−	0.116926i
$931$	2.06925	−	6.36851i	0.0678171	−	0.208719i
$932$	−9.62454	−	29.6213i	−0.315262	−	0.970277i
$933$	−2.83865	+	2.06240i	−0.0929331	+	0.0675198i
$934$	−23.0045			−0.752732
$935$	17.9180	−	0.787512i	0.585980	−	0.0257544i
$936$	−11.9325			−0.390025
$937$	−6.04953	+	4.39524i	−0.197630	+	0.143586i	−0.682199	−	0.731166i	$-0.738976\pi$
$937$	−6.04953	+	4.39524i	−0.197630	+	0.143586i	0.484570	+	0.874753i	$0.338976\pi$
$938$	0.403051	+	1.24046i	0.0131601	+	0.0405026i
$939$	−3.67070	+	11.2973i	−0.119789	+	0.368672i
$940$	16.3386	+	11.8707i	0.532906	+	0.387179i
$941$	−14.9518	−	10.8631i	−0.487415	−	0.354128i	0.316774	−	0.948501i	$-0.397400\pi$
$941$	−14.9518	−	10.8631i	−0.487415	−	0.354128i	−0.804189	+	0.594373i	$0.797400\pi$
$942$	2.84166	−	8.74572i	0.0925862	−	0.284951i
$943$	7.47564	+	23.0077i	0.243440	+	0.749232i
$944$	−0.464450	+	0.337443i	−0.0151166	+	0.0109828i
$945$	4.84000			0.157445
$946$	−8.28805	−	22.1479i	−0.269468	−	0.720089i
$947$	−13.7749			−0.447625			−0.223812	−	0.974632i	$-0.571850\pi$
$947$	−13.7749			−0.447625			−0.223812	+	0.974632i	$0.571850\pi$
$948$	−0.969186	+	0.704155i	−0.0314777	+	0.0228699i
$949$	0.144282	+	0.444055i	0.00468360	+	0.0144146i
$950$	−0.721287	+	2.21989i	−0.0234017	+	0.0720229i
$951$	7.95766	+	5.78158i	0.258045	+	0.187481i
$952$	2.52137	+	1.83188i	0.0817181	+	0.0593716i
$953$	−5.52220	+	16.9956i	−0.178882	+	0.550541i	−0.999789	−	0.0205196i	$-0.993468\pi$
$953$	−5.52220	+	16.9956i	−0.178882	+	0.550541i	0.820908	+	0.571061i	$0.193468\pi$
$954$	2.99451	+	9.21615i	0.0969508	+	0.298384i
$955$	54.3148	−	39.4620i	1.75758	−	1.27696i
$956$	−6.28178			−0.203167
$957$	−0.637586	+	2.30165i	−0.0206102	+	0.0744017i
$958$	15.3223			0.495042
$959$	4.76835	−	3.46441i	0.153978	−	0.111872i
$960$	−2.62463	−	8.07777i	−0.0847094	−	0.260709i
$961$	−3.76057	+	11.5738i	−0.121309	+	0.373350i
$962$	−8.41589	−	6.11450i	−0.271339	−	0.197139i
$963$	−8.13629	−	5.91136i	−0.262188	−	0.190491i
$964$	−9.48745	+	29.1994i	−0.305570	+	0.940449i
$965$	−4.47800	−	13.7819i	−0.144152	−	0.443654i
$966$	−0.777726	+	0.565051i	−0.0250229	+	0.0181802i
$967$	17.3962			0.559423			0.279711	−	0.960084i	$-0.409761\pi$
$967$	17.3962			0.559423			0.279711	+	0.960084i	$0.409761\pi$
$968$	−7.10568	+	30.8596i	−0.228385	+	0.991865i
$969$	1.10214			0.0354058
$970$	38.7646	−	28.1642i	1.24466	−	0.904296i
$971$	−3.82848	−	11.7828i	−0.122862	−	0.378130i	0.870644	−	0.491914i	$-0.163703\pi$
$971$	−3.82848	−	11.7828i	−0.122862	−	0.378130i	−0.993505	+	0.113785i	$0.963703\pi$
$972$	4.77517	−	14.6965i	0.153164	−	0.471389i
$973$	−5.13189	−	3.72854i	−0.164521	−	0.119531i
$974$	4.31721	+	3.13664i	0.138332	+	0.100504i
$975$	0.690273	−	2.12444i	0.0221064	−	0.0680366i
$976$	−0.171198	−	0.526892i	−0.00547991	−	0.0168654i
$977$	−15.8592	+	11.5224i	−0.507379	+	0.368633i	−0.811829	−	0.583896i	$-0.801528\pi$
$977$	−15.8592	+	11.5224i	−0.507379	+	0.368633i	0.304449	+	0.952529i	$0.401528\pi$
$978$	−4.79003			−0.153168
$979$	10.0984	−	36.4545i	0.322745	−	1.16509i
$980$	21.7701			0.695421
$981$	24.5436	−	17.8320i	0.783618	−	0.569332i
$982$	8.38782	+	25.8151i	0.267666	+	0.823792i
$983$	−1.20657	+	3.71344i	−0.0384836	+	0.118440i	−0.968453	−	0.249197i	$-0.919833\pi$
$983$	−1.20657	+	3.71344i	−0.0384836	+	0.118440i	0.929969	+	0.367638i	$0.119833\pi$
$984$	9.20365	+	6.68684i	0.293402	+	0.213169i
$985$	−60.3079	−	43.8163i	−1.92157	−	1.39610i
$986$	0.705036	−	2.16988i	0.0224529	−	0.0691030i
$987$	−0.593614	−	1.82695i	−0.0188949	−	0.0581526i
$988$	1.47476	−	1.07147i	0.0469183	−	0.0340881i
$989$	27.0611			0.860492
$990$	−7.77680	−	20.7817i	−0.247163	−	0.660485i
$991$	−33.0046			−1.04842			−0.524212	−	0.851588i	$-0.675640\pi$
$991$	−33.0046			−1.04842			−0.524212	+	0.851588i	$0.675640\pi$
$992$	19.4393	−	14.1235i	0.617198	−	0.448420i
$993$	−4.35998	−	13.4186i	−0.138360	−	0.425828i
$994$	−1.84809	+	5.68785i	−0.0586179	+	0.180407i
$995$	−3.65920	−	2.65856i	−0.116004	−	0.0842821i
$996$	−5.72802	−	4.16165i	−0.181499	−	0.131867i
$997$	−7.45839	+	22.9546i	−0.236210	+	0.726979i	0.760749	+	0.649046i	$0.224832\pi$
$997$	−7.45839	+	22.9546i	−0.236210	+	0.726979i	−0.996959	+	0.0779325i	$0.975168\pi$
$998$	9.97874	+	30.7114i	0.315871	+	0.972152i
$999$	19.2164	−	13.9616i	0.607981	−	0.441724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.f.b.58.3	✓	28
11.2	odd	10		2299.2.a.u.1.5		14
11.4	even	5	inner	209.2.f.b.191.3	yes	28
11.9	even	5		2299.2.a.t.1.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.f.b.58.3	✓	28	1.1	even	1	trivial
209.2.f.b.191.3	yes	28	11.4	even	5	inner
2299.2.a.t.1.10		14	11.9	even	5
2299.2.a.u.1.5		14	11.2	odd	10

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.732184 + 0.531963i) q^{2} +(-0.173387 - 0.533629i) q^{3} +(-0.364925 + 1.12312i) q^{4} +(-2.22723 - 1.61818i) q^{5} +(0.410822 + 0.298480i) q^{6} +(0.170311 - 0.524163i) q^{7} +(-0.889607 - 2.73793i) q^{8} +(2.17235 - 1.57831i) q^{9} +2.49156 q^{10} +(0.885404 - 3.19626i) q^{11} +0.662605 q^{12} +(1.24882 - 0.907320i) q^{13} +(0.154136 + 0.474383i) q^{14} +(-0.477336 + 1.46909i) q^{15} +(0.197059 + 0.143172i) q^{16} +(-1.58913 - 1.15457i) q^{17} +(-0.750962 + 2.31122i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(2.63019 - 1.91094i) q^{20} -0.309239 q^{21} +(1.05201 + 2.81125i) q^{22} -3.43489 q^{23} +(-1.30679 + 0.949441i) q^{24} +(0.796977 + 2.45284i) q^{25} +(-0.431705 + 1.32865i) q^{26} +(-2.58069 - 1.87498i) q^{27} +(0.526549 + 0.382561i) q^{28} +(0.396594 - 1.22059i) q^{29} +(-0.432003 - 1.32957i) q^{30} +(3.51066 - 2.55065i) q^{31} +5.53721 q^{32} +(-1.85913 + 0.0817108i) q^{33} +1.77773 q^{34} +(-1.22751 + 0.891840i) q^{35} +(0.979888 + 3.01579i) q^{36} +(-2.30102 + 7.08181i) q^{37} +(0.732184 + 0.531963i) q^{38} +(-0.700701 - 0.509089i) q^{39} +(-2.44910 + 7.53755i) q^{40} +(-2.17638 - 6.69822i) q^{41} +(0.226420 - 0.164503i) q^{42} -7.87829 q^{43} +(3.26669 + 2.16081i) q^{44} -7.39232 q^{45} +(2.51497 - 1.82723i) q^{46} +(1.91960 + 5.90791i) q^{47} +(0.0422332 - 0.129980i) q^{48} +(5.41738 + 3.93596i) q^{49} +(-1.88835 - 1.37197i) q^{50} +(-0.340580 + 1.04820i) q^{51} +(0.563307 + 1.73368i) q^{52} +(3.22601 - 2.34383i) q^{53} +2.88695 q^{54} +(-7.14412 + 5.68607i) q^{55} -1.58663 q^{56} +(-0.453932 + 0.329801i) q^{57} +(0.358929 + 1.10467i) q^{58} +(-0.728326 + 2.24156i) q^{59} +(-1.47578 - 1.07221i) q^{60} +(-1.84007 - 1.33689i) q^{61} +(-1.21360 + 3.73508i) q^{62} +(-0.457315 - 1.40747i) q^{63} +(-4.44837 + 3.23193i) q^{64} -4.24962 q^{65} +(1.31776 - 1.04882i) q^{66} +2.61490 q^{67} +(1.87664 - 1.36346i) q^{68} +(0.595564 + 1.83296i) q^{69} +(0.424339 - 1.30598i) q^{70} +(9.70010 + 7.04754i) q^{71} +(-6.25383 - 4.54367i) q^{72} +(-0.0934697 + 0.287670i) q^{73} +(-2.08249 - 6.40924i) q^{74} +(1.17072 - 0.850581i) q^{75} +1.18092 q^{76} +(-1.52457 - 1.00845i) q^{77} +0.783859 q^{78} +(-1.46269 + 1.06271i) q^{79} +(-0.207219 - 0.637753i) q^{80} +(1.93621 - 5.95904i) q^{81} +(5.15672 + 3.74658i) q^{82} +(-8.64470 - 6.28074i) q^{83} +(0.112849 - 0.347313i) q^{84} +(1.67107 + 5.14301i) q^{85} +(5.76836 - 4.19096i) q^{86} -0.720107 q^{87} +(-9.53878 + 0.419239i) q^{88} +11.4054 q^{89} +(5.41254 - 3.93244i) q^{90} +(-0.262896 - 0.809111i) q^{91} +(1.25348 - 3.85781i) q^{92} +(-1.96980 - 1.43114i) q^{93} +(-4.54829 - 3.30453i) q^{94} +(-0.850727 + 2.61827i) q^{95} +(-0.960079 - 2.95482i) q^{96} +(15.5584 - 11.3038i) q^{97} -6.06030 q^{98} +(-3.12126 - 8.34084i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + q^{3} - 6 q^{4} + 7 q^{5} - 14 q^{6} - 12 q^{7} + 4 q^{8} + 6 q^{9} - 12 q^{10} + 2 q^{11} - 16 q^{12} + 5 q^{13} + 23 q^{14} + 15 q^{15} + 30 q^{16} - 15 q^{17} - 38 q^{18} + 7 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + q^3 - 6 * q^4 + 7 * q^5 - 14 * q^6 - 12 * q^7 + 4 * q^8 + 6 * q^9 - 12 * q^10 + 2 * q^11 - 16 * q^12 + 5 * q^13 + 23 * q^14 + 15 * q^15 + 30 * q^16 - 15 * q^17 - 38 * q^18 + 7 * q^19 + 8 * q^20 - 18 * q^21 + 18 * q^22 - 42 * q^23 - 4 * q^24 + 2 * q^25 + 14 * q^26 + 28 * q^27 - 15 * q^28 - 21 * q^29 + 10 * q^30 + 19 * q^31 - 4 * q^32 - 28 * q^33 - 20 * q^34 - 16 * q^35 + 46 * q^36 + 23 * q^37 + 2 * q^38 - 4 * q^39 - 84 * q^40 + 5 * q^41 + 34 * q^42 - 12 * q^43 - 11 * q^44 - 22 * q^45 + 19 * q^46 + 43 * q^47 + 28 * q^48 - q^49 - 43 * q^50 - 6 * q^51 - 21 * q^52 + 46 * q^53 + 60 * q^54 - 92 * q^55 - 60 * q^56 - q^57 + 63 * q^58 + 3 * q^59 + 40 * q^60 - 12 * q^61 - 25 * q^62 + 9 * q^63 + 44 * q^64 + 26 * q^65 + 13 * q^66 + 24 * q^67 - 19 * q^68 - q^69 - 14 * q^70 + 14 * q^71 - 7 * q^72 + 7 * q^73 - 58 * q^74 + 50 * q^75 - 14 * q^76 - 60 * q^77 + 6 * q^78 - 62 * q^79 + 85 * q^80 + 31 * q^81 + 36 * q^82 + 5 * q^83 - 59 * q^84 - 9 * q^85 + 34 * q^86 - 34 * q^87 - 16 * q^88 - 108 * q^89 - 28 * q^90 + 45 * q^91 + 62 * q^92 + 13 * q^93 - 80 * q^94 - 7 * q^95 - 40 * q^96 + 38 * q^97 + 84 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more