LMFDB - Embedded newform 738.2.v.a.137.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(137,738)] 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("738.137"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([4, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.v (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [168,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$21$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			137.18
Character	$\chi$	$=$	738.137
Dual form			738.2.v.a.167.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{2} +(1.45241 - 0.943659i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.08080 + 4.03360i) q^{5} +(1.28742 + 1.15869i) q^{6} +(-4.10812 - 0.540844i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.21902 - 2.74117i) q^{9} -4.17589 q^{10} +(0.661956 + 0.0871482i) q^{11} +(-0.785999 + 1.54344i) q^{12} +(-0.905717 + 1.18035i) q^{13} +(-0.540844 - 4.10812i) q^{14} +(2.23657 + 6.87836i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.52530 - 1.46023i) q^{17} +(2.96327 + 0.468013i) q^{18} +(-2.03375 + 4.90991i) q^{19} +(-1.08080 - 4.03360i) q^{20} +(-6.47706 + 3.09113i) q^{21} +(0.0871482 + 0.661956i) q^{22} +(1.90657 + 3.30227i) q^{23} +(-1.69428 - 0.359745i) q^{24} +(-10.7717 - 6.21903i) q^{25} +(-1.37455 - 0.569357i) q^{26} +(-0.816209 - 5.13165i) q^{27} +(3.82816 - 1.58567i) q^{28} +(-0.166650 + 1.26584i) q^{29} +(-6.06512 + 3.94061i) q^{30} +(-7.53940 + 4.35288i) q^{31} +(0.965926 + 0.258819i) q^{32} +(1.04367 - 0.498085i) q^{33} +(0.498057 - 3.78311i) q^{34} +(6.62160 - 15.9860i) q^{35} +(0.314884 + 2.98343i) q^{36} +7.52750 q^{37} +(-5.26898 - 0.693674i) q^{38} +(-0.201626 + 2.56905i) q^{39} +(3.61643 - 2.08794i) q^{40} +(4.59721 - 4.45709i) q^{41} +(-4.66219 - 5.45632i) q^{42} +(-6.49708 + 1.74089i) q^{43} +(-0.616845 + 0.255506i) q^{44} +(9.73926 + 7.87968i) q^{45} +(-2.69629 + 2.69629i) q^{46} +(0.240703 - 0.184698i) q^{47} +(-0.0910250 - 1.72966i) q^{48} +(9.82265 + 2.63197i) q^{49} +(3.21920 - 12.0142i) q^{50} +(-6.49816 + 1.20583i) q^{51} +(0.194197 - 1.47507i) q^{52} +(1.03902 + 2.50841i) q^{53} +(4.74554 - 2.11656i) q^{54} +(-1.06696 + 2.57588i) q^{55} +(2.52244 + 3.28731i) q^{56} +(1.67943 + 9.05039i) q^{57} +(-1.26584 + 0.166650i) q^{58} +(-3.69949 + 2.13590i) q^{59} +(-5.37611 - 4.83855i) q^{60} +(3.91255 - 1.04836i) q^{61} +(-6.15590 - 6.15590i) q^{62} +(-6.49041 + 10.6017i) q^{63} +1.00000i q^{64} +(-3.78217 - 4.92902i) q^{65} +(0.751236 + 0.879197i) q^{66} +(3.89663 - 0.513002i) q^{67} +(3.78311 - 0.498057i) q^{68} +(5.88534 + 2.99712i) q^{69} +(17.1550 + 2.25851i) q^{70} +(-12.4184 + 5.14386i) q^{71} +(-2.80027 + 1.07632i) q^{72} +(9.56653 + 9.56653i) q^{73} +(1.94826 + 7.27101i) q^{74} +(-21.5136 + 1.13217i) q^{75} +(-0.693674 - 5.26898i) q^{76} +(-2.67226 - 0.716030i) q^{77} +(-2.53370 + 0.470163i) q^{78} +(-1.64296 + 12.4795i) q^{79} +(2.95280 + 2.95280i) q^{80} +(-6.02800 - 6.68306i) q^{81} +(5.49506 + 3.28698i) q^{82} +(11.9759 + 6.91428i) q^{83} +(4.06374 - 5.91553i) q^{84} +(9.70012 - 12.6414i) q^{85} +(-3.36314 - 5.82513i) q^{86} +(0.952471 + 1.99578i) q^{87} +(-0.406451 - 0.529697i) q^{88} +(14.8193 - 6.13837i) q^{89} +(-5.09048 + 11.4468i) q^{90} +(4.35918 - 4.35918i) q^{91} +(-3.30227 - 1.90657i) q^{92} +(-6.84271 + 13.4368i) q^{93} +(0.240703 + 0.184698i) q^{94} +(-17.6065 - 13.5100i) q^{95} +(1.64716 - 0.535592i) q^{96} +(0.422726 - 0.324369i) q^{97} +10.1692i q^{98} +(1.04582 - 1.70830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 4 q^{3} - 12 q^{7} - 4 q^{9} + 8 q^{15} + 84 q^{16} - 12 q^{17} - 8 q^{21} - 12 q^{22} + 48 q^{25} - 40 q^{27} + 16 q^{30} - 64 q^{33} - 36 q^{34} + 24 q^{35} - 4 q^{36} + 32 q^{39} - 32 q^{42}+ \cdots + 68 q^{99}+O(q^{100}) $ 168 * q - 4 * q^3 - 12 * q^7 - 4 * q^9 + 8 * q^15 + 84 * q^16 - 12 * q^17 - 8 * q^21 - 12 * q^22 + 48 * q^25 - 40 * q^27 + 16 * q^30 - 64 * q^33 - 36 * q^34 + 24 * q^35 - 4 * q^36 + 32 * q^39 - 32 * q^42 + 12 * q^44 + 72 * q^45 - 12 * q^47 - 8 * q^48 + 12 * q^49 - 44 * q^51 + 12 * q^56 - 64 * q^57 - 24 * q^58 - 108 * q^61 + 48 * q^63 - 84 * q^65 - 4 * q^66 - 60 * q^67 + 40 * q^69 + 12 * q^70 + 20 * q^75 - 60 * q^79 + 68 * q^81 + 12 * q^82 - 120 * q^83 + 8 * q^84 + 24 * q^85 + 72 * q^89 + 40 * q^90 - 16 * q^93 - 12 * q^94 - 120 * q^95 + 96 * q^97 + 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	1.45241	−	0.943659i	0.838552	−	0.544822i
$3$	1.45241	−	0.943659i	0.838552	−	0.544822i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.08080	+	4.03360i	−0.483348	+	1.80388i	0.104038	+	0.994573i	$0.466824\pi$
$5$	−1.08080	+	4.03360i	−0.483348	+	1.80388i	−0.587386	+	0.809307i	$0.699843\pi$
$6$	1.28742	+	1.15869i	0.525586	+	0.473032i
$7$	−4.10812	−	0.540844i	−1.55272	−	0.204420i	−0.695181	−	0.718834i	$-0.744676\pi$
$7$	−4.10812	−	0.540844i	−1.55272	−	0.204420i	−0.857542	+	0.514415i	$0.828009\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.21902	−	2.74117i	0.406339	−	0.913722i
$10$	−4.17589			−1.32053
$11$	0.661956	+	0.0871482i	0.199587	+	0.0262762i	0.229657	−	0.973272i	$-0.426240\pi$
$11$	0.661956	+	0.0871482i	0.199587	+	0.0262762i	−0.0300697	+	0.999548i	$0.509573\pi$
$12$	−0.785999	+	1.54344i	−0.226898	+	0.445553i
$13$	−0.905717	+	1.18035i	−0.251201	+	0.327371i	−0.901884	−	0.431978i	$-0.857816\pi$
$13$	−0.905717	+	1.18035i	−0.251201	+	0.327371i	0.650684	+	0.759349i	$0.274482\pi$
$14$	−0.540844	−	4.10812i	−0.144547	−	1.09794i
$15$	2.23657	+	6.87836i	0.577480	+	1.77599i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.52530	−	1.46023i	−0.855011	−	0.354157i	−0.0882568	−	0.996098i	$-0.528130\pi$
$17$	−3.52530	−	1.46023i	−0.855011	−	0.354157i	−0.766754	+	0.641940i	$0.778130\pi$
$18$	2.96327	+	0.468013i	0.698449	+	0.110312i
$19$	−2.03375	+	4.90991i	−0.466574	+	1.12641i	0.499074	+	0.866559i	$0.333673\pi$
$19$	−2.03375	+	4.90991i	−0.466574	+	1.12641i	−0.965649	+	0.259851i	$0.916327\pi$
$20$	−1.08080	−	4.03360i	−0.241674	−	0.901940i
$21$	−6.47706	+	3.09113i	−1.41341	+	0.674540i
$22$	0.0871482	+	0.661956i	0.0185801	+	0.141130i
$23$	1.90657	+	3.30227i	0.397547	+	0.688571i	0.993423	−	0.114506i	$-0.0365284\pi$
$23$	1.90657	+	3.30227i	0.397547	+	0.688571i	−0.595876	+	0.803076i	$0.703195\pi$
$24$	−1.69428	−	0.359745i	−0.345843	−	0.0734326i
$25$	−10.7717	−	6.21903i	−2.15433	−	1.24381i
$26$	−1.37455	−	0.569357i	−0.269571	−	0.111660i
$27$	−0.816209	−	5.13165i	−0.157079	−	0.987586i
$28$	3.82816	−	1.58567i	0.723454	−	0.299664i
$29$	−0.166650	+	1.26584i	−0.0309462	+	0.235060i	−0.999927	−	0.0120760i	$-0.996156\pi$
$29$	−0.166650	+	1.26584i	−0.0309462	+	0.235060i	0.968981	+	0.247136i	$0.0794893\pi$
$30$	−6.06512	+	3.94061i	−1.10733	+	0.719454i
$31$	−7.53940	+	4.35288i	−1.35412	+	0.781800i	−0.988823	−	0.149092i	$-0.952365\pi$
$31$	−7.53940	+	4.35288i	−1.35412	+	0.781800i	−0.365294	+	0.930892i	$0.619031\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	1.04367	−	0.498085i	0.181680	−	0.0867055i
$34$	0.498057	−	3.78311i	0.0854160	−	0.648799i
$35$	6.62160	−	15.9860i	1.11925	−	2.70212i
$36$	0.314884	+	2.98343i	0.0524807	+	0.497238i
$37$	7.52750			1.23751			0.618757	−	0.785582i	$-0.287637\pi$
$37$	7.52750			1.23751			0.618757	+	0.785582i	$0.287637\pi$
$38$	−5.26898	−	0.693674i	−0.854741	−	0.112529i
$39$	−0.201626	+	2.56905i	−0.0322860	+	0.411377i
$40$	3.61643	−	2.08794i	0.571807	−	0.330133i
$41$	4.59721	−	4.45709i	0.717964	−	0.696081i
$41$	4.59721	−	4.45709i	0.717964	−	0.696081i
$42$	−4.66219	−	5.45632i	−0.719392	−	0.841928i
$43$	−6.49708	+	1.74089i	−0.990796	+	0.265483i	−0.717585	−	0.696471i	$-0.754752\pi$
$43$	−6.49708	+	1.74089i	−0.990796	+	0.265483i	−0.273211	+	0.961954i	$0.588086\pi$
$44$	−0.616845	+	0.255506i	−0.0929929	+	0.0385189i
$45$	9.73926	+	7.87968i	1.45184	+	1.17463i
$46$	−2.69629	+	2.69629i	−0.397547	+	0.397547i
$47$	0.240703	−	0.184698i	0.0351102	−	0.0269410i	−0.591057	−	0.806630i	$-0.701289\pi$
$47$	0.240703	−	0.184698i	0.0351102	−	0.0269410i	0.626167	+	0.779689i	$0.284623\pi$
$48$	−0.0910250	−	1.72966i	−0.0131383	−	0.249655i
$49$	9.82265	+	2.63197i	1.40324	+	0.375996i
$50$	3.21920	−	12.0142i	0.455264	−	1.69907i
$51$	−6.49816	+	1.20583i	−0.909924	+	0.168849i
$52$	0.194197	−	1.47507i	0.0269303	−	0.204556i
$53$	1.03902	+	2.50841i	0.142720	+	0.344557i	0.979035	−	0.203693i	$-0.0652944\pi$
$53$	1.03902	+	2.50841i	0.142720	+	0.344557i	−0.836315	+	0.548250i	$0.815294\pi$
$54$	4.74554	−	2.11656i	0.645786	−	0.288028i
$55$	−1.06696	+	2.57588i	−0.143869	+	0.347331i
$56$	2.52244	+	3.28731i	0.337076	+	0.439286i
$57$	1.67943	+	9.05039i	0.222446	+	1.19875i
$58$	−1.26584	+	0.166650i	−0.166212	+	0.0218823i
$59$	−3.69949	+	2.13590i	−0.481633	+	0.278071i	−0.721097	−	0.692834i	$-0.756362\pi$
$59$	−3.69949	+	2.13590i	−0.481633	+	0.278071i	0.239464	+	0.970905i	$0.423028\pi$
$60$	−5.37611	−	4.83855i	−0.694053	−	0.624654i
$61$	3.91255	−	1.04836i	0.500950	−	0.134229i	0.000509339	−	1.00000i	$-0.499838\pi$
$61$	3.91255	−	1.04836i	0.500950	−	0.134229i	0.500441	+	0.865771i	$0.333171\pi$
$62$	−6.15590	−	6.15590i	−0.781800	−	0.781800i
$63$	−6.49041	+	10.6017i	−0.817715	+	1.33569i
$64$			1.00000i			0.125000i
$65$	−3.78217	−	4.92902i	−0.469121	−	0.611370i
$66$	0.751236	+	0.879197i	0.0924708	+	0.108222i
$67$	3.89663	−	0.513002i	0.476050	−	0.0626731i	0.111316	−	0.993785i	$-0.464493\pi$
$67$	3.89663	−	0.513002i	0.476050	−	0.0626731i	0.364734	+	0.931112i	$0.381160\pi$
$68$	3.78311	−	0.498057i	0.458770	−	0.0603982i
$69$	5.88534	+	2.99712i	0.708512	+	0.360811i
$70$	17.1550	+	2.25851i	2.05042	+	0.269943i
$71$	−12.4184	+	5.14386i	−1.47379	+	0.610464i	−0.967720	−	0.252028i	$-0.918903\pi$
$71$	−12.4184	+	5.14386i	−1.47379	+	0.610464i	−0.506071	+	0.862492i	$0.668903\pi$
$72$	−2.80027	+	1.07632i	−0.330015	+	0.126846i
$73$	9.56653	+	9.56653i	1.11968	+	1.11968i	0.991788	+	0.127889i	$0.0408201\pi$
$73$	9.56653	+	9.56653i	1.11968	+	1.11968i	0.127889	+	0.991788i	$0.459180\pi$
$74$	1.94826	+	7.27101i	0.226481	+	0.845238i
$75$	−21.5136	+	1.13217i	−2.48417	+	0.130732i
$76$	−0.693674	−	5.26898i	−0.0795699	−	0.604394i
$77$	−2.67226	−	0.716030i	−0.304532	−	0.0815992i
$78$	−2.53370	+	0.470163i	−0.286885	+	0.0532355i
$79$	−1.64296	+	12.4795i	−0.184848	+	1.40406i	0.607661	+	0.794197i	$0.292108\pi$
$79$	−1.64296	+	12.4795i	−0.184848	+	1.40406i	−0.792509	+	0.609861i	$0.791225\pi$
$80$	2.95280	+	2.95280i	0.330133	+	0.330133i
$81$	−6.02800	−	6.68306i	−0.669777	−	0.742562i
$82$	5.49506	+	3.28698i	0.606828	+	0.362987i
$83$	11.9759	+	6.91428i	1.31452	+	0.758941i	0.982842	−	0.184450i	$-0.0590504\pi$
$83$	11.9759	+	6.91428i	1.31452	+	0.758941i	0.331683	+	0.943391i	$0.392384\pi$
$84$	4.06374	−	5.91553i	0.443390	−	0.645437i
$85$	9.70012	−	12.6414i	1.05213	−	1.37116i
$86$	−3.36314	−	5.82513i	−0.362657	−	0.628140i
$87$	0.952471	+	1.99578i	0.102116	+	0.213970i
$88$	−0.406451	−	0.529697i	−0.0433278	−	0.0564659i
$89$	14.8193	−	6.13837i	1.57085	−	0.650666i	0.583916	−	0.811814i	$-0.301520\pi$
$89$	14.8193	−	6.13837i	1.57085	−	0.650666i	0.986930	+	0.161148i	$0.0515196\pi$
$90$	−5.09048	+	11.4468i	−0.536584	+	1.20660i
$91$	4.35918	−	4.35918i	0.456966	−	0.456966i
$92$	−3.30227	−	1.90657i	−0.344285	−	0.198773i
$93$	−6.84271	+	13.4368i	−0.709556	+	1.39333i
$94$	0.240703	+	0.184698i	0.0248267	+	0.0190502i
$95$	−17.6065	−	13.5100i	−1.80639	−	1.38609i
$96$	1.64716	−	0.535592i	0.168113	−	0.0546636i
$97$	0.422726	−	0.324369i	0.0429213	−	0.0329347i	−0.587078	−	0.809530i	$-0.699722\pi$
$97$	0.422726	−	0.324369i	0.0429213	−	0.0329347i	0.629999	+	0.776596i	$0.283055\pi$
$98$			10.1692i			1.02724i
$99$	1.04582	−	1.70830i	0.105109	−	0.171690i
$100$	12.4381			1.24381
$101$	−4.79053	+	3.67590i	−0.476676	+	0.365766i	−0.818979	−	0.573823i	$-0.805460\pi$
$101$	−4.79053	+	3.67590i	−0.476676	+	0.365766i	0.342303	+	0.939589i	$0.388793\pi$
$102$	−2.84658	−	5.96465i	−0.281854	−	0.590588i
$103$	12.7353	+	3.41240i	1.25484	+	0.336234i	0.824205	−	0.566291i	$-0.191622\pi$
$103$	12.7353	+	3.41240i	1.25484	+	0.336234i	0.430637	+	0.902525i	$0.358289\pi$
$104$	1.47507	−	0.194197i	0.144643	−	0.0190426i
$105$	−5.46798	−	29.4668i	−0.533620	−	2.87566i
$106$	−2.15402	+	1.65284i	−0.209217	+	0.160538i
$107$	4.58911			0.443646			0.221823	−	0.975087i	$-0.428799\pi$
$107$	4.58911			0.443646			0.221823	+	0.975087i	$0.428799\pi$
$108$	3.27268	+	4.03603i	0.314914	+	0.388367i
$109$	−5.74013	−	2.37764i	−0.549805	−	0.227737i	0.0904474	−	0.995901i	$-0.471170\pi$
$109$	−5.74013	−	2.37764i	−0.549805	−	0.227737i	−0.640253	+	0.768164i	$0.721170\pi$
$110$	−2.76426	−	0.363921i	−0.263561	−	0.0346985i
$111$	10.9331	−	7.10340i	1.03772	−	0.674224i
$112$	−2.52244	+	3.28731i	−0.238349	+	0.310622i
$113$	2.10213	+	3.64099i	0.197752	+	0.342516i	0.947799	−	0.318868i	$-0.103303\pi$
$113$	2.10213	+	3.64099i	0.197752	+	0.342516i	−0.750048	+	0.661384i	$0.769969\pi$
$114$	−8.30734	+	3.96462i	−0.778053	+	0.371320i
$115$	−15.3807	+	4.12123i	−1.43425	+	0.384307i
$116$	−0.488594	−	1.17957i	−0.0453648	−	0.109520i
$117$	2.13146	+	3.92159i	0.197054	+	0.362551i
$118$	−3.02062	−	3.02062i	−0.278071	−	0.278071i
$119$	13.6926	+	7.90543i	1.25520	+	0.724689i
$120$	3.28224	−	6.44523i	0.299626	−	0.588367i
$121$	−10.1946	−	2.73163i	−0.926781	−	0.248330i
$122$	2.02528	+	3.50789i	0.183361	+	0.317590i
$123$	2.47108	−	10.8117i	0.222810	−	0.974862i
$124$	4.35288	−	7.53940i	0.390900	−	0.677059i
$125$	21.9631	−	21.9631i	1.96444	−	1.96444i
$126$	−11.9203	−	3.52532i	−1.06195	−	0.314061i
$127$			10.3830i			0.921340i	0.887571	+	0.460670i	$0.152391\pi$
$127$			10.3830i			0.921340i	−0.887571	+	0.460670i	$0.847609\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−7.79366	+	8.65952i	−0.686193	+	0.762428i
$130$	3.78217	−	4.92902i	0.331718	−	0.432304i
$131$	4.23311	−	15.7982i	0.369849	−	1.38029i	−0.490878	−	0.871228i	$-0.663324\pi$
$131$	4.23311	−	15.7982i	0.369849	−	1.38029i	0.860727	−	0.509067i	$-0.170009\pi$
$132$	−0.654805	+	0.953191i	−0.0569934	+	0.0829646i
$133$	11.0104	−	19.0705i	0.954721	−	1.65363i
$134$	1.50404	+	3.63108i	0.129930	+	0.313678i
$135$	21.5812	+	2.25402i	1.85741	+	0.193996i
$136$	1.46023	+	3.52530i	0.125214	+	0.302292i
$137$	−9.79036	+	7.51241i	−0.836447	+	0.641829i	−0.935529	−	0.353251i	$-0.885076\pi$
$137$	−9.79036	+	7.51241i	−0.836447	+	0.641829i	0.0990814	+	0.995079i	$0.468410\pi$
$138$	−1.37175	+	6.46051i	−0.116772	+	0.549955i
$139$	−7.78588	−	13.4855i	−0.660390	−	1.14383i	−0.980513	−	0.196453i	$-0.937058\pi$
$139$	−7.78588	−	13.4855i	−0.660390	−	1.14383i	0.320124	−	0.947376i	$-0.396276\pi$
$140$	2.25851	+	17.1550i	0.190879	+	1.44987i
$141$	0.175309	−	0.495400i	0.0147637	−	0.0417202i
$142$	−8.18270	−	10.6639i	−0.686677	−	0.894895i
$143$	−0.702410	+	0.702410i	−0.0587385	+	0.0587385i
$144$	−1.76441	−	2.42628i	−0.147034	−	0.202190i
$145$	−4.92576	−	2.04032i	−0.409062	−	0.169439i
$146$	−6.76456	+	11.7166i	−0.559839	+	0.969669i
$147$	16.7502	−	5.44651i	1.38154	−	0.449221i
$148$	−6.51901	+	3.76375i	−0.535859	+	0.309379i
$149$	−1.74108	−	13.2248i	−0.142634	−	1.08342i	−0.901688	−	0.432388i	$-0.857671\pi$
$149$	−1.74108	−	13.2248i	−0.142634	−	1.08342i	0.759053	−	0.651028i	$-0.225662\pi$
$150$	−6.66172	−	20.4875i	−0.543927	−	1.67280i
$151$	0.0425070	−	0.322873i	0.00345917	−	0.0262750i	−0.989628	−	0.143652i	$-0.954115\pi$
$151$	0.0425070	−	0.322873i	0.00345917	−	0.0262750i	0.993087	+	0.117377i	$0.0374487\pi$
$152$	4.90991	−	2.03375i	0.398246	−	0.164959i
$153$	−8.30013	+	7.88340i	−0.671026	+	0.637335i
$154$		−	2.76653i		−	0.222933i
$155$	−9.40918	−	35.1155i	−0.755763	−	2.82055i
$156$	−1.10991	−	2.32568i	−0.0888640	−	0.186203i
$157$	6.40881	+	4.91765i	0.511478	+	0.392471i	0.832005	−	0.554768i	$-0.187193\pi$
$157$	6.40881	+	4.91765i	0.511478	+	0.392471i	−0.320526	+	0.947240i	$0.603860\pi$
$158$	−12.4795	+	1.64296i	−0.992818	+	0.130707i
$159$	3.87617	+	2.66277i	0.307400	+	0.211172i
$160$	−2.08794	+	3.61643i	−0.165067	+	0.285904i
$161$	−6.04639	−	14.5973i	−0.476522	−	1.15043i
$162$	4.89518	−	7.55230i	0.384601	−	0.593365i
$163$			14.1024i			1.10458i	0.833652	+	0.552291i	$0.186246\pi$
$163$			14.1024i			1.10458i	−0.833652	+	0.552291i	$0.813754\pi$
$164$	−1.75276	+	6.15856i	−0.136867	+	0.480903i
$165$	0.881075	+	4.74809i	0.0685916	+	0.369638i
$166$	−3.57910	+	13.3574i	−0.277792	+	1.03673i
$167$	9.68249	+	7.42963i	0.749253	+	0.574922i	0.911242	−	0.411870i	$-0.135124\pi$
$167$	9.68249	+	7.42963i	0.749253	+	0.574922i	−0.161989	+	0.986793i	$0.551791\pi$
$168$	6.76574	+	2.39422i	0.521988	+	0.184718i
$169$	2.79174	+	10.4189i	0.214749	+	0.801454i
$170$	14.7213	+	6.09775i	1.12907	+	0.467676i
$171$	10.9797	+	11.5601i	0.839639	+	0.884024i
$172$	4.75620	−	4.75620i	0.362657	−	0.362657i
$173$	3.03096	−	0.812143i	0.230440	−	0.0617461i	−0.141751	−	0.989902i	$-0.545273\pi$
$173$	3.03096	−	0.812143i	0.230440	−	0.0617461i	0.372191	+	0.928156i	$0.378607\pi$
$174$	−1.68126	+	1.43656i	−0.127456	+	0.108905i
$175$	40.8878	+	31.3743i	3.09082	+	2.37167i
$176$	0.406451	−	0.529697i	0.0306374	−	0.0399274i
$177$	−3.35763	+	6.59327i	−0.252375	+	0.495581i
$178$	9.76474	+	12.7257i	0.731898	+	0.953828i
$179$	−7.46883	+	18.0313i	−0.558246	+	1.34773i	0.352907	+	0.935658i	$0.385193\pi$
$179$	−7.46883	+	18.0313i	−0.558246	+	1.34773i	−0.911153	+	0.412068i	$0.864807\pi$
$180$	−12.3743	−	1.95437i	−0.922325	−	0.145670i
$181$	4.88106	−	11.7839i	0.362806	−	0.875892i	−0.632081	−	0.774902i	$-0.717799\pi$
$181$	4.88106	−	11.7839i	0.362806	−	0.875892i	0.994887	−	0.100990i	$-0.0322010\pi$
$182$	5.33888	+	3.08241i	0.395744	+	0.228483i
$183$	4.69334	−	5.21477i	0.346942	−	0.385487i
$184$	0.986911	−	3.68320i	0.0727561	−	0.271529i
$185$	−8.13572	+	30.3629i	−0.598150	+	2.23233i
$186$	−14.7500	−	3.13185i	−1.08152	−	0.229638i
$187$	−2.20634	−	1.27383i	−0.161343	−	0.0931517i
$188$	−0.116106	+	0.280305i	−0.00846791	+	0.0204434i
$189$	0.577660	+	21.5229i	0.0420186	+	1.56556i
$190$	8.49272	−	20.5032i	0.616126	−	1.48746i
$191$	−11.7731	−	15.3430i	−0.851873	−	1.11018i	−0.992755	−	0.120156i	$-0.961660\pi$
$191$	−11.7731	−	15.3430i	−0.851873	−	1.11018i	0.140882	−	0.990026i	$-0.455006\pi$
$192$	0.943659	+	1.45241i	0.0681027	+	0.104819i
$193$	−2.64248	+	3.44374i	−0.190210	+	0.247886i	−0.878717	−	0.477344i	$-0.841600\pi$
$193$	−2.64248	+	3.44374i	−0.190210	+	0.247886i	0.688507	+	0.725230i	$0.258266\pi$
$194$	0.422726	+	0.324369i	0.0303500	+	0.0232883i
$195$	−10.1446	−	3.58991i	−0.726470	−	0.257079i
$196$	−9.82265	+	2.63197i	−0.701618	+	0.187998i
$197$	5.03031	−	5.03031i	0.358395	−	0.358395i	−0.504826	−	0.863221i	$-0.668443\pi$
$197$	5.03031	−	5.03031i	0.358395	−	0.358395i	0.863221	+	0.504826i	$0.168443\pi$
$198$	1.92077	+	0.568048i	0.136503	+	0.0403694i
$199$	−17.3948	−	7.20515i	−1.23308	−	0.510760i	−0.331537	−	0.943442i	$-0.607567\pi$
$199$	−17.3948	−	7.20515i	−1.23308	−	0.510760i	−0.901546	+	0.432683i	$0.857567\pi$
$200$	3.21920	+	12.0142i	0.227632	+	0.849535i
$201$	5.17543	−	4.42218i	0.365047	−	0.311917i
$202$	−4.79053	−	3.67590i	−0.337061	−	0.258636i
$203$	1.36924	−	5.11007i	0.0961018	−	0.358657i
$204$	5.02466	−	4.29335i	0.351796	−	0.300595i
$205$	13.0095	+	23.3605i	0.908619	+	1.63157i
$206$			13.1845i			0.918608i
$207$	11.3762	−	1.20070i	0.790701	−	0.0834541i
$208$	0.569357	+	1.37455i	0.0394778	+	0.0953079i
$209$	−1.77414	+	3.07291i	−0.122720	+	0.212557i
$210$	27.0475	−	12.9082i	1.86645	−	0.890752i
$211$	−21.8567	+	2.87749i	−1.50468	+	0.198095i	−0.837350	−	0.546667i	$-0.815896\pi$
$211$	−21.8567	+	2.87749i	−1.50468	+	0.198095i	−0.667330	+	0.744762i	$0.732563\pi$
$212$	−2.15402	−	1.65284i	−0.147939	−	0.113517i
$213$	−13.1826	+	19.1897i	−0.903256	+	1.31486i
$214$	1.18775	+	4.43274i	0.0811929	+	0.303016i
$215$		−	28.0882i		−	1.91560i
$216$	−3.05148	+	4.20577i	−0.207627	+	0.286166i
$217$	33.3270	−	13.8045i	2.26238	−	0.937110i
$218$	0.810969	−	6.15992i	0.0549258	−	0.417203i
$219$	22.9221	+	4.86703i	1.54893	+	0.328883i
$220$	−0.363921	−	2.76426i	−0.0245356	−	0.186366i
$221$	4.91651	−	2.83855i	0.330720	−	0.190941i
$222$	9.69104	+	8.72203i	0.650420	+	0.585384i
$223$	−10.9083	+	18.8938i	−0.730477	+	1.26522i	0.226203	+	0.974080i	$0.427369\pi$
$223$	−10.9083	+	18.8938i	−0.730477	+	1.26522i	−0.956680	+	0.291143i	$0.905964\pi$
$224$	−3.82816	−	1.58567i	−0.255780	−	0.105947i
$225$	−30.1782	+	21.9458i	−2.01188	+	1.46306i
$226$	−2.97286	+	2.97286i	−0.197752	+	0.197752i
$227$	4.27423	+	5.57029i	0.283691	+	0.369713i	0.913362	−	0.407149i	$-0.133477\pi$
$227$	4.27423	+	5.57029i	0.283691	+	0.369713i	−0.629671	+	0.776862i	$0.716810\pi$
$228$	−5.97962	−	6.99815i	−0.396010	−	0.463464i
$229$	−0.0443591	−	0.336941i	−0.00293133	−	0.0222657i	0.989917	−	0.141651i	$-0.0452410\pi$
$229$	−0.0443591	−	0.336941i	−0.00293133	−	0.0222657i	−0.992848	+	0.119385i	$0.961908\pi$
$230$	−7.96161	−	13.7899i	−0.524973	−	0.909280i
$231$	−4.55692	+	1.48173i	−0.299823	+	0.0974906i
$232$	1.01292	−	0.777241i	0.0665015	−	0.0510284i
$233$	−3.60581	−	8.70520i	−0.236225	−	0.570296i	0.760662	−	0.649148i	$-0.224875\pi$
$233$	−3.60581	−	8.70520i	−0.236225	−	0.570296i	−0.996886	+	0.0788519i	$0.974875\pi$
$234$	−3.23630	+	3.07382i	−0.211564	+	0.200942i
$235$	0.484847	+	1.17052i	0.0316279	+	0.0763565i
$236$	2.13590	−	3.69949i	0.139035	−	0.240816i
$237$	9.39016	+	19.6759i	0.609956	+	1.27808i
$238$	−4.09215	+	15.2721i	−0.265255	+	0.989944i
$239$	2.59563	−	3.38269i	0.167897	−	0.218808i	−0.701825	−	0.712349i	$-0.747631\pi$
$239$	2.59563	−	3.38269i	0.167897	−	0.218808i	0.869722	+	0.493541i	$0.164298\pi$
$240$	7.07512	+	1.50225i	0.456697	+	0.0969701i
$241$	−0.760797	+	0.203855i	−0.0490073	+	0.0131315i	−0.283239	−	0.959049i	$-0.591409\pi$
$241$	−0.760797	+	0.203855i	−0.0490073	+	0.0131315i	0.234232	+	0.972181i	$0.424742\pi$
$242$		−	10.5542i		−	0.678451i
$243$	−15.0617	−	4.01820i	−0.966207	−	0.257768i
$244$	−2.86418	+	2.86418i	−0.183361	+	0.183361i
$245$	−21.2326	+	36.7760i	−1.35650	+	2.34953i
$246$	11.0829	−	0.411400i	0.706620	−	0.0262299i
$247$	−3.95342	−	6.84753i	−0.251550	−	0.435698i
$248$	8.40911	+	2.25322i	0.533979	+	0.143079i
$249$	23.9187	−	1.25875i	1.51578	−	0.0797698i
$250$	26.8992	+	15.5302i	1.70125	+	0.982218i
$251$	17.2249	+	17.2249i	1.08723	+	1.08723i	0.995813	+	0.0914136i	$0.0291385\pi$
$251$	17.2249	+	17.2249i	1.08723	+	1.08723i	0.0914136	+	0.995813i	$0.470861\pi$
$252$	0.319988	−	12.4266i	0.0201574	−	0.782801i
$253$	0.974277	+	2.35211i	0.0612522	+	0.147876i
$254$	−10.0292	+	2.68731i	−0.629287	+	0.168617i
$255$	2.15939	−	27.5142i	0.135226	−	1.72301i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.89551	+	7.68318i	−0.367752	+	0.479264i	−0.940174	−	0.340696i	$-0.889337\pi$
$257$	−5.89551	+	7.68318i	−0.367752	+	0.479264i	0.572422	+	0.819959i	$0.306004\pi$
$258$	−10.3816	−	5.28684i	−0.646330	−	0.329145i
$259$	−30.9239	−	4.07121i	−1.92152	−	0.252972i
$260$	5.73997	+	2.37757i	0.355978	+	0.147451i
$261$	3.26672	+	1.99989i	0.202205	+	0.123790i
$262$	16.3555			1.01045
$263$	11.5143	−	8.83527i	0.710005	−	0.544806i	−0.189412	−	0.981898i	$-0.560658\pi$
$263$	11.5143	−	8.83527i	0.710005	−	0.544806i	0.899417	+	0.437092i	$0.143992\pi$
$264$	−1.09019	−	0.385789i	−0.0670964	−	0.0237437i
$265$	−11.2409	+	1.47989i	−0.690523	+	0.0909090i
$266$	21.2704	+	5.69939i	1.30417	+	0.349452i
$267$	15.7313	−	22.8999i	0.962740	−	1.40145i
$268$	−3.11808	+	2.39259i	−0.190467	+	0.146151i
$269$	24.0607			1.46701			0.733504	−	0.679685i	$-0.237884\pi$
$269$	24.0607			1.46701			0.733504	+	0.679685i	$0.237884\pi$
$270$	3.40840	+	21.4292i	0.207428	+	1.30414i
$271$		−	14.1356i		−	0.858675i	−0.903144	−	0.429338i	$-0.858747\pi$
$271$		−	14.1356i		−	0.858675i	0.903144	−	0.429338i	$-0.141253\pi$
$272$	−3.02725	+	2.32289i	−0.183554	+	0.140846i
$273$	2.21776	−	10.4449i	0.134225	−	0.632155i
$274$	−9.79036	−	7.51241i	−0.591458	−	0.453841i
$275$	−6.58839	−	5.05545i	−0.397295	−	0.304855i
$276$	−6.59541	+	0.347091i	−0.396997	+	0.0208924i
$277$	−12.9859	−	7.49740i	−0.780246	−	0.450475i	0.0562717	−	0.998415i	$-0.482079\pi$
$277$	−12.9859	−	7.49740i	−0.780246	−	0.450475i	−0.836517	+	0.547941i	$0.815412\pi$
$278$	11.0109	−	11.0109i	0.660390	−	0.660390i
$279$	2.74130	+	25.9730i	0.164118	+	1.55496i
$280$	−15.9860	+	6.62160i	−0.955344	+	0.395716i
$281$	−12.7697	−	16.6418i	−0.761776	−	0.992765i	−0.999769	−	0.0214986i	$-0.993156\pi$
$281$	−12.7697	−	16.6418i	−0.761776	−	0.992765i	0.237993	−	0.971267i	$-0.423510\pi$
$282$	0.523893	+	0.0411166i	0.0311974	+	0.00244846i
$283$	−4.35826	−	7.54873i	−0.259072	−	0.448725i	0.706922	−	0.707292i	$-0.250083\pi$
$283$	−4.35826	−	7.54873i	−0.259072	−	0.448725i	−0.965993	+	0.258566i	$0.916750\pi$
$284$	8.18270	−	10.6639i	0.485554	−	0.632786i
$285$	−38.3208	−	3.00752i	−2.26993	−	0.178150i
$286$	−0.860274	−	0.496679i	−0.0508690	−	0.0293693i
$287$	−21.2965	+	15.8239i	−1.25709	+	0.934054i
$288$	1.88695	−	2.33226i	0.111189	−	0.137430i
$289$	−1.72533	−	1.72533i	−0.101490	−	0.101490i
$290$	0.695914	−	5.28599i	0.0408655	−	0.310404i
$291$	0.307880	−	0.870027i	0.0180482	−	0.0510019i
$292$	−13.0681	−	3.50159i	−0.764754	−	0.204915i
$293$	−3.06415	−	23.2745i	−0.179009	−	1.35971i	−0.811141	−	0.584850i	$-0.801153\pi$
$293$	−3.06415	−	23.2745i	−0.179009	−	1.35971i	0.632132	−	0.774861i	$-0.282180\pi$
$294$	9.59621	+	14.7698i	0.559662	+	0.861394i
$295$	−4.61696	−	17.2307i	−0.268810	−	1.00321i
$296$	−5.32275	−	5.32275i	−0.309379	−	0.309379i
$297$	−0.0930805	−	3.46806i	−0.00540108	−	0.201237i
$298$	12.3235	−	5.10457i	0.713883	−	0.295700i
$299$	−5.62465	−	0.740500i	−0.325282	−	0.0428242i
$300$	18.0652	−	11.7373i	1.04300	−	0.677652i
$301$	27.6323	−	3.63787i	1.59270	−	0.209683i
$302$	0.322873	−	0.0425070i	0.0185792	−	0.00244600i
$303$	−3.48904	+	9.85957i	−0.200440	+	0.566417i
$304$	3.23523	+	4.21623i	0.185553	+	0.241818i
$305$			16.9147i			0.968534i
$306$	−9.76301	−	5.97694i	−0.558114	−	0.341679i
$307$	−11.3182	−	11.3182i	−0.645965	−	0.645965i	0.306050	−	0.952015i	$-0.400993\pi$
$307$	−11.3182	−	11.3182i	−0.645965	−	0.645965i	−0.952015	+	0.306050i	$0.900993\pi$
$308$	2.67226	−	0.716030i	0.152266	−	0.0407996i
$309$	21.7170	−	7.06151i	1.23544	−	0.401715i
$310$	31.4837	−	18.1771i	1.78816	−	1.03239i
$311$	2.23510	−	0.294257i	0.126741	−	0.0166858i	−0.0668888	−	0.997760i	$-0.521307\pi$
$311$	2.23510	−	0.294257i	0.126741	−	0.0166858i	0.193630	+	0.981075i	$0.437974\pi$
$312$	1.95916	−	1.67402i	0.110916	−	0.0947728i
$313$	9.35525	+	12.1920i	0.528790	+	0.689133i	0.979016	−	0.203782i	$-0.0653233\pi$
$313$	9.35525	+	12.1920i	0.528790	+	0.689133i	−0.450226	+	0.892915i	$0.648657\pi$
$314$	−3.09136	+	7.46321i	−0.174456	+	0.421174i
$315$	−35.7484	−	37.6381i	−2.01419	−	2.12067i
$316$	−4.81692	−	11.6291i	−0.270973	−	0.654187i
$317$	−1.66829	+	12.6719i	−0.0937007	+	0.711728i	0.878527	+	0.477692i	$0.158527\pi$
$317$	−1.66829	+	12.6719i	−0.0937007	+	0.711728i	−0.972228	+	0.234036i	$0.924807\pi$
$318$	−1.56882	+	4.43327i	−0.0879749	+	0.248605i
$319$	−0.220631	+	0.823404i	−0.0123529	+	0.0461018i
$320$	−4.03360	−	1.08080i	−0.225485	−	0.0604185i
$321$	6.66529	−	4.33055i	0.372020	−	0.241708i
$322$	12.5350	−	9.61842i	0.698546	−	0.536013i
$323$	14.3392	−	14.3392i	0.797853	−	0.797853i
$324$	8.56193	+	2.77370i	0.475663	+	0.154094i
$325$	17.0967	−	7.08170i	0.948356	−	0.392822i
$326$	−13.6218	+	3.64996i	−0.754443	+	0.202152i
$327$	−10.5807	+	1.96341i	−0.585116	+	0.108577i
$328$	−6.40236	−	0.0990803i	−0.353511	−	0.00547079i
$329$	−1.08873	+	0.628579i	−0.0600237	+	0.0346547i
$330$	−4.35826	+	2.07995i	−0.239914	+	0.114497i
$331$	17.3238	+	2.28072i	0.952201	+	0.125360i	0.590592	−	0.806970i	$-0.298894\pi$
$331$	17.3238	+	2.28072i	0.952201	+	0.125360i	0.361609	+	0.932330i	$0.382228\pi$
$332$	−13.8286			−0.758941
$333$	9.17615	−	20.6342i	0.502850	−	1.13074i
$334$	−4.67046	+	11.2755i	−0.255556	+	0.616968i
$335$	−2.14224	+	16.2719i	−0.117043	+	0.889029i
$336$	−0.561533	+	7.15487i	−0.0306342	+	0.390330i
$337$	−33.6368	−	9.01296i	−1.83232	−	0.490967i	−0.834151	−	0.551536i	$-0.814042\pi$
$337$	−33.6368	−	9.01296i	−1.83232	−	0.490967i	−0.998164	+	0.0605683i	$0.980709\pi$
$338$	−9.34133	+	5.39322i	−0.508102	+	0.293353i
$339$	6.48901	+	3.30454i	0.352435	+	0.179478i
$340$	−2.07983	+	15.7979i	−0.112795	+	0.856760i
$341$	−5.37010	+	2.22437i	−0.290807	+	0.120456i
$342$	−8.32445	+	13.5976i	−0.450135	+	0.735272i
$343$	−12.1320	−	5.02525i	−0.655067	−	0.271338i
$344$	5.82513	+	3.36314i	0.314070	+	0.181328i
$345$	−18.4500	+	20.4998i	−0.993317	+	1.10367i
$346$	1.56894	+	2.71748i	0.0843467	+	0.146093i
$347$	−3.39577	−	25.7934i	−0.182295	−	1.38466i	−0.800822	−	0.598902i	$-0.795604\pi$
$347$	−3.39577	−	25.7934i	−0.182295	−	1.38466i	0.618528	−	0.785763i	$-0.287729\pi$
$348$	−1.82275	−	1.25216i	−0.0977099	−	0.0671228i
$349$	3.19167	+	11.9115i	0.170846	+	0.637607i	0.997222	+	0.0744876i	$0.0237321\pi$
$349$	3.19167	+	11.9115i	0.170846	+	0.637607i	−0.826376	+	0.563119i	$0.809601\pi$
$350$	−19.7227	+	47.6148i	−1.05422	+	2.54512i
$351$	6.79641	+	3.68440i	0.362765	+	0.196659i
$352$	0.616845	+	0.255506i	0.0328779	+	0.0136185i
$353$	3.95531	−	6.85079i	0.210520	−	0.364631i	−0.741358	−	0.671110i	$-0.765818\pi$
$353$	3.95531	−	6.85079i	0.210520	−	0.364631i	0.951877	+	0.306479i	$0.0991511\pi$
$354$	−7.23763	−	1.53676i	−0.384676	−	0.0816778i
$355$	−7.32650	−	55.6503i	−0.388850	−	2.95361i
$356$	−9.76474	+	12.7257i	−0.517530	+	0.674458i
$357$	27.3474	−	1.43918i	1.44738	−	0.0761697i
$358$	−19.3500	−	2.54748i	−1.02268	−	0.134638i
$359$	−1.39805			−0.0737864			−0.0368932	−	0.999319i	$-0.511746\pi$
$359$	−1.39805			−0.0737864			−0.0368932	+	0.999319i	$0.511746\pi$
$360$	−1.31492	−	12.4585i	−0.0693025	−	0.656619i
$361$	−6.53603	−	6.53603i	−0.344001	−	0.344001i
$362$	12.6457	+	1.66484i	0.664644	+	0.0875020i
$363$	−17.3845	+	5.65275i	−0.912450	+	0.296693i
$364$	−1.59557	+	5.95475i	−0.0836306	+	0.312114i
$365$	−48.9270	+	28.2480i	−2.56096	+	1.47857i
$366$	6.25181	+	3.18374i	0.326787	+	0.166417i
$367$	2.02106	+	7.54270i	0.105498	+	0.393726i	0.998401	−	0.0565238i	$-0.0180017\pi$
$367$	2.02106	+	7.54270i	0.105498	+	0.393726i	−0.892903	+	0.450250i	$0.851335\pi$
$368$	3.81313			0.198773
$369$	−6.61355	−	18.0350i	−0.344288	−	0.938864i
$370$	−31.4340			−1.63418
$371$	−2.91175	−	10.8668i	−0.151170	−	0.564176i
$372$	−0.792442	−	15.0580i	−0.0410862	−	0.780720i
$373$	−19.6461	+	11.3427i	−1.01724	+	0.587301i	−0.913302	−	0.407283i	$-0.866476\pi$
$373$	−19.6461	+	11.3427i	−1.01724	+	0.587301i	−0.103934	+	0.994584i	$0.533143\pi$
$374$	0.659383	−	2.46085i	0.0340959	−	0.127248i
$375$	11.1738	−	52.6251i	0.577015	−	2.71755i
$376$	−0.300804	−	0.0396017i	−0.0155128	−	0.00204230i
$377$	−1.34319	−	1.34319i	−0.0691780	−	0.0691780i
$378$	−20.6400	+	6.12850i	−1.06161	+	0.315216i
$379$	7.71169			0.396123			0.198061	−	0.980190i	$-0.436535\pi$
$379$	7.71169			0.396123			0.198061	+	0.980190i	$0.436535\pi$
$380$	22.0027	+	2.89671i	1.12871	+	0.148598i
$381$	9.79799	+	15.0804i	0.501966	+	0.772592i
$382$	11.7731	−	15.3430i	0.602365	−	0.785018i
$383$	−0.574300	−	4.36224i	−0.0293453	−	0.222900i	0.970488	−	0.241149i	$-0.0775242\pi$
$383$	−0.574300	−	4.36224i	−0.0293453	−	0.222900i	−0.999833	+	0.0182489i	$0.994191\pi$
$384$	−1.15869	+	1.28742i	−0.0591290	+	0.0656982i
$385$	5.77636	−	10.0049i	0.294390	−	0.509899i
$386$	−4.01032	−	1.66113i	−0.204120	−	0.0845493i
$387$	−3.14799	+	19.9318i	−0.160021	+	1.01319i
$388$	−0.203907	+	0.492275i	−0.0103518	+	0.0249915i
$389$	4.98490	+	18.6039i	0.252744	+	0.943255i	0.969331	+	0.245757i	$0.0790365\pi$
$389$	4.98490	+	18.6039i	0.252744	+	0.943255i	−0.716587	+	0.697498i	$0.754297\pi$
$390$	0.841968	−	10.7281i	0.0426347	−	0.543237i
$391$	−1.89916	−	14.4255i	−0.0960444	−	0.729530i
$392$	−5.08458	−	8.80674i	−0.256810	−	0.444808i
$393$	−8.75987	−	26.9401i	−0.441877	−	1.35895i
$394$	6.16084	+	3.55696i	0.310379	+	0.179197i
$395$	−48.5617	−	20.1149i	−2.44341	−	1.01209i
$396$	−0.0515609	+	2.00234i	−0.00259103	+	0.100621i
$397$	−0.854656	+	0.354010i	−0.0428940	+	0.0177673i	−0.404027	−	0.914747i	$-0.632390\pi$
$397$	−0.854656	+	0.354010i	−0.0428940	+	0.0177673i	0.361133	+	0.932514i	$0.382390\pi$
$398$	2.45754	−	18.6669i	0.123186	−	0.935687i
$399$	−2.00444	−	38.0884i	−0.100348	−	1.90680i
$400$	−10.7717	+	6.21903i	−0.538583	+	0.310951i
$401$	8.30830	+	2.22620i	0.414897	+	0.111171i	0.460228	−	0.887801i	$-0.347768\pi$
$401$	8.30830	+	2.22620i	0.414897	+	0.111171i	−0.0453312	+	0.998972i	$0.514434\pi$
$402$	5.61100	+	3.85454i	0.279851	+	0.192247i
$403$	1.69063	−	12.8416i	0.0842164	−	0.639687i
$404$	2.31077	−	5.57869i	0.114965	−	0.277550i
$405$	33.4718	−	17.0915i	1.66323	−	0.849282i
$406$	5.29033			0.262555
$407$	4.98288	+	0.656008i	0.246992	+	0.0325171i
$408$	5.44754	+	3.74224i	0.269693	+	0.185269i
$409$	−21.9904	+	12.6962i	−1.08735	+	0.627785i	−0.932871	−	0.360211i	$-0.882705\pi$
$409$	−21.9904	+	12.6962i	−1.08735	+	0.627785i	−0.154484	+	0.987995i	$0.549371\pi$
$410$	−19.1974	+	18.6123i	−0.948094	+	0.919197i
$411$	−7.13052	+	20.1499i	−0.351722	+	0.993921i
$412$	−12.7353	+	3.41240i	−0.627421	+	0.168117i
$413$	16.3531	−	6.77369i	0.804685	−	0.333312i
$414$	4.10416	+	10.6778i	0.201709	+	0.524786i
$415$	−40.8330	+	40.8330i	−2.00441	+	2.00441i
$416$	−1.18035	+	0.905717i	−0.0578716	+	0.0444064i
$417$	−24.0341	−	12.2394i	−1.17695	−	0.599365i
$418$	−3.42738	−	0.918364i	−0.167639	−	0.0449187i
$419$	−2.69361	+	10.0527i	−0.131591	+	0.491106i	−0.999989	−	0.00476341i	$-0.998484\pi$
$419$	−2.69361	+	10.0527i	−0.131591	+	0.491106i	0.868397	+	0.495869i	$0.165150\pi$
$420$	19.4688	+	22.7850i	0.949980	+	1.11179i
$421$	3.21509	−	24.4211i	0.156694	−	1.19021i	−0.714630	−	0.699502i	$-0.753405\pi$
$421$	3.21509	−	24.4211i	0.156694	−	1.19021i	0.871324	−	0.490708i	$-0.163262\pi$
$422$	−8.43639	−	20.3672i	−0.410677	−	0.991462i
$423$	−0.212867	−	0.884959i	−0.0103500	−	0.0430282i
$424$	1.03902	−	2.50841i	0.0504592	−	0.121819i
$425$	28.8922	+	37.6530i	1.40148	+	1.82644i
$426$	−21.9478	−	7.76674i	−1.06337	−	0.376300i
$427$	−16.6402	+	2.19073i	−0.805276	+	0.106017i
$428$	−3.97429	+	2.29456i	−0.192104	+	0.110912i
$429$	−0.357356	+	1.68303i	−0.0172533	+	0.0812573i
$430$	27.1311	−	7.26976i	1.30838	−	0.350579i
$431$	10.5762	+	10.5762i	0.509439	+	0.509439i	0.914354	−	0.404915i	$-0.132699\pi$
$431$	10.5762	+	10.5762i	0.509439	+	0.509439i	−0.404915	+	0.914354i	$0.632699\pi$
$432$	−4.85224	−	1.85897i	−0.233454	−	0.0894396i
$433$			24.4464i			1.17482i	0.809290	+	0.587409i	$0.199852\pi$
$433$			24.4464i			1.17482i	−0.809290	+	0.587409i	$0.800148\pi$
$434$	21.9598	+	28.6185i	1.05410	+	1.37373i
$435$	−9.07960	+	1.68485i	−0.435334	+	0.0807823i
$436$	6.15992	−	0.810969i	0.295007	−	0.0388384i
$437$	−20.0913	+	2.64507i	−0.961098	+	0.126531i
$438$	1.23149	+	23.4007i	0.0588428	+	1.11813i
$439$	−12.8066	−	1.68602i	−0.611225	−	0.0804692i	−0.181442	−	0.983402i	$-0.558076\pi$
$439$	−12.8066	−	1.68602i	−0.611225	−	0.0804692i	−0.429783	+	0.902932i	$0.641410\pi$
$440$	2.57588	−	1.06696i	0.122800	−	0.0508655i
$441$	19.1886	−	23.7171i	0.913745	−	1.12939i
$442$	4.01431	+	4.01431i	0.190941	+	0.190941i
$443$	1.97663	+	7.37690i	0.0939127	+	0.350487i	0.996852	−	0.0792804i	$-0.0252622\pi$
$443$	1.97663	+	7.37690i	0.0939127	+	0.350487i	−0.902940	+	0.429767i	$0.858596\pi$
$444$	−5.91661	+	11.6182i	−0.280790	+	0.551378i
$445$	8.74299	+	66.4096i	0.414458	+	3.14812i
$446$	−21.0733	−	5.64658i	−0.997850	−	0.267373i
$447$	−15.0084	−	17.5649i	−0.709875	−	0.830790i
$448$	0.540844	−	4.10812i	0.0255525	−	0.194090i
$449$	26.6466	+	26.6466i	1.25753	+	1.25753i	0.952267	+	0.305266i	$0.0987453\pi$
$449$	26.6466	+	26.6466i	1.25753	+	1.25753i	0.305266	+	0.952267i	$0.401255\pi$
$450$	−29.0088	−	23.4699i	−1.36749	−	1.10638i
$451$	3.43158	−	2.54976i	0.161587	−	0.120063i
$452$	−3.64099	−	2.10213i	−0.171258	−	0.0988758i
$453$	−0.242944	−	0.509057i	−0.0114145	−	0.0239176i
$454$	−4.27423	+	5.57029i	−0.200600	+	0.261427i
$455$	12.8718	+	22.2946i	0.603438	+	1.04519i
$456$	5.21206	−	7.58713i	0.244077	−	0.355300i
$457$	−9.19411	−	11.9820i	−0.430082	−	0.560494i	0.527166	−	0.849763i	$-0.323255\pi$
$457$	−9.19411	−	11.9820i	−0.430082	−	0.560494i	−0.957248	+	0.289268i	$0.906588\pi$
$458$	0.313979	−	0.130054i	0.0146713	−	0.00607704i
$459$	−4.61599	+	19.2825i	−0.215456	+	0.900028i
$460$	11.2594	−	11.2594i	0.524973	−	0.524973i
$461$	0.696729	+	0.402257i	0.0324499	+	0.0187350i	0.516137	−	0.856506i	$-0.327369\pi$
$461$	0.696729	+	0.402257i	0.0324499	+	0.0187350i	−0.483687	+	0.875241i	$0.660703\pi$
$462$	−2.61066	−	4.01815i	−0.121459	−	0.186941i
$463$	22.4861	+	17.2542i	1.04502	+	0.801871i	0.980594	−	0.196051i	$-0.0628118\pi$
$463$	22.4861	+	17.2542i	1.04502	+	0.801871i	0.0644255	+	0.997923i	$0.479479\pi$
$464$	1.01292	+	0.777241i	0.0470237	+	0.0360825i
$465$	−46.8031	−	42.1233i	−2.17044	−	1.95342i
$466$	7.47532	−	5.73602i	0.346288	−	0.265716i
$467$		−	1.27434i		−	0.0589696i	−0.999565	−	0.0294848i	$-0.990613\pi$
$467$		−	1.27434i		−	0.0589696i	0.999565	−	0.0294848i	$-0.00938666\pi$
$468$	−3.80670	−	2.33047i	−0.175965	−	0.107726i
$469$	−16.2853			−0.751985
$470$	−1.00515	+	0.771279i	−0.0463642	+	0.0355765i
$471$	13.9488	+	1.09474i	0.642728	+	0.0504430i
$472$	4.12625	+	1.10562i	0.189926	+	0.0508905i
$473$	−4.45250	+	0.586183i	−0.204726	+	0.0269527i
$474$	−16.5751	+	14.1627i	−0.761318	+	0.650514i
$475$	52.4417	−	40.2400i	2.40619	−	1.84634i
$476$	−15.8109			−0.724689
$477$	8.14255	+	0.209673i	0.372822	+	0.00960027i
$478$	3.93922	+	1.63168i	0.180176	+	0.0746313i
$479$	4.01764	+	0.528932i	0.183571	+	0.0241675i	0.221751	−	0.975103i	$-0.428823\pi$
$479$	4.01764	+	0.528932i	0.183571	+	0.0241675i	−0.0381804	+	0.999271i	$0.512156\pi$
$480$	0.380110	+	7.22286i	0.0173496	+	0.329677i
$481$	−6.81779	+	8.88511i	−0.310864	+	0.405126i
$482$	−0.393818	−	0.682112i	−0.0179379	−	0.0310694i
$483$	−22.5567	−	15.4956i	−1.02637	−	0.705073i
$484$	10.1946	−	2.73163i	0.463391	−	0.124165i
$485$	0.851492	+	2.05568i	0.0386643	+	0.0933438i
$486$	−0.0169656	−	15.5884i	−0.000769577	−	0.707106i
$487$	−7.30878	−	7.30878i	−0.331193	−	0.331193i	0.521847	−	0.853039i	$-0.325243\pi$
$487$	−7.30878	−	7.30878i	−0.331193	−	0.331193i	−0.853039	+	0.521847i	$0.825243\pi$
$488$	−3.50789	−	2.02528i	−0.158795	−	0.0916803i
$489$	13.3078	+	20.4825i	0.601800	+	0.926249i
$490$	−41.0183	−	10.9908i	−1.85302	−	0.496515i
$491$	12.9223	+	22.3821i	0.583177	+	1.01009i	0.995100	+	0.0988735i	$0.0315239\pi$
$491$	12.9223	+	22.3821i	0.583177	+	1.01009i	−0.411923	+	0.911219i	$0.635143\pi$
$492$	3.26585	+	10.5988i	0.147236	+	0.477830i
$493$	2.43590	−	4.21910i	0.109707	−	0.190019i
$494$	5.59098	−	5.59098i	0.251550	−	0.251550i
$495$	5.76026	+	6.06476i	0.258905	+	0.272591i
$496$			8.70575i			0.390900i
$497$	53.7982	−	14.4152i	2.41318	−	0.646610i
$498$	7.40646	+	22.7779i	0.331892	+	1.02070i
$499$	23.5215	−	30.6538i	1.05297	−	1.37225i	0.128185	−	0.991750i	$-0.459085\pi$
$499$	23.5215	−	30.6538i	1.05297	−	1.37225i	0.924781	−	0.380501i	$-0.124248\pi$
$500$	−8.03904	+	30.0021i	−0.359517	+	1.34174i
$501$	21.0740	+	1.65395i	0.941518	+	0.0738929i
$502$	−12.1798	+	21.0961i	−0.543613	+	0.941566i
$503$	−1.73106	−	4.17914i	−0.0771840	−	0.186339i	0.880578	−	0.473902i	$-0.157155\pi$
$503$	−1.73106	−	4.17914i	−0.0771840	−	0.186339i	−0.957762	+	0.287563i	$0.907155\pi$
$504$	12.0860	−	2.90715i	0.538352	−	0.129495i
$505$	−9.64952	−	23.2960i	−0.429398	−	1.03666i
$506$	−2.01980	+	1.54985i	−0.0897913	+	0.0688993i
$507$	13.8866	+	12.4981i	0.616728	+	0.555061i
$508$	−5.19149	−	8.99192i	−0.230335	−	0.398952i
$509$	3.07424	+	23.3512i	0.136263	+	1.03502i	0.913794	+	0.406178i	$0.133139\pi$
$509$	3.07424	+	23.3512i	0.136263	+	1.03502i	−0.777531	+	0.628845i	$0.783528\pi$
$510$	27.1356	−	5.03539i	1.20158	−	0.222971i
$511$	−34.1264	−	44.4744i	−1.50966	−	1.96743i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	26.8559	+	6.42898i	1.18572	+	0.283846i
$514$	−8.94725	−	3.70607i	−0.394646	−	0.163468i
$515$	−27.5285	+	47.6808i	−1.21305	+	2.10107i
$516$	2.41974	−	11.3962i	0.106523	−	0.501690i
$517$	0.175431	−	0.101285i	0.00771546	−	0.00445452i
$518$	−4.07121	−	30.9239i	−0.178879	−	1.35872i
$519$	3.63582	−	4.03976i	0.159595	−	0.177326i
$520$	−0.810946	+	6.15975i	−0.0355623	+	0.270123i
$521$	14.2780	−	5.91414i	0.625531	−	0.259103i	−0.0473221	−	0.998880i	$-0.515069\pi$
$521$	14.2780	−	5.91414i	0.625531	−	0.259103i	0.672853	+	0.739776i	$0.265069\pi$
$522$	−1.08626	+	3.67302i	−0.0475442	+	0.160764i
$523$			36.6814i			1.60396i	0.597348	+	0.801982i	$0.296221\pi$
$523$			36.6814i			1.60396i	−0.597348	+	0.801982i	$0.703779\pi$
$524$	4.23311	+	15.7982i	0.184924	+	0.690147i
$525$	88.9926	+	6.98438i	3.88396	+	0.304823i
$526$	11.5143	+	8.83527i	0.502049	+	0.385236i
$527$	32.9349	−	4.33596i	1.43467	−	0.188877i
$528$	0.0904819	−	1.15289i	0.00393772	−	0.0501731i
$529$	4.23001	−	7.32659i	0.183913	−	0.318547i
$530$	−4.33882	−	10.4748i	−0.188466	−	0.454998i
$531$	1.34512	+	12.7446i	0.0583734	+	0.553070i
$532$			22.0208i			0.954721i
$533$	1.09717	+	9.46319i	0.0475237	+	0.409896i
$534$	26.1911	+	9.26835i	1.13340	+	0.401081i
$535$	−4.95991	+	18.5106i	−0.214436	+	0.800284i
$536$	−3.11808	−	2.39259i	−0.134681	−	0.103344i
$537$	6.16760	+	33.2370i	0.266152	+	1.43428i
$538$	6.22737	+	23.2409i	0.268481	+	1.00198i
$539$	6.27279	+	2.59827i	0.270188	+	0.111916i
$540$	−19.8169	+	8.83854i	−0.852781	+	0.380350i
$541$	−20.1613	+	20.1613i	−0.866800	+	0.866800i	−0.992117	−	0.125317i	$-0.960005\pi$
$541$	−20.1613	+	20.1613i	−0.866800	+	0.866800i	0.125317	+	0.992117i	$0.460005\pi$
$542$	13.6539	−	3.65856i	0.586486	−	0.157148i
$543$	−4.03068	−	21.7212i	−0.172973	−	0.932146i
$544$	−3.02725	−	2.32289i	−0.129792	−	0.0995930i
$545$	15.7944	−	20.5836i	0.676557	−	0.881707i
$546$	10.6630	−	0.561152i	0.456335	−	0.0240151i
$547$	−5.34017	−	6.95944i	−0.228329	−	0.297564i	0.665113	−	0.746743i	$-0.268383\pi$
$547$	−5.34017	−	6.95944i	−0.228329	−	0.297564i	−0.893442	+	0.449179i	$0.851717\pi$
$548$	4.72250	−	11.4011i	0.201735	−	0.487032i
$549$	1.89572	−	12.0029i	0.0809073	−	0.512272i
$550$	3.17799	−	7.67235i	0.135510	−	0.327150i
$551$	−5.87621	−	3.39263i	−0.250335	−	0.144531i
$552$	−2.04228	−	6.28085i	−0.0869253	−	0.267331i
$553$	13.4990	−	50.3788i	0.574034	−	2.14233i
$554$	3.88094	−	14.4839i	0.164885	−	0.615360i
$555$	16.8358	+	51.7769i	0.714640	+	2.19781i
$556$	13.4855	+	7.78588i	0.571914	+	0.330195i
$557$	−17.0667	+	41.2026i	−0.723139	+	1.74581i	−0.0589336	+	0.998262i	$0.518770\pi$
$557$	−17.0667	+	41.2026i	−0.723139	+	1.74581i	−0.664205	+	0.747550i	$0.731230\pi$
$558$	−24.3785	+	9.37020i	−1.03202	+	0.396672i
$559$	3.82966	−	9.24561i	0.161977	−	0.391047i
$560$	−10.5334	−	13.7275i	−0.445119	−	0.580091i
$561$	−4.40658	+	0.231901i	−0.186046	+	0.00979086i
$562$	12.7697	−	16.6418i	0.538657	−	0.701991i
$563$	−1.17265	−	0.899805i	−0.0494212	−	0.0379223i	0.583755	−	0.811930i	$-0.301583\pi$
$563$	−1.17265	−	0.899805i	−0.0494212	−	0.0379223i	−0.633177	+	0.774007i	$0.718249\pi$
$564$	0.0958780	+	0.516684i	0.00403719	+	0.0217563i
$565$	−16.9583	+	4.54396i	−0.713440	+	0.191166i
$566$	6.16351	−	6.16351i	0.259072	−	0.259072i
$567$	21.1492	+	30.7150i	0.888184	+	1.28991i
$568$	12.4184	+	5.14386i	0.521064	+	0.215832i
$569$	4.30737	+	16.0753i	0.180574	+	0.673913i	0.995535	+	0.0943959i	$0.0300920\pi$
$569$	4.30737	+	16.0753i	0.180574	+	0.673913i	−0.814960	+	0.579517i	$0.803241\pi$
$570$	−7.01311	−	37.7934i	−0.293747	−	1.58299i
$571$	−18.0990	−	13.8879i	−0.757421	−	0.581189i	0.156215	−	0.987723i	$-0.450071\pi$
$571$	−18.0990	−	13.8879i	−0.757421	−	0.581189i	−0.913636	+	0.406534i	$0.866737\pi$
$572$	0.257100	−	0.959510i	0.0107499	−	0.0401191i
$573$	−31.5780	−	11.1746i	−1.31919	−	0.466827i
$574$	−20.7966	−	16.4753i	−0.868035	−	0.687666i
$575$		−	47.4279i		−	1.97788i
$576$	2.74117	+	1.21902i	0.114215	+	0.0507924i
$577$	1.43876	+	3.47349i	0.0598966	+	0.144603i	0.950994	−	0.309208i	$-0.100064\pi$
$577$	1.43876	+	3.47349i	0.0598966	+	0.144603i	−0.891098	+	0.453811i	$0.850064\pi$
$578$	1.21999	−	2.11309i	0.0507449	−	0.0878928i
$579$	−0.588254	+	7.49534i	−0.0244470	+	0.311496i
$580$	5.28599	−	0.695914i	0.219489	−	0.0288962i
$581$	−45.4588	−	34.8818i	−1.88595	−	1.44714i
$582$	0.920067	+	0.0722093i	0.0381380	+	0.00299317i
$583$	0.469181	+	1.75101i	0.0194315	+	0.0725193i
$584$		−	13.5291i		−	0.559839i
$585$	−18.1218	+	4.35901i	−0.749245	+	0.180223i
$586$	21.6884	−	8.98362i	0.895939	−	0.371110i
$587$	3.58072	−	27.1983i	0.147792	−	1.12259i	−0.743361	−	0.668891i	$-0.766769\pi$
$587$	3.58072	−	27.1983i	0.147792	−	1.12259i	0.891153	−	0.453703i	$-0.149897\pi$
$588$	−11.7829	+	13.0919i	−0.485918	+	0.539902i
$589$	−6.03896	−	45.8705i	−0.248831	−	1.89006i
$590$	15.4487	−	8.91929i	0.636011	−	0.367201i
$591$	2.55920	−	12.0530i	0.105271	−	0.495794i
$592$	3.76375	−	6.51901i	0.154689	−	0.267930i
$593$	31.6269	+	13.1003i	1.29876	+	0.537964i	0.921584	−	0.388178i	$-0.126896\pi$
$593$	31.6269	+	13.1003i	1.29876	+	0.537964i	0.377175	+	0.926142i	$0.376896\pi$
$594$	3.32579	−	0.987508i	0.136459	−	0.0405179i
$595$	−46.6863	+	46.6863i	−1.91395	+	1.91395i
$596$	8.12021	+	10.5825i	0.332617	+	0.433474i
$597$	−32.0636	+	5.94986i	−1.31228	+	0.243512i
$598$	−0.740500	−	5.62465i	−0.0302813	−	0.230009i
$599$	−18.1525	−	31.4411i	−0.741692	−	1.28465i	−0.951724	−	0.306954i	$-0.900690\pi$
$599$	−18.1525	−	31.4411i	−0.741692	−	1.28465i	0.210032	−	0.977695i	$-0.432643\pi$
$600$	16.0130	+	14.4118i	0.653726	+	0.588360i
$601$	−19.3922	+	14.8802i	−0.791024	+	0.606974i	−0.923230	−	0.384248i	$-0.874461\pi$
$601$	−19.3922	+	14.8802i	−0.791024	+	0.606974i	0.132206	+	0.991222i	$0.457794\pi$
$602$	10.6657	+	25.7492i	0.434701	+	1.04946i
$603$	3.34384	−	11.3067i	0.136172	−	0.460444i
$604$	0.124624	+	0.300869i	0.00507089	+	0.0122422i
$605$	22.0366	−	38.1686i	0.895916	−	1.55177i
$606$	−10.4266	−	0.818311i	−0.423553	−	0.0332416i
$607$	−6.23346	+	23.2636i	−0.253008	+	0.944240i	0.716179	+	0.697916i	$0.245889\pi$
$607$	−6.23346	+	23.2636i	−0.253008	+	0.944240i	−0.969188	+	0.246323i	$0.920777\pi$
$608$	−3.23523	+	4.21623i	−0.131206	+	0.170991i
$609$	−2.83346	−	8.71404i	−0.114818	−	0.353111i
$610$	−16.3384	+	4.37785i	−0.661521	+	0.177254i
$611$			0.451399i			0.0182617i
$612$	3.24642	−	10.9773i	0.131229	−	0.443731i
$613$	13.6328	−	13.6328i	0.550625	−	0.550625i	−0.375996	−	0.926621i	$-0.622700\pi$
$613$	13.6328	−	13.6328i	0.550625	−	0.550625i	0.926621	+	0.375996i	$0.122700\pi$
$614$	8.00320	−	13.8619i	0.322983	−	0.559423i
$615$	40.9395	+	21.6527i	1.65084	+	0.873121i
$616$	1.38326	+	2.39588i	0.0557333	+	0.0965329i
$617$	18.2610	+	4.89301i	0.735159	+	0.196985i	0.606925	−	0.794759i	$-0.292403\pi$
$617$	18.2610	+	4.89301i	0.735159	+	0.196985i	0.128233	+	0.991744i	$0.459069\pi$
$618$	12.4417	+	19.1494i	0.500478	+	0.770301i
$619$	−16.6946	−	9.63863i	−0.671013	−	0.387409i	0.125448	−	0.992100i	$-0.459963\pi$
$619$	−16.6946	−	9.63863i	−0.671013	−	0.387409i	−0.796460	+	0.604691i	$0.793297\pi$
$620$	25.7063	+	25.7063i	1.03239	+	1.03239i
$621$	15.3899	−	12.4792i	0.617577	−	0.500772i
$622$	0.862717	+	2.08278i	0.0345918	+	0.0835120i
$623$	−64.1995	+	17.2022i	−2.57210	+	0.689192i
$624$	2.12405	+	1.45914i	0.0850300	+	0.0584123i
$625$	33.7574	+	58.4696i	1.35030	+	2.33878i
$626$	−9.35525	+	12.1920i	−0.373911	+	0.487291i
$627$	0.322983	+	6.13732i	0.0128987	+	0.245101i
$628$	−8.00901	−	1.05441i	−0.319594	−	0.0420754i
$629$	−26.5367	−	10.9919i	−1.05809	−	0.438275i
$630$	27.1032	−	44.2717i	1.07982	−	1.76383i
$631$	−41.4339			−1.64946			−0.824728	−	0.565529i	$-0.808672\pi$
$631$	−41.4339			−1.64946			−0.824728	+	0.565529i	$0.808672\pi$
$632$	9.98611	−	7.66261i	0.397226	−	0.304802i
$633$	−29.0297	+	24.8046i	−1.15383	+	0.985895i
$634$	−12.6719	+	1.66829i	−0.503267	+	0.0662564i
$635$	−41.8808	−	11.2219i	−1.66199	−	0.445328i
$636$	−4.68825	−	0.367946i	−0.185901	−	0.0145900i
$637$	−12.0032	+	9.21037i	−0.475584	+	0.364928i
$638$	−0.852451			−0.0337489
$639$	−1.03803	+	40.3113i	−0.0410638	+	1.59469i
$640$		−	4.17589i		−	0.165067i
$641$	16.7269	−	12.8350i	0.660675	−	0.506954i	−0.223143	−	0.974786i	$-0.571632\pi$
$641$	16.7269	−	12.8350i	0.660675	−	0.506954i	0.883817	+	0.467832i	$0.154965\pi$
$642$	5.90810	+	5.31735i	0.233174	+	0.209859i
$643$	15.8015	+	12.1249i	0.623149	+	0.478159i	0.871424	−	0.490530i	$-0.163197\pi$
$643$	15.8015	+	12.1249i	0.623149	+	0.478159i	−0.248275	+	0.968690i	$0.579864\pi$
$644$	12.5350	+	9.61842i	0.493947	+	0.379019i
$645$	−26.5057	−	40.7957i	−1.04366	−	1.60633i
$646$	17.5618	+	10.1393i	0.690961	+	0.398926i
$647$	7.76294	−	7.76294i	0.305193	−	0.305193i	−0.537849	−	0.843041i	$-0.680763\pi$
$647$	7.76294	−	7.76294i	0.305193	−	0.305193i	0.843041	+	0.537849i	$0.180763\pi$
$648$	−0.463198	+	8.98807i	−0.0181961	+	0.353085i
$649$	−2.63504	+	1.09147i	−0.103434	+	0.0428439i
$650$	11.2654	+	14.6813i	0.441863	+	0.575848i
$651$	35.3779	−	51.4992i	1.38657	−	2.01841i
$652$	−7.05118	−	12.2130i	−0.276145	−	0.478298i
$653$	17.3715	−	22.6390i	0.679801	−	0.885933i	−0.318271	−	0.948000i	$-0.603102\pi$
$653$	17.3715	−	22.6390i	0.679801	−	0.885933i	0.998072	+	0.0620662i	$0.0197690\pi$
$654$	−4.63500	−	9.71204i	−0.181243	−	0.379771i
$655$	59.1484	+	34.1494i	2.31112	+	1.33433i
$656$	−1.56135	−	6.20985i	−0.0609604	−	0.242454i
$657$	37.8852	−	14.5617i	1.47804	−	0.568106i
$658$	−0.888946	−	0.888946i	−0.0346547	−	0.0346547i
$659$	3.25167	−	24.6988i	0.126667	−	0.962131i	−0.803580	−	0.595197i	$-0.797074\pi$
$659$	3.25167	−	24.6988i	0.126667	−	0.962131i	0.930247	−	0.366934i	$-0.119592\pi$
$660$	−3.13708	−	3.67143i	−0.122111	−	0.142910i
$661$	11.1235	+	2.98052i	0.432653	+	0.115929i	0.468571	−	0.883426i	$-0.344769\pi$
$661$	11.1235	+	2.98052i	0.432653	+	0.115929i	−0.0359185	+	0.999355i	$0.511436\pi$
$662$	2.28072	+	17.3238i	0.0886426	+	0.673308i
$663$	4.46219	−	8.76226i	0.173297	−	0.340298i
$664$	−3.57910	−	13.3574i	−0.138896	−	0.518366i
$665$	65.0229	+	65.0229i	2.52148	+	2.52148i
$666$	22.3060	+	3.52297i	0.864341	+	0.136512i
$667$	−4.49786	+	1.86307i	−0.174158	+	0.0721386i
$668$	−12.1001	−	1.59301i	−0.468167	−	0.0616353i
$669$	1.98587	+	37.7354i	0.0767780	+	1.45894i
$670$	−16.2719	+	2.14224i	−0.628639	+	0.0827619i
$671$	2.68130	−	0.353000i	0.103510	−	0.0136274i
$672$	−7.05641	+	1.30942i	−0.272207	+	0.0505118i
$673$	−22.9713	−	29.9368i	−0.885480	−	1.15398i	−0.987251	−	0.159173i	$-0.949117\pi$
$673$	−22.9713	−	29.9368i	−0.885480	−	1.15398i	0.101770	−	0.994808i	$-0.467549\pi$
$674$		−	34.8234i		−	1.34135i
$675$	−23.1219	+	60.3524i	−0.889963	+	2.32297i
$676$	−7.62717	−	7.62717i	−0.293353	−	0.293353i
$677$	−25.1968	+	6.75146i	−0.968391	+	0.259480i	−0.708148	−	0.706064i	$-0.750469\pi$
$677$	−25.1968	+	6.75146i	−0.968391	+	0.259480i	−0.260243	+	0.965543i	$0.583803\pi$
$678$	−1.51246	+	7.12318i	−0.0580856	+	0.273564i
$679$	−1.91204	+	1.10392i	−0.0733774	+	0.0423645i
$680$	−15.7979	+	2.07983i	−0.605821	+	0.0797578i
$681$	11.4644	+	4.05695i	0.439317	+	0.155463i
$682$	−3.53846	−	4.61141i	−0.135495	−	0.176580i
$683$	−12.9766	+	31.3283i	−0.496536	+	1.19874i	0.454802	+	0.890593i	$0.349710\pi$
$683$	−12.9766	+	31.3283i	−0.496536	+	1.19874i	−0.951338	+	0.308150i	$0.900290\pi$
$684$	−15.2888	−	4.52150i	−0.584580	−	0.172884i
$685$	−19.7206	−	47.6098i	−0.753487	−	1.81908i
$686$	1.71402	−	13.0193i	0.0654415	−	0.497078i
$687$	−0.382385	−	0.447518i	−0.0145889	−	0.0170739i
$688$	−1.74089	+	6.49708i	−0.0663708	+	0.247699i
$689$	−3.90187	−	1.04550i	−0.148649	−	0.0398304i
$690$	−24.5765	−	12.5156i	−0.935613	−	0.476462i
$691$	−36.0511	+	27.6630i	−1.37145	+	1.05235i	−0.379568	+	0.925164i	$0.623927\pi$
$691$	−36.0511	+	27.6630i	−1.37145	+	1.05235i	−0.991879	+	0.127185i	$0.959406\pi$
$692$	−2.21882	+	2.21882i	−0.0843467	+	0.0843467i
$693$	−5.22029	+	6.45226i	−0.198302	+	0.245101i
$694$	24.0357	−	9.95590i	0.912381	−	0.377921i
$695$	62.8102	−	16.8300i	2.38253	−	0.638396i
$696$	0.737730	−	2.08473i	0.0279636	−	0.0790214i
$697$	−22.7149	+	8.99961i	−0.860389	+	0.340885i
$698$	−10.6795	+	6.16583i	−0.404226	+	0.233380i
$699$	−13.4519	−	9.24090i	−0.508796	−	0.349523i
$700$	−51.0970	−	6.72705i	−1.93128	−	0.254258i
$701$	−15.9177			−0.601202			−0.300601	−	0.953750i	$-0.597187\pi$
$701$	−15.9177			−0.601202			−0.300601	+	0.953750i	$0.597187\pi$
$702$	−1.79982	+	7.51842i	−0.0679299	+	0.283765i
$703$	−15.3091	+	36.9594i	−0.577392	+	1.39395i
$704$	−0.0871482	+	0.661956i	−0.00328452	+	0.0249484i
$705$	1.80877	+	1.24256i	0.0681223	+	0.0467973i
$706$	7.64107	+	2.04742i	0.287575	+	0.0770556i
$707$	21.6682	−	12.5101i	0.814915	−	0.470492i
$708$	−0.388841	−	7.38876i	−0.0146135	−	0.277687i
$709$	−4.79866	+	36.4495i	−0.180218	+	1.36889i	0.627177	+	0.778877i	$0.284210\pi$
$709$	−4.79866	+	36.4495i	−0.180218	+	1.36889i	−0.807394	+	0.590012i	$0.799123\pi$
$710$	51.8578	−	21.4802i	1.94619	−	0.806137i
$711$	32.2057	+	19.7164i	1.20781	+	0.739423i
$712$	−14.8193	−	6.13837i	−0.555378	−	0.230045i
$713$	−28.7488	−	16.5981i	−1.07665	−	0.621604i
$714$	8.46816	+	26.0430i	0.316913	+	0.974636i
$715$	−2.07408	−	3.59241i	−0.0775661	−	0.134348i
$716$	−2.54748	−	19.3500i	−0.0952037	−	0.723144i
$717$	0.577825	−	7.36245i	0.0215793	−	0.274956i
$718$	−0.361843	−	1.35042i	−0.0135038	−	0.0503970i
$719$	−14.4781	+	34.9532i	−0.539942	+	1.30354i	0.384821	+	0.922991i	$0.374263\pi$
$719$	−14.4781	+	34.9532i	−0.539942	+	1.30354i	−0.924763	+	0.380544i	$0.875737\pi$
$720$	11.6936	−	4.49461i	0.435796	−	0.167504i
$721$	−50.4724	−	20.9063i	−1.87969	−	0.778593i
$722$	4.62167	−	8.00497i	0.172001	−	0.297914i
$723$	−0.912624	+	1.01402i	−0.0339408	+	0.0377116i
$724$	1.66484	+	12.6457i	0.0618733	+	0.469974i
$725$	9.66737	−	12.5988i	0.359037	−	0.467906i
$726$	−9.95958	−	15.3291i	−0.369635	−	0.568916i
$727$	41.3531	+	5.44423i	1.53370	+	0.201915i	0.849582	−	0.527456i	$-0.176854\pi$
$727$	41.3531	+	5.44423i	1.53370	+	0.201915i	0.684118	+	0.729371i	$0.260187\pi$
$728$	−6.16481			−0.228483
$729$	−25.6676	+	8.37699i	−0.950652	+	0.310259i
$730$	−39.9488	−	39.9488i	−1.47857	−	1.47857i
$731$	25.4463	+	3.35007i	0.941165	+	0.123907i
$732$	−1.45717	+	6.86279i	−0.0538586	+	0.253656i
$733$	8.19585	−	30.5873i	0.302721	−	1.12977i	−0.632169	−	0.774830i	$-0.717835\pi$
$733$	8.19585	−	30.5873i	0.302721	−	1.12977i	0.934890	−	0.354938i	$-0.115498\pi$
$734$	−6.76260	+	3.90439i	−0.249612	+	0.144114i
$735$	3.86540	+	73.4503i	0.142577	+	2.70926i
$736$	0.986911	+	3.68320i	0.0363780	+	0.135765i
$737$	2.62411			0.0966602
$738$	15.7088	−	11.0560i	0.578247	−	0.406977i
$739$	2.40666			0.0885305			0.0442653	−	0.999020i	$-0.485905\pi$
$739$	2.40666			0.0885305			0.0442653	+	0.999020i	$0.485905\pi$
$740$	−8.13572	−	30.3629i	−0.299075	−	1.11616i
$741$	−12.2037	−	6.21477i	−0.448316	−	0.228305i
$742$	9.74290	−	5.62507i	0.357673	−	0.206503i
$743$	0.00102684	−	0.00383221i	3.76710e−5	−	0.000140590i	−0.965907	−	0.258889i	$-0.916644\pi$
$743$	0.00102684	−	0.00383221i	3.76710e−5	−	0.000140590i	0.965945	+	0.258749i	$0.0833102\pi$
$744$	14.3398	−	4.66273i	0.525722	−	0.170944i
$745$	55.2252	+	7.27054i	2.02330	+	0.266372i
$746$	−16.0410	−	16.0410i	−0.587301	−	0.587301i
$747$	33.5520	−	24.3993i	1.22760	−	0.892723i
$748$	2.54766			0.0931517
$749$	−18.8526	−	2.48199i	−0.688859	−	0.0906901i
$750$	53.7240	−	2.82728i	1.96172	−	0.103238i
$751$	13.6424	−	17.7791i	0.497819	−	0.648770i	−0.475096	−	0.879934i	$-0.657587\pi$
$751$	13.6424	−	17.7791i	0.497819	−	0.648770i	0.972915	+	0.231164i	$0.0742533\pi$
$752$	−0.0396017	−	0.300804i	−0.00144412	−	0.0109692i
$753$	41.2721	+	8.76328i	1.50404	+	0.319352i
$754$	0.949782	−	1.64507i	0.0345890	−	0.0599099i
$755$	1.25640	+	0.520417i	0.0457250	+	0.0189399i
$756$	−11.2617	−	18.3505i	−0.409584	−	0.667402i
$757$	−11.0799	+	26.7492i	−0.402706	+	0.972217i	0.584301	+	0.811537i	$0.301369\pi$
$757$	−11.0799	+	26.7492i	−0.402706	+	0.972217i	−0.987007	+	0.160680i	$0.948631\pi$
$758$	1.99593	+	7.44892i	0.0724955	+	0.270557i
$759$	3.63464	+	2.49686i	0.131929	+	0.0906302i
$760$	2.89671	+	22.0027i	0.105075	+	0.798121i
$761$	−2.09053	−	3.62090i	−0.0757816	−	0.131258i	0.825644	−	0.564191i	$-0.190812\pi$
$761$	−2.09053	−	3.62090i	−0.0757816	−	0.131258i	−0.901426	+	0.432933i	$0.857479\pi$
$762$	−12.0306	+	13.3672i	−0.435824	+	0.484243i
$763$	22.2952	+	12.8722i	0.807141	+	0.466003i
$764$	17.8673	+	7.40089i	0.646418	+	0.267755i
$765$	−22.8277	−	41.9998i	−0.825337	−	1.51851i
$766$	4.06496	−	1.68376i	0.146873	−	0.0608368i
$767$	0.829572	−	6.30123i	0.0299541	−	0.227524i
$768$	−1.54344	−	0.785999i	−0.0556941	−	0.0283623i
$769$	42.8217	−	24.7231i	1.54419	−	0.891538i	0.545621	−	0.838032i	$-0.316294\pi$
$769$	42.8217	−	24.7231i	1.54419	−	0.891538i	0.998568	−	0.0535054i	$-0.0170394\pi$
$770$	11.1591	+	2.99006i	0.402145	+	0.107754i
$771$	−1.31243	+	16.7225i	−0.0472659	+	0.602247i
$772$	0.566581	−	4.30361i	0.0203917	−	0.154890i
$773$	−5.01452	+	12.1061i	−0.180360	+	0.435427i	−0.988041	−	0.154193i	$-0.950722\pi$
$773$	−5.01452	+	12.1061i	−0.180360	+	0.435427i	0.807681	+	0.589620i	$0.200722\pi$
$774$	−20.0674	+	2.11800i	−0.721307	+	0.0761299i
$775$	108.283			3.88963
$776$	−0.528276	−	0.0695488i	−0.0189640	−	0.00249666i
$777$	−48.7561	+	23.2685i	−1.74912	+	0.834753i
$778$	−16.6798	+	9.63008i	−0.597999	+	0.345255i
$779$	12.5343	+	31.6365i	0.449089	+	1.13349i
$780$	10.5804	−	1.96335i	0.378840	−	0.0702992i
$781$	−8.66870	+	2.32277i	−0.310191	+	0.0831153i
$782$	13.4424	−	5.56804i	0.480701	−	0.199113i
$783$	6.63184	−	0.177995i	0.237003	−	0.00636101i
$784$	7.19068	−	7.19068i	0.256810	−	0.256810i
$785$	−26.7625	+	20.5356i	−0.955193	+	0.732946i
$786$	23.7550	−	15.4340i	0.847312	−	0.550513i
$787$	35.9789	+	9.64051i	1.28251	+	0.343647i	0.834810	−	0.550538i	$-0.185577\pi$
$787$	35.9789	+	9.64051i	1.28251	+	0.343647i	0.447698	+	0.894185i	$0.352244\pi$
$788$	−1.84122	+	6.87153i	−0.0655907	+	0.244788i
$789$	8.38613	−	23.6981i	0.298554	−	0.843674i
$790$	6.86083	−	52.1131i	0.244097	−	1.85410i
$791$	−6.66658	−	16.0946i	−0.237036	−	0.572256i
$792$	−1.94746	+	0.468440i	−0.0691999	+	0.0166453i
$793$	−2.30622	+	5.56771i	−0.0818963	+	0.197715i
$794$	−0.563149	−	0.733910i	−0.0199854	−	0.0260455i
$795$	−14.9299	+	12.7570i	−0.529510	+	0.452444i
$796$	18.6669	−	2.45754i	0.661630	−	0.0871053i
$797$	35.5821	−	20.5434i	1.26038	−	0.727683i	0.287235	−	0.957860i	$-0.407264\pi$
$797$	35.5821	−	20.5434i	1.26038	−	0.727683i	0.973149	+	0.230177i	$0.0739304\pi$
$798$	36.2718	−	11.7941i	1.28401	−	0.417508i
$799$	−1.11825	+	0.299635i	−0.0395610	+	0.0106003i
$800$	−8.79503	−	8.79503i	−0.310951	−	0.310951i
$801$	1.23872	−	48.1051i	0.0437680	−	1.69971i
$802$			8.60139i			0.303726i
$803$	5.49892	+	7.16633i	0.194053	+	0.252894i
$804$	−2.27096	+	6.41744i	−0.0800906	+	0.226326i
$805$	65.4145	−	8.61198i	2.30556	−	0.303532i
$806$	12.8416	−	1.69063i	0.452327	−	0.0595500i
$807$	34.9461	−	22.7051i	1.23016	−	0.799257i
$808$	5.98668	+	0.788161i	0.210610	+	0.0277274i
$809$	43.6373	−	18.0752i	1.53421	−	0.635489i	0.553830	−	0.832630i	$-0.313166\pi$
$809$	43.6373	−	18.0752i	1.53421	−	0.635489i	0.980375	+	0.197141i	$0.0631657\pi$
$810$	25.1722	+	27.9077i	0.884463	+	0.980577i
$811$	4.37703	+	4.37703i	0.153698	+	0.153698i	0.779767	−	0.626069i	$-0.215337\pi$
$811$	4.37703	+	4.37703i	0.153698	+	0.153698i	−0.626069	+	0.779767i	$0.715337\pi$
$812$	1.36924	+	5.11007i	0.0480509	+	0.179328i
$813$	−13.3392	−	20.5307i	−0.467825	−	0.720044i
$814$	0.656008	+	4.98288i	0.0229931	+	0.174650i
$815$	−56.8832	−	15.2418i	−1.99253	−	0.533898i
$816$	−2.20480	+	6.23048i	−0.0771835	+	0.218110i
$817$	4.66585	−	35.4406i	0.163237	−	1.23991i
$818$	−17.9551	−	17.9551i	−0.627785	−	0.627785i
$819$	−6.63533	−	17.2632i	−0.231857	−	0.603223i
$820$	−22.9468	−	13.7261i	−0.801336	−	0.479336i
$821$	−0.210061	−	0.121279i	−0.00733117	−	0.00423265i	0.496330	−	0.868134i	$-0.334681\pi$
$821$	−0.210061	−	0.121279i	−0.00733117	−	0.00423265i	−0.503661	+	0.863901i	$0.668014\pi$
$822$	−21.3088	−	1.67237i	−0.743230	−	0.0583307i
$823$	7.99810	−	10.4233i	0.278796	−	0.363334i	−0.632876	−	0.774254i	$-0.718126\pi$
$823$	7.99810	−	10.4233i	0.278796	−	0.363334i	0.911672	+	0.410919i	$0.134792\pi$
$824$	−6.59225	−	11.4181i	−0.229652	−	0.397769i
$825$	−14.3397	−	1.12542i	−0.499244	−	0.0391820i
$826$	10.7754	+	14.0428i	0.374924	+	0.488610i
$827$	−8.21788	+	3.40396i	−0.285764	+	0.118367i	−0.520961	−	0.853580i	$-0.674426\pi$
$827$	−8.21788	+	3.40396i	−0.285764	+	0.118367i	0.235197	+	0.971948i	$0.424426\pi$
$828$	−9.25174	+	6.72794i	−0.321520	+	0.233812i
$829$	7.40688	−	7.40688i	0.257252	−	0.257252i	−0.566684	−	0.823935i	$-0.691774\pi$
$829$	7.40688	−	7.40688i	0.257252	−	0.257252i	0.823935	+	0.566684i	$0.191774\pi$
$830$	−50.0100	−	28.8733i	−1.73587	−	1.00221i
$831$	−25.9359	+	1.36490i	−0.899705	+	0.0473479i
$832$	−1.18035	−	0.905717i	−0.0409214	−	0.0314001i
$833$	−30.7845	−	23.6218i	−1.06662	−	0.818447i
$834$	5.60186	−	26.3829i	0.193977	−	0.913566i
$835$	−40.4330	+	31.0253i	−1.39924	+	1.07368i
$836$		−	3.54829i		−	0.122720i
$837$	28.4912	+	35.1367i	0.984798	+	1.21450i
$838$	−10.4073			−0.359514
$839$	39.2257	−	30.0989i	1.35422	−	1.03913i	0.359867	−	0.933004i	$-0.382822\pi$
$839$	39.2257	−	30.0989i	1.35422	−	1.03913i	0.994353	−	0.106126i	$-0.0338446\pi$
$840$	−16.9697	+	24.7026i	−0.585511	+	0.852321i
$841$	26.4373	+	7.08385i	0.911630	+	0.244271i
$842$	24.4211	−	3.21509i	0.841606	−	0.110799i
$843$	−34.2510	−	12.1205i	−1.17967	−	0.417454i
$844$	17.4897	−	13.4204i	0.602022	−	0.461948i
$845$	−45.0430			−1.54953
$846$	0.799710	−	0.434658i	0.0274946	−	0.0149439i
$847$	40.4032	+	16.7356i	1.38827	+	0.575041i
$848$	2.69186	+	0.354390i	0.0924387	+	0.0121698i
$849$	−13.4534	−	6.85117i	−0.461720	−	0.235132i
$850$	−28.8922	+	37.6530i	−0.990994	+	1.29149i
$851$	14.3517	+	24.8579i	0.491970	+	0.852116i
$852$	1.82159	−	23.2101i	0.0624067	−	0.795165i
$853$	37.1049	−	9.94222i	1.27045	−	0.340415i	0.440244	−	0.897878i	$-0.354892\pi$
$853$	37.1049	−	9.94222i	1.27045	−	0.340415i	0.830202	+	0.557463i	$0.188225\pi$
$854$	−6.42288	−	15.5062i	−0.219786	−	0.530612i
$855$	−58.4957	+	31.7936i	−2.00051	+	1.08732i
$856$	−3.24499	−	3.24499i	−0.110912	−	0.110912i
$857$	23.5931	+	13.6215i	0.805926	+	0.465302i	0.845539	−	0.533913i	$-0.179279\pi$
$857$	23.5931	+	13.6215i	0.805926	+	0.465302i	−0.0396130	+	0.999215i	$0.512613\pi$
$858$	−1.71817	+	0.0904205i	−0.0586573	+	0.00308690i
$859$	0.149972	+	0.0401849i	0.00511698	+	0.00137109i	0.261377	−	0.965237i	$-0.415824\pi$
$859$	0.149972	+	0.0401849i	0.00511698	+	0.00137109i	−0.256260	+	0.966608i	$0.582490\pi$
$860$	14.0441	+	24.3251i	0.478900	+	0.829478i
$861$	−15.9990	+	43.0794i	−0.545244	+	1.46814i
$862$	−7.47852	+	12.9532i	−0.254719	+	0.441187i
$863$	−15.6569	+	15.6569i	−0.532968	+	0.532968i	−0.921455	−	0.388486i	$-0.872998\pi$
$863$	−15.6569	+	15.6569i	−0.532968	+	0.532968i	0.388486	+	0.921455i	$0.372998\pi$
$864$	0.539771	−	5.16804i	0.0183634	−	0.175820i
$865$			13.1034i			0.445530i
$866$	−23.6134	+	6.32719i	−0.802416	+	0.215007i
$867$	−4.13401	−	0.877771i	−0.140398	−	0.0298107i
$868$	−21.9598	+	28.6185i	−0.745364	+	0.971377i
$869$	−2.17514	+	8.11772i	−0.0737865	+	0.275375i
$870$	−3.97741	−	8.33415i	−0.134847	−	0.282554i
$871$	−2.92372	+	5.06404i	−0.0990666	+	0.171588i
$872$	2.37764	+	5.74013i	0.0805171	+	0.194385i
$873$	−0.373840	−	1.55417i	−0.0126526	−	0.0526008i
$874$	−7.75496	−	18.7221i	−0.262315	−	0.633286i
$875$	−102.106	+	78.3483i	−3.45180	+	2.64866i
$876$	−22.2846	+	7.24608i	−0.752928	+	0.244822i
$877$	3.23885	+	5.60984i	0.109368	+	0.189431i	0.915514	−	0.402285i	$-0.131784\pi$
$877$	3.23885	+	5.60984i	0.109368	+	0.189431i	−0.806146	+	0.591716i	$0.798451\pi$
$878$	−1.68602	−	12.8066i	−0.0569003	−	0.432201i
$879$	−26.4136	−	30.9127i	−0.890908	−	1.04266i
$880$	1.69729	+	2.21195i	0.0572157	+	0.0745650i
$881$	32.9627	−	32.9627i	1.11054	−	1.11054i	0.117463	−	0.993077i	$-0.462524\pi$
$881$	32.9627	−	32.9627i	1.11054	−	1.11054i	0.993077	−	0.117463i	$-0.0374762\pi$
$882$	27.8754	+	12.3964i	0.938612	+	0.417407i
$883$	37.8528	+	15.6791i	1.27385	+	0.527645i	0.914132	−	0.405416i	$-0.132873\pi$
$883$	37.8528	+	15.6791i	1.27385	+	0.527645i	0.359716	+	0.933062i	$0.382873\pi$
$884$	−2.83855	+	4.91651i	−0.0954707	+	0.165360i
$885$	−22.9657	−	20.6693i	−0.771983	−	0.694793i
$886$	−6.61395	+	3.81856i	−0.222200	+	0.128287i
$887$	7.47557	+	56.7826i	0.251005	+	1.90657i	0.397914	+	0.917423i	$0.369734\pi$
$887$	7.47557	+	56.7826i	0.251005	+	1.90657i	−0.146909	+	0.989150i	$0.546932\pi$
$888$	−12.7537	−	2.70798i	−0.427986	−	0.0908739i
$889$	5.61557	−	42.6545i	0.188340	−	1.43059i
$890$	−61.8839	+	25.6332i	−2.07435	+	0.859225i
$891$	−3.40785	−	4.94922i	−0.114167	−	0.165805i
$892$		−	21.8167i		−	0.730477i
$893$	0.417321	+	1.55746i	0.0139651	+	0.0521185i
$894$	13.0819	−	19.0432i	0.437524	−	0.636899i
$895$	−64.6589	−	49.6145i	−2.16131	−	1.65843i
$896$	4.10812	−	0.540844i	0.137243	−	0.0180683i
$897$	−8.86811	+	4.23224i	−0.296098	+	0.141310i
$898$	−18.8420	+	32.6353i	−0.628766	+	1.08906i
$899$	−4.25358	−	10.2691i	−0.141865	−	0.342492i
$900$	15.1622	−	34.0948i	0.505406	−	1.13649i
$901$		−	10.3601i		−	0.345145i
$902$	3.35104	+	2.65472i	0.111577	+	0.0883927i
$903$	36.7007	−	31.3592i	1.22132	−	1.04357i
$904$	1.08814	−	4.06100i	0.0361910	−	0.135067i
$905$	42.2562	+	32.4243i	1.40464	+	1.07782i
$906$	0.428833	−	0.366419i	0.0142470	−	0.0121735i
$907$	−9.39292	−	35.0548i	−0.311887	−	1.16398i	−0.926853	−	0.375424i	$-0.877497\pi$
$907$	−9.39292	−	35.0548i	−0.311887	−	1.16398i	0.614967	−	0.788553i	$-0.289169\pi$
$908$	−6.48674	−	2.68690i	−0.215270	−	0.0891677i
$909$	4.23653	+	17.6126i	0.140517	+	0.584174i
$910$	−18.2034	+	18.2034i	−0.603438	+	0.603438i
$911$	−14.1992	+	3.80468i	−0.470442	+	0.126055i	−0.486249	−	0.873821i	$-0.661635\pi$
$911$	−14.1992	+	3.80468i	−0.470442	+	0.126055i	0.0158066	+	0.999875i	$0.494968\pi$
$912$	8.67758	+	3.07077i	0.287343	+	0.101683i
$913$	7.32495	+	5.62063i	0.242420	+	0.186016i
$914$	9.19411	−	11.9820i	0.304114	−	0.396329i
$915$	15.9617	+	24.5672i	0.527678	+	0.812166i
$916$	0.206887	+	0.269620i	0.00683573	+	0.00890849i
$917$	−25.9345	+	62.6114i	−0.856433	+	2.06761i
$918$	−19.8201	+	0.531960i	−0.654162	+	0.0175573i
$919$	8.26339	−	19.9496i	0.272584	−	0.658076i	−0.727008	−	0.686629i	$-0.759090\pi$
$919$	8.26339	−	19.9496i	0.272584	−	0.658076i	0.999592	+	0.0285525i	$0.00908978\pi$
$920$	13.7899	+	7.96161i	0.454640	+	0.262487i
$921$	−27.1193	−	5.75822i	−0.893612	−	0.189740i
$922$	−0.208223	+	0.777100i	−0.00685747	+	0.0255924i
$923$	5.17596	−	19.3170i	0.170369	−	0.635825i
$924$	3.20554	−	3.56167i	0.105455	−	0.117171i
$925$	−81.0838	−	46.8137i	−2.66602	−	1.53923i
$926$	−10.8465	+	26.1857i	−0.356437	+	0.860514i
$927$	24.8785	−	30.7497i	0.817116	−	1.00995i
$928$	−0.488594	+	1.17957i	−0.0160389	+	0.0387213i
$929$	−5.06965	−	6.60690i	−0.166330	−	0.216765i	0.702750	−	0.711437i	$-0.251955\pi$
$929$	−5.06965	−	6.60690i	−0.166330	−	0.216765i	−0.869080	+	0.494671i	$0.835288\pi$
$930$	28.5744	−	56.1106i	0.936992	−	1.83994i
$931$	−32.8995	+	42.8755i	−1.07824	+	1.40519i
$932$	7.47532	+	5.73602i	0.244862	+	0.187889i
$933$	2.96862	−	2.53655i	0.0971881	−	0.0830431i
$934$	1.23092	−	0.329824i	0.0402770	−	0.0107922i
$935$	7.52273	−	7.52273i	0.246020	−	0.246020i
$936$	1.26581	−	4.28015i	0.0413744	−	0.139901i
$937$	26.0309	+	10.7824i	0.850393	+	0.352244i	0.764943	−	0.644098i	$-0.222767\pi$
$937$	26.0309	+	10.7824i	0.850393	+	0.352244i	0.0854503	+	0.996342i	$0.472767\pi$
$938$	−4.21494	−	15.7304i	−0.137623	−	0.513615i
$939$	25.0928	+	8.87968i	0.818873	+	0.289777i
$940$	−1.00515	−	0.771279i	−0.0327844	−	0.0251564i
$941$	−3.06180	+	11.4268i	−0.0998120	+	0.372503i	−0.997705	−	0.0677103i	$-0.978431\pi$
$941$	−3.06180	+	11.4268i	−0.0998120	+	0.372503i	0.897893	+	0.440214i	$0.145097\pi$
$942$	2.55278	+	13.7569i	0.0831742	+	0.448223i
$943$	23.4834	+	6.68349i	0.764725	+	0.217644i
$944$			4.27180i			0.139035i
$945$	−87.4389	−	20.9318i	−2.84439	−	0.680913i
$946$	−1.71860	−	4.14907i	−0.0558765	−	0.134898i
$947$	0.986474	−	1.70862i	0.0320561	−	0.0555228i	−0.849552	−	0.527504i	$-0.823128\pi$
$947$	0.986474	−	1.70862i	0.0320561	−	0.0555228i	0.881608	+	0.471982i	$0.156461\pi$
$948$	−17.9700	−	12.3447i	−0.583640	−	0.400938i
$949$	−19.9564	+	2.62732i	−0.647814	+	0.0852863i
$950$	52.4417	+	40.2400i	1.70143	+	1.30556i
$951$	9.53494	+	19.9792i	0.309192	+	0.647871i
$952$	−4.09215	−	15.2721i	−0.132627	−	0.494972i
$953$			9.93606i			0.321861i	0.986966	+	0.160930i	$0.0514494\pi$
$953$			9.93606i			0.321861i	−0.986966	+	0.160930i	$0.948551\pi$
$954$	1.90492	+	7.91937i	0.0616740	+	0.256399i
$955$	74.6120	−	30.9053i	2.41439	−	1.00007i
$956$	−0.556535	+	4.22731i	−0.0179996	+	0.136721i
$957$	0.456566	+	1.40412i	0.0147587	+	0.0453889i
$958$	0.528932	+	4.01764i	0.0170890	+	0.129804i
$959$	44.2830	−	25.5668i	1.42997	−	0.825596i
$960$	−6.87836	+	2.23657i	−0.221998	+	0.0721850i
$961$	22.3951	−	38.7894i	0.722422	−	1.25127i
$962$	−10.3469	−	4.28584i	−0.333599	−	0.138181i
$963$	5.59420	−	12.5795i	0.180271	−	0.405369i
$964$	0.556942	−	0.556942i	0.0179379	−	0.0179379i
$965$	−11.0347	−	14.3807i	−0.355219	−	0.462931i
$966$	9.12946	−	25.7987i	0.293736	−	0.830058i
$967$	−5.06165	−	38.4470i	−0.162772	−	1.23637i	−0.856504	−	0.516140i	$-0.827368\pi$
$967$	−5.06165	−	38.4470i	−0.162772	−	1.23637i	0.693732	−	0.720233i	$-0.255965\pi$
$968$	5.27711	+	9.14022i	0.169613	+	0.293778i
$969$	7.29514	−	34.3577i	0.234354	−	1.10373i
$970$	−1.76526	+	1.35453i	−0.0566790	+	0.0434913i
$971$	13.8089	+	33.3377i	0.443149	+	1.06986i	0.974837	+	0.222917i	$0.0715579\pi$
$971$	13.8089	+	33.3377i	0.443149	+	1.06986i	−0.531688	+	0.846940i	$0.678442\pi$
$972$	15.0529	−	4.05097i	0.482822	−	0.129935i
$973$	24.6917	+	59.6111i	0.791581	+	1.91105i
$974$	5.16809	−	8.95140i	0.165596	−	0.286821i
$975$	18.1488	−	26.4190i	0.581228	−	0.846086i
$976$	1.04836	−	3.91255i	0.0335573	−	0.125238i
$977$	−18.5266	+	24.1443i	−0.592717	+	0.772444i	−0.989354	−	0.145532i	$-0.953511\pi$
$977$	−18.5266	+	24.1443i	−0.592717	+	0.772444i	0.396636	+	0.917976i	$0.370177\pi$
$978$	−16.3402	+	18.1556i	−0.522503	+	0.580552i
$979$	10.3447	−	2.77185i	0.330618	−	0.0885888i
$980$		−	42.4653i		−	1.35650i
$981$	−13.5148	+	12.8363i	−0.431495	+	0.409831i
$982$	−18.2749	+	18.2749i	−0.583177	+	0.583177i
$983$	−8.70139	+	15.0713i	−0.277531	+	0.480698i	−0.970771	−	0.240009i	$-0.922850\pi$
$983$	−8.70139	+	15.0713i	−0.277531	+	0.480698i	0.693239	+	0.720707i	$0.256183\pi$
$984$	−9.39238	+	5.89773i	−0.299418	+	0.188013i
$985$	14.8535	+	25.7270i	0.473271	+	0.819730i
$986$	4.70580	+	1.26092i	0.149863	+	0.0401557i
$987$	−0.988125	+	1.94035i	−0.0314524	+	0.0617620i
$988$	6.84753	+	3.95342i	0.217849	+	0.125775i
$989$	−18.1360	−	18.1360i	−0.576692	−	0.576692i
$990$	−4.36724	+	7.13366i	−0.138800	+	0.226723i
$991$	−10.3968	−	25.1001i	−0.330265	−	0.797330i	−0.998571	−	0.0534433i	$-0.982980\pi$
$991$	−10.3968	−	25.1001i	−0.330265	−	0.797330i	0.668306	−	0.743886i	$-0.267020\pi$
$992$	−8.40911	+	2.25322i	−0.266990	+	0.0715397i
$993$	27.3135	−	13.0352i	0.866768	−	0.413659i
$994$	27.8480	+	48.2342i	0.883285	+	1.52989i
$995$	47.8630	−	62.3762i	1.51736	−	1.97746i
$996$	−20.0848	+	13.0494i	−0.636412	+	0.413487i
$997$	20.6931	+	2.72430i	0.655357	+	0.0862794i	0.450870	−	0.892590i	$-0.351114\pi$
$997$	20.6931	+	2.72430i	0.655357	+	0.0862794i	0.204488	+	0.978869i	$0.434447\pi$
$998$	35.6971	+	14.7862i	1.12997	+	0.468049i
$999$	−6.14401	−	38.6285i	−0.194388	−	1.22215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.v.a.137.18	✓	168
9.5	odd	6		738.2.v.b.383.3	yes	168
41.3	odd	8		738.2.v.b.659.3	yes	168
369.167	even	24	inner	738.2.v.a.167.18	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.v.a.137.18	✓	168	1.1	even	1	trivial
738.2.v.a.167.18	yes	168	369.167	even	24	inner
738.2.v.b.383.3	yes	168	9.5	odd	6
738.2.v.b.659.3	yes	168	41.3	odd	8

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:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.v (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(1.45241 - 0.943659i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.08080 + 4.03360i) q^{5} +(1.28742 + 1.15869i) q^{6} +(-4.10812 - 0.540844i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.21902 - 2.74117i) q^{9} -4.17589 q^{10} +(0.661956 + 0.0871482i) q^{11} +(-0.785999 + 1.54344i) q^{12} +(-0.905717 + 1.18035i) q^{13} +(-0.540844 - 4.10812i) q^{14} +(2.23657 + 6.87836i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.52530 - 1.46023i) q^{17} +(2.96327 + 0.468013i) q^{18} +(-2.03375 + 4.90991i) q^{19} +(-1.08080 - 4.03360i) q^{20} +(-6.47706 + 3.09113i) q^{21} +(0.0871482 + 0.661956i) q^{22} +(1.90657 + 3.30227i) q^{23} +(-1.69428 - 0.359745i) q^{24} +(-10.7717 - 6.21903i) q^{25} +(-1.37455 - 0.569357i) q^{26} +(-0.816209 - 5.13165i) q^{27} +(3.82816 - 1.58567i) q^{28} +(-0.166650 + 1.26584i) q^{29} +(-6.06512 + 3.94061i) q^{30} +(-7.53940 + 4.35288i) q^{31} +(0.965926 + 0.258819i) q^{32} +(1.04367 - 0.498085i) q^{33} +(0.498057 - 3.78311i) q^{34} +(6.62160 - 15.9860i) q^{35} +(0.314884 + 2.98343i) q^{36} +7.52750 q^{37} +(-5.26898 - 0.693674i) q^{38} +(-0.201626 + 2.56905i) q^{39} +(3.61643 - 2.08794i) q^{40} +(4.59721 - 4.45709i) q^{41} +(-4.66219 - 5.45632i) q^{42} +(-6.49708 + 1.74089i) q^{43} +(-0.616845 + 0.255506i) q^{44} +(9.73926 + 7.87968i) q^{45} +(-2.69629 + 2.69629i) q^{46} +(0.240703 - 0.184698i) q^{47} +(-0.0910250 - 1.72966i) q^{48} +(9.82265 + 2.63197i) q^{49} +(3.21920 - 12.0142i) q^{50} +(-6.49816 + 1.20583i) q^{51} +(0.194197 - 1.47507i) q^{52} +(1.03902 + 2.50841i) q^{53} +(4.74554 - 2.11656i) q^{54} +(-1.06696 + 2.57588i) q^{55} +(2.52244 + 3.28731i) q^{56} +(1.67943 + 9.05039i) q^{57} +(-1.26584 + 0.166650i) q^{58} +(-3.69949 + 2.13590i) q^{59} +(-5.37611 - 4.83855i) q^{60} +(3.91255 - 1.04836i) q^{61} +(-6.15590 - 6.15590i) q^{62} +(-6.49041 + 10.6017i) q^{63} +1.00000i q^{64} +(-3.78217 - 4.92902i) q^{65} +(0.751236 + 0.879197i) q^{66} +(3.89663 - 0.513002i) q^{67} +(3.78311 - 0.498057i) q^{68} +(5.88534 + 2.99712i) q^{69} +(17.1550 + 2.25851i) q^{70} +(-12.4184 + 5.14386i) q^{71} +(-2.80027 + 1.07632i) q^{72} +(9.56653 + 9.56653i) q^{73} +(1.94826 + 7.27101i) q^{74} +(-21.5136 + 1.13217i) q^{75} +(-0.693674 - 5.26898i) q^{76} +(-2.67226 - 0.716030i) q^{77} +(-2.53370 + 0.470163i) q^{78} +(-1.64296 + 12.4795i) q^{79} +(2.95280 + 2.95280i) q^{80} +(-6.02800 - 6.68306i) q^{81} +(5.49506 + 3.28698i) q^{82} +(11.9759 + 6.91428i) q^{83} +(4.06374 - 5.91553i) q^{84} +(9.70012 - 12.6414i) q^{85} +(-3.36314 - 5.82513i) q^{86} +(0.952471 + 1.99578i) q^{87} +(-0.406451 - 0.529697i) q^{88} +(14.8193 - 6.13837i) q^{89} +(-5.09048 + 11.4468i) q^{90} +(4.35918 - 4.35918i) q^{91} +(-3.30227 - 1.90657i) q^{92} +(-6.84271 + 13.4368i) q^{93} +(0.240703 + 0.184698i) q^{94} +(-17.6065 - 13.5100i) q^{95} +(1.64716 - 0.535592i) q^{96} +(0.422726 - 0.324369i) q^{97} +10.1692i q^{98} +(1.04582 - 1.70830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 4 q^{3} - 12 q^{7} - 4 q^{9} + 8 q^{15} + 84 q^{16} - 12 q^{17} - 8 q^{21} - 12 q^{22} + 48 q^{25} - 40 q^{27} + 16 q^{30} - 64 q^{33} - 36 q^{34} + 24 q^{35} - 4 q^{36} + 32 q^{39} - 32 q^{42}+ \cdots + 68 q^{99}+O(q^{100}) \) 168 * q - 4 * q^3 - 12 * q^7 - 4 * q^9 + 8 * q^15 + 84 * q^16 - 12 * q^17 - 8 * q^21 - 12 * q^22 + 48 * q^25 - 40 * q^27 + 16 * q^30 - 64 * q^33 - 36 * q^34 + 24 * q^35 - 4 * q^36 + 32 * q^39 - 32 * q^42 + 12 * q^44 + 72 * q^45 - 12 * q^47 - 8 * q^48 + 12 * q^49 - 44 * q^51 + 12 * q^56 - 64 * q^57 - 24 * q^58 - 108 * q^61 + 48 * q^63 - 84 * q^65 - 4 * q^66 - 60 * q^67 + 40 * q^69 + 12 * q^70 + 20 * q^75 - 60 * q^79 + 68 * q^81 + 12 * q^82 - 120 * q^83 + 8 * q^84 + 24 * q^85 + 72 * q^89 + 40 * q^90 - 16 * q^93 - 12 * q^94 - 120 * q^95 + 96 * q^97 + 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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