LMFDB - Embedded newform 372.2.p.a.191.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [372,2,Mod(191,372)] 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("372.191"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(372, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 372 = 2^{2} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	372.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.97043495519$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.5
Character	$\chi$	$=$	372.191
Dual form			372.2.p.a.335.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37366 - 0.336245i) q^{2} +(-1.53913 - 0.794402i) q^{3} +(1.77388 + 0.923772i) q^{4} +(-3.42031 + 1.97472i) q^{5} +(1.84713 + 1.60876i) q^{6} +(-2.26131 - 1.30557i) q^{7} +(-2.12609 - 1.86541i) q^{8} +(1.73785 + 2.44538i) q^{9} +(5.36233 - 1.56253i) q^{10} +(0.103767 + 0.179731i) q^{11} +(-1.99639 - 2.83098i) q^{12} +(-1.71430 - 2.96925i) q^{13} +(2.66728 + 2.55376i) q^{14} +(6.83302 - 0.322246i) q^{15} +(2.29329 + 3.27732i) q^{16} +(3.39107 + 1.95784i) q^{17} +(-1.56497 - 3.94346i) q^{18} +(4.86040 + 2.80615i) q^{19} +(-7.89140 + 0.343323i) q^{20} +(2.44331 + 3.80583i) q^{21} +(-0.0821077 - 0.281780i) q^{22} -1.56206 q^{23} +(1.79045 + 4.56008i) q^{24} +(5.29901 - 9.17816i) q^{25} +(1.35647 + 4.65516i) q^{26} +(-0.732164 - 5.14431i) q^{27} +(-2.80525 - 4.40486i) q^{28} -7.63843i q^{29} +(-9.49460 - 1.85491i) q^{30} +(5.45799 + 1.10016i) q^{31} +(-2.04822 - 5.27303i) q^{32} +(-0.0169334 - 0.359062i) q^{33} +(-3.99987 - 3.82963i) q^{34} +10.3125 q^{35} +(0.823763 + 5.94318i) q^{36} +(-3.79678 + 6.57622i) q^{37} +(-5.73298 - 5.48898i) q^{38} +(0.279749 + 5.93191i) q^{39} +(10.9555 + 2.18183i) q^{40} +(4.66304 - 2.69221i) q^{41} +(-2.07658 - 6.04947i) q^{42} +(-0.114409 - 0.0660539i) q^{43} +(0.0180409 + 0.414678i) q^{44} +(-10.7729 - 4.93219i) q^{45} +(2.14574 + 0.525234i) q^{46} +12.5078 q^{47} +(-0.926168 - 6.86602i) q^{48} +(-0.0909767 - 0.157576i) q^{49} +(-10.3651 + 10.8259i) q^{50} +(-3.66400 - 5.70725i) q^{51} +(-0.298047 - 6.85071i) q^{52} +(1.04024 - 0.600584i) q^{53} +(-0.724005 + 7.31272i) q^{54} +(-0.709834 - 0.409823i) q^{55} +(2.37234 + 6.99402i) q^{56} +(-5.25158 - 8.18015i) q^{57} +(-2.56838 + 10.4926i) q^{58} +(-1.23031 + 2.13097i) q^{59} +(12.4186 + 5.74053i) q^{60} +0.154002 q^{61} +(-7.12750 - 3.34646i) q^{62} +(-0.737209 - 7.79865i) q^{63} +(1.04053 + 7.93204i) q^{64} +(11.7269 + 6.77050i) q^{65} +(-0.0974721 + 0.498923i) q^{66} +(-4.26005 + 2.45954i) q^{67} +(4.20676 + 6.60554i) q^{68} +(2.40421 + 1.24090i) q^{69} +(-14.1659 - 3.46753i) q^{70} +(-4.14969 - 7.18748i) q^{71} +(0.866795 - 8.44089i) q^{72} +(7.27086 + 12.5935i) q^{73} +(7.42671 - 7.75684i) q^{74} +(-15.4470 + 9.91684i) q^{75} +(6.02951 + 9.46767i) q^{76} -0.541903i q^{77} +(1.61029 - 8.24248i) q^{78} +(-3.59507 - 2.07561i) q^{79} +(-14.3155 - 6.68084i) q^{80} +(-2.95976 + 8.49940i) q^{81} +(-7.31067 + 2.13025i) q^{82} +(4.05426 + 7.02219i) q^{83} +(0.818412 + 9.00815i) q^{84} -15.4647 q^{85} +(0.134948 + 0.129205i) q^{86} +(-6.06799 + 11.7565i) q^{87} +(0.114651 - 0.575692i) q^{88} +7.41534i q^{89} +(13.1399 + 10.3975i) q^{90} +8.95254i q^{91} +(-2.77090 - 1.44299i) q^{92} +(-7.52660 - 6.02913i) q^{93} +(-17.1814 - 4.20568i) q^{94} -22.1654 q^{95} +(-1.03642 + 9.74299i) q^{96} +1.34931 q^{97} +(0.0719868 + 0.247047i) q^{98} +(-0.259177 + 0.566096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) $ 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.37366	−	0.336245i	−0.971324	−	0.237761i
$2$	−1.37366	−	0.336245i	−0.971324	−	0.237761i
$3$	−1.53913	−	0.794402i	−0.888618	−	0.458648i
$3$	−1.53913	−	0.794402i	−0.888618	−	0.458648i
$4$	1.77388	+	0.923772i	0.886939	+	0.461886i
$5$	−3.42031	+	1.97472i	−1.52961	+	0.883120i	−0.530231	+	0.847853i	$0.677895\pi$
$5$	−3.42031	+	1.97472i	−1.52961	+	0.883120i	−0.999378	+	0.0352669i	$0.988772\pi$
$6$	1.84713	+	1.60876i	0.754087	+	0.656775i
$7$	−2.26131	−	1.30557i	−0.854696	−	0.493459i	0.00753664	−	0.999972i	$-0.497601\pi$
$7$	−2.26131	−	1.30557i	−0.854696	−	0.493459i	−0.862232	+	0.506513i	$0.830934\pi$
$8$	−2.12609	−	1.86541i	−0.751687	−	0.659520i
$9$	1.73785	+	2.44538i	0.579283	+	0.815126i
$10$	5.36233	−	1.56253i	1.69572	−	0.494114i
$11$	0.103767	+	0.179731i	0.0312871	+	0.0541908i	0.881245	−	0.472660i	$-0.156706\pi$
$11$	0.103767	+	0.179731i	0.0312871	+	0.0541908i	−0.849958	+	0.526851i	$0.823373\pi$
$12$	−1.99639	−	2.83098i	−0.576307	−	0.817233i
$13$	−1.71430	−	2.96925i	−0.475461	−	0.823522i	0.524144	−	0.851629i	$-0.324385\pi$
$13$	−1.71430	−	2.96925i	−0.475461	−	0.823522i	−0.999605	+	0.0281076i	$0.991052\pi$
$14$	2.66728	+	2.55376i	0.712861	+	0.682522i
$15$	6.83302	−	0.322246i	1.76428	−	0.0832035i
$16$	2.29329	+	3.27732i	0.573323	+	0.819329i
$17$	3.39107	+	1.95784i	0.822456	+	0.474845i	0.851263	−	0.524740i	$-0.175837\pi$
$17$	3.39107	+	1.95784i	0.822456	+	0.474845i	−0.0288065	+	0.999585i	$0.509171\pi$
$18$	−1.56497	−	3.94346i	−0.368866	−	0.929482i
$19$	4.86040	+	2.80615i	1.11505	+	0.643775i	0.940133	−	0.340808i	$-0.110700\pi$
$19$	4.86040	+	2.80615i	1.11505	+	0.643775i	0.174919	+	0.984583i	$0.444034\pi$
$20$	−7.89140	+	0.343323i	−1.76457	+	0.0767693i
$21$	2.44331	+	3.80583i	0.533174	+	0.830501i
$22$	−0.0821077	−	0.281780i	−0.0175054	−	0.0600757i
$23$	−1.56206			−0.325712			−0.162856	−	0.986650i	$-0.552071\pi$
$23$	−1.56206			−0.325712			−0.162856	+	0.986650i	$0.552071\pi$
$24$	1.79045	+	4.56008i	0.365474	+	0.930821i
$25$	5.29901	−	9.17816i	1.05980	−	1.83563i
$26$	1.35647	+	4.65516i	0.266025	+	0.912952i
$27$	−0.732164	−	5.14431i	−0.140905	−	0.990023i
$28$	−2.80525	−	4.40486i	−0.530142	−	0.832440i
$29$		−	7.63843i		−	1.41842i	−0.704997	−	0.709210i	$-0.749052\pi$
$29$		−	7.63843i		−	1.41842i	0.704997	−	0.709210i	$-0.250948\pi$
$30$	−9.49460	−	1.85491i	−1.73347	−	0.338659i
$31$	5.45799	+	1.10016i	0.980284	+	0.197594i
$31$	5.45799	+	1.10016i	0.980284	+	0.197594i
$32$	−2.04822	−	5.27303i	−0.362078	−	0.932148i
$33$	−0.0169334	−	0.359062i	−0.00294772	−	0.0625047i
$34$	−3.99987	−	3.82963i	−0.685972	−	0.656777i
$35$	10.3125			1.74313
$36$	0.823763	+	5.94318i	0.137294	+	0.990530i
$37$	−3.79678	+	6.57622i	−0.624187	+	1.08112i	0.364510	+	0.931199i	$0.381236\pi$
$37$	−3.79678	+	6.57622i	−0.624187	+	1.08112i	−0.988697	+	0.149925i	$0.952097\pi$
$38$	−5.73298	−	5.48898i	−0.930011	−	0.890430i
$39$	0.279749	+	5.93191i	0.0447957	+	0.949865i
$40$	10.9555	+	2.18183i	1.73222	+	0.344978i
$41$	4.66304	−	2.69221i	0.728245	−	0.420452i	−0.0895350	−	0.995984i	$-0.528538\pi$
$41$	4.66304	−	2.69221i	0.728245	−	0.420452i	0.817780	+	0.575531i	$0.195205\pi$
$42$	−2.07658	−	6.04947i	−0.320424	−	0.933453i
$43$	−0.114409	−	0.0660539i	−0.0174472	−	0.0100731i	0.491251	−	0.871018i	$-0.336540\pi$
$43$	−0.114409	−	0.0660539i	−0.0174472	−	0.0100731i	−0.508698	+	0.860945i	$0.669873\pi$
$44$	0.0180409	+	0.414678i	0.00271977	+	0.0625150i
$45$	−10.7729	−	4.93219i	−1.60593	−	0.735248i
$46$	2.14574	+	0.525234i	0.316372	+	0.0774416i
$47$	12.5078			1.82445			0.912225	−	0.409690i	$-0.134363\pi$
$47$	12.5078			1.82445			0.912225	+	0.409690i	$0.134363\pi$
$48$	−0.926168	−	6.86602i	−0.133681	−	0.991024i
$49$	−0.0909767	−	0.157576i	−0.0129967	−	0.0225109i
$50$	−10.3651	+	10.8259i	−1.46585	+	1.53101i
$51$	−3.66400	−	5.70725i	−0.513062	−	0.799174i
$52$	−0.298047	−	6.85071i	−0.0413316	−	0.950022i
$53$	1.04024	−	0.600584i	0.142888	−	0.0824966i	−0.426852	−	0.904322i	$-0.640377\pi$
$53$	1.04024	−	0.600584i	0.142888	−	0.0824966i	0.569740	+	0.821825i	$0.307044\pi$
$54$	−0.724005	+	7.31272i	−0.0985246	+	0.995135i
$55$	−0.709834	−	0.409823i	−0.0957140	−	0.0552605i
$56$	2.37234	+	6.99402i	0.317017	+	0.934616i
$57$	−5.25158	−	8.18015i	−0.695588	−	1.08349i
$58$	−2.56838	+	10.4926i	−0.337245	+	1.37775i
$59$	−1.23031	+	2.13097i	−0.160173	+	0.277428i	−0.934931	−	0.354830i	$-0.884539\pi$
$59$	−1.23031	+	2.13097i	−0.160173	+	0.277428i	0.774758	+	0.632258i	$0.217872\pi$
$60$	12.4186	+	5.74053i	1.60324	+	0.741099i
$61$	0.154002			0.0197180			0.00985898	−	0.999951i	$-0.496862\pi$
$61$	0.154002			0.0197180			0.00985898	+	0.999951i	$0.496862\pi$
$62$	−7.12750	−	3.34646i	−0.905193	−	0.425001i
$63$	−0.737209	−	7.79865i	−0.0928796	−	0.982538i
$64$	1.04053	+	7.93204i	0.130066	+	0.991505i
$65$	11.7269	+	6.77050i	1.45454	+	0.839778i
$66$	−0.0974721	+	0.498923i	−0.0119980	+	0.0614131i
$67$	−4.26005	+	2.45954i	−0.520448	+	0.300481i	−0.737118	−	0.675764i	$-0.763814\pi$
$67$	−4.26005	+	2.45954i	−0.520448	+	0.300481i	0.216670	+	0.976245i	$0.430481\pi$
$68$	4.20676	+	6.60554i	0.510145	+	0.801040i
$69$	2.40421	+	1.24090i	0.289433	+	0.149387i
$70$	−14.1659	−	3.46753i	−1.69315	−	0.414449i
$71$	−4.14969	−	7.18748i	−0.492478	−	0.852997i	0.507484	−	0.861661i	$-0.330576\pi$
$71$	−4.14969	−	7.18748i	−0.492478	−	0.852997i	−0.999962	+	0.00866383i	$0.997242\pi$
$72$	0.866795	−	8.44089i	0.102153	−	0.994769i
$73$	7.27086	+	12.5935i	0.850989	+	1.47396i	0.880317	+	0.474387i	$0.157330\pi$
$73$	7.27086	+	12.5935i	0.850989	+	1.47396i	−0.0293272	+	0.999570i	$0.509336\pi$
$74$	7.42671	−	7.75684i	0.863337	−	0.901714i
$75$	−15.4470	+	9.91684i	−1.78367	+	1.14510i
$76$	6.02951	+	9.46767i	0.691632	+	1.08602i
$77$		−	0.541903i		−	0.0617555i
$78$	1.61029	−	8.24248i	0.182330	−	0.933277i
$79$	−3.59507	−	2.07561i	−0.404477	−	0.233525i	0.283937	−	0.958843i	$-0.408359\pi$
$79$	−3.59507	−	2.07561i	−0.404477	−	0.233525i	−0.688414	+	0.725318i	$0.741693\pi$
$80$	−14.3155	−	6.68084i	−1.60053	−	0.746941i
$81$	−2.95976	+	8.49940i	−0.328862	+	0.944378i
$82$	−7.31067	+	2.13025i	−0.807328	+	0.235247i
$83$	4.05426	+	7.02219i	0.445013	+	0.770786i	0.998053	−	0.0623691i	$-0.0198656\pi$
$83$	4.05426	+	7.02219i	0.445013	+	0.770786i	−0.553040	+	0.833155i	$0.686532\pi$
$84$	0.818412	+	9.00815i	0.0892961	+	0.982870i
$85$	−15.4647			−1.67738
$86$	0.134948	+	0.129205i	0.0145519	+	0.0139325i
$87$	−6.06799	+	11.7565i	−0.650556	+	1.26043i
$88$	0.114651	−	0.575692i	0.0122219	−	0.0613690i
$89$			7.41534i			0.786024i	0.919533	+	0.393012i	$0.128567\pi$
$89$			7.41534i			0.786024i	−0.919533	+	0.393012i	$0.871433\pi$
$90$	13.1399	+	10.3975i	1.38507	+	1.09599i
$91$			8.95254i			0.938481i
$92$	−2.77090	−	1.44299i	−0.288887	−	0.150442i
$93$	−7.52660	−	6.02913i	−0.780472	−	0.625191i
$94$	−17.1814	−	4.20568i	−1.77213	−	0.433783i
$95$	−22.1654			−2.27412
$96$	−1.03642	+	9.74299i	−0.105780	+	0.994390i
$97$	1.34931			0.137002			0.0685008	−	0.997651i	$-0.478178\pi$
$97$	1.34931			0.137002			0.0685008	+	0.997651i	$0.478178\pi$
$98$	0.0719868	+	0.247047i	0.00727176	+	0.0249555i
$99$	−0.259177	+	0.566096i	−0.0260483	+	0.0568947i
$100$	17.8783	−	11.3859i	1.78783	−	1.13859i
$101$		−	3.09100i		−	0.307566i	−0.988105	−	0.153783i	$-0.950854\pi$
$101$		−	3.09100i		−	0.307566i	0.988105	−	0.153783i	$-0.0491457\pi$
$102$	3.11405	+	9.07181i	0.308337	+	0.898243i
$103$	6.00461	−	3.46676i	0.591652	−	0.341590i	−0.174099	−	0.984728i	$-0.555701\pi$
$103$	6.00461	−	3.46676i	0.591652	−	0.341590i	0.765750	+	0.643138i	$0.222368\pi$
$104$	−1.89410	+	9.51076i	−0.185732	+	0.932606i
$105$	−15.8723	−	8.19229i	−1.54898	−	0.799486i
$106$	−1.63088	+	0.475222i	−0.158405	+	0.0461576i
$107$	7.20284	−	12.4757i	0.696324	−	1.20607i	−0.273408	−	0.961898i	$-0.588151\pi$
$107$	7.20284	−	12.4757i	0.696324	−	1.20607i	0.969732	−	0.244171i	$-0.0785159\pi$
$108$	3.45340	−	9.80174i	0.332303	−	0.943173i
$109$	−5.14668			−0.492962			−0.246481	−	0.969148i	$-0.579274\pi$
$109$	−5.14668			−0.492962			−0.246481	+	0.969148i	$0.579274\pi$
$110$	0.837269	+	0.801635i	0.0798305	+	0.0764329i
$111$	11.0679	−	7.10549i	1.05052	−	0.674424i
$112$	−0.907083	−	10.4051i	−0.0857113	−	0.983189i
$113$	6.32002	−	3.64886i	0.594537	−	0.343256i	−0.172352	−	0.985035i	$-0.555137\pi$
$113$	6.32002	−	3.64886i	0.594537	−	0.343256i	0.766890	+	0.641779i	$0.221803\pi$
$114$	4.46334	+	13.0025i	0.418030	+	1.21780i
$115$	5.34273	−	3.08462i	0.498212	−	0.287643i
$116$	7.05616	−	13.5496i	0.655148	−	1.25805i
$117$	4.28175	−	9.35222i	0.395848	−	0.864613i
$118$	2.40656	−	2.51353i	0.221542	−	0.231389i
$119$	−5.11219	−	8.85457i	−0.468633	−	0.811697i
$120$	−15.1288	−	12.0612i	−1.38106	−	1.10104i
$121$	5.47846	−	9.48898i	0.498042	−	0.862634i
$122$	−0.211547	−	0.0517825i	−0.0191525	−	0.00468816i
$123$	−9.31573	+	0.439330i	−0.839971	+	0.0396131i
$124$	8.66552	+	6.99348i	0.778187	+	0.628033i
$125$			22.1090i			1.97749i
$126$	−1.60958	+	10.9606i	−0.143393	+	0.976445i
$127$	10.7362	+	6.19857i	0.952688	+	0.550035i	0.893915	−	0.448237i	$-0.147948\pi$
$127$	10.7362	+	6.19857i	0.952688	+	0.550035i	0.0587729	+	0.998271i	$0.481281\pi$
$128$	1.23778	−	11.2458i	0.109405	−	0.993997i
$129$	0.123617	+	0.192552i	0.0108838	+	0.0169533i
$130$	−13.8322	−	13.2435i	−1.21316	−	1.16153i
$131$	−2.00451	+	3.47191i	−0.175135	+	0.303342i	−0.940208	−	0.340601i	$-0.889369\pi$
$131$	−2.00451	+	3.47191i	−0.175135	+	0.303342i	0.765073	+	0.643943i	$0.222703\pi$
$132$	0.301654	−	0.652575i	0.0262556	−	0.0567994i
$133$	−7.32725	−	12.6912i	−0.635353	−	1.10046i
$134$	6.67887	−	1.94615i	0.576966	−	0.168122i
$135$	12.6628	+	16.1493i	1.08984	+	1.38991i
$136$	−3.55757	−	10.4883i	−0.305059	−	0.899362i
$137$	−16.6428	+	9.60871i	−1.42189	+	0.820928i	−0.996460	−	0.0840645i	$-0.973210\pi$
$137$	−16.6428	+	9.60871i	−1.42189	+	0.820928i	−0.425428	+	0.904992i	$0.639876\pi$
$138$	−2.88532	−	2.51298i	−0.245615	−	0.213919i
$139$		−	1.32937i		−	0.112756i	−0.998409	−	0.0563780i	$-0.982045\pi$
$139$		−	1.32937i		−	0.112756i	0.998409	−	0.0563780i	$-0.0179552\pi$
$140$	18.2932	+	9.52641i	1.54605	+	0.805129i
$141$	−19.2511	−	9.93622i	−1.62124	−	0.836781i
$142$	3.28351	+	11.2685i	0.275546	+	0.945628i
$143$	0.355777	−	0.616223i	0.0297515	−	0.0515312i
$144$	−4.02889	+	11.3035i	−0.335741	+	0.941954i
$145$	15.0837	+	26.1258i	1.25264	+	2.16963i
$146$	−5.75318	−	19.7440i	−0.476137	−	1.63402i
$147$	0.0148461	+	0.314803i	0.00122449	+	0.0259645i
$148$	−12.8100	+	8.15806i	−1.05297	+	0.670588i
$149$	17.4403	+	10.0691i	1.42876	+	0.824896i	0.997023	−	0.0771031i	$-0.0245671\pi$
$149$	17.4403	+	10.0691i	1.42876	+	0.824896i	0.431738	+	0.901999i	$0.357900\pi$
$150$	24.5534	−	8.42838i	2.00478	−	0.688174i
$151$		−	6.32563i		−	0.514772i	−0.966309	−	0.257386i	$-0.917139\pi$
$151$		−	6.32563i		−	0.514772i	0.966309	−	0.257386i	$-0.0828612\pi$
$152$	−5.09904	−	15.0327i	−0.413587	−	1.21932i
$153$	1.10552	+	11.6949i	0.0893762	+	0.945476i
$154$	−0.182212	+	0.744389i	−0.0146831	+	0.0599846i
$155$	−20.8405	+	7.01511i	−1.67395	+	0.563467i
$156$	−4.98349	+	10.7809i	−0.398998	+	0.863163i
$157$	22.4951			1.79531			0.897653	−	0.440703i	$-0.145271\pi$
$157$	22.4951			1.79531			0.897653	+	0.440703i	$0.145271\pi$
$158$	4.24048	+	4.06001i	0.337355	+	0.322997i
$159$	−2.07818	+	0.0980069i	−0.164810	+	0.00777245i
$160$	17.4183	+	13.9907i	1.37704	+	1.10606i
$161$	3.53230	+	2.03938i	0.278385	+	0.160725i
$162$	6.92358	−	10.6801i	0.543968	−	0.839106i
$163$		−	16.3193i		−	1.27823i	−0.769112	−	0.639113i	$-0.779301\pi$
$163$		−	16.3193i		−	1.27823i	0.769112	−	0.639113i	$-0.220699\pi$
$164$	10.7587	−	0.468065i	0.840110	−	0.0365498i
$165$	0.766963	+	1.19466i	0.0597080	+	0.0930045i
$166$	−3.20800	−	11.0093i	−0.248989	−	0.854489i
$167$	8.27206	−	14.3276i	0.640111	−	1.10871i	−0.345296	−	0.938494i	$-0.612221\pi$
$167$	8.27206	−	14.3276i	0.640111	−	1.10871i	0.985408	−	0.170212i	$-0.0544452\pi$
$168$	1.90472	−	12.6493i	0.146953	−	0.975916i
$169$	0.622370	−	1.07798i	0.0478746	−	0.0829212i
$170$	21.2432	+	5.19993i	1.62928	+	0.398816i
$171$	1.58454	+	16.7622i	0.121172	+	1.28184i
$172$	−0.141929	−	0.222859i	−0.0108220	−	0.0169929i
$173$	4.53164	−	2.61634i	0.344534	−	0.198917i	−0.317741	−	0.948178i	$-0.602924\pi$
$173$	4.53164	−	2.61634i	0.344534	−	0.198917i	0.662275	+	0.749261i	$0.269591\pi$
$174$	12.2884	−	14.1092i	0.931583	−	1.06961i
$175$	−23.9654	+	13.8365i	−1.81162	+	1.04594i
$176$	−0.351065	+	0.752254i	−0.0264625	+	0.0567033i
$177$	3.58646	−	2.30247i	0.269575	−	0.173064i
$178$	2.49337	−	10.1861i	0.186886	−	0.763484i
$179$	−4.26889	+	7.39393i	−0.319072	+	0.552648i	−0.980295	−	0.197541i	$-0.936704\pi$
$179$	−4.26889	+	7.39393i	−0.319072	+	0.552648i	0.661223	+	0.750189i	$0.270038\pi$
$180$	−14.5536	−	18.7008i	−1.08476	−	1.39388i
$181$	−8.16415	−	14.1407i	−0.606837	−	1.05107i	−0.991758	−	0.128123i	$-0.959105\pi$
$181$	−8.16415	−	14.1407i	−0.606837	−	1.05107i	0.384922	−	0.922949i	$-0.374228\pi$
$182$	3.01024	−	12.2977i	0.223134	−	0.911569i
$183$	−0.237030	−	0.122340i	−0.0175217	−	0.00904361i
$184$	3.32108	+	2.91387i	0.244833	+	0.214814i
$185$		−	29.9903i		−	2.20493i
$186$	8.31171	+	10.8127i	0.609444	+	0.792829i
$187$			0.812639i			0.0594261i
$188$	22.1873	+	11.5543i	1.61818	+	0.842687i
$189$	−5.06060	+	12.5888i	−0.368105	+	0.915699i
$190$	30.4477	+	7.45301i	2.20891	+	0.540698i
$191$	2.18511	+	3.78472i	0.158109	+	0.273853i	0.934187	−	0.356785i	$-0.116127\pi$
$191$	2.18511	+	3.78472i	0.158109	+	0.273853i	−0.776078	+	0.630637i	$0.782794\pi$
$192$	4.69972	−	13.0351i	0.339173	−	0.940724i
$193$	8.35283	−	14.4675i	0.601250	−	1.04140i	−0.391382	−	0.920228i	$-0.628003\pi$
$193$	8.35283	−	14.4675i	0.601250	−	1.04140i	0.992632	−	0.121167i	$-0.0386638\pi$
$194$	−1.85349	−	0.453698i	−0.133073	−	0.0325736i
$195$	−12.6707	−	19.7365i	−0.907365	−	1.41336i
$196$	−0.0158171	−	0.363563i	−0.00112980	−	0.0259688i
$197$	9.40039	−	5.42732i	0.669750	−	0.386681i	−0.126232	−	0.992001i	$-0.540288\pi$
$197$	9.40039	−	5.42732i	0.669750	−	0.386681i	0.795982	+	0.605320i	$0.206955\pi$
$198$	0.546368	−	0.690475i	0.0388287	−	0.0490699i
$199$	14.6129	−	8.43677i	1.03588	−	0.598067i	0.117218	−	0.993106i	$-0.462602\pi$
$199$	14.6129	−	8.43677i	1.03588	−	0.598067i	0.918664	+	0.395039i	$0.129269\pi$
$200$	−28.3872	+	9.62880i	−2.00728	+	0.680859i
$201$	8.51065	−	0.401363i	0.600295	−	0.0283099i
$202$	−1.03933	+	4.24599i	−0.0731273	+	0.298747i
$203$	−9.97250	+	17.2729i	−0.699932	+	1.21232i
$204$	−1.22729	−	13.5087i	−0.0859278	−	0.945795i
$205$	−10.6327	+	18.4164i	−0.742620	+	1.28626i
$206$	−9.41397	+	2.74313i	−0.655902	+	0.191123i
$207$	−2.71462	−	3.81983i	−0.188679	−	0.265496i
$208$	5.79979	−	12.4277i	0.402143	−	0.861703i
$209$			1.16475i			0.0805674i
$210$	19.0485	+	16.5904i	1.31447	+	1.14485i
$211$	−3.26296	−	1.88387i	−0.224632	−	0.129691i	0.383461	−	0.923557i	$-0.374732\pi$
$211$	−3.26296	−	1.88387i	−0.224632	−	0.129691i	−0.608093	+	0.793866i	$0.708065\pi$
$212$	2.40007	−	0.104417i	0.164837	−	0.00717140i
$213$	0.677172	+	14.3590i	0.0463990	+	0.983863i
$214$	−14.0891	+	14.7154i	−0.963113	+	1.00592i
$215$	0.521751			0.0355831
$216$	−8.03958	+	12.3031i	−0.547024	+	0.837117i
$217$	−10.9059	−	9.61358i	−0.740340	−	0.652613i
$218$	7.06978	+	1.73054i	0.478826	+	0.117207i
$219$	−1.18650	−	25.1590i	−0.0801763	−	1.70009i
$220$	−0.880576	−	1.38270i	−0.0593685	−	0.0932216i
$221$		−	13.4253i		−	0.903081i
$222$	−17.5927	+	6.03900i	−1.18075	+	0.405311i
$223$	−19.9649	−	11.5267i	−1.33695	−	0.771887i	−0.350594	−	0.936528i	$-0.614020\pi$
$223$	−19.9649	−	11.5267i	−1.33695	−	0.771887i	−0.986354	+	0.164640i	$0.947354\pi$
$224$	−2.25264	+	14.5981i	−0.150511	+	0.975373i
$225$	31.6530	−	2.99217i	2.11020	−	0.199478i
$226$	−9.90846	+	2.88722i	−0.659101	+	0.192055i
$227$	1.63294	+	2.82833i	0.108382	+	0.187723i	0.915115	−	0.403193i	$-0.132100\pi$
$227$	1.63294	+	2.82833i	0.108382	+	0.187723i	−0.806733	+	0.590916i	$0.798766\pi$
$228$	−1.75907	−	19.3618i	−0.116497	−	1.28227i
$229$	−11.2661	+	19.5134i	−0.744483	+	1.28948i	0.205953	+	0.978562i	$0.433971\pi$
$229$	−11.2661	+	19.5134i	−0.744483	+	1.28948i	−0.950436	+	0.310920i	$0.899363\pi$
$230$	−8.37627	+	2.44076i	−0.552315	+	0.160939i
$231$	−0.430489	+	0.834059i	−0.0283241	+	0.0548771i
$232$	−14.2488	+	16.2400i	−0.935477	+	1.06621i
$233$			13.6684i			0.895448i	0.894172	+	0.447724i	$0.147765\pi$
$233$			13.6684i			0.895448i	−0.894172	+	0.447724i	$0.852235\pi$
$234$	−9.02630	+	11.4070i	−0.590068	+	0.745702i
$235$	−42.7805	+	24.6994i	−2.79069	+	1.61121i
$236$	−4.15095	+	2.64355i	−0.270204	+	0.172080i
$237$	3.88441	+	6.05057i	0.252319	+	0.393027i
$238$	4.04510	+	13.8821i	0.262205	+	0.899843i
$239$	3.28285	+	5.68607i	0.212350	+	0.367801i	0.952450	−	0.304696i	$-0.0985549\pi$
$239$	3.28285	+	5.68607i	0.212350	+	0.367801i	−0.740099	+	0.672497i	$0.765222\pi$
$240$	16.7262	+	21.6550i	1.07967	+	1.39782i
$241$	7.65184	−	13.2534i	0.492898	−	0.853725i	−0.507068	−	0.861906i	$-0.669271\pi$
$241$	7.65184	−	13.2534i	0.492898	−	0.853725i	0.999967	+	0.00818079i	$0.00260406\pi$
$242$	−10.7162	+	11.1925i	−0.688861	+	0.719482i
$243$	11.3074	−	10.7305i	0.725370	−	0.688359i
$244$	0.273181	+	0.142263i	0.0174886	+	0.00910745i
$245$	0.622337	+	0.359306i	0.0397597	+	0.0229552i
$246$	12.9444	+	2.52888i	0.825302	+	0.161235i
$247$		−	19.2423i		−	1.22436i
$248$	−9.55195	−	12.5204i	−0.606549	−	0.795046i
$249$	−0.661599	−	14.0288i	−0.0419271	−	0.889039i
$250$	7.43404	−	30.3703i	0.470170	−	1.92078i
$251$	9.82770	−	17.0221i	0.620319	−	1.07442i	−0.369108	−	0.929387i	$-0.620337\pi$
$251$	9.82770	−	17.0221i	0.620319	−	1.07442i	0.989426	−	0.145037i	$-0.0463300\pi$
$252$	5.89645	−	14.5149i	0.371442	−	0.914351i
$253$	−0.162091	−	0.280750i	−0.0101906	−	0.0176506i
$254$	−12.6637	−	12.1247i	−0.794591	−	0.760774i
$255$	23.8022	+	12.2852i	1.49055	+	0.769329i
$256$	−5.48163	+	15.0317i	−0.342602	+	0.939481i
$257$	−13.3298	+	7.69598i	−0.831492	+	0.480062i	−0.854363	−	0.519676i	$-0.826053\pi$
$257$	−13.3298	+	7.69598i	−0.831492	+	0.480062i	0.0228711	+	0.999738i	$0.492719\pi$
$258$	−0.105063	−	0.306067i	−0.00654091	−	0.0190549i
$259$	17.1714	−	9.91393i	1.06698	−	0.616022i
$260$	14.5476	+	22.8430i	0.902205	+	1.41666i
$261$	18.6789	−	13.2744i	1.15619	−	0.821667i
$262$	3.92092	−	4.09521i	0.242235	−	0.253003i
$263$	−13.5866			−0.837783			−0.418891	−	0.908036i	$-0.637581\pi$
$263$	−13.5866			−0.837783			−0.418891	+	0.908036i	$0.637581\pi$
$264$	−0.633794	+	0.794986i	−0.0390073	+	0.0489280i
$265$	−2.37197	+	4.10837i	−0.145709	+	0.252375i
$266$	5.79780	+	19.8971i	0.355486	+	1.21997i
$267$	5.89076	−	11.4132i	0.360509	−	0.698475i
$268$	−9.82887	+	0.427614i	−0.600394	+	0.0261207i
$269$	−11.8869	+	6.86288i	−0.724754	+	0.418437i	−0.816500	−	0.577345i	$-0.804089\pi$
$269$	−11.8869	+	6.86288i	−0.724754	+	0.418437i	0.0917457	+	0.995782i	$0.470755\pi$
$270$	−11.9642	−	26.4415i	−0.728119	−	1.60918i
$271$		−	1.75353i		−	0.106519i	−0.998581	−	0.0532597i	$-0.983039\pi$
$271$		−	1.75353i		−	0.106519i	0.998581	−	0.0532597i	$-0.0169611\pi$
$272$	1.36027	+	15.6035i	0.0824783	+	0.946102i
$273$	7.11192	−	13.7791i	0.430433	−	0.833951i
$274$	26.0924	−	7.60305i	1.57630	−	0.459317i
$275$	2.19946			0.132632
$276$	3.11847	+	4.42216i	0.187710	+	0.266183i
$277$	−15.1715			−0.911567			−0.455783	−	0.890091i	$-0.650641\pi$
$277$	−15.1715			−0.911567			−0.455783	+	0.890091i	$0.650641\pi$
$278$	−0.446995	+	1.82610i	−0.0268090	+	0.109522i
$279$	6.79487	+	15.2588i	0.406798	+	0.913518i
$280$	−21.9254	−	19.2370i	−1.31029	−	1.14963i
$281$		−	8.60821i		−	0.513523i	−0.966475	−	0.256761i	$-0.917345\pi$
$281$		−	8.60821i		−	0.513523i	0.966475	−	0.256761i	$-0.0826555\pi$
$282$	23.1035	+	20.1221i	1.37579	+	1.19825i
$283$			10.2357i			0.608451i	0.952600	+	0.304225i	$0.0983976\pi$
$283$			10.2357i			0.608451i	−0.952600	+	0.304225i	$0.901602\pi$
$284$	−0.721463	−	16.5831i	−0.0428109	−	0.984025i
$285$	34.1155	+	17.6083i	2.02083	+	1.04302i
$286$	−0.695918	+	0.726853i	−0.0411505	+	0.0429797i
$287$	−14.0595			−0.829904
$288$	9.33505	−	14.1724i	0.550073	−	0.835117i
$289$	−0.833745	−	1.44409i	−0.0490438	−	0.0849464i
$290$	−11.9352	−	40.9598i	−0.700862	−	2.40524i
$291$	−2.07676	−	1.07189i	−0.121742	−	0.0628355i
$292$	1.26411	+	29.0559i	0.0739762	+	1.70037i
$293$	19.7156	+	11.3828i	1.15180	+	0.664991i	0.949325	−	0.314297i	$-0.101769\pi$
$293$	19.7156	+	11.3828i	1.15180	+	0.664991i	0.202473	+	0.979288i	$0.435102\pi$
$294$	0.0854573	−	0.437424i	0.00498397	−	0.0255111i
$295$		−	9.71808i		−	0.565808i
$296$	20.3396	−	6.89911i	1.18222	−	0.401003i
$297$	0.848615	−	0.665404i	0.0492416	−	0.0386107i
$298$	−20.5713	−	19.6958i	−1.19166	−	1.14094i
$299$	2.67783	+	4.63815i	0.154863	+	0.268231i
$300$	−36.5620	+	3.32175i	−2.11091	+	0.191781i
$301$	0.172476	+	0.298737i	0.00994135	+	0.0172189i
$302$	−2.12696	+	8.68926i	−0.122393	+	0.500011i
$303$	−2.45550	+	4.75746i	−0.141065	+	0.273309i
$304$	1.94966	+	22.3644i	0.111821	+	1.28269i
$305$	−0.526735	+	0.304111i	−0.0301608	+	0.0174133i
$306$	2.41374	−	16.4365i	0.137984	−	0.939613i
$307$	16.0339	+	9.25716i	0.915101	+	0.528334i	0.882069	−	0.471120i	$-0.156150\pi$
$307$	16.0339	+	9.25716i	0.915101	+	0.528334i	0.0330325	+	0.999454i	$0.489484\pi$
$308$	0.500594	−	0.961270i	0.0285240	−	0.0547734i
$309$	−11.9959	+	0.565727i	−0.682422	+	0.0321831i
$310$	30.9866	−	2.62885i	1.75992	−	0.149309i
$311$	10.2620			0.581904			0.290952	−	0.956738i	$-0.406028\pi$
$311$	10.2620			0.581904			0.290952	+	0.956738i	$0.406028\pi$
$312$	10.4706	−	13.1336i	0.592783	−	0.743545i
$313$	1.01466	−	1.75745i	0.0573522	−	0.0993369i	−0.835924	−	0.548845i	$-0.815068\pi$
$313$	1.01466	−	1.75745i	0.0573522	−	0.0993369i	0.893276	+	0.449509i	$0.148401\pi$
$314$	−30.9006	−	7.56387i	−1.74382	−	0.426854i
$315$	17.9216	+	25.2180i	1.00977	+	1.42087i
$316$	−4.45982	−	7.00291i	−0.250885	−	0.393944i
$317$	−8.17576	−	4.72028i	−0.459196	−	0.265117i	0.252510	−	0.967594i	$-0.418744\pi$
$317$	−8.17576	−	4.72028i	−0.459196	−	0.265117i	−0.711706	+	0.702477i	$0.752077\pi$
$318$	2.88766	+	0.564148i	0.161932	+	0.0316358i
$319$	1.37286	−	0.792620i	0.0768653	−	0.0443782i
$320$	−19.2225	−	25.0753i	−1.07457	−	1.40175i
$321$	−20.9968	+	13.4798i	−1.17193	+	0.752367i
$322$	−4.16645	−	3.98913i	−0.232187	−	0.222305i
$323$	10.9880	+	19.0317i	0.611387	+	1.05895i
$324$	−13.1018	+	12.3428i	−0.727875	+	0.685709i
$325$	−36.3363			−2.01558
$326$	−5.48728	+	22.4172i	−0.303913	+	1.24157i
$327$	7.92141	+	4.08853i	0.438055	+	0.226096i
$328$	−14.9361	−	2.97458i	−0.824709	−	0.164244i
$329$	−28.2840	−	16.3298i	−1.55935	−	0.900291i
$330$	−0.651846	−	1.89895i	−0.0358829	−	0.104534i
$331$	11.4961	−	6.63730i	0.631885	−	0.364819i	−0.149597	−	0.988747i	$-0.547798\pi$
$331$	11.4961	−	6.63730i	0.631885	−	0.364819i	0.781482	+	0.623928i	$0.214464\pi$
$332$	0.704872	+	16.2017i	0.0386849	+	0.889186i
$333$	−22.6796	+	2.14391i	−1.24283	+	0.117486i
$334$	−16.1806	+	16.8998i	−0.885362	+	0.924718i
$335$	9.71380	−	16.8248i	0.530722	−	0.919237i
$336$	−6.86971	+	16.7354i	−0.374773	+	0.912990i
$337$	16.9738			0.924623			0.462311	−	0.886718i	$-0.347020\pi$
$337$	16.9738			0.924623			0.462311	+	0.886718i	$0.347020\pi$
$338$	−1.21739	+	1.27150i	−0.0662172	+	0.0691606i
$339$	−12.6260	+	0.595443i	−0.685750	+	0.0323400i
$340$	−27.4325	−	14.2858i	−1.48774	−	0.774759i
$341$	0.368630	+	1.09513i	0.0199624	+	0.0593045i
$342$	3.45959	−	23.5583i	0.187073	−	1.27389i
$343$			18.7531i			1.01257i
$344$	0.120026	+	0.353855i	0.00647138	+	0.0190786i
$345$	−10.6736	+	0.503367i	−0.574647	+	0.0271004i
$346$	−7.10466	+	2.07022i	−0.381949	+	0.111296i
$347$	17.2853	−	29.9390i	0.927922	−	1.60721i	0.141128	−	0.989991i	$-0.454927\pi$
$347$	17.2853	−	29.9390i	0.927922	−	1.60721i	0.786793	−	0.617216i	$-0.211740\pi$
$348$	−21.6242	+	15.2492i	−1.15918	+	0.817446i
$349$	14.5272			0.777621			0.388810	−	0.921318i	$-0.372886\pi$
$349$	14.5272			0.777621			0.388810	+	0.921318i	$0.372886\pi$
$350$	37.5728	−	10.9483i	2.00835	−	0.585212i
$351$	−14.0196	+	10.9929i	−0.748311	+	0.586755i
$352$	0.735185	−	0.915296i	0.0391855	−	0.0487855i
$353$	−2.94141	−	1.69822i	−0.156555	−	0.0903873i	0.419676	−	0.907674i	$-0.362144\pi$
$353$	−2.94141	−	1.69822i	−0.156555	−	0.0903873i	−0.576231	+	0.817287i	$0.695477\pi$
$354$	−5.70076	+	1.95688i	−0.302992	+	0.104007i
$355$	28.3865	+	16.3889i	1.50660	+	0.869835i
$356$	−6.85008	+	13.1539i	−0.363053	+	0.697156i
$357$	0.834237	+	17.6895i	0.0441525	+	0.936226i
$358$	8.35017	−	8.72135i	0.441320	−	0.460937i
$359$	13.3436	+	23.1118i	0.704248	+	1.21979i	0.966962	+	0.254920i	$0.0820491\pi$
$359$	13.3436	+	23.1118i	0.704248	+	1.21979i	−0.262714	+	0.964874i	$0.584618\pi$
$360$	13.7037	+	30.5821i	0.722246	+	1.61182i
$361$	6.24897	+	10.8235i	0.328893	+	0.569660i
$362$	6.46002	+	22.1697i	0.339531	+	1.16521i
$363$	−15.9701	+	10.2527i	−0.838215	+	0.538126i
$364$	−8.27010	+	15.8807i	−0.433471	+	0.832376i
$365$	−49.7372	−	28.7158i	−2.60336	−	1.50305i
$366$	0.284462	+	0.247753i	0.0148691	+	0.0129503i
$367$	−24.6665	+	14.2412i	−1.28758	+	0.743387i	−0.978223	−	0.207558i	$-0.933448\pi$
$367$	−24.6665	+	14.2412i	−1.28758	+	0.743387i	−0.309361	+	0.950945i	$0.600115\pi$
$368$	−3.58226	−	5.11937i	−0.186738	−	0.266865i
$369$	14.6871	+	6.72425i	0.764582	+	0.350050i
$370$	−10.0841	+	41.1964i	−0.524246	+	2.14170i
$371$	−3.13642			−0.162835
$372$	−7.78173	−	17.6478i	−0.403464	−	0.914995i
$373$	13.9489			0.722249			0.361124	−	0.932518i	$-0.382393\pi$
$373$	13.9489			0.722249			0.361124	+	0.932518i	$0.382393\pi$
$374$	0.273246	−	1.11629i	0.0141292	−	0.0577220i
$375$	17.5635	−	34.0287i	0.906973	−	1.75723i
$376$	−26.5927	−	23.3321i	−1.37141	−	1.20326i
$377$	−22.6804	+	13.0945i	−1.16810	+	0.674403i
$378$	11.1845	−	15.5911i	0.575267	−	0.801920i
$379$	10.1809	+	5.87792i	0.522955	+	0.301928i	0.738143	−	0.674644i	$-0.235703\pi$
$379$	10.1809	+	5.87792i	0.522955	+	0.301928i	−0.215188	+	0.976573i	$0.569036\pi$
$380$	−39.3188	−	20.4758i	−2.01701	−	1.05039i
$381$	−11.6003	−	18.0693i	−0.594303	−	0.925719i
$382$	−1.72900	−	5.93364i	−0.0884634	−	0.303592i
$383$	8.97682	+	15.5483i	0.458694	+	0.794481i	0.998892	−	0.0470564i	$-0.0149840\pi$
$383$	8.97682	+	15.5483i	0.458694	+	0.794481i	−0.540198	+	0.841538i	$0.681651\pi$
$384$	−10.8388	+	16.3255i	−0.553115	+	0.833105i
$385$	1.07010	+	1.85347i	0.0545376	+	0.0944618i
$386$	−16.3386	+	17.0649i	−0.831612	+	0.868578i
$387$	−0.0372983	−	0.394565i	−0.00189598	−	0.0200568i
$388$	2.39351	+	1.24645i	0.121512	+	0.0632791i
$389$	14.7547	+	8.51860i	0.748091	+	0.431910i	0.825004	−	0.565127i	$-0.191173\pi$
$389$	14.7547	+	8.51860i	0.748091	+	0.431910i	−0.0769129	+	0.997038i	$0.524506\pi$
$390$	10.7689	+	31.3717i	0.545303	+	1.58857i
$391$	−5.29706	−	3.05826i	−0.267884	−	0.154663i
$392$	−0.100519	+	0.504730i	−0.00507697	+	0.0254927i
$393$	5.84329	−	3.75134i	0.294755	−	0.189230i
$394$	−14.7378	+	4.29445i	−0.742482	+	0.216351i
$395$	16.3950			0.824921
$396$	−0.982692	+	0.764764i	−0.0493821	+	0.0384309i
$397$	−9.59407	+	16.6174i	−0.481512	+	0.834004i	−0.999775	−	0.0212177i	$-0.993246\pi$
$397$	−9.59407	+	16.6174i	−0.481512	+	0.834004i	0.518263	+	0.855222i	$0.326579\pi$
$398$	−22.9100	+	6.67573i	−1.14837	+	0.334624i
$399$	1.19570	+	25.3542i	0.0598601	+	1.26930i
$400$	42.2319	−	3.68165i	2.11160	−	0.184082i
$401$		−	21.4586i		−	1.07159i	−0.844347	−	0.535797i	$-0.820011\pi$
$401$		−	21.4586i		−	1.07159i	0.844347	−	0.535797i	$-0.179989\pi$
$402$	−11.8257	−	2.31033i	−0.589812	−	0.115229i
$403$	−6.08998	−	18.0921i	−0.303363	−	0.901233i
$404$	2.85538	−	5.48307i	0.142061	−	0.272793i
$405$	−6.66063	−	34.9153i	−0.330969	−	1.73495i
$406$	19.5067	−	20.3738i	0.968103	−	1.01114i
$407$	−1.57593			−0.0781160
$408$	−2.85633	+	18.9690i	−0.141410	+	0.939104i
$409$	−5.88083	+	10.1859i	−0.290788	+	0.503660i	−0.973996	−	0.226564i	$-0.927251\pi$
$409$	−5.88083	+	10.1859i	−0.290788	+	0.503660i	0.683208	+	0.730224i	$0.260584\pi$
$410$	20.7981	−	21.7226i	1.02715	−	1.07280i
$411$	33.2486	−	1.56801i	1.64003	−	0.0773441i
$412$	13.8539	−	0.602729i	0.682535	−	0.0296943i
$413$	5.56425	−	3.21252i	0.273799	−	0.158078i
$414$	2.44457	+	6.15992i	0.120144	+	0.302744i
$415$	−27.7337	−	16.0120i	−1.36139	−	0.786000i
$416$	−12.1457	+	15.1212i	−0.595491	+	0.741378i
$417$	−1.05606	+	2.04608i	−0.0517153	+	0.100197i
$418$	0.391641	−	1.59997i	0.0191558	−	0.0782570i
$419$	−0.826543			−0.0403793			−0.0201896	−	0.999796i	$-0.506427\pi$
$419$	−0.826543			−0.0403793			−0.0201896	+	0.999796i	$0.506427\pi$
$420$	−20.5878	−	29.1945i	−1.00458	−	1.42455i
$421$	3.90144	+	6.75750i	0.190145	+	0.329340i	0.945298	−	0.326208i	$-0.105771\pi$
$421$	3.90144	+	6.75750i	0.190145	+	0.329340i	−0.755153	+	0.655548i	$0.772438\pi$
$422$	3.84876	+	3.68495i	0.187355	+	0.179381i
$423$	21.7367	+	30.5863i	1.05687	+	1.48716i
$424$	−3.33198	−	0.663577i	−0.161815	−	0.0322261i
$425$	35.9387	−	20.7492i	1.74328	−	1.00648i
$426$	3.89794	−	19.9521i	0.188856	−	0.966681i
$427$	−0.348247	−	0.201061i	−0.0168529	−	0.00973000i
$428$	24.3016	−	15.4766i	1.17466	−	0.748088i
$429$	−1.03712	+	0.665819i	−0.0500724	+	0.0321460i
$430$	−0.716708	−	0.175436i	−0.0345627	−	0.00846028i
$431$	2.78276	−	4.81989i	0.134041	−	0.232166i	−0.791190	−	0.611571i	$-0.790538\pi$
$431$	2.78276	−	4.81989i	0.134041	−	0.232166i	0.925231	+	0.379405i	$0.123871\pi$
$432$	15.1805	−	14.1969i	0.730371	−	0.683051i
$433$	9.56018			0.459433			0.229716	−	0.973258i	$-0.426220\pi$
$433$	9.56018			0.459433			0.229716	+	0.973258i	$0.426220\pi$
$434$	11.7485	+	16.8728i	0.563944	+	0.809922i
$435$	−2.46145	−	52.1936i	−0.118018	−	2.50249i
$436$	−9.12958	−	4.75435i	−0.437228	−	0.227692i
$437$	−7.59223	−	4.38338i	−0.363186	−	0.209685i
$438$	−6.82974	+	34.9589i	−0.326338	+	1.67040i
$439$	−21.9459	+	12.6705i	−1.04742	+	0.604728i	−0.921926	−	0.387366i	$-0.873385\pi$
$439$	−21.9459	+	12.6705i	−1.04742	+	0.604728i	−0.125494	+	0.992094i	$0.540052\pi$
$440$	0.744686	+	2.19545i	0.0355015	+	0.104664i
$441$	0.227230	−	0.496316i	0.0108205	−	0.0236341i
$442$	−4.51418	+	18.4417i	−0.214717	+	0.877184i
$443$	6.16615	+	10.6801i	0.292963	+	0.507426i	0.974509	−	0.224349i	$-0.0720255\pi$
$443$	6.16615	+	10.6801i	0.292963	+	0.507426i	−0.681546	+	0.731775i	$0.738692\pi$
$444$	26.1970	−	2.38006i	1.24325	−	0.112953i
$445$	−14.6432	−	25.3628i	−0.694154	−	1.20231i
$446$	23.5491	+	22.5469i	1.11508	+	1.06763i
$447$	−18.8439	−	29.3523i	−0.891286	−	1.38832i
$448$	8.00287	−	19.2953i	0.378100	−	0.911618i
$449$			26.5483i			1.25289i	0.779465	+	0.626446i	$0.215491\pi$
$449$			26.5483i			1.25289i	−0.779465	+	0.626446i	$0.784509\pi$
$450$	−44.4865	−	6.53293i	−2.09711	−	0.307965i
$451$	0.967744	+	0.558727i	0.0455693	+	0.0263094i
$452$	14.5817	−	0.634389i	0.685864	−	0.0298391i
$453$	−5.02509	+	9.73597i	−0.236100	+	0.457436i
$454$	−1.29209	−	4.43424i	−0.0606408	−	0.208109i
$455$	−17.6787	−	30.6204i	−0.828791	−	1.43551i
$456$	−4.09396	+	27.1881i	−0.191717	+	1.27320i
$457$	−11.3089			−0.529008			−0.264504	−	0.964385i	$-0.585208\pi$
$457$	−11.3089			−0.529008			−0.264504	+	0.964385i	$0.585208\pi$
$458$	22.0370	−	23.0166i	1.02972	−	1.07550i
$459$	7.58890	−	18.8782i	0.354220	−	0.881159i
$460$	12.3268	−	0.536291i	0.574742	−	0.0250047i
$461$		−	3.46910i		−	0.161572i	−0.996731	−	0.0807860i	$-0.974257\pi$
$461$		−	3.46910i		−	0.161572i	0.996731	−	0.0807860i	$-0.0257430\pi$
$462$	0.871793	−	1.00096i	0.0405595	−	0.0465690i
$463$			17.4348i			0.810266i	0.914258	+	0.405133i	$0.132775\pi$
$463$			17.4348i			0.810266i	−0.914258	+	0.405133i	$0.867225\pi$
$464$	25.0336	−	17.5171i	1.16215	−	0.813213i
$465$	37.6491	+	5.75858i	1.74594	+	0.267048i
$466$	4.59593	−	18.7757i	0.212903	−	0.869769i
$467$	24.2213			1.12083			0.560413	−	0.828213i	$-0.310642\pi$
$467$	24.2213			1.12083			0.560413	+	0.828213i	$0.310642\pi$
$468$	16.2346	−	12.6343i	0.750446	−	0.584023i
$469$	12.8444			0.593100
$470$	67.0709	−	19.5438i	3.09375	−	0.901486i
$471$	−34.6229	−	17.8702i	−1.59534	−	0.823414i
$472$	6.59087	−	2.23559i	0.303369	−	0.102902i
$473$		−	0.0274170i		−	0.00126064i
$474$	−3.30138	−	9.61753i	−0.151637	−	0.441748i
$475$	51.5106	−	29.7397i	2.36347	−	1.36455i
$476$	−0.888801	−	20.4294i	−0.0407381	−	0.936381i
$477$	3.27644	+	1.50006i	0.150018	+	0.0686831i
$478$	−2.59761	−	8.91457i	−0.118812	−	0.407743i
$479$	−4.12563	+	7.14581i	−0.188505	+	0.326500i	−0.944752	−	0.327786i	$-0.893698\pi$
$479$	−4.12563	+	7.14581i	−0.188505	+	0.326500i	0.756247	+	0.654286i	$0.227031\pi$
$480$	−15.6947	−	35.3707i	−0.716364	−	1.61444i
$481$	26.0353			1.18711
$482$	−14.9674	+	15.6327i	−0.681747	+	0.712051i
$483$	−3.81659	−	5.94494i	−0.173661	−	0.270504i
$484$	18.4838	−	11.7714i	0.840172	−	0.535066i
$485$	−4.61505	+	2.66450i	−0.209559	+	0.120989i
$486$	−19.1406	+	10.9379i	−0.868234	+	0.496155i
$487$	11.8489	−	6.84094i	0.536923	−	0.309993i	−0.206908	−	0.978360i	$-0.566340\pi$
$487$	11.8489	−	6.84094i	0.536923	−	0.309993i	0.743831	+	0.668368i	$0.233007\pi$
$488$	−0.327423	−	0.287277i	−0.0148217	−	0.0130044i
$489$	−12.9641	+	25.1176i	−0.586257	+	1.13586i
$490$	−0.734064	−	0.702822i	−0.0331616	−	0.0317503i
$491$	−8.58572	−	14.8709i	−0.387468	−	0.671114i	0.604640	−	0.796499i	$-0.293317\pi$
$491$	−8.58572	−	14.8709i	−0.387468	−	0.671114i	−0.992108	+	0.125384i	$0.959984\pi$
$492$	−16.9308	−	7.82629i	−0.763300	−	0.352836i
$493$	14.9548	−	25.9025i	0.673530	−	1.16659i
$494$	−6.47013	+	26.4324i	−0.291105	+	1.18925i
$495$	−0.231413	−	2.44802i	−0.0104012	−	0.110030i
$496$	8.91120	+	20.4105i	0.400125	+	0.916461i
$497$			21.6709i			0.972071i
$498$	−3.80830	+	19.4932i	−0.170654	+	0.873513i
$499$	24.9843	+	14.4247i	1.11845	+	0.645737i	0.941005	−	0.338393i	$-0.109883\pi$
$499$	24.9843	+	14.4247i	1.11845	+	0.645737i	0.177445	+	0.984131i	$0.443217\pi$
$500$	−20.4237	+	39.2187i	−0.913375	+	1.75391i
$501$	−24.1137	+	15.4808i	−1.07732	+	0.691629i
$502$	−19.2235	+	20.0780i	−0.857986	+	0.896125i
$503$	−20.0784	+	34.7769i	−0.895254	+	1.55062i	−0.0617635	+	0.998091i	$0.519672\pi$
$503$	−20.0784	+	34.7769i	−0.895254	+	1.55062i	−0.833490	+	0.552534i	$0.813661\pi$
$504$	−12.9803	+	17.9558i	−0.578187	+	0.799816i
$505$	6.10386	+	10.5722i	0.271618	+	0.470456i
$506$	0.128257	+	0.440157i	0.00570172	+	0.0195674i
$507$	−1.81426	+	1.16473i	−0.0805739	+	0.0517277i
$508$	13.3187	+	20.9134i	0.590923	+	0.927880i
$509$	11.1221	−	6.42137i	0.492980	−	0.284622i	−0.232830	−	0.972517i	$-0.574799\pi$
$509$	11.1221	−	6.42137i	0.492980	−	0.284622i	0.725810	+	0.687895i	$0.241465\pi$
$510$	−28.5653	−	24.8790i	−1.26489	−	1.10166i
$511$		−	37.9704i		−	1.67971i
$512$	12.5842	−	18.8053i	0.556149	−	0.831083i
$513$	10.8771	−	27.0580i	0.480236	−	1.19464i
$514$	20.8984	−	6.08957i	0.921788	−	0.268599i
$515$	−13.6918	+	23.7148i	−0.603331	+	1.04500i
$516$	0.0414067	+	0.455758i	0.00182283	+	0.0200636i
$517$	1.29790	+	2.24803i	0.0570817	+	0.0988684i
$518$	−26.9212	+	7.84455i	−1.18285	+	0.344670i
$519$	−9.05322	+	0.426951i	−0.397392	+	0.0187411i
$520$	−12.3026	−	36.2700i	−0.539506	−	1.59055i
$521$	−8.48268	−	4.89748i	−0.371633	−	0.214562i	0.302539	−	0.953137i	$-0.402166\pi$
$521$	−8.48268	−	4.89748i	−0.371633	−	0.214562i	−0.674172	+	0.738575i	$0.735499\pi$
$522$	−30.1218	+	11.9539i	−1.31840	+	0.523207i
$523$		−	26.4240i		−	1.15544i	−0.816235	−	0.577721i	$-0.803942\pi$
$523$		−	26.4240i		−	1.15544i	0.816235	−	0.577721i	$-0.196058\pi$
$524$	−6.76300	+	4.30704i	−0.295443	+	0.188154i
$525$	47.8777	−	2.25791i	2.08955	−	0.0985435i
$526$	18.6633	+	4.56841i	0.813758	+	0.199192i
$527$	16.3545	+	14.4166i	0.712414	+	0.627996i
$528$	1.13793	−	0.878930i	0.0495219	−	0.0382505i
$529$	−20.5600			−0.893912
$530$	4.63969	−	4.84594i	0.201535	−	0.210494i
$531$	−7.34912	+	0.694715i	−0.318924	+	0.0301481i
$532$	−1.27391	−	29.2813i	−0.0552310	−	1.26951i
$533$	−15.9877	−	9.23049i	−0.692503	−	0.399817i
$534$	−11.9295	+	13.6971i	−0.516241	+	0.592731i
$535$			56.8942i			2.45975i
$536$	13.6453	+	2.71751i	0.589387	+	0.117379i
$537$	12.4441	−	7.98901i	0.537004	−	0.344751i
$538$	18.6361	−	5.43036i	0.803459	−	0.234120i
$539$	0.0188808	−	0.0327026i	0.000813256	−	0.00140860i
$540$	7.54396	+	40.3445i	0.324640	+	1.73615i
$541$	4.50911	−	7.81002i	0.193862	−	0.335779i	−0.752665	−	0.658404i	$-0.771232\pi$
$541$	4.50911	−	7.81002i	0.193862	−	0.335779i	0.946527	+	0.322625i	$0.104565\pi$
$542$	−0.589616	+	2.40875i	−0.0253262	+	0.103465i
$543$	1.33227	+	28.2501i	0.0571734	+	1.21233i
$544$	3.37806	−	21.8913i	0.144833	−	0.938582i
$545$	17.6032	−	10.1632i	0.754039	−	0.435345i
$546$	−14.4025	+	16.5365i	−0.616371	+	0.707696i
$547$	−12.4420	+	7.18337i	−0.531980	+	0.307139i	−0.741822	−	0.670596i	$-0.766038\pi$
$547$	−12.4420	+	7.18337i	−0.531980	+	0.307139i	0.209842	+	0.977735i	$0.432705\pi$
$548$	−38.3985	+	1.67056i	−1.64030	+	0.0713630i
$549$	0.267633	+	0.376594i	0.0114223	+	0.0160726i
$550$	−3.02131	−	0.739557i	−0.128829	−	0.0315348i
$551$	21.4346	−	37.1258i	0.913144	−	1.58161i
$552$	−2.79679	−	7.12311i	−0.119039	−	0.303180i
$553$	5.41971	+	9.38722i	0.230470	+	0.399185i
$554$	20.8405	+	5.10134i	0.885427	+	0.216735i
$555$	−23.8244	+	46.1590i	−1.01129	+	1.95934i
$556$	1.22804	−	2.35815i	0.0520804	−	0.100008i
$557$			2.78690i			0.118085i	0.998255	+	0.0590423i	$0.0188047\pi$
$557$			2.78690i			0.118085i	−0.998255	+	0.0590423i	$0.981195\pi$
$558$	−4.20315	−	23.2451i	−0.177934	−	0.984043i
$559$			0.452944i			0.0191575i
$560$	23.6496	+	33.7974i	0.999379	+	1.42820i
$561$	0.645563	−	1.25076i	0.0272557	−	0.0528071i
$562$	−2.89447	+	11.8247i	−0.122096	+	0.498797i
$563$	−5.77934	−	10.0101i	−0.243570	−	0.421876i	0.718158	−	0.695880i	$-0.244985\pi$
$563$	−5.77934	−	10.0101i	−0.243570	−	0.421876i	−0.961729	+	0.274004i	$0.911652\pi$
$564$	−24.9704	−	35.4093i	−1.05144	−	1.49100i
$565$	−14.4109	+	24.9605i	−0.606273	+	1.05010i
$566$	3.44171	−	14.0604i	0.144666	−	0.591002i
$567$	17.7895	−	15.3556i	0.747089	−	0.644876i
$568$	−4.58494	+	23.0221i	−0.192380	+	0.965986i
$569$	−23.0044	+	13.2816i	−0.964394	+	0.556793i	−0.897522	−	0.440969i	$-0.854635\pi$
$569$	−23.0044	+	13.2816i	−0.964394	+	0.556793i	−0.0668711	+	0.997762i	$0.521302\pi$
$570$	−40.9424	−	35.6589i	−1.71489	−	1.49359i
$571$	−6.87059	+	3.96674i	−0.287525	+	0.166003i	−0.636825	−	0.771008i	$-0.719753\pi$
$571$	−6.87059	+	3.96674i	−0.287525	+	0.166003i	0.349300	+	0.937011i	$0.386419\pi$
$572$	1.20035	−	0.764449i	0.0501893	−	0.0319632i
$573$	−0.356579	−	7.56103i	−0.0148963	−	0.315867i
$574$	19.3129	+	4.72742i	0.806105	+	0.197319i
$575$	−8.27737	+	14.3368i	−0.345190	+	0.597887i
$576$	−17.5886	+	16.3292i	−0.732857	+	0.680383i
$577$	19.6286	−	33.9977i	0.817150	−	1.41534i	−0.0906243	−	0.995885i	$-0.528886\pi$
$577$	19.6286	−	33.9977i	0.817150	−	1.41534i	0.907774	−	0.419460i	$-0.137780\pi$
$578$	0.659714	+	2.26403i	0.0274405	+	0.0941711i
$579$	−24.3491	+	15.6319i	−1.01192	+	0.649640i
$580$	2.62245	+	60.2779i	0.108891	+	2.50290i
$581$		−	21.1725i		−	0.878383i
$582$	2.49235	+	2.17072i	0.103311	+	0.0899792i
$583$	0.215887	+	0.124642i	0.00894111	+	0.00516215i
$584$	8.03346	−	40.3380i	0.332427	−	1.66920i
$585$	3.82307	+	40.4427i	0.158064	+	1.67210i
$586$	−23.2551	−	22.2654i	−0.960659	−	0.919774i
$587$	−46.7434			−1.92930			−0.964652	−	0.263525i	$-0.915115\pi$
$587$	−46.7434			−1.92930			−0.964652	+	0.263525i	$0.915115\pi$
$588$	−0.264471	+	0.572136i	−0.0109066	+	0.0235945i
$589$	23.4408	+	20.6631i	0.965861	+	0.851410i
$590$	−3.26765	+	13.3493i	−0.134527	+	0.549583i
$591$	−18.7799	+	0.885662i	−0.772502	+	0.0364313i
$592$	−30.2595	+	2.63793i	−1.24366	+	0.108418i
$593$		−	33.9827i		−	1.39550i	−0.716340	−	0.697751i	$-0.754184\pi$
$593$		−	33.9827i		−	1.39550i	0.716340	−	0.697751i	$-0.245816\pi$
$594$	−1.38945	+	0.628696i	−0.0570097	+	0.0257957i
$595$	34.9705	+	20.1902i	1.43365	+	0.827719i
$596$	21.6353	+	33.9722i	0.886217	+	1.39156i
$597$	−29.1934	+	1.37676i	−1.19481	+	0.0563471i
$598$	−2.11888	−	7.27164i	−0.0866474	−	0.297359i
$599$	3.14601	+	5.44904i	0.128542	+	0.222642i	0.923112	−	0.384531i	$-0.125637\pi$
$599$	3.14601	+	5.44904i	0.128542	+	0.222642i	−0.794570	+	0.607173i	$0.792304\pi$
$600$	51.3407	+	7.73085i	2.09598	+	0.315611i
$601$	0.0599165	−	0.103778i	0.00244404	−	0.00423321i	−0.864801	−	0.502115i	$-0.832555\pi$
$601$	0.0599165	−	0.103778i	0.00244404	−	0.00423321i	0.867245	+	0.497882i	$0.165889\pi$
$602$	−0.136474	−	0.468357i	−0.00556228	−	0.0190888i
$603$	−13.4178	−	6.14313i	−0.546417	−	0.250168i
$604$	5.84344	−	11.2209i	0.237766	−	0.456572i
$605$			43.2737i			1.75932i
$606$	4.97269	−	5.70948i	0.202002	−	0.231932i
$607$	−3.75868	+	2.17008i	−0.152560	+	0.0880807i	−0.574337	−	0.818619i	$-0.694740\pi$
$607$	−3.75868	+	2.17008i	−0.152560	+	0.0880807i	0.421777	+	0.906700i	$0.361407\pi$
$608$	4.84175	−	31.3766i	0.196359	−	1.27249i
$609$	29.0706	−	18.6630i	1.17800	−	0.756265i
$610$	0.825810	−	0.240632i	0.0334361	−	0.00974292i
$611$	−21.4421	−	37.1388i	−0.867454	−	1.50247i
$612$	−8.84234	+	21.7666i	−0.357431	+	0.879861i
$613$	−0.674030	+	1.16745i	−0.0272238	+	0.0471531i	−0.879316	−	0.476238i	$-0.842000\pi$
$613$	−0.674030	+	1.16745i	−0.0272238	+	0.0471531i	0.852093	+	0.523391i	$0.175333\pi$
$614$	−18.9124	−	18.1075i	−0.763242	−	0.730759i
$615$	30.9951	−	19.8986i	1.24984	−	0.802388i
$616$	−1.01087	+	1.15213i	−0.0407290	+	0.0464208i
$617$	14.4949	+	8.36865i	0.583544	+	0.336909i	0.762540	−	0.646940i	$-0.223952\pi$
$617$	14.4949	+	8.36865i	0.583544	+	0.336909i	−0.178997	+	0.983850i	$0.557285\pi$
$618$	16.6685	+	3.25644i	0.670505	+	0.130993i
$619$		−	15.8050i		−	0.635256i	−0.948215	−	0.317628i	$-0.897114\pi$
$619$		−	15.8050i		−	0.635256i	0.948215	−	0.317628i	$-0.102886\pi$
$620$	−43.4489	−	6.80793i	−1.74495	−	0.273413i
$621$	1.14368	+	8.03572i	0.0458944	+	0.322462i
$622$	−14.0965	−	3.45054i	−0.565217	−	0.138354i
$623$	9.68124	−	16.7684i	0.387871	−	0.671812i
$624$	−18.7992	+	14.5204i	−0.752570	+	0.581282i
$625$	−17.1640	−	29.7289i	−0.686560	−	1.18916i
$626$	−1.98473	+	2.07296i	−0.0793260	+	0.0828521i
$627$	0.925280	−	1.79270i	0.0369521	−	0.0715936i
$628$	39.9036	+	20.7804i	1.59233	+	0.829227i
$629$	−25.7503	+	14.8670i	−1.02673	+	0.592785i
$630$	−16.1388	−	40.6670i	−0.642983	−	1.62021i
$631$	11.5518	−	6.66943i	0.459870	−	0.265506i	−0.252120	−	0.967696i	$-0.581128\pi$
$631$	11.5518	−	6.66943i	0.459870	−	0.265506i	0.711989	+	0.702190i	$0.247794\pi$
$632$	3.77158	+	11.1192i	0.150025	+	0.442298i
$633$	3.52558	+	5.49163i	0.140129	+	0.218273i
$634$	9.64354	+	9.23311i	0.382994	+	0.366694i
$635$	−48.9617			−1.94299
$636$	−3.77697	−	1.74591i	−0.149766	−	0.0692297i
$637$	−0.311922	+	0.540265i	−0.0123588	+	0.0214061i
$638$	−2.15235	+	0.627174i	−0.0852125	+	0.0248300i
$639$	10.3646	−	22.6383i	0.410016	−	0.895559i
$640$	17.9737	+	40.9084i	0.710472	+	1.61704i
$641$	8.90301	−	5.14016i	0.351648	−	0.203024i	−0.313763	−	0.949501i	$-0.601590\pi$
$641$	8.90301	−	5.14016i	0.351648	−	0.203024i	0.665411	+	0.746477i	$0.268256\pi$
$642$	33.3750	−	11.4565i	1.31721	−	0.452153i
$643$			2.24083i			0.0883697i	0.999023	+	0.0441849i	$0.0140691\pi$
$643$			2.24083i			0.0883697i	−0.999023	+	0.0441849i	$0.985931\pi$
$644$	4.38196	+	6.88065i	0.172673	+	0.271136i
$645$	−0.803044	−	0.414480i	−0.0316198	−	0.0163202i
$646$	−8.69441	−	29.8378i	−0.342077	−	1.17395i
$647$	26.1082			1.02642			0.513210	−	0.858263i	$-0.328456\pi$
$647$	26.1082			1.02642			0.513210	+	0.858263i	$0.328456\pi$
$648$	22.1475	−	12.5494i	0.870038	−	0.492985i
$649$	−0.510666			−0.0200454
$650$	49.9137	+	12.2179i	1.95778	+	0.479226i
$651$	9.14854	+	23.4602i	0.358560	+	0.919479i
$652$	15.0753	−	28.9485i	0.590395	−	1.13371i
$653$		−	32.7751i		−	1.28259i	−0.767296	−	0.641293i	$-0.778398\pi$
$653$		−	32.7751i		−	1.28259i	0.767296	−	0.641293i	$-0.221602\pi$
$654$	−9.50657	−	8.27978i	−0.371736	−	0.323765i
$655$		−	15.8333i		−	0.618659i
$656$	19.5169	+	9.10825i	0.762008	+	0.355617i
$657$	−18.1602	+	39.6656i	−0.708497	+	1.54750i
$658$	33.3618	+	31.9419i	1.30058	+	1.24523i
$659$	38.0025			1.48037			0.740185	−	0.672404i	$-0.234738\pi$
$659$	38.0025			1.48037			0.740185	+	0.672404i	$0.234738\pi$
$660$	0.256902	+	2.82769i	0.00999991	+	0.110068i
$661$	−8.45454	−	14.6437i	−0.328843	−	0.569574i	0.653439	−	0.756979i	$-0.273326\pi$
$661$	−8.45454	−	14.6437i	−0.328843	−	0.569574i	−0.982283	+	0.187405i	$0.939992\pi$
$662$	−18.0235	+	5.25187i	−0.700504	+	0.204120i
$663$	−10.6651	+	20.6632i	−0.414197	+	0.802494i
$664$	4.47950	−	22.4927i	0.173838	−	0.872885i
$665$	50.1229	+	28.9385i	1.94368	+	1.12219i
$666$	31.8749	+	4.68089i	1.23513	+	0.181381i
$667$			11.9317i			0.461996i
$668$	27.9091	−	17.7740i	1.07984	−	0.687696i
$669$	21.5717	+	33.6013i	0.834011	+	1.29910i
$670$	−19.0007	+	19.8453i	−0.734061	+	0.766692i
$671$	0.0159804	+	0.0276789i	0.000616917	+	0.00106853i
$672$	15.0638	−	20.6788i	0.581100	−	0.797703i
$673$	10.4297	+	18.0648i	0.402036	+	0.696347i	0.993972	−	0.109639i	$-0.0349694\pi$
$673$	10.4297	+	18.0648i	0.402036	+	0.696347i	−0.591936	+	0.805985i	$0.701636\pi$
$674$	−23.3162	−	5.70736i	−0.898108	−	0.219839i
$675$	−51.0950	−	20.5398i	−1.96665	−	0.790579i
$676$	2.09981	−	1.33727i	0.0807620	−	0.0514335i
$677$	−12.7648	+	7.36976i	−0.490591	+	0.283243i	−0.724820	−	0.688939i	$-0.758077\pi$
$677$	−12.7648	+	7.36976i	−0.490591	+	0.283243i	0.234228	+	0.972182i	$0.424744\pi$
$678$	17.5440	+	3.42749i	0.673775	+	0.131632i
$679$	−3.05121	−	1.76162i	−0.117095	−	0.0676046i
$680$	32.8794	+	28.8479i	1.26087	+	1.10627i
$681$	−0.266473	−	5.65039i	−0.0102113	−	0.216523i
$682$	−0.138141	−	1.62828i	−0.00528969	−	0.0623502i
$683$	−31.9631			−1.22304			−0.611518	−	0.791231i	$-0.709441\pi$
$683$	−31.9631			−1.22304			−0.611518	+	0.791231i	$0.709441\pi$
$684$	−12.6737	+	31.1978i	−0.484589	+	1.19288i
$685$	37.9490	−	65.7295i	1.44996	−	2.51140i
$686$	6.30563	−	25.7603i	0.240750	−	0.983534i
$687$	32.8415	−	21.0839i	1.25298	−	0.804401i
$688$	−0.0458930	−	0.526435i	−0.00174965	−	0.0200701i
$689$	−3.56657	−	2.05916i	−0.135875	−	0.0784477i
$690$	14.8311	+	2.89749i	0.564611	+	0.110305i
$691$	−9.86252	+	5.69413i	−0.375188	+	0.216615i	−0.675722	−	0.737156i	$-0.736168\pi$
$691$	−9.86252	+	5.69413i	−0.375188	+	0.216615i	0.300535	+	0.953771i	$0.402835\pi$
$692$	10.4555	−	0.454876i	0.397458	−	0.0172918i
$693$	1.32516	−	0.941745i	0.0503386	−	0.0357739i
$694$	−33.8109	+	35.3138i	−1.28344	+	1.34050i
$695$	2.62513	+	4.54687i	0.0995770	+	0.172472i
$696$	34.8318	−	13.6762i	1.32030	−	0.518396i
$697$	21.0836			0.798599
$698$	−19.9554	−	4.88468i	−0.755321	−	0.184888i
$699$	10.8582	−	21.0375i	0.410696	−	0.795711i
$700$	−55.2935	+	2.40560i	−2.08990	+	0.0909230i
$701$	25.8765	+	14.9398i	0.977342	+	0.564269i	0.901467	−	0.432849i	$-0.142492\pi$
$701$	25.8765	+	14.9398i	0.977342	+	0.564269i	0.0758752	+	0.997117i	$0.475825\pi$
$702$	22.9544	−	10.3864i	0.866360	−	0.392010i
$703$	−36.9077	+	21.3087i	−1.39200	+	0.803673i
$704$	−1.31766	+	1.01010i	−0.0496611	+	0.0380697i
$705$	85.4661	−	4.03059i	3.21884	−	0.151801i
$706$	3.46948	+	3.32182i	0.130575	+	0.125018i
$707$	−4.03552	+	6.98973i	−0.151771	+	0.262876i
$708$	8.48890	−	0.771237i	0.319032	−	0.0289849i
$709$	−45.4639			−1.70743			−0.853717	−	0.520737i	$-0.825657\pi$
$709$	−45.4639			−1.70743			−0.853717	+	0.520737i	$0.825657\pi$
$710$	−33.4826	−	32.0576i	−1.25658	−	1.20310i
$711$	−1.17203	−	12.3984i	−0.0439544	−	0.464977i
$712$	13.8326	−	15.7657i	0.518399	−	0.590844i
$713$	−8.52571	−	1.71851i	−0.319290	−	0.0643587i
$714$	4.80204	−	24.5798i	0.179712	−	0.919876i
$715$			2.81023i			0.105097i
$716$	−14.4028	+	9.17246i	−0.538258	+	0.342791i
$717$	−0.535716	−	11.3595i	−0.0200067	−	0.424229i
$718$	−10.5583	−	36.2344i	−0.394034	−	1.35226i
$719$	−13.7548	+	23.8239i	−0.512966	+	0.888483i	0.486921	+	0.873446i	$0.338120\pi$
$719$	−13.7548	+	23.8239i	−0.512966	+	0.888483i	−0.999887	+	0.0150372i	$0.995213\pi$
$720$	−8.54107	−	46.6172i	−0.318307	−	1.73732i
$721$	−18.1044			−0.674243
$722$	−4.94460	−	16.9690i	−0.184019	−	0.631522i
$723$	−22.3057	+	14.3200i	−0.829558	+	0.532568i
$724$	−1.41941	−	32.6257i	−0.0527521	−	1.21253i
$725$	−70.1067	−	40.4761i	−2.60370	−	1.50325i
$726$	25.3849	−	8.71381i	0.942124	−	0.323400i
$727$	−32.1309	−	18.5508i	−1.19167	−	0.688010i	−0.232984	−	0.972481i	$-0.574849\pi$
$727$	−32.1309	−	18.5508i	−1.19167	−	0.688010i	−0.958685	+	0.284471i	$0.908182\pi$
$728$	16.7001	−	19.0339i	0.618947	−	0.705444i
$729$	−25.9279	+	7.53296i	−0.960292	+	0.278998i
$730$	58.6664	+	56.1695i	2.17134	+	2.07893i
$731$	−0.258646	−	0.447988i	−0.00956636	−	0.0165694i
$732$	−0.307448	−	0.435977i	−0.0113636	−	0.0161142i
$733$	−1.33480	−	2.31194i	−0.0493018	−	0.0853933i	0.840321	−	0.542089i	$-0.182366\pi$
$733$	−1.33480	−	2.31194i	−0.0493018	−	0.0853933i	−0.889623	+	0.456695i	$0.849033\pi$
$734$	38.6720	−	11.2686i	1.42741	−	0.415932i
$735$	−0.672424	−	1.04741i	−0.0248027	−	0.0386341i
$736$	3.19944	+	8.23678i	0.117933	+	0.303612i
$737$	−0.884110	−	0.510441i	−0.0325666	−	0.0188023i
$738$	−17.9141	−	14.1753i	−0.659428	−	0.521800i
$739$	0.860757	−	0.496958i	0.0316635	−	0.0182809i	−0.484085	−	0.875021i	$-0.660847\pi$
$739$	0.860757	−	0.496958i	0.0316635	−	0.0182809i	0.515748	+	0.856740i	$0.327514\pi$
$740$	27.7042	−	53.1991i	1.01843	−	1.95564i
$741$	−15.2861	+	29.6164i	−0.561550	+	1.08799i
$742$	4.30837	+	1.05460i	0.158165	+	0.0387157i
$743$	−50.8770			−1.86650			−0.933249	−	0.359231i	$-0.883039\pi$
$743$	−50.8770			−1.86650			−0.933249	+	0.359231i	$0.883039\pi$
$744$	4.75547	+	26.8586i	0.174344	+	0.984685i
$745$	−79.5348			−2.91393
$746$	−19.1611	−	4.69026i	−0.701537	−	0.171723i
$747$	−10.1262	+	22.1177i	−0.370499	+	0.809245i
$748$	−0.750693	+	1.44152i	−0.0274481	+	0.0527073i
$749$	−32.5757	+	18.8076i	−1.19029	+	0.687215i
$750$	−35.5682	+	40.8382i	−1.29877	+	1.49120i
$751$	−33.6978	−	19.4555i	−1.22965	−	0.709940i	−0.262695	−	0.964879i	$-0.584611\pi$
$751$	−33.6978	−	19.4555i	−1.22965	−	0.709940i	−0.966957	+	0.254939i	$0.917945\pi$
$752$	28.6840	+	40.9920i	1.04600	+	1.49483i
$753$	−28.6485	+	18.3921i	−1.04401	+	0.670244i
$754$	35.5581	−	10.3613i	1.29495	−	0.377335i
$755$	12.4913	+	21.6356i	0.454606	+	0.787400i
$756$	−20.6061	+	17.6561i	−0.749435	+	0.642148i
$757$	3.37956	+	5.85356i	0.122832	+	0.212751i	0.920883	−	0.389838i	$-0.127469\pi$
$757$	3.37956	+	5.85356i	0.122832	+	0.212751i	−0.798051	+	0.602589i	$0.794136\pi$
$758$	−12.0086	−	11.4975i	−0.436172	−	0.417609i
$759$	0.0264510	+	0.560876i	0.000960109	+	0.0203585i
$760$	47.1257	+	41.3475i	1.70943	+	1.49983i
$761$	−4.28604	−	2.47455i	−0.155369	−	0.0897023i	0.420300	−	0.907385i	$-0.361925\pi$
$761$	−4.28604	−	2.47455i	−0.155369	−	0.0897023i	−0.575669	+	0.817683i	$0.695258\pi$
$762$	9.85918	+	28.7216i	0.357160	+	1.04048i
$763$	11.6382	+	6.71934i	0.421333	+	0.243257i
$764$	0.379901	+	8.73217i	0.0137443	+	0.315919i
$765$	−26.8753	−	37.8170i	−0.971679	−	1.36728i
$766$	−7.10305	−	24.3765i	−0.256644	−	0.880758i
$767$	8.43649			0.304624
$768$	20.3782	−	18.7811i	0.735333	−	0.677706i
$769$	−14.7527	+	25.5525i	−0.531997	+	0.921447i	0.467305	+	0.884096i	$0.345225\pi$
$769$	−14.7527	+	25.5525i	−0.531997	+	0.921447i	−0.999302	+	0.0373504i	$0.988108\pi$
$770$	−0.846737	−	2.90586i	−0.0305143	−	0.104720i
$771$	26.6301	−	1.25588i	0.959059	−	0.0452293i
$772$	28.1816	−	17.9475i	1.01428	−	0.645946i
$773$			7.73134i			0.278077i	0.990287	+	0.139039i	$0.0444012\pi$
$773$			7.73134i			0.278077i	−0.990287	+	0.139039i	$0.955599\pi$
$774$	−0.0814351	+	0.554539i	−0.00292713	+	0.0199325i
$775$	39.0194	−	44.2645i	1.40162	−	1.59003i
$776$	−2.86875	−	2.51701i	−0.102982	−	0.0903553i
$777$	−34.3047	+	1.61781i	−1.23068	+	0.0580387i
$778$	−17.4035	−	16.6628i	−0.623947	−	0.597392i
$779$	30.2190			1.08271
$780$	−4.24417	−	46.7150i	−0.151966	−	1.67267i
$781$	0.861207	−	1.49165i	0.0308164	−	0.0533756i
$782$	6.24803	+	5.98211i	0.223429	+	0.213920i
$783$	−39.2945	+	5.59258i	−1.40427	+	0.199863i
$784$	0.307791	−	0.659528i	0.0109926	−	0.0235546i
$785$	−76.9403	+	44.4215i	−2.74612	+	1.58547i
$786$	−9.28806	+	3.18828i	−0.331294	+	0.113722i
$787$	−10.7691	−	6.21757i	−0.383878	−	0.221632i	0.295626	−	0.955304i	$-0.404472\pi$
$787$	−10.7691	−	6.21757i	−0.383878	−	0.221632i	−0.679504	+	0.733671i	$0.737805\pi$
$788$	21.6888	−	0.943590i	0.772630	−	0.0336140i
$789$	20.9115	+	10.7932i	0.744469	+	0.384248i
$790$	−22.5211	−	5.51273i	−0.801266	−	0.196134i
$791$	−19.0554			−0.677531
$792$	1.60703	−	0.720101i	0.0571034	−	0.0255877i
$793$	−0.264006	−	0.457271i	−0.00937511	−	0.0162382i
$794$	18.7665	−	19.6007i	0.665998	−	0.695603i
$795$	6.91447	−	4.43902i	0.245231	−	0.157436i
$796$	33.7152	−	1.46681i	1.19500	−	0.0519898i
$797$	41.0026	−	23.6729i	1.45239	−	0.838537i	0.453772	−	0.891118i	$-0.350078\pi$
$797$	41.0026	−	23.6729i	1.45239	−	0.838537i	0.998617	+	0.0525812i	$0.0167448\pi$
$798$	6.88272	−	35.2300i	0.243646	−	1.24713i
$799$	42.4149	+	24.4882i	1.50053	+	0.866331i
$800$	−59.2502	−	9.14294i	−2.09481	−	0.323252i
$801$	−18.1333	+	12.8867i	−0.640709	+	0.455331i
$802$	−7.21536	+	29.4769i	−0.254783	+	1.04086i
$803$	−1.50896	+	2.61359i	−0.0532499	+	0.0922316i
$804$	15.4676	+	7.14993i	0.545501	+	0.252158i
$805$	−16.1088			−0.567759
$806$	2.28217	+	26.9001i	0.0803859	+	0.947517i
$807$	23.7473	−	1.11993i	0.835945	−	0.0394232i
$808$	−5.76598	+	6.57176i	−0.202846	+	0.231194i
$809$	12.0541	+	6.95941i	0.423798	+	0.244680i	0.696701	−	0.717362i	$-0.254650\pi$
$809$	12.0541	+	6.95941i	0.423798	+	0.244680i	−0.272903	+	0.962042i	$0.587984\pi$
$810$	−2.59065	+	50.2013i	−0.0910262	+	1.76389i
$811$	−15.0353	+	8.68061i	−0.527959	+	0.304817i	−0.740185	−	0.672403i	$-0.765262\pi$
$811$	−15.0353	+	8.68061i	−0.527959	+	0.304817i	0.212226	+	0.977221i	$0.431929\pi$
$812$	−33.6462	+	21.4277i	−1.18075	+	0.751964i
$813$	−1.39301	+	2.69891i	−0.0488550	+	0.0946550i
$814$	2.16479	+	0.529899i	0.0758759	+	0.0185729i
$815$	32.2260	+	55.8171i	1.12883	+	1.95519i
$816$	10.3018	−	25.0965i	0.360637	−	0.878552i
$817$	−0.370715	−	0.642097i	−0.0129697	−	0.0224641i
$818$	11.5032	−	12.0146i	0.402200	−	0.420079i
$819$	−21.8923	+	15.5582i	−0.764980	+	0.543646i
$820$	−35.8736	+	22.8462i	−1.25276	+	0.797825i
$821$		−	43.8618i		−	1.53079i	−0.643563	−	0.765393i	$-0.722545\pi$
$821$		−	43.8618i		−	1.53079i	0.643563	−	0.765393i	$-0.277455\pi$
$822$	−46.1995	−	9.02577i	−1.61139	−	0.314810i
$823$	46.0561	+	26.5905i	1.60542	+	0.926887i	0.990378	+	0.138389i	$0.0441925\pi$
$823$	46.0561	+	26.5905i	1.60542	+	0.926887i	0.615038	+	0.788498i	$0.289141\pi$
$824$	−19.2333	−	3.83037i	−0.670023	−	0.133437i
$825$	−3.38526	−	1.74726i	−0.117860	−	0.0608317i
$826$	−8.72357	+	2.54196i	−0.303532	+	0.0884460i
$827$	−5.54499	−	9.60421i	−0.192818	−	0.333971i	0.753365	−	0.657603i	$-0.228429\pi$
$827$	−5.54499	−	9.60421i	−0.192818	−	0.333971i	−0.946183	+	0.323632i	$0.895096\pi$
$828$	−1.28677	−	9.28360i	−0.0447182	−	0.322628i
$829$	28.9104			1.00410			0.502050	−	0.864839i	$-0.332579\pi$
$829$	28.9104			1.00410			0.502050	+	0.864839i	$0.332579\pi$
$830$	32.7127	+	31.3204i	1.13547	+	1.08715i
$831$	23.3509	+	12.0523i	0.810035	+	0.418089i
$832$	21.7684	−	16.6875i	0.754685	−	0.578534i
$833$		−	0.712470i		−	0.0246856i
$834$	2.13865	−	2.45552i	0.0740552	−	0.0850277i
$835$			65.3399i			2.26118i
$836$	−1.07596	+	2.06612i	−0.0372129	+	0.0714584i
$837$	1.66341	−	28.8831i	0.0574957	−	0.998346i
$838$	1.13539	+	0.277921i	0.0392213	+	0.00960062i
$839$	−49.0946			−1.69493			−0.847467	−	0.530848i	$-0.821874\pi$
$839$	−49.0946			−1.69493			−0.847467	+	0.530848i	$0.821874\pi$
$840$	18.4641	+	47.0259i	0.637071	+	1.62255i
$841$	−29.3456			−1.01192
$842$	−3.08708	−	10.5943i	−0.106388	−	0.365105i
$843$	−6.83838	+	13.2492i	−0.235526	+	0.456326i
$844$	−4.04783	−	6.35600i	−0.139332	−	0.218782i
$845$			4.91602i			0.169116i
$846$	−19.5743	−	49.3240i	−0.672978	−	1.69579i
$847$	−24.7770	+	14.3050i	−0.851349	+	0.491527i
$848$	4.35388	+	2.03189i	0.149513	+	0.0697754i
$849$	8.13128	−	15.7541i	0.279065	−	0.540680i
$850$	−56.3443	+	16.4181i	−1.93259	+	0.563138i
$851$	5.93080	−	10.2724i	0.203305	−	0.352135i
$852$	−12.0632	+	26.0967i	−0.413279	+	0.894058i
$853$	11.4826			0.393158			0.196579	−	0.980488i	$-0.437017\pi$
$853$	11.4826			0.393158			0.196579	+	0.980488i	$0.437017\pi$
$854$	0.410767	+	0.393285i	0.0140562	+	0.0134579i
$855$	−38.5202	−	54.2028i	−1.31736	−	1.85370i
$856$	−38.5861	+	13.0882i	−1.31885	+	0.447346i
$857$	23.1206	−	13.3487i	0.789783	−	0.455982i	−0.0501030	−	0.998744i	$-0.515955\pi$
$857$	23.1206	−	13.3487i	0.789783	−	0.455982i	0.839886	+	0.542762i	$0.182622\pi$
$858$	1.64852	−	0.565883i	0.0562796	−	0.0193189i
$859$	17.6320	−	10.1799i	0.601597	−	0.347332i	−0.168073	−	0.985775i	$-0.553754\pi$
$859$	17.6320	−	10.1799i	0.601597	−	0.347332i	0.769670	+	0.638442i	$0.220421\pi$
$860$	0.925523	+	0.481979i	0.0315601	+	0.0164353i
$861$	21.6394	+	11.1689i	0.737467	+	0.380634i
$862$	−5.44323	+	5.68519i	−0.185397	+	0.193638i
$863$	2.40752	+	4.16994i	0.0819529	+	0.141947i	0.904089	−	0.427345i	$-0.140551\pi$
$863$	2.40752	+	4.16994i	0.0819529	+	0.141947i	−0.822136	+	0.569291i	$0.807218\pi$
$864$	−25.6264	+	14.3974i	−0.871830	+	0.489809i
$865$	−10.3331	+	17.8974i	−0.351335	+	0.608530i
$866$	−13.1324	−	3.21456i	−0.446258	−	0.109235i
$867$	0.136055	+	2.88497i	0.00462068	+	0.0979787i
$868$	−10.4650	−	27.1279i	−0.355204	−	0.920780i
$869$		−	0.861525i		−	0.0292252i
$870$	−14.1686	+	72.5238i	−0.480361	+	2.45879i
$871$	14.6060	+	8.43277i	0.494905	+	0.285734i
$872$	10.9423	+	9.60064i	0.370553	+	0.325119i
$873$	2.34490	+	3.29957i	0.0793627	+	0.111674i
$874$	8.95525	+	8.57411i	0.302916	+	0.290024i
$875$	28.8649	−	49.9954i	0.975810	−	1.69015i
$876$	21.1365	−	45.7251i	0.714136	−	1.54491i
$877$	20.6798	+	35.8185i	0.698309	+	1.20951i	0.969053	+	0.246855i	$0.0793970\pi$
$877$	20.6798	+	35.8185i	0.698309	+	1.20951i	−0.270744	+	0.962651i	$0.587270\pi$
$878$	34.4065	−	10.0257i	1.16116	−	0.338351i
$879$	−21.3024	−	33.1818i	−0.718511	−	1.11919i
$880$	−0.284737	−	3.26619i	−0.00959847	−	0.110103i
$881$	3.74458	−	2.16194i	0.126158	−	0.0728375i	−0.435593	−	0.900144i	$-0.643461\pi$
$881$	3.74458	−	2.16194i	0.126158	−	0.0728375i	0.561751	+	0.827306i	$0.310128\pi$
$882$	−0.479020	+	0.605365i	−0.0161295	+	0.0203837i
$883$		−	31.3586i		−	1.05530i	−0.849461	−	0.527651i	$-0.823073\pi$
$883$		−	31.3586i		−	1.05530i	0.849461	−	0.527651i	$-0.176927\pi$
$884$	12.4019	−	23.8148i	0.417120	−	0.800978i
$885$	−7.72007	+	14.9574i	−0.259507	+	0.502788i
$886$	−4.87907	−	16.7441i	−0.163915	−	0.562530i
$887$	−15.2611	+	26.4330i	−0.512418	+	0.887533i	0.487479	+	0.873135i	$0.337917\pi$
$887$	−15.2611	+	26.4330i	−0.512418	+	0.887533i	−0.999896	+	0.0143985i	$0.995417\pi$
$888$	−36.7860	−	5.53921i	−1.23446	−	0.185884i
$889$	−16.1853	−	28.0338i	−0.542839	−	0.940224i
$890$	11.5867	+	39.7635i	0.388386	+	1.33287i
$891$	−1.83473	+	0.350003i	−0.0614657	+	0.0117255i
$892$	−24.7672	−	38.8900i	−0.829268	−	1.30213i
$893$	60.7929	+	35.0988i	2.03436	+	1.17454i
$894$	16.0155	+	46.6562i	0.535639	+	1.56042i
$895$		−	33.7194i		−	1.12711i
$896$	−17.4812	+	23.8143i	−0.584005	+	0.795578i
$897$	−0.436985	−	9.26599i	−0.0145905	−	0.309382i
$898$	8.92673	−	36.4683i	0.297889	−	1.21696i
$899$	8.40347	−	41.6905i	0.280271	−	1.39045i
$900$	58.9126	+	23.9324i	1.96375	+	0.797746i
$901$	4.70339			0.156692
$902$	−1.14148	−	1.09290i	−0.0380072	−	0.0363896i
$903$	−0.0281457	−	0.596811i	−0.000936629	−	0.0198606i
$904$	−20.2435	−	4.03158i	−0.673290	−	0.134088i
$905$	55.8479	+	32.2438i	1.85645	+	1.07182i
$906$	10.1764	−	11.6842i	0.338090	−	0.388183i
$907$			16.6955i			0.554364i	0.960817	+	0.277182i	$0.0894005\pi$
$907$			16.6955i			0.554364i	−0.960817	+	0.277182i	$0.910599\pi$
$908$	0.283902	+	6.52559i	0.00942161	+	0.216559i
$909$	7.55868	−	5.37170i	0.250706	−	0.178168i
$910$	13.9886	+	48.0064i	0.463717	+	1.59140i
$911$	14.9874	−	25.9589i	0.496554	−	0.860057i	−0.503438	−	0.864031i	$-0.667932\pi$
$911$	14.9874	−	25.9589i	0.496554	−	0.860057i	0.999992	+	0.00397470i	$0.00126519\pi$
$912$	14.7655	−	35.9705i	0.488936	−	1.19110i
$913$	−0.841402	+	1.45735i	−0.0278463	+	0.0482313i
$914$	15.5346	+	3.80256i	0.513838	+	0.125778i
$915$	1.05230	−	0.0496266i	0.0347880	−	0.00164060i
$916$	−38.0106	+	24.2071i	−1.25590	+	0.799827i
$917$	9.06563	−	5.23404i	0.299374	−	0.172843i
$918$	−16.7723	+	23.3805i	−0.553567	+	0.771671i
$919$	−11.7495	+	6.78358i	−0.387580	+	0.223770i	−0.681111	−	0.732180i	$-0.738503\pi$
$919$	−11.7495	+	6.78358i	−0.387580	+	0.223770i	0.293531	+	0.955950i	$0.405170\pi$
$920$	−17.1132	−	3.40816i	−0.564205	−	0.112364i
$921$	−17.3243	−	26.9853i	−0.570856	−	0.889197i
$922$	−1.16647	+	4.76536i	−0.0384155	+	0.156939i
$923$	−14.2276	+	24.6430i	−0.468308	+	0.811133i
$924$	−1.53412	+	1.08185i	−0.0504687	+	0.0355901i
$925$	40.2384	+	69.6949i	1.32303	+	2.29156i
$926$	5.86238	−	23.9495i	0.192650	−	0.787031i
$927$	18.9127	+	8.65883i	0.621173	+	0.284393i
$928$	−40.2776	+	15.6452i	−1.32218	+	0.513578i
$929$		−	28.5186i		−	0.935666i	−0.883817	−	0.467833i	$-0.845035\pi$
$929$		−	28.5186i		−	0.935666i	0.883817	−	0.467833i	$-0.154965\pi$
$930$	−49.7807	−	20.5696i	−1.63237	−	0.674505i
$931$		−	1.02118i		−	0.0334678i
$932$	−12.6265	+	24.2461i	−0.413595	+	0.794208i
$933$	−15.7946	−	8.15215i	−0.517090	−	0.266889i
$934$	−33.2717	−	8.14427i	−1.08868	−	0.266489i
$935$	−1.60473	−	2.77948i	−0.0524804	−	0.0908987i
$936$	−26.5491	+	11.8965i	−0.867783	+	0.388848i
$937$	24.2221	−	41.9539i	0.791301	−	1.37057i	−0.133861	−	0.991000i	$-0.542738\pi$
$937$	24.2221	−	41.9539i	0.791301	−	1.37057i	0.925162	−	0.379573i	$-0.123929\pi$
$938$	−17.6438	−	4.31887i	−0.576092	−	0.141016i
$939$	−2.95782	+	1.89889i	−0.0965249	+	0.0619680i
$940$	−98.7040	+	4.29421i	−3.21937	+	0.140062i
$941$	−15.1143	+	8.72622i	−0.492711	+	0.284467i	−0.725698	−	0.688013i	$-0.758483\pi$
$941$	−15.1143	+	8.72622i	−0.492711	+	0.284467i	0.232988	+	0.972480i	$0.425150\pi$
$942$	41.5514	+	36.1893i	1.35382	+	1.17911i
$943$	−7.28395	+	4.20539i	−0.237198	+	0.136946i
$944$	−9.80532	+	0.854797i	−0.319136	+	0.0278213i
$945$	−7.55045	−	53.0508i	−0.245616	−	1.72574i
$946$	−0.00921883	+	0.0376616i	−0.000299730	+	0.00122448i
$947$	−11.8017	+	20.4411i	−0.383503	+	0.664247i	−0.991560	−	0.129647i	$-0.958616\pi$
$947$	−11.8017	+	20.4411i	−0.383503	+	0.664247i	0.608057	+	0.793893i	$0.291949\pi$
$948$	1.30112	+	14.3213i	0.0422585	+	0.465134i
$949$	24.9288	−	43.1780i	0.809224	−	1.40162i
$950$	−80.7578	+	23.5320i	−2.62013	+	0.763478i
$951$	8.83377	+	13.7600i	0.286454	+	0.446197i
$952$	−5.64838	+	28.3619i	−0.183065	+	0.919215i
$953$			11.4941i			0.372329i	0.982519	+	0.186165i	$0.0596058\pi$
$953$			11.4941i			0.372329i	−0.982519	+	0.186165i	$0.940394\pi$
$954$	−3.99632	−	3.16226i	−0.129386	−	0.102382i
$955$	−14.9475	−	8.62994i	−0.483689	−	0.279258i
$956$	0.570755	+	13.1190i	0.0184595	+	0.424299i
$957$	−2.74267	+	0.129344i	−0.0886579	+	0.00418111i
$958$	8.06996	−	8.42868i	0.260728	−	0.272318i
$959$	50.1794			1.62038
$960$	9.66602	+	53.8645i	0.311970	+	1.73847i
$961$	28.5793	+	12.0093i	0.921913	+	0.387396i
$962$	−35.7636	−	8.75422i	−1.15306	−	0.282247i
$963$	43.0252	−	4.06719i	1.38647	−	0.131063i
$964$	25.8165	−	16.4413i	0.831495	−	0.529540i
$965$			65.9779i			2.12390i
$966$	3.24374	+	9.44963i	0.104366	+	0.304037i
$967$	−34.4429	−	19.8856i	−1.10761	−	0.639478i	−0.169400	−	0.985547i	$-0.554183\pi$
$967$	−34.4429	−	19.8856i	−1.10761	−	0.639478i	−0.938209	+	0.346069i	$0.887516\pi$
$968$	−29.3485	+	9.95488i	−0.943297	+	0.319962i
$969$	−1.79308	−	38.0212i	−0.0576021	−	1.22142i
$970$	7.23544	−	2.10833i	0.232316	−	0.0676944i
$971$	−19.7790	−	34.2582i	−0.634737	−	1.09940i	−0.986571	−	0.163335i	$-0.947775\pi$
$971$	−19.7790	−	34.2582i	−0.634737	−	1.09940i	0.351834	−	0.936063i	$-0.385558\pi$
$972$	29.9704	−	8.58907i	0.961303	−	0.275495i
$973$	−1.73559	+	3.00613i	−0.0556404	+	0.0963720i
$974$	−18.5765	+	5.41300i	−0.595230	+	0.173444i
$975$	55.9264	+	28.8657i	1.79108	+	0.924441i
$976$	0.353172	+	0.504714i	0.0113048	+	0.0161555i
$977$		−	48.9599i		−	1.56637i	−0.621791	−	0.783183i	$-0.713595\pi$
$977$		−	48.9599i		−	1.56637i	0.621791	−	0.783183i	$-0.286405\pi$
$978$	26.2539	−	30.1438i	0.839507	−	0.963894i
$979$	−1.33276	+	0.769471i	−0.0425953	+	0.0245924i
$980$	0.772033	+	1.21226i	0.0246617	+	0.0387243i
$981$	−8.94415	−	12.5856i	−0.285565	−	0.401826i
$982$	6.79359	+	23.3144i	0.216792	+	0.743994i
$983$	22.0725	+	38.2307i	0.704004	+	1.21937i	0.967050	+	0.254588i	$0.0819399\pi$
$983$	22.0725	+	38.2307i	0.704004	+	1.21937i	−0.263045	+	0.964784i	$0.584727\pi$
$984$	20.6256	+	16.4436i	0.657521	+	0.524201i
$985$	−21.4348	+	37.1262i	−0.682971	+	1.18294i
$986$	−29.2524	+	30.5527i	−0.931585	+	0.972996i
$987$	30.5604	+	47.6026i	0.972749	+	1.51521i
$988$	17.7755	−	34.1335i	0.565514	−	1.08593i
$989$	0.178713	+	0.103180i	0.00568275	+	0.00328094i
$990$	−0.505253	+	3.44056i	−0.0160580	+	0.109348i
$991$			29.5417i			0.938424i	0.883086	+	0.469212i	$0.155462\pi$
$991$			29.5417i			0.938424i	−0.883086	+	0.469212i	$0.844538\pi$
$992$	−5.37801	−	31.0335i	−0.170752	−	0.985314i
$993$	−22.9667	+	1.08311i	−0.728828	+	0.0343716i
$994$	7.28671	−	29.7684i	0.231121	−	0.944195i
$995$	−33.3205	+	57.7128i	−1.05633	+	1.82962i
$996$	11.7858	−	25.4965i	0.373448	−	0.807889i
$997$	21.9127	+	37.9540i	0.693983	+	1.20201i	0.970522	+	0.241012i	$0.0774792\pi$
$997$	21.9127	+	37.9540i	0.693983	+	1.20201i	−0.276539	+	0.961003i	$0.589187\pi$
$998$	−29.4697	−	28.2154i	−0.932846	−	0.893144i
$999$	36.6100	+	14.7170i	1.15829	+	0.465624i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	372.2.p.a.191.5	✓	120
3.2	odd	2	inner	372.2.p.a.191.56	yes	120
4.3	odd	2	inner	372.2.p.a.191.55	yes	120
12.11	even	2	inner	372.2.p.a.191.6	yes	120
31.25	even	3	inner	372.2.p.a.335.5	yes	120
93.56	odd	6	inner	372.2.p.a.335.56	yes	120
124.87	odd	6	inner	372.2.p.a.335.55	yes	120
372.335	even	6	inner	372.2.p.a.335.6	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.p.a.191.5	✓	120	1.1	even	1	trivial
372.2.p.a.191.6	yes	120	12.11	even	2	inner
372.2.p.a.191.55	yes	120	4.3	odd	2	inner
372.2.p.a.191.56	yes	120	3.2	odd	2	inner
372.2.p.a.335.5	yes	120	31.25	even	3	inner
372.2.p.a.335.6	yes	120	372.335	even	6	inner
372.2.p.a.335.55	yes	120	124.87	odd	6	inner
372.2.p.a.335.56	yes	120	93.56	odd	6	inner

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:	\( N \)	\(=\)	\( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	372.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37366 - 0.336245i) q^{2} +(-1.53913 - 0.794402i) q^{3} +(1.77388 + 0.923772i) q^{4} +(-3.42031 + 1.97472i) q^{5} +(1.84713 + 1.60876i) q^{6} +(-2.26131 - 1.30557i) q^{7} +(-2.12609 - 1.86541i) q^{8} +(1.73785 + 2.44538i) q^{9} +(5.36233 - 1.56253i) q^{10} +(0.103767 + 0.179731i) q^{11} +(-1.99639 - 2.83098i) q^{12} +(-1.71430 - 2.96925i) q^{13} +(2.66728 + 2.55376i) q^{14} +(6.83302 - 0.322246i) q^{15} +(2.29329 + 3.27732i) q^{16} +(3.39107 + 1.95784i) q^{17} +(-1.56497 - 3.94346i) q^{18} +(4.86040 + 2.80615i) q^{19} +(-7.89140 + 0.343323i) q^{20} +(2.44331 + 3.80583i) q^{21} +(-0.0821077 - 0.281780i) q^{22} -1.56206 q^{23} +(1.79045 + 4.56008i) q^{24} +(5.29901 - 9.17816i) q^{25} +(1.35647 + 4.65516i) q^{26} +(-0.732164 - 5.14431i) q^{27} +(-2.80525 - 4.40486i) q^{28} -7.63843i q^{29} +(-9.49460 - 1.85491i) q^{30} +(5.45799 + 1.10016i) q^{31} +(-2.04822 - 5.27303i) q^{32} +(-0.0169334 - 0.359062i) q^{33} +(-3.99987 - 3.82963i) q^{34} +10.3125 q^{35} +(0.823763 + 5.94318i) q^{36} +(-3.79678 + 6.57622i) q^{37} +(-5.73298 - 5.48898i) q^{38} +(0.279749 + 5.93191i) q^{39} +(10.9555 + 2.18183i) q^{40} +(4.66304 - 2.69221i) q^{41} +(-2.07658 - 6.04947i) q^{42} +(-0.114409 - 0.0660539i) q^{43} +(0.0180409 + 0.414678i) q^{44} +(-10.7729 - 4.93219i) q^{45} +(2.14574 + 0.525234i) q^{46} +12.5078 q^{47} +(-0.926168 - 6.86602i) q^{48} +(-0.0909767 - 0.157576i) q^{49} +(-10.3651 + 10.8259i) q^{50} +(-3.66400 - 5.70725i) q^{51} +(-0.298047 - 6.85071i) q^{52} +(1.04024 - 0.600584i) q^{53} +(-0.724005 + 7.31272i) q^{54} +(-0.709834 - 0.409823i) q^{55} +(2.37234 + 6.99402i) q^{56} +(-5.25158 - 8.18015i) q^{57} +(-2.56838 + 10.4926i) q^{58} +(-1.23031 + 2.13097i) q^{59} +(12.4186 + 5.74053i) q^{60} +0.154002 q^{61} +(-7.12750 - 3.34646i) q^{62} +(-0.737209 - 7.79865i) q^{63} +(1.04053 + 7.93204i) q^{64} +(11.7269 + 6.77050i) q^{65} +(-0.0974721 + 0.498923i) q^{66} +(-4.26005 + 2.45954i) q^{67} +(4.20676 + 6.60554i) q^{68} +(2.40421 + 1.24090i) q^{69} +(-14.1659 - 3.46753i) q^{70} +(-4.14969 - 7.18748i) q^{71} +(0.866795 - 8.44089i) q^{72} +(7.27086 + 12.5935i) q^{73} +(7.42671 - 7.75684i) q^{74} +(-15.4470 + 9.91684i) q^{75} +(6.02951 + 9.46767i) q^{76} -0.541903i q^{77} +(1.61029 - 8.24248i) q^{78} +(-3.59507 - 2.07561i) q^{79} +(-14.3155 - 6.68084i) q^{80} +(-2.95976 + 8.49940i) q^{81} +(-7.31067 + 2.13025i) q^{82} +(4.05426 + 7.02219i) q^{83} +(0.818412 + 9.00815i) q^{84} -15.4647 q^{85} +(0.134948 + 0.129205i) q^{86} +(-6.06799 + 11.7565i) q^{87} +(0.114651 - 0.575692i) q^{88} +7.41534i q^{89} +(13.1399 + 10.3975i) q^{90} +8.95254i q^{91} +(-2.77090 - 1.44299i) q^{92} +(-7.52660 - 6.02913i) q^{93} +(-17.1814 - 4.20568i) q^{94} -22.1654 q^{95} +(-1.03642 + 9.74299i) q^{96} +1.34931 q^{97} +(0.0719868 + 0.247047i) q^{98} +(-0.259177 + 0.566096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) \) 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

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