LMFDB - Embedded newform 684.2.o.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("684.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	684.11
Dual form			684.2.o.a.311.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30529 - 0.544263i) q^{2} +(1.25014 - 1.19881i) q^{3} +(1.40756 + 1.42084i) q^{4} +1.79274i q^{5} +(-2.28426 + 0.884390i) q^{6} +(-2.43772 - 1.40742i) q^{7} +(-1.06395 - 2.62069i) q^{8} +(0.125699 - 2.99737i) q^{9} +(0.975721 - 2.34004i) q^{10} +(2.00035 - 3.46471i) q^{11} +(3.46296 + 0.0888553i) q^{12} +(-2.05352 + 3.55679i) q^{13} +(2.41592 + 3.16385i) q^{14} +(2.14916 + 2.24117i) q^{15} +(-0.0375763 + 3.99982i) q^{16} +(-6.65138 - 3.84018i) q^{17} +(-1.79543 + 3.84401i) q^{18} +(2.29881 - 3.70344i) q^{19} +(-2.54719 + 2.52338i) q^{20} +(-4.73472 + 1.16290i) q^{21} +(-4.49675 + 3.43373i) q^{22} +(0.417491 - 0.723116i) q^{23} +(-4.47180 - 2.00074i) q^{24} +1.78609 q^{25} +(4.61626 - 3.52499i) q^{26} +(-3.43614 - 3.89782i) q^{27} +(-1.43151 - 5.44463i) q^{28} -6.45469i q^{29} +(-1.58548 - 4.09508i) q^{30} +(-3.07334 + 1.77440i) q^{31} +(2.22600 - 5.20047i) q^{32} +(-1.65282 - 6.72941i) q^{33} +(6.59190 + 8.63264i) q^{34} +(2.52313 - 4.37019i) q^{35} +(4.43571 - 4.04036i) q^{36} +4.43303 q^{37} +(-5.01625 + 3.58291i) q^{38} +(1.69675 + 6.90827i) q^{39} +(4.69820 - 1.90739i) q^{40} -7.35803i q^{41} +(6.81310 + 1.05902i) q^{42} +(2.11621 - 1.22179i) q^{43} +(7.73840 - 2.03459i) q^{44} +(5.37349 + 0.225346i) q^{45} +(-0.938512 + 0.716650i) q^{46} -4.37304 q^{47} +(4.74806 + 5.04539i) q^{48} +(0.461654 + 0.799607i) q^{49} +(-2.33136 - 0.972104i) q^{50} +(-12.9188 + 3.17300i) q^{51} +(-7.94407 + 2.08866i) q^{52} +(-2.21477 + 1.27870i) q^{53} +(2.36371 + 6.95794i) q^{54} +(6.21131 + 3.58610i) q^{55} +(-1.09478 + 7.88593i) q^{56} +(-1.56590 - 7.38566i) q^{57} +(-3.51305 + 8.42523i) q^{58} +6.16527 q^{59} +(-0.159294 + 6.20818i) q^{60} -0.777566 q^{61} +(4.97734 - 0.643390i) q^{62} +(-4.52497 + 7.12983i) q^{63} +(-5.73600 + 5.57658i) q^{64} +(-6.37640 - 3.68142i) q^{65} +(-1.50517 + 9.68339i) q^{66} +(0.683087 + 0.394381i) q^{67} +(-3.90591 - 14.8558i) q^{68} +(-0.344958 - 1.40449i) q^{69} +(-5.67195 + 4.33111i) q^{70} +(3.39181 - 5.87479i) q^{71} +(-7.98890 + 2.85964i) q^{72} +(-5.70240 + 9.87685i) q^{73} +(-5.78638 - 2.41273i) q^{74} +(2.23286 - 2.14119i) q^{75} +(8.49770 - 1.94656i) q^{76} +(-9.75259 + 5.63066i) q^{77} +(1.54517 - 9.94076i) q^{78} +(1.34514 - 0.776617i) q^{79} +(-7.17063 - 0.0673645i) q^{80} +(-8.96840 - 0.753534i) q^{81} +(-4.00470 + 9.60435i) q^{82} +(1.25828 - 2.17940i) q^{83} +(-8.31668 - 5.09044i) q^{84} +(6.88443 - 11.9242i) q^{85} +(-3.42723 + 0.443018i) q^{86} +(-7.73796 - 8.06927i) q^{87} +(-11.2082 - 1.55600i) q^{88} +(-14.2251 + 8.21288i) q^{89} +(-6.89131 - 3.21873i) q^{90} +(10.0118 - 5.78031i) q^{91} +(1.61508 - 0.424637i) q^{92} +(-1.71494 + 5.90260i) q^{93} +(5.70807 + 2.38008i) q^{94} +(6.63930 + 4.12116i) q^{95} +(-3.45157 - 9.16988i) q^{96} +(3.35880 + 5.81762i) q^{97} +(-0.167394 - 1.29498i) q^{98} +(-10.1336 - 6.43129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 232 q - 3 q^{2} + q^{4} + 3 q^{6} + 2 q^{10} - q^{12} + 2 q^{13} + q^{16} - 12 q^{17} - 16 q^{18} - 27 q^{20} - 14 q^{21} + 6 q^{22} - 10 q^{24} - 204 q^{25} - 6 q^{28} - 9 q^{30} - 3 q^{32} - 12 q^{33}+ \cdots - 162 q^{98}+O(q^{100}) $ 232 * q - 3 * q^2 + q^4 + 3 * q^6 + 2 * q^10 - q^12 + 2 * q^13 + q^16 - 12 * q^17 - 16 * q^18 - 27 * q^20 - 14 * q^21 + 6 * q^22 - 10 * q^24 - 204 * q^25 - 6 * q^28 - 9 * q^30 - 3 * q^32 - 12 * q^33 + 2 * q^34 + 13 * q^36 - 16 * q^37 - 3 * q^38 - 16 * q^40 - 43 * q^42 + 21 * q^44 + 2 * q^45 - 24 * q^46 + 58 * q^48 + 88 * q^49 + 9 * q^50 + 17 * q^52 + 41 * q^54 - 48 * q^56 - 12 * q^57 + 2 * q^58 + 16 * q^60 - 4 * q^61 + 6 * q^62 + 16 * q^64 + 12 * q^65 - 27 * q^66 - 18 * q^68 - 14 * q^69 + 60 * q^70 + 15 * q^72 + 2 * q^73 - 30 * q^74 + 3 * q^76 - 12 * q^77 - 64 * q^78 + 54 * q^80 + 4 * q^81 + 2 * q^82 - 10 * q^84 + 22 * q^85 + 51 * q^86 - 18 * q^88 + 14 * q^90 + 57 * q^92 + 4 * q^93 - 6 * q^94 - 17 * q^96 - 4 * q^97 - 162 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−1.30529	−	0.544263i	−0.922978	−	0.384852i
$2$	−1.30529	−	0.544263i	−0.922978	−	0.384852i
$3$	1.25014	−	1.19881i	0.721769	−	0.692134i
$3$	1.25014	−	1.19881i	0.721769	−	0.692134i
$4$	1.40756	+	1.42084i	0.703778	+	0.710420i
$5$			1.79274i			0.801737i	0.916136	+	0.400868i	$0.131292\pi$
$5$			1.79274i			0.801737i	−0.916136	+	0.400868i	$0.868708\pi$
$6$	−2.28426	+	0.884390i	−0.932546	+	0.361051i
$7$	−2.43772	−	1.40742i	−0.921372	−	0.531954i	−0.0372993	−	0.999304i	$-0.511875\pi$
$7$	−2.43772	−	1.40742i	−0.921372	−	0.531954i	−0.884072	+	0.467350i	$0.845209\pi$
$8$	−1.06395	−	2.62069i	−0.376165	−	0.926553i
$9$	0.125699	−	2.99737i	0.0418998	−	0.999122i
$10$	0.975721	−	2.34004i	0.308550	−	0.739985i
$11$	2.00035	−	3.46471i	0.603128	−	1.04465i	−0.389216	−	0.921146i	$-0.627254\pi$
$11$	2.00035	−	3.46471i	0.603128	−	1.04465i	0.992344	−	0.123502i	$-0.0394126\pi$
$12$	3.46296	+	0.0888553i	0.999671	+	0.0256503i
$13$	−2.05352	+	3.55679i	−0.569543	+	0.986477i	0.427068	+	0.904219i	$0.359546\pi$
$13$	−2.05352	+	3.55679i	−0.569543	+	0.986477i	−0.996611	+	0.0822577i	$0.973787\pi$
$14$	2.41592	+	3.16385i	0.645682	+	0.845574i
$15$	2.14916	+	2.24117i	0.554910	+	0.578668i
$16$	−0.0375763	+	3.99982i	−0.00939408	+	0.999956i
$17$	−6.65138	−	3.84018i	−1.61320	−	0.931380i	−0.988623	−	0.150414i	$-0.951939\pi$
$17$	−6.65138	−	3.84018i	−1.61320	−	0.931380i	−0.624574	−	0.780966i	$-0.714727\pi$
$18$	−1.79543	+	3.84401i	−0.423187	+	0.906042i
$19$	2.29881	−	3.70344i	0.527382	−	0.849628i
$19$	2.29881	−	3.70344i	0.527382	−	0.849628i
$20$	−2.54719	+	2.52338i	−0.569570	+	0.564244i
$21$	−4.73472	+	1.16290i	−1.03320	+	0.253765i
$22$	−4.49675	+	3.43373i	−0.958709	+	0.732073i
$23$	0.417491	−	0.723116i	0.0870530	−	0.150780i	−0.819211	−	0.573492i	$-0.805588\pi$
$23$	0.417491	−	0.723116i	0.0870530	−	0.150780i	0.906264	+	0.422712i	$0.138922\pi$
$24$	−4.47180	−	2.00074i	−0.912803	−	0.408400i
$25$	1.78609			0.357218
$26$	4.61626	−	3.52499i	0.905323	−	0.691307i
$27$	−3.43614	−	3.89782i	−0.661285	−	0.750135i
$28$	−1.43151	−	5.44463i	−0.270530	−	1.02894i
$29$		−	6.45469i		−	1.19861i	−0.800522	−	0.599303i	$-0.795444\pi$
$29$		−	6.45469i		−	1.19861i	0.800522	−	0.599303i	$-0.204556\pi$
$30$	−1.58548	−	4.09508i	−0.289468	−	0.747656i
$31$	−3.07334	+	1.77440i	−0.551989	+	0.318691i	−0.749924	−	0.661524i	$-0.769910\pi$
$31$	−3.07334	+	1.77440i	−0.551989	+	0.318691i	0.197935	+	0.980215i	$0.436577\pi$
$32$	2.22600	−	5.20047i	0.393506	−	0.919322i
$33$	−1.65282	−	6.72941i	−0.287718	−	1.17144i
$34$	6.59190	+	8.63264i	1.13050	+	1.48049i
$35$	2.52313	−	4.37019i	0.426487	−	0.738697i
$36$	4.43571	−	4.04036i	0.739285	−	0.673393i
$37$	4.43303			0.728785			0.364392	−	0.931245i	$-0.381277\pi$
$37$	4.43303			0.728785			0.364392	+	0.931245i	$0.381277\pi$
$38$	−5.01625	+	3.58291i	−0.813744	+	0.581224i
$39$	1.69675	+	6.90827i	0.271697	+	1.10621i
$40$	4.69820	−	1.90739i	0.742851	−	0.301585i
$41$		−	7.35803i		−	1.14913i	−0.818459	−	0.574566i	$-0.805171\pi$
$41$		−	7.35803i		−	1.14913i	0.818459	−	0.574566i	$-0.194829\pi$
$42$	6.81310	+	1.05902i	1.05128	+	0.163410i
$43$	2.11621	−	1.22179i	0.322718	−	0.186322i	−0.329885	−	0.944021i	$-0.607010\pi$
$43$	2.11621	−	1.22179i	0.322718	−	0.186322i	0.652604	+	0.757700i	$0.273677\pi$
$44$	7.73840	−	2.03459i	1.16661	−	0.306726i
$45$	5.37349	+	0.225346i	0.801033	+	0.0335926i
$46$	−0.938512	+	0.716650i	−0.138376	+	0.105664i
$47$	−4.37304			−0.637873			−0.318937	−	0.947776i	$-0.603326\pi$
$47$	−4.37304			−0.637873			−0.318937	+	0.947776i	$0.603326\pi$
$48$	4.74806	+	5.04539i	0.685324	+	0.728239i
$49$	0.461654	+	0.799607i	0.0659505	+	0.114230i
$50$	−2.33136	−	0.972104i	−0.329705	−	0.137476i
$51$	−12.9188	+	3.17300i	−1.80899	+	0.444309i
$52$	−7.94407	+	2.08866i	−1.10164	+	0.289646i
$53$	−2.21477	+	1.27870i	−0.304222	+	0.175643i	−0.644338	−	0.764741i	$-0.722867\pi$
$53$	−2.21477	+	1.27870i	−0.304222	+	0.175643i	0.340116	+	0.940383i	$0.389534\pi$
$54$	2.36371	+	6.95794i	0.321660	+	0.946855i
$55$	6.21131	+	3.58610i	0.837533	+	0.483550i
$56$	−1.09478	+	7.88593i	−0.146296	+	1.05380i
$57$	−1.56590	−	7.38566i	−0.207409	−	0.978254i
$58$	−3.51305	+	8.42523i	−0.461286	+	1.10629i
$59$	6.16527			0.802650			0.401325	−	0.915936i	$-0.368550\pi$
$59$	6.16527			0.802650			0.401325	+	0.915936i	$0.368550\pi$
$60$	−0.159294	+	6.20818i	−0.0205648	+	0.801473i
$61$	−0.777566			−0.0995571			−0.0497786	−	0.998760i	$-0.515852\pi$
$61$	−0.777566			−0.0995571			−0.0497786	+	0.998760i	$0.515852\pi$
$62$	4.97734	−	0.643390i	0.632122	−	0.0817107i
$63$	−4.52497	+	7.12983i	−0.570092	+	0.898274i
$64$	−5.73600	+	5.57658i	−0.717000	+	0.697073i
$65$	−6.37640	−	3.68142i	−0.790895	−	0.456623i
$66$	−1.50517	+	9.68339i	−0.185274	+	1.19194i
$67$	0.683087	+	0.394381i	0.0834524	+	0.0481812i	0.541145	−	0.840929i	$-0.317991\pi$
$67$	0.683087	+	0.394381i	0.0834524	+	0.0481812i	−0.457693	+	0.889110i	$0.651324\pi$
$68$	−3.90591	−	14.8558i	−0.473661	−	1.80153i
$69$	−0.344958	−	1.40449i	−0.0415280	−	0.169081i
$70$	−5.67195	+	4.33111i	−0.677928	+	0.517667i
$71$	3.39181	−	5.87479i	0.402534	−	0.697209i	−0.591497	−	0.806307i	$-0.701463\pi$
$71$	3.39181	−	5.87479i	0.402534	−	0.697209i	0.994031	+	0.109098i	$0.0347963\pi$
$72$	−7.98890	+	2.85964i	−0.941500	+	0.337012i
$73$	−5.70240	+	9.87685i	−0.667416	+	1.15600i	0.311209	+	0.950342i	$0.399266\pi$
$73$	−5.70240	+	9.87685i	−0.667416	+	1.15600i	−0.978624	+	0.205656i	$0.934067\pi$
$74$	−5.78638	−	2.41273i	−0.672653	−	0.280474i
$75$	2.23286	−	2.14119i	0.257829	−	0.247243i
$76$	8.49770	−	1.94656i	0.974753	−	0.223286i
$77$	−9.75259	+	5.63066i	−1.11141	+	0.641673i
$78$	1.54517	−	9.94076i	0.174957	−	1.12557i
$79$	1.34514	−	0.776617i	0.151340	−	0.0873763i	−0.422418	−	0.906401i	$-0.638818\pi$
$79$	1.34514	−	0.776617i	0.151340	−	0.0873763i	0.573758	+	0.819025i	$0.305485\pi$
$80$	−7.17063	−	0.0673645i	−0.801701	−	0.00753158i
$81$	−8.96840	−	0.753534i	−0.996489	−	0.0837260i
$82$	−4.00470	+	9.60435i	−0.442246	+	1.06062i
$83$	1.25828	−	2.17940i	0.138114	−	0.239220i	−0.788669	−	0.614818i	$-0.789229\pi$
$83$	1.25828	−	2.17940i	0.138114	−	0.239220i	0.926783	+	0.375598i	$0.122563\pi$
$84$	−8.31668	−	5.09044i	−0.907424	−	0.555413i
$85$	6.88443	−	11.9242i	0.746721	−	1.29336i
$86$	−3.42723	+	0.443018i	−0.369568	+	0.0477719i
$87$	−7.73796	−	8.06927i	−0.829597	−	0.865116i
$88$	−11.2082	−	1.55600i	−1.19480	−	0.165870i
$89$	−14.2251	+	8.21288i	−1.50786	+	0.870563i	−0.507902	+	0.861415i	$0.669579\pi$
$89$	−14.2251	+	8.21288i	−1.50786	+	0.870563i	−0.999958	+	0.00914830i	$0.997088\pi$
$90$	−6.89131	−	3.21873i	−0.726407	−	0.339284i
$91$	10.0118	−	5.78031i	1.04952	−	0.605941i
$92$	1.61508	−	0.424637i	0.168383	−	0.0442715i
$93$	−1.71494	+	5.90260i	−0.177831	+	0.612071i
$94$	5.70807	+	2.38008i	0.588743	+	0.245487i
$95$	6.63930	+	4.12116i	0.681178	+	0.422822i
$96$	−3.45157	−	9.16988i	−0.352274	−	0.935897i
$97$	3.35880	+	5.81762i	0.341035	+	0.590689i	0.984625	−	0.174681i	$-0.0558893\pi$
$97$	3.35880	+	5.81762i	0.341035	+	0.590689i	−0.643590	+	0.765370i	$0.722556\pi$
$98$	−0.167394	−	1.29498i	−0.0169094	−	0.130813i
$99$	−10.1336	−	6.43129i	−1.01846	−	0.646369i
$100$	2.51402	+	2.53775i	0.251402	+	0.253775i
$101$			8.68436i			0.864126i	0.901843	+	0.432063i	$0.142214\pi$
$101$			8.68436i			0.864126i	−0.901843	+	0.432063i	$0.857786\pi$
$102$	18.5897	+	2.88955i	1.84066	+	0.286108i
$103$	−2.06089	+	1.18985i	−0.203065	+	0.117240i	−0.598084	−	0.801433i	$-0.704071\pi$
$103$	−2.06089	+	1.18985i	−0.203065	+	0.117240i	0.395019	+	0.918673i	$0.370738\pi$
$104$	11.5061	+	1.59736i	1.12827	+	0.156634i
$105$	−2.08477	−	8.48811i	−0.203453	−	0.828355i
$106$	3.58686	−	0.463652i	0.348387	−	0.0450339i
$107$	0.151752			0.0146704			0.00733522	−	0.999973i	$-0.497665\pi$
$107$	0.151752			0.0146704			0.00733522	+	0.999973i	$0.497665\pi$
$108$	0.701624	−	10.3686i	0.0675138	−	0.997718i
$109$	9.30823	−	16.1223i	0.891567	−	1.54424i	0.0535700	−	0.998564i	$-0.482940\pi$
$109$	9.30823	−	16.1223i	0.891567	−	1.54424i	0.837997	−	0.545675i	$-0.183727\pi$
$110$	−6.15577	−	8.06149i	−0.586930	−	0.768633i
$111$	5.54190	−	5.31436i	0.526014	−	0.504417i
$112$	5.72103	−	9.69757i	0.540586	−	0.916334i
$113$	12.3814	−	7.14841i	1.16474	−	0.672466i	0.212308	−	0.977203i	$-0.431902\pi$
$113$	12.3814	−	7.14841i	1.16474	−	0.672466i	0.952436	+	0.304737i	$0.0985687\pi$
$114$	−1.97579	+	10.4927i	−0.185049	+	0.982729i
$115$	1.29636	+	0.748452i	0.120886	+	0.0697936i
$116$	9.17109	−	9.08534i	0.851514	−	0.843552i
$117$	10.4029	+	6.60222i	0.961747	+	0.610376i
$118$	−8.04746	−	3.35553i	−0.740829	−	0.308902i
$119$	10.8095	+	18.7226i	0.990903	+	1.71629i
$120$	3.58681	−	8.01677i	0.327429	−	0.731828i
$121$	−2.50280	−	4.33498i	−0.227527	−	0.394089i
$122$	1.01495	+	0.423201i	0.0918891	+	0.0383148i
$123$	−8.82090	−	9.19857i	−0.795353	−	0.829407i
$124$	−6.84703	−	1.86917i	−0.614882	−	0.167857i
$125$			12.1657i			1.08813i
$126$	9.78689	−	6.84371i	0.871885	−	0.609686i
$127$	−2.59683	+	1.49928i	−0.230431	+	0.133040i	−0.610771	−	0.791807i	$-0.709140\pi$
$127$	−2.59683	+	1.49928i	−0.230431	+	0.133040i	0.380340	+	0.924847i	$0.375807\pi$
$128$	10.5223	−	4.15715i	0.930046	−	0.367444i
$129$	1.18085	−	4.06434i	0.103968	−	0.357845i
$130$	6.31938	+	8.27575i	0.554246	+	0.725831i
$131$	−8.28796			−0.724123			−0.362061	−	0.932154i	$-0.617927\pi$
$131$	−8.28796			−0.724123			−0.362061	+	0.932154i	$0.617927\pi$
$132$	7.23499	−	11.8204i	0.629725	−	1.02883i
$133$	−10.8161	+	5.79258i	−0.937878	+	0.502280i
$134$	−0.676979	−	0.886559i	−0.0584821	−	0.0765871i
$135$	6.98776	−	6.16009i	0.601411	−	0.530176i
$136$	−2.98714	+	21.5170i	−0.256145	+	1.84506i
$137$			14.4636i			1.23571i	0.786293	+	0.617854i	$0.211998\pi$
$137$			14.4636i			1.23571i	−0.786293	+	0.617854i	$0.788002\pi$
$138$	−0.314143	+	2.02101i	−0.0267416	+	0.172040i
$139$	17.9404	+	10.3579i	1.52169	+	0.878546i	0.999672	+	0.0256085i	$0.00815232\pi$
$139$	17.9404	+	10.3579i	1.52169	+	0.878546i	0.522014	+	0.852937i	$0.325181\pi$
$140$	9.76080	−	2.56632i	0.824938	−	0.216894i
$141$	−5.46691	+	5.24245i	−0.460397	+	0.441494i
$142$	−7.62472	+	5.82225i	−0.639852	+	0.488593i
$143$	8.21550	+	14.2297i	0.687015	+	1.18994i
$144$	11.9842	+	0.615405i	0.998684	+	0.0512838i
$145$	11.5716			0.960967
$146$	12.8189	−	9.78853i	1.06090	−	0.810105i
$147$	1.53571	+	0.446185i	0.126663	+	0.0368007i
$148$	6.23973	+	6.29862i	0.512903	+	0.517744i
$149$			9.49001i			0.777452i	0.921354	+	0.388726i	$0.127085\pi$
$149$			9.49001i			0.777452i	−0.921354	+	0.388726i	$0.872915\pi$
$150$	−4.07990	+	1.57960i	−0.333123	+	0.128974i
$151$	−15.1692	−	8.75796i	−1.23446	−	0.712713i	−0.266500	−	0.963835i	$-0.585867\pi$
$151$	−15.1692	−	8.75796i	−1.23446	−	0.712713i	−0.967955	+	0.251122i	$0.919200\pi$
$152$	−12.1514	−	2.08416i	−0.985608	−	0.169048i
$153$	−12.3465	+	19.4539i	−0.998154	+	1.57276i
$154$	15.7945	−	2.04166i	1.27276	−	0.164522i
$155$	−3.18103	−	5.50970i	−0.255506	−	0.442550i
$156$	−7.42729	+	12.1346i	−0.594659	+	0.971544i
$157$	−18.2677			−1.45792			−0.728961	−	0.684555i	$-0.759996\pi$
$157$	−18.2677			−1.45792			−0.728961	+	0.684555i	$0.759996\pi$
$158$	−2.17848	+	0.281599i	−0.173311	+	0.0224028i
$159$	−1.23585	+	4.25364i	−0.0980096	+	0.337336i
$160$	9.32308	+	3.99064i	0.737054	+	0.315488i
$161$	−2.03545	+	1.17517i	−0.160416	+	0.0926164i
$162$	11.2962	+	5.86475i	0.887515	+	0.460778i
$163$			5.04086i			0.394831i	0.980320	+	0.197415i	$0.0632547\pi$
$163$			5.04086i			0.394831i	−0.980320	+	0.197415i	$0.936745\pi$
$164$	10.4546	−	10.3568i	0.816366	−	0.808733i
$165$	12.0641	−	2.96307i	0.939187	−	0.230674i
$166$	−2.82858	+	2.15991i	−0.219541	+	0.167642i
$167$	6.07102	−	10.5153i	0.469790	−	0.813699i	−0.529614	−	0.848239i	$-0.677663\pi$
$167$	6.07102	−	10.5153i	0.469790	−	0.813699i	0.999403	+	0.0345395i	$0.0109964\pi$
$168$	8.08512	+	11.1710i	0.623781	+	0.861858i
$169$	−1.93385	−	3.34953i	−0.148758	−	0.257656i
$170$	−15.4761	+	11.8176i	−1.18696	+	0.906365i
$171$	−10.8116	−	7.35588i	−0.826785	−	0.562518i
$172$	4.71465	+	1.28705i	0.359489	+	0.0981367i
$173$	20.6152	−	11.9022i	1.56735	−	0.904908i	0.570870	−	0.821040i	$-0.306606\pi$
$173$	20.6152	−	11.9022i	1.56735	−	0.904908i	0.996477	−	0.0838681i	$-0.0267274\pi$
$174$	5.70847	+	14.7442i	0.432758	+	1.11776i
$175$	−4.35399	−	2.51378i	−0.329131	−	0.190024i
$176$	13.7831	+	8.13124i	1.03894	+	0.612915i
$177$	7.70745	−	7.39100i	0.579328	−	0.555542i
$178$	23.0379	−	2.97796i	1.72676	−	0.223208i
$179$	24.6916			1.84553			0.922767	−	0.385359i	$-0.125922\pi$
$179$	24.6916			1.84553			0.922767	+	0.385359i	$0.125922\pi$
$180$	7.24330	+	7.95206i	0.539884	+	0.592712i
$181$	3.56559	+	6.17578i	0.265028	+	0.459042i	0.967571	−	0.252599i	$-0.0812855\pi$
$181$	3.56559	+	6.17578i	0.265028	+	0.459042i	−0.702543	+	0.711641i	$0.747952\pi$
$182$	−16.2143	+	2.09592i	−1.20188	+	0.155360i
$183$	−0.972066	+	0.932156i	−0.0718572	+	0.0689069i
$184$	−2.33925	−	0.324752i	−0.172452	−	0.0239410i
$185$			7.94725i			0.584294i
$186$	5.45106	−	6.77122i	0.399691	−	0.496490i
$187$	−26.6102	+	15.3634i	−1.94593	+	1.12348i
$188$	−6.15529	−	6.21339i	−0.448921	−	0.453158i
$189$	2.89048	+	14.3379i	0.210252	+	1.04293i
$190$	−6.42321	−	8.99283i	−0.465989	−	0.652408i
$191$	11.7234	−	20.3056i	0.848277	−	1.46926i	−0.0344679	−	0.999406i	$-0.510974\pi$
$191$	11.7234	−	20.3056i	0.848277	−	1.46926i	0.882745	−	0.469853i	$-0.155693\pi$
$192$	−0.485531	+	13.8479i	−0.0350402	+	0.999386i
$193$	3.14592			0.226449			0.113224	−	0.993569i	$-0.463882\pi$
$193$	3.14592			0.226449			0.113224	+	0.993569i	$0.463882\pi$
$194$	−1.21789	−	9.42174i	−0.0874395	−	0.676441i
$195$	−12.3847	+	3.04182i	−0.886888	+	0.217829i
$196$	−0.486312	+	1.78143i	−0.0347366	+	0.127245i
$197$			19.5577i			1.39343i	0.717349	+	0.696714i	$0.245355\pi$
$197$			19.5577i			1.39343i	−0.717349	+	0.696714i	$0.754645\pi$
$198$	9.72689	+	13.9100i	0.691260	+	0.988541i
$199$	19.6330	−	11.3351i	1.39174	−	0.803523i	0.398235	−	0.917283i	$-0.369623\pi$
$199$	19.6330	−	11.3351i	1.39174	−	0.803523i	0.993508	+	0.113760i	$0.0362895\pi$
$200$	−1.90032	−	4.68079i	−0.134373	−	0.330982i
$201$	1.32674	−	0.325862i	0.0935812	−	0.0229845i
$202$	4.72657	−	11.3356i	0.332561	−	0.797569i
$203$	−9.08445	+	15.7347i	−0.637604	+	1.10436i
$204$	−22.6923	−	13.8894i	−1.58878	−	0.972452i
$205$	13.1910			0.921301
$206$	3.33764	−	0.431437i	0.232545	−	0.0300596i
$207$	−2.11497	−	1.34227i	−0.147000	−	0.0932942i
$208$	−14.1494	−	8.34735i	−0.981083	−	0.578785i
$209$	−8.23293	−	15.3729i	−0.569484	−	1.06336i
$210$	−1.89854	+	12.2141i	−0.131012	+	0.842853i
$211$		−	27.7223i		−	1.90848i	−0.299040	−	0.954240i	$-0.596667\pi$
$211$		−	27.7223i		−	1.90848i	0.299040	−	0.954240i	$-0.403333\pi$
$212$	−4.93424	−	1.34700i	−0.338885	−	0.0925121i
$213$	−2.80253	−	11.4104i	−0.192026	−	0.781831i
$214$	−0.198081	−	0.0825932i	−0.0135405	−	0.00564595i
$215$	2.19035	+	3.79380i	0.149381	+	0.258735i
$216$	−6.55906	+	13.1521i	−0.446288	+	0.894889i
$217$	9.98927			0.678116
$218$	−20.9247	+	15.9782i	−1.41720	+	1.08218i
$219$	4.71169	+	19.1836i	0.318386	+	1.29630i
$220$	3.64748	+	13.8729i	0.245913	+	0.935312i
$221$	27.3174	−	15.7717i	1.83757	−	1.06092i
$222$	−10.1262	+	3.92053i	−0.679626	+	0.263128i
$223$	9.98765	−	5.76637i	0.668822	−	0.386145i	−0.126808	−	0.991927i	$-0.540473\pi$
$223$	9.98765	−	5.76637i	0.668822	−	0.386145i	0.795630	+	0.605782i	$0.207140\pi$
$224$	−12.7456	+	9.54438i	−0.851602	+	0.637710i
$225$	0.224511	−	5.35357i	0.0149674	−	0.356905i
$226$	−20.0519	+	2.59199i	−1.33383	+	0.172417i
$227$	−8.12056	+	14.0652i	−0.538981	+	0.933542i	0.459979	+	0.887930i	$0.347857\pi$
$227$	−8.12056	+	14.0652i	−0.538981	+	0.933542i	−0.998959	+	0.0456119i	$0.985476\pi$
$228$	8.28975	−	12.6206i	0.549002	−	0.835821i
$229$	1.91127	+	3.31041i	0.126300	+	0.218758i	0.922240	−	0.386617i	$-0.126356\pi$
$229$	1.91127	+	3.31041i	0.126300	+	0.218758i	−0.795940	+	0.605375i	$0.793023\pi$
$230$	−1.28477	−	1.68251i	−0.0847149	−	0.110941i
$231$	−5.44200	+	18.7306i	−0.358057	+	1.23238i
$232$	−16.9157	+	6.86750i	−1.11057	+	0.450873i
$233$	16.8430	+	9.72434i	1.10342	+	0.637063i	0.937118	−	0.349012i	$-0.113483\pi$
$233$	16.8430	+	9.72434i	1.10342	+	0.637063i	0.166306	+	0.986074i	$0.446816\pi$
$234$	−9.98542	−	14.2797i	−0.652767	−	0.933494i
$235$		−	7.83971i		−	0.511406i
$236$	8.67796	+	8.75987i	0.564887	+	0.570219i
$237$	0.750596	−	2.58345i	0.0487564	−	0.167813i
$238$	−3.91948	−	30.3215i	−0.254062	−	1.96545i
$239$	8.39290	+	14.5369i	0.542892	+	0.940316i	0.998736	+	0.0502564i	$0.0160039\pi$
$239$	8.39290	+	14.5369i	0.542892	+	0.940316i	−0.455845	+	0.890059i	$0.650663\pi$
$240$	−9.04505	+	8.51203i	−0.583856	+	0.549449i
$241$	12.3210			0.793665			0.396833	−	0.917891i	$-0.370109\pi$
$241$	12.3210			0.793665			0.396833	+	0.917891i	$0.370109\pi$
$242$	0.907507	+	7.02057i	0.0583368	+	0.451300i
$243$	−12.1151	+	9.80940i	−0.777184	+	0.629273i
$244$	−1.09447	−	1.10480i	−0.0700661	−	0.0707274i
$245$	−1.43349	+	0.827624i	−0.0915821	+	0.0528749i
$246$	6.50737	+	16.8077i	0.414895	+	1.07162i
$247$	8.45175	+	15.7815i	0.537772	+	1.00415i
$248$	7.92003	+	6.16640i	0.502923	+	0.391567i
$249$	−1.03967	−	4.23300i	−0.0658864	−	0.268255i
$250$	6.62133	−	15.8797i	0.418770	−	1.00432i
$251$	−6.35327	−	11.0042i	−0.401015	−	0.694578i	0.592834	−	0.805325i	$-0.298009\pi$
$251$	−6.35327	−	11.0042i	−0.401015	−	0.694578i	−0.993849	+	0.110747i	$0.964676\pi$
$252$	−16.4995	+	3.60637i	−1.03937	+	0.227180i
$253$	−1.67026	−	2.89297i	−0.105008	−	0.181880i
$254$	4.20561	−	0.543634i	0.263884	−	0.0341106i
$255$	−5.68835	−	23.1600i	−0.356218	−	1.45034i
$256$	−15.9972	−	0.300597i	−0.999824	−	0.0187873i
$257$	1.83140	+	1.05736i	0.114240	+	0.0659562i	0.556031	−	0.831162i	$-0.312324\pi$
$257$	1.83140	+	1.05736i	0.114240	+	0.0659562i	−0.441791	+	0.897118i	$0.645657\pi$
$258$	−3.75343	+	4.66244i	−0.233678	+	0.290271i
$259$	−10.8065	−	6.23912i	−0.671482	−	0.387680i
$260$	−3.74443	−	14.2416i	−0.232220	−	0.883229i
$261$	−19.3471	−	0.811351i	−1.19755	−	0.0502214i
$262$	10.8182	+	4.51083i	0.668349	+	0.278680i
$263$	0.980055	+	1.69750i	0.0604328	+	0.104673i	0.894659	−	0.446750i	$-0.147419\pi$
$263$	0.980055	+	1.69750i	0.0604328	+	0.104673i	−0.834226	+	0.551422i	$0.814085\pi$
$264$	−15.8772	+	11.4913i	−0.977172	+	0.707241i
$265$	−2.29237	−	3.97050i	−0.140819	−	0.243906i
$266$	17.2709	−	1.67415i	1.05894	−	0.102649i
$267$	−7.93769	+	27.3205i	−0.485779	+	1.67199i
$268$	0.401131	+	1.52567i	0.0245030	+	0.0931951i
$269$	−21.4693	−	12.3953i	−1.30901	−	0.755757i	−0.327078	−	0.944997i	$-0.606064\pi$
$269$	−21.4693	−	12.3953i	−1.30901	−	0.755757i	−0.981931	+	0.189241i	$0.939397\pi$
$270$	−12.4738	+	4.23751i	−0.759128	+	0.257887i
$271$	1.11291	+	0.642537i	0.0676042	+	0.0390313i	0.533421	−	0.845850i	$-0.320906\pi$
$271$	1.11291	+	0.642537i	0.0676042	+	0.0390313i	−0.465817	+	0.884881i	$0.654239\pi$
$272$	15.6100	−	26.4600i	0.946493	−	1.60438i
$273$	5.58664	−	19.2285i	0.338119	−	1.16376i
$274$	7.87200	−	18.8792i	0.475565	−	1.14053i
$275$	3.57281	−	6.18829i	0.215448	−	0.373168i
$276$	1.51001	−	2.46703i	0.0908919	−	0.148498i
$277$	2.99077	−	5.18016i	0.179698	−	0.311246i	−0.762079	−	0.647484i	$-0.775821\pi$
$277$	2.99077	−	5.18016i	0.179698	−	0.311246i	0.941777	+	0.336238i	$0.109155\pi$
$278$	−17.7800	−	23.2843i	−1.06637	−	1.39650i
$279$	4.93219	+	9.43497i	0.295283	+	0.564857i
$280$	−14.1374	−	1.96265i	−0.844872	−	0.117291i
$281$		−	9.01630i		−	0.537867i	−0.963159	−	0.268934i	$-0.913329\pi$
$281$		−	9.01630i		−	0.537867i	0.963159	−	0.268934i	$-0.0866712\pi$
$282$	9.98916	−	3.86747i	0.594846	−	0.230305i
$283$		−	31.9615i		−	1.89991i	−0.312383	−	0.949956i	$-0.601127\pi$
$283$		−	31.9615i		−	1.89991i	0.312383	−	0.949956i	$-0.398873\pi$
$284$	13.1213	−	3.44987i	0.778606	−	0.204712i
$285$	13.2405	−	2.80725i	0.784302	−	0.166287i
$286$	−2.97892	−	23.0452i	−0.176147	−	1.36269i
$287$	−10.3558	+	17.9368i	−0.611285	+	1.05878i
$288$	−15.3079	−	7.32584i	−0.902027	−	0.431680i
$289$	20.9939	+	36.3625i	1.23494	+	2.13897i
$290$	−15.1042	−	6.29798i	−0.886951	−	0.369830i
$291$	11.1732	+	3.24626i	0.654985	+	0.190299i
$292$	−22.0599	+	5.80001i	−1.29096	+	0.339420i
$293$	−12.7570	+	7.36523i	−0.745270	+	0.430282i	−0.823982	−	0.566616i	$-0.808252\pi$
$293$	−12.7570	+	7.36523i	−0.745270	+	0.430282i	0.0787126	+	0.996897i	$0.474919\pi$
$294$	−1.76170	−	1.41823i	−0.102745	−	0.0827129i
$295$			11.0527i			0.643514i
$296$	−4.71654	−	11.6176i	−0.274143	−	0.675258i
$297$	−20.3783	+	4.10821i	−1.18247	+	0.238383i
$298$	5.16506	−	12.3872i	0.299204	−	0.717571i
$299$	1.71465	+	2.96986i	0.0991608	+	0.171751i
$300$	6.18517	+	0.158704i	0.357101	+	0.00916277i
$301$	−6.87829			−0.396458
$302$	15.0336	+	19.6877i	0.865086	+	1.13290i
$303$	10.4109	+	10.8567i	0.598091	+	0.623699i
$304$	14.7267	+	9.33398i	0.844636	+	0.535341i
$305$		−	1.39397i		−	0.0798186i
$306$	26.7038	−	18.6732i	1.52655	−	1.06748i
$307$	4.99607	+	2.88448i	0.285141	+	0.164626i	0.635748	−	0.771896i	$-0.280692\pi$
$307$	4.99607	+	2.88448i	0.285141	+	0.164626i	−0.350608	+	0.936522i	$0.614025\pi$
$308$	−21.7276	−	5.93141i	−1.23804	−	0.337973i
$309$	−1.14999	+	3.95810i	−0.0654204	+	0.225168i
$310$	1.15343	+	8.92306i	0.0655104	+	0.506796i
$311$	−2.57758	−	4.46449i	−0.146161	−	0.253158i	0.783645	−	0.621210i	$-0.213358\pi$
$311$	−2.57758	−	4.46449i	−0.146161	−	0.253158i	−0.929805	+	0.368051i	$0.880025\pi$
$312$	16.2992	−	11.7967i	0.922758	−	0.667858i
$313$	16.2255			0.917121			0.458560	−	0.888663i	$-0.348365\pi$
$313$	16.2255			0.917121			0.458560	+	0.888663i	$0.348365\pi$
$314$	23.8446	+	9.94244i	1.34563	+	0.561084i
$315$	−12.7819	−	8.11208i	−0.720179	−	0.457064i
$316$	2.99681	+	0.818099i	0.168584	+	0.0460216i
$317$		−	0.108879i		−	0.00611525i	−0.999995	−	0.00305762i	$-0.999027\pi$
$317$		−	0.108879i		−	0.00611525i	0.999995	−	0.00305762i	$-0.000973273\pi$
$318$	3.92825	−	4.87960i	0.220285	−	0.273635i
$319$	−22.3636	−	12.9116i	−1.25212	−	0.722913i
$320$	−9.99735	−	10.2831i	−0.558869	−	0.574845i
$321$	0.189712	−	0.181922i	0.0105887	−	0.0101539i
$322$	3.29646	−	0.426113i	0.183704	−	0.0237464i
$323$	−29.5121	+	15.8052i	−1.64210	+	0.879424i
$324$	−11.5529	−	13.8033i	−0.641826	−	0.766850i
$325$	−3.66777	+	6.35276i	−0.203451	+	0.352388i
$326$	2.74355	−	6.57977i	0.151951	−	0.364420i
$327$	−7.69105	−	31.3140i	−0.425316	−	1.73167i
$328$	−19.2831	+	7.82861i	−1.06473	+	0.432263i
$329$	10.6602	+	6.15469i	0.587718	+	0.339319i
$330$	−17.3598	−	2.69837i	−0.955624	−	0.148541i
$331$	2.75516	+	1.59069i	0.151437	+	0.0874325i	0.573804	−	0.818993i	$-0.305467\pi$
$331$	2.75516	+	1.59069i	0.151437	+	0.0874325i	−0.422366	+	0.906425i	$0.638800\pi$
$332$	4.86768	−	1.27982i	0.267149	−	0.0702390i
$333$	0.557229	−	13.2874i	0.0305359	−	0.728145i
$334$	−13.6475	+	10.4213i	−0.746760	+	0.570227i
$335$	−0.707021	+	1.22460i	−0.0386287	+	0.0669068i
$336$	−4.47348	−	18.9817i	−0.244048	−	1.03554i
$337$	21.4509			1.16851			0.584253	−	0.811571i	$-0.301387\pi$
$337$	21.4509			1.16851			0.584253	+	0.811571i	$0.301387\pi$
$338$	0.701210	+	5.42463i	0.0381408	+	0.295061i
$339$	6.90889	−	23.7795i	0.375239	−	1.29152i
$340$	26.6326	−	7.00227i	1.44435	−	0.379751i
$341$			14.1976i			0.768846i
$342$	10.1087	+	15.4859i	0.546618	+	0.837382i
$343$			17.1049i			0.923578i
$344$	−5.45348	−	4.24598i	−0.294032	−	0.228928i
$345$	2.51788	−	0.618419i	0.135558	−	0.0332946i
$346$	−33.3868	+	4.31570i	−1.79488	+	0.232014i
$347$	−27.2356			−1.46208			−0.731042	−	0.682333i	$-0.760965\pi$
$347$	−27.2356			−1.46208			−0.731042	+	0.682333i	$0.760965\pi$
$348$	0.573534	−	22.3524i	0.0307446	−	1.19821i
$349$	−7.95134	+	13.7721i	−0.425626	+	0.737205i	−0.996479	−	0.0838470i	$-0.973279\pi$
$349$	−7.95134	+	13.7721i	−0.425626	+	0.737205i	0.570853	+	0.821052i	$0.306613\pi$
$350$	4.31506	+	5.65092i	0.230650	+	0.302055i
$351$	20.9199	−	4.21740i	1.11662	−	0.225108i
$352$	−13.5653	−	18.1152i	−0.723034	−	0.965544i
$353$	−20.1971	−	11.6608i	−1.07498	−	0.620642i	−0.145445	−	0.989366i	$-0.546461\pi$
$353$	−20.1971	−	11.6608i	−1.07498	−	0.620642i	−0.929539	+	0.368724i	$0.879795\pi$
$354$	−14.0831	+	5.45251i	−0.748508	+	0.289798i
$355$	10.5320	+	6.08063i	0.558978	+	0.322726i
$356$	−31.6918	−	8.65155i	−1.67966	−	0.458531i
$357$	35.9582	+	10.4473i	1.90311	+	0.552929i
$358$	−32.2296	−	13.4387i	−1.70339	−	0.710257i
$359$	−3.75437	+	6.50276i	−0.198148	+	0.343203i	−0.947928	−	0.318485i	$-0.896826\pi$
$359$	−3.75437	+	6.50276i	−0.198148	+	0.343203i	0.749780	+	0.661687i	$0.230159\pi$
$360$	−5.12659	−	14.3220i	−0.270195	−	0.754835i
$361$	−8.43098	−	17.0270i	−0.443736	−	0.896158i
$362$	−1.29287	−	10.0018i	−0.0679518	−	0.525682i
$363$	−8.32567	−	2.41894i	−0.436984	−	0.126961i
$364$	22.3051	+	6.08906i	1.16910	+	0.319153i
$365$	−17.7066	−	10.2229i	−0.926806	−	0.535092i
$366$	1.77616	−	0.687672i	0.0928416	−	0.0359452i
$367$		−	21.2697i		−	1.11027i	−0.831761	−	0.555134i	$-0.812667\pi$
$367$		−	21.2697i		−	1.11027i	0.831761	−	0.555134i	$-0.187333\pi$
$368$	2.87665	+	1.69706i	0.149956	+	0.0884656i
$369$	−22.0547	−	0.924900i	−1.14812	−	0.0481484i
$370$	4.32540	−	10.3735i	0.224867	−	0.539290i
$371$	7.19865			0.373735
$372$	−10.8005	+	5.87158i	−0.559982	+	0.304427i
$373$	−3.99784	−	6.92447i	−0.207000	−	0.358535i	0.743768	−	0.668438i	$-0.233037\pi$
$373$	−3.99784	−	6.92447i	−0.207000	−	0.358535i	−0.950768	+	0.309903i	$0.899703\pi$
$374$	43.0957	−	5.57072i	2.22842	−	0.288055i
$375$	14.5844	+	15.2088i	0.753133	+	0.785379i
$376$	4.65271	+	11.4604i	0.239945	+	0.591023i
$377$	22.9580	+	13.2548i	1.18240	+	0.682658i
$378$	4.03066	−	20.2882i	0.207315	−	1.04351i
$379$			26.4444i			1.35836i	0.733972	+	0.679180i	$0.237664\pi$
$379$			26.4444i			1.35836i	−0.733972	+	0.679180i	$0.762336\pi$
$380$	3.48968	+	15.2341i	0.179017	+	0.781495i
$381$	−1.44904	+	4.98742i	−0.0742368	+	0.255513i
$382$	−26.3540	+	20.1240i	−1.34839	+	1.02963i
$383$	−20.3853			−1.04164			−0.520819	−	0.853667i	$-0.674373\pi$
$383$	−20.3853			−1.04164			−0.520819	+	0.853667i	$0.674373\pi$
$384$	8.17066	−	17.8112i	0.416957	−	0.908926i
$385$	−10.0943	−	17.4838i	−0.514453	−	0.891059i
$386$	−4.10634	−	1.71221i	−0.209007	−	0.0871492i
$387$	−3.39615	−	6.49662i	−0.172636	−	0.330242i
$388$	−3.53821	+	12.9609i	−0.179625	+	0.657992i
$389$			0.341040i			0.0172914i	0.999963	+	0.00864570i	$0.00275204\pi$
$389$			0.341040i			0.0172914i	−0.999963	+	0.00864570i	$0.997248\pi$
$390$	17.8212	+	2.77009i	0.902410	+	0.140269i
$391$	−5.55379	+	3.20648i	−0.280867	+	0.162159i
$392$	1.60434	−	2.06060i	0.0810315	−	0.104076i
$393$	−10.3611	+	9.93571i	−0.522649	+	0.501190i
$394$	10.6445	−	25.5284i	0.536264	−	1.28610i
$395$	1.39227	+	2.41148i	0.0700527	+	0.121335i
$396$	−5.12569	−	23.4506i	−0.257576	−	1.17844i
$397$	−6.00936	+	10.4085i	−0.301601	+	0.522389i	−0.976499	−	0.215523i	$-0.930855\pi$
$397$	−6.00936	+	10.4085i	−0.301601	+	0.522389i	0.674897	+	0.737912i	$0.264188\pi$
$398$	−31.7959	+	4.11007i	−1.59379	+	0.206019i
$399$	−6.57748	+	20.2080i	−0.329286	+	1.01167i
$400$	−0.0671148	+	7.14405i	−0.00335574	+	0.357203i
$401$			5.16485i			0.257920i	0.991650	+	0.128960i	$0.0411639\pi$
$401$			5.16485i			0.257920i	−0.991650	+	0.128960i	$0.958836\pi$
$402$	−1.90914	−	0.296753i	−0.0952191	−	0.0148007i
$403$		−	14.5750i		−	0.726032i
$404$	−12.3391	+	12.2237i	−0.613892	+	0.608152i
$405$	1.35089	−	16.0780i	0.0671262	−	0.798922i
$406$	20.4217	−	15.5940i	1.01351	−	0.773919i
$407$	8.86760	−	15.3591i	0.439551	−	0.761324i
$408$	22.0605	+	30.4802i	1.09216	+	1.50900i
$409$	3.69305	−	6.39656i	0.182610	−	0.316289i	−0.760159	−	0.649737i	$-0.774879\pi$
$409$	3.69305	−	6.39656i	0.182610	−	0.316289i	0.942768	+	0.333448i	$0.108212\pi$
$410$	−17.2181	−	7.17938i	−0.850340	−	0.354565i
$411$	17.3391	+	18.0815i	0.855277	+	0.891896i
$412$	−4.59140	−	1.25341i	−0.226202	−	0.0617509i
$413$	−15.0292	−	8.67712i	−0.739539	−	0.426973i
$414$	2.03009	+	2.90315i	0.0997736	+	0.142682i
$415$	3.90710	+	2.25576i	0.191792	+	0.110731i
$416$	13.9259	+	18.5967i	0.682772	+	0.911778i
$417$	34.8452	−	8.55835i	1.70638	−	0.419104i
$418$	2.37946	+	24.5469i	0.116383	+	1.20063i
$419$	−1.79225	−	3.10427i	−0.0875573	−	0.151654i	0.818921	−	0.573907i	$-0.194573\pi$
$419$	−1.79225	−	3.10427i	−0.0875573	−	0.151654i	−0.906478	+	0.422253i	$0.861239\pi$
$420$	9.12583	−	14.9096i	0.445295	−	0.727515i
$421$	−3.28516	−	5.69006i	−0.160109	−	0.277317i	0.774799	−	0.632208i	$-0.217851\pi$
$421$	−3.28516	−	5.69006i	−0.160109	−	0.277317i	−0.934908	+	0.354891i	$0.884518\pi$
$422$	−15.0882	+	36.1856i	−0.734483	+	1.76149i
$423$	−0.549688	+	13.1076i	−0.0267267	+	0.637313i
$424$	5.70748	+	4.44374i	0.277180	+	0.215807i
$425$	−11.8800	−	6.85891i	−0.576263	−	0.332706i
$426$	−2.55218	+	16.4192i	−0.123653	+	0.795515i
$427$	1.89549	+	1.09436i	0.0917291	+	0.0529598i
$428$	0.213600	+	0.215616i	0.0103247	+	0.0104222i
$429$	27.3292	+	7.94023i	1.31947	+	0.383358i
$430$	−0.794215	−	6.14413i	−0.0383004	−	0.296296i
$431$	10.2172	+	17.6968i	0.492147	+	0.852423i	0.999959	−	0.00904469i	$-0.00287905\pi$
$431$	10.2172	+	17.6968i	0.492147	+	0.852423i	−0.507812	+	0.861468i	$0.669546\pi$
$432$	15.7197	−	13.5975i	0.756314	−	0.654209i
$433$	−12.8544	−	22.2645i	−0.617743	−	1.06996i	−0.989897	−	0.141791i	$-0.954714\pi$
$433$	−12.8544	−	22.2645i	−0.617743	−	1.06996i	0.372154	−	0.928171i	$-0.378619\pi$
$434$	−13.0389	−	5.43679i	−0.625886	−	0.260974i
$435$	14.4661	−	13.8721i	0.693596	−	0.665118i
$436$	36.0091	−	9.46756i	1.72452	−	0.453414i
$437$	−1.71829	−	3.20846i	−0.0821969	−	0.153481i
$438$	4.29079	−	27.6045i	0.205022	−	1.31899i
$439$	−29.6483	+	17.1175i	−1.41504	+	0.816972i	−0.995857	−	0.0909320i	$-0.971015\pi$
$439$	−29.6483	+	17.1175i	−1.41504	+	0.816972i	−0.419179	+	0.907904i	$0.637682\pi$
$440$	2.78950	−	20.0934i	0.132984	−	0.957913i
$441$	2.45475	−	1.28323i	0.116893	−	0.0611064i
$442$	−44.2411	+	5.71878i	−2.10433	+	0.272015i
$443$	−20.9145			−0.993677			−0.496839	−	0.867843i	$-0.665506\pi$
$443$	−20.9145			−0.993677			−0.496839	+	0.867843i	$0.665506\pi$
$444$	15.3514	+	0.393898i	0.728545	+	0.0186936i
$445$	−14.7235	−	25.5019i	−0.697963	−	1.20891i
$446$	−16.1752	+	2.09087i	−0.765917	+	0.0990055i
$447$	11.3767	+	11.8638i	0.538101	+	0.561140i
$448$	21.8314	−	5.52119i	1.03143	−	0.260852i
$449$			10.7359i			0.506659i	0.967380	+	0.253329i	$0.0815257\pi$
$449$			10.7359i			0.506659i	−0.967380	+	0.253329i	$0.918474\pi$
$450$	−3.20680	+	6.86576i	−0.151170	+	0.323655i
$451$	−25.4934	−	14.7186i	−1.20044	−	0.693073i
$452$	27.5843	+	7.53022i	1.29745	+	0.354192i
$453$	−29.4628	+	7.23639i	−1.38428	+	0.339995i
$454$	18.2549	−	13.9395i	0.856743	−	0.654211i
$455$	10.3626	+	17.9485i	0.485805	+	0.841440i
$456$	−17.6895	+	11.9617i	−0.828384	+	0.560160i
$457$	5.37257	−	9.30557i	0.251318	−	0.435296i	−0.712571	−	0.701600i	$-0.752469\pi$
$457$	5.37257	−	9.30557i	0.251318	−	0.435296i	0.963889	+	0.266304i	$0.0858026\pi$
$458$	−0.693019	−	5.36127i	−0.0323827	−	0.250516i
$459$	7.88675	+	39.1212i	0.368122	+	1.82602i
$460$	0.761263	+	2.89541i	0.0354941	+	0.134999i
$461$	−5.64696	+	3.26027i	−0.263005	+	0.151846i	−0.625705	−	0.780060i	$-0.715188\pi$
$461$	−5.64696	+	3.26027i	−0.263005	+	0.151846i	0.362700	+	0.931906i	$0.381855\pi$
$462$	17.2978	−	21.4870i	0.804765	−	0.999665i
$463$	33.3422	−	19.2501i	1.54954	−	0.894629i	0.551366	−	0.834264i	$-0.314107\pi$
$463$	33.3422	−	19.2501i	1.54954	−	0.894629i	0.998176	−	0.0603651i	$-0.0192265\pi$
$464$	25.8176	+	0.242544i	1.19855	+	0.0112598i
$465$	−10.5818	−	3.07444i	−0.490720	−	0.142574i
$466$	−16.6924	−	21.8601i	−0.773262	−	1.01265i
$467$	20.5044			0.948828			0.474414	−	0.880302i	$-0.342660\pi$
$467$	20.5044			0.948828			0.474414	+	0.880302i	$0.342660\pi$
$468$	5.26193	+	24.0738i	0.243233	+	1.11281i
$469$	−1.11012	−	1.92278i	−0.0512604	−	0.0887857i
$470$	−4.26686	+	10.2331i	−0.196816	+	0.472017i
$471$	−22.8372	+	21.8995i	−1.05228	+	1.00908i
$472$	−6.55957	−	16.1573i	−0.301929	−	0.743698i
$473$		−	9.77604i		−	0.449503i
$474$	−2.38582	+	2.96363i	−0.109584	+	0.136124i
$475$	4.10588	−	6.61469i	0.188391	−	0.303503i
$476$	−11.3868	+	41.7116i	−0.521915	+	1.91185i
$477$	3.55433	+	6.79921i	0.162742	+	0.311314i
$478$	−3.04324	−	23.5428i	−0.139195	−	1.07682i
$479$	−22.8821			−1.04551			−0.522756	−	0.852483i	$-0.675096\pi$
$479$	−22.8821			−1.04551			−0.522756	+	0.852483i	$0.675096\pi$
$480$	16.4392	−	6.18776i	0.750343	−	0.282431i
$481$	−9.10329	+	15.7674i	−0.415074	+	0.718930i
$482$	−16.0825	−	6.70587i	−0.732536	−	0.305444i
$483$	−1.13579	+	3.90925i	−0.0516804	+	0.177877i
$484$	2.63648	−	9.65780i	0.119840	−	0.438991i
$485$	−10.4295	+	6.02145i	−0.473577	+	0.273420i
$486$	21.1526	−	6.21030i	0.959501	−	0.281705i
$487$			6.02934i			0.273215i	0.990625	+	0.136608i	$0.0436200\pi$
$487$			6.02934i			0.273215i	−0.990625	+	0.136608i	$0.956380\pi$
$488$	0.827295	+	2.03776i	0.0374499	+	0.0922449i
$489$	6.04304	+	6.30178i	0.273276	+	0.284976i
$490$	2.32156	−	0.300094i	0.104877	−	0.0135569i
$491$	−4.50019			−0.203091			−0.101545	−	0.994831i	$-0.532379\pi$
$491$	−4.50019			−0.203091			−0.101545	+	0.994831i	$0.532379\pi$
$492$	0.653800	−	25.4806i	0.0294756	−	1.14875i
$493$	−24.7872	+	42.9326i	−1.11636	+	1.93359i
$494$	−2.44270	−	25.1993i	−0.109902	−	1.13377i
$495$	11.5296	−	18.1668i	0.518218	−	0.816537i
$496$	−6.98178	−	12.3595i	−0.313491	−	0.554958i
$497$	−16.5366	+	9.54739i	−0.741766	+	0.428259i
$498$	−0.946795	+	6.09113i	−0.0424269	+	0.272950i
$499$			10.6457i			0.476566i	0.971196	+	0.238283i	$0.0765846\pi$
$499$			10.6457i			0.476566i	−0.971196	+	0.238283i	$0.923415\pi$
$500$	−17.2855	+	17.1239i	−0.773031	+	0.765803i
$501$	−5.01626	−	20.4236i	−0.224110	−	0.912460i
$502$	2.30367	+	17.8215i	0.102818	+	0.795411i
$503$	9.46733	+	16.3979i	0.422127	+	0.731146i	0.996147	−	0.0876952i	$-0.0279502\pi$
$503$	9.46733	+	16.3979i	0.422127	+	0.731146i	−0.574020	+	0.818841i	$0.694617\pi$
$504$	23.4994	+	4.27271i	1.04675	+	0.190322i
$505$	−15.5688			−0.692801
$506$	0.605630	+	4.68522i	0.0269235	+	0.208283i
$507$	−6.43305	−	1.86906i	−0.285702	−	0.0830078i
$508$	−5.78542	−	1.57936i	−0.256686	−	0.0700728i
$509$	33.8244	+	19.5285i	1.49924	+	0.865586i	1.00000		0.000877837i	$-0.000279424\pi$
$509$	33.8244	+	19.5285i	1.49924	+	0.865586i	0.499240	+	0.866464i	$0.333613\pi$
$510$	−5.18021	+	33.3265i	−0.229384	+	1.47572i
$511$	27.8017	−	16.0513i	1.22988	−	0.710069i
$512$	20.7173	+	9.09904i	0.915585	+	0.402125i
$513$	−22.3344	+	3.76521i	−0.986086	+	0.166238i
$514$	−1.81502	−	2.37692i	−0.0800572	−	0.104842i
$515$	−2.13309	−	3.69463i	−0.0939954	−	0.162805i
$516$	7.43690	−	4.04298i	0.327391	−	0.177982i
$517$	−8.74760	+	15.1513i	−0.384719	+	0.666353i
$518$	10.7098	+	14.0254i	0.470564	+	0.616242i
$519$	11.5034	−	39.5932i	0.504944	−	1.73795i
$520$	−2.86364	+	20.6274i	−0.125579	+	0.904571i
$521$		−	22.1149i		−	0.968871i	−0.874827	−	0.484435i	$-0.839025\pi$
$521$		−	22.1149i		−	0.968871i	0.874827	−	0.484435i	$-0.160975\pi$
$522$	24.8119	+	11.5889i	1.08599	+	0.507234i
$523$	−10.2374	+	5.91056i	−0.447650	+	0.258451i	−0.706837	−	0.707376i	$-0.749879\pi$
$523$	−10.2374	+	5.91056i	−0.447650	+	0.258451i	0.259187	+	0.965827i	$0.416545\pi$
$524$	−11.6658	−	11.7759i	−0.509621	−	0.514431i
$525$	−8.45665	+	2.07704i	−0.369078	+	0.0906496i
$526$	−0.355365	−	2.74914i	−0.0154946	−	0.119868i
$527$	27.2560			1.18729
$528$	26.9786	−	6.35811i	1.17409	−	0.276701i
$529$	11.1514	+	19.3148i	0.484844	+	0.839774i
$530$	0.831206	+	6.43030i	0.0361053	+	0.279314i
$531$	0.774971	−	18.4796i	0.0336309	−	0.801945i
$532$	−23.4546	−	7.21464i	−1.01689	−	0.312794i
$533$	26.1710	+	15.1098i	1.13359	+	0.654479i
$534$	25.2305	−	31.3409i	1.09183	−	1.35625i
$535$			0.272052i			0.0117618i
$536$	0.306775	−	2.20976i	0.0132506	−	0.0954471i
$537$	30.8679	−	29.6005i	1.33205	−	1.27736i
$538$	21.2774	+	27.8645i	0.917332	+	1.20132i
$539$	3.69387			0.159106
$540$	18.5882	+	1.25783i	0.799907	+	0.0541283i
$541$	3.39836	+	5.88613i	0.146107	+	0.253064i	0.929785	−	0.368102i	$-0.119992\pi$
$541$	3.39836	+	5.88613i	0.146107	+	0.253064i	−0.783679	+	0.621167i	$0.786659\pi$
$542$	−1.10295	−	1.44441i	−0.0473760	−	0.0620427i
$543$	11.8611	+	3.44612i	0.509008	+	0.147887i
$544$	−34.7767	+	26.0421i	−1.49104	+	1.11654i
$545$	28.9031	+	16.6872i	1.23807	+	0.714802i
$546$	−17.7575	+	22.0581i	−0.759951	+	0.943999i
$547$		−	43.3641i		−	1.85411i	−0.374921	−	0.927057i	$-0.622330\pi$
$547$		−	43.3641i		−	1.85411i	0.374921	−	0.927057i	$-0.377670\pi$
$548$	−20.5505	+	20.3583i	−0.877873	+	0.869664i
$549$	−0.0977396	+	2.33065i	−0.00417142	+	0.0994697i
$550$	−8.03160	+	6.13295i	−0.342469	+	0.261510i
$551$	−23.9046	−	14.8381i	−1.01837	−	0.632124i
$552$	−3.31371	+	2.39834i	−0.141041	+	0.102080i
$553$	−4.37210			−0.185921
$554$	−6.72319	+	5.13384i	−0.285641	+	0.218116i
$555$	9.52726	+	9.93518i	0.404410	+	0.421725i
$556$	10.5352	+	40.0698i	0.446792	+	1.69934i
$557$	19.8699	−	11.4719i	0.841913	−	0.486079i	−0.0160009	−	0.999872i	$-0.505093\pi$
$557$	19.8699	−	11.4719i	0.841913	−	0.486079i	0.857914	+	0.513793i	$0.171760\pi$
$558$	−1.30283	−	14.9998i	−0.0551531	−	0.634991i
$559$			10.0359i			0.424472i
$560$	17.3852	+	10.2563i	0.734658	+	0.433408i
$561$	−14.8486	+	51.1070i	−0.626909	+	2.15774i
$562$	−4.90724	+	11.7689i	−0.206999	+	0.496440i
$563$	−12.8515	−	22.2595i	−0.541627	−	0.938125i	−0.998811	−	0.0487529i	$-0.984475\pi$
$563$	−12.8515	−	22.2595i	−0.541627	−	0.938125i	0.457184	−	0.889372i	$-0.348858\pi$
$564$	−15.1437	−	0.388568i	−0.637663	−	0.0163617i
$565$	12.8152	+	22.1966i	0.539140	+	0.933818i
$566$	−17.3955	+	41.7189i	−0.731185	+	1.75358i
$567$	20.8019	+	14.4592i	0.873598	+	0.607229i
$568$	−19.0047	−	2.63837i	−0.797420	−	0.110703i
$569$	9.75621	+	5.63275i	0.409002	+	0.236137i	0.690361	−	0.723465i	$-0.257452\pi$
$569$	9.75621	+	5.63275i	0.409002	+	0.236137i	−0.281359	+	0.959603i	$0.590785\pi$
$570$	−18.8106	−	3.54207i	−0.787890	−	0.148361i
$571$	−17.0698	+	9.85524i	−0.714348	+	0.412429i	−0.812669	−	0.582726i	$-0.801986\pi$
$571$	−17.0698	+	9.85524i	−0.714348	+	0.412429i	0.0983209	+	0.995155i	$0.468653\pi$
$572$	−8.65431	+	31.7020i	−0.361855	+	1.32553i
$573$	−9.68663	−	39.4390i	−0.404665	−	1.64759i
$574$	23.2797	−	17.7764i	0.971676	−	0.741974i
$575$	0.745678	−	1.29155i	0.0310969	−	0.0538614i
$576$	15.9940	+	17.8939i	0.666419	+	0.745578i
$577$	37.4911			1.56078			0.780388	−	0.625295i	$-0.215021\pi$
$577$	37.4911			1.56078			0.780388	+	0.625295i	$0.215021\pi$
$578$	−7.61233	−	58.8898i	−0.316631	−	2.44949i
$579$	3.93285	−	3.77137i	0.163443	−	0.156733i
$580$	16.2876	+	16.4414i	0.676307	+	0.682690i
$581$	−6.13466	+	3.54185i	−0.254509	+	0.146941i
$582$	−12.8174	−	10.3185i	−0.531299	−	0.427714i
$583$			10.2314i			0.423740i
$584$	31.9512	+	4.43570i	1.32215	+	0.183550i
$585$	−11.8361	+	18.6496i	−0.489361	+	0.771068i
$586$	20.6601	−	2.67061i	0.853462	−	0.110322i
$587$	−3.14952	−	5.45513i	−0.129995	−	0.225157i	0.793680	−	0.608336i	$-0.208163\pi$
$587$	−3.14952	−	5.45513i	−0.129995	−	0.225157i	−0.923674	+	0.383179i	$0.874829\pi$
$588$	1.52764	+	2.81003i	0.0629988	+	0.115884i
$589$	−0.493649	+	15.4609i	−0.0203404	+	0.637057i
$590$	6.01559	−	14.4270i	0.247658	−	0.593950i
$591$	23.4460	+	24.4499i	0.964440	+	1.00573i
$592$	−0.166577	+	17.7313i	−0.00684627	+	0.728753i
$593$	30.8163	−	17.7918i	1.26547	−	0.730621i	0.291345	−	0.956618i	$-0.405897\pi$
$593$	30.8163	−	17.7918i	1.26547	−	0.730621i	0.974128	+	0.225997i	$0.0725641\pi$
$594$	28.8355	+	5.72874i	1.18313	+	0.235053i
$595$	−33.5646	+	19.3785i	−1.37602	+	0.794443i
$596$	−13.4838	+	13.3577i	−0.552317	+	0.547153i
$597$	10.9553	−	37.7067i	0.448370	−	1.54323i
$598$	−0.621727	−	4.80975i	−0.0254243	−	0.196685i
$599$	1.96321	−	3.40038i	0.0802147	−	0.138936i	−0.823127	−	0.567857i	$-0.807773\pi$
$599$	1.96321	−	3.40038i	0.0802147	−	0.138936i	0.903342	+	0.428921i	$0.141106\pi$
$600$	−7.98705	−	3.57351i	−0.326070	−	0.145888i
$601$	−17.9063	+	31.0147i	−0.730415	+	1.26512i	0.226291	+	0.974060i	$0.427340\pi$
$601$	−17.9063	+	31.0147i	−0.730415	+	1.26512i	−0.956706	+	0.291056i	$0.905993\pi$
$602$	8.97815	+	3.74360i	0.365922	+	0.152578i
$603$	1.26797	−	1.99789i	0.0516356	−	0.0813603i
$604$	−8.90787	−	33.8804i	−0.362456	−	1.37857i
$605$	7.77147	−	4.48686i	0.315955	−	0.182417i
$606$	−7.68036	−	19.8373i	−0.311993	−	0.805837i
$607$	18.5677	−	10.7201i	0.753641	−	0.435115i	−0.0733673	−	0.997305i	$-0.523375\pi$
$607$	18.5677	−	10.7201i	0.753641	−	0.435115i	0.827008	+	0.562190i	$0.190041\pi$
$608$	−14.1425	−	20.1988i	−0.573554	−	0.819168i
$609$	7.50615	+	30.5612i	0.304165	+	1.23840i
$610$	−0.758688	+	1.81954i	−0.0307184	+	0.0736708i
$611$	8.98010	−	15.5540i	0.363296	−	0.629247i
$612$	−45.0193	+	9.84006i	−1.81980	+	0.397761i
$613$	21.6932	−	37.5738i	0.876182	−	1.51759i	0.0206840	−	0.999786i	$-0.493416\pi$
$613$	21.6932	−	37.5738i	0.876182	−	1.51759i	0.855498	−	0.517806i	$-0.173251\pi$
$614$	−4.95139	−	6.48425i	−0.199822	−	0.261683i
$615$	16.4906	−	15.8136i	0.664966	−	0.637664i
$616$	25.1325	+	19.5677i	1.01262	+	0.788406i
$617$	−36.0362	−	20.8055i	−1.45076	−	0.837599i	−0.452239	−	0.891897i	$-0.649375\pi$
$617$	−36.0362	−	20.8055i	−1.45076	−	0.837599i	−0.998525	+	0.0542976i	$0.982708\pi$
$618$	3.65531	−	4.54056i	0.147038	−	0.182648i
$619$	12.7039	+	7.33463i	0.510615	+	0.294804i	0.733086	−	0.680136i	$-0.238079\pi$
$619$	12.7039	+	7.33463i	0.510615	+	0.294804i	−0.222472	+	0.974939i	$0.571412\pi$
$620$	3.35093	−	12.2749i	0.134577	−	0.492973i
$621$	−4.25313	+	0.857421i	−0.170672	+	0.0344071i
$622$	0.934622	+	7.23033i	0.0374749	+	0.289910i
$623$	46.2358			1.85240
$624$	−27.6956	+	6.52709i	−1.10871	+	0.261293i
$625$	−12.8794			−0.515177
$626$	−21.1790	−	8.83095i	−0.846482	−	0.352956i
$627$	−28.7215	−	9.34851i	−1.14703	−	0.373343i
$628$	−25.7128	−	25.9555i	−1.02605	−	1.03574i
$629$	−29.4857	−	17.0236i	−1.17567	−	0.678775i
$630$	12.2690	+	17.5453i	0.488808	+	0.699022i
$631$	7.23451	−	4.17685i	0.288001	−	0.166278i	−0.349039	−	0.937108i	$-0.613492\pi$
$631$	7.23451	−	4.17685i	0.288001	−	0.166278i	0.637040	+	0.770831i	$0.280159\pi$
$632$	−3.46644	−	2.69891i	−0.137888	−	0.107357i
$633$	−33.2338	−	34.6567i	−1.32093	−	1.37748i
$634$	−0.0592587	+	0.142118i	−0.00235347	+	0.00564424i
$635$	−2.68782	−	4.65543i	−0.106663	−	0.184745i
$636$	−7.78328	+	4.23129i	−0.308627	+	0.167781i
$637$	−3.79205			−0.150247
$638$	22.1636	+	29.0251i	0.877467	+	1.14912i
$639$	−17.1825	−	10.9050i	−0.679731	−	0.431393i
$640$	7.45269	+	18.8637i	0.294593	+	0.745652i
$641$	5.96935	−	3.44640i	0.235775	−	0.136125i	−0.377458	−	0.926027i	$-0.623202\pi$
$641$	5.96935	−	3.44640i	0.235775	−	0.136125i	0.613233	+	0.789902i	$0.289869\pi$
$642$	−0.346642	+	0.134208i	−0.0136809	+	0.00529678i
$643$		−	16.8686i		−	0.665234i	−0.943062	−	0.332617i	$-0.892068\pi$
$643$		−	16.8686i		−	0.665234i	0.943062	−	0.332617i	$-0.107932\pi$
$644$	−4.53474	−	1.23794i	−0.178694	−	0.0487816i
$645$	7.28630	+	2.11696i	0.286898	+	0.0833553i
$646$	47.1240	−	4.56797i	1.85407	−	0.179724i
$647$	−15.5815			−0.612572			−0.306286	−	0.951939i	$-0.599086\pi$
$647$	−15.5815			−0.612572			−0.306286	+	0.951939i	$0.599086\pi$
$648$	7.56719	+	24.3051i	0.297267	+	0.954794i
$649$	12.3327	−	21.3609i	0.484101	−	0.838488i
$650$	8.24507	−	6.29595i	0.323398	−	0.246948i
$651$	12.4880	−	11.9753i	0.489443	−	0.469347i
$652$	−7.16226	+	7.09529i	−0.280496	+	0.277873i
$653$	−32.7006	+	18.8797i	−1.27967	+	0.738819i	−0.976788	−	0.214208i	$-0.931283\pi$
$653$	−32.7006	+	18.8797i	−1.27967	+	0.738819i	−0.302885	+	0.953027i	$0.597950\pi$
$654$	−7.00401	+	45.0597i	−0.273878	+	1.76198i
$655$		−	14.8581i		−	0.580556i
$656$	29.4308	+	0.276488i	1.14908	+	0.0107950i
$657$	28.8877	+	18.3337i	1.12702	+	0.715266i
$658$	−10.5649	−	13.8356i	−0.411863	−	0.539369i
$659$	−2.48029			−0.0966185			−0.0483092	−	0.998832i	$-0.515383\pi$
$659$	−2.48029			−0.0966185			−0.0483092	+	0.998832i	$0.515383\pi$
$660$	21.1909	+	12.9704i	0.824854	+	0.504874i
$661$	20.2831	−	35.1314i	0.788922	−	1.36645i	−0.137706	−	0.990473i	$-0.543973\pi$
$661$	20.2831	−	35.1314i	0.788922	−	1.36645i	0.926628	−	0.375980i	$-0.122694\pi$
$662$	−2.73053	−	3.57585i	−0.106125	−	0.138979i
$663$	15.2433	−	52.4653i	0.592000	−	2.03758i
$664$	−7.05028	−	0.978770i	−0.273604	−	0.0379836i
$665$	−10.3846	−	19.3905i	−0.402696	−	0.751931i
$666$	−7.95919	+	17.0406i	−0.308412	+	0.660310i
$667$	−4.66749	−	2.69478i	−0.180726	−	0.104342i
$668$	23.4859	−	6.17493i	0.908696	−	0.238915i
$669$	5.57316	−	19.1821i	0.215471	−	0.741622i
$670$	1.58937	−	1.21365i	0.0614027	−	0.0468872i
$671$	−1.55540	+	2.69404i	−0.0600457	+	0.104002i
$672$	−4.49189	+	27.2114i	−0.173278	+	1.04970i
$673$	3.10684	−	5.38120i	0.119760	−	0.207430i	−0.799913	−	0.600117i	$-0.795121\pi$
$673$	3.10684	−	5.38120i	0.119760	−	0.207430i	0.919672	+	0.392686i	$0.128454\pi$
$674$	−27.9997	−	11.6750i	−1.07851	−	0.449702i
$675$	−6.13725	−	6.96186i	−0.236223	−	0.267962i
$676$	2.03715	−	7.46235i	0.0783518	−	0.287014i
$677$	12.2111	+	7.05007i	0.469310	+	0.270956i	0.715951	−	0.698151i	$-0.245993\pi$
$677$	12.2111	+	7.05007i	0.469310	+	0.270956i	−0.246641	+	0.969107i	$0.579327\pi$
$678$	−21.9604	+	27.2788i	−0.843384	+	1.04764i
$679$		−	18.9090i		−	0.725659i
$680$	−38.5743	−	5.35515i	−1.47926	−	0.205361i
$681$	6.70973	+	27.3185i	0.257117	+	1.04685i
$682$	7.72726	−	18.5320i	0.295892	−	0.709628i
$683$	−30.2520			−1.15756			−0.578780	−	0.815483i	$-0.696471\pi$
$683$	−30.2520			−1.15756			−0.578780	+	0.815483i	$0.696471\pi$
$684$	−4.76641	−	25.7154i	−0.182248	−	0.983253i
$685$	−25.9294			−0.990713
$686$	9.30957	−	22.3268i	0.355441	−	0.852442i
$687$	6.35791	+	1.84723i	0.242569	+	0.0704761i
$688$	4.80743	+	8.51036i	0.183282	+	0.324454i
$689$		−	10.5033i		−	0.400144i
$690$	−3.62314	−	0.563175i	−0.137931	−	0.0214397i
$691$	27.2410	+	15.7276i	1.03630	+	0.598306i	0.918782	−	0.394766i	$-0.129174\pi$
$691$	27.2410	+	15.7276i	1.03630	+	0.598306i	0.117514	+	0.993071i	$0.462508\pi$
$692$	45.9282	+	12.5379i	1.74593	+	0.476621i
$693$	15.6512	+	29.9398i	0.594542	+	1.13732i
$694$	35.5503	+	14.8233i	1.34947	+	0.562686i
$695$	−18.5690	+	32.1624i	−0.704362	+	1.21999i
$696$	−12.9142	+	28.8641i	−0.489511	+	1.09409i
$697$	−28.2561	+	48.9411i	−1.07028	+	1.85377i
$698$	17.8745	−	13.6490i	0.676558	−	0.516621i
$699$	32.7138	−	8.03487i	1.23735	−	0.303907i
$700$	−2.55681	−	9.72461i	−0.0966382	−	0.367556i
$701$	−12.2607	−	7.07872i	−0.463080	−	0.267359i	0.250258	−	0.968179i	$-0.419484\pi$
$701$	−12.2607	−	7.07872i	−0.463080	−	0.267359i	−0.713339	+	0.700820i	$0.752818\pi$
$702$	−29.6019	−	5.88100i	−1.11725	−	0.221964i
$703$	10.1907	−	16.4175i	0.384348	−	0.619196i
$704$	7.84722	+	31.0287i	0.295753	+	1.16944i
$705$	−9.39834	−	9.80073i	−0.353962	−	0.369117i
$706$	20.0165	+	26.2133i	0.753332	+	0.986550i
$707$	12.2225	−	21.1700i	0.459675	−	0.796181i
$708$	21.3501	+	0.547817i	0.802386	+	0.0205882i
$709$	−33.3208			−1.25139			−0.625694	−	0.780069i	$-0.715184\pi$
$709$	−33.3208			−1.25139			−0.625694	+	0.780069i	$0.715184\pi$
$710$	−10.4378	−	13.6691i	−0.391723	−	0.512993i
$711$	−2.15872	−	4.12950i	−0.0809584	−	0.154868i
$712$	36.6583	+	28.5415i	1.37383	+	1.06964i
$713$			2.96318i			0.110972i
$714$	−41.2497	−	33.2074i	−1.54373	−	1.24276i
$715$	−25.5101	+	14.7282i	−0.954022	+	0.550805i
$716$	34.7547	+	35.0828i	1.29885	+	1.31110i
$717$	27.9193	+	8.11168i	1.04267	+	0.302936i
$718$	8.43975	−	6.44462i	0.314969	−	0.240511i
$719$	26.6582	−	46.1734i	0.994184	−	1.72198i	0.403827	−	0.914835i	$-0.367680\pi$
$719$	26.6582	−	46.1734i	0.994184	−	1.72198i	0.590357	−	0.807142i	$-0.298987\pi$
$720$	−1.10326	+	21.4845i	−0.0411161	+	0.800682i
$721$	6.69849			0.249465
$722$	1.73769	+	26.8138i	0.0646702	+	0.997907i
$723$	15.4030	−	14.7706i	0.572843	−	0.549323i
$724$	−3.75604	+	13.7589i	−0.139592	+	0.511345i
$725$		−	11.5287i		−	0.428164i
$726$	9.55086	+	7.68877i	0.354466	+	0.285357i
$727$	−21.0858	+	12.1739i	−0.782028	+	0.451504i	−0.837148	−	0.546976i	$-0.815779\pi$
$727$	−21.0858	+	12.1739i	−0.782028	+	0.451504i	0.0551207	+	0.998480i	$0.482446\pi$
$728$	−25.8005	−	20.0878i	−0.956229	−	0.744503i
$729$	−3.38594	+	26.7869i	−0.125405	+	0.992106i
$730$	17.5483	+	22.9809i	0.649491	+	0.850561i
$731$	−18.7676			−0.694144
$732$	−2.69268	−	0.0690909i	−0.0995244	−	0.00255367i
$733$	−16.2281	−	28.1079i	−0.599399	−	1.03819i	−0.992910	−	0.118870i	$-0.962073\pi$
$733$	−16.2281	−	28.1079i	−0.599399	−	1.03819i	0.393511	−	0.919320i	$-0.371260\pi$
$734$	−11.5763	+	27.7631i	−0.427289	+	1.02475i
$735$	−0.799893	+	2.75313i	−0.0295045	+	0.101551i
$736$	−2.83121	−	3.78081i	−0.104360	−	0.139363i
$737$	2.73283	−	1.57780i	0.100665	−	0.0581189i
$738$	28.2844	+	13.2108i	1.04116	+	0.486297i
$739$	−28.6574	−	16.5454i	−1.05418	−	0.608632i	−0.130364	−	0.991466i	$-0.541615\pi$
$739$	−28.6574	−	16.5454i	−1.05418	−	0.608632i	−0.923817	+	0.382834i	$0.874948\pi$
$740$	−11.2918	+	11.1862i	−0.415094	+	0.411213i
$741$	29.4849	+	9.59697i	1.08315	+	0.352554i
$742$	−9.39632	−	3.91796i	−0.344950	−	0.143833i
$743$	23.2405			0.852610			0.426305	−	0.904580i	$-0.359815\pi$
$743$	23.2405			0.852610			0.426305	+	0.904580i	$0.359815\pi$
$744$	17.2935	−	1.78577i	0.634010	−	0.0654696i
$745$	−17.0131			−0.623311
$746$	1.44961	+	11.2143i	0.0530738	+	0.410585i
$747$	−6.37430	−	4.04547i	−0.233223	−	0.148016i
$748$	−59.2842	−	16.1840i	−2.16765	−	0.591746i
$749$	−0.369930	−	0.213579i	−0.0135169	−	0.00780401i
$750$	−10.7592	−	27.7896i	−0.392871	−	1.01473i
$751$	37.6530	+	21.7389i	1.37398	+	0.793265i	0.991426	−	0.130670i	$-0.0417127\pi$
$751$	37.6530	+	21.7389i	1.37398	+	0.793265i	0.382550	+	0.923935i	$0.375046\pi$
$752$	0.164323	−	17.4914i	0.00599223	−	0.637845i
$753$	−21.1344	−	6.14039i	−0.770181	−	0.223768i
$754$	−22.7527	−	29.7966i	−0.828605	−	1.08513i
$755$	15.7007	−	27.1945i	0.571408	−	0.989708i
$756$	−16.3033	+	24.2883i	−0.592946	+	0.883355i
$757$	21.6050	−	37.4210i	0.785248	−	1.36009i	−0.143603	−	0.989635i	$-0.545869\pi$
$757$	21.6050	−	37.4210i	0.785248	−	1.36009i	0.928851	−	0.370454i	$-0.120798\pi$
$758$	14.3927	−	34.5176i	0.522768	−	1.25374i
$759$	−5.55618	−	1.61429i	−0.201677	−	0.0585951i
$760$	3.73635	−	21.7843i	0.135532	−	0.790198i
$761$	−21.3438	+	12.3229i	−0.773712	+	0.446703i	−0.834197	−	0.551466i	$-0.814069\pi$
$761$	−21.3438	+	12.3229i	−0.773712	+	0.446703i	0.0604849	+	0.998169i	$0.480735\pi$
$762$	4.60589	−	5.72136i	0.166854	−	0.207263i
$763$	−45.3817	+	26.2012i	−1.64293	+	0.948545i
$764$	45.3523	−	11.9241i	1.64079	−	0.431398i
$765$	−34.8758	−	22.1340i	−1.26094	−	0.800257i
$766$	26.6087	+	11.0949i	0.961410	+	0.400877i
$767$	−12.6605	+	21.9286i	−0.457144	+	0.791796i
$768$	−20.3591	+	18.8018i	−0.734645	+	0.678452i
$769$	4.91758	−	8.51750i	0.177333	−	0.307149i	−0.763633	−	0.645650i	$-0.776586\pi$
$769$	4.91758	−	8.51750i	0.177333	−	0.307149i	0.940966	+	0.338501i	$0.109920\pi$
$770$	3.66016	+	28.3154i	0.131903	+	1.02042i
$771$	3.55708	−	0.873657i	0.128105	−	0.0314640i
$772$	4.42806	+	4.46986i	0.159369	+	0.160874i
$773$	24.8976	−	14.3746i	0.895505	−	0.517020i	0.0197660	−	0.999805i	$-0.493708\pi$
$773$	24.8976	−	14.3746i	0.895505	−	0.517020i	0.875739	+	0.482784i	$0.160375\pi$
$774$	0.897085	+	10.3284i	0.0322451	+	0.371245i
$775$	−5.48927	+	3.16923i	−0.197180	+	0.113842i
$776$	11.6725	−	14.9920i	0.419020	−	0.538183i
$777$	−20.9891	+	5.15516i	−0.752981	+	0.184940i
$778$	0.185615	−	0.445155i	0.00665463	−	0.0159596i
$779$	−27.2500	−	16.9147i	−0.976334	−	0.606032i
$780$	−21.7541	−	13.3152i	−0.778922	−	0.476760i
$781$	−13.5696	−	23.5033i	−0.485559	−	0.841013i
$782$	8.99446	−	1.16266i	0.321641	−	0.0415766i
$783$	−25.1592	+	22.1792i	−0.899117	+	0.792620i
$784$	−3.21564	+	1.81649i	−0.114844	+	0.0648745i
$785$		−	32.7492i		−	1.16887i
$786$	18.9319	−	7.32979i	0.675278	−	0.261445i
$787$	−8.15443	+	4.70796i	−0.290674	+	0.167821i	−0.638246	−	0.769833i	$-0.720340\pi$
$787$	−8.15443	+	4.70796i	−0.290674	+	0.167821i	0.347572	+	0.937653i	$0.387006\pi$
$788$	−27.7884	+	27.5285i	−0.989920	+	0.980664i
$789$	3.26019	+	0.947217i	0.116066	+	0.0337218i
$790$	−0.504833	−	3.90544i	−0.0179612	−	0.138949i
$791$	−40.2432			−1.43088
$792$	−6.07277	+	33.3995i	−0.215786	+	1.18680i
$793$	1.59674	−	2.76564i	0.0567021	−	0.0982108i
$794$	13.5089	−	10.3155i	0.479414	−	0.366082i
$795$	−7.62567	−	2.21556i	−0.270455	−	0.0785779i
$796$	43.7398	+	11.9405i	1.55032	+	0.423221i
$797$	10.9915	−	6.34592i	0.389338	−	0.224784i	−0.292536	−	0.956255i	$-0.594499\pi$
$797$	10.9915	−	6.34592i	0.389338	−	0.224784i	0.681873	+	0.731471i	$0.261166\pi$
$798$	19.5840	−	22.7975i	0.693266	−	0.807021i
$799$	29.0867	+	16.7932i	1.02901	+	0.594102i
$800$	3.97585	−	9.28852i	0.140567	−	0.328399i
$801$	22.8289	+	43.6702i	0.806620	+	1.54301i
$802$	2.81104	−	6.74162i	0.0992612	−	0.238055i
$803$	22.8136	+	39.5143i	0.805074	+	1.39443i
$804$	2.33046	+	1.42642i	0.0821890	+	0.0503060i
$805$	−2.10677	−	3.64904i	−0.0742539	−	0.128612i
$806$	−7.93263	+	19.0246i	−0.279415	+	0.670112i
$807$	−41.6993	+	10.2418i	−1.46789	+	0.360529i
$808$	22.7590	−	9.23976i	0.800658	−	0.325054i
$809$			7.68181i			0.270078i	0.990840	+	0.135039i	$0.0431160\pi$
$809$			7.68181i			0.270078i	−0.990840	+	0.135039i	$0.956884\pi$
$810$	−10.5140	+	20.2512i	−0.369423	+	0.711554i
$811$	8.25992	−	4.76887i	0.290045	−	0.167458i	−0.347917	−	0.937525i	$-0.613111\pi$
$811$	8.25992	−	4.76887i	0.290045	−	0.167458i	0.637962	+	0.770068i	$0.279778\pi$
$812$	−35.1434	+	9.23995i	−1.23329	+	0.324259i
$813$	2.16157	−	0.530905i	0.0758095	−	0.0186196i
$814$	−19.9342	+	15.2218i	−0.698693	+	0.533524i
$815$	−9.03694			−0.316550
$816$	−12.2060	−	51.7922i	−0.427295	−	1.81309i
$817$	0.339911	−	10.6459i	0.0118920	−	0.372453i
$818$	−8.30191	+	6.33936i	−0.290269	+	0.221650i
$819$	−16.0672	−	30.7356i	−0.561435	−	1.07399i
$820$	18.5671	+	18.7423i	0.648391	+	0.654511i
$821$			31.8166i			1.11041i	0.831715	+	0.555203i	$0.187359\pi$
$821$			31.8166i			1.11041i	−0.831715	+	0.555203i	$0.812641\pi$
$822$	−12.7915	−	33.0387i	−0.446154	−	1.15236i
$823$	15.0649	+	8.69770i	0.525128	+	0.303183i	0.739030	−	0.673672i	$-0.235284\pi$
$823$	15.0649	+	8.69770i	0.525128	+	0.303183i	−0.213902	+	0.976855i	$0.568617\pi$
$824$	5.31092	+	4.13499i	0.185015	+	0.144049i
$825$	−2.95208	−	12.0193i	−0.102778	−	0.418460i
$826$	14.8948	+	19.5060i	0.518257	+	0.678700i
$827$	−9.71682	−	16.8300i	−0.337887	−	0.585237i	0.646148	−	0.763212i	$-0.276379\pi$
$827$	−9.71682	−	16.8300i	−0.337887	−	0.585237i	−0.984035	+	0.177975i	$0.943046\pi$
$828$	−1.06978	−	4.89435i	−0.0371774	−	0.170090i
$829$	−32.3396			−1.12320			−0.561600	−	0.827409i	$-0.689814\pi$
$829$	−32.3396			−1.12320			−0.561600	+	0.827409i	$0.689814\pi$
$830$	−3.87216	−	5.07091i	−0.134405	−	0.176014i
$831$	−2.47116	−	10.0613i	−0.0857237	−	0.349023i
$832$	−8.05578	−	31.8534i	−0.279284	−	1.10432i
$833$		−	7.09132i		−	0.245700i
$834$	−50.1410	−	7.79384i	−1.73624	−	0.269878i
$835$	18.8512	+	10.8837i	0.652373	+	0.376648i
$836$	10.2541	−	33.3359i	0.354645	−	1.15294i
$837$	17.4767	+	5.88226i	0.604083	+	0.203321i
$838$	0.649866	+	5.02743i	0.0224492	+	0.173670i
$839$	−19.0029	−	32.9139i	−0.656052	−	1.13631i	−0.981629	−	0.190799i	$-0.938892\pi$
$839$	−19.0029	−	32.9139i	−0.656052	−	1.13631i	0.325577	−	0.945515i	$-0.394441\pi$
$840$	−20.0266	+	14.4945i	−0.690983	+	0.500108i
$841$	−12.6631			−0.436657
$842$	1.19119	+	9.21516i	0.0410511	+	0.317575i
$843$	−10.8088	−	11.2716i	−0.372276	−	0.388216i
$844$	39.3890	−	39.0207i	1.35582	−	1.34315i
$845$	6.00484	−	3.46689i	0.206573	−	0.119265i
$846$	7.85148	−	16.8100i	0.269939	−	0.577940i
$847$			14.0899i			0.484136i
$848$	−5.03134	−	8.90674i	−0.172777	−	0.305859i
$849$	−38.3158	−	39.9563i	−1.31499	−	1.37130i
$850$	11.7737	+	15.4187i	0.403836	+	0.528856i
$851$	1.85075	−	3.20559i	0.0634429	−	0.109886i
$852$	12.2677	−	20.0428i	0.420285	−	0.686654i
$853$	13.0648	+	22.6289i	0.447331	+	0.774800i	0.998211	−	0.0597840i	$-0.0190412\pi$
$853$	13.0648	+	22.6289i	0.447331	+	0.774800i	−0.550880	+	0.834584i	$0.685708\pi$
$854$	−1.87854	−	2.46010i	−0.0642823	−	0.0841829i
$855$	13.1872	−	19.3824i	0.450992	−	0.662864i
$856$	−0.161458	−	0.397695i	−0.00551850	−	0.0135929i
$857$	−7.80328	+	4.50523i	−0.266555	+	0.153896i	−0.627321	−	0.778761i	$-0.715849\pi$
$857$	−7.80328	+	4.50523i	−0.266555	+	0.153896i	0.360766	+	0.932656i	$0.382515\pi$
$858$	−31.3509	−	25.2386i	−1.07030	−	0.861631i
$859$	−24.8568	−	14.3511i	−0.848104	−	0.489653i	0.0119065	−	0.999929i	$-0.496210\pi$
$859$	−24.8568	−	14.3511i	−0.848104	−	0.489653i	−0.860011	+	0.510276i	$0.829543\pi$
$860$	−2.30735	+	8.45213i	−0.0786798	+	0.288215i
$861$	8.55664	+	34.8382i	0.291610	+	1.18728i
$862$	−3.70474	−	28.6602i	−0.126184	−	0.976172i
$863$	−52.3373			−1.78158			−0.890792	−	0.454412i	$-0.849849\pi$
$863$	−52.3373			−1.78158			−0.890792	+	0.454412i	$0.849849\pi$
$864$	−27.9193	+	9.19297i	−0.949835	+	0.312751i
$865$	21.3375	+	36.9577i	0.725498	+	1.25660i
$866$	4.66096	+	36.0577i	0.158386	+	1.22529i
$867$	69.8371	+	20.2905i	2.37179	+	0.689101i
$868$	14.0604	+	14.1932i	0.477243	+	0.481747i
$869$		−	6.21402i		−	0.210796i
$870$	−26.4325	+	10.2338i	−0.896146	+	0.346958i
$871$	−2.80546	+	1.61973i	−0.0950594	+	0.0548826i
$872$	−52.1551	−	7.24054i	−1.76620	−	0.245196i
$873$	17.8597	−	9.33629i	0.604460	−	0.315985i
$874$	0.496615	+	5.12317i	0.0167982	+	0.173294i
$875$	17.1222	−	29.6565i	0.578836	−	1.00257i
$876$	−20.6248	+	33.6965i	−0.696848	+	1.13850i
$877$	−3.60999			−0.121901			−0.0609503	−	0.998141i	$-0.519413\pi$
$877$	−3.60999			−0.121901			−0.0609503	+	0.998141i	$0.519413\pi$
$878$	48.0160	−	6.20674i	1.62046	−	0.209467i
$879$	−7.11845	+	24.5008i	−0.240099	+	0.826390i
$880$	−14.5772	+	24.7094i	−0.491397	+	0.832954i
$881$		−	2.96110i		−	0.0997620i	−0.998755	−	0.0498810i	$-0.984116\pi$
$881$		−	2.96110i		−	0.0997620i	0.998755	−	0.0498810i	$-0.0158842\pi$
$882$	−3.90257	+	0.338963i	−0.131406	+	0.0114135i
$883$	−20.9235	+	12.0802i	−0.704133	+	0.406531i	−0.808885	−	0.587967i	$-0.799929\pi$
$883$	−20.9235	+	12.0802i	−0.704133	+	0.406531i	0.104752	+	0.994498i	$0.466595\pi$
$884$	60.8599	+	16.6141i	2.04694	+	0.558794i
$885$	13.2501	+	13.8174i	0.445398	+	0.464468i
$886$	27.2994	+	11.3830i	0.917142	+	0.382419i
$887$	25.8310	−	44.7405i	0.867319	−	1.50224i	0.00259288	−	0.999997i	$-0.499175\pi$
$887$	25.8310	−	44.7405i	0.867319	−	1.50224i	0.864726	−	0.502244i	$-0.167492\pi$
$888$	−19.8236	−	8.86935i	−0.665237	−	0.297636i
$889$	8.44046			0.283084
$890$	5.33871	+	41.3008i	0.178954	+	1.38441i
$891$	−20.5507	+	29.5656i	−0.688475	+	0.990483i
$892$	22.2513	+	6.07437i	0.745027	+	0.203385i
$893$	−10.0528	+	16.1953i	−0.336403	+	0.541955i
$894$	−8.39287	−	21.6777i	−0.280700	−	0.725009i
$895$			44.2655i			1.47963i
$896$	−31.5012	−	4.67525i	−1.05238	−	0.156189i
$897$	5.70386	+	1.65720i	0.190446	+	0.0553322i
$898$	5.84316	−	14.0135i	0.194989	−	0.467635i
$899$	11.4532	+	19.8375i	0.381985	+	0.661617i
$900$	7.92258	−	7.21645i	0.264086	−	0.240548i
$901$	19.6417			0.654360
$902$	25.2655	+	33.0872i	0.841248	+	1.10168i
$903$	−8.59882	+	8.24578i	−0.286151	+	0.274402i
$904$	−31.9070	−	24.8422i	−1.06121	−	0.826240i
$905$	−11.0715	+	6.39216i	−0.368031	+	0.212483i
$906$	42.3960	+	6.58996i	1.40851	+	0.218937i
$907$	32.3448	−	18.6743i	1.07399	−	0.620070i	0.144723	−	0.989472i	$-0.453771\pi$
$907$	32.3448	−	18.6743i	1.07399	−	0.620070i	0.929269	+	0.369403i	$0.120438\pi$
$908$	−31.4146	+	8.25956i	−1.04253	+	0.274103i
$909$	26.0302	+	1.09162i	0.863367	+	0.0362067i
$910$	−3.75744	−	29.0680i	−0.124558	−	0.963594i
$911$	−2.46360	+	4.26707i	−0.0816226	+	0.141374i	−0.903947	−	0.427644i	$-0.859344\pi$
$911$	−2.46360	+	4.26707i	−0.0816226	+	0.141374i	0.822324	+	0.569019i	$0.192677\pi$
$912$	29.6002	−	5.98581i	0.980160	−	0.198210i
$913$	−5.03399	−	8.71913i	−0.166601	−	0.288561i
$914$	−12.0774	+	9.22236i	−0.399486	+	0.305048i
$915$	−1.67111	−	1.74266i	−0.0552452	−	0.0576106i
$916$	−2.01335	+	7.37519i	−0.0665230	+	0.243683i
$917$	20.2037	+	11.6646i	0.667186	+	0.385200i
$918$	10.9978	−	55.3569i	0.362980	−	1.82705i
$919$			57.3260i			1.89101i	0.325606	+	0.945506i	$0.394432\pi$
$919$			57.3260i			1.89101i	−0.325606	+	0.945506i	$0.605568\pi$
$920$	0.582194	−	4.19367i	0.0191944	−	0.138261i
$921$	9.70373	−	2.38334i	0.319749	−	0.0785337i
$922$	9.14535	−	1.18216i	0.301186	−	0.0389325i
$923$	13.9303	+	24.1279i	0.458520	+	0.794181i
$924$	−34.2732	+	18.6322i	−1.12750	+	0.612954i
$925$	7.91779			0.260335
$926$	−53.9983	+	6.98003i	−1.77449	+	0.229378i
$927$	3.30737	+	6.32679i	0.108628	+	0.207799i
$928$	−33.5674	−	14.3682i	−1.10191	−	0.471658i
$929$	−10.1343	+	5.85103i	−0.332495	+	0.191966i	−0.656948	−	0.753936i	$-0.728153\pi$
$929$	−10.1343	+	5.85103i	−0.332495	+	0.191966i	0.324453	+	0.945902i	$0.394820\pi$
$930$	12.1390	+	9.77233i	0.398054	+	0.320447i
$931$	4.02255	+	0.128435i	0.131834	+	0.00420929i
$932$	9.89079	+	37.6188i	0.323983	+	1.23225i
$933$	−8.57442	−	2.49121i	−0.280714	−	0.0815586i
$934$	−26.7641	−	11.1598i	−0.875748	−	0.365159i
$935$	−27.5425	−	47.7051i	−0.900737	−	1.56012i
$936$	6.23417	−	34.2872i	0.203770	−	1.12071i
$937$	3.22655	+	5.58855i	0.105407	+	0.182570i	0.913904	−	0.405930i	$-0.133052\pi$
$937$	3.22655	+	5.58855i	0.105407	+	0.182570i	−0.808498	+	0.588500i	$0.799719\pi$
$938$	0.402525	+	3.11398i	0.0131429	+	0.101675i
$939$	20.2842	−	19.4513i	0.661949	−	0.634771i
$940$	11.1390	−	11.0348i	0.363313	−	0.359916i
$941$	−16.3924	−	9.46418i	−0.534378	−	0.308524i	0.208419	−	0.978040i	$-0.433168\pi$
$941$	−16.3924	−	9.46418i	−0.534378	−	0.308524i	−0.742798	+	0.669516i	$0.766502\pi$
$942$	41.7282	−	16.1558i	1.35958	−	0.526384i
$943$	−5.32071	−	3.07191i	−0.173266	−	0.100035i
$944$	−0.231668	+	24.6600i	−0.00754016	+	0.802615i
$945$	−25.7040	+	5.18187i	−0.836152	+	0.168566i
$946$	−5.32074	+	12.7606i	−0.172992	+	0.414881i
$947$	−3.37692	−	5.84899i	−0.109735	−	0.190067i	0.805928	−	0.592014i	$-0.201667\pi$
$947$	−3.37692	−	5.84899i	−0.109735	−	0.190067i	−0.915663	+	0.401947i	$0.868334\pi$
$948$	4.72718	−	2.56987i	0.153532	−	0.0834656i
$949$	−23.4199	−	40.5645i	−0.760244	−	1.31678i
$950$	−8.95949	+	6.39940i	−0.290684	+	0.207624i
$951$	−0.130525	−	0.136114i	−0.00423257	−	0.00441379i
$952$	37.5652	−	48.2482i	1.21749	−	1.56373i
$953$	−4.85581	−	2.80350i	−0.157295	−	0.0908143i	0.419286	−	0.907854i	$-0.362280\pi$
$953$	−4.85581	−	2.80350i	−0.157295	−	0.0908143i	−0.576581	+	0.817040i	$0.695614\pi$
$954$	−0.938868	−	10.8094i	−0.0303970	−	0.349968i
$955$	36.4025	+	21.0170i	1.17796	+	0.680095i
$956$	−8.84119	+	32.3865i	−0.285944	+	1.04745i
$957$	−43.4363	+	10.6684i	−1.40410	+	0.344861i
$958$	29.8678	+	12.4539i	0.964984	+	0.402367i
$959$	20.3563	−	35.2582i	0.657340	−	1.13855i
$960$	−24.8256	−	0.870430i	−0.801244	−	0.0280930i
$961$	−9.20304	+	15.9401i	−0.296872	+	0.514198i
$962$	20.4640	−	15.6264i	0.659786	−	0.503814i
$963$	0.0190752	−	0.454857i	0.000614689	−	0.0146576i
$964$	17.3425	+	17.5062i	0.558564	+	0.563836i
$965$			5.63982i			0.181552i
$966$	3.61020	−	4.48453i	0.116156	−	0.144287i
$967$			4.66646i			0.150063i	0.997181	+	0.0750315i	$0.0239057\pi$
$967$			4.66646i			0.150063i	−0.997181	+	0.0750315i	$0.976094\pi$
$968$	−8.69775	+	11.1713i	−0.279556	+	0.359058i
$969$	−17.9468	+	55.1382i	−0.576535	+	1.77129i
$970$	16.8907	−	2.18336i	0.542328	−	0.0701034i
$971$	26.9215	−	46.6295i	0.863953	−	1.49641i	−0.00412986	−	0.999991i	$-0.501315\pi$
$971$	26.9215	−	46.6295i	0.863953	−	1.49641i	0.868083	−	0.496419i	$-0.165352\pi$
$972$	−30.9903	−	3.40635i	−0.994013	−	0.109259i
$973$	−29.1558	−	50.4993i	−0.934692	−	1.61893i
$974$	3.28155	−	7.87002i	0.105147	−	0.252172i
$975$	3.03054	+	12.3388i	0.0970550	+	0.395158i
$976$	0.0292181	−	3.11013i	0.000935248	−	0.0995527i
$977$	35.8836	−	20.7174i	1.14802	−	0.662808i	0.199614	−	0.979875i	$-0.436031\pi$
$977$	35.8836	−	20.7174i	1.14802	−	0.662808i	0.948403	+	0.317067i	$0.102698\pi$
$978$	−4.45809	−	11.5146i	−0.142554	−	0.368198i
$979$			65.7145i			2.10025i
$980$	−3.19363	−	0.871830i	−0.102017	−	0.0278496i
$981$	−47.1545	−	29.9267i	−1.50553	−	0.955487i
$982$	5.87404	+	2.44929i	0.187448	+	0.0781599i
$983$	22.5154	+	38.9978i	0.718130	+	1.24384i	0.961740	+	0.273964i	$0.0883349\pi$
$983$	22.5154	+	38.9978i	0.718130	+	1.24384i	−0.243610	+	0.969873i	$0.578332\pi$
$984$	−14.7215	+	32.9037i	−0.469305	+	1.04893i
$985$	−35.0618			−1.11716
$986$	55.7210	−	42.5487i	1.77452	−	1.35503i
$987$	20.7051	−	5.08540i	0.659051	−	0.161870i
$988$	−10.5266	+	34.2219i	−0.334897	+	1.08874i
$989$		−	2.04035i		−	0.0648794i
$990$	−24.9370	+	17.4378i	−0.792550	+	0.554209i
$991$	7.73322	+	4.46477i	0.245654	+	0.141828i	0.617772	−	0.786357i	$-0.288035\pi$
$991$	7.73322	+	4.46477i	0.245654	+	0.141828i	−0.372119	+	0.928185i	$0.621369\pi$
$992$	2.38642	+	19.9326i	0.0757688	+	0.632862i
$993$	5.35128	−	1.31433i	0.169818	−	0.0417091i
$994$	26.7813	−	3.46185i	0.849451	−	0.109803i
$995$	20.3208	+	35.1967i	0.644214	+	1.11581i
$996$	4.55102	−	7.43538i	0.144205	−	0.235599i
$997$	−32.7263			−1.03645			−0.518226	−	0.855244i	$-0.673407\pi$
$997$	−32.7263			−1.03645			−0.518226	+	0.855244i	$0.673407\pi$
$998$	5.79406	−	13.8957i	0.183408	−	0.439860i
$999$	−15.2325	−	17.2791i	−0.481934	−	0.546687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.o.a.11.15	✓	232
4.3	odd	2	inner	684.2.o.a.11.54	yes	232
9.5	odd	6		684.2.bi.a.239.25	yes	232
19.7	even	3		684.2.bi.a.83.92	yes	232
36.23	even	6		684.2.bi.a.239.92	yes	232
76.7	odd	6		684.2.bi.a.83.25	yes	232
171.140	odd	6	inner	684.2.o.a.311.54	yes	232
684.311	even	6	inner	684.2.o.a.311.15	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.o.a.11.15	✓	232	1.1	even	1	trivial
684.2.o.a.11.54	yes	232	4.3	odd	2	inner
684.2.o.a.311.15	yes	232	684.311	even	6	inner
684.2.o.a.311.54	yes	232	171.140	odd	6	inner
684.2.bi.a.83.25	yes	232	76.7	odd	6
684.2.bi.a.83.92	yes	232	19.7	even	3
684.2.bi.a.239.25	yes	232	9.5	odd	6
684.2.bi.a.239.92	yes	232	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.30529 - 0.544263i) q^{2} +(1.25014 - 1.19881i) q^{3} +(1.40756 + 1.42084i) q^{4} +1.79274i q^{5} +(-2.28426 + 0.884390i) q^{6} +(-2.43772 - 1.40742i) q^{7} +(-1.06395 - 2.62069i) q^{8} +(0.125699 - 2.99737i) q^{9} +(0.975721 - 2.34004i) q^{10} +(2.00035 - 3.46471i) q^{11} +(3.46296 + 0.0888553i) q^{12} +(-2.05352 + 3.55679i) q^{13} +(2.41592 + 3.16385i) q^{14} +(2.14916 + 2.24117i) q^{15} +(-0.0375763 + 3.99982i) q^{16} +(-6.65138 - 3.84018i) q^{17} +(-1.79543 + 3.84401i) q^{18} +(2.29881 - 3.70344i) q^{19} +(-2.54719 + 2.52338i) q^{20} +(-4.73472 + 1.16290i) q^{21} +(-4.49675 + 3.43373i) q^{22} +(0.417491 - 0.723116i) q^{23} +(-4.47180 - 2.00074i) q^{24} +1.78609 q^{25} +(4.61626 - 3.52499i) q^{26} +(-3.43614 - 3.89782i) q^{27} +(-1.43151 - 5.44463i) q^{28} -6.45469i q^{29} +(-1.58548 - 4.09508i) q^{30} +(-3.07334 + 1.77440i) q^{31} +(2.22600 - 5.20047i) q^{32} +(-1.65282 - 6.72941i) q^{33} +(6.59190 + 8.63264i) q^{34} +(2.52313 - 4.37019i) q^{35} +(4.43571 - 4.04036i) q^{36} +4.43303 q^{37} +(-5.01625 + 3.58291i) q^{38} +(1.69675 + 6.90827i) q^{39} +(4.69820 - 1.90739i) q^{40} -7.35803i q^{41} +(6.81310 + 1.05902i) q^{42} +(2.11621 - 1.22179i) q^{43} +(7.73840 - 2.03459i) q^{44} +(5.37349 + 0.225346i) q^{45} +(-0.938512 + 0.716650i) q^{46} -4.37304 q^{47} +(4.74806 + 5.04539i) q^{48} +(0.461654 + 0.799607i) q^{49} +(-2.33136 - 0.972104i) q^{50} +(-12.9188 + 3.17300i) q^{51} +(-7.94407 + 2.08866i) q^{52} +(-2.21477 + 1.27870i) q^{53} +(2.36371 + 6.95794i) q^{54} +(6.21131 + 3.58610i) q^{55} +(-1.09478 + 7.88593i) q^{56} +(-1.56590 - 7.38566i) q^{57} +(-3.51305 + 8.42523i) q^{58} +6.16527 q^{59} +(-0.159294 + 6.20818i) q^{60} -0.777566 q^{61} +(4.97734 - 0.643390i) q^{62} +(-4.52497 + 7.12983i) q^{63} +(-5.73600 + 5.57658i) q^{64} +(-6.37640 - 3.68142i) q^{65} +(-1.50517 + 9.68339i) q^{66} +(0.683087 + 0.394381i) q^{67} +(-3.90591 - 14.8558i) q^{68} +(-0.344958 - 1.40449i) q^{69} +(-5.67195 + 4.33111i) q^{70} +(3.39181 - 5.87479i) q^{71} +(-7.98890 + 2.85964i) q^{72} +(-5.70240 + 9.87685i) q^{73} +(-5.78638 - 2.41273i) q^{74} +(2.23286 - 2.14119i) q^{75} +(8.49770 - 1.94656i) q^{76} +(-9.75259 + 5.63066i) q^{77} +(1.54517 - 9.94076i) q^{78} +(1.34514 - 0.776617i) q^{79} +(-7.17063 - 0.0673645i) q^{80} +(-8.96840 - 0.753534i) q^{81} +(-4.00470 + 9.60435i) q^{82} +(1.25828 - 2.17940i) q^{83} +(-8.31668 - 5.09044i) q^{84} +(6.88443 - 11.9242i) q^{85} +(-3.42723 + 0.443018i) q^{86} +(-7.73796 - 8.06927i) q^{87} +(-11.2082 - 1.55600i) q^{88} +(-14.2251 + 8.21288i) q^{89} +(-6.89131 - 3.21873i) q^{90} +(10.0118 - 5.78031i) q^{91} +(1.61508 - 0.424637i) q^{92} +(-1.71494 + 5.90260i) q^{93} +(5.70807 + 2.38008i) q^{94} +(6.63930 + 4.12116i) q^{95} +(-3.45157 - 9.16988i) q^{96} +(3.35880 + 5.81762i) q^{97} +(-0.167394 - 1.29498i) q^{98} +(-10.1336 - 6.43129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - 3 q^{2} + q^{4} + 3 q^{6} + 2 q^{10} - q^{12} + 2 q^{13} + q^{16} - 12 q^{17} - 16 q^{18} - 27 q^{20} - 14 q^{21} + 6 q^{22} - 10 q^{24} - 204 q^{25} - 6 q^{28} - 9 q^{30} - 3 q^{32} - 12 q^{33}+ \cdots - 162 q^{98}+O(q^{100}) \) 232 * q - 3 * q^2 + q^4 + 3 * q^6 + 2 * q^10 - q^12 + 2 * q^13 + q^16 - 12 * q^17 - 16 * q^18 - 27 * q^20 - 14 * q^21 + 6 * q^22 - 10 * q^24 - 204 * q^25 - 6 * q^28 - 9 * q^30 - 3 * q^32 - 12 * q^33 + 2 * q^34 + 13 * q^36 - 16 * q^37 - 3 * q^38 - 16 * q^40 - 43 * q^42 + 21 * q^44 + 2 * q^45 - 24 * q^46 + 58 * q^48 + 88 * q^49 + 9 * q^50 + 17 * q^52 + 41 * q^54 - 48 * q^56 - 12 * q^57 + 2 * q^58 + 16 * q^60 - 4 * q^61 + 6 * q^62 + 16 * q^64 + 12 * q^65 - 27 * q^66 - 18 * q^68 - 14 * q^69 + 60 * q^70 + 15 * q^72 + 2 * q^73 - 30 * q^74 + 3 * q^76 - 12 * q^77 - 64 * q^78 + 54 * q^80 + 4 * q^81 + 2 * q^82 - 10 * q^84 + 22 * q^85 + 51 * q^86 - 18 * q^88 + 14 * q^90 + 57 * q^92 + 4 * q^93 - 6 * q^94 - 17 * q^96 - 4 * q^97 - 162 * q^98

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