LMFDB - Embedded newform 425.2.k.b.86.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] 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("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.14
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.742425 - 0.539403i) q^{2} +(0.213285 - 0.656424i) q^{3} +(-0.357795 + 1.10118i) q^{4} +(2.18854 - 0.458598i) q^{5} +(-0.195729 - 0.602392i) q^{6} +1.08853 q^{7} +(0.895506 + 2.75609i) q^{8} +(2.04165 + 1.48335i) q^{9} +(1.37745 - 1.52098i) q^{10} +(-3.50028 + 2.54310i) q^{11} +(0.646528 + 0.469730i) q^{12} +(0.552867 + 0.401681i) q^{13} +(0.808152 - 0.587157i) q^{14} +(0.165747 - 1.53442i) q^{15} +(0.278050 + 0.202015i) q^{16} +(0.309017 + 0.951057i) q^{17} +2.31589 q^{18} +(-2.07999 - 6.40154i) q^{19} +(-0.278048 + 2.57405i) q^{20} +(0.232167 - 0.714537i) q^{21} +(-1.22694 + 3.77613i) q^{22} +(0.469902 - 0.341404i) q^{23} +2.00016 q^{24} +(4.57937 - 2.00732i) q^{25} +0.627130 q^{26} +(3.08432 - 2.24089i) q^{27} +(-0.389470 + 1.19867i) q^{28} +(2.36319 - 7.27315i) q^{29} +(-0.704616 - 1.22860i) q^{30} +(0.276832 + 0.852003i) q^{31} -5.48044 q^{32} +(0.922796 + 2.84007i) q^{33} +(0.742425 + 0.539403i) q^{34} +(2.38229 - 0.499198i) q^{35} +(-2.36392 + 1.71749i) q^{36} +(0.318361 + 0.231303i) q^{37} +(-4.99724 - 3.63071i) q^{38} +(0.381591 - 0.277242i) q^{39} +(3.22378 + 5.62111i) q^{40} +(4.54428 + 3.30161i) q^{41} +(-0.213057 - 0.655722i) q^{42} -5.18004 q^{43} +(-1.54803 - 4.76435i) q^{44} +(5.14848 + 2.31006i) q^{45} +(0.164713 - 0.506934i) q^{46} +(-1.90830 + 5.87313i) q^{47} +(0.191911 - 0.139432i) q^{48} -5.81510 q^{49} +(2.31709 - 3.96041i) q^{50} +0.690205 q^{51} +(-0.640136 + 0.465086i) q^{52} +(2.70532 - 8.32612i) q^{53} +(1.08113 - 3.32738i) q^{54} +(-6.49423 + 7.17090i) q^{55} +(0.974785 + 3.00008i) q^{56} -4.64575 q^{57} +(-2.16867 - 6.67448i) q^{58} +(-11.7992 - 8.57264i) q^{59} +(1.63037 + 0.731524i) q^{60} +(-4.85982 + 3.53087i) q^{61} +(0.665101 + 0.483224i) q^{62} +(2.22240 + 1.61467i) q^{63} +(-4.62492 + 3.36020i) q^{64} +(1.39418 + 0.625550i) q^{65} +(2.21705 + 1.61078i) q^{66} +(-1.41290 - 4.34845i) q^{67} -1.15785 q^{68} +(-0.123883 - 0.381271i) q^{69} +(1.49940 - 1.65563i) q^{70} +(2.67782 - 8.24148i) q^{71} +(-2.25992 + 6.95531i) q^{72} +(-10.6963 + 7.77135i) q^{73} +0.361125 q^{74} +(-0.340939 - 3.43414i) q^{75} +7.79345 q^{76} +(-3.81016 + 2.76824i) q^{77} +(0.133757 - 0.411663i) q^{78} +(1.24328 - 3.82643i) q^{79} +(0.701166 + 0.314604i) q^{80} +(1.52639 + 4.69774i) q^{81} +5.15469 q^{82} +(2.80123 + 8.62129i) q^{83} +(0.703765 + 0.511315i) q^{84} +(1.11245 + 1.93971i) q^{85} +(-3.84579 + 2.79413i) q^{86} +(-4.27023 - 3.10251i) q^{87} +(-10.1435 - 7.36971i) q^{88} +(7.35359 - 5.34270i) q^{89} +(5.06842 - 1.06207i) q^{90} +(0.601812 + 0.437242i) q^{91} +(0.207818 + 0.639599i) q^{92} +0.618319 q^{93} +(1.75122 + 5.38970i) q^{94} +(-7.48786 - 13.0561i) q^{95} +(-1.16890 + 3.59749i) q^{96} +(-0.975963 + 3.00371i) q^{97} +(-4.31728 + 3.13669i) q^{98} -10.9187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.742425	−	0.539403i	0.524974	−	0.381416i	−0.293500	−	0.955959i	$-0.594820\pi$
$2$	0.742425	−	0.539403i	0.524974	−	0.381416i	0.818474	+	0.574543i	$0.194820\pi$
$3$	0.213285	−	0.656424i	0.123140	−	0.378986i	−0.870418	−	0.492314i	$-0.836151\pi$
$3$	0.213285	−	0.656424i	0.123140	−	0.378986i	0.993558	+	0.113328i	$0.0361511\pi$
$4$	−0.357795	+	1.10118i	−0.178897	+	0.550590i
$5$	2.18854	−	0.458598i	0.978743	−	0.205091i
$5$	2.18854	−	0.458598i	0.978743	−	0.205091i
$6$	−0.195729	−	0.602392i	−0.0799060	−	0.245926i
$7$	1.08853			0.411426			0.205713	−	0.978612i	$-0.434049\pi$
$7$	1.08853			0.411426			0.205713	+	0.978612i	$0.434049\pi$
$8$	0.895506	+	2.75609i	0.316609	+	0.974423i
$9$	2.04165	+	1.48335i	0.680550	+	0.494448i
$10$	1.37745	−	1.52098i	0.435589	−	0.480976i
$11$	−3.50028	+	2.54310i	−1.05537	+	0.766775i	−0.973227	−	0.229845i	$-0.926178\pi$
$11$	−3.50028	+	2.54310i	−1.05537	+	0.766775i	−0.0821477	+	0.996620i	$0.526178\pi$
$12$	0.646528	+	0.469730i	0.186637	+	0.135599i
$13$	0.552867	+	0.401681i	0.153338	+	0.111406i	0.661809	−	0.749673i	$-0.269789\pi$
$13$	0.552867	+	0.401681i	0.153338	+	0.111406i	−0.508471	+	0.861079i	$0.669789\pi$
$14$	0.808152	−	0.587157i	0.215988	−	0.156924i
$15$	0.165747	−	1.53442i	0.0427956	−	0.396185i
$16$	0.278050	+	0.202015i	0.0695125	+	0.0505038i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	2.31589			0.545861
$19$	−2.07999	−	6.40154i	−0.477181	−	1.46861i	−0.842993	−	0.537924i	$-0.819209\pi$
$19$	−2.07999	−	6.40154i	−0.477181	−	1.46861i	0.365812	−	0.930689i	$-0.380791\pi$
$20$	−0.278048	+	2.57405i	−0.0621733	+	0.575576i
$21$	0.232167	−	0.714537i	0.0506630	−	0.155925i
$22$	−1.22694	+	3.77613i	−0.261584	+	0.805073i
$23$	0.469902	−	0.341404i	0.0979814	−	0.0711876i	−0.537716	−	0.843126i	$-0.680713\pi$
$23$	0.469902	−	0.341404i	0.0979814	−	0.0711876i	0.635697	+	0.771938i	$0.280713\pi$
$24$	2.00016			0.408280
$25$	4.57937	−	2.00732i	0.915875	−	0.401464i
$26$	0.627130			0.122990
$27$	3.08432	−	2.24089i	0.593577	−	0.431259i
$28$	−0.389470	+	1.19867i	−0.0736030	+	0.226527i
$29$	2.36319	−	7.27315i	0.438833	−	1.35059i	−0.450274	−	0.892890i	$-0.648674\pi$
$29$	2.36319	−	7.27315i	0.438833	−	1.35059i	0.889107	−	0.457699i	$-0.151326\pi$
$30$	−0.704616	−	1.22860i	−0.128645	−	0.224310i
$31$	0.276832	+	0.852003i	0.0497206	+	0.153024i	0.972834	−	0.231503i	$-0.0743644\pi$
$31$	0.276832	+	0.852003i	0.0497206	+	0.153024i	−0.923114	+	0.384527i	$0.874364\pi$
$32$	−5.48044			−0.968814
$33$	0.922796	+	2.84007i	0.160638	+	0.494393i
$34$	0.742425	+	0.539403i	0.127325	+	0.0925069i
$35$	2.38229	−	0.499198i	0.402680	−	0.0843799i
$36$	−2.36392	+	1.71749i	−0.393987	+	0.286248i
$37$	0.318361	+	0.231303i	0.0523382	+	0.0380259i	0.613647	−	0.789581i	$-0.289702\pi$
$37$	0.318361	+	0.231303i	0.0523382	+	0.0380259i	−0.561309	+	0.827607i	$0.689702\pi$
$38$	−4.99724	−	3.63071i	−0.810660	−	0.588979i
$39$	0.381591	−	0.277242i	0.0611035	−	0.0443943i
$40$	3.22378	+	5.62111i	0.509725	+	0.888776i
$41$	4.54428	+	3.30161i	0.709697	+	0.515625i	0.883076	−	0.469230i	$-0.155468\pi$
$41$	4.54428	+	3.30161i	0.709697	+	0.515625i	−0.173379	+	0.984855i	$0.555468\pi$
$42$	−0.213057	−	0.655722i	−0.0328754	−	0.101180i
$43$	−5.18004			−0.789949			−0.394974	−	0.918692i	$-0.629247\pi$
$43$	−5.18004			−0.789949			−0.394974	+	0.918692i	$0.629247\pi$
$44$	−1.54803	−	4.76435i	−0.233374	−	0.718253i
$45$	5.14848	+	2.31006i	0.767490	+	0.344363i
$46$	0.164713	−	0.506934i	0.0242856	−	0.0747433i
$47$	−1.90830	+	5.87313i	−0.278354	+	0.856684i	0.709959	+	0.704243i	$0.248713\pi$
$47$	−1.90830	+	5.87313i	−0.278354	+	0.856684i	−0.988313	+	0.152441i	$0.951287\pi$
$48$	0.191911	−	0.139432i	0.0277000	−	0.0201252i
$49$	−5.81510			−0.830729
$50$	2.31709	−	3.96041i	0.327686	−	0.560087i
$51$	0.690205			0.0966480
$52$	−0.640136	+	0.465086i	−0.0887709	+	0.0644958i
$53$	2.70532	−	8.32612i	0.371604	−	1.14368i	−0.574137	−	0.818759i	$-0.694662\pi$
$53$	2.70532	−	8.32612i	0.371604	−	1.14368i	0.945741	−	0.324921i	$-0.105338\pi$
$54$	1.08113	−	3.32738i	0.147123	−	0.452799i
$55$	−6.49423	+	7.17090i	−0.875682	+	0.966924i
$56$	0.974785	+	3.00008i	0.130261	+	0.400903i
$57$	−4.64575			−0.615344
$58$	−2.16867	−	6.67448i	−0.284760	−	0.876402i
$59$	−11.7992	−	8.57264i	−1.53613	−	1.11606i	−0.952706	−	0.303894i	$-0.901713\pi$
$59$	−11.7992	−	8.57264i	−1.53613	−	1.11606i	−0.583423	−	0.812168i	$-0.698287\pi$
$60$	1.63037	+	0.731524i	0.210479	+	0.0944394i
$61$	−4.85982	+	3.53087i	−0.622236	+	0.452081i	−0.853702	−	0.520762i	$-0.825648\pi$
$61$	−4.85982	+	3.53087i	−0.622236	+	0.452081i	0.231466	+	0.972843i	$0.425648\pi$
$62$	0.665101	+	0.483224i	0.0844679	+	0.0613695i
$63$	2.22240	+	1.61467i	0.279996	+	0.203429i
$64$	−4.62492	+	3.36020i	−0.578115	+	0.420025i
$65$	1.39418	+	0.625550i	0.172927	+	0.0775899i
$66$	2.21705	+	1.61078i	0.272900	+	0.198274i
$67$	−1.41290	−	4.34845i	−0.172613	−	0.531248i	0.826903	−	0.562344i	$-0.190100\pi$
$67$	−1.41290	−	4.34845i	−0.172613	−	0.531248i	−0.999516	+	0.0310959i	$0.990100\pi$
$68$	−1.15785			−0.140410
$69$	−0.123883	−	0.381271i	−0.0149137	−	0.0458997i
$70$	1.49940	−	1.65563i	0.179213	−	0.197886i
$71$	2.67782	−	8.24148i	0.317799	−	0.978084i	−0.656788	−	0.754075i	$-0.728086\pi$
$71$	2.67782	−	8.24148i	0.317799	−	0.978084i	0.974587	−	0.224009i	$-0.0719144\pi$
$72$	−2.25992	+	6.95531i	−0.266334	+	0.819691i
$73$	−10.6963	+	7.77135i	−1.25191	+	0.909568i	−0.998331	−	0.0577462i	$-0.981609\pi$
$73$	−10.6963	+	7.77135i	−1.25191	+	0.909568i	−0.253581	+	0.967314i	$0.581609\pi$
$74$	0.361125			0.0419799
$75$	−0.340939	−	3.43414i	−0.0393683	−	0.396540i
$76$	7.79345			0.893970
$77$	−3.81016	+	2.76824i	−0.434208	+	0.315471i
$78$	0.133757	−	0.411663i	0.0151451	−	0.0466117i
$79$	1.24328	−	3.82643i	0.139880	−	0.430507i	−0.856437	−	0.516252i	$-0.827327\pi$
$79$	1.24328	−	3.82643i	0.139880	−	0.430507i	0.996317	+	0.0857445i	$0.0273269\pi$
$80$	0.701166	+	0.314604i	0.0783928	+	0.0351738i
$81$	1.52639	+	4.69774i	0.169599	+	0.521971i
$82$	5.15469			0.569240
$83$	2.80123	+	8.62129i	0.307475	+	0.946309i	0.978742	+	0.205094i	$0.0657501\pi$
$83$	2.80123	+	8.62129i	0.307475	+	0.946309i	−0.671268	+	0.741215i	$0.734250\pi$
$84$	0.703765	+	0.511315i	0.0767870	+	0.0557891i
$85$	1.11245	+	1.93971i	0.120662	+	0.210391i
$86$	−3.84579	+	2.79413i	−0.414702	+	0.301299i
$87$	−4.27023	−	3.10251i	−0.457817	−	0.332623i
$88$	−10.1435	−	7.36971i	−1.08130	−	0.785614i
$89$	7.35359	−	5.34270i	0.779479	−	0.566325i	−0.125344	−	0.992113i	$-0.540003\pi$
$89$	7.35359	−	5.34270i	0.779479	−	0.566325i	0.904823	+	0.425789i	$0.140003\pi$
$90$	5.06842	−	1.06207i	0.534258	−	0.111952i
$91$	0.601812	+	0.437242i	0.0630870	+	0.0458354i
$92$	0.207818	+	0.639599i	0.0216666	+	0.0666828i
$93$	0.618319			0.0641167
$94$	1.75122	+	5.38970i	0.180625	+	0.555905i
$95$	−7.48786	−	13.0561i	−0.768238	−	1.33953i
$96$	−1.16890	+	3.59749i	−0.119300	+	0.367167i
$97$	−0.975963	+	3.00371i	−0.0990940	+	0.304980i	−0.988299	−	0.152529i	$-0.951258\pi$
$97$	−0.975963	+	3.00371i	−0.0990940	+	0.304980i	0.889205	+	0.457509i	$0.151258\pi$
$98$	−4.31728	+	3.13669i	−0.436111	+	0.316853i
$99$	−10.9187			−1.09737
$100$	0.571940	+	5.76092i	0.0571940	+	0.576092i
$101$	−10.3561			−1.03047			−0.515237	−	0.857048i	$-0.672296\pi$
$101$	−10.3561			−1.03047			−0.515237	+	0.857048i	$0.672296\pi$
$102$	0.512425	−	0.372299i	0.0507377	−	0.0368631i
$103$	−3.91633	+	12.0532i	−0.385888	+	1.18764i	0.549947	+	0.835200i	$0.314648\pi$
$103$	−3.91633	+	12.0532i	−0.385888	+	1.18764i	−0.935834	+	0.352440i	$0.885352\pi$
$104$	−0.611972	+	1.88346i	−0.0600088	+	0.184688i
$105$	0.180420	−	1.67026i	0.0176072	−	0.163001i
$106$	−2.48264	−	7.64078i	−0.241135	−	0.742138i
$107$	7.45827			0.721018			0.360509	−	0.932756i	$-0.382603\pi$
$107$	7.45827			0.721018			0.360509	+	0.932756i	$0.382603\pi$
$108$	1.36407	+	4.19817i	0.131257	+	0.403969i
$109$	8.68481	+	6.30989i	0.831854	+	0.604377i	0.920083	−	0.391723i	$-0.128121\pi$
$109$	8.68481	+	6.30989i	0.831854	+	0.604377i	−0.0882291	+	0.996100i	$0.528121\pi$
$110$	−0.953472	+	8.82686i	−0.0909100	+	0.841609i
$111$	0.219734	−	0.159646i	0.0208562	−	0.0151529i
$112$	0.302666	+	0.219900i	0.0285992	+	0.0207786i
$113$	0.189020	+	0.137331i	0.0177815	+	0.0129190i	0.596641	−	0.802509i	$-0.296502\pi$
$113$	0.189020	+	0.137331i	0.0177815	+	0.0129190i	−0.578859	+	0.815428i	$0.696502\pi$
$114$	−3.44912	+	2.50593i	−0.323040	+	0.234702i
$115$	0.871830	−	0.962671i	0.0812986	−	0.0897695i
$116$	7.16350	+	5.20459i	0.665115	+	0.483234i
$117$	0.532928	+	1.64018i	0.0492692	+	0.151635i
$118$	−13.3842			−1.23211
$119$	0.336374	+	1.03525i	0.0308354	+	0.0949015i
$120$	4.37742	−	0.917269i	0.399602	−	0.0837348i
$121$	2.38541	−	7.34154i	0.216856	−	0.667413i
$122$	−1.70349	+	5.24281i	−0.154227	+	0.474662i
$123$	3.13648	−	2.27879i	0.282807	−	0.205471i
$124$	−1.03726			−0.0931485
$125$	9.10157	−	6.49318i	0.814069	−	0.580768i
$126$	2.52092			0.224581
$127$	−1.92267	+	1.39690i	−0.170610	+	0.123955i	−0.669813	−	0.742529i	$-0.733626\pi$
$127$	−1.92267	+	1.39690i	−0.170610	+	0.123955i	0.499204	+	0.866485i	$0.333626\pi$
$128$	1.76595	−	5.43502i	0.156089	−	0.480393i
$129$	−1.10482	+	3.40030i	−0.0972744	+	0.299380i
$130$	1.37250	−	0.287601i	0.120376	−	0.0252243i
$131$	4.90098	+	15.0837i	0.428200	+	1.31787i	0.899896	+	0.436104i	$0.143642\pi$
$131$	4.90098	+	15.0837i	0.428200	+	1.31787i	−0.471696	+	0.881761i	$0.656358\pi$
$132$	−3.45760			−0.300946
$133$	−2.26413	−	6.96826i	−0.196325	−	0.604225i
$134$	−3.39454	−	2.46628i	−0.293244	−	0.213054i
$135$	5.72247	−	6.31873i	0.492512	−	0.543829i
$136$	−2.34447	+	1.70335i	−0.201036	+	0.146061i
$137$	−10.6904	−	7.76700i	−0.913339	−	0.663580i	0.0285181	−	0.999593i	$-0.490921\pi$
$137$	−10.6904	−	7.76700i	−0.913339	−	0.663580i	−0.941857	+	0.336014i	$0.890921\pi$
$138$	−0.297632	−	0.216243i	−0.0253362	−	0.0184078i
$139$	14.9705	−	10.8767i	1.26978	−	0.922552i	0.270590	−	0.962695i	$-0.412781\pi$
$139$	14.9705	−	10.8767i	1.26978	−	0.922552i	0.999194	+	0.0401425i	$0.0127812\pi$
$140$	−0.302663	+	2.80194i	−0.0255797	+	0.236807i
$141$	3.44825	+	2.50530i	0.290395	+	0.210984i
$142$	−2.45740	−	7.56311i	−0.206221	−	0.634682i
$143$	−2.95671			−0.247252
$144$	0.268023	+	0.824888i	0.0223352	+	0.0687407i
$145$	1.83647	−	17.0013i	0.152510	−	1.41188i
$146$	−3.74934	+	11.5393i	−0.310298	+	0.954999i
$147$	−1.24027	+	3.81717i	−0.102296	+	0.314835i
$148$	−0.368614	+	0.267814i	−0.0302999	+	0.0220141i
$149$	19.1299			1.56718			0.783592	−	0.621276i	$-0.213385\pi$
$149$	19.1299			1.56718			0.783592	+	0.621276i	$0.213385\pi$
$150$	−2.10551	−	2.36569i	−0.171914	−	0.193158i
$151$	−0.568340			−0.0462509			−0.0231254	−	0.999733i	$-0.507362\pi$
$151$	−0.568340			−0.0462509			−0.0231254	+	0.999733i	$0.507362\pi$
$152$	15.7805	−	11.4652i	1.27997	−	0.929953i
$153$	−0.779841	+	2.40010i	−0.0630464	+	0.194037i
$154$	−1.33556	+	4.11043i	−0.107622	+	0.331228i
$155$	0.996585	+	1.73768i	0.0800476	+	0.139574i
$156$	0.168762	+	0.519396i	0.0135118	+	0.0415850i
$157$	−11.6875			−0.932763			−0.466381	−	0.884584i	$-0.654443\pi$
$157$	−11.6875			−0.932763			−0.466381	+	0.884584i	$0.654443\pi$
$158$	−1.14095	−	3.51147i	−0.0907688	−	0.279358i
$159$	−4.88846	−	3.55167i	−0.387680	−	0.281666i
$160$	−11.9941	+	2.51332i	−0.948220	+	0.198696i
$161$	0.511502	−	0.371628i	0.0403120	−	0.0292884i
$162$	3.66721	+	2.66438i	0.288123	+	0.209334i
$163$	−15.8706	−	11.5307i	−1.24308	−	0.903152i	−0.245282	−	0.969452i	$-0.578880\pi$
$163$	−15.8706	−	11.5307i	−1.24308	−	0.903152i	−0.997800	+	0.0663003i	$0.978880\pi$
$164$	−5.26159	+	3.82277i	−0.410861	+	0.298508i
$165$	3.32202	+	5.79241i	0.258619	+	0.450938i
$166$	6.73005	+	4.88967i	0.522353	+	0.379512i
$167$	4.86792	+	14.9819i	0.376691	+	1.15933i	0.942331	+	0.334683i	$0.108629\pi$
$167$	4.86792	+	14.9819i	0.376691	+	1.15933i	−0.565640	+	0.824652i	$0.691371\pi$
$168$	2.17723			0.167977
$169$	−3.87291	−	11.9196i	−0.297916	−	0.916891i
$170$	1.87219	+	0.840029i	0.143591	+	0.0644272i
$171$	5.24909	−	16.1550i	0.401408	−	1.23541i
$172$	1.85339	−	5.70415i	0.141320	−	0.434938i
$173$	15.9326	−	11.5757i	1.21133	−	0.880083i	0.215979	−	0.976398i	$-0.430706\pi$
$173$	15.9326	−	11.5757i	1.21133	−	0.880083i	0.995351	+	0.0963149i	$0.0307056\pi$
$174$	−4.84383			−0.367210
$175$	4.98479	−	2.18503i	0.376814	−	0.165172i
$176$	−1.48700			−0.112087
$177$	−8.14388	+	5.91688i	−0.612132	+	0.444740i
$178$	2.57762	−	7.93310i	0.193201	−	0.594611i
$179$	0.288758	−	0.888706i	0.0215828	−	0.0664250i	−0.939685	−	0.342041i	$-0.888882\pi$
$179$	0.288758	−	0.888706i	0.0215828	−	0.0664250i	0.961268	+	0.275616i	$0.0888818\pi$
$180$	−4.38589	+	4.84288i	−0.326905	+	0.360967i
$181$	3.91959	+	12.0633i	0.291341	+	0.896656i	0.984426	+	0.175800i	$0.0562511\pi$
$181$	3.91959	+	12.0633i	0.291341	+	0.896656i	−0.693085	+	0.720856i	$0.743749\pi$
$182$	0.682650			0.0506014
$183$	1.28122	+	3.94318i	0.0947103	+	0.291488i
$184$	1.36174	+	0.989361i	0.100389	+	0.0729367i
$185$	0.802819	+	0.360214i	0.0590245	+	0.0264835i
$186$	0.459056	−	0.333523i	0.0336596	−	0.0244551i
$187$	−3.50028	−	2.54310i	−0.255966	−	0.185970i
$188$	−5.78459	−	4.20275i	−0.421885	−	0.306517i
$189$	3.35737	−	2.43927i	0.244213	−	0.177431i
$190$	−12.6017	−	5.65421i	−0.914222	−	0.410200i
$191$	−4.63361	−	3.36651i	−0.335276	−	0.243592i	0.407390	−	0.913254i	$-0.366439\pi$
$191$	−4.63361	−	3.36651i	−0.335276	−	0.243592i	−0.742666	+	0.669662i	$0.766439\pi$
$192$	1.21929	+	3.75258i	0.0879946	+	0.270819i
$193$	−12.0001			−0.863783			−0.431891	−	0.901926i	$-0.642154\pi$
$193$	−12.0001			−0.863783			−0.431891	+	0.901926i	$0.642154\pi$
$194$	0.895629	+	2.75646i	0.0643024	+	0.197903i
$195$	0.707983	−	0.781751i	0.0506997	−	0.0559824i
$196$	2.08061	−	6.40347i	0.148615	−	0.457391i
$197$	2.64900	−	8.15278i	0.188733	−	0.580861i	−0.811259	−	0.584686i	$-0.801218\pi$
$197$	2.64900	−	8.15278i	0.188733	−	0.580861i	0.999993	+	0.00382506i	$0.00121756\pi$
$198$	−8.10628	+	5.88956i	−0.576088	+	0.418553i
$199$	−14.0246			−0.994180			−0.497090	−	0.867699i	$-0.665598\pi$
$199$	−14.0246			−0.994180			−0.497090	+	0.867699i	$0.665598\pi$
$200$	9.63320	+	10.8236i	0.681170	+	0.765343i
$201$	−3.15578			−0.222591
$202$	−7.68865	+	5.58613i	−0.540972	+	0.393039i
$203$	2.57240	−	7.91704i	0.180547	−	0.555667i
$204$	−0.246952	+	0.760039i	−0.0172901	+	0.0532134i
$205$	11.4594	+	5.14170i	0.800362	+	0.359112i
$206$	3.59397	+	11.0611i	0.250404	+	0.770664i
$207$	1.46580			0.101880
$208$	0.0725789	+	0.223375i	0.00503244	+	0.0154883i
$209$	23.5603	+	17.1176i	1.62970	+	1.18405i
$210$	−0.766995	−	1.33736i	−0.0529277	−	0.0922868i
$211$	−5.12870	+	3.72622i	−0.353075	+	0.256524i	−0.750158	−	0.661259i	$-0.770022\pi$
$211$	−5.12870	+	3.72622i	−0.353075	+	0.256524i	0.397083	+	0.917783i	$0.370022\pi$
$212$	8.20060	+	5.95809i	0.563220	+	0.409203i
$213$	−4.83876	−	3.51557i	−0.331547	−	0.240883i
$214$	5.53721	−	4.02302i	0.378516	−	0.275008i
$215$	−11.3367	+	2.37556i	−0.773157	+	0.162012i
$216$	8.93810	+	6.49391i	0.608161	+	0.441855i
$217$	0.301340	+	0.927430i	0.0204563	+	0.0629581i
$218$	9.85140			0.667221
$219$	2.81993	+	8.67885i	0.190553	+	0.586462i
$220$	−5.57284	−	9.71702i	−0.375721	−	0.655122i
$221$	−0.211176	+	0.649934i	−0.0142053	+	0.0437193i
$222$	0.0770225	−	0.237051i	0.00516941	−	0.0159098i
$223$	13.7009	−	9.95426i	0.917478	−	0.666587i	−0.0254170	−	0.999677i	$-0.508091\pi$
$223$	13.7009	−	9.95426i	0.917478	−	0.666587i	0.942895	+	0.333090i	$0.108091\pi$
$224$	−5.96562			−0.398595
$225$	12.3270	+	2.69455i	0.821802	+	0.179637i
$226$	0.214410			0.0142623
$227$	−16.0708	+	11.6761i	−1.06666	+	0.774972i	−0.975309	−	0.220846i	$-0.929118\pi$
$227$	−16.0708	+	11.6761i	−1.06666	+	0.774972i	−0.0913495	+	0.995819i	$0.529118\pi$
$228$	1.66223	−	5.11580i	0.110084	−	0.338802i
$229$	3.66688	−	11.2855i	0.242314	−	0.745766i	−0.753752	−	0.657159i	$-0.771758\pi$
$229$	3.66688	−	11.2855i	0.242314	−	0.745766i	0.996067	−	0.0886078i	$-0.0282418\pi$
$230$	0.128001	−	1.18498i	0.00844011	−	0.0781352i
$231$	1.00449	+	3.09150i	0.0660906	+	0.203406i
$232$	22.1617			1.45498
$233$	8.61306	+	26.5083i	0.564260	+	1.73661i	0.670139	+	0.742235i	$0.266234\pi$
$233$	8.61306	+	26.5083i	0.564260	+	1.73661i	−0.105879	+	0.994379i	$0.533766\pi$
$234$	1.28038	+	0.930251i	0.0837011	+	0.0608124i
$235$	−1.48296	+	13.7287i	−0.0967379	+	0.895561i
$236$	13.6617	−	9.92582i	0.889302	−	0.646116i
$237$	−2.24659	−	1.63224i	−0.145931	−	0.106025i
$238$	0.808152	+	0.587157i	0.0523847	+	0.0380597i
$239$	11.0336	−	8.01642i	0.713707	−	0.518539i	−0.170660	−	0.985330i	$-0.554590\pi$
$239$	11.0336	−	8.01642i	0.713707	−	0.518539i	0.884368	+	0.466791i	$0.154590\pi$
$240$	0.356062	−	0.393162i	0.0229837	−	0.0253785i
$241$	10.9872	+	7.98270i	0.707750	+	0.514211i	0.882447	−	0.470411i	$-0.155895\pi$
$241$	10.9872	+	7.98270i	0.707750	+	0.514211i	−0.174697	+	0.984622i	$0.555895\pi$
$242$	−2.18906	−	6.73725i	−0.140718	−	0.433087i
$243$	14.8465			0.952406
$244$	−2.14930	−	6.61486i	−0.137595	−	0.423473i
$245$	−12.7266	+	2.66680i	−0.813070	+	0.170375i
$246$	1.09942	−	3.38366i	0.0700963	−	0.215734i
$247$	1.42142	−	4.37469i	0.0904429	−	0.278355i
$248$	−2.10029	+	1.52595i	−0.133368	+	0.0968978i
$249$	6.25668			0.396501
$250$	3.25479	−	9.73012i	0.205851	−	0.615387i
$251$	−13.8900			−0.876726			−0.438363	−	0.898798i	$-0.644442\pi$
$251$	−13.8900			−0.876726			−0.438363	+	0.898798i	$0.644442\pi$
$252$	−2.57320	+	1.86954i	−0.162096	+	0.117770i
$253$	−0.776565	+	2.39002i	−0.0488222	+	0.150259i
$254$	−0.673946	+	2.07419i	−0.0422872	+	0.130146i
$255$	1.51054	−	0.316527i	0.0945935	−	0.0198217i
$256$	−5.15371	−	15.8615i	−0.322107	−	0.991343i
$257$	1.32445			0.0826167			0.0413084	−	0.999146i	$-0.486847\pi$
$257$	1.32445			0.0826167			0.0413084	+	0.999146i	$0.486847\pi$
$258$	1.01388	+	3.12041i	0.0631217	+	0.194269i
$259$	0.346545	+	0.251780i	0.0215333	+	0.0156448i
$260$	−1.18767	+	1.31142i	−0.0736563	+	0.0813310i
$261$	15.6134	−	11.3438i	0.966445	−	0.702163i
$262$	11.7748	+	8.55488i	0.727449	+	0.528522i
$263$	16.5625	+	12.0334i	1.02129	+	0.742009i	0.966547	−	0.256491i	$-0.0825665\pi$
$263$	16.5625	+	12.0334i	1.02129	+	0.742009i	0.0547416	+	0.998501i	$0.482567\pi$
$264$	−7.00112	+	5.08661i	−0.430889	+	0.313059i
$265$	2.10234	−	19.4627i	0.129146	−	1.19558i
$266$	−5.43965	−	3.95214i	−0.333526	−	0.242321i
$267$	−1.93866	−	5.96659i	−0.118644	−	0.365149i
$268$	5.29395			0.323380
$269$	−2.50521	−	7.71026i	−0.152746	−	0.470103i	0.845180	−	0.534482i	$-0.179493\pi$
$269$	−2.50521	−	7.71026i	−0.152746	−	0.470103i	−0.997926	+	0.0643793i	$0.979493\pi$
$270$	0.840164	−	7.77790i	0.0511307	−	0.473348i
$271$	5.43801	−	16.7365i	0.330336	−	1.01667i	−0.638639	−	0.769507i	$-0.720502\pi$
$271$	5.43801	−	16.7365i	0.330336	−	1.01667i	0.968974	−	0.247162i	$-0.0794978\pi$
$272$	−0.106206	+	0.326867i	−0.00643966	+	0.0198193i
$273$	0.415373	−	0.301786i	0.0251395	−	0.0182649i
$274$	−12.1263			−0.732579
$275$	−10.9243	+	18.6720i	−0.658759	+	1.12596i
$276$	0.464173			0.0279399
$277$	−10.1541	+	7.37737i	−0.610100	+	0.443263i	−0.849449	−	0.527670i	$-0.823066\pi$
$277$	−10.1541	+	7.37737i	−0.610100	+	0.443263i	0.239350	+	0.970933i	$0.423066\pi$
$278$	5.24756	−	16.1503i	0.314727	−	0.968632i
$279$	−0.698619	+	2.15013i	−0.0418252	+	0.128725i
$280$	3.50918	+	6.11875i	0.209714	+	0.365665i
$281$	−4.03886	−	12.4303i	−0.240938	−	0.741531i	−0.996278	−	0.0861979i	$-0.972528\pi$
$281$	−4.03886	−	12.4303i	−0.240938	−	0.741531i	0.755340	−	0.655333i	$-0.227472\pi$
$282$	3.91144			0.232923
$283$	3.85796	+	11.8736i	0.229332	+	0.705812i	0.997823	+	0.0659507i	$0.0210080\pi$
$283$	3.85796	+	11.8736i	0.229332	+	0.705812i	−0.768491	+	0.639861i	$0.778992\pi$
$284$	8.11724	+	5.89752i	0.481670	+	0.349953i
$285$	−10.1674	+	2.13053i	−0.602264	+	0.126202i
$286$	−2.19513	+	1.59486i	−0.129801	+	0.0943059i
$287$	4.94658	+	3.59390i	0.291988	+	0.212141i
$288$	−11.1891	−	8.12939i	−0.659326	−	0.479029i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−7.80712	−	13.6128i	−0.458450	−	0.799370i
$291$	1.76354	+	1.28129i	0.103381	+	0.0751106i
$292$	−4.73055	−	14.5591i	−0.276835	−	0.852010i
$293$	17.3250			1.01214			0.506068	−	0.862494i	$-0.331099\pi$
$293$	17.3250			1.01214			0.506068	+	0.862494i	$0.331099\pi$
$294$	1.13818	+	3.50297i	0.0663803	+	0.204297i
$295$	−29.7544	−	13.3504i	−1.73237	−	0.777292i
$296$	−0.352396	+	1.08456i	−0.0204826	+	0.0630390i
$297$	−5.09717	+	15.6875i	−0.295768	+	0.910280i
$298$	14.2025	−	10.3187i	0.822731	−	0.597749i
$299$	0.396929			0.0229550
$300$	3.90359	+	0.853283i	0.225374	+	0.0492643i
$301$	−5.63863			−0.325005
$302$	−0.421950	+	0.306565i	−0.0242805	+	0.0176408i
$303$	−2.20881	+	6.79801i	−0.126893	+	0.390535i
$304$	0.714868	−	2.20014i	0.0410005	−	0.126186i
$305$	−9.01664	+	9.95613i	−0.516291	+	0.570086i
$306$	0.715650	+	2.20255i	0.0409110	+	0.125911i
$307$	−11.1620			−0.637052			−0.318526	−	0.947914i	$-0.603188\pi$
$307$	−11.1620			−0.637052			−0.318526	+	0.947914i	$0.603188\pi$
$308$	−1.68508	−	5.18614i	−0.0960162	−	0.295508i
$309$	7.07673	+	5.14154i	0.402581	+	0.292492i
$310$	1.67720	+	0.752539i	0.0952587	+	0.0427413i
$311$	0.348244	−	0.253014i	0.0197471	−	0.0143471i	−0.577868	−	0.816130i	$-0.696115\pi$
$311$	0.348244	−	0.253014i	0.0197471	−	0.0143471i	0.597615	+	0.801783i	$0.296115\pi$
$312$	1.10582	+	0.803426i	0.0626048	+	0.0454850i
$313$	9.20918	+	6.69086i	0.520533	+	0.378190i	0.816805	−	0.576914i	$-0.195743\pi$
$313$	9.20918	+	6.69086i	0.520533	+	0.378190i	−0.296271	+	0.955104i	$0.595743\pi$
$314$	−8.67708	+	6.30427i	−0.489676	+	0.355771i
$315$	5.60428	+	2.51456i	0.315765	+	0.141680i
$316$	3.76875	+	2.73816i	0.212009	+	0.154033i
$317$	7.47682	+	23.0113i	0.419940	+	1.29244i	0.907757	+	0.419496i	$0.137793\pi$
$317$	7.47682	+	23.0113i	0.419940	+	1.29244i	−0.487817	+	0.872946i	$0.662207\pi$
$318$	−5.54510			−0.310954
$319$	10.2245	+	31.4679i	0.572464	+	1.76186i
$320$	−8.58081	+	9.47489i	−0.479682	+	0.529663i
$321$	1.59074	−	4.89579i	0.0887863	−	0.273256i
$322$	0.179295	−	0.551812i	0.00999170	−	0.0307513i
$323$	5.44547	−	3.95637i	0.302994	−	0.220138i
$324$	−5.71919			−0.317733
$325$	3.33809	+	0.729669i	0.185164	+	0.0404748i
$326$	−18.0024			−0.997062
$327$	5.99430	−	4.35511i	0.331485	−	0.240838i
$328$	−5.03010	+	15.4810i	−0.277741	+	0.854797i
$329$	−2.07724	+	6.39308i	−0.114522	+	0.352462i
$330$	5.59080	+	2.50852i	0.307763	+	0.138089i
$331$	−4.80955	−	14.8023i	−0.264357	−	0.813607i	−0.991841	−	0.127482i	$-0.959311\pi$
$331$	−4.80955	−	14.8023i	−0.264357	−	0.813607i	0.727484	−	0.686125i	$-0.240689\pi$
$332$	−10.4959			−0.576035
$333$	0.306880	+	0.944478i	0.0168169	+	0.0517571i
$334$	11.6954	+	8.49718i	0.639942	+	0.464945i
$335$	−5.08637	−	8.86879i	−0.277898	−	0.484554i
$336$	0.208901	−	0.151776i	0.0113965	−	0.00828004i
$337$	13.2229	+	9.60703i	0.720299	+	0.523328i	0.886480	−	0.462767i	$-0.153143\pi$
$337$	13.2229	+	9.60703i	0.720299	+	0.523328i	−0.166181	+	0.986095i	$0.553143\pi$
$338$	−9.30481	−	6.76034i	−0.506115	−	0.367714i
$339$	0.130462	−	0.0947865i	0.00708575	−	0.00514810i
$340$	−2.53399	+	0.530988i	−0.137425	+	0.0287968i
$341$	−3.13572	−	2.27824i	−0.169809	−	0.123373i
$342$	−4.81702	−	14.8253i	−0.260475	−	0.801659i
$343$	−13.9496			−0.753209
$344$	−4.63876	−	14.2766i	−0.250105	−	0.769745i
$345$	−0.445972	−	0.777613i	−0.0240103	−	0.0418653i
$346$	5.58477	−	17.1882i	0.300239	−	0.924041i
$347$	7.04722	−	21.6891i	0.378314	−	1.16433i	−0.562901	−	0.826524i	$-0.690315\pi$
$347$	7.04722	−	21.6891i	0.378314	−	1.16433i	0.941215	−	0.337808i	$-0.109685\pi$
$348$	4.94428	−	3.59223i	0.265041	−	0.192564i
$349$	−7.96544			−0.426380			−0.213190	−	0.977011i	$-0.568385\pi$
$349$	−7.96544			−0.426380			−0.213190	+	0.977011i	$0.568385\pi$
$350$	2.52222	−	4.31103i	0.134818	−	0.230434i
$351$	2.60534			0.139063
$352$	19.1831	−	13.9373i	1.02246	−	0.742862i
$353$	6.94968	−	21.3889i	0.369894	−	1.13842i	−0.576965	−	0.816769i	$-0.695763\pi$
$353$	6.94968	−	21.3889i	0.369894	−	1.13842i	0.946859	−	0.321648i	$-0.104237\pi$
$354$	−2.85464	+	8.78568i	−0.151722	+	0.466953i
$355$	2.08097	−	19.2648i	0.110447	−	1.02247i
$356$	3.25219	+	10.0092i	0.172366	+	0.530487i
$357$	0.751308			0.0397634
$358$	−0.264990	−	0.815555i	−0.0140051	−	0.0431034i
$359$	−21.5120	−	15.6294i	−1.13536	−	0.824887i	−0.148894	−	0.988853i	$-0.547571\pi$
$359$	−21.5120	−	15.6294i	−1.13536	−	0.824887i	−0.986466	+	0.163966i	$0.947571\pi$
$360$	−1.75621	+	16.2583i	−0.0925606	+	0.856889i
$361$	−21.2820	+	15.4623i	−1.12011	+	0.813805i
$362$	9.41698	+	6.84183i	0.494945	+	0.359599i
$363$	−4.31039	−	3.13168i	−0.226237	−	0.164371i
$364$	−0.696807	+	0.506260i	−0.0365226	+	0.0265352i
$365$	−19.8454	+	21.9132i	−1.03876	+	1.14699i
$366$	3.07817	+	2.23642i	0.160899	+	0.116900i
$367$	−0.562999	−	1.73273i	−0.0293883	−	0.0904479i	0.935287	−	0.353891i	$-0.115142\pi$
$367$	−0.562999	−	1.73273i	−0.0293883	−	0.0904479i	−0.964675	+	0.263444i	$0.915142\pi$
$368$	0.199625			0.0104062
$369$	4.38040	+	13.4815i	0.228034	+	0.701817i
$370$	0.790334	−	0.165611i	0.0410875	−	0.00860972i
$371$	2.94482	−	9.06323i	0.152887	−	0.470539i
$372$	−0.221231	+	0.680880i	−0.0114703	+	0.0353020i
$373$	−26.7717	+	19.4508i	−1.38619	+	1.00712i	−0.389916	+	0.920850i	$0.627496\pi$
$373$	−26.7717	+	19.4508i	−1.38619	+	1.00712i	−0.996271	+	0.0862741i	$0.972504\pi$
$374$	−3.97046			−0.205307
$375$	−2.32105	−	7.35938i	−0.119858	−	0.380037i
$376$	−17.8957			−0.922902
$377$	4.22801	−	3.07183i	0.217754	−	0.158207i
$378$	1.17684	−	3.62196i	0.0605304	−	0.186293i
$379$	−3.79407	+	11.6769i	−0.194888	+	0.599804i	0.805090	+	0.593153i	$0.202117\pi$
$379$	−3.79407	+	11.6769i	−0.194888	+	0.599804i	−0.999978	+	0.00665099i	$0.997883\pi$
$380$	17.0562	−	3.57406i	0.874967	−	0.183346i
$381$	0.506883	+	1.56003i	0.0259684	+	0.0799226i
$382$	−5.25602			−0.268921
$383$	8.69480	+	26.7598i	0.444284	+	1.36736i	0.883267	+	0.468869i	$0.155339\pi$
$383$	8.69480	+	26.7598i	0.444284	+	1.36736i	−0.438984	+	0.898495i	$0.644661\pi$
$384$	−3.19103	−	2.31842i	−0.162841	−	0.118311i
$385$	−7.06916	+	7.80574i	−0.360278	+	0.397817i
$386$	−8.90914	+	6.47287i	−0.453463	+	0.329460i
$387$	−10.5758	−	7.68379i	−0.537600	−	0.390589i
$388$	−2.95842	−	2.14942i	−0.150191	−	0.109120i
$389$	−0.887010	+	0.644450i	−0.0449732	+	0.0326749i	−0.610045	−	0.792367i	$-0.708849\pi$
$389$	−0.887010	+	0.644450i	−0.0449732	+	0.0326749i	0.565072	+	0.825042i	$0.308849\pi$
$390$	0.103945	−	0.962280i	0.00526345	−	0.0487270i
$391$	0.469902	+	0.341404i	0.0237640	+	0.0172655i
$392$	−5.20746	−	16.0269i	−0.263017	−	0.809482i
$393$	10.9466			0.552181
$394$	−2.43095	−	7.48171i	−0.122470	−	0.376923i
$395$	0.966173	−	8.94445i	0.0486135	−	0.450044i
$396$	3.90664	−	12.0234i	0.196316	−	0.604198i
$397$	−6.02919	+	18.5560i	−0.302597	+	0.931297i	0.677967	+	0.735093i	$0.262861\pi$
$397$	−6.02919	+	18.5560i	−0.302597	+	0.931297i	−0.980563	+	0.196204i	$0.937139\pi$
$398$	−10.4122	+	7.56494i	−0.521919	+	0.379196i
$399$	−5.05704			−0.253168
$400$	1.67880	+	0.366968i	0.0839402	+	0.0183484i
$401$	6.51268			0.325228			0.162614	−	0.986690i	$-0.448008\pi$
$401$	6.51268			0.325228			0.162614	+	0.986690i	$0.448008\pi$
$402$	−2.34293	+	1.70224i	−0.116855	+	0.0848998i
$403$	−0.189182	+	0.582242i	−0.00942383	+	0.0290036i
$404$	3.70537	−	11.4040i	0.184349	−	0.567368i
$405$	5.49493	+	9.58118i	0.273045	+	0.476093i
$406$	−2.36066	−	7.26537i	−0.117158	−	0.360574i
$407$	−1.70258			−0.0843938
$408$	0.618083	+	1.90226i	0.0305997	+	0.0941760i
$409$	3.47453	+	2.52440i	0.171805	+	0.124823i	0.670365	−	0.742032i	$-0.266138\pi$
$409$	3.47453	+	2.52440i	0.171805	+	0.124823i	−0.498560	+	0.866855i	$0.666138\pi$
$410$	11.2812	−	2.36393i	0.557140	−	0.116746i
$411$	−7.37853	+	5.36082i	−0.363956	+	0.264430i
$412$	−11.8715	−	8.62517i	−0.584868	−	0.424932i
$413$	−12.8438	−	9.33157i	−0.632003	−	0.459177i
$414$	1.08824	−	0.790655i	0.0534842	−	0.0388586i
$415$	10.0843	+	17.5834i	0.495018	+	0.863133i
$416$	−3.02995	−	2.20139i	−0.148556	−	0.107932i
$417$	−3.94675	−	12.1469i	−0.193273	−	0.594834i
$418$	26.7250			1.30716
$419$	−0.131928	−	0.406034i	−0.00644512	−	0.0198361i	0.947782	−	0.318918i	$-0.103320\pi$
$419$	−0.131928	−	0.406034i	−0.00644512	−	0.0198361i	−0.954227	+	0.299082i	$0.903320\pi$
$420$	1.77470	+	0.796286i	0.0865966	+	0.0388548i
$421$	−7.72782	+	23.7838i	−0.376631	+	1.15915i	0.565741	+	0.824583i	$0.308590\pi$
$421$	−7.72782	+	23.7838i	−0.376631	+	1.15915i	−0.942372	+	0.334567i	$0.891410\pi$
$422$	−1.79774	+	5.53288i	−0.0875127	+	0.269336i
$423$	−12.6080	+	9.16021i	−0.613020	+	0.445385i
$424$	25.3701			1.23208
$425$	3.32418	+	3.73495i	0.161246	+	0.181172i
$426$	−5.48873			−0.265930
$427$	−5.29006	+	3.84345i	−0.256004	+	0.185998i
$428$	−2.66853	+	8.21290i	−0.128988	+	0.396985i
$429$	−0.630621	+	1.94085i	−0.0304467	+	0.0937052i
$430$	−7.13527	+	7.87873i	−0.344093	+	0.379946i
$431$	−7.83367	−	24.1096i	−0.377335	−	1.16132i	−0.941890	−	0.335922i	$-0.890952\pi$
$431$	−7.83367	−	24.1096i	−0.377335	−	1.16132i	0.564555	−	0.825395i	$-0.309048\pi$
$432$	1.31029			0.0630413
$433$	5.85158	+	18.0093i	0.281209	+	0.865473i	0.987509	+	0.157560i	$0.0503629\pi$
$433$	5.85158	+	18.0093i	0.281209	+	0.865473i	−0.706300	+	0.707912i	$0.749637\pi$
$434$	0.723982	+	0.526004i	0.0347522	+	0.0252490i
$435$	−10.7684	−	4.83162i	−0.516303	−	0.231658i
$436$	−10.0557	+	7.30589i	−0.481581	+	0.349889i
$437$	−3.16290	−	2.29798i	−0.151302	−	0.109927i
$438$	6.77498	+	4.92231i	0.323721	+	0.235197i
$439$	−13.3279	+	9.68331i	−0.636108	+	0.462159i	−0.858511	−	0.512796i	$-0.828610\pi$
$439$	−13.3279	+	9.68331i	−0.636108	+	0.462159i	0.222403	+	0.974955i	$0.428610\pi$
$440$	−25.5792	−	11.4771i	−1.21944	−	0.547148i
$441$	−11.8724	−	8.62581i	−0.565353	−	0.410753i
$442$	0.193794	+	0.596436i	0.00921784	+	0.0283696i
$443$	28.9881			1.37726			0.688632	−	0.725111i	$-0.258211\pi$
$443$	28.9881			1.37726			0.688632	+	0.725111i	$0.258211\pi$
$444$	0.0971794	+	0.299087i	0.00461193	+	0.0141941i
$445$	13.6434	−	15.0650i	0.646761	−	0.714151i
$446$	4.80251	−	14.7806i	0.227405	−	0.699881i
$447$	4.08012	−	12.5573i	0.192983	−	0.593941i
$448$	−5.03436	+	3.65768i	−0.237851	+	0.172809i
$449$	6.81855			0.321787			0.160894	−	0.986972i	$-0.448562\pi$
$449$	6.81855			0.321787			0.160894	+	0.986972i	$0.448562\pi$
$450$	10.6053	−	4.64874i	0.499941	−	0.219143i
$451$	−24.3026			−1.14437
$452$	−0.218857	+	0.159009i	−0.0102941	+	0.00747913i
$453$	−0.121218	+	0.373072i	−0.00569534	+	0.0175284i
$454$	−5.63324	+	17.3373i	−0.264381	+	0.813681i
$455$	1.51761	+	0.680929i	0.0711464	+	0.0319225i
$456$	−4.16030	−	12.8041i	−0.194824	−	0.599606i
$457$	12.0182			0.562189			0.281094	−	0.959680i	$-0.409303\pi$
$457$	12.0182			0.562189			0.281094	+	0.959680i	$0.409303\pi$
$458$	−3.36505	−	10.3566i	−0.157238	−	0.483930i
$459$	3.08432	+	2.24089i	0.143964	+	0.104596i
$460$	0.748137	+	1.30448i	0.0348821	+	0.0608217i
$461$	−25.9056	+	18.8215i	−1.20655	+	0.876607i	−0.994913	−	0.100742i	$-0.967878\pi$
$461$	−25.9056	+	18.8215i	−1.20655	+	0.876607i	−0.211633	+	0.977349i	$0.567878\pi$
$462$	2.41333	+	1.75339i	0.112278	+	0.0815749i
$463$	0.778128	+	0.565343i	0.0361627	+	0.0262737i	0.605720	−	0.795678i	$-0.292885\pi$
$463$	0.778128	+	0.565343i	0.0361627	+	0.0262737i	−0.569557	+	0.821952i	$0.692885\pi$
$464$	2.12637	−	1.54490i	0.0987143	−	0.0717201i
$465$	1.35321	−	0.283560i	0.0627537	−	0.0131498i
$466$	20.6932	+	15.0345i	0.958594	+	0.696459i
$467$	11.0462	+	33.9966i	0.511156	+	1.57318i	0.790169	+	0.612889i	$0.209993\pi$
$467$	11.0462	+	33.9966i	0.511156	+	1.57318i	−0.279013	+	0.960287i	$0.590007\pi$
$468$	−1.99682			−0.0923029
$469$	−1.53798	−	4.73342i	−0.0710174	−	0.218569i
$470$	6.30432	+	10.9924i	0.290796	+	0.507044i
$471$	−2.49276	+	7.67194i	−0.114861	+	0.353504i
$472$	13.0606	−	40.1965i	0.601165	−	1.85020i
$473$	18.1316	−	13.1734i	0.833692	−	0.605713i
$474$	−2.54836			−0.117050
$475$	−22.3750	−	25.1398i	−1.02663	−	1.15350i
$476$	−1.26035			−0.0577682
$477$	17.8738	−	12.9861i	0.818386	−	0.594592i
$478$	3.86758	−	11.9032i	0.176899	−	0.544439i
$479$	−9.11134	+	28.0418i	−0.416308	+	1.28126i	0.494768	+	0.869025i	$0.335253\pi$
$479$	−9.11134	+	28.0418i	−0.416308	+	1.28126i	−0.911076	+	0.412238i	$0.864747\pi$
$480$	−0.908366	+	8.40929i	−0.0414610	+	0.383830i
$481$	0.0831012	+	0.255759i	0.00378909	+	0.0116616i
$482$	12.4631			0.567679
$483$	−0.134850	−	0.415025i	−0.00613588	−	0.0188843i
$484$	7.23087	+	5.25353i	0.328676	+	0.238797i
$485$	−0.758435	+	7.02129i	−0.0344388	+	0.318820i
$486$	11.0224	−	8.00828i	0.499988	−	0.363263i
$487$	−20.8075	−	15.1175i	−0.942877	−	0.685040i	0.00623421	−	0.999981i	$-0.498016\pi$
$487$	−20.8075	−	15.1175i	−0.942877	−	0.685040i	−0.949112	+	0.314940i	$0.898016\pi$
$488$	−14.0834	−	10.2322i	−0.637524	−	0.463188i
$489$	−10.9540	+	7.95852i	−0.495355	+	0.359897i
$490$	−8.01004	+	8.84465i	−0.361857	+	0.399560i
$491$	16.7882	+	12.1974i	0.757642	+	0.550459i	0.898186	−	0.439615i	$-0.144885\pi$
$491$	16.7882	+	12.1974i	0.757642	+	0.550459i	−0.140544	+	0.990074i	$0.544885\pi$
$492$	1.38714	+	4.26917i	0.0625370	+	0.192469i
$493$	7.64744			0.344423
$494$	−1.30442	−	4.01460i	−0.0586887	−	0.180625i
$495$	−23.8959	+	5.00728i	−1.07404	+	0.225060i
$496$	−0.0951442	+	0.292824i	−0.00427210	+	0.0131482i
$497$	2.91489	−	8.97109i	0.130750	−	0.402409i
$498$	4.64511	−	3.37487i	0.208153	−	0.151232i
$499$	1.58208			0.0708236			0.0354118	−	0.999373i	$-0.488726\pi$
$499$	1.58208			0.0708236			0.0354118	+	0.999373i	$0.488726\pi$
$500$	3.89366	+	12.3457i	0.174130	+	0.552116i
$501$	10.8727			0.485758
$502$	−10.3123	+	7.49229i	−0.460259	+	0.334397i
$503$	−3.79818	+	11.6896i	−0.169353	+	0.521214i	−0.999331	−	0.0365823i	$-0.988353\pi$
$503$	−3.79818	+	11.6896i	−0.169353	+	0.521214i	0.829978	+	0.557796i	$0.188353\pi$
$504$	−2.45999	+	7.57106i	−0.109576	+	0.337242i
$505$	−22.6648	+	4.74931i	−1.00857	+	0.211341i
$506$	0.712644	+	2.19329i	0.0316809	+	0.0975038i
$507$	−8.65033			−0.384175
$508$	−0.850319	−	2.61701i	−0.0377268	−	0.116111i
$509$	−31.5152	−	22.8972i	−1.39689	−	1.01490i	−0.995069	−	0.0991802i	$-0.968378\pi$
$509$	−31.5152	−	22.8972i	−1.39689	−	1.01490i	−0.401819	−	0.915719i	$-0.631622\pi$
$510$	0.950725	−	1.04979i	0.0420988	−	0.0464853i
$511$	−11.6433	+	8.45935i	−0.515069	+	0.374219i
$512$	−3.13537	−	2.27798i	−0.138565	−	0.100673i
$513$	−20.7605	−	15.0834i	−0.916597	−	0.665947i
$514$	0.983303	−	0.714411i	0.0433716	−	0.0315113i
$515$	−3.04344	+	28.1749i	−0.134110	+	1.24154i
$516$	−3.34904	−	2.43322i	−0.147433	−	0.107117i
$517$	−8.25641	−	25.4106i	−0.363116	−	1.11756i
$518$	0.393095			0.0172716
$519$	−4.20038	−	12.9274i	−0.184376	−	0.567451i
$520$	−0.475572	+	4.40266i	−0.0208552	+	0.193069i
$521$	12.7825	−	39.3406i	0.560013	−	1.72354i	−0.122311	−	0.992492i	$-0.539031\pi$
$521$	12.7825	−	39.3406i	0.560013	−	1.72354i	0.682324	−	0.731050i	$-0.260969\pi$
$522$	5.47289	−	16.8438i	0.239542	−	0.737235i
$523$	−22.2181	+	16.1424i	−0.971530	+	0.705858i	−0.955800	−	0.294019i	$-0.905007\pi$
$523$	−22.2181	+	16.1424i	−0.971530	+	0.705858i	−0.0157300	+	0.999876i	$0.505007\pi$
$524$	−18.3634			−0.802207
$525$	−0.371122	−	3.73816i	−0.0161971	−	0.163147i
$526$	18.7873			0.819164
$527$	−0.724757	+	0.526567i	−0.0315709	+	0.0229376i
$528$	−0.317155	+	0.976101i	−0.0138024	+	0.0424794i
$529$	−7.00314	+	21.5534i	−0.304484	+	0.937106i
$530$	−8.93739	−	15.5836i	−0.388216	−	0.676907i
$531$	−11.3737	−	35.0047i	−0.493577	−	1.51907i
$532$	8.48340			0.367802
$533$	1.18619	+	3.65070i	0.0513794	+	0.158130i
$534$	−4.65771	−	3.38402i	−0.201559	−	0.146441i
$535$	16.3227	−	3.42035i	0.705692	−	0.147875i
$536$	10.7194	−	7.78813i	0.463010	−	0.336396i
$537$	−0.521780	−	0.379095i	−0.0225165	−	0.0163592i
$538$	−6.01887	−	4.37297i	−0.259492	−	0.188532i
$539$	20.3545	−	14.7884i	0.876731	−	0.636982i
$540$	4.91058	+	8.56228i	0.211318	+	0.368462i
$541$	6.63497	+	4.82059i	0.285260	+	0.207253i	0.721208	−	0.692718i	$-0.243587\pi$
$541$	6.63497	+	4.82059i	0.285260	+	0.207253i	−0.435949	+	0.899972i	$0.643587\pi$
$542$	−4.99040	−	15.3589i	−0.214356	−	0.659719i
$543$	8.75460			0.375696
$544$	−1.69355	−	5.21221i	−0.0726103	−	0.223472i
$545$	21.9007	+	9.82657i	0.938124	+	0.420924i
$546$	0.145599	−	0.448108i	0.00623106	−	0.0191772i
$547$	11.0118	−	33.8910i	0.470832	−	1.44907i	−0.380665	−	0.924713i	$-0.624305\pi$
$547$	11.0118	−	33.8910i	0.470832	−	1.44907i	0.851497	−	0.524360i	$-0.175695\pi$
$548$	12.3778	−	8.99301i	0.528754	−	0.384162i
$549$	−15.1595			−0.646994
$550$	1.96128	+	19.7552i	0.0836292	+	0.842363i
$551$	−51.4747			−2.19290
$552$	0.939878	−	0.682862i	0.0400039	−	0.0290645i
$553$	1.35335	−	4.16519i	0.0575503	−	0.177122i
$554$	−3.55927	+	10.9543i	−0.151219	+	0.465403i
$555$	0.407683	−	0.450161i	0.0173052	−	0.0191083i
$556$	6.62085	+	20.3769i	0.280787	+	0.864172i
$557$	36.0760			1.52859			0.764294	−	0.644868i	$-0.223088\pi$
$557$	36.0760			1.52859			0.764294	+	0.644868i	$0.223088\pi$
$558$	0.641115	+	1.97315i	0.0271405	+	0.0835300i
$559$	−2.86387	−	2.08072i	−0.121129	−	0.0880053i
$560$	0.763240	+	0.342456i	0.0322528	+	0.0144714i
$561$	−2.41591	+	1.75526i	−0.102000	+	0.0741072i
$562$	−9.70351	−	7.05001i	−0.409318	−	0.297387i
$563$	17.6320	+	12.8104i	0.743101	+	0.539895i	0.893681	−	0.448703i	$-0.148114\pi$
$563$	17.6320	+	12.8104i	0.743101	+	0.539895i	−0.150580	+	0.988598i	$0.548114\pi$
$564$	−3.99255	+	2.90076i	−0.168117	+	0.122144i
$565$	0.476657	+	0.213870i	0.0200531	+	0.00899756i
$566$	9.26890	+	6.73425i	0.389601	+	0.283062i
$567$	1.66152	+	5.11363i	0.0697773	+	0.214752i
$568$	25.1122			1.05369
$569$	−0.210957	−	0.649258i	−0.00884377	−	0.0272183i	0.946537	−	0.322595i	$-0.104555\pi$
$569$	−0.210957	−	0.649258i	−0.00884377	−	0.0272183i	−0.955381	+	0.295376i	$0.904555\pi$
$570$	−6.39931	+	7.06609i	−0.268037	+	0.295966i
$571$	11.8417	−	36.4450i	0.495559	−	1.52517i	−0.320524	−	0.947240i	$-0.603859\pi$
$571$	11.8417	−	36.4450i	0.495559	−	1.52517i	0.816084	−	0.577934i	$-0.196141\pi$
$572$	1.05789	−	3.25587i	0.0442328	−	0.136135i
$573$	−3.19814	+	2.32358i	−0.133604	+	0.0970691i
$574$	5.61103			0.234200
$575$	1.46655	−	2.50666i	0.0611594	−	0.104535i
$576$	−14.4268			−0.601116
$577$	32.3981	−	23.5386i	1.34875	−	0.979926i	0.349679	−	0.936869i	$-0.386291\pi$
$577$	32.3981	−	23.5386i	1.34875	−	0.979926i	0.999073	−	0.0430561i	$-0.0137094\pi$
$578$	−0.283581	+	0.872773i	−0.0117954	+	0.0363026i
$579$	−2.55943	+	7.87712i	−0.106366	+	0.327362i
$580$	18.0644	+	8.10526i	0.750083	+	0.336553i
$581$	3.04922	+	9.38453i	0.126503	+	0.389336i
$582$	2.00043			0.0829206
$583$	11.7048	+	36.0237i	0.484763	+	1.49195i
$584$	−30.9972	−	22.5208i	−1.28267	−	0.931915i
$585$	1.91852	+	3.34520i	0.0793210	+	0.138307i
$586$	12.8625	−	9.34515i	0.531345	−	0.386045i
$587$	9.62229	+	6.99100i	0.397154	+	0.288550i	0.768381	−	0.639993i	$-0.221063\pi$
$587$	9.62229	+	6.99100i	0.397154	+	0.288550i	−0.371227	+	0.928542i	$0.621063\pi$
$588$	−3.75963	−	2.73153i	−0.155044	−	0.112646i
$589$	4.87832	−	3.54431i	0.201008	−	0.146041i
$590$	−29.2917	+	6.13795i	−1.20592	+	0.252696i
$591$	−4.78668	−	3.47773i	−0.196898	−	0.143055i
$592$	0.0417936	+	0.128627i	0.00171771	+	0.00528656i
$593$	2.08395			0.0855774			0.0427887	−	0.999084i	$-0.486376\pi$
$593$	2.08395			0.0855774			0.0427887	+	0.999084i	$0.486376\pi$
$594$	4.67761	+	14.3962i	0.191925	+	0.590684i
$595$	1.21093	+	2.11143i	0.0496434	+	0.0865601i
$596$	−6.84459	+	21.0655i	−0.280365	+	0.862876i
$597$	−2.99124	+	9.20610i	−0.122423	+	0.376781i
$598$	0.294690	−	0.214105i	0.0120508	−	0.00875540i
$599$	29.8447			1.21942			0.609711	−	0.792624i	$-0.291286\pi$
$599$	29.8447			1.21942			0.609711	+	0.792624i	$0.291286\pi$
$600$	9.15947	−	4.01495i	0.373934	−	0.163910i
$601$	14.4824			0.590750			0.295375	−	0.955381i	$-0.404555\pi$
$601$	14.4824			0.590750			0.295375	+	0.955381i	$0.404555\pi$
$602$	−4.18626	+	3.04150i	−0.170619	+	0.123962i
$603$	3.56561	−	10.9738i	0.145203	−	0.446889i
$604$	0.203349	−	0.625845i	0.00827416	−	0.0254653i
$605$	1.85374	−	17.1612i	0.0753652	−	0.697701i
$606$	2.02700	+	6.23845i	0.0823411	+	0.253420i
$607$	26.5315			1.07688			0.538440	−	0.842664i	$-0.319014\pi$
$607$	26.5315			1.07688			0.538440	+	0.842664i	$0.319014\pi$
$608$	11.3992	+	35.0832i	0.462300	+	1.42281i
$609$	−4.64827	−	3.37717i	−0.188358	−	0.136850i
$610$	−1.32381	+	12.2553i	−0.0535994	+	0.496202i
$611$	−3.41416	+	2.48053i	−0.138122	+	0.100352i
$612$	−2.36392	−	1.71749i	−0.0955559	−	0.0694254i
$613$	15.7892	+	11.4715i	0.637718	+	0.463329i	0.859066	−	0.511866i	$-0.171045\pi$
$613$	15.7892	+	11.4715i	0.637718	+	0.463329i	−0.221347	+	0.975195i	$0.571045\pi$
$614$	−8.28698	+	6.02085i	−0.334435	+	0.242982i
$615$	5.81926	−	6.42559i	0.234655	−	0.259105i
$616$	−11.0415	−	8.02215i	−0.444876	−	0.323222i
$617$	14.0842	+	43.3467i	0.567009	+	1.74507i	0.661906	+	0.749587i	$0.269748\pi$
$617$	14.0842	+	43.3467i	0.567009	+	1.74507i	−0.0948971	+	0.995487i	$0.530252\pi$
$618$	8.02731			0.322906
$619$	3.62517	+	11.1571i	0.145708	+	0.448443i	0.997101	−	0.0760847i	$-0.0242419\pi$
$619$	3.62517	+	11.1571i	0.145708	+	0.448443i	−0.851393	+	0.524528i	$0.824242\pi$
$620$	−2.27007	+	0.475685i	−0.0911684	+	0.0191040i
$621$	0.684280	−	2.10600i	0.0274592	−	0.0845107i
$622$	0.122068	−	0.375688i	0.00489450	−	0.0150637i
$623$	8.00460	−	5.81568i	0.320698	−	0.233000i
$624$	0.162109			0.00648954
$625$	16.9413	−	18.3845i	0.677654	−	0.735381i
$626$	10.4462			0.417514
$627$	16.2614	−	11.8146i	0.649419	−	0.471831i
$628$	4.18172	−	12.8700i	0.166869	−	0.513570i
$629$	−0.121603	+	0.374256i	−0.00484863	+	0.0149226i
$630$	5.51712	−	1.15609i	0.219807	−	0.0460597i
$631$	−1.70652	−	5.25213i	−0.0679355	−	0.209084i	0.911326	−	0.411686i	$-0.135060\pi$
$631$	−1.70652	−	5.25213i	−0.0679355	−	0.209084i	−0.979261	+	0.202602i	$0.935060\pi$
$632$	11.6593			0.463784
$633$	1.35210	+	4.16135i	0.0537413	+	0.165399i
$634$	17.9633	+	13.0511i	0.713415	+	0.518326i
$635$	−3.56722	+	3.93891i	−0.141561	+	0.156311i
$636$	5.66009	−	4.11230i	0.224437	−	0.163063i
$637$	−3.21498	−	2.33582i	−0.127382	−	0.0925485i
$638$	24.5649	+	17.8474i	0.972532	+	0.706586i
$639$	17.6921	−	12.8541i	0.699890	−	0.508500i
$640$	1.37234	−	12.7046i	0.0542466	−	0.502194i
$641$	15.9557	+	11.5925i	0.630211	+	0.457875i	0.856473	−	0.516191i	$-0.172651\pi$
$641$	15.9557	+	11.5925i	0.630211	+	0.457875i	−0.226262	+	0.974066i	$0.572651\pi$
$642$	−1.45980	−	4.49280i	−0.0576137	−	0.177317i
$643$	32.1042			1.26607			0.633033	−	0.774125i	$-0.281810\pi$
$643$	32.1042			1.26607			0.633033	+	0.774125i	$0.281810\pi$
$644$	0.226216	+	0.696223i	0.00891418	+	0.0274350i
$645$	−0.858575	+	7.94835i	−0.0338064	+	0.312966i
$646$	1.90878	−	5.87461i	0.0750999	−	0.231134i
$647$	−10.1593	+	31.2671i	−0.399404	+	1.22924i	0.526075	+	0.850438i	$0.323663\pi$
$647$	−10.1593	+	31.2671i	−0.399404	+	1.22924i	−0.925479	+	0.378800i	$0.876337\pi$
$648$	−11.5805	+	8.41372i	−0.454925	+	0.330522i
$649$	63.1018			2.47696
$650$	2.87187	−	1.25885i	0.112644	−	0.0493762i
$651$	0.673058			0.0263792
$652$	18.3758	−	13.3508i	0.719650	−	0.522856i
$653$	7.39931	−	22.7727i	0.289558	−	0.891166i	−0.695438	−	0.718586i	$-0.744790\pi$
$653$	7.39931	−	22.7727i	0.289558	−	0.891166i	0.984995	−	0.172580i	$-0.0552104\pi$
$654$	2.10115	−	6.46669i	0.0821616	−	0.252868i
$655$	17.6433	+	30.7635i	0.689381	+	1.20203i
$656$	0.596561	+	1.83603i	0.0232918	+	0.0716848i
$657$	−33.3658			−1.30172
$658$	1.90626	+	5.86685i	0.0743136	+	0.228714i
$659$	24.1862	+	17.5723i	0.942159	+	0.684518i	0.948939	−	0.315459i	$-0.102158\pi$
$659$	24.1862	+	17.5723i	0.942159	+	0.684518i	−0.00678051	+	0.999977i	$0.502158\pi$
$660$	−7.56709	+	1.58565i	−0.294548	+	0.0617214i
$661$	−19.1528	+	13.9153i	−0.744958	+	0.541243i	−0.894260	−	0.447548i	$-0.852297\pi$
$661$	−19.1528	+	13.9153i	−0.744958	+	0.541243i	0.149302	+	0.988792i	$0.452297\pi$
$662$	−11.5551	−	8.39529i	−0.449103	−	0.326292i
$663$	0.381591	+	0.277242i	0.0148198	+	0.0107672i
$664$	−21.2525	+	15.4408i	−0.824757	+	0.599221i
$665$	−8.15075	−	14.2120i	−0.316073	−	0.551116i
$666$	0.737290	+	0.535673i	0.0285694	+	0.0207569i
$667$	−1.37261	−	4.22447i	−0.0531478	−	0.163572i
$668$	−18.2395			−0.705707
$669$	−3.61202	−	11.1167i	−0.139649	−	0.429795i
$670$	−8.56011	−	3.84081i	−0.330706	−	0.148383i
$671$	8.03138	−	24.7181i	0.310048	−	0.954230i
$672$	−1.27238	+	3.91597i	−0.0490830	+	0.151062i
$673$	−28.5931	+	20.7741i	−1.10218	+	0.800784i	−0.981415	−	0.191896i	$-0.938536\pi$
$673$	−28.5931	+	20.7741i	−1.10218	+	0.800784i	−0.120770	+	0.992681i	$0.538536\pi$
$674$	14.9991			0.577744
$675$	9.62607	−	16.4531i	0.370508	−	0.633279i
$676$	14.5113			0.558127
$677$	−3.38473	+	2.45915i	−0.130086	+	0.0945127i	−0.650925	−	0.759142i	$-0.725619\pi$
$677$	−3.38473	+	2.45915i	−0.130086	+	0.0945127i	0.520840	+	0.853654i	$0.325619\pi$
$678$	0.0457304	−	0.140744i	0.00175627	−	0.00540523i
$679$	−1.06236	+	3.26962i	−0.0407698	+	0.125477i
$680$	−4.34979	+	4.80302i	−0.166807	+	0.184187i
$681$	4.23683	+	13.0396i	0.162356	+	0.499679i
$682$	−3.55693			−0.136202
$683$	−1.08139	−	3.32816i	−0.0413781	−	0.127349i	0.928234	−	0.371998i	$-0.121327\pi$
$683$	−1.08139	−	3.32816i	−0.0413781	−	0.127349i	−0.969612	+	0.244649i	$0.921327\pi$
$684$	15.9115	+	11.5604i	0.608391	+	0.442022i
$685$	−26.9582	−	12.0958i	−1.03002	−	0.462156i
$686$	−10.3565	+	7.52447i	−0.395415	+	0.287286i
$687$	−6.62597	−	4.81405i	−0.252797	−	0.183668i
$688$	−1.44031	−	1.04645i	−0.0549113	−	0.0398954i
$689$	4.84013	−	3.51656i	0.184394	−	0.133970i
$690$	−0.750548	−	0.336761i	−0.0285729	−	0.0128203i
$691$	10.3596	+	7.52666i	0.394096	+	0.286328i	0.767132	−	0.641489i	$-0.221683\pi$
$691$	10.3596	+	7.52666i	0.394096	+	0.286328i	−0.373036	+	0.927817i	$0.621683\pi$
$692$	7.04632	+	21.6863i	0.267861	+	0.824391i
$693$	−11.8853			−0.451484
$694$	−6.46715	−	19.9038i	−0.245489	−	0.755539i
$695$	27.7755	−	30.6696i	1.05358	−	1.16336i
$696$	4.72675	−	14.5474i	0.179167	−	0.551419i
$697$	−1.73576	+	5.34212i	−0.0657466	+	0.202347i
$698$	−5.91374	+	4.29659i	−0.223838	+	0.162628i
$699$	19.2377			0.727636
$700$	0.622574	+	6.27094i	0.0235311	+	0.237019i
$701$	−24.4708			−0.924249			−0.462124	−	0.886815i	$-0.652913\pi$
$701$	−24.4708			−0.924249			−0.462124	+	0.886815i	$0.652913\pi$
$702$	1.93427	−	1.40533i	0.0730043	−	0.0530407i
$703$	0.818507	−	2.51911i	0.0308706	−	0.0950099i
$704$	7.64318	−	23.5233i	0.288063	−	0.886567i
$705$	8.69554	+	3.90158i	0.327493	+	0.146942i
$706$	−6.37764	−	19.6284i	−0.240026	−	0.738723i
$707$	−11.2730			−0.423963
$708$	−3.60170	−	11.0849i	−0.135360	−	0.416596i
$709$	26.1274	+	18.9826i	0.981234	+	0.712908i	0.957984	−	0.286822i	$-0.0925987\pi$
$709$	26.1274	+	18.9826i	0.981234	+	0.712908i	0.0232497	+	0.999730i	$0.492599\pi$
$710$	−8.84654	−	15.4252i	−0.332005	−	0.578896i
$711$	8.21427	−	5.96802i	0.308059	−	0.223818i
$712$	21.3101	+	15.4827i	0.798630	+	0.580239i
$713$	0.420961	+	0.305846i	0.0157651	+	0.0114540i
$714$	0.557790	−	0.405258i	0.0208748	−	0.0151664i
$715$	−6.47086	+	1.35594i	−0.241996	+	0.0507093i
$716$	0.875308	+	0.635949i	0.0327118	+	0.0237665i
$717$	−2.90885	−	8.95253i	−0.108633	−	0.334338i
$718$	−24.4016			−0.910659
$719$	−11.7145	−	36.0535i	−0.436877	−	1.34457i	−0.891150	−	0.453708i	$-0.850101\pi$
$719$	−11.7145	−	36.0535i	−0.436877	−	1.34457i	0.454273	−	0.890862i	$-0.349899\pi$
$720$	0.964869	+	1.68238i	0.0359586	+	0.0626987i
$721$	−4.26304	+	13.1203i	−0.158764	+	0.488625i
$722$	−7.45989	+	22.9592i	−0.277628	+	0.854452i
$723$	7.58344	−	5.50969i	0.282031	−	0.204908i
$724$	−14.6862			−0.545810
$725$	−3.77759	−	38.0501i	−0.140296	−	1.41315i
$726$	−4.88938			−0.181462
$727$	−22.0416	+	16.0142i	−0.817478	+	0.593933i	−0.915989	−	0.401203i	$-0.868592\pi$
$727$	−22.0416	+	16.0142i	−0.817478	+	0.593933i	0.0985106	+	0.995136i	$0.468592\pi$
$728$	−0.666150	+	2.05020i	−0.0246892	+	0.0759854i
$729$	−1.41262	+	4.34761i	−0.0523194	+	0.161023i
$730$	−2.91367	+	26.9736i	−0.107840	+	0.998338i
$731$	−1.60072	−	4.92651i	−0.0592048	−	0.182214i
$732$	−4.80056			−0.177434
$733$	−5.19943	−	16.0022i	−0.192045	−	0.591055i	−0.999998	−	0.00180788i	$-0.999425\pi$
$733$	−5.19943	−	16.0022i	−0.192045	−	0.591055i	0.807953	−	0.589247i	$-0.200575\pi$
$734$	−1.35263	−	0.982740i	−0.0499263	−	0.0362736i
$735$	−0.963835	+	8.92280i	−0.0355516	+	0.329122i
$736$	−2.57527	+	1.87104i	−0.0949257	+	0.0689676i
$737$	16.0041	+	11.6277i	0.589519	+	0.428311i
$738$	10.5241	+	7.64618i	0.387396	+	0.281460i
$739$	−30.6041	+	22.2352i	−1.12579	+	0.817935i	−0.985077	−	0.172115i	$-0.944940\pi$
$739$	−30.6041	+	22.2352i	−1.12579	+	0.817935i	−0.140714	+	0.990050i	$0.544940\pi$
$740$	−0.683906	+	0.755165i	−0.0251409	+	0.0277604i
$741$	−2.56848	−	1.86611i	−0.0943555	−	0.0685533i
$742$	−2.70243	−	8.31721i	−0.0992092	−	0.305335i
$743$	−43.2330			−1.58607			−0.793033	−	0.609179i	$-0.791499\pi$
$743$	−43.2330			−1.58607			−0.793033	+	0.609179i	$0.791499\pi$
$744$	0.553709	+	1.70414i	0.0202999	+	0.0624768i
$745$	41.8665	−	8.77295i	1.53387	−	0.321416i
$746$	−9.38418	+	28.8815i	−0.343579	+	1.05743i
$747$	−7.06922	+	21.7568i	−0.258649	+	0.796041i
$748$	4.05280	−	2.94453i	0.148185	−	0.107663i
$749$	8.11855			0.296645
$750$	−5.69288	−	4.21181i	−0.207875	−	0.153794i
$751$	−8.22782			−0.300238			−0.150119	−	0.988668i	$-0.547966\pi$
$751$	−8.22782			−0.300238			−0.150119	+	0.988668i	$0.547966\pi$
$752$	−1.71706	+	1.24752i	−0.0626149	+	0.0454924i
$753$	−2.96252	+	9.11770i	−0.107960	+	0.332267i
$754$	1.48203	−	4.56121i	0.0539723	−	0.166110i
$755$	−1.24383	+	0.260640i	−0.0452677	+	0.00948566i
$756$	1.48483	+	4.56983i	0.0540026	+	0.166203i
$757$	−33.1776			−1.20586			−0.602929	−	0.797795i	$-0.706000\pi$
$757$	−33.1776			−1.20586			−0.602929	+	0.797795i	$0.706000\pi$
$758$	3.48177	+	10.7158i	0.126464	+	0.389215i
$759$	1.40324	+	1.01951i	0.0509342	+	0.0370059i
$760$	29.2783	−	32.3290i	1.06204	−	1.17270i
$761$	−16.9819	+	12.3381i	−0.615594	+	0.447255i	−0.851380	−	0.524550i	$-0.824234\pi$
$761$	−16.9819	+	12.3381i	−0.615594	+	0.447255i	0.235786	+	0.971805i	$0.424234\pi$
$762$	1.21781	+	0.884789i	0.0441165	+	0.0320525i
$763$	9.45368	+	6.86850i	0.342246	+	0.248656i
$764$	5.36502	−	3.89791i	0.194100	−	0.141022i
$765$	−0.606026	+	5.61034i	−0.0219109	+	0.202842i
$766$	20.8896	+	15.1772i	0.754772	+	0.548374i
$767$	−3.07993	−	9.47906i	−0.111210	−	0.342269i
$768$	−11.5111			−0.415370
$769$	7.28786	+	22.4297i	0.262807	+	0.808836i	0.992191	+	0.124731i	$0.0398069\pi$
$769$	7.28786	+	22.4297i	0.262807	+	0.808836i	−0.729384	+	0.684105i	$0.760193\pi$
$770$	−1.03788	+	9.60830i	−0.0374027	+	0.346259i
$771$	0.282485	−	0.869398i	0.0101734	−	0.0313106i
$772$	4.29356	−	13.2142i	0.154529	−	0.475590i
$773$	−7.84964	+	5.70310i	−0.282332	+	0.205126i	−0.719934	−	0.694043i	$-0.755828\pi$
$773$	−7.84964	+	5.70310i	−0.282332	+	0.205126i	0.437602	+	0.899169i	$0.355828\pi$
$774$	−11.9964			−0.431203
$775$	2.97796	+	3.34595i	0.106971	+	0.120190i
$776$	−9.15245			−0.328554
$777$	0.239187	−	0.173780i	0.00858079	−	0.00623431i
$778$	−0.310920	+	0.956912i	−0.0111470	+	0.0343070i
$779$	11.6834	−	35.9577i	0.418600	−	1.28832i
$780$	0.607536	+	1.05932i	0.0217533	+	0.0379298i
$781$	11.5858	+	35.6575i	0.414573	+	1.27592i
$782$	0.533022			0.0190608
$783$	−9.00948	−	27.7283i	−0.321973	−	0.990930i
$784$	−1.61689	−	1.17474i	−0.0577461	−	0.0419550i
$785$	−25.5785	+	5.35986i	−0.912935	+	0.191302i
$786$	8.12701	−	5.90462i	0.289881	−	0.210611i
$787$	−9.68333	−	7.03535i	−0.345173	−	0.250783i	0.401668	−	0.915785i	$-0.368431\pi$
$787$	−9.68333	−	7.03535i	−0.345173	−	0.250783i	−0.746841	+	0.665002i	$0.768431\pi$
$788$	8.02987	+	5.83405i	0.286052	+	0.207829i
$789$	11.4315	−	8.30549i	0.406973	−	0.295683i
$790$	−4.10736	−	7.16174i	−0.146133	−	0.254803i
$791$	0.205754	+	0.149489i	0.00731576	+	0.00531521i
$792$	−9.77772	−	30.0927i	−0.347436	−	1.06930i
$793$	−4.10512			−0.145777
$794$	5.53292	+	17.0286i	0.196356	+	0.604322i
$795$	−12.3273	−	5.53112i	−0.437206	−	0.196169i
$796$	5.01795	−	15.4436i	0.177856	−	0.547386i
$797$	15.3255	−	47.1670i	0.542857	−	1.67074i	−0.183174	−	0.983080i	$-0.558637\pi$
$797$	15.3255	−	47.1670i	0.542857	−	1.67074i	0.726031	−	0.687662i	$-0.241363\pi$
$798$	−3.75447	+	2.72778i	−0.132907	+	0.0965625i
$799$	−6.17537			−0.218469
$800$	−25.0970	+	11.0010i	−0.887313	+	0.388944i
$801$	22.9385			0.810493
$802$	4.83518	−	3.51296i	0.170736	−	0.124047i
$803$	17.6769	−	54.4038i	0.623804	−	1.91987i
$804$	1.12912	−	3.47508i	0.0398210	−	0.122556i
$805$	0.949013	−	1.04790i	0.0334483	−	0.0369335i
$806$	0.173610	+	0.534317i	0.00611515	+	0.0188205i
$807$	−5.59552			−0.196972
$808$	−9.27398	−	28.5424i	−0.326258	−	1.00412i
$809$	−10.1948	−	7.40697i	−0.358431	−	0.260415i	0.393966	−	0.919125i	$-0.371103\pi$
$809$	−10.1948	−	7.40697i	−0.358431	−	0.260415i	−0.752397	+	0.658710i	$0.771103\pi$
$810$	9.24770	+	4.14932i	0.324931	+	0.145792i
$811$	−1.72623	+	1.25418i	−0.0606163	+	0.0440403i	−0.617681	−	0.786429i	$-0.711928\pi$
$811$	−1.72623	+	1.25418i	−0.0606163	+	0.0440403i	0.557065	+	0.830469i	$0.311928\pi$
$812$	7.79769	+	5.66535i	0.273645	+	0.198815i
$813$	−9.82637	−	7.13927i	−0.344626	−	0.250385i
$814$	−1.26404	+	0.918378i	−0.0443045	+	0.0321891i
$815$	−40.0213	−	17.9570i	−1.40189	−	0.629008i
$816$	0.191911	+	0.139432i	0.00671824	+	0.00488109i
$817$	10.7744	+	33.1602i	0.376949	+	1.16013i
$818$	3.94125			0.137803
$819$	0.580108	+	1.78539i	0.0202706	+	0.0623866i
$820$	−9.76206	+	10.7792i	−0.340906	+	0.376427i
$821$	−4.66063	+	14.3439i	−0.162657	+	0.500607i	−0.998856	−	0.0478195i	$-0.984773\pi$
$821$	−4.66063	+	14.3439i	−0.162657	+	0.500607i	0.836199	+	0.548426i	$0.184773\pi$
$822$	−2.58637	+	7.96001i	−0.0902099	+	0.277637i
$823$	−24.8177	+	18.0311i	−0.865091	+	0.628525i	−0.929265	−	0.369414i	$-0.879559\pi$
$823$	−24.8177	+	18.0311i	−0.865091	+	0.628525i	0.0641745	+	0.997939i	$0.479559\pi$
$824$	−36.7268			−1.27944
$825$	9.92676	+	11.1534i	0.345605	+	0.388312i
$826$	−14.5691			−0.506922
$827$	33.3355	−	24.2197i	1.15919	−	0.842201i	0.169515	−	0.985528i	$-0.445780\pi$
$827$	33.3355	−	24.2197i	1.15919	−	0.842201i	0.989675	+	0.143326i	$0.0457799\pi$
$828$	−0.524454	+	1.61410i	−0.0182260	+	0.0560940i
$829$	11.7784	−	36.2501i	0.409079	−	1.25902i	−0.508361	−	0.861144i	$-0.669749\pi$
$829$	11.7784	−	36.2501i	0.409079	−	1.25902i	0.917441	−	0.397873i	$-0.130251\pi$
$830$	16.9714	+	7.61482i	0.589084	+	0.264314i
$831$	2.67697	+	8.23886i	0.0928630	+	0.285803i
$832$	−3.90669			−0.135440
$833$	−1.79697	−	5.53049i	−0.0622612	−	0.191620i
$834$	−9.48222	−	6.88924i	−0.328343	−	0.238555i
$835$	17.5243	+	30.5560i	0.606453	+	1.05743i
$836$	−27.2793	+	19.8196i	−0.943474	+	0.685474i
$837$	2.76308	+	2.00750i	0.0955061	+	0.0693892i
$838$	−0.316963	−	0.230287i	−0.0109493	−	0.00795514i
$839$	−21.3219	+	15.4912i	−0.736113	+	0.534817i	−0.891491	−	0.453038i	$-0.850340\pi$
$839$	−21.3219	+	15.4912i	−0.736113	+	0.534817i	0.155379	+	0.987855i	$0.450340\pi$
$840$	4.76495	−	0.998475i	0.164406	−	0.0344507i
$841$	−23.8525	−	17.3299i	−0.822500	−	0.597581i
$842$	7.09173	+	21.8261i	0.244397	+	0.752177i
$843$	−9.02098			−0.310699
$844$	−2.26822	−	6.98085i	−0.0780752	−	0.240291i
$845$	−13.9423	−	24.3103i	−0.479630	−	0.836300i
$846$	−4.41941	+	13.6015i	−0.151942	+	0.467631i
$847$	2.59659	−	7.99149i	0.0892200	−	0.274591i
$848$	2.43422	−	1.76856i	0.0835913	−	0.0607327i
$849$	8.61695			0.295733
$850$	4.48260	+	0.979847i	0.153752	+	0.0336085i
$851$	0.228566			0.00783515
$852$	5.60256	−	4.07049i	0.191940	−	0.139453i
$853$	−7.55157	+	23.2413i	−0.258561	+	0.795768i	0.734546	+	0.678559i	$0.237395\pi$
$853$	−7.55157	+	23.2413i	−0.258561	+	0.795768i	−0.993107	+	0.117210i	$0.962605\pi$
$854$	−1.85430	+	5.70695i	−0.0634529	+	0.195288i
$855$	4.07914	−	37.7631i	0.139504	−	1.29147i
$856$	6.67893	+	20.5556i	0.228281	+	0.702577i
$857$	−34.8556			−1.19065			−0.595323	−	0.803487i	$-0.702976\pi$
$857$	−34.8556			−1.19065			−0.595323	+	0.803487i	$0.702976\pi$
$858$	0.578713	+	1.78110i	0.0197569	+	0.0608056i
$859$	−21.1330	−	15.3541i	−0.721050	−	0.523874i	0.165669	−	0.986181i	$-0.447022\pi$
$859$	−21.1330	−	15.3541i	−0.721050	−	0.523874i	−0.886720	+	0.462308i	$0.847022\pi$
$860$	1.44030	−	13.3337i	0.0491138	−	0.454676i
$861$	3.41415	−	2.48053i	0.116354	−	0.0845362i
$862$	−18.8207	−	13.6740i	−0.641036	−	0.465740i
$863$	−23.3386	−	16.9565i	−0.794456	−	0.577206i	0.114827	−	0.993386i	$-0.463369\pi$
$863$	−23.3386	−	16.9565i	−0.794456	−	0.577206i	−0.909282	+	0.416180i	$0.863369\pi$
$864$	−16.9034	+	12.2811i	−0.575066	+	0.417810i
$865$	29.5604	−	32.6404i	1.00508	−	1.10981i
$866$	14.0587	+	10.2142i	0.477732	+	0.347093i
$867$	0.213285	+	0.656424i	0.00724354	+	0.0222933i
$868$	−1.12909			−0.0383237
$869$	5.37917	+	16.5554i	0.182476	+	0.561603i
$870$	−10.6009	+	2.22137i	−0.359404	+	0.0753116i
$871$	0.965547	−	2.97165i	0.0327163	−	0.100690i
$872$	−9.61328	+	29.5866i	−0.325547	+	1.00193i
$873$	−6.44811	+	4.68482i	−0.218235	+	0.158557i
$874$	−3.58775			−0.121358
$875$	9.90733	−	7.06802i	0.334929	−	0.238943i
$876$	−10.5659			−0.356989
$877$	−8.91958	+	6.48046i	−0.301193	+	0.218829i	−0.728108	−	0.685462i	$-0.759600\pi$
$877$	−8.91958	+	6.48046i	−0.301193	+	0.218829i	0.426915	+	0.904292i	$0.359600\pi$
$878$	−4.67178	+	14.3783i	−0.157665	+	0.485243i
$879$	3.69516	−	11.3725i	0.124634	−	0.383586i
$880$	−3.25435	+	0.681936i	−0.109704	+	0.0229880i
$881$	−13.1603	−	40.5032i	−0.443382	−	1.36459i	−0.884249	−	0.467016i	$-0.845329\pi$
$881$	−13.1603	−	40.5032i	−0.443382	−	1.36459i	0.440867	−	0.897572i	$-0.354671\pi$
$882$	−13.4672			−0.453463
$883$	−7.41907	−	22.8335i	−0.249671	−	0.768410i	−0.994833	−	0.101526i	$-0.967628\pi$
$883$	−7.41907	−	22.8335i	−0.249671	−	0.768410i	0.745161	−	0.666884i	$-0.232372\pi$
$884$	−0.640136	−	0.465086i	−0.0215301	−	0.0156425i
$885$	−15.1097	+	16.6841i	−0.507907	+	0.560829i
$886$	21.5215	−	15.6363i	0.723028	−	0.525311i
$887$	38.5219	+	27.9878i	1.29344	+	0.939739i	0.999869	−	0.0161981i	$-0.00515625\pi$
$887$	38.5219	+	27.9878i	1.29344	+	0.939739i	0.293571	+	0.955937i	$0.405156\pi$
$888$	0.636772	+	0.462642i	0.0213687	+	0.0155252i
$889$	−2.09289	+	1.52057i	−0.0701932	+	0.0509983i
$890$	2.00311	−	18.5440i	0.0671443	−	0.621595i
$891$	−17.2896	−	12.5617i	−0.579225	−	0.420831i
$892$	6.05933	+	18.6487i	0.202881	+	0.624405i
$893$	41.5663			1.39096
$894$	−3.74428	−	11.5237i	−0.125227	−	0.385411i
$895$	0.224398	−	2.07739i	0.00750080	−	0.0694394i
$896$	1.92229	−	5.91619i	0.0642190	−	0.197646i
$897$	0.0846589	−	0.260553i	0.00282668	−	0.00869962i
$898$	5.06226	−	3.67795i	0.168930	−	0.122735i
$899$	6.85095			0.228492
$900$	−7.37773	+	12.6102i	−0.245924	+	0.420339i
$901$	8.75460			0.291658
$902$	−18.0429	+	13.1089i	−0.600762	+	0.436479i
$903$	−1.20263	+	3.70133i	−0.0400212	+	0.123172i
$904$	−0.209228	+	0.643936i	−0.00695880	+	0.0214170i
$905$	14.1104	+	24.6034i	0.469044	+	0.817844i
$906$	0.111241	+	0.342364i	0.00369572	+	0.0113743i
$907$	30.5790			1.01536			0.507679	−	0.861546i	$-0.330503\pi$
$907$	30.5790			1.01536			0.507679	+	0.861546i	$0.330503\pi$
$908$	−7.10746	−	21.8745i	−0.235869	−	0.725932i
$909$	−21.1436	−	15.3617i	−0.701289	−	0.509516i
$910$	1.49400	−	0.313062i	0.0495257	−	0.0103779i
$911$	−14.9146	+	10.8361i	−0.494142	+	0.359015i	−0.806775	−	0.590859i	$-0.798789\pi$
$911$	−14.9146	+	10.8361i	−0.494142	+	0.359015i	0.312633	+	0.949874i	$0.398789\pi$
$912$	−1.29175	−	0.938512i	−0.0427741	−	0.0310772i
$913$	−31.7299	−	23.0531i	−1.05011	−	0.762947i
$914$	8.92263	−	6.48267i	0.295134	−	0.214428i
$915$	4.61233	+	8.04223i	0.152479	+	0.265868i
$916$	11.1154	+	8.07578i	0.367262	+	0.266831i
$917$	5.33486	+	16.4190i	0.176173	+	0.542203i
$918$	3.49862			0.115472
$919$	8.03444	+	24.7275i	0.265032	+	0.815684i	0.991686	+	0.128681i	$0.0410742\pi$
$919$	8.03444	+	24.7275i	0.265032	+	0.815684i	−0.726654	+	0.687003i	$0.758926\pi$
$920$	3.43393	+	1.54076i	0.113213	+	0.0507974i
$921$	−2.38070	+	7.32703i	−0.0784466	+	0.241434i
$922$	−9.08059	+	27.9472i	−0.299053	+	0.920391i
$923$	4.79092	−	3.48081i	0.157695	−	0.114572i
$924$	−3.76370			−0.123817
$925$	1.92219	+	0.420170i	0.0632013	+	0.0138151i
$926$	0.882650			0.0290057
$927$	−25.8749	+	18.7992i	−0.849842	+	0.617447i
$928$	−12.9513	+	39.8600i	−0.425148	+	1.30847i
$929$	5.54508	−	17.0660i	0.181928	−	0.559917i	−0.817954	−	0.575284i	$-0.804892\pi$
$929$	5.54508	−	17.0660i	0.181928	−	0.559917i	0.999882	+	0.0153668i	$0.00489158\pi$
$930$	0.851706	−	0.940450i	0.0279285	−	0.0308386i
$931$	12.0953	+	37.2256i	0.396408	+	1.22002i
$932$	−32.2721			−1.05711
$933$	−0.0918091	−	0.282559i	−0.00300570	−	0.00925058i
$934$	26.5389	+	19.2816i	0.868378	+	0.630914i
$935$	−8.82676	−	3.96045i	−0.288666	−	0.129521i
$936$	−4.04325	+	2.93759i	−0.132158	+	0.0960182i
$937$	−31.6728	−	23.0116i	−1.03471	−	0.751757i	−0.0654601	−	0.997855i	$-0.520852\pi$
$937$	−31.6728	−	23.0116i	−1.03471	−	0.751757i	−0.969245	+	0.246098i	$0.920852\pi$
$938$	−3.69506	−	2.68462i	−0.120648	−	0.0876559i
$939$	6.35621	−	4.61806i	0.207427	−	0.150705i
$940$	−14.5872	−	6.54507i	−0.475781	−	0.213477i
$941$	3.49819	+	2.54158i	0.114038	+	0.0828533i	0.643342	−	0.765579i	$-0.277547\pi$
$941$	3.49819	+	2.54158i	0.114038	+	0.0828533i	−0.529305	+	0.848432i	$0.677547\pi$
$942$	2.28758	+	7.04045i	0.0745334	+	0.229390i
$943$	3.26255			0.106243
$944$	−1.54897	−	4.76725i	−0.0504148	−	0.155161i
$945$	6.22908	−	6.87812i	0.202632	−	0.223745i
$946$	6.35559	−	19.5605i	0.206638	−	0.635967i
$947$	15.6269	−	48.0947i	0.507807	−	1.56287i	−0.288194	−	0.957572i	$-0.593055\pi$
$947$	15.6269	−	48.0947i	0.507807	−	1.56287i	0.796000	−	0.605296i	$-0.206945\pi$
$948$	2.60121	−	1.88989i	0.0844833	−	0.0613807i
$949$	−9.03526			−0.293297
$950$	−30.1722	−	6.59533i	−0.978917	−	0.213981i
$951$	16.6998			0.541529
$952$	−2.55202	+	1.85415i	−0.0827115	+	0.0600934i
$953$	8.36670	−	25.7500i	0.271024	−	0.834126i	−0.719220	−	0.694782i	$-0.755501\pi$
$953$	8.36670	−	25.7500i	0.271024	−	0.834126i	0.990244	−	0.139344i	$-0.0444992\pi$
$954$	6.26523	−	19.2824i	0.202844	−	0.624291i
$955$	−11.6847	−	5.24277i	−0.378108	−	0.169652i
$956$	4.87973	+	15.0183i	0.157822	+	0.485725i
$957$	22.8370			0.738216
$958$	8.36136	+	25.7336i	0.270143	+	0.831416i
$959$	−11.6368	−	8.45461i	−0.375771	−	0.273014i
$960$	4.38939	+	7.65350i	0.141667	+	0.247016i
$961$	24.4303	−	17.7496i	0.788073	−	0.572568i
$962$	0.199654	+	0.145057i	0.00643710	+	0.00467683i
$963$	15.2272	+	11.0632i	0.490689	+	0.356506i
$964$	−12.7216	+	9.24276i	−0.409734	+	0.297689i
$965$	−26.2625	+	5.50321i	−0.845421	+	0.177154i
$966$	−0.323982	−	0.235387i	−0.0104239	−	0.00757344i
$967$	5.27235	+	16.2266i	0.169547	+	0.521813i	0.999343	−	0.0362551i	$-0.0115429\pi$
$967$	5.27235	+	16.2266i	0.169547	+	0.521813i	−0.829795	+	0.558068i	$0.811543\pi$
$968$	22.3701			0.719001
$969$	−1.43562	−	4.41837i	−0.0461186	−	0.141938i
$970$	3.22423	+	5.62189i	0.103524	+	0.180508i
$971$	7.74881	−	23.8484i	0.248671	−	0.765331i	−0.746340	−	0.665565i	$-0.768191\pi$
$971$	7.74881	−	23.8484i	0.248671	−	0.765331i	0.995011	−	0.0997658i	$-0.0318093\pi$
$972$	−5.31202	+	16.3487i	−0.170383	+	0.524385i
$973$	16.2959	−	11.8396i	0.522422	−	0.379562i
$974$	−23.6024			−0.756271
$975$	1.19094	−	2.03557i	0.0381405	−	0.0651904i
$976$	−2.06456			−0.0660850
$977$	−47.7604	+	34.7000i	−1.52799	+	1.11015i	−0.570648	+	0.821195i	$0.693308\pi$
$977$	−47.7604	+	34.7000i	−1.52799	+	1.11015i	−0.957343	+	0.288955i	$0.906692\pi$
$978$	−3.83964	+	11.8172i	−0.122778	+	0.377873i
$979$	−12.1526	+	37.4019i	−0.388399	+	1.19537i
$980$	1.61688	−	14.9684i	0.0516492	−	0.478148i
$981$	8.37160	+	25.7651i	0.267285	+	0.822618i
$982$	19.0433			0.607696
$983$	−6.26771	−	19.2900i	−0.199909	−	0.615257i	−0.999884	−	0.0152235i	$-0.995154\pi$
$983$	−6.26771	−	19.2900i	−0.199909	−	0.615257i	0.799975	−	0.600033i	$-0.204846\pi$
$984$	9.08928	+	6.60375i	0.289756	+	0.210520i
$985$	2.05857	−	19.0575i	0.0655916	−	0.607221i
$986$	5.67765	−	4.12506i	0.180813	−	0.131369i
$987$	3.75352	+	2.72709i	0.119476	+	0.0868044i
$988$	4.30874	+	3.13048i	0.137079	+	0.0995939i
$989$	−2.43411	+	1.76849i	−0.0774003	+	0.0562346i
$990$	−15.0399	+	16.6070i	−0.478001	+	0.527806i
$991$	30.5882	+	22.2236i	0.971666	+	0.705957i	0.955831	−	0.293918i	$-0.0949593\pi$
$991$	30.5882	+	22.2236i	0.971666	+	0.705957i	0.0158352	+	0.999875i	$0.494959\pi$
$992$	−1.51716	−	4.66935i	−0.0481700	−	0.148252i
$993$	−10.7424			−0.340899
$994$	−2.67496	−	8.23267i	−0.0848444	−	0.261124i
$995$	−30.6934	+	6.43168i	−0.973047	+	0.203898i
$996$	−2.23861	+	6.88972i	−0.0709330	+	0.218309i
$997$	−14.8934	+	45.8370i	−0.471677	+	1.45167i	0.378710	+	0.925516i	$0.376368\pi$
$997$	−14.8934	+	45.8370i	−0.471677	+	1.45167i	−0.850387	+	0.526158i	$0.823632\pi$
$998$	1.17458	−	0.853379i	0.0371805	−	0.0270132i
$999$	1.50025			0.0474658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.14	✓	76
25.16	even	5	inner	425.2.k.b.341.14	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.14	✓	76	1.1	even	1	trivial
425.2.k.b.341.14	yes	76	25.16	even	5	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.742425 - 0.539403i) q^{2} +(0.213285 - 0.656424i) q^{3} +(-0.357795 + 1.10118i) q^{4} +(2.18854 - 0.458598i) q^{5} +(-0.195729 - 0.602392i) q^{6} +1.08853 q^{7} +(0.895506 + 2.75609i) q^{8} +(2.04165 + 1.48335i) q^{9} +(1.37745 - 1.52098i) q^{10} +(-3.50028 + 2.54310i) q^{11} +(0.646528 + 0.469730i) q^{12} +(0.552867 + 0.401681i) q^{13} +(0.808152 - 0.587157i) q^{14} +(0.165747 - 1.53442i) q^{15} +(0.278050 + 0.202015i) q^{16} +(0.309017 + 0.951057i) q^{17} +2.31589 q^{18} +(-2.07999 - 6.40154i) q^{19} +(-0.278048 + 2.57405i) q^{20} +(0.232167 - 0.714537i) q^{21} +(-1.22694 + 3.77613i) q^{22} +(0.469902 - 0.341404i) q^{23} +2.00016 q^{24} +(4.57937 - 2.00732i) q^{25} +0.627130 q^{26} +(3.08432 - 2.24089i) q^{27} +(-0.389470 + 1.19867i) q^{28} +(2.36319 - 7.27315i) q^{29} +(-0.704616 - 1.22860i) q^{30} +(0.276832 + 0.852003i) q^{31} -5.48044 q^{32} +(0.922796 + 2.84007i) q^{33} +(0.742425 + 0.539403i) q^{34} +(2.38229 - 0.499198i) q^{35} +(-2.36392 + 1.71749i) q^{36} +(0.318361 + 0.231303i) q^{37} +(-4.99724 - 3.63071i) q^{38} +(0.381591 - 0.277242i) q^{39} +(3.22378 + 5.62111i) q^{40} +(4.54428 + 3.30161i) q^{41} +(-0.213057 - 0.655722i) q^{42} -5.18004 q^{43} +(-1.54803 - 4.76435i) q^{44} +(5.14848 + 2.31006i) q^{45} +(0.164713 - 0.506934i) q^{46} +(-1.90830 + 5.87313i) q^{47} +(0.191911 - 0.139432i) q^{48} -5.81510 q^{49} +(2.31709 - 3.96041i) q^{50} +0.690205 q^{51} +(-0.640136 + 0.465086i) q^{52} +(2.70532 - 8.32612i) q^{53} +(1.08113 - 3.32738i) q^{54} +(-6.49423 + 7.17090i) q^{55} +(0.974785 + 3.00008i) q^{56} -4.64575 q^{57} +(-2.16867 - 6.67448i) q^{58} +(-11.7992 - 8.57264i) q^{59} +(1.63037 + 0.731524i) q^{60} +(-4.85982 + 3.53087i) q^{61} +(0.665101 + 0.483224i) q^{62} +(2.22240 + 1.61467i) q^{63} +(-4.62492 + 3.36020i) q^{64} +(1.39418 + 0.625550i) q^{65} +(2.21705 + 1.61078i) q^{66} +(-1.41290 - 4.34845i) q^{67} -1.15785 q^{68} +(-0.123883 - 0.381271i) q^{69} +(1.49940 - 1.65563i) q^{70} +(2.67782 - 8.24148i) q^{71} +(-2.25992 + 6.95531i) q^{72} +(-10.6963 + 7.77135i) q^{73} +0.361125 q^{74} +(-0.340939 - 3.43414i) q^{75} +7.79345 q^{76} +(-3.81016 + 2.76824i) q^{77} +(0.133757 - 0.411663i) q^{78} +(1.24328 - 3.82643i) q^{79} +(0.701166 + 0.314604i) q^{80} +(1.52639 + 4.69774i) q^{81} +5.15469 q^{82} +(2.80123 + 8.62129i) q^{83} +(0.703765 + 0.511315i) q^{84} +(1.11245 + 1.93971i) q^{85} +(-3.84579 + 2.79413i) q^{86} +(-4.27023 - 3.10251i) q^{87} +(-10.1435 - 7.36971i) q^{88} +(7.35359 - 5.34270i) q^{89} +(5.06842 - 1.06207i) q^{90} +(0.601812 + 0.437242i) q^{91} +(0.207818 + 0.639599i) q^{92} +0.618319 q^{93} +(1.75122 + 5.38970i) q^{94} +(-7.48786 - 13.0561i) q^{95} +(-1.16890 + 3.59749i) q^{96} +(-0.975963 + 3.00371i) q^{97} +(-4.31728 + 3.13669i) q^{98} -10.9187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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