LMFDB - Embedded newform 640.2.bm.a.221.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			221.33
Character	$\chi$	$=$	640.221
Dual form			640.2.bm.a.501.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0344201 + 1.41379i) q^{2} +(-1.37377 - 0.135304i) q^{3} +(-1.99763 + 0.0973258i) q^{4} +(-0.471397 - 0.881921i) q^{5} +(0.144007 - 1.94688i) q^{6} +(0.0886862 + 0.445856i) q^{7} +(-0.206357 - 2.82089i) q^{8} +(-1.07343 - 0.213518i) q^{9} +O(q^{10})$	\(q+(0.0344201 + 1.41379i) q^{2} +(-1.37377 - 0.135304i) q^{3} +(-1.99763 + 0.0973258i) q^{4} +(-0.471397 - 0.881921i) q^{5} +(0.144007 - 1.94688i) q^{6} +(0.0886862 + 0.445856i) q^{7} +(-0.206357 - 2.82089i) q^{8} +(-1.07343 - 0.213518i) q^{9} +(1.23063 - 0.696814i) q^{10} +(1.21482 + 0.996974i) q^{11} +(2.75745 + 0.136585i) q^{12} +(-0.544469 - 0.291025i) q^{13} +(-0.627296 + 0.140730i) q^{14} +(0.528262 + 1.27534i) q^{15} +(3.98106 - 0.388842i) q^{16} +(-0.0852558 + 0.205826i) q^{17} +(0.264923 - 1.52496i) q^{18} +(3.47569 - 1.05434i) q^{19} +(1.02751 + 1.71587i) q^{20} +(-0.0615080 - 0.624501i) q^{21} +(-1.36770 + 1.75182i) q^{22} +(5.94991 - 3.97560i) q^{23} +(-0.0981914 + 3.90317i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(0.392709 - 0.779785i) q^{26} +(5.40867 + 1.64070i) q^{27} +(-0.220555 - 0.882023i) q^{28} +(4.56886 + 5.56718i) q^{29} +(-1.78488 + 0.790751i) q^{30} +(5.48803 - 5.48803i) q^{31} +(0.686771 + 5.61501i) q^{32} +(-1.53398 - 1.53398i) q^{33} +(-0.293930 - 0.113450i) q^{34} +(0.351403 - 0.288389i) q^{35} +(2.16509 + 0.322058i) q^{36} +(-2.72193 + 8.97302i) q^{37} +(1.61025 + 4.87762i) q^{38} +(0.708597 + 0.473469i) q^{39} +(-2.39053 + 1.51175i) q^{40} +(1.41663 + 2.12014i) q^{41} +(0.880799 - 0.108455i) q^{42} +(-3.29543 + 0.324572i) q^{43} +(-2.52378 - 1.87335i) q^{44} +(0.317704 + 1.04733i) q^{45} +(5.82548 + 8.27511i) q^{46} +(-5.84726 - 2.42201i) q^{47} +(-5.52165 - 0.00447526i) q^{48} +(6.27623 - 2.59970i) q^{49} +(-1.19465 - 0.756843i) q^{50} +(0.144971 - 0.271221i) q^{51} +(1.11597 + 0.528369i) q^{52} +(0.560619 - 0.683116i) q^{53} +(-2.13345 + 7.70322i) q^{54} +(0.306592 - 1.54134i) q^{55} +(1.23941 - 0.342179i) q^{56} +(-4.91744 + 0.978140i) q^{57} +(-7.71358 + 6.65106i) q^{58} +(-0.316105 + 0.168961i) q^{59} +(-1.17939 - 2.49624i) q^{60} +(0.281848 - 2.86166i) q^{61} +(7.94784 + 7.57005i) q^{62} -0.497530i q^{63} +(-7.91483 + 1.16422i) q^{64} +0.617367i q^{65} +(2.11593 - 2.22153i) q^{66} +(0.392935 - 3.98954i) q^{67} +(0.150277 - 0.419461i) q^{68} +(-8.71170 + 4.65650i) q^{69} +(0.419818 + 0.486885i) q^{70} +(12.3308 - 2.45275i) q^{71} +(-0.380801 + 3.07208i) q^{72} +(1.09232 - 5.49146i) q^{73} +(-12.7797 - 3.53940i) q^{74} +(0.875725 - 1.06707i) q^{75} +(-6.84053 + 2.44445i) q^{76} +(-0.336769 + 0.630050i) q^{77} +(-0.644999 + 1.01811i) q^{78} +(14.2413 - 5.89893i) q^{79} +(-2.21958 - 3.32768i) q^{80} +(-4.17482 - 1.72927i) q^{81} +(-2.94868 + 2.07580i) q^{82} +(-2.16532 - 7.13812i) q^{83} +(0.183650 + 1.24154i) q^{84} +(0.221711 - 0.0218367i) q^{85} +(-0.572307 - 4.64790i) q^{86} +(-5.52329 - 8.26619i) q^{87} +(2.56167 - 3.63259i) q^{88} +(6.80047 + 4.54393i) q^{89} +(-1.46977 + 0.485218i) q^{90} +(0.0814682 - 0.268565i) q^{91} +(-11.4988 + 8.52086i) q^{92} +(-8.28183 + 6.79672i) q^{93} +(3.22297 - 8.35019i) q^{94} +(-2.56827 - 2.56827i) q^{95} +(-0.183729 - 7.80664i) q^{96} +(3.85381 - 3.85381i) q^{97} +(3.89147 + 8.78383i) q^{98} +(-1.09114 - 1.32956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{11}{32}\right)$	$1$

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 $

$2$	0.0344201	+	1.41379i	0.0243387	+	0.999704i
$2$	0.0344201	+	1.41379i	0.0243387	+	0.999704i
$3$	−1.37377	−	0.135304i	−0.793145	−	0.0781179i	−0.306674	−	0.951815i	$-0.599216\pi$
$3$	−1.37377	−	0.135304i	−0.793145	−	0.0781179i	−0.486471	+	0.873697i	$0.661716\pi$
$4$	−1.99763	+	0.0973258i	−0.998815	+	0.0486629i
$5$	−0.471397	−	0.881921i	−0.210815	−	0.394407i
$5$	−0.471397	−	0.881921i	−0.210815	−	0.394407i
$6$	0.144007	−	1.94688i	0.0587907	−	0.794811i
$7$	0.0886862	+	0.445856i	0.0335202	+	0.168518i	0.993919	−	0.110110i	$-0.0351204\pi$
$7$	0.0886862	+	0.445856i	0.0335202	+	0.168518i	−0.960399	+	0.278628i	$0.910120\pi$
$8$	−0.206357	−	2.82089i	−0.0729583	−	0.997335i
$9$	−1.07343	−	0.213518i	−0.357809	−	0.0711727i
$10$	1.23063	−	0.696814i	0.389159	−	0.220352i
$11$	1.21482	+	0.996974i	0.366281	+	0.300599i	0.799472	−	0.600703i	$-0.205113\pi$
$11$	1.21482	+	0.996974i	0.366281	+	0.300599i	−0.433191	+	0.901302i	$0.642613\pi$
$12$	2.75745	+	0.136585i	0.796006	+	0.0394287i
$13$	−0.544469	−	0.291025i	−0.151009	−	0.0807158i	0.394162	−	0.919041i	$-0.371035\pi$
$13$	−0.544469	−	0.291025i	−0.151009	−	0.0807158i	−0.545170	+	0.838325i	$0.683535\pi$
$14$	−0.627296	+	0.140730i	−0.167652	+	0.0376118i
$15$	0.528262	+	1.27534i	0.136397	+	0.329290i
$16$	3.98106	−	0.388842i	0.995264	−	0.0972105i
$17$	−0.0852558	+	0.205826i	−0.0206776	+	0.0499201i	−0.933881	−	0.357584i	$-0.883601\pi$
$17$	−0.0852558	+	0.205826i	−0.0206776	+	0.0499201i	0.913204	+	0.407504i	$0.133601\pi$
$18$	0.264923	−	1.52496i	0.0624430	−	0.359435i
$19$	3.47569	−	1.05434i	0.797378	−	0.241882i	0.134798	−	0.990873i	$-0.456962\pi$
$19$	3.47569	−	1.05434i	0.797378	−	0.241882i	0.662580	+	0.748991i	$0.269462\pi$
$20$	1.02751	+	1.71587i	0.229758	+	0.383681i
$21$	−0.0615080	−	0.624501i	−0.0134221	−	0.136277i
$22$	−1.36770	+	1.75182i	−0.291595	+	0.373488i
$23$	5.94991	−	3.97560i	1.24064	−	0.828970i	0.250374	−	0.968149i	$-0.419446\pi$
$23$	5.94991	−	3.97560i	1.24064	−	0.828970i	0.990267	+	0.139179i	$0.0444464\pi$
$24$	−0.0981914	+	3.90317i	−0.0200432	+	0.796730i
$25$	−0.555570	+	0.831470i	−0.111114	+	0.166294i
$26$	0.392709	−	0.779785i	0.0770165	−	0.152928i
$27$	5.40867	+	1.64070i	1.04090	+	0.315753i
$28$	−0.220555	−	0.882023i	−0.0416811	−	0.166687i
$29$	4.56886	+	5.56718i	0.848417	+	1.03380i	0.998978	+	0.0451981i	$0.0143919\pi$
$29$	4.56886	+	5.56718i	0.848417	+	1.03380i	−0.150561	+	0.988601i	$0.548108\pi$
$30$	−1.78488	+	0.790751i	−0.325873	+	0.144371i
$31$	5.48803	−	5.48803i	0.985679	−	0.985679i	−0.0142197	−	0.999899i	$-0.504526\pi$
$31$	5.48803	−	5.48803i	0.985679	−	0.985679i	0.999899	+	0.0142197i	$0.00452643\pi$
$32$	0.686771	+	5.61501i	0.121405	+	0.992603i
$33$	−1.53398	−	1.53398i	−0.267031	−	0.267031i
$34$	−0.293930	−	0.113450i	−0.0504085	−	0.0194565i
$35$	0.351403	−	0.288389i	0.0593980	−	0.0487466i
$36$	2.16509	+	0.322058i	0.360849	+	0.0536763i
$37$	−2.72193	+	8.97302i	−0.447483	+	1.47515i	0.385942	+	0.922523i	$0.373876\pi$
$37$	−2.72193	+	8.97302i	−0.447483	+	1.47515i	−0.833425	+	0.552632i	$0.813624\pi$
$38$	1.61025	+	4.87762i	0.261217	+	0.791254i
$39$	0.708597	+	0.473469i	0.113466	+	0.0758158i
$40$	−2.39053	+	1.51175i	−0.377975	+	0.239028i
$41$	1.41663	+	2.12014i	0.221240	+	0.331110i	0.925441	−	0.378891i	$-0.123695\pi$
$41$	1.41663	+	2.12014i	0.221240	+	0.331110i	−0.704201	+	0.710001i	$0.748695\pi$
$42$	0.880799	−	0.108455i	0.135910	−	0.0167350i
$43$	−3.29543	+	0.324572i	−0.502549	+	0.0494968i	−0.346116	−	0.938192i	$-0.612500\pi$
$43$	−3.29543	+	0.324572i	−0.502549	+	0.0494968i	−0.156433	+	0.987689i	$0.550000\pi$
$44$	−2.52378	−	1.87335i	−0.380475	−	0.282418i
$45$	0.317704	+	1.04733i	0.0473605	+	0.156127i
$46$	5.82548	+	8.27511i	0.858920	+	1.22010i
$47$	−5.84726	−	2.42201i	−0.852911	−	0.353287i	−0.0869797	−	0.996210i	$-0.527722\pi$
$47$	−5.84726	−	2.42201i	−0.852911	−	0.353287i	−0.765931	+	0.642923i	$0.777722\pi$
$48$	−5.52165	−	0.00447526i	−0.796982	−	0.000645948i
$49$	6.27623	−	2.59970i	0.896605	−	0.371386i
$50$	−1.19465	−	0.756843i	−0.168949	−	0.107034i
$51$	0.144971	−	0.271221i	0.0203000	−	0.0379785i
$52$	1.11597	+	0.528369i	0.154758	+	0.0732716i
$53$	0.560619	−	0.683116i	0.0770069	−	0.0938332i	−0.733082	−	0.680140i	$-0.761919\pi$
$53$	0.560619	−	0.683116i	0.0770069	−	0.0938332i	0.810089	+	0.586307i	$0.199419\pi$
$54$	−2.13345	+	7.70322i	−0.290326	+	1.04828i
$55$	0.306592	−	1.54134i	0.0413409	−	0.207835i
$56$	1.23941	−	0.342179i	0.165623	−	0.0457257i
$57$	−4.91744	+	0.978140i	−0.651331	+	0.129558i
$58$	−7.71358	+	6.65106i	−1.01284	+	0.873327i
$59$	−0.316105	+	0.168961i	−0.0411533	+	0.0219969i	−0.491845	−	0.870683i	$-0.663677\pi$
$59$	−0.316105	+	0.168961i	−0.0411533	+	0.0219969i	0.450692	+	0.892680i	$0.351177\pi$
$60$	−1.17939	−	2.49624i	−0.152259	−	0.322263i
$61$	0.281848	−	2.86166i	0.0360870	−	0.366397i	−0.960134	−	0.279541i	$-0.909818\pi$
$61$	0.281848	−	2.86166i	0.0360870	−	0.366397i	0.996221	−	0.0868567i	$-0.0276822\pi$
$62$	7.94784	+	7.57005i	1.00938	+	0.961397i
$63$		−	0.497530i		−	0.0626829i
$64$	−7.91483	+	1.16422i	−0.989354	+	0.145528i
$65$			0.617367i			0.0765750i
$66$	2.11593	−	2.22153i	0.260453	−	0.273452i
$67$	0.392935	−	3.98954i	0.0480046	−	0.487399i	−0.940883	−	0.338733i	$-0.890002\pi$
$67$	0.392935	−	3.98954i	0.0480046	−	0.487399i	0.988887	−	0.148667i	$-0.0474982\pi$
$68$	0.150277	−	0.419461i	0.0182238	−	0.0508671i
$69$	−8.71170	+	4.65650i	−1.04877	+	0.560577i
$70$	0.419818	+	0.486885i	0.0501779	+	0.0581939i
$71$	12.3308	−	2.45275i	1.46340	−	0.291088i	0.601786	−	0.798658i	$-0.294456\pi$
$71$	12.3308	−	2.45275i	1.46340	−	0.291088i	0.861611	+	0.507570i	$0.169456\pi$
$72$	−0.380801	+	3.07208i	−0.0448778	+	0.362048i
$73$	1.09232	−	5.49146i	0.127846	−	0.642727i	−0.862719	−	0.505684i	$-0.831240\pi$
$73$	1.09232	−	5.49146i	0.127846	−	0.642727i	0.990565	−	0.137043i	$-0.0437598\pi$
$74$	−12.7797	−	3.53940i	−1.48561	−	0.411447i
$75$	0.875725	−	1.06707i	0.101120	−	0.123215i
$76$	−6.84053	+	2.44445i	−0.784662	+	0.280398i
$77$	−0.336769	+	0.630050i	−0.0383784	+	0.0718009i
$78$	−0.644999	+	1.01811i	−0.0730317	+	0.115278i
$79$	14.2413	−	5.89893i	1.60227	−	0.663681i	0.610534	−	0.791990i	$-0.290955\pi$
$79$	14.2413	−	5.89893i	1.60227	−	0.663681i	0.991734	+	0.128308i	$0.0409547\pi$
$80$	−2.21958	−	3.32768i	−0.248157	−	0.372046i
$81$	−4.17482	−	1.72927i	−0.463869	−	0.192141i
$82$	−2.94868	+	2.07580i	−0.325627	+	0.229234i
$83$	−2.16532	−	7.13812i	−0.237675	−	0.783510i	−0.991914	−	0.126910i	$-0.959494\pi$
$83$	−2.16532	−	7.13812i	−0.237675	−	0.783510i	0.754239	−	0.656600i	$-0.228006\pi$
$84$	0.183650	+	1.24154i	0.0200379	+	0.135463i
$85$	0.221711	−	0.0218367i	0.0240480	−	0.00236852i
$86$	−0.572307	−	4.64790i	−0.0617135	−	0.501196i
$87$	−5.52329	−	8.26619i	−0.592159	−	0.886229i
$88$	2.56167	−	3.63259i	0.273075	−	0.387236i
$89$	6.80047	+	4.54393i	0.720848	+	0.481655i	0.861084	−	0.508463i	$-0.169786\pi$
$89$	6.80047	+	4.54393i	0.720848	+	0.481655i	−0.140236	+	0.990118i	$0.544786\pi$
$90$	−1.46977	+	0.485218i	−0.154928	+	0.0511464i
$91$	0.0814682	−	0.268565i	0.00854018	−	0.0281532i
$92$	−11.4988	+	8.52086i	−1.19883	+	0.888361i
$93$	−8.28183	+	6.79672i	−0.858785	+	0.704787i
$94$	3.22297	−	8.35019i	0.332424	−	0.861256i
$95$	−2.56827	−	2.56827i	−0.263499	−	0.263499i
$96$	−0.183729	−	7.80664i	−0.0187517	−	0.796762i
$97$	3.85381	−	3.85381i	0.391295	−	0.391295i	−0.483854	−	0.875149i	$-0.660763\pi$
$97$	3.85381	−	3.85381i	0.391295	−	0.391295i	0.875149	+	0.483854i	$0.160763\pi$
$98$	3.89147	+	8.78383i	0.393098	+	0.887300i
$99$	−1.09114	−	1.32956i	−0.109664	−	0.133626i
$100$	1.02890	−	1.71504i	0.102890	−	0.171504i
$101$	−17.0386	−	5.16860i	−1.69540	−	0.514295i	−0.713016	−	0.701148i	$-0.752671\pi$
$101$	−17.0386	−	5.16860i	−1.69540	−	0.514295i	−0.982388	+	0.186853i	$0.940171\pi$
$102$	0.388441	+	0.195623i	0.0384614	+	0.0193696i
$103$	−3.62468	+	5.42471i	−0.357150	+	0.534513i	−0.965922	−	0.258832i	$-0.916662\pi$
$103$	−3.62468	+	5.42471i	−0.357150	+	0.534513i	0.608772	+	0.793345i	$0.291662\pi$
$104$	−0.708594	+	1.59594i	−0.0694834	+	0.156495i
$105$	−0.521766	+	0.348633i	−0.0509192	+	0.0340231i
$106$	0.985082	+	0.769087i	0.0956797	+	0.0747003i
$107$	0.899471	+	9.13249i	0.0869552	+	0.882871i	0.935401	+	0.353589i	$0.115039\pi$
$107$	0.899471	+	9.13249i	0.0869552	+	0.882871i	−0.848446	+	0.529282i	$0.822461\pi$
$108$	−10.9642	−	2.75111i	−1.05503	−	0.264726i
$109$	12.8423	−	3.89568i	1.23007	−	0.373138i	0.392647	−	0.919689i	$-0.371560\pi$
$109$	12.8423	−	3.89568i	1.23007	−	0.373138i	0.837426	+	0.546551i	$0.184060\pi$
$110$	2.18969	+	0.380405i	0.208779	+	0.0362702i
$111$	4.95339	−	11.9585i	0.470155	−	1.13505i
$112$	0.526432	+	1.74049i	0.0497431	+	0.164461i
$113$	0.930775	+	2.24709i	0.0875599	+	0.211388i	0.961594	−	0.274477i	$-0.0885046\pi$
$113$	0.930775	+	2.24709i	0.0875599	+	0.211388i	−0.874034	+	0.485865i	$0.838505\pi$
$114$	−1.55215	−	6.91859i	−0.145372	−	0.647985i
$115$	−6.31093	−	3.37326i	−0.588498	−	0.314559i
$116$	−9.66873	−	10.6765i	−0.897719	−	0.991288i
$117$	0.522309	+	0.428648i	0.0482875	+	0.0396285i
$118$	−0.249757	−	0.441091i	−0.0229920	−	0.0406058i
$119$	−0.0993295	−	0.0197579i	−0.00910552	−	0.00181120i
$120$	3.48857	−	1.75334i	0.318462	−	0.160058i
$121$	−1.66417	−	8.36636i	−0.151288	−	0.760578i
$122$	4.05549	+	0.299977i	0.367167	+	0.0271587i
$123$	−1.65926	−	3.10425i	−0.149610	−	0.279901i
$124$	−10.4289	+	11.4972i	−0.936545	+	1.03248i
$125$	0.995185	+	0.0980171i	0.0890120	+	0.00876692i
$126$	0.703405	−	0.0171250i	0.0626643	−	0.00152562i
$127$	5.60744			0.497580			0.248790	−	0.968557i	$-0.419967\pi$
$127$	5.60744			0.497580			0.248790	+	0.968557i	$0.419967\pi$
$128$	−1.91840	−	11.1499i	−0.169564	−	0.985519i
$129$	4.57108			0.402461
$130$	−0.872831	+	0.0212498i	−0.0765523	+	0.00186373i
$131$	5.67136	+	0.558580i	0.495509	+	0.0488034i	0.342686	−	0.939450i	$-0.388663\pi$
$131$	5.67136	+	0.558580i	0.495509	+	0.0488034i	0.152823	+	0.988254i	$0.451163\pi$
$132$	3.21362	+	2.91503i	0.279710	+	0.253721i
$133$	0.778328	+	1.45615i	0.0674896	+	0.126264i
$134$	5.65391	+	0.418209i	0.488423	+	0.0361278i
$135$	−1.10266	−	5.54344i	−0.0949018	−	0.477104i
$136$	0.598205	+	0.198024i	0.0512956	+	0.0169804i
$137$	−21.4398	−	4.26464i	−1.83172	−	0.364353i	−0.846062	−	0.533085i	$-0.821033\pi$
$137$	−21.4398	−	4.26464i	−1.83172	−	0.364353i	−0.985662	+	0.168732i	$0.946033\pi$
$138$	−6.88319	−	12.1563i	−0.585936	−	1.03481i
$139$	0.0348871	+	0.0286311i	0.00295909	+	0.00242846i	0.635872	−	0.771795i	$-0.280641\pi$
$139$	0.0348871	+	0.0286311i	0.00295909	+	0.00242846i	−0.632913	+	0.774223i	$0.718141\pi$
$140$	−0.673906	+	0.610295i	−0.0569554	+	0.0515794i
$141$	7.70506	+	4.11844i	0.648883	+	0.346835i
$142$	3.89211	+	17.3488i	0.326619	+	1.45588i
$143$	−0.371286	−	0.896363i	−0.0310485	−	0.0749577i
$144$	−4.35640	−	0.432633i	−0.363033	−	0.0360528i
$145$	2.75606	−	6.65373i	0.228879	−	0.552562i
$146$	7.80139	+	1.35530i	0.645648	+	0.112165i
$147$	−8.97383	+	2.72218i	−0.740149	+	0.224522i
$148$	4.56411	−	18.1897i	0.375168	−	1.49518i
$149$	0.983567	+	9.98632i	0.0805769	+	0.818111i	0.947518	+	0.319701i	$0.103583\pi$
$149$	0.983567	+	9.98632i	0.0805769	+	0.818111i	−0.866941	+	0.498410i	$0.833917\pi$
$150$	1.53877	+	1.20137i	0.125640	+	0.0980912i
$151$	1.79153	−	1.19706i	0.145793	−	0.0974155i	−0.480535	−	0.876976i	$-0.659557\pi$
$151$	1.79153	−	1.19706i	0.145793	−	0.0974155i	0.626327	+	0.779560i	$0.284557\pi$
$152$	−3.69141	−	9.58696i	−0.299413	−	0.777605i
$153$	0.135463	−	0.202735i	0.0109516	−	0.0163902i
$154$	−0.902353	−	0.454436i	−0.0727137	−	0.0366195i
$155$	−7.42705	−	2.25297i	−0.596555	−	0.180963i
$156$	−1.46160	−	0.876852i	−0.117021	−	0.0702044i
$157$	0.377876	+	0.460443i	0.0301578	+	0.0367474i	0.787871	−	0.615840i	$-0.211183\pi$
$157$	0.377876	+	0.460443i	0.0301578	+	0.0367474i	−0.757713	+	0.652588i	$0.773683\pi$
$158$	8.83006	+	19.9312i	0.702482	+	1.58564i
$159$	−0.862588	+	0.862588i	−0.0684077	+	0.0684077i
$160$	4.62826	−	3.25258i	0.365896	−	0.257139i
$161$	2.30022	+	2.30022i	0.181283	+	0.181283i
$162$	2.30113	−	5.96186i	0.180794	−	0.468408i
$163$	5.15161	−	4.22782i	0.403505	−	0.331148i	−0.410652	−	0.911792i	$-0.634699\pi$
$163$	5.15161	−	4.22782i	0.403505	−	0.331148i	0.814158	+	0.580644i	$0.197199\pi$
$164$	−3.03625	−	4.09738i	−0.237091	−	0.319951i
$165$	−0.629736	+	2.07596i	−0.0490249	+	0.161613i
$166$	10.0173	−	3.30702i	0.777493	−	0.256674i
$167$	17.4105	+	11.6333i	1.34727	+	0.900215i	0.999304	−	0.0372932i	$-0.0118736\pi$
$167$	17.4105	+	11.6333i	1.34727	+	0.900215i	0.347963	+	0.937508i	$0.386874\pi$
$168$	−1.74896	+	0.302378i	−0.134935	+	0.0233289i
$169$	−7.01066	−	10.4922i	−0.539282	−	0.807092i
$170$	0.0385039	+	0.312703i	0.00295311	+	0.0239832i
$171$	−3.95602	+	0.389634i	−0.302524	+	0.0297961i
$172$	6.55147	−	0.969106i	0.499545	−	0.0738936i
$173$	3.86510	+	12.7415i	0.293858	+	0.968722i	0.972235	+	0.234007i	$0.0751839\pi$
$173$	3.86510	+	12.7415i	0.293858	+	0.968722i	−0.678376	+	0.734715i	$0.737316\pi$
$174$	11.4966	−	8.09332i	0.871554	−	0.613553i
$175$	−0.419987	−	0.173964i	−0.0317480	−	0.0131505i
$176$	5.22391	+	3.49664i	0.393767	+	0.263569i
$177$	0.457115	−	0.189343i	0.0343589	−	0.0142319i
$178$	−6.19011	+	9.77087i	−0.463968	+	0.732358i
$179$	−3.81811	+	7.14318i	−0.285379	+	0.533907i	−0.983238	−	0.182329i	$-0.941636\pi$
$179$	−3.81811	+	7.14318i	−0.285379	+	0.533907i	0.697859	+	0.716236i	$0.254136\pi$
$180$	−0.736588	−	2.06126i	−0.0549020	−	0.153637i
$181$	−0.900556	+	1.09733i	−0.0669378	+	0.0815640i	−0.805403	−	0.592728i	$-0.798051\pi$
$181$	−0.900556	+	1.09733i	−0.0669378	+	0.0815640i	0.738465	+	0.674292i	$0.235551\pi$
$182$	0.382499	+	0.105935i	0.0283527	+	0.00785244i
$183$	−0.774388	+	3.89311i	−0.0572444	+	0.287787i
$184$	−12.4425	−	15.9636i	−0.917276	−	1.17685i
$185$	9.19661	−	1.82932i	0.676148	−	0.134494i
$186$	−9.89423	−	11.4749i	−0.725480	−	0.841377i
$187$	−0.308773	+	0.165043i	−0.0225797	+	0.0120691i
$188$	11.9164	+	4.26920i	0.869092	+	0.311363i
$189$	−0.251842	+	2.55699i	−0.0183188	+	0.185994i
$190$	3.54261	−	3.71941i	0.257008	−	0.269834i
$191$			5.60080i			0.405260i	0.979255	+	0.202630i	$0.0649489\pi$
$191$			5.60080i			0.405260i	−0.979255	+	0.202630i	$0.935051\pi$
$192$	11.0307	−	0.528460i	0.796069	−	0.0381383i
$193$		−	8.60101i		−	0.619114i	−0.950881	−	0.309557i	$-0.899819\pi$
$193$		−	8.60101i		−	0.619114i	0.950881	−	0.309557i	$-0.100181\pi$
$194$	5.58114	+	5.31584i	0.400702	+	0.381655i
$195$	0.0835324	−	0.848119i	0.00598188	−	0.0607350i
$196$	−12.2846	+	5.80408i	−0.877470	+	0.414577i
$197$	−5.61750	+	3.00262i	−0.400230	+	0.213928i	−0.659216	−	0.751954i	$-0.729112\pi$
$197$	−5.61750	+	3.00262i	−0.400230	+	0.213928i	0.258986	+	0.965881i	$0.416612\pi$
$198$	1.84217	−	1.58842i	0.130918	−	0.112884i
$199$	−4.68305	+	0.931517i	−0.331973	+	0.0660335i	−0.358263	−	0.933621i	$-0.616631\pi$
$199$	−4.68305	+	0.931517i	−0.331973	+	0.0660335i	0.0262898	+	0.999654i	$0.491631\pi$
$200$	2.46013	+	1.39562i	0.173957	+	0.0986854i
$201$	−1.07960	+	5.42753i	−0.0761493	+	0.382828i
$202$	6.72087	−	24.2670i	0.472879	−	1.70742i
$203$	−2.07696	+	2.53078i	−0.145774	+	0.177626i
$204$	−0.263201	+	0.555909i	−0.0184278	+	0.0389214i
$205$	1.20200	−	2.24878i	0.0839512	−	0.157062i
$206$	−7.79419	−	4.93783i	−0.543047	−	0.344035i
$207$	−7.23566	+	2.99711i	−0.502913	+	0.208313i
$208$	−2.28073	−	0.946874i	−0.158140	−	0.0656539i
$209$	5.27347	+	2.18434i	0.364773	+	0.151094i
$210$	−0.510855	−	0.725670i	−0.0352523	−	0.0500760i
$211$	−1.97790	−	6.52026i	−0.136164	−	0.448873i	0.862167	−	0.506625i	$-0.169107\pi$
$211$	−1.97790	−	6.52026i	−0.136164	−	0.448873i	−0.998331	+	0.0577513i	$0.981607\pi$
$212$	−1.05342	+	1.41918i	−0.0723495	+	0.0974694i
$213$	−17.2715	+	1.70110i	−1.18342	+	0.116557i
$214$	−12.8805	+	1.58601i	−0.880493	+	0.108417i
$215$	1.83970	+	2.75331i	0.125467	+	0.187774i
$216$	3.51212	−	15.5958i	0.238970	−	1.06116i
$217$	2.93358	+	1.96016i	0.199144	+	0.133064i
$218$	5.94972	+	18.0223i	0.402966	+	1.22063i
$219$	−2.24361	+	7.39619i	−0.151609	+	0.499788i
$220$	−0.462445	+	3.10887i	−0.0311780	+	0.209600i
$221$	0.106320	−	0.0872542i	0.00715183	−	0.00586935i
$222$	17.0774	+	6.59146i	1.14616	+	0.442390i
$223$	0.426784	+	0.426784i	0.0285796	+	0.0285796i	0.721252	−	0.692673i	$-0.243567\pi$
$223$	0.426784	+	0.426784i	0.0285796	+	0.0285796i	−0.692673	+	0.721252i	$0.743567\pi$
$224$	−2.44258	+	0.804175i	−0.163202	+	0.0537312i
$225$	0.773898	−	0.773898i	0.0515932	−	0.0515932i
$226$	−3.14488	+	1.39327i	−0.209195	+	0.0926789i
$227$	−11.7253	−	14.2874i	−0.778237	−	0.948285i	0.221401	−	0.975183i	$-0.428937\pi$
$227$	−11.7253	−	14.2874i	−0.778237	−	0.948285i	−0.999638	+	0.0268978i	$0.991437\pi$
$228$	9.72803	−	2.43256i	0.644255	−	0.161100i
$229$	4.93693	+	1.49760i	0.326241	+	0.0989642i	0.449157	−	0.893453i	$-0.351724\pi$
$229$	4.93693	+	1.49760i	0.326241	+	0.0989642i	−0.122916	+	0.992417i	$0.539224\pi$
$230$	4.55188	−	9.03847i	0.300142	−	0.595979i
$231$	0.547890	−	0.819976i	0.0360485	−	0.0539504i
$232$	14.7616	−	14.0371i	0.969145	−	0.921580i
$233$	−5.72281	+	3.82386i	−0.374914	+	0.250509i	−0.728724	−	0.684808i	$-0.759886\pi$
$233$	−5.72281	+	3.82386i	−0.374914	+	0.250509i	0.353810	+	0.935317i	$0.384886\pi$
$234$	−0.588043	+	0.753192i	−0.0384415	+	0.0492377i
$235$	0.620353	+	6.29855i	0.0404674	+	0.410872i
$236$	0.615016	−	0.368288i	0.0400341	−	0.0239735i
$237$	−20.3623	+	6.17685i	−1.32268	+	0.401230i
$238$	0.0245146	−	0.141112i	0.00158905	−	0.00914691i
$239$	1.93619	−	4.67438i	0.125242	−	0.302360i	−0.848805	−	0.528705i	$-0.822678\pi$
$239$	1.93619	−	4.67438i	0.125242	−	0.302360i	0.974047	+	0.226345i	$0.0726777\pi$
$240$	2.59894	+	4.87177i	0.167761	+	0.314472i
$241$	−5.78679	−	13.9706i	−0.372760	−	0.899923i	−0.993280	−	0.115732i	$-0.963079\pi$
$241$	−5.78679	−	13.9706i	−0.372760	−	0.899923i	0.620520	−	0.784190i	$-0.286921\pi$
$242$	11.7710	−	2.64077i	0.756671	−	0.169755i
$243$	−9.45273	−	5.05259i	−0.606393	−	0.324124i
$244$	−0.284516	+	5.74396i	−0.0182143	+	0.367719i
$245$	−5.25133	−	4.30965i	−0.335495	−	0.275334i
$246$	4.33166	−	2.45270i	0.276177	−	0.156378i
$247$	−2.19924	−	0.437457i	−0.139935	−	0.0278347i
$248$	−16.6136	−	14.3486i	−1.05497	−	0.911139i
$249$	2.00883	+	10.0991i	0.127305	+	0.640004i
$250$	−0.104322	+	1.41036i	−0.00659789	+	0.0891990i
$251$	5.53091	+	10.3476i	0.349108	+	0.653134i	0.993785	−	0.111321i	$-0.0355081\pi$
$251$	5.53091	+	10.3476i	0.349108	+	0.653134i	−0.644677	+	0.764455i	$0.723008\pi$
$252$	0.0484225	+	0.993881i	0.00305033	+	0.0626086i
$253$	11.1916	+	1.10228i	0.703610	+	0.0692996i
$254$	0.193009	+	7.92777i	0.0121104	+	0.497433i
$255$	−0.307534			−0.0192585
$256$	15.6976	−	3.09600i	0.981100	−	0.193500i
$257$	−25.3252			−1.57974			−0.789870	−	0.613274i	$-0.789852\pi$
$257$	−25.3252			−1.57974			−0.789870	+	0.613274i	$0.789852\pi$
$258$	0.157337	+	6.46256i	0.00979536	+	0.402341i
$259$	−4.24207	−	0.417807i	−0.263589	−	0.0259613i
$260$	−0.0600858	−	1.23327i	−0.00372636	−	0.0764843i
$261$	−3.71565	−	6.95150i	−0.229993	−	0.430287i
$262$	−0.594509	+	8.03737i	−0.0367289	+	0.496550i
$263$	5.26302	+	26.4590i	0.324532	+	1.63153i	0.706753	+	0.707461i	$0.250159\pi$
$263$	5.26302	+	26.4590i	0.324532	+	1.63153i	−0.382221	+	0.924071i	$0.624841\pi$
$264$	−4.01064	+	4.64373i	−0.246838	+	0.285802i
$265$	−0.866728	−	0.172403i	−0.0532427	−	0.0105906i
$266$	−2.03191	+	1.15052i	−0.124584	+	0.0705427i
$267$	−8.72745	−	7.16243i	−0.534111	−	0.438334i
$268$	−0.396654	+	8.00786i	−0.0242295	+	0.489158i
$269$	15.6686	+	8.37503i	0.955330	+	0.510634i	0.873932	−	0.486047i	$-0.161562\pi$
$269$	15.6686	+	8.37503i	0.955330	+	0.510634i	0.0813973	+	0.996682i	$0.474062\pi$
$270$	7.79934	−	1.74974i	0.474653	−	0.106486i
$271$	6.28153	+	15.1650i	0.381576	+	0.921206i	0.991661	+	0.128870i	$0.0411350\pi$
$271$	6.28153	+	15.1650i	0.381576	+	0.921206i	−0.610086	+	0.792335i	$0.708865\pi$
$272$	−0.259374	+	0.852554i	−0.0157269	+	0.0516937i
$273$	−0.148256	+	0.357922i	−0.00897287	+	0.0216624i
$274$	5.29136	−	30.4582i	0.319663	−	1.84005i
$275$	−1.50387	+	0.456194i	−0.0906867	+	0.0275095i
$276$	16.9496	−	10.1498i	1.02024	−	0.610949i
$277$	−1.18507	−	12.0322i	−0.0712037	−	0.722943i	−0.962819	−	0.270149i	$-0.912927\pi$
$277$	−1.18507	−	12.0322i	−0.0712037	−	0.722943i	0.891615	−	0.452795i	$-0.149573\pi$
$278$	−0.0392777	+	0.0503087i	−0.00235572	+	0.00301731i
$279$	−7.06280	+	4.71921i	−0.422838	+	0.282532i
$280$	−0.886028	−	0.931758i	−0.0529503	−	0.0556832i
$281$	−12.6498	+	18.9318i	−0.754625	+	1.12938i	0.232990	+	0.972479i	$0.425149\pi$
$281$	−12.6498	+	18.9318i	−0.754625	+	1.12938i	−0.987615	+	0.156897i	$0.949851\pi$
$282$	−5.55742	+	11.0351i	−0.330940	+	0.657133i
$283$	12.6900	+	3.84947i	0.754342	+	0.228827i	0.643957	−	0.765062i	$-0.277292\pi$
$283$	12.6900	+	3.84947i	0.754342	+	0.228827i	0.110385	+	0.993889i	$0.464792\pi$
$284$	−24.3937	+	6.09979i	−1.44750	+	0.361956i
$285$	3.18071	+	3.87570i	0.188409	+	0.229577i
$286$	1.25449	−	0.555775i	0.0741798	−	0.0328637i
$287$	−0.819639	+	0.819639i	−0.0483818	+	0.0483818i
$288$	0.461707	−	6.17395i	0.0272063	−	0.363803i
$289$	11.9857	+	11.9857i	0.705042	+	0.705042i
$290$	9.50187	+	3.66749i	0.557969	+	0.215362i
$291$	−5.81567	+	4.77279i	−0.340920	+	0.279786i
$292$	−1.64759	+	11.0762i	−0.0964178	+	0.648186i
$293$	−5.69669	+	18.7795i	−0.332804	+	1.09711i	0.617704	+	0.786411i	$0.288063\pi$
$293$	−5.69669	+	18.7795i	−0.332804	+	1.09711i	−0.950509	+	0.310699i	$0.899437\pi$
$294$	−4.15749	−	12.5935i	−0.242470	−	0.734466i
$295$	0.298021	+	0.199132i	0.0173515	+	0.0115939i
$296$	25.8736	+	5.82663i	1.50387	+	0.338666i
$297$	4.93480	+	7.38545i	0.286346	+	0.428547i
$298$	−14.0848	+	1.73429i	−0.815908	+	0.100465i
$299$	−4.39654	+	0.433022i	−0.254259	+	0.0250423i
$300$	−1.64552	+	2.21685i	−0.0950042	+	0.127990i
$301$	−0.436972	−	1.44050i	−0.0251866	−	0.0830292i
$302$	1.75406	+	2.49165i	0.100935	+	0.143378i
$303$	22.7077	+	9.40585i	1.30452	+	0.540352i
$304$	13.4269	−	5.54887i	0.770088	−	0.318250i
$305$	−2.65662	+	1.10041i	−0.152117	+	0.0630091i
$306$	0.291289	+	0.184539i	0.0166519	+	0.0105494i
$307$	3.12592	−	5.84819i	0.178406	−	0.333774i	−0.776784	−	0.629767i	$-0.783150\pi$
$307$	3.12592	−	5.84819i	0.178406	−	0.333774i	0.955190	+	0.295993i	$0.0956504\pi$
$308$	0.611419	−	1.29138i	0.0348389	−	0.0735834i
$309$	5.71345	−	6.96185i	0.325027	−	0.396046i
$310$	2.92960	−	10.5779i	0.166390	−	0.600783i
$311$	6.02461	−	30.2878i	0.341624	−	1.71746i	−0.303025	−	0.952983i	$-0.597997\pi$
$311$	6.02461	−	30.2878i	0.341624	−	1.71746i	0.644649	−	0.764479i	$-0.277003\pi$
$312$	1.18938	−	2.09658i	0.0673354	−	0.118695i
$313$	7.39353	−	1.47066i	0.417907	−	0.0831269i	0.0183421	−	0.999832i	$-0.494161\pi$
$313$	7.39353	−	1.47066i	0.417907	−	0.0831269i	0.399565	+	0.916705i	$0.369161\pi$
$314$	−0.637965	+	0.550087i	−0.0360025	+	0.0310432i
$315$	−0.438782	+	0.234534i	−0.0247226	+	0.0132145i
$316$	−27.8747	+	13.1699i	−1.56807	+	0.740866i
$317$	−0.853209	+	8.66277i	−0.0479210	+	0.486550i	0.941032	+	0.338318i	$0.109858\pi$
$317$	−0.853209	+	8.66277i	−0.0479210	+	0.486550i	−0.988953	+	0.148231i	$0.952642\pi$
$318$	−1.24921	−	1.18983i	−0.0700524	−	0.0667225i
$319$			11.3181i			0.633694i
$320$	4.75778	+	6.43145i	0.265968	+	0.359529i
$321$		−	12.6676i		−	0.707037i
$322$	−3.17286	+	3.33121i	−0.176817	+	0.185641i
$323$	−0.0793126	+	0.805274i	−0.00441307	+	0.0448067i
$324$	8.50805	+	3.04812i	0.472669	+	0.169340i
$325$	0.544469	−	0.291025i	0.0302017	−	0.0161432i
$326$	6.15458	+	7.13780i	0.340871	+	0.395326i
$327$	−18.1695	+	3.61413i	−1.00477	+	0.199862i
$328$	5.68834	−	4.43366i	0.314086	−	0.244808i
$329$	0.561297	−	2.82183i	0.0309453	−	0.155573i
$330$	−2.95666	−	0.818863i	−0.162759	−	0.0450769i
$331$	−12.4797	+	15.2065i	−0.685945	+	0.835827i	−0.993275	−	0.115776i	$-0.963064\pi$
$331$	−12.4797	+	15.2065i	−0.685945	+	0.835827i	0.307330	+	0.951603i	$0.400564\pi$
$332$	5.02024	+	14.0486i	0.275522	+	0.771016i
$333$	4.83770	−	9.05070i	0.265104	−	0.495975i
$334$	−15.8479	+	25.0153i	−0.867158	+	1.36878i
$335$	−3.70368	+	1.53412i	−0.202354	+	0.0838177i
$336$	−0.487699	−	2.46226i	−0.0266062	−	0.134327i
$337$	−24.4497	−	10.1274i	−1.33186	−	0.551674i	−0.400674	−	0.916221i	$-0.631224\pi$
$337$	−24.4497	−	10.1274i	−1.33186	−	0.551674i	−0.931185	+	0.364547i	$0.881224\pi$
$338$	14.5925	−	10.2728i	0.793728	−	0.558765i
$339$	−0.974627	−	3.21291i	−0.0529345	−	0.174502i
$340$	−0.440772	+	0.0651998i	−0.0239042	+	0.00353596i
$341$	12.1384	−	1.19552i	0.657329	−	0.0647413i
$342$	−0.687029	−	5.57959i	−0.0371503	−	0.301710i
$343$	3.48360	+	5.21358i	0.188097	+	0.281507i
$344$	1.59562	+	9.22908i	0.0860300	+	0.497599i
$345$	8.21333	+	5.48797i	0.442191	+	0.295463i
$346$	−17.8809	+	5.90303i	−0.961283	+	0.317349i
$347$	−7.24469	+	23.8825i	−0.388915	+	1.28208i	0.516036	+	0.856567i	$0.327407\pi$
$347$	−7.24469	+	23.8825i	−0.388915	+	1.28208i	−0.904951	+	0.425515i	$0.860093\pi$
$348$	11.8380	+	15.9752i	0.634584	+	0.856362i
$349$	−4.36881	+	3.58539i	−0.233857	+	0.191922i	−0.744022	−	0.668155i	$-0.767084\pi$
$349$	−4.36881	+	3.58539i	−0.233857	+	0.191922i	0.510165	+	0.860077i	$0.329584\pi$
$350$	0.231494	−	0.599763i	0.0123739	−	0.0320587i
$351$	−2.46737	−	2.46737i	−0.131698	−	0.131698i
$352$	−4.76372	+	7.50590i	−0.253907	+	0.400066i
$353$	17.8983	−	17.8983i	0.952632	−	0.952632i	−0.0462962	−	0.998928i	$-0.514742\pi$
$353$	17.8983	−	17.8983i	0.952632	−	0.952632i	0.998928	+	0.0462962i	$0.0147418\pi$
$354$	0.283427	+	0.639750i	0.0150640	+	0.0340023i
$355$	−7.97583	−	9.71857i	−0.423313	−	0.515808i
$356$	−14.0271	−	8.41523i	−0.743433	−	0.446006i
$357$	0.133782	+	0.0405824i	0.00708051	+	0.00214785i
$358$	−10.2304	−	5.15216i	−0.540694	−	0.272300i
$359$	−17.1067	+	25.6019i	−0.902855	+	1.35122i	0.0332314	+	0.999448i	$0.489420\pi$
$359$	−17.1067	+	25.6019i	−0.902855	+	1.35122i	−0.936086	+	0.351770i	$0.885580\pi$
$360$	2.88884	−	1.11233i	0.152255	−	0.0586251i
$361$	−4.82914	+	3.22673i	−0.254165	+	0.169828i
$362$	−1.58240	−	1.23543i	−0.0831690	−	0.0649328i
$363$	1.15418	+	11.7186i	0.0605788	+	0.615067i
$364$	−0.136605	+	0.544422i	−0.00716005	+	0.0285355i
$365$	−5.35795	+	1.62532i	−0.280448	+	0.0850729i
$366$	−5.53072	−	0.960825i	−0.289095	−	0.0502231i
$367$	6.06443	−	14.6408i	0.316561	−	0.764245i	−0.682871	−	0.730539i	$-0.739269\pi$
$367$	6.06443	−	14.6408i	0.316561	−	0.764245i	0.999432	−	0.0337061i	$-0.0107310\pi$
$368$	22.1410	−	18.1407i	1.15418	−	0.945647i
$369$	−1.06796	−	2.57829i	−0.0555959	−	0.134220i
$370$	2.90283	+	12.9391i	0.150911	+	0.672674i
$371$	0.354290	+	0.189372i	0.0183938	+	0.00983171i
$372$	15.8825	−	14.3834i	0.823471	−	0.745743i
$373$	3.40728	+	2.79628i	0.176422	+	0.144786i	0.718460	−	0.695568i	$-0.244847\pi$
$373$	3.40728	+	2.79628i	0.176422	+	0.144786i	−0.542038	+	0.840354i	$0.682347\pi$
$374$	−0.243964	−	0.430861i	−0.0126151	−	0.0222793i
$375$	−1.35389	−	0.269305i	−0.0699146	−	0.0139069i
$376$	−5.62561	+	16.9943i	−0.290119	+	0.876413i
$377$	−0.867419	−	4.36081i	−0.0446744	−	0.224593i
$378$	−3.62373	−	0.268041i	−0.186385	−	0.0137865i
$379$	−10.4309	−	19.5149i	−0.535801	−	1.00241i	−0.993557	−	0.113335i	$-0.963847\pi$
$379$	−10.4309	−	19.5149i	−0.535801	−	1.00241i	0.457756	−	0.889078i	$-0.348653\pi$
$380$	5.38042	+	4.88050i	0.276010	+	0.250364i
$381$	−7.70332	−	0.758711i	−0.394653	−	0.0388699i
$382$	−7.91839	+	0.192780i	−0.405140	+	0.00986349i
$383$	37.5178			1.91707			0.958535	−	0.284974i	$-0.0919848\pi$
$383$	37.5178			1.91707			0.958535	+	0.284974i	$0.0919848\pi$
$384$	1.12681	+	15.5769i	0.0575023	+	0.794905i
$385$	0.714406			0.0364095
$386$	12.1601	−	0.296047i	0.618931	−	0.0150684i
$387$	3.60671	+	0.355230i	0.183339	+	0.0180574i
$388$	−7.32341	+	8.07355i	−0.371790	+	0.409873i
$389$	15.6248	+	29.2319i	0.792208	+	1.48212i	0.874243	+	0.485488i	$0.161358\pi$
$389$	15.6248	+	29.2319i	0.792208	+	1.48212i	−0.0820353	+	0.996629i	$0.526142\pi$
$390$	1.20194	+	0.0889054i	0.0608626	+	0.00450190i
$391$	0.311017	+	1.56359i	0.0157288	+	0.0790740i
$392$	−8.62862	−	17.1681i	−0.435811	−	0.867120i
$393$	−7.71555	−	1.53472i	−0.389198	−	0.0774163i
$394$	−4.43844	−	7.83864i	−0.223605	−	0.394905i
$395$	−11.9157	−	9.77895i	−0.599543	−	0.492032i
$396$	2.30911	+	2.54978i	0.116037	+	0.128131i
$397$	24.2138	+	12.9425i	1.21526	+	0.649568i	0.949286	−	0.314414i	$-0.101808\pi$
$397$	24.2138	+	12.9425i	1.21526	+	0.649568i	0.265970	+	0.963981i	$0.414308\pi$
$398$	−1.47816	−	6.58881i	−0.0740937	−	0.330267i
$399$	−0.872218	−	2.10572i	−0.0436655	−	0.105418i
$400$	−1.88845	+	3.52616i	−0.0944223	+	0.176308i
$401$	−6.28487	+	15.1730i	−0.313852	+	0.757705i	0.685704	+	0.727881i	$0.259495\pi$
$401$	−6.28487	+	15.1730i	−0.313852	+	0.757705i	−0.999555	+	0.0298238i	$0.990505\pi$
$402$	−7.71057	−	1.33952i	−0.384568	−	0.0668092i
$403$	−4.58522	+	1.39091i	−0.228406	+	0.0692862i
$404$	34.5399	+	8.66666i	1.71842	+	0.431183i
$405$	0.442919	+	4.49703i	0.0220088	+	0.223459i
$406$	−3.64950	−	2.84929i	−0.181122	−	0.141408i
$407$	−12.2525	+	8.18687i	−0.607334	+	0.405808i
$408$	−0.795000	−	0.352978i	−0.0393584	−	0.0174750i
$409$	7.40586	−	11.0837i	0.366196	−	0.548051i	−0.601919	−	0.798557i	$-0.705597\pi$
$409$	7.40586	−	11.0837i	0.366196	−	0.548051i	0.968115	+	0.250506i	$0.0805970\pi$
$410$	3.22069	+	1.62198i	0.159058	+	0.0801037i
$411$	28.8762	+	8.75951i	1.42436	+	0.432075i
$412$	6.71280	−	11.1893i	0.330716	−	0.551259i
$413$	−0.103367	−	0.125952i	−0.00508633	−	0.00619772i
$414$	−4.48635	−	10.1266i	−0.220492	−	0.497694i
$415$	−5.27453	+	5.27453i	−0.258917	+	0.258917i
$416$	1.26018	−	3.25707i	0.0617855	−	0.159691i
$417$	−0.0440528	−	0.0440528i	−0.00215728	−	0.00215728i
$418$	−2.90670	+	7.53079i	−0.142171	+	0.368343i
$419$	12.0478	−	9.88733i	0.588571	−	0.483028i	−0.292337	−	0.956315i	$-0.594433\pi$
$419$	12.0478	−	9.88733i	0.588571	−	0.483028i	0.880908	+	0.473288i	$0.156933\pi$
$420$	1.00837	−	0.747221i	0.0492032	−	0.0364607i
$421$	−6.35610	+	20.9533i	−0.309778	+	1.02120i	0.654446	+	0.756109i	$0.272902\pi$
$421$	−6.35610	+	20.9533i	−0.309778	+	1.02120i	−0.964223	+	0.265091i	$0.914598\pi$
$422$	9.15023	−	3.02077i	0.445426	−	0.147049i
$423$	5.75947	+	3.84835i	0.280035	+	0.187113i
$424$	−2.04268	−	1.44048i	−0.0992014	−	0.0699558i
$425$	−0.123772	−	0.185238i	−0.00600383	−	0.00898537i
$426$	−2.99949	−	24.3598i	−0.145326	−	1.18024i
$427$	1.30088	−	0.128126i	0.0629540	−	0.00620043i
$428$	−2.68564	−	18.1558i	−0.129815	−	0.877593i
$429$	0.388778	+	1.28163i	0.0187704	+	0.0618777i
$430$	−3.82929	+	2.69573i	−0.184665	+	0.130000i
$431$	−5.62271	−	2.32900i	−0.270836	−	0.112184i	0.243132	−	0.969993i	$-0.421825\pi$
$431$	−5.62271	−	2.32900i	−0.270836	−	0.112184i	−0.513968	+	0.857809i	$0.671825\pi$
$432$	22.1702	+	4.42861i	1.06666	+	0.213072i
$433$	13.4931	−	5.58903i	0.648438	−	0.268592i	−0.0341262	−	0.999418i	$-0.510865\pi$
$433$	13.4931	−	5.58903i	0.648438	−	0.268592i	0.682564	+	0.730826i	$0.260865\pi$
$434$	−2.67028	+	4.21495i	−0.128178	+	0.202324i
$435$	−4.68647	+	8.76776i	−0.224699	+	0.420382i
$436$	−25.2751	+	9.03202i	−1.21046	+	0.432555i
$437$	16.4884	−	20.0912i	0.788747	−	0.961091i
$438$	−10.5339	−	2.91742i	−0.503330	−	0.139400i
$439$	1.09311	−	5.49543i	0.0521712	−	0.262282i	−0.945893	−	0.324480i	$-0.894811\pi$
$439$	1.09311	−	5.49543i	0.0521712	−	0.262282i	0.998064	+	0.0621973i	$0.0198108\pi$
$440$	−4.41122	−	0.546795i	−0.210297	−	0.0260674i
$441$	−7.29217	+	1.45050i	−0.347246	+	0.0690715i
$442$	0.127019	+	0.147311i	0.00604168	+	0.00700686i
$443$	23.3098	−	12.4594i	1.10748	−	0.591962i	0.186849	−	0.982389i	$-0.440172\pi$
$443$	23.3098	−	12.4594i	1.10748	−	0.591962i	0.920634	+	0.390426i	$0.127672\pi$
$444$	−8.73117	+	24.3708i	−0.414363	+	1.15659i
$445$	0.801668	−	8.13947i	0.0380027	−	0.385848i
$446$	−0.588695	+	0.618075i	−0.0278755	+	0.0292667i
$447$		−	13.8520i		−	0.655175i
$448$	−1.22101	−	3.42562i	−0.0576874	−	0.161845i
$449$		−	7.60710i		−	0.359001i	−0.983758	−	0.179501i	$-0.942552\pi$
$449$		−	7.60710i		−	0.359001i	0.983758	−	0.179501i	$-0.0574482\pi$
$450$	1.12077	+	1.06750i	0.0528336	+	0.0503222i
$451$	−0.392776	+	3.98792i	−0.0184951	+	0.187784i
$452$	−2.07804	−	4.39827i	−0.0977430	−	0.206877i
$453$	−2.62311	+	1.40208i	−0.123245	+	0.0658756i
$454$	19.7958	−	17.0690i	0.929063	−	0.801087i
$455$	−0.275257	+	0.0547519i	−0.0129042	+	0.00256681i
$456$	3.77397	+	13.6697i	0.176733	+	0.640143i
$457$	4.09378	−	20.5808i	0.191499	−	0.962729i	−0.758784	−	0.651342i	$-0.774206\pi$
$457$	4.09378	−	20.5808i	0.191499	−	0.962729i	0.950283	−	0.311387i	$-0.100794\pi$
$458$	−1.94737	+	7.03135i	−0.0909946	+	0.328553i
$459$	−0.798819	+	0.973364i	−0.0372857	+	0.0454327i
$460$	12.9352	+	6.12432i	0.603108	+	0.285548i
$461$	16.1262	−	30.1701i	0.751074	−	1.40516i	−0.157536	−	0.987513i	$-0.550355\pi$
$461$	16.1262	−	30.1701i	0.751074	−	1.40516i	0.908610	−	0.417647i	$-0.137145\pi$
$462$	1.17814	+	0.746381i	0.0548118	+	0.0347248i
$463$	28.1894	−	11.6764i	1.31007	−	0.542650i	0.385168	−	0.922847i	$-0.374144\pi$
$463$	28.1894	−	11.6764i	1.31007	−	0.542650i	0.924906	+	0.380196i	$0.124144\pi$
$464$	20.3537	+	20.3867i	0.944895	+	0.946428i
$465$	9.89820	+	4.09997i	0.459018	+	0.190131i
$466$	−5.60313	−	7.95926i	−0.259560	−	0.368706i
$467$	−5.37882	−	17.7316i	−0.248902	−	0.820520i	−0.988986	−	0.148006i	$-0.952714\pi$
$467$	−5.37882	−	17.7316i	−0.248902	−	0.820520i	0.740084	−	0.672514i	$-0.234786\pi$
$468$	−1.08510	−	0.805447i	−0.0501588	−	0.0372318i
$469$	1.81360	−	0.178624i	0.0837445	−	0.00824811i
$470$	−8.88351	+	1.09385i	−0.409766	+	0.0504555i
$471$	−0.456813	−	0.683670i	−0.0210489	−	0.0315018i
$472$	0.541852	+	0.856830i	0.0249408	+	0.0394388i
$473$	−4.32694	−	2.89117i	−0.198953	−	0.132936i
$474$	−9.43367	−	28.5756i	−0.433303	−	1.31252i
$475$	−1.05434	+	3.47569i	−0.0483764	+	0.159476i
$476$	0.200347	+	0.0298016i	0.00918287	+	0.00136595i
$477$	−0.747641	+	0.613573i	−0.0342321	+	0.0280936i
$478$	6.67525	+	2.57648i	0.305319	+	0.117846i
$479$	−10.3318	−	10.3318i	−0.472073	−	0.472073i	0.430512	−	0.902585i	$-0.358333\pi$
$479$	−10.3318	−	10.3318i	−0.472073	−	0.472073i	−0.902585	+	0.430512i	$0.858333\pi$
$480$	−6.79823	+	3.84206i	−0.310295	+	0.175365i
$481$	4.09338	−	4.09338i	0.186642	−	0.186642i
$482$	19.5523	−	8.66221i	0.890584	−	0.394553i
$483$	−2.84873	−	3.47119i	−0.129622	−	0.157945i
$484$	4.13866	+	16.5509i	0.188121	+	0.752315i
$485$	−5.21542	−	1.58208i	−0.236820	−	0.0718386i
$486$	6.81796	−	13.5381i	0.309269	−	0.614102i
$487$	−16.2521	+	24.3230i	−0.736454	+	1.10218i	0.254382	+	0.967104i	$0.418128\pi$
$487$	−16.2521	+	24.3230i	−0.736454	+	1.10218i	−0.990835	+	0.135077i	$0.956872\pi$
$488$	−8.13058	−	0.204540i	−0.368054	−	0.00925908i
$489$	−7.64915	+	5.11100i	−0.345907	+	0.231127i
$490$	5.91221	−	7.57264i	0.267087	−	0.342097i
$491$	0.221753	+	2.25149i	0.0100076	+	0.101608i	0.998891	−	0.0470851i	$-0.0149932\pi$
$491$	0.221753	+	2.25149i	0.0100076	+	0.101608i	−0.988883	+	0.148694i	$0.952493\pi$
$492$	3.61670	+	6.03966i	0.163054	+	0.272289i
$493$	−1.53539	+	0.465755i	−0.0691505	+	0.0209766i
$494$	0.542776	−	3.12434i	0.0244207	−	0.140571i
$495$	−0.658209	+	1.58906i	−0.0295843	+	0.0714228i
$496$	19.7142	−	23.9821i	0.885192	−	1.07683i
$497$	2.18714	+	5.28023i	0.0981068	+	0.236851i
$498$	−14.2089	+	3.18769i	−0.636716	+	0.142844i
$499$	−24.5524	−	13.1235i	−1.09912	−	0.587489i	−0.180872	−	0.983507i	$-0.557892\pi$
$499$	−24.5524	−	13.1235i	−1.09912	−	0.587489i	−0.918243	+	0.396017i	$0.870392\pi$
$500$	−1.99755	−	0.0989449i	−0.0893332	−	0.00442495i
$501$	−22.3440	−	18.3372i	−0.998255	−	0.819247i
$502$	−14.4390	+	8.17573i	−0.644444	+	0.364901i
$503$	−17.9723	−	3.57492i	−0.801347	−	0.159398i	−0.222605	−	0.974909i	$-0.571456\pi$
$503$	−17.9723	−	3.57492i	−0.801347	−	0.159398i	−0.578742	+	0.815511i	$0.696456\pi$
$504$	−1.40348	+	0.102669i	−0.0625158	+	0.00457324i
$505$	3.47364	+	17.4632i	0.154575	+	0.777101i
$506$	−1.17318	+	15.8606i	−0.0521541	+	0.705089i
$507$	8.21138	+	15.3624i	0.364680	+	0.682268i
$508$	−11.2016	+	0.545749i	−0.496991	+	0.0242137i
$509$	21.0732	+	2.07553i	0.934053	+	0.0919962i	0.553580	−	0.832796i	$-0.313261\pi$
$509$	21.0732	+	2.07553i	0.934053	+	0.0919962i	0.380473	+	0.924792i	$0.375761\pi$
$510$	−0.0105854	−	0.434790i	−0.000468727	−	0.0192528i
$511$	2.54527			0.112596
$512$	4.91743	+	22.0866i	0.217322	+	0.976100i
$513$	20.5287			0.906365
$514$	−0.871694	−	35.8046i	−0.0384488	−	1.57927i
$515$	6.49283	+	0.639488i	0.286108	+	0.0281792i
$516$	−9.13132	+	0.444884i	−0.401984	+	0.0195849i
$517$	−4.68866	−	8.77187i	−0.206207	−	0.385786i
$518$	0.444681	−	6.01179i	0.0195382	−	0.264143i
$519$	−3.58577	−	18.0269i	−0.157398	−	0.791292i
$520$	1.74152	−	0.127398i	0.0763709	−	0.00558678i
$521$	−27.0863	−	5.38779i	−1.18667	−	0.236043i	−0.437993	−	0.898978i	$-0.644311\pi$
$521$	−27.0863	−	5.38779i	−1.18667	−	0.236043i	−0.748677	+	0.662935i	$0.769311\pi$
$522$	9.70010	−	5.49244i	0.424562	−	0.240398i
$523$	−20.8403	−	17.1032i	−0.911284	−	0.747871i	0.0568297	−	0.998384i	$-0.481901\pi$
$523$	−20.8403	−	17.1032i	−0.911284	−	0.747871i	−0.968113	+	0.250513i	$0.919401\pi$
$524$	−11.3836	−	0.563867i	−0.497297	−	0.0246327i
$525$	0.553426	+	0.295812i	0.0241535	+	0.0129103i
$526$	−37.2264	+	8.35155i	−1.62315	+	0.364145i
$527$	0.661691	+	1.59746i	0.0288237	+	0.0695866i
$528$	−6.70333	−	5.51038i	−0.291725	−	0.239808i
$529$	10.7943	−	26.0597i	0.469316	−	1.13303i
$530$	0.213910	−	1.23131i	0.00929164	−	0.0534847i
$531$	0.375392	−	0.113874i	0.0162906	−	0.00494170i
$532$	−1.69653	−	2.83310i	−0.0735540	−	0.122830i
$533$	−0.154299	−	1.56662i	−0.00668343	−	0.0678580i
$534$	9.82581	−	12.5853i	0.425204	−	0.544621i
$535$	7.63013	−	5.09829i	0.329879	−	0.220418i
$536$	−11.3351	−	0.285156i	−0.489603	−	0.0123169i
$537$	6.21170	−	9.29646i	0.268055	−	0.401172i
$538$	−11.3013	+	22.4404i	−0.487232	+	0.967475i
$539$	10.2163	+	3.09908i	0.440047	+	0.133487i
$540$	2.74223	+	10.9664i	0.118007	+	0.471920i
$541$	14.8700	+	18.1192i	0.639311	+	0.779003i	0.987363	−	0.158472i	$-0.0506568\pi$
$541$	14.8700	+	18.1192i	0.639311	+	0.779003i	−0.348052	+	0.937475i	$0.613157\pi$
$542$	−21.2239	+	9.40277i	−0.911646	+	0.403884i
$543$	1.38563	−	1.38563i	0.0594630	−	0.0594630i
$544$	−1.21426	−	0.337357i	−0.0520612	−	0.0144641i
$545$	−9.48951	−	9.48951i	−0.406486	−	0.406486i
$546$	−0.511131	−	0.197284i	−0.0218744	−	0.00844298i
$547$	13.3812	−	10.9817i	0.572140	−	0.469543i	−0.303283	−	0.952900i	$-0.598083\pi$
$547$	13.3812	−	10.9817i	0.572140	−	0.469543i	0.875423	+	0.483357i	$0.160583\pi$
$548$	43.2438	+	6.43253i	1.84728	+	0.274784i
$549$	−0.913559	+	3.01160i	−0.0389897	+	0.128532i
$550$	−0.696727	−	2.11046i	−0.0297086	−	0.0899903i
$551$	21.7496	+	14.5326i	0.926566	+	0.619111i
$552$	14.9332	+	23.6138i	0.635599	+	1.00507i
$553$	3.89307	+	5.82640i	0.165550	+	0.247764i
$554$	16.9702	−	2.08959i	0.720996	−	0.0887781i
$555$	−12.8815	+	1.26872i	−0.546789	+	0.0538541i
$556$	−0.0724781	−	0.0537989i	−0.00307376	−	0.00228158i
$557$	3.21935	+	10.6128i	0.136408	+	0.449678i	0.998356	−	0.0573196i	$-0.0182554\pi$
$557$	3.21935	+	10.6128i	0.136408	+	0.449678i	−0.861948	+	0.506997i	$0.830755\pi$
$558$	−6.91509	−	9.82291i	−0.292739	−	0.415837i
$559$	1.88872	+	0.782334i	0.0798844	+	0.0330892i
$560$	1.28682	−	1.28473i	0.0543780	−	0.0542899i
$561$	0.446513	−	0.184952i	0.0188518	−	0.00780867i
$562$	−27.2011	−	17.2326i	−1.14741	−	0.726914i
$563$	6.18283	−	11.5673i	0.260575	−	0.487502i	−0.717280	−	0.696785i	$-0.754613\pi$
$563$	6.18283	−	11.5673i	0.260575	−	0.487502i	0.977855	+	0.209283i	$0.0671131\pi$
$564$	−15.7927	−	7.47722i	−0.664993	−	0.314848i
$565$	1.54299	−	1.88014i	0.0649141	−	0.0790981i
$566$	−5.00557	+	18.0736i	−0.210400	+	0.759688i
$567$	0.400754	−	2.01473i	0.0168301	−	0.0846106i
$568$	−9.46348	−	34.2777i	−0.397079	−	1.43826i
$569$	−12.0309	+	2.39310i	−0.504363	+	0.100324i	−0.440713	−	0.897648i	$-0.645274\pi$
$569$	−12.0309	+	2.39310i	−0.504363	+	0.100324i	−0.0636502	+	0.997972i	$0.520274\pi$
$570$	−5.36997	+	4.63027i	−0.224923	+	0.193941i
$571$	−29.7340	+	15.8931i	−1.24433	+	0.665107i	−0.956264	−	0.292504i	$-0.905511\pi$
$571$	−29.7340	+	15.8931i	−1.24433	+	0.665107i	−0.288064	+	0.957611i	$0.593011\pi$
$572$	0.828931	+	1.75447i	0.0346594	+	0.0733579i
$573$	0.757812	−	7.69420i	0.0316581	−	0.321430i
$574$	−1.18701	−	1.13059i	−0.0495450	−	0.0471899i
$575$			7.15589i			0.298421i
$576$	8.74458	+	0.440251i	0.364358	+	0.0183438i
$577$		−	36.1352i		−	1.50433i	−0.658976	−	0.752164i	$-0.729010\pi$
$577$		−	36.1352i		−	1.50433i	0.658976	−	0.752164i	$-0.270990\pi$
$578$	−16.5328	+	17.3579i	−0.687674	+	0.721993i
$579$	−1.16375	+	11.8158i	−0.0483639	+	0.491047i
$580$	−4.85802	+	13.5599i	−0.201718	+	0.563045i
$581$	2.99054	−	1.59847i	0.124068	−	0.0663159i
$582$	−6.94793	−	8.05788i	−0.288001	−	0.334010i
$583$	1.36210	−	0.270938i	0.0564123	−	0.0112211i
$584$	−15.7162	−	1.94811i	−0.650341	−	0.0806133i
$585$	0.131819	−	0.662699i	0.00545005	−	0.0273992i
$586$	−26.7464	−	7.40756i	−1.10488	−	0.306004i
$587$	5.07560	−	6.18464i	0.209492	−	0.255267i	−0.657654	−	0.753320i	$-0.728451\pi$
$587$	5.07560	−	6.18464i	0.209492	−	0.255267i	0.867147	+	0.498052i	$0.165951\pi$
$588$	17.6615	−	6.31130i	0.728347	−	0.260274i
$589$	13.2884	−	24.8609i	0.547541	−	1.02438i
$590$	−0.271273	+	0.428195i	−0.0111681	+	0.0176285i
$591$	8.12340	−	3.36482i	0.334152	−	0.138410i
$592$	−7.34709	+	36.7805i	−0.301963	+	1.51167i
$593$	−22.2702	−	9.22460i	−0.914526	−	0.378809i	−0.124738	−	0.992190i	$-0.539809\pi$
$593$	−22.2702	−	9.22460i	−0.914526	−	0.378809i	−0.789787	+	0.613381i	$0.789809\pi$
$594$	−10.2717	+	7.23100i	−0.421451	+	0.296692i
$595$	0.0293987	+	0.0969146i	0.00120523	+	0.00397311i
$596$	−2.93673	−	19.8533i	−0.120293	−	0.813221i
$597$	6.55946	−	0.646050i	0.268461	−	0.0264411i
$598$	−0.763533	−	6.20090i	−0.0312232	−	0.253574i
$599$	−11.7119	−	17.5281i	−0.478535	−	0.716179i	0.511141	−	0.859497i	$-0.329223\pi$
$599$	−11.7119	−	17.5281i	−0.478535	−	0.716179i	−0.989677	+	0.143318i	$0.954223\pi$
$600$	−3.19081	−	2.25013i	−0.130264	−	0.0918610i
$601$	31.4268	+	20.9987i	1.28192	+	0.856555i	0.994850	−	0.101354i	$-0.0323173\pi$
$601$	31.4268	+	20.9987i	1.28192	+	0.856555i	0.287074	+	0.957908i	$0.407317\pi$
$602$	2.02153	−	0.667370i	0.0823916	−	0.0272000i
$603$	−1.27362	+	4.19858i	−0.0518660	+	0.170979i
$604$	−3.46231	+	2.56565i	−0.140879	+	0.104395i
$605$	−6.59399	+	5.41154i	−0.268084	+	0.220011i
$606$	−12.5163	+	32.4278i	−0.508441	+	1.31729i
$607$	−5.05148	−	5.05148i	−0.205033	−	0.205033i	0.597119	−	0.802153i	$-0.296312\pi$
$607$	−5.05148	−	5.05148i	−0.205033	−	0.205033i	−0.802153	+	0.597119i	$0.796312\pi$
$608$	8.30712	+	18.7919i	0.336898	+	0.762114i
$609$	3.19569	−	3.19569i	0.129496	−	0.129496i
$610$	−1.64719	−	3.71804i	−0.0666928	−	0.150539i
$611$	2.47879	+	3.02041i	0.100281	+	0.122193i
$612$	−0.250874	+	0.418174i	−0.0101410	+	0.0169037i
$613$	−36.3665	−	11.0316i	−1.46883	−	0.445564i	−0.548313	−	0.836273i	$-0.684730\pi$
$613$	−36.3665	−	11.0316i	−1.46883	−	0.445564i	−0.920514	+	0.390709i	$0.872230\pi$
$614$	8.37574	+	4.21812i	0.338017	+	0.170229i
$615$	−1.95554	+	2.92667i	−0.0788548	+	0.118015i
$616$	1.84680	+	0.819972i	0.0744095	+	0.0330376i
$617$	−7.58402	+	5.06748i	−0.305321	+	0.204009i	−0.698786	−	0.715331i	$-0.746276\pi$
$617$	−7.58402	+	5.06748i	−0.305321	+	0.204009i	0.393465	+	0.919339i	$0.371276\pi$
$618$	10.0393	+	7.83801i	0.403839	+	0.315291i
$619$	2.16635	+	21.9954i	0.0870731	+	0.884068i	0.935164	+	0.354216i	$0.115252\pi$
$619$	2.16635	+	21.9954i	0.0870731	+	0.884068i	−0.848090	+	0.529851i	$0.822248\pi$
$620$	15.0558	+	3.77776i	0.604654	+	0.151718i
$621$	38.7039	−	11.7407i	1.55313	−	0.471138i
$622$	43.0280	+	7.47505i	1.72527	+	0.299722i
$623$	−1.42283	+	3.43501i	−0.0570044	+	0.137621i
$624$	3.00507	+	1.60938i	0.120299	+	0.0644266i
$625$	−0.382683	−	0.923880i	−0.0153073	−	0.0369552i
$626$	2.33370	+	10.4023i	0.0932735	+	0.415760i
$627$	−6.94897	−	3.71430i	−0.277515	−	0.148335i
$628$	−0.799669	−	0.883018i	−0.0319103	−	0.0352363i
$629$	−1.61482	−	1.32525i	−0.0643869	−	0.0528410i
$630$	−0.346686	−	0.612275i	−0.0138123	−	0.0243936i
$631$	−37.4835	−	7.45593i	−1.49219	−	0.296816i	−0.619467	−	0.785023i	$-0.712651\pi$
$631$	−37.4835	−	7.45593i	−1.49219	−	0.296816i	−0.872728	+	0.488207i	$0.837651\pi$
$632$	−19.5790	−	38.9558i	−0.778812	−	1.54958i
$633$	1.83495	+	9.22494i	0.0729329	+	0.366658i
$634$	−12.2768	−	0.908089i	−0.487572	−	0.0360648i
$635$	−2.64333	−	4.94532i	−0.104897	−	0.196249i
$636$	1.63918	−	1.80708i	0.0649977	−	0.0716556i
$637$	−4.17380	−	0.411083i	−0.165372	−	0.0162877i
$638$	−16.0015	+	0.389571i	−0.633506	+	0.0154233i
$639$	−13.7599			−0.544334
$640$	−8.92899	+	6.94789i	−0.352949	+	0.274640i
$641$	−13.2647			−0.523923			−0.261962	−	0.965078i	$-0.584369\pi$
$641$	−13.2647			−0.523923			−0.261962	+	0.965078i	$0.584369\pi$
$642$	17.9094	−	0.436020i	0.706828	−	0.0172083i
$643$	−13.1180	−	1.29201i	−0.517323	−	0.0509518i	−0.164013	−	0.986458i	$-0.552444\pi$
$643$	−13.1180	−	1.29201i	−0.517323	−	0.0509518i	−0.353310	+	0.935506i	$0.614944\pi$
$644$	−4.81886	−	4.37112i	−0.189890	−	0.172246i
$645$	−2.15479	−	4.03133i	−0.0848448	−	0.158733i
$646$	−1.14122	−	0.0844141i	−0.0449008	−	0.00332123i
$647$	−3.64186	−	18.3089i	−0.143176	−	0.719797i	−0.983955	−	0.178417i	$-0.942902\pi$
$647$	−3.64186	−	18.3089i	−0.143176	−	0.719797i	0.840778	−	0.541379i	$-0.182098\pi$
$648$	−4.01657	+	12.1335i	−0.157786	+	0.476651i
$649$	−0.552459	−	0.109891i	−0.0216859	−	0.00431360i
$650$	0.430190	+	0.759751i	0.0168734	+	0.0297999i
$651$	−3.76484	−	3.08972i	−0.147556	−	0.121096i
$652$	−9.87954	+	8.94700i	−0.386913	+	0.350392i
$653$	−23.0169	−	12.3028i	−0.900719	−	0.481444i	−0.0450599	−	0.998984i	$-0.514348\pi$
$653$	−23.0169	−	12.3028i	−0.900719	−	0.481444i	−0.855659	+	0.517540i	$0.826848\pi$
$654$	−5.73504	−	25.5635i	−0.224258	−	0.999612i
$655$	−2.18084	−	5.26501i	−0.0852124	−	0.205721i
$656$	6.46408	+	7.88954i	0.252380	+	0.308035i
$657$	−2.34505	+	5.66145i	−0.0914891	+	0.220874i
$658$	4.00881	+	0.696432i	0.156280	+	0.0271497i
$659$	−28.9679	+	8.78732i	−1.12843	+	0.342306i	−0.798676	−	0.601761i	$-0.794466\pi$
$659$	−28.9679	+	8.78732i	−1.12843	+	0.342306i	−0.329754	+	0.944067i	$0.606966\pi$
$660$	1.05594	−	4.20829i	0.0411022	−	0.163808i
$661$	−3.55149	−	36.0589i	−0.138137	−	1.40253i	−0.775199	−	0.631717i	$-0.782351\pi$
$661$	−3.55149	−	36.0589i	−0.138137	−	1.40253i	0.637062	−	0.770813i	$-0.280149\pi$
$662$	−21.9285	−	17.1203i	−0.852274	−	0.665399i
$663$	−0.157864	+	0.105481i	−0.00613094	+	0.00409656i
$664$	−19.6890	+	7.58114i	−0.764082	+	0.294205i
$665$	0.917308	−	1.37285i	0.0355717	−	0.0532368i
$666$	12.9623	+	6.52799i	0.502281	+	0.252954i
$667$	49.3172	+	14.9602i	1.90957	+	0.579261i
$668$	−35.9120	−	21.5446i	−1.38948	−	0.833587i
$669$	−0.528556	−	0.644047i	−0.0204352	−	0.0249003i
$670$	−2.29641	−	5.18344i	−0.0887179	−	0.200254i
$671$	3.19539	−	3.19539i	0.123357	−	0.123357i
$672$	3.46434	−	0.774257i	0.133640	−	0.0298676i
$673$	13.8771	+	13.8771i	0.534922	+	0.534922i	0.922033	−	0.387111i	$-0.126527\pi$
$673$	13.8771	+	13.8771i	0.534922	+	0.534922i	−0.387111	+	0.922033i	$0.626527\pi$
$674$	13.4765	−	34.9154i	0.519095	−	1.34489i
$675$	−4.36909	+	3.58562i	−0.168166	+	0.138011i
$676$	15.0259	+	20.2772i	0.577918	+	0.779893i
$677$	3.34705	−	11.0337i	0.128638	−	0.424061i	−0.868836	−	0.495100i	$-0.835131\pi$
$677$	3.34705	−	11.0337i	0.128638	−	0.424061i	0.997474	+	0.0710387i	$0.0226314\pi$
$678$	4.50885	−	1.48851i	0.173161	−	0.0571659i
$679$	2.06002	+	1.37646i	0.0790563	+	0.0528237i
$680$	−0.107351	−	0.620917i	−0.00411671	−	0.0238111i
$681$	14.1747	+	21.2140i	0.543177	+	0.812922i
$682$	2.10803	+	17.1200i	0.0807206	+	0.655559i
$683$	6.59060	−	0.649118i	0.252182	−	0.0248378i	0.0288640	−	0.999583i	$-0.490811\pi$
$683$	6.59060	−	0.649118i	0.252182	−	0.0248378i	0.223318	+	0.974746i	$0.428311\pi$
$684$	7.86474	−	1.16337i	0.300716	−	0.0444825i
$685$	6.34557	+	20.9185i	0.242452	+	0.799256i
$686$	−7.25103	+	5.10455i	−0.276846	+	0.194893i
$687$	−6.57955	−	2.72534i	−0.251026	−	0.103978i
$688$	−12.9931	+	2.57354i	−0.495357	+	0.0981154i
$689$	−0.504044	+	0.208782i	−0.0192025	+	0.00795395i
$690$	−7.47617	+	11.8009i	−0.284613	+	0.449251i
$691$	−17.3261	+	32.4148i	−0.659114	+	1.23312i	0.301031	+	0.953614i	$0.402669\pi$
$691$	−17.3261	+	32.4148i	−0.659114	+	1.23312i	−0.960145	+	0.279502i	$0.909831\pi$
$692$	−8.96113	−	25.0767i	−0.340651	−	0.953274i
$693$	0.496024	−	0.604407i	0.0188424	−	0.0229595i
$694$	−34.0144	−	9.42046i	−1.29117	−	0.357596i
$695$	0.00880471	−	0.0442643i	0.000333982	−	0.00167904i
$696$	−22.1782	+	17.2864i	−0.840664	+	0.655239i
$697$	−0.557154	+	0.110825i	−0.0211037	+	0.00419779i
$698$	−5.21938	−	6.05320i	−0.197557	−	0.229117i
$699$	8.37919	−	4.47877i	0.316930	−	0.169403i
$700$	0.855910	+	0.306641i	0.0323503	+	0.0115899i
$701$	0.791821	−	8.03949i	0.0299067	−	0.303647i	−0.968582	−	0.248693i	$-0.919999\pi$
$701$	0.791821	−	8.03949i	0.0299067	−	0.303647i	0.998489	−	0.0549539i	$-0.0175012\pi$
$702$	3.40343	−	3.57328i	0.128454	−	0.134865i
$703$			34.0572i			1.28449i
$704$	−10.7758	−	6.47656i	−0.406127	−	0.244095i
$705$		−	8.73668i		−	0.329042i
$706$	25.9206	+	24.6885i	0.975535	+	0.929164i
$707$	0.793362	−	8.05514i	0.0298374	−	0.302945i
$708$	−0.894720	+	0.422727i	−0.0336256	+	0.0158871i
$709$	31.7398	−	16.9653i	1.19201	−	0.637144i	0.248548	−	0.968619i	$-0.420047\pi$
$709$	31.7398	−	16.9653i	1.19201	−	0.637144i	0.943464	+	0.331476i	$0.107547\pi$
$710$	13.4655	−	11.6107i	0.505353	−	0.435742i
$711$	−16.5465	+	3.29130i	−0.620542	+	0.123434i
$712$	11.4146	−	20.1210i	0.427780	−	0.754068i
$713$	10.8351	−	54.4715i	0.405776	−	2.03997i
$714$	−0.0527704	+	0.190538i	−0.00197488	+	0.00713069i
$715$	−0.615499	+	0.749988i	−0.0230184	+	0.0280479i
$716$	6.93196	−	14.6410i	0.259059	−	0.547161i
$717$	−3.29234	+	6.15953i	−0.122955	+	0.230032i
$718$	−36.7847	−	23.3041i	−1.37279	−	0.869701i
$719$	21.4996	−	8.90542i	0.801799	−	0.332116i	0.0561223	−	0.998424i	$-0.482126\pi$
$719$	21.4996	−	8.90542i	0.801799	−	0.332116i	0.745677	+	0.666308i	$0.232126\pi$
$720$	1.67204	+	4.04594i	0.0623134	+	0.150783i
$721$	−2.74010	−	1.13498i	−0.102046	−	0.0422690i
$722$	−4.72815	−	6.71635i	−0.175964	−	0.249957i
$723$	6.05943	+	19.9753i	0.225353	+	0.742888i
$724$	1.69218	−	2.27971i	0.0628894	−	0.0847247i
$725$	−7.16726	+	0.705914i	−0.266185	+	0.0262170i
$726$	−16.5280	+	2.03513i	−0.613410	+	0.0755308i
$727$	10.1095	+	15.1299i	0.374941	+	0.561138i	0.970172	−	0.242416i	$-0.0779398\pi$
$727$	10.1095	+	15.1299i	0.374941	+	0.561138i	−0.595232	+	0.803554i	$0.702940\pi$
$728$	−0.774402	−	0.174392i	−0.0287013	−	0.00646341i
$729$	23.5739	+	15.7516i	0.873108	+	0.583392i
$730$	−2.48228	−	7.51910i	−0.0918735	−	0.278294i
$731$	0.214150	−	0.705957i	0.00792061	−	0.0261108i
$732$	1.16804	−	7.85237i	0.0431720	−	0.290232i
$733$	−39.8560	+	32.7090i	−1.47212	+	1.20813i	−0.542261	+	0.840210i	$0.682431\pi$
$733$	−39.8560	+	32.7090i	−1.47212	+	1.20813i	−0.929856	+	0.367924i	$0.880069\pi$
$734$	20.9079	+	8.06992i	0.771723	+	0.297866i
$735$	6.63099	+	6.63099i	0.244588	+	0.244588i
$736$	26.4093	+	30.6785i	0.973458	+	1.13082i
$737$	4.45480	−	4.45480i	0.164095	−	0.164095i
$738$	3.60841	−	1.59862i	0.132827	−	0.0588462i
$739$	−21.4852	−	26.1798i	−0.790346	−	0.963039i	0.209545	−	0.977799i	$-0.432802\pi$
$739$	−21.4852	−	26.1798i	−0.790346	−	0.963039i	−0.999891	+	0.0147599i	$0.995302\pi$
$740$	−18.1934	+	4.54937i	−0.668802	+	0.167238i
$741$	2.96206	+	0.898531i	0.108814	+	0.0330084i
$742$	−0.255539	+	0.507412i	−0.00938111	+	0.0186277i
$743$	−5.00308	+	7.48764i	−0.183545	+	0.274695i	−0.911820	−	0.410591i	$-0.865323\pi$
$743$	−5.00308	+	7.48764i	−0.183545	+	0.274695i	0.728275	+	0.685285i	$0.240323\pi$
$744$	20.8818	+	21.9596i	0.765564	+	0.805077i
$745$	8.34350	−	5.57495i	0.305682	−	0.204250i
$746$	−3.83609	+	4.91345i	−0.140449	+	0.179894i
$747$	0.800202	+	8.12459i	0.0292779	+	0.297263i
$748$	0.600751	−	0.359746i	0.0219656	−	0.0131536i
$749$	−3.99200	+	1.21096i	−0.145864	+	0.0442475i
$750$	0.334142	−	1.92339i	0.0122011	−	0.0702323i
$751$	6.79881	−	16.4138i	0.248092	−	0.598947i	−0.749950	−	0.661495i	$-0.769922\pi$
$751$	6.79881	−	16.4138i	0.248092	−	0.598947i	0.998042	+	0.0625474i	$0.0199225\pi$
$752$	−24.2200	−	7.36851i	−0.883214	−	0.268702i
$753$	−6.19810	−	14.9635i	−0.225871	−	0.545302i
$754$	6.13543	−	1.37645i	0.223439	−	0.0501274i
$755$	−1.90024	−	1.01570i	−0.0691567	−	0.0369650i
$756$	0.254226	−	5.13244i	0.00924609	−	0.186665i
$757$	9.66850	+	7.93473i	0.351407	+	0.288393i	0.793492	−	0.608581i	$-0.208261\pi$
$757$	9.66850	+	7.93473i	0.351407	+	0.288393i	−0.442084	+	0.896973i	$0.645761\pi$
$758$	27.2310	−	15.4189i	0.989075	−	0.560039i
$759$	−15.2255	−	3.02854i	−0.552651	−	0.109929i
$760$	−6.71483	+	7.77479i	−0.243572	+	0.282021i
$761$	6.79973	+	34.1845i	0.246490	+	1.23919i	0.883536	+	0.468363i	$0.155156\pi$
$761$	6.79973	+	34.1845i	0.246490	+	1.23919i	−0.637046	+	0.770826i	$0.719844\pi$
$762$	0.807512	−	10.9170i	0.0292531	−	0.395482i
$763$	2.87585	+	5.38033i	0.104113	+	0.194781i
$764$	−0.545103	−	11.1883i	−0.0197211	−	0.404780i
$765$	−0.242654	−	0.0238993i	−0.00877316	−	0.000864081i
$766$	1.29137	+	53.0425i	0.0466589	+	1.91650i
$767$	0.221281			0.00799001
$768$	−21.9838	+	2.12924i	−0.793270	+	0.0768322i
$769$	16.4482			0.593136			0.296568	−	0.955012i	$-0.404158\pi$
$769$	16.4482			0.593136			0.296568	+	0.955012i	$0.404158\pi$
$770$	0.0245899	+	1.01002i	0.000886159	+	0.0363987i
$771$	34.7909	+	3.42660i	1.25296	+	0.123406i
$772$	0.837100	+	17.1816i	0.0301279	+	0.618381i
$773$	−11.9457	−	22.3489i	−0.429659	−	0.803835i	0.570185	−	0.821516i	$-0.306872\pi$
$773$	−11.9457	−	22.3489i	−0.429659	−	0.803835i	−0.999844	+	0.0176815i	$0.994372\pi$
$774$	−0.378079	+	5.11138i	−0.0135898	+	0.183725i
$775$	1.51414	+	7.61212i	0.0543897	+	0.273435i
$776$	−11.6664	−	10.0759i	−0.418800	−	0.361704i
$777$	5.77108	+	1.14794i	0.207036	+	0.0411821i
$778$	−40.7901	+	23.0964i	−1.46240	+	0.828046i
$779$	7.15911	+	5.87533i	0.256502	+	0.210505i
$780$	−0.0843230	+	1.70236i	−0.00301925	+	0.0609542i
$781$	17.4250	+	9.31384i	0.623515	+	0.333275i
$782$	−2.19989	+	0.493533i	−0.0786677	+	0.0176487i
$783$	15.5774	+	37.6072i	0.556691	+	1.34397i
$784$	23.9752	−	12.7900i	0.856256	−	0.456786i
$785$	0.227945	−	0.550308i	0.00813571	−	0.0196413i
$786$	1.90421	−	10.9610i	0.0679208	−	0.390967i
$787$	−24.5590	+	7.44988i	−0.875432	+	0.265560i	−0.695853	−	0.718184i	$-0.744974\pi$
$787$	−24.5590	+	7.44988i	−0.875432	+	0.265560i	−0.179579	+	0.983744i	$0.557474\pi$
$788$	10.9295	−	6.54485i	0.389346	−	0.233150i
$789$	−3.65015	−	37.0606i	−0.129949	−	1.31939i
$790$	13.4153	−	17.1829i	0.477294	−	0.611341i
$791$	−0.919330	+	0.614277i	−0.0326876	+	0.0218412i
$792$	−3.52539	+	3.35236i	−0.125269	+	0.119121i
$793$	−0.986271	+	1.47606i	−0.0350235	+	0.0524164i
$794$	−17.4647	+	34.6788i	−0.619798	+	1.23071i
$795$	1.16736	+	0.354114i	0.0414019	+	0.0125591i
$796$	9.26435	−	2.31661i	0.328366	−	0.0821100i
$797$	−7.99443	−	9.74124i	−0.283177	−	0.345052i	0.611923	−	0.790917i	$-0.290396\pi$
$797$	−7.99443	−	9.74124i	−0.283177	−	0.345052i	−0.895100	+	0.445865i	$0.852896\pi$
$798$	2.94704	−	1.30562i	0.104324	−	0.0462183i
$799$	0.997026	−	0.997026i	0.0352722	−	0.0352722i
$800$	−5.05026	−	2.54850i	−0.178554	−	0.0901032i
$801$	−6.32960	−	6.32960i	−0.223645	−	0.223645i
$802$	−21.6679	−	8.36326i	−0.765119	−	0.295317i
$803$	6.80180	−	5.58210i	0.240030	−	0.196988i
$804$	1.62841	−	10.9473i	0.0574295	−	0.386080i
$805$	0.944296	−	3.11293i	0.0332821	−	0.109716i
$806$	−2.12429	−	6.43468i	−0.0748248	−	0.226652i
$807$	−20.3918	−	13.6254i	−0.717825	−	0.479635i
$808$	−11.0640	+	49.1306i	−0.389231	+	1.72841i
$809$	2.51188	+	3.75929i	0.0883128	+	0.132170i	0.872996	−	0.487728i	$-0.162174\pi$
$809$	2.51188	+	3.75929i	0.0883128	+	0.132170i	−0.784683	+	0.619897i	$0.787174\pi$
$810$	−6.34263	+	0.780985i	−0.222857	+	0.0274410i
$811$	−13.0350	+	1.28384i	−0.457721	+	0.0450816i	−0.324251	−	0.945971i	$-0.605112\pi$
$811$	−13.0350	+	1.28384i	−0.457721	+	0.0450816i	−0.133470	+	0.991053i	$0.542612\pi$
$812$	3.90269	−	5.25772i	0.136958	−	0.184510i
$813$	−6.57748	−	21.6830i	−0.230682	−	0.760457i
$814$	−11.9963	−	17.0407i	−0.420469	−	0.597278i
$815$	−6.15705	−	2.55034i	−0.215672	−	0.0893344i
$816$	0.471674	−	1.13612i	0.0165119	−	0.0397720i
$817$	−11.1117	+	4.60261i	−0.388749	+	0.161025i
$818$	15.9249	+	10.0889i	0.556802	+	0.352749i
$819$	−0.144794	+	0.270890i	−0.00505950	+	0.00946565i
$820$	−2.18229	+	4.60922i	−0.0762087	+	0.160961i
$821$	−5.08581	+	6.19708i	−0.177496	+	0.216280i	−0.854157	−	0.520015i	$-0.825926\pi$
$821$	−5.08581	+	6.19708i	−0.177496	+	0.216280i	0.676661	+	0.736295i	$0.263426\pi$
$822$	−11.3902	+	41.1266i	−0.397280	+	1.43445i
$823$	−1.06948	+	5.37662i	−0.0372796	+	0.187417i	−0.994938	−	0.100489i	$-0.967959\pi$
$823$	−1.06948	+	5.37662i	−0.0372796	+	0.187417i	0.957659	+	0.287906i	$0.0929592\pi$
$824$	16.0505	+	9.10538i	0.559145	+	0.317201i
$825$	2.12769	−	0.423224i	0.0740767	−	0.0147348i
$826$	0.174513	−	0.150474i	0.00607209	−	0.00523567i
$827$	16.6628	−	8.90645i	0.579422	−	0.309707i	−0.155525	−	0.987832i	$-0.549707\pi$
$827$	16.6628	−	8.90645i	0.579422	−	0.309707i	0.734947	+	0.678124i	$0.237207\pi$
$828$	14.1625	−	6.69133i	0.492180	−	0.232540i
$829$	4.83532	−	49.0938i	0.167938	−	1.70510i	−0.429404	−	0.903113i	$-0.641276\pi$
$829$	4.83532	−	49.0938i	0.167938	−	1.70510i	0.597341	−	0.801987i	$-0.296224\pi$
$830$	−7.63865	−	7.27555i	−0.265142	−	0.252538i
$831$			16.6898i			0.578961i
$832$	4.64820	+	1.66953i	0.161147	+	0.0578806i
$833$			1.51345i			0.0524379i
$834$	0.0607654	−	0.0637980i	0.00210413	−	0.00220914i
$835$	2.05243	−	20.8386i	0.0710271	−	0.721151i
$836$	−10.7470	−	3.85026i	−0.371694	−	0.133164i
$837$	38.6872	−	20.6787i	1.33722	−	0.714761i
$838$	14.3933	+	16.6927i	0.497210	+	0.576641i
$839$	−53.8812	+	10.7176i	−1.86019	+	0.370014i	−0.992002	−	0.126225i	$-0.959714\pi$
$839$	−53.8812	+	10.7176i	−1.86019	+	0.370014i	−0.868186	+	0.496239i	$0.834714\pi$
$840$	1.09113	+	1.39990i	0.0376474	+	0.0483012i
$841$	−4.46132	+	22.4286i	−0.153839	+	0.773399i
$842$	−29.8424	−	8.26501i	−1.02844	−	0.284831i
$843$	19.9395	−	24.2963i	0.686751	−	0.836809i
$844$	4.58570	+	12.8326i	0.157846	+	0.441715i
$845$	−5.94849	+	11.1288i	−0.204634	+	0.382844i
$846$	−5.24254	+	8.27516i	−0.180242	+	0.284506i
$847$	3.58260	−	1.48396i	0.123100	−	0.0509895i
$848$	1.96623	−	2.93752i	0.0675206	−	0.100875i
$849$	−16.9123	−	7.00529i	−0.580427	−	0.240421i
$850$	0.257629	−	0.181364i	0.00883659	−	0.00622075i
$851$	19.4779	+	64.2099i	0.667693	+	2.20109i
$852$	34.3365	−	5.07912i	1.17635	−	0.174008i
$853$	16.6390	−	1.63880i	0.569710	−	0.0561115i	0.190939	−	0.981602i	$-0.438847\pi$
$853$	16.6390	−	1.63880i	0.569710	−	0.0561115i	0.378771	+	0.925490i	$0.376347\pi$
$854$	0.225920	+	1.83477i	0.00773081	+	0.0627845i
$855$	2.20848	+	3.30523i	0.0755285	+	0.113036i
$856$	25.5761	−	4.42186i	0.874174	−	0.151136i
$857$	39.4280	+	26.3449i	1.34683	+	0.899925i	0.999288	−	0.0377375i	$-0.0120151\pi$
$857$	39.4280	+	26.3449i	1.34683	+	0.899925i	0.347546	+	0.937663i	$0.387015\pi$
$858$	−1.79858	+	0.593767i	−0.0614025	+	0.0202709i
$859$	4.92756	−	16.2440i	0.168126	−	0.554237i	−0.831874	−	0.554965i	$-0.812732\pi$
$859$	4.92756	−	16.2440i	0.168126	−	0.554237i	1.00000		0.000727618i	$0.000231608\pi$
$860$	−3.94302	−	5.32105i	−0.134456	−	0.181446i
$861$	1.23689	−	1.01509i	0.0421532	−	0.0345943i
$862$	3.09920	−	8.02952i	0.105559	−	0.273487i
$863$	−31.6447	−	31.6447i	−1.07720	−	1.07720i	−0.996760	−	0.0804384i	$-0.974368\pi$
$863$	−31.6447	−	31.6447i	−1.07720	−	1.07720i	−0.0804384	−	0.996760i	$-0.525632\pi$
$864$	−5.49804	+	31.4965i	−0.187047	+	1.07153i
$865$	9.41504	−	9.41504i	0.320121	−	0.320121i
$866$	8.36618	+	18.8841i	0.284294	+	0.641709i
$867$	−14.8439	−	18.0873i	−0.504124	−	0.614277i
$868$	−6.05098	−	3.63015i	−0.205384	−	0.123215i
$869$	23.1816	+	7.03206i	0.786382	+	0.238546i
$870$	−12.5571	−	6.32392i	−0.425726	−	0.214401i
$871$	−1.37500	+	2.05783i	−0.0465899	+	0.0697268i
$872$	−13.6394	−	35.4229i	−0.461888	−	1.19957i
$873$	−4.95964	+	3.31392i	−0.167858	+	0.112159i
$874$	28.9723	+	22.6197i	0.980003	+	0.765121i
$875$	0.0445576	+	0.452401i	0.00150632	+	0.0152940i
$876$	3.76206	−	14.9932i	0.127108	−	0.506574i
$877$	0.961450	−	0.291653i	0.0324659	−	0.00984841i	−0.274010	−	0.961727i	$-0.588350\pi$
$877$	0.961450	−	0.291653i	0.0324659	−	0.00984841i	0.306476	+	0.951878i	$0.400850\pi$
$878$	7.80703	+	1.35628i	0.263475	+	0.0457722i
$879$	10.3669	−	25.0278i	0.349666	−	0.844168i
$880$	0.621221	−	6.25538i	0.0209414	−	0.210869i
$881$	9.19739	+	22.2045i	0.309868	+	0.748088i	0.999709	+	0.0241266i	$0.00768048\pi$
$881$	9.19739	+	22.2045i	0.309868	+	0.748088i	−0.689841	+	0.723961i	$0.742320\pi$
$882$	−2.30171	−	10.2597i	−0.0775026	−	0.345462i
$883$	41.8079	+	22.3468i	1.40695	+	0.752029i	0.987776	−	0.155878i	$-0.0498207\pi$
$883$	41.8079	+	22.3468i	1.40695	+	0.752029i	0.419171	+	0.907907i	$0.362321\pi$
$884$	−0.203895	+	0.184649i	−0.00685774	+	0.00621043i
$885$	−0.382469	−	0.313884i	−0.0128565	−	0.0105511i
$886$	18.4173	+	32.5265i	0.618742	+	1.09275i
$887$	−11.4668	−	2.28088i	−0.385016	−	0.0765845i	−0.00121275	−	0.999999i	$-0.500386\pi$
$887$	−11.4668	−	2.28088i	−0.385016	−	0.0765845i	−0.383804	+	0.923415i	$0.625386\pi$
$888$	−34.7559	−	11.5052i	−1.16633	−	0.386090i
$889$	0.497303	+	2.50011i	0.0166790	+	0.0838510i
$890$	11.5351	+	0.853233i	0.386659	+	0.0286004i
$891$	−3.34760	−	6.26292i	−0.112149	−	0.209816i
$892$	−0.894094	−	0.811019i	−0.0299365	−	0.0271549i
$893$	−22.8769	−	2.25318i	−0.765546	−	0.0753997i
$894$	19.5838	−	0.476785i	0.654981	−	0.0159461i
$895$	8.09957			0.270739
$896$	4.80110	−	1.84417i	0.160393	−	0.0616094i
$897$	6.09841			0.203620
$898$	10.7549	−	0.261837i	0.358895	−	0.00873761i
$899$	55.6269	+	5.47877i	1.85526	+	0.182727i
$900$	−1.47064	+	1.62128i	−0.0490214	+	0.0540428i
$901$	0.0928068	+	0.173629i	0.00309184	+	0.00578443i
$902$	−5.65162	−	0.418040i	−0.188178	−	0.0139192i
$903$	0.405391	+	2.03804i	0.0134906	+	0.0678217i
$904$	6.14672	−	3.08932i	0.204437	−	0.102749i
$905$	1.39228	+	0.276941i	0.0462809	+	0.00920585i
$906$	−2.07254	−	3.66028i	−0.0688557	−	0.121605i
$907$	6.79570	+	5.57709i	0.225648	+	0.185184i	0.740424	−	0.672141i	$-0.234625\pi$
$907$	6.79570	+	5.57709i	0.225648	+	0.185184i	−0.514776	+	0.857325i	$0.672125\pi$
$908$	24.8134	+	27.3997i	0.823462	+	0.909290i
$909$	17.1861	+	9.18617i	0.570027	+	0.304686i
$910$	−0.0868824	−	0.387272i	−0.00288012	−	0.0128379i
$911$	6.12407	+	14.7848i	0.202899	+	0.489843i	0.992273	−	0.124070i	$-0.0395947\pi$
$911$	6.12407	+	14.7848i	0.202899	+	0.489843i	−0.789374	+	0.613913i	$0.789595\pi$
$912$	−19.1963	+	5.80614i	−0.635652	+	0.192260i
$913$	4.48604	−	10.8303i	0.148466	−	0.358430i
$914$	29.2379	+	5.07937i	0.967105	+	0.168010i
$915$	3.79846	−	1.15225i	0.125573	−	0.0380922i
$916$	−10.0079	−	2.51116i	−0.330671	−	0.0829711i
$917$	0.253925	+	2.57815i	0.00838535	+	0.0851379i
$918$	−1.40363	−	1.09586i	−0.0463268	−	0.0361689i
$919$	−1.80755	+	1.20777i	−0.0596257	+	0.0398406i	−0.585026	−	0.811015i	$-0.698916\pi$
$919$	−1.80755	+	1.20777i	−0.0596257	+	0.0398406i	0.525400	+	0.850855i	$0.323916\pi$
$920$	−8.21330	+	18.4985i	−0.270784	+	0.609879i
$921$	−5.08558	+	7.61110i	−0.167575	+	0.250794i
$922$	43.2093	+	21.7607i	1.42302	+	0.716651i
$923$	−7.42755	−	2.25312i	−0.244481	−	0.0741625i
$924$	−1.01468	+	1.69133i	−0.0333804	+	0.0556408i
$925$	−5.94856	−	7.24835i	−0.195588	−	0.238324i
$926$	17.4784	+	39.4522i	0.574375	+	1.29648i
$927$	5.04910	−	5.04910i	0.165834	−	0.165834i
$928$	−28.1220	+	29.4776i	−0.923150	+	0.967650i
$929$	38.9900	+	38.9900i	1.27922	+	1.27922i	0.941105	+	0.338114i	$0.109789\pi$
$929$	38.9900	+	38.9900i	1.27922	+	1.27922i	0.338114	+	0.941105i	$0.390211\pi$
$930$	−5.45582	+	14.1351i	−0.178903	+	0.463509i
$931$	19.0733	−	15.6530i	0.625101	−	0.513007i
$932$	11.0599	−	8.19564i	0.362279	−	0.268457i
$933$	−12.3745	+	40.7932i	−0.405122	+	1.33551i
$934$	24.8837	−	8.21487i	0.814219	−	0.268799i
$935$	0.291109	+	0.194513i	0.00952028	+	0.00636125i
$936$	1.10139	−	1.56183i	0.0360000	−	0.0510501i
$937$	−11.7995	−	17.6591i	−0.385472	−	0.576899i	0.587097	−	0.809517i	$-0.300271\pi$
$937$	−11.7995	−	17.6591i	−0.385472	−	0.576899i	−0.972568	+	0.232618i	$0.925271\pi$
$938$	0.314963	+	2.55792i	0.0102839	+	0.0835189i
$939$	−10.3560	+	1.01997i	−0.337954	+	0.0332856i
$940$	−1.85225	−	12.5218i	−0.0604137	−	0.408416i
$941$	−8.37258	−	27.6007i	−0.272938	−	0.899757i	−0.981066	−	0.193673i	$-0.937960\pi$
$941$	−8.37258	−	27.6007i	−0.272938	−	0.899757i	0.708128	−	0.706084i	$-0.249540\pi$
$942$	0.950845	−	0.669372i	0.0309802	−	0.0218093i
$943$	16.8576	+	6.98266i	0.548960	+	0.227387i
$944$	−1.19273	+	0.795560i	−0.0388201	+	0.0258933i
$945$	2.37378	−	0.983254i	0.0772192	−	0.0319852i
$946$	3.93858	−	6.21691i	0.128054	−	0.202129i
$947$	−2.75786	+	5.15960i	−0.0896184	+	0.167664i	−0.922737	−	0.385430i	$-0.874053\pi$
$947$	−2.75786	+	5.15960i	−0.0896184	+	0.167664i	0.833119	+	0.553094i	$0.186553\pi$
$948$	40.0753	−	14.3208i	1.30158	−	0.465119i
$949$	−2.19289	+	2.67204i	−0.0711841	+	0.0867380i
$950$	−4.95020	−	1.37098i	−0.160606	−	0.0444806i
$951$	2.34422	−	11.7852i	0.0760165	−	0.382161i
$952$	−0.0352374	+	0.284275i	−0.00114205	+	0.00921340i
$953$	−22.7208	+	4.51944i	−0.735998	+	0.146399i	−0.548836	−	0.835930i	$-0.684929\pi$
$953$	−22.7208	+	4.51944i	−0.735998	+	0.146399i	−0.187162	+	0.982329i	$0.559929\pi$
$954$	−0.893201	−	1.03589i	−0.0289184	−	0.0335382i
$955$	4.93947	−	2.64020i	0.159837	−	0.0854349i
$956$	−3.41286	+	9.52612i	−0.110380	+	0.308097i
$957$	1.53139	−	15.5485i	0.0495028	−	0.502611i
$958$	14.2514	−	14.9627i	0.460443	−	0.483422i
$959$		−	9.93726i		−	0.320891i
$960$	−5.66588	−	9.47906i	−0.182865	−	0.305935i
$961$		−	29.2369i		−	0.943127i
$962$	5.92810	+	5.64631i	0.191129	+	0.182044i
$963$	0.984433	−	9.99512i	0.0317229	−	0.322088i
$964$	12.9196	+	27.3448i	0.416111	+	0.880717i
$965$	−7.58541	+	4.05449i	−0.244183	+	0.130519i
$966$	4.80950	−	4.14700i	0.154743	−	0.133428i
$967$	18.4798	−	3.67585i	0.594269	−	0.118208i	0.111213	−	0.993797i	$-0.464527\pi$
$967$	18.4798	−	3.67585i	0.594269	−	0.118208i	0.483057	+	0.875589i	$0.339527\pi$
$968$	−23.2572	+	6.42091i	−0.747513	+	0.206376i
$969$	0.217914	−	1.09553i	0.00700041	−	0.0351934i
$970$	2.05722	−	7.42799i	0.0660535	−	0.238499i
$971$	35.8214	−	43.6485i	1.14956	−	1.40075i	0.247640	−	0.968852i	$-0.420345\pi$
$971$	35.8214	−	43.6485i	1.14956	−	1.40075i	0.901924	−	0.431896i	$-0.142155\pi$
$972$	19.3748	+	9.17321i	0.621447	+	0.294231i
$973$	−0.00967133	+	0.0180938i	−0.000310049	+	0.000580060i
$974$	−34.9471	−	22.1400i	−1.11978	−	0.709410i
$975$	−0.787351	+	0.326131i	−0.0252154	+	0.0104446i
$976$	0.00932229	−	11.5020i	0.000298399	−	0.368170i
$977$	34.5300	+	14.3028i	1.10471	+	0.457586i	0.859113	−	0.511786i	$-0.171016\pi$
$977$	34.5300	+	14.3028i	1.10471	+	0.457586i	0.245598	+	0.969372i	$0.421016\pi$
$978$	−7.48919	−	10.6384i	−0.239478	−	0.340179i
$979$	3.73114	+	12.2999i	0.119248	+	0.393107i
$980$	10.9097	+	8.09801i	0.348496	+	0.258681i
$981$	−14.6171	+	1.43966i	−0.466688	+	0.0459648i
$982$	−3.17551	+	0.391009i	−0.101335	+	0.0124776i
$983$	−3.84890	−	5.76029i	−0.122761	−	0.183725i	0.764999	−	0.644031i	$-0.222739\pi$
$983$	−3.84890	−	5.76029i	−0.122761	−	0.183725i	−0.887760	+	0.460307i	$0.847739\pi$
$984$	−8.41435	+	5.32116i	−0.268240	+	0.169632i
$985$	5.29614	+	3.53877i	0.168749	+	0.112755i
$986$	−0.711331	−	2.15469i	−0.0226534	−	0.0686195i
$987$	−1.15290	+	3.80059i	−0.0366971	+	0.120974i
$988$	4.43585	+	0.659834i	0.141123	+	0.0209921i
$989$	−18.3172	+	15.0325i	−0.582452	+	0.478006i
$990$	−2.26925	−	0.875876i	−0.0721216	−	0.0278372i
$991$	−26.8783	−	26.8783i	−0.853817	−	0.853817i	0.136784	−	0.990601i	$-0.456323\pi$
$991$	−26.8783	−	26.8783i	−0.853817	−	0.853817i	−0.990601	+	0.136784i	$0.956323\pi$
$992$	34.5844	+	27.0463i	1.09805	+	0.858722i
$993$	19.2017	−	19.2017i	0.609347	−	0.609347i
$994$	−7.38988	+	3.27392i	−0.234393	+	0.103842i
$995$	3.02910	+	3.69097i	0.0960289	+	0.117012i
$996$	−4.99581	−	19.9787i	−0.158298	−	0.633050i
$997$	−5.67364	−	1.72108i	−0.179686	−	0.0545072i	0.199159	−	0.979967i	$-0.436179\pi$
$997$	−5.67364	−	1.72108i	−0.179686	−	0.0545072i	−0.378846	+	0.925460i	$0.623679\pi$
$998$	17.7089	−	35.1637i	0.560564	−	1.11309i
$999$	−29.4441	+	44.0662i	−0.931570	+	1.39419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.221.33	✓	1024
128.117	even	32	inner	640.2.bm.a.501.33	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.221.33	✓	1024	1.1	even	1	trivial
640.2.bm.a.501.33	yes	1024	128.117	even	32	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0344201 + 1.41379i) q^{2} +(-1.37377 - 0.135304i) q^{3} +(-1.99763 + 0.0973258i) q^{4} +(-0.471397 - 0.881921i) q^{5} +(0.144007 - 1.94688i) q^{6} +(0.0886862 + 0.445856i) q^{7} +(-0.206357 - 2.82089i) q^{8} +(-1.07343 - 0.213518i) q^{9} +O(q^{10})\)	\(q+(0.0344201 + 1.41379i) q^{2} +(-1.37377 - 0.135304i) q^{3} +(-1.99763 + 0.0973258i) q^{4} +(-0.471397 - 0.881921i) q^{5} +(0.144007 - 1.94688i) q^{6} +(0.0886862 + 0.445856i) q^{7} +(-0.206357 - 2.82089i) q^{8} +(-1.07343 - 0.213518i) q^{9} +(1.23063 - 0.696814i) q^{10} +(1.21482 + 0.996974i) q^{11} +(2.75745 + 0.136585i) q^{12} +(-0.544469 - 0.291025i) q^{13} +(-0.627296 + 0.140730i) q^{14} +(0.528262 + 1.27534i) q^{15} +(3.98106 - 0.388842i) q^{16} +(-0.0852558 + 0.205826i) q^{17} +(0.264923 - 1.52496i) q^{18} +(3.47569 - 1.05434i) q^{19} +(1.02751 + 1.71587i) q^{20} +(-0.0615080 - 0.624501i) q^{21} +(-1.36770 + 1.75182i) q^{22} +(5.94991 - 3.97560i) q^{23} +(-0.0981914 + 3.90317i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(0.392709 - 0.779785i) q^{26} +(5.40867 + 1.64070i) q^{27} +(-0.220555 - 0.882023i) q^{28} +(4.56886 + 5.56718i) q^{29} +(-1.78488 + 0.790751i) q^{30} +(5.48803 - 5.48803i) q^{31} +(0.686771 + 5.61501i) q^{32} +(-1.53398 - 1.53398i) q^{33} +(-0.293930 - 0.113450i) q^{34} +(0.351403 - 0.288389i) q^{35} +(2.16509 + 0.322058i) q^{36} +(-2.72193 + 8.97302i) q^{37} +(1.61025 + 4.87762i) q^{38} +(0.708597 + 0.473469i) q^{39} +(-2.39053 + 1.51175i) q^{40} +(1.41663 + 2.12014i) q^{41} +(0.880799 - 0.108455i) q^{42} +(-3.29543 + 0.324572i) q^{43} +(-2.52378 - 1.87335i) q^{44} +(0.317704 + 1.04733i) q^{45} +(5.82548 + 8.27511i) q^{46} +(-5.84726 - 2.42201i) q^{47} +(-5.52165 - 0.00447526i) q^{48} +(6.27623 - 2.59970i) q^{49} +(-1.19465 - 0.756843i) q^{50} +(0.144971 - 0.271221i) q^{51} +(1.11597 + 0.528369i) q^{52} +(0.560619 - 0.683116i) q^{53} +(-2.13345 + 7.70322i) q^{54} +(0.306592 - 1.54134i) q^{55} +(1.23941 - 0.342179i) q^{56} +(-4.91744 + 0.978140i) q^{57} +(-7.71358 + 6.65106i) q^{58} +(-0.316105 + 0.168961i) q^{59} +(-1.17939 - 2.49624i) q^{60} +(0.281848 - 2.86166i) q^{61} +(7.94784 + 7.57005i) q^{62} -0.497530i q^{63} +(-7.91483 + 1.16422i) q^{64} +0.617367i q^{65} +(2.11593 - 2.22153i) q^{66} +(0.392935 - 3.98954i) q^{67} +(0.150277 - 0.419461i) q^{68} +(-8.71170 + 4.65650i) q^{69} +(0.419818 + 0.486885i) q^{70} +(12.3308 - 2.45275i) q^{71} +(-0.380801 + 3.07208i) q^{72} +(1.09232 - 5.49146i) q^{73} +(-12.7797 - 3.53940i) q^{74} +(0.875725 - 1.06707i) q^{75} +(-6.84053 + 2.44445i) q^{76} +(-0.336769 + 0.630050i) q^{77} +(-0.644999 + 1.01811i) q^{78} +(14.2413 - 5.89893i) q^{79} +(-2.21958 - 3.32768i) q^{80} +(-4.17482 - 1.72927i) q^{81} +(-2.94868 + 2.07580i) q^{82} +(-2.16532 - 7.13812i) q^{83} +(0.183650 + 1.24154i) q^{84} +(0.221711 - 0.0218367i) q^{85} +(-0.572307 - 4.64790i) q^{86} +(-5.52329 - 8.26619i) q^{87} +(2.56167 - 3.63259i) q^{88} +(6.80047 + 4.54393i) q^{89} +(-1.46977 + 0.485218i) q^{90} +(0.0814682 - 0.268565i) q^{91} +(-11.4988 + 8.52086i) q^{92} +(-8.28183 + 6.79672i) q^{93} +(3.22297 - 8.35019i) q^{94} +(-2.56827 - 2.56827i) q^{95} +(-0.183729 - 7.80664i) q^{96} +(3.85381 - 3.85381i) q^{97} +(3.89147 + 8.78383i) q^{98} +(-1.09114 - 1.32956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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