LMFDB - Embedded newform 140.2.o.a.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(31,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("140.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$140 = 2^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	140.o (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	140.31
Dual form			140.2.o.a.131.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26796 - 0.626319i) q^{2} +(-1.49907 + 2.59647i) q^{3} +(1.21545 + 1.58830i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(3.52698 - 2.35332i) q^{6} +(-2.06101 - 1.65899i) q^{7} +(-0.546365 - 2.77516i) q^{8} +(-2.99443 - 5.18651i) q^{9} +(1.41125 - 0.0915727i) q^{10} +(-1.93693 - 1.11828i) q^{11} +(-5.94600 + 0.774910i) q^{12} +3.17109i q^{13} +(1.57423 + 3.39438i) q^{14} -2.99814i q^{15} +(-1.04536 + 3.86099i) q^{16} +(-2.98390 - 1.72275i) q^{17} +(0.548417 + 8.45176i) q^{18} +(1.02618 + 1.77739i) q^{19} +(-1.84676 - 0.767779i) q^{20} +(7.39711 - 2.86441i) q^{21} +(1.75554 + 2.63107i) q^{22} +(-2.30481 + 1.33068i) q^{23} +(8.02464 + 2.74154i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.98611 - 4.02082i) q^{26} +8.96105 q^{27} +(0.129905 - 5.28991i) q^{28} -7.38092 q^{29} +(-1.87779 + 3.80153i) q^{30} +(-2.44599 + 4.23658i) q^{31} +(3.74369 - 4.24085i) q^{32} +(5.80718 - 3.35278i) q^{33} +(2.70447 + 4.05325i) q^{34} +(2.61438 + 0.406219i) q^{35} +(4.59812 - 11.0600i) q^{36} +(5.59689 + 9.69410i) q^{37} +(-0.187940 - 2.89637i) q^{38} +(-8.23364 - 4.75369i) q^{39} +(1.86074 + 2.13017i) q^{40} +1.46011i q^{41} +(-11.1733 - 1.00099i) q^{42} -9.95752i q^{43} +(-0.578071 - 4.43563i) q^{44} +(5.18651 + 2.99443i) q^{45} +(3.75585 - 0.243709i) q^{46} +(3.06343 + 5.30601i) q^{47} +(-8.45786 - 8.50215i) q^{48} +(1.49553 + 6.83838i) q^{49} +(-1.17639 + 0.784927i) q^{50} +(8.94615 - 5.16506i) q^{51} +(-5.03663 + 3.85430i) q^{52} +(-2.32888 + 4.03374i) q^{53} +(-11.3623 - 5.61247i) q^{54} +2.23657 q^{55} +(-3.47788 + 6.62604i) q^{56} -6.15325 q^{57} +(9.35872 + 4.62281i) q^{58} +(-3.55938 + 6.16503i) q^{59} +(4.76194 - 3.64409i) q^{60} +(-2.19681 + 1.26833i) q^{61} +(5.75488 - 3.83985i) q^{62} +(-2.43279 + 15.6572i) q^{63} +(-7.40297 + 3.03249i) q^{64} +(-1.58555 - 2.74625i) q^{65} +(-9.46318 + 0.614046i) q^{66} +(-0.0456998 - 0.0263848i) q^{67} +(-0.890536 - 6.83323i) q^{68} -7.97917i q^{69} +(-3.06051 - 2.15251i) q^{70} -0.212347i q^{71} +(-12.7573 + 11.1437i) q^{72} +(-12.8816 - 7.43720i) q^{73} +(-1.02505 - 15.7972i) q^{74} +(1.49907 + 2.59647i) q^{75} +(-1.57575 + 3.79020i) q^{76} +(2.13680 + 5.51813i) q^{77} +(7.46261 + 11.1844i) q^{78} +(0.399413 - 0.230601i) q^{79} +(-1.02518 - 3.86639i) q^{80} +(-4.44995 + 7.70755i) q^{81} +(0.914496 - 1.85137i) q^{82} +10.9174 q^{83} +(13.5403 + 8.26724i) q^{84} +3.44551 q^{85} +(-6.23658 + 12.6257i) q^{86} +(11.0645 - 19.1643i) q^{87} +(-2.04514 + 5.98626i) q^{88} +(6.07992 - 3.51024i) q^{89} +(-4.70082 - 7.04523i) q^{90} +(5.26080 - 6.53565i) q^{91} +(-4.91490 - 2.04334i) q^{92} +(-7.33344 - 12.7019i) q^{93} +(-0.561053 - 8.64650i) q^{94} +(-1.77739 - 1.02618i) q^{95} +(5.39918 + 16.0777i) q^{96} -0.185459i q^{97} +(2.38673 - 9.60747i) q^{98} +13.3945i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38}+ \cdots + 78 q^{98}+O(q^{100})$ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$ .

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.26796	−	0.626319i	−0.896584	−	0.442874i
$2$	−1.26796	−	0.626319i	−0.896584	−	0.442874i
$3$	−1.49907	+	2.59647i	−0.865490	+	1.49907i	0.00107081	+	0.999999i	$0.499659\pi$
$3$	−1.49907	+	2.59647i	−0.865490	+	1.49907i	−0.866560	+	0.499072i	$0.833674\pi$
$4$	1.21545	+	1.58830i	0.607725	+	0.794148i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	3.52698	−	2.35332i	1.43988	−	0.960741i
$7$	−2.06101	−	1.65899i	−0.778989	−	0.627038i
$7$	−2.06101	−	1.65899i	−0.778989	−	0.627038i
$8$	−0.546365	−	2.77516i	−0.193169	−	0.981165i
$9$	−2.99443	−	5.18651i	−0.998144	−	1.72884i
$10$	1.41125	−	0.0915727i	0.446275	−	0.0289578i
$11$	−1.93693	−	1.11828i	−0.584005	−	0.337175i	0.178718	−	0.983900i	$-0.442805\pi$
$11$	−1.93693	−	1.11828i	−0.584005	−	0.337175i	−0.762723	+	0.646725i	$0.776138\pi$
$12$	−5.94600	+	0.774910i	−1.71646	+	0.223697i
$13$			3.17109i			0.879502i	0.898120	+	0.439751i	$0.144933\pi$
$13$			3.17109i			0.879502i	−0.898120	+	0.439751i	$0.855067\pi$
$14$	1.57423	+	3.39438i	0.420730	+	0.907186i
$15$		−	2.99814i		−	0.774117i
$16$	−1.04536	+	3.86099i	−0.261341	+	0.965247i
$17$	−2.98390	−	1.72275i	−0.723701	−	0.417829i	0.0924124	−	0.995721i	$-0.470542\pi$
$17$	−2.98390	−	1.72275i	−0.723701	−	0.417829i	−0.816113	+	0.577892i	$0.803876\pi$
$18$	0.548417	+	8.45176i	0.129263	+	1.99210i
$19$	1.02618	+	1.77739i	0.235421	+	0.407761i	0.959395	−	0.282066i	$-0.0910198\pi$
$19$	1.02618	+	1.77739i	0.235421	+	0.407761i	−0.723974	+	0.689827i	$0.757686\pi$
$20$	−1.84676	−	0.767779i	−0.412948	−	0.171681i
$21$	7.39711	−	2.86441i	1.61418	−	0.625065i
$22$	1.75554	+	2.63107i	0.374283	+	0.560947i
$23$	−2.30481	+	1.33068i	−0.480587	+	0.277467i	−0.720661	−	0.693288i	$-0.756162\pi$
$23$	−2.30481	+	1.33068i	−0.480587	+	0.277467i	0.240074	+	0.970755i	$0.422828\pi$
$24$	8.02464	+	2.74154i	1.63802	+	0.559614i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.98611	−	4.02082i	0.389509	−	0.788548i
$27$	8.96105			1.72455
$28$	0.129905	−	5.28991i	0.0245497	−	0.999699i
$29$	−7.38092			−1.37060			−0.685301	−	0.728260i	$-0.740329\pi$
$29$	−7.38092			−1.37060			−0.685301	+	0.728260i	$0.740329\pi$
$30$	−1.87779	+	3.80153i	−0.342837	+	0.694061i
$31$	−2.44599	+	4.23658i	−0.439313	+	0.760913i	−0.997637	−	0.0687104i	$-0.978112\pi$
$31$	−2.44599	+	4.23658i	−0.439313	+	0.760913i	0.558323	+	0.829623i	$0.311445\pi$
$32$	3.74369	−	4.24085i	0.661796	−	0.749684i
$33$	5.80718	−	3.35278i	1.01090	−	0.583643i
$34$	2.70447	+	4.05325i	0.463813	+	0.695127i
$35$	2.61438	+	0.406219i	0.441911	+	0.0686636i
$36$	4.59812	−	11.0600i	0.766354	−	1.84333i
$37$	5.59689	+	9.69410i	0.920123	+	1.59370i	0.799222	+	0.601036i	$0.205245\pi$
$37$	5.59689	+	9.69410i	0.920123	+	1.59370i	0.120902	+	0.992664i	$0.461421\pi$
$38$	−0.187940	−	2.89637i	−0.0304878	−	0.469854i
$39$	−8.23364	−	4.75369i	−1.31844	−	0.761200i
$40$	1.86074	+	2.13017i	0.294209	+	0.336810i
$41$			1.46011i			0.228031i	0.993479	+	0.114016i	$0.0363714\pi$
$41$			1.46011i			0.228031i	−0.993479	+	0.114016i	$0.963629\pi$
$42$	−11.1733	−	1.00099i	−1.72407	−	0.154456i
$43$		−	9.95752i		−	1.51851i	−0.650794	−	0.759254i	$-0.725564\pi$
$43$		−	9.95752i		−	1.51851i	0.650794	−	0.759254i	$-0.274436\pi$
$44$	−0.578071	−	4.43563i	−0.0871474	−	0.668696i
$45$	5.18651	+	2.99443i	0.773159	+	0.446384i
$46$	3.75585	−	0.243709i	0.553769	−	0.0359329i
$47$	3.06343	+	5.30601i	0.446847	+	0.773962i	0.998179	−	0.0603243i	$-0.0192135\pi$
$47$	3.06343	+	5.30601i	0.446847	+	0.773962i	−0.551332	+	0.834286i	$0.685880\pi$
$48$	−8.45786	−	8.50215i	−1.22079	−	1.22718i
$49$	1.49553	+	6.83838i	0.213647	+	0.976911i
$50$	−1.17639	+	0.784927i	−0.166366	+	0.111005i
$51$	8.94615	−	5.16506i	1.25271	−	0.723253i
$52$	−5.03663	+	3.85430i	−0.698455	+	0.534496i
$53$	−2.32888	+	4.03374i	−0.319897	+	0.554077i	−0.980466	−	0.196688i	$-0.936982\pi$
$53$	−2.32888	+	4.03374i	−0.319897	+	0.554077i	0.660570	+	0.750765i	$0.270315\pi$
$54$	−11.3623	−	5.61247i	−1.54621	−	0.763760i
$55$	2.23657			0.301579
$56$	−3.47788	+	6.62604i	−0.464751	+	0.885441i
$57$	−6.15325			−0.815018
$58$	9.35872	+	4.62281i	1.22886	+	0.607004i
$59$	−3.55938	+	6.16503i	−0.463392	+	0.802619i	−0.999127	−	0.0417674i	$-0.986701\pi$
$59$	−3.55938	+	6.16503i	−0.463392	+	0.802619i	0.535735	+	0.844386i	$0.320035\pi$
$60$	4.76194	−	3.64409i	0.614763	−	0.470451i
$61$	−2.19681	+	1.26833i	−0.281272	+	0.162393i	−0.633999	−	0.773334i	$-0.718588\pi$
$61$	−2.19681	+	1.26833i	−0.281272	+	0.162393i	0.352727	+	0.935726i	$0.385254\pi$
$62$	5.75488	−	3.83985i	0.730870	−	0.487662i
$63$	−2.43279	+	15.6572i	−0.306503	+	1.97262i
$64$	−7.40297	+	3.03249i	−0.925371	+	0.379062i
$65$	−1.58555	−	2.74625i	−0.196663	−	0.340630i
$66$	−9.46318	+	0.614046i	−1.16484	+	0.0755838i
$67$	−0.0456998	−	0.0263848i	−0.00558311	−	0.00322341i	0.497206	−	0.867633i	$-0.334359\pi$
$67$	−0.0456998	−	0.0263848i	−0.00558311	−	0.00322341i	−0.502789	+	0.864409i	$0.667693\pi$
$68$	−0.890536	−	6.83323i	−0.107993	−	0.828650i
$69$		−	7.97917i		−	0.960579i
$70$	−3.06051	−	2.15251i	−0.365801	−	0.257274i
$71$		−	0.212347i		−	0.0252009i	−0.999921	−	0.0126005i	$-0.995989\pi$
$71$		−	0.212347i		−	0.0252009i	0.999921	−	0.0126005i	$-0.00401095\pi$
$72$	−12.7573	+	11.1437i	−1.50346	+	1.31330i
$73$	−12.8816	−	7.43720i	−1.50768	−	0.870459i	−0.999960	−	0.00893589i	$-0.997156\pi$
$73$	−12.8816	−	7.43720i	−1.50768	−	0.870459i	−0.507719	−	0.861523i	$-0.669511\pi$
$74$	−1.02505	−	15.7972i	−0.119159	−	1.83639i
$75$	1.49907	+	2.59647i	0.173098	+	0.299814i
$76$	−1.57575	+	3.79020i	−0.180751	+	0.434766i
$77$	2.13680	+	5.51813i	0.243511	+	0.628849i
$78$	7.46261	+	11.1844i	0.844974	+	1.26638i
$79$	0.399413	−	0.230601i	0.0449375	−	0.0259447i	−0.477363	−	0.878706i	$-0.658407\pi$
$79$	0.399413	−	0.230601i	0.0449375	−	0.0259447i	0.522300	+	0.852762i	$0.325074\pi$
$80$	−1.02518	−	3.86639i	−0.114619	−	0.432276i
$81$	−4.44995	+	7.70755i	−0.494439	+	0.856394i
$82$	0.914496	−	1.85137i	0.100989	−	0.204449i
$83$	10.9174			1.19834			0.599168	−	0.800624i	$-0.295498\pi$
$83$	10.9174			1.19834			0.599168	+	0.800624i	$0.295498\pi$
$84$	13.5403	+	8.26724i	1.47737	+	0.902030i
$85$	3.44551			0.373718
$86$	−6.23658	+	12.6257i	−0.672508	+	1.36147i
$87$	11.0645	−	19.1643i	1.18624	−	2.05463i
$88$	−2.04514	+	5.98626i	−0.218013	+	0.638137i
$89$	6.07992	−	3.51024i	0.644470	−	0.372085i	−0.141864	−	0.989886i	$-0.545310\pi$
$89$	6.07992	−	3.51024i	0.644470	−	0.372085i	0.786334	+	0.617801i	$0.211976\pi$
$90$	−4.70082	−	7.04523i	−0.495510	−	0.742633i
$91$	5.26080	−	6.53565i	0.551481	−	0.685122i
$92$	−4.91490	−	2.04334i	−0.512414	−	0.213033i
$93$	−7.33344	−	12.7019i	−0.760442	−	1.31712i
$94$	−0.561053	−	8.64650i	−0.0578682	−	0.891819i
$95$	−1.77739	−	1.02618i	−0.182356	−	0.105284i
$96$	5.39918	+	16.0777i	0.551052	+	1.64092i
$97$		−	0.185459i		−	0.0188305i	−0.999956	−	0.00941523i	$-0.997003\pi$
$97$		−	0.185459i		−	0.0188305i	0.999956	−	0.00941523i	$-0.00299701\pi$
$98$	2.38673	−	9.60747i	0.241096	−	0.970501i
$99$			13.3945i			1.34620i
$100$	1.98323	−	0.258463i	0.198323	−	0.0258463i
$101$	−5.41172	−	3.12446i	−0.538486	−	0.310895i	0.205979	−	0.978556i	$-0.433962\pi$
$101$	−5.41172	−	3.12446i	−0.538486	−	0.310895i	−0.744465	+	0.667661i	$0.767295\pi$
$102$	−14.5783	+	0.945957i	−1.44347	+	0.0936637i
$103$	−5.70918	−	9.88858i	−0.562542	−	0.974351i	−0.997274	−	0.0737911i	$-0.976490\pi$
$103$	−5.70918	−	9.88858i	−0.562542	−	0.974351i	0.434732	−	0.900560i	$-0.356843\pi$
$104$	8.80027	−	1.73257i	0.862937	−	0.169893i
$105$	−4.97388	+	6.17921i	−0.485401	+	0.603029i
$106$	5.47934	−	3.65601i	0.532201	−	0.355103i
$107$	2.25502	−	1.30194i	0.218001	−	0.125863i	−0.387023	−	0.922070i	$-0.626497\pi$
$107$	2.25502	−	1.30194i	0.218001	−	0.125863i	0.605024	+	0.796207i	$0.293163\pi$
$108$	10.8917	+	14.2328i	1.04805	+	1.36955i
$109$	−0.500946	+	0.867663i	−0.0479819	+	0.0831071i	−0.889019	−	0.457871i	$-0.848612\pi$
$109$	−0.500946	+	0.867663i	−0.0479819	+	0.0831071i	0.841037	+	0.540978i	$0.181946\pi$
$110$	−2.83588	−	1.40080i	−0.270391	−	0.133561i
$111$	−33.5606			−3.18543
$112$	8.55983	−	6.22329i	0.808828	−	0.588046i
$113$	14.8588			1.39780			0.698899	−	0.715220i	$-0.253674\pi$
$113$	14.8588			1.39780			0.698899	+	0.715220i	$0.253674\pi$
$114$	7.80208	+	3.85389i	0.730732	+	0.360950i
$115$	1.33068	−	2.30481i	0.124087	−	0.214925i
$116$	−8.97114	−	11.7231i	−0.832949	−	1.08846i
$117$	16.4469	−	9.49562i	1.52052	−	0.877870i
$118$	8.37443	−	5.58771i	0.770929	−	0.514391i
$119$	3.29182	+	8.50085i	0.301760	+	0.779272i
$120$	−8.32031	+	1.63808i	−0.759537	+	0.149536i
$121$	−2.99888	−	5.19421i	−0.272626	−	0.472201i
$122$	3.57984	−	0.232288i	0.324104	−	0.0210304i
$123$	−3.79114	−	2.18882i	−0.341836	−	0.197359i
$124$	−9.70193	+	1.26440i	−0.871259	+	0.113546i
$125$			1.00000i			0.0894427i
$126$	12.8911	−	18.3290i	1.14843	−	1.63288i
$127$			3.02360i			0.268301i	0.990961	+	0.134151i	$0.0428306\pi$
$127$			3.02360i			0.268301i	−0.990961	+	0.134151i	$0.957169\pi$
$128$	11.2860	+	0.791535i	0.997550	+	0.0699625i
$129$	25.8544	+	14.9270i	2.27635	+	1.31425i
$130$	0.290385	+	4.47519i	0.0254685	+	0.392500i
$131$	7.85267	+	13.6012i	0.686091	+	1.18834i	0.973093	+	0.230414i	$0.0740081\pi$
$131$	7.85267	+	13.6012i	0.686091	+	1.18834i	−0.287002	+	0.957930i	$0.592659\pi$
$132$	12.3835	+	5.14838i	1.07785	+	0.448109i
$133$	0.833705	−	5.36563i	0.0722914	−	0.465259i
$134$	0.0414202	+	0.0620775i	0.00357816	+	0.00536268i
$135$	−7.76049	+	4.48052i	−0.667917	+	0.385622i
$136$	−3.15061	+	9.22202i	−0.270163	+	0.790782i
$137$	−4.80718	+	8.32628i	−0.410705	+	0.711362i	−0.994967	−	0.100203i	$-0.968051\pi$
$137$	−4.80718	+	8.32628i	−0.410705	+	0.711362i	0.584262	+	0.811565i	$0.301384\pi$
$138$	−4.99750	+	10.1173i	−0.425415	+	0.861239i
$139$	−7.49745			−0.635925			−0.317963	−	0.948103i	$-0.602999\pi$
$139$	−7.49745			−0.635925			−0.317963	+	0.948103i	$0.602999\pi$
$140$	2.53245	+	4.64615i	0.214031	+	0.392671i
$141$	−18.3692			−1.54697
$142$	−0.132997	+	0.269247i	−0.0111608	+	0.0225947i
$143$	3.54618	−	6.14217i	0.296547	−	0.513634i
$144$	23.1553	−	6.13968i	1.92961	−	0.511640i
$145$	6.39206	−	3.69046i	0.530832	−	0.306476i
$146$	11.6753	+	17.4981i	0.966257	+	1.44815i
$147$	−19.9975	−	6.36813i	−1.64937	−	0.525234i
$148$	−8.59435	+	20.6722i	−0.706451	+	1.69925i
$149$	−3.25066	−	5.63031i	−0.266305	−	0.461253i	0.701600	−	0.712571i	$-0.252469\pi$
$149$	−3.25066	−	5.63031i	−0.266305	−	0.461253i	−0.967905	+	0.251318i	$0.919136\pi$
$150$	−0.274548	−	4.23112i	−0.0224168	−	0.345469i
$151$	20.5029	+	11.8373i	1.66850	+	0.963309i	0.968448	+	0.249217i	$0.0801731\pi$
$151$	20.5029	+	11.8373i	1.66850	+	0.963309i	0.700052	+	0.714092i	$0.253160\pi$
$152$	4.37187	−	3.81890i	0.354605	−	0.309754i
$153$			20.6347i			1.66821i
$154$	0.746721	−	8.33509i	0.0601725	−	0.671661i
$155$		−	4.89199i		−	0.392934i
$156$	−2.45731	−	18.8553i	−0.196742	−	1.50963i
$157$	6.78313	+	3.91624i	0.541353	+	0.312550i	0.745627	−	0.666363i	$-0.232150\pi$
$157$	6.78313	+	3.91624i	0.541353	+	0.312550i	−0.204274	+	0.978914i	$0.565483\pi$
$158$	−0.650870	+	0.0422336i	−0.0517805	+	0.00335992i
$159$	−6.98233	−	12.0937i	−0.553734	−	0.959096i
$160$	−1.12170	+	5.54453i	−0.0886783	+	0.438333i
$161$	6.95783	+	1.08110i	0.548354	+	0.0852026i
$162$	10.4697	−	6.98578i	0.822581	−	0.548855i
$163$	−9.39774	+	5.42579i	−0.736088	+	0.424980i	−0.820645	−	0.571438i	$-0.806386\pi$
$163$	−9.39774	+	5.42579i	−0.736088	+	0.424980i	0.0845574	+	0.996419i	$0.473052\pi$
$164$	−2.31909	+	1.77470i	−0.181091	+	0.138580i
$165$	−3.35278	+	5.80718i	−0.261013	+	0.452088i
$166$	−13.8428	−	6.83774i	−1.07441	−	0.530712i
$167$	−11.7476			−0.909058			−0.454529	−	0.890732i	$-0.650192\pi$
$167$	−11.7476			−0.909058			−0.454529	+	0.890732i	$0.650192\pi$
$168$	−11.9907	−	18.9631i	−0.925102	−	1.46304i
$169$	2.94418			0.226476
$170$	−4.36877	−	2.15798i	−0.335069	−	0.165510i
$171$	6.14563	−	10.6445i	0.469968	−	0.814009i
$172$	15.8155	−	12.1029i	1.20592	−	0.922835i
$173$	−14.2785	+	8.24371i	−1.08558	+	0.626758i	−0.932395	−	0.361440i	$-0.882285\pi$
$173$	−14.2785	+	8.24371i	−1.08558	+	0.626758i	−0.153181	+	0.988198i	$0.548952\pi$
$174$	−26.0324	+	17.3697i	−1.97351	+	1.31679i
$175$	−2.46723	+	0.955394i	−0.186505	+	0.0722210i
$176$	6.34247	−	6.30943i	0.478082	−	0.475591i
$177$	−10.6715	−	18.4836i	−0.802122	−	1.38932i
$178$	−9.90763	+	0.642885i	−0.742608	+	0.0481863i
$179$	−7.88914	−	4.55480i	−0.589662	−	0.340441i	0.175302	−	0.984515i	$-0.443910\pi$
$179$	−7.88914	−	4.55480i	−0.589662	−	0.340441i	−0.764964	+	0.644073i	$0.777243\pi$
$180$	1.54790	+	11.8773i	0.115374	+	0.885281i
$181$		−	16.5755i		−	1.23205i	−0.787728	−	0.616023i	$-0.788743\pi$
$181$		−	16.5755i		−	1.23205i	0.787728	−	0.616023i	$-0.211257\pi$
$182$	−10.7639	+	4.99202i	−0.797872	+	0.370033i
$183$		−	7.60525i		−	0.562196i
$184$	4.95212	+	5.66917i	0.365075	+	0.417937i
$185$	−9.69410	−	5.59689i	−0.712725	−	0.411492i
$186$	1.34309	+	20.6986i	0.0984798	+	1.51769i
$187$	3.85305	+	6.67369i	0.281763	+	0.488028i
$188$	−4.70407	+	11.3148i	−0.343080	+	0.825218i
$189$	−18.4688	−	14.8663i	−1.34341	−	1.08136i
$190$	1.61095	+	2.41436i	0.116870	+	0.175156i
$191$	−2.59197	+	1.49648i	−0.187549	+	0.108281i	−0.590834	−	0.806793i	$-0.701201\pi$
$191$	−2.59197	+	1.49648i	−0.187549	+	0.108281i	0.403286	+	0.915074i	$0.367868\pi$
$192$	3.22381	−	23.7675i	0.232659	−	1.71527i
$193$	7.35442	−	12.7382i	0.529383	−	0.916918i	−0.470030	−	0.882651i	$-0.655757\pi$
$193$	7.35442	−	12.7382i	0.529383	−	0.916918i	0.999413	−	0.0342676i	$-0.0109098\pi$
$194$	−0.116156	+	0.235154i	−0.00833953	+	0.0168831i
$195$	9.50739			0.680838
$196$	−9.04362	+	10.6870i	−0.645973	+	0.763360i
$197$	4.81748			0.343231			0.171616	−	0.985164i	$-0.445101\pi$
$197$	4.81748			0.343231			0.171616	+	0.985164i	$0.445101\pi$
$198$	8.38923	−	16.9837i	0.596196	−	1.20698i
$199$	−0.637180	+	1.10363i	−0.0451685	+	0.0782342i	−0.887726	−	0.460373i	$-0.847716\pi$
$199$	−0.637180	+	1.10363i	−0.0451685	+	0.0782342i	0.842557	+	0.538607i	$0.181049\pi$
$200$	−2.67654	−	0.914412i	−0.189260	−	0.0646587i
$201$	0.137014	−	0.0791053i	0.00966425	−	0.00557966i
$202$	4.90494	+	7.35115i	0.345110	+	0.517225i
$203$	15.2122	+	12.2448i	1.06768	+	0.859420i
$204$	19.0772	+	7.93125i	1.33567	+	0.555298i
$205$	−0.730057	−	1.26450i	−0.0509894	−	0.0883162i
$206$	1.04561	+	16.1141i	0.0728511	+	1.12272i
$207$	13.8032	+	7.96929i	0.959390	+	0.553904i
$208$	−12.2435	−	3.31494i	−0.848937	−	0.229850i
$209$		−	4.59023i		−	0.317513i
$210$	10.1768	−	4.71976i	0.702268	−	0.325694i
$211$			3.70986i			0.255397i	0.991813	+	0.127698i	$0.0407590\pi$
$211$			3.70986i			0.255397i	−0.991813	+	0.127698i	$0.959241\pi$
$212$	−9.23742	+	1.20386i	−0.634428	+	0.0826815i
$213$	0.551351	+	0.318323i	0.0377780	+	0.0218111i
$214$	−3.67471	+	0.238444i	−0.251198	+	0.0162997i
$215$	4.97876	+	8.62347i	0.339549	+	0.588116i
$216$	−4.89600	−	24.8683i	−0.333131	−	1.69207i
$217$	12.0697	−	4.67378i	0.819342	−	0.317277i
$218$	1.17861	−	0.786412i	0.0798258	−	0.0532625i
$219$	38.6209	−	22.2978i	2.60976	−	1.50675i
$220$	2.71844	+	3.55233i	0.183277	+	0.239498i
$221$	5.46301	−	9.46220i	0.367482	−	0.636497i
$222$	42.5535	+	21.0196i	2.85600	+	1.41074i
$223$	−12.9581			−0.867737			−0.433869	−	0.900976i	$-0.642852\pi$
$223$	−12.9581			−0.867737			−0.433869	+	0.900976i	$0.642852\pi$
$224$	−14.7513	+	2.52971i	−0.985612	+	0.169024i
$225$	−5.98886			−0.399258
$226$	−18.8404	−	9.30634i	−1.25324	−	0.619049i
$227$	−4.44626	+	7.70115i	−0.295109	+	0.511143i	−0.975010	−	0.222160i	$-0.928689\pi$
$227$	−4.44626	+	7.70115i	−0.295109	+	0.511143i	0.679901	+	0.733304i	$0.262023\pi$
$228$	−7.47897	−	9.77318i	−0.495307	−	0.647244i
$229$	−11.2113	+	6.47287i	−0.740866	+	0.427739i	−0.822384	−	0.568933i	$-0.807357\pi$
$229$	−11.2113	+	6.47287i	−0.740866	+	0.427739i	0.0815180	+	0.996672i	$0.474023\pi$
$230$	−3.13080	+	2.08898i	−0.206439	+	0.137743i
$231$	−17.5309	−	2.72392i	−1.15345	−	0.179221i
$232$	4.03267	+	20.4832i	0.264758	+	1.34479i
$233$	7.60809	+	13.1776i	0.498423	+	0.863294i	0.999998	−	0.00182020i	$-0.000579387\pi$
$233$	7.60809	+	13.1776i	0.498423	+	0.863294i	−0.501576	+	0.865114i	$0.667246\pi$
$234$	−26.8013	+	1.73908i	−1.75206	+	0.113687i
$235$	−5.30601	−	3.06343i	−0.346126	−	0.199836i
$236$	−14.1181	+	1.83994i	−0.919013	+	0.119770i
$237$			1.38275i			0.0898194i
$238$	1.15035	−	12.8405i	0.0745660	−	0.832324i
$239$		−	0.0438513i		−	0.00283650i	−0.999999	−	0.00141825i	$-0.999549\pi$
$239$		−	0.0438513i		−	0.00283650i	0.999999	−	0.00141825i	$-0.000451444\pi$
$240$	11.5758	+	3.13415i	0.747214	+	0.202308i
$241$	1.99236	+	1.15029i	0.128339	+	0.0740968i	0.562795	−	0.826596i	$-0.309726\pi$
$241$	1.99236	+	1.15029i	0.128339	+	0.0740968i	−0.434456	+	0.900693i	$0.643059\pi$
$242$	0.549231	+	8.46432i	0.0353059	+	0.544107i
$243$	0.0999675	+	0.173149i	0.00641292	+	0.0111075i
$244$	−4.68458	−	1.94759i	−0.299900	−	0.124682i
$245$	−4.71435	−	5.17444i	−0.301189	−	0.330583i
$246$	3.43612	+	5.14979i	0.219079	+	0.328339i
$247$	−5.63627	+	3.25410i	−0.358627	+	0.207053i
$248$	13.0936	+	4.47329i	0.831443	+	0.284054i
$249$	−16.3659	+	28.3466i	−1.03715	+	1.79639i
$250$	0.626319	−	1.26796i	0.0396119	−	0.0801929i
$251$	6.32409			0.399173			0.199587	−	0.979880i	$-0.436040\pi$
$251$	6.32409			0.399173			0.199587	+	0.979880i	$0.436040\pi$
$252$	−27.8251	+	15.1665i	−1.75282	+	0.955401i
$253$	5.95233			0.374220
$254$	1.89374	−	3.83381i	0.118824	−	0.240554i
$255$	−5.16506	+	8.94615i	−0.323449	+	0.560229i
$256$	−13.8144	−	8.07226i	−0.863402	−	0.504516i
$257$	−12.3334	+	7.12068i	−0.769335	+	0.444176i	−0.832637	−	0.553819i	$-0.813170\pi$
$257$	−12.3334	+	7.12068i	−0.769335	+	0.444176i	0.0633025	+	0.997994i	$0.479837\pi$
$258$	−23.4333	−	35.1200i	−1.45889	−	2.18648i
$259$	4.54713	−	29.2648i	0.282545	−	1.81843i
$260$	2.43470	−	5.85624i	0.150993	−	0.363188i
$261$	22.1017	+	38.2812i	1.36806	+	2.36955i
$262$	−1.43818	−	22.1641i	−0.0888511	−	1.36930i
$263$	10.1744	+	5.87421i	0.627382	+	0.362219i	0.779738	−	0.626107i	$-0.215353\pi$
$263$	10.1744	+	5.87421i	0.627382	+	0.362219i	−0.152355	+	0.988326i	$0.548686\pi$
$264$	−12.4773	−	14.2840i	−0.767925	−	0.879118i
$265$		−	4.65777i		−	0.286124i
$266$	−4.41770	+	6.28125i	−0.270867	+	0.385128i
$267$			21.0484i			1.28814i
$268$	−0.0136390	−	0.104654i	−0.000833133	−	0.00639276i
$269$	−7.35196	−	4.24466i	−0.448257	−	0.258801i	0.258837	−	0.965921i	$-0.416661\pi$
$269$	−7.35196	−	4.24466i	−0.448257	−	0.258801i	−0.707094	+	0.707120i	$0.749994\pi$
$270$	12.6462	−	0.820587i	0.769626	−	0.0499393i
$271$	−3.98686	−	6.90544i	−0.242184	−	0.419476i	0.719152	−	0.694853i	$-0.244531\pi$
$271$	−3.98686	−	6.90544i	−0.242184	−	0.419476i	−0.961336	+	0.275377i	$0.911197\pi$
$272$	9.77078	−	9.71988i	0.592440	−	0.589354i
$273$	9.08330	+	23.4569i	0.549746	+	1.41968i
$274$	11.3102	−	7.54657i	0.683275	−	0.455905i
$275$	−1.93693	+	1.11828i	−0.116801	+	0.0674351i
$276$	12.6733	−	9.69828i	0.762841	−	0.583768i
$277$	6.79754	−	11.7737i	0.408425	−	0.707412i	−0.586289	−	0.810102i	$-0.699412\pi$
$277$	6.79754	−	11.7737i	0.408425	−	0.707412i	0.994713	+	0.102690i	$0.0327449\pi$
$278$	9.50647	+	4.69579i	0.570160	+	0.281635i
$279$	29.2974			1.75399
$280$	−0.301084	−	7.47726i	−0.0179932	−	0.446851i
$281$	9.48286			0.565700			0.282850	−	0.959164i	$-0.408720\pi$
$281$	9.48286			0.565700			0.282850	+	0.959164i	$0.408720\pi$
$282$	23.2914	+	11.5050i	1.38698	+	0.685111i
$283$	−10.7746	+	18.6621i	−0.640483	+	1.10935i	0.344842	+	0.938661i	$0.387933\pi$
$283$	−10.7746	+	18.6621i	−0.640483	+	1.10935i	−0.985325	+	0.170689i	$0.945401\pi$
$284$	0.337269	−	0.258097i	0.0200132	−	0.0153152i
$285$	5.32887	−	3.07662i	0.315655	−	0.182244i
$286$	−8.34337	+	5.56699i	−0.493354	+	0.329183i
$287$	2.42231	−	3.00931i	0.142984	−	0.177634i
$288$	−33.2054	−	6.71772i	−1.95665	−	0.395845i
$289$	−2.56424	−	4.44140i	−0.150838	−	0.261259i
$290$	−10.4163	+	0.675891i	−0.611666	+	0.0396897i
$291$	0.481537	+	0.278016i	0.0282282	+	0.0162976i
$292$	−3.84449	−	29.4994i	−0.224982	−	1.72632i
$293$			28.9496i			1.69125i	0.533776	+	0.845626i	$0.320773\pi$
$293$			28.9496i			1.69125i	−0.533776	+	0.845626i	$0.679227\pi$
$294$	21.3676	+	20.5994i	1.24618	+	1.20138i
$295$		−	7.11876i		−	0.414470i
$296$	23.8447	−	20.8288i	1.38594	−	1.21065i
$297$	−17.3569	−	10.0210i	−1.00715	−	0.581477i
$298$	0.595344	+	9.17496i	0.0344873	+	0.531491i
$299$	−4.21972	−	7.30877i	−0.244033	−	0.422677i
$300$	−2.30191	+	5.53685i	−0.132901	+	0.319670i
$301$	−16.5194	+	20.5226i	−0.952162	+	1.18290i
$302$	−18.5829	−	27.8506i	−1.06933	−	1.60262i
$303$	16.2251	−	9.36757i	0.932108	−	0.538153i
$304$	−7.93521	+	2.10404i	−0.455115	+	0.120675i
$305$	1.26833	−	2.19681i	0.0726242	−	0.125789i
$306$	12.9239	−	26.1640i	0.738809	−	1.49569i
$307$	−8.00589			−0.456920			−0.228460	−	0.973553i	$-0.573369\pi$
$307$	−8.00589			−0.456920			−0.228460	+	0.973553i	$0.573369\pi$
$308$	−6.16724	+	10.1009i	−0.351411	+	0.575551i
$309$	34.2339			1.94750
$310$	−3.06394	+	6.20285i	−0.174020	+	0.352298i
$311$	6.87633	−	11.9101i	0.389921	−	0.675363i	−0.602518	−	0.798105i	$-0.705836\pi$
$311$	6.87633	−	11.9101i	0.389921	−	0.675363i	0.992438	+	0.122743i	$0.0391691\pi$
$312$	−8.69367	+	25.4469i	−0.492182	+	1.44065i
$313$	9.21091	−	5.31792i	0.520631	−	0.300587i	−0.216562	−	0.976269i	$-0.569484\pi$
$313$	9.21091	−	5.31792i	0.520631	−	0.300587i	0.737193	+	0.675682i	$0.236151\pi$
$314$	−6.14793	−	9.21404i	−0.346948	−	0.519979i
$315$	−5.72173	−	14.7759i	−0.322383	−	0.832528i
$316$	0.851730	+	0.354102i	0.0479136	+	0.0199198i
$317$	8.49175	+	14.7081i	0.476944	+	0.826091i	0.999651	−	0.0264211i	$-0.00841107\pi$
$317$	8.49175	+	14.7081i	0.476944	+	0.826091i	−0.522707	+	0.852513i	$0.675078\pi$
$318$	1.27878	+	19.7076i	0.0717105	+	1.10514i
$319$	14.2963	+	8.25397i	0.800439	+	0.462133i
$320$	4.89491	−	6.32770i	0.273634	−	0.353729i
$321$			7.80679i			0.435732i
$322$	−8.14515	−	5.72861i	−0.453911	−	0.319243i
$323$		−	7.07140i		−	0.393463i
$324$	−17.6506	+	2.30030i	−0.980586	+	0.127794i
$325$	2.74625	+	1.58555i	0.152334	+	0.0879502i
$326$	15.3142	−	0.993708i	0.848177	−	0.0550364i
$327$	−1.50191	−	2.60138i	−0.0830557	−	0.143857i
$328$	4.05204	−	0.797755i	0.223737	−	0.0440486i
$329$	2.48885	−	16.0179i	0.137215	−	0.883097i
$330$	7.88833	−	5.26337i	0.434239	−	0.289739i
$331$	7.21415	−	4.16509i	0.396525	−	0.228934i	−0.288458	−	0.957492i	$-0.593143\pi$
$331$	7.21415	−	4.16509i	0.396525	−	0.228934i	0.684984	+	0.728558i	$0.259809\pi$
$332$	13.2695	+	17.3400i	0.728258	+	0.951655i
$333$	33.5190	−	58.0567i	1.83683	−	3.18149i
$334$	14.8955	+	7.35775i	0.815046	+	0.402598i
$335$	0.0527695			0.00288311
$336$	3.32679	+	31.5545i	0.181491	+	1.72144i
$337$	−27.0772			−1.47499			−0.737495	−	0.675353i	$-0.763991\pi$
$337$	−27.0772			−1.47499			−0.737495	+	0.675353i	$0.763991\pi$
$338$	−3.73311	−	1.84400i	−0.203054	−	0.100300i
$339$	−22.2744	+	38.5804i	−1.20978	+	2.09540i
$340$	4.18784	+	5.47248i	0.227118	+	0.296787i
$341$	9.47541	−	5.47063i	0.513122	−	0.296251i
$342$	−14.4593	+	9.64775i	−0.781870	+	0.521690i
$343$	8.26248	−	16.5750i	0.446132	−	0.894967i
$344$	−27.6337	+	5.44044i	−1.48991	+	0.293329i
$345$	3.98958	+	6.91016i	0.214792	+	0.372031i
$346$	23.2678	−	1.50980i	1.25089	−	0.0811672i
$347$	−24.0514	−	13.8861i	−1.29115	−	0.745443i	−0.312288	−	0.949987i	$-0.601095\pi$
$347$	−24.0514	−	13.8861i	−1.29115	−	0.745443i	−0.978857	+	0.204544i	$0.934429\pi$
$348$	43.8870	−	5.71955i	2.35259	−	0.306600i
$349$			9.64063i			0.516051i	0.966138	+	0.258026i	$0.0830719\pi$
$349$			9.64063i			0.516051i	−0.966138	+	0.258026i	$0.916928\pi$
$350$	3.72673	+	0.333869i	0.199202	+	0.0178461i
$351$			28.4163i			1.51675i
$352$	−11.9937	+	4.02771i	−0.639267	+	0.214677i
$353$	−14.1283	−	8.15697i	−0.751973	−	0.434152i	0.0744333	−	0.997226i	$-0.476285\pi$
$353$	−14.1283	−	8.15697i	−0.751973	−	0.434152i	−0.826406	+	0.563074i	$0.809619\pi$
$354$	1.95444	+	30.1203i	0.103877	+	1.60088i
$355$	0.106173	+	0.183898i	0.00563509	+	0.00976027i
$356$	12.9651	+	5.39018i	0.687151	+	0.285679i
$357$	−27.0069	−	4.19629i	−1.42936	−	0.222091i
$358$	7.15037	+	10.7164i	0.377909	+	0.566380i
$359$	1.38744	−	0.801040i	0.0732264	−	0.0422773i	−0.462940	−	0.886390i	$-0.653205\pi$
$359$	1.38744	−	0.801040i	0.0732264	−	0.0422773i	0.536166	+	0.844112i	$0.319872\pi$
$360$	5.47629	−	16.0294i	0.288626	−	0.844825i
$361$	7.39392	−	12.8067i	0.389154	−	0.674034i
$362$	−10.3815	+	21.0171i	−0.545642	+	1.10463i
$363$	17.9822			0.943818
$364$	16.7748	+	0.411939i	0.879237	+	0.0215915i
$365$	14.8744			0.778562
$366$	−4.76331	+	9.64316i	−0.248982	+	0.504056i
$367$	−0.630259	+	1.09164i	−0.0328993	+	0.0569832i	−0.882006	−	0.471238i	$-0.843807\pi$
$367$	−0.630259	+	1.09164i	−0.0328993	+	0.0569832i	0.849107	+	0.528221i	$0.177141\pi$
$368$	−2.72839	−	10.2899i	−0.142227	−	0.536398i
$369$	7.57289	−	4.37221i	0.394229	−	0.227608i
$370$	8.78631	+	13.1682i	0.456778	+	0.684584i
$371$	11.4918	−	4.45000i	0.596623	−	0.231033i
$372$	11.2609	−	27.0862i	0.583851	−	1.40435i
$373$	−4.61372	−	7.99120i	−0.238889	−	0.413768i	0.721507	−	0.692408i	$-0.243450\pi$
$373$	−4.61372	−	7.99120i	−0.238889	−	0.413768i	−0.960396	+	0.278639i	$0.910117\pi$
$374$	−0.705669	−	10.8752i	−0.0364893	−	0.562344i
$375$	−2.59647	−	1.49907i	−0.134081	−	0.0774117i
$376$	13.0513	−	11.4005i	0.673068	−	0.587936i
$377$		−	23.4056i		−	1.20545i
$378$	14.1067	+	30.4172i	0.725571	+	1.56449i
$379$			2.53516i			0.130223i	0.997878	+	0.0651113i	$0.0207403\pi$
$379$			2.53516i			0.130223i	−0.997878	+	0.0651113i	$0.979260\pi$
$380$	−0.530458	−	4.07029i	−0.0272119	−	0.208801i
$381$	−7.85068	−	4.53259i	−0.402203	−	0.232212i
$382$	4.22379	−	0.274073i	0.216108	−	0.0140228i
$383$	−0.662435	−	1.14737i	−0.0338489	−	0.0586279i	0.848605	−	0.529027i	$-0.177443\pi$
$383$	−0.662435	−	1.14737i	−0.0338489	−	0.0586279i	−0.882454	+	0.470400i	$0.844110\pi$
$384$	−18.9737	+	28.1171i	−0.968248	+	1.43485i
$385$	−4.60959	−	3.71044i	−0.234926	−	0.189101i
$386$	−17.3033	+	11.5454i	−0.880715	+	0.587644i
$387$	−51.6448	+	29.8171i	−2.62525	+	1.51569i
$388$	0.294563	−	0.225416i	0.0149542	−	0.0114437i
$389$	−16.1134	+	27.9093i	−0.816983	+	1.41506i	0.0909120	+	0.995859i	$0.471022\pi$
$389$	−16.1134	+	27.9093i	−0.816983	+	1.41506i	−0.907895	+	0.419197i	$0.862312\pi$
$390$	−12.0550	−	5.95465i	−0.610428	−	0.301526i
$391$	9.16976			0.463735
$392$	18.1605	−	7.88657i	0.917241	−	0.398332i
$393$	−47.0869			−2.37522
$394$	−6.10838	−	3.01728i	−0.307736	−	0.152008i
$395$	−0.230601	+	0.399413i	−0.0116028	+	0.0200967i
$396$	−21.2744	+	16.2804i	−1.06908	+	0.818119i
$397$	−30.4617	+	17.5871i	−1.52883	+	0.882670i	−0.529419	+	0.848361i	$0.677590\pi$
$397$	−30.4617	+	17.5871i	−1.52883	+	0.882670i	−0.999411	+	0.0343095i	$0.989077\pi$
$398$	1.49914	−	1.00028i	0.0751452	−	0.0501395i
$399$	12.6819	+	10.2082i	0.634890	+	0.511047i
$400$	2.82103	+	2.83580i	0.141052	+	0.141790i
$401$	−15.9623	−	27.6476i	−0.797120	−	1.38065i	−0.921484	−	0.388416i	$-0.873022\pi$
$401$	−15.9623	−	27.6476i	−0.797120	−	1.38065i	0.124364	−	0.992237i	$-0.460311\pi$
$402$	−0.223274	+	0.0144878i	−0.0111359	+	0.000722585i
$403$	−13.4346	−	7.75647i	−0.669225	−	0.386377i
$404$	−1.61511	−	12.3930i	−0.0803549	−	0.616576i
$405$		−	8.89991i		−	0.442240i
$406$	−11.6192	−	25.0536i	−0.576653	−	1.24339i
$407$		−	25.0357i		−	1.24097i
$408$	−19.2217	−	22.0049i	−0.951616	−	1.08941i
$409$	14.2151	+	8.20712i	0.702894	+	0.405816i	0.808424	−	0.588600i	$-0.200321\pi$
$409$	14.2151	+	8.20712i	0.702894	+	0.405816i	−0.105530	+	0.994416i	$0.533654\pi$
$410$	0.133707	+	2.06058i	0.00660330	+	0.101765i
$411$	−14.4126	−	24.9634i	−0.710922	−	1.23135i
$412$	8.76677	−	21.0869i	0.431908	−	1.03888i
$413$	17.5636	−	6.80123i	0.864250	−	0.334666i
$414$	−12.5106	−	18.7500i	−0.614864	−	0.921510i
$415$	−9.45470	+	5.45868i	−0.464113	+	0.267956i
$416$	13.4481	+	11.8716i	0.659349	+	0.582052i
$417$	11.2392	−	19.4669i	0.550387	−	0.953298i
$418$	−2.87495	+	5.82023i	−0.140618	+	0.284677i
$419$	−11.8654			−0.579665			−0.289832	−	0.957077i	$-0.593600\pi$
$419$	−11.8654			−0.579665			−0.289832	+	0.957077i	$0.593600\pi$
$420$	−15.8599	−	0.389473i	−0.773884	−	0.0190043i
$421$	10.3433			0.504101			0.252051	−	0.967714i	$-0.418895\pi$
$421$	10.3433			0.504101			0.252051	+	0.967714i	$0.418895\pi$
$422$	2.32355	−	4.70395i	0.113109	−	0.228985i
$423$	18.3465	−	31.7770i	0.892035	−	1.54505i
$424$	12.4667	+	4.25912i	0.605436	+	0.206841i
$425$	−2.98390	+	1.72275i	−0.144740	+	0.0835658i
$426$	−0.499720	−	0.748942i	−0.0242115	−	0.0362864i
$427$	6.63178	+	1.03044i	0.320934	+	0.0498663i
$428$	4.80873	+	1.99920i	0.232439	+	0.0966349i
$429$	10.6320	+	18.4151i	0.513316	+	0.889089i
$430$	−0.911837	−	14.0525i	−0.0439727	−	0.677672i
$431$	−25.6838	−	14.8286i	−1.23715	−	0.714267i	−0.268636	−	0.963242i	$-0.586573\pi$
$431$	−25.6838	−	14.8286i	−1.23715	−	0.714267i	−0.968510	+	0.248975i	$0.919906\pi$
$432$	−9.36754	+	34.5985i	−0.450696	+	1.66462i
$433$		−	29.4107i		−	1.41339i	−0.707520	−	0.706693i	$-0.750186\pi$
$433$		−	29.4107i		−	1.41339i	0.707520	−	0.706693i	$-0.249814\pi$
$434$	−18.2311	−	1.63328i	−0.875122	−	0.0784001i
$435$			22.1291i			1.06101i
$436$	−1.98698	+	0.258952i	−0.0951591	+	0.0124016i
$437$	−4.73029	−	2.73103i	−0.226280	−	0.130643i
$438$	−62.9354	+	4.08374i	−3.00717	+	0.195129i
$439$	4.41191	+	7.64165i	0.210569	+	0.364716i	0.951893	−	0.306432i	$-0.0991351\pi$
$439$	4.41191	+	7.64165i	0.210569	+	0.364716i	−0.741324	+	0.671147i	$0.765802\pi$
$440$	−1.22198	−	6.20682i	−0.0582557	−	0.295899i
$441$	30.9890	−	28.2336i	1.47567	−	1.34446i
$442$	−12.8532	+	8.57612i	−0.611366	+	0.407925i
$443$	−16.9454	+	9.78342i	−0.805099	+	0.464824i	−0.845251	−	0.534369i	$-0.820549\pi$
$443$	−16.9454	+	9.78342i	−0.805099	+	0.464824i	0.0401518	+	0.999194i	$0.487216\pi$
$444$	−40.7912	−	53.3041i	−1.93586	−	2.52970i
$445$	−3.51024	+	6.07992i	−0.166402	+	0.288216i
$446$	16.4303	+	8.11589i	0.777999	+	0.384298i
$447$	19.4919			0.921935
$448$	20.2885	+	6.03143i	0.958540	+	0.284958i
$449$	5.02309			0.237054			0.118527	−	0.992951i	$-0.462183\pi$
$449$	5.02309			0.237054			0.118527	+	0.992951i	$0.462183\pi$
$450$	7.59365	+	3.75094i	0.357968	+	0.176821i
$451$	1.63282	−	2.82813i	0.0768866	−	0.133171i
$452$	18.0601	+	23.6002i	0.849477	+	1.11006i
$453$	−61.4705	+	35.4900i	−2.88814	+	1.66747i
$454$	10.4611	−	6.97998i	0.490962	−	0.327587i
$455$	−1.28816	+	8.29044i	−0.0603898	+	0.388662i
$456$	3.36192	+	17.0762i	0.157436	+	0.799667i
$457$	13.9225	+	24.1144i	0.651265	+	1.12802i	0.982816	+	0.184587i	$0.0590946\pi$
$457$	13.9225	+	24.1144i	0.651265	+	1.12802i	−0.331551	+	0.943437i	$0.607572\pi$
$458$	18.2696	−	1.18548i	0.853683	−	0.0553937i
$459$	−26.7388	−	15.4377i	−1.24806	−	0.720569i
$460$	5.27810	−	0.687866i	0.246093	−	0.0320719i
$461$			19.8494i			0.924481i	0.886755	+	0.462240i	$0.152954\pi$
$461$			19.8494i			0.924481i	−0.886755	+	0.462240i	$0.847046\pi$
$462$	20.5224	+	14.4337i	0.954789	+	0.671518i
$463$			35.7118i			1.65967i	0.558012	+	0.829833i	$0.311564\pi$
$463$			35.7118i			1.65967i	−0.558012	+	0.829833i	$0.688436\pi$
$464$	7.71573	−	28.4976i	0.358194	−	1.32297i
$465$	12.7019	+	7.33344i	0.589036	+	0.340080i
$466$	−1.39339	−	21.4738i	−0.0645474	−	0.994754i
$467$	11.3055	+	19.5818i	0.523158	+	0.906136i	0.999637	+	0.0269503i	$0.00857959\pi$
$467$	11.3055	+	19.5818i	0.523158	+	0.906136i	−0.476479	+	0.879186i	$0.658087\pi$
$468$	35.0722	+	14.5811i	1.62121	+	0.674010i
$469$	0.0504157	+	0.130195i	0.00232798	+	0.00601183i
$470$	4.80914	+	7.20756i	0.221829	+	0.332460i
$471$	−20.3368	+	11.7415i	−0.937070	+	0.541018i
$472$	19.0536	+	6.50948i	0.877015	+	0.299623i
$473$	−11.1353	+	19.2870i	−0.512003	+	0.886816i
$474$	0.866043	−	1.75328i	0.0397787	−	0.0805306i
$475$	2.05235			0.0941684
$476$	−9.50083	+	15.5607i	−0.435470	+	0.713225i
$477$	27.8947			1.27721
$478$	−0.0274649	+	0.0556017i	−0.00125621	+	0.00254316i
$479$	−4.28200	+	7.41664i	−0.195649	+	0.338875i	−0.947113	−	0.320900i	$-0.896015\pi$
$479$	−4.28200	+	7.41664i	−0.195649	+	0.338875i	0.751464	+	0.659774i	$0.229348\pi$
$480$	−12.7147	−	11.2241i	−0.580343	−	0.512308i
$481$	−30.7409	+	17.7483i	−1.40166	+	0.809251i
$482$	−1.80579	−	2.70638i	−0.0822515	−	0.123272i
$483$	−13.2373	+	16.4451i	−0.602319	+	0.748280i
$484$	4.60495	−	11.0764i	0.209316	−	0.503473i
$485$	0.0927293	+	0.160612i	0.00421062	+	0.00729301i
$486$	−0.0183086	−	0.282157i	−0.000830494	−	0.0127989i
$487$	27.4054	+	15.8225i	1.24186	+	0.716987i	0.969472	−	0.245201i	$-0.0788539\pi$
$487$	27.4054	+	15.8225i	1.24186	+	0.716987i	0.272386	+	0.962188i	$0.412187\pi$
$488$	4.72006	+	5.40351i	0.213667	+	0.244605i
$489$		−	32.5346i		−	1.47126i
$490$	2.73677	+	9.51368i	0.123634	+	0.429784i
$491$		−	35.7781i		−	1.61464i	−0.590113	−	0.807321i	$-0.700917\pi$
$491$		−	35.7781i		−	1.61464i	0.590113	−	0.807321i	$-0.299083\pi$
$492$	−1.13146	−	8.68184i	−0.0510100	−	0.391408i
$493$	22.0239	+	12.7155i	0.991906	+	0.572677i
$494$	9.18467	−	0.595973i	0.413238	−	0.0268141i
$495$	−6.69725	−	11.6000i	−0.301019	−	0.521380i
$496$	−13.8004	−	13.8727i	−0.619658	−	0.622903i
$497$	−0.352280	+	0.437649i	−0.0158019	+	0.0196312i
$498$	38.5053	−	25.6921i	1.72546	−	1.15129i
$499$	−35.7797	+	20.6574i	−1.60172	+	0.924752i	−0.610574	+	0.791959i	$0.709061\pi$
$499$	−35.7797	+	20.6574i	−1.60172	+	0.924752i	−0.991144	+	0.132793i	$0.957605\pi$
$500$	−1.58830	+	1.21545i	−0.0710307	+	0.0543566i
$501$	17.6105	−	30.5023i	0.786780	−	1.36274i
$502$	−8.01870	−	3.96090i	−0.357892	−	0.176783i
$503$	−29.0170			−1.29381			−0.646903	−	0.762572i	$-0.723936\pi$
$503$	−29.0170			−1.29381			−0.646903	+	0.762572i	$0.723936\pi$
$504$	44.7803	−	1.80315i	1.99467	−	0.0803187i
$505$	6.24891			0.278073
$506$	−7.54733	−	3.72806i	−0.335520	−	0.165732i
$507$	−4.41354	+	7.64448i	−0.196012	+	0.339503i
$508$	−4.80237	+	3.67503i	−0.213071	+	0.163053i
$509$	17.3474	−	10.0155i	0.768910	−	0.443931i	−0.0635754	−	0.997977i	$-0.520250\pi$
$509$	17.3474	−	10.0155i	0.768910	−	0.443931i	0.832486	+	0.554046i	$0.186917\pi$
$510$	12.1522	−	8.10839i	0.538110	−	0.359046i
$511$	14.2109	+	36.6986i	0.628654	+	1.62345i
$512$	12.4604	+	18.8875i	0.550675	+	0.834720i
$513$	9.19562	+	15.9273i	0.405996	+	0.703206i
$514$	20.0981	−	1.30412i	0.886487	−	0.0575222i
$515$	9.88858	+	5.70918i	0.435743	+	0.251576i
$516$	7.71618	+	59.2075i	0.339686	+	2.60646i
$517$		−	13.7031i		−	0.602663i
$518$	−24.0947	+	34.2587i	−1.05866	+	1.50524i
$519$		−	49.4317i		−	2.16981i
$520$	−6.75497	+	5.90059i	−0.296225	+	0.258758i
$521$	18.5712	+	10.7221i	0.813620	+	0.469743i	0.848211	−	0.529658i	$-0.177680\pi$
$521$	18.5712	+	10.7221i	0.813620	+	0.469743i	−0.0345917	+	0.999402i	$0.511013\pi$
$522$	−4.04782	−	62.3818i	−0.177168	−	2.73038i
$523$	−20.5020	−	35.5105i	−0.896491	−	1.55277i	−0.831949	−	0.554852i	$-0.812775\pi$
$523$	−20.5020	−	35.5105i	−0.896491	−	1.55277i	−0.0645418	−	0.997915i	$-0.520559\pi$
$524$	−12.0582	+	29.0040i	−0.526766	+	1.26704i
$525$	1.21790	−	7.83829i	0.0531537	−	0.342091i
$526$	−9.22165	−	13.8207i	−0.402083	−	0.602611i
$527$	14.5972	−	8.42768i	0.635863	−	0.367116i
$528$	6.87442	+	25.9263i	0.299171	+	1.12830i
$529$	−7.95856	+	13.7846i	−0.346024	+	0.599332i
$530$	−2.91725	+	5.90587i	−0.126717	+	0.256534i
$531$	42.6333			1.85013
$532$	9.53553	−	5.19749i	0.413418	−	0.225340i
$533$	−4.63015			−0.200554
$534$	13.1830	−	26.6886i	0.570485	−	1.15493i
$535$	−1.30194	+	2.25502i	−0.0562876	+	0.0974931i
$536$	−0.0482531	+	0.141240i	−0.00208422	+	0.00610062i
$537$	23.6528	−	13.6559i	1.02069	−	0.589297i
$538$	6.66349	+	9.98673i	0.287284	+	0.430559i
$539$	4.75052	−	14.9178i	0.204620	−	0.642557i
$540$	−16.5489	−	6.88010i	−0.712151	−	0.296072i
$541$	−1.72641	−	2.99023i	−0.0742242	−	0.128560i	0.826524	−	0.562901i	$-0.190315\pi$
$541$	−1.72641	−	2.99023i	−0.0742242	−	0.128560i	−0.900749	+	0.434341i	$0.856981\pi$
$542$	0.730175	+	11.2529i	0.0313637	+	0.483352i
$543$	43.0377	+	24.8479i	1.84693	+	1.06632i
$544$	−18.4767	+	6.20481i	−0.792182	+	0.266029i
$545$		−	1.00189i		−	0.0429163i
$546$	3.17422	−	35.4315i	0.135844	−	1.51633i
$547$		−	28.2607i		−	1.20834i	−0.796855	−	0.604170i	$-0.793505\pi$
$547$		−	28.2607i		−	1.20834i	0.796855	−	0.604170i	$-0.206495\pi$
$548$	−19.0675	+	2.48496i	−0.814522	+	0.106152i
$549$	13.1564	+	7.59584i	0.561500	+	0.324182i
$550$	3.15635	−	0.204809i	0.134587	−	0.00873307i
$551$	−7.57413	−	13.1188i	−0.322669	−	0.558879i
$552$	−22.1434	+	4.35953i	−0.942487	+	0.185554i
$553$	−1.20576	−	0.187349i	−0.0512741	−	0.00796691i
$554$	−15.9931	+	10.6711i	−0.679481	+	0.453374i
$555$	29.0643	−	16.7803i	1.23371	−	0.712284i
$556$	−9.11277	−	11.9082i	−0.386468	−	0.505018i
$557$	−1.03826	+	1.79833i	−0.0439927	+	0.0761976i	−0.887183	−	0.461417i	$-0.847341\pi$
$557$	−1.03826	+	1.79833i	−0.0439927	+	0.0761976i	0.843191	+	0.537615i	$0.180674\pi$
$558$	−37.1480	−	18.3495i	−1.57260	−	0.776798i
$559$	31.5762			1.33553
$560$	−4.30138	+	9.66944i	−0.181767	+	0.408609i
$561$	−23.1040			−0.975453
$562$	−12.0239	−	5.93929i	−0.507197	−	0.250534i
$563$	22.9547	−	39.7588i	0.967426	−	1.67563i	0.264477	−	0.964392i	$-0.414801\pi$
$563$	22.9547	−	39.7588i	0.967426	−	1.67563i	0.702949	−	0.711240i	$-0.251866\pi$
$564$	−22.3268	−	29.1757i	−0.940130	−	1.22852i
$565$	−12.8681	+	7.42940i	−0.541365	+	0.312557i
$566$	25.3502	−	16.9145i	1.06555	−	0.710971i
$567$	21.9581	−	8.50292i	0.922154	−	0.357089i
$568$	−0.589295	+	0.116019i	−0.0247263	+	0.00486803i
$569$	−3.96413	−	6.86607i	−0.166185	−	0.287840i	0.770891	−	0.636968i	$-0.219811\pi$
$569$	−3.96413	−	6.86607i	−0.166185	−	0.287840i	−0.937075	+	0.349127i	$0.886478\pi$
$570$	−8.68375	+	0.563470i	−0.363722	+	0.0236011i
$571$	18.3314	+	10.5837i	0.767147	+	0.442912i	0.831856	−	0.554992i	$-0.187279\pi$
$571$	18.3314	+	10.5837i	0.767147	+	0.442912i	−0.0647092	+	0.997904i	$0.520612\pi$
$572$	14.0658	−	1.83311i	0.588120	−	0.0766464i
$573$		−	8.97330i		−	0.374865i
$574$	−4.95618	+	2.29855i	−0.206867	+	0.0959396i
$575$			2.66137i			0.110987i
$576$	37.8958	+	29.3150i	1.57899	+	1.22146i
$577$	8.94731	+	5.16573i	0.372481	+	0.215052i	0.674542	−	0.738237i	$-0.264341\pi$
$577$	8.94731	+	5.16573i	0.372481	+	0.215052i	−0.302061	+	0.953289i	$0.597675\pi$
$578$	0.469630	+	7.23756i	0.0195340	+	0.301043i
$579$	22.0496	+	38.1911i	0.916351	+	1.58717i
$580$	13.6308	+	5.66691i	0.565987	+	0.235306i
$581$	−22.5008	−	18.1117i	−0.933490	−	0.751402i
$582$	−0.436444	−	0.654109i	−0.0180912	−	0.0271137i
$583$	9.02174	−	5.20871i	0.373642	−	0.215723i
$584$	−13.6013	+	39.8119i	−0.562827	+	1.64743i
$585$	−9.49562	+	16.4469i	−0.392595	+	0.679995i
$586$	18.1317	−	36.7069i	0.749012	−	1.51635i
$587$	−20.4660			−0.844722			−0.422361	−	0.906428i	$-0.638799\pi$
$587$	−20.4660			−0.844722			−0.422361	+	0.906428i	$0.638799\pi$
$588$	−14.1915	−	39.5021i	−0.585249	−	1.62904i
$589$	−10.0401			−0.413694
$590$	−4.45861	+	9.02632i	−0.183558	+	0.371608i
$591$	−7.22175	+	12.5084i	−0.297063	+	0.514529i
$592$	−43.2796	+	11.4757i	−1.77878	+	0.471648i
$593$	38.8389	−	22.4236i	1.59492	−	0.920828i	0.602477	−	0.798136i	$-0.294181\pi$
$593$	38.8389	−	22.4236i	1.59492	−	0.920828i	0.992445	−	0.122692i	$-0.0391527\pi$
$594$	15.7315	+	23.5772i	0.645471	+	0.967383i
$595$	−7.10122	−	5.71605i	−0.291122	−	0.234335i
$596$	4.99158	−	12.0064i	0.204463	−	0.491800i
$597$	−1.91036	−	3.30884i	−0.0781857	−	0.135422i
$598$	0.772823	+	11.9101i	0.0316031	+	0.487041i
$599$	−14.1499	−	8.16942i	−0.578147	−	0.333793i	0.182250	−	0.983252i	$-0.441662\pi$
$599$	−14.1499	−	8.16942i	−0.578147	−	0.333793i	−0.760397	+	0.649459i	$0.774995\pi$
$600$	6.38656	−	5.57878i	0.260730	−	0.227753i
$601$			39.8029i			1.62359i	0.583941	+	0.811796i	$0.301510\pi$
$601$			39.8029i			1.62359i	−0.583941	+	0.811796i	$0.698490\pi$
$602$	33.7996	−	15.6754i	1.37757	−	0.638882i
$603$			0.316030i			0.0128697i
$604$	6.11903	+	46.9523i	0.248980	+	1.91046i
$605$	5.19421	+	2.99888i	0.211175	+	0.121922i
$606$	−26.4399	+	1.71563i	−1.07405	+	0.0696926i
$607$	4.70373	+	8.14710i	0.190919	+	0.330681i	0.945555	−	0.325463i	$-0.105520\pi$
$607$	4.70373	+	8.14710i	0.190919	+	0.330681i	−0.754636	+	0.656143i	$0.772187\pi$
$608$	11.3793	+	2.30213i	0.461493	+	0.0933636i
$609$	−54.5975	+	21.1420i	−2.21240	+	0.856716i
$610$	−2.98409	+	1.99109i	−0.120822	+	0.0806168i
$611$	−16.8259	+	9.71441i	−0.680701	+	0.393003i
$612$	−32.7739	+	25.0804i	−1.32481	+	1.01382i
$613$	−6.81796	+	11.8091i	−0.275375	+	0.476963i	−0.970230	−	0.242187i	$-0.922135\pi$
$613$	−6.81796	+	11.8091i	−0.275375	+	0.476963i	0.694855	+	0.719150i	$0.255469\pi$
$614$	10.1512	+	5.01423i	0.409667	+	0.202358i
$615$	4.37763			0.176523
$616$	14.1462	−	8.94487i	0.569966	−	0.360399i
$617$	39.1144			1.57469			0.787343	−	0.616515i	$-0.211456\pi$
$617$	39.1144			1.57469			0.787343	+	0.616515i	$0.211456\pi$
$618$	−43.4072	−	21.4413i	−1.74609	−	0.862496i
$619$	9.50950	−	16.4709i	0.382219	−	0.662023i	−0.609160	−	0.793047i	$-0.708493\pi$
$619$	9.50950	−	16.4709i	0.382219	−	0.662023i	0.991379	+	0.131024i	$0.0418266\pi$
$620$	7.76992	−	5.94597i	0.312047	−	0.238796i
$621$	−20.6535	+	11.9243i	−0.828798	+	0.478507i
$622$	−16.1785	+	10.7948i	−0.648697	+	0.432833i
$623$	−18.3542	−	2.85186i	−0.735347	−	0.114257i
$624$	26.9611	−	26.8206i	1.07931	−	1.07368i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−15.0098	+	0.973953i	−0.599912	+	0.0389270i
$627$	11.9184	+	6.88108i	0.475974	+	0.274804i
$628$	2.02441	+	15.5336i	0.0807827	+	0.619859i
$629$		−	38.5683i		−	1.53782i
$630$	−1.99950	+	22.3189i	−0.0796619	+	0.889206i
$631$			16.4987i			0.656802i	0.944538	+	0.328401i	$0.106510\pi$
$631$			16.4987i			0.656802i	−0.944538	+	0.328401i	$0.893490\pi$
$632$	−0.858180	−	0.982441i	−0.0341366	−	0.0390794i
$633$	−9.63252	−	5.56134i	−0.382858	−	0.221043i
$634$	−1.55522	−	23.9679i	−0.0617659	−	0.951886i
$635$	−1.51180	−	2.61851i	−0.0599939	−	0.103913i
$636$	10.7218	−	25.7893i	0.425146	−	1.02261i
$637$	−21.6851	+	4.74245i	−0.859196	+	0.187903i
$638$	−12.9575	−	19.4197i	−0.512993	−	0.768835i
$639$	−1.10134	+	0.635857i	−0.0435682	+	0.0251541i
$640$	−10.1697	+	4.95750i	−0.401993	+	0.195963i
$641$	−13.4723	+	23.3347i	−0.532124	+	0.921665i	0.467173	+	0.884166i	$0.345272\pi$
$641$	−13.4723	+	23.3347i	−0.532124	+	0.921665i	−0.999297	+	0.0374991i	$0.988061\pi$
$642$	4.88954	−	9.89870i	0.192975	−	0.390671i
$643$	−43.6730			−1.72229			−0.861147	−	0.508355i	$-0.830254\pi$
$643$	−43.6730			−1.72229			−0.861147	+	0.508355i	$0.830254\pi$
$644$	6.73979	+	12.3651i	0.265585	+	0.487254i
$645$	−29.8541			−1.17550
$646$	−4.42895	+	8.96625i	−0.174255	+	0.352773i
$647$	14.0540	−	24.3422i	0.552518	−	0.956989i	−0.445574	−	0.895245i	$-0.647000\pi$
$647$	14.0540	−	24.3422i	0.552518	−	0.956989i	0.998092	−	0.0617443i	$-0.0196663\pi$
$648$	23.8209	+	8.13818i	0.935775	+	0.319698i
$649$	13.7885	−	7.96080i	0.541246	−	0.312489i
$650$	−2.48908	−	3.73043i	−0.0976296	−	0.146320i
$651$	−5.95797	+	38.3448i	−0.233511	+	1.50285i
$652$	−20.0402	−	8.33161i	−0.784836	−	0.326291i
$653$	20.8367	+	36.0902i	0.815403	+	1.41232i	0.909038	+	0.416713i	$0.136818\pi$
$653$	20.8367	+	36.0902i	0.815403	+	1.41232i	−0.0936346	+	0.995607i	$0.529849\pi$
$654$	0.275067	+	4.23912i	0.0107560	+	0.165763i
$655$	−13.6012	−	7.85267i	−0.531444	−	0.306829i
$656$	−5.63748	−	1.52635i	−0.220107	−	0.0595939i
$657$			89.0808i			3.47537i
$658$	−13.1881	+	18.7513i	−0.514125	+	0.731002i
$659$			47.0951i			1.83457i	0.398236	+	0.917283i	$0.369622\pi$
$659$			47.0951i			1.83457i	−0.398236	+	0.917283i	$0.630378\pi$
$660$	−13.2986	+	1.73314i	−0.517649	+	0.0674623i
$661$	−10.0792	−	5.81924i	−0.392036	−	0.226342i	0.291006	−	0.956721i	$-0.406010\pi$
$661$	−10.0792	−	5.81924i	−0.392036	−	0.226342i	−0.683042	+	0.730379i	$0.739343\pi$
$662$	−11.7559	+	0.762817i	−0.456907	+	0.0296477i
$663$	16.3789	+	28.3690i	0.636103	+	1.10176i
$664$	−5.96486	−	30.2973i	−0.231481	−	1.17577i
$665$	1.96081	+	5.06363i	0.0760368	+	0.196359i
$666$	−78.8628	+	52.6200i	−3.05587	+	2.03898i
$667$	17.0116	−	9.82168i	0.658693	−	0.380297i
$668$	−14.2786	−	18.6587i	−0.552457	−	0.721926i
$669$	19.4251	−	33.6452i	0.751017	−	1.30080i
$670$	−0.0669097	−	0.0330505i	−0.00258495	−	0.00127685i
$671$	5.67340			0.219019
$672$	15.5449	−	42.0935i	0.599658	−	1.62379i
$673$	14.9849			0.577626			0.288813	−	0.957385i	$-0.406739\pi$
$673$	14.9849			0.577626			0.288813	+	0.957385i	$0.406739\pi$
$674$	34.3328	+	16.9590i	1.32245	+	0.653234i
$675$	4.48052	−	7.76049i	0.172455	−	0.298702i
$676$	3.57851	+	4.67623i	0.137635	+	0.179855i
$677$	19.9347	−	11.5093i	0.766154	−	0.442339i	−0.0653470	−	0.997863i	$-0.520815\pi$
$677$	19.9347	−	11.5093i	0.766154	−	0.442339i	0.831501	+	0.555524i	$0.187482\pi$
$678$	52.4067	−	34.9676i	2.01267	−	1.34292i
$679$	−0.307673	+	0.382232i	−0.0118074	+	0.0146687i
$680$	−1.88250	−	9.56181i	−0.0721907	−	0.366679i
$681$	−13.3305	−	23.0892i	−0.510827	−	0.884779i
$682$	−15.4408	+	1.00192i	−0.591259	+	0.0383655i
$683$	32.2762	+	18.6347i	1.23502	+	0.713037i	0.968071	−	0.250675i	$-0.0806525\pi$
$683$	32.2762	+	18.6347i	1.23502	+	0.713037i	0.266945	+	0.963712i	$0.413986\pi$
$684$	24.3764	−	3.17684i	0.932055	−	0.121469i
$685$		−	9.61436i		−	0.367346i
$686$	−20.8577	+	15.8415i	−0.796352	+	0.604833i
$687$		−	38.8132i		−	1.48082i
$688$	38.4459	+	10.4092i	1.46573	+	0.396848i
$689$	−12.7914	−	7.38510i	−0.487312	−	0.281350i
$690$	−0.730674	−	11.2606i	−0.0278163	−	0.428682i
$691$	−13.9969	−	24.2433i	−0.532467	−	0.922260i	−0.999281	−	0.0379044i	$-0.987932\pi$
$691$	−13.9969	−	24.2433i	−0.532467	−	0.922260i	0.466815	−	0.884355i	$-0.345402\pi$
$692$	−30.4483	−	12.6587i	−1.15747	−	0.481211i
$693$	22.2213	−	27.6062i	0.844118	−	1.04867i
$694$	21.7991	+	32.6708i	0.827483	+	1.24017i
$695$	6.49298	−	3.74872i	0.246293	−	0.142197i
$696$	−59.2292	−	20.2351i	−2.24508	−	0.767009i
$697$	2.51542	−	4.35683i	0.0952782	−	0.165027i
$698$	6.03811	−	12.2239i	0.228546	−	0.462683i
$699$	−45.6203			−1.72552
$700$	−4.51624	−	2.75745i	−0.170698	−	0.104222i
$701$	29.2334			1.10413			0.552065	−	0.833801i	$-0.313840\pi$
$701$	29.2334			1.10413			0.552065	+	0.833801i	$0.313840\pi$
$702$	17.7977	−	36.0308i	0.671729	−	1.35989i
$703$	−11.4868	+	19.8957i	−0.433233	+	0.750381i
$704$	17.7302	+	2.40491i	0.668232	+	0.0906386i
$705$	15.9082	−	9.18460i	0.599137	−	0.345912i
$706$	12.8053	+	19.1915i	0.481932	+	0.722283i
$707$	5.97017	+	15.4175i	0.224532	+	0.579835i
$708$	16.3868	−	39.4155i	0.615852	−	1.48133i
$709$	2.08074	+	3.60395i	0.0781440	+	0.135349i	0.902449	−	0.430796i	$-0.141767\pi$
$709$	2.08074	+	3.60395i	0.0781440	+	0.135349i	−0.824305	+	0.566146i	$0.808434\pi$
$710$	−0.0194451	−	0.299673i	−0.000729763	−	0.0112465i
$711$	−2.39203	−	1.38104i	−0.0897082	−	0.0517931i
$712$	−13.0633	−	14.9548i	−0.489569	−	0.560457i
$713$		−	13.0194i		−	0.487580i
$714$	31.6154	+	22.2356i	1.18318	+	0.832148i
$715$			7.09236i			0.265239i
$716$	−2.35449	−	18.0664i	−0.0879916	−	0.675173i
$717$	0.113858	+	0.0657362i	0.00425212	+	0.00245496i
$718$	−2.26093	+	0.146707i	−0.0843771	+	0.00547505i
$719$	−21.1113	−	36.5658i	−0.787318	−	1.36368i	−0.927604	−	0.373564i	$-0.878135\pi$
$719$	−21.1113	−	36.5658i	−0.787318	−	1.36368i	0.140286	−	0.990111i	$-0.455198\pi$
$720$	−16.9832	+	16.8948i	−0.632928	+	0.629631i
$721$	−4.63835	+	29.8519i	−0.172741	+	1.11174i
$722$	−17.3962	+	11.6074i	−0.647421	+	0.431982i
$723$	−5.97339	+	3.44874i	−0.222153	+	0.128260i
$724$	26.3268	−	20.1467i	0.978427	−	0.748746i
$725$	−3.69046	+	6.39206i	−0.137060	+	0.237395i
$726$	−22.8007	−	11.2626i	−0.846212	−	0.417993i
$727$	27.2605			1.01104			0.505519	−	0.862816i	$-0.331301\pi$
$727$	27.2605			1.01104			0.505519	+	0.862816i	$0.331301\pi$
$728$	−21.0118	−	11.0287i	−0.778748	−	0.408750i
$729$	−27.2992			−1.01108
$730$	−18.8602	−	9.31612i	−0.698046	−	0.344805i
$731$	−17.1544	+	29.7122i	−0.634477	+	1.09895i
$732$	12.0794	−	9.24380i	0.446467	−	0.341661i
$733$	13.2554	−	7.65300i	0.489599	−	0.282670i	−0.234809	−	0.972041i	$-0.575447\pi$
$733$	13.2554	−	7.65300i	0.489599	−	0.282670i	0.724408	+	0.689372i	$0.242113\pi$
$734$	1.48286	−	0.989415i	0.0547333	−	0.0365200i
$735$	20.5024	−	4.48381i	0.756244	−	0.165388i
$736$	−2.98526	+	14.7560i	−0.110038	+	0.543915i
$737$	0.0590113	+	0.102211i	0.00217371	+	0.00376498i
$738$	−12.3405	+	0.800751i	−0.454261	+	0.0294760i
$739$	42.5694	+	24.5774i	1.56594	+	0.904096i	0.996635	+	0.0819692i	$0.0261209\pi$
$739$	42.5694	+	24.5774i	1.56594	+	0.904096i	0.569305	+	0.822126i	$0.307212\pi$
$740$	−2.89318	−	22.1998i	−0.106355	−	0.816082i
$741$		−	19.5125i		−	0.716810i
$742$	−17.3582	−	1.55508i	−0.637241	−	0.0570890i
$743$			35.2067i			1.29161i	0.763503	+	0.645805i	$0.223478\pi$
$743$			35.2067i			1.29161i	−0.763503	+	0.645805i	$0.776522\pi$
$744$	−31.2430	+	27.2913i	−1.14542	+	1.00055i
$745$	5.63031	+	3.25066i	0.206279	+	0.119095i
$746$	0.844982	+	13.0222i	0.0309370	+	0.476776i
$747$	−32.6913	−	56.6229i	−1.19611	−	2.07173i
$748$	−5.91659	+	14.2313i	−0.216332	+	0.520349i
$749$	−6.80752	−	1.05774i	−0.248741	−	0.0386491i
$750$	2.35332	+	3.52698i	0.0859313	+	0.128787i
$751$	0.584292	−	0.337341i	0.0213211	−	0.0123098i	−0.489302	−	0.872115i	$-0.662748\pi$
$751$	0.584292	−	0.337341i	0.0213211	−	0.0123098i	0.510623	+	0.859805i	$0.329415\pi$
$752$	−23.6888	+	6.28115i	−0.863843	+	0.229050i
$753$	−9.48027	+	16.4203i	−0.345480	+	0.598389i
$754$	−14.6593	+	29.6773i	−0.533862	+	1.08079i
$755$	−23.6747			−0.861609
$756$	1.16408	−	47.4031i	0.0423372	−	1.72403i
$757$	−45.8640			−1.66695			−0.833477	−	0.552553i	$-0.813654\pi$
$757$	−45.8640			−1.66695			−0.833477	+	0.552553i	$0.813654\pi$
$758$	1.58782	−	3.21449i	0.0576723	−	0.116756i
$759$	−8.92298	+	15.4550i	−0.323883	+	0.560983i
$760$	−1.87670	+	5.49320i	−0.0680749	+	0.199259i
$761$	18.9229	−	10.9252i	0.685956	−	0.396037i	−0.116139	−	0.993233i	$-0.537052\pi$
$761$	18.9229	−	10.9252i	0.685956	−	0.396037i	0.802095	+	0.597196i	$0.203719\pi$
$762$	7.11551	+	10.6642i	0.257768	+	0.386322i
$763$	2.47190	−	0.957201i	0.0894886	−	0.0346530i
$764$	−5.52726	−	2.29793i	−0.199969	−	0.0831360i
$765$	−10.3173	−	17.8701i	−0.373024	−	0.646097i
$766$	0.121322	+	1.86972i	0.00438354	+	0.0675556i
$767$	−19.5499	−	11.2871i	−0.705905	−	0.407554i
$768$	41.6682	−	23.7679i	1.50357	−	0.857649i
$769$		−	16.0214i		−	0.577745i	−0.957368	−	0.288872i	$-0.906720\pi$
$769$		−	16.0214i		−	0.577745i	0.957368	−	0.288872i	$-0.0932803\pi$
$770$	3.52087	+	7.59176i	0.126883	+	0.273588i
$771$		−	42.6976i		−	1.53772i
$772$	29.1710	−	3.80169i	1.04989	−	0.136826i
$773$	−36.6688	−	21.1707i	−1.31888	−	0.761458i	−0.335335	−	0.942099i	$-0.608850\pi$
$773$	−36.6688	−	21.1707i	−1.31888	−	0.761458i	−0.983549	+	0.180641i	$0.942183\pi$
$774$	84.1586	−	5.46087i	3.02502	−	0.196287i
$775$	2.44599	+	4.23658i	0.0878627	+	0.152183i
$776$	−0.514676	+	0.101328i	−0.0184758	+	0.00363746i
$777$	69.1687	+	55.6765i	2.48141	+	1.99738i
$778$	37.9113	−	25.2957i	1.35919	−	0.906896i
$779$	−2.59519	+	1.49833i	−0.0929824	+	0.0536834i
$780$	11.5558	+	15.1005i	0.413762	+	0.540686i
$781$	−0.237464	+	0.411299i	−0.00849712	+	0.0147174i
$782$	−11.6269	−	5.74319i	−0.415777	−	0.205376i
$783$	−66.1408			−2.36368
$784$	−27.9662	−	1.37437i	−0.998795	−	0.0490845i
$785$	−7.83249			−0.279553
$786$	59.7043	+	29.4914i	2.12958	+	1.05192i
$787$	−2.19121	+	3.79528i	−0.0781081	+	0.135287i	−0.902434	−	0.430829i	$-0.858221\pi$
$787$	−2.19121	+	3.79528i	−0.0781081	+	0.135287i	0.824326	+	0.566116i	$0.191555\pi$
$788$	5.85541	+	7.65158i	0.208590	+	0.272576i
$789$	−30.5044	+	17.6117i	−1.08599	+	0.626994i
$790$	0.542554	−	0.362011i	0.0193032	−	0.0128798i
$791$	−30.6241	−	24.6506i	−1.08887	−	0.876473i
$792$	37.1718	−	7.31828i	1.32084	−	0.260044i
$793$	−4.02198	−	6.96627i	−0.142825	−	0.247380i
$794$	49.6394	−	3.22099i	1.76164	−	0.114309i
$795$	12.0937	+	6.98233i	0.428921	+	0.247638i
$796$	−2.52735	+	0.329375i	−0.0895795	+	0.0116744i
$797$		−	53.6019i		−	1.89868i	−0.314255	−	0.949339i	$-0.601755\pi$
$797$		−	53.6019i		−	1.89868i	0.314255	−	0.949339i	$-0.398245\pi$
$798$	−9.68661	−	20.8865i	−0.342902	−	0.739373i
$799$		−	21.1101i		−	0.746822i
$800$	−1.80084	−	5.36255i	−0.0636694	−	0.189595i
$801$	−36.4118	−	21.0224i	−1.28655	−	0.742789i
$802$	2.92343	+	45.0535i	0.103230	+	1.59090i
$803$	16.6338	+	28.8106i	0.586995	+	1.01670i
$804$	0.292177	+	0.121471i	0.0103043	+	0.00428394i
$805$	−6.56621	+	2.54266i	−0.231428	+	0.0896169i
$806$	12.1765	+	18.2492i	0.428900	+	0.642802i
$807$	22.0422	−	12.7261i	0.775924	−	0.447980i
$808$	−5.71408	+	16.7254i	−0.201021	+	0.588399i
$809$	0.754693	−	1.30717i	0.0265336	−	0.0459575i	−0.852454	−	0.522803i	$-0.824886\pi$
$809$	0.754693	−	1.30717i	0.0265336	−	0.0459575i	0.878987	+	0.476845i	$0.158220\pi$
$810$	−5.57418	+	11.2847i	−0.195857	+	0.396505i
$811$	43.1894			1.51658			0.758292	−	0.651915i	$-0.226034\pi$
$811$	43.1894			1.51658			0.758292	+	0.651915i	$0.226034\pi$
$812$	−0.958815	+	39.0444i	−0.0336478	+	1.37019i
$813$	23.9063			0.838432
$814$	−15.6803	+	31.7442i	−0.549594	+	1.11264i
$815$	5.42579	−	9.39774i	0.190057	−	0.329188i
$816$	10.5903	+	39.9403i	0.370733	+	1.39819i
$817$	17.6984	−	10.2182i	0.619189	−	0.357489i
$818$	−12.8840	−	19.3095i	−0.450478	−	0.675142i
$819$	−49.6503	−	7.71460i	−1.73492	−	0.269570i
$820$	1.12104	−	2.69648i	0.0391486	−	0.0941651i
$821$	4.56478	+	7.90644i	0.159312	+	0.275937i	0.934621	−	0.355646i	$-0.115739\pi$
$821$	4.56478	+	7.90644i	0.159312	+	0.275937i	−0.775309	+	0.631582i	$0.782406\pi$
$822$	2.63960	+	40.6795i	0.0920668	+	1.41886i
$823$	−0.329424	−	0.190193i	−0.0114830	−	0.00662972i	0.494248	−	0.869321i	$-0.335444\pi$
$823$	−0.329424	−	0.190193i	−0.0114830	−	0.00662972i	−0.505731	+	0.862692i	$0.668777\pi$
$824$	−24.3231	+	21.2466i	−0.847334	+	0.740161i
$825$		−	6.70555i		−	0.233457i
$826$	−26.5297	−	2.37674i	−0.923087	−	0.0826972i
$827$			23.9044i			0.831236i	0.909539	+	0.415618i	$0.136435\pi$
$827$			23.9044i			0.831236i	−0.909539	+	0.415618i	$0.863565\pi$
$828$	4.11954	+	31.6099i	0.143164	+	1.09852i
$829$	35.8241	+	20.6830i	1.24422	+	0.718352i	0.969951	−	0.243301i	$-0.0782303\pi$
$829$	35.8241	+	20.6830i	1.24422	+	0.718352i	0.274271	+	0.961653i	$0.411564\pi$
$830$	15.4071	−	0.999731i	0.534787	−	0.0347012i
$831$	20.3800	+	35.2992i	0.706974	+	1.22452i
$832$	−9.61631	−	23.4755i	−0.333386	−	0.813866i
$833$	7.31833	−	22.9814i	0.253565	−	0.796259i
$834$	−26.4434	+	17.6439i	−0.915659	+	0.610959i
$835$	10.1737	−	5.87381i	0.352076	−	0.203271i
$836$	7.29064	−	5.57919i	0.252152	−	0.192960i
$837$	−21.9187	+	37.9642i	−0.757620	+	1.31224i
$838$	15.0449	+	7.43155i	0.519718	+	0.256718i
$839$	46.4174			1.60251			0.801253	−	0.598326i	$-0.204167\pi$
$839$	46.4174			1.60251			0.801253	+	0.598326i	$0.204167\pi$
$840$	19.8658	+	10.4272i	0.685435	+	0.359772i
$841$	25.4780			0.878551
$842$	−13.1149	−	6.47819i	−0.451969	−	0.223253i
$843$	−14.2155	+	24.6219i	−0.489607	+	0.848025i
$844$	−5.89234	+	4.50914i	−0.202823	+	0.155211i
$845$	−2.54974	+	1.47209i	−0.0877136	+	0.0506415i
$846$	−43.1651	+	28.8013i	−1.48405	+	0.990208i
$847$	−2.43641	+	15.6804i	−0.0837159	+	0.538786i
$848$	−13.1397	−	13.2085i	−0.451219	−	0.453582i
$849$	−32.3038	−	55.9518i	−1.10866	−	1.92026i
$850$	4.86246	−	0.315514i	0.166781	−	0.0108221i
$851$	−25.7996	−	14.8954i	−0.884398	−	0.510608i
$852$	0.164549	+	1.26261i	0.00563737	+	0.0432564i
$853$		−	10.5928i		−	0.362692i	−0.983419	−	0.181346i	$-0.941955\pi$
$853$		−	10.5928i		−	0.362692i	0.983419	−	0.181346i	$-0.0580454\pi$
$854$	−7.76345	−	5.46016i	−0.265660	−	0.186843i
$855$			12.2913i			0.420352i
$856$	−4.84514	−	5.54670i	−0.165604	−	0.189582i
$857$	−0.245410	−	0.141688i	−0.00838305	−	0.00483996i	0.495803	−	0.868435i	$-0.334874\pi$
$857$	−0.245410	−	0.141688i	−0.00838305	−	0.00483996i	−0.504186	+	0.863595i	$0.668207\pi$
$858$	−1.94719	−	30.0086i	−0.0664761	−	1.02448i
$859$	4.93861	+	8.55393i	0.168503	+	0.291856i	0.937894	−	0.346922i	$-0.112773\pi$
$859$	4.93861	+	8.55393i	0.168503	+	0.291856i	−0.769391	+	0.638779i	$0.779440\pi$
$860$	−7.64517	+	18.3891i	−0.260698	+	0.627064i
$861$	4.18236	+	10.8006i	0.142535	+	0.368084i
$862$	23.2787	+	34.8883i	0.792875	+	1.18830i
$863$	28.2007	−	16.2817i	0.959963	−	0.554235i	0.0638012	−	0.997963i	$-0.479678\pi$
$863$	28.2007	−	16.2817i	0.959963	−	0.554235i	0.896162	+	0.443728i	$0.146344\pi$
$864$	33.5473	−	38.0025i	1.14130	−	1.29287i
$865$	8.24371	−	14.2785i	0.280295	−	0.485485i
$866$	−18.4205	+	37.2916i	−0.625952	+	1.26722i
$867$	15.3759			0.522195
$868$	22.0934	+	13.4894i	0.749899	+	0.457861i
$869$	−1.03151			−0.0349916
$870$	13.8598	−	28.0588i	0.469893	−	0.951282i
$871$	0.0836685	−	0.144918i	0.00283500	−	0.00491036i
$872$	2.68160	+	0.916141i	0.0908104	+	0.0310245i
$873$	−0.961883	+	0.555343i	−0.0325548	+	0.0187955i
$874$	4.28733	+	6.42551i	0.145021	+	0.217346i
$875$	1.65899	−	2.06101i	0.0560840	−	0.0696749i
$876$	82.3573	+	34.2396i	2.78260	+	1.15685i
$877$	−19.0353	−	32.9700i	−0.642775	−	1.11332i	−0.984811	−	0.173632i	$-0.944450\pi$
$877$	−19.0353	−	32.9700i	−0.642775	−	1.11332i	0.342036	−	0.939687i	$-0.388884\pi$
$878$	−0.808020	−	12.4526i	−0.0272694	−	0.420254i
$879$	−75.1666	−	43.3975i	−2.53531	−	1.46376i
$880$	−2.33802	+	8.63536i	−0.0788148	+	0.291098i
$881$			27.7529i			0.935019i	0.883988	+	0.467509i	$0.154849\pi$
$881$			27.7529i			0.935019i	−0.883988	+	0.467509i	$0.845151\pi$
$882$	−56.9761	+	16.3901i	−1.91849	+	0.551884i
$883$		−	44.1707i		−	1.48646i	−0.669034	−	0.743232i	$-0.733292\pi$
$883$		−	44.1707i		−	1.48646i	0.669034	−	0.743232i	$-0.266708\pi$
$884$	21.6688	−	2.82397i	0.728800	−	0.0949804i
$885$	18.4836	+	10.6715i	0.621321	+	0.358720i
$886$	27.6136	−	1.79179i	0.927698	−	0.0601963i
$887$	10.0638	+	17.4310i	0.337909	+	0.585275i	0.984039	−	0.177952i	$-0.0569471\pi$
$887$	10.0638	+	17.4310i	0.337909	+	0.585275i	−0.646130	+	0.763227i	$0.723614\pi$
$888$	18.3363	+	93.1358i	0.615326	+	3.12543i
$889$	5.01611	−	6.23167i	0.168235	−	0.209003i
$890$	8.25882	−	5.51057i	0.276836	−	0.184715i
$891$	17.2385	−	9.95263i	0.577510	−	0.333426i
$892$	−15.7499	−	20.5813i	−0.527346	−	0.689111i
$893$	−6.28724	+	10.8898i	−0.210394	+	0.364414i
$894$	−24.7150	−	12.2081i	−0.826592	−	0.408301i
$895$	9.10959			0.304500
$896$	−21.9474	−	20.3547i	−0.733211	−	0.680001i
$897$	25.3027			0.844831
$898$	−6.36909	−	3.14606i	−0.212539	−	0.104985i
$899$	18.0537	−	31.2699i	0.602124	−	1.04291i
$900$	−7.27917	−	9.51208i	−0.242639	−	0.317069i
$901$	13.8983	−	8.02418i	0.463019	−	0.267324i
$902$	−3.84167	+	2.56329i	−0.127913	+	0.0853483i
$903$	−28.5224	−	73.6569i	−0.949167	−	2.45115i
$904$	−8.11832	−	41.2355i	−0.270011	−	1.37147i
$905$	8.28775	+	14.3548i	0.275494	+	0.477170i
$906$	100.170	−	6.49984i	3.32794	−	0.215943i
$907$	−13.0052	−	7.50854i	−0.431830	−	0.249317i	0.268296	−	0.963336i	$-0.413539\pi$
$907$	−13.0052	−	7.50854i	−0.431830	−	0.249317i	−0.700126	+	0.714020i	$0.746873\pi$
$908$	−17.6359	+	2.29839i	−0.585268	+	0.0762748i
$909$			37.4239i			1.24127i
$910$	6.82579	−	9.70516i	0.226273	−	0.321723i
$911$			24.0198i			0.795811i	0.917426	+	0.397906i	$0.130263\pi$
$911$			24.0198i			0.795811i	−0.917426	+	0.397906i	$0.869737\pi$
$912$	6.43237	−	23.7576i	0.212997	−	0.786693i
$913$	−21.1461	−	12.2087i	−0.699834	−	0.404049i
$914$	−2.54983	−	39.2960i	−0.0843410	−	1.29980i
$915$	3.80262	+	6.58634i	0.125711	+	0.217738i
$916$	−23.9076	−	9.93946i	−0.789931	−	0.328409i
$917$	6.37981	−	41.0597i	0.210680	−	1.35591i
$918$	24.2349	+	36.3214i	0.799871	+	1.19878i
$919$	−49.7575	+	28.7275i	−1.64135	+	0.947632i	−0.660992	+	0.750393i	$0.729864\pi$
$919$	−49.7575	+	28.7275i	−1.64135	+	0.947632i	−0.980355	+	0.197239i	$0.936802\pi$
$920$	−7.12325	−	2.43359i	−0.234847	−	0.0802330i
$921$	12.0014	−	20.7870i	0.395459	−	0.684956i
$922$	12.4321	−	25.1683i	0.409429	−	0.828875i
$923$	0.673370			0.0221643
$924$	−16.9815	−	31.1550i	−0.558650	−	1.02492i
$925$	11.1938			0.368049
$926$	22.3669	−	45.2811i	0.735023	−	1.48803i
$927$	−34.1915	+	59.2214i	−1.12300	+	1.94509i
$928$	−27.6318	+	31.3014i	−0.907060	+	1.02752i
$929$	3.45964	−	1.99743i	0.113507	−	0.0655334i	−0.442172	−	0.896930i	$-0.645792\pi$
$929$	3.45964	−	1.99743i	0.113507	−	0.0655334i	0.555679	+	0.831397i	$0.312458\pi$
$930$	−11.5124	−	17.2539i	−0.377507	−	0.565779i
$931$	−10.6198	+	9.67552i	−0.348049	+	0.317102i
$932$	−11.6827	+	28.1006i	−0.382678	+	0.920466i
$933$	20.6162	+	35.7083i	0.674945	+	1.16904i
$934$	−2.07056	−	31.9098i	−0.0677507	−	1.04412i
$935$	−6.67369	−	3.85305i	−0.218253	−	0.126008i
$936$	−35.3378	−	40.4546i	−1.15505	−	1.32230i
$937$			43.2204i			1.41195i	0.708237	+	0.705975i	$0.249491\pi$
$937$			43.2204i			1.41195i	−0.708237	+	0.705975i	$0.750509\pi$
$938$	0.0176181	−	0.196658i	0.000575252	−	0.00642111i
$939$			31.8878i			1.04062i
$940$	−1.58357	−	12.1510i	−0.0516503	−	0.396321i
$941$	−30.6731	−	17.7091i	−0.999915	−	0.577301i	−0.0916918	−	0.995787i	$-0.529227\pi$
$941$	−30.6731	−	17.7091i	−0.999915	−	0.577301i	−0.908223	+	0.418486i	$0.862561\pi$
$942$	33.1402	−	2.15039i	1.07976	−	0.0700636i
$943$	−1.94295	−	3.36529i	−0.0632712	−	0.109589i
$944$	−20.0823	−	20.1874i	−0.653622	−	0.657044i
$945$	23.4276	+	3.64015i	0.762099	+	0.118414i
$946$	26.1990	−	17.4809i	0.851802	−	0.568352i
$947$	42.1696	−	24.3466i	1.37033	−	0.791159i	0.379358	−	0.925250i	$-0.376145\pi$
$947$	42.1696	−	24.3466i	1.37033	−	0.791159i	0.990969	+	0.134091i	$0.0428116\pi$
$948$	−2.19622	+	1.68067i	−0.0713299	+	0.0545855i
$949$	23.5840	−	40.8488i	0.765571	−	1.32601i
$950$	−2.60230	−	1.28543i	−0.0844299	−	0.0417048i
$951$	−50.9190			−1.65116
$952$	21.7927	−	13.7799i	0.706304	−	0.446608i
$953$	−47.5308			−1.53967			−0.769837	−	0.638241i	$-0.779662\pi$
$953$	−47.5308			−1.53967			−0.769837	+	0.638241i	$0.779662\pi$
$954$	−35.3694	−	17.4710i	−1.14513	−	0.565644i
$955$	1.49648	−	2.59197i	0.0484248	−	0.0838743i
$956$	0.0696488	−	0.0532990i	0.00225260	−	0.00172381i
$957$	−42.8623	+	24.7466i	−1.38554	+	0.799943i
$958$	10.0746	−	6.72211i	0.325495	−	0.217182i
$959$	23.7208	−	9.18550i	0.765986	−	0.296615i
$960$	9.09185	+	22.1952i	0.293438	+	0.716346i
$961$	3.53423	+	6.12147i	0.114008	+	0.197467i
$962$	50.0943	−	3.25051i	1.61510	−	0.104801i
$963$	−13.5050	−	7.79713i	−0.435193	−	0.251259i
$964$	0.594616	+	4.56258i	0.0191513	+	0.146951i
$965$			14.7088i			0.473494i
$966$	27.0843	−	12.5610i	0.871424	−	0.404144i
$967$			29.3643i			0.944292i	0.881520	+	0.472146i	$0.156521\pi$
$967$			29.3643i			0.944292i	−0.881520	+	0.472146i	$0.843479\pi$
$968$	−12.7763	+	11.1603i	−0.410645	+	0.358705i
$969$	18.3607	+	10.6005i	0.589829	+	0.340538i
$970$	−0.0169829	−	0.261728i	−0.000545289	−	0.00840357i
$971$	13.3188	+	23.0688i	0.427419	+	0.740312i	0.996643	−	0.0818708i	$-0.0260895\pi$
$971$	13.3188	+	23.0688i	0.427419	+	0.740312i	−0.569224	+	0.822183i	$0.692756\pi$
$972$	−0.153506	+	0.369231i	−0.00492370	+	0.0118431i
$973$	15.4523	+	12.4382i	0.495379	+	0.398749i
$974$	−24.8391	−	37.2269i	−0.795895	−	1.19283i
$975$	−8.23364	+	4.75369i	−0.263687	+	0.152240i
$976$	−2.60053	−	9.80770i	−0.0832411	−	0.313937i
$977$	−7.73476	+	13.3970i	−0.247457	+	0.428608i	−0.962819	−	0.270146i	$-0.912928\pi$
$977$	−7.73476	+	13.3970i	−0.247457	+	0.428608i	0.715363	+	0.698753i	$0.246261\pi$
$978$	−20.3770	+	41.2526i	−0.651585	+	1.31911i
$979$	−15.7018			−0.501832
$980$	2.48848	−	13.7771i	0.0794916	−	0.440092i
$981$	6.00019			0.191571
$982$	−22.4085	+	45.3652i	−0.715083	+	1.44766i
$983$	22.0131	−	38.1277i	0.702107	−	1.21609i	−0.265618	−	0.964078i	$-0.585576\pi$
$983$	22.0131	−	38.1277i	0.702107	−	1.21609i	0.967725	−	0.252007i	$-0.0810907\pi$
$984$	−4.00296	+	11.7169i	−0.127610	+	0.373521i
$985$	−4.17206	+	2.40874i	−0.132933	+	0.0767489i
$986$	−19.9615	−	29.9167i	−0.635703	−	0.952743i
$987$	37.8591	+	30.4743i	1.20507	+	0.970006i
$988$	−12.0191	−	4.99686i	−0.382378	−	0.158971i
$989$	13.2503	+	22.9502i	0.421336	+	0.729775i
$990$	1.22657	+	18.9029i	0.0389830	+	0.600775i
$991$	−14.4776	−	8.35865i	−0.459896	−	0.265521i	0.252104	−	0.967700i	$-0.418877\pi$
$991$	−14.4776	−	8.35865i	−0.459896	−	0.265521i	−0.712001	+	0.702179i	$0.752211\pi$
$992$	8.80969	+	26.2335i	0.279708	+	0.832916i
$993$			24.9751i			0.792560i
$994$	0.720785	−	0.334282i	0.0228619	−	0.0106028i
$995$		−	1.27436i		−	0.0403999i
$996$	−64.9146	+	8.45996i	−2.05690	+	0.268064i
$997$	23.8844	+	13.7897i	0.756427	+	0.436723i	0.828011	−	0.560711i	$-0.189472\pi$
$997$	23.8844	+	13.7897i	0.756427	+	0.436723i	−0.0715845	+	0.997435i	$0.522806\pi$
$998$	58.3053	−	3.78331i	1.84562	−	0.119759i
$999$	50.1540	+	86.8693i	1.58680	+	2.74842i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.o.a.31.3	✓	32
4.3	odd	2	inner	140.2.o.a.31.8	yes	32
5.2	odd	4		700.2.t.c.199.11		32
5.3	odd	4		700.2.t.d.199.6		32
5.4	even	2		700.2.p.c.451.14		32
7.2	even	3		980.2.o.f.411.8		32
7.3	odd	6		980.2.g.a.391.25		32
7.4	even	3		980.2.g.a.391.26		32
7.5	odd	6	inner	140.2.o.a.131.8	yes	32
7.6	odd	2		980.2.o.f.31.3		32
20.3	even	4		700.2.t.d.199.1		32
20.7	even	4		700.2.t.c.199.16		32
20.19	odd	2		700.2.p.c.451.9		32
28.3	even	6		980.2.g.a.391.28		32
28.11	odd	6		980.2.g.a.391.27		32
28.19	even	6	inner	140.2.o.a.131.3	yes	32
28.23	odd	6		980.2.o.f.411.3		32
28.27	even	2		980.2.o.f.31.8		32
35.12	even	12		700.2.t.d.299.1		32
35.19	odd	6		700.2.p.c.551.9		32
35.33	even	12		700.2.t.c.299.16		32
140.19	even	6		700.2.p.c.551.14		32
140.47	odd	12		700.2.t.d.299.6		32
140.103	odd	12		700.2.t.c.299.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.3	✓	32	1.1	even	1	trivial
140.2.o.a.31.8	yes	32	4.3	odd	2	inner
140.2.o.a.131.3	yes	32	28.19	even	6	inner
140.2.o.a.131.8	yes	32	7.5	odd	6	inner
700.2.p.c.451.9		32	20.19	odd	2
700.2.p.c.451.14		32	5.4	even	2
700.2.p.c.551.9		32	35.19	odd	6
700.2.p.c.551.14		32	140.19	even	6
700.2.t.c.199.11		32	5.2	odd	4
700.2.t.c.199.16		32	20.7	even	4
700.2.t.c.299.11		32	140.103	odd	12
700.2.t.c.299.16		32	35.33	even	12
700.2.t.d.199.1		32	20.3	even	4
700.2.t.d.199.6		32	5.3	odd	4
700.2.t.d.299.1		32	35.12	even	12
700.2.t.d.299.6		32	140.47	odd	12
980.2.g.a.391.25		32	7.3	odd	6
980.2.g.a.391.26		32	7.4	even	3
980.2.g.a.391.27		32	28.11	odd	6
980.2.g.a.391.28		32	28.3	even	6
980.2.o.f.31.3		32	7.6	odd	2
980.2.o.f.31.8		32	28.27	even	2
980.2.o.f.411.3		32	28.23	odd	6
980.2.o.f.411.8		32	7.2	even	3

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

Introduction

L-functions

Modular forms

Varieties

Fields

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Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	140.2.o.a.31.3

Level	$140$
Weight	$2$
Character	140.31
Analytic conductor	$1.118$
Analytic rank	$0$
Dimension	$32$
Inner twists	$4$