LMFDB - Embedded newform 425.2.k.b.86.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			86.17
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.55652 - 1.13088i) q^{2} +(0.803039 - 2.47150i) q^{3} +(0.525836 - 1.61836i) q^{4} +(-1.36443 - 1.77154i) q^{5} +(-1.54502 - 4.75508i) q^{6} +3.93026 q^{7} +(0.177386 + 0.545938i) q^{8} +(-3.03639 - 2.20607i) q^{9} +(-4.12715 - 1.21443i) q^{10} +(-3.76030 + 2.73201i) q^{11} +(-3.57750 - 2.59921i) q^{12} +(1.58924 + 1.15465i) q^{13} +(6.11753 - 4.44465i) q^{14} +(-5.47404 + 1.94957i) q^{15} +(3.64681 + 2.64956i) q^{16} +(0.309017 + 0.951057i) q^{17} -7.22100 q^{18} +(0.639301 + 1.96757i) q^{19} +(-3.58444 + 1.27659i) q^{20} +(3.15615 - 9.71365i) q^{21} +(-2.76340 + 8.50487i) q^{22} +(-4.36700 + 3.17281i) q^{23} +1.49173 q^{24} +(-1.27668 + 4.83426i) q^{25} +3.77944 q^{26} +(-1.58348 + 1.15047i) q^{27} +(2.06667 - 6.36057i) q^{28} +(0.927920 - 2.85584i) q^{29} +(-6.31573 + 9.22502i) q^{30} +(-1.99713 - 6.14652i) q^{31} +7.52459 q^{32} +(3.73251 + 11.4875i) q^{33} +(1.55652 + 1.13088i) q^{34} +(-5.36256 - 6.96260i) q^{35} +(-5.16685 + 3.75393i) q^{36} +(1.10767 + 0.804766i) q^{37} +(3.22016 + 2.33959i) q^{38} +(4.12993 - 3.00057i) q^{39} +(0.725118 - 1.05914i) q^{40} +(-6.04391 - 4.39116i) q^{41} +(-6.07233 - 18.6887i) q^{42} -6.18377 q^{43} +(2.44408 + 7.52209i) q^{44} +(0.234807 + 8.38909i) q^{45} +(-3.20926 + 9.87709i) q^{46} +(2.33983 - 7.20126i) q^{47} +(9.47692 - 6.88538i) q^{48} +8.44696 q^{49} +(3.47979 + 8.96839i) q^{50} +2.59869 q^{51} +(2.70431 - 1.96479i) q^{52} +(-1.43999 + 4.43182i) q^{53} +(-1.16369 + 3.58146i) q^{54} +(9.97051 + 2.93386i) q^{55} +(0.697173 + 2.14568i) q^{56} +5.37622 q^{57} +(-1.78529 - 5.49455i) q^{58} +(9.22330 + 6.70112i) q^{59} +(0.276651 + 9.88410i) q^{60} +(-9.46018 + 6.87323i) q^{61} +(-10.0595 - 7.30868i) q^{62} +(-11.9338 - 8.67042i) q^{63} +(4.41857 - 3.21028i) q^{64} +(-0.122897 - 4.39082i) q^{65} +(18.8007 + 13.6595i) q^{66} +(3.87128 + 11.9146i) q^{67} +1.70164 q^{68} +(4.33473 + 13.3409i) q^{69} +(-16.2208 - 4.77303i) q^{70} +(1.42335 - 4.38063i) q^{71} +(0.665762 - 2.04901i) q^{72} +(11.7723 - 8.55307i) q^{73} +2.63420 q^{74} +(10.9227 + 7.03741i) q^{75} +3.52039 q^{76} +(-14.7790 + 10.7375i) q^{77} +(3.03504 - 9.34089i) q^{78} +(2.94078 - 9.05078i) q^{79} +(-0.282011 - 10.0756i) q^{80} +(-1.90761 - 5.87102i) q^{81} -14.3733 q^{82} +(-3.24121 - 9.97543i) q^{83} +(-14.0605 - 10.2156i) q^{84} +(1.26320 - 1.84508i) q^{85} +(-9.62516 + 6.99309i) q^{86} +(-6.31307 - 4.58671i) q^{87} +(-2.15853 - 1.56827i) q^{88} +(-5.12278 + 3.72192i) q^{89} +(9.85252 + 12.7923i) q^{90} +(6.24611 + 4.53807i) q^{91} +(2.83841 + 8.73574i) q^{92} -16.7949 q^{93} +(-4.50175 - 13.8550i) q^{94} +(2.61333 - 3.81715i) q^{95} +(6.04254 - 18.5970i) q^{96} +(0.162858 - 0.501227i) q^{97} +(13.1479 - 9.55249i) q^{98} +17.4447 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	1.55652	−	1.13088i	1.10063	−	0.799652i	0.119464	−	0.992839i	$-0.461882\pi$
$2$	1.55652	−	1.13088i	1.10063	−	0.799652i	0.981162	+	0.193187i	$0.0618824\pi$
$3$	0.803039	−	2.47150i	0.463635	−	1.42692i	−0.397056	−	0.917794i	$-0.629968\pi$
$3$	0.803039	−	2.47150i	0.463635	−	1.42692i	0.860691	−	0.509127i	$-0.170032\pi$
$4$	0.525836	−	1.61836i	0.262918	−	0.809178i
$5$	−1.36443	−	1.77154i	−0.610190	−	0.792255i
$5$	−1.36443	−	1.77154i	−0.610190	−	0.792255i
$6$	−1.54502	−	4.75508i	−0.630751	−	1.94125i
$7$	3.93026			1.48550			0.742750	−	0.669569i	$-0.233521\pi$
$7$	3.93026			1.48550			0.742750	+	0.669569i	$0.233521\pi$
$8$	0.177386	+	0.545938i	0.0627154	+	0.193018i
$9$	−3.03639	−	2.20607i	−1.01213	−	0.735356i
$10$	−4.12715	−	1.21443i	−1.30512	−	0.384037i
$11$	−3.76030	+	2.73201i	−1.13377	+	0.823733i	−0.986239	−	0.165324i	$-0.947133\pi$
$11$	−3.76030	+	2.73201i	−1.13377	+	0.823733i	−0.147533	+	0.989057i	$0.547133\pi$
$12$	−3.57750	−	2.59921i	−1.03274	−	0.750326i
$13$	1.58924	+	1.15465i	0.440775	+	0.320242i	0.785943	−	0.618299i	$-0.212178\pi$
$13$	1.58924	+	1.15465i	0.440775	+	0.320242i	−0.345168	+	0.938541i	$0.612178\pi$
$14$	6.11753	−	4.44465i	1.63498	−	1.18788i
$15$	−5.47404	+	1.94957i	−1.41339	+	0.503377i
$16$	3.64681	+	2.64956i	0.911702	+	0.662390i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	−7.22100			−1.70201
$19$	0.639301	+	1.96757i	0.146666	+	0.451391i	0.997221	−	0.0744943i	$-0.0237342\pi$
$19$	0.639301	+	1.96757i	0.146666	+	0.451391i	−0.850556	+	0.525885i	$0.823734\pi$
$20$	−3.58444	+	1.27659i	−0.801505	+	0.285455i
$21$	3.15615	−	9.71365i	0.688729	−	2.11969i
$22$	−2.76340	+	8.50487i	−0.589159	+	1.81325i
$23$	−4.36700	+	3.17281i	−0.910582	+	0.661577i	−0.941162	−	0.337956i	$-0.890265\pi$
$23$	−4.36700	+	3.17281i	−0.910582	+	0.661577i	0.0305798	+	0.999532i	$0.490265\pi$
$24$	1.49173			0.304499
$25$	−1.27668	+	4.83426i	−0.255336	+	0.966852i
$26$	3.77944			0.741210
$27$	−1.58348	+	1.15047i	−0.304742	+	0.221408i
$28$	2.06667	−	6.36057i	0.390565	−	1.20203i
$29$	0.927920	−	2.85584i	0.172310	−	0.530317i	−0.827190	−	0.561922i	$-0.810062\pi$
$29$	0.927920	−	2.85584i	0.172310	−	0.530317i	0.999500	+	0.0316053i	$0.0100620\pi$
$30$	−6.31573	+	9.22502i	−1.15309	+	1.68425i
$31$	−1.99713	−	6.14652i	−0.358694	−	1.10395i	−0.953836	−	0.300327i	$-0.902904\pi$
$31$	−1.99713	−	6.14652i	−0.358694	−	1.10395i	0.595142	−	0.803621i	$-0.297096\pi$
$32$	7.52459			1.33017
$33$	3.73251	+	11.4875i	0.649747	+	1.99971i
$34$	1.55652	+	1.13088i	0.266941	+	0.193944i
$35$	−5.36256	−	6.96260i	−0.906437	−	1.17689i
$36$	−5.16685	+	3.75393i	−0.861141	+	0.625656i
$37$	1.10767	+	0.804766i	0.182099	+	0.132303i	0.675100	−	0.737726i	$-0.264100\pi$
$37$	1.10767	+	0.804766i	0.182099	+	0.132303i	−0.493001	+	0.870029i	$0.664100\pi$
$38$	3.22016	+	2.33959i	0.522379	+	0.379531i
$39$	4.12993	−	3.00057i	0.661318	−	0.480476i
$40$	0.725118	−	1.05914i	0.114651	−	0.167464i
$41$	−6.04391	−	4.39116i	−0.943900	−	0.685783i	0.00545631	−	0.999985i	$-0.498263\pi$
$41$	−6.04391	−	4.39116i	−0.943900	−	0.685783i	−0.949356	+	0.314202i	$0.898263\pi$
$42$	−6.07233	−	18.6887i	−0.936981	−	2.88373i
$43$	−6.18377			−0.943016			−0.471508	−	0.881862i	$-0.656290\pi$
$43$	−6.18377			−0.943016			−0.471508	+	0.881862i	$0.656290\pi$
$44$	2.44408	+	7.52209i	0.368458	+	1.13400i
$45$	0.234807	+	8.38909i	0.0350029	+	1.25057i
$46$	−3.20926	+	9.87709i	−0.473180	+	1.45630i
$47$	2.33983	−	7.20126i	0.341299	−	1.05041i	−0.622236	−	0.782830i	$-0.713775\pi$
$47$	2.33983	−	7.20126i	0.341299	−	1.05041i	0.963535	−	0.267582i	$-0.0862245\pi$
$48$	9.47692	−	6.88538i	1.36787	−	0.993819i
$49$	8.44696			1.20671
$50$	3.47979	+	8.96839i	0.492116	+	1.26832i
$51$	2.59869			0.363889
$52$	2.70431	−	1.96479i	0.375020	−	0.272468i
$53$	−1.43999	+	4.43182i	−0.197797	+	0.608758i	0.802135	+	0.597142i	$0.203697\pi$
$53$	−1.43999	+	4.43182i	−0.197797	+	0.608758i	−0.999933	+	0.0116152i	$0.996303\pi$
$54$	−1.16369	+	3.58146i	−0.158358	+	0.487375i
$55$	9.97051	+	2.93386i	1.34442	+	0.395602i
$56$	0.697173	+	2.14568i	0.0931637	+	0.286728i
$57$	5.37622			0.712098
$58$	−1.78529	−	5.49455i	−0.234420	−	0.721469i
$59$	9.22330	+	6.70112i	1.20077	+	0.872412i	0.994360	−	0.106053i	$-0.0338214\pi$
$59$	9.22330	+	6.70112i	1.20077	+	0.872412i	0.206412	+	0.978465i	$0.433821\pi$
$60$	0.276651	+	9.88410i	0.0357155	+	1.27603i
$61$	−9.46018	+	6.87323i	−1.21125	+	0.880026i	−0.995344	−	0.0963873i	$-0.969271\pi$
$61$	−9.46018	+	6.87323i	−1.21125	+	0.880026i	−0.215908	+	0.976414i	$0.569271\pi$
$62$	−10.0595	−	7.30868i	−1.27756	−	0.928203i
$63$	−11.9338	−	8.67042i	−1.50352	−	1.09237i
$64$	4.41857	−	3.21028i	0.552321	−	0.401285i
$65$	−0.122897	−	4.39082i	−0.0152435	−	0.544614i
$66$	18.8007	+	13.6595i	2.31420	+	1.68137i
$67$	3.87128	+	11.9146i	0.472952	+	1.45560i	0.848699	+	0.528876i	$0.177386\pi$
$67$	3.87128	+	11.9146i	0.472952	+	1.45560i	−0.375747	+	0.926722i	$0.622614\pi$
$68$	1.70164			0.206354
$69$	4.33473	+	13.3409i	0.521840	+	1.60606i
$70$	−16.2208	−	4.77303i	−1.93875	−	0.570486i
$71$	1.42335	−	4.38063i	0.168921	−	0.519885i	−0.830383	−	0.557193i	$-0.811878\pi$
$71$	1.42335	−	4.38063i	0.168921	−	0.519885i	0.999304	+	0.0373083i	$0.0118783\pi$
$72$	0.665762	−	2.04901i	0.0784608	−	0.241478i
$73$	11.7723	−	8.55307i	1.37784	−	1.00106i	0.380764	−	0.924672i	$-0.375661\pi$
$73$	11.7723	−	8.55307i	1.37784	−	1.00106i	0.997078	−	0.0763891i	$-0.0243391\pi$
$74$	2.63420			0.306219
$75$	10.9227	+	7.03741i	1.26124	+	0.812610i
$76$	3.52039			0.403817
$77$	−14.7790	+	10.7375i	−1.68422	+	1.22366i
$78$	3.03504	−	9.34089i	0.343651	−	1.05765i
$79$	2.94078	−	9.05078i	0.330863	−	1.01829i	−0.637861	−	0.770152i	$-0.720180\pi$
$79$	2.94078	−	9.05078i	0.330863	−	1.01829i	0.968724	−	0.248141i	$-0.0798195\pi$
$80$	−0.282011	−	10.0756i	−0.0315297	−	1.12648i
$81$	−1.90761	−	5.87102i	−0.211957	−	0.652336i
$82$	−14.3733			−1.58727
$83$	−3.24121	−	9.97543i	−0.355769	−	1.09495i	−0.955562	−	0.294790i	$-0.904750\pi$
$83$	−3.24121	−	9.97543i	−0.355769	−	1.09495i	0.599793	−	0.800156i	$-0.295250\pi$
$84$	−14.0605	−	10.2156i	−1.53413	−	1.11461i
$85$	1.26320	−	1.84508i	0.137013	−	0.200127i
$86$	−9.62516	+	6.99309i	−1.03791	+	0.754084i
$87$	−6.31307	−	4.58671i	−0.676832	−	0.491747i
$88$	−2.15853	−	1.56827i	−0.230100	−	0.167178i
$89$	−5.12278	+	3.72192i	−0.543014	+	0.394522i	−0.825203	−	0.564836i	$-0.808939\pi$
$89$	−5.12278	+	3.72192i	−0.543014	+	0.394522i	0.282189	+	0.959359i	$0.408939\pi$
$90$	9.85252	+	12.7923i	1.03855	+	1.34842i
$91$	6.24611	+	4.53807i	0.654771	+	0.475719i
$92$	2.83841	+	8.73574i	0.295925	+	0.910764i
$93$	−16.7949			−1.74155
$94$	−4.50175	−	13.8550i	−0.464320	−	1.42903i
$95$	2.61333	−	3.81715i	0.268122	−	0.391631i
$96$	6.04254	−	18.5970i	0.616714	−	1.89805i
$97$	0.162858	−	0.501227i	0.0165358	−	0.0508919i	−0.942448	−	0.334352i	$-0.891482\pi$
$97$	0.162858	−	0.501227i	0.0165358	−	0.0508919i	0.958984	+	0.283460i	$0.0914825\pi$
$98$	13.1479	−	9.55249i	1.32814	−	0.964947i
$99$	17.4447			1.75326
$100$	7.15224	+	4.60815i	0.715224	+	0.460815i
$101$	−11.7714			−1.17130			−0.585651	−	0.810563i	$-0.699161\pi$
$101$	−11.7714			−1.17130			−0.585651	+	0.810563i	$0.699161\pi$
$102$	4.04491	−	2.93880i	0.400506	−	0.290985i
$103$	0.806326	−	2.48162i	0.0794497	−	0.244521i	−0.903440	−	0.428714i	$-0.858967\pi$
$103$	0.806326	−	2.48162i	0.0794497	−	0.244521i	0.982890	+	0.184192i	$0.0589670\pi$
$104$	−0.348457	+	1.07244i	−0.0341691	+	0.105162i
$105$	−21.5144	+	7.66232i	−2.09959	+	0.747766i
$106$	2.77048	+	8.52667i	0.269093	+	0.828183i
$107$	−7.19863			−0.695918			−0.347959	−	0.937510i	$-0.613125\pi$
$107$	−7.19863			−0.695918			−0.347959	+	0.937510i	$0.613125\pi$
$108$	1.02922	+	3.16760i	0.0990363	+	0.304803i
$109$	8.53326	+	6.19977i	0.817338	+	0.593831i	0.915949	−	0.401295i	$-0.131440\pi$
$109$	8.53326	+	6.19977i	0.817338	+	0.593831i	−0.0986109	+	0.995126i	$0.531440\pi$
$110$	18.8371	−	6.70881i	1.79605	−	0.639660i
$111$	2.87848	−	2.09134i	0.273213	−	0.198501i
$112$	14.3329	+	10.4135i	1.35433	+	0.983980i
$113$	5.94807	+	4.32153i	0.559548	+	0.406535i	0.831293	−	0.555834i	$-0.187601\pi$
$113$	5.94807	+	4.32153i	0.559548	+	0.406535i	−0.271746	+	0.962369i	$0.587601\pi$
$114$	8.36820	−	6.07985i	0.783754	−	0.569431i
$115$	11.5792	+	3.40723i	1.07977	+	0.317726i
$116$	−4.13384	−	3.00341i	−0.383818	−	0.278860i
$117$	−2.27831	−	7.01192i	−0.210630	−	0.648252i
$118$	21.9344			2.01923
$119$	1.21452	+	3.73790i	0.111335	+	0.342653i
$120$	−2.03536	−	2.64266i	−0.185802	−	0.241241i
$121$	3.27673	−	10.0847i	0.297885	−	0.916795i
$122$	−6.95219	+	21.3966i	−0.629421	+	1.93716i
$123$	−15.7062	+	11.4113i	−1.41618	+	1.02892i
$124$	−10.9974			−0.987598
$125$	10.3060	−	4.33432i	0.921797	−	0.387673i
$126$	−28.3804			−2.52833
$127$	−3.47951	+	2.52801i	−0.308756	+	0.224325i	−0.731363	−	0.681989i	$-0.761115\pi$
$127$	−3.47951	+	2.52801i	−0.308756	+	0.224325i	0.422606	+	0.906313i	$0.361115\pi$
$128$	−1.40330	+	4.31890i	−0.124035	+	0.381741i
$129$	−4.96581	+	15.2832i	−0.437215	+	1.34561i
$130$	−5.15677	−	6.69542i	−0.452279	−	0.587227i
$131$	6.54583	+	20.1460i	0.571912	+	1.76016i	0.646463	+	0.762945i	$0.276248\pi$
$131$	6.54583	+	20.1460i	0.571912	+	1.76016i	−0.0745514	+	0.997217i	$0.523752\pi$
$132$	20.5535			1.78896
$133$	2.51262	+	7.73305i	0.217872	+	0.670541i
$134$	19.4997	+	14.1673i	1.68452	+	1.22387i
$135$	4.19865	+	1.23547i	0.361362	+	0.106332i
$136$	−0.464402	+	0.337408i	−0.0398222	+	0.0289325i
$137$	−16.4874	−	11.9788i	−1.40862	−	1.02342i	−0.993522	−	0.113643i	$-0.963748\pi$
$137$	−16.4874	−	11.9788i	−1.40862	−	1.02342i	−0.415096	−	0.909778i	$-0.636252\pi$
$138$	21.8341	+	15.8634i	1.85864	+	1.35038i
$139$	−6.13935	+	4.46050i	−0.520733	+	0.378335i	−0.816880	−	0.576808i	$-0.804298\pi$
$139$	−6.13935	+	4.46050i	−0.520733	+	0.378335i	0.296147	+	0.955142i	$0.404298\pi$
$140$	−14.0878	+	5.01734i	−1.19064	+	0.424043i
$141$	−15.9189	−	11.5658i	−1.34062	−	0.974015i
$142$	−2.73848	−	8.42817i	−0.229808	−	0.707276i
$143$	−9.13051			−0.763532
$144$	−5.22802	−	16.0902i	−0.435669	−	1.34085i
$145$	−6.32531	+	2.25275i	−0.525288	+	0.187081i
$146$	8.65133	−	26.6261i	0.715989	−	2.20359i
$147$	6.78324	−	20.8767i	0.559472	−	1.72188i
$148$	1.88485	−	1.36942i	0.154934	−	0.112566i
$149$	0.328955			0.0269490			0.0134745	−	0.999909i	$-0.495711\pi$
$149$	0.328955			0.0269490			0.0134745	+	0.999909i	$0.495711\pi$
$150$	24.9598	−	1.39832i	2.03796	−	0.114172i
$151$	−8.05689			−0.655661			−0.327830	−	0.944737i	$-0.606317\pi$
$151$	−8.05689			−0.655661			−0.327830	+	0.944737i	$0.606317\pi$
$152$	−0.960766	+	0.698037i	−0.0779284	+	0.0566183i
$153$	1.15980	−	3.56949i	0.0937641	−	0.288576i
$154$	−10.8609	+	33.4264i	−0.875196	+	2.69357i
$155$	−8.16385	+	11.9245i	−0.655736	+	0.957796i
$156$	−2.68433	−	8.26150i	−0.214918	−	0.661450i
$157$	19.3565			1.54481			0.772407	−	0.635127i	$-0.219052\pi$
$157$	19.3565			1.54481			0.772407	+	0.635127i	$0.219052\pi$
$158$	−5.65795	−	17.4134i	−0.450122	−	1.38533i
$159$	9.79689	+	7.11785i	0.776944	+	0.564483i
$160$	−10.2668	−	13.3301i	−0.811658	−	1.05384i
$161$	−17.1635	+	12.4700i	−1.35267	+	0.982772i
$162$	−9.60864	−	6.98109i	−0.754926	−	0.548486i
$163$	−17.7434	−	12.8913i	−1.38977	−	1.00972i	−0.995891	−	0.0905608i	$-0.971134\pi$
$163$	−17.7434	−	12.8913i	−1.38977	−	1.00972i	−0.393876	−	0.919164i	$-0.628866\pi$
$164$	−10.2846	+	7.47217i	−0.803089	+	0.583479i
$165$	15.2578	−	22.2861i	1.18781	−	1.73497i
$166$	−16.3260	−	11.8615i	−1.26714	−	0.920634i
$167$	6.68399	+	20.5712i	0.517223	+	1.59185i	0.779201	+	0.626774i	$0.215625\pi$
$167$	6.68399	+	20.5712i	0.517223	+	1.59185i	−0.261979	+	0.965074i	$0.584375\pi$
$168$	5.86290			0.452333
$169$	−2.82476	−	8.69372i	−0.217289	−	0.668748i
$170$	−0.120367	−	4.30043i	−0.00923173	−	0.329828i
$171$	2.39942	−	7.38464i	0.183488	−	0.564718i
$172$	−3.25165	+	10.0075i	−0.247936	+	0.763068i
$173$	−8.54279	+	6.20670i	−0.649496	+	0.471887i	−0.863100	−	0.505034i	$-0.831480\pi$
$173$	−8.54279	+	6.20670i	−0.649496	+	0.471887i	0.213603	+	0.976921i	$0.431480\pi$
$174$	−15.0134			−1.13816
$175$	−5.01768	+	18.9999i	−0.379301	+	1.43626i
$176$	−20.9517			−1.57929
$177$	23.9685	−	17.4141i	1.80158	−	1.30893i
$178$	−3.76468	+	11.5865i	−0.282174	+	0.868443i
$179$	−1.28544	+	3.95618i	−0.0960784	+	0.295699i	−0.987533	−	0.157411i	$-0.949685\pi$
$179$	−1.28544	+	3.95618i	−0.0960784	+	0.295699i	0.891455	+	0.453110i	$0.149685\pi$
$180$	13.7000	+	4.03128i	1.02114	+	0.300474i
$181$	−2.37586	−	7.31214i	−0.176596	−	0.543507i	0.823107	−	0.567887i	$-0.192239\pi$
$181$	−2.37586	−	7.31214i	−0.176596	−	0.543507i	−0.999703	+	0.0243800i	$0.992239\pi$
$182$	14.8542			1.10107
$183$	9.39028	+	28.9003i	0.694150	+	2.13637i
$184$	−2.50680	−	1.82130i	−0.184804	−	0.134268i
$185$	−0.0856567	−	3.06031i	−0.00629761	−	0.224999i
$186$	−26.1416	+	18.9930i	−1.91680	+	1.39263i
$187$	−3.76030	−	2.73201i	−0.274980	−	0.199785i
$188$	−10.4238	−	7.57336i	−0.760237	−	0.552344i
$189$	−6.22351	+	4.52165i	−0.452694	+	0.328901i
$190$	−0.249018	−	8.89683i	−0.0180657	−	0.645444i
$191$	6.79383	+	4.93601i	0.491584	+	0.357157i	0.805793	−	0.592197i	$-0.201739\pi$
$191$	6.79383	+	4.93601i	0.491584	+	0.357157i	−0.314209	+	0.949354i	$0.601739\pi$
$192$	−4.38592	−	13.4985i	−0.316526	−	0.974168i
$193$	7.00251			0.504052			0.252026	−	0.967720i	$-0.418903\pi$
$193$	7.00251			0.504052			0.252026	+	0.967720i	$0.418903\pi$
$194$	−0.313334	−	0.964343i	−0.0224961	−	0.0692358i
$195$	−10.9506	−	3.22226i	−0.784189	−	0.230751i
$196$	4.44172	−	13.6702i	0.317265	−	0.976443i
$197$	−0.397087	+	1.22211i	−0.0282913	+	0.0870716i	−0.964205	−	0.265157i	$-0.914576\pi$
$197$	−0.397087	+	1.22211i	−0.0282913	+	0.0870716i	0.935914	+	0.352229i	$0.114576\pi$
$198$	27.1531	−	19.7279i	1.92969	−	1.40200i
$199$	−4.23070			−0.299907			−0.149953	−	0.988693i	$-0.547912\pi$
$199$	−4.23070			−0.299907			−0.149953	+	0.988693i	$0.547912\pi$
$200$	−2.86567	+	0.160543i	−0.202634	+	0.0113521i
$201$	32.5557			2.29630
$202$	−18.3225	+	13.3121i	−1.28917	+	0.936633i
$203$	3.64697	−	11.2242i	0.255967	−	0.787786i
$204$	1.36648	−	4.20561i	0.0956730	−	0.294451i
$205$	0.467381	+	16.6984i	0.0326433	+	1.16627i
$206$	−1.55134	−	4.77455i	−0.108087	−	0.332658i
$207$	20.2593			1.40812
$208$	2.73633	+	8.42155i	0.189730	+	0.583929i
$209$	−7.77938	−	5.65205i	−0.538111	−	0.390961i
$210$	−24.8225	+	36.2567i	−1.71291	+	2.50195i
$211$	6.76615	−	4.91590i	0.465801	−	0.338424i	−0.330001	−	0.943980i	$-0.607049\pi$
$211$	6.76615	−	4.91590i	0.465801	−	0.338424i	0.795803	+	0.605556i	$0.207049\pi$
$212$	6.41507	+	4.66082i	0.440589	+	0.320107i
$213$	−9.68371	−	7.03563i	−0.663517	−	0.482073i
$214$	−11.2048	+	8.14077i	−0.765945	+	0.556492i
$215$	8.43730	+	10.9548i	0.575419	+	0.747109i
$216$	−0.908972	−	0.660407i	−0.0618477	−	0.0449350i
$217$	−7.84923	−	24.1574i	−0.532840	−	1.63991i
$218$	20.2934			1.37444
$219$	−11.6853	−	35.9637i	−0.789620	−	2.43020i
$220$	9.99089	−	14.5931i	0.673586	−	0.983867i
$221$	−0.607034	+	1.86826i	−0.0408335	+	0.125673i
$222$	2.11536	−	6.51042i	0.141974	−	0.436951i
$223$	4.31680	−	3.13634i	0.289074	−	0.210025i	−0.433791	−	0.901013i	$-0.642825\pi$
$223$	4.31680	−	3.13634i	0.289074	−	0.210025i	0.722866	+	0.690989i	$0.242825\pi$
$224$	29.5736			1.97597
$225$	14.5412	−	11.8623i	0.969413	−	0.790818i
$226$	14.1454			0.940939
$227$	6.85628	−	4.98138i	0.455067	−	0.330626i	−0.336526	−	0.941674i	$-0.609252\pi$
$227$	6.85628	−	4.98138i	0.455067	−	0.330626i	0.791593	+	0.611048i	$0.209252\pi$
$228$	2.82701	−	8.70065i	0.187223	−	0.576214i
$229$	−5.34386	+	16.4467i	−0.353132	+	1.08683i	0.603953	+	0.797020i	$0.293592\pi$
$229$	−5.34386	+	16.4467i	−0.353132	+	1.08683i	−0.957085	+	0.289809i	$0.906408\pi$
$230$	21.8764	−	7.79125i	1.44249	−	0.513739i
$231$	14.6697	+	45.1488i	0.965199	+	2.97058i
$232$	1.72371			0.113167
$233$	−2.37955	−	7.32349i	−0.155889	−	0.479778i	0.842361	−	0.538914i	$-0.181165\pi$
$233$	−2.37955	−	7.32349i	−0.155889	−	0.479778i	−0.998250	+	0.0591364i	$0.981165\pi$
$234$	−11.4759	−	8.33770i	−0.750201	−	0.545053i
$235$	−15.9498	+	5.68050i	−1.04045	+	0.370555i
$236$	15.6948	−	11.4029i	1.02164	−	0.742266i
$237$	−20.0075	−	14.5363i	−1.29962	−	0.944232i
$238$	6.11753	+	4.44465i	0.396541	+	0.288104i
$239$	6.44657	−	4.68371i	0.416994	−	0.302964i	−0.359433	−	0.933171i	$-0.617030\pi$
$239$	6.44657	−	4.68371i	0.416994	−	0.302964i	0.776427	+	0.630207i	$0.217030\pi$
$240$	−25.1283	−	7.39409i	−1.62202	−	0.477287i
$241$	−0.951995	−	0.691665i	−0.0613234	−	0.0445541i	0.556701	−	0.830713i	$-0.312067\pi$
$241$	−0.951995	−	0.691665i	−0.0613234	−	0.0445541i	−0.618025	+	0.786159i	$0.712067\pi$
$242$	−6.30432	−	19.4027i	−0.405257	−	1.24725i
$243$	−21.9140			−1.40578
$244$	6.14882	+	18.9241i	0.393638	+	1.21149i
$245$	−11.5253	−	14.9641i	−0.736322	−	0.956021i
$246$	−11.5423	+	35.5237i	−0.735913	+	2.26491i
$247$	−1.25584	+	3.86509i	−0.0799075	+	0.245930i
$248$	3.00136	−	2.18061i	0.190586	−	0.138469i
$249$	−27.2571			−1.72735
$250$	11.1399	−	18.4013i	0.704550	−	1.16380i
$251$	17.6387			1.11334			0.556672	−	0.830732i	$-0.312078\pi$
$251$	17.6387			1.11334			0.556672	+	0.830732i	$0.312078\pi$
$252$	−20.3071	+	14.7539i	−1.27922	+	0.929411i
$253$	7.75304	−	23.8614i	0.487430	−	1.50015i
$254$	−2.55705	+	7.86979i	−0.160444	+	0.493795i
$255$	−3.54572	−	4.60367i	−0.222042	−	0.288293i
$256$	6.07538	+	18.6981i	0.379711	+	1.16863i
$257$	−28.5502			−1.78091			−0.890455	−	0.455071i	$-0.849614\pi$
$257$	−28.5502			−1.78091			−0.890455	+	0.455071i	$0.849614\pi$
$258$	9.55404	+	29.4043i	0.594809	+	1.83063i
$259$	4.35342	+	3.16294i	0.270508	+	0.196536i
$260$	−7.17053	−	2.10996i	−0.444698	−	0.130854i
$261$	−9.11771	+	6.62441i	−0.564372	+	0.410040i
$262$	32.9714	+	23.9551i	2.03698	+	1.47995i
$263$	−9.66679	−	7.02334i	−0.596080	−	0.433078i	0.248405	−	0.968656i	$-0.420094\pi$
$263$	−9.66679	−	7.02334i	−0.596080	−	0.433078i	−0.844485	+	0.535579i	$0.820094\pi$
$264$	−5.60936	+	4.07544i	−0.345232	+	0.250826i
$265$	9.81589	−	3.49591i	0.602985	−	0.214752i
$266$	12.6561	+	9.19518i	0.775994	+	0.563793i
$267$	5.08493	+	15.6498i	0.311192	+	0.957752i
$268$	21.3177			1.30219
$269$	−9.93517	−	30.5773i	−0.605758	−	1.86433i	−0.491495	−	0.870880i	$-0.663549\pi$
$269$	−9.93517	−	30.5773i	−0.605758	−	1.86433i	−0.114263	−	0.993451i	$-0.536451\pi$
$270$	7.93244	−	2.82512i	0.482753	−	0.171932i
$271$	−3.28658	+	10.1151i	−0.199646	+	0.614446i	0.800245	+	0.599673i	$0.204703\pi$
$271$	−3.28658	+	10.1151i	−0.199646	+	0.614446i	−0.999891	+	0.0147732i	$0.995297\pi$
$272$	−1.39296	+	4.28708i	−0.0844604	+	0.259942i
$273$	16.2317	−	11.7930i	0.982388	−	0.713746i
$274$	−39.2096			−2.36874
$275$	−8.40659	−	21.6662i	−0.506936	−	1.30652i
$276$	23.8697			1.43679
$277$	16.5920	−	12.0548i	0.996915	−	0.724301i	0.0354905	−	0.999370i	$-0.488701\pi$
$277$	16.5920	−	12.0548i	0.996915	−	0.724301i	0.961425	+	0.275069i	$0.0887007\pi$
$278$	−4.51174	+	13.8857i	−0.270596	+	0.832810i
$279$	−7.49558	+	23.0690i	−0.448749	+	1.38111i
$280$	2.84990	−	4.16269i	0.170314	−	0.248768i
$281$	−3.18134	−	9.79117i	−0.189783	−	0.584092i	0.810215	−	0.586133i	$-0.199350\pi$
$281$	−3.18134	−	9.79117i	−0.189783	−	0.584092i	−0.999998	+	0.00204078i	$0.999350\pi$
$282$	−37.8576			−2.25439
$283$	7.58200	+	23.3350i	0.450703	+	1.38712i	0.876106	+	0.482118i	$0.160132\pi$
$283$	7.58200	+	23.3350i	0.450703	+	1.38712i	−0.425403	+	0.905004i	$0.639868\pi$
$284$	−6.34097	−	4.60698i	−0.376267	−	0.273374i
$285$	−7.33547	−	9.52417i	−0.434515	−	0.564163i
$286$	−14.2118	+	10.3255i	−0.840363	+	0.610559i
$287$	−23.7541	−	17.2584i	−1.40216	−	1.01873i
$288$	−22.8476	−	16.5998i	−1.34631	−	0.978150i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−7.29789	+	10.6596i	−0.428547	+	0.625953i
$291$	−1.10800	−	0.805009i	−0.0649521	−	0.0471905i
$292$	−7.65162	−	23.5493i	−0.447777	−	1.37812i
$293$	−9.21889			−0.538573			−0.269287	−	0.963060i	$-0.586788\pi$
$293$	−9.21889			−0.538573			−0.269287	+	0.963060i	$0.586788\pi$
$294$	−13.0507	−	40.1660i	−0.761133	−	2.34253i
$295$	−0.713246	−	25.4826i	−0.0415268	−	1.48365i
$296$	−0.242868	+	0.747471i	−0.0141164	+	0.0434458i
$297$	2.81127	−	8.65221i	0.163127	−	0.502052i
$298$	0.512025	−	0.372008i	0.0296608	−	0.0215498i
$299$	−10.6037			−0.613226
$300$	17.1326	−	13.9762i	0.989149	−	0.806918i
$301$	−24.3038			−1.40085
$302$	−12.5407	+	9.11137i	−0.721637	+	0.524300i
$303$	−9.45292	+	29.0931i	−0.543056	+	1.67136i
$304$	−2.88178	+	8.86920i	−0.165281	+	0.508683i
$305$	25.0839	+	7.38104i	1.43630	+	0.422637i
$306$	−2.23141	−	6.86758i	−0.127561	−	0.392593i
$307$	24.9040			1.42135			0.710674	−	0.703521i	$-0.248390\pi$
$307$	24.9040			1.42135			0.710674	+	0.703521i	$0.248390\pi$
$308$	9.60586	+	29.5638i	0.547345	+	1.68455i
$309$	−5.48581	−	3.98567i	−0.312077	−	0.226737i
$310$	0.777912	+	27.7930i	0.0441825	+	1.57854i
$311$	27.2572	−	19.8035i	1.54561	−	1.12295i	0.598925	−	0.800805i	$-0.295595\pi$
$311$	27.2572	−	19.8035i	1.54561	−	1.12295i	0.946689	−	0.322149i	$-0.104405\pi$
$312$	2.37071	+	1.72243i	0.134215	+	0.0975131i
$313$	−10.7413	−	7.80401i	−0.607134	−	0.441109i	0.241270	−	0.970458i	$-0.422436\pi$
$313$	−10.7413	−	7.80401i	−0.607134	−	0.441109i	−0.848404	+	0.529349i	$0.822436\pi$
$314$	30.1287	−	21.8898i	1.70026	−	1.23531i
$315$	0.922852	+	32.9713i	0.0519968	+	1.85772i
$316$	−13.1010	−	9.51845i	−0.736990	−	0.535455i
$317$	3.52801	+	10.8581i	0.198153	+	0.609852i	0.999925	+	0.0122225i	$0.00389063\pi$
$317$	3.52801	+	10.8581i	0.198153	+	0.609852i	−0.801772	+	0.597630i	$0.796109\pi$
$318$	23.2985			1.30651
$319$	4.31296	+	13.2739i	0.241479	+	0.743197i
$320$	−11.7159	−	3.44746i	−0.654940	−	0.192719i
$321$	−5.78078	+	17.7914i	−0.322652	+	0.993020i
$322$	−12.6132	+	38.8195i	−0.702908	+	2.16333i
$323$	−1.67371	+	1.21602i	−0.0931278	+	0.0676613i
$324$	−10.5045			−0.583583
$325$	−7.61081	+	6.20867i	−0.422172	+	0.344395i
$326$	−42.1964			−2.33704
$327$	22.1753	−	16.1113i	1.22630	−	0.890956i
$328$	1.32519	−	4.07853i	0.0731716	−	0.225199i
$329$	9.19615	−	28.3028i	0.507000	−	1.56039i
$330$	−1.45387	−	51.9435i	−0.0800330	−	2.85939i
$331$	1.43054	+	4.40274i	0.0786295	+	0.241997i	0.982643	−	0.185508i	$-0.0593929\pi$
$331$	1.43054	+	4.40274i	0.0786295	+	0.241997i	−0.904013	+	0.427504i	$0.859393\pi$
$332$	−17.8481			−0.979544
$333$	−1.58794	−	4.88717i	−0.0870184	−	0.267815i
$334$	33.6673	+	24.4607i	1.84219	+	1.33843i
$335$	15.8250	−	23.1147i	0.864614	−	1.26289i
$336$	37.2468	−	27.0614i	2.03198	−	1.47632i
$337$	−0.154693	−	0.112391i	−0.00842668	−	0.00612234i	0.583564	−	0.812067i	$-0.301658\pi$
$337$	−0.154693	−	0.112391i	−0.00842668	−	0.00612234i	−0.591991	+	0.805945i	$0.701658\pi$
$338$	−14.2283	−	10.3375i	−0.773920	−	0.562285i
$339$	15.4572	−	11.2303i	0.839520	−	0.609947i
$340$	−2.32176	−	3.01452i	−0.125915	−	0.163485i
$341$	24.3022	+	17.6566i	1.31604	+	0.956156i
$342$	−4.61639	−	14.2078i	−0.249626	−	0.768269i
$343$	5.68695			0.307066
$344$	−1.09691	−	3.37595i	−0.0591416	−	0.182019i
$345$	17.7195	−	25.8819i	0.953986	−	1.39343i
$346$	−6.27800	+	19.3217i	−0.337508	+	1.03874i
$347$	7.10907	−	21.8795i	0.381635	−	1.17455i	−0.557258	−	0.830340i	$-0.688146\pi$
$347$	7.10907	−	21.8795i	0.381635	−	1.17455i	0.938892	−	0.344211i	$-0.111854\pi$
$348$	−10.7426	+	7.80493i	−0.575862	+	0.418388i
$349$	16.8342			0.901113			0.450557	−	0.892748i	$-0.351226\pi$
$349$	16.8342			0.901113			0.450557	+	0.892748i	$0.351226\pi$
$350$	13.6765	+	35.2481i	0.731038	+	1.88409i
$351$	−3.84492			−0.205226
$352$	−28.2947	+	20.5573i	−1.50811	+	1.09571i
$353$	1.47190	−	4.53003i	0.0783411	−	0.241109i	−0.904214	−	0.427079i	$-0.859543\pi$
$353$	1.47190	−	4.53003i	0.0783411	−	0.241109i	0.982555	+	0.185970i	$0.0595427\pi$
$354$	17.6142	−	54.2109i	0.936184	−	2.88128i
$355$	−9.70250	+	3.45553i	−0.514955	+	0.183400i
$356$	3.32965	+	10.2476i	0.176471	+	0.543122i
$357$	10.2135			0.540557
$358$	2.47314	+	7.61155i	0.130710	+	0.402283i
$359$	16.2441	+	11.8020i	0.857332	+	0.622888i	0.927158	−	0.374671i	$-0.122244\pi$
$359$	16.2441	+	11.8020i	0.857332	+	0.622888i	−0.0698261	+	0.997559i	$0.522244\pi$
$360$	−4.53827	+	1.61630i	−0.239188	+	0.0851863i
$361$	11.9087	−	8.65219i	0.626774	−	0.455378i
$362$	−11.9672	−	8.69468i	−0.628982	−	0.456982i
$363$	−22.2931	−	16.1969i	−1.17008	−	0.850116i
$364$	10.6286	−	7.72216i	0.557092	−	0.404751i
$365$	−31.2145	−	9.18500i	−1.63384	−	0.480765i
$366$	47.2989	+	34.3647i	2.47235	+	1.79627i
$367$	0.909991	+	2.80066i	0.0475012	+	0.146194i	0.971994	−	0.235006i	$-0.0755110\pi$
$367$	0.909991	+	2.80066i	0.0475012	+	0.146194i	−0.924493	+	0.381200i	$0.875511\pi$
$368$	−24.3322			−1.26840
$369$	8.66448	+	26.6665i	0.451055	+	1.38820i
$370$	−3.59417	−	4.66657i	−0.186852	−	0.242604i
$371$	−5.65952	+	17.4182i	−0.293828	+	0.904309i
$372$	−8.83136	+	27.1801i	−0.457885	+	1.40922i
$373$	−29.1118	+	21.1509i	−1.50735	+	1.09515i	−0.540014	+	0.841656i	$0.681581\pi$
$373$	−29.1118	+	21.1509i	−1.50735	+	1.09515i	−0.967336	+	0.253498i	$0.918419\pi$
$374$	−8.94255			−0.462408
$375$	−2.43614	−	28.9519i	−0.125802	−	1.49507i
$376$	4.34649			0.224153
$377$	4.77218	−	3.46719i	0.245780	−	0.178569i
$378$	−4.57359	+	14.0761i	−0.235240	+	0.723995i
$379$	−1.35389	+	4.16683i	−0.0695444	+	0.214036i	−0.979788	−	0.200036i	$-0.935894\pi$
$379$	−1.35389	+	4.16683i	−0.0695444	+	0.214036i	0.910244	+	0.414072i	$0.135894\pi$
$380$	−4.80332	−	6.23650i	−0.246405	−	0.319926i
$381$	3.45380	+	10.6297i	0.176943	+	0.544576i
$382$	16.1568			0.826652
$383$	6.20211	+	19.0881i	0.316913	+	0.975357i	0.974960	+	0.222381i	$0.0713827\pi$
$383$	6.20211	+	19.0881i	0.316913	+	0.975357i	−0.658047	+	0.752977i	$0.728617\pi$
$384$	9.54727	+	6.93650i	0.487207	+	0.353977i
$385$	39.1867	+	11.5309i	1.99714	+	0.587667i
$386$	10.8996	−	7.91899i	0.554773	−	0.403066i
$387$	18.7763	+	13.6418i	0.954455	+	0.693452i
$388$	−0.725527	−	0.527126i	−0.0368330	−	0.0267608i
$389$	25.1330	−	18.2602i	1.27429	−	0.925829i	0.274929	−	0.961465i	$-0.411346\pi$
$389$	25.1330	−	18.2602i	1.27429	−	0.925829i	0.999365	+	0.0356361i	$0.0113457\pi$
$390$	−20.6888	+	7.36828i	−1.04762	+	0.373108i
$391$	−4.36700	−	3.17281i	−0.220849	−	0.160456i
$392$	1.49837	+	4.61152i	0.0756792	+	0.232917i
$393$	55.0474			2.77677
$394$	0.763981	+	2.35129i	0.0384888	+	0.118456i
$395$	−20.0463	+	7.13944i	−1.00864	+	0.359224i
$396$	9.17307	−	28.2318i	0.460964	−	1.41870i
$397$	−7.51927	+	23.1419i	−0.377382	+	1.16146i	0.564476	+	0.825449i	$0.309078\pi$
$397$	−7.51927	+	23.1419i	−0.377382	+	1.16146i	−0.941858	+	0.336012i	$0.890922\pi$
$398$	−6.58518	+	4.78441i	−0.330085	+	0.239821i
$399$	21.1300			1.05782
$400$	−17.4645	+	14.2470i	−0.873223	+	0.712349i
$401$	6.83556			0.341352			0.170676	−	0.985327i	$-0.445405\pi$
$401$	6.83556			0.341352			0.170676	+	0.985327i	$0.445405\pi$
$402$	50.6736	−	36.8165i	2.52737	−	1.83624i
$403$	3.92316	−	12.0742i	0.195427	−	0.601461i
$404$	−6.18984	+	19.0504i	−0.307956	+	0.947792i
$405$	−7.79793	+	11.3900i	−0.387482	+	0.565972i
$406$	−7.01664	−	21.5950i	−0.348230	−	1.07174i
$407$	−6.36378			−0.315441
$408$	0.460971	+	1.41872i	0.0228215	+	0.0702372i
$409$	−29.8399	−	21.6799i	−1.47549	−	1.07200i	−0.978977	−	0.203973i	$-0.934615\pi$
$409$	−29.8399	−	21.6799i	−1.47549	−	1.07200i	−0.496510	−	0.868031i	$-0.665385\pi$
$410$	19.6114	+	25.4629i	0.968536	+	1.25752i
$411$	−42.8457	+	31.1293i	−2.11342	+	1.53549i
$412$	−3.59215	−	2.60985i	−0.176972	−	0.128578i
$413$	36.2500	+	26.3372i	1.78375	+	1.29597i
$414$	31.5341	−	22.9109i	1.54982	−	1.12601i
$415$	−13.2494	+	19.3527i	−0.650389	+	0.949985i
$416$	11.9583	+	8.68825i	0.586306	+	0.425976i
$417$	6.09399	+	18.7554i	0.298424	+	0.918454i
$418$	−18.5005			−0.904891
$419$	−1.71146	−	5.26732i	−0.0836101	−	0.257326i	0.900508	−	0.434839i	$-0.143195\pi$
$419$	−1.71146	−	5.26732i	−0.0836101	−	0.257326i	−0.984118	+	0.177513i	$0.943195\pi$
$420$	1.08731	+	38.8471i	0.0530554	+	1.89554i
$421$	4.65660	−	14.3316i	0.226949	−	0.698477i	−0.771139	−	0.636667i	$-0.780313\pi$
$421$	4.65660	−	14.3316i	0.226949	−	0.698477i	0.998088	−	0.0618103i	$-0.0196874\pi$
$422$	4.97237	−	15.3034i	0.242051	−	0.744957i
$423$	−22.9911	+	16.7040i	−1.11787	+	0.812177i
$424$	−2.67493			−0.129906
$425$	−4.99217	+	0.279676i	−0.242156	+	0.0135663i
$426$	−23.0293			−1.11577
$427$	−37.1810	+	27.0136i	−1.79931	+	1.30728i
$428$	−3.78530	+	11.6500i	−0.182969	+	0.563122i
$429$	−7.33216	+	22.5661i	−0.354000	+	1.08950i
$430$	25.5213	+	7.50976i	1.23075	+	0.362153i
$431$	3.26009	+	10.0335i	0.157033	+	0.483297i	0.998361	−	0.0572270i	$-0.0182259\pi$
$431$	3.26009	+	10.0335i	0.157033	+	0.483297i	−0.841328	+	0.540524i	$0.818226\pi$
$432$	−8.82290			−0.424492
$433$	−9.92136	−	30.5348i	−0.476790	−	1.46741i	−0.843529	−	0.537084i	$-0.819526\pi$
$433$	−9.92136	−	30.5348i	−0.476790	−	1.46741i	0.366739	−	0.930324i	$-0.380474\pi$
$434$	−39.5366	−	28.7250i	−1.89782	−	1.37885i
$435$	0.488195	+	17.4421i	0.0234071	+	0.836282i
$436$	14.5205	−	10.5498i	0.695408	−	0.505243i
$437$	−9.03454	−	6.56398i	−0.432181	−	0.313998i
$438$	−58.8589	−	42.7635i	−2.81239	−	2.04332i
$439$	9.63245	−	6.99838i	0.459732	−	0.334015i	−0.333694	−	0.942681i	$-0.608295\pi$
$439$	9.63245	−	6.99838i	0.459732	−	0.334015i	0.793426	+	0.608667i	$0.208295\pi$
$440$	0.166921	+	5.96370i	0.00795766	+	0.284308i
$441$	−25.6483	−	18.6346i	−1.22135	−	0.887360i
$442$	1.16791	+	3.59446i	0.0555519	+	0.170971i
$443$	−22.6230			−1.07485			−0.537425	−	0.843312i	$-0.680603\pi$
$443$	−22.6230			−1.07485			−0.537425	+	0.843312i	$0.680603\pi$
$444$	−1.87092	−	5.75810i	−0.0887900	−	0.273268i
$445$	13.5832	+	3.99690i	0.643904	+	0.189471i
$446$	3.17237	−	9.76355i	0.150216	−	0.462317i
$447$	0.264164	−	0.813012i	0.0124945	−	0.0384542i
$448$	17.3661	−	12.6172i	0.820472	−	0.596108i
$449$	1.77633			0.0838301			0.0419151	−	0.999121i	$-0.486654\pi$
$449$	1.77633			0.0838301			0.0419151	+	0.999121i	$0.486654\pi$
$450$	9.21889	−	34.9082i	0.434583	−	1.64559i
$451$	34.7236			1.63507
$452$	10.1215	−	7.35369i	0.476075	−	0.345888i
$453$	−6.47000	+	19.9126i	−0.303987	+	0.935576i
$454$	5.03861	−	15.5072i	0.236474	−	0.727791i
$455$	−0.483017	−	17.2571i	−0.0226442	−	0.809024i
$456$	0.953666	+	2.93508i	0.0446595	+	0.137448i
$457$	8.97124			0.419657			0.209828	−	0.977738i	$-0.432709\pi$
$457$	8.97124			0.419657			0.209828	+	0.977738i	$0.432709\pi$
$458$	10.2814	+	31.6429i	0.480418	+	1.47857i
$459$	−1.58348	−	1.15047i	−0.0739107	−	0.0536993i
$460$	11.6029	−	16.9476i	0.540986	−	0.790187i
$461$	20.2920	−	14.7430i	0.945091	−	0.686649i	−0.00455000	−	0.999990i	$-0.501448\pi$
$461$	20.2920	−	14.7430i	0.945091	−	0.686649i	0.949641	+	0.313341i	$0.101448\pi$
$462$	73.8916	+	53.6854i	3.43775	+	2.49767i
$463$	18.9342	+	13.7565i	0.879945	+	0.639317i	0.933237	−	0.359262i	$-0.116971\pi$
$463$	18.9342	+	13.7565i	0.879945	+	0.639317i	−0.0532921	+	0.998579i	$0.516971\pi$
$464$	10.9507	−	7.95613i	0.508372	−	0.369354i
$465$	22.9154	+	29.7528i	1.06268	+	1.37975i
$466$	−11.9858	−	8.70818i	−0.555231	−	0.403399i
$467$	−5.97177	−	18.3792i	−0.276341	−	0.850489i	−0.988862	−	0.148838i	$-0.952447\pi$
$467$	−5.97177	−	18.3792i	−0.276341	−	0.850489i	0.712521	−	0.701651i	$-0.247553\pi$
$468$	−12.5458			−0.579930
$469$	15.2152	+	46.8274i	0.702571	+	2.16229i
$470$	−18.4023	+	26.8791i	−0.848833	+	1.23984i
$471$	15.5440	−	47.8395i	0.716230	−	2.20433i
$472$	−2.02231	+	6.22403i	−0.0930844	+	0.286484i
$473$	23.2528	−	16.8942i	1.06917	−	0.776794i
$474$	−47.5807			−2.18546
$475$	−10.3279	+	0.578600i	−0.473877	+	0.0265480i
$476$	6.68789			0.306539
$477$	14.1493	−	10.2800i	0.647850	−	0.470691i
$478$	4.73751	−	14.5806i	0.216689	−	0.666900i
$479$	−0.128806	+	0.396425i	−0.00588531	+	0.0181131i	−0.953956	−	0.299946i	$-0.903031\pi$
$479$	−0.128806	+	0.396425i	−0.00588531	+	0.0181131i	0.948071	+	0.318060i	$0.103031\pi$
$480$	−41.1899	+	14.6697i	−1.88005	+	0.669578i
$481$	0.831121	+	2.55793i	0.0378958	+	0.116631i
$482$	−2.26399			−0.103122
$483$	17.0366	+	52.4334i	0.775194	+	2.38580i
$484$	−14.5977	−	10.6058i	−0.663531	−	0.482084i
$485$	−1.11015	+	0.395378i	−0.0504093	+	0.0179532i
$486$	−34.1096	+	24.7821i	−1.54724	+	1.12414i
$487$	1.27733	+	0.928033i	0.0578813	+	0.0420532i	0.616350	−	0.787473i	$-0.288611\pi$
$487$	1.27733	+	0.928033i	0.0578813	+	0.0420532i	−0.558468	+	0.829526i	$0.688611\pi$
$488$	−5.43046	−	3.94546i	−0.245825	−	0.178602i
$489$	−46.1095	+	33.5005i	−2.08514	+	1.51494i
$490$	−34.8619	−	10.2583i	−1.57490	−	0.463421i
$491$	21.7874	+	15.8294i	0.983250	+	0.714373i	0.958432	−	0.285319i	$-0.0920997\pi$
$491$	21.7874	+	15.8294i	0.983250	+	0.714373i	0.0248171	+	0.999692i	$0.492100\pi$
$492$	10.2086	+	31.4187i	0.460238	+	1.41647i
$493$	3.00281			0.135240
$494$	2.41620	+	7.43630i	0.108710	+	0.334575i
$495$	−23.8021	−	30.9040i	−1.06982	−	1.38903i
$496$	9.00245	−	27.7067i	0.404222	−	1.24407i
$497$	5.59415	−	17.2170i	0.250932	−	0.772289i
$498$	−42.4262	+	30.8245i	−1.90116	+	1.38128i
$499$	−13.4622			−0.602650			−0.301325	−	0.953522i	$-0.597429\pi$
$499$	−13.4622			−0.602650			−0.301325	+	0.953522i	$0.597429\pi$
$500$	−1.59520	−	18.9579i	−0.0713397	−	0.847824i
$501$	56.2092			2.51124
$502$	27.4550	−	19.9472i	1.22538	−	0.890288i
$503$	4.93154	−	15.1777i	0.219887	−	0.676741i	−0.778884	−	0.627168i	$-0.784214\pi$
$503$	4.93154	−	15.1777i	0.219887	−	0.676741i	0.998770	−	0.0495732i	$-0.0157861\pi$
$504$	2.61662	−	8.05313i	0.116554	−	0.358715i
$505$	16.0613	+	20.8535i	0.714717	+	0.927970i
$506$	−14.9166	−	45.9085i	−0.663123	−	2.04088i
$507$	−23.7549			−1.05499
$508$	2.26157	+	6.96040i	0.100341	+	0.308818i
$509$	30.1024	+	21.8707i	1.33427	+	0.969401i	0.999634	+	0.0270525i	$0.00861214\pi$
$509$	30.1024	+	21.8707i	1.33427	+	0.969401i	0.334632	+	0.942349i	$0.391388\pi$
$510$	−10.7252	−	3.15593i	−0.474919	−	0.139747i
$511$	46.2682	−	33.6158i	2.04678	−	1.48708i
$512$	23.2540	+	16.8950i	1.02769	+	0.746660i
$513$	−3.27595	−	2.38012i	−0.144637	−	0.105085i
$514$	−44.4389	+	32.2868i	−1.96012	+	1.42411i
$515$	−5.49645	+	1.95755i	−0.242202	+	0.0862600i
$516$	22.1224	+	16.0729i	0.973887	+	0.707570i
$517$	10.8755	+	33.4713i	0.478304	+	1.47207i
$518$	10.3531			0.454888
$519$	8.47967	+	26.0977i	0.372216	+	1.14556i
$520$	2.37531	−	0.845964i	0.104164	−	0.0370980i
$521$	9.32667	−	28.7045i	0.408609	−	1.25757i	−0.509235	−	0.860627i	$-0.670072\pi$
$521$	9.32667	−	28.7045i	0.408609	−	1.25757i	0.917844	−	0.396941i	$-0.129928\pi$
$522$	−6.70051	+	20.6220i	−0.293273	+	0.902602i
$523$	−4.04776	+	2.94087i	−0.176996	+	0.128595i	−0.672756	−	0.739864i	$-0.734890\pi$
$523$	−4.04776	+	2.94087i	−0.176996	+	0.128595i	0.495760	+	0.868460i	$0.334890\pi$
$524$	36.0454			1.57465
$525$	42.9289	+	27.6589i	1.87357	+	1.20713i
$526$	−22.9891			−1.00237
$527$	5.22854	−	3.79876i	0.227759	−	0.165477i
$528$	−16.8250	+	51.7822i	−0.732216	+	2.25353i
$529$	1.89656	−	5.83702i	0.0824593	−	0.253784i
$530$	11.3252	−	16.5420i	0.491934	−	0.718540i
$531$	−13.2224	−	40.6945i	−0.573805	−	1.76599i
$532$	13.8361			0.599869
$533$	−4.53496	−	13.9572i	−0.196431	−	0.604552i
$534$	25.6128	+	18.6088i	1.10837	+	0.805281i
$535$	9.82201	+	12.7526i	0.424642	+	0.551344i
$536$	−5.81791	+	4.22696i	−0.251295	+	0.182577i
$537$	8.74544	+	6.35394i	0.377394	+	0.274193i
$538$	−50.0435	−	36.3587i	−2.15753	−	1.56754i
$539$	−31.7631	+	23.0772i	−1.36813	+	0.994007i
$540$	4.20723	−	6.14525i	0.181050	−	0.264450i
$541$	−26.0628	−	18.9358i	−1.12053	−	0.814112i	−0.136239	−	0.990676i	$-0.543502\pi$
$541$	−26.0628	−	18.9358i	−1.12053	−	0.814112i	−0.984289	+	0.176564i	$0.943502\pi$
$542$	6.32327	+	19.4610i	0.271608	+	0.835922i
$543$	−19.9799			−0.857418
$544$	2.32523	+	7.15631i	0.0996933	+	0.306824i
$545$	−0.659884	−	23.5761i	−0.0282663	−	1.00989i
$546$	11.9285	−	36.7122i	0.510493	−	1.57114i
$547$	4.84260	−	14.9040i	0.207055	−	0.637249i	−0.792568	−	0.609783i	$-0.791256\pi$
$547$	4.84260	−	14.9040i	0.207055	−	0.637249i	0.999623	−	0.0274653i	$-0.00874358\pi$
$548$	−28.0557	+	20.3837i	−1.19848	+	0.870747i
$549$	43.8876			1.87308
$550$	−37.5868	−	24.2170i	−1.60271	−	1.03262i
$551$	6.21228			0.264652
$552$	−6.51440	+	4.73299i	−0.277271	+	0.201449i
$553$	11.5580	−	35.5719i	0.491497	−	1.51267i
$554$	12.1933	−	37.5270i	0.518042	−	1.59437i
$555$	−7.63235	−	2.24585i	−0.323975	−	0.0953311i
$556$	3.99039	+	12.2811i	0.169230	+	0.520837i
$557$	−22.9717			−0.973343			−0.486672	−	0.873585i	$-0.661789\pi$
$557$	−22.9717			−0.973343			−0.486672	+	0.873585i	$0.661789\pi$
$558$	14.4212	+	44.3840i	0.610500	+	1.87893i
$559$	−9.82747	−	7.14007i	−0.415658	−	0.301993i
$560$	−1.10838	−	39.5997i	−0.0468374	−	1.67339i
$561$	−9.77184	+	7.09966i	−0.412567	+	0.299748i
$562$	−16.0244	−	11.6424i	−0.675950	−	0.491107i
$563$	27.7697	+	20.1759i	1.17035	+	0.850312i	0.991051	−	0.133482i	$-0.0426157\pi$
$563$	27.7697	+	20.1759i	1.17035	+	0.850312i	0.179303	+	0.983794i	$0.442616\pi$
$564$	−27.0883	+	19.6808i	−1.14062	+	0.828712i
$565$	−0.459970	−	16.4336i	−0.0193511	−	0.691368i
$566$	38.1906	+	27.7471i	1.60527	+	1.16630i
$567$	−7.49741	−	23.0746i	−0.314862	−	0.969044i
$568$	2.64403			0.110941
$569$	2.18325	+	6.71936i	0.0915267	+	0.281690i	0.986333	−	0.164765i	$-0.0526864\pi$
$569$	2.18325	+	6.71936i	0.0915267	+	0.281690i	−0.894806	+	0.446455i	$0.852686\pi$
$570$	−22.1885	−	6.52905i	−0.929373	−	0.273472i
$571$	−5.58999	+	17.2042i	−0.233934	+	0.719974i	0.763327	+	0.646012i	$0.223564\pi$
$571$	−5.58999	+	17.2042i	−0.233934	+	0.719974i	−0.997261	+	0.0739619i	$0.976436\pi$
$572$	−4.80115	+	14.7764i	−0.200746	+	0.617833i
$573$	17.6551	−	12.8271i	0.737550	−	0.535862i
$574$	−56.4910			−2.35789
$575$	−9.76295	−	25.1619i	−0.407143	−	1.04932i
$576$	−20.4986			−0.854107
$577$	−8.05198	+	5.85011i	−0.335208	+	0.243543i	−0.742637	−	0.669694i	$-0.766425\pi$
$577$	−8.05198	+	5.85011i	−0.335208	+	0.243543i	0.407429	+	0.913237i	$0.366425\pi$
$578$	−0.594538	+	1.82980i	−0.0247295	+	0.0761096i
$579$	5.62329	−	17.3067i	0.233696	−	0.719242i
$580$	0.319673	+	11.4212i	0.0132737	+	0.474239i
$581$	−12.7388	−	39.2061i	−0.528495	−	1.62654i
$582$	−2.63499			−0.109224
$583$	−6.69303	−	20.5990i	−0.277197	−	0.853125i
$584$	6.75768	+	4.90974i	0.279635	+	0.203167i
$585$	−9.31328	+	13.6034i	−0.385057	+	0.562430i
$586$	−14.3494	+	10.4254i	−0.592768	+	0.430671i
$587$	−0.333532	−	0.242325i	−0.0137663	−	0.0100018i	0.580881	−	0.813989i	$-0.302708\pi$
$587$	−0.333532	−	0.242325i	−0.0137663	−	0.0100018i	−0.594647	+	0.803987i	$0.702708\pi$
$588$	−30.2190	−	21.9554i	−1.24621	−	0.905426i
$589$	10.8169	−	7.85896i	0.445704	−	0.323823i
$590$	−29.9279	−	38.8576i	−1.23211	−	1.59974i
$591$	2.70156	+	1.96280i	0.111127	+	0.0807388i
$592$	1.90717	+	5.86965i	0.0783840	+	0.241241i
$593$	−32.6956			−1.34265			−0.671324	−	0.741164i	$-0.734274\pi$
$593$	−32.6956			−1.34265			−0.671324	+	0.741164i	$0.734274\pi$
$594$	−5.40879	−	16.6465i	−0.221925	−	0.683016i
$595$	4.96471	−	7.25166i	0.203533	−	0.297289i
$596$	0.172976	−	0.532367i	0.00708539	−	0.0218066i
$597$	−3.39742	+	10.4562i	−0.139047	+	0.427943i
$598$	−16.5048	+	11.9915i	−0.674932	+	0.490367i
$599$	0.479884			0.0196075			0.00980376	−	0.999952i	$-0.496879\pi$
$599$	0.479884			0.0196075			0.00980376	+	0.999952i	$0.496879\pi$
$600$	−1.90446	+	7.21143i	−0.0777494	+	0.294405i
$601$	−1.86028			−0.0758824			−0.0379412	−	0.999280i	$-0.512080\pi$
$601$	−1.86028			−0.0758824			−0.0379412	+	0.999280i	$0.512080\pi$
$602$	−37.8294	+	27.4847i	−1.54181	+	1.12019i
$603$	14.5296	−	44.7176i	0.591693	−	1.82104i
$604$	−4.23660	+	13.0389i	−0.172385	+	0.530546i
$605$	−22.3364	+	7.95505i	−0.908102	+	0.323419i
$606$	18.1871	+	55.9741i	0.738800	+	2.27379i
$607$	7.27635			0.295338			0.147669	−	0.989037i	$-0.452823\pi$
$607$	7.27635			0.295338			0.147669	+	0.989037i	$0.452823\pi$
$608$	4.81048	+	14.8051i	0.195091	+	0.600427i
$609$	−24.8120	−	18.0270i	−1.00543	−	0.730490i
$610$	47.3906	−	16.8781i	1.91879	−	0.683374i
$611$	12.0335	−	8.74282i	0.486822	−	0.353697i
$612$	−5.16685	−	3.75393i	−0.208857	−	0.151744i
$613$	−15.7524	−	11.4448i	−0.636234	−	0.462251i	0.222320	−	0.974974i	$-0.428637\pi$
$613$	−15.7524	−	11.4448i	−0.636234	−	0.462251i	−0.858554	+	0.512723i	$0.828637\pi$
$614$	38.7636	−	28.1634i	1.56437	−	1.13658i
$615$	41.6455	+	12.2543i	1.67931	+	0.494143i
$616$	−8.48360	−	6.16370i	−0.341814	−	0.248342i
$617$	2.87979	+	8.86307i	0.115936	+	0.356814i	0.992141	−	0.125124i	$-0.0399330\pi$
$617$	2.87979	+	8.86307i	0.115936	+	0.356814i	−0.876205	+	0.481938i	$0.839933\pi$
$618$	−13.0461			−0.524790
$619$	−6.61176	−	20.3489i	−0.265749	−	0.817891i	−0.991520	−	0.129955i	$-0.958517\pi$
$619$	−6.61176	−	20.3489i	−0.265749	−	0.817891i	0.725771	−	0.687936i	$-0.241483\pi$
$620$	15.0052	+	19.4823i	0.602623	+	0.782429i
$621$	3.26486	−	10.0482i	0.131014	−	0.403220i
$622$	20.0310	−	61.6491i	0.803171	−	2.47190i
$623$	−20.1339	+	14.6281i	−0.806646	+	0.586063i
$624$	23.0112			0.921187
$625$	−21.7402	−	12.3436i	−0.869607	−	0.493744i
$626$	−25.5444			−1.02096
$627$	−20.2162	+	14.6879i	−0.807357	+	0.586579i
$628$	10.1783	−	31.3257i	0.406160	−	1.25003i
$629$	−0.423091	+	1.30214i	−0.0168697	+	0.0519197i
$630$	38.7230	+	50.2769i	1.54276	+	2.00308i
$631$	11.4771	+	35.3228i	0.456895	+	1.40618i	0.868896	+	0.494994i	$0.164830\pi$
$631$	11.4771	+	35.3228i	0.456895	+	1.40618i	−0.412001	+	0.911183i	$0.635170\pi$
$632$	5.46281			0.217299
$633$	−6.71616	−	20.6702i	−0.266943	−	0.821567i
$634$	17.7706	+	12.9111i	0.705761	+	0.512766i
$635$	9.22599	+	2.71479i	0.366122	+	0.107733i
$636$	16.6708	−	12.1120i	0.661039	−	0.480273i
$637$	13.4242	+	9.75326i	0.531887	+	0.386438i
$638$	21.7244	+	15.7837i	0.860077	+	0.624882i
$639$	−13.9858	+	10.1613i	−0.553270	+	0.401974i
$640$	9.56579	−	3.40684i	0.378121	−	0.134667i
$641$	−3.86754	−	2.80994i	−0.152759	−	0.110986i	0.508780	−	0.860896i	$-0.330096\pi$
$641$	−3.86754	−	2.80994i	−0.152759	−	0.110986i	−0.661539	+	0.749911i	$0.730096\pi$
$642$	11.1220	+	34.2301i	0.438951	+	1.35095i
$643$	−42.2542			−1.66634			−0.833171	−	0.553016i	$-0.813477\pi$
$643$	−42.2542			−1.66634			−0.833171	+	0.553016i	$0.813477\pi$
$644$	11.1557	+	34.3337i	0.439597	+	1.35294i
$645$	33.8502	−	12.0557i	1.33285	−	0.474692i
$646$	−1.22999	+	3.78553i	−0.0483934	+	0.148940i
$647$	−8.39763	+	25.8453i	−0.330145	+	1.01608i	0.638919	+	0.769274i	$0.279382\pi$
$647$	−8.39763	+	25.8453i	−0.330145	+	1.01608i	−0.969064	+	0.246808i	$0.920618\pi$
$648$	2.86683	−	2.08287i	0.112620	−	0.0818229i
$649$	−52.9899			−2.08004
$650$	−4.82513	+	18.2708i	−0.189257	+	0.716640i
$651$	−66.0084			−2.58707
$652$	−30.1928	+	21.9364i	−1.18244	+	0.859094i
$653$	0.780297	−	2.40151i	0.0305354	−	0.0939783i	−0.934627	−	0.355629i	$-0.884267\pi$
$653$	0.780297	−	2.40151i	0.0305354	−	0.0939783i	0.965163	+	0.261650i	$0.0842668\pi$
$654$	16.2964	−	50.1551i	0.637239	−	1.96122i
$655$	26.7580	−	39.0839i	1.04552	−	1.52713i
$656$	−10.4063	−	32.0274i	−0.406299	−	1.25046i
$657$	−54.6139			−2.13069
$658$	−17.6931	−	54.4537i	−0.689748	−	2.12283i
$659$	24.5275	+	17.8203i	0.955455	+	0.694178i	0.952091	−	0.305816i	$-0.0989292\pi$
$659$	24.5275	+	17.8203i	0.955455	+	0.694178i	0.00336405	+	0.999994i	$0.498929\pi$
$660$	−28.0438	−	36.4113i	−1.09160	−	1.41731i
$661$	−16.1944	+	11.7659i	−0.629890	+	0.457642i	−0.856362	−	0.516376i	$-0.827281\pi$
$661$	−16.1944	+	11.7659i	−0.629890	+	0.457642i	0.226472	+	0.974018i	$0.427281\pi$
$662$	7.20563	+	5.23519i	0.280055	+	0.203472i
$663$	4.12993	+	3.00057i	0.160393	+	0.116532i
$664$	4.87102	−	3.53900i	0.189032	−	0.137340i
$665$	10.2711	−	15.0024i	0.398296	−	0.581767i
$666$	−7.99845	−	5.81121i	−0.309934	−	0.225180i
$667$	5.00883	+	15.4156i	0.193943	+	0.596894i
$668$	36.8062			1.42408
$669$	−4.28490	−	13.1876i	−0.165664	−	0.509861i
$670$	−1.50793	−	53.8747i	−0.0582563	−	2.08136i
$671$	16.7953	−	51.6907i	0.648377	−	1.99550i
$672$	23.7488	−	73.0912i	0.916129	−	2.81955i
$673$	−24.4961	+	17.7975i	−0.944256	+	0.686042i	−0.949441	−	0.313944i	$-0.898349\pi$
$673$	−24.4961	+	17.7975i	−0.944256	+	0.686042i	0.00518518	+	0.999987i	$0.498349\pi$
$674$	−0.367884			−0.0141704
$675$	−3.54007	−	9.12376i	−0.136257	−	0.351174i
$676$	−15.5549			−0.598265
$677$	−19.7449	+	14.3455i	−0.758858	+	0.551342i	−0.898560	−	0.438851i	$-0.855386\pi$
$677$	−19.7449	+	14.3455i	−0.758858	+	0.551342i	0.139702	+	0.990194i	$0.455386\pi$
$678$	11.3593	−	34.9604i	0.436252	−	1.34265i
$679$	0.640076	−	1.96995i	0.0245639	−	0.0755998i
$680$	1.23137	+	0.362337i	0.0472210	+	0.0138950i
$681$	−6.80562	−	20.9455i	−0.260792	−	0.802635i
$682$	57.7942			2.21306
$683$	−6.58116	−	20.2547i	−0.251821	−	0.775026i	−0.994439	−	0.105311i	$-0.966416\pi$
$683$	−6.58116	−	20.2547i	−0.251821	−	0.775026i	0.742618	−	0.669715i	$-0.233584\pi$
$684$	−10.6893	−	7.76622i	−0.408715	−	0.296949i
$685$	1.27499	+	45.5523i	0.0487148	+	1.74047i
$686$	8.85185	−	6.43125i	0.337965	−	0.245546i
$687$	36.3567	+	26.4147i	1.38709	+	1.00778i
$688$	−22.5510	−	16.3843i	−0.859749	−	0.624644i
$689$	−7.40567	+	5.38053i	−0.282134	+	0.204982i
$690$	−1.68845	−	60.3242i	−0.0642781	−	2.29650i
$691$	−5.08827	−	3.69684i	−0.193567	−	0.140635i	0.486781	−	0.873524i	$-0.338171\pi$
$691$	−5.08827	−	3.69684i	−0.193567	−	0.140635i	−0.680347	+	0.732890i	$0.738171\pi$
$692$	5.55255	+	17.0890i	0.211076	+	0.649626i
$693$	68.5624			2.60447
$694$	−13.6776	−	42.0953i	−0.519194	−	1.59792i
$695$	16.2786	+	4.79005i	0.617483	+	0.181697i
$696$	1.38421	−	4.26016i	0.0524683	−	0.161481i
$697$	2.30857	−	7.10504i	0.0874432	−	0.269123i
$698$	26.2028	−	19.0374i	0.991789	−	0.720577i
$699$	−20.0109			−0.756881
$700$	28.1102	+	18.1112i	1.06246	+	0.684540i
$701$	−17.4810			−0.660248			−0.330124	−	0.943938i	$-0.607091\pi$
$701$	−17.4810			−0.660248			−0.330124	+	0.943938i	$0.607091\pi$
$702$	−5.98469	+	4.34813i	−0.225878	+	0.164110i
$703$	−0.875299	+	2.69389i	−0.0330125	+	0.101602i
$704$	−7.84459	+	24.1432i	−0.295654	+	0.909930i
$705$	1.23103	+	43.9816i	0.0463631	+	1.65644i
$706$	−2.83187	−	8.71561i	−0.106579	−	0.328016i
$707$	−46.2648			−1.73997
$708$	−15.5788	−	47.9466i	−0.585486	−	1.80194i
$709$	2.46608	+	1.79171i	0.0926157	+	0.0672892i	0.633129	−	0.774046i	$-0.281770\pi$
$709$	2.46608	+	1.79171i	0.0926157	+	0.0672892i	−0.540514	+	0.841335i	$0.681770\pi$
$710$	−11.1944	+	16.3509i	−0.420117	+	0.613640i
$711$	−28.8960	+	20.9942i	−1.08368	+	0.787342i
$712$	−2.94064	−	2.13650i	−0.110205	−	0.0800688i
$713$	28.2232	+	20.5054i	1.05697	+	0.767931i
$714$	15.8976	−	11.5503i	0.594952	−	0.432258i
$715$	12.4579	+	16.1750i	0.465900	+	0.604912i
$716$	5.72658	+	4.16060i	0.214012	+	0.155489i
$717$	−6.39894	−	19.6939i	−0.238973	−	0.735482i
$718$	38.6310			1.44169
$719$	7.86226	+	24.1976i	0.293213	+	0.902417i	0.983816	+	0.179183i	$0.0573453\pi$
$719$	7.86226	+	24.1976i	0.293213	+	0.902417i	−0.690603	+	0.723234i	$0.742655\pi$
$720$	−21.3711	+	31.2155i	−0.796454	+	1.16333i
$721$	3.16907	−	9.75341i	0.118023	−	0.363236i
$722$	8.75158	−	26.9346i	0.325700	−	1.00240i
$723$	−2.47394	+	1.79742i	−0.0920068	+	0.0668468i
$724$	−13.0830			−0.486224
$725$	12.6212	+	8.13180i	0.468741	+	0.302008i
$726$	−53.0164			−1.96762
$727$	31.0202	−	22.5375i	1.15048	−	0.835870i	0.161932	−	0.986802i	$-0.448228\pi$
$727$	31.0202	−	22.5375i	1.15048	−	0.835870i	0.988544	+	0.150932i	$0.0482276\pi$
$728$	−1.36953	+	4.21498i	−0.0507581	+	0.156217i
$729$	−11.8750	+	36.5474i	−0.439814	+	1.35361i
$730$	−58.9731	+	21.0032i	−2.18269	+	0.777362i
$731$	−1.91089	−	5.88112i	−0.0706768	−	0.217521i
$732$	51.7088			1.91121
$733$	−6.62643	−	20.3941i	−0.244753	−	0.753272i	−0.995677	−	0.0928832i	$-0.970392\pi$
$733$	−6.62643	−	20.3941i	−0.244753	−	0.753272i	0.750924	−	0.660388i	$-0.229608\pi$
$734$	4.58363	+	3.33020i	0.169185	+	0.122920i
$735$	−46.2390	+	16.4679i	−1.70555	+	0.607429i
$736$	−32.8599	+	23.8741i	−1.21123	+	0.880011i
$737$	−47.1080	−	34.2260i	−1.73525	−	1.26073i
$738$	43.6430	+	31.7085i	1.60652	+	1.16721i
$739$	24.4604	−	17.7715i	0.899790	−	0.653736i	−0.0386218	−	0.999254i	$-0.512297\pi$
$739$	24.4604	−	17.7715i	0.899790	−	0.653736i	0.938412	+	0.345518i	$0.112297\pi$
$740$	−4.99772	−	1.47060i	−0.183720	−	0.0540603i
$741$	8.54409	+	6.20764i	0.313875	+	0.228043i
$742$	10.8887	+	33.5121i	0.399738	+	1.23027i
$743$	15.1406			0.555454			0.277727	−	0.960660i	$-0.410419\pi$
$743$	15.1406			0.555454			0.277727	+	0.960660i	$0.410419\pi$
$744$	−2.97918	−	9.16897i	−0.109222	−	0.336151i
$745$	−0.448835	−	0.582756i	−0.0164440	−	0.0213505i
$746$	−21.3939	+	65.8437i	−0.783287	+	2.41071i
$747$	−12.1649	+	37.4396i	−0.445090	+	1.36984i
$748$	−6.39867	+	4.64891i	−0.233959	+	0.169981i
$749$	−28.2925			−1.03379
$750$	−36.5330	−	42.3093i	−1.33400	−	1.54492i
$751$	−0.622963			−0.0227322			−0.0113661	−	0.999935i	$-0.503618\pi$
$751$	−0.622963			−0.0227322			−0.0113661	+	0.999935i	$0.503618\pi$
$752$	27.6131	−	20.0621i	1.00695	−	0.731589i
$753$	14.1646	−	43.5940i	0.516185	−	1.58866i
$754$	3.50702	−	10.7935i	0.127718	−	0.393076i
$755$	10.9930	+	14.2731i	0.400078	+	0.519450i
$756$	4.04509	+	12.4495i	0.147118	+	0.452784i
$757$	22.4025			0.814232			0.407116	−	0.913376i	$-0.366534\pi$
$757$	22.4025			0.814232			0.407116	+	0.913376i	$0.366534\pi$
$758$	2.60483	+	8.01684i	0.0946116	+	0.291185i
$759$	−52.7475	−	38.3233i	−1.91461	−	1.39105i
$760$	2.54749	+	0.749610i	0.0924072	+	0.0271912i
$761$	2.42880	−	1.76463i	0.0880441	−	0.0639678i	−0.542892	−	0.839802i	$-0.682671\pi$
$761$	2.42880	−	1.76463i	0.0880441	−	0.0639678i	0.630936	+	0.775834i	$0.282671\pi$
$762$	17.3968	+	12.6395i	0.630219	+	0.457881i
$763$	33.5379	+	24.3667i	1.21416	+	0.882135i
$764$	11.5607	−	8.39931i	0.418250	−	0.303876i
$765$	−7.90594	+	2.81569i	−0.285840	+	0.101801i
$766$	31.2400	+	22.6972i	1.12875	+	0.820084i
$767$	6.92057	+	21.2993i	0.249887	+	0.769074i
$768$	51.0911			1.84359
$769$	−5.11742	−	15.7498i	−0.184539	−	0.567953i	0.815401	−	0.578896i	$-0.196516\pi$
$769$	−5.11742	−	15.7498i	−0.184539	−	0.567953i	−0.999940	+	0.0109438i	$0.996516\pi$
$770$	74.0349	−	26.3674i	2.66803	−	0.950215i
$771$	−22.9269	+	70.5617i	−0.825692	+	2.54122i
$772$	3.68217	−	11.3326i	0.132524	−	0.407868i
$773$	−37.4290	+	27.1937i	−1.34623	+	0.978091i	−0.347037	+	0.937851i	$0.612812\pi$
$773$	−37.4290	+	27.1937i	−1.34623	+	0.978091i	−0.999190	+	0.0402396i	$0.987188\pi$
$774$	44.6530			1.60502
$775$	32.2636	−	1.80750i	1.15894	−	0.0649273i
$776$	0.302527			0.0108601
$777$	11.3132	−	8.21950i	0.405858	−	0.294873i
$778$	18.4700	−	56.8447i	0.662180	−	2.03798i
$779$	4.77601	−	14.6991i	0.171118	−	0.526649i
$780$	−10.9730	+	16.0276i	−0.392896	+	0.573880i
$781$	6.61571	+	20.3611i	0.236729	+	0.728576i
$782$	−10.3854			−0.371381
$783$	1.81621	+	5.58973i	0.0649062	+	0.199761i
$784$	30.8044	+	22.3807i	1.10016	+	0.799312i
$785$	−26.4105	−	34.2907i	−0.942631	−	1.22389i
$786$	85.6823	−	62.2519i	3.05619	−	2.22045i
$787$	−32.2738	−	23.4483i	−1.15044	−	0.835841i	−0.161898	−	0.986808i	$-0.551761\pi$
$787$	−32.2738	−	23.4483i	−1.15044	−	0.835841i	−0.988539	+	0.150967i	$0.951761\pi$
$788$	1.76900	+	1.28526i	0.0630181	+	0.0457853i
$789$	−25.1210	+	18.2515i	−0.894331	+	0.649770i
$790$	−23.1286	+	33.7826i	−0.822878	+	1.20193i
$791$	23.3775	+	16.9847i	0.831208	+	0.603908i
$792$	3.09445	+	9.52374i	0.109956	+	0.338411i
$793$	−22.9706			−0.815710
$794$	14.4668	+	44.5243i	0.513408	+	1.58011i
$795$	−0.757601	−	27.0673i	−0.0268694	−	0.959979i
$796$	−2.22466	+	6.84679i	−0.0788508	+	0.242678i
$797$	14.0643	−	43.2856i	0.498184	−	1.53325i	−0.313751	−	0.949505i	$-0.601586\pi$
$797$	14.0643	−	43.2856i	0.498184	−	1.53325i	0.811935	−	0.583748i	$-0.198414\pi$
$798$	32.8892	−	23.8954i	1.16427	−	0.845889i
$799$	7.57185			0.267873
$800$	−9.60648	+	36.3758i	−0.339640	+	1.28608i
$801$	23.7656			0.839715
$802$	10.6397	−	7.73019i	0.375701	−	0.272962i
$803$	−20.9002	+	64.3242i	−0.737551	+	2.26995i
$804$	17.1189	−	52.6867i	0.603739	−	1.85812i
$805$	45.5093	+	13.3913i	1.60399	+	0.471981i
$806$	−7.54802	−	23.2304i	−0.265868	−	0.818257i
$807$	−83.5501			−2.94110
$808$	−2.08809	−	6.42647i	−0.0734586	−	0.226082i
$809$	−36.4671	−	26.4949i	−1.28211	−	0.931511i	−0.282500	−	0.959267i	$-0.591164\pi$
$809$	−36.4671	−	26.4949i	−1.28211	−	0.931511i	−0.999615	+	0.0277568i	$0.991164\pi$
$810$	0.743044	+	26.5472i	0.0261079	+	0.932775i
$811$	−27.3217	+	19.8503i	−0.959393	+	0.697040i	−0.953010	−	0.302940i	$-0.902032\pi$
$811$	−27.3217	+	19.8503i	−0.959393	+	0.697040i	−0.00638343	+	0.999980i	$0.502032\pi$
$812$	−16.2471	−	11.8042i	−0.570161	−	0.414246i
$813$	22.3601	+	16.2456i	0.784204	+	0.569757i
$814$	−9.90536	+	7.19666i	−0.347183	+	0.252243i
$815$	1.37211	+	49.0222i	0.0480629	+	1.71717i
$816$	9.47692	+	6.88538i	0.331758	+	0.241037i
$817$	−3.95329	−	12.1670i	−0.138308	−	0.425669i
$818$	−70.9637			−2.48119
$819$	−8.95436	−	27.5587i	−0.312891	−	0.962979i
$820$	27.2698	+	8.02424i	0.952301	+	0.280218i
$821$	1.11527	−	3.43244i	0.0389232	−	0.119793i	−0.929707	−	0.368300i	$-0.879940\pi$
$821$	1.11527	−	3.43244i	0.0389232	−	0.119793i	0.968630	+	0.248507i	$0.0799399\pi$
$822$	−31.4869	+	96.9066i	−1.09823	+	3.38001i
$823$	19.4702	−	14.1460i	0.678690	−	0.493097i	−0.194233	−	0.980955i	$-0.562222\pi$
$823$	19.4702	−	14.1460i	0.678690	−	0.493097i	0.872923	+	0.487858i	$0.162222\pi$
$824$	1.49784			0.0521797
$825$	−60.2987	+	3.37811i	−2.09933	+	0.117611i
$826$	86.2080			2.99956
$827$	−12.1867	+	8.85415i	−0.423773	+	0.307889i	−0.779154	−	0.626833i	$-0.784351\pi$
$827$	−12.1867	+	8.85415i	−0.423773	+	0.307889i	0.355381	+	0.934721i	$0.384351\pi$
$828$	10.6531	−	32.7868i	0.370221	−	1.13942i
$829$	12.5899	−	38.7479i	0.437267	−	1.34577i	−0.453479	−	0.891267i	$-0.649817\pi$
$829$	12.5899	−	38.7479i	0.437267	−	1.34577i	0.890746	−	0.454502i	$-0.150183\pi$
$830$	1.26250	+	45.1063i	0.0438222	+	1.56566i
$831$	−16.4694	−	50.6875i	−0.571316	−	1.75833i
$832$	10.7289			0.371957
$833$	2.61026	+	8.03354i	0.0904400	+	0.278346i
$834$	30.6954	+	22.3015i	1.06290	+	0.772239i
$835$	27.3228	−	39.9088i	0.945545	−	1.38110i
$836$	−13.2377	+	9.61776i	−0.457836	+	0.332637i
$837$	10.2338	+	7.43529i	0.353732	+	0.257001i
$838$	−8.62062	−	6.26324i	−0.297794	−	0.216360i
$839$	−21.9115	+	15.9196i	−0.756468	+	0.549606i	−0.897825	−	0.440352i	$-0.854854\pi$
$839$	−21.9115	+	15.9196i	−0.756468	+	0.549606i	0.141357	+	0.989959i	$0.454854\pi$
$840$	−7.99950	−	10.3863i	−0.276009	−	0.358363i
$841$	16.1667	+	11.7458i	0.557472	+	0.405027i
$842$	−8.95914	−	27.5734i	−0.308752	−	0.950242i
$843$	−26.7536			−0.921444
$844$	−4.39779	−	13.5350i	−0.151378	−	0.465894i
$845$	−11.5471	+	16.8661i	−0.397231	+	0.580212i
$846$	−16.8959	+	52.0003i	−0.580893	+	1.78781i
$847$	12.8784	−	39.6357i	0.442508	−	1.36190i
$848$	−16.9937	+	12.3467i	−0.583567	+	0.423986i
$849$	63.7611			2.18828
$850$	−7.45414	+	6.08086i	−0.255675	+	0.208572i
$851$	−7.39055			−0.253345
$852$	−16.4782	+	11.9721i	−0.564534	+	0.410158i
$853$	2.11322	−	6.50382i	0.0723553	−	0.222687i	−0.908339	−	0.418235i	$-0.862649\pi$
$853$	2.11322	−	6.50382i	0.0723553	−	0.222687i	0.980694	+	0.195549i	$0.0626487\pi$
$854$	−27.3239	+	84.0944i	−0.935005	+	2.87765i
$855$	−16.3560	+	5.82515i	−0.559363	+	0.199216i
$856$	−1.27694	−	3.93000i	−0.0436448	−	0.134325i
$857$	−5.64889			−0.192963			−0.0964813	−	0.995335i	$-0.530759\pi$
$857$	−5.64889			−0.192963			−0.0964813	+	0.995335i	$0.530759\pi$
$858$	14.1068	+	43.4163i	0.481599	+	1.48221i
$859$	22.1032	+	16.0589i	0.754153	+	0.547924i	0.897111	−	0.441804i	$-0.145662\pi$
$859$	22.1032	+	16.0589i	0.754153	+	0.547924i	−0.142958	+	0.989729i	$0.545662\pi$
$860$	22.1654	−	7.89415i	0.755833	−	0.269188i
$861$	−61.7296	+	44.8492i	−2.10374	+	1.52846i
$862$	16.4211	+	11.9306i	0.559304	+	0.406358i
$863$	−34.3727	−	24.9733i	−1.17006	−	0.850099i	−0.179045	−	0.983841i	$-0.557301\pi$
$863$	−34.3727	−	24.9733i	−1.17006	−	0.850099i	−0.991016	+	0.133742i	$0.957301\pi$
$864$	−11.9151	+	8.65681i	−0.405359	+	0.294511i
$865$	22.6514	+	6.66527i	0.770171	+	0.226626i
$866$	−49.9739	−	36.3082i	−1.69818	−	1.23380i
$867$	0.803039	+	2.47150i	0.0272726	+	0.0839365i
$868$	−43.2228			−1.46708
$869$	13.6687	+	42.0679i	0.463678	+	1.42705i
$870$	20.4847	+	26.5968i	0.694497	+	0.901717i
$871$	−7.60476	+	23.4050i	−0.257677	+	0.793050i
$872$	−1.87101	+	5.75838i	−0.0633604	+	0.195003i
$873$	−1.60024	+	1.16264i	−0.0541600	+	0.0393495i
$874$	−21.4855			−0.726758
$875$	40.5053	−	17.0350i	1.36933	−	0.575888i
$876$	−64.3466			−2.17407
$877$	−23.1283	+	16.8037i	−0.780989	+	0.567421i	−0.905276	−	0.424825i	$-0.860336\pi$
$877$	−23.1283	+	16.8037i	−0.780989	+	0.567421i	0.124287	+	0.992246i	$0.460336\pi$
$878$	7.07878	−	21.7862i	0.238897	−	0.735250i
$879$	−7.40313	+	22.7845i	−0.249701	+	0.768501i
$880$	28.5871	+	37.1167i	0.963670	+	1.25120i
$881$	1.38986	+	4.27755i	0.0468256	+	0.144114i	0.971736	−	0.236072i	$-0.0758600\pi$
$881$	1.38986	+	4.27755i	0.0468256	+	0.144114i	−0.924910	+	0.380186i	$0.875860\pi$
$882$	−60.9955			−2.05383
$883$	−8.62785	−	26.5538i	−0.290350	−	0.893606i	−0.984744	−	0.174011i	$-0.944327\pi$
$883$	−8.62785	−	26.5538i	−0.290350	−	0.893606i	0.694393	−	0.719595i	$-0.255673\pi$
$884$	2.70431	+	1.96479i	0.0909557	+	0.0660832i
$885$	−63.5530	−	18.7007i	−2.13631	−	0.628619i
$886$	−35.2131	+	25.5838i	−1.18301	+	0.859505i
$887$	33.9339	+	24.6544i	1.13939	+	0.827815i	0.987034	−	0.160510i	$-0.0513140\pi$
$887$	33.9339	+	24.6544i	1.13939	+	0.827815i	0.152356	+	0.988326i	$0.451314\pi$
$888$	1.65234	+	1.20050i	0.0554489	+	0.0402860i
$889$	−13.6754	+	9.93574i	−0.458657	+	0.333234i
$890$	25.6625	−	9.13965i	0.860208	−	0.306362i
$891$	23.2129	+	16.8652i	0.777661	+	0.565004i
$892$	−2.80579	−	8.63532i	−0.0939446	−	0.289132i
$893$	15.6648			0.524203
$894$	−0.508242	−	1.56421i	−0.0169981	−	0.0523149i
$895$	8.76241	−	3.12071i	0.292895	−	0.104314i
$896$	−5.51532	+	16.9744i	−0.184254	+	0.567076i
$897$	−8.51516	+	26.2070i	−0.284313	+	0.875025i
$898$	2.76489	−	2.00881i	0.0922656	−	0.0670349i
$899$	−19.4067			−0.647249
$900$	−11.5511	−	29.7705i	−0.385037	−	0.992348i
$901$	−4.65989			−0.155244
$902$	54.0480	−	39.2682i	1.79960	−	1.30749i
$903$	−19.5169	+	60.0670i	−0.649483	+	1.99890i
$904$	−1.30418	+	4.01386i	−0.0433764	+	0.133499i
$905$	−9.71203	+	14.1858i	−0.322839	+	0.471552i
$906$	12.4481	+	38.3112i	0.413559	+	1.27280i
$907$	−34.7635			−1.15430			−0.577152	−	0.816637i	$-0.695836\pi$
$907$	−34.7635			−1.15430			−0.577152	+	0.816637i	$0.695836\pi$
$908$	−4.45637	−	13.7153i	−0.147890	−	0.455158i
$909$	35.7427	+	25.9686i	1.18551	+	0.861323i
$910$	−20.2675	−	26.3148i	−0.671860	−	0.872325i
$911$	3.94279	−	2.86460i	0.130630	−	0.0949086i	−0.520551	−	0.853830i	$-0.674274\pi$
$911$	3.94279	−	2.86460i	0.130630	−	0.0949086i	0.651182	+	0.758922i	$0.274274\pi$
$912$	19.6060	+	14.2446i	0.649221	+	0.471687i
$913$	39.4409	+	28.6555i	1.30530	+	0.948360i
$914$	13.9639	−	10.1454i	0.461885	−	0.335579i
$915$	38.3856	−	56.0676i	1.26899	−	1.85354i
$916$	23.8066	+	17.2965i	0.786593	+	0.571494i
$917$	25.7268	+	79.1790i	0.849574	+	2.61472i
$918$	−3.76577			−0.124289
$919$	11.5386	+	35.5122i	0.380624	+	1.17144i	0.939605	+	0.342260i	$0.111192\pi$
$919$	11.5386	+	35.5122i	0.380624	+	1.17144i	−0.558981	+	0.829180i	$0.688808\pi$
$920$	0.193853	+	6.92591i	0.00639115	+	0.228341i
$921$	19.9989	−	61.5503i	0.658987	−	2.02815i
$922$	14.9123	−	45.8955i	0.491112	−	1.51149i
$923$	7.32012	−	5.31838i	0.240945	−	0.175057i
$924$	80.7808			2.65749
$925$	−5.30458	+	4.32732i	−0.174414	+	0.142281i
$926$	45.0283			1.47972
$927$	−7.92294	+	5.75635i	−0.260223	+	0.189063i
$928$	6.98222	−	21.4891i	0.229203	−	0.705413i
$929$	−5.86768	+	18.0589i	−0.192512	+	0.592492i	0.807484	+	0.589889i	$0.200829\pi$
$929$	−5.86768	+	18.0589i	−0.192512	+	0.592492i	−0.999997	+	0.00260291i	$0.999171\pi$
$930$	69.3151	+	20.3962i	2.27293	+	0.668819i
$931$	5.40015	+	16.6200i	0.176983	+	0.544697i
$932$	−13.1033			−0.429212
$933$	−27.0558	−	83.2692i	−0.885767	−	2.72611i
$934$	−30.0798	−	21.8543i	−0.984243	−	0.715094i
$935$	0.290787	+	10.3891i	0.00950975	+	0.339761i
$936$	3.42393	−	2.48763i	0.111915	−	0.0813108i
$937$	11.5260	+	8.37412i	0.376538	+	0.273571i	0.759917	−	0.650021i	$-0.225240\pi$
$937$	11.5260	+	8.37412i	0.376538	+	0.273571i	−0.383379	+	0.923591i	$0.625240\pi$
$938$	76.6388	+	55.6814i	2.50235	+	1.81806i
$939$	−27.9133	+	20.2802i	−0.910916	+	0.661819i
$940$	0.806084	+	28.7995i	0.0262916	+	0.939336i
$941$	17.0318	+	12.3743i	0.555220	+	0.403391i	0.829706	−	0.558200i	$-0.188508\pi$
$941$	17.0318	+	12.3743i	0.555220	+	0.403391i	−0.274486	+	0.961591i	$0.588508\pi$
$942$	−29.9061	−	92.0416i	−0.974394	−	2.99888i
$943$	40.3261			1.31320
$944$	15.8806	+	48.8754i	0.516869	+	1.59076i
$945$	16.5018	+	4.85572i	0.536803	+	0.157957i
$946$	17.0882	−	52.5922i	0.555586	−	1.70992i
$947$	7.43367	−	22.8785i	0.241562	−	0.743451i	−0.754621	−	0.656161i	$-0.772179\pi$
$947$	7.43367	−	22.8785i	0.241562	−	0.743451i	0.996183	−	0.0872903i	$-0.0278208\pi$
$948$	−34.0455	+	24.7355i	−1.10575	+	0.803372i
$949$	28.5847			0.927899
$950$	−15.4213	+	12.5802i	−0.500332	+	0.408156i
$951$	29.6689			0.962081
$952$	−1.82522	+	1.32610i	−0.0591558	+	0.0429792i
$953$	−3.51902	+	10.8304i	−0.113992	+	0.350832i	−0.991736	−	0.128299i	$-0.959048\pi$
$953$	−3.51902	+	10.8304i	−0.113992	+	0.350832i	0.877743	+	0.479131i	$0.159048\pi$
$954$	10.3981	−	32.0022i	0.336652	−	1.03611i
$955$	−0.525373	−	18.7703i	−0.0170007	−	0.607394i
$956$	−4.19007	−	12.8957i	−0.135517	−	0.417077i
$957$	36.2700			1.17244
$958$	0.247819	+	0.762708i	0.00800667	+	0.0246420i
$959$	−64.8000	−	47.0799i	−2.09250	−	1.52029i
$960$	−17.9288	+	26.1875i	−0.578648	+	0.845197i
$961$	−8.71169	+	6.32941i	−0.281022	+	0.204175i
$962$	4.18636	+	3.04157i	0.134974	+	0.0980641i
$963$	21.8579	+	15.8807i	0.704360	+	0.511747i
$964$	−1.61995	+	1.17697i	−0.0521752	+	0.0379075i
$965$	−9.55442	−	12.4052i	−0.307568	−	0.399338i
$966$	85.8136	+	62.3472i	2.76101	+	2.00599i
$967$	7.04965	+	21.6966i	0.226702	+	0.697715i	0.998114	+	0.0613806i	$0.0195503\pi$
$967$	7.04965	+	21.6966i	0.226702	+	0.697715i	−0.771413	+	0.636335i	$0.780450\pi$
$968$	6.08689			0.195640
$969$	1.66134	+	5.11309i	0.0533701	+	0.164256i
$970$	−1.28085	+	1.87086i	−0.0411255	+	0.0600696i
$971$	5.72325	−	17.6143i	0.183668	−	0.565271i	−0.816255	−	0.577692i	$-0.803954\pi$
$971$	5.72325	−	17.6143i	0.183668	−	0.565271i	0.999923	+	0.0124204i	$0.00395362\pi$
$972$	−11.5232	+	35.4647i	−0.369606	+	1.13753i
$973$	−24.1293	+	17.5309i	−0.773548	+	0.562016i
$974$	3.03768			0.0973335
$975$	9.23295	+	23.7959i	0.295691	+	0.762079i
$976$	−52.7105			−1.68722
$977$	−0.857887	+	0.623291i	−0.0274462	+	0.0199409i	−0.601424	−	0.798930i	$-0.705400\pi$
$977$	−0.857887	+	0.623291i	−0.0274462	+	0.0199409i	0.573978	+	0.818871i	$0.305400\pi$
$978$	−33.8853	+	104.288i	−1.08353	+	3.33477i
$979$	9.09483	−	27.9910i	0.290672	−	0.894597i
$980$	−30.2776	+	10.7833i	−0.967184	+	0.344461i
$981$	−12.2332	−	37.6499i	−0.390576	−	1.20207i
$982$	51.8136			1.65344
$983$	11.8660	+	36.5197i	0.378466	+	1.16480i	0.941110	+	0.338099i	$0.109784\pi$
$983$	11.8660	+	36.5197i	0.378466	+	1.16480i	−0.562645	+	0.826699i	$0.690216\pi$
$984$	−9.01590	−	6.55043i	−0.287416	−	0.208820i
$985$	2.70680	−	0.964023i	0.0862459	−	0.0307163i
$986$	4.67394	−	3.39582i	0.148849	−	0.108145i
$987$	−62.5656	−	45.4566i	−1.99149	−	1.44690i
$988$	5.59473	+	4.06481i	0.177992	+	0.129319i
$989$	27.0045	−	19.6199i	0.858694	−	0.623878i
$990$	−71.9970	−	21.1854i	−2.28822	−	0.673317i
$991$	19.6262	+	14.2592i	0.623446	+	0.452960i	0.854123	−	0.520070i	$-0.174094\pi$
$991$	19.6262	+	14.2592i	0.623446	+	0.452960i	−0.230678	+	0.973030i	$0.574094\pi$
$992$	−15.0276	−	46.2501i	−0.477125	−	1.46844i
$993$	12.0302			0.381766
$994$	−10.7629	−	33.1249i	−0.341380	−	1.05066i
$995$	5.77249	+	7.49484i	0.183000	+	0.237602i
$996$	−14.3328	+	44.1117i	−0.454151	+	1.39773i
$997$	−1.24216	+	3.82298i	−0.0393396	+	0.121075i	−0.968798	−	0.247853i	$-0.920275\pi$
$997$	−1.24216	+	3.82298i	−0.0393396	+	0.121075i	0.929458	+	0.368928i	$0.120275\pi$
$998$	−20.9541	+	15.2241i	−0.663292	+	0.481910i
$999$	−2.67983			−0.0847861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.17	✓	76
25.16	even	5	inner	425.2.k.b.341.17	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.17	✓	76	1.1	even	1	trivial
425.2.k.b.341.17	yes	76	25.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.55652 - 1.13088i) q^{2} +(0.803039 - 2.47150i) q^{3} +(0.525836 - 1.61836i) q^{4} +(-1.36443 - 1.77154i) q^{5} +(-1.54502 - 4.75508i) q^{6} +3.93026 q^{7} +(0.177386 + 0.545938i) q^{8} +(-3.03639 - 2.20607i) q^{9} +(-4.12715 - 1.21443i) q^{10} +(-3.76030 + 2.73201i) q^{11} +(-3.57750 - 2.59921i) q^{12} +(1.58924 + 1.15465i) q^{13} +(6.11753 - 4.44465i) q^{14} +(-5.47404 + 1.94957i) q^{15} +(3.64681 + 2.64956i) q^{16} +(0.309017 + 0.951057i) q^{17} -7.22100 q^{18} +(0.639301 + 1.96757i) q^{19} +(-3.58444 + 1.27659i) q^{20} +(3.15615 - 9.71365i) q^{21} +(-2.76340 + 8.50487i) q^{22} +(-4.36700 + 3.17281i) q^{23} +1.49173 q^{24} +(-1.27668 + 4.83426i) q^{25} +3.77944 q^{26} +(-1.58348 + 1.15047i) q^{27} +(2.06667 - 6.36057i) q^{28} +(0.927920 - 2.85584i) q^{29} +(-6.31573 + 9.22502i) q^{30} +(-1.99713 - 6.14652i) q^{31} +7.52459 q^{32} +(3.73251 + 11.4875i) q^{33} +(1.55652 + 1.13088i) q^{34} +(-5.36256 - 6.96260i) q^{35} +(-5.16685 + 3.75393i) q^{36} +(1.10767 + 0.804766i) q^{37} +(3.22016 + 2.33959i) q^{38} +(4.12993 - 3.00057i) q^{39} +(0.725118 - 1.05914i) q^{40} +(-6.04391 - 4.39116i) q^{41} +(-6.07233 - 18.6887i) q^{42} -6.18377 q^{43} +(2.44408 + 7.52209i) q^{44} +(0.234807 + 8.38909i) q^{45} +(-3.20926 + 9.87709i) q^{46} +(2.33983 - 7.20126i) q^{47} +(9.47692 - 6.88538i) q^{48} +8.44696 q^{49} +(3.47979 + 8.96839i) q^{50} +2.59869 q^{51} +(2.70431 - 1.96479i) q^{52} +(-1.43999 + 4.43182i) q^{53} +(-1.16369 + 3.58146i) q^{54} +(9.97051 + 2.93386i) q^{55} +(0.697173 + 2.14568i) q^{56} +5.37622 q^{57} +(-1.78529 - 5.49455i) q^{58} +(9.22330 + 6.70112i) q^{59} +(0.276651 + 9.88410i) q^{60} +(-9.46018 + 6.87323i) q^{61} +(-10.0595 - 7.30868i) q^{62} +(-11.9338 - 8.67042i) q^{63} +(4.41857 - 3.21028i) q^{64} +(-0.122897 - 4.39082i) q^{65} +(18.8007 + 13.6595i) q^{66} +(3.87128 + 11.9146i) q^{67} +1.70164 q^{68} +(4.33473 + 13.3409i) q^{69} +(-16.2208 - 4.77303i) q^{70} +(1.42335 - 4.38063i) q^{71} +(0.665762 - 2.04901i) q^{72} +(11.7723 - 8.55307i) q^{73} +2.63420 q^{74} +(10.9227 + 7.03741i) q^{75} +3.52039 q^{76} +(-14.7790 + 10.7375i) q^{77} +(3.03504 - 9.34089i) q^{78} +(2.94078 - 9.05078i) q^{79} +(-0.282011 - 10.0756i) q^{80} +(-1.90761 - 5.87102i) q^{81} -14.3733 q^{82} +(-3.24121 - 9.97543i) q^{83} +(-14.0605 - 10.2156i) q^{84} +(1.26320 - 1.84508i) q^{85} +(-9.62516 + 6.99309i) q^{86} +(-6.31307 - 4.58671i) q^{87} +(-2.15853 - 1.56827i) q^{88} +(-5.12278 + 3.72192i) q^{89} +(9.85252 + 12.7923i) q^{90} +(6.24611 + 4.53807i) q^{91} +(2.83841 + 8.73574i) q^{92} -16.7949 q^{93} +(-4.50175 - 13.8550i) q^{94} +(2.61333 - 3.81715i) q^{95} +(6.04254 - 18.5970i) q^{96} +(0.162858 - 0.501227i) q^{97} +(13.1479 - 9.55249i) q^{98} +17.4447 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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