LMFDB - Embedded newform 841.2.e.m.236.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			236.2
Character	$\chi$	$=$	841.236
Dual form			841.2.e.m.196.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.33424 - 0.532775i) q^{2} +(-0.911751 - 1.89327i) q^{3} +(3.36289 + 1.61948i) q^{4} +(-0.540264 + 2.36705i) q^{5} +(1.11956 + 4.90511i) q^{6} +(0.340899 - 0.164169i) q^{7} +(-3.24315 - 2.58633i) q^{8} +(-0.882711 + 1.10689i) q^{9} +(2.52221 - 5.23743i) q^{10} +(-3.00251 + 2.39442i) q^{11} -7.84343i q^{12} +(-3.48744 - 4.37311i) q^{13} +(-0.883206 + 0.201586i) q^{14} +(4.97405 - 1.13529i) q^{15} +(1.53798 + 1.92857i) q^{16} -1.82620i q^{17} +(2.65018 - 2.11345i) q^{18} +(-0.242234 + 0.503004i) q^{19} +(-5.65025 + 7.08519i) q^{20} +(-0.621631 - 0.495734i) q^{21} +(8.28428 - 3.98950i) q^{22} +(0.0745967 + 0.326829i) q^{23} +(-1.93967 + 8.49825i) q^{24} +(-0.806195 - 0.388243i) q^{25} +(5.81064 + 12.0659i) q^{26} +(-3.24561 - 0.740789i) q^{27} +1.41228 q^{28} -12.2155 q^{30} +(3.96609 + 0.905234i) q^{31} +(1.03710 + 2.15357i) q^{32} +(7.27084 + 3.50145i) q^{33} +(-0.972955 + 4.26280i) q^{34} +(0.204419 + 0.895620i) q^{35} +(-4.76105 + 2.29280i) q^{36} +(6.30168 + 5.02542i) q^{37} +(0.833420 - 1.04508i) q^{38} +(-5.09980 + 10.5898i) q^{39} +(7.87413 - 6.27941i) q^{40} +7.79555i q^{41} +(1.18692 + 1.48835i) q^{42} +(0.0221259 - 0.00505009i) q^{43} +(-13.9749 + 3.18967i) q^{44} +(-2.14316 - 2.68743i) q^{45} -0.802642i q^{46} +(5.96453 - 4.75655i) q^{47} +(2.24904 - 4.67019i) q^{48} +(-4.27517 + 5.36089i) q^{49} +(1.67501 + 1.33577i) q^{50} +(-3.45749 + 1.66504i) q^{51} +(-4.64570 - 20.3542i) q^{52} +(-1.41804 + 6.21282i) q^{53} +(7.18136 + 3.45836i) q^{54} +(-4.04557 - 8.40072i) q^{55} +(-1.53018 - 0.349254i) q^{56} +1.17318 q^{57} +8.13681 q^{59} +(18.5658 + 4.23752i) q^{60} +(-4.50012 - 9.34460i) q^{61} +(-8.77553 - 4.22607i) q^{62} +(-0.119200 + 0.522250i) q^{63} +(-2.37128 - 10.3893i) q^{64} +(12.2355 - 5.89231i) q^{65} +(-15.1064 - 12.0470i) q^{66} +(7.50404 - 9.40977i) q^{67} +(2.95751 - 6.14133i) q^{68} +(0.550763 - 0.439219i) q^{69} -2.19950i q^{70} +(9.70090 + 12.1645i) q^{71} +(5.72554 - 1.30682i) q^{72} +(6.76071 - 1.54309i) q^{73} +(-12.0322 - 15.0879i) q^{74} +1.88033i q^{75} +(-1.62921 + 1.29925i) q^{76} +(-0.630466 + 1.30918i) q^{77} +(17.5462 - 22.0022i) q^{78} +(5.83344 + 4.65202i) q^{79} +(-5.39593 + 2.59854i) q^{80} +(2.50178 + 10.9610i) q^{81} +(4.15328 - 18.1967i) q^{82} +(-0.604821 - 0.291266i) q^{83} +(-1.28764 - 2.67382i) q^{84} +(4.32271 + 0.986631i) q^{85} -0.0543377 q^{86} +15.9304 q^{88} +(-9.39749 - 2.14492i) q^{89} +(3.57084 + 7.41493i) q^{90} +(-1.90679 - 0.918263i) q^{91} +(-0.278434 + 1.21990i) q^{92} +(-1.90223 - 8.33423i) q^{93} +(-16.4568 + 7.92519i) q^{94} +(-1.05976 - 0.845134i) q^{95} +(3.13171 - 3.92703i) q^{96} +(-1.93304 + 4.01399i) q^{97} +(12.8354 - 10.2359i) q^{98} -5.43702i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} - 2 q^{5} + 6 q^{6} + 16 q^{9} - 8 q^{13} + 4 q^{16} + 14 q^{20} + 50 q^{22} + 14 q^{23} - 50 q^{24} + 26 q^{25} - 300 q^{28} - 312 q^{30} + 24 q^{34} - 10 q^{35} + 38 q^{36} - 28 q^{38}+ \cdots - 4 q^{96}+O(q^{100}) $ 96 * q + 12 * q^4 - 2 * q^5 + 6 * q^6 + 16 * q^9 - 8 * q^13 + 4 * q^16 + 14 * q^20 + 50 * q^22 + 14 * q^23 - 50 * q^24 + 26 * q^25 - 300 * q^28 - 312 * q^30 + 24 * q^34 - 10 * q^35 + 38 * q^36 - 28 * q^38 + 30 * q^42 + 2 * q^45 - 8 * q^49 + 46 * q^51 - 4 * q^52 - 38 * q^53 + 92 * q^54 + 72 * q^57 - 12 * q^59 - 24 * q^62 - 20 * q^63 + 2 * q^64 + 34 * q^65 + 4 * q^67 - 24 * q^71 + 54 * q^74 - 12 * q^78 - 82 * q^80 - 24 * q^81 + 44 * q^82 + 6 * q^83 + 60 * q^86 - 180 * q^88 - 8 * q^92 + 4 * q^93 - 26 * q^94 - 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

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 $

$2$	−2.33424	−	0.532775i	−1.65056	−	0.376729i	−0.706812	−	0.707401i	$-0.749867\pi$
$2$	−2.33424	−	0.532775i	−1.65056	−	0.376729i	−0.943746	+	0.330672i	$0.892725\pi$
$3$	−0.911751	−	1.89327i	−0.526399	−	1.09308i	−0.979467	−	0.201604i	$-0.935385\pi$
$3$	−0.911751	−	1.89327i	−0.526399	−	1.09308i	0.453068	−	0.891476i	$-0.350330\pi$
$4$	3.36289	+	1.61948i	1.68145	+	0.809742i
$5$	−0.540264	+	2.36705i	−0.241613	+	1.05858i	0.697935	+	0.716161i	$0.254102\pi$
$5$	−0.540264	+	2.36705i	−0.241613	+	1.05858i	−0.939548	+	0.342416i	$0.888755\pi$
$6$	1.11956	+	4.90511i	0.457058	+	2.00250i
$7$	0.340899	−	0.164169i	0.128848	−	0.0620499i	−0.368349	−	0.929688i	$-0.620077\pi$
$7$	0.340899	−	0.164169i	0.128848	−	0.0620499i	0.497197	+	0.867638i	$0.334363\pi$
$8$	−3.24315	−	2.58633i	−1.14663	−	0.914405i
$9$	−0.882711	+	1.10689i	−0.294237	+	0.368962i
$10$	2.52221	−	5.23743i	0.797593	−	1.65622i
$11$	−3.00251	+	2.39442i	−0.905292	+	0.721946i	−0.961014	−	0.276500i	$-0.910825\pi$
$11$	−3.00251	+	2.39442i	−0.905292	+	0.721946i	0.0557220	+	0.998446i	$0.482254\pi$
$12$		−	7.84343i		−	2.26420i
$13$	−3.48744	−	4.37311i	−0.967241	−	1.21288i	−0.977067	−	0.212930i	$-0.931699\pi$
$13$	−3.48744	−	4.37311i	−0.967241	−	1.21288i	0.00982613	−	0.999952i	$-0.496872\pi$
$14$	−0.883206	+	0.201586i	−0.236047	+	0.0538762i
$15$	4.97405	−	1.13529i	1.28429	−	0.293132i
$16$	1.53798	+	1.92857i	0.384495	+	0.482142i
$17$		−	1.82620i		−	0.442919i	−0.975170	−	0.221460i	$-0.928918\pi$
$17$		−	1.82620i		−	0.442919i	0.975170	−	0.221460i	$-0.0710821\pi$
$18$	2.65018	−	2.11345i	0.624654	−	0.498145i
$19$	−0.242234	+	0.503004i	−0.0555723	+	0.115397i	−0.926906	−	0.375295i	$-0.877542\pi$
$19$	−0.242234	+	0.503004i	−0.0555723	+	0.115397i	0.871333	+	0.490692i	$0.163256\pi$
$20$	−5.65025	+	7.08519i	−1.26343	+	1.58430i
$21$	−0.621631	−	0.495734i	−0.135651	−	0.108178i
$22$	8.28428	−	3.98950i	1.76621	−	0.850564i
$23$	0.0745967	+	0.326829i	0.0155545	+	0.0681486i	0.982110	−	0.188311i	$-0.0603012\pi$
$23$	0.0745967	+	0.326829i	0.0155545	+	0.0681486i	−0.966555	+	0.256459i	$0.917444\pi$
$24$	−1.93967	+	8.49825i	−0.395934	+	1.73470i
$25$	−0.806195	−	0.388243i	−0.161239	−	0.0776487i
$26$	5.81064	+	12.0659i	1.13956	+	2.36632i
$27$	−3.24561	−	0.740789i	−0.624618	−	0.142565i
$28$	1.41228			0.266895
$29$		0			0
$29$		0			0
$30$	−12.2155			−2.23023
$31$	3.96609	+	0.905234i	0.712331	+	0.162585i	0.563306	−	0.826249i	$-0.309529\pi$
$31$	3.96609	+	0.905234i	0.712331	+	0.162585i	0.149025	+	0.988833i	$0.452386\pi$
$32$	1.03710	+	2.15357i	0.183336	+	0.380701i
$33$	7.27084	+	3.50145i	1.26569	+	0.609524i
$34$	−0.972955	+	4.26280i	−0.166860	+	0.731063i
$35$	0.204419	+	0.895620i	0.0345532	+	0.151387i
$36$	−4.76105	+	2.29280i	−0.793508	+	0.382133i
$37$	6.30168	+	5.02542i	1.03599	+	0.826174i	0.985005	−	0.172526i	$-0.0551928\pi$
$37$	6.30168	+	5.02542i	1.03599	+	0.826174i	0.0509842	+	0.998699i	$0.483764\pi$
$38$	0.833420	−	1.04508i	0.135199	−	0.169534i
$39$	−5.09980	+	10.5898i	−0.816622	+	1.69573i
$40$	7.87413	−	6.27941i	1.24501	−	0.992862i
$41$			7.79555i			1.21746i	0.793377	+	0.608730i	$0.208321\pi$
$41$			7.79555i			1.21746i	−0.793377	+	0.608730i	$0.791679\pi$
$42$	1.18692	+	1.48835i	0.183146	+	0.229658i
$43$	0.0221259	−	0.00505009i	0.00337417	−	0.000770132i	−0.220834	−	0.975312i	$-0.570878\pi$
$43$	0.0221259	−	0.00505009i	0.00337417	−	0.000770132i	0.224208	+	0.974541i	$0.428021\pi$
$44$	−13.9749	+	3.18967i	−2.10679	+	0.480861i
$45$	−2.14316	−	2.68743i	−0.319483	−	0.400619i
$46$		−	0.802642i		−	0.118343i
$47$	5.96453	−	4.75655i	0.870016	−	0.693815i	−0.0830603	−	0.996545i	$-0.526469\pi$
$47$	5.96453	−	4.75655i	0.870016	−	0.693815i	0.953076	+	0.302730i	$0.0978980\pi$
$48$	2.24904	−	4.67019i	0.324621	−	0.674083i
$49$	−4.27517	+	5.36089i	−0.610738	+	0.765841i
$50$	1.67501	+	1.33577i	0.236882	+	0.188907i
$51$	−3.45749	+	1.66504i	−0.484146	+	0.233152i
$52$	−4.64570	−	20.3542i	−0.644243	−	2.82261i
$53$	−1.41804	+	6.21282i	−0.194782	+	0.853396i	0.779201	+	0.626775i	$0.215625\pi$
$53$	−1.41804	+	6.21282i	−0.194782	+	0.853396i	−0.973983	+	0.226622i	$0.927232\pi$
$54$	7.18136	+	3.45836i	0.977260	+	0.470623i
$55$	−4.04557	−	8.40072i	−0.545505	−	1.13275i
$56$	−1.53018	−	0.349254i	−0.204479	−	0.0466711i
$57$	1.17318			0.155391
$58$		0			0
$59$	8.13681			1.05932			0.529661	−	0.848209i	$-0.322319\pi$
$59$	8.13681			1.05932			0.529661	+	0.848209i	$0.322319\pi$
$60$	18.5658	+	4.23752i	2.39683	+	0.547062i
$61$	−4.50012	−	9.34460i	−0.576181	−	1.19645i	−0.961789	−	0.273790i	$-0.911723\pi$
$61$	−4.50012	−	9.34460i	−0.576181	−	1.19645i	0.385608	−	0.922663i	$-0.373992\pi$
$62$	−8.77553	−	4.22607i	−1.11449	−	0.536711i
$63$	−0.119200	+	0.522250i	−0.0150178	+	0.0657973i
$64$	−2.37128	−	10.3893i	−0.296410	−	1.29866i
$65$	12.2355	−	5.89231i	1.51763	−	0.730851i
$66$	−15.1064	−	12.0470i	−1.85947	−	1.48288i
$67$	7.50404	−	9.40977i	0.916764	−	1.14959i	−0.0715926	−	0.997434i	$-0.522808\pi$
$67$	7.50404	−	9.40977i	0.916764	−	1.14959i	0.988357	−	0.152152i	$-0.0486204\pi$
$68$	2.95751	−	6.14133i	0.358650	−	0.744745i
$69$	0.550763	−	0.439219i	0.0663040	−	0.0528757i
$70$		−	2.19950i		−	0.262891i
$71$	9.70090	+	12.1645i	1.15128	+	1.44367i	0.876005	+	0.482302i	$0.160199\pi$
$71$	9.70090	+	12.1645i	1.15128	+	1.44367i	0.275280	+	0.961364i	$0.411230\pi$
$72$	5.72554	−	1.30682i	0.674761	−	0.154010i
$73$	6.76071	−	1.54309i	0.791282	−	0.180605i	0.192267	−	0.981343i	$-0.438416\pi$
$73$	6.76071	−	1.54309i	0.791282	−	0.180605i	0.599015	+	0.800738i	$0.295559\pi$
$74$	−12.0322	−	15.0879i	−1.39872	−	1.75393i
$75$			1.88033i			0.217121i
$76$	−1.62921	+	1.29925i	−0.186884	+	0.149035i
$77$	−0.630466	+	1.30918i	−0.0718483	+	0.149194i
$78$	17.5462	−	22.0022i	1.98671	−	2.49126i
$79$	5.83344	+	4.65202i	0.656314	+	0.523393i	0.894067	−	0.447933i	$-0.147840\pi$
$79$	5.83344	+	4.65202i	0.656314	+	0.523393i	−0.237754	+	0.971326i	$0.576411\pi$
$80$	−5.39593	+	2.59854i	−0.603283	+	0.290526i
$81$	2.50178	+	10.9610i	0.277976	+	1.21789i
$82$	4.15328	−	18.1967i	0.458653	−	2.00949i
$83$	−0.604821	−	0.291266i	−0.0663877	−	0.0319706i	0.400395	−	0.916343i	$-0.368873\pi$
$83$	−0.604821	−	0.291266i	−0.0663877	−	0.0319706i	−0.466783	+	0.884372i	$0.654587\pi$
$84$	−1.28764	−	2.67382i	−0.140494	−	0.291738i
$85$	4.32271	+	0.986631i	0.468864	+	0.107015i
$86$	−0.0543377			−0.00585939
$87$		0			0
$88$	15.9304			1.69818
$89$	−9.39749	−	2.14492i	−0.996132	−	0.227361i	−0.306775	−	0.951782i	$-0.599250\pi$
$89$	−9.39749	−	2.14492i	−0.996132	−	0.227361i	−0.689357	+	0.724422i	$0.742107\pi$
$90$	3.57084	+	7.41493i	0.376400	+	0.781603i
$91$	−1.90679	−	0.918263i	−0.199886	−	0.0962601i
$92$	−0.278434	+	1.21990i	−0.0290288	+	0.127183i
$93$	−1.90223	−	8.33423i	−0.197252	−	0.864219i
$94$	−16.4568	+	7.92519i	−1.69739	+	0.817421i
$95$	−1.05976	−	0.845134i	−0.108730	−	0.0867089i
$96$	3.13171	−	3.92703i	0.319628	−	0.400801i
$97$	−1.93304	+	4.01399i	−0.196270	+	0.407559i	−0.975756	−	0.218861i	$-0.929766\pi$
$97$	−1.93304	+	4.01399i	−0.196270	+	0.407559i	0.779486	+	0.626419i	$0.215480\pi$
$98$	12.8354	−	10.2359i	1.29657	−	1.03398i
$99$		−	5.43702i		−	0.546441i
$100$	−2.08240	−	2.61124i	−0.208240	−	0.261124i
$101$	5.88761	−	1.34381i	0.585839	−	0.133714i	0.0806798	−	0.996740i	$-0.474291\pi$
$101$	5.88761	−	1.34381i	0.585839	−	0.133714i	0.505159	+	0.863026i	$0.331434\pi$
$102$	8.95772	−	2.04454i	0.886946	−	0.202440i
$103$	3.86467	+	4.84615i	0.380797	+	0.477505i	0.934884	−	0.354954i	$-0.115504\pi$
$103$	3.86467	+	4.84615i	0.380797	+	0.477505i	−0.554086	+	0.832459i	$0.686932\pi$
$104$			23.2023i			2.27518i
$105$	1.50927	−	1.20360i	0.147290	−	0.117460i
$106$	6.62007	−	13.7467i	0.642998	−	1.33520i
$107$	3.30545	−	4.14490i	0.319550	−	0.400703i	−0.595950	−	0.803022i	$-0.703224\pi$
$107$	3.30545	−	4.14490i	0.319550	−	0.400703i	0.915500	+	0.402319i	$0.131796\pi$
$108$	−9.71495	−	7.74741i	−0.934821	−	0.745495i
$109$	5.67548	−	2.73316i	0.543612	−	0.261790i	−0.141863	−	0.989886i	$-0.545309\pi$
$109$	5.67548	−	2.73316i	0.543612	−	0.261790i	0.685474	+	0.728097i	$0.259595\pi$
$110$	4.96765	+	21.7647i	0.473647	+	2.07518i
$111$	3.76892	−	16.5127i	0.357730	−	1.56732i
$112$	0.840907	+	0.404959i	0.0794582	+	0.0382651i
$113$	5.81841	+	12.0821i	0.547350	+	1.13658i	0.972809	+	0.231607i	$0.0743984\pi$
$113$	5.81841	+	12.0821i	0.547350	+	1.13658i	−0.425459	+	0.904978i	$0.639887\pi$
$114$	−2.73848	−	0.625041i	−0.256482	−	0.0585404i
$115$	−0.813923			−0.0758987
$116$		0			0
$117$	7.91893			0.732105
$118$	−18.9933	−	4.33509i	−1.74847	−	0.399078i
$119$	−0.299805	−	0.622551i	−0.0274831	−	0.0570692i
$120$	−19.0679	−	9.18259i	−1.74065	−	0.838252i
$121$	0.834088	−	3.65438i	0.0758262	−	0.332216i
$122$	5.52580	+	24.2101i	0.500282	+	2.19188i
$123$	14.7591	−	7.10760i	1.33078	−	0.640871i
$124$	11.8715	+	9.46723i	1.06610	+	0.850182i
$125$	−6.21438	+	7.79258i	−0.555831	+	0.696990i
$126$	0.556484	−	1.15555i	0.0495755	−	0.102945i
$127$	4.55833	−	3.63515i	0.404486	−	0.322567i	−0.400025	−	0.916504i	$-0.630999\pi$
$127$	4.55833	−	3.63515i	0.404486	−	0.322567i	0.804512	+	0.593937i	$0.202427\pi$
$128$			20.7338i			1.83263i
$129$	−0.0297345	−	0.0372859i	−0.00261798	−	0.00328284i
$130$	−31.6999	+	7.23529i	−2.78026	+	0.634577i
$131$	0.514963	−	0.117537i	0.0449925	−	0.0102692i	−0.199965	−	0.979803i	$-0.564083\pi$
$131$	0.514963	−	0.117537i	0.0449925	−	0.0102692i	0.244958	+	0.969534i	$0.421226\pi$
$132$	18.7805	+	23.5500i	1.63463	+	2.04977i
$133$			0.211241i			0.0183169i
$134$	−22.5295	+	17.9667i	−1.94626	+	1.55209i
$135$	3.50697	−	7.28230i	0.301832	−	0.626761i
$136$	−4.72316	+	5.92265i	−0.405008	+	0.507863i
$137$	6.14676	+	4.90188i	0.525153	+	0.418796i	0.849852	−	0.527022i	$-0.176691\pi$
$137$	6.14676	+	4.90188i	0.525153	+	0.418796i	−0.324698	+	0.945818i	$0.605263\pi$
$138$	−1.51962	+	0.731809i	−0.129358	+	0.0622957i
$139$	2.05793	+	9.01638i	0.174551	+	0.764760i	0.984087	+	0.177689i	$0.0568620\pi$
$139$	2.05793	+	9.01638i	0.174551	+	0.764760i	−0.809535	+	0.587071i	$0.800281\pi$
$140$	−0.763002	+	3.34293i	−0.0644855	+	0.282529i
$141$	−14.4436	−	6.95567i	−1.21637	−	0.585773i
$142$	−16.1633	−	33.5634i	−1.35639	−	2.81658i
$143$	20.9422	+	4.77991i	1.75127	+	0.399716i
$144$	−3.49230			−0.291025
$145$		0			0
$146$	−16.6033			−1.37410
$147$	14.0475	+	3.20625i	1.15862	+	0.264447i
$148$	13.0533	+	27.1054i	1.07297	+	2.22805i
$149$	−0.463346	−	0.223136i	−0.0379588	−	0.0182800i	0.414808	−	0.909909i	$-0.363849\pi$
$149$	−0.463346	−	0.223136i	−0.0379588	−	0.0182800i	−0.452767	+	0.891629i	$0.649563\pi$
$150$	1.00179	−	4.38914i	0.0817959	−	0.358371i
$151$	−1.45803	−	6.38806i	−0.118653	−	0.519853i	−0.998966	−	0.0454597i	$-0.985525\pi$
$151$	−1.45803	−	6.38806i	−0.118653	−	0.519853i	0.880313	−	0.474393i	$-0.157332\pi$
$152$	2.08654	−	1.00482i	0.169240	−	0.0815019i
$153$	2.02140	+	1.61201i	0.163420	+	0.130323i
$154$	2.16916	−	2.72004i	0.174796	−	0.219187i
$155$	−4.28547	+	8.89887i	−0.344217	+	0.714774i
$156$	−34.3002	+	27.3535i	−2.74621	+	2.19003i
$157$		−	11.4559i		−	0.914282i	−0.889394	−	0.457141i	$-0.848874\pi$
$157$		−	11.4559i		−	0.914282i	0.889394	−	0.457141i	$-0.151126\pi$
$158$	−11.1382	−	13.9668i	−0.886106	−	1.11114i
$159$	13.0554	−	2.97982i	1.03536	−	0.236315i
$160$	−5.65791	+	1.29138i	−0.447297	+	0.102093i
$161$	0.0790851	+	0.0991695i	0.00623278	+	0.00781565i
$162$		−	26.9186i		−	2.11492i
$163$	14.2551	−	11.3681i	1.11655	−	0.890418i	0.121779	−	0.992557i	$-0.461140\pi$
$163$	14.2551	−	11.3681i	1.11655	−	0.890418i	0.994770	+	0.102139i	$0.0325687\pi$
$164$	−12.6248	+	26.2156i	−0.985830	+	2.04710i
$165$	−12.2163	+	15.3187i	−0.951036	+	1.19256i
$166$	1.25662	+	1.00212i	0.0975325	+	0.0777796i
$167$	2.28291	−	1.09939i	0.176657	−	0.0850735i	−0.343465	−	0.939165i	$-0.611601\pi$
$167$	2.28291	−	1.09939i	0.176657	−	0.0850735i	0.520122	+	0.854092i	$0.325886\pi$
$168$	0.733913	+	3.21548i	0.0566226	+	0.248080i
$169$	−4.06909	+	17.8278i	−0.313007	+	1.37137i
$170$	−9.56460	−	4.60607i	−0.733571	−	0.353269i
$171$	−0.342945	−	0.712132i	−0.0262256	−	0.0544581i
$172$	0.0825856	+	0.0188496i	0.00629709	+	0.00143727i
$173$	−8.48473			−0.645082			−0.322541	−	0.946556i	$-0.604537\pi$
$173$	−8.48473			−0.645082			−0.322541	+	0.946556i	$0.604537\pi$
$174$		0			0
$175$	−0.338569			−0.0255934
$176$	−9.23562	−	2.10797i	−0.696161	−	0.158894i
$177$	−7.41874	−	15.4052i	−0.557627	−	1.15792i
$178$	20.7932	+	10.0135i	1.55852	+	0.750544i
$179$	2.88229	−	12.6282i	0.215433	−	0.943873i	−0.745372	−	0.666648i	$-0.767728\pi$
$179$	2.88229	−	12.6282i	0.215433	−	0.943873i	0.960805	−	0.277224i	$-0.0894145\pi$
$180$	−2.85495	−	12.5084i	−0.212796	−	0.932318i
$181$	−14.7912	+	7.12306i	−1.09942	+	0.529453i	−0.893476	−	0.449111i	$-0.851741\pi$
$181$	−14.7912	+	7.12306i	−1.09942	+	0.529453i	−0.205944	+	0.978564i	$0.566027\pi$
$182$	3.96169	+	3.15934i	0.293660	+	0.234186i
$183$	−13.5889	+	17.0399i	−1.00452	+	1.25962i
$184$	0.603360	−	1.25289i	0.0444803	−	0.0923643i
$185$	−15.3000	+	12.2013i	−1.12488	+	0.897060i
$186$			20.4676i			1.50075i
$187$	4.37270	+	5.48320i	0.319764	+	0.400971i
$188$	27.7613	−	6.33633i	2.02470	−	0.462124i
$189$	−1.22804	+	0.280292i	−0.0893268	+	0.0203883i
$190$	2.02348	+	2.53736i	0.146799	+	0.184080i
$191$			7.42138i			0.536992i	0.963281	+	0.268496i	$0.0865266\pi$
$191$			7.42138i			0.536992i	−0.963281	+	0.268496i	$0.913473\pi$
$192$	−17.5077	+	13.9619i	−1.26351	+	1.00761i
$193$	−9.53227	+	19.7940i	−0.686147	+	1.42480i	0.208498	+	0.978023i	$0.433143\pi$
$193$	−9.53227	+	19.7940i	−0.686147	+	1.42480i	−0.894645	+	0.446777i	$0.852572\pi$
$194$	6.65072	−	8.33975i	0.477494	−	0.598759i
$195$	−22.3115	−	17.7928i	−1.59776	−	1.27417i
$196$	−23.0588	+	11.1045i	−1.64706	+	0.793182i
$197$	−4.38461	−	19.2102i	−0.312391	−	1.36867i	−0.850578	−	0.525848i	$-0.823748\pi$
$197$	−4.38461	−	19.2102i	−0.312391	−	1.36867i	0.538188	−	0.842825i	$-0.319109\pi$
$198$	−2.89671	+	12.6913i	−0.205860	+	0.901933i
$199$	14.6301	+	7.04551i	1.03710	+	0.499443i	0.873368	−	0.487061i	$-0.161931\pi$
$199$	14.6301	+	7.04551i	1.03710	+	0.499443i	0.163736	+	0.986504i	$0.447645\pi$
$200$	1.61049	+	3.34422i	0.113879	+	0.236472i
$201$	−24.6570	−	5.62781i	−1.73917	−	0.396955i
$202$	−14.4591			−1.01734
$203$		0			0
$204$	−14.3237			−1.00286
$205$	−18.4525	−	4.21165i	−1.28878	−	0.294155i
$206$	−6.43917	−	13.3711i	−0.448638	−	0.931607i
$207$	−0.427610	−	0.205926i	−0.0297209	−	0.0143129i
$208$	3.07022	−	13.4515i	0.212882	−	0.932695i
$209$	−0.477094	−	2.09029i	−0.0330013	−	0.144588i
$210$	−4.16425	+	2.00540i	−0.287361	+	0.138386i
$211$	18.4011	+	14.6744i	1.26678	+	1.01023i	0.998906	+	0.0467726i	$0.0148936\pi$
$211$	18.4011	+	14.6744i	1.26678	+	1.01023i	0.267877	+	0.963453i	$0.413678\pi$
$212$	−14.8303	+	18.5966i	−1.01855	+	1.27722i
$213$	14.1860	−	29.4574i	0.972006	−	2.01839i
$214$	−9.92401	+	7.91414i	−0.678392	+	0.540999i
$215$			0.0551015i			0.00375789i
$216$	8.61009	+	10.7967i	0.585842	+	0.734623i
$217$	1.50065	−	0.342513i	0.101871	−	0.0232513i
$218$	−14.7041	+	3.35611i	−0.995887	+	0.227305i
$219$	−9.08557	−	11.3929i	−0.613946	−	0.769864i
$220$		−	34.8025i		−	2.34638i
$221$	−7.98618	+	6.36877i	−0.537209	+	0.428410i
$222$	−17.5951	+	36.5366i	−1.18091	+	2.45218i
$223$	−0.437647	+	0.548792i	−0.0293070	+	0.0367498i	−0.796269	−	0.604943i	$-0.793196\pi$
$223$	−0.437647	+	0.548792i	−0.0293070	+	0.0367498i	0.766962	+	0.641692i	$0.221767\pi$
$224$	0.707096	+	0.563890i	0.0472448	+	0.0376765i
$225$	1.14138	−	0.549659i	0.0760919	−	0.0366439i
$226$	−7.14456	−	31.3024i	−0.475249	−	2.08220i
$227$	1.64721	−	7.21690i	0.109329	−	0.479002i	−0.890388	−	0.455203i	$-0.849567\pi$
$227$	1.64721	−	7.21690i	0.109329	−	0.479002i	0.999717	−	0.0237991i	$-0.00757622\pi$
$228$	3.94528	+	1.89995i	0.261282	+	0.125827i
$229$	4.66238	+	9.68152i	0.308098	+	0.639773i	0.996318	−	0.0857290i	$-0.0273219\pi$
$229$	4.66238	+	9.68152i	0.308098	+	0.639773i	−0.688220	+	0.725502i	$0.741608\pi$
$230$	1.89989	+	0.433638i	0.125275	+	0.0285933i
$231$	3.05345			0.200902
$232$		0			0
$233$	−15.5888			−1.02126			−0.510630	−	0.859801i	$-0.670588\pi$
$233$	−15.5888			−1.02126			−0.510630	+	0.859801i	$0.670588\pi$
$234$	−18.4847	−	4.21901i	−1.20838	−	0.275805i
$235$	8.03658	+	16.6881i	0.524249	+	1.08861i
$236$	27.3632	+	13.1774i	1.78120	+	0.857779i
$237$	3.48887	−	15.2858i	0.226627	−	0.992917i
$238$	0.368137	+	1.61291i	0.0238628	+	0.104550i
$239$	−6.70681	+	3.22983i	−0.433828	+	0.208920i	−0.638035	−	0.770007i	$-0.720253\pi$
$239$	−6.70681	+	3.22983i	−0.433828	+	0.208920i	0.204208	+	0.978928i	$0.434538\pi$
$240$	9.83949	+	7.84673i	0.635136	+	0.506504i
$241$	3.28385	−	4.11781i	0.211531	−	0.265252i	−0.664735	−	0.747079i	$-0.731455\pi$
$241$	3.28385	−	4.11781i	0.211531	−	0.265252i	0.876266	+	0.481828i	$0.160027\pi$
$242$	−3.89393	+	8.08582i	−0.250311	+	0.519776i
$243$	10.6628	−	8.50333i	0.684021	−	0.545489i
$244$		−	38.7128i		−	2.47833i
$245$	−10.3798	−	13.0158i	−0.663140	−	0.831551i
$246$	−38.2380	+	8.72758i	−2.43797	+	0.556450i
$247$	3.04447	−	0.694879i	0.193715	−	0.0442141i
$248$	−10.5214	−	13.1934i	−0.668110	−	0.837784i
$249$			1.41065i			0.0893964i
$250$	18.6575	−	14.8789i	1.18001	−	0.941024i
$251$	12.1329	−	25.1943i	0.765825	−	1.59025i	−0.0407853	−	0.999168i	$-0.512986\pi$
$251$	12.1329	−	25.1943i	0.765825	−	1.59025i	0.806610	−	0.591084i	$-0.201300\pi$
$252$	−1.24663	+	1.56323i	−0.0785305	+	0.0984742i
$253$	−1.00655	−	0.802694i	−0.0632810	−	0.0504649i
$254$	−12.5770	+	6.05675i	−0.789149	+	0.380034i
$255$	−2.07328	−	9.08362i	−0.129834	−	0.568838i
$256$	6.30392	−	27.6193i	0.393995	−	1.72620i
$257$	17.1802	+	8.27355i	1.07167	+	0.516090i	0.884645	−	0.466265i	$-0.154401\pi$
$257$	17.1802	+	8.27355i	1.07167	+	0.516090i	0.187027	+	0.982355i	$0.440115\pi$
$258$	0.0495425	+	0.102876i	0.00308438	+	0.00640478i
$259$	2.97325	+	0.678626i	0.184749	+	0.0421677i
$260$	50.6892			3.14361
$261$		0			0
$262$	−1.26467			−0.0781315
$263$	6.93648	+	1.58321i	0.427722	+	0.0976247i	0.430962	−	0.902370i	$-0.358174\pi$
$263$	6.93648	+	1.58321i	0.427722	+	0.0976247i	−0.00324031	+	0.999995i	$0.501031\pi$
$264$	−14.5245	−	30.1605i	−0.893924	−	1.85625i
$265$	−13.9399	−	6.71312i	−0.856324	−	0.412384i
$266$	0.112544	−	0.493087i	0.00690051	−	0.0302331i
$267$	4.50726	+	19.7476i	0.275840	+	1.20853i
$268$	40.4743	−	19.4914i	2.47236	−	1.19063i
$269$	−4.65665	−	3.71355i	−0.283921	−	0.226419i	0.471165	−	0.882045i	$-0.343834\pi$
$269$	−4.65665	−	3.71355i	−0.283921	−	0.226419i	−0.755086	+	0.655626i	$0.772405\pi$
$270$	−12.0659	+	15.1302i	−0.734310	+	0.920796i
$271$	2.22735	−	4.62514i	0.135302	−	0.280957i	−0.822299	−	0.569056i	$-0.807309\pi$
$271$	2.22735	−	4.62514i	0.135302	−	0.280957i	0.957601	+	0.288099i	$0.0930231\pi$
$272$	3.52195	−	2.80866i	0.213550	−	0.170300i
$273$			4.44730i			0.269163i
$274$	−11.7364	−	14.7170i	−0.709023	−	0.889087i
$275$	3.35023	−	0.764669i	0.202027	−	0.0461113i
$276$	2.56346	−	0.585094i	0.154302	−	0.0352185i
$277$	12.4733	+	15.6410i	0.749448	+	0.939778i	0.999596	−	0.0284299i	$-0.00905073\pi$
$277$	12.4733	+	15.6410i	0.749448	+	0.939778i	−0.250148	+	0.968208i	$0.580479\pi$
$278$		−	22.1428i		−	1.32804i
$279$	−4.50290	+	3.59095i	−0.269582	+	0.214984i
$280$	1.65340	−	3.43333i	0.0988098	−	0.205181i
$281$	−7.31426	+	9.17179i	−0.436332	+	0.547143i	−0.950572	−	0.310503i	$-0.899503\pi$
$281$	−7.31426	+	9.17179i	−0.436332	+	0.547143i	0.514240	+	0.857646i	$0.328074\pi$
$282$	30.0090	+	23.9314i	1.78701	+	1.42510i
$283$	−26.6889	+	12.8527i	−1.58649	+	0.764013i	−0.998978	−	0.0452037i	$-0.985606\pi$
$283$	−26.6889	+	12.8527i	−1.58649	+	0.764013i	−0.587511	+	0.809216i	$0.699892\pi$
$284$	12.9228	+	56.6185i	0.766828	+	3.35969i
$285$	−0.633826	+	2.77697i	−0.0375446	+	0.164494i
$286$	−46.3374	−	22.3149i	−2.73999	−	1.31951i
$287$	1.27978	+	2.65750i	0.0755433	+	0.156867i
$288$	−3.29922	−	0.753025i	−0.194408	−	0.0443724i
$289$	13.6650			0.803823
$290$		0			0
$291$	9.36201			0.548811
$292$	25.2346	+	5.75963i	1.47674	+	0.337057i
$293$	3.41113	+	7.08328i	0.199280	+	0.413809i	0.976530	−	0.215383i	$-0.0691000\pi$
$293$	3.41113	+	7.08328i	0.199280	+	0.413809i	−0.777250	+	0.629192i	$0.783386\pi$
$294$	−31.0820	−	14.9683i	−1.81274	−	0.872970i
$295$	−4.39602	+	19.2602i	−0.255946	+	1.12137i
$296$	−7.43992	−	32.5964i	−0.432437	−	1.89463i
$297$	11.5188	−	5.54714i	0.668386	−	0.321878i
$298$	0.962681	+	0.767712i	0.0557666	+	0.0444724i
$299$	1.16911	−	1.46602i	0.0676113	−	0.0847819i
$300$	−3.04516	+	6.32334i	−0.175812	+	0.365078i
$301$	0.00671364	−	0.00535395i	0.000386968	−	0.000308596i
$302$			15.6881i			0.902747i
$303$	−7.91222	−	9.92162i	−0.454545	−	0.569982i
$304$	−1.34263	+	0.306446i	−0.0770050	+	0.0175759i
$305$	24.5504	−	5.60346i	1.40575	−	0.320853i
$306$	−3.85959	−	4.83977i	−0.220638	−	0.276671i
$307$			28.3811i			1.61979i	0.586572	+	0.809897i	$0.300477\pi$
$307$			28.3811i			1.61979i	−0.586572	+	0.809897i	$0.699523\pi$
$308$	−4.24038	+	3.38159i	−0.241618	+	0.192684i
$309$	5.65144	−	11.7353i	0.321499	−	0.667600i
$310$	14.7444	−	18.4889i	0.837427	−	1.05010i
$311$	6.70169	+	5.34442i	0.380018	+	0.303054i	0.794806	−	0.606864i	$-0.207573\pi$
$311$	6.70169	+	5.34442i	0.380018	+	0.303054i	−0.414788	+	0.909918i	$0.636144\pi$
$312$	43.9283	−	21.1547i	2.48695	−	1.19765i
$313$	−0.195597	−	0.856966i	−0.0110558	−	0.0484386i	0.969099	−	0.246672i	$-0.0793369\pi$
$313$	−0.195597	−	0.856966i	−0.0110558	−	0.0484386i	−0.980155	+	0.198233i	$0.936480\pi$
$314$	−6.10343	+	26.7409i	−0.344436	+	1.50907i
$315$	−1.17179	−	0.564305i	−0.0660230	−	0.0317950i
$316$	12.0834	+	25.0914i	0.679744	+	1.41150i
$317$	−25.9581	−	5.92476i	−1.45795	−	0.332767i	−0.581218	−	0.813748i	$-0.697424\pi$
$317$	−25.9581	−	5.92476i	−1.45795	−	0.332767i	−0.876731	+	0.480980i	$0.840281\pi$
$318$	−32.0621			−1.79795
$319$		0			0
$320$	25.8730			1.44635
$321$	−10.8612	−	2.47899i	−0.606211	−	0.138364i
$322$	−0.131769	−	0.273620i	−0.00734317	−	0.0152483i
$323$	0.918586	+	0.442368i	0.0511115	+	0.0246140i
$324$	−9.33798	+	40.9124i	−0.518777	+	2.27291i
$325$	1.11373	+	4.87955i	0.0617784	+	0.270669i
$326$	−39.3316	+	18.9411i	−2.17838	+	1.04905i
$327$	−10.3492	−	8.25324i	−0.572314	−	0.456405i
$328$	20.1619	−	25.2822i	1.11325	−	1.39598i
$329$	1.25243	−	2.60069i	0.0690486	−	0.143381i
$330$	36.6772	−	29.2491i	2.01901	−	1.61011i
$331$		−	18.6487i		−	1.02502i	−0.858680	−	0.512512i	$-0.828715\pi$
$331$		−	18.6487i		−	1.02502i	0.858680	−	0.512512i	$-0.171285\pi$
$332$	−1.56225	−	1.95900i	−0.0857395	−	0.107514i
$333$	−11.1251	+	2.53924i	−0.609653	+	0.139149i
$334$	−5.91459	+	1.34997i	−0.323632	+	0.0738669i
$335$	18.2192	+	22.8462i	0.995423	+	1.24822i
$336$		−	1.96129i		−	0.106997i
$337$	−4.72830	+	3.77070i	−0.257567	+	0.205403i	−0.743757	−	0.668450i	$-0.766958\pi$
$337$	−4.72830	+	3.77070i	−0.257567	+	0.205403i	0.486190	+	0.873853i	$0.338386\pi$
$338$	18.9965	−	39.4465i	1.03327	−	2.14561i
$339$	17.5697	−	22.0317i	0.954253	−	1.19660i
$340$	12.9390	+	10.3185i	0.701715	+	0.559599i
$341$	−14.0758	+	6.77853i	−0.762245	+	0.367078i
$342$	0.421109	+	1.84500i	0.0227710	+	0.0997662i
$343$	−1.16668	+	5.11156i	−0.0629948	+	0.275998i
$344$	−0.0848189	−	0.0408466i	−0.00457313	−	0.00220230i
$345$	0.742095	+	1.54098i	0.0399531	+	0.0829634i
$346$	19.8054	+	4.52045i	1.06474	+	0.243021i
$347$	14.4469			0.775548			0.387774	−	0.921754i	$-0.373244\pi$
$347$	14.4469			0.775548			0.387774	+	0.921754i	$0.373244\pi$
$348$		0			0
$349$	11.5232			0.616825			0.308413	−	0.951253i	$-0.400202\pi$
$349$	11.5232			0.616825			0.308413	+	0.951253i	$0.400202\pi$
$350$	0.790301	+	0.180381i	0.0422434	+	0.00964178i
$351$	8.07931	+	16.7769i	0.431242	+	0.895483i
$352$	−8.27048	−	3.98285i	−0.440818	−	0.212287i
$353$	−1.88547	+	8.26080i	−0.100354	+	0.439678i	0.899642	+	0.436629i	$0.143828\pi$
$353$	−1.88547	+	8.26080i	−0.100354	+	0.439678i	−0.999995	+	0.00304918i	$0.999029\pi$
$354$	9.10964	+	39.9119i	0.484172	+	2.12130i
$355$	−34.0351	+	16.3905i	−1.80640	+	0.869915i
$356$	−28.1291	−	22.4322i	−1.49084	−	1.18891i
$357$	−0.905310	+	1.13522i	−0.0479141	+	0.0600824i
$358$	−13.4559	+	27.9415i	−0.711168	+	1.47676i
$359$	3.85854	−	3.07709i	0.203646	−	0.162402i	−0.516356	−	0.856374i	$-0.672712\pi$
$359$	3.85854	−	3.07709i	0.203646	−	0.162402i	0.720003	+	0.693971i	$0.244141\pi$
$360$			14.2587i			0.751497i
$361$	11.6520	+	14.6111i	0.613262	+	0.769006i
$362$	38.3212	−	8.74656i	2.01412	−	0.459709i
$363$	−7.67920	+	1.75273i	−0.403054	+	0.0919944i
$364$	−4.92523	−	6.17604i	−0.258152	−	0.323713i
$365$			16.8366i			0.881269i
$366$	40.7981	−	32.5354i	2.13255	−	1.70065i
$367$	1.26131	−	2.61914i	0.0658398	−	0.136718i	−0.865452	−	0.500992i	$-0.832969\pi$
$367$	1.26131	−	2.61914i	0.0658398	−	0.136718i	0.931292	+	0.364274i	$0.118683\pi$
$368$	−0.515584	+	0.646522i	−0.0268767	+	0.0337023i
$369$	−8.62878	−	6.88122i	−0.449196	−	0.358222i
$370$	42.2144	−	20.3294i	2.19462	−	1.05687i
$371$	0.536542	+	2.35074i	0.0278559	+	0.122045i
$372$	7.10014	−	31.1078i	0.368125	−	1.61286i
$373$	28.0616	+	13.5138i	1.45297	+	0.699716i	0.983109	−	0.183022i	$-0.0585880\pi$
$373$	28.0616	+	13.5138i	1.45297	+	0.699716i	0.469866	+	0.882738i	$0.344302\pi$
$374$	−7.28563	−	15.1288i	−0.376731	−	0.782290i
$375$	20.4194	+	4.66060i	1.05445	+	0.240672i
$376$	−31.6459			−1.63201
$377$		0			0
$378$	3.01588			0.155120
$379$	23.6671	+	5.40187i	1.21570	+	0.277476i	0.781825	−	0.623498i	$-0.214289\pi$
$379$	23.6671	+	5.40187i	1.21570	+	0.277476i	0.433875	+	0.900973i	$0.357146\pi$
$380$	−2.19520	−	4.55837i	−0.112611	−	0.233839i
$381$	−11.0384	−	5.31580i	−0.565513	−	0.272337i
$382$	3.95393	−	17.3233i	0.202300	−	0.886336i
$383$	−6.62397	−	29.0215i	−0.338469	−	1.48293i	−0.802254	−	0.596982i	$-0.796366\pi$
$383$	−6.62397	−	29.0215i	−0.338469	−	1.48293i	0.463785	−	0.885948i	$-0.346491\pi$
$384$	39.2547	−	18.9041i	2.00321	−	0.964695i
$385$	−2.75827	−	2.19964i	−0.140574	−	0.112104i
$386$	32.7963	−	41.1253i	1.66929	−	2.09322i
$387$	−0.0139409	+	0.0289486i	−0.000708656	+	0.00147154i
$388$	−13.0012	+	10.3681i	−0.660035	+	0.526361i
$389$			10.7861i			0.546879i	0.961889	+	0.273440i	$0.0881614\pi$
$389$			10.7861i			0.546879i	−0.961889	+	0.273440i	$0.911839\pi$
$390$	42.6008	+	53.4197i	2.15717	+	2.70501i
$391$	0.596857	−	0.136229i	0.0301843	−	0.00688938i
$392$	27.7301	−	6.32920i	1.40058	−	0.319673i
$393$	−0.692047	−	0.867799i	−0.0349091	−	0.0437747i
$394$			47.1774i			2.37676i
$395$	−14.1632	+	11.2947i	−0.712625	+	0.568300i
$396$	8.80518	−	18.2841i	0.442477	−	0.918813i
$397$	0.712354	−	0.893264i	0.0357520	−	0.0448316i	−0.763634	−	0.645649i	$-0.776587\pi$
$397$	0.712354	−	0.893264i	0.0357520	−	0.0448316i	0.799386	+	0.600818i	$0.205158\pi$
$398$	−30.3966	−	24.2405i	−1.52365	−	1.21507i
$399$	0.399936	−	0.192599i	0.0200218	−	0.00964201i
$400$	−0.491160	−	2.15191i	−0.0245580	−	0.107596i
$401$	0.857065	−	3.75505i	0.0427998	−	0.187518i	−0.949009	−	0.315249i	$-0.897912\pi$
$401$	0.857065	−	3.75505i	0.0427998	−	0.187518i	0.991809	+	0.127731i	$0.0407693\pi$
$402$	54.5571	+	26.2733i	2.72106	+	1.31039i
$403$	−9.87281	−	20.5011i	−0.491799	−	1.02123i
$404$	21.9757	+	5.01581i	1.09333	+	0.249546i
$405$	−27.2969			−1.35639
$406$		0			0
$407$	−30.9539			−1.53433
$408$	15.5195	+	3.54223i	0.768331	+	0.175367i
$409$	−8.35245	−	17.3440i	−0.413002	−	0.857607i	−0.998885	−	0.0472117i	$-0.984966\pi$
$409$	−8.35245	−	17.3440i	−0.413002	−	0.857607i	0.585883	−	0.810396i	$-0.300748\pi$
$410$	40.8286	+	19.6620i	2.01638	+	0.971039i
$411$	3.67627	−	16.1068i	0.181337	−	0.794488i
$412$	5.14823	+	22.5559i	0.253635	+	1.11125i
$413$	2.77383	−	1.33581i	0.136491	−	0.0657308i
$414$	0.888433	+	0.708501i	0.0436641	+	0.0348209i
$415$	1.01621	−	1.27428i	0.0498835	−	0.0625520i
$416$	5.80095	−	12.0458i	0.284415	−	0.590594i
$417$	15.1941	−	12.1169i	0.744060	−	0.593368i
$418$			5.13342i			0.251084i
$419$	1.24992	+	1.56734i	0.0610624	+	0.0765698i	0.811425	−	0.584457i	$-0.198692\pi$
$419$	1.24992	+	1.56734i	0.0610624	+	0.0765698i	−0.750362	+	0.661027i	$0.770121\pi$
$420$	7.02474	−	1.60335i	0.342772	−	0.0782355i
$421$	−38.8570	+	8.86887i	−1.89378	+	0.432242i	−0.999872	−	0.0160147i	$-0.994902\pi$
$421$	−38.8570	+	8.86887i	−1.89378	+	0.432242i	−0.893905	+	0.448257i	$0.852045\pi$
$422$	−35.1344	−	44.0572i	−1.71032	−	2.14467i
$423$			10.8007i			0.525149i
$424$	20.6673	−	16.4816i	1.00369	−	0.800418i
$425$	−0.709011	+	1.47228i	−0.0343921	+	0.0714159i
$426$	−48.8077	+	61.2029i	−2.36474	+	2.96529i
$427$	−3.06818	−	2.44679i	−0.148479	−	0.118408i
$428$	17.8285	−	8.58574i	0.861772	−	0.415008i
$429$	−10.0444	−	44.0072i	−0.484947	−	2.12469i
$430$	0.0293567	−	0.128620i	0.00141571	−	0.00620261i
$431$	−12.8972	−	6.21096i	−0.621236	−	0.299171i	0.0966647	−	0.995317i	$-0.469183\pi$
$431$	−12.8972	−	6.21096i	−0.621236	−	0.299171i	−0.717901	+	0.696146i	$0.754897\pi$
$432$	−3.56303	−	7.39870i	−0.171426	−	0.355970i
$433$	8.61255	+	1.96576i	0.413893	+	0.0944683i	0.424396	−	0.905477i	$-0.360486\pi$
$433$	8.61255	+	1.96576i	0.413893	+	0.0944683i	−0.0105037	+	0.999945i	$0.503343\pi$
$434$	−3.68536			−0.176903
$435$		0			0
$436$	23.5123			1.12604
$437$	−0.182466	−	0.0416467i	−0.00872855	−	0.00199223i
$438$	15.1380	+	31.4344i	0.723323	+	1.50200i
$439$	−10.4355	−	5.02550i	−0.498062	−	0.239854i	0.167950	−	0.985796i	$-0.446285\pi$
$439$	−10.4355	−	5.02550i	−0.498062	−	0.239854i	−0.666011	+	0.745942i	$0.732000\pi$
$440$	−8.60661	+	37.7080i	−0.410304	+	1.79766i
$441$	−2.16015	−	9.46424i	−0.102864	−	0.450678i
$442$	22.0348	−	10.6114i	1.04809	−	0.504733i
$443$	−27.7465	−	22.1271i	−1.31827	−	1.05129i	−0.994454	−	0.105170i	$-0.966461\pi$
$443$	−27.7465	−	22.1271i	−1.31827	−	1.05129i	−0.323820	−	0.946119i	$-0.604967\pi$
$444$	39.4165	−	49.4268i	1.87063	−	2.34569i
$445$	10.1542	−	21.0855i	0.481357	−	0.999549i
$446$	1.31396	−	1.04784i	0.0622176	−	0.0496169i
$447$			1.08068i			0.0511146i
$448$	−2.51396	−	3.15240i	−0.118773	−	0.148937i
$449$	−20.2283	+	4.61698i	−0.954633	+	0.217889i	−0.671344	−	0.741146i	$-0.734283\pi$
$449$	−20.2283	+	4.61698i	−0.954633	+	0.217889i	−0.283289	+	0.959035i	$0.591426\pi$
$450$	−2.95710	+	0.674938i	−0.139399	+	0.0318169i
$451$	−18.6659	−	23.4063i	−0.878941	−	1.10216i
$452$			50.0535i			2.35432i
$453$	−10.7650	+	8.58476i	−0.505781	+	0.403347i
$454$	−7.68997	+	15.9684i	−0.360908	+	0.749434i
$455$	3.20374	−	4.01737i	0.150194	−	0.188337i
$456$	−3.80480	−	3.03423i	−0.178176	−	0.142091i
$457$	34.3302	−	16.5326i	1.60590	−	0.773361i	0.606142	−	0.795356i	$-0.292716\pi$
$457$	34.3302	−	16.5326i	1.60590	−	0.773361i	0.999758	+	0.0219951i	$0.00700183\pi$
$458$	−5.72503	−	25.0830i	−0.267513	−	1.17205i
$459$	−1.35283	+	5.92714i	−0.0631447	+	0.276655i
$460$	−2.73714	−	1.31814i	−0.127620	−	0.0614584i
$461$	−7.69032	−	15.9691i	−0.358174	−	0.743756i	0.641554	−	0.767078i	$-0.278290\pi$
$461$	−7.69032	−	15.9691i	−0.358174	−	0.743756i	−0.999728	+	0.0233222i	$0.992576\pi$
$462$	−7.12749	−	1.62680i	−0.331601	−	0.0756858i
$463$	−9.21914			−0.428450			−0.214225	−	0.976784i	$-0.568723\pi$
$463$	−9.21914			−0.428450			−0.214225	+	0.976784i	$0.568723\pi$
$464$		0			0
$465$	20.7552			0.962501
$466$	36.3881	+	8.30535i	1.68565	+	0.384738i
$467$	3.38523	+	7.02951i	0.156650	+	0.325287i	0.964492	−	0.264112i	$-0.0850789\pi$
$467$	3.38523	+	7.02951i	0.156650	+	0.325287i	−0.807842	+	0.589399i	$0.799365\pi$
$468$	26.6305	+	12.8246i	1.23100	+	0.592817i
$469$	1.01334	−	4.43971i	0.0467915	−	0.205007i
$470$	−9.86829	−	43.2358i	−0.455190	−	1.99432i
$471$	−21.6891	+	10.4449i	−0.999383	+	0.481277i
$472$	−26.3889	−	21.0445i	−1.21465	−	0.968650i
$473$	−0.0543412	+	0.0681418i	−0.00249861	+	0.00313316i
$474$	−16.2878	+	33.8219i	−0.748121	+	1.55349i
$475$	0.390576	−	0.311474i	0.0179208	−	0.0142914i
$476$		−	2.57910i		−	0.118213i
$477$	−5.62516	−	7.05373i	−0.257558	−	0.322968i
$478$	17.3761	−	3.96598i	0.794764	−	0.181400i
$479$	−17.2783	+	3.94367i	−0.789467	+	0.180191i	−0.598200	−	0.801347i	$-0.704117\pi$
$479$	−17.2783	+	3.94367i	−0.789467	+	0.180191i	−0.191268	+	0.981538i	$0.561260\pi$
$480$	7.60354	+	9.53454i	0.347052	+	0.435190i
$481$		−	45.0838i		−	2.05564i
$482$	−9.85916	+	7.86242i	−0.449072	+	0.358123i
$483$	0.115649	−	0.240147i	0.00526220	−	0.0109271i
$484$	8.72316	−	10.9385i	0.396507	−	0.497204i
$485$	−8.45696	−	6.74420i	−0.384011	−	0.306238i
$486$	−29.4200	+	14.1679i	−1.33452	+	0.642670i
$487$	4.70832	+	20.6285i	0.213354	+	0.934766i	0.962269	+	0.272100i	$0.0877181\pi$
$487$	4.70832	+	20.6285i	0.213354	+	0.934766i	−0.748915	+	0.662666i	$0.769425\pi$
$488$	−9.57362	+	41.9448i	−0.433377	+	1.89875i
$489$	−34.5200	−	16.6240i	−1.56105	−	0.751762i
$490$	17.2944	+	35.9122i	0.781281	+	1.62235i
$491$	−17.2624	−	3.94003i	−0.779042	−	0.177811i	−0.185532	−	0.982638i	$-0.559401\pi$
$491$	−17.2624	−	3.94003i	−0.779042	−	0.177811i	−0.593509	+	0.804827i	$0.702258\pi$
$492$	61.1439			2.75658
$493$		0			0
$494$	−7.47673			−0.336394
$495$	12.8697	+	2.93743i	0.578450	+	0.132028i
$496$	4.35397	+	9.04111i	0.195499	+	0.405958i
$497$	5.30407	+	2.55430i	0.237920	+	0.114576i
$498$	0.751561	−	3.29280i	0.0336782	−	0.147554i
$499$	6.49875	+	28.4729i	0.290924	+	1.27462i	0.883242	+	0.468917i	$0.155356\pi$
$499$	6.49875	+	28.4729i	0.290924	+	1.27462i	−0.592318	+	0.805704i	$0.701787\pi$
$500$	−33.5183	+	16.1415i	−1.49898	+	0.721872i
$501$	−4.16289	−	3.31979i	−0.185984	−	0.148317i
$502$	−41.7441	+	52.3455i	−1.86313	+	2.33629i
$503$	−18.6936	+	38.8176i	−0.833504	+	1.73079i	−0.166080	+	0.986112i	$0.553111\pi$
$503$	−18.6936	+	38.8176i	−0.833504	+	1.73079i	−0.667425	+	0.744677i	$0.732603\pi$
$504$	1.73729	−	1.38545i	0.0773853	−	0.0617127i
$505$			14.6623i			0.652463i
$506$	1.92187	+	2.40994i	0.0854374	+	0.107135i
$507$	37.4629	−	8.55066i	1.66378	−	0.379748i
$508$	21.2163	−	4.84247i	0.941319	−	0.214850i
$509$	20.2588	+	25.4037i	0.897955	+	1.12600i	0.991464	+	0.130381i	$0.0416202\pi$
$509$	20.2588	+	25.4037i	0.897955	+	1.12600i	−0.0935090	+	0.995618i	$0.529808\pi$
$510$			22.3079i			0.987813i
$511$	2.05140	−	1.63593i	0.0907484	−	0.0723695i
$512$	−11.4376	+	23.7504i	−0.505474	+	1.04963i
$513$	1.15882	−	1.45311i	0.0511630	−	0.0641564i
$514$	−35.6948	−	28.4657i	−1.57443	−	1.25557i
$515$	−13.5590	+	6.52967i	−0.597481	+	0.287732i
$516$	−0.0396101	−	0.173543i	−0.00174374	−	0.00763980i
$517$	−6.51937	+	28.5632i	−0.286722	+	1.25621i
$518$	−6.57874	−	3.16815i	−0.289053	−	0.139201i
$519$	7.73595	+	16.0639i	0.339571	+	0.705126i
$520$	−54.9211	−	12.5354i	−2.40845	−	0.549713i
$521$	−28.2658			−1.23835			−0.619173	−	0.785254i	$-0.712532\pi$
$521$	−28.2658			−1.23835			−0.619173	+	0.785254i	$0.712532\pi$
$522$		0			0
$523$	−8.63499			−0.377582			−0.188791	−	0.982017i	$-0.560457\pi$
$523$	−8.63499			−0.377582			−0.188791	+	0.982017i	$0.560457\pi$
$524$	1.92211	+	0.438710i	0.0839680	+	0.0191651i
$525$	0.308690	+	0.641002i	0.0134724	+	0.0279756i
$526$	−15.3479	−	7.39117i	−0.669201	−	0.322270i
$527$	1.65314	−	7.24288i	0.0720119	−	0.315505i
$528$	4.42963	+	19.4075i	0.192775	+	0.844601i
$529$	20.6210	−	9.93057i	0.896567	−	0.431764i
$530$	28.9626	+	23.0969i	1.25805	+	1.00327i
$531$	−7.18246	+	9.00652i	−0.311692	+	0.390850i
$532$	−0.342101	+	0.710381i	−0.0148320	+	0.0307989i
$533$	34.0908	−	27.1865i	1.47664	−	1.17758i
$534$		−	48.4970i		−	2.09867i
$535$	8.02537	+	10.0635i	0.346967	+	0.435083i
$536$	−48.6735	+	11.1094i	−2.10238	+	0.479854i
$537$	−26.5364	+	6.05677i	−1.14513	+	0.261369i
$538$	8.89125	+	11.1493i	0.383329	+	0.480679i
$539$		−	26.3327i		−	1.13423i
$540$	23.5871	−	18.8101i	1.01503	−	0.809459i
$541$	4.57517	−	9.50045i	0.196702	−	0.408456i	−0.779166	−	0.626818i	$-0.784357\pi$
$541$	4.57517	−	9.50045i	0.196702	−	0.408456i	0.975868	+	0.218362i	$0.0700713\pi$
$542$	−7.66333	+	9.60951i	−0.329168	+	0.412764i
$543$	26.9717	+	21.5093i	1.15747	+	0.923050i
$544$	3.93285	−	1.89396i	0.168620	−	0.0812029i
$545$	3.40328	+	14.9108i	0.145781	+	0.638707i
$546$	2.36941	−	10.3811i	0.101401	−	0.444269i
$547$	−34.8853	−	16.7999i	−1.49159	−	0.718310i	−0.502354	−	0.864662i	$-0.667533\pi$
$547$	−34.8853	−	16.7999i	−1.49159	−	0.718310i	−0.989233	+	0.146352i	$0.953247\pi$
$548$	12.7324	+	26.4391i	0.543901	+	1.12942i
$549$	14.3157	+	3.26747i	0.610979	+	0.139452i
$550$	−8.22765			−0.350828
$551$		0			0
$552$	−2.92217			−0.124376
$553$	2.75233	+	0.628202i	0.117041	+	0.0267139i
$554$	−20.7825	−	43.1554i	−0.882965	−	1.83350i
$555$	37.0502	+	17.8424i	1.57269	+	0.757369i
$556$	−7.68129	+	33.6539i	−0.325759	+	1.42724i
$557$	1.86634	+	8.17695i	0.0790792	+	0.346469i	0.998953	−	0.0457456i	$-0.0145664\pi$
$557$	1.86634	+	8.17695i	0.0790792	+	0.346469i	−0.919874	+	0.392214i	$0.871709\pi$
$558$	12.4240	−	5.98310i	0.525951	−	0.253285i
$559$	−0.0992473	−	0.0791471i	−0.00419771	−	0.00334756i
$560$	−1.41287	+	1.77168i	−0.0597047	+	0.0748673i
$561$	6.39435	−	13.2780i	0.269970	−	0.560598i
$562$	21.9598	−	17.5123i	0.926316	−	0.738713i
$563$		−	27.6892i		−	1.16696i	−0.812127	−	0.583480i	$-0.801691\pi$
$563$		−	27.6892i		−	1.16696i	0.812127	−	0.583480i	$-0.198309\pi$
$564$	−37.3077	−	46.7824i	−1.57094	−	1.96989i
$565$	−31.7423	+	7.24498i	−1.33541	+	0.304798i
$566$	69.1459	−	15.7821i	2.90642	−	0.663371i
$567$	2.65231	+	3.32589i	0.111387	+	0.139674i
$568$		−	64.5412i		−	2.70809i
$569$	7.66072	−	6.10922i	0.321154	−	0.256112i	−0.449621	−	0.893220i	$-0.648441\pi$
$569$	7.66072	−	6.10922i	0.321154	−	0.256112i	0.770775	+	0.637108i	$0.219869\pi$
$570$	2.95900	−	6.14444i	0.123939	−	0.257362i
$571$	−8.97937	+	11.2598i	−0.375775	+	0.471207i	−0.933375	−	0.358903i	$-0.883151\pi$
$571$	−8.97937	+	11.2598i	−0.375775	+	0.471207i	0.557600	+	0.830110i	$0.311722\pi$
$572$	62.6853	+	49.9898i	2.62100	+	2.09018i
$573$	14.0507	−	6.76644i	0.586975	−	0.282672i
$574$	−1.57148	−	6.88508i	−0.0655921	−	0.287378i
$575$	0.0667498	−	0.292450i	0.00278366	−	0.0121960i
$576$	13.5929	+	6.54598i	0.566370	+	0.272749i
$577$	−4.50822	−	9.36141i	−0.187680	−	0.389721i	0.785805	−	0.618475i	$-0.212249\pi$
$577$	−4.50822	−	9.36141i	−0.187680	−	0.389721i	−0.973484	+	0.228754i	$0.926535\pi$
$578$	−31.8974	−	7.28037i	−1.32676	−	0.302823i
$579$	46.1663			1.91861
$580$		0			0
$581$	−0.254000			−0.0105377
$582$	−21.8532	−	4.98785i	−0.905844	−	0.206753i
$583$	−10.6185	−	22.0495i	−0.439772	−	0.913195i
$584$	−25.9170	−	12.4810i	−1.07245	−	0.516466i
$585$	−4.27831	+	18.7445i	−0.176886	+	0.774990i
$586$	−4.18860	−	18.3514i	−0.173029	−	0.758091i
$587$	−1.46591	+	0.705943i	−0.0605044	+	0.0291374i	−0.463891	−	0.885892i	$-0.653547\pi$
$587$	−1.46591	+	0.705943i	−0.0605044	+	0.0291374i	0.403387	+	0.915030i	$0.367833\pi$
$588$	42.0478	+	33.5320i	1.73402	+	1.38284i
$589$	−1.41606	+	1.77568i	−0.0583476	+	0.0731656i
$590$	20.5228	−	42.6160i	0.844909	−	1.75447i
$591$	−32.3725	+	25.8162i	−1.33163	+	1.06194i
$592$			19.8822i			0.817154i
$593$	−19.3646	−	24.2824i	−0.795208	−	0.997159i	−0.999832	−	0.0183183i	$-0.994169\pi$
$593$	−19.3646	−	24.2824i	−0.795208	−	0.997159i	0.204625	−	0.978841i	$-0.434403\pi$
$594$	−29.8429	+	6.81145i	−1.22447	+	0.279477i
$595$	1.63558	−	0.373311i	0.0670524	−	0.0153043i
$596$	−1.19682	−	1.50076i	−0.0490237	−	0.0614737i
$597$		−	34.1226i		−	1.39654i
$598$	−3.51004	+	2.79916i	−0.143536	+	0.114466i
$599$	−7.08818	+	14.7188i	−0.289615	+	0.601392i	−0.994117	−	0.108310i	$-0.965456\pi$
$599$	−7.08818	+	14.7188i	−0.289615	+	0.601392i	0.704502	+	0.709702i	$0.251170\pi$
$600$	4.86314	−	6.09819i	0.198537	−	0.248958i
$601$	−7.78199	−	6.20593i	−0.317434	−	0.253145i	0.451790	−	0.892124i	$-0.350786\pi$
$601$	−7.78199	−	6.20593i	−0.317434	−	0.253145i	−0.769224	+	0.638979i	$0.779357\pi$
$602$	−0.0185237	+	0.00892055i	−0.000754970	+	0.000363574i
$603$	3.79163	+	16.6122i	0.154407	+	0.676502i
$604$	5.44215	−	23.8436i	0.221438	−	0.970183i
$605$	8.19947	+	3.94866i	0.333356	+	0.160536i
$606$	13.1830	+	27.3749i	0.535525	+	1.11203i
$607$	25.5531	+	5.83233i	1.03717	+	0.236727i	0.707013	−	0.707200i	$-0.250042\pi$
$607$	25.5531	+	5.83233i	1.03717	+	0.236727i	0.330155	+	0.943927i	$0.392899\pi$
$608$	−1.33447			−0.0541201
$609$		0			0
$610$	−60.2919			−2.44115
$611$	−41.6019	−	9.49535i	−1.68303	−	0.384141i
$612$	4.18712	+	8.69464i	0.169254	+	0.351460i
$613$	−41.8439	−	20.1510i	−1.69006	−	0.813890i	−0.995532	−	0.0944251i	$-0.969899\pi$
$613$	−41.8439	−	20.1510i	−1.69006	−	0.813890i	−0.694529	−	0.719465i	$-0.744387\pi$
$614$	15.1207	−	66.2483i	0.610224	−	2.67356i
$615$	8.85025	+	38.7755i	0.356876	+	1.56358i
$616$	5.43066	−	2.61527i	0.218807	−	0.105372i
$617$	7.48659	+	5.97036i	0.301399	+	0.240358i	0.762497	−	0.646991i	$-0.223973\pi$
$617$	7.48659	+	5.97036i	0.301399	+	0.240358i	−0.461098	+	0.887349i	$0.652544\pi$
$618$	−19.4441	+	24.3822i	−0.782158	+	0.980795i
$619$	8.70941	−	18.0853i	0.350061	−	0.726909i	−0.649376	−	0.760467i	$-0.724970\pi$
$619$	8.70941	−	18.0853i	0.350061	−	0.726909i	0.999437	+	0.0335589i	$0.0106841\pi$
$620$	−28.8232	+	22.9857i	−1.15757	+	0.923128i
$621$		−	1.11602i		−	0.0447844i
$622$	−12.7960	−	16.0457i	−0.513072	−	0.643372i
$623$	−3.55573	+	0.811571i	−0.142457	+	0.0325149i
$624$	−28.2666	+	6.45167i	−1.13157	+	0.258274i
$625$	−17.8775	−	22.4177i	−0.715102	−	0.896710i
$626$			2.10457i			0.0841157i
$627$	−3.52248	+	2.80909i	−0.140674	+	0.112184i
$628$	18.5527	−	38.5250i	0.740333	−	1.53732i
$629$	9.17743	−	11.5081i	0.365928	−	0.458859i
$630$	2.43460	+	1.94153i	0.0969967	+	0.0773523i
$631$	−25.7365	+	12.3940i	−1.02455	+	0.493399i	−0.869201	−	0.494460i	$-0.835366\pi$
$631$	−25.7365	+	12.3940i	−1.02455	+	0.493399i	−0.155354	+	0.987859i	$0.549652\pi$
$632$	−6.88711	−	30.1744i	−0.273955	−	1.20027i
$633$	11.0053	−	48.2176i	0.437423	−	1.91648i
$634$	57.4358	+	27.6596i	2.28107	+	1.09850i
$635$	6.14187	+	12.7537i	0.243733	+	0.506116i
$636$	48.7298	+	11.1223i	1.93226	+	0.441027i
$637$	38.3531			1.51961
$638$		0			0
$639$	−22.0278			−0.871408
$640$	−49.0780	−	11.2017i	−1.93998	−	0.442788i
$641$	3.24196	+	6.73199i	0.128050	+	0.265898i	0.955131	−	0.296185i	$-0.0957145\pi$
$641$	3.24196	+	6.73199i	0.128050	+	0.265898i	−0.827081	+	0.562083i	$0.810000\pi$
$642$	24.0318	+	11.5731i	0.948460	+	0.456754i
$643$	−4.65243	+	20.3836i	−0.183474	+	0.803851i	0.796486	+	0.604657i	$0.206690\pi$
$643$	−4.65243	+	20.3836i	−0.183474	+	0.803851i	−0.979960	+	0.199195i	$0.936167\pi$
$644$	0.105351	+	0.461574i	0.00415142	+	0.0181886i
$645$	0.104322	−	0.0502388i	0.00410767	−	0.00197815i
$646$	−1.90852	−	1.52199i	−0.0750897	−	0.0598820i
$647$	5.69771	−	7.14470i	0.224000	−	0.280887i	−0.657114	−	0.753791i	$-0.728223\pi$
$647$	5.69771	−	7.14470i	0.224000	−	0.280887i	0.881114	+	0.472904i	$0.156794\pi$
$648$	20.2351	−	42.0187i	0.794912	−	1.65065i
$649$	−24.4309	+	19.4830i	−0.958996	+	0.764774i
$650$		−	11.9834i		−	0.470029i
$651$	−2.01669	−	2.52885i	−0.0790402	−	0.0991133i
$652$	66.3490	−	15.1437i	2.59843	−	0.593074i
$653$	−14.2722	+	3.25753i	−0.558513	+	0.127477i	−0.492454	−	0.870339i	$-0.663900\pi$
$653$	−14.2722	+	3.25753i	−0.558513	+	0.127477i	−0.0660595	+	0.997816i	$0.521043\pi$
$654$	19.7605	+	24.7789i	0.772696	+	0.968931i
$655$			1.28244i			0.0501092i
$656$	−15.0343	+	11.9894i	−0.586989	+	0.468108i
$657$	−4.25974	+	8.84544i	−0.166188	+	0.345093i
$658$	−4.30906	+	5.40339i	−0.167985	+	0.210646i
$659$	29.9785	+	23.9070i	1.16780	+	0.931286i	0.998526	−	0.0542837i	$-0.0172875\pi$
$659$	29.9785	+	23.9070i	1.16780	+	0.931286i	0.169270	+	0.985570i	$0.445859\pi$
$660$	−65.8905	+	31.7312i	−2.56478	+	1.23513i
$661$	5.36029	+	23.4850i	0.208491	+	0.913459i	0.965572	+	0.260138i	$0.0837680\pi$
$661$	5.36029	+	23.4850i	0.208491	+	0.913459i	−0.757080	+	0.653322i	$0.773375\pi$
$662$	−9.93555	+	43.5305i	−0.386156	+	1.69186i
$663$	19.3392	+	9.31327i	0.751072	+	0.361697i
$664$	1.20822	+	2.50889i	0.0468879	+	0.0973638i
$665$	−0.500018	−	0.114126i	−0.0193899	−	0.00442561i
$666$	27.3216			1.05869
$667$		0			0
$668$	9.45763			0.365927
$669$	1.43804	+	0.328222i	0.0555977	+	0.0126898i
$670$	−30.3562	−	63.0353i	−1.17276	−	2.43527i
$671$	35.8866	+	17.2821i	1.38539	+	0.667167i
$672$	0.422901	−	1.85285i	0.0163138	−	0.0714753i
$673$	−0.447342	−	1.95993i	−0.0172438	−	0.0755499i	0.965574	−	0.260129i	$-0.0837650\pi$
$673$	−0.447342	−	1.95993i	−0.0172438	−	0.0755499i	−0.982818	+	0.184579i	$0.940908\pi$
$674$	13.0459	−	6.28259i	0.502510	−	0.241996i
$675$	2.32899	+	1.85731i	0.0896429	+	0.0714878i
$676$	−42.5558	+	53.3633i	−1.63676	+	2.05243i
$677$	7.14374	−	14.8341i	0.274556	−	0.570122i	−0.717406	−	0.696655i	$-0.754671\pi$
$677$	7.14374	−	14.8341i	0.274556	−	0.570122i	0.991962	+	0.126533i	$0.0403850\pi$
$678$	−52.7497	+	42.0665i	−2.02584	+	1.61555i
$679$			1.68571i			0.0646916i
$680$	−11.4675	−	14.3797i	−0.439757	−	0.551438i
$681$	−15.1654	+	3.46140i	−0.581139	+	0.132641i
$682$	36.4676	−	8.32350i	1.39642	−	0.318723i
$683$	−2.76382	−	3.46572i	−0.105755	−	0.132612i	0.726137	−	0.687550i	$-0.241314\pi$
$683$	−2.76382	−	3.46572i	−0.105755	−	0.132612i	−0.831892	+	0.554937i	$0.812742\pi$
$684$		−	2.95022i		−	0.112804i
$685$	−14.9239	+	11.9014i	−0.570212	+	0.454729i
$686$	5.44662	−	11.3100i	0.207953	−	0.431819i
$687$	14.0788	−	17.6543i	0.537140	−	0.673552i
$688$	0.0437686	+	0.0349043i	0.00166866	+	0.00133072i
$689$	32.1146	−	15.4656i	1.22347	−	0.589192i
$690$	−0.911235	−	3.99238i	−0.0346901	−	0.151987i
$691$	−4.48891	+	19.6672i	−0.170766	+	0.748176i	0.814918	+	0.579576i	$0.196782\pi$
$691$	−4.48891	+	19.6672i	−0.170766	+	0.748176i	−0.985685	+	0.168600i	$0.946075\pi$
$692$	−28.5332	−	13.7409i	−1.08467	−	0.522350i
$693$	−0.892588	−	1.85348i	−0.0339066	−	0.0704078i
$694$	−33.7225	−	7.69693i	−1.28009	−	0.292172i
$695$	−22.4541			−0.851731
$696$		0			0
$697$	14.2363			0.539237
$698$	−26.8980	−	6.13930i	−1.01811	−	0.232376i
$699$	14.2131	+	29.5139i	0.537590	+	1.11632i
$700$	−1.13857	−	0.548307i	−0.0430340	−	0.0207241i
$701$	−7.09085	+	31.0671i	−0.267818	+	1.17339i	0.644728	+	0.764412i	$0.276971\pi$
$701$	−7.09085	+	31.0671i	−0.267818	+	1.17339i	−0.912546	+	0.408975i	$0.865886\pi$
$702$	−9.92076	−	43.4657i	−0.374435	−	1.64051i
$703$	−4.05428	+	1.95244i	−0.152910	+	0.0736377i
$704$	31.9961	+	25.5160i	1.20590	+	0.961672i
$705$	24.2678	−	30.4308i	0.913977	−	1.14609i
$706$	8.80230	−	18.2782i	0.331279	−	0.687908i
$707$	1.78647	−	1.42466i	0.0671872	−	0.0535800i
$708$		−	63.8205i		−	2.39852i
$709$	29.1581	+	36.5631i	1.09506	+	1.37316i	0.921521	+	0.388330i	$0.126948\pi$
$709$	29.1581	+	36.5631i	1.09506	+	1.37316i	0.173536	+	0.984828i	$0.444481\pi$
$710$	88.1786	−	20.1262i	3.30928	−	0.755323i
$711$	−10.2985	+	2.35056i	−0.386224	+	0.0881530i
$712$	24.9300	+	31.2613i	0.934293	+	1.17157i
$713$			1.36376i			0.0510733i
$714$	2.71803	−	2.16756i	0.101720	−	0.0811188i
$715$	−22.6286	+	46.9887i	−0.846261	+	1.75728i
$716$	30.1440	−	37.7993i	1.12653	−	1.41263i
$717$	12.2299	+	9.75300i	0.456733	+	0.364233i
$718$	−10.6462	+	5.12693i	−0.397312	+	0.191335i
$719$	−7.73658	−	33.8962i	−0.288526	−	1.26411i	−0.886549	−	0.462635i	$-0.846904\pi$
$719$	−7.73658	−	33.8962i	−0.288526	−	1.26411i	0.598023	−	0.801479i	$-0.295953\pi$
$720$	1.88676	−	8.26644i	0.0703154	−	0.308072i
$721$	2.11305	+	1.01759i	0.0786941	+	0.0378971i
$722$	−19.4141	−	40.3137i	−0.722517	−	1.50032i
$723$	−10.7902	−	2.46279i	−0.401291	−	0.0915921i
$724$	−61.2769			−2.27734
$725$		0			0
$726$	18.8589			0.699920
$727$	−22.4821	−	5.13139i	−0.833814	−	0.190313i	−0.215758	−	0.976447i	$-0.569222\pi$
$727$	−22.4821	−	5.13139i	−0.833814	−	0.190313i	−0.618056	+	0.786134i	$0.712079\pi$
$728$	3.80909	+	7.90966i	0.141174	+	0.293152i
$729$	4.56758	+	2.19963i	0.169170	+	0.0814678i
$730$	8.97014	−	39.3007i	0.332000	−	1.45459i
$731$	−0.00922249	−	0.0404063i	−0.000341106	−	0.00149448i
$732$	−73.2937	+	35.2964i	−2.70901	+	1.30459i
$733$	−30.0623	−	23.9739i	−1.11038	−	0.885496i	−0.116196	−	0.993226i	$-0.537070\pi$
$733$	−30.0623	−	23.9739i	−1.11038	−	0.885496i	−0.994180	+	0.107731i	$0.965642\pi$
$734$	−4.33961	+	5.44170i	−0.160178	+	0.200857i
$735$	−15.1787	+	31.5189i	−0.559875	+	1.16259i
$736$	−0.626485	+	0.499605i	−0.0230925	+	0.0184157i
$737$			46.2208i			1.70257i
$738$	16.4755	+	20.6596i	0.606472	+	0.760492i
$739$	−28.3509	+	6.47090i	−1.04290	+	0.238036i	−0.709468	−	0.704737i	$-0.751065\pi$
$739$	−28.3509	+	6.47090i	−1.04290	+	0.238036i	−0.333435	+	0.942773i	$0.608208\pi$
$740$	−71.2121	+	16.2537i	−2.61781	+	0.597498i
$741$	−4.09139	−	5.13044i	−0.150301	−	0.188471i
$742$		−	5.77306i		−	0.211936i
$743$	25.5189	−	20.3506i	0.936197	−	0.746592i	−0.0312906	−	0.999510i	$-0.509962\pi$
$743$	25.5189	−	20.3506i	0.936197	−	0.746592i	0.967488	+	0.252918i	$0.0813903\pi$
$744$	−15.3858	+	31.9490i	−0.564072	+	1.17131i
$745$	0.778503	−	0.976212i	0.0285221	−	0.0357656i
$746$	−58.3028	−	46.4949i	−2.13462	−	1.70230i
$747$	0.856281	−	0.412363i	0.0313297	−	0.0150876i
$748$	5.82499	+	25.5209i	0.212983	+	0.933138i
$749$	0.446363	−	1.95564i	0.0163098	−	0.0714577i
$750$	−45.1808	−	21.7579i	−1.64977	−	0.794487i
$751$	−0.0603884	−	0.125398i	−0.00220360	−	0.00457583i	0.899864	−	0.436170i	$-0.143665\pi$
$751$	−0.0603884	−	0.125398i	−0.00220360	−	0.00457583i	−0.902068	+	0.431594i	$0.857951\pi$
$752$	18.3467	+	4.18751i	0.669034	+	0.152703i
$753$	−58.7619			−2.14140
$754$		0			0
$755$	15.9086			0.578972
$756$	−4.58370	−	1.04620i	−0.166708	−	0.0380499i
$757$	−0.743366	−	1.54361i	−0.0270181	−	0.0561036i	0.887023	−	0.461725i	$-0.152769\pi$
$757$	−0.743366	−	1.54361i	−0.0270181	−	0.0561036i	−0.914041	+	0.405622i	$0.867055\pi$
$758$	−52.3668	−	25.2185i	−1.90205	−	0.915979i
$759$	−0.601997	+	2.63752i	−0.0218511	+	0.0957359i
$760$	1.25119	+	5.48180i	0.0453853	+	0.198846i
$761$	34.8731	−	16.7940i	1.26415	−	0.608783i	0.322881	−	0.946440i	$-0.395349\pi$
$761$	34.8731	−	16.7940i	1.26415	−	0.608783i	0.941269	+	0.337657i	$0.109634\pi$
$762$	22.9341	+	18.2893i	0.830815	+	0.662553i
$763$	1.48607	−	1.86347i	0.0537992	−	0.0674621i
$764$	−12.0188	+	24.9573i	−0.434825	+	0.902924i
$765$	−4.90779	+	3.91383i	−0.177442	+	0.141505i
$766$			71.2723i			2.57517i
$767$	−28.3766	−	35.5832i	−1.02462	−	1.28483i
$768$	−58.0383	+	13.2469i	−2.09428	+	0.478005i
$769$	44.2877	−	10.1084i	1.59706	−	0.364517i	0.670867	−	0.741578i	$-0.265922\pi$
$769$	44.2877	−	10.1084i	1.59706	−	0.364517i	0.926189	+	0.377061i	$0.123065\pi$
$770$	5.26654	+	6.60404i	0.189793	+	0.237993i
$771$		−	40.0702i		−	1.44309i
$772$	−64.1120	+	51.1276i	−2.30744	+	1.84012i
$773$	−21.9810	+	45.6439i	−0.790600	+	1.64170i	−0.0238818	+	0.999715i	$0.507603\pi$
$773$	−21.9810	+	45.6439i	−0.790600	+	1.64170i	−0.766718	+	0.641984i	$0.778112\pi$
$774$	0.0479645	−	0.0601456i	0.00172405	−	0.00216189i
$775$	−2.84599	−	2.26960i	−0.102231	−	0.0815266i
$776$	16.6506	−	8.01852i	0.597723	−	0.287848i
$777$	−1.42604	−	6.24791i	−0.0511590	−	0.224142i
$778$	5.74659	−	25.1775i	0.206025	−	0.902656i
$779$	−3.92119	−	1.88835i	−0.140491	−	0.0676570i
$780$	−46.2159	−	95.9683i	−1.65480	−	3.43622i
$781$	−58.2542	−	13.2961i	−2.08450	−	0.475773i
$782$	−1.46579			−0.0524164
$783$		0			0
$784$	−16.9140			−0.604070
$785$	27.1167	+	6.18921i	0.967837	+	0.220903i
$786$	1.15306	+	2.39436i	0.0411284	+	0.0854039i
$787$	36.1003	+	17.3850i	1.28684	+	0.619708i	0.947138	−	0.320827i	$-0.103961\pi$
$787$	36.1003	+	17.3850i	1.28684	+	0.619708i	0.339698	+	0.940534i	$0.389675\pi$
$788$	16.3657	−	71.7029i	0.583004	−	2.55431i
$789$	−3.32690	−	14.5761i	−0.118441	−	0.518924i
$790$	39.0778	−	18.8189i	1.39032	−	0.669545i
$791$	3.96699	+	3.16357i	0.141050	+	0.112484i
$792$	−14.0619	+	17.6331i	−0.499669	+	0.626565i
$793$	−25.1710	+	52.2682i	−0.893850	+	1.85610i
$794$	−2.13872	+	1.70557i	−0.0759002	+	0.0605284i
$795$			32.5128i			1.15311i
$796$	37.7896	+	47.3866i	1.33942	+	1.67957i
$797$	−8.88907	+	2.02887i	−0.314867	+	0.0718664i	−0.377034	−	0.926199i	$-0.623056\pi$
$797$	−8.88907	+	2.02887i	−0.314867	+	0.0718664i	0.0621669	+	0.998066i	$0.480199\pi$
$798$	−1.03616	+	0.236497i	−0.0366796	+	0.00837189i
$799$	−8.68643	−	10.8924i	−0.307304	−	0.385347i
$800$		−	2.13885i		−	0.0756196i
$801$	10.6694	−	8.50860i	0.376986	−	0.300637i
$802$	−4.00119	+	8.30856i	−0.141287	+	0.293385i
$803$	−16.6043	+	20.8212i	−0.585954	+	0.734763i
$804$	−73.8049	−	58.8574i	−2.60290	−	2.07574i
$805$	−0.277466	+	0.133621i	−0.00977939	+	0.00470951i
$806$	12.1230	+	53.1145i	0.427016	+	1.87088i
$807$	−2.78505	+	12.2021i	−0.0980385	+	0.429535i
$808$	−22.5700	−	10.8691i	−0.794008	−	0.382374i
$809$	1.87212	+	3.88749i	0.0658201	+	0.136677i	0.931283	−	0.364295i	$-0.118690\pi$
$809$	1.87212	+	3.88749i	0.0658201	+	0.136677i	−0.865463	+	0.500972i	$0.832976\pi$
$810$	63.7176	+	14.5431i	2.23881	+	0.510993i
$811$	46.7124			1.64029			0.820147	−	0.572153i	$-0.193892\pi$
$811$	46.7124			1.64029			0.820147	+	0.572153i	$0.193892\pi$
$812$		0			0
$813$	−10.7874			−0.378331
$814$	72.2538	+	16.4915i	2.53249	+	0.578025i
$815$	19.2073	+	39.8844i	0.672803	+	1.39709i
$816$	−8.52870	−	4.10721i	−0.298564	−	0.143781i
$817$	−0.00281943	+	0.0123527i	−9.86392e−5	+	0.000432167i
$818$	10.2562	+	44.9351i	0.358598	+	1.57112i
$819$	2.69956	−	1.30004i	0.0943302	−	0.0454270i
$820$	−55.2330	−	44.0468i	−1.92882	−	1.53818i
$821$	1.42116	−	1.78208i	0.0495989	−	0.0621950i	−0.756413	−	0.654094i	$-0.773050\pi$
$821$	1.42116	−	1.78208i	0.0495989	−	0.0621950i	0.806012	+	0.591899i	$0.201622\pi$
$822$	−17.1626	+	35.6385i	−0.598614	+	1.24303i
$823$	−20.4148	+	16.2803i	−0.711616	+	0.567495i	−0.910990	−	0.412429i	$-0.864681\pi$
$823$	−20.4148	+	16.2803i	−0.711616	+	0.567495i	0.199374	+	0.979923i	$0.436109\pi$
$824$		−	25.7121i		−	0.895724i
$825$	−4.50230	−	5.64571i	−0.156750	−	0.196558i
$826$	−7.18648	+	1.64027i	−0.250050	+	0.0570722i
$827$	24.9617	−	5.69735i	0.868005	−	0.198116i	0.234746	−	0.972057i	$-0.424574\pi$
$827$	24.9617	−	5.69735i	0.868005	−	0.198116i	0.633259	+	0.773940i	$0.281717\pi$
$828$	−1.10451	−	1.38502i	−0.0383845	−	0.0481326i
$829$			43.4804i			1.51014i	0.655645	+	0.755069i	$0.272397\pi$
$829$			43.4804i			1.51014i	−0.655645	+	0.755069i	$0.727603\pi$
$830$	−3.05097	+	2.43307i	−0.105901	+	0.0844531i
$831$	18.2401	−	37.8760i	0.632743	−	1.31390i
$832$	−37.1637	+	46.6018i	−1.28842	+	1.61563i
$833$	9.79007	+	7.80732i	0.339206	+	0.270508i
$834$	−41.9223	+	20.1887i	−1.45165	+	0.699079i
$835$	1.36894	+	5.99772i	0.0473742	+	0.207560i
$836$	1.78077	−	7.80206i	0.0615892	−	0.269840i
$837$	−12.2018	−	5.87608i	−0.421756	−	0.203107i
$838$	−2.08256	−	4.32449i	−0.0719409	−	0.149387i
$839$	45.8155	+	10.4571i	1.58173	+	0.361019i	0.920986	−	0.389595i	$-0.127385\pi$
$839$	45.8155	+	10.4571i	1.58173	+	0.361019i	0.660741	+	0.750614i	$0.270242\pi$
$840$	−8.00771			−0.276292
$841$		0			0
$842$	95.4268			3.28863
$843$	24.0335	+	5.48548i	0.827756	+	0.188930i
$844$	38.1160	+	79.1487i	1.31201	+	2.72441i
$845$	−40.0010	−	19.2635i	−1.37608	−	0.662683i
$846$	5.75435	−	25.2115i	0.197839	−	0.866788i
$847$	−0.315594	−	1.38271i	−0.0108439	−	0.0475104i
$848$	−14.1628	+	6.82042i	−0.486351	+	0.234214i
$849$	48.6672	+	38.8108i	1.67025	+	1.33198i
$850$	2.43939	−	3.05890i	0.0836705	−	0.104920i
$851$	−1.17237	+	2.43445i	−0.0401883	+	0.0834520i
$852$	95.4118	−	76.0884i	3.26875	−	2.60674i
$853$			25.7853i			0.882872i	0.897293	+	0.441436i	$0.145531\pi$
$853$			25.7853i			0.882872i	−0.897293	+	0.441436i	$0.854469\pi$
$854$	5.85828	+	7.34605i	0.200466	+	0.251376i
$855$	1.87093	−	0.427028i	0.0639846	−	0.0146041i
$856$	−21.4402	+	4.89358i	−0.732810	+	0.167259i
$857$	−32.0355	−	40.1712i	−1.09431	−	1.37222i	−0.922005	−	0.387179i	$-0.873449\pi$
$857$	−32.0355	−	40.1712i	−1.09431	−	1.37222i	−0.172306	−	0.985043i	$-0.555122\pi$
$858$			108.075i			3.68962i
$859$	−14.2066	+	11.3293i	−0.484721	+	0.386552i	−0.835137	−	0.550042i	$-0.814612\pi$
$859$	−14.2066	+	11.3293i	−0.484721	+	0.386552i	0.350416	+	0.936594i	$0.386040\pi$
$860$	−0.0892360	+	0.185300i	−0.00304292	+	0.00631869i
$861$	3.86452	−	4.84595i	0.131702	−	0.165150i
$862$	26.7961	+	21.3692i	0.912679	+	0.727837i
$863$	−13.1896	+	6.35179i	−0.448980	+	0.216217i	−0.644689	−	0.764445i	$-0.723013\pi$
$863$	−13.1896	+	6.35179i	−0.448980	+	0.216217i	0.195710	+	0.980662i	$0.437299\pi$
$864$	−1.77069	−	7.75792i	−0.0602402	−	0.263930i
$865$	4.58399	−	20.0838i	0.155860	−	0.682869i
$866$	−19.0565	−	9.17711i	−0.647565	−	0.311851i
$867$	−12.4591	−	25.8715i	−0.423132	−	0.878642i
$868$	5.60122	+	1.27844i	0.190118	+	0.0433931i
$869$	−28.6539			−0.972017
$870$		0			0
$871$	−67.3198			−2.28105
$872$	−25.4753	−	5.81457i	−0.862703	−	0.196906i
$873$	−2.73671	−	5.68284i	−0.0926237	−	0.192335i
$874$	0.403732	+	0.194427i	0.0136564	+	0.00657659i
$875$	−0.839181	+	3.67669i	−0.0283695	+	0.124295i
$876$	−12.1031	−	53.0272i	−0.408926	−	1.79162i
$877$	−18.1825	+	8.75625i	−0.613981	+	0.295678i	−0.714910	−	0.699216i	$-0.753533\pi$
$877$	−18.1825	+	8.75625i	−0.613981	+	0.295678i	0.100930	+	0.994894i	$0.467818\pi$
$878$	21.6816	+	17.2905i	0.731719	+	0.583527i
$879$	10.3005	−	12.9164i	0.347426	−	0.435658i
$880$	9.97934	−	20.7223i	0.336403	−	0.698549i
$881$	13.7280	−	10.9477i	0.462509	−	0.368839i	−0.364337	−	0.931267i	$-0.618704\pi$
$881$	13.7280	−	10.9477i	0.462509	−	0.368839i	0.826846	+	0.562428i	$0.190133\pi$
$882$			23.2427i			0.782622i
$883$	5.29462	+	6.63925i	0.178178	+	0.223428i	0.862898	−	0.505378i	$-0.168647\pi$
$883$	5.29462	+	6.63925i	0.178178	+	0.223428i	−0.684720	+	0.728806i	$0.740075\pi$
$884$	−37.1708	+	8.48399i	−1.25019	+	0.285348i
$885$	40.4729	−	9.23768i	1.36048	−	0.310521i
$886$	52.9782	+	66.4326i	1.77984	+	2.23185i
$887$			9.27160i			0.311310i	0.987812	+	0.155655i	$0.0497488\pi$
$887$			9.27160i			0.311310i	−0.987812	+	0.155655i	$0.950251\pi$
$888$	−54.9305	+	43.8056i	−1.84335	+	1.47002i
$889$	0.957156	−	1.98755i	0.0321020	−	0.0666604i
$890$	−34.9363	+	43.8087i	−1.17107	+	1.46847i
$891$	−33.7570	−	26.9203i	−1.13090	−	0.901864i
$892$	−2.36052	+	1.13677i	−0.0790361	+	0.0380618i
$893$	0.947754	+	4.15238i	0.0317154	+	0.138954i
$894$	0.575762	−	2.52258i	0.0192564	−	0.0843676i
$895$	28.3343	+	13.6451i	0.947110	+	0.456104i
$896$	3.40384	+	7.06815i	0.113714	+	0.236130i
$897$	−3.84150	−	0.876798i	−0.128264	−	0.0292754i
$898$	49.6776			1.65776
$899$		0			0
$900$	4.72850			0.157617
$901$	11.3459	+	2.58962i	0.377986	+	0.0862727i
$902$	31.1004	+	64.5806i	1.03553	+	2.15030i
$903$	−0.0162576	−	0.00782926i	−0.000541020	−	0.000260542i
$904$	12.3782	−	54.2323i	0.411692	−	1.80374i
$905$	−8.86950	−	38.8598i	−0.294832	−	1.29174i
$906$	29.7017	−	14.3036i	0.986774	−	0.475205i
$907$	15.6254	+	12.4608i	0.518832	+	0.413754i	0.847584	−	0.530662i	$-0.178057\pi$
$907$	15.6254	+	12.4608i	0.518832	+	0.413754i	−0.328752	+	0.944416i	$0.606628\pi$
$908$	17.2270	−	21.6020i	0.571700	−	0.716889i
$909$	−3.70962	+	7.70310i	−0.123040	+	0.255496i
$910$	−9.61867	+	7.67063i	−0.318856	+	0.254279i
$911$		−	14.2969i		−	0.473676i	−0.971549	−	0.236838i	$-0.923889\pi$
$911$		−	14.2969i		−	0.473676i	0.971549	−	0.236838i	$-0.0761111\pi$
$912$	1.80433	+	2.26255i	0.0597472	+	0.0749207i
$913$	2.51340	−	0.573667i	0.0831814	−	0.0189856i
$914$	−88.9432	+	20.3007i	−2.94198	+	0.671488i
$915$	−32.9927	−	41.3715i	−1.09070	−	1.36770i
$916$			40.1086i			1.32523i
$917$	0.156255	−	0.124609i	0.00515998	−	0.00411495i
$918$	6.31567	−	13.1146i	0.208448	−	0.432847i
$919$	36.0978	−	45.2652i	1.19076	−	1.49316i	0.363265	−	0.931686i	$-0.381662\pi$
$919$	36.0978	−	45.2652i	1.19076	−	1.49316i	0.827492	−	0.561477i	$-0.189767\pi$
$920$	2.63968	+	2.10507i	0.0870276	+	0.0694022i
$921$	53.7331	−	25.8765i	1.77056	−	0.852659i
$922$	9.44311	+	41.3730i	0.310992	+	1.36255i
$923$	19.3656	−	84.8462i	0.637426	−	2.79275i
$924$	10.2684	+	4.94502i	0.337807	+	0.162679i
$925$	−3.12930	−	6.49805i	−0.102891	−	0.213655i
$926$	21.5197	+	4.91173i	0.707181	+	0.161409i
$927$	−8.77552			−0.288226
$928$		0			0
$929$	28.1340			0.923048			0.461524	−	0.887128i	$-0.347303\pi$
$929$	28.1340			0.923048			0.461524	+	0.887128i	$0.347303\pi$
$930$	−48.4477	−	11.0579i	−1.58866	−	0.362602i
$931$	−1.66096	−	3.44901i	−0.0544357	−	0.113037i
$932$	−52.4236	−	25.2459i	−1.71719	−	0.826957i
$933$	4.00816	−	17.5609i	0.131221	−	0.574917i
$934$	−4.15680	−	18.2121i	−0.136015	−	0.595919i
$935$	−15.3414	+	7.38803i	−0.501718	+	0.241615i
$936$	−25.6823	−	20.4810i	−0.839453	−	0.669441i
$937$	29.4214	−	36.8933i	0.961155	−	1.20525i	−0.0175226	−	0.999846i	$-0.505578\pi$
$937$	29.4214	−	36.8933i	0.961155	−	1.20525i	0.978677	−	0.205404i	$-0.0658507\pi$
$938$	−4.73074	+	9.82348i	−0.154464	+	0.320748i
$939$	−1.44413	+	1.15166i	−0.0471275	+	0.0375829i
$940$			69.1356i			2.25495i
$941$	13.8310	+	17.3436i	0.450878	+	0.565384i	0.954374	−	0.298614i	$-0.0965244\pi$
$941$	13.8310	+	17.3436i	0.450878	+	0.565384i	−0.503496	+	0.863998i	$0.667953\pi$
$942$	56.1925	−	12.8256i	1.83085	−	0.417880i
$943$	−2.54782	+	0.581522i	−0.0829683	+	0.0189370i
$944$	12.5143	+	15.6924i	0.407305	+	0.510744i
$945$		−	3.05827i		−	0.0994854i
$946$	0.163150	−	0.130108i	0.00530446	−	0.00423016i
$947$	−13.4797	+	27.9909i	−0.438031	+	0.909581i	0.558744	+	0.829340i	$0.311283\pi$
$947$	−13.4797	+	27.9909i	−0.438031	+	0.909581i	−0.996775	+	0.0802413i	$0.974431\pi$
$948$	36.4878	−	45.7542i	1.18507	−	1.48603i
$949$	−30.3257	−	24.1839i	−0.984413	−	0.785043i
$950$	−1.07764	+	0.518966i	−0.0349634	+	0.0168375i
$951$	12.4501	+	54.5475i	0.403723	+	1.76882i
$952$	−0.637809	+	2.79442i	−0.0206715	+	0.0905678i
$953$	−18.2506	−	8.78900i	−0.591193	−	0.284704i	0.114270	−	0.993450i	$-0.463547\pi$
$953$	−18.2506	−	8.78900i	−0.591193	−	0.284704i	−0.705464	+	0.708746i	$0.749261\pi$
$954$	9.37243	+	19.4621i	0.303444	+	0.630107i
$955$	−17.5668	−	4.00950i	−0.568447	−	0.129744i
$956$	−27.7850			−0.898630
$957$		0			0
$958$	42.4329			1.37094
$959$	2.90016	+	0.661943i	0.0936511	+	0.0213753i
$960$	−23.5897	−	48.9846i	−0.761355	−	1.58097i
$961$	−13.0196	−	6.26991i	−0.419987	−	0.202255i
$962$	−24.0195	+	105.236i	−0.774420	+	3.39296i
$963$	1.67017	+	7.31750i	0.0538206	+	0.235803i
$964$	17.7120	−	8.52963i	0.570464	−	0.274721i
$965$	−41.7033	−	33.2573i	−1.34248	−	1.07059i
$966$	−0.397897	+	0.498947i	−0.0128021	+	0.0160533i
$967$	11.3197	−	23.5056i	0.364016	−	0.755888i	−0.635857	−	0.771807i	$-0.719353\pi$
$967$	11.3197	−	23.5056i	0.364016	−	0.755888i	0.999873	+	0.0159190i	$0.00506740\pi$
$968$	−12.1565	+	9.69449i	−0.390725	+	0.311593i
$969$		−	2.14246i		−	0.0688258i
$970$	16.1474	+	20.2483i	0.518463	+	0.650132i
$971$	14.9769	−	3.41838i	0.480632	−	0.109701i	0.0246613	−	0.999696i	$-0.492149\pi$
$971$	14.9769	−	3.41838i	0.480632	−	0.109701i	0.455971	+	0.889995i	$0.349292\pi$
$972$	49.6290	−	11.3275i	1.59185	−	0.363330i
$973$	2.18175	+	2.73583i	0.0699438	+	0.0877068i
$974$		−	50.6603i		−	1.62326i
$975$	8.22287	−	6.55752i	0.263343	−	0.210009i
$976$	11.1006	−	23.0506i	0.355321	−	0.737832i
$977$	26.4633	−	33.1839i	0.846635	−	1.06165i	−0.150692	−	0.988581i	$-0.548150\pi$
$977$	26.4633	−	33.1839i	0.846635	−	1.06165i	0.997327	−	0.0730659i	$-0.0232784\pi$
$978$	71.7212	+	57.1957i	2.29339	+	1.82892i
$979$	33.3519	−	16.0614i	1.06593	−	0.513326i
$980$	−13.8272	−	60.5808i	−0.441692	−	1.93518i
$981$	−1.98451	+	8.69470i	−0.0633605	+	0.277600i
$982$	38.1955	+	18.3940i	1.21887	+	0.586975i
$983$	12.9898	+	26.9736i	0.414310	+	0.860323i	0.998803	+	0.0489240i	$0.0155792\pi$
$983$	12.9898	+	26.9736i	0.414310	+	0.860323i	−0.584493	+	0.811399i	$0.698706\pi$
$984$	−66.2486	−	15.1208i	−2.11193	−	0.482034i
$985$	47.8405			1.52432
$986$		0			0
$987$	−6.06572			−0.193074
$988$	11.3636	+	2.59366i	0.361523	+	0.0825153i
$989$	0.00330104	+	0.00685467i	0.000104967	+	0.000217966i
$990$	−28.4760	−	13.7133i	−0.905027	−	0.435838i
$991$	−11.2958	+	49.4902i	−0.358823	+	1.57211i	0.397306	+	0.917686i	$0.369945\pi$
$991$	−11.2958	+	49.4902i	−0.358823	+	1.57211i	−0.756130	+	0.654422i	$0.772912\pi$
$992$	2.16376	+	9.48007i	0.0686996	+	0.300992i
$993$	−35.3070	+	17.0029i	−1.12043	+	0.539572i
$994$	−11.0201	−	8.78824i	−0.349536	−	0.278746i
$995$	−24.5812	+	30.8239i	−0.779277	+	0.977182i
$996$	−2.28453	+	4.74387i	−0.0723881	+	0.150315i
$997$	6.42116	−	5.12070i	0.203360	−	0.162174i	−0.516514	−	0.856278i	$-0.672771\pi$
$997$	6.42116	−	5.12070i	0.203360	−	0.162174i	0.719875	+	0.694104i	$0.244199\pi$
$998$		−	69.9250i		−	2.21344i
$999$	−16.7300	−	20.9788i	−0.529314	−	0.663739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.m.236.2		96
29.2	odd	28		841.2.d.p.190.2		48
29.3	odd	28		841.2.d.p.645.2		48
29.4	even	14	inner	841.2.e.m.267.2		96
29.5	even	14	inner	841.2.e.m.651.2		96
29.6	even	14		841.2.b.f.840.2		16
29.7	even	7	inner	841.2.e.m.196.15		96
29.8	odd	28		841.2.d.q.778.2		48
29.9	even	14	inner	841.2.e.m.63.15		96
29.10	odd	28		841.2.d.q.574.2		48
29.11	odd	28		841.2.d.p.571.2		48
29.12	odd	4		841.2.d.q.605.7		48
29.13	even	14	inner	841.2.e.m.270.15		96
29.14	odd	28		841.2.a.j.1.7	yes	8
29.15	odd	28		841.2.a.i.1.2	✓	8
29.16	even	7	inner	841.2.e.m.270.2		96
29.17	odd	4		841.2.d.p.605.2		48
29.18	odd	28		841.2.d.q.571.7		48
29.19	odd	28		841.2.d.p.574.7		48
29.20	even	7	inner	841.2.e.m.63.2		96
29.21	odd	28		841.2.d.p.778.7		48
29.22	even	14	inner	841.2.e.m.196.2		96
29.23	even	7		841.2.b.f.840.15		16
29.24	even	7	inner	841.2.e.m.651.15		96
29.25	even	7	inner	841.2.e.m.267.15		96
29.26	odd	28		841.2.d.q.645.7		48
29.27	odd	28		841.2.d.q.190.7		48
29.28	even	2	inner	841.2.e.m.236.15		96
87.14	even	28		7569.2.a.bd.1.2		8
87.44	even	28		7569.2.a.bi.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.i.1.2	✓	8	29.15	odd	28
841.2.a.j.1.7	yes	8	29.14	odd	28
841.2.b.f.840.2		16	29.6	even	14
841.2.b.f.840.15		16	29.23	even	7
841.2.d.p.190.2		48	29.2	odd	28
841.2.d.p.571.2		48	29.11	odd	28
841.2.d.p.574.7		48	29.19	odd	28
841.2.d.p.605.2		48	29.17	odd	4
841.2.d.p.645.2		48	29.3	odd	28
841.2.d.p.778.7		48	29.21	odd	28
841.2.d.q.190.7		48	29.27	odd	28
841.2.d.q.571.7		48	29.18	odd	28
841.2.d.q.574.2		48	29.10	odd	28
841.2.d.q.605.7		48	29.12	odd	4
841.2.d.q.645.7		48	29.26	odd	28
841.2.d.q.778.2		48	29.8	odd	28
841.2.e.m.63.2		96	29.20	even	7	inner
841.2.e.m.63.15		96	29.9	even	14	inner
841.2.e.m.196.2		96	29.22	even	14	inner
841.2.e.m.196.15		96	29.7	even	7	inner
841.2.e.m.236.2		96	1.1	even	1	trivial
841.2.e.m.236.15		96	29.28	even	2	inner
841.2.e.m.267.2		96	29.4	even	14	inner
841.2.e.m.267.15		96	29.25	even	7	inner
841.2.e.m.270.2		96	29.16	even	7	inner
841.2.e.m.270.15		96	29.13	even	14	inner
841.2.e.m.651.2		96	29.5	even	14	inner
841.2.e.m.651.15		96	29.24	even	7	inner
7569.2.a.bd.1.2		8	87.14	even	28
7569.2.a.bi.1.7		8	87.44	even	28

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.33424 - 0.532775i) q^{2} +(-0.911751 - 1.89327i) q^{3} +(3.36289 + 1.61948i) q^{4} +(-0.540264 + 2.36705i) q^{5} +(1.11956 + 4.90511i) q^{6} +(0.340899 - 0.164169i) q^{7} +(-3.24315 - 2.58633i) q^{8} +(-0.882711 + 1.10689i) q^{9} +(2.52221 - 5.23743i) q^{10} +(-3.00251 + 2.39442i) q^{11} -7.84343i q^{12} +(-3.48744 - 4.37311i) q^{13} +(-0.883206 + 0.201586i) q^{14} +(4.97405 - 1.13529i) q^{15} +(1.53798 + 1.92857i) q^{16} -1.82620i q^{17} +(2.65018 - 2.11345i) q^{18} +(-0.242234 + 0.503004i) q^{19} +(-5.65025 + 7.08519i) q^{20} +(-0.621631 - 0.495734i) q^{21} +(8.28428 - 3.98950i) q^{22} +(0.0745967 + 0.326829i) q^{23} +(-1.93967 + 8.49825i) q^{24} +(-0.806195 - 0.388243i) q^{25} +(5.81064 + 12.0659i) q^{26} +(-3.24561 - 0.740789i) q^{27} +1.41228 q^{28} -12.2155 q^{30} +(3.96609 + 0.905234i) q^{31} +(1.03710 + 2.15357i) q^{32} +(7.27084 + 3.50145i) q^{33} +(-0.972955 + 4.26280i) q^{34} +(0.204419 + 0.895620i) q^{35} +(-4.76105 + 2.29280i) q^{36} +(6.30168 + 5.02542i) q^{37} +(0.833420 - 1.04508i) q^{38} +(-5.09980 + 10.5898i) q^{39} +(7.87413 - 6.27941i) q^{40} +7.79555i q^{41} +(1.18692 + 1.48835i) q^{42} +(0.0221259 - 0.00505009i) q^{43} +(-13.9749 + 3.18967i) q^{44} +(-2.14316 - 2.68743i) q^{45} -0.802642i q^{46} +(5.96453 - 4.75655i) q^{47} +(2.24904 - 4.67019i) q^{48} +(-4.27517 + 5.36089i) q^{49} +(1.67501 + 1.33577i) q^{50} +(-3.45749 + 1.66504i) q^{51} +(-4.64570 - 20.3542i) q^{52} +(-1.41804 + 6.21282i) q^{53} +(7.18136 + 3.45836i) q^{54} +(-4.04557 - 8.40072i) q^{55} +(-1.53018 - 0.349254i) q^{56} +1.17318 q^{57} +8.13681 q^{59} +(18.5658 + 4.23752i) q^{60} +(-4.50012 - 9.34460i) q^{61} +(-8.77553 - 4.22607i) q^{62} +(-0.119200 + 0.522250i) q^{63} +(-2.37128 - 10.3893i) q^{64} +(12.2355 - 5.89231i) q^{65} +(-15.1064 - 12.0470i) q^{66} +(7.50404 - 9.40977i) q^{67} +(2.95751 - 6.14133i) q^{68} +(0.550763 - 0.439219i) q^{69} -2.19950i q^{70} +(9.70090 + 12.1645i) q^{71} +(5.72554 - 1.30682i) q^{72} +(6.76071 - 1.54309i) q^{73} +(-12.0322 - 15.0879i) q^{74} +1.88033i q^{75} +(-1.62921 + 1.29925i) q^{76} +(-0.630466 + 1.30918i) q^{77} +(17.5462 - 22.0022i) q^{78} +(5.83344 + 4.65202i) q^{79} +(-5.39593 + 2.59854i) q^{80} +(2.50178 + 10.9610i) q^{81} +(4.15328 - 18.1967i) q^{82} +(-0.604821 - 0.291266i) q^{83} +(-1.28764 - 2.67382i) q^{84} +(4.32271 + 0.986631i) q^{85} -0.0543377 q^{86} +15.9304 q^{88} +(-9.39749 - 2.14492i) q^{89} +(3.57084 + 7.41493i) q^{90} +(-1.90679 - 0.918263i) q^{91} +(-0.278434 + 1.21990i) q^{92} +(-1.90223 - 8.33423i) q^{93} +(-16.4568 + 7.92519i) q^{94} +(-1.05976 - 0.845134i) q^{95} +(3.13171 - 3.92703i) q^{96} +(-1.93304 + 4.01399i) q^{97} +(12.8354 - 10.2359i) q^{98} -5.43702i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} - 2 q^{5} + 6 q^{6} + 16 q^{9} - 8 q^{13} + 4 q^{16} + 14 q^{20} + 50 q^{22} + 14 q^{23} - 50 q^{24} + 26 q^{25} - 300 q^{28} - 312 q^{30} + 24 q^{34} - 10 q^{35} + 38 q^{36} - 28 q^{38}+ \cdots - 4 q^{96}+O(q^{100}) \) 96 * q + 12 * q^4 - 2 * q^5 + 6 * q^6 + 16 * q^9 - 8 * q^13 + 4 * q^16 + 14 * q^20 + 50 * q^22 + 14 * q^23 - 50 * q^24 + 26 * q^25 - 300 * q^28 - 312 * q^30 + 24 * q^34 - 10 * q^35 + 38 * q^36 - 28 * q^38 + 30 * q^42 + 2 * q^45 - 8 * q^49 + 46 * q^51 - 4 * q^52 - 38 * q^53 + 92 * q^54 + 72 * q^57 - 12 * q^59 - 24 * q^62 - 20 * q^63 + 2 * q^64 + 34 * q^65 + 4 * q^67 - 24 * q^71 + 54 * q^74 - 12 * q^78 - 82 * q^80 - 24 * q^81 + 44 * q^82 + 6 * q^83 + 60 * q^86 - 180 * q^88 - 8 * q^92 + 4 * q^93 - 26 * q^94 - 4 * q^96

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