LMFDB - Embedded newform 847.2.n.g.632.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(9,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 18]))

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

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

chi := DirichletCharacter("847.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			632.3
Character	$\chi$	$=$	847.632
Dual form			847.2.n.g.130.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.49861 + 0.318539i) q^{2} +(-0.300978 + 2.86361i) q^{3} +(0.317271 + 0.141258i) q^{4} +(1.57065 + 1.74438i) q^{5} +(-1.36322 + 4.19556i) q^{6} +(-0.680015 + 2.55687i) q^{7} +(-2.04850 - 1.48832i) q^{8} +(-5.17524 - 1.10003i) q^{9} +(1.79813 + 3.11446i) q^{10} +(-0.500000 + 0.866025i) q^{12} +(-0.0571040 - 0.175748i) q^{13} +(-1.83354 + 3.61514i) q^{14} +(-5.46796 + 3.97271i) q^{15} +(-3.06059 - 3.39913i) q^{16} +(3.83559 - 0.815279i) q^{17} +(-7.40526 - 3.29703i) q^{18} +(0.706462 - 0.314537i) q^{19} +(0.251913 + 0.775308i) q^{20} +(-7.11721 - 2.71686i) q^{21} +(-4.17752 + 7.23567i) q^{23} +(4.87854 - 5.41816i) q^{24} +(-0.0532886 + 0.507007i) q^{25} +(-0.0295940 - 0.281568i) q^{26} +(2.03836 - 6.27342i) q^{27} +(-0.576928 + 0.715163i) q^{28} +(6.60987 - 4.80235i) q^{29} +(-9.45980 + 4.21177i) q^{30} +(1.77501 - 1.97134i) q^{31} +(-0.971782 - 1.68317i) q^{32} +6.00774 q^{34} +(-5.52822 + 2.82974i) q^{35} +(-1.48657 - 1.08005i) q^{36} +(0.713192 + 6.78557i) q^{37} +(1.15890 - 0.246332i) q^{38} +(0.520461 - 0.110628i) q^{39} +(-0.621272 - 5.91100i) q^{40} +(-0.344659 - 0.250409i) q^{41} +(-9.80049 - 6.33862i) q^{42} +1.18479 q^{43} +(-6.20961 - 10.7554i) q^{45} +(-8.56531 + 9.51274i) q^{46} +(-7.01607 + 3.12376i) q^{47} +(10.6550 - 7.74128i) q^{48} +(-6.07516 - 3.47742i) q^{49} +(-0.241361 + 0.742831i) q^{50} +(1.18022 + 11.2290i) q^{51} +(0.00670840 - 0.0638262i) q^{52} +(4.38573 - 4.87085i) q^{53} +(5.05303 - 8.75211i) q^{54} +(5.19846 - 4.22567i) q^{56} +(0.688082 + 2.11770i) q^{57} +(11.4353 - 5.09134i) q^{58} +(0.186722 + 0.0831341i) q^{59} +(-2.29600 + 0.488030i) q^{60} +(9.75707 + 10.8363i) q^{61} +(3.28799 - 2.38886i) q^{62} +(6.33188 - 12.4844i) q^{63} +(1.90671 + 5.86825i) q^{64} +(0.216881 - 0.375650i) q^{65} +(-1.87939 - 3.25519i) q^{67} +(1.33208 + 0.283143i) q^{68} +(-19.4628 - 14.1406i) q^{69} +(-9.18602 + 2.47971i) q^{70} +(-3.07962 + 9.47809i) q^{71} +(8.96429 + 9.95586i) q^{72} +(0.110187 + 0.0490584i) q^{73} +(-1.09267 + 10.3961i) q^{74} +(-1.43583 - 0.305196i) q^{75} +0.268571 q^{76} +0.815207 q^{78} +(-0.320535 - 0.0681318i) q^{79} +(1.12227 - 10.6777i) q^{80} +(2.85082 + 1.26927i) q^{81} +(-0.436744 - 0.485053i) q^{82} +(1.03676 - 3.19083i) q^{83} +(-1.87431 - 1.86734i) q^{84} +(7.44651 + 5.41021i) q^{85} +(1.77554 + 0.377403i) q^{86} +(11.7626 + 20.3735i) q^{87} +(2.32635 - 4.02936i) q^{89} +(-5.87977 - 18.0961i) q^{90} +(0.488197 - 0.0264962i) q^{91} +(-2.34750 + 1.70556i) q^{92} +(5.11092 + 5.67626i) q^{93} +(-11.5094 + 2.44640i) q^{94} +(1.65827 + 0.738311i) q^{95} +(5.11244 - 2.27621i) q^{96} +(4.05449 + 12.4784i) q^{97} +(-7.99660 - 7.14647i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} + 6 q^{5} + 6 q^{6} - 6 q^{8} - 12 q^{10} - 12 q^{12} - 6 q^{13} + 12 q^{14} - 18 q^{15} - 6 q^{16} - 3 q^{17} - 12 q^{18} + 9 q^{19} - 12 q^{20} - 48 q^{21} + 6 q^{24} + 3 q^{25} + 9 q^{26}+ \cdots - 24 q^{98}+O(q^{100}) $ 24 * q + 3 * q^3 + 6 * q^5 + 6 * q^6 - 6 * q^8 - 12 * q^10 - 12 * q^12 - 6 * q^13 + 12 * q^14 - 18 * q^15 - 6 * q^16 - 3 * q^17 - 12 * q^18 + 9 * q^19 - 12 * q^20 - 48 * q^21 + 6 * q^24 + 3 * q^25 + 9 * q^26 - 12 * q^27 - 3 * q^28 + 6 * q^29 - 6 * q^30 + 9 * q^31 + 36 * q^32 - 48 * q^34 + 15 * q^35 - 6 * q^36 + 3 * q^39 + 3 * q^40 - 18 * q^41 + 18 * q^42 - 12 * q^45 - 24 * q^46 - 3 * q^47 + 36 * q^48 - 30 * q^50 - 18 * q^51 + 9 * q^52 + 9 * q^53 + 72 * q^54 + 12 * q^56 + 15 * q^58 + 6 * q^60 + 12 * q^61 + 6 * q^62 - 6 * q^63 + 6 * q^64 - 60 * q^65 - 21 * q^68 - 42 * q^69 - 45 * q^70 + 18 * q^71 + 12 * q^72 + 6 * q^73 + 18 * q^74 + 9 * q^75 - 72 * q^76 + 48 * q^78 - 3 * q^79 - 27 * q^80 + 15 * q^81 - 3 * q^82 + 30 * q^83 + 54 * q^85 - 9 * q^86 + 96 * q^87 + 60 * q^89 + 72 * q^90 - 9 * q^91 + 6 * q^92 + 6 * q^93 + 9 * q^95 + 3 * q^96 - 90 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	1.49861	+	0.318539i	1.05968	+	0.225241i	0.704606	−	0.709598i	$-0.251124\pi$
$2$	1.49861	+	0.318539i	1.05968	+	0.225241i	0.355070	+	0.934840i	$0.384457\pi$
$3$	−0.300978	+	2.86361i	−0.173770	+	1.65331i	0.466033	+	0.884767i	$0.345683\pi$
$3$	−0.300978	+	2.86361i	−0.173770	+	1.65331i	−0.639802	+	0.768540i	$0.720984\pi$
$4$	0.317271	+	0.141258i	0.158636	+	0.0706291i
$5$	1.57065	+	1.74438i	0.702415	+	0.780111i	0.983759	−	0.179496i	$-0.0574467\pi$
$5$	1.57065	+	1.74438i	0.702415	+	0.780111i	−0.281344	+	0.959607i	$0.590780\pi$
$6$	−1.36322	+	4.19556i	−0.556532	+	1.71283i
$7$	−0.680015	+	2.55687i	−0.257021	+	0.966406i
$7$	−0.680015	+	2.55687i	−0.257021	+	0.966406i
$8$	−2.04850	−	1.48832i	−0.724255	−	0.526202i
$9$	−5.17524	−	1.10003i	−1.72508	−	0.366677i
$10$	1.79813	+	3.11446i	0.568620	+	0.984878i
$11$		0			0
$11$		0			0
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.0571040	−	0.175748i	−0.0158378	−	0.0487438i	0.942825	−	0.333287i	$-0.108158\pi$
$13$	−0.0571040	−	0.175748i	−0.0158378	−	0.0487438i	−0.958663	+	0.284544i	$0.908158\pi$
$14$	−1.83354	+	3.61514i	−0.490034	+	0.966186i
$15$	−5.46796	+	3.97271i	−1.41182	+	1.02575i
$16$	−3.06059	−	3.39913i	−0.765147	−	0.849782i
$17$	3.83559	−	0.815279i	0.930266	−	0.197734i	0.282233	−	0.959346i	$-0.408925\pi$
$17$	3.83559	−	0.815279i	0.930266	−	0.197734i	0.648033	+	0.761612i	$0.275592\pi$
$18$	−7.40526	−	3.29703i	−1.74544	−	0.777118i
$19$	0.706462	−	0.314537i	0.162073	−	0.0721597i	−0.324097	−	0.946024i	$-0.605060\pi$
$19$	0.706462	−	0.314537i	0.162073	−	0.0721597i	0.486170	+	0.873864i	$0.338394\pi$
$20$	0.251913	+	0.775308i	0.0563295	+	0.173364i
$21$	−7.11721	−	2.71686i	−1.55310	−	0.592867i
$22$		0			0
$23$	−4.17752	+	7.23567i	−0.871073	+	1.50874i	−0.0101847	+	0.999948i	$0.503242\pi$
$23$	−4.17752	+	7.23567i	−0.871073	+	1.50874i	−0.860888	+	0.508794i	$0.830091\pi$
$24$	4.87854	−	5.41816i	0.995827	−	1.10598i
$25$	−0.0532886	+	0.507007i	−0.0106577	+	0.101401i
$26$	−0.0295940	−	0.281568i	−0.00580385	−	0.0552200i
$27$	2.03836	−	6.27342i	0.392282	−	1.20732i
$28$	−0.576928	+	0.715163i	−0.109029	+	0.135153i
$29$	6.60987	−	4.80235i	1.22742	−	0.891774i	0.230727	−	0.973018i	$-0.425889\pi$
$29$	6.60987	−	4.80235i	1.22742	−	0.891774i	0.996694	+	0.0812446i	$0.0258895\pi$
$30$	−9.45980	+	4.21177i	−1.72711	+	0.768961i
$31$	1.77501	−	1.97134i	0.318800	−	0.354064i	−0.562350	−	0.826899i	$-0.690103\pi$
$31$	1.77501	−	1.97134i	0.318800	−	0.354064i	0.881151	+	0.472835i	$0.156769\pi$
$32$	−0.971782	−	1.68317i	−0.171788	−	0.297546i
$33$		0			0
$34$	6.00774			1.03032
$35$	−5.52822	+	2.82974i	−0.934439	+	0.478313i
$36$	−1.48657	−	1.08005i	−0.247761	−	0.180009i
$37$	0.713192	+	6.78557i	0.117248	+	1.11554i	0.882011	+	0.471229i	$0.156189\pi$
$37$	0.713192	+	6.78557i	0.117248	+	1.11554i	−0.764763	+	0.644312i	$0.777144\pi$
$38$	1.15890	−	0.246332i	0.187999	−	0.0399604i
$39$	0.520461	−	0.110628i	0.0833405	−	0.0177146i
$40$	−0.621272	−	5.91100i	−0.0982317	−	0.934612i
$41$	−0.344659	−	0.250409i	−0.0538267	−	0.0391074i	0.560547	−	0.828123i	$-0.310591\pi$
$41$	−0.344659	−	0.250409i	−0.0538267	−	0.0391074i	−0.614373	+	0.789016i	$0.710591\pi$
$42$	−9.80049	−	6.33862i	−1.51225	−	0.978070i
$43$	1.18479			0.180679			0.0903396	−	0.995911i	$-0.471205\pi$
$43$	1.18479			0.180679			0.0903396	+	0.995911i	$0.471205\pi$
$44$		0			0
$45$	−6.20961	−	10.7554i	−0.925674	−	1.60331i
$46$	−8.56531	+	9.51274i	−1.26289	+	1.40258i
$47$	−7.01607	+	3.12376i	−1.02340	+	0.455647i	−0.848643	−	0.528965i	$-0.822580\pi$
$47$	−7.01607	+	3.12376i	−1.02340	+	0.455647i	−0.174756	+	0.984612i	$0.555914\pi$
$48$	10.6550	−	7.74128i	1.53791	−	1.11736i
$49$	−6.07516	−	3.47742i	−0.867880	−	0.496774i
$50$	−0.241361	+	0.742831i	−0.0341335	+	0.105052i
$51$	1.18022	+	11.2290i	0.165263	+	1.57238i
$52$	0.00670840	−	0.0638262i	0.000930288	−	0.00885110i
$53$	4.38573	−	4.87085i	0.602427	−	0.669063i	−0.362377	−	0.932031i	$-0.618035\pi$
$53$	4.38573	−	4.87085i	0.602427	−	0.669063i	0.964804	+	0.262968i	$0.0847015\pi$
$54$	5.05303	−	8.75211i	0.687631	−	1.19101i
$55$		0			0
$56$	5.19846	−	4.22567i	0.694674	−	0.564679i
$57$	0.688082	+	2.11770i	0.0911387	+	0.280496i
$58$	11.4353	−	5.09134i	1.50153	−	0.668526i
$59$	0.186722	+	0.0831341i	0.0243092	+	0.0108231i	0.418855	−	0.908053i	$-0.362431\pi$
$59$	0.186722	+	0.0831341i	0.0243092	+	0.0108231i	−0.394546	+	0.918876i	$0.629098\pi$
$60$	−2.29600	+	0.488030i	−0.296413	+	0.0630044i
$61$	9.75707	+	10.8363i	1.24927	+	1.38745i	0.891110	+	0.453788i	$0.149928\pi$
$61$	9.75707	+	10.8363i	1.24927	+	1.38745i	0.358156	+	0.933662i	$0.383406\pi$
$62$	3.28799	−	2.38886i	0.417575	−	0.303386i
$63$	6.33188	−	12.4844i	0.797741	−	1.57288i
$64$	1.90671	+	5.86825i	0.238339	+	0.733531i
$65$	0.216881	−	0.375650i	0.0269008	−	0.0465936i
$66$		0			0
$67$	−1.87939	−	3.25519i	−0.229603	−	0.397685i	0.728087	−	0.685485i	$-0.240410\pi$
$67$	−1.87939	−	3.25519i	−0.229603	−	0.397685i	−0.957691	+	0.287800i	$0.907076\pi$
$68$	1.33208	+	0.283143i	0.161539	+	0.0343362i
$69$	−19.4628	−	14.1406i	−2.34305	−	1.70232i
$70$	−9.18602	+	2.47971i	−1.09794	+	0.296383i
$71$	−3.07962	+	9.47809i	−0.365483	+	1.12484i	0.584194	+	0.811614i	$0.301411\pi$
$71$	−3.07962	+	9.47809i	−0.365483	+	1.12484i	−0.949678	+	0.313228i	$0.898589\pi$
$72$	8.96429	+	9.95586i	1.05645	+	1.17331i
$73$	0.110187	+	0.0490584i	0.0128964	+	0.00574186i	0.413175	−	0.910652i	$-0.364420\pi$
$73$	0.110187	+	0.0490584i	0.0128964	+	0.00574186i	−0.400278	+	0.916394i	$0.631087\pi$
$74$	−1.09267	+	10.3961i	−0.127021	+	1.20852i
$75$	−1.43583	−	0.305196i	−0.165796	−	0.0352410i
$76$	0.268571			0.0308072
$77$		0			0
$78$	0.815207			0.0923041
$79$	−0.320535	−	0.0681318i	−0.0360630	−	0.00766543i	0.189845	−	0.981814i	$-0.439201\pi$
$79$	−0.320535	−	0.0681318i	−0.0360630	−	0.00766543i	−0.225908	+	0.974149i	$0.572535\pi$
$80$	1.12227	−	10.6777i	0.125473	−	1.19380i
$81$	2.85082	+	1.26927i	0.316758	+	0.141030i
$82$	−0.436744	−	0.485053i	−0.0482303	−	0.0535652i
$83$	1.03676	−	3.19083i	0.113800	−	0.350239i	−0.877895	−	0.478853i	$-0.841053\pi$
$83$	1.03676	−	3.19083i	0.113800	−	0.350239i	0.991695	+	0.128614i	$0.0410527\pi$
$84$	−1.87431	−	1.86734i	−0.204504	−	0.203744i
$85$	7.44651	+	5.41021i	0.807687	+	0.586819i
$86$	1.77554	+	0.377403i	0.191461	+	0.0406964i
$87$	11.7626	+	20.3735i	1.26109	+	2.18427i
$88$		0			0
$89$	2.32635	−	4.02936i	0.246593	−	0.427111i	−0.715985	−	0.698115i	$-0.754022\pi$
$89$	2.32635	−	4.02936i	0.246593	−	0.427111i	0.962578	+	0.271004i	$0.0873557\pi$
$90$	−5.87977	−	18.0961i	−0.619782	−	1.90749i
$91$	0.488197	−	0.0264962i	0.0511769	−	0.00277756i
$92$	−2.34750	+	1.70556i	−0.244744	+	0.177817i
$93$	5.11092	+	5.67626i	0.529978	+	0.588600i
$94$	−11.5094	+	2.44640i	−1.18710	+	0.252326i
$95$	1.65827	+	0.738311i	0.170135	+	0.0757492i
$96$	5.11244	−	2.27621i	0.521787	−	0.232314i
$97$	4.05449	+	12.4784i	0.411671	+	1.26699i	0.915194	+	0.403012i	$0.132037\pi$
$97$	4.05449	+	12.4784i	0.411671	+	1.26699i	−0.503523	+	0.863982i	$0.667963\pi$
$98$	−7.99660	−	7.14647i	−0.807778	−	0.721902i
$99$		0			0
$100$	−0.0885259	+	0.153331i	−0.00885259	+	0.0153331i
$101$	−3.94899	+	4.38580i	−0.392939	+	0.436403i	−0.906858	−	0.421435i	$-0.861526\pi$
$101$	−3.94899	+	4.38580i	−0.392939	+	0.436403i	0.513919	+	0.857839i	$0.328193\pi$
$102$	−1.80820	+	17.2038i	−0.179038	+	1.70343i
$103$	−0.0962994	−	0.916227i	−0.00948866	−	0.0902786i	0.988753	−	0.149560i	$-0.0477857\pi$
$103$	−0.0962994	−	0.916227i	−0.00948866	−	0.0902786i	−0.998241	+	0.0592815i	$0.981119\pi$
$104$	−0.144592	+	0.445010i	−0.0141785	+	0.0436368i
$105$	−6.43940	−	16.6824i	−0.628421	−	1.62803i
$106$	8.12406	−	5.90247i	0.789078	−	0.573299i
$107$	−9.45273	+	4.20862i	−0.913829	+	0.406863i	−0.809122	−	0.587640i	$-0.800057\pi$
$107$	−9.45273	+	4.20862i	−0.913829	+	0.406863i	−0.104707	+	0.994503i	$0.533390\pi$
$108$	1.53288	−	1.70244i	0.147502	−	0.163817i
$109$	−0.237826	−	0.411927i	−0.0227796	−	0.0394554i	0.854411	−	0.519598i	$-0.173918\pi$
$109$	−0.237826	−	0.411927i	−0.0227796	−	0.0394554i	−0.877190	+	0.480143i	$0.840585\pi$
$110$		0			0
$111$	−19.6459			−1.86471
$112$	10.7724	−	5.51407i	1.01789	−	0.521030i
$113$	2.54266	+	1.84735i	0.239194	+	0.173784i	0.700924	−	0.713236i	$-0.252771\pi$
$113$	2.54266	+	1.84735i	0.239194	+	0.173784i	−0.461730	+	0.887020i	$0.652771\pi$
$114$	0.356596	+	3.39279i	0.0333983	+	0.317763i
$115$	−19.1832	+	4.07751i	−1.78884	+	0.380230i
$116$	2.77549	−	0.589949i	0.257698	−	0.0547754i
$117$	0.102199	+	0.972355i	0.00944827	+	0.0898943i
$118$	0.253342	+	0.184064i	0.0233220	+	0.0169444i
$119$	−0.523693	+	10.3615i	−0.0480068	+	0.949836i
$120$	17.1138			1.56227
$121$		0			0
$122$	11.1702	+	19.3474i	1.01131	+	1.75163i
$123$	0.820810	−	0.911602i	0.0740100	−	0.0821964i
$124$	0.841626	−	0.374716i	0.0755802	−	0.0336505i
$125$	8.52690	−	6.19516i	0.762669	−	0.554112i
$126$	13.4658	−	16.6923i	1.19963	−	1.48706i
$127$	−0.137705	+	0.423812i	−0.0122193	+	0.0376072i	−0.956980	−	0.290153i	$-0.906294\pi$
$127$	−0.137705	+	0.423812i	−0.0122193	+	0.0376072i	0.944761	+	0.327760i	$0.106294\pi$
$128$	1.39446	+	13.2674i	0.123254	+	1.17268i
$129$	−0.356596	+	3.39279i	−0.0313965	+	0.298718i
$130$	0.444680	−	0.493867i	0.0390010	−	0.0433150i
$131$	6.04323	−	10.4672i	0.528000	−	0.914522i	−0.471467	−	0.881883i	$-0.656276\pi$
$131$	6.04323	−	10.4672i	0.528000	−	0.914522i	0.999467	−	0.0326389i	$-0.0103911\pi$
$132$		0			0
$133$	0.323826	+	2.02022i	0.0280792	+	0.175175i
$134$	−1.77956	−	5.47692i	−0.153730	−	0.473133i
$135$	14.1448	−	6.29766i	1.21739	−	0.542017i
$136$	−9.07061	−	4.03849i	−0.777798	−	0.346298i
$137$	15.9910	−	3.39899i	1.36620	−	0.290395i	0.534289	−	0.845302i	$-0.320579\pi$
$137$	15.9910	−	3.39899i	1.36620	−	0.290395i	0.831913	+	0.554907i	$0.187246\pi$
$138$	−24.6628	−	27.3909i	−2.09944	−	2.33166i
$139$	16.7707	−	12.1846i	1.42247	−	1.03348i	0.431111	−	0.902299i	$-0.358122\pi$
$139$	16.7707	−	12.1846i	1.42247	−	1.03348i	0.991358	−	0.131185i	$-0.0418782\pi$
$140$	−2.15367	+	0.116887i	−0.182018	+	0.00987879i
$141$	−6.83354	−	21.0315i	−0.575488	−	1.77117i
$142$	−7.63429	+	13.2230i	−0.640655	+	1.10965i
$143$		0			0
$144$	12.1001	+	20.9581i	1.00834	+	1.74650i
$145$	18.7589	+	3.98733i	1.55784	+	0.331130i
$146$	0.149500	+	0.108618i	0.0123727	+	0.00898932i
$147$	11.7865	−	16.3503i	0.972131	−	1.34855i
$148$	−0.732242	+	2.25361i	−0.0601899	+	0.185246i
$149$	−0.477888	−	0.530749i	−0.0391501	−	0.0434806i	0.723252	−	0.690585i	$-0.242647\pi$
$149$	−0.477888	−	0.530749i	−0.0391501	−	0.0434806i	−0.762402	+	0.647104i	$0.775980\pi$
$150$	−2.05454	−	0.914739i	−0.167752	−	0.0746881i
$151$	0.997712	−	9.49259i	0.0811926	−	0.772496i	−0.875857	−	0.482571i	$-0.839703\pi$
$151$	0.997712	−	9.49259i	0.0811926	−	0.772496i	0.957049	−	0.289925i	$-0.0936304\pi$
$152$	−1.91532	−	0.407114i	−0.155353	−	0.0330213i
$153$	−20.7469			−1.67729
$154$		0			0
$155$	6.22668			0.500139
$156$	0.180754	+	0.0384205i	0.0144719	+	0.00307610i
$157$	−0.965972	+	9.19061i	−0.0770929	+	0.733490i	0.885884	+	0.463907i	$0.153553\pi$
$157$	−0.965972	+	9.19061i	−0.0770929	+	0.733490i	−0.962977	+	0.269584i	$0.913114\pi$
$158$	−0.458654	−	0.204206i	−0.0364886	−	0.0162458i
$159$	12.6282	+	14.0251i	1.00148	+	1.11226i
$160$	1.40977	−	4.33883i	0.111452	−	0.343015i
$161$	−15.6599	−	15.6017i	−1.23417	−	1.22959i
$162$	3.86796	+	2.81024i	0.303895	+	0.220793i
$163$	8.61097	+	1.83032i	0.674464	+	0.143362i	0.532396	−	0.846495i	$-0.321292\pi$
$163$	8.61097	+	1.83032i	0.674464	+	0.143362i	0.142067	+	0.989857i	$0.454625\pi$
$164$	−0.0739780	−	0.128134i	−0.00577671	−	0.0100056i
$165$		0			0
$166$	2.57011	−	4.45156i	0.199479	−	0.345508i
$167$	2.59030	+	7.97212i	0.200443	+	0.616901i	0.999870	+	0.0161370i	$0.00513679\pi$
$167$	2.59030	+	7.97212i	0.200443	+	0.616901i	−0.799427	+	0.600764i	$0.794863\pi$
$168$	10.5361	+	16.1582i	0.812875	+	1.24663i
$169$	10.4896	−	7.62114i	0.806892	−	0.586241i
$170$	9.43605	+	10.4798i	0.723712	+	0.803763i
$171$	−4.00211	+	0.850675i	−0.306049	+	0.0650527i
$172$	0.375900	+	0.167362i	0.0286621	+	0.0127612i
$173$	4.97482	−	2.21493i	0.378229	−	0.168398i	−0.208812	−	0.977956i	$-0.566960\pi$
$173$	4.97482	−	2.21493i	0.378229	−	0.168398i	0.587041	+	0.809558i	$0.300293\pi$
$174$	11.1378	+	34.2788i	0.844358	+	2.59867i
$175$	−1.26011	−	0.481025i	−0.0952557	−	0.0363620i
$176$		0			0
$177$	−0.294263	+	0.509678i	−0.0221182	+	0.0383098i
$178$	4.76980	−	5.29740i	0.357512	−	0.397057i
$179$	1.05485	−	10.0362i	0.0788433	−	0.750144i	−0.881662	−	0.471882i	$-0.843575\pi$
$179$	1.05485	−	10.0362i	0.0788433	−	0.750144i	0.960505	−	0.278262i	$-0.0897583\pi$
$180$	−0.450847	−	4.28952i	−0.0336041	−	0.319722i
$181$	6.14307	−	18.9064i	0.456611	−	1.40530i	−0.412623	−	0.910902i	$-0.635387\pi$
$181$	6.14307	−	18.9064i	0.456611	−	1.40530i	0.869234	−	0.494401i	$-0.164613\pi$
$182$	0.740056	+	0.115802i	0.0548566	+	0.00858383i
$183$	−33.9677	+	24.6790i	−2.51096	+	1.82432i
$184$	19.3267	−	8.60480i	1.42478	−	0.634354i
$185$	−10.7164	+	11.9018i	−0.787889	+	0.875039i
$186$	5.85117	+	10.1345i	0.429028	+	0.743099i
$187$		0			0
$188$	−2.66725			−0.194529
$189$	14.6542	+	9.47784i	1.06594	+	0.689411i
$190$	2.24992	+	1.63467i	0.163227	+	0.118591i
$191$	2.65346	+	25.2460i	0.191998	+	1.82674i	0.489486	+	0.872011i	$0.337184\pi$
$191$	2.65346	+	25.2460i	0.191998	+	1.82674i	−0.297488	+	0.954726i	$0.596149\pi$
$192$	−17.3783	+	3.69387i	−1.25417	+	0.266582i
$193$	7.56248	−	1.60745i	0.544359	−	0.115707i	0.0724792	−	0.997370i	$-0.476909\pi$
$193$	7.56248	−	1.60745i	0.544359	−	0.115707i	0.471880	+	0.881663i	$0.343576\pi$
$194$	2.10123	+	19.9918i	0.150859	+	1.43533i
$195$	1.01044	+	0.734126i	0.0723590	+	0.0525719i
$196$	−1.43626	−	1.96145i	−0.102590	−	0.140104i
$197$	−5.37464			−0.382927			−0.191464	−	0.981500i	$-0.561323\pi$
$197$	−5.37464			−0.382927			−0.191464	+	0.981500i	$0.561323\pi$
$198$		0			0
$199$	−4.39053	−	7.60462i	−0.311236	−	0.539077i	0.667394	−	0.744705i	$-0.267410\pi$
$199$	−4.39053	−	7.60462i	−0.311236	−	0.539077i	−0.978630	+	0.205628i	$0.934076\pi$
$200$	0.863754	−	0.959295i	0.0610766	−	0.0678324i
$201$	9.88726	−	4.40209i	0.697393	−	0.310499i
$202$	−7.31504	+	5.31469i	−0.514685	+	0.373940i
$203$	7.78417	+	20.1662i	0.546342	+	1.41539i
$204$	−1.21174	+	3.72935i	−0.0848388	+	0.261107i
$205$	−0.104528	−	0.994522i	−0.00730058	−	0.0694604i
$206$	0.147539	−	1.40374i	0.0102795	−	0.0978033i
$207$	29.5791	−	32.8510i	2.05589	−	2.28330i
$208$	−0.422618	+	0.731997i	−0.0293033	+	0.0507548i
$209$		0			0
$210$	−4.33615	−	27.0515i	−0.299223	−	1.86673i
$211$	1.31061	+	4.03365i	0.0902263	+	0.277688i	0.985980	−	0.166862i	$-0.0533635\pi$
$211$	1.31061	+	4.03365i	0.0902263	+	0.277688i	−0.895754	+	0.444550i	$0.853364\pi$
$212$	2.07951	−	0.925859i	0.142822	−	0.0635883i
$213$	−26.2147	−	11.6715i	−1.79620	−	0.799720i
$214$	−15.5066	+	3.29602i	−1.06001	+	0.225311i
$215$	1.86089	+	2.06673i	0.126912	+	0.140950i
$216$	−13.5125	+	9.81739i	−0.919407	+	0.667988i
$217$	3.83344	+	5.87900i	0.260231	+	0.399092i
$218$	−0.225193	−	0.693074i	−0.0152520	−	0.0469409i
$219$	−0.173648	+	0.300767i	−0.0117341	+	0.0203240i
$220$		0			0
$221$	−0.362311	−	0.627541i	−0.0243717	−	0.0422130i
$222$	−29.4415	−	6.25799i	−1.97599	−	0.420009i
$223$	14.5907	+	10.6008i	0.977065	+	0.709879i	0.957051	−	0.289921i	$-0.0936289\pi$
$223$	14.5907	+	10.6008i	0.977065	+	0.709879i	0.0200140	+	0.999800i	$0.493629\pi$
$224$	4.96448	−	1.34013i	0.331704	−	0.0895415i
$225$	0.833506	−	2.56527i	0.0555670	−	0.171018i
$226$	3.22200	+	3.57840i	0.214324	+	0.238031i
$227$	16.6314	+	7.40477i	1.10386	+	0.491472i	0.876044	−	0.482231i	$-0.160173\pi$
$227$	16.6314	+	7.40477i	1.10386	+	0.491472i	0.227820	+	0.973703i	$0.426840\pi$
$228$	−0.0808338	+	0.769082i	−0.00535335	+	0.0509337i
$229$	−18.8208	−	4.00048i	−1.24371	−	0.264359i	−0.461369	−	0.887208i	$-0.652642\pi$
$229$	−18.8208	−	4.00048i	−1.24371	−	0.264359i	−0.782342	+	0.622849i	$0.785975\pi$
$230$	−30.0469			−1.98124
$231$		0			0
$232$	−20.6878			−1.35822
$233$	−9.12123	−	1.93878i	−0.597552	−	0.127014i	−0.100801	−	0.994907i	$-0.532140\pi$
$233$	−9.12123	−	1.93878i	−0.597552	−	0.127014i	−0.496751	+	0.867893i	$0.665474\pi$
$234$	−0.156577	+	1.48973i	−0.0102358	+	0.0973870i
$235$	−16.4688	−	7.33238i	−1.07431	−	0.478312i
$236$	0.0474982	+	0.0527521i	0.00309187	+	0.00343387i
$237$	0.291577	−	0.897382i	0.0189400	−	0.0582912i
$238$	−4.08535	+	15.3610i	−0.264814	+	0.995706i
$239$	−9.05277	−	6.57723i	−0.585575	−	0.425445i	0.255154	−	0.966900i	$-0.417874\pi$
$239$	−9.05277	−	6.57723i	−0.585575	−	0.425445i	−0.840730	+	0.541455i	$0.817874\pi$
$240$	30.2389	+	6.42748i	1.95191	+	0.414892i
$241$	−10.1022	−	17.4975i	−0.650740	−	1.12711i	−0.982944	−	0.183907i	$-0.941126\pi$
$241$	−10.1022	−	17.4975i	−0.650740	−	1.12711i	0.332204	−	0.943208i	$-0.392208\pi$
$242$		0			0
$243$	5.40167	−	9.35597i	0.346518	−	0.600186i
$244$	1.56492	+	4.81632i	0.100184	+	0.308333i
$245$	−3.47600	−	16.0592i	−0.222073	−	1.02598i
$246$	1.52045	−	1.10467i	0.0969406	−	0.0704315i
$247$	−0.0956211	−	0.106198i	−0.00608422	−	0.00675722i
$248$	−6.57010	+	1.39652i	−0.417202	+	0.0886790i
$249$	8.82526	+	3.92926i	0.559278	+	0.249007i
$250$	14.7519	−	6.56797i	0.932992	−	0.415395i
$251$	−1.82078	−	5.60379i	−0.114927	−	0.353708i	0.877005	−	0.480481i	$-0.159538\pi$
$251$	−1.82078	−	5.60379i	−0.114927	−	0.353708i	−0.991932	+	0.126773i	$0.959538\pi$
$252$	3.77244	−	3.06650i	0.237641	−	0.193171i
$253$		0			0
$254$	−0.341367	+	0.591264i	−0.0214192	+	0.0370992i
$255$	−17.7340	+	19.6956i	−1.11054	+	1.23338i
$256$	−0.846506	+	8.05396i	−0.0529066	+	0.503373i
$257$	0.286040	+	2.72149i	0.0178427	+	0.169762i	0.999814	−	0.0192661i	$-0.00613296\pi$
$257$	0.286040	+	2.72149i	0.0178427	+	0.169762i	−0.981972	+	0.189028i	$0.939466\pi$
$258$	−1.61513	+	4.97087i	−0.100554	+	0.309473i
$259$	−17.8348	−	2.79075i	−1.10820	−	0.173409i
$260$	0.121874	−	0.0885465i	0.00755829	−	0.00549142i
$261$	−39.4904	+	17.5823i	−2.44439	+	1.08831i
$262$	12.3907	−	13.7612i	0.765497	−	0.850171i
$263$	−3.09879	−	5.36727i	−0.191080	−	0.330960i	0.754529	−	0.656267i	$-0.227866\pi$
$263$	−3.09879	−	5.36727i	−0.191080	−	0.330960i	−0.945608	+	0.325307i	$0.894532\pi$
$264$		0			0
$265$	15.3851			0.945097
$266$	−0.158231	+	3.13067i	−0.00970177	+	0.191954i
$267$	10.8383	+	7.87452i	0.663296	+	0.481913i
$268$	−0.136452	−	1.29826i	−0.00833515	−	0.0793036i
$269$	4.11746	−	0.875193i	0.251046	−	0.0533615i	−0.0806697	−	0.996741i	$-0.525706\pi$
$269$	4.11746	−	0.875193i	0.251046	−	0.0533615i	0.331716	+	0.943379i	$0.392373\pi$
$270$	23.2036	−	4.93207i	1.41212	−	0.300156i
$271$	−2.67402	−	25.4416i	−0.162435	−	1.54547i	−0.707283	−	0.706931i	$-0.750079\pi$
$271$	−2.67402	−	25.4416i	−0.162435	−	1.54547i	0.544848	−	0.838535i	$-0.316587\pi$
$272$	−14.5104	−	10.5424i	−0.879821	−	0.639228i
$273$	−0.0710614	+	1.40598i	−0.00430083	+	0.0850938i
$274$	25.0469			1.51314
$275$		0			0
$276$	−4.17752	−	7.23567i	−0.251457	−	0.435536i
$277$	−10.2763	+	11.4130i	−0.617444	+	0.685742i	−0.968043	−	0.250784i	$-0.919312\pi$
$277$	−10.2763	+	11.4130i	−0.617444	+	0.685742i	0.350599	+	0.936526i	$0.385978\pi$
$278$	29.0139	−	12.9178i	1.74014	−	0.774760i
$279$	−11.3546	+	8.24961i	−0.679783	+	0.493891i
$280$	15.5361	+	2.43106i	0.928462	+	0.145284i
$281$	5.94982	−	18.3117i	0.354937	−	1.09238i	−0.601110	−	0.799166i	$-0.705275\pi$
$281$	5.94982	−	18.3117i	0.354937	−	1.09238i	0.956046	−	0.293216i	$-0.0947254\pi$
$282$	−3.54146	−	33.6947i	−0.210891	−	2.00649i
$283$	2.82907	−	26.9168i	0.168171	−	1.60004i	−0.506712	−	0.862116i	$-0.669139\pi$
$283$	2.82907	−	26.9168i	0.168171	−	1.60004i	0.674883	−	0.737925i	$-0.264194\pi$
$284$	−2.31593	+	2.57210i	−0.137425	+	0.152626i
$285$	−2.61334	+	4.52644i	−0.154801	+	0.268123i
$286$		0			0
$287$	0.874638	−	0.710966i	0.0516282	−	0.0419670i
$288$	3.17766	+	9.77983i	0.187245	+	0.576282i
$289$	−1.48324	+	0.660381i	−0.0872494	+	0.0388459i
$290$	26.8421	+	11.9509i	1.57622	+	0.701780i
$291$	−36.9537	+	7.85476i	−2.16627	+	0.460454i
$292$	0.0280293	+	0.0311296i	0.00164029	+	0.00182172i
$293$	−3.26445	+	2.37176i	−0.190711	+	0.138560i	−0.679044	−	0.734098i	$-0.737605\pi$
$293$	−3.26445	+	2.37176i	−0.190711	+	0.138560i	0.488333	+	0.872658i	$0.337605\pi$
$294$	22.8715	−	20.7482i	1.33389	−	1.21006i
$295$	0.148257	+	0.456289i	0.00863187	+	0.0265662i
$296$	8.63816	−	14.9617i	0.502083	−	0.869633i
$297$		0			0
$298$	−0.547104	−	0.947611i	−0.0316929	−	0.0548936i
$299$	1.51021	+	0.321005i	0.0873377	+	0.0185642i
$300$	−0.412437	−	0.299653i	−0.0238121	−	0.0173005i
$301$	−0.805676	+	3.02936i	−0.0464384	+	0.174609i
$302$	4.51894	−	13.9079i	0.260036	−	0.800308i
$303$	−11.3707	−	12.6284i	−0.653228	−	0.725483i
$304$	−3.23134	−	1.43868i	−0.185330	−	0.0825142i
$305$	−3.57776	+	34.0401i	−0.204862	+	1.94913i
$306$	−31.0915	−	6.60870i	−1.77738	−	0.377794i
$307$	2.92902			0.167168			0.0835839	−	0.996501i	$-0.473363\pi$
$307$	2.92902			0.167168			0.0835839	+	0.996501i	$0.473363\pi$
$308$		0			0
$309$	2.65270			0.150907
$310$	9.33136	+	1.98344i	0.529986	+	0.112652i
$311$	−1.63311	+	15.5380i	−0.0926053	+	0.881080i	0.845324	+	0.534254i	$0.179407\pi$
$311$	−1.63311	+	15.5380i	−0.0926053	+	0.881080i	−0.937929	+	0.346826i	$0.887259\pi$
$312$	−1.23082	−	0.547995i	−0.0696813	−	0.0310241i
$313$	−14.7048	−	16.3313i	−0.831164	−	0.923101i	0.166857	−	0.985981i	$-0.446638\pi$
$313$	−14.7048	−	16.3313i	−0.831164	−	0.923101i	−0.998021	+	0.0628803i	$0.979971\pi$
$314$	−4.37518	+	13.4654i	−0.246906	+	0.759898i
$315$	31.7227	−	8.56335i	1.78737	−	0.482490i
$316$	−0.0920723	−	0.0668944i	−0.00517947	−	0.00376311i
$317$	2.94604	+	0.626201i	0.165466	+	0.0351709i	0.289900	−	0.957057i	$-0.406378\pi$
$317$	2.94604	+	0.626201i	0.165466	+	0.0351709i	−0.124434	+	0.992228i	$0.539711\pi$
$318$	14.4572	+	25.0407i	0.810721	+	1.40421i
$319$		0			0
$320$	−7.24170	+	12.5430i	−0.404823	+	0.701174i
$321$	−9.20681	−	28.3356i	−0.513874	−	1.58154i
$322$	−18.4983	−	28.3692i	−1.03087	−	1.58095i
$323$	2.45326	−	1.78240i	0.136503	−	0.0991752i
$324$	0.725189	+	0.805404i	0.0402883	+	0.0447447i
$325$	0.0921486	−	0.0195868i	0.00511149	−	0.00108648i
$326$	12.3215	+	5.48587i	0.682422	+	0.303834i
$327$	1.25118	−	0.557060i	0.0691903	−	0.0308055i
$328$	0.333345	+	1.02593i	0.0184059	+	0.0566475i
$329$	−3.21600	−	20.0634i	−0.177304	−	1.10613i
$330$		0			0
$331$	−13.7344	+	23.7887i	−0.754912	+	1.30755i	0.190506	+	0.981686i	$0.438987\pi$
$331$	−13.7344	+	23.7887i	−0.754912	+	1.30755i	−0.945418	+	0.325860i	$0.894346\pi$
$332$	0.779666	−	0.865907i	0.0427897	−	0.0475228i
$333$	3.77340	−	35.9015i	0.206781	−	1.96739i
$334$	1.34241	+	12.7722i	0.0734535	+	0.698863i
$335$	2.72644	−	8.39112i	0.148961	−	0.458456i
$336$	12.5479	+	32.5075i	0.684544	+	1.77343i
$337$	−13.9492	+	10.1347i	−0.759862	+	0.552072i	−0.898868	−	0.438220i	$-0.855609\pi$
$337$	−13.9492	+	10.1347i	−0.759862	+	0.552072i	0.139006	+	0.990291i	$0.455609\pi$
$338$	18.1474	−	8.07976i	0.987090	−	0.439481i
$339$	−6.05538	+	6.72519i	−0.328883	+	0.365262i
$340$	1.59833	+	2.76838i	0.0866814	+	0.150137i
$341$		0			0
$342$	−6.26857			−0.338965
$343$	13.0225	−	13.1687i	0.703149	−	0.711043i
$344$	−2.42705	−	1.76336i	−0.130858	−	0.0950738i
$345$	−5.90270	−	56.1604i	−0.317791	−	3.02358i
$346$	8.16086	−	1.73464i	0.438731	−	0.0932550i
$347$	11.1813	−	2.37665i	0.600242	−	0.127585i	0.102238	−	0.994760i	$-0.467400\pi$
$347$	11.1813	−	2.37665i	0.600242	−	0.127585i	0.498004	+	0.867174i	$0.334066\pi$
$348$	0.854023	+	8.12549i	0.0457804	+	0.435572i
$349$	−22.9121	−	16.6466i	−1.22646	−	0.891072i	−0.229836	−	0.973229i	$-0.573819\pi$
$349$	−22.9121	−	16.6466i	−1.22646	−	0.891072i	−0.996619	+	0.0821572i	$0.973819\pi$
$350$	−1.73519	−	1.12226i	−0.0927500	−	0.0599875i
$351$	−1.21894			−0.0650622
$352$		0			0
$353$	−8.21806	−	14.2341i	−0.437403	−	0.757605i	0.560085	−	0.828435i	$-0.310768\pi$
$353$	−8.21806	−	14.2341i	−0.437403	−	0.757605i	−0.997488	+	0.0708303i	$0.977435\pi$
$354$	−0.603338	+	0.670074i	−0.0320670	+	0.0356140i
$355$	−21.3704	+	9.51471i	−1.13422	+	0.504988i
$356$	1.30726	−	0.949783i	0.0692848	−	0.0503384i
$357$	−29.5137	−	4.61823i	−1.56203	−	0.244423i
$358$	4.77774	−	14.7044i	0.252512	−	0.777151i
$359$	−2.59890	−	24.7269i	−0.137165	−	1.30503i	−0.819112	−	0.573634i	$-0.805533\pi$
$359$	−2.59890	−	24.7269i	−0.137165	−	1.30503i	0.681947	−	0.731401i	$-0.261133\pi$
$360$	−3.28706	+	31.2743i	−0.173243	+	1.64830i
$361$	−12.3133	+	13.6753i	−0.648070	+	0.719754i
$362$	15.2285	−	26.3765i	0.800392	−	1.38632i
$363$		0			0
$364$	0.158633	+	0.0605553i	0.00831465	+	0.00317396i
$365$	0.0874885	+	0.269262i	0.00457935	+	0.0140938i
$366$	−58.7655	+	26.1641i	−3.07172	+	1.36762i
$367$	3.92697	+	1.74840i	0.204986	+	0.0912656i	0.506662	−	0.862145i	$-0.330879\pi$
$367$	3.92697	+	1.74840i	0.204986	+	0.0912656i	−0.301676	+	0.953411i	$0.597546\pi$
$368$	37.3806	−	7.94550i	1.94860	−	0.414188i
$369$	1.50824	+	1.67507i	0.0785156	+	0.0872004i
$370$	−19.8510	+	14.4226i	−1.03200	+	0.749794i
$371$	9.47177	+	14.5260i	0.491750	+	0.754152i
$372$	0.819731	+	2.52287i	0.0425010	+	0.130805i
$373$	1.36484	−	2.36397i	0.0706686	−	0.122402i	−0.828526	−	0.559951i	$-0.810820\pi$
$373$	1.36484	−	2.36397i	0.0706686	−	0.122402i	0.899195	+	0.437549i	$0.144153\pi$
$374$		0			0
$375$	15.1741	+	26.2823i	0.783588	+	1.35721i
$376$	19.0216	+	4.04317i	0.980964	+	0.208510i
$377$	−1.22145	−	0.887438i	−0.0629081	−	0.0457054i
$378$	18.9419	+	18.8715i	0.974264	+	0.970646i
$379$	−5.08593	+	15.6529i	−0.261247	+	0.804035i	0.731288	+	0.682069i	$0.238920\pi$
$379$	−5.08593	+	15.6529i	−0.261247	+	0.804035i	−0.992534	+	0.121965i	$0.961080\pi$
$380$	0.421830	+	0.468490i	0.0216394	+	0.0240330i
$381$	−1.17219	−	0.521891i	−0.0600530	−	0.0267373i
$382$	−4.06534	+	38.6791i	−0.208001	+	1.97900i
$383$	7.68803	+	1.63414i	0.392840	+	0.0835007i	0.400097	−	0.916473i	$-0.368977\pi$
$383$	7.68803	+	1.63414i	0.392840	+	0.0835007i	−0.00725667	+	0.999974i	$0.502310\pi$
$384$	−38.4124			−1.96022
$385$		0			0
$386$	11.8452			0.602907
$387$	−6.13159	−	1.30331i	−0.311686	−	0.0662509i
$388$	−0.476309	+	4.53178i	−0.0241809	+	0.230066i
$389$	8.80951	+	3.92225i	0.446660	+	0.198866i	0.617725	−	0.786394i	$-0.288054\pi$
$389$	8.80951	+	3.92225i	0.446660	+	0.198866i	−0.171066	+	0.985260i	$0.554721\pi$
$390$	1.28040	+	1.42203i	0.0648358	+	0.0720074i
$391$	−10.1241	+	31.1589i	−0.512000	+	1.57577i
$392$	7.26946	+	16.1653i	0.367163	+	0.816471i
$393$	28.1551	+	20.4559i	1.42024	+	1.03186i
$394$	−8.05448	−	1.71203i	−0.405779	−	0.0862510i
$395$	−0.384600	−	0.666146i	−0.0193513	−	0.0335175i
$396$		0			0
$397$	4.71688	−	8.16988i	0.236733	−	0.410034i	−0.723042	−	0.690805i	$-0.757257\pi$
$397$	4.71688	−	8.16988i	0.236733	−	0.410034i	0.959775	+	0.280770i	$0.0905898\pi$
$398$	−4.15732	−	12.7949i	−0.208388	−	0.641351i
$399$	−5.88259	+	0.319270i	−0.294498	+	0.0159835i
$400$	1.88648	−	1.37061i	0.0943239	−	0.0685303i
$401$	−12.1915	−	13.5400i	−0.608813	−	0.676156i	0.357385	−	0.933957i	$-0.383669\pi$
$401$	−12.1915	−	13.5400i	−0.608813	−	0.676156i	−0.966198	+	0.257802i	$0.917002\pi$
$402$	16.2194	−	3.44753i	0.808949	−	0.171947i
$403$	−0.447820	−	0.199382i	−0.0223075	−	0.00993194i
$404$	−1.87243	+	0.833660i	−0.0931569	+	0.0414761i
$405$	2.26355	+	6.96650i	0.112477	+	0.346168i
$406$	5.24170	+	32.7009i	0.260141	+	1.62292i
$407$		0			0
$408$	14.2947	−	24.7592i	0.707695	−	1.22576i
$409$	4.29011	−	4.76465i	0.212132	−	0.235597i	−0.627683	−	0.778469i	$-0.715997\pi$
$409$	4.29011	−	4.76465i	0.212132	−	0.235597i	0.839815	+	0.542872i	$0.182663\pi$
$410$	0.160147	−	1.52370i	0.00790909	−	0.0752500i
$411$	4.92045	+	46.8150i	0.242708	+	2.30921i
$412$	0.0988716	−	0.304295i	0.00487105	−	0.0149916i
$413$	−0.339537	+	0.420892i	−0.0167075	+	0.0207107i
$414$	54.7919	−	39.8086i	2.69287	−	1.95649i
$415$	7.19441	−	3.20316i	0.353160	−	0.157237i
$416$	−0.240322	+	0.266905i	−0.0117828	+	0.0130861i
$417$	29.8444	+	51.6919i	1.46148	+	2.53137i
$418$		0			0
$419$	1.62092			0.0791871			0.0395935	−	0.999216i	$-0.487394\pi$
$419$	1.62092			0.0791871			0.0395935	+	0.999216i	$0.487394\pi$
$420$	0.313485	−	6.20245i	0.0152965	−	0.302648i
$421$	−25.2000	−	18.3089i	−1.22817	−	0.892319i	−0.231420	−	0.972854i	$-0.574337\pi$
$421$	−25.2000	−	18.3089i	−1.22817	−	0.892319i	−0.996752	+	0.0805348i	$0.974337\pi$
$422$	0.679220	+	6.46234i	0.0330639	+	0.314582i
$423$	39.7461	−	8.44829i	1.93252	−	0.410770i
$424$	−16.2336	+	3.45056i	−0.788373	+	0.167574i
$425$	0.208959	+	1.98812i	0.0101360	+	0.0964378i
$426$	−35.5677	−	25.8414i	−1.72326	−	1.25202i
$427$	−34.3420	+	17.5787i	−1.66193	+	0.850693i
$428$	−3.59358			−0.173702
$429$		0			0
$430$	2.13041	+	3.68999i	0.102738	+	0.177947i
$431$	22.8896	−	25.4215i	1.10255	−	1.22451i	0.130080	−	0.991504i	$-0.458477\pi$
$431$	22.8896	−	25.4215i	1.10255	−	1.22451i	0.972475	−	0.233007i	$-0.0748567\pi$
$432$	−27.5627	+	12.2717i	−1.32611	+	0.590424i
$433$	16.5832	−	12.0484i	0.796937	−	0.579009i	−0.113077	−	0.993586i	$-0.536071\pi$
$433$	16.5832	−	12.0484i	0.796937	−	0.579009i	0.910014	+	0.414578i	$0.136071\pi$
$434$	3.87213	+	10.0314i	0.185868	+	0.481524i
$435$	−17.0642	+	52.5181i	−0.818164	+	2.51805i
$436$	−0.0172673	−	0.164287i	−0.000826953	−	0.00786793i
$437$	−0.675369	+	6.42571i	−0.0323073	+	0.307383i
$438$	−0.356037	+	0.395419i	−0.0170121	+	0.0188939i
$439$	−15.6609	+	27.1255i	−0.747455	+	1.29463i	0.201585	+	0.979471i	$0.435391\pi$
$439$	−15.6609	+	27.1255i	−0.747455	+	1.29463i	−0.949039	+	0.315158i	$0.897942\pi$
$440$		0			0
$441$	27.6152	+	24.6793i	1.31501	+	1.17521i
$442$	−0.343066	−	1.05585i	−0.0163180	−	0.0502216i
$443$	−26.8563	+	11.9572i	−1.27598	+	0.568103i	−0.929108	−	0.369809i	$-0.879423\pi$
$443$	−26.8563	+	11.9572i	−1.27598	+	0.568103i	−0.346873	+	0.937912i	$0.612756\pi$
$444$	−6.23307	−	2.77514i	−0.295809	−	0.131702i
$445$	10.6826	−	2.27066i	0.506405	−	0.107640i
$446$	18.4890	+	20.5341i	0.875479	+	0.972318i
$447$	1.66369	−	1.20874i	0.0786900	−	0.0571716i
$448$	−16.3009	+	0.884712i	−0.770147	+	0.0417987i
$449$	−2.13245	−	6.56299i	−0.100636	−	0.309727i	0.888045	−	0.459756i	$-0.152063\pi$
$449$	−2.13245	−	6.56299i	−0.100636	−	0.309727i	−0.988682	+	0.150029i	$0.952063\pi$
$450$	2.06624	−	3.57883i	0.0974034	−	0.168708i
$451$		0			0
$452$	0.545759	+	0.945283i	0.0256704	+	0.0444624i
$453$	26.8828	+	5.71412i	1.26306	+	0.268473i
$454$	22.5652	+	16.3946i	1.05904	+	0.769437i
$455$	0.813004	+	0.809985i	0.0381142	+	0.0379727i
$456$	1.74229	−	5.36220i	0.0815900	−	0.251108i
$457$	8.28025	+	9.19615i	0.387334	+	0.430178i	0.905004	−	0.425402i	$-0.139867\pi$
$457$	8.28025	+	9.19615i	0.387334	+	0.430178i	−0.517671	+	0.855580i	$0.673201\pi$
$458$	−26.9307	−	11.9903i	−1.25839	−	0.560270i
$459$	2.70371	−	25.7241i	0.126198	−	1.20070i
$460$	−6.66225	−	1.41610i	−0.310629	−	0.0660262i
$461$	20.0942			0.935881			0.467940	−	0.883760i	$-0.344996\pi$
$461$	20.0942			0.935881			0.467940	+	0.883760i	$0.344996\pi$
$462$		0			0
$463$	8.69190			0.403947			0.201974	−	0.979391i	$-0.435265\pi$
$463$	8.69190			0.403947			0.201974	+	0.979391i	$0.435265\pi$
$464$	−36.5539	−	7.76977i	−1.69697	−	0.360702i
$465$	−1.87409	+	17.8308i	−0.0869090	+	0.826883i
$466$	−13.0516	−	5.81094i	−0.604603	−	0.269187i
$467$	3.19122	+	3.54421i	0.147672	+	0.164006i	0.812443	−	0.583041i	$-0.198137\pi$
$467$	3.19122	+	3.54421i	0.147672	+	0.164006i	−0.664771	+	0.747048i	$0.731471\pi$
$468$	−0.104928	+	0.322937i	−0.00485032	+	0.0149277i
$469$	9.60111	−	2.59176i	0.443338	−	0.119677i
$470$	−22.3446	−	16.2343i	−1.03068	−	0.748834i
$471$	−26.0276	−	5.53233i	−1.19929	−	0.254917i
$472$	−0.258770	−	0.448204i	−0.0119109	−	0.0206302i
$473$		0			0
$474$	0.722811	−	1.25195i	0.0331998	−	0.0575038i
$475$	0.121826	+	0.374942i	0.00558977	+	0.0172035i
$476$	−1.62980	+	3.21342i	−0.0747017	+	0.147287i
$477$	−28.0553	+	20.3834i	−1.28457	+	0.933291i
$478$	−11.4715	−	12.7404i	−0.524693	−	0.582730i
$479$	38.7484	−	8.23624i	1.77046	−	0.376323i	0.796786	−	0.604261i	$-0.206532\pi$
$479$	38.7484	−	8.23624i	1.77046	−	0.376323i	0.973676	+	0.227938i	$0.0731984\pi$
$480$	12.0004	+	5.34293i	0.547742	+	0.243870i
$481$	1.15183	−	0.512826i	0.0525187	−	0.0233828i
$482$	−9.56560	−	29.4399i	−0.435701	−	1.34095i
$483$	49.3906	−	40.1481i	2.24735	−	1.82680i
$484$		0			0
$485$	−15.3990	+	26.6718i	−0.699232	+	1.21111i
$486$	11.0752	−	12.3003i	0.502383	−	0.557953i
$487$	−0.538917	+	5.12745i	−0.0244207	+	0.232347i	0.975503	+	0.219986i	$0.0706013\pi$
$487$	−0.538917	+	5.12745i	−0.0244207	+	0.232347i	−0.999924	+	0.0123607i	$0.996065\pi$
$488$	−3.85942	−	36.7199i	−0.174708	−	1.66223i
$489$	−7.83303	+	24.1076i	−0.354222	+	1.09018i
$490$	−0.0936775	−	25.1737i	−0.00423192	−	1.13723i
$491$	−8.24593	+	5.99102i	−0.372134	+	0.270371i	−0.758095	−	0.652144i	$-0.773870\pi$
$491$	−8.24593	+	5.99102i	−0.372134	+	0.270371i	0.385961	+	0.922515i	$0.373870\pi$
$492$	0.389191	−	0.173279i	0.0175461	−	0.00781201i
$493$	21.4375	−	23.8087i	0.965494	−	1.07229i
$494$	−0.109470	−	0.189608i	−0.00492531	−	0.00853088i
$495$		0			0
$496$	−12.1334			−0.544806
$497$	−22.1400	−	14.3194i	−0.993117	−	0.642314i
$498$	11.9740	+	8.69961i	0.536567	+	0.389839i
$499$	−0.615653	−	5.85755i	−0.0275604	−	0.262220i	−0.999622	−	0.0274938i	$-0.991247\pi$
$499$	−0.615653	−	5.85755i	−0.0275604	−	0.262220i	0.972062	−	0.234726i	$-0.0754193\pi$
$500$	3.58045	−	0.761049i	0.160123	−	0.0340352i
$501$	−23.6087	+	5.01818i	−1.05476	+	0.224196i
$502$	−0.943614	−	8.97789i	−0.0421156	−	0.400703i
$503$	10.3836	+	7.54411i	0.462981	+	0.336375i	0.794699	−	0.607003i	$-0.207628\pi$
$503$	10.3836	+	7.54411i	0.462981	+	0.336375i	−0.331719	+	0.943378i	$0.607628\pi$
$504$	−31.5517	+	16.1504i	−1.40542	+	0.719396i
$505$	−13.8530			−0.616449
$506$		0			0
$507$	18.6668	+	32.3319i	0.829024	+	1.43591i
$508$	−0.103557	+	0.115011i	−0.00459458	+	0.00510280i
$509$	29.4281	−	13.1022i	1.30438	−	0.580746i	0.367376	−	0.930072i	$-0.380256\pi$
$509$	29.4281	−	13.1022i	1.30438	−	0.580746i	0.937001	+	0.349326i	$0.113589\pi$
$510$	−32.8501	+	23.8670i	−1.45463	+	1.05685i
$511$	−0.200365	+	0.248373i	−0.00886362	+	0.0109874i
$512$	4.41079	−	13.5750i	0.194931	−	0.599937i
$513$	−0.533201	−	5.07307i	−0.0235414	−	0.223982i
$514$	−0.438239	+	4.16957i	−0.0193299	+	0.183912i
$515$	1.44700	−	1.60705i	0.0637623	−	0.0708152i
$516$	−0.592396	+	1.02606i	−0.0260788	+	0.0451698i
$517$		0			0
$518$	−25.8384	−	9.86332i	−1.13528	−	0.433370i
$519$	4.84540	+	14.9126i	0.212689	+	0.654591i
$520$	−1.00337	+	0.446729i	−0.0440007	+	0.0195904i
$521$	16.9261	+	7.53600i	0.741548	+	0.330158i	0.742504	−	0.669841i	$-0.233638\pi$
$521$	16.9261	+	7.53600i	0.741548	+	0.330158i	−0.000956606		1.00000i	$0.500304\pi$
$522$	−64.7813	+	13.7697i	−2.83540	+	0.602683i
$523$	−24.9199	−	27.6763i	−1.08967	−	1.21020i	−0.976248	−	0.216654i	$-0.930486\pi$
$523$	−24.9199	−	27.6763i	−1.08967	−	1.21020i	−0.113421	−	0.993547i	$-0.536181\pi$
$524$	3.39592	−	2.46728i	0.148351	−	0.107784i
$525$	1.75673	−	3.46370i	0.0766702	−	0.151168i
$526$	−2.93419	−	9.03052i	−0.127937	−	0.393749i
$527$	5.20099	−	9.00838i	0.226559	−	0.392411i
$528$		0			0
$529$	−23.4033	−	40.5357i	−1.01754	−	1.76242i
$530$	23.0562	+	4.90075i	1.00150	+	0.212875i
$531$	−0.874882	−	0.635639i	−0.0379667	−	0.0275844i
$532$	−0.182632	+	0.686700i	−0.00791810	+	0.0297722i
$533$	−0.0243276	+	0.0748726i	−0.00105374	+	0.00324309i
$534$	13.7341	+	15.2533i	0.594332	+	0.660073i
$535$	−22.1883	−	9.87889i	−0.959286	−	0.427102i
$536$	−0.994854	+	9.46540i	−0.0429711	+	0.408843i
$537$	28.4224	+	6.04137i	1.22652	+	0.260704i
$538$	6.44924			0.278047
$539$		0			0
$540$	5.37733			0.231403
$541$	−35.3665	−	7.51739i	−1.52053	−	0.323198i	−0.629446	−	0.777044i	$-0.716718\pi$
$541$	−35.3665	−	7.51739i	−1.52053	−	0.323198i	−0.891080	+	0.453847i	$0.850051\pi$
$542$	4.09683	−	38.9788i	0.175974	−	1.67428i
$543$	52.2917	+	23.2818i	2.24405	+	0.999116i
$544$	−5.09961	−	5.66369i	−0.218644	−	0.242829i
$545$	0.345016	−	1.06185i	0.0147789	−	0.0454847i
$546$	−0.554353	+	2.08438i	−0.0237241	+	0.0892032i
$547$	−10.3538	−	7.52246i	−0.442696	−	0.321637i	0.344010	−	0.938966i	$-0.388215\pi$
$547$	−10.3538	−	7.52246i	−0.442696	−	0.321637i	−0.786705	+	0.617329i	$0.788215\pi$
$548$	5.55361	+	1.18046i	0.237238	+	0.0504266i
$549$	−38.5749	−	66.8137i	−1.64634	−	2.85154i
$550$		0			0
$551$	3.15910	−	5.47172i	0.134582	−	0.233103i
$552$	18.8239	+	57.9340i	0.801198	+	2.46583i
$553$	0.392173	−	0.773236i	0.0166769	−	0.0328813i
$554$	−19.0357	+	13.8302i	−0.808749	+	0.587590i
$555$	−30.8568	−	34.2699i	−1.30980	−	1.45468i
$556$	7.04202	−	1.49683i	0.298648	−	0.0634796i
$557$	−28.0081	−	12.4700i	−1.18674	−	0.528371i	−0.284113	−	0.958791i	$-0.591699\pi$
$557$	−28.0081	−	12.4700i	−1.18674	−	0.528371i	−0.902629	+	0.430420i	$0.858366\pi$
$558$	−19.6440	+	8.74606i	−0.831595	+	0.370250i
$559$	−0.0676564	−	0.208225i	−0.00286156	−	0.00880698i
$560$	26.5382	+	10.1305i	1.12145	+	0.428090i
$561$		0			0
$562$	14.7494	−	25.5468i	0.622167	−	1.07763i
$563$	−9.70557	+	10.7791i	−0.409041	+	0.454286i	−0.912101	−	0.409965i	$-0.865541\pi$
$563$	−9.70557	+	10.7791i	−0.409041	+	0.454286i	0.503060	+	0.864251i	$0.332207\pi$
$564$	0.802783	−	7.63797i	0.0338033	−	0.321617i
$565$	0.771141	+	7.33691i	0.0324421	+	0.308666i
$566$	12.8137	−	39.4367i	0.538602	−	1.65765i
$567$	−5.18395	+	6.42606i	−0.217706	+	0.269869i
$568$	20.4151	−	14.8324i	0.856598	−	0.622355i
$569$	17.3620	−	7.73005i	0.727852	−	0.324061i	−0.00914352	−	0.999958i	$-0.502911\pi$
$569$	17.3620	−	7.73005i	0.727852	−	0.324061i	0.736996	+	0.675898i	$0.236244\pi$
$570$	−5.35822	+	5.95091i	−0.224431	+	0.249256i
$571$	10.5005	+	18.1873i	0.439431	+	0.761117i	0.997646	−	0.0685799i	$-0.0218468\pi$
$571$	10.5005	+	18.1873i	0.439431	+	0.761117i	−0.558215	+	0.829696i	$0.688513\pi$
$572$		0			0
$573$	−73.0934			−3.05352
$574$	1.53721	−	0.786854i	0.0641619	−	0.0328426i
$575$	−3.44593	−	2.50361i	−0.143705	−	0.104408i
$576$	−3.41243	−	32.4671i	−0.142184	−	1.35279i
$577$	5.07412	−	1.07854i	0.211238	−	0.0449001i	−0.101077	−	0.994879i	$-0.532229\pi$
$577$	5.07412	−	1.07854i	0.211238	−	0.0449001i	0.312315	+	0.949979i	$0.398895\pi$
$578$	−2.43315	+	0.517183i	−0.101206	+	0.0215120i
$579$	2.32699	+	22.1398i	0.0967063	+	0.920099i
$580$	5.38841	+	3.91491i	0.223742	+	0.162558i
$581$	7.45352	+	4.82068i	0.309224	+	0.199995i
$582$	−57.8813			−2.39926
$583$		0			0
$584$	−0.152704	−	0.264490i	−0.00631892	−	0.0109447i
$585$	−1.53564	+	1.70550i	−0.0634909	+	0.0705138i
$586$	−5.64763	+	2.51449i	−0.233302	+	0.103873i
$587$	−6.74568	+	4.90103i	−0.278424	+	0.202287i	−0.718230	−	0.695806i	$-0.755047\pi$
$587$	−6.74568	+	4.90103i	−0.278424	+	0.202287i	0.439806	+	0.898093i	$0.355047\pi$
$588$	6.04911	−	3.52253i	0.249461	−	0.145267i
$589$	0.633913	−	1.95098i	0.0261199	−	0.0803888i
$590$	0.0768338	+	0.731025i	0.00316320	+	0.0300958i
$591$	1.61765	−	15.3909i	0.0665411	−	0.633096i
$592$	20.8822	−	23.1921i	0.858255	−	0.953188i
$593$	−3.05097	+	5.28444i	−0.125288	+	0.217006i	−0.921846	−	0.387557i	$-0.873319\pi$
$593$	−3.05097	+	5.28444i	−0.125288	+	0.217006i	0.796557	+	0.604563i	$0.206652\pi$
$594$		0			0
$595$	−18.8969	+	15.3607i	−0.774698	+	0.629729i
$596$	−0.0766475	−	0.235897i	−0.00313961	−	0.00966271i
$597$	23.0981	−	10.2840i	0.945344	−	0.420894i
$598$	2.16096	+	0.962122i	0.0883683	+	0.0393441i
$599$	13.5476	−	2.87964i	0.553541	−	0.117659i	0.0773554	−	0.997004i	$-0.475352\pi$
$599$	13.5476	−	2.87964i	0.553541	−	0.117659i	0.476186	+	0.879345i	$0.342019\pi$
$600$	2.48708	+	2.76218i	0.101535	+	0.112766i
$601$	−25.2976	+	18.3798i	−1.03191	+	0.749726i	−0.968690	−	0.248274i	$-0.920137\pi$
$601$	−25.2976	+	18.3798i	−1.03191	+	0.749726i	−0.0632191	+	0.998000i	$0.520137\pi$
$602$	−2.17236	+	4.28319i	−0.0885389	+	0.174570i
$603$	6.14546	+	18.9138i	0.250262	+	0.770229i
$604$	1.65745	−	2.87079i	0.0674407	−	0.116811i
$605$		0			0
$606$	−13.0175	−	22.5470i	−0.528801	−	0.915911i
$607$	−36.9703	−	7.85828i	−1.50058	−	0.318958i	−0.616895	−	0.787045i	$-0.711610\pi$
$607$	−36.9703	−	7.85828i	−1.50058	−	0.318958i	−0.883682	+	0.468088i	$0.844943\pi$
$608$	−1.21595	−	0.883437i	−0.0493132	−	0.0358281i
$609$	−60.0911	+	16.2213i	−2.43502	+	0.657319i
$610$	−16.2048	+	49.8732i	−0.656112	+	2.01931i
$611$	0.949640	+	1.05468i	0.0384183	+	0.0426679i
$612$	−6.58239	−	2.93067i	−0.266077	−	0.118465i
$613$	−2.20914	+	21.0186i	−0.0892263	+	0.848932i	0.854777	+	0.518996i	$0.173694\pi$
$613$	−2.20914	+	21.0186i	−0.0892263	+	0.848932i	−0.944003	+	0.329936i	$0.892973\pi$
$614$	4.38945	+	0.933006i	0.177144	+	0.0376531i
$615$	2.87939			0.116108
$616$		0			0
$617$	23.7743			0.957115			0.478558	−	0.878056i	$-0.341160\pi$
$617$	23.7743			0.957115			0.478558	+	0.878056i	$0.341160\pi$
$618$	3.97537	+	0.844990i	0.159913	+	0.0339905i
$619$	−1.41135	+	13.4281i	−0.0567269	+	0.539721i	0.928846	+	0.370467i	$0.120802\pi$
$619$	−1.41135	+	13.4281i	−0.0567269	+	0.539721i	−0.985573	+	0.169254i	$0.945864\pi$
$620$	1.97555	+	0.879570i	0.0793398	+	0.0353244i
$621$	36.8772	+	40.9562i	1.47983	+	1.64352i
$622$	−7.39686	+	22.7652i	−0.296587	+	0.912802i
$623$	8.72059	+	8.68820i	0.349383	+	0.348085i
$624$	−1.96896	−	1.43053i	−0.0788213	−	0.0572670i
$625$	26.6928	+	5.67372i	1.06771	+	0.226949i
$626$	−16.8346	−	29.1583i	−0.672844	−	1.16540i
$627$		0			0
$628$	−1.60472	+	2.77946i	−0.0640354	+	0.110913i
$629$	8.26764	+	25.4452i	0.329652	+	1.01457i
$630$	50.2676	−	2.72821i	2.00271	−	0.108694i
$631$	30.9331	−	22.4742i	1.23143	−	0.894683i	0.234429	−	0.972133i	$-0.424678\pi$
$631$	30.9331	−	22.4742i	1.23143	−	0.894683i	0.996996	+	0.0774503i	$0.0246779\pi$
$632$	0.555215	+	0.616628i	0.0220853	+	0.0245282i
$633$	−11.9453	+	2.53905i	−0.474782	+	0.100918i
$634$	4.21550	+	1.87686i	0.167419	+	0.0745397i
$635$	−0.955576	+	0.425450i	−0.0379209	+	0.0168835i
$636$	2.02541	+	6.23358i	0.0803129	+	0.247178i
$637$	−0.264233	+	1.26627i	−0.0104693	+	0.0501715i
$638$		0			0
$639$	26.3640	−	45.6637i	1.04294	−	1.80643i
$640$	−20.9532	+	23.2709i	−0.828248	+	0.919863i
$641$	−4.03013	+	38.3441i	−0.159180	+	1.51450i	0.565116	+	0.825012i	$0.308832\pi$
$641$	−4.03013	+	38.3441i	−0.159180	+	1.51450i	−0.724296	+	0.689489i	$0.757835\pi$
$642$	−4.77139	−	45.3968i	−0.188312	−	1.79167i
$643$	5.95250	−	18.3199i	0.234744	−	0.722467i	−0.762412	−	0.647092i	$-0.775985\pi$
$643$	5.95250	−	18.3199i	0.234744	−	0.722467i	0.997155	−	0.0753745i	$-0.0240152\pi$
$644$	−2.76456	−	7.16207i	−0.108939	−	0.282225i
$645$	−6.47840	+	4.70683i	−0.255087	+	0.185331i
$646$	4.24424	−	1.88966i	0.166987	−	0.0743475i
$647$	26.6209	−	29.5655i	1.04658	−	1.16234i	0.0601416	−	0.998190i	$-0.480845\pi$
$647$	26.6209	−	29.5655i	1.04658	−	1.16234i	0.986435	−	0.164151i	$-0.0524886\pi$
$648$	−3.95084	−	6.84305i	−0.155204	−	0.268820i
$649$		0			0
$650$	0.144334			0.00566124
$651$	−17.9889	+	9.20803i	−0.705042	+	0.360891i
$652$	2.47346	+	1.79708i	0.0968684	+	0.0703790i
$653$	−0.498236	−	4.74040i	−0.0194975	−	0.185506i	0.980438	−	0.196826i	$-0.0630634\pi$
$653$	−0.498236	−	4.74040i	−0.0194975	−	0.185506i	−0.999936	+	0.0113198i	$0.996397\pi$
$654$	2.05247	−	0.436267i	0.0802580	−	0.0170594i
$655$	27.7506	−	5.89856i	1.08430	−	0.230476i
$656$	0.203686	+	1.93794i	0.00795259	+	0.0756639i
$657$	−0.516279	−	0.375099i	−0.0201420	−	0.0146340i
$658$	1.57144	−	31.0916i	0.0612610	−	1.21208i
$659$	−38.3550			−1.49410			−0.747050	−	0.664768i	$-0.768530\pi$
$659$	−38.3550			−1.49410			−0.747050	+	0.664768i	$0.768530\pi$
$660$		0			0
$661$	5.18139	+	8.97443i	0.201533	+	0.349065i	0.949022	−	0.315208i	$-0.102074\pi$
$661$	5.18139	+	8.97443i	0.201533	+	0.349065i	−0.747490	+	0.664273i	$0.768741\pi$
$662$	−28.1602	+	31.2750i	−1.09448	+	1.21554i
$663$	1.90608	−	0.848642i	0.0740261	−	0.0329585i
$664$	−6.87280	+	4.99338i	−0.266717	+	0.193781i
$665$	−3.01542	+	3.73793i	−0.116933	+	0.144951i
$666$	17.0909	−	52.6003i	0.662258	−	2.03822i
$667$	7.13539	+	67.8887i	0.276284	+	2.62866i
$668$	−0.304300	+	2.89522i	−0.0117737	+	0.112019i
$669$	−34.7479	+	38.5915i	−1.34343	+	1.49203i
$670$	6.75877	−	11.7065i	0.261114	−	0.452263i
$671$		0			0
$672$	2.34343	+	14.6197i	0.0903996	+	0.563967i
$673$	−7.91603	−	24.3630i	−0.305140	−	0.939126i	−0.979625	−	0.200836i	$-0.935634\pi$
$673$	−7.91603	−	24.3630i	−0.305140	−	0.939126i	0.674484	−	0.738289i	$-0.264366\pi$
$674$	−24.1327	+	10.7446i	−0.929557	+	0.413865i
$675$	3.07205	+	1.36777i	0.118243	+	0.0526453i
$676$	4.40459	−	0.936225i	0.169407	−	0.0360086i
$677$	27.9947	+	31.0913i	1.07593	+	1.19494i	0.979886	+	0.199559i	$0.0639509\pi$
$677$	27.9947	+	31.0913i	1.07593	+	1.19494i	0.0960398	+	0.995377i	$0.469382\pi$
$678$	−11.2169	+	8.14955i	−0.430782	+	0.312981i
$679$	−34.6629	+	1.88128i	−1.33024	+	0.0721970i
$680$	−7.20206	−	22.1656i	−0.276186	−	0.850014i
$681$	−26.2101	+	45.3972i	−1.00437	+	1.73962i
$682$		0			0
$683$	23.0214	+	39.8743i	0.880890	+	1.52575i	0.850353	+	0.526212i	$0.176388\pi$
$683$	23.0214	+	39.8743i	0.880890	+	1.52575i	0.0305366	+	0.999534i	$0.490278\pi$
$684$	−1.38992	−	0.295436i	−0.0531448	−	0.0112963i
$685$	31.0453	+	22.5558i	1.18618	+	0.861811i
$686$	23.7104	−	15.5865i	0.905267	−	0.595097i
$687$	17.1204	−	52.6913i	0.653186	−	2.01030i
$688$	−3.62616	−	4.02726i	−0.138246	−	0.153538i
$689$	−1.10649	−	0.492639i	−0.0421538	−	0.0187681i
$690$	9.04346	−	86.0428i	0.344279	−	3.27559i
$691$	−7.82518	−	1.66329i	−0.297684	−	0.0632747i	0.0566486	−	0.998394i	$-0.481959\pi$
$691$	−7.82518	−	1.66329i	−0.297684	−	0.0632747i	−0.354332	+	0.935120i	$0.615292\pi$
$692$	1.89124			0.0718943
$693$		0			0
$694$	17.5134			0.664800
$695$	47.5954	+	10.1167i	1.80540	+	0.383749i
$696$	6.22656	−	59.2418i	0.236017	−	2.24555i
$697$	−1.52612	−	0.679474i	−0.0578060	−	0.0257369i
$698$	−29.0337	−	32.2451i	−1.09894	−	1.22050i
$699$	8.29720	−	25.5361i	0.313829	−	0.965866i
$700$	−0.331849	−	0.330617i	−0.0125427	−	0.0124961i
$701$	26.5474	+	19.2878i	1.00268	+	0.728491i	0.962661	−	0.270708i	$-0.0872579\pi$
$701$	26.5474	+	19.2878i	1.00268	+	0.728491i	0.0400199	+	0.999199i	$0.487258\pi$
$702$	−1.82672	−	0.388280i	−0.0689449	−	0.0146547i
$703$	2.63816	+	4.56942i	0.0994999	+	0.172339i
$704$		0			0
$705$	25.9538	−	44.9534i	0.977478	−	1.69304i
$706$	−7.78154	−	23.9491i	−0.292862	−	0.901337i
$707$	−8.52854	−	13.0795i	−0.320749	−	0.491904i
$708$	−0.165357	+	0.120139i	−0.00621451	+	0.00451510i
$709$	4.95289	+	5.50074i	0.186010	+	0.206585i	0.828936	−	0.559343i	$-0.188947\pi$
$709$	4.95289	+	5.50074i	0.186010	+	0.206585i	−0.642926	+	0.765928i	$0.722280\pi$
$710$	−35.0567	+	7.45153i	−1.31565	+	0.279651i
$711$	1.58390	+	0.705197i	0.0594009	+	0.0264470i
$712$	−10.7625	+	4.79179i	−0.403343	+	0.179580i
$713$	6.84888	+	21.0787i	0.256493	+	0.789403i
$714$	−42.7584	−	16.3222i	−1.60019	−	0.610842i
$715$		0			0
$716$	1.75237	−	3.03520i	0.0654893	−	0.113431i
$717$	21.5593	−	23.9440i	0.805147	−	0.894206i
$718$	3.98175	−	37.8838i	0.148597	−	1.41381i
$719$	1.47772	+	14.0596i	0.0551097	+	0.524334i	0.986900	+	0.161336i	$0.0515802\pi$
$719$	1.47772	+	14.0596i	0.0551097	+	0.524334i	−0.931790	+	0.362998i	$0.881753\pi$
$720$	−17.5538	+	54.0250i	−0.654191	+	2.01339i
$721$	2.40816	+	0.376823i	0.0896845	+	0.0140336i
$722$	−22.8090	+	16.5717i	−0.848863	+	0.616735i
$723$	53.1466	−	23.6624i	1.97654	−	0.880014i
$724$	4.61970	−	5.13070i	0.171690	−	0.190681i
$725$	2.08260	+	3.60716i	0.0773457	+	0.133967i
$726$		0			0
$727$	15.2790			0.566667			0.283333	−	0.959021i	$-0.408560\pi$
$727$	15.2790			0.566667			0.283333	+	0.959021i	$0.408560\pi$
$728$	−1.03951	−	0.672317i	−0.0385267	−	0.0249177i
$729$	32.7400	+	23.7870i	1.21259	+	0.881000i
$730$	0.0453406	+	0.431387i	0.00167813	+	0.0159663i
$731$	4.54437	−	0.965936i	0.168080	−	0.0357264i
$732$	−14.2631	+	3.03171i	−0.527178	+	0.112055i
$733$	−0.140584	−	1.33756i	−0.00519258	−	0.0494041i	0.991619	−	0.129198i	$-0.0412404\pi$
$733$	−0.140584	−	1.33756i	−0.00519258	−	0.0494041i	−0.996811	+	0.0797942i	$0.974574\pi$
$734$	5.32805	+	3.87106i	0.196662	+	0.142883i
$735$	47.0335	−	5.12044i	1.73486	−	0.188870i
$736$	16.2385			0.598561
$737$		0			0
$738$	1.72668	+	2.99070i	0.0635600	+	0.110089i
$739$	−17.1656	+	19.0644i	−0.631448	+	0.701294i	−0.970942	−	0.239314i	$-0.923077\pi$
$739$	−17.1656	+	19.0644i	−0.631448	+	0.701294i	0.339494	+	0.940608i	$0.389744\pi$
$740$	−5.08125	+	2.26232i	−0.186790	+	0.0831644i
$741$	0.332890	−	0.241858i	0.0122290	−	0.00888489i
$742$	9.56738	+	24.7859i	0.351229	+	0.909920i
$743$	−1.87916	+	5.78346i	−0.0689397	+	0.212175i	−0.979591	−	0.201001i	$-0.935580\pi$
$743$	−1.87916	+	5.78346i	−0.0689397	+	0.212175i	0.910651	+	0.413176i	$0.135580\pi$
$744$	−2.02163	−	19.2345i	−0.0741166	−	0.705172i
$745$	0.175234	−	1.66724i	0.00642007	−	0.0610829i
$746$	2.79837	−	3.10791i	0.102456	−	0.113789i
$747$	−8.87551	+	15.3728i	−0.324738	+	0.562463i
$748$		0			0
$749$	−4.33291	−	27.0313i	−0.158321	−	0.987703i
$750$	14.3681	+	44.2205i	0.524649	+	1.61470i
$751$	19.0116	−	8.46450i	0.693742	−	0.308874i	−0.0294052	−	0.999568i	$-0.509361\pi$
$751$	19.0116	−	8.46450i	0.693742	−	0.308874i	0.723148	+	0.690694i	$0.242695\pi$
$752$	32.0913	+	14.2880i	1.17025	+	0.521029i
$753$	16.5951	−	3.52740i	0.604759	−	0.128546i
$754$	−1.54780	−	1.71900i	−0.0563675	−	0.0626024i
$755$	18.1258	−	13.1691i	0.659664	−	0.479274i
$756$	3.31053	+	5.07707i	0.120403	+	0.184651i
$757$	−1.62358	−	4.99687i	−0.0590101	−	0.181614i	0.917206	−	0.398412i	$-0.130439\pi$
$757$	−1.62358	−	4.99687i	−0.0590101	−	0.181614i	−0.976216	+	0.216798i	$0.930439\pi$
$758$	−12.6079	+	21.8375i	−0.457939	+	0.793173i
$759$		0			0
$760$	−2.29813	−	3.98048i	−0.0833621	−	0.144387i
$761$	40.0858	+	8.52050i	1.45311	+	0.308868i	0.865757	−	0.500464i	$-0.166837\pi$
$761$	40.0858	+	8.52050i	1.45311	+	0.308868i	0.587352	+	0.809332i	$0.300171\pi$
$762$	−1.59041	−	1.15550i	−0.0576144	−	0.0418593i
$763$	1.21497	−	0.327974i	0.0439848	−	0.0118734i
$764$	−2.72434	+	8.38465i	−0.0985631	+	0.303346i
$765$	−32.5861	−	36.1905i	−1.17815	−	1.30847i
$766$	11.0008	+	4.89788i	0.397476	+	0.176968i
$767$	0.00394807	−	0.0375634i	0.000142557	−	0.00135633i
$768$	−22.8086	−	4.84813i	−0.823036	−	0.174942i
$769$	47.5580			1.71499			0.857493	−	0.514496i	$-0.172021\pi$
$769$	47.5580			1.71499			0.857493	+	0.514496i	$0.172021\pi$
$770$		0			0
$771$	−7.87939			−0.283769
$772$	2.62642	+	0.558263i	0.0945270	+	0.0200923i
$773$	−2.14209	+	20.3806i	−0.0770456	+	0.733040i	0.885997	+	0.463691i	$0.153475\pi$
$773$	−2.14209	+	20.3806i	−0.0770456	+	0.733040i	−0.963043	+	0.269349i	$0.913191\pi$
$774$	−8.77370	−	3.90630i	−0.315364	−	0.140409i
$775$	0.904898	+	1.00499i	0.0325049	+	0.0361003i
$776$	10.2663	−	31.5965i	0.368540	−	1.13425i
$777$	13.3595	−	50.2320i	0.479269	−	1.80206i
$778$	11.9526	+	8.68409i	0.428522	+	0.311340i
$779$	−0.322251	−	0.0684966i	−0.0115459	−	0.00245415i
$780$	0.216881	+	0.375650i	0.00776560	+	0.0134504i
$781$		0			0
$782$	−25.0974	+	43.4701i	−0.897483	+	1.55449i
$783$	−16.6539	−	51.2554i	−0.595161	−	1.83172i
$784$	6.77338	+	31.2932i	0.241906	+	1.11761i
$785$	−17.5491	+	12.7502i	−0.626355	+	0.455073i
$786$	35.6775	+	39.6238i	1.27257	+	1.41334i
$787$	18.7028	−	3.97540i	0.666682	−	0.141708i	0.137875	−	0.990450i	$-0.455973\pi$
$787$	18.7028	−	3.97540i	0.666682	−	0.141708i	0.528807	+	0.848742i	$0.322639\pi$
$788$	−1.70522	−	0.759211i	−0.0607458	−	0.0270458i
$789$	16.3024	−	7.25831i	0.580382	−	0.258403i
$790$	−0.364171	−	1.12080i	−0.0129566	−	0.0398764i
$791$	−6.45249	+	5.24503i	−0.229424	+	0.186492i
$792$		0			0
$793$	1.34730	−	2.33359i	0.0478439	−	0.0828681i
$794$	9.67119	−	10.7409i	0.343218	−	0.381182i
$795$	−4.63056	+	44.0569i	−0.164229	+	1.56254i
$796$	−0.318773	−	3.03292i	−0.0112986	−	0.107499i
$797$	−16.2278	+	49.9441i	−0.574819	+	1.76911i	0.0619750	+	0.998078i	$0.480260\pi$
$797$	−16.2278	+	49.9441i	−0.574819	+	1.76911i	−0.636794	+	0.771034i	$0.719740\pi$
$798$	−8.91740	−	1.39537i	−0.315673	−	0.0493957i
$799$	−24.3640	+	17.7015i	−0.861936	+	0.626233i
$800$	0.905167	−	0.403006i	0.0320025	−	0.0142484i
$801$	−16.4719	+	18.2938i	−0.582004	+	0.646381i
$802$	−13.9572	−	24.1746i	−0.492847	−	0.853636i
$803$		0			0
$804$	3.75877			0.132562
$805$	2.61918	−	51.8217i	0.0923141	−	1.82647i
$806$	−0.607596	−	0.441444i	−0.0214016	−	0.0155492i
$807$	1.26695	+	12.0542i	0.0445987	+	0.424329i
$808$	14.6170	−	3.10694i	0.514225	−	0.109302i
$809$	−39.7827	+	8.45608i	−1.39869	+	0.297300i	−0.844706	−	0.535230i	$-0.820225\pi$
$809$	−39.7827	+	8.45608i	−1.39869	+	0.297300i	−0.553980	+	0.832530i	$0.686891\pi$
$810$	1.17308	+	11.1611i	0.0412177	+	0.392161i
$811$	16.6373	+	12.0877i	0.584214	+	0.424456i	0.840241	−	0.542213i	$-0.182414\pi$
$811$	16.6373	+	12.0877i	0.584214	+	0.424456i	−0.256027	+	0.966670i	$0.582414\pi$
$812$	−0.378952	+	7.49774i	−0.0132986	+	0.263119i
$813$	73.6596			2.58336
$814$		0			0
$815$	10.3320	+	17.8956i	0.361915	+	0.626856i
$816$	34.5567	−	38.3791i	1.20973	−	1.34354i
$817$	0.837010	−	0.372661i	0.0292833	−	0.0130378i
$818$	7.94693	−	5.77378i	0.277858	−	0.201876i
$819$	−2.55568	−	0.399907i	−0.0893028	−	0.0139739i
$820$	0.107320	−	0.330298i	0.00374779	−	0.0115345i
$821$	−0.665091	−	6.32792i	−0.0232118	−	0.220846i	−0.999979	−	0.00654084i	$-0.997918\pi$
$821$	−0.665091	−	6.32792i	−0.0232118	−	0.220846i	0.976767	−	0.214305i	$-0.0687487\pi$
$822$	−7.53857	+	71.7247i	−0.262938	+	2.50169i
$823$	−1.67876	+	1.86445i	−0.0585179	+	0.0649907i	−0.771693	−	0.635995i	$-0.780590\pi$
$823$	−1.67876	+	1.86445i	−0.0585179	+	0.0649907i	0.713175	+	0.700986i	$0.247256\pi$
$824$	−1.16637	+	2.02022i	−0.0406326	+	0.0703777i
$825$		0			0
$826$	−0.642903	+	0.522597i	−0.0223695	+	0.0181835i
$827$	−12.7514	−	39.2448i	−0.443410	−	1.36468i	−0.884218	−	0.467075i	$-0.845308\pi$
$827$	−12.7514	−	39.2448i	−0.443410	−	1.36468i	0.440808	−	0.897602i	$-0.354692\pi$
$828$	14.0251	−	6.24436i	0.487405	−	0.217007i
$829$	−42.7337	−	19.0263i	−1.48420	−	0.660810i	−0.504894	−	0.863181i	$-0.668469\pi$
$829$	−42.7337	−	19.0263i	−1.48420	−	0.660810i	−0.979309	+	0.202371i	$0.935135\pi$
$830$	11.8019	−	2.50858i	0.409652	−	0.0870741i
$831$	−29.5895	−	32.8625i	−1.02645	−	1.13999i
$832$	0.922453	−	0.670202i	0.0319803	−	0.0232351i
$833$	−26.1369	−	8.38498i	−0.905588	−	0.290522i
$834$	28.2591	+	86.9726i	0.978533	+	3.01162i
$835$	−9.83796	+	17.0399i	−0.340457	+	0.589688i
$836$		0			0
$837$	−8.74897	−	15.1537i	−0.302409	−	0.523787i
$838$	2.42912	+	0.516326i	0.0839127	+	0.0178362i
$839$	−13.3843	−	9.72429i	−0.462079	−	0.335720i	0.332268	−	0.943185i	$-0.392186\pi$
$839$	−13.3843	−	9.72429i	−0.462079	−	0.335720i	−0.794346	+	0.607465i	$0.792186\pi$
$840$	−11.6376	+	43.7578i	−0.401537	+	1.50979i
$841$	11.6663	−	35.9051i	0.402286	−	1.23811i
$842$	−31.9328	−	35.4650i	−1.10048	−	1.22220i
$843$	50.6467	+	22.5494i	1.74437	+	0.776642i
$844$	−0.153967	+	1.46489i	−0.00529975	+	0.0504237i
$845$	29.7696	+	6.32773i	1.02411	+	0.217681i
$846$	62.2550			2.14037
$847$		0			0
$848$	−29.9796			−1.02950
$849$	76.2279	+	16.2027i	2.61613	+	0.556077i
$850$	−0.320144	+	3.04597i	−0.0109809	+	0.104476i
$851$	−52.0776	−	23.1864i	−1.78520	−	0.794820i
$852$	−6.66846	−	7.40607i	−0.228458	−	0.253728i
$853$	4.08405	−	12.5694i	0.139835	−	0.430368i	−0.856476	−	0.516187i	$-0.827351\pi$
$853$	4.08405	−	12.5694i	0.139835	−	0.430368i	0.996311	+	0.0858193i	$0.0273508\pi$
$854$	−57.0648	+	15.4043i	−1.95272	+	0.527125i
$855$	−7.76981	−	5.64509i	−0.265722	−	0.193058i
$856$	25.6277	+	5.44734i	0.875938	+	0.186186i
$857$	25.3606	+	43.9258i	0.866300	+	1.50048i	0.865750	+	0.500476i	$0.166842\pi$
$857$	25.3606	+	43.9258i	0.866300	+	1.50048i	0.000549663		1.00000i	$0.499825\pi$
$858$		0			0
$859$	−27.5562	+	47.7287i	−0.940205	+	1.62848i	−0.175126	+	0.984546i	$0.556033\pi$
$859$	−27.5562	+	47.7287i	−0.940205	+	1.62848i	−0.765079	+	0.643937i	$0.777300\pi$
$860$	0.298465	+	0.918580i	0.0101776	+	0.0313233i
$861$	1.77268	+	2.71861i	0.0604129	+	0.0926499i
$862$	42.4004	−	30.8057i	1.44416	−	1.04924i
$863$	7.03941	+	7.81805i	0.239624	+	0.266130i	0.850947	−	0.525252i	$-0.176029\pi$
$863$	7.03941	+	7.81805i	0.239624	+	0.266130i	−0.611323	+	0.791381i	$0.709362\pi$
$864$	−12.5401	+	2.66548i	−0.426623	+	0.0906815i
$865$	11.6774	+	5.19911i	0.397043	+	0.176775i
$866$	28.6896	−	12.7734i	0.974912	−	0.434059i
$867$	−1.44465	−	4.44618i	−0.0490630	−	0.151000i
$868$	0.385782	+	2.40674i	0.0130943	+	0.0816901i
$869$		0			0
$870$	−42.3016	+	73.2685i	−1.43416	+	2.48404i
$871$	−0.464773	+	0.516183i	−0.0157482	+	0.0174902i
$872$	−0.125893	+	1.19780i	−0.00426329	+	0.0405625i
$873$	−7.25630	−	69.0390i	−0.245588	−	2.33662i
$874$	−3.05895	+	9.41449i	−0.103471	+	0.318450i
$875$	10.0418	+	26.0150i	0.339474	+	0.879466i
$876$	−0.0975794	+	0.0708956i	−0.00329690	+	0.00239534i
$877$	−36.2254	+	16.1286i	−1.22324	+	0.544624i	−0.913750	−	0.406277i	$-0.866827\pi$
$877$	−36.2254	+	16.1286i	−1.22324	+	0.544624i	−0.309495	+	0.950901i	$0.600160\pi$
$878$	−32.1101	+	35.6619i	−1.08366	+	1.20353i
$879$	−5.80928	−	10.0620i	−0.195942	−	0.339382i
$880$		0			0
$881$	25.0077			0.842532			0.421266	−	0.906937i	$-0.361586\pi$
$881$	25.0077			0.842532			0.421266	+	0.906937i	$0.361586\pi$
$882$	33.5230	+	45.7812i	1.12878	+	1.54153i
$883$	−41.2065	−	29.9383i	−1.38671	−	1.00750i	−0.996217	−	0.0868978i	$-0.972305\pi$
$883$	−41.2065	−	29.9383i	−1.38671	−	1.00750i	−0.390493	−	0.920606i	$-0.627695\pi$
$884$	−0.0263055	−	0.250280i	−0.000884749	−	0.00841783i
$885$	−1.35126	+	0.287218i	−0.0454220	+	0.00965474i
$886$	−44.0559	+	9.36437i	−1.48009	+	0.314602i
$887$	−3.34868	−	31.8605i	−0.112438	−	1.06977i	−0.894652	−	0.446763i	$-0.852577\pi$
$887$	−3.34868	−	31.8605i	−0.112438	−	1.06977i	0.782215	−	0.623009i	$-0.214090\pi$
$888$	40.2447	+	29.2395i	1.35052	+	0.981212i
$889$	−0.989991	−	0.640292i	−0.0332032	−	0.0214747i
$890$	16.7324			0.560870
$891$		0			0
$892$	3.13176	+	5.42437i	0.104859	+	0.181621i
$893$	−3.97405	+	4.41363i	−0.132986	+	0.147696i
$894$	2.87826	−	1.28148i	0.0962633	−	0.0428592i
$895$	19.1638	−	13.9233i	0.640576	−	0.465406i
$896$	−34.8713	−	5.45658i	−1.16497	−	0.182291i
$897$	−1.37377	+	4.22804i	−0.0458689	+	0.141170i
$898$	−1.10513	−	10.5146i	−0.0368787	−	0.350878i
$899$	2.26547	−	21.5545i	0.0755577	−	0.718883i
$900$	0.626812	−	0.696145i	0.0208937	−	0.0232048i
$901$	12.8508	−	22.2582i	0.428121	−	0.741527i
$902$		0			0
$903$	−8.43242	−	3.21891i	−0.280613	−	0.107119i
$904$	−2.45919	−	7.56861i	−0.0817915	−	0.251728i
$905$	42.6286	−	18.9795i	1.41702	−	0.630899i
$906$	38.4667	+	17.1265i	1.27797	+	0.568989i
$907$	16.1130	−	3.42492i	0.535023	−	0.113723i	0.0675264	−	0.997717i	$-0.478489\pi$
$907$	16.1130	−	3.42492i	0.535023	−	0.113723i	0.467497	+	0.883995i	$0.345156\pi$
$908$	4.23067	+	4.69864i	0.140400	+	0.155930i
$909$	25.2615	−	18.3536i	0.837871	−	0.608749i
$910$	0.960364	+	1.47282i	0.0318358	+	0.0488236i
$911$	−14.0287	−	43.1759i	−0.464792	−	1.43048i	−0.859244	−	0.511566i	$-0.829066\pi$
$911$	−14.0287	−	43.1759i	−0.464792	−	1.43048i	0.394452	−	0.918916i	$-0.370934\pi$
$912$	5.09240	−	8.82029i	0.168626	−	0.292069i
$913$		0			0
$914$	9.47952	+	16.4190i	0.313555	+	0.543093i
$915$	−96.4008	−	20.4906i	−3.18691	−	0.677399i
$916$	−5.40618	−	3.92782i	−0.178625	−	0.129779i
$917$	22.6537	+	22.5696i	0.748092	+	0.745314i
$918$	12.2459	−	37.6891i	0.404176	−	1.24393i
$919$	−8.24428	−	9.15620i	−0.271954	−	0.302035i	0.591662	−	0.806186i	$-0.298472\pi$
$919$	−8.24428	−	9.15620i	−0.271954	−	0.302035i	−0.863615	+	0.504151i	$0.831805\pi$
$920$	45.3655	+	20.1980i	1.49566	+	0.665909i
$921$	−0.881568	+	8.38756i	−0.0290487	+	0.276380i
$922$	30.1134	+	6.40079i	0.991731	+	0.210799i
$923$	1.84161			0.0606175
$924$		0			0
$925$	−3.47834			−0.114367
$926$	13.0258	+	2.76871i	0.428053	+	0.0909855i
$927$	−0.509507	+	4.84763i	−0.0167344	+	0.159217i
$928$	−14.5065	−	6.45873i	−0.476201	−	0.212018i
$929$	3.97004	+	4.40918i	0.130253	+	0.144660i	0.804743	−	0.593623i	$-0.202303\pi$
$929$	3.97004	+	4.40918i	0.130253	+	0.144660i	−0.674490	+	0.738284i	$0.735636\pi$
$930$	−8.48834	+	26.1244i	−0.278344	+	0.856654i
$931$	−5.38564	−	0.545799i	−0.176507	−	0.0178878i
$932$	−2.62003	−	1.90357i	−0.0858221	−	0.0623534i
$933$	−44.0033	−	9.35320i	−1.44060	−	0.306210i
$934$	3.65342	+	6.32791i	0.119544	+	0.207055i
$935$		0			0
$936$	1.23783	−	2.14398i	0.0404596	−	0.0700781i
$937$	−13.9132	−	42.8205i	−0.454525	−	1.39889i	−0.871691	−	0.490055i	$-0.836977\pi$
$937$	−13.9132	−	42.8205i	−0.454525	−	1.39889i	0.417166	−	0.908830i	$-0.363023\pi$
$938$	15.2139	−	0.825714i	0.496751	−	0.0269605i
$939$	51.1924	−	37.1934i	1.67060	−	1.21376i
$940$	−4.18931	−	4.65270i	−0.136640	−	0.151754i
$941$	5.92994	−	1.26045i	0.193311	−	0.0410895i	−0.110239	−	0.993905i	$-0.535162\pi$
$941$	5.92994	−	1.26045i	0.193311	−	0.0410895i	0.303549	+	0.952816i	$0.401828\pi$
$942$	−37.2429	−	16.5816i	−1.21344	−	0.540258i
$943$	3.25170	−	1.44775i	0.105890	−	0.0471452i
$944$	−0.288896	−	0.889132i	−0.00940278	−	0.0289388i
$945$	6.48364	+	40.4489i	0.210913	+	1.31580i
$946$		0			0
$947$	9.47131	−	16.4048i	0.307776	−	0.533084i	−0.670099	−	0.742272i	$-0.733748\pi$
$947$	9.47131	−	16.4048i	0.307776	−	0.533084i	0.977876	+	0.209187i	$0.0670818\pi$
$948$	0.219271	−	0.243526i	0.00712160	−	0.00790934i
$949$	0.00232980	−	0.0221666i	7.56286e−5	−	0.000719558i
$950$	0.0631360	+	0.600699i	0.00204840	+	0.0194892i
$951$	−2.67989	+	8.24785i	−0.0869014	+	0.267455i
$952$	16.4940	−	20.4461i	0.534575	−	0.662663i
$953$	10.1103	−	7.34556i	0.327504	−	0.237946i	−0.411867	−	0.911244i	$-0.635123\pi$
$953$	10.1103	−	7.34556i	0.327504	−	0.237946i	0.739371	+	0.673298i	$0.235123\pi$
$954$	−48.5369	+	21.6100i	−1.57144	+	0.699650i
$955$	−39.8710	+	44.2812i	−1.29020	+	1.43291i
$956$	−1.94310	−	3.36554i	−0.0628442	−	0.108849i
$957$		0			0
$958$	60.6923			1.96088
$959$	−2.18333	+	43.1982i	−0.0705035	+	1.39494i
$960$	−33.7387	−	24.5126i	−1.08891	−	0.791140i
$961$	2.50483	+	23.8319i	0.0808011	+	0.768771i
$962$	1.88949	−	0.401624i	0.0609196	−	0.0129489i
$963$	53.5498	−	11.3824i	1.72562	−	0.366791i
$964$	−0.733467	−	6.97847i	−0.0236234	−	0.224761i
$965$	14.6820	+	10.6671i	0.472630	+	0.343386i
$966$	86.8059	−	44.4335i	2.79293	−	1.42962i
$967$	−18.5294			−0.595865			−0.297933	−	0.954587i	$-0.596297\pi$
$967$	−18.5294			−0.595865			−0.297933	+	0.954587i	$0.596297\pi$
$968$		0			0
$969$	4.36571	+	7.56164i	0.140247	+	0.242915i
$970$	−31.5731	+	35.0655i	−1.01375	+	1.12588i
$971$	37.8883	−	16.8690i	1.21589	−	0.541350i	0.304352	−	0.952560i	$-0.401560\pi$
$971$	37.8883	−	16.8690i	1.21589	−	0.541350i	0.911541	+	0.411209i	$0.134893\pi$
$972$	3.03540	−	2.20535i	0.0973606	−	0.0707366i
$973$	19.7501	+	51.1661i	0.633160	+	1.64031i
$974$	−2.44092	+	7.51238i	−0.0782121	+	0.240712i
$975$	0.0283543	+	0.269773i	0.000908064	+	0.00863965i
$976$	6.97168	−	66.3311i	0.223158	−	2.12321i
$977$	−14.8762	+	16.5216i	−0.475930	+	0.528574i	−0.932527	−	0.361100i	$-0.882401\pi$
$977$	−14.8762	+	16.5216i	−0.475930	+	0.528574i	0.456597	+	0.889674i	$0.349068\pi$
$978$	−19.4179	+	33.6327i	−0.620915	+	1.07546i
$979$		0			0
$980$	1.16566	−	5.58613i	0.0372356	−	0.178442i
$981$	0.777674	+	2.39344i	0.0248292	+	0.0764165i
$982$	−14.2658	+	6.35155i	−0.455240	+	0.202686i
$983$	32.3508	+	14.4035i	1.03183	+	0.459401i	0.851583	−	0.524220i	$-0.175643\pi$
$983$	32.3508	+	14.4035i	1.03183	+	0.459401i	0.180249	+	0.983621i	$0.442310\pi$
$984$	−3.03819	+	0.645788i	−0.0968540	+	0.0205870i
$985$	−8.44166	−	9.37542i	−0.268974	−	0.298726i
$986$	39.7104	−	28.8513i	1.26464	−	0.918812i
$987$	58.4217	−	3.17076i	1.85958	−	0.100926i
$988$	−0.0153365	−	0.0472008i	−0.000487918	−	0.00150166i
$989$	−4.94949	+	8.57277i	−0.157385	+	0.272598i
$990$		0			0
$991$	−22.7863	−	39.4670i	−0.723830	−	1.25371i	−0.959454	−	0.281866i	$-0.909047\pi$
$991$	−22.7863	−	39.4670i	−0.723830	−	1.25371i	0.235624	−	0.971844i	$-0.424287\pi$
$992$	−5.04303	−	1.07193i	−0.160116	−	0.0340338i
$993$	−63.9879	−	46.4899i	−2.03059	−	1.47531i
$994$	−28.6180	−	28.5117i	−0.907707	−	0.904336i
$995$	6.36938	−	19.6029i	0.201923	−	0.621455i
$996$	2.24496	+	2.49328i	0.0711342	+	0.0790026i
$997$	20.8623	+	9.28851i	0.660717	+	0.294170i	0.709569	−	0.704636i	$-0.248890\pi$
$997$	20.8623	+	9.28851i	0.660717	+	0.294170i	−0.0488521	+	0.998806i	$0.515556\pi$
$998$	0.943235	−	8.97429i	0.0298576	−	0.284076i
$999$	44.0225	+	9.35727i	1.39281	+	0.296051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.g.632.3		24
7.4	even	3	inner	847.2.n.g.753.1		24
11.2	odd	10		847.2.n.f.9.3		24
11.3	even	5		77.2.e.a.23.3	✓	6
11.4	even	5	inner	847.2.n.g.366.3		24
11.5	even	5	inner	847.2.n.g.807.1		24
11.6	odd	10		847.2.n.f.807.3		24
11.7	odd	10		847.2.n.f.366.1		24
11.8	odd	10		847.2.e.c.485.1		6
11.9	even	5	inner	847.2.n.g.9.1		24
11.10	odd	2		847.2.n.f.632.1		24
33.14	odd	10		693.2.i.h.100.1		6
44.3	odd	10		1232.2.q.m.177.3		6
77.3	odd	30		539.2.e.m.67.3		6
77.4	even	15	inner	847.2.n.g.487.1		24
77.18	odd	30		847.2.n.f.487.3		24
77.19	even	30		5929.2.a.u.1.3		3
77.25	even	15		77.2.e.a.67.3	yes	6
77.30	odd	30		5929.2.a.x.1.3		3
77.32	odd	6		847.2.n.f.753.3		24
77.39	odd	30		847.2.n.f.81.1		24
77.46	odd	30		847.2.n.f.130.1		24
77.47	odd	30		539.2.a.g.1.1		3
77.53	even	15	inner	847.2.n.g.130.3		24
77.58	even	15		539.2.a.j.1.1		3
77.60	even	15	inner	847.2.n.g.81.3		24
77.69	odd	10		539.2.e.m.177.3		6
77.74	odd	30		847.2.e.c.606.1		6
231.47	even	30		4851.2.a.bk.1.3		3
231.179	odd	30		693.2.i.h.298.1		6
231.212	odd	30		4851.2.a.bj.1.3		3
308.47	even	30		8624.2.a.co.1.3		3
308.135	odd	30		8624.2.a.ch.1.1		3
308.179	odd	30		1232.2.q.m.529.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.3	✓	6	11.3	even	5
77.2.e.a.67.3	yes	6	77.25	even	15
539.2.a.g.1.1		3	77.47	odd	30
539.2.a.j.1.1		3	77.58	even	15
539.2.e.m.67.3		6	77.3	odd	30
539.2.e.m.177.3		6	77.69	odd	10
693.2.i.h.100.1		6	33.14	odd	10
693.2.i.h.298.1		6	231.179	odd	30
847.2.e.c.485.1		6	11.8	odd	10
847.2.e.c.606.1		6	77.74	odd	30
847.2.n.f.9.3		24	11.2	odd	10
847.2.n.f.81.1		24	77.39	odd	30
847.2.n.f.130.1		24	77.46	odd	30
847.2.n.f.366.1		24	11.7	odd	10
847.2.n.f.487.3		24	77.18	odd	30
847.2.n.f.632.1		24	11.10	odd	2
847.2.n.f.753.3		24	77.32	odd	6
847.2.n.f.807.3		24	11.6	odd	10
847.2.n.g.9.1		24	11.9	even	5	inner
847.2.n.g.81.3		24	77.60	even	15	inner
847.2.n.g.130.3		24	77.53	even	15	inner
847.2.n.g.366.3		24	11.4	even	5	inner
847.2.n.g.487.1		24	77.4	even	15	inner
847.2.n.g.632.3		24	1.1	even	1	trivial
847.2.n.g.753.1		24	7.4	even	3	inner
847.2.n.g.807.1		24	11.5	even	5	inner
1232.2.q.m.177.3		6	44.3	odd	10
1232.2.q.m.529.3		6	308.179	odd	30
4851.2.a.bj.1.3		3	231.212	odd	30
4851.2.a.bk.1.3		3	231.47	even	30
5929.2.a.u.1.3		3	77.19	even	30
5929.2.a.x.1.3		3	77.30	odd	30
8624.2.a.ch.1.1		3	308.135	odd	30
8624.2.a.co.1.3		3	308.47	even	30

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.49861 + 0.318539i) q^{2} +(-0.300978 + 2.86361i) q^{3} +(0.317271 + 0.141258i) q^{4} +(1.57065 + 1.74438i) q^{5} +(-1.36322 + 4.19556i) q^{6} +(-0.680015 + 2.55687i) q^{7} +(-2.04850 - 1.48832i) q^{8} +(-5.17524 - 1.10003i) q^{9} +(1.79813 + 3.11446i) q^{10} +(-0.500000 + 0.866025i) q^{12} +(-0.0571040 - 0.175748i) q^{13} +(-1.83354 + 3.61514i) q^{14} +(-5.46796 + 3.97271i) q^{15} +(-3.06059 - 3.39913i) q^{16} +(3.83559 - 0.815279i) q^{17} +(-7.40526 - 3.29703i) q^{18} +(0.706462 - 0.314537i) q^{19} +(0.251913 + 0.775308i) q^{20} +(-7.11721 - 2.71686i) q^{21} +(-4.17752 + 7.23567i) q^{23} +(4.87854 - 5.41816i) q^{24} +(-0.0532886 + 0.507007i) q^{25} +(-0.0295940 - 0.281568i) q^{26} +(2.03836 - 6.27342i) q^{27} +(-0.576928 + 0.715163i) q^{28} +(6.60987 - 4.80235i) q^{29} +(-9.45980 + 4.21177i) q^{30} +(1.77501 - 1.97134i) q^{31} +(-0.971782 - 1.68317i) q^{32} +6.00774 q^{34} +(-5.52822 + 2.82974i) q^{35} +(-1.48657 - 1.08005i) q^{36} +(0.713192 + 6.78557i) q^{37} +(1.15890 - 0.246332i) q^{38} +(0.520461 - 0.110628i) q^{39} +(-0.621272 - 5.91100i) q^{40} +(-0.344659 - 0.250409i) q^{41} +(-9.80049 - 6.33862i) q^{42} +1.18479 q^{43} +(-6.20961 - 10.7554i) q^{45} +(-8.56531 + 9.51274i) q^{46} +(-7.01607 + 3.12376i) q^{47} +(10.6550 - 7.74128i) q^{48} +(-6.07516 - 3.47742i) q^{49} +(-0.241361 + 0.742831i) q^{50} +(1.18022 + 11.2290i) q^{51} +(0.00670840 - 0.0638262i) q^{52} +(4.38573 - 4.87085i) q^{53} +(5.05303 - 8.75211i) q^{54} +(5.19846 - 4.22567i) q^{56} +(0.688082 + 2.11770i) q^{57} +(11.4353 - 5.09134i) q^{58} +(0.186722 + 0.0831341i) q^{59} +(-2.29600 + 0.488030i) q^{60} +(9.75707 + 10.8363i) q^{61} +(3.28799 - 2.38886i) q^{62} +(6.33188 - 12.4844i) q^{63} +(1.90671 + 5.86825i) q^{64} +(0.216881 - 0.375650i) q^{65} +(-1.87939 - 3.25519i) q^{67} +(1.33208 + 0.283143i) q^{68} +(-19.4628 - 14.1406i) q^{69} +(-9.18602 + 2.47971i) q^{70} +(-3.07962 + 9.47809i) q^{71} +(8.96429 + 9.95586i) q^{72} +(0.110187 + 0.0490584i) q^{73} +(-1.09267 + 10.3961i) q^{74} +(-1.43583 - 0.305196i) q^{75} +0.268571 q^{76} +0.815207 q^{78} +(-0.320535 - 0.0681318i) q^{79} +(1.12227 - 10.6777i) q^{80} +(2.85082 + 1.26927i) q^{81} +(-0.436744 - 0.485053i) q^{82} +(1.03676 - 3.19083i) q^{83} +(-1.87431 - 1.86734i) q^{84} +(7.44651 + 5.41021i) q^{85} +(1.77554 + 0.377403i) q^{86} +(11.7626 + 20.3735i) q^{87} +(2.32635 - 4.02936i) q^{89} +(-5.87977 - 18.0961i) q^{90} +(0.488197 - 0.0264962i) q^{91} +(-2.34750 + 1.70556i) q^{92} +(5.11092 + 5.67626i) q^{93} +(-11.5094 + 2.44640i) q^{94} +(1.65827 + 0.738311i) q^{95} +(5.11244 - 2.27621i) q^{96} +(4.05449 + 12.4784i) q^{97} +(-7.99660 - 7.14647i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} + 6 q^{5} + 6 q^{6} - 6 q^{8} - 12 q^{10} - 12 q^{12} - 6 q^{13} + 12 q^{14} - 18 q^{15} - 6 q^{16} - 3 q^{17} - 12 q^{18} + 9 q^{19} - 12 q^{20} - 48 q^{21} + 6 q^{24} + 3 q^{25} + 9 q^{26}+ \cdots - 24 q^{98}+O(q^{100}) \) 24 * q + 3 * q^3 + 6 * q^5 + 6 * q^6 - 6 * q^8 - 12 * q^10 - 12 * q^12 - 6 * q^13 + 12 * q^14 - 18 * q^15 - 6 * q^16 - 3 * q^17 - 12 * q^18 + 9 * q^19 - 12 * q^20 - 48 * q^21 + 6 * q^24 + 3 * q^25 + 9 * q^26 - 12 * q^27 - 3 * q^28 + 6 * q^29 - 6 * q^30 + 9 * q^31 + 36 * q^32 - 48 * q^34 + 15 * q^35 - 6 * q^36 + 3 * q^39 + 3 * q^40 - 18 * q^41 + 18 * q^42 - 12 * q^45 - 24 * q^46 - 3 * q^47 + 36 * q^48 - 30 * q^50 - 18 * q^51 + 9 * q^52 + 9 * q^53 + 72 * q^54 + 12 * q^56 + 15 * q^58 + 6 * q^60 + 12 * q^61 + 6 * q^62 - 6 * q^63 + 6 * q^64 - 60 * q^65 - 21 * q^68 - 42 * q^69 - 45 * q^70 + 18 * q^71 + 12 * q^72 + 6 * q^73 + 18 * q^74 + 9 * q^75 - 72 * q^76 + 48 * q^78 - 3 * q^79 - 27 * q^80 + 15 * q^81 - 3 * q^82 + 30 * q^83 + 54 * q^85 - 9 * q^86 + 96 * q^87 + 60 * q^89 + 72 * q^90 - 9 * q^91 + 6 * q^92 + 6 * q^93 + 9 * q^95 + 3 * q^96 - 90 * q^97 - 24 * q^98

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