LMFDB - Embedded newform 1210.2.b.j.969.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1210,2,Mod(969,1210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1210, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1210.969");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1210 = 2 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1210.b (of order $2$, degree $1$, 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:	$9.66189864457$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			969.4
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1210.969
Dual form			1210.2.b.j.969.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +0.732051i q^{3} -1.00000 q^{4} +(0.133975 + 2.23205i) q^{5} -0.732051 q^{6} +1.26795i q^{7} -1.00000i q^{8} +2.46410 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +0.732051i q^{3} -1.00000 q^{4} +(0.133975 + 2.23205i) q^{5} -0.732051 q^{6} +1.26795i q^{7} -1.00000i q^{8} +2.46410 q^{9} +(-2.23205 + 0.133975i) q^{10} -0.732051i q^{12} +2.46410i q^{13} -1.26795 q^{14} +(-1.63397 + 0.0980762i) q^{15} +1.00000 q^{16} +1.73205i q^{17} +2.46410i q^{18} -4.19615 q^{19} +(-0.133975 - 2.23205i) q^{20} -0.928203 q^{21} +2.73205i q^{23} +0.732051 q^{24} +(-4.96410 + 0.598076i) q^{25} -2.46410 q^{26} +4.00000i q^{27} -1.26795i q^{28} +3.73205 q^{29} +(-0.0980762 - 1.63397i) q^{30} +8.73205 q^{31} +1.00000i q^{32} -1.73205 q^{34} +(-2.83013 + 0.169873i) q^{35} -2.46410 q^{36} +7.92820i q^{37} -4.19615i q^{38} -1.80385 q^{39} +(2.23205 - 0.133975i) q^{40} -10.4641 q^{41} -0.928203i q^{42} -9.46410i q^{43} +(0.330127 + 5.50000i) q^{45} -2.73205 q^{46} -6.73205i q^{47} +0.732051i q^{48} +5.39230 q^{49} +(-0.598076 - 4.96410i) q^{50} -1.26795 q^{51} -2.46410i q^{52} +3.00000i q^{53} -4.00000 q^{54} +1.26795 q^{56} -3.07180i q^{57} +3.73205i q^{58} -13.8564 q^{59} +(1.63397 - 0.0980762i) q^{60} -8.92820 q^{61} +8.73205i q^{62} +3.12436i q^{63} -1.00000 q^{64} +(-5.50000 + 0.330127i) q^{65} -7.26795i q^{67} -1.73205i q^{68} -2.00000 q^{69} +(-0.169873 - 2.83013i) q^{70} +6.92820 q^{71} -2.46410i q^{72} -12.9282i q^{73} -7.92820 q^{74} +(-0.437822 - 3.63397i) q^{75} +4.19615 q^{76} -1.80385i q^{78} -7.26795 q^{79} +(0.133975 + 2.23205i) q^{80} +4.46410 q^{81} -10.4641i q^{82} +3.26795i q^{83} +0.928203 q^{84} +(-3.86603 + 0.232051i) q^{85} +9.46410 q^{86} +2.73205i q^{87} -0.464102 q^{89} +(-5.50000 + 0.330127i) q^{90} -3.12436 q^{91} -2.73205i q^{92} +6.39230i q^{93} +6.73205 q^{94} +(-0.562178 - 9.36603i) q^{95} -0.732051 q^{96} +17.1962i q^{97} +5.39230i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{9} - 2 q^{10} - 12 q^{14} - 10 q^{15} + 4 q^{16} + 4 q^{19} - 4 q^{20} + 24 q^{21} - 4 q^{24} - 6 q^{25} + 4 q^{26} + 8 q^{29} + 10 q^{30} + 28 q^{31} + 6 q^{35} + 4 q^{36} - 28 q^{39} + 2 q^{40} - 28 q^{41} - 16 q^{45} - 4 q^{46} - 20 q^{49} + 8 q^{50} - 12 q^{51} - 16 q^{54} + 12 q^{56} + 10 q^{60} - 8 q^{61} - 4 q^{64} - 22 q^{65} - 8 q^{69} - 18 q^{70} - 4 q^{74} - 26 q^{75} - 4 q^{76} - 36 q^{79} + 4 q^{80} + 4 q^{81} - 24 q^{84} - 12 q^{85} + 24 q^{86} + 12 q^{89} - 22 q^{90} + 36 q^{91} + 20 q^{94} + 22 q^{95} + 4 q^{96}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^9 - 2 * q^10 - 12 * q^14 - 10 * q^15 + 4 * q^16 + 4 * q^19 - 4 * q^20 + 24 * q^21 - 4 * q^24 - 6 * q^25 + 4 * q^26 + 8 * q^29 + 10 * q^30 + 28 * q^31 + 6 * q^35 + 4 * q^36 - 28 * q^39 + 2 * q^40 - 28 * q^41 - 16 * q^45 - 4 * q^46 - 20 * q^49 + 8 * q^50 - 12 * q^51 - 16 * q^54 + 12 * q^56 + 10 * q^60 - 8 * q^61 - 4 * q^64 - 22 * q^65 - 8 * q^69 - 18 * q^70 - 4 * q^74 - 26 * q^75 - 4 * q^76 - 36 * q^79 + 4 * q^80 + 4 * q^81 - 24 * q^84 - 12 * q^85 + 24 * q^86 + 12 * q^89 - 22 * q^90 + 36 * q^91 + 20 * q^94 + 22 * q^95 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1210\mathbb{Z}\right)^\times$.

$n$	$727$	$1091$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			0.732051i			0.422650i	0.977416	+	0.211325i	$0.0677778\pi$
$3$			0.732051i			0.422650i	−0.977416	+	0.211325i	$0.932222\pi$
$4$	−1.00000			−0.500000
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$	−0.732051			−0.298858
$7$			1.26795i			0.479240i	0.970867	+	0.239620i	$0.0770228\pi$
$7$			1.26795i			0.479240i	−0.970867	+	0.239620i	$0.922977\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.46410			0.821367
$10$	−2.23205	+	0.133975i	−0.705836	+	0.0423665i
$11$		0			0
$11$		0			0
$12$		−	0.732051i		−	0.211325i
$13$			2.46410i			0.683419i	0.939806	+	0.341709i	$0.111006\pi$
$13$			2.46410i			0.683419i	−0.939806	+	0.341709i	$0.888994\pi$
$14$	−1.26795			−0.338874
$15$	−1.63397	+	0.0980762i	−0.421890	+	0.0253232i
$16$	1.00000			0.250000
$17$			1.73205i			0.420084i	0.977692	+	0.210042i	$0.0673601\pi$
$17$			1.73205i			0.420084i	−0.977692	+	0.210042i	$0.932640\pi$
$18$			2.46410i			0.580794i
$19$	−4.19615			−0.962663			−0.481332	−	0.876539i	$-0.659847\pi$
$19$	−4.19615			−0.962663			−0.481332	+	0.876539i	$0.659847\pi$
$20$	−0.133975	−	2.23205i	−0.0299576	−	0.499102i
$21$	−0.928203			−0.202551
$22$		0			0
$23$			2.73205i			0.569672i	0.958576	+	0.284836i	$0.0919391\pi$
$23$			2.73205i			0.569672i	−0.958576	+	0.284836i	$0.908061\pi$
$24$	0.732051			0.149429
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	−2.46410			−0.483250
$27$			4.00000i			0.769800i
$28$		−	1.26795i		−	0.239620i
$29$	3.73205			0.693024			0.346512	−	0.938045i	$-0.387366\pi$
$29$	3.73205			0.693024			0.346512	+	0.938045i	$0.387366\pi$
$30$	−0.0980762	−	1.63397i	−0.0179062	−	0.298322i
$31$	8.73205			1.56832			0.784161	−	0.620557i	$-0.213093\pi$
$31$	8.73205			1.56832			0.784161	+	0.620557i	$0.213093\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−1.73205			−0.297044
$35$	−2.83013	+	0.169873i	−0.478379	+	0.0287138i
$36$	−2.46410			−0.410684
$37$			7.92820i			1.30339i	0.758482	+	0.651694i	$0.225941\pi$
$37$			7.92820i			1.30339i	−0.758482	+	0.651694i	$0.774059\pi$
$38$		−	4.19615i		−	0.680706i
$39$	−1.80385			−0.288847
$40$	2.23205	−	0.133975i	0.352918	−	0.0211832i
$41$	−10.4641			−1.63422			−0.817109	−	0.576483i	$-0.804425\pi$
$41$	−10.4641			−1.63422			−0.817109	+	0.576483i	$0.804425\pi$
$42$		−	0.928203i		−	0.143225i
$43$		−	9.46410i		−	1.44326i	−0.692278	−	0.721631i	$-0.743393\pi$
$43$		−	9.46410i		−	1.44326i	0.692278	−	0.721631i	$-0.256607\pi$
$44$		0			0
$45$	0.330127	+	5.50000i	0.0492124	+	0.819892i
$46$	−2.73205			−0.402819
$47$		−	6.73205i		−	0.981971i	−0.871168	−	0.490985i	$-0.836637\pi$
$47$		−	6.73205i		−	0.981971i	0.871168	−	0.490985i	$-0.163363\pi$
$48$			0.732051i			0.105662i
$49$	5.39230			0.770329
$50$	−0.598076	−	4.96410i	−0.0845807	−	0.702030i
$51$	−1.26795			−0.177548
$52$		−	2.46410i		−	0.341709i
$53$			3.00000i			0.412082i	0.978543	+	0.206041i	$0.0660580\pi$
$53$			3.00000i			0.412082i	−0.978543	+	0.206041i	$0.933942\pi$
$54$	−4.00000			−0.544331
$55$		0			0
$56$	1.26795			0.169437
$57$		−	3.07180i		−	0.406869i
$58$			3.73205i			0.490042i
$59$	−13.8564			−1.80395			−0.901975	−	0.431788i	$-0.857883\pi$
$59$	−13.8564			−1.80395			−0.901975	+	0.431788i	$0.857883\pi$
$60$	1.63397	−	0.0980762i	0.210945	−	0.0126616i
$61$	−8.92820			−1.14314			−0.571570	−	0.820554i	$-0.693665\pi$
$61$	−8.92820			−1.14314			−0.571570	+	0.820554i	$0.693665\pi$
$62$			8.73205i			1.10897i
$63$			3.12436i			0.393632i
$64$	−1.00000			−0.125000
$65$	−5.50000	+	0.330127i	−0.682191	+	0.0409472i
$66$		0			0
$67$		−	7.26795i		−	0.887921i	−0.896046	−	0.443961i	$-0.853573\pi$
$67$		−	7.26795i		−	0.887921i	0.896046	−	0.443961i	$-0.146427\pi$
$68$		−	1.73205i		−	0.210042i
$69$	−2.00000			−0.240772
$70$	−0.169873	−	2.83013i	−0.0203037	−	0.338265i
$71$	6.92820			0.822226			0.411113	−	0.911584i	$-0.365140\pi$
$71$	6.92820			0.822226			0.411113	+	0.911584i	$0.365140\pi$
$72$		−	2.46410i		−	0.290397i
$73$		−	12.9282i		−	1.51313i	−0.653917	−	0.756566i	$-0.726876\pi$
$73$		−	12.9282i		−	1.51313i	0.653917	−	0.756566i	$-0.273124\pi$
$74$	−7.92820			−0.921635
$75$	−0.437822	−	3.63397i	−0.0505553	−	0.419615i
$76$	4.19615			0.481332
$77$		0			0
$78$		−	1.80385i		−	0.204246i
$79$	−7.26795			−0.817708			−0.408854	−	0.912600i	$-0.634072\pi$
$79$	−7.26795			−0.817708			−0.408854	+	0.912600i	$0.634072\pi$
$80$	0.133975	+	2.23205i	0.0149788	+	0.249551i
$81$	4.46410			0.496011
$82$		−	10.4641i		−	1.15557i
$83$			3.26795i			0.358704i	0.983785	+	0.179352i	$0.0574001\pi$
$83$			3.26795i			0.358704i	−0.983785	+	0.179352i	$0.942600\pi$
$84$	0.928203			0.101275
$85$	−3.86603	+	0.232051i	−0.419329	+	0.0251694i
$86$	9.46410			1.02054
$87$			2.73205i			0.292907i
$88$		0			0
$89$	−0.464102			−0.0491947			−0.0245973	−	0.999697i	$-0.507830\pi$
$89$	−0.464102			−0.0491947			−0.0245973	+	0.999697i	$0.507830\pi$
$90$	−5.50000	+	0.330127i	−0.579751	+	0.0347984i
$91$	−3.12436			−0.327521
$92$		−	2.73205i		−	0.284836i
$93$			6.39230i			0.662851i
$94$	6.73205			0.694358
$95$	−0.562178	−	9.36603i	−0.0576782	−	0.960934i
$96$	−0.732051			−0.0747146
$97$			17.1962i			1.74600i	0.487716	+	0.873002i	$0.337830\pi$
$97$			17.1962i			1.74600i	−0.487716	+	0.873002i	$0.662170\pi$
$98$			5.39230i			0.544705i
$99$		0			0
$100$	4.96410	−	0.598076i	0.496410	−	0.0598076i
$101$	10.0000			0.995037			0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000			0.995037			0.497519	+	0.867453i	$0.334245\pi$
$102$		−	1.26795i		−	0.125546i
$103$		−	8.00000i		−	0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$		−	8.00000i		−	0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$	2.46410			0.241625
$105$	−0.124356	−	2.07180i	−0.0121359	−	0.202187i
$106$	−3.00000			−0.291386
$107$			11.6603i			1.12724i	0.826034	+	0.563620i	$0.190592\pi$
$107$			11.6603i			1.12724i	−0.826034	+	0.563620i	$0.809408\pi$
$108$		−	4.00000i		−	0.384900i
$109$	−8.26795			−0.791926			−0.395963	−	0.918266i	$-0.629589\pi$
$109$	−8.26795			−0.791926			−0.395963	+	0.918266i	$0.629589\pi$
$110$		0			0
$111$	−5.80385			−0.550877
$112$			1.26795i			0.119810i
$113$			6.80385i			0.640052i	0.947409	+	0.320026i	$0.103692\pi$
$113$			6.80385i			0.640052i	−0.947409	+	0.320026i	$0.896308\pi$
$114$	3.07180			0.287700
$115$	−6.09808	+	0.366025i	−0.568649	+	0.0341320i
$116$	−3.73205			−0.346512
$117$			6.07180i			0.561338i
$118$		−	13.8564i		−	1.27559i
$119$	−2.19615			−0.201321
$120$	0.0980762	+	1.63397i	0.00895309	+	0.149161i
$121$		0			0
$122$		−	8.92820i		−	0.808322i
$123$		−	7.66025i		−	0.690702i
$124$	−8.73205			−0.784161
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	−3.12436			−0.278340
$127$			21.8564i			1.93944i	0.244215	+	0.969721i	$0.421470\pi$
$127$			21.8564i			1.93944i	−0.244215	+	0.969721i	$0.578530\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	6.92820			0.609994
$130$	−0.330127	−	5.50000i	−0.0289541	−	0.482382i
$131$	5.46410			0.477401			0.238700	−	0.971093i	$-0.423279\pi$
$131$	5.46410			0.477401			0.238700	+	0.971093i	$0.423279\pi$
$132$		0			0
$133$		−	5.32051i		−	0.461347i
$134$	7.26795			0.627855
$135$	−8.92820	+	0.535898i	−0.768417	+	0.0461228i
$136$	1.73205			0.148522
$137$			6.00000i			0.512615i	0.966595	+	0.256307i	$0.0825059\pi$
$137$			6.00000i			0.512615i	−0.966595	+	0.256307i	$0.917494\pi$
$138$		−	2.00000i		−	0.170251i
$139$	9.26795			0.786097			0.393049	−	0.919518i	$-0.371420\pi$
$139$	9.26795			0.786097			0.393049	+	0.919518i	$0.371420\pi$
$140$	2.83013	−	0.169873i	0.239189	−	0.0143569i
$141$	4.92820			0.415030
$142$			6.92820i			0.581402i
$143$		0			0
$144$	2.46410			0.205342
$145$	0.500000	+	8.33013i	0.0415227	+	0.691779i
$146$	12.9282			1.06995
$147$			3.94744i			0.325579i
$148$		−	7.92820i		−	0.651694i
$149$	13.5885			1.11321			0.556605	−	0.830777i	$-0.312104\pi$
$149$	13.5885			1.11321			0.556605	+	0.830777i	$0.312104\pi$
$150$	3.63397	−	0.437822i	0.296713	−	0.0357480i
$151$	10.9282			0.889325			0.444662	−	0.895698i	$-0.353324\pi$
$151$	10.9282			0.889325			0.444662	+	0.895698i	$0.353324\pi$
$152$			4.19615i			0.340353i
$153$			4.26795i			0.345043i
$154$		0			0
$155$	1.16987	+	19.4904i	0.0939665	+	1.56551i
$156$	1.80385			0.144423
$157$		−	10.0000i		−	0.798087i	−0.916932	−	0.399043i	$-0.869342\pi$
$157$		−	10.0000i		−	0.798087i	0.916932	−	0.399043i	$-0.130658\pi$
$158$		−	7.26795i		−	0.578207i
$159$	−2.19615			−0.174166
$160$	−2.23205	+	0.133975i	−0.176459	+	0.0105916i
$161$	−3.46410			−0.273009
$162$			4.46410i			0.350733i
$163$		−	9.12436i		−	0.714675i	−0.933975	−	0.357337i	$-0.883685\pi$
$163$		−	9.12436i		−	0.714675i	0.933975	−	0.357337i	$-0.116315\pi$
$164$	10.4641			0.817109
$165$		0			0
$166$	−3.26795			−0.253642
$167$		−	15.3205i		−	1.18554i	−0.805373	−	0.592768i	$-0.798035\pi$
$167$		−	15.3205i		−	1.18554i	0.805373	−	0.592768i	$-0.201965\pi$
$168$			0.928203i			0.0716124i
$169$	6.92820			0.532939
$170$	−0.232051	−	3.86603i	−0.0177975	−	0.296511i
$171$	−10.3397			−0.790700
$172$			9.46410i			0.721631i
$173$			6.53590i			0.496915i	0.968643	+	0.248458i	$0.0799237\pi$
$173$			6.53590i			0.496915i	−0.968643	+	0.248458i	$0.920076\pi$
$174$	−2.73205			−0.207116
$175$	−0.758330	−	6.29423i	−0.0573244	−	0.475799i
$176$		0			0
$177$		−	10.1436i		−	0.762439i
$178$		−	0.464102i		−	0.0347859i
$179$	21.8564			1.63362			0.816812	−	0.576904i	$-0.195739\pi$
$179$	21.8564			1.63362			0.816812	+	0.576904i	$0.195739\pi$
$180$	−0.330127	−	5.50000i	−0.0246062	−	0.409946i
$181$	−8.66025			−0.643712			−0.321856	−	0.946789i	$-0.604307\pi$
$181$	−8.66025			−0.643712			−0.321856	+	0.946789i	$0.604307\pi$
$182$		−	3.12436i		−	0.231593i
$183$		−	6.53590i		−	0.483148i
$184$	2.73205			0.201409
$185$	−17.6962	+	1.06218i	−1.30105	+	0.0780929i
$186$	−6.39230			−0.468707
$187$		0			0
$188$			6.73205i			0.490985i
$189$	−5.07180			−0.368919
$190$	9.36603	−	0.562178i	0.679483	−	0.0407847i
$191$	1.46410			0.105939			0.0529693	−	0.998596i	$-0.483131\pi$
$191$	1.46410			0.105939			0.0529693	+	0.998596i	$0.483131\pi$
$192$		−	0.732051i		−	0.0528312i
$193$		−	13.1962i		−	0.949880i	−0.880018	−	0.474940i	$-0.842470\pi$
$193$		−	13.1962i		−	0.949880i	0.880018	−	0.474940i	$-0.157530\pi$
$194$	−17.1962			−1.23461
$195$	−0.241670	−	4.02628i	−0.0173063	−	0.288328i
$196$	−5.39230			−0.385165
$197$			10.0718i			0.717586i	0.933417	+	0.358793i	$0.116812\pi$
$197$			10.0718i			0.717586i	−0.933417	+	0.358793i	$0.883188\pi$
$198$		0			0
$199$	13.0718			0.926635			0.463318	−	0.886192i	$-0.346659\pi$
$199$	13.0718			0.926635			0.463318	+	0.886192i	$0.346659\pi$
$200$	0.598076	+	4.96410i	0.0422904	+	0.351015i
$201$	5.32051			0.375280
$202$			10.0000i			0.703598i
$203$			4.73205i			0.332125i
$204$	1.26795			0.0887742
$205$	−1.40192	−	23.3564i	−0.0979146	−	1.63128i
$206$	8.00000			0.557386
$207$			6.73205i			0.467910i
$208$			2.46410i			0.170855i
$209$		0			0
$210$	2.07180	−	0.124356i	0.142968	−	0.00858136i
$211$	9.07180			0.624528			0.312264	−	0.949995i	$-0.398913\pi$
$211$	9.07180			0.624528			0.312264	+	0.949995i	$0.398913\pi$
$212$		−	3.00000i		−	0.206041i
$213$			5.07180i			0.347514i
$214$	−11.6603			−0.797079
$215$	21.1244	−	1.26795i	1.44067	−	0.0864734i
$216$	4.00000			0.272166
$217$			11.0718i			0.751603i
$218$		−	8.26795i		−	0.559976i
$219$	9.46410			0.639525
$220$		0			0
$221$	−4.26795			−0.287093
$222$		−	5.80385i		−	0.389529i
$223$		−	20.3923i		−	1.36557i	−0.730619	−	0.682785i	$-0.760769\pi$
$223$		−	20.3923i		−	1.36557i	0.730619	−	0.682785i	$-0.239231\pi$
$224$	−1.26795			−0.0847184
$225$	−12.2321	+	1.47372i	−0.815470	+	0.0982480i
$226$	−6.80385			−0.452585
$227$			28.3923i			1.88446i	0.334962	+	0.942232i	$0.391277\pi$
$227$			28.3923i			1.88446i	−0.334962	+	0.942232i	$0.608723\pi$
$228$			3.07180i			0.203435i
$229$	−9.33975			−0.617188			−0.308594	−	0.951194i	$-0.599858\pi$
$229$	−9.33975			−0.617188			−0.308594	+	0.951194i	$0.599858\pi$
$230$	−0.366025	−	6.09808i	−0.0241350	−	0.402095i
$231$		0			0
$232$		−	3.73205i		−	0.245021i
$233$			13.1962i			0.864509i	0.901752	+	0.432254i	$0.142282\pi$
$233$			13.1962i			0.864509i	−0.901752	+	0.432254i	$0.857718\pi$
$234$	−6.07180			−0.396926
$235$	15.0263	−	0.901924i	0.980206	−	0.0588350i
$236$	13.8564			0.901975
$237$		−	5.32051i		−	0.345604i
$238$		−	2.19615i		−	0.142355i
$239$	16.7321			1.08231			0.541153	−	0.840924i	$-0.317988\pi$
$239$	16.7321			1.08231			0.541153	+	0.840924i	$0.317988\pi$
$240$	−1.63397	+	0.0980762i	−0.105473	+	0.00633079i
$241$	19.3205			1.24454			0.622272	−	0.782801i	$-0.286210\pi$
$241$	19.3205			1.24454			0.622272	+	0.782801i	$0.286210\pi$
$242$		0			0
$243$			15.2679i			0.979439i
$244$	8.92820			0.571570
$245$	0.722432	+	12.0359i	0.0461545	+	0.768945i
$246$	7.66025			0.488400
$247$		−	10.3397i		−	0.657902i
$248$		−	8.73205i		−	0.554486i
$249$	−2.39230			−0.151606
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$	−16.5885			−1.04705			−0.523527	−	0.852009i	$-0.675384\pi$
$251$	−16.5885			−1.04705			−0.523527	+	0.852009i	$0.675384\pi$
$252$		−	3.12436i		−	0.196816i
$253$		0			0
$254$	−21.8564			−1.37139
$255$	−0.169873	−	2.83013i	−0.0106379	−	0.177229i
$256$	1.00000			0.0625000
$257$			27.9808i			1.74539i	0.488264	+	0.872696i	$0.337630\pi$
$257$			27.9808i			1.74539i	−0.488264	+	0.872696i	$0.662370\pi$
$258$			6.92820i			0.431331i
$259$	−10.0526			−0.624636
$260$	5.50000	−	0.330127i	0.341096	−	0.0204736i
$261$	9.19615			0.569228
$262$			5.46410i			0.337573i
$263$		−	10.0526i		−	0.619867i	−0.950758	−	0.309934i	$-0.899693\pi$
$263$		−	10.0526i		−	0.619867i	0.950758	−	0.309934i	$-0.100307\pi$
$264$		0			0
$265$	−6.69615	+	0.401924i	−0.411341	+	0.0246900i
$266$	5.32051			0.326221
$267$		−	0.339746i		−	0.0207921i
$268$			7.26795i			0.443961i
$269$	5.19615			0.316815			0.158408	−	0.987374i	$-0.449364\pi$
$269$	5.19615			0.316815			0.158408	+	0.987374i	$0.449364\pi$
$270$	−0.535898	−	8.92820i	−0.0326137	−	0.543353i
$271$	−17.8564			−1.08470			−0.542350	−	0.840153i	$-0.682465\pi$
$271$	−17.8564			−1.08470			−0.542350	+	0.840153i	$0.682465\pi$
$272$			1.73205i			0.105021i
$273$		−	2.28719i		−	0.138427i
$274$	−6.00000			−0.362473
$275$		0			0
$276$	2.00000			0.120386
$277$			13.9282i			0.836865i	0.908248	+	0.418432i	$0.137420\pi$
$277$			13.9282i			0.836865i	−0.908248	+	0.418432i	$0.862580\pi$
$278$			9.26795i			0.555855i
$279$	21.5167			1.28817
$280$	0.169873	+	2.83013i	0.0101519	+	0.169132i
$281$	28.3923			1.69374			0.846871	−	0.531798i	$-0.178483\pi$
$281$	28.3923			1.69374			0.846871	+	0.531798i	$0.178483\pi$
$282$			4.92820i			0.293470i
$283$		−	10.5359i		−	0.626294i	−0.949705	−	0.313147i	$-0.898617\pi$
$283$		−	10.5359i		−	0.626294i	0.949705	−	0.313147i	$-0.101383\pi$
$284$	−6.92820			−0.411113
$285$	6.85641	−	0.411543i	0.406138	−	0.0243777i
$286$		0			0
$287$		−	13.2679i		−	0.783182i
$288$			2.46410i			0.145199i
$289$	14.0000			0.823529
$290$	−8.33013	+	0.500000i	−0.489162	+	0.0293610i
$291$	−12.5885			−0.737948
$292$			12.9282i			0.756566i
$293$		−	1.53590i		−	0.0897281i	−0.998993	−	0.0448641i	$-0.985715\pi$
$293$		−	1.53590i		−	0.0897281i	0.998993	−	0.0448641i	$-0.0142855\pi$
$294$	−3.94744			−0.230219
$295$	−1.85641	−	30.9282i	−0.108084	−	1.80071i
$296$	7.92820			0.460817
$297$		0			0
$298$			13.5885i			0.787158i
$299$	−6.73205			−0.389325
$300$	0.437822	+	3.63397i	0.0252777	+	0.209808i
$301$	12.0000			0.691669
$302$			10.9282i			0.628847i
$303$			7.32051i			0.420552i
$304$	−4.19615			−0.240666
$305$	−1.19615	−	19.9282i	−0.0684915	−	1.14109i
$306$	−4.26795			−0.243982
$307$		−	8.73205i		−	0.498364i	−0.968457	−	0.249182i	$-0.919838\pi$
$307$		−	8.73205i		−	0.498364i	0.968457	−	0.249182i	$-0.0801618\pi$
$308$		0			0
$309$	5.85641			0.333159
$310$	−19.4904	+	1.16987i	−1.10698	+	0.0664443i
$311$	12.3923			0.702703			0.351352	−	0.936244i	$-0.385722\pi$
$311$	12.3923			0.702703			0.351352	+	0.936244i	$0.385722\pi$
$312$			1.80385i			0.102123i
$313$			6.26795i			0.354285i	0.984185	+	0.177143i	$0.0566854\pi$
$313$			6.26795i			0.354285i	−0.984185	+	0.177143i	$0.943315\pi$
$314$	10.0000			0.564333
$315$	−6.97372	+	0.418584i	−0.392925	+	0.0235846i
$316$	7.26795			0.408854
$317$			25.4641i			1.43021i	0.699019	+	0.715103i	$0.253620\pi$
$317$			25.4641i			1.43021i	−0.699019	+	0.715103i	$0.746380\pi$
$318$		−	2.19615i		−	0.123154i
$319$		0			0
$320$	−0.133975	−	2.23205i	−0.00748941	−	0.124775i
$321$	−8.53590			−0.476427
$322$		−	3.46410i		−	0.193047i
$323$		−	7.26795i		−	0.404400i
$324$	−4.46410			−0.248006
$325$	−1.47372	−	12.2321i	−0.0817473	−	0.678512i
$326$	9.12436			0.505351
$327$		−	6.05256i		−	0.334707i
$328$			10.4641i			0.577783i
$329$	8.53590			0.470599
$330$		0			0
$331$	−9.46410			−0.520194			−0.260097	−	0.965582i	$-0.583755\pi$
$331$	−9.46410			−0.520194			−0.260097	+	0.965582i	$0.583755\pi$
$332$		−	3.26795i		−	0.179352i
$333$			19.5359i			1.07056i
$334$	15.3205			0.838301
$335$	16.2224	−	0.973721i	0.886326	−	0.0532000i
$336$	−0.928203			−0.0506376
$337$			22.6603i			1.23438i	0.786813	+	0.617191i	$0.211730\pi$
$337$			22.6603i			1.23438i	−0.786813	+	0.617191i	$0.788270\pi$
$338$			6.92820i			0.376845i
$339$	−4.98076			−0.270518
$340$	3.86603	−	0.232051i	0.209665	−	0.0125847i
$341$		0			0
$342$		−	10.3397i		−	0.559109i
$343$			15.7128i			0.848412i
$344$	−9.46410			−0.510270
$345$	−0.267949	−	4.46410i	−0.0144259	−	0.240339i
$346$	−6.53590			−0.351372
$347$			21.4641i			1.15225i	0.817360	+	0.576127i	$0.195437\pi$
$347$			21.4641i			1.15225i	−0.817360	+	0.576127i	$0.804563\pi$
$348$		−	2.73205i		−	0.146453i
$349$	26.1244			1.39840			0.699202	−	0.714924i	$-0.253539\pi$
$349$	26.1244			1.39840			0.699202	+	0.714924i	$0.253539\pi$
$350$	6.29423	−	0.758330i	0.336441	−	0.0405345i
$351$	−9.85641			−0.526096
$352$		0			0
$353$			8.12436i			0.432416i	0.976347	+	0.216208i	$0.0693689\pi$
$353$			8.12436i			0.432416i	−0.976347	+	0.216208i	$0.930631\pi$
$354$	10.1436			0.539126
$355$	0.928203	+	15.4641i	0.0492639	+	0.820749i
$356$	0.464102			0.0245973
$357$		−	1.60770i		−	0.0850883i
$358$			21.8564i			1.15515i
$359$	13.5167			0.713382			0.356691	−	0.934222i	$-0.383905\pi$
$359$	13.5167			0.713382			0.356691	+	0.934222i	$0.383905\pi$
$360$	5.50000	−	0.330127i	0.289875	−	0.0173992i
$361$	−1.39230			−0.0732792
$362$		−	8.66025i		−	0.455173i
$363$		0			0
$364$	3.12436			0.163761
$365$	28.8564	−	1.73205i	1.51041	−	0.0906597i
$366$	6.53590			0.341637
$367$			3.41154i			0.178081i	0.996028	+	0.0890405i	$0.0283801\pi$
$367$			3.41154i			0.178081i	−0.996028	+	0.0890405i	$0.971620\pi$
$368$			2.73205i			0.142418i
$369$	−25.7846			−1.34229
$370$	−1.06218	−	17.6962i	−0.0552200	−	0.919979i
$371$	−3.80385			−0.197486
$372$		−	6.39230i		−	0.331426i
$373$			12.3923i			0.641649i	0.947139	+	0.320825i	$0.103960\pi$
$373$			12.3923i			0.641649i	−0.947139	+	0.320825i	$0.896040\pi$
$374$		0			0
$375$	8.05256	−	1.46410i	0.415832	−	0.0756059i
$376$	−6.73205			−0.347179
$377$			9.19615i			0.473626i
$378$		−	5.07180i		−	0.260865i
$379$	−14.2487			−0.731907			−0.365954	−	0.930633i	$-0.619257\pi$
$379$	−14.2487			−0.731907			−0.365954	+	0.930633i	$0.619257\pi$
$380$	0.562178	+	9.36603i	0.0288391	+	0.480467i
$381$	−16.0000			−0.819705
$382$			1.46410i			0.0749100i
$383$		−	23.3205i		−	1.19162i	−0.803125	−	0.595811i	$-0.796831\pi$
$383$		−	23.3205i		−	1.19162i	0.803125	−	0.595811i	$-0.203169\pi$
$384$	0.732051			0.0373573
$385$		0			0
$386$	13.1962			0.671666
$387$		−	23.3205i		−	1.18545i
$388$		−	17.1962i		−	0.873002i
$389$	−28.2679			−1.43324			−0.716621	−	0.697463i	$-0.754312\pi$
$389$	−28.2679			−1.43324			−0.716621	+	0.697463i	$0.754312\pi$
$390$	4.02628	−	0.241670i	0.203879	−	0.0122374i
$391$	−4.73205			−0.239310
$392$		−	5.39230i		−	0.272353i
$393$			4.00000i			0.201773i
$394$	−10.0718			−0.507410
$395$	−0.973721	−	16.2224i	−0.0489932	−	0.816239i
$396$		0			0
$397$		−	26.7128i		−	1.34068i	−0.742055	−	0.670339i	$-0.766149\pi$
$397$		−	26.7128i		−	1.34068i	0.742055	−	0.670339i	$-0.233851\pi$
$398$			13.0718i			0.655230i
$399$	3.89488			0.194988
$400$	−4.96410	+	0.598076i	−0.248205	+	0.0299038i
$401$	2.32051			0.115881			0.0579403	−	0.998320i	$-0.481547\pi$
$401$	2.32051			0.115881			0.0579403	+	0.998320i	$0.481547\pi$
$402$			5.32051i			0.265363i
$403$			21.5167i			1.07182i
$404$	−10.0000			−0.497519
$405$	0.598076	+	9.96410i	0.0297186	+	0.495120i
$406$	−4.73205			−0.234848
$407$		0			0
$408$			1.26795i			0.0627728i
$409$	−17.3923			−0.859994			−0.429997	−	0.902830i	$-0.641485\pi$
$409$	−17.3923			−0.859994			−0.429997	+	0.902830i	$0.641485\pi$
$410$	23.3564	−	1.40192i	1.15349	−	0.0692361i
$411$	−4.39230			−0.216656
$412$			8.00000i			0.394132i
$413$		−	17.5692i		−	0.864525i
$414$	−6.73205			−0.330862
$415$	−7.29423	+	0.437822i	−0.358060	+	0.0214918i
$416$	−2.46410			−0.120813
$417$			6.78461i			0.332244i
$418$		0			0
$419$	−3.41154			−0.166665			−0.0833324	−	0.996522i	$-0.526556\pi$
$419$	−3.41154			−0.166665			−0.0833324	+	0.996522i	$0.526556\pi$
$420$	0.124356	+	2.07180i	0.00606793	+	0.101093i
$421$	−17.0526			−0.831091			−0.415545	−	0.909572i	$-0.636409\pi$
$421$	−17.0526			−0.831091			−0.415545	+	0.909572i	$0.636409\pi$
$422$			9.07180i			0.441608i
$423$		−	16.5885i		−	0.806558i
$424$	3.00000			0.145693
$425$	−1.03590	−	8.59808i	−0.0502485	−	0.417068i
$426$	−5.07180			−0.245729
$427$		−	11.3205i		−	0.547838i
$428$		−	11.6603i		−	0.563620i
$429$		0			0
$430$	1.26795	+	21.1244i	0.0611459	+	1.01871i
$431$	17.8564			0.860113			0.430056	−	0.902802i	$-0.358494\pi$
$431$	17.8564			0.860113			0.430056	+	0.902802i	$0.358494\pi$
$432$			4.00000i			0.192450i
$433$		−	19.5885i		−	0.941361i	−0.882304	−	0.470681i	$-0.844008\pi$
$433$		−	19.5885i		−	0.941361i	0.882304	−	0.470681i	$-0.155992\pi$
$434$	−11.0718			−0.531463
$435$	−6.09808	+	0.366025i	−0.292380	+	0.0175496i
$436$	8.26795			0.395963
$437$		−	11.4641i		−	0.548402i
$438$			9.46410i			0.452212i
$439$	−17.1244			−0.817301			−0.408650	−	0.912691i	$-0.634000\pi$
$439$	−17.1244			−0.817301			−0.408650	+	0.912691i	$0.634000\pi$
$440$		0			0
$441$	13.2872			0.632723
$442$		−	4.26795i		−	0.203006i
$443$			12.7846i			0.607415i	0.952765	+	0.303708i	$0.0982246\pi$
$443$			12.7846i			0.607415i	−0.952765	+	0.303708i	$0.901775\pi$
$444$	5.80385			0.275438
$445$	−0.0621778	−	1.03590i	−0.00294751	−	0.0491063i
$446$	20.3923			0.965604
$447$			9.94744i			0.470498i
$448$		−	1.26795i		−	0.0599050i
$449$	21.9282			1.03486			0.517428	−	0.855727i	$-0.326890\pi$
$449$	21.9282			1.03486			0.517428	+	0.855727i	$0.326890\pi$
$450$	−1.47372	−	12.2321i	−0.0694719	−	0.576624i
$451$		0			0
$452$		−	6.80385i		−	0.320026i
$453$			8.00000i			0.375873i
$454$	−28.3923			−1.33252
$455$	−0.418584	−	6.97372i	−0.0196235	−	0.326933i
$456$	−3.07180			−0.143850
$457$		−	15.5885i		−	0.729197i	−0.931165	−	0.364599i	$-0.881206\pi$
$457$		−	15.5885i		−	0.729197i	0.931165	−	0.364599i	$-0.118794\pi$
$458$		−	9.33975i		−	0.436418i
$459$	−6.92820			−0.323381
$460$	6.09808	−	0.366025i	0.284324	−	0.0170660i
$461$	8.51666			0.396660			0.198330	−	0.980135i	$-0.436448\pi$
$461$	8.51666			0.396660			0.198330	+	0.980135i	$0.436448\pi$
$462$		0			0
$463$		−	4.00000i		−	0.185896i	−0.995671	−	0.0929479i	$-0.970371\pi$
$463$		−	4.00000i		−	0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$	3.73205			0.173256
$465$	−14.2679	+	0.856406i	−0.661660	+	0.0397149i
$466$	−13.1962			−0.611300
$467$		−	25.1769i		−	1.16505i	−0.812813	−	0.582524i	$-0.802065\pi$
$467$		−	25.1769i		−	1.16505i	0.812813	−	0.582524i	$-0.197935\pi$
$468$		−	6.07180i		−	0.280669i
$469$	9.21539			0.425527
$470$	0.901924	+	15.0263i	0.0416026	+	0.693111i
$471$	7.32051			0.337311
$472$			13.8564i			0.637793i
$473$		0			0
$474$	5.32051			0.244379
$475$	20.8301	−	2.50962i	0.955752	−	0.115149i
$476$	2.19615			0.100660
$477$			7.39230i			0.338470i
$478$			16.7321i			0.765306i
$479$	−2.14359			−0.0979433			−0.0489716	−	0.998800i	$-0.515594\pi$
$479$	−2.14359			−0.0979433			−0.0489716	+	0.998800i	$0.515594\pi$
$480$	−0.0980762	−	1.63397i	−0.00447655	−	0.0745804i
$481$	−19.5359			−0.890760
$482$			19.3205i			0.880025i
$483$		−	2.53590i		−	0.115387i
$484$		0			0
$485$	−38.3827	+	2.30385i	−1.74287	+	0.104612i
$486$	−15.2679			−0.692568
$487$		−	38.8372i		−	1.75988i	−0.475085	−	0.879940i	$-0.657583\pi$
$487$		−	38.8372i		−	1.75988i	0.475085	−	0.879940i	$-0.342417\pi$
$488$			8.92820i			0.404161i
$489$	6.67949			0.302057
$490$	−12.0359	+	0.722432i	−0.543726	+	0.0326361i
$491$	35.9090			1.62055			0.810274	−	0.586051i	$-0.199318\pi$
$491$	35.9090			1.62055			0.810274	+	0.586051i	$0.199318\pi$
$492$			7.66025i			0.345351i
$493$			6.46410i			0.291128i
$494$	10.3397			0.465207
$495$		0			0
$496$	8.73205			0.392081
$497$			8.78461i			0.394044i
$498$		−	2.39230i		−	0.107202i
$499$	10.9282			0.489214			0.244607	−	0.969622i	$-0.421341\pi$
$499$	10.9282			0.489214			0.244607	+	0.969622i	$0.421341\pi$
$500$	2.00000	+	11.0000i	0.0894427	+	0.491935i
$501$	11.2154			0.501067
$502$		−	16.5885i		−	0.740379i
$503$		−	15.1244i		−	0.674362i	−0.941440	−	0.337181i	$-0.890527\pi$
$503$		−	15.1244i		−	0.674362i	0.941440	−	0.337181i	$-0.109473\pi$
$504$	3.12436			0.139170
$505$	1.33975	+	22.3205i	0.0596179	+	0.993250i
$506$		0			0
$507$			5.07180i			0.225246i
$508$		−	21.8564i		−	0.969721i
$509$	8.92820			0.395736			0.197868	−	0.980229i	$-0.436598\pi$
$509$	8.92820			0.395736			0.197868	+	0.980229i	$0.436598\pi$
$510$	2.83013	−	0.169873i	0.125320	−	0.00752210i
$511$	16.3923			0.725153
$512$			1.00000i			0.0441942i
$513$		−	16.7846i		−	0.741059i
$514$	−27.9808			−1.23418
$515$	17.8564	−	1.07180i	0.786847	−	0.0472290i
$516$	−6.92820			−0.304997
$517$		0			0
$518$		−	10.0526i		−	0.441684i
$519$	−4.78461			−0.210021
$520$	0.330127	+	5.50000i	0.0144770	+	0.241191i
$521$	−21.1769			−0.927777			−0.463889	−	0.885893i	$-0.653546\pi$
$521$	−21.1769			−0.927777			−0.463889	+	0.885893i	$0.653546\pi$
$522$			9.19615i			0.402505i
$523$		−	26.9282i		−	1.17749i	−0.808320	−	0.588744i	$-0.799623\pi$
$523$		−	26.9282i		−	1.17749i	0.808320	−	0.588744i	$-0.200377\pi$
$524$	−5.46410			−0.238700
$525$	4.60770	−	0.555136i	0.201096	−	0.0242281i
$526$	10.0526			0.438312
$527$			15.1244i			0.658827i
$528$		0			0
$529$	15.5359			0.675474
$530$	−0.401924	−	6.69615i	−0.0174585	−	0.290862i
$531$	−34.1436			−1.48171
$532$			5.32051i			0.230673i
$533$		−	25.7846i		−	1.11686i
$534$	0.339746			0.0147022
$535$	−26.0263	+	1.56218i	−1.12521	+	0.0675388i
$536$	−7.26795			−0.313928
$537$			16.0000i			0.690451i
$538$			5.19615i			0.224022i
$539$		0			0
$540$	8.92820	−	0.535898i	0.384209	−	0.0230614i
$541$	−25.0718			−1.07792			−0.538960	−	0.842331i	$-0.681183\pi$
$541$	−25.0718			−1.07792			−0.538960	+	0.842331i	$0.681183\pi$
$542$		−	17.8564i		−	0.766998i
$543$		−	6.33975i		−	0.272065i
$544$	−1.73205			−0.0742611
$545$	−1.10770	−	18.4545i	−0.0474484	−	0.790503i
$546$	2.28719			0.0978826
$547$			31.3205i			1.33917i	0.742736	+	0.669584i	$0.233528\pi$
$547$			31.3205i			1.33917i	−0.742736	+	0.669584i	$0.766472\pi$
$548$		−	6.00000i		−	0.256307i
$549$	−22.0000			−0.938937
$550$		0			0
$551$	−15.6603			−0.667149
$552$			2.00000i			0.0851257i
$553$		−	9.21539i		−	0.391878i
$554$	−13.9282			−0.591753
$555$	−0.777568	−	12.9545i	−0.0330059	−	0.549887i
$556$	−9.26795			−0.393049
$557$			1.46410i			0.0620360i	0.999519	+	0.0310180i	$0.00987492\pi$
$557$			1.46410i			0.0620360i	−0.999519	+	0.0310180i	$0.990125\pi$
$558$			21.5167i			0.910873i
$559$	23.3205			0.986352
$560$	−2.83013	+	0.169873i	−0.119595	+	0.00717844i
$561$		0			0
$562$			28.3923i			1.19766i
$563$		−	43.3731i		−	1.82796i	−0.405763	−	0.913978i	$-0.632994\pi$
$563$		−	43.3731i		−	1.82796i	0.405763	−	0.913978i	$-0.367006\pi$
$564$	−4.92820			−0.207515
$565$	−15.1865	+	0.911543i	−0.638902	+	0.0383489i
$566$	10.5359			0.442857
$567$			5.66025i			0.237708i
$568$		−	6.92820i		−	0.290701i
$569$	−3.32051			−0.139203			−0.0696015	−	0.997575i	$-0.522173\pi$
$569$	−3.32051			−0.139203			−0.0696015	+	0.997575i	$0.522173\pi$
$570$	0.411543	+	6.85641i	0.0172376	+	0.287183i
$571$	−38.4449			−1.60887			−0.804434	−	0.594042i	$-0.797531\pi$
$571$	−38.4449			−1.60887			−0.804434	+	0.594042i	$0.797531\pi$
$572$		0			0
$573$			1.07180i			0.0447750i
$574$	13.2679			0.553793
$575$	−1.63397	−	13.5622i	−0.0681415	−	0.565582i
$576$	−2.46410			−0.102671
$577$		−	12.2679i		−	0.510721i	−0.966846	−	0.255361i	$-0.917806\pi$
$577$		−	12.2679i		−	0.510721i	0.966846	−	0.255361i	$-0.0821942\pi$
$578$			14.0000i			0.582323i
$579$	9.66025			0.401466
$580$	−0.500000	−	8.33013i	−0.0207614	−	0.345890i
$581$	−4.14359			−0.171905
$582$		−	12.5885i		−	0.521808i
$583$		0			0
$584$	−12.9282			−0.534973
$585$	−13.5526	+	0.813467i	−0.560329	+	0.0336327i
$586$	1.53590			0.0634474
$587$		−	24.7321i		−	1.02080i	−0.859937	−	0.510400i	$-0.829497\pi$
$587$		−	24.7321i		−	1.02080i	0.859937	−	0.510400i	$-0.170503\pi$
$588$		−	3.94744i		−	0.162790i
$589$	−36.6410			−1.50977
$590$	30.9282	−	1.85641i	1.27329	−	0.0764270i
$591$	−7.37307			−0.303287
$592$			7.92820i			0.325847i
$593$			38.9090i			1.59780i	0.601464	+	0.798900i	$0.294584\pi$
$593$			38.9090i			1.59780i	−0.601464	+	0.798900i	$0.705416\pi$
$594$		0			0
$595$	−0.294229	−	4.90192i	−0.0120622	−	0.200959i
$596$	−13.5885			−0.556605
$597$			9.56922i			0.391642i
$598$		−	6.73205i		−	0.275294i
$599$	36.7321			1.50083			0.750415	−	0.660966i	$-0.229853\pi$
$599$	36.7321			1.50083			0.750415	+	0.660966i	$0.229853\pi$
$600$	−3.63397	+	0.437822i	−0.148356	+	0.0178740i
$601$	15.7846			0.643868			0.321934	−	0.946762i	$-0.395667\pi$
$601$	15.7846			0.643868			0.321934	+	0.946762i	$0.395667\pi$
$602$			12.0000i			0.489083i
$603$		−	17.9090i		−	0.729309i
$604$	−10.9282			−0.444662
$605$		0			0
$606$	−7.32051			−0.297375
$607$			13.6603i			0.554453i	0.960805	+	0.277226i	$0.0894152\pi$
$607$			13.6603i			0.554453i	−0.960805	+	0.277226i	$0.910585\pi$
$608$		−	4.19615i		−	0.170176i
$609$	−3.46410			−0.140372
$610$	19.9282	−	1.19615i	0.806869	−	0.0484308i
$611$	16.5885			0.671097
$612$		−	4.26795i		−	0.172522i
$613$		−	27.0000i		−	1.09052i	−0.838267	−	0.545260i	$-0.816431\pi$
$613$		−	27.0000i		−	1.09052i	0.838267	−	0.545260i	$-0.183569\pi$
$614$	8.73205			0.352397
$615$	17.0981	−	1.02628i	0.689461	−	0.0413836i
$616$		0			0
$617$		−	9.33975i		−	0.376004i	−0.982169	−	0.188002i	$-0.939799\pi$
$617$		−	9.33975i		−	0.376004i	0.982169	−	0.188002i	$-0.0602011\pi$
$618$			5.85641i			0.235579i
$619$	−2.33975			−0.0940423			−0.0470212	−	0.998894i	$-0.514973\pi$
$619$	−2.33975			−0.0940423			−0.0470212	+	0.998894i	$0.514973\pi$
$620$	−1.16987	−	19.4904i	−0.0469832	−	0.782753i
$621$	−10.9282			−0.438534
$622$			12.3923i			0.496886i
$623$		−	0.588457i		−	0.0235760i
$624$	−1.80385			−0.0722117
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	−6.26795			−0.250518
$627$		0			0
$628$			10.0000i			0.399043i
$629$	−13.7321			−0.547533
$630$	−0.418584	−	6.97372i	−0.0166768	−	0.277840i
$631$	−11.2679			−0.448570			−0.224285	−	0.974524i	$-0.572005\pi$
$631$	−11.2679			−0.448570			−0.224285	+	0.974524i	$0.572005\pi$
$632$			7.26795i			0.289103i
$633$			6.64102i			0.263957i
$634$	−25.4641			−1.01131
$635$	−48.7846	+	2.92820i	−1.93596	+	0.116202i
$636$	2.19615			0.0870831
$637$			13.2872i			0.526458i
$638$		0			0
$639$	17.0718			0.675350
$640$	2.23205	−	0.133975i	0.0882296	−	0.00529581i
$641$	−2.32051			−0.0916546			−0.0458273	−	0.998949i	$-0.514592\pi$
$641$	−2.32051			−0.0916546			−0.0458273	+	0.998949i	$0.514592\pi$
$642$		−	8.53590i		−	0.336885i
$643$			26.5885i			1.04855i	0.851550	+	0.524273i	$0.175663\pi$
$643$			26.5885i			1.04855i	−0.851550	+	0.524273i	$0.824337\pi$
$644$	3.46410			0.136505
$645$	0.928203	+	15.4641i	0.0365480	+	0.608898i
$646$	7.26795			0.285954
$647$		−	25.8564i		−	1.01652i	−0.861204	−	0.508260i	$-0.830289\pi$
$647$		−	25.8564i		−	1.01652i	0.861204	−	0.508260i	$-0.169711\pi$
$648$		−	4.46410i		−	0.175366i
$649$		0			0
$650$	12.2321	−	1.47372i	0.479781	−	0.0578041i
$651$	−8.10512			−0.317665
$652$			9.12436i			0.357337i
$653$			18.0000i			0.704394i	0.935926	+	0.352197i	$0.114565\pi$
$653$			18.0000i			0.704394i	−0.935926	+	0.352197i	$0.885435\pi$
$654$	6.05256			0.236674
$655$	0.732051	+	12.1962i	0.0286036	+	0.476543i
$656$	−10.4641			−0.408555
$657$		−	31.8564i		−	1.24284i
$658$			8.53590i			0.332764i
$659$	26.7321			1.04133			0.520666	−	0.853760i	$-0.325684\pi$
$659$	26.7321			1.04133			0.520666	+	0.853760i	$0.325684\pi$
$660$		0			0
$661$	42.3731			1.64812			0.824061	−	0.566502i	$-0.191703\pi$
$661$	42.3731			1.64812			0.824061	+	0.566502i	$0.191703\pi$
$662$		−	9.46410i		−	0.367833i
$663$		−	3.12436i		−	0.121340i
$664$	3.26795			0.126821
$665$	11.8756	−	0.712813i	0.460518	−	0.0276417i
$666$	−19.5359			−0.757001
$667$			10.1962i			0.394797i
$668$			15.3205i			0.592768i
$669$	14.9282			0.577158
$670$	0.973721	+	16.2224i	0.0376181	+	0.626727i
$671$		0			0
$672$		−	0.928203i		−	0.0358062i
$673$		−	10.7846i		−	0.415716i	−0.978159	−	0.207858i	$-0.933351\pi$
$673$		−	10.7846i		−	0.415716i	0.978159	−	0.207858i	$-0.0666492\pi$
$674$	−22.6603			−0.872840
$675$	−2.39230	−	19.8564i	−0.0920799	−	0.764273i
$676$	−6.92820			−0.266469
$677$		−	5.14359i		−	0.197684i	−0.995103	−	0.0988422i	$-0.968486\pi$
$677$		−	5.14359i		−	0.197684i	0.995103	−	0.0988422i	$-0.0315139\pi$
$678$		−	4.98076i		−	0.191285i
$679$	−21.8038			−0.836755
$680$	0.232051	+	3.86603i	0.00889874	+	0.148255i
$681$	−20.7846			−0.796468
$682$		0			0
$683$		−	8.33975i		−	0.319112i	−0.987189	−	0.159556i	$-0.948994\pi$
$683$		−	8.33975i		−	0.319112i	0.987189	−	0.159556i	$-0.0510062\pi$
$684$	10.3397			0.395350
$685$	−13.3923	+	0.803848i	−0.511694	+	0.0307134i
$686$	−15.7128			−0.599918
$687$		−	6.83717i		−	0.260854i
$688$		−	9.46410i		−	0.360815i
$689$	−7.39230			−0.281624
$690$	4.46410	−	0.267949i	0.169945	−	0.0102007i
$691$	−31.3205			−1.19149			−0.595744	−	0.803174i	$-0.703143\pi$
$691$	−31.3205			−1.19149			−0.595744	+	0.803174i	$0.703143\pi$
$692$		−	6.53590i		−	0.248458i
$693$		0			0
$694$	−21.4641			−0.814766
$695$	1.24167	+	20.6865i	0.0470992	+	0.784685i
$696$	2.73205			0.103558
$697$		−	18.1244i		−	0.686509i
$698$			26.1244i			0.988821i
$699$	−9.66025			−0.365384
$700$	0.758330	+	6.29423i	0.0286622	+	0.237899i
$701$	−47.4449			−1.79197			−0.895984	−	0.444087i	$-0.853528\pi$
$701$	−47.4449			−1.79197			−0.895984	+	0.444087i	$0.853528\pi$
$702$		−	9.85641i		−	0.372006i
$703$		−	33.2679i		−	1.25472i
$704$		0			0
$705$	0.660254	+	11.0000i	0.0248666	+	0.414284i
$706$	−8.12436			−0.305764
$707$			12.6795i			0.476861i
$708$			10.1436i			0.381220i
$709$	14.0000			0.525781			0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000			0.525781			0.262891	+	0.964826i	$0.415324\pi$
$710$	−15.4641	+	0.928203i	−0.580357	+	0.0348348i
$711$	−17.9090			−0.671639
$712$			0.464102i			0.0173929i
$713$			23.8564i			0.893429i
$714$	1.60770			0.0601665
$715$		0			0
$716$	−21.8564			−0.816812
$717$			12.2487i			0.457437i
$718$			13.5167i			0.504437i
$719$	−32.4449			−1.20999			−0.604995	−	0.796230i	$-0.706825\pi$
$719$	−32.4449			−1.20999			−0.604995	+	0.796230i	$0.706825\pi$
$720$	0.330127	+	5.50000i	0.0123031	+	0.204973i
$721$	10.1436			0.377767
$722$		−	1.39230i		−	0.0518162i
$723$			14.1436i			0.526006i
$724$	8.66025			0.321856
$725$	−18.5263	+	2.23205i	−0.688049	+	0.0828963i
$726$		0			0
$727$		−	3.12436i		−	0.115876i	−0.998320	−	0.0579380i	$-0.981547\pi$
$727$		−	3.12436i		−	0.115876i	0.998320	−	0.0579380i	$-0.0184526\pi$
$728$			3.12436i			0.115796i
$729$	2.21539			0.0820515
$730$	1.73205	+	28.8564i	0.0641061	+	1.06802i
$731$	16.3923			0.606291
$732$			6.53590i			0.241574i
$733$		−	2.21539i		−	0.0818273i	−0.999163	−	0.0409137i	$-0.986973\pi$
$733$		−	2.21539i		−	0.0818273i	0.999163	−	0.0409137i	$-0.0130269\pi$
$734$	−3.41154			−0.125922
$735$	−8.81089	+	0.528857i	−0.324995	+	0.0195072i
$736$	−2.73205			−0.100705
$737$		0			0
$738$		−	25.7846i		−	0.949145i
$739$	−23.8038			−0.875639			−0.437819	−	0.899063i	$-0.644249\pi$
$739$	−23.8038			−0.875639			−0.437819	+	0.899063i	$0.644249\pi$
$740$	17.6962	−	1.06218i	0.650524	−	0.0390464i
$741$	7.56922			0.278062
$742$		−	3.80385i		−	0.139644i
$743$			44.9808i			1.65018i	0.564998	+	0.825092i	$0.308877\pi$
$743$			44.9808i			1.65018i	−0.564998	+	0.825092i	$0.691123\pi$
$744$	6.39230			0.234353
$745$	1.82051	+	30.3301i	0.0666983	+	1.11121i
$746$	−12.3923			−0.453715
$747$			8.05256i			0.294628i
$748$		0			0
$749$	−14.7846			−0.540218
$750$	1.46410	+	8.05256i	0.0534614	+	0.294038i
$751$	−40.3923			−1.47394			−0.736968	−	0.675928i	$-0.763743\pi$
$751$	−40.3923			−1.47394			−0.736968	+	0.675928i	$0.763743\pi$
$752$		−	6.73205i		−	0.245493i
$753$		−	12.1436i		−	0.442537i
$754$	−9.19615			−0.334904
$755$	1.46410	+	24.3923i	0.0532841	+	0.887727i
$756$	5.07180			0.184459
$757$		−	18.4641i		−	0.671089i	−0.942024	−	0.335545i	$-0.891080\pi$
$757$		−	18.4641i		−	0.671089i	0.942024	−	0.335545i	$-0.108920\pi$
$758$		−	14.2487i		−	0.517537i
$759$		0			0
$760$	−9.36603	+	0.562178i	−0.339741	+	0.0203923i
$761$	3.24871			0.117766			0.0588828	−	0.998265i	$-0.481246\pi$
$761$	3.24871			0.117766			0.0588828	+	0.998265i	$0.481246\pi$
$762$		−	16.0000i		−	0.579619i
$763$		−	10.4833i		−	0.379522i
$764$	−1.46410			−0.0529693
$765$	−9.52628	+	0.571797i	−0.344423	+	0.0206734i
$766$	23.3205			0.842604
$767$		−	34.1436i		−	1.23285i
$768$			0.732051i			0.0264156i
$769$	−9.00000			−0.324548			−0.162274	−	0.986746i	$-0.551883\pi$
$769$	−9.00000			−0.324548			−0.162274	+	0.986746i	$0.551883\pi$
$770$		0			0
$771$	−20.4833			−0.737689
$772$			13.1962i			0.474940i
$773$			13.4641i			0.484270i	0.970243	+	0.242135i	$0.0778477\pi$
$773$			13.4641i			0.484270i	−0.970243	+	0.242135i	$0.922152\pi$
$774$	23.3205			0.838238
$775$	−43.3468	+	5.22243i	−1.55706	+	0.187595i
$776$	17.1962			0.617306
$777$		−	7.35898i		−	0.264002i
$778$		−	28.2679i		−	1.01346i
$779$	43.9090			1.57320
$780$	0.241670	+	4.02628i	0.00865317	+	0.144164i
$781$		0			0
$782$		−	4.73205i		−	0.169218i
$783$			14.9282i			0.533490i
$784$	5.39230			0.192582
$785$	22.3205	−	1.33975i	0.796653	−	0.0478176i
$786$	−4.00000			−0.142675
$787$		−	32.3923i		−	1.15466i	−0.816511	−	0.577330i	$-0.804094\pi$
$787$		−	32.3923i		−	1.15466i	0.816511	−	0.577330i	$-0.195906\pi$
$788$		−	10.0718i		−	0.358793i
$789$	7.35898			0.261987
$790$	16.2224	−	0.973721i	0.577168	−	0.0346434i
$791$	−8.62693			−0.306738
$792$		0			0
$793$		−	22.0000i		−	0.781243i
$794$	26.7128			0.948002
$795$	−0.294229	−	4.90192i	−0.0104352	−	0.173853i
$796$	−13.0718			−0.463318
$797$			42.2487i			1.49653i	0.663402	+	0.748263i	$0.269112\pi$
$797$			42.2487i			1.49653i	−0.663402	+	0.748263i	$0.730888\pi$
$798$			3.89488i			0.137877i
$799$	11.6603			0.412510
$800$	−0.598076	−	4.96410i	−0.0211452	−	0.175507i
$801$	−1.14359			−0.0404069
$802$			2.32051i			0.0819400i
$803$		0			0
$804$	−5.32051			−0.187640
$805$	−0.464102	−	7.73205i	−0.0163574	−	0.272519i
$806$	−21.5167			−0.757892
$807$			3.80385i			0.133902i
$808$		−	10.0000i		−	0.351799i
$809$	20.3923			0.716955			0.358478	−	0.933538i	$-0.383296\pi$
$809$	20.3923			0.716955			0.358478	+	0.933538i	$0.383296\pi$
$810$	−9.96410	+	0.598076i	−0.350103	+	0.0210143i
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$		−	4.73205i		−	0.166062i
$813$		−	13.0718i		−	0.458448i
$814$		0			0
$815$	20.3660	−	1.22243i	0.713391	−	0.0428199i
$816$	−1.26795			−0.0443871
$817$			39.7128i			1.38938i
$818$		−	17.3923i		−	0.608108i
$819$	−7.69873			−0.269015
$820$	1.40192	+	23.3564i	0.0489573	+	0.815641i
$821$	31.0718			1.08441			0.542207	−	0.840245i	$-0.317589\pi$
$821$	31.0718			1.08441			0.542207	+	0.840245i	$0.317589\pi$
$822$		−	4.39230i		−	0.153199i
$823$			13.4641i			0.469329i	0.972076	+	0.234665i	$0.0753992\pi$
$823$			13.4641i			0.469329i	−0.972076	+	0.234665i	$0.924601\pi$
$824$	−8.00000			−0.278693
$825$		0			0
$826$	17.5692			0.611311
$827$		−	31.3731i		−	1.09095i	−0.838128	−	0.545474i	$-0.816350\pi$
$827$		−	31.3731i		−	1.09095i	0.838128	−	0.545474i	$-0.183650\pi$
$828$		−	6.73205i		−	0.233955i
$829$	1.87564			0.0651438			0.0325719	−	0.999469i	$-0.489630\pi$
$829$	1.87564			0.0651438			0.0325719	+	0.999469i	$0.489630\pi$
$830$	−0.437822	−	7.29423i	−0.0151970	−	0.253186i
$831$	−10.1962			−0.353701
$832$		−	2.46410i		−	0.0854274i
$833$			9.33975i			0.323603i
$834$	−6.78461			−0.234932
$835$	34.1962	−	2.05256i	1.18341	−	0.0710317i
$836$		0			0
$837$			34.9282i			1.20730i
$838$		−	3.41154i		−	0.117850i
$839$	23.6603			0.816843			0.408421	−	0.912794i	$-0.366079\pi$
$839$	23.6603			0.816843			0.408421	+	0.912794i	$0.366079\pi$
$840$	−2.07180	+	0.124356i	−0.0714838	+	0.00429068i
$841$	−15.0718			−0.519717
$842$		−	17.0526i		−	0.587670i
$843$			20.7846i			0.715860i
$844$	−9.07180			−0.312264
$845$	0.928203	+	15.4641i	0.0319312	+	0.531981i
$846$	16.5885			0.570323
$847$		0			0
$848$			3.00000i			0.103020i
$849$	7.71281			0.264703
$850$	8.59808	−	1.03590i	0.294912	−	0.0355310i
$851$	−21.6603			−0.742504
$852$		−	5.07180i		−	0.173757i
$853$		−	21.3923i		−	0.732459i	−0.930525	−	0.366229i	$-0.880649\pi$
$853$		−	21.3923i		−	0.732459i	0.930525	−	0.366229i	$-0.119351\pi$
$854$	11.3205			0.387380
$855$	−1.38526	−	23.0788i	−0.0473750	−	0.789280i
$856$	11.6603			0.398539
$857$		−	32.0000i		−	1.09310i	−0.837427	−	0.546550i	$-0.815941\pi$
$857$		−	32.0000i		−	1.09310i	0.837427	−	0.546550i	$-0.184059\pi$
$858$		0			0
$859$	13.4641			0.459389			0.229695	−	0.973263i	$-0.426227\pi$
$859$	13.4641			0.459389			0.229695	+	0.973263i	$0.426227\pi$
$860$	−21.1244	+	1.26795i	−0.720335	+	0.0432367i
$861$	9.71281			0.331012
$862$			17.8564i			0.608192i
$863$		−	38.4449i		−	1.30868i	−0.756201	−	0.654339i	$-0.772947\pi$
$863$		−	38.4449i		−	1.30868i	0.756201	−	0.654339i	$-0.227053\pi$
$864$	−4.00000			−0.136083
$865$	−14.5885	+	0.875644i	−0.496022	+	0.0297728i
$866$	19.5885			0.665643
$867$			10.2487i			0.348064i
$868$		−	11.0718i		−	0.375801i
$869$		0			0
$870$	−0.366025	−	6.09808i	−0.0124094	−	0.206744i
$871$	17.9090			0.606822
$872$			8.26795i			0.279988i
$873$			42.3731i			1.43411i
$874$	11.4641			0.387779
$875$	13.9474	−	2.53590i	0.471510	−	0.0857290i
$876$	−9.46410			−0.319762
$877$			33.7846i			1.14083i	0.821358	+	0.570413i	$0.193217\pi$
$877$			33.7846i			1.14083i	−0.821358	+	0.570413i	$0.806783\pi$
$878$		−	17.1244i		−	0.577919i
$879$	1.12436			0.0379236
$880$		0			0
$881$	7.39230			0.249053			0.124527	−	0.992216i	$-0.460259\pi$
$881$	7.39230			0.249053			0.124527	+	0.992216i	$0.460259\pi$
$882$			13.2872i			0.447403i
$883$			17.0718i			0.574512i	0.957854	+	0.287256i	$0.0927430\pi$
$883$			17.0718i			0.574512i	−0.957854	+	0.287256i	$0.907257\pi$
$884$	4.26795			0.143547
$885$	22.6410	−	1.35898i	0.761069	−	0.0456817i
$886$	−12.7846			−0.429507
$887$		−	48.9808i		−	1.64461i	−0.569045	−	0.822307i	$-0.692687\pi$
$887$		−	48.9808i		−	1.64461i	0.569045	−	0.822307i	$-0.307313\pi$
$888$			5.80385i			0.194764i
$889$	−27.7128			−0.929458
$890$	1.03590	−	0.0621778i	0.0347234	−	0.00208421i
$891$		0			0
$892$			20.3923i			0.682785i
$893$			28.2487i			0.945307i
$894$	−9.94744			−0.332692
$895$	2.92820	+	48.7846i	0.0978790	+	1.63069i
$896$	1.26795			0.0423592
$897$		−	4.92820i		−	0.164548i
$898$			21.9282i			0.731754i
$899$	32.5885			1.08689
$900$	12.2321	−	1.47372i	0.407735	−	0.0491240i
$901$	−5.19615			−0.173109
$902$		0			0
$903$			8.78461i			0.292334i
$904$	6.80385			0.226293
$905$	−1.16025	−	19.3301i	−0.0385681	−	0.642555i
$906$	−8.00000			−0.265782
$907$			8.39230i			0.278662i	0.990246	+	0.139331i	$0.0444952\pi$
$907$			8.39230i			0.278662i	−0.990246	+	0.139331i	$0.955505\pi$
$908$		−	28.3923i		−	0.942232i
$909$	24.6410			0.817291
$910$	6.97372	−	0.418584i	0.231177	−	0.0138759i
$911$	−17.4641			−0.578612			−0.289306	−	0.957237i	$-0.593424\pi$
$911$	−17.4641			−0.578612			−0.289306	+	0.957237i	$0.593424\pi$
$912$		−	3.07180i		−	0.101717i
$913$		0			0
$914$	15.5885			0.515620
$915$	14.5885	−	0.875644i	0.482280	−	0.0289479i
$916$	9.33975			0.308594
$917$			6.92820i			0.228789i
$918$		−	6.92820i		−	0.228665i
$919$	28.1051			0.927102			0.463551	−	0.886070i	$-0.346575\pi$
$919$	28.1051			0.927102			0.463551	+	0.886070i	$0.346575\pi$
$920$	0.366025	+	6.09808i	0.0120675	+	0.201048i
$921$	6.39230			0.210634
$922$			8.51666i			0.280481i
$923$			17.0718i			0.561925i
$924$		0			0
$925$	−4.74167	−	39.3564i	−0.155905	−	1.29403i
$926$	4.00000			0.131448
$927$		−	19.7128i		−	0.647454i
$928$			3.73205i			0.122511i
$929$	−14.0718			−0.461681			−0.230840	−	0.972992i	$-0.574148\pi$
$929$	−14.0718			−0.461681			−0.230840	+	0.972992i	$0.574148\pi$
$930$	−0.856406	−	14.2679i	−0.0280827	−	0.467864i
$931$	−22.6269			−0.741568
$932$		−	13.1962i		−	0.432254i
$933$			9.07180i			0.296997i
$934$	25.1769			0.823814
$935$		0			0
$936$	6.07180			0.198463
$937$			16.2679i			0.531451i	0.964049	+	0.265725i	$0.0856114\pi$
$937$			16.2679i			0.531451i	−0.964049	+	0.265725i	$0.914389\pi$
$938$			9.21539i			0.300893i
$939$	−4.58846			−0.149739
$940$	−15.0263	+	0.901924i	−0.490103	+	0.0294175i
$941$	2.51666			0.0820408			0.0410204	−	0.999158i	$-0.486939\pi$
$941$	2.51666			0.0820408			0.0410204	+	0.999158i	$0.486939\pi$
$942$			7.32051i			0.238515i
$943$		−	28.5885i		−	0.930968i
$944$	−13.8564			−0.450988
$945$	−0.679492	−	11.3205i	−0.0221039	−	0.368256i
$946$		0			0
$947$			45.9090i			1.49184i	0.666035	+	0.745920i	$0.267990\pi$
$947$			45.9090i			1.49184i	−0.666035	+	0.745920i	$0.732010\pi$
$948$			5.32051i			0.172802i
$949$	31.8564			1.03410
$950$	2.50962	+	20.8301i	0.0814228	+	0.675819i
$951$	−18.6410			−0.604476
$952$			2.19615i			0.0711777i
$953$			19.3397i			0.626476i	0.949675	+	0.313238i	$0.101414\pi$
$953$			19.3397i			0.626476i	−0.949675	+	0.313238i	$0.898586\pi$
$954$	−7.39230			−0.239335
$955$	0.196152	+	3.26795i	0.00634734	+	0.105748i
$956$	−16.7321			−0.541153
$957$		0			0
$958$		−	2.14359i		−	0.0692564i
$959$	−7.60770			−0.245665
$960$	1.63397	−	0.0980762i	0.0527363	−	0.00316540i
$961$	45.2487			1.45964
$962$		−	19.5359i		−	0.629863i
$963$			28.7321i			0.925877i
$964$	−19.3205			−0.622272
$965$	29.4545	−	1.76795i	0.948173	−	0.0569123i
$966$	2.53590			0.0815912
$967$		−	53.3731i		−	1.71636i	−0.513347	−	0.858181i	$-0.671595\pi$
$967$		−	53.3731i		−	1.71636i	0.513347	−	0.858181i	$-0.328405\pi$
$968$		0			0
$969$	5.32051			0.170919
$970$	−2.30385	−	38.3827i	−0.0739721	−	1.23239i
$971$	18.7321			0.601140			0.300570	−	0.953760i	$-0.402823\pi$
$971$	18.7321			0.601140			0.300570	+	0.953760i	$0.402823\pi$
$972$		−	15.2679i		−	0.489720i
$973$			11.7513i			0.376729i
$974$	38.8372			1.24442
$975$	8.95448	−	1.07884i	0.286773	−	0.0345505i
$976$	−8.92820			−0.285785
$977$		−	41.0526i		−	1.31339i	−0.754157	−	0.656694i	$-0.771954\pi$
$977$		−	41.0526i		−	1.31339i	0.754157	−	0.656694i	$-0.228046\pi$
$978$			6.67949i			0.213587i
$979$		0			0
$980$	−0.722432	−	12.0359i	−0.0230772	−	0.384473i
$981$	−20.3731			−0.650462
$982$			35.9090i			1.14590i
$983$			44.0000i			1.40338i	0.712481	+	0.701691i	$0.247571\pi$
$983$			44.0000i			1.40338i	−0.712481	+	0.701691i	$0.752429\pi$
$984$	−7.66025			−0.244200
$985$	−22.4808	+	1.34936i	−0.716297	+	0.0429943i
$986$	−6.46410			−0.205859
$987$			6.24871i			0.198899i
$988$			10.3397i			0.328951i
$989$	25.8564			0.822186
$990$		0			0
$991$	−38.2487			−1.21501			−0.607505	−	0.794316i	$-0.707830\pi$
$991$	−38.2487			−1.21501			−0.607505	+	0.794316i	$0.707830\pi$
$992$			8.73205i			0.277243i
$993$		−	6.92820i		−	0.219860i
$994$	−8.78461			−0.278631
$995$	1.75129	+	29.1769i	0.0555196	+	0.924970i
$996$	2.39230			0.0758031
$997$		−	21.1436i		−	0.669624i	−0.942285	−	0.334812i	$-0.891327\pi$
$997$		−	21.1436i		−	0.669624i	0.942285	−	0.334812i	$-0.108673\pi$
$998$			10.9282i			0.345926i
$999$	−31.7128			−1.00335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1210.2.b.j.969.4	yes	4
5.2	odd	4		6050.2.a.bt.1.2		2
5.3	odd	4		6050.2.a.cu.1.1		2
5.4	even	2	inner	1210.2.b.j.969.1	yes	4
11.10	odd	2		1210.2.b.i.969.2	✓	4
55.32	even	4		6050.2.a.cn.1.2		2
55.43	even	4		6050.2.a.cd.1.1		2
55.54	odd	2		1210.2.b.i.969.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1210.2.b.i.969.2	✓	4	11.10	odd	2
1210.2.b.i.969.3	yes	4	55.54	odd	2
1210.2.b.j.969.1	yes	4	5.4	even	2	inner
1210.2.b.j.969.4	yes	4	1.1	even	1	trivial
6050.2.a.bt.1.2		2	5.2	odd	4
6050.2.a.cd.1.1		2	55.43	even	4
6050.2.a.cn.1.2		2	55.32	even	4
6050.2.a.cu.1.1		2	5.3	odd	4

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:	\( N \)	\(=\)	\( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1210.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +0.732051i q^{3} -1.00000 q^{4} +(0.133975 + 2.23205i) q^{5} -0.732051 q^{6} +1.26795i q^{7} -1.00000i q^{8} +2.46410 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +0.732051i q^{3} -1.00000 q^{4} +(0.133975 + 2.23205i) q^{5} -0.732051 q^{6} +1.26795i q^{7} -1.00000i q^{8} +2.46410 q^{9} +(-2.23205 + 0.133975i) q^{10} -0.732051i q^{12} +2.46410i q^{13} -1.26795 q^{14} +(-1.63397 + 0.0980762i) q^{15} +1.00000 q^{16} +1.73205i q^{17} +2.46410i q^{18} -4.19615 q^{19} +(-0.133975 - 2.23205i) q^{20} -0.928203 q^{21} +2.73205i q^{23} +0.732051 q^{24} +(-4.96410 + 0.598076i) q^{25} -2.46410 q^{26} +4.00000i q^{27} -1.26795i q^{28} +3.73205 q^{29} +(-0.0980762 - 1.63397i) q^{30} +8.73205 q^{31} +1.00000i q^{32} -1.73205 q^{34} +(-2.83013 + 0.169873i) q^{35} -2.46410 q^{36} +7.92820i q^{37} -4.19615i q^{38} -1.80385 q^{39} +(2.23205 - 0.133975i) q^{40} -10.4641 q^{41} -0.928203i q^{42} -9.46410i q^{43} +(0.330127 + 5.50000i) q^{45} -2.73205 q^{46} -6.73205i q^{47} +0.732051i q^{48} +5.39230 q^{49} +(-0.598076 - 4.96410i) q^{50} -1.26795 q^{51} -2.46410i q^{52} +3.00000i q^{53} -4.00000 q^{54} +1.26795 q^{56} -3.07180i q^{57} +3.73205i q^{58} -13.8564 q^{59} +(1.63397 - 0.0980762i) q^{60} -8.92820 q^{61} +8.73205i q^{62} +3.12436i q^{63} -1.00000 q^{64} +(-5.50000 + 0.330127i) q^{65} -7.26795i q^{67} -1.73205i q^{68} -2.00000 q^{69} +(-0.169873 - 2.83013i) q^{70} +6.92820 q^{71} -2.46410i q^{72} -12.9282i q^{73} -7.92820 q^{74} +(-0.437822 - 3.63397i) q^{75} +4.19615 q^{76} -1.80385i q^{78} -7.26795 q^{79} +(0.133975 + 2.23205i) q^{80} +4.46410 q^{81} -10.4641i q^{82} +3.26795i q^{83} +0.928203 q^{84} +(-3.86603 + 0.232051i) q^{85} +9.46410 q^{86} +2.73205i q^{87} -0.464102 q^{89} +(-5.50000 + 0.330127i) q^{90} -3.12436 q^{91} -2.73205i q^{92} +6.39230i q^{93} +6.73205 q^{94} +(-0.562178 - 9.36603i) q^{95} -0.732051 q^{96} +17.1962i q^{97} +5.39230i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{9} - 2 q^{10} - 12 q^{14} - 10 q^{15} + 4 q^{16} + 4 q^{19} - 4 q^{20} + 24 q^{21} - 4 q^{24} - 6 q^{25} + 4 q^{26} + 8 q^{29} + 10 q^{30} + 28 q^{31} + 6 q^{35} + 4 q^{36} - 28 q^{39} + 2 q^{40} - 28 q^{41} - 16 q^{45} - 4 q^{46} - 20 q^{49} + 8 q^{50} - 12 q^{51} - 16 q^{54} + 12 q^{56} + 10 q^{60} - 8 q^{61} - 4 q^{64} - 22 q^{65} - 8 q^{69} - 18 q^{70} - 4 q^{74} - 26 q^{75} - 4 q^{76} - 36 q^{79} + 4 q^{80} + 4 q^{81} - 24 q^{84} - 12 q^{85} + 24 q^{86} + 12 q^{89} - 22 q^{90} + 36 q^{91} + 20 q^{94} + 22 q^{95} + 4 q^{96}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^9 - 2 * q^10 - 12 * q^14 - 10 * q^15 + 4 * q^16 + 4 * q^19 - 4 * q^20 + 24 * q^21 - 4 * q^24 - 6 * q^25 + 4 * q^26 + 8 * q^29 + 10 * q^30 + 28 * q^31 + 6 * q^35 + 4 * q^36 - 28 * q^39 + 2 * q^40 - 28 * q^41 - 16 * q^45 - 4 * q^46 - 20 * q^49 + 8 * q^50 - 12 * q^51 - 16 * q^54 + 12 * q^56 + 10 * q^60 - 8 * q^61 - 4 * q^64 - 22 * q^65 - 8 * q^69 - 18 * q^70 - 4 * q^74 - 26 * q^75 - 4 * q^76 - 36 * q^79 + 4 * q^80 + 4 * q^81 - 24 * q^84 - 12 * q^85 + 24 * q^86 + 12 * q^89 - 22 * q^90 + 36 * q^91 + 20 * q^94 + 22 * q^95 + 4 * q^96

Introduction

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