LMFDB - Embedded newform 1210.2.b.k.969.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1210,2,Mod(969,1210)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1210.969"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [8,0,0,-8,2,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$9.66189864457$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.12904960000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 6x^{5} + 59x^{4} - 86x^{3} + 72x^{2} + 132x + 121 $ x^8 - 2x^7 + 2x^6 + 6x^5 + 59x^4 - 86x^3 + 72x^2 + 132*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			969.8
Root			$-0.549472 - 0.549472i$ of defining polynomial
Character	$\chi$	$=$	1210.969
Dual form			1210.2.b.k.969.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +1.61803i q^{3} -1.00000 q^{4} +(2.16751 + 0.549472i) q^{5} -1.61803 q^{6} -3.77813i q^{7} -1.00000i q^{8} +0.381966 q^{9} +(-0.549472 + 2.16751i) q^{10} -1.61803i q^{12} -3.09894i q^{13} +3.77813 q^{14} +(-0.889064 + 3.50710i) q^{15} +1.00000 q^{16} +3.29722i q^{17} +0.381966i q^{18} -1.29722 q^{19} +(-2.16751 - 0.549472i) q^{20} +6.11314 q^{21} +0.556884i q^{23} +1.61803 q^{24} +(4.39616 + 2.38197i) q^{25} +3.09894 q^{26} +5.47214i q^{27} +3.77813i q^{28} +9.57108 q^{29} +(-3.50710 - 0.889064i) q^{30} +5.34921 q^{31} +1.00000i q^{32} -3.29722 q^{34} +(2.07597 - 8.18911i) q^{35} -0.381966 q^{36} -7.91525i q^{37} -1.29722i q^{38} +5.01420 q^{39} +(0.549472 - 2.16751i) q^{40} +6.28806 q^{41} +6.11314i q^{42} +3.61803i q^{43} +(0.827913 + 0.209880i) q^{45} -0.556884 q^{46} +5.34921i q^{47} +1.61803i q^{48} -7.27425 q^{49} +(-2.38197 + 4.39616i) q^{50} -5.33501 q^{51} +3.09894i q^{52} +11.0142i q^{53} -5.47214 q^{54} -3.77813 q^{56} -2.09894i q^{57} +9.57108i q^{58} -5.29722 q^{59} +(0.889064 - 3.50710i) q^{60} +2.45731 q^{61} +5.34921i q^{62} -1.44312i q^{63} -1.00000 q^{64} +(1.70278 - 6.71698i) q^{65} -9.21247i q^{67} -3.29722i q^{68} -0.901057 q^{69} +(8.18911 + 2.07597i) q^{70} +10.8919 q^{71} -0.381966i q^{72} -3.39616i q^{73} +7.91525 q^{74} +(-3.85410 + 7.11314i) q^{75} +1.29722 q^{76} +5.01420i q^{78} -16.3634 q^{79} +(2.16751 + 0.549472i) q^{80} -7.70820 q^{81} +6.28806i q^{82} +0.184079i q^{83} -6.11314 q^{84} +(-1.81173 + 7.14674i) q^{85} -3.61803 q^{86} +15.4863i q^{87} -6.09017 q^{89} +(-0.209880 + 0.827913i) q^{90} -11.7082 q^{91} -0.556884i q^{92} +8.65520i q^{93} -5.34921 q^{94} +(-2.81173 - 0.712785i) q^{95} -1.61803 q^{96} -12.3580i q^{97} -7.27425i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 2 q^{5} - 4 q^{6} + 12 q^{9} + 2 q^{10} + 4 q^{14} + 6 q^{15} + 8 q^{16} + 12 q^{19} - 2 q^{20} - 8 q^{21} + 4 q^{24} + 12 q^{26} + 28 q^{29} - 6 q^{30} - 32 q^{31} - 4 q^{34} + 16 q^{35}+ \cdots - 4 q^{96}+O(q^{100}) $ 8 * q - 8 * q^4 + 2 * q^5 - 4 * q^6 + 12 * q^9 + 2 * q^10 + 4 * q^14 + 6 * q^15 + 8 * q^16 + 12 * q^19 - 2 * q^20 - 8 * q^21 + 4 * q^24 + 12 * q^26 + 28 * q^29 - 6 * q^30 - 32 * q^31 - 4 * q^34 + 16 * q^35 - 12 * q^36 - 4 * q^39 - 2 * q^40 - 20 * q^41 - 2 * q^45 - 48 * q^49 - 28 * q^50 - 12 * q^51 - 8 * q^54 - 4 * q^56 - 20 * q^59 - 6 * q^60 - 20 * q^61 - 8 * q^64 + 36 * q^65 - 20 * q^69 + 8 * q^70 + 52 * q^71 + 32 * q^74 - 4 * q^75 - 12 * q^76 - 12 * q^79 + 2 * q^80 - 8 * q^81 + 8 * q^84 + 28 * q^85 - 20 * q^86 - 4 * q^89 - 2 * q^90 - 40 * q^91 + 32 * q^94 + 20 * q^95 - 4 * q^96

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
$3$			1.61803i			0.934172i	0.884212	+	0.467086i	$0.154696\pi$
$3$			1.61803i			0.934172i	−0.884212	+	0.467086i	$0.845304\pi$
$4$	−1.00000			−0.500000
$5$	2.16751	+	0.549472i	0.969338	+	0.245731i
$5$	2.16751	+	0.549472i	0.969338	+	0.245731i
$6$	−1.61803			−0.660560
$7$		−	3.77813i		−	1.42800i	−0.700147	−	0.713999i	$-0.746882\pi$
$7$		−	3.77813i		−	1.42800i	0.700147	−	0.713999i	$-0.253118\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.381966			0.127322
$10$	−0.549472	+	2.16751i	−0.173758	+	0.685425i
$11$		0			0
$11$		0			0
$12$		−	1.61803i		−	0.467086i
$13$		−	3.09894i		−	0.859492i	−0.902950	−	0.429746i	$-0.858603\pi$
$13$		−	3.09894i		−	0.859492i	0.902950	−	0.429746i	$-0.141397\pi$
$14$	3.77813			1.00975
$15$	−0.889064	+	3.50710i	−0.229555	+	0.905529i
$16$	1.00000			0.250000
$17$			3.29722i			0.799693i	0.916582	+	0.399846i	$0.130937\pi$
$17$			3.29722i			0.799693i	−0.916582	+	0.399846i	$0.869063\pi$
$18$			0.381966i			0.0900303i
$19$	−1.29722			−0.297602			−0.148801	−	0.988867i	$-0.547541\pi$
$19$	−1.29722			−0.297602			−0.148801	+	0.988867i	$0.547541\pi$
$20$	−2.16751	−	0.549472i	−0.484669	−	0.122866i
$21$	6.11314			1.33400
$22$		0			0
$23$			0.556884i			0.116118i	0.998313	+	0.0580591i	$0.0184912\pi$
$23$			0.556884i			0.116118i	−0.998313	+	0.0580591i	$0.981509\pi$
$24$	1.61803			0.330280
$25$	4.39616	+	2.38197i	0.879232	+	0.476393i
$26$	3.09894			0.607753
$27$			5.47214i			1.05311i
$28$			3.77813i			0.713999i
$29$	9.57108			1.77730			0.888652	−	0.458581i	$-0.151642\pi$
$29$	9.57108			1.77730			0.888652	+	0.458581i	$0.151642\pi$
$30$	−3.50710	−	0.889064i	−0.640306	−	0.162320i
$31$	5.34921			0.960746			0.480373	−	0.877064i	$-0.340501\pi$
$31$	5.34921			0.960746			0.480373	+	0.877064i	$0.340501\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−3.29722			−0.565468
$35$	2.07597	−	8.18911i	0.350904	−	1.38421i
$36$	−0.381966			−0.0636610
$37$		−	7.91525i		−	1.30126i	−0.759395	−	0.650630i	$-0.774505\pi$
$37$		−	7.91525i		−	1.30126i	0.759395	−	0.650630i	$-0.225495\pi$
$38$		−	1.29722i		−	0.210437i
$39$	5.01420			0.802914
$40$	0.549472	−	2.16751i	0.0868791	−	0.342713i
$41$	6.28806			0.982029			0.491015	−	0.871151i	$-0.336626\pi$
$41$	6.28806			0.982029			0.491015	+	0.871151i	$0.336626\pi$
$42$			6.11314i			0.943278i
$43$			3.61803i			0.551745i	0.961194	+	0.275873i	$0.0889668\pi$
$43$			3.61803i			0.551745i	−0.961194	+	0.275873i	$0.911033\pi$
$44$		0			0
$45$	0.827913	+	0.209880i	0.123418	+	0.0312870i
$46$	−0.556884			−0.0821080
$47$			5.34921i			0.780262i	0.920759	+	0.390131i	$0.127570\pi$
$47$			5.34921i			0.780262i	−0.920759	+	0.390131i	$0.872430\pi$
$48$			1.61803i			0.233543i
$49$	−7.27425			−1.03918
$50$	−2.38197	+	4.39616i	−0.336861	+	0.621711i
$51$	−5.33501			−0.747051
$52$			3.09894i			0.429746i
$53$			11.0142i			1.51292i	0.654042	+	0.756458i	$0.273072\pi$
$53$			11.0142i			1.51292i	−0.654042	+	0.756458i	$0.726928\pi$
$54$	−5.47214			−0.744663
$55$		0			0
$56$	−3.77813			−0.504874
$57$		−	2.09894i		−	0.278012i
$58$			9.57108i			1.25674i
$59$	−5.29722			−0.689639			−0.344820	−	0.938669i	$-0.612060\pi$
$59$	−5.29722			−0.689639			−0.344820	+	0.938669i	$0.612060\pi$
$60$	0.889064	−	3.50710i	0.114778	−	0.452764i
$61$	2.45731			0.314627			0.157313	−	0.987549i	$-0.449717\pi$
$61$	2.45731			0.314627			0.157313	+	0.987549i	$0.449717\pi$
$62$			5.34921i			0.679350i
$63$		−	1.44312i		−	0.181816i
$64$	−1.00000			−0.125000
$65$	1.70278	−	6.71698i	0.211204	−	0.833139i
$66$		0			0
$67$		−	9.21247i		−	1.12548i	−0.826633	−	0.562741i	$-0.809747\pi$
$67$		−	9.21247i		−	1.12548i	0.826633	−	0.562741i	$-0.190253\pi$
$68$		−	3.29722i		−	0.399846i
$69$	−0.901057			−0.108474
$70$	8.18911	+	2.07597i	0.978786	+	0.248126i
$71$	10.8919			1.29263			0.646315	−	0.763071i	$-0.276309\pi$
$71$	10.8919			1.29263			0.646315	+	0.763071i	$0.276309\pi$
$72$		−	0.381966i		−	0.0450151i
$73$		−	3.39616i		−	0.397491i	−0.980051	−	0.198745i	$-0.936313\pi$
$73$		−	3.39616i		−	0.397491i	0.980051	−	0.198745i	$-0.0636867\pi$
$74$	7.91525			0.920129
$75$	−3.85410	+	7.11314i	−0.445033	+	0.821355i
$76$	1.29722			0.148801
$77$		0			0
$78$			5.01420i			0.567746i
$79$	−16.3634			−1.84103			−0.920513	−	0.390711i	$-0.872229\pi$
$79$	−16.3634			−1.84103			−0.920513	+	0.390711i	$0.872229\pi$
$80$	2.16751	+	0.549472i	0.242335	+	0.0614328i
$81$	−7.70820			−0.856467
$82$			6.28806i			0.694400i
$83$			0.184079i			0.0202053i	0.999949	+	0.0101027i	$0.00321583\pi$
$83$			0.184079i			0.0202053i	−0.999949	+	0.0101027i	$0.996784\pi$
$84$	−6.11314			−0.666998
$85$	−1.81173	+	7.14674i	−0.196510	+	0.775173i
$86$	−3.61803			−0.390143
$87$			15.4863i			1.66031i
$88$		0			0
$89$	−6.09017			−0.645557			−0.322778	−	0.946475i	$-0.604617\pi$
$89$	−6.09017			−0.645557			−0.322778	+	0.946475i	$0.604617\pi$
$90$	−0.209880	+	0.827913i	−0.0221232	+	0.0872697i
$91$	−11.7082			−1.22735
$92$		−	0.556884i		−	0.0580591i
$93$			8.65520i			0.897502i
$94$	−5.34921			−0.551729
$95$	−2.81173	−	0.712785i	−0.288477	−	0.0731302i
$96$	−1.61803			−0.165140
$97$		−	12.3580i		−	1.25476i	−0.778712	−	0.627381i	$-0.784127\pi$
$97$		−	12.3580i		−	1.25476i	0.778712	−	0.627381i	$-0.215873\pi$
$98$		−	7.27425i		−	0.734810i
$99$		0			0
$100$	−4.39616	−	2.38197i	−0.439616	−	0.238197i
$101$	−9.01420			−0.896946			−0.448473	−	0.893796i	$-0.648032\pi$
$101$	−9.01420			−0.896946			−0.448473	+	0.893796i	$0.648032\pi$
$102$		−	5.33501i		−	0.528245i
$103$			11.4340i			1.12662i	0.826245	+	0.563311i	$0.190473\pi$
$103$			11.4340i			1.12662i	−0.826245	+	0.563311i	$0.809527\pi$
$104$	−3.09894			−0.303876
$105$	13.2503	+	3.35900i	1.29309	+	0.327805i
$106$	−11.0142			−1.06979
$107$		−	15.3546i		−	1.48439i	−0.670185	−	0.742194i	$-0.733785\pi$
$107$		−	15.3546i		−	1.48439i	0.670185	−	0.742194i	$-0.266215\pi$
$108$		−	5.47214i		−	0.526557i
$109$	−2.42892			−0.232648			−0.116324	−	0.993211i	$-0.537111\pi$
$109$	−2.42892			−0.232648			−0.116324	+	0.993211i	$0.537111\pi$
$110$		0			0
$111$	12.8071			1.21560
$112$		−	3.77813i		−	0.357000i
$113$			8.38134i			0.788450i	0.919014	+	0.394225i	$0.128987\pi$
$113$			8.38134i			0.788450i	−0.919014	+	0.394225i	$0.871013\pi$
$114$	2.09894			0.196584
$115$	−0.305992	+	1.20705i	−0.0285339	+	0.112558i
$116$	−9.57108			−0.888652
$117$		−	1.18369i		−	0.109432i
$118$		−	5.29722i		−	0.487648i
$119$	12.4573			1.14196
$120$	3.50710	+	0.889064i	0.320153	+	0.0811601i
$121$		0			0
$122$			2.45731i			0.222475i
$123$			10.1743i			0.917385i
$124$	−5.34921			−0.480373
$125$	8.21988	+	7.57849i	0.735209	+	0.677841i
$126$	1.44312			0.128563
$127$		−	6.95343i		−	0.617017i	−0.951222	−	0.308509i	$-0.900170\pi$
$127$		−	6.95343i		−	0.617017i	0.951222	−	0.308509i	$-0.0998299\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−5.85410			−0.515425
$130$	6.71698	+	1.70278i	0.589118	+	0.149344i
$131$	−5.61741			−0.490795			−0.245398	−	0.969423i	$-0.578918\pi$
$131$	−5.61741			−0.490795			−0.245398	+	0.969423i	$0.578918\pi$
$132$		0			0
$133$			4.90106i			0.424976i
$134$	9.21247			0.795836
$135$	−3.00678	+	11.8609i	−0.258783	+	1.02082i
$136$	3.29722			0.282734
$137$		−	7.68796i		−	0.656827i	−0.944534	−	0.328413i	$-0.893486\pi$
$137$		−	7.68796i		−	0.656827i	0.944534	−	0.328413i	$-0.106514\pi$
$138$		−	0.901057i		−	0.0767030i
$139$	−0.961819			−0.0815804			−0.0407902	−	0.999168i	$-0.512988\pi$
$139$	−0.961819			−0.0815804			−0.0407902	+	0.999168i	$0.512988\pi$
$140$	−2.07597	+	8.18911i	−0.175452	+	0.692106i
$141$	−8.65520			−0.728899
$142$			10.8919i			0.914028i
$143$		0			0
$144$	0.381966			0.0318305
$145$	20.7454	+	5.25904i	1.72281	+	0.436739i
$146$	3.39616			0.281068
$147$		−	11.7700i		−	0.970772i
$148$			7.91525i			0.650630i
$149$	8.79232			0.720295			0.360148	−	0.932895i	$-0.382726\pi$
$149$	8.79232			0.720295			0.360148	+	0.932895i	$0.382726\pi$
$150$	−7.11314	−	3.85410i	−0.580785	−	0.314686i
$151$	−8.93783			−0.727351			−0.363675	−	0.931526i	$-0.618478\pi$
$151$	−8.93783			−0.727351			−0.363675	+	0.931526i	$0.618478\pi$
$152$			1.29722i			0.105218i
$153$			1.25943i			0.101819i
$154$		0			0
$155$	11.5944	+	2.93924i	0.931288	+	0.236085i
$156$	−5.01420			−0.401457
$157$		−	17.6410i		−	1.40791i	−0.710247	−	0.703953i	$-0.751417\pi$
$157$		−	17.6410i		−	1.40791i	0.710247	−	0.703953i	$-0.248583\pi$
$158$		−	16.3634i		−	1.30180i
$159$	−17.8213			−1.41332
$160$	−0.549472	+	2.16751i	−0.0434396	+	0.171356i
$161$	2.10398			0.165817
$162$		−	7.70820i		−	0.605614i
$163$		−	0.174289i		−	0.0136514i	−0.999977	−	0.00682570i	$-0.997827\pi$
$163$		−	0.174289i		−	0.0136514i	0.999977	−	0.00682570i	$-0.00217271\pi$
$164$	−6.28806			−0.491015
$165$		0			0
$166$	−0.184079			−0.0142873
$167$			5.48633i			0.424545i	0.977211	+	0.212273i	$0.0680865\pi$
$167$			5.48633i			0.424545i	−0.977211	+	0.212273i	$0.931914\pi$
$168$		−	6.11314i		−	0.471639i
$169$	3.39655			0.261273
$170$	−7.14674	−	1.81173i	−0.548130	−	0.138953i
$171$	−0.495493			−0.0378913
$172$		−	3.61803i		−	0.275873i
$173$			23.9960i			1.82438i	0.409763	+	0.912192i	$0.365611\pi$
$173$			23.9960i			1.82438i	−0.409763	+	0.912192i	$0.634389\pi$
$174$	−15.4863			−1.17402
$175$	8.99937	−	16.6093i	0.680289	−	1.25554i
$176$		0			0
$177$		−	8.57108i		−	0.644242i
$178$		−	6.09017i		−	0.456478i
$179$	0.213099			0.0159278			0.00796388	−	0.999968i	$-0.497465\pi$
$179$	0.213099			0.0159278			0.00796388	+	0.999968i	$0.497465\pi$
$180$	−0.827913	−	0.209880i	−0.0617090	−	0.0156435i
$181$	1.03818			0.0771674			0.0385837	−	0.999255i	$-0.487715\pi$
$181$	1.03818			0.0771674			0.0385837	+	0.999255i	$0.487715\pi$
$182$		−	11.7082i		−	0.867870i
$183$			3.97601i			0.293915i
$184$	0.556884			0.0410540
$185$	4.34921	−	17.1564i	0.319760	−	1.26136i
$186$	−8.65520			−0.634630
$187$		0			0
$188$		−	5.34921i		−	0.390131i
$189$	20.6744			1.50384
$190$	0.712785	−	2.81173i	0.0517108	−	0.203984i
$191$	−17.9345			−1.29769			−0.648847	−	0.760919i	$-0.724748\pi$
$191$	−17.9345			−1.29769			−0.648847	+	0.760919i	$0.724748\pi$
$192$		−	1.61803i		−	0.116772i
$193$			9.01986i			0.649264i	0.945840	+	0.324632i	$0.105240\pi$
$193$			9.01986i			0.649264i	−0.945840	+	0.324632i	$0.894760\pi$
$194$	12.3580			0.887251
$195$	10.8683	+	2.75516i	0.778295	+	0.197301i
$196$	7.27425			0.519589
$197$		−	3.68422i		−	0.262490i	−0.991350	−	0.131245i	$-0.958103\pi$
$197$		−	3.68422i		−	0.262490i	0.991350	−	0.131245i	$-0.0418974\pi$
$198$		0			0
$199$	4.23544			0.300242			0.150121	−	0.988668i	$-0.452034\pi$
$199$	4.23544			0.300242			0.150121	+	0.988668i	$0.452034\pi$
$200$	2.38197	−	4.39616i	0.168430	−	0.310856i
$201$	14.9061			1.05139
$202$		−	9.01420i		−	0.634237i
$203$		−	36.1608i		−	2.53799i
$204$	5.33501			0.373526
$205$	13.6294	+	3.45511i	0.951918	+	0.241315i
$206$	−11.4340			−0.796641
$207$			0.212711i			0.0147844i
$208$		−	3.09894i		−	0.214873i
$209$		0			0
$210$	−3.35900	+	13.2503i	−0.231793	+	0.914355i
$211$	−13.6704			−0.941110			−0.470555	−	0.882371i	$-0.655946\pi$
$211$	−13.6704			−0.941110			−0.470555	+	0.882371i	$0.655946\pi$
$212$		−	11.0142i		−	0.756458i
$213$			17.6235i			1.20754i
$214$	15.3546			1.04962
$215$	−1.98801	+	7.84211i	−0.135581	+	0.534827i
$216$	5.47214			0.372332
$217$		−	20.2100i		−	1.37194i
$218$		−	2.42892i		−	0.164507i
$219$	5.49511			0.371325
$220$		0			0
$221$	10.2179			0.687330
$222$			12.8071i			0.859559i
$223$		−	23.9720i		−	1.60529i	−0.596460	−	0.802643i	$-0.703426\pi$
$223$		−	23.9720i		−	1.60529i	0.596460	−	0.802643i	$-0.296574\pi$
$224$	3.77813			0.252437
$225$	1.67918	+	0.909830i	0.111946	+	0.0606553i
$226$	−8.38134			−0.557518
$227$			20.7045i			1.37420i	0.726561	+	0.687102i	$0.241117\pi$
$227$			20.7045i			1.37420i	−0.726561	+	0.687102i	$0.758883\pi$
$228$			2.09894i			0.139006i
$229$	16.3407			1.07982			0.539911	−	0.841722i	$-0.318458\pi$
$229$	16.3407			1.07982			0.539911	+	0.841722i	$0.318458\pi$
$230$	−1.20705	−	0.305992i	−0.0795904	−	0.0201765i
$231$		0			0
$232$		−	9.57108i		−	0.628372i
$233$		−	0.480281i		−	0.0314643i	−0.999876	−	0.0157321i	$-0.994992\pi$
$233$		−	0.480281i		−	0.0314643i	0.999876	−	0.0157321i	$-0.00500790\pi$
$234$	1.18369			0.0773803
$235$	−2.93924	+	11.5944i	−0.191735	+	0.756338i
$236$	5.29722			0.344820
$237$		−	26.4765i		−	1.71984i
$238$			12.4573i			0.807488i
$239$	−1.12859			−0.0730025			−0.0365012	−	0.999334i	$-0.511621\pi$
$239$	−1.12859			−0.0730025			−0.0365012	+	0.999334i	$0.511621\pi$
$240$	−0.889064	+	3.50710i	−0.0573888	+	0.226382i
$241$	−12.7220			−0.819497			−0.409748	−	0.912199i	$-0.634384\pi$
$241$	−12.7220			−0.819497			−0.409748	+	0.912199i	$0.634384\pi$
$242$		0			0
$243$			3.94427i			0.253025i
$244$	−2.45731			−0.157313
$245$	−15.7670	−	3.99699i	−1.00732	−	0.255359i
$246$	−10.1743			−0.648689
$247$			4.02001i			0.255787i
$248$		−	5.34921i		−	0.339675i
$249$	−0.297846			−0.0188753
$250$	−7.57849	+	8.21988i	−0.479306	+	0.519871i
$251$	−2.83952			−0.179229			−0.0896144	−	0.995977i	$-0.528563\pi$
$251$	−2.83952			−0.179229			−0.0896144	+	0.995977i	$0.528563\pi$
$252$			1.44312i			0.0909078i
$253$		0			0
$254$	6.95343			0.436297
$255$	−11.5637	−	2.93144i	−0.724145	−	0.183574i
$256$	1.00000			0.0625000
$257$		−	30.8410i		−	1.92381i	−0.273390	−	0.961903i	$-0.588145\pi$
$257$		−	30.8410i		−	1.92381i	0.273390	−	0.961903i	$-0.411855\pi$
$258$		−	5.85410i		−	0.364460i
$259$	−29.9048			−1.85820
$260$	−1.70278	+	6.71698i	−0.105602	+	0.416569i
$261$	3.65583			0.226290
$262$		−	5.61741i		−	0.347044i
$263$		−	27.7069i		−	1.70848i	−0.519876	−	0.854242i	$-0.674022\pi$
$263$		−	27.7069i		−	1.70848i	0.519876	−	0.854242i	$-0.325978\pi$
$264$		0			0
$265$	−6.05199	+	23.8733i	−0.371771	+	1.46653i
$266$	−4.90106			−0.300503
$267$		−	9.85410i		−	0.603061i
$268$			9.21247i			0.562741i
$269$	−12.7592			−0.777941			−0.388970	−	0.921250i	$-0.627169\pi$
$269$	−12.7592			−0.777941			−0.388970	+	0.921250i	$0.627169\pi$
$270$	−11.8609	−	3.00678i	−0.721831	−	0.182987i
$271$	5.70254			0.346405			0.173202	−	0.984886i	$-0.444589\pi$
$271$	5.70254			0.346405			0.173202	+	0.984886i	$0.444589\pi$
$272$			3.29722i			0.199923i
$273$		−	18.9443i		−	1.14656i
$274$	7.68796			0.464447
$275$		0			0
$276$	0.901057			0.0542372
$277$			31.7274i			1.90632i	0.302472	+	0.953158i	$0.402188\pi$
$277$			31.7274i			1.90632i	−0.302472	+	0.953158i	$0.597812\pi$
$278$		−	0.961819i		−	0.0576861i
$279$	2.04322			0.122324
$280$	−8.18911	−	2.07597i	−0.489393	−	0.124063i
$281$	−1.93822			−0.115625			−0.0578123	−	0.998327i	$-0.518412\pi$
$281$	−1.93822			−0.115625			−0.0578123	+	0.998327i	$0.518412\pi$
$282$		−	8.65520i		−	0.515410i
$283$			4.91588i			0.292219i	0.989268	+	0.146109i	$0.0466751\pi$
$283$			4.91588i			0.292219i	−0.989268	+	0.146109i	$0.953325\pi$
$284$	−10.8919			−0.646315
$285$	1.15331	−	4.54947i	0.0683162	−	0.269487i
$286$		0			0
$287$		−	23.7571i		−	1.40234i
$288$			0.381966i			0.0225076i
$289$	6.12835			0.360491
$290$	−5.25904	+	20.7454i	−0.308821	+	1.21821i
$291$	19.9956			1.17216
$292$			3.39616i			0.198745i
$293$		−	0.188725i		−	0.0110254i	−0.999985	−	0.00551272i	$-0.998245\pi$
$293$		−	0.188725i		−	0.0110254i	0.999985	−	0.00551272i	$-0.00175476\pi$
$294$	11.7700			0.686439
$295$	−11.4818	−	2.91067i	−0.668493	−	0.169466i
$296$	−7.91525			−0.460065
$297$		0			0
$298$			8.79232i			0.509326i
$299$	1.72575			0.0998027
$300$	3.85410	−	7.11314i	0.222517	−	0.410677i
$301$	13.6694			0.787891
$302$		−	8.93783i		−	0.514315i
$303$		−	14.5853i		−	0.837902i
$304$	−1.29722			−0.0744006
$305$	5.32624	+	1.35022i	0.304979	+	0.0773136i
$306$	−1.25943			−0.0719966
$307$			12.3820i			0.706676i	0.935496	+	0.353338i	$0.114953\pi$
$307$			12.3820i			0.706676i	−0.935496	+	0.353338i	$0.885047\pi$
$308$		0			0
$309$	−18.5005			−1.05246
$310$	−2.93924	+	11.5944i	−0.166937	+	0.658520i
$311$	−21.1182			−1.19750			−0.598751	−	0.800935i	$-0.704336\pi$
$311$	−21.1182			−1.19750			−0.598751	+	0.800935i	$0.704336\pi$
$312$		−	5.01420i		−	0.283873i
$313$			16.5792i			0.937113i	0.883433	+	0.468557i	$0.155226\pi$
$313$			16.5792i			0.937113i	−0.883433	+	0.468557i	$0.844774\pi$
$314$	17.6410			0.995539
$315$	0.792952	−	3.12796i	0.0446778	−	0.176241i
$316$	16.3634			0.920513
$317$			19.6370i			1.10293i	0.834200	+	0.551463i	$0.185930\pi$
$317$			19.6370i			1.10293i	−0.834200	+	0.551463i	$0.814070\pi$
$318$		−	17.8213i		−	0.999371i
$319$		0			0
$320$	−2.16751	−	0.549472i	−0.121167	−	0.0307164i
$321$	24.8443			1.38667
$322$			2.10398i			0.117250i
$323$		−	4.27721i		−	0.237990i
$324$	7.70820			0.428234
$325$	7.38158	−	13.6235i	0.409456	−	0.755693i
$326$	0.174289			0.00965300
$327$		−	3.93008i		−	0.217334i
$328$		−	6.28806i		−	0.347200i
$329$	20.2100			1.11421
$330$		0			0
$331$	−23.4826			−1.29072			−0.645360	−	0.763879i	$-0.723293\pi$
$331$	−23.4826			−1.29072			−0.645360	+	0.763879i	$0.723293\pi$
$332$		−	0.184079i		−	0.0101027i
$333$		−	3.02336i		−	0.165679i
$334$	−5.48633			−0.300199
$335$	5.06199	−	19.9681i	0.276566	−	1.09097i
$336$	6.11314			0.333499
$337$		−	12.8251i		−	0.698627i	−0.937006	−	0.349313i	$-0.886415\pi$
$337$		−	12.8251i		−	0.698627i	0.937006	−	0.349313i	$-0.113585\pi$
$338$			3.39655i			0.184748i
$339$	−13.5613			−0.736548
$340$	1.81173	−	7.14674i	0.0982548	−	0.387586i
$341$		0			0
$342$		−	0.495493i		−	0.0267932i
$343$			1.03615i			0.0559468i
$344$	3.61803			0.195071
$345$	−1.95305	−	0.495105i	−0.105148	−	0.0266556i
$346$	−23.9960			−1.29003
$347$		−	20.6936i		−	1.11089i	−0.831553	−	0.555446i	$-0.812548\pi$
$347$		−	20.6936i		−	1.11089i	0.831553	−	0.555446i	$-0.187452\pi$
$348$		−	15.4863i		−	0.830155i
$349$	−21.7174			−1.16250			−0.581252	−	0.813724i	$-0.697437\pi$
$349$	−21.7174			−1.16250			−0.581252	+	0.813724i	$0.697437\pi$
$350$	16.6093	+	8.99937i	0.887802	+	0.481037i
$351$	16.9578			0.905143
$352$		0			0
$353$		−	0.260293i		−	0.0138540i	−0.999976	−	0.00692701i	$-0.997795\pi$
$353$		−	0.260293i		−	0.0138540i	0.999976	−	0.00692701i	$-0.00220495\pi$
$354$	8.57108			0.455548
$355$	23.6082	+	5.98479i	1.25300	+	0.317640i
$356$	6.09017			0.322778
$357$			20.1564i			1.06679i
$358$			0.213099i			0.0112626i
$359$	−8.22187			−0.433934			−0.216967	−	0.976179i	$-0.569616\pi$
$359$	−8.22187			−0.433934			−0.216967	+	0.976179i	$0.569616\pi$
$360$	0.209880	−	0.827913i	0.0110616	−	0.0436349i
$361$	−17.3172			−0.911433
$362$			1.03818i			0.0545656i
$363$		0			0
$364$	11.7082			0.613677
$365$	1.86609	−	7.36120i	0.0976759	−	0.385303i
$366$	−3.97601			−0.207830
$367$		−	7.21334i		−	0.376533i	−0.982118	−	0.188267i	$-0.939713\pi$
$367$		−	7.21334i		−	0.376533i	0.982118	−	0.188267i	$-0.0602869\pi$
$368$			0.556884i			0.0290296i
$369$	2.40182			0.125034
$370$	17.1564	+	4.34921i	0.891916	+	0.226105i
$371$	41.6130			2.16044
$372$		−	8.65520i		−	0.448751i
$373$			29.9629i			1.55142i	0.631090	+	0.775709i	$0.282608\pi$
$373$			29.9629i			1.55142i	−0.631090	+	0.775709i	$0.717392\pi$
$374$		0			0
$375$	−12.2623	+	13.3000i	−0.633220	+	0.686812i
$376$	5.34921			0.275864
$377$		−	29.6602i		−	1.52758i
$378$			20.6744i			1.06338i
$379$	36.7066			1.88549			0.942745	−	0.333515i	$-0.108235\pi$
$379$	36.7066			1.88549			0.942745	+	0.333515i	$0.108235\pi$
$380$	2.81173	+	0.712785i	0.144239	+	0.0365651i
$381$	11.2509			0.576401
$382$		−	17.9345i		−	0.917608i
$383$		−	6.44815i		−	0.329485i	−0.986337	−	0.164743i	$-0.947321\pi$
$383$		−	6.44815i		−	0.329485i	0.986337	−	0.164743i	$-0.0526793\pi$
$384$	1.61803			0.0825700
$385$		0			0
$386$	−9.01986			−0.459099
$387$			1.38197i			0.0702493i
$388$			12.3580i			0.627381i
$389$	28.6001			1.45008			0.725041	−	0.688705i	$-0.241821\pi$
$389$	28.6001			1.45008			0.725041	+	0.688705i	$0.241821\pi$
$390$	−2.75516	+	10.8683i	−0.139513	+	0.550338i
$391$	−1.83617			−0.0928590
$392$			7.27425i			0.367405i
$393$		−	9.08915i		−	0.458487i
$394$	3.68422			0.185608
$395$	−35.4678	−	8.99123i	−1.78458	−	0.452398i
$396$		0			0
$397$			24.5049i			1.22987i	0.788579	+	0.614934i	$0.210817\pi$
$397$			24.5049i			1.22987i	−0.788579	+	0.614934i	$0.789183\pi$
$398$			4.23544i			0.212303i
$399$	−7.93008			−0.397000
$400$	4.39616	+	2.38197i	0.219808	+	0.119098i
$401$	−30.7122			−1.53370			−0.766848	−	0.641829i	$-0.778176\pi$
$401$	−30.7122			−1.53370			−0.766848	+	0.641829i	$0.778176\pi$
$402$			14.9061i			0.743448i
$403$		−	16.5769i		−	0.825754i
$404$	9.01420			0.448473
$405$	−16.7076	−	4.23544i	−0.830206	−	0.210461i
$406$	36.1608			1.79463
$407$		0			0
$408$			5.33501i			0.264122i
$409$	−21.8581			−1.08081			−0.540407	−	0.841404i	$-0.681730\pi$
$409$	−21.8581			−1.08081			−0.540407	+	0.841404i	$0.681730\pi$
$410$	−3.45511	+	13.6294i	−0.170636	+	0.673108i
$411$	12.4394			0.613589
$412$		−	11.4340i		−	0.563311i
$413$			20.0136i			0.984803i
$414$	−0.212711			−0.0104542
$415$	−0.101146	+	0.398993i	−0.00496508	+	0.0195858i
$416$	3.09894			0.151938
$417$		−	1.55626i		−	0.0762102i
$418$		0			0
$419$	−4.17764			−0.204091			−0.102046	−	0.994780i	$-0.532539\pi$
$419$	−4.17764			−0.204091			−0.102046	+	0.994780i	$0.532539\pi$
$420$	−13.2503	−	3.35900i	−0.646547	−	0.163902i
$421$	12.6940			0.618668			0.309334	−	0.950953i	$-0.399894\pi$
$421$	12.6940			0.618668			0.309334	+	0.950953i	$0.399894\pi$
$422$		−	13.6704i		−	0.665465i
$423$			2.04322i			0.0993445i
$424$	11.0142			0.534897
$425$	−7.85386	+	14.4951i	−0.380968	+	0.703116i
$426$	−17.6235			−0.853859
$427$		−	9.28404i		−	0.449286i
$428$			15.3546i			0.742194i
$429$		0			0
$430$	−7.84211	−	1.98801i	−0.378180	−	0.0958702i
$431$	−0.730785			−0.0352007			−0.0176003	−	0.999845i	$-0.505603\pi$
$431$	−0.730785			−0.0352007			−0.0176003	+	0.999845i	$0.505603\pi$
$432$			5.47214i			0.263278i
$433$		−	5.64580i		−	0.271320i	−0.990755	−	0.135660i	$-0.956685\pi$
$433$		−	5.64580i		−	0.271320i	0.990755	−	0.135660i	$-0.0433154\pi$
$434$	20.2100			0.970110
$435$	−8.50930	+	33.5667i	−0.407990	+	1.60940i
$436$	2.42892			0.116324
$437$		−	0.722400i		−	0.0345571i
$438$			5.49511i			0.262566i
$439$	−13.7074			−0.654220			−0.327110	−	0.944986i	$-0.606075\pi$
$439$	−13.7074			−0.654220			−0.327110	+	0.944986i	$0.606075\pi$
$440$		0			0
$441$	−2.77852			−0.132310
$442$			10.2179i			0.486016i
$443$		−	14.0435i		−	0.667225i	−0.942710	−	0.333612i	$-0.891732\pi$
$443$		−	14.0435i		−	0.667225i	0.942710	−	0.333612i	$-0.108268\pi$
$444$	−12.8071			−0.607800
$445$	−13.2005	−	3.34638i	−0.625763	−	0.158633i
$446$	23.9720			1.13511
$447$			14.2263i			0.672880i
$448$			3.77813i			0.178500i
$449$	−9.65544			−0.455668			−0.227834	−	0.973700i	$-0.573164\pi$
$449$	−9.65544			−0.455668			−0.227834	+	0.973700i	$0.573164\pi$
$450$	−0.909830	+	1.67918i	−0.0428898	+	0.0791575i
$451$		0			0
$452$		−	8.38134i		−	0.394225i
$453$		−	14.4617i		−	0.679471i
$454$	−20.7045			−0.971709
$455$	−25.3776	−	6.43333i	−1.18972	−	0.301599i
$456$	−2.09894			−0.0982920
$457$		−	1.02878i		−	0.0481243i	−0.999710	−	0.0240621i	$-0.992340\pi$
$457$		−	1.02878i		−	0.0481243i	0.999710	−	0.0240621i	$-0.00765996\pi$
$458$			16.3407i			0.763550i
$459$	−18.0428			−0.842167
$460$	0.305992	−	1.20705i	0.0142669	−	0.0562789i
$461$	−8.05882			−0.375336			−0.187668	−	0.982232i	$-0.560093\pi$
$461$	−8.05882			−0.375336			−0.187668	+	0.982232i	$0.560093\pi$
$462$		0			0
$463$			7.46633i			0.346990i	0.984835	+	0.173495i	$0.0555060\pi$
$463$			7.46633i			0.346990i	−0.984835	+	0.173495i	$0.944494\pi$
$464$	9.57108			0.444326
$465$	−4.75579	+	18.7602i	−0.220544	+	0.869983i
$466$	0.480281			0.0222486
$467$			11.1894i			0.517782i	0.965907	+	0.258891i	$0.0833570\pi$
$467$			11.1894i			0.517782i	−0.965907	+	0.258891i	$0.916643\pi$
$468$			1.18369i			0.0547161i
$469$	−34.8059			−1.60719
$470$	−11.5944	−	2.93924i	−0.534811	−	0.135577i
$471$	28.5437			1.31523
$472$			5.29722i			0.243824i
$473$		0			0
$474$	26.4765			1.21611
$475$	−5.70278	−	3.08993i	−0.261662	−	0.141776i
$476$	−12.4573			−0.570980
$477$			4.20705i			0.192628i
$478$		−	1.12859i		−	0.0516206i
$479$	−26.7696			−1.22313			−0.611567	−	0.791193i	$-0.709461\pi$
$479$	−26.7696			−1.22313			−0.611567	+	0.791193i	$0.709461\pi$
$480$	−3.50710	−	0.889064i	−0.160076	−	0.0405800i
$481$	−24.5289			−1.11842
$482$		−	12.7220i		−	0.579472i
$483$			3.40431i			0.154901i
$484$		0			0
$485$	6.79036	−	26.7860i	0.308334	−	1.21629i
$486$	−3.94427			−0.178916
$487$			18.3782i			0.832797i	0.909182	+	0.416398i	$0.136708\pi$
$487$			18.3782i			0.832797i	−0.909182	+	0.416398i	$0.863292\pi$
$488$		−	2.45731i		−	0.111237i
$489$	0.282006			0.0127528
$490$	3.99699	−	15.7670i	0.180566	−	0.712279i
$491$	−25.9831			−1.17260			−0.586301	−	0.810093i	$-0.699416\pi$
$491$	−25.9831			−1.17260			−0.586301	+	0.810093i	$0.699416\pi$
$492$		−	10.1743i		−	0.458692i
$493$			31.5579i			1.42130i
$494$	−4.02001			−0.180869
$495$		0			0
$496$	5.34921			0.240186
$497$		−	41.1510i		−	1.84587i
$498$		−	0.297846i		−	0.0133468i
$499$	−16.9808			−0.760165			−0.380083	−	0.924953i	$-0.624104\pi$
$499$	−16.9808			−0.760165			−0.380083	+	0.924953i	$0.624104\pi$
$500$	−8.21988	−	7.57849i	−0.367604	−	0.338920i
$501$	−8.87707			−0.396598
$502$		−	2.83952i		−	0.126734i
$503$			13.3916i			0.597104i	0.954393	+	0.298552i	$0.0965036\pi$
$503$			13.3916i			0.597104i	−0.954393	+	0.298552i	$0.903496\pi$
$504$	−1.44312			−0.0642815
$505$	−19.5383	−	4.95305i	−0.869444	−	0.220408i
$506$		0			0
$507$			5.49573i			0.244074i
$508$			6.95343i			0.308509i
$509$	20.0301			0.887817			0.443909	−	0.896072i	$-0.353591\pi$
$509$	20.0301			0.887817			0.443909	+	0.896072i	$0.353591\pi$
$510$	2.93144	−	11.5637i	0.129806	−	0.512048i
$511$	−12.8311			−0.567616
$512$			1.00000i			0.0441942i
$513$		−	7.09856i		−	0.313409i
$514$	30.8410			1.36034
$515$	−6.28263	+	24.7832i	−0.276846	+	1.09208i
$516$	5.85410			0.257712
$517$		0			0
$518$		−	29.9048i		−	1.31394i
$519$	−38.8264			−1.70429
$520$	−6.71698	−	1.70278i	−0.294559	−	0.0746719i
$521$	2.32624			0.101914			0.0509572	−	0.998701i	$-0.483773\pi$
$521$	2.32624			0.101914			0.0509572	+	0.998701i	$0.483773\pi$
$522$			3.65583i			0.160011i
$523$			19.1186i			0.835996i	0.908448	+	0.417998i	$0.137268\pi$
$523$			19.1186i			0.835996i	−0.908448	+	0.417998i	$0.862732\pi$
$524$	5.61741			0.245398
$525$	26.8743	+	14.5613i	1.17289	+	0.635507i
$526$	27.7069			1.20808
$527$			17.6375i			0.768302i
$528$		0			0
$529$	22.6899			0.986517
$530$	−23.8733	−	6.05199i	−1.03699	−	0.262882i
$531$	−2.02336			−0.0878062
$532$		−	4.90106i		−	0.212488i
$533$		−	19.4863i		−	0.844047i
$534$	9.85410			0.426429
$535$	8.43693	−	33.2812i	0.364760	−	1.43887i
$536$	−9.21247			−0.397918
$537$			0.344801i			0.0148793i
$538$		−	12.7592i		−	0.550087i
$539$		0			0
$540$	3.00678	−	11.8609i	0.129391	−	0.510411i
$541$	29.8025			1.28131			0.640656	−	0.767828i	$-0.278663\pi$
$541$	29.8025			1.28131			0.640656	+	0.767828i	$0.278663\pi$
$542$			5.70254i			0.244945i
$543$			1.67981i			0.0720877i
$544$	−3.29722			−0.141367
$545$	−5.26470	−	1.33462i	−0.225515	−	0.0571690i
$546$	18.9443			0.810740
$547$			18.9495i			0.810224i	0.914267	+	0.405112i	$0.132767\pi$
$547$			18.9495i			0.810224i	−0.914267	+	0.405112i	$0.867233\pi$
$548$			7.68796i			0.328413i
$549$	0.938610			0.0400589
$550$		0			0
$551$	−12.4158			−0.528930
$552$			0.901057i			0.0383515i
$553$			61.8230i			2.62898i
$554$	−31.7274			−1.34797
$555$	27.7596	+	7.03716i	1.17833	+	0.298711i
$556$	0.961819			0.0407902
$557$			6.68359i			0.283193i	0.989924	+	0.141596i	$0.0452235\pi$
$557$			6.68359i			0.283193i	−0.989924	+	0.141596i	$0.954776\pi$
$558$			2.04322i			0.0864962i
$559$	11.2121			0.474221
$560$	2.07597	−	8.18911i	0.0877259	−	0.346053i
$561$		0			0
$562$		−	1.93822i		−	0.0817589i
$563$		−	9.52412i		−	0.401394i	−0.979653	−	0.200697i	$-0.935679\pi$
$563$		−	9.52412i		−	0.401394i	0.979653	−	0.200697i	$-0.0643207\pi$
$564$	8.65520			0.364450
$565$	−4.60531	+	18.1666i	−0.193747	+	0.764274i
$566$	−4.91588			−0.206630
$567$			29.1226i			1.22303i
$568$		−	10.8919i		−	0.457014i
$569$	−28.0616			−1.17640			−0.588201	−	0.808715i	$-0.700164\pi$
$569$	−28.0616			−1.17640			−0.588201	+	0.808715i	$0.700164\pi$
$570$	4.54947	+	1.15331i	0.190556	+	0.0483068i
$571$	−1.61429			−0.0675561			−0.0337781	−	0.999429i	$-0.510754\pi$
$571$	−1.61429			−0.0675561			−0.0337781	+	0.999429i	$0.510754\pi$
$572$		0			0
$573$		−	29.0186i		−	1.21227i
$574$	23.7571			0.991601
$575$	−1.32648	+	2.44815i	−0.0553180	+	0.102095i
$576$	−0.381966			−0.0159153
$577$		−	3.26960i		−	0.136115i	−0.997681	−	0.0680577i	$-0.978320\pi$
$577$		−	3.26960i		−	0.136115i	0.997681	−	0.0680577i	$-0.0216802\pi$
$578$			6.12835i			0.254906i
$579$	−14.5944			−0.606524
$580$	−20.7454	−	5.25904i	−0.861405	−	0.218370i
$581$	0.695475			0.0288532
$582$			19.9956i			0.828846i
$583$		0			0
$584$	−3.39616			−0.140534
$585$	0.650405	−	2.56566i	0.0268909	−	0.106077i
$586$	0.188725			0.00779616
$587$		−	3.50427i		−	0.144637i	−0.997382	−	0.0723183i	$-0.976960\pi$
$587$		−	3.50427i		−	0.144637i	0.997382	−	0.0723183i	$-0.0230397\pi$
$588$			11.7700i			0.485386i
$589$	−6.93909			−0.285920
$590$	2.91067	−	11.4818i	0.119830	−	0.472696i
$591$	5.96119			0.245211
$592$		−	7.91525i		−	0.325315i
$593$		−	27.6283i		−	1.13456i	−0.823526	−	0.567278i	$-0.807996\pi$
$593$		−	27.6283i		−	1.13456i	0.823526	−	0.567278i	$-0.192004\pi$
$594$		0			0
$595$	27.0013	+	6.84494i	1.10695	+	0.280615i
$596$	−8.79232			−0.360148
$597$			6.85309i			0.280478i
$598$			1.72575i			0.0705712i
$599$	7.95329			0.324962			0.162481	−	0.986712i	$-0.448050\pi$
$599$	7.95329			0.324962			0.162481	+	0.986712i	$0.448050\pi$
$600$	7.11314	+	3.85410i	0.290393	+	0.157343i
$601$	6.53391			0.266524			0.133262	−	0.991081i	$-0.457455\pi$
$601$	6.53391			0.266524			0.133262	+	0.991081i	$0.457455\pi$
$602$			13.6694i			0.557123i
$603$		−	3.51885i		−	0.143299i
$604$	8.93783			0.363675
$605$		0			0
$606$	14.5853			0.592486
$607$			8.37823i			0.340062i	0.985439	+	0.170031i	$0.0543867\pi$
$607$			8.37823i			0.340062i	−0.985439	+	0.170031i	$0.945613\pi$
$608$		−	1.29722i		−	0.0526092i
$609$	58.5093			2.37092
$610$	−1.35022	+	5.32624i	−0.0546689	+	0.215653i
$611$	16.5769			0.670629
$612$		−	1.25943i		−	0.0509093i
$613$		−	17.9125i		−	0.723480i	−0.932279	−	0.361740i	$-0.882183\pi$
$613$		−	17.9125i		−	0.723480i	0.932279	−	0.361740i	$-0.117817\pi$
$614$	−12.3820			−0.499695
$615$	−5.59048	+	22.0528i	−0.225430	+	0.889256i
$616$		0			0
$617$		−	21.3999i		−	0.861529i	−0.902464	−	0.430765i	$-0.858244\pi$
$617$		−	21.3999i		−	0.861529i	0.902464	−	0.430765i	$-0.141756\pi$
$618$		−	18.5005i		−	0.744200i
$619$	5.92053			0.237966			0.118983	−	0.992896i	$-0.462037\pi$
$619$	5.92053			0.237966			0.118983	+	0.992896i	$0.462037\pi$
$620$	−11.5944	−	2.93924i	−0.465644	−	0.118043i
$621$	−3.04734			−0.122286
$622$		−	21.1182i		−	0.846762i
$623$			23.0094i			0.921854i
$624$	5.01420			0.200728
$625$	13.6525	+	20.9430i	0.546099	+	0.837721i
$626$	−16.5792			−0.662639
$627$		0			0
$628$			17.6410i			0.703953i
$629$	26.0983			1.04061
$630$	3.12796	+	0.792952i	0.124621	+	0.0315919i
$631$	18.2035			0.724672			0.362336	−	0.932048i	$-0.381979\pi$
$631$	18.2035			0.724672			0.362336	+	0.932048i	$0.381979\pi$
$632$			16.3634i			0.650901i
$633$		−	22.1192i		−	0.879159i
$634$	−19.6370			−0.779886
$635$	3.82071	−	15.0716i	0.151620	−	0.598098i
$636$	17.8213			0.706662
$637$			22.5425i			0.893166i
$638$		0			0
$639$	4.16033			0.164580
$640$	0.549472	−	2.16751i	0.0217198	−	0.0856782i
$641$	17.6343			0.696514			0.348257	−	0.937399i	$-0.386774\pi$
$641$	17.6343			0.696514			0.348257	+	0.937399i	$0.386774\pi$
$642$			24.8443i			0.980527i
$643$			43.9495i			1.73320i	0.499003	+	0.866600i	$0.333700\pi$
$643$			43.9495i			1.73320i	−0.499003	+	0.866600i	$0.666300\pi$
$644$	−2.10398			−0.0829083
$645$	−12.6888	−	3.21666i	−0.499621	−	0.126656i
$646$	4.27721			0.168285
$647$			0.496121i			0.0195045i	0.999952	+	0.00975227i	$0.00310429\pi$
$647$			0.496121i			0.0195045i	−0.999952	+	0.00975227i	$0.996896\pi$
$648$			7.70820i			0.302807i
$649$		0			0
$650$	13.6235	+	7.38158i	0.534356	+	0.289529i
$651$	32.7004			1.28163
$652$			0.174289i			0.00682570i
$653$		−	18.1571i		−	0.710543i	−0.934763	−	0.355272i	$-0.884388\pi$
$653$		−	18.1571i		−	0.710543i	0.934763	−	0.355272i	$-0.115612\pi$
$654$	3.93008			0.153678
$655$	−12.1758	−	3.08661i	−0.475746	−	0.120604i
$656$	6.28806			0.245507
$657$		−	1.29722i		−	0.0506093i
$658$			20.2100i			0.787867i
$659$	14.4974			0.564739			0.282370	−	0.959306i	$-0.408880\pi$
$659$	14.4974			0.564739			0.282370	+	0.959306i	$0.408880\pi$
$660$		0			0
$661$	−11.6178			−0.451880			−0.225940	−	0.974141i	$-0.572545\pi$
$661$	−11.6178			−0.451880			−0.225940	+	0.974141i	$0.572545\pi$
$662$		−	23.4826i		−	0.912677i
$663$			16.5329i			0.642085i
$664$	0.184079			0.00714366
$665$	−2.69299	+	10.6231i	−0.104430	+	0.411945i
$666$	3.02336			0.117153
$667$			5.32998i			0.206378i
$668$		−	5.48633i		−	0.212273i
$669$	38.7876			1.49961
$670$	19.9681	+	5.06199i	0.771434	+	0.195562i
$671$		0			0
$672$			6.11314i			0.235819i
$673$		−	35.6283i		−	1.37337i	−0.726956	−	0.686684i	$-0.759066\pi$
$673$		−	35.6283i		−	1.37337i	0.726956	−	0.686684i	$-0.240934\pi$
$674$	12.8251			0.494004
$675$	−13.0344	+	24.0564i	−0.501696	+	0.925931i
$676$	−3.39655			−0.130637
$677$			24.5097i			0.941984i	0.882138	+	0.470992i	$0.156104\pi$
$677$			24.5097i			0.941984i	−0.882138	+	0.470992i	$0.843896\pi$
$678$		−	13.5613i		−	0.520818i
$679$	−46.6900			−1.79180
$680$	7.14674	+	1.81173i	0.274065	+	0.0694766i
$681$	−33.5005			−1.28374
$682$		0			0
$683$			25.5212i			0.976540i	0.872693	+	0.488270i	$0.162372\pi$
$683$			25.5212i			0.976540i	−0.872693	+	0.488270i	$0.837628\pi$
$684$	0.495493			0.0189457
$685$	4.22432	−	16.6637i	0.161403	−	0.636687i
$686$	−1.03615			−0.0395603
$687$			26.4398i			1.00874i
$688$			3.61803i			0.137936i
$689$	34.1324			1.30034
$690$	0.495105	−	1.95305i	0.0188483	−	0.0743512i
$691$	−45.4864			−1.73038			−0.865192	−	0.501442i	$-0.832803\pi$
$691$	−45.4864			−1.73038			−0.865192	+	0.501442i	$0.832803\pi$
$692$		−	23.9960i		−	0.912192i
$693$		0			0
$694$	20.6936			0.785519
$695$	−2.08475	−	0.528492i	−0.0790790	−	0.0200469i
$696$	15.4863			0.587008
$697$			20.7331i			0.785322i
$698$		−	21.7174i		−	0.822014i
$699$	0.777111			0.0293931
$700$	−8.99937	+	16.6093i	−0.340144	+	0.627771i
$701$	−29.1466			−1.10085			−0.550425	−	0.834884i	$-0.685534\pi$
$701$	−29.1466			−1.10085			−0.550425	+	0.834884i	$0.685534\pi$
$702$			16.9578i			0.640032i
$703$			10.2678i			0.387258i
$704$		0			0
$705$	−18.7602	−	4.75579i	−0.706550	−	0.179113i
$706$	0.260293			0.00979627
$707$			34.0568i			1.28084i
$708$			8.57108i			0.322121i
$709$	−30.9168			−1.16110			−0.580552	−	0.814223i	$-0.697163\pi$
$709$	−30.9168			−1.16110			−0.580552	+	0.814223i	$0.697163\pi$
$710$	−5.98479	+	23.6082i	−0.224605	+	0.886002i
$711$	−6.25026			−0.234403
$712$			6.09017i			0.228239i
$713$			2.97889i			0.111560i
$714$	−20.1564			−0.754333
$715$		0			0
$716$	−0.213099			−0.00796388
$717$		−	1.82610i		−	0.0681969i
$718$		−	8.22187i		−	0.306838i
$719$	17.5471			0.654396			0.327198	−	0.944956i	$-0.393896\pi$
$719$	17.5471			0.654396			0.327198	+	0.944956i	$0.393896\pi$
$720$	0.827913	+	0.209880i	0.0308545	+	0.00782175i
$721$	43.1989			1.60881
$722$		−	17.3172i		−	0.644480i
$723$		−	20.5846i		−	0.765551i
$724$	−1.03818			−0.0385837
$725$	42.0760	+	22.7980i	1.56266	+	0.846696i
$726$		0			0
$727$		−	16.7731i		−	0.622080i	−0.950397	−	0.311040i	$-0.899323\pi$
$727$		−	16.7731i		−	0.622080i	0.950397	−	0.311040i	$-0.100677\pi$
$728$			11.7082i			0.433935i
$729$	−29.5066			−1.09284
$730$	7.36120	+	1.86609i	0.272450	+	0.0690673i
$731$	−11.9294			−0.441227
$732$		−	3.97601i		−	0.146958i
$733$			9.25089i			0.341689i	0.985298	+	0.170845i	$0.0546497\pi$
$733$			9.25089i			0.341689i	−0.985298	+	0.170845i	$0.945350\pi$
$734$	7.21334			0.266249
$735$	6.46727	−	25.5115i	0.238549	−	0.941006i
$736$	−0.556884			−0.0205270
$737$		0			0
$738$			2.40182i			0.0884124i
$739$	−7.49636			−0.275758			−0.137879	−	0.990449i	$-0.544029\pi$
$739$	−7.49636			−0.275758			−0.137879	+	0.990449i	$0.544029\pi$
$740$	−4.34921	+	17.1564i	−0.159880	+	0.630680i
$741$	−6.50451			−0.238949
$742$			41.6130i			1.52766i
$743$			6.50325i			0.238581i	0.992859	+	0.119291i	$0.0380620\pi$
$743$			6.50325i			0.238581i	−0.992859	+	0.119291i	$0.961938\pi$
$744$	8.65520			0.317315
$745$	19.0574	+	4.83113i	0.698210	+	0.176999i
$746$	−29.9629			−1.09702
$747$			0.0703120i			0.00257258i
$748$		0			0
$749$	−58.0118			−2.11970
$750$	−13.3000	−	12.2623i	−0.485649	−	0.447754i
$751$	20.2922			0.740474			0.370237	−	0.928937i	$-0.379277\pi$
$751$	20.2922			0.740474			0.370237	+	0.928937i	$0.379277\pi$
$752$			5.34921i			0.195066i
$753$		−	4.59444i		−	0.167431i
$754$	29.6602			1.08016
$755$	−19.3728	−	4.91109i	−0.705049	−	0.178733i
$756$	−20.6744			−0.751922
$757$			18.4509i			0.670608i	0.942110	+	0.335304i	$0.108839\pi$
$757$			18.4509i			0.670608i	−0.942110	+	0.335304i	$0.891161\pi$
$758$			36.7066i			1.33324i
$759$		0			0
$760$	−0.712785	+	2.81173i	−0.0258554	+	0.101992i
$761$	−13.6441			−0.494599			−0.247299	−	0.968939i	$-0.579543\pi$
$761$	−13.6441			−0.494599			−0.247299	+	0.968939i	$0.579543\pi$
$762$			11.2509i			0.407577i
$763$			9.17677i			0.332221i
$764$	17.9345			0.648847
$765$	−0.692019	+	2.72981i	−0.0250200	+	0.0986965i
$766$	6.44815			0.232981
$767$			16.4158i			0.592739i
$768$			1.61803i			0.0583858i
$769$	6.77400			0.244277			0.122138	−	0.992513i	$-0.461025\pi$
$769$	6.77400			0.244277			0.122138	+	0.992513i	$0.461025\pi$
$770$		0			0
$771$	49.9017			1.79717
$772$		−	9.01986i		−	0.324632i
$773$		−	18.7748i		−	0.675282i	−0.941275	−	0.337641i	$-0.890371\pi$
$773$		−	18.7748i		−	0.675282i	0.941275	−	0.337641i	$-0.109629\pi$
$774$	−1.38197			−0.0496737
$775$	23.5160	+	12.7416i	0.844719	+	0.457693i
$776$	−12.3580			−0.443626
$777$		−	48.3870i		−	1.73588i
$778$			28.6001i			1.02536i
$779$	−8.15698			−0.292254
$780$	−10.8683	−	2.75516i	−0.389147	−	0.0986505i
$781$		0			0
$782$		−	1.83617i		−	0.0656612i
$783$			52.3742i			1.87170i
$784$	−7.27425			−0.259795
$785$	9.69323	−	38.2370i	0.345966	−	1.36474i
$786$	9.08915			0.324199
$787$			27.4395i			0.978113i	0.872252	+	0.489057i	$0.162659\pi$
$787$			27.4395i			0.978113i	−0.872252	+	0.489057i	$0.837341\pi$
$788$			3.68422i			0.131245i
$789$	44.8308			1.59602
$790$	8.99123	−	35.4678i	0.319893	−	1.26189i
$791$	31.6658			1.12590
$792$		0			0
$793$		−	7.61507i		−	0.270419i
$794$	−24.5049			−0.869648
$795$	−38.6279	−	9.79232i	−1.36999	−	0.347298i
$796$	−4.23544			−0.150121
$797$		−	53.8746i		−	1.90834i	−0.299270	−	0.954169i	$-0.596743\pi$
$797$		−	53.8746i		−	1.90834i	0.299270	−	0.954169i	$-0.403257\pi$
$798$		−	7.93008i		−	0.280722i
$799$	−17.6375			−0.623970
$800$	−2.38197	+	4.39616i	−0.0842152	+	0.155428i
$801$	−2.32624			−0.0821936
$802$		−	30.7122i		−	1.08449i
$803$		0			0
$804$	−14.9061			−0.525697
$805$	4.56038	+	1.15608i	0.160732	+	0.0407463i
$806$	16.5769			0.583896
$807$		−	20.6448i		−	0.726731i
$808$			9.01420i			0.317118i
$809$	−32.3371			−1.13691			−0.568456	−	0.822714i	$-0.692459\pi$
$809$	−32.3371			−1.13691			−0.568456	+	0.822714i	$0.692459\pi$
$810$	4.23544	−	16.7076i	0.148818	−	0.587044i
$811$	45.9263			1.61269			0.806346	−	0.591444i	$-0.201442\pi$
$811$	45.9263			1.61269			0.806346	+	0.591444i	$0.201442\pi$
$812$			36.1608i			1.26899i
$813$			9.22691i			0.323602i
$814$		0			0
$815$	0.0957671	−	0.377773i	0.00335458	−	0.0132328i
$816$	−5.33501			−0.186763
$817$		−	4.69338i		−	0.164201i
$818$		−	21.8581i		−	0.764251i
$819$	−4.47214			−0.156269
$820$	−13.6294	−	3.45511i	−0.475959	−	0.120658i
$821$	28.4350			0.992389			0.496194	−	0.868211i	$-0.334730\pi$
$821$	28.4350			0.992389			0.496194	+	0.868211i	$0.334730\pi$
$822$			12.4394i			0.433873i
$823$			10.3634i			0.361246i	0.983552	+	0.180623i	$0.0578113\pi$
$823$			10.3634i			0.361246i	−0.983552	+	0.180623i	$0.942189\pi$
$824$	11.4340			0.398321
$825$		0			0
$826$	−20.0136			−0.696361
$827$			19.6082i			0.681845i	0.940091	+	0.340923i	$0.110739\pi$
$827$			19.6082i			0.681845i	−0.940091	+	0.340923i	$0.889261\pi$
$828$		−	0.212711i		−	0.00739220i
$829$	−49.8737			−1.73219			−0.866093	−	0.499883i	$-0.833376\pi$
$829$	−49.8737			−1.73219			−0.866093	+	0.499883i	$0.833376\pi$
$830$	−0.398993	−	0.101146i	−0.0138492	−	0.00351084i
$831$	−51.3361			−1.78083
$832$			3.09894i			0.107437i
$833$		−	23.9848i		−	0.831024i
$834$	1.55626			0.0538887
$835$	−3.01458	+	11.8917i	−0.104324	+	0.411528i
$836$		0			0
$837$			29.2716i			1.01177i
$838$		−	4.17764i		−	0.144314i
$839$	10.5253			0.363373			0.181687	−	0.983356i	$-0.441844\pi$
$839$	10.5253			0.363373			0.181687	+	0.983356i	$0.441844\pi$
$840$	3.35900	−	13.2503i	0.115896	−	0.457178i
$841$	62.6056			2.15881
$842$			12.6940i			0.437464i
$843$		−	3.13611i		−	0.108013i
$844$	13.6704			0.470555
$845$	7.36204	+	1.86631i	0.253262	+	0.0642029i
$846$	−2.04322			−0.0702472
$847$		0			0
$848$			11.0142i			0.378229i
$849$	−7.95406			−0.272983
$850$	−14.4951	−	7.85386i	−0.497178	−	0.269385i
$851$	4.40787			0.151100
$852$		−	17.6235i		−	0.603770i
$853$			15.7203i			0.538253i	0.963105	+	0.269126i	$0.0867350\pi$
$853$			15.7203i			0.538253i	−0.963105	+	0.269126i	$0.913265\pi$
$854$	9.28404			0.317693
$855$	−1.07398	−	0.272260i	−0.0367295	−	0.00931108i
$856$	−15.3546			−0.524810
$857$		−	37.8967i		−	1.29453i	−0.762267	−	0.647263i	$-0.775914\pi$
$857$		−	37.8967i		−	1.29453i	0.762267	−	0.647263i	$-0.224086\pi$
$858$		0			0
$859$	−20.5913			−0.702567			−0.351283	−	0.936269i	$-0.614255\pi$
$859$	−20.5913			−0.702567			−0.351283	+	0.936269i	$0.614255\pi$
$860$	1.98801	−	7.84211i	0.0677905	−	0.267414i
$861$	38.4398			1.31002
$862$		−	0.730785i		−	0.0248906i
$863$			8.59318i			0.292515i	0.989247	+	0.146258i	$0.0467228\pi$
$863$			8.59318i			0.292515i	−0.989247	+	0.146258i	$0.953277\pi$
$864$	−5.47214			−0.186166
$865$	−13.1851	+	52.0115i	−0.448308	+	1.76844i
$866$	5.64580			0.191852
$867$			9.91588i			0.336761i
$868$			20.2100i			0.685972i
$869$		0			0
$870$	−33.5667	−	8.50930i	−1.13802	−	0.288492i
$871$	−28.5489			−0.967343
$872$			2.42892i			0.0822536i
$873$		−	4.72033i		−	0.159759i
$874$	0.722400			0.0244355
$875$	28.6325	−	31.0558i	0.967955	−	1.04988i
$876$	−5.49511			−0.185662
$877$		−	45.1493i		−	1.52458i	−0.647234	−	0.762292i	$-0.724074\pi$
$877$		−	45.1493i		−	1.52458i	0.647234	−	0.762292i	$-0.275926\pi$
$878$		−	13.7074i		−	0.462603i
$879$	0.305364			0.0102997
$880$		0			0
$881$	−38.4847			−1.29658			−0.648291	−	0.761393i	$-0.724516\pi$
$881$	−38.4847			−1.29658			−0.648291	+	0.761393i	$0.724516\pi$
$882$		−	2.77852i		−	0.0935575i
$883$			39.3195i			1.32321i	0.749854	+	0.661604i	$0.230124\pi$
$883$			39.3195i			1.32321i	−0.749854	+	0.661604i	$0.769876\pi$
$884$	−10.2179			−0.343665
$885$	4.70957	−	18.5779i	0.158310	−	0.624488i
$886$	14.0435			0.471799
$887$		−	7.84407i		−	0.263378i	−0.991291	−	0.131689i	$-0.957960\pi$
$887$		−	7.84407i		−	0.263378i	0.991291	−	0.131689i	$-0.0420400\pi$
$888$		−	12.8071i		−	0.429780i
$889$	−26.2710			−0.881100
$890$	3.34638	−	13.2005i	0.112171	−	0.442481i
$891$		0			0
$892$			23.9720i			0.802643i
$893$		−	6.93909i		−	0.232208i
$894$	−14.2263			−0.475798
$895$	0.461893	+	0.117092i	0.0154394	+	0.00391395i
$896$	−3.77813			−0.126218
$897$			2.79232i			0.0932330i
$898$		−	9.65544i		−	0.322206i
$899$	51.1977			1.70754
$900$	−1.67918	−	0.909830i	−0.0559728	−	0.0303277i
$901$	−36.3162			−1.20987
$902$		0			0
$903$			22.1175i			0.736026i
$904$	8.38134			0.278759
$905$	2.25026	+	0.570451i	0.0748013	+	0.0189624i
$906$	14.4617			0.480458
$907$		−	44.3634i		−	1.47306i	−0.676403	−	0.736532i	$-0.736462\pi$
$907$		−	44.3634i		−	1.47306i	0.676403	−	0.736532i	$-0.263538\pi$
$908$		−	20.7045i		−	0.687102i
$909$	−3.44312			−0.114201
$910$	6.43333	−	25.3776i	0.213263	−	0.841259i
$911$	13.8518			0.458930			0.229465	−	0.973317i	$-0.426302\pi$
$911$	13.8518			0.458930			0.229465	+	0.973317i	$0.426302\pi$
$912$		−	2.09894i		−	0.0695030i
$913$		0			0
$914$	1.02878			0.0340290
$915$	−2.18471	+	8.61803i	−0.0722242	+	0.284903i
$916$	−16.3407			−0.539911
$917$			21.2233i			0.700854i
$918$		−	18.0428i		−	0.595502i
$919$	15.2390			0.502688			0.251344	−	0.967898i	$-0.419127\pi$
$919$	15.2390			0.502688			0.251344	+	0.967898i	$0.419127\pi$
$920$	1.20705	+	0.305992i	0.0397952	+	0.0100883i
$921$	−20.0344			−0.660157
$922$		−	8.05882i		−	0.265403i
$923$		−	33.7534i		−	1.11101i
$924$		0			0
$925$	18.8539	−	34.7967i	0.619911	−	1.14411i
$926$	−7.46633			−0.245359
$927$			4.36738i			0.143444i
$928$			9.57108i			0.314186i
$929$	−37.9217			−1.24417			−0.622086	−	0.782949i	$-0.713715\pi$
$929$	−37.9217			−1.24417			−0.622086	+	0.782949i	$0.713715\pi$
$930$	−18.7602	−	4.75579i	−0.615171	−	0.155948i
$931$	9.43629			0.309262
$932$			0.480281i			0.0157321i
$933$		−	34.1699i		−	1.11867i
$934$	−11.1894			−0.366127
$935$		0			0
$936$	−1.18369			−0.0386902
$937$		−	5.47756i		−	0.178944i	−0.995989	−	0.0894720i	$-0.971482\pi$
$937$		−	5.47756i		−	0.178944i	0.995989	−	0.0894720i	$-0.0285180\pi$
$938$		−	34.8059i		−	1.13645i
$939$	−26.8257			−0.875425
$940$	2.93924	−	11.5944i	0.0958674	−	0.378169i
$941$	46.4407			1.51392			0.756961	−	0.653460i	$-0.226683\pi$
$941$	46.4407			1.51392			0.756961	+	0.653460i	$0.226683\pi$
$942$			28.5437i			0.930005i
$943$			3.50172i			0.114032i
$944$	−5.29722			−0.172410
$945$	44.8119	+	11.3600i	1.45773	+	0.369541i
$946$		0			0
$947$		−	22.7220i		−	0.738366i	−0.929357	−	0.369183i	$-0.879638\pi$
$947$		−	22.7220i		−	0.738366i	0.929357	−	0.369183i	$-0.120362\pi$
$948$			26.4765i			0.859918i
$949$	−10.5245			−0.341640
$950$	3.08993	−	5.70278i	0.100251	−	0.185023i
$951$	−31.7734			−1.03032
$952$		−	12.4573i		−	0.403744i
$953$			36.0182i			1.16674i	0.812205	+	0.583372i	$0.198267\pi$
$953$			36.0182i			1.16674i	−0.812205	+	0.583372i	$0.801733\pi$
$954$	−4.20705			−0.136208
$955$	−38.8731	−	9.85449i	−1.25790	−	0.318884i
$956$	1.12859			0.0365012
$957$		0			0
$958$		−	26.7696i		−	0.864886i
$959$	−29.0461			−0.937947
$960$	0.889064	−	3.50710i	0.0286944	−	0.113191i
$961$	−2.38598			−0.0769672
$962$		−	24.5289i		−	0.790844i
$963$		−	5.86495i		−	0.188995i
$964$	12.7220			0.409748
$965$	−4.95616	+	19.5506i	−0.159544	+	0.629356i
$966$	−3.40431			−0.109532
$967$		−	23.8349i		−	0.766479i	−0.923649	−	0.383240i	$-0.874808\pi$
$967$		−	23.8349i		−	0.766479i	0.923649	−	0.383240i	$-0.125192\pi$
$968$		0			0
$969$	6.92067			0.222324
$970$	26.7860	+	6.79036i	0.860046	+	0.218025i
$971$	−35.3692			−1.13505			−0.567526	−	0.823355i	$-0.692099\pi$
$971$	−35.3692			−1.13505			−0.567526	+	0.823355i	$0.692099\pi$
$972$		−	3.94427i		−	0.126513i
$973$			3.63387i			0.116497i
$974$	−18.3782			−0.588876
$975$	22.0432	+	11.9436i	0.705948	+	0.382503i
$976$	2.45731			0.0786566
$977$		−	11.2807i		−	0.360903i	−0.983584	−	0.180452i	$-0.942244\pi$
$977$		−	11.2807i		−	0.360903i	0.983584	−	0.180452i	$-0.0577559\pi$
$978$			0.282006i			0.00901757i
$979$		0			0
$980$	15.7670	+	3.99699i	0.503658	+	0.127679i
$981$	−0.927765			−0.0296213
$982$		−	25.9831i		−	0.829155i
$983$			8.56401i			0.273150i	0.990630	+	0.136575i	$0.0436094\pi$
$983$			8.56401i			0.273150i	−0.990630	+	0.136575i	$0.956391\pi$
$984$	10.1743			0.324345
$985$	2.02437	−	7.98556i	0.0645019	−	0.254441i
$986$	−31.5579			−1.00501
$987$			32.7004i			1.04087i
$988$		−	4.02001i		−	0.127893i
$989$	−2.01482			−0.0640677
$990$		0			0
$991$	−15.9978			−0.508185			−0.254093	−	0.967180i	$-0.581777\pi$
$991$	−15.9978			−0.508185			−0.254093	+	0.967180i	$0.581777\pi$
$992$			5.34921i			0.169837i
$993$		−	37.9956i		−	1.20575i
$994$	41.1510			1.30523
$995$	9.18034	+	2.32725i	0.291036	+	0.0737789i
$996$	0.297846			0.00943763
$997$		−	28.4039i		−	0.899560i	−0.893139	−	0.449780i	$-0.851502\pi$
$997$		−	28.4039i		−	0.899560i	0.893139	−	0.449780i	$-0.148498\pi$
$998$		−	16.9808i		−	0.537518i
$999$	43.3133			1.37037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1210.2.b.k.969.8		8
5.2	odd	4		6050.2.a.dd.1.4		4
5.3	odd	4		6050.2.a.di.1.1		4
5.4	even	2	inner	1210.2.b.k.969.2		8
11.5	even	5		110.2.j.b.69.1	yes	16
11.9	even	5		110.2.j.b.59.3	yes	16
11.10	odd	2		1210.2.b.l.969.4		8
33.5	odd	10		990.2.ba.h.289.4		16
33.20	odd	10		990.2.ba.h.829.2		16
44.27	odd	10		880.2.cd.b.289.3		16
44.31	odd	10		880.2.cd.b.609.1		16
55.9	even	10		110.2.j.b.59.1	✓	16
55.27	odd	20		550.2.h.n.201.2		8
55.32	even	4		6050.2.a.dl.1.3		4
55.38	odd	20		550.2.h.j.201.1		8
55.42	odd	20		550.2.h.n.301.2		8
55.43	even	4		6050.2.a.da.1.2		4
55.49	even	10		110.2.j.b.69.3	yes	16
55.53	odd	20		550.2.h.j.301.1		8
55.54	odd	2		1210.2.b.l.969.6		8
165.104	odd	10		990.2.ba.h.289.2		16
165.119	odd	10		990.2.ba.h.829.4		16
220.119	odd	10		880.2.cd.b.609.3		16
220.159	odd	10		880.2.cd.b.289.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.1	✓	16	55.9	even	10
110.2.j.b.59.3	yes	16	11.9	even	5
110.2.j.b.69.1	yes	16	11.5	even	5
110.2.j.b.69.3	yes	16	55.49	even	10
550.2.h.j.201.1		8	55.38	odd	20
550.2.h.j.301.1		8	55.53	odd	20
550.2.h.n.201.2		8	55.27	odd	20
550.2.h.n.301.2		8	55.42	odd	20
880.2.cd.b.289.1		16	220.159	odd	10
880.2.cd.b.289.3		16	44.27	odd	10
880.2.cd.b.609.1		16	44.31	odd	10
880.2.cd.b.609.3		16	220.119	odd	10
990.2.ba.h.289.2		16	165.104	odd	10
990.2.ba.h.289.4		16	33.5	odd	10
990.2.ba.h.829.2		16	33.20	odd	10
990.2.ba.h.829.4		16	165.119	odd	10
1210.2.b.k.969.2		8	5.4	even	2	inner
1210.2.b.k.969.8		8	1.1	even	1	trivial
1210.2.b.l.969.4		8	11.10	odd	2
1210.2.b.l.969.6		8	55.54	odd	2
6050.2.a.da.1.2		4	55.43	even	4
6050.2.a.dd.1.4		4	5.2	odd	4
6050.2.a.di.1.1		4	5.3	odd	4
6050.2.a.dl.1.3		4	55.32	even	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.61803i q^{3} -1.00000 q^{4} +(2.16751 + 0.549472i) q^{5} -1.61803 q^{6} -3.77813i q^{7} -1.00000i q^{8} +0.381966 q^{9} +(-0.549472 + 2.16751i) q^{10} -1.61803i q^{12} -3.09894i q^{13} +3.77813 q^{14} +(-0.889064 + 3.50710i) q^{15} +1.00000 q^{16} +3.29722i q^{17} +0.381966i q^{18} -1.29722 q^{19} +(-2.16751 - 0.549472i) q^{20} +6.11314 q^{21} +0.556884i q^{23} +1.61803 q^{24} +(4.39616 + 2.38197i) q^{25} +3.09894 q^{26} +5.47214i q^{27} +3.77813i q^{28} +9.57108 q^{29} +(-3.50710 - 0.889064i) q^{30} +5.34921 q^{31} +1.00000i q^{32} -3.29722 q^{34} +(2.07597 - 8.18911i) q^{35} -0.381966 q^{36} -7.91525i q^{37} -1.29722i q^{38} +5.01420 q^{39} +(0.549472 - 2.16751i) q^{40} +6.28806 q^{41} +6.11314i q^{42} +3.61803i q^{43} +(0.827913 + 0.209880i) q^{45} -0.556884 q^{46} +5.34921i q^{47} +1.61803i q^{48} -7.27425 q^{49} +(-2.38197 + 4.39616i) q^{50} -5.33501 q^{51} +3.09894i q^{52} +11.0142i q^{53} -5.47214 q^{54} -3.77813 q^{56} -2.09894i q^{57} +9.57108i q^{58} -5.29722 q^{59} +(0.889064 - 3.50710i) q^{60} +2.45731 q^{61} +5.34921i q^{62} -1.44312i q^{63} -1.00000 q^{64} +(1.70278 - 6.71698i) q^{65} -9.21247i q^{67} -3.29722i q^{68} -0.901057 q^{69} +(8.18911 + 2.07597i) q^{70} +10.8919 q^{71} -0.381966i q^{72} -3.39616i q^{73} +7.91525 q^{74} +(-3.85410 + 7.11314i) q^{75} +1.29722 q^{76} +5.01420i q^{78} -16.3634 q^{79} +(2.16751 + 0.549472i) q^{80} -7.70820 q^{81} +6.28806i q^{82} +0.184079i q^{83} -6.11314 q^{84} +(-1.81173 + 7.14674i) q^{85} -3.61803 q^{86} +15.4863i q^{87} -6.09017 q^{89} +(-0.209880 + 0.827913i) q^{90} -11.7082 q^{91} -0.556884i q^{92} +8.65520i q^{93} -5.34921 q^{94} +(-2.81173 - 0.712785i) q^{95} -1.61803 q^{96} -12.3580i q^{97} -7.27425i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 2 q^{5} - 4 q^{6} + 12 q^{9} + 2 q^{10} + 4 q^{14} + 6 q^{15} + 8 q^{16} + 12 q^{19} - 2 q^{20} - 8 q^{21} + 4 q^{24} + 12 q^{26} + 28 q^{29} - 6 q^{30} - 32 q^{31} - 4 q^{34} + 16 q^{35}+ \cdots - 4 q^{96}+O(q^{100}) \) 8 * q - 8 * q^4 + 2 * q^5 - 4 * q^6 + 12 * q^9 + 2 * q^10 + 4 * q^14 + 6 * q^15 + 8 * q^16 + 12 * q^19 - 2 * q^20 - 8 * q^21 + 4 * q^24 + 12 * q^26 + 28 * q^29 - 6 * q^30 - 32 * q^31 - 4 * q^34 + 16 * q^35 - 12 * q^36 - 4 * q^39 - 2 * q^40 - 20 * q^41 - 2 * q^45 - 48 * q^49 - 28 * q^50 - 12 * q^51 - 8 * q^54 - 4 * q^56 - 20 * q^59 - 6 * q^60 - 20 * q^61 - 8 * q^64 + 36 * q^65 - 20 * q^69 + 8 * q^70 + 52 * q^71 + 32 * q^74 - 4 * q^75 - 12 * q^76 - 12 * q^79 + 2 * q^80 - 8 * q^81 + 8 * q^84 + 28 * q^85 - 20 * q^86 - 4 * q^89 - 2 * q^90 - 40 * q^91 + 32 * q^94 + 20 * q^95 - 4 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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