LMFDB - Embedded newform 1150.2.e.a.1057.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(643,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("1150.643");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.e (of order $4$, degree $2$, 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:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.1
Root			$-0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	1150.1057
Dual form			1150.2.e.a.643.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-2.00000 + 2.00000i) q^{3} +1.00000i q^{4} +2.82843 q^{6} +(-2.61313 + 2.61313i) q^{7} +(0.707107 - 0.707107i) q^{8} -5.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-2.00000 + 2.00000i) q^{3} +1.00000i q^{4} +2.82843 q^{6} +(-2.61313 + 2.61313i) q^{7} +(0.707107 - 0.707107i) q^{8} -5.00000i q^{9} -0.317025i q^{11} +(-2.00000 - 2.00000i) q^{12} +(3.41421 - 3.41421i) q^{13} +3.69552 q^{14} -1.00000 q^{16} +(3.69552 - 3.69552i) q^{17} +(-3.53553 + 3.53553i) q^{18} +5.09494 q^{19} -10.4525i q^{21} +(-0.224171 + 0.224171i) q^{22} +(3.67139 + 3.08560i) q^{23} +2.82843i q^{24} -4.82843 q^{26} +(4.00000 + 4.00000i) q^{27} +(-2.61313 - 2.61313i) q^{28} +3.65685i q^{29} +2.24264 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.634051 + 0.634051i) q^{33} -5.22625 q^{34} +5.00000 q^{36} +(2.07193 - 2.07193i) q^{37} +(-3.60266 - 3.60266i) q^{38} +13.6569i q^{39} -9.89949 q^{41} +(-7.39104 + 7.39104i) q^{42} +(5.76745 + 5.76745i) q^{43} +0.317025 q^{44} +(-0.414214 - 4.77791i) q^{46} +(-1.58579 - 1.58579i) q^{47} +(2.00000 - 2.00000i) q^{48} -6.65685i q^{49} +14.7821i q^{51} +(3.41421 + 3.41421i) q^{52} +(-5.00208 - 5.00208i) q^{53} -5.65685i q^{54} +3.69552i q^{56} +(-10.1899 + 10.1899i) q^{57} +(2.58579 - 2.58579i) q^{58} -9.65685i q^{59} +11.8519i q^{61} +(-1.58579 - 1.58579i) q^{62} +(13.0656 + 13.0656i) q^{63} -1.00000i q^{64} -0.896683i q^{66} +(-2.38896 + 2.38896i) q^{67} +(3.69552 + 3.69552i) q^{68} +(-13.5140 + 1.17157i) q^{69} -4.82843 q^{71} +(-3.53553 - 3.53553i) q^{72} +(-6.82843 + 6.82843i) q^{73} -2.93015 q^{74} +5.09494i q^{76} +(0.828427 + 0.828427i) q^{77} +(9.65685 - 9.65685i) q^{78} +4.59220 q^{79} -1.00000 q^{81} +(7.00000 + 7.00000i) q^{82} +(1.94061 + 1.94061i) q^{83} +10.4525 q^{84} -8.15640i q^{86} +(-7.31371 - 7.31371i) q^{87} +(-0.224171 - 0.224171i) q^{88} +14.7821 q^{89} +17.8435i q^{91} +(-3.08560 + 3.67139i) q^{92} +(-4.48528 + 4.48528i) q^{93} +2.24264i q^{94} -2.82843 q^{96} +(-3.06147 + 3.06147i) q^{97} +(-4.70711 + 4.70711i) q^{98} -1.58513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{3}+O(q^{10}) $ 8 * q - 16 * q^3	$ 8 q - 16 q^{3} - 16 q^{12} + 16 q^{13} - 8 q^{16} + 8 q^{23} - 16 q^{26} + 32 q^{27} - 16 q^{31} + 40 q^{36} + 8 q^{46} - 24 q^{47} + 16 q^{48} + 16 q^{52} + 32 q^{58} - 24 q^{62} - 16 q^{71} - 32 q^{73} - 16 q^{77} + 32 q^{78} - 8 q^{81} + 56 q^{82} + 32 q^{87} + 8 q^{92} + 32 q^{93} - 32 q^{98}+O(q^{100}) $ 8 * q - 16 * q^3 - 16 * q^12 + 16 * q^13 - 8 * q^16 + 8 * q^23 - 16 * q^26 + 32 * q^27 - 16 * q^31 + 40 * q^36 + 8 * q^46 - 24 * q^47 + 16 * q^48 + 16 * q^52 + 32 * q^58 - 24 * q^62 - 16 * q^71 - 32 * q^73 - 16 * q^77 + 32 * q^78 - 8 * q^81 + 56 * q^82 + 32 * q^87 + 8 * q^92 + 32 * q^93 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−2.00000	+	2.00000i	−1.15470	+	1.15470i	−0.169102	+	0.985599i	$0.554087\pi$
$3$	−2.00000	+	2.00000i	−1.15470	+	1.15470i	−0.985599	+	0.169102i	$0.945913\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	2.82843			1.15470
$7$	−2.61313	+	2.61313i	−0.987669	+	0.987669i	−0.999925	−	0.0122561i	$-0.996099\pi$
$7$	−2.61313	+	2.61313i	−0.987669	+	0.987669i	0.0122561	+	0.999925i	$0.496099\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	5.00000i		−	1.66667i
$10$		0			0
$11$		−	0.317025i		−	0.0955867i	−0.998857	−	0.0477934i	$-0.984781\pi$
$11$		−	0.317025i		−	0.0955867i	0.998857	−	0.0477934i	$-0.0152189\pi$
$12$	−2.00000	−	2.00000i	−0.577350	−	0.577350i
$13$	3.41421	−	3.41421i	0.946932	−	0.946932i	−0.0517287	−	0.998661i	$-0.516473\pi$
$13$	3.41421	−	3.41421i	0.946932	−	0.946932i	0.998661	+	0.0517287i	$0.0164731\pi$
$14$	3.69552			0.987669
$15$		0			0
$16$	−1.00000			−0.250000
$17$	3.69552	−	3.69552i	0.896295	−	0.896295i	−0.0988114	−	0.995106i	$-0.531504\pi$
$17$	3.69552	−	3.69552i	0.896295	−	0.896295i	0.995106	+	0.0988114i	$0.0315040\pi$
$18$	−3.53553	+	3.53553i	−0.833333	+	0.833333i
$19$	5.09494			1.16886			0.584429	−	0.811445i	$-0.301318\pi$
$19$	5.09494			1.16886			0.584429	+	0.811445i	$0.301318\pi$
$20$		0			0
$21$		−	10.4525i		−	2.28092i
$22$	−0.224171	+	0.224171i	−0.0477934	+	0.0477934i
$23$	3.67139	+	3.08560i	0.765537	+	0.643392i
$23$	3.67139	+	3.08560i	0.765537	+	0.643392i
$24$			2.82843i			0.577350i
$25$		0			0
$26$	−4.82843			−0.946932
$27$	4.00000	+	4.00000i	0.769800	+	0.769800i
$28$	−2.61313	−	2.61313i	−0.493834	−	0.493834i
$29$			3.65685i			0.679061i	0.940595	+	0.339530i	$0.110268\pi$
$29$			3.65685i			0.679061i	−0.940595	+	0.339530i	$0.889732\pi$
$30$		0			0
$31$	2.24264			0.402790			0.201395	−	0.979510i	$-0.435452\pi$
$31$	2.24264			0.402790			0.201395	+	0.979510i	$0.435452\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.634051	+	0.634051i	0.110374	+	0.110374i
$34$	−5.22625			−0.896295
$35$		0			0
$36$	5.00000			0.833333
$37$	2.07193	−	2.07193i	0.340623	−	0.340623i	−0.515978	−	0.856602i	$-0.672572\pi$
$37$	2.07193	−	2.07193i	0.340623	−	0.340623i	0.856602	+	0.515978i	$0.172572\pi$
$38$	−3.60266	−	3.60266i	−0.584429	−	0.584429i
$39$			13.6569i			2.18685i
$40$		0			0
$41$	−9.89949			−1.54604			−0.773021	−	0.634381i	$-0.781255\pi$
$41$	−9.89949			−1.54604			−0.773021	+	0.634381i	$0.781255\pi$
$42$	−7.39104	+	7.39104i	−1.14046	+	1.14046i
$43$	5.76745	+	5.76745i	0.879528	+	0.879528i	0.993486	−	0.113958i	$-0.0363529\pi$
$43$	5.76745	+	5.76745i	0.879528	+	0.879528i	−0.113958	+	0.993486i	$0.536353\pi$
$44$	0.317025			0.0477934
$45$		0			0
$46$	−0.414214	−	4.77791i	−0.0610725	−	0.704464i
$47$	−1.58579	−	1.58579i	−0.231311	−	0.231311i	0.581929	−	0.813240i	$-0.302298\pi$
$47$	−1.58579	−	1.58579i	−0.231311	−	0.231311i	−0.813240	+	0.581929i	$0.802298\pi$
$48$	2.00000	−	2.00000i	0.288675	−	0.288675i
$49$		−	6.65685i		−	0.950979i
$50$		0			0
$51$			14.7821i			2.06990i
$52$	3.41421	+	3.41421i	0.473466	+	0.473466i
$53$	−5.00208	−	5.00208i	−0.687089	−	0.687089i	0.274499	−	0.961587i	$-0.411488\pi$
$53$	−5.00208	−	5.00208i	−0.687089	−	0.687089i	−0.961587	+	0.274499i	$0.911488\pi$
$54$		−	5.65685i		−	0.769800i
$55$		0			0
$56$			3.69552i			0.493834i
$57$	−10.1899	+	10.1899i	−1.34968	+	1.34968i
$58$	2.58579	−	2.58579i	0.339530	−	0.339530i
$59$		−	9.65685i		−	1.25722i	−0.777723	−	0.628608i	$-0.783625\pi$
$59$		−	9.65685i		−	1.25722i	0.777723	−	0.628608i	$-0.216375\pi$
$60$		0			0
$61$			11.8519i			1.51748i	0.651392	+	0.758742i	$0.274185\pi$
$61$			11.8519i			1.51748i	−0.651392	+	0.758742i	$0.725815\pi$
$62$	−1.58579	−	1.58579i	−0.201395	−	0.201395i
$63$	13.0656	+	13.0656i	1.64611	+	1.64611i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		−	0.896683i		−	0.110374i
$67$	−2.38896	+	2.38896i	−0.291857	+	0.291857i	−0.837814	−	0.545956i	$-0.816166\pi$
$67$	−2.38896	+	2.38896i	−0.291857	+	0.291857i	0.545956	+	0.837814i	$0.316166\pi$
$68$	3.69552	+	3.69552i	0.448147	+	0.448147i
$69$	−13.5140	+	1.17157i	−1.62689	+	0.141041i
$70$		0			0
$71$	−4.82843			−0.573029			−0.286514	−	0.958076i	$-0.592497\pi$
$71$	−4.82843			−0.573029			−0.286514	+	0.958076i	$0.592497\pi$
$72$	−3.53553	−	3.53553i	−0.416667	−	0.416667i
$73$	−6.82843	+	6.82843i	−0.799207	+	0.799207i	−0.982970	−	0.183764i	$-0.941172\pi$
$73$	−6.82843	+	6.82843i	−0.799207	+	0.799207i	0.183764	+	0.982970i	$0.441172\pi$
$74$	−2.93015			−0.340623
$75$		0			0
$76$			5.09494i			0.584429i
$77$	0.828427	+	0.828427i	0.0944080	+	0.0944080i
$78$	9.65685	−	9.65685i	1.09342	−	1.09342i
$79$	4.59220			0.516663			0.258331	−	0.966056i	$-0.416827\pi$
$79$	4.59220			0.516663			0.258331	+	0.966056i	$0.416827\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	7.00000	+	7.00000i	0.773021	+	0.773021i
$83$	1.94061	+	1.94061i	0.213010	+	0.213010i	0.805545	−	0.592535i	$-0.201873\pi$
$83$	1.94061	+	1.94061i	0.213010	+	0.213010i	−0.592535	+	0.805545i	$0.701873\pi$
$84$	10.4525			1.14046
$85$		0			0
$86$		−	8.15640i		−	0.879528i
$87$	−7.31371	−	7.31371i	−0.784112	−	0.784112i
$88$	−0.224171	−	0.224171i	−0.0238967	−	0.0238967i
$89$	14.7821			1.56690			0.783448	−	0.621457i	$-0.213459\pi$
$89$	14.7821			1.56690			0.783448	+	0.621457i	$0.213459\pi$
$90$		0			0
$91$			17.8435i			1.87051i
$92$	−3.08560	+	3.67139i	−0.321696	+	0.382768i
$93$	−4.48528	+	4.48528i	−0.465102	+	0.465102i
$94$			2.24264i			0.231311i
$95$		0			0
$96$	−2.82843			−0.288675
$97$	−3.06147	+	3.06147i	−0.310845	+	0.310845i	−0.845237	−	0.534392i	$-0.820541\pi$
$97$	−3.06147	+	3.06147i	−0.310845	+	0.310845i	0.534392	+	0.845237i	$0.320541\pi$
$98$	−4.70711	+	4.70711i	−0.475490	+	0.475490i
$99$	−1.58513			−0.159311
$100$		0			0
$101$	18.4853			1.83935			0.919677	−	0.392675i	$-0.128450\pi$
$101$	18.4853			1.83935			0.919677	+	0.392675i	$0.128450\pi$
$102$	10.4525	−	10.4525i	1.03495	−	1.03495i
$103$	8.28772	+	8.28772i	0.816613	+	0.816613i	0.985616	−	0.169002i	$-0.0540546\pi$
$103$	8.28772	+	8.28772i	0.816613	+	0.816613i	−0.169002	+	0.985616i	$0.554055\pi$
$104$		−	4.82843i		−	0.473466i
$105$		0			0
$106$			7.07401i			0.687089i
$107$	−6.66413	+	6.66413i	−0.644246	+	0.644246i	−0.951596	−	0.307351i	$-0.900558\pi$
$107$	−6.66413	+	6.66413i	−0.644246	+	0.644246i	0.307351	+	0.951596i	$0.400558\pi$
$108$	−4.00000	+	4.00000i	−0.384900	+	0.384900i
$109$	0.951076			0.0910966			0.0455483	−	0.998962i	$-0.485497\pi$
$109$	0.951076			0.0910966			0.0455483	+	0.998962i	$0.485497\pi$
$110$		0			0
$111$			8.28772i			0.786636i
$112$	2.61313	−	2.61313i	0.246917	−	0.246917i
$113$	6.94269	+	6.94269i	0.653114	+	0.653114i	0.953742	−	0.300628i	$-0.0971962\pi$
$113$	6.94269	+	6.94269i	0.653114	+	0.653114i	−0.300628	+	0.953742i	$0.597196\pi$
$114$	14.4107			1.34968
$115$		0			0
$116$	−3.65685			−0.339530
$117$	−17.0711	−	17.0711i	−1.57822	−	1.57822i
$118$	−6.82843	+	6.82843i	−0.628608	+	0.628608i
$119$			19.3137i			1.77048i
$120$		0			0
$121$	10.8995			0.990863
$122$	8.38057	−	8.38057i	0.758742	−	0.758742i
$123$	19.7990	−	19.7990i	1.78521	−	1.78521i
$124$			2.24264i			0.201395i
$125$		0			0
$126$		−	18.4776i		−	1.64611i
$127$	2.41421	+	2.41421i	0.214227	+	0.214227i	0.806060	−	0.591833i	$-0.201596\pi$
$127$	2.41421	+	2.41421i	0.214227	+	0.214227i	−0.591833	+	0.806060i	$0.701596\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−23.0698			−2.03118
$130$		0			0
$131$	10.1421			0.886123			0.443061	−	0.896491i	$-0.353892\pi$
$131$	10.1421			0.886123			0.443061	+	0.896491i	$0.353892\pi$
$132$	−0.634051	+	0.634051i	−0.0551870	+	0.0551870i
$133$	−13.3137	+	13.3137i	−1.15444	+	1.15444i
$134$	3.37849			0.291857
$135$		0			0
$136$		−	5.22625i		−	0.448147i
$137$	14.7821	−	14.7821i	1.26292	−	1.26292i	0.313246	−	0.949672i	$-0.398584\pi$
$137$	14.7821	−	14.7821i	1.26292	−	1.26292i	0.949672	−	0.313246i	$-0.101416\pi$
$138$	10.3842	+	8.72739i	0.883966	+	0.742925i
$139$		−	13.1716i		−	1.11720i	−0.829438	−	0.558599i	$-0.811339\pi$
$139$		−	13.1716i		−	1.11720i	0.829438	−	0.558599i	$-0.188661\pi$
$140$		0			0
$141$	6.34315			0.534189
$142$	3.41421	+	3.41421i	0.286514	+	0.286514i
$143$	−1.08239	−	1.08239i	−0.0905142	−	0.0905142i
$144$			5.00000i			0.416667i
$145$		0			0
$146$	9.65685			0.799207
$147$	13.3137	+	13.3137i	1.09810	+	1.09810i
$148$	2.07193	+	2.07193i	0.170312	+	0.170312i
$149$	−5.99162			−0.490853			−0.245426	−	0.969415i	$-0.578928\pi$
$149$	−5.99162			−0.490853			−0.245426	+	0.969415i	$0.578928\pi$
$150$		0			0
$151$	−19.4142			−1.57991			−0.789953	−	0.613167i	$-0.789895\pi$
$151$	−19.4142			−1.57991			−0.789953	+	0.613167i	$0.789895\pi$
$152$	3.60266	−	3.60266i	0.292215	−	0.292215i
$153$	−18.4776	−	18.4776i	−1.49382	−	1.49382i
$154$		−	1.17157i		−	0.0944080i
$155$		0			0
$156$	−13.6569			−1.09342
$157$	−5.45042	+	5.45042i	−0.434991	+	0.434991i	−0.890322	−	0.455331i	$-0.849521\pi$
$157$	−5.45042	+	5.45042i	−0.434991	+	0.434991i	0.455331	+	0.890322i	$0.349521\pi$
$158$	−3.24718	−	3.24718i	−0.258331	−	0.258331i
$159$	20.0083			1.58676
$160$		0			0
$161$	−17.6569	+	1.53073i	−1.39156	+	0.120639i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−6.48528	+	6.48528i	−0.507966	+	0.507966i	−0.913902	−	0.405935i	$-0.866946\pi$
$163$	−6.48528	+	6.48528i	−0.507966	+	0.507966i	0.405935	+	0.913902i	$0.366946\pi$
$164$		−	9.89949i		−	0.773021i
$165$		0			0
$166$		−	2.74444i		−	0.213010i
$167$	−8.07107	−	8.07107i	−0.624558	−	0.624558i	0.322136	−	0.946694i	$-0.395599\pi$
$167$	−8.07107	−	8.07107i	−0.624558	−	0.624558i	−0.946694	+	0.322136i	$0.895599\pi$
$168$	−7.39104	−	7.39104i	−0.570231	−	0.570231i
$169$		−	10.3137i		−	0.793362i
$170$		0			0
$171$		−	25.4747i		−	1.94810i
$172$	−5.76745	+	5.76745i	−0.439764	+	0.439764i
$173$	−3.41421	+	3.41421i	−0.259578	+	0.259578i	−0.824882	−	0.565304i	$-0.808759\pi$
$173$	−3.41421	+	3.41421i	−0.259578	+	0.259578i	0.565304	+	0.824882i	$0.308759\pi$
$174$			10.3431i			0.784112i
$175$		0			0
$176$			0.317025i			0.0238967i
$177$	19.3137	+	19.3137i	1.45171	+	1.45171i
$178$	−10.4525	−	10.4525i	−0.783448	−	0.783448i
$179$			16.0000i			1.19590i	0.801535	+	0.597948i	$0.204017\pi$
$179$			16.0000i			1.19590i	−0.801535	+	0.597948i	$0.795983\pi$
$180$		0			0
$181$			3.37849i			0.251121i	0.992086	+	0.125561i	$0.0400730\pi$
$181$			3.37849i			0.251121i	−0.992086	+	0.125561i	$0.959927\pi$
$182$	12.6173	−	12.6173i	0.935256	−	0.935256i
$183$	−23.7038	−	23.7038i	−1.75224	−	1.75224i
$184$	4.77791	−	0.414214i	0.352232	−	0.0305362i
$185$		0			0
$186$	6.34315			0.465102
$187$	−1.17157	−	1.17157i	−0.0856739	−	0.0856739i
$188$	1.58579	−	1.58579i	0.115655	−	0.115655i
$189$	−20.9050			−1.52062
$190$		0			0
$191$		−	2.42742i		−	0.175642i	−0.996136	−	0.0878209i	$-0.972010\pi$
$191$		−	2.42742i		−	0.175642i	0.996136	−	0.0878209i	$-0.0279903\pi$
$192$	2.00000	+	2.00000i	0.144338	+	0.144338i
$193$	11.1421	−	11.1421i	0.802028	−	0.802028i	−0.181384	−	0.983412i	$-0.558058\pi$
$193$	11.1421	−	11.1421i	0.802028	−	0.802028i	0.983412	+	0.181384i	$0.0580577\pi$
$194$	4.32957			0.310845
$195$		0			0
$196$	6.65685			0.475490
$197$	7.07107	+	7.07107i	0.503793	+	0.503793i	0.912614	−	0.408822i	$-0.134060\pi$
$197$	7.07107	+	7.07107i	0.503793	+	0.503793i	−0.408822	+	0.912614i	$0.634060\pi$
$198$	1.12085	+	1.12085i	0.0796556	+	0.0796556i
$199$	9.81845			0.696012			0.348006	−	0.937492i	$-0.386859\pi$
$199$	9.81845			0.696012			0.348006	+	0.937492i	$0.386859\pi$
$200$		0			0
$201$		−	9.55582i		−	0.674016i
$202$	−13.0711	−	13.0711i	−0.919677	−	0.919677i
$203$	−9.55582	−	9.55582i	−0.670687	−	0.670687i
$204$	−14.7821			−1.03495
$205$		0			0
$206$		−	11.7206i		−	0.816613i
$207$	15.4280	−	18.3569i	1.07232	−	1.27589i
$208$	−3.41421	+	3.41421i	−0.236733	+	0.236733i
$209$		−	1.61522i		−	0.111727i
$210$		0			0
$211$	−13.6569			−0.940177			−0.470088	−	0.882619i	$-0.655778\pi$
$211$	−13.6569			−0.940177			−0.470088	+	0.882619i	$0.655778\pi$
$212$	5.00208	−	5.00208i	0.343544	−	0.343544i
$213$	9.65685	−	9.65685i	0.661677	−	0.661677i
$214$	9.42450			0.644246
$215$		0			0
$216$	5.65685			0.384900
$217$	−5.86030	+	5.86030i	−0.397823	+	0.397823i
$218$	−0.672512	−	0.672512i	−0.0455483	−	0.0455483i
$219$		−	27.3137i		−	1.84569i
$220$		0			0
$221$		−	25.2346i		−	1.69746i
$222$	5.86030	−	5.86030i	0.393318	−	0.393318i
$223$	6.24264	−	6.24264i	0.418038	−	0.418038i	−0.466489	−	0.884527i	$-0.654481\pi$
$223$	6.24264	−	6.24264i	0.418038	−	0.418038i	0.884527	+	0.466489i	$0.154481\pi$
$224$	−3.69552			−0.246917
$225$		0			0
$226$		−	9.81845i		−	0.653114i
$227$	−1.12085	+	1.12085i	−0.0743937	+	0.0743937i	−0.743325	−	0.668931i	$-0.766752\pi$
$227$	−1.12085	+	1.12085i	−0.0743937	+	0.0743937i	0.668931	+	0.743325i	$0.266752\pi$
$228$	−10.1899	−	10.1899i	−0.674841	−	0.674841i
$229$	−9.50143			−0.627872			−0.313936	−	0.949444i	$-0.601648\pi$
$229$	−9.50143			−0.627872			−0.313936	+	0.949444i	$0.601648\pi$
$230$		0			0
$231$	−3.31371			−0.218026
$232$	2.58579	+	2.58579i	0.169765	+	0.169765i
$233$	14.6569	−	14.6569i	0.960202	−	0.960202i	−0.0390354	−	0.999238i	$-0.512429\pi$
$233$	14.6569	−	14.6569i	0.960202	−	0.960202i	0.999238	+	0.0390354i	$0.0124285\pi$
$234$			24.1421i			1.57822i
$235$		0			0
$236$	9.65685			0.628608
$237$	−9.18440	+	9.18440i	−0.596591	+	0.596591i
$238$	13.6569	−	13.6569i	0.885242	−	0.885242i
$239$			5.75736i			0.372413i	0.982511	+	0.186206i	$0.0596193\pi$
$239$			5.75736i			0.372413i	−0.982511	+	0.186206i	$0.940381\pi$
$240$		0			0
$241$			29.8268i			1.92131i	0.277742	+	0.960656i	$0.410414\pi$
$241$			29.8268i			1.92131i	−0.277742	+	0.960656i	$0.589586\pi$
$242$	−7.70711	−	7.70711i	−0.495432	−	0.495432i
$243$	−10.0000	+	10.0000i	−0.641500	+	0.641500i
$244$	−11.8519			−0.758742
$245$		0			0
$246$	−28.0000			−1.78521
$247$	17.3952	−	17.3952i	1.10683	−	1.10683i
$248$	1.58579	−	1.58579i	0.100698	−	0.100698i
$249$	−7.76245			−0.491926
$250$		0			0
$251$			15.8101i			0.997923i	0.866624	+	0.498961i	$0.166285\pi$
$251$			15.8101i			0.997923i	−0.866624	+	0.498961i	$0.833715\pi$
$252$	−13.0656	+	13.0656i	−0.823057	+	0.823057i
$253$	0.978213	−	1.16392i	0.0614997	−	0.0731752i
$254$		−	3.41421i		−	0.214227i
$255$		0			0
$256$	1.00000			0.0625000
$257$	1.17157	+	1.17157i	0.0730807	+	0.0730807i	0.742702	−	0.669622i	$-0.233544\pi$
$257$	1.17157	+	1.17157i	0.0730807	+	0.0730807i	−0.669622	+	0.742702i	$0.733544\pi$
$258$	16.3128	+	16.3128i	1.01559	+	1.01559i
$259$			10.8284i			0.672846i
$260$		0			0
$261$	18.2843			1.13177
$262$	−7.17157	−	7.17157i	−0.443061	−	0.443061i
$263$	17.2095	+	17.2095i	1.06118	+	1.06118i	0.998002	+	0.0631805i	$0.0201244\pi$
$263$	17.2095	+	17.2095i	1.06118	+	1.06118i	0.0631805	+	0.998002i	$0.479876\pi$
$264$	0.896683			0.0551870
$265$		0			0
$266$	18.8284			1.15444
$267$	−29.5641	+	29.5641i	−1.80930	+	1.80930i
$268$	−2.38896	−	2.38896i	−0.145929	−	0.145929i
$269$		−	2.00000i		−	0.121942i	−0.998140	−	0.0609711i	$-0.980580\pi$
$269$		−	2.00000i		−	0.121942i	0.998140	−	0.0609711i	$-0.0194197\pi$
$270$		0			0
$271$	9.51472			0.577978			0.288989	−	0.957332i	$-0.406681\pi$
$271$	9.51472			0.577978			0.288989	+	0.957332i	$0.406681\pi$
$272$	−3.69552	+	3.69552i	−0.224074	+	0.224074i
$273$	−35.6871	−	35.6871i	−2.15988	−	2.15988i
$274$	−20.9050			−1.26292
$275$		0			0
$276$	−1.17157	−	13.5140i	−0.0705204	−	0.813445i
$277$	−5.41421	−	5.41421i	−0.325309	−	0.325309i	0.525491	−	0.850799i	$-0.323882\pi$
$277$	−5.41421	−	5.41421i	−0.325309	−	0.325309i	−0.850799	+	0.525491i	$0.823882\pi$
$278$	−9.31371	+	9.31371i	−0.558599	+	0.558599i
$279$		−	11.2132i		−	0.671317i
$280$		0			0
$281$		−	13.8854i		−	0.828333i	−0.910201	−	0.414166i	$-0.864073\pi$
$281$		−	13.8854i		−	0.828333i	0.910201	−	0.414166i	$-0.135927\pi$
$282$	−4.48528	−	4.48528i	−0.267095	−	0.267095i
$283$	1.43788	+	1.43788i	0.0854730	+	0.0854730i	0.748551	−	0.663078i	$-0.230750\pi$
$283$	1.43788	+	1.43788i	0.0854730	+	0.0854730i	−0.663078	+	0.748551i	$0.730750\pi$
$284$		−	4.82843i		−	0.286514i
$285$		0			0
$286$			1.53073i			0.0905142i
$287$	25.8686	−	25.8686i	1.52698	−	1.52698i
$288$	3.53553	−	3.53553i	0.208333	−	0.208333i
$289$		−	10.3137i		−	0.606689i
$290$		0			0
$291$		−	12.2459i		−	0.717866i
$292$	−6.82843	−	6.82843i	−0.399603	−	0.399603i
$293$	3.34003	+	3.34003i	0.195127	+	0.195127i	0.797907	−	0.602780i	$-0.205941\pi$
$293$	3.34003	+	3.34003i	0.195127	+	0.195127i	−0.602780	+	0.797907i	$0.705941\pi$
$294$		−	18.8284i		−	1.09810i
$295$		0			0
$296$		−	2.93015i		−	0.170312i
$297$	1.26810	−	1.26810i	0.0735827	−	0.0735827i
$298$	4.23671	+	4.23671i	0.245426	+	0.245426i
$299$	23.0698	−	2.00000i	1.33416	−	0.115663i
$300$		0			0
$301$	−30.1421			−1.73736
$302$	13.7279	+	13.7279i	0.789953	+	0.789953i
$303$	−36.9706	+	36.9706i	−2.12390	+	2.12390i
$304$	−5.09494			−0.292215
$305$		0			0
$306$			26.1313i			1.49382i
$307$	9.65685	+	9.65685i	0.551146	+	0.551146i	0.926771	−	0.375626i	$-0.122572\pi$
$307$	9.65685	+	9.65685i	0.551146	+	0.551146i	−0.375626	+	0.926771i	$0.622572\pi$
$308$	−0.828427	+	0.828427i	−0.0472040	+	0.0472040i
$309$	−33.1509			−1.88589
$310$		0			0
$311$	−11.4142			−0.647241			−0.323620	−	0.946187i	$-0.604900\pi$
$311$	−11.4142			−0.647241			−0.323620	+	0.946187i	$0.604900\pi$
$312$	9.65685	+	9.65685i	0.546712	+	0.546712i
$313$	19.3743	+	19.3743i	1.09510	+	1.09510i	0.994975	+	0.100124i	$0.0319239\pi$
$313$	19.3743	+	19.3743i	1.09510	+	1.09510i	0.100124	+	0.994975i	$0.468076\pi$
$314$	7.70806			0.434991
$315$		0			0
$316$			4.59220i			0.258331i
$317$	7.75736	+	7.75736i	0.435697	+	0.435697i	0.890561	−	0.454864i	$-0.150312\pi$
$317$	7.75736	+	7.75736i	0.435697	+	0.435697i	−0.454864	+	0.890561i	$0.650312\pi$
$318$	−14.1480	−	14.1480i	−0.793382	−	0.793382i
$319$	1.15932			0.0649092
$320$		0			0
$321$		−	26.6565i		−	1.48782i
$322$	13.5677	+	11.4029i	0.756097	+	0.635458i
$323$	18.8284	−	18.8284i	1.04764	−	1.04764i
$324$		−	1.00000i		−	0.0555556i
$325$		0			0
$326$	9.17157			0.507966
$327$	−1.90215	+	1.90215i	−0.105189	+	0.105189i
$328$	−7.00000	+	7.00000i	−0.386510	+	0.386510i
$329$	8.28772			0.456917
$330$		0			0
$331$	−1.65685			−0.0910689			−0.0455345	−	0.998963i	$-0.514499\pi$
$331$	−1.65685			−0.0910689			−0.0455345	+	0.998963i	$0.514499\pi$
$332$	−1.94061	+	1.94061i	−0.106505	+	0.106505i
$333$	−10.3596	−	10.3596i	−0.567705	−	0.567705i
$334$			11.4142i			0.624558i
$335$		0			0
$336$			10.4525i			0.570231i
$337$	−1.08239	+	1.08239i	−0.0589617	+	0.0589617i	−0.735973	−	0.677011i	$-0.763275\pi$
$337$	−1.08239	+	1.08239i	−0.0589617	+	0.0589617i	0.677011	+	0.735973i	$0.263275\pi$
$338$	−7.29289	+	7.29289i	−0.396681	+	0.396681i
$339$	−27.7708			−1.50830
$340$		0			0
$341$		−	0.710974i		−	0.0385014i
$342$	−18.0133	+	18.0133i	−0.974049	+	0.974049i
$343$	−0.896683	−	0.896683i	−0.0484163	−	0.0484163i
$344$	8.15640			0.439764
$345$		0			0
$346$	4.82843			0.259578
$347$	−18.8284	−	18.8284i	−1.01076	−	1.01076i	−0.999941	−	0.0108215i	$-0.996555\pi$
$347$	−18.8284	−	18.8284i	−1.01076	−	1.01076i	−0.0108215	−	0.999941i	$-0.503445\pi$
$348$	7.31371	−	7.31371i	0.392056	−	0.392056i
$349$			32.6274i			1.74651i	0.487267	+	0.873253i	$0.337994\pi$
$349$			32.6274i			1.74651i	−0.487267	+	0.873253i	$0.662006\pi$
$350$		0			0
$351$	27.3137			1.45790
$352$	0.224171	−	0.224171i	0.0119483	−	0.0119483i
$353$	2.31371	−	2.31371i	0.123146	−	0.123146i	−0.642848	−	0.765994i	$-0.722247\pi$
$353$	2.31371	−	2.31371i	0.123146	−	0.123146i	0.765994	+	0.642848i	$0.222247\pi$
$354$		−	27.3137i		−	1.45171i
$355$		0			0
$356$			14.7821i			0.783448i
$357$	−38.6274	−	38.6274i	−2.04438	−	2.04438i
$358$	11.3137	−	11.3137i	0.597948	−	0.597948i
$359$	−12.8799			−0.679776			−0.339888	−	0.940466i	$-0.610389\pi$
$359$	−12.8799			−0.679776			−0.339888	+	0.940466i	$0.610389\pi$
$360$		0			0
$361$	6.95837			0.366230
$362$	2.38896	−	2.38896i	0.125561	−	0.125561i
$363$	−21.7990	+	21.7990i	−1.14415	+	1.14415i
$364$	−17.8435			−0.935256
$365$		0			0
$366$			33.5223i			1.75224i
$367$	−18.6633	+	18.6633i	−0.974216	+	0.974216i	−0.999676	−	0.0254595i	$-0.991895\pi$
$367$	−18.6633	+	18.6633i	−0.974216	+	0.974216i	0.0254595	+	0.999676i	$0.491895\pi$
$368$	−3.67139	−	3.08560i	−0.191384	−	0.160848i
$369$			49.4975i			2.57674i
$370$		0			0
$371$	26.1421			1.35723
$372$	−4.48528	−	4.48528i	−0.232551	−	0.232551i
$373$	−19.3358	−	19.3358i	−1.00117	−	1.00117i	−0.999999	−	0.00117109i	$-0.999627\pi$
$373$	−19.3358	−	19.3358i	−1.00117	−	1.00117i	−0.00117109	−	0.999999i	$-0.500373\pi$
$374$			1.65685i			0.0856739i
$375$		0			0
$376$	−2.24264			−0.115655
$377$	12.4853	+	12.4853i	0.643025	+	0.643025i
$378$	14.7821	+	14.7821i	0.760308	+	0.760308i
$379$	−0.765367			−0.0393143			−0.0196571	−	0.999807i	$-0.506257\pi$
$379$	−0.765367			−0.0393143			−0.0196571	+	0.999807i	$0.506257\pi$
$380$		0			0
$381$	−9.65685			−0.494736
$382$	−1.71644	+	1.71644i	−0.0878209	+	0.0878209i
$383$	15.4161	+	15.4161i	0.787727	+	0.787727i	0.981121	−	0.193394i	$-0.0619496\pi$
$383$	15.4161	+	15.4161i	0.787727	+	0.787727i	−0.193394	+	0.981121i	$0.561950\pi$
$384$		−	2.82843i		−	0.144338i
$385$		0			0
$386$	−15.7574			−0.802028
$387$	28.8372	−	28.8372i	1.46588	−	1.46588i
$388$	−3.06147	−	3.06147i	−0.155422	−	0.155422i
$389$	−6.99709			−0.354766			−0.177383	−	0.984142i	$-0.556763\pi$
$389$	−6.99709			−0.354766			−0.177383	+	0.984142i	$0.556763\pi$
$390$		0			0
$391$	24.9706	−	2.16478i	1.26282	−	0.109478i
$392$	−4.70711	−	4.70711i	−0.237745	−	0.237745i
$393$	−20.2843	+	20.2843i	−1.02321	+	1.02321i
$394$		−	10.0000i		−	0.503793i
$395$		0			0
$396$		−	1.58513i		−	0.0796556i
$397$	0.585786	+	0.585786i	0.0293998	+	0.0293998i	0.721654	−	0.692254i	$-0.243382\pi$
$397$	0.585786	+	0.585786i	0.0293998	+	0.0293998i	−0.692254	+	0.721654i	$0.743382\pi$
$398$	−6.94269	−	6.94269i	−0.348006	−	0.348006i
$399$		−	53.2548i		−	2.66608i
$400$		0			0
$401$		−	15.9414i		−	0.796075i	−0.917369	−	0.398037i	$-0.869691\pi$
$401$		−	15.9414i		−	0.796075i	0.917369	−	0.398037i	$-0.130309\pi$
$402$	−6.75699	+	6.75699i	−0.337008	+	0.337008i
$403$	7.65685	−	7.65685i	0.381415	−	0.381415i
$404$			18.4853i			0.919677i
$405$		0			0
$406$			13.5140i			0.670687i
$407$	−0.656854	−	0.656854i	−0.0325591	−	0.0325591i
$408$	10.4525	+	10.4525i	0.517476	+	0.517476i
$409$			9.65685i			0.477501i	0.971081	+	0.238750i	$0.0767378\pi$
$409$			9.65685i			0.477501i	−0.971081	+	0.238750i	$0.923262\pi$
$410$		0			0
$411$			59.1283i			2.91658i
$412$	−8.28772	+	8.28772i	−0.408307	+	0.408307i
$413$	25.2346	+	25.2346i	1.24171	+	1.24171i
$414$	−23.8896	+	2.07107i	−1.17411	+	0.101787i
$415$		0			0
$416$	4.82843			0.236733
$417$	26.3431	+	26.3431i	1.29003	+	1.29003i
$418$	−1.14214	+	1.14214i	−0.0558637	+	0.0558637i
$419$	20.0627			0.980128			0.490064	−	0.871686i	$-0.336973\pi$
$419$	20.0627			0.980128			0.490064	+	0.871686i	$0.336973\pi$
$420$		0			0
$421$		−	3.37849i		−	0.164658i	−0.996605	−	0.0823288i	$-0.973764\pi$
$421$		−	3.37849i		−	0.164658i	0.996605	−	0.0823288i	$-0.0262358\pi$
$422$	9.65685	+	9.65685i	0.470088	+	0.470088i
$423$	−7.92893	+	7.92893i	−0.385518	+	0.385518i
$424$	−7.07401			−0.343544
$425$		0			0
$426$	−13.6569			−0.661677
$427$	−30.9706	−	30.9706i	−1.49877	−	1.49877i
$428$	−6.66413	−	6.66413i	−0.322123	−	0.322123i
$429$	4.32957			0.209034
$430$		0			0
$431$		−	27.6620i		−	1.33243i	−0.745759	−	0.666216i	$-0.767913\pi$
$431$		−	27.6620i		−	1.33243i	0.745759	−	0.666216i	$-0.232087\pi$
$432$	−4.00000	−	4.00000i	−0.192450	−	0.192450i
$433$	−6.75699	−	6.75699i	−0.324720	−	0.324720i	0.525855	−	0.850575i	$-0.323746\pi$
$433$	−6.75699	−	6.75699i	−0.324720	−	0.324720i	−0.850575	+	0.525855i	$0.823746\pi$
$434$	8.28772			0.397823
$435$		0			0
$436$			0.951076i			0.0455483i
$437$	18.7055	+	15.7209i	0.894804	+	0.752034i
$438$	−19.3137	+	19.3137i	−0.922845	+	0.922845i
$439$			20.1421i			0.961332i	0.876904	+	0.480666i	$0.159605\pi$
$439$			20.1421i			0.961332i	−0.876904	+	0.480666i	$0.840395\pi$
$440$		0			0
$441$	−33.2843			−1.58497
$442$	−17.8435	+	17.8435i	−0.848731	+	0.848731i
$443$	−5.31371	+	5.31371i	−0.252462	+	0.252462i	−0.821979	−	0.569517i	$-0.807130\pi$
$443$	−5.31371	+	5.31371i	−0.252462	+	0.252462i	0.569517	+	0.821979i	$0.307130\pi$
$444$	−8.28772			−0.393318
$445$		0			0
$446$	−8.82843			−0.418038
$447$	11.9832	−	11.9832i	0.566788	−	0.566788i
$448$	2.61313	+	2.61313i	0.123459	+	0.123459i
$449$		−	12.7279i		−	0.600668i	−0.953834	−	0.300334i	$-0.902902\pi$
$449$		−	12.7279i		−	0.600668i	0.953834	−	0.300334i	$-0.0970981\pi$
$450$		0			0
$451$			3.13839i			0.147781i
$452$	−6.94269	+	6.94269i	−0.326557	+	0.326557i
$453$	38.8284	−	38.8284i	1.82432	−	1.82432i
$454$	1.58513			0.0743937
$455$		0			0
$456$			14.4107i			0.674841i
$457$	18.7402	−	18.7402i	0.876631	−	0.876631i	−0.116554	−	0.993184i	$-0.537185\pi$
$457$	18.7402	−	18.7402i	0.876631	−	0.876631i	0.993184	+	0.116554i	$0.0371847\pi$
$458$	6.71852	+	6.71852i	0.313936	+	0.313936i
$459$	29.5641			1.37994
$460$		0			0
$461$	−12.8284			−0.597479			−0.298740	−	0.954335i	$-0.596566\pi$
$461$	−12.8284			−0.597479			−0.298740	+	0.954335i	$0.596566\pi$
$462$	2.34315	+	2.34315i	0.109013	+	0.109013i
$463$	16.2132	−	16.2132i	0.753491	−	0.753491i	−0.221638	−	0.975129i	$-0.571140\pi$
$463$	16.2132	−	16.2132i	0.753491	−	0.753491i	0.975129	+	0.221638i	$0.0711402\pi$
$464$		−	3.65685i		−	0.169765i
$465$		0			0
$466$	−20.7279			−0.960202
$467$	6.84984	−	6.84984i	0.316973	−	0.316973i	−0.530630	−	0.847603i	$-0.678045\pi$
$467$	6.84984	−	6.84984i	0.316973	−	0.316973i	0.847603	+	0.530630i	$0.178045\pi$
$468$	17.0711	−	17.0711i	0.789110	−	0.789110i
$469$		−	12.4853i		−	0.576517i
$470$		0			0
$471$		−	21.8017i		−	1.00457i
$472$	−6.82843	−	6.82843i	−0.314304	−	0.314304i
$473$	1.82843	−	1.82843i	0.0840712	−	0.0840712i
$474$	12.9887			0.596591
$475$		0			0
$476$	−19.3137			−0.885242
$477$	−25.0104	+	25.0104i	−1.14515	+	1.14515i
$478$	4.07107	−	4.07107i	0.186206	−	0.186206i
$479$	35.6871			1.63058			0.815292	−	0.579050i	$-0.196576\pi$
$479$	35.6871			1.63058			0.815292	+	0.579050i	$0.196576\pi$
$480$		0			0
$481$		−	14.1480i		−	0.645094i
$482$	21.0907	−	21.0907i	0.960656	−	0.960656i
$483$	32.2522	−	38.3752i	1.46753	−	1.74613i
$484$			10.8995i			0.495432i
$485$		0			0
$486$	14.1421			0.641500
$487$	23.2426	+	23.2426i	1.05322	+	1.05322i	0.998502	+	0.0547230i	$0.0174276\pi$
$487$	23.2426	+	23.2426i	1.05322	+	1.05322i	0.0547230	+	0.998502i	$0.482572\pi$
$488$	8.38057	+	8.38057i	0.379371	+	0.379371i
$489$		−	25.9411i		−	1.17310i
$490$		0			0
$491$	7.79899			0.351963			0.175982	−	0.984393i	$-0.443690\pi$
$491$	7.79899			0.351963			0.175982	+	0.984393i	$0.443690\pi$
$492$	19.7990	+	19.7990i	0.892607	+	0.892607i
$493$	13.5140	+	13.5140i	0.608639	+	0.608639i
$494$	−24.6005			−1.10683
$495$		0			0
$496$	−2.24264			−0.100698
$497$	12.6173	−	12.6173i	0.565963	−	0.565963i
$498$	5.48888	+	5.48888i	0.245963	+	0.245963i
$499$		−	2.14214i		−	0.0958952i	−0.998850	−	0.0479476i	$-0.984732\pi$
$499$		−	2.14214i		−	0.0958952i	0.998850	−	0.0479476i	$-0.0152680\pi$
$500$		0			0
$501$	32.2843			1.44235
$502$	11.1794	−	11.1794i	0.498961	−	0.498961i
$503$	−1.71644	−	1.71644i	−0.0765324	−	0.0765324i	0.667804	−	0.744337i	$-0.267234\pi$
$503$	−1.71644	−	1.71644i	−0.0765324	−	0.0765324i	−0.744337	+	0.667804i	$0.767234\pi$
$504$	18.4776			0.823057
$505$		0			0
$506$	−1.51472	+	0.131316i	−0.0673375	+	0.00583772i
$507$	20.6274	+	20.6274i	0.916096	+	0.916096i
$508$	−2.41421	+	2.41421i	−0.107113	+	0.107113i
$509$		−	7.65685i		−	0.339384i	−0.985497	−	0.169692i	$-0.945723\pi$
$509$		−	7.65685i		−	0.339384i	0.985497	−	0.169692i	$-0.0542773\pi$
$510$		0			0
$511$		−	35.6871i		−	1.57870i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	20.3797	+	20.3797i	0.899788	+	0.899788i
$514$		−	1.65685i		−	0.0730807i
$515$		0			0
$516$		−	23.0698i		−	1.01559i
$517$	−0.502734	+	0.502734i	−0.0221102	+	0.0221102i
$518$	7.65685	−	7.65685i	0.336423	−	0.336423i
$519$		−	13.6569i		−	0.599469i
$520$		0			0
$521$		−	16.3128i		−	0.714677i	−0.933975	−	0.357339i	$-0.883684\pi$
$521$		−	16.3128i		−	0.714677i	0.933975	−	0.357339i	$-0.116316\pi$
$522$	−12.9289	−	12.9289i	−0.565884	−	0.565884i
$523$	2.83730	+	2.83730i	0.124066	+	0.124066i	0.766414	−	0.642347i	$-0.222039\pi$
$523$	2.83730	+	2.83730i	0.124066	+	0.124066i	−0.642347	+	0.766414i	$0.722039\pi$
$524$			10.1421i			0.443061i
$525$		0			0
$526$		−	24.3379i		−	1.06118i
$527$	8.28772	−	8.28772i	0.361019	−	0.361019i
$528$	−0.634051	−	0.634051i	−0.0275935	−	0.0275935i
$529$	3.95815	+	22.6569i	0.172094	+	0.985081i
$530$		0			0
$531$	−48.2843			−2.09536
$532$	−13.3137	−	13.3137i	−0.577222	−	0.577222i
$533$	−33.7990	+	33.7990i	−1.46400	+	1.46400i
$534$	41.8100			1.80930
$535$		0			0
$536$			3.37849i			0.145929i
$537$	−32.0000	−	32.0000i	−1.38090	−	1.38090i
$538$	−1.41421	+	1.41421i	−0.0609711	+	0.0609711i
$539$	−2.11039			−0.0909010
$540$		0			0
$541$	25.1127			1.07968			0.539840	−	0.841768i	$-0.318485\pi$
$541$	25.1127			1.07968			0.539840	+	0.841768i	$0.318485\pi$
$542$	−6.72792	−	6.72792i	−0.288989	−	0.288989i
$543$	−6.75699	−	6.75699i	−0.289970	−	0.289970i
$544$	5.22625			0.224074
$545$		0			0
$546$			50.4692i			2.15988i
$547$	−8.48528	−	8.48528i	−0.362804	−	0.362804i	0.502040	−	0.864844i	$-0.332583\pi$
$547$	−8.48528	−	8.48528i	−0.362804	−	0.362804i	−0.864844	+	0.502040i	$0.832583\pi$
$548$	14.7821	+	14.7821i	0.631459	+	0.631459i
$549$	59.2596			2.52914
$550$		0			0
$551$			18.6314i			0.793726i
$552$	−8.72739	+	10.3842i	−0.371463	+	0.441983i
$553$	−12.0000	+	12.0000i	−0.510292	+	0.510292i
$554$			7.65685i			0.325309i
$555$		0			0
$556$	13.1716			0.558599
$557$	0.803828	−	0.803828i	0.0340593	−	0.0340593i	−0.689872	−	0.723931i	$-0.742333\pi$
$557$	0.803828	−	0.803828i	0.0340593	−	0.0340593i	0.723931	+	0.689872i	$0.242333\pi$
$558$	−7.92893	+	7.92893i	−0.335658	+	0.335658i
$559$	39.3826			1.66571
$560$		0			0
$561$	4.68629			0.197855
$562$	−9.81845	+	9.81845i	−0.414166	+	0.414166i
$563$	−15.9029	−	15.9029i	−0.670228	−	0.670228i	0.287540	−	0.957769i	$-0.407163\pi$
$563$	−15.9029	−	15.9029i	−0.670228	−	0.670228i	−0.957769	+	0.287540i	$0.907163\pi$
$564$			6.34315i			0.267095i
$565$		0			0
$566$		−	2.03347i		−	0.0854730i
$567$	2.61313	−	2.61313i	0.109741	−	0.109741i
$568$	−3.41421	+	3.41421i	−0.143257	+	0.143257i
$569$	38.4859			1.61341			0.806707	−	0.590952i	$-0.201248\pi$
$569$	38.4859			1.61341			0.806707	+	0.590952i	$0.201248\pi$
$570$		0			0
$571$			39.6996i			1.66138i	0.556737	+	0.830689i	$0.312053\pi$
$571$			39.6996i			1.66138i	−0.556737	+	0.830689i	$0.687947\pi$
$572$	1.08239	−	1.08239i	0.0452571	−	0.0452571i
$573$	4.85483	+	4.85483i	0.202814	+	0.202814i
$574$	−36.5838			−1.52698
$575$		0			0
$576$	−5.00000			−0.208333
$577$	−28.7279	−	28.7279i	−1.19596	−	1.19596i	−0.975366	−	0.220593i	$-0.929201\pi$
$577$	−28.7279	−	28.7279i	−1.19596	−	1.19596i	−0.220593	−	0.975366i	$-0.570799\pi$
$578$	−7.29289	+	7.29289i	−0.303344	+	0.303344i
$579$			44.5685i			1.85221i
$580$		0			0
$581$	−10.1421			−0.420767
$582$	−8.65914	+	8.65914i	−0.358933	+	0.358933i
$583$	−1.58579	+	1.58579i	−0.0656766	+	0.0656766i
$584$			9.65685i			0.399603i
$585$		0			0
$586$		−	4.72352i		−	0.195127i
$587$	4.00000	+	4.00000i	0.165098	+	0.165098i	0.784821	−	0.619723i	$-0.212755\pi$
$587$	4.00000	+	4.00000i	0.165098	+	0.165098i	−0.619723	+	0.784821i	$0.712755\pi$
$588$	−13.3137	+	13.3137i	−0.549048	+	0.549048i
$589$	11.4261			0.470805
$590$		0			0
$591$	−28.2843			−1.16346
$592$	−2.07193	+	2.07193i	−0.0851558	+	0.0851558i
$593$	20.7279	−	20.7279i	0.851194	−	0.851194i	−0.139086	−	0.990280i	$-0.544417\pi$
$593$	20.7279	−	20.7279i	0.851194	−	0.851194i	0.990280	+	0.139086i	$0.0444166\pi$
$594$	−1.79337			−0.0735827
$595$		0			0
$596$		−	5.99162i		−	0.245426i
$597$	−19.6369	+	19.6369i	−0.803685	+	0.803685i
$598$	−17.7270	−	14.8986i	−0.724912	−	0.609249i
$599$		−	1.27208i		−	0.0519757i	−0.999662	−	0.0259878i	$-0.991727\pi$
$599$		−	1.27208i		−	0.0519757i	0.999662	−	0.0259878i	$-0.00827312\pi$
$600$		0			0
$601$	36.0416			1.47017			0.735084	−	0.677976i	$-0.237143\pi$
$601$	36.0416			1.47017			0.735084	+	0.677976i	$0.237143\pi$
$602$	21.3137	+	21.3137i	0.868682	+	0.868682i
$603$	11.9448	+	11.9448i	0.486429	+	0.486429i
$604$		−	19.4142i		−	0.789953i
$605$		0			0
$606$	52.2843			2.12390
$607$	29.6569	+	29.6569i	1.20373	+	1.20373i	0.973022	+	0.230713i	$0.0741057\pi$
$607$	29.6569	+	29.6569i	1.20373	+	1.20373i	0.230713	+	0.973022i	$0.425894\pi$
$608$	3.60266	+	3.60266i	0.146107	+	0.146107i
$609$	38.2233			1.54889
$610$		0			0
$611$	−10.8284			−0.438071
$612$	18.4776	−	18.4776i	0.746912	−	0.746912i
$613$	−11.0481	−	11.0481i	−0.446228	−	0.446228i	0.447870	−	0.894099i	$-0.352183\pi$
$613$	−11.0481	−	11.0481i	−0.446228	−	0.446228i	−0.894099	+	0.447870i	$0.852183\pi$
$614$		−	13.6569i		−	0.551146i
$615$		0			0
$616$	1.17157			0.0472040
$617$	−21.3533	+	21.3533i	−0.859653	+	0.859653i	−0.991297	−	0.131644i	$-0.957975\pi$
$617$	−21.3533	+	21.3533i	−0.859653	+	0.859653i	0.131644	+	0.991297i	$0.457975\pi$
$618$	23.4412	+	23.4412i	0.942944	+	0.942944i
$619$	−32.9426			−1.32408			−0.662038	−	0.749470i	$-0.730308\pi$
$619$	−32.9426			−1.32408			−0.662038	+	0.749470i	$0.730308\pi$
$620$		0			0
$621$	2.34315	+	27.0279i	0.0940272	+	1.08459i
$622$	8.07107	+	8.07107i	0.323620	+	0.323620i
$623$	−38.6274	+	38.6274i	−1.54757	+	1.54757i
$624$		−	13.6569i		−	0.546712i
$625$		0			0
$626$		−	27.3994i		−	1.09510i
$627$	3.23045	+	3.23045i	0.129012	+	0.129012i
$628$	−5.45042	−	5.45042i	−0.217496	−	0.217496i
$629$		−	15.3137i		−	0.610598i
$630$		0			0
$631$			24.7093i			0.983662i	0.870691	+	0.491831i	$0.163672\pi$
$631$			24.7093i			0.983662i	−0.870691	+	0.491831i	$0.836328\pi$
$632$	3.24718	−	3.24718i	0.129166	−	0.129166i
$633$	27.3137	−	27.3137i	1.08562	−	1.08562i
$634$		−	10.9706i		−	0.435697i
$635$		0			0
$636$			20.0083i			0.793382i
$637$	−22.7279	−	22.7279i	−0.900513	−	0.900513i
$638$	−0.819760	−	0.819760i	−0.0324546	−	0.0324546i
$639$			24.1421i			0.955048i
$640$		0			0
$641$		−	21.5391i		−	0.850742i	−0.905019	−	0.425371i	$-0.860144\pi$
$641$		−	21.5391i		−	0.850742i	0.905019	−	0.425371i	$-0.139856\pi$
$642$	−18.8490	+	18.8490i	−0.743911	+	0.743911i
$643$	−26.8038	−	26.8038i	−1.05704	−	1.05704i	−0.998272	−	0.0587658i	$-0.981283\pi$
$643$	−26.8038	−	26.8038i	−1.05704	−	1.05704i	−0.0587658	−	0.998272i	$-0.518717\pi$
$644$	−1.53073	−	17.6569i	−0.0603194	−	0.695778i
$645$		0			0
$646$	−26.6274			−1.04764
$647$	12.9706	+	12.9706i	0.509925	+	0.509925i	0.914503	−	0.404578i	$-0.132582\pi$
$647$	12.9706	+	12.9706i	0.509925	+	0.509925i	−0.404578	+	0.914503i	$0.632582\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	−3.06147			−0.120173
$650$		0			0
$651$		−	23.4412i		−	0.918733i
$652$	−6.48528	−	6.48528i	−0.253983	−	0.253983i
$653$	3.75736	−	3.75736i	0.147037	−	0.147037i	−0.629756	−	0.776793i	$-0.716845\pi$
$653$	3.75736	−	3.75736i	0.147037	−	0.147037i	0.776793	+	0.629756i	$0.216845\pi$
$654$	2.69005			0.105189
$655$		0			0
$656$	9.89949			0.386510
$657$	34.1421	+	34.1421i	1.33201	+	1.33201i
$658$	−5.86030	−	5.86030i	−0.228458	−	0.228458i
$659$	−40.5194			−1.57841			−0.789206	−	0.614129i	$-0.789507\pi$
$659$	−40.5194			−1.57841			−0.789206	+	0.614129i	$0.789507\pi$
$660$		0			0
$661$			19.5056i			0.758680i	0.925257	+	0.379340i	$0.123849\pi$
$661$			19.5056i			0.758680i	−0.925257	+	0.379340i	$0.876151\pi$
$662$	1.17157	+	1.17157i	0.0455345	+	0.0455345i
$663$	50.4692	+	50.4692i	1.96006	+	1.96006i
$664$	2.74444			0.106505
$665$		0			0
$666$			14.6508i			0.567705i
$667$	−11.2836	+	13.4257i	−0.436902	+	0.519846i
$668$	8.07107	−	8.07107i	0.312279	−	0.312279i
$669$			24.9706i			0.965418i
$670$		0			0
$671$	3.75736			0.145051
$672$	7.39104	−	7.39104i	0.285115	−	0.285115i
$673$	−29.2132	+	29.2132i	−1.12609	+	1.12609i	−0.135279	+	0.990808i	$0.543193\pi$
$673$	−29.2132	+	29.2132i	−1.12609	+	1.12609i	−0.990808	+	0.135279i	$0.956807\pi$
$674$	1.53073			0.0589617
$675$		0			0
$676$	10.3137			0.396681
$677$	0.0928546	−	0.0928546i	0.00356869	−	0.00356869i	−0.705320	−	0.708889i	$-0.749197\pi$
$677$	0.0928546	−	0.0928546i	0.00356869	−	0.00356869i	0.708889	+	0.705320i	$0.249197\pi$
$678$	19.6369	+	19.6369i	0.754151	+	0.754151i
$679$		−	16.0000i		−	0.614024i
$680$		0			0
$681$		−	4.48342i		−	0.171805i
$682$	−0.502734	+	0.502734i	−0.0192507	+	0.0192507i
$683$	−16.9706	+	16.9706i	−0.649361	+	0.649361i	−0.952838	−	0.303478i	$-0.901852\pi$
$683$	−16.9706	+	16.9706i	−0.649361	+	0.649361i	0.303478	+	0.952838i	$0.401852\pi$
$684$	25.4747			0.974049
$685$		0			0
$686$			1.26810i			0.0484163i
$687$	19.0029	−	19.0029i	0.725004	−	0.725004i
$688$	−5.76745	−	5.76745i	−0.219882	−	0.219882i
$689$	−34.1563			−1.30125
$690$		0			0
$691$	−12.4853			−0.474962			−0.237481	−	0.971392i	$-0.576322\pi$
$691$	−12.4853			−0.474962			−0.237481	+	0.971392i	$0.576322\pi$
$692$	−3.41421	−	3.41421i	−0.129789	−	0.129789i
$693$	4.14214	−	4.14214i	0.157347	−	0.157347i
$694$			26.6274i			1.01076i
$695$		0			0
$696$	−10.3431			−0.392056
$697$	−36.5838	+	36.5838i	−1.38571	+	1.38571i
$698$	23.0711	−	23.0711i	0.873253	−	0.873253i
$699$			58.6274i			2.21749i
$700$		0			0
$701$		−	13.3057i		−	0.502551i	−0.967916	−	0.251275i	$-0.919150\pi$
$701$		−	13.3057i		−	0.502551i	0.967916	−	0.251275i	$-0.0808499\pi$
$702$	−19.3137	−	19.3137i	−0.728949	−	0.728949i
$703$	10.5563	−	10.5563i	0.398140	−	0.398140i
$704$	−0.317025			−0.0119483
$705$		0			0
$706$	−3.27208			−0.123146
$707$	−48.3044	+	48.3044i	−1.81667	+	1.81667i
$708$	−19.3137	+	19.3137i	−0.725854	+	0.725854i
$709$	−3.19278			−0.119908			−0.0599538	−	0.998201i	$-0.519095\pi$
$709$	−3.19278			−0.119908			−0.0599538	+	0.998201i	$0.519095\pi$
$710$		0			0
$711$		−	22.9610i		−	0.861105i
$712$	10.4525	−	10.4525i	0.391724	−	0.391724i
$713$	8.23360	+	6.91989i	0.308351	+	0.259152i
$714$			54.6274i			2.04438i
$715$		0			0
$716$	−16.0000			−0.597948
$717$	−11.5147	−	11.5147i	−0.430025	−	0.430025i
$718$	9.10748	+	9.10748i	0.339888	+	0.339888i
$719$		−	38.5269i		−	1.43681i	−0.695624	−	0.718406i	$-0.744872\pi$
$719$		−	38.5269i		−	1.43681i	0.695624	−	0.718406i	$-0.255128\pi$
$720$		0			0
$721$	−43.3137			−1.61309
$722$	−4.92031	−	4.92031i	−0.183115	−	0.183115i
$723$	−59.6536	−	59.6536i	−2.21854	−	2.21854i
$724$	−3.37849			−0.125561
$725$		0			0
$726$	30.8284			1.14415
$727$	30.6465	−	30.6465i	1.13662	−	1.13662i	0.147565	−	0.989052i	$-0.452857\pi$
$727$	30.6465	−	30.6465i	1.13662	−	1.13662i	0.989052	−	0.147565i	$-0.0471435\pi$
$728$	12.6173	+	12.6173i	0.467628	+	0.467628i
$729$		−	43.0000i		−	1.59259i
$730$		0			0
$731$	42.6274			1.57663
$732$	23.7038	−	23.7038i	0.876119	−	0.876119i
$733$	11.0481	+	11.0481i	0.408071	+	0.408071i	0.881065	−	0.472995i	$-0.156827\pi$
$733$	11.0481	+	11.0481i	0.408071	+	0.408071i	−0.472995	+	0.881065i	$0.656827\pi$
$734$	26.3939			0.974216
$735$		0			0
$736$	0.414214	+	4.77791i	0.0152681	+	0.176116i
$737$	0.757359	+	0.757359i	0.0278977	+	0.0278977i
$738$	35.0000	−	35.0000i	1.28837	−	1.28837i
$739$		−	15.7990i		−	0.581175i	−0.956848	−	0.290588i	$-0.906149\pi$
$739$		−	15.7990i		−	0.581175i	0.956848	−	0.290588i	$-0.0938508\pi$
$740$		0			0
$741$			69.5808i			2.55611i
$742$	−18.4853	−	18.4853i	−0.678616	−	0.678616i
$743$	−25.4972	−	25.4972i	−0.935402	−	0.935402i	0.0626347	−	0.998037i	$-0.480050\pi$
$743$	−25.4972	−	25.4972i	−0.935402	−	0.935402i	−0.998037	+	0.0626347i	$0.980050\pi$
$744$			6.34315i			0.232551i
$745$		0			0
$746$			27.3450i			1.00117i
$747$	9.70307	−	9.70307i	0.355017	−	0.355017i
$748$	1.17157	−	1.17157i	0.0428369	−	0.0428369i
$749$		−	34.8284i		−	1.27260i
$750$		0			0
$751$			1.79337i			0.0654409i	0.999465	+	0.0327204i	$0.0104171\pi$
$751$			1.79337i			0.0654409i	−0.999465	+	0.0327204i	$0.989583\pi$
$752$	1.58579	+	1.58579i	0.0578277	+	0.0578277i
$753$	−31.6201	−	31.6201i	−1.15230	−	1.15230i
$754$		−	17.6569i		−	0.643025i
$755$		0			0
$756$		−	20.9050i		−	0.760308i
$757$	−9.64868	+	9.64868i	−0.350687	+	0.350687i	−0.860365	−	0.509678i	$-0.829764\pi$
$757$	−9.64868	+	9.64868i	−0.350687	+	0.350687i	0.509678	+	0.860365i	$0.329764\pi$
$758$	0.541196	+	0.541196i	0.0196571	+	0.0196571i
$759$	0.371418	+	4.28427i	0.0134816	+	0.155509i
$760$		0			0
$761$	−9.65685			−0.350061			−0.175030	−	0.984563i	$-0.556002\pi$
$761$	−9.65685			−0.350061			−0.175030	+	0.984563i	$0.556002\pi$
$762$	6.82843	+	6.82843i	0.247368	+	0.247368i
$763$	−2.48528	+	2.48528i	−0.0899732	+	0.0899732i
$764$	2.42742			0.0878209
$765$		0			0
$766$		−	21.8017i		−	0.787727i
$767$	−32.9706	−	32.9706i	−1.19050	−	1.19050i
$768$	−2.00000	+	2.00000i	−0.0721688	+	0.0721688i
$769$	9.44703			0.340669			0.170334	−	0.985386i	$-0.445515\pi$
$769$	9.44703			0.340669			0.170334	+	0.985386i	$0.445515\pi$
$770$		0			0
$771$	−4.68629			−0.168773
$772$	11.1421	+	11.1421i	0.401014	+	0.401014i
$773$	37.9447	+	37.9447i	1.36478	+	1.36478i	0.867715	+	0.497061i	$0.165588\pi$
$773$	37.9447	+	37.9447i	1.36478	+	1.36478i	0.497061	+	0.867715i	$0.334412\pi$
$774$	−40.7820			−1.46588
$775$		0			0
$776$			4.32957i			0.155422i
$777$	−21.6569	−	21.6569i	−0.776935	−	0.776935i
$778$	4.94769	+	4.94769i	0.177383	+	0.177383i
$779$	−50.4373			−1.80710
$780$		0			0
$781$			1.53073i			0.0547740i
$782$	−19.1876	−	16.1261i	−0.686147	−	0.576669i
$783$	−14.6274	+	14.6274i	−0.522741	+	0.522741i
$784$			6.65685i			0.237745i
$785$		0			0
$786$	28.6863			1.02321
$787$	13.3442	−	13.3442i	0.475669	−	0.475669i	−0.428074	−	0.903744i	$-0.640808\pi$
$787$	13.3442	−	13.3442i	0.475669	−	0.475669i	0.903744	+	0.428074i	$0.140808\pi$
$788$	−7.07107	+	7.07107i	−0.251896	+	0.251896i
$789$	−68.8380			−2.45070
$790$		0			0
$791$	−36.2843			−1.29012
$792$	−1.12085	+	1.12085i	−0.0398278	+	0.0398278i
$793$	40.4650	+	40.4650i	1.43695	+	1.43695i
$794$		−	0.828427i		−	0.0293998i
$795$		0			0
$796$			9.81845i			0.348006i
$797$	8.88331	−	8.88331i	0.314663	−	0.314663i	−0.532050	−	0.846713i	$-0.678578\pi$
$797$	8.88331	−	8.88331i	0.314663	−	0.314663i	0.846713	+	0.532050i	$0.178578\pi$
$798$	−37.6569	+	37.6569i	−1.33304	+	1.33304i
$799$	−11.7206			−0.414645
$800$		0			0
$801$		−	73.9104i		−	2.61149i
$802$	−11.2723	+	11.2723i	−0.398037	+	0.398037i
$803$	2.16478	+	2.16478i	0.0763936	+	0.0763936i
$804$	9.55582			0.337008
$805$		0			0
$806$	−10.8284			−0.381415
$807$	4.00000	+	4.00000i	0.140807	+	0.140807i
$808$	13.0711	−	13.0711i	0.459839	−	0.459839i
$809$		−	30.3431i		−	1.06681i	−0.845861	−	0.533404i	$-0.820913\pi$
$809$		−	30.3431i		−	1.06681i	0.845861	−	0.533404i	$-0.179087\pi$
$810$		0			0
$811$	41.6569			1.46277			0.731385	−	0.681965i	$-0.238874\pi$
$811$	41.6569			1.46277			0.731385	+	0.681965i	$0.238874\pi$
$812$	9.55582	−	9.55582i	0.335344	−	0.335344i
$813$	−19.0294	+	19.0294i	−0.667392	+	0.667392i
$814$			0.928932i			0.0325591i
$815$		0			0
$816$		−	14.7821i		−	0.517476i
$817$	29.3848	+	29.3848i	1.02804	+	1.02804i
$818$	6.82843	−	6.82843i	0.238750	−	0.238750i
$819$	89.2177			3.11752
$820$		0			0
$821$	2.68629			0.0937522			0.0468761	−	0.998901i	$-0.485073\pi$
$821$	2.68629			0.0937522			0.0468761	+	0.998901i	$0.485073\pi$
$822$	41.8100	−	41.8100i	1.45829	−	1.45829i
$823$	27.2132	−	27.2132i	0.948593	−	0.948593i	−0.0501491	−	0.998742i	$-0.515970\pi$
$823$	27.2132	−	27.2132i	0.948593	−	0.948593i	0.998742	+	0.0501491i	$0.0159697\pi$
$824$	11.7206			0.408307
$825$		0			0
$826$		−	35.6871i		−	1.24171i
$827$	−0.541196	+	0.541196i	−0.0188192	+	0.0188192i	−0.716454	−	0.697635i	$-0.754236\pi$
$827$	−0.541196	+	0.541196i	−0.0188192	+	0.0188192i	0.697635	+	0.716454i	$0.254236\pi$
$828$	18.3569	+	15.4280i	0.637947	+	0.536160i
$829$			50.0000i			1.73657i	0.496064	+	0.868286i	$0.334778\pi$
$829$			50.0000i			1.73657i	−0.496064	+	0.868286i	$0.665222\pi$
$830$		0			0
$831$	21.6569			0.751268
$832$	−3.41421	−	3.41421i	−0.118367	−	0.118367i
$833$	−24.6005	−	24.6005i	−0.852358	−	0.852358i
$834$		−	37.2548i		−	1.29003i
$835$		0			0
$836$	1.61522			0.0558637
$837$	8.97056	+	8.97056i	0.310068	+	0.310068i
$838$	−14.1865	−	14.1865i	−0.490064	−	0.490064i
$839$	−56.0668			−1.93564			−0.967821	−	0.251640i	$-0.919030\pi$
$839$	−56.0668			−1.93564			−0.967821	+	0.251640i	$0.919030\pi$
$840$		0			0
$841$	15.6274			0.538876
$842$	−2.38896	+	2.38896i	−0.0823288	+	0.0823288i
$843$	27.7708	+	27.7708i	0.956476	+	0.956476i
$844$		−	13.6569i		−	0.470088i
$845$		0			0
$846$	11.2132			0.385518
$847$	−28.4818	+	28.4818i	−0.978645	+	0.978645i
$848$	5.00208	+	5.00208i	0.171772	+	0.171772i
$849$	−5.75152			−0.197392
$850$		0			0
$851$	14.0000	−	1.21371i	0.479914	−	0.0416054i
$852$	9.65685	+	9.65685i	0.330838	+	0.330838i
$853$	1.41421	−	1.41421i	0.0484218	−	0.0484218i	−0.682481	−	0.730903i	$-0.739099\pi$
$853$	1.41421	−	1.41421i	0.0484218	−	0.0484218i	0.730903	+	0.682481i	$0.239099\pi$
$854$			43.7990i			1.49877i
$855$		0			0
$856$			9.42450i			0.322123i
$857$	−34.7990	−	34.7990i	−1.18871	−	1.18871i	−0.977424	−	0.211287i	$-0.932235\pi$
$857$	−34.7990	−	34.7990i	−1.18871	−	1.18871i	−0.211287	−	0.977424i	$-0.567765\pi$
$858$	−3.06147	−	3.06147i	−0.104517	−	0.104517i
$859$		−	21.4558i		−	0.732064i	−0.930602	−	0.366032i	$-0.880716\pi$
$859$		−	21.4558i		−	0.732064i	0.930602	−	0.366032i	$-0.119284\pi$
$860$		0			0
$861$			103.475i			3.52640i
$862$	−19.5600	+	19.5600i	−0.666216	+	0.666216i
$863$	14.3431	−	14.3431i	0.488246	−	0.488246i	−0.419506	−	0.907752i	$-0.637797\pi$
$863$	14.3431	−	14.3431i	0.488246	−	0.488246i	0.907752	+	0.419506i	$0.137797\pi$
$864$			5.65685i			0.192450i
$865$		0			0
$866$			9.55582i			0.324720i
$867$	20.6274	+	20.6274i	0.700544	+	0.700544i
$868$	−5.86030	−	5.86030i	−0.198912	−	0.198912i
$869$		−	1.45584i		−	0.0493861i
$870$		0			0
$871$			16.3128i			0.552738i
$872$	0.672512	−	0.672512i	0.0227741	−	0.0227741i
$873$	15.3073	+	15.3073i	0.518075	+	0.518075i
$874$	−2.11039	−	24.3431i	−0.0713851	−	0.823419i
$875$		0			0
$876$	27.3137			0.922845
$877$	23.8995	+	23.8995i	0.807029	+	0.807029i	0.984183	−	0.177154i	$-0.0566892\pi$
$877$	23.8995	+	23.8995i	0.807029	+	0.807029i	−0.177154	+	0.984183i	$0.556689\pi$
$878$	14.2426	−	14.2426i	0.480666	−	0.480666i
$879$	−13.3601			−0.450626
$880$		0			0
$881$		−	15.6788i		−	0.528231i	−0.964491	−	0.264115i	$-0.914920\pi$
$881$		−	15.6788i		−	0.528231i	0.964491	−	0.264115i	$-0.0850800\pi$
$882$	23.5355	+	23.5355i	0.792483	+	0.792483i
$883$	−10.9706	+	10.9706i	−0.369189	+	0.369189i	−0.867181	−	0.497993i	$-0.834071\pi$
$883$	−10.9706	+	10.9706i	−0.369189	+	0.369189i	0.497993	+	0.867181i	$0.334071\pi$
$884$	25.2346			0.848731
$885$		0			0
$886$	7.51472			0.252462
$887$	2.55635	+	2.55635i	0.0858338	+	0.0858338i	0.748720	−	0.662886i	$-0.230669\pi$
$887$	2.55635	+	2.55635i	0.0858338	+	0.0858338i	−0.662886	+	0.748720i	$0.730669\pi$
$888$	5.86030	+	5.86030i	0.196659	+	0.196659i
$889$	−12.6173			−0.423170
$890$		0			0
$891$			0.317025i			0.0106207i
$892$	6.24264	+	6.24264i	0.209019	+	0.209019i
$893$	−8.07948	−	8.07948i	−0.270369	−	0.270369i
$894$	−16.9469			−0.566788
$895$		0			0
$896$		−	3.69552i		−	0.123459i
$897$	−42.1396	+	50.1396i	−1.40700	+	1.67411i
$898$	−9.00000	+	9.00000i	−0.300334	+	0.300334i
$899$			8.20101i			0.273519i
$900$		0			0
$901$	−36.9706			−1.23167
$902$	2.21918	−	2.21918i	0.0738905	−	0.0738905i
$903$	60.2843	−	60.2843i	2.00613	−	2.00613i
$904$	9.81845			0.326557
$905$		0			0
$906$	−54.9117			−1.82432
$907$	−5.89876	+	5.89876i	−0.195865	+	0.195865i	−0.798225	−	0.602360i	$-0.794227\pi$
$907$	−5.89876	+	5.89876i	−0.195865	+	0.195865i	0.602360	+	0.798225i	$0.294227\pi$
$908$	−1.12085	−	1.12085i	−0.0371968	−	0.0371968i
$909$		−	92.4264i		−	3.06559i
$910$		0			0
$911$			4.06694i			0.134744i	0.997728	+	0.0673718i	$0.0214614\pi$
$911$			4.06694i			0.134744i	−0.997728	+	0.0673718i	$0.978539\pi$
$912$	10.1899	−	10.1899i	0.337420	−	0.337420i
$913$	0.615224	−	0.615224i	0.0203609	−	0.0203609i
$914$	−26.5027			−0.876631
$915$		0			0
$916$		−	9.50143i		−	0.313936i
$917$	−26.5027	+	26.5027i	−0.875196	+	0.875196i
$918$	−20.9050	−	20.9050i	−0.689968	−	0.689968i
$919$	40.2793			1.32869			0.664345	−	0.747426i	$-0.268710\pi$
$919$	40.2793			1.32869			0.664345	+	0.747426i	$0.268710\pi$
$920$		0			0
$921$	−38.6274			−1.27282
$922$	9.07107	+	9.07107i	0.298740	+	0.298740i
$923$	−16.4853	+	16.4853i	−0.542620	+	0.542620i
$924$		−	3.31371i		−	0.109013i
$925$		0			0
$926$	−22.9289			−0.753491
$927$	41.4386	−	41.4386i	1.36102	−	1.36102i
$928$	−2.58579	+	2.58579i	−0.0848826	+	0.0848826i
$929$			1.41421i			0.0463988i	0.999731	+	0.0231994i	$0.00738527\pi$
$929$			1.41421i			0.0463988i	−0.999731	+	0.0231994i	$0.992615\pi$
$930$		0			0
$931$		−	33.9162i		−	1.11156i
$932$	14.6569	+	14.6569i	0.480101	+	0.480101i
$933$	22.8284	−	22.8284i	0.747369	−	0.747369i
$934$	−9.68714			−0.316973
$935$		0			0
$936$	−24.1421			−0.789110
$937$	2.87576	−	2.87576i	0.0939469	−	0.0939469i	−0.658571	−	0.752518i	$-0.728839\pi$
$937$	2.87576	−	2.87576i	0.0939469	−	0.0939469i	0.752518	+	0.658571i	$0.228839\pi$
$938$	−8.82843	+	8.82843i	−0.288258	+	0.288258i
$939$	−77.4971			−2.52902
$940$		0			0
$941$			46.9819i			1.53157i	0.643099	+	0.765783i	$0.277648\pi$
$941$			46.9819i			1.53157i	−0.643099	+	0.765783i	$0.722352\pi$
$942$	−15.4161	+	15.4161i	−0.502284	+	0.502284i
$943$	−36.3449	−	30.5459i	−1.18355	−	0.994711i
$944$			9.65685i			0.314304i
$945$		0			0
$946$	−2.58579			−0.0840712
$947$	−16.8284	−	16.8284i	−0.546850	−	0.546850i	0.378678	−	0.925528i	$-0.376379\pi$
$947$	−16.8284	−	16.8284i	−0.546850	−	0.546850i	−0.925528	+	0.378678i	$0.876379\pi$
$948$	−9.18440	−	9.18440i	−0.298296	−	0.298296i
$949$			46.6274i			1.51359i
$950$		0			0
$951$	−31.0294			−1.00620
$952$	13.6569	+	13.6569i	0.442621	+	0.442621i
$953$	−37.5892	−	37.5892i	−1.21763	−	1.21763i	−0.968458	−	0.249177i	$-0.919840\pi$
$953$	−37.5892	−	37.5892i	−1.21763	−	1.21763i	−0.249177	−	0.968458i	$-0.580160\pi$
$954$	35.3701			1.14515
$955$		0			0
$956$	−5.75736			−0.186206
$957$	−2.31863	+	2.31863i	−0.0749507	+	0.0749507i
$958$	−25.2346	−	25.2346i	−0.815292	−	0.815292i
$959$			77.2548i			2.49469i
$960$		0			0
$961$	−25.9706			−0.837760
$962$	−10.0042	+	10.0042i	−0.322547	+	0.322547i
$963$	33.3207	+	33.3207i	1.07374	+	1.07374i
$964$	−29.8268			−0.960656
$965$		0			0
$966$	−49.9411	+	4.32957i	−1.60683	+	0.139302i
$967$	24.0000	+	24.0000i	0.771788	+	0.771788i	0.978419	−	0.206631i	$-0.0662500\pi$
$967$	24.0000	+	24.0000i	0.771788	+	0.771788i	−0.206631	+	0.978419i	$0.566250\pi$
$968$	7.70711	−	7.70711i	0.247716	−	0.247716i
$969$			75.3137i			2.41942i
$970$		0			0
$971$			9.94977i			0.319303i	0.987173	+	0.159652i	$0.0510371\pi$
$971$			9.94977i			0.319303i	−0.987173	+	0.159652i	$0.948963\pi$
$972$	−10.0000	−	10.0000i	−0.320750	−	0.320750i
$973$	34.4190	+	34.4190i	1.10342	+	1.10342i
$974$		−	32.8701i		−	1.05322i
$975$		0			0
$976$		−	11.8519i		−	0.379371i
$977$	11.9832	−	11.9832i	0.383378	−	0.383378i	−0.488940	−	0.872318i	$-0.662616\pi$
$977$	11.9832	−	11.9832i	0.383378	−	0.383378i	0.872318	+	0.488940i	$0.162616\pi$
$978$	−18.3431	+	18.3431i	−0.586549	+	0.586549i
$979$		−	4.68629i		−	0.149775i
$980$		0			0
$981$		−	4.75538i		−	0.151828i
$982$	−5.51472	−	5.51472i	−0.175982	−	0.175982i
$983$	21.3533	+	21.3533i	0.681066	+	0.681066i	0.960240	−	0.279174i	$-0.0900607\pi$
$983$	21.3533	+	21.3533i	0.681066	+	0.681066i	−0.279174	+	0.960240i	$0.590061\pi$
$984$		−	28.0000i		−	0.892607i
$985$		0			0
$986$		−	19.1116i		−	0.608639i
$987$	−16.5754	+	16.5754i	−0.527602	+	0.527602i
$988$	17.3952	+	17.3952i	0.553415	+	0.553415i
$989$	3.37849	+	38.9706i	0.107430	+	1.23919i
$990$		0			0
$991$	−2.44365			−0.0776251			−0.0388126	−	0.999247i	$-0.512358\pi$
$991$	−2.44365			−0.0776251			−0.0388126	+	0.999247i	$0.512358\pi$
$992$	1.58579	+	1.58579i	0.0503488	+	0.0503488i
$993$	3.31371	−	3.31371i	0.105157	−	0.105157i
$994$	−17.8435			−0.565963
$995$		0			0
$996$		−	7.76245i		−	0.245963i
$997$	−18.0416	−	18.0416i	−0.571384	−	0.571384i	0.361131	−	0.932515i	$-0.382391\pi$
$997$	−18.0416	−	18.0416i	−0.571384	−	0.571384i	−0.932515	+	0.361131i	$0.882391\pi$
$998$	−1.51472	+	1.51472i	−0.0479476	+	0.0479476i
$999$	16.5754			0.524424

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.e.a.1057.1		8
5.2	odd	4		230.2.e.c.183.4	yes	8
5.3	odd	4	inner	1150.2.e.a.643.2		8
5.4	even	2		230.2.e.c.137.3	✓	8
23.22	odd	2	inner	1150.2.e.a.1057.2		8
115.22	even	4		230.2.e.c.183.3	yes	8
115.68	even	4	inner	1150.2.e.a.643.1		8
115.114	odd	2		230.2.e.c.137.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.e.c.137.3	✓	8	5.4	even	2
230.2.e.c.137.4	yes	8	115.114	odd	2
230.2.e.c.183.3	yes	8	115.22	even	4
230.2.e.c.183.4	yes	8	5.2	odd	4
1150.2.e.a.643.1		8	115.68	even	4	inner
1150.2.e.a.643.2		8	5.3	odd	4	inner
1150.2.e.a.1057.1		8	1.1	even	1	trivial
1150.2.e.a.1057.2		8	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-2.00000 + 2.00000i) q^{3} +1.00000i q^{4} +2.82843 q^{6} +(-2.61313 + 2.61313i) q^{7} +(0.707107 - 0.707107i) q^{8} -5.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-2.00000 + 2.00000i) q^{3} +1.00000i q^{4} +2.82843 q^{6} +(-2.61313 + 2.61313i) q^{7} +(0.707107 - 0.707107i) q^{8} -5.00000i q^{9} -0.317025i q^{11} +(-2.00000 - 2.00000i) q^{12} +(3.41421 - 3.41421i) q^{13} +3.69552 q^{14} -1.00000 q^{16} +(3.69552 - 3.69552i) q^{17} +(-3.53553 + 3.53553i) q^{18} +5.09494 q^{19} -10.4525i q^{21} +(-0.224171 + 0.224171i) q^{22} +(3.67139 + 3.08560i) q^{23} +2.82843i q^{24} -4.82843 q^{26} +(4.00000 + 4.00000i) q^{27} +(-2.61313 - 2.61313i) q^{28} +3.65685i q^{29} +2.24264 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.634051 + 0.634051i) q^{33} -5.22625 q^{34} +5.00000 q^{36} +(2.07193 - 2.07193i) q^{37} +(-3.60266 - 3.60266i) q^{38} +13.6569i q^{39} -9.89949 q^{41} +(-7.39104 + 7.39104i) q^{42} +(5.76745 + 5.76745i) q^{43} +0.317025 q^{44} +(-0.414214 - 4.77791i) q^{46} +(-1.58579 - 1.58579i) q^{47} +(2.00000 - 2.00000i) q^{48} -6.65685i q^{49} +14.7821i q^{51} +(3.41421 + 3.41421i) q^{52} +(-5.00208 - 5.00208i) q^{53} -5.65685i q^{54} +3.69552i q^{56} +(-10.1899 + 10.1899i) q^{57} +(2.58579 - 2.58579i) q^{58} -9.65685i q^{59} +11.8519i q^{61} +(-1.58579 - 1.58579i) q^{62} +(13.0656 + 13.0656i) q^{63} -1.00000i q^{64} -0.896683i q^{66} +(-2.38896 + 2.38896i) q^{67} +(3.69552 + 3.69552i) q^{68} +(-13.5140 + 1.17157i) q^{69} -4.82843 q^{71} +(-3.53553 - 3.53553i) q^{72} +(-6.82843 + 6.82843i) q^{73} -2.93015 q^{74} +5.09494i q^{76} +(0.828427 + 0.828427i) q^{77} +(9.65685 - 9.65685i) q^{78} +4.59220 q^{79} -1.00000 q^{81} +(7.00000 + 7.00000i) q^{82} +(1.94061 + 1.94061i) q^{83} +10.4525 q^{84} -8.15640i q^{86} +(-7.31371 - 7.31371i) q^{87} +(-0.224171 - 0.224171i) q^{88} +14.7821 q^{89} +17.8435i q^{91} +(-3.08560 + 3.67139i) q^{92} +(-4.48528 + 4.48528i) q^{93} +2.24264i q^{94} -2.82843 q^{96} +(-3.06147 + 3.06147i) q^{97} +(-4.70711 + 4.70711i) q^{98} -1.58513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{3}+O(q^{10}) \) 8 * q - 16 * q^3	\( 8 q - 16 q^{3} - 16 q^{12} + 16 q^{13} - 8 q^{16} + 8 q^{23} - 16 q^{26} + 32 q^{27} - 16 q^{31} + 40 q^{36} + 8 q^{46} - 24 q^{47} + 16 q^{48} + 16 q^{52} + 32 q^{58} - 24 q^{62} - 16 q^{71} - 32 q^{73} - 16 q^{77} + 32 q^{78} - 8 q^{81} + 56 q^{82} + 32 q^{87} + 8 q^{92} + 32 q^{93} - 32 q^{98}+O(q^{100}) \) 8 * q - 16 * q^3 - 16 * q^12 + 16 * q^13 - 8 * q^16 + 8 * q^23 - 16 * q^26 + 32 * q^27 - 16 * q^31 + 40 * q^36 + 8 * q^46 - 24 * q^47 + 16 * q^48 + 16 * q^52 + 32 * q^58 - 24 * q^62 - 16 * q^71 - 32 * q^73 - 16 * q^77 + 32 * q^78 - 8 * q^81 + 56 * q^82 + 32 * q^87 + 8 * q^92 + 32 * q^93 - 32 * q^98

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