LMFDB - Embedded newform 1890.2.z.b.1009.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1009,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("1890.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.z (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1009.1
Character	$\chi$	$=$	1890.1009
Dual form			1890.2.z.b.1639.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.482247 - 2.18345i) q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.482247 - 2.18345i) q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(1.50936 + 1.64980i) q^{10} +(-0.563211 - 0.975509i) q^{11} +(0.109484 + 0.0632106i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +0.941713i q^{17} +0.696778 q^{19} +(-2.13204 - 0.674085i) q^{20} +(0.975509 + 0.563211i) q^{22} +(-1.71677 - 0.991178i) q^{23} +(-4.53488 + 2.10592i) q^{25} -0.126421 q^{26} +1.00000i q^{28} +(-1.60428 - 2.77870i) q^{29} +(5.32069 - 9.21571i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.470856 - 0.815547i) q^{34} +(1.50936 + 1.64980i) q^{35} -0.277671i q^{37} +(-0.603427 + 0.348389i) q^{38} +(2.18345 - 0.482247i) q^{40} +(-3.56146 + 6.16862i) q^{41} +(-4.02294 + 2.32264i) q^{43} -1.12642 q^{44} +1.98236 q^{46} +(1.07142 - 0.618584i) q^{47} +(0.500000 - 0.866025i) q^{49} +(2.87436 - 4.09122i) q^{50} +(0.109484 - 0.0632106i) q^{52} -1.76768i q^{53} +(-1.85837 + 1.70018i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(2.77870 + 1.60428i) q^{58} +(-5.61814 + 9.73091i) q^{59} +(-3.62772 - 6.28340i) q^{61} +10.6414i q^{62} -1.00000 q^{64} +(0.0852186 - 0.269535i) q^{65} +(-9.15175 - 5.28376i) q^{67} +(0.815547 + 0.470856i) q^{68} +(-2.13204 - 0.674085i) q^{70} -10.4340 q^{71} +2.66901i q^{73} +(0.138836 + 0.240470i) q^{74} +(0.348389 - 0.603427i) q^{76} +(0.975509 + 0.563211i) q^{77} +(5.40386 + 9.35976i) q^{79} +(-1.64980 + 1.50936i) q^{80} -7.12291i q^{82} +(-9.57479 + 5.52801i) q^{83} +(2.05618 - 0.454138i) q^{85} +(2.32264 - 4.02294i) q^{86} +(0.975509 - 0.563211i) q^{88} -2.79337 q^{89} -0.126421 q^{91} +(-1.71677 + 0.991178i) q^{92} +(-0.618584 + 1.07142i) q^{94} +(-0.336019 - 1.52138i) q^{95} +(-1.50021 + 0.866148i) q^{97} +1.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 2 q^{5}+O(q^{10}) $ 24 * q + 12 * q^4 + 2 * q^5	$ 24 q + 12 q^{4} + 2 q^{5} - 4 q^{10} - 4 q^{11} + 12 q^{14} - 12 q^{16} + 32 q^{19} - 2 q^{20} + 16 q^{26} - 20 q^{29} + 36 q^{31} - 4 q^{35} - 2 q^{40} + 20 q^{41} - 8 q^{44} - 32 q^{46} + 12 q^{49} + 28 q^{55} - 12 q^{56} + 16 q^{61} - 24 q^{64} - 16 q^{65} - 2 q^{70} - 24 q^{71} - 44 q^{74} + 16 q^{76} - 68 q^{79} - 4 q^{80} + 26 q^{85} + 24 q^{86} - 40 q^{89} + 16 q^{91} - 48 q^{94} + 50 q^{95}+O(q^{100}) $ 24 * q + 12 * q^4 + 2 * q^5 - 4 * q^10 - 4 * q^11 + 12 * q^14 - 12 * q^16 + 32 * q^19 - 2 * q^20 + 16 * q^26 - 20 * q^29 + 36 * q^31 - 4 * q^35 - 2 * q^40 + 20 * q^41 - 8 * q^44 - 32 * q^46 + 12 * q^49 + 28 * q^55 - 12 * q^56 + 16 * q^61 - 24 * q^64 - 16 * q^65 - 2 * q^70 - 24 * q^71 - 44 * q^74 + 16 * q^76 - 68 * q^79 - 4 * q^80 + 26 * q^85 + 24 * q^86 - 40 * q^89 + 16 * q^91 - 48 * q^94 + 50 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.482247	−	2.18345i	−0.215667	−	0.976467i
$5$	−0.482247	−	2.18345i	−0.215667	−	0.976467i
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.50936	+	1.64980i	0.477302	+	0.521711i
$11$	−0.563211	−	0.975509i	−0.169814	−	0.294127i	0.768540	−	0.639802i	$-0.220983\pi$
$11$	−0.563211	−	0.975509i	−0.169814	−	0.294127i	−0.938354	+	0.345674i	$0.887650\pi$
$12$		0			0
$13$	0.109484	+	0.0632106i	0.0303654	+	0.0175315i	0.515106	−	0.857127i	$-0.327753\pi$
$13$	0.109484	+	0.0632106i	0.0303654	+	0.0175315i	−0.484740	+	0.874658i	$0.661086\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$			0.941713i			0.228399i	0.993458	+	0.114199i	$0.0364303\pi$
$17$			0.941713i			0.228399i	−0.993458	+	0.114199i	$0.963570\pi$
$18$		0			0
$19$	0.696778			0.159852			0.0799259	−	0.996801i	$-0.474532\pi$
$19$	0.696778			0.159852			0.0799259	+	0.996801i	$0.474532\pi$
$20$	−2.13204	−	0.674085i	−0.476739	−	0.150730i
$21$		0			0
$22$	0.975509	+	0.563211i	0.207979	+	0.120077i
$23$	−1.71677	−	0.991178i	−0.357972	−	0.206675i	0.310219	−	0.950665i	$-0.399598\pi$
$23$	−1.71677	−	0.991178i	−0.357972	−	0.206675i	−0.668191	+	0.743990i	$0.732931\pi$
$24$		0			0
$25$	−4.53488	+	2.10592i	−0.906975	+	0.421184i
$26$	−0.126421			−0.0247932
$27$		0			0
$28$			1.00000i			0.188982i
$29$	−1.60428	−	2.77870i	−0.297908	−	0.515992i	0.677749	−	0.735293i	$-0.262956\pi$
$29$	−1.60428	−	2.77870i	−0.297908	−	0.515992i	−0.975657	+	0.219301i	$0.929622\pi$
$30$		0			0
$31$	5.32069	−	9.21571i	0.955624	−	1.65519i	0.222691	−	0.974889i	$-0.428516\pi$
$31$	5.32069	−	9.21571i	0.955624	−	1.65519i	0.732933	−	0.680301i	$-0.238151\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	−0.470856	−	0.815547i	−0.0807512	−	0.139865i
$35$	1.50936	+	1.64980i	0.255129	+	0.278867i
$36$		0			0
$37$		−	0.277671i		−	0.0456489i	−0.999739	−	0.0228244i	$-0.992734\pi$
$37$		−	0.277671i		−	0.0456489i	0.999739	−	0.0228244i	$-0.00726588\pi$
$38$	−0.603427	+	0.348389i	−0.0978888	+	0.0565161i
$39$		0			0
$40$	2.18345	−	0.482247i	0.345233	−	0.0762499i
$41$	−3.56146	+	6.16862i	−0.556206	+	0.963377i	0.441603	+	0.897211i	$0.354410\pi$
$41$	−3.56146	+	6.16862i	−0.556206	+	0.963377i	−0.997809	+	0.0661664i	$0.978923\pi$
$42$		0			0
$43$	−4.02294	+	2.32264i	−0.613492	+	0.354200i	−0.774331	−	0.632781i	$-0.781913\pi$
$43$	−4.02294	+	2.32264i	−0.613492	+	0.354200i	0.160839	+	0.986981i	$0.448580\pi$
$44$	−1.12642			−0.169814
$45$		0			0
$46$	1.98236			0.292283
$47$	1.07142	−	0.618584i	0.156282	−	0.0902297i	−0.419819	−	0.907608i	$-0.637907\pi$
$47$	1.07142	−	0.618584i	0.156282	−	0.0902297i	0.576102	+	0.817378i	$0.304573\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	2.87436	−	4.09122i	0.406496	−	0.578586i
$51$		0			0
$52$	0.109484	−	0.0632106i	0.0151827	−	0.00876573i
$53$		−	1.76768i		−	0.242810i	−0.992603	−	0.121405i	$-0.961260\pi$
$53$		−	1.76768i		−	0.242810i	0.992603	−	0.121405i	$-0.0387399\pi$
$54$		0			0
$55$	−1.85837	+	1.70018i	−0.250582	+	0.229252i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	2.77870	+	1.60428i	0.364862	+	0.210653i
$59$	−5.61814	+	9.73091i	−0.731420	+	1.26686i	0.224856	+	0.974392i	$0.427809\pi$
$59$	−5.61814	+	9.73091i	−0.731420	+	1.26686i	−0.956276	+	0.292465i	$0.905525\pi$
$60$		0			0
$61$	−3.62772	−	6.28340i	−0.464482	−	0.804506i	0.534696	−	0.845044i	$-0.320426\pi$
$61$	−3.62772	−	6.28340i	−0.464482	−	0.804506i	−0.999178	+	0.0405381i	$0.987093\pi$
$62$			10.6414i			1.35146i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.0852186	−	0.269535i	0.0105701	−	0.0334318i
$66$		0			0
$67$	−9.15175	−	5.28376i	−1.11806	−	0.645515i	−0.177158	−	0.984182i	$-0.556690\pi$
$67$	−9.15175	−	5.28376i	−1.11806	−	0.645515i	−0.940906	+	0.338668i	$0.890024\pi$
$68$	0.815547	+	0.470856i	0.0988996	+	0.0570997i
$69$		0			0
$70$	−2.13204	−	0.674085i	−0.254828	−	0.0805686i
$71$	−10.4340			−1.23829			−0.619147	−	0.785275i	$-0.712521\pi$
$71$	−10.4340			−1.23829			−0.619147	+	0.785275i	$0.712521\pi$
$72$		0			0
$73$			2.66901i			0.312384i	0.987727	+	0.156192i	$0.0499219\pi$
$73$			2.66901i			0.312384i	−0.987727	+	0.156192i	$0.950078\pi$
$74$	0.138836	+	0.240470i	0.0161393	+	0.0279541i
$75$		0			0
$76$	0.348389	−	0.603427i	0.0399630	−	0.0692179i
$77$	0.975509	+	0.563211i	0.111170	+	0.0641838i
$78$		0			0
$79$	5.40386	+	9.35976i	0.607982	+	1.05306i	0.991573	+	0.129552i	$0.0413541\pi$
$79$	5.40386	+	9.35976i	0.607982	+	1.05306i	−0.383591	+	0.923503i	$0.625313\pi$
$80$	−1.64980	+	1.50936i	−0.184453	+	0.168752i
$81$		0			0
$82$		−	7.12291i		−	0.786594i
$83$	−9.57479	+	5.52801i	−1.05097	+	0.606777i	−0.922921	−	0.384990i	$-0.874205\pi$
$83$	−9.57479	+	5.52801i	−1.05097	+	0.606777i	−0.128049	+	0.991768i	$0.540871\pi$
$84$		0			0
$85$	2.05618	−	0.454138i	0.223024	−	0.0492582i
$86$	2.32264	−	4.02294i	0.250457	−	0.433804i
$87$		0			0
$88$	0.975509	−	0.563211i	0.103990	−	0.0600384i
$89$	−2.79337			−0.296097			−0.148048	−	0.988980i	$-0.547299\pi$
$89$	−2.79337			−0.296097			−0.148048	+	0.988980i	$0.547299\pi$
$90$		0			0
$91$	−0.126421			−0.0132525
$92$	−1.71677	+	0.991178i	−0.178986	+	0.103337i
$93$		0			0
$94$	−0.618584	+	1.07142i	−0.0638020	+	0.110508i
$95$	−0.336019	−	1.52138i	−0.0344748	−	0.156090i
$96$		0			0
$97$	−1.50021	+	0.866148i	−0.152323	+	0.0879440i	−0.574224	−	0.818698i	$-0.694696\pi$
$97$	−1.50021	+	0.866148i	−0.152323	+	0.0879440i	0.421901	+	0.906642i	$0.361363\pi$
$98$			1.00000i			0.101015i
$99$		0			0
$100$	−0.443657	+	4.98028i	−0.0443657	+	0.498028i
$101$	1.14231	+	1.97854i	0.113664	+	0.196872i	0.917245	−	0.398324i	$-0.130408\pi$
$101$	1.14231	+	1.97854i	0.113664	+	0.196872i	−0.803581	+	0.595196i	$0.797075\pi$
$102$		0			0
$103$	−12.6776	−	7.31942i	−1.24916	−	0.721203i	−0.278219	−	0.960518i	$-0.589744\pi$
$103$	−12.6776	−	7.31942i	−1.24916	−	0.721203i	−0.970942	+	0.239314i	$0.923077\pi$
$104$	−0.0632106	+	0.109484i	−0.00619831	+	0.0107358i
$105$		0			0
$106$	0.883840	+	1.53086i	0.0858462	+	0.148690i
$107$			13.4843i			1.30357i	0.758402	+	0.651787i	$0.225980\pi$
$107$			13.4843i			1.30357i	−0.758402	+	0.651787i	$0.774020\pi$
$108$		0			0
$109$	−11.6040			−1.11146			−0.555732	−	0.831362i	$-0.687562\pi$
$109$	−11.6040			−1.11146			−0.555732	+	0.831362i	$0.687562\pi$
$110$	0.759304	−	2.40158i	0.0723968	−	0.228982i
$111$		0			0
$112$	0.866025	+	0.500000i	0.0818317	+	0.0472456i
$113$	0.377266	+	0.217815i	0.0354902	+	0.0204903i	0.517640	−	0.855598i	$-0.326811\pi$
$113$	0.377266	+	0.217815i	0.0354902	+	0.0204903i	−0.482150	+	0.876089i	$0.660144\pi$
$114$		0			0
$115$	−1.33628	+	4.22647i	−0.124608	+	0.394120i
$116$	−3.20857			−0.297908
$117$		0			0
$118$		−	11.2363i		−	1.03438i
$119$	−0.470856	−	0.815547i	−0.0431633	−	0.0747611i
$120$		0			0
$121$	4.86559	−	8.42745i	0.442326	−	0.766131i
$122$	6.28340	+	3.62772i	0.568872	+	0.328438i
$123$		0			0
$124$	−5.32069	−	9.21571i	−0.477812	−	0.827595i
$125$	6.78509	+	8.88608i	0.606877	+	0.794796i
$126$		0			0
$127$			15.3059i			1.35818i	0.734054	+	0.679091i	$0.237626\pi$
$127$			15.3059i			1.35818i	−0.734054	+	0.679091i	$0.762374\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	0.0609662	+	0.276034i	0.00534709	+	0.0242098i
$131$	−5.68968	+	9.85481i	−0.497109	+	0.861019i	−0.999994	−	0.00333461i	$-0.998939\pi$
$131$	−5.68968	+	9.85481i	−0.497109	+	0.861019i	0.502885	+	0.864353i	$0.332272\pi$
$132$		0			0
$133$	−0.603427	+	0.348389i	−0.0523238	+	0.0302092i
$134$	10.5675			0.912895
$135$		0			0
$136$	−0.941713			−0.0807512
$137$	8.14260	−	4.70113i	0.695669	−	0.401645i	−0.110063	−	0.993925i	$-0.535105\pi$
$137$	8.14260	−	4.70113i	0.695669	−	0.401645i	0.805732	+	0.592280i	$0.201772\pi$
$138$		0			0
$139$	−9.58719	+	16.6055i	−0.813175	+	1.40846i	0.0974561	+	0.995240i	$0.468929\pi$
$139$	−9.58719	+	16.6055i	−0.813175	+	1.40846i	−0.910631	+	0.413220i	$0.864404\pi$
$140$	2.18345	−	0.482247i	0.184535	−	0.0407573i
$141$		0			0
$142$	9.03615	−	5.21702i	0.758297	−	0.437803i
$143$		−	0.142403i		−	0.0119084i
$144$		0			0
$145$	−5.29349	+	4.84289i	−0.439600	+	0.402180i
$146$	−1.33451	−	2.31143i	−0.110444	−	0.191295i
$147$		0			0
$148$	−0.240470	−	0.138836i	−0.0197666	−	0.0114122i
$149$	1.89688	−	3.28548i	0.155398	−	0.269157i	−0.777806	−	0.628505i	$-0.783667\pi$
$149$	1.89688	−	3.28548i	0.155398	−	0.269157i	0.933204	+	0.359347i	$0.117001\pi$
$150$		0			0
$151$	3.54177	+	6.13453i	0.288225	+	0.499221i	0.973386	−	0.229171i	$-0.0736014\pi$
$151$	3.54177	+	6.13453i	0.288225	+	0.499221i	−0.685161	+	0.728392i	$0.740268\pi$
$152$			0.696778i			0.0565161i
$153$		0			0
$154$	−1.12642			−0.0907696
$155$	−22.6879	−	7.17320i	−1.82233	−	0.576165i
$156$		0			0
$157$	0.269315	+	0.155489i	0.0214936	+	0.0124094i	0.510708	−	0.859754i	$-0.329383\pi$
$157$	0.269315	+	0.155489i	0.0214936	+	0.0124094i	−0.489215	+	0.872163i	$0.662717\pi$
$158$	−9.35976	−	5.40386i	−0.744623	−	0.429908i
$159$		0			0
$160$	0.674085	−	2.13204i	0.0532911	−	0.168553i
$161$	1.98236			0.156232
$162$		0			0
$163$		−	14.3505i		−	1.12402i	−0.827131	−	0.562009i	$-0.810028\pi$
$163$		−	14.3505i		−	1.12402i	0.827131	−	0.562009i	$-0.189972\pi$
$164$	3.56146	+	6.16862i	0.278103	+	0.481689i
$165$		0			0
$166$	5.52801	−	9.57479i	0.429056	−	0.743148i
$167$	−19.8898	−	11.4834i	−1.53912	−	0.888611i	−0.998891	−	0.0470932i	$-0.985004\pi$
$167$	−19.8898	−	11.4834i	−1.53912	−	0.888611i	−0.540229	−	0.841518i	$-0.681662\pi$
$168$		0			0
$169$	−6.49201	−	11.2445i	−0.499385	−	0.864961i
$170$	−1.55363	+	1.42138i	−0.119158	+	0.109015i
$171$		0			0
$172$			4.64529i			0.354200i
$173$	17.5779	−	10.1486i	1.33642	−	0.771584i	0.350147	−	0.936695i	$-0.386132\pi$
$173$	17.5779	−	10.1486i	1.33642	−	0.771584i	0.986275	+	0.165111i	$0.0527983\pi$
$174$		0			0
$175$	2.87436	−	4.09122i	0.217281	−	0.309267i
$176$	−0.563211	+	0.975509i	−0.0424536	+	0.0735318i
$177$		0			0
$178$	2.41913	−	1.39668i	0.181321	−	0.104686i
$179$	9.22172			0.689264			0.344632	−	0.938738i	$-0.388004\pi$
$179$	9.22172			0.689264			0.344632	+	0.938738i	$0.388004\pi$
$180$		0			0
$181$	−17.0649			−1.26842			−0.634211	−	0.773160i	$-0.718675\pi$
$181$	−17.0649			−1.26842			−0.634211	+	0.773160i	$0.718675\pi$
$182$	0.109484	−	0.0632106i	0.00811549	−	0.00468548i
$183$		0			0
$184$	0.991178	−	1.71677i	0.0730706	−	0.126562i
$185$	−0.606281	+	0.133906i	−0.0445746	+	0.00984498i
$186$		0			0
$187$	0.918649	−	0.530383i	0.0671783	−	0.0387854i
$188$		−	1.23717i		−	0.0902297i
$189$		0			0
$190$	1.05169	+	1.14954i	0.0762976	+	0.0833965i
$191$	−9.37825	−	16.2436i	−0.678586	−	1.17535i	−0.975407	−	0.220412i	$-0.929260\pi$
$191$	−9.37825	−	16.2436i	−0.678586	−	1.17535i	0.296821	−	0.954933i	$-0.404074\pi$
$192$		0			0
$193$	−20.6301	−	11.9108i	−1.48499	−	0.857357i	−0.485133	−	0.874441i	$-0.661229\pi$
$193$	−20.6301	−	11.9108i	−1.48499	−	0.857357i	−0.999854	+	0.0170831i	$0.994562\pi$
$194$	0.866148	−	1.50021i	0.0621858	−	0.107709i
$195$		0			0
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$		−	9.08570i		−	0.647329i	−0.946172	−	0.323665i	$-0.895085\pi$
$197$		−	9.08570i		−	0.647329i	0.946172	−	0.323665i	$-0.104915\pi$
$198$		0			0
$199$	−1.42266			−0.100850			−0.0504250	−	0.998728i	$-0.516058\pi$
$199$	−1.42266			−0.100850			−0.0504250	+	0.998728i	$0.516058\pi$
$200$	−2.10592	−	4.53488i	−0.148911	−	0.320664i
$201$		0			0
$202$	−1.97854	−	1.14231i	−0.139210	−	0.0803727i
$203$	2.77870	+	1.60428i	0.195027	+	0.112599i
$204$		0			0
$205$	15.1864	+	4.80145i	1.06066	+	0.335348i
$206$	14.6388			1.01994
$207$		0			0
$208$		−	0.126421i		−	0.00876573i
$209$	−0.392433	−	0.679713i	−0.0271451	−	0.0470168i
$210$		0			0
$211$	8.65477	−	14.9905i	0.595819	−	1.03199i	−0.397611	−	0.917554i	$-0.630161\pi$
$211$	8.65477	−	14.9905i	0.595819	−	1.03199i	0.993431	−	0.114435i	$-0.0365059\pi$
$212$	−1.53086	−	0.883840i	−0.105140	−	0.0607024i
$213$		0			0
$214$	−6.74214	−	11.6777i	−0.460883	−	0.798273i
$215$	7.01142	+	7.66378i	0.478175	+	0.522665i
$216$		0			0
$217$			10.6414i			0.722384i
$218$	10.0494	−	5.80201i	0.680629	−	0.392962i
$219$		0			0
$220$	0.543213	+	2.45948i	0.0366234	+	0.165818i
$221$	−0.0595262	+	0.103102i	−0.00400417	+	0.00693542i
$222$		0			0
$223$	4.86638	−	2.80961i	0.325877	−	0.188145i	−0.328132	−	0.944632i	$-0.606419\pi$
$223$	4.86638	−	2.80961i	0.325877	−	0.188145i	0.654009	+	0.756487i	$0.273086\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	−0.435629			−0.0289776
$227$	6.03886	−	3.48654i	0.400813	−	0.231410i	−0.286021	−	0.958223i	$-0.592333\pi$
$227$	6.03886	−	3.48654i	0.400813	−	0.231410i	0.686835	+	0.726813i	$0.259000\pi$
$228$		0			0
$229$	−11.1762	+	19.3577i	−0.738544	+	1.27920i	0.214607	+	0.976701i	$0.431153\pi$
$229$	−11.1762	+	19.3577i	−0.738544	+	1.27920i	−0.953151	+	0.302496i	$0.902180\pi$
$230$	−0.955985	−	4.32837i	−0.0630358	−	0.285404i
$231$		0			0
$232$	2.77870	−	1.60428i	0.182431	−	0.105326i
$233$		−	15.0528i		−	0.986143i	−0.869989	−	0.493072i	$-0.835874\pi$
$233$		−	15.0528i		−	0.986143i	0.869989	−	0.493072i	$-0.164126\pi$
$234$		0			0
$235$	−1.86733	−	2.04107i	−0.121811	−	0.133145i
$236$	5.61814	+	9.73091i	0.365710	+	0.633428i
$237$		0			0
$238$	0.815547	+	0.470856i	0.0528641	+	0.0305211i
$239$	−7.82955	+	13.5612i	−0.506452	+	0.877200i	0.493521	+	0.869734i	$0.335710\pi$
$239$	−7.82955	+	13.5612i	−0.506452	+	0.877200i	−0.999972	+	0.00746575i	$0.997624\pi$
$240$		0			0
$241$	5.56703	+	9.64239i	0.358604	+	0.621121i	0.987728	−	0.156185i	$-0.0499195\pi$
$241$	5.56703	+	9.64239i	0.358604	+	0.621121i	−0.629124	+	0.777305i	$0.716586\pi$
$242$			9.73118i			0.625544i
$243$		0			0
$244$	−7.25544			−0.464482
$245$	−2.13204	−	0.674085i	−0.136211	−	0.0430657i
$246$		0			0
$247$	0.0762860	+	0.0440437i	0.00485396	+	0.00280244i
$248$	9.21571	+	5.32069i	0.585198	+	0.337864i
$249$		0			0
$250$	−10.3191	−	4.30303i	−0.652638	−	0.272147i
$251$	−3.56765			−0.225188			−0.112594	−	0.993641i	$-0.535916\pi$
$251$	−3.56765			−0.225188			−0.112594	+	0.993641i	$0.535916\pi$
$252$		0			0
$253$			2.23297i			0.140386i
$254$	−7.65297	−	13.2553i	−0.480190	−	0.831713i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.14054	+	1.23584i	0.133523	+	0.0770898i	0.565274	−	0.824903i	$-0.308771\pi$
$257$	2.14054	+	1.23584i	0.133523	+	0.0770898i	−0.431750	+	0.901993i	$0.642104\pi$
$258$		0			0
$259$	0.138836	+	0.240470i	0.00862683	+	0.0149421i
$260$	−0.190815	−	0.208569i	−0.0118339	−	0.0129349i
$261$		0			0
$262$		−	11.3794i		−	0.703019i
$263$	8.34220	−	4.81637i	0.514402	−	0.296990i	−0.220239	−	0.975446i	$-0.570684\pi$
$263$	8.34220	−	4.81637i	0.514402	−	0.296990i	0.734641	+	0.678456i	$0.237351\pi$
$264$		0			0
$265$	−3.85964	+	0.852459i	−0.237096	+	0.0523661i
$266$	0.348389	−	0.603427i	0.0213611	−	0.0369985i
$267$		0			0
$268$	−9.15175	+	5.28376i	−0.559032	+	0.322757i
$269$	7.67021			0.467661			0.233830	−	0.972277i	$-0.424874\pi$
$269$	7.67021			0.467661			0.233830	+	0.972277i	$0.424874\pi$
$270$		0			0
$271$	23.7130			1.44046			0.720232	−	0.693733i	$-0.244035\pi$
$271$	23.7130			1.44046			0.720232	+	0.693733i	$0.244035\pi$
$272$	0.815547	−	0.470856i	0.0494498	−	0.0285499i
$273$		0			0
$274$	−4.70113	+	8.14260i	−0.284006	+	0.491912i
$275$	4.60843	+	3.23774i	0.277899	+	0.195243i
$276$		0			0
$277$	−3.32984	+	1.92248i	−0.200070	+	0.115511i	−0.596688	−	0.802473i	$-0.703517\pi$
$277$	−3.32984	+	1.92248i	−0.200070	+	0.115511i	0.396618	+	0.917984i	$0.370184\pi$
$278$		−	19.1744i		−	1.15000i
$279$		0			0
$280$	−1.64980	+	1.50936i	−0.0985942	+	0.0902016i
$281$	−12.1543	−	21.0519i	−0.725067	−	1.25585i	−0.958947	−	0.283587i	$-0.908476\pi$
$281$	−12.1543	−	21.0519i	−0.725067	−	1.25585i	0.233880	−	0.972266i	$-0.424858\pi$
$282$		0			0
$283$	−27.4006	−	15.8198i	−1.62880	−	0.940387i	−0.984452	−	0.175653i	$-0.943796\pi$
$283$	−27.4006	−	15.8198i	−1.62880	−	0.940387i	−0.644346	−	0.764734i	$-0.722870\pi$
$284$	−5.21702	+	9.03615i	−0.309573	+	0.536197i
$285$		0			0
$286$	0.0712017	+	0.123325i	0.00421025	+	0.00729236i
$287$		−	7.12291i		−	0.420452i
$288$		0			0
$289$	16.1132			0.947834
$290$	2.16285	−	6.84081i	0.127007	−	0.401706i
$291$		0			0
$292$	2.31143	+	1.33451i	0.135266	+	0.0780960i
$293$	−23.0999	−	13.3367i	−1.34951	−	0.779141i	−0.361331	−	0.932437i	$-0.617678\pi$
$293$	−23.0999	−	13.3367i	−1.34951	−	0.779141i	−0.988180	+	0.153297i	$0.951011\pi$
$294$		0			0
$295$	23.9563	+	7.57421i	1.39479	+	0.440988i
$296$	0.277671			0.0161393
$297$		0			0
$298$			3.79375i			0.219766i
$299$	−0.125306	−	0.217036i	−0.00724663	−	0.0125515i
$300$		0			0
$301$	2.32264	−	4.02294i	0.133875	−	0.231878i
$302$	−6.13453	−	3.54177i	−0.353003	−	0.203806i
$303$		0			0
$304$	−0.348389	−	0.603427i	−0.0199815	−	0.0346089i
$305$	−11.9700	+	10.9511i	−0.685400	+	0.627057i
$306$		0			0
$307$			8.60830i			0.491302i	0.969358	+	0.245651i	$0.0790017\pi$
$307$			8.60830i			0.491302i	−0.969358	+	0.245651i	$0.920998\pi$
$308$	0.975509	−	0.563211i	0.0555848	−	0.0320919i
$309$		0			0
$310$	23.2349	−	5.13177i	1.31965	−	0.291465i
$311$	−16.6871	+	28.9028i	−0.946237	+	1.63893i	−0.192981	+	0.981203i	$0.561816\pi$
$311$	−16.6871	+	28.9028i	−0.946237	+	1.63893i	−0.753256	+	0.657728i	$0.771518\pi$
$312$		0			0
$313$	11.4076	−	6.58617i	0.644795	−	0.372272i	−0.141664	−	0.989915i	$-0.545245\pi$
$313$	11.4076	−	6.58617i	0.644795	−	0.372272i	0.786459	+	0.617642i	$0.211912\pi$
$314$	−0.310978			−0.0175495
$315$		0			0
$316$	10.8077			0.607982
$317$	6.27066	−	3.62037i	0.352195	−	0.203340i	−0.313456	−	0.949603i	$-0.601487\pi$
$317$	6.27066	−	3.62037i	0.352195	−	0.203340i	0.665652	+	0.746262i	$0.268154\pi$
$318$		0			0
$319$	−1.80710	+	3.12999i	−0.101178	+	0.175246i
$320$	0.482247	+	2.18345i	0.0269584	+	0.122058i
$321$		0			0
$322$	−1.71677	+	0.991178i	−0.0956719	+	0.0552362i
$323$			0.656165i			0.0365100i
$324$		0			0
$325$	−0.629612	−	0.0560877i	−0.0349246	−	0.00311119i
$326$	7.17526	+	12.4279i	0.397401	+	0.688318i
$327$		0			0
$328$	−6.16862	−	3.56146i	−0.340605	−	0.196649i
$329$	−0.618584	+	1.07142i	−0.0341036	+	0.0590692i
$330$		0			0
$331$	11.7693	+	20.3850i	0.646900	+	1.12046i	0.983859	+	0.178944i	$0.0572682\pi$
$331$	11.7693	+	20.3850i	0.646900	+	1.12046i	−0.336959	+	0.941519i	$0.609399\pi$
$332$			11.0560i			0.606777i
$333$		0			0
$334$	22.9668			1.25669
$335$	−7.12341	+	22.5304i	−0.389194	+	1.23097i
$336$		0			0
$337$	18.9095	+	10.9174i	1.03007	+	0.594709i	0.917003	−	0.398879i	$-0.130601\pi$
$337$	18.9095	+	10.9174i	1.03007	+	0.594709i	0.113062	+	0.993588i	$0.463934\pi$
$338$	11.2445	+	6.49201i	0.611620	+	0.353119i
$339$		0			0
$340$	0.634795	−	2.00777i	0.0344266	−	0.108887i
$341$	−11.9867			−0.649115
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−2.32264	−	4.02294i	−0.125229	−	0.216902i
$345$		0			0
$346$	−10.1486	+	17.5779i	−0.545592	+	0.944993i
$347$	−29.4643	−	17.0112i	−1.58172	−	0.913209i	−0.994608	−	0.103707i	$-0.966930\pi$
$347$	−29.4643	−	17.0112i	−1.58172	−	0.913209i	−0.587117	−	0.809502i	$-0.699737\pi$
$348$		0			0
$349$	11.9598	+	20.7149i	0.640192	+	1.10884i	0.985390	+	0.170315i	$0.0544785\pi$
$349$	11.9598	+	20.7149i	0.640192	+	1.10884i	−0.345198	+	0.938530i	$0.612188\pi$
$350$	−0.443657	+	4.98028i	−0.0237145	+	0.266207i
$351$		0			0
$352$		−	1.12642i		−	0.0600384i
$353$	27.5513	−	15.9068i	1.46641	−	0.846631i	0.467115	−	0.884197i	$-0.345294\pi$
$353$	27.5513	−	15.9068i	1.46641	−	0.846631i	0.999294	+	0.0375654i	$0.0119602\pi$
$354$		0			0
$355$	5.03178	+	22.7822i	0.267059	+	1.20915i
$356$	−1.39668	+	2.41913i	−0.0740242	+	0.128214i
$357$		0			0
$358$	−7.98625	+	4.61086i	−0.422086	+	0.243692i
$359$	4.11764			0.217320			0.108660	−	0.994079i	$-0.465344\pi$
$359$	4.11764			0.217320			0.108660	+	0.994079i	$0.465344\pi$
$360$		0			0
$361$	−18.5145			−0.974447
$362$	14.7786	−	8.53244i	0.776747	−	0.448455i
$363$		0			0
$364$	−0.0632106	+	0.109484i	−0.00331313	+	0.00573852i
$365$	5.82764	−	1.28712i	0.305033	−	0.0673710i
$366$		0			0
$367$	22.5910	−	13.0429i	1.17924	−	0.680836i	0.223403	−	0.974726i	$-0.428283\pi$
$367$	22.5910	−	13.0429i	1.17924	−	0.680836i	0.955839	+	0.293890i	$0.0949499\pi$
$368$			1.98236i			0.103337i
$369$		0			0
$370$	0.458101	−	0.419106i	0.0238156	−	0.0217883i
$371$	0.883840	+	1.53086i	0.0458867	+	0.0794781i
$372$		0			0
$373$	20.4740	+	11.8207i	1.06010	+	0.612051i	0.925461	−	0.378843i	$-0.123678\pi$
$373$	20.4740	+	11.8207i	1.06010	+	0.612051i	0.134643	+	0.990894i	$0.457011\pi$
$374$	−0.530383	+	0.918649i	−0.0274254	+	0.0475022i
$375$		0			0
$376$	0.618584	+	1.07142i	0.0319010	+	0.0552542i
$377$		−	0.405631i		−	0.0208911i
$378$		0			0
$379$	−5.53772			−0.284454			−0.142227	−	0.989834i	$-0.545426\pi$
$379$	−5.53772			−0.284454			−0.142227	+	0.989834i	$0.545426\pi$
$380$	−1.48556	−	0.469688i	−0.0762077	−	0.0240945i
$381$		0			0
$382$	16.2436	+	9.37825i	0.831095	+	0.479833i
$383$	−5.99337	−	3.46027i	−0.306247	−	0.176812i	0.338999	−	0.940787i	$-0.389912\pi$
$383$	−5.99337	−	3.46027i	−0.306247	−	0.176812i	−0.645246	+	0.763975i	$0.723245\pi$
$384$		0			0
$385$	0.759304	−	2.40158i	0.0386977	−	0.122396i
$386$	23.8216			1.21249
$387$		0			0
$388$			1.73230i			0.0879440i
$389$	7.37426	+	12.7726i	0.373890	+	0.647596i	0.990160	−	0.139938i	$-0.0446904\pi$
$389$	7.37426	+	12.7726i	0.373890	+	0.647596i	−0.616270	+	0.787535i	$0.711357\pi$
$390$		0			0
$391$	0.933405	−	1.61671i	0.0472043	−	0.0817603i
$392$	0.866025	+	0.500000i	0.0437409	+	0.0252538i
$393$		0			0
$394$	4.54285	+	7.86845i	0.228865	+	0.396407i
$395$	17.8305	−	16.3128i	0.897152	−	0.820784i
$396$		0			0
$397$			18.8856i			0.947839i	0.880568	+	0.473919i	$0.157161\pi$
$397$			18.8856i			0.947839i	−0.880568	+	0.473919i	$0.842839\pi$
$398$	1.23206	−	0.711331i	0.0617577	−	0.0356558i
$399$		0			0
$400$	4.09122	+	2.87436i	0.204561	+	0.143718i
$401$	15.0742	−	26.1093i	0.752769	−	1.30383i	−0.193707	−	0.981059i	$-0.562051\pi$
$401$	15.0742	−	26.1093i	0.752769	−	1.30383i	0.946476	−	0.322775i	$-0.104616\pi$
$402$		0			0
$403$	1.16506	−	0.672648i	0.0580358	−	0.0335070i
$404$	2.28462			0.113664
$405$		0			0
$406$	−3.20857			−0.159239
$407$	−0.270871	+	0.156387i	−0.0134266	+	0.00775184i
$408$		0			0
$409$	−5.49050	+	9.50983i	−0.271488	+	0.470231i	−0.969243	−	0.246106i	$-0.920849\pi$
$409$	−5.49050	+	9.50983i	−0.271488	+	0.470231i	0.697755	+	0.716336i	$0.254182\pi$
$410$	−15.5525	+	3.43500i	−0.768083	+	0.169643i
$411$		0			0
$412$	−12.6776	+	7.31942i	−0.624580	+	0.360602i
$413$		−	11.2363i		−	0.552902i
$414$		0			0
$415$	16.6875	+	18.2402i	0.819158	+	0.895375i
$416$	0.0632106	+	0.109484i	0.00309915	+	0.00536789i
$417$		0			0
$418$	0.679713	+	0.392433i	0.0332459	+	0.0191945i
$419$	−15.7875	+	27.3447i	−0.771268	+	1.33588i	0.165600	+	0.986193i	$0.447044\pi$
$419$	−15.7875	+	27.3447i	−0.771268	+	1.33588i	−0.936868	+	0.349683i	$0.886289\pi$
$420$		0			0
$421$	−6.89078	−	11.9352i	−0.335836	−	0.581685i	0.647809	−	0.761803i	$-0.275685\pi$
$421$	−6.89078	−	11.9352i	−0.335836	−	0.581685i	−0.983645	+	0.180118i	$0.942352\pi$
$422$			17.3095i			0.842616i
$423$		0			0
$424$	1.76768			0.0858462
$425$	−1.98317	−	4.27055i	−0.0961980	−	0.207152i
$426$		0			0
$427$	6.28340	+	3.62772i	0.304075	+	0.175558i
$428$	11.6777	+	6.74214i	0.564464	+	0.325893i
$429$		0			0
$430$	−9.90395	−	3.13132i	−0.477611	−	0.151006i
$431$	20.8591			1.00475			0.502374	−	0.864650i	$-0.332460\pi$
$431$	20.8591			1.00475			0.502374	+	0.864650i	$0.332460\pi$
$432$		0			0
$433$		−	38.0425i		−	1.82821i	−0.405483	−	0.914103i	$-0.632897\pi$
$433$		−	38.0425i		−	1.82821i	0.405483	−	0.914103i	$-0.367103\pi$
$434$	−5.32069	−	9.21571i	−0.255401	−	0.442368i
$435$		0			0
$436$	−5.80201	+	10.0494i	−0.277866	+	0.481278i
$437$	−1.19621	−	0.690631i	−0.0572224	−	0.0330374i
$438$		0			0
$439$	−4.09765	−	7.09733i	−0.195570	−	0.338737i	0.751517	−	0.659713i	$-0.229322\pi$
$439$	−4.09765	−	7.09733i	−0.195570	−	0.338737i	−0.947087	+	0.320976i	$0.895989\pi$
$440$	−1.70018	−	1.85837i	−0.0810527	−	0.0885941i
$441$		0			0
$442$		−	0.119052i		−	0.00566275i
$443$	33.7419	−	19.4809i	1.60313	−	0.925567i	0.612272	−	0.790647i	$-0.290256\pi$
$443$	33.7419	−	19.4809i	1.60313	−	0.925567i	0.990857	−	0.134919i	$-0.0430775\pi$
$444$		0			0
$445$	1.34709	+	6.09917i	0.0638584	+	0.289129i
$446$	−2.80961	+	4.86638i	−0.133039	+	0.230430i
$447$		0			0
$448$	0.866025	−	0.500000i	0.0409159	−	0.0236228i
$449$	17.2573			0.814424			0.407212	−	0.913334i	$-0.366501\pi$
$449$	17.2573			0.814424			0.407212	+	0.913334i	$0.366501\pi$
$450$		0			0
$451$	8.02340			0.377807
$452$	0.377266	−	0.217815i	0.0177451	−	0.0102451i
$453$		0			0
$454$	−3.48654	+	6.03886i	−0.163631	+	0.283418i
$455$	0.0609662	+	0.276034i	0.00285814	+	0.0129407i
$456$		0			0
$457$	4.13649	−	2.38821i	0.193497	−	0.111716i	−0.400122	−	0.916462i	$-0.631032\pi$
$457$	4.13649	−	2.38821i	0.193497	−	0.111716i	0.593619	+	0.804746i	$0.297699\pi$
$458$		−	22.3524i		−	1.04446i
$459$		0			0
$460$	2.99209	+	3.27049i	0.139507	+	0.152487i
$461$	4.70834	+	8.15509i	0.219289	+	0.379821i	0.954591	−	0.297920i	$-0.0962928\pi$
$461$	4.70834	+	8.15509i	0.219289	+	0.379821i	−0.735301	+	0.677740i	$0.762959\pi$
$462$		0			0
$463$	13.6991	+	7.90915i	0.636649	+	0.367569i	0.783323	−	0.621615i	$-0.213523\pi$
$463$	13.6991	+	7.90915i	0.636649	+	0.367569i	−0.146674	+	0.989185i	$0.546857\pi$
$464$	−1.60428	+	2.77870i	−0.0744770	+	0.128998i
$465$		0			0
$466$	7.52641	+	13.0361i	0.348654	+	0.603887i
$467$			31.3856i			1.45235i	0.687508	+	0.726177i	$0.258705\pi$
$467$			31.3856i			1.45235i	−0.687508	+	0.726177i	$0.741295\pi$
$468$		0			0
$469$	10.5675			0.487963
$470$	2.63769	+	0.833956i	0.121668	+	0.0384675i
$471$		0			0
$472$	−9.73091	−	5.61814i	−0.447901	−	0.258596i
$473$	4.53152	+	2.61628i	0.208360	+	0.120296i
$474$		0			0
$475$	−3.15980	+	1.46736i	−0.144982	+	0.0673270i
$476$	−0.941713			−0.0431633
$477$		0			0
$478$		−	15.6591i		−	0.716231i
$479$	14.4530	+	25.0333i	0.660374	+	1.14380i	0.980517	+	0.196432i	$0.0629355\pi$
$479$	14.4530	+	25.0333i	0.660374	+	1.14380i	−0.320144	+	0.947369i	$0.603731\pi$
$480$		0			0
$481$	0.0175518	−	0.0304006i	0.000800292	−	0.00138615i
$482$	−9.64239	−	5.56703i	−0.439199	−	0.253571i
$483$		0			0
$484$	−4.86559	−	8.42745i	−0.221163	−	0.383066i
$485$	2.61466	+	2.85794i	0.118726	+	0.129772i
$486$		0			0
$487$			15.6946i			0.711192i	0.934640	+	0.355596i	$0.115722\pi$
$487$			15.6946i			0.711192i	−0.934640	+	0.355596i	$0.884278\pi$
$488$	6.28340	−	3.62772i	0.284436	−	0.164219i
$489$		0			0
$490$	2.18345	−	0.482247i	0.0986381	−	0.0217857i
$491$	10.5822	−	18.3289i	0.477568	−	0.827171i	−0.522102	−	0.852883i	$-0.674852\pi$
$491$	10.5822	−	18.3289i	0.477568	−	0.827171i	0.999669	+	0.0257117i	$0.00818520\pi$
$492$		0			0
$493$	2.61674	−	1.51078i	0.117852	−	0.0680419i
$494$	−0.0880875			−0.00396324
$495$		0			0
$496$	−10.6414			−0.477812
$497$	9.03615	−	5.21702i	0.405327	−	0.234015i
$498$		0			0
$499$	7.75002	−	13.4234i	0.346938	−	0.600915i	−0.638766	−	0.769401i	$-0.720555\pi$
$499$	7.75002	−	13.4234i	0.346938	−	0.600915i	0.985704	+	0.168486i	$0.0538879\pi$
$500$	11.0881	−	1.43302i	0.495876	−	0.0640866i
$501$		0			0
$502$	3.08968	−	1.78382i	0.137899	−	0.0796160i
$503$		−	26.6280i		−	1.18728i	−0.804730	−	0.593641i	$-0.797690\pi$
$503$		−	26.6280i		−	1.18728i	0.804730	−	0.593641i	$-0.202310\pi$
$504$		0			0
$505$	3.76916	−	3.44832i	0.167725	−	0.153448i
$506$	−1.11648	−	1.93381i	−0.0496338	−	0.0859682i
$507$		0			0
$508$	13.2553	+	7.65297i	0.588110	+	0.339545i
$509$	18.7982	−	32.5595i	0.833216	−	1.44317i	−0.0622581	−	0.998060i	$-0.519830\pi$
$509$	18.7982	−	32.5595i	0.833216	−	1.44317i	0.895474	−	0.445113i	$-0.146836\pi$
$510$		0			0
$511$	−1.33451	−	2.31143i	−0.0590350	−	0.102252i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−2.47169			−0.109021
$515$	−9.86782	+	31.2106i	−0.434828	+	1.37530i
$516$		0			0
$517$	−1.20687	−	0.696786i	−0.0530780	−	0.0306446i
$518$	−0.240470	−	0.138836i	−0.0105657	−	0.00610009i
$519$		0			0
$520$	0.269535	+	0.0852186i	0.0118199	+	0.00373708i
$521$	7.32398			0.320869			0.160435	−	0.987046i	$-0.448710\pi$
$521$	7.32398			0.320869			0.160435	+	0.987046i	$0.448710\pi$
$522$		0			0
$523$			7.32858i			0.320457i	0.987080	+	0.160228i	$0.0512230\pi$
$523$			7.32858i			0.320457i	−0.987080	+	0.160228i	$0.948777\pi$
$524$	5.68968	+	9.85481i	0.248555	+	0.430509i
$525$		0			0
$526$	−4.81637	+	8.34220i	−0.210004	+	0.363737i
$527$	8.67855	+	5.01056i	0.378043	+	0.218263i
$528$		0			0
$529$	−9.53513	−	16.5153i	−0.414571	−	0.718058i
$530$	2.91631	−	2.66807i	0.126677	−	0.115894i
$531$		0			0
$532$			0.696778i			0.0302092i
$533$	−0.779845	+	0.450243i	−0.0337788	+	0.0195022i
$534$		0			0
$535$	29.4422	−	6.50275i	1.27290	−	0.281138i
$536$	5.28376	−	9.15175i	0.228224	−	0.395295i
$537$		0			0
$538$	−6.64260	+	3.83511i	−0.286383	+	0.165343i
$539$	−1.12642			−0.0485184
$540$		0			0
$541$	−43.7178			−1.87958			−0.939788	−	0.341758i	$-0.888978\pi$
$541$	−43.7178			−1.87958			−0.939788	+	0.341758i	$0.888978\pi$
$542$	−20.5361	+	11.8565i	−0.882101	+	0.509281i
$543$		0			0
$544$	−0.470856	+	0.815547i	−0.0201878	+	0.0349663i
$545$	5.59600	+	25.3367i	0.239706	+	1.08531i
$546$		0			0
$547$	−15.3447	+	8.85925i	−0.656090	+	0.378794i	−0.790786	−	0.612093i	$-0.790328\pi$
$547$	−15.3447	+	8.85925i	−0.656090	+	0.378794i	0.134695	+	0.990887i	$0.456994\pi$
$548$		−	9.40226i		−	0.401645i
$549$		0			0
$550$	−5.60989	−	0.499745i	−0.239207	−	0.0213092i
$551$	−1.11783	−	1.93614i	−0.0476212	−	0.0824823i
$552$		0			0
$553$	−9.35976	−	5.40386i	−0.398018	−	0.229796i
$554$	1.92248	−	3.32984i	0.0816784	−	0.141471i
$555$		0			0
$556$	9.58719	+	16.6055i	0.406587	+	0.704230i
$557$			8.35979i			0.354216i	0.984191	+	0.177108i	$0.0566741\pi$
$557$			8.35979i			0.354216i	−0.984191	+	0.177108i	$0.943326\pi$
$558$		0			0
$559$	−0.587263			−0.0248386
$560$	0.674085	−	2.13204i	0.0284853	−	0.0900953i
$561$		0			0
$562$	21.0519	+	12.1543i	0.888022	+	0.512700i
$563$	−0.640004	−	0.369507i	−0.0269730	−	0.0155728i	0.486453	−	0.873707i	$-0.338291\pi$
$563$	−0.640004	−	0.369507i	−0.0269730	−	0.0155728i	−0.513426	+	0.858134i	$0.671624\pi$
$564$		0			0
$565$	0.293651	−	0.928780i	0.0123540	−	0.0390741i
$566$	31.6395			1.32991
$567$		0			0
$568$		−	10.4340i		−	0.437803i
$569$	11.4249	+	19.7886i	0.478959	+	0.829581i	0.999709	−	0.0241284i	$-0.00768105\pi$
$569$	11.4249	+	19.7886i	0.478959	+	0.829581i	−0.520750	+	0.853709i	$0.674348\pi$
$570$		0			0
$571$	−3.92185	+	6.79284i	−0.164124	+	0.284272i	−0.936344	−	0.351084i	$-0.885813\pi$
$571$	−3.92185	+	6.79284i	−0.164124	+	0.284272i	0.772220	+	0.635356i	$0.219146\pi$
$572$	−0.123325	−	0.0712017i	−0.00515648	−	0.00297709i
$573$		0			0
$574$	3.56146	+	6.16862i	0.148652	+	0.257473i
$575$	9.87269	+	0.879487i	0.411720	+	0.0366772i
$576$		0			0
$577$		−	41.4320i		−	1.72484i	−0.506197	−	0.862418i	$-0.668949\pi$
$577$		−	41.4320i		−	1.72484i	0.506197	−	0.862418i	$-0.331051\pi$
$578$	−13.9544	+	8.05659i	−0.580427	+	0.335110i
$579$		0			0
$580$	1.54732	+	7.00574i	0.0642491	+	0.290897i
$581$	5.52801	−	9.57479i	0.229340	−	0.397229i
$582$		0			0
$583$	−1.72439	+	0.995577i	−0.0714169	+	0.0412326i
$584$	−2.66901			−0.110444
$585$		0			0
$586$	26.6735			1.10187
$587$	−19.0433	+	10.9947i	−0.786003	+	0.453799i	−0.838554	−	0.544819i	$-0.816598\pi$
$587$	−19.0433	+	10.9947i	−0.786003	+	0.453799i	0.0525504	+	0.998618i	$0.483265\pi$
$588$		0			0
$589$	3.70734	−	6.42130i	0.152758	−	0.264585i
$590$	−24.5338	+	5.41866i	−1.01004	+	0.223083i
$591$		0			0
$592$	−0.240470	+	0.138836i	−0.00988328	+	0.00570611i
$593$			13.8580i			0.569081i	0.958664	+	0.284540i	$0.0918410\pi$
$593$			13.8580i			0.569081i	−0.958664	+	0.284540i	$0.908159\pi$
$594$		0			0
$595$	−1.55363	+	1.42138i	−0.0636928	+	0.0582711i
$596$	−1.89688	−	3.28548i	−0.0776991	−	0.134579i
$597$		0			0
$598$	0.217036	+	0.125306i	0.00887527	+	0.00512414i
$599$	15.1548	−	26.2489i	0.619209	−	1.07250i	−0.370421	−	0.928864i	$-0.620787\pi$
$599$	15.1548	−	26.2489i	0.619209	−	1.07250i	0.989630	−	0.143638i	$-0.0458800\pi$
$600$		0			0
$601$	−10.4476	−	18.0958i	−0.426167	−	0.738143i	0.570361	−	0.821394i	$-0.306803\pi$
$601$	−10.4476	−	18.0958i	−0.426167	−	0.738143i	−0.996529	+	0.0832505i	$0.973470\pi$
$602$			4.64529i			0.189328i
$603$		0			0
$604$	7.08355			0.288225
$605$	−20.7473	−	6.55964i	−0.843497	−	0.266687i
$606$		0			0
$607$	26.3561	+	15.2167i	1.06976	+	0.617628i	0.928117	−	0.372290i	$-0.121427\pi$
$607$	26.3561	+	15.2167i	1.06976	+	0.617628i	0.141646	+	0.989917i	$0.454761\pi$
$608$	0.603427	+	0.348389i	0.0244722	+	0.0141290i
$609$		0			0
$610$	4.89078	−	15.4689i	0.198022	−	0.626318i
$611$	0.156404			0.00632743
$612$		0			0
$613$		−	24.1562i		−	0.975658i	−0.872939	−	0.487829i	$-0.837789\pi$
$613$		−	24.1562i		−	0.975658i	0.872939	−	0.487829i	$-0.162211\pi$
$614$	−4.30415	−	7.45501i	−0.173701	−	0.300860i
$615$		0			0
$616$	−0.563211	+	0.975509i	−0.0226924	+	0.0393044i
$617$	9.65499	+	5.57431i	0.388695	+	0.224413i	0.681595	−	0.731730i	$-0.261287\pi$
$617$	9.65499	+	5.57431i	0.388695	+	0.224413i	−0.292899	+	0.956143i	$0.594620\pi$
$618$		0			0
$619$	−8.12051	−	14.0651i	−0.326391	−	0.565326i	0.655402	−	0.755280i	$-0.272499\pi$
$619$	−8.12051	−	14.0651i	−0.326391	−	0.565326i	−0.981793	+	0.189955i	$0.939166\pi$
$620$	−17.5561	+	16.0617i	−0.705070	+	0.645053i
$621$		0			0
$622$		−	33.3741i		−	1.33818i
$623$	2.41913	−	1.39668i	0.0969204	−	0.0559570i
$624$		0			0
$625$	16.1302	−	19.1002i	0.645208	−	0.764007i
$626$	−6.58617	+	11.4076i	−0.263236	+	0.455939i
$627$		0			0
$628$	0.269315	−	0.155489i	0.0107468	−	0.00620468i
$629$	0.261487			0.0104262
$630$		0			0
$631$	−17.7403			−0.706230			−0.353115	−	0.935580i	$-0.614877\pi$
$631$	−17.7403			−0.706230			−0.353115	+	0.935580i	$0.614877\pi$
$632$	−9.35976	+	5.40386i	−0.372311	+	0.214954i
$633$		0			0
$634$	−3.62037	+	6.27066i	−0.143783	+	0.249040i
$635$	33.4197	−	7.38124i	1.32622	−	0.292915i
$636$		0			0
$637$	0.109484	−	0.0632106i	0.00433791	−	0.00250449i
$638$		−	3.61420i		−	0.143088i
$639$		0			0
$640$	−1.50936	−	1.64980i	−0.0596627	−	0.0652139i
$641$	1.11952	+	1.93907i	0.0442185	+	0.0765887i	0.887288	−	0.461217i	$-0.152587\pi$
$641$	1.11952	+	1.93907i	0.0442185	+	0.0765887i	−0.843069	+	0.537805i	$0.819254\pi$
$642$		0			0
$643$	−33.7529	−	19.4872i	−1.33108	−	0.768501i	−0.345617	−	0.938376i	$-0.612330\pi$
$643$	−33.7529	−	19.4872i	−1.33108	−	0.768501i	−0.985466	+	0.169875i	$0.945664\pi$
$644$	0.991178	−	1.71677i	0.0390579	−	0.0676503i
$645$		0			0
$646$	−0.328082	−	0.568255i	−0.0129082	−	0.0223577i
$647$			27.8364i			1.09436i	0.837014	+	0.547182i	$0.184299\pi$
$647$			27.8364i			1.09436i	−0.837014	+	0.547182i	$0.815701\pi$
$648$		0			0
$649$	12.6568			0.496823
$650$	0.573304	−	0.266233i	0.0224868	−	0.0104425i
$651$		0			0
$652$	−12.4279	−	7.17526i	−0.486714	−	0.281005i
$653$	−15.8311	−	9.14010i	−0.619519	−	0.357680i	0.157163	−	0.987573i	$-0.449765\pi$
$653$	−15.8311	−	9.14010i	−0.619519	−	0.357680i	−0.776682	+	0.629893i	$0.783099\pi$
$654$		0			0
$655$	24.2613	+	7.67065i	0.947966	+	0.299717i
$656$	7.12291			0.278103
$657$		0			0
$658$		−	1.23717i		−	0.0482298i
$659$	−1.72824	−	2.99341i	−0.0673228	−	0.116607i	0.830399	−	0.557169i	$-0.188112\pi$
$659$	−1.72824	−	2.99341i	−0.0673228	−	0.116607i	−0.897722	+	0.440562i	$0.854779\pi$
$660$		0			0
$661$	−2.51296	+	4.35257i	−0.0977428	+	0.169295i	−0.910750	−	0.412958i	$-0.864496\pi$
$661$	−2.51296	+	4.35257i	−0.0977428	+	0.169295i	0.813007	+	0.582254i	$0.197829\pi$
$662$	−20.3850	−	11.7693i	−0.792287	−	0.457427i
$663$		0			0
$664$	−5.52801	−	9.57479i	−0.214528	−	0.371574i
$665$	1.05169	+	1.14954i	0.0407828	+	0.0445773i
$666$		0			0
$667$			6.36053i			0.246281i
$668$	−19.8898	+	11.4834i	−0.769560	+	0.444306i
$669$		0			0
$670$	−5.09616	−	23.0736i	−0.196882	−	0.891412i
$671$	−4.08634	+	7.07775i	−0.157751	+	0.273234i
$672$		0			0
$673$	−19.6091	+	11.3213i	−0.755873	+	0.436404i	−0.827812	−	0.561005i	$-0.810415\pi$
$673$	−19.6091	+	11.3213i	−0.755873	+	0.436404i	0.0719387	+	0.997409i	$0.477081\pi$
$674$	−21.8348			−0.841045
$675$		0			0
$676$	−12.9840			−0.499385
$677$	3.83963	−	2.21681i	0.147569	−	0.0851990i	−0.424397	−	0.905476i	$-0.639514\pi$
$677$	3.83963	−	2.21681i	0.147569	−	0.0851990i	0.571966	+	0.820277i	$0.306181\pi$
$678$		0			0
$679$	0.866148	−	1.50021i	0.0332397	−	0.0575729i
$680$	0.454138	+	2.05618i	0.0174154	+	0.0788509i
$681$		0			0
$682$	10.3808	−	5.99334i	0.397500	−	0.229497i
$683$			21.9857i			0.841259i	0.907232	+	0.420630i	$0.138191\pi$
$683$			21.9857i			0.841259i	−0.907232	+	0.420630i	$0.861809\pi$
$684$		0			0
$685$	−14.1914	−	15.5118i	−0.542226	−	0.592676i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	4.02294	+	2.32264i	0.153373	+	0.0885500i
$689$	0.111736	−	0.193533i	0.00425681	−	0.00737301i
$690$		0			0
$691$	1.50848	+	2.61277i	0.0573853	+	0.0993943i	0.893291	−	0.449479i	$-0.148390\pi$
$691$	1.50848	+	2.61277i	0.0573853	+	0.0993943i	−0.835906	+	0.548873i	$0.815057\pi$
$692$		−	20.2972i		−	0.771584i
$693$		0			0
$694$	34.0224			1.29147
$695$	40.8806	+	12.9252i	1.55069	+	0.490279i
$696$		0			0
$697$	−5.80907	−	3.35387i	−0.220034	−	0.127037i
$698$	−20.7149	−	11.9598i	−0.784072	−	0.452684i
$699$		0			0
$700$	−2.10592	−	4.53488i	−0.0795963	−	0.171402i
$701$	−10.1916			−0.384932			−0.192466	−	0.981304i	$-0.561649\pi$
$701$	−10.1916			−0.384932			−0.192466	+	0.981304i	$0.561649\pi$
$702$		0			0
$703$		−	0.193475i		−	0.00729706i
$704$	0.563211	+	0.975509i	0.0212268	+	0.0367659i
$705$		0			0
$706$	−15.9068	+	27.5513i	−0.598659	+	1.03691i
$707$	−1.97854	−	1.14231i	−0.0744106	−	0.0429610i
$708$		0			0
$709$	−15.4814	−	26.8145i	−0.581415	−	1.00704i	−0.995312	−	0.0967162i	$-0.969166\pi$
$709$	−15.4814	−	26.8145i	−0.581415	−	1.00704i	0.413897	−	0.910324i	$-0.364167\pi$
$710$	−15.7487	−	17.2140i	−0.591040	−	0.646032i
$711$		0			0
$712$		−	2.79337i		−	0.104686i
$713$	−18.2688	+	10.5475i	−0.684173	+	0.395007i
$714$		0			0
$715$	−0.310930	+	0.0686736i	−0.0116281	+	0.00256825i
$716$	4.61086	−	7.98625i	0.172316	−	0.298460i
$717$		0			0
$718$	−3.56598	+	2.05882i	−0.133081	+	0.0768344i
$719$	−9.42171			−0.351370			−0.175685	−	0.984446i	$-0.556214\pi$
$719$	−9.42171			−0.351370			−0.175685	+	0.984446i	$0.556214\pi$
$720$		0			0
$721$	14.6388			0.545179
$722$	16.0340	−	9.25725i	0.596725	−	0.344519i
$723$		0			0
$724$	−8.53244	+	14.7786i	−0.317105	+	0.549243i
$725$	13.1270	+	9.22258i	0.487523	+	0.342518i
$726$		0			0
$727$	−28.1303	+	16.2410i	−1.04329	+	0.602346i	−0.920764	−	0.390119i	$-0.872434\pi$
$727$	−28.1303	+	16.2410i	−1.04329	+	0.602346i	−0.122529	+	0.992465i	$0.539101\pi$
$728$		−	0.126421i		−	0.00468548i
$729$		0			0
$730$	−4.40332	+	4.02850i	−0.162974	+	0.149101i
$731$	−2.18726	−	3.78845i	−0.0808988	−	0.140121i
$732$		0			0
$733$	16.5097	+	9.53190i	0.609801	+	0.352069i	0.772888	−	0.634543i	$-0.218812\pi$
$733$	16.5097	+	9.53190i	0.609801	+	0.352069i	−0.163086	+	0.986612i	$0.552145\pi$
$734$	−13.0429	+	22.5910i	−0.481424	+	0.833851i
$735$		0			0
$736$	−0.991178	−	1.71677i	−0.0365353	−	0.0632810i
$737$			11.9035i			0.438471i
$738$		0			0
$739$	18.9602			0.697462			0.348731	−	0.937223i	$-0.386613\pi$
$739$	18.9602			0.697462			0.348731	+	0.937223i	$0.386613\pi$
$740$	−0.187174	+	0.592008i	−0.00688066	+	0.0217626i
$741$		0			0
$742$	−1.53086	−	0.883840i	−0.0561995	−	0.0324468i
$743$	44.7056	+	25.8108i	1.64009	+	0.946907i	0.980799	+	0.195020i	$0.0624770\pi$
$743$	44.7056	+	25.8108i	1.64009	+	0.946907i	0.659292	+	0.751887i	$0.270856\pi$
$744$		0			0
$745$	−8.08844	−	2.55731i	−0.296338	−	0.0936926i
$746$	−23.6414			−0.865571
$747$		0			0
$748$		−	1.06077i		−	0.0387854i
$749$	−6.74214	−	11.6777i	−0.246352	−	0.426695i
$750$		0			0
$751$	22.3112	−	38.6440i	0.814145	−	1.41014i	−0.0957944	−	0.995401i	$-0.530539\pi$
$751$	22.3112	−	38.6440i	0.814145	−	1.41014i	0.909940	−	0.414740i	$-0.136128\pi$
$752$	−1.07142	−	0.618584i	−0.0390706	−	0.0225574i
$753$		0			0
$754$	0.202816	+	0.351287i	0.00738611	+	0.0127931i
$755$	11.6864	−	10.6916i	0.425312	−	0.389108i
$756$		0			0
$757$			2.04073i			0.0741715i	0.999312	+	0.0370857i	$0.0118075\pi$
$757$			2.04073i			0.0741715i	−0.999312	+	0.0370857i	$0.988193\pi$
$758$	4.79581	−	2.76886i	0.174191	−	0.100570i
$759$		0			0
$760$	1.52138	−	0.336019i	0.0551861	−	0.0121887i
$761$	2.28880	−	3.96431i	0.0829688	−	0.143706i	−0.821555	−	0.570129i	$-0.806893\pi$
$761$	2.28880	−	3.96431i	0.0829688	−	0.143706i	0.904524	+	0.426423i	$0.140226\pi$
$762$		0			0
$763$	10.0494	−	5.80201i	0.363812	−	0.210047i
$764$	−18.7565			−0.678586
$765$		0			0
$766$	6.92055			0.250050
$767$	−1.23019	+	0.710252i	−0.0444197	+	0.0256457i
$768$		0			0
$769$	−19.2465	+	33.3359i	−0.694047	+	1.20212i	0.276454	+	0.961027i	$0.410841\pi$
$769$	−19.2465	+	33.3359i	−0.694047	+	1.20212i	−0.970501	+	0.241097i	$0.922493\pi$
$770$	0.543213	+	2.45948i	0.0195760	+	0.0886335i
$771$		0			0
$772$	−20.6301	+	11.9108i	−0.742493	+	0.428679i
$773$		−	28.2743i		−	1.01696i	−0.861075	−	0.508478i	$-0.830208\pi$
$773$		−	28.2743i		−	1.01696i	0.861075	−	0.508478i	$-0.169792\pi$
$774$		0			0
$775$	−4.72113	+	52.9970i	−0.169588	+	1.90371i
$776$	−0.866148	−	1.50021i	−0.0310929	−	0.0538545i
$777$		0			0
$778$	−12.7726	−	7.37426i	−0.457920	−	0.264380i
$779$	−2.48154	+	4.29816i	−0.0889105	+	0.153998i
$780$		0			0
$781$	5.87656	+	10.1785i	0.210280	+	0.364216i
$782$			1.86681i			0.0667570i
$783$		0			0
$784$	−1.00000			−0.0357143
$785$	0.209625	−	0.663018i	0.00748185	−	0.0236641i
$786$		0			0
$787$	−19.0732	−	11.0119i	−0.679888	−	0.392533i	0.119925	−	0.992783i	$-0.461735\pi$
$787$	−19.0732	−	11.0119i	−0.679888	−	0.392533i	−0.799813	+	0.600250i	$0.795068\pi$
$788$	−7.86845	−	4.54285i	−0.280302	−	0.161832i
$789$		0			0
$790$	−7.28533	+	23.0425i	−0.259200	+	0.819817i
$791$	−0.435629			−0.0154892
$792$		0			0
$793$		−	0.917241i		−	0.0325722i
$794$	−9.44278	−	16.3554i	−0.335112	−	0.580430i
$795$		0			0
$796$	−0.711331	+	1.23206i	−0.0252125	+	0.0436693i
$797$	39.3563	+	22.7224i	1.39407	+	0.804867i	0.993763	−	0.111514i	$-0.0355699\pi$
$797$	39.3563	+	22.7224i	1.39407	+	0.804867i	0.400308	+	0.916381i	$0.368903\pi$
$798$		0			0
$799$	0.582528	+	1.00897i	0.0206084	+	0.0356947i
$800$	−4.98028	−	0.443657i	−0.176079	−	0.0156857i
$801$		0			0
$802$			30.1484i			1.06458i
$803$	2.60364	−	1.50321i	0.0918806	−	0.0530473i
$804$		0			0
$805$	−0.955985	−	4.32837i	−0.0336941	−	0.152555i
$806$	−0.672648	+	1.16506i	−0.0236930	+	0.0410375i
$807$		0			0
$808$	−1.97854	+	1.14231i	−0.0696048	+	0.0401863i
$809$	−14.9303			−0.524923			−0.262461	−	0.964943i	$-0.584534\pi$
$809$	−14.9303			−0.524923			−0.262461	+	0.964943i	$0.584534\pi$
$810$		0			0
$811$	−42.9560			−1.50839			−0.754195	−	0.656650i	$-0.771973\pi$
$811$	−42.9560			−1.50839			−0.754195	+	0.656650i	$0.771973\pi$
$812$	2.77870	−	1.60428i	0.0975133	−	0.0562994i
$813$		0			0
$814$	0.156387	−	0.270871i	0.00548138	−	0.00949403i
$815$	−31.3336	+	6.92049i	−1.09757	+	0.242414i
$816$		0			0
$817$	−2.80309	+	1.61837i	−0.0980678	+	0.0566195i
$818$		−	10.9810i		−	0.383942i
$819$		0			0
$820$	11.7514	−	10.7510i	0.410375	−	0.375443i
$821$	−15.1594	−	26.2569i	−0.529067	−	0.916371i	−0.999425	−	0.0338954i	$-0.989209\pi$
$821$	−15.1594	−	26.2569i	−0.529067	−	0.916371i	0.470358	−	0.882475i	$-0.344125\pi$
$822$		0			0
$823$	−24.8088	−	14.3234i	−0.864780	−	0.499281i	0.000829765	−	1.00000i	$-0.499736\pi$
$823$	−24.8088	−	14.3234i	−0.864780	−	0.499281i	−0.865610	+	0.500718i	$0.833069\pi$
$824$	7.31942	−	12.6776i	0.254984	−	0.441645i
$825$		0			0
$826$	5.61814	+	9.73091i	0.195480	+	0.338582i
$827$		−	38.5735i		−	1.34133i	−0.741760	−	0.670665i	$-0.766009\pi$
$827$		−	38.5735i		−	1.34133i	0.741760	−	0.670665i	$-0.233991\pi$
$828$		0			0
$829$	34.5996			1.20169			0.600847	−	0.799364i	$-0.294830\pi$
$829$	34.5996			1.20169			0.600847	+	0.799364i	$0.294830\pi$
$830$	−23.5719	−	7.45269i	−0.818192	−	0.258687i
$831$		0			0
$832$	−0.109484	−	0.0632106i	−0.00379567	−	0.00219143i
$833$	0.815547	+	0.470856i	0.0282570	+	0.0163142i
$834$		0			0
$835$	−15.4816	+	48.9662i	−0.535761	+	1.69454i
$836$	−0.784865			−0.0271451
$837$		0			0
$838$		−	31.5749i		−	1.09074i
$839$	−5.25612	−	9.10387i	−0.181461	−	0.314300i	0.760917	−	0.648849i	$-0.224749\pi$
$839$	−5.25612	−	9.10387i	−0.181461	−	0.314300i	−0.942378	+	0.334549i	$0.891416\pi$
$840$		0			0
$841$	9.35254	−	16.1991i	0.322501	−	0.558589i
$842$	11.9352	+	6.89078i	0.411313	+	0.237472i
$843$		0			0
$844$	−8.65477	−	14.9905i	−0.297910	−	0.515995i
$845$	−21.4210	+	19.5976i	−0.736904	+	0.674177i
$846$		0			0
$847$			9.73118i			0.334367i
$848$	−1.53086	+	0.883840i	−0.0525698	+	0.0303512i
$849$		0			0
$850$	3.85275	+	2.70682i	0.132148	+	0.0928431i
$851$	−0.275222	+	0.476698i	−0.00943449	+	0.0163410i
$852$		0			0
$853$	30.3232	−	17.5071i	1.03825	−	0.599433i	0.118911	−	0.992905i	$-0.462060\pi$
$853$	30.3232	−	17.5071i	1.03825	−	0.599433i	0.919337	+	0.393472i	$0.128726\pi$
$854$	−7.25544			−0.248276
$855$		0			0
$856$	−13.4843			−0.460883
$857$	−27.5306	+	15.8948i	−0.940427	+	0.542956i	−0.890094	−	0.455777i	$-0.849362\pi$
$857$	−27.5306	+	15.8948i	−0.940427	+	0.542956i	−0.0503330	+	0.998732i	$0.516028\pi$
$858$		0			0
$859$	4.66921	−	8.08731i	0.159311	−	0.275936i	−0.775309	−	0.631582i	$-0.782406\pi$
$859$	4.66921	−	8.08731i	0.159311	−	0.275936i	0.934621	+	0.355646i	$0.115739\pi$
$860$	10.1427	−	2.24018i	0.345864	−	0.0763893i
$861$		0			0
$862$	−18.0645	+	10.4296i	−0.615281	+	0.355232i
$863$		−	10.0896i		−	0.343453i	−0.985145	−	0.171727i	$-0.945065\pi$
$863$		−	10.0896i		−	0.343453i	0.985145	−	0.171727i	$-0.0549346\pi$
$864$		0			0
$865$	−30.6358	−	33.4862i	−1.04165	−	1.13857i
$866$	19.0212	+	32.9458i	0.646368	+	1.11954i
$867$		0			0
$868$	9.21571	+	5.32069i	0.312801	+	0.180596i
$869$	6.08702	−	10.5430i	0.206488	−	0.357648i
$870$		0			0
$871$	−0.667980	−	1.15697i	−0.0226336	−	0.0392026i
$872$		−	11.6040i		−	0.392962i
$873$		0			0
$874$	1.38126			0.0467219
$875$	−10.3191	−	4.30303i	−0.348849	−	0.145469i
$876$		0			0
$877$	−21.5364	−	12.4340i	−0.727231	−	0.419867i	0.0901771	−	0.995926i	$-0.471257\pi$
$877$	−21.5364	−	12.4340i	−0.727231	−	0.419867i	−0.817408	+	0.576059i	$0.804590\pi$
$878$	7.09733	+	4.09765i	0.239523	+	0.138289i
$879$		0			0
$880$	2.40158	+	0.759304i	0.0809572	+	0.0255961i
$881$	−15.0500			−0.507048			−0.253524	−	0.967329i	$-0.581590\pi$
$881$	−15.0500			−0.507048			−0.253524	+	0.967329i	$0.581590\pi$
$882$		0			0
$883$			24.2908i			0.817449i	0.912658	+	0.408725i	$0.134026\pi$
$883$			24.2908i			0.817449i	−0.912658	+	0.408725i	$0.865974\pi$
$884$	0.0595262	+	0.103102i	0.00200208	+	0.00346771i
$885$		0			0
$886$	−19.4809	+	33.7419i	−0.654474	+	1.13358i
$887$	−12.3219	−	7.11402i	−0.413727	−	0.238866i	0.278663	−	0.960389i	$-0.410109\pi$
$887$	−12.3219	−	7.11402i	−0.413727	−	0.238866i	−0.692390	+	0.721523i	$0.743442\pi$
$888$		0			0
$889$	−7.65297	−	13.2553i	−0.256672	−	0.444569i
$890$	−4.21620	−	4.60849i	−0.141327	−	0.154477i
$891$		0			0
$892$		−	5.61922i		−	0.188145i
$893$	0.746541	−	0.431015i	0.0249820	−	0.0144234i
$894$		0			0
$895$	−4.44715	−	20.1351i	−0.148652	−	0.673043i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$		0			0
$898$	−14.9453	+	8.62866i	−0.498731	+	0.287942i
$899$	−34.1436			−1.13875
$900$		0			0
$901$	1.66465			0.0554574
$902$	−6.94847	+	4.01170i	−0.231359	+	0.133575i
$903$		0			0
$904$	−0.217815	+	0.377266i	−0.00724441	+	0.0125477i
$905$	8.22948	+	37.2602i	0.273557	+	1.23857i
$906$		0			0
$907$	6.40949	−	3.70052i	0.212824	−	0.122874i	−0.389799	−	0.920900i	$-0.627456\pi$
$907$	6.40949	−	3.70052i	0.212824	−	0.122874i	0.602623	+	0.798026i	$0.294122\pi$
$908$		−	6.97308i		−	0.231410i
$909$		0			0
$910$	−0.190815	−	0.208569i	−0.00632546	−	0.00691400i
$911$	−6.43693	−	11.1491i	−0.213265	−	0.369386i	0.739469	−	0.673190i	$-0.235076\pi$
$911$	−6.43693	−	11.1491i	−0.213265	−	0.369386i	−0.952734	+	0.303804i	$0.901743\pi$
$912$		0			0
$913$	10.7852	+	6.22686i	0.356939	+	0.206079i
$914$	−2.38821	+	4.13649i	−0.0789948	+	0.136823i
$915$		0			0
$916$	11.1762	+	19.3577i	0.369272	+	0.639598i
$917$		−	11.3794i		−	0.375779i
$918$		0			0
$919$	22.8152			0.752603			0.376302	−	0.926497i	$-0.377196\pi$
$919$	22.8152			0.752603			0.376302	+	0.926497i	$0.377196\pi$
$920$	−4.22647	−	1.33628i	−0.139343	−	0.0440558i
$921$		0			0
$922$	−8.15509	−	4.70834i	−0.268574	−	0.155061i
$923$	−1.14236	−	0.659542i	−0.0376012	−	0.0217091i
$924$		0			0
$925$	0.584754	+	1.25921i	0.0192266	+	0.0414024i
$926$	−15.8183			−0.519822
$927$		0			0
$928$		−	3.20857i		−	0.105326i
$929$	−20.0830	−	34.7848i	−0.658902	−	1.14125i	−0.980900	−	0.194511i	$-0.937688\pi$
$929$	−20.0830	−	34.7848i	−0.658902	−	1.14125i	0.321999	−	0.946740i	$-0.395645\pi$
$930$		0			0
$931$	0.348389	−	0.603427i	0.0114180	−	0.0197765i
$932$	−13.0361	−	7.52641i	−0.427012	−	0.246536i
$933$		0			0
$934$	−15.6928	−	27.1808i	−0.513485	−	0.889382i
$935$	−1.60108	−	1.75005i	−0.0523608	−	0.0572326i
$936$		0			0
$937$			16.1624i			0.528001i	0.964522	+	0.264001i	$0.0850421\pi$
$937$			16.1624i			0.528001i	−0.964522	+	0.264001i	$0.914958\pi$
$938$	−9.15175	+	5.28376i	−0.298815	+	0.172521i
$939$		0			0
$940$	−2.70129	+	0.596620i	−0.0881063	+	0.0194596i
$941$	12.7272	−	22.0442i	0.414896	−	0.718621i	−0.580521	−	0.814245i	$-0.697151\pi$
$941$	12.7272	−	22.0442i	0.414896	−	0.718621i	0.995418	+	0.0956239i	$0.0304846\pi$
$942$		0			0
$943$	12.2284	−	7.06008i	0.398212	−	0.229908i
$944$	11.2363			0.365710
$945$		0			0
$946$	−5.23255			−0.170125
$947$	22.3214	−	12.8873i	0.725349	−	0.418780i	−0.0913692	−	0.995817i	$-0.529124\pi$
$947$	22.3214	−	12.8873i	0.725349	−	0.418780i	0.816718	+	0.577037i	$0.195791\pi$
$948$		0			0
$949$	−0.168710	+	0.292214i	−0.00547655	+	0.00948566i
$950$	2.00279	−	2.85067i	0.0649790	−	0.0924880i
$951$		0			0
$952$	0.815547	−	0.470856i	0.0264320	−	0.0152605i
$953$			22.9367i			0.742993i	0.928434	+	0.371496i	$0.121155\pi$
$953$			22.9367i			0.742993i	−0.928434	+	0.371496i	$0.878845\pi$
$954$		0			0
$955$	−30.9444	+	28.3103i	−1.00134	+	0.916101i
$956$	7.82955	+	13.5612i	0.253226	+	0.438600i
$957$		0			0
$958$	−25.0333	−	14.4530i	−0.808790	−	0.466955i
$959$	−4.70113	+	8.14260i	−0.151807	+	0.262938i
$960$		0			0
$961$	−41.1195	−	71.2210i	−1.32644	−	2.29745i
$962$			0.0351035i			0.00113178i
$963$		0			0
$964$	11.1341			0.358604
$965$	−16.0578	+	50.7886i	−0.516918	+	1.63494i
$966$		0			0
$967$	32.6257	+	18.8365i	1.04917	+	0.605740i	0.922418	−	0.386194i	$-0.126211\pi$
$967$	32.6257	+	18.8365i	1.04917	+	0.605740i	0.126755	+	0.991934i	$0.459544\pi$
$968$	8.42745	+	4.86559i	0.270868	+	0.156386i
$969$		0			0
$970$	−3.69333	−	1.16771i	−0.118586	−	0.0374931i
$971$	−38.7928			−1.24492			−0.622461	−	0.782651i	$-0.713867\pi$
$971$	−38.7928			−1.24492			−0.622461	+	0.782651i	$0.713867\pi$
$972$		0			0
$973$		−	19.1744i		−	0.614702i
$974$	−7.84732	−	13.5920i	−0.251444	−	0.435514i
$975$		0			0
$976$	−3.62772	+	6.28340i	−0.116120	+	0.201127i
$977$	−4.46694	−	2.57899i	−0.142910	−	0.0825092i	0.426840	−	0.904327i	$-0.359627\pi$
$977$	−4.46694	−	2.57899i	−0.142910	−	0.0825092i	−0.569750	+	0.821818i	$0.692960\pi$
$978$		0			0
$979$	1.57326	+	2.72496i	0.0502815	+	0.0870900i
$980$	−1.64980	+	1.50936i	−0.0527008	+	0.0482148i
$981$		0			0
$982$			21.1644i			0.675383i
$983$	−35.2161	+	20.3320i	−1.12322	+	0.648491i	−0.942221	−	0.334993i	$-0.891266\pi$
$983$	−35.2161	+	20.3320i	−1.12322	+	0.648491i	−0.180998	+	0.983483i	$0.557933\pi$
$984$		0			0
$985$	−19.8381	+	4.38155i	−0.632096	+	0.139608i
$986$	−1.51078	+	2.61674i	−0.0481129	+	0.0833340i
$987$		0			0
$988$	0.0762860	−	0.0440437i	0.00242698	−	0.00140122i
$989$	9.20862			0.292817
$990$		0			0
$991$	22.8853			0.726974			0.363487	−	0.931599i	$-0.381586\pi$
$991$	22.8853			0.726974			0.363487	+	0.931599i	$0.381586\pi$
$992$	9.21571	−	5.32069i	0.292599	−	0.168932i
$993$		0			0
$994$	−5.21702	+	9.03615i	−0.165474	+	0.286609i
$995$	0.686075	+	3.10631i	0.0217500	+	0.0984766i
$996$		0			0
$997$	26.9663	−	15.5690i	0.854031	−	0.493075i	−0.00797786	−	0.999968i	$-0.502539\pi$
$997$	26.9663	−	15.5690i	0.854031	−	0.493075i	0.862009	+	0.506893i	$0.169206\pi$
$998$			15.5000i			0.490645i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.z.b.1009.1		24
3.2	odd	2		630.2.z.b.589.11	yes	24
5.4	even	2	inner	1890.2.z.b.1009.11		24
9.2	odd	6		630.2.z.b.169.2	✓	24
9.7	even	3	inner	1890.2.z.b.1639.11		24
15.14	odd	2		630.2.z.b.589.2	yes	24
45.29	odd	6		630.2.z.b.169.11	yes	24
45.34	even	6	inner	1890.2.z.b.1639.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.z.b.169.2	✓	24	9.2	odd	6
630.2.z.b.169.11	yes	24	45.29	odd	6
630.2.z.b.589.2	yes	24	15.14	odd	2
630.2.z.b.589.11	yes	24	3.2	odd	2
1890.2.z.b.1009.1		24	1.1	even	1	trivial
1890.2.z.b.1009.11		24	5.4	even	2	inner
1890.2.z.b.1639.1		24	45.34	even	6	inner
1890.2.z.b.1639.11		24	9.7	even	3	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.482247 - 2.18345i) q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.482247 - 2.18345i) q^{5} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(1.50936 + 1.64980i) q^{10} +(-0.563211 - 0.975509i) q^{11} +(0.109484 + 0.0632106i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +0.941713i q^{17} +0.696778 q^{19} +(-2.13204 - 0.674085i) q^{20} +(0.975509 + 0.563211i) q^{22} +(-1.71677 - 0.991178i) q^{23} +(-4.53488 + 2.10592i) q^{25} -0.126421 q^{26} +1.00000i q^{28} +(-1.60428 - 2.77870i) q^{29} +(5.32069 - 9.21571i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.470856 - 0.815547i) q^{34} +(1.50936 + 1.64980i) q^{35} -0.277671i q^{37} +(-0.603427 + 0.348389i) q^{38} +(2.18345 - 0.482247i) q^{40} +(-3.56146 + 6.16862i) q^{41} +(-4.02294 + 2.32264i) q^{43} -1.12642 q^{44} +1.98236 q^{46} +(1.07142 - 0.618584i) q^{47} +(0.500000 - 0.866025i) q^{49} +(2.87436 - 4.09122i) q^{50} +(0.109484 - 0.0632106i) q^{52} -1.76768i q^{53} +(-1.85837 + 1.70018i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(2.77870 + 1.60428i) q^{58} +(-5.61814 + 9.73091i) q^{59} +(-3.62772 - 6.28340i) q^{61} +10.6414i q^{62} -1.00000 q^{64} +(0.0852186 - 0.269535i) q^{65} +(-9.15175 - 5.28376i) q^{67} +(0.815547 + 0.470856i) q^{68} +(-2.13204 - 0.674085i) q^{70} -10.4340 q^{71} +2.66901i q^{73} +(0.138836 + 0.240470i) q^{74} +(0.348389 - 0.603427i) q^{76} +(0.975509 + 0.563211i) q^{77} +(5.40386 + 9.35976i) q^{79} +(-1.64980 + 1.50936i) q^{80} -7.12291i q^{82} +(-9.57479 + 5.52801i) q^{83} +(2.05618 - 0.454138i) q^{85} +(2.32264 - 4.02294i) q^{86} +(0.975509 - 0.563211i) q^{88} -2.79337 q^{89} -0.126421 q^{91} +(-1.71677 + 0.991178i) q^{92} +(-0.618584 + 1.07142i) q^{94} +(-0.336019 - 1.52138i) q^{95} +(-1.50021 + 0.866148i) q^{97} +1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 2 q^{5}+O(q^{10}) \) 24 * q + 12 * q^4 + 2 * q^5	\( 24 q + 12 q^{4} + 2 q^{5} - 4 q^{10} - 4 q^{11} + 12 q^{14} - 12 q^{16} + 32 q^{19} - 2 q^{20} + 16 q^{26} - 20 q^{29} + 36 q^{31} - 4 q^{35} - 2 q^{40} + 20 q^{41} - 8 q^{44} - 32 q^{46} + 12 q^{49} + 28 q^{55} - 12 q^{56} + 16 q^{61} - 24 q^{64} - 16 q^{65} - 2 q^{70} - 24 q^{71} - 44 q^{74} + 16 q^{76} - 68 q^{79} - 4 q^{80} + 26 q^{85} + 24 q^{86} - 40 q^{89} + 16 q^{91} - 48 q^{94} + 50 q^{95}+O(q^{100}) \) 24 * q + 12 * q^4 + 2 * q^5 - 4 * q^10 - 4 * q^11 + 12 * q^14 - 12 * q^16 + 32 * q^19 - 2 * q^20 + 16 * q^26 - 20 * q^29 + 36 * q^31 - 4 * q^35 - 2 * q^40 + 20 * q^41 - 8 * q^44 - 32 * q^46 + 12 * q^49 + 28 * q^55 - 12 * q^56 + 16 * q^61 - 24 * q^64 - 16 * q^65 - 2 * q^70 - 24 * q^71 - 44 * q^74 + 16 * q^76 - 68 * q^79 - 4 * q^80 + 26 * q^85 + 24 * q^86 - 40 * q^89 + 16 * q^91 - 48 * q^94 + 50 * q^95

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