LMFDB - Embedded newform 1458.2.c.f.973.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1458,2,Mod(487,1458)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1458.487"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1458, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1458 = 2 \cdot 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1458.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-6,0,-6,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$11.6421886147$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			973.3
Root			$0.500000 + 1.80139i$ of defining polynomial
Character	$\chi$	$=$	1458.973
Dual form			1458.2.c.f.487.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.04401 + 1.80828i) q^{5} +(2.00610 + 3.47467i) q^{7} +1.00000 q^{8} +2.08802 q^{10} +(-0.106223 - 0.183984i) q^{11} +(-2.59951 + 4.50249i) q^{13} +(2.00610 - 3.47467i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.78552 q^{17} -1.27281 q^{19} +(-1.04401 - 1.80828i) q^{20} +(-0.106223 + 0.183984i) q^{22} +(-0.414721 + 0.718318i) q^{23} +(0.320093 + 0.554417i) q^{25} +5.19903 q^{26} -4.01220 q^{28} +(-4.60562 - 7.97716i) q^{29} +(-1.76795 + 3.06218i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.89276 - 3.27836i) q^{34} -8.37755 q^{35} +3.55460 q^{37} +(0.636405 + 1.10229i) q^{38} +(-1.04401 + 1.80828i) q^{40} +(-1.36970 + 2.37239i) q^{41} +(-3.44827 - 5.97257i) q^{43} +0.212447 q^{44} +0.829442 q^{46} +(0.638637 + 1.10615i) q^{47} +(-4.54889 + 7.87892i) q^{49} +(0.320093 - 0.554417i) q^{50} +(-2.59951 - 4.50249i) q^{52} -11.2992 q^{53} +0.443592 q^{55} +(2.00610 + 3.47467i) q^{56} +(-4.60562 + 7.97716i) q^{58} +(4.27993 - 7.41305i) q^{59} +(-1.41684 - 2.45404i) q^{61} +3.53590 q^{62} +1.00000 q^{64} +(-5.42783 - 9.40127i) q^{65} +(-4.88028 + 8.45289i) q^{67} +(-1.89276 + 3.27836i) q^{68} +(4.18878 + 7.25517i) q^{70} -11.7241 q^{71} +0.750325 q^{73} +(-1.77730 - 3.07838i) q^{74} +(0.636405 - 1.10229i) q^{76} +(0.426190 - 0.738183i) q^{77} +(1.18389 + 2.05056i) q^{79} +2.08802 q^{80} +2.73940 q^{82} +(5.70024 + 9.87311i) q^{83} +(-3.95212 + 6.84527i) q^{85} +(-3.44827 + 5.97257i) q^{86} +(-0.106223 - 0.183984i) q^{88} +5.39625 q^{89} -20.8596 q^{91} +(-0.414721 - 0.718318i) q^{92} +(0.638637 - 1.10615i) q^{94} +(1.32882 - 2.30159i) q^{95} +(6.28158 + 10.8800i) q^{97} +9.09779 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 12 q^{8} + 6 q^{10} - 3 q^{11} - 9 q^{13} - 6 q^{14} - 6 q^{16} + 12 q^{17} + 18 q^{19} - 3 q^{20} - 3 q^{22} + 3 q^{23} - 15 q^{25} + 18 q^{26} + 12 q^{28}+ \cdots + 24 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 12 * q^8 + 6 * q^10 - 3 * q^11 - 9 * q^13 - 6 * q^14 - 6 * q^16 + 12 * q^17 + 18 * q^19 - 3 * q^20 - 3 * q^22 + 3 * q^23 - 15 * q^25 + 18 * q^26 + 12 * q^28 - 3 * q^29 - 12 * q^31 - 6 * q^32 - 6 * q^34 - 6 * q^35 + 30 * q^37 - 9 * q^38 - 3 * q^40 - 3 * q^41 - 12 * q^43 + 6 * q^44 - 6 * q^46 + 9 * q^47 - 12 * q^49 - 15 * q^50 - 9 * q^52 - 12 * q^53 + 18 * q^55 - 6 * q^56 - 3 * q^58 + 3 * q^59 - 12 * q^61 + 24 * q^62 + 12 * q^64 + 3 * q^65 - 21 * q^67 - 6 * q^68 + 3 * q^70 - 24 * q^71 + 42 * q^73 - 15 * q^74 - 9 * q^76 + 3 * q^77 + 6 * q^80 + 6 * q^82 + 27 * q^83 - 12 * q^86 - 3 * q^88 - 24 * q^89 + 12 * q^91 + 3 * q^92 + 9 * q^94 + 30 * q^95 - 18 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1458\mathbb{Z}\right)^\times$.

$n$	$731$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.04401	+	1.80828i	−0.466895	+	0.808685i	−0.999285	−	0.0378137i	$-0.987961\pi$
$5$	−1.04401	+	1.80828i	−0.466895	+	0.808685i	0.532390	+	0.846499i	$0.321294\pi$
$6$		0			0
$7$	2.00610	+	3.47467i	0.758235	+	1.31330i	0.943750	+	0.330661i	$0.107272\pi$
$7$	2.00610	+	3.47467i	0.758235	+	1.31330i	−0.185514	+	0.982642i	$0.559395\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	2.08802			0.660289
$11$	−0.106223	−	0.183984i	−0.0320276	−	0.0554733i	0.849567	−	0.527480i	$-0.176863\pi$
$11$	−0.106223	−	0.183984i	−0.0320276	−	0.0554733i	−0.881595	+	0.472007i	$0.843530\pi$
$12$		0			0
$13$	−2.59951	+	4.50249i	−0.720975	+	1.24877i	0.239634	+	0.970863i	$0.422973\pi$
$13$	−2.59951	+	4.50249i	−0.720975	+	1.24877i	−0.960609	+	0.277903i	$0.910361\pi$
$14$	2.00610	−	3.47467i	0.536153	−	0.928645i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.78552			0.918124			0.459062	−	0.888404i	$-0.348186\pi$
$17$	3.78552			0.918124			0.459062	+	0.888404i	$0.348186\pi$
$18$		0			0
$19$	−1.27281			−0.292002			−0.146001	−	0.989284i	$-0.546640\pi$
$19$	−1.27281			−0.292002			−0.146001	+	0.989284i	$0.546640\pi$
$20$	−1.04401	−	1.80828i	−0.233447	−	0.404343i
$21$		0			0
$22$	−0.106223	+	0.183984i	−0.0226469	+	0.0392256i
$23$	−0.414721	+	0.718318i	−0.0864753	+	0.149780i	−0.906019	−	0.423237i	$-0.860894\pi$
$23$	−0.414721	+	0.718318i	−0.0864753	+	0.149780i	0.819544	+	0.573017i	$0.194227\pi$
$24$		0			0
$25$	0.320093	+	0.554417i	0.0640186	+	0.110883i
$26$	5.19903			1.01961
$27$		0			0
$28$	−4.01220			−0.758235
$29$	−4.60562	−	7.97716i	−0.855241	−	1.48132i	−0.876421	−	0.481546i	$-0.840075\pi$
$29$	−4.60562	−	7.97716i	−0.855241	−	1.48132i	0.0211794	−	0.999776i	$-0.493258\pi$
$30$		0			0
$31$	−1.76795	+	3.06218i	−0.317534	+	0.549984i	−0.979973	−	0.199131i	$-0.936188\pi$
$31$	−1.76795	+	3.06218i	−0.317534	+	0.549984i	0.662439	+	0.749116i	$0.269521\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−1.89276	−	3.27836i	−0.324606	−	0.562234i
$35$	−8.37755			−1.41606
$36$		0			0
$37$	3.55460			0.584373			0.292187	−	0.956361i	$-0.405617\pi$
$37$	3.55460			0.584373			0.292187	+	0.956361i	$0.405617\pi$
$38$	0.636405	+	1.10229i	0.103238	+	0.178814i
$39$		0			0
$40$	−1.04401	+	1.80828i	−0.165072	+	0.285913i
$41$	−1.36970	+	2.37239i	−0.213911	+	0.370504i	−0.952935	−	0.303174i	$-0.901954\pi$
$41$	−1.36970	+	2.37239i	−0.213911	+	0.370504i	0.739024	+	0.673679i	$0.235287\pi$
$42$		0			0
$43$	−3.44827	−	5.97257i	−0.525856	−	0.910809i	−0.999546	−	0.0301176i	$-0.990412\pi$
$43$	−3.44827	−	5.97257i	−0.525856	−	0.910809i	0.473691	−	0.880691i	$-0.342922\pi$
$44$	0.212447			0.0320276
$45$		0			0
$46$	0.829442			0.122295
$47$	0.638637	+	1.10615i	0.0931547	+	0.161349i	0.908837	−	0.417151i	$-0.136972\pi$
$47$	0.638637	+	1.10615i	0.0931547	+	0.161349i	−0.815682	+	0.578500i	$0.803638\pi$
$48$		0			0
$49$	−4.54889	+	7.87892i	−0.649842	+	1.12556i
$50$	0.320093	−	0.554417i	0.0452680	−	0.0784064i
$51$		0			0
$52$	−2.59951	−	4.50249i	−0.360488	−	0.624383i
$53$	−11.2992			−1.55207			−0.776036	−	0.630689i	$-0.782772\pi$
$53$	−11.2992			−1.55207			−0.776036	+	0.630689i	$0.782772\pi$
$54$		0			0
$55$	0.443592			0.0598140
$56$	2.00610	+	3.47467i	0.268077	+	0.464322i
$57$		0			0
$58$	−4.60562	+	7.97716i	−0.604747	+	1.04745i
$59$	4.27993	−	7.41305i	0.557199	−	0.965097i	−0.440530	−	0.897738i	$-0.645209\pi$
$59$	4.27993	−	7.41305i	0.557199	−	0.965097i	0.997729	−	0.0673590i	$-0.0214573\pi$
$60$		0			0
$61$	−1.41684	−	2.45404i	−0.181408	−	0.314208i	0.760952	−	0.648808i	$-0.224732\pi$
$61$	−1.41684	−	2.45404i	−0.181408	−	0.314208i	−0.942360	+	0.334600i	$0.891399\pi$
$62$	3.53590			0.449060
$63$		0			0
$64$	1.00000			0.125000
$65$	−5.42783	−	9.40127i	−0.673239	−	1.16608i
$66$		0			0
$67$	−4.88028	+	8.45289i	−0.596221	+	1.03268i	0.397153	+	0.917753i	$0.369998\pi$
$67$	−4.88028	+	8.45289i	−0.596221	+	1.03268i	−0.993373	+	0.114932i	$0.963335\pi$
$68$	−1.89276	+	3.27836i	−0.229531	+	0.397559i
$69$		0			0
$70$	4.18878	+	7.25517i	0.500654	+	0.867159i
$71$	−11.7241			−1.39140			−0.695700	−	0.718333i	$-0.744906\pi$
$71$	−11.7241			−1.39140			−0.695700	+	0.718333i	$0.744906\pi$
$72$		0			0
$73$	0.750325			0.0878189			0.0439094	−	0.999036i	$-0.486019\pi$
$73$	0.750325			0.0878189			0.0439094	+	0.999036i	$0.486019\pi$
$74$	−1.77730	−	3.07838i	−0.206607	−	0.357854i
$75$		0			0
$76$	0.636405	−	1.10229i	0.0730006	−	0.126441i
$77$	0.426190	−	0.738183i	0.0485689	−	0.0841237i
$78$		0			0
$79$	1.18389	+	2.05056i	0.133198	+	0.230706i	0.924908	−	0.380192i	$-0.124142\pi$
$79$	1.18389	+	2.05056i	0.133198	+	0.230706i	−0.791710	+	0.610898i	$0.790809\pi$
$80$	2.08802			0.233447
$81$		0			0
$82$	2.73940			0.302516
$83$	5.70024	+	9.87311i	0.625683	+	1.08371i	0.988408	+	0.151819i	$0.0485130\pi$
$83$	5.70024	+	9.87311i	0.625683	+	1.08371i	−0.362725	+	0.931896i	$0.618154\pi$
$84$		0			0
$85$	−3.95212	+	6.84527i	−0.428667	+	0.742474i
$86$	−3.44827	+	5.97257i	−0.371836	+	0.644039i
$87$		0			0
$88$	−0.106223	−	0.183984i	−0.0113235	−	0.0196128i
$89$	5.39625			0.572001			0.286001	−	0.958229i	$-0.407674\pi$
$89$	5.39625			0.572001			0.286001	+	0.958229i	$0.407674\pi$
$90$		0			0
$91$	−20.8596			−2.18668
$92$	−0.414721	−	0.718318i	−0.0432377	−	0.0748898i
$93$		0			0
$94$	0.638637	−	1.10615i	0.0658703	−	0.114091i
$95$	1.32882	−	2.30159i	0.136334	−	0.236138i
$96$		0			0
$97$	6.28158	+	10.8800i	0.637798	+	1.10470i	0.985915	+	0.167247i	$0.0534878\pi$
$97$	6.28158	+	10.8800i	0.637798	+	1.10470i	−0.348117	+	0.937451i	$0.613179\pi$
$98$	9.09779			0.919015
$99$		0			0
$100$	−0.640186			−0.0640186
$101$	1.44726	+	2.50673i	0.144008	+	0.249429i	0.929002	−	0.370074i	$-0.120668\pi$
$101$	1.44726	+	2.50673i	0.144008	+	0.249429i	−0.784995	+	0.619503i	$0.787334\pi$
$102$		0			0
$103$	−8.34501	+	14.4540i	−0.822258	+	1.42419i	0.0817382	+	0.996654i	$0.473953\pi$
$103$	−8.34501	+	14.4540i	−0.822258	+	1.42419i	−0.903997	+	0.427540i	$0.859380\pi$
$104$	−2.59951	+	4.50249i	−0.254903	+	0.441505i
$105$		0			0
$106$	5.64962	+	9.78544i	0.548740	+	0.950446i
$107$	0.321371			0.0310681			0.0155341	−	0.999879i	$-0.495055\pi$
$107$	0.321371			0.0310681			0.0155341	+	0.999879i	$0.495055\pi$
$108$		0			0
$109$	0.568378			0.0544407			0.0272204	−	0.999629i	$-0.491334\pi$
$109$	0.568378			0.0544407			0.0272204	+	0.999629i	$0.491334\pi$
$110$	−0.221796	−	0.384162i	−0.0211474	−	0.0366284i
$111$		0			0
$112$	2.00610	−	3.47467i	0.189559	−	0.328326i
$113$	0.679907	−	1.17763i	0.0639603	−	0.110782i	−0.832272	−	0.554367i	$-0.812960\pi$
$113$	0.679907	−	1.17763i	0.0639603	−	0.110782i	0.896232	+	0.443585i	$0.146294\pi$
$114$		0			0
$115$	−0.865945	−	1.49986i	−0.0807498	−	0.139863i
$116$	9.21123			0.855241
$117$		0			0
$118$	−8.55985			−0.787998
$119$	7.59415	+	13.1534i	0.696154	+	1.20577i
$120$		0			0
$121$	5.47743	−	9.48719i	0.497948	−	0.862472i
$122$	−1.41684	+	2.45404i	−0.128275	+	0.222178i
$123$		0			0
$124$	−1.76795	−	3.06218i	−0.158767	−	0.274992i
$125$	−11.7768			−1.05335
$126$		0			0
$127$	1.80401			0.160080			0.0800402	−	0.996792i	$-0.474495\pi$
$127$	1.80401			0.160080			0.0800402	+	0.996792i	$0.474495\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−5.42783	+	9.40127i	−0.476052	+	0.824546i
$131$	4.85721	−	8.41294i	0.424377	−	0.735042i	−0.571985	−	0.820264i	$-0.693827\pi$
$131$	4.85721	−	8.41294i	0.424377	−	0.735042i	0.996362	+	0.0852218i	$0.0271599\pi$
$132$		0			0
$133$	−2.55339	−	4.42259i	−0.221407	−	0.383488i
$134$	9.76056			0.843184
$135$		0			0
$136$	3.78552			0.324606
$137$	4.53396	+	7.85305i	0.387363	+	0.670932i	0.992094	−	0.125498i	$-0.0400528\pi$
$137$	4.53396	+	7.85305i	0.387363	+	0.670932i	−0.604731	+	0.796430i	$0.706720\pi$
$138$		0			0
$139$	5.02044	−	8.69565i	0.425828	−	0.737555i	−0.570670	−	0.821180i	$-0.693316\pi$
$139$	5.02044	−	8.69565i	0.425828	−	0.737555i	0.996497	+	0.0836244i	$0.0266496\pi$
$140$	4.18878	−	7.25517i	0.354016	−	0.613174i
$141$		0			0
$142$	5.86207	+	10.1534i	0.491934	+	0.852055i
$143$	1.10452			0.0923643
$144$		0			0
$145$	19.2332			1.59723
$146$	−0.375162	−	0.649800i	−0.0310487	−	0.0537779i
$147$		0			0
$148$	−1.77730	+	3.07838i	−0.146093	+	0.253041i
$149$	−7.92122	+	13.7200i	−0.648931	+	1.12398i	0.334447	+	0.942415i	$0.391450\pi$
$149$	−7.92122	+	13.7200i	−0.648931	+	1.12398i	−0.983378	+	0.181568i	$0.941883\pi$
$150$		0			0
$151$	−2.65377	−	4.59647i	−0.215961	−	0.374056i	0.737608	−	0.675229i	$-0.235955\pi$
$151$	−2.65377	−	4.59647i	−0.215961	−	0.374056i	−0.953569	+	0.301173i	$0.902622\pi$
$152$	−1.27281			−0.103238
$153$		0			0
$154$	−0.852380			−0.0686867
$155$	−3.69151	−	6.39389i	−0.296510	−	0.513570i
$156$		0			0
$157$	5.75852	−	9.97404i	0.459580	−	0.796015i	−0.539359	−	0.842076i	$-0.681333\pi$
$157$	5.75852	−	9.97404i	0.459580	−	0.796015i	0.998939	+	0.0460607i	$0.0146668\pi$
$158$	1.18389	−	2.05056i	0.0941852	−	0.163134i
$159$		0			0
$160$	−1.04401	−	1.80828i	−0.0825361	−	0.142957i
$161$	−3.32789			−0.262275
$162$		0			0
$163$	7.66336			0.600241			0.300120	−	0.953901i	$-0.402973\pi$
$163$	7.66336			0.600241			0.300120	+	0.953901i	$0.402973\pi$
$164$	−1.36970	−	2.37239i	−0.106955	−	0.185252i
$165$		0			0
$166$	5.70024	−	9.87311i	0.442425	−	0.766302i
$167$	−3.05500	+	5.29141i	−0.236403	+	0.409461i	−0.959679	−	0.281097i	$-0.909302\pi$
$167$	−3.05500	+	5.29141i	−0.236403	+	0.409461i	0.723277	+	0.690558i	$0.242635\pi$
$168$		0			0
$169$	−7.01494	−	12.1502i	−0.539611	−	0.934634i
$170$	7.90424			0.606227
$171$		0			0
$172$	6.89653			0.525856
$173$	5.65174	+	9.78911i	0.429694	+	0.744252i	0.996846	−	0.0793612i	$-0.0252881\pi$
$173$	5.65174	+	9.78911i	0.429694	+	0.744252i	−0.567152	+	0.823613i	$0.691955\pi$
$174$		0			0
$175$	−1.28428	+	2.22444i	−0.0970823	+	0.168151i
$176$	−0.106223	+	0.183984i	−0.00800689	+	0.0138683i
$177$		0			0
$178$	−2.69813	−	4.67329i	−0.202233	−	0.350278i
$179$	6.92990			0.517965			0.258982	−	0.965882i	$-0.416613\pi$
$179$	6.92990			0.517965			0.258982	+	0.965882i	$0.416613\pi$
$180$		0			0
$181$	3.03763			0.225785			0.112893	−	0.993607i	$-0.463988\pi$
$181$	3.03763			0.225785			0.112893	+	0.993607i	$0.463988\pi$
$182$	10.4298	+	18.0649i	0.773107	+	1.33906i
$183$		0			0
$184$	−0.414721	+	0.718318i	−0.0305736	+	0.0529551i
$185$	−3.71104	+	6.42770i	−0.272841	+	0.472574i
$186$		0			0
$187$	−0.402111	−	0.696477i	−0.0294053	−	0.0509314i
$188$	−1.27727			−0.0931547
$189$		0			0
$190$	−2.65765			−0.192806
$191$	2.54859	+	4.41429i	0.184409	+	0.319407i	0.943377	−	0.331721i	$-0.107629\pi$
$191$	2.54859	+	4.41429i	0.184409	+	0.319407i	−0.758968	+	0.651128i	$0.774296\pi$
$192$		0			0
$193$	−9.43413	+	16.3404i	−0.679084	+	1.17621i	0.296173	+	0.955134i	$0.404289\pi$
$193$	−9.43413	+	16.3404i	−0.679084	+	1.17621i	−0.975257	+	0.221073i	$0.929044\pi$
$194$	6.28158	−	10.8800i	0.450991	−	0.781140i
$195$		0			0
$196$	−4.54889	−	7.87892i	−0.324921	−	0.562780i
$197$	−20.0440			−1.42807			−0.714036	−	0.700109i	$-0.753135\pi$
$197$	−20.0440			−1.42807			−0.714036	+	0.700109i	$0.753135\pi$
$198$		0			0
$199$	5.50212			0.390035			0.195018	−	0.980800i	$-0.437524\pi$
$199$	5.50212			0.390035			0.195018	+	0.980800i	$0.437524\pi$
$200$	0.320093	+	0.554417i	0.0226340	+	0.0392032i
$201$		0			0
$202$	1.44726	−	2.50673i	0.101829	−	0.176373i
$203$	18.4787	−	32.0060i	1.29695	−	2.24638i
$204$		0			0
$205$	−2.85995	−	4.95358i	−0.199748	−	0.345973i
$206$	16.6900			1.16285
$207$		0			0
$208$	5.19903			0.360488
$209$	0.135202	+	0.234177i	0.00935213	+	0.0161984i
$210$		0			0
$211$	12.5726	−	21.7763i	0.865531	−	1.49914i	−0.000987489	−	1.00000i	$-0.500314\pi$
$211$	12.5726	−	21.7763i	0.865531	−	1.49914i	0.866519	−	0.499145i	$-0.166352\pi$
$212$	5.64962	−	9.78544i	0.388018	−	0.672067i
$213$		0			0
$214$	−0.160686	−	0.278316i	−0.0109842	−	0.0190253i
$215$	14.4001			0.982077
$216$		0			0
$217$	−14.1868			−0.963061
$218$	−0.284189	−	0.492229i	−0.0192477	−	0.0333380i
$219$		0			0
$220$	−0.221796	+	0.384162i	−0.0149535	+	0.0259002i
$221$	−9.84052	+	17.0443i	−0.661945	+	1.14652i
$222$		0			0
$223$	1.87620	+	3.24967i	0.125639	+	0.217614i	0.921983	−	0.387231i	$-0.126568\pi$
$223$	1.87620	+	3.24967i	0.125639	+	0.217614i	−0.796343	+	0.604845i	$0.793235\pi$
$224$	−4.01220			−0.268077
$225$		0			0
$226$	−1.35981			−0.0904535
$227$	−9.36384	−	16.2186i	−0.621500	−	1.07647i	−0.989207	−	0.146528i	$-0.953190\pi$
$227$	−9.36384	−	16.2186i	−0.621500	−	1.07647i	0.367707	−	0.929942i	$-0.380143\pi$
$228$		0			0
$229$	2.07166	−	3.58822i	0.136899	−	0.237117i	−0.789422	−	0.613851i	$-0.789620\pi$
$229$	2.07166	−	3.58822i	0.136899	−	0.237117i	0.926321	+	0.376734i	$0.122953\pi$
$230$	−0.865945	+	1.49986i	−0.0570987	+	0.0988979i
$231$		0			0
$232$	−4.60562	−	7.97716i	−0.302374	−	0.523726i
$233$	−1.91711			−0.125594			−0.0627971	−	0.998026i	$-0.520002\pi$
$233$	−1.91711			−0.125594			−0.0627971	+	0.998026i	$0.520002\pi$
$234$		0			0
$235$	−2.66697			−0.173974
$236$	4.27993	+	7.41305i	0.278600	+	0.482548i
$237$		0			0
$238$	7.59415	−	13.1534i	0.492255	−	0.852611i
$239$	−12.0996	+	20.9572i	−0.782660	+	1.35561i	0.147727	+	0.989028i	$0.452804\pi$
$239$	−12.0996	+	20.9572i	−0.782660	+	1.35561i	−0.930387	+	0.366579i	$0.880529\pi$
$240$		0			0
$241$	−6.60247	−	11.4358i	−0.425302	−	0.736645i	0.571146	−	0.820848i	$-0.306499\pi$
$241$	−6.60247	−	11.4358i	−0.425302	−	0.736645i	−0.996449	+	0.0842031i	$0.973166\pi$
$242$	−10.9549			−0.704205
$243$		0			0
$244$	2.83368			0.181408
$245$	−9.49817	−	16.4513i	−0.606816	−	1.05104i
$246$		0			0
$247$	3.30869	−	5.73081i	0.210527	−	0.364643i
$248$	−1.76795	+	3.06218i	−0.112265	+	0.194449i
$249$		0			0
$250$	5.88840	+	10.1990i	0.372415	+	0.645042i
$251$	−8.65988			−0.546607			−0.273303	−	0.961928i	$-0.588116\pi$
$251$	−8.65988			−0.546607			−0.273303	+	0.961928i	$0.588116\pi$
$252$		0			0
$253$	0.176212			0.0110784
$254$	−0.902007	−	1.56232i	−0.0565970	−	0.0980288i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.9154	+	18.9060i	−0.680883	+	1.17932i	0.293829	+	0.955858i	$0.405071\pi$
$257$	−10.9154	+	18.9060i	−0.680883	+	1.17932i	−0.974712	+	0.223466i	$0.928263\pi$
$258$		0			0
$259$	7.13090	+	12.3511i	0.443092	+	0.767459i
$260$	10.8557			0.673239
$261$		0			0
$262$	−9.71443			−0.600159
$263$	2.84376	+	4.92554i	0.175354	+	0.303722i	0.940284	−	0.340392i	$-0.110560\pi$
$263$	2.84376	+	4.92554i	0.175354	+	0.303722i	−0.764930	+	0.644114i	$0.777226\pi$
$264$		0			0
$265$	11.7965	−	20.4322i	0.724654	−	1.25514i
$266$	−2.55339	+	4.42259i	−0.156558	+	0.271167i
$267$		0			0
$268$	−4.88028	−	8.45289i	−0.298110	−	0.516342i
$269$	−22.7662			−1.38808			−0.694041	−	0.719936i	$-0.744171\pi$
$269$	−22.7662			−1.38808			−0.694041	+	0.719936i	$0.744171\pi$
$270$		0			0
$271$	−19.8340			−1.20483			−0.602414	−	0.798184i	$-0.705794\pi$
$271$	−19.8340			−1.20483			−0.602414	+	0.798184i	$0.705794\pi$
$272$	−1.89276	−	3.27836i	−0.114766	−	0.198780i
$273$		0			0
$274$	4.53396	−	7.85305i	0.273907	−	0.474420i
$275$	0.0680027	−	0.117784i	0.00410072	−	0.00710265i
$276$		0			0
$277$	12.0684	+	20.9031i	0.725121	+	1.25595i	0.958924	+	0.283662i	$0.0915495\pi$
$277$	12.0684	+	20.9031i	0.725121	+	1.25595i	−0.233803	+	0.972284i	$0.575117\pi$
$278$	−10.0409			−0.602211
$279$		0			0
$280$	−8.37755			−0.500654
$281$	11.8276	+	20.4861i	0.705578	+	1.22210i	0.966483	+	0.256732i	$0.0826458\pi$
$281$	11.8276	+	20.4861i	0.705578	+	1.22210i	−0.260905	+	0.965365i	$0.584021\pi$
$282$		0			0
$283$	5.81208	−	10.0668i	0.345492	−	0.598410i	−0.639951	−	0.768416i	$-0.721045\pi$
$283$	5.81208	−	10.0668i	0.345492	−	0.598410i	0.985443	+	0.170006i	$0.0543787\pi$
$284$	5.86207	−	10.1534i	0.347850	−	0.602494i
$285$		0			0
$286$	−0.552258	−	0.956539i	−0.0326557	−	0.0565614i
$287$	−10.9910			−0.648779
$288$		0			0
$289$	−2.66981			−0.157048
$290$	−9.61660	−	16.6564i	−0.564706	−	0.978100i
$291$		0			0
$292$	−0.375162	+	0.649800i	−0.0219547	+	0.0380267i
$293$	5.35546	−	9.27593i	0.312869	−	0.541906i	−0.666113	−	0.745851i	$-0.732043\pi$
$293$	5.35546	−	9.27593i	0.312869	−	0.541906i	0.978982	+	0.203945i	$0.0653765\pi$
$294$		0			0
$295$	8.93656	+	15.4786i	0.520307	+	0.901197i
$296$	3.55460			0.206607
$297$		0			0
$298$	15.8424			0.917728
$299$	−2.15615	−	3.73456i	−0.124693	−	0.215975i
$300$		0			0
$301$	13.8352	−	23.9632i	0.797445	−	1.38122i
$302$	−2.65377	+	4.59647i	−0.152708	+	0.264497i
$303$		0			0
$304$	0.636405	+	1.10229i	0.0365003	+	0.0632204i
$305$	5.91677			0.338793
$306$		0			0
$307$	24.7876			1.41470			0.707351	−	0.706862i	$-0.249890\pi$
$307$	24.7876			1.41470			0.707351	+	0.706862i	$0.249890\pi$
$308$	0.426190	+	0.738183i	0.0242844	+	0.0420619i
$309$		0			0
$310$	−3.69151	+	6.39389i	−0.209664	+	0.363148i
$311$	10.8918	−	18.8651i	0.617615	−	1.06974i	−0.372305	−	0.928111i	$-0.621432\pi$
$311$	10.8918	−	18.8651i	0.617615	−	1.06974i	0.989920	−	0.141630i	$-0.0452343\pi$
$312$		0			0
$313$	4.70123	+	8.14277i	0.265729	+	0.460257i	0.967754	−	0.251896i	$-0.0810539\pi$
$313$	4.70123	+	8.14277i	0.265729	+	0.460257i	−0.702025	+	0.712152i	$0.747721\pi$
$314$	−11.5170			−0.649944
$315$		0			0
$316$	−2.36778			−0.133198
$317$	7.25293	+	12.5625i	0.407365	+	0.705578i	0.994594	−	0.103844i	$-0.0331142\pi$
$317$	7.25293	+	12.5625i	0.407365	+	0.705578i	−0.587228	+	0.809421i	$0.699781\pi$
$318$		0			0
$319$	−0.978448	+	1.69472i	−0.0547826	+	0.0948862i
$320$	−1.04401	+	1.80828i	−0.0583618	+	0.101086i
$321$		0			0
$322$	1.66395	+	2.88204i	0.0927281	+	0.160610i
$323$	−4.81825			−0.268095
$324$		0			0
$325$	−3.32834			−0.184623
$326$	−3.83168	−	6.63666i	−0.212217	−	0.367571i
$327$		0			0
$328$	−1.36970	+	2.37239i	−0.0756289	+	0.130993i
$329$	−2.56234	+	4.43811i	−0.141266	+	0.244681i
$330$		0			0
$331$	−0.403370	−	0.698657i	−0.0221712	−	0.0384017i	0.854727	−	0.519078i	$-0.173725\pi$
$331$	−0.403370	−	0.698657i	−0.0221712	−	0.0384017i	−0.876898	+	0.480676i	$0.840391\pi$
$332$	−11.4005			−0.625683
$333$		0			0
$334$	6.10999			0.334324
$335$	−10.1901	−	17.6498i	−0.556745	−	0.964310i
$336$		0			0
$337$	13.3329	−	23.0933i	0.726289	−	1.25797i	−0.232152	−	0.972680i	$-0.574577\pi$
$337$	13.3329	−	23.0933i	0.726289	−	1.25797i	0.958441	−	0.285291i	$-0.0920901\pi$
$338$	−7.01494	+	12.1502i	−0.381563	+	0.660886i
$339$		0			0
$340$	−3.95212	−	6.84527i	−0.214334	−	0.371237i
$341$	0.751191			0.0406793
$342$		0			0
$343$	−8.41675			−0.454462
$344$	−3.44827	−	5.97257i	−0.185918	−	0.322020i
$345$		0			0
$346$	5.65174	−	9.78911i	0.303840	−	0.526266i
$347$	14.5521	−	25.2051i	0.781200	−	1.35308i	−0.150043	−	0.988680i	$-0.547941\pi$
$347$	14.5521	−	25.2051i	0.781200	−	1.35308i	0.931243	−	0.364399i	$-0.118726\pi$
$348$		0			0
$349$	14.7743	+	25.5898i	0.790848	+	1.36979i	0.925443	+	0.378888i	$0.123693\pi$
$349$	14.7743	+	25.5898i	0.790848	+	1.36979i	−0.134595	+	0.990901i	$0.542973\pi$
$350$	2.56856			0.137295
$351$		0			0
$352$	0.212447			0.0113235
$353$	−3.12628	−	5.41487i	−0.166395	−	0.288205i	0.770755	−	0.637132i	$-0.219879\pi$
$353$	−3.12628	−	5.41487i	−0.166395	−	0.288205i	−0.937150	+	0.348927i	$0.886546\pi$
$354$		0			0
$355$	12.2401	−	21.2005i	0.649637	−	1.12520i
$356$	−2.69813	+	4.67329i	−0.143000	+	0.247684i
$357$		0			0
$358$	−3.46495	−	6.00147i	−0.183128	−	0.317187i
$359$	−2.58629			−0.136499			−0.0682495	−	0.997668i	$-0.521741\pi$
$359$	−2.58629			−0.136499			−0.0682495	+	0.997668i	$0.521741\pi$
$360$		0			0
$361$	−17.3800			−0.914735
$362$	−1.51882	−	2.63067i	−0.0798272	−	0.138265i
$363$		0			0
$364$	10.4298	−	18.0649i	0.546669	−	0.946859i
$365$	−0.783345	+	1.35679i	−0.0410022	+	0.0710178i
$366$		0			0
$367$	−9.34060	−	16.1784i	−0.487575	−	0.844505i	0.512323	−	0.858793i	$-0.328785\pi$
$367$	−9.34060	−	16.1784i	−0.487575	−	0.844505i	−0.999898	+	0.0142879i	$0.995452\pi$
$368$	0.829442			0.0432377
$369$		0			0
$370$	7.42207			0.385855
$371$	−22.6675	−	39.2612i	−1.17684	−	2.03834i
$372$		0			0
$373$	−6.76307	+	11.7140i	−0.350178	+	0.606527i	−0.986281	−	0.165078i	$-0.947212\pi$
$373$	−6.76307	+	11.7140i	−0.350178	+	0.606527i	0.636102	+	0.771605i	$0.280546\pi$
$374$	−0.402111	+	0.696477i	−0.0207927	+	0.0360140i
$375$		0			0
$376$	0.638637	+	1.10615i	0.0329352	+	0.0570454i
$377$	47.8894			2.46643
$378$		0			0
$379$	30.2178			1.55218			0.776092	−	0.630620i	$-0.217199\pi$
$379$	30.2178			1.55218			0.776092	+	0.630620i	$0.217199\pi$
$380$	1.32882	+	2.30159i	0.0681672	+	0.118069i
$381$		0			0
$382$	2.54859	−	4.41429i	0.130397	−	0.225855i
$383$	19.2945	−	33.4191i	0.985904	−	1.70764i	0.348058	−	0.937473i	$-0.386841\pi$
$383$	19.2945	−	33.4191i	0.985904	−	1.70764i	0.637847	−	0.770163i	$-0.279825\pi$
$384$		0			0
$385$	0.889892	+	1.54134i	0.0453531	+	0.0785538i
$386$	18.8683			0.960369
$387$		0			0
$388$	−12.5632			−0.637798
$389$	2.81309	+	4.87242i	0.142629	+	0.247041i	0.928486	−	0.371367i	$-0.121111\pi$
$389$	2.81309	+	4.87242i	0.142629	+	0.247041i	−0.785857	+	0.618409i	$0.787778\pi$
$390$		0			0
$391$	−1.56994	+	2.71921i	−0.0793951	+	0.137516i
$392$	−4.54889	+	7.87892i	−0.229754	+	0.397945i
$393$		0			0
$394$	10.0220	+	17.3586i	0.504900	+	0.874512i
$395$	−4.94397			−0.248758
$396$		0			0
$397$	7.71618			0.387264			0.193632	−	0.981074i	$-0.437973\pi$
$397$	7.71618			0.387264			0.193632	+	0.981074i	$0.437973\pi$
$398$	−2.75106	−	4.76498i	−0.137898	−	0.238847i
$399$		0			0
$400$	0.320093	−	0.554417i	0.0160046	−	0.0277209i
$401$	−18.1897	+	31.5054i	−0.908349	+	1.57331i	−0.0919915	+	0.995760i	$0.529323\pi$
$401$	−18.1897	+	31.5054i	−0.908349	+	1.57331i	−0.816358	+	0.577547i	$0.804010\pi$
$402$		0			0
$403$	−9.19163	−	15.9204i	−0.457868	−	0.793050i
$404$	−2.89452			−0.144008
$405$		0			0
$406$	−36.9574			−1.83416
$407$	−0.377582	−	0.653991i	−0.0187160	−	0.0324171i
$408$		0			0
$409$	−2.93384	+	5.08156i	−0.145069	+	0.251267i	−0.929399	−	0.369077i	$-0.879674\pi$
$409$	−2.93384	+	5.08156i	−0.145069	+	0.251267i	0.784330	+	0.620344i	$0.213007\pi$
$410$	−2.85995	+	4.95358i	−0.141243	+	0.244640i
$411$		0			0
$412$	−8.34501	−	14.4540i	−0.411129	−	0.712097i
$413$	34.3439			1.68995
$414$		0			0
$415$	−23.8044			−1.16851
$416$	−2.59951	−	4.50249i	−0.127452	−	0.220753i
$417$		0			0
$418$	0.135202	−	0.234177i	0.00661295	−	0.0114540i
$419$	−10.5678	+	18.3040i	−0.516270	+	0.894207i	0.483551	+	0.875316i	$0.339347\pi$
$419$	−10.5678	+	18.3040i	−0.516270	+	0.894207i	−0.999822	+	0.0188905i	$0.993987\pi$
$420$		0			0
$421$	−3.72146	−	6.44575i	−0.181373	−	0.314147i	0.760976	−	0.648781i	$-0.224721\pi$
$421$	−3.72146	−	6.44575i	−0.181373	−	0.314147i	−0.942348	+	0.334634i	$0.891387\pi$
$422$	−25.1451			−1.22405
$423$		0			0
$424$	−11.2992			−0.548740
$425$	1.21172	+	2.09876i	0.0587770	+	0.101805i
$426$		0			0
$427$	5.68465	−	9.84611i	0.275100	−	0.476487i
$428$	−0.160686	+	0.278316i	−0.00776703	+	0.0134529i
$429$		0			0
$430$	−7.20004	−	12.4708i	−0.347217	−	0.601397i
$431$	−13.0502			−0.628607			−0.314303	−	0.949323i	$-0.601771\pi$
$431$	−13.0502			−0.628607			−0.314303	+	0.949323i	$0.601771\pi$
$432$		0			0
$433$	0.143533			0.00689775			0.00344887	−	0.999994i	$-0.498902\pi$
$433$	0.143533			0.00689775			0.00344887	+	0.999994i	$0.498902\pi$
$434$	7.09339	+	12.2861i	0.340493	+	0.589752i
$435$		0			0
$436$	−0.284189	+	0.492229i	−0.0136102	+	0.0235735i
$437$	0.527861	−	0.914282i	0.0252510	−	0.0437360i
$438$		0			0
$439$	−6.77826	−	11.7403i	−0.323509	−	0.560333i	0.657701	−	0.753279i	$-0.271529\pi$
$439$	−6.77826	−	11.7403i	−0.323509	−	0.560333i	−0.981209	+	0.192946i	$0.938196\pi$
$440$	0.443592			0.0211474
$441$		0			0
$442$	19.6810			0.936132
$443$	−6.14064	−	10.6359i	−0.291750	−	0.505327i	0.682473	−	0.730911i	$-0.260904\pi$
$443$	−6.14064	−	10.6359i	−0.291750	−	0.505327i	−0.974224	+	0.225584i	$0.927571\pi$
$444$		0			0
$445$	−5.63373	+	9.75791i	−0.267064	+	0.462569i
$446$	1.87620	−	3.24967i	0.0888405	−	0.153876i
$447$		0			0
$448$	2.00610	+	3.47467i	0.0947794	+	0.164163i
$449$	40.6646			1.91908			0.959540	−	0.281573i	$-0.0908563\pi$
$449$	40.6646			1.91908			0.959540	+	0.281573i	$0.0908563\pi$
$450$		0			0
$451$	0.581976			0.0274042
$452$	0.679907	+	1.17763i	0.0319801	+	0.0553912i
$453$		0			0
$454$	−9.36384	+	16.2186i	−0.439467	+	0.761179i
$455$	21.7776	−	37.7198i	1.02095	−	1.76833i
$456$		0			0
$457$	−16.2955	−	28.2246i	−0.762271	−	1.32029i	−0.941677	−	0.336517i	$-0.890751\pi$
$457$	−16.2955	−	28.2246i	−0.762271	−	1.32029i	0.179407	−	0.983775i	$-0.442582\pi$
$458$	−4.14333			−0.193605
$459$		0			0
$460$	1.73189			0.0807498
$461$	13.6602	+	23.6602i	0.636220	+	1.10197i	0.986255	+	0.165229i	$0.0528362\pi$
$461$	13.6602	+	23.6602i	0.636220	+	1.10197i	−0.350035	+	0.936736i	$0.613830\pi$
$462$		0			0
$463$	1.69959	−	2.94378i	0.0789868	−	0.136809i	−0.823826	−	0.566842i	$-0.808165\pi$
$463$	1.69959	−	2.94378i	0.0789868	−	0.136809i	0.902813	+	0.430033i	$0.141498\pi$
$464$	−4.60562	+	7.97716i	−0.213810	+	0.370330i
$465$		0			0
$466$	0.958556	+	1.66027i	0.0444042	+	0.0769104i
$467$	32.9976			1.52695			0.763473	−	0.645840i	$-0.223493\pi$
$467$	32.9976			1.52695			0.763473	+	0.645840i	$0.223493\pi$
$468$		0			0
$469$	−39.1613			−1.80830
$470$	1.33348	+	2.30966i	0.0615090	+	0.106537i
$471$		0			0
$472$	4.27993	−	7.41305i	0.197000	−	0.341213i
$473$	−0.732573	+	1.26885i	−0.0336837	+	0.0583420i
$474$		0			0
$475$	−0.407417	−	0.705667i	−0.0186936	−	0.0323782i
$476$	−15.1883			−0.696154
$477$		0			0
$478$	24.1993			1.10685
$479$	11.5216	+	19.9561i	0.526437	+	0.911815i	0.999526	+	0.0308006i	$0.00980567\pi$
$479$	11.5216	+	19.9561i	0.526437	+	0.911815i	−0.473089	+	0.881015i	$0.656861\pi$
$480$		0			0
$481$	−9.24024	+	16.0046i	−0.421319	+	0.729745i
$482$	−6.60247	+	11.4358i	−0.300734	+	0.520887i
$483$		0			0
$484$	5.47743	+	9.48719i	0.248974	+	0.431236i
$485$	−26.2321			−1.19114
$486$		0			0
$487$	26.9315			1.22038			0.610192	−	0.792254i	$-0.291092\pi$
$487$	26.9315			1.22038			0.610192	+	0.792254i	$0.291092\pi$
$488$	−1.41684	−	2.45404i	−0.0641374	−	0.111089i
$489$		0			0
$490$	−9.49817	+	16.4513i	−0.429083	+	0.743194i
$491$	0.123997	−	0.214768i	0.00559589	−	0.00969236i	−0.863214	−	0.504838i	$-0.831552\pi$
$491$	0.123997	−	0.214768i	0.00559589	−	0.00969236i	0.868810	+	0.495146i	$0.164885\pi$
$492$		0			0
$493$	−17.4347	−	30.1977i	−0.785218	−	1.36004i
$494$	−6.61737			−0.297730
$495$		0			0
$496$	3.53590			0.158767
$497$	−23.5198	−	40.7375i	−1.05501	−	1.82733i
$498$		0			0
$499$	13.3591	−	23.1387i	0.598037	−	1.03583i	−0.395073	−	0.918650i	$-0.629281\pi$
$499$	13.3591	−	23.1387i	0.598037	−	1.03583i	0.993111	−	0.117182i	$-0.0373859\pi$
$500$	5.88840	−	10.1990i	0.263337	−	0.456114i
$501$		0			0
$502$	4.32994	+	7.49967i	0.193255	+	0.334727i
$503$	26.1743			1.16705			0.583527	−	0.812094i	$-0.301672\pi$
$503$	26.1743			1.16705			0.583527	+	0.812094i	$0.301672\pi$
$504$		0			0
$505$	−6.04381			−0.268946
$506$	−0.0881062	−	0.152604i	−0.00391680	−	0.00678409i
$507$		0			0
$508$	−0.902007	+	1.56232i	−0.0400201	+	0.0693168i
$509$	−2.72891	+	4.72660i	−0.120957	+	0.209503i	−0.920145	−	0.391577i	$-0.871930\pi$
$509$	−2.72891	+	4.72660i	−0.120957	+	0.209503i	0.799189	+	0.601080i	$0.205263\pi$
$510$		0			0
$511$	1.50523	+	2.60713i	0.0665874	+	0.115333i
$512$	1.00000			0.0441942
$513$		0			0
$514$	21.8308			0.962914
$515$	−17.4245	−	30.1802i	−0.767816	−	1.32990i
$516$		0			0
$517$	0.135676	−	0.234998i	0.00596704	−	0.0103352i
$518$	7.13090	−	12.3511i	0.313314	−	0.542675i
$519$		0			0
$520$	−5.42783	−	9.40127i	−0.238026	−	0.412273i
$521$	−26.1192			−1.14430			−0.572151	−	0.820148i	$-0.693891\pi$
$521$	−26.1192			−1.14430			−0.572151	+	0.820148i	$0.693891\pi$
$522$		0			0
$523$	7.40765			0.323914			0.161957	−	0.986798i	$-0.448219\pi$
$523$	7.40765			0.323914			0.161957	+	0.986798i	$0.448219\pi$
$524$	4.85721	+	8.41294i	0.212188	+	0.367521i
$525$		0			0
$526$	2.84376	−	4.92554i	0.123994	−	0.214764i
$527$	−6.69262	+	11.5920i	−0.291535	+	0.504954i
$528$		0			0
$529$	11.1560	+	19.3228i	0.485044	+	0.840121i
$530$	−23.5930			−1.02482
$531$		0			0
$532$	5.10677			0.221407
$533$	−7.12110	−	12.3341i	−0.308449	−	0.534249i
$534$		0			0
$535$	−0.335514	+	0.581128i	−0.0145055	+	0.0251243i
$536$	−4.88028	+	8.45289i	−0.210796	+	0.365109i
$537$		0			0
$538$	11.3831	+	19.7161i	0.490761	+	0.850023i
$539$	1.93280			0.0832514
$540$		0			0
$541$	11.3209			0.486725			0.243362	−	0.969935i	$-0.421750\pi$
$541$	11.3209			0.486725			0.243362	+	0.969935i	$0.421750\pi$
$542$	9.91698	+	17.1767i	0.425971	+	0.737803i
$543$		0			0
$544$	−1.89276	+	3.27836i	−0.0811515	+	0.140558i
$545$	−0.593391	+	1.02778i	−0.0254181	+	0.0440254i
$546$		0			0
$547$	5.31884	+	9.21249i	0.227417	+	0.393898i	0.957042	−	0.289950i	$-0.0936386\pi$
$547$	5.31884	+	9.21249i	0.227417	+	0.393898i	−0.729625	+	0.683848i	$0.760305\pi$
$548$	−9.06792			−0.387363
$549$		0			0
$550$	−0.136005			−0.00579929
$551$	5.86207	+	10.1534i	0.249733	+	0.432550i
$552$		0			0
$553$	−4.75001	+	8.22726i	−0.201991	+	0.349859i
$554$	12.0684	−	20.9031i	0.512738	−	0.888088i
$555$		0			0
$556$	5.02044	+	8.69565i	0.212914	+	0.368778i
$557$	−11.8477			−0.502003			−0.251001	−	0.967987i	$-0.580760\pi$
$557$	−11.8477			−0.502003			−0.251001	+	0.967987i	$0.580760\pi$
$558$		0			0
$559$	35.8553			1.51652
$560$	4.18878	+	7.25517i	0.177008	+	0.306587i
$561$		0			0
$562$	11.8276	−	20.4861i	0.498919	−	0.864153i
$563$	−3.00397	+	5.20304i	−0.126602	+	0.219282i	−0.922358	−	0.386336i	$-0.873741\pi$
$563$	−3.00397	+	5.20304i	−0.126602	+	0.219282i	0.795756	+	0.605618i	$0.207074\pi$
$564$		0			0
$565$	1.41966	+	2.45892i	0.0597254	+	0.103447i
$566$	−11.6242			−0.488600
$567$		0			0
$568$	−11.7241			−0.491934
$569$	14.5942	+	25.2779i	0.611820	+	1.05970i	0.990934	+	0.134353i	$0.0428956\pi$
$569$	14.5942	+	25.2779i	0.611820	+	1.05970i	−0.379114	+	0.925350i	$0.623771\pi$
$570$		0			0
$571$	−10.9070	+	18.8915i	−0.456445	+	0.790586i	−0.998770	−	0.0495830i	$-0.984211\pi$
$571$	−10.9070	+	18.8915i	−0.456445	+	0.790586i	0.542325	+	0.840169i	$0.317544\pi$
$572$	−0.552258	+	0.956539i	−0.0230911	+	0.0399949i
$573$		0			0
$574$	5.49551	+	9.51850i	0.229378	+	0.397294i
$575$	−0.530997			−0.0221441
$576$		0			0
$577$	40.0799			1.66855			0.834273	−	0.551351i	$-0.185888\pi$
$577$	40.0799			1.66855			0.834273	+	0.551351i	$0.185888\pi$
$578$	1.33491	+	2.31213i	0.0555248	+	0.0961718i
$579$		0			0
$580$	−9.61660	+	16.6564i	−0.399308	+	0.691621i
$581$	−22.8705	+	39.6130i	−0.948830	+	1.64342i
$582$		0			0
$583$	1.20024	+	2.07888i	0.0497090	+	0.0860986i
$584$	0.750325			0.0310487
$585$		0			0
$586$	−10.7109			−0.442464
$587$	13.4329	+	23.2664i	0.554433	+	0.960306i	0.997947	+	0.0640391i	$0.0203982\pi$
$587$	13.4329	+	23.2664i	0.554433	+	0.960306i	−0.443514	+	0.896267i	$0.646268\pi$
$588$		0			0
$589$	2.25027	−	3.89757i	0.0927206	−	0.160597i
$590$	8.93656	−	15.4786i	0.367912	−	0.637243i
$591$		0			0
$592$	−1.77730	−	3.07838i	−0.0730466	−	0.126520i
$593$	30.4609			1.25088			0.625440	−	0.780272i	$-0.284919\pi$
$593$	30.4609			1.25088			0.625440	+	0.780272i	$0.284919\pi$
$594$		0			0
$595$	−31.7134			−1.30012
$596$	−7.92122	−	13.7200i	−0.324466	−	0.561991i
$597$		0			0
$598$	−2.15615	+	3.73456i	−0.0881714	+	0.152717i
$599$	14.5944	−	25.2783i	0.596312	−	1.03284i	−0.397048	−	0.917798i	$-0.629965\pi$
$599$	14.5944	−	25.2783i	0.596312	−	1.03284i	0.993360	−	0.115045i	$-0.0367012\pi$
$600$		0			0
$601$	11.6109	+	20.1107i	0.473619	+	0.820332i	0.999544	−	0.0301987i	$-0.00961402\pi$
$601$	11.6109	+	20.1107i	0.473619	+	0.820332i	−0.525925	+	0.850531i	$0.676281\pi$
$602$	−27.6703			−1.12776
$603$		0			0
$604$	5.30755			0.215961
$605$	11.4370	+	19.8094i	0.464979	+	0.805367i
$606$		0			0
$607$	−21.3357	+	36.9545i	−0.865988	+	1.49994i	7.49778e−5		1.00000i	$0.499976\pi$
$607$	−21.3357	+	36.9545i	−0.865988	+	1.49994i	−0.866063	+	0.499935i	$0.833357\pi$
$608$	0.636405	−	1.10229i	0.0258096	−	0.0447036i
$609$		0			0
$610$	−2.95839	−	5.12408i	−0.119782	−	0.207468i
$611$	−6.64058			−0.268649
$612$		0			0
$613$	−13.6082			−0.549631			−0.274815	−	0.961497i	$-0.588617\pi$
$613$	−13.6082			−0.549631			−0.274815	+	0.961497i	$0.588617\pi$
$614$	−12.3938	−	21.4667i	−0.500173	−	0.866325i
$615$		0			0
$616$	0.426190	−	0.738183i	0.0171717	−	0.0297422i
$617$	−14.0643	+	24.3600i	−0.566206	+	0.980697i	0.430731	+	0.902481i	$0.358256\pi$
$617$	−14.0643	+	24.3600i	−0.566206	+	0.980697i	−0.996936	+	0.0782166i	$0.975077\pi$
$618$		0			0
$619$	9.74843	+	16.8848i	0.391822	+	0.678656i	0.992690	−	0.120692i	$-0.0385114\pi$
$619$	9.74843	+	16.8848i	0.391822	+	0.678656i	−0.600868	+	0.799349i	$0.705178\pi$
$620$	7.38303			0.296510
$621$		0			0
$622$	−21.7835			−0.873439
$623$	10.8254	+	18.7502i	0.433712	+	0.751211i
$624$		0			0
$625$	10.6946	−	18.5236i	0.427785	−	0.740945i
$626$	4.70123	−	8.14277i	0.187899	−	0.325451i
$627$		0			0
$628$	5.75852	+	9.97404i	0.229790	+	0.398008i
$629$	13.4560			0.536527
$630$		0			0
$631$	12.5494			0.499584			0.249792	−	0.968299i	$-0.419638\pi$
$631$	12.5494			0.499584			0.249792	+	0.968299i	$0.419638\pi$
$632$	1.18389	+	2.05056i	0.0470926	+	0.0815668i
$633$		0			0
$634$	7.25293	−	12.5625i	0.288051	−	0.498919i
$635$	−1.88341	+	3.26216i	−0.0747407	+	0.129455i
$636$		0			0
$637$	−23.6498	−	40.9627i	−0.937040	−	1.62300i
$638$	1.95690			0.0774743
$639$		0			0
$640$	2.08802			0.0825361
$641$	6.97641	+	12.0835i	0.275552	+	0.477270i	0.970274	−	0.242008i	$-0.0778061\pi$
$641$	6.97641	+	12.0835i	0.275552	+	0.477270i	−0.694722	+	0.719278i	$0.744473\pi$
$642$		0			0
$643$	−20.5255	+	35.5513i	−0.809449	+	1.40201i	0.103798	+	0.994598i	$0.466901\pi$
$643$	−20.5255	+	35.5513i	−0.809449	+	1.40201i	−0.913246	+	0.407408i	$0.866433\pi$
$644$	1.66395	−	2.88204i	0.0655687	−	0.113568i
$645$		0			0
$646$	2.40912	+	4.17273i	0.0947857	+	0.164174i
$647$	0.303995			0.0119513			0.00597563	−	0.999982i	$-0.498098\pi$
$647$	0.303995			0.0119513			0.00597563	+	0.999982i	$0.498098\pi$
$648$		0			0
$649$	−1.81851			−0.0713829
$650$	1.66417	+	2.88243i	0.0652742	+	0.113058i
$651$		0			0
$652$	−3.83168	+	6.63666i	−0.150060	+	0.259912i
$653$	−23.5585	+	40.8045i	−0.921915	+	1.59680i	−0.125465	+	0.992098i	$0.540042\pi$
$653$	−23.5585	+	40.8045i	−0.921915	+	1.59680i	−0.796450	+	0.604705i	$0.793291\pi$
$654$		0			0
$655$	10.1419	+	17.5664i	0.396279	+	0.686375i
$656$	2.73940			0.106955
$657$		0			0
$658$	5.12468			0.199781
$659$	21.4829	+	37.2095i	0.836855	+	1.44947i	0.892512	+	0.451025i	$0.148941\pi$
$659$	21.4829	+	37.2095i	0.836855	+	1.44947i	−0.0556570	+	0.998450i	$0.517725\pi$
$660$		0			0
$661$	−13.7631	+	23.8384i	−0.535322	+	0.927205i	0.463826	+	0.885927i	$0.346476\pi$
$661$	−13.7631	+	23.8384i	−0.535322	+	0.927205i	−0.999148	+	0.0412786i	$0.986857\pi$
$662$	−0.403370	+	0.698657i	−0.0156774	+	0.0271541i
$663$		0			0
$664$	5.70024	+	9.87311i	0.221212	+	0.383151i
$665$	10.6630			0.413494
$666$		0			0
$667$	7.64019			0.295829
$668$	−3.05500	−	5.29141i	−0.118201	−	0.204731i
$669$		0			0
$670$	−10.1901	+	17.6498i	−0.393678	+	0.681870i
$671$	−0.301003	+	0.521353i	−0.0116201	+	0.0201266i
$672$		0			0
$673$	16.8214	+	29.1355i	0.648417	+	1.12309i	0.983501	+	0.180903i	$0.0579021\pi$
$673$	16.8214	+	29.1355i	0.648417	+	1.12309i	−0.335084	+	0.942188i	$0.608765\pi$
$674$	−26.6658			−1.02713
$675$		0			0
$676$	14.0299			0.539611
$677$	−17.0445	−	29.5220i	−0.655075	−	1.13462i	−0.981875	−	0.189530i	$-0.939304\pi$
$677$	−17.0445	−	29.5220i	−0.655075	−	1.13462i	0.326800	−	0.945094i	$-0.394030\pi$
$678$		0			0
$679$	−25.2030	+	43.6528i	−0.967202	+	1.67524i
$680$	−3.95212	+	6.84527i	−0.151557	+	0.262504i
$681$		0			0
$682$	−0.375596	−	0.650551i	−0.0143823	−	0.0249109i
$683$	−16.4530			−0.629557			−0.314778	−	0.949165i	$-0.601930\pi$
$683$	−16.4530			−0.629557			−0.314778	+	0.949165i	$0.601930\pi$
$684$		0			0
$685$	−18.9340			−0.723430
$686$	4.20838	+	7.28912i	0.160677	+	0.278300i
$687$		0			0
$688$	−3.44827	+	5.97257i	−0.131464	+	0.227702i
$689$	29.3726	−	50.8748i	1.11901	−	1.93817i
$690$		0			0
$691$	7.13457	+	12.3574i	0.271412	+	0.470099i	0.969224	−	0.246182i	$-0.0791762\pi$
$691$	7.13457	+	12.3574i	0.271412	+	0.470099i	−0.697812	+	0.716281i	$0.745843\pi$
$692$	−11.3035			−0.429694
$693$		0			0
$694$	−29.1043			−1.10478
$695$	10.4828	+	18.1567i	0.397634	+	0.688721i
$696$		0			0
$697$	−5.18502	+	8.98072i	−0.196397	+	0.340169i
$698$	14.7743	−	25.5898i	0.559214	−	0.968587i
$699$		0			0
$700$	−1.28428	−	2.22444i	−0.0485412	−	0.0840757i
$701$	15.8891			0.600123			0.300062	−	0.953920i	$-0.402993\pi$
$701$	15.8891			0.600123			0.300062	+	0.953920i	$0.402993\pi$
$702$		0			0
$703$	−4.52433			−0.170638
$704$	−0.106223	−	0.183984i	−0.00400344	−	0.00693417i
$705$		0			0
$706$	−3.12628	+	5.41487i	−0.117659	+	0.203791i
$707$	−5.80671	+	10.0575i	−0.218384	+	0.378252i
$708$		0			0
$709$	4.12090	+	7.13761i	0.154764	+	0.268058i	0.932973	−	0.359947i	$-0.117205\pi$
$709$	4.12090	+	7.13761i	0.154764	+	0.268058i	−0.778209	+	0.628005i	$0.783872\pi$
$710$	−24.4802			−0.918726
$711$		0			0
$712$	5.39625			0.202233
$713$	−1.46641	−	2.53990i	−0.0549176	−	0.0951201i
$714$		0			0
$715$	−1.15312	+	1.99727i	−0.0431244	+	0.0746937i
$716$	−3.46495	+	6.00147i	−0.129491	+	0.224285i
$717$		0			0
$718$	1.29314	+	2.23979i	0.0482597	+	0.0835883i
$719$	21.8697			0.815601			0.407801	−	0.913071i	$-0.366296\pi$
$719$	21.8697			0.815601			0.407801	+	0.913071i	$0.366296\pi$
$720$		0			0
$721$	−66.9638			−2.49386
$722$	8.68998	+	15.0515i	0.323407	+	0.560158i
$723$		0			0
$724$	−1.51882	+	2.63067i	−0.0564464	+	0.0977680i
$725$	2.94845	−	5.10686i	0.109503	−	0.189664i
$726$		0			0
$727$	−24.3290	−	42.1391i	−0.902314	−	1.56285i	−0.824483	−	0.565886i	$-0.808534\pi$
$727$	−24.3290	−	42.1391i	−0.902314	−	1.56285i	−0.0778304	−	0.996967i	$-0.524799\pi$
$728$	−20.8596			−0.773107
$729$		0			0
$730$	1.56669			0.0579858
$731$	−13.0535	−	22.6093i	−0.482801	−	0.836236i
$732$		0			0
$733$	13.0891	−	22.6710i	0.483458	−	0.837373i	−0.516362	−	0.856371i	$-0.672714\pi$
$733$	13.0891	−	22.6710i	0.483458	−	0.837373i	0.999820	+	0.0189972i	$0.00604736\pi$
$734$	−9.34060	+	16.1784i	−0.344768	+	0.597155i
$735$		0			0
$736$	−0.414721	−	0.718318i	−0.0152868	−	0.0264776i
$737$	2.07360			0.0763820
$738$		0			0
$739$	2.57311			0.0946534			0.0473267	−	0.998879i	$-0.484930\pi$
$739$	2.57311			0.0946534			0.0473267	+	0.998879i	$0.484930\pi$
$740$	−3.71104	−	6.42770i	−0.136420	−	0.236287i
$741$		0			0
$742$	−22.6675	+	39.2612i	−0.832148	+	1.44132i
$743$	24.4985	−	42.4327i	0.898763	−	1.55670i	0.0696865	−	0.997569i	$-0.477800\pi$
$743$	24.4985	−	42.4327i	0.898763	−	1.55670i	0.829077	−	0.559135i	$-0.188867\pi$
$744$		0			0
$745$	−16.5396	−	28.6475i	−0.605965	−	1.04956i
$746$	13.5261			0.495227
$747$		0			0
$748$	0.804222			0.0294053
$749$	0.644703	+	1.11666i	0.0235570	+	0.0408018i
$750$		0			0
$751$	−4.25544	+	7.37063i	−0.155283	+	0.268958i	−0.933162	−	0.359456i	$-0.882962\pi$
$751$	−4.25544	+	7.37063i	−0.155283	+	0.268958i	0.777879	+	0.628414i	$0.216296\pi$
$752$	0.638637	−	1.10615i	0.0232887	−	0.0403372i
$753$		0			0
$754$	−23.9447	−	41.4735i	−0.872015	−	1.51038i
$755$	11.0822			0.403324
$756$		0			0
$757$	17.3242			0.629658			0.314829	−	0.949148i	$-0.398053\pi$
$757$	17.3242			0.629658			0.314829	+	0.949148i	$0.398053\pi$
$758$	−15.1089	−	26.1694i	−0.548780	−	0.950514i
$759$		0			0
$760$	1.32882	−	2.30159i	0.0482015	−	0.0834874i
$761$	−5.22338	+	9.04715i	−0.189347	+	0.327959i	−0.945033	−	0.326976i	$-0.893971\pi$
$761$	−5.22338	+	9.04715i	−0.189347	+	0.327959i	0.755686	+	0.654935i	$0.227304\pi$
$762$		0			0
$763$	1.14022	+	1.97493i	0.0412789	+	0.0714971i
$764$	−5.09718			−0.184409
$765$		0			0
$766$	−38.5891			−1.39428
$767$	22.2515	+	38.5407i	0.803454	+	1.39162i
$768$		0			0
$769$	−19.7248	+	34.1644i	−0.711295	+	1.23200i	0.253076	+	0.967446i	$0.418558\pi$
$769$	−19.7248	+	34.1644i	−0.711295	+	1.23200i	−0.964371	+	0.264553i	$0.914776\pi$
$770$	0.889892	−	1.54134i	0.0320695	−	0.0555460i
$771$		0			0
$772$	−9.43413	−	16.3404i	−0.339542	−	0.588104i
$773$	−23.3425			−0.839572			−0.419786	−	0.907623i	$-0.637895\pi$
$773$	−23.3425			−0.839572			−0.419786	+	0.907623i	$0.637895\pi$
$774$		0			0
$775$	−2.26364			−0.0813122
$776$	6.28158	+	10.8800i	0.225496	+	0.390570i
$777$		0			0
$778$	2.81309	−	4.87242i	0.100854	−	0.174685i
$779$	1.74336	−	3.01960i	0.0624625	−	0.108188i
$780$		0			0
$781$	1.24538	+	2.15706i	0.0445631	+	0.0771856i
$782$	3.13987			0.112282
$783$		0			0
$784$	9.09779			0.324921
$785$	12.0239	+	20.8260i	0.429151	+	0.743311i
$786$		0			0
$787$	−18.9448	+	32.8133i	−0.675308	+	1.16967i	0.301070	+	0.953602i	$0.402656\pi$
$787$	−18.9448	+	32.8133i	−0.675308	+	1.16967i	−0.976379	+	0.216066i	$0.930677\pi$
$788$	10.0220	−	17.3586i	0.357018	−	0.618373i
$789$		0			0
$790$	2.47198	+	4.28160i	0.0879492	+	0.152332i
$791$	5.45585			0.193988
$792$		0			0
$793$	14.7324			0.523162
$794$	−3.85809	−	6.68240i	−0.136918	−	0.237150i
$795$		0			0
$796$	−2.75106	+	4.76498i	−0.0975088	+	0.168890i
$797$	1.35224	−	2.34215i	0.0478989	−	0.0829633i	−0.841082	−	0.540908i	$-0.818081\pi$
$797$	1.35224	−	2.34215i	0.0478989	−	0.0829633i	0.888981	+	0.457944i	$0.151414\pi$
$798$		0			0
$799$	2.41757	+	4.18736i	0.0855276	+	0.148138i
$800$	−0.640186			−0.0226340
$801$		0			0
$802$	36.3793			1.28460
$803$	−0.0797020	−	0.138048i	−0.00281262	−	0.00487161i
$804$		0			0
$805$	3.47435	−	6.01775i	0.122455	−	0.212098i
$806$	−9.19163	+	15.9204i	−0.323761	+	0.560771i
$807$		0			0
$808$	1.44726	+	2.50673i	0.0509145	+	0.0881864i
$809$	−22.3977			−0.787460			−0.393730	−	0.919226i	$-0.628815\pi$
$809$	−22.3977			−0.787460			−0.393730	+	0.919226i	$0.628815\pi$
$810$		0			0
$811$	−35.0916			−1.23223			−0.616117	−	0.787655i	$-0.711295\pi$
$811$	−35.0916			−1.23223			−0.616117	+	0.787655i	$0.711295\pi$
$812$	18.4787	+	32.0060i	0.648474	+	1.12319i
$813$		0			0
$814$	−0.377582	+	0.653991i	−0.0132342	+	0.0229224i
$815$	−8.00061	+	13.8575i	−0.280249	+	0.485406i
$816$		0			0
$817$	4.38899	+	7.60195i	0.153551	+	0.265958i
$818$	5.86768			0.205158
$819$		0			0
$820$	5.71990			0.199748
$821$	−7.08396	−	12.2698i	−0.247232	−	0.428218i	0.715525	−	0.698587i	$-0.246188\pi$
$821$	−7.08396	−	12.2698i	−0.247232	−	0.428218i	−0.962757	+	0.270369i	$0.912854\pi$
$822$		0			0
$823$	17.2999	−	29.9644i	0.603038	−	1.04449i	−0.389321	−	0.921102i	$-0.627290\pi$
$823$	17.2999	−	29.9644i	0.603038	−	1.04449i	0.992358	−	0.123390i	$-0.0393765\pi$
$824$	−8.34501	+	14.4540i	−0.290712	+	0.503528i
$825$		0			0
$826$	−17.1719	−	29.7427i	−0.597488	−	1.03488i
$827$	50.7694			1.76543			0.882713	−	0.469912i	$-0.155714\pi$
$827$	50.7694			1.76543			0.882713	+	0.469912i	$0.155714\pi$
$828$		0			0
$829$	54.5822			1.89572			0.947859	−	0.318691i	$-0.103243\pi$
$829$	54.5822			1.89572			0.947859	+	0.318691i	$0.103243\pi$
$830$	11.9022	+	20.6152i	0.413132	+	0.715565i
$831$		0			0
$832$	−2.59951	+	4.50249i	−0.0901219	+	0.156096i
$833$	−17.2199	+	29.8258i	−0.596636	+	1.03340i
$834$		0			0
$835$	−6.37888	−	11.0486i	−0.220750	−	0.382351i
$836$	−0.270404			−0.00935213
$837$		0			0
$838$	21.1356			0.730117
$839$	5.53924	+	9.59425i	0.191236	+	0.331230i	0.945660	−	0.325157i	$-0.105417\pi$
$839$	5.53924	+	9.59425i	0.191236	+	0.331230i	−0.754424	+	0.656387i	$0.772084\pi$
$840$		0			0
$841$	−27.9234	+	48.3647i	−0.962876	+	1.66775i
$842$	−3.72146	+	6.44575i	−0.128250	+	0.222135i
$843$		0			0
$844$	12.5726	+	21.7763i	0.432766	+	0.749572i
$845$	29.2946			1.00777
$846$		0			0
$847$	43.9532			1.51025
$848$	5.64962	+	9.78544i	0.194009	+	0.336033i
$849$		0			0
$850$	1.21172	−	2.09876i	0.0415616	−	0.0719868i
$851$	−1.47417	+	2.55334i	−0.0505339	+	0.0875272i
$852$		0			0
$853$	12.7190	+	22.0300i	0.435490	+	0.754291i	0.997336	−	0.0729510i	$-0.0232417\pi$
$853$	12.7190	+	22.0300i	0.435490	+	0.754291i	−0.561845	+	0.827242i	$0.689908\pi$
$854$	−11.3693			−0.389050
$855$		0			0
$856$	0.321371			0.0109842
$857$	−23.5990	−	40.8746i	−0.806125	−	1.39625i	−0.915529	−	0.402252i	$-0.868228\pi$
$857$	−23.5990	−	40.8746i	−0.806125	−	1.39625i	0.109404	−	0.993997i	$-0.465106\pi$
$858$		0			0
$859$	12.2684	−	21.2496i	0.418594	−	0.725026i	−0.577204	−	0.816600i	$-0.695856\pi$
$859$	12.2684	−	21.2496i	0.418594	−	0.725026i	0.995798	+	0.0915737i	$0.0291897\pi$
$860$	−7.20004	+	12.4708i	−0.245519	+	0.425252i
$861$		0			0
$862$	6.52511	+	11.3018i	0.222246	+	0.384941i
$863$	28.4215			0.967479			0.483740	−	0.875212i	$-0.339278\pi$
$863$	28.4215			0.967479			0.483740	+	0.875212i	$0.339278\pi$
$864$		0			0
$865$	−23.6019			−0.802488
$866$	−0.0717664	−	0.124303i	−0.00243872	−	0.00422399i
$867$		0			0
$868$	7.09339	−	12.2861i	0.240765	−	0.417018i
$869$	0.251514	−	0.435634i	0.00853202	−	0.0147779i
$870$		0			0
$871$	−25.3727	−	43.9468i	−0.859721	−	1.48908i
$872$	0.568378			0.0192477
$873$		0			0
$874$	−1.05572			−0.0357103
$875$	−23.6255	−	40.9205i	−0.798687	−	1.38337i
$876$		0			0
$877$	−21.6256	+	37.4566i	−0.730244	+	1.26482i	0.226534	+	0.974003i	$0.427261\pi$
$877$	−21.6256	+	37.4566i	−0.730244	+	1.26482i	−0.956779	+	0.290817i	$0.906073\pi$
$878$	−6.77826	+	11.7403i	−0.228755	+	0.396215i
$879$		0			0
$880$	−0.221796	−	0.384162i	−0.00747675	−	0.0129501i
$881$	−20.4436			−0.688762			−0.344381	−	0.938830i	$-0.611911\pi$
$881$	−20.4436			−0.688762			−0.344381	+	0.938830i	$0.611911\pi$
$882$		0			0
$883$	−28.2937			−0.952160			−0.476080	−	0.879402i	$-0.657943\pi$
$883$	−28.2937			−0.952160			−0.476080	+	0.879402i	$0.657943\pi$
$884$	−9.84052	−	17.0443i	−0.330972	−	0.573261i
$885$		0			0
$886$	−6.14064	+	10.6359i	−0.206299	+	0.357320i
$887$	28.7206	−	49.7456i	0.964344	−	1.67029i	0.252976	−	0.967473i	$-0.418591\pi$
$887$	28.7206	−	49.7456i	0.964344	−	1.67029i	0.711368	−	0.702820i	$-0.248076\pi$
$888$		0			0
$889$	3.61904	+	6.26836i	0.121379	+	0.210234i
$890$	11.2675			0.377686
$891$		0			0
$892$	−3.75239			−0.125639
$893$	−0.812863	−	1.40792i	−0.0272014	−	0.0471142i
$894$		0			0
$895$	−7.23487	+	12.5312i	−0.241835	+	0.418871i
$896$	2.00610	−	3.47467i	0.0670192	−	0.116081i
$897$		0			0
$898$	−20.3323	−	35.2165i	−0.678497	−	1.17519i
$899$	32.5700			1.08627
$900$		0			0
$901$	−42.7736			−1.42499
$902$	−0.290988	−	0.504006i	−0.00968884	−	0.0167816i
$903$		0			0
$904$	0.679907	−	1.17763i	0.0226134	−	0.0391675i
$905$	−3.17131	+	5.49288i	−0.105418	+	0.182589i
$906$		0			0
$907$	14.2444	+	24.6720i	0.472978	+	0.819222i	0.999522	−	0.0309263i	$-0.00984572\pi$
$907$	14.2444	+	24.6720i	0.472978	+	0.819222i	−0.526544	+	0.850148i	$0.676512\pi$
$908$	18.7277			0.621500
$909$		0			0
$910$	−43.5551			−1.44384
$911$	9.48930	+	16.4359i	0.314394	+	0.544547i	0.979309	−	0.202373i	$-0.0648652\pi$
$911$	9.48930	+	16.4359i	0.314394	+	0.544547i	−0.664914	+	0.746920i	$0.731532\pi$
$912$		0			0
$913$	1.21100	−	2.09751i	0.0400782	−	0.0694175i
$914$	−16.2955	+	28.2246i	−0.539007	+	0.933587i
$915$		0			0
$916$	2.07166	+	3.58822i	0.0684497	+	0.118558i
$917$	38.9763			1.28711
$918$		0			0
$919$	−13.1481			−0.433715			−0.216857	−	0.976203i	$-0.569581\pi$
$919$	−13.1481			−0.433715			−0.216857	+	0.976203i	$0.569581\pi$
$920$	−0.865945	−	1.49986i	−0.0285494	−	0.0494489i
$921$		0			0
$922$	13.6602	−	23.6602i	0.449875	−	0.779207i
$923$	30.4771	−	52.7878i	1.00316	−	1.73753i
$924$		0			0
$925$	1.13780	+	1.97073i	0.0374107	+	0.0647973i
$926$	−3.39919			−0.111704
$927$		0			0
$928$	9.21123			0.302374
$929$	−13.6910	−	23.7135i	−0.449187	−	0.778014i	0.549147	−	0.835726i	$-0.314953\pi$
$929$	−13.6910	−	23.7135i	−0.449187	−	0.778014i	−0.998333	+	0.0577119i	$0.981620\pi$
$930$		0			0
$931$	5.78987	−	10.0284i	0.189755	−	0.328666i
$932$	0.958556	−	1.66027i	0.0313985	−	0.0543839i
$933$		0			0
$934$	−16.4988	−	28.5767i	−0.539857	−	0.935060i
$935$	1.67923			0.0549167
$936$		0			0
$937$	40.0933			1.30979			0.654895	−	0.755720i	$-0.272713\pi$
$937$	40.0933			1.30979			0.654895	+	0.755720i	$0.272713\pi$
$938$	19.5807	+	33.9147i	0.639332	+	1.10735i
$939$		0			0
$940$	1.33348	−	2.30966i	0.0434935	−	0.0753329i
$941$	1.70453	−	2.95233i	0.0555661	−	0.0962434i	−0.836904	−	0.547349i	$-0.815637\pi$
$941$	1.70453	−	2.95233i	0.0555661	−	0.0962434i	0.892470	+	0.451106i	$0.148970\pi$
$942$		0			0
$943$	−1.13609	−	1.96776i	−0.0369960	−	0.0640790i
$944$	−8.55985			−0.278600
$945$		0			0
$946$	1.46515			0.0476360
$947$	−1.91753	−	3.32126i	−0.0623114	−	0.107927i	0.833187	−	0.552992i	$-0.186514\pi$
$947$	−1.91753	−	3.32126i	−0.0623114	−	0.107927i	−0.895498	+	0.445065i	$0.853181\pi$
$948$		0			0
$949$	−1.95048	+	3.37833i	−0.0633152	+	0.109665i
$950$	−0.407417	+	0.705667i	−0.0132184	+	0.0228949i
$951$		0			0
$952$	7.59415	+	13.1534i	0.246128	+	0.426306i
$953$	−52.7929			−1.71013			−0.855065	−	0.518522i	$-0.826483\pi$
$953$	−52.7929			−1.71013			−0.855065	+	0.518522i	$0.826483\pi$
$954$		0			0
$955$	−10.6430			−0.344399
$956$	−12.0996	−	20.9572i	−0.391330	−	0.677804i
$957$		0			0
$958$	11.5216	−	19.9561i	0.372247	−	0.644751i
$959$	−18.1912	+	31.5081i	−0.587424	+	1.01745i
$960$		0			0
$961$	9.24869	+	16.0192i	0.298345	+	0.516748i
$962$	18.4805			0.595835
$963$		0			0
$964$	13.2049			0.425302
$965$	−19.6986	−	34.1190i	−0.634121	−	1.09833i
$966$		0			0
$967$	−5.02186	+	8.69812i	−0.161492	+	0.279713i	−0.935404	−	0.353581i	$-0.884964\pi$
$967$	−5.02186	+	8.69812i	−0.161492	+	0.279713i	0.773912	+	0.633293i	$0.218297\pi$
$968$	5.47743	−	9.48719i	0.176051	−	0.304930i
$969$		0			0
$970$	13.1160	+	22.7177i	0.421131	+	0.729420i
$971$	4.06174			0.130348			0.0651738	−	0.997874i	$-0.479240\pi$
$971$	4.06174			0.130348			0.0651738	+	0.997874i	$0.479240\pi$
$972$		0			0
$973$	40.2860			1.29151
$974$	−13.4658	−	23.3234i	−0.431471	−	0.747330i
$975$		0			0
$976$	−1.41684	+	2.45404i	−0.0453520	+	0.0785519i
$977$	−9.11452	+	15.7868i	−0.291599	+	0.505065i	−0.974188	−	0.225738i	$-0.927521\pi$
$977$	−9.11452	+	15.7868i	−0.291599	+	0.505065i	0.682589	+	0.730803i	$0.260854\pi$
$978$		0			0
$979$	−0.573208	−	0.992825i	−0.0183198	−	0.0317308i
$980$	18.9963			0.606816
$981$		0			0
$982$	−0.247993			−0.00791378
$983$	21.0216	+	36.4104i	0.670484	+	1.16131i	0.977767	+	0.209694i	$0.0672468\pi$
$983$	21.0216	+	36.4104i	0.670484	+	1.16131i	−0.307283	+	0.951618i	$0.599420\pi$
$984$		0			0
$985$	20.9261	−	36.2450i	0.666760	−	1.15486i
$986$	−17.4347	+	30.1977i	−0.555233	+	0.961692i
$987$		0			0
$988$	3.30869	+	5.73081i	0.105263	+	0.182321i
$989$	5.72028			0.181894
$990$		0			0
$991$	−31.8731			−1.01248			−0.506241	−	0.862392i	$-0.668965\pi$
$991$	−31.8731			−1.01248			−0.506241	+	0.862392i	$0.668965\pi$
$992$	−1.76795	−	3.06218i	−0.0561325	−	0.0972244i
$993$		0			0
$994$	−23.5198	+	40.7375i	−0.746004	+	1.29212i
$995$	−5.74426	+	9.94935i	−0.182105	+	0.315416i
$996$		0			0
$997$	15.9999	+	27.7126i	0.506721	+	0.877666i	0.999970	+	0.00777813i	$0.00247588\pi$
$997$	15.9999	+	27.7126i	0.506721	+	0.877666i	−0.493249	+	0.869888i	$0.664191\pi$
$998$	−26.7183			−0.845753
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1458.2.c.f.973.3		12
3.2	odd	2		1458.2.c.g.973.4		12
9.2	odd	6		1458.2.c.g.487.4		12
9.4	even	3		1458.2.a.g.1.4		6
9.5	odd	6		1458.2.a.f.1.3		6
9.7	even	3	inner	1458.2.c.f.487.3		12
27.2	odd	18		486.2.e.g.271.1		12
27.4	even	9		486.2.e.f.217.2		12
27.5	odd	18		486.2.e.e.55.1		12
27.7	even	9		486.2.e.h.433.2		12
27.11	odd	18		162.2.e.b.37.2		12
27.13	even	9		54.2.e.b.43.2	✓	12
27.14	odd	18		162.2.e.b.127.2		12
27.16	even	9		54.2.e.b.49.2	yes	12
27.20	odd	18		486.2.e.e.433.1		12
27.22	even	9		486.2.e.h.55.2		12
27.23	odd	18		486.2.e.g.217.1		12
27.25	even	9		486.2.e.f.271.2		12
108.43	odd	18		432.2.u.b.49.1		12
108.67	odd	18		432.2.u.b.97.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.43.2	✓	12	27.13	even	9
54.2.e.b.49.2	yes	12	27.16	even	9
162.2.e.b.37.2		12	27.11	odd	18
162.2.e.b.127.2		12	27.14	odd	18
432.2.u.b.49.1		12	108.43	odd	18
432.2.u.b.97.1		12	108.67	odd	18
486.2.e.e.55.1		12	27.5	odd	18
486.2.e.e.433.1		12	27.20	odd	18
486.2.e.f.217.2		12	27.4	even	9
486.2.e.f.271.2		12	27.25	even	9
486.2.e.g.217.1		12	27.23	odd	18
486.2.e.g.271.1		12	27.2	odd	18
486.2.e.h.55.2		12	27.22	even	9
486.2.e.h.433.2		12	27.7	even	9
1458.2.a.f.1.3		6	9.5	odd	6
1458.2.a.g.1.4		6	9.4	even	3
1458.2.c.f.487.3		12	9.7	even	3	inner
1458.2.c.f.973.3		12	1.1	even	1	trivial
1458.2.c.g.487.4		12	9.2	odd	6
1458.2.c.g.973.4		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1458 = 2 \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1458.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.04401 + 1.80828i) q^{5} +(2.00610 + 3.47467i) q^{7} +1.00000 q^{8} +2.08802 q^{10} +(-0.106223 - 0.183984i) q^{11} +(-2.59951 + 4.50249i) q^{13} +(2.00610 - 3.47467i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.78552 q^{17} -1.27281 q^{19} +(-1.04401 - 1.80828i) q^{20} +(-0.106223 + 0.183984i) q^{22} +(-0.414721 + 0.718318i) q^{23} +(0.320093 + 0.554417i) q^{25} +5.19903 q^{26} -4.01220 q^{28} +(-4.60562 - 7.97716i) q^{29} +(-1.76795 + 3.06218i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.89276 - 3.27836i) q^{34} -8.37755 q^{35} +3.55460 q^{37} +(0.636405 + 1.10229i) q^{38} +(-1.04401 + 1.80828i) q^{40} +(-1.36970 + 2.37239i) q^{41} +(-3.44827 - 5.97257i) q^{43} +0.212447 q^{44} +0.829442 q^{46} +(0.638637 + 1.10615i) q^{47} +(-4.54889 + 7.87892i) q^{49} +(0.320093 - 0.554417i) q^{50} +(-2.59951 - 4.50249i) q^{52} -11.2992 q^{53} +0.443592 q^{55} +(2.00610 + 3.47467i) q^{56} +(-4.60562 + 7.97716i) q^{58} +(4.27993 - 7.41305i) q^{59} +(-1.41684 - 2.45404i) q^{61} +3.53590 q^{62} +1.00000 q^{64} +(-5.42783 - 9.40127i) q^{65} +(-4.88028 + 8.45289i) q^{67} +(-1.89276 + 3.27836i) q^{68} +(4.18878 + 7.25517i) q^{70} -11.7241 q^{71} +0.750325 q^{73} +(-1.77730 - 3.07838i) q^{74} +(0.636405 - 1.10229i) q^{76} +(0.426190 - 0.738183i) q^{77} +(1.18389 + 2.05056i) q^{79} +2.08802 q^{80} +2.73940 q^{82} +(5.70024 + 9.87311i) q^{83} +(-3.95212 + 6.84527i) q^{85} +(-3.44827 + 5.97257i) q^{86} +(-0.106223 - 0.183984i) q^{88} +5.39625 q^{89} -20.8596 q^{91} +(-0.414721 - 0.718318i) q^{92} +(0.638637 - 1.10615i) q^{94} +(1.32882 - 2.30159i) q^{95} +(6.28158 + 10.8800i) q^{97} +9.09779 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 12 q^{8} + 6 q^{10} - 3 q^{11} - 9 q^{13} - 6 q^{14} - 6 q^{16} + 12 q^{17} + 18 q^{19} - 3 q^{20} - 3 q^{22} + 3 q^{23} - 15 q^{25} + 18 q^{26} + 12 q^{28}+ \cdots + 24 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 12 * q^8 + 6 * q^10 - 3 * q^11 - 9 * q^13 - 6 * q^14 - 6 * q^16 + 12 * q^17 + 18 * q^19 - 3 * q^20 - 3 * q^22 + 3 * q^23 - 15 * q^25 + 18 * q^26 + 12 * q^28 - 3 * q^29 - 12 * q^31 - 6 * q^32 - 6 * q^34 - 6 * q^35 + 30 * q^37 - 9 * q^38 - 3 * q^40 - 3 * q^41 - 12 * q^43 + 6 * q^44 - 6 * q^46 + 9 * q^47 - 12 * q^49 - 15 * q^50 - 9 * q^52 - 12 * q^53 + 18 * q^55 - 6 * q^56 - 3 * q^58 + 3 * q^59 - 12 * q^61 + 24 * q^62 + 12 * q^64 + 3 * q^65 - 21 * q^67 - 6 * q^68 + 3 * q^70 - 24 * q^71 + 42 * q^73 - 15 * q^74 - 9 * q^76 + 3 * q^77 + 6 * q^80 + 6 * q^82 + 27 * q^83 - 12 * q^86 - 3 * q^88 - 24 * q^89 + 12 * q^91 + 3 * q^92 + 9 * q^94 + 30 * q^95 - 18 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more