LMFDB - Embedded newform 3024.2.q.i.2881.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.q (of order $3$, 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2881.3
Root			$-1.02682 + 1.77851i$ of defining polynomial
Character	$\chi$	$=$	3024.2881
Dual form			3024.2.q.i.2305.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0731228 + 0.126652i) q^{5} +(2.33035 - 1.25278i) q^{7} +O(q^{10})$	$q+(-0.0731228 + 0.126652i) q^{5} +(2.33035 - 1.25278i) q^{7} +(-0.832020 - 1.44110i) q^{11} +(0.0999454 + 0.173111i) q^{13} +(-3.13555 + 5.43093i) q^{17} +(-3.45879 - 5.99080i) q^{19} +(3.09092 - 5.35363i) q^{23} +(2.48931 + 4.31160i) q^{25} +(2.46757 - 4.27396i) q^{29} +2.51780 q^{31} +(-0.0117348 + 0.386752i) q^{35} +(-3.50023 - 6.06257i) q^{37} +(-1.15895 - 2.00736i) q^{41} +(0.940993 - 1.62985i) q^{43} -1.81177 q^{47} +(3.86110 - 5.83883i) q^{49} +(2.67307 - 4.62989i) q^{53} +0.243359 q^{55} -4.57099 q^{59} -0.678276 q^{61} -0.0292332 q^{65} +6.18684 q^{67} +1.27749 q^{71} +(-0.778603 + 1.34858i) q^{73} +(-3.74428 - 2.31594i) q^{77} -12.7957 q^{79} +(3.75687 - 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(-4.53394 - 7.85301i) q^{89} +(0.449777 + 0.278199i) q^{91} +1.01167 q^{95} +(-3.98514 + 6.90246i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{5} + 4 q^{7}+O(q^{10}) $ 10 * q - 4 * q^5 + 4 * q^7	$ 10 q - 4 q^{5} + 4 q^{7} + 4 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} + 3 q^{23} - q^{25} - 7 q^{29} - 6 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} - 54 q^{47} - 8 q^{49} + 21 q^{53} - 4 q^{55} - 60 q^{59} + 28 q^{61} - 22 q^{65} - 4 q^{67} - 6 q^{71} + 15 q^{73} - 11 q^{77} - 8 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} + 28 q^{95} - 12 q^{97}+O(q^{100}) $ 10 * q - 4 * q^5 + 4 * q^7 + 4 * q^11 - 8 * q^13 - 12 * q^17 - q^19 + 3 * q^23 - q^25 - 7 * q^29 - 6 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 - 54 * q^47 - 8 * q^49 + 21 * q^53 - 4 * q^55 - 60 * q^59 + 28 * q^61 - 22 * q^65 - 4 * q^67 - 6 * q^71 + 15 * q^73 - 11 * q^77 - 8 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 + 28 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.0731228	+	0.126652i	−0.0327015	+	0.0566407i	−0.881913	−	0.471412i	$-0.843744\pi$
$5$	−0.0731228	+	0.126652i	−0.0327015	+	0.0566407i	0.849211	+	0.528053i	$0.177078\pi$
$6$		0			0
$7$	2.33035	−	1.25278i	0.880791	−	0.473505i
$7$	2.33035	−	1.25278i	0.880791	−	0.473505i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.832020	−	1.44110i	−0.250864	−	0.434508i	0.712900	−	0.701265i	$-0.247381\pi$
$11$	−0.832020	−	1.44110i	−0.250864	−	0.434508i	−0.963764	+	0.266757i	$0.914048\pi$
$12$		0			0
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	0.879553	−	0.475802i	$-0.157842\pi$
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	−0.851833	+	0.523814i	$0.824509\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.13555	+	5.43093i	−0.760483	+	1.31720i	0.182119	+	0.983277i	$0.441704\pi$
$17$	−3.13555	+	5.43093i	−0.760483	+	1.31720i	−0.942602	+	0.333919i	$0.891629\pi$
$18$		0			0
$19$	−3.45879	−	5.99080i	−0.793500	−	1.37438i	−0.923787	−	0.382907i	$-0.874923\pi$
$19$	−3.45879	−	5.99080i	−0.793500	−	1.37438i	0.130287	−	0.991476i	$-0.458410\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.09092	−	5.35363i	0.644501	−	1.11631i	−0.339916	−	0.940456i	$-0.610399\pi$
$23$	3.09092	−	5.35363i	0.644501	−	1.11631i	0.984417	−	0.175852i	$-0.0562682\pi$
$24$		0			0
$25$	2.48931	+	4.31160i	0.497861	+	0.862321i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.46757	−	4.27396i	0.458217	−	0.793655i	−0.540650	−	0.841248i	$-0.681822\pi$
$29$	2.46757	−	4.27396i	0.458217	−	0.793655i	0.998867	+	0.0475930i	$0.0151551\pi$
$30$		0			0
$31$	2.51780			0.452209			0.226105	−	0.974103i	$-0.427401\pi$
$31$	2.51780			0.452209			0.226105	+	0.974103i	$0.427401\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.0117348	+	0.386752i	−0.00198354	+	0.0653730i
$36$		0			0
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	−0.995994	−	0.0894162i	$-0.971500\pi$
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	0.420560	−	0.907264i	$-0.361833\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.15895	−	2.00736i	−0.180998	−	0.313498i	0.761223	−	0.648491i	$-0.224599\pi$
$41$	−1.15895	−	2.00736i	−0.180998	−	0.313498i	−0.942221	+	0.334993i	$0.891266\pi$
$42$		0			0
$43$	0.940993	−	1.62985i	0.143500	−	0.248550i	−0.785312	−	0.619100i	$-0.787498\pi$
$43$	0.940993	−	1.62985i	0.143500	−	0.248550i	0.928812	+	0.370550i	$0.120831\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.81177			−0.264275			−0.132137	−	0.991231i	$-0.542184\pi$
$47$	−1.81177			−0.264275			−0.132137	+	0.991231i	$0.542184\pi$
$48$		0			0
$49$	3.86110	−	5.83883i	0.551586	−	0.834118i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.67307	−	4.62989i	0.367174	−	0.635964i	−0.621948	−	0.783058i	$-0.713659\pi$
$53$	2.67307	−	4.62989i	0.367174	−	0.635964i	0.989123	+	0.147094i	$0.0469920\pi$
$54$		0			0
$55$	0.243359			0.0328145
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.57099			−0.595092			−0.297546	−	0.954708i	$-0.596168\pi$
$59$	−4.57099			−0.595092			−0.297546	+	0.954708i	$0.596168\pi$
$60$		0			0
$61$	−0.678276			−0.0868443			−0.0434221	−	0.999057i	$-0.513826\pi$
$61$	−0.678276			−0.0868443			−0.0434221	+	0.999057i	$0.513826\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0292332			−0.00362593
$66$		0			0
$67$	6.18684			0.755842			0.377921	−	0.925838i	$-0.376639\pi$
$67$	6.18684			0.755842			0.377921	+	0.925838i	$0.376639\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.27749			0.151611			0.0758053	−	0.997123i	$-0.475847\pi$
$71$	1.27749			0.151611			0.0758053	+	0.997123i	$0.475847\pi$
$72$		0			0
$73$	−0.778603	+	1.34858i	−0.0911286	+	0.157839i	−0.907986	−	0.419000i	$-0.862381\pi$
$73$	−0.778603	+	1.34858i	−0.0911286	+	0.157839i	0.816858	+	0.576839i	$0.195714\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.74428	−	2.31594i	−0.426700	−	0.263926i
$78$		0			0
$79$	−12.7957			−1.43963			−0.719817	−	0.694164i	$-0.755774\pi$
$79$	−12.7957			−1.43963			−0.719817	+	0.694164i	$0.755774\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.75687	−	6.50709i	0.412370	−	0.714246i	−0.582778	−	0.812631i	$-0.698034\pi$
$83$	3.75687	−	6.50709i	0.412370	−	0.714246i	0.995148	+	0.0983854i	$0.0313678\pi$
$84$		0			0
$85$	−0.458561	−	0.794251i	−0.0497379	−	0.0861486i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.53394	−	7.85301i	−0.480597	−	0.832418i	0.519155	−	0.854680i	$-0.326247\pi$
$89$	−4.53394	−	7.85301i	−0.480597	−	0.832418i	−0.999752	+	0.0222619i	$0.992913\pi$
$90$		0			0
$91$	0.449777	+	0.278199i	0.0471494	+	0.0291632i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.01167			0.103795
$96$		0			0
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	−0.994278	−	0.106821i	$-0.965933\pi$
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	0.589649	+	0.807660i	$0.299266\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.42150	+	12.8544i	0.738467	+	1.27906i	0.953186	+	0.302386i	$0.0977832\pi$
$101$	7.42150	+	12.8544i	0.738467	+	1.27906i	−0.214719	+	0.976676i	$0.568883\pi$
$102$		0			0
$103$	−0.101974	+	0.176624i	−0.0100478	+	0.0174033i	−0.871006	−	0.491273i	$-0.836532\pi$
$103$	−0.101974	+	0.176624i	−0.0100478	+	0.0174033i	0.860958	+	0.508676i	$0.169865\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.48444	+	6.03524i	0.336854	+	0.583448i	0.983839	−	0.179054i	$-0.0573038\pi$
$107$	3.48444	+	6.03524i	0.336854	+	0.583448i	−0.646985	+	0.762503i	$0.723970\pi$
$108$		0			0
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	−0.661270	−	0.750148i	$-0.729982\pi$
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	0.980282	+	0.197603i	$0.0633157\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.0193234	+	0.0334691i	0.00181779	+	0.00314851i	0.866933	−	0.498425i	$-0.166088\pi$
$113$	0.0193234	+	0.0334691i	0.00181779	+	0.00314851i	−0.865115	+	0.501573i	$0.832755\pi$
$114$		0			0
$115$	0.452033	+	0.782945i	0.0421523	+	0.0730100i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.503195	+	16.5841i	−0.0461278	+	1.52027i
$120$		0			0
$121$	4.11548	−	7.12823i	0.374135	−	0.648021i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.45933			−0.130526
$126$		0			0
$127$	−13.4788			−1.19605			−0.598027	−	0.801476i	$-0.704048\pi$
$127$	−13.4788			−1.19605			−0.598027	+	0.801476i	$0.704048\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.91665	−	17.1761i	0.866422	−	1.50069i	0.000793988	−	1.00000i	$-0.499747\pi$
$131$	9.91665	−	17.1761i	0.866422	−	1.50069i	0.865628	−	0.500687i	$-0.166919\pi$
$132$		0			0
$133$	−15.5653	−	9.62759i	−1.34969	−	0.834818i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.22255	−	5.58162i	−0.275321	−	0.476870i	0.694895	−	0.719111i	$-0.255451\pi$
$137$	−3.22255	−	5.58162i	−0.275321	−	0.476870i	−0.970216	+	0.242241i	$0.922117\pi$
$138$		0			0
$139$	−6.26527	−	10.8518i	−0.531413	−	0.920435i	−0.999328	−	0.0366611i	$-0.988328\pi$
$139$	−6.26527	−	10.8518i	−0.531413	−	0.920435i	0.467914	−	0.883774i	$-0.345006\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.166313	−	0.288063i	0.0139078	−	0.0240890i
$144$		0			0
$145$	0.360872	+	0.625048i	0.0299688	+	0.0519074i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.88364	−	15.3869i	0.727776	−	1.26054i	−0.230045	−	0.973180i	$-0.573887\pi$
$149$	8.88364	−	15.3869i	0.727776	−	1.26054i	0.957821	−	0.287365i	$-0.0927792\pi$
$150$		0			0
$151$	4.23300	+	7.33177i	0.344476	+	0.596651i	0.985259	−	0.171072i	$-0.0547231\pi$
$151$	4.23300	+	7.33177i	0.344476	+	0.596651i	−0.640782	+	0.767723i	$0.721390\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.184108	+	0.318885i	−0.0147879	+	0.0256135i
$156$		0			0
$157$	5.69935			0.454858			0.227429	−	0.973795i	$-0.426968\pi$
$157$	5.69935			0.454858			0.227429	+	0.973795i	$0.426968\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.496032	−	16.3481i	0.0390928	−	1.28841i
$162$		0			0
$163$	1.06267	+	1.84060i	0.0832349	+	0.144167i	0.904638	−	0.426181i	$-0.140141\pi$
$163$	1.06267	+	1.84060i	0.0832349	+	0.144167i	−0.821403	+	0.570349i	$0.806808\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.78723	−	10.0238i	−0.447829	−	0.775663i	0.550415	−	0.834891i	$-0.314470\pi$
$167$	−5.78723	−	10.0238i	−0.447829	−	0.775663i	−0.998244	+	0.0592278i	$0.981136\pi$
$168$		0			0
$169$	6.48002	−	11.2237i	0.498463	−	0.863364i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	15.9109			1.20968			0.604842	−	0.796345i	$-0.293236\pi$
$173$	15.9109			1.20968			0.604842	+	0.796345i	$0.293236\pi$
$174$		0			0
$175$	11.2024	+	6.92902i	0.846825	+	0.523785i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.87665	−	6.71456i	0.289755	−	0.501870i	−0.683996	−	0.729485i	$-0.739760\pi$
$179$	3.87665	−	6.71456i	0.289755	−	0.501870i	0.973751	+	0.227615i	$0.0730929\pi$
$180$		0			0
$181$	−12.1618			−0.903982			−0.451991	−	0.892022i	$-0.649286\pi$
$181$	−12.1618			−0.903982			−0.451991	+	0.892022i	$0.649286\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.02379			0.0752703
$186$		0			0
$187$	10.4354			0.763110
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.96765			−0.359447			−0.179723	−	0.983717i	$-0.557520\pi$
$191$	−4.96765			−0.359447			−0.179723	+	0.983717i	$0.557520\pi$
$192$		0			0
$193$	−14.9044			−1.07284			−0.536422	−	0.843950i	$-0.680224\pi$
$193$	−14.9044			−1.07284			−0.536422	+	0.843950i	$0.680224\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	21.2608			1.51477			0.757386	−	0.652968i	$-0.226476\pi$
$197$	21.2608			1.51477			0.757386	+	0.652968i	$0.226476\pi$
$198$		0			0
$199$	9.97208	−	17.2722i	0.706902	−	1.22439i	−0.259098	−	0.965851i	$-0.583425\pi$
$199$	9.97208	−	17.2722i	0.706902	−	1.22439i	0.966001	−	0.258540i	$-0.0832413\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.395997	−	13.0512i	0.0277935	−	0.916012i
$204$		0			0
$205$	0.338983			0.0236756
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.75556	+	9.96893i	−0.398121	+	0.689565i
$210$		0			0
$211$	−11.7569	−	20.3636i	−0.809381	−	1.40189i	−0.913293	−	0.407303i	$-0.866469\pi$
$211$	−11.7569	−	20.3636i	−0.809381	−	1.40189i	0.103912	−	0.994587i	$-0.466864\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.137616	+	0.238358i	0.00938535	+	0.0162559i
$216$		0			0
$217$	5.86735	−	3.15424i	0.398302	−	0.214123i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.25354			−0.0843220
$222$		0			0
$223$	−2.03052	+	3.51696i	−0.135974	+	0.235513i	−0.925969	−	0.377600i	$-0.876750\pi$
$223$	−2.03052	+	3.51696i	−0.135974	+	0.235513i	0.789995	+	0.613113i	$0.210083\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.92643	+	3.33667i	0.127861	+	0.221462i	0.922848	−	0.385165i	$-0.125855\pi$
$227$	1.92643	+	3.33667i	0.127861	+	0.221462i	−0.794986	+	0.606627i	$0.792522\pi$
$228$		0			0
$229$	−6.55812	+	11.3590i	−0.433373	+	0.750624i	−0.997161	−	0.0752952i	$-0.976010\pi$
$229$	−6.55812	+	11.3590i	−0.433373	+	0.750624i	0.563788	+	0.825919i	$0.309343\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.75115	+	15.1574i	0.573307	+	0.992997i	0.996223	+	0.0868284i	$0.0276732\pi$
$233$	8.75115	+	15.1574i	0.573307	+	0.992997i	−0.422916	+	0.906169i	$0.638993\pi$
$234$		0			0
$235$	0.132482	−	0.229466i	0.00864218	−	0.0149687i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.65857	+	6.33683i	0.236653	+	0.409895i	0.959752	−	0.280849i	$-0.0906161\pi$
$239$	3.65857	+	6.33683i	0.236653	+	0.409895i	−0.723099	+	0.690745i	$0.757283\pi$
$240$		0			0
$241$	−3.11553	−	5.39626i	−0.200689	−	0.347604i	0.748062	−	0.663629i	$-0.230985\pi$
$241$	−3.11553	−	5.39626i	−0.200689	−	0.347604i	−0.948751	+	0.316026i	$0.897651\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.457167	+	0.915969i	0.0292074	+	0.0585191i
$246$		0			0
$247$	0.691380	−	1.19751i	0.0439915	−	0.0761954i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5.65283			0.356803			0.178402	−	0.983958i	$-0.442907\pi$
$251$	5.65283			0.356803			0.178402	+	0.983958i	$0.442907\pi$
$252$		0			0
$253$	−10.2868			−0.646727
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.90082	−	10.2205i	0.368083	−	0.637539i	−0.621183	−	0.783666i	$-0.713347\pi$
$257$	5.90082	−	10.2205i	0.368083	−	0.637539i	0.989266	+	0.146127i	$0.0466808\pi$
$258$		0			0
$259$	−15.7518	−	9.74293i	−0.978770	−	0.605396i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	11.1200	+	19.2605i	0.685691	+	1.18765i	0.973219	+	0.229879i	$0.0738331\pi$
$263$	11.1200	+	19.2605i	0.685691	+	1.18765i	−0.287528	+	0.957772i	$0.592834\pi$
$264$		0			0
$265$	0.390925	+	0.677101i	0.0240143	+	0.0415940i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.19442	−	2.06880i	0.0728251	−	0.126137i	−0.827313	−	0.561741i	$-0.810132\pi$
$269$	1.19442	−	2.06880i	0.0728251	−	0.126137i	0.900138	+	0.435604i	$0.143465\pi$
$270$		0			0
$271$	11.6129	+	20.1142i	0.705435	+	1.22185i	0.966534	+	0.256537i	$0.0825815\pi$
$271$	11.6129	+	20.1142i	0.705435	+	1.22185i	−0.261100	+	0.965312i	$0.584085\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.14231	−	7.17469i	0.249790	−	0.432650i
$276$		0			0
$277$	2.30900	+	3.99931i	0.138734	+	0.240295i	0.927018	−	0.375017i	$-0.122363\pi$
$277$	2.30900	+	3.99931i	0.138734	+	0.240295i	−0.788283	+	0.615312i	$0.789030\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.90841	+	10.2337i	−0.352466	+	0.610489i	−0.986681	−	0.162668i	$-0.947990\pi$
$281$	−5.90841	+	10.2337i	−0.352466	+	0.610489i	0.634215	+	0.773157i	$0.281324\pi$
$282$		0			0
$283$	−15.8497			−0.942165			−0.471082	−	0.882089i	$-0.656137\pi$
$283$	−15.8497			−0.942165			−0.471082	+	0.882089i	$0.656137\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.21555	−	3.22596i	−0.307864	−	0.190422i
$288$		0			0
$289$	−11.1634	−	19.3355i	−0.656669	−	1.13738i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.04804	−	12.2076i	−0.411751	−	0.713173i	0.583330	−	0.812235i	$-0.301749\pi$
$293$	−7.04804	−	12.2076i	−0.411751	−	0.713173i	−0.995081	+	0.0990615i	$0.968416\pi$
$294$		0			0
$295$	0.334243	−	0.578927i	0.0194604	−	0.0337064i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.23569			0.0714619
$300$		0			0
$301$	0.151011	−	4.97698i	0.00870413	−	0.286868i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.0495974	−	0.0859053i	0.00283994	−	0.00491892i
$306$		0			0
$307$	−27.3916			−1.56332			−0.781660	−	0.623704i	$-0.785627\pi$
$307$	−27.3916			−1.56332			−0.781660	+	0.623704i	$0.785627\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−14.0557			−0.797026			−0.398513	−	0.917163i	$-0.630474\pi$
$311$	−14.0557			−0.797026			−0.398513	+	0.917163i	$0.630474\pi$
$312$		0			0
$313$	21.7446			1.22908			0.614540	−	0.788886i	$-0.289342\pi$
$313$	21.7446			1.22908			0.614540	+	0.788886i	$0.289342\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.56297			−0.480944			−0.240472	−	0.970656i	$-0.577302\pi$
$317$	−8.56297			−0.480944			−0.240472	+	0.970656i	$0.577302\pi$
$318$		0			0
$319$	−8.21228			−0.459799
$320$		0			0
$321$		0			0
$322$		0			0
$323$	43.3808			2.41377
$324$		0			0
$325$	−0.497589	+	0.861850i	−0.0276013	+	0.0478068i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−4.22208	+	2.26975i	−0.232771	+	0.125135i
$330$		0			0
$331$	−10.8472			−0.596216			−0.298108	−	0.954532i	$-0.596356\pi$
$331$	−10.8472			−0.596216			−0.298108	+	0.954532i	$0.596356\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.452399	+	0.783578i	−0.0247172	+	0.0428114i
$336$		0			0
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	0.908014	−	0.418940i	$-0.137598\pi$
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	−0.816819	+	0.576893i	$0.804265\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.09486	−	3.62840i	−0.113443	−	0.196489i
$342$		0			0
$343$	1.68298	−	18.4436i	0.0908723	−	0.995863i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−11.5330			−0.619126			−0.309563	−	0.950879i	$-0.600183\pi$
$347$	−11.5330			−0.619126			−0.309563	+	0.950879i	$0.600183\pi$
$348$		0			0
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	−0.960186	−	0.279362i	$-0.909877\pi$
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	0.722027	+	0.691865i	$0.243211\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.32349	−	2.29236i	−0.0704424	−	0.122010i	0.828653	−	0.559763i	$-0.189108\pi$
$353$	−1.32349	−	2.29236i	−0.0704424	−	0.122010i	−0.899095	+	0.437753i	$0.855774\pi$
$354$		0			0
$355$	−0.0934139	+	0.161798i	−0.00495790	+	0.00858733i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.9835	−	22.4882i	−0.685245	−	1.18688i	−0.973360	−	0.229284i	$-0.926362\pi$
$359$	−12.9835	−	22.4882i	−0.685245	−	1.18688i	0.288114	−	0.957596i	$-0.406972\pi$
$360$		0			0
$361$	−14.4264	+	24.9873i	−0.759286	+	1.31512i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.113867	−	0.197224i	−0.00596009	−	0.0103232i
$366$		0			0
$367$	8.79371	+	15.2312i	0.459028	+	0.795060i	0.998910	−	0.0466808i	$-0.0148644\pi$
$367$	8.79371	+	15.2312i	0.459028	+	0.795060i	−0.539882	+	0.841741i	$0.681531\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.428975	−	14.1380i	0.0222713	−	0.734011i
$372$		0			0
$373$	−0.407538	+	0.705876i	−0.0211015	+	0.0365489i	−0.876383	−	0.481614i	$-0.840051\pi$
$373$	−0.407538	+	0.705876i	−0.0211015	+	0.0365489i	0.855282	+	0.518163i	$0.173384\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.986490			0.0508068
$378$		0			0
$379$	20.4312			1.04948			0.524741	−	0.851262i	$-0.324162\pi$
$379$	20.4312			1.04948			0.524741	+	0.851262i	$0.324162\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−8.94638	+	15.4956i	−0.457139	+	0.791788i	−0.998808	−	0.0488039i	$-0.984459\pi$
$383$	−8.94638	+	15.4956i	−0.457139	+	0.791788i	0.541670	+	0.840591i	$0.317792\pi$
$384$		0			0
$385$	0.567112	−	0.304874i	0.0289027	−	0.0155378i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	7.81392	+	13.5341i	0.396181	+	0.686206i	0.993251	−	0.115983i	$-0.0370018\pi$
$389$	7.81392	+	13.5341i	0.396181	+	0.686206i	−0.597070	+	0.802189i	$0.703669\pi$
$390$		0			0
$391$	19.3835	+	33.5731i	0.980264	+	1.69787i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.935661	−	1.62061i	0.0470782	−	0.0815419i
$396$		0			0
$397$	9.63064	+	16.6808i	0.483348	+	0.837183i	0.999817	−	0.0191225i	$-0.00608724\pi$
$397$	9.63064	+	16.6808i	0.483348	+	0.837183i	−0.516469	+	0.856306i	$0.672754\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.15064	−	12.3853i	0.357086	−	0.618491i	−0.630387	−	0.776281i	$-0.717104\pi$
$401$	7.15064	−	12.3853i	0.357086	−	0.618491i	0.987473	+	0.157790i	$0.0504370\pi$
$402$		0			0
$403$	0.251642	+	0.435857i	0.0125352	+	0.0217116i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.82452	+	10.0884i	−0.288711	+	0.500062i
$408$		0			0
$409$	31.8610			1.57542			0.787712	−	0.616044i	$-0.211266\pi$
$409$	31.8610			1.57542			0.787712	+	0.616044i	$0.211266\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.6520	+	5.72643i	−0.524151	+	0.281779i
$414$		0			0
$415$	0.549426	+	0.951633i	0.0269702	+	0.0467138i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.9480	+	20.6945i	0.583697	+	1.01099i	0.995036	+	0.0995110i	$0.0317278\pi$
$419$	11.9480	+	20.6945i	0.583697	+	1.01099i	−0.411339	+	0.911482i	$0.634939\pi$
$420$		0			0
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	−0.894278	−	0.447513i	$-0.852310\pi$
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	0.834696	+	0.550711i	$0.185643\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−31.2214			−1.51446
$426$		0			0
$427$	−1.58062	+	0.849728i	−0.0764917	+	0.0411212i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.46382	−	4.26746i	0.118678	−	0.205556i	−0.800566	−	0.599244i	$-0.795468\pi$
$431$	2.46382	−	4.26746i	0.118678	−	0.205556i	0.919244	+	0.393688i	$0.128801\pi$
$432$		0			0
$433$	30.8539			1.48274			0.741371	−	0.671095i	$-0.234176\pi$
$433$	30.8539			1.48274			0.741371	+	0.671095i	$0.234176\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−42.7633			−2.04565
$438$		0			0
$439$	−2.44822			−0.116847			−0.0584235	−	0.998292i	$-0.518607\pi$
$439$	−2.44822			−0.116847			−0.0584235	+	0.998292i	$0.518607\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−26.2950			−1.24931			−0.624657	−	0.780899i	$-0.714761\pi$
$443$	−26.2950			−1.24931			−0.624657	+	0.780899i	$0.714761\pi$
$444$		0			0
$445$	1.32614			0.0628650
$446$		0			0
$447$		0			0
$448$		0			0
$449$	38.7077			1.82673			0.913365	−	0.407141i	$-0.133474\pi$
$449$	38.7077			1.82673			0.913365	+	0.407141i	$0.133474\pi$
$450$		0			0
$451$	−1.92854	+	3.34034i	−0.0908116	+	0.157290i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.0681236	+	0.0366226i	−0.00319368	+	0.00171690i
$456$		0			0
$457$	−9.15511			−0.428258			−0.214129	−	0.976805i	$-0.568691\pi$
$457$	−9.15511			−0.428258			−0.214129	+	0.976805i	$0.568691\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−14.6152	+	25.3143i	−0.680698	+	1.17900i	0.294070	+	0.955784i	$0.404990\pi$
$461$	−14.6152	+	25.3143i	−0.680698	+	1.17900i	−0.974768	+	0.223220i	$0.928343\pi$
$462$		0			0
$463$	8.21031	+	14.2207i	0.381565	+	0.660891i	0.991286	−	0.131726i	$-0.0420518\pi$
$463$	8.21031	+	14.2207i	0.381565	+	0.660891i	−0.609721	+	0.792616i	$0.708718\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.68632	+	13.3131i	0.355680	+	0.616057i	0.987234	−	0.159276i	$-0.0509158\pi$
$467$	7.68632	+	13.3131i	0.355680	+	0.616057i	−0.631554	+	0.775332i	$0.717582\pi$
$468$		0			0
$469$	14.4175	−	7.75073i	0.665739	−	0.357895i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.13170			−0.143996
$474$		0			0
$475$	17.2200	−	29.8259i	0.790106	−	1.36850i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	18.9646	+	32.8476i	0.866513	+	1.50084i	0.865537	+	0.500844i	$0.166977\pi$
$479$	18.9646	+	32.8476i	0.866513	+	1.50084i	0.000975329		1.00000i	$0.499690\pi$
$480$		0			0
$481$	0.699663	−	1.21185i	0.0319019	−	0.0552557i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.582809	−	1.00946i	−0.0264640	−	0.0458370i
$486$		0			0
$487$	−2.30247	+	3.98800i	−0.104335	+	0.180714i	−0.913466	−	0.406914i	$-0.866605\pi$
$487$	−2.30247	+	3.98800i	−0.104335	+	0.180714i	0.809131	+	0.587628i	$0.199938\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−15.1876	−	26.3056i	−0.685405	−	1.18716i	−0.973309	−	0.229497i	$-0.926292\pi$
$491$	−15.1876	−	26.3056i	−0.685405	−	1.18716i	0.287904	−	0.957659i	$-0.407042\pi$
$492$		0			0
$493$	15.4744	+	26.8024i	0.696932	+	1.20712i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.97701	−	1.60041i	0.133537	−	0.0717884i
$498$		0			0
$499$	4.63436	−	8.02694i	0.207462	−	0.359335i	−0.743452	−	0.668789i	$-0.766813\pi$
$499$	4.63436	−	8.02694i	0.207462	−	0.359335i	0.950914	+	0.309454i	$0.100146\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−22.4230			−0.999791			−0.499896	−	0.866086i	$-0.666628\pi$
$503$	−22.4230			−0.999791			−0.499896	+	0.866086i	$0.666628\pi$
$504$		0			0
$505$	−2.17072			−0.0965960
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−18.8207	+	32.5984i	−0.834213	+	1.44490i	0.0604572	+	0.998171i	$0.480744\pi$
$509$	−18.8207	+	32.5984i	−0.834213	+	1.44490i	−0.894670	+	0.446728i	$0.852589\pi$
$510$		0			0
$511$	−0.124951	+	4.11808i	−0.00552748	+	0.182173i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.0149133	−	0.0258306i	−0.000657158	−	0.00113823i
$516$		0			0
$517$	1.50743	+	2.61095i	0.0662969	+	0.114830i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.4641	+	30.2488i	−0.765117	+	1.32522i	0.175067	+	0.984556i	$0.443986\pi$
$521$	−17.4641	+	30.2488i	−0.765117	+	1.32522i	−0.940185	+	0.340666i	$0.889348\pi$
$522$		0			0
$523$	11.8735	+	20.5656i	0.519194	+	0.899270i	0.999751	+	0.0223069i	$0.00710109\pi$
$523$	11.8735	+	20.5656i	0.519194	+	0.899270i	−0.480557	+	0.876963i	$0.659566\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.89468	+	13.6740i	−0.343898	+	0.595648i
$528$		0			0
$529$	−7.60755	−	13.1767i	−0.330763	−	0.572898i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.231664	−	0.401254i	0.0100345	−	0.0173802i
$534$		0			0
$535$	−1.01917			−0.0440626
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−11.6269	−	0.706212i	−0.500804	−	0.0304187i
$540$		0			0
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	0.989428	−	0.145028i	$-0.0463271\pi$
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	−0.620311	+	0.784356i	$0.712994\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.487083	+	0.843653i	0.0208643	+	0.0361381i
$546$		0			0
$547$	10.0046	−	17.3284i	0.427765	−	0.740910i	−0.568910	−	0.822400i	$-0.692635\pi$
$547$	10.0046	−	17.3284i	0.427765	−	0.740910i	0.996674	+	0.0814901i	$0.0259679\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−34.1392			−1.45438
$552$		0			0
$553$	−29.8186	+	16.0302i	−1.26802	+	0.681674i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.122740	−	0.212593i	0.00520068	−	0.00900784i	−0.863413	−	0.504497i	$-0.831678\pi$
$557$	0.122740	−	0.212593i	0.00520068	−	0.00900784i	0.868614	+	0.495489i	$0.165011\pi$
$558$		0			0
$559$	0.376192			0.0159112
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−44.2509			−1.86495			−0.932477	−	0.361230i	$-0.882357\pi$
$563$	−44.2509			−1.86495			−0.932477	+	0.361230i	$0.882357\pi$
$564$		0			0
$565$	−0.00565192			−0.000237778
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.53533			0.232053			0.116027	−	0.993246i	$-0.462984\pi$
$569$	5.53533			0.232053			0.116027	+	0.993246i	$0.462984\pi$
$570$		0			0
$571$	4.10381			0.171739			0.0858696	−	0.996306i	$-0.472633\pi$
$571$	4.10381			0.171739			0.0858696	+	0.996306i	$0.472633\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	30.7770			1.28349
$576$		0			0
$577$	−2.82275	+	4.88915i	−0.117513	+	0.203538i	−0.918781	−	0.394767i	$-0.870825\pi$
$577$	−2.82275	+	4.88915i	−0.117513	+	0.203538i	0.801269	+	0.598305i	$0.204159\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.602904	−	19.8703i	0.0250127	−	0.824360i
$582$		0			0
$583$	−8.89619			−0.368442
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.36644	−	16.2232i	0.386595	−	0.669601i	−0.605394	−	0.795926i	$-0.706985\pi$
$587$	9.36644	−	16.2232i	0.386595	−	0.669601i	0.991989	+	0.126324i	$0.0403180\pi$
$588$		0			0
$589$	−8.70852	−	15.0836i	−0.358828	−	0.621509i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.43516	+	16.3422i	0.387456	+	0.671093i	0.992107	−	0.125398i	$-0.0400207\pi$
$593$	9.43516	+	16.3422i	0.387456	+	0.671093i	−0.604651	+	0.796491i	$0.706687\pi$
$594$		0			0
$595$	−2.06363	−	1.27641i	−0.0846005	−	0.0523277i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.67451			0.109278			0.0546388	−	0.998506i	$-0.482599\pi$
$599$	2.67451			0.109278			0.0546388	+	0.998506i	$0.482599\pi$
$600$		0			0
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	−0.968736	−	0.248095i	$-0.920196\pi$
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	0.699224	+	0.714902i	$0.253529\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.601872	+	1.04247i	0.0244696	+	0.0423825i
$606$		0			0
$607$	12.9026	−	22.3480i	0.523701	−	0.907076i	−0.475919	−	0.879489i	$-0.657884\pi$
$607$	12.9026	−	22.3480i	0.523701	−	0.907076i	0.999619	−	0.0275869i	$-0.00878231\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.181079	−	0.313637i	−0.00732565	−	0.0126884i
$612$		0			0
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	−0.454333	−	0.890832i	$-0.650122\pi$
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	0.998650	−	0.0519519i	$-0.0165443\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.76588	+	8.25474i	0.191867	+	0.332323i	0.945869	−	0.324549i	$-0.105212\pi$
$617$	4.76588	+	8.25474i	0.191867	+	0.332323i	−0.754002	+	0.656872i	$0.771879\pi$
$618$		0			0
$619$	17.3536	+	30.0573i	0.697499	+	1.20810i	0.969331	+	0.245759i	$0.0790371\pi$
$619$	17.3536	+	30.0573i	0.697499	+	1.20810i	−0.271832	+	0.962345i	$0.587630\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−20.4038	−	12.6203i	−0.817459	−	0.505621i
$624$		0			0
$625$	−12.3398	+	21.3732i	−0.493593	+	0.854928i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	43.9006			1.75043
$630$		0			0
$631$	36.7963			1.46484			0.732419	−	0.680854i	$-0.238391\pi$
$631$	36.7963			1.46484			0.732419	+	0.680854i	$0.238391\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.985611	−	1.70713i	0.0391128	−	0.0677453i
$636$		0			0
$637$	1.39666	+	0.0848329i	0.0553378	+	0.00336120i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−22.0922	−	38.2648i	−0.872590	−	1.51137i	−0.859308	−	0.511458i	$-0.829106\pi$
$641$	−22.0922	−	38.2648i	−0.872590	−	1.51137i	−0.0132813	−	0.999912i	$-0.504228\pi$
$642$		0			0
$643$	−7.24065	−	12.5412i	−0.285543	−	0.494575i	0.687197	−	0.726471i	$-0.258841\pi$
$643$	−7.24065	−	12.5412i	−0.285543	−	0.494575i	−0.972741	+	0.231895i	$0.925507\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16.6536	+	28.8448i	−0.654719	+	1.13401i	0.327245	+	0.944940i	$0.393880\pi$
$647$	−16.6536	+	28.8448i	−0.654719	+	1.13401i	−0.981964	+	0.189068i	$0.939453\pi$
$648$		0			0
$649$	3.80315	+	6.58725i	0.149287	+	0.258572i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.53322	+	7.85176i	−0.177398	+	0.307263i	−0.940989	−	0.338438i	$-0.890101\pi$
$653$	−4.53322	+	7.85176i	−0.177398	+	0.307263i	0.763590	+	0.645701i	$0.223435\pi$
$654$		0			0
$655$	1.45027	+	2.51194i	0.0566666	+	0.0981495i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	16.1806	−	28.0256i	0.630305	−	1.09172i	−0.357184	−	0.934034i	$-0.616263\pi$
$659$	16.1806	−	28.0256i	0.630305	−	1.09172i	0.987489	−	0.157686i	$-0.0504035\pi$
$660$		0			0
$661$	−8.65915			−0.336802			−0.168401	−	0.985719i	$-0.553860\pi$
$661$	−8.65915			−0.336802			−0.168401	+	0.985719i	$0.553860\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.35754	−	1.26739i	0.0914214	−	0.0491473i
$666$		0			0
$667$	−15.2541	−	26.4209i	−0.590642	−	1.02302i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.564339	+	0.977464i	0.0217861	+	0.0377346i
$672$		0			0
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	−0.691831	−	0.722059i	$-0.743196\pi$
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	0.971237	+	0.238114i	$0.0765291\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−38.3315			−1.47320			−0.736600	−	0.676329i	$-0.763570\pi$
$677$	−38.3315			−1.47320			−0.736600	+	0.676329i	$0.763570\pi$
$678$		0			0
$679$	−0.639537	+	21.0777i	−0.0245432	+	0.808887i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.31659	+	5.74450i	−0.126906	+	0.219807i	−0.922476	−	0.386054i	$-0.873838\pi$
$683$	−3.31659	+	5.74450i	−0.126906	+	0.219807i	0.795570	+	0.605861i	$0.207171\pi$
$684$		0			0
$685$	0.942567			0.0360136
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.06864			0.0407121
$690$		0			0
$691$	23.3875			0.889704			0.444852	−	0.895604i	$-0.353256\pi$
$691$	23.3875			0.889704			0.444852	+	0.895604i	$0.353256\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.83254			0.0695121
$696$		0			0
$697$	14.5358			0.550583
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−9.26736			−0.350023			−0.175012	−	0.984566i	$-0.555996\pi$
$701$	−9.26736			−0.350023			−0.175012	+	0.984566i	$0.555996\pi$
$702$		0			0
$703$	−24.2131	+	41.9383i	−0.913214	+	1.58173i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	33.3984	+	20.6579i	1.25608	+	0.776918i
$708$		0			0
$709$	14.2355			0.534626			0.267313	−	0.963610i	$-0.413864\pi$
$709$	14.2355			0.534626			0.267313	+	0.963610i	$0.413864\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	7.78230	−	13.4793i	0.291449	−	0.504805i
$714$		0			0
$715$	0.0243226	+	0.0421280i	0.000909613	+	0.00157550i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.92848	+	12.0005i	0.258389	+	0.447542i	0.965810	−	0.259249i	$-0.0834752\pi$
$719$	6.92848	+	12.0005i	0.258389	+	0.447542i	−0.707422	+	0.706792i	$0.750142\pi$
$720$		0			0
$721$	−0.0163649	+	0.539348i	−0.000609459	+	0.0200864i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	24.5702			0.912513
$726$		0			0
$727$	−15.7000	+	27.1932i	−0.582280	+	1.00854i	0.412928	+	0.910764i	$0.364506\pi$
$727$	−15.7000	+	27.1932i	−0.582280	+	1.00854i	−0.995208	+	0.0977755i	$0.968827\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.90107	+	10.2209i	0.218259	+	0.378035i
$732$		0			0
$733$	13.3003	−	23.0368i	0.491257	−	0.850883i	−0.508692	−	0.860949i	$-0.669871\pi$
$733$	13.3003	−	23.0368i	0.491257	−	0.850883i	0.999949	+	0.0100658i	$0.00320409\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.14757	−	8.91586i	−0.189613	−	0.328420i
$738$		0			0
$739$	−16.5019	+	28.5822i	−0.607034	+	1.05141i	0.384693	+	0.923045i	$0.374307\pi$
$739$	−16.5019	+	28.5822i	−0.607034	+	1.05141i	−0.991727	+	0.128368i	$0.959026\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	19.3008	+	33.4299i	0.708076	+	1.22642i	0.965570	+	0.260144i	$0.0837701\pi$
$743$	19.3008	+	33.4299i	0.708076	+	1.22642i	−0.257493	+	0.966280i	$0.582897\pi$
$744$		0			0
$745$	1.29919	+	2.25027i	0.0475988	+	0.0824435i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	15.6808	+	9.69900i	0.572964	+	0.354394i
$750$		0			0
$751$	−18.9498	+	32.8220i	−0.691487	+	1.19769i	0.279863	+	0.960040i	$0.409711\pi$
$751$	−18.9498	+	32.8220i	−0.691487	+	1.19769i	−0.971351	+	0.237651i	$0.923622\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−1.23811			−0.0450596
$756$		0			0
$757$	22.5927			0.821147			0.410573	−	0.911828i	$-0.365329\pi$
$757$	22.5927			0.821147			0.410573	+	0.911828i	$0.365329\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.8735	−	24.0296i	0.502913	−	0.871072i	−0.497081	−	0.867704i	$-0.665595\pi$
$761$	13.8735	−	24.0296i	0.502913	−	0.871072i	0.999994	−	0.00336738i	$-0.00107187\pi$
$762$		0			0
$763$	0.534493	−	17.6157i	0.0193500	−	0.637730i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.456849	−	0.791286i	−0.0164959	−	0.0285717i
$768$		0			0
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	0.735412	−	0.677621i	$-0.236989\pi$
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	−0.954542	+	0.298075i	$0.903655\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	20.7795	−	35.9912i	0.747388	−	1.29451i	−0.201682	−	0.979451i	$-0.564641\pi$
$773$	20.7795	−	35.9912i	0.747388	−	1.29451i	0.949071	−	0.315063i	$-0.102026\pi$
$774$		0			0
$775$	6.26756	+	10.8557i	0.225137	+	0.389950i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−8.01714	+	13.8861i	−0.287244	+	0.497521i
$780$		0			0
$781$	−1.06290	−	1.84100i	−0.0380336	−	0.0658761i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.416753	+	0.721837i	−0.0148746	+	0.0257635i
$786$		0			0
$787$	20.8969			0.744893			0.372446	−	0.928054i	$-0.378519\pi$
$787$	20.8969			0.744893			0.372446	+	0.928054i	$0.378519\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.0869596	+	0.0537869i	0.00309193	+	0.00191244i
$792$		0			0
$793$	−0.0677905	−	0.117417i	−0.00240731	−	0.00416959i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.319383	+	0.553188i	0.0113131	+	0.0195949i	0.871627	−	0.490171i	$-0.163066\pi$
$797$	0.319383	+	0.553188i	0.0113131	+	0.0195949i	−0.860313	+	0.509765i	$0.829732\pi$
$798$		0			0
$799$	5.68091	−	9.83963i	0.200976	−	0.348101i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.59125			0.0914433
$804$		0			0
$805$	2.03425	+	1.25824i	0.0716980	+	0.0443472i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−25.2796	+	43.7856i	−0.888783	+	1.53942i	−0.0474686	+	0.998873i	$0.515115\pi$
$809$	−25.2796	+	43.7856i	−0.888783	+	1.53942i	−0.841315	+	0.540545i	$0.818218\pi$
$810$		0			0
$811$	0.784071			0.0275325			0.0137662	−	0.999905i	$-0.495618\pi$
$811$	0.784071			0.0275325			0.0137662	+	0.999905i	$0.495618\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.310823			−0.0108876
$816$		0			0
$817$	−13.0188			−0.455470
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−43.4413			−1.51611			−0.758056	−	0.652189i	$-0.773851\pi$
$821$	−43.4413			−1.51611			−0.758056	+	0.652189i	$0.773851\pi$
$822$		0			0
$823$	−3.96546			−0.138227			−0.0691136	−	0.997609i	$-0.522017\pi$
$823$	−3.96546			−0.138227			−0.0691136	+	0.997609i	$0.522017\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	29.3159			1.01941			0.509707	−	0.860348i	$-0.329754\pi$
$827$	29.3159			1.01941			0.509707	+	0.860348i	$0.329754\pi$
$828$		0			0
$829$	−17.5213	+	30.3478i	−0.608541	+	1.05402i	0.382940	+	0.923773i	$0.374912\pi$
$829$	−17.5213	+	30.3478i	−0.608541	+	1.05402i	−0.991481	+	0.130251i	$0.958422\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	19.6036	+	39.2773i	0.679225	+	1.36088i
$834$		0			0
$835$	1.69272			0.0585788
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−18.7921	+	32.5489i	−0.648777	+	1.12371i	0.334639	+	0.942347i	$0.391386\pi$
$839$	−18.7921	+	32.5489i	−0.648777	+	1.12371i	−0.983415	+	0.181368i	$0.941948\pi$
$840$		0			0
$841$	2.32218	+	4.02213i	0.0800750	+	0.138694i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.947675	+	1.64142i	0.0326010	+	0.0564666i
$846$		0			0
$847$	0.660455	−	21.7671i	0.0226935	−	0.747926i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−43.2757			−1.48347
$852$		0			0
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	−0.436400	−	0.899753i	$-0.643747\pi$
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	0.997409	−	0.0719434i	$-0.0229201\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	13.7673	+	23.8457i	0.470283	+	0.814554i	0.999422	−	0.0339808i	$-0.0108185\pi$
$857$	13.7673	+	23.8457i	0.470283	+	0.814554i	−0.529139	+	0.848535i	$0.677485\pi$
$858$		0			0
$859$	−23.2550	+	40.2789i	−0.793451	+	1.37430i	0.130366	+	0.991466i	$0.458385\pi$
$859$	−23.2550	+	40.2789i	−0.793451	+	1.37430i	−0.923818	+	0.382832i	$0.874949\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.44007	+	4.22633i	0.0830610	+	0.143866i	0.904563	−	0.426339i	$-0.140197\pi$
$863$	2.44007	+	4.22633i	0.0830610	+	0.143866i	−0.821502	+	0.570205i	$0.806864\pi$
$864$		0			0
$865$	−1.16345	+	2.01516i	−0.0395585	+	0.0685174i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	10.6463	+	18.4400i	0.361152	+	0.625533i
$870$		0			0
$871$	0.618346	+	1.07101i	0.0209518	+	0.0362897i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.40075	+	1.82821i	−0.114966	+	0.0618049i
$876$		0			0
$877$	−19.6446	+	34.0255i	−0.663352	+	1.14896i	0.316378	+	0.948633i	$0.397533\pi$
$877$	−19.6446	+	34.0255i	−0.663352	+	1.14896i	−0.979729	+	0.200326i	$0.935800\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−47.3713			−1.59598			−0.797990	−	0.602670i	$-0.794103\pi$
$881$	−47.3713			−1.59598			−0.797990	+	0.602670i	$0.794103\pi$
$882$		0			0
$883$	2.67206			0.0899221			0.0449610	−	0.998989i	$-0.485684\pi$
$883$	2.67206			0.0899221			0.0449610	+	0.998989i	$0.485684\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.4800	−	19.8840i	0.385461	−	0.667638i	−0.606372	−	0.795181i	$-0.707376\pi$
$887$	11.4800	−	19.8840i	0.385461	−	0.667638i	0.991833	+	0.127543i	$0.0407091\pi$
$888$		0			0
$889$	−31.4105	+	16.8860i	−1.05347	+	0.566338i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.26655	+	10.8540i	0.209702	+	0.363214i
$894$		0			0
$895$	0.566944	+	0.981976i	0.0189508	+	0.0328238i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	6.21284	−	10.7610i	0.207210	−	0.358898i
$900$		0			0
$901$	16.7631	+	29.0345i	0.558459	+	0.967280i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.889308	−	1.54033i	0.0295616	−	0.0512022i
$906$		0			0
$907$	−13.9491	−	24.1606i	−0.463173	−	0.802238i	0.535944	−	0.844253i	$-0.319956\pi$
$907$	−13.9491	−	24.1606i	−0.463173	−	0.802238i	−0.999117	+	0.0420148i	$0.986622\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−18.7381	+	32.4553i	−0.620820	+	1.07529i	0.368513	+	0.929623i	$0.379867\pi$
$911$	−18.7381	+	32.4553i	−0.620820	+	1.07529i	−0.989333	+	0.145670i	$0.953466\pi$
$912$		0			0
$913$	−12.5032			−0.413794
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.59143	−	52.4499i	0.0525536	−	1.73205i
$918$		0			0
$919$	15.1073	+	26.1667i	0.498345	+	0.863160i	0.999998	−	0.00190951i	$-0.000607816\pi$
$919$	15.1073	+	26.1667i	0.498345	+	0.863160i	−0.501653	+	0.865069i	$0.667274\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.127680	+	0.221147i	0.00420262	+	0.00727916i
$924$		0			0
$925$	17.4263	−	30.1832i	0.572972	−	0.992417i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	45.9351			1.50708			0.753540	−	0.657402i	$-0.228344\pi$
$929$	45.9351			1.50708			0.753540	+	0.657402i	$0.228344\pi$
$930$		0			0
$931$	−48.3340	−	2.93579i	−1.58408	−	0.0962167i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.763064	+	1.32167i	−0.0249549	+	0.0432231i
$936$		0			0
$937$	−45.3797			−1.48249			−0.741245	−	0.671235i	$-0.765764\pi$
$937$	−45.3797			−1.48249			−0.741245	+	0.671235i	$0.765764\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−49.4003			−1.61040			−0.805202	−	0.593000i	$-0.797943\pi$
$941$	−49.4003			−1.61040			−0.805202	+	0.593000i	$0.797943\pi$
$942$		0			0
$943$	−14.3289			−0.466613
$944$		0			0
$945$		0			0
$946$		0			0
$947$	31.6505			1.02850			0.514252	−	0.857639i	$-0.328070\pi$
$947$	31.6505			1.02850			0.514252	+	0.857639i	$0.328070\pi$
$948$		0			0
$949$	−0.311271			−0.0101043
$950$		0			0
$951$		0			0
$952$		0			0
$953$	19.1237			0.619477			0.309739	−	0.950822i	$-0.399758\pi$
$953$	19.1237			0.619477			0.309739	+	0.950822i	$0.399758\pi$
$954$		0			0
$955$	0.363249	−	0.629165i	0.0117545	−	0.0203593i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−14.5022	−	8.97001i	−0.468300	−	0.289657i
$960$		0			0
$961$	−24.6607			−0.795507
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.08985	−	1.88768i	0.0350836	−	0.0607666i
$966$		0			0
$967$	−4.98525	−	8.63470i	−0.160315	−	0.277673i	0.774667	−	0.632370i	$-0.217918\pi$
$967$	−4.98525	−	8.63470i	−0.160315	−	0.277673i	−0.934982	+	0.354696i	$0.884584\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	0.522554	+	0.905090i	0.0167695	+	0.0290457i	0.874288	−	0.485407i	$-0.161329\pi$
$971$	0.522554	+	0.905090i	0.0167695	+	0.0290457i	−0.857519	+	0.514453i	$0.827995\pi$
$972$		0			0
$973$	−28.1951	−	17.4395i	−0.903895	−	0.559084i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	18.8862			0.604222			0.302111	−	0.953273i	$-0.402309\pi$
$977$	18.8862			0.604222			0.302111	+	0.953273i	$0.402309\pi$
$978$		0			0
$979$	−7.54466	+	13.0677i	−0.241128	+	0.417647i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.14446	−	1.98226i	−0.0365025	−	0.0632242i	0.847197	−	0.531279i	$-0.178288\pi$
$983$	−1.14446	−	1.98226i	−0.0365025	−	0.0632242i	−0.883700	+	0.468055i	$0.844955\pi$
$984$		0			0
$985$	−1.55465	+	2.69274i	−0.0495353	+	0.0857977i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−5.81707	−	10.0755i	−0.184972	−	0.320381i
$990$		0			0
$991$	9.53491	−	16.5150i	0.302886	−	0.524615i	−0.673902	−	0.738821i	$-0.735383\pi$
$991$	9.53491	−	16.5150i	0.302886	−	0.524615i	0.976789	+	0.214206i	$0.0687164\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.45837	+	2.52598i	0.0462336	+	0.0800789i
$996$		0			0
$997$	−18.5075	−	32.0560i	−0.586139	−	1.01522i	−0.994732	−	0.102507i	$-0.967314\pi$
$997$	−18.5075	−	32.0560i	−0.586139	−	1.01522i	0.408593	−	0.912717i	$-0.366020\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.i.2881.3		10
3.2	odd	2		1008.2.q.i.529.5		10
4.3	odd	2		189.2.h.b.46.1		10
7.2	even	3		3024.2.t.i.289.3		10
9.4	even	3		3024.2.t.i.1873.3		10
9.5	odd	6		1008.2.t.i.193.2		10
12.11	even	2		63.2.h.b.25.5	yes	10
21.2	odd	6		1008.2.t.i.961.2		10
28.3	even	6		1323.2.f.f.883.5		10
28.11	odd	6		1323.2.f.e.883.5		10
28.19	even	6		1323.2.g.f.667.5		10
28.23	odd	6		189.2.g.b.100.5		10
28.27	even	2		1323.2.h.f.802.1		10
36.7	odd	6		567.2.e.e.487.5		10
36.11	even	6		567.2.e.f.487.1		10
36.23	even	6		63.2.g.b.4.1	✓	10
36.31	odd	6		189.2.g.b.172.5		10
63.23	odd	6		1008.2.q.i.625.5		10
63.58	even	3	inner	3024.2.q.i.2305.3		10
84.11	even	6		441.2.f.e.295.1		10
84.23	even	6		63.2.g.b.16.1	yes	10
84.47	odd	6		441.2.g.f.79.1		10
84.59	odd	6		441.2.f.f.295.1		10
84.83	odd	2		441.2.h.f.214.5		10
252.11	even	6		3969.2.a.z.1.5		5
252.23	even	6		63.2.h.b.58.5	yes	10
252.31	even	6		1323.2.f.f.442.5		10
252.59	odd	6		441.2.f.f.148.1		10
252.67	odd	6		1323.2.f.e.442.5		10
252.79	odd	6		567.2.e.e.163.5		10
252.95	even	6		441.2.f.e.148.1		10
252.103	even	6		1323.2.h.f.226.1		10
252.115	even	6		3969.2.a.bb.1.1		5
252.131	odd	6		441.2.h.f.373.5		10
252.139	even	6		1323.2.g.f.361.5		10
252.151	odd	6		3969.2.a.bc.1.1		5
252.167	odd	6		441.2.g.f.67.1		10
252.191	even	6		567.2.e.f.163.1		10
252.227	odd	6		3969.2.a.ba.1.5		5
252.247	odd	6		189.2.h.b.37.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.1	✓	10	36.23	even	6
63.2.g.b.16.1	yes	10	84.23	even	6
63.2.h.b.25.5	yes	10	12.11	even	2
63.2.h.b.58.5	yes	10	252.23	even	6
189.2.g.b.100.5		10	28.23	odd	6
189.2.g.b.172.5		10	36.31	odd	6
189.2.h.b.37.1		10	252.247	odd	6
189.2.h.b.46.1		10	4.3	odd	2
441.2.f.e.148.1		10	252.95	even	6
441.2.f.e.295.1		10	84.11	even	6
441.2.f.f.148.1		10	252.59	odd	6
441.2.f.f.295.1		10	84.59	odd	6
441.2.g.f.67.1		10	252.167	odd	6
441.2.g.f.79.1		10	84.47	odd	6
441.2.h.f.214.5		10	84.83	odd	2
441.2.h.f.373.5		10	252.131	odd	6
567.2.e.e.163.5		10	252.79	odd	6
567.2.e.e.487.5		10	36.7	odd	6
567.2.e.f.163.1		10	252.191	even	6
567.2.e.f.487.1		10	36.11	even	6
1008.2.q.i.529.5		10	3.2	odd	2
1008.2.q.i.625.5		10	63.23	odd	6
1008.2.t.i.193.2		10	9.5	odd	6
1008.2.t.i.961.2		10	21.2	odd	6
1323.2.f.e.442.5		10	252.67	odd	6
1323.2.f.e.883.5		10	28.11	odd	6
1323.2.f.f.442.5		10	252.31	even	6
1323.2.f.f.883.5		10	28.3	even	6
1323.2.g.f.361.5		10	252.139	even	6
1323.2.g.f.667.5		10	28.19	even	6
1323.2.h.f.226.1		10	252.103	even	6
1323.2.h.f.802.1		10	28.27	even	2
3024.2.q.i.2305.3		10	63.58	even	3	inner
3024.2.q.i.2881.3		10	1.1	even	1	trivial
3024.2.t.i.289.3		10	7.2	even	3
3024.2.t.i.1873.3		10	9.4	even	3
3969.2.a.z.1.5		5	252.11	even	6
3969.2.a.ba.1.5		5	252.227	odd	6
3969.2.a.bb.1.1		5	252.115	even	6
3969.2.a.bc.1.1		5	252.151	odd	6

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0731228 + 0.126652i) q^{5} +(2.33035 - 1.25278i) q^{7} +O(q^{10})\)	\(q+(-0.0731228 + 0.126652i) q^{5} +(2.33035 - 1.25278i) q^{7} +(-0.832020 - 1.44110i) q^{11} +(0.0999454 + 0.173111i) q^{13} +(-3.13555 + 5.43093i) q^{17} +(-3.45879 - 5.99080i) q^{19} +(3.09092 - 5.35363i) q^{23} +(2.48931 + 4.31160i) q^{25} +(2.46757 - 4.27396i) q^{29} +2.51780 q^{31} +(-0.0117348 + 0.386752i) q^{35} +(-3.50023 - 6.06257i) q^{37} +(-1.15895 - 2.00736i) q^{41} +(0.940993 - 1.62985i) q^{43} -1.81177 q^{47} +(3.86110 - 5.83883i) q^{49} +(2.67307 - 4.62989i) q^{53} +0.243359 q^{55} -4.57099 q^{59} -0.678276 q^{61} -0.0292332 q^{65} +6.18684 q^{67} +1.27749 q^{71} +(-0.778603 + 1.34858i) q^{73} +(-3.74428 - 2.31594i) q^{77} -12.7957 q^{79} +(3.75687 - 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(-4.53394 - 7.85301i) q^{89} +(0.449777 + 0.278199i) q^{91} +1.01167 q^{95} +(-3.98514 + 6.90246i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{5} + 4 q^{7}+O(q^{10}) \) 10 * q - 4 * q^5 + 4 * q^7	\( 10 q - 4 q^{5} + 4 q^{7} + 4 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} + 3 q^{23} - q^{25} - 7 q^{29} - 6 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} - 54 q^{47} - 8 q^{49} + 21 q^{53} - 4 q^{55} - 60 q^{59} + 28 q^{61} - 22 q^{65} - 4 q^{67} - 6 q^{71} + 15 q^{73} - 11 q^{77} - 8 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} + 28 q^{95} - 12 q^{97}+O(q^{100}) \) 10 * q - 4 * q^5 + 4 * q^7 + 4 * q^11 - 8 * q^13 - 12 * q^17 - q^19 + 3 * q^23 - q^25 - 7 * q^29 - 6 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 - 54 * q^47 - 8 * q^49 + 21 * q^53 - 4 * q^55 - 60 * q^59 + 28 * q^61 - 22 * q^65 - 4 * q^67 - 6 * q^71 + 15 * q^73 - 11 * q^77 - 8 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 + 28 * q^95 - 12 * q^97

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