LMFDB - Embedded newform 585.2.h.g.64.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(64,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("585.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.h (of order $2$, degree $1$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.2593100598870016.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{10} + 9x^{8} - 16x^{6} + 36x^{4} - 64x^{2} + 64 $ x^12 - 4x^10 + 9x^8 - 16x^6 + 36x^4 - 64*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.7
Root			$-1.25694 + 0.648161i$ of defining polynomial
Character	$\chi$	$=$	585.64
Dual form			585.2.h.g.64.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.246506 q^{2} -1.93923 q^{4} +(-2.15160 - 0.608775i) q^{5} +2.59264 q^{7} -0.971044 q^{8} +O(q^{10})$	\(q+0.246506 q^{2} -1.93923 q^{4} +(-2.15160 - 0.608775i) q^{5} +2.59264 q^{7} -0.971044 q^{8} +(-0.530383 - 0.150067i) q^{10} +3.81019i q^{11} +(1.54283 - 3.25879i) q^{13} +0.639102 q^{14} +3.63910 q^{16} +4.63910i q^{17} +5.02774i q^{19} +(4.17246 + 1.18056i) q^{20} +0.939235i q^{22} -4.00000i q^{23} +(4.25879 + 2.61968i) q^{25} +(0.380316 - 0.803310i) q^{26} -5.02774 q^{28} +7.87847 q^{29} +10.2130i q^{31} +2.83915 q^{32} +1.14357i q^{34} +(-5.57834 - 1.57834i) q^{35} +4.53473 q^{37} +1.23937i q^{38} +(2.08930 + 0.591148i) q^{40} +6.40284i q^{41} +0.639102i q^{43} -7.38886i q^{44} -0.986023i q^{46} +3.81019 q^{47} -0.278203 q^{49} +(1.04982 + 0.645767i) q^{50} +(-2.99190 + 6.31955i) q^{52} -6.51757i q^{53} +(2.31955 - 8.19802i) q^{55} -2.51757 q^{56} +1.94209 q^{58} +6.24529i q^{59} -3.23937 q^{61} +2.51757i q^{62} -6.57834 q^{64} +(-5.30342 + 6.07238i) q^{65} -13.6342 q^{67} -8.99631i q^{68} +(-1.37509 - 0.389069i) q^{70} -13.4026i q^{71} +3.08565 q^{73} +1.11784 q^{74} -9.74998i q^{76} +9.87847i q^{77} -3.36090 q^{79} +(-7.82990 - 2.21539i) q^{80} +1.57834i q^{82} -7.23132 q^{83} +(2.82417 - 9.98150i) q^{85} +0.157542i q^{86} -3.69987i q^{88} -8.83794i q^{89} +(4.00000 - 8.44887i) q^{91} +7.75694i q^{92} +0.939235 q^{94} +(3.06077 - 10.8177i) q^{95} +14.1272 q^{97} -0.0685787 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{4}+O(q^{10}) $ 12 * q + 12 * q^4	$ 12 q + 12 q^{4} - 24 q^{10} - 16 q^{14} + 20 q^{16} + 4 q^{25} + 28 q^{26} + 24 q^{29} - 8 q^{35} - 16 q^{40} + 44 q^{49} + 16 q^{55} + 64 q^{56} + 8 q^{61} - 20 q^{64} - 28 q^{65} - 104 q^{74} - 64 q^{79} + 48 q^{91} - 24 q^{94} + 72 q^{95}+O(q^{100}) $ 12 * q + 12 * q^4 - 24 * q^10 - 16 * q^14 + 20 * q^16 + 4 * q^25 + 28 * q^26 + 24 * q^29 - 8 * q^35 - 16 * q^40 + 44 * q^49 + 16 * q^55 + 64 * q^56 + 8 * q^61 - 20 * q^64 - 28 * q^65 - 104 * q^74 - 64 * q^79 + 48 * q^91 - 24 * q^94 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.246506			0.174306			0.0871530	−	0.996195i	$-0.472223\pi$
$2$	0.246506			0.174306			0.0871530	+	0.996195i	$0.472223\pi$
$3$		0			0
$3$		0			0
$4$	−1.93923			−0.969617
$5$	−2.15160	−	0.608775i	−0.962226	−	0.272253i
$5$	−2.15160	−	0.608775i	−0.962226	−	0.272253i
$6$		0			0
$7$	2.59264			0.979927			0.489963	−	0.871743i	$-0.337010\pi$
$7$	2.59264			0.979927			0.489963	+	0.871743i	$0.337010\pi$
$8$	−0.971044			−0.343316
$9$		0			0
$10$	−0.530383	−	0.150067i	−0.167722	−	0.0474552i
$11$			3.81019i			1.14882i	0.818569	+	0.574408i	$0.194768\pi$
$11$			3.81019i			1.14882i	−0.818569	+	0.574408i	$0.805232\pi$
$12$		0			0
$13$	1.54283	−	3.25879i	0.427903	−	0.903825i
$13$	1.54283	−	3.25879i	0.427903	−	0.903825i
$14$	0.639102			0.170807
$15$		0			0
$16$	3.63910			0.909775
$17$			4.63910i			1.12515i	0.826747	+	0.562574i	$0.190189\pi$
$17$			4.63910i			1.12515i	−0.826747	+	0.562574i	$0.809811\pi$
$18$		0			0
$19$			5.02774i			1.15344i	0.816941	+	0.576722i	$0.195668\pi$
$19$			5.02774i			1.15344i	−0.816941	+	0.576722i	$0.804332\pi$
$20$	4.17246	+	1.18056i	0.932991	+	0.263981i
$21$		0			0
$22$			0.939235i			0.200246i
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$		0			0
$25$	4.25879	+	2.61968i	0.851757	+	0.523937i
$26$	0.380316	−	0.803310i	0.0745861	−	0.157542i
$27$		0			0
$28$	−5.02774			−0.950154
$29$	7.87847			1.46300			0.731498	−	0.681844i	$-0.238822\pi$
$29$	7.87847			1.46300			0.731498	+	0.681844i	$0.238822\pi$
$30$		0			0
$31$			10.2130i			1.83431i	0.398526	+	0.917157i	$0.369522\pi$
$31$			10.2130i			1.83431i	−0.398526	+	0.917157i	$0.630478\pi$
$32$	2.83915			0.501895
$33$		0			0
$34$			1.14357i			0.196120i
$35$	−5.57834	−	1.57834i	−0.942911	−	0.266788i
$36$		0			0
$37$	4.53473			0.745505			0.372753	−	0.927931i	$-0.378414\pi$
$37$	4.53473			0.745505			0.372753	+	0.927931i	$0.378414\pi$
$38$			1.23937i			0.201052i
$39$		0			0
$40$	2.08930	+	0.591148i	0.330348	+	0.0934687i
$41$			6.40284i			0.999955i	0.866038	+	0.499977i	$0.166658\pi$
$41$			6.40284i			0.999955i	−0.866038	+	0.499977i	$0.833342\pi$
$42$		0			0
$43$			0.639102i			0.0974621i	0.998812	+	0.0487310i	$0.0155177\pi$
$43$			0.639102i			0.0974621i	−0.998812	+	0.0487310i	$0.984482\pi$
$44$		−	7.38886i		−	1.11391i
$45$		0			0
$46$		−	0.986023i		−	0.145381i
$47$	3.81019			0.555774			0.277887	−	0.960614i	$-0.410366\pi$
$47$	3.81019			0.555774			0.277887	+	0.960614i	$0.410366\pi$
$48$		0			0
$49$	−0.278203			−0.0397433
$50$	1.04982	+	0.645767i	0.148466	+	0.0913253i
$51$		0			0
$52$	−2.99190	+	6.31955i	−0.414902	+	0.876364i
$53$		−	6.51757i		−	0.895257i	−0.894220	−	0.447629i	$-0.852269\pi$
$53$		−	6.51757i		−	0.895257i	0.894220	−	0.447629i	$-0.147731\pi$
$54$		0			0
$55$	2.31955	−	8.19802i	0.312768	−	1.10542i
$56$	−2.51757			−0.336425
$57$		0			0
$58$	1.94209			0.255009
$59$			6.24529i			0.813068i	0.913636	+	0.406534i	$0.133263\pi$
$59$			6.24529i			0.813068i	−0.913636	+	0.406534i	$0.866737\pi$
$60$		0			0
$61$	−3.23937			−0.414759			−0.207379	−	0.978261i	$-0.566493\pi$
$61$	−3.23937			−0.414759			−0.207379	+	0.978261i	$0.566493\pi$
$62$			2.51757i			0.319732i
$63$		0			0
$64$	−6.57834			−0.822292
$65$	−5.30342	+	6.07238i	−0.657808	+	0.753186i
$66$		0			0
$67$	−13.6342			−1.66568			−0.832838	−	0.553516i	$-0.813286\pi$
$67$	−13.6342			−1.66568			−0.832838	+	0.553516i	$0.813286\pi$
$68$		−	8.99631i		−	1.09096i
$69$		0			0
$70$	−1.37509	−	0.389069i	−0.164355	−	0.0465027i
$71$		−	13.4026i		−	1.59060i	−0.606217	−	0.795300i	$-0.707314\pi$
$71$		−	13.4026i		−	1.59060i	0.606217	−	0.795300i	$-0.292686\pi$
$72$		0			0
$73$	3.08565			0.361149			0.180574	−	0.983561i	$-0.442204\pi$
$73$	3.08565			0.361149			0.180574	+	0.983561i	$0.442204\pi$
$74$	1.11784			0.129946
$75$		0			0
$76$		−	9.74998i		−	1.11840i
$77$			9.87847i			1.12576i
$78$		0			0
$79$	−3.36090			−0.378131			−0.189065	−	0.981965i	$-0.560546\pi$
$79$	−3.36090			−0.378131			−0.189065	+	0.981965i	$0.560546\pi$
$80$	−7.82990	−	2.21539i	−0.875409	−	0.247689i
$81$		0			0
$82$			1.57834i			0.174298i
$83$	−7.23132			−0.793740			−0.396870	−	0.917875i	$-0.629904\pi$
$83$	−7.23132			−0.793740			−0.396870	+	0.917875i	$0.629904\pi$
$84$		0			0
$85$	2.82417	−	9.98150i	0.306324	−	1.08265i
$86$			0.157542i			0.0169882i
$87$		0			0
$88$		−	3.69987i		−	0.394407i
$89$		−	8.83794i		−	0.936819i	−0.883511	−	0.468410i	$-0.844827\pi$
$89$		−	8.83794i		−	0.936819i	0.883511	−	0.468410i	$-0.155173\pi$
$90$		0			0
$91$	4.00000	−	8.44887i	0.419314	−	0.885682i
$92$			7.75694i			0.808717i
$93$		0			0
$94$	0.939235			0.0968747
$95$	3.06077	−	10.8177i	0.314028	−	1.10987i
$96$		0			0
$97$	14.1272			1.43440			0.717198	−	0.696869i	$-0.245424\pi$
$97$	14.1272			1.43440			0.717198	+	0.696869i	$0.245424\pi$
$98$	−0.0685787			−0.00692750
$99$		0			0
$100$	−8.25879	−	5.08018i	−0.825879	−	0.508018i
$101$	3.27820			0.326193			0.163097	−	0.986610i	$-0.447852\pi$
$101$	3.27820			0.326193			0.163097	+	0.986610i	$0.447852\pi$
$102$		0			0
$103$		−	4.39604i		−	0.433155i	−0.976265	−	0.216577i	$-0.930511\pi$
$103$		−	4.39604i		−	0.433155i	0.976265	−	0.216577i	$-0.0694894\pi$
$104$	−1.49815	+	3.16443i	−0.146906	+	0.310297i
$105$		0			0
$106$		−	1.60662i		−	0.156049i
$107$			7.15667i			0.691862i	0.938260	+	0.345931i	$0.112437\pi$
$107$			7.15667i			0.691862i	−0.938260	+	0.345931i	$0.887563\pi$
$108$		0			0
$109$			4.40715i			0.422128i	0.977472	+	0.211064i	$0.0676929\pi$
$109$			4.40715i			0.422128i	−0.977472	+	0.211064i	$0.932307\pi$
$110$	0.571783	−	2.02086i	0.0545174	−	0.192681i
$111$		0			0
$112$	9.43489			0.891513
$113$			15.1178i			1.42217i	0.703108	+	0.711083i	$0.251795\pi$
$113$			15.1178i			1.42217i	−0.703108	+	0.711083i	$0.748205\pi$
$114$		0			0
$115$	−2.43510	+	8.60641i	−0.227074	+	0.802552i
$116$	−15.2782			−1.41855
$117$		0			0
$118$			1.53950i			0.141723i
$119$			12.0275i			1.10256i
$120$		0			0
$121$	−3.51757			−0.319779
$122$	−0.798523			−0.0722949
$123$		0			0
$124$		−	19.8055i		−	1.77858i
$125$	−7.56841	−	8.22916i	−0.676940	−	0.736039i
$126$		0			0
$127$			13.2782i			1.17825i	0.808042	+	0.589125i	$0.200527\pi$
$127$			13.2782i			1.17825i	−0.808042	+	0.589125i	$0.799473\pi$
$128$	−7.29990			−0.645226
$129$		0			0
$130$	−1.30732	+	1.49688i	−0.114660	+	0.131285i
$131$	7.75694			0.677727			0.338863	−	0.940836i	$-0.389958\pi$
$131$	7.75694			0.677727			0.338863	+	0.940836i	$0.389958\pi$
$132$		0			0
$133$			13.0351i			1.13029i
$134$	−3.36090			−0.290337
$135$		0			0
$136$		−	4.50477i		−	0.386281i
$137$	9.48849			0.810656			0.405328	−	0.914171i	$-0.367157\pi$
$137$	9.48849			0.810656			0.405328	+	0.914171i	$0.367157\pi$
$138$		0			0
$139$	7.75694			0.657935			0.328968	−	0.944341i	$-0.393299\pi$
$139$	7.75694			0.657935			0.328968	+	0.944341i	$0.393299\pi$
$140$	10.8177	+	3.06077i	0.914263	+	0.258682i
$141$		0			0
$142$		−	3.30383i		−	0.277251i
$143$	12.4166	+	5.87847i	1.03833	+	0.491582i
$144$		0			0
$145$	−16.9513	−	4.79622i	−1.40773	−	0.398304i
$146$	0.760632			0.0629503
$147$		0			0
$148$	−8.79391			−0.722855
$149$		−	1.21755i		−	0.0997456i	−0.998756	−	0.0498728i	$-0.984118\pi$
$149$		−	1.21755i		−	0.0997456i	0.998756	−	0.0498728i	$-0.0158816\pi$
$150$		0			0
$151$			10.2130i			0.831125i	0.909565	+	0.415562i	$0.136415\pi$
$151$			10.2130i			0.831125i	−0.909565	+	0.415562i	$0.863585\pi$
$152$		−	4.88216i		−	0.395996i
$153$		0			0
$154$			2.43510i			0.196226i
$155$	6.21744	−	21.9744i	0.499397	−	1.76502i
$156$		0			0
$157$		−	8.00000i		−	0.638470i	−0.947676	−	0.319235i	$-0.896574\pi$
$157$		−	8.00000i		−	0.638470i	0.947676	−	0.319235i	$-0.103426\pi$
$158$	−0.828481			−0.0659104
$159$		0			0
$160$	−6.10872	−	1.72840i	−0.482937	−	0.136642i
$161$		−	10.3706i		−	0.817316i
$162$		0			0
$163$	0.828481			0.0648916			0.0324458	−	0.999473i	$-0.489670\pi$
$163$	0.828481			0.0648916			0.0324458	+	0.999473i	$0.489670\pi$
$164$		−	12.4166i		−	0.969574i
$165$		0			0
$166$	−1.78256			−0.138354
$167$	11.4306			0.884525			0.442262	−	0.896886i	$-0.354176\pi$
$167$	11.4306			0.884525			0.442262	+	0.896886i	$0.354176\pi$
$168$		0			0
$169$	−8.23937	−	10.0555i	−0.633798	−	0.773499i
$170$	0.696174	−	2.46050i	0.0533941	−	0.188712i
$171$		0			0
$172$		−	1.23937i		−	0.0945009i
$173$		−	3.96116i		−	0.301162i	−0.988598	−	0.150581i	$-0.951886\pi$
$173$		−	3.96116i		−	0.301162i	0.988598	−	0.150581i	$-0.0481144\pi$
$174$		0			0
$175$	11.0415	+	6.79191i	0.834660	+	0.513420i
$176$			13.8657i			1.04516i
$177$		0			0
$178$		−	2.17860i		−	0.163293i
$179$	−20.7921			−1.55407			−0.777037	−	0.629455i	$-0.783278\pi$
$179$	−20.7921			−1.55407			−0.777037	+	0.629455i	$0.783278\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$	0.986023	−	2.08270i	0.0730889	−	0.154380i
$183$		0			0
$184$			3.88418i			0.286345i
$185$	−9.75694	−	2.76063i	−0.717344	−	0.202966i
$186$		0			0
$187$	−17.6759			−1.29259
$188$	−7.38886			−0.538888
$189$		0			0
$190$	0.754496	−	2.66663i	0.0547369	−	0.193457i
$191$	−0.600267			−0.0434338			−0.0217169	−	0.999764i	$-0.506913\pi$
$191$	−0.600267			−0.0434338			−0.0217169	+	0.999764i	$0.506913\pi$
$192$		0			0
$193$	−10.7060			−0.770638			−0.385319	−	0.922784i	$-0.625909\pi$
$193$	−10.7060			−0.770638			−0.385319	+	0.922784i	$0.625909\pi$
$194$	3.48243			0.250024
$195$		0			0
$196$	0.539501			0.0385358
$197$	−14.6738			−1.04546			−0.522732	−	0.852497i	$-0.675087\pi$
$197$	−14.6738			−1.04546			−0.522732	+	0.852497i	$0.675087\pi$
$198$		0			0
$199$	25.6742			1.82000			0.909999	−	0.414609i	$-0.136082\pi$
$199$	25.6742			1.82000			0.909999	+	0.414609i	$0.136082\pi$
$200$	−4.13547	−	2.54383i	−0.292422	−	0.179876i
$201$		0			0
$202$	0.808096			0.0568575
$203$	20.4261			1.43363
$204$		0			0
$205$	3.89789	−	13.7764i	0.272240	−	0.962183i
$206$		−	1.08365i		−	0.0755015i
$207$		0			0
$208$	5.61451	−	11.8591i	0.389296	−	0.822277i
$209$	−19.1567			−1.32509
$210$		0			0
$211$	−13.6742			−0.941374			−0.470687	−	0.882300i	$-0.655994\pi$
$211$	−13.6742			−0.941374			−0.470687	+	0.882300i	$0.655994\pi$
$212$			12.6391i			0.868057i
$213$		0			0
$214$			1.76416i			0.120596i
$215$	0.389069	−	1.37509i	0.0265343	−	0.0937805i
$216$		0			0
$217$			26.4787i			1.79749i
$218$			1.08639i			0.0735795i
$219$		0			0
$220$	−4.49815	+	15.8979i	−0.303265	+	1.07184i
$221$	15.1178	+	7.15733i	1.01694	+	0.481454i
$222$		0			0
$223$	−9.89794			−0.662815			−0.331408	−	0.943488i	$-0.607524\pi$
$223$	−9.89794			−0.662815			−0.331408	+	0.943488i	$0.607524\pi$
$224$	7.36090			0.491821
$225$		0			0
$226$			3.72664i			0.247892i
$227$	7.54640			0.500872			0.250436	−	0.968133i	$-0.419426\pi$
$227$	7.54640			0.500872			0.250436	+	0.968133i	$0.419426\pi$
$228$		0			0
$229$		−	14.7777i		−	0.976539i	−0.872693	−	0.488270i	$-0.837628\pi$
$229$		−	14.7777i		−	0.976539i	0.872693	−	0.488270i	$-0.162372\pi$
$230$	−0.600267	+	2.12153i	−0.0395804	+	0.139890i
$231$		0			0
$232$	−7.65034			−0.502270
$233$		−	1.48243i		−	0.0971171i	−0.998820	−	0.0485586i	$-0.984537\pi$
$233$		−	1.48243i		−	0.0971171i	0.998820	−	0.0485586i	$-0.0154628\pi$
$234$		0			0
$235$	−8.19802	−	2.31955i	−0.534780	−	0.151311i
$236$		−	12.1111i		−	0.788365i
$237$		0			0
$238$			2.96486i			0.192183i
$239$			6.56038i			0.424356i	0.977231	+	0.212178i	$0.0680556\pi$
$239$			6.56038i			0.424356i	−0.977231	+	0.212178i	$0.931944\pi$
$240$		0			0
$241$			9.59243i			0.617903i	0.951078	+	0.308951i	$0.0999781\pi$
$241$			9.59243i			0.617903i	−0.951078	+	0.308951i	$0.900022\pi$
$242$	−0.867102			−0.0557394
$243$		0			0
$244$	6.28190			0.402157
$245$	0.598583	+	0.169363i	0.0382420	+	0.0108202i
$246$		0			0
$247$	16.3843	+	7.75694i	1.04251	+	0.493562i
$248$		−	9.91730i		−	0.629749i
$249$		0			0
$250$	−1.86566	−	2.02854i	−0.117995	−	0.128296i
$251$	21.8785			1.38096			0.690478	−	0.723353i	$-0.257400\pi$
$251$	21.8785			1.38096			0.690478	+	0.723353i	$0.257400\pi$
$252$		0			0
$253$	15.2408			0.958179
$254$			3.27315i			0.205376i
$255$		0			0
$256$	11.3572			0.709825
$257$		−	5.23937i		−	0.326823i	−0.986558	−	0.163411i	$-0.947750\pi$
$257$		−	5.23937i		−	0.326823i	0.986558	−	0.163411i	$-0.0522498\pi$
$258$		0			0
$259$	11.7569			0.730541
$260$	10.2846	−	11.7758i	0.637822	−	0.730302i
$261$		0			0
$262$	1.91213			0.118132
$263$			5.87847i			0.362482i	0.983439	+	0.181241i	$0.0580114\pi$
$263$			5.87847i			0.362482i	−0.983439	+	0.181241i	$0.941989\pi$
$264$		0			0
$265$	−3.96774	+	14.0232i	−0.243736	+	0.861440i
$266$			3.21324i			0.197016i
$267$		0			0
$268$	26.4398			1.61507
$269$	8.91361			0.543473			0.271736	−	0.962372i	$-0.412402\pi$
$269$	8.91361			0.543473			0.271736	+	0.962372i	$0.412402\pi$
$270$		0			0
$271$			7.77793i			0.472476i	0.971695	+	0.236238i	$0.0759144\pi$
$271$			7.77793i			0.472476i	−0.971695	+	0.236238i	$0.924086\pi$
$272$			16.8822i			1.02363i
$273$		0			0
$274$	2.33897			0.141302
$275$	−9.98150	+	16.2268i	−0.601907	+	0.978513i
$276$		0			0
$277$		−	27.7569i		−	1.66775i	−0.551951	−	0.833876i	$-0.686117\pi$
$277$		−	27.7569i		−	1.66775i	0.551951	−	0.833876i	$-0.313883\pi$
$278$	1.91213			0.114682
$279$		0			0
$280$	5.41681	+	1.53263i	0.323716	+	0.0915925i
$281$			11.2730i			0.672493i	0.941774	+	0.336247i	$0.109158\pi$
$281$			11.2730i			0.672493i	−0.941774	+	0.336247i	$0.890842\pi$
$282$		0			0
$283$		−	4.00000i		−	0.237775i	−0.992908	−	0.118888i	$-0.962067\pi$
$283$		−	4.00000i		−	0.237775i	0.992908	−	0.118888i	$-0.0379328\pi$
$284$			25.9908i			1.54227i
$285$		0			0
$286$	3.06077	+	1.44908i	0.180987	+	0.0856857i
$287$			16.6003i			0.979883i
$288$		0			0
$289$	−4.52126			−0.265957
$290$	−4.17860	−	1.18230i	−0.245376	−	0.0694268i
$291$		0			0
$292$	−5.98381			−0.350176
$293$	−23.7432			−1.38709			−0.693547	−	0.720411i	$-0.743953\pi$
$293$	−23.7432			−1.38709			−0.693547	+	0.720411i	$0.743953\pi$
$294$		0			0
$295$	3.80198	−	13.4374i	0.221360	−	0.782355i
$296$	−4.40343			−0.255944
$297$		0			0
$298$		−	0.300133i		−	0.0173863i
$299$	−13.0351	−	6.17131i	−0.753842	−	0.356896i
$300$		0			0
$301$			1.65696i			0.0955057i
$302$			2.51757i			0.144870i
$303$		0			0
$304$			18.2965i			1.04937i
$305$	6.96983	+	1.97205i	0.399091	+	0.112919i
$306$		0			0
$307$	26.9029			1.53543			0.767714	−	0.640792i	$-0.221394\pi$
$307$	26.9029			1.53543			0.767714	+	0.640792i	$0.221394\pi$
$308$		−	19.1567i		−	1.09155i
$309$		0			0
$310$	1.53263	−	5.41681i	0.0870478	−	0.307654i
$311$	4.43488			0.251479			0.125739	−	0.992063i	$-0.459870\pi$
$311$	4.43488			0.251479			0.125739	+	0.992063i	$0.459870\pi$
$312$		0			0
$313$			18.2745i			1.03294i	0.856306	+	0.516468i	$0.172754\pi$
$313$			18.2745i			1.03294i	−0.856306	+	0.516468i	$0.827246\pi$
$314$		−	1.97205i		−	0.111289i
$315$		0			0
$316$	6.51757			0.366642
$317$	−25.7153			−1.44431			−0.722157	−	0.691729i	$-0.756849\pi$
$317$	−25.7153			−1.44431			−0.722157	+	0.691729i	$0.756849\pi$
$318$		0			0
$319$			30.0185i			1.68071i
$320$	14.1540	+	4.00473i	0.791231	+	0.223871i
$321$		0			0
$322$		−	2.55641i		−	0.142463i
$323$	−23.3242			−1.29779
$324$		0			0
$325$	15.1076	−	9.83675i	0.838017	−	0.545645i
$326$	0.204225			0.0113110
$327$		0			0
$328$		−	6.21744i		−	0.343301i
$329$	9.87847			0.544618
$330$		0			0
$331$		−	0.620596i		−	0.0341110i	−0.999855	−	0.0170555i	$-0.994571\pi$
$331$		−	0.620596i		−	0.0341110i	0.999855	−	0.0170555i	$-0.00542920\pi$
$332$	14.0232			0.769624
$333$		0			0
$334$	2.81770			0.154178
$335$	29.3353	+	8.30013i	1.60276	+	0.453485i
$336$		0			0
$337$		−	24.9963i		−	1.36164i	−0.732453	−	0.680818i	$-0.761625\pi$
$337$		−	24.9963i		−	1.36164i	0.732453	−	0.680818i	$-0.238375\pi$
$338$	−2.03105	−	2.47874i	−0.110475	−	0.134825i
$339$		0			0
$340$	−5.47673	+	19.3565i	−0.297017	+	1.04975i
$341$	−38.9136			−2.10729
$342$		0			0
$343$	−18.8698			−1.01887
$344$		−	0.620596i		−	0.0334603i
$345$		0			0
$346$		−	0.976450i		−	0.0524943i
$347$		−	31.7569i		−	1.70480i	−0.522889	−	0.852401i	$-0.675146\pi$
$347$		−	31.7569i		−	1.70480i	0.522889	−	0.852401i	$-0.324854\pi$
$348$		0			0
$349$			1.97205i			0.105561i	0.998606	+	0.0527806i	$0.0168084\pi$
$349$			1.97205i			0.105561i	−0.998606	+	0.0527806i	$0.983192\pi$
$350$	2.72180	+	1.67424i	0.145486	+	0.0894921i
$351$		0			0
$352$			10.8177i			0.576586i
$353$	15.6598			0.833487			0.416744	−	0.909024i	$-0.363171\pi$
$353$	15.6598			0.833487			0.416744	+	0.909024i	$0.363171\pi$
$354$		0			0
$355$	−8.15919	+	28.8371i	−0.433045	+	1.53052i
$356$			17.1388i			0.908356i
$357$		0			0
$358$	−5.12537			−0.270884
$359$			13.7177i			0.723993i	0.932179	+	0.361997i	$0.117905\pi$
$359$			13.7177i			0.723993i	−0.932179	+	0.361997i	$0.882095\pi$
$360$		0			0
$361$	−6.27820			−0.330432
$362$	−1.47904			−0.0777364
$363$		0			0
$364$	−7.75694	+	16.3843i	−0.406574	+	0.858773i
$365$	−6.63910	−	1.87847i	−0.347506	−	0.0983236i
$366$		0			0
$367$			8.63910i			0.450957i	0.974248	+	0.225479i	$0.0723946\pi$
$367$			8.63910i			0.450957i	−0.974248	+	0.225479i	$0.927605\pi$
$368$		−	14.5564i		−	0.758805i
$369$		0			0
$370$	−2.40514	−	0.680512i	−0.125037	−	0.0353781i
$371$		−	16.8977i		−	0.877287i
$372$		0			0
$373$		−	31.7958i		−	1.64632i	−0.567807	−	0.823161i	$-0.692208\pi$
$373$		−	31.7958i		−	1.64632i	0.567807	−	0.823161i	$-0.307792\pi$
$374$	−4.35721			−0.225306
$375$		0			0
$376$	−3.69987			−0.190806
$377$	12.1551	−	25.6742i	0.626020	−	1.32229i
$378$		0			0
$379$		−	2.12959i		−	0.109390i	−0.998503	−	0.0546948i	$-0.982581\pi$
$379$		−	2.12959i		−	0.109390i	0.998503	−	0.0546948i	$-0.0174186\pi$
$380$	−5.93554	+	20.9781i	−0.304487	+	1.07615i
$381$		0			0
$382$	−0.147969			−0.00757076
$383$	13.4026			0.684842			0.342421	−	0.939547i	$-0.388753\pi$
$383$	13.4026			0.684842			0.342421	+	0.939547i	$0.388753\pi$
$384$		0			0
$385$	6.01377	−	21.2545i	0.306490	−	1.08323i
$386$	−2.63910			−0.134327
$387$		0			0
$388$	−27.3959			−1.39082
$389$	16.9136			0.857554			0.428777	−	0.903410i	$-0.358945\pi$
$389$	16.9136			0.857554			0.428777	+	0.903410i	$0.358945\pi$
$390$		0			0
$391$	18.5564			0.938438
$392$	0.270148			0.0136445
$393$		0			0
$394$	−3.61717			−0.182230
$395$	7.23132	+	2.04603i	0.363847	+	0.102947i
$396$		0			0
$397$	−15.8913			−0.797563			−0.398781	−	0.917046i	$-0.630567\pi$
$397$	−15.8913			−0.797563			−0.398781	+	0.917046i	$0.630567\pi$
$398$	6.32885			0.317237
$399$		0			0
$400$	15.4982	+	9.53330i	0.774908	+	0.476665i
$401$		−	14.3383i		−	0.716021i	−0.933718	−	0.358010i	$-0.883455\pi$
$401$		−	14.3383i		−	0.716021i	0.933718	−	0.358010i	$-0.116545\pi$
$402$		0			0
$403$	33.2821	+	15.7569i	1.65790	+	0.784909i
$404$	−6.35721			−0.316283
$405$		0			0
$406$	5.03514			0.249890
$407$			17.2782i			0.856449i
$408$		0			0
$409$		−	22.5461i		−	1.11483i	−0.830233	−	0.557416i	$-0.811793\pi$
$409$		−	22.5461i		−	1.11483i	0.830233	−	0.557416i	$-0.188207\pi$
$410$	0.960852	−	3.39595i	0.0474531	−	0.167714i
$411$		0			0
$412$			8.52496i			0.419994i
$413$			16.1918i			0.796747i
$414$		0			0
$415$	15.5589	+	4.40225i	0.763757	+	0.216098i
$416$	4.38032	−	9.25218i	0.214763	−	0.453625i
$417$		0			0
$418$	−4.72223			−0.230972
$419$	20.7921			1.01576			0.507880	−	0.861428i	$-0.330429\pi$
$419$	20.7921			1.01576			0.507880	+	0.861428i	$0.330429\pi$
$420$		0			0
$421$		−	30.0185i		−	1.46301i	−0.681835	−	0.731506i	$-0.738818\pi$
$421$		−	30.0185i		−	1.46301i	0.681835	−	0.731506i	$-0.261182\pi$
$422$	−3.37078			−0.164087
$423$		0			0
$424$			6.32885i			0.307356i
$425$	−12.1530	+	19.7569i	−0.589506	+	0.958352i
$426$		0			0
$427$	−8.39852			−0.406433
$428$		−	13.8785i		−	0.670841i
$429$		0			0
$430$	0.0959078	−	0.338968i	0.00462509	−	0.0163465i
$431$		−	1.37509i		−	0.0662359i	−0.999451	−	0.0331179i	$-0.989456\pi$
$431$		−	1.37509i		−	0.0662359i	0.999451	−	0.0331179i	$-0.0105437\pi$
$432$		0			0
$433$			7.79577i			0.374641i	0.982299	+	0.187321i	$0.0599803\pi$
$433$			7.79577i			0.374641i	−0.982299	+	0.187321i	$0.940020\pi$
$434$			6.52716i			0.313314i
$435$		0			0
$436$		−	8.54649i		−	0.409303i
$437$	20.1110			0.962038
$438$		0			0
$439$	−19.7569			−0.942947			−0.471474	−	0.881880i	$-0.656278\pi$
$439$	−19.7569			−0.942947			−0.471474	+	0.881880i	$0.656278\pi$
$440$	−2.25239	+	7.96064i	−0.107378	+	0.379509i
$441$		0			0
$442$	3.72664	+	1.76432i	0.177258	+	0.0839203i
$443$			20.1918i			0.959342i	0.877448	+	0.479671i	$0.159244\pi$
$443$			20.1918i			0.959342i	−0.877448	+	0.479671i	$0.840756\pi$
$444$		0			0
$445$	−5.38032	+	19.0157i	−0.255051	+	0.901432i
$446$	−2.43990			−0.115533
$447$		0			0
$448$	−17.0553			−0.805786
$449$		−	40.8285i		−	1.92681i	−0.268041	−	0.963407i	$-0.586376\pi$
$449$		−	40.8285i		−	1.92681i	0.268041	−	0.963407i	$-0.413624\pi$
$450$		0			0
$451$	−24.3960			−1.14876
$452$		−	29.3170i		−	1.37896i
$453$		0			0
$454$	1.86023			0.0873050
$455$	−13.7499	+	15.7435i	−0.644604	+	0.738067i
$456$		0			0
$457$	−25.4838			−1.19208			−0.596040	−	0.802955i	$-0.703260\pi$
$457$	−25.4838			−1.19208			−0.596040	+	0.802955i	$0.703260\pi$
$458$		−	3.64279i		−	0.170217i
$459$		0			0
$460$	4.72223	−	16.6898i	0.220175	−	0.778168i
$461$			11.5881i			0.539713i	0.962901	+	0.269856i	$0.0869762\pi$
$461$			11.5881i			0.539713i	−0.962901	+	0.269856i	$0.913024\pi$
$462$		0			0
$463$	7.77793			0.361471			0.180735	−	0.983532i	$-0.442152\pi$
$463$	7.77793			0.361471			0.180735	+	0.983532i	$0.442152\pi$
$464$	28.6706			1.33100
$465$		0			0
$466$		−	0.365427i		−	0.0169281i
$467$			14.4787i			0.669996i	0.942219	+	0.334998i	$0.108736\pi$
$467$			14.4787i			0.669996i	−0.942219	+	0.334998i	$0.891264\pi$
$468$		0			0
$469$	−35.3485			−1.63224
$470$	−2.02086	−	0.571783i	−0.0932153	−	0.0263744i
$471$		0			0
$472$		−	6.06446i		−	0.279139i
$473$	−2.43510			−0.111966
$474$		0			0
$475$	−13.1711	+	21.4121i	−0.604331	+	0.982454i
$476$		−	23.3242i		−	1.06906i
$477$		0			0
$478$			1.61717i			0.0739677i
$479$		−	9.45853i		−	0.432171i	−0.976374	−	0.216086i	$-0.930671\pi$
$479$		−	9.45853i		−	0.432171i	0.976374	−	0.216086i	$-0.0693291\pi$
$480$		0			0
$481$	6.99631	−	14.7777i	0.319004	−	0.673806i
$482$			2.36459i			0.107704i
$483$		0			0
$484$	6.82140			0.310064
$485$	−30.3960	−	8.60027i	−1.38021	−	0.390518i
$486$		0			0
$487$	12.1851			0.552158			0.276079	−	0.961135i	$-0.410965\pi$
$487$	12.1851			0.552158			0.276079	+	0.961135i	$0.410965\pi$
$488$	3.14557			0.142393
$489$		0			0
$490$	0.147554	+	0.0417490i	0.00666582	+	0.00188603i
$491$	−44.1918			−1.99435			−0.997174	−	0.0751219i	$-0.976065\pi$
$491$	−44.1918			−1.99435			−0.997174	+	0.0751219i	$0.976065\pi$
$492$		0			0
$493$			36.5490i			1.64609i
$494$	4.03884	+	1.91213i	0.181716	+	0.0860308i
$495$		0			0
$496$			37.1663i			1.66881i
$497$		−	34.7482i		−	1.55867i
$498$		0			0
$499$		−	33.3893i		−	1.49471i	−0.664425	−	0.747355i	$-0.731324\pi$
$499$		−	33.3893i		−	1.49471i	0.664425	−	0.747355i	$-0.268676\pi$
$500$	14.6769	+	15.9583i	0.656372	+	0.713676i
$501$		0			0
$502$	5.39317			0.240709
$503$			20.6779i			0.921984i	0.887404	+	0.460992i	$0.152506\pi$
$503$			20.6779i			0.921984i	−0.887404	+	0.460992i	$0.847494\pi$
$504$		0			0
$505$	−7.05339	−	1.99569i	−0.313872	−	0.0888070i
$506$	3.75694			0.167016
$507$		0			0
$508$		−	25.7496i		−	1.14245i
$509$		−	26.8289i		−	1.18917i	−0.804033	−	0.594585i	$-0.797316\pi$
$509$		−	26.8289i		−	1.18917i	0.804033	−	0.594585i	$-0.202684\pi$
$510$		0			0
$511$	8.00000			0.353899
$512$	17.3994			0.768953
$513$		0			0
$514$		−	1.29153i		−	0.0569672i
$515$	−2.67620	+	9.45853i	−0.117927	+	0.416793i
$516$		0			0
$517$			14.5176i			0.638482i
$518$	2.89815			0.127338
$519$		0			0
$520$	5.14985	−	5.89655i	0.225836	−	0.258581i
$521$	42.1918			1.84846			0.924229	−	0.381840i	$-0.124709\pi$
$521$	42.1918			1.84846			0.924229	+	0.381840i	$0.124709\pi$
$522$		0			0
$523$		−	30.9524i		−	1.35346i	−0.736233	−	0.676728i	$-0.763397\pi$
$523$		−	30.9524i		−	1.35346i	0.736233	−	0.676728i	$-0.236603\pi$
$524$	−15.0425			−0.657136
$525$		0			0
$526$			1.44908i			0.0631828i
$527$	−47.3793			−2.06387
$528$		0			0
$529$	7.00000			0.304348
$530$	−0.978070	+	3.45681i	−0.0424846	+	0.150154i
$531$		0			0
$532$		−	25.2782i		−	1.09595i
$533$	20.8655	+	9.87847i	0.903784	+	0.427884i
$534$		0			0
$535$	4.35680	−	15.3983i	0.188361	−	0.665727i
$536$	13.2394			0.571854
$537$		0			0
$538$	2.19726			0.0947305
$539$		−	1.06001i		−	0.0456578i
$540$		0			0
$541$		−	37.1758i		−	1.59831i	−0.601123	−	0.799157i	$-0.705280\pi$
$541$		−	37.1758i		−	1.59831i	0.601123	−	0.799157i	$-0.294720\pi$
$542$			1.91730i			0.0823553i
$543$		0			0
$544$			13.1711i			0.564706i
$545$	2.68296	−	9.48243i	0.114925	−	0.406183i
$546$		0			0
$547$		−	30.9524i		−	1.32343i	−0.749755	−	0.661716i	$-0.769829\pi$
$547$		−	30.9524i		−	1.32343i	0.749755	−	0.661716i	$-0.230171\pi$
$548$	−18.4004			−0.786027
$549$		0			0
$550$	−2.46050	+	4.00000i	−0.104916	+	0.170561i
$551$			39.6109i			1.68748i
$552$		0			0
$553$	−8.71361			−0.370540
$554$		−	6.84225i		−	0.290699i
$555$		0			0
$556$	−15.0425			−0.637945
$557$	−43.3912			−1.83854			−0.919271	−	0.393625i	$-0.871221\pi$
$557$	−43.3912			−1.83854			−0.919271	+	0.393625i	$0.871221\pi$
$558$		0			0
$559$	2.08270	+	0.986023i	0.0880886	+	0.0417043i
$560$	−20.3001	−	5.74373i	−0.857837	−	0.242717i
$561$		0			0
$562$			2.77887i			0.117220i
$563$			3.39973i			0.143282i	0.997430	+	0.0716408i	$0.0228235\pi$
$563$			3.39973i			0.143282i	−0.997430	+	0.0716408i	$0.977176\pi$
$564$		0			0
$565$	9.20336	−	32.5276i	0.387188	−	1.36845i
$566$		−	0.986023i		−	0.0414457i
$567$		0			0
$568$			13.0145i			0.546078i
$569$	19.2782			0.808184			0.404092	−	0.914718i	$-0.367588\pi$
$569$	19.2782			0.808184			0.404092	+	0.914718i	$0.367588\pi$
$570$		0			0
$571$	5.67424			0.237460			0.118730	−	0.992927i	$-0.462118\pi$
$571$	5.67424			0.237460			0.118730	+	0.992927i	$0.462118\pi$
$572$	−24.0787	−	11.3997i	−1.00678	−	0.476647i
$573$		0			0
$574$			4.09206i			0.170799i
$575$	10.4787	−	17.0351i	0.436994	−	0.710415i
$576$		0			0
$577$	−32.4332			−1.35021			−0.675106	−	0.737721i	$-0.735902\pi$
$577$	−32.4332			−1.35021			−0.675106	+	0.737721i	$0.735902\pi$
$578$	−1.11452			−0.0463578
$579$		0			0
$580$	32.8726	+	9.30099i	1.36496	+	0.386203i
$581$	−18.7482			−0.777807
$582$		0			0
$583$	24.8332			1.02849
$584$	−2.99631			−0.123988
$585$		0			0
$586$	−5.85285			−0.241779
$587$	−14.7037			−0.606888			−0.303444	−	0.952849i	$-0.598137\pi$
$587$	−14.7037			−0.606888			−0.303444	+	0.952849i	$0.598137\pi$
$588$		0			0
$589$	−51.3485			−2.11578
$590$	0.937210	−	3.31239i	0.0385843	−	0.136369i
$591$		0			0
$592$	16.5023			0.678242
$593$	−10.7896			−0.443076			−0.221538	−	0.975152i	$-0.571108\pi$
$593$	−10.7896			−0.443076			−0.221538	+	0.975152i	$0.571108\pi$
$594$		0			0
$595$	7.32206	−	25.8785i	0.300175	−	1.06091i
$596$			2.36112i			0.0967151i
$597$		0			0
$598$	−3.21324	−	1.52126i	−0.131399	−	0.0622091i
$599$	−24.7921			−1.01298			−0.506489	−	0.862247i	$-0.669057\pi$
$599$	−24.7921			−1.01298			−0.506489	+	0.862247i	$0.669057\pi$
$600$		0			0
$601$	8.51757			0.347439			0.173719	−	0.984795i	$-0.444421\pi$
$601$	8.51757			0.347439			0.173719	+	0.984795i	$0.444421\pi$
$602$			0.408451i			0.0166472i
$603$		0			0
$604$		−	19.8055i		−	0.805873i
$605$	7.56841	+	2.14141i	0.307700	+	0.0870607i
$606$		0			0
$607$			21.6742i			0.879730i	0.898064	+	0.439865i	$0.144974\pi$
$607$			21.6742i			0.879730i	−0.898064	+	0.439865i	$0.855026\pi$
$608$			14.2745i			0.578908i
$609$		0			0
$610$	1.71810	+	0.486121i	0.0695640	+	0.0196825i
$611$	5.87847	−	12.4166i	0.237817	−	0.502322i
$612$		0			0
$613$	12.3630			0.499337			0.249668	−	0.968331i	$-0.419678\pi$
$613$	12.3630			0.499337			0.249668	+	0.968331i	$0.419678\pi$
$614$	6.63172			0.267634
$615$		0			0
$616$		−	9.59243i		−	0.386490i
$617$	19.2289			0.774126			0.387063	−	0.922053i	$-0.373490\pi$
$617$	19.2289			0.774126			0.387063	+	0.922053i	$0.373490\pi$
$618$		0			0
$619$		−	4.56469i		−	0.183470i	−0.995783	−	0.0917352i	$-0.970759\pi$
$619$		−	4.56469i		−	0.183470i	0.995783	−	0.0917352i	$-0.0292413\pi$
$620$	−12.0571	+	42.6135i	−0.484224	+	1.71140i
$621$		0			0
$622$	1.09322			0.0438342
$623$		−	22.9136i		−	0.918014i
$624$		0			0
$625$	11.2745	+	22.3133i	0.450980	+	0.892534i
$626$			4.50477i			0.180047i
$627$		0			0
$628$			15.5139i			0.619071i
$629$			21.0371i			0.838803i
$630$		0			0
$631$			4.71266i			0.187608i	0.995591	+	0.0938040i	$0.0299027\pi$
$631$			4.71266i			0.187608i	−0.995591	+	0.0938040i	$0.970097\pi$
$632$	3.26358			0.129818
$633$		0			0
$634$	−6.33897			−0.251753
$635$	8.08344	−	28.5694i	0.320782	−	1.13374i
$636$		0			0
$637$	−0.429220	+	0.906605i	−0.0170063	+	0.0359210i
$638$			7.39973i			0.292958i
$639$		0			0
$640$	15.7065	+	4.44399i	0.620853	+	0.175664i
$641$	1.56512			0.0618187			0.0309093	−	0.999522i	$-0.490160\pi$
$641$	1.56512			0.0618187			0.0309093	+	0.999522i	$0.490160\pi$
$642$		0			0
$643$	−0.365427			−0.0144110			−0.00720552	−	0.999974i	$-0.502294\pi$
$643$	−0.365427			−0.0144110			−0.00720552	+	0.999974i	$0.502294\pi$
$644$			20.1110i			0.792483i
$645$		0			0
$646$	−5.74955			−0.226213
$647$		−	24.3572i		−	0.957581i	−0.877929	−	0.478790i	$-0.841075\pi$
$647$		−	24.3572i		−	0.957581i	0.877929	−	0.478790i	$-0.158925\pi$
$648$		0			0
$649$	−23.7958			−0.934066
$650$	3.72410	−	2.42482i	0.146071	−	0.0951091i
$651$		0			0
$652$	−1.60662			−0.0629201
$653$			46.6317i			1.82484i	0.409255	+	0.912420i	$0.365789\pi$
$653$			46.6317i			1.82484i	−0.409255	+	0.912420i	$0.634211\pi$
$654$		0			0
$655$	−16.6898	−	4.72223i	−0.652126	−	0.184513i
$656$			23.3006i			0.909734i
$657$		0			0
$658$	2.43510			0.0949301
$659$	15.0790			0.587395			0.293697	−	0.955898i	$-0.405114\pi$
$659$	15.0790			0.587395			0.293697	+	0.955898i	$0.405114\pi$
$660$		0			0
$661$			32.4536i			1.26230i	0.775661	+	0.631149i	$0.217416\pi$
$661$			32.4536i			1.26230i	−0.775661	+	0.631149i	$0.782584\pi$
$662$		−	0.152981i		−	0.00594576i
$663$		0			0
$664$	7.02193			0.272504
$665$	7.93547	−	28.0464i	0.307724	−	1.08759i
$666$		0			0
$667$		−	31.5139i		−	1.22022i
$668$	−22.1666			−0.857651
$669$		0			0
$670$	7.23132	+	2.04603i	0.279370	+	0.0790451i
$671$		−	12.3426i		−	0.476481i
$672$		0			0
$673$			25.2782i			0.974403i	0.873290	+	0.487202i	$0.161982\pi$
$673$			25.2782i			0.974403i	−0.873290	+	0.487202i	$0.838018\pi$
$674$		−	6.16174i		−	0.237341i
$675$		0			0
$676$	15.9781	+	19.5000i	0.614541	+	0.749998i
$677$		−	46.0315i		−	1.76913i	−0.466415	−	0.884566i	$-0.654455\pi$
$677$		−	46.0315i		−	1.76913i	0.466415	−	0.884566i	$-0.345545\pi$
$678$		0			0
$679$	36.6267			1.40560
$680$	−2.74239	+	9.69248i	−0.105166	+	0.371690i
$681$		0			0
$682$	−9.59243			−0.367313
$683$	28.4355			1.08805			0.544027	−	0.839067i	$-0.316899\pi$
$683$	28.4355			1.08805			0.544027	+	0.839067i	$0.316899\pi$
$684$		0			0
$685$	−20.4155	−	5.77636i	−0.780035	−	0.220703i
$686$	−4.65151			−0.177596
$687$		0			0
$688$			2.32576i			0.0886686i
$689$	−21.2394	−	10.0555i	−0.809155	−	0.383084i
$690$		0			0
$691$		−	14.3051i		−	0.544191i	−0.962270	−	0.272096i	$-0.912283\pi$
$691$		−	14.3051i		−	0.544191i	0.962270	−	0.272096i	$-0.0877167\pi$
$692$			7.68163i			0.292012i
$693$		0			0
$694$		−	7.82827i		−	0.297157i
$695$	−16.6898	−	4.72223i	−0.633082	−	0.179124i
$696$		0			0
$697$	−29.7034			−1.12510
$698$			0.486121i			0.0184000i
$699$		0			0
$700$	−21.4121	−	13.1711i	−0.809301	−	0.497821i
$701$	−40.6706			−1.53611			−0.768053	−	0.640387i	$-0.778774\pi$
$701$	−40.6706			−1.53611			−0.768053	+	0.640387i	$0.778774\pi$
$702$		0			0
$703$			22.7995i			0.859898i
$704$		−	25.0647i		−	0.944663i
$705$		0			0
$706$	3.86023			0.145282
$707$	8.49921			0.319646
$708$		0			0
$709$			16.4347i			0.617217i	0.951189	+	0.308609i	$0.0998634\pi$
$709$			16.4347i			0.617217i	−0.951189	+	0.308609i	$0.900137\pi$
$710$	−2.01129	+	7.10852i	−0.0754823	+	0.266778i
$711$		0			0
$712$			8.58203i			0.321625i
$713$	40.8521			1.52992
$714$		0			0
$715$	−23.1369	−	20.2070i	−0.865272	−	0.755701i
$716$	40.3207			1.50686
$717$		0			0
$718$			3.38150i			0.126196i
$719$	7.39973			0.275963			0.137982	−	0.990435i	$-0.455938\pi$
$719$	7.39973			0.275963			0.137982	+	0.990435i	$0.455938\pi$
$720$		0			0
$721$		−	11.3974i		−	0.424460i
$722$	−1.54761			−0.0575962
$723$		0			0
$724$	11.6354			0.432427
$725$	33.5527	+	20.6391i	1.24612	+	0.766517i
$726$		0			0
$727$		−	44.7921i		−	1.66125i	−0.556835	−	0.830623i	$-0.687984\pi$
$727$		−	44.7921i		−	1.66125i	0.556835	−	0.830623i	$-0.312016\pi$
$728$	−3.88418	+	8.20423i	−0.143957	+	0.304069i
$729$		0			0
$730$	−1.63658	−	0.463054i	−0.0605724	−	0.0171384i
$731$	−2.96486			−0.109659
$732$		0			0
$733$	−36.2102			−1.33745			−0.668727	−	0.743508i	$-0.733160\pi$
$733$	−36.2102			−1.33745			−0.668727	+	0.743508i	$0.733160\pi$
$734$			2.12959i			0.0786046i
$735$		0			0
$736$		−	11.3566i		−	0.418610i
$737$		−	51.9488i		−	1.91356i
$738$		0			0
$739$		−	16.5922i		−	0.610355i	−0.952296	−	0.305177i	$-0.901284\pi$
$739$		−	16.5922i		−	0.610355i	0.952296	−	0.305177i	$-0.0987158\pi$
$740$	18.9210	+	5.35351i	0.695550	+	0.196799i
$741$		0			0
$742$		−	4.16539i		−	0.152916i
$743$	−11.7457			−0.430907			−0.215453	−	0.976514i	$-0.569123\pi$
$743$	−11.7457			−0.430907			−0.215453	+	0.976514i	$0.569123\pi$
$744$		0			0
$745$	−0.741214	+	2.61968i	−0.0271560	+	0.0959778i
$746$		−	7.83784i		−	0.286964i
$747$		0			0
$748$	34.2777			1.25332
$749$			18.5547i			0.677974i
$750$		0			0
$751$	−15.5139			−0.566109			−0.283055	−	0.959104i	$-0.591348\pi$
$751$	−15.5139			−0.566109			−0.283055	+	0.959104i	$0.591348\pi$
$752$	13.8657			0.505629
$753$		0			0
$754$	2.99631	−	6.32885i	0.109119	−	0.230483i
$755$	6.21744	−	21.9744i	0.226276	−	0.799729i
$756$		0			0
$757$		−	5.31704i		−	0.193251i	−0.995321	−	0.0966255i	$-0.969195\pi$
$757$		−	5.31704i		−	0.193251i	0.995321	−	0.0966255i	$-0.0308049\pi$
$758$		−	0.524956i		−	0.0190673i
$759$		0			0
$760$	−2.97214	+	10.5045i	−0.107811	+	0.381037i
$761$		−	29.5791i		−	1.07224i	−0.844142	−	0.536120i	$-0.819889\pi$
$761$		−	29.5791i		−	1.07224i	0.844142	−	0.536120i	$-0.180111\pi$
$762$		0			0
$763$			11.4262i			0.413655i
$764$	1.16406			0.0421141
$765$		0			0
$766$	3.30383			0.119372
$767$	20.3521	+	9.63541i	0.734871	+	0.347914i
$768$		0			0
$769$			27.8985i			1.00604i	0.864273	+	0.503022i	$0.167779\pi$
$769$			27.8985i			1.00604i	−0.864273	+	0.503022i	$0.832221\pi$
$770$	1.48243	−	5.23937i	0.0534230	−	0.188814i
$771$		0			0
$772$	20.7615			0.747224
$773$	7.36847			0.265026			0.132513	−	0.991181i	$-0.457695\pi$
$773$	7.36847			0.265026			0.132513	+	0.991181i	$0.457695\pi$
$774$		0			0
$775$	−26.7549	+	43.4951i	−0.961065	+	1.56239i
$776$	−13.7181			−0.492451
$777$		0			0
$778$	4.16930			0.149477
$779$	−32.1918			−1.15339
$780$		0			0
$781$	51.0666			1.82731
$782$	4.57426			0.163575
$783$		0			0
$784$	−1.01241			−0.0361575
$785$	−4.87020	+	17.2128i	−0.173825	+	0.614352i
$786$		0			0
$787$	11.6621			0.415709			0.207855	−	0.978160i	$-0.433352\pi$
$787$	11.6621			0.415709			0.207855	+	0.978160i	$0.433352\pi$
$788$	28.4559			1.01370
$789$		0			0
$790$	1.78256	+	0.504359i	0.0634207	+	0.0179443i
$791$			39.1952i			1.39362i
$792$		0			0
$793$	−4.99779	+	10.5564i	−0.177477	+	0.374869i
$794$	−3.91730			−0.139020
$795$		0			0
$796$	−49.7884			−1.76470
$797$		−	8.47371i		−	0.300154i	−0.988674	−	0.150077i	$-0.952048\pi$
$797$		−	8.47371i		−	0.300154i	0.988674	−	0.150077i	$-0.0479522\pi$
$798$		0			0
$799$			17.6759i			0.625327i
$800$	12.0913	+	7.43767i	0.427493	+	0.262961i
$801$		0			0
$802$		−	3.53448i		−	0.124807i
$803$			11.7569i			0.414893i
$804$		0			0
$805$	−6.31335	+	22.3133i	−0.222516	+	0.786442i
$806$	8.20423	+	3.88418i	0.288982	+	0.136814i
$807$		0			0
$808$	−3.18328			−0.111987
$809$	16.9136			0.594651			0.297325	−	0.954776i	$-0.403905\pi$
$809$	16.9136			0.594651			0.297325	+	0.954776i	$0.403905\pi$
$810$		0			0
$811$			23.4818i			0.824556i	0.911058	+	0.412278i	$0.135267\pi$
$811$			23.4818i			0.824556i	−0.911058	+	0.412278i	$0.864733\pi$
$812$	−39.6109			−1.39007
$813$		0			0
$814$			4.25918i			0.149284i
$815$	−1.78256	−	0.504359i	−0.0624404	−	0.0176669i
$816$		0			0
$817$	−3.21324			−0.112417
$818$		−	5.55774i		−	0.194322i
$819$		0			0
$820$	−7.55892	+	26.7156i	−0.263969	+	0.932949i
$821$			19.5236i			0.681378i	0.940176	+	0.340689i	$0.110660\pi$
$821$			19.5236i			0.681378i	−0.940176	+	0.340689i	$0.889340\pi$
$822$		0			0
$823$		−	12.4737i		−	0.434806i	−0.976082	−	0.217403i	$-0.930241\pi$
$823$		−	12.4737i		−	0.434806i	0.976082	−	0.217403i	$-0.0697586\pi$
$824$			4.26875i			0.148709i
$825$		0			0
$826$			3.99138i			0.138878i
$827$	−27.0272			−0.939828			−0.469914	−	0.882712i	$-0.655715\pi$
$827$	−27.0272			−0.939828			−0.469914	+	0.882712i	$0.655715\pi$
$828$		0			0
$829$	44.3522			1.54041			0.770207	−	0.637793i	$-0.220153\pi$
$829$	44.3522			1.54041			0.770207	+	0.637793i	$0.220153\pi$
$830$	3.83536	+	1.08518i	0.133127	+	0.0376671i
$831$		0			0
$832$	−10.1492	+	21.4374i	−0.351861	+	0.743208i
$833$		−	1.29061i		−	0.0447171i
$834$		0			0
$835$	−24.5941	−	6.95865i	−0.851113	−	0.240814i
$836$	37.1493			1.28483
$837$		0			0
$838$	5.12537			0.177053
$839$			6.70835i			0.231598i	0.993273	+	0.115799i	$0.0369428\pi$
$839$			6.70835i			0.231598i	−0.993273	+	0.115799i	$0.963057\pi$
$840$		0			0
$841$	33.0703			1.14035
$842$		−	7.39973i		−	0.255012i
$843$		0			0
$844$	26.5176			0.912772
$845$	11.6063	+	26.6513i	0.399269	+	0.916834i
$846$		0			0
$847$	−9.11981			−0.313360
$848$		−	23.7181i		−	0.814483i
$849$		0			0
$850$	−2.99578	+	4.87020i	−0.102754	+	0.167047i
$851$		−	18.1389i		−	0.621794i
$852$		0			0
$853$	−22.7336			−0.778383			−0.389191	−	0.921157i	$-0.627246\pi$
$853$	−22.7336			−0.778383			−0.389191	+	0.921157i	$0.627246\pi$
$854$	−2.07029			−0.0708437
$855$		0			0
$856$		−	6.94945i		−	0.237527i
$857$			50.2745i			1.71734i	0.512525	+	0.858672i	$0.328710\pi$
$857$			50.2745i			1.71734i	−0.512525	+	0.858672i	$0.671290\pi$
$858$		0			0
$859$	24.1530			0.824089			0.412045	−	0.911164i	$-0.364815\pi$
$859$	24.1530			0.824089			0.412045	+	0.911164i	$0.364815\pi$
$860$	−0.754496	+	2.66663i	−0.0257281	+	0.0909312i
$861$		0			0
$862$		−	0.338968i		−	0.0115453i
$863$	32.3197			1.10018			0.550088	−	0.835107i	$-0.314594\pi$
$863$	32.3197			1.10018			0.550088	+	0.835107i	$0.314594\pi$
$864$		0			0
$865$	−2.41146	+	8.52285i	−0.0819921	+	0.289786i
$866$			1.92170i			0.0653022i
$867$		0			0
$868$		−	51.3485i		−	1.74288i
$869$		−	12.8057i		−	0.434403i
$870$		0			0
$871$	−21.0351	+	44.4308i	−0.712749	+	1.50548i
$872$		−	4.27954i		−	0.144923i
$873$		0			0
$874$	4.95747			0.167689
$875$	−19.6222	−	21.3353i	−0.663351	−	0.721264i
$876$		0			0
$877$	39.9464			1.34889			0.674447	−	0.738323i	$-0.264382\pi$
$877$	39.9464			1.34889			0.674447	+	0.738323i	$0.264382\pi$
$878$	−4.87020			−0.164361
$879$		0			0
$880$	8.44108	−	29.8334i	0.284549	−	1.00568i
$881$	−28.2357			−0.951284			−0.475642	−	0.879639i	$-0.657784\pi$
$881$	−28.2357			−0.951284			−0.475642	+	0.879639i	$0.657784\pi$
$882$		0			0
$883$			39.2708i			1.32157i	0.750576	+	0.660784i	$0.229776\pi$
$883$			39.2708i			1.32157i	−0.750576	+	0.660784i	$0.770224\pi$
$884$	−29.3170	−	13.8797i	−0.986039	−	0.466826i
$885$		0			0
$886$			4.97740i			0.167219i
$887$		−	17.0351i		−	0.571984i	−0.958232	−	0.285992i	$-0.907677\pi$
$887$		−	17.0351i		−	0.571984i	0.958232	−	0.285992i	$-0.0923231\pi$
$888$		0			0
$889$			34.4256i			1.15460i
$890$	−1.32628	+	4.68749i	−0.0444570	+	0.157125i
$891$		0			0
$892$	19.1944			0.642677
$893$			19.1567i			0.641054i
$894$		0			0
$895$	44.7363	+	12.6577i	1.49537	+	0.423100i
$896$	−18.9260			−0.632274
$897$		0			0
$898$		−	10.0645i		−	0.335855i
$899$			80.4630i			2.68359i
$900$		0			0
$901$	30.2357			1.00730
$902$	−6.01377			−0.200237
$903$		0			0
$904$		−	14.6801i		−	0.488253i
$905$	12.9096	+	3.65265i	0.429130	+	0.121418i
$906$		0			0
$907$			13.2005i			0.438317i	0.975689	+	0.219158i	$0.0703311\pi$
$907$			13.2005i			0.438317i	−0.975689	+	0.219158i	$0.929669\pi$
$908$	−14.6342			−0.485654
$909$		0			0
$910$	−3.38942	+	3.88087i	−0.112358	+	0.128649i
$911$	32.6003			1.08010			0.540048	−	0.841635i	$-0.318406\pi$
$911$	32.6003			1.08010			0.540048	+	0.841635i	$0.318406\pi$
$912$		0			0
$913$		−	27.5527i		−	0.911862i
$914$	−6.28190			−0.207787
$915$		0			0
$916$			28.6575i			0.946869i
$917$	20.1110			0.664123
$918$		0			0
$919$	−3.36090			−0.110866			−0.0554329	−	0.998462i	$-0.517654\pi$
$919$	−3.36090			−0.110866			−0.0554329	+	0.998462i	$0.517654\pi$
$920$	2.36459	−	8.35721i	0.0779582	−	0.275529i
$921$		0			0
$922$			2.85654i			0.0940751i
$923$	−43.6763	−	20.6779i	−1.43762	−	0.680623i
$924$		0			0
$925$	19.3125	+	11.8796i	0.634989	+	0.390598i
$926$	1.91730			0.0630065
$927$		0			0
$928$	22.3681			0.734270
$929$			26.5138i			0.869890i	0.900457	+	0.434945i	$0.143232\pi$
$929$			26.5138i			0.869890i	−0.900457	+	0.434945i	$0.856768\pi$
$930$		0			0
$931$		−	1.39873i		−	0.0458417i
$932$			2.87478i			0.0941665i
$933$		0			0
$934$			3.56909i			0.116784i
$935$	38.0315	+	10.7606i	1.24376	+	0.351910i
$936$		0			0
$937$		−	15.7181i		−	0.513488i	−0.966479	−	0.256744i	$-0.917350\pi$
$937$		−	15.7181i		−	0.513488i	0.966479	−	0.256744i	$-0.0826497\pi$
$938$	−8.71361			−0.284509
$939$		0			0
$940$	15.8979	+	4.49815i	0.518532	+	0.146714i
$941$		−	54.2452i		−	1.76834i	−0.467163	−	0.884171i	$-0.654724\pi$
$941$		−	54.2452i		−	1.76834i	0.467163	−	0.884171i	$-0.345276\pi$
$942$		0			0
$943$	25.6113			0.834020
$944$			22.7273i			0.739709i
$945$		0			0
$946$	−0.600267			−0.0195163
$947$	21.5460			0.700150			0.350075	−	0.936722i	$-0.386156\pi$
$947$	21.5460			0.700150			0.350075	+	0.936722i	$0.386156\pi$
$948$		0			0
$949$	4.76063	−	10.0555i	0.154537	−	0.326415i
$950$	−3.24675	+	5.27820i	−0.105339	+	0.171248i
$951$		0			0
$952$		−	11.6793i		−	0.378527i
$953$			18.2745i			0.591969i	0.955193	+	0.295985i	$0.0956478\pi$
$953$			18.2745i			0.591969i	−0.955193	+	0.295985i	$0.904352\pi$
$954$		0			0
$955$	1.29153	+	0.365427i	0.0417931	+	0.0118250i
$956$		−	12.7221i		−	0.411463i
$957$		0			0
$958$		−	2.33158i		−	0.0753300i
$959$	24.6003			0.794384
$960$		0			0
$961$	−73.3060			−2.36471
$962$	1.72463	−	3.64279i	0.0556043	−	0.117448i
$963$		0			0
$964$		−	18.6020i		−	0.599129i
$965$	23.0351	+	6.51757i	0.741527	+	0.209808i
$966$		0			0
$967$	40.6946			1.30865			0.654325	−	0.756214i	$-0.272953\pi$
$967$	40.6946			1.30865			0.654325	+	0.756214i	$0.272953\pi$
$968$	3.41572			0.109785
$969$		0			0
$970$	−7.49280	−	2.12002i	−0.240579	−	0.0680696i
$971$	41.7131			1.33864			0.669318	−	0.742976i	$-0.266586\pi$
$971$	41.7131			1.33864			0.669318	+	0.742976i	$0.266586\pi$
$972$		0			0
$973$	20.1110			0.644728
$974$	3.00369			0.0962445
$975$		0			0
$976$	−11.7884			−0.377337
$977$	−26.7013			−0.854251			−0.427125	−	0.904192i	$-0.640474\pi$
$977$	−26.7013			−0.854251			−0.427125	+	0.904192i	$0.640474\pi$
$978$		0			0
$979$	33.6742			1.07623
$980$	−1.16079	−	0.328435i	−0.0370802	−	0.0104915i
$981$		0			0
$982$	−10.8935			−0.347627
$983$	−54.0876			−1.72513			−0.862564	−	0.505949i	$-0.831143\pi$
$983$	−54.0876			−1.72513			−0.862564	+	0.505949i	$0.831143\pi$
$984$		0			0
$985$	31.5721	+	8.93303i	1.00597	+	0.284630i
$986$			9.00955i			0.286922i
$987$		0			0
$988$	−31.7731	−	15.0425i	−1.01084	−	0.478567i
$989$	2.55641			0.0812890
$990$		0			0
$991$	18.0703			0.574022			0.287011	−	0.957927i	$-0.407338\pi$
$991$	18.0703			0.574022			0.287011	+	0.957927i	$0.407338\pi$
$992$			28.9963i			0.920634i
$993$		0			0
$994$		−	8.56564i		−	0.271686i
$995$	−55.2408	−	15.6298i	−1.75125	−	0.495499i
$996$		0			0
$997$		−	6.23568i		−	0.197486i	−0.995113	−	0.0987429i	$-0.968518\pi$
$997$		−	6.23568i		−	0.197486i	0.995113	−	0.0987429i	$-0.0314821\pi$
$998$		−	8.23065i		−	0.260537i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.h.g.64.7		12
3.2	odd	2		195.2.h.c.64.5	✓	12
5.4	even	2	inner	585.2.h.g.64.5		12
12.11	even	2		3120.2.r.n.2209.12		12
13.12	even	2	inner	585.2.h.g.64.6		12
15.2	even	4		975.2.b.j.376.3		6
15.8	even	4		975.2.b.l.376.4		6
15.14	odd	2		195.2.h.c.64.8	yes	12
39.38	odd	2		195.2.h.c.64.7	yes	12
60.59	even	2		3120.2.r.n.2209.1		12
65.64	even	2	inner	585.2.h.g.64.8		12
156.155	even	2		3120.2.r.n.2209.7		12
195.38	even	4		975.2.b.l.376.3		6
195.77	even	4		975.2.b.j.376.4		6
195.194	odd	2		195.2.h.c.64.6	yes	12
780.779	even	2		3120.2.r.n.2209.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.h.c.64.5	✓	12	3.2	odd	2
195.2.h.c.64.6	yes	12	195.194	odd	2
195.2.h.c.64.7	yes	12	39.38	odd	2
195.2.h.c.64.8	yes	12	15.14	odd	2
585.2.h.g.64.5		12	5.4	even	2	inner
585.2.h.g.64.6		12	13.12	even	2	inner
585.2.h.g.64.7		12	1.1	even	1	trivial
585.2.h.g.64.8		12	65.64	even	2	inner
975.2.b.j.376.3		6	15.2	even	4
975.2.b.j.376.4		6	195.77	even	4
975.2.b.l.376.3		6	195.38	even	4
975.2.b.l.376.4		6	15.8	even	4
3120.2.r.n.2209.1		12	60.59	even	2
3120.2.r.n.2209.6		12	780.779	even	2
3120.2.r.n.2209.7		12	156.155	even	2
3120.2.r.n.2209.12		12	12.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.246506 q^{2} -1.93923 q^{4} +(-2.15160 - 0.608775i) q^{5} +2.59264 q^{7} -0.971044 q^{8} +O(q^{10})\)	\(q+0.246506 q^{2} -1.93923 q^{4} +(-2.15160 - 0.608775i) q^{5} +2.59264 q^{7} -0.971044 q^{8} +(-0.530383 - 0.150067i) q^{10} +3.81019i q^{11} +(1.54283 - 3.25879i) q^{13} +0.639102 q^{14} +3.63910 q^{16} +4.63910i q^{17} +5.02774i q^{19} +(4.17246 + 1.18056i) q^{20} +0.939235i q^{22} -4.00000i q^{23} +(4.25879 + 2.61968i) q^{25} +(0.380316 - 0.803310i) q^{26} -5.02774 q^{28} +7.87847 q^{29} +10.2130i q^{31} +2.83915 q^{32} +1.14357i q^{34} +(-5.57834 - 1.57834i) q^{35} +4.53473 q^{37} +1.23937i q^{38} +(2.08930 + 0.591148i) q^{40} +6.40284i q^{41} +0.639102i q^{43} -7.38886i q^{44} -0.986023i q^{46} +3.81019 q^{47} -0.278203 q^{49} +(1.04982 + 0.645767i) q^{50} +(-2.99190 + 6.31955i) q^{52} -6.51757i q^{53} +(2.31955 - 8.19802i) q^{55} -2.51757 q^{56} +1.94209 q^{58} +6.24529i q^{59} -3.23937 q^{61} +2.51757i q^{62} -6.57834 q^{64} +(-5.30342 + 6.07238i) q^{65} -13.6342 q^{67} -8.99631i q^{68} +(-1.37509 - 0.389069i) q^{70} -13.4026i q^{71} +3.08565 q^{73} +1.11784 q^{74} -9.74998i q^{76} +9.87847i q^{77} -3.36090 q^{79} +(-7.82990 - 2.21539i) q^{80} +1.57834i q^{82} -7.23132 q^{83} +(2.82417 - 9.98150i) q^{85} +0.157542i q^{86} -3.69987i q^{88} -8.83794i q^{89} +(4.00000 - 8.44887i) q^{91} +7.75694i q^{92} +0.939235 q^{94} +(3.06077 - 10.8177i) q^{95} +14.1272 q^{97} -0.0685787 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{4}+O(q^{10}) \) 12 * q + 12 * q^4	\( 12 q + 12 q^{4} - 24 q^{10} - 16 q^{14} + 20 q^{16} + 4 q^{25} + 28 q^{26} + 24 q^{29} - 8 q^{35} - 16 q^{40} + 44 q^{49} + 16 q^{55} + 64 q^{56} + 8 q^{61} - 20 q^{64} - 28 q^{65} - 104 q^{74} - 64 q^{79} + 48 q^{91} - 24 q^{94} + 72 q^{95}+O(q^{100}) \) 12 * q + 12 * q^4 - 24 * q^10 - 16 * q^14 + 20 * q^16 + 4 * q^25 + 28 * q^26 + 24 * q^29 - 8 * q^35 - 16 * q^40 + 44 * q^49 + 16 * q^55 + 64 * q^56 + 8 * q^61 - 20 * q^64 - 28 * q^65 - 104 * q^74 - 64 * q^79 + 48 * q^91 - 24 * q^94 + 72 * q^95

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