LMFDB - Embedded newform 585.2.c.c.469.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(469,585)]

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, 0]))

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

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

chi := DirichletCharacter("585.469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.c (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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 16x^{8} + 90x^{6} + 208x^{4} + 169x^{2} + 16 $ x^10 + 16x^8 + 90x^6 + 208x^4 + 169x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.3
Root			$-1.77159i$ of defining polynomial
Character	$\chi$	$=$	585.469
Dual form			585.2.c.c.469.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.77159i q^{2} -1.13853 q^{4} +(-1.51036 + 1.64888i) q^{5} -0.437634i q^{7} -1.52618i q^{8} +O(q^{10})$	\(q-1.77159i q^{2} -1.13853 q^{4} +(-1.51036 + 1.64888i) q^{5} -0.437634i q^{7} -1.52618i q^{8} +(2.92114 + 2.67573i) q^{10} -5.73540 q^{11} -1.00000i q^{13} -0.775308 q^{14} -4.98081 q^{16} -3.98081i q^{17} -4.77531 q^{19} +(1.71958 - 1.87730i) q^{20} +10.1608i q^{22} +0.337673i q^{23} +(-0.437634 - 4.98081i) q^{25} -1.77159 q^{26} +0.498258i q^{28} +1.72295 q^{29} -7.86166 q^{31} +5.77159i q^{32} -7.05236 q^{34} +(0.721608 + 0.660985i) q^{35} +1.66233i q^{37} +8.45988i q^{38} +(2.51649 + 2.30508i) q^{40} -2.68304 q^{41} -2.27705i q^{43} +6.52990 q^{44} +0.598218 q^{46} +11.7162i q^{47} +6.80848 q^{49} +(-8.82395 + 0.775308i) q^{50} +1.13853i q^{52} -14.2993i q^{53} +(8.66251 - 9.45701i) q^{55} -0.667908 q^{56} -3.05236i q^{58} +11.4392 q^{59} -2.25786 q^{61} +13.9276i q^{62} +0.263257 q^{64} +(1.64888 + 1.51036i) q^{65} +2.17977i q^{67} +4.53225i q^{68} +(1.17099 - 1.27839i) q^{70} +13.6970 q^{71} +2.55410i q^{73} +2.94496 q^{74} +5.43681 q^{76} +2.51001i q^{77} -2.55144 q^{79} +(7.52281 - 8.21278i) q^{80} +4.75325i q^{82} -5.41158i q^{83} +(6.56389 + 6.01245i) q^{85} -4.03400 q^{86} +8.75325i q^{88} -4.72448 q^{89} -0.437634 q^{91} -0.384450i q^{92} +20.7563 q^{94} +(7.21243 - 7.87393i) q^{95} -14.7901i q^{97} -12.0618i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 12 q^{4} + 2 q^{5}+O(q^{10}) $ 10 * q - 12 * q^4 + 2 * q^5	$ 10 q - 12 q^{4} + 2 q^{5} + 4 q^{10} - 10 q^{11} + 24 q^{14} - 16 q^{19} - 32 q^{20} + 10 q^{25} + 16 q^{29} + 24 q^{31} - 40 q^{34} - 12 q^{35} + 36 q^{40} - 10 q^{41} + 36 q^{44} - 24 q^{46} - 44 q^{49} - 40 q^{50} + 2 q^{55} + 16 q^{59} + 26 q^{61} + 32 q^{64} + 56 q^{70} - 10 q^{71} + 24 q^{74} - 2 q^{79} + 12 q^{80} - 4 q^{85} + 38 q^{89} + 10 q^{91} + 24 q^{94} + 48 q^{95}+O(q^{100}) $ 10 * q - 12 * q^4 + 2 * q^5 + 4 * q^10 - 10 * q^11 + 24 * q^14 - 16 * q^19 - 32 * q^20 + 10 * q^25 + 16 * q^29 + 24 * q^31 - 40 * q^34 - 12 * q^35 + 36 * q^40 - 10 * q^41 + 36 * q^44 - 24 * q^46 - 44 * q^49 - 40 * q^50 + 2 * q^55 + 16 * q^59 + 26 * q^61 + 32 * q^64 + 56 * q^70 - 10 * q^71 + 24 * q^74 - 2 * q^79 + 12 * q^80 - 4 * q^85 + 38 * q^89 + 10 * q^91 + 24 * q^94 + 48 * 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 $

$2$		−	1.77159i		−	1.25270i	−0.779541	−	0.626351i	$-0.784548\pi$
$2$		−	1.77159i		−	1.25270i	0.779541	−	0.626351i	$-0.215452\pi$
$3$		0			0
$3$		0			0
$4$	−1.13853			−0.569263
$5$	−1.51036	+	1.64888i	−0.675453	+	0.737403i
$5$	−1.51036	+	1.64888i	−0.675453	+	0.737403i
$6$		0			0
$7$		−	0.437634i		−	0.165410i	−0.996574	−	0.0827051i	$-0.973644\pi$
$7$		−	0.437634i		−	0.165410i	0.996574	−	0.0827051i	$-0.0263560\pi$
$8$		−	1.52618i		−	0.539586i
$9$		0			0
$10$	2.92114	+	2.67573i	0.923746	+	0.846141i
$11$	−5.73540			−1.72929			−0.864644	−	0.502385i	$-0.832456\pi$
$11$	−5.73540			−1.72929			−0.864644	+	0.502385i	$0.832456\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−0.775308			−0.207210
$15$		0			0
$16$	−4.98081			−1.24520
$17$		−	3.98081i		−	0.965488i	−0.875761	−	0.482744i	$-0.839640\pi$
$17$		−	3.98081i		−	0.965488i	0.875761	−	0.482744i	$-0.160360\pi$
$18$		0			0
$19$	−4.77531			−1.09553			−0.547765	−	0.836632i	$-0.684521\pi$
$19$	−4.77531			−1.09553			−0.547765	+	0.836632i	$0.684521\pi$
$20$	1.71958	−	1.87730i	0.384510	−	0.419776i
$21$		0			0
$22$			10.1608i			2.16628i
$23$			0.337673i			0.0704098i	0.999380	+	0.0352049i	$0.0112084\pi$
$23$			0.337673i			0.0704098i	−0.999380	+	0.0352049i	$0.988792\pi$
$24$		0			0
$25$	−0.437634	−	4.98081i	−0.0875268	−	0.996162i
$26$	−1.77159			−0.347437
$27$		0			0
$28$			0.498258i			0.0941618i
$29$	1.72295			0.319944			0.159972	−	0.987122i	$-0.448860\pi$
$29$	1.72295			0.319944			0.159972	+	0.987122i	$0.448860\pi$
$30$		0			0
$31$	−7.86166			−1.41200			−0.705998	−	0.708214i	$-0.749501\pi$
$31$	−7.86166			−1.41200			−0.705998	+	0.708214i	$0.749501\pi$
$32$			5.77159i			1.02028i
$33$		0			0
$34$	−7.05236			−1.20947
$35$	0.721608	+	0.660985i	0.121974	+	0.111727i
$36$		0			0
$37$			1.66233i			0.273285i	0.990620	+	0.136642i	$0.0436311\pi$
$37$			1.66233i			0.273285i	−0.990620	+	0.136642i	$0.956369\pi$
$38$			8.45988i			1.37237i
$39$		0			0
$40$	2.51649	+	2.30508i	0.397892	+	0.364465i
$41$	−2.68304			−0.419021			−0.209511	−	0.977806i	$-0.567187\pi$
$41$	−2.68304			−0.419021			−0.209511	+	0.977806i	$0.567187\pi$
$42$		0			0
$43$		−	2.27705i		−	0.347247i	−0.984812	−	0.173623i	$-0.944452\pi$
$43$		−	2.27705i		−	0.347247i	0.984812	−	0.173623i	$-0.0555476\pi$
$44$	6.52990			0.984419
$45$		0			0
$46$	0.598218			0.0882025
$47$			11.7162i			1.70899i	0.519464	+	0.854493i	$0.326132\pi$
$47$			11.7162i			1.70899i	−0.519464	+	0.854493i	$0.673868\pi$
$48$		0			0
$49$	6.80848			0.972639
$50$	−8.82395	+	0.775308i	−1.24789	+	0.109645i
$51$		0			0
$52$			1.13853i			0.157885i
$53$		−	14.2993i		−	1.96416i	−0.188467	−	0.982080i	$-0.560352\pi$
$53$		−	14.2993i		−	1.96416i	0.188467	−	0.982080i	$-0.439648\pi$
$54$		0			0
$55$	8.66251	−	9.45701i	1.16805	−	1.27518i
$56$	−0.667908			−0.0892530
$57$		0			0
$58$		−	3.05236i		−	0.400794i
$59$	11.4392			1.48925			0.744626	−	0.667482i	$-0.232628\pi$
$59$	11.4392			1.48925			0.744626	+	0.667482i	$0.232628\pi$
$60$		0			0
$61$	−2.25786			−0.289089			−0.144545	−	0.989498i	$-0.546172\pi$
$61$	−2.25786			−0.289089			−0.144545	+	0.989498i	$0.546172\pi$
$62$			13.9276i			1.76881i
$63$		0			0
$64$	0.263257			0.0329071
$65$	1.64888	+	1.51036i	0.204519	+	0.187337i
$66$		0			0
$67$			2.17977i			0.266302i	0.991096	+	0.133151i	$0.0425095\pi$
$67$			2.17977i			0.266302i	−0.991096	+	0.133151i	$0.957491\pi$
$68$			4.53225i			0.549616i
$69$		0			0
$70$	1.17099	−	1.27839i	0.139960	−	0.152797i
$71$	13.6970			1.62554			0.812769	−	0.582586i	$-0.197959\pi$
$71$	13.6970			1.62554			0.812769	+	0.582586i	$0.197959\pi$
$72$		0			0
$73$			2.55410i			0.298935i	0.988767	+	0.149467i	$0.0477559\pi$
$73$			2.55410i			0.298935i	−0.988767	+	0.149467i	$0.952244\pi$
$74$	2.94496			0.342344
$75$		0			0
$76$	5.43681			0.623645
$77$			2.51001i			0.286042i
$78$		0			0
$79$	−2.55144			−0.287060			−0.143530	−	0.989646i	$-0.545845\pi$
$79$	−2.55144			−0.287060			−0.143530	+	0.989646i	$0.545845\pi$
$80$	7.52281	−	8.21278i	0.841076	−	0.918216i
$81$		0			0
$82$			4.75325i			0.524909i
$83$		−	5.41158i		−	0.593998i	−0.954878	−	0.296999i	$-0.904014\pi$
$83$		−	5.41158i		−	0.593998i	0.954878	−	0.296999i	$-0.0959857\pi$
$84$		0			0
$85$	6.56389	+	6.01245i	0.711954	+	0.652142i
$86$	−4.03400			−0.434997
$87$		0			0
$88$			8.75325i			0.933099i
$89$	−4.72448			−0.500794			−0.250397	−	0.968143i	$-0.580561\pi$
$89$	−4.72448			−0.500794			−0.250397	+	0.968143i	$0.580561\pi$
$90$		0			0
$91$	−0.437634			−0.0458765
$92$		−	0.384450i		−	0.0400817i
$93$		0			0
$94$	20.7563			2.14085
$95$	7.21243	−	7.87393i	0.739979	−	0.807848i
$96$		0			0
$97$		−	14.7901i		−	1.50171i	−0.660468	−	0.750854i	$-0.729642\pi$
$97$		−	14.7901i		−	1.50171i	0.660468	−	0.750854i	$-0.270358\pi$
$98$		−	12.0618i		−	1.21843i
$99$		0			0
$100$	0.498258	+	5.67078i	0.0498258	+	0.567078i
$101$	−12.5955			−1.25330			−0.626651	−	0.779300i	$-0.715575\pi$
$101$	−12.5955			−1.25330			−0.626651	+	0.779300i	$0.715575\pi$
$102$		0			0
$103$			6.23867i			0.614715i	0.951594	+	0.307357i	$0.0994447\pi$
$103$			6.23867i			0.614715i	−0.951594	+	0.307357i	$0.900555\pi$
$104$	−1.52618			−0.149654
$105$		0			0
$106$	−25.3325			−2.46051
$107$			1.10554i			0.106877i	0.998571	+	0.0534384i	$0.0170181\pi$
$107$			1.10554i			0.106877i	−0.998571	+	0.0534384i	$0.982982\pi$
$108$		0			0
$109$	−7.92019			−0.758616			−0.379308	−	0.925270i	$-0.623838\pi$
$109$	−7.92019			−0.758616			−0.379308	+	0.925270i	$0.623838\pi$
$110$	−16.7539	−	15.3464i	−1.59742	−	1.46322i
$111$		0			0
$112$			2.17977i			0.205969i
$113$		−	11.4432i		−	1.07649i	−0.842789	−	0.538244i	$-0.819088\pi$
$113$		−	11.4432i		−	1.07649i	0.842789	−	0.538244i	$-0.180912\pi$
$114$		0			0
$115$	−0.556784	−	0.510008i	−0.0519204	−	0.0475585i
$116$	−1.96162			−0.182132
$117$		0			0
$118$		−	20.2655i		−	1.86559i
$119$	−1.74214			−0.159702
$120$		0			0
$121$	21.8948			1.99044
$122$			4.00000i			0.362143i
$123$		0			0
$124$	8.95070			0.803796
$125$	8.87376	+	6.80120i	0.793693	+	0.608318i
$126$		0			0
$127$			1.42937i			0.126836i	0.997987	+	0.0634180i	$0.0202001\pi$
$127$			1.42937i			0.126836i	−0.997987	+	0.0634180i	$0.979800\pi$
$128$			11.0768i			0.979060i
$129$		0			0
$130$	2.67573	−	2.92114i	0.234677	−	0.256201i
$131$	−17.6819			−1.54487			−0.772437	−	0.635092i	$-0.780962\pi$
$131$	−17.6819			−1.54487			−0.772437	+	0.635092i	$0.780962\pi$
$132$		0			0
$133$			2.08984i			0.181212i
$134$	3.86166			0.333597
$135$		0			0
$136$	−6.07543			−0.520964
$137$		−	10.7686i		−	0.920021i	−0.887913	−	0.460011i	$-0.847846\pi$
$137$		−	10.7686i		−	0.920021i	0.887913	−	0.460011i	$-0.152154\pi$
$138$		0			0
$139$	−3.80848			−0.323031			−0.161515	−	0.986870i	$-0.551638\pi$
$139$	−3.80848			−0.323031			−0.161515	+	0.986870i	$0.551638\pi$
$140$	−0.821569	−	0.752548i	−0.0694352	−	0.0636019i
$141$		0			0
$142$		−	24.2655i		−	2.03631i
$143$			5.73540i			0.479618i
$144$		0			0
$145$	−2.60227	+	2.84094i	−0.216107	+	0.235928i
$146$	4.52481			0.374476
$147$		0			0
$148$		−	1.89260i		−	0.155571i
$149$	−16.3649			−1.34067			−0.670334	−	0.742060i	$-0.733849\pi$
$149$	−16.3649			−1.34067			−0.670334	+	0.742060i	$0.733849\pi$
$150$		0			0
$151$	20.3774			1.65829			0.829144	−	0.559035i	$-0.188828\pi$
$151$	20.3774			1.65829			0.829144	+	0.559035i	$0.188828\pi$
$152$			7.28797i			0.591133i
$153$		0			0
$154$	4.44670			0.358325
$155$	11.8739	−	12.9630i	0.953737	−	1.04121i
$156$		0			0
$157$		−	13.1911i		−	1.05276i	−0.850249	−	0.526381i	$-0.823549\pi$
$157$		−	13.1911i		−	1.05276i	0.850249	−	0.526381i	$-0.176451\pi$
$158$			4.52010i			0.359600i
$159$		0			0
$160$	−9.51668	−	8.71717i	−0.752359	−	0.689153i
$161$	0.147777			0.0116465
$162$		0			0
$163$		−	10.3578i		−	0.811287i	−0.914031	−	0.405644i	$-0.867047\pi$
$163$		−	10.3578i		−	0.811287i	0.914031	−	0.405644i	$-0.132953\pi$
$164$	3.05471			0.238533
$165$		0			0
$166$	−9.58708			−0.744102
$167$			10.6713i			0.825769i	0.910783	+	0.412885i	$0.135479\pi$
$167$			10.6713i			0.825769i	−0.910783	+	0.412885i	$0.864521\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	10.6516	−	11.6285i	0.816940	−	0.891867i
$171$		0			0
$172$			2.59248i			0.197675i
$173$			5.64045i			0.428836i	0.976742	+	0.214418i	$0.0687854\pi$
$173$			5.64045i			0.428836i	−0.976742	+	0.214418i	$0.931215\pi$
$174$		0			0
$175$	−2.17977	+	0.191524i	−0.164775	+	0.0144778i
$176$	28.5669			2.15331
$177$		0			0
$178$			8.36983i			0.627345i
$179$	−11.9616			−0.894054			−0.447027	−	0.894521i	$-0.647517\pi$
$179$	−11.9616			−0.894054			−0.447027	+	0.894521i	$0.647517\pi$
$180$		0			0
$181$	11.3442			0.843209			0.421604	−	0.906780i	$-0.361467\pi$
$181$	11.3442			0.843209			0.421604	+	0.906780i	$0.361467\pi$
$182$			0.775308i			0.0574696i
$183$		0			0
$184$	0.515350			0.0379921
$185$	−2.74098	−	2.51071i	−0.201521	−	0.184591i
$186$		0			0
$187$			22.8315i			1.66961i
$188$		−	13.3392i		−	0.972861i
$189$		0			0
$190$	−13.9494	−	12.7775i	−1.01199	−	0.926974i
$191$	19.8691			1.43768			0.718839	−	0.695177i	$-0.244674\pi$
$191$	19.8691			1.43768			0.718839	+	0.695177i	$0.244674\pi$
$192$		0			0
$193$		−	1.10823i		−	0.0797719i	−0.999204	−	0.0398859i	$-0.987301\pi$
$193$		−	1.10823i		−	0.0797719i	0.999204	−	0.0398859i	$-0.0126995\pi$
$194$	−26.2020			−1.88119
$195$		0			0
$196$	−7.75162			−0.553687
$197$		−	5.37758i		−	0.383137i	−0.981479	−	0.191568i	$-0.938643\pi$
$197$		−	5.37758i		−	0.383137i	0.981479	−	0.191568i	$-0.0613574\pi$
$198$		0			0
$199$	11.2736			0.799162			0.399581	−	0.916698i	$-0.369156\pi$
$199$	11.2736			0.799162			0.399581	+	0.916698i	$0.369156\pi$
$200$	−7.60161	+	0.667908i	−0.537515	+	0.0472282i
$201$		0			0
$202$			22.3141i			1.57001i
$203$		−	0.754022i		−	0.0529220i
$204$		0			0
$205$	4.05236	−	4.42403i	0.283029	−	0.308987i
$206$	11.0524			0.770054
$207$		0			0
$208$			4.98081i			0.345357i
$209$	27.3883			1.89449
$210$		0			0
$211$	−16.4498			−1.13245			−0.566224	−	0.824251i	$-0.691596\pi$
$211$	−16.4498			−1.13245			−0.566224	+	0.824251i	$0.691596\pi$
$212$			16.2801i			1.11812i
$213$		0			0
$214$	1.95857			0.133885
$215$	3.75459	+	3.43916i	0.256061	+	0.234549i
$216$		0			0
$217$			3.44053i			0.233559i
$218$			14.0313i			0.950320i
$219$		0			0
$220$	−9.86249	+	10.7670i	−0.664929	+	0.725914i
$221$	−3.98081			−0.267778
$222$		0			0
$223$		−	25.0527i		−	1.67765i	−0.544397	−	0.838827i	$-0.683242\pi$
$223$		−	25.0527i		−	1.67765i	0.544397	−	0.838827i	$-0.316758\pi$
$224$	2.52584			0.168765
$225$		0			0
$226$	−20.2727			−1.34852
$227$			8.11414i			0.538554i	0.963063	+	0.269277i	$0.0867847\pi$
$227$			8.11414i			0.538554i	−0.963063	+	0.269277i	$0.913215\pi$
$228$		0			0
$229$	−9.57717			−0.632877			−0.316439	−	0.948613i	$-0.602487\pi$
$229$	−9.57717			−0.632877			−0.316439	+	0.948613i	$0.602487\pi$
$230$	−0.903524	+	0.986392i	−0.0595766	+	0.0650408i
$231$		0			0
$232$		−	2.62953i		−	0.172637i
$233$		−	16.3791i		−	1.07303i	−0.843890	−	0.536516i	$-0.819740\pi$
$233$		−	16.3791i		−	1.07303i	0.843890	−	0.536516i	$-0.180260\pi$
$234$		0			0
$235$	−19.3187	−	17.6957i	−1.26021	−	1.15434i
$236$	−13.0238			−0.847775
$237$		0			0
$238$			3.08635i			0.200059i
$239$	−22.2511			−1.43931			−0.719653	−	0.694334i	$-0.755699\pi$
$239$	−22.2511			−1.43931			−0.719653	+	0.694334i	$0.755699\pi$
$240$		0			0
$241$	23.8031			1.53329			0.766647	−	0.642068i	$-0.221924\pi$
$241$	23.8031			1.53329			0.766647	+	0.642068i	$0.221924\pi$
$242$		−	38.7886i		−	2.49343i
$243$		0			0
$244$	2.57063			0.164568
$245$	−10.2832	+	11.2264i	−0.656972	+	0.717227i
$246$		0			0
$247$			4.77531i			0.303846i
$248$			11.9983i			0.761893i
$249$		0			0
$250$	12.0489	−	15.7207i	0.762041	−	0.994261i
$251$	4.35992			0.275196			0.137598	−	0.990488i	$-0.456062\pi$
$251$	4.35992			0.275196			0.137598	+	0.990488i	$0.456062\pi$
$252$		0			0
$253$		−	1.93669i		−	0.121759i
$254$	2.53225			0.158888
$255$		0			0
$256$	20.1500			1.25938
$257$			14.9965i			0.935457i	0.883872	+	0.467728i	$0.154927\pi$
$257$			14.9965i			0.935457i	−0.883872	+	0.467728i	$0.845073\pi$
$258$		0			0
$259$	0.727491			0.0452041
$260$	−1.87730	−	1.71958i	−0.116425	−	0.106644i
$261$		0			0
$262$			31.3250i			1.93527i
$263$		−	10.7029i		−	0.659971i	−0.943986	−	0.329986i	$-0.892956\pi$
$263$		−	10.7029i		−	0.659971i	0.943986	−	0.329986i	$-0.107044\pi$
$264$		0			0
$265$	23.5779	+	21.5971i	1.44838	+	1.32670i
$266$	3.70233			0.227005
$267$		0			0
$268$		−	2.48173i		−	0.151596i
$269$	15.0076			0.915028			0.457514	−	0.889202i	$-0.348740\pi$
$269$	15.0076			0.915028			0.457514	+	0.889202i	$0.348740\pi$
$270$		0			0
$271$	−1.71386			−0.104109			−0.0520547	−	0.998644i	$-0.516577\pi$
$271$	−1.71386			−0.104109			−0.0520547	+	0.998644i	$0.516577\pi$
$272$			19.8277i			1.20223i
$273$		0			0
$274$	−19.0775			−1.15251
$275$	2.51001	+	28.5669i	0.151359	+	1.72265i
$276$		0			0
$277$			21.1527i			1.27094i	0.772125	+	0.635471i	$0.219194\pi$
$277$			21.1527i			1.27094i	−0.772125	+	0.635471i	$0.780806\pi$
$278$			6.74705i			0.404661i
$279$		0			0
$280$	1.00878	−	1.10130i	0.0602862	−	0.0658154i
$281$	−18.7440			−1.11818			−0.559088	−	0.829108i	$-0.688849\pi$
$281$	−18.7440			−1.11818			−0.559088	+	0.829108i	$0.688849\pi$
$282$		0			0
$283$			9.29744i			0.552675i	0.961061	+	0.276338i	$0.0891208\pi$
$283$			9.29744i			0.552675i	−0.961061	+	0.276338i	$0.910879\pi$
$284$	−15.5944			−0.925358
$285$		0			0
$286$	10.1608			0.600819
$287$			1.17419i			0.0693103i
$288$		0			0
$289$	1.15315			0.0678321
$290$	5.03298	+	4.61015i	0.295547	+	0.270718i
$291$		0			0
$292$		−	2.90791i		−	0.170172i
$293$			17.9762i			1.05018i	0.851047	+	0.525090i	$0.175968\pi$
$293$			17.9762i			1.05018i	−0.851047	+	0.525090i	$0.824032\pi$
$294$		0			0
$295$	−17.2772	+	18.8618i	−1.00592	+	1.09818i
$296$	2.53701			0.147461
$297$		0			0
$298$			28.9919i			1.67946i
$299$	0.337673			0.0195282
$300$		0			0
$301$	−0.996515			−0.0574382
$302$		−	36.1003i		−	2.07734i
$303$		0			0
$304$	23.7849			1.36416
$305$	3.41018	−	3.72295i	0.195266	−	0.213175i
$306$		0			0
$307$			13.3129i			0.759807i	0.925026	+	0.379904i	$0.124043\pi$
$307$			13.3129i			0.759807i	−0.925026	+	0.379904i	$0.875957\pi$
$308$		−	2.85771i		−	0.162833i
$309$		0			0
$310$	−22.9650	−	21.0357i	−1.30433	−	1.19475i
$311$	−2.64776			−0.150141			−0.0750703	−	0.997178i	$-0.523918\pi$
$311$	−2.64776			−0.150141			−0.0750703	+	0.997178i	$0.523918\pi$
$312$		0			0
$313$			15.8718i			0.897126i	0.893751	+	0.448563i	$0.148064\pi$
$313$			15.8718i			0.897126i	−0.893751	+	0.448563i	$0.851936\pi$
$314$	−23.3691			−1.31880
$315$		0			0
$316$	2.90488			0.163412
$317$			3.85187i			0.216342i	0.994132	+	0.108171i	$0.0344995\pi$
$317$			3.85187i			0.216342i	−0.994132	+	0.108171i	$0.965501\pi$
$318$		0			0
$319$	−9.88181			−0.553275
$320$	−0.397612	+	0.434080i	−0.0222272	+	0.0242658i
$321$		0			0
$322$		−	0.261801i		−	0.0145896i
$323$			19.0096i			1.05772i
$324$		0			0
$325$	−4.98081	+	0.437634i	−0.276286	+	0.0242756i
$326$	−18.3498			−1.01630
$327$		0			0
$328$			4.09480i			0.226098i
$329$	5.12742			0.282684
$330$		0			0
$331$	−8.15256			−0.448105			−0.224053	−	0.974577i	$-0.571929\pi$
$331$	−8.15256			−0.448105			−0.224053	+	0.974577i	$0.571929\pi$
$332$			6.16121i			0.338141i
$333$		0			0
$334$	18.9051			1.03444
$335$	−3.59419	−	3.29224i	−0.196372	−	0.179874i
$336$		0			0
$337$		−	0.343016i		−	0.0186852i	−0.999956	−	0.00934262i	$-0.997026\pi$
$337$		−	0.343016i		−	0.0186852i	0.999956	−	0.00934262i	$-0.00297389\pi$
$338$			1.77159i			0.0963617i
$339$		0			0
$340$	−7.47316	−	6.84533i	−0.405289	−	0.371240i
$341$	45.0898			2.44175
$342$		0			0
$343$		−	6.04306i		−	0.326295i
$344$	−3.47519			−0.187369
$345$		0			0
$346$	9.99256			0.537203
$347$			32.2306i			1.73023i	0.501572	+	0.865116i	$0.332755\pi$
$347$			32.2306i			1.73023i	−0.501572	+	0.865116i	$0.667245\pi$
$348$		0			0
$349$	−23.6186			−1.26427			−0.632137	−	0.774856i	$-0.717822\pi$
$349$	−23.6186			−1.26427			−0.632137	+	0.774856i	$0.717822\pi$
$350$	0.339301	+	3.86166i	0.0181364	+	0.206414i
$351$		0			0
$352$		−	33.1024i		−	1.76436i
$353$		−	30.5552i		−	1.62629i	−0.582063	−	0.813144i	$-0.697754\pi$
$353$		−	30.5552i		−	1.62629i	0.582063	−	0.813144i	$-0.302246\pi$
$354$		0			0
$355$	−20.6874	+	22.5848i	−1.09797	+	1.19868i
$356$	5.37894			0.285083
$357$		0			0
$358$			21.1911i			1.11998i
$359$	−30.2293			−1.59544			−0.797719	−	0.603029i	$-0.793960\pi$
$359$	−30.2293			−1.59544			−0.797719	+	0.603029i	$0.793960\pi$
$360$		0			0
$361$	3.80356			0.200188
$362$		−	20.0973i		−	1.05629i
$363$		0			0
$364$	0.498258			0.0261158
$365$	−4.21141	−	3.85761i	−0.220435	−	0.201916i
$366$		0			0
$367$			10.0441i			0.524299i	0.965027	+	0.262149i	$0.0844313\pi$
$367$			10.0441i			0.524299i	−0.965027	+	0.262149i	$0.915569\pi$
$368$		−	1.68189i		−	0.0876744i
$369$		0			0
$370$	−4.44794	+	4.85589i	−0.231238	+	0.252446i
$371$	−6.25786			−0.324892
$372$		0			0
$373$		−	28.8097i		−	1.49171i	−0.666109	−	0.745854i	$-0.732042\pi$
$373$		−	28.8097i		−	1.49171i	0.666109	−	0.745854i	$-0.267958\pi$
$374$	40.4481			2.09152
$375$		0			0
$376$	17.8810			0.922144
$377$		−	1.72295i		−	0.0887364i
$378$		0			0
$379$	−17.0581			−0.876216			−0.438108	−	0.898922i	$-0.644351\pi$
$379$	−17.0581			−0.876216			−0.438108	+	0.898922i	$0.644351\pi$
$380$	−8.21153	+	8.96466i	−0.421243	+	0.459877i
$381$		0			0
$382$		−	35.1999i		−	1.80098i
$383$		−	6.58842i		−	0.336653i	−0.985731	−	0.168326i	$-0.946164\pi$
$383$		−	6.58842i		−	0.336653i	0.985731	−	0.168326i	$-0.0538363\pi$
$384$		0			0
$385$	−4.13871	−	3.79101i	−0.210928	−	0.193208i
$386$	−1.96332			−0.0999304
$387$		0			0
$388$			16.8389i			0.854866i
$389$	30.5741			1.55017			0.775083	−	0.631859i	$-0.217708\pi$
$389$	30.5741			1.55017			0.775083	+	0.631859i	$0.217708\pi$
$390$		0			0
$391$	1.34421			0.0679798
$392$		−	10.3910i		−	0.524822i
$393$		0			0
$394$	−9.52686			−0.479956
$395$	3.85359	−	4.20703i	0.193895	−	0.211679i
$396$		0			0
$397$		−	21.5069i		−	1.07940i	−0.841857	−	0.539700i	$-0.818538\pi$
$397$		−	21.5069i		−	1.07940i	0.841857	−	0.539700i	$-0.181462\pi$
$398$		−	19.9721i		−	1.00111i
$399$		0			0
$400$	2.17977	+	24.8085i	0.108989	+	1.24042i
$401$	17.8990			0.893835			0.446918	−	0.894575i	$-0.352522\pi$
$401$	17.8990			0.893835			0.446918	+	0.894575i	$0.352522\pi$
$402$		0			0
$403$			7.86166i			0.391617i
$404$	14.3403			0.713458
$405$		0			0
$406$	−1.33582			−0.0662954
$407$		−	9.53411i		−	0.472588i
$408$		0			0
$409$	−22.3844			−1.10684			−0.553420	−	0.832902i	$-0.686678\pi$
$409$	−22.3844			−1.10684			−0.553420	+	0.832902i	$0.686678\pi$
$410$	−7.83755	−	7.17911i	−0.387069	−	0.354551i
$411$		0			0
$412$		−	7.10288i		−	0.349934i
$413$		−	5.00617i		−	0.246337i
$414$		0			0
$415$	8.92306	+	8.17342i	0.438016	+	0.401217i
$416$	5.77159			0.282975
$417$		0			0
$418$		−	48.5208i		−	2.37323i
$419$	−27.5153			−1.34421			−0.672105	−	0.740456i	$-0.734610\pi$
$419$	−27.5153			−1.34421			−0.672105	+	0.740456i	$0.734610\pi$
$420$		0			0
$421$	6.34607			0.309289			0.154644	−	0.987970i	$-0.450577\pi$
$421$	6.34607			0.309289			0.154644	+	0.987970i	$0.450577\pi$
$422$			29.1422i			1.41862i
$423$		0			0
$424$	−21.8233			−1.05983
$425$	−19.8277	+	1.74214i	−0.961783	+	0.0845062i
$426$		0			0
$427$			0.988117i			0.0478183i
$428$		−	1.25869i		−	0.0608410i
$429$		0			0
$430$	6.09278	−	6.65159i	0.293820	−	0.320768i
$431$	3.78383			0.182261			0.0911304	−	0.995839i	$-0.470952\pi$
$431$	3.78383			0.182261			0.0911304	+	0.995839i	$0.470952\pi$
$432$		0			0
$433$			2.55410i			0.122742i	0.998115	+	0.0613711i	$0.0195473\pi$
$433$			2.55410i			0.122742i	−0.998115	+	0.0613711i	$0.980453\pi$
$434$	6.09521			0.292579
$435$		0			0
$436$	9.01733			0.431852
$437$		−	1.61249i		−	0.0771361i
$438$		0			0
$439$	−2.34073			−0.111717			−0.0558585	−	0.998439i	$-0.517790\pi$
$439$	−2.34073			−0.111717			−0.0558585	+	0.998439i	$0.517790\pi$
$440$	−14.4331	−	13.2205i	−0.688070	−	0.630265i
$441$		0			0
$442$			7.05236i			0.335446i
$443$		−	0.468574i		−	0.0222626i	−0.999938	−	0.0111313i	$-0.996457\pi$
$443$		−	0.468574i		−	0.0222626i	0.999938	−	0.0111313i	$-0.00354328\pi$
$444$		0			0
$445$	7.13566	−	7.79011i	0.338262	−	0.369287i
$446$	−44.3831			−2.10160
$447$		0			0
$448$		−	0.115210i		−	0.00544317i
$449$	−17.5863			−0.829947			−0.414974	−	0.909833i	$-0.636209\pi$
$449$	−17.5863			−0.829947			−0.414974	+	0.909833i	$0.636209\pi$
$450$		0			0
$451$	15.3883			0.724608
$452$			13.0284i			0.612804i
$453$		0			0
$454$	14.3749			0.674648
$455$	0.660985	−	0.721608i	0.0309874	−	0.0338295i
$456$		0			0
$457$		−	11.9132i		−	0.557276i	−0.960396	−	0.278638i	$-0.910117\pi$
$457$		−	11.9132i		−	0.557276i	0.960396	−	0.278638i	$-0.0898829\pi$
$458$			16.9668i			0.792807i
$459$		0			0
$460$	0.633913	+	0.580657i	0.0295563	+	0.0270733i
$461$	17.7540			0.826886			0.413443	−	0.910530i	$-0.364326\pi$
$461$	17.7540			0.826886			0.413443	+	0.910530i	$0.364326\pi$
$462$		0			0
$463$		−	39.4856i		−	1.83505i	−0.397676	−	0.917526i	$-0.630183\pi$
$463$		−	39.4856i		−	1.83505i	0.397676	−	0.917526i	$-0.369817\pi$
$464$	−8.58169			−0.398395
$465$		0			0
$466$	−29.0170			−1.34419
$467$		−	19.2793i		−	0.892139i	−0.894998	−	0.446069i	$-0.852823\pi$
$467$		−	19.2793i		−	0.892139i	0.894998	−	0.446069i	$-0.147177\pi$
$468$		0			0
$469$	0.953943			0.0440490
$470$	−31.3495	+	34.2247i	−1.44604	+	1.57867i
$471$		0			0
$472$		−	17.4582i		−	0.803579i
$473$			13.0598i			0.600490i
$474$		0			0
$475$	2.08984	+	23.7849i	0.0958883	+	1.09133i
$476$	1.98347			0.0909122
$477$		0			0
$478$			39.4198i			1.80302i
$479$	38.8194			1.77371			0.886853	−	0.462052i	$-0.152887\pi$
$479$	38.8194			1.77371			0.886853	+	0.462052i	$0.152887\pi$
$480$		0			0
$481$	1.66233			0.0757956
$482$		−	42.1694i		−	1.92076i
$483$		0			0
$484$	−24.9278			−1.13308
$485$	24.3872	+	22.3384i	1.10736	+	1.01433i
$486$		0			0
$487$		−	29.8866i		−	1.35429i	−0.735849	−	0.677145i	$-0.763217\pi$
$487$		−	29.8866i		−	1.35429i	0.735849	−	0.677145i	$-0.236783\pi$
$488$			3.44590i			0.155989i
$489$		0			0
$490$	19.8885	+	18.2177i	0.898472	+	0.822990i
$491$	−26.7474			−1.20709			−0.603547	−	0.797327i	$-0.706246\pi$
$491$	−26.7474			−1.20709			−0.603547	+	0.797327i	$0.706246\pi$
$492$		0			0
$493$		−	6.85874i		−	0.308902i
$494$	8.45988			0.380628
$495$		0			0
$496$	39.1574			1.75822
$497$		−	5.99429i		−	0.268880i
$498$		0			0
$499$	−31.9694			−1.43115			−0.715574	−	0.698537i	$-0.753835\pi$
$499$	−31.9694			−1.43115			−0.715574	+	0.698537i	$0.753835\pi$
$500$	−10.1030	−	7.74334i	−0.451820	−	0.346293i
$501$		0			0
$502$		−	7.72398i		−	0.344738i
$503$		−	9.37993i		−	0.418231i	−0.977891	−	0.209115i	$-0.932942\pi$
$503$		−	9.37993i		−	0.418231i	0.977891	−	0.209115i	$-0.0670584\pi$
$504$		0			0
$505$	19.0238	−	20.7686i	0.846547	−	0.924189i
$506$	−3.43102			−0.152528
$507$		0			0
$508$		−	1.62737i		−	0.0722030i
$509$	11.0042			0.487753			0.243877	−	0.969806i	$-0.421581\pi$
$509$	11.0042			0.487753			0.243877	+	0.969806i	$0.421581\pi$
$510$		0			0
$511$	1.11776			0.0494469
$512$		−	13.5440i		−	0.598565i
$513$		0			0
$514$	26.5677			1.17185
$515$	−10.2868	−	9.42263i	−0.453292	−	0.415211i
$516$		0			0
$517$		−	67.1972i		−	2.95533i
$518$		−	1.28881i		−	0.0566273i
$519$		0			0
$520$	2.30508	−	2.51649i	0.101084	−	0.110355i
$521$	−29.1305			−1.27623			−0.638115	−	0.769941i	$-0.720285\pi$
$521$	−29.1305			−1.27623			−0.638115	+	0.769941i	$0.720285\pi$
$522$		0			0
$523$			13.5675i			0.593266i	0.954992	+	0.296633i	$0.0958638\pi$
$523$			13.5675i			0.593266i	−0.954992	+	0.296633i	$0.904136\pi$
$524$	20.1313			0.879439
$525$		0			0
$526$	−18.9612			−0.826747
$527$			31.2958i			1.36327i
$528$		0			0
$529$	22.8860			0.995042
$530$	38.2611	−	41.7703i	1.66196	−	1.81439i
$531$		0			0
$532$		−	2.37933i		−	0.103157i
$533$			2.68304i			0.116216i
$534$		0			0
$535$	−1.82291	−	1.66977i	−0.0788113	−	0.0721902i
$536$	3.32672			0.143693
$537$		0			0
$538$		−	26.5872i		−	1.14626i
$539$	−39.0493			−1.68197
$540$		0			0
$541$	−22.6672			−0.974541			−0.487270	−	0.873251i	$-0.662007\pi$
$541$	−22.6672			−0.974541			−0.487270	+	0.873251i	$0.662007\pi$
$542$			3.03625i			0.130418i
$543$		0			0
$544$	22.9756			0.985071
$545$	11.9623	−	13.0595i	0.512410	−	0.559406i
$546$		0			0
$547$			33.5014i			1.43242i	0.697886	+	0.716209i	$0.254124\pi$
$547$			33.5014i			1.43242i	−0.697886	+	0.716209i	$0.745876\pi$
$548$			12.2603i			0.523734i
$549$		0			0
$550$	50.6089	−	4.44670i	2.15797	−	0.189608i
$551$	−8.22762			−0.350508
$552$		0			0
$553$			1.11660i			0.0474826i
$554$	37.4739			1.59211
$555$		0			0
$556$	4.33605			0.183889
$557$		−	42.6185i		−	1.80580i	−0.429846	−	0.902902i	$-0.641432\pi$
$557$		−	42.6185i		−	1.80580i	0.429846	−	0.902902i	$-0.358568\pi$
$558$		0			0
$559$	−2.27705			−0.0963090
$560$	−3.59419	−	3.29224i	−0.151882	−	0.139122i
$561$		0			0
$562$			33.2067i			1.40074i
$563$		−	17.1688i		−	0.723580i	−0.932260	−	0.361790i	$-0.882166\pi$
$563$		−	17.1688i		−	0.723580i	0.932260	−	0.361790i	$-0.117834\pi$
$564$		0			0
$565$	18.8685	+	17.2834i	0.793805	+	0.727116i
$566$	16.4712			0.692338
$567$		0			0
$568$		−	20.9041i		−	0.877117i
$569$	16.9018			0.708561			0.354281	−	0.935139i	$-0.384726\pi$
$569$	16.9018			0.708561			0.354281	+	0.935139i	$0.384726\pi$
$570$		0			0
$571$	−29.9408			−1.25298			−0.626491	−	0.779428i	$-0.715510\pi$
$571$	−29.9408			−1.25298			−0.626491	+	0.779428i	$0.715510\pi$
$572$		−	6.52990i		−	0.273029i
$573$		0			0
$574$	2.08018			0.0868252
$575$	1.68189	−	0.147777i	0.0701396	−	0.00616275i
$576$		0			0
$577$			44.8430i			1.86684i	0.358789	+	0.933419i	$0.383190\pi$
$577$			44.8430i			1.86684i	−0.358789	+	0.933419i	$0.616810\pi$
$578$		−	2.04290i		−	0.0849734i
$579$		0			0
$580$	2.96275	−	3.23449i	0.123022	−	0.134305i
$581$	−2.36829			−0.0982532
$582$		0			0
$583$			82.0122i			3.39660i
$584$	3.89801			0.161301
$585$		0			0
$586$	31.8464			1.31556
$587$		−	24.2703i		−	1.00174i	−0.865522	−	0.500872i	$-0.833013\pi$
$587$		−	24.2703i		−	1.00174i	0.865522	−	0.500872i	$-0.166987\pi$
$588$		0			0
$589$	37.5418			1.54688
$590$	33.4154	+	30.6081i	1.37569	+	1.26012i
$591$		0			0
$592$		−	8.27973i		−	0.340295i
$593$			44.2659i			1.81778i	0.417032	+	0.908892i	$0.363070\pi$
$593$			44.2659i			1.81778i	−0.417032	+	0.908892i	$0.636930\pi$
$594$		0			0
$595$	2.63125	−	2.87258i	0.107871	−	0.117764i
$596$	18.6319			0.763192
$597$		0			0
$598$		−	0.598218i		−	0.0244630i
$599$	−18.9996			−0.776301			−0.388151	−	0.921596i	$-0.626886\pi$
$599$	−18.9996			−0.776301			−0.388151	+	0.921596i	$0.626886\pi$
$600$		0			0
$601$	0.722123			0.0294560			0.0147280	−	0.999892i	$-0.495312\pi$
$601$	0.722123			0.0294560			0.0147280	+	0.999892i	$0.495312\pi$
$602$			1.76541i			0.0719529i
$603$		0			0
$604$	−23.2002			−0.944001
$605$	−33.0690	+	36.1020i	−1.34445	+	1.46776i
$606$		0			0
$607$			29.9236i			1.21456i	0.794487	+	0.607281i	$0.207740\pi$
$607$			29.9236i			1.21456i	−0.794487	+	0.607281i	$0.792260\pi$
$608$		−	27.5611i		−	1.11775i
$609$		0			0
$610$	−6.59553	−	6.04143i	−0.267045	−	0.244611i
$611$	11.7162			0.473987
$612$		0			0
$613$		−	34.6980i		−	1.40144i	−0.713438	−	0.700719i	$-0.752863\pi$
$613$		−	34.6980i		−	1.40144i	0.713438	−	0.700719i	$-0.247137\pi$
$614$	23.5850			0.951812
$615$		0			0
$616$	3.83072			0.154344
$617$		−	25.8247i		−	1.03966i	−0.854269	−	0.519831i	$-0.825995\pi$
$617$		−	25.8247i		−	1.03966i	0.854269	−	0.519831i	$-0.174005\pi$
$618$		0			0
$619$	29.3106			1.17809			0.589047	−	0.808099i	$-0.299503\pi$
$619$	29.3106			1.17809			0.589047	+	0.808099i	$0.299503\pi$
$620$	−13.5188	+	14.7587i	−0.542927	+	0.592722i
$621$		0			0
$622$			4.69074i			0.188082i
$623$			2.06759i			0.0828364i
$624$		0			0
$625$	−24.6170	+	4.35955i	−0.984678	+	0.174382i
$626$	28.1183			1.12383
$627$		0			0
$628$			15.0184i			0.599298i
$629$	6.61741			0.263853
$630$		0			0
$631$	−22.9480			−0.913546			−0.456773	−	0.889583i	$-0.650995\pi$
$631$	−22.9480			−0.913546			−0.456773	+	0.889583i	$0.650995\pi$
$632$			3.89396i			0.154893i
$633$		0			0
$634$	6.82392			0.271013
$635$	−2.35686	−	2.15886i	−0.0935292	−	0.0856717i
$636$		0			0
$637$		−	6.80848i		−	0.269762i
$638$			17.5065i			0.693089i
$639$		0			0
$640$	−18.2643	−	16.7299i	−0.721962	−	0.661309i
$641$	−24.3185			−0.960522			−0.480261	−	0.877126i	$-0.659458\pi$
$641$	−24.3185			−0.960522			−0.480261	+	0.877126i	$0.659458\pi$
$642$		0			0
$643$		−	11.2911i		−	0.445276i	−0.974901	−	0.222638i	$-0.928533\pi$
$643$		−	11.2911i		−	0.445276i	0.974901	−	0.222638i	$-0.0714668\pi$
$644$	−0.168248			−0.00662991
$645$		0			0
$646$	33.6772			1.32501
$647$		−	7.55633i		−	0.297070i	−0.988907	−	0.148535i	$-0.952544\pi$
$647$		−	7.55633i		−	0.297070i	0.988907	−	0.148535i	$-0.0474558\pi$
$648$		0			0
$649$	−65.6082			−2.57535
$650$	0.775308	+	8.82395i	0.0304101	+	0.346104i
$651$		0			0
$652$			11.7926i			0.461835i
$653$			33.6711i			1.31765i	0.752295	+	0.658826i	$0.228947\pi$
$653$			33.6711i			1.31765i	−0.752295	+	0.658826i	$0.771053\pi$
$654$		0			0
$655$	26.7060	−	29.1554i	1.04349	−	1.13919i
$656$	13.3637			0.521766
$657$		0			0
$658$		−	9.08367i		−	0.354118i
$659$	−17.1039			−0.666274			−0.333137	−	0.942878i	$-0.608107\pi$
$659$	−17.1039			−0.666274			−0.333137	+	0.942878i	$0.608107\pi$
$660$		0			0
$661$	19.1964			0.746655			0.373327	−	0.927700i	$-0.378217\pi$
$661$	19.1964			0.746655			0.373327	+	0.927700i	$0.378217\pi$
$662$			14.4430i			0.561342i
$663$		0			0
$664$	−8.25903			−0.320513
$665$	−3.44590	−	3.15640i	−0.133626	−	0.122400i
$666$		0			0
$667$			0.581794i			0.0225272i
$668$		−	12.1495i		−	0.470080i
$669$		0			0
$670$	−5.83249	+	6.36743i	−0.225329	+	0.245995i
$671$	12.9497			0.499919
$672$		0			0
$673$			27.9616i			1.07784i	0.842357	+	0.538921i	$0.181168\pi$
$673$			27.9616i			1.07784i	−0.842357	+	0.538921i	$0.818832\pi$
$674$	−0.607682			−0.0234070
$675$		0			0
$676$	1.13853			0.0437894
$677$			6.98533i			0.268468i	0.990950	+	0.134234i	$0.0428574\pi$
$677$			6.98533i			0.268468i	−0.990950	+	0.134234i	$0.957143\pi$
$678$		0			0
$679$	−6.47266			−0.248398
$680$	9.17608	−	10.0177i	0.351886	−	0.384160i
$681$		0			0
$682$		−	79.8805i		−	3.05878i
$683$		−	18.0969i		−	0.692460i	−0.938150	−	0.346230i	$-0.887462\pi$
$683$		−	18.0969i		−	0.692460i	0.938150	−	0.346230i	$-0.112538\pi$
$684$		0			0
$685$	17.7561	+	16.2644i	0.678426	+	0.621431i
$686$	−10.7058			−0.408750
$687$		0			0
$688$			11.3416i			0.432393i
$689$	−14.2993			−0.544760
$690$		0			0
$691$	13.9818			0.531892			0.265946	−	0.963988i	$-0.414316\pi$
$691$	13.9818			0.531892			0.265946	+	0.963988i	$0.414316\pi$
$692$		−	6.42180i		−	0.244120i
$693$		0			0
$694$	57.0994			2.16746
$695$	5.75216	−	6.27973i	0.218192	−	0.238204i
$696$		0			0
$697$			10.6807i			0.404560i
$698$			41.8424i			1.58376i
$699$		0			0
$700$	2.48173	−	0.218055i	0.0938004	−	0.00824169i
$701$	2.64470			0.0998891			0.0499445	−	0.998752i	$-0.484096\pi$
$701$	2.64470			0.0998891			0.0499445	+	0.998752i	$0.484096\pi$
$702$		0			0
$703$		−	7.93812i		−	0.299392i
$704$	−1.50988			−0.0569058
$705$		0			0
$706$	−54.1312			−2.03725
$707$			5.51224i			0.207309i
$708$		0			0
$709$	−9.89834			−0.371740			−0.185870	−	0.982574i	$-0.559510\pi$
$709$	−9.89834			−0.371740			−0.185870	+	0.982574i	$0.559510\pi$
$710$	40.0110	+	36.6496i	1.50158	+	1.37543i
$711$		0			0
$712$			7.21040i			0.270221i
$713$		−	2.65467i		−	0.0994183i
$714$		0			0
$715$	−9.45701	−	8.66251i	−0.353672	−	0.323960i
$716$	13.6186			0.508951
$717$		0			0
$718$			53.5538i			1.99861i
$719$	21.1288			0.787972			0.393986	−	0.919116i	$-0.371096\pi$
$719$	21.1288			0.787972			0.393986	+	0.919116i	$0.371096\pi$
$720$		0			0
$721$	2.73026			0.101680
$722$		−	6.73835i		−	0.250775i
$723$		0			0
$724$	−12.9157			−0.480007
$725$	−0.754022	−	8.58169i	−0.0280037	−	0.318716i
$726$		0			0
$727$		−	18.7471i		−	0.695290i	−0.937626	−	0.347645i	$-0.886981\pi$
$727$		−	18.7471i		−	0.695290i	0.937626	−	0.347645i	$-0.113019\pi$
$728$			0.667908i			0.0247543i
$729$		0			0
$730$	−6.83409	+	7.46089i	−0.252941	+	0.276140i
$731$	−9.06451			−0.335263
$732$		0			0
$733$		−	47.2675i		−	1.74586i	−0.487842	−	0.872932i	$-0.662216\pi$
$733$		−	47.2675i		−	1.74586i	0.487842	−	0.872932i	$-0.337784\pi$
$734$	17.7940			0.656790
$735$		0			0
$736$	−1.94891			−0.0718379
$737$		−	12.5019i		−	0.460512i
$738$		0			0
$739$	40.6501			1.49534			0.747670	−	0.664071i	$-0.231173\pi$
$739$	40.6501			1.49534			0.747670	+	0.664071i	$0.231173\pi$
$740$	3.12068	+	2.85851i	0.114718	+	0.105081i
$741$		0			0
$742$			11.0864i			0.406993i
$743$		−	1.06271i		−	0.0389871i	−0.999810	−	0.0194936i	$-0.993795\pi$
$743$		−	1.06271i		−	0.0389871i	0.999810	−	0.0194936i	$-0.00620539\pi$
$744$		0			0
$745$	24.7169	−	26.9839i	0.905558	−	0.988612i
$746$	−51.0389			−1.86867
$747$		0			0
$748$		−	25.9943i		−	0.950445i
$749$	0.483823			0.0176785
$750$		0			0
$751$	−10.8780			−0.396945			−0.198473	−	0.980106i	$-0.563598\pi$
$751$	−10.8780			−0.396945			−0.198473	+	0.980106i	$0.563598\pi$
$752$		−	58.3562i		−	2.12803i
$753$		0			0
$754$	−3.05236			−0.111160
$755$	−30.7772	+	33.5999i	−1.12010	+	1.22283i
$756$		0			0
$757$		−	16.2279i		−	0.589812i	−0.955526	−	0.294906i	$-0.904712\pi$
$757$		−	16.2279i		−	0.589812i	0.955526	−	0.294906i	$-0.0952884\pi$
$758$			30.2199i			1.09764i
$759$		0			0
$760$	−12.0170	−	11.0075i	−0.435903	−	0.399282i
$761$	−37.3880			−1.35531			−0.677657	−	0.735379i	$-0.737004\pi$
$761$	−37.3880			−1.35531			−0.677657	+	0.735379i	$0.737004\pi$
$762$		0			0
$763$			3.46615i			0.125483i
$764$	−22.6215			−0.818416
$765$		0			0
$766$	−11.6720			−0.421726
$767$		−	11.4392i		−	0.413044i
$768$		0			0
$769$	12.5874			0.453914			0.226957	−	0.973905i	$-0.427122\pi$
$769$	12.5874			0.453914			0.226957	+	0.973905i	$0.427122\pi$
$770$	−6.71611	+	7.33209i	−0.242032	+	0.264230i
$771$		0			0
$772$			1.26174i			0.0454111i
$773$		−	0.746723i		−	0.0268577i	−0.999910	−	0.0134289i	$-0.995725\pi$
$773$		−	0.746723i		−	0.0268577i	0.999910	−	0.0134289i	$-0.00427467\pi$
$774$		0			0
$775$	3.44053	+	39.1574i	0.123588	+	1.40658i
$776$	−22.5724			−0.810300
$777$		0			0
$778$		−	54.1646i		−	1.94190i
$779$	12.8124			0.459050
$780$		0			0
$781$	−78.5579			−2.81102
$782$		−	2.38139i		−	0.0851585i
$783$		0			0
$784$	−33.9117			−1.21113
$785$	21.7505	+	19.9232i	0.776310	+	0.711091i
$786$		0			0
$787$			33.3585i			1.18910i	0.804058	+	0.594551i	$0.202670\pi$
$787$			33.3585i			1.18910i	−0.804058	+	0.594551i	$0.797330\pi$
$788$			6.12251i			0.218105i
$789$		0			0
$790$	−7.45313	−	6.82698i	−0.265170	−	0.242893i
$791$	−5.00794			−0.178062
$792$		0			0
$793$			2.25786i			0.0801790i
$794$	−38.1014			−1.35217
$795$		0			0
$796$	−12.8352			−0.454933
$797$		−	0.233988i		−	0.00828829i	−0.999991	−	0.00414415i	$-0.998681\pi$
$797$		−	0.233988i		−	0.00828829i	0.999991	−	0.00414415i	$-0.00131913\pi$
$798$		0			0
$799$	46.6400			1.65001
$800$	28.7472	−	2.52584i	1.01637	−	0.0893021i
$801$		0			0
$802$		−	31.7097i		−	1.11971i
$803$		−	14.6488i		−	0.516945i
$804$		0			0
$805$	−0.223197	+	0.243668i	−0.00786666	+	0.00858816i
$806$	13.9276			0.490580
$807$		0			0
$808$			19.2230i			0.676264i
$809$	−22.2003			−0.780521			−0.390260	−	0.920705i	$-0.627615\pi$
$809$	−22.2003			−0.780521			−0.390260	+	0.920705i	$0.627615\pi$
$810$		0			0
$811$	−43.4456			−1.52558			−0.762791	−	0.646645i	$-0.776171\pi$
$811$	−43.4456			−1.52558			−0.762791	+	0.646645i	$0.776171\pi$
$812$			0.858473i			0.0301265i
$813$		0			0
$814$	−16.8905			−0.592012
$815$	17.0788	+	15.6440i	0.598246	+	0.547986i
$816$		0			0
$817$			10.8736i			0.380420i
$818$			39.6560i			1.38654i
$819$		0			0
$820$	−4.61371	+	5.03687i	−0.161118	+	0.175895i
$821$	6.76172			0.235986			0.117993	−	0.993014i	$-0.462354\pi$
$821$	6.76172			0.235986			0.117993	+	0.993014i	$0.462354\pi$
$822$		0			0
$823$			28.6208i			0.997659i	0.866700	+	0.498829i	$0.166237\pi$
$823$			28.6208i			0.997659i	−0.866700	+	0.498829i	$0.833763\pi$
$824$	9.52133			0.331691
$825$		0			0
$826$	−8.86887			−0.308587
$827$		−	8.19215i		−	0.284869i	−0.989804	−	0.142435i	$-0.954507\pi$
$827$		−	8.19215i		−	0.284869i	0.989804	−	0.142435i	$-0.0454930\pi$
$828$		0			0
$829$	3.60208			0.125105			0.0625526	−	0.998042i	$-0.480076\pi$
$829$	3.60208			0.125105			0.0625526	+	0.998042i	$0.480076\pi$
$830$	14.4799	−	15.8080i	0.502606	−	0.548703i
$831$		0			0
$832$		−	0.263257i		−	0.00912678i
$833$		−	27.1033i		−	0.939072i
$834$		0			0
$835$	−17.5957	−	16.1175i	−0.608925	−	0.557768i
$836$	−31.1823			−1.07846
$837$		0			0
$838$			48.7458i			1.68389i
$839$	1.50713			0.0520318			0.0260159	−	0.999662i	$-0.491718\pi$
$839$	1.50713			0.0520318			0.0260159	+	0.999662i	$0.491718\pi$
$840$		0			0
$841$	−26.0314			−0.897636
$842$		−	11.2426i		−	0.387446i
$843$		0			0
$844$	18.7285			0.644660
$845$	1.51036	−	1.64888i	0.0519579	−	0.0567233i
$846$		0			0
$847$		−	9.58193i		−	0.329239i
$848$			71.2221i			2.44578i
$849$		0			0
$850$	3.08635	+	35.1265i	0.105861	+	1.20483i
$851$	−0.561324			−0.0192419
$852$		0			0
$853$		−	8.35952i		−	0.286225i	−0.989706	−	0.143112i	$-0.954289\pi$
$853$		−	8.35952i		−	0.286225i	0.989706	−	0.143112i	$-0.0457110\pi$
$854$	1.75054			0.0599021
$855$		0			0
$856$	1.68726			0.0576692
$857$			12.8565i			0.439168i	0.975594	+	0.219584i	$0.0704700\pi$
$857$			12.8565i			0.439168i	−0.975594	+	0.219584i	$0.929530\pi$
$858$		0			0
$859$	16.3734			0.558652			0.279326	−	0.960196i	$-0.409889\pi$
$859$	16.3734			0.558652			0.279326	+	0.960196i	$0.409889\pi$
$860$	−4.27470	−	3.91557i	−0.145766	−	0.133520i
$861$		0			0
$862$		−	6.70339i		−	0.228318i
$863$		−	50.0600i		−	1.70406i	−0.523492	−	0.852031i	$-0.675371\pi$
$863$		−	50.0600i		−	1.70406i	0.523492	−	0.852031i	$-0.324629\pi$
$864$		0			0
$865$	−9.30045	−	8.51911i	−0.316225	−	0.289658i
$866$	4.52481			0.153759
$867$		0			0
$868$		−	3.91713i		−	0.132956i
$869$	14.6335			0.496409
$870$		0			0
$871$	2.17977			0.0738588
$872$			12.0876i			0.409339i
$873$		0			0
$874$	−2.85668			−0.0966285
$875$	2.97644	−	3.88346i	0.100622	−	0.131285i
$876$		0			0
$877$			48.1027i			1.62431i	0.583439	+	0.812157i	$0.301707\pi$
$877$			48.1027i			1.62431i	−0.583439	+	0.812157i	$0.698293\pi$
$878$			4.14681i			0.139948i
$879$		0			0
$880$	−43.1463	+	47.1036i	−1.45446	+	1.58786i
$881$	41.2109			1.38843			0.694216	−	0.719767i	$-0.255751\pi$
$881$	41.2109			1.38843			0.694216	+	0.719767i	$0.255751\pi$
$882$		0			0
$883$			13.9344i			0.468930i	0.972125	+	0.234465i	$0.0753338\pi$
$883$			13.9344i			0.468930i	−0.972125	+	0.234465i	$0.924666\pi$
$884$	4.53225			0.152436
$885$		0			0
$886$	−0.830120			−0.0278884
$887$		−	47.8092i		−	1.60528i	−0.596466	−	0.802638i	$-0.703429\pi$
$887$		−	47.8092i		−	1.60528i	0.596466	−	0.802638i	$-0.296571\pi$
$888$		0			0
$889$	0.625541			0.0209800
$890$	−13.8009	−	12.6414i	−0.462606	−	0.423742i
$891$		0			0
$892$			28.5232i			0.955026i
$893$		−	55.9485i		−	1.87225i
$894$		0			0
$895$	18.0663	−	19.7233i	0.603891	−	0.659278i
$896$	4.84758			0.161946
$897$		0			0
$898$			31.1556i			1.03968i
$899$	−13.5452			−0.451759
$900$		0			0
$901$	−56.9228			−1.89637
$902$		−	27.2618i		−	0.907718i
$903$		0			0
$904$	−17.4644			−0.580857
$905$	−17.1338	+	18.7053i	−0.569548	+	0.621785i
$906$		0			0
$907$		−	8.74334i		−	0.290318i	−0.989408	−	0.145159i	$-0.953631\pi$
$907$		−	8.74334i		−	0.290318i	0.989408	−	0.145159i	$-0.0463693\pi$
$908$		−	9.23815i		−	0.306579i
$909$		0			0
$910$	−1.27839	−	1.17099i	−0.0423783	−	0.0388180i
$911$	2.67266			0.0885493			0.0442746	−	0.999019i	$-0.485902\pi$
$911$	2.67266			0.0885493			0.0442746	+	0.999019i	$0.485902\pi$
$912$		0			0
$913$			31.0376i			1.02719i
$914$	−21.1053			−0.698100
$915$		0			0
$916$	10.9039			0.360273
$917$			7.73820i			0.255538i
$918$		0			0
$919$	15.4118			0.508389			0.254195	−	0.967153i	$-0.418190\pi$
$919$	15.4118			0.508389			0.254195	+	0.967153i	$0.418190\pi$
$920$	−0.778363	+	0.849752i	−0.0256619	+	0.0280155i
$921$		0			0
$922$		−	31.4528i		−	1.03584i
$923$		−	13.6970i		−	0.450843i
$924$		0			0
$925$	8.27973	−	0.727491i	0.272236	−	0.0239198i
$926$	−69.9522			−2.29877
$927$		0			0
$928$			9.94416i			0.326433i
$929$	16.7575			0.549795			0.274898	−	0.961473i	$-0.411356\pi$
$929$	16.7575			0.549795			0.274898	+	0.961473i	$0.411356\pi$
$930$		0			0
$931$	−32.5126			−1.06556
$932$			18.6480i			0.610836i
$933$		0			0
$934$	−34.1549			−1.11758
$935$	−37.6466	−	34.4838i	−1.23117	−	1.12774i
$936$		0			0
$937$		−	34.3945i		−	1.12362i	−0.827267	−	0.561809i	$-0.810105\pi$
$937$		−	34.3945i		−	1.12362i	0.827267	−	0.561809i	$-0.189895\pi$
$938$		−	1.68999i		−	0.0551803i
$939$		0			0
$940$	21.9948	+	20.1470i	0.717391	+	0.657122i
$941$	−3.90298			−0.127234			−0.0636168	−	0.997974i	$-0.520264\pi$
$941$	−3.90298			−0.127234			−0.0636168	+	0.997974i	$0.520264\pi$
$942$		0			0
$943$		−	0.905993i		−	0.0295032i
$944$	−56.9763			−1.85442
$945$		0			0
$946$	23.1366			0.752235
$947$			32.7611i			1.06459i	0.846558	+	0.532297i	$0.178671\pi$
$947$			32.7611i			1.06459i	−0.846558	+	0.532297i	$0.821329\pi$
$948$		0			0
$949$	2.55410			0.0829096
$950$	42.1371	−	3.70233i	1.36711	−	0.120120i
$951$		0			0
$952$			2.65882i			0.0861727i
$953$			3.05611i			0.0989970i	0.998774	+	0.0494985i	$0.0157623\pi$
$953$			3.05611i			0.0989970i	−0.998774	+	0.0494985i	$0.984238\pi$
$954$		0			0
$955$	−30.0095	+	32.7618i	−0.971083	+	1.06015i
$956$	25.3335			0.819343
$957$		0			0
$958$		−	68.7721i		−	2.22192i
$959$	−4.71269			−0.152181
$960$		0			0
$961$	30.8057			0.993733
$962$		−	2.94496i		−	0.0949493i
$963$		0			0
$964$	−27.1005			−0.872847
$965$	1.82734	+	1.67382i	0.0588240	+	0.0538821i
$966$		0			0
$967$		−	20.5538i		−	0.660966i	−0.943812	−	0.330483i	$-0.892788\pi$
$967$		−	20.5538i		−	0.660966i	0.943812	−	0.330483i	$-0.107212\pi$
$968$		−	33.4154i		−	1.07401i
$969$		0			0
$970$	39.5744	−	43.2040i	1.27066	−	1.38720i
$971$	49.3281			1.58301			0.791507	−	0.611160i	$-0.209297\pi$
$971$	49.3281			1.58301			0.791507	+	0.611160i	$0.209297\pi$
$972$		0			0
$973$			1.66672i			0.0534326i
$974$	−52.9467			−1.69652
$975$		0			0
$976$	11.2460			0.359975
$977$		−	19.0164i		−	0.608390i	−0.952610	−	0.304195i	$-0.901613\pi$
$977$		−	19.0164i		−	0.608390i	0.952610	−	0.304195i	$-0.0983874\pi$
$978$		0			0
$979$	27.0968			0.866017
$980$	11.7077	−	12.7815i	0.373990	−	0.408291i
$981$		0			0
$982$			47.3854i			1.51213i
$983$			20.8696i			0.665636i	0.942991	+	0.332818i	$0.107999\pi$
$983$			20.8696i			0.665636i	−0.942991	+	0.332818i	$0.892001\pi$
$984$		0			0
$985$	8.86700	+	8.12207i	0.282526	+	0.258791i
$986$	−12.1509			−0.386962
$987$		0			0
$988$		−	5.43681i		−	0.172968i
$989$	0.768899			0.0244496
$990$		0			0
$991$	15.6435			0.496932			0.248466	−	0.968641i	$-0.420074\pi$
$991$	15.6435			0.496932			0.248466	+	0.968641i	$0.420074\pi$
$992$		−	45.3743i		−	1.44063i
$993$		0			0
$994$	−10.6194			−0.336827
$995$	−17.0271	+	18.5888i	−0.539796	+	0.589304i
$996$		0			0
$997$			6.21108i			0.196707i	0.995152	+	0.0983535i	$0.0313576\pi$
$997$			6.21108i			0.196707i	−0.995152	+	0.0983535i	$0.968642\pi$
$998$			56.6367i			1.79280i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.c.c.469.3		10
3.2	odd	2		195.2.c.b.79.8	yes	10
5.2	odd	4		2925.2.a.bl.1.4		5
5.3	odd	4		2925.2.a.bm.1.2		5
5.4	even	2	inner	585.2.c.c.469.8		10
12.11	even	2		3120.2.l.p.1249.9		10
15.2	even	4		975.2.a.r.1.2		5
15.8	even	4		975.2.a.s.1.4		5
15.14	odd	2		195.2.c.b.79.3	✓	10
60.59	even	2		3120.2.l.p.1249.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.c.b.79.3	✓	10	15.14	odd	2
195.2.c.b.79.8	yes	10	3.2	odd	2
585.2.c.c.469.3		10	1.1	even	1	trivial
585.2.c.c.469.8		10	5.4	even	2	inner
975.2.a.r.1.2		5	15.2	even	4
975.2.a.s.1.4		5	15.8	even	4
2925.2.a.bl.1.4		5	5.2	odd	4
2925.2.a.bm.1.2		5	5.3	odd	4
3120.2.l.p.1249.4		10	60.59	even	2
3120.2.l.p.1249.9		10	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.77159i q^{2} -1.13853 q^{4} +(-1.51036 + 1.64888i) q^{5} -0.437634i q^{7} -1.52618i q^{8} +O(q^{10})\)	\(q-1.77159i q^{2} -1.13853 q^{4} +(-1.51036 + 1.64888i) q^{5} -0.437634i q^{7} -1.52618i q^{8} +(2.92114 + 2.67573i) q^{10} -5.73540 q^{11} -1.00000i q^{13} -0.775308 q^{14} -4.98081 q^{16} -3.98081i q^{17} -4.77531 q^{19} +(1.71958 - 1.87730i) q^{20} +10.1608i q^{22} +0.337673i q^{23} +(-0.437634 - 4.98081i) q^{25} -1.77159 q^{26} +0.498258i q^{28} +1.72295 q^{29} -7.86166 q^{31} +5.77159i q^{32} -7.05236 q^{34} +(0.721608 + 0.660985i) q^{35} +1.66233i q^{37} +8.45988i q^{38} +(2.51649 + 2.30508i) q^{40} -2.68304 q^{41} -2.27705i q^{43} +6.52990 q^{44} +0.598218 q^{46} +11.7162i q^{47} +6.80848 q^{49} +(-8.82395 + 0.775308i) q^{50} +1.13853i q^{52} -14.2993i q^{53} +(8.66251 - 9.45701i) q^{55} -0.667908 q^{56} -3.05236i q^{58} +11.4392 q^{59} -2.25786 q^{61} +13.9276i q^{62} +0.263257 q^{64} +(1.64888 + 1.51036i) q^{65} +2.17977i q^{67} +4.53225i q^{68} +(1.17099 - 1.27839i) q^{70} +13.6970 q^{71} +2.55410i q^{73} +2.94496 q^{74} +5.43681 q^{76} +2.51001i q^{77} -2.55144 q^{79} +(7.52281 - 8.21278i) q^{80} +4.75325i q^{82} -5.41158i q^{83} +(6.56389 + 6.01245i) q^{85} -4.03400 q^{86} +8.75325i q^{88} -4.72448 q^{89} -0.437634 q^{91} -0.384450i q^{92} +20.7563 q^{94} +(7.21243 - 7.87393i) q^{95} -14.7901i q^{97} -12.0618i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 12 q^{4} + 2 q^{5}+O(q^{10}) \) 10 * q - 12 * q^4 + 2 * q^5	\( 10 q - 12 q^{4} + 2 q^{5} + 4 q^{10} - 10 q^{11} + 24 q^{14} - 16 q^{19} - 32 q^{20} + 10 q^{25} + 16 q^{29} + 24 q^{31} - 40 q^{34} - 12 q^{35} + 36 q^{40} - 10 q^{41} + 36 q^{44} - 24 q^{46} - 44 q^{49} - 40 q^{50} + 2 q^{55} + 16 q^{59} + 26 q^{61} + 32 q^{64} + 56 q^{70} - 10 q^{71} + 24 q^{74} - 2 q^{79} + 12 q^{80} - 4 q^{85} + 38 q^{89} + 10 q^{91} + 24 q^{94} + 48 q^{95}+O(q^{100}) \) 10 * q - 12 * q^4 + 2 * q^5 + 4 * q^10 - 10 * q^11 + 24 * q^14 - 16 * q^19 - 32 * q^20 + 10 * q^25 + 16 * q^29 + 24 * q^31 - 40 * q^34 - 12 * q^35 + 36 * q^40 - 10 * q^41 + 36 * q^44 - 24 * q^46 - 44 * q^49 - 40 * q^50 + 2 * q^55 + 16 * q^59 + 26 * q^61 + 32 * q^64 + 56 * q^70 - 10 * q^71 + 24 * q^74 - 2 * q^79 + 12 * q^80 - 4 * q^85 + 38 * q^89 + 10 * q^91 + 24 * q^94 + 48 * q^95

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