LMFDB - Embedded newform 585.2.c.c.469.1

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			469.1
Root			$-2.47948i$ of defining polynomial
Character	$\chi$	$=$	585.469
Dual form			585.2.c.c.469.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47948i q^{2} -4.14785 q^{4} +(1.72481 - 1.42303i) q^{5} -0.949959i q^{7} +5.32555i q^{8} +O(q^{10})$	\(q-2.47948i q^{2} -4.14785 q^{4} +(1.72481 - 1.42303i) q^{5} -0.949959i q^{7} +5.32555i q^{8} +(-3.52839 - 4.27665i) q^{10} -3.89611 q^{11} +1.00000i q^{13} -2.35541 q^{14} +4.90893 q^{16} -5.90893i q^{17} -6.35541 q^{19} +(-7.15426 + 5.90252i) q^{20} +9.66033i q^{22} -3.30537i q^{23} +(0.949959 - 4.90893i) q^{25} +2.47948 q^{26} +3.94028i q^{28} -4.29569 q^{29} +7.56253 q^{31} -1.52052i q^{32} -14.6511 q^{34} +(-1.35182 - 1.63850i) q^{35} +1.30537i q^{37} +15.7581i q^{38} +(7.57843 + 9.18558i) q^{40} +6.75499 q^{41} +8.29569i q^{43} +16.1604 q^{44} -8.19561 q^{46} +0.0128228i q^{47} +6.09758 q^{49} +(-12.1716 - 2.35541i) q^{50} -4.14785i q^{52} -2.51249i q^{53} +(-6.72005 + 5.54428i) q^{55} +5.05905 q^{56} +10.6511i q^{58} -6.30851 q^{59} +1.61324 q^{61} -18.7512i q^{62} +6.04776 q^{64} +(1.42303 + 1.72481i) q^{65} -4.66328i q^{67} +24.5093i q^{68} +(-4.06264 + 3.35182i) q^{70} -7.92175 q^{71} -14.5914i q^{73} +3.23664 q^{74} +26.3612 q^{76} +3.70114i q^{77} +16.6004 q^{79} +(8.46698 - 6.98556i) q^{80} -16.7489i q^{82} -12.8044i q^{83} +(-8.40860 - 10.1918i) q^{85} +20.5690 q^{86} -20.7489i q^{88} +17.6542 q^{89} +0.949959 q^{91} +13.7102i q^{92} +0.0317940 q^{94} +(-10.9619 + 9.04395i) q^{95} -18.1226i q^{97} -15.1189i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.47948i		−	1.75326i	−0.481165	−	0.876630i	$-0.659786\pi$
$2$		−	2.47948i		−	1.75326i	0.481165	−	0.876630i	$-0.340214\pi$
$3$		0			0
$3$		0			0
$4$	−4.14785			−2.07392
$5$	1.72481	−	1.42303i	0.771360	−	0.636399i
$5$	1.72481	−	1.42303i	0.771360	−	0.636399i
$6$		0			0
$7$		−	0.949959i		−	0.359051i	−0.983753	−	0.179525i	$-0.942544\pi$
$7$		−	0.949959i		−	0.359051i	0.983753	−	0.179525i	$-0.0574562\pi$
$8$			5.32555i			1.88287i
$9$		0			0
$10$	−3.52839	−	4.27665i	−1.11577	−	1.35239i
$11$	−3.89611			−1.17472			−0.587360	−	0.809326i	$-0.699833\pi$
$11$	−3.89611			−1.17472			−0.587360	+	0.809326i	$0.699833\pi$
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−2.35541			−0.629509
$15$		0			0
$16$	4.90893			1.22723
$17$		−	5.90893i		−	1.43313i	−0.697523	−	0.716563i	$-0.745714\pi$
$17$		−	5.90893i		−	1.43313i	0.697523	−	0.716563i	$-0.254286\pi$
$18$		0			0
$19$	−6.35541			−1.45803			−0.729015	−	0.684497i	$-0.760022\pi$
$19$	−6.35541			−1.45803			−0.729015	+	0.684497i	$0.760022\pi$
$20$	−7.15426	+	5.90252i	−1.59974	+	1.31984i
$21$		0			0
$22$			9.66033i			2.05959i
$23$		−	3.30537i		−	0.689217i	−0.938747	−	0.344608i	$-0.888012\pi$
$23$		−	3.30537i		−	0.689217i	0.938747	−	0.344608i	$-0.111988\pi$
$24$		0			0
$25$	0.949959	−	4.90893i	0.189992	−	0.981786i
$26$	2.47948			0.486267
$27$		0			0
$28$			3.94028i			0.744643i
$29$	−4.29569			−0.797690			−0.398845	−	0.917018i	$-0.630589\pi$
$29$	−4.29569			−0.797690			−0.398845	+	0.917018i	$0.630589\pi$
$30$		0			0
$31$	7.56253			1.35827			0.679135	−	0.734013i	$-0.262355\pi$
$31$	7.56253			1.35827			0.679135	+	0.734013i	$0.262355\pi$
$32$		−	1.52052i		−	0.268792i
$33$		0			0
$34$	−14.6511			−2.51264
$35$	−1.35182	−	1.63850i	−0.228500	−	0.276957i
$36$		0			0
$37$			1.30537i			0.214601i	0.994227	+	0.107301i	$0.0342207\pi$
$37$			1.30537i			0.214601i	−0.994227	+	0.107301i	$0.965779\pi$
$38$			15.7581i			2.55631i
$39$		0			0
$40$	7.57843	+	9.18558i	1.19825	+	1.45237i
$41$	6.75499			1.05495			0.527476	−	0.849570i	$-0.323138\pi$
$41$	6.75499			1.05495			0.527476	+	0.849570i	$0.323138\pi$
$42$		0			0
$43$			8.29569i			1.26508i	0.774527	+	0.632540i	$0.217988\pi$
$43$			8.29569i			1.26508i	−0.774527	+	0.632540i	$0.782012\pi$
$44$	16.1604			2.43628
$45$		0			0
$46$	−8.19561			−1.20838
$47$			0.0128228i			0.00187040i	1.00000		0.000935200i	$0.000297683\pi$
$47$			0.0128228i			0.00187040i	−1.00000		0.000935200i	$0.999702\pi$
$48$		0			0
$49$	6.09758			0.871083
$50$	−12.1716	−	2.35541i	−1.72133	−	0.333105i
$51$		0			0
$52$		−	4.14785i		−	0.575203i
$53$		−	2.51249i		−	0.345117i	−0.984999	−	0.172559i	$-0.944797\pi$
$53$		−	2.51249i		−	0.345117i	0.984999	−	0.172559i	$-0.0552034\pi$
$54$		0			0
$55$	−6.72005	+	5.54428i	−0.906132	+	0.747591i
$56$	5.05905			0.676044
$57$		0			0
$58$			10.6511i			1.39856i
$59$	−6.30851			−0.821298			−0.410649	−	0.911793i	$-0.634698\pi$
$59$	−6.30851			−0.821298			−0.410649	+	0.911793i	$0.634698\pi$
$60$		0			0
$61$	1.61324			0.206554			0.103277	−	0.994653i	$-0.467067\pi$
$61$	1.61324			0.206554			0.103277	+	0.994653i	$0.467067\pi$
$62$		−	18.7512i		−	2.38140i
$63$		0			0
$64$	6.04776			0.755970
$65$	1.42303	+	1.72481i	0.176505	+	0.213937i
$66$		0			0
$67$		−	4.66328i		−	0.569710i	−0.958571	−	0.284855i	$-0.908055\pi$
$67$		−	4.66328i		−	0.569710i	0.958571	−	0.284855i	$-0.0919455\pi$
$68$			24.5093i			2.97219i
$69$		0			0
$70$	−4.06264	+	3.35182i	−0.485578	+	0.400619i
$71$	−7.92175			−0.940139			−0.470069	−	0.882629i	$-0.655771\pi$
$71$	−7.92175			−0.940139			−0.470069	+	0.882629i	$0.655771\pi$
$72$		0			0
$73$		−	14.5914i		−	1.70779i	−0.520444	−	0.853896i	$-0.674233\pi$
$73$		−	14.5914i		−	1.70779i	0.520444	−	0.853896i	$-0.325767\pi$
$74$	3.23664			0.376252
$75$		0			0
$76$	26.3612			3.02384
$77$			3.70114i			0.421784i
$78$		0			0
$79$	16.6004			1.86769			0.933845	−	0.357678i	$-0.116431\pi$
$79$	16.6004			1.86769			0.933845	+	0.357678i	$0.116431\pi$
$80$	8.46698	−	6.98556i	0.946637	−	0.781010i
$81$		0			0
$82$		−	16.7489i		−	1.84961i
$83$		−	12.8044i		−	1.40546i	−0.711456	−	0.702731i	$-0.751964\pi$
$83$		−	12.8044i		−	1.40546i	0.711456	−	0.702731i	$-0.248036\pi$
$84$		0			0
$85$	−8.40860	−	10.1918i	−0.912040	−	1.10546i
$86$	20.5690			2.21802
$87$		0			0
$88$		−	20.7489i		−	2.21184i
$89$	17.6542			1.87135			0.935673	−	0.352868i	$-0.114794\pi$
$89$	17.6542			1.87135			0.935673	+	0.352868i	$0.114794\pi$
$90$		0			0
$91$	0.949959			0.0995827
$92$			13.7102i			1.42938i
$93$		0			0
$94$	0.0317940			0.00327930
$95$	−10.9619	+	9.04395i	−1.12467	+	0.927890i
$96$		0			0
$97$		−	18.1226i		−	1.84007i	−0.391840	−	0.920033i	$-0.628161\pi$
$97$		−	18.1226i		−	1.84007i	0.391840	−	0.920033i	$-0.371839\pi$
$98$		−	15.1189i		−	1.52723i
$99$		0			0
$100$	−3.94028	+	20.3615i	−0.394028	+	2.03615i
$101$	−11.6921			−1.16341			−0.581705	−	0.813400i	$-0.697614\pi$
$101$	−11.6921			−1.16341			−0.581705	+	0.813400i	$0.697614\pi$
$102$		0			0
$103$			7.52217i			0.741181i	0.928796	+	0.370591i	$0.120845\pi$
$103$			7.52217i			0.741181i	−0.928796	+	0.370591i	$0.879155\pi$
$104$	−5.32555			−0.522213
$105$		0			0
$106$	−6.22968			−0.605080
$107$			6.00901i			0.580913i	0.956888	+	0.290457i	$0.0938072\pi$
$107$			6.00901i			0.580913i	−0.956888	+	0.290457i	$0.906193\pi$
$108$		0			0
$109$	−1.08139			−0.103579			−0.0517894	−	0.998658i	$-0.516492\pi$
$109$	−1.08139			−0.103579			−0.0517894	+	0.998658i	$0.516492\pi$
$110$	13.7470	+	16.6623i	1.31072	+	1.58869i
$111$		0			0
$112$		−	4.66328i		−	0.440639i
$113$			7.29636i			0.686383i	0.939265	+	0.343192i	$0.111508\pi$
$113$			7.29636i			0.686383i	−0.939265	+	0.343192i	$0.888492\pi$
$114$		0			0
$115$	−4.70364	−	5.70114i	−0.438617	−	0.531634i
$116$	17.8179			1.65435
$117$		0			0
$118$			15.6419i			1.43995i
$119$	−5.61324			−0.514565
$120$		0			0
$121$	4.17964			0.379967
$122$		−	4.00000i		−	0.362143i
$123$		0			0
$124$	−31.3682			−2.81695
$125$	−5.34706	−	9.81880i	−0.478256	−	0.878221i
$126$		0			0
$127$		−	10.6915i		−	0.948714i	−0.880333	−	0.474357i	$-0.842681\pi$
$127$		−	10.6915i		−	0.948714i	0.880333	−	0.474357i	$-0.157319\pi$
$128$		−	18.0364i		−	1.59420i
$129$		0			0
$130$	4.27665	−	3.52839i	0.375087	−	0.309460i
$131$	0.225811			0.0197292			0.00986458	−	0.999951i	$-0.496860\pi$
$131$	0.225811			0.0197292			0.00986458	+	0.999951i	$0.496860\pi$
$132$		0			0
$133$			6.03738i			0.523507i
$134$	−11.5625			−0.998851
$135$		0			0
$136$	31.4683			2.69838
$137$			6.63828i			0.567146i	0.958951	+	0.283573i	$0.0915199\pi$
$137$			6.63828i			0.567146i	−0.958951	+	0.283573i	$0.908480\pi$
$138$		0			0
$139$	−3.09758			−0.262733			−0.131367	−	0.991334i	$-0.541936\pi$
$139$	−3.09758			−0.262733			−0.131367	+	0.991334i	$0.541936\pi$
$140$	5.60715	+	6.79625i	0.473890	+	0.574388i
$141$		0			0
$142$			19.6419i			1.64831i
$143$		−	3.89611i		−	0.325809i
$144$		0			0
$145$	−7.40926	+	6.11291i	−0.615306	+	0.507649i
$146$	−36.1791			−2.99420
$147$		0			0
$148$		−	5.41446i		−	0.445066i
$149$	10.9808			0.899582			0.449791	−	0.893134i	$-0.351498\pi$
$149$	10.9808			0.899582			0.449791	+	0.893134i	$0.351498\pi$
$150$		0			0
$151$	−2.78901			−0.226966			−0.113483	−	0.993540i	$-0.536201\pi$
$151$	−2.78901			−0.226966			−0.113483	+	0.993540i	$0.536201\pi$
$152$		−	33.8460i		−	2.74528i
$153$		0			0
$154$	9.17692			0.739497
$155$	13.0440	−	10.7617i	1.04772	−	0.864403i
$156$		0			0
$157$			11.3843i			0.908563i	0.890858	+	0.454281i	$0.150104\pi$
$157$			11.3843i			0.908563i	−0.890858	+	0.454281i	$0.849896\pi$
$158$		−	41.1604i		−	3.27455i
$159$		0			0
$160$	−2.16374	−	2.62260i	−0.171059	−	0.207335i
$161$	−3.13996			−0.247464
$162$		0			0
$163$			2.13144i			0.166947i	0.996510	+	0.0834735i	$0.0266014\pi$
$163$			2.13144i			0.166947i	−0.996510	+	0.0834735i	$0.973399\pi$
$164$	−28.0187			−2.18789
$165$		0			0
$166$	−31.7482			−2.46414
$167$		−	3.00587i		−	0.232601i	−0.993214	−	0.116300i	$-0.962896\pi$
$167$		−	3.00587i		−	0.232601i	0.993214	−	0.116300i	$-0.0371035\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	−25.2704	+	20.8490i	−1.93815	+	1.59904i
$171$		0			0
$172$		−	34.4092i		−	2.62368i
$173$		−	0.673441i		−	0.0512008i	−0.999672	−	0.0256004i	$-0.991850\pi$
$173$		−	0.673441i		−	0.0512008i	0.999672	−	0.0256004i	$-0.00814974\pi$
$174$		0			0
$175$	−4.66328	−	0.902422i	−0.352511	−	0.0682167i
$176$	−19.1257			−1.44165
$177$		0			0
$178$		−	43.7734i		−	3.28096i
$179$	7.81786			0.584334			0.292167	−	0.956367i	$-0.405624\pi$
$179$	7.81786			0.584334			0.292167	+	0.956367i	$0.405624\pi$
$180$		0			0
$181$	−9.53118			−0.708447			−0.354223	−	0.935161i	$-0.615255\pi$
$181$	−9.53118			−0.708447			−0.354223	+	0.935161i	$0.615255\pi$
$182$		−	2.35541i		−	0.174594i
$183$		0			0
$184$	17.6029			1.29770
$185$	1.85758	+	2.25151i	0.136572	+	0.165535i
$186$		0			0
$187$			23.0218i			1.68352i
$188$		−	0.0531870i		−	0.00387906i
$189$		0			0
$190$	22.4243	+	27.1798i	1.62683	+	1.97183i
$191$	16.1073			1.16548			0.582740	−	0.812659i	$-0.301981\pi$
$191$	16.1073			1.16548			0.582740	+	0.812659i	$0.301981\pi$
$192$		0			0
$193$		−	13.8967i		−	1.00031i	−0.865936	−	0.500155i	$-0.833276\pi$
$193$		−	13.8967i		−	1.00031i	0.865936	−	0.500155i	$-0.166724\pi$
$194$	−44.9346			−3.22612
$195$		0			0
$196$	−25.2918			−1.80656
$197$			11.7647i			0.838198i	0.907941	+	0.419099i	$0.137654\pi$
$197$			11.7647i			0.838198i	−0.907941	+	0.419099i	$0.862346\pi$
$198$		0			0
$199$	8.41513			0.596533			0.298266	−	0.954483i	$-0.403592\pi$
$199$	8.41513			0.596533			0.298266	+	0.954483i	$0.403592\pi$
$200$	26.1427	+	5.05905i	1.84857	+	0.357729i
$201$		0			0
$202$			28.9905i			2.03976i
$203$			4.08073i			0.286411i
$204$		0			0
$205$	11.6511	−	9.61257i	0.813748	−	0.671371i
$206$	18.6511			1.29948
$207$		0			0
$208$			4.90893i			0.340373i
$209$	24.7613			1.71278
$210$		0			0
$211$	11.5402			0.794459			0.397230	−	0.917719i	$-0.369972\pi$
$211$	11.5402			0.794459			0.397230	+	0.917719i	$0.369972\pi$
$212$			10.4214i			0.715746i
$213$		0			0
$214$	14.8993			1.01849
$215$	11.8050	+	14.3085i	0.805097	+	0.975832i
$216$		0			0
$217$		−	7.18409i		−	0.487688i
$218$			2.68130i			0.181601i
$219$		0			0
$220$	27.8737	−	22.9968i	1.87925	−	1.55045i
$221$	5.90893			0.397478
$222$		0			0
$223$			7.82173i			0.523782i	0.965098	+	0.261891i	$0.0843460\pi$
$223$			7.82173i			0.523782i	−0.965098	+	0.261891i	$0.915654\pi$
$224$	−1.44443			−0.0965098
$225$		0			0
$226$	18.0912			1.20341
$227$		−	21.1316i		−	1.40255i	−0.712889	−	0.701277i	$-0.752614\pi$
$227$		−	21.1316i		−	1.40255i	0.712889	−	0.701277i	$-0.247386\pi$
$228$		0			0
$229$	23.5280			1.55477			0.777387	−	0.629022i	$-0.216545\pi$
$229$	23.5280			1.55477			0.777387	+	0.629022i	$0.216545\pi$
$230$	−14.1359	+	11.6626i	−0.932093	+	0.769010i
$231$		0			0
$232$		−	22.8769i		−	1.50194i
$233$			6.40612i			0.419679i	0.977736	+	0.209839i	$0.0672941\pi$
$233$			6.40612i			0.419679i	−0.977736	+	0.209839i	$0.932706\pi$
$234$		0			0
$235$	0.0182473	+	0.0221169i	0.00119032	+	0.00144275i
$236$	26.1667			1.70331
$237$		0			0
$238$			13.9179i			0.902166i
$239$	−12.6696			−0.819530			−0.409765	−	0.912191i	$-0.634389\pi$
$239$	−12.6696			−0.819530			−0.409765	+	0.912191i	$0.634389\pi$
$240$		0			0
$241$	−0.206457			−0.0132990			−0.00664952	−	0.999978i	$-0.502117\pi$
$241$	−0.206457			−0.0132990			−0.00664952	+	0.999978i	$0.502117\pi$
$242$		−	10.3634i		−	0.666181i
$243$		0			0
$244$	−6.69146			−0.428377
$245$	10.5172	−	8.67705i	0.671918	−	0.554356i
$246$		0			0
$247$		−	6.35541i		−	0.404385i
$248$			40.2746i			2.55744i
$249$		0			0
$250$	−24.3456	+	13.2580i	−1.53975	+	0.838507i
$251$	−15.5028			−0.978529			−0.489264	−	0.872135i	$-0.662735\pi$
$251$	−15.5028			−0.978529			−0.489264	+	0.872135i	$0.662735\pi$
$252$		0			0
$253$			12.8781i			0.809637i
$254$	−26.5093			−1.66334
$255$		0			0
$256$	−32.6254			−2.03909
$257$		−	6.11944i		−	0.381720i	−0.981617	−	0.190860i	$-0.938872\pi$
$257$		−	6.11944i		−	0.381720i	0.981617	−	0.190860i	$-0.0611276\pi$
$258$		0			0
$259$	1.24004			0.0770526
$260$	−5.90252	−	7.15426i	−0.366059	−	0.443688i
$261$		0			0
$262$		−	0.559894i		−	0.0345904i
$263$			17.1066i			1.05484i	0.849605	+	0.527419i	$0.176840\pi$
$263$			17.1066i			1.05484i	−0.849605	+	0.527419i	$0.823160\pi$
$264$		0			0
$265$	−3.57535	−	4.33357i	−0.219632	−	0.266209i
$266$	14.9696			0.917844
$267$		0			0
$268$			19.3426i			1.18153i
$269$	27.8981			1.70098			0.850490	−	0.525992i	$-0.176306\pi$
$269$	27.8981			1.70098			0.850490	+	0.525992i	$0.176306\pi$
$270$		0			0
$271$	−28.6569			−1.74079			−0.870393	−	0.492358i	$-0.836135\pi$
$271$	−28.6569			−1.74079			−0.870393	+	0.492358i	$0.836135\pi$
$272$		−	29.0065i		−	1.75878i
$273$		0			0
$274$	16.4595			0.994355
$275$	−3.70114	+	19.1257i	−0.223187	+	1.15332i
$276$		0			0
$277$			0.433599i			0.0260525i	0.999915	+	0.0130262i	$0.00414649\pi$
$277$			0.433599i			0.0260525i	−0.999915	+	0.0130262i	$0.995854\pi$
$278$			7.68040i			0.460640i
$279$		0			0
$280$	8.72592	−	7.19919i	0.521473	−	0.430234i
$281$	18.5747			1.10807			0.554036	−	0.832492i	$-0.313087\pi$
$281$	18.5747			1.10807			0.554036	+	0.832492i	$0.313087\pi$
$282$		0			0
$283$			21.9360i			1.30396i	0.758237	+	0.651979i	$0.226061\pi$
$283$			21.9360i			1.30396i	−0.758237	+	0.651979i	$0.773939\pi$
$284$	32.8582			1.94978
$285$		0			0
$286$	−9.66033			−0.571228
$287$		−	6.41696i		−	0.378781i
$288$		0			0
$289$	−17.9154			−1.05385
$290$	15.1569	+	18.3712i	0.890041	+	1.07879i
$291$		0			0
$292$			60.5228i			3.54183i
$293$			9.26031i			0.540993i	0.962721	+	0.270497i	$0.0871879\pi$
$293$			9.26031i			0.540993i	−0.962721	+	0.270497i	$0.912812\pi$
$294$		0			0
$295$	−10.8810	+	8.97722i	−0.633517	+	0.522674i
$296$	−6.95180			−0.404065
$297$		0			0
$298$		−	27.2267i		−	1.57720i
$299$	3.30537			0.191154
$300$		0			0
$301$	7.88056			0.454228
$302$			6.91530i			0.397931i
$303$		0			0
$304$	−31.1982			−1.78934
$305$	2.78253	−	2.29569i	0.159327	−	0.131451i
$306$		0			0
$307$		−	9.15012i		−	0.522225i	−0.965308	−	0.261113i	$-0.915911\pi$
$307$		−	9.15012i		−	0.522225i	0.965308	−	0.261113i	$-0.0840894\pi$
$308$		−	15.3518i		−	0.874747i
$309$		0			0
$310$	−26.6835	−	32.3423i	−1.51552	−	1.83692i
$311$	−8.11488			−0.460153			−0.230076	−	0.973173i	$-0.573898\pi$
$311$	−8.11488			−0.460153			−0.230076	+	0.973173i	$0.573898\pi$
$312$		0			0
$313$		−	4.21952i		−	0.238501i	−0.992864	−	0.119251i	$-0.961951\pi$
$313$		−	4.21952i		−	0.238501i	0.992864	−	0.119251i	$-0.0380492\pi$
$314$	28.2271			1.59295
$315$		0			0
$316$	−68.8558			−3.87344
$317$		−	15.4374i		−	0.867053i	−0.901141	−	0.433527i	$-0.857269\pi$
$317$		−	15.4374i		−	0.867053i	0.901141	−	0.433527i	$-0.142731\pi$
$318$		0			0
$319$	16.7365			0.937062
$320$	10.4313	−	8.60616i	0.583125	−	0.481099i
$321$		0			0
$322$			7.78549i			0.433868i
$323$			37.5537i			2.08954i
$324$		0			0
$325$	4.90893	+	0.949959i	0.272298	+	0.0526942i
$326$	5.28486			0.292701
$327$		0			0
$328$			35.9740i			1.98633i
$329$	0.0121811			0.000671568
$330$		0			0
$331$	14.6619			0.805894			0.402947	−	0.915223i	$-0.367986\pi$
$331$	14.6619			0.805894			0.402947	+	0.915223i	$0.367986\pi$
$332$			53.1105i			2.91482i
$333$		0			0
$334$	−7.45300			−0.407810
$335$	−6.63600	−	8.04328i	−0.362563	−	0.439452i
$336$		0			0
$337$			26.6094i			1.44951i	0.689009	+	0.724753i	$0.258046\pi$
$337$			26.6094i			1.44951i	−0.689009	+	0.724753i	$0.741954\pi$
$338$			2.47948i			0.134866i
$339$		0			0
$340$	34.8776	+	42.2740i	1.89150	+	2.29263i
$341$	−29.4644			−1.59559
$342$		0			0
$343$		−	12.4422i		−	0.671813i
$344$	−44.1791			−2.38198
$345$		0			0
$346$	−1.66979			−0.0897683
$347$		−	3.06153i		−	0.164352i	−0.996618	−	0.0821759i	$-0.973813\pi$
$347$		−	3.06153i		−	0.164352i	0.996618	−	0.0821759i	$-0.0261869\pi$
$348$		0			0
$349$	22.4273			1.20050			0.600252	−	0.799811i	$-0.295067\pi$
$349$	22.4273			1.20050			0.600252	+	0.799811i	$0.295067\pi$
$350$	−2.23754	+	11.5625i	−0.119602	+	0.618043i
$351$		0			0
$352$			5.92409i			0.315755i
$353$			23.7147i			1.26220i	0.775700	+	0.631102i	$0.217397\pi$
$353$			23.7147i			1.26220i	−0.775700	+	0.631102i	$0.782603\pi$
$354$		0			0
$355$	−13.6635	+	11.2729i	−0.725185	+	0.598304i
$356$	−73.2271			−3.88103
$357$		0			0
$358$		−	19.3843i		−	1.02449i
$359$	−18.6484			−0.984227			−0.492113	−	0.870531i	$-0.663775\pi$
$359$	−18.6484			−0.984227			−0.492113	+	0.870531i	$0.663775\pi$
$360$		0			0
$361$	21.3912			1.12585
$362$			23.6324i			1.24209i
$363$		0			0
$364$	−3.94028			−0.206527
$365$	−20.7640	−	25.1674i	−1.08684	−	1.31732i
$366$		0			0
$367$			10.7870i			0.563076i	0.959550	+	0.281538i	$0.0908446\pi$
$367$			10.7870i			0.563076i	−0.959550	+	0.281538i	$0.909155\pi$
$368$		−	16.2258i		−	0.845829i
$369$		0			0
$370$	5.58259	−	4.60584i	0.290225	−	0.239446i
$371$	−2.38676			−0.123914
$372$		0			0
$373$		−	19.0430i		−	0.986009i	−0.870027	−	0.493005i	$-0.835899\pi$
$373$		−	19.0430i		−	0.986009i	0.870027	−	0.493005i	$-0.164101\pi$
$374$	57.0822			2.95165
$375$		0			0
$376$	−0.0682885			−0.00352171
$377$		−	4.29569i		−	0.221239i
$378$		0			0
$379$	15.9537			0.819489			0.409744	−	0.912200i	$-0.365618\pi$
$379$	15.9537			0.819489			0.409744	+	0.912200i	$0.365618\pi$
$380$	45.4682	−	37.5129i	2.33247	−	1.92437i
$381$		0			0
$382$		−	39.9377i		−	2.04339i
$383$			24.8044i			1.26744i	0.773561	+	0.633722i	$0.218474\pi$
$383$			24.8044i			1.26744i	−0.773561	+	0.633722i	$0.781526\pi$
$384$		0			0
$385$	5.26684	+	6.38377i	0.268423	+	0.325347i
$386$	−34.4568			−1.75380
$387$		0			0
$388$			75.1696i			3.81616i
$389$	−36.2379			−1.83734			−0.918668	−	0.395030i	$-0.870734\pi$
$389$	−36.2379			−1.83734			−0.918668	+	0.395030i	$0.870734\pi$
$390$		0			0
$391$	−19.5312			−0.987734
$392$			32.4730i			1.64013i
$393$		0			0
$394$	29.1703			1.46958
$395$	28.6326	−	23.6229i	1.44066	−	1.18860i
$396$		0			0
$397$		−	18.4111i		−	0.924025i	−0.886873	−	0.462013i	$-0.847127\pi$
$397$		−	18.4111i		−	0.924025i	0.886873	−	0.462013i	$-0.152873\pi$
$398$		−	20.8652i		−	1.04588i
$399$		0			0
$400$	4.66328	−	24.0976i	0.233164	−	1.20488i
$401$	−24.0667			−1.20183			−0.600916	−	0.799312i	$-0.705197\pi$
$401$	−24.0667			−1.20183			−0.600916	+	0.799312i	$0.705197\pi$
$402$		0			0
$403$			7.56253i			0.376717i
$404$	48.4971			2.41282
$405$		0			0
$406$	10.1181			0.502153
$407$		−	5.08585i		−	0.252096i
$408$		0			0
$409$	−35.7102			−1.76575			−0.882877	−	0.469605i	$-0.844396\pi$
$409$	−35.7102			−1.76575			−0.882877	+	0.469605i	$0.844396\pi$
$410$	−23.8342	−	28.8887i	−1.17709	−	1.42671i
$411$		0			0
$412$		−	31.2008i		−	1.53715i
$413$			5.99283i			0.294888i
$414$		0			0
$415$	−18.2210	−	22.0851i	−0.894435	−	1.08412i
$416$	1.52052			0.0745494
$417$		0			0
$418$		−	61.3954i		−	3.00295i
$419$	21.8241			1.06618			0.533090	−	0.846059i	$-0.321031\pi$
$419$	21.8241			1.06618			0.533090	+	0.846059i	$0.321031\pi$
$420$		0			0
$421$	−0.107706			−0.00524928			−0.00262464	−	0.999997i	$-0.500835\pi$
$421$	−0.107706			−0.00524928			−0.00262464	+	0.999997i	$0.500835\pi$
$422$		−	28.6137i		−	1.39289i
$423$		0			0
$424$	13.3804			0.649809
$425$	−29.0065	−	5.61324i	−1.40702	−	0.272282i
$426$		0			0
$427$		−	1.53251i		−	0.0741634i
$428$		−	24.9244i		−	1.20477i
$429$		0			0
$430$	35.4777	−	29.2704i	1.71089	−	1.41154i
$431$	−32.3215			−1.55687			−0.778437	−	0.627723i	$-0.783987\pi$
$431$	−32.3215			−1.55687			−0.778437	+	0.627723i	$0.783987\pi$
$432$		0			0
$433$		−	14.5914i		−	0.701217i	−0.936522	−	0.350608i	$-0.885975\pi$
$433$		−	14.5914i		−	0.701217i	0.936522	−	0.350608i	$-0.114025\pi$
$434$	−17.8128			−0.855044
$435$		0			0
$436$	4.48546			0.214814
$437$			21.0070i			1.00490i
$438$		0			0
$439$	27.4117			1.30829			0.654146	−	0.756369i	$-0.273028\pi$
$439$	27.4117			1.30829			0.654146	+	0.756369i	$0.273028\pi$
$440$	−29.5264	−	35.7880i	−1.40761	−	1.70612i
$441$		0			0
$442$		−	14.6511i		−	0.696882i
$443$			7.19811i			0.341993i	0.985272	+	0.170996i	$0.0546986\pi$
$443$			7.19811i			0.341993i	−0.985272	+	0.170996i	$0.945301\pi$
$444$		0			0
$445$	30.4503	−	25.1226i	1.44348	−	1.19092i
$446$	19.3939			0.918326
$447$		0			0
$448$		−	5.74513i		−	0.271432i
$449$	18.9884			0.896119			0.448060	−	0.894004i	$-0.352115\pi$
$449$	18.9884			0.896119			0.448060	+	0.894004i	$0.352115\pi$
$450$		0			0
$451$	−26.3182			−1.23927
$452$		−	30.2642i		−	1.42351i
$453$		0			0
$454$	−52.3955			−2.45904
$455$	1.63850	−	1.35182i	0.0768141	−	0.0633744i
$456$		0			0
$457$			26.3998i			1.23493i	0.786599	+	0.617465i	$0.211840\pi$
$457$			26.3998i			1.23493i	−0.786599	+	0.617465i	$0.788160\pi$
$458$		−	58.3373i		−	2.72592i
$459$		0			0
$460$	19.5100	+	23.6474i	0.909658	+	1.10257i
$461$	22.0585			1.02737			0.513684	−	0.857980i	$-0.328280\pi$
$461$	22.0585			1.02737			0.513684	+	0.857980i	$0.328280\pi$
$462$		0			0
$463$			1.31425i			0.0610781i	0.999534	+	0.0305391i	$0.00972240\pi$
$463$			1.31425i			0.0610781i	−0.999534	+	0.0305391i	$0.990278\pi$
$464$	−21.0872			−0.978950
$465$		0			0
$466$	15.8839			0.735806
$467$			14.8898i			0.689017i	0.938783	+	0.344509i	$0.111954\pi$
$467$			14.8898i			0.689017i	−0.938783	+	0.344509i	$0.888046\pi$
$468$		0			0
$469$	−4.42992			−0.204555
$470$	0.0548386	−	0.0452438i	0.00252952	−	0.00208694i
$471$		0			0
$472$		−	33.5963i		−	1.54639i
$473$		−	32.3209i		−	1.48612i
$474$		0			0
$475$	−6.03738	+	31.1982i	−0.277014	+	1.43147i
$476$	23.2828			1.06717
$477$		0			0
$478$			31.4142i			1.43685i
$479$	3.03653			0.138743			0.0693713	−	0.997591i	$-0.477901\pi$
$479$	3.03653			0.138743			0.0693713	+	0.997591i	$0.477901\pi$
$480$		0			0
$481$	−1.30537			−0.0595196
$482$			0.511906i			0.0233167i
$483$		0			0
$484$	−17.3365			−0.788022
$485$	−25.7890	−	31.2580i	−1.17102	−	1.41935i
$486$		0			0
$487$		−	16.2584i		−	0.736741i	−0.929679	−	0.368370i	$-0.879916\pi$
$487$		−	16.2584i		−	0.736741i	0.929679	−	0.368370i	$-0.120084\pi$
$488$			8.59138i			0.388914i
$489$		0			0
$490$	−21.5146	−	26.0772i	−0.971931	−	1.17805i
$491$	12.5098			0.564558			0.282279	−	0.959332i	$-0.408910\pi$
$491$	12.5098			0.564558			0.282279	+	0.959332i	$0.408910\pi$
$492$		0			0
$493$			25.3829i			1.14319i
$494$	−15.7581			−0.708992
$495$		0			0
$496$	37.1239			1.66691
$497$			7.52534i			0.337557i
$498$		0			0
$499$	0.977442			0.0437563			0.0218782	−	0.999761i	$-0.493035\pi$
$499$	0.977442			0.0437563			0.0218782	+	0.999761i	$0.493035\pi$
$500$	22.1788	+	40.7269i	0.991865	+	1.82136i
$501$		0			0
$502$			38.4390i			1.71562i
$503$		−	22.9051i		−	1.02129i	−0.859792	−	0.510644i	$-0.829407\pi$
$503$		−	22.9051i		−	1.02129i	0.859792	−	0.510644i	$-0.170593\pi$
$504$		0			0
$505$	−20.1667	+	16.6383i	−0.897408	+	0.740394i
$506$	31.9310			1.41950
$507$		0			0
$508$			44.3465i			1.96756i
$509$	−13.2463			−0.587132			−0.293566	−	0.955939i	$-0.594842\pi$
$509$	−13.2463			−0.587132			−0.293566	+	0.955939i	$0.594842\pi$
$510$		0			0
$511$	−13.8612			−0.613184
$512$			44.8214i			1.98084i
$513$		0			0
$514$	−15.1731			−0.669255
$515$	10.7043	+	12.9743i	0.471687	+	0.571717i
$516$		0			0
$517$		−	0.0499590i		−	0.00219720i
$518$		−	3.07467i		−	0.135093i
$519$		0			0
$520$	−9.18558	+	7.57843i	−0.402814	+	0.332336i
$521$	8.70493			0.381370			0.190685	−	0.981651i	$-0.438929\pi$
$521$	8.70493			0.381370			0.190685	+	0.981651i	$0.438929\pi$
$522$		0			0
$523$			29.4014i			1.28563i	0.766020	+	0.642817i	$0.222234\pi$
$523$			29.4014i			1.28563i	−0.766020	+	0.642817i	$0.777766\pi$
$524$	−0.936627			−0.0409168
$525$		0			0
$526$	42.4155			1.84940
$527$		−	44.6865i		−	1.94657i
$528$		0			0
$529$	12.0745			0.524980
$530$	−10.7450	+	8.86504i	−0.466734	+	0.385073i
$531$		0			0
$532$		−	25.0421i		−	1.08571i
$533$			6.75499i			0.292591i
$534$		0			0
$535$	8.55102	+	10.3644i	0.369693	+	0.448093i
$536$	24.8345			1.07269
$537$		0			0
$538$		−	69.1730i		−	2.98226i
$539$	−23.7568			−1.02328
$540$		0			0
$541$	−1.40100			−0.0602335			−0.0301168	−	0.999546i	$-0.509588\pi$
$541$	−1.40100			−0.0602335			−0.0301168	+	0.999546i	$0.509588\pi$
$542$			71.0544i			3.05205i
$543$		0			0
$544$	−8.98462			−0.385212
$545$	−1.86520	+	1.53886i	−0.0798965	+	0.0659175i
$546$		0			0
$547$			2.42904i			0.103858i	0.998651	+	0.0519292i	$0.0165370\pi$
$547$			2.42904i			0.103858i	−0.998651	+	0.0519292i	$0.983463\pi$
$548$		−	27.5345i		−	1.17622i
$549$		0			0
$550$	47.4219	+	9.17692i	2.02208	+	0.391305i
$551$	27.3009			1.16306
$552$		0			0
$553$		−	15.7697i		−	0.670595i
$554$	1.07510			0.0456767
$555$		0			0
$556$	12.8483			0.544888
$557$		−	14.2429i		−	0.603491i	−0.953388	−	0.301746i	$-0.902431\pi$
$557$		−	14.2429i		−	0.603491i	0.953388	−	0.301746i	$-0.0975693\pi$
$558$		0			0
$559$	−8.29569			−0.350870
$560$	−6.63600	−	8.04328i	−0.280422	−	0.339891i
$561$		0			0
$562$		−	46.0557i		−	1.94274i
$563$			38.1924i			1.60962i	0.593533	+	0.804810i	$0.297733\pi$
$563$			38.1924i			1.60962i	−0.593533	+	0.804810i	$0.702267\pi$
$564$		0			0
$565$	10.3829	+	12.5848i	0.436814	+	0.529449i
$566$	54.3899			2.28618
$567$		0			0
$568$		−	42.1877i		−	1.77016i
$569$	−22.1387			−0.928104			−0.464052	−	0.885808i	$-0.653605\pi$
$569$	−22.1387			−0.928104			−0.464052	+	0.885808i	$0.653605\pi$
$570$		0			0
$571$	−44.8956			−1.87882			−0.939412	−	0.342791i	$-0.888628\pi$
$571$	−44.8956			−1.87882			−0.939412	+	0.342791i	$0.888628\pi$
$572$			16.1604i			0.675702i
$573$		0			0
$574$	−15.9108			−0.664103
$575$	−16.2258	−	3.13996i	−0.676663	−	0.130945i
$576$		0			0
$577$			4.07248i			0.169540i	0.996401	+	0.0847698i	$0.0270155\pi$
$577$			4.07248i			0.169540i	−0.996401	+	0.0847698i	$0.972984\pi$
$578$			44.4210i			1.84767i
$579$		0			0
$580$	30.7325	−	25.3554i	1.27610	−	1.05283i
$581$	−12.1636			−0.504632
$582$		0			0
$583$			9.78893i			0.405416i
$584$	77.7071			3.21554
$585$		0			0
$586$	22.9608			0.948502
$587$			24.5786i			1.01447i	0.861809	+	0.507233i	$0.169332\pi$
$587$			24.5786i			1.01447i	−0.861809	+	0.507233i	$0.830668\pi$
$588$		0			0
$589$	−48.0630			−1.98040
$590$	22.2589	+	26.9793i	0.916383	+	1.11072i
$591$		0			0
$592$			6.40795i			0.263365i
$593$		−	0.191663i		−	0.00787065i	−0.999992	−	0.00393532i	$-0.998747\pi$
$593$		−	0.191663i		−	0.00787065i	0.999992	−	0.00393532i	$-0.00125266\pi$
$594$		0			0
$595$	−9.68179	+	7.98782i	−0.396915	+	0.327469i
$596$	−45.5467			−1.86566
$597$		0			0
$598$		−	8.19561i		−	0.335143i
$599$	22.5977			0.923316			0.461658	−	0.887058i	$-0.347255\pi$
$599$	22.5977			0.923316			0.461658	+	0.887058i	$0.347255\pi$
$600$		0			0
$601$	17.0155			0.694077			0.347039	−	0.937851i	$-0.387187\pi$
$601$	17.0155			0.694077			0.347039	+	0.937851i	$0.387187\pi$
$602$		−	19.5397i		−	0.796380i
$603$		0			0
$604$	11.5684			0.470710
$605$	7.20910	−	5.94776i	0.293091	−	0.241811i
$606$		0			0
$607$			34.4651i			1.39889i	0.714684	+	0.699447i	$0.246570\pi$
$607$			34.4651i			1.39889i	−0.714684	+	0.699447i	$0.753430\pi$
$608$			9.66349i			0.391906i
$609$		0			0
$610$	−5.69213	−	6.89925i	−0.230468	−	0.279343i
$611$	−0.0128228			−0.000518755
$612$		0			0
$613$		−	7.02682i		−	0.283810i	−0.989880	−	0.141905i	$-0.954677\pi$
$613$		−	7.02682i		−	0.283810i	0.989880	−	0.141905i	$-0.0453228\pi$
$614$	−22.6876			−0.915597
$615$		0			0
$616$	−19.7106			−0.794163
$617$			12.1122i			0.487620i	0.969823	+	0.243810i	$0.0783973\pi$
$617$			12.1122i			0.487620i	−0.969823	+	0.243810i	$0.921603\pi$
$618$		0			0
$619$	−30.8710			−1.24081			−0.620406	−	0.784281i	$-0.713032\pi$
$619$	−30.8710			−1.24081			−0.620406	+	0.784281i	$0.713032\pi$
$620$	−54.1043	+	44.6380i	−2.17288	+	1.79270i
$621$		0			0
$622$			20.1207i			0.806767i
$623$		−	16.7708i		−	0.671908i
$624$		0			0
$625$	−23.1952	−	9.32656i	−0.927806	−	0.373062i
$626$	−10.4622			−0.418155
$627$		0			0
$628$		−	47.2201i		−	1.88429i
$629$	7.71332			0.307550
$630$		0			0
$631$	9.48047			0.377412			0.188706	−	0.982034i	$-0.439571\pi$
$631$	9.48047			0.377412			0.188706	+	0.982034i	$0.439571\pi$
$632$			88.4062i			3.51661i
$633$		0			0
$634$	−38.2769			−1.52017
$635$	−15.2143	−	18.4408i	−0.603761	−	0.731800i
$636$		0			0
$637$			6.09758i			0.241595i
$638$		−	41.4978i		−	1.64291i
$639$		0			0
$640$	−25.6663	−	31.1094i	−1.01455	−	1.22971i
$641$	−17.3964			−0.687118			−0.343559	−	0.939131i	$-0.611633\pi$
$641$	−17.3964			−0.687118			−0.343559	+	0.939131i	$0.611633\pi$
$642$		0			0
$643$		−	33.9506i		−	1.33888i	−0.742866	−	0.669440i	$-0.766534\pi$
$643$		−	33.9506i		−	1.33888i	0.742866	−	0.669440i	$-0.233466\pi$
$644$	13.0241			0.513221
$645$		0			0
$646$	93.1137			3.66351
$647$			9.18548i			0.361118i	0.983564	+	0.180559i	$0.0577908\pi$
$647$			9.18548i			0.361118i	−0.983564	+	0.180559i	$0.942209\pi$
$648$		0			0
$649$	24.5786			0.964796
$650$	2.35541	−	12.1716i	0.0923867	−	0.477410i
$651$		0			0
$652$		−	8.84087i		−	0.346235i
$653$			3.54781i			0.138837i	0.997588	+	0.0694183i	$0.0221143\pi$
$653$			3.54781i			0.138837i	−0.997588	+	0.0694183i	$0.977886\pi$
$654$		0			0
$655$	0.389481	−	0.321336i	0.0152183	−	0.0125556i
$656$	33.1598			1.29467
$657$		0			0
$658$		−	0.0302030i		−	0.00117743i
$659$	−15.5339			−0.605115			−0.302557	−	0.953131i	$-0.597840\pi$
$659$	−15.5339			−0.605115			−0.302557	+	0.953131i	$0.597840\pi$
$660$		0			0
$661$	1.60878			0.0625745			0.0312872	−	0.999510i	$-0.490039\pi$
$661$	1.60878			0.0625745			0.0312872	+	0.999510i	$0.490039\pi$
$662$		−	36.3541i		−	1.41294i
$663$		0			0
$664$	68.1903			2.64630
$665$	8.59138	+	10.4133i	0.333159	+	0.403812i
$666$		0			0
$667$			14.1988i			0.549781i
$668$			12.4679i			0.482396i
$669$		0			0
$670$	−19.9432	+	16.4539i	−0.770473	+	0.635668i
$671$	−6.28535			−0.242643
$672$		0			0
$673$		−	8.18214i		−	0.315398i	−0.987487	−	0.157699i	$-0.949592\pi$
$673$		−	8.18214i		−	0.315398i	0.987487	−	0.157699i	$-0.0504076\pi$
$674$	65.9776			2.54136
$675$		0			0
$676$	4.14785			0.159533
$677$		−	42.7063i		−	1.64134i	−0.571405	−	0.820668i	$-0.693601\pi$
$677$		−	42.7063i		−	1.64134i	0.571405	−	0.820668i	$-0.306399\pi$
$678$		0			0
$679$	−17.2157			−0.660677
$680$	54.2769	−	44.7804i	2.08142	−	1.71725i
$681$		0			0
$682$			73.0566i			2.79748i
$683$		−	9.14962i		−	0.350100i	−0.984560	−	0.175050i	$-0.943991\pi$
$683$		−	9.14962i		−	0.350100i	0.984560	−	0.175050i	$-0.0560088\pi$
$684$		0			0
$685$	9.44648	+	11.4498i	0.360931	+	0.437474i
$686$	−30.8501			−1.17786
$687$		0			0
$688$			40.7229i			1.55255i
$689$	2.51249			0.0957182
$690$		0			0
$691$	−16.9918			−0.646398			−0.323199	−	0.946331i	$-0.604758\pi$
$691$	−16.9918			−0.646398			−0.323199	+	0.946331i	$0.604758\pi$
$692$			2.79333i			0.106186i
$693$		0			0
$694$	−7.59103			−0.288152
$695$	−5.34274	+	4.40795i	−0.202662	+	0.167203i
$696$		0			0
$697$		−	39.9148i		−	1.51188i
$698$		−	55.6080i		−	2.10480i
$699$		0			0
$700$	19.3426	+	3.74311i	0.731080	+	0.141476i
$701$	40.8320			1.54220			0.771101	−	0.636712i	$-0.219706\pi$
$701$	40.8320			1.54220			0.771101	+	0.636712i	$0.219706\pi$
$702$		0			0
$703$		−	8.29614i		−	0.312895i
$704$	−23.5627			−0.888053
$705$		0			0
$706$	58.8001			2.21297
$707$			11.1070i			0.417723i
$708$		0			0
$709$	38.0193			1.42784			0.713922	−	0.700225i	$-0.246917\pi$
$709$	38.0193			1.42784			0.713922	+	0.700225i	$0.246917\pi$
$710$	27.9510	+	33.8785i	1.04898	+	1.27144i
$711$		0			0
$712$			94.0185i			3.52349i
$713$		−	24.9969i		−	0.936143i
$714$		0			0
$715$	−5.54428	−	6.72005i	−0.207344	−	0.251316i
$716$	−32.4273			−1.21186
$717$		0			0
$718$			46.2385i			1.72561i
$719$	27.9175			1.04115			0.520573	−	0.853817i	$-0.325718\pi$
$719$	27.9175			1.04115			0.520573	+	0.853817i	$0.325718\pi$
$720$		0			0
$721$	7.14575			0.266122
$722$		−	53.0392i		−	1.97391i
$723$		0			0
$724$	39.5338			1.46926
$725$	−4.08073	+	21.0872i	−0.151554	+	0.783160i
$726$		0			0
$727$			4.31960i			0.160205i	0.996787	+	0.0801026i	$0.0255248\pi$
$727$			4.31960i			0.160205i	−0.996787	+	0.0801026i	$0.974475\pi$
$728$			5.05905i			0.187501i
$729$		0			0
$730$	−62.4022	+	51.4840i	−2.30961	+	1.90551i
$731$	49.0186			1.81302
$732$		0			0
$733$		−	13.1669i		−	0.486330i	−0.969985	−	0.243165i	$-0.921814\pi$
$733$		−	13.1669i		−	0.486330i	0.969985	−	0.243165i	$-0.0781857\pi$
$734$	26.7462			0.987219
$735$		0			0
$736$	−5.02586			−0.185256
$737$			18.1686i			0.669250i
$738$		0			0
$739$	−2.14218			−0.0788014			−0.0394007	−	0.999223i	$-0.512545\pi$
$739$	−2.14218			−0.0788014			−0.0394007	+	0.999223i	$0.512545\pi$
$740$	−7.70495	−	9.33893i	−0.283240	−	0.343306i
$741$		0			0
$742$			5.91794i			0.217254i
$743$			24.4771i			0.897979i	0.893537	+	0.448990i	$0.148216\pi$
$743$			24.4771i			0.897979i	−0.893537	+	0.448990i	$0.851784\pi$
$744$		0			0
$745$	18.9398	−	15.6260i	0.693902	−	0.572494i
$746$	−47.2168			−1.72873
$747$		0			0
$748$		−	95.4909i		−	3.49149i
$749$	5.70831			0.208577
$750$		0			0
$751$	−12.0058			−0.438097			−0.219049	−	0.975714i	$-0.570295\pi$
$751$	−12.0058			−0.438097			−0.219049	+	0.975714i	$0.570295\pi$
$752$			0.0629463i			0.00229541i
$753$		0			0
$754$	−10.6511			−0.387890
$755$	−4.81052	+	3.96885i	−0.175073	+	0.144441i
$756$		0			0
$757$		−	16.8442i		−	0.612212i	−0.951997	−	0.306106i	$-0.900974\pi$
$757$		−	16.8442i		−	0.612212i	0.951997	−	0.306106i	$-0.0990262\pi$
$758$		−	39.5571i		−	1.43678i
$759$		0			0
$760$	−48.1640	−	58.3781i	−1.74709	−	2.11760i
$761$	−3.97932			−0.144250			−0.0721251	−	0.997396i	$-0.522978\pi$
$761$	−3.97932			−0.144250			−0.0721251	+	0.997396i	$0.522978\pi$
$762$		0			0
$763$			1.02728i			0.0371900i
$764$	−66.8104			−2.41712
$765$		0			0
$766$	61.5021			2.22216
$767$		−	6.30851i		−	0.227787i
$768$		0			0
$769$	−15.5176			−0.559579			−0.279790	−	0.960061i	$-0.590265\pi$
$769$	−15.5176			−0.559579			−0.279790	+	0.960061i	$0.590265\pi$
$770$	15.8285	−	13.0591i	0.570418	−	0.470616i
$771$		0			0
$772$			57.6416i			2.07456i
$773$		−	44.4624i		−	1.59920i	−0.600531	−	0.799601i	$-0.705044\pi$
$773$		−	44.4624i		−	1.59920i	0.600531	−	0.799601i	$-0.294956\pi$
$774$		0			0
$775$	7.18409	−	37.1239i	0.258060	−	1.33353i
$776$	96.5126			3.46460
$777$		0			0
$778$			89.8514i			3.22133i
$779$	−42.9307			−1.53815
$780$		0			0
$781$	30.8640			1.10440
$782$			48.4273i			1.73176i
$783$		0			0
$784$	29.9326			1.06902
$785$	16.2002	+	19.6357i	0.578209	+	0.700829i
$786$		0			0
$787$		−	32.0619i		−	1.14288i	−0.820643	−	0.571441i	$-0.806384\pi$
$787$		−	32.0619i		−	1.14288i	0.820643	−	0.571441i	$-0.193616\pi$
$788$		−	48.7980i		−	1.73836i
$789$		0			0
$790$	−58.5726	−	70.9940i	−2.08392	−	2.52585i
$791$	6.93124			0.246446
$792$		0			0
$793$			1.61324i			0.0572878i
$794$	−45.6500			−1.62006
$795$		0			0
$796$	−34.9046			−1.23716
$797$			24.7378i			0.876260i	0.898912	+	0.438130i	$0.144359\pi$
$797$			24.7378i			0.876260i	−0.898912	+	0.438130i	$0.855641\pi$
$798$		0			0
$799$	0.0757691			0.00268052
$800$	−7.46410	−	1.44443i	−0.263896	−	0.0510682i
$801$		0			0
$802$			59.6729i			2.10712i
$803$			56.8496i			2.00618i
$804$		0			0
$805$	−5.41585	+	4.46827i	−0.190884	+	0.157486i
$806$	18.7512			0.660482
$807$		0			0
$808$		−	62.2670i		−	2.19055i
$809$	11.3400			0.398694			0.199347	−	0.979929i	$-0.436118\pi$
$809$	11.3400			0.398694			0.199347	+	0.979929i	$0.436118\pi$
$810$		0			0
$811$	8.96070			0.314653			0.157326	−	0.987547i	$-0.449713\pi$
$811$	8.96070			0.314653			0.157326	+	0.987547i	$0.449713\pi$
$812$		−	16.9262i		−	0.593994i
$813$		0			0
$814$	−12.6103			−0.441990
$815$	3.03310	+	3.67633i	0.106245	+	0.128776i
$816$		0			0
$817$		−	52.7225i		−	1.84453i
$818$			88.5428i			3.09583i
$819$		0			0
$820$	−48.3270	+	39.8715i	−1.68765	+	1.39237i
$821$	−5.28500			−0.184448			−0.0922239	−	0.995738i	$-0.529398\pi$
$821$	−5.28500			−0.184448			−0.0922239	+	0.995738i	$0.529398\pi$
$822$		0			0
$823$		−	11.2463i		−	0.392023i	−0.980602	−	0.196012i	$-0.937201\pi$
$823$		−	11.2463i		−	0.392023i	0.980602	−	0.196012i	$-0.0627990\pi$
$824$	−40.0597			−1.39554
$825$		0			0
$826$	14.8591			0.517015
$827$		−	42.9625i		−	1.49395i	−0.664851	−	0.746976i	$-0.731505\pi$
$827$		−	42.9625i		−	1.49395i	0.664851	−	0.746976i	$-0.268495\pi$
$828$		0			0
$829$	−21.1444			−0.734376			−0.367188	−	0.930147i	$-0.619679\pi$
$829$	−21.1444			−0.734376			−0.367188	+	0.930147i	$0.619679\pi$
$830$	−54.7598	+	45.1788i	−1.90074	+	1.56818i
$831$		0			0
$832$			6.04776i			0.209668i
$833$		−	36.0302i		−	1.24837i
$834$		0			0
$835$	−4.27744	−	5.18455i	−0.148027	−	0.179419i
$836$	−102.706			−3.55217
$837$		0			0
$838$		−	54.1126i		−	1.86929i
$839$	−26.3671			−0.910293			−0.455146	−	0.890417i	$-0.650413\pi$
$839$	−26.3671			−0.910293			−0.455146	+	0.890417i	$0.650413\pi$
$840$		0			0
$841$	−10.5470			−0.363691
$842$			0.267056i			0.00920336i
$843$		0			0
$844$	−47.8669			−1.64765
$845$	−1.72481	+	1.42303i	−0.0593354	+	0.0489538i
$846$		0			0
$847$		−	3.97048i		−	0.136427i
$848$		−	12.3336i		−	0.423539i
$849$		0			0
$850$	−13.9179	+	71.9212i	−0.477381	+	2.46688i
$851$	4.31472			0.147907
$852$		0			0
$853$			52.4061i			1.79435i	0.441676	+	0.897175i	$0.354384\pi$
$853$			52.4061i			1.79435i	−0.441676	+	0.897175i	$0.645616\pi$
$854$	−3.79984			−0.130028
$855$		0			0
$856$	−32.0013			−1.09378
$857$			24.6382i			0.841625i	0.907148	+	0.420813i	$0.138255\pi$
$857$			24.6382i			0.841625i	−0.907148	+	0.420813i	$0.861745\pi$
$858$		0			0
$859$	47.0110			1.60399			0.801997	−	0.597329i	$-0.203771\pi$
$859$	47.0110			1.60399			0.801997	+	0.597329i	$0.203771\pi$
$860$	−48.9655	−	59.3495i	−1.66971	−	2.02380i
$861$		0			0
$862$			80.1407i			2.72960i
$863$			14.9378i			0.508490i	0.967140	+	0.254245i	$0.0818269\pi$
$863$			14.9378i			0.508490i	−0.967140	+	0.254245i	$0.918173\pi$
$864$		0			0
$865$	−0.958328	−	1.16156i	−0.0325841	−	0.0394942i
$866$	−36.1791			−1.22942
$867$		0			0
$868$			29.7985i			1.01143i
$869$	−64.6769			−2.19401
$870$		0			0
$871$	4.66328			0.158009
$872$		−	5.75902i		−	0.195025i
$873$		0			0
$874$	52.0864			1.76185
$875$	−9.32746	+	5.07949i	−0.315326	+	0.171718i
$876$		0			0
$877$			29.3418i			0.990801i	0.868665	+	0.495400i	$0.164979\pi$
$877$			29.3418i			0.990801i	−0.868665	+	0.495400i	$0.835021\pi$
$878$		−	67.9670i		−	2.29378i
$879$		0			0
$880$	−32.9883	+	27.2165i	−1.11203	+	0.917468i
$881$	−12.1590			−0.409647			−0.204824	−	0.978799i	$-0.565662\pi$
$881$	−12.1590			−0.409647			−0.204824	+	0.978799i	$0.565662\pi$
$882$		0			0
$883$			31.1431i			1.04805i	0.851703	+	0.524024i	$0.175570\pi$
$883$			31.1431i			1.04805i	−0.851703	+	0.524024i	$0.824430\pi$
$884$	−24.5093			−0.824338
$885$		0			0
$886$	17.8476			0.599602
$887$		−	2.56117i		−	0.0859955i	−0.999075	−	0.0429978i	$-0.986309\pi$
$887$		−	2.56117i		−	0.0859955i	0.999075	−	0.0429978i	$-0.0136908\pi$
$888$		0			0
$889$	−10.1564			−0.340636
$890$	−62.2910	−	75.5010i	−2.08800	−	2.53080i
$891$		0			0
$892$		−	32.4433i		−	1.08628i
$893$		−	0.0814942i		−	0.00272710i
$894$		0			0
$895$	13.4843	−	11.1251i	0.450732	−	0.371870i
$896$	−17.1338			−0.572400
$897$		0			0
$898$		−	47.0815i		−	1.57113i
$899$	−32.4863			−1.08348
$900$		0			0
$901$	−14.8461			−0.494596
$902$			65.2555i			2.17277i
$903$		0			0
$904$	−38.8571			−1.29237
$905$	−16.4395	+	13.5632i	−0.546467	+	0.450855i
$906$		0			0
$907$		−	34.5273i		−	1.14646i	−0.819394	−	0.573231i	$-0.805690\pi$
$907$		−	34.5273i		−	1.14646i	0.819394	−	0.573231i	$-0.194310\pi$
$908$			87.6506i			2.90879i
$909$		0			0
$910$	−3.35182	−	4.06264i	−0.111112	−	0.134675i
$911$	16.4985			0.546619			0.273309	−	0.961926i	$-0.411882\pi$
$911$	16.4985			0.546619			0.273309	+	0.961926i	$0.411882\pi$
$912$		0			0
$913$			49.8872i			1.65102i
$914$	65.4578			2.16515
$915$		0			0
$916$	−97.5905			−3.22448
$917$		−	0.214511i		−	0.00708377i
$918$		0			0
$919$	−29.8399			−0.984327			−0.492163	−	0.870503i	$-0.663794\pi$
$919$	−29.8399			−0.984327			−0.492163	+	0.870503i	$0.663794\pi$
$920$	30.3617	−	25.0495i	1.00100	−	0.825857i
$921$		0			0
$922$		−	54.6938i		−	1.80124i
$923$		−	7.92175i		−	0.260748i
$924$		0			0
$925$	6.40795	+	1.24004i	0.210692	+	0.0407724i
$926$	3.25865			0.107086
$927$		0			0
$928$			6.53166i			0.214412i
$929$	29.9391			0.982270			0.491135	−	0.871084i	$-0.336582\pi$
$929$	29.9391			0.982270			0.491135	+	0.871084i	$0.336582\pi$
$930$		0			0
$931$	−38.7526			−1.27007
$932$		−	26.5716i		−	0.870381i
$933$		0			0
$934$	36.9190			1.20803
$935$	32.7608	+	39.7083i	1.07139	+	1.29860i
$936$		0			0
$937$			32.7542i			1.07003i	0.844842	+	0.535016i	$0.179694\pi$
$937$			32.7542i			1.07003i	−0.844842	+	0.535016i	$0.820306\pi$
$938$			10.9839i			0.358638i
$939$		0			0
$940$	−0.0756869	−	0.0917377i	−0.00246863	−	0.00299215i
$941$	26.6679			0.869349			0.434675	−	0.900588i	$-0.356863\pi$
$941$	26.6679			0.869349			0.434675	+	0.900588i	$0.356863\pi$
$942$		0			0
$943$		−	22.3277i		−	0.727091i
$944$	−30.9680			−1.00792
$945$		0			0
$946$	−80.1391			−2.60555
$947$		−	16.9685i		−	0.551402i	−0.961243	−	0.275701i	$-0.911090\pi$
$947$		−	16.9685i		−	0.551402i	0.961243	−	0.275701i	$-0.0889099\pi$
$948$		0			0
$949$	14.5914			0.473656
$950$	77.3556	+	14.9696i	2.50975	+	0.485677i
$951$		0			0
$952$		−	29.8936i		−	0.968856i
$953$			45.6056i			1.47731i	0.674084	+	0.738655i	$0.264539\pi$
$953$			45.6056i			1.47731i	−0.674084	+	0.738655i	$0.735461\pi$
$954$		0			0
$955$	27.7820	−	22.9211i	0.899004	−	0.741711i
$956$	52.5517			1.69964
$957$		0			0
$958$		−	7.52903i		−	0.243252i
$959$	6.30609			0.203634
$960$		0			0
$961$	26.1919			0.844899
$962$			3.23664i			0.104353i
$963$		0			0
$964$	0.856350			0.0275812
$965$	−19.7755	−	23.9693i	−0.636596	−	0.771599i
$966$		0			0
$967$		−	7.77794i		−	0.250122i	−0.992149	−	0.125061i	$-0.960087\pi$
$967$		−	7.77794i		−	0.250122i	0.992149	−	0.125061i	$-0.0399126\pi$
$968$			22.2589i			0.715427i
$969$		0			0
$970$	−77.5038	+	63.9434i	−2.48850	+	2.05310i
$971$	−14.1572			−0.454327			−0.227163	−	0.973857i	$-0.572945\pi$
$971$	−14.1572			−0.454327			−0.227163	+	0.973857i	$0.572945\pi$
$972$		0			0
$973$			2.94257i			0.0943345i
$974$	−40.3126			−1.29170
$975$		0			0
$976$	7.91927			0.253490
$977$		−	13.0985i		−	0.419058i	−0.977802	−	0.209529i	$-0.932807\pi$
$977$		−	13.0985i		−	0.419058i	0.977802	−	0.209529i	$-0.0671930\pi$
$978$		0			0
$979$	−68.7828			−2.19831
$980$	−43.6236	+	35.9911i	−1.39351	+	1.14969i
$981$		0			0
$982$		−	31.0178i		−	0.989817i
$983$		−	49.1176i		−	1.56661i	−0.621638	−	0.783305i	$-0.713533\pi$
$983$		−	49.1176i		−	1.56661i	0.621638	−	0.783305i	$-0.286467\pi$
$984$		0			0
$985$	16.7415	+	20.2919i	0.533429	+	0.646552i
$986$	62.9366			2.00431
$987$		0			0
$988$			26.3612i			0.838663i
$989$	27.4203			0.871915
$990$		0			0
$991$	17.0358			0.541161			0.270581	−	0.962697i	$-0.412784\pi$
$991$	17.0358			0.541161			0.270581	+	0.962697i	$0.412784\pi$
$992$		−	11.4989i		−	0.365092i
$993$		0			0
$994$	18.6590			0.591826
$995$	14.5145	−	11.9750i	0.460141	−	0.379633i
$996$		0			0
$997$			8.01802i			0.253933i	0.991907	+	0.126967i	$0.0405241\pi$
$997$			8.01802i			0.253933i	−0.991907	+	0.126967i	$0.959476\pi$
$998$		−	2.42355i		−	0.0767162i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.c.c.469.1		10
3.2	odd	2		195.2.c.b.79.10	yes	10
5.2	odd	4		2925.2.a.bm.1.5		5
5.3	odd	4		2925.2.a.bl.1.1		5
5.4	even	2	inner	585.2.c.c.469.10		10
12.11	even	2		3120.2.l.p.1249.2		10
15.2	even	4		975.2.a.s.1.1		5
15.8	even	4		975.2.a.r.1.5		5
15.14	odd	2		195.2.c.b.79.1	✓	10
60.59	even	2		3120.2.l.p.1249.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.c.b.79.1	✓	10	15.14	odd	2
195.2.c.b.79.10	yes	10	3.2	odd	2
585.2.c.c.469.1		10	1.1	even	1	trivial
585.2.c.c.469.10		10	5.4	even	2	inner
975.2.a.r.1.5		5	15.8	even	4
975.2.a.s.1.1		5	15.2	even	4
2925.2.a.bl.1.1		5	5.3	odd	4
2925.2.a.bm.1.5		5	5.2	odd	4
3120.2.l.p.1249.2		10	12.11	even	2
3120.2.l.p.1249.7		10	60.59	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)

\(f(q)\)	\(=\)	\(q-2.47948i q^{2} -4.14785 q^{4} +(1.72481 - 1.42303i) q^{5} -0.949959i q^{7} +5.32555i q^{8} +O(q^{10})\)	\(q-2.47948i q^{2} -4.14785 q^{4} +(1.72481 - 1.42303i) q^{5} -0.949959i q^{7} +5.32555i q^{8} +(-3.52839 - 4.27665i) q^{10} -3.89611 q^{11} +1.00000i q^{13} -2.35541 q^{14} +4.90893 q^{16} -5.90893i q^{17} -6.35541 q^{19} +(-7.15426 + 5.90252i) q^{20} +9.66033i q^{22} -3.30537i q^{23} +(0.949959 - 4.90893i) q^{25} +2.47948 q^{26} +3.94028i q^{28} -4.29569 q^{29} +7.56253 q^{31} -1.52052i q^{32} -14.6511 q^{34} +(-1.35182 - 1.63850i) q^{35} +1.30537i q^{37} +15.7581i q^{38} +(7.57843 + 9.18558i) q^{40} +6.75499 q^{41} +8.29569i q^{43} +16.1604 q^{44} -8.19561 q^{46} +0.0128228i q^{47} +6.09758 q^{49} +(-12.1716 - 2.35541i) q^{50} -4.14785i q^{52} -2.51249i q^{53} +(-6.72005 + 5.54428i) q^{55} +5.05905 q^{56} +10.6511i q^{58} -6.30851 q^{59} +1.61324 q^{61} -18.7512i q^{62} +6.04776 q^{64} +(1.42303 + 1.72481i) q^{65} -4.66328i q^{67} +24.5093i q^{68} +(-4.06264 + 3.35182i) q^{70} -7.92175 q^{71} -14.5914i q^{73} +3.23664 q^{74} +26.3612 q^{76} +3.70114i q^{77} +16.6004 q^{79} +(8.46698 - 6.98556i) q^{80} -16.7489i q^{82} -12.8044i q^{83} +(-8.40860 - 10.1918i) q^{85} +20.5690 q^{86} -20.7489i q^{88} +17.6542 q^{89} +0.949959 q^{91} +13.7102i q^{92} +0.0317940 q^{94} +(-10.9619 + 9.04395i) q^{95} -18.1226i q^{97} -15.1189i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 12 q^{4} + 2 q^{5}+O(q^{10}) \) 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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