LMFDB - Embedded newform 961.2.g.u.816.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{15}]$

Embedding invariants

Embedding label			816.3
Character	$\chi$	$=$	961.816
Dual form			961.2.g.u.338.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.91047 + 1.38804i) q^{2} +(1.10521 + 3.40149i) q^{4} +(-1.96900 - 3.41041i) q^{5} +(0.767781 + 0.163197i) q^{7} +(-1.15045 + 3.54072i) q^{8} +(2.93444 - 0.623735i) q^{9} +(0.972060 - 9.24853i) q^{10} +(1.24030 + 1.37749i) q^{14} +(-1.32560 + 0.963104i) q^{16} +(6.47193 + 2.88149i) q^{18} +(7.91216 - 3.52272i) q^{19} +(9.42431 - 10.4668i) q^{20} +(-5.25394 + 9.10008i) q^{25} +(0.293447 + 2.79196i) q^{28} +3.57653 q^{32} +(-0.955194 - 2.93979i) q^{35} +(5.36480 + 9.29211i) q^{36} +(20.0056 + 4.25232i) q^{38} +(14.3406 - 3.04818i) q^{40} +(-0.247538 + 2.35516i) q^{41} +(-7.90512 - 8.77952i) q^{45} +(-6.47214 + 4.70228i) q^{47} +(-5.83196 - 2.59656i) q^{49} +(-22.6687 + 10.0928i) q^{50} +(-1.46113 + 2.53075i) q^{56} +(-1.06941 - 10.1748i) q^{59} +2.35480 q^{63} +(9.48406 + 6.89057i) q^{64} +(6.00000 + 10.3923i) q^{67} +(2.25566 - 6.94221i) q^{70} +(-16.1756 + 3.43822i) q^{71} +(-1.16746 + 11.1076i) q^{72} +(20.7271 + 23.0198i) q^{76} +(5.89469 + 2.62449i) q^{80} +(8.22191 - 3.66063i) q^{81} +(-3.74196 + 4.15587i) q^{82} +(-2.91618 - 27.7456i) q^{90} -18.8918 q^{94} +(-27.5930 - 20.0475i) q^{95} +(3.16561 + 9.74276i) q^{97} +(-7.53766 - 13.0556i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 6 q^{8} - 9 q^{9} - 9 q^{10} + 15 q^{14} - 24 q^{16} + 21 q^{20} - 60 q^{25} + 27 q^{28} + 48 q^{32} - 24 q^{35} + 72 q^{36} - 33 q^{38} - 18 q^{40} - 48 q^{47} + 21 q^{49} - 39 q^{50}+ \cdots - 228 q^{98}+O(q^{100}) $ 24 * q - 12 * q^4 - 6 * q^8 - 9 * q^9 - 9 * q^10 + 15 * q^14 - 24 * q^16 + 21 * q^20 - 60 * q^25 + 27 * q^28 + 48 * q^32 - 24 * q^35 + 72 * q^36 - 33 * q^38 - 18 * q^40 - 48 * q^47 + 21 * q^49 - 39 * q^50 - 120 * q^56 + 42 * q^64 + 144 * q^67 - 6 * q^70 - 9 * q^72 + 15 * q^76 - 9 * q^80 + 27 * q^81 + 21 * q^82 + 27 * q^90 - 96 * q^95 - 228 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

Coefficient data

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

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

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

$2$	1.91047	+	1.38804i	1.35091	+	0.981490i	0.998966	+	0.0454672i	$0.0144777\pi$
$2$	1.91047	+	1.38804i	1.35091	+	0.981490i	0.351939	+	0.936023i	$0.385522\pi$
$3$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$3$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$4$	1.10521	+	3.40149i	0.552605	+	1.70074i
$5$	−1.96900	−	3.41041i	−0.880564	−	1.52518i	−0.850715	−	0.525628i	$-0.823830\pi$
$5$	−1.96900	−	3.41041i	−0.880564	−	1.52518i	−0.0298497	−	0.999554i	$-0.509503\pi$
$6$		0			0
$7$	0.767781	+	0.163197i	0.290194	+	0.0616827i	0.350709	−	0.936485i	$-0.385941\pi$
$7$	0.767781	+	0.163197i	0.290194	+	0.0616827i	−0.0605145	+	0.998167i	$0.519274\pi$
$8$	−1.15045	+	3.54072i	−0.406746	+	1.25183i
$9$	2.93444	−	0.623735i	0.978148	−	0.207912i
$10$	0.972060	−	9.24853i	0.307392	−	2.92464i
$11$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$11$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$12$		0			0
$13$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$13$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$14$	1.24030	+	1.37749i	0.331484	+	0.368150i
$15$		0			0
$16$	−1.32560	+	0.963104i	−0.331400	+	0.240776i
$17$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$17$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$18$	6.47193	+	2.88149i	1.52545	+	0.679173i
$19$	7.91216	−	3.52272i	1.81517	−	0.808168i	0.861210	−	0.508249i	$-0.169707\pi$
$19$	7.91216	−	3.52272i	1.81517	−	0.808168i	0.953965	−	0.299918i	$-0.0969595\pi$
$20$	9.42431	−	10.4668i	2.10734	−	2.34044i
$21$		0			0
$22$		0			0
$23$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$23$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$24$		0			0
$25$	−5.25394	+	9.10008i	−1.05079	+	1.82002i
$26$		0			0
$27$		0			0
$28$	0.293447	+	2.79196i	0.0554563	+	0.527632i
$29$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$29$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$30$		0			0
$31$		0			0
$31$		0			0
$32$	3.57653			0.632248
$33$		0			0
$34$		0			0
$35$	−0.955194	−	2.93979i	−0.161457	−	0.496914i
$36$	5.36480	+	9.29211i	0.894134	+	1.54868i
$37$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$37$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$38$	20.0056	+	4.25232i	3.24534	+	0.689818i
$39$		0			0
$40$	14.3406	−	3.04818i	2.26744	−	0.481960i
$41$	−0.247538	+	2.35516i	−0.0386589	+	0.367815i	0.958040	+	0.286633i	$0.0925360\pi$
$41$	−0.247538	+	2.35516i	−0.0386589	+	0.367815i	−0.996699	+	0.0811816i	$0.974131\pi$
$42$		0			0
$43$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$43$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$44$		0			0
$45$	−7.90512	−	8.77952i	−1.17843	−	1.30877i
$46$		0			0
$47$	−6.47214	+	4.70228i	−0.944058	+	0.685898i	−0.949394	−	0.314087i	$-0.898301\pi$
$47$	−6.47214	+	4.70228i	−0.944058	+	0.685898i	0.00533600	+	0.999986i	$0.498301\pi$
$48$		0			0
$49$	−5.83196	−	2.59656i	−0.833138	−	0.370937i
$50$	−22.6687	+	10.0928i	−3.20584	+	1.42733i
$51$		0			0
$52$		0			0
$53$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$53$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$54$		0			0
$55$		0			0
$56$	−1.46113	+	2.53075i	−0.195252	+	0.338186i
$57$		0			0
$58$		0			0
$59$	−1.06941	−	10.1748i	−0.139225	−	1.32464i	−0.811506	−	0.584345i	$-0.801352\pi$
$59$	−1.06941	−	10.1748i	−0.139225	−	1.32464i	0.672280	−	0.740297i	$-0.265315\pi$
$60$		0			0
$61$		0			0			−	1.00000i	$-0.5\pi$
$61$		0			0				1.00000i	$0.5\pi$
$62$		0			0
$63$	2.35480			0.296677
$64$	9.48406	+	6.89057i	1.18551	+	0.861321i
$65$		0			0
$66$		0			0
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	0.955588	+	0.294706i	$0.0952216\pi$
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	−0.222571	+	0.974916i	$0.571445\pi$
$68$		0			0
$69$		0			0
$70$	2.25566	−	6.94221i	0.269603	−	0.829753i
$71$	−16.1756	+	3.43822i	−1.91969	+	0.408042i	−0.919811	+	0.392363i	$0.871658\pi$
$71$	−16.1756	+	3.43822i	−1.91969	+	0.408042i	−0.999877	+	0.0156796i	$0.995009\pi$
$72$	−1.16746	+	11.1076i	−0.137586	+	1.30905i
$73$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$73$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$74$		0			0
$75$		0			0
$76$	20.7271	+	23.0198i	2.37756	+	2.64055i
$77$		0			0
$78$		0			0
$79$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$79$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$80$	5.89469	+	2.62449i	0.659046	+	0.293426i
$81$	8.22191	−	3.66063i	0.913545	−	0.406737i
$82$	−3.74196	+	4.15587i	−0.413231	+	0.458939i
$83$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$83$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$89$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$90$	−2.91618	−	27.7456i	−0.307392	−	2.92464i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−18.8918			−1.94854
$95$	−27.5930	−	20.0475i	−2.83098	−	2.05683i
$96$		0			0
$97$	3.16561	+	9.74276i	0.321419	+	0.989227i	0.973031	+	0.230674i	$0.0740932\pi$
$97$	3.16561	+	9.74276i	0.321419	+	0.989227i	−0.651612	+	0.758553i	$0.725907\pi$
$98$	−7.53766	−	13.0556i	−0.761419	−	1.31882i
$99$		0			0
$100$	−36.7605	−	7.81369i	−3.67605	−	0.781369i
$101$	2.18714	−	6.73133i	0.217629	−	0.669792i	−0.781328	−	0.624121i	$-0.785457\pi$
$101$	2.18714	−	6.73133i	0.217629	−	0.669792i	0.998957	−	0.0456715i	$-0.0145427\pi$
$102$		0			0
$103$	1.56449	−	14.8851i	0.154153	−	1.46667i	−0.594706	−	0.803943i	$-0.702732\pi$
$103$	1.56449	−	14.8851i	0.154153	−	1.46667i	0.748860	−	0.662728i	$-0.230602\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.69441	+	4.10305i	0.357152	+	0.396657i	0.894767	−	0.446533i	$-0.147341\pi$
$107$	3.69441	+	4.10305i	0.357152	+	0.396657i	−0.537615	+	0.843190i	$0.680675\pi$
$108$		0			0
$109$	−12.0978	+	8.78959i	−1.15876	+	0.841890i	−0.989621	−	0.143702i	$-0.954099\pi$
$109$	−12.0978	+	8.78959i	−1.15876	+	0.841890i	−0.169141	+	0.985592i	$0.554099\pi$
$110$		0			0
$111$		0			0
$112$	−1.17495	+	0.523120i	−0.111022	+	0.0494302i
$113$	−14.2256	+	15.7992i	−1.33824	+	1.48626i	−0.664525	+	0.747266i	$0.731366\pi$
$113$	−14.2256	+	15.7992i	−1.33824	+	1.48626i	−0.673711	+	0.738995i	$0.735301\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	12.0799	−	20.9229i	1.11204	−	1.92611i
$119$		0			0
$120$		0			0
$121$	1.14981	+	10.9397i	0.104528	+	0.994522i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	21.6900			1.94001
$126$	4.49877	+	3.26855i	0.400783	+	0.291186i
$127$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$127$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$128$	6.34421	+	19.5255i	0.560754	+	1.72582i
$129$		0			0
$130$		0			0
$131$	−19.5630	−	4.15823i	−1.70922	−	0.363307i	−0.753471	−	0.657481i	$-0.771622\pi$
$131$	−19.5630	−	4.15823i	−1.70922	−	0.363307i	−0.955752	+	0.294174i	$0.904955\pi$
$132$		0			0
$133$	6.64971	−	1.41344i	0.576603	−	0.122561i
$134$	−2.96209	+	28.1824i	−0.255885	+	2.43459i
$135$		0			0
$136$		0			0
$137$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$137$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$138$		0			0
$139$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$139$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$140$	8.94395	−	6.49816i	0.755902	−	0.549195i
$141$		0			0
$142$	−35.6753	−	15.8837i	−2.99381	−	1.33293i
$143$		0			0
$144$	−3.28917	+	3.65300i	−0.274098	+	0.304417i
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$		0			0
$151$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$151$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$152$	3.37043	+	32.0675i	0.273378	+	2.60102i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	18.4697	+	13.4190i	1.47404	+	1.07095i	0.979418	+	0.201844i	$0.0646933\pi$
$157$	18.4697	+	13.4190i	1.47404	+	1.07095i	0.494621	+	0.869109i	$0.335307\pi$
$158$		0			0
$159$		0			0
$160$	−7.04220	−	12.1975i	−0.556735	−	0.964293i
$161$		0			0
$162$	20.7888	+	4.41879i	1.63332	+	0.347173i
$163$	7.54402	−	23.2181i	0.590893	−	1.81858i	0.0167022	−	0.999861i	$-0.494683\pi$
$163$	7.54402	−	23.2181i	0.590893	−	1.81858i	0.574191	−	0.818721i	$-0.305317\pi$
$164$	−8.28463	+	1.76095i	−0.646921	+	0.137507i
$165$		0			0
$166$		0			0
$167$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$167$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$168$		0			0
$169$	−8.69870	−	9.66088i	−0.669131	−	0.743145i
$170$		0			0
$171$	21.0205	−	15.2723i	1.60748	−	1.16790i
$172$		0			0
$173$	12.7896	+	5.69431i	0.972378	+	0.432931i	0.830540	−	0.556959i	$-0.188032\pi$
$173$	12.7896	+	5.69431i	0.972378	+	0.432931i	0.141838	+	0.989890i	$0.454699\pi$
$174$		0			0
$175$	−5.51898	+	6.12945i	−0.417196	+	0.463343i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$179$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$180$	21.1266	−	36.5924i	1.57468	−	2.72743i
$181$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$181$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−23.1478	−	16.8179i	−1.68823	−	1.22657i
$189$		0			0
$190$	−24.8889	−	76.6002i	−1.80563	−	5.55716i
$191$	6.69861	+	11.6023i	0.484694	+	0.839515i	0.999845	−	0.0175844i	$-0.00559759\pi$
$191$	6.69861	+	11.6023i	0.484694	+	0.839515i	−0.515151	+	0.857099i	$0.672264\pi$
$192$		0			0
$193$	17.7242	+	3.76739i	1.27581	+	0.271183i	0.795521	−	0.605925i	$-0.207197\pi$
$193$	17.7242	+	3.76739i	1.27581	+	0.271183i	0.480293	+	0.877108i	$0.340530\pi$
$194$	−7.47550	+	23.0072i	−0.536710	+	1.65182i
$195$		0			0
$196$	2.38661	−	22.7071i	0.170472	−	1.62193i
$197$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$197$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$198$		0			0
$199$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$199$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$200$	−26.1765	−	29.0719i	−1.85096	−	2.05570i
$201$		0			0
$202$	13.5218	−	9.82416i	0.951390	−	0.691226i
$203$		0			0
$204$		0			0
$205$	8.51947	−	3.79311i	0.595026	−	0.264923i
$206$	23.6499	−	26.2659i	1.64777	−	1.83003i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−11.4215	+	19.7827i	−0.786291	+	1.36190i	0.141933	+	0.989876i	$0.454668\pi$
$211$	−11.4215	+	19.7827i	−0.786291	+	1.36190i	−0.928225	+	0.372021i	$0.878665\pi$
$212$		0			0
$213$		0			0
$214$	1.36286	+	12.9667i	0.0931631	+	0.886387i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−35.3128			−2.39168
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$223$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$224$	2.74600	+	0.583680i	0.183475	+	0.0389987i
$225$	−9.74133	+	29.9807i	−0.649422	+	1.99872i
$226$	−49.1075	+	10.4381i	−3.26658	+	0.694333i
$227$	−2.92680	+	27.8466i	−0.194258	+	1.84824i	0.270392	+	0.962750i	$0.412847\pi$
$227$	−2.92680	+	27.8466i	−0.194258	+	1.84824i	−0.464650	+	0.885494i	$0.653820\pi$
$228$		0			0
$229$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$229$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.99606	−	5.08294i	0.458327	−	0.332994i	−0.334547	−	0.942379i	$-0.608583\pi$
$233$	6.99606	−	5.08294i	0.458327	−	0.332994i	0.792875	+	0.609385i	$0.208583\pi$
$234$		0			0
$235$	28.7804	+	12.8138i	1.87742	+	0.835883i
$236$	33.4274	−	14.8828i	2.17594	−	0.968790i
$237$		0			0
$238$		0			0
$239$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$239$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$240$		0			0
$241$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$241$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$242$	−12.9881	+	22.4960i	−0.834905	+	1.44610i
$243$		0			0
$244$		0			0
$245$	2.62782	+	25.0020i	0.167885	+	1.59732i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	41.4381	+	30.1065i	2.62078	+	1.90410i
$251$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$251$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$252$	2.60255	+	8.00983i	0.163945	+	0.504572i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−7.73647	+	23.8104i	−0.483529	+	1.48815i
$257$	23.8664	−	5.07297i	1.48875	−	0.316443i	0.609491	−	0.792793i	$-0.291374\pi$
$257$	23.8664	−	5.07297i	1.48875	−	0.316443i	0.879256	+	0.476350i	$0.158040\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−31.6026	−	35.0983i	−1.95242	−	2.16838i
$263$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$263$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$264$		0			0
$265$		0			0
$266$	14.6660	+	6.52971i	0.899228	+	0.400362i
$267$		0			0
$268$	−28.7180	+	31.8946i	−1.75423	+	1.94827i
$269$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$269$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$270$		0			0
$271$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$271$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$277$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$278$		0			0
$279$		0			0
$280$	11.5079			0.687727
$281$	−0.624238	−	0.453536i	−0.0372389	−	0.0270557i	0.569010	−	0.822331i	$-0.307327\pi$
$281$	−0.624238	−	0.453536i	−0.0372389	−	0.0270557i	−0.606249	+	0.795275i	$0.707327\pi$
$282$		0			0
$283$	1.23607	+	3.80423i	0.0734766	+	0.226138i	0.981050	−	0.193756i	$-0.0620672\pi$
$283$	1.23607	+	3.80423i	0.0734766	+	0.226138i	−0.907573	+	0.419894i	$0.862067\pi$
$284$	−29.5725	−	51.2210i	−1.75480	−	3.03941i
$285$		0			0
$286$		0			0
$287$	−0.574410	+	1.76785i	−0.0339064	+	0.104353i
$288$	10.4951	−	2.23081i	0.618432	−	0.131452i
$289$	1.77698	−	16.9069i	0.104528	−	0.994522i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−17.3974	−	19.3218i	−1.01637	−	1.12879i	−0.991632	−	0.129096i	$-0.958793\pi$
$293$	−17.3974	−	19.3218i	−1.01637	−	1.12879i	−0.0247346	−	0.999694i	$-0.507874\pi$
$294$		0			0
$295$	−32.5945	+	23.6813i	−1.89772	+	1.37878i
$296$		0			0
$297$		0			0
$298$	−21.5731	+	9.60496i	−1.24970	+	0.556400i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−7.09561	+	12.2900i	−0.406961	+	0.704877i
$305$		0			0
$306$		0			0
$307$	1.39760	+	13.2973i	0.0797654	+	0.758917i	0.959168	+	0.282838i	$0.0912758\pi$
$307$	1.39760	+	13.2973i	0.0797654	+	0.758917i	−0.879402	+	0.476079i	$0.842058\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−21.2466			−1.20478			−0.602391	−	0.798201i	$-0.705785\pi$
$311$	−21.2466			−1.20478			−0.602391	+	0.798201i	$0.705785\pi$
$312$		0			0
$313$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$313$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$314$	16.6596	+	51.2731i	0.940158	+	2.89351i
$315$	−4.63661	−	8.03084i	−0.261243	−	0.452487i
$316$		0			0
$317$	−16.1886	−	3.44100i	−0.909243	−	0.193266i	−0.270531	−	0.962711i	$-0.587199\pi$
$317$	−16.1886	−	3.44100i	−0.909243	−	0.193266i	−0.638712	+	0.769446i	$0.720533\pi$
$318$		0			0
$319$		0			0
$320$	4.82555	−	45.9121i	0.269757	−	2.56656i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	21.5385	+	23.9209i	1.19658	+	1.32894i
$325$		0			0
$326$	46.6402	−	33.8861i	2.58316	−	1.87678i
$327$		0			0
$328$	−8.05420	−	3.58596i	−0.444719	−	0.198002i
$329$	−5.73658	+	2.55409i	−0.316268	+	0.140812i
$330$		0			0
$331$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$331$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	23.6280	−	40.9249i	1.29094	−	2.23597i
$336$		0			0
$337$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$337$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$338$	−3.20893	−	30.5309i	−0.174543	−	1.66066i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	61.3576			3.31784
$343$	−8.49910	−	6.17496i	−0.458908	−	0.333416i
$344$		0			0
$345$		0			0
$346$	16.5303	+	28.6313i	0.888673	+	1.53923i
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$	−9.27051	+	28.5317i	−0.496239	+	1.52727i	0.318778	+	0.947829i	$0.396728\pi$
$349$	−9.27051	+	28.5317i	−0.496239	+	1.52727i	−0.815017	+	0.579437i	$0.803272\pi$
$350$	−19.0517	+	4.04957i	−1.01836	+	0.216459i
$351$		0			0
$352$		0			0
$353$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$353$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$354$		0			0
$355$	43.5755	+	48.3955i	2.31275	+	2.56857i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−28.0633	−	12.4946i	−1.48112	−	0.659439i	−0.502403	−	0.864634i	$-0.667550\pi$
$359$	−28.0633	−	12.4946i	−1.48112	−	0.659439i	−0.978721	+	0.205195i	$0.934217\pi$
$360$	40.1803	−	17.8894i	2.11769	−	0.942856i
$361$	37.4793	−	41.6250i	1.97259	−	2.19079i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$367$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$368$		0			0
$369$	0.742613	+	7.06549i	0.0386589	+	0.367815i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−38.5818			−1.99769			−0.998844	−	0.0480672i	$-0.984694\pi$
$373$	−38.5818			−1.99769			−0.998844	+	0.0480672i	$0.984694\pi$
$374$		0			0
$375$		0			0
$376$	−9.20361	−	28.3258i	−0.474640	−	1.46079i
$377$		0			0
$378$		0			0
$379$	−19.5630	−	4.15823i	−1.00488	−	0.213594i	−0.324054	−	0.946038i	$-0.605046\pi$
$379$	−19.5630	−	4.15823i	−1.00488	−	0.213594i	−0.680827	+	0.732444i	$0.738379\pi$
$380$	37.6952	−	116.014i	1.93372	−	5.95139i
$381$		0			0
$382$	−3.30698	+	31.4638i	−0.169200	+	1.60983i
$383$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$383$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$384$		0			0
$385$		0			0
$386$	28.6322	+	31.7993i	1.45734	+	1.61854i
$387$		0			0
$388$	−29.6412	+	21.5356i	−1.50480	+	1.09330i
$389$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$389$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$390$		0			0
$391$		0			0
$392$	15.9031	−	17.6622i	0.803227	−	0.892074i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	9.04674	−	15.6694i	0.454043	−	0.786425i	−0.544590	−	0.838703i	$-0.683315\pi$
$397$	9.04674	−	15.6694i	0.454043	−	0.786425i	0.998633	+	0.0522772i	$0.0166479\pi$
$398$		0			0
$399$		0			0
$400$	−1.79972	−	17.1232i	−0.0899858	−	0.856158i
$401$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$401$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$402$		0			0
$403$		0			0
$404$	25.3138			1.25941
$405$	−28.6732	−	20.8323i	−1.42478	−	1.03517i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$409$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$410$	21.5412	+	4.57872i	1.06384	+	0.226127i
$411$		0			0
$412$	52.3605	−	11.1296i	2.57962	−	0.548315i
$413$	0.839417	−	7.98652i	0.0413050	−	0.392991i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.92665	−	1.39979i	0.0941229	−	0.0683843i	−0.539728	−	0.841839i	$-0.681473\pi$
$419$	1.92665	−	1.39979i	0.0941229	−	0.0683843i	0.633851	+	0.773455i	$0.281473\pi$
$420$		0			0
$421$	9.33413	+	4.15582i	0.454918	+	0.202542i	0.621386	−	0.783504i	$-0.286570\pi$
$421$	9.33413	+	4.15582i	0.454918	+	0.202542i	−0.166469	+	0.986047i	$0.553236\pi$
$422$	−49.2796	+	21.9407i	−2.39889	+	1.06806i
$423$	−16.0591	+	17.8355i	−0.780822	+	0.867191i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−9.87339	+	17.1012i	−0.477248	+	0.826618i
$429$		0			0
$430$		0			0
$431$	−4.18114	−	39.7809i	−0.201398	−	1.91618i	−0.367420	−	0.930055i	$-0.619759\pi$
$431$	−4.18114	−	39.7809i	−0.201398	−	1.91618i	0.166021	−	0.986122i	$-0.446908\pi$
$432$		0			0
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$		0			0
$436$	−43.2683	−	31.4363i	−2.07218	−	1.50552i
$437$		0			0
$438$		0			0
$439$	18.4993	+	32.0417i	0.882923	+	1.52927i	0.848076	+	0.529874i	$0.177761\pi$
$439$	18.4993	+	32.0417i	0.882923	+	1.52927i	0.0348463	+	0.999393i	$0.488906\pi$
$440$		0			0
$441$	−18.7331	−	3.98185i	−0.892054	−	0.189612i
$442$		0			0
$443$	40.8228	−	8.67716i	1.93955	−	0.412264i	0.942632	−	0.333835i	$-0.108343\pi$
$443$	40.8228	−	8.67716i	1.93955	−	0.412264i	0.996920	−	0.0784294i	$-0.0249905\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	6.15716	+	6.83822i	0.290899	+	0.323076i
$449$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$449$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$450$	−60.2249	+	43.7559i	−2.83903	+	2.06267i
$451$		0			0
$452$	−69.4630	−	30.9269i	−3.26726	−	1.45468i
$453$		0			0
$454$	−44.2437	+	49.1376i	−2.07646	+	2.30614i
$455$		0			0
$456$		0			0
$457$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$457$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$461$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$462$		0			0
$463$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$463$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$464$		0			0
$465$		0			0
$466$	20.4211			0.945987
$467$	32.4941	+	23.6084i	1.50365	+	1.09247i	0.968899	+	0.247455i	$0.0795943\pi$
$467$	32.4941	+	23.6084i	1.50365	+	1.09247i	0.534750	+	0.845010i	$0.320406\pi$
$468$		0			0
$469$	2.91070	+	8.95820i	0.134403	+	0.413651i
$470$	37.1979	+	64.4286i	1.71581	+	2.97187i
$471$		0			0
$472$	37.2563	+	7.91908i	1.71486	+	0.364505i
$473$		0			0
$474$		0			0
$475$	−9.51293	+	90.5095i	−0.436483	+	4.15286i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−19.5046	−	21.6621i	−0.891190	−	0.989766i	0.108801	−	0.994064i	$-0.465299\pi$
$479$	−19.5046	−	21.6621i	−0.891190	−	0.989766i	−0.999991	+	0.00429710i	$0.998632\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−35.9406	+	16.0018i	−1.63366	+	0.727354i
$485$	26.9937	−	29.9796i	1.22572	−	1.36130i
$486$		0			0
$487$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$487$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$488$		0			0
$489$		0			0
$490$	−29.6834	+	51.4131i	−1.34096	+	2.32261i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.9804			−0.582251
$498$		0			0
$499$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$499$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$500$	23.9720	+	73.7783i	1.07206	+	3.29947i
$501$		0			0
$502$		0			0
$503$	−22.3178	−	4.74380i	−0.995103	−	0.211516i	−0.318547	−	0.947907i	$-0.603195\pi$
$503$	−22.3178	−	4.74380i	−0.995103	−	0.211516i	−0.676556	+	0.736391i	$0.736528\pi$
$504$	−2.70908	+	8.33770i	−0.120672	+	0.371391i
$505$	−27.2631	+	5.79495i	−1.21319	+	0.257872i
$506$		0			0
$507$		0			0
$508$		0			0
$509$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$509$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$510$		0			0
$511$		0			0
$512$	−14.6113	+	10.6157i	−0.645734	+	0.469154i
$513$		0			0
$514$	52.6375	+	23.4357i	2.32174	+	1.03371i
$515$	−53.8447	+	23.9732i	−2.37268	+	1.05639i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	−0.954519	−	0.298150i	$-0.903630\pi$
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	0.735465	+	0.677563i	$0.236964\pi$
$522$		0			0
$523$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$523$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$524$	−7.47699	−	71.1388i	−0.326634	−	3.10771i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	18.6074	+	13.5191i	0.809017	+	0.587785i
$530$		0			0
$531$	−9.48448	−	29.1902i	−0.411591	−	1.26675i
$532$	12.1571	+	21.0567i	0.527078	+	0.912926i
$533$		0			0
$534$		0			0
$535$	6.71881	−	20.6784i	0.290479	−	0.894004i
$536$	−43.6990	+	9.28851i	−1.88751	+	0.401202i
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	31.0863	+	34.5249i	1.33651	+	1.48434i	0.706310	+	0.707903i	$0.250359\pi$
$541$	31.0863	+	34.5249i	1.33651	+	1.48434i	0.630196	+	0.776436i	$0.282975\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	53.7968	+	23.9519i	2.30440	+	1.02599i
$546$		0			0
$547$	−25.8252	+	28.6817i	−1.10420	+	1.22634i	−0.132239	+	0.991218i	$0.542217\pi$
$547$	−25.8252	+	28.6817i	−1.10420	+	1.22634i	−0.971965	+	0.235125i	$0.924450\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$	4.09753	+	2.97703i	0.173152	+	0.125802i
$561$		0			0
$562$	−0.563063	−	1.73293i	−0.0237514	−	0.0730993i
$563$	−22.4373	−	38.8625i	−0.945619	−	1.63786i	−0.754507	−	0.656292i	$-0.772124\pi$
$563$	−22.4373	−	38.8625i	−0.945619	−	1.63786i	−0.191112	−	0.981568i	$-0.561209\pi$
$564$		0			0
$565$	81.8920	+	17.4067i	3.44522	+	0.732305i
$566$	−2.91894	+	8.98356i	−0.122692	+	0.377607i
$567$	6.91003	−	1.46877i	0.290194	−	0.0616827i
$568$	6.43540	−	61.2288i	0.270023	−	2.56910i
$569$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$569$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$570$		0			0
$571$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$571$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$572$		0			0
$573$		0			0
$574$	−3.55124	+	2.58012i	−0.148226	+	0.107692i
$575$		0			0
$576$	32.1283	+	14.3044i	1.33868	+	0.596019i
$577$	16.4438	−	7.32126i	0.684565	−	0.304788i	−0.0348259	−	0.999393i	$-0.511088\pi$
$577$	16.4438	−	7.32126i	0.684565	−	0.304788i	0.719391	+	0.694605i	$0.244421\pi$
$578$	26.8622	−	29.8335i	1.11732	−	1.24091i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−6.41786	−	61.0618i	−0.265119	−	2.52244i
$587$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$587$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$588$		0			0
$589$		0			0
$590$	−95.1411			−3.91690
$591$		0			0
$592$		0			0
$593$	−14.8414	−	45.6770i	−0.609462	−	1.87573i	−0.462585	−	0.886575i	$-0.653078\pi$
$593$	−14.8414	−	45.6770i	−0.609462	−	1.87573i	−0.146876	−	0.989155i	$-0.546922\pi$
$594$		0			0
$595$		0			0
$596$	−34.9838	−	7.43603i	−1.43299	−	0.304592i
$597$		0			0
$598$		0			0
$599$	4.03150	−	38.3572i	0.164723	−	1.56723i	−0.530028	−	0.847980i	$-0.677819\pi$
$599$	4.03150	−	38.3572i	0.164723	−	1.56723i	0.694751	−	0.719251i	$-0.255515\pi$
$600$		0			0
$601$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$601$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$602$		0			0
$603$	24.0887	+	26.7532i	0.980968	+	1.08948i
$604$		0			0
$605$	35.0450	−	25.4617i	1.42478	−	1.03517i
$606$		0			0
$607$	−43.8502	−	19.5234i	−1.77982	−	0.792429i	−0.981830	−	0.189764i	$-0.939228\pi$
$607$	−43.8502	−	19.5234i	−1.77982	−	0.792429i	−0.797994	−	0.602665i	$-0.794105\pi$
$608$	28.2981	−	12.5991i	1.14764	−	0.510963i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$613$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$614$	−15.7871	+	27.3440i	−0.637114	+	1.10351i
$615$		0			0
$616$		0			0
$617$	2.29963	+	21.8795i	0.0925795	+	0.880835i	0.937977	+	0.346697i	$0.112697\pi$
$617$	2.29963	+	21.8795i	0.0925795	+	0.880835i	−0.845398	+	0.534138i	$0.820636\pi$
$618$		0			0
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$		0			0
$622$	−40.5909	−	29.4910i	−1.62755	−	1.18248i
$623$		0			0
$624$		0			0
$625$	−16.4380	−	28.4715i	−0.657520	−	1.13886i
$626$		0			0
$627$		0			0
$628$	−25.2317	+	77.6551i	−1.00685	+	3.09878i
$629$		0			0
$630$	2.28901	−	21.7785i	0.0911963	−	0.867674i
$631$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$631$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$632$		0			0
$633$		0			0
$634$	−26.1516	−	29.0443i	−1.03861	−	1.15350i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−45.3218	+	20.1785i	−1.79290	+	0.798251i
$640$	54.0981	−	60.0820i	2.13841	−	2.37495i
$641$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$641$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$642$		0			0
$643$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$643$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$647$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$648$	3.50238	+	33.3229i	0.137586	+	1.30905i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	87.3138			3.41947
$653$	37.2148	+	27.0381i	1.45633	+	1.05808i	0.984301	+	0.176499i	$0.0564772\pi$
$653$	37.2148	+	27.0381i	1.45633	+	1.05808i	0.472026	+	0.881585i	$0.343523\pi$
$654$		0			0
$655$	24.3382	+	74.9053i	0.950972	+	2.92679i
$656$	−1.94013	−	3.36041i	−0.0757494	−	0.131202i
$657$		0			0
$658$	−14.5047	−	3.08308i	−0.565453	−	0.120191i
$659$	0.250798	−	0.771878i	0.00976972	−	0.0300681i	−0.946053	−	0.324012i	$-0.894968\pi$
$659$	0.250798	−	0.771878i	0.00976972	−	0.0300681i	0.955823	+	0.293944i	$0.0949680\pi$
$660$		0			0
$661$	3.37651	−	32.1253i	0.131331	−	1.24953i	−0.708119	−	0.706093i	$-0.750456\pi$
$661$	3.37651	−	32.1253i	0.131331	−	1.24953i	0.839450	−	0.543437i	$-0.182877\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−17.9137	−	19.8952i	−0.694663	−	0.771502i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$	101.946	−	45.3892i	3.93851	−	1.75354i
$671$		0			0
$672$		0			0
$673$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$673$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$674$		0			0
$675$		0			0
$676$	23.2475	−	40.2658i	0.894134	−	1.54868i
$677$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$677$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$678$		0			0
$679$	0.840511	+	7.99693i	0.0322558	+	0.306894i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	37.0252			1.41673			0.708366	−	0.705846i	$-0.249433\pi$
$683$	37.0252			1.41673			0.708366	+	0.705846i	$0.249433\pi$
$684$	75.1807	+	54.6220i	2.87461	+	2.08852i
$685$		0			0
$686$	−7.66619	−	23.5941i	−0.292697	−	0.900827i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	17.7372	−	3.77016i	0.674756	−	0.143424i	0.142225	−	0.989834i	$-0.454574\pi$
$691$	17.7372	−	3.77016i	0.674756	−	0.143424i	0.532531	+	0.846411i	$0.321241\pi$
$692$	−5.23390	+	49.7972i	−0.198963	+	1.89301i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−57.3141	+	41.6411i	−2.16937	+	1.57614i
$699$		0			0
$700$	−26.9489	−	11.9984i	−1.01857	−	0.453497i
$701$	45.3096	−	20.1731i	1.71132	−	0.761928i	0.713178	−	0.700983i	$-0.247255\pi$
$701$	45.3096	−	20.1731i	1.71132	−	0.761928i	0.998141	−	0.0609456i	$-0.0194116\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.77778	−	4.81125i	0.104469	−	0.180946i
$708$		0			0
$709$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$709$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$710$	16.0749	+	152.942i	0.603280	+	5.73983i
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−36.2711	−	62.8234i	−1.35363	−	2.34455i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	18.9346	+	4.02468i	0.705651	+	0.149991i
$721$	3.63038	−	11.1732i	0.135203	−	0.416111i
$722$	129.380	−	27.5006i	4.81502	−	1.02346i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−35.2970	−	39.2013i	−1.30909	−	1.45390i	−0.808854	−	0.588010i	$-0.799912\pi$
$727$	−35.2970	−	39.2013i	−1.30909	−	1.45390i	−0.500241	−	0.865886i	$-0.666755\pi$
$728$		0			0
$729$	21.8435	−	15.8702i	0.809017	−	0.587785i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	8.97341	−	9.96598i	0.331440	−	0.368102i	−0.554273	−	0.832335i	$-0.687003\pi$
$733$	8.97341	−	9.96598i	0.331440	−	0.368102i	0.885713	+	0.464233i	$0.153670\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−8.38842	+	14.5292i	−0.308782	+	0.534826i
$739$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$739$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$		0			0
$745$	39.3800			1.44277
$746$	−73.7092	−	53.5529i	−2.69869	−	1.96071i
$747$		0			0
$748$		0			0
$749$	2.16689	+	3.75316i	0.0791765	+	0.137138i
$750$		0			0
$751$	23.8534	+	5.07019i	0.870423	+	0.185014i	0.621409	−	0.783486i	$-0.286560\pi$
$751$	23.8534	+	5.07019i	0.870423	+	0.185014i	0.249013	+	0.968500i	$0.419894\pi$
$752$	4.05067	−	12.4667i	0.147713	−	0.454613i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$757$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$758$	−31.6026	−	35.0983i	−1.14786	−	1.27483i
$759$		0			0
$760$	102.727	−	74.6355i	3.72630	−	2.70732i
$761$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$761$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$762$		0			0
$763$	−10.7229	+	4.77415i	−0.388196	+	0.172836i
$764$	−32.0618	+	35.6082i	−1.15995	+	1.28826i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	26.3820	−	45.6949i	0.951358	−	1.64780i	0.208866	−	0.977944i	$-0.433023\pi$
$769$	26.3820	−	45.6949i	0.951358	−	1.64780i	0.742491	−	0.669856i	$-0.233644\pi$
$770$		0			0
$771$		0			0
$772$	6.77421	+	64.4523i	0.243809	+	2.31969i
$773$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$773$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$774$		0			0
$775$		0			0
$776$	−38.1383			−1.36909
$777$		0			0
$778$		0			0
$779$	6.33803	+	19.5064i	0.227083	+	0.698891i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	10.2316	−	2.17479i	0.365414	−	0.0776712i
$785$	9.39749	−	89.4111i	0.335411	−	3.19122i
$786$		0			0
$787$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$787$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−13.5006	+	9.80873i	−0.480025	+	0.348758i
$792$		0			0
$793$		0			0
$794$	39.0332	−	17.3787i	1.38524	−	0.616748i
$795$		0			0
$796$		0			0
$797$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$797$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$798$		0			0
$799$		0			0
$800$	−18.7909	+	32.5468i	−0.664358	+	1.15070i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	21.3176	+	15.4881i	0.749950	+	0.544871i
$809$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$809$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$810$	−25.8633	−	79.5989i	−0.908742	−	2.79682i
$811$	6.00000	+	10.3923i	0.210688	+	0.364923i	0.951930	−	0.306315i	$-0.0990961\pi$
$811$	6.00000	+	10.3923i	0.210688	+	0.364923i	−0.741242	+	0.671238i	$0.765763\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−94.0374	+	19.9883i	−3.29399	+	0.700159i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	22.3180	+	24.7867i	0.779380	+	0.865589i
$821$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$821$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$822$		0			0
$823$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$823$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$824$	50.9041	+	22.6640i	1.77333	+	0.789537i
$825$		0			0
$826$	12.6893	−	14.0928i	0.441516	−	0.490353i
$827$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$827$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$828$		0			0
$829$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$829$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	5.62376			0.194270
$839$	−12.9443	−	9.40456i	−0.446886	−	0.324682i	0.341479	−	0.939889i	$-0.389072\pi$
$839$	−12.9443	−	9.40456i	−0.446886	−	0.324682i	−0.788365	+	0.615208i	$0.789072\pi$
$840$		0			0
$841$	−8.96149	−	27.5806i	−0.309017	−	0.951057i
$842$	12.0641	+	20.8957i	0.415757	+	0.720113i
$843$		0			0
$844$	−79.9138	−	16.9862i	−2.75075	−	0.584689i
$845$	−15.8198	+	48.6884i	−0.544219	+	1.67493i
$846$	−55.4368	+	11.7834i	−1.90596	+	0.405123i
$847$	−0.902527	+	8.58697i	−0.0310112	+	0.295052i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	43.6869	−	31.7404i	1.49581	−	1.08677i	0.523799	−	0.851842i	$-0.324514\pi$
$853$	43.6869	−	31.7404i	1.49581	−	1.08677i	0.972013	−	0.234929i	$-0.0754857\pi$
$854$		0			0
$855$	−93.4744	−	41.6175i	−3.19676	−	1.42329i
$856$	−18.7780	+	8.36051i	−0.641819	+	0.285756i
$857$	25.4270	−	28.2395i	0.868569	−	0.964643i	−0.131074	−	0.991373i	$-0.541843\pi$
$857$	25.4270	−	28.2395i	0.868569	−	0.964643i	0.999643	+	0.0267295i	$0.00850928\pi$
$858$		0			0
$859$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$859$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$860$		0			0
$861$		0			0
$862$	47.2294	−	81.8037i	1.60864	−	2.78624i
$863$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$863$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$864$		0			0
$865$	−5.76287	−	54.8300i	−0.195943	−	1.86428i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−17.2036	−	52.9471i	−0.582586	−	1.79301i
$873$	15.3662	+	26.6151i	0.520068	+	0.900783i
$874$		0			0
$875$	16.6532	+	3.53974i	0.562981	+	0.119665i
$876$		0			0
$877$	−56.2176	+	11.9494i	−1.89833	+	0.403503i	−0.999402	−	0.0345867i	$-0.988989\pi$
$877$	−56.2176	+	11.9494i	−1.89833	+	0.403503i	−0.898931	+	0.438090i	$0.855655\pi$
$878$	−9.13275	+	86.8923i	−0.308215	+	2.93247i
$879$		0			0
$880$		0			0
$881$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$881$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$882$	−30.2621	−	33.6095i	−1.01898	−	1.13169i
$883$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$883$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$884$		0			0
$885$		0			0
$886$	90.0349	+	40.0861i	3.02478	+	1.34672i
$887$	−23.7609	+	10.5790i	−0.797811	+	0.355208i	−0.764817	−	0.644247i	$-0.777171\pi$
$887$	−23.7609	+	10.5790i	−0.797811	+	0.355208i	−0.0329939	+	0.999456i	$0.510504\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−34.6438	+	60.0048i	−1.15931	+	2.00798i
$894$		0			0
$895$		0			0
$896$	1.68447	+	16.0266i	0.0562741	+	0.535412i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−112.745			−3.75818
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−39.5746	−	68.5452i	−1.31623	−	2.27978i
$905$		0			0
$906$		0			0
$907$	14.8372	−	45.6643i	0.492662	−	1.51626i	−0.327906	−	0.944710i	$-0.606343\pi$
$907$	14.8372	−	45.6643i	0.492662	−	1.51626i	0.820568	−	0.571549i	$-0.193657\pi$
$908$	−97.9546	+	20.8209i	−3.25074	+	0.690966i
$909$	2.21948	−	21.1169i	0.0736154	−	0.700403i
$910$		0			0
$911$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$911$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−14.3415	−	6.38523i	−0.473597	−	0.210859i
$918$		0			0
$919$	−16.0591	+	17.8355i	−0.529742	+	0.588338i	−0.947314	−	0.320306i	$-0.896214\pi$
$919$	−16.0591	+	17.8355i	−0.529742	+	0.588338i	0.417572	+	0.908644i	$0.362881\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−4.69346	−	44.6553i	−0.154153	−	1.46667i
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$		0			0
$931$	−55.2904			−1.81207
$932$	25.0217	+	18.1793i	0.819612	+	0.595483i
$933$		0			0
$934$	29.3097	+	90.2061i	0.959044	+	2.95163i
$935$		0			0
$936$		0			0
$937$	41.0822	+	8.73229i	1.34210	+	0.285272i	0.822317	−	0.569029i	$-0.192681\pi$
$937$	41.0822	+	8.73229i	1.34210	+	0.285272i	0.519779	+	0.854300i	$0.326014\pi$
$938$	−6.87352	+	21.1545i	−0.224428	+	0.690719i
$939$		0			0
$940$	−11.7778	+	112.058i	−0.384149	+	3.65493i
$941$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$941$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$942$		0			0
$943$		0			0
$944$	11.2170	+	12.4577i	0.365081	+	0.405464i
$945$		0			0
$946$		0			0
$947$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$947$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$948$		0			0
$949$		0			0
$950$	−143.805	+	159.711i	−4.66564	+	5.18172i
$951$		0			0
$952$		0			0
$953$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$953$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$954$		0			0
$955$	26.3791	−	45.6900i	0.853609	−	1.47849i
$956$		0			0
$957$		0			0
$958$	−7.19522	−	68.4579i	−0.232467	−	2.21177i
$959$		0			0
$960$		0			0
$961$		0			0
$962$		0			0
$963$	13.4002	+	9.73585i	0.431817	+	0.313733i
$964$		0			0
$965$	−22.0506	−	67.8647i	−0.709834	−	2.18464i
$966$		0			0
$967$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$967$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$968$	−40.0574	−	8.51446i	−1.28749	−	0.273665i
$969$		0			0
$970$	93.1833	−	19.8067i	2.99194	−	0.635956i
$971$	−2.92680	+	27.8466i	−0.0939254	+	0.893640i	0.841534	+	0.540205i	$0.181653\pi$
$971$	−2.92680	+	27.8466i	−0.0939254	+	0.893640i	−0.935459	+	0.353435i	$0.885013\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−40.1468	+	29.1684i	−1.28441	+	0.933179i	−0.999677	−	0.0254283i	$-0.991905\pi$
$977$	−40.1468	+	29.1684i	−1.28441	+	0.933179i	−0.284733	+	0.958607i	$0.591905\pi$
$978$		0			0
$979$		0			0
$980$	−82.1397	+	36.5710i	−2.62386	+	1.16822i
$981$	−30.0180	+	33.3384i	−0.958402	+	1.06441i
$982$		0			0
$983$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$983$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0			−	1.00000i	$-0.5\pi$
$991$		0			0				1.00000i	$0.5\pi$
$992$		0			0
$993$		0			0
$994$	−24.7987	−	18.0173i	−0.786566	−	0.571474i
$995$		0			0
$996$		0			0
$997$	−31.1049	−	53.8753i	−0.985102	−	1.70625i	−0.641483	−	0.767137i	$-0.721680\pi$
$997$	−31.1049	−	53.8753i	−0.985102	−	1.70625i	−0.343619	−	0.939109i	$-0.611653\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.u.816.3		24
31.2	even	5	inner	961.2.g.u.846.1		24
31.3	odd	30	inner	961.2.g.u.338.3		24
31.4	even	5		961.2.c.g.439.1		6
31.5	even	3		961.2.d.m.374.3		12
31.6	odd	6	inner	961.2.g.u.732.3		24
31.7	even	15		961.2.c.g.521.1		6
31.8	even	5	inner	961.2.g.u.547.1		24
31.9	even	15		961.2.d.m.531.1		12
31.10	even	15		961.2.d.m.628.1		12
31.11	odd	30		961.2.a.g.1.1	✓	3
31.12	odd	30	inner	961.2.g.u.448.1		24
31.13	odd	30		961.2.d.m.388.3		12
31.14	even	15	inner	961.2.g.u.844.1		24
31.15	odd	10	inner	961.2.g.u.235.3		24
31.16	even	5	inner	961.2.g.u.235.3		24
31.17	odd	30	inner	961.2.g.u.844.1		24
31.18	even	15		961.2.d.m.388.3		12
31.19	even	15	inner	961.2.g.u.448.1		24
31.20	even	15		961.2.a.g.1.1	✓	3
31.21	odd	30		961.2.d.m.628.1		12
31.22	odd	30		961.2.d.m.531.1		12
31.23	odd	10	inner	961.2.g.u.547.1		24
31.24	odd	30		961.2.c.g.521.1		6
31.25	even	3	inner	961.2.g.u.732.3		24
31.26	odd	6		961.2.d.m.374.3		12
31.27	odd	10		961.2.c.g.439.1		6
31.28	even	15	inner	961.2.g.u.338.3		24
31.29	odd	10	inner	961.2.g.u.846.1		24
31.30	odd	2	CM	961.2.g.u.816.3		24
93.11	even	30		8649.2.a.q.1.3		3
93.20	odd	30		8649.2.a.q.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.g.1.1	✓	3	31.11	odd	30
961.2.a.g.1.1	✓	3	31.20	even	15
961.2.c.g.439.1		6	31.4	even	5
961.2.c.g.439.1		6	31.27	odd	10
961.2.c.g.521.1		6	31.7	even	15
961.2.c.g.521.1		6	31.24	odd	30
961.2.d.m.374.3		12	31.5	even	3
961.2.d.m.374.3		12	31.26	odd	6
961.2.d.m.388.3		12	31.13	odd	30
961.2.d.m.388.3		12	31.18	even	15
961.2.d.m.531.1		12	31.9	even	15
961.2.d.m.531.1		12	31.22	odd	30
961.2.d.m.628.1		12	31.10	even	15
961.2.d.m.628.1		12	31.21	odd	30
961.2.g.u.235.3		24	31.15	odd	10	inner
961.2.g.u.235.3		24	31.16	even	5	inner
961.2.g.u.338.3		24	31.3	odd	30	inner
961.2.g.u.338.3		24	31.28	even	15	inner
961.2.g.u.448.1		24	31.12	odd	30	inner
961.2.g.u.448.1		24	31.19	even	15	inner
961.2.g.u.547.1		24	31.8	even	5	inner
961.2.g.u.547.1		24	31.23	odd	10	inner
961.2.g.u.732.3		24	31.6	odd	6	inner
961.2.g.u.732.3		24	31.25	even	3	inner
961.2.g.u.816.3		24	1.1	even	1	trivial
961.2.g.u.816.3		24	31.30	odd	2	CM
961.2.g.u.844.1		24	31.14	even	15	inner
961.2.g.u.844.1		24	31.17	odd	30	inner
961.2.g.u.846.1		24	31.2	even	5	inner
961.2.g.u.846.1		24	31.29	odd	10	inner
8649.2.a.q.1.3		3	93.11	even	30
8649.2.a.q.1.3		3	93.20	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.91047 + 1.38804i) q^{2} +(1.10521 + 3.40149i) q^{4} +(-1.96900 - 3.41041i) q^{5} +(0.767781 + 0.163197i) q^{7} +(-1.15045 + 3.54072i) q^{8} +(2.93444 - 0.623735i) q^{9} +(0.972060 - 9.24853i) q^{10} +(1.24030 + 1.37749i) q^{14} +(-1.32560 + 0.963104i) q^{16} +(6.47193 + 2.88149i) q^{18} +(7.91216 - 3.52272i) q^{19} +(9.42431 - 10.4668i) q^{20} +(-5.25394 + 9.10008i) q^{25} +(0.293447 + 2.79196i) q^{28} +3.57653 q^{32} +(-0.955194 - 2.93979i) q^{35} +(5.36480 + 9.29211i) q^{36} +(20.0056 + 4.25232i) q^{38} +(14.3406 - 3.04818i) q^{40} +(-0.247538 + 2.35516i) q^{41} +(-7.90512 - 8.77952i) q^{45} +(-6.47214 + 4.70228i) q^{47} +(-5.83196 - 2.59656i) q^{49} +(-22.6687 + 10.0928i) q^{50} +(-1.46113 + 2.53075i) q^{56} +(-1.06941 - 10.1748i) q^{59} +2.35480 q^{63} +(9.48406 + 6.89057i) q^{64} +(6.00000 + 10.3923i) q^{67} +(2.25566 - 6.94221i) q^{70} +(-16.1756 + 3.43822i) q^{71} +(-1.16746 + 11.1076i) q^{72} +(20.7271 + 23.0198i) q^{76} +(5.89469 + 2.62449i) q^{80} +(8.22191 - 3.66063i) q^{81} +(-3.74196 + 4.15587i) q^{82} +(-2.91618 - 27.7456i) q^{90} -18.8918 q^{94} +(-27.5930 - 20.0475i) q^{95} +(3.16561 + 9.74276i) q^{97} +(-7.53766 - 13.0556i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 6 q^{8} - 9 q^{9} - 9 q^{10} + 15 q^{14} - 24 q^{16} + 21 q^{20} - 60 q^{25} + 27 q^{28} + 48 q^{32} - 24 q^{35} + 72 q^{36} - 33 q^{38} - 18 q^{40} - 48 q^{47} + 21 q^{49} - 39 q^{50}+ \cdots - 228 q^{98}+O(q^{100}) \) 24 * q - 12 * q^4 - 6 * q^8 - 9 * q^9 - 9 * q^10 + 15 * q^14 - 24 * q^16 + 21 * q^20 - 60 * q^25 + 27 * q^28 + 48 * q^32 - 24 * q^35 + 72 * q^36 - 33 * q^38 - 18 * q^40 - 48 * q^47 + 21 * q^49 - 39 * q^50 - 120 * q^56 + 42 * q^64 + 144 * q^67 - 6 * q^70 - 9 * q^72 + 15 * q^76 - 9 * q^80 + 27 * q^81 + 21 * q^82 + 27 * q^90 - 96 * q^95 - 228 * q^98

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