LMFDB - Embedded newform 2070.2.d.e.829.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(829,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, 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("2070.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.d (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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 690)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			829.6
Root			$0.403032 + 0.403032i$ of defining polynomial
Character	$\chi$	$=$	2070.829
Dual form			2070.2.d.e.829.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(1.67513 + 1.48119i) q^{5} +2.96239i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.67513 + 1.48119i) q^{5} +2.96239i q^{7} -1.00000i q^{8} +(-1.48119 + 1.67513i) q^{10} +3.35026 q^{11} +4.96239i q^{13} -2.96239 q^{14} +1.00000 q^{16} -1.35026i q^{17} +4.96239 q^{19} +(-1.67513 - 1.48119i) q^{20} +3.35026i q^{22} -1.00000i q^{23} +(0.612127 + 4.96239i) q^{25} -4.96239 q^{26} -2.96239i q^{28} +7.73813 q^{29} -4.00000 q^{31} +1.00000i q^{32} +1.35026 q^{34} +(-4.38787 + 4.96239i) q^{35} -7.61213i q^{37} +4.96239i q^{38} +(1.48119 - 1.67513i) q^{40} -4.70052 q^{41} +10.3127i q^{43} -3.35026 q^{44} +1.00000 q^{46} -3.22425i q^{47} -1.77575 q^{49} +(-4.96239 + 0.612127i) q^{50} -4.96239i q^{52} -6.96239i q^{53} +(5.61213 + 4.96239i) q^{55} +2.96239 q^{56} +7.73813i q^{58} +1.22425 q^{59} -11.0884 q^{61} -4.00000i q^{62} -1.00000 q^{64} +(-7.35026 + 8.31265i) q^{65} -7.61213i q^{67} +1.35026i q^{68} +(-4.96239 - 4.38787i) q^{70} +2.18664 q^{71} +9.92478i q^{73} +7.61213 q^{74} -4.96239 q^{76} +9.92478i q^{77} +4.12601 q^{79} +(1.67513 + 1.48119i) q^{80} -4.70052i q^{82} -6.38787i q^{83} +(2.00000 - 2.26187i) q^{85} -10.3127 q^{86} -3.35026i q^{88} +9.92478 q^{89} -14.7005 q^{91} +1.00000i q^{92} +3.22425 q^{94} +(8.31265 + 7.35026i) q^{95} +12.8872i q^{97} -1.77575i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4}+O(q^{10}) $ 6 * q - 6 * q^4	$ 6 q - 6 q^{4} + 2 q^{10} + 4 q^{14} + 6 q^{16} + 8 q^{19} + 2 q^{25} - 8 q^{26} + 28 q^{29} - 24 q^{31} - 12 q^{34} - 28 q^{35} - 2 q^{40} + 12 q^{41} + 6 q^{46} - 14 q^{49} - 8 q^{50} + 32 q^{55} - 4 q^{56} + 4 q^{59} - 28 q^{61} - 6 q^{64} - 24 q^{65} - 8 q^{70} - 12 q^{71} + 44 q^{74} - 8 q^{76} + 8 q^{79} + 12 q^{85} - 20 q^{86} + 16 q^{89} - 48 q^{91} + 16 q^{94} + 8 q^{95}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^10 + 4 * q^14 + 6 * q^16 + 8 * q^19 + 2 * q^25 - 8 * q^26 + 28 * q^29 - 24 * q^31 - 12 * q^34 - 28 * q^35 - 2 * q^40 + 12 * q^41 + 6 * q^46 - 14 * q^49 - 8 * q^50 + 32 * q^55 - 4 * q^56 + 4 * q^59 - 28 * q^61 - 6 * q^64 - 24 * q^65 - 8 * q^70 - 12 * q^71 + 44 * q^74 - 8 * q^76 + 8 * q^79 + 12 * q^85 - 20 * q^86 + 16 * q^89 - 48 * q^91 + 16 * q^94 + 8 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.67513	+	1.48119i	0.749141	+	0.662410i
$5$	1.67513	+	1.48119i	0.749141	+	0.662410i
$6$		0			0
$7$			2.96239i			1.11968i	0.828602	+	0.559839i	$0.189137\pi$
$7$			2.96239i			1.11968i	−0.828602	+	0.559839i	$0.810863\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.48119	+	1.67513i	−0.468395	+	0.529723i
$11$	3.35026			1.01014			0.505071	−	0.863078i	$-0.331466\pi$
$11$	3.35026			1.01014			0.505071	+	0.863078i	$0.331466\pi$
$12$		0			0
$13$			4.96239i			1.37632i	0.725559	+	0.688159i	$0.241581\pi$
$13$			4.96239i			1.37632i	−0.725559	+	0.688159i	$0.758419\pi$
$14$	−2.96239			−0.791732
$15$		0			0
$16$	1.00000			0.250000
$17$		−	1.35026i		−	0.327487i	−0.986503	−	0.163743i	$-0.947643\pi$
$17$		−	1.35026i		−	0.327487i	0.986503	−	0.163743i	$-0.0523569\pi$
$18$		0			0
$19$	4.96239			1.13845			0.569225	−	0.822182i	$-0.307243\pi$
$19$	4.96239			1.13845			0.569225	+	0.822182i	$0.307243\pi$
$20$	−1.67513	−	1.48119i	−0.374571	−	0.331205i
$21$		0			0
$22$			3.35026i			0.714278i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$		0			0
$25$	0.612127	+	4.96239i	0.122425	+	0.992478i
$26$	−4.96239			−0.973204
$27$		0			0
$28$		−	2.96239i		−	0.559839i
$29$	7.73813			1.43694			0.718468	−	0.695560i	$-0.244844\pi$
$29$	7.73813			1.43694			0.718468	+	0.695560i	$0.244844\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	1.35026			0.231568
$35$	−4.38787	+	4.96239i	−0.741686	+	0.838797i
$36$		0			0
$37$		−	7.61213i		−	1.25143i	−0.780053	−	0.625713i	$-0.784808\pi$
$37$		−	7.61213i		−	1.25143i	0.780053	−	0.625713i	$-0.215192\pi$
$38$			4.96239i			0.805006i
$39$		0			0
$40$	1.48119	−	1.67513i	0.234197	−	0.264861i
$41$	−4.70052			−0.734098			−0.367049	−	0.930202i	$-0.619632\pi$
$41$	−4.70052			−0.734098			−0.367049	+	0.930202i	$0.619632\pi$
$42$		0			0
$43$			10.3127i			1.57266i	0.617804	+	0.786332i	$0.288023\pi$
$43$			10.3127i			1.57266i	−0.617804	+	0.786332i	$0.711977\pi$
$44$	−3.35026			−0.505071
$45$		0			0
$46$	1.00000			0.147442
$47$		−	3.22425i		−	0.470306i	−0.971958	−	0.235153i	$-0.924441\pi$
$47$		−	3.22425i		−	0.470306i	0.971958	−	0.235153i	$-0.0755591\pi$
$48$		0			0
$49$	−1.77575			−0.253678
$50$	−4.96239	+	0.612127i	−0.701788	+	0.0865678i
$51$		0			0
$52$		−	4.96239i		−	0.688159i
$53$		−	6.96239i		−	0.956358i	−0.878263	−	0.478179i	$-0.841297\pi$
$53$		−	6.96239i		−	0.956358i	0.878263	−	0.478179i	$-0.158703\pi$
$54$		0			0
$55$	5.61213	+	4.96239i	0.756739	+	0.669128i
$56$	2.96239			0.395866
$57$		0			0
$58$			7.73813i			1.01607i
$59$	1.22425			0.159384			0.0796921	−	0.996820i	$-0.474606\pi$
$59$	1.22425			0.159384			0.0796921	+	0.996820i	$0.474606\pi$
$60$		0			0
$61$	−11.0884			−1.41972			−0.709862	−	0.704341i	$-0.751243\pi$
$61$	−11.0884			−1.41972			−0.709862	+	0.704341i	$0.751243\pi$
$62$		−	4.00000i		−	0.508001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−7.35026	+	8.31265i	−0.911688	+	1.03106i
$66$		0			0
$67$		−	7.61213i		−	0.929969i	−0.885319	−	0.464985i	$-0.846060\pi$
$67$		−	7.61213i		−	0.929969i	0.885319	−	0.464985i	$-0.153940\pi$
$68$			1.35026i			0.163743i
$69$		0			0
$70$	−4.96239	−	4.38787i	−0.593119	−	0.524451i
$71$	2.18664			0.259507			0.129753	−	0.991546i	$-0.458581\pi$
$71$	2.18664			0.259507			0.129753	+	0.991546i	$0.458581\pi$
$72$		0			0
$73$			9.92478i			1.16161i	0.814044	+	0.580804i	$0.197262\pi$
$73$			9.92478i			1.16161i	−0.814044	+	0.580804i	$0.802738\pi$
$74$	7.61213			0.884892
$75$		0			0
$76$	−4.96239			−0.569225
$77$			9.92478i			1.13103i
$78$		0			0
$79$	4.12601			0.464212			0.232106	−	0.972690i	$-0.425438\pi$
$79$	4.12601			0.464212			0.232106	+	0.972690i	$0.425438\pi$
$80$	1.67513	+	1.48119i	0.187285	+	0.165603i
$81$		0			0
$82$		−	4.70052i		−	0.519086i
$83$		−	6.38787i		−	0.701160i	−0.936533	−	0.350580i	$-0.885984\pi$
$83$		−	6.38787i		−	0.701160i	0.936533	−	0.350580i	$-0.114016\pi$
$84$		0			0
$85$	2.00000	−	2.26187i	0.216930	−	0.245334i
$86$	−10.3127			−1.11204
$87$		0			0
$88$		−	3.35026i		−	0.357139i
$89$	9.92478			1.05202			0.526012	−	0.850477i	$-0.323687\pi$
$89$	9.92478			1.05202			0.526012	+	0.850477i	$0.323687\pi$
$90$		0			0
$91$	−14.7005			−1.54103
$92$			1.00000i			0.104257i
$93$		0			0
$94$	3.22425			0.332556
$95$	8.31265	+	7.35026i	0.852860	+	0.754121i
$96$		0			0
$97$			12.8872i			1.30849i	0.756281	+	0.654247i	$0.227014\pi$
$97$			12.8872i			1.30849i	−0.756281	+	0.654247i	$0.772986\pi$
$98$		−	1.77575i		−	0.179377i
$99$		0			0
$100$	−0.612127	−	4.96239i	−0.0612127	−	0.496239i
$101$	−4.26187			−0.424071			−0.212036	−	0.977262i	$-0.568009\pi$
$101$	−4.26187			−0.424071			−0.212036	+	0.977262i	$0.568009\pi$
$102$		0			0
$103$			0.261865i			0.0258023i	0.999917	+	0.0129012i	$0.00410668\pi$
$103$			0.261865i			0.0258023i	−0.999917	+	0.0129012i	$0.995893\pi$
$104$	4.96239			0.486602
$105$		0			0
$106$	6.96239			0.676247
$107$			9.08840i			0.878608i	0.898338	+	0.439304i	$0.144775\pi$
$107$			9.08840i			0.878608i	−0.898338	+	0.439304i	$0.855225\pi$
$108$		0			0
$109$	−18.9380			−1.81393			−0.906963	−	0.421210i	$-0.861606\pi$
$109$	−18.9380			−1.81393			−0.906963	+	0.421210i	$0.861606\pi$
$110$	−4.96239	+	5.61213i	−0.473145	+	0.535095i
$111$		0			0
$112$			2.96239i			0.279919i
$113$		−	6.64974i		−	0.625555i	−0.949826	−	0.312777i	$-0.898741\pi$
$113$		−	6.64974i		−	0.625555i	0.949826	−	0.312777i	$-0.101259\pi$
$114$		0			0
$115$	1.48119	−	1.67513i	0.138122	−	0.156207i
$116$	−7.73813			−0.718468
$117$		0			0
$118$			1.22425i			0.112702i
$119$	4.00000			0.366679
$120$		0			0
$121$	0.224254			0.0203867
$122$		−	11.0884i		−	1.00390i
$123$		0			0
$124$	4.00000			0.359211
$125$	−6.32487	+	9.21933i	−0.565713	+	0.824602i
$126$		0			0
$127$			0.186642i			0.0165618i	0.999966	+	0.00828091i	$0.00263593\pi$
$127$			0.186642i			0.0165618i	−0.999966	+	0.00828091i	$0.997364\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−8.31265	−	7.35026i	−0.729068	−	0.644661i
$131$	−7.92478			−0.692391			−0.346196	−	0.938162i	$-0.612527\pi$
$131$	−7.92478			−0.692391			−0.346196	+	0.938162i	$0.612527\pi$
$132$		0			0
$133$			14.7005i			1.27470i
$134$	7.61213			0.657588
$135$		0			0
$136$	−1.35026			−0.115784
$137$		−	9.19982i		−	0.785993i	−0.919540	−	0.392997i	$-0.871438\pi$
$137$		−	9.19982i		−	0.785993i	0.919540	−	0.392997i	$-0.128562\pi$
$138$		0			0
$139$	−8.62530			−0.731588			−0.365794	−	0.930696i	$-0.619203\pi$
$139$	−8.62530			−0.731588			−0.365794	+	0.930696i	$0.619203\pi$
$140$	4.38787	−	4.96239i	0.370843	−	0.419398i
$141$		0			0
$142$			2.18664i			0.183499i
$143$			16.6253i			1.39028i
$144$		0			0
$145$	12.9624	+	11.4617i	1.07647	+	0.951841i
$146$	−9.92478			−0.821380
$147$		0			0
$148$			7.61213i			0.625713i
$149$	4.64974			0.380921			0.190461	−	0.981695i	$-0.439002\pi$
$149$	4.64974			0.380921			0.190461	+	0.981695i	$0.439002\pi$
$150$		0			0
$151$	10.7005			0.870796			0.435398	−	0.900238i	$-0.356608\pi$
$151$	10.7005			0.870796			0.435398	+	0.900238i	$0.356608\pi$
$152$		−	4.96239i		−	0.402503i
$153$		0			0
$154$	−9.92478			−0.799761
$155$	−6.70052	−	5.92478i	−0.538199	−	0.475890i
$156$		0			0
$157$		−	17.0132i		−	1.35780i	−0.734231	−	0.678900i	$-0.762457\pi$
$157$		−	17.0132i		−	1.35780i	0.734231	−	0.678900i	$-0.237543\pi$
$158$			4.12601i			0.328248i
$159$		0			0
$160$	−1.48119	+	1.67513i	−0.117099	+	0.132431i
$161$	2.96239			0.233469
$162$		0			0
$163$		−	12.6253i		−	0.988890i	−0.869209	−	0.494445i	$-0.835371\pi$
$163$		−	12.6253i		−	0.988890i	0.869209	−	0.494445i	$-0.164629\pi$
$164$	4.70052			0.367049
$165$		0			0
$166$	6.38787			0.495795
$167$			24.6253i			1.90556i	0.303657	+	0.952781i	$0.401792\pi$
$167$			24.6253i			1.90556i	−0.303657	+	0.952781i	$0.598208\pi$
$168$		0			0
$169$	−11.6253			−0.894254
$170$	2.26187	+	2.00000i	0.173477	+	0.153393i
$171$		0			0
$172$		−	10.3127i		−	0.786332i
$173$		−	4.44851i		−	0.338214i	−0.985598	−	0.169107i	$-0.945912\pi$
$173$		−	4.44851i		−	0.338214i	0.985598	−	0.169107i	$-0.0540883\pi$
$174$		0			0
$175$	−14.7005	+	1.81336i	−1.11126	+	0.137077i
$176$	3.35026			0.252535
$177$		0			0
$178$			9.92478i			0.743894i
$179$	−13.8496			−1.03516			−0.517582	−	0.855634i	$-0.673168\pi$
$179$	−13.8496			−1.03516			−0.517582	+	0.855634i	$0.673168\pi$
$180$		0			0
$181$	−22.6859			−1.68623			−0.843116	−	0.537732i	$-0.819281\pi$
$181$	−22.6859			−1.68623			−0.843116	+	0.537732i	$0.819281\pi$
$182$		−	14.7005i		−	1.08968i
$183$		0			0
$184$	−1.00000			−0.0737210
$185$	11.2750	−	12.7513i	0.828957	−	0.937495i
$186$		0			0
$187$		−	4.52373i		−	0.330808i
$188$			3.22425i			0.235153i
$189$		0			0
$190$	−7.35026	+	8.31265i	−0.533244	+	0.603063i
$191$	19.3258			1.39837			0.699184	−	0.714942i	$-0.253547\pi$
$191$	19.3258			1.39837			0.699184	+	0.714942i	$0.253547\pi$
$192$		0			0
$193$			5.92478i			0.426475i	0.977000	+	0.213237i	$0.0684008\pi$
$193$			5.92478i			0.426475i	−0.977000	+	0.213237i	$0.931599\pi$
$194$	−12.8872			−0.925245
$195$		0			0
$196$	1.77575			0.126839
$197$		−	8.07522i		−	0.575336i	−0.957730	−	0.287668i	$-0.907120\pi$
$197$		−	8.07522i		−	0.575336i	0.957730	−	0.287668i	$-0.0928799\pi$
$198$		0			0
$199$	−15.9756			−1.13248			−0.566239	−	0.824241i	$-0.691602\pi$
$199$	−15.9756			−1.13248			−0.566239	+	0.824241i	$0.691602\pi$
$200$	4.96239	−	0.612127i	0.350894	−	0.0432839i
$201$		0			0
$202$		−	4.26187i		−	0.299864i
$203$			22.9234i			1.60890i
$204$		0			0
$205$	−7.87399	−	6.96239i	−0.549943	−	0.486274i
$206$	−0.261865			−0.0182450
$207$		0			0
$208$			4.96239i			0.344080i
$209$	16.6253			1.15000
$210$		0			0
$211$	21.7743			1.49901			0.749503	−	0.662000i	$-0.230292\pi$
$211$	21.7743			1.49901			0.749503	+	0.662000i	$0.230292\pi$
$212$			6.96239i			0.478179i
$213$		0			0
$214$	−9.08840			−0.621270
$215$	−15.2750	+	17.2750i	−1.04175	+	1.17815i
$216$		0			0
$217$		−	11.8496i		−	0.804400i
$218$		−	18.9380i		−	1.28264i
$219$		0			0
$220$	−5.61213	−	4.96239i	−0.378370	−	0.334564i
$221$	6.70052			0.450726
$222$		0			0
$223$			3.81336i			0.255361i	0.991815	+	0.127681i	$0.0407533\pi$
$223$			3.81336i			0.255361i	−0.991815	+	0.127681i	$0.959247\pi$
$224$	−2.96239			−0.197933
$225$		0			0
$226$	6.64974			0.442334
$227$			16.9380i			1.12421i	0.827065	+	0.562106i	$0.190009\pi$
$227$			16.9380i			1.12421i	−0.827065	+	0.562106i	$0.809991\pi$
$228$		0			0
$229$	26.9380			1.78011			0.890055	−	0.455853i	$-0.150666\pi$
$229$	26.9380			1.78011			0.890055	+	0.455853i	$0.150666\pi$
$230$	1.67513	+	1.48119i	0.110455	+	0.0976671i
$231$		0			0
$232$		−	7.73813i		−	0.508033i
$233$		−	27.4010i		−	1.79510i	−0.440910	−	0.897551i	$-0.645344\pi$
$233$		−	27.4010i		−	1.79510i	0.440910	−	0.897551i	$-0.354656\pi$
$234$		0			0
$235$	4.77575	−	5.40105i	0.311535	−	0.352325i
$236$	−1.22425			−0.0796921
$237$		0			0
$238$			4.00000i			0.259281i
$239$	7.48612			0.484237			0.242118	−	0.970247i	$-0.422158\pi$
$239$	7.48612			0.484237			0.242118	+	0.970247i	$0.422158\pi$
$240$		0			0
$241$	−13.0738			−0.842158			−0.421079	−	0.907024i	$-0.638348\pi$
$241$	−13.0738			−0.842158			−0.421079	+	0.907024i	$0.638348\pi$
$242$			0.224254i			0.0144156i
$243$		0			0
$244$	11.0884			0.709862
$245$	−2.97461	−	2.63023i	−0.190041	−	0.168039i
$246$		0			0
$247$			24.6253i			1.56687i
$248$			4.00000i			0.254000i
$249$		0			0
$250$	−9.21933	−	6.32487i	−0.583082	−	0.400020i
$251$	5.02302			0.317050			0.158525	−	0.987355i	$-0.449326\pi$
$251$	5.02302			0.317050			0.158525	+	0.987355i	$0.449326\pi$
$252$		0			0
$253$		−	3.35026i		−	0.210629i
$254$	−0.186642			−0.0117110
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	19.4010i		−	1.21020i	−0.796148	−	0.605102i	$-0.793132\pi$
$257$		−	19.4010i		−	1.21020i	0.796148	−	0.605102i	$-0.206868\pi$
$258$		0			0
$259$	22.5501			1.40119
$260$	7.35026	−	8.31265i	0.455844	−	0.515529i
$261$		0			0
$262$		−	7.92478i		−	0.489594i
$263$			15.4763i			0.954308i	0.878820	+	0.477154i	$0.158332\pi$
$263$			15.4763i			0.954308i	−0.878820	+	0.477154i	$0.841668\pi$
$264$		0			0
$265$	10.3127	−	11.6629i	0.633501	−	0.716447i
$266$	−14.7005			−0.901347
$267$		0			0
$268$			7.61213i			0.464985i
$269$	−20.2130			−1.23241			−0.616204	−	0.787587i	$-0.711330\pi$
$269$	−20.2130			−1.23241			−0.616204	+	0.787587i	$0.711330\pi$
$270$		0			0
$271$	30.3996			1.84665			0.923323	−	0.384024i	$-0.125462\pi$
$271$	30.3996			1.84665			0.923323	+	0.384024i	$0.125462\pi$
$272$		−	1.35026i		−	0.0818716i
$273$		0			0
$274$	9.19982			0.555781
$275$	2.05079	+	16.6253i	0.123667	+	1.00254i
$276$		0			0
$277$			20.8119i			1.25047i	0.780437	+	0.625234i	$0.214997\pi$
$277$			20.8119i			1.25047i	−0.780437	+	0.625234i	$0.785003\pi$
$278$		−	8.62530i		−	0.517311i
$279$		0			0
$280$	4.96239	+	4.38787i	0.296559	+	0.262226i
$281$	−19.8496			−1.18413			−0.592063	−	0.805892i	$-0.701686\pi$
$281$	−19.8496			−1.18413			−0.592063	+	0.805892i	$0.701686\pi$
$282$		0			0
$283$		−	12.3879i		−	0.736383i	−0.929750	−	0.368191i	$-0.879977\pi$
$283$		−	12.3879i		−	0.736383i	0.929750	−	0.368191i	$-0.120023\pi$
$284$	−2.18664			−0.129753
$285$		0			0
$286$	−16.6253			−0.983075
$287$		−	13.9248i		−	0.821954i
$288$		0			0
$289$	15.1768			0.892753
$290$	−11.4617	+	12.9624i	−0.673053	+	0.761178i
$291$		0			0
$292$		−	9.92478i		−	0.580804i
$293$			9.03761i			0.527983i	0.964525	+	0.263991i	$0.0850391\pi$
$293$			9.03761i			0.527983i	−0.964525	+	0.263991i	$0.914961\pi$
$294$		0			0
$295$	2.05079	+	1.81336i	0.119401	+	0.105578i
$296$	−7.61213			−0.442446
$297$		0			0
$298$			4.64974i			0.269352i
$299$	4.96239			0.286982
$300$		0			0
$301$	−30.5501			−1.76088
$302$			10.7005i			0.615746i
$303$		0			0
$304$	4.96239			0.284613
$305$	−18.5745	−	16.4241i	−1.06357	−	0.940440i
$306$		0			0
$307$		−	30.5501i		−	1.74359i	−0.489875	−	0.871793i	$-0.662958\pi$
$307$		−	30.5501i		−	1.74359i	0.489875	−	0.871793i	$-0.337042\pi$
$308$		−	9.92478i		−	0.565517i
$309$		0			0
$310$	5.92478	−	6.70052i	0.336505	−	0.380564i
$311$	−14.4387			−0.818741			−0.409371	−	0.912368i	$-0.634252\pi$
$311$	−14.4387			−0.818741			−0.409371	+	0.912368i	$0.634252\pi$
$312$		0			0
$313$		−	27.9610i		−	1.58045i	−0.612818	−	0.790224i	$-0.709964\pi$
$313$		−	27.9610i		−	1.58045i	0.612818	−	0.790224i	$-0.290036\pi$
$314$	17.0132			0.960109
$315$		0			0
$316$	−4.12601			−0.232106
$317$		−	1.47627i		−	0.0829156i	−0.999140	−	0.0414578i	$-0.986800\pi$
$317$		−	1.47627i		−	0.0829156i	0.999140	−	0.0414578i	$-0.0132002\pi$
$318$		0			0
$319$	25.9248			1.45151
$320$	−1.67513	−	1.48119i	−0.0936427	−	0.0828013i
$321$		0			0
$322$			2.96239i			0.165087i
$323$		−	6.70052i		−	0.372827i
$324$		0			0
$325$	−24.6253	+	3.03761i	−1.36597	+	0.168496i
$326$	12.6253			0.699251
$327$		0			0
$328$			4.70052i			0.259543i
$329$	9.55149			0.526591
$330$		0			0
$331$	23.1754			1.27383			0.636917	−	0.770932i	$-0.280209\pi$
$331$	23.1754			1.27383			0.636917	+	0.770932i	$0.280209\pi$
$332$			6.38787i			0.350580i
$333$		0			0
$334$	−24.6253			−1.34744
$335$	11.2750	−	12.7513i	0.616021	−	0.696678i
$336$		0			0
$337$		−	21.0376i		−	1.14599i	−0.819558	−	0.572996i	$-0.805781\pi$
$337$		−	21.0376i		−	1.14599i	0.819558	−	0.572996i	$-0.194219\pi$
$338$		−	11.6253i		−	0.632333i
$339$		0			0
$340$	−2.00000	+	2.26187i	−0.108465	+	0.122667i
$341$	−13.4010			−0.725707
$342$		0			0
$343$			15.4763i			0.835640i
$344$	10.3127			0.556021
$345$		0			0
$346$	4.44851			0.239153
$347$		−	3.37470i		−	0.181163i	−0.995889	−	0.0905817i	$-0.971127\pi$
$347$		−	3.37470i		−	0.181163i	0.995889	−	0.0905817i	$-0.0288726\pi$
$348$		0			0
$349$	4.44851			0.238123			0.119062	−	0.992887i	$-0.462011\pi$
$349$	4.44851			0.238123			0.119062	+	0.992887i	$0.462011\pi$
$350$	−1.81336	−	14.7005i	−0.0969280	−	0.785776i
$351$		0			0
$352$			3.35026i			0.178570i
$353$		−	35.4010i		−	1.88421i	−0.335321	−	0.942104i	$-0.608845\pi$
$353$		−	35.4010i		−	1.88421i	0.335321	−	0.942104i	$-0.391155\pi$
$354$		0			0
$355$	3.66291	+	3.23884i	0.194407	+	0.171900i
$356$	−9.92478			−0.526012
$357$		0			0
$358$		−	13.8496i		−	0.731972i
$359$	−34.5501			−1.82348			−0.911742	−	0.410764i	$-0.865262\pi$
$359$	−34.5501			−1.82348			−0.911742	+	0.410764i	$0.865262\pi$
$360$		0			0
$361$	5.62530			0.296068
$362$		−	22.6859i		−	1.19235i
$363$		0			0
$364$	14.7005			0.770517
$365$	−14.7005	+	16.6253i	−0.769461	+	0.870208i
$366$		0			0
$367$			22.8119i			1.19077i	0.803439	+	0.595387i	$0.203001\pi$
$367$			22.8119i			1.19077i	−0.803439	+	0.595387i	$0.796999\pi$
$368$		−	1.00000i		−	0.0521286i
$369$		0			0
$370$	12.7513	+	11.2750i	0.662909	+	0.586161i
$371$	20.6253			1.07081
$372$		0			0
$373$		−	10.8364i		−	0.561087i	−0.959841	−	0.280543i	$-0.909485\pi$
$373$		−	10.8364i		−	0.561087i	0.959841	−	0.280543i	$-0.0905146\pi$
$374$	4.52373			0.233917
$375$		0			0
$376$	−3.22425			−0.166278
$377$			38.3996i			1.97768i
$378$		0			0
$379$	32.4387			1.66626			0.833131	−	0.553076i	$-0.186546\pi$
$379$	32.4387			1.66626			0.833131	+	0.553076i	$0.186546\pi$
$380$	−8.31265	−	7.35026i	−0.426430	−	0.377060i
$381$		0			0
$382$			19.3258i			0.988795i
$383$		−	32.9986i		−	1.68615i	−0.537797	−	0.843074i	$-0.680743\pi$
$383$		−	32.9986i		−	1.68615i	0.537797	−	0.843074i	$-0.319257\pi$
$384$		0			0
$385$	−14.7005	+	16.6253i	−0.749208	+	0.847304i
$386$	−5.92478			−0.301563
$387$		0			0
$388$		−	12.8872i		−	0.654247i
$389$	29.1246			1.47668			0.738338	−	0.674431i	$-0.235611\pi$
$389$	29.1246			1.47668			0.738338	+	0.674431i	$0.235611\pi$
$390$		0			0
$391$	−1.35026			−0.0682857
$392$			1.77575i			0.0896887i
$393$		0			0
$394$	8.07522			0.406824
$395$	6.91160	+	6.11142i	0.347761	+	0.307499i
$396$		0			0
$397$			13.7381i			0.689497i	0.938695	+	0.344749i	$0.112036\pi$
$397$			13.7381i			0.689497i	−0.938695	+	0.344749i	$0.887964\pi$
$398$		−	15.9756i		−	0.800783i
$399$		0			0
$400$	0.612127	+	4.96239i	0.0306063	+	0.248119i
$401$	1.44992			0.0724057			0.0362028	−	0.999344i	$-0.488474\pi$
$401$	1.44992			0.0724057			0.0362028	+	0.999344i	$0.488474\pi$
$402$		0			0
$403$		−	19.8496i		−	0.988777i
$404$	4.26187			0.212036
$405$		0			0
$406$	−22.9234			−1.13767
$407$		−	25.5026i		−	1.26412i
$408$		0			0
$409$	17.8496			0.882604			0.441302	−	0.897359i	$-0.354517\pi$
$409$	17.8496			0.882604			0.441302	+	0.897359i	$0.354517\pi$
$410$	6.96239	−	7.87399i	0.343848	−	0.388869i
$411$		0			0
$412$		−	0.261865i		−	0.0129012i
$413$			3.62672i			0.178459i
$414$		0			0
$415$	9.46168	−	10.7005i	0.464456	−	0.525268i
$416$	−4.96239			−0.243301
$417$		0			0
$418$			16.6253i			0.813170i
$419$	17.9003			0.874489			0.437244	−	0.899343i	$-0.355954\pi$
$419$	17.9003			0.874489			0.437244	+	0.899343i	$0.355954\pi$
$420$		0			0
$421$	7.61213			0.370992			0.185496	−	0.982645i	$-0.440611\pi$
$421$	7.61213			0.370992			0.185496	+	0.982645i	$0.440611\pi$
$422$			21.7743i			1.05996i
$423$		0			0
$424$	−6.96239			−0.338123
$425$	6.70052	−	0.826531i	0.325023	−	0.0400927i
$426$		0			0
$427$		−	32.8481i		−	1.58963i
$428$		−	9.08840i		−	0.439304i
$429$		0			0
$430$	−17.2750	−	15.2750i	−0.833076	−	0.736628i
$431$	22.9525			1.10558			0.552792	−	0.833319i	$-0.313562\pi$
$431$	22.9525			1.10558			0.552792	+	0.833319i	$0.313562\pi$
$432$		0			0
$433$		−	33.7645i		−	1.62262i	−0.584618	−	0.811309i	$-0.698756\pi$
$433$		−	33.7645i		−	1.62262i	0.584618	−	0.811309i	$-0.301244\pi$
$434$	11.8496			0.568797
$435$		0			0
$436$	18.9380			0.906963
$437$		−	4.96239i		−	0.237383i
$438$		0			0
$439$	23.4763			1.12046			0.560231	−	0.828337i	$-0.310713\pi$
$439$	23.4763			1.12046			0.560231	+	0.828337i	$0.310713\pi$
$440$	4.96239	−	5.61213i	0.236573	−	0.267548i
$441$		0			0
$442$			6.70052i			0.318711i
$443$		−	30.5501i		−	1.45148i	−0.687970	−	0.725739i	$-0.741498\pi$
$443$		−	30.5501i		−	1.45148i	0.687970	−	0.725739i	$-0.258502\pi$
$444$		0			0
$445$	16.6253	+	14.7005i	0.788115	+	0.696872i
$446$	−3.81336			−0.180568
$447$		0			0
$448$		−	2.96239i		−	0.139960i
$449$	32.7005			1.54323			0.771617	−	0.636088i	$-0.219448\pi$
$449$	32.7005			1.54323			0.771617	+	0.636088i	$0.219448\pi$
$450$		0			0
$451$	−15.7480			−0.741544
$452$			6.64974i			0.312777i
$453$		0			0
$454$	−16.9380			−0.794937
$455$	−24.6253	−	21.7743i	−1.15445	−	1.02080i
$456$		0			0
$457$			5.81336i			0.271937i	0.990713	+	0.135969i	$0.0434147\pi$
$457$			5.81336i			0.271937i	−0.990713	+	0.135969i	$0.956585\pi$
$458$			26.9380i			1.25873i
$459$		0			0
$460$	−1.48119	+	1.67513i	−0.0690610	+	0.0781034i
$461$	23.9902			1.11733			0.558666	−	0.829392i	$-0.311313\pi$
$461$	23.9902			1.11733			0.558666	+	0.829392i	$0.311313\pi$
$462$		0			0
$463$			35.3620i			1.64341i	0.569911	+	0.821706i	$0.306978\pi$
$463$			35.3620i			1.64341i	−0.569911	+	0.821706i	$0.693022\pi$
$464$	7.73813			0.359234
$465$		0			0
$466$	27.4010			1.26933
$467$			1.98541i			0.0918739i	0.998944	+	0.0459369i	$0.0146273\pi$
$467$			1.98541i			0.0918739i	−0.998944	+	0.0459369i	$0.985373\pi$
$468$		0			0
$469$	22.5501			1.04127
$470$	5.40105	+	4.77575i	0.249132	+	0.220289i
$471$		0			0
$472$		−	1.22425i		−	0.0563508i
$473$			34.5501i			1.58861i
$474$		0			0
$475$	3.03761	+	24.6253i	0.139375	+	1.12989i
$476$	−4.00000			−0.183340
$477$		0			0
$478$			7.48612i			0.342407i
$479$	11.0738			0.505975			0.252988	−	0.967470i	$-0.418587\pi$
$479$	11.0738			0.505975			0.252988	+	0.967470i	$0.418587\pi$
$480$		0			0
$481$	37.7743			1.72236
$482$		−	13.0738i		−	0.595496i
$483$		0			0
$484$	−0.224254			−0.0101934
$485$	−19.0884	+	21.5877i	−0.866759	+	0.980246i
$486$		0			0
$487$			17.4372i			0.790157i	0.918647	+	0.395078i	$0.129283\pi$
$487$			17.4372i			0.790157i	−0.918647	+	0.395078i	$0.870717\pi$
$488$			11.0884i			0.501948i
$489$		0			0
$490$	2.63023	−	2.97461i	0.118821	−	0.134379i
$491$	−14.8773			−0.671404			−0.335702	−	0.941968i	$-0.608973\pi$
$491$	−14.8773			−0.671404			−0.335702	+	0.941968i	$0.608973\pi$
$492$		0			0
$493$		−	10.4485i		−	0.470577i
$494$	−24.6253			−1.10794
$495$		0			0
$496$	−4.00000			−0.179605
$497$			6.47768i			0.290564i
$498$		0			0
$499$	16.1016			0.720805			0.360403	−	0.932797i	$-0.382639\pi$
$499$	16.1016			0.720805			0.360403	+	0.932797i	$0.382639\pi$
$500$	6.32487	−	9.21933i	0.282857	−	0.412301i
$501$		0			0
$502$			5.02302i			0.224188i
$503$			38.8021i			1.73010i	0.501686	+	0.865050i	$0.332713\pi$
$503$			38.8021i			1.73010i	−0.501686	+	0.865050i	$0.667287\pi$
$504$		0			0
$505$	−7.13918	−	6.31265i	−0.317689	−	0.280909i
$506$	3.35026			0.148937
$507$		0			0
$508$		−	0.186642i		−	0.00828091i
$509$	23.4372			1.03884			0.519419	−	0.854520i	$-0.326148\pi$
$509$	23.4372			1.03884			0.519419	+	0.854520i	$0.326148\pi$
$510$		0			0
$511$	−29.4010			−1.30063
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	19.4010			0.855743
$515$	−0.387873	+	0.438658i	−0.0170917	+	0.0193296i
$516$		0			0
$517$		−	10.8021i		−	0.475076i
$518$			22.5501i			0.990794i
$519$		0			0
$520$	8.31265	+	7.35026i	0.364534	+	0.322330i
$521$	−21.1490			−0.926556			−0.463278	−	0.886213i	$-0.653327\pi$
$521$	−21.1490			−0.926556			−0.463278	+	0.886213i	$0.653327\pi$
$522$		0			0
$523$		−	11.7626i		−	0.514341i	−0.966366	−	0.257171i	$-0.917210\pi$
$523$		−	11.7626i		−	0.514341i	0.966366	−	0.257171i	$-0.0827903\pi$
$524$	7.92478			0.346196
$525$		0			0
$526$	−15.4763			−0.674797
$527$			5.40105i			0.235273i
$528$		0			0
$529$	−1.00000			−0.0434783
$530$	11.6629	+	10.3127i	0.506605	+	0.447953i
$531$		0			0
$532$		−	14.7005i		−	0.637349i
$533$		−	23.3258i		−	1.01035i
$534$		0			0
$535$	−13.4617	+	15.2243i	−0.581999	+	0.658202i
$536$	−7.61213			−0.328794
$537$		0			0
$538$		−	20.2130i		−	0.871444i
$539$	−5.94921			−0.256251
$540$		0			0
$541$	−21.1754			−0.910401			−0.455200	−	0.890389i	$-0.650432\pi$
$541$	−21.1754			−0.910401			−0.455200	+	0.890389i	$0.650432\pi$
$542$			30.3996i			1.30578i
$543$		0			0
$544$	1.35026			0.0578920
$545$	−31.7235	−	28.0508i	−1.35889	−	1.20156i
$546$		0			0
$547$			5.29948i			0.226589i	0.993561	+	0.113295i	$0.0361404\pi$
$547$			5.29948i			0.226589i	−0.993561	+	0.113295i	$0.963860\pi$
$548$			9.19982i			0.392997i
$549$		0			0
$550$	−16.6253	+	2.05079i	−0.708905	+	0.0874458i
$551$	38.3996			1.63588
$552$		0			0
$553$			12.2228i			0.519768i
$554$	−20.8119			−0.884215
$555$		0			0
$556$	8.62530			0.365794
$557$			7.99015i			0.338554i	0.985569	+	0.169277i	$0.0541432\pi$
$557$			7.99015i			0.338554i	−0.985569	+	0.169277i	$0.945857\pi$
$558$		0			0
$559$	−51.1754			−2.16449
$560$	−4.38787	+	4.96239i	−0.185421	+	0.209699i
$561$		0			0
$562$		−	19.8496i		−	0.837303i
$563$			15.1636i			0.639070i	0.947574	+	0.319535i	$0.103527\pi$
$563$			15.1636i			0.639070i	−0.947574	+	0.319535i	$0.896473\pi$
$564$		0			0
$565$	9.84955	−	11.1392i	0.414374	−	0.468629i
$566$	12.3879			0.520701
$567$		0			0
$568$		−	2.18664i		−	0.0917495i
$569$	−25.5223			−1.06995			−0.534976	−	0.844868i	$-0.679679\pi$
$569$	−25.5223			−1.06995			−0.534976	+	0.844868i	$0.679679\pi$
$570$		0			0
$571$	6.76590			0.283144			0.141572	−	0.989928i	$-0.454784\pi$
$571$	6.76590			0.283144			0.141572	+	0.989928i	$0.454784\pi$
$572$		−	16.6253i		−	0.695139i
$573$		0			0
$574$	13.9248			0.581209
$575$	4.96239	−	0.612127i	0.206946	−	0.0255275i
$576$		0			0
$577$			4.00000i			0.166522i	0.996528	+	0.0832611i	$0.0265335\pi$
$577$			4.00000i			0.166522i	−0.996528	+	0.0832611i	$0.973466\pi$
$578$			15.1768i			0.631271i
$579$		0			0
$580$	−12.9624	−	11.4617i	−0.538234	−	0.475920i
$581$	18.9234			0.785073
$582$		0			0
$583$		−	23.3258i		−	0.966057i
$584$	9.92478			0.410690
$585$		0			0
$586$	−9.03761			−0.373340
$587$			12.8773i			0.531504i	0.964041	+	0.265752i	$0.0856202\pi$
$587$			12.8773i			0.531504i	−0.964041	+	0.265752i	$0.914380\pi$
$588$		0			0
$589$	−19.8496			−0.817887
$590$	−1.81336	+	2.05079i	−0.0746548	+	0.0844295i
$591$		0			0
$592$		−	7.61213i		−	0.312856i
$593$			16.2981i			0.669281i	0.942346	+	0.334641i	$0.108615\pi$
$593$			16.2981i			0.669281i	−0.942346	+	0.334641i	$0.891385\pi$
$594$		0			0
$595$	6.70052	+	5.92478i	0.274695	+	0.242892i
$596$	−4.64974			−0.190461
$597$		0			0
$598$			4.96239i			0.202927i
$599$	9.91493			0.405113			0.202556	−	0.979271i	$-0.435075\pi$
$599$	9.91493			0.405113			0.202556	+	0.979271i	$0.435075\pi$
$600$		0			0
$601$	−7.40105			−0.301895			−0.150948	−	0.988542i	$-0.548232\pi$
$601$	−7.40105			−0.301895			−0.150948	+	0.988542i	$0.548232\pi$
$602$		−	30.5501i		−	1.24513i
$603$		0			0
$604$	−10.7005			−0.435398
$605$	0.375654	+	0.332163i	0.0152725	+	0.0135044i
$606$		0			0
$607$		−	13.9610i		−	0.566658i	−0.959023	−	0.283329i	$-0.908561\pi$
$607$		−	13.9610i		−	0.566658i	0.959023	−	0.283329i	$-0.0914389\pi$
$608$			4.96239i			0.201251i
$609$		0			0
$610$	16.4241	−	18.5745i	0.664991	−	0.752060i
$611$	16.0000			0.647291
$612$		0			0
$613$			41.3865i			1.67158i	0.549047	+	0.835792i	$0.314991\pi$
$613$			41.3865i			1.67158i	−0.549047	+	0.835792i	$0.685009\pi$
$614$	30.5501			1.23290
$615$		0			0
$616$	9.92478			0.399881
$617$		−	29.3014i		−	1.17963i	−0.807539	−	0.589815i	$-0.799201\pi$
$617$		−	29.3014i		−	1.17963i	0.807539	−	0.589815i	$-0.200799\pi$
$618$		0			0
$619$	19.0376			0.765186			0.382593	−	0.923917i	$-0.375031\pi$
$619$	19.0376			0.765186			0.382593	+	0.923917i	$0.375031\pi$
$620$	6.70052	+	5.92478i	0.269099	+	0.237945i
$621$		0			0
$622$		−	14.4387i		−	0.578937i
$623$			29.4010i			1.17793i
$624$		0			0
$625$	−24.2506	+	6.07522i	−0.970024	+	0.243009i
$626$	27.9610			1.11755
$627$		0			0
$628$			17.0132i			0.678900i
$629$	−10.2784			−0.409825
$630$		0			0
$631$	12.4993			0.497589			0.248794	−	0.968556i	$-0.419966\pi$
$631$	12.4993			0.497589			0.248794	+	0.968556i	$0.419966\pi$
$632$		−	4.12601i		−	0.164124i
$633$		0			0
$634$	1.47627			0.0586302
$635$	−0.276454	+	0.312650i	−0.0109707	+	0.0124072i
$636$		0			0
$637$		−	8.81194i		−	0.349142i
$638$			25.9248i			1.02637i
$639$		0			0
$640$	1.48119	−	1.67513i	0.0585493	−	0.0662154i
$641$	34.0263			1.34396			0.671980	−	0.740569i	$-0.265444\pi$
$641$	34.0263			1.34396			0.671980	+	0.740569i	$0.265444\pi$
$642$		0			0
$643$			7.34041i			0.289478i	0.989470	+	0.144739i	$0.0462342\pi$
$643$			7.34041i			0.289478i	−0.989470	+	0.144739i	$0.953766\pi$
$644$	−2.96239			−0.116734
$645$		0			0
$646$	6.70052			0.263629
$647$			14.9525i			0.587845i	0.955829	+	0.293922i	$0.0949608\pi$
$647$			14.9525i			0.587845i	−0.955829	+	0.293922i	$0.905039\pi$
$648$		0			0
$649$	4.10157			0.161001
$650$	−3.03761	−	24.6253i	−0.119145	−	0.965884i
$651$		0			0
$652$			12.6253i			0.494445i
$653$			20.4485i			0.800212i	0.916469	+	0.400106i	$0.131027\pi$
$653$			20.4485i			0.800212i	−0.916469	+	0.400106i	$0.868973\pi$
$654$		0			0
$655$	−13.2750	−	11.7381i	−0.518699	−	0.458647i
$656$	−4.70052			−0.183525
$657$		0			0
$658$			9.55149i			0.372356i
$659$	38.4241			1.49679			0.748395	−	0.663254i	$-0.230825\pi$
$659$	38.4241			1.49679			0.748395	+	0.663254i	$0.230825\pi$
$660$		0			0
$661$	−39.3112			−1.52903			−0.764515	−	0.644606i	$-0.777021\pi$
$661$	−39.3112			−1.52903			−0.764515	+	0.644606i	$0.777021\pi$
$662$			23.1754i			0.900737i
$663$		0			0
$664$	−6.38787			−0.247898
$665$	−21.7743	+	24.6253i	−0.844372	+	0.954928i
$666$		0			0
$667$		−	7.73813i		−	0.299622i
$668$		−	24.6253i		−	0.952781i
$669$		0			0
$670$	12.7513	+	11.2750i	0.492626	+	0.435593i
$671$	−37.1490			−1.43412
$672$		0			0
$673$		−	25.5515i		−	0.984938i	−0.870330	−	0.492469i	$-0.836095\pi$
$673$		−	25.5515i		−	0.984938i	0.870330	−	0.492469i	$-0.163905\pi$
$674$	21.0376			0.810339
$675$		0			0
$676$	11.6253			0.447127
$677$		−	36.2130i		−	1.39178i	−0.718149	−	0.695889i	$-0.755010\pi$
$677$		−	36.2130i		−	1.39178i	0.718149	−	0.695889i	$-0.244990\pi$
$678$		0			0
$679$	−38.1768			−1.46509
$680$	−2.26187	−	2.00000i	−0.0867386	−	0.0766965i
$681$		0			0
$682$		−	13.4010i		−	0.513153i
$683$		−	15.4763i		−	0.592183i	−0.955160	−	0.296092i	$-0.904317\pi$
$683$		−	15.4763i		−	0.592183i	0.955160	−	0.296092i	$-0.0956833\pi$
$684$		0			0
$685$	13.6267	−	15.4109i	0.520650	−	0.588820i
$686$	−15.4763			−0.590887
$687$		0			0
$688$			10.3127i			0.393166i
$689$	34.5501			1.31625
$690$		0			0
$691$	−37.6531			−1.43239			−0.716195	−	0.697900i	$-0.754118\pi$
$691$	−37.6531			−1.43239			−0.716195	+	0.697900i	$0.754118\pi$
$692$			4.44851i			0.169107i
$693$		0			0
$694$	3.37470			0.128102
$695$	−14.4485	−	12.7757i	−0.548063	−	0.484612i
$696$		0			0
$697$			6.34694i			0.240407i
$698$			4.44851i			0.168378i
$699$		0			0
$700$	14.7005	−	1.81336i	0.555628	−	0.0685385i
$701$	−28.3488			−1.07072			−0.535361	−	0.844624i	$-0.679824\pi$
$701$	−28.3488			−1.07072			−0.535361	+	0.844624i	$0.679824\pi$
$702$		0			0
$703$		−	37.7743i		−	1.42469i
$704$	−3.35026			−0.126268
$705$		0			0
$706$	35.4010			1.33234
$707$		−	12.6253i		−	0.474823i
$708$		0			0
$709$	43.5633			1.63605			0.818026	−	0.575181i	$-0.195068\pi$
$709$	43.5633			1.63605			0.818026	+	0.575181i	$0.195068\pi$
$710$	−3.23884	+	3.66291i	−0.121552	+	0.137467i
$711$		0			0
$712$		−	9.92478i		−	0.371947i
$713$			4.00000i			0.149801i
$714$		0			0
$715$	−24.6253	+	27.8496i	−0.920934	+	1.04151i
$716$	13.8496			0.517582
$717$		0			0
$718$		−	34.5501i		−	1.28940i
$719$	32.3634			1.20695			0.603476	−	0.797381i	$-0.293782\pi$
$719$	32.3634			1.20695			0.603476	+	0.797381i	$0.293782\pi$
$720$		0			0
$721$	−0.775746			−0.0288903
$722$			5.62530i			0.209352i
$723$		0			0
$724$	22.6859			0.843116
$725$	4.73672	+	38.3996i	0.175917	+	1.42613i
$726$		0			0
$727$		−	6.96239i		−	0.258221i	−0.991630	−	0.129110i	$-0.958788\pi$
$727$		−	6.96239i		−	0.258221i	0.991630	−	0.129110i	$-0.0412121\pi$
$728$			14.7005i			0.544838i
$729$		0			0
$730$	−16.6253	−	14.7005i	−0.615330	−	0.544091i
$731$	13.9248			0.515026
$732$		0			0
$733$		−	9.68735i		−	0.357810i	−0.983866	−	0.178905i	$-0.942744\pi$
$733$		−	9.68735i		−	0.357810i	0.983866	−	0.178905i	$-0.0572555\pi$
$734$	−22.8119			−0.842004
$735$		0			0
$736$	1.00000			0.0368605
$737$		−	25.5026i		−	0.939401i
$738$		0			0
$739$	42.9234			1.57896			0.789481	−	0.613775i	$-0.210350\pi$
$739$	42.9234			1.57896			0.789481	+	0.613775i	$0.210350\pi$
$740$	−11.2750	+	12.7513i	−0.414479	+	0.468747i
$741$		0			0
$742$			20.6253i			0.757179i
$743$		−	16.9986i		−	0.623618i	−0.950145	−	0.311809i	$-0.899065\pi$
$743$		−	16.9986i		−	0.623618i	0.950145	−	0.311809i	$-0.100935\pi$
$744$		0			0
$745$	7.78892	+	6.88717i	0.285364	+	0.252326i
$746$	10.8364			0.396748
$747$		0			0
$748$			4.52373i			0.165404i
$749$	−26.9234			−0.983758
$750$		0			0
$751$	−17.9003			−0.653193			−0.326596	−	0.945164i	$-0.605902\pi$
$751$	−17.9003			−0.653193			−0.326596	+	0.945164i	$0.605902\pi$
$752$		−	3.22425i		−	0.117576i
$753$		0			0
$754$	−38.3996			−1.39843
$755$	17.9248	+	15.8496i	0.652349	+	0.576824i
$756$		0			0
$757$			12.3879i			0.450245i	0.974330	+	0.225122i	$0.0722782\pi$
$757$			12.3879i			0.450245i	−0.974330	+	0.225122i	$0.927722\pi$
$758$			32.4387i			1.17823i
$759$		0			0
$760$	7.35026	−	8.31265i	0.266622	−	0.301532i
$761$	−38.5764			−1.39839			−0.699197	−	0.714929i	$-0.746459\pi$
$761$	−38.5764			−1.39839			−0.699197	+	0.714929i	$0.746459\pi$
$762$		0			0
$763$		−	56.1016i		−	2.03101i
$764$	−19.3258			−0.699184
$765$		0			0
$766$	32.9986			1.19229
$767$			6.07522i			0.219364i
$768$		0			0
$769$	−34.2228			−1.23411			−0.617054	−	0.786921i	$-0.711674\pi$
$769$	−34.2228			−1.23411			−0.617054	+	0.786921i	$0.711674\pi$
$770$	−16.6253	−	14.7005i	−0.599134	−	0.529770i
$771$		0			0
$772$		−	5.92478i		−	0.213237i
$773$		−	13.5613i		−	0.487768i	−0.969804	−	0.243884i	$-0.921578\pi$
$773$		−	13.5613i		−	0.487768i	0.969804	−	0.243884i	$-0.0784215\pi$
$774$		0			0
$775$	−2.44851	−	19.8496i	−0.0879530	−	0.713017i
$776$	12.8872			0.462622
$777$		0			0
$778$			29.1246i			1.04417i
$779$	−23.3258			−0.835734
$780$		0			0
$781$	7.32582			0.262139
$782$		−	1.35026i		−	0.0482853i
$783$		0			0
$784$	−1.77575			−0.0634195
$785$	25.1998	−	28.4993i	0.899420	−	1.01718i
$786$		0			0
$787$			37.0132i			1.31938i	0.751539	+	0.659689i	$0.229312\pi$
$787$			37.0132i			1.31938i	−0.751539	+	0.659689i	$0.770688\pi$
$788$			8.07522i			0.287668i
$789$		0			0
$790$	−6.11142	+	6.91160i	−0.217435	+	0.245904i
$791$	19.6991			0.700420
$792$		0			0
$793$		−	55.0249i		−	1.95399i
$794$	−13.7381			−0.487548
$795$		0			0
$796$	15.9756			0.566239
$797$		−	47.6893i		−	1.68924i	−0.535366	−	0.844620i	$-0.679826\pi$
$797$		−	47.6893i		−	1.68924i	0.535366	−	0.844620i	$-0.320174\pi$
$798$		0			0
$799$	−4.35359			−0.154019
$800$	−4.96239	+	0.612127i	−0.175447	+	0.0216420i
$801$		0			0
$802$			1.44992i			0.0511985i
$803$			33.2506i			1.17339i
$804$		0			0
$805$	4.96239	+	4.38787i	0.174901	+	0.154652i
$806$	19.8496			0.699171
$807$		0			0
$808$			4.26187i			0.149932i
$809$	−9.17538			−0.322589			−0.161295	−	0.986906i	$-0.551567\pi$
$809$	−9.17538			−0.322589			−0.161295	+	0.986906i	$0.551567\pi$
$810$		0			0
$811$	−38.5501			−1.35368			−0.676838	−	0.736132i	$-0.736650\pi$
$811$	−38.5501			−1.35368			−0.676838	+	0.736132i	$0.736650\pi$
$812$		−	22.9234i		−	0.804452i
$813$		0			0
$814$	25.5026			0.893866
$815$	18.7005	−	21.1490i	0.655051	−	0.740818i
$816$		0			0
$817$			51.1754i			1.79040i
$818$			17.8496i			0.624095i
$819$		0			0
$820$	7.87399	+	6.96239i	0.274972	+	0.243137i
$821$	−43.4372			−1.51597			−0.757985	−	0.652272i	$-0.773816\pi$
$821$	−43.4372			−1.51597			−0.757985	+	0.652272i	$0.773816\pi$
$822$		0			0
$823$			3.51247i			0.122437i	0.998124	+	0.0612184i	$0.0194986\pi$
$823$			3.51247i			0.122437i	−0.998124	+	0.0612184i	$0.980501\pi$
$824$	0.261865			0.00912250
$825$		0			0
$826$	−3.62672			−0.126190
$827$			9.56325i			0.332547i	0.986080	+	0.166273i	$0.0531734\pi$
$827$			9.56325i			0.332547i	−0.986080	+	0.166273i	$0.946827\pi$
$828$		0			0
$829$	−30.5764			−1.06196			−0.530982	−	0.847383i	$-0.678177\pi$
$829$	−30.5764			−1.06196			−0.530982	+	0.847383i	$0.678177\pi$
$830$	10.7005	+	9.46168i	0.371421	+	0.328420i
$831$		0			0
$832$		−	4.96239i		−	0.172040i
$833$			2.39772i			0.0830762i
$834$		0			0
$835$	−36.4749	+	41.2506i	−1.26226	+	1.42754i
$836$	−16.6253			−0.574998
$837$		0			0
$838$			17.9003i			0.618357i
$839$	22.1768			0.765628			0.382814	−	0.923825i	$-0.374955\pi$
$839$	22.1768			0.765628			0.382814	+	0.923825i	$0.374955\pi$
$840$		0			0
$841$	30.8787			1.06478
$842$			7.61213i			0.262331i
$843$		0			0
$844$	−21.7743			−0.749503
$845$	−19.4739	−	17.2193i	−0.669923	−	0.592363i
$846$		0			0
$847$			0.664327i			0.0228265i
$848$		−	6.96239i		−	0.239089i
$849$		0			0
$850$	0.826531	+	6.70052i	0.0283498	+	0.229826i
$851$	−7.61213			−0.260940
$852$		0			0
$853$		−	29.7381i		−	1.01821i	−0.860703	−	0.509107i	$-0.829976\pi$
$853$		−	29.7381i		−	1.01821i	0.860703	−	0.509107i	$-0.170024\pi$
$854$	32.8481			1.12404
$855$		0			0
$856$	9.08840			0.310635
$857$			22.2520i			0.760114i	0.924963	+	0.380057i	$0.124096\pi$
$857$			22.2520i			0.760114i	−0.924963	+	0.380057i	$0.875904\pi$
$858$		0			0
$859$	−11.0738			−0.377833			−0.188917	−	0.981993i	$-0.560498\pi$
$859$	−11.0738			−0.377833			−0.188917	+	0.981993i	$0.560498\pi$
$860$	15.2750	−	17.2750i	0.520875	−	0.589074i
$861$		0			0
$862$			22.9525i			0.781767i
$863$			22.8218i			0.776863i	0.921478	+	0.388431i	$0.126983\pi$
$863$			22.8218i			0.776863i	−0.921478	+	0.388431i	$0.873017\pi$
$864$		0			0
$865$	6.58910	−	7.45183i	0.224036	−	0.253370i
$866$	33.7645			1.14736
$867$		0			0
$868$			11.8496i			0.402200i
$869$	13.8232			0.468920
$870$		0			0
$871$	37.7743			1.27993
$872$			18.9380i			0.641320i
$873$		0			0
$874$	4.96239			0.167855
$875$	−27.3112	−	18.7367i	−0.923288	−	0.633417i
$876$		0			0
$877$			8.81194i			0.297558i	0.988870	+	0.148779i	$0.0475343\pi$
$877$			8.81194i			0.297558i	−0.988870	+	0.148779i	$0.952466\pi$
$878$			23.4763i			0.792286i
$879$		0			0
$880$	5.61213	+	4.96239i	0.189185	+	0.167282i
$881$	−21.4010			−0.721020			−0.360510	−	0.932755i	$-0.617397\pi$
$881$	−21.4010			−0.721020			−0.360510	+	0.932755i	$0.617397\pi$
$882$		0			0
$883$			6.17679i			0.207866i	0.994584	+	0.103933i	$0.0331427\pi$
$883$			6.17679i			0.207866i	−0.994584	+	0.103933i	$0.966857\pi$
$884$	−6.70052			−0.225363
$885$		0			0
$886$	30.5501			1.02635
$887$		−	35.5975i		−	1.19525i	−0.801776	−	0.597624i	$-0.796111\pi$
$887$		−	35.5975i		−	1.19525i	0.801776	−	0.597624i	$-0.203889\pi$
$888$		0			0
$889$	−0.552907			−0.0185439
$890$	−14.7005	+	16.6253i	−0.492763	+	0.557281i
$891$		0			0
$892$		−	3.81336i		−	0.127681i
$893$		−	16.0000i		−	0.535420i
$894$		0			0
$895$	−23.1998	−	20.5139i	−0.775484	−	0.685703i
$896$	2.96239			0.0989665
$897$		0			0
$898$			32.7005i			1.09123i
$899$	−30.9525			−1.03232
$900$		0			0
$901$	−9.40105			−0.313194
$902$		−	15.7480i		−	0.524351i
$903$		0			0
$904$	−6.64974			−0.221167
$905$	−38.0019	−	33.6023i	−1.26323	−	1.11698i
$906$		0			0
$907$		−	5.53690i		−	0.183850i	−0.995766	−	0.0919249i	$-0.970698\pi$
$907$		−	5.53690i		−	0.183850i	0.995766	−	0.0919249i	$-0.0293020\pi$
$908$		−	16.9380i		−	0.562106i
$909$		0			0
$910$	21.7743	−	24.6253i	0.721812	−	0.816321i
$911$	15.4763			0.512752			0.256376	−	0.966577i	$-0.417472\pi$
$911$	15.4763			0.512752			0.256376	+	0.966577i	$0.417472\pi$
$912$		0			0
$913$		−	21.4010i		−	0.708271i
$914$	−5.81336			−0.192289
$915$		0			0
$916$	−26.9380			−0.890055
$917$		−	23.4763i		−	0.775255i
$918$		0			0
$919$	5.17347			0.170657			0.0853285	−	0.996353i	$-0.472806\pi$
$919$	5.17347			0.170657			0.0853285	+	0.996353i	$0.472806\pi$
$920$	−1.67513	−	1.48119i	−0.0552274	−	0.0488335i
$921$		0			0
$922$			23.9902i			0.790074i
$923$			10.8510i			0.357164i
$924$		0			0
$925$	37.7743	−	4.65959i	1.24201	−	0.153206i
$926$	−35.3620			−1.16207
$927$		0			0
$928$			7.73813i			0.254017i
$929$	−44.3996			−1.45670			−0.728352	−	0.685203i	$-0.759714\pi$
$929$	−44.3996			−1.45670			−0.728352	+	0.685203i	$0.759714\pi$
$930$		0			0
$931$	−8.81194			−0.288800
$932$			27.4010i			0.897551i
$933$		0			0
$934$	−1.98541			−0.0649647
$935$	6.70052	−	7.57784i	0.219131	−	0.247822i
$936$		0			0
$937$		−	3.99015i		−	0.130353i	−0.997874	−	0.0651763i	$-0.979239\pi$
$937$		−	3.99015i		−	0.130353i	0.997874	−	0.0651763i	$-0.0207610\pi$
$938$			22.5501i			0.736286i
$939$		0			0
$940$	−4.77575	+	5.40105i	−0.155768	+	0.176163i
$941$	2.30280			0.0750692			0.0375346	−	0.999295i	$-0.488050\pi$
$941$	2.30280			0.0750692			0.0375346	+	0.999295i	$0.488050\pi$
$942$		0			0
$943$			4.70052i			0.153070i
$944$	1.22425			0.0398461
$945$		0			0
$946$	−34.5501			−1.12332
$947$		−	24.7269i		−	0.803515i	−0.915746	−	0.401758i	$-0.868399\pi$
$947$		−	24.7269i		−	0.803515i	0.915746	−	0.401758i	$-0.131601\pi$
$948$		0			0
$949$	−49.2506			−1.59874
$950$	−24.6253	+	3.03761i	−0.798950	+	0.0985531i
$951$		0			0
$952$		−	4.00000i		−	0.129641i
$953$		−	11.6775i		−	0.378271i	−0.981951	−	0.189136i	$-0.939431\pi$
$953$		−	11.6775i		−	0.378271i	0.981951	−	0.189136i	$-0.0605686\pi$
$954$		0			0
$955$	32.3733	+	28.6253i	1.04757	+	0.926293i
$956$	−7.48612			−0.242118
$957$		0			0
$958$			11.0738i			0.357779i
$959$	27.2534			0.880059
$960$		0			0
$961$	−15.0000			−0.483871
$962$			37.7743i			1.21789i
$963$		0			0
$964$	13.0738			0.421079
$965$	−8.77575	+	9.92478i	−0.282501	+	0.319490i
$966$		0			0
$967$			51.2116i			1.64685i	0.567423	+	0.823427i	$0.307941\pi$
$967$			51.2116i			1.64685i	−0.567423	+	0.823427i	$0.692059\pi$
$968$		−	0.224254i		−	0.00720779i
$969$		0			0
$970$	−21.5877	−	19.0884i	−0.693139	−	0.612891i
$971$	−14.8265			−0.475806			−0.237903	−	0.971289i	$-0.576460\pi$
$971$	−14.8265			−0.475806			−0.237903	+	0.971289i	$0.576460\pi$
$972$		0			0
$973$		−	25.5515i		−	0.819143i
$974$	−17.4372			−0.558725
$975$		0			0
$976$	−11.0884			−0.354931
$977$			16.6958i			0.534145i	0.963676	+	0.267073i	$0.0860564\pi$
$977$			16.6958i			0.534145i	−0.963676	+	0.267073i	$0.913944\pi$
$978$		0			0
$979$	33.2506			1.06269
$980$	2.97461	+	2.63023i	0.0950203	+	0.0840195i
$981$		0			0
$982$		−	14.8773i		−	0.474754i
$983$		−	30.0263i		−	0.957692i	−0.877899	−	0.478846i	$-0.841055\pi$
$983$		−	30.0263i		−	0.957692i	0.877899	−	0.478846i	$-0.158945\pi$
$984$		0			0
$985$	11.9610	−	13.5271i	0.381108	−	0.431008i
$986$	10.4485			0.332748
$987$		0			0
$988$		−	24.6253i		−	0.783435i
$989$	10.3127			0.327923
$990$		0			0
$991$	−1.40105			−0.0445057			−0.0222529	−	0.999752i	$-0.507084\pi$
$991$	−1.40105			−0.0445057			−0.0222529	+	0.999752i	$0.507084\pi$
$992$		−	4.00000i		−	0.127000i
$993$		0			0
$994$	−6.47768			−0.205460
$995$	−26.7612	−	23.6629i	−0.848386	−	0.750165i
$996$		0			0
$997$			13.2144i			0.418504i	0.977862	+	0.209252i	$0.0671030\pi$
$997$			13.2144i			0.418504i	−0.977862	+	0.209252i	$0.932897\pi$
$998$			16.1016i			0.509686i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.d.e.829.6		6
3.2	odd	2		690.2.d.c.139.1	✓	6
5.4	even	2	inner	2070.2.d.e.829.3		6
15.2	even	4		3450.2.a.bt.1.1		3
15.8	even	4		3450.2.a.bo.1.3		3
15.14	odd	2		690.2.d.c.139.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.d.c.139.1	✓	6	3.2	odd	2
690.2.d.c.139.4	yes	6	15.14	odd	2
2070.2.d.e.829.3		6	5.4	even	2	inner
2070.2.d.e.829.6		6	1.1	even	1	trivial
3450.2.a.bo.1.3		3	15.8	even	4
3450.2.a.bt.1.1		3	15.2	even	4

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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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.67513 + 1.48119i) q^{5} +2.96239i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.67513 + 1.48119i) q^{5} +2.96239i q^{7} -1.00000i q^{8} +(-1.48119 + 1.67513i) q^{10} +3.35026 q^{11} +4.96239i q^{13} -2.96239 q^{14} +1.00000 q^{16} -1.35026i q^{17} +4.96239 q^{19} +(-1.67513 - 1.48119i) q^{20} +3.35026i q^{22} -1.00000i q^{23} +(0.612127 + 4.96239i) q^{25} -4.96239 q^{26} -2.96239i q^{28} +7.73813 q^{29} -4.00000 q^{31} +1.00000i q^{32} +1.35026 q^{34} +(-4.38787 + 4.96239i) q^{35} -7.61213i q^{37} +4.96239i q^{38} +(1.48119 - 1.67513i) q^{40} -4.70052 q^{41} +10.3127i q^{43} -3.35026 q^{44} +1.00000 q^{46} -3.22425i q^{47} -1.77575 q^{49} +(-4.96239 + 0.612127i) q^{50} -4.96239i q^{52} -6.96239i q^{53} +(5.61213 + 4.96239i) q^{55} +2.96239 q^{56} +7.73813i q^{58} +1.22425 q^{59} -11.0884 q^{61} -4.00000i q^{62} -1.00000 q^{64} +(-7.35026 + 8.31265i) q^{65} -7.61213i q^{67} +1.35026i q^{68} +(-4.96239 - 4.38787i) q^{70} +2.18664 q^{71} +9.92478i q^{73} +7.61213 q^{74} -4.96239 q^{76} +9.92478i q^{77} +4.12601 q^{79} +(1.67513 + 1.48119i) q^{80} -4.70052i q^{82} -6.38787i q^{83} +(2.00000 - 2.26187i) q^{85} -10.3127 q^{86} -3.35026i q^{88} +9.92478 q^{89} -14.7005 q^{91} +1.00000i q^{92} +3.22425 q^{94} +(8.31265 + 7.35026i) q^{95} +12.8872i q^{97} -1.77575i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4}+O(q^{10}) \) 6 * q - 6 * q^4	\( 6 q - 6 q^{4} + 2 q^{10} + 4 q^{14} + 6 q^{16} + 8 q^{19} + 2 q^{25} - 8 q^{26} + 28 q^{29} - 24 q^{31} - 12 q^{34} - 28 q^{35} - 2 q^{40} + 12 q^{41} + 6 q^{46} - 14 q^{49} - 8 q^{50} + 32 q^{55} - 4 q^{56} + 4 q^{59} - 28 q^{61} - 6 q^{64} - 24 q^{65} - 8 q^{70} - 12 q^{71} + 44 q^{74} - 8 q^{76} + 8 q^{79} + 12 q^{85} - 20 q^{86} + 16 q^{89} - 48 q^{91} + 16 q^{94} + 8 q^{95}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^10 + 4 * q^14 + 6 * q^16 + 8 * q^19 + 2 * q^25 - 8 * q^26 + 28 * q^29 - 24 * q^31 - 12 * q^34 - 28 * q^35 - 2 * q^40 + 12 * q^41 + 6 * q^46 - 14 * q^49 - 8 * q^50 + 32 * q^55 - 4 * q^56 + 4 * q^59 - 28 * q^61 - 6 * q^64 - 24 * q^65 - 8 * q^70 - 12 * q^71 + 44 * q^74 - 8 * q^76 + 8 * q^79 + 12 * q^85 - 20 * q^86 + 16 * q^89 - 48 * q^91 + 16 * q^94 + 8 * q^95

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