LMFDB - Embedded newform 1386.2.e.a.307.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(307,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1386.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.e (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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.6679465984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14x^{6} + 61x^{4} + 88x^{2} + 36 $ x^8 + 14x^6 + 61x^4 + 88*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			307.7
Root			$-1.25051i$ of defining polynomial
Character	$\chi$	$=$	1386.307
Dual form			1386.2.e.a.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +1.18572i q^{5} +(1.74138 + 1.99189i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +1.18572i q^{5} +(1.74138 + 1.99189i) q^{7} -1.00000i q^{8} -1.18572 q^{10} +(2.25051 - 2.43623i) q^{11} +5.98377 q^{13} +(-1.99189 + 1.74138i) q^{14} +1.00000 q^{16} -4.29703 q^{17} -0.203984 q^{19} -1.18572i q^{20} +(2.43623 + 2.25051i) q^{22} +3.11131 q^{23} +3.59407 q^{25} +5.98377i q^{26} +(-1.74138 - 1.99189i) q^{28} -2.50102i q^{29} +2.79805i q^{31} +1.00000i q^{32} -4.29703i q^{34} +(-2.36182 + 2.06479i) q^{35} +8.96551 q^{37} -0.203984i q^{38} +1.18572 q^{40} -2.20398 q^{41} -4.37144i q^{43} +(-2.25051 + 2.43623i) q^{44} +3.11131i q^{46} +2.05818i q^{47} +(-0.935213 + 6.93725i) q^{49} +3.59407i q^{50} -5.98377 q^{52} -1.51928 q^{53} +(2.88869 + 2.66847i) q^{55} +(1.99189 - 1.74138i) q^{56} +2.50102 q^{58} +7.96754i q^{59} -11.6123 q^{61} -2.79805 q^{62} -1.00000 q^{64} +7.09508i q^{65} -12.4686 q^{67} +4.29703 q^{68} +(-2.06479 - 2.36182i) q^{70} +15.8217 q^{71} -2.29703 q^{73} +8.96551i q^{74} +0.203984 q^{76} +(8.77167 + 0.240361i) q^{77} +9.85420i q^{79} +1.18572i q^{80} -2.20398i q^{82} -10.0419 q^{83} -5.09508i q^{85} +4.37144 q^{86} +(-2.43623 - 2.25051i) q^{88} +8.87246i q^{89} +(10.4200 + 11.9190i) q^{91} -3.11131 q^{92} -2.05818 q^{94} -0.241868i q^{95} +9.46652i q^{97} +(-6.93725 - 0.935213i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} - 4 q^{10} + 8 q^{11} + 8 q^{14} + 8 q^{16} - 12 q^{17} - 4 q^{19} + 4 q^{22} + 8 q^{23} - 16 q^{25} + 8 q^{35} + 16 q^{37} + 4 q^{40} - 20 q^{41} - 8 q^{44} - 12 q^{49} + 40 q^{55} - 8 q^{56} - 56 q^{61} + 20 q^{62} - 8 q^{64} + 16 q^{67} + 12 q^{68} - 12 q^{70} - 8 q^{71} + 4 q^{73} + 4 q^{76} - 4 q^{77} + 4 q^{83} + 24 q^{86} - 4 q^{88} + 20 q^{91} - 8 q^{92} + 20 q^{94} - 20 q^{98}+O(q^{100}) $ 8 * q - 8 * q^4 - 4 * q^10 + 8 * q^11 + 8 * q^14 + 8 * q^16 - 12 * q^17 - 4 * q^19 + 4 * q^22 + 8 * q^23 - 16 * q^25 + 8 * q^35 + 16 * q^37 + 4 * q^40 - 20 * q^41 - 8 * q^44 - 12 * q^49 + 40 * q^55 - 8 * q^56 - 56 * q^61 + 20 * q^62 - 8 * q^64 + 16 * q^67 + 12 * q^68 - 12 * q^70 - 8 * q^71 + 4 * q^73 + 4 * q^76 - 4 * q^77 + 4 * q^83 + 24 * q^86 - 4 * q^88 + 20 * q^91 - 8 * q^92 + 20 * q^94 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$-1$	$-1$

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
$5$			1.18572i			0.530271i	0.964211	+	0.265135i	$0.0854166\pi$
$5$			1.18572i			0.530271i	−0.964211	+	0.265135i	$0.914583\pi$
$6$		0			0
$7$	1.74138	+	1.99189i	0.658179	+	0.752862i
$7$	1.74138	+	1.99189i	0.658179	+	0.752862i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.18572			−0.374958
$11$	2.25051	−	2.43623i	0.678554	−	0.734551i
$11$	2.25051	−	2.43623i	0.678554	−	0.734551i
$12$		0			0
$13$	5.98377			1.65960			0.829800	−	0.558061i	$-0.188455\pi$
$13$	5.98377			1.65960			0.829800	+	0.558061i	$0.188455\pi$
$14$	−1.99189	+	1.74138i	−0.532354	+	0.465403i
$15$		0			0
$16$	1.00000			0.250000
$17$	−4.29703			−1.04218			−0.521092	−	0.853501i	$-0.674475\pi$
$17$	−4.29703			−1.04218			−0.521092	+	0.853501i	$0.674475\pi$
$18$		0			0
$19$	−0.203984			−0.0467970			−0.0233985	−	0.999726i	$-0.507449\pi$
$19$	−0.203984			−0.0467970			−0.0233985	+	0.999726i	$0.507449\pi$
$20$		−	1.18572i		−	0.265135i
$21$		0			0
$22$	2.43623	+	2.25051i	0.519406	+	0.479810i
$23$	3.11131			0.648753			0.324377	−	0.945928i	$-0.394845\pi$
$23$	3.11131			0.648753			0.324377	+	0.945928i	$0.394845\pi$
$24$		0			0
$25$	3.59407			0.718813
$26$			5.98377i			1.17351i
$27$		0			0
$28$	−1.74138	−	1.99189i	−0.329089	−	0.376431i
$29$		−	2.50102i		−	0.464427i	−0.972665	−	0.232214i	$-0.925403\pi$
$29$		−	2.50102i		−	0.464427i	0.972665	−	0.232214i	$-0.0745968\pi$
$30$		0			0
$31$			2.79805i			0.502544i	0.967916	+	0.251272i	$0.0808489\pi$
$31$			2.79805i			0.502544i	−0.967916	+	0.251272i	$0.919151\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$		−	4.29703i		−	0.736935i
$35$	−2.36182	+	2.06479i	−0.399220	+	0.349013i
$36$		0			0
$37$	8.96551			1.47392			0.736960	−	0.675936i	$-0.236260\pi$
$37$	8.96551			1.47392			0.736960	+	0.675936i	$0.236260\pi$
$38$		−	0.203984i		−	0.0330905i
$39$		0			0
$40$	1.18572			0.187479
$41$	−2.20398			−0.344204			−0.172102	−	0.985079i	$-0.555056\pi$
$41$	−2.20398			−0.344204			−0.172102	+	0.985079i	$0.555056\pi$
$42$		0			0
$43$		−	4.37144i		−	0.666639i	−0.942814	−	0.333319i	$-0.891831\pi$
$43$		−	4.37144i		−	0.666639i	0.942814	−	0.333319i	$-0.108169\pi$
$44$	−2.25051	+	2.43623i	−0.339277	+	0.367275i
$45$		0			0
$46$			3.11131i			0.458738i
$47$			2.05818i			0.300216i	0.988670	+	0.150108i	$0.0479622\pi$
$47$			2.05818i			0.300216i	−0.988670	+	0.150108i	$0.952038\pi$
$48$		0			0
$49$	−0.935213	+	6.93725i	−0.133602	+	0.991035i
$50$			3.59407i			0.508278i
$51$		0			0
$52$	−5.98377			−0.829800
$53$	−1.51928			−0.208689			−0.104345	−	0.994541i	$-0.533274\pi$
$53$	−1.51928			−0.208689			−0.104345	+	0.994541i	$0.533274\pi$
$54$		0			0
$55$	2.88869	+	2.66847i	0.389511	+	0.359817i
$56$	1.99189	−	1.74138i	0.266177	−	0.232701i
$57$		0			0
$58$	2.50102			0.328400
$59$			7.96754i			1.03729i	0.854991	+	0.518643i	$0.173563\pi$
$59$			7.96754i			1.03729i	−0.854991	+	0.518643i	$0.826437\pi$
$60$		0			0
$61$	−11.6123			−1.48681			−0.743403	−	0.668844i	$-0.766790\pi$
$61$	−11.6123			−1.48681			−0.743403	+	0.668844i	$0.766790\pi$
$62$	−2.79805			−0.355353
$63$		0			0
$64$	−1.00000			−0.125000
$65$			7.09508i			0.880037i
$66$		0			0
$67$	−12.4686			−1.52328			−0.761638	−	0.648002i	$-0.775605\pi$
$67$	−12.4686			−1.52328			−0.761638	+	0.648002i	$0.775605\pi$
$68$	4.29703			0.521092
$69$		0			0
$70$	−2.06479	−	2.36182i	−0.246789	−	0.282291i
$71$	15.8217			1.87769			0.938847	−	0.344334i	$-0.111895\pi$
$71$	15.8217			1.87769			0.938847	+	0.344334i	$0.111895\pi$
$72$		0			0
$73$	−2.29703			−0.268847			−0.134424	−	0.990924i	$-0.542918\pi$
$73$	−2.29703			−0.268847			−0.134424	+	0.990924i	$0.542918\pi$
$74$			8.96551i			1.04222i
$75$		0			0
$76$	0.203984			0.0233985
$77$	8.77167	+	0.240361i	0.999625	+	0.0273916i
$78$		0			0
$79$			9.85420i			1.10868i	0.832289	+	0.554342i	$0.187030\pi$
$79$			9.85420i			1.10868i	−0.832289	+	0.554342i	$0.812970\pi$
$80$			1.18572i			0.132568i
$81$		0			0
$82$		−	2.20398i		−	0.243389i
$83$	−10.0419			−1.10225			−0.551124	−	0.834424i	$-0.685801\pi$
$83$	−10.0419			−1.10225			−0.551124	+	0.834424i	$0.685801\pi$
$84$		0			0
$85$		−	5.09508i		−	0.552639i
$86$	4.37144			0.471385
$87$		0			0
$88$	−2.43623	−	2.25051i	−0.259703	−	0.239905i
$89$			8.87246i			0.940479i	0.882539	+	0.470239i	$0.155832\pi$
$89$			8.87246i			0.940479i	−0.882539	+	0.470239i	$0.844168\pi$
$90$		0			0
$91$	10.4200	+	11.9190i	1.09231	+	1.24945i
$92$	−3.11131			−0.324377
$93$		0			0
$94$	−2.05818			−0.212285
$95$		−	0.241868i		−	0.0248151i
$96$		0			0
$97$			9.46652i			0.961180i	0.876945	+	0.480590i	$0.159577\pi$
$97$			9.46652i			0.961180i	−0.876945	+	0.480590i	$0.840423\pi$
$98$	−6.93725	−	0.935213i	−0.700768	−	0.0944708i
$99$		0			0
$100$	−3.59407			−0.359407
$101$	3.12754			0.311202			0.155601	−	0.987820i	$-0.450269\pi$
$101$	3.12754			0.311202			0.155601	+	0.987820i	$0.450269\pi$
$102$		0			0
$103$		−	8.54297i		−	0.841763i	−0.907116	−	0.420882i	$-0.861721\pi$
$103$		−	8.54297i		−	0.841763i	0.907116	−	0.420882i	$-0.138279\pi$
$104$		−	5.98377i		−	0.586757i
$105$		0			0
$106$		−	1.51928i		−	0.147565i
$107$			3.12754i			0.302351i	0.988507	+	0.151175i	$0.0483058\pi$
$107$			3.12754i			0.302351i	−0.988507	+	0.151175i	$0.951694\pi$
$108$		0			0
$109$		−	6.22564i		−	0.596308i	−0.954518	−	0.298154i	$-0.903629\pi$
$109$		−	6.22564i		−	0.596308i	0.954518	−	0.298154i	$-0.0963709\pi$
$110$	−2.66847	+	2.88869i	−0.254429	+	0.275426i
$111$		0			0
$112$	1.74138	+	1.99189i	0.164545	+	0.188215i
$113$	13.8745			1.30520			0.652601	−	0.757702i	$-0.273678\pi$
$113$	13.8745			1.30520			0.652601	+	0.757702i	$0.273678\pi$
$114$		0			0
$115$			3.68915i			0.344015i
$116$			2.50102i			0.232214i
$117$		0			0
$118$	−7.96754			−0.733472
$119$	−7.48275	−	8.55920i	−0.685943	−	0.784620i
$120$		0			0
$121$	−0.870426	−	10.9655i	−0.0791296	−	0.996864i
$122$		−	11.6123i		−	1.05133i
$123$		0			0
$124$		−	2.79805i		−	0.251272i
$125$			10.1902i			0.911436i
$126$		0			0
$127$			11.0423i			0.979848i	0.871765	+	0.489924i	$0.162975\pi$
$127$			11.0423i			0.979848i	−0.871765	+	0.489924i	$0.837025\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−7.09508			−0.622280
$131$	10.3011			0.900011			0.450006	−	0.893026i	$-0.351422\pi$
$131$	10.3011			0.900011			0.450006	+	0.893026i	$0.351422\pi$
$132$		0			0
$133$	−0.355212	−	0.406312i	−0.0308008	−	0.0352317i
$134$		−	12.4686i		−	1.07712i
$135$		0			0
$136$			4.29703i			0.368468i
$137$	−1.90695			−0.162922			−0.0814609	−	0.996677i	$-0.525959\pi$
$137$	−1.90695			−0.162922			−0.0814609	+	0.996677i	$0.525959\pi$
$138$		0			0
$139$	5.80008			0.491957			0.245978	−	0.969275i	$-0.420891\pi$
$139$	5.80008			0.491957			0.245978	+	0.969275i	$0.420891\pi$
$140$	2.36182	−	2.06479i	0.199610	−	0.174506i
$141$		0			0
$142$			15.8217i			1.32773i
$143$	13.4665	−	14.5778i	1.12613	−	1.21906i
$144$		0			0
$145$	2.96551			0.246272
$146$		−	2.29703i		−	0.190104i
$147$		0			0
$148$	−8.96551			−0.736960
$149$			3.74492i			0.306796i	0.988165	+	0.153398i	$0.0490216\pi$
$149$			3.74492i			0.306796i	−0.988165	+	0.153398i	$0.950978\pi$
$150$		0			0
$151$			2.23885i			0.182195i	0.995842	+	0.0910977i	$0.0290375\pi$
$151$			2.23885i			0.182195i	−0.995842	+	0.0910977i	$0.970962\pi$
$152$			0.203984i			0.0165453i
$153$		0			0
$154$	−0.240361	+	8.77167i	−0.0193688	+	0.706841i
$155$	−3.31771			−0.266485
$156$		0			0
$157$		−	21.2666i		−	1.69726i	−0.528987	−	0.848630i	$-0.677428\pi$
$157$		−	21.2666i		−	1.69726i	0.528987	−	0.848630i	$-0.322572\pi$
$158$	−9.85420			−0.783958
$159$		0			0
$160$	−1.18572			−0.0937395
$161$	5.41797	+	6.19738i	0.426996	+	0.488422i
$162$		0			0
$163$	−11.8380			−0.927221			−0.463611	−	0.886039i	$-0.653446\pi$
$163$	−11.8380			−0.927221			−0.463611	+	0.886039i	$0.653446\pi$
$164$	2.20398			0.172102
$165$		0			0
$166$		−	10.0419i		−	0.779406i
$167$	−19.3735			−1.49916			−0.749582	−	0.661911i	$-0.769746\pi$
$167$	−19.3735			−1.49916			−0.749582	+	0.661911i	$0.769746\pi$
$168$		0			0
$169$	22.8055			1.75427
$170$	5.09508			0.390775
$171$		0			0
$172$			4.37144i			0.333319i
$173$	11.8380			0.900024			0.450012	−	0.893023i	$-0.351420\pi$
$173$	11.8380			0.900024			0.450012	+	0.893023i	$0.351420\pi$
$174$		0			0
$175$	6.25862	+	7.15897i	0.473107	+	0.541167i
$176$	2.25051	−	2.43623i	0.169638	−	0.183638i
$177$		0			0
$178$	−8.87246			−0.665019
$179$	−19.0819			−1.42625			−0.713123	−	0.701039i	$-0.752720\pi$
$179$	−19.0819			−1.42625			−0.713123	+	0.701039i	$0.752720\pi$
$180$		0			0
$181$			15.7869i			1.17343i	0.809794	+	0.586714i	$0.199579\pi$
$181$			15.7869i			1.17343i	−0.809794	+	0.586714i	$0.800421\pi$
$182$	−11.9190	+	10.4200i	−0.883494	+	0.772382i
$183$		0			0
$184$		−	3.11131i		−	0.229369i
$185$			10.6306i			0.781577i
$186$		0			0
$187$	−9.67051	+	10.4686i	−0.707178	+	0.765537i
$188$		−	2.05818i		−	0.150108i
$189$		0			0
$190$	0.241868			0.0175469
$191$	−10.0768			−0.729133			−0.364567	−	0.931177i	$-0.618783\pi$
$191$	−10.0768			−0.729133			−0.364567	+	0.931177i	$0.618783\pi$
$192$		0			0
$193$		−	10.2226i		−	0.735841i	−0.929857	−	0.367920i	$-0.880070\pi$
$193$		−	10.2226i		−	0.735841i	0.929857	−	0.367920i	$-0.119930\pi$
$194$	−9.46652			−0.679657
$195$		0			0
$196$	0.935213	−	6.93725i	0.0668009	−	0.495518i
$197$		−	7.53551i		−	0.536883i	−0.963296	−	0.268441i	$-0.913491\pi$
$197$		−	7.53551i		−	0.536883i	0.963296	−	0.268441i	$-0.0865086\pi$
$198$		0			0
$199$		−	20.1025i		−	1.42503i	−0.701656	−	0.712516i	$-0.747556\pi$
$199$		−	20.1025i		−	1.42503i	0.701656	−	0.712516i	$-0.252444\pi$
$200$		−	3.59407i		−	0.254139i
$201$		0			0
$202$			3.12754i			0.220053i
$203$	4.98174	−	4.35521i	0.349649	−	0.305676i
$204$		0			0
$205$		−	2.61331i		−	0.182521i
$206$	8.54297			0.595217
$207$		0			0
$208$	5.98377			0.414900
$209$	−0.459067	+	0.496951i	−0.0317543	+	0.0343748i
$210$		0			0
$211$		−	26.5616i		−	1.82858i	−0.405064	−	0.914288i	$-0.632751\pi$
$211$		−	26.5616i		−	1.82858i	0.405064	−	0.914288i	$-0.367249\pi$
$212$	1.51928			0.104345
$213$		0			0
$214$	−3.12754			−0.213794
$215$	5.18331			0.353499
$216$		0			0
$217$	−5.57339	+	4.87246i	−0.378347	+	0.330764i
$218$	6.22564			0.421653
$219$		0			0
$220$	−2.88869	−	2.66847i	−0.194755	−	0.179909i
$221$	−25.7125			−1.72961
$222$		0			0
$223$		−	22.7656i		−	1.52450i	−0.647285	−	0.762248i	$-0.724096\pi$
$223$		−	22.7656i		−	1.52450i	0.647285	−	0.762248i	$-0.275904\pi$
$224$	−1.99189	+	1.74138i	−0.133088	+	0.116351i
$225$		0			0
$226$			13.8745i			0.922917i
$227$	−18.5064			−1.22832			−0.614158	−	0.789183i	$-0.710504\pi$
$227$	−18.5064			−1.22832			−0.614158	+	0.789183i	$0.710504\pi$
$228$		0			0
$229$		−	20.5995i		−	1.36125i	−0.732631	−	0.680626i	$-0.761708\pi$
$229$		−	20.5995i		−	1.36125i	0.732631	−	0.680626i	$-0.238292\pi$
$230$	−3.68915			−0.243255
$231$		0			0
$232$	−2.50102			−0.164200
$233$		−	28.9330i		−	1.89547i	−0.319063	−	0.947734i	$-0.603368\pi$
$233$		−	28.9330i		−	1.89547i	0.319063	−	0.947734i	$-0.396632\pi$
$234$		0			0
$235$	−2.44043			−0.159196
$236$		−	7.96754i		−	0.518643i
$237$		0			0
$238$	8.55920	−	7.48275i	0.554810	−	0.485035i
$239$		−	27.1922i		−	1.75892i	−0.475976	−	0.879459i	$-0.657905\pi$
$239$		−	27.1922i		−	1.75892i	0.475976	−	0.879459i	$-0.342095\pi$
$240$		0			0
$241$	4.07441			0.262456			0.131228	−	0.991352i	$-0.458108\pi$
$241$	4.07441			0.262456			0.131228	+	0.991352i	$0.458108\pi$
$242$	10.9655	−	0.870426i	0.704890	−	0.0559531i
$243$		0			0
$244$	11.6123			0.743403
$245$	−8.22564	−	1.10890i	−0.525517	−	0.0708451i
$246$		0			0
$247$	−1.22059			−0.0776643
$248$	2.79805			0.177676
$249$		0			0
$250$	−10.1902			−0.644483
$251$		−	11.3735i		−	0.717887i	−0.933359	−	0.358944i	$-0.883137\pi$
$251$		−	11.3735i		−	0.717887i	0.933359	−	0.358944i	$-0.116863\pi$
$252$		0			0
$253$	7.00203	−	7.57987i	0.440214	−	0.476542i
$254$	−11.0423			−0.692857
$255$		0			0
$256$	1.00000			0.0625000
$257$			5.46652i			0.340992i	0.985358	+	0.170496i	$0.0545371\pi$
$257$			5.46652i			0.340992i	−0.985358	+	0.170496i	$0.945463\pi$
$258$		0			0
$259$	15.6123	+	17.8583i	0.970103	+	1.10966i
$260$		−	7.09508i		−	0.440018i
$261$		0			0
$262$			10.3011i			0.636404i
$263$			29.9543i			1.84706i	0.383523	+	0.923531i	$0.374711\pi$
$263$			29.9543i			1.84706i	−0.383523	+	0.923531i	$0.625289\pi$
$264$		0			0
$265$		−	1.80144i		−	0.110662i
$266$	0.406312	−	0.355212i	0.0249126	−	0.0217795i
$267$		0			0
$268$	12.4686			0.761638
$269$			16.4428i			1.00254i	0.865292	+	0.501269i	$0.167133\pi$
$269$			16.4428i			1.00254i	−0.865292	+	0.501269i	$0.832867\pi$
$270$		0			0
$271$	−0.633605			−0.0384888			−0.0192444	−	0.999815i	$-0.506126\pi$
$271$	−0.633605			−0.0384888			−0.0192444	+	0.999815i	$0.506126\pi$
$272$	−4.29703			−0.260546
$273$		0			0
$274$		−	1.90695i		−	0.115203i
$275$	8.08847	−	8.75597i	0.487753	−	0.528005i
$276$		0			0
$277$		−	9.00505i		−	0.541061i	−0.962711	−	0.270530i	$-0.912801\pi$
$277$		−	9.00505i		−	0.541061i	0.962711	−	0.270530i	$-0.0871991\pi$
$278$			5.80008i			0.347866i
$279$		0			0
$280$	2.06479	+	2.36182i	0.123395	+	0.141146i
$281$		−	3.90695i		−	0.233069i	−0.993187	−	0.116535i	$-0.962821\pi$
$281$		−	3.90695i		−	0.233069i	0.993187	−	0.116535i	$-0.0371786\pi$
$282$		0			0
$283$	17.5085			1.04077			0.520385	−	0.853932i	$-0.325788\pi$
$283$	17.5085			1.04077			0.520385	+	0.853932i	$0.325788\pi$
$284$	−15.8217			−0.938847
$285$		0			0
$286$	14.5778	+	13.4665i	0.862006	+	0.796292i
$287$	−3.83797	−	4.39008i	−0.226548	−	0.259138i
$288$		0			0
$289$	1.46449			0.0861465
$290$			2.96551i			0.174141i
$291$		0			0
$292$	2.29703			0.134424
$293$	30.4361			1.77810			0.889048	−	0.457814i	$-0.151368\pi$
$293$	30.4361			1.77810			0.889048	+	0.457814i	$0.151368\pi$
$294$		0			0
$295$	−9.44728			−0.550042
$296$		−	8.96551i		−	0.521110i
$297$		0			0
$298$	−3.74492			−0.216937
$299$	18.6174			1.07667
$300$		0			0
$301$	8.70741	−	7.61233i	0.501887	−	0.438767i
$302$	−2.23885			−0.128832
$303$		0			0
$304$	−0.203984			−0.0116993
$305$		−	13.7690i		−	0.788410i
$306$		0			0
$307$	−17.8001			−1.01590			−0.507952	−	0.861385i	$-0.669597\pi$
$307$	−17.8001			−1.01590			−0.507952	+	0.861385i	$0.669597\pi$
$308$	−8.77167	−	0.240361i	−0.499812	−	0.0136958i
$309$		0			0
$310$		−	3.31771i		−	0.188433i
$311$			26.6522i			1.51131i	0.654970	+	0.755655i	$0.272681\pi$
$311$			26.6522i			1.51131i	−0.654970	+	0.755655i	$0.727319\pi$
$312$		0			0
$313$			31.1191i			1.75896i	0.475938	+	0.879479i	$0.342109\pi$
$313$			31.1191i			1.75896i	−0.475938	+	0.879479i	$0.657891\pi$
$314$	21.2666			1.20014
$315$		0			0
$316$		−	9.85420i		−	0.554342i
$317$	7.48275			0.420273			0.210137	−	0.977672i	$-0.432609\pi$
$317$	7.48275			0.420273			0.210137	+	0.977672i	$0.432609\pi$
$318$		0			0
$319$	−6.09305	−	5.62856i	−0.341145	−	0.315139i
$320$		−	1.18572i		−	0.0662838i
$321$		0			0
$322$	−6.19738	+	5.41797i	−0.345366	+	0.301931i
$323$	0.876524			0.0487711
$324$		0			0
$325$	21.5061			1.19294
$326$		−	11.8380i		−	0.655644i
$327$		0			0
$328$			2.20398i			0.121695i
$329$	−4.09966	+	3.58407i	−0.226021	+	0.197596i
$330$		0			0
$331$	−2.37551			−0.130570			−0.0652849	−	0.997867i	$-0.520796\pi$
$331$	−2.37551			−0.130570			−0.0652849	+	0.997867i	$0.520796\pi$
$332$	10.0419			0.551124
$333$		0			0
$334$		−	19.3735i		−	1.06007i
$335$		−	14.7842i		−	0.807749i
$336$		0			0
$337$			14.7469i			0.803318i	0.915789	+	0.401659i	$0.131566\pi$
$337$			14.7469i			0.803318i	−0.915789	+	0.401659i	$0.868434\pi$
$338$			22.8055i			1.24046i
$339$		0			0
$340$			5.09508i			0.276320i
$341$	6.81669	+	6.29703i	0.369144	+	0.341003i
$342$		0			0
$343$	−15.4468	+	10.2175i	−0.834046	+	0.551694i
$344$	−4.37144			−0.235692
$345$		0			0
$346$			11.8380i			0.636413i
$347$		−	2.73882i		−	0.147027i	−0.997294	−	0.0735137i	$-0.976579\pi$
$347$		−	2.73882i		−	0.147027i	0.997294	−	0.0735137i	$-0.0234213\pi$
$348$		0			0
$349$	20.1739			1.07989			0.539943	−	0.841702i	$-0.318446\pi$
$349$	20.1739			1.07989			0.539943	+	0.841702i	$0.318446\pi$
$350$	−7.15897	+	6.25862i	−0.382663	+	0.334537i
$351$		0			0
$352$	2.43623	+	2.25051i	0.129851	+	0.119952i
$353$		−	30.3955i		−	1.61779i	−0.587953	−	0.808895i	$-0.700066\pi$
$353$		−	30.3955i		−	1.61779i	0.587953	−	0.808895i	$-0.299934\pi$
$354$		0			0
$355$			18.7602i			0.995686i
$356$		−	8.87246i		−	0.470239i
$357$		0			0
$358$		−	19.0819i		−	1.00851i
$359$			2.43203i			0.128358i	0.997938	+	0.0641789i	$0.0204428\pi$
$359$			2.43203i			0.128358i	−0.997938	+	0.0641789i	$0.979557\pi$
$360$		0			0
$361$	−18.9584			−0.997810
$362$	−15.7869			−0.829739
$363$		0			0
$364$	−10.4200	−	11.9190i	−0.546156	−	0.624724i
$365$		−	2.72364i		−	0.142562i
$366$		0			0
$367$			26.2473i			1.37010i	0.728497	+	0.685049i	$0.240219\pi$
$367$			26.2473i			1.37010i	−0.728497	+	0.685049i	$0.759781\pi$
$368$	3.11131			0.162188
$369$		0			0
$370$	−10.6306			−0.552658
$371$	−2.64564	−	3.02623i	−0.137355	−	0.157114i
$372$		0			0
$373$		−	26.8370i		−	1.38957i	−0.719219	−	0.694783i	$-0.755500\pi$
$373$		−	26.8370i		−	1.38957i	0.719219	−	0.694783i	$-0.244500\pi$
$374$	−10.4686	−	9.67051i	−0.541316	−	0.500050i
$375$		0			0
$376$	2.05818			0.106143
$377$		−	14.9655i		−	0.770763i
$378$		0			0
$379$	21.8420			1.12195			0.560975	−	0.827833i	$-0.310426\pi$
$379$	21.8420			1.12195			0.560975	+	0.827833i	$0.310426\pi$
$380$			0.241868i			0.0124075i
$381$		0			0
$382$		−	10.0768i		−	0.515575i
$383$		−	27.2139i		−	1.39056i	−0.718738	−	0.695281i	$-0.755280\pi$
$383$		−	27.2139i		−	1.39056i	0.718738	−	0.695281i	$-0.244720\pi$
$384$		0			0
$385$	−0.285001	+	10.4008i	−0.0145250	+	0.530072i
$386$	10.2226			0.520318
$387$		0			0
$388$		−	9.46652i		−	0.480590i
$389$	4.51725			0.229033			0.114517	−	0.993421i	$-0.463468\pi$
$389$	4.51725			0.229033			0.114517	+	0.993421i	$0.463468\pi$
$390$		0			0
$391$	−13.3694			−0.676120
$392$	6.93725	+	0.935213i	0.350384	+	0.0472354i
$393$		0			0
$394$	7.53551			0.379633
$395$	−11.6843			−0.587902
$396$		0			0
$397$		−	24.2970i		−	1.21943i	−0.792620	−	0.609717i	$-0.791283\pi$
$397$		−	24.2970i		−	1.21943i	0.792620	−	0.609717i	$-0.208717\pi$
$398$	20.1025			1.00765
$399$		0			0
$400$	3.59407			0.179703
$401$	23.8380			1.19041			0.595206	−	0.803573i	$-0.297071\pi$
$401$	23.8380			1.19041			0.595206	+	0.803573i	$0.297071\pi$
$402$		0			0
$403$			16.7429i			0.834022i
$404$	−3.12754			−0.155601
$405$		0			0
$406$	4.35521	+	4.98174i	0.216146	+	0.247239i
$407$	20.1769	−	21.8420i	1.00013	−	1.08267i
$408$		0			0
$409$	7.00746			0.346496			0.173248	−	0.984878i	$-0.444574\pi$
$409$	7.00746			0.346496			0.173248	+	0.984878i	$0.444574\pi$
$410$	2.61331			0.129062
$411$		0			0
$412$			8.54297i			0.420882i
$413$	−15.8704	+	13.8745i	−0.780933	+	0.682719i
$414$		0			0
$415$		−	11.9070i		−	0.584489i
$416$			5.98377i			0.293378i
$417$		0			0
$418$	−0.496951	−	0.459067i	−0.0243067	−	0.0224537i
$419$		−	1.36941i		−	0.0669000i	−0.999440	−	0.0334500i	$-0.989351\pi$
$419$		−	1.36941i		−	0.0669000i	0.999440	−	0.0334500i	$-0.0106495\pi$
$420$		0			0
$421$	22.2267			1.08326			0.541631	−	0.840616i	$-0.317807\pi$
$421$	22.2267			1.08326			0.541631	+	0.840616i	$0.317807\pi$
$422$	26.5616			1.29300
$423$		0			0
$424$			1.51928i			0.0737827i
$425$	−15.4438			−0.749135
$426$		0			0
$427$	−20.2214	−	23.1304i	−0.978584	−	1.11936i
$428$		−	3.12754i		−	0.151175i
$429$		0			0
$430$			5.18331i			0.249961i
$431$			11.2074i			0.539840i	0.962883	+	0.269920i	$0.0869973\pi$
$431$			11.2074i			0.539840i	−0.962883	+	0.269920i	$0.913003\pi$
$432$		0			0
$433$			12.4452i			0.598080i	0.954241	+	0.299040i	$0.0966665\pi$
$433$			12.4452i			0.598080i	−0.954241	+	0.299040i	$0.903334\pi$
$434$	−4.87246	−	5.57339i	−0.233885	−	0.267531i
$435$		0			0
$436$			6.22564i			0.298154i
$437$	−0.634657			−0.0303597
$438$		0			0
$439$	−36.9036			−1.76131			−0.880656	−	0.473755i	$-0.842898\pi$
$439$	−36.9036			−1.76131			−0.880656	+	0.473755i	$0.842898\pi$
$440$	2.66847	−	2.88869i	0.127215	−	0.137713i
$441$		0			0
$442$		−	25.7125i		−	1.22302i
$443$	−19.8512			−0.943158			−0.471579	−	0.881824i	$-0.656316\pi$
$443$	−19.8512			−0.943158			−0.471579	+	0.881824i	$0.656316\pi$
$444$		0			0
$445$	−10.5203			−0.498708
$446$	22.7656			1.07798
$447$		0			0
$448$	−1.74138	−	1.99189i	−0.0822723	−	0.0941077i
$449$	6.90898			0.326055			0.163028	−	0.986622i	$-0.447874\pi$
$449$	6.90898			0.326055			0.163028	+	0.986622i	$0.447874\pi$
$450$		0			0
$451$	−4.96008	+	5.36941i	−0.233561	+	0.252836i
$452$	−13.8745			−0.652601
$453$		0			0
$454$		−	18.5064i		−	0.868550i
$455$	−14.1326	+	12.3552i	−0.662546	+	0.579221i
$456$		0			0
$457$			0.218558i			0.0102237i	0.999987	+	0.00511186i	$0.00162716\pi$
$457$			0.218558i			0.0102237i	−0.999987	+	0.00511186i	$0.998373\pi$
$458$	20.5995			0.962551
$459$		0			0
$460$		−	3.68915i		−	0.172007i
$461$	27.5788			1.28447			0.642237	−	0.766506i	$-0.278007\pi$
$461$	27.5788			1.28447			0.642237	+	0.766506i	$0.278007\pi$
$462$		0			0
$463$	−40.0887			−1.86308			−0.931540	−	0.363638i	$-0.881535\pi$
$463$	−40.0887			−1.86308			−0.931540	+	0.363638i	$0.881535\pi$
$464$		−	2.50102i		−	0.116107i
$465$		0			0
$466$	28.9330			1.34030
$467$		−	25.4100i		−	1.17583i	−0.808921	−	0.587917i	$-0.799948\pi$
$467$		−	25.4100i		−	1.17583i	0.808921	−	0.587917i	$-0.200052\pi$
$468$		0			0
$469$	−21.7125	−	24.8359i	−1.00259	−	1.14682i
$470$		−	2.44043i		−	0.112568i
$471$		0			0
$472$	7.96754			0.366736
$473$	−10.6498	−	9.83797i	−0.489680	−	0.452350i
$474$		0			0
$475$	−0.733130			−0.0336383
$476$	7.48275	+	8.55920i	0.342971	+	0.392310i
$477$		0			0
$478$	27.1922			1.24374
$479$	−33.3045			−1.52172			−0.760861	−	0.648915i	$-0.775223\pi$
$479$	−33.3045			−1.52172			−0.760861	+	0.648915i	$0.775223\pi$
$480$		0			0
$481$	53.6475			2.44612
$482$			4.07441i			0.185584i
$483$		0			0
$484$	0.870426	+	10.9655i	0.0395648	+	0.498432i
$485$	−11.2247			−0.509685
$486$		0			0
$487$	−23.1922			−1.05094			−0.525469	−	0.850813i	$-0.676110\pi$
$487$	−23.1922			−1.05094			−0.525469	+	0.850813i	$0.676110\pi$
$488$			11.6123i			0.525665i
$489$		0			0
$490$	1.10890	−	8.22564i	0.0500951	−	0.371596i
$491$			23.0626i			1.04080i	0.853922	+	0.520401i	$0.174217\pi$
$491$			23.0626i			1.04080i	−0.853922	+	0.520401i	$0.825783\pi$
$492$		0			0
$493$			10.7469i			0.484018i
$494$		−	1.22059i		−	0.0549170i
$495$		0			0
$496$			2.79805i			0.125636i
$497$	27.5516	+	31.5151i	1.23586	+	1.41364i
$498$		0			0
$499$	11.1184			0.497728			0.248864	−	0.968538i	$-0.419943\pi$
$499$	11.1184			0.497728			0.248864	+	0.968538i	$0.419943\pi$
$500$		−	10.1902i		−	0.455718i
$501$		0			0
$502$	11.3735			0.507623
$503$	−2.85518			−0.127306			−0.0636530	−	0.997972i	$-0.520275\pi$
$503$	−2.85518			−0.127306			−0.0636530	+	0.997972i	$0.520275\pi$
$504$		0			0
$505$			3.70839i			0.165021i
$506$	7.57987	+	7.00203i	0.336966	+	0.311278i
$507$		0			0
$508$		−	11.0423i		−	0.489924i
$509$		−	10.9631i		−	0.485931i	−0.970035	−	0.242965i	$-0.921880\pi$
$509$		−	10.9631i		−	0.485931i	0.970035	−	0.242965i	$-0.0781201\pi$
$510$		0			0
$511$	−4.00000	−	4.57543i	−0.176950	−	0.202405i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−5.46652			−0.241118
$515$	10.1296			0.446362
$516$		0			0
$517$	5.01420	+	4.63195i	0.220524	+	0.203713i
$518$	−17.8583	+	15.6123i	−0.784647	+	0.685966i
$519$		0			0
$520$	7.09508			0.311140
$521$			12.9888i			0.569050i	0.958669	+	0.284525i	$0.0918359\pi$
$521$			12.9888i			0.569050i	−0.958669	+	0.284525i	$0.908164\pi$
$522$		0			0
$523$	−13.7595			−0.601661			−0.300830	−	0.953678i	$-0.597264\pi$
$523$	−13.7595			−0.601661			−0.300830	+	0.953678i	$0.597264\pi$
$524$	−10.3011			−0.450006
$525$		0			0
$526$	−29.9543			−1.30607
$527$		−	12.0233i		−	0.523744i
$528$		0			0
$529$	−13.3197			−0.579119
$530$	1.80144			0.0782496
$531$		0			0
$532$	0.355212	+	0.406312i	0.0154004	+	0.0176159i
$533$	−13.1881			−0.571241
$534$		0			0
$535$	−3.70839			−0.160328
$536$			12.4686i			0.538560i
$537$		0			0
$538$	−16.4428			−0.708901
$539$	14.7960	+	17.8907i	0.637310	+	0.770608i
$540$		0			0
$541$			12.6468i			0.543729i	0.962336	+	0.271865i	$0.0876403\pi$
$541$			12.6468i			0.543729i	−0.962336	+	0.271865i	$0.912360\pi$
$542$		−	0.633605i		−	0.0272157i
$543$		0			0
$544$		−	4.29703i		−	0.184234i
$545$	7.38187			0.316205
$546$		0			0
$547$			23.5230i			1.00577i	0.864352	+	0.502886i	$0.167729\pi$
$547$			23.5230i			1.00577i	−0.864352	+	0.502886i	$0.832271\pi$
$548$	1.90695			0.0814609
$549$		0			0
$550$	8.75597	+	8.08847i	0.373356	+	0.344894i
$551$			0.510166i			0.0217338i
$552$		0			0
$553$	−19.6284	+	17.1599i	−0.834686	+	0.729712i
$554$	9.00505			0.382588
$555$		0			0
$556$	−5.80008			−0.245978
$557$			34.6222i			1.46699i	0.679695	+	0.733495i	$0.262112\pi$
$557$			34.6222i			1.46699i	−0.679695	+	0.733495i	$0.737888\pi$
$558$		0			0
$559$		−	26.1577i		−	1.10635i
$560$	−2.36182	+	2.06479i	−0.0998051	+	0.0872532i
$561$		0			0
$562$	3.90695			0.164805
$563$	22.3576			0.942261			0.471131	−	0.882063i	$-0.343846\pi$
$563$	22.3576			0.942261			0.471131	+	0.882063i	$0.343846\pi$
$564$		0			0
$565$			16.4513i			0.692110i
$566$			17.5085i			0.735936i
$567$		0			0
$568$		−	15.8217i		−	0.663865i
$569$		−	44.7061i		−	1.87418i	−0.349092	−	0.937089i	$-0.613510\pi$
$569$		−	44.7061i		−	1.87418i	0.349092	−	0.937089i	$-0.386490\pi$
$570$		0			0
$571$			3.92017i			0.164054i	0.996630	+	0.0820269i	$0.0261394\pi$
$571$			3.92017i			0.164054i	−0.996630	+	0.0820269i	$0.973861\pi$
$572$	−13.4665	+	14.5778i	−0.563064	+	0.609530i
$573$		0			0
$574$	4.39008	−	3.83797i	0.183238	−	0.160194i
$575$	11.1823			0.466332
$576$		0			0
$577$		−	22.2094i		−	0.924590i	−0.886726	−	0.462295i	$-0.847026\pi$
$577$		−	22.2094i		−	0.924590i	0.886726	−	0.462295i	$-0.152974\pi$
$578$			1.46449i			0.0609148i
$579$		0			0
$580$	−2.96551			−0.123136
$581$	−17.4868	−	20.0024i	−0.725476	−	0.829840i
$582$		0			0
$583$	−3.41915	+	3.70131i	−0.141607	+	0.153293i
$584$			2.29703i			0.0950519i
$585$		0			0
$586$			30.4361i			1.25730i
$587$			28.7104i			1.18501i	0.805568	+	0.592503i	$0.201860\pi$
$587$			28.7104i			1.18501i	−0.805568	+	0.592503i	$0.798140\pi$
$588$		0			0
$589$		−	0.570756i		−	0.0235176i
$590$		−	9.44728i		−	0.388938i
$591$		0			0
$592$	8.96551			0.368480
$593$	−38.4608			−1.57939			−0.789697	−	0.613497i	$-0.789762\pi$
$593$	−38.4608			−1.57939			−0.789697	+	0.613497i	$0.789762\pi$
$594$		0			0
$595$	10.1488	−	8.87246i	0.416061	−	0.363735i
$596$		−	3.74492i		−	0.153398i
$597$		0			0
$598$			18.6174i			0.761321i
$599$	−23.8542			−0.974656			−0.487328	−	0.873219i	$-0.662028\pi$
$599$	−23.8542			−0.974656			−0.487328	+	0.873219i	$0.662028\pi$
$600$		0			0
$601$	−25.8972			−1.05637			−0.528184	−	0.849130i	$-0.677127\pi$
$601$	−25.8972			−1.05637			−0.528184	+	0.849130i	$0.677127\pi$
$602$	7.61233	+	8.70741i	0.310255	+	0.354888i
$603$		0			0
$604$		−	2.23885i		−	0.0910977i
$605$	13.0020	−	1.03208i	0.528608	−	0.0419601i
$606$		0			0
$607$	−0.787244			−0.0319533			−0.0159766	−	0.999872i	$-0.505086\pi$
$607$	−0.787244			−0.0319533			−0.0159766	+	0.999872i	$0.505086\pi$
$608$		−	0.203984i		−	0.00827263i
$609$		0			0
$610$	13.7690			0.557490
$611$			12.3157i			0.498239i
$612$		0			0
$613$			31.5799i			1.27550i	0.770244	+	0.637749i	$0.220134\pi$
$613$			31.5799i			1.27550i	−0.770244	+	0.637749i	$0.779866\pi$
$614$		−	17.8001i		−	0.718353i
$615$		0			0
$616$	0.240361	−	8.77167i	0.00968440	−	0.353421i
$617$	39.6800			1.59746			0.798728	−	0.601692i	$-0.205506\pi$
$617$	39.6800			1.59746			0.798728	+	0.601692i	$0.205506\pi$
$618$		0			0
$619$		−	26.3522i		−	1.05918i	−0.848252	−	0.529592i	$-0.822345\pi$
$619$		−	26.3522i		−	1.05918i	0.848252	−	0.529592i	$-0.177655\pi$
$620$	3.31771			0.133242
$621$		0			0
$622$	−26.6522			−1.06866
$623$	−17.6729	+	15.4503i	−0.708051	+	0.619003i
$624$		0			0
$625$	5.88764			0.235505
$626$	−31.1191			−1.24377
$627$		0			0
$628$			21.2666i			0.848630i
$629$	−38.5251			−1.53610
$630$		0			0
$631$	15.4574			0.615348			0.307674	−	0.951492i	$-0.400449\pi$
$631$	15.4574			0.615348			0.307674	+	0.951492i	$0.400449\pi$
$632$	9.85420			0.391979
$633$		0			0
$634$			7.48275i			0.297178i
$635$	−13.0931			−0.519585
$636$		0			0
$637$	−5.59610	+	41.5109i	−0.221725	+	1.64472i
$638$	5.62856	−	6.09305i	0.222837	−	0.241226i
$639$		0			0
$640$	1.18572			0.0468697
$641$	8.96551			0.354116			0.177058	−	0.984200i	$-0.443342\pi$
$641$	8.96551			0.354116			0.177058	+	0.984200i	$0.443342\pi$
$642$		0			0
$643$		−	18.2500i		−	0.719710i	−0.933008	−	0.359855i	$-0.882826\pi$
$643$		−	18.2500i		−	0.719710i	0.933008	−	0.359855i	$-0.117174\pi$
$644$	−5.41797	−	6.19738i	−0.213498	−	0.244211i
$645$		0			0
$646$			0.876524i			0.0344864i
$647$		−	7.20300i		−	0.283179i	−0.989925	−	0.141590i	$-0.954779\pi$
$647$		−	7.20300i		−	0.283179i	0.989925	−	0.141590i	$-0.0452213\pi$
$648$		0			0
$649$	19.4108	+	17.9310i	0.761939	+	0.703854i
$650$			21.5061i			0.843537i
$651$		0			0
$652$	11.8380			0.463611
$653$	28.4523			1.11343			0.556713	−	0.830705i	$-0.312062\pi$
$653$	28.4523			1.11343			0.556713	+	0.830705i	$0.312062\pi$
$654$		0			0
$655$			12.2142i			0.477249i
$656$	−2.20398			−0.0860511
$657$		0			0
$658$	−3.58407	−	4.09966i	−0.139721	−	0.159821i
$659$		−	10.1336i		−	0.394751i	−0.980328	−	0.197375i	$-0.936758\pi$
$659$		−	10.1336i		−	0.394751i	0.980328	−	0.197375i	$-0.0632417\pi$
$660$		0			0
$661$		−	4.00542i		−	0.155793i	−0.996961	−	0.0778965i	$-0.975180\pi$
$661$		−	4.00542i		−	0.155793i	0.996961	−	0.0778965i	$-0.0248204\pi$
$662$		−	2.37551i		−	0.0923267i
$663$		0			0
$664$			10.0419i			0.389703i
$665$	0.481772	−	0.421183i	0.0186823	−	0.0163328i
$666$		0			0
$667$		−	7.78144i		−	0.301299i
$668$	19.3735			0.749582
$669$		0			0
$670$	14.7842			0.571165
$671$	−26.1336	+	28.2903i	−1.00888	+	1.09213i
$672$		0			0
$673$			30.8357i			1.18863i	0.804233	+	0.594314i	$0.202576\pi$
$673$			30.8357i			1.18863i	−0.804233	+	0.594314i	$0.797424\pi$
$674$	−14.7469			−0.568031
$675$		0			0
$676$	−22.8055			−0.877135
$677$	−20.7318			−0.796787			−0.398393	−	0.917215i	$-0.630432\pi$
$677$	−20.7318			−0.796787			−0.398393	+	0.917215i	$0.630432\pi$
$678$		0			0
$679$	−18.8562	+	16.4848i	−0.723636	+	0.632628i
$680$	−5.09508			−0.195387
$681$		0			0
$682$	−6.29703	+	6.81669i	−0.241126	+	0.261025i
$683$	−9.59610			−0.367185			−0.183592	−	0.983002i	$-0.558773\pi$
$683$	−9.59610			−0.367185			−0.183592	+	0.983002i	$0.558773\pi$
$684$		0			0
$685$		−	2.26111i		−	0.0863926i
$686$	−10.2175	−	15.4468i	−0.390107	−	0.589760i
$687$		0			0
$688$		−	4.37144i		−	0.166660i
$689$	−9.09102			−0.346340
$690$		0			0
$691$		−	18.6871i		−	0.710891i	−0.934697	−	0.355446i	$-0.884329\pi$
$691$		−	18.6871i		−	0.710891i	0.934697	−	0.355446i	$-0.115671\pi$
$692$	−11.8380			−0.450012
$693$		0			0
$694$	2.73882			0.103964
$695$			6.87728i			0.260870i
$696$		0			0
$697$	9.47059			0.358724
$698$			20.1739i			0.763595i
$699$		0			0
$700$	−6.25862	−	7.15897i	−0.236554	−	0.270583i
$701$		−	10.7104i		−	0.404527i	−0.979331	−	0.202264i	$-0.935170\pi$
$701$		−	10.7104i		−	0.404527i	0.979331	−	0.202264i	$-0.0648298\pi$
$702$		0			0
$703$	−1.82882			−0.0689751
$704$	−2.25051	+	2.43623i	−0.0848192	+	0.0918188i
$705$		0			0
$706$	30.3955			1.14395
$707$	5.44623	+	6.22970i	0.204827	+	0.234292i
$708$		0			0
$709$	−1.07102			−0.0402229			−0.0201115	−	0.999798i	$-0.506402\pi$
$709$	−1.07102			−0.0402229			−0.0201115	+	0.999798i	$0.506402\pi$
$710$	−18.7602			−0.704056
$711$		0			0
$712$	8.87246			0.332509
$713$			8.70560i			0.326027i
$714$		0			0
$715$	17.2852	+	15.9675i	0.646432	+	0.597152i
$716$	19.0819			0.713123
$717$		0			0
$718$	−2.43203			−0.0907626
$719$		−	23.6949i		−	0.883669i	−0.897096	−	0.441835i	$-0.854328\pi$
$719$		−	23.6949i		−	0.883669i	0.897096	−	0.441835i	$-0.145672\pi$
$720$		0			0
$721$	17.0166	−	14.8765i	0.633732	−	0.554031i
$722$		−	18.9584i		−	0.705558i
$723$		0			0
$724$		−	15.7869i		−	0.586714i
$725$		−	8.98882i		−	0.333836i
$726$		0			0
$727$		−	14.7656i		−	0.547625i	−0.961783	−	0.273813i	$-0.911715\pi$
$727$		−	14.7656i		−	0.547625i	0.961783	−	0.273813i	$-0.0882848\pi$
$728$	11.9190	−	10.4200i	0.441747	−	0.386191i
$729$		0			0
$730$	2.72364			0.100806
$731$			18.7842i			0.694760i
$732$		0			0
$733$	−13.7294			−0.507109			−0.253554	−	0.967321i	$-0.581600\pi$
$733$	−13.7294			−0.507109			−0.253554	+	0.967321i	$0.581600\pi$
$734$	−26.2473			−0.968805
$735$		0			0
$736$			3.11131i			0.114684i
$737$	−28.0606	+	30.3763i	−1.03363	+	1.11892i
$738$		0			0
$739$			20.1204i			0.740142i	0.929004	+	0.370071i	$0.120667\pi$
$739$			20.1204i			0.740142i	−0.929004	+	0.370071i	$0.879333\pi$
$740$		−	10.6306i		−	0.390788i
$741$		0			0
$742$	3.02623	−	2.64564i	0.111096	−	0.0971244i
$743$		−	5.22059i		−	0.191525i	−0.995404	−	0.0957625i	$-0.969471\pi$
$743$		−	5.22059i		−	0.191525i	0.995404	−	0.0957625i	$-0.0305289\pi$
$744$		0			0
$745$	−4.44043			−0.162685
$746$	26.8370			0.982572
$747$		0			0
$748$	9.67051	−	10.4686i	0.353589	−	0.382768i
$749$	−6.22970	+	5.44623i	−0.227628	+	0.199001i
$750$		0			0
$751$	−37.1557			−1.35583			−0.677915	−	0.735140i	$-0.737116\pi$
$751$	−37.1557			−1.35583			−0.677915	+	0.735140i	$0.737116\pi$
$752$			2.05818i			0.0750541i
$753$		0			0
$754$	14.9655			0.545012
$755$	−2.65466			−0.0966128
$756$		0			0
$757$	22.7835			0.828079			0.414040	−	0.910259i	$-0.364117\pi$
$757$	22.7835			0.828079			0.414040	+	0.910259i	$0.364117\pi$
$758$			21.8420i			0.793338i
$759$		0			0
$760$	−0.241868			−0.00877346
$761$	−40.7889			−1.47860			−0.739298	−	0.673378i	$-0.764843\pi$
$761$	−40.7889			−1.47860			−0.739298	+	0.673378i	$0.764843\pi$
$762$		0			0
$763$	12.4008	−	10.8412i	0.448937	−	0.392477i
$764$	10.0768			0.364567
$765$		0			0
$766$	27.2139			0.983276
$767$			47.6759i			1.72148i
$768$		0			0
$769$	−0.398477			−0.0143694			−0.00718472	−	0.999974i	$-0.502287\pi$
$769$	−0.398477			−0.0143694			−0.00718472	+	0.999974i	$0.502287\pi$
$770$	−10.4008	−	0.285001i	−0.374817	−	0.0102707i
$771$		0			0
$772$			10.2226i			0.367920i
$773$		−	12.0863i		−	0.434714i	−0.976092	−	0.217357i	$-0.930256\pi$
$773$		−	12.0863i		−	0.434714i	0.976092	−	0.217357i	$-0.0697436\pi$
$774$		0			0
$775$			10.0564i			0.361236i
$776$	9.46652			0.339828
$777$		0			0
$778$			4.51725i			0.161951i
$779$	0.449576			0.0161077
$780$		0			0
$781$	35.6069	−	38.5454i	1.27412	−	1.37926i
$782$		−	13.3694i		−	0.478089i
$783$		0			0
$784$	−0.935213	+	6.93725i	−0.0334005	+	0.247759i
$785$	25.2163			0.900007
$786$		0			0
$787$	8.94084			0.318706			0.159353	−	0.987222i	$-0.449059\pi$
$787$	8.94084			0.318706			0.159353	+	0.987222i	$0.449059\pi$
$788$			7.53551i			0.268441i
$789$		0			0
$790$		−	11.6843i		−	0.415710i
$791$	24.1607	+	27.6364i	0.859056	+	0.982637i
$792$		0			0
$793$	−69.4855			−2.46750
$794$	24.2970			0.862269
$795$		0			0
$796$			20.1025i			0.712516i
$797$			52.6479i			1.86488i	0.361319	+	0.932442i	$0.382327\pi$
$797$			52.6479i			1.86488i	−0.361319	+	0.932442i	$0.617673\pi$
$798$		0			0
$799$		−	8.84406i		−	0.312881i
$800$			3.59407i			0.127069i
$801$		0			0
$802$			23.8380i			0.841748i
$803$	−5.16949	+	5.59610i	−0.182427	+	0.197482i
$804$		0			0
$805$	−7.34836	+	6.42420i	−0.258996	+	0.226423i
$806$	−16.7429			−0.589743
$807$		0			0
$808$		−	3.12754i		−	0.110027i
$809$		−	4.06898i		−	0.143058i	−0.997439	−	0.0715289i	$-0.977212\pi$
$809$		−	4.06898i		−	0.143058i	0.997439	−	0.0715289i	$-0.0227878\pi$
$810$		0			0
$811$	16.5795			0.582185			0.291092	−	0.956695i	$-0.405981\pi$
$811$	16.5795			0.582185			0.291092	+	0.956695i	$0.405981\pi$
$812$	−4.98174	+	4.35521i	−0.174825	+	0.152838i
$813$		0			0
$814$	21.8420	+	20.1769i	0.765563	+	0.707202i
$815$		−	14.0365i		−	0.491678i
$816$		0			0
$817$			0.891702i			0.0311967i
$818$			7.00746i			0.245010i
$819$		0			0
$820$			2.61331i			0.0912607i
$821$		−	8.06898i		−	0.281610i	−0.990037	−	0.140805i	$-0.955031\pi$
$821$		−	8.06898i		−	0.281610i	0.990037	−	0.140805i	$-0.0449690\pi$
$822$		0			0
$823$	8.07305			0.281409			0.140704	−	0.990052i	$-0.455063\pi$
$823$	8.07305			0.281409			0.140704	+	0.990052i	$0.455063\pi$
$824$	−8.54297			−0.297608
$825$		0			0
$826$	−13.8745	−	15.8704i	−0.482755	−	0.552203i
$827$			30.0522i			1.04502i	0.852634	+	0.522509i	$0.175004\pi$
$827$			30.0522i			1.04502i	−0.852634	+	0.522509i	$0.824996\pi$
$828$		0			0
$829$			49.3878i			1.71531i	0.514227	+	0.857654i	$0.328079\pi$
$829$			49.3878i			1.71531i	−0.514227	+	0.857654i	$0.671921\pi$
$830$	11.9070			0.413296
$831$		0			0
$832$	−5.98377			−0.207450
$833$	4.01864	−	29.8096i	0.139238	−	1.03284i
$834$		0			0
$835$		−	22.9715i		−	0.794963i
$836$	0.459067	−	0.496951i	0.0158772	−	0.0171874i
$837$		0			0
$838$	1.36941			0.0473055
$839$			39.9134i			1.37796i	0.724778	+	0.688982i	$0.241942\pi$
$839$			39.9134i			1.37796i	−0.724778	+	0.688982i	$0.758058\pi$
$840$		0			0
$841$	22.7449			0.784307
$842$			22.2267i			0.765982i
$843$		0			0
$844$			26.5616i			0.914288i
$845$			27.0410i			0.930238i
$846$		0			0
$847$	20.3263	−	20.8289i	0.698420	−	0.715688i
$848$	−1.51928			−0.0521723
$849$		0			0
$850$		−	15.4438i		−	0.529719i
$851$	27.8945			0.956211
$852$		0			0
$853$	−54.9533			−1.88157			−0.940783	−	0.339008i	$-0.889908\pi$
$853$	−54.9533			−1.88157			−0.940783	+	0.339008i	$0.889908\pi$
$854$	23.1304	−	20.2214i	0.791507	−	0.691963i
$855$		0			0
$856$	3.12754			0.106897
$857$	−33.1370			−1.13194			−0.565970	−	0.824426i	$-0.691498\pi$
$857$	−33.1370			−1.13194			−0.565970	+	0.824426i	$0.691498\pi$
$858$		0			0
$859$		−	25.1151i		−	0.856916i	−0.903562	−	0.428458i	$-0.859057\pi$
$859$		−	25.1151i		−	0.856916i	0.903562	−	0.428458i	$-0.140943\pi$
$860$	−5.18331			−0.176749
$861$		0			0
$862$	−11.2074			−0.381725
$863$	−6.55453			−0.223119			−0.111559	−	0.993758i	$-0.535585\pi$
$863$	−6.55453			−0.223119			−0.111559	+	0.993758i	$0.535585\pi$
$864$		0			0
$865$			14.0365i			0.477256i
$866$	−12.4452			−0.422907
$867$		0			0
$868$	5.57339	−	4.87246i	0.189173	−	0.165382i
$869$	24.0071	+	22.1769i	0.814384	+	0.752301i
$870$		0			0
$871$	−74.6090			−2.52803
$872$	−6.22564			−0.210827
$873$		0			0
$874$		−	0.634657i		−	0.0214676i
$875$	−20.2976	+	17.7449i	−0.686185	+	0.599888i
$876$		0			0
$877$		−	51.9787i		−	1.75520i	−0.479398	−	0.877598i	$-0.659145\pi$
$877$		−	51.9787i		−	1.75520i	0.479398	−	0.877598i	$-0.340855\pi$
$878$		−	36.9036i		−	1.24544i
$879$		0			0
$880$	2.88869	+	2.66847i	0.0973777	+	0.0899543i
$881$		−	47.2114i		−	1.59059i	−0.606220	−	0.795297i	$-0.707315\pi$
$881$		−	47.2114i		−	1.59059i	0.606220	−	0.795297i	$-0.292685\pi$
$882$		0			0
$883$	−7.19220			−0.242037			−0.121018	−	0.992650i	$-0.538616\pi$
$883$	−7.19220			−0.242037			−0.121018	+	0.992650i	$0.538616\pi$
$884$	25.7125			0.864804
$885$		0			0
$886$		−	19.8512i		−	0.666913i
$887$	1.84712			0.0620201			0.0310100	−	0.999519i	$-0.490128\pi$
$887$	1.84712			0.0620201			0.0310100	+	0.999519i	$0.490128\pi$
$888$		0			0
$889$	−21.9950	+	19.2289i	−0.737690	+	0.644915i
$890$		−	10.5203i		−	0.352640i
$891$		0			0
$892$			22.7656i			0.762248i
$893$		−	0.419835i		−	0.0140492i
$894$		0			0
$895$		−	22.6258i		−	0.756296i
$896$	1.99189	−	1.74138i	0.0665442	−	0.0581753i
$897$		0			0
$898$			6.90898i			0.230556i
$899$	6.99797			0.233395
$900$		0			0
$901$	6.52839			0.217492
$902$	−5.36941	−	4.96008i	−0.178782	−	0.165153i
$903$		0			0
$904$		−	13.8745i		−	0.461459i
$905$	−18.7188			−0.622235
$906$		0			0
$907$	28.9523			0.961345			0.480673	−	0.876900i	$-0.340393\pi$
$907$	28.9523			0.961345			0.480673	+	0.876900i	$0.340393\pi$
$908$	18.5064			0.614158
$909$		0			0
$910$	−12.3552	−	14.1326i	−0.409571	−	0.468491i
$911$	−39.8217			−1.31935			−0.659676	−	0.751550i	$-0.729307\pi$
$911$	−39.8217			−1.31935			−0.659676	+	0.751550i	$0.729307\pi$
$912$		0			0
$913$	−22.5995	+	24.4645i	−0.747934	+	0.809656i
$914$	−0.218558			−0.00722926
$915$		0			0
$916$			20.5995i			0.680626i
$917$	17.9381	+	20.5186i	0.592368	+	0.677584i
$918$		0			0
$919$			37.2450i			1.22860i	0.789073	+	0.614299i	$0.210561\pi$
$919$			37.2450i			1.22860i	−0.789073	+	0.614299i	$0.789439\pi$
$920$	3.68915			0.121628
$921$		0			0
$922$			27.5788i			0.908260i
$923$	94.6736			3.11622
$924$		0			0
$925$	32.2226			1.05947
$926$		−	40.0887i		−	1.31740i
$927$		0			0
$928$	2.50102			0.0820999
$929$			0.653900i			0.0214538i	0.999942	+	0.0107269i	$0.00341454\pi$
$929$			0.653900i			0.0214538i	−0.999942	+	0.0107269i	$0.996585\pi$
$930$		0			0
$931$	0.190768	−	1.41508i	0.00625217	−	0.0463775i
$932$			28.9330i			0.947734i
$933$		0			0
$934$	25.4100			0.831441
$935$	−12.4128	−	11.4665i	−0.405942	−	0.374995i
$936$		0			0
$937$	12.7740			0.417308			0.208654	−	0.977990i	$-0.433092\pi$
$937$	12.7740			0.417308			0.208654	+	0.977990i	$0.433092\pi$
$938$	24.8359	−	21.7125i	0.810922	−	0.708937i
$939$		0			0
$940$	2.44043			0.0795979
$941$	32.8914			1.07223			0.536115	−	0.844145i	$-0.319891\pi$
$941$	32.8914			1.07223			0.536115	+	0.844145i	$0.319891\pi$
$942$		0			0
$943$	−6.85728			−0.223304
$944$			7.96754i			0.259321i
$945$		0			0
$946$	9.83797	−	10.6498i	0.319860	−	0.346256i
$947$	−18.3190			−0.595287			−0.297643	−	0.954677i	$-0.596201\pi$
$947$	−18.3190			−0.595287			−0.297643	+	0.954677i	$0.596201\pi$
$948$		0			0
$949$	−13.7449			−0.446179
$950$		−	0.733130i		−	0.0237859i
$951$		0			0
$952$	−8.55920	+	7.48275i	−0.277405	+	0.242517i
$953$			19.4858i			0.631206i	0.948891	+	0.315603i	$0.102207\pi$
$953$			19.4858i			0.631206i	−0.948891	+	0.315603i	$0.897793\pi$
$954$		0			0
$955$		−	11.9483i		−	0.386638i
$956$			27.1922i			0.879459i
$957$		0			0
$958$		−	33.3045i		−	1.07602i
$959$	−3.32072	−	3.79843i	−0.107232	−	0.122658i
$960$		0			0
$961$	23.1709			0.747449
$962$			53.6475i			1.72967i
$963$		0			0
$964$	−4.07441			−0.131228
$965$	12.1212			0.390195
$966$		0			0
$967$		−	38.0684i		−	1.22420i	−0.790781	−	0.612099i	$-0.790325\pi$
$967$		−	38.0684i		−	1.22420i	0.790781	−	0.612099i	$-0.209675\pi$
$968$	−10.9655	+	0.870426i	−0.352445	+	0.0279765i
$969$		0			0
$970$		−	11.2247i		−	0.360402i
$971$		−	49.1292i		−	1.57663i	−0.615270	−	0.788316i	$-0.710953\pi$
$971$		−	49.1292i		−	1.57663i	0.615270	−	0.788316i	$-0.289047\pi$
$972$		0			0
$973$	10.1001	+	11.5531i	0.323795	+	0.370375i
$974$		−	23.1922i		−	0.743126i
$975$		0			0
$976$	−11.6123			−0.371702
$977$	−22.9047			−0.732785			−0.366392	−	0.930460i	$-0.619407\pi$
$977$	−22.9047			−0.732785			−0.366392	+	0.930460i	$0.619407\pi$
$978$		0			0
$979$	21.6153	+	19.9675i	0.690829	+	0.638165i
$980$	8.22564	+	1.10890i	0.262758	+	0.0354226i
$981$		0			0
$982$	−23.0626			−0.735958
$983$		−	58.5906i		−	1.86875i	−0.356290	−	0.934376i	$-0.615958\pi$
$983$		−	58.5906i		−	1.86875i	0.356290	−	0.934376i	$-0.384042\pi$
$984$		0			0
$985$	8.93501			0.284693
$986$	−10.7469			−0.342253
$987$		0			0
$988$	1.22059			0.0388322
$989$		−	13.6009i		−	0.432484i
$990$		0			0
$991$	−12.4513			−0.395528			−0.197764	−	0.980250i	$-0.563368\pi$
$991$	−12.4513			−0.395528			−0.197764	+	0.980250i	$0.563368\pi$
$992$	−2.79805			−0.0888382
$993$		0			0
$994$	−31.5151	+	27.5516i	−0.999598	+	0.873884i
$995$	23.8360			0.755652
$996$		0			0
$997$	0.420131			0.0133057			0.00665284	−	0.999978i	$-0.497882\pi$
$997$	0.420131			0.0133057			0.00665284	+	0.999978i	$0.497882\pi$
$998$			11.1184i			0.351947i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.e.a.307.7		8
3.2	odd	2		462.2.e.b.307.2	yes	8
7.6	odd	2		1386.2.e.e.307.6		8
11.10	odd	2		1386.2.e.e.307.3		8
12.11	even	2		3696.2.q.c.769.2		8
21.20	even	2		462.2.e.a.307.3	✓	8
33.32	even	2		462.2.e.a.307.6	yes	8
77.76	even	2	inner	1386.2.e.a.307.2		8
84.83	odd	2		3696.2.q.b.769.7		8
132.131	odd	2		3696.2.q.b.769.2		8
231.230	odd	2		462.2.e.b.307.7	yes	8
924.923	even	2		3696.2.q.c.769.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.e.a.307.3	✓	8	21.20	even	2
462.2.e.a.307.6	yes	8	33.32	even	2
462.2.e.b.307.2	yes	8	3.2	odd	2
462.2.e.b.307.7	yes	8	231.230	odd	2
1386.2.e.a.307.2		8	77.76	even	2	inner
1386.2.e.a.307.7		8	1.1	even	1	trivial
1386.2.e.e.307.3		8	11.10	odd	2
1386.2.e.e.307.6		8	7.6	odd	2
3696.2.q.b.769.2		8	132.131	odd	2
3696.2.q.b.769.7		8	84.83	odd	2
3696.2.q.c.769.2		8	12.11	even	2
3696.2.q.c.769.7		8	924.923	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +1.18572i q^{5} +(1.74138 + 1.99189i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +1.18572i q^{5} +(1.74138 + 1.99189i) q^{7} -1.00000i q^{8} -1.18572 q^{10} +(2.25051 - 2.43623i) q^{11} +5.98377 q^{13} +(-1.99189 + 1.74138i) q^{14} +1.00000 q^{16} -4.29703 q^{17} -0.203984 q^{19} -1.18572i q^{20} +(2.43623 + 2.25051i) q^{22} +3.11131 q^{23} +3.59407 q^{25} +5.98377i q^{26} +(-1.74138 - 1.99189i) q^{28} -2.50102i q^{29} +2.79805i q^{31} +1.00000i q^{32} -4.29703i q^{34} +(-2.36182 + 2.06479i) q^{35} +8.96551 q^{37} -0.203984i q^{38} +1.18572 q^{40} -2.20398 q^{41} -4.37144i q^{43} +(-2.25051 + 2.43623i) q^{44} +3.11131i q^{46} +2.05818i q^{47} +(-0.935213 + 6.93725i) q^{49} +3.59407i q^{50} -5.98377 q^{52} -1.51928 q^{53} +(2.88869 + 2.66847i) q^{55} +(1.99189 - 1.74138i) q^{56} +2.50102 q^{58} +7.96754i q^{59} -11.6123 q^{61} -2.79805 q^{62} -1.00000 q^{64} +7.09508i q^{65} -12.4686 q^{67} +4.29703 q^{68} +(-2.06479 - 2.36182i) q^{70} +15.8217 q^{71} -2.29703 q^{73} +8.96551i q^{74} +0.203984 q^{76} +(8.77167 + 0.240361i) q^{77} +9.85420i q^{79} +1.18572i q^{80} -2.20398i q^{82} -10.0419 q^{83} -5.09508i q^{85} +4.37144 q^{86} +(-2.43623 - 2.25051i) q^{88} +8.87246i q^{89} +(10.4200 + 11.9190i) q^{91} -3.11131 q^{92} -2.05818 q^{94} -0.241868i q^{95} +9.46652i q^{97} +(-6.93725 - 0.935213i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} - 4 q^{10} + 8 q^{11} + 8 q^{14} + 8 q^{16} - 12 q^{17} - 4 q^{19} + 4 q^{22} + 8 q^{23} - 16 q^{25} + 8 q^{35} + 16 q^{37} + 4 q^{40} - 20 q^{41} - 8 q^{44} - 12 q^{49} + 40 q^{55} - 8 q^{56} - 56 q^{61} + 20 q^{62} - 8 q^{64} + 16 q^{67} + 12 q^{68} - 12 q^{70} - 8 q^{71} + 4 q^{73} + 4 q^{76} - 4 q^{77} + 4 q^{83} + 24 q^{86} - 4 q^{88} + 20 q^{91} - 8 q^{92} + 20 q^{94} - 20 q^{98}+O(q^{100}) \) 8 * q - 8 * q^4 - 4 * q^10 + 8 * q^11 + 8 * q^14 + 8 * q^16 - 12 * q^17 - 4 * q^19 + 4 * q^22 + 8 * q^23 - 16 * q^25 + 8 * q^35 + 16 * q^37 + 4 * q^40 - 20 * q^41 - 8 * q^44 - 12 * q^49 + 40 * q^55 - 8 * q^56 - 56 * q^61 + 20 * q^62 - 8 * q^64 + 16 * q^67 + 12 * q^68 - 12 * q^70 - 8 * q^71 + 4 * q^73 + 4 * q^76 - 4 * q^77 + 4 * q^83 + 24 * q^86 - 4 * q^88 + 20 * q^91 - 8 * q^92 + 20 * q^94 - 20 * q^98

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