LMFDB - Embedded newform 1386.2.e.e.307.1

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			307.1
Root			$-2.20392i$ of defining polynomial
Character	$\chi$	$=$	1386.307
Dual form			1386.2.e.e.307.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} -3.06118i q^{5} +(2.37330 + 1.16938i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} -3.06118i q^{5} +(2.37330 + 1.16938i) q^{7} +1.00000i q^{8} -3.06118 q^{10} +(3.20392 - 0.857262i) q^{11} +0.338760 q^{13} +(1.16938 - 2.37330i) q^{14} +1.00000 q^{16} +0.314583 q^{17} +6.09326 q^{19} +3.06118i q^{20} +(-0.857262 - 3.20392i) q^{22} +3.37576 q^{23} -4.37083 q^{25} -0.338760i q^{26} +(-2.37330 - 1.16938i) q^{28} +4.40784i q^{29} +0.722422i q^{31} -1.00000i q^{32} -0.314583i q^{34} +(3.57968 - 7.26510i) q^{35} -7.49320 q^{37} -6.09326i q^{38} +3.06118 q^{40} +8.09326 q^{41} -4.12236i q^{43} +(-3.20392 + 0.857262i) q^{44} -3.37576i q^{46} -8.77571i q^{47} +(4.26510 + 5.55058i) q^{49} +4.37083i q^{50} -0.338760 q^{52} -13.5623 q^{53} +(-2.62424 - 9.80778i) q^{55} +(-1.16938 + 2.37330i) q^{56} +4.40784 q^{58} -4.67752i q^{59} +13.7836 q^{61} +0.722422 q^{62} -1.00000 q^{64} -1.03700i q^{65} -1.73032 q^{67} -0.314583 q^{68} +(-7.26510 - 3.57968i) q^{70} -13.5465 q^{71} -1.68542 q^{73} +7.49320i q^{74} -6.09326 q^{76} +(8.60633 + 1.71206i) q^{77} +6.86896i q^{79} -3.06118i q^{80} -8.09326i q^{82} -7.11447 q^{83} -0.962995i q^{85} -4.12236 q^{86} +(0.857262 + 3.20392i) q^{88} +2.28548i q^{89} +(0.803978 + 0.396139i) q^{91} -3.37576 q^{92} -8.77571 q^{94} -18.6526i q^{95} -5.08536i q^{97} +(5.55058 - 4.26510i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 20 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 + 20 * 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
$5$		−	3.06118i		−	1.36900i	−0.729012	−	0.684501i	$-0.760020\pi$
$5$		−	3.06118i		−	1.36900i	0.729012	−	0.684501i	$-0.239980\pi$
$6$		0			0
$7$	2.37330	+	1.16938i	0.897023	+	0.441984i
$7$	2.37330	+	1.16938i	0.897023	+	0.441984i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−3.06118			−0.968031
$11$	3.20392	−	0.857262i	0.966018	−	0.258474i
$11$	3.20392	−	0.857262i	0.966018	−	0.258474i
$12$		0			0
$13$	0.338760			0.0939550			0.0469775	−	0.998896i	$-0.485041\pi$
$13$	0.338760			0.0939550			0.0469775	+	0.998896i	$0.485041\pi$
$14$	1.16938	−	2.37330i	0.312530	−	0.634291i
$15$		0			0
$16$	1.00000			0.250000
$17$	0.314583			0.0762975			0.0381488	−	0.999272i	$-0.487854\pi$
$17$	0.314583			0.0762975			0.0381488	+	0.999272i	$0.487854\pi$
$18$		0			0
$19$	6.09326			1.39789			0.698944	−	0.715176i	$-0.253653\pi$
$19$	6.09326			1.39789			0.698944	+	0.715176i	$0.253653\pi$
$20$			3.06118i			0.684501i
$21$		0			0
$22$	−0.857262	−	3.20392i	−0.182769	−	0.683078i
$23$	3.37576			0.703896			0.351948	−	0.936020i	$-0.385519\pi$
$23$	3.37576			0.703896			0.351948	+	0.936020i	$0.385519\pi$
$24$		0			0
$25$	−4.37083			−0.874167
$26$		−	0.338760i		−	0.0664362i
$27$		0			0
$28$	−2.37330	−	1.16938i	−0.448511	−	0.220992i
$29$			4.40784i			0.818515i	0.912419	+	0.409258i	$0.134212\pi$
$29$			4.40784i			0.818515i	−0.912419	+	0.409258i	$0.865788\pi$
$30$		0			0
$31$			0.722422i			0.129751i	0.997893	+	0.0648754i	$0.0206650\pi$
$31$			0.722422i			0.129751i	−0.997893	+	0.0648754i	$0.979335\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$		−	0.314583i		−	0.0539505i
$35$	3.57968	−	7.26510i	0.605077	−	1.22803i
$36$		0			0
$37$	−7.49320			−1.23187			−0.615937	−	0.787795i	$-0.711222\pi$
$37$	−7.49320			−1.23187			−0.615937	+	0.787795i	$0.711222\pi$
$38$		−	6.09326i		−	0.988457i
$39$		0			0
$40$	3.06118			0.484015
$41$	8.09326			1.26395			0.631977	−	0.774987i	$-0.282244\pi$
$41$	8.09326			1.26395			0.631977	+	0.774987i	$0.282244\pi$
$42$		0			0
$43$		−	4.12236i		−	0.628655i	−0.949315	−	0.314327i	$-0.898221\pi$
$43$		−	4.12236i		−	0.628655i	0.949315	−	0.314327i	$-0.101779\pi$
$44$	−3.20392	+	0.857262i	−0.483009	+	0.129237i
$45$		0			0
$46$		−	3.37576i		−	0.497729i
$47$		−	8.77571i		−	1.28007i	−0.768346	−	0.640034i	$-0.778920\pi$
$47$		−	8.77571i		−	1.28007i	0.768346	−	0.640034i	$-0.221080\pi$
$48$		0			0
$49$	4.26510	+	5.55058i	0.609300	+	0.792940i
$50$			4.37083i			0.618129i
$51$		0			0
$52$	−0.338760			−0.0469775
$53$	−13.5623			−1.86292			−0.931461	−	0.363841i	$-0.881465\pi$
$53$	−13.5623			−1.86292			−0.931461	+	0.363841i	$0.881465\pi$
$54$		0			0
$55$	−2.62424	−	9.80778i	−0.353852	−	1.32248i
$56$	−1.16938	+	2.37330i	−0.156265	+	0.317145i
$57$		0			0
$58$	4.40784			0.578778
$59$		−	4.67752i		−	0.608961i	−0.952519	−	0.304481i	$-0.901517\pi$
$59$		−	4.67752i		−	0.608961i	0.952519	−	0.304481i	$-0.0984829\pi$
$60$		0			0
$61$	13.7836			1.76481			0.882405	−	0.470491i	$-0.155923\pi$
$61$	13.7836			1.76481			0.882405	+	0.470491i	$0.155923\pi$
$62$	0.722422			0.0917477
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	1.03700i		−	0.128625i
$66$		0			0
$67$	−1.73032			−0.211392			−0.105696	−	0.994398i	$-0.533707\pi$
$67$	−1.73032			−0.211392			−0.105696	+	0.994398i	$0.533707\pi$
$68$	−0.314583			−0.0381488
$69$		0			0
$70$	−7.26510	−	3.57968i	−0.868346	−	0.427854i
$71$	−13.5465			−1.60767			−0.803836	−	0.594851i	$-0.797211\pi$
$71$	−13.5465			−1.60767			−0.803836	+	0.594851i	$0.797211\pi$
$72$		0			0
$73$	−1.68542			−0.197263			−0.0986316	−	0.995124i	$-0.531447\pi$
$73$	−1.68542			−0.197263			−0.0986316	+	0.995124i	$0.531447\pi$
$74$			7.49320i			0.871067i
$75$		0			0
$76$	−6.09326			−0.698944
$77$	8.60633	+	1.71206i	0.980782	+	0.195107i
$78$		0			0
$79$			6.86896i			0.772819i	0.922327	+	0.386409i	$0.126285\pi$
$79$			6.86896i			0.772819i	−0.922327	+	0.386409i	$0.873715\pi$
$80$		−	3.06118i		−	0.342251i
$81$		0			0
$82$		−	8.09326i		−	0.893751i
$83$	−7.11447			−0.780914			−0.390457	−	0.920621i	$-0.627683\pi$
$83$	−7.11447			−0.780914			−0.390457	+	0.920621i	$0.627683\pi$
$84$		0			0
$85$		−	0.962995i		−	0.104451i
$86$	−4.12236			−0.444526
$87$		0			0
$88$	0.857262	+	3.20392i	0.0913845	+	0.341539i
$89$			2.28548i			0.242260i	0.992637	+	0.121130i	$0.0386518\pi$
$89$			2.28548i			0.242260i	−0.992637	+	0.121130i	$0.961348\pi$
$90$		0			0
$91$	0.803978	+	0.396139i	0.0842798	+	0.0415266i
$92$	−3.37576			−0.351948
$93$		0			0
$94$	−8.77571			−0.905145
$95$		−	18.6526i		−	1.91371i
$96$		0			0
$97$		−	5.08536i		−	0.516340i	−0.966100	−	0.258170i	$-0.916881\pi$
$97$		−	5.08536i		−	0.516340i	0.966100	−	0.258170i	$-0.0831195\pi$
$98$	5.55058	−	4.26510i	0.560693	−	0.430840i
$99$		0			0
$100$	4.37083			0.437083
$101$	−9.71452			−0.966631			−0.483316	−	0.875446i	$-0.660568\pi$
$101$	−9.71452			−0.966631			−0.483316	+	0.875446i	$0.660568\pi$
$102$		0			0
$103$			6.70663i			0.660824i	0.943837	+	0.330412i	$0.107188\pi$
$103$			6.70663i			0.660824i	−0.943837	+	0.330412i	$0.892812\pi$
$104$			0.338760i			0.0332181i
$105$		0			0
$106$			13.5623i			1.31728i
$107$		−	9.71452i		−	0.939139i	−0.882896	−	0.469569i	$-0.844409\pi$
$107$		−	9.71452i		−	0.939139i	0.882896	−	0.469569i	$-0.155591\pi$
$108$		0			0
$109$		−	18.9913i		−	1.81904i	−0.415661	−	0.909520i	$-0.636450\pi$
$109$		−	18.9913i		−	1.81904i	0.415661	−	0.909520i	$-0.363550\pi$
$110$	−9.80778	+	2.62424i	−0.935135	+	0.250211i
$111$		0			0
$112$	2.37330	+	1.16938i	0.224256	+	0.110496i
$113$	11.1012			1.04431			0.522154	−	0.852851i	$-0.325128\pi$
$113$	11.1012			1.04431			0.522154	+	0.852851i	$0.325128\pi$
$114$		0			0
$115$		−	10.3338i		−	0.963635i
$116$		−	4.40784i		−	0.409258i
$117$		0			0
$118$	−4.67752			−0.430601
$119$	0.746599	+	0.367867i	0.0684406	+	0.0337223i
$120$		0			0
$121$	9.53020	−	5.49320i	0.866382	−	0.499382i
$122$		−	13.7836i		−	1.24791i
$123$		0			0
$124$		−	0.722422i		−	0.0648754i
$125$		−	1.92599i		−	0.172266i
$126$		0			0
$127$			21.6106i			1.91763i	0.284025	+	0.958817i	$0.408330\pi$
$127$			21.6106i			1.91763i	−0.284025	+	0.958817i	$0.591670\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−1.03700			−0.0909514
$131$	−13.9459			−1.21846			−0.609231	−	0.792993i	$-0.708522\pi$
$131$	−13.9459			−1.21846			−0.609231	+	0.792993i	$0.708522\pi$
$132$		0			0
$133$	14.4611	+	7.12533i	1.25394	+	0.617845i
$134$			1.73032i			0.149477i
$135$		0			0
$136$			0.314583i			0.0269752i
$137$	−11.7787			−1.00632			−0.503160	−	0.864193i	$-0.667829\pi$
$137$	−11.7787			−1.00632			−0.503160	+	0.864193i	$0.667829\pi$
$138$		0			0
$139$	−7.53810			−0.639373			−0.319687	−	0.947523i	$-0.603578\pi$
$139$	−7.53810			−0.639373			−0.319687	+	0.947523i	$0.603578\pi$
$140$	−3.57968	+	7.26510i	−0.302539	+	0.614013i
$141$		0			0
$142$			13.5465i			1.13680i
$143$	1.08536	−	0.290406i	0.0907623	−	0.0242850i
$144$		0			0
$145$	13.4932			1.12055
$146$			1.68542i			0.139486i
$147$		0			0
$148$	7.49320			0.615937
$149$			9.42905i			0.772458i	0.922403	+	0.386229i	$0.126223\pi$
$149$			9.42905i			0.772458i	−0.922403	+	0.386229i	$0.873777\pi$
$150$		0			0
$151$		−	9.09029i		−	0.739757i	−0.929080	−	0.369879i	$-0.879399\pi$
$151$		−	9.09029i		−	0.739757i	0.929080	−	0.369879i	$-0.120601\pi$
$152$			6.09326i			0.494228i
$153$		0			0
$154$	1.71206	−	8.60633i	0.137962	−	0.693518i
$155$	2.21147			0.177629
$156$		0			0
$157$		−	8.45274i		−	0.674602i	−0.941397	−	0.337301i	$-0.890486\pi$
$157$		−	8.45274i		−	0.674602i	0.941397	−	0.337301i	$-0.109514\pi$
$158$	6.86896			0.546465
$159$		0			0
$160$	−3.06118			−0.242008
$161$	8.01170	+	3.94755i	0.631410	+	0.311111i
$162$		0			0
$163$	11.2077			0.877857			0.438928	−	0.898522i	$-0.355358\pi$
$163$	11.2077			0.877857			0.438928	+	0.898522i	$0.355358\pi$
$164$	−8.09326			−0.631977
$165$		0			0
$166$			7.11447i			0.552190i
$167$	14.6933			1.13700			0.568501	−	0.822682i	$-0.307523\pi$
$167$	14.6933			1.13700			0.568501	+	0.822682i	$0.307523\pi$
$168$		0			0
$169$	−12.8852			−0.991172
$170$	−0.962995			−0.0738583
$171$		0			0
$172$			4.12236i			0.314327i
$173$	11.2077			0.852107			0.426054	−	0.904698i	$-0.359903\pi$
$173$	11.2077			0.852107			0.426054	+	0.904698i	$0.359903\pi$
$174$		0			0
$175$	−10.3733	−	5.11117i	−0.784148	−	0.386368i
$176$	3.20392	−	0.857262i	0.241505	−	0.0646186i
$177$		0			0
$178$	2.28548			0.171304
$179$	19.0446			1.42346			0.711731	−	0.702453i	$-0.247912\pi$
$179$	19.0446			1.42346			0.711731	+	0.702453i	$0.247912\pi$
$180$		0			0
$181$		−	14.5435i		−	1.08101i	−0.841341	−	0.540505i	$-0.818233\pi$
$181$		−	14.5435i		−	1.08101i	0.841341	−	0.540505i	$-0.181767\pi$
$182$	0.396139	−	0.803978i	0.0293638	−	0.0595948i
$183$		0			0
$184$			3.37576i			0.248865i
$185$			22.9380i			1.68644i
$186$		0			0
$187$	1.00790	−	0.269680i	0.0737048	−	0.0197209i
$188$			8.77571i			0.640034i
$189$		0			0
$190$	−18.6526			−1.35320
$191$	6.11743			0.442642			0.221321	−	0.975201i	$-0.428963\pi$
$191$	6.11743			0.442642			0.221321	+	0.975201i	$0.428963\pi$
$192$		0			0
$193$			10.7515i			0.773912i	0.922098	+	0.386956i	$0.126473\pi$
$193$			10.7515i			0.773912i	−0.922098	+	0.386956i	$0.873527\pi$
$194$	−5.08536			−0.365107
$195$		0			0
$196$	−4.26510	−	5.55058i	−0.304650	−	0.396470i
$197$			25.9010i			1.84537i	0.385552	+	0.922686i	$0.374011\pi$
$197$			25.9010i			1.84537i	−0.385552	+	0.922686i	$0.625989\pi$
$198$		0			0
$199$			19.5707i			1.38733i	0.720299	+	0.693664i	$0.244005\pi$
$199$			19.5707i			1.38733i	−0.720299	+	0.693664i	$0.755995\pi$
$200$		−	4.37083i		−	0.309065i
$201$		0			0
$202$			9.71452i			0.683512i
$203$	−5.15444	+	10.4611i	−0.361771	+	0.734227i
$204$		0			0
$205$		−	24.7749i		−	1.73036i
$206$	6.70663			0.467273
$207$		0			0
$208$	0.338760			0.0234888
$209$	19.5223	−	5.22352i	1.35039	−	0.361318i
$210$		0			0
$211$			5.95165i			0.409728i	0.978790	+	0.204864i	$0.0656752\pi$
$211$			5.95165i			0.409728i	−0.978790	+	0.204864i	$0.934325\pi$
$212$	13.5623			0.931461
$213$		0			0
$214$	−9.71452			−0.664071
$215$	−12.6193			−0.860629
$216$		0			0
$217$	−0.844786	+	1.71452i	−0.0573478	+	0.116389i
$218$	−18.9913			−1.28625
$219$		0			0
$220$	2.62424	+	9.80778i	0.176926	+	0.661240i
$221$	0.106568			0.00716854
$222$		0			0
$223$		−	8.04490i		−	0.538727i	−0.963039	−	0.269363i	$-0.913187\pi$
$223$		−	8.04490i		−	0.538727i	0.963039	−	0.269363i	$-0.0868132\pi$
$224$	1.16938	−	2.37330i	0.0781325	−	0.158573i
$225$		0			0
$226$		−	11.1012i		−	0.738438i
$227$	−17.0155			−1.12936			−0.564679	−	0.825310i	$-0.691000\pi$
$227$	−17.0155			−1.12936			−0.564679	+	0.825310i	$0.691000\pi$
$228$		0			0
$229$			24.7942i			1.63845i	0.573476	+	0.819223i	$0.305595\pi$
$229$			24.7942i			1.63845i	−0.573476	+	0.819223i	$0.694405\pi$
$230$	−10.3338			−0.681393
$231$		0			0
$232$	−4.40784			−0.289389
$233$		−	0.170718i		−	0.0111841i	−0.999984	−	0.00559204i	$-0.998220\pi$
$233$		−	0.170718i		−	0.0111841i	0.999984	−	0.00559204i	$-0.00178001\pi$
$234$		0			0
$235$	−26.8640			−1.75242
$236$			4.67752i			0.304481i
$237$		0			0
$238$	0.367867	−	0.746599i	0.0238453	−	0.0483948i
$239$			18.8897i			1.22187i	0.791680	+	0.610936i	$0.209207\pi$
$239$			18.8897i			1.22187i	−0.791680	+	0.610936i	$0.790793\pi$
$240$		0			0
$241$	0.436947			0.0281462			0.0140731	−	0.999901i	$-0.495520\pi$
$241$	0.436947			0.0281462			0.0140731	+	0.999901i	$0.495520\pi$
$242$	−5.49320	−	9.53020i	−0.353116	−	0.612625i
$243$		0			0
$244$	−13.7836			−0.882405
$245$	16.9913	−	13.0563i	1.08554	−	0.834133i
$246$		0			0
$247$	2.06415			0.131339
$248$	−0.722422			−0.0458739
$249$		0			0
$250$	−1.92599			−0.121810
$251$		−	6.69332i		−	0.422478i	−0.977434	−	0.211239i	$-0.932250\pi$
$251$		−	6.69332i		−	0.422478i	0.977434	−	0.211239i	$-0.0677499\pi$
$252$		0			0
$253$	10.8157	−	2.89392i	0.679976	−	0.181939i
$254$	21.6106			1.35597
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	9.08536i		−	0.566729i	−0.959012	−	0.283365i	$-0.908549\pi$
$257$		−	9.08536i		−	0.566729i	0.959012	−	0.283365i	$-0.0914506\pi$
$258$		0			0
$259$	−17.7836	−	8.76239i	−1.10502	−	0.544469i
$260$			1.03700i			0.0643123i
$261$		0			0
$262$			13.9459i			0.861583i
$263$			14.7591i			0.910087i	0.890469	+	0.455044i	$0.150376\pi$
$263$			14.7591i			0.910087i	−0.890469	+	0.455044i	$0.849624\pi$
$264$		0			0
$265$			41.5166i			2.55034i
$266$	7.12533	−	14.4611i	0.436882	−	0.886668i
$267$		0			0
$268$	1.73032			0.105696
$269$			29.1835i			1.77935i	0.456592	+	0.889676i	$0.349070\pi$
$269$			29.1835i			1.77935i	−0.456592	+	0.889676i	$0.650930\pi$
$270$		0			0
$271$	−12.8048			−0.777837			−0.388919	−	0.921272i	$-0.627151\pi$
$271$	−12.8048			−0.777837			−0.388919	+	0.921272i	$0.627151\pi$
$272$	0.314583			0.0190744
$273$		0			0
$274$			11.7787i			0.711576i
$275$	−14.0038	+	3.74695i	−0.844461	+	0.225950i
$276$		0			0
$277$		−	12.9272i		−	0.776719i	−0.921508	−	0.388359i	$-0.873042\pi$
$277$		−	12.9272i		−	0.776719i	0.921508	−	0.388359i	$-0.126958\pi$
$278$			7.53810i			0.452105i
$279$		0			0
$280$	7.26510	+	3.57968i	0.434173	+	0.213927i
$281$			13.7787i			0.821967i	0.911643	+	0.410983i	$0.134815\pi$
$281$			13.7787i			0.821967i	−0.911643	+	0.410983i	$0.865185\pi$
$282$		0			0
$283$	14.1998			0.844092			0.422046	−	0.906574i	$-0.361312\pi$
$283$	14.1998			0.844092			0.422046	+	0.906574i	$0.361312\pi$
$284$	13.5465			0.803836
$285$		0			0
$286$	−0.290406	−	1.08536i	−0.0171721	−	0.0641786i
$287$	19.2077	+	9.46409i	1.13380	+	0.558648i
$288$		0			0
$289$	−16.9010			−0.994179
$290$		−	13.4932i		−	0.792348i
$291$		0			0
$292$	1.68542			0.0986316
$293$	−7.05280			−0.412029			−0.206015	−	0.978549i	$-0.566049\pi$
$293$	−7.05280			−0.412029			−0.206015	+	0.978549i	$0.566049\pi$
$294$		0			0
$295$	−14.3187			−0.833669
$296$		−	7.49320i		−	0.435533i
$297$		0			0
$298$	9.42905			0.546210
$299$	1.14357			0.0661345
$300$		0			0
$301$	4.82061	−	9.78360i	0.277855	−	0.563918i
$302$	−9.09029			−0.523087
$303$		0			0
$304$	6.09326			0.349472
$305$		−	42.1941i		−	2.41603i
$306$		0			0
$307$	19.5381			1.11510			0.557549	−	0.830144i	$-0.311742\pi$
$307$	19.5381			1.11510			0.557549	+	0.830144i	$0.311742\pi$
$308$	−8.60633	−	1.71206i	−0.490391	−	0.0975536i
$309$		0			0
$310$		−	2.21147i		−	0.125603i
$311$			7.85346i			0.445329i	0.974895	+	0.222664i	$0.0714754\pi$
$311$			7.85346i			0.445329i	−0.974895	+	0.222664i	$0.928525\pi$
$312$		0			0
$313$		−	17.7281i		−	1.00205i	−0.865433	−	0.501025i	$-0.832957\pi$
$313$		−	17.7281i		−	1.00205i	0.865433	−	0.501025i	$-0.167043\pi$
$314$	−8.45274			−0.477016
$315$		0			0
$316$		−	6.86896i		−	0.386409i
$317$	−0.746599			−0.0419332			−0.0209666	−	0.999780i	$-0.506674\pi$
$317$	−0.746599			−0.0419332			−0.0209666	+	0.999780i	$0.506674\pi$
$318$		0			0
$319$	3.77867	+	14.1224i	0.211565	+	0.790701i
$320$			3.06118i			0.171125i
$321$		0			0
$322$	3.94755	−	8.01170i	0.219988	−	0.446475i
$323$	1.91683			0.106655
$324$		0			0
$325$	−1.48066			−0.0821324
$326$		−	11.2077i		−	0.620738i
$327$		0			0
$328$			8.09326i			0.446875i
$329$	10.2621	−	20.8274i	0.565770	−	1.14825i
$330$		0			0
$331$	−1.50899			−0.0829418			−0.0414709	−	0.999140i	$-0.513204\pi$
$331$	−1.50899			−0.0829418			−0.0414709	+	0.999140i	$0.513204\pi$
$332$	7.11447			0.390457
$333$		0			0
$334$		−	14.6933i		−	0.803982i
$335$			5.29682i			0.289396i
$336$		0			0
$337$		−	5.38663i		−	0.293428i	−0.989179	−	0.146714i	$-0.953130\pi$
$337$		−	5.38663i		−	0.293428i	0.989179	−	0.146714i	$-0.0468698\pi$
$338$			12.8852i			0.700865i
$339$		0			0
$340$			0.962995i			0.0522257i
$341$	0.619305	+	2.31458i	0.0335373	+	0.125342i
$342$		0			0
$343$	3.63163	+	18.1607i	0.196090	+	0.980586i
$344$	4.12236			0.222263
$345$		0			0
$346$		−	11.2077i		−	0.602531i
$347$		−	21.8761i		−	1.17437i	−0.809453	−	0.587185i	$-0.800236\pi$
$347$		−	21.8761i		−	1.17437i	0.809453	−	0.587185i	$-0.199764\pi$
$348$		0			0
$349$	−1.73525			−0.0928858			−0.0464429	−	0.998921i	$-0.514789\pi$
$349$	−1.73525			−0.0928858			−0.0464429	+	0.998921i	$0.514789\pi$
$350$	−5.11117	+	10.3733i	−0.273203	+	0.554476i
$351$		0			0
$352$	−0.857262	−	3.20392i	−0.0456922	−	0.170769i
$353$			20.8874i			1.11173i	0.831274	+	0.555863i	$0.187612\pi$
$353$			20.8874i			1.11173i	−0.831274	+	0.555863i	$0.812388\pi$
$354$		0			0
$355$			41.4682i			2.20091i
$356$		−	2.28548i		−	0.121130i
$357$		0			0
$358$		−	19.0446i		−	1.00654i
$359$			28.5786i			1.50832i	0.656692	+	0.754159i	$0.271955\pi$
$359$			28.5786i			1.50832i	−0.656692	+	0.754159i	$0.728045\pi$
$360$		0			0
$361$	18.1278			0.954094
$362$	−14.5435			−0.764390
$363$		0			0
$364$	−0.803978	−	0.396139i	−0.0421399	−	0.0207633i
$365$			5.15937i			0.270054i
$366$		0			0
$367$		−	30.0759i		−	1.56995i	−0.619528	−	0.784975i	$-0.712676\pi$
$367$		−	30.0759i		−	1.56995i	0.619528	−	0.784975i	$-0.287324\pi$
$368$	3.37576			0.175974
$369$		0			0
$370$	22.9380			1.19249
$371$	−32.1873	−	15.8595i	−1.67108	−	0.823382i
$372$		0			0
$373$			33.3508i			1.72684i	0.504486	+	0.863420i	$0.331682\pi$
$373$			33.3508i			1.72684i	−0.504486	+	0.863420i	$0.668318\pi$
$374$	−0.269680	−	1.00790i	−0.0139448	−	0.0521172i
$375$		0			0
$376$	8.77571			0.452572
$377$			1.49320i			0.0769036i
$378$		0			0
$379$	6.42364			0.329960			0.164980	−	0.986297i	$-0.447244\pi$
$379$	6.42364			0.329960			0.164980	+	0.986297i	$0.447244\pi$
$380$			18.6526i			0.956856i
$381$		0			0
$382$		−	6.11743i		−	0.312995i
$383$			12.1949i			0.623130i	0.950225	+	0.311565i	$0.100853\pi$
$383$			12.1949i			0.623130i	−0.950225	+	0.311565i	$0.899147\pi$
$384$		0			0
$385$	5.24092	−	26.3455i	0.267102	−	1.34269i
$386$	10.7515			0.547238
$387$		0			0
$388$			5.08536i			0.258170i
$389$	12.7466			0.646278			0.323139	−	0.946351i	$-0.395262\pi$
$389$	12.7466			0.646278			0.323139	+	0.946351i	$0.395262\pi$
$390$		0			0
$391$	1.06196			0.0537055
$392$	−5.55058	+	4.26510i	−0.280346	+	0.215420i
$393$		0			0
$394$	25.9010			1.30488
$395$	21.0271			1.05799
$396$		0			0
$397$		−	20.3146i		−	1.01956i	−0.860305	−	0.509780i	$-0.829727\pi$
$397$		−	20.3146i		−	1.01956i	0.860305	−	0.509780i	$-0.170273\pi$
$398$	19.5707			0.980989
$399$		0			0
$400$	−4.37083			−0.218542
$401$	0.792277			0.0395644			0.0197822	−	0.999804i	$-0.493703\pi$
$401$	0.792277			0.0395644			0.0197822	+	0.999804i	$0.493703\pi$
$402$		0			0
$403$			0.244728i			0.0121907i
$404$	9.71452			0.483316
$405$		0			0
$406$	10.4611	+	5.15444i	0.519177	+	0.255810i
$407$	−24.0076	+	6.42364i	−1.19001	+	0.318408i
$408$		0			0
$409$	26.6077			1.31566			0.657832	−	0.753165i	$-0.271474\pi$
$409$	26.6077			1.31566			0.657832	+	0.753165i	$0.271474\pi$
$410$	−24.7749			−1.22355
$411$		0			0
$412$		−	6.70663i		−	0.330412i
$413$	5.46980	−	11.1012i	0.269151	−	0.546252i
$414$		0			0
$415$			21.7787i			1.06907i
$416$		−	0.338760i		−	0.0166091i
$417$		0			0
$418$	−5.22352	−	19.5223i	−0.255491	−	0.954867i
$419$			10.9380i			0.534358i	0.963647	+	0.267179i	$0.0860916\pi$
$419$			10.9380i			0.534358i	−0.963647	+	0.267179i	$0.913908\pi$
$420$		0			0
$421$	30.3829			1.48077			0.740386	−	0.672182i	$-0.234643\pi$
$421$	30.3829			1.48077			0.740386	+	0.672182i	$0.234643\pi$
$422$	5.95165			0.289722
$423$		0			0
$424$		−	13.5623i		−	0.658642i
$425$	−1.37499			−0.0666968
$426$		0			0
$427$	32.7126	+	16.1183i	1.58307	+	0.780018i
$428$			9.71452i			0.469569i
$429$		0			0
$430$			12.6193i			0.608557i
$431$			24.1458i			1.16306i	0.813525	+	0.581530i	$0.197546\pi$
$431$			24.1458i			1.16306i	−0.813525	+	0.581530i	$0.802454\pi$
$432$		0			0
$433$			13.5031i			0.648916i	0.945900	+	0.324458i	$0.105182\pi$
$433$			13.5031i			0.648916i	−0.945900	+	0.324458i	$0.894818\pi$
$434$	1.71452	+	0.844786i	0.0822998	+	0.0405510i
$435$		0			0
$436$			18.9913i			0.909520i
$437$	20.5694			0.983968
$438$		0			0
$439$	−30.5911			−1.46003			−0.730017	−	0.683429i	$-0.760488\pi$
$439$	−30.5911			−1.46003			−0.730017	+	0.683429i	$0.760488\pi$
$440$	9.80778	−	2.62424i	0.467568	−	0.125106i
$441$		0			0
$442$		−	0.106568i		−	0.00506892i
$443$	−28.8739			−1.37184			−0.685920	−	0.727677i	$-0.740600\pi$
$443$	−28.8739			−1.37184			−0.685920	+	0.727677i	$0.740600\pi$
$444$		0			0
$445$	6.99626			0.331654
$446$	−8.04490			−0.380937
$447$		0			0
$448$	−2.37330	−	1.16938i	−0.112128	−	0.0552480i
$449$	20.5944			0.971908			0.485954	−	0.873984i	$-0.338472\pi$
$449$	20.5944			0.971908			0.485954	+	0.873984i	$0.338472\pi$
$450$		0			0
$451$	25.9301	−	6.93804i	1.22100	−	0.326700i
$452$	−11.1012			−0.522154
$453$		0			0
$454$			17.0155i			0.798577i
$455$	1.21265	−	2.46112i	0.0568500	−	0.115379i
$456$		0			0
$457$			6.87983i			0.321825i	0.986969	+	0.160912i	$0.0514437\pi$
$457$			6.87983i			0.321825i	−0.986969	+	0.160912i	$0.948556\pi$
$458$	24.7942			1.15856
$459$		0			0
$460$			10.3338i			0.481817i
$461$	16.2681			0.757682			0.378841	−	0.925462i	$-0.376323\pi$
$461$	16.2681			0.757682			0.378841	+	0.925462i	$0.376323\pi$
$462$		0			0
$463$	17.5899			0.817472			0.408736	−	0.912653i	$-0.365970\pi$
$463$	17.5899			0.817472			0.408736	+	0.912653i	$0.365970\pi$
$464$			4.40784i			0.204629i
$465$		0			0
$466$	−0.170718			−0.00790834
$467$		−	41.0022i		−	1.89736i	−0.316245	−	0.948678i	$-0.602422\pi$
$467$		−	41.0022i		−	1.89736i	0.316245	−	0.948678i	$-0.397578\pi$
$468$		0			0
$469$	−4.10657	−	2.02340i	−0.189624	−	0.0934320i
$470$			26.8640i			1.23915i
$471$		0			0
$472$	4.67752			0.215300
$473$	−3.53395	−	13.2077i	−0.162491	−	0.607292i
$474$		0			0
$475$	−26.6326			−1.22199
$476$	−0.746599	−	0.367867i	−0.0342203	−	0.0168611i
$477$		0			0
$478$	18.8897			0.863994
$479$	−4.29308			−0.196156			−0.0980779	−	0.995179i	$-0.531269\pi$
$479$	−4.29308			−0.196156			−0.0980779	+	0.995179i	$0.531269\pi$
$480$		0			0
$481$	−2.53839			−0.115741
$482$		−	0.436947i		−	0.0199024i
$483$		0			0
$484$	−9.53020	+	5.49320i	−0.433191	+	0.249691i
$485$	−15.5672			−0.706871
$486$		0			0
$487$	−14.8897			−0.674716			−0.337358	−	0.941376i	$-0.609533\pi$
$487$	−14.8897			−0.674716			−0.337358	+	0.941376i	$0.609533\pi$
$488$			13.7836i			0.623954i
$489$		0			0
$490$	−13.0563	−	16.9913i	−0.589821	−	0.767590i
$491$		−	4.35949i		−	0.196741i	−0.995150	−	0.0983704i	$-0.968637\pi$
$491$		−	4.35949i		−	0.196741i	0.995150	−	0.0983704i	$-0.0313630\pi$
$492$		0			0
$493$			1.38663i			0.0624507i
$494$		−	2.06415i		−	0.0928705i
$495$		0			0
$496$			0.722422i			0.0324377i
$497$	−32.1499	−	15.8410i	−1.44212	−	0.710565i
$498$		0			0
$499$	−6.73573			−0.301533			−0.150766	−	0.988569i	$-0.548174\pi$
$499$	−6.73573			−0.301533			−0.150766	+	0.988569i	$0.548174\pi$
$500$			1.92599i			0.0861329i
$501$		0			0
$502$	−6.69332			−0.298737
$503$	−43.4275			−1.93634			−0.968168	−	0.250300i	$-0.919471\pi$
$503$	−43.4275			−1.93634			−0.968168	+	0.250300i	$0.919471\pi$
$504$		0			0
$505$			29.7379i			1.32332i
$506$	−2.89392	−	10.8157i	−0.128650	−	0.480816i
$507$		0			0
$508$		−	21.6106i		−	0.958817i
$509$		−	6.18729i		−	0.274247i	−0.990554	−	0.137123i	$-0.956214\pi$
$509$		−	6.18729i		−	0.274247i	0.990554	−	0.137123i	$-0.0437857\pi$
$510$		0			0
$511$	−4.00000	−	1.97089i	−0.176950	−	0.0871872i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−9.08536			−0.400738
$515$	20.5302			0.904669
$516$		0			0
$517$	−7.52308	−	28.1167i	−0.330865	−	1.23657i
$518$	−8.76239	+	17.7836i	−0.384998	+	0.781367i
$519$		0			0
$520$	1.03700			0.0454757
$521$		−	15.2659i		−	0.668813i	−0.942429	−	0.334406i	$-0.891464\pi$
$521$		−	15.2659i		−	0.668813i	0.942429	−	0.334406i	$-0.108536\pi$
$522$		0			0
$523$	−12.4021			−0.542307			−0.271154	−	0.962536i	$-0.587405\pi$
$523$	−12.4021			−0.542307			−0.271154	+	0.962536i	$0.587405\pi$
$524$	13.9459			0.609231
$525$		0			0
$526$	14.7591			0.643529
$527$			0.227262i			0.00989967i
$528$		0			0
$529$	−11.6042			−0.504531
$530$	41.5166			1.80337
$531$		0			0
$532$	−14.4611	−	7.12533i	−0.626969	−	0.308922i
$533$	2.74167			0.118755
$534$		0			0
$535$	−29.7379			−1.28568
$536$		−	1.73032i		−	0.0747384i
$537$		0			0
$538$	29.1835			1.25819
$539$	18.4233	+	14.1273i	0.793550	+	0.608506i
$540$		0			0
$541$		−	31.2768i		−	1.34469i	−0.740236	−	0.672347i	$-0.765286\pi$
$541$		−	31.2768i		−	1.34469i	0.740236	−	0.672347i	$-0.234714\pi$
$542$			12.8048i			0.550014i
$543$		0			0
$544$		−	0.314583i		−	0.0134876i
$545$	−58.1359			−2.49027
$546$		0			0
$547$			21.1729i			0.905288i	0.891691	+	0.452644i	$0.149519\pi$
$547$			21.1729i			0.905288i	−0.891691	+	0.452644i	$0.850481\pi$
$548$	11.7787			0.503160
$549$		0			0
$550$	3.74695	+	14.0038i	0.159771	+	0.597124i
$551$			26.8581i			1.14419i
$552$		0			0
$553$	−8.03243	+	16.3021i	−0.341574	+	0.693236i
$554$	−12.9272			−0.549223
$555$		0			0
$556$	7.53810			0.319687
$557$			8.50455i			0.360349i	0.983635	+	0.180175i	$0.0576663\pi$
$557$			8.50455i			0.360349i	−0.983635	+	0.180175i	$0.942334\pi$
$558$		0			0
$559$		−	1.39649i		−	0.0590653i
$560$	3.57968	−	7.26510i	0.151269	−	0.307007i
$561$		0			0
$562$	13.7787			0.581218
$563$	4.14161			0.174548			0.0872740	−	0.996184i	$-0.472184\pi$
$563$	4.14161			0.174548			0.0872740	+	0.996184i	$0.472184\pi$
$564$		0			0
$565$		−	33.9827i		−	1.42966i
$566$		−	14.1998i		−	0.596863i
$567$		0			0
$568$		−	13.5465i		−	0.568398i
$569$		−	32.7335i		−	1.37226i	−0.727480	−	0.686129i	$-0.759308\pi$
$569$		−	32.7335i		−	1.37226i	0.727480	−	0.686129i	$-0.240692\pi$
$570$		0			0
$571$		−	45.8603i		−	1.91919i	−0.281379	−	0.959597i	$-0.590792\pi$
$571$		−	45.8603i		−	1.91919i	0.281379	−	0.959597i	$-0.409208\pi$
$572$	−1.08536	+	0.290406i	−0.0453811	+	0.0121425i
$573$		0			0
$574$	9.46409	−	19.2077i	0.395024	−	0.801715i
$575$	−14.7549			−0.615322
$576$		0			0
$577$			9.33009i			0.388417i	0.980960	+	0.194208i	$0.0622138\pi$
$577$			9.33009i			0.388417i	−0.980960	+	0.194208i	$0.937786\pi$
$578$			16.9010i			0.702990i
$579$		0			0
$580$	−13.4932			−0.560275
$581$	−16.8848	−	8.31951i	−0.700498	−	0.345152i
$582$		0			0
$583$	−43.4525	+	11.6264i	−1.79962	+	0.481517i
$584$		−	1.68542i		−	0.0697431i
$585$		0			0
$586$			7.05280i			0.291349i
$587$		−	0.922247i		−	0.0380652i	−0.999819	−	0.0190326i	$-0.993941\pi$
$587$		−	0.922247i		−	0.0380652i	0.999819	−	0.0190326i	$-0.00605863\pi$
$588$		0			0
$589$			4.40190i			0.181377i
$590$			14.3187i			0.589493i
$591$		0			0
$592$	−7.49320			−0.307969
$593$	−41.7746			−1.71548			−0.857739	−	0.514085i	$-0.828132\pi$
$593$	−41.7746			−1.71548			−0.857739	+	0.514085i	$0.828132\pi$
$594$		0			0
$595$	1.12611	−	2.28548i	0.0461659	−	0.0936954i
$596$		−	9.42905i		−	0.386229i
$597$		0			0
$598$		−	1.14357i		−	0.0467642i
$599$	−7.13104			−0.291366			−0.145683	−	0.989331i	$-0.546538\pi$
$599$	−7.13104			−0.291366			−0.145683	+	0.989331i	$0.546538\pi$
$600$		0			0
$601$	25.3908			1.03571			0.517856	−	0.855468i	$-0.326730\pi$
$601$	25.3908			1.03571			0.517856	+	0.855468i	$0.326730\pi$
$602$	−9.78360	−	4.82061i	−0.398750	−	0.196473i
$603$		0			0
$604$			9.09029i			0.369879i
$605$	−16.8157	−	29.1737i	−0.683655	−	1.18608i
$606$		0			0
$607$	−45.0397			−1.82810			−0.914052	−	0.405597i	$-0.867064\pi$
$607$	−45.0397			−1.82810			−0.914052	+	0.405597i	$0.867064\pi$
$608$		−	6.09326i		−	0.247114i
$609$		0			0
$610$	−42.1941			−1.70839
$611$		−	2.97286i		−	0.120269i
$612$		0			0
$613$		−	21.1061i		−	0.852467i	−0.904613	−	0.426233i	$-0.859840\pi$
$613$		−	21.1061i		−	0.852467i	0.904613	−	0.426233i	$-0.140160\pi$
$614$		−	19.5381i		−	0.788494i
$615$		0			0
$616$	−1.71206	+	8.60633i	−0.0689808	+	0.346759i
$617$	1.21591			0.0489508			0.0244754	−	0.999700i	$-0.492208\pi$
$617$	1.21591			0.0489508			0.0244754	+	0.999700i	$0.492208\pi$
$618$		0			0
$619$		−	37.2817i		−	1.49848i	−0.662299	−	0.749240i	$-0.730419\pi$
$619$		−	37.2817i		−	1.49848i	0.662299	−	0.749240i	$-0.269581\pi$
$620$	−2.21147			−0.0888146
$621$		0			0
$622$	7.85346			0.314895
$623$	−2.67259	+	5.42412i	−0.107075	+	0.217313i
$624$		0			0
$625$	−27.7500			−1.11000
$626$	−17.7281			−0.708556
$627$		0			0
$628$			8.45274i			0.337301i
$629$	−2.35723			−0.0939890
$630$		0			0
$631$	−23.5356			−0.936938			−0.468469	−	0.883480i	$-0.655194\pi$
$631$	−23.5356			−0.936938			−0.468469	+	0.883480i	$0.655194\pi$
$632$	−6.86896			−0.273233
$633$		0			0
$634$			0.746599i			0.0296512i
$635$	66.1541			2.62524
$636$		0			0
$637$	1.44484	+	1.88031i	0.0572468	+	0.0745007i
$638$	14.1224	−	3.77867i	0.559110	−	0.149599i
$639$		0			0
$640$	3.06118			0.121004
$641$	−7.49320			−0.295964			−0.147982	−	0.988990i	$-0.547278\pi$
$641$	−7.49320			−0.295964			−0.147982	+	0.988990i	$0.547278\pi$
$642$		0			0
$643$		−	14.6101i		−	0.576168i	−0.957605	−	0.288084i	$-0.906982\pi$
$643$		−	14.6101i		−	0.576168i	0.957605	−	0.288084i	$-0.0930182\pi$
$644$	−8.01170	−	3.94755i	−0.315705	−	0.155555i
$645$		0			0
$646$		−	1.91683i		−	0.0754168i
$647$		−	42.6518i		−	1.67681i	−0.545044	−	0.838407i	$-0.683487\pi$
$647$		−	42.6518i		−	1.67681i	0.545044	−	0.838407i	$-0.316513\pi$
$648$		0			0
$649$	−4.00986	−	14.9864i	−0.157401	−	0.588268i
$650$			1.48066i			0.0580764i
$651$		0			0
$652$	−11.2077			−0.438928
$653$	11.3916			0.445786			0.222893	−	0.974843i	$-0.428450\pi$
$653$	11.3916			0.445786			0.222893	+	0.974843i	$0.428450\pi$
$654$		0			0
$655$			42.6911i			1.66808i
$656$	8.09326			0.315989
$657$		0			0
$658$	−20.8274	−	10.2621i	−0.811936	−	0.400060i
$659$			28.1616i			1.09702i	0.836144	+	0.548509i	$0.184804\pi$
$659$			28.1616i			1.09702i	−0.836144	+	0.548509i	$0.815196\pi$
$660$		0			0
$661$			33.4233i			1.30002i	0.759927	+	0.650009i	$0.225235\pi$
$661$			33.4233i			1.30002i	−0.759927	+	0.650009i	$0.774765\pi$
$662$			1.50899i			0.0586487i
$663$		0			0
$664$		−	7.11447i		−	0.276095i
$665$	21.8119	−	44.2681i	0.845831	−	1.71664i
$666$		0			0
$667$			14.8798i			0.576149i
$668$	−14.6933			−0.568501
$669$		0			0
$670$	5.29682			0.204634
$671$	44.1616	−	11.8162i	1.70484	−	0.456158i
$672$		0			0
$673$			36.2033i			1.39553i	0.716325	+	0.697767i	$0.245823\pi$
$673$			36.2033i			1.39553i	−0.716325	+	0.697767i	$0.754177\pi$
$674$	−5.38663			−0.207485
$675$		0			0
$676$	12.8852			0.495586
$677$	38.4221			1.47668			0.738340	−	0.674428i	$-0.235610\pi$
$677$	38.4221			1.47668			0.738340	+	0.674428i	$0.235610\pi$
$678$		0			0
$679$	5.94672	−	12.0691i	0.228214	−	0.463169i
$680$	0.962995			0.0369292
$681$		0			0
$682$	2.31458	−	0.619305i	0.0886300	−	0.0237144i
$683$	−5.44484			−0.208341			−0.104171	−	0.994559i	$-0.533219\pi$
$683$	−5.44484			−0.208341			−0.104171	+	0.994559i	$0.533219\pi$
$684$		0			0
$685$			36.0567i			1.37765i
$686$	18.1607	−	3.63163i	0.693379	−	0.138656i
$687$		0			0
$688$		−	4.12236i		−	0.157164i
$689$	−4.59435			−0.175031
$690$		0			0
$691$		−	0.850492i		−	0.0323542i	−0.999869	−	0.0161771i	$-0.994850\pi$
$691$		−	0.850492i		−	0.0323542i	0.999869	−	0.0161771i	$-0.00514956\pi$
$692$	−11.2077			−0.426054
$693$		0			0
$694$	−21.8761			−0.830405
$695$			23.0755i			0.875304i
$696$		0			0
$697$	2.54600			0.0964366
$698$			1.73525i			0.0656802i
$699$		0			0
$700$	10.3733	+	5.11117i	0.392074	+	0.193184i
$701$		−	18.9222i		−	0.714683i	−0.933974	−	0.357342i	$-0.883683\pi$
$701$		−	18.9222i		−	0.714683i	0.933974	−	0.357342i	$-0.116317\pi$
$702$		0			0
$703$	−45.6580			−1.72202
$704$	−3.20392	+	0.857262i	−0.120752	+	0.0323093i
$705$		0			0
$706$	20.8874			0.786109
$707$	−23.0555	−	11.3600i	−0.867090	−	0.427236i
$708$		0			0
$709$	−37.8021			−1.41969			−0.709843	−	0.704360i	$-0.751234\pi$
$709$	−37.8021			−1.41969			−0.709843	+	0.704360i	$0.751234\pi$
$710$	41.4682			1.55628
$711$		0			0
$712$	−2.28548			−0.0856518
$713$			2.43873i			0.0913311i
$714$		0			0
$715$	−0.888985	−	3.32248i	−0.0332462	−	0.124254i
$716$	−19.0446			−0.711731
$717$		0			0
$718$	28.5786			1.06654
$719$		−	36.6094i		−	1.36530i	−0.730746	−	0.682650i	$-0.760828\pi$
$719$		−	36.6094i		−	1.36530i	0.730746	−	0.682650i	$-0.239172\pi$
$720$		0			0
$721$	−7.84259	+	15.9168i	−0.292073	+	0.592774i
$722$		−	18.1278i		−	0.674646i
$723$		0			0
$724$			14.5435i			0.540505i
$725$		−	19.2659i		−	0.715519i
$726$		0			0
$727$		−	0.0449029i		−	0.00166536i	−1.00000		0.000832678i	$-0.999735\pi$
$727$		−	0.0449029i		−	0.00166536i	1.00000		0.000832678i	$-0.000265050\pi$
$728$	−0.396139	+	0.803978i	−0.0146819	+	0.0297974i
$729$		0			0
$730$	5.15937			0.190957
$731$		−	1.29682i		−	0.0479648i
$732$		0			0
$733$	−36.7601			−1.35777			−0.678883	−	0.734246i	$-0.737536\pi$
$733$	−36.7601			−1.35777			−0.678883	+	0.734246i	$0.737536\pi$
$734$	−30.0759			−1.11012
$735$		0			0
$736$		−	3.37576i		−	0.124432i
$737$	−5.54381	+	1.48334i	−0.204209	+	0.0546395i
$738$		0			0
$739$		−	6.07995i		−	0.223654i	−0.993728	−	0.111827i	$-0.964330\pi$
$739$		−	6.07995i		−	0.223654i	0.993728	−	0.111827i	$-0.0356703\pi$
$740$		−	22.9380i		−	0.843219i
$741$		0			0
$742$	−15.8595	+	32.1873i	−0.582219	+	1.18163i
$743$			1.93585i			0.0710195i	0.999369	+	0.0355097i	$0.0113055\pi$
$743$			1.93585i			0.0710195i	−0.999369	+	0.0355097i	$0.988695\pi$
$744$		0			0
$745$	28.8640			1.05750
$746$	33.3508			1.22106
$747$		0			0
$748$	−1.00790	+	0.269680i	−0.0368524	+	0.00986047i
$749$	11.3600	−	23.0555i	0.415084	−	0.842429i
$750$		0			0
$751$	−8.58081			−0.313118			−0.156559	−	0.987669i	$-0.550040\pi$
$751$	−8.58081			−0.313118			−0.156559	+	0.987669i	$0.550040\pi$
$752$		−	8.77571i		−	0.320017i
$753$		0			0
$754$	1.49320			0.0543791
$755$	−27.8270			−1.01273
$756$		0			0
$757$	33.6955			1.22468			0.612342	−	0.790593i	$-0.290228\pi$
$757$	33.6955			1.22468			0.612342	+	0.790593i	$0.290228\pi$
$758$		−	6.42364i		−	0.233317i
$759$		0			0
$760$	18.6526			0.676600
$761$	14.2722			0.517366			0.258683	−	0.965962i	$-0.416712\pi$
$761$	14.2722			0.517366			0.258683	+	0.965962i	$0.416712\pi$
$762$		0			0
$763$	22.2081	−	45.0721i	0.803986	−	1.63172i
$764$	−6.11743			−0.221321
$765$		0			0
$766$	12.1949			0.440619
$767$		−	1.58455i		−	0.0572150i
$768$		0			0
$769$	41.9785			1.51378			0.756892	−	0.653540i	$-0.226717\pi$
$769$	41.9785			1.51378			0.756892	+	0.653540i	$0.226717\pi$
$770$	−26.3455	−	5.24092i	−0.949427	−	0.188870i
$771$		0			0
$772$		−	10.7515i		−	0.386956i
$773$			33.9094i			1.21964i	0.792541	+	0.609819i	$0.208758\pi$
$773$			33.9094i			1.21964i	−0.792541	+	0.609819i	$0.791242\pi$
$774$		0			0
$775$		−	3.15759i		−	0.113424i
$776$	5.08536			0.182554
$777$		0			0
$778$		−	12.7466i		−	0.456988i
$779$	49.3143			1.76687
$780$		0			0
$781$	−43.4018	+	11.6129i	−1.55304	+	0.415542i
$782$		−	1.06196i		−	0.0379755i
$783$		0			0
$784$	4.26510	+	5.55058i	0.152325	+	0.198235i
$785$	−25.8754			−0.923532
$786$		0			0
$787$	−49.3342			−1.75858			−0.879288	−	0.476291i	$-0.841981\pi$
$787$	−49.3342			−1.75858			−0.879288	+	0.476291i	$0.841981\pi$
$788$		−	25.9010i		−	0.922686i
$789$		0			0
$790$		−	21.0271i		−	0.748112i
$791$	26.3464	+	12.9815i	0.936769	+	0.461568i
$792$		0			0
$793$	4.66933			0.165813
$794$	−20.3146			−0.720938
$795$		0			0
$796$		−	19.5707i		−	0.693664i
$797$		−	13.9578i		−	0.494410i	−0.968963	−	0.247205i	$-0.920488\pi$
$797$		−	13.9578i		−	0.494410i	0.968963	−	0.247205i	$-0.0795121\pi$
$798$		0			0
$799$		−	2.76069i		−	0.0976660i
$800$			4.37083i			0.154532i
$801$		0			0
$802$		−	0.792277i		−	0.0279763i
$803$	−5.39994	+	1.44484i	−0.190560	+	0.0509875i
$804$		0			0
$805$	12.0842	−	24.5253i	0.425911	−	0.864402i
$806$	0.244728			0.00862016
$807$		0			0
$808$		−	9.71452i		−	0.341756i
$809$			36.9864i			1.30037i	0.759775	+	0.650186i	$0.225309\pi$
$809$			36.9864i			1.30037i	−0.759775	+	0.650186i	$0.774691\pi$
$810$		0			0
$811$	−21.6023			−0.758558			−0.379279	−	0.925282i	$-0.623828\pi$
$811$	−21.6023			−0.758558			−0.379279	+	0.925282i	$0.623828\pi$
$812$	5.15444	−	10.4611i	0.180885	−	0.367113i
$813$		0			0
$814$	6.42364	+	24.0076i	0.225148	+	0.841466i
$815$		−	34.3089i		−	1.20179i
$816$		0			0
$817$		−	25.1186i		−	0.878789i
$818$		−	26.6077i		−	0.930315i
$819$		0			0
$820$			24.7749i			0.865178i
$821$			40.9864i			1.43044i	0.698902	+	0.715218i	$0.253672\pi$
$821$			40.9864i			1.43044i	−0.698902	+	0.715218i	$0.746328\pi$
$822$		0			0
$823$	48.6178			1.69471			0.847354	−	0.531028i	$-0.178194\pi$
$823$	48.6178			1.69471			0.847354	+	0.531028i	$0.178194\pi$
$824$	−6.70663			−0.233636
$825$		0			0
$826$	−11.1012	−	5.46980i	−0.386259	−	0.190319i
$827$			47.8988i			1.66560i	0.553571	+	0.832802i	$0.313265\pi$
$827$			47.8988i			1.66560i	−0.553571	+	0.832802i	$0.686735\pi$
$828$		0			0
$829$		−	8.45964i		−	0.293816i	−0.989150	−	0.146908i	$-0.953068\pi$
$829$		−	8.45964i		−	0.293816i	0.989150	−	0.146908i	$-0.0469321\pi$
$830$	21.7787			0.755949
$831$		0			0
$832$	−0.338760			−0.0117444
$833$	1.34173	+	1.74612i	0.0464881	+	0.0604993i
$834$		0			0
$835$		−	44.9789i		−	1.55656i
$836$	−19.5223	+	5.22352i	−0.675193	+	0.180659i
$837$		0			0
$838$	10.9380			0.377848
$839$			45.7295i			1.57876i	0.613905	+	0.789380i	$0.289598\pi$
$839$			45.7295i			1.57876i	−0.613905	+	0.789380i	$0.710402\pi$
$840$		0			0
$841$	9.57095			0.330033
$842$		−	30.3829i		−	1.04706i
$843$		0			0
$844$		−	5.95165i		−	0.204864i
$845$			39.4441i			1.35692i
$846$		0			0
$847$	29.0417	−	1.89258i	0.997883	−	0.0650297i
$848$	−13.5623			−0.465731
$849$		0			0
$850$			1.37499i			0.0471617i
$851$	−25.2953			−0.867111
$852$		0			0
$853$	39.7994			1.36271			0.681353	−	0.731955i	$-0.261392\pi$
$853$	39.7994			1.36271			0.681353	+	0.731955i	$0.261392\pi$
$854$	16.1183	−	32.7126i	0.551556	−	1.11940i
$855$		0			0
$856$	9.71452			0.332036
$857$	9.92254			0.338947			0.169474	−	0.985535i	$-0.445793\pi$
$857$	9.92254			0.338947			0.169474	+	0.985535i	$0.445793\pi$
$858$		0			0
$859$			31.3594i			1.06997i	0.844862	+	0.534985i	$0.179683\pi$
$859$			31.3594i			1.06997i	−0.844862	+	0.534985i	$0.820317\pi$
$860$	12.6193			0.430315
$861$		0			0
$862$	24.1458			0.822408
$863$	−4.06314			−0.138311			−0.0691555	−	0.997606i	$-0.522030\pi$
$863$	−4.06314			−0.138311			−0.0691555	+	0.997606i	$0.522030\pi$
$864$		0			0
$865$		−	34.3089i		−	1.16654i
$866$	13.5031			0.458853
$867$		0			0
$868$	0.844786	−	1.71452i	0.0286739	−	0.0581947i
$869$	5.88850	+	22.0076i	0.199754	+	0.746557i
$870$		0			0
$871$	−0.586163			−0.0198614
$872$	18.9913			0.643127
$873$		0			0
$874$		−	20.5694i		−	0.695770i
$875$	2.25221	−	4.57095i	0.0761387	−	0.154526i
$876$		0			0
$877$			28.8423i			0.973937i	0.873420	+	0.486968i	$0.161897\pi$
$877$			28.8423i			0.973937i	−0.873420	+	0.486968i	$0.838103\pi$
$878$			30.5911i			1.03240i
$879$		0			0
$880$	−2.62424	−	9.80778i	−0.0884630	−	0.330620i
$881$		−	19.4856i		−	0.656486i	−0.944593	−	0.328243i	$-0.893543\pi$
$881$		−	19.4856i		−	0.656486i	0.944593	−	0.328243i	$-0.106457\pi$
$882$		0			0
$883$	1.11031			0.0373649			0.0186825	−	0.999825i	$-0.494053\pi$
$883$	1.11031			0.0373649			0.0186825	+	0.999825i	$0.494053\pi$
$884$	−0.106568			−0.00358427
$885$		0			0
$886$			28.8739i			0.970037i
$887$	−3.24254			−0.108874			−0.0544368	−	0.998517i	$-0.517336\pi$
$887$	−3.24254			−0.108874			−0.0544368	+	0.998517i	$0.517336\pi$
$888$		0			0
$889$	−25.2710	+	51.2885i	−0.847563	+	1.72016i
$890$		−	6.99626i		−	0.234515i
$891$		0			0
$892$			8.04490i			0.269363i
$893$		−	53.4726i		−	1.78939i
$894$		0			0
$895$		−	58.2990i		−	1.94872i
$896$	−1.16938	+	2.37330i	−0.0390662	+	0.0792864i
$897$		0			0
$898$		−	20.5944i		−	0.687242i
$899$	−3.18432			−0.106203
$900$		0			0
$901$	−4.26646			−0.142136
$902$	−6.93804	−	25.9301i	−0.231012	−	0.863379i
$903$		0			0
$904$			11.1012i			0.369219i
$905$	−44.5203			−1.47991
$906$		0			0
$907$	−19.5748			−0.649971			−0.324986	−	0.945719i	$-0.605359\pi$
$907$	−19.5748			−0.649971			−0.324986	+	0.945719i	$0.605359\pi$
$908$	17.0155			0.564679
$909$		0			0
$910$	−2.46112	−	1.21265i	−0.0815854	−	0.0401990i
$911$	−10.4535			−0.346340			−0.173170	−	0.984892i	$-0.555401\pi$
$911$	−10.4535			−0.346340			−0.173170	+	0.984892i	$0.555401\pi$
$912$		0			0
$913$	−22.7942	+	6.09896i	−0.754377	+	0.201846i
$914$	6.87983			0.227565
$915$		0			0
$916$		−	24.7942i		−	0.819223i
$917$	−33.0979	−	16.3081i	−1.09299	−	0.538541i
$918$		0			0
$919$		−	55.5373i		−	1.83201i	−0.401170	−	0.916004i	$-0.631396\pi$
$919$		−	55.5373i		−	1.83201i	0.401170	−	0.916004i	$-0.368604\pi$
$920$	10.3338			0.340696
$921$		0			0
$922$		−	16.2681i		−	0.535762i
$923$	−4.58900			−0.151049
$924$		0			0
$925$	32.7515			1.07686
$926$		−	17.5899i		−	0.578040i
$927$		0			0
$928$	4.40784			0.144694
$929$			1.16530i			0.0382324i	0.999817	+	0.0191162i	$0.00608524\pi$
$929$			1.16530i			0.0382324i	−0.999817	+	0.0191162i	$0.993915\pi$
$930$		0			0
$931$	25.9884	+	33.8211i	0.851734	+	1.10844i
$932$			0.170718i			0.00559204i
$933$		0			0
$934$	−41.0022			−1.34163
$935$	−0.825539	−	3.08536i	−0.0269980	−	0.100902i
$936$		0			0
$937$	−53.4875			−1.74736			−0.873680	−	0.486501i	$-0.838273\pi$
$937$	−53.4875			−1.74736			−0.873680	+	0.486501i	$0.838273\pi$
$938$	−2.02340	+	4.10657i	−0.0660664	+	0.134084i
$939$		0			0
$940$	26.8640			0.876208
$941$	33.2985			1.08550			0.542750	−	0.839894i	$-0.317383\pi$
$941$	33.2985			1.08550			0.542750	+	0.839894i	$0.317383\pi$
$942$		0			0
$943$	27.3209			0.889692
$944$		−	4.67752i		−	0.152240i
$945$		0			0
$946$	−13.2077	+	3.53395i	−0.429420	+	0.114899i
$947$	−47.5965			−1.54668			−0.773340	−	0.633992i	$-0.781415\pi$
$947$	−47.5965			−1.54668			−0.773340	+	0.633992i	$0.781415\pi$
$948$		0			0
$949$	−0.570951			−0.0185339
$950$			26.6326i			0.864076i
$951$		0			0
$952$	−0.367867	+	0.746599i	−0.0119226	+	0.0241974i
$953$			14.4895i			0.469359i	0.972073	+	0.234680i	$0.0754041\pi$
$953$			14.4895i			0.469359i	−0.972073	+	0.234680i	$0.924596\pi$
$954$		0			0
$955$		−	18.7266i		−	0.605978i
$956$		−	18.8897i		−	0.610936i
$957$		0			0
$958$			4.29308i			0.138703i
$959$	−27.9543	−	13.7737i	−0.902692	−	0.444777i
$960$		0			0
$961$	30.4781			0.983165
$962$			2.53839i			0.0818411i
$963$		0			0
$964$	−0.436947			−0.0140731
$965$	32.9124			1.05949
$966$		0			0
$967$		−	33.5600i		−	1.07922i	−0.841916	−	0.539609i	$-0.818572\pi$
$967$		−	33.5600i		−	1.07922i	0.841916	−	0.539609i	$-0.181428\pi$
$968$	5.49320	+	9.53020i	0.176558	+	0.306312i
$969$		0			0
$970$			15.5672i			0.499833i
$971$			43.5824i			1.39863i	0.714815	+	0.699313i	$0.246511\pi$
$971$			43.5824i			1.39863i	−0.714815	+	0.699313i	$0.753489\pi$
$972$		0			0
$973$	−17.8902	−	8.81490i	−0.573533	−	0.282593i
$974$			14.8897i			0.477096i
$975$		0			0
$976$	13.7836			0.441202
$977$	11.2169			0.358860			0.179430	−	0.983771i	$-0.442575\pi$
$977$	11.2169			0.358860			0.179430	+	0.983771i	$0.442575\pi$
$978$		0			0
$979$	1.95925	+	7.32248i	0.0626180	+	0.234027i
$980$	−16.9913	+	13.0563i	−0.542768	+	0.417067i
$981$		0			0
$982$	−4.35949			−0.139117
$983$		−	53.1221i		−	1.69433i	−0.531328	−	0.847166i	$-0.678307\pi$
$983$		−	53.1221i		−	1.69433i	0.531328	−	0.847166i	$-0.321693\pi$
$984$		0			0
$985$	79.2878			2.52632
$986$	1.38663			0.0441593
$987$		0			0
$988$	−2.06415			−0.0656693
$989$		−	13.9161i		−	0.442507i
$990$		0			0
$991$	37.9827			1.20656			0.603279	−	0.797530i	$-0.293860\pi$
$991$	37.9827			1.20656			0.603279	+	0.797530i	$0.293860\pi$
$992$	0.722422			0.0229369
$993$		0			0
$994$	−15.8410	+	32.1499i	−0.502445	+	1.01973i
$995$	59.9093			1.89925
$996$		0			0
$997$	−10.8939			−0.345014			−0.172507	−	0.985008i	$-0.555187\pi$
$997$	−10.8939			−0.345014			−0.172507	+	0.985008i	$0.555187\pi$
$998$			6.73573i			0.213216i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.e.e.307.1		8
3.2	odd	2		462.2.e.a.307.8	yes	8
7.6	odd	2		1386.2.e.a.307.4		8
11.10	odd	2		1386.2.e.a.307.5		8
12.11	even	2		3696.2.q.b.769.4		8
21.20	even	2		462.2.e.b.307.5	yes	8
33.32	even	2		462.2.e.b.307.4	yes	8
77.76	even	2	inner	1386.2.e.e.307.8		8
84.83	odd	2		3696.2.q.c.769.5		8
132.131	odd	2		3696.2.q.c.769.4		8
231.230	odd	2		462.2.e.a.307.1	✓	8
924.923	even	2		3696.2.q.b.769.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.e.a.307.1	✓	8	231.230	odd	2
462.2.e.a.307.8	yes	8	3.2	odd	2
462.2.e.b.307.4	yes	8	33.32	even	2
462.2.e.b.307.5	yes	8	21.20	even	2
1386.2.e.a.307.4		8	7.6	odd	2
1386.2.e.a.307.5		8	11.10	odd	2
1386.2.e.e.307.1		8	1.1	even	1	trivial
1386.2.e.e.307.8		8	77.76	even	2	inner
3696.2.q.b.769.4		8	12.11	even	2
3696.2.q.b.769.5		8	924.923	even	2
3696.2.q.c.769.4		8	132.131	odd	2
3696.2.q.c.769.5		8	84.83	odd	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} -3.06118i q^{5} +(2.37330 + 1.16938i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} -3.06118i q^{5} +(2.37330 + 1.16938i) q^{7} +1.00000i q^{8} -3.06118 q^{10} +(3.20392 - 0.857262i) q^{11} +0.338760 q^{13} +(1.16938 - 2.37330i) q^{14} +1.00000 q^{16} +0.314583 q^{17} +6.09326 q^{19} +3.06118i q^{20} +(-0.857262 - 3.20392i) q^{22} +3.37576 q^{23} -4.37083 q^{25} -0.338760i q^{26} +(-2.37330 - 1.16938i) q^{28} +4.40784i q^{29} +0.722422i q^{31} -1.00000i q^{32} -0.314583i q^{34} +(3.57968 - 7.26510i) q^{35} -7.49320 q^{37} -6.09326i q^{38} +3.06118 q^{40} +8.09326 q^{41} -4.12236i q^{43} +(-3.20392 + 0.857262i) q^{44} -3.37576i q^{46} -8.77571i q^{47} +(4.26510 + 5.55058i) q^{49} +4.37083i q^{50} -0.338760 q^{52} -13.5623 q^{53} +(-2.62424 - 9.80778i) q^{55} +(-1.16938 + 2.37330i) q^{56} +4.40784 q^{58} -4.67752i q^{59} +13.7836 q^{61} +0.722422 q^{62} -1.00000 q^{64} -1.03700i q^{65} -1.73032 q^{67} -0.314583 q^{68} +(-7.26510 - 3.57968i) q^{70} -13.5465 q^{71} -1.68542 q^{73} +7.49320i q^{74} -6.09326 q^{76} +(8.60633 + 1.71206i) q^{77} +6.86896i q^{79} -3.06118i q^{80} -8.09326i q^{82} -7.11447 q^{83} -0.962995i q^{85} -4.12236 q^{86} +(0.857262 + 3.20392i) q^{88} +2.28548i q^{89} +(0.803978 + 0.396139i) q^{91} -3.37576 q^{92} -8.77571 q^{94} -18.6526i q^{95} -5.08536i q^{97} +(5.55058 - 4.26510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} + 4 q^{10} + 8 q^{11} + 8 q^{14} + 8 q^{16} + 12 q^{17} + 4 q^{19} + 4 q^{22} + 8 q^{23} - 16 q^{25} - 8 q^{35} + 16 q^{37} - 4 q^{40} + 20 q^{41} - 8 q^{44} - 12 q^{49} - 40 q^{55} - 8 q^{56} + 56 q^{61} - 20 q^{62} - 8 q^{64} + 16 q^{67} - 12 q^{68} - 12 q^{70} - 8 q^{71} - 4 q^{73} - 4 q^{76} + 20 q^{77} - 4 q^{83} + 24 q^{86} - 4 q^{88} + 20 q^{91} - 8 q^{92} - 20 q^{94} + 20 q^{98}+O(q^{100}) \) 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 + 20 * 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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