LMFDB - Embedded newform 1305.2.c.k.784.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1305,2,Mod(784,1305)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1305, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1305.784");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1305 = 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1305.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.4204774638$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 148x^{8} + 502x^{6} + 792x^{4} + 496x^{2} + 45 $ x^12 + 20x^10 + 148x^8 + 502x^6 + 792x^4 + 496*x^2 + 45
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			784.2
Root			$-2.51930i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.k.784.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.51930i q^{2} -4.34685 q^{4} +(-2.08236 + 0.814730i) q^{5} +4.08323i q^{7} +5.91241i q^{8} +(2.05255 + 5.24608i) q^{10} -1.07928 q^{11} -1.43381i q^{13} +10.2869 q^{14} +6.20142 q^{16} -6.88737i q^{17} +7.42874 q^{19} +(9.05170 - 3.54151i) q^{20} +2.71902i q^{22} -1.01996i q^{23} +(3.67243 - 3.39312i) q^{25} -3.61219 q^{26} -17.7492i q^{28} -1.00000 q^{29} -7.37006 q^{31} -3.79838i q^{32} -17.3513 q^{34} +(-3.32673 - 8.50274i) q^{35} +10.8961i q^{37} -18.7152i q^{38} +(-4.81702 - 12.3118i) q^{40} +3.02388 q^{41} -10.6232i q^{43} +4.69147 q^{44} -2.56957 q^{46} -6.88737i q^{47} -9.67273 q^{49} +(-8.54827 - 9.25194i) q^{50} +6.23256i q^{52} -7.61354i q^{53} +(2.24745 - 0.879321i) q^{55} -24.1417 q^{56} +2.51930i q^{58} +9.45393 q^{59} -0.265337 q^{61} +18.5674i q^{62} +2.83360 q^{64} +(1.16817 + 2.98570i) q^{65} -11.1316i q^{67} +29.9384i q^{68} +(-21.4209 + 8.38101i) q^{70} +12.1375 q^{71} -3.54019i q^{73} +27.4506 q^{74} -32.2916 q^{76} -4.40694i q^{77} +6.13029 q^{79} +(-12.9136 + 5.05248i) q^{80} -7.61805i q^{82} -0.615986i q^{83} +(5.61135 + 14.3420i) q^{85} -26.7630 q^{86} -6.38115i q^{88} -2.11822 q^{89} +5.85457 q^{91} +4.43360i q^{92} -17.3513 q^{94} +(-15.4693 + 6.05242i) q^{95} -1.52207i q^{97} +24.3685i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 16 q^{4} - 10 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{16} + 20 q^{19} + 14 q^{20} + 8 q^{25} - 56 q^{26} - 12 q^{29} - 16 q^{31} - 4 q^{34} - 16 q^{35} + 16 q^{40} - 32 q^{41} + 68 q^{44} + 20 q^{46}+ \cdots - 8 q^{95}+O(q^{100}) $ 12 * q - 16 * q^4 - 10 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^16 + 20 * q^19 + 14 * q^20 + 8 * q^25 - 56 * q^26 - 12 * q^29 - 16 * q^31 - 4 * q^34 - 16 * q^35 + 16 * q^40 - 32 * q^41 + 68 * q^44 + 20 * q^46 + 4 * q^49 - 8 * q^50 + 4 * q^55 - 76 * q^56 + 44 * q^59 - 52 * q^61 - 36 * q^64 - 8 * q^65 - 30 * q^70 - 20 * q^71 + 20 * q^74 - 28 * q^76 + 4 * q^79 + 34 * q^80 + 20 * q^85 - 36 * q^86 + 68 * q^89 + 48 * q^91 - 4 * q^94 - 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times$.

$n$	$146$	$262$	$901$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	2.51930i		−	1.78141i	−0.454581	−	0.890706i	$-0.650211\pi$
$2$		−	2.51930i		−	1.78141i	0.454581	−	0.890706i	$-0.349789\pi$
$3$		0			0
$3$		0			0
$4$	−4.34685			−2.17343
$5$	−2.08236	+	0.814730i	−0.931259	+	0.364358i
$5$	−2.08236	+	0.814730i	−0.931259	+	0.364358i
$6$		0			0
$7$			4.08323i			1.54331i	0.636039	+	0.771657i	$0.280572\pi$
$7$			4.08323i			1.54331i	−0.636039	+	0.771657i	$0.719428\pi$
$8$			5.91241i			2.09035i
$9$		0			0
$10$	2.05255	+	5.24608i	0.649072	+	1.65895i
$11$	−1.07928			−0.325415			−0.162708	−	0.986674i	$-0.552023\pi$
$11$	−1.07928			−0.325415			−0.162708	+	0.986674i	$0.552023\pi$
$12$		0			0
$13$		−	1.43381i		−	0.397667i	−0.980033	−	0.198834i	$-0.936285\pi$
$13$		−	1.43381i		−	0.397667i	0.980033	−	0.198834i	$-0.0637153\pi$
$14$	10.2869			2.74928
$15$		0			0
$16$	6.20142			1.55035
$17$		−	6.88737i		−	1.67043i	−0.549922	−	0.835216i	$-0.685342\pi$
$17$		−	6.88737i		−	1.67043i	0.549922	−	0.835216i	$-0.314658\pi$
$18$		0			0
$19$	7.42874			1.70427			0.852135	−	0.523322i	$-0.175308\pi$
$19$	7.42874			1.70427			0.852135	+	0.523322i	$0.175308\pi$
$20$	9.05170	−	3.54151i	2.02402	−	0.791906i
$21$		0			0
$22$			2.71902i			0.579698i
$23$		−	1.01996i		−	0.212676i	−0.994330	−	0.106338i	$-0.966087\pi$
$23$		−	1.01996i		−	0.212676i	0.994330	−	0.106338i	$-0.0339125\pi$
$24$		0			0
$25$	3.67243	−	3.39312i	0.734486	−	0.678624i
$26$	−3.61219			−0.708409
$27$		0			0
$28$		−	17.7492i		−	3.35428i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$		0			0
$31$	−7.37006			−1.32370			−0.661851	−	0.749636i	$-0.730229\pi$
$31$	−7.37006			−1.32370			−0.661851	+	0.749636i	$0.730229\pi$
$32$		−	3.79838i		−	0.671465i
$33$		0			0
$34$	−17.3513			−2.97573
$35$	−3.32673	−	8.50274i	−0.562319	−	1.43723i
$36$		0			0
$37$			10.8961i			1.79131i	0.444748	+	0.895656i	$0.353293\pi$
$37$			10.8961i			1.79131i	−0.444748	+	0.895656i	$0.646707\pi$
$38$		−	18.7152i		−	3.03601i
$39$		0			0
$40$	−4.81702	−	12.3118i	−0.761638	−	1.94666i
$41$	3.02388			0.472251			0.236125	−	0.971723i	$-0.424122\pi$
$41$	3.02388			0.472251			0.236125	+	0.971723i	$0.424122\pi$
$42$		0			0
$43$		−	10.6232i		−	1.62002i	−0.586413	−	0.810012i	$-0.699460\pi$
$43$		−	10.6232i		−	1.62002i	0.586413	−	0.810012i	$-0.300540\pi$
$44$	4.69147			0.707266
$45$		0			0
$46$	−2.56957			−0.378863
$47$		−	6.88737i		−	1.00463i	−0.864686	−	0.502313i	$-0.832483\pi$
$47$		−	6.88737i		−	1.00463i	0.864686	−	0.502313i	$-0.167517\pi$
$48$		0			0
$49$	−9.67273			−1.38182
$50$	−8.54827	−	9.25194i	−1.20891	−	1.30842i
$51$		0			0
$52$			6.23256i			0.864300i
$53$		−	7.61354i		−	1.04580i	−0.852394	−	0.522900i	$-0.824850\pi$
$53$		−	7.61354i		−	1.04580i	0.852394	−	0.522900i	$-0.175150\pi$
$54$		0			0
$55$	2.24745	−	0.879321i	0.303046	−	0.118568i
$56$	−24.1417			−3.22607
$57$		0			0
$58$			2.51930i			0.330800i
$59$	9.45393			1.23080			0.615399	−	0.788216i	$-0.288995\pi$
$59$	9.45393			1.23080			0.615399	+	0.788216i	$0.288995\pi$
$60$		0			0
$61$	−0.265337			−0.0339729			−0.0169865	−	0.999856i	$-0.505407\pi$
$61$	−0.265337			−0.0339729			−0.0169865	+	0.999856i	$0.505407\pi$
$62$			18.5674i			2.35806i
$63$		0			0
$64$	2.83360			0.354200
$65$	1.16817	+	2.98570i	0.144893	+	0.370331i
$66$		0			0
$67$		−	11.1316i		−	1.35994i	−0.733240	−	0.679970i	$-0.761993\pi$
$67$		−	11.1316i		−	1.35994i	0.733240	−	0.679970i	$-0.238007\pi$
$68$			29.9384i			3.63056i
$69$		0			0
$70$	−21.4209	+	8.38101i	−2.56029	+	1.00172i
$71$	12.1375			1.44046			0.720228	−	0.693737i	$-0.244037\pi$
$71$	12.1375			1.44046			0.720228	+	0.693737i	$0.244037\pi$
$72$		0			0
$73$		−	3.54019i		−	0.414348i	−0.978304	−	0.207174i	$-0.933573\pi$
$73$		−	3.54019i		−	0.414348i	0.978304	−	0.207174i	$-0.0664266\pi$
$74$	27.4506			3.19106
$75$		0			0
$76$	−32.2916			−3.70410
$77$		−	4.40694i		−	0.502218i
$78$		0			0
$79$	6.13029			0.689711			0.344856	−	0.938656i	$-0.387928\pi$
$79$	6.13029			0.689711			0.344856	+	0.938656i	$0.387928\pi$
$80$	−12.9136	+	5.05248i	−1.44378	+	0.564885i
$81$		0			0
$82$		−	7.61805i		−	0.841273i
$83$		−	0.615986i		−	0.0676132i	−0.999428	−	0.0338066i	$-0.989237\pi$
$83$		−	0.615986i		−	0.0676132i	0.999428	−	0.0338066i	$-0.0107630\pi$
$84$		0			0
$85$	5.61135	+	14.3420i	0.608636	+	1.55561i
$86$	−26.7630			−2.88593
$87$		0			0
$88$		−	6.38115i		−	0.680233i
$89$	−2.11822			−0.224531			−0.112265	−	0.993678i	$-0.535811\pi$
$89$	−2.11822			−0.224531			−0.112265	+	0.993678i	$0.535811\pi$
$90$		0			0
$91$	5.85457			0.613725
$92$			4.43360i			0.462235i
$93$		0			0
$94$	−17.3513			−1.78965
$95$	−15.4693	+	6.05242i	−1.58712	+	0.620965i
$96$		0			0
$97$		−	1.52207i		−	0.154543i	−0.997010	−	0.0772713i	$-0.975379\pi$
$97$		−	1.52207i		−	0.154543i	0.997010	−	0.0772713i	$-0.0246208\pi$
$98$			24.3685i			2.46159i
$99$		0			0
$100$	−15.9635	+	14.7494i	−1.59635	+	1.47494i
$101$	8.28909			0.824795			0.412398	−	0.911004i	$-0.364691\pi$
$101$	8.28909			0.824795			0.412398	+	0.911004i	$0.364691\pi$
$102$		0			0
$103$		−	3.32888i		−	0.328004i	−0.986460	−	0.164002i	$-0.947560\pi$
$103$		−	3.32888i		−	0.328004i	0.986460	−	0.164002i	$-0.0524404\pi$
$104$	8.47727			0.831265
$105$		0			0
$106$	−19.1808			−1.86300
$107$		−	8.74777i		−	0.845679i	−0.906205	−	0.422840i	$-0.861033\pi$
$107$		−	8.74777i		−	0.845679i	0.906205	−	0.422840i	$-0.138967\pi$
$108$		0			0
$109$	15.5289			1.48739			0.743697	−	0.668516i	$-0.233070\pi$
$109$	15.5289			1.48739			0.743697	+	0.668516i	$0.233070\pi$
$110$	−2.21527	−	5.66198i	−0.211218	−	0.539849i
$111$		0			0
$112$			25.3218i			2.39268i
$113$		−	0.339380i		−	0.0319262i	−0.999873	−	0.0159631i	$-0.994919\pi$
$113$		−	0.339380i		−	0.0319262i	0.999873	−	0.0159631i	$-0.00508143\pi$
$114$		0			0
$115$	0.830990	+	2.12392i	0.0774902	+	0.198056i
$116$	4.34685			0.403595
$117$		0			0
$118$		−	23.8173i		−	2.19256i
$119$	28.1227			2.57800
$120$		0			0
$121$	−9.83516			−0.894105
$122$			0.668463i			0.0605198i
$123$		0			0
$124$	32.0365			2.87697
$125$	−4.88284	+	10.0577i	−0.436734	+	0.899590i
$126$		0			0
$127$		−	12.1171i		−	1.07522i	−0.843194	−	0.537609i	$-0.819328\pi$
$127$		−	12.1171i		−	1.07522i	0.843194	−	0.537609i	$-0.180672\pi$
$128$		−	14.7354i		−	1.30244i
$129$		0			0
$130$	7.52187	−	2.94296i	0.659712	−	0.258115i
$131$	−16.8007			−1.46789			−0.733943	−	0.679211i	$-0.762322\pi$
$131$	−16.8007			−1.46789			−0.733943	+	0.679211i	$0.762322\pi$
$132$		0			0
$133$			30.3332i			2.63022i
$134$	−28.0437			−2.42261
$135$		0			0
$136$	40.7210			3.49180
$137$			0.956886i			0.0817523i	0.999164	+	0.0408762i	$0.0130149\pi$
$137$			0.956886i			0.0817523i	−0.999164	+	0.0408762i	$0.986985\pi$
$138$		0			0
$139$	1.85457			0.157302			0.0786511	−	0.996902i	$-0.474939\pi$
$139$	1.85457			0.157302			0.0786511	+	0.996902i	$0.474939\pi$
$140$	14.4608	+	36.9601i	1.22216	+	3.12370i
$141$		0			0
$142$		−	30.5780i		−	2.56604i
$143$			1.54748i			0.129407i
$144$		0			0
$145$	2.08236	−	0.814730i	0.172930	−	0.0676596i
$146$	−8.91879			−0.738124
$147$		0			0
$148$		−	47.3638i		−	3.89328i
$149$	−16.6324			−1.36258			−0.681289	−	0.732014i	$-0.738580\pi$
$149$	−16.6324			−1.36258			−0.681289	+	0.732014i	$0.738580\pi$
$150$		0			0
$151$	14.7060			1.19676			0.598379	−	0.801213i	$-0.295812\pi$
$151$	14.7060			1.19676			0.598379	+	0.801213i	$0.295812\pi$
$152$			43.9218i			3.56253i
$153$		0			0
$154$	−11.1024			−0.894656
$155$	15.3471	−	6.00460i	1.23271	−	0.482301i
$156$		0			0
$157$			5.86462i			0.468048i	0.972231	+	0.234024i	$0.0751894\pi$
$157$			5.86462i			0.468048i	−0.972231	+	0.234024i	$0.924811\pi$
$158$		−	15.4440i		−	1.22866i
$159$		0			0
$160$	3.09465	+	7.90958i	0.244654	+	0.625308i
$161$	4.16472			0.328226
$162$		0			0
$163$		−	5.06226i		−	0.396507i	−0.980151	−	0.198253i	$-0.936473\pi$
$163$		−	5.06226i		−	0.396507i	0.980151	−	0.198253i	$-0.0635269\pi$
$164$	−13.1444			−1.02640
$165$		0			0
$166$	−1.55185			−0.120447
$167$			4.25070i			0.328929i	0.986383	+	0.164464i	$0.0525895\pi$
$167$			4.25070i			0.328929i	−0.986383	+	0.164464i	$0.947410\pi$
$168$		0			0
$169$	10.9442			0.841861
$170$	36.1317	−	14.1366i	2.77117	−	1.08423i
$171$		0			0
$172$			46.1775i			3.52100i
$173$		−	3.69756i		−	0.281120i	−0.990072	−	0.140560i	$-0.955110\pi$
$173$		−	3.69756i		−	0.281120i	0.990072	−	0.140560i	$-0.0448903\pi$
$174$		0			0
$175$	13.8549	+	14.9954i	1.04733	+	1.13354i
$176$	−6.69306			−0.504509
$177$		0			0
$178$			5.33642i			0.399981i
$179$	17.2381			1.28843			0.644217	−	0.764842i	$-0.277183\pi$
$179$	17.2381			1.28843			0.644217	+	0.764842i	$0.277183\pi$
$180$		0			0
$181$	3.97382			0.295371			0.147686	−	0.989034i	$-0.452818\pi$
$181$	3.97382			0.295371			0.147686	+	0.989034i	$0.452818\pi$
$182$		−	14.7494i		−	1.09330i
$183$		0			0
$184$	6.03041			0.444568
$185$	−8.87740	−	22.6896i	−0.652679	−	1.66817i
$186$		0			0
$187$			7.43340i			0.543584i
$188$			29.9384i			2.18348i
$189$		0			0
$190$	15.2478	+	38.9717i	1.10619	+	2.82731i
$191$	−22.0235			−1.59357			−0.796783	−	0.604266i	$-0.793466\pi$
$191$	−22.0235			−1.59357			−0.796783	+	0.604266i	$0.793466\pi$
$192$		0			0
$193$			12.2161i			0.879336i	0.898160	+	0.439668i	$0.144904\pi$
$193$			12.2161i			0.879336i	−0.898160	+	0.439668i	$0.855096\pi$
$194$	−3.83454			−0.275304
$195$		0			0
$196$	42.0459			3.00328
$197$		−	12.0979i		−	0.861943i	−0.902366	−	0.430971i	$-0.858171\pi$
$197$		−	12.0979i		−	0.861943i	0.902366	−	0.430971i	$-0.141829\pi$
$198$		0			0
$199$	0.590878			0.0418863			0.0209431	−	0.999781i	$-0.493333\pi$
$199$	0.590878			0.0418863			0.0209431	+	0.999781i	$0.493333\pi$
$200$	20.0615	+	21.7129i	1.41856	+	1.53534i
$201$		0			0
$202$		−	20.8827i		−	1.46930i
$203$		−	4.08323i		−	0.286586i
$204$		0			0
$205$	−6.29680	+	2.46365i	−0.439788	+	0.172069i
$206$	−8.38643			−0.584310
$207$		0			0
$208$		−	8.89165i		−	0.616525i
$209$	−8.01769			−0.554595
$210$		0			0
$211$	−17.4117			−1.19867			−0.599334	−	0.800499i	$-0.704568\pi$
$211$	−17.4117			−1.19867			−0.599334	+	0.800499i	$0.704568\pi$
$212$			33.0949i			2.27297i
$213$		0			0
$214$	−22.0382			−1.50650
$215$	8.65505	+	22.1213i	0.590269	+	1.50866i
$216$		0			0
$217$		−	30.0936i		−	2.04289i
$218$		−	39.1218i		−	2.64966i
$219$		0			0
$220$	−9.76932	+	3.82228i	−0.658647	+	0.257698i
$221$	−9.87517			−0.664276
$222$		0			0
$223$			14.3494i			0.960910i	0.877019	+	0.480455i	$0.159528\pi$
$223$			14.3494i			0.960910i	−0.877019	+	0.480455i	$0.840472\pi$
$224$	15.5096			1.03628
$225$		0			0
$226$	−0.854999			−0.0568737
$227$			1.37659i			0.0913678i	0.998956	+	0.0456839i	$0.0145467\pi$
$227$			1.37659i			0.0913678i	−0.998956	+	0.0456839i	$0.985453\pi$
$228$		0			0
$229$	15.1027			0.998014			0.499007	−	0.866598i	$-0.333698\pi$
$229$	15.1027			0.998014			0.499007	+	0.866598i	$0.333698\pi$
$230$	5.35077	−	2.09351i	0.352820	−	0.138042i
$231$		0			0
$232$		−	5.91241i		−	0.388169i
$233$			8.73802i			0.572447i	0.958163	+	0.286223i	$0.0924000\pi$
$233$			8.73802i			0.572447i	−0.958163	+	0.286223i	$0.907600\pi$
$234$		0			0
$235$	5.61135	+	14.3420i	0.366044	+	0.935567i
$236$	−41.0949			−2.67505
$237$		0			0
$238$		−	70.8494i		−	4.59248i
$239$	3.46703			0.224264			0.112132	−	0.993693i	$-0.464232\pi$
$239$	3.46703			0.224264			0.112132	+	0.993693i	$0.464232\pi$
$240$		0			0
$241$	14.6327			0.942574			0.471287	−	0.881980i	$-0.343790\pi$
$241$	14.6327			0.942574			0.471287	+	0.881980i	$0.343790\pi$
$242$			24.7777i			1.59277i
$243$		0			0
$244$	1.15338			0.0738377
$245$	20.1421	−	7.88067i	1.28683	−	0.503477i
$246$		0			0
$247$		−	10.6514i		−	0.677732i
$248$		−	43.5748i		−	2.76700i
$249$		0			0
$250$	25.3384	+	12.3013i	1.60254	+	0.778004i
$251$	−21.2431			−1.34085			−0.670425	−	0.741977i	$-0.733888\pi$
$251$	−21.2431			−1.34085			−0.670425	+	0.741977i	$0.733888\pi$
$252$		0			0
$253$			1.10082i			0.0692079i
$254$	−30.5266			−1.91541
$255$		0			0
$256$	−31.4557			−1.96598
$257$		−	10.8916i		−	0.679400i	−0.940534	−	0.339700i	$-0.889674\pi$
$257$		−	10.8916i		−	0.679400i	0.940534	−	0.339700i	$-0.110326\pi$
$258$		0			0
$259$	−44.4913			−2.76456
$260$	−5.07785	−	12.9784i	−0.314915	−	0.804887i
$261$		0			0
$262$			42.3260i			2.61491i
$263$			27.6093i			1.70246i	0.524789	+	0.851232i	$0.324144\pi$
$263$			27.6093i			1.70246i	−0.524789	+	0.851232i	$0.675856\pi$
$264$		0			0
$265$	6.20298	+	15.8541i	0.381046	+	0.973910i
$266$	76.4184			4.68551
$267$		0			0
$268$			48.3873i			2.95573i
$269$	10.5729			0.644639			0.322319	−	0.946631i	$-0.395538\pi$
$269$	10.5729			0.644639			0.322319	+	0.946631i	$0.395538\pi$
$270$		0			0
$271$	−3.60438			−0.218950			−0.109475	−	0.993990i	$-0.534917\pi$
$271$	−3.60438			−0.218950			−0.109475	+	0.993990i	$0.534917\pi$
$272$		−	42.7115i		−	2.58976i
$273$		0			0
$274$	2.41068			0.145635
$275$	−3.96358	+	3.66212i	−0.239013	+	0.220834i
$276$		0			0
$277$			0.855958i			0.0514295i	0.999669	+	0.0257148i	$0.00818616\pi$
$277$			0.855958i			0.0514295i	−0.999669	+	0.0257148i	$0.991814\pi$
$278$		−	4.67220i		−	0.280220i
$279$		0			0
$280$	50.2717	−	19.6690i	3.00431	−	1.17545i
$281$	10.7917			0.643779			0.321889	−	0.946777i	$-0.395682\pi$
$281$	10.7917			0.643779			0.321889	+	0.946777i	$0.395682\pi$
$282$		0			0
$283$		−	29.9813i		−	1.78220i	−0.453802	−	0.891102i	$-0.649933\pi$
$283$		−	29.9813i		−	1.78220i	0.453802	−	0.891102i	$-0.350067\pi$
$284$	−52.7599			−3.13072
$285$		0			0
$286$	3.89856			0.230527
$287$			12.3472i			0.728832i
$288$		0			0
$289$	−30.4359			−1.79034
$290$	−2.05255	−	5.24608i	−0.120530	−	0.308060i
$291$		0			0
$292$			15.3887i			0.900555i
$293$			0.468563i			0.0273738i	0.999906	+	0.0136869i	$0.00435680\pi$
$293$			0.468563i			0.0273738i	−0.999906	+	0.0136869i	$0.995643\pi$
$294$		0			0
$295$	−19.6865	+	7.70240i	−1.14619	+	0.448451i
$296$	−64.4224			−3.74448
$297$		0			0
$298$			41.9019i			2.42731i
$299$	−1.46242			−0.0845742
$300$		0			0
$301$	43.3770			2.50021
$302$		−	37.0488i		−	2.13192i
$303$		0			0
$304$	46.0687			2.64222
$305$	0.552527	−	0.216178i	0.0316376	−	0.0123783i
$306$		0			0
$307$			2.56354i			0.146309i	0.997321	+	0.0731546i	$0.0233067\pi$
$307$			2.56354i			0.146309i	−0.997321	+	0.0731546i	$0.976693\pi$
$308$			19.1563i			1.09153i
$309$		0			0
$310$	−15.1274	−	38.6639i	−0.859177	−	2.19596i
$311$	16.1147			0.913782			0.456891	−	0.889523i	$-0.348963\pi$
$311$	16.1147			0.913782			0.456891	+	0.889523i	$0.348963\pi$
$312$		0			0
$313$		−	7.11492i		−	0.402159i	−0.979575	−	0.201079i	$-0.935555\pi$
$313$		−	7.11492i		−	0.402159i	0.979575	−	0.201079i	$-0.0644449\pi$
$314$	14.7747			0.833786
$315$		0			0
$316$	−26.6474			−1.49904
$317$		−	27.1389i		−	1.52427i	−0.647417	−	0.762136i	$-0.724151\pi$
$317$		−	27.1389i		−	1.52427i	0.647417	−	0.762136i	$-0.275849\pi$
$318$		0			0
$319$	1.07928			0.0604281
$320$	−5.90056	+	2.30862i	−0.329852	+	0.129056i
$321$		0			0
$322$		−	10.4922i		−	0.584705i
$323$		−	51.1645i		−	2.84687i
$324$		0			0
$325$	−4.86508	−	5.26556i	−0.269866	−	0.292081i
$326$	−12.7533			−0.706342
$327$		0			0
$328$			17.8784i			0.987172i
$329$	28.1227			1.55045
$330$		0			0
$331$	−9.73035			−0.534828			−0.267414	−	0.963582i	$-0.586169\pi$
$331$	−9.73035			−0.534828			−0.267414	+	0.963582i	$0.586169\pi$
$332$			2.67760i			0.146952i
$333$		0			0
$334$	10.7088			0.585957
$335$	9.06923	+	23.1799i	0.495505	+	1.26646i
$336$		0			0
$337$			4.34813i			0.236858i	0.992963	+	0.118429i	$0.0377858\pi$
$337$			4.34813i			0.236858i	−0.992963	+	0.118429i	$0.962214\pi$
$338$		−	27.5717i		−	1.49970i
$339$		0			0
$340$	−24.3917	−	62.3424i	−1.32283	−	3.38099i
$341$	7.95435			0.430752
$342$		0			0
$343$		−	10.9134i		−	0.589267i
$344$	62.8088			3.38643
$345$		0			0
$346$	−9.31524			−0.500790
$347$		−	1.49087i		−	0.0800343i	−0.999199	−	0.0400171i	$-0.987259\pi$
$347$		−	1.49087i		−	0.0800343i	0.999199	−	0.0400171i	$-0.0127413\pi$
$348$		0			0
$349$	5.48041			0.293359			0.146680	−	0.989184i	$-0.453141\pi$
$349$	5.48041			0.293359			0.146680	+	0.989184i	$0.453141\pi$
$350$	37.7778	−	34.9045i	2.01931	−	1.86573i
$351$		0			0
$352$			4.09951i			0.218505i
$353$			2.97765i			0.158484i	0.996855	+	0.0792421i	$0.0252500\pi$
$353$			2.97765i			0.158484i	−0.996855	+	0.0792421i	$0.974750\pi$
$354$		0			0
$355$	−25.2746	+	9.88878i	−1.34144	+	0.524842i
$356$	9.20758			0.488001
$357$		0			0
$358$		−	43.4278i		−	2.29523i
$359$	−25.1271			−1.32616			−0.663080	−	0.748548i	$-0.730751\pi$
$359$	−25.1271			−1.32616			−0.663080	+	0.748548i	$0.730751\pi$
$360$		0			0
$361$	36.1862			1.90454
$362$		−	10.0112i		−	0.526178i
$363$		0			0
$364$	−25.4489			−1.33389
$365$	2.88430	+	7.37195i	0.150971	+	0.385865i
$366$		0			0
$367$		−	10.7689i		−	0.562133i	−0.959688	−	0.281066i	$-0.909312\pi$
$367$		−	10.7689i		−	0.562133i	0.959688	−	0.281066i	$-0.0906881\pi$
$368$		−	6.32518i		−	0.329723i
$369$		0			0
$370$	−57.1619	+	22.3648i	−2.97171	+	1.16269i
$371$	31.0878			1.61400
$372$		0			0
$373$			32.3686i			1.67598i	0.545683	+	0.837992i	$0.316270\pi$
$373$			32.3686i			1.67598i	−0.545683	+	0.837992i	$0.683730\pi$
$374$	18.7269			0.968346
$375$		0			0
$376$	40.7210			2.10002
$377$			1.43381i			0.0738449i
$378$		0			0
$379$	19.9236			1.02341			0.511704	−	0.859162i	$-0.329015\pi$
$379$	19.9236			1.02341			0.511704	+	0.859162i	$0.329015\pi$
$380$	67.2427	−	26.3090i	3.44948	−	1.34962i
$381$		0			0
$382$			55.4837i			2.83879i
$383$			11.9116i			0.608653i	0.952568	+	0.304326i	$0.0984313\pi$
$383$			11.9116i			0.608653i	−0.952568	+	0.304326i	$0.901569\pi$
$384$		0			0
$385$	3.59047	+	9.17683i	0.182987	+	0.467695i
$386$	30.7760			1.56646
$387$		0			0
$388$			6.61620i			0.335887i
$389$	−32.8327			−1.66468			−0.832342	−	0.554263i	$-0.813000\pi$
$389$	−32.8327			−1.66468			−0.832342	+	0.554263i	$0.813000\pi$
$390$		0			0
$391$	−7.02482			−0.355261
$392$		−	57.1892i		−	2.88849i
$393$		0			0
$394$	−30.4783			−1.53547
$395$	−12.7655	+	4.99453i	−0.642300	+	0.251302i
$396$		0			0
$397$		−	30.5279i		−	1.53215i	−0.642749	−	0.766076i	$-0.722206\pi$
$397$		−	30.5279i		−	1.53215i	0.642749	−	0.766076i	$-0.277794\pi$
$398$		−	1.48860i		−	0.0746166i
$399$		0			0
$400$	22.7743	−	21.0421i	1.13871	−	1.05211i
$401$	30.9549			1.54582			0.772908	−	0.634519i	$-0.218802\pi$
$401$	30.9549			1.54582			0.772908	+	0.634519i	$0.218802\pi$
$402$		0			0
$403$			10.5673i			0.526392i
$404$	−36.0314			−1.79263
$405$		0			0
$406$	−10.2869			−0.510528
$407$		−	11.7600i		−	0.582920i
$408$		0			0
$409$	29.2998			1.44878			0.724392	−	0.689388i	$-0.242121\pi$
$409$	29.2998			1.44878			0.724392	+	0.689388i	$0.242121\pi$
$410$	6.20665	+	15.8635i	0.306525	+	0.783443i
$411$		0			0
$412$			14.4701i			0.712892i
$413$			38.6026i			1.89951i
$414$		0			0
$415$	0.501862	+	1.28270i	0.0246354	+	0.0629654i
$416$	−5.44615			−0.267019
$417$		0			0
$418$			20.1989i			0.987962i
$419$	3.86228			0.188685			0.0943424	−	0.995540i	$-0.469925\pi$
$419$	3.86228			0.188685			0.0943424	+	0.995540i	$0.469925\pi$
$420$		0			0
$421$	2.06057			0.100426			0.0502129	−	0.998739i	$-0.484010\pi$
$421$	2.06057			0.100426			0.0502129	+	0.998739i	$0.484010\pi$
$422$			43.8651i			2.13532i
$423$		0			0
$424$	45.0144			2.18609
$425$	−23.3697	−	25.2934i	−1.13360	−	1.22691i
$426$		0			0
$427$		−	1.08343i		−	0.0524309i
$428$			38.0253i			1.83802i
$429$		0			0
$430$	55.7302	−	21.8046i	2.68755	−	1.05151i
$431$	19.2642			0.927925			0.463962	−	0.885855i	$-0.346427\pi$
$431$	19.2642			0.927925			0.463962	+	0.885855i	$0.346427\pi$
$432$		0			0
$433$		−	12.5317i		−	0.602236i	−0.953587	−	0.301118i	$-0.902640\pi$
$433$		−	12.5317i		−	0.602236i	0.953587	−	0.301118i	$-0.0973598\pi$
$434$	−75.8147			−3.63922
$435$		0			0
$436$	−67.5017			−3.23274
$437$		−	7.57700i		−	0.362457i
$438$		0			0
$439$	10.1415			0.484025			0.242013	−	0.970273i	$-0.422192\pi$
$439$	10.1415			0.484025			0.242013	+	0.970273i	$0.422192\pi$
$440$	5.19891	+	13.2878i	0.247848	+	0.633473i
$441$		0			0
$442$			24.8785i			1.18335i
$443$			31.5129i			1.49722i	0.663010	+	0.748611i	$0.269279\pi$
$443$			31.5129i			1.49722i	−0.663010	+	0.748611i	$0.730721\pi$
$444$		0			0
$445$	4.41089	−	1.72577i	0.209096	−	0.0818096i
$446$	36.1505			1.71178
$447$		0			0
$448$			11.5702i			0.546641i
$449$	−16.9679			−0.800762			−0.400381	−	0.916349i	$-0.631122\pi$
$449$	−16.9679			−0.800762			−0.400381	+	0.916349i	$0.631122\pi$
$450$		0			0
$451$	−3.26361			−0.153678
$452$			1.47524i			0.0693892i
$453$		0			0
$454$	3.46805			0.162764
$455$	−12.1913	+	4.76989i	−0.571537	+	0.223616i
$456$		0			0
$457$		−	23.0976i		−	1.08046i	−0.841518	−	0.540229i	$-0.818337\pi$
$457$		−	23.0976i		−	1.08046i	0.841518	−	0.540229i	$-0.181663\pi$
$458$		−	38.0482i		−	1.77787i
$459$		0			0
$460$	−3.61219	−	9.23235i	−0.168419	−	0.430461i
$461$	−36.4118			−1.69587			−0.847933	−	0.530104i	$-0.822153\pi$
$461$	−36.4118			−1.69587			−0.847933	+	0.530104i	$0.822153\pi$
$462$		0			0
$463$		−	19.1964i		−	0.892134i	−0.895000	−	0.446067i	$-0.852824\pi$
$463$		−	19.1964i		−	0.892134i	0.895000	−	0.446067i	$-0.147176\pi$
$464$	−6.20142			−0.287894
$465$		0			0
$466$	22.0137			1.01976
$467$			23.9688i			1.10915i	0.832135	+	0.554573i	$0.187118\pi$
$467$			23.9688i			1.10915i	−0.832135	+	0.554573i	$0.812882\pi$
$468$		0			0
$469$	45.4528			2.09881
$470$	36.1317	−	14.1366i	1.66663	−	0.652075i
$471$		0			0
$472$			55.8956i			2.57280i
$473$			11.4654i			0.527180i
$474$		0			0
$475$	27.2815	−	25.2066i	1.25176	−	1.15656i
$476$	−122.245			−5.60310
$477$		0			0
$478$		−	8.73447i		−	0.399506i
$479$	2.07329			0.0947310			0.0473655	−	0.998878i	$-0.484917\pi$
$479$	2.07329			0.0947310			0.0473655	+	0.998878i	$0.484917\pi$
$480$		0			0
$481$	15.6230			0.712346
$482$		−	36.8641i		−	1.67911i
$483$		0			0
$484$	42.7520			1.94327
$485$	1.24007	+	3.16949i	0.0563089	+	0.143919i
$486$		0			0
$487$		−	27.7050i		−	1.25544i	−0.778441	−	0.627718i	$-0.783989\pi$
$487$		−	27.7050i		−	1.25544i	0.778441	−	0.627718i	$-0.216011\pi$
$488$		−	1.56878i		−	0.0710155i
$489$		0			0
$490$	−19.8537	−	50.7439i	−0.896900	−	2.29238i
$491$	−25.0080			−1.12859			−0.564297	−	0.825572i	$-0.690853\pi$
$491$	−25.0080			−1.12859			−0.564297	+	0.825572i	$0.690853\pi$
$492$		0			0
$493$			6.88737i			0.310192i
$494$	−26.8340			−1.20732
$495$		0			0
$496$	−45.7048			−2.05221
$497$			49.5602i			2.22308i
$498$		0			0
$499$	8.83260			0.395402			0.197701	−	0.980262i	$-0.436653\pi$
$499$	8.83260			0.395402			0.197701	+	0.980262i	$0.436653\pi$
$500$	21.2250	−	43.7195i	0.949210	−	1.95519i
$501$		0			0
$502$			53.5175i			2.38860i
$503$		−	41.3878i		−	1.84539i	−0.385530	−	0.922695i	$-0.625982\pi$
$503$		−	41.3878i		−	1.84539i	0.385530	−	0.922695i	$-0.374018\pi$
$504$		0			0
$505$	−17.2609	+	6.75337i	−0.768098	+	0.300521i
$506$	2.77329			0.123288
$507$		0			0
$508$			52.6712i			2.33691i
$509$	−37.5015			−1.66223			−0.831113	−	0.556104i	$-0.812296\pi$
$509$	−37.5015			−1.66223			−0.831113	+	0.556104i	$0.812296\pi$
$510$		0			0
$511$	14.4554			0.639469
$512$			49.7754i			2.19978i
$513$		0			0
$514$	−27.4392			−1.21029
$515$	2.71214	+	6.93191i	0.119511	+	0.305457i
$516$		0			0
$517$			7.43340i			0.326920i
$518$			112.087i			4.92481i
$519$		0			0
$520$	−17.6527	+	6.90669i	−0.774123	+	0.302878i
$521$	−28.1345			−1.23259			−0.616297	−	0.787514i	$-0.711368\pi$
$521$	−28.1345			−1.23259			−0.616297	+	0.787514i	$0.711368\pi$
$522$		0			0
$523$			18.2249i			0.796921i	0.917186	+	0.398460i	$0.130455\pi$
$523$			18.2249i			0.796921i	−0.917186	+	0.398460i	$0.869545\pi$
$524$	73.0303			3.19034
$525$		0			0
$526$	69.5561			3.03279
$527$			50.7603i			2.21115i
$528$		0			0
$529$	21.9597			0.954769
$530$	39.9412	−	15.6271i	1.73493	−	0.678799i
$531$		0			0
$532$		−	131.854i		−	5.71660i
$533$		−	4.33567i		−	0.187799i
$534$		0			0
$535$	7.12707	+	18.2160i	0.308130	+	0.787546i
$536$	65.8145			2.84275
$537$		0			0
$538$		−	26.6362i		−	1.14837i
$539$	10.4396			0.449665
$540$		0			0
$541$	−45.7584			−1.96731			−0.983655	−	0.180066i	$-0.942369\pi$
$541$	−45.7584			−1.96731			−0.983655	+	0.180066i	$0.942369\pi$
$542$			9.08049i			0.390040i
$543$		0			0
$544$	−26.1608			−1.12164
$545$	−32.3366	+	12.6518i	−1.38515	+	0.541945i
$546$		0			0
$547$			17.7250i			0.757868i	0.925424	+	0.378934i	$0.123709\pi$
$547$			17.7250i			0.757868i	−0.925424	+	0.378934i	$0.876291\pi$
$548$		−	4.15944i		−	0.177683i
$549$		0			0
$550$	9.22597	+	9.98543i	0.393397	+	0.425780i
$551$	−7.42874			−0.316475
$552$		0			0
$553$			25.0313i			1.06444i
$554$	2.15641			0.0916171
$555$		0			0
$556$	−8.06152			−0.341885
$557$			16.2072i			0.686720i	0.939204	+	0.343360i	$0.111565\pi$
$557$			16.2072i			0.686720i	−0.939204	+	0.343360i	$0.888435\pi$
$558$		0			0
$559$	−15.2317			−0.644230
$560$	−20.6304	−	52.7290i	−0.871794	−	2.22821i
$561$		0			0
$562$		−	27.1875i		−	1.14683i
$563$		−	38.2802i		−	1.61332i	−0.591018	−	0.806658i	$-0.701274\pi$
$563$		−	38.2802i		−	1.61332i	0.591018	−	0.806658i	$-0.298726\pi$
$564$		0			0
$565$	0.276503	+	0.706711i	0.0116326	+	0.0297316i
$566$	−75.5318			−3.17484
$567$		0			0
$568$			71.7619i			3.01106i
$569$	21.3031			0.893075			0.446537	−	0.894765i	$-0.352657\pi$
$569$	21.3031			0.893075			0.446537	+	0.894765i	$0.352657\pi$
$570$		0			0
$571$	0.776929			0.0325135			0.0162567	−	0.999868i	$-0.494825\pi$
$571$	0.776929			0.0325135			0.0162567	+	0.999868i	$0.494825\pi$
$572$		−	6.72667i		−	0.281256i
$573$		0			0
$574$	31.1062			1.29835
$575$	−3.46084	−	3.74572i	−0.144327	−	0.156207i
$576$		0			0
$577$		−	32.6201i		−	1.35799i	−0.734142	−	0.678996i	$-0.762415\pi$
$577$		−	32.6201i		−	1.35799i	0.734142	−	0.678996i	$-0.237585\pi$
$578$			76.6769i			3.18934i
$579$		0			0
$580$	−9.05170	+	3.54151i	−0.375851	+	0.147053i
$581$	2.51521			0.104348
$582$		0			0
$583$			8.21714i			0.340319i
$584$	20.9311			0.866134
$585$		0			0
$586$	1.18045			0.0487639
$587$		−	23.9622i		−	0.989025i	−0.869171	−	0.494512i	$-0.835347\pi$
$587$		−	23.9622i		−	0.989025i	0.869171	−	0.494512i	$-0.164653\pi$
$588$		0			0
$589$	−54.7502			−2.25594
$590$	19.4046	+	49.5961i	0.798876	+	2.04184i
$591$		0			0
$592$			67.5714i			2.77717i
$593$			24.7871i			1.01788i	0.860801	+	0.508942i	$0.169963\pi$
$593$			24.7871i			1.01788i	−0.860801	+	0.508942i	$0.830037\pi$
$594$		0			0
$595$	−58.5615	+	22.9124i	−2.40079	+	0.939317i
$596$	72.2985			2.96146
$597$		0			0
$598$			3.68428i			0.150661i
$599$	−19.5390			−0.798340			−0.399170	−	0.916877i	$-0.630702\pi$
$599$	−19.5390			−0.798340			−0.399170	+	0.916877i	$0.630702\pi$
$600$		0			0
$601$	28.1306			1.14747			0.573735	−	0.819041i	$-0.305494\pi$
$601$	28.1306			1.14747			0.573735	+	0.819041i	$0.305494\pi$
$602$		−	109.279i		−	4.45390i
$603$		0			0
$604$	−63.9249			−2.60107
$605$	20.4803	−	8.01300i	0.832643	−	0.325775i
$606$		0			0
$607$		−	7.48051i		−	0.303624i	−0.988409	−	0.151812i	$-0.951489\pi$
$607$		−	7.48051i		−	0.303624i	0.988409	−	0.151812i	$-0.0485109\pi$
$608$		−	28.2172i		−	1.14436i
$609$		0			0
$610$	−0.544617	−	1.39198i	−0.0220509	−	0.0563596i
$611$	−9.87517			−0.399507
$612$		0			0
$613$			14.2166i			0.574203i	0.957900	+	0.287101i	$0.0926917\pi$
$613$			14.2166i			0.574203i	−0.957900	+	0.287101i	$0.907308\pi$
$614$	6.45833			0.260637
$615$		0			0
$616$	26.0557			1.04981
$617$			42.3238i			1.70389i	0.523630	+	0.851945i	$0.324577\pi$
$617$			42.3238i			1.70389i	−0.523630	+	0.851945i	$0.675423\pi$
$618$		0			0
$619$	−34.3853			−1.38206			−0.691032	−	0.722824i	$-0.742844\pi$
$619$	−34.3853			−1.38206			−0.691032	+	0.722824i	$0.742844\pi$
$620$	−66.7116	+	26.1011i	−2.67920	+	1.04825i
$621$		0			0
$622$		−	40.5978i		−	1.62782i
$623$		−	8.64916i		−	0.346521i
$624$		0			0
$625$	1.97349	−	24.9220i	0.0789396	−	0.996879i
$626$	−17.9246			−0.716410
$627$		0			0
$628$		−	25.4926i		−	1.01727i
$629$	75.0456			2.99227
$630$		0			0
$631$	−1.48894			−0.0592738			−0.0296369	−	0.999561i	$-0.509435\pi$
$631$	−1.48894			−0.0592738			−0.0296369	+	0.999561i	$0.509435\pi$
$632$			36.2448i			1.44174i
$633$		0			0
$634$	−68.3709			−2.71536
$635$	9.87216	+	25.2321i	0.391765	+	1.00131i
$636$		0			0
$637$			13.8689i			0.549504i
$638$		−	2.71902i		−	0.107647i
$639$		0			0
$640$	12.0054	+	30.6844i	0.474555	+	1.21291i
$641$	−29.9790			−1.18410			−0.592050	−	0.805901i	$-0.701681\pi$
$641$	−29.9790			−1.18410			−0.592050	+	0.805901i	$0.701681\pi$
$642$		0			0
$643$		−	9.90934i		−	0.390786i	−0.980725	−	0.195393i	$-0.937402\pi$
$643$		−	9.90934i		−	0.390786i	0.980725	−	0.195393i	$-0.0625983\pi$
$644$	−18.1034			−0.713374
$645$		0			0
$646$	−128.898			−5.07144
$647$		−	46.6922i		−	1.83566i	−0.396976	−	0.917829i	$-0.629940\pi$
$647$		−	46.6922i		−	1.83566i	0.396976	−	0.917829i	$-0.370060\pi$
$648$		0			0
$649$	−10.2034			−0.400520
$650$	−13.2655	+	12.2566i	−0.520316	+	0.480743i
$651$		0			0
$652$			22.0049i			0.861778i
$653$			18.4037i			0.720193i	0.932915	+	0.360096i	$0.117256\pi$
$653$			18.4037i			0.720193i	−0.932915	+	0.360096i	$0.882744\pi$
$654$		0			0
$655$	34.9851	−	13.6881i	1.36698	−	0.534837i
$656$	18.7524			0.732156
$657$		0			0
$658$		−	70.8494i		−	2.76200i
$659$	−31.2481			−1.21725			−0.608626	−	0.793457i	$-0.708279\pi$
$659$	−31.2481			−1.21725			−0.608626	+	0.793457i	$0.708279\pi$
$660$		0			0
$661$	−24.1806			−0.940517			−0.470259	−	0.882529i	$-0.655839\pi$
$661$	−24.1806			−0.940517			−0.470259	+	0.882529i	$0.655839\pi$
$662$			24.5136i			0.952749i
$663$		0			0
$664$	3.64196			0.141336
$665$	−24.7134	−	63.1646i	−0.958344	−	2.44942i
$666$		0			0
$667$			1.01996i			0.0394929i
$668$		−	18.4771i		−	0.714902i
$669$		0			0
$670$	58.3971	−	22.8481i	2.25608	−	0.882698i
$671$	0.286373			0.0110553
$672$		0			0
$673$			17.6115i			0.678873i	0.940629	+	0.339437i	$0.110236\pi$
$673$			17.6115i			0.678873i	−0.940629	+	0.339437i	$0.889764\pi$
$674$	10.9542			0.421941
$675$		0			0
$676$	−47.5728			−1.82972
$677$			28.2582i			1.08605i	0.839717	+	0.543025i	$0.182721\pi$
$677$			28.2582i			1.08605i	−0.839717	+	0.543025i	$0.817279\pi$
$678$		0			0
$679$	6.21495			0.238508
$680$	−84.7957	+	33.1766i	−3.25177	+	1.27226i
$681$		0			0
$682$		−	20.0394i		−	0.767347i
$683$		−	36.4236i		−	1.39371i	−0.717212	−	0.696855i	$-0.754582\pi$
$683$		−	36.4236i		−	1.39371i	0.717212	−	0.696855i	$-0.245418\pi$
$684$		0			0
$685$	−0.779604	−	1.99258i	−0.0297871	−	0.0761326i
$686$	−27.4940			−1.04973
$687$		0			0
$688$		−	65.8790i		−	2.51161i
$689$	−10.9164			−0.415880
$690$		0			0
$691$	−2.76187			−0.105067			−0.0525333	−	0.998619i	$-0.516730\pi$
$691$	−2.76187			−0.105067			−0.0525333	+	0.998619i	$0.516730\pi$
$692$			16.0727i			0.610993i
$693$		0			0
$694$	−3.75595			−0.142574
$695$	−3.86187	+	1.51097i	−0.146489	+	0.0573144i
$696$		0			0
$697$		−	20.8266i		−	0.788863i
$698$		−	13.8068i		−	0.522594i
$699$		0			0
$700$	−60.2251	−	65.1826i	−2.27629	−	2.46367i
$701$	−0.823616			−0.0311076			−0.0155538	−	0.999879i	$-0.504951\pi$
$701$	−0.823616			−0.0311076			−0.0155538	+	0.999879i	$0.504951\pi$
$702$		0			0
$703$			80.9445i			3.05288i
$704$	−3.05824			−0.115262
$705$		0			0
$706$	7.50158			0.282326
$707$			33.8462i			1.27292i
$708$		0			0
$709$	−37.0407			−1.39109			−0.695546	−	0.718482i	$-0.744837\pi$
$709$	−37.0407			−1.39109			−0.695546	+	0.718482i	$0.744837\pi$
$710$	24.9128	+	63.6742i	0.934960	+	2.38965i
$711$		0			0
$712$		−	12.5238i		−	0.469348i
$713$			7.51714i			0.281519i
$714$		0			0
$715$	−1.26078	−	3.22241i	−0.0471505	−	0.120511i
$716$	−74.9314			−2.80032
$717$		0			0
$718$			63.3027i			2.36244i
$719$	47.2494			1.76211			0.881053	−	0.473018i	$-0.156836\pi$
$719$	47.2494			1.76211			0.881053	+	0.473018i	$0.156836\pi$
$720$		0			0
$721$	13.5926			0.506213
$722$		−	91.1637i		−	3.39276i
$723$		0			0
$724$	−17.2736			−0.641968
$725$	−3.67243	+	3.39312i	−0.136391	+	0.126017i
$726$		0			0
$727$		−	17.7601i		−	0.658686i	−0.944210	−	0.329343i	$-0.893173\pi$
$727$		−	17.7601i		−	0.658686i	0.944210	−	0.329343i	$-0.106827\pi$
$728$			34.6146i			1.28290i
$729$		0			0
$730$	18.5721	−	7.26640i	0.687385	−	0.268942i
$731$	−73.1660			−2.70614
$732$		0			0
$733$		−	18.6106i		−	0.687397i	−0.939080	−	0.343699i	$-0.888320\pi$
$733$		−	18.6106i		−	0.687397i	0.939080	−	0.343699i	$-0.111680\pi$
$734$	−27.1301			−1.00139
$735$		0			0
$736$	−3.87418			−0.142804
$737$			12.0141i			0.442545i
$738$		0			0
$739$	−29.8386			−1.09763			−0.548815	−	0.835944i	$-0.684921\pi$
$739$	−29.8386			−1.09763			−0.548815	+	0.835944i	$0.684921\pi$
$740$	38.5887	+	98.6285i	1.41855	+	3.62565i
$741$		0			0
$742$		−	78.3194i		−	2.87519i
$743$		−	2.81047i		−	0.103106i	−0.998670	−	0.0515532i	$-0.983583\pi$
$743$		−	2.81047i		−	0.103106i	0.998670	−	0.0515532i	$-0.0164172\pi$
$744$		0			0
$745$	34.6346	−	13.5509i	1.26891	−	0.496467i
$746$	81.5461			2.98562
$747$		0			0
$748$		−	32.3119i		−	1.18144i
$749$	35.7191			1.30515
$750$		0			0
$751$	0.199733			0.00728835			0.00364417	−	0.999993i	$-0.498840\pi$
$751$	0.199733			0.00728835			0.00364417	+	0.999993i	$0.498840\pi$
$752$		−	42.7115i		−	1.55753i
$753$		0			0
$754$	3.61219			0.131548
$755$	−30.6232	+	11.9814i	−1.11449	+	0.436049i
$756$		0			0
$757$		−	4.12493i		−	0.149923i	−0.997186	−	0.0749616i	$-0.976117\pi$
$757$		−	4.12493i		−	0.149923i	0.997186	−	0.0749616i	$-0.0238834\pi$
$758$		−	50.1935i		−	1.82311i
$759$		0			0
$760$	−35.7844	−	91.4609i	−1.29804	−	3.31764i
$761$	21.3155			0.772685			0.386343	−	0.922355i	$-0.373738\pi$
$761$	21.3155			0.772685			0.386343	+	0.922355i	$0.373738\pi$
$762$		0			0
$763$			63.4078i			2.29552i
$764$	95.7329			3.46350
$765$		0			0
$766$	30.0088			1.08426
$767$		−	13.5551i		−	0.489448i
$768$		0			0
$769$	29.9808			1.08113			0.540567	−	0.841301i	$-0.318210\pi$
$769$	29.9808			1.08113			0.540567	+	0.841301i	$0.318210\pi$
$770$	23.1192	−	9.04545i	0.833157	−	0.325975i
$771$		0			0
$772$		−	53.1017i		−	1.91117i
$773$			33.7161i			1.21268i	0.795204	+	0.606342i	$0.207364\pi$
$773$			33.7161i			1.21268i	−0.795204	+	0.606342i	$0.792636\pi$
$774$		0			0
$775$	−27.0660	+	25.0075i	−0.972240	+	0.898295i
$776$	8.99910			0.323049
$777$		0			0
$778$			82.7153i			2.96549i
$779$	22.4636			0.804843
$780$		0			0
$781$	−13.0998			−0.468746
$782$			17.6976i			0.632865i
$783$		0			0
$784$	−59.9847			−2.14231
$785$	−4.77808	−	12.2122i	−0.170537	−	0.435874i
$786$		0			0
$787$			31.6643i			1.12871i	0.825532	+	0.564355i	$0.190875\pi$
$787$			31.6643i			1.12871i	−0.825532	+	0.564355i	$0.809125\pi$
$788$			52.5880i			1.87337i
$789$		0			0
$790$	12.5827	+	32.1600i	0.447672	+	1.14420i
$791$	1.38577			0.0492722
$792$		0			0
$793$			0.380443i			0.0135099i
$794$	−76.9089			−2.72939
$795$		0			0
$796$	−2.56846			−0.0910367
$797$			18.4025i			0.651851i	0.945395	+	0.325925i	$0.105676\pi$
$797$			18.4025i			0.651851i	−0.945395	+	0.325925i	$0.894324\pi$
$798$		0			0
$799$	−47.4359			−1.67816
$800$	−12.8883	−	13.9493i	−0.455672	−	0.493182i
$801$		0			0
$802$		−	77.9846i		−	2.75373i
$803$			3.82086i			0.134835i
$804$		0			0
$805$	−8.67243	+	3.39312i	−0.305663	+	0.119592i
$806$	26.6220			0.937721
$807$		0			0
$808$			49.0085i			1.72411i
$809$	34.5242			1.21381			0.606903	−	0.794776i	$-0.292412\pi$
$809$	34.5242			1.21381			0.606903	+	0.794776i	$0.292412\pi$
$810$		0			0
$811$	−34.1567			−1.19941			−0.599703	−	0.800223i	$-0.704715\pi$
$811$	−34.1567			−1.19941			−0.599703	+	0.800223i	$0.704715\pi$
$812$			17.7492i			0.622874i
$813$		0			0
$814$	−29.6268			−1.03842
$815$	4.12437	+	10.5414i	0.144471	+	0.369250i
$816$		0			0
$817$		−	78.9171i		−	2.76096i
$818$		−	73.8150i		−	2.58088i
$819$		0			0
$820$	27.3713	−	10.7091i	0.955846	−	0.373978i
$821$	14.8753			0.519151			0.259575	−	0.965723i	$-0.416417\pi$
$821$	14.8753			0.519151			0.259575	+	0.965723i	$0.416417\pi$
$822$		0			0
$823$		−	1.54163i		−	0.0537378i	−0.999639	−	0.0268689i	$-0.991446\pi$
$823$		−	1.54163i		−	0.0537378i	0.999639	−	0.0268689i	$-0.00855366\pi$
$824$	19.6817			0.685645
$825$		0			0
$826$	97.2513			3.38380
$827$			33.7827i			1.17474i	0.809319	+	0.587369i	$0.199836\pi$
$827$			33.7827i			1.17474i	−0.809319	+	0.587369i	$0.800164\pi$
$828$		0			0
$829$	48.7491			1.69312			0.846562	−	0.532290i	$-0.178668\pi$
$829$	48.7491			1.69312			0.846562	+	0.532290i	$0.178668\pi$
$830$	3.23151	−	1.26434i	0.112167	−	0.0438858i
$831$		0			0
$832$		−	4.06284i		−	0.140854i
$833$			66.6197i			2.30824i
$834$		0			0
$835$	−3.46317	−	8.85147i	−0.119848	−	0.306318i
$836$	34.8517			1.20537
$837$		0			0
$838$		−	9.73023i		−	0.336125i
$839$	42.6991			1.47414			0.737069	−	0.675818i	$-0.236209\pi$
$839$	42.6991			1.47414			0.737069	+	0.675818i	$0.236209\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$		−	5.19118i		−	0.178900i
$843$		0			0
$844$	75.6859			2.60522
$845$	−22.7897	+	8.91656i	−0.783990	+	0.306739i
$846$		0			0
$847$		−	40.1592i		−	1.37989i
$848$		−	47.2147i		−	1.62136i
$849$		0			0
$850$	−63.7215	+	58.8751i	−2.18563	+	2.01940i
$851$	11.1136			0.380969
$852$		0			0
$853$			1.49646i			0.0512379i	0.999672	+	0.0256189i	$0.00815566\pi$
$853$			1.49646i			0.0512379i	−0.999672	+	0.0256189i	$0.991844\pi$
$854$	−2.72949			−0.0934011
$855$		0			0
$856$	51.7205			1.76777
$857$			13.9153i			0.475336i	0.971346	+	0.237668i	$0.0763831\pi$
$857$			13.9153i			0.475336i	−0.971346	+	0.237668i	$0.923617\pi$
$858$		0			0
$859$	14.0417			0.479098			0.239549	−	0.970884i	$-0.423000\pi$
$859$	14.0417			0.479098			0.239549	+	0.970884i	$0.423000\pi$
$860$	−37.6222	−	96.1582i	−1.28291	−	3.27897i
$861$		0			0
$862$		−	48.5323i		−	1.65302i
$863$			34.0731i			1.15986i	0.814665	+	0.579931i	$0.196921\pi$
$863$			34.0731i			1.15986i	−0.814665	+	0.579931i	$0.803079\pi$
$864$		0			0
$865$	3.01251	+	7.69963i	0.102428	+	0.261795i
$866$	−31.5711			−1.07283
$867$		0			0
$868$			130.812i			4.44006i
$869$	−6.61629			−0.224442
$870$		0			0
$871$	−15.9606			−0.540803
$872$			91.8131i			3.10918i
$873$		0			0
$874$	−19.0887			−0.645685
$875$	−41.0680	−	19.9377i	−1.38835	−	0.674019i
$876$		0			0
$877$			29.3593i			0.991393i	0.868496	+	0.495697i	$0.165087\pi$
$877$			29.3593i			0.991393i	−0.868496	+	0.495697i	$0.834913\pi$
$878$		−	25.5493i		−	0.862248i
$879$		0			0
$880$	13.9374	−	5.45304i	0.469828	−	0.183822i
$881$	43.2369			1.45669			0.728344	−	0.685212i	$-0.240290\pi$
$881$	43.2369			1.45669			0.728344	+	0.685212i	$0.240290\pi$
$882$		0			0
$883$		−	26.0177i		−	0.875566i	−0.899081	−	0.437783i	$-0.855764\pi$
$883$		−	26.0177i		−	0.875566i	0.899081	−	0.437783i	$-0.144236\pi$
$884$	42.9259			1.44375
$885$		0			0
$886$	79.3902			2.66717
$887$			8.13241i			0.273060i	0.990636	+	0.136530i	$0.0435950\pi$
$887$			8.13241i			0.273060i	−0.990636	+	0.136530i	$0.956405\pi$
$888$		0			0
$889$	49.4769			1.65940
$890$	−4.34774	−	11.1123i	−0.145736	−	0.372486i
$891$		0			0
$892$		−	62.3749i		−	2.08847i
$893$		−	51.1645i		−	1.71215i
$894$		0			0
$895$	−35.8959	+	14.0444i	−1.19987	+	0.469452i
$896$	60.1681			2.01007
$897$		0			0
$898$			42.7470i			1.42649i
$899$	7.37006			0.245805
$900$		0			0
$901$	−52.4372			−1.74694
$902$			8.22201i			0.273763i
$903$		0			0
$904$	2.00656			0.0667371
$905$	−8.27491	+	3.23759i	−0.275067	+	0.107621i
$906$		0			0
$907$		−	18.7226i		−	0.621673i	−0.950463	−	0.310836i	$-0.899391\pi$
$907$		−	18.7226i		−	0.621673i	0.950463	−	0.310836i	$-0.100609\pi$
$908$		−	5.98385i		−	0.198581i
$909$		0			0
$910$	12.0168	+	30.7135i	0.398352	+	1.01814i
$911$	14.9915			0.496690			0.248345	−	0.968672i	$-0.420113\pi$
$911$	14.9915			0.496690			0.248345	+	0.968672i	$0.420113\pi$
$912$		0			0
$913$			0.664821i			0.0220024i
$914$	−58.1896			−1.92474
$915$		0			0
$916$	−65.6492			−2.16911
$917$		−	68.6012i		−	2.26541i
$918$		0			0
$919$	−33.4011			−1.10180			−0.550901	−	0.834571i	$-0.685716\pi$
$919$	−33.4011			−1.10180			−0.550901	+	0.834571i	$0.685716\pi$
$920$	−12.5575	+	4.91316i	−0.414008	+	0.161982i
$921$		0			0
$922$			91.7320i			3.02103i
$923$		−	17.4029i		−	0.572822i
$924$		0			0
$925$	36.9718	+	40.0153i	1.21563	+	1.31569i
$926$	−48.3615			−1.58926
$927$		0			0
$928$			3.79838i			0.124688i
$929$	35.1088			1.15188			0.575941	−	0.817491i	$-0.304636\pi$
$929$	35.1088			1.15188			0.575941	+	0.817491i	$0.304636\pi$
$930$		0			0
$931$	−71.8562			−2.35499
$932$		−	37.9829i		−	1.24417i
$933$		0			0
$934$	60.3846			1.97584
$935$	−6.05621	−	15.4790i	−0.198059	−	0.506217i
$936$		0			0
$937$			52.6199i			1.71902i	0.511122	+	0.859508i	$0.329230\pi$
$937$			52.6199i			1.71902i	−0.511122	+	0.859508i	$0.670770\pi$
$938$		−	114.509i		−	3.73885i
$939$		0			0
$940$	−24.3917	−	62.3424i	−0.795569	−	2.03339i
$941$	−11.5423			−0.376269			−0.188135	−	0.982143i	$-0.560244\pi$
$941$	−11.5423			−0.376269			−0.188135	+	0.982143i	$0.560244\pi$
$942$		0			0
$943$		−	3.08423i		−	0.100436i
$944$	58.6278			1.90817
$945$		0			0
$946$	28.8848			0.939125
$947$			32.3450i			1.05107i	0.850771	+	0.525536i	$0.176135\pi$
$947$			32.3450i			1.05107i	−0.850771	+	0.525536i	$0.823865\pi$
$948$		0			0
$949$	−5.07596			−0.164773
$950$	−63.5029	−	68.7302i	−2.06031	−	2.22990i
$951$		0			0
$952$			166.273i			5.38894i
$953$		−	5.16960i		−	0.167460i	−0.996488	−	0.0837299i	$-0.973317\pi$
$953$		−	5.16960i		−	0.167460i	0.996488	−	0.0837299i	$-0.0266833\pi$
$954$		0			0
$955$	45.8608	−	17.9432i	1.48402	−	0.580629i
$956$	−15.0707			−0.487420
$957$		0			0
$958$		−	5.22323i		−	0.168755i
$959$	−3.90718			−0.126170
$960$		0			0
$961$	23.3177			0.752185
$962$		−	39.3589i		−	1.26898i
$963$		0			0
$964$	−63.6061			−2.04861
$965$	−9.95285	−	25.4384i	−0.320393	−	0.818890i
$966$		0			0
$967$		−	38.2056i		−	1.22861i	−0.789069	−	0.614305i	$-0.789436\pi$
$967$		−	38.2056i		−	1.22861i	0.789069	−	0.614305i	$-0.210564\pi$
$968$		−	58.1495i		−	1.86900i
$969$		0			0
$970$	7.98488	−	3.12411i	0.256379	−	0.100309i
$971$	−13.1039			−0.420524			−0.210262	−	0.977645i	$-0.567432\pi$
$971$	−13.1039			−0.420524			−0.210262	+	0.977645i	$0.567432\pi$
$972$		0			0
$973$			7.57261i			0.242767i
$974$	−69.7972			−2.23645
$975$		0			0
$976$	−1.64547			−0.0526701
$977$		−	32.4219i		−	1.03727i	−0.854997	−	0.518633i	$-0.826441\pi$
$977$		−	32.4219i		−	1.03727i	0.854997	−	0.518633i	$-0.173559\pi$
$978$		0			0
$979$	2.28615			0.0730656
$980$	−87.5547	+	34.2561i	−2.79683	+	1.09427i
$981$		0			0
$982$			63.0024i			2.01049i
$983$			18.5976i			0.593172i	0.955006	+	0.296586i	$0.0958482\pi$
$983$			18.5976i			0.593172i	−0.955006	+	0.296586i	$0.904152\pi$
$984$		0			0
$985$	9.85656	+	25.1923i	0.314056	+	0.802692i
$986$	17.3513			0.552579
$987$		0			0
$988$			46.3000i			1.47300i
$989$	−10.8352			−0.344540
$990$		0			0
$991$	−18.9551			−0.602128			−0.301064	−	0.953604i	$-0.597342\pi$
$991$	−18.9551			−0.602128			−0.301064	+	0.953604i	$0.597342\pi$
$992$			27.9943i			0.888819i
$993$		0			0
$994$	124.857			3.96021
$995$	−1.23042	+	0.481406i	−0.0390069	+	0.0152616i
$996$		0			0
$997$		−	22.5731i		−	0.714896i	−0.933933	−	0.357448i	$-0.883647\pi$
$997$		−	22.5731i		−	0.714896i	0.933933	−	0.357448i	$-0.116353\pi$
$998$		−	22.2519i		−	0.704373i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.k.784.2	✓	12
3.2	odd	2		1305.2.c.l.784.11	yes	12
5.2	odd	4		6525.2.a.ce.1.11		12
5.3	odd	4		6525.2.a.ce.1.2		12
5.4	even	2	inner	1305.2.c.k.784.11	yes	12
15.2	even	4		6525.2.a.cf.1.2		12
15.8	even	4		6525.2.a.cf.1.11		12
15.14	odd	2		1305.2.c.l.784.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1305.2.c.k.784.2	✓	12	1.1	even	1	trivial
1305.2.c.k.784.11	yes	12	5.4	even	2	inner
1305.2.c.l.784.2	yes	12	15.14	odd	2
1305.2.c.l.784.11	yes	12	3.2	odd	2
6525.2.a.ce.1.2		12	5.3	odd	4
6525.2.a.ce.1.11		12	5.2	odd	4
6525.2.a.cf.1.2		12	15.2	even	4
6525.2.a.cf.1.11		12	15.8	even	4

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:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.51930i q^{2} -4.34685 q^{4} +(-2.08236 + 0.814730i) q^{5} +4.08323i q^{7} +5.91241i q^{8} +(2.05255 + 5.24608i) q^{10} -1.07928 q^{11} -1.43381i q^{13} +10.2869 q^{14} +6.20142 q^{16} -6.88737i q^{17} +7.42874 q^{19} +(9.05170 - 3.54151i) q^{20} +2.71902i q^{22} -1.01996i q^{23} +(3.67243 - 3.39312i) q^{25} -3.61219 q^{26} -17.7492i q^{28} -1.00000 q^{29} -7.37006 q^{31} -3.79838i q^{32} -17.3513 q^{34} +(-3.32673 - 8.50274i) q^{35} +10.8961i q^{37} -18.7152i q^{38} +(-4.81702 - 12.3118i) q^{40} +3.02388 q^{41} -10.6232i q^{43} +4.69147 q^{44} -2.56957 q^{46} -6.88737i q^{47} -9.67273 q^{49} +(-8.54827 - 9.25194i) q^{50} +6.23256i q^{52} -7.61354i q^{53} +(2.24745 - 0.879321i) q^{55} -24.1417 q^{56} +2.51930i q^{58} +9.45393 q^{59} -0.265337 q^{61} +18.5674i q^{62} +2.83360 q^{64} +(1.16817 + 2.98570i) q^{65} -11.1316i q^{67} +29.9384i q^{68} +(-21.4209 + 8.38101i) q^{70} +12.1375 q^{71} -3.54019i q^{73} +27.4506 q^{74} -32.2916 q^{76} -4.40694i q^{77} +6.13029 q^{79} +(-12.9136 + 5.05248i) q^{80} -7.61805i q^{82} -0.615986i q^{83} +(5.61135 + 14.3420i) q^{85} -26.7630 q^{86} -6.38115i q^{88} -2.11822 q^{89} +5.85457 q^{91} +4.43360i q^{92} -17.3513 q^{94} +(-15.4693 + 6.05242i) q^{95} -1.52207i q^{97} +24.3685i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{4} - 10 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{16} + 20 q^{19} + 14 q^{20} + 8 q^{25} - 56 q^{26} - 12 q^{29} - 16 q^{31} - 4 q^{34} - 16 q^{35} + 16 q^{40} - 32 q^{41} + 68 q^{44} + 20 q^{46}+ \cdots - 8 q^{95}+O(q^{100}) \) 12 * q - 16 * q^4 - 10 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^16 + 20 * q^19 + 14 * q^20 + 8 * q^25 - 56 * q^26 - 12 * q^29 - 16 * q^31 - 4 * q^34 - 16 * q^35 + 16 * q^40 - 32 * q^41 + 68 * q^44 + 20 * q^46 + 4 * q^49 - 8 * q^50 + 4 * q^55 - 76 * q^56 + 44 * q^59 - 52 * q^61 - 36 * q^64 - 8 * q^65 - 30 * q^70 - 20 * q^71 + 20 * q^74 - 28 * q^76 + 4 * q^79 + 34 * q^80 + 20 * q^85 - 36 * q^86 + 68 * q^89 + 48 * q^91 - 4 * q^94 - 8 * q^95

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