LMFDB - Embedded newform 637.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(1,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("637.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.a (trivial)

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:	yes
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.4507648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 1 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 7x^2 - 6*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.35100$ of defining polynomial
Character	$\chi$	$=$	637.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.17619 q^{2} +3.35100 q^{3} -0.616586 q^{4} +3.14862 q^{5} -3.94140 q^{6} +3.07759 q^{8} +8.22917 q^{9} +O(q^{10})$	\(q-1.17619 q^{2} +3.35100 q^{3} -0.616586 q^{4} +3.14862 q^{5} -3.94140 q^{6} +3.07759 q^{8} +8.22917 q^{9} -3.70337 q^{10} -0.773390 q^{11} -2.06618 q^{12} +1.00000 q^{13} +10.5510 q^{15} -2.38665 q^{16} -5.75340 q^{17} -9.67904 q^{18} -1.22298 q^{19} -1.94140 q^{20} +0.909650 q^{22} -2.99182 q^{23} +10.3130 q^{24} +4.91383 q^{25} -1.17619 q^{26} +17.5229 q^{27} -2.46882 q^{29} -12.4100 q^{30} -6.13487 q^{31} -3.34804 q^{32} -2.59163 q^{33} +6.76707 q^{34} -5.07399 q^{36} +4.99933 q^{37} +1.43845 q^{38} +3.35100 q^{39} +9.69018 q^{40} -2.55981 q^{41} -2.73150 q^{43} +0.476861 q^{44} +25.9106 q^{45} +3.51894 q^{46} +5.37169 q^{47} -7.99766 q^{48} -5.77958 q^{50} -19.2796 q^{51} -0.616586 q^{52} -9.79015 q^{53} -20.6102 q^{54} -2.43511 q^{55} -4.09820 q^{57} +2.90379 q^{58} +2.50456 q^{59} -6.50561 q^{60} -10.9167 q^{61} +7.21575 q^{62} +8.71122 q^{64} +3.14862 q^{65} +3.04823 q^{66} +4.32518 q^{67} +3.54746 q^{68} -10.0256 q^{69} +10.6649 q^{71} +25.3260 q^{72} -5.17450 q^{73} -5.88014 q^{74} +16.4662 q^{75} +0.754072 q^{76} -3.94140 q^{78} -0.542038 q^{79} -7.51467 q^{80} +34.0318 q^{81} +3.01081 q^{82} +15.2259 q^{83} -18.1153 q^{85} +3.21275 q^{86} -8.27301 q^{87} -2.38018 q^{88} +9.23208 q^{89} -30.4757 q^{90} +1.84471 q^{92} -20.5579 q^{93} -6.31811 q^{94} -3.85070 q^{95} -11.2193 q^{96} -1.26291 q^{97} -6.36436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) $ 6 * q + 8 * q^3 + 4 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^9	$ 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} + 6 q^{13} + 12 q^{15} + 16 q^{17} - 4 q^{18} + 2 q^{19} + 16 q^{20} - 12 q^{22} - 6 q^{23} + 12 q^{24} - 4 q^{25} + 20 q^{27} - 6 q^{29} + 6 q^{31} - 20 q^{32} + 4 q^{33} - 24 q^{36} + 8 q^{38} + 8 q^{39} + 4 q^{40} - 8 q^{41} + 2 q^{43} - 4 q^{44} + 14 q^{45} + 8 q^{46} + 30 q^{47} - 8 q^{48} + 8 q^{50} - 4 q^{51} + 4 q^{52} - 14 q^{53} - 48 q^{54} - 8 q^{55} + 4 q^{57} - 8 q^{58} + 24 q^{59} + 12 q^{60} + 28 q^{62} - 20 q^{64} + 6 q^{65} - 4 q^{66} + 16 q^{67} + 28 q^{68} - 20 q^{69} + 8 q^{71} + 28 q^{72} - 6 q^{73} - 12 q^{74} + 12 q^{75} - 16 q^{76} + 4 q^{78} - 22 q^{79} - 28 q^{80} + 46 q^{81} - 40 q^{82} + 50 q^{83} - 8 q^{85} - 16 q^{86} - 16 q^{87} - 44 q^{88} + 26 q^{89} - 40 q^{90} + 20 q^{92} + 16 q^{93} - 32 q^{94} - 6 q^{95} - 20 q^{96} - 14 q^{97} + 12 q^{99}+O(q^{100}) $ 6 * q + 8 * q^3 + 4 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 + 6 * q^13 + 12 * q^15 + 16 * q^17 - 4 * q^18 + 2 * q^19 + 16 * q^20 - 12 * q^22 - 6 * q^23 + 12 * q^24 - 4 * q^25 + 20 * q^27 - 6 * q^29 + 6 * q^31 - 20 * q^32 + 4 * q^33 - 24 * q^36 + 8 * q^38 + 8 * q^39 + 4 * q^40 - 8 * q^41 + 2 * q^43 - 4 * q^44 + 14 * q^45 + 8 * q^46 + 30 * q^47 - 8 * q^48 + 8 * q^50 - 4 * q^51 + 4 * q^52 - 14 * q^53 - 48 * q^54 - 8 * q^55 + 4 * q^57 - 8 * q^58 + 24 * q^59 + 12 * q^60 + 28 * q^62 - 20 * q^64 + 6 * q^65 - 4 * q^66 + 16 * q^67 + 28 * q^68 - 20 * q^69 + 8 * q^71 + 28 * q^72 - 6 * q^73 - 12 * q^74 + 12 * q^75 - 16 * q^76 + 4 * q^78 - 22 * q^79 - 28 * q^80 + 46 * q^81 - 40 * q^82 + 50 * q^83 - 8 * q^85 - 16 * q^86 - 16 * q^87 - 44 * q^88 + 26 * q^89 - 40 * q^90 + 20 * q^92 + 16 * q^93 - 32 * q^94 - 6 * q^95 - 20 * q^96 - 14 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.17619	−0.831689	−0.415845	−	0.909436i	$-0.636514\pi$
$2$	−1.17619	−0.831689	−0.415845	+	0.909436i	$0.636514\pi$
$3$	3.35100	1.93470	0.967349	−	0.253447i	$-0.0815644\pi$
$3$	3.35100	1.93470	0.967349	+	0.253447i	$0.0815644\pi$
$4$	−0.616586	−0.308293
$5$	3.14862	1.40811	0.704054	−	0.710147i	$-0.251371\pi$
$5$	3.14862	1.40811	0.704054	+	0.710147i	$0.251371\pi$
$6$	−3.94140	−1.60907
$7$	0	0
$7$	0	0
$8$	3.07759	1.08809
$9$	8.22917	2.74306
$10$	−3.70337	−1.17111
$11$	−0.773390	−0.233186	−0.116593	−	0.993180i	$-0.537197\pi$
$11$	−0.773390	−0.233186	−0.116593	+	0.993180i	$0.537197\pi$
$12$	−2.06618	−0.596454
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	10.5510	2.72426
$16$	−2.38665	−0.596663
$17$	−5.75340	−1.39540	−0.697702	−	0.716388i	$-0.745794\pi$
$17$	−5.75340	−1.39540	−0.697702	+	0.716388i	$0.745794\pi$
$18$	−9.67904	−2.28137
$19$	−1.22298	−0.280571	−0.140285	−	0.990111i	$-0.544802\pi$
$19$	−1.22298	−0.280571	−0.140285	+	0.990111i	$0.544802\pi$
$20$	−1.94140	−0.434109
$21$	0	0
$22$	0.909650	0.193938
$23$	−2.99182	−0.623838	−0.311919	−	0.950109i	$-0.600972\pi$
$23$	−2.99182	−0.623838	−0.311919	+	0.950109i	$0.600972\pi$
$24$	10.3130	2.10513
$25$	4.91383	0.982767
$26$	−1.17619	−0.230669
$27$	17.5229	3.37229
$28$	0	0
$29$	−2.46882	−0.458449	−0.229224	−	0.973374i	$-0.573619\pi$
$29$	−2.46882	−0.458449	−0.229224	+	0.973374i	$0.573619\pi$
$30$	−12.4100	−2.26574
$31$	−6.13487	−1.10185	−0.550927	−	0.834553i	$-0.685726\pi$
$31$	−6.13487	−1.10185	−0.550927	+	0.834553i	$0.685726\pi$
$32$	−3.34804	−0.591855
$33$	−2.59163	−0.451144
$34$	6.76707	1.16054
$35$	0	0
$36$	−5.07399	−0.845665
$37$	4.99933	0.821884	0.410942	−	0.911661i	$-0.365200\pi$
$37$	4.99933	0.821884	0.410942	+	0.911661i	$0.365200\pi$
$38$	1.43845	0.233348
$39$	3.35100	0.536589
$40$	9.69018	1.53215
$41$	−2.55981	−0.399774	−0.199887	−	0.979819i	$-0.564058\pi$
$41$	−2.55981	−0.399774	−0.199887	+	0.979819i	$0.564058\pi$
$42$	0	0
$43$	−2.73150	−0.416550	−0.208275	−	0.978070i	$-0.566785\pi$
$43$	−2.73150	−0.416550	−0.208275	+	0.978070i	$0.566785\pi$
$44$	0.476861	0.0718895
$45$	25.9106	3.86252
$46$	3.51894	0.518839
$47$	5.37169	0.783542	0.391771	−	0.920063i	$-0.371863\pi$
$47$	5.37169	0.783542	0.391771	+	0.920063i	$0.371863\pi$
$48$	−7.99766	−1.15436
$49$	0	0
$50$	−5.77958	−0.817357
$51$	−19.2796	−2.69969
$52$	−0.616586	−0.0855050
$53$	−9.79015	−1.34478	−0.672390	−	0.740197i	$-0.734732\pi$
$53$	−9.79015	−1.34478	−0.672390	+	0.740197i	$0.734732\pi$
$54$	−20.6102	−2.80470
$55$	−2.43511	−0.328351
$56$	0	0
$57$	−4.09820	−0.542820
$58$	2.90379	0.381287
$59$	2.50456	0.326066	0.163033	−	0.986621i	$-0.447872\pi$
$59$	2.50456	0.326066	0.163033	+	0.986621i	$0.447872\pi$
$60$	−6.50561	−0.839871
$61$	−10.9167	−1.39774	−0.698870	−	0.715248i	$-0.746314\pi$
$61$	−10.9167	−1.39774	−0.698870	+	0.715248i	$0.746314\pi$
$62$	7.21575	0.916401
$63$	0	0
$64$	8.71122	1.08890
$65$	3.14862	0.390539
$66$	3.04823	0.375212
$67$	4.32518	0.528404	0.264202	−	0.964467i	$-0.414891\pi$
$67$	4.32518	0.528404	0.264202	+	0.964467i	$0.414891\pi$
$68$	3.54746	0.430193
$69$	−10.0256	−1.20694
$70$	0	0
$71$	10.6649	1.26570	0.632848	−	0.774276i	$-0.281886\pi$
$71$	10.6649	1.26570	0.632848	+	0.774276i	$0.281886\pi$
$72$	25.3260	2.98470
$73$	−5.17450	−0.605630	−0.302815	−	0.953049i	$-0.597926\pi$
$73$	−5.17450	−0.605630	−0.302815	+	0.953049i	$0.597926\pi$
$74$	−5.88014	−0.683552
$75$	16.4662	1.90136
$76$	0.754072	0.0864979
$77$	0	0
$78$	−3.94140	−0.446275
$79$	−0.542038	−0.0609841	−0.0304920	−	0.999535i	$-0.509707\pi$
$79$	−0.542038	−0.0609841	−0.0304920	+	0.999535i	$0.509707\pi$
$80$	−7.51467	−0.840165
$81$	34.0318	3.78131
$82$	3.01081	0.332488
$83$	15.2259	1.67125	0.835627	−	0.549297i	$-0.185104\pi$
$83$	15.2259	1.67125	0.835627	+	0.549297i	$0.185104\pi$
$84$	0	0
$85$	−18.1153	−1.96488
$86$	3.21275	0.346440
$87$	−8.27301	−0.886960
$88$	−2.38018	−0.253728
$89$	9.23208	0.978599	0.489299	−	0.872116i	$-0.337253\pi$
$89$	9.23208	0.978599	0.489299	+	0.872116i	$0.337253\pi$
$90$	−30.4757	−3.21242
$91$	0	0
$92$	1.84471	0.192325
$93$	−20.5579	−2.13176
$94$	−6.31811	−0.651663
$95$	−3.85070	−0.395074
$96$	−11.2193	−1.14506
$97$	−1.26291	−0.128229	−0.0641145	−	0.997943i	$-0.520422\pi$
$97$	−1.26291	−0.128229	−0.0641145	+	0.997943i	$0.520422\pi$
$98$	0	0
$99$	−6.36436	−0.639642
$100$	−3.02980	−0.302980
$101$	0.605447	0.0602443	0.0301221	−	0.999546i	$-0.490410\pi$
$101$	0.605447	0.0602443	0.0301221	+	0.999546i	$0.490410\pi$
$102$	22.6764	2.24530
$103$	7.64804	0.753584	0.376792	−	0.926298i	$-0.377027\pi$
$103$	7.64804	0.753584	0.376792	+	0.926298i	$0.377027\pi$
$104$	3.07759	0.301783
$105$	0	0
$106$	11.5150	1.11844
$107$	4.82965	0.466900	0.233450	−	0.972369i	$-0.424999\pi$
$107$	4.82965	0.466900	0.233450	+	0.972369i	$0.424999\pi$
$108$	−10.8044	−1.03965
$109$	7.23092	0.692596	0.346298	−	0.938125i	$-0.387439\pi$
$109$	7.23092	0.692596	0.346298	+	0.938125i	$0.387439\pi$
$110$	2.86415	0.273086
$111$	16.7527	1.59010
$112$	0	0
$113$	−9.19375	−0.864875	−0.432438	−	0.901664i	$-0.642346\pi$
$113$	−9.19375	−0.864875	−0.432438	+	0.901664i	$0.642346\pi$
$114$	4.82025	0.451458
$115$	−9.42012	−0.878430
$116$	1.52224	0.141336
$117$	8.22917	0.760787
$118$	−2.94583	−0.271186
$119$	0	0
$120$	32.4718	2.96425
$121$	−10.4019	−0.945624
$122$	12.8401	1.16249
$123$	−8.57790	−0.773443
$124$	3.78267	0.339694
$125$	−0.271305	−0.0242663
$126$	0	0
$127$	−11.2118	−0.994888	−0.497444	−	0.867496i	$-0.665728\pi$
$127$	−11.2118	−0.994888	−0.497444	+	0.867496i	$0.665728\pi$
$128$	−3.54994	−0.313773
$129$	−9.15325	−0.805899
$130$	−3.70337	−0.324807
$131$	15.7380	1.37503	0.687517	−	0.726169i	$-0.258701\pi$
$131$	15.7380	1.37503	0.687517	+	0.726169i	$0.258701\pi$
$132$	1.59796	0.139084
$133$	0	0
$134$	−5.08721	−0.439468
$135$	55.1732	4.74855
$136$	−17.7066	−1.51833
$137$	−18.6210	−1.59090	−0.795449	−	0.606020i	$-0.792765\pi$
$137$	−18.6210	−1.59090	−0.795449	+	0.606020i	$0.792765\pi$
$138$	11.7919	1.00380
$139$	−11.9137	−1.01050	−0.505252	−	0.862972i	$-0.668601\pi$
$139$	−11.9137	−1.01050	−0.505252	+	0.862972i	$0.668601\pi$
$140$	0	0
$141$	18.0005	1.51592
$142$	−12.5440	−1.05267
$143$	−0.773390	−0.0646741
$144$	−19.6402	−1.63668
$145$	−7.77339	−0.645545
$146$	6.08618	0.503696
$147$	0	0
$148$	−3.08251	−0.253381
$149$	11.3753	0.931904	0.465952	−	0.884810i	$-0.345712\pi$
$149$	11.3753	0.931904	0.465952	+	0.884810i	$0.345712\pi$
$150$	−19.3674	−1.58134
$151$	−3.69250	−0.300492	−0.150246	−	0.988649i	$-0.548007\pi$
$151$	−3.69250	−0.300492	−0.150246	+	0.988649i	$0.548007\pi$
$152$	−3.76383	−0.305287
$153$	−47.3457	−3.82767
$154$	0	0
$155$	−19.3164	−1.55153
$156$	−2.06618	−0.165426
$157$	1.12065	0.0894374	0.0447187	−	0.999000i	$-0.485761\pi$
$157$	1.12065	0.0894374	0.0447187	+	0.999000i	$0.485761\pi$
$158$	0.637538	0.0507198
$159$	−32.8068	−2.60175
$160$	−10.5417	−0.833396
$161$	0	0
$162$	−40.0277	−3.14488
$163$	−20.3435	−1.59342	−0.796712	−	0.604359i	$-0.793429\pi$
$163$	−20.3435	−1.59342	−0.796712	+	0.604359i	$0.793429\pi$
$164$	1.57834	0.123248
$165$	−8.16005	−0.635259
$166$	−17.9084	−1.38996
$167$	13.0063	1.00646	0.503228	−	0.864154i	$-0.332146\pi$
$167$	13.0063	1.00646	0.503228	+	0.864154i	$0.332146\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	21.3070	1.63417
$171$	−10.0641	−0.769622
$172$	1.68420	0.128419
$173$	−25.9110	−1.96998	−0.984989	−	0.172616i	$-0.944778\pi$
$173$	−25.9110	−1.96998	−0.984989	+	0.172616i	$0.944778\pi$
$174$	9.73060	0.737675
$175$	0	0
$176$	1.84581	0.139133
$177$	8.39278	0.630840
$178$	−10.8587	−0.813890
$179$	9.64163	0.720649	0.360325	−	0.932827i	$-0.382666\pi$
$179$	9.64163	0.720649	0.360325	+	0.932827i	$0.382666\pi$
$180$	−15.9761	−1.19079
$181$	−2.92683	−0.217550	−0.108775	−	0.994066i	$-0.534693\pi$
$181$	−2.92683	−0.217550	−0.108775	+	0.994066i	$0.534693\pi$
$182$	0	0
$183$	−36.5818	−2.70421
$184$	−9.20760	−0.678793
$185$	15.7410	1.15730
$186$	24.1799	1.77296
$187$	4.44962	0.325388
$188$	−3.31211	−0.241560
$189$	0	0
$190$	4.52914	0.328579
$191$	−16.1364	−1.16759	−0.583796	−	0.811901i	$-0.698433\pi$
$191$	−16.1364	−1.16759	−0.583796	+	0.811901i	$0.698433\pi$
$192$	29.1913	2.10670
$193$	−0.0863817	−0.00621789	−0.00310894	−	0.999995i	$-0.500990\pi$
$193$	−0.0863817	−0.00621789	−0.00310894	+	0.999995i	$0.500990\pi$
$194$	1.48542	0.106647
$195$	10.5510	0.755575
$196$	0	0
$197$	15.0589	1.07290	0.536451	−	0.843932i	$-0.319765\pi$
$197$	15.0589	1.07290	0.536451	+	0.843932i	$0.319765\pi$
$198$	7.48567	0.531983
$199$	15.4466	1.09498	0.547492	−	0.836811i	$-0.315583\pi$
$199$	15.4466	1.09498	0.547492	+	0.836811i	$0.315583\pi$
$200$	15.1228	1.06934
$201$	14.4936	1.02230
$202$	−0.712119	−0.0501045
$203$	0	0
$204$	11.8875	0.832294
$205$	−8.05987	−0.562925
$206$	−8.99552	−0.626748
$207$	−24.6202	−1.71122
$208$	−2.38665	−0.165484
$209$	0.945840	0.0654251
$210$	0	0
$211$	−25.0561	−1.72493	−0.862466	−	0.506115i	$-0.831081\pi$
$211$	−25.0561	−1.72493	−0.862466	+	0.506115i	$0.831081\pi$
$212$	6.03647	0.414586
$213$	35.7382	2.44874
$214$	−5.68057	−0.388316
$215$	−8.60047	−0.586547
$216$	53.9285	3.66937
$217$	0	0
$218$	−8.50491	−0.576025
$219$	−17.3397	−1.17171
$220$	1.50146	0.101228
$221$	−5.75340	−0.387015
$222$	−19.7043	−1.32247
$223$	−20.6640	−1.38376	−0.691881	−	0.722012i	$-0.743218\pi$
$223$	−20.6640	−1.38376	−0.691881	+	0.722012i	$0.743218\pi$
$224$	0	0
$225$	40.4368	2.69579
$226$	10.8136	0.719307
$227$	0.982378	0.0652027	0.0326013	−	0.999468i	$-0.489621\pi$
$227$	0.982378	0.0652027	0.0326013	+	0.999468i	$0.489621\pi$
$228$	2.52689	0.167347
$229$	−14.2742	−0.943269	−0.471634	−	0.881794i	$-0.656336\pi$
$229$	−14.2742	−0.943269	−0.471634	+	0.881794i	$0.656336\pi$
$230$	11.0798	0.730581
$231$	0	0
$232$	−7.59802	−0.498835
$233$	1.39534	0.0914119	0.0457060	−	0.998955i	$-0.485446\pi$
$233$	1.39534	0.0914119	0.0457060	+	0.998955i	$0.485446\pi$
$234$	−9.67904	−0.632739
$235$	16.9134	1.10331
$236$	−1.54428	−0.100524
$237$	−1.81637	−0.117986
$238$	0	0
$239$	2.54875	0.164865	0.0824326	−	0.996597i	$-0.473731\pi$
$239$	2.54875	0.164865	0.0824326	+	0.996597i	$0.473731\pi$
$240$	−25.1816	−1.62547
$241$	29.6746	1.91151	0.955755	−	0.294164i	$-0.0950413\pi$
$241$	29.6746	1.91151	0.955755	+	0.294164i	$0.0950413\pi$
$242$	12.2345	0.786466
$243$	61.4716	3.94340
$244$	6.73108	0.430913
$245$	0	0
$246$	10.0892	0.643264
$247$	−1.22298	−0.0778163
$248$	−18.8806	−1.19892
$249$	51.0218	3.23337
$250$	0.319106	0.0201820
$251$	18.0858	1.14157	0.570784	−	0.821100i	$-0.306639\pi$
$251$	18.0858	1.14157	0.570784	+	0.821100i	$0.306639\pi$
$252$	0	0
$253$	2.31384	0.145470
$254$	13.1872	0.827437
$255$	−60.7043	−3.80145
$256$	−13.2470	−0.827940
$257$	14.7403	0.919473	0.459737	−	0.888055i	$-0.347944\pi$
$257$	14.7403	0.919473	0.459737	+	0.888055i	$0.347944\pi$
$258$	10.7659	0.670257
$259$	0	0
$260$	−1.94140	−0.120400
$261$	−20.3164	−1.25755
$262$	−18.5108	−1.14360
$263$	−8.15922	−0.503119	−0.251560	−	0.967842i	$-0.580943\pi$
$263$	−8.15922	−0.503119	−0.251560	+	0.967842i	$0.580943\pi$
$264$	−7.97597	−0.490887
$265$	−30.8255	−1.89360
$266$	0	0
$267$	30.9367	1.89329
$268$	−2.66684	−0.162903
$269$	0.442582	0.0269847	0.0134924	−	0.999909i	$-0.495705\pi$
$269$	0.442582	0.0269847	0.0134924	+	0.999909i	$0.495705\pi$
$270$	−64.8939	−3.94932
$271$	−21.0831	−1.28071	−0.640354	−	0.768080i	$-0.721212\pi$
$271$	−21.0831	−1.28071	−0.640354	+	0.768080i	$0.721212\pi$
$272$	13.7314	0.832586
$273$	0	0
$274$	21.9018	1.32313
$275$	−3.80031	−0.229167
$276$	6.18163	0.372090
$277$	3.59421	0.215955	0.107977	−	0.994153i	$-0.465563\pi$
$277$	3.59421	0.215955	0.107977	+	0.994153i	$0.465563\pi$
$278$	14.0127	0.840426
$279$	−50.4849	−3.02245
$280$	0	0
$281$	−9.01252	−0.537642	−0.268821	−	0.963190i	$-0.586634\pi$
$281$	−9.01252	−0.537642	−0.268821	+	0.963190i	$0.586634\pi$
$282$	−21.1720	−1.26077
$283$	27.7411	1.64904	0.824520	−	0.565833i	$-0.191445\pi$
$283$	27.7411	1.64904	0.824520	+	0.565833i	$0.191445\pi$
$284$	−6.57585	−0.390205
$285$	−12.9037	−0.764349
$286$	0.909650	0.0537887
$287$	0	0
$288$	−27.5516	−1.62349
$289$	16.1016	0.947153
$290$	9.14296	0.536893
$291$	−4.23201	−0.248085
$292$	3.19052	0.186711
$293$	12.7409	0.744333	0.372167	−	0.928166i	$-0.378615\pi$
$293$	12.7409	0.744333	0.372167	+	0.928166i	$0.378615\pi$
$294$	0	0
$295$	7.88593	0.459137
$296$	15.3859	0.894287
$297$	−13.5521	−0.786370
$298$	−13.3795	−0.775055
$299$	−2.99182	−0.173021
$300$	−10.1528	−0.586175
$301$	0	0
$302$	4.34307	0.249916
$303$	2.02885	0.116555
$304$	2.91883	0.167406
$305$	−34.3726	−1.96817
$306$	55.6874	3.18344
$307$	10.1384	0.578626	0.289313	−	0.957235i	$-0.406573\pi$
$307$	10.1384	0.578626	0.289313	+	0.957235i	$0.406573\pi$
$308$	0	0
$309$	25.6286	1.45796
$310$	22.7197	1.29039
$311$	20.6013	1.16819	0.584096	−	0.811685i	$-0.301449\pi$
$311$	20.6013	1.16819	0.584096	+	0.811685i	$0.301449\pi$
$312$	10.3130	0.583859
$313$	16.5456	0.935213	0.467606	−	0.883937i	$-0.345117\pi$
$313$	16.5456	0.935213	0.467606	+	0.883937i	$0.345117\pi$
$314$	−1.31809	−0.0743841
$315$	0	0
$316$	0.334213	0.0188010
$317$	−21.2340	−1.19262	−0.596310	−	0.802754i	$-0.703367\pi$
$317$	−21.2340	−1.19262	−0.596310	+	0.802754i	$0.703367\pi$
$318$	38.5869	2.16384
$319$	1.90936	0.106904
$320$	27.4284	1.53329
$321$	16.1841	0.903310
$322$	0	0
$323$	7.03629	0.391510
$324$	−20.9835	−1.16575
$325$	4.91383	0.272570
$326$	23.9277	1.32523
$327$	24.2308	1.33996
$328$	−7.87804	−0.434992
$329$	0	0
$330$	9.59774	0.528338
$331$	16.2415	0.892712	0.446356	−	0.894855i	$-0.352721\pi$
$331$	16.2415	0.892712	0.446356	+	0.894855i	$0.352721\pi$
$332$	−9.38804	−0.515236
$333$	41.1403	2.25448
$334$	−15.2978	−0.837058
$335$	13.6184	0.744050
$336$	0	0
$337$	6.42141	0.349797	0.174898	−	0.984586i	$-0.444040\pi$
$337$	6.42141	0.349797	0.174898	+	0.984586i	$0.444040\pi$
$338$	−1.17619	−0.0639761
$339$	−30.8082	−1.67327
$340$	11.1696	0.605758
$341$	4.74464	0.256937
$342$	11.8373	0.640086
$343$	0	0
$344$	−8.40645	−0.453245
$345$	−31.5668	−1.69950
$346$	30.4762	1.63841
$347$	14.4809	0.777376	0.388688	−	0.921369i	$-0.372928\pi$
$347$	14.4809	0.777376	0.388688	+	0.921369i	$0.372928\pi$
$348$	5.10102	0.273443
$349$	1.74500	0.0934079	0.0467040	−	0.998909i	$-0.485128\pi$
$349$	1.74500	0.0934079	0.0467040	+	0.998909i	$0.485128\pi$
$350$	0	0
$351$	17.5229	0.935306
$352$	2.58934	0.138012
$353$	15.9580	0.849358	0.424679	−	0.905344i	$-0.360387\pi$
$353$	15.9580	0.849358	0.424679	+	0.905344i	$0.360387\pi$
$354$	−9.87148	−0.524663
$355$	33.5799	1.78224
$356$	−5.69237	−0.301695
$357$	0	0
$358$	−11.3404	−0.599356
$359$	8.81400	0.465185	0.232593	−	0.972574i	$-0.425279\pi$
$359$	8.81400	0.465185	0.232593	+	0.972574i	$0.425279\pi$
$360$	79.7422	4.20278
$361$	−17.5043	−0.921280
$362$	3.44250	0.180934
$363$	−34.8566	−1.82950
$364$	0	0
$365$	−16.2926	−0.852792
$366$	43.0271	2.24906
$367$	−19.7080	−1.02875	−0.514374	−	0.857566i	$-0.671976\pi$
$367$	−19.7080	−1.02875	−0.514374	+	0.857566i	$0.671976\pi$
$368$	7.14043	0.372221
$369$	−21.0651	−1.09660
$370$	−18.5144	−0.962515
$371$	0	0
$372$	12.6757	0.657205
$373$	−0.365792	−0.0189400	−0.00947000	−	0.999955i	$-0.503014\pi$
$373$	−0.365792	−0.0189400	−0.00947000	+	0.999955i	$0.503014\pi$
$374$	−5.23358	−0.270622
$375$	−0.909143	−0.0469479
$376$	16.5319	0.852566
$377$	−2.46882	−0.127151
$378$	0	0
$379$	7.39215	0.379709	0.189855	−	0.981812i	$-0.439198\pi$
$379$	7.39215	0.379709	0.189855	+	0.981812i	$0.439198\pi$
$380$	2.37429	0.121798
$381$	−37.5707	−1.92481
$382$	18.9795	0.971073
$383$	−3.35364	−0.171363	−0.0856814	−	0.996323i	$-0.527307\pi$
$383$	−3.35364	−0.171363	−0.0856814	+	0.996323i	$0.527307\pi$
$384$	−11.8958	−0.607057
$385$	0	0
$386$	0.101601	0.00517135
$387$	−22.4780	−1.14262
$388$	0.778692	0.0395321
$389$	−2.59344	−0.131492	−0.0657462	−	0.997836i	$-0.520943\pi$
$389$	−2.59344	−0.131492	−0.0657462	+	0.997836i	$0.520943\pi$
$390$	−12.4100	−0.628403
$391$	17.2131	0.870506
$392$	0	0
$393$	52.7379	2.66027
$394$	−17.7121	−0.892321
$395$	−1.70668	−0.0858721
$396$	3.92417	0.197197
$397$	−33.4914	−1.68088	−0.840441	−	0.541902i	$-0.817704\pi$
$397$	−33.4914	−1.68088	−0.840441	+	0.541902i	$0.817704\pi$
$398$	−18.1681	−0.910686
$399$	0	0
$400$	−11.7276	−0.586380
$401$	39.5156	1.97331	0.986657	−	0.162811i	$-0.0520561\pi$
$401$	39.5156	1.97331	0.986657	+	0.162811i	$0.0520561\pi$
$402$	−17.0472	−0.850239
$403$	−6.13487	−0.305599
$404$	−0.373310	−0.0185729
$405$	107.153	5.32449
$406$	0	0
$407$	−3.86643	−0.191652
$408$	−59.3348	−2.93751
$409$	−10.9799	−0.542922	−0.271461	−	0.962449i	$-0.587507\pi$
$409$	−10.9799	−0.542922	−0.271461	+	0.962449i	$0.587507\pi$
$410$	9.47990	0.468179
$411$	−62.3989	−3.07791
$412$	−4.71567	−0.232324
$413$	0	0
$414$	28.9580	1.42321
$415$	47.9405	2.35331
$416$	−3.34804	−0.164151
$417$	−39.9227	−1.95502
$418$	−1.11248	−0.0544134
$419$	31.5621	1.54191	0.770954	−	0.636891i	$-0.219780\pi$
$419$	31.5621	1.54191	0.770954	+	0.636891i	$0.219780\pi$
$420$	0	0
$421$	−17.7055	−0.862914	−0.431457	−	0.902134i	$-0.642000\pi$
$421$	−17.7055	−0.862914	−0.431457	+	0.902134i	$0.642000\pi$
$422$	29.4706	1.43461
$423$	44.2046	2.14930
$424$	−30.1301	−1.46325
$425$	−28.2712	−1.37136
$426$	−42.0348	−2.03659
$427$	0	0
$428$	−2.97789	−0.143942
$429$	−2.59163	−0.125125
$430$	10.1158	0.487825
$431$	−21.4816	−1.03473	−0.517367	−	0.855764i	$-0.673088\pi$
$431$	−21.4816	−1.03473	−0.517367	+	0.855764i	$0.673088\pi$
$432$	−41.8212	−2.01212
$433$	34.7200	1.66854	0.834269	−	0.551358i	$-0.185890\pi$
$433$	34.7200	1.66854	0.834269	+	0.551358i	$0.185890\pi$
$434$	0	0
$435$	−26.0486	−1.24893
$436$	−4.45848	−0.213522
$437$	3.65894	0.175031
$438$	20.3948	0.974500
$439$	0.728505	0.0347697	0.0173848	−	0.999849i	$-0.494466\pi$
$439$	0.728505	0.0347697	0.0173848	+	0.999849i	$0.494466\pi$
$440$	−7.49428	−0.357276
$441$	0	0
$442$	6.76707	0.321877
$443$	0.837291	0.0397809	0.0198904	−	0.999802i	$-0.493668\pi$
$443$	0.837291	0.0397809	0.0198904	+	0.999802i	$0.493668\pi$
$444$	−10.3295	−0.490216
$445$	29.0684	1.37797
$446$	24.3047	1.15086
$447$	38.1187	1.80295
$448$	0	0
$449$	26.4312	1.24737	0.623683	−	0.781677i	$-0.285635\pi$
$449$	26.4312	1.24737	0.623683	+	0.781677i	$0.285635\pi$
$450$	−47.5612	−2.24206
$451$	1.97973	0.0932217
$452$	5.66873	0.266635
$453$	−12.3736	−0.581361
$454$	−1.15546	−0.0542284
$455$	0	0
$456$	−12.6126	−0.590639
$457$	−2.40475	−0.112489	−0.0562447	−	0.998417i	$-0.517913\pi$
$457$	−2.40475	−0.112489	−0.0562447	+	0.998417i	$0.517913\pi$
$458$	16.7892	0.784507
$459$	−100.816	−4.70571
$460$	5.80831	0.270814
$461$	−22.2702	−1.03722	−0.518612	−	0.855010i	$-0.673551\pi$
$461$	−22.2702	−1.03722	−0.518612	+	0.855010i	$0.673551\pi$
$462$	0	0
$463$	32.3085	1.50151	0.750753	−	0.660583i	$-0.229691\pi$
$463$	32.3085	1.50151	0.750753	+	0.660583i	$0.229691\pi$
$464$	5.89221	0.273539
$465$	−64.7291	−3.00174
$466$	−1.64118	−0.0760263
$467$	−12.8744	−0.595756	−0.297878	−	0.954604i	$-0.596279\pi$
$467$	−12.8744	−0.595756	−0.297878	+	0.954604i	$0.596279\pi$
$468$	−5.07399	−0.234545
$469$	0	0
$470$	−19.8934	−0.917612
$471$	3.75528	0.173034
$472$	7.70802	0.354791
$473$	2.11251	0.0971335
$474$	2.13639	0.0981275
$475$	−6.00952	−0.275736
$476$	0	0
$477$	−80.5649	−3.68881
$478$	−2.99781	−0.137117
$479$	10.5419	0.481670	0.240835	−	0.970566i	$-0.422579\pi$
$479$	10.5419	0.481670	0.240835	+	0.970566i	$0.422579\pi$
$480$	−35.3252	−1.61237
$481$	4.99933	0.227950
$482$	−34.9029	−1.58978
$483$	0	0
$484$	6.41364	0.291529
$485$	−3.97643	−0.180560
$486$	−72.3020	−3.27969
$487$	38.2416	1.73289	0.866446	−	0.499271i	$-0.166399\pi$
$487$	38.2416	1.73289	0.866446	+	0.499271i	$0.166399\pi$
$488$	−33.5972	−1.52087
$489$	−68.1709	−3.08280
$490$	0	0
$491$	−15.4291	−0.696306	−0.348153	−	0.937438i	$-0.613191\pi$
$491$	−15.4291	−0.696306	−0.348153	+	0.937438i	$0.613191\pi$
$492$	5.28901	0.238447
$493$	14.2041	0.639721
$494$	1.43845	0.0647190
$495$	−20.0390	−0.900685
$496$	14.6418	0.657436
$497$	0	0
$498$	−60.0111	−2.68916
$499$	−38.8212	−1.73788	−0.868938	−	0.494921i	$-0.835197\pi$
$499$	−38.8212	−1.73788	−0.868938	+	0.494921i	$0.835197\pi$
$500$	0.167283	0.00748112
$501$	43.5840	1.94719
$502$	−21.2723	−0.949430
$503$	−27.0935	−1.20804	−0.604020	−	0.796969i	$-0.706435\pi$
$503$	−27.0935	−1.20804	−0.604020	+	0.796969i	$0.706435\pi$
$504$	0	0
$505$	1.90633	0.0848304
$506$	−2.72151	−0.120986
$507$	3.35100	0.148823
$508$	6.91304	0.306717
$509$	−15.7693	−0.698961	−0.349480	−	0.936944i	$-0.613642\pi$
$509$	−15.7693	−0.698961	−0.349480	+	0.936944i	$0.613642\pi$
$510$	71.3995	3.16162
$511$	0	0
$512$	22.6809	1.00236
$513$	−21.4302	−0.946167
$514$	−17.3373	−0.764716
$515$	24.0808	1.06113
$516$	5.64376	0.248453
$517$	−4.15441	−0.182711
$518$	0	0
$519$	−86.8277	−3.81131
$520$	9.69018	0.424943
$521$	7.30737	0.320142	0.160071	−	0.987106i	$-0.448828\pi$
$521$	7.30737	0.320142	0.160071	+	0.987106i	$0.448828\pi$
$522$	23.8958	1.04589
$523$	14.0826	0.615788	0.307894	−	0.951421i	$-0.400376\pi$
$523$	14.0826	0.615788	0.307894	+	0.951421i	$0.400376\pi$
$524$	−9.70381	−0.423913
$525$	0	0
$526$	9.59677	0.418439
$527$	35.2963	1.53753
$528$	6.18531	0.269181
$529$	−14.0490	−0.610827
$530$	36.2565	1.57488
$531$	20.6105	0.894419
$532$	0	0
$533$	−2.55981	−0.110877
$534$	−36.3873	−1.57463
$535$	15.2067	0.657445
$536$	13.3111	0.574953
$537$	32.3091	1.39424
$538$	−0.520559	−0.0224429
$539$	0	0
$540$	−34.0190	−1.46394
$541$	−39.1750	−1.68426	−0.842132	−	0.539271i	$-0.818700\pi$
$541$	−39.1750	−1.68426	−0.842132	+	0.539271i	$0.818700\pi$
$542$	24.7977	1.06515
$543$	−9.80781	−0.420893
$544$	19.2626	0.825877
$545$	22.7674	0.975250
$546$	0	0
$547$	38.7917	1.65862	0.829308	−	0.558792i	$-0.188735\pi$
$547$	38.7917	1.65862	0.829308	+	0.558792i	$0.188735\pi$
$548$	11.4814	0.490463
$549$	−89.8355	−3.83408
$550$	4.46987	0.190596
$551$	3.01932	0.128627
$552$	−30.8546	−1.31326
$553$	0	0
$554$	−4.22746	−0.179607
$555$	52.7480	2.23903
$556$	7.34580	0.311531
$557$	−27.4693	−1.16391	−0.581956	−	0.813220i	$-0.697713\pi$
$557$	−27.4693	−1.16391	−0.581956	+	0.813220i	$0.697713\pi$
$558$	59.3796	2.51374
$559$	−2.73150	−0.115530
$560$	0	0
$561$	14.9107	0.629528
$562$	10.6004	0.447151
$563$	14.1210	0.595129	0.297565	−	0.954702i	$-0.403826\pi$
$563$	14.1210	0.595129	0.297565	+	0.954702i	$0.403826\pi$
$564$	−11.0989	−0.467346
$565$	−28.9477	−1.21784
$566$	−32.6288	−1.37149
$567$	0	0
$568$	32.8223	1.37720
$569$	−8.28649	−0.347388	−0.173694	−	0.984800i	$-0.555570\pi$
$569$	−8.28649	−0.347388	−0.173694	+	0.984800i	$0.555570\pi$
$570$	15.1771	0.635701
$571$	−23.5274	−0.984591	−0.492295	−	0.870428i	$-0.663842\pi$
$571$	−23.5274	−0.984591	−0.492295	+	0.870428i	$0.663842\pi$
$572$	0.476861	0.0199386
$573$	−54.0731	−2.25894
$574$	0	0
$575$	−14.7013	−0.613087
$576$	71.6861	2.98692
$577$	−17.7732	−0.739906	−0.369953	−	0.929050i	$-0.620626\pi$
$577$	−17.7732	−0.739906	−0.369953	+	0.929050i	$0.620626\pi$
$578$	−18.9385	−0.787737
$579$	−0.289465	−0.0120297
$580$	4.79296	0.199017
$581$	0	0
$582$	4.97763	0.206329
$583$	7.57160	0.313584
$584$	−15.9250	−0.658982
$585$	25.9106	1.07127
$586$	−14.9857	−0.619054
$587$	−6.64096	−0.274102	−0.137051	−	0.990564i	$-0.543762\pi$
$587$	−6.64096	−0.274102	−0.137051	+	0.990564i	$0.543762\pi$
$588$	0	0
$589$	7.50282	0.309148
$590$	−9.27532	−0.381859
$591$	50.4623	2.07574
$592$	−11.9317	−0.490388
$593$	34.0504	1.39828	0.699141	−	0.714984i	$-0.253566\pi$
$593$	34.0504	1.39828	0.699141	+	0.714984i	$0.253566\pi$
$594$	15.9398	0.654016
$595$	0	0
$596$	−7.01387	−0.287299
$597$	51.7616	2.11846
$598$	3.51894	0.143900
$599$	9.38441	0.383437	0.191718	−	0.981450i	$-0.438594\pi$
$599$	9.38441	0.383437	0.191718	+	0.981450i	$0.438594\pi$
$600$	50.6764	2.06885
$601$	8.80294	0.359079	0.179540	−	0.983751i	$-0.442539\pi$
$601$	8.80294	0.359079	0.179540	+	0.983751i	$0.442539\pi$
$602$	0	0
$603$	35.5926	1.44944
$604$	2.27675	0.0926394
$605$	−32.7516	−1.33154
$606$	−2.38631	−0.0969371
$607$	17.7720	0.721342	0.360671	−	0.932693i	$-0.382548\pi$
$607$	17.7720	0.721342	0.360671	+	0.932693i	$0.382548\pi$
$608$	4.09458	0.166057
$609$	0	0
$610$	40.4286	1.63691
$611$	5.37169	0.217315
$612$	29.1927	1.18004
$613$	10.6081	0.428457	0.214228	−	0.976784i	$-0.431276\pi$
$613$	10.6081	0.428457	0.214228	+	0.976784i	$0.431276\pi$
$614$	−11.9246	−0.481237
$615$	−27.0086	−1.08909
$616$	0	0
$617$	49.3483	1.98669	0.993344	−	0.115188i	$-0.0367469\pi$
$617$	49.3483	1.98669	0.993344	+	0.115188i	$0.0367469\pi$
$618$	−30.1440	−1.21257
$619$	7.42203	0.298317	0.149158	−	0.988813i	$-0.452344\pi$
$619$	7.42203	0.298317	0.149158	+	0.988813i	$0.452344\pi$
$620$	11.9102	0.478325
$621$	−52.4255	−2.10376
$622$	−24.2309	−0.971573
$623$	0	0
$624$	−7.99766	−0.320163
$625$	−25.4234	−1.01694
$626$	−19.4607	−0.777806
$627$	3.16951	0.126578
$628$	−0.690975	−0.0275729
$629$	−28.7631	−1.14686
$630$	0	0
$631$	35.5184	1.41396	0.706982	−	0.707231i	$-0.250056\pi$
$631$	35.5184	1.41396	0.706982	+	0.707231i	$0.250056\pi$
$632$	−1.66817	−0.0663564
$633$	−83.9628	−3.33722
$634$	24.9752	0.991890
$635$	−35.3018	−1.40091
$636$	20.2282	0.802099
$637$	0	0
$638$	−2.24576	−0.0889106
$639$	87.7637	3.47188
$640$	−11.1774	−0.441827
$641$	37.1554	1.46755	0.733775	−	0.679393i	$-0.237757\pi$
$641$	37.1554	1.46755	0.733775	+	0.679393i	$0.237757\pi$
$642$	−19.0356	−0.751274
$643$	39.7694	1.56835	0.784176	−	0.620538i	$-0.213086\pi$
$643$	39.7694	1.56835	0.784176	+	0.620538i	$0.213086\pi$
$644$	0	0
$645$	−28.8201	−1.13479
$646$	−8.27599	−0.325614
$647$	22.9754	0.903256	0.451628	−	0.892206i	$-0.350843\pi$
$647$	22.9754	0.903256	0.451628	+	0.892206i	$0.350843\pi$
$648$	104.736	4.11442
$649$	−1.93700	−0.0760340
$650$	−5.77958	−0.226694
$651$	0	0
$652$	12.5435	0.491241
$653$	18.1757	0.711268	0.355634	−	0.934625i	$-0.384265\pi$
$653$	18.1757	0.711268	0.355634	+	0.934625i	$0.384265\pi$
$654$	−28.4999	−1.11443
$655$	49.5530	1.93619
$656$	6.10936	0.238531
$657$	−42.5819	−1.66128
$658$	0	0
$659$	14.1044	0.549431	0.274716	−	0.961526i	$-0.411416\pi$
$659$	14.1044	0.549431	0.274716	+	0.961526i	$0.411416\pi$
$660$	5.03137	0.195846
$661$	−12.8557	−0.500027	−0.250013	−	0.968242i	$-0.580435\pi$
$661$	−12.8557	−0.500027	−0.250013	+	0.968242i	$0.580435\pi$
$662$	−19.1030	−0.742459
$663$	−19.2796	−0.748758
$664$	46.8590	1.81848
$665$	0	0
$666$	−48.3887	−1.87502
$667$	7.38627	0.285997
$668$	−8.01948	−0.310283
$669$	−69.2449	−2.67716
$670$	−16.0177	−0.618819
$671$	8.44287	0.325933
$672$	0	0
$673$	−45.6138	−1.75828	−0.879141	−	0.476561i	$-0.841883\pi$
$673$	−45.6138	−1.75828	−0.879141	+	0.476561i	$0.841883\pi$
$674$	−7.55278	−0.290922
$675$	86.1048	3.31418
$676$	−0.616586	−0.0237148
$677$	10.2469	0.393821	0.196910	−	0.980421i	$-0.436909\pi$
$677$	10.2469	0.393821	0.196910	+	0.980421i	$0.436909\pi$
$678$	36.2362	1.39164
$679$	0	0
$680$	−55.7515	−2.13797
$681$	3.29194	0.126148
$682$	−5.58058	−0.213692
$683$	2.90040	0.110981	0.0554904	−	0.998459i	$-0.482328\pi$
$683$	2.90040	0.110981	0.0554904	+	0.998459i	$0.482328\pi$
$684$	6.20539	0.237269
$685$	−58.6305	−2.24016
$686$	0	0
$687$	−47.8329	−1.82494
$688$	6.51914	0.248540
$689$	−9.79015	−0.372975
$690$	37.1284	1.41345
$691$	6.91470	0.263048	0.131524	−	0.991313i	$-0.458013\pi$
$691$	6.91470	0.263048	0.131524	+	0.991313i	$0.458013\pi$
$692$	15.9764	0.607330
$693$	0	0
$694$	−17.0323	−0.646536
$695$	−37.5117	−1.42290
$696$	−25.4610	−0.965095
$697$	14.7276	0.557847
$698$	−2.05245	−0.0776864
$699$	4.67579	0.176855
$700$	0	0
$701$	−26.0973	−0.985682	−0.492841	−	0.870119i	$-0.664042\pi$
$701$	−26.0973	−0.985682	−0.492841	+	0.870119i	$0.664042\pi$
$702$	−20.6102	−0.777884
$703$	−6.11408	−0.230597
$704$	−6.73717	−0.253916
$705$	56.6769	2.13457
$706$	−18.7696	−0.706402
$707$	0	0
$708$	−5.17487	−0.194483
$709$	−3.38472	−0.127116	−0.0635580	−	0.997978i	$-0.520245\pi$
$709$	−3.38472	−0.127116	−0.0635580	+	0.997978i	$0.520245\pi$
$710$	−39.4962	−1.48227
$711$	−4.46053	−0.167283
$712$	28.4126	1.06481
$713$	18.3544	0.687378
$714$	0	0
$715$	−2.43511	−0.0910681
$716$	−5.94489	−0.222171
$717$	8.54087	0.318964
$718$	−10.3669	−0.386890
$719$	−2.41574	−0.0900918	−0.0450459	−	0.998985i	$-0.514343\pi$
$719$	−2.41574	−0.0900918	−0.0450459	+	0.998985i	$0.514343\pi$
$720$	−61.8395	−2.30462
$721$	0	0
$722$	20.5883	0.766219
$723$	99.4395	3.69819
$724$	1.80464	0.0670691
$725$	−12.1314	−0.450548
$726$	40.9979	1.52157
$727$	17.0150	0.631050	0.315525	−	0.948917i	$-0.397819\pi$
$727$	17.0150	0.631050	0.315525	+	0.948917i	$0.397819\pi$
$728$	0	0
$729$	103.896	3.84799
$730$	19.1631	0.709258
$731$	15.7154	0.581256
$732$	22.5558	0.833687
$733$	4.18453	0.154559	0.0772795	−	0.997009i	$-0.475377\pi$
$733$	4.18453	0.154559	0.0772795	+	0.997009i	$0.475377\pi$
$734$	23.1803	0.855599
$735$	0	0
$736$	10.0167	0.369221
$737$	−3.34505	−0.123216
$738$	24.7765	0.912034
$739$	−28.0794	−1.03292	−0.516458	−	0.856312i	$-0.672750\pi$
$739$	−28.0794	−1.03292	−0.516458	+	0.856312i	$0.672750\pi$
$740$	−9.70567	−0.356788
$741$	−4.09820	−0.150551
$742$	0	0
$743$	−26.5210	−0.972961	−0.486481	−	0.873691i	$-0.661720\pi$
$743$	−26.5210	−0.972961	−0.486481	+	0.873691i	$0.661720\pi$
$744$	−63.2689	−2.31955
$745$	35.8167	1.31222
$746$	0.430240	0.0157522
$747$	125.296	4.58435
$748$	−2.74357	−0.100315
$749$	0	0
$750$	1.06932	0.0390461
$751$	−23.7162	−0.865418	−0.432709	−	0.901534i	$-0.642442\pi$
$751$	−23.7162	−0.865418	−0.432709	+	0.901534i	$0.642442\pi$
$752$	−12.8204	−0.467510
$753$	60.6056	2.20859
$754$	2.90379	0.105750
$755$	−11.6263	−0.423125
$756$	0	0
$757$	−52.3661	−1.90328	−0.951639	−	0.307219i	$-0.900602\pi$
$757$	−52.3661	−1.90328	−0.951639	+	0.307219i	$0.900602\pi$
$758$	−8.69454	−0.315800
$759$	7.75368	0.281441
$760$	−11.8509	−0.429877
$761$	23.8695	0.865268	0.432634	−	0.901570i	$-0.357584\pi$
$761$	23.8695	0.865268	0.432634	+	0.901570i	$0.357584\pi$
$762$	44.1902	1.60084
$763$	0	0
$764$	9.94949	0.359960
$765$	−149.074	−5.38978
$766$	3.94450	0.142521
$767$	2.50456	0.0904345
$768$	−44.3908	−1.60181
$769$	41.7599	1.50590	0.752950	−	0.658077i	$-0.228630\pi$
$769$	41.7599	1.50590	0.752950	+	0.658077i	$0.228630\pi$
$770$	0	0
$771$	49.3946	1.77890
$772$	0.0532617	0.00191693
$773$	2.97178	0.106888	0.0534438	−	0.998571i	$-0.482980\pi$
$773$	2.97178	0.106888	0.0534438	+	0.998571i	$0.482980\pi$
$774$	26.4383	0.950306
$775$	−30.1457	−1.08287
$776$	−3.88672	−0.139525
$777$	0	0
$778$	3.05037	0.109361
$779$	3.13059	0.112165
$780$	−6.50561	−0.232938
$781$	−8.24815	−0.295142
$782$	−20.2459	−0.723990
$783$	−43.2610	−1.54602
$784$	0	0
$785$	3.52850	0.125937
$786$	−62.0296	−2.21252
$787$	−48.6142	−1.73291	−0.866454	−	0.499256i	$-0.833607\pi$
$787$	−48.6142	−1.73291	−0.866454	+	0.499256i	$0.833607\pi$
$788$	−9.28509	−0.330768
$789$	−27.3415	−0.973384
$790$	2.00737	0.0714189
$791$	0	0
$792$	−19.5869	−0.695990
$793$	−10.9167	−0.387664
$794$	39.3921	1.39797
$795$	−103.296	−3.66354
$796$	−9.52418	−0.337576
$797$	25.6470	0.908463	0.454232	−	0.890884i	$-0.349914\pi$
$797$	25.6470	0.908463	0.454232	+	0.890884i	$0.349914\pi$
$798$	0	0
$799$	−30.9055	−1.09336
$800$	−16.4517	−0.581655
$801$	75.9724	2.68435
$802$	−46.4777	−1.64118
$803$	4.00191	0.141224
$804$	−8.93657	−0.315169
$805$	0	0
$806$	7.21575	0.254164
$807$	1.48309	0.0522073
$808$	1.86332	0.0655514
$809$	−11.9205	−0.419101	−0.209550	−	0.977798i	$-0.567200\pi$
$809$	−11.9205	−0.419101	−0.209550	+	0.977798i	$0.567200\pi$
$810$	−126.032	−4.42832
$811$	−10.5564	−0.370685	−0.185343	−	0.982674i	$-0.559339\pi$
$811$	−10.5564	−0.370685	−0.185343	+	0.982674i	$0.559339\pi$
$812$	0	0
$813$	−70.6494	−2.47778
$814$	4.54764	0.159395
$815$	−64.0540	−2.24371
$816$	46.0137	1.61080
$817$	3.34057	0.116872
$818$	12.9144	0.451543
$819$	0	0
$820$	4.96960	0.173546
$821$	−46.2139	−1.61288	−0.806438	−	0.591319i	$-0.798607\pi$
$821$	−46.2139	−1.61288	−0.806438	+	0.591319i	$0.798607\pi$
$822$	73.3927	2.55986
$823$	41.2171	1.43674	0.718368	−	0.695663i	$-0.244889\pi$
$823$	41.2171	1.43674	0.718368	+	0.695663i	$0.244889\pi$
$824$	23.5375	0.819969
$825$	−12.7348	−0.443369
$826$	0	0
$827$	5.94430	0.206704	0.103352	−	0.994645i	$-0.467043\pi$
$827$	5.94430	0.206704	0.103352	+	0.994645i	$0.467043\pi$
$828$	15.1805	0.527558
$829$	34.8106	1.20902	0.604511	−	0.796596i	$-0.293368\pi$
$829$	34.8106	1.20902	0.604511	+	0.796596i	$0.293368\pi$
$830$	−56.3869	−1.95722
$831$	12.0442	0.417808
$832$	8.71122	0.302007
$833$	0	0
$834$	46.9565	1.62597
$835$	40.9519	1.41720
$836$	−0.583191	−0.0201701
$837$	−107.501	−3.71578
$838$	−37.1229	−1.28239
$839$	10.7896	0.372500	0.186250	−	0.982502i	$-0.440367\pi$
$839$	10.7896	0.372500	0.186250	+	0.982502i	$0.440367\pi$
$840$	0	0
$841$	−22.9049	−0.789825
$842$	20.8250	0.717676
$843$	−30.2009	−1.04018
$844$	15.4492	0.531784
$845$	3.14862	0.108316
$846$	−51.9928	−1.78755
$847$	0	0
$848$	23.3657	0.802381
$849$	92.9605	3.19039
$850$	33.2523	1.14054
$851$	−14.9571	−0.512722
$852$	−22.0356	−0.754929
$853$	39.1053	1.33894	0.669470	−	0.742839i	$-0.266521\pi$
$853$	39.1053	1.33894	0.669470	+	0.742839i	$0.266521\pi$
$854$	0	0
$855$	−31.6881	−1.08371
$856$	14.8637	0.508030
$857$	−33.3654	−1.13974	−0.569870	−	0.821735i	$-0.693006\pi$
$857$	−33.3654	−1.13974	−0.569870	+	0.821735i	$0.693006\pi$
$858$	3.04823	0.104065
$859$	−29.4914	−1.00623	−0.503116	−	0.864219i	$-0.667813\pi$
$859$	−29.4914	−1.00623	−0.503116	+	0.864219i	$0.667813\pi$
$860$	5.30293	0.180828
$861$	0	0
$862$	25.2664	0.860578
$863$	−24.6224	−0.838157	−0.419079	−	0.907950i	$-0.637647\pi$
$863$	−24.6224	−0.838157	−0.419079	+	0.907950i	$0.637647\pi$
$864$	−58.6675	−1.99591
$865$	−81.5841	−2.77394
$866$	−40.8372	−1.38771
$867$	53.9564	1.83246
$868$	0	0
$869$	0.419207	0.0142206
$870$	30.6380	1.03873
$871$	4.32518	0.146553
$872$	22.2538	0.753609
$873$	−10.3927	−0.351740
$874$	−4.30359	−0.145571
$875$	0	0
$876$	10.6914	0.361230
$877$	−4.62556	−0.156194	−0.0780971	−	0.996946i	$-0.524884\pi$
$877$	−4.62556	−0.156194	−0.0780971	+	0.996946i	$0.524884\pi$
$878$	−0.856858	−0.0289176
$879$	42.6948	1.44006
$880$	5.81177	0.195915
$881$	−42.1720	−1.42081	−0.710405	−	0.703793i	$-0.751488\pi$
$881$	−42.1720	−1.42081	−0.710405	+	0.703793i	$0.751488\pi$
$882$	0	0
$883$	20.7992	0.699950	0.349975	−	0.936759i	$-0.386190\pi$
$883$	20.7992	0.699950	0.349975	+	0.936759i	$0.386190\pi$
$884$	3.54746	0.119314
$885$	26.4257	0.888291
$886$	−0.984810	−0.0330853
$887$	34.4889	1.15802	0.579012	−	0.815319i	$-0.303438\pi$
$887$	34.4889	1.15802	0.579012	+	0.815319i	$0.303438\pi$
$888$	51.5581	1.73018
$889$	0	0
$890$	−34.1898	−1.14605
$891$	−26.3198	−0.881748
$892$	12.7411	0.426604
$893$	−6.56947	−0.219839
$894$	−44.8347	−1.49950
$895$	30.3579	1.01475
$896$	0	0
$897$	−10.0256	−0.334744
$898$	−31.0880	−1.03742
$899$	15.1459	0.505144
$900$	−24.9327	−0.831091
$901$	56.3267	1.87651
$902$	−2.32853	−0.0775315
$903$	0	0
$904$	−28.2946	−0.941065
$905$	−9.21550	−0.306334
$906$	14.5536	0.483512
$907$	13.3619	0.443675	0.221838	−	0.975084i	$-0.428795\pi$
$907$	13.3619	0.443675	0.221838	+	0.975084i	$0.428795\pi$
$908$	−0.605720	−0.0201015
$909$	4.98233	0.165254
$910$	0	0
$911$	5.29058	0.175285	0.0876424	−	0.996152i	$-0.472067\pi$
$911$	5.29058	0.175285	0.0876424	+	0.996152i	$0.472067\pi$
$912$	9.78097	0.323880
$913$	−11.7755	−0.389713
$914$	2.82843	0.0935562
$915$	−115.182	−3.80781
$916$	8.80129	0.290803
$917$	0	0
$918$	118.579	3.91369
$919$	−18.8306	−0.621164	−0.310582	−	0.950547i	$-0.600524\pi$
$919$	−18.8306	−0.621164	−0.310582	+	0.950547i	$0.600524\pi$
$920$	−28.9913	−0.955814
$921$	33.9736	1.11947
$922$	26.1939	0.862649
$923$	10.6649	0.351041
$924$	0	0
$925$	24.5659	0.807721
$926$	−38.0009	−1.24879
$927$	62.9371	2.06712
$928$	8.26571	0.271335
$929$	−44.9537	−1.47488	−0.737442	−	0.675411i	$-0.763966\pi$
$929$	−44.9537	−1.47488	−0.737442	+	0.675411i	$0.763966\pi$
$930$	76.1335	2.49652
$931$	0	0
$932$	−0.860348	−0.0281816
$933$	69.0348	2.26010
$934$	15.1427	0.495484
$935$	14.0102	0.458182
$936$	25.3260	0.827808
$937$	37.9272	1.23903	0.619514	−	0.784986i	$-0.287330\pi$
$937$	37.9272	1.23903	0.619514	+	0.784986i	$0.287330\pi$
$938$	0	0
$939$	55.4442	1.80935
$940$	−10.4286	−0.340143
$941$	35.7869	1.16662	0.583310	−	0.812250i	$-0.301757\pi$
$941$	35.7869	1.16662	0.583310	+	0.812250i	$0.301757\pi$
$942$	−4.41691	−0.143911
$943$	7.65848	0.249394
$944$	−5.97752	−0.194552
$945$	0	0
$946$	−2.48471	−0.0807849
$947$	−14.7443	−0.479125	−0.239563	−	0.970881i	$-0.577004\pi$
$947$	−14.7443	−0.479125	−0.239563	+	0.970881i	$0.577004\pi$
$948$	1.11995	0.0363742
$949$	−5.17450	−0.167971
$950$	7.06831	0.229326
$951$	−71.1551	−2.30736
$952$	0	0
$953$	0.649669	0.0210448	0.0105224	−	0.999945i	$-0.496651\pi$
$953$	0.649669	0.0210448	0.0105224	+	0.999945i	$0.496651\pi$
$954$	94.7593	3.06795
$955$	−50.8076	−1.64409
$956$	−1.57153	−0.0508268
$957$	6.39826	0.206826
$958$	−12.3992	−0.400600
$959$	0	0
$960$	91.9123	2.96646
$961$	6.63659	0.214083
$962$	−5.88014	−0.189583
$963$	39.7440	1.28073
$964$	−18.2969	−0.589305
$965$	−0.271983	−0.00875545
$966$	0	0
$967$	−13.0802	−0.420632	−0.210316	−	0.977633i	$-0.567449\pi$
$967$	−13.0802	−0.420632	−0.210316	+	0.977633i	$0.567449\pi$
$968$	−32.0127	−1.02893
$969$	23.5786	0.757453
$970$	4.67702	0.150170
$971$	−29.1203	−0.934515	−0.467258	−	0.884121i	$-0.654758\pi$
$971$	−29.1203	−0.934515	−0.467258	+	0.884121i	$0.654758\pi$
$972$	−37.9025	−1.21572
$973$	0	0
$974$	−44.9792	−1.44123
$975$	16.4662	0.527342
$976$	26.0544	0.833980
$977$	−18.5000	−0.591868	−0.295934	−	0.955208i	$-0.595631\pi$
$977$	−18.5000	−0.591868	−0.295934	+	0.955208i	$0.595631\pi$
$978$	80.1817	2.56393
$979$	−7.14000	−0.228195
$980$	0	0
$981$	59.5045	1.89983
$982$	18.1475	0.579111
$983$	−11.0462	−0.352318	−0.176159	−	0.984362i	$-0.556367\pi$
$983$	−11.0462	−0.352318	−0.176159	+	0.984362i	$0.556367\pi$
$984$	−26.3993	−0.841578
$985$	47.4148	1.51076
$986$	−16.7067	−0.532049
$987$	0	0
$988$	0.754072	0.0239902
$989$	8.17216	0.259860
$990$	23.5696	0.749090
$991$	−40.4757	−1.28575	−0.642877	−	0.765969i	$-0.722259\pi$
$991$	−40.4757	−1.28575	−0.642877	+	0.765969i	$0.722259\pi$
$992$	20.5398	0.652138
$993$	54.4251	1.72713
$994$	0	0
$995$	48.6357	1.54185
$996$	−31.4593	−0.996826
$997$	−12.0623	−0.382018	−0.191009	−	0.981588i	$-0.561176\pi$
$997$	−12.0623	−0.382018	−0.191009	+	0.981588i	$0.561176\pi$
$998$	45.6610	1.44537
$999$	87.6029	2.77163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.a.n.1.2	yes	6
3.2	odd	2		5733.2.a.br.1.5		6
7.2	even	3		637.2.e.n.508.5		12
7.3	odd	6		637.2.e.o.79.5		12
7.4	even	3		637.2.e.n.79.5		12
7.5	odd	6		637.2.e.o.508.5		12
7.6	odd	2		637.2.a.m.1.2	✓	6
13.12	even	2		8281.2.a.cd.1.5		6
21.20	even	2		5733.2.a.bu.1.5		6
91.90	odd	2		8281.2.a.cc.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.m.1.2	✓	6	7.6	odd	2
637.2.a.n.1.2	yes	6	1.1	even	1	trivial
637.2.e.n.79.5		12	7.4	even	3
637.2.e.n.508.5		12	7.2	even	3
637.2.e.o.79.5		12	7.3	odd	6
637.2.e.o.508.5		12	7.5	odd	6
5733.2.a.br.1.5		6	3.2	odd	2
5733.2.a.bu.1.5		6	21.20	even	2
8281.2.a.cc.1.5		6	91.90	odd	2
8281.2.a.cd.1.5		6	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.a (trivial)

\(f(q)\)	\(=\)	\(q-1.17619 q^{2} +3.35100 q^{3} -0.616586 q^{4} +3.14862 q^{5} -3.94140 q^{6} +3.07759 q^{8} +8.22917 q^{9} +O(q^{10})\)	\(q-1.17619 q^{2} +3.35100 q^{3} -0.616586 q^{4} +3.14862 q^{5} -3.94140 q^{6} +3.07759 q^{8} +8.22917 q^{9} -3.70337 q^{10} -0.773390 q^{11} -2.06618 q^{12} +1.00000 q^{13} +10.5510 q^{15} -2.38665 q^{16} -5.75340 q^{17} -9.67904 q^{18} -1.22298 q^{19} -1.94140 q^{20} +0.909650 q^{22} -2.99182 q^{23} +10.3130 q^{24} +4.91383 q^{25} -1.17619 q^{26} +17.5229 q^{27} -2.46882 q^{29} -12.4100 q^{30} -6.13487 q^{31} -3.34804 q^{32} -2.59163 q^{33} +6.76707 q^{34} -5.07399 q^{36} +4.99933 q^{37} +1.43845 q^{38} +3.35100 q^{39} +9.69018 q^{40} -2.55981 q^{41} -2.73150 q^{43} +0.476861 q^{44} +25.9106 q^{45} +3.51894 q^{46} +5.37169 q^{47} -7.99766 q^{48} -5.77958 q^{50} -19.2796 q^{51} -0.616586 q^{52} -9.79015 q^{53} -20.6102 q^{54} -2.43511 q^{55} -4.09820 q^{57} +2.90379 q^{58} +2.50456 q^{59} -6.50561 q^{60} -10.9167 q^{61} +7.21575 q^{62} +8.71122 q^{64} +3.14862 q^{65} +3.04823 q^{66} +4.32518 q^{67} +3.54746 q^{68} -10.0256 q^{69} +10.6649 q^{71} +25.3260 q^{72} -5.17450 q^{73} -5.88014 q^{74} +16.4662 q^{75} +0.754072 q^{76} -3.94140 q^{78} -0.542038 q^{79} -7.51467 q^{80} +34.0318 q^{81} +3.01081 q^{82} +15.2259 q^{83} -18.1153 q^{85} +3.21275 q^{86} -8.27301 q^{87} -2.38018 q^{88} +9.23208 q^{89} -30.4757 q^{90} +1.84471 q^{92} -20.5579 q^{93} -6.31811 q^{94} -3.85070 q^{95} -11.2193 q^{96} -1.26291 q^{97} -6.36436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) \) 6 * q + 8 * q^3 + 4 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^9	\( 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} + 6 q^{13} + 12 q^{15} + 16 q^{17} - 4 q^{18} + 2 q^{19} + 16 q^{20} - 12 q^{22} - 6 q^{23} + 12 q^{24} - 4 q^{25} + 20 q^{27} - 6 q^{29} + 6 q^{31} - 20 q^{32} + 4 q^{33} - 24 q^{36} + 8 q^{38} + 8 q^{39} + 4 q^{40} - 8 q^{41} + 2 q^{43} - 4 q^{44} + 14 q^{45} + 8 q^{46} + 30 q^{47} - 8 q^{48} + 8 q^{50} - 4 q^{51} + 4 q^{52} - 14 q^{53} - 48 q^{54} - 8 q^{55} + 4 q^{57} - 8 q^{58} + 24 q^{59} + 12 q^{60} + 28 q^{62} - 20 q^{64} + 6 q^{65} - 4 q^{66} + 16 q^{67} + 28 q^{68} - 20 q^{69} + 8 q^{71} + 28 q^{72} - 6 q^{73} - 12 q^{74} + 12 q^{75} - 16 q^{76} + 4 q^{78} - 22 q^{79} - 28 q^{80} + 46 q^{81} - 40 q^{82} + 50 q^{83} - 8 q^{85} - 16 q^{86} - 16 q^{87} - 44 q^{88} + 26 q^{89} - 40 q^{90} + 20 q^{92} + 16 q^{93} - 32 q^{94} - 6 q^{95} - 20 q^{96} - 14 q^{97} + 12 q^{99}+O(q^{100}) \) 6 * q + 8 * q^3 + 4 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 + 6 * q^13 + 12 * q^15 + 16 * q^17 - 4 * q^18 + 2 * q^19 + 16 * q^20 - 12 * q^22 - 6 * q^23 + 12 * q^24 - 4 * q^25 + 20 * q^27 - 6 * q^29 + 6 * q^31 - 20 * q^32 + 4 * q^33 - 24 * q^36 + 8 * q^38 + 8 * q^39 + 4 * q^40 - 8 * q^41 + 2 * q^43 - 4 * q^44 + 14 * q^45 + 8 * q^46 + 30 * q^47 - 8 * q^48 + 8 * q^50 - 4 * q^51 + 4 * q^52 - 14 * q^53 - 48 * q^54 - 8 * q^55 + 4 * q^57 - 8 * q^58 + 24 * q^59 + 12 * q^60 + 28 * q^62 - 20 * q^64 + 6 * q^65 - 4 * q^66 + 16 * q^67 + 28 * q^68 - 20 * q^69 + 8 * q^71 + 28 * q^72 - 6 * q^73 - 12 * q^74 + 12 * q^75 - 16 * q^76 + 4 * q^78 - 22 * q^79 - 28 * q^80 + 46 * q^81 - 40 * q^82 + 50 * q^83 - 8 * q^85 - 16 * q^86 - 16 * q^87 - 44 * q^88 + 26 * q^89 - 40 * q^90 + 20 * q^92 + 16 * q^93 - 32 * q^94 - 6 * q^95 - 20 * q^96 - 14 * q^97 + 12 * q^99

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