LMFDB - Embedded newform 637.2.a.m.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:	$1$
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	$-0.918436\pi$
$3$	−3.35100	−1.93470	−0.967349	+	0.253447i	$0.918436\pi$
$4$	−0.616586	−0.308293
$5$	−3.14862	−1.40811	−0.704054	−	0.710147i	$-0.748629\pi$
$5$	−3.14862	−1.40811	−0.704054	+	0.710147i	$0.748629\pi$
$6$	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	$-0.254206\pi$
$17$	5.75340	1.39540	0.697702	+	0.716388i	$0.254206\pi$
$18$	−9.67904	−2.28137
$19$	1.22298	0.280571	0.140285	−	0.990111i	$-0.455198\pi$
$19$	1.22298	0.280571	0.140285	+	0.990111i	$0.455198\pi$
$20$	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	$-0.314274\pi$
$31$	6.13487	1.10185	0.550927	+	0.834553i	$0.314274\pi$
$32$	−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	$-0.435942\pi$
$41$	2.55981	0.399774	0.199887	+	0.979819i	$0.435942\pi$
$42$	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	$-0.628137\pi$
$47$	−5.37169	−0.783542	−0.391771	+	0.920063i	$0.628137\pi$
$48$	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	$-0.552128\pi$
$59$	−2.50456	−0.326066	−0.163033	+	0.986621i	$0.552128\pi$
$60$	−6.50561	−0.839871
$61$	10.9167	1.39774	0.698870	−	0.715248i	$-0.253686\pi$
$61$	10.9167	1.39774	0.698870	+	0.715248i	$0.253686\pi$
$62$	−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	$-0.402074\pi$
$73$	5.17450	0.605630	0.302815	+	0.953049i	$0.402074\pi$
$74$	−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	$-0.814896\pi$
$83$	−15.2259	−1.67125	−0.835627	+	0.549297i	$0.814896\pi$
$84$	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	$-0.662747\pi$
$89$	−9.23208	−0.978599	−0.489299	+	0.872116i	$0.662747\pi$
$90$	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	$-0.479578\pi$
$97$	1.26291	0.128229	0.0641145	+	0.997943i	$0.479578\pi$
$98$	0	0
$99$	−6.36436	−0.639642
$100$	−3.02980	−0.302980
$101$	−0.605447	−0.0602443	−0.0301221	−	0.999546i	$-0.509590\pi$
$101$	−0.605447	−0.0602443	−0.0301221	+	0.999546i	$0.509590\pi$
$102$	22.6764	2.24530
$103$	−7.64804	−0.753584	−0.376792	−	0.926298i	$-0.622973\pi$
$103$	−7.64804	−0.753584	−0.376792	+	0.926298i	$0.622973\pi$
$104$	−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	$-0.741299\pi$
$131$	−15.7380	−1.37503	−0.687517	+	0.726169i	$0.741299\pi$
$132$	−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	$-0.331399\pi$
$139$	11.9137	1.01050	0.505252	+	0.862972i	$0.331399\pi$
$140$	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	$-0.514239\pi$
$157$	−1.12065	−0.0894374	−0.0447187	+	0.999000i	$0.514239\pi$
$158$	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	$-0.667854\pi$
$167$	−13.0063	−1.00646	−0.503228	+	0.864154i	$0.667854\pi$
$168$	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	$-0.0552221\pi$
$173$	25.9110	1.96998	0.984989	+	0.172616i	$0.0552221\pi$
$174$	−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	$-0.465307\pi$
$181$	2.92683	0.217550	0.108775	+	0.994066i	$0.465307\pi$
$182$	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	$-0.684417\pi$
$199$	−15.4466	−1.09498	−0.547492	+	0.836811i	$0.684417\pi$
$200$	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	$-0.256782\pi$
$223$	20.6640	1.38376	0.691881	+	0.722012i	$0.256782\pi$
$224$	0	0
$225$	40.4368	2.69579
$226$	10.8136	0.719307
$227$	−0.982378	−0.0652027	−0.0326013	−	0.999468i	$-0.510379\pi$
$227$	−0.982378	−0.0652027	−0.0326013	+	0.999468i	$0.510379\pi$
$228$	2.52689	0.167347
$229$	14.2742	0.943269	0.471634	−	0.881794i	$-0.343664\pi$
$229$	14.2742	0.943269	0.471634	+	0.881794i	$0.343664\pi$
$230$	−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	$-0.904959\pi$
$241$	−29.6746	−1.91151	−0.955755	+	0.294164i	$0.904959\pi$
$242$	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	$-0.693361\pi$
$251$	−18.0858	−1.14157	−0.570784	+	0.821100i	$0.693361\pi$
$252$	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	$-0.652056\pi$
$257$	−14.7403	−0.919473	−0.459737	+	0.888055i	$0.652056\pi$
$258$	−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	$-0.504295\pi$
$269$	−0.442582	−0.0269847	−0.0134924	+	0.999909i	$0.504295\pi$
$270$	−64.8939	−3.94932
$271$	21.0831	1.28071	0.640354	−	0.768080i	$-0.278788\pi$
$271$	21.0831	1.28071	0.640354	+	0.768080i	$0.278788\pi$
$272$	−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	$-0.808555\pi$
$283$	−27.7411	−1.64904	−0.824520	+	0.565833i	$0.808555\pi$
$284$	−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	$-0.621385\pi$
$293$	−12.7409	−0.744333	−0.372167	+	0.928166i	$0.621385\pi$
$294$	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	$-0.593427\pi$
$307$	−10.1384	−0.578626	−0.289313	+	0.957235i	$0.593427\pi$
$308$	0	0
$309$	25.6286	1.45796
$310$	22.7197	1.29039
$311$	−20.6013	−1.16819	−0.584096	−	0.811685i	$-0.698551\pi$
$311$	−20.6013	−1.16819	−0.584096	+	0.811685i	$0.698551\pi$
$312$	10.3130	0.583859
$313$	−16.5456	−0.935213	−0.467606	−	0.883937i	$-0.654883\pi$
$313$	−16.5456	−0.935213	−0.467606	+	0.883937i	$0.654883\pi$
$314$	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	$-0.514872\pi$
$349$	−1.74500	−0.0934079	−0.0467040	+	0.998909i	$0.514872\pi$
$350$	0	0
$351$	17.5229	0.935306
$352$	2.58934	0.138012
$353$	−15.9580	−0.849358	−0.424679	−	0.905344i	$-0.639613\pi$
$353$	−15.9580	−0.849358	−0.424679	+	0.905344i	$0.639613\pi$
$354$	−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	$-0.328024\pi$
$367$	19.7080	1.02875	0.514374	+	0.857566i	$0.328024\pi$
$368$	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	$-0.472693\pi$
$383$	3.35364	0.171363	0.0856814	+	0.996323i	$0.472693\pi$
$384$	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	$-0.182296\pi$
$397$	33.4914	1.68088	0.840441	+	0.541902i	$0.182296\pi$
$398$	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	$-0.412493\pi$
$409$	10.9799	0.542922	0.271461	+	0.962449i	$0.412493\pi$
$410$	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	$-0.780220\pi$
$419$	−31.5621	−1.54191	−0.770954	+	0.636891i	$0.780220\pi$
$420$	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	$-0.814110\pi$
$433$	−34.7200	−1.66854	−0.834269	+	0.551358i	$0.814110\pi$
$434$	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	$-0.505534\pi$
$439$	−0.728505	−0.0347697	−0.0173848	+	0.999849i	$0.505534\pi$
$440$	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	$-0.326449\pi$
$461$	22.2702	1.03722	0.518612	+	0.855010i	$0.326449\pi$
$462$	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	$-0.403721\pi$
$467$	12.8744	0.595756	0.297878	+	0.954604i	$0.403721\pi$
$468$	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	$-0.577421\pi$
$479$	−10.5419	−0.481670	−0.240835	+	0.970566i	$0.577421\pi$
$480$	−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	$-0.293565\pi$
$503$	27.0935	1.20804	0.604020	+	0.796969i	$0.293565\pi$
$504$	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	$-0.386358\pi$
$509$	15.7693	0.698961	0.349480	+	0.936944i	$0.386358\pi$
$510$	−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	$-0.551172\pi$
$521$	−7.30737	−0.320142	−0.160071	+	0.987106i	$0.551172\pi$
$522$	23.8958	1.04589
$523$	−14.0826	−0.615788	−0.307894	−	0.951421i	$-0.599624\pi$
$523$	−14.0826	−0.615788	−0.307894	+	0.951421i	$0.599624\pi$
$524$	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	$-0.596174\pi$
$563$	−14.1210	−0.595129	−0.297565	+	0.954702i	$0.596174\pi$
$564$	−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	$-0.379374\pi$
$577$	17.7732	0.739906	0.369953	+	0.929050i	$0.379374\pi$
$578$	−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	$-0.456238\pi$
$587$	6.64096	0.274102	0.137051	+	0.990564i	$0.456238\pi$
$588$	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	$-0.746434\pi$
$593$	−34.0504	−1.39828	−0.699141	+	0.714984i	$0.746434\pi$
$594$	−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	$-0.557461\pi$
$601$	−8.80294	−0.359079	−0.179540	+	0.983751i	$0.557461\pi$
$602$	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	$-0.617452\pi$
$607$	−17.7720	−0.721342	−0.360671	+	0.932693i	$0.617452\pi$
$608$	−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	$-0.547656\pi$
$619$	−7.42203	−0.298317	−0.149158	+	0.988813i	$0.547656\pi$
$620$	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	$-0.786914\pi$
$643$	−39.7694	−1.56835	−0.784176	+	0.620538i	$0.786914\pi$
$644$	0	0
$645$	−28.8201	−1.13479
$646$	−8.27599	−0.325614
$647$	−22.9754	−0.903256	−0.451628	−	0.892206i	$-0.649157\pi$
$647$	−22.9754	−0.903256	−0.451628	+	0.892206i	$0.649157\pi$
$648$	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	$-0.419565\pi$
$661$	12.8557	0.500027	0.250013	+	0.968242i	$0.419565\pi$
$662$	−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	$-0.563091\pi$
$677$	−10.2469	−0.393821	−0.196910	+	0.980421i	$0.563091\pi$
$678$	−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	$-0.541987\pi$
$691$	−6.91470	−0.263048	−0.131524	+	0.991313i	$0.541987\pi$
$692$	−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	$-0.485657\pi$
$719$	2.41574	0.0900918	0.0450459	+	0.998985i	$0.485657\pi$
$720$	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	$-0.602181\pi$
$727$	−17.0150	−0.631050	−0.315525	+	0.948917i	$0.602181\pi$
$728$	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	$-0.524623\pi$
$733$	−4.18453	−0.154559	−0.0772795	+	0.997009i	$0.524623\pi$
$734$	−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	$-0.642416\pi$
$761$	−23.8695	−0.865268	−0.432634	+	0.901570i	$0.642416\pi$
$762$	−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	$-0.771370\pi$
$769$	−41.7599	−1.50590	−0.752950	+	0.658077i	$0.771370\pi$
$770$	0	0
$771$	49.3946	1.77890
$772$	0.0532617	0.00191693
$773$	−2.97178	−0.106888	−0.0534438	−	0.998571i	$-0.517020\pi$
$773$	−2.97178	−0.106888	−0.0534438	+	0.998571i	$0.517020\pi$
$774$	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	$-0.166393\pi$
$787$	48.6142	1.73291	0.866454	+	0.499256i	$0.166393\pi$
$788$	−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	$-0.650086\pi$
$797$	−25.6470	−0.908463	−0.454232	+	0.890884i	$0.650086\pi$
$798$	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	$-0.440661\pi$
$811$	10.5564	0.370685	0.185343	+	0.982674i	$0.440661\pi$
$812$	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	$-0.706632\pi$
$829$	−34.8106	−1.20902	−0.604511	+	0.796596i	$0.706632\pi$
$830$	−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	$-0.559633\pi$
$839$	−10.7896	−0.372500	−0.186250	+	0.982502i	$0.559633\pi$
$840$	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	$-0.733479\pi$
$853$	−39.1053	−1.33894	−0.669470	+	0.742839i	$0.733479\pi$
$854$	0	0
$855$	−31.6881	−1.08371
$856$	14.8637	0.508030
$857$	33.3654	1.13974	0.569870	−	0.821735i	$-0.306994\pi$
$857$	33.3654	1.13974	0.569870	+	0.821735i	$0.306994\pi$
$858$	3.04823	0.104065
$859$	29.4914	1.00623	0.503116	−	0.864219i	$-0.332187\pi$
$859$	29.4914	1.00623	0.503116	+	0.864219i	$0.332187\pi$
$860$	−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	$-0.248512\pi$
$881$	42.1720	1.42081	0.710405	+	0.703793i	$0.248512\pi$
$882$	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	$-0.696562\pi$
$887$	−34.4889	−1.15802	−0.579012	+	0.815319i	$0.696562\pi$
$888$	−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	$-0.236034\pi$
$929$	44.9537	1.47488	0.737442	+	0.675411i	$0.236034\pi$
$930$	−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	$-0.712670\pi$
$937$	−37.9272	−1.23903	−0.619514	+	0.784986i	$0.712670\pi$
$938$	0	0
$939$	55.4442	1.80935
$940$	−10.4286	−0.340143
$941$	−35.7869	−1.16662	−0.583310	−	0.812250i	$-0.698243\pi$
$941$	−35.7869	−1.16662	−0.583310	+	0.812250i	$0.698243\pi$
$942$	−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	$-0.345242\pi$
$971$	29.1203	0.934515	0.467258	+	0.884121i	$0.345242\pi$
$972$	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	$-0.443633\pi$
$983$	11.0462	0.352318	0.176159	+	0.984362i	$0.443633\pi$
$984$	−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	$-0.438824\pi$
$997$	12.0623	0.382018	0.191009	+	0.981588i	$0.438824\pi$
$998$	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.m.1.2	✓	6
3.2	odd	2		5733.2.a.bu.1.5		6
7.2	even	3		637.2.e.o.508.5		12
7.3	odd	6		637.2.e.n.79.5		12
7.4	even	3		637.2.e.o.79.5		12
7.5	odd	6		637.2.e.n.508.5		12
7.6	odd	2		637.2.a.n.1.2	yes	6
13.12	even	2		8281.2.a.cc.1.5		6
21.20	even	2		5733.2.a.br.1.5		6
91.90	odd	2		8281.2.a.cd.1.5		6

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
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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