LMFDB - Embedded newform 475.3.c.h.151.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,3,Mod(151,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("475.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	475.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.9428125571$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 42x^{12} + 677x^{10} + 5313x^{8} + 21125x^{6} + 40138x^{4} + 30565x^{2} + 3675 $ x^14 + 42x^12 + 677x^10 + 5313x^8 + 21125x^6 + 40138x^4 + 30565x^2 + 3675
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.11
Root			$2.34822i$ of defining polynomial
Character	$\chi$	$=$	475.151
Dual form			475.3.c.h.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.34822i q^{2} +5.73703i q^{3} -1.51415 q^{4} -13.4718 q^{6} -9.56678 q^{7} +5.83734i q^{8} -23.9135 q^{9} +O(q^{10})$	\(q+2.34822i q^{2} +5.73703i q^{3} -1.51415 q^{4} -13.4718 q^{6} -9.56678 q^{7} +5.83734i q^{8} -23.9135 q^{9} +4.15630 q^{11} -8.68670i q^{12} +4.55775i q^{13} -22.4649i q^{14} -19.7639 q^{16} +27.9397 q^{17} -56.1541i q^{18} +(7.04287 + 17.6465i) q^{19} -54.8849i q^{21} +9.75992i q^{22} +13.9626 q^{23} -33.4890 q^{24} -10.7026 q^{26} -85.5590i q^{27} +14.4855 q^{28} +14.6141i q^{29} -28.9385i q^{31} -23.0608i q^{32} +23.8448i q^{33} +65.6087i q^{34} +36.2085 q^{36} +30.8172i q^{37} +(-41.4378 + 16.5382i) q^{38} -26.1479 q^{39} -44.2953i q^{41} +128.882 q^{42} -69.2593 q^{43} -6.29325 q^{44} +32.7872i q^{46} -30.1880 q^{47} -113.386i q^{48} +42.5233 q^{49} +160.291i q^{51} -6.90110i q^{52} +54.3939i q^{53} +200.912 q^{54} -55.8445i q^{56} +(-101.238 + 40.4051i) q^{57} -34.3171 q^{58} -31.3331i q^{59} +99.9646 q^{61} +67.9540 q^{62} +228.775 q^{63} -24.9039 q^{64} -55.9929 q^{66} -3.05833i q^{67} -42.3049 q^{68} +80.1037i q^{69} +23.0099i q^{71} -139.591i q^{72} -21.1499 q^{73} -72.3655 q^{74} +(-10.6639 - 26.7193i) q^{76} -39.7625 q^{77} -61.4012i q^{78} -77.7042i q^{79} +275.633 q^{81} +104.015 q^{82} -93.1651 q^{83} +83.1038i q^{84} -162.636i q^{86} -83.8415 q^{87} +24.2617i q^{88} +126.623i q^{89} -43.6030i q^{91} -21.1414 q^{92} +166.021 q^{93} -70.8882i q^{94} +132.300 q^{96} +77.2807i q^{97} +99.8542i q^{98} -99.3917 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 28 q^{4} - 4 q^{6} - 20 q^{7} - 36 q^{9}+O(q^{10}) $ 14 * q - 28 * q^4 - 4 * q^6 - 20 * q^7 - 36 * q^9	$ 14 q - 28 q^{4} - 4 q^{6} - 20 q^{7} - 36 q^{9} - 4 q^{11} + 36 q^{16} + 22 q^{17} + 39 q^{19} + 12 q^{23} - 44 q^{24} + 30 q^{26} + 98 q^{28} + 4 q^{36} + 37 q^{38} - 32 q^{39} + 250 q^{42} + 90 q^{43} - 52 q^{44} + 148 q^{47} + 234 q^{49} + 98 q^{54} - 195 q^{57} - 274 q^{58} + 222 q^{61} + 518 q^{62} + 198 q^{63} - 218 q^{64} + 92 q^{66} + 80 q^{68} - 228 q^{73} - 92 q^{74} - 351 q^{76} - 260 q^{77} + 402 q^{81} + 58 q^{82} - 280 q^{83} - 282 q^{87} + 302 q^{92} - 358 q^{93} + 190 q^{96} - 180 q^{99}+O(q^{100}) $ 14 * q - 28 * q^4 - 4 * q^6 - 20 * q^7 - 36 * q^9 - 4 * q^11 + 36 * q^16 + 22 * q^17 + 39 * q^19 + 12 * q^23 - 44 * q^24 + 30 * q^26 + 98 * q^28 + 4 * q^36 + 37 * q^38 - 32 * q^39 + 250 * q^42 + 90 * q^43 - 52 * q^44 + 148 * q^47 + 234 * q^49 + 98 * q^54 - 195 * q^57 - 274 * q^58 + 222 * q^61 + 518 * q^62 + 198 * q^63 - 218 * q^64 + 92 * q^66 + 80 * q^68 - 228 * q^73 - 92 * q^74 - 351 * q^76 - 260 * q^77 + 402 * q^81 + 58 * q^82 - 280 * q^83 - 282 * q^87 + 302 * q^92 - 358 * q^93 + 190 * q^96 - 180 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$			2.34822i			1.17411i	0.809547	+	0.587055i	$0.199713\pi$
$2$			2.34822i			1.17411i	−0.809547	+	0.587055i	$0.800287\pi$
$3$			5.73703i			1.91234i	0.292809	+	0.956171i	$0.405410\pi$
$3$			5.73703i			1.91234i	−0.292809	+	0.956171i	$0.594590\pi$
$4$	−1.51415			−0.378537
$5$		0			0
$5$		0			0
$6$	−13.4718			−2.24530
$7$	−9.56678			−1.36668			−0.683342	−	0.730099i	$-0.739474\pi$
$7$	−9.56678			−1.36668			−0.683342	+	0.730099i	$0.739474\pi$
$8$			5.83734i			0.729667i
$9$	−23.9135			−2.65705
$10$		0			0
$11$	4.15630			0.377846			0.188923	−	0.981992i	$-0.439500\pi$
$11$	4.15630			0.377846			0.188923	+	0.981992i	$0.439500\pi$
$12$		−	8.68670i		−	0.723891i
$13$			4.55775i			0.350596i	0.984515	+	0.175298i	$0.0560889\pi$
$13$			4.55775i			0.350596i	−0.984515	+	0.175298i	$0.943911\pi$
$14$		−	22.4649i		−	1.60464i
$15$		0			0
$16$	−19.7639			−1.23525
$17$	27.9397			1.64351			0.821757	−	0.569838i	$-0.192994\pi$
$17$	27.9397			1.64351			0.821757	+	0.569838i	$0.192994\pi$
$18$		−	56.1541i		−	3.11967i
$19$	7.04287	+	17.6465i	0.370677	+	0.928762i
$19$	7.04287	+	17.6465i	0.370677	+	0.928762i
$20$		0			0
$21$		−	54.8849i		−	2.61357i
$22$			9.75992i			0.443633i
$23$	13.9626			0.607069			0.303534	−	0.952820i	$-0.401833\pi$
$23$	13.9626			0.607069			0.303534	+	0.952820i	$0.401833\pi$
$24$	−33.4890			−1.39537
$25$		0			0
$26$	−10.7026			−0.411639
$27$		−	85.5590i		−	3.16885i
$28$	14.4855			0.517340
$29$			14.6141i			0.503934i	0.967736	+	0.251967i	$0.0810775\pi$
$29$			14.6141i			0.503934i	−0.967736	+	0.251967i	$0.918923\pi$
$30$		0			0
$31$		−	28.9385i		−	0.933499i	−0.884389	−	0.466750i	$-0.845425\pi$
$31$		−	28.9385i		−	0.933499i	0.884389	−	0.466750i	$-0.154575\pi$
$32$		−	23.0608i		−	0.720650i
$33$			23.8448i			0.722570i
$34$			65.6087i			1.92967i
$35$		0			0
$36$	36.2085			1.00579
$37$			30.8172i			0.832896i	0.909160	+	0.416448i	$0.136725\pi$
$37$			30.8172i			0.832896i	−0.909160	+	0.416448i	$0.863275\pi$
$38$	−41.4378	+	16.5382i	−1.09047	+	0.435216i
$39$	−26.1479			−0.670460
$40$		0			0
$41$		−	44.2953i		−	1.08037i	−0.841545	−	0.540187i	$-0.818354\pi$
$41$		−	44.2953i		−	1.08037i	0.841545	−	0.540187i	$-0.181646\pi$
$42$	128.882			3.06862
$43$	−69.2593			−1.61068			−0.805340	−	0.592813i	$-0.798017\pi$
$43$	−69.2593			−1.61068			−0.805340	+	0.592813i	$0.798017\pi$
$44$	−6.29325			−0.143028
$45$		0			0
$46$			32.7872i			0.712766i
$47$	−30.1880			−0.642299			−0.321149	−	0.947029i	$-0.604069\pi$
$47$	−30.1880			−0.642299			−0.321149	+	0.947029i	$0.604069\pi$
$48$		−	113.386i		−	2.36221i
$49$	42.5233			0.867823
$50$		0			0
$51$			160.291i			3.14296i
$52$		−	6.90110i		−	0.132714i
$53$			54.3939i			1.02630i	0.858299	+	0.513150i	$0.171522\pi$
$53$			54.3939i			1.02630i	−0.858299	+	0.513150i	$0.828478\pi$
$54$	200.912			3.72058
$55$		0			0
$56$		−	55.8445i		−	0.997224i
$57$	−101.238	+	40.4051i	−1.77611	+	0.708862i
$58$	−34.3171			−0.591675
$59$		−	31.3331i		−	0.531069i	−0.964101	−	0.265534i	$-0.914452\pi$
$59$		−	31.3331i		−	0.531069i	0.964101	−	0.265534i	$-0.0855484\pi$
$60$		0			0
$61$	99.9646			1.63876			0.819382	−	0.573248i	$-0.194317\pi$
$61$	99.9646			1.63876			0.819382	+	0.573248i	$0.194317\pi$
$62$	67.9540			1.09603
$63$	228.775			3.63135
$64$	−24.9039			−0.389124
$65$		0			0
$66$	−55.9929			−0.848378
$67$		−	3.05833i		−	0.0456468i	−0.999740	−	0.0228234i	$-0.992734\pi$
$67$		−	3.05833i		−	0.0456468i	0.999740	−	0.0228234i	$-0.00726554\pi$
$68$	−42.3049			−0.622130
$69$			80.1037i			1.16092i
$70$		0			0
$71$			23.0099i			0.324084i	0.986784	+	0.162042i	$0.0518079\pi$
$71$			23.0099i			0.324084i	−0.986784	+	0.162042i	$0.948192\pi$
$72$		−	139.591i		−	1.93876i
$73$	−21.1499			−0.289724			−0.144862	−	0.989452i	$-0.546274\pi$
$73$	−21.1499			−0.289724			−0.144862	+	0.989452i	$0.546274\pi$
$74$	−72.3655			−0.977912
$75$		0			0
$76$	−10.6639	−	26.7193i	−0.140315	−	0.351570i
$77$	−39.7625			−0.516395
$78$		−	61.4012i		−	0.787195i
$79$		−	77.7042i		−	0.983597i	−0.870709	−	0.491799i	$-0.836340\pi$
$79$		−	77.7042i		−	0.983597i	0.870709	−	0.491799i	$-0.163660\pi$
$80$		0			0
$81$	275.633			3.40288
$82$	104.015			1.26848
$83$	−93.1651			−1.12247			−0.561236	−	0.827656i	$-0.689674\pi$
$83$	−93.1651			−1.12247			−0.561236	+	0.827656i	$0.689674\pi$
$84$			83.1038i			0.989330i
$85$		0			0
$86$		−	162.636i		−	1.89112i
$87$	−83.8415			−0.963695
$88$			24.2617i			0.275702i
$89$			126.623i			1.42273i	0.702821	+	0.711366i	$0.251923\pi$
$89$			126.623i			1.42273i	−0.702821	+	0.711366i	$0.748077\pi$
$90$		0			0
$91$		−	43.6030i		−	0.479154i
$92$	−21.1414			−0.229798
$93$	166.021			1.78517
$94$		−	70.8882i		−	0.754130i
$95$		0			0
$96$	132.300			1.37813
$97$			77.2807i			0.796708i	0.917232	+	0.398354i	$0.130418\pi$
$97$			77.2807i			0.796708i	−0.917232	+	0.398354i	$0.869582\pi$
$98$			99.8542i			1.01892i
$99$	−99.3917			−1.00396
$100$		0			0
$101$	−145.782			−1.44339			−0.721693	−	0.692213i	$-0.756636\pi$
$101$	−145.782			−1.44339			−0.721693	+	0.692213i	$0.756636\pi$
$102$	−376.399			−3.69019
$103$		−	7.27524i		−	0.0706334i	−0.999376	−	0.0353167i	$-0.988756\pi$
$103$		−	7.27524i		−	0.0706334i	0.999376	−	0.0353167i	$-0.0112440\pi$
$104$	−26.6051			−0.255819
$105$		0			0
$106$	−127.729			−1.20499
$107$		−	128.949i		−	1.20513i	−0.798068	−	0.602567i	$-0.794145\pi$
$107$		−	128.949i		−	1.20513i	0.798068	−	0.602567i	$-0.205855\pi$
$108$			129.549i			1.19953i
$109$			74.4133i			0.682691i	0.939938	+	0.341346i	$0.110883\pi$
$109$			74.4133i			0.682691i	−0.939938	+	0.341346i	$0.889117\pi$
$110$		0			0
$111$	−176.799			−1.59278
$112$	189.077			1.68819
$113$			174.597i			1.54511i	0.634949	+	0.772554i	$0.281021\pi$
$113$			174.597i			1.54511i	−0.634949	+	0.772554i	$0.718979\pi$
$114$	−94.8802	−	237.730i	−0.832283	−	2.08535i
$115$		0			0
$116$		−	22.1279i		−	0.190758i
$117$		−	108.992i		−	0.931553i
$118$	73.5770			0.623534
$119$	−267.293			−2.24616
$120$		0			0
$121$	−103.725			−0.857233
$122$			234.739i			1.92409i
$123$	254.123			2.06604
$124$			43.8171i			0.353364i
$125$		0			0
$126$			537.215i			4.26361i
$127$			81.1228i			0.638762i	0.947626	+	0.319381i	$0.103475\pi$
$127$			81.1228i			0.638762i	−0.947626	+	0.319381i	$0.896525\pi$
$128$		−	150.723i		−	1.17752i
$129$		−	397.342i		−	3.08017i
$130$		0			0
$131$	−51.8609			−0.395885			−0.197942	−	0.980214i	$-0.563426\pi$
$131$	−51.8609			−0.395885			−0.197942	+	0.980214i	$0.563426\pi$
$132$		−	36.1046i		−	0.273519i
$133$	−67.3776	−	168.820i	−0.506599	−	1.26932i
$134$	7.18165			0.0535944
$135$		0			0
$136$			163.094i			1.19922i
$137$	−11.6713			−0.0851920			−0.0425960	−	0.999092i	$-0.513563\pi$
$137$	−11.6713			−0.0851920			−0.0425960	+	0.999092i	$0.513563\pi$
$138$	−188.101			−1.36305
$139$	115.309			0.829564			0.414782	−	0.909921i	$-0.363858\pi$
$139$	115.309			0.829564			0.414782	+	0.909921i	$0.363858\pi$
$140$		0			0
$141$		−	173.190i		−	1.22830i
$142$	−54.0324			−0.380510
$143$			18.9434i			0.132471i
$144$	472.625			3.28212
$145$		0			0
$146$		−	49.6645i		−	0.340168i
$147$			243.958i			1.65957i
$148$		−	46.6617i		−	0.315282i
$149$	149.512			1.00343			0.501717	−	0.865032i	$-0.332702\pi$
$149$	149.512			1.00343			0.501717	+	0.865032i	$0.332702\pi$
$150$		0			0
$151$			262.436i			1.73799i	0.494823	+	0.868994i	$0.335233\pi$
$151$			262.436i			1.73799i	−0.494823	+	0.868994i	$0.664767\pi$
$152$	−103.008	+	41.1116i	−0.677687	+	0.270471i
$153$	−668.136			−4.36690
$154$		−	93.3711i		−	0.606306i
$155$		0			0
$156$	39.5918			0.253794
$157$	106.277			0.676926			0.338463	−	0.940980i	$-0.390093\pi$
$157$	106.277			0.676926			0.338463	+	0.940980i	$0.390093\pi$
$158$	182.467			1.15485
$159$	−312.059			−1.96264
$160$		0			0
$161$	−133.577			−0.829671
$162$			647.247i			3.99535i
$163$	−173.109			−1.06202			−0.531009	−	0.847366i	$-0.678187\pi$
$163$	−173.109			−1.06202			−0.531009	+	0.847366i	$0.678187\pi$
$164$			67.0696i			0.408961i
$165$		0			0
$166$		−	218.772i		−	1.31791i
$167$			30.8456i			0.184704i	0.995726	+	0.0923522i	$0.0294386\pi$
$167$			30.8456i			0.184704i	−0.995726	+	0.0923522i	$0.970561\pi$
$168$	320.382			1.90703
$169$	148.227			0.877082
$170$		0			0
$171$	−168.419	−	421.988i	−0.984909	−	2.46777i
$172$	104.869			0.609702
$173$			14.7393i			0.0851981i	0.999092	+	0.0425990i	$0.0135638\pi$
$173$			14.7393i			0.0851981i	−0.999092	+	0.0425990i	$0.986436\pi$
$174$		−	196.878i		−	1.13148i
$175$		0			0
$176$	−82.1450			−0.466733
$177$	179.759			1.01559
$178$	−297.339			−1.67045
$179$		−	166.782i		−	0.931745i	−0.884852	−	0.465873i	$-0.845741\pi$
$179$		−	166.782i		−	0.931745i	0.884852	−	0.465873i	$-0.154259\pi$
$180$		0			0
$181$		−	200.231i		−	1.10625i	−0.833099	−	0.553124i	$-0.813436\pi$
$181$		−	200.231i		−	1.10625i	0.833099	−	0.553124i	$-0.186564\pi$
$182$	102.390			0.562580
$183$			573.499i			3.13388i
$184$			81.5043i			0.442958i
$185$		0			0
$186$			389.854i			2.09599i
$187$	116.126			0.620995
$188$	45.7091			0.243134
$189$			818.524i			4.33082i
$190$		0			0
$191$	264.646			1.38558			0.692792	−	0.721138i	$-0.256381\pi$
$191$	264.646			1.38558			0.692792	+	0.721138i	$0.256381\pi$
$192$		−	142.875i		−	0.744138i
$193$		−	170.535i		−	0.883600i	−0.897113	−	0.441800i	$-0.854340\pi$
$193$		−	170.535i		−	0.883600i	0.897113	−	0.441800i	$-0.145660\pi$
$194$	−181.472			−0.935423
$195$		0			0
$196$	−64.3866			−0.328503
$197$	193.450			0.981979			0.490989	−	0.871166i	$-0.336635\pi$
$197$	193.450			0.981979			0.490989	+	0.871166i	$0.336635\pi$
$198$		−	233.394i		−	1.17876i
$199$	247.455			1.24349			0.621747	−	0.783218i	$-0.286423\pi$
$199$	247.455			1.24349			0.621747	+	0.783218i	$0.286423\pi$
$200$		0			0
$201$	17.5457			0.0872923
$202$		−	342.329i		−	1.69470i
$203$		−	139.810i		−	0.688719i
$204$		−	242.704i		−	1.18973i
$205$		0			0
$206$	17.0839			0.0829315
$207$	−333.894			−1.61301
$208$		−	90.0792i		−	0.433073i
$209$	29.2723	+	73.3441i	0.140059	+	0.350929i
$210$		0			0
$211$		−	103.882i		−	0.492331i	−0.969228	−	0.246166i	$-0.920829\pi$
$211$		−	103.882i		−	0.492331i	0.969228	−	0.246166i	$-0.0791707\pi$
$212$		−	82.3604i		−	0.388492i
$213$	−132.009			−0.619759
$214$	302.802			1.41496
$215$		0			0
$216$	499.437			2.31221
$217$			276.848i			1.27580i
$218$	−174.739			−0.801555
$219$		−	121.337i		−	0.554051i
$220$		0			0
$221$			127.342i			0.576210i
$222$		−	415.163i		−	1.87010i
$223$			68.3811i			0.306642i	0.988176	+	0.153321i	$0.0489968\pi$
$223$			68.3811i			0.306642i	−0.988176	+	0.153321i	$0.951003\pi$
$224$			220.618i			0.984900i
$225$		0			0
$226$	−409.993			−1.81413
$227$			199.560i			0.879121i	0.898213	+	0.439560i	$0.144866\pi$
$227$			199.560i			0.879121i	−0.898213	+	0.439560i	$0.855134\pi$
$228$	153.290	−	61.1793i	0.672323	−	0.268330i
$229$	−75.3592			−0.329079			−0.164540	−	0.986370i	$-0.552614\pi$
$229$	−75.3592			−0.329079			−0.164540	+	0.986370i	$0.552614\pi$
$230$		0			0
$231$		−	228.118i		−	0.987525i
$232$	−85.3074			−0.367704
$233$	−10.3384			−0.0443709			−0.0221854	−	0.999754i	$-0.507062\pi$
$233$	−10.3384			−0.0443709			−0.0221854	+	0.999754i	$0.507062\pi$
$234$	255.937			1.09375
$235$		0			0
$236$			47.4428i			0.201029i
$237$	445.791			1.88097
$238$		−	627.664i		−	2.63724i
$239$	−360.813			−1.50968			−0.754840	−	0.655909i	$-0.772285\pi$
$239$	−360.813			−1.50968			−0.754840	+	0.655909i	$0.772285\pi$
$240$		0			0
$241$			446.555i			1.85293i	0.376384	+	0.926464i	$0.377167\pi$
$241$			446.555i			1.85293i	−0.376384	+	0.926464i	$0.622833\pi$
$242$		−	243.570i		−	1.00649i
$243$			811.283i			3.33861i
$244$	−151.361			−0.620332
$245$		0			0
$246$			596.738i			2.42577i
$247$	−80.4282	+	32.0997i	−0.325620	+	0.129958i
$248$	168.924			0.681144
$249$		−	534.491i		−	2.14655i
$250$		0			0
$251$	−295.147			−1.17588			−0.587942	−	0.808903i	$-0.700062\pi$
$251$	−295.147			−1.17588			−0.587942	+	0.808903i	$0.700062\pi$
$252$	−346.399			−1.37460
$253$	58.0327			0.229378
$254$	−190.494			−0.749978
$255$		0			0
$256$	254.316			0.993420
$257$			96.9364i			0.377185i	0.982055	+	0.188592i	$0.0603925\pi$
$257$			96.9364i			0.377185i	−0.982055	+	0.188592i	$0.939608\pi$
$258$	933.048			3.61646
$259$		−	294.821i		−	1.13831i
$260$		0			0
$261$		−	349.474i		−	1.33898i
$262$		−	121.781i		−	0.464812i
$263$	−288.418			−1.09665			−0.548323	−	0.836267i	$-0.684733\pi$
$263$	−288.418			−1.09665			−0.548323	+	0.836267i	$0.684733\pi$
$264$	−139.190			−0.527236
$265$		0			0
$266$	396.427	−	158.218i	1.49033	−	0.594803i
$267$	−726.441			−2.72075
$268$			4.63077i			0.0172790i
$269$			174.475i			0.648607i	0.945953	+	0.324304i	$0.105130\pi$
$269$			174.475i			0.648607i	−0.945953	+	0.324304i	$0.894870\pi$
$270$		0			0
$271$	127.454			0.470311			0.235155	−	0.971958i	$-0.424440\pi$
$271$	127.454			0.470311			0.235155	+	0.971958i	$0.424440\pi$
$272$	−552.199			−2.03015
$273$	250.152			0.916307
$274$		−	27.4068i		−	0.100025i
$275$		0			0
$276$		−	121.289i		−	0.439452i
$277$	424.528			1.53259			0.766295	−	0.642488i	$-0.222098\pi$
$277$	424.528			1.53259			0.766295	+	0.642488i	$0.222098\pi$
$278$			270.772i			0.974001i
$279$			692.020i			2.48036i
$280$		0			0
$281$			166.293i			0.591791i	0.955220	+	0.295895i	$0.0956180\pi$
$281$			166.293i			0.591791i	−0.955220	+	0.295895i	$0.904382\pi$
$282$	406.688			1.44215
$283$	−221.482			−0.782621			−0.391310	−	0.920259i	$-0.627978\pi$
$283$	−221.482			−0.782621			−0.391310	+	0.920259i	$0.627978\pi$
$284$		−	34.8404i		−	0.122677i
$285$		0			0
$286$	−44.4833			−0.155536
$287$			423.764i			1.47653i
$288$			551.464i			1.91480i
$289$	491.629			1.70114
$290$		0			0
$291$	−443.361			−1.52358
$292$	32.0240			0.109671
$293$		−	38.0208i		−	0.129764i	−0.997893	−	0.0648819i	$-0.979333\pi$
$293$		−	38.0208i		−	0.129764i	0.997893	−	0.0648819i	$-0.0206671\pi$
$294$	−572.866			−1.94853
$295$		0			0
$296$	−179.890			−0.607737
$297$		−	355.609i		−	1.19734i
$298$			351.087i			1.17814i
$299$			63.6380i			0.212836i
$300$		0			0
$301$	662.588			2.20129
$302$	−616.258			−2.04059
$303$		−	836.355i		−	2.76025i
$304$	−139.195	−	348.764i	−0.457878	−	1.14725i
$305$		0			0
$306$		−	1568.93i		−	5.12723i
$307$		−	285.495i		−	0.929950i	−0.885324	−	0.464975i	$-0.846063\pi$
$307$		−	285.495i		−	0.929950i	0.885324	−	0.464975i	$-0.153937\pi$
$308$	60.2062			0.195475
$309$	41.7382			0.135075
$310$		0			0
$311$	−4.55195			−0.0146365			−0.00731825	−	0.999973i	$-0.502329\pi$
$311$	−4.55195			−0.0146365			−0.00731825	+	0.999973i	$0.502329\pi$
$312$		−	152.634i		−	0.489213i
$313$	298.019			0.952136			0.476068	−	0.879408i	$-0.342062\pi$
$313$	298.019			0.952136			0.476068	+	0.879408i	$0.342062\pi$
$314$			249.563i			0.794786i
$315$		0			0
$316$			117.655i			0.372327i
$317$		−	179.077i		−	0.564910i	−0.959280	−	0.282455i	$-0.908851\pi$
$317$		−	179.077i		−	0.564910i	0.959280	−	0.282455i	$-0.0911489\pi$
$318$		−	732.785i		−	2.30435i
$319$			60.7406i			0.190409i
$320$		0			0
$321$	739.786			2.30463
$322$		−	313.668i		−	0.974126i
$323$	196.776	+	493.038i	0.609213	+	1.52643i
$324$	−417.349			−1.28811
$325$		0			0
$326$		−	406.499i		−	1.24693i
$327$	−426.911			−1.30554
$328$	258.567			0.788313
$329$	288.802			0.877819
$330$		0			0
$331$			330.043i			0.997109i	0.866858	+	0.498554i	$0.166136\pi$
$331$			330.043i			0.997109i	−0.866858	+	0.498554i	$0.833864\pi$
$332$	141.066			0.424896
$333$		−	736.945i		−	2.21305i
$334$	−72.4324			−0.216863
$335$		0			0
$336$			1084.74i			3.22840i
$337$			7.17182i			0.0212814i	0.999943	+	0.0106407i	$0.00338710\pi$
$337$			7.17182i			0.0212814i	−0.999943	+	0.0106407i	$0.996613\pi$
$338$			348.070i			1.02979i
$339$	−1001.67			−2.95477
$340$		0			0
$341$		−	120.277i		−	0.352719i
$342$	990.923	−	395.486i	2.89743	−	1.15639i
$343$	61.9608			0.180644
$344$		−	404.290i		−	1.17526i
$345$		0			0
$346$	−34.6111			−0.100032
$347$	38.9167			0.112152			0.0560759	−	0.998427i	$-0.482141\pi$
$347$	38.9167			0.112152			0.0560759	+	0.998427i	$0.482141\pi$
$348$	126.948			0.364794
$349$	342.266			0.980704			0.490352	−	0.871525i	$-0.336868\pi$
$349$	342.266			0.980704			0.490352	+	0.871525i	$0.336868\pi$
$350$		0			0
$351$	389.957			1.11099
$352$		−	95.8476i		−	0.272294i
$353$	17.5325			0.0496671			0.0248335	−	0.999692i	$-0.492094\pi$
$353$	17.5325			0.0496671			0.0248335	+	0.999692i	$0.492094\pi$
$354$			422.113i			1.19241i
$355$		0			0
$356$		−	191.726i		−	0.538556i
$357$		−	1533.47i		−	4.29543i
$358$	391.642			1.09397
$359$	452.975			1.26177			0.630885	−	0.775876i	$-0.282692\pi$
$359$	452.975			1.26177			0.630885	+	0.775876i	$0.282692\pi$
$360$		0			0
$361$	−261.796	+	248.564i	−0.725197	+	0.688542i
$362$	470.186			1.29886
$363$		−	595.074i		−	1.63932i
$364$			66.0214i			0.181377i
$365$		0			0
$366$	−1346.70			−3.67952
$367$	290.156			0.790615			0.395308	−	0.918549i	$-0.370638\pi$
$367$	290.156			0.790615			0.395308	+	0.918549i	$0.370638\pi$
$368$	−275.956			−0.749880
$369$			1059.26i			2.87061i
$370$		0			0
$371$		−	520.375i		−	1.40263i
$372$	−251.380			−0.675752
$373$		−	555.723i		−	1.48987i	−0.667136	−	0.744936i	$-0.732480\pi$
$373$		−	555.723i		−	1.48987i	0.667136	−	0.744936i	$-0.267520\pi$
$374$			272.690i			0.729117i
$375$		0			0
$376$		−	176.218i		−	0.468664i
$377$	−66.6074			−0.176678
$378$	−1922.08			−5.08486
$379$			4.05619i			0.0107023i	0.999986	+	0.00535117i	$0.00170334\pi$
$379$			4.05619i			0.0107023i	−0.999986	+	0.00535117i	$0.998297\pi$
$380$		0			0
$381$	−465.404			−1.22153
$382$			621.449i			1.62683i
$383$			392.529i			1.02488i	0.858723	+	0.512439i	$0.171258\pi$
$383$			392.529i			1.02488i	−0.858723	+	0.512439i	$0.828742\pi$
$384$	864.703			2.25183
$385$		0			0
$386$	400.454			1.03744
$387$	1656.23			4.27966
$388$		−	117.014i		−	0.301583i
$389$	0.819385			0.00210639			0.00105319	−	0.999999i	$-0.499665\pi$
$389$	0.819385			0.00210639			0.00105319	+	0.999999i	$0.499665\pi$
$390$		0			0
$391$	390.111			0.997726
$392$			248.223i			0.633222i
$393$		−	297.527i		−	0.757067i
$394$			454.263i			1.15295i
$395$		0			0
$396$	150.494			0.380034
$397$	−132.366			−0.333414			−0.166707	−	0.986006i	$-0.553313\pi$
$397$	−132.366			−0.333414			−0.166707	+	0.986006i	$0.553313\pi$
$398$			581.080i			1.46000i
$399$	968.525	−	386.547i	2.42738	−	0.968790i
$400$		0			0
$401$		−	50.7026i		−	0.126440i	−0.998000	−	0.0632202i	$-0.979863\pi$
$401$		−	50.7026i		−	0.126440i	0.998000	−	0.0632202i	$-0.0201370\pi$
$402$			41.2013i			0.102491i
$403$	131.894			0.327281
$404$	220.735			0.546375
$405$		0			0
$406$	328.305			0.808632
$407$			128.085i			0.314706i
$408$	−935.673			−2.29332
$409$			67.8086i			0.165791i	0.996558	+	0.0828956i	$0.0264168\pi$
$409$			67.8086i			0.165791i	−0.996558	+	0.0828956i	$0.973583\pi$
$410$		0			0
$411$		−	66.9586i		−	0.162916i
$412$			11.0158i			0.0267373i
$413$			299.757i			0.725803i
$414$		−	784.057i		−	1.89386i
$415$		0			0
$416$	105.105			0.252657
$417$			661.533i			1.58641i
$418$	−172.228	+	68.7379i	−0.412029	+	0.164445i
$419$	−222.546			−0.531135			−0.265568	−	0.964092i	$-0.585559\pi$
$419$	−222.546			−0.531135			−0.265568	+	0.964092i	$0.585559\pi$
$420$		0			0
$421$			205.736i			0.488684i	0.969689	+	0.244342i	$0.0785719\pi$
$421$			205.736i			0.488684i	−0.969689	+	0.244342i	$0.921428\pi$
$422$	243.938			0.578051
$423$	721.901			1.70662
$424$	−317.516			−0.748858
$425$		0			0
$426$		−	309.985i		−	0.727665i
$427$	−956.339			−2.23967
$428$			195.248i			0.456187i
$429$	−108.679			−0.253331
$430$		0			0
$431$			479.116i			1.11164i	0.831303	+	0.555819i	$0.187595\pi$
$431$			479.116i			1.11164i	−0.831303	+	0.555819i	$0.812405\pi$
$432$			1690.98i			3.91431i
$433$			566.880i			1.30919i	0.755979	+	0.654596i	$0.227161\pi$
$433$			566.880i			1.30919i	−0.755979	+	0.654596i	$0.772839\pi$
$434$	−650.101			−1.49793
$435$		0			0
$436$		−	112.673i		−	0.258424i
$437$	98.3367	+	246.390i	0.225027	+	0.563822i
$438$	284.927			0.650518
$439$			684.577i			1.55940i	0.626152	+	0.779701i	$0.284629\pi$
$439$			684.577i			1.55940i	−0.626152	+	0.779701i	$0.715371\pi$
$440$		0			0
$441$	−1016.88			−2.30585
$442$	−299.028			−0.676534
$443$	−473.575			−1.06902			−0.534509	−	0.845163i	$-0.679504\pi$
$443$	−473.575			−1.06902			−0.534509	+	0.845163i	$0.679504\pi$
$444$	267.699			0.602926
$445$		0			0
$446$	−160.574			−0.360031
$447$			857.752i			1.91891i
$448$	238.251			0.531809
$449$			315.053i			0.701677i	0.936436	+	0.350839i	$0.114103\pi$
$449$			315.053i			0.701677i	−0.936436	+	0.350839i	$0.885897\pi$
$450$		0			0
$451$		−	184.105i		−	0.408215i
$452$		−	264.366i		−	0.584880i
$453$	−1505.60			−3.32363
$454$	−468.612			−1.03219
$455$		0			0
$456$	−235.858	−	590.962i	−0.517233	−	1.29597i
$457$	−259.302			−0.567401			−0.283700	−	0.958913i	$-0.591562\pi$
$457$	−259.302			−0.567401			−0.283700	+	0.958913i	$0.591562\pi$
$458$		−	176.960i		−	0.386376i
$459$		−	2390.50i		−	5.20805i
$460$		0			0
$461$	681.783			1.47892			0.739461	−	0.673200i	$-0.235081\pi$
$461$	681.783			1.47892			0.739461	+	0.673200i	$0.235081\pi$
$462$	535.672			1.15946
$463$	640.879			1.38419			0.692094	−	0.721808i	$-0.256689\pi$
$463$	640.879			1.38419			0.692094	+	0.721808i	$0.256689\pi$
$464$		−	288.832i		−	0.622483i
$465$		0			0
$466$		−	24.2769i		−	0.0520963i
$467$	142.309			0.304730			0.152365	−	0.988324i	$-0.451311\pi$
$467$	142.309			0.304730			0.152365	+	0.988324i	$0.451311\pi$
$468$			165.029i			0.352627i
$469$			29.2584i			0.0623847i
$470$		0			0
$471$			609.716i			1.29451i
$472$	182.902			0.387503
$473$	−287.863			−0.608589
$474$			1046.82i			2.20847i
$475$		0			0
$476$	404.721			0.850255
$477$		−	1300.75i		−	2.72693i
$478$		−	847.270i		−	1.77253i
$479$	303.821			0.634283			0.317141	−	0.948378i	$-0.397277\pi$
$479$	303.821			0.634283			0.317141	+	0.948378i	$0.397277\pi$
$480$		0			0
$481$	−140.457			−0.292010
$482$	−1048.61			−2.17554
$483$		−	766.335i		−	1.58661i
$484$	157.055			0.324494
$485$		0			0
$486$	−1905.07			−3.91990
$487$			0.541296i			0.00111149i	1.00000		0.000555746i	$0.000176899\pi$
$487$			0.541296i			0.00111149i	−1.00000		0.000555746i	$0.999823\pi$
$488$			583.527i			1.19575i
$489$		−	993.131i		−	2.03094i
$490$		0			0
$491$	463.173			0.943326			0.471663	−	0.881779i	$-0.343654\pi$
$491$	463.173			0.943326			0.471663	+	0.881779i	$0.343654\pi$
$492$	−384.780			−0.782073
$493$			408.314i			0.828223i
$494$	−75.3771	−	188.863i	−0.152585	−	0.382315i
$495$		0			0
$496$			571.939i			1.15310i
$497$		−	220.131i		−	0.442920i
$498$	1255.10			2.52029
$499$	174.865			0.350431			0.175215	−	0.984530i	$-0.443938\pi$
$499$	174.865			0.350431			0.175215	+	0.984530i	$0.443938\pi$
$500$		0			0
$501$	−176.962			−0.353218
$502$		−	693.070i		−	1.38062i
$503$	−503.015			−1.00003			−0.500015	−	0.866017i	$-0.666672\pi$
$503$	−503.015			−1.00003			−0.500015	+	0.866017i	$0.666672\pi$
$504$			1335.44i			2.64968i
$505$		0			0
$506$			136.274i			0.269316i
$507$			850.382i			1.67728i
$508$		−	122.832i		−	0.241795i
$509$		−	358.496i		−	0.704315i	−0.935941	−	0.352157i	$-0.885448\pi$
$509$		−	358.496i		−	0.704315i	0.935941	−	0.352157i	$-0.114552\pi$
$510$		0			0
$511$	202.336			0.395961
$512$		−	5.70303i		−	0.0111387i
$513$	1509.81	−	602.581i	2.94311	−	1.17462i
$514$	−227.628			−0.442857
$515$		0			0
$516$			601.634i			1.16596i
$517$	−125.471			−0.242690
$518$	692.305			1.33650
$519$	−84.5596			−0.162928
$520$		0			0
$521$		−	882.596i		−	1.69404i	−0.531559	−	0.847022i	$-0.678393\pi$
$521$		−	882.596i		−	1.69404i	0.531559	−	0.847022i	$-0.321607\pi$
$522$	820.642			1.57211
$523$			2.57808i			0.00492941i	0.999997	+	0.00246471i	$0.000784541\pi$
$523$			2.57808i			0.00492941i	−0.999997	+	0.00246471i	$0.999215\pi$
$524$	78.5250			0.149857
$525$		0			0
$526$		−	677.269i		−	1.28758i
$527$		−	808.534i		−	1.53422i
$528$		−	471.268i		−	0.892553i
$529$	−334.046			−0.631467
$530$		0			0
$531$			749.282i			1.41108i
$532$	102.020	+	255.618i	0.191766	+	0.480485i
$533$	201.887			0.378775
$534$		−	1705.84i		−	3.19446i
$535$		0			0
$536$	17.8525			0.0333070
$537$	956.835			1.78182
$538$	−409.707			−0.761537
$539$	176.740			0.327903
$540$		0			0
$541$	382.112			0.706307			0.353154	−	0.935565i	$-0.385109\pi$
$541$	382.112			0.706307			0.353154	+	0.935565i	$0.385109\pi$
$542$			299.291i			0.552197i
$543$	1148.73			2.11552
$544$		−	644.312i		−	1.18440i
$545$		0			0
$546$			587.412i			1.07585i
$547$			93.8141i			0.171506i	0.996316	+	0.0857532i	$0.0273297\pi$
$547$			93.8141i			0.171506i	−0.996316	+	0.0857532i	$0.972670\pi$
$548$	17.6721			0.0322483
$549$	−2390.50			−4.35428
$550$		0			0
$551$	−257.887	+	102.925i	−0.468035	+	0.186797i
$552$	−467.592			−0.847088
$553$			743.379i			1.34427i
$554$			996.885i			1.79943i
$555$		0			0
$556$	−174.595			−0.314020
$557$	−799.561			−1.43548			−0.717739	−	0.696313i	$-0.754823\pi$
$557$	−799.561			−1.43548			−0.717739	+	0.696313i	$0.754823\pi$
$558$	−1625.02			−2.91221
$559$		−	315.667i		−	0.564699i
$560$		0			0
$561$			666.218i			1.18755i
$562$	−390.493			−0.694828
$563$			676.517i			1.20163i	0.799389	+	0.600814i	$0.205157\pi$
$563$			676.517i			1.20163i	−0.799389	+	0.600814i	$0.794843\pi$
$564$			262.234i			0.464955i
$565$		0			0
$566$		−	520.088i		−	0.918884i
$567$	−2636.92			−4.65065
$568$	−134.317			−0.236473
$569$			710.658i			1.24896i	0.781041	+	0.624480i	$0.214689\pi$
$569$			710.658i			1.24896i	−0.781041	+	0.624480i	$0.785311\pi$
$570$		0			0
$571$	−812.896			−1.42363			−0.711817	−	0.702364i	$-0.752128\pi$
$571$	−812.896			−1.42363			−0.711817	+	0.702364i	$0.752128\pi$
$572$		−	28.6831i		−	0.0501452i
$573$			1518.28i			2.64971i
$574$	−995.091			−1.73361
$575$		0			0
$576$	595.540			1.03392
$577$	−812.174			−1.40758			−0.703790	−	0.710408i	$-0.748510\pi$
$577$	−812.174			−1.40758			−0.703790	+	0.710408i	$0.748510\pi$
$578$			1154.45i			1.99733i
$579$	978.363			1.68975
$580$		0			0
$581$	891.291			1.53406
$582$		−	1041.11i		−	1.78885i
$583$			226.078i			0.387783i
$584$		−	123.459i		−	0.211402i
$585$		0			0
$586$	89.2812			0.152357
$587$	332.138			0.565823			0.282912	−	0.959146i	$-0.408700\pi$
$587$	332.138			0.565823			0.282912	+	0.959146i	$0.408700\pi$
$588$		−	369.387i		−	0.628210i
$589$	510.662	−	203.810i	0.866998	−	0.346027i
$590$		0			0
$591$			1109.83i			1.87788i
$592$		−	609.069i		−	1.02883i
$593$	−381.895			−0.644005			−0.322003	−	0.946739i	$-0.604356\pi$
$593$	−381.895			−0.644005			−0.322003	+	0.946739i	$0.604356\pi$
$594$	835.049			1.40581
$595$		0			0
$596$	−226.383			−0.379837
$597$			1419.66i			2.37798i
$598$	−149.436			−0.249893
$599$			391.286i			0.653232i	0.945157	+	0.326616i	$0.105908\pi$
$599$			391.286i			0.653232i	−0.945157	+	0.326616i	$0.894092\pi$
$600$		0			0
$601$			708.847i			1.17945i	0.807606	+	0.589723i	$0.200763\pi$
$601$			708.847i			1.17945i	−0.807606	+	0.589723i	$0.799237\pi$
$602$			1555.90i			2.58456i
$603$			73.1354i			0.121286i
$604$		−	397.367i		−	0.657892i
$605$		0			0
$606$	1963.95			3.24084
$607$			256.683i			0.422872i	0.977392	+	0.211436i	$0.0678140\pi$
$607$			256.683i			0.422872i	−0.977392	+	0.211436i	$0.932186\pi$
$608$	406.942	−	162.414i	0.669312	−	0.267129i
$609$	802.093			1.31707
$610$		0			0
$611$		−	137.590i		−	0.225188i
$612$	1011.66			1.65303
$613$	730.296			1.19135			0.595674	−	0.803226i	$-0.296885\pi$
$613$	730.296			1.19135			0.595674	+	0.803226i	$0.296885\pi$
$614$	670.405			1.09186
$615$		0			0
$616$		−	232.107i		−	0.376797i
$617$	−91.8108			−0.148802			−0.0744009	−	0.997228i	$-0.523704\pi$
$617$	−91.8108			−0.148802			−0.0744009	+	0.997228i	$0.523704\pi$
$618$			98.0107i			0.158593i
$619$	28.4153			0.0459052			0.0229526	−	0.999737i	$-0.492693\pi$
$619$	28.4153			0.0459052			0.0229526	+	0.999737i	$0.492693\pi$
$620$		0			0
$621$		−	1194.62i		−	1.92371i
$622$		−	10.6890i		−	0.0171849i
$623$		−	1211.38i		−	1.94442i
$624$	516.787			0.828184
$625$		0			0
$626$			699.814i			1.11791i
$627$	−420.777	+	167.936i	−0.671096	+	0.267840i
$628$	−160.919			−0.256241
$629$			861.023i			1.36888i
$630$		0			0
$631$	430.427			0.682134			0.341067	−	0.940039i	$-0.389212\pi$
$631$	430.427			0.682134			0.341067	+	0.940039i	$0.389212\pi$
$632$	453.585			0.717698
$633$	595.973			0.941506
$634$	420.512			0.663268
$635$		0			0
$636$	472.504			0.742930
$637$			193.811i			0.304256i
$638$	−142.632			−0.223562
$639$		−	550.247i		−	0.861107i
$640$		0			0
$641$		−	340.928i		−	0.531868i	−0.963991	−	0.265934i	$-0.914320\pi$
$641$		−	340.928i		−	0.531868i	0.963991	−	0.265934i	$-0.0856804\pi$
$642$			1737.18i			2.70589i
$643$	−245.635			−0.382014			−0.191007	−	0.981589i	$-0.561175\pi$
$643$	−245.635			−0.382014			−0.191007	+	0.981589i	$0.561175\pi$
$644$	202.255			0.314061
$645$		0			0
$646$	−1157.76	+	462.074i	−1.79220	+	0.715284i
$647$	728.400			1.12581			0.562906	−	0.826521i	$-0.309683\pi$
$647$	728.400			1.12581			0.562906	+	0.826521i	$0.309683\pi$
$648$			1608.96i			2.48297i
$649$		−	130.230i		−	0.200662i
$650$		0			0
$651$	−1588.29			−2.43976
$652$	262.112			0.402013
$653$	−394.958			−0.604836			−0.302418	−	0.953175i	$-0.597794\pi$
$653$	−394.958			−0.604836			−0.302418	+	0.953175i	$0.597794\pi$
$654$		−	1002.48i		−	1.53285i
$655$		0			0
$656$			875.450i			1.33453i
$657$	505.766			0.769812
$658$			678.172i			1.03066i
$659$			115.919i			0.175901i	0.996125	+	0.0879504i	$0.0280317\pi$
$659$			115.919i			0.175901i	−0.996125	+	0.0879504i	$0.971968\pi$
$660$		0			0
$661$		−	1088.21i		−	1.64631i	−0.567818	−	0.823154i	$-0.692212\pi$
$661$		−	1088.21i		−	1.64631i	0.567818	−	0.823154i	$-0.307788\pi$
$662$	−775.014			−1.17072
$663$	−730.567			−1.10191
$664$		−	543.836i		−	0.819030i
$665$		0			0
$666$	1730.51			2.59836
$667$			204.051i			0.305923i
$668$		−	46.7048i		−	0.0699174i
$669$	−392.304			−0.586404
$670$		0			0
$671$	415.483			0.619200
$672$	−1265.69			−1.88347
$673$		−	1183.83i		−	1.75903i	−0.475868	−	0.879517i	$-0.657866\pi$
$673$		−	1183.83i		−	1.75903i	0.475868	−	0.879517i	$-0.342134\pi$
$674$	−16.8410			−0.0249867
$675$		0			0
$676$	−224.437			−0.332008
$677$			833.194i			1.23071i	0.788248	+	0.615357i	$0.210988\pi$
$677$			833.194i			1.23071i	−0.788248	+	0.615357i	$0.789012\pi$
$678$		−	2352.14i		−	3.46923i
$679$		−	739.327i		−	1.08885i
$680$		0			0
$681$	−1144.88			−1.68118
$682$	282.437			0.414131
$683$		−	979.686i		−	1.43439i	−0.696874	−	0.717193i	$-0.745427\pi$
$683$		−	979.686i		−	1.43439i	0.696874	−	0.717193i	$-0.254573\pi$
$684$	255.012	+	638.952i	0.372824	+	0.934141i
$685$		0			0
$686$			145.498i			0.212096i
$687$		−	432.338i		−	0.629312i
$688$	1368.84			1.98959
$689$	−247.914			−0.359817
$690$		0			0
$691$	268.944			0.389211			0.194605	−	0.980882i	$-0.437657\pi$
$691$	268.944			0.389211			0.194605	+	0.980882i	$0.437657\pi$
$692$		−	22.3174i		−	0.0322506i
$693$	950.858			1.37209
$694$			91.3850i			0.131679i
$695$		0			0
$696$		−	489.411i		−	0.703176i
$697$		−	1237.60i		−	1.77561i
$698$			803.715i			1.15145i
$699$		−	59.3118i		−	0.0848523i
$700$		0			0
$701$	555.168			0.791966			0.395983	−	0.918258i	$-0.370404\pi$
$701$	555.168			0.791966			0.395983	+	0.918258i	$0.370404\pi$
$702$			915.705i			1.30442i
$703$	−543.814	+	217.041i	−0.773562	+	0.308736i
$704$	−103.508			−0.147029
$705$		0			0
$706$			41.1702i			0.0583147i
$707$	1394.66			1.97265
$708$	−272.181			−0.384436
$709$	−409.398			−0.577430			−0.288715	−	0.957415i	$-0.593228\pi$
$709$	−409.398			−0.577430			−0.288715	+	0.957415i	$0.593228\pi$
$710$		0			0
$711$			1858.18i			2.61347i
$712$	−739.142			−1.03812
$713$		−	404.056i		−	0.566698i
$714$	3600.93			5.04331
$715$		0			0
$716$			252.533i			0.352700i
$717$		−	2070.00i		−	2.88702i
$718$			1063.69i			1.48146i
$719$	530.021			0.737164			0.368582	−	0.929595i	$-0.379843\pi$
$719$	530.021			0.737164			0.368582	+	0.929595i	$0.379843\pi$
$720$		0			0
$721$			69.6006i			0.0965335i
$722$	−583.683	−	614.755i	−0.808425	−	0.851461i
$723$	−2561.90			−3.54343
$724$			303.179i			0.418755i
$725$		0			0
$726$	1397.37			1.92475
$727$	−60.1205			−0.0826967			−0.0413483	−	0.999145i	$-0.513165\pi$
$727$	−60.1205			−0.0826967			−0.0413483	+	0.999145i	$0.513165\pi$
$728$	254.526			0.349623
$729$	−2173.65			−2.98169
$730$		0			0
$731$	−1935.09			−2.64718
$732$		−	868.362i		−	1.18629i
$733$	625.418			0.853231			0.426616	−	0.904433i	$-0.359706\pi$
$733$	625.418			0.853231			0.426616	+	0.904433i	$0.359706\pi$
$734$			681.350i			0.928270i
$735$		0			0
$736$		−	321.988i		−	0.437484i
$737$		−	12.7114i		−	0.0172474i
$738$	−2487.37			−3.37042
$739$	−110.100			−0.148985			−0.0744923	−	0.997222i	$-0.523734\pi$
$739$	−110.100			−0.148985			−0.0744923	+	0.997222i	$0.523734\pi$
$740$		0			0
$741$	−184.157	−	461.419i	−0.248524	−	0.622698i
$742$	1221.96			1.64684
$743$		−	194.296i		−	0.261503i	−0.991415	−	0.130751i	$-0.958261\pi$
$743$		−	194.296i		−	0.261503i	0.991415	−	0.130751i	$-0.0417389\pi$
$744$			969.119i			1.30258i
$745$		0			0
$746$	1304.96			1.74928
$747$	2227.90			2.98247
$748$	−175.832			−0.235069
$749$			1233.63i			1.64704i
$750$		0			0
$751$		−	62.7172i		−	0.0835115i	−0.999128	−	0.0417558i	$-0.986705\pi$
$751$		−	62.7172i		−	0.0835115i	0.999128	−	0.0417558i	$-0.0132951\pi$
$752$	596.635			0.793397
$753$		−	1693.27i		−	2.24869i
$754$		−	156.409i		−	0.207439i
$755$		0			0
$756$		−	1239.37i		−	1.63937i
$757$	580.530			0.766882			0.383441	−	0.923565i	$-0.374739\pi$
$757$	580.530			0.766882			0.383441	+	0.923565i	$0.374739\pi$
$758$	−9.52483			−0.0125657
$759$			332.935i			0.438650i
$760$		0			0
$761$	599.456			0.787721			0.393861	−	0.919170i	$-0.371139\pi$
$761$	599.456			0.787721			0.393861	+	0.919170i	$0.371139\pi$
$762$		−	1092.87i		−	1.43421i
$763$		−	711.896i		−	0.933023i
$764$	−400.713			−0.524494
$765$		0			0
$766$	−921.744			−1.20332
$767$	142.808			0.186191
$768$			1459.02i			1.89976i
$769$	−227.963			−0.296441			−0.148220	−	0.988954i	$-0.547354\pi$
$769$	−227.963			−0.296441			−0.148220	+	0.988954i	$0.547354\pi$
$770$		0			0
$771$	−556.127			−0.721306
$772$			258.215i			0.334475i
$773$		−	984.904i		−	1.27413i	−0.770809	−	0.637066i	$-0.780148\pi$
$773$		−	984.904i		−	1.27413i	0.770809	−	0.637066i	$-0.219852\pi$
$774$			3889.19i			5.02480i
$775$		0			0
$776$	−451.113			−0.581331
$777$	1691.40			2.17683
$778$			1.92410i			0.00247313i
$779$	781.656	−	311.966i	1.00341	−	0.400470i
$780$		0			0
$781$			95.6363i			0.122454i
$782$			916.067i			1.17144i
$783$	1250.37			1.59689
$784$	−840.429			−1.07198
$785$		0			0
$786$	698.660			0.888880
$787$			567.593i			0.721211i	0.932718	+	0.360605i	$0.117430\pi$
$787$			567.593i			0.721211i	−0.932718	+	0.360605i	$0.882570\pi$
$788$	−292.911			−0.371715
$789$		−	1654.66i		−	2.09716i
$790$		0			0
$791$		−	1670.33i		−	2.11167i
$792$		−	580.183i		−	0.732554i
$793$			455.614i			0.574544i
$794$		−	310.824i		−	0.391466i
$795$		0			0
$796$	−374.683			−0.470708
$797$		−	1174.98i		−	1.47425i	−0.675757	−	0.737124i	$-0.736183\pi$
$797$		−	1174.98i		−	1.47425i	0.675757	−	0.737124i	$-0.263817\pi$
$798$	907.698	+	2274.31i	1.13747	+	2.85001i
$799$	−843.446			−1.05563
$800$		0			0
$801$		−	3028.00i		−	3.78028i
$802$	119.061			0.148455
$803$	−87.9052			−0.109471
$804$	−26.5668			−0.0330433
$805$		0			0
$806$			309.717i			0.384265i
$807$	−1000.97			−1.24036
$808$		−	850.979i		−	1.05319i
$809$	−944.954			−1.16805			−0.584026	−	0.811735i	$-0.698523\pi$
$809$	−944.954			−1.16805			−0.584026	+	0.811735i	$0.698523\pi$
$810$		0			0
$811$			502.942i			0.620151i	0.950712	+	0.310075i	$0.100354\pi$
$811$			502.942i			0.620151i	−0.950712	+	0.310075i	$0.899646\pi$
$812$			211.693i			0.260705i
$813$			731.208i			0.899395i
$814$	−300.773			−0.369500
$815$		0			0
$816$		−	3167.98i		−	3.88233i
$817$	−487.784	−	1222.18i	−0.597043	−	1.49594i
$818$	−159.230			−0.194657
$819$			1042.70i			1.27314i
$820$		0			0
$821$	−1622.74			−1.97654			−0.988268	−	0.152732i	$-0.951193\pi$
$821$	−1622.74			−1.97654			−0.988268	+	0.152732i	$0.951193\pi$
$822$	157.234			0.191282
$823$	525.320			0.638299			0.319150	−	0.947704i	$-0.396603\pi$
$823$	525.320			0.638299			0.319150	+	0.947704i	$0.396603\pi$
$824$	42.4680			0.0515389
$825$		0			0
$826$	−703.895			−0.852173
$827$		−	1529.88i		−	1.84991i	−0.380075	−	0.924956i	$-0.624102\pi$
$827$		−	1529.88i		−	1.84991i	0.380075	−	0.924956i	$-0.375898\pi$
$828$	505.564			0.610585
$829$		−	940.737i		−	1.13479i	−0.823447	−	0.567393i	$-0.807952\pi$
$829$		−	940.737i		−	1.13479i	0.823447	−	0.567393i	$-0.192048\pi$
$830$		0			0
$831$			2435.53i			2.93084i
$832$		−	113.506i		−	0.136425i
$833$	1188.09			1.42628
$834$	−1553.43			−1.86262
$835$		0			0
$836$	−44.3226	−	111.054i	−0.0530174	−	0.132839i
$837$	−2475.95			−2.95812
$838$		−	522.586i		−	0.623611i
$839$		−	584.666i		−	0.696861i	−0.937335	−	0.348430i	$-0.886715\pi$
$839$		−	584.666i		−	0.696861i	0.937335	−	0.348430i	$-0.113285\pi$
$840$		0			0
$841$	627.428			0.746050
$842$	−483.113			−0.573769
$843$	−954.029			−1.13171
$844$			157.292i			0.186365i
$845$		0			0
$846$			1695.18i			2.00376i
$847$	992.316			1.17157
$848$		−	1075.04i		−	1.26773i
$849$		−	1270.65i		−	1.49664i
$850$		0			0
$851$			430.287i			0.505625i
$852$	199.880			0.234601
$853$	1035.83			1.21433			0.607167	−	0.794574i	$-0.292306\pi$
$853$	1035.83			1.21433			0.607167	+	0.794574i	$0.292306\pi$
$854$		−	2245.70i		−	2.62962i
$855$		0			0
$856$	752.721			0.879347
$857$			488.572i			0.570096i	0.958513	+	0.285048i	$0.0920096\pi$
$857$			488.572i			0.570096i	−0.958513	+	0.285048i	$0.907990\pi$
$858$		−	255.202i		−	0.297438i
$859$	55.9552			0.0651399			0.0325699	−	0.999469i	$-0.489631\pi$
$859$	55.9552			0.0651399			0.0325699	+	0.999469i	$0.489631\pi$
$860$		0			0
$861$	−2431.14			−2.82363
$862$	−1125.07			−1.30519
$863$		−	740.616i		−	0.858188i	−0.903260	−	0.429094i	$-0.858833\pi$
$863$		−	740.616i		−	0.858188i	0.903260	−	0.429094i	$-0.141167\pi$
$864$	−1973.06			−2.28363
$865$		0			0
$866$	−1331.16			−1.53714
$867$			2820.49i			3.25316i
$868$		−	419.189i		−	0.482936i
$869$		−	322.962i		−	0.371648i
$870$		0			0
$871$	13.9391			0.0160036
$872$	−434.376			−0.498137
$873$		−	1848.05i		−	2.11689i
$874$	−578.579	+	230.916i	−0.661990	+	0.264206i
$875$		0			0
$876$			183.722i			0.209729i
$877$			1241.85i			1.41602i	0.706204	+	0.708009i	$0.250406\pi$
$877$			1241.85i			1.41602i	−0.706204	+	0.708009i	$0.749594\pi$
$878$	−1607.54			−1.83091
$879$	218.126			0.248153
$880$		0			0
$881$	−812.952			−0.922761			−0.461380	−	0.887202i	$-0.652646\pi$
$881$	−812.952			−0.922761			−0.461380	+	0.887202i	$0.652646\pi$
$882$		−	2387.86i		−	2.70733i
$883$	−512.623			−0.580547			−0.290274	−	0.956944i	$-0.593746\pi$
$883$	−512.623			−0.580547			−0.290274	+	0.956944i	$0.593746\pi$
$884$		−	192.815i		−	0.218117i
$885$		0			0
$886$		−	1112.06i		−	1.25515i
$887$		−	600.453i		−	0.676948i	−0.940976	−	0.338474i	$-0.890089\pi$
$887$		−	600.453i		−	0.676948i	0.940976	−	0.338474i	$-0.109911\pi$
$888$		−	1032.03i		−	1.16220i
$889$		−	776.085i		−	0.872986i
$890$		0			0
$891$	1145.61			1.28576
$892$		−	103.539i		−	0.116075i
$893$	−212.610	−	532.713i	−0.238086	−	0.596543i
$894$	−2014.19			−2.25301
$895$		0			0
$896$			1441.94i			1.60930i
$897$	−365.093			−0.407015
$898$	−739.815			−0.823847
$899$	422.910			0.470422
$900$		0			0
$901$			1519.75i			1.68674i
$902$	432.319			0.479289
$903$			3801.29i			4.20962i
$904$	−1019.18			−1.12741
$905$		0			0
$906$		−	3535.49i		−	3.90231i
$907$		−	139.480i		−	0.153782i	−0.997040	−	0.0768910i	$-0.975501\pi$
$907$		−	139.480i		−	0.153782i	0.997040	−	0.0768910i	$-0.0244993\pi$
$908$		−	302.164i		−	0.332779i
$909$	3486.15			3.83515
$910$		0			0
$911$		−	897.235i		−	0.984890i	−0.870344	−	0.492445i	$-0.836103\pi$
$911$		−	897.235i		−	0.984890i	0.870344	−	0.492445i	$-0.163897\pi$
$912$	2000.87	−	798.565i	2.19393	−	0.875619i
$913$	−387.223			−0.424121
$914$		−	608.899i		−	0.666191i
$915$		0			0
$916$	114.105			0.124569
$917$	496.142			0.541049
$918$	5613.42			6.11483
$919$	−79.2393			−0.0862234			−0.0431117	−	0.999070i	$-0.513727\pi$
$919$	−79.2393			−0.0862234			−0.0431117	+	0.999070i	$0.513727\pi$
$920$		0			0
$921$	1637.89			1.77838
$922$			1600.98i			1.73642i
$923$	−104.874			−0.113623
$924$			345.404i			0.373814i
$925$		0			0
$926$			1504.93i			1.62519i
$927$			173.976i			0.187677i
$928$	337.013			0.363160
$929$	−535.116			−0.576013			−0.288007	−	0.957628i	$-0.592993\pi$
$929$	−535.116			−0.576013			−0.288007	+	0.957628i	$0.592993\pi$
$930$		0			0
$931$	299.486	+	750.387i	0.321682	+	0.806001i
$932$	15.6539			0.0167960
$933$		−	26.1147i		−	0.0279900i
$934$			334.173i			0.357787i
$935$		0			0
$936$	636.221			0.679723
$937$	−1523.13			−1.62554			−0.812768	−	0.582587i	$-0.802041\pi$
$937$	−1523.13			−1.62554			−0.812768	+	0.582587i	$0.802041\pi$
$938$	−68.7053			−0.0732466
$939$			1709.74i			1.82081i
$940$		0			0
$941$			283.647i			0.301432i	0.988577	+	0.150716i	$0.0481578\pi$
$941$			283.647i			0.301432i	−0.988577	+	0.150716i	$0.951842\pi$
$942$	−1431.75			−1.51990
$943$		−	618.477i		−	0.655861i
$944$			619.265i			0.656001i
$945$		0			0
$946$		−	675.965i		−	0.714551i
$947$	1604.67			1.69448			0.847239	−	0.531211i	$-0.178263\pi$
$947$	1604.67			1.69448			0.847239	+	0.531211i	$0.178263\pi$
$948$	−674.993			−0.712018
$949$		−	96.3958i		−	0.101576i
$950$		0			0
$951$	1027.37			1.08030
$952$		−	1560.28i		−	1.63895i
$953$		−	490.181i		−	0.514356i	−0.966364	−	0.257178i	$-0.917207\pi$
$953$		−	490.181i		−	0.514356i	0.966364	−	0.257178i	$-0.0827927\pi$
$954$	3054.44			3.20172
$955$		0			0
$956$	546.324			0.571469
$957$	−348.471			−0.364128
$958$			713.440i			0.744718i
$959$	111.657			0.116431
$960$		0			0
$961$	123.564			0.128579
$962$		−	329.824i		−	0.342853i
$963$			3083.63i			3.20211i
$964$		−	676.150i		−	0.701401i
$965$		0			0
$966$	1799.52			1.86286
$967$	−969.777			−1.00287			−0.501436	−	0.865195i	$-0.667195\pi$
$967$	−969.777			−1.00287			−0.501436	+	0.865195i	$0.667195\pi$
$968$		−	605.479i		−	0.625494i
$969$	−2828.57	+	1128.91i	−2.91906	+	1.16502i
$970$		0			0
$971$		−	521.725i		−	0.537307i	−0.963237	−	0.268653i	$-0.913421\pi$
$971$		−	521.725i		−	0.537307i	0.963237	−	0.268653i	$-0.0865786\pi$
$972$		−	1228.40i		−	1.26379i
$973$	−1103.14			−1.13375
$974$	−1.27108			−0.00130501
$975$		0			0
$976$	−1975.69			−2.02428
$977$		−	631.913i		−	0.646790i	−0.946264	−	0.323395i	$-0.895176\pi$
$977$		−	631.913i		−	0.646790i	0.946264	−	0.323395i	$-0.104824\pi$
$978$	2332.09			2.38455
$979$			526.284i			0.537573i
$980$		0			0
$981$		−	1779.48i		−	1.81395i
$982$			1087.63i			1.10757i
$983$			903.596i			0.919223i	0.888120	+	0.459611i	$0.152011\pi$
$983$			903.596i			0.919223i	−0.888120	+	0.459611i	$0.847989\pi$
$984$			1483.40i			1.50752i
$985$		0			0
$986$	−958.812			−0.972426
$987$			1656.87i			1.67869i
$988$	121.780	−	48.6036i	0.123259	−	0.0491939i
$989$	−967.038			−0.977794
$990$		0			0
$991$		−	691.185i		−	0.697462i	−0.937223	−	0.348731i	$-0.886613\pi$
$991$		−	691.185i		−	0.697462i	0.937223	−	0.348731i	$-0.113387\pi$
$992$	−667.344			−0.672726
$993$	−1893.47			−1.90681
$994$	516.917			0.520037
$995$		0			0
$996$			809.297i			0.812547i
$997$	−285.575			−0.286435			−0.143217	−	0.989691i	$-0.545745\pi$
$997$	−285.575			−0.286435			−0.143217	+	0.989691i	$0.545745\pi$
$998$			410.622i			0.411445i
$999$	2636.69			2.63932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.3.c.h.151.11	yes	14
5.2	odd	4		475.3.d.d.474.8		28
5.3	odd	4		475.3.d.d.474.21		28
5.4	even	2		475.3.c.i.151.4	yes	14
19.18	odd	2	inner	475.3.c.h.151.4	✓	14
95.18	even	4		475.3.d.d.474.7		28
95.37	even	4		475.3.d.d.474.22		28
95.94	odd	2		475.3.c.i.151.11	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.3.c.h.151.4	✓	14	19.18	odd	2	inner
475.3.c.h.151.11	yes	14	1.1	even	1	trivial
475.3.c.i.151.4	yes	14	5.4	even	2
475.3.c.i.151.11	yes	14	95.94	odd	2
475.3.d.d.474.7		28	95.18	even	4
475.3.d.d.474.8		28	5.2	odd	4
475.3.d.d.474.21		28	5.3	odd	4
475.3.d.d.474.22		28	95.37	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	475.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.34822i q^{2} +5.73703i q^{3} -1.51415 q^{4} -13.4718 q^{6} -9.56678 q^{7} +5.83734i q^{8} -23.9135 q^{9} +O(q^{10})\)	\(q+2.34822i q^{2} +5.73703i q^{3} -1.51415 q^{4} -13.4718 q^{6} -9.56678 q^{7} +5.83734i q^{8} -23.9135 q^{9} +4.15630 q^{11} -8.68670i q^{12} +4.55775i q^{13} -22.4649i q^{14} -19.7639 q^{16} +27.9397 q^{17} -56.1541i q^{18} +(7.04287 + 17.6465i) q^{19} -54.8849i q^{21} +9.75992i q^{22} +13.9626 q^{23} -33.4890 q^{24} -10.7026 q^{26} -85.5590i q^{27} +14.4855 q^{28} +14.6141i q^{29} -28.9385i q^{31} -23.0608i q^{32} +23.8448i q^{33} +65.6087i q^{34} +36.2085 q^{36} +30.8172i q^{37} +(-41.4378 + 16.5382i) q^{38} -26.1479 q^{39} -44.2953i q^{41} +128.882 q^{42} -69.2593 q^{43} -6.29325 q^{44} +32.7872i q^{46} -30.1880 q^{47} -113.386i q^{48} +42.5233 q^{49} +160.291i q^{51} -6.90110i q^{52} +54.3939i q^{53} +200.912 q^{54} -55.8445i q^{56} +(-101.238 + 40.4051i) q^{57} -34.3171 q^{58} -31.3331i q^{59} +99.9646 q^{61} +67.9540 q^{62} +228.775 q^{63} -24.9039 q^{64} -55.9929 q^{66} -3.05833i q^{67} -42.3049 q^{68} +80.1037i q^{69} +23.0099i q^{71} -139.591i q^{72} -21.1499 q^{73} -72.3655 q^{74} +(-10.6639 - 26.7193i) q^{76} -39.7625 q^{77} -61.4012i q^{78} -77.7042i q^{79} +275.633 q^{81} +104.015 q^{82} -93.1651 q^{83} +83.1038i q^{84} -162.636i q^{86} -83.8415 q^{87} +24.2617i q^{88} +126.623i q^{89} -43.6030i q^{91} -21.1414 q^{92} +166.021 q^{93} -70.8882i q^{94} +132.300 q^{96} +77.2807i q^{97} +99.8542i q^{98} -99.3917 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 28 q^{4} - 4 q^{6} - 20 q^{7} - 36 q^{9}+O(q^{10}) \) 14 * q - 28 * q^4 - 4 * q^6 - 20 * q^7 - 36 * q^9	\( 14 q - 28 q^{4} - 4 q^{6} - 20 q^{7} - 36 q^{9} - 4 q^{11} + 36 q^{16} + 22 q^{17} + 39 q^{19} + 12 q^{23} - 44 q^{24} + 30 q^{26} + 98 q^{28} + 4 q^{36} + 37 q^{38} - 32 q^{39} + 250 q^{42} + 90 q^{43} - 52 q^{44} + 148 q^{47} + 234 q^{49} + 98 q^{54} - 195 q^{57} - 274 q^{58} + 222 q^{61} + 518 q^{62} + 198 q^{63} - 218 q^{64} + 92 q^{66} + 80 q^{68} - 228 q^{73} - 92 q^{74} - 351 q^{76} - 260 q^{77} + 402 q^{81} + 58 q^{82} - 280 q^{83} - 282 q^{87} + 302 q^{92} - 358 q^{93} + 190 q^{96} - 180 q^{99}+O(q^{100}) \) 14 * q - 28 * q^4 - 4 * q^6 - 20 * q^7 - 36 * q^9 - 4 * q^11 + 36 * q^16 + 22 * q^17 + 39 * q^19 + 12 * q^23 - 44 * q^24 + 30 * q^26 + 98 * q^28 + 4 * q^36 + 37 * q^38 - 32 * q^39 + 250 * q^42 + 90 * q^43 - 52 * q^44 + 148 * q^47 + 234 * q^49 + 98 * q^54 - 195 * q^57 - 274 * q^58 + 222 * q^61 + 518 * q^62 + 198 * q^63 - 218 * q^64 + 92 * q^66 + 80 * q^68 - 228 * q^73 - 92 * q^74 - 351 * q^76 - 260 * q^77 + 402 * q^81 + 58 * q^82 - 280 * q^83 - 282 * q^87 + 302 * q^92 - 358 * q^93 + 190 * q^96 - 180 * q^99

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