LMFDB - Embedded newform 3525.2.a.bi.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 17 x^{11} + 51 x^{10} + 106 x^{9} - 316 x^{8} - 288 x^{7} + 852 x^{6} + 309 x^{5} + \cdots - 2 $ x^13 - 3x^12 - 17x^11 + 51x^10 + 106x^9 - 316x^8 - 288x^7 + 852x^6 + 309x^5 - 923x^4 - 107x^3 + 293x^2 + 12x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$1.32490$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.32490 q^{2} +1.00000 q^{3} -0.244653 q^{4} +1.32490 q^{6} +1.72082 q^{7} -2.97393 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.32490 q^{2} +1.00000 q^{3} -0.244653 q^{4} +1.32490 q^{6} +1.72082 q^{7} -2.97393 q^{8} +1.00000 q^{9} +3.57955 q^{11} -0.244653 q^{12} -3.93183 q^{13} +2.27991 q^{14} -3.45084 q^{16} -6.66126 q^{17} +1.32490 q^{18} +4.90105 q^{19} +1.72082 q^{21} +4.74252 q^{22} +3.18055 q^{23} -2.97393 q^{24} -5.20926 q^{26} +1.00000 q^{27} -0.421004 q^{28} +8.59522 q^{29} +8.88675 q^{31} +1.37586 q^{32} +3.57955 q^{33} -8.82547 q^{34} -0.244653 q^{36} +6.83266 q^{37} +6.49338 q^{38} -3.93183 q^{39} +8.76229 q^{41} +2.27991 q^{42} -4.62605 q^{43} -0.875747 q^{44} +4.21389 q^{46} +1.00000 q^{47} -3.45084 q^{48} -4.03878 q^{49} -6.66126 q^{51} +0.961933 q^{52} +1.04207 q^{53} +1.32490 q^{54} -5.11760 q^{56} +4.90105 q^{57} +11.3878 q^{58} -2.48419 q^{59} -1.98065 q^{61} +11.7740 q^{62} +1.72082 q^{63} +8.72455 q^{64} +4.74252 q^{66} +0.398498 q^{67} +1.62970 q^{68} +3.18055 q^{69} +8.09686 q^{71} -2.97393 q^{72} +14.8867 q^{73} +9.05255 q^{74} -1.19906 q^{76} +6.15976 q^{77} -5.20926 q^{78} +1.37945 q^{79} +1.00000 q^{81} +11.6091 q^{82} +3.17610 q^{83} -0.421004 q^{84} -6.12903 q^{86} +8.59522 q^{87} -10.6453 q^{88} -9.17752 q^{89} -6.76597 q^{91} -0.778131 q^{92} +8.88675 q^{93} +1.32490 q^{94} +1.37586 q^{96} -7.76972 q^{97} -5.35096 q^{98} +3.57955 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9	$ 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9} + 16 q^{11} + 17 q^{12} - 8 q^{13} - 4 q^{14} + 29 q^{16} + 12 q^{17} + 3 q^{18} + 28 q^{19} - 4 q^{21} + 6 q^{23} + 15 q^{24} + 4 q^{26} + 13 q^{27} - 20 q^{28} + 12 q^{29} + 26 q^{31} + 53 q^{32} + 16 q^{33} + 8 q^{34} + 17 q^{36} - 4 q^{37} + 2 q^{38} - 8 q^{39} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{44} + 16 q^{46} + 13 q^{47} + 29 q^{48} + 21 q^{49} + 12 q^{51} - 32 q^{52} + 6 q^{53} + 3 q^{54} + 28 q^{57} - 4 q^{58} + 34 q^{59} + 24 q^{61} + 30 q^{62} - 4 q^{63} + 13 q^{64} - 24 q^{67} + 44 q^{68} + 6 q^{69} + 20 q^{71} + 15 q^{72} - 6 q^{73} + 20 q^{74} + 66 q^{76} - 2 q^{77} + 4 q^{78} + 6 q^{79} + 13 q^{81} + 20 q^{82} + 14 q^{83} - 20 q^{84} + 48 q^{86} + 12 q^{87} - 22 q^{88} + 36 q^{89} + 4 q^{91} + 4 q^{92} + 26 q^{93} + 3 q^{94} + 53 q^{96} - 32 q^{97} - 39 q^{98} + 16 q^{99}+O(q^{100}) $ 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9 + 16 * q^11 + 17 * q^12 - 8 * q^13 - 4 * q^14 + 29 * q^16 + 12 * q^17 + 3 * q^18 + 28 * q^19 - 4 * q^21 + 6 * q^23 + 15 * q^24 + 4 * q^26 + 13 * q^27 - 20 * q^28 + 12 * q^29 + 26 * q^31 + 53 * q^32 + 16 * q^33 + 8 * q^34 + 17 * q^36 - 4 * q^37 + 2 * q^38 - 8 * q^39 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 4 * q^44 + 16 * q^46 + 13 * q^47 + 29 * q^48 + 21 * q^49 + 12 * q^51 - 32 * q^52 + 6 * q^53 + 3 * q^54 + 28 * q^57 - 4 * q^58 + 34 * q^59 + 24 * q^61 + 30 * q^62 - 4 * q^63 + 13 * q^64 - 24 * q^67 + 44 * q^68 + 6 * q^69 + 20 * q^71 + 15 * q^72 - 6 * q^73 + 20 * q^74 + 66 * q^76 - 2 * q^77 + 4 * q^78 + 6 * q^79 + 13 * q^81 + 20 * q^82 + 14 * q^83 - 20 * q^84 + 48 * q^86 + 12 * q^87 - 22 * q^88 + 36 * q^89 + 4 * q^91 + 4 * q^92 + 26 * q^93 + 3 * q^94 + 53 * q^96 - 32 * q^97 - 39 * q^98 + 16 * 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 $

$2$	1.32490	0.936842	0.468421	−	0.883505i	$-0.344823\pi$
$2$	1.32490	0.936842	0.468421	+	0.883505i	$0.344823\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.244653	−0.122327
$5$	0	0
$5$	0	0
$6$	1.32490	0.540886
$7$	1.72082	0.650409	0.325204	−	0.945644i	$-0.394567\pi$
$7$	1.72082	0.650409	0.325204	+	0.945644i	$0.394567\pi$
$8$	−2.97393	−1.05144
$9$	1.00000	0.333333
$10$	0	0
$11$	3.57955	1.07927	0.539637	−	0.841898i	$-0.318562\pi$
$11$	3.57955	1.07927	0.539637	+	0.841898i	$0.318562\pi$
$12$	−0.244653	−0.0706253
$13$	−3.93183	−1.09049	−0.545246	−	0.838276i	$-0.683564\pi$
$13$	−3.93183	−1.09049	−0.545246	+	0.838276i	$0.683564\pi$
$14$	2.27991	0.609331
$15$	0	0
$16$	−3.45084	−0.862710
$17$	−6.66126	−1.61559	−0.807796	−	0.589462i	$-0.799340\pi$
$17$	−6.66126	−1.61559	−0.807796	+	0.589462i	$0.799340\pi$
$18$	1.32490	0.312281
$19$	4.90105	1.12438	0.562189	−	0.827009i	$-0.309959\pi$
$19$	4.90105	1.12438	0.562189	+	0.827009i	$0.309959\pi$
$20$	0	0
$21$	1.72082	0.375514
$22$	4.74252	1.01111
$23$	3.18055	0.663190	0.331595	−	0.943422i	$-0.392413\pi$
$23$	3.18055	0.663190	0.331595	+	0.943422i	$0.392413\pi$
$24$	−2.97393	−0.607051
$25$	0	0
$26$	−5.20926	−1.02162
$27$	1.00000	0.192450
$28$	−0.421004	−0.0795623
$29$	8.59522	1.59609	0.798046	−	0.602597i	$-0.205867\pi$
$29$	8.59522	1.59609	0.798046	+	0.602597i	$0.205867\pi$
$30$	0	0
$31$	8.88675	1.59611	0.798054	−	0.602586i	$-0.205863\pi$
$31$	8.88675	1.59611	0.798054	+	0.602586i	$0.205863\pi$
$32$	1.37586	0.243220
$33$	3.57955	0.623119
$34$	−8.82547	−1.51355
$35$	0	0
$36$	−0.244653	−0.0407755
$37$	6.83266	1.12328	0.561641	−	0.827381i	$-0.310170\pi$
$37$	6.83266	1.12328	0.561641	+	0.827381i	$0.310170\pi$
$38$	6.49338	1.05337
$39$	−3.93183	−0.629596
$40$	0	0
$41$	8.76229	1.36844	0.684220	−	0.729276i	$-0.260143\pi$
$41$	8.76229	1.36844	0.684220	+	0.729276i	$0.260143\pi$
$42$	2.27991	0.351797
$43$	−4.62605	−0.705465	−0.352733	−	0.935724i	$-0.614748\pi$
$43$	−4.62605	−0.705465	−0.352733	+	0.935724i	$0.614748\pi$
$44$	−0.875747	−0.132024
$45$	0	0
$46$	4.21389	0.621305
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−3.45084	−0.498086
$49$	−4.03878	−0.576968
$50$	0	0
$51$	−6.66126	−0.932762
$52$	0.961933	0.133396
$53$	1.04207	0.143139	0.0715696	−	0.997436i	$-0.477199\pi$
$53$	1.04207	0.143139	0.0715696	+	0.997436i	$0.477199\pi$
$54$	1.32490	0.180295
$55$	0	0
$56$	−5.11760	−0.683868
$57$	4.90105	0.649160
$58$	11.3878	1.49529
$59$	−2.48419	−0.323415	−0.161707	−	0.986839i	$-0.551700\pi$
$59$	−2.48419	−0.323415	−0.161707	+	0.986839i	$0.551700\pi$
$60$	0	0
$61$	−1.98065	−0.253596	−0.126798	−	0.991929i	$-0.540470\pi$
$61$	−1.98065	−0.253596	−0.126798	+	0.991929i	$0.540470\pi$
$62$	11.7740	1.49530
$63$	1.72082	0.216803
$64$	8.72455	1.09057
$65$	0	0
$66$	4.74252	0.583764
$67$	0.398498	0.0486843	0.0243422	−	0.999704i	$-0.492251\pi$
$67$	0.398498	0.0486843	0.0243422	+	0.999704i	$0.492251\pi$
$68$	1.62970	0.197630
$69$	3.18055	0.382893
$70$	0	0
$71$	8.09686	0.960921	0.480460	−	0.877016i	$-0.340470\pi$
$71$	8.09686	0.960921	0.480460	+	0.877016i	$0.340470\pi$
$72$	−2.97393	−0.350481
$73$	14.8867	1.74236	0.871179	−	0.490965i	$-0.163356\pi$
$73$	14.8867	1.74236	0.871179	+	0.490965i	$0.163356\pi$
$74$	9.05255	1.05234
$75$	0	0
$76$	−1.19906	−0.137541
$77$	6.15976	0.701969
$78$	−5.20926	−0.589832
$79$	1.37945	0.155200	0.0776002	−	0.996985i	$-0.475274\pi$
$79$	1.37945	0.155200	0.0776002	+	0.996985i	$0.475274\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	11.6091	1.28201
$83$	3.17610	0.348622	0.174311	−	0.984691i	$-0.444230\pi$
$83$	3.17610	0.348622	0.174311	+	0.984691i	$0.444230\pi$
$84$	−0.421004	−0.0459353
$85$	0	0
$86$	−6.12903	−0.660910
$87$	8.59522	0.921504
$88$	−10.6453	−1.13479
$89$	−9.17752	−0.972815	−0.486407	−	0.873732i	$-0.661693\pi$
$89$	−9.17752	−0.972815	−0.486407	+	0.873732i	$0.661693\pi$
$90$	0	0
$91$	−6.76597	−0.709266
$92$	−0.778131	−0.0811258
$93$	8.88675	0.921513
$94$	1.32490	0.136652
$95$	0	0
$96$	1.37586	0.140423
$97$	−7.76972	−0.788895	−0.394448	−	0.918918i	$-0.629064\pi$
$97$	−7.76972	−0.788895	−0.394448	+	0.918918i	$0.629064\pi$
$98$	−5.35096	−0.540528
$99$	3.57955	0.359758
$100$	0	0
$101$	−8.93100	−0.888668	−0.444334	−	0.895861i	$-0.646560\pi$
$101$	−8.93100	−0.888668	−0.444334	+	0.895861i	$0.646560\pi$
$102$	−8.82547	−0.873851
$103$	−10.7508	−1.05931	−0.529654	−	0.848214i	$-0.677678\pi$
$103$	−10.7508	−1.05931	−0.529654	+	0.848214i	$0.677678\pi$
$104$	11.6930	1.14659
$105$	0	0
$106$	1.38063	0.134099
$107$	−14.8150	−1.43222	−0.716108	−	0.697990i	$-0.754078\pi$
$107$	−14.8150	−1.43222	−0.716108	+	0.697990i	$0.754078\pi$
$108$	−0.244653	−0.0235418
$109$	−2.57789	−0.246917	−0.123458	−	0.992350i	$-0.539399\pi$
$109$	−2.57789	−0.246917	−0.123458	+	0.992350i	$0.539399\pi$
$110$	0	0
$111$	6.83266	0.648527
$112$	−5.93827	−0.561114
$113$	17.2178	1.61971	0.809855	−	0.586630i	$-0.199546\pi$
$113$	17.2178	1.61971	0.809855	+	0.586630i	$0.199546\pi$
$114$	6.49338	0.608161
$115$	0	0
$116$	−2.10285	−0.195244
$117$	−3.93183	−0.363497
$118$	−3.29130	−0.302988
$119$	−11.4628	−1.05080
$120$	0	0
$121$	1.81315	0.164832
$122$	−2.62415	−0.237579
$123$	8.76229	0.790069
$124$	−2.17417	−0.195246
$125$	0	0
$126$	2.27991	0.203110
$127$	−16.7495	−1.48627	−0.743137	−	0.669139i	$-0.766663\pi$
$127$	−16.7495	−1.48627	−0.743137	+	0.669139i	$0.766663\pi$
$128$	8.80739	0.778471
$129$	−4.62605	−0.407301
$130$	0	0
$131$	1.52308	0.133072	0.0665360	−	0.997784i	$-0.478805\pi$
$131$	1.52308	0.133072	0.0665360	+	0.997784i	$0.478805\pi$
$132$	−0.875747	−0.0762240
$133$	8.43383	0.731306
$134$	0.527968	0.0456095
$135$	0	0
$136$	19.8101	1.69870
$137$	0.968228	0.0827213	0.0413607	−	0.999144i	$-0.486831\pi$
$137$	0.968228	0.0827213	0.0413607	+	0.999144i	$0.486831\pi$
$138$	4.21389	0.358710
$139$	13.4756	1.14298	0.571491	−	0.820608i	$-0.306365\pi$
$139$	13.4756	1.14298	0.571491	+	0.820608i	$0.306365\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	10.7275	0.900231
$143$	−14.0742	−1.17694
$144$	−3.45084	−0.287570
$145$	0	0
$146$	19.7233	1.63232
$147$	−4.03878	−0.333113
$148$	−1.67163	−0.137407
$149$	−9.94401	−0.814645	−0.407322	−	0.913284i	$-0.633537\pi$
$149$	−9.94401	−0.814645	−0.407322	+	0.913284i	$0.633537\pi$
$150$	0	0
$151$	14.0456	1.14301	0.571505	−	0.820598i	$-0.306360\pi$
$151$	14.0456	1.14301	0.571505	+	0.820598i	$0.306360\pi$
$152$	−14.5754	−1.18222
$153$	−6.66126	−0.538531
$154$	8.16103	0.657635
$155$	0	0
$156$	0.961933	0.0770163
$157$	9.24149	0.737551	0.368775	−	0.929519i	$-0.379777\pi$
$157$	9.24149	0.737551	0.368775	+	0.929519i	$0.379777\pi$
$158$	1.82763	0.145398
$159$	1.04207	0.0826414
$160$	0	0
$161$	5.47315	0.431345
$162$	1.32490	0.104094
$163$	−8.48720	−0.664768	−0.332384	−	0.943144i	$-0.607853\pi$
$163$	−8.48720	−0.664768	−0.332384	+	0.943144i	$0.607853\pi$
$164$	−2.14372	−0.167397
$165$	0	0
$166$	4.20800	0.326604
$167$	19.8121	1.53311	0.766554	−	0.642180i	$-0.221970\pi$
$167$	19.8121	1.53311	0.766554	+	0.642180i	$0.221970\pi$
$168$	−5.11760	−0.394831
$169$	2.45926	0.189174
$170$	0	0
$171$	4.90105	0.374793
$172$	1.13178	0.0862971
$173$	24.6668	1.87538	0.937691	−	0.347469i	$-0.112959\pi$
$173$	24.6668	1.87538	0.937691	+	0.347469i	$0.112959\pi$
$174$	11.3878	0.863304
$175$	0	0
$176$	−12.3524	−0.931100
$177$	−2.48419	−0.186723
$178$	−12.1592	−0.911374
$179$	−2.12720	−0.158994	−0.0794971	−	0.996835i	$-0.525331\pi$
$179$	−2.12720	−0.158994	−0.0794971	+	0.996835i	$0.525331\pi$
$180$	0	0
$181$	16.3890	1.21818	0.609092	−	0.793099i	$-0.291534\pi$
$181$	16.3890	1.21818	0.609092	+	0.793099i	$0.291534\pi$
$182$	−8.96420	−0.664470
$183$	−1.98065	−0.146414
$184$	−9.45873	−0.697307
$185$	0	0
$186$	11.7740	0.863312
$187$	−23.8443	−1.74367
$188$	−0.244653	−0.0178432
$189$	1.72082	0.125171
$190$	0	0
$191$	−1.69373	−0.122554	−0.0612770	−	0.998121i	$-0.519517\pi$
$191$	−1.69373	−0.122554	−0.0612770	+	0.998121i	$0.519517\pi$
$192$	8.72455	0.629640
$193$	−6.15701	−0.443192	−0.221596	−	0.975139i	$-0.571127\pi$
$193$	−6.15701	−0.443192	−0.221596	+	0.975139i	$0.571127\pi$
$194$	−10.2941	−0.739071
$195$	0	0
$196$	0.988099	0.0705785
$197$	−16.3325	−1.16364	−0.581821	−	0.813317i	$-0.697660\pi$
$197$	−16.3325	−1.16364	−0.581821	+	0.813317i	$0.697660\pi$
$198$	4.74252	0.337036
$199$	−16.8744	−1.19619	−0.598097	−	0.801423i	$-0.704076\pi$
$199$	−16.8744	−1.19619	−0.598097	+	0.801423i	$0.704076\pi$
$200$	0	0
$201$	0.398498	0.0281079
$202$	−11.8326	−0.832542
$203$	14.7908	1.03811
$204$	1.62970	0.114102
$205$	0	0
$206$	−14.2437	−0.992404
$207$	3.18055	0.221063
$208$	13.5681	0.940778
$209$	17.5435	1.21351
$210$	0	0
$211$	−17.8582	−1.22941	−0.614703	−	0.788758i	$-0.710724\pi$
$211$	−17.8582	−1.22941	−0.614703	+	0.788758i	$0.710724\pi$
$212$	−0.254945	−0.0175097
$213$	8.09686	0.554788
$214$	−19.6283	−1.34176
$215$	0	0
$216$	−2.97393	−0.202350
$217$	15.2925	1.03812
$218$	−3.41543	−0.231322
$219$	14.8867	1.00595
$220$	0	0
$221$	26.1909	1.76179
$222$	9.05255	0.607567
$223$	−24.1423	−1.61669	−0.808344	−	0.588710i	$-0.799636\pi$
$223$	−24.1423	−1.61669	−0.808344	+	0.588710i	$0.799636\pi$
$224$	2.36761	0.158192
$225$	0	0
$226$	22.8117	1.51741
$227$	14.8919	0.988413	0.494207	−	0.869344i	$-0.335459\pi$
$227$	14.8919	0.988413	0.494207	+	0.869344i	$0.335459\pi$
$228$	−1.19906	−0.0794095
$229$	23.5710	1.55761	0.778807	−	0.627264i	$-0.215825\pi$
$229$	23.5710	1.55761	0.778807	+	0.627264i	$0.215825\pi$
$230$	0	0
$231$	6.15976	0.405282
$232$	−25.5616	−1.67820
$233$	17.9935	1.17879	0.589397	−	0.807844i	$-0.299366\pi$
$233$	17.9935	1.17879	0.589397	+	0.807844i	$0.299366\pi$
$234$	−5.20926	−0.340540
$235$	0	0
$236$	0.607766	0.0395622
$237$	1.37945	0.0896050
$238$	−15.1870	−0.984430
$239$	−18.3015	−1.18383	−0.591914	−	0.806001i	$-0.701628\pi$
$239$	−18.3015	−1.18383	−0.591914	+	0.806001i	$0.701628\pi$
$240$	0	0
$241$	−0.0352775	−0.00227242	−0.00113621	−	0.999999i	$-0.500362\pi$
$241$	−0.0352775	−0.00227242	−0.00113621	+	0.999999i	$0.500362\pi$
$242$	2.40224	0.154422
$243$	1.00000	0.0641500
$244$	0.484571	0.0310215
$245$	0	0
$246$	11.6091	0.740170
$247$	−19.2701	−1.22613
$248$	−26.4286	−1.67822
$249$	3.17610	0.201277
$250$	0	0
$251$	11.8864	0.750264	0.375132	−	0.926971i	$-0.377597\pi$
$251$	11.8864	0.750264	0.375132	+	0.926971i	$0.377597\pi$
$252$	−0.421004	−0.0265208
$253$	11.3849	0.715764
$254$	−22.1913	−1.39240
$255$	0	0
$256$	−5.78023	−0.361264
$257$	−4.62328	−0.288392	−0.144196	−	0.989549i	$-0.546060\pi$
$257$	−4.62328	−0.288392	−0.144196	+	0.989549i	$0.546060\pi$
$258$	−6.12903	−0.381576
$259$	11.7578	0.730592
$260$	0	0
$261$	8.59522	0.532031
$262$	2.01792	0.124667
$263$	−8.40096	−0.518025	−0.259013	−	0.965874i	$-0.583397\pi$
$263$	−8.40096	−0.518025	−0.259013	+	0.965874i	$0.583397\pi$
$264$	−10.6453	−0.655174
$265$	0	0
$266$	11.1739	0.685118
$267$	−9.17752	−0.561655
$268$	−0.0974938	−0.00595538
$269$	12.9347	0.788644	0.394322	−	0.918972i	$-0.370979\pi$
$269$	12.9347	0.788644	0.394322	+	0.918972i	$0.370979\pi$
$270$	0	0
$271$	18.9185	1.14922	0.574608	−	0.818429i	$-0.305155\pi$
$271$	18.9185	1.14922	0.574608	+	0.818429i	$0.305155\pi$
$272$	22.9869	1.39379
$273$	−6.76597	−0.409495
$274$	1.28280	0.0774968
$275$	0	0
$276$	−0.778131	−0.0468380
$277$	−0.945084	−0.0567846	−0.0283923	−	0.999597i	$-0.509039\pi$
$277$	−0.945084	−0.0567846	−0.0283923	+	0.999597i	$0.509039\pi$
$278$	17.8537	1.07079
$279$	8.88675	0.532036
$280$	0	0
$281$	−13.5465	−0.808114	−0.404057	−	0.914734i	$-0.632400\pi$
$281$	−13.5465	−0.808114	−0.404057	+	0.914734i	$0.632400\pi$
$282$	1.32490	0.0788964
$283$	9.37570	0.557328	0.278664	−	0.960389i	$-0.410108\pi$
$283$	9.37570	0.557328	0.278664	+	0.960389i	$0.410108\pi$
$284$	−1.98092	−0.117546
$285$	0	0
$286$	−18.6468	−1.10261
$287$	15.0783	0.890046
$288$	1.37586	0.0810733
$289$	27.3723	1.61014
$290$	0	0
$291$	−7.76972	−0.455469
$292$	−3.64208	−0.213137
$293$	12.4775	0.728942	0.364471	−	0.931215i	$-0.381250\pi$
$293$	12.4775	0.728942	0.364471	+	0.931215i	$0.381250\pi$
$294$	−5.35096	−0.312074
$295$	0	0
$296$	−20.3198	−1.18107
$297$	3.57955	0.207706
$298$	−13.1748	−0.763194
$299$	−12.5054	−0.723204
$300$	0	0
$301$	−7.96059	−0.458841
$302$	18.6089	1.07082
$303$	−8.93100	−0.513073
$304$	−16.9127	−0.970012
$305$	0	0
$306$	−8.82547	−0.504518
$307$	−7.93479	−0.452862	−0.226431	−	0.974027i	$-0.572706\pi$
$307$	−7.93479	−0.452862	−0.226431	+	0.974027i	$0.572706\pi$
$308$	−1.50700	−0.0858695
$309$	−10.7508	−0.611591
$310$	0	0
$311$	−30.5352	−1.73149	−0.865746	−	0.500484i	$-0.833155\pi$
$311$	−30.5352	−1.73149	−0.865746	+	0.500484i	$0.833155\pi$
$312$	11.6930	0.661984
$313$	−0.794157	−0.0448884	−0.0224442	−	0.999748i	$-0.507145\pi$
$313$	−0.794157	−0.0448884	−0.0224442	+	0.999748i	$0.507145\pi$
$314$	12.2440	0.690969
$315$	0	0
$316$	−0.337487	−0.0189851
$317$	−12.2562	−0.688378	−0.344189	−	0.938900i	$-0.611846\pi$
$317$	−12.2562	−0.688378	−0.344189	+	0.938900i	$0.611846\pi$
$318$	1.38063	0.0774220
$319$	30.7670	1.72262
$320$	0	0
$321$	−14.8150	−0.826890
$322$	7.25135	0.404102
$323$	−32.6472	−1.81654
$324$	−0.244653	−0.0135918
$325$	0	0
$326$	−11.2446	−0.622783
$327$	−2.57789	−0.142558
$328$	−26.0584	−1.43884
$329$	1.72082	0.0948719
$330$	0	0
$331$	−29.6790	−1.63130	−0.815651	−	0.578544i	$-0.803621\pi$
$331$	−29.6790	−1.63130	−0.815651	+	0.578544i	$0.803621\pi$
$332$	−0.777042	−0.0426457
$333$	6.83266	0.374427
$334$	26.2490	1.43628
$335$	0	0
$336$	−5.93827	−0.323959
$337$	−33.5995	−1.83028	−0.915141	−	0.403135i	$-0.867921\pi$
$337$	−33.5995	−1.83028	−0.915141	+	0.403135i	$0.867921\pi$
$338$	3.25826	0.177226
$339$	17.2178	0.935140
$340$	0	0
$341$	31.8105	1.72264
$342$	6.49338	0.351122
$343$	−18.9958	−1.02567
$344$	13.7575	0.741757
$345$	0	0
$346$	32.6809	1.75694
$347$	−31.1032	−1.66971	−0.834853	−	0.550472i	$-0.814448\pi$
$347$	−31.1032	−1.66971	−0.834853	+	0.550472i	$0.814448\pi$
$348$	−2.10285	−0.112724
$349$	−16.5391	−0.885317	−0.442658	−	0.896690i	$-0.645965\pi$
$349$	−16.5391	−0.885317	−0.442658	+	0.896690i	$0.645965\pi$
$350$	0	0
$351$	−3.93183	−0.209865
$352$	4.92496	0.262501
$353$	−22.1981	−1.18149	−0.590744	−	0.806859i	$-0.701166\pi$
$353$	−22.1981	−1.18149	−0.590744	+	0.806859i	$0.701166\pi$
$354$	−3.29130	−0.174930
$355$	0	0
$356$	2.24531	0.119001
$357$	−11.4628	−0.606677
$358$	−2.81831	−0.148952
$359$	30.3420	1.60139	0.800693	−	0.599074i	$-0.204465\pi$
$359$	30.3420	1.60139	0.800693	+	0.599074i	$0.204465\pi$
$360$	0	0
$361$	5.02032	0.264227
$362$	21.7137	1.14125
$363$	1.81315	0.0951658
$364$	1.65531	0.0867621
$365$	0	0
$366$	−2.62415	−0.137166
$367$	5.71813	0.298484	0.149242	−	0.988801i	$-0.452317\pi$
$367$	5.71813	0.298484	0.149242	+	0.988801i	$0.452317\pi$
$368$	−10.9756	−0.572141
$369$	8.76229	0.456147
$370$	0	0
$371$	1.79321	0.0930989
$372$	−2.17417	−0.112725
$373$	8.43711	0.436857	0.218429	−	0.975853i	$-0.429907\pi$
$373$	8.43711	0.436857	0.218429	+	0.975853i	$0.429907\pi$
$374$	−31.5912	−1.63354
$375$	0	0
$376$	−2.97393	−0.153369
$377$	−33.7949	−1.74053
$378$	2.27991	0.117266
$379$	24.0426	1.23498	0.617492	−	0.786577i	$-0.288149\pi$
$379$	24.0426	1.23498	0.617492	+	0.786577i	$0.288149\pi$
$380$	0	0
$381$	−16.7495	−0.858101
$382$	−2.24401	−0.114814
$383$	−17.7302	−0.905973	−0.452986	−	0.891517i	$-0.649641\pi$
$383$	−17.7302	−0.905973	−0.452986	+	0.891517i	$0.649641\pi$
$384$	8.80739	0.449450
$385$	0	0
$386$	−8.15740	−0.415201
$387$	−4.62605	−0.235155
$388$	1.90089	0.0965028
$389$	−25.3604	−1.28582	−0.642912	−	0.765940i	$-0.722274\pi$
$389$	−25.3604	−1.28582	−0.642912	+	0.765940i	$0.722274\pi$
$390$	0	0
$391$	−21.1865	−1.07144
$392$	12.0110	0.606649
$393$	1.52308	0.0768291
$394$	−21.6388	−1.09015
$395$	0	0
$396$	−0.875747	−0.0440079
$397$	0.670952	0.0336741	0.0168370	−	0.999858i	$-0.494640\pi$
$397$	0.670952	0.0336741	0.0168370	+	0.999858i	$0.494640\pi$
$398$	−22.3568	−1.12065
$399$	8.43383	0.422220
$400$	0	0
$401$	4.72278	0.235844	0.117922	−	0.993023i	$-0.462377\pi$
$401$	4.72278	0.235844	0.117922	+	0.993023i	$0.462377\pi$
$402$	0.527968	0.0263327
$403$	−34.9412	−1.74054
$404$	2.18500	0.108708
$405$	0	0
$406$	19.5963	0.972548
$407$	24.4578	1.21233
$408$	19.8101	0.980747
$409$	6.74847	0.333690	0.166845	−	0.985983i	$-0.446642\pi$
$409$	6.74847	0.333690	0.166845	+	0.985983i	$0.446642\pi$
$410$	0	0
$411$	0.968228	0.0477592
$412$	2.63022	0.129581
$413$	−4.27485	−0.210352
$414$	4.21389	0.207102
$415$	0	0
$416$	−5.40964	−0.265230
$417$	13.4756	0.659901
$418$	23.2434	1.13687
$419$	−27.9946	−1.36763	−0.683813	−	0.729658i	$-0.739679\pi$
$419$	−27.9946	−1.36763	−0.683813	+	0.729658i	$0.739679\pi$
$420$	0	0
$421$	−4.71812	−0.229947	−0.114974	−	0.993369i	$-0.536678\pi$
$421$	−4.71812	−0.229947	−0.114974	+	0.993369i	$0.536678\pi$
$422$	−23.6602	−1.15176
$423$	1.00000	0.0486217
$424$	−3.09904	−0.150503
$425$	0	0
$426$	10.7275	0.519749
$427$	−3.40833	−0.164941
$428$	3.62452	0.175198
$429$	−14.0742	−0.679507
$430$	0	0
$431$	19.9391	0.960433	0.480217	−	0.877150i	$-0.340558\pi$
$431$	19.9391	0.960433	0.480217	+	0.877150i	$0.340558\pi$
$432$	−3.45084	−0.166029
$433$	−11.2317	−0.539759	−0.269879	−	0.962894i	$-0.586984\pi$
$433$	−11.2317	−0.539759	−0.269879	+	0.962894i	$0.586984\pi$
$434$	20.2610	0.972557
$435$	0	0
$436$	0.630688	0.0302045
$437$	15.5880	0.745677
$438$	19.7233	0.942418
$439$	−29.8530	−1.42481	−0.712404	−	0.701770i	$-0.752394\pi$
$439$	−29.8530	−1.42481	−0.712404	+	0.701770i	$0.752394\pi$
$440$	0	0
$441$	−4.03878	−0.192323
$442$	34.7002	1.65052
$443$	−27.5951	−1.31108	−0.655541	−	0.755159i	$-0.727559\pi$
$443$	−27.5951	−1.31108	−0.655541	+	0.755159i	$0.727559\pi$
$444$	−1.67163	−0.0793321
$445$	0	0
$446$	−31.9860	−1.51458
$447$	−9.94401	−0.470335
$448$	15.0134	0.709315
$449$	0.0145040	0.000684488 0	0.000342244	−	1.00000i	$-0.499891\pi$
$449$	0.0145040	0.000684488 0	0.000342244		1.00000i	$0.499891\pi$
$450$	0	0
$451$	31.3650	1.47692
$452$	−4.21238	−0.198134
$453$	14.0456	0.659918
$454$	19.7303	0.925987
$455$	0	0
$456$	−14.5754	−0.682555
$457$	38.6287	1.80697	0.903487	−	0.428616i	$-0.140999\pi$
$457$	38.6287	1.80697	0.903487	+	0.428616i	$0.140999\pi$
$458$	31.2291	1.45924
$459$	−6.66126	−0.310921
$460$	0	0
$461$	−33.0956	−1.54141	−0.770707	−	0.637190i	$-0.780097\pi$
$461$	−33.0956	−1.54141	−0.770707	+	0.637190i	$0.780097\pi$
$462$	8.16103	0.379685
$463$	4.57920	0.212814	0.106407	−	0.994323i	$-0.466065\pi$
$463$	4.57920	0.212814	0.106407	+	0.994323i	$0.466065\pi$
$464$	−29.6607	−1.37696
$465$	0	0
$466$	23.8395	1.10434
$467$	29.8815	1.38275	0.691375	−	0.722496i	$-0.257005\pi$
$467$	29.8815	1.38275	0.691375	+	0.722496i	$0.257005\pi$
$468$	0.961933	0.0444654
$469$	0.685744	0.0316647
$470$	0	0
$471$	9.24149	0.425825
$472$	7.38782	0.340052
$473$	−16.5591	−0.761390
$474$	1.82763	0.0839458
$475$	0	0
$476$	2.80442	0.128540
$477$	1.04207	0.0477130
$478$	−24.2476	−1.10906
$479$	−19.7989	−0.904635	−0.452317	−	0.891857i	$-0.649403\pi$
$479$	−19.7989	−0.904635	−0.452317	+	0.891857i	$0.649403\pi$
$480$	0	0
$481$	−26.8648	−1.22493
$482$	−0.0467389	−0.00212890
$483$	5.47315	0.249037
$484$	−0.443593	−0.0201633
$485$	0	0
$486$	1.32490	0.0600985
$487$	−8.12540	−0.368197	−0.184098	−	0.982908i	$-0.558937\pi$
$487$	−8.12540	−0.368197	−0.184098	+	0.982908i	$0.558937\pi$
$488$	5.89030	0.266641
$489$	−8.48720	−0.383804
$490$	0	0
$491$	6.60332	0.298003	0.149002	−	0.988837i	$-0.452394\pi$
$491$	6.60332	0.298003	0.149002	+	0.988837i	$0.452394\pi$
$492$	−2.14372	−0.0966465
$493$	−57.2549	−2.57863
$494$	−25.5308	−1.14869
$495$	0	0
$496$	−30.6667	−1.37698
$497$	13.9332	0.624991
$498$	4.20800	0.188565
$499$	10.0174	0.448442	0.224221	−	0.974538i	$-0.428016\pi$
$499$	10.0174	0.448442	0.224221	+	0.974538i	$0.428016\pi$
$500$	0	0
$501$	19.8121	0.885140
$502$	15.7482	0.702879
$503$	21.1010	0.940847	0.470423	−	0.882441i	$-0.344101\pi$
$503$	21.1010	0.940847	0.470423	+	0.882441i	$0.344101\pi$
$504$	−5.11760	−0.227956
$505$	0	0
$506$	15.0838	0.670558
$507$	2.45926	0.109220
$508$	4.09781	0.181811
$509$	−1.96317	−0.0870160	−0.0435080	−	0.999053i	$-0.513853\pi$
$509$	−1.96317	−0.0870160	−0.0435080	+	0.999053i	$0.513853\pi$
$510$	0	0
$511$	25.6174	1.13325
$512$	−25.2730	−1.11692
$513$	4.90105	0.216387
$514$	−6.12536	−0.270178
$515$	0	0
$516$	1.13178	0.0498237
$517$	3.57955	0.157428
$518$	15.5778	0.684450
$519$	24.6668	1.08275
$520$	0	0
$521$	42.6843	1.87003	0.935016	−	0.354605i	$-0.115385\pi$
$521$	42.6843	1.87003	0.935016	+	0.354605i	$0.115385\pi$
$522$	11.3878	0.498429
$523$	0.874906	0.0382570	0.0191285	−	0.999817i	$-0.493911\pi$
$523$	0.874906	0.0382570	0.0191285	+	0.999817i	$0.493911\pi$
$524$	−0.372626	−0.0162782
$525$	0	0
$526$	−11.1304	−0.485308
$527$	−59.1969	−2.57866
$528$	−12.3524	−0.537571
$529$	−12.8841	−0.560179
$530$	0	0
$531$	−2.48419	−0.107805
$532$	−2.06336	−0.0894581
$533$	−34.4518	−1.49227
$534$	−12.1592	−0.526182
$535$	0	0
$536$	−1.18511	−0.0511888
$537$	−2.12720	−0.0917953
$538$	17.1372	0.738835
$539$	−14.4570	−0.622707
$540$	0	0
$541$	−29.8053	−1.28143	−0.640715	−	0.767779i	$-0.721362\pi$
$541$	−29.8053	−1.28143	−0.640715	+	0.767779i	$0.721362\pi$
$542$	25.0650	1.07663
$543$	16.3890	0.703319
$544$	−9.16496	−0.392944
$545$	0	0
$546$	−8.96420	−0.383632
$547$	−17.4534	−0.746253	−0.373127	−	0.927780i	$-0.621714\pi$
$547$	−17.4534	−0.746253	−0.373127	+	0.927780i	$0.621714\pi$
$548$	−0.236880	−0.0101190
$549$	−1.98065	−0.0845319
$550$	0	0
$551$	42.1256	1.79461
$552$	−9.45873	−0.402590
$553$	2.37379	0.100944
$554$	−1.25214	−0.0531982
$555$	0	0
$556$	−3.29684	−0.139817
$557$	13.1467	0.557045	0.278523	−	0.960430i	$-0.410155\pi$
$557$	13.1467	0.557045	0.278523	+	0.960430i	$0.410155\pi$
$558$	11.7740	0.498434
$559$	18.1888	0.769305
$560$	0	0
$561$	−23.8443	−1.00671
$562$	−17.9476	−0.757075
$563$	5.85778	0.246876	0.123438	−	0.992352i	$-0.460608\pi$
$563$	5.85778	0.246876	0.123438	+	0.992352i	$0.460608\pi$
$564$	−0.244653	−0.0103018
$565$	0	0
$566$	12.4218	0.522128
$567$	1.72082	0.0722677
$568$	−24.0795	−1.01035
$569$	45.7303	1.91712	0.958558	−	0.284899i	$-0.0919601\pi$
$569$	45.7303	1.91712	0.958558	+	0.284899i	$0.0919601\pi$
$570$	0	0
$571$	−36.3944	−1.52306	−0.761529	−	0.648131i	$-0.775551\pi$
$571$	−36.3944	−1.52306	−0.761529	+	0.648131i	$0.775551\pi$
$572$	3.44329	0.143971
$573$	−1.69373	−0.0707566
$574$	19.9772	0.833832
$575$	0	0
$576$	8.72455	0.363523
$577$	−5.81554	−0.242104	−0.121052	−	0.992646i	$-0.538627\pi$
$577$	−5.81554	−0.242104	−0.121052	+	0.992646i	$0.538627\pi$
$578$	36.2655	1.50844
$579$	−6.15701	−0.255877
$580$	0	0
$581$	5.46549	0.226747
$582$	−10.2941	−0.426703
$583$	3.73013	0.154486
$584$	−44.2720	−1.83199
$585$	0	0
$586$	16.5314	0.682904
$587$	34.2619	1.41414	0.707069	−	0.707144i	$-0.250017\pi$
$587$	34.2619	1.41414	0.707069	+	0.707144i	$0.250017\pi$
$588$	0.988099	0.0407485
$589$	43.5544	1.79463
$590$	0	0
$591$	−16.3325	−0.671829
$592$	−23.5784	−0.969066
$593$	14.4349	0.592769	0.296384	−	0.955069i	$-0.404219\pi$
$593$	14.4349	0.592769	0.296384	+	0.955069i	$0.404219\pi$
$594$	4.74252	0.194588
$595$	0	0
$596$	2.43283	0.0996527
$597$	−16.8744	−0.690623
$598$	−16.5683	−0.677528
$599$	7.81197	0.319188	0.159594	−	0.987183i	$-0.448981\pi$
$599$	7.81197	0.319188	0.159594	+	0.987183i	$0.448981\pi$
$600$	0	0
$601$	23.5792	0.961817	0.480908	−	0.876771i	$-0.340307\pi$
$601$	23.5792	0.961817	0.480908	+	0.876771i	$0.340307\pi$
$602$	−10.5470	−0.429862
$603$	0.398498	0.0162281
$604$	−3.43629	−0.139821
$605$	0	0
$606$	−11.8326	−0.480668
$607$	0.252862	0.0102634	0.00513168	−	0.999987i	$-0.498367\pi$
$607$	0.252862	0.0102634	0.00513168	+	0.999987i	$0.498367\pi$
$608$	6.74316	0.273471
$609$	14.7908	0.599354
$610$	0	0
$611$	−3.93183	−0.159065
$612$	1.62970	0.0658766
$613$	−44.6432	−1.80312	−0.901560	−	0.432653i	$-0.857577\pi$
$613$	−44.6432	−1.80312	−0.901560	+	0.432653i	$0.857577\pi$
$614$	−10.5128	−0.424261
$615$	0	0
$616$	−18.3187	−0.738081
$617$	−10.8385	−0.436343	−0.218171	−	0.975910i	$-0.570009\pi$
$617$	−10.8385	−0.436343	−0.218171	+	0.975910i	$0.570009\pi$
$618$	−14.2437	−0.572965
$619$	11.7930	0.473999	0.237000	−	0.971510i	$-0.423836\pi$
$619$	11.7930	0.473999	0.237000	+	0.971510i	$0.423836\pi$
$620$	0	0
$621$	3.18055	0.127631
$622$	−40.4559	−1.62213
$623$	−15.7929	−0.632727
$624$	13.5681	0.543159
$625$	0	0
$626$	−1.05217	−0.0420534
$627$	17.5435	0.700622
$628$	−2.26096	−0.0902221
$629$	−45.5141	−1.81476
$630$	0	0
$631$	−23.1228	−0.920505	−0.460253	−	0.887788i	$-0.652241\pi$
$631$	−23.1228	−0.920505	−0.460253	+	0.887788i	$0.652241\pi$
$632$	−4.10239	−0.163184
$633$	−17.8582	−0.709798
$634$	−16.2382	−0.644901
$635$	0	0
$636$	−0.254945	−0.0101092
$637$	15.8798	0.629180
$638$	40.7630	1.61382
$639$	8.09686	0.320307
$640$	0	0
$641$	−19.3572	−0.764564	−0.382282	−	0.924046i	$-0.624862\pi$
$641$	−19.3572	−0.764564	−0.382282	+	0.924046i	$0.624862\pi$
$642$	−19.6283	−0.774665
$643$	3.44971	0.136043	0.0680216	−	0.997684i	$-0.478331\pi$
$643$	3.44971	0.136043	0.0680216	+	0.997684i	$0.478331\pi$
$644$	−1.33902	−0.0527649
$645$	0	0
$646$	−43.2541	−1.70181
$647$	26.6979	1.04960	0.524801	−	0.851225i	$-0.324140\pi$
$647$	26.6979	1.04960	0.524801	+	0.851225i	$0.324140\pi$
$648$	−2.97393	−0.116827
$649$	−8.89229	−0.349053
$650$	0	0
$651$	15.2925	0.599360
$652$	2.07642	0.0813188
$653$	28.8587	1.12933	0.564665	−	0.825320i	$-0.309005\pi$
$653$	28.8587	1.12933	0.564665	+	0.825320i	$0.309005\pi$
$654$	−3.41543	−0.133554
$655$	0	0
$656$	−30.2373	−1.18057
$657$	14.8867	0.580786
$658$	2.27991	0.0888800
$659$	44.8655	1.74771	0.873855	−	0.486187i	$-0.161612\pi$
$659$	44.8655	1.74771	0.873855	+	0.486187i	$0.161612\pi$
$660$	0	0
$661$	−22.7311	−0.884138	−0.442069	−	0.896981i	$-0.645755\pi$
$661$	−22.7311	−0.884138	−0.442069	+	0.896981i	$0.645755\pi$
$662$	−39.3215	−1.52827
$663$	26.1909	1.01717
$664$	−9.44549	−0.366556
$665$	0	0
$666$	9.05255	0.350779
$667$	27.3375	1.05851
$668$	−4.84710	−0.187540
$669$	−24.1423	−0.933395
$670$	0	0
$671$	−7.08981	−0.273699
$672$	2.36761	0.0913325
$673$	−22.9214	−0.883555	−0.441777	−	0.897125i	$-0.645652\pi$
$673$	−22.9214	−0.883555	−0.441777	+	0.897125i	$0.645652\pi$
$674$	−44.5158	−1.71468
$675$	0	0
$676$	−0.601665	−0.0231410
$677$	12.3019	0.472802	0.236401	−	0.971656i	$-0.424032\pi$
$677$	12.3019	0.472802	0.236401	+	0.971656i	$0.424032\pi$
$678$	22.8117	0.876079
$679$	−13.3703	−0.513105
$680$	0	0
$681$	14.8919	0.570661
$682$	42.1456	1.61384
$683$	−14.6365	−0.560049	−0.280025	−	0.959993i	$-0.590343\pi$
$683$	−14.6365	−0.560049	−0.280025	+	0.959993i	$0.590343\pi$
$684$	−1.19906	−0.0458471
$685$	0	0
$686$	−25.1674	−0.960895
$687$	23.5710	0.899289
$688$	15.9637	0.608612
$689$	−4.09723	−0.156092
$690$	0	0
$691$	−9.76820	−0.371600	−0.185800	−	0.982588i	$-0.559488\pi$
$691$	−9.76820	−0.371600	−0.185800	+	0.982588i	$0.559488\pi$
$692$	−6.03481	−0.229409
$693$	6.15976	0.233990
$694$	−41.2085	−1.56425
$695$	0	0
$696$	−25.5616	−0.968909
$697$	−58.3679	−2.21084
$698$	−21.9125	−0.829402
$699$	17.9935	0.680577
$700$	0	0
$701$	−32.8337	−1.24011	−0.620056	−	0.784558i	$-0.712890\pi$
$701$	−32.8337	−1.24011	−0.620056	+	0.784558i	$0.712890\pi$
$702$	−5.20926	−0.196611
$703$	33.4872	1.26299
$704$	31.2299	1.17702
$705$	0	0
$706$	−29.4102	−1.10687
$707$	−15.3686	−0.577997
$708$	0.607766	0.0228412
$709$	−24.5644	−0.922536	−0.461268	−	0.887261i	$-0.652605\pi$
$709$	−24.5644	−0.922536	−0.461268	+	0.887261i	$0.652605\pi$
$710$	0	0
$711$	1.37945	0.0517335
$712$	27.2933	1.02286
$713$	28.2647	1.05852
$714$	−15.1870	−0.568361
$715$	0	0
$716$	0.520425	0.0194492
$717$	−18.3015	−0.683484
$718$	40.1999	1.50025
$719$	27.7530	1.03501	0.517506	−	0.855680i	$-0.326861\pi$
$719$	27.7530	1.03501	0.517506	+	0.855680i	$0.326861\pi$
$720$	0	0
$721$	−18.5002	−0.688983
$722$	6.65140	0.247539
$723$	−0.0352775	−0.00131198
$724$	−4.00962	−0.149016
$725$	0	0
$726$	2.40224	0.0891553
$727$	−31.4271	−1.16557	−0.582783	−	0.812628i	$-0.698036\pi$
$727$	−31.4271	−1.16557	−0.582783	+	0.812628i	$0.698036\pi$
$728$	20.1215	0.745753
$729$	1.00000	0.0370370
$730$	0	0
$731$	30.8153	1.13974
$732$	0.484571	0.0179103
$733$	−13.9078	−0.513696	−0.256848	−	0.966452i	$-0.582684\pi$
$733$	−13.9078	−0.513696	−0.256848	+	0.966452i	$0.582684\pi$
$734$	7.57592	0.279632
$735$	0	0
$736$	4.37599	0.161301
$737$	1.42644	0.0525437
$738$	11.6091	0.427338
$739$	−21.4649	−0.789597	−0.394799	−	0.918768i	$-0.629186\pi$
$739$	−21.4649	−0.789597	−0.394799	+	0.918768i	$0.629186\pi$
$740$	0	0
$741$	−19.2701	−0.707904
$742$	2.37582	0.0872190
$743$	1.53026	0.0561399	0.0280700	−	0.999606i	$-0.491064\pi$
$743$	1.53026	0.0561399	0.0280700	+	0.999606i	$0.491064\pi$
$744$	−26.4286	−0.968918
$745$	0	0
$746$	11.1783	0.409266
$747$	3.17610	0.116207
$748$	5.83358	0.213297
$749$	−25.4939	−0.931526
$750$	0	0
$751$	−46.1716	−1.68482	−0.842412	−	0.538834i	$-0.818865\pi$
$751$	−46.1716	−1.68482	−0.842412	+	0.538834i	$0.818865\pi$
$752$	−3.45084	−0.125839
$753$	11.8864	0.433165
$754$	−44.7747	−1.63060
$755$	0	0
$756$	−0.421004	−0.0153118
$757$	−27.6091	−1.00347	−0.501735	−	0.865021i	$-0.667305\pi$
$757$	−27.6091	−1.00347	−0.501735	+	0.865021i	$0.667305\pi$
$758$	31.8539	1.15699
$759$	11.3849	0.413246
$760$	0	0
$761$	−8.29745	−0.300782	−0.150391	−	0.988627i	$-0.548053\pi$
$761$	−8.29745	−0.300782	−0.150391	+	0.988627i	$0.548053\pi$
$762$	−22.1913	−0.803905
$763$	−4.43608	−0.160597
$764$	0.414376	0.0149916
$765$	0	0
$766$	−23.4907	−0.848754
$767$	9.76742	0.352681
$768$	−5.78023	−0.208576
$769$	−45.8484	−1.65333	−0.826667	−	0.562691i	$-0.809766\pi$
$769$	−45.8484	−1.65333	−0.826667	+	0.562691i	$0.809766\pi$
$770$	0	0
$771$	−4.62328	−0.166503
$772$	1.50633	0.0542141
$773$	14.7944	0.532118	0.266059	−	0.963957i	$-0.414278\pi$
$773$	14.7944	0.532118	0.266059	+	0.963957i	$0.414278\pi$
$774$	−6.12903	−0.220303
$775$	0	0
$776$	23.1066	0.829478
$777$	11.7578	0.421808
$778$	−33.5999	−1.20462
$779$	42.9445	1.53865
$780$	0	0
$781$	28.9831	1.03710
$782$	−28.0698	−1.00377
$783$	8.59522	0.307168
$784$	13.9372	0.497756
$785$	0	0
$786$	2.01792	0.0719768
$787$	7.84922	0.279795	0.139897	−	0.990166i	$-0.455323\pi$
$787$	7.84922	0.279795	0.139897	+	0.990166i	$0.455323\pi$
$788$	3.99580	0.142344
$789$	−8.40096	−0.299082
$790$	0	0
$791$	29.6287	1.05347
$792$	−10.6453	−0.378265
$793$	7.78755	0.276544
$794$	0.888940	0.0315473
$795$	0	0
$796$	4.12838	0.146326
$797$	22.4134	0.793923	0.396961	−	0.917835i	$-0.370065\pi$
$797$	22.4134	0.793923	0.396961	+	0.917835i	$0.370065\pi$
$798$	11.1739	0.395553
$799$	−6.66126	−0.235658
$800$	0	0
$801$	−9.17752	−0.324272
$802$	6.25719	0.220949
$803$	53.2877	1.88048
$804$	−0.0974938	−0.00343834
$805$	0	0
$806$	−46.2934	−1.63061
$807$	12.9347	0.455324
$808$	26.5602	0.934384
$809$	48.4038	1.70179	0.850894	−	0.525338i	$-0.176061\pi$
$809$	48.4038	1.70179	0.850894	+	0.525338i	$0.176061\pi$
$810$	0	0
$811$	15.1666	0.532572	0.266286	−	0.963894i	$-0.414203\pi$
$811$	15.1666	0.532572	0.266286	+	0.963894i	$0.414203\pi$
$812$	−3.61862	−0.126989
$813$	18.9185	0.663500
$814$	32.4040	1.13576
$815$	0	0
$816$	22.9869	0.804703
$817$	−22.6725	−0.793210
$818$	8.94101	0.312615
$819$	−6.76597	−0.236422
$820$	0	0
$821$	−56.4030	−1.96848	−0.984240	−	0.176840i	$-0.943412\pi$
$821$	−56.4030	−1.96848	−0.984240	+	0.176840i	$0.943412\pi$
$822$	1.28280	0.0447428
$823$	45.5549	1.58794	0.793971	−	0.607955i	$-0.208010\pi$
$823$	45.5549	1.58794	0.793971	+	0.607955i	$0.208010\pi$
$824$	31.9721	1.11380
$825$	0	0
$826$	−5.66373	−0.197066
$827$	24.0051	0.834741	0.417370	−	0.908737i	$-0.362952\pi$
$827$	24.0051	0.834741	0.417370	+	0.908737i	$0.362952\pi$
$828$	−0.778131	−0.0270419
$829$	13.8097	0.479631	0.239815	−	0.970818i	$-0.422913\pi$
$829$	13.8097	0.479631	0.239815	+	0.970818i	$0.422913\pi$
$830$	0	0
$831$	−0.945084	−0.0327846
$832$	−34.3034	−1.18926
$833$	26.9033	0.932145
$834$	17.8537	0.618223
$835$	0	0
$836$	−4.29208	−0.148445
$837$	8.88675	0.307171
$838$	−37.0899	−1.28125
$839$	10.9580	0.378312	0.189156	−	0.981947i	$-0.439425\pi$
$839$	10.9580	0.378312	0.189156	+	0.981947i	$0.439425\pi$
$840$	0	0
$841$	44.8778	1.54751
$842$	−6.25102	−0.215424
$843$	−13.5465	−0.466565
$844$	4.36905	0.150389
$845$	0	0
$846$	1.32490	0.0455508
$847$	3.12011	0.107208
$848$	−3.59601	−0.123487
$849$	9.37570	0.321773
$850$	0	0
$851$	21.7316	0.744949
$852$	−1.98092	−0.0678653
$853$	43.9890	1.50615	0.753077	−	0.657932i	$-0.228569\pi$
$853$	43.9890	1.50615	0.753077	+	0.657932i	$0.228569\pi$
$854$	−4.51569	−0.154524
$855$	0	0
$856$	44.0586	1.50589
$857$	19.3253	0.660138	0.330069	−	0.943957i	$-0.392928\pi$
$857$	19.3253	0.660138	0.330069	+	0.943957i	$0.392928\pi$
$858$	−18.6468	−0.636591
$859$	22.4739	0.766800	0.383400	−	0.923582i	$-0.374753\pi$
$859$	22.4739	0.766800	0.383400	+	0.923582i	$0.374753\pi$
$860$	0	0
$861$	15.0783	0.513868
$862$	26.4172	0.899774
$863$	−20.9239	−0.712258	−0.356129	−	0.934437i	$-0.615904\pi$
$863$	−20.9239	−0.712258	−0.356129	+	0.934437i	$0.615904\pi$
$864$	1.37586	0.0468077
$865$	0	0
$866$	−14.8808	−0.505669
$867$	27.3723	0.929613
$868$	−3.74136	−0.126990
$869$	4.93781	0.167504
$870$	0	0
$871$	−1.56683	−0.0530899
$872$	7.66646	0.259619
$873$	−7.76972	−0.262965
$874$	20.6525	0.698582
$875$	0	0
$876$	−3.64208	−0.123055
$877$	20.8412	0.703758	0.351879	−	0.936045i	$-0.385543\pi$
$877$	20.8412	0.703758	0.351879	+	0.936045i	$0.385543\pi$
$878$	−39.5521	−1.33482
$879$	12.4775	0.420855
$880$	0	0
$881$	28.8102	0.970640	0.485320	−	0.874337i	$-0.338703\pi$
$881$	28.8102	0.970640	0.485320	+	0.874337i	$0.338703\pi$
$882$	−5.35096	−0.180176
$883$	−20.9425	−0.704770	−0.352385	−	0.935855i	$-0.614629\pi$
$883$	−20.9425	−0.704770	−0.352385	+	0.935855i	$0.614629\pi$
$884$	−6.40769	−0.215514
$885$	0	0
$886$	−36.5606	−1.22828
$887$	57.9503	1.94578	0.972890	−	0.231269i	$-0.0742877\pi$
$887$	57.9503	1.94578	0.972890	+	0.231269i	$0.0742877\pi$
$888$	−20.3198	−0.681889
$889$	−28.8228	−0.966686
$890$	0	0
$891$	3.57955	0.119919
$892$	5.90649	0.197764
$893$	4.90105	0.164007
$894$	−13.1748	−0.440630
$895$	0	0
$896$	15.1559	0.506324
$897$	−12.5054	−0.417542
$898$	0.0192163	0.000641258 0
$899$	76.3835	2.54753
$900$	0	0
$901$	−6.94149	−0.231254
$902$	41.5554	1.38364
$903$	−7.96059	−0.264912
$904$	−51.2044	−1.70303
$905$	0	0
$906$	18.6089	0.618239
$907$	−7.94256	−0.263728	−0.131864	−	0.991268i	$-0.542096\pi$
$907$	−7.94256	−0.263728	−0.131864	+	0.991268i	$0.542096\pi$
$908$	−3.64336	−0.120909
$909$	−8.93100	−0.296223
$910$	0	0
$911$	11.7797	0.390279	0.195140	−	0.980775i	$-0.437484\pi$
$911$	11.7797	0.390279	0.195140	+	0.980775i	$0.437484\pi$
$912$	−16.9127	−0.560037
$913$	11.3690	0.376259
$914$	51.1790	1.69285
$915$	0	0
$916$	−5.76671	−0.190538
$917$	2.62094	0.0865512
$918$	−8.82547	−0.291284
$919$	−3.42364	−0.112936	−0.0564678	−	0.998404i	$-0.517984\pi$
$919$	−3.42364	−0.112936	−0.0564678	+	0.998404i	$0.517984\pi$
$920$	0	0
$921$	−7.93479	−0.261460
$922$	−43.8481	−1.44406
$923$	−31.8355	−1.04788
$924$	−1.50700	−0.0495768
$925$	0	0
$926$	6.06696	0.199373
$927$	−10.7508	−0.353103
$928$	11.8258	0.388202
$929$	8.73527	0.286595	0.143297	−	0.989680i	$-0.454229\pi$
$929$	8.73527	0.286595	0.143297	+	0.989680i	$0.454229\pi$
$930$	0	0
$931$	−19.7943	−0.648731
$932$	−4.40216	−0.144198
$933$	−30.5352	−0.999677
$934$	39.5898	1.29542
$935$	0	0
$936$	11.6930	0.382197
$937$	−50.9852	−1.66561	−0.832807	−	0.553563i	$-0.813268\pi$
$937$	−50.9852	−1.66561	−0.832807	+	0.553563i	$0.813268\pi$
$938$	0.908539	0.0296648
$939$	−0.794157	−0.0259163
$940$	0	0
$941$	9.39351	0.306220	0.153110	−	0.988209i	$-0.451071\pi$
$941$	9.39351	0.306220	0.153110	+	0.988209i	$0.451071\pi$
$942$	12.2440	0.398931
$943$	27.8689	0.907536
$944$	8.57255	0.279013
$945$	0	0
$946$	−21.9391	−0.713303
$947$	−15.7922	−0.513178	−0.256589	−	0.966521i	$-0.582599\pi$
$947$	−15.7922	−0.513178	−0.256589	+	0.966521i	$0.582599\pi$
$948$	−0.337487	−0.0109611
$949$	−58.5320	−1.90003
$950$	0	0
$951$	−12.2562	−0.397435
$952$	34.0896	1.10485
$953$	58.1590	1.88395	0.941977	−	0.335679i	$-0.108966\pi$
$953$	58.1590	1.88395	0.941977	+	0.335679i	$0.108966\pi$
$954$	1.38063	0.0446996
$955$	0	0
$956$	4.47753	0.144814
$957$	30.7670	0.994555
$958$	−26.2315	−0.847500
$959$	1.66615	0.0538027
$960$	0	0
$961$	47.9743	1.54756
$962$	−35.5931	−1.14757
$963$	−14.8150	−0.477405
$964$	0.00863074	0.000277977 0
$965$	0	0
$966$	7.25135	0.233308
$967$	47.9801	1.54294	0.771468	−	0.636268i	$-0.219523\pi$
$967$	47.9801	1.54294	0.771468	+	0.636268i	$0.219523\pi$
$968$	−5.39219	−0.173311
$969$	−32.6472	−1.04878
$970$	0	0
$971$	33.3840	1.07134	0.535671	−	0.844427i	$-0.320059\pi$
$971$	33.3840	1.07134	0.535671	+	0.844427i	$0.320059\pi$
$972$	−0.244653	−0.00784725
$973$	23.1890	0.743405
$974$	−10.7653	−0.344942
$975$	0	0
$976$	6.83489	0.218779
$977$	4.14339	0.132559	0.0662793	−	0.997801i	$-0.478887\pi$
$977$	4.14339	0.132559	0.0662793	+	0.997801i	$0.478887\pi$
$978$	−11.2446	−0.359564
$979$	−32.8513	−1.04993
$980$	0	0
$981$	−2.57789	−0.0823056
$982$	8.74870	0.279182
$983$	−27.9452	−0.891312	−0.445656	−	0.895204i	$-0.647030\pi$
$983$	−27.9452	−0.891312	−0.445656	+	0.895204i	$0.647030\pi$
$984$	−26.0584	−0.830713
$985$	0	0
$986$	−75.8568	−2.41577
$987$	1.72082	0.0547743
$988$	4.71449	0.149988
$989$	−14.7134	−0.467858
$990$	0	0
$991$	−5.93447	−0.188515	−0.0942574	−	0.995548i	$-0.530048\pi$
$991$	−5.93447	−0.188515	−0.0942574	+	0.995548i	$0.530048\pi$
$992$	12.2269	0.388205
$993$	−29.6790	−0.941833
$994$	18.4601	0.585518
$995$	0	0
$996$	−0.777042	−0.0246215
$997$	−34.3187	−1.08688	−0.543442	−	0.839447i	$-0.682879\pi$
$997$	−34.3187	−1.08688	−0.543442	+	0.839447i	$0.682879\pi$
$998$	13.2721	0.420119
$999$	6.83266	0.216176

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bi.1.9		13
5.2	odd	4		705.2.c.c.424.19	yes	26
5.3	odd	4		705.2.c.c.424.8	✓	26
5.4	even	2		3525.2.a.bh.1.5		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.c.424.8	✓	26	5.3	odd	4
705.2.c.c.424.19	yes	26	5.2	odd	4
3525.2.a.bh.1.5		13	5.4	even	2
3525.2.a.bi.1.9		13	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+1.32490 q^{2} +1.00000 q^{3} -0.244653 q^{4} +1.32490 q^{6} +1.72082 q^{7} -2.97393 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.32490 q^{2} +1.00000 q^{3} -0.244653 q^{4} +1.32490 q^{6} +1.72082 q^{7} -2.97393 q^{8} +1.00000 q^{9} +3.57955 q^{11} -0.244653 q^{12} -3.93183 q^{13} +2.27991 q^{14} -3.45084 q^{16} -6.66126 q^{17} +1.32490 q^{18} +4.90105 q^{19} +1.72082 q^{21} +4.74252 q^{22} +3.18055 q^{23} -2.97393 q^{24} -5.20926 q^{26} +1.00000 q^{27} -0.421004 q^{28} +8.59522 q^{29} +8.88675 q^{31} +1.37586 q^{32} +3.57955 q^{33} -8.82547 q^{34} -0.244653 q^{36} +6.83266 q^{37} +6.49338 q^{38} -3.93183 q^{39} +8.76229 q^{41} +2.27991 q^{42} -4.62605 q^{43} -0.875747 q^{44} +4.21389 q^{46} +1.00000 q^{47} -3.45084 q^{48} -4.03878 q^{49} -6.66126 q^{51} +0.961933 q^{52} +1.04207 q^{53} +1.32490 q^{54} -5.11760 q^{56} +4.90105 q^{57} +11.3878 q^{58} -2.48419 q^{59} -1.98065 q^{61} +11.7740 q^{62} +1.72082 q^{63} +8.72455 q^{64} +4.74252 q^{66} +0.398498 q^{67} +1.62970 q^{68} +3.18055 q^{69} +8.09686 q^{71} -2.97393 q^{72} +14.8867 q^{73} +9.05255 q^{74} -1.19906 q^{76} +6.15976 q^{77} -5.20926 q^{78} +1.37945 q^{79} +1.00000 q^{81} +11.6091 q^{82} +3.17610 q^{83} -0.421004 q^{84} -6.12903 q^{86} +8.59522 q^{87} -10.6453 q^{88} -9.17752 q^{89} -6.76597 q^{91} -0.778131 q^{92} +8.88675 q^{93} +1.32490 q^{94} +1.37586 q^{96} -7.76972 q^{97} -5.35096 q^{98} +3.57955 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9} + 16 q^{11} + 17 q^{12} - 8 q^{13} - 4 q^{14} + 29 q^{16} + 12 q^{17} + 3 q^{18} + 28 q^{19} - 4 q^{21} + 6 q^{23} + 15 q^{24} + 4 q^{26} + 13 q^{27} - 20 q^{28} + 12 q^{29} + 26 q^{31} + 53 q^{32} + 16 q^{33} + 8 q^{34} + 17 q^{36} - 4 q^{37} + 2 q^{38} - 8 q^{39} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{44} + 16 q^{46} + 13 q^{47} + 29 q^{48} + 21 q^{49} + 12 q^{51} - 32 q^{52} + 6 q^{53} + 3 q^{54} + 28 q^{57} - 4 q^{58} + 34 q^{59} + 24 q^{61} + 30 q^{62} - 4 q^{63} + 13 q^{64} - 24 q^{67} + 44 q^{68} + 6 q^{69} + 20 q^{71} + 15 q^{72} - 6 q^{73} + 20 q^{74} + 66 q^{76} - 2 q^{77} + 4 q^{78} + 6 q^{79} + 13 q^{81} + 20 q^{82} + 14 q^{83} - 20 q^{84} + 48 q^{86} + 12 q^{87} - 22 q^{88} + 36 q^{89} + 4 q^{91} + 4 q^{92} + 26 q^{93} + 3 q^{94} + 53 q^{96} - 32 q^{97} - 39 q^{98} + 16 q^{99}+O(q^{100}) \) 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9 + 16 * q^11 + 17 * q^12 - 8 * q^13 - 4 * q^14 + 29 * q^16 + 12 * q^17 + 3 * q^18 + 28 * q^19 - 4 * q^21 + 6 * q^23 + 15 * q^24 + 4 * q^26 + 13 * q^27 - 20 * q^28 + 12 * q^29 + 26 * q^31 + 53 * q^32 + 16 * q^33 + 8 * q^34 + 17 * q^36 - 4 * q^37 + 2 * q^38 - 8 * q^39 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 4 * q^44 + 16 * q^46 + 13 * q^47 + 29 * q^48 + 21 * q^49 + 12 * q^51 - 32 * q^52 + 6 * q^53 + 3 * q^54 + 28 * q^57 - 4 * q^58 + 34 * q^59 + 24 * q^61 + 30 * q^62 - 4 * q^63 + 13 * q^64 - 24 * q^67 + 44 * q^68 + 6 * q^69 + 20 * q^71 + 15 * q^72 - 6 * q^73 + 20 * q^74 + 66 * q^76 - 2 * q^77 + 4 * q^78 + 6 * q^79 + 13 * q^81 + 20 * q^82 + 14 * q^83 - 20 * q^84 + 48 * q^86 + 12 * q^87 - 22 * q^88 + 36 * q^89 + 4 * q^91 + 4 * q^92 + 26 * q^93 + 3 * q^94 + 53 * q^96 - 32 * q^97 - 39 * q^98 + 16 * q^99

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