LMFDB - Embedded newform 3725.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3725,2,Mod(1,3725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3725, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3725.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3725 = 5^{2} \cdot 149 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3725.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:	$29.7442747529$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 15x^{7} + 12x^{6} + 75x^{5} - 48x^{4} - 137x^{3} + 76x^{2} + 68x - 39 $ x^9 - x^8 - 15x^7 + 12x^6 + 75x^5 - 48x^4 - 137x^3 + 76x^2 + 68*x - 39
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 149)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.917233$ of defining polynomial
Character	$\chi$	$=$	3725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.917233 q^{2} -1.10671 q^{3} -1.15868 q^{4} +1.01511 q^{6} -1.87253 q^{7} +2.89725 q^{8} -1.77520 q^{9} +O(q^{10})$	\(q-0.917233 q^{2} -1.10671 q^{3} -1.15868 q^{4} +1.01511 q^{6} -1.87253 q^{7} +2.89725 q^{8} -1.77520 q^{9} +0.565636 q^{11} +1.28232 q^{12} +0.286153 q^{13} +1.71755 q^{14} -0.340081 q^{16} -0.408284 q^{17} +1.62827 q^{18} -4.88410 q^{19} +2.07234 q^{21} -0.518820 q^{22} +1.65405 q^{23} -3.20641 q^{24} -0.262469 q^{26} +5.28475 q^{27} +2.16967 q^{28} -1.05763 q^{29} +0.534502 q^{31} -5.48256 q^{32} -0.625994 q^{33} +0.374491 q^{34} +2.05690 q^{36} -0.861959 q^{37} +4.47985 q^{38} -0.316688 q^{39} -4.66258 q^{41} -1.90082 q^{42} -11.5852 q^{43} -0.655394 q^{44} -1.51715 q^{46} -6.74604 q^{47} +0.376370 q^{48} -3.49363 q^{49} +0.451851 q^{51} -0.331561 q^{52} +4.36079 q^{53} -4.84734 q^{54} -5.42519 q^{56} +5.40527 q^{57} +0.970093 q^{58} -1.11518 q^{59} +6.97770 q^{61} -0.490262 q^{62} +3.32412 q^{63} +5.70895 q^{64} +0.574182 q^{66} -11.4482 q^{67} +0.473072 q^{68} -1.83055 q^{69} +5.35274 q^{71} -5.14319 q^{72} -6.70971 q^{73} +0.790617 q^{74} +5.65913 q^{76} -1.05917 q^{77} +0.290476 q^{78} +13.4604 q^{79} -0.523072 q^{81} +4.27667 q^{82} +13.9308 q^{83} -2.40119 q^{84} +10.6264 q^{86} +1.17049 q^{87} +1.63879 q^{88} -1.79226 q^{89} -0.535831 q^{91} -1.91653 q^{92} -0.591537 q^{93} +6.18769 q^{94} +6.06759 q^{96} -16.7891 q^{97} +3.20447 q^{98} -1.00412 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + q^{2} - 6 q^{3} + 13 q^{4} + q^{6} - 3 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + q^2 - 6 * q^3 + 13 * q^4 + q^6 - 3 * q^7 + 6 * q^8 + 9 * q^9	$ 9 q + q^{2} - 6 q^{3} + 13 q^{4} + q^{6} - 3 q^{7} + 6 q^{8} + 9 q^{9} + 5 q^{11} + q^{12} - 7 q^{13} - 8 q^{14} + 13 q^{16} + 5 q^{17} + 15 q^{18} + 30 q^{19} - 6 q^{21} + 7 q^{22} + 4 q^{23} - 11 q^{24} - 15 q^{26} - 15 q^{27} + 12 q^{28} - 16 q^{29} + 22 q^{31} + 38 q^{32} + 15 q^{33} + 9 q^{34} - 26 q^{36} + 7 q^{37} + 18 q^{38} - 13 q^{39} + 6 q^{41} + 11 q^{42} - 4 q^{43} + 6 q^{44} + q^{46} + 6 q^{47} + 6 q^{48} + 14 q^{49} - 11 q^{51} - 50 q^{52} + 2 q^{53} + 12 q^{54} + 7 q^{56} - 5 q^{57} - 2 q^{58} + 43 q^{59} + q^{61} - 33 q^{62} + 6 q^{63} + 18 q^{64} + 51 q^{66} - 33 q^{67} + 16 q^{68} - 14 q^{69} + 15 q^{71} - 3 q^{72} + 11 q^{73} + 33 q^{74} + 59 q^{76} + 30 q^{77} + 21 q^{78} + q^{79} + q^{81} - 5 q^{82} + 4 q^{83} + 24 q^{84} - 7 q^{86} - 17 q^{87} + 37 q^{88} - 19 q^{89} + 62 q^{91} - 17 q^{92} - 3 q^{93} + 17 q^{94} - 43 q^{96} + q^{97} - 36 q^{98} + q^{99}+O(q^{100}) $ 9 * q + q^2 - 6 * q^3 + 13 * q^4 + q^6 - 3 * q^7 + 6 * q^8 + 9 * q^9 + 5 * q^11 + q^12 - 7 * q^13 - 8 * q^14 + 13 * q^16 + 5 * q^17 + 15 * q^18 + 30 * q^19 - 6 * q^21 + 7 * q^22 + 4 * q^23 - 11 * q^24 - 15 * q^26 - 15 * q^27 + 12 * q^28 - 16 * q^29 + 22 * q^31 + 38 * q^32 + 15 * q^33 + 9 * q^34 - 26 * q^36 + 7 * q^37 + 18 * q^38 - 13 * q^39 + 6 * q^41 + 11 * q^42 - 4 * q^43 + 6 * q^44 + q^46 + 6 * q^47 + 6 * q^48 + 14 * q^49 - 11 * q^51 - 50 * q^52 + 2 * q^53 + 12 * q^54 + 7 * q^56 - 5 * q^57 - 2 * q^58 + 43 * q^59 + q^61 - 33 * q^62 + 6 * q^63 + 18 * q^64 + 51 * q^66 - 33 * q^67 + 16 * q^68 - 14 * q^69 + 15 * q^71 - 3 * q^72 + 11 * q^73 + 33 * q^74 + 59 * q^76 + 30 * q^77 + 21 * q^78 + q^79 + q^81 - 5 * q^82 + 4 * q^83 + 24 * q^84 - 7 * q^86 - 17 * q^87 + 37 * q^88 - 19 * q^89 + 62 * q^91 - 17 * q^92 - 3 * q^93 + 17 * q^94 - 43 * q^96 + q^97 - 36 * q^98 + 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 $

$2$	−0.917233	−0.648581	−0.324291	−	0.945957i	$-0.605126\pi$
$2$	−0.917233	−0.648581	−0.324291	+	0.945957i	$0.605126\pi$
$3$	−1.10671	−0.638958	−0.319479	−	0.947593i	$-0.603508\pi$
$3$	−1.10671	−0.638958	−0.319479	+	0.947593i	$0.603508\pi$
$4$	−1.15868	−0.579342
$5$	0	0
$5$	0	0
$6$	1.01511	0.414416
$7$	−1.87253	−0.707750	−0.353875	−	0.935293i	$-0.615136\pi$
$7$	−1.87253	−0.707750	−0.353875	+	0.935293i	$0.615136\pi$
$8$	2.89725	1.02433
$9$	−1.77520	−0.591733
$10$	0	0
$11$	0.565636	0.170546	0.0852729	−	0.996358i	$-0.472824\pi$
$11$	0.565636	0.170546	0.0852729	+	0.996358i	$0.472824\pi$
$12$	1.28232	0.370175
$13$	0.286153	0.0793646	0.0396823	−	0.999212i	$-0.487365\pi$
$13$	0.286153	0.0793646	0.0396823	+	0.999212i	$0.487365\pi$
$14$	1.71755	0.459034
$15$	0	0
$16$	−0.340081	−0.0850203
$17$	−0.408284	−0.0990234	−0.0495117	−	0.998774i	$-0.515767\pi$
$17$	−0.408284	−0.0990234	−0.0495117	+	0.998774i	$0.515767\pi$
$18$	1.62827	0.383787
$19$	−4.88410	−1.12049	−0.560244	−	0.828327i	$-0.689293\pi$
$19$	−4.88410	−1.12049	−0.560244	+	0.828327i	$0.689293\pi$
$20$	0	0
$21$	2.07234	0.452223
$22$	−0.518820	−0.110613
$23$	1.65405	0.344894	0.172447	−	0.985019i	$-0.444833\pi$
$23$	1.65405	0.344894	0.172447	+	0.985019i	$0.444833\pi$
$24$	−3.20641	−0.654505
$25$	0	0
$26$	−0.262469	−0.0514744
$27$	5.28475	1.01705
$28$	2.16967	0.410030
$29$	−1.05763	−0.196397	−0.0981986	−	0.995167i	$-0.531308\pi$
$29$	−1.05763	−0.196397	−0.0981986	+	0.995167i	$0.531308\pi$
$30$	0	0
$31$	0.534502	0.0959993	0.0479997	−	0.998847i	$-0.484715\pi$
$31$	0.534502	0.0959993	0.0479997	+	0.998847i	$0.484715\pi$
$32$	−5.48256	−0.969189
$33$	−0.625994	−0.108972
$34$	0.374491	0.0642247
$35$	0	0
$36$	2.05690	0.342816
$37$	−0.861959	−0.141705	−0.0708526	−	0.997487i	$-0.522572\pi$
$37$	−0.861959	−0.141705	−0.0708526	+	0.997487i	$0.522572\pi$
$38$	4.47985	0.726728
$39$	−0.316688	−0.0507107
$40$	0	0
$41$	−4.66258	−0.728173	−0.364087	−	0.931365i	$-0.618619\pi$
$41$	−4.66258	−0.728173	−0.364087	+	0.931365i	$0.618619\pi$
$42$	−1.90082	−0.293303
$43$	−11.5852	−1.76673	−0.883366	−	0.468684i	$-0.844728\pi$
$43$	−11.5852	−1.76673	−0.883366	+	0.468684i	$0.844728\pi$
$44$	−0.655394	−0.0988044
$45$	0	0
$46$	−1.51715	−0.223692
$47$	−6.74604	−0.984012	−0.492006	−	0.870592i	$-0.663736\pi$
$47$	−6.74604	−0.984012	−0.492006	+	0.870592i	$0.663736\pi$
$48$	0.376370	0.0543244
$49$	−3.49363	−0.499090
$50$	0	0
$51$	0.451851	0.0632718
$52$	−0.331561	−0.0459793
$53$	4.36079	0.599001	0.299501	−	0.954096i	$-0.403180\pi$
$53$	4.36079	0.599001	0.299501	+	0.954096i	$0.403180\pi$
$54$	−4.84734	−0.659640
$55$	0	0
$56$	−5.42519	−0.724971
$57$	5.40527	0.715945
$58$	0.970093	0.127380
$59$	−1.11518	−0.145183	−0.0725917	−	0.997362i	$-0.523127\pi$
$59$	−1.11518	−0.145183	−0.0725917	+	0.997362i	$0.523127\pi$
$60$	0	0
$61$	6.97770	0.893403	0.446702	−	0.894683i	$-0.352599\pi$
$61$	6.97770	0.893403	0.446702	+	0.894683i	$0.352599\pi$
$62$	−0.490262	−0.0622634
$63$	3.32412	0.418799
$64$	5.70895	0.713618
$65$	0	0
$66$	0.574182	0.0706769
$67$	−11.4482	−1.39863	−0.699313	−	0.714816i	$-0.746511\pi$
$67$	−11.4482	−1.39863	−0.699313	+	0.714816i	$0.746511\pi$
$68$	0.473072	0.0573684
$69$	−1.83055	−0.220373
$70$	0	0
$71$	5.35274	0.635254	0.317627	−	0.948216i	$-0.397114\pi$
$71$	5.35274	0.635254	0.317627	+	0.948216i	$0.397114\pi$
$72$	−5.14319	−0.606131
$73$	−6.70971	−0.785312	−0.392656	−	0.919685i	$-0.628444\pi$
$73$	−6.70971	−0.785312	−0.392656	+	0.919685i	$0.628444\pi$
$74$	0.790617	0.0919074
$75$	0	0
$76$	5.65913	0.649146
$77$	−1.05917	−0.120704
$78$	0.290476	0.0328900
$79$	13.4604	1.51441	0.757205	−	0.653177i	$-0.226564\pi$
$79$	13.4604	1.51441	0.757205	+	0.653177i	$0.226564\pi$
$80$	0	0
$81$	−0.523072	−0.0581191
$82$	4.27667	0.472280
$83$	13.9308	1.52910	0.764551	−	0.644564i	$-0.222961\pi$
$83$	13.9308	1.52910	0.764551	+	0.644564i	$0.222961\pi$
$84$	−2.40119	−0.261992
$85$	0	0
$86$	10.6264	1.14587
$87$	1.17049	0.125489
$88$	1.63879	0.174695
$89$	−1.79226	−0.189979	−0.0949896	−	0.995478i	$-0.530282\pi$
$89$	−1.79226	−0.189979	−0.0949896	+	0.995478i	$0.530282\pi$
$90$	0	0
$91$	−0.535831	−0.0561703
$92$	−1.91653	−0.199812
$93$	−0.591537	−0.0613395
$94$	6.18769	0.638212
$95$	0	0
$96$	6.06759	0.619271
$97$	−16.7891	−1.70468	−0.852339	−	0.522989i	$-0.824817\pi$
$97$	−16.7891	−1.70468	−0.852339	+	0.522989i	$0.824817\pi$
$98$	3.20447	0.323700
$99$	−1.00412	−0.100918
$100$	0	0
$101$	−17.9374	−1.78484	−0.892420	−	0.451205i	$-0.850994\pi$
$101$	−17.9374	−1.78484	−0.892420	+	0.451205i	$0.850994\pi$
$102$	−0.414452	−0.0410369
$103$	−5.51395	−0.543305	−0.271653	−	0.962395i	$-0.587570\pi$
$103$	−5.51395	−0.543305	−0.271653	+	0.962395i	$0.587570\pi$
$104$	0.829057	0.0812957
$105$	0	0
$106$	−3.99986	−0.388501
$107$	−4.19776	−0.405813	−0.202906	−	0.979198i	$-0.565039\pi$
$107$	−4.19776	−0.405813	−0.202906	+	0.979198i	$0.565039\pi$
$108$	−6.12335	−0.589220
$109$	−11.5156	−1.10300	−0.551499	−	0.834176i	$-0.685944\pi$
$109$	−11.5156	−1.10300	−0.551499	+	0.834176i	$0.685944\pi$
$110$	0	0
$111$	0.953937	0.0905437
$112$	0.636813	0.0601731
$113$	−4.67917	−0.440180	−0.220090	−	0.975480i	$-0.570635\pi$
$113$	−4.67917	−0.440180	−0.220090	+	0.975480i	$0.570635\pi$
$114$	−4.95789	−0.464348
$115$	0	0
$116$	1.22546	0.113781
$117$	−0.507979	−0.0469627
$118$	1.02288	0.0941633
$119$	0.764525	0.0700838
$120$	0	0
$121$	−10.6801	−0.970914
$122$	−6.40017	−0.579445
$123$	5.16011	0.465272
$124$	−0.619319	−0.0556165
$125$	0	0
$126$	−3.04899	−0.271625
$127$	12.3387	1.09488	0.547441	−	0.836845i	$-0.315602\pi$
$127$	12.3387	1.09488	0.547441	+	0.836845i	$0.315602\pi$
$128$	5.72869	0.506350
$129$	12.8215	1.12887
$130$	0	0
$131$	21.0350	1.83784	0.918920	−	0.394443i	$-0.129063\pi$
$131$	21.0350	1.83784	0.918920	+	0.394443i	$0.129063\pi$
$132$	0.725329	0.0631318
$133$	9.14562	0.793026
$134$	10.5007	0.907123
$135$	0	0
$136$	−1.18290	−0.101433
$137$	21.4192	1.82997	0.914985	−	0.403489i	$-0.132203\pi$
$137$	21.4192	1.82997	0.914985	+	0.403489i	$0.132203\pi$
$138$	1.67904	0.142930
$139$	1.36490	0.115769	0.0578846	−	0.998323i	$-0.481564\pi$
$139$	1.36490	0.115769	0.0578846	+	0.998323i	$0.481564\pi$
$140$	0	0
$141$	7.46590	0.628742
$142$	−4.90971	−0.412014
$143$	0.161859	0.0135353
$144$	0.603712	0.0503093
$145$	0	0
$146$	6.15436	0.509339
$147$	3.86642	0.318897
$148$	0.998739	0.0820958
$149$	1.00000	0.0819232
$149$	1.00000	0.0819232
$150$	0	0
$151$	−5.71378	−0.464981	−0.232491	−	0.972599i	$-0.574687\pi$
$151$	−5.71378	−0.464981	−0.232491	+	0.972599i	$0.574687\pi$
$152$	−14.1504	−1.14775
$153$	0.724785	0.0585954
$154$	0.971507	0.0782862
$155$	0	0
$156$	0.366941	0.0293788
$157$	−4.35818	−0.347821	−0.173910	−	0.984762i	$-0.555640\pi$
$157$	−4.35818	−0.347821	−0.173910	+	0.984762i	$0.555640\pi$
$158$	−12.3463	−0.982218
$159$	−4.82612	−0.382736
$160$	0	0
$161$	−3.09727	−0.244099
$162$	0.479778	0.0376949
$163$	−1.74339	−0.136553	−0.0682763	−	0.997666i	$-0.521750\pi$
$163$	−1.74339	−0.136553	−0.0682763	+	0.997666i	$0.521750\pi$
$164$	5.40246	0.421861
$165$	0	0
$166$	−12.7778	−0.991747
$167$	14.8082	1.14590	0.572948	−	0.819592i	$-0.305800\pi$
$167$	14.8082	1.14590	0.572948	+	0.819592i	$0.305800\pi$
$168$	6.00409	0.463226
$169$	−12.9181	−0.993701
$170$	0	0
$171$	8.67024	0.663030
$172$	13.4236	1.02354
$173$	18.1760	1.38190	0.690949	−	0.722903i	$-0.257193\pi$
$173$	18.1760	1.38190	0.690949	+	0.722903i	$0.257193\pi$
$174$	−1.07361	−0.0813901
$175$	0	0
$176$	−0.192362	−0.0144999
$177$	1.23417	0.0927661
$178$	1.64392	0.123217
$179$	−9.07690	−0.678439	−0.339220	−	0.940707i	$-0.610163\pi$
$179$	−9.07690	−0.678439	−0.339220	+	0.940707i	$0.610163\pi$
$180$	0	0
$181$	2.07446	0.154193	0.0770965	−	0.997024i	$-0.475435\pi$
$181$	2.07446	0.154193	0.0770965	+	0.997024i	$0.475435\pi$
$182$	0.491482	0.0364310
$183$	−7.72227	−0.570847
$184$	4.79221	0.353286
$185$	0	0
$186$	0.542577	0.0397837
$187$	−0.230940	−0.0168880
$188$	7.81654	0.570080
$189$	−9.89585	−0.719818
$190$	0	0
$191$	12.4374	0.899941	0.449971	−	0.893043i	$-0.351434\pi$
$191$	12.4374	0.899941	0.449971	+	0.893043i	$0.351434\pi$
$192$	−6.31813	−0.455972
$193$	8.38609	0.603644	0.301822	−	0.953364i	$-0.402405\pi$
$193$	8.38609	0.603644	0.301822	+	0.953364i	$0.402405\pi$
$194$	15.3995	1.10562
$195$	0	0
$196$	4.04801	0.289144
$197$	1.57577	0.112269	0.0561343	−	0.998423i	$-0.482122\pi$
$197$	1.57577	0.112269	0.0561343	+	0.998423i	$0.482122\pi$
$198$	0.921009	0.0654532
$199$	10.6640	0.755948	0.377974	−	0.925816i	$-0.376621\pi$
$199$	10.6640	0.755948	0.377974	+	0.925816i	$0.376621\pi$
$200$	0	0
$201$	12.6699	0.893663
$202$	16.4528	1.15761
$203$	1.98045	0.139000
$204$	−0.523553	−0.0366560
$205$	0	0
$206$	5.05757	0.352378
$207$	−2.93628	−0.204085
$208$	−0.0973154	−0.00674761
$209$	−2.76262	−0.191095
$210$	0	0
$211$	19.7462	1.35939	0.679694	−	0.733496i	$-0.262113\pi$
$211$	19.7462	1.35939	0.679694	+	0.733496i	$0.262113\pi$
$212$	−5.05279	−0.347027
$213$	−5.92392	−0.405900
$214$	3.85032	0.263203
$215$	0	0
$216$	15.3112	1.04180
$217$	−1.00087	−0.0679436
$218$	10.5625	0.715384
$219$	7.42568	0.501781
$220$	0	0
$221$	−0.116832	−0.00785896
$222$	−0.874982	−0.0587249
$223$	17.3499	1.16184	0.580918	−	0.813962i	$-0.302694\pi$
$223$	17.3499	1.16184	0.580918	+	0.813962i	$0.302694\pi$
$224$	10.2663	0.685944
$225$	0	0
$226$	4.29189	0.285492
$227$	−16.3677	−1.08636	−0.543182	−	0.839615i	$-0.682781\pi$
$227$	−16.3677	−1.08636	−0.543182	+	0.839615i	$0.682781\pi$
$228$	−6.26300	−0.414777
$229$	23.3088	1.54029	0.770145	−	0.637869i	$-0.220184\pi$
$229$	23.3088	1.54029	0.770145	+	0.637869i	$0.220184\pi$
$230$	0	0
$231$	1.17219	0.0771246
$232$	−3.06422	−0.201176
$233$	−8.61238	−0.564216	−0.282108	−	0.959383i	$-0.591034\pi$
$233$	−8.61238	−0.564216	−0.282108	+	0.959383i	$0.591034\pi$
$234$	0.465935	0.0304591
$235$	0	0
$236$	1.29214	0.0841109
$237$	−14.8967	−0.967644
$238$	−0.701247	−0.0454551
$239$	−22.1203	−1.43084	−0.715420	−	0.698694i	$-0.753765\pi$
$239$	−22.1203	−1.43084	−0.715420	+	0.698694i	$0.753765\pi$
$240$	0	0
$241$	21.0537	1.35619	0.678094	−	0.734976i	$-0.262806\pi$
$241$	21.0537	1.35619	0.678094	+	0.734976i	$0.262806\pi$
$242$	9.79609	0.629717
$243$	−15.2754	−0.979915
$244$	−8.08495	−0.517586
$245$	0	0
$246$	−4.73303	−0.301767
$247$	−1.39760	−0.0889272
$248$	1.54858	0.0983352
$249$	−15.4173	−0.977031
$250$	0	0
$251$	−3.36484	−0.212387	−0.106193	−	0.994346i	$-0.533866\pi$
$251$	−3.36484	−0.212387	−0.106193	+	0.994346i	$0.533866\pi$
$252$	−3.85160	−0.242628
$253$	0.935593	0.0588202
$254$	−11.3174	−0.710119
$255$	0	0
$256$	−16.6724	−1.04203
$257$	−2.77532	−0.173120	−0.0865598	−	0.996247i	$-0.527587\pi$
$257$	−2.77532	−0.173120	−0.0865598	+	0.996247i	$0.527587\pi$
$258$	−11.7603	−0.732162
$259$	1.61405	0.100292
$260$	0	0
$261$	1.87751	0.116215
$262$	−19.2940	−1.19199
$263$	9.38711	0.578834	0.289417	−	0.957203i	$-0.406539\pi$
$263$	9.38711	0.578834	0.289417	+	0.957203i	$0.406539\pi$
$264$	−1.81366	−0.111623
$265$	0	0
$266$	−8.38866	−0.514342
$267$	1.98351	0.121389
$268$	13.2649	0.810283
$269$	20.9968	1.28020	0.640099	−	0.768292i	$-0.278893\pi$
$269$	20.9968	1.28020	0.640099	+	0.768292i	$0.278893\pi$
$270$	0	0
$271$	3.05773	0.185744	0.0928718	−	0.995678i	$-0.470395\pi$
$271$	3.05773	0.185744	0.0928718	+	0.995678i	$0.470395\pi$
$272$	0.138850	0.00841900
$273$	0.593008	0.0358905
$274$	−19.6464	−1.18688
$275$	0	0
$276$	2.12103	0.127671
$277$	20.7336	1.24576	0.622880	−	0.782317i	$-0.285963\pi$
$277$	20.7336	1.24576	0.622880	+	0.782317i	$0.285963\pi$
$278$	−1.25193	−0.0750858
$279$	−0.948847	−0.0568060
$280$	0	0
$281$	15.2889	0.912058	0.456029	−	0.889965i	$-0.349271\pi$
$281$	15.2889	0.912058	0.456029	+	0.889965i	$0.349271\pi$
$282$	−6.84796	−0.407790
$283$	−14.2544	−0.847339	−0.423669	−	0.905817i	$-0.639258\pi$
$283$	−14.2544	−0.847339	−0.423669	+	0.905817i	$0.639258\pi$
$284$	−6.20214	−0.368029
$285$	0	0
$286$	−0.148462	−0.00877874
$287$	8.73083	0.515365
$288$	9.73264	0.573501
$289$	−16.8333	−0.990194
$290$	0	0
$291$	18.5807	1.08922
$292$	7.77444	0.454964
$293$	19.6344	1.14706	0.573528	−	0.819186i	$-0.305574\pi$
$293$	19.6344	1.14706	0.573528	+	0.819186i	$0.305574\pi$
$294$	−3.54641	−0.206831
$295$	0	0
$296$	−2.49731	−0.145153
$297$	2.98924	0.173454
$298$	−0.917233	−0.0531339
$299$	0.473313	0.0273724
$300$	0	0
$301$	21.6937	1.25040
$302$	5.24087	0.301578
$303$	19.8515	1.14044
$304$	1.66099	0.0952643
$305$	0	0
$306$	−0.664797	−0.0380039
$307$	12.5027	0.713569	0.356784	−	0.934187i	$-0.383873\pi$
$307$	12.5027	0.713569	0.356784	+	0.934187i	$0.383873\pi$
$308$	1.22725	0.0699288
$309$	6.10232	0.347149
$310$	0	0
$311$	−3.41403	−0.193592	−0.0967961	−	0.995304i	$-0.530859\pi$
$311$	−3.41403	−0.193592	−0.0967961	+	0.995304i	$0.530859\pi$
$312$	−0.917524	−0.0519445
$313$	4.96058	0.280388	0.140194	−	0.990124i	$-0.455227\pi$
$313$	4.96058	0.280388	0.140194	+	0.990124i	$0.455227\pi$
$314$	3.99746	0.225590
$315$	0	0
$316$	−15.5963	−0.877362
$317$	19.1015	1.07285	0.536423	−	0.843949i	$-0.319775\pi$
$317$	19.1015	1.07285	0.536423	+	0.843949i	$0.319775\pi$
$318$	4.42668	0.248236
$319$	−0.598234	−0.0334947
$320$	0	0
$321$	4.64569	0.259297
$322$	2.84092	0.158318
$323$	1.99410	0.110955
$324$	0.606075	0.0336708
$325$	0	0
$326$	1.59909	0.0885655
$327$	12.7444	0.704769
$328$	−13.5087	−0.745891
$329$	12.6322	0.696435
$330$	0	0
$331$	−0.233014	−0.0128076	−0.00640380	−	0.999979i	$-0.502038\pi$
$331$	−0.233014	−0.0128076	−0.00640380	+	0.999979i	$0.502038\pi$
$332$	−16.1414	−0.885873
$333$	1.53015	0.0838517
$334$	−13.5826	−0.743206
$335$	0	0
$336$	−0.704765	−0.0384481
$337$	15.3599	0.836707	0.418354	−	0.908284i	$-0.362607\pi$
$337$	15.3599	0.836707	0.418354	+	0.908284i	$0.362607\pi$
$338$	11.8489	0.644496
$339$	5.17848	0.281256
$340$	0	0
$341$	0.302334	0.0163723
$342$	−7.95263	−0.430029
$343$	19.6496	1.06098
$344$	−33.5653	−1.80972
$345$	0	0
$346$	−16.6717	−0.896274
$347$	−21.2975	−1.14331	−0.571655	−	0.820494i	$-0.693699\pi$
$347$	−21.2975	−1.14331	−0.571655	+	0.820494i	$0.693699\pi$
$348$	−1.35623	−0.0727013
$349$	4.19874	0.224754	0.112377	−	0.993666i	$-0.464154\pi$
$349$	4.19874	0.224754	0.112377	+	0.993666i	$0.464154\pi$
$350$	0	0
$351$	1.51225	0.0807178
$352$	−3.10114	−0.165291
$353$	−10.4363	−0.555467	−0.277733	−	0.960658i	$-0.589583\pi$
$353$	−10.4363	−0.555467	−0.277733	+	0.960658i	$0.589583\pi$
$354$	−1.13202	−0.0601664
$355$	0	0
$356$	2.07666	0.110063
$357$	−0.846105	−0.0447806
$358$	8.32562	0.440023
$359$	11.9334	0.629819	0.314910	−	0.949122i	$-0.398026\pi$
$359$	11.9334	0.629819	0.314910	+	0.949122i	$0.398026\pi$
$360$	0	0
$361$	4.85440	0.255495
$362$	−1.90276	−0.100007
$363$	11.8197	0.620373
$364$	0.620859	0.0325419
$365$	0	0
$366$	7.08312	0.370241
$367$	25.2159	1.31626	0.658129	−	0.752906i	$-0.271348\pi$
$367$	25.2159	1.31626	0.658129	+	0.752906i	$0.271348\pi$
$368$	−0.562513	−0.0293230
$369$	8.27701	0.430884
$370$	0	0
$371$	−8.16572	−0.423943
$372$	0.685405	0.0355366
$373$	−33.9024	−1.75540	−0.877700	−	0.479211i	$-0.840923\pi$
$373$	−33.9024	−1.75540	−0.877700	+	0.479211i	$0.840923\pi$
$374$	0.211826	0.0109533
$375$	0	0
$376$	−19.5450	−1.00795
$377$	−0.302645	−0.0155870
$378$	9.07680	0.466860
$379$	30.0510	1.54361	0.771807	−	0.635857i	$-0.219353\pi$
$379$	30.0510	1.54361	0.771807	+	0.635857i	$0.219353\pi$
$380$	0	0
$381$	−13.6553	−0.699583
$382$	−11.4080	−0.583685
$383$	−4.69532	−0.239920	−0.119960	−	0.992779i	$-0.538277\pi$
$383$	−4.69532	−0.239920	−0.119960	+	0.992779i	$0.538277\pi$
$384$	−6.33999	−0.323536
$385$	0	0
$386$	−7.69199	−0.391512
$387$	20.5661	1.04543
$388$	19.4533	0.987592
$389$	22.6121	1.14648	0.573239	−	0.819388i	$-0.305687\pi$
$389$	22.6121	1.14648	0.573239	+	0.819388i	$0.305687\pi$
$390$	0	0
$391$	−0.675324	−0.0341526
$392$	−10.1219	−0.511233
$393$	−23.2796	−1.17430
$394$	−1.44534	−0.0728153
$395$	0	0
$396$	1.16345	0.0584658
$397$	2.59293	0.130135	0.0650677	−	0.997881i	$-0.479274\pi$
$397$	2.59293	0.130135	0.0650677	+	0.997881i	$0.479274\pi$
$398$	−9.78132	−0.490293
$399$	−10.1215	−0.506710
$400$	0	0
$401$	25.3844	1.26764	0.633818	−	0.773482i	$-0.281487\pi$
$401$	25.3844	1.26764	0.633818	+	0.773482i	$0.281487\pi$
$402$	−11.6212	−0.579613
$403$	0.152949	0.00761895
$404$	20.7838	1.03403
$405$	0	0
$406$	−1.81653	−0.0901529
$407$	−0.487555	−0.0241672
$408$	1.30912	0.0648113
$409$	−12.3394	−0.610144	−0.305072	−	0.952329i	$-0.598680\pi$
$409$	−12.3394	−0.610144	−0.305072	+	0.952329i	$0.598680\pi$
$410$	0	0
$411$	−23.7048	−1.16927
$412$	6.38892	0.314760
$413$	2.08820	0.102754
$414$	2.69325	0.132366
$415$	0	0
$416$	−1.56885	−0.0769194
$417$	−1.51054	−0.0739717
$418$	2.53397	0.123940
$419$	5.41456	0.264519	0.132259	−	0.991215i	$-0.457777\pi$
$419$	5.41456	0.264519	0.132259	+	0.991215i	$0.457777\pi$
$420$	0	0
$421$	−10.5952	−0.516377	−0.258188	−	0.966095i	$-0.583126\pi$
$421$	−10.5952	−0.516377	−0.258188	+	0.966095i	$0.583126\pi$
$422$	−18.1119	−0.881674
$423$	11.9756	0.582272
$424$	12.6343	0.613576
$425$	0	0
$426$	5.43361	0.263259
$427$	−13.0660	−0.632306
$428$	4.86388	0.235105
$429$	−0.179130	−0.00864849
$430$	0	0
$431$	−32.9560	−1.58743	−0.793717	−	0.608287i	$-0.791857\pi$
$431$	−32.9560	−1.58743	−0.793717	+	0.608287i	$0.791857\pi$
$432$	−1.79724	−0.0864699
$433$	−28.5380	−1.37145	−0.685724	−	0.727862i	$-0.740514\pi$
$433$	−28.5380	−1.37145	−0.685724	+	0.727862i	$0.740514\pi$
$434$	0.918031	0.0440669
$435$	0	0
$436$	13.3430	0.639013
$437$	−8.07856	−0.386450
$438$	−6.81108	−0.325446
$439$	11.0455	0.527171	0.263586	−	0.964636i	$-0.415095\pi$
$439$	11.0455	0.527171	0.263586	+	0.964636i	$0.415095\pi$
$440$	0	0
$441$	6.20188	0.295328
$442$	0.107162	0.00509717
$443$	20.7463	0.985687	0.492844	−	0.870118i	$-0.335957\pi$
$443$	20.7463	0.985687	0.492844	+	0.870118i	$0.335957\pi$
$444$	−1.10531	−0.0524558
$445$	0	0
$446$	−15.9139	−0.753545
$447$	−1.10671	−0.0523455
$448$	−10.6902	−0.505064
$449$	17.3638	0.819451	0.409725	−	0.912209i	$-0.365625\pi$
$449$	17.3638	0.819451	0.409725	+	0.912209i	$0.365625\pi$
$450$	0	0
$451$	−2.63733	−0.124187
$452$	5.42169	0.255015
$453$	6.32348	0.297103
$454$	15.0130	0.704596
$455$	0	0
$456$	15.6604	0.733365
$457$	31.6155	1.47891	0.739456	−	0.673204i	$-0.235083\pi$
$457$	31.6155	1.47891	0.739456	+	0.673204i	$0.235083\pi$
$458$	−21.3796	−0.999003
$459$	−2.15768	−0.100712
$460$	0	0
$461$	−32.9871	−1.53636	−0.768182	−	0.640232i	$-0.778838\pi$
$461$	−32.9871	−1.53636	−0.768182	+	0.640232i	$0.778838\pi$
$462$	−1.07517	−0.0500216
$463$	37.9302	1.76277	0.881384	−	0.472401i	$-0.156612\pi$
$463$	37.9302	1.76277	0.881384	+	0.472401i	$0.156612\pi$
$464$	0.359680	0.0166977
$465$	0	0
$466$	7.89956	0.365940
$467$	0.187312	0.00866775	0.00433387	−	0.999991i	$-0.498620\pi$
$467$	0.187312	0.00866775	0.00433387	+	0.999991i	$0.498620\pi$
$468$	0.588587	0.0272075
$469$	21.4372	0.989878
$470$	0	0
$471$	4.82323	0.222243
$472$	−3.23094	−0.148716
$473$	−6.55303	−0.301309
$474$	13.6637	0.627596
$475$	0	0
$476$	−0.885843	−0.0406025
$477$	−7.74128	−0.354449
$478$	20.2894	0.928016
$479$	−29.8144	−1.36225	−0.681126	−	0.732166i	$-0.738510\pi$
$479$	−29.8144	−1.36225	−0.681126	+	0.732166i	$0.738510\pi$
$480$	0	0
$481$	−0.246652	−0.0112464
$482$	−19.3111	−0.879598
$483$	3.42777	0.155969
$484$	12.3748	0.562492
$485$	0	0
$486$	14.0111	0.635554
$487$	1.32261	0.0599332	0.0299666	−	0.999551i	$-0.490460\pi$
$487$	1.32261	0.0599332	0.0299666	+	0.999551i	$0.490460\pi$
$488$	20.2161	0.915141
$489$	1.92942	0.0872514
$490$	0	0
$491$	−39.9039	−1.80084	−0.900419	−	0.435023i	$-0.856740\pi$
$491$	−39.9039	−1.80084	−0.900419	+	0.435023i	$0.856740\pi$
$492$	−5.97894	−0.269552
$493$	0.431814	0.0194479
$494$	1.28192	0.0576765
$495$	0	0
$496$	−0.181774	−0.00816189
$497$	−10.0232	−0.449601
$498$	14.1412	0.633684
$499$	3.27391	0.146561	0.0732803	−	0.997311i	$-0.476653\pi$
$499$	3.27391	0.146561	0.0732803	+	0.997311i	$0.476653\pi$
$500$	0	0
$501$	−16.3884	−0.732179
$502$	3.08634	0.137750
$503$	25.9554	1.15729	0.578647	−	0.815578i	$-0.303581\pi$
$503$	25.9554	1.15729	0.578647	+	0.815578i	$0.303581\pi$
$504$	9.63079	0.428989
$505$	0	0
$506$	−0.858156	−0.0381497
$507$	14.2966	0.634933
$508$	−14.2966	−0.634311
$509$	30.7164	1.36148	0.680740	−	0.732525i	$-0.261658\pi$
$509$	30.7164	1.36148	0.680740	+	0.732525i	$0.261658\pi$
$510$	0	0
$511$	12.5641	0.555805
$512$	3.83512	0.169490
$513$	−25.8112	−1.13959
$514$	2.54561	0.112282
$515$	0	0
$516$	−14.8560	−0.654000
$517$	−3.81581	−0.167819
$518$	−1.48046	−0.0650475
$519$	−20.1156	−0.882975
$520$	0	0
$521$	8.48557	0.371760	0.185880	−	0.982572i	$-0.440486\pi$
$521$	8.48557	0.371760	0.185880	+	0.982572i	$0.440486\pi$
$522$	−1.72211	−0.0753747
$523$	−21.0834	−0.921911	−0.460956	−	0.887423i	$-0.652493\pi$
$523$	−21.0834	−0.921911	−0.460956	+	0.887423i	$0.652493\pi$
$524$	−24.3730	−1.06474
$525$	0	0
$526$	−8.61016	−0.375421
$527$	−0.218228	−0.00950618
$528$	0.212889	0.00926479
$529$	−20.2641	−0.881048
$530$	0	0
$531$	1.97966	0.0859099
$532$	−10.5969	−0.459434
$533$	−1.33421	−0.0577912
$534$	−1.81934	−0.0787305
$535$	0	0
$536$	−33.1684	−1.43266
$537$	10.0455	0.433494
$538$	−19.2590	−0.830313
$539$	−1.97612	−0.0851176
$540$	0	0
$541$	19.4919	0.838023	0.419011	−	0.907981i	$-0.362377\pi$
$541$	19.4919	0.838023	0.419011	+	0.907981i	$0.362377\pi$
$542$	−2.80465	−0.120470
$543$	−2.29581	−0.0985228
$544$	2.23844	0.0959724
$545$	0	0
$546$	−0.543926	−0.0232779
$547$	11.4894	0.491253	0.245626	−	0.969365i	$-0.421006\pi$
$547$	11.4894	0.491253	0.245626	+	0.969365i	$0.421006\pi$
$548$	−24.8181	−1.06018
$549$	−12.3868	−0.528656
$550$	0	0
$551$	5.16557	0.220061
$552$	−5.30357	−0.225735
$553$	−25.2050	−1.07182
$554$	−19.0175	−0.807977
$555$	0	0
$556$	−1.58149	−0.0670700
$557$	−20.4299	−0.865643	−0.432821	−	0.901480i	$-0.642482\pi$
$557$	−20.4299	−0.865643	−0.432821	+	0.901480i	$0.642482\pi$
$558$	0.870313	0.0368433
$559$	−3.31515	−0.140216
$560$	0	0
$561$	0.255583	0.0107907
$562$	−14.0235	−0.591544
$563$	21.5845	0.909678	0.454839	−	0.890574i	$-0.349697\pi$
$563$	21.5845	0.909678	0.454839	+	0.890574i	$0.349697\pi$
$564$	−8.65062	−0.364257
$565$	0	0
$566$	13.0746	0.549568
$567$	0.979468	0.0411338
$568$	15.5082	0.650711
$569$	−29.9182	−1.25424	−0.627119	−	0.778923i	$-0.715766\pi$
$569$	−29.9182	−1.25424	−0.627119	+	0.778923i	$0.715766\pi$
$570$	0	0
$571$	37.2624	1.55938	0.779692	−	0.626163i	$-0.215376\pi$
$571$	37.2624	1.55938	0.779692	+	0.626163i	$0.215376\pi$
$572$	−0.187543	−0.00784157
$573$	−13.7646	−0.575024
$574$	−8.00820	−0.334256
$575$	0	0
$576$	−10.1345	−0.422272
$577$	−31.9938	−1.33192	−0.665960	−	0.745988i	$-0.731978\pi$
$577$	−31.9938	−1.33192	−0.665960	+	0.745988i	$0.731978\pi$
$578$	15.4401	0.642222
$579$	−9.28095	−0.385703
$580$	0	0
$581$	−26.0858	−1.08222
$582$	−17.0428	−0.706446
$583$	2.46662	0.102157
$584$	−19.4397	−0.804420
$585$	0	0
$586$	−18.0093	−0.743959
$587$	9.38116	0.387202	0.193601	−	0.981080i	$-0.437983\pi$
$587$	9.38116	0.387202	0.193601	+	0.981080i	$0.437983\pi$
$588$	−4.47996	−0.184751
$589$	−2.61056	−0.107566
$590$	0	0
$591$	−1.74391	−0.0717349
$592$	0.293136	0.0120478
$593$	−6.46540	−0.265502	−0.132751	−	0.991149i	$-0.542381\pi$
$593$	−6.46540	−0.265502	−0.132751	+	0.991149i	$0.542381\pi$
$594$	−2.74183	−0.112499
$595$	0	0
$596$	−1.15868	−0.0474616
$597$	−11.8019	−0.483019
$598$	−0.434138	−0.0177532
$599$	30.6077	1.25060	0.625299	−	0.780385i	$-0.284977\pi$
$599$	30.6077	1.25060	0.625299	+	0.780385i	$0.284977\pi$
$600$	0	0
$601$	−36.3059	−1.48095	−0.740474	−	0.672085i	$-0.765399\pi$
$601$	−36.3059	−1.48095	−0.740474	+	0.672085i	$0.765399\pi$
$602$	−19.8982	−0.810989
$603$	20.3229	0.827613
$604$	6.62047	0.269383
$605$	0	0
$606$	−18.2084	−0.739667
$607$	28.0923	1.14023	0.570116	−	0.821564i	$-0.306898\pi$
$607$	28.0923	1.14023	0.570116	+	0.821564i	$0.306898\pi$
$608$	26.7774	1.08597
$609$	−2.19177	−0.0888152
$610$	0	0
$611$	−1.93040	−0.0780957
$612$	−0.839798	−0.0339468
$613$	6.37604	0.257526	0.128763	−	0.991675i	$-0.458899\pi$
$613$	6.37604	0.257526	0.128763	+	0.991675i	$0.458899\pi$
$614$	−11.4679	−0.462808
$615$	0	0
$616$	−3.06868	−0.123641
$617$	27.1335	1.09236	0.546178	−	0.837669i	$-0.316082\pi$
$617$	27.1335	1.09236	0.546178	+	0.837669i	$0.316082\pi$
$618$	−5.59725	−0.225154
$619$	29.4675	1.18440	0.592200	−	0.805791i	$-0.298259\pi$
$619$	29.4675	1.18440	0.592200	+	0.805791i	$0.298259\pi$
$620$	0	0
$621$	8.74126	0.350775
$622$	3.13146	0.125560
$623$	3.35606	0.134458
$624$	0.107700	0.00431144
$625$	0	0
$626$	−4.55000	−0.181855
$627$	3.05741	0.122101
$628$	5.04975	0.201507
$629$	0.351924	0.0140321
$630$	0	0
$631$	3.58965	0.142902	0.0714508	−	0.997444i	$-0.477237\pi$
$631$	3.58965	0.142902	0.0714508	+	0.997444i	$0.477237\pi$
$632$	38.9980	1.55126
$633$	−21.8533	−0.868591
$634$	−17.5205	−0.695827
$635$	0	0
$636$	5.59195	0.221735
$637$	−0.999713	−0.0396101
$638$	0.548720	0.0217240
$639$	−9.50218	−0.375901
$640$	0	0
$641$	−33.9847	−1.34231	−0.671157	−	0.741315i	$-0.734202\pi$
$641$	−33.9847	−1.34231	−0.671157	+	0.741315i	$0.734202\pi$
$642$	−4.26118	−0.168175
$643$	−40.1205	−1.58220	−0.791099	−	0.611688i	$-0.790491\pi$
$643$	−40.1205	−1.58220	−0.791099	+	0.611688i	$0.790491\pi$
$644$	3.58876	0.141417
$645$	0	0
$646$	−1.82905	−0.0719631
$647$	28.2002	1.10867	0.554333	−	0.832295i	$-0.312974\pi$
$647$	28.2002	1.10867	0.554333	+	0.832295i	$0.312974\pi$
$648$	−1.51547	−0.0595332
$649$	−0.630784	−0.0247604
$650$	0	0
$651$	1.10767	0.0434131
$652$	2.02004	0.0791107
$653$	−50.2823	−1.96770	−0.983849	−	0.179002i	$-0.942713\pi$
$653$	−50.2823	−1.96770	−0.983849	+	0.179002i	$0.942713\pi$
$654$	−11.6896	−0.457100
$655$	0	0
$656$	1.58566	0.0619095
$657$	11.9111	0.464695
$658$	−11.5866	−0.451694
$659$	−3.02422	−0.117807	−0.0589034	−	0.998264i	$-0.518760\pi$
$659$	−3.02422	−0.117807	−0.0589034	+	0.998264i	$0.518760\pi$
$660$	0	0
$661$	−38.2920	−1.48938	−0.744692	−	0.667408i	$-0.767404\pi$
$661$	−38.2920	−1.48938	−0.744692	+	0.667408i	$0.767404\pi$
$662$	0.213728	0.00830677
$663$	0.129299	0.00502154
$664$	40.3609	1.56631
$665$	0	0
$666$	−1.40350	−0.0543846
$667$	−1.74938	−0.0677362
$668$	−17.1581	−0.663866
$669$	−19.2013	−0.742364
$670$	0	0
$671$	3.94684	0.152366
$672$	−11.3618	−0.438289
$673$	3.88998	0.149948	0.0749738	−	0.997186i	$-0.476113\pi$
$673$	3.88998	0.149948	0.0749738	+	0.997186i	$0.476113\pi$
$674$	−14.0886	−0.542673
$675$	0	0
$676$	14.9680	0.575693
$677$	−34.5430	−1.32760	−0.663798	−	0.747912i	$-0.731056\pi$
$677$	−34.5430	−1.32760	−0.663798	+	0.747912i	$0.731056\pi$
$678$	−4.74987	−0.182418
$679$	31.4382	1.20649
$680$	0	0
$681$	18.1143	0.694141
$682$	−0.277310	−0.0106188
$683$	−32.3876	−1.23928	−0.619639	−	0.784887i	$-0.712721\pi$
$683$	−32.3876	−1.23928	−0.619639	+	0.784887i	$0.712721\pi$
$684$	−10.0461	−0.384121
$685$	0	0
$686$	−18.0233	−0.688133
$687$	−25.7960	−0.984180
$688$	3.93992	0.150208
$689$	1.24786	0.0475395
$690$	0	0
$691$	21.0226	0.799736	0.399868	−	0.916573i	$-0.369056\pi$
$691$	21.0226	0.799736	0.399868	+	0.916573i	$0.369056\pi$
$692$	−21.0603	−0.800592
$693$	1.88024	0.0714244
$694$	19.5348	0.741530
$695$	0	0
$696$	3.39119	0.128543
$697$	1.90366	0.0721062
$698$	−3.85122	−0.145771
$699$	9.53139	0.360510
$700$	0	0
$701$	−16.0195	−0.605049	−0.302524	−	0.953142i	$-0.597829\pi$
$701$	−16.0195	−0.605049	−0.302524	+	0.953142i	$0.597829\pi$
$702$	−1.38708	−0.0523521
$703$	4.20989	0.158779
$704$	3.22919	0.121705
$705$	0	0
$706$	9.57249	0.360265
$707$	33.5884	1.26322
$708$	−1.43002	−0.0537433
$709$	20.0689	0.753703	0.376852	−	0.926274i	$-0.377007\pi$
$709$	20.0689	0.753703	0.376852	+	0.926274i	$0.377007\pi$
$710$	0	0
$711$	−23.8948	−0.896126
$712$	−5.19262	−0.194602
$713$	0.884095	0.0331096
$714$	0.776075	0.0290439
$715$	0	0
$716$	10.5173	0.393048
$717$	24.4806	0.914247
$718$	−10.9457	−0.408489
$719$	−11.7275	−0.437361	−0.218681	−	0.975797i	$-0.570175\pi$
$719$	−11.7275	−0.437361	−0.218681	+	0.975797i	$0.570175\pi$
$720$	0	0
$721$	10.3250	0.384524
$722$	−4.45261	−0.165709
$723$	−23.3003	−0.866546
$724$	−2.40364	−0.0893305
$725$	0	0
$726$	−10.8414	−0.402362
$727$	11.1660	0.414124	0.207062	−	0.978328i	$-0.433610\pi$
$727$	11.1660	0.414124	0.207062	+	0.978328i	$0.433610\pi$
$728$	−1.55244	−0.0575371
$729$	18.4746	0.684243
$730$	0	0
$731$	4.73006	0.174948
$732$	8.94768	0.330716
$733$	7.46809	0.275840	0.137920	−	0.990443i	$-0.455958\pi$
$733$	7.46809	0.275840	0.137920	+	0.990443i	$0.455958\pi$
$734$	−23.1288	−0.853700
$735$	0	0
$736$	−9.06846	−0.334268
$737$	−6.47554	−0.238530
$738$	−7.59195	−0.279463
$739$	−40.8417	−1.50238	−0.751192	−	0.660083i	$-0.770521\pi$
$739$	−40.8417	−1.50238	−0.751192	+	0.660083i	$0.770521\pi$
$740$	0	0
$741$	1.54673	0.0568207
$742$	7.48987	0.274962
$743$	−19.2057	−0.704590	−0.352295	−	0.935889i	$-0.614599\pi$
$743$	−19.2057	−0.704590	−0.352295	+	0.935889i	$0.614599\pi$
$744$	−1.71383	−0.0628320
$745$	0	0
$746$	31.0964	1.13852
$747$	−24.7299	−0.904820
$748$	0.267587	0.00978394
$749$	7.86044	0.287214
$750$	0	0
$751$	12.5439	0.457733	0.228866	−	0.973458i	$-0.426498\pi$
$751$	12.5439	0.457733	0.228866	+	0.973458i	$0.426498\pi$
$752$	2.29420	0.0836610
$753$	3.72389	0.135706
$754$	0.277595	0.0101094
$755$	0	0
$756$	11.4662	0.417021
$757$	41.5862	1.51148	0.755738	−	0.654874i	$-0.227278\pi$
$757$	41.5862	1.51148	0.755738	+	0.654874i	$0.227278\pi$
$758$	−27.5637	−1.00116
$759$	−1.03543	−0.0375836
$760$	0	0
$761$	21.3217	0.772913	0.386456	−	0.922308i	$-0.373699\pi$
$761$	21.3217	0.772913	0.386456	+	0.922308i	$0.373699\pi$
$762$	12.5251	0.453736
$763$	21.5634	0.780647
$764$	−14.4111	−0.521374
$765$	0	0
$766$	4.30670	0.155607
$767$	−0.319111	−0.0115224
$768$	18.4515	0.665811
$769$	44.5402	1.60616	0.803079	−	0.595872i	$-0.203193\pi$
$769$	44.5402	1.60616	0.803079	+	0.595872i	$0.203193\pi$
$770$	0	0
$771$	3.07147	0.110616
$772$	−9.71683	−0.349716
$773$	−37.2677	−1.34043	−0.670214	−	0.742168i	$-0.733798\pi$
$773$	−37.2677	−1.34043	−0.670214	+	0.742168i	$0.733798\pi$
$774$	−18.8639	−0.678048
$775$	0	0
$776$	−48.6423	−1.74616
$777$	−1.78628	−0.0640823
$778$	−20.7405	−0.743585
$779$	22.7725	0.815910
$780$	0	0
$781$	3.02771	0.108340
$782$	0.619429	0.0221507
$783$	−5.58931	−0.199746
$784$	1.18812	0.0424328
$785$	0	0
$786$	21.3528	0.761631
$787$	28.8907	1.02984	0.514921	−	0.857238i	$-0.327821\pi$
$787$	28.8907	1.02984	0.514921	+	0.857238i	$0.327821\pi$
$788$	−1.82582	−0.0650420
$789$	−10.3888	−0.369850
$790$	0	0
$791$	8.76190	0.311537
$792$	−2.90918	−0.103373
$793$	1.99669	0.0709046
$794$	−2.37832	−0.0844034
$795$	0	0
$796$	−12.3562	−0.437952
$797$	−39.6656	−1.40503	−0.702513	−	0.711671i	$-0.747939\pi$
$797$	−39.6656	−1.40503	−0.702513	+	0.711671i	$0.747939\pi$
$798$	9.28379	0.328643
$799$	2.75430	0.0974402
$800$	0	0
$801$	3.18162	0.112417
$802$	−23.2834	−0.822165
$803$	−3.79525	−0.133932
$804$	−14.6804	−0.517737
$805$	0	0
$806$	−0.140290	−0.00494151
$807$	−23.2373	−0.817993
$808$	−51.9692	−1.82827
$809$	−33.0670	−1.16257	−0.581287	−	0.813698i	$-0.697451\pi$
$809$	−33.0670	−1.16257	−0.581287	+	0.813698i	$0.697451\pi$
$810$	0	0
$811$	39.5697	1.38948	0.694740	−	0.719261i	$-0.255520\pi$
$811$	39.5697	1.38948	0.694740	+	0.719261i	$0.255520\pi$
$812$	−2.29471	−0.0805286
$813$	−3.38401	−0.118682
$814$	0.447202	0.0156744
$815$	0	0
$816$	−0.153666	−0.00537939
$817$	56.5834	1.97960
$818$	11.3181	0.395728
$819$	0.951207	0.0332378
$820$	0	0
$821$	27.9100	0.974065	0.487032	−	0.873384i	$-0.338079\pi$
$821$	27.9100	0.974065	0.487032	+	0.873384i	$0.338079\pi$
$822$	21.7428	0.758369
$823$	−42.9361	−1.49666	−0.748329	−	0.663328i	$-0.769143\pi$
$823$	−42.9361	−1.49666	−0.748329	+	0.663328i	$0.769143\pi$
$824$	−15.9753	−0.556525
$825$	0	0
$826$	−1.91537	−0.0666441
$827$	18.7519	0.652067	0.326033	−	0.945358i	$-0.394288\pi$
$827$	18.7519	0.652067	0.326033	+	0.945358i	$0.394288\pi$
$828$	3.40222	0.118235
$829$	18.5597	0.644603	0.322302	−	0.946637i	$-0.395543\pi$
$829$	18.5597	0.644603	0.322302	+	0.946637i	$0.395543\pi$
$830$	0	0
$831$	−22.9460	−0.795988
$832$	1.63363	0.0566361
$833$	1.42639	0.0494216
$834$	1.38552	0.0479766
$835$	0	0
$836$	3.20101	0.110709
$837$	2.82471	0.0976361
$838$	−4.96641	−0.171562
$839$	0.529963	0.0182964	0.00914818	−	0.999958i	$-0.497088\pi$
$839$	0.529963	0.0182964	0.00914818	+	0.999958i	$0.497088\pi$
$840$	0	0
$841$	−27.8814	−0.961428
$842$	9.71823	0.334912
$843$	−16.9203	−0.582766
$844$	−22.8797	−0.787551
$845$	0	0
$846$	−10.9844	−0.377651
$847$	19.9987	0.687165
$848$	−1.48302	−0.0509273
$849$	15.7755	0.541414
$850$	0	0
$851$	−1.42573	−0.0488733
$852$	6.86395	0.235155
$853$	−38.8749	−1.33105	−0.665525	−	0.746376i	$-0.731792\pi$
$853$	−38.8749	−1.33105	−0.665525	+	0.746376i	$0.731792\pi$
$854$	11.9845	0.410102
$855$	0	0
$856$	−12.1620	−0.415687
$857$	23.7643	0.811771	0.405886	−	0.913924i	$-0.366963\pi$
$857$	23.7643	0.811771	0.405886	+	0.913924i	$0.366963\pi$
$858$	0.164304	0.00560925
$859$	38.9859	1.33018	0.665090	−	0.746763i	$-0.268393\pi$
$859$	38.9859	1.33018	0.665090	+	0.746763i	$0.268393\pi$
$860$	0	0
$861$	−9.66248	−0.329296
$862$	30.2283	1.02958
$863$	0.542999	0.0184839	0.00924195	−	0.999957i	$-0.497058\pi$
$863$	0.542999	0.0184839	0.00924195	+	0.999957i	$0.497058\pi$
$864$	−28.9740	−0.985714
$865$	0	0
$866$	26.1760	0.889496
$867$	18.6295	0.632692
$868$	1.15969	0.0393626
$869$	7.61367	0.258276
$870$	0	0
$871$	−3.27595	−0.111001
$872$	−33.3637	−1.12984
$873$	29.8041	1.00871
$874$	7.40992	0.250644
$875$	0	0
$876$	−8.60402	−0.290703
$877$	−13.9025	−0.469453	−0.234726	−	0.972061i	$-0.575419\pi$
$877$	−13.9025	−0.469453	−0.234726	+	0.972061i	$0.575419\pi$
$878$	−10.1313	−0.341913
$879$	−21.7296	−0.732920
$880$	0	0
$881$	−34.8859	−1.17533	−0.587667	−	0.809103i	$-0.699954\pi$
$881$	−34.8859	−1.17533	−0.587667	+	0.809103i	$0.699954\pi$
$882$	−5.68857	−0.191544
$883$	−2.77333	−0.0933299	−0.0466649	−	0.998911i	$-0.514859\pi$
$883$	−2.77333	−0.0933299	−0.0466649	+	0.998911i	$0.514859\pi$
$884$	0.135371	0.00455303
$885$	0	0
$886$	−19.0292	−0.639298
$887$	−31.6941	−1.06418	−0.532091	−	0.846687i	$-0.678594\pi$
$887$	−31.6941	−1.06418	−0.532091	+	0.846687i	$0.678594\pi$
$888$	2.76379	0.0927468
$889$	−23.1046	−0.774902
$890$	0	0
$891$	−0.295868	−0.00991196
$892$	−20.1031	−0.673100
$893$	32.9483	1.10257
$894$	1.01511	0.0339503
$895$	0	0
$896$	−10.7272	−0.358369
$897$	−0.523819	−0.0174898
$898$	−15.9267	−0.531480
$899$	−0.565305	−0.0188540
$900$	0	0
$901$	−1.78044	−0.0593151
$902$	2.41904	0.0805453
$903$	−24.0086	−0.798956
$904$	−13.5567	−0.450890
$905$	0	0
$906$	−5.80011	−0.192696
$907$	−12.7658	−0.423880	−0.211940	−	0.977283i	$-0.567978\pi$
$907$	−12.7658	−0.423880	−0.211940	+	0.977283i	$0.567978\pi$
$908$	18.9650	0.629377
$909$	31.8425	1.05615
$910$	0	0
$911$	13.9226	0.461276	0.230638	−	0.973040i	$-0.425919\pi$
$911$	13.9226	0.461276	0.230638	+	0.973040i	$0.425919\pi$
$912$	−1.83823	−0.0608699
$913$	7.87975	0.260782
$914$	−28.9988	−0.959195
$915$	0	0
$916$	−27.0076	−0.892355
$917$	−39.3888	−1.30073
$918$	1.97909	0.0653198
$919$	−5.11045	−0.168578	−0.0842890	−	0.996441i	$-0.526862\pi$
$919$	−5.11045	−0.168578	−0.0842890	+	0.996441i	$0.526862\pi$
$920$	0	0
$921$	−13.8369	−0.455940
$922$	30.2569	0.996457
$923$	1.53170	0.0504167
$924$	−1.35820	−0.0446816
$925$	0	0
$926$	−34.7909	−1.14330
$927$	9.78835	0.321492
$928$	5.79853	0.190346
$929$	45.7107	1.49972	0.749859	−	0.661597i	$-0.230121\pi$
$929$	45.7107	1.49972	0.749859	+	0.661597i	$0.230121\pi$
$930$	0	0
$931$	17.0632	0.559224
$932$	9.97904	0.326874
$933$	3.77834	0.123697
$934$	−0.171808	−0.00562174
$935$	0	0
$936$	−1.47174	−0.0481054
$937$	−12.7921	−0.417899	−0.208949	−	0.977926i	$-0.567004\pi$
$937$	−12.7921	−0.417899	−0.208949	+	0.977926i	$0.567004\pi$
$938$	−19.6629	−0.642016
$939$	−5.48991	−0.179156
$940$	0	0
$941$	19.7575	0.644076	0.322038	−	0.946727i	$-0.395632\pi$
$941$	19.7575	0.644076	0.322038	+	0.946727i	$0.395632\pi$
$942$	−4.42402	−0.144142
$943$	−7.71217	−0.251143
$944$	0.379250	0.0123435
$945$	0	0
$946$	6.01065	0.195423
$947$	−28.9373	−0.940335	−0.470168	−	0.882577i	$-0.655807\pi$
$947$	−28.9373	−0.940335	−0.470168	+	0.882577i	$0.655807\pi$
$948$	17.2606	0.560597
$949$	−1.92001	−0.0623260
$950$	0	0
$951$	−21.1397	−0.685503
$952$	2.21502	0.0717891
$953$	−14.7569	−0.478022	−0.239011	−	0.971017i	$-0.576823\pi$
$953$	−14.7569	−0.478022	−0.239011	+	0.971017i	$0.576823\pi$
$954$	7.10055	0.229889
$955$	0	0
$956$	25.6304	0.828946
$957$	0.662070	0.0214017
$958$	27.3467	0.883532
$959$	−40.1082	−1.29516
$960$	0	0
$961$	−30.7143	−0.990784
$962$	0.226238	0.00729420
$963$	7.45186	0.240133
$964$	−24.3946	−0.785696
$965$	0	0
$966$	−3.14406	−0.101159
$967$	29.9776	0.964014	0.482007	−	0.876167i	$-0.339908\pi$
$967$	29.9776	0.964014	0.482007	+	0.876167i	$0.339908\pi$
$968$	−30.9428	−0.994538
$969$	−2.20688	−0.0708953
$970$	0	0
$971$	−24.7539	−0.794391	−0.397195	−	0.917734i	$-0.630016\pi$
$971$	−24.7539	−0.794391	−0.397195	+	0.917734i	$0.630016\pi$
$972$	17.6993	0.567706
$973$	−2.55582	−0.0819357
$974$	−1.21314	−0.0388715
$975$	0	0
$976$	−2.37299	−0.0759574
$977$	0.640419	0.0204888	0.0102444	−	0.999948i	$-0.496739\pi$
$977$	0.640419	0.0204888	0.0102444	+	0.999948i	$0.496739\pi$
$978$	−1.76973	−0.0565896
$979$	−1.01377	−0.0324002
$980$	0	0
$981$	20.4425	0.652680
$982$	36.6012	1.16799
$983$	28.4300	0.906777	0.453388	−	0.891313i	$-0.350215\pi$
$983$	28.4300	0.906777	0.453388	+	0.891313i	$0.350215\pi$
$984$	14.9501	0.476593
$985$	0	0
$986$	−0.396074	−0.0126136
$987$	−13.9801	−0.444992
$988$	1.61938	0.0515193
$989$	−19.1626	−0.609335
$990$	0	0
$991$	44.3441	1.40864	0.704318	−	0.709884i	$-0.251253\pi$
$991$	44.3441	1.40864	0.704318	+	0.709884i	$0.251253\pi$
$992$	−2.93044	−0.0930415
$993$	0.257878	0.00818351
$994$	9.19358	0.291603
$995$	0	0
$996$	17.8638	0.566035
$997$	38.2765	1.21223	0.606115	−	0.795377i	$-0.292727\pi$
$997$	38.2765	1.21223	0.606115	+	0.795377i	$0.292727\pi$
$998$	−3.00294	−0.0950564
$999$	−4.55524	−0.144121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3725.2.a.c.1.4		9
5.4	even	2		149.2.a.b.1.6	✓	9
15.14	odd	2		1341.2.a.e.1.4		9
20.19	odd	2		2384.2.a.j.1.5		9
35.34	odd	2		7301.2.a.j.1.6		9
40.19	odd	2		9536.2.a.w.1.5		9
40.29	even	2		9536.2.a.v.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
149.2.a.b.1.6	✓	9	5.4	even	2
1341.2.a.e.1.4		9	15.14	odd	2
2384.2.a.j.1.5		9	20.19	odd	2
3725.2.a.c.1.4		9	1.1	even	1	trivial
7301.2.a.j.1.6		9	35.34	odd	2
9536.2.a.v.1.5		9	40.29	even	2
9536.2.a.w.1.5		9	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3725 = 5^{2} \cdot 149 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3725.a (trivial)

\(f(q)\)	\(=\)	\(q-0.917233 q^{2} -1.10671 q^{3} -1.15868 q^{4} +1.01511 q^{6} -1.87253 q^{7} +2.89725 q^{8} -1.77520 q^{9} +O(q^{10})\)	\(q-0.917233 q^{2} -1.10671 q^{3} -1.15868 q^{4} +1.01511 q^{6} -1.87253 q^{7} +2.89725 q^{8} -1.77520 q^{9} +0.565636 q^{11} +1.28232 q^{12} +0.286153 q^{13} +1.71755 q^{14} -0.340081 q^{16} -0.408284 q^{17} +1.62827 q^{18} -4.88410 q^{19} +2.07234 q^{21} -0.518820 q^{22} +1.65405 q^{23} -3.20641 q^{24} -0.262469 q^{26} +5.28475 q^{27} +2.16967 q^{28} -1.05763 q^{29} +0.534502 q^{31} -5.48256 q^{32} -0.625994 q^{33} +0.374491 q^{34} +2.05690 q^{36} -0.861959 q^{37} +4.47985 q^{38} -0.316688 q^{39} -4.66258 q^{41} -1.90082 q^{42} -11.5852 q^{43} -0.655394 q^{44} -1.51715 q^{46} -6.74604 q^{47} +0.376370 q^{48} -3.49363 q^{49} +0.451851 q^{51} -0.331561 q^{52} +4.36079 q^{53} -4.84734 q^{54} -5.42519 q^{56} +5.40527 q^{57} +0.970093 q^{58} -1.11518 q^{59} +6.97770 q^{61} -0.490262 q^{62} +3.32412 q^{63} +5.70895 q^{64} +0.574182 q^{66} -11.4482 q^{67} +0.473072 q^{68} -1.83055 q^{69} +5.35274 q^{71} -5.14319 q^{72} -6.70971 q^{73} +0.790617 q^{74} +5.65913 q^{76} -1.05917 q^{77} +0.290476 q^{78} +13.4604 q^{79} -0.523072 q^{81} +4.27667 q^{82} +13.9308 q^{83} -2.40119 q^{84} +10.6264 q^{86} +1.17049 q^{87} +1.63879 q^{88} -1.79226 q^{89} -0.535831 q^{91} -1.91653 q^{92} -0.591537 q^{93} +6.18769 q^{94} +6.06759 q^{96} -16.7891 q^{97} +3.20447 q^{98} -1.00412 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + q^{2} - 6 q^{3} + 13 q^{4} + q^{6} - 3 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + q^2 - 6 * q^3 + 13 * q^4 + q^6 - 3 * q^7 + 6 * q^8 + 9 * q^9	\( 9 q + q^{2} - 6 q^{3} + 13 q^{4} + q^{6} - 3 q^{7} + 6 q^{8} + 9 q^{9} + 5 q^{11} + q^{12} - 7 q^{13} - 8 q^{14} + 13 q^{16} + 5 q^{17} + 15 q^{18} + 30 q^{19} - 6 q^{21} + 7 q^{22} + 4 q^{23} - 11 q^{24} - 15 q^{26} - 15 q^{27} + 12 q^{28} - 16 q^{29} + 22 q^{31} + 38 q^{32} + 15 q^{33} + 9 q^{34} - 26 q^{36} + 7 q^{37} + 18 q^{38} - 13 q^{39} + 6 q^{41} + 11 q^{42} - 4 q^{43} + 6 q^{44} + q^{46} + 6 q^{47} + 6 q^{48} + 14 q^{49} - 11 q^{51} - 50 q^{52} + 2 q^{53} + 12 q^{54} + 7 q^{56} - 5 q^{57} - 2 q^{58} + 43 q^{59} + q^{61} - 33 q^{62} + 6 q^{63} + 18 q^{64} + 51 q^{66} - 33 q^{67} + 16 q^{68} - 14 q^{69} + 15 q^{71} - 3 q^{72} + 11 q^{73} + 33 q^{74} + 59 q^{76} + 30 q^{77} + 21 q^{78} + q^{79} + q^{81} - 5 q^{82} + 4 q^{83} + 24 q^{84} - 7 q^{86} - 17 q^{87} + 37 q^{88} - 19 q^{89} + 62 q^{91} - 17 q^{92} - 3 q^{93} + 17 q^{94} - 43 q^{96} + q^{97} - 36 q^{98} + q^{99}+O(q^{100}) \) 9 * q + q^2 - 6 * q^3 + 13 * q^4 + q^6 - 3 * q^7 + 6 * q^8 + 9 * q^9 + 5 * q^11 + q^12 - 7 * q^13 - 8 * q^14 + 13 * q^16 + 5 * q^17 + 15 * q^18 + 30 * q^19 - 6 * q^21 + 7 * q^22 + 4 * q^23 - 11 * q^24 - 15 * q^26 - 15 * q^27 + 12 * q^28 - 16 * q^29 + 22 * q^31 + 38 * q^32 + 15 * q^33 + 9 * q^34 - 26 * q^36 + 7 * q^37 + 18 * q^38 - 13 * q^39 + 6 * q^41 + 11 * q^42 - 4 * q^43 + 6 * q^44 + q^46 + 6 * q^47 + 6 * q^48 + 14 * q^49 - 11 * q^51 - 50 * q^52 + 2 * q^53 + 12 * q^54 + 7 * q^56 - 5 * q^57 - 2 * q^58 + 43 * q^59 + q^61 - 33 * q^62 + 6 * q^63 + 18 * q^64 + 51 * q^66 - 33 * q^67 + 16 * q^68 - 14 * q^69 + 15 * q^71 - 3 * q^72 + 11 * q^73 + 33 * q^74 + 59 * q^76 + 30 * q^77 + 21 * q^78 + q^79 + q^81 - 5 * q^82 + 4 * q^83 + 24 * q^84 - 7 * q^86 - 17 * q^87 + 37 * q^88 - 19 * q^89 + 62 * q^91 - 17 * q^92 - 3 * q^93 + 17 * q^94 - 43 * q^96 + q^97 - 36 * q^98 + q^99

Introduction

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