LMFDB - Embedded newform 3725.2.a.c.1.7

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			1.7
Root			$1.60510$ 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)

$f(q)$	$=$	$q+1.60510 q^{2} -1.97240 q^{3} +0.576343 q^{4} -3.16589 q^{6} -4.58029 q^{7} -2.28511 q^{8} +0.890348 q^{9} +O(q^{10})$	\(q+1.60510 q^{2} -1.97240 q^{3} +0.576343 q^{4} -3.16589 q^{6} -4.58029 q^{7} -2.28511 q^{8} +0.890348 q^{9} -2.18841 q^{11} -1.13678 q^{12} -4.15663 q^{13} -7.35182 q^{14} -4.82051 q^{16} -4.56008 q^{17} +1.42910 q^{18} +1.14926 q^{19} +9.03414 q^{21} -3.51262 q^{22} -0.565875 q^{23} +4.50714 q^{24} -6.67180 q^{26} +4.16107 q^{27} -2.63982 q^{28} +0.935532 q^{29} -6.36311 q^{31} -3.16718 q^{32} +4.31642 q^{33} -7.31938 q^{34} +0.513146 q^{36} -1.90519 q^{37} +1.84467 q^{38} +8.19852 q^{39} -10.5238 q^{41} +14.5007 q^{42} +3.11444 q^{43} -1.26128 q^{44} -0.908286 q^{46} +12.6142 q^{47} +9.50797 q^{48} +13.9790 q^{49} +8.99428 q^{51} -2.39565 q^{52} +5.73780 q^{53} +6.67893 q^{54} +10.4665 q^{56} -2.26679 q^{57} +1.50162 q^{58} +11.8479 q^{59} -8.30754 q^{61} -10.2134 q^{62} -4.07805 q^{63} +4.55739 q^{64} +6.92828 q^{66} -15.6061 q^{67} -2.62817 q^{68} +1.11613 q^{69} -0.851833 q^{71} -2.03454 q^{72} -3.90582 q^{73} -3.05802 q^{74} +0.662366 q^{76} +10.0236 q^{77} +13.1594 q^{78} -12.2344 q^{79} -10.8783 q^{81} -16.8917 q^{82} -13.9499 q^{83} +5.20677 q^{84} +4.99899 q^{86} -1.84524 q^{87} +5.00077 q^{88} +1.15067 q^{89} +19.0386 q^{91} -0.326138 q^{92} +12.5506 q^{93} +20.2470 q^{94} +6.24694 q^{96} +7.77105 q^{97} +22.4377 q^{98} -1.94845 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.60510	1.13498	0.567488	−	0.823381i	$-0.307915\pi$
$2$	1.60510	1.13498	0.567488	+	0.823381i	$0.307915\pi$
$3$	−1.97240	−1.13876	−0.569382	−	0.822073i	$-0.692817\pi$
$3$	−1.97240	−1.13876	−0.569382	+	0.822073i	$0.692817\pi$
$4$	0.576343	0.288172
$5$	0	0
$5$	0	0
$6$	−3.16589	−1.29247
$7$	−4.58029	−1.73119	−0.865593	−	0.500748i	$-0.833058\pi$
$7$	−4.58029	−1.73119	−0.865593	+	0.500748i	$0.833058\pi$
$8$	−2.28511	−0.807908
$9$	0.890348	0.296783
$10$	0	0
$11$	−2.18841	−0.659831	−0.329916	−	0.944010i	$-0.607020\pi$
$11$	−2.18841	−0.659831	−0.329916	+	0.944010i	$0.607020\pi$
$12$	−1.13678	−0.328159
$13$	−4.15663	−1.15284	−0.576421	−	0.817153i	$-0.695551\pi$
$13$	−4.15663	−1.15284	−0.576421	+	0.817153i	$0.695551\pi$
$14$	−7.35182	−1.96486
$15$	0	0
$16$	−4.82051	−1.20513
$17$	−4.56008	−1.10598	−0.552991	−	0.833187i	$-0.686513\pi$
$17$	−4.56008	−1.10598	−0.552991	+	0.833187i	$0.686513\pi$
$18$	1.42910	0.336842
$19$	1.14926	0.263657	0.131829	−	0.991273i	$-0.457915\pi$
$19$	1.14926	0.263657	0.131829	+	0.991273i	$0.457915\pi$
$20$	0	0
$21$	9.03414	1.97141
$22$	−3.51262	−0.748893
$23$	−0.565875	−0.117993	−0.0589966	−	0.998258i	$-0.518790\pi$
$23$	−0.565875	−0.117993	−0.0589966	+	0.998258i	$0.518790\pi$
$24$	4.50714	0.920017
$25$	0	0
$26$	−6.67180	−1.30845
$27$	4.16107	0.800798
$28$	−2.63982	−0.498879
$29$	0.935532	0.173724	0.0868620	−	0.996220i	$-0.472316\pi$
$29$	0.935532	0.173724	0.0868620	+	0.996220i	$0.472316\pi$
$30$	0	0
$31$	−6.36311	−1.14285	−0.571425	−	0.820655i	$-0.693609\pi$
$31$	−6.36311	−1.14285	−0.571425	+	0.820655i	$0.693609\pi$
$32$	−3.16718	−0.559884
$33$	4.31642	0.751392
$34$	−7.31938	−1.25526
$35$	0	0
$36$	0.513146	0.0855244
$37$	−1.90519	−0.313212	−0.156606	−	0.987661i	$-0.550055\pi$
$37$	−1.90519	−0.313212	−0.156606	+	0.987661i	$0.550055\pi$
$38$	1.84467	0.299245
$39$	8.19852	1.31281
$40$	0	0
$41$	−10.5238	−1.64354	−0.821769	−	0.569821i	$-0.807013\pi$
$41$	−10.5238	−1.64354	−0.821769	+	0.569821i	$0.807013\pi$
$42$	14.5007	2.23751
$43$	3.11444	0.474948	0.237474	−	0.971394i	$-0.423681\pi$
$43$	3.11444	0.474948	0.237474	+	0.971394i	$0.423681\pi$
$44$	−1.26128	−0.190145
$45$	0	0
$46$	−0.908286	−0.133919
$47$	12.6142	1.83997	0.919984	−	0.391955i	$-0.128201\pi$
$47$	12.6142	1.83997	0.919984	+	0.391955i	$0.128201\pi$
$48$	9.50797	1.37236
$49$	13.9790	1.99700
$50$	0	0
$51$	8.99428	1.25945
$52$	−2.39565	−0.332216
$53$	5.73780	0.788148	0.394074	−	0.919079i	$-0.371065\pi$
$53$	5.73780	0.788148	0.394074	+	0.919079i	$0.371065\pi$
$54$	6.67893	0.908887
$55$	0	0
$56$	10.4665	1.39864
$57$	−2.26679	−0.300243
$58$	1.50162	0.197173
$59$	11.8479	1.54246	0.771232	−	0.636555i	$-0.219641\pi$
$59$	11.8479	1.54246	0.771232	+	0.636555i	$0.219641\pi$
$60$	0	0
$61$	−8.30754	−1.06367	−0.531836	−	0.846848i	$-0.678498\pi$
$61$	−8.30754	−1.06367	−0.531836	+	0.846848i	$0.678498\pi$
$62$	−10.2134	−1.29711
$63$	−4.07805	−0.513786
$64$	4.55739	0.569673
$65$	0	0
$66$	6.92828	0.852812
$67$	−15.6061	−1.90658	−0.953291	−	0.302052i	$-0.902328\pi$
$67$	−15.6061	−1.90658	−0.953291	+	0.302052i	$0.902328\pi$
$68$	−2.62817	−0.318712
$69$	1.11613	0.134366
$70$	0	0
$71$	−0.851833	−0.101094	−0.0505470	−	0.998722i	$-0.516096\pi$
$71$	−0.851833	−0.101094	−0.0505470	+	0.998722i	$0.516096\pi$
$72$	−2.03454	−0.239773
$73$	−3.90582	−0.457142	−0.228571	−	0.973527i	$-0.573405\pi$
$73$	−3.90582	−0.457142	−0.228571	+	0.973527i	$0.573405\pi$
$74$	−3.05802	−0.355488
$75$	0	0
$76$	0.662366	0.0759786
$77$	10.0236	1.14229
$78$	13.1594	1.49001
$79$	−12.2344	−1.37648	−0.688241	−	0.725482i	$-0.741617\pi$
$79$	−12.2344	−1.37648	−0.688241	+	0.725482i	$0.741617\pi$
$80$	0	0
$81$	−10.8783	−1.20870
$82$	−16.8917	−1.86538
$83$	−13.9499	−1.53120	−0.765602	−	0.643315i	$-0.777559\pi$
$83$	−13.9499	−1.53120	−0.765602	+	0.643315i	$0.777559\pi$
$84$	5.20677	0.568105
$85$	0	0
$86$	4.99899	0.539055
$87$	−1.84524	−0.197830
$88$	5.00077	0.533083
$89$	1.15067	0.121971	0.0609853	−	0.998139i	$-0.480576\pi$
$89$	1.15067	0.121971	0.0609853	+	0.998139i	$0.480576\pi$
$90$	0	0
$91$	19.0386	1.99578
$92$	−0.326138	−0.0340023
$93$	12.5506	1.30144
$94$	20.2470	2.08832
$95$	0	0
$96$	6.24694	0.637576
$97$	7.77105	0.789030	0.394515	−	0.918889i	$-0.370913\pi$
$97$	7.77105	0.789030	0.394515	+	0.918889i	$0.370913\pi$
$98$	22.4377	2.26655
$99$	−1.94845	−0.195827
$100$	0	0
$101$	2.59676	0.258387	0.129194	−	0.991619i	$-0.458761\pi$
$101$	2.59676	0.258387	0.129194	+	0.991619i	$0.458761\pi$
$102$	14.4367	1.42945
$103$	16.3525	1.61126	0.805630	−	0.592419i	$-0.201827\pi$
$103$	16.3525	1.61126	0.805630	+	0.592419i	$0.201827\pi$
$104$	9.49836	0.931391
$105$	0	0
$106$	9.20974	0.894529
$107$	−13.5767	−1.31251	−0.656257	−	0.754538i	$-0.727861\pi$
$107$	−13.5767	−1.31251	−0.656257	+	0.754538i	$0.727861\pi$
$108$	2.39820	0.230767
$109$	1.94406	0.186207	0.0931037	−	0.995656i	$-0.470321\pi$
$109$	1.94406	0.186207	0.0931037	+	0.995656i	$0.470321\pi$
$110$	0	0
$111$	3.75780	0.356674
$112$	22.0793	2.08630
$113$	−5.94772	−0.559514	−0.279757	−	0.960071i	$-0.590254\pi$
$113$	−5.94772	−0.559514	−0.279757	+	0.960071i	$0.590254\pi$
$114$	−3.63842	−0.340769
$115$	0	0
$116$	0.539188	0.0500623
$117$	−3.70085	−0.342144
$118$	19.0170	1.75066
$119$	20.8865	1.91466
$120$	0	0
$121$	−6.21085	−0.564622
$122$	−13.3344	−1.20724
$123$	20.7571	1.87160
$124$	−3.66734	−0.329337
$125$	0	0
$126$	−6.54568	−0.583135
$127$	−1.14813	−0.101880	−0.0509398	−	0.998702i	$-0.516222\pi$
$127$	−1.14813	−0.101880	−0.0509398	+	0.998702i	$0.516222\pi$
$128$	13.6494	1.20645
$129$	−6.14292	−0.540854
$130$	0	0
$131$	−5.62287	−0.491272	−0.245636	−	0.969362i	$-0.578997\pi$
$131$	−5.62287	−0.491272	−0.245636	+	0.969362i	$0.578997\pi$
$132$	2.48774	0.216530
$133$	−5.26392	−0.456440
$134$	−25.0493	−2.16393
$135$	0	0
$136$	10.4203	0.893532
$137$	−0.803810	−0.0686741	−0.0343371	−	0.999410i	$-0.510932\pi$
$137$	−0.803810	−0.0686741	−0.0343371	+	0.999410i	$0.510932\pi$
$138$	1.79150	0.152503
$139$	0.931286	0.0789906	0.0394953	−	0.999220i	$-0.487425\pi$
$139$	0.931286	0.0789906	0.0394953	+	0.999220i	$0.487425\pi$
$140$	0	0
$141$	−24.8802	−2.09529
$142$	−1.36728	−0.114739
$143$	9.09643	0.760681
$144$	−4.29194	−0.357662
$145$	0	0
$146$	−6.26923	−0.518845
$147$	−27.5722	−2.27412
$148$	−1.09805	−0.0902588
$149$	1.00000	0.0819232
$149$	1.00000	0.0819232
$150$	0	0
$151$	19.2396	1.56569	0.782847	−	0.622215i	$-0.213767\pi$
$151$	19.2396	1.56569	0.782847	+	0.622215i	$0.213767\pi$
$152$	−2.62618	−0.213011
$153$	−4.06006	−0.328236
$154$	16.0888	1.29647
$155$	0	0
$156$	4.72516	0.378316
$157$	−2.58762	−0.206515	−0.103257	−	0.994655i	$-0.532927\pi$
$157$	−2.58762	−0.206515	−0.103257	+	0.994655i	$0.532927\pi$
$158$	−19.6375	−1.56228
$159$	−11.3172	−0.897514
$160$	0	0
$161$	2.59187	0.204268
$162$	−17.4608	−1.37185
$163$	8.64759	0.677332	0.338666	−	0.940907i	$-0.390024\pi$
$163$	8.64759	0.677332	0.338666	+	0.940907i	$0.390024\pi$
$164$	−6.06531	−0.473621
$165$	0	0
$166$	−22.3910	−1.73788
$167$	9.71609	0.751854	0.375927	−	0.926649i	$-0.377324\pi$
$167$	9.71609	0.751854	0.375927	+	0.926649i	$0.377324\pi$
$168$	−20.6440	−1.59272
$169$	4.27758	0.329045
$170$	0	0
$171$	1.02324	0.0782490
$172$	1.79499	0.136867
$173$	6.60313	0.502027	0.251014	−	0.967984i	$-0.419236\pi$
$173$	6.60313	0.502027	0.251014	+	0.967984i	$0.419236\pi$
$174$	−2.96179	−0.224533
$175$	0	0
$176$	10.5493	0.795182
$177$	−23.3687	−1.75650
$178$	1.84694	0.138434
$179$	−6.85957	−0.512708	−0.256354	−	0.966583i	$-0.582521\pi$
$179$	−6.85957	−0.512708	−0.256354	+	0.966583i	$0.582521\pi$
$180$	0	0
$181$	−22.9083	−1.70276	−0.851381	−	0.524547i	$-0.824235\pi$
$181$	−22.9083	−1.70276	−0.851381	+	0.524547i	$0.824235\pi$
$182$	30.5588	2.26517
$183$	16.3858	1.21127
$184$	1.29309	0.0953276
$185$	0	0
$186$	20.1449	1.47710
$187$	9.97933	0.729761
$188$	7.27010	0.530227
$189$	−19.0589	−1.38633
$190$	0	0
$191$	−7.15017	−0.517368	−0.258684	−	0.965962i	$-0.583289\pi$
$191$	−7.15017	−0.517368	−0.258684	+	0.965962i	$0.583289\pi$
$192$	−8.98897	−0.648723
$193$	7.96445	0.573293	0.286647	−	0.958036i	$-0.407459\pi$
$193$	7.96445	0.573293	0.286647	+	0.958036i	$0.407459\pi$
$194$	12.4733	0.895531
$195$	0	0
$196$	8.05672	0.575480
$197$	4.57914	0.326250	0.163125	−	0.986605i	$-0.447843\pi$
$197$	4.57914	0.326250	0.163125	+	0.986605i	$0.447843\pi$
$198$	−3.12746	−0.222259
$199$	11.9473	0.846918	0.423459	−	0.905915i	$-0.360816\pi$
$199$	11.9473	0.846918	0.423459	+	0.905915i	$0.360816\pi$
$200$	0	0
$201$	30.7813	2.17115
$202$	4.16806	0.293264
$203$	−4.28501	−0.300748
$204$	5.18379	0.362938
$205$	0	0
$206$	26.2474	1.82874
$207$	−0.503826	−0.0350183
$208$	20.0371	1.38932
$209$	−2.51505	−0.173969
$210$	0	0
$211$	−16.5224	−1.13745	−0.568724	−	0.822528i	$-0.692563\pi$
$211$	−16.5224	−1.13745	−0.568724	+	0.822528i	$0.692563\pi$
$212$	3.30694	0.227122
$213$	1.68015	0.115122
$214$	−21.7920	−1.48967
$215$	0	0
$216$	−9.50850	−0.646972
$217$	29.1449	1.97848
$218$	3.12041	0.211341
$219$	7.70383	0.520577
$220$	0	0
$221$	18.9546	1.27502
$222$	6.03164	0.404817
$223$	−23.4598	−1.57098	−0.785491	−	0.618873i	$-0.787590\pi$
$223$	−23.4598	−1.57098	−0.785491	+	0.618873i	$0.787590\pi$
$224$	14.5066	0.969264
$225$	0	0
$226$	−9.54667	−0.635035
$227$	−21.2145	−1.40806	−0.704029	−	0.710171i	$-0.748618\pi$
$227$	−21.2145	−1.40806	−0.704029	+	0.710171i	$0.748618\pi$
$228$	−1.30645	−0.0865217
$229$	2.56128	0.169254	0.0846272	−	0.996413i	$-0.473030\pi$
$229$	2.56128	0.169254	0.0846272	+	0.996413i	$0.473030\pi$
$230$	0	0
$231$	−19.7704	−1.30080
$232$	−2.13779	−0.140353
$233$	−29.3104	−1.92019	−0.960093	−	0.279681i	$-0.909771\pi$
$233$	−29.3104	−1.92019	−0.960093	+	0.279681i	$0.909771\pi$
$234$	−5.94023	−0.388325
$235$	0	0
$236$	6.82845	0.444494
$237$	24.1312	1.56749
$238$	33.5248	2.17309
$239$	0.786631	0.0508829	0.0254415	−	0.999676i	$-0.491901\pi$
$239$	0.786631	0.0508829	0.0254415	+	0.999676i	$0.491901\pi$
$240$	0	0
$241$	−25.0809	−1.61560	−0.807801	−	0.589455i	$-0.799343\pi$
$241$	−25.0809	−1.61560	−0.807801	+	0.589455i	$0.799343\pi$
$242$	−9.96902	−0.640833
$243$	8.97316	0.575629
$244$	−4.78799	−0.306520
$245$	0	0
$246$	33.3172	2.12422
$247$	−4.77703	−0.303955
$248$	14.5404	0.923317
$249$	27.5148	1.74368
$250$	0	0
$251$	26.4649	1.67045	0.835225	−	0.549908i	$-0.185337\pi$
$251$	26.4649	1.67045	0.835225	+	0.549908i	$0.185337\pi$
$252$	−2.35036	−0.148059
$253$	1.23837	0.0778556
$254$	−1.84286	−0.115631
$255$	0	0
$256$	12.7939	0.799619
$257$	18.4020	1.14788	0.573942	−	0.818896i	$-0.305414\pi$
$257$	18.4020	1.14788	0.573942	+	0.818896i	$0.305414\pi$
$258$	−9.85999	−0.613856
$259$	8.72633	0.542228
$260$	0	0
$261$	0.832949	0.0515583
$262$	−9.02526	−0.557583
$263$	−2.50403	−0.154405	−0.0772025	−	0.997015i	$-0.524599\pi$
$263$	−2.50403	−0.154405	−0.0772025	+	0.997015i	$0.524599\pi$
$264$	−9.86349	−0.607056
$265$	0	0
$266$	−8.44912	−0.518049
$267$	−2.26957	−0.138896
$268$	−8.99444	−0.549423
$269$	−12.5575	−0.765645	−0.382822	−	0.923822i	$-0.625048\pi$
$269$	−12.5575	−0.765645	−0.382822	+	0.923822i	$0.625048\pi$
$270$	0	0
$271$	28.2606	1.71671	0.858356	−	0.513055i	$-0.171486\pi$
$271$	28.2606	1.71671	0.858356	+	0.513055i	$0.171486\pi$
$272$	21.9819	1.33285
$273$	−37.5516	−2.27273
$274$	−1.29019	−0.0779435
$275$	0	0
$276$	0.643274	0.0387205
$277$	−9.64560	−0.579548	−0.289774	−	0.957095i	$-0.593580\pi$
$277$	−9.64560	−0.579548	−0.289774	+	0.957095i	$0.593580\pi$
$278$	1.49481	0.0896525
$279$	−5.66539	−0.339178
$280$	0	0
$281$	29.9804	1.78848	0.894241	−	0.447586i	$-0.147716\pi$
$281$	29.9804	1.78848	0.894241	+	0.447586i	$0.147716\pi$
$282$	−39.9352	−2.37810
$283$	11.3871	0.676893	0.338446	−	0.940986i	$-0.390099\pi$
$283$	11.3871	0.676893	0.338446	+	0.940986i	$0.390099\pi$
$284$	−0.490948	−0.0291324
$285$	0	0
$286$	14.6007	0.863356
$287$	48.2019	2.84527
$288$	−2.81990	−0.166164
$289$	3.79430	0.223194
$290$	0	0
$291$	−15.3276	−0.898519
$292$	−2.25109	−0.131735
$293$	−19.3369	−1.12967	−0.564836	−	0.825203i	$-0.691061\pi$
$293$	−19.3369	−1.12967	−0.564836	+	0.825203i	$0.691061\pi$
$294$	−44.2561	−2.58107
$295$	0	0
$296$	4.35358	0.253047
$297$	−9.10614	−0.528392
$298$	1.60510	0.0929809
$299$	2.35213	0.136027
$300$	0	0
$301$	−14.2650	−0.822223
$302$	30.8814	1.77702
$303$	−5.12184	−0.294242
$304$	−5.54001	−0.317741
$305$	0	0
$306$	−6.51680	−0.372540
$307$	−19.9732	−1.13993	−0.569964	−	0.821670i	$-0.693043\pi$
$307$	−19.9732	−1.13993	−0.569964	+	0.821670i	$0.693043\pi$
$308$	5.77701	0.329176
$309$	−32.2536	−1.83484
$310$	0	0
$311$	21.5927	1.22441	0.612204	−	0.790700i	$-0.290283\pi$
$311$	21.5927	1.22441	0.612204	+	0.790700i	$0.290283\pi$
$312$	−18.7345	−1.06063
$313$	−28.7932	−1.62749	−0.813744	−	0.581223i	$-0.802574\pi$
$313$	−28.7932	−1.62749	−0.813744	+	0.581223i	$0.802574\pi$
$314$	−4.15339	−0.234389
$315$	0	0
$316$	−7.05124	−0.396663
$317$	9.81392	0.551204	0.275602	−	0.961272i	$-0.411123\pi$
$317$	9.81392	0.551204	0.275602	+	0.961272i	$0.411123\pi$
$318$	−18.1653	−1.01866
$319$	−2.04733	−0.114629
$320$	0	0
$321$	26.7787	1.49464
$322$	4.16021	0.231839
$323$	−5.24070	−0.291600
$324$	−6.26965	−0.348314
$325$	0	0
$326$	13.8802	0.768756
$327$	−3.83446	−0.212046
$328$	24.0480	1.32783
$329$	−57.7766	−3.18533
$330$	0	0
$331$	10.6126	0.583320	0.291660	−	0.956522i	$-0.405792\pi$
$331$	10.6126	0.583320	0.291660	+	0.956522i	$0.405792\pi$
$332$	−8.03995	−0.441249
$333$	−1.69629	−0.0929559
$334$	15.5953	0.853336
$335$	0	0
$336$	−43.5492	−2.37581
$337$	17.2831	0.941472	0.470736	−	0.882274i	$-0.343988\pi$
$337$	17.2831	0.941472	0.470736	+	0.882274i	$0.343988\pi$
$338$	6.86594	0.373458
$339$	11.7313	0.637154
$340$	0	0
$341$	13.9251	0.754088
$342$	1.64240	0.0888108
$343$	−31.9660	−1.72600
$344$	−7.11685	−0.383715
$345$	0	0
$346$	10.5987	0.569789
$347$	26.3745	1.41586	0.707929	−	0.706284i	$-0.249630\pi$
$347$	26.3745	1.41586	0.707929	+	0.706284i	$0.249630\pi$
$348$	−1.06349	−0.0570091
$349$	−19.0250	−1.01838	−0.509192	−	0.860653i	$-0.670056\pi$
$349$	−19.0250	−1.01838	−0.509192	+	0.860653i	$0.670056\pi$
$350$	0	0
$351$	−17.2960	−0.923194
$352$	6.93111	0.369429
$353$	15.0218	0.799530	0.399765	−	0.916618i	$-0.369092\pi$
$353$	15.0218	0.799530	0.399765	+	0.916618i	$0.369092\pi$
$354$	−37.5091	−1.99359
$355$	0	0
$356$	0.663180	0.0351485
$357$	−41.1964	−2.18034
$358$	−11.0103	−0.581912
$359$	0.226039	0.0119299	0.00596493	−	0.999982i	$-0.498101\pi$
$359$	0.226039	0.0119299	0.00596493	+	0.999982i	$0.498101\pi$
$360$	0	0
$361$	−17.6792	−0.930485
$362$	−36.7701	−1.93260
$363$	12.2503	0.642972
$364$	10.9727	0.575128
$365$	0	0
$366$	26.3008	1.37476
$367$	23.6050	1.23217	0.616084	−	0.787680i	$-0.288718\pi$
$367$	23.6050	1.23217	0.616084	+	0.787680i	$0.288718\pi$
$368$	2.72781	0.142197
$369$	−9.36983	−0.487774
$370$	0	0
$371$	−26.2808	−1.36443
$372$	7.23344	0.375037
$373$	−16.8003	−0.869885	−0.434942	−	0.900458i	$-0.643231\pi$
$373$	−16.8003	−0.869885	−0.434942	+	0.900458i	$0.643231\pi$
$374$	16.0178	0.828262
$375$	0	0
$376$	−28.8248	−1.48653
$377$	−3.88866	−0.200276
$378$	−30.5914	−1.57345
$379$	32.2575	1.65695	0.828477	−	0.560023i	$-0.189208\pi$
$379$	32.2575	1.65695	0.828477	+	0.560023i	$0.189208\pi$
$380$	0	0
$381$	2.26456	0.116017
$382$	−11.4767	−0.587200
$383$	1.33342	0.0681348	0.0340674	−	0.999420i	$-0.489154\pi$
$383$	1.33342	0.0681348	0.0340674	+	0.999420i	$0.489154\pi$
$384$	−26.9221	−1.37386
$385$	0	0
$386$	12.7837	0.650674
$387$	2.77294	0.140956
$388$	4.47879	0.227376
$389$	−2.10792	−0.106876	−0.0534380	−	0.998571i	$-0.517018\pi$
$389$	−2.10792	−0.106876	−0.0534380	+	0.998571i	$0.517018\pi$
$390$	0	0
$391$	2.58043	0.130498
$392$	−31.9436	−1.61340
$393$	11.0905	0.559443
$394$	7.34997	0.370286
$395$	0	0
$396$	−1.12298	−0.0564317
$397$	−15.3814	−0.771971	−0.385985	−	0.922505i	$-0.626139\pi$
$397$	−15.3814	−0.771971	−0.385985	+	0.922505i	$0.626139\pi$
$398$	19.1765	0.961232
$399$	10.3825	0.519777
$400$	0	0
$401$	−5.31766	−0.265551	−0.132776	−	0.991146i	$-0.542389\pi$
$401$	−5.31766	−0.265551	−0.132776	+	0.991146i	$0.542389\pi$
$402$	49.4071	2.46420
$403$	26.4491	1.31752
$404$	1.49663	0.0744599
$405$	0	0
$406$	−6.87786	−0.341342
$407$	4.16935	0.206667
$408$	−20.5529	−1.01752
$409$	14.1544	0.699888	0.349944	−	0.936771i	$-0.386201\pi$
$409$	14.1544	0.699888	0.349944	+	0.936771i	$0.386201\pi$
$410$	0	0
$411$	1.58543	0.0782036
$412$	9.42465	0.464319
$413$	−54.2667	−2.67029
$414$	−0.808691	−0.0397450
$415$	0	0
$416$	13.1648	0.645458
$417$	−1.83687	−0.0899517
$418$	−4.03690	−0.197451
$419$	−1.90815	−0.0932192	−0.0466096	−	0.998913i	$-0.514842\pi$
$419$	−1.90815	−0.0932192	−0.0466096	+	0.998913i	$0.514842\pi$
$420$	0	0
$421$	−23.0811	−1.12491	−0.562453	−	0.826829i	$-0.690142\pi$
$421$	−23.0811	−1.12491	−0.562453	+	0.826829i	$0.690142\pi$
$422$	−26.5201	−1.29098
$423$	11.2310	0.546071
$424$	−13.1115	−0.636751
$425$	0	0
$426$	2.69681	0.130661
$427$	38.0509	1.84141
$428$	−7.82486	−0.378229
$429$	−17.9418	−0.866236
$430$	0	0
$431$	−21.7118	−1.04582	−0.522911	−	0.852387i	$-0.675154\pi$
$431$	−21.7118	−1.04582	−0.522911	+	0.852387i	$0.675154\pi$
$432$	−20.0585	−0.965065
$433$	1.36060	0.0653862	0.0326931	−	0.999465i	$-0.489592\pi$
$433$	1.36060	0.0653862	0.0326931	+	0.999465i	$0.489592\pi$
$434$	46.7804	2.24553
$435$	0	0
$436$	1.12045	0.0536597
$437$	−0.650335	−0.0311098
$438$	12.3654	0.590842
$439$	27.7517	1.32452	0.662258	−	0.749275i	$-0.269598\pi$
$439$	27.7517	1.32452	0.662258	+	0.749275i	$0.269598\pi$
$440$	0	0
$441$	12.4462	0.592677
$442$	30.4239	1.44712
$443$	16.4055	0.779450	0.389725	−	0.920931i	$-0.372570\pi$
$443$	16.4055	0.779450	0.389725	+	0.920931i	$0.372570\pi$
$444$	2.16578	0.102783
$445$	0	0
$446$	−37.6553	−1.78303
$447$	−1.97240	−0.0932912
$448$	−20.8741	−0.986210
$449$	18.7210	0.883499	0.441749	−	0.897139i	$-0.354358\pi$
$449$	18.7210	0.883499	0.441749	+	0.897139i	$0.354358\pi$
$450$	0	0
$451$	23.0304	1.08446
$452$	−3.42793	−0.161236
$453$	−37.9480	−1.78295
$454$	−34.0514	−1.59811
$455$	0	0
$456$	5.17986	0.242569
$457$	−26.6978	−1.24887	−0.624436	−	0.781076i	$-0.714671\pi$
$457$	−26.6978	−1.24887	−0.624436	+	0.781076i	$0.714671\pi$
$458$	4.11112	0.192100
$459$	−18.9748	−0.885668
$460$	0	0
$461$	−15.2809	−0.711704	−0.355852	−	0.934542i	$-0.615809\pi$
$461$	−15.2809	−0.711704	−0.355852	+	0.934542i	$0.615809\pi$
$462$	−31.7335	−1.47638
$463$	−36.2380	−1.68412	−0.842061	−	0.539383i	$-0.818658\pi$
$463$	−36.2380	−1.68412	−0.842061	+	0.539383i	$0.818658\pi$
$464$	−4.50975	−0.209360
$465$	0	0
$466$	−47.0460	−2.17937
$467$	−8.01421	−0.370853	−0.185427	−	0.982658i	$-0.559367\pi$
$467$	−8.01421	−0.370853	−0.185427	+	0.982658i	$0.559367\pi$
$468$	−2.13296	−0.0985961
$469$	71.4802	3.30065
$470$	0	0
$471$	5.10382	0.235172
$472$	−27.0737	−1.24617
$473$	−6.81569	−0.313386
$474$	38.7329	1.77906
$475$	0	0
$476$	12.0378	0.551750
$477$	5.10864	0.233909
$478$	1.26262	0.0577509
$479$	−12.1072	−0.553194	−0.276597	−	0.960986i	$-0.589207\pi$
$479$	−12.1072	−0.553194	−0.276597	+	0.960986i	$0.589207\pi$
$480$	0	0
$481$	7.91919	0.361084
$482$	−40.2573	−1.83367
$483$	−5.11220	−0.232613
$484$	−3.57958	−0.162708
$485$	0	0
$486$	14.4028	0.653325
$487$	13.7922	0.624982	0.312491	−	0.949921i	$-0.398837\pi$
$487$	13.7922	0.624982	0.312491	+	0.949921i	$0.398837\pi$
$488$	18.9836	0.859349
$489$	−17.0565	−0.771321
$490$	0	0
$491$	21.4486	0.967960	0.483980	−	0.875079i	$-0.339191\pi$
$491$	21.4486	0.967960	0.483980	+	0.875079i	$0.339191\pi$
$492$	11.9632	0.539343
$493$	−4.26610	−0.192135
$494$	−7.66761	−0.344982
$495$	0	0
$496$	30.6735	1.37728
$497$	3.90164	0.175013
$498$	44.1640	1.97903
$499$	−15.3767	−0.688356	−0.344178	−	0.938904i	$-0.611842\pi$
$499$	−15.3767	−0.688356	−0.344178	+	0.938904i	$0.611842\pi$
$500$	0	0
$501$	−19.1640	−0.856184
$502$	42.4788	1.89592
$503$	22.7495	1.01435	0.507176	−	0.861842i	$-0.330689\pi$
$503$	22.7495	1.01435	0.507176	+	0.861842i	$0.330689\pi$
$504$	9.31880	0.415092
$505$	0	0
$506$	1.98770	0.0883642
$507$	−8.43708	−0.374704
$508$	−0.661714	−0.0293588
$509$	14.5956	0.646939	0.323469	−	0.946239i	$-0.395151\pi$
$509$	14.5956	0.646939	0.323469	+	0.946239i	$0.395151\pi$
$510$	0	0
$511$	17.8898	0.791398
$512$	−6.76336	−0.298901
$513$	4.78213	0.211136
$514$	29.5370	1.30282
$515$	0	0
$516$	−3.54043	−0.155859
$517$	−27.6051	−1.21407
$518$	14.0066	0.615416
$519$	−13.0240	−0.571690
$520$	0	0
$521$	27.5974	1.20906	0.604532	−	0.796581i	$-0.293360\pi$
$521$	27.5974	1.20906	0.604532	+	0.796581i	$0.293360\pi$
$522$	1.33697	0.0585174
$523$	−6.56814	−0.287205	−0.143602	−	0.989635i	$-0.545869\pi$
$523$	−6.56814	−0.287205	−0.143602	+	0.989635i	$0.545869\pi$
$524$	−3.24070	−0.141571
$525$	0	0
$526$	−4.01921	−0.175246
$527$	29.0163	1.26397
$528$	−20.8074	−0.905524
$529$	−22.6798	−0.986078
$530$	0	0
$531$	10.5487	0.457777
$532$	−3.03383	−0.131533
$533$	43.7435	1.89474
$534$	−3.64289	−0.157643
$535$	0	0
$536$	35.6616	1.54034
$537$	13.5298	0.583854
$538$	−20.1560	−0.868989
$539$	−30.5919	−1.31769
$540$	0	0
$541$	1.51611	0.0651826	0.0325913	−	0.999469i	$-0.489624\pi$
$541$	1.51611	0.0651826	0.0325913	+	0.999469i	$0.489624\pi$
$542$	45.3611	1.94843
$543$	45.1843	1.93904
$544$	14.4426	0.619222
$545$	0	0
$546$	−60.2740	−2.57949
$547$	−22.2054	−0.949435	−0.474718	−	0.880138i	$-0.657450\pi$
$547$	−22.2054	−0.949435	−0.474718	+	0.880138i	$0.657450\pi$
$548$	−0.463271	−0.0197899
$549$	−7.39660	−0.315679
$550$	0	0
$551$	1.07517	0.0458036
$552$	−2.55048	−0.108556
$553$	56.0373	2.38295
$554$	−15.4821	−0.657773
$555$	0	0
$556$	0.536740	0.0227629
$557$	4.56601	0.193468	0.0967340	−	0.995310i	$-0.469160\pi$
$557$	4.56601	0.193468	0.0967340	+	0.995310i	$0.469160\pi$
$558$	−9.09351	−0.384959
$559$	−12.9456	−0.547540
$560$	0	0
$561$	−19.6832	−0.831026
$562$	48.1215	2.02988
$563$	−1.81784	−0.0766127	−0.0383063	−	0.999266i	$-0.512196\pi$
$563$	−1.81784	−0.0766127	−0.0383063	+	0.999266i	$0.512196\pi$
$564$	−14.3395	−0.603803
$565$	0	0
$566$	18.2774	0.768257
$567$	49.8259	2.09249
$568$	1.94653	0.0816747
$569$	−18.2290	−0.764199	−0.382100	−	0.924121i	$-0.624799\pi$
$569$	−18.2290	−0.764199	−0.382100	+	0.924121i	$0.624799\pi$
$570$	0	0
$571$	−6.71113	−0.280852	−0.140426	−	0.990091i	$-0.544847\pi$
$571$	−6.71113	−0.280852	−0.140426	+	0.990091i	$0.544847\pi$
$572$	5.24266	0.219207
$573$	14.1030	0.589160
$574$	77.3689	3.22932
$575$	0	0
$576$	4.05766	0.169069
$577$	1.54458	0.0643019	0.0321509	−	0.999483i	$-0.489764\pi$
$577$	1.54458	0.0643019	0.0321509	+	0.999483i	$0.489764\pi$
$578$	6.09023	0.253320
$579$	−15.7090	−0.652846
$580$	0	0
$581$	63.8947	2.65080
$582$	−24.6023	−1.01980
$583$	−12.5567	−0.520045
$584$	8.92524	0.369329
$585$	0	0
$586$	−31.0376	−1.28215
$587$	−6.07810	−0.250870	−0.125435	−	0.992102i	$-0.540033\pi$
$587$	−6.07810	−0.250870	−0.125435	+	0.992102i	$0.540033\pi$
$588$	−15.8911	−0.655336
$589$	−7.31285	−0.301321
$590$	0	0
$591$	−9.03188	−0.371522
$592$	9.18401	0.377461
$593$	−16.9776	−0.697185	−0.348592	−	0.937274i	$-0.613340\pi$
$593$	−16.9776	−0.697185	−0.348592	+	0.937274i	$0.613340\pi$
$594$	−14.6163	−0.599712
$595$	0	0
$596$	0.576343	0.0236079
$597$	−23.5647	−0.964440
$598$	3.77541	0.154388
$599$	3.77340	0.154177	0.0770886	−	0.997024i	$-0.475438\pi$
$599$	3.77340	0.154177	0.0770886	+	0.997024i	$0.475438\pi$
$600$	0	0
$601$	−16.2959	−0.664723	−0.332361	−	0.943152i	$-0.607845\pi$
$601$	−16.2959	−0.664723	−0.332361	+	0.943152i	$0.607845\pi$
$602$	−22.8968	−0.933204
$603$	−13.8948	−0.565841
$604$	11.0886	0.451188
$605$	0	0
$606$	−8.22106	−0.333958
$607$	−27.0629	−1.09845	−0.549224	−	0.835675i	$-0.685077\pi$
$607$	−27.0629	−1.09845	−0.549224	+	0.835675i	$0.685077\pi$
$608$	−3.63991	−0.147618
$609$	8.45173	0.342481
$610$	0	0
$611$	−52.4325	−2.12119
$612$	−2.33999	−0.0945884
$613$	2.03060	0.0820150	0.0410075	−	0.999159i	$-0.486943\pi$
$613$	2.03060	0.0820150	0.0410075	+	0.999159i	$0.486943\pi$
$614$	−32.0589	−1.29379
$615$	0	0
$616$	−22.9049	−0.922867
$617$	−17.7024	−0.712673	−0.356336	−	0.934358i	$-0.615974\pi$
$617$	−17.7024	−0.712673	−0.356336	+	0.934358i	$0.615974\pi$
$618$	−51.7703	−2.08250
$619$	36.2600	1.45741	0.728706	−	0.684826i	$-0.240122\pi$
$619$	36.2600	1.45741	0.728706	+	0.684826i	$0.240122\pi$
$620$	0	0
$621$	−2.35465	−0.0944887
$622$	34.6584	1.38967
$623$	−5.27039	−0.211154
$624$	−39.5211	−1.58211
$625$	0	0
$626$	−46.2160	−1.84716
$627$	4.96067	0.198110
$628$	−1.49136	−0.0595117
$629$	8.68783	0.346406
$630$	0	0
$631$	−43.3373	−1.72523	−0.862614	−	0.505862i	$-0.831175\pi$
$631$	−43.3373	−1.72523	−0.862614	+	0.505862i	$0.831175\pi$
$632$	27.9571	1.11207
$633$	32.5887	1.29528
$634$	15.7523	0.625604
$635$	0	0
$636$	−6.52261	−0.258638
$637$	−58.1057	−2.30223
$638$	−3.28617	−0.130101
$639$	−0.758429	−0.0300030
$640$	0	0
$641$	−8.63702	−0.341142	−0.170571	−	0.985345i	$-0.554561\pi$
$641$	−8.63702	−0.341142	−0.170571	+	0.985345i	$0.554561\pi$
$642$	42.9825	1.69638
$643$	−0.609504	−0.0240365	−0.0120182	−	0.999928i	$-0.503826\pi$
$643$	−0.609504	−0.0240365	−0.0120182	+	0.999928i	$0.503826\pi$
$644$	1.49381	0.0588642
$645$	0	0
$646$	−8.41184	−0.330959
$647$	−4.34556	−0.170842	−0.0854208	−	0.996345i	$-0.527223\pi$
$647$	−4.34556	−0.170842	−0.0854208	+	0.996345i	$0.527223\pi$
$648$	24.8582	0.976521
$649$	−25.9281	−1.01777
$650$	0	0
$651$	−57.4853	−2.25303
$652$	4.98398	0.195188
$653$	7.19764	0.281666	0.140833	−	0.990033i	$-0.455022\pi$
$653$	7.19764	0.281666	0.140833	+	0.990033i	$0.455022\pi$
$654$	−6.15469	−0.240667
$655$	0	0
$656$	50.7300	1.98068
$657$	−3.47754	−0.135672
$658$	−92.7372	−3.61527
$659$	25.1558	0.979930	0.489965	−	0.871742i	$-0.337010\pi$
$659$	25.1558	0.979930	0.489965	+	0.871742i	$0.337010\pi$
$660$	0	0
$661$	−11.0508	−0.429825	−0.214912	−	0.976633i	$-0.568947\pi$
$661$	−11.0508	−0.429825	−0.214912	+	0.976633i	$0.568947\pi$
$662$	17.0342	0.662055
$663$	−37.3859	−1.45195
$664$	31.8771	1.23707
$665$	0	0
$666$	−2.72271	−0.105503
$667$	−0.529394	−0.0204982
$668$	5.59980	0.216663
$669$	46.2720	1.78898
$670$	0	0
$671$	18.1803	0.701844
$672$	−28.6128	−1.10376
$673$	−15.9152	−0.613485	−0.306743	−	0.951793i	$-0.599239\pi$
$673$	−15.9152	−0.613485	−0.306743	+	0.951793i	$0.599239\pi$
$674$	27.7411	1.06855
$675$	0	0
$676$	2.46535	0.0948213
$677$	18.0453	0.693538	0.346769	−	0.937951i	$-0.387279\pi$
$677$	18.0453	0.693538	0.346769	+	0.937951i	$0.387279\pi$
$678$	18.8298	0.723155
$679$	−35.5936	−1.36596
$680$	0	0
$681$	41.8435	1.60345
$682$	22.3512	0.855872
$683$	−6.40694	−0.245155	−0.122577	−	0.992459i	$-0.539116\pi$
$683$	−6.40694	−0.245155	−0.122577	+	0.992459i	$0.539116\pi$
$684$	0.589737	0.0225491
$685$	0	0
$686$	−51.3086	−1.95897
$687$	−5.05187	−0.192741
$688$	−15.0132	−0.572374
$689$	−23.8499	−0.908610
$690$	0	0
$691$	47.5301	1.80813	0.904065	−	0.427395i	$-0.140569\pi$
$691$	47.5301	1.80813	0.904065	+	0.427395i	$0.140569\pi$
$692$	3.80567	0.144670
$693$	8.92446	0.339012
$694$	42.3337	1.60697
$695$	0	0
$696$	4.21658	0.159829
$697$	47.9892	1.81772
$698$	−30.5370	−1.15584
$699$	57.8117	2.18664
$700$	0	0
$701$	−20.6766	−0.780944	−0.390472	−	0.920615i	$-0.627688\pi$
$701$	−20.6766	−0.780944	−0.390472	+	0.920615i	$0.627688\pi$
$702$	−27.7618	−1.04780
$703$	−2.18955	−0.0825806
$704$	−9.97344	−0.375888
$705$	0	0
$706$	24.1115	0.907447
$707$	−11.8939	−0.447316
$708$	−13.4684	−0.506174
$709$	−21.1294	−0.793532	−0.396766	−	0.917920i	$-0.629867\pi$
$709$	−21.1294	−0.793532	−0.396766	+	0.917920i	$0.629867\pi$
$710$	0	0
$711$	−10.8929	−0.408516
$712$	−2.62940	−0.0985411
$713$	3.60073	0.134848
$714$	−66.1243	−2.47464
$715$	0	0
$716$	−3.95347	−0.147748
$717$	−1.55155	−0.0579436
$718$	0.362814	0.0135401
$719$	−7.53028	−0.280832	−0.140416	−	0.990093i	$-0.544844\pi$
$719$	−7.53028	−0.280832	−0.140416	+	0.990093i	$0.544844\pi$
$720$	0	0
$721$	−74.8992	−2.78939
$722$	−28.3769	−1.05608
$723$	49.4695	1.83979
$724$	−13.2031	−0.490688
$725$	0	0
$726$	19.6629	0.729758
$727$	−28.8353	−1.06944	−0.534721	−	0.845029i	$-0.679583\pi$
$727$	−28.8353	−1.06944	−0.534721	+	0.845029i	$0.679583\pi$
$728$	−43.5052	−1.61241
$729$	14.9363	0.553198
$730$	0	0
$731$	−14.2021	−0.525284
$732$	9.44382	0.349054
$733$	−17.5591	−0.648560	−0.324280	−	0.945961i	$-0.605122\pi$
$733$	−17.5591	−0.648560	−0.324280	+	0.945961i	$0.605122\pi$
$734$	37.8883	1.39848
$735$	0	0
$736$	1.79223	0.0660625
$737$	34.1525	1.25802
$738$	−15.0395	−0.553612
$739$	38.3981	1.41250	0.706248	−	0.707964i	$-0.250386\pi$
$739$	38.3981	1.41250	0.706248	+	0.707964i	$0.250386\pi$
$740$	0	0
$741$	9.42220	0.346133
$742$	−42.1833	−1.54860
$743$	−23.4989	−0.862091	−0.431045	−	0.902330i	$-0.641855\pi$
$743$	−23.4989	−0.862091	−0.431045	+	0.902330i	$0.641855\pi$
$744$	−28.6795	−1.05144
$745$	0	0
$746$	−26.9661	−0.987299
$747$	−12.4203	−0.454435
$748$	5.75152	0.210296
$749$	62.1854	2.27220
$750$	0	0
$751$	15.8551	0.578563	0.289281	−	0.957244i	$-0.406584\pi$
$751$	15.8551	0.578563	0.289281	+	0.957244i	$0.406584\pi$
$752$	−60.8069	−2.21740
$753$	−52.1993	−1.90225
$754$	−6.24169	−0.227309
$755$	0	0
$756$	−10.9845	−0.399501
$757$	−2.29130	−0.0832788	−0.0416394	−	0.999133i	$-0.513258\pi$
$757$	−2.29130	−0.0832788	−0.0416394	+	0.999133i	$0.513258\pi$
$758$	51.7764	1.88060
$759$	−2.44255	−0.0886591
$760$	0	0
$761$	−24.1144	−0.874145	−0.437072	−	0.899426i	$-0.643985\pi$
$761$	−24.1144	−0.874145	−0.437072	+	0.899426i	$0.643985\pi$
$762$	3.63484	0.131676
$763$	−8.90436	−0.322359
$764$	−4.12095	−0.149091
$765$	0	0
$766$	2.14028	0.0773314
$767$	−49.2473	−1.77822
$768$	−25.2347	−0.910577
$769$	−50.2033	−1.81038	−0.905188	−	0.425011i	$-0.860270\pi$
$769$	−50.2033	−1.81038	−0.905188	+	0.425011i	$0.860270\pi$
$770$	0	0
$771$	−36.2960	−1.30717
$772$	4.59025	0.165207
$773$	47.2029	1.69777	0.848886	−	0.528576i	$-0.177274\pi$
$773$	47.2029	1.69777	0.848886	+	0.528576i	$0.177274\pi$
$774$	4.45084	0.159982
$775$	0	0
$776$	−17.7577	−0.637464
$777$	−17.2118	−0.617470
$778$	−3.38343	−0.121302
$779$	−12.0945	−0.433331
$780$	0	0
$781$	1.86416	0.0667050
$782$	4.14185	0.148112
$783$	3.89281	0.139118
$784$	−67.3861	−2.40665
$785$	0	0
$786$	17.8014	0.634955
$787$	17.6905	0.630599	0.315299	−	0.948992i	$-0.397895\pi$
$787$	17.6905	0.630599	0.315299	+	0.948992i	$0.397895\pi$
$788$	2.63916	0.0940160
$789$	4.93894	0.175831
$790$	0	0
$791$	27.2423	0.968623
$792$	4.45242	0.158210
$793$	34.5314	1.22624
$794$	−24.6887	−0.876169
$795$	0	0
$796$	6.88572	0.244058
$797$	−8.31270	−0.294451	−0.147225	−	0.989103i	$-0.547034\pi$
$797$	−8.31270	−0.294451	−0.147225	+	0.989103i	$0.547034\pi$
$798$	16.6650	0.589935
$799$	−57.5217	−2.03497
$800$	0	0
$801$	1.02450	0.0361988
$802$	−8.53537	−0.301395
$803$	8.54756	0.301637
$804$	17.7406	0.625663
$805$	0	0
$806$	42.4535	1.49536
$807$	24.7684	0.871888
$808$	−5.93388	−0.208753
$809$	−34.7175	−1.22060	−0.610301	−	0.792169i	$-0.708952\pi$
$809$	−34.7175	−1.22060	−0.610301	+	0.792169i	$0.708952\pi$
$810$	0	0
$811$	48.7191	1.71076	0.855379	−	0.518002i	$-0.173324\pi$
$811$	48.7191	1.71076	0.855379	+	0.518002i	$0.173324\pi$
$812$	−2.46963	−0.0866672
$813$	−55.7412	−1.95493
$814$	6.69222	0.234562
$815$	0	0
$816$	−43.3571	−1.51780
$817$	3.57929	0.125224
$818$	22.7191	0.794356
$819$	16.9510	0.592314
$820$	0	0
$821$	−11.1342	−0.388585	−0.194292	−	0.980944i	$-0.562241\pi$
$821$	−11.1342	−0.388585	−0.194292	+	0.980944i	$0.562241\pi$
$822$	2.54478	0.0887593
$823$	26.0154	0.906840	0.453420	−	0.891297i	$-0.350204\pi$
$823$	26.0154	0.906840	0.453420	+	0.891297i	$0.350204\pi$
$824$	−37.3673	−1.30175
$825$	0	0
$826$	−87.1035	−3.03072
$827$	37.6183	1.30812	0.654058	−	0.756444i	$-0.273065\pi$
$827$	37.6183	1.30812	0.654058	+	0.756444i	$0.273065\pi$
$828$	−0.290377	−0.0100913
$829$	45.3259	1.57423	0.787116	−	0.616805i	$-0.211573\pi$
$829$	45.3259	1.57423	0.787116	+	0.616805i	$0.211573\pi$
$830$	0	0
$831$	19.0249	0.659968
$832$	−18.9434	−0.656743
$833$	−63.7455	−2.20865
$834$	−2.94835	−0.102093
$835$	0	0
$836$	−1.44953	−0.0501331
$837$	−26.4774	−0.915191
$838$	−3.06277	−0.105802
$839$	−37.5412	−1.29606	−0.648032	−	0.761613i	$-0.724408\pi$
$839$	−37.5412	−1.29606	−0.648032	+	0.761613i	$0.724408\pi$
$840$	0	0
$841$	−28.1248	−0.969820
$842$	−37.0475	−1.27674
$843$	−59.1333	−2.03666
$844$	−9.52256	−0.327780
$845$	0	0
$846$	18.0269	0.619778
$847$	28.4475	0.977466
$848$	−27.6592	−0.949820
$849$	−22.4599	−0.770821
$850$	0	0
$851$	1.07810	0.0369568
$852$	0.968345	0.0331750
$853$	−3.62937	−0.124267	−0.0621336	−	0.998068i	$-0.519790\pi$
$853$	−3.62937	−0.124267	−0.0621336	+	0.998068i	$0.519790\pi$
$854$	61.0755	2.08996
$855$	0	0
$856$	31.0244	1.06039
$857$	30.1700	1.03059	0.515293	−	0.857014i	$-0.327683\pi$
$857$	30.1700	1.03059	0.515293	+	0.857014i	$0.327683\pi$
$858$	−28.7983	−0.983158
$859$	25.4804	0.869380	0.434690	−	0.900580i	$-0.356858\pi$
$859$	25.4804	0.869380	0.434690	+	0.900580i	$0.356858\pi$
$860$	0	0
$861$	−95.0733	−3.24009
$862$	−34.8497	−1.18698
$863$	41.9712	1.42871	0.714357	−	0.699781i	$-0.246719\pi$
$863$	41.9712	1.42871	0.714357	+	0.699781i	$0.246719\pi$
$864$	−13.1789	−0.448354
$865$	0	0
$866$	2.18390	0.0742118
$867$	−7.48387	−0.254166
$868$	16.7975	0.570143
$869$	26.7740	0.908247
$870$	0	0
$871$	64.8686	2.19799
$872$	−4.44239	−0.150438
$873$	6.91894	0.234171
$874$	−1.04385	−0.0353088
$875$	0	0
$876$	4.44005	0.150015
$877$	5.40315	0.182451	0.0912257	−	0.995830i	$-0.470922\pi$
$877$	5.40315	0.182451	0.0912257	+	0.995830i	$0.470922\pi$
$878$	44.5442	1.50330
$879$	38.1400	1.28643
$880$	0	0
$881$	46.6700	1.57235	0.786176	−	0.618003i	$-0.212058\pi$
$881$	46.6700	1.57235	0.786176	+	0.618003i	$0.212058\pi$
$882$	19.9774	0.672674
$883$	16.0855	0.541321	0.270660	−	0.962675i	$-0.412758\pi$
$883$	16.0855	0.541321	0.270660	+	0.962675i	$0.412758\pi$
$884$	10.9243	0.367425
$885$	0	0
$886$	26.3325	0.884658
$887$	−22.9835	−0.771709	−0.385855	−	0.922560i	$-0.626093\pi$
$887$	−22.9835	−0.771709	−0.385855	+	0.922560i	$0.626093\pi$
$888$	−8.58698	−0.288160
$889$	5.25875	0.176373
$890$	0	0
$891$	23.8063	0.797540
$892$	−13.5209	−0.452713
$893$	14.4969	0.485121
$894$	−3.16589	−0.105883
$895$	0	0
$896$	−62.5183	−2.08859
$897$	−4.63934	−0.154903
$898$	30.0491	1.00275
$899$	−5.95290	−0.198540
$900$	0	0
$901$	−26.1648	−0.871677
$902$	36.9660	1.23083
$903$	28.1363	0.936318
$904$	13.5912	0.452036
$905$	0	0
$906$	−60.9104	−2.02361
$907$	−36.6183	−1.21589	−0.607946	−	0.793979i	$-0.708006\pi$
$907$	−36.6183	−1.21589	−0.607946	+	0.793979i	$0.708006\pi$
$908$	−12.2269	−0.405762
$909$	2.31202	0.0766849
$910$	0	0
$911$	−3.73066	−0.123602	−0.0618011	−	0.998088i	$-0.519684\pi$
$911$	−3.73066	−0.123602	−0.0618011	+	0.998088i	$0.519684\pi$
$912$	10.9271	0.361832
$913$	30.5282	1.01034
$914$	−42.8527	−1.41744
$915$	0	0
$916$	1.47618	0.0487743
$917$	25.7544	0.850484
$918$	−30.4564	−1.00521
$919$	−18.1560	−0.598911	−0.299456	−	0.954110i	$-0.596805\pi$
$919$	−18.1560	−0.598911	−0.299456	+	0.954110i	$0.596805\pi$
$920$	0	0
$921$	39.3950	1.29811
$922$	−24.5274	−0.807768
$923$	3.54076	0.116545
$924$	−11.3946	−0.374854
$925$	0	0
$926$	−58.1656	−1.91144
$927$	14.5594	0.478194
$928$	−2.96300	−0.0972653
$929$	52.2751	1.71509	0.857545	−	0.514409i	$-0.171989\pi$
$929$	52.2751	1.71509	0.857545	+	0.514409i	$0.171989\pi$
$930$	0	0
$931$	16.0655	0.526525
$932$	−16.8928	−0.553343
$933$	−42.5893	−1.39431
$934$	−12.8636	−0.420910
$935$	0	0
$936$	8.45685	0.276421
$937$	37.0812	1.21139	0.605694	−	0.795697i	$-0.292895\pi$
$937$	37.0812	1.21139	0.605694	+	0.795697i	$0.292895\pi$
$938$	114.733	3.74616
$939$	56.7916	1.85333
$940$	0	0
$941$	−56.6561	−1.84694	−0.923468	−	0.383676i	$-0.874658\pi$
$941$	−56.6561	−1.84694	−0.923468	+	0.383676i	$0.874658\pi$
$942$	8.19213	0.266914
$943$	5.95514	0.193926
$944$	−57.1129	−1.85887
$945$	0	0
$946$	−10.9399	−0.355685
$947$	5.52652	0.179588	0.0897938	−	0.995960i	$-0.471379\pi$
$947$	5.52652	0.179588	0.0897938	+	0.995960i	$0.471379\pi$
$948$	13.9078	0.451706
$949$	16.2351	0.527012
$950$	0	0
$951$	−19.3569	−0.627692
$952$	−47.7279	−1.54687
$953$	−29.2755	−0.948326	−0.474163	−	0.880437i	$-0.657249\pi$
$953$	−29.2755	−0.948326	−0.474163	+	0.880437i	$0.657249\pi$
$954$	8.19988	0.265481
$955$	0	0
$956$	0.453370	0.0146630
$957$	4.03815	0.130535
$958$	−19.4333	−0.627862
$959$	3.68168	0.118888
$960$	0	0
$961$	9.48922	0.306104
$962$	12.7111	0.409822
$963$	−12.0880	−0.389531
$964$	−14.4552	−0.465571
$965$	0	0
$966$	−8.20558	−0.264010
$967$	48.2493	1.55159	0.775797	−	0.630983i	$-0.217348\pi$
$967$	48.2493	1.55159	0.775797	+	0.630983i	$0.217348\pi$
$968$	14.1925	0.456163
$969$	10.3367	0.332064
$970$	0	0
$971$	13.7662	0.441777	0.220889	−	0.975299i	$-0.429104\pi$
$971$	13.7662	0.441777	0.220889	+	0.975299i	$0.429104\pi$
$972$	5.17162	0.165880
$973$	−4.26556	−0.136747
$974$	22.1378	0.709340
$975$	0	0
$976$	40.0466	1.28186
$977$	4.49107	0.143682	0.0718410	−	0.997416i	$-0.477113\pi$
$977$	4.49107	0.143682	0.0718410	+	0.997416i	$0.477113\pi$
$978$	−27.3773	−0.875431
$979$	−2.51814	−0.0804800
$980$	0	0
$981$	1.73089	0.0552631
$982$	34.4271	1.09861
$983$	−21.0432	−0.671175	−0.335587	−	0.942009i	$-0.608935\pi$
$983$	−21.0432	−0.671175	−0.335587	+	0.942009i	$0.608935\pi$
$984$	−47.4322	−1.51208
$985$	0	0
$986$	−6.84751	−0.218069
$987$	113.958	3.62734
$988$	−2.75321	−0.0875913
$989$	−1.76239	−0.0560406
$990$	0	0
$991$	20.2185	0.642263	0.321132	−	0.947035i	$-0.395937\pi$
$991$	20.2185	0.642263	0.321132	+	0.947035i	$0.395937\pi$
$992$	20.1532	0.639863
$993$	−20.9322	−0.664264
$994$	6.26252	0.198635
$995$	0	0
$996$	15.8580	0.502479
$997$	−0.392026	−0.0124156	−0.00620780	−	0.999981i	$-0.501976\pi$
$997$	−0.392026	−0.0124156	−0.00620780	+	0.999981i	$0.501976\pi$
$998$	−24.6812	−0.781268
$999$	−7.92764	−0.250819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3725.2.a.c.1.7		9
5.4	even	2		149.2.a.b.1.3	✓	9
15.14	odd	2		1341.2.a.e.1.7		9
20.19	odd	2		2384.2.a.j.1.3		9
35.34	odd	2		7301.2.a.j.1.3		9
40.19	odd	2		9536.2.a.w.1.7		9
40.29	even	2		9536.2.a.v.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
149.2.a.b.1.3	✓	9	5.4	even	2
1341.2.a.e.1.7		9	15.14	odd	2
2384.2.a.j.1.3		9	20.19	odd	2
3725.2.a.c.1.7		9	1.1	even	1	trivial
7301.2.a.j.1.3		9	35.34	odd	2
9536.2.a.v.1.3		9	40.29	even	2
9536.2.a.w.1.7		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)

\(f(q)\)	\(=\)	\(q+1.60510 q^{2} -1.97240 q^{3} +0.576343 q^{4} -3.16589 q^{6} -4.58029 q^{7} -2.28511 q^{8} +0.890348 q^{9} +O(q^{10})\)	\(q+1.60510 q^{2} -1.97240 q^{3} +0.576343 q^{4} -3.16589 q^{6} -4.58029 q^{7} -2.28511 q^{8} +0.890348 q^{9} -2.18841 q^{11} -1.13678 q^{12} -4.15663 q^{13} -7.35182 q^{14} -4.82051 q^{16} -4.56008 q^{17} +1.42910 q^{18} +1.14926 q^{19} +9.03414 q^{21} -3.51262 q^{22} -0.565875 q^{23} +4.50714 q^{24} -6.67180 q^{26} +4.16107 q^{27} -2.63982 q^{28} +0.935532 q^{29} -6.36311 q^{31} -3.16718 q^{32} +4.31642 q^{33} -7.31938 q^{34} +0.513146 q^{36} -1.90519 q^{37} +1.84467 q^{38} +8.19852 q^{39} -10.5238 q^{41} +14.5007 q^{42} +3.11444 q^{43} -1.26128 q^{44} -0.908286 q^{46} +12.6142 q^{47} +9.50797 q^{48} +13.9790 q^{49} +8.99428 q^{51} -2.39565 q^{52} +5.73780 q^{53} +6.67893 q^{54} +10.4665 q^{56} -2.26679 q^{57} +1.50162 q^{58} +11.8479 q^{59} -8.30754 q^{61} -10.2134 q^{62} -4.07805 q^{63} +4.55739 q^{64} +6.92828 q^{66} -15.6061 q^{67} -2.62817 q^{68} +1.11613 q^{69} -0.851833 q^{71} -2.03454 q^{72} -3.90582 q^{73} -3.05802 q^{74} +0.662366 q^{76} +10.0236 q^{77} +13.1594 q^{78} -12.2344 q^{79} -10.8783 q^{81} -16.8917 q^{82} -13.9499 q^{83} +5.20677 q^{84} +4.99899 q^{86} -1.84524 q^{87} +5.00077 q^{88} +1.15067 q^{89} +19.0386 q^{91} -0.326138 q^{92} +12.5506 q^{93} +20.2470 q^{94} +6.24694 q^{96} +7.77105 q^{97} +22.4377 q^{98} -1.94845 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + q^{2} - 6 q^{3} + 13 q^{4} + q^{6} - 3 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 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

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