LMFDB - Embedded newform 6025.2.a.n.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.628757 q^{2} -2.03617 q^{3} -1.60466 q^{4} +1.28026 q^{6} +0.952044 q^{7} +2.26646 q^{8} +1.14599 q^{9} +O(q^{10})$	\(q-0.628757 q^{2} -2.03617 q^{3} -1.60466 q^{4} +1.28026 q^{6} +0.952044 q^{7} +2.26646 q^{8} +1.14599 q^{9} +0.264542 q^{11} +3.26737 q^{12} +4.33167 q^{13} -0.598604 q^{14} +1.78428 q^{16} -5.23651 q^{17} -0.720546 q^{18} +5.12219 q^{19} -1.93852 q^{21} -0.166333 q^{22} -0.0255499 q^{23} -4.61489 q^{24} -2.72356 q^{26} +3.77509 q^{27} -1.52771 q^{28} +0.821055 q^{29} -2.30029 q^{31} -5.65479 q^{32} -0.538653 q^{33} +3.29249 q^{34} -1.83892 q^{36} +10.0379 q^{37} -3.22061 q^{38} -8.82000 q^{39} +11.6490 q^{41} +1.21886 q^{42} +6.04017 q^{43} -0.424502 q^{44} +0.0160647 q^{46} +5.20680 q^{47} -3.63309 q^{48} -6.09361 q^{49} +10.6624 q^{51} -6.95087 q^{52} +11.7212 q^{53} -2.37361 q^{54} +2.15777 q^{56} -10.4296 q^{57} -0.516244 q^{58} -3.73401 q^{59} -3.68964 q^{61} +1.44632 q^{62} +1.09103 q^{63} -0.0130678 q^{64} +0.338682 q^{66} -7.24621 q^{67} +8.40285 q^{68} +0.0520240 q^{69} +4.51346 q^{71} +2.59733 q^{72} +7.27765 q^{73} -6.31137 q^{74} -8.21939 q^{76} +0.251856 q^{77} +5.54564 q^{78} -8.91035 q^{79} -11.1247 q^{81} -7.32441 q^{82} -5.32080 q^{83} +3.11068 q^{84} -3.79780 q^{86} -1.67181 q^{87} +0.599574 q^{88} -4.87575 q^{89} +4.12394 q^{91} +0.0409991 q^{92} +4.68377 q^{93} -3.27381 q^{94} +11.5141 q^{96} -12.6624 q^{97} +3.83140 q^{98} +0.303162 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9	$ 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) $ 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9 + q^11 + 26 * q^12 + 11 * q^13 - q^14 + 43 * q^16 + 20 * q^17 + 18 * q^18 + 2 * q^21 + 23 * q^22 + 79 * q^23 - 2 * q^24 + 2 * q^26 + 26 * q^27 + 30 * q^28 + 2 * q^29 + q^31 + 68 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 16 * q^37 + 45 * q^38 - 2 * q^39 - 2 * q^41 + 19 * q^42 + 25 * q^43 + 3 * q^44 + 14 * q^46 + 88 * q^47 + 75 * q^48 + 40 * q^49 - 10 * q^51 + 18 * q^52 + 34 * q^53 + 4 * q^54 - 15 * q^56 + 51 * q^57 + 53 * q^58 + q^59 + 9 * q^61 + 39 * q^62 + 110 * q^63 + 17 * q^64 + 26 * q^66 + 30 * q^67 + 44 * q^68 - 7 * q^69 + 5 * q^71 + 18 * q^72 + 23 * q^73 - 18 * q^74 + 43 * q^76 + 30 * q^77 + 46 * q^78 + 5 * q^79 + 44 * q^81 + 5 * q^82 + 65 * q^83 - 65 * q^84 + 40 * q^86 + 33 * q^87 + 71 * q^88 - 9 * q^89 + q^91 + 117 * q^92 + 68 * q^93 - 72 * q^94 + 83 * q^96 - 8 * q^97 + 76 * q^98 - 40 * 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 $

$2$	−0.628757	−0.444598	−0.222299	−	0.974979i	$-0.571356\pi$
$2$	−0.628757	−0.444598	−0.222299	+	0.974979i	$0.571356\pi$
$3$	−2.03617	−1.17558	−0.587791	−	0.809013i	$-0.700002\pi$
$3$	−2.03617	−1.17558	−0.587791	+	0.809013i	$0.700002\pi$
$4$	−1.60466	−0.802332
$5$	0	0
$5$	0	0
$6$	1.28026	0.522662
$7$	0.952044	0.359839	0.179919	−	0.983681i	$-0.442416\pi$
$7$	0.952044	0.359839	0.179919	+	0.983681i	$0.442416\pi$
$8$	2.26646	0.801314
$9$	1.14599	0.381995
$10$	0	0
$11$	0.264542	0.0797625	0.0398813	−	0.999204i	$-0.487302\pi$
$11$	0.264542	0.0797625	0.0398813	+	0.999204i	$0.487302\pi$
$12$	3.26737	0.943208
$13$	4.33167	1.20139	0.600694	−	0.799479i	$-0.294891\pi$
$13$	4.33167	1.20139	0.600694	+	0.799479i	$0.294891\pi$
$14$	−0.598604	−0.159984
$15$	0	0
$16$	1.78428	0.446070
$17$	−5.23651	−1.27004	−0.635020	−	0.772495i	$-0.719008\pi$
$17$	−5.23651	−1.27004	−0.635020	+	0.772495i	$0.719008\pi$
$18$	−0.720546	−0.169834
$19$	5.12219	1.17511	0.587555	−	0.809184i	$-0.300090\pi$
$19$	5.12219	1.17511	0.587555	+	0.809184i	$0.300090\pi$
$20$	0	0
$21$	−1.93852	−0.423020
$22$	−0.166333	−0.0354623
$23$	−0.0255499	−0.00532753	−0.00266376	−	0.999996i	$-0.500848\pi$
$23$	−0.0255499	−0.00532753	−0.00266376	+	0.999996i	$0.500848\pi$
$24$	−4.61489	−0.942011
$25$	0	0
$26$	−2.72356	−0.534135
$27$	3.77509	0.726516
$28$	−1.52771	−0.288710
$29$	0.821055	0.152466	0.0762330	−	0.997090i	$-0.475711\pi$
$29$	0.821055	0.152466	0.0762330	+	0.997090i	$0.475711\pi$
$30$	0	0
$31$	−2.30029	−0.413144	−0.206572	−	0.978431i	$-0.566231\pi$
$31$	−2.30029	−0.413144	−0.206572	+	0.978431i	$0.566231\pi$
$32$	−5.65479	−0.999636
$33$	−0.538653	−0.0937675
$34$	3.29249	0.564658
$35$	0	0
$36$	−1.83892	−0.306487
$37$	10.0379	1.65021	0.825106	−	0.564978i	$-0.191115\pi$
$37$	10.0379	1.65021	0.825106	+	0.564978i	$0.191115\pi$
$38$	−3.22061	−0.522452
$39$	−8.82000	−1.41233
$40$	0	0
$41$	11.6490	1.81927	0.909637	−	0.415405i	$-0.136360\pi$
$41$	11.6490	1.81927	0.909637	+	0.415405i	$0.136360\pi$
$42$	1.21886	0.188074
$43$	6.04017	0.921117	0.460559	−	0.887629i	$-0.347649\pi$
$43$	6.04017	0.921117	0.460559	+	0.887629i	$0.347649\pi$
$44$	−0.424502	−0.0639961
$45$	0	0
$46$	0.0160647	0.00236861
$47$	5.20680	0.759490	0.379745	−	0.925091i	$-0.376012\pi$
$47$	5.20680	0.759490	0.379745	+	0.925091i	$0.376012\pi$
$48$	−3.63309	−0.524392
$49$	−6.09361	−0.870516
$50$	0	0
$51$	10.6624	1.49304
$52$	−6.95087	−0.963912
$53$	11.7212	1.61004	0.805018	−	0.593250i	$-0.202155\pi$
$53$	11.7212	1.61004	0.805018	+	0.593250i	$0.202155\pi$
$54$	−2.37361	−0.323008
$55$	0	0
$56$	2.15777	0.288344
$57$	−10.4296	−1.38144
$58$	−0.516244	−0.0677861
$59$	−3.73401	−0.486126	−0.243063	−	0.970010i	$-0.578152\pi$
$59$	−3.73401	−0.486126	−0.243063	+	0.970010i	$0.578152\pi$
$60$	0	0
$61$	−3.68964	−0.472410	−0.236205	−	0.971703i	$-0.575904\pi$
$61$	−3.68964	−0.472410	−0.236205	+	0.971703i	$0.575904\pi$
$62$	1.44632	0.183683
$63$	1.09103	0.137457
$64$	−0.0130678	−0.00163347
$65$	0	0
$66$	0.338682	0.0416889
$67$	−7.24621	−0.885266	−0.442633	−	0.896703i	$-0.645956\pi$
$67$	−7.24621	−0.885266	−0.442633	+	0.896703i	$0.645956\pi$
$68$	8.40285	1.01899
$69$	0.0520240	0.00626295
$70$	0	0
$71$	4.51346	0.535649	0.267825	−	0.963468i	$-0.413695\pi$
$71$	4.51346	0.535649	0.267825	+	0.963468i	$0.413695\pi$
$72$	2.59733	0.306098
$73$	7.27765	0.851784	0.425892	−	0.904774i	$-0.359960\pi$
$73$	7.27765	0.851784	0.425892	+	0.904774i	$0.359960\pi$
$74$	−6.31137	−0.733682
$75$	0	0
$76$	−8.21939	−0.942829
$77$	0.251856	0.0287017
$78$	5.54564	0.627920
$79$	−8.91035	−1.00249	−0.501247	−	0.865305i	$-0.667125\pi$
$79$	−8.91035	−1.00249	−0.501247	+	0.865305i	$0.667125\pi$
$80$	0	0
$81$	−11.1247	−1.23607
$82$	−7.32441	−0.808846
$83$	−5.32080	−0.584033	−0.292017	−	0.956413i	$-0.594326\pi$
$83$	−5.32080	−0.584033	−0.292017	+	0.956413i	$0.594326\pi$
$84$	3.11068	0.339403
$85$	0	0
$86$	−3.79780	−0.409527
$87$	−1.67181	−0.179236
$88$	0.599574	0.0639148
$89$	−4.87575	−0.516829	−0.258414	−	0.966034i	$-0.583200\pi$
$89$	−4.87575	−0.516829	−0.258414	+	0.966034i	$0.583200\pi$
$90$	0	0
$91$	4.12394	0.432306
$92$	0.0409991	0.00427445
$93$	4.68377	0.485685
$94$	−3.27381	−0.337668
$95$	0	0
$96$	11.5141	1.17515
$97$	−12.6624	−1.28567	−0.642836	−	0.766004i	$-0.722242\pi$
$97$	−12.6624	−1.28567	−0.642836	+	0.766004i	$0.722242\pi$
$98$	3.83140	0.387030
$99$	0.303162	0.0304689
$100$	0	0
$101$	−0.0741327	−0.00737648	−0.00368824	−	0.999993i	$-0.501174\pi$
$101$	−0.0741327	−0.00737648	−0.00368824	+	0.999993i	$0.501174\pi$
$102$	−6.70407	−0.663802
$103$	15.1012	1.48797	0.743984	−	0.668197i	$-0.232934\pi$
$103$	15.1012	1.48797	0.743984	+	0.668197i	$0.232934\pi$
$104$	9.81754	0.962689
$105$	0	0
$106$	−7.36981	−0.715819
$107$	9.41840	0.910511	0.455256	−	0.890361i	$-0.349548\pi$
$107$	9.41840	0.910511	0.455256	+	0.890361i	$0.349548\pi$
$108$	−6.05775	−0.582907
$109$	−18.2069	−1.74390	−0.871951	−	0.489592i	$-0.837146\pi$
$109$	−18.2069	−1.74390	−0.871951	+	0.489592i	$0.837146\pi$
$110$	0	0
$111$	−20.4388	−1.93996
$112$	1.69871	0.160513
$113$	−6.72559	−0.632690	−0.316345	−	0.948644i	$-0.602456\pi$
$113$	−6.72559	−0.632690	−0.316345	+	0.948644i	$0.602456\pi$
$114$	6.55771	0.614186
$115$	0	0
$116$	−1.31752	−0.122328
$117$	4.96402	0.458924
$118$	2.34778	0.216131
$119$	−4.98539	−0.457010
$120$	0	0
$121$	−10.9300	−0.993638
$122$	2.31989	0.210033
$123$	−23.7194	−2.13871
$124$	3.69119	0.331479
$125$	0	0
$126$	−0.685992	−0.0611130
$127$	−19.7025	−1.74831	−0.874157	−	0.485644i	$-0.838585\pi$
$127$	−19.7025	−1.74831	−0.874157	+	0.485644i	$0.838585\pi$
$128$	11.3178	1.00036
$129$	−12.2988	−1.08285
$130$	0	0
$131$	14.9092	1.30263	0.651313	−	0.758809i	$-0.274219\pi$
$131$	14.9092	1.30263	0.651313	+	0.758809i	$0.274219\pi$
$132$	0.864358	0.0752327
$133$	4.87655	0.422850
$134$	4.55611	0.393588
$135$	0	0
$136$	−11.8683	−1.01770
$137$	−9.05504	−0.773625	−0.386812	−	0.922158i	$-0.626424\pi$
$137$	−9.05504	−0.773625	−0.386812	+	0.922158i	$0.626424\pi$
$138$	−0.0327104	−0.00278450
$139$	−17.2453	−1.46273	−0.731365	−	0.681986i	$-0.761117\pi$
$139$	−17.2453	−1.46273	−0.731365	+	0.681986i	$0.761117\pi$
$140$	0	0
$141$	−10.6019	−0.892843
$142$	−2.83787	−0.238149
$143$	1.14591	0.0958258
$144$	2.04476	0.170396
$145$	0	0
$146$	−4.57587	−0.378702
$147$	12.4076	1.02336
$148$	−16.1074	−1.32402
$149$	−7.67806	−0.629011	−0.314506	−	0.949256i	$-0.601839\pi$
$149$	−7.67806	−0.629011	−0.314506	+	0.949256i	$0.601839\pi$
$150$	0	0
$151$	−20.0367	−1.63056	−0.815280	−	0.579067i	$-0.803417\pi$
$151$	−20.0367	−1.63056	−0.815280	+	0.579067i	$0.803417\pi$
$152$	11.6092	0.941632
$153$	−6.00097	−0.485149
$154$	−0.158356	−0.0127607
$155$	0	0
$156$	14.1532	1.13316
$157$	12.0723	0.963474	0.481737	−	0.876316i	$-0.340006\pi$
$157$	12.0723	0.963474	0.481737	+	0.876316i	$0.340006\pi$
$158$	5.60245	0.445707
$159$	−23.8664	−1.89273
$160$	0	0
$161$	−0.0243247	−0.00191705
$162$	6.99471	0.549557
$163$	17.2267	1.34930	0.674648	−	0.738139i	$-0.264295\pi$
$163$	17.2267	1.34930	0.674648	+	0.738139i	$0.264295\pi$
$164$	−18.6928	−1.45966
$165$	0	0
$166$	3.34549	0.259660
$167$	22.9575	1.77650	0.888251	−	0.459358i	$-0.151920\pi$
$167$	22.9575	1.77650	0.888251	+	0.459358i	$0.151920\pi$
$168$	−4.39358	−0.338972
$169$	5.76333	0.443333
$170$	0	0
$171$	5.86995	0.448886
$172$	−9.69245	−0.739042
$173$	17.2038	1.30798	0.653990	−	0.756504i	$-0.273094\pi$
$173$	17.2038	1.30798	0.653990	+	0.756504i	$0.273094\pi$
$174$	1.05116	0.0796882
$175$	0	0
$176$	0.472017	0.0355797
$177$	7.60307	0.571482
$178$	3.06566	0.229781
$179$	14.5587	1.08817	0.544086	−	0.839030i	$-0.316877\pi$
$179$	14.5587	1.08817	0.544086	+	0.839030i	$0.316877\pi$
$180$	0	0
$181$	15.0862	1.12135	0.560675	−	0.828036i	$-0.310542\pi$
$181$	15.0862	1.12135	0.560675	+	0.828036i	$0.310542\pi$
$182$	−2.59295	−0.192203
$183$	7.51274	0.555358
$184$	−0.0579078	−0.00426902
$185$	0	0
$186$	−2.94495	−0.215935
$187$	−1.38528	−0.101302
$188$	−8.35517	−0.609363
$189$	3.59405	0.261429
$190$	0	0
$191$	4.06886	0.294413	0.147206	−	0.989106i	$-0.452972\pi$
$191$	4.06886	0.294413	0.147206	+	0.989106i	$0.452972\pi$
$192$	0.0266082	0.00192028
$193$	15.4660	1.11326	0.556632	−	0.830759i	$-0.312093\pi$
$193$	15.4660	1.11326	0.556632	+	0.830759i	$0.312093\pi$
$194$	7.96157	0.571608
$195$	0	0
$196$	9.77820	0.698443
$197$	−1.04073	−0.0741489	−0.0370745	−	0.999313i	$-0.511804\pi$
$197$	−1.04073	−0.0741489	−0.0370745	+	0.999313i	$0.511804\pi$
$198$	−0.190615	−0.0135464
$199$	−15.4725	−1.09681	−0.548407	−	0.836212i	$-0.684766\pi$
$199$	−15.4725	−1.09681	−0.548407	+	0.836212i	$0.684766\pi$
$200$	0	0
$201$	14.7545	1.04070
$202$	0.0466114	0.00327957
$203$	0.781680	0.0548632
$204$	−17.1096	−1.19791
$205$	0	0
$206$	−9.49500	−0.661548
$207$	−0.0292798	−0.00203509
$208$	7.72890	0.535903
$209$	1.35504	0.0937298
$210$	0	0
$211$	3.68052	0.253378	0.126689	−	0.991943i	$-0.459565\pi$
$211$	3.68052	0.253378	0.126689	+	0.991943i	$0.459565\pi$
$212$	−18.8087	−1.29178
$213$	−9.19017	−0.629700
$214$	−5.92188	−0.404812
$215$	0	0
$216$	8.55608	0.582167
$217$	−2.18997	−0.148665
$218$	11.4477	0.775336
$219$	−14.8185	−1.00134
$220$	0	0
$221$	−22.6828	−1.52581
$222$	12.8510	0.862504
$223$	−14.7058	−0.984771	−0.492386	−	0.870377i	$-0.663875\pi$
$223$	−14.7058	−0.984771	−0.492386	+	0.870377i	$0.663875\pi$
$224$	−5.38361	−0.359708
$225$	0	0
$226$	4.22876	0.281293
$227$	9.64410	0.640102	0.320051	−	0.947400i	$-0.396300\pi$
$227$	9.64410	0.640102	0.320051	+	0.947400i	$0.396300\pi$
$228$	16.7361	1.10837
$229$	9.28207	0.613376	0.306688	−	0.951810i	$-0.400779\pi$
$229$	9.28207	0.613376	0.306688	+	0.951810i	$0.400779\pi$
$230$	0	0
$231$	−0.512822	−0.0337412
$232$	1.86089	0.122173
$233$	−6.56766	−0.430262	−0.215131	−	0.976585i	$-0.569018\pi$
$233$	−6.56766	−0.430262	−0.215131	+	0.976585i	$0.569018\pi$
$234$	−3.12116	−0.204037
$235$	0	0
$236$	5.99183	0.390035
$237$	18.1430	1.17851
$238$	3.13460	0.203186
$239$	18.2412	1.17992	0.589962	−	0.807431i	$-0.299143\pi$
$239$	18.2412	1.17992	0.589962	+	0.807431i	$0.299143\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	6.87232	0.441770
$243$	11.3265	0.726592
$244$	5.92064	0.379030
$245$	0	0
$246$	14.9137	0.950865
$247$	22.1876	1.41176
$248$	−5.21350	−0.331058
$249$	10.8340	0.686579
$250$	0	0
$251$	13.6625	0.862370	0.431185	−	0.902264i	$-0.358096\pi$
$251$	13.6625	0.862370	0.431185	+	0.902264i	$0.358096\pi$
$252$	−1.75074	−0.110286
$253$	−0.00675904	−0.000424937 0
$254$	12.3881	0.777297
$255$	0	0
$256$	−7.09001	−0.443126
$257$	−21.3617	−1.33250	−0.666252	−	0.745727i	$-0.732102\pi$
$257$	−21.3617	−1.33250	−0.666252	+	0.745727i	$0.732102\pi$
$258$	7.73296	0.481433
$259$	9.55648	0.593811
$260$	0	0
$261$	0.940916	0.0582413
$262$	−9.37428	−0.579145
$263$	−0.824406	−0.0508350	−0.0254175	−	0.999677i	$-0.508092\pi$
$263$	−0.824406	−0.0508350	−0.0254175	+	0.999677i	$0.508092\pi$
$264$	−1.22083	−0.0751372
$265$	0	0
$266$	−3.06616	−0.187999
$267$	9.92786	0.607575
$268$	11.6277	0.710278
$269$	23.6553	1.44229	0.721144	−	0.692785i	$-0.243617\pi$
$269$	23.6553	1.44229	0.721144	+	0.692785i	$0.243617\pi$
$270$	0	0
$271$	−3.56396	−0.216495	−0.108248	−	0.994124i	$-0.534524\pi$
$271$	−3.56396	−0.216495	−0.108248	+	0.994124i	$0.534524\pi$
$272$	−9.34340	−0.566527
$273$	−8.39703	−0.508212
$274$	5.69342	0.343952
$275$	0	0
$276$	−0.0834810	−0.00502497
$277$	−4.66351	−0.280203	−0.140102	−	0.990137i	$-0.544743\pi$
$277$	−4.66351	−0.280203	−0.140102	+	0.990137i	$0.544743\pi$
$278$	10.8431	0.650327
$279$	−2.63609	−0.157819
$280$	0	0
$281$	−3.00462	−0.179241	−0.0896203	−	0.995976i	$-0.528565\pi$
$281$	−3.00462	−0.179241	−0.0896203	+	0.995976i	$0.528565\pi$
$282$	6.66603	0.396956
$283$	−2.00606	−0.119248	−0.0596239	−	0.998221i	$-0.518990\pi$
$283$	−2.00606	−0.119248	−0.0596239	+	0.998221i	$0.518990\pi$
$284$	−7.24259	−0.429769
$285$	0	0
$286$	−0.720498	−0.0426040
$287$	11.0904	0.654645
$288$	−6.48031	−0.381856
$289$	10.4211	0.613004
$290$	0	0
$291$	25.7828	1.51141
$292$	−11.6782	−0.683414
$293$	−9.22768	−0.539087	−0.269543	−	0.962988i	$-0.586873\pi$
$293$	−9.22768	−0.539087	−0.269543	+	0.962988i	$0.586873\pi$
$294$	−7.80138	−0.454986
$295$	0	0
$296$	22.7504	1.32234
$297$	0.998671	0.0579488
$298$	4.82763	0.279657
$299$	−0.110674	−0.00640043
$300$	0	0
$301$	5.75051	0.331454
$302$	12.5982	0.724944
$303$	0.150947	0.00867166
$304$	9.13941	0.524181
$305$	0	0
$306$	3.77315	0.215697
$307$	15.9909	0.912647	0.456323	−	0.889814i	$-0.349166\pi$
$307$	15.9909	0.912647	0.456323	+	0.889814i	$0.349166\pi$
$308$	−0.404145	−0.0230283
$309$	−30.7487	−1.74923
$310$	0	0
$311$	−24.9158	−1.41284	−0.706422	−	0.707791i	$-0.749692\pi$
$311$	−24.9158	−1.41284	−0.706422	+	0.707791i	$0.749692\pi$
$312$	−19.9902	−1.13172
$313$	−26.0178	−1.47061	−0.735306	−	0.677736i	$-0.762961\pi$
$313$	−26.0178	−1.47061	−0.735306	+	0.677736i	$0.762961\pi$
$314$	−7.59054	−0.428359
$315$	0	0
$316$	14.2981	0.804333
$317$	26.8197	1.50635	0.753173	−	0.657823i	$-0.228522\pi$
$317$	26.8197	1.50635	0.753173	+	0.657823i	$0.228522\pi$
$318$	15.0062	0.841505
$319$	0.217204	0.0121611
$320$	0	0
$321$	−19.1775	−1.07038
$322$	0.0152943	0.000852318 0
$323$	−26.8224	−1.49244
$324$	17.8514	0.991743
$325$	0	0
$326$	−10.8314	−0.599895
$327$	37.0723	2.05010
$328$	26.4020	1.45781
$329$	4.95710	0.273294
$330$	0	0
$331$	28.7527	1.58039	0.790197	−	0.612853i	$-0.209978\pi$
$331$	28.7527	1.58039	0.790197	+	0.612853i	$0.209978\pi$
$332$	8.53809	0.468589
$333$	11.5032	0.630373
$334$	−14.4347	−0.789830
$335$	0	0
$336$	−3.45887	−0.188697
$337$	12.5805	0.685303	0.342651	−	0.939463i	$-0.388675\pi$
$337$	12.5805	0.685303	0.342651	+	0.939463i	$0.388675\pi$
$338$	−3.62373	−0.197105
$339$	13.6944	0.743779
$340$	0	0
$341$	−0.608523	−0.0329534
$342$	−3.69077	−0.199574
$343$	−12.4657	−0.673084
$344$	13.6898	0.738104
$345$	0	0
$346$	−10.8170	−0.581525
$347$	−12.7938	−0.686809	−0.343405	−	0.939188i	$-0.611580\pi$
$347$	−12.7938	−0.686809	−0.343405	+	0.939188i	$0.611580\pi$
$348$	2.68269	0.143807
$349$	−30.4705	−1.63105	−0.815524	−	0.578723i	$-0.803551\pi$
$349$	−30.4705	−1.63105	−0.815524	+	0.578723i	$0.803551\pi$
$350$	0	0
$351$	16.3524	0.872828
$352$	−1.49593	−0.0797335
$353$	34.0445	1.81201	0.906003	−	0.423270i	$-0.139118\pi$
$353$	34.0445	1.81201	0.906003	+	0.423270i	$0.139118\pi$
$354$	−4.78048	−0.254080
$355$	0	0
$356$	7.82395	0.414669
$357$	10.1511	0.537253
$358$	−9.15391	−0.483799
$359$	20.8737	1.10167	0.550837	−	0.834613i	$-0.314309\pi$
$359$	20.8737	1.10167	0.550837	+	0.834613i	$0.314309\pi$
$360$	0	0
$361$	7.23681	0.380885
$362$	−9.48556	−0.498550
$363$	22.2554	1.16810
$364$	−6.61754	−0.346853
$365$	0	0
$366$	−4.72369	−0.246911
$367$	−8.27931	−0.432176	−0.216088	−	0.976374i	$-0.569330\pi$
$367$	−8.27931	−0.432176	−0.216088	+	0.976374i	$0.569330\pi$
$368$	−0.0455882	−0.00237645
$369$	13.3496	0.694953
$370$	0	0
$371$	11.1591	0.579354
$372$	−7.51589	−0.389680
$373$	−23.5937	−1.22163	−0.610817	−	0.791772i	$-0.709159\pi$
$373$	−23.5937	−1.22163	−0.610817	+	0.791772i	$0.709159\pi$
$374$	0.871004	0.0450386
$375$	0	0
$376$	11.8010	0.608589
$377$	3.55653	0.183171
$378$	−2.25978	−0.116231
$379$	16.9480	0.870558	0.435279	−	0.900296i	$-0.356650\pi$
$379$	16.9480	0.870558	0.435279	+	0.900296i	$0.356650\pi$
$380$	0	0
$381$	40.1176	2.05529
$382$	−2.55833	−0.130895
$383$	−1.44759	−0.0739682	−0.0369841	−	0.999316i	$-0.511775\pi$
$383$	−1.44759	−0.0739682	−0.0369841	+	0.999316i	$0.511775\pi$
$384$	−23.0450	−1.17601
$385$	0	0
$386$	−9.72433	−0.494955
$387$	6.92194	0.351862
$388$	20.3189	1.03154
$389$	31.5016	1.59720	0.798598	−	0.601865i	$-0.205575\pi$
$389$	31.5016	1.59720	0.798598	+	0.601865i	$0.205575\pi$
$390$	0	0
$391$	0.133792	0.00676618
$392$	−13.8109	−0.697556
$393$	−30.3577	−1.53134
$394$	0.654366	0.0329665
$395$	0	0
$396$	−0.486473	−0.0244462
$397$	−17.8910	−0.897925	−0.448962	−	0.893551i	$-0.648206\pi$
$397$	−17.8910	−0.897925	−0.448962	+	0.893551i	$0.648206\pi$
$398$	9.72842	0.487642
$399$	−9.92948	−0.497096
$400$	0	0
$401$	−20.4076	−1.01911	−0.509554	−	0.860439i	$-0.670190\pi$
$401$	−20.4076	−1.01911	−0.509554	+	0.860439i	$0.670190\pi$
$402$	−9.27700	−0.462695
$403$	−9.96407	−0.496346
$404$	0.118958	0.00591839
$405$	0	0
$406$	−0.491487	−0.0243921
$407$	2.65544	0.131625
$408$	24.1659	1.19639
$409$	39.5932	1.95776	0.978879	−	0.204442i	$-0.0655380\pi$
$409$	39.5932	1.95776	0.978879	+	0.204442i	$0.0655380\pi$
$410$	0	0
$411$	18.4376	0.909460
$412$	−24.2324	−1.19385
$413$	−3.55494	−0.174927
$414$	0.0184099	0.000904797 0
$415$	0	0
$416$	−24.4947	−1.20095
$417$	35.1144	1.71956
$418$	−0.851988	−0.0416721
$419$	−18.6922	−0.913175	−0.456588	−	0.889678i	$-0.650928\pi$
$419$	−18.6922	−0.913175	−0.456588	+	0.889678i	$0.650928\pi$
$420$	0	0
$421$	8.88795	0.433172	0.216586	−	0.976264i	$-0.430508\pi$
$421$	8.88795	0.433172	0.216586	+	0.976264i	$0.430508\pi$
$422$	−2.31415	−0.112651
$423$	5.96691	0.290121
$424$	26.5657	1.29014
$425$	0	0
$426$	5.77838	0.279963
$427$	−3.51270	−0.169992
$428$	−15.1134	−0.730533
$429$	−2.33327	−0.112651
$430$	0	0
$431$	29.5644	1.42407	0.712034	−	0.702145i	$-0.247774\pi$
$431$	29.5644	1.42407	0.712034	+	0.702145i	$0.247774\pi$
$432$	6.73581	0.324077
$433$	30.3450	1.45829	0.729143	−	0.684361i	$-0.239919\pi$
$433$	30.3450	1.45829	0.729143	+	0.684361i	$0.239919\pi$
$434$	1.37696	0.0660963
$435$	0	0
$436$	29.2159	1.39919
$437$	−0.130871	−0.00626043
$438$	9.31725	0.445195
$439$	−31.4495	−1.50100	−0.750502	−	0.660868i	$-0.770188\pi$
$439$	−31.4495	−1.50100	−0.750502	+	0.660868i	$0.770188\pi$
$440$	0	0
$441$	−6.98319	−0.332533
$442$	14.2620	0.678373
$443$	−16.0616	−0.763110	−0.381555	−	0.924346i	$-0.624611\pi$
$443$	−16.0616	−0.763110	−0.381555	+	0.924346i	$0.624611\pi$
$444$	32.7974	1.55649
$445$	0	0
$446$	9.24635	0.437828
$447$	15.6338	0.739455
$448$	−0.0124411	−0.000587787 0
$449$	−1.96649	−0.0928043	−0.0464021	−	0.998923i	$-0.514776\pi$
$449$	−1.96649	−0.0928043	−0.0464021	+	0.998923i	$0.514776\pi$
$450$	0	0
$451$	3.08166	0.145110
$452$	10.7923	0.507628
$453$	40.7980	1.91686
$454$	−6.06380	−0.284588
$455$	0	0
$456$	−23.6383	−1.10697
$457$	31.6735	1.48162	0.740811	−	0.671714i	$-0.234441\pi$
$457$	31.6735	1.48162	0.740811	+	0.671714i	$0.234441\pi$
$458$	−5.83616	−0.272706
$459$	−19.7683	−0.922705
$460$	0	0
$461$	−0.909527	−0.0423609	−0.0211804	−	0.999776i	$-0.506742\pi$
$461$	−0.909527	−0.0423609	−0.0211804	+	0.999776i	$0.506742\pi$
$462$	0.322440	0.0150013
$463$	29.8260	1.38613	0.693067	−	0.720873i	$-0.256259\pi$
$463$	29.8260	1.38613	0.693067	+	0.720873i	$0.256259\pi$
$464$	1.46499	0.0680105
$465$	0	0
$466$	4.12946	0.191294
$467$	35.2758	1.63237	0.816185	−	0.577791i	$-0.196085\pi$
$467$	35.2758	1.63237	0.816185	+	0.577791i	$0.196085\pi$
$468$	−7.96560	−0.368210
$469$	−6.89872	−0.318553
$470$	0	0
$471$	−24.5812	−1.13264
$472$	−8.46297	−0.389540
$473$	1.59788	0.0734707
$474$	−11.4075	−0.523965
$475$	0	0
$476$	7.99988	0.366674
$477$	13.4324	0.615026
$478$	−11.4693	−0.524592
$479$	−15.6794	−0.716408	−0.358204	−	0.933643i	$-0.616611\pi$
$479$	−15.6794	−0.716408	−0.358204	+	0.933643i	$0.616611\pi$
$480$	0	0
$481$	43.4806	1.98255
$482$	−0.628757	−0.0286391
$483$	0.0495291	0.00225365
$484$	17.5390	0.797228
$485$	0	0
$486$	−7.12159	−0.323042
$487$	−7.17915	−0.325318	−0.162659	−	0.986682i	$-0.552007\pi$
$487$	−7.17915	−0.325318	−0.162659	+	0.986682i	$0.552007\pi$
$488$	−8.36242	−0.378549
$489$	−35.0764	−1.58621
$490$	0	0
$491$	16.1289	0.727888	0.363944	−	0.931421i	$-0.381430\pi$
$491$	16.1289	0.727888	0.363944	+	0.931421i	$0.381430\pi$
$492$	38.0617	1.71595
$493$	−4.29946	−0.193638
$494$	−13.9506	−0.627668
$495$	0	0
$496$	−4.10435	−0.184291
$497$	4.29701	0.192747
$498$	−6.81198	−0.305252
$499$	21.7008	0.971459	0.485730	−	0.874109i	$-0.338554\pi$
$499$	21.7008	0.971459	0.485730	+	0.874109i	$0.338554\pi$
$500$	0	0
$501$	−46.7453	−2.08843
$502$	−8.59039	−0.383408
$503$	−33.4196	−1.49011	−0.745053	−	0.667005i	$-0.767576\pi$
$503$	−33.4196	−1.49011	−0.745053	+	0.667005i	$0.767576\pi$
$504$	2.47277	0.110146
$505$	0	0
$506$	0.00424979	0.000188926 0
$507$	−11.7351	−0.521175
$508$	31.6159	1.40273
$509$	18.3142	0.811765	0.405882	−	0.913925i	$-0.366964\pi$
$509$	18.3142	0.811765	0.405882	+	0.913925i	$0.366964\pi$
$510$	0	0
$511$	6.92864	0.306505
$512$	−18.1777	−0.803349
$513$	19.3367	0.853737
$514$	13.4313	0.592429
$515$	0	0
$516$	19.7355	0.868805
$517$	1.37742	0.0605788
$518$	−6.00870	−0.264007
$519$	−35.0298	−1.53764
$520$	0	0
$521$	−28.6616	−1.25569	−0.627843	−	0.778340i	$-0.716062\pi$
$521$	−28.6616	−1.25569	−0.627843	+	0.778340i	$0.716062\pi$
$522$	−0.591608	−0.0258940
$523$	−28.1483	−1.23084	−0.615420	−	0.788199i	$-0.711014\pi$
$523$	−28.1483	−1.23084	−0.615420	+	0.788199i	$0.711014\pi$
$524$	−23.9243	−1.04514
$525$	0	0
$526$	0.518351	0.0226012
$527$	12.0455	0.524709
$528$	−0.961107	−0.0418268
$529$	−22.9993	−0.999972
$530$	0	0
$531$	−4.27912	−0.185698
$532$	−7.82523	−0.339267
$533$	50.4597	2.18565
$534$	−6.24221	−0.270127
$535$	0	0
$536$	−16.4232	−0.709376
$537$	−29.6441	−1.27924
$538$	−14.8734	−0.641239
$539$	−1.61202	−0.0694346
$540$	0	0
$541$	−20.0834	−0.863455	−0.431727	−	0.902004i	$-0.642096\pi$
$541$	−20.0834	−0.863455	−0.431727	+	0.902004i	$0.642096\pi$
$542$	2.24086	0.0962533
$543$	−30.7181	−1.31824
$544$	29.6114	1.26958
$545$	0	0
$546$	5.27969	0.225950
$547$	24.5628	1.05023	0.525115	−	0.851032i	$-0.324022\pi$
$547$	24.5628	1.05023	0.525115	+	0.851032i	$0.324022\pi$
$548$	14.5303	0.620704
$549$	−4.22828	−0.180458
$550$	0	0
$551$	4.20560	0.179164
$552$	0.117910	0.00501859
$553$	−8.48305	−0.360736
$554$	2.93222	0.124578
$555$	0	0
$556$	27.6730	1.17360
$557$	−13.4850	−0.571378	−0.285689	−	0.958322i	$-0.592223\pi$
$557$	−13.4850	−0.571378	−0.285689	+	0.958322i	$0.592223\pi$
$558$	1.65746	0.0701660
$559$	26.1640	1.10662
$560$	0	0
$561$	2.82066	0.119089
$562$	1.88918	0.0796901
$563$	11.8930	0.501231	0.250616	−	0.968087i	$-0.419367\pi$
$563$	11.8930	0.501231	0.250616	+	0.968087i	$0.419367\pi$
$564$	17.0125	0.716357
$565$	0	0
$566$	1.26132	0.0530174
$567$	−10.5912	−0.444788
$568$	10.2296	0.429223
$569$	−5.70015	−0.238963	−0.119481	−	0.992836i	$-0.538123\pi$
$569$	−5.70015	−0.238963	−0.119481	+	0.992836i	$0.538123\pi$
$570$	0	0
$571$	−29.3310	−1.22747	−0.613733	−	0.789514i	$-0.710333\pi$
$571$	−29.3310	−1.22747	−0.613733	+	0.789514i	$0.710333\pi$
$572$	−1.83880	−0.0768841
$573$	−8.28489	−0.346106
$574$	−6.97316	−0.291054
$575$	0	0
$576$	−0.0149755	−0.000623978 0
$577$	15.5613	0.647826	0.323913	−	0.946087i	$-0.395001\pi$
$577$	15.5613	0.647826	0.323913	+	0.946087i	$0.395001\pi$
$578$	−6.55232	−0.272540
$579$	−31.4913	−1.30873
$580$	0	0
$581$	−5.06563	−0.210158
$582$	−16.2111	−0.671972
$583$	3.10077	0.128421
$584$	16.4945	0.682547
$585$	0	0
$586$	5.80197	0.239677
$587$	−27.3626	−1.12938	−0.564688	−	0.825305i	$-0.691003\pi$
$587$	−27.3626	−1.12938	−0.564688	+	0.825305i	$0.691003\pi$
$588$	−19.9101	−0.821078
$589$	−11.7825	−0.485489
$590$	0	0
$591$	2.11910	0.0871682
$592$	17.9103	0.736110
$593$	−40.3381	−1.65649	−0.828243	−	0.560370i	$-0.810659\pi$
$593$	−40.3381	−1.65649	−0.828243	+	0.560370i	$0.810659\pi$
$594$	−0.627921	−0.0257639
$595$	0	0
$596$	12.3207	0.504676
$597$	31.5046	1.28940
$598$	0.0695869	0.00284562
$599$	46.2943	1.89153	0.945766	−	0.324847i	$-0.105313\pi$
$599$	46.2943	1.89153	0.945766	+	0.324847i	$0.105313\pi$
$600$	0	0
$601$	−6.94462	−0.283277	−0.141639	−	0.989918i	$-0.545237\pi$
$601$	−6.94462	−0.283277	−0.141639	+	0.989918i	$0.545237\pi$
$602$	−3.61567	−0.147364
$603$	−8.30405	−0.338167
$604$	32.1521	1.30825
$605$	0	0
$606$	−0.0949088	−0.00385541
$607$	19.9253	0.808742	0.404371	−	0.914595i	$-0.367491\pi$
$607$	19.9253	0.808742	0.404371	+	0.914595i	$0.367491\pi$
$608$	−28.9649	−1.17468
$609$	−1.59163	−0.0644962
$610$	0	0
$611$	22.5541	0.912442
$612$	9.62954	0.389251
$613$	33.5828	1.35640	0.678198	−	0.734879i	$-0.262761\pi$
$613$	33.5828	1.35640	0.678198	+	0.734879i	$0.262761\pi$
$614$	−10.0544	−0.405761
$615$	0	0
$616$	0.570821	0.0229990
$617$	−16.0045	−0.644319	−0.322159	−	0.946685i	$-0.604409\pi$
$617$	−16.0045	−0.644319	−0.322159	+	0.946685i	$0.604409\pi$
$618$	19.3334	0.777705
$619$	−1.42600	−0.0573160	−0.0286580	−	0.999589i	$-0.509123\pi$
$619$	−1.42600	−0.0573160	−0.0286580	+	0.999589i	$0.509123\pi$
$620$	0	0
$621$	−0.0964532	−0.00387053
$622$	15.6660	0.628148
$623$	−4.64193	−0.185975
$624$	−15.7373	−0.629998
$625$	0	0
$626$	16.3588	0.653831
$627$	−2.75908	−0.110187
$628$	−19.3720	−0.773027
$629$	−52.5633	−2.09584
$630$	0	0
$631$	−4.47508	−0.178150	−0.0890751	−	0.996025i	$-0.528391\pi$
$631$	−4.47508	−0.178150	−0.0890751	+	0.996025i	$0.528391\pi$
$632$	−20.1949	−0.803312
$633$	−7.49417	−0.297867
$634$	−16.8631	−0.669719
$635$	0	0
$636$	38.2976	1.51860
$637$	−26.3955	−1.04583
$638$	−0.136568	−0.00540679
$639$	5.17236	0.204615
$640$	0	0
$641$	32.1482	1.26978	0.634890	−	0.772603i	$-0.281046\pi$
$641$	32.1482	1.26978	0.634890	+	0.772603i	$0.281046\pi$
$642$	12.0580	0.475890
$643$	31.1494	1.22841	0.614206	−	0.789145i	$-0.289476\pi$
$643$	31.1494	1.22841	0.614206	+	0.789145i	$0.289476\pi$
$644$	0.0390329	0.00153811
$645$	0	0
$646$	16.8648	0.663535
$647$	47.5414	1.86904	0.934522	−	0.355905i	$-0.115827\pi$
$647$	47.5414	1.86904	0.934522	+	0.355905i	$0.115827\pi$
$648$	−25.2136	−0.990484
$649$	−0.987803	−0.0387747
$650$	0	0
$651$	4.45916	0.174768
$652$	−27.6430	−1.08258
$653$	41.6205	1.62874	0.814368	−	0.580348i	$-0.197084\pi$
$653$	41.6205	1.62874	0.814368	+	0.580348i	$0.197084\pi$
$654$	−23.3095	−0.911472
$655$	0	0
$656$	20.7851	0.811523
$657$	8.34008	0.325377
$658$	−3.11681	−0.121506
$659$	−1.02036	−0.0397474	−0.0198737	−	0.999802i	$-0.506326\pi$
$659$	−1.02036	−0.0397474	−0.0198737	+	0.999802i	$0.506326\pi$
$660$	0	0
$661$	31.4248	1.22228	0.611141	−	0.791521i	$-0.290711\pi$
$661$	31.4248	1.22228	0.611141	+	0.791521i	$0.290711\pi$
$662$	−18.0785	−0.702640
$663$	46.1861	1.79372
$664$	−12.0594	−0.467994
$665$	0	0
$666$	−7.23273	−0.280263
$667$	−0.0209779	−0.000812267 0
$668$	−36.8391	−1.42535
$669$	29.9434	1.15768
$670$	0	0
$671$	−0.976067	−0.0376807
$672$	10.9619	0.422866
$673$	36.0874	1.39107	0.695533	−	0.718495i	$-0.255168\pi$
$673$	36.0874	1.39107	0.695533	+	0.718495i	$0.255168\pi$
$674$	−7.91007	−0.304684
$675$	0	0
$676$	−9.24821	−0.355700
$677$	−32.9926	−1.26801	−0.634004	−	0.773329i	$-0.718590\pi$
$677$	−32.9926	−1.26801	−0.634004	+	0.773329i	$0.718590\pi$
$678$	−8.61047	−0.330683
$679$	−12.0552	−0.462635
$680$	0	0
$681$	−19.6370	−0.752493
$682$	0.382613	0.0146510
$683$	−25.6771	−0.982508	−0.491254	−	0.871016i	$-0.663461\pi$
$683$	−25.6771	−0.982508	−0.491254	+	0.871016i	$0.663461\pi$
$684$	−9.41930	−0.360156
$685$	0	0
$686$	7.83789	0.299252
$687$	−18.8999	−0.721075
$688$	10.7773	0.410882
$689$	50.7725	1.93428
$690$	0	0
$691$	32.1870	1.22445	0.612226	−	0.790683i	$-0.290274\pi$
$691$	32.1870	1.22445	0.612226	+	0.790683i	$0.290274\pi$
$692$	−27.6063	−1.04943
$693$	0.288623	0.0109639
$694$	8.04422	0.305354
$695$	0	0
$696$	−3.78908	−0.143625
$697$	−61.0003	−2.31055
$698$	19.1585	0.725161
$699$	13.3729	0.505808
$700$	0	0
$701$	27.3708	1.03378	0.516890	−	0.856052i	$-0.327090\pi$
$701$	27.3708	1.03378	0.516890	+	0.856052i	$0.327090\pi$
$702$	−10.2817	−0.388058
$703$	51.4158	1.93918
$704$	−0.00345698	−0.000130290 0
$705$	0	0
$706$	−21.4057	−0.805615
$707$	−0.0705776	−0.00265434
$708$	−12.2004	−0.458518
$709$	21.1432	0.794048	0.397024	−	0.917808i	$-0.370043\pi$
$709$	21.1432	0.794048	0.397024	+	0.917808i	$0.370043\pi$
$710$	0	0
$711$	−10.2111	−0.382947
$712$	−11.0507	−0.414142
$713$	0.0587721	0.00220103
$714$	−6.38257	−0.238862
$715$	0	0
$716$	−23.3619	−0.873075
$717$	−37.1421	−1.38710
$718$	−13.1245	−0.489802
$719$	37.7075	1.40625	0.703126	−	0.711065i	$-0.251787\pi$
$719$	37.7075	1.40625	0.703126	+	0.711065i	$0.251787\pi$
$720$	0	0
$721$	14.3770	0.535429
$722$	−4.55019	−0.169341
$723$	−2.03617	−0.0757259
$724$	−24.2083	−0.899695
$725$	0	0
$726$	−13.9932	−0.519337
$727$	−2.15608	−0.0799646	−0.0399823	−	0.999200i	$-0.512730\pi$
$727$	−2.15608	−0.0799646	−0.0399823	+	0.999200i	$0.512730\pi$
$728$	9.34673	0.346413
$729$	10.3114	0.381905
$730$	0	0
$731$	−31.6294	−1.16986
$732$	−12.0554	−0.445581
$733$	16.0911	0.594337	0.297169	−	0.954825i	$-0.403958\pi$
$733$	16.0911	0.594337	0.297169	+	0.954825i	$0.403958\pi$
$734$	5.20567	0.192145
$735$	0	0
$736$	0.144480	0.00532559
$737$	−1.91693	−0.0706111
$738$	−8.39366	−0.308975
$739$	20.2731	0.745759	0.372880	−	0.927880i	$-0.378370\pi$
$739$	20.2731	0.745759	0.372880	+	0.927880i	$0.378370\pi$
$740$	0	0
$741$	−45.1777	−1.65965
$742$	−7.01639	−0.257580
$743$	−31.9105	−1.17068	−0.585342	−	0.810787i	$-0.699040\pi$
$743$	−31.9105	−1.17068	−0.585342	+	0.810787i	$0.699040\pi$
$744$	10.6156	0.389186
$745$	0	0
$746$	14.8347	0.543137
$747$	−6.09755	−0.223098
$748$	2.22291	0.0812776
$749$	8.96673	0.327637
$750$	0	0
$751$	−8.76408	−0.319806	−0.159903	−	0.987133i	$-0.551118\pi$
$751$	−8.76408	−0.319806	−0.159903	+	0.987133i	$0.551118\pi$
$752$	9.29038	0.338785
$753$	−27.8192	−1.01379
$754$	−2.23620	−0.0814374
$755$	0	0
$756$	−5.76725	−0.209753
$757$	−49.2099	−1.78856	−0.894282	−	0.447504i	$-0.852313\pi$
$757$	−49.2099	−1.78856	−0.894282	+	0.447504i	$0.852313\pi$
$758$	−10.6561	−0.387049
$759$	0.0137625	0.000499549 0
$760$	0	0
$761$	−22.6015	−0.819304	−0.409652	−	0.912242i	$-0.634350\pi$
$761$	−22.6015	−0.819304	−0.409652	+	0.912242i	$0.634350\pi$
$762$	−25.2242	−0.913777
$763$	−17.3338	−0.627524
$764$	−6.52916	−0.236217
$765$	0	0
$766$	0.910180	0.0328861
$767$	−16.1745	−0.584026
$768$	14.4365	0.520931
$769$	−21.0272	−0.758259	−0.379130	−	0.925344i	$-0.623777\pi$
$769$	−21.0272	−0.758259	−0.379130	+	0.925344i	$0.623777\pi$
$770$	0	0
$771$	43.4959	1.56647
$772$	−24.8177	−0.893208
$773$	−43.1560	−1.55221	−0.776107	−	0.630602i	$-0.782808\pi$
$773$	−43.1560	−1.55221	−0.776107	+	0.630602i	$0.782808\pi$
$774$	−4.35222	−0.156437
$775$	0	0
$776$	−28.6988	−1.03023
$777$	−19.4586	−0.698074
$778$	−19.8069	−0.710110
$779$	59.6685	2.13785
$780$	0	0
$781$	1.19400	0.0427247
$782$	−0.0841229	−0.00300823
$783$	3.09955	0.110769
$784$	−10.8727	−0.388311
$785$	0	0
$786$	19.0876	0.680833
$787$	19.1286	0.681861	0.340931	−	0.940088i	$-0.389258\pi$
$787$	19.1286	0.681861	0.340931	+	0.940088i	$0.389258\pi$
$788$	1.67002	0.0594921
$789$	1.67863	0.0597608
$790$	0	0
$791$	−6.40306	−0.227666
$792$	0.687103	0.0244151
$793$	−15.9823	−0.567548
$794$	11.2491	0.399216
$795$	0	0
$796$	24.8281	0.880009
$797$	34.1131	1.20835	0.604173	−	0.796853i	$-0.293503\pi$
$797$	34.1131	1.20835	0.604173	+	0.796853i	$0.293503\pi$
$798$	6.24323	0.221008
$799$	−27.2655	−0.964583
$800$	0	0
$801$	−5.58754	−0.197426
$802$	12.8314	0.453093
$803$	1.92525	0.0679405
$804$	−23.6761	−0.834990
$805$	0	0
$806$	6.26498	0.220674
$807$	−48.1662	−1.69553
$808$	−0.168019	−0.00591088
$809$	−25.2656	−0.888293	−0.444146	−	0.895954i	$-0.646493\pi$
$809$	−25.2656	−0.888293	−0.444146	+	0.895954i	$0.646493\pi$
$810$	0	0
$811$	17.0125	0.597390	0.298695	−	0.954349i	$-0.403449\pi$
$811$	17.0125	0.597390	0.298695	+	0.954349i	$0.403449\pi$
$812$	−1.25434	−0.0440185
$813$	7.25682	0.254508
$814$	−1.66962	−0.0585203
$815$	0	0
$816$	19.0247	0.665999
$817$	30.9389	1.08241
$818$	−24.8945	−0.870415
$819$	4.72597	0.165139
$820$	0	0
$821$	7.04839	0.245990	0.122995	−	0.992407i	$-0.460750\pi$
$821$	7.04839	0.245990	0.122995	+	0.992407i	$0.460750\pi$
$822$	−11.5928	−0.404344
$823$	21.7844	0.759355	0.379677	−	0.925119i	$-0.376035\pi$
$823$	21.7844	0.759355	0.379677	+	0.925119i	$0.376035\pi$
$824$	34.2263	1.19233
$825$	0	0
$826$	2.23519	0.0777723
$827$	10.7476	0.373731	0.186865	−	0.982386i	$-0.440167\pi$
$827$	10.7476	0.373731	0.186865	+	0.982386i	$0.440167\pi$
$828$	0.0469843	0.00163282
$829$	−3.63058	−0.126095	−0.0630476	−	0.998011i	$-0.520082\pi$
$829$	−3.63058	−0.126095	−0.0630476	+	0.998011i	$0.520082\pi$
$830$	0	0
$831$	9.49570	0.329402
$832$	−0.0566053	−0.00196243
$833$	31.9093	1.10559
$834$	−22.0784	−0.764514
$835$	0	0
$836$	−2.17438	−0.0752025
$837$	−8.68378	−0.300155
$838$	11.7529	0.405996
$839$	28.2546	0.975456	0.487728	−	0.872996i	$-0.337826\pi$
$839$	28.2546	0.975456	0.487728	+	0.872996i	$0.337826\pi$
$840$	0	0
$841$	−28.3259	−0.976754
$842$	−5.58836	−0.192588
$843$	6.11792	0.210712
$844$	−5.90601	−0.203293
$845$	0	0
$846$	−3.75174	−0.128987
$847$	−10.4059	−0.357550
$848$	20.9140	0.718189
$849$	4.08468	0.140186
$850$	0	0
$851$	−0.256466	−0.00879155
$852$	14.7471	0.505229
$853$	−34.1367	−1.16882	−0.584410	−	0.811459i	$-0.698674\pi$
$853$	−34.1367	−1.16882	−0.584410	+	0.811459i	$0.698674\pi$
$854$	2.20864	0.0755780
$855$	0	0
$856$	21.3464	0.729605
$857$	33.8648	1.15680	0.578400	−	0.815753i	$-0.303677\pi$
$857$	33.8648	1.15680	0.578400	+	0.815753i	$0.303677\pi$
$858$	1.46706	0.0500845
$859$	4.88183	0.166566	0.0832829	−	0.996526i	$-0.473459\pi$
$859$	4.88183	0.166566	0.0832829	+	0.996526i	$0.473459\pi$
$860$	0	0
$861$	−22.5819	−0.769590
$862$	−18.5888	−0.633138
$863$	0.615531	0.0209529	0.0104765	−	0.999945i	$-0.496665\pi$
$863$	0.615531	0.0209529	0.0104765	+	0.999945i	$0.496665\pi$
$864$	−21.3473	−0.726251
$865$	0	0
$866$	−19.0796	−0.648351
$867$	−21.2191	−0.720637
$868$	3.51417	0.119279
$869$	−2.35717	−0.0799614
$870$	0	0
$871$	−31.3882	−1.06355
$872$	−41.2651	−1.39741
$873$	−14.5109	−0.491120
$874$	0.0822863	0.00278338
$875$	0	0
$876$	23.7788	0.803410
$877$	2.38404	0.0805033	0.0402516	−	0.999190i	$-0.487184\pi$
$877$	2.38404	0.0805033	0.0402516	+	0.999190i	$0.487184\pi$
$878$	19.7741	0.667344
$879$	18.7891	0.633741
$880$	0	0
$881$	−46.5964	−1.56987	−0.784936	−	0.619577i	$-0.787304\pi$
$881$	−46.5964	−1.56987	−0.784936	+	0.619577i	$0.787304\pi$
$882$	4.39073	0.147843
$883$	−38.5110	−1.29600	−0.647999	−	0.761641i	$-0.724394\pi$
$883$	−38.5110	−1.29600	−0.647999	+	0.761641i	$0.724394\pi$
$884$	36.3983	1.22421
$885$	0	0
$886$	10.0988	0.339277
$887$	55.9698	1.87928	0.939642	−	0.342160i	$-0.111159\pi$
$887$	55.9698	1.87928	0.939642	+	0.342160i	$0.111159\pi$
$888$	−46.3236	−1.55452
$889$	−18.7576	−0.629111
$890$	0	0
$891$	−2.94295	−0.0985925
$892$	23.5978	0.790114
$893$	26.6702	0.892484
$894$	−9.82988	−0.328760
$895$	0	0
$896$	10.7750	0.359969
$897$	0.225350	0.00752423
$898$	1.23644	0.0412606
$899$	−1.88866	−0.0629904
$900$	0	0
$901$	−61.3784	−2.04481
$902$	−1.93762	−0.0645156
$903$	−11.7090	−0.389651
$904$	−15.2433	−0.506983
$905$	0	0
$906$	−25.6520	−0.852232
$907$	−5.56428	−0.184759	−0.0923794	−	0.995724i	$-0.529447\pi$
$907$	−5.56428	−0.184759	−0.0923794	+	0.995724i	$0.529447\pi$
$908$	−15.4756	−0.513574
$909$	−0.0849550	−0.00281778
$910$	0	0
$911$	−20.0731	−0.665051	−0.332526	−	0.943094i	$-0.607901\pi$
$911$	−20.0731	−0.665051	−0.332526	+	0.943094i	$0.607901\pi$
$912$	−18.6094	−0.616218
$913$	−1.40758	−0.0465840
$914$	−19.9149	−0.658726
$915$	0	0
$916$	−14.8946	−0.492132
$917$	14.1942	0.468735
$918$	12.4295	0.410233
$919$	−27.1686	−0.896209	−0.448104	−	0.893981i	$-0.647901\pi$
$919$	−27.1686	−0.896209	−0.448104	+	0.893981i	$0.647901\pi$
$920$	0	0
$921$	−32.5601	−1.07289
$922$	0.571871	0.0188336
$923$	19.5508	0.643522
$924$	0.822907	0.0270716
$925$	0	0
$926$	−18.7533	−0.616273
$927$	17.3058	0.568397
$928$	−4.64289	−0.152410
$929$	33.8660	1.11111	0.555554	−	0.831481i	$-0.312506\pi$
$929$	33.8660	1.11111	0.555554	+	0.831481i	$0.312506\pi$
$930$	0	0
$931$	−31.2126	−1.02295
$932$	10.5389	0.345213
$933$	50.7327	1.66092
$934$	−22.1799	−0.725749
$935$	0	0
$936$	11.2508	0.367742
$937$	−5.50918	−0.179977	−0.0899886	−	0.995943i	$-0.528683\pi$
$937$	−5.50918	−0.179977	−0.0899886	+	0.995943i	$0.528683\pi$
$938$	4.33762	0.141628
$939$	52.9766	1.72883
$940$	0	0
$941$	8.92172	0.290840	0.145420	−	0.989370i	$-0.453547\pi$
$941$	8.92172	0.290840	0.145420	+	0.989370i	$0.453547\pi$
$942$	15.4556	0.503572
$943$	−0.297632	−0.00969223
$944$	−6.66251	−0.216846
$945$	0	0
$946$	−1.00468	−0.0326649
$947$	−8.31141	−0.270084	−0.135042	−	0.990840i	$-0.543117\pi$
$947$	−8.31141	−0.270084	−0.135042	+	0.990840i	$0.543117\pi$
$948$	−29.1134	−0.945560
$949$	31.5243	1.02332
$950$	0	0
$951$	−54.6095	−1.77083
$952$	−11.2992	−0.366208
$953$	48.4860	1.57062	0.785308	−	0.619106i	$-0.212505\pi$
$953$	48.4860	1.57062	0.785308	+	0.619106i	$0.212505\pi$
$954$	−8.44570	−0.273439
$955$	0	0
$956$	−29.2710	−0.946691
$957$	−0.442264	−0.0142964
$958$	9.85851	0.318514
$959$	−8.62080	−0.278380
$960$	0	0
$961$	−25.7087	−0.829312
$962$	−27.3387	−0.881436
$963$	10.7933	0.347811
$964$	−1.60466	−0.0516828
$965$	0	0
$966$	−0.0311418	−0.00100197
$967$	43.8818	1.41114	0.705572	−	0.708638i	$-0.250690\pi$
$967$	43.8818	1.41114	0.705572	+	0.708638i	$0.250690\pi$
$968$	−24.7724	−0.796216
$969$	54.6149	1.75448
$970$	0	0
$971$	43.2355	1.38749	0.693747	−	0.720219i	$-0.255959\pi$
$971$	43.2355	1.38749	0.693747	+	0.720219i	$0.255959\pi$
$972$	−18.1752	−0.582969
$973$	−16.4183	−0.526347
$974$	4.51394	0.144636
$975$	0	0
$976$	−6.58335	−0.210728
$977$	−10.9350	−0.349842	−0.174921	−	0.984582i	$-0.555967\pi$
$977$	−10.9350	−0.349842	−0.174921	+	0.984582i	$0.555967\pi$
$978$	22.0545	0.705226
$979$	−1.28984	−0.0412236
$980$	0	0
$981$	−20.8648	−0.666162
$982$	−10.1412	−0.323618
$983$	−44.2970	−1.41286	−0.706428	−	0.707785i	$-0.749695\pi$
$983$	−44.2970	−1.41286	−0.706428	+	0.707785i	$0.749695\pi$
$984$	−53.7590	−1.71378
$985$	0	0
$986$	2.70332	0.0860912
$987$	−10.0935	−0.321280
$988$	−35.6037	−1.13270
$989$	−0.154326	−0.00490728
$990$	0	0
$991$	−22.8148	−0.724736	−0.362368	−	0.932035i	$-0.618032\pi$
$991$	−22.8148	−0.724736	−0.362368	+	0.932035i	$0.618032\pi$
$992$	13.0076	0.412993
$993$	−58.5454	−1.85788
$994$	−2.70178	−0.0856951
$995$	0	0
$996$	−17.3850	−0.550865
$997$	−55.6421	−1.76220	−0.881102	−	0.472926i	$-0.843198\pi$
$997$	−55.6421	−1.76220	−0.881102	+	0.472926i	$0.843198\pi$
$998$	−13.6445	−0.431909
$999$	37.8938	1.19891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.n.1.14	yes	40
5.4	even	2		6025.2.a.m.1.27	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.27	✓	40	5.4	even	2
6025.2.a.n.1.14	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.628757 q^{2} -2.03617 q^{3} -1.60466 q^{4} +1.28026 q^{6} +0.952044 q^{7} +2.26646 q^{8} +1.14599 q^{9} +O(q^{10})\)	\(q-0.628757 q^{2} -2.03617 q^{3} -1.60466 q^{4} +1.28026 q^{6} +0.952044 q^{7} +2.26646 q^{8} +1.14599 q^{9} +0.264542 q^{11} +3.26737 q^{12} +4.33167 q^{13} -0.598604 q^{14} +1.78428 q^{16} -5.23651 q^{17} -0.720546 q^{18} +5.12219 q^{19} -1.93852 q^{21} -0.166333 q^{22} -0.0255499 q^{23} -4.61489 q^{24} -2.72356 q^{26} +3.77509 q^{27} -1.52771 q^{28} +0.821055 q^{29} -2.30029 q^{31} -5.65479 q^{32} -0.538653 q^{33} +3.29249 q^{34} -1.83892 q^{36} +10.0379 q^{37} -3.22061 q^{38} -8.82000 q^{39} +11.6490 q^{41} +1.21886 q^{42} +6.04017 q^{43} -0.424502 q^{44} +0.0160647 q^{46} +5.20680 q^{47} -3.63309 q^{48} -6.09361 q^{49} +10.6624 q^{51} -6.95087 q^{52} +11.7212 q^{53} -2.37361 q^{54} +2.15777 q^{56} -10.4296 q^{57} -0.516244 q^{58} -3.73401 q^{59} -3.68964 q^{61} +1.44632 q^{62} +1.09103 q^{63} -0.0130678 q^{64} +0.338682 q^{66} -7.24621 q^{67} +8.40285 q^{68} +0.0520240 q^{69} +4.51346 q^{71} +2.59733 q^{72} +7.27765 q^{73} -6.31137 q^{74} -8.21939 q^{76} +0.251856 q^{77} +5.54564 q^{78} -8.91035 q^{79} -11.1247 q^{81} -7.32441 q^{82} -5.32080 q^{83} +3.11068 q^{84} -3.79780 q^{86} -1.67181 q^{87} +0.599574 q^{88} -4.87575 q^{89} +4.12394 q^{91} +0.0409991 q^{92} +4.68377 q^{93} -3.27381 q^{94} +11.5141 q^{96} -12.6624 q^{97} +3.83140 q^{98} +0.303162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) \) 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9 + q^11 + 26 * q^12 + 11 * q^13 - q^14 + 43 * q^16 + 20 * q^17 + 18 * q^18 + 2 * q^21 + 23 * q^22 + 79 * q^23 - 2 * q^24 + 2 * q^26 + 26 * q^27 + 30 * q^28 + 2 * q^29 + q^31 + 68 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 16 * q^37 + 45 * q^38 - 2 * q^39 - 2 * q^41 + 19 * q^42 + 25 * q^43 + 3 * q^44 + 14 * q^46 + 88 * q^47 + 75 * q^48 + 40 * q^49 - 10 * q^51 + 18 * q^52 + 34 * q^53 + 4 * q^54 - 15 * q^56 + 51 * q^57 + 53 * q^58 + q^59 + 9 * q^61 + 39 * q^62 + 110 * q^63 + 17 * q^64 + 26 * q^66 + 30 * q^67 + 44 * q^68 - 7 * q^69 + 5 * q^71 + 18 * q^72 + 23 * q^73 - 18 * q^74 + 43 * q^76 + 30 * q^77 + 46 * q^78 + 5 * q^79 + 44 * q^81 + 5 * q^82 + 65 * q^83 - 65 * q^84 + 40 * q^86 + 33 * q^87 + 71 * q^88 - 9 * q^89 + q^91 + 117 * q^92 + 68 * q^93 - 72 * q^94 + 83 * q^96 - 8 * q^97 + 76 * q^98 - 40 * q^99

Introduction

L-functions

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Database

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