LMFDB - Embedded newform 6025.2.a.k.1.18

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:	$25$
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q+1.43128 q^{2} -1.25448 q^{3} +0.0485743 q^{4} -1.79552 q^{6} +2.72576 q^{7} -2.79304 q^{8} -1.42627 q^{9} +O(q^{10})$	\(q+1.43128 q^{2} -1.25448 q^{3} +0.0485743 q^{4} -1.79552 q^{6} +2.72576 q^{7} -2.79304 q^{8} -1.42627 q^{9} +6.42128 q^{11} -0.0609357 q^{12} +4.50692 q^{13} +3.90133 q^{14} -4.09479 q^{16} -7.34936 q^{17} -2.04139 q^{18} -2.46559 q^{19} -3.41942 q^{21} +9.19068 q^{22} +6.02048 q^{23} +3.50383 q^{24} +6.45068 q^{26} +5.55269 q^{27} +0.132402 q^{28} +0.229668 q^{29} +4.08364 q^{31} -0.274717 q^{32} -8.05540 q^{33} -10.5190 q^{34} -0.0692799 q^{36} +0.420726 q^{37} -3.52896 q^{38} -5.65386 q^{39} +5.97215 q^{41} -4.89416 q^{42} -6.55939 q^{43} +0.311909 q^{44} +8.61702 q^{46} -10.8362 q^{47} +5.13685 q^{48} +0.429757 q^{49} +9.21966 q^{51} +0.218920 q^{52} +2.49871 q^{53} +7.94747 q^{54} -7.61316 q^{56} +3.09305 q^{57} +0.328720 q^{58} +8.13951 q^{59} +11.1504 q^{61} +5.84484 q^{62} -3.88766 q^{63} +7.79638 q^{64} -11.5296 q^{66} -8.55624 q^{67} -0.356990 q^{68} -7.55260 q^{69} +3.64665 q^{71} +3.98363 q^{72} -8.50154 q^{73} +0.602178 q^{74} -0.119764 q^{76} +17.5029 q^{77} -8.09228 q^{78} -3.50107 q^{79} -2.68696 q^{81} +8.54784 q^{82} -4.47496 q^{83} -0.166096 q^{84} -9.38835 q^{86} -0.288114 q^{87} -17.9349 q^{88} -4.39063 q^{89} +12.2848 q^{91} +0.292440 q^{92} -5.12286 q^{93} -15.5096 q^{94} +0.344629 q^{96} +12.9749 q^{97} +0.615104 q^{98} -9.15847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9}+O(q^{10}) $ 25 * q + 4 * q^2 - 9 * q^3 + 36 * q^4 + 7 * q^6 - 7 * q^7 + 15 * q^8 + 36 * q^9	$ 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9} + 10 q^{11} - 22 q^{12} - 10 q^{13} + 13 q^{14} + 54 q^{16} - q^{17} + 13 q^{18} + 50 q^{19} + 9 q^{21} - 11 q^{22} + 31 q^{23} + 22 q^{24} + 8 q^{26} - 42 q^{27} - 14 q^{28} + 4 q^{29} + 34 q^{31} + 44 q^{32} - 28 q^{33} + 33 q^{34} + 83 q^{36} - 14 q^{37} + 10 q^{38} + 23 q^{39} + 11 q^{41} - 23 q^{42} - 49 q^{43} + 20 q^{44} + 27 q^{46} + 28 q^{47} - 30 q^{48} + 66 q^{49} + 49 q^{51} - 39 q^{52} + 16 q^{53} + 5 q^{54} + 51 q^{56} - 10 q^{57} + 8 q^{58} + 30 q^{59} + 35 q^{61} + 18 q^{62} + 73 q^{64} - 13 q^{66} - 37 q^{67} - 11 q^{68} - 4 q^{69} + 12 q^{71} + 90 q^{72} - 36 q^{73} - 12 q^{74} + 57 q^{76} + 31 q^{77} + 9 q^{78} + 16 q^{79} + 65 q^{81} + 11 q^{82} - 43 q^{83} - 62 q^{84} - 9 q^{86} + 22 q^{87} - 20 q^{88} + 38 q^{89} + 86 q^{91} + 119 q^{92} - 10 q^{93} - 18 q^{94} - 34 q^{96} - 17 q^{97} + 32 q^{98} + 26 q^{99}+O(q^{100}) $ 25 * q + 4 * q^2 - 9 * q^3 + 36 * q^4 + 7 * q^6 - 7 * q^7 + 15 * q^8 + 36 * q^9 + 10 * q^11 - 22 * q^12 - 10 * q^13 + 13 * q^14 + 54 * q^16 - q^17 + 13 * q^18 + 50 * q^19 + 9 * q^21 - 11 * q^22 + 31 * q^23 + 22 * q^24 + 8 * q^26 - 42 * q^27 - 14 * q^28 + 4 * q^29 + 34 * q^31 + 44 * q^32 - 28 * q^33 + 33 * q^34 + 83 * q^36 - 14 * q^37 + 10 * q^38 + 23 * q^39 + 11 * q^41 - 23 * q^42 - 49 * q^43 + 20 * q^44 + 27 * q^46 + 28 * q^47 - 30 * q^48 + 66 * q^49 + 49 * q^51 - 39 * q^52 + 16 * q^53 + 5 * q^54 + 51 * q^56 - 10 * q^57 + 8 * q^58 + 30 * q^59 + 35 * q^61 + 18 * q^62 + 73 * q^64 - 13 * q^66 - 37 * q^67 - 11 * q^68 - 4 * q^69 + 12 * q^71 + 90 * q^72 - 36 * q^73 - 12 * q^74 + 57 * q^76 + 31 * q^77 + 9 * q^78 + 16 * q^79 + 65 * q^81 + 11 * q^82 - 43 * q^83 - 62 * q^84 - 9 * q^86 + 22 * q^87 - 20 * q^88 + 38 * q^89 + 86 * q^91 + 119 * q^92 - 10 * q^93 - 18 * q^94 - 34 * q^96 - 17 * q^97 + 32 * q^98 + 26 * 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 $

$2$	1.43128	1.01207	0.506035	−	0.862513i	$-0.331111\pi$
$2$	1.43128	1.01207	0.506035	+	0.862513i	$0.331111\pi$
$3$	−1.25448	−0.724277	−0.362139	−	0.932124i	$-0.617953\pi$
$3$	−1.25448	−0.724277	−0.362139	+	0.932124i	$0.617953\pi$
$4$	0.0485743	0.0242871
$5$	0	0
$5$	0	0
$6$	−1.79552	−0.733020
$7$	2.72576	1.03024	0.515120	−	0.857118i	$-0.327747\pi$
$7$	2.72576	1.03024	0.515120	+	0.857118i	$0.327747\pi$
$8$	−2.79304	−0.987490
$9$	−1.42627	−0.475423
$10$	0	0
$11$	6.42128	1.93609	0.968045	−	0.250777i	$-0.0806860\pi$
$11$	6.42128	1.93609	0.968045	+	0.250777i	$0.0806860\pi$
$12$	−0.0609357	−0.0175906
$13$	4.50692	1.24999	0.624997	−	0.780627i	$-0.285100\pi$
$13$	4.50692	1.24999	0.624997	+	0.780627i	$0.285100\pi$
$14$	3.90133	1.04268
$15$	0	0
$16$	−4.09479	−1.02370
$17$	−7.34936	−1.78248	−0.891240	−	0.453531i	$-0.850164\pi$
$17$	−7.34936	−1.78248	−0.891240	+	0.453531i	$0.850164\pi$
$18$	−2.04139	−0.481161
$19$	−2.46559	−0.565646	−0.282823	−	0.959172i	$-0.591271\pi$
$19$	−2.46559	−0.565646	−0.282823	+	0.959172i	$0.591271\pi$
$20$	0	0
$21$	−3.41942	−0.746179
$22$	9.19068	1.95946
$23$	6.02048	1.25536	0.627679	−	0.778473i	$-0.284005\pi$
$23$	6.02048	1.25536	0.627679	+	0.778473i	$0.284005\pi$
$24$	3.50383	0.715217
$25$	0	0
$26$	6.45068	1.26508
$27$	5.55269	1.06861
$28$	0.132402	0.0250216
$29$	0.229668	0.0426482	0.0213241	−	0.999773i	$-0.493212\pi$
$29$	0.229668	0.0426482	0.0213241	+	0.999773i	$0.493212\pi$
$30$	0	0
$31$	4.08364	0.733443	0.366721	−	0.930331i	$-0.380480\pi$
$31$	4.08364	0.733443	0.366721	+	0.930331i	$0.380480\pi$
$32$	−0.274717	−0.0485636
$33$	−8.05540	−1.40227
$34$	−10.5190	−1.80400
$35$	0	0
$36$	−0.0692799	−0.0115466
$37$	0.420726	0.0691669	0.0345835	−	0.999402i	$-0.488990\pi$
$37$	0.420726	0.0691669	0.0345835	+	0.999402i	$0.488990\pi$
$38$	−3.52896	−0.572474
$39$	−5.65386	−0.905343
$40$	0	0
$41$	5.97215	0.932693	0.466346	−	0.884602i	$-0.345570\pi$
$41$	5.97215	0.932693	0.466346	+	0.884602i	$0.345570\pi$
$42$	−4.89416	−0.755186
$43$	−6.55939	−1.00030	−0.500149	−	0.865939i	$-0.666721\pi$
$43$	−6.55939	−1.00030	−0.500149	+	0.865939i	$0.666721\pi$
$44$	0.311909	0.0470221
$45$	0	0
$46$	8.61702	1.27051
$47$	−10.8362	−1.58062	−0.790308	−	0.612710i	$-0.790079\pi$
$47$	−10.8362	−1.58062	−0.790308	+	0.612710i	$0.790079\pi$
$48$	5.13685	0.741441
$49$	0.429757	0.0613938
$50$	0	0
$51$	9.21966	1.29101
$52$	0.218920	0.0303588
$53$	2.49871	0.343224	0.171612	−	0.985165i	$-0.445102\pi$
$53$	2.49871	0.343224	0.171612	+	0.985165i	$0.445102\pi$
$54$	7.94747	1.08151
$55$	0	0
$56$	−7.61316	−1.01735
$57$	3.09305	0.409684
$58$	0.328720	0.0431630
$59$	8.13951	1.05967	0.529837	−	0.848099i	$-0.322253\pi$
$59$	8.13951	1.05967	0.529837	+	0.848099i	$0.322253\pi$
$60$	0	0
$61$	11.1504	1.42766	0.713828	−	0.700321i	$-0.246960\pi$
$61$	11.1504	1.42766	0.713828	+	0.700321i	$0.246960\pi$
$62$	5.84484	0.742296
$63$	−3.88766	−0.489799
$64$	7.79638	0.974547
$65$	0	0
$66$	−11.5296	−1.41919
$67$	−8.55624	−1.04531	−0.522655	−	0.852544i	$-0.675059\pi$
$67$	−8.55624	−1.04531	−0.522655	+	0.852544i	$0.675059\pi$
$68$	−0.356990	−0.0432914
$69$	−7.55260	−0.909227
$70$	0	0
$71$	3.64665	0.432777	0.216389	−	0.976307i	$-0.430572\pi$
$71$	3.64665	0.432777	0.216389	+	0.976307i	$0.430572\pi$
$72$	3.98363	0.469475
$73$	−8.50154	−0.995030	−0.497515	−	0.867455i	$-0.665754\pi$
$73$	−8.50154	−0.995030	−0.497515	+	0.867455i	$0.665754\pi$
$74$	0.602178	0.0700018
$75$	0	0
$76$	−0.119764	−0.0137379
$77$	17.5029	1.99464
$78$	−8.09228	−0.916271
$79$	−3.50107	−0.393901	−0.196950	−	0.980413i	$-0.563104\pi$
$79$	−3.50107	−0.393901	−0.196950	+	0.980413i	$0.563104\pi$
$80$	0	0
$81$	−2.68696	−0.298551
$82$	8.54784	0.943951
$83$	−4.47496	−0.491191	−0.245595	−	0.969372i	$-0.578983\pi$
$83$	−4.47496	−0.491191	−0.245595	+	0.969372i	$0.578983\pi$
$84$	−0.166096	−0.0181226
$85$	0	0
$86$	−9.38835	−1.01237
$87$	−0.288114	−0.0308891
$88$	−17.9349	−1.91187
$89$	−4.39063	−0.465406	−0.232703	−	0.972548i	$-0.574757\pi$
$89$	−4.39063	−0.465406	−0.232703	+	0.972548i	$0.574757\pi$
$90$	0	0
$91$	12.2848	1.28779
$92$	0.292440	0.0304890
$93$	−5.12286	−0.531216
$94$	−15.5096	−1.59969
$95$	0	0
$96$	0.344629	0.0351735
$97$	12.9749	1.31740	0.658700	−	0.752406i	$-0.271107\pi$
$97$	12.9749	1.31740	0.658700	+	0.752406i	$0.271107\pi$
$98$	0.615104	0.0621349
$99$	−9.15847	−0.920461
$100$	0	0
$101$	8.70475	0.866155	0.433077	−	0.901357i	$-0.357428\pi$
$101$	8.70475	0.866155	0.433077	+	0.901357i	$0.357428\pi$
$102$	13.1960	1.30659
$103$	6.06555	0.597656	0.298828	−	0.954307i	$-0.403404\pi$
$103$	6.06555	0.597656	0.298828	+	0.954307i	$0.403404\pi$
$104$	−12.5880	−1.23436
$105$	0	0
$106$	3.57636	0.347367
$107$	8.17191	0.790009	0.395004	−	0.918679i	$-0.370743\pi$
$107$	8.17191	0.790009	0.395004	+	0.918679i	$0.370743\pi$
$108$	0.269718	0.0259536
$109$	15.0385	1.44043	0.720215	−	0.693751i	$-0.244043\pi$
$109$	15.0385	1.44043	0.720215	+	0.693751i	$0.244043\pi$
$110$	0	0
$111$	−0.527794	−0.0500960
$112$	−11.1614	−1.05465
$113$	−1.44086	−0.135545	−0.0677725	−	0.997701i	$-0.521589\pi$
$113$	−1.44086	−0.135545	−0.0677725	+	0.997701i	$0.521589\pi$
$114$	4.42703	0.414630
$115$	0	0
$116$	0.0111559	0.00103580
$117$	−6.42807	−0.594275
$118$	11.6500	1.07247
$119$	−20.0326	−1.83638
$120$	0	0
$121$	30.2329	2.74844
$122$	15.9593	1.44489
$123$	−7.49197	−0.675528
$124$	0.198360	0.0178132
$125$	0	0
$126$	−5.56435	−0.495711
$127$	−9.57494	−0.849639	−0.424819	−	0.905278i	$-0.639662\pi$
$127$	−9.57494	−0.849639	−0.424819	+	0.905278i	$0.639662\pi$
$128$	11.7083	1.03487
$129$	8.22866	0.724493
$130$	0	0
$131$	−10.0280	−0.876154	−0.438077	−	0.898937i	$-0.644340\pi$
$131$	−10.0280	−0.876154	−0.438077	+	0.898937i	$0.644340\pi$
$132$	−0.391285	−0.0340570
$133$	−6.72061	−0.582751
$134$	−12.2464	−1.05793
$135$	0	0
$136$	20.5271	1.76018
$137$	−23.1668	−1.97927	−0.989635	−	0.143605i	$-0.954130\pi$
$137$	−23.1668	−1.97927	−0.989635	+	0.143605i	$0.954130\pi$
$138$	−10.8099	−0.920202
$139$	8.41735	0.713951	0.356975	−	0.934114i	$-0.383808\pi$
$139$	8.41735	0.713951	0.356975	+	0.934114i	$0.383808\pi$
$140$	0	0
$141$	13.5938	1.14480
$142$	5.21939	0.438001
$143$	28.9402	2.42010
$144$	5.84026	0.486689
$145$	0	0
$146$	−12.1681	−1.00704
$147$	−0.539123	−0.0444661
$148$	0.0204365	0.00167987
$149$	13.3137	1.09070	0.545351	−	0.838208i	$-0.316396\pi$
$149$	13.3137	1.09070	0.545351	+	0.838208i	$0.316396\pi$
$150$	0	0
$151$	−14.1749	−1.15354	−0.576769	−	0.816907i	$-0.695687\pi$
$151$	−14.1749	−1.15354	−0.576769	+	0.816907i	$0.695687\pi$
$152$	6.88651	0.558570
$153$	10.4821	0.847432
$154$	25.0516	2.01871
$155$	0	0
$156$	−0.274632	−0.0219882
$157$	5.97542	0.476891	0.238445	−	0.971156i	$-0.423362\pi$
$157$	5.97542	0.476891	0.238445	+	0.971156i	$0.423362\pi$
$158$	−5.01102	−0.398655
$159$	−3.13459	−0.248589
$160$	0	0
$161$	16.4104	1.29332
$162$	−3.84580	−0.302155
$163$	25.1548	1.97027	0.985136	−	0.171776i	$-0.0549504\pi$
$163$	25.1548	1.97027	0.985136	+	0.171776i	$0.0549504\pi$
$164$	0.290093	0.0226524
$165$	0	0
$166$	−6.40494	−0.497120
$167$	16.6419	1.28779	0.643894	−	0.765114i	$-0.277318\pi$
$167$	16.6419	1.28779	0.643894	+	0.765114i	$0.277318\pi$
$168$	9.55060	0.736845
$169$	7.31232	0.562486
$170$	0	0
$171$	3.51660	0.268921
$172$	−0.318618	−0.0242944
$173$	2.39950	0.182430	0.0912152	−	0.995831i	$-0.470925\pi$
$173$	2.39950	0.182430	0.0912152	+	0.995831i	$0.470925\pi$
$174$	−0.412374	−0.0312620
$175$	0	0
$176$	−26.2938	−1.98197
$177$	−10.2109	−0.767498
$178$	−6.28425	−0.471024
$179$	25.4679	1.90356	0.951779	−	0.306785i	$-0.0992534\pi$
$179$	25.4679	1.90356	0.951779	+	0.306785i	$0.0992534\pi$
$180$	0	0
$181$	7.99948	0.594597	0.297298	−	0.954785i	$-0.403914\pi$
$181$	7.99948	0.594597	0.297298	+	0.954785i	$0.403914\pi$
$182$	17.5830	1.30334
$183$	−13.9879	−1.03402
$184$	−16.8155	−1.23965
$185$	0	0
$186$	−7.33227	−0.537628
$187$	−47.1923	−3.45104
$188$	−0.526358	−0.0383886
$189$	15.1353	1.10093
$190$	0	0
$191$	13.5056	0.977234	0.488617	−	0.872498i	$-0.337502\pi$
$191$	13.5056	0.977234	0.488617	+	0.872498i	$0.337502\pi$
$192$	−9.78044	−0.705843
$193$	1.24421	0.0895602	0.0447801	−	0.998997i	$-0.485741\pi$
$193$	1.24421	0.0895602	0.0447801	+	0.998997i	$0.485741\pi$
$194$	18.5707	1.33330
$195$	0	0
$196$	0.0208751	0.00149108
$197$	12.5227	0.892205	0.446103	−	0.894982i	$-0.352812\pi$
$197$	12.5227	0.892205	0.446103	+	0.894982i	$0.352812\pi$
$198$	−13.1084	−0.931571
$199$	5.20215	0.368771	0.184385	−	0.982854i	$-0.440971\pi$
$199$	5.20215	0.368771	0.184385	+	0.982854i	$0.440971\pi$
$200$	0	0
$201$	10.7337	0.757095
$202$	12.4590	0.876610
$203$	0.626018	0.0439379
$204$	0.447838	0.0313549
$205$	0	0
$206$	8.68152	0.604870
$207$	−8.58682	−0.596825
$208$	−18.4549	−1.27962
$209$	−15.8323	−1.09514
$210$	0	0
$211$	3.75204	0.258301	0.129151	−	0.991625i	$-0.458775\pi$
$211$	3.75204	0.258301	0.129151	+	0.991625i	$0.458775\pi$
$212$	0.121373	0.00833592
$213$	−4.57466	−0.313451
$214$	11.6963	0.799545
$215$	0	0
$216$	−15.5089	−1.05525
$217$	11.1310	0.755622
$218$	21.5244	1.45782
$219$	10.6651	0.720678
$220$	0	0
$221$	−33.1230	−2.22809
$222$	−0.755424	−0.0507007
$223$	−18.1649	−1.21641	−0.608207	−	0.793778i	$-0.708111\pi$
$223$	−18.1649	−1.21641	−0.608207	+	0.793778i	$0.708111\pi$
$224$	−0.748813	−0.0500322
$225$	0	0
$226$	−2.06229	−0.137181
$227$	1.55378	0.103128	0.0515639	−	0.998670i	$-0.483579\pi$
$227$	1.55378	0.103128	0.0515639	+	0.998670i	$0.483579\pi$
$228$	0.150243	0.00995006
$229$	−0.469326	−0.0310140	−0.0155070	−	0.999880i	$-0.504936\pi$
$229$	−0.469326	−0.0310140	−0.0155070	+	0.999880i	$0.504936\pi$
$230$	0	0
$231$	−21.9571	−1.44467
$232$	−0.641472	−0.0421147
$233$	−9.22233	−0.604175	−0.302087	−	0.953280i	$-0.597683\pi$
$233$	−9.22233	−0.604175	−0.302087	+	0.953280i	$0.597683\pi$
$234$	−9.20040	−0.601449
$235$	0	0
$236$	0.395371	0.0257365
$237$	4.39204	0.285293
$238$	−28.6723	−1.85855
$239$	−0.225938	−0.0146147	−0.00730736	−	0.999973i	$-0.502326\pi$
$239$	−0.225938	−0.0146147	−0.00730736	+	0.999973i	$0.502326\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	43.2718	2.78162
$243$	−13.2873	−0.852381
$244$	0.541620	0.0346737
$245$	0	0
$246$	−10.7231	−0.683682
$247$	−11.1122	−0.707054
$248$	−11.4058	−0.724268
$249$	5.61377	0.355758
$250$	0	0
$251$	−11.1989	−0.706870	−0.353435	−	0.935459i	$-0.614987\pi$
$251$	−11.1989	−0.706870	−0.353435	+	0.935459i	$0.614987\pi$
$252$	−0.188840	−0.0118958
$253$	38.6592	2.43048
$254$	−13.7045	−0.859895
$255$	0	0
$256$	1.16510	0.0728188
$257$	28.9074	1.80319	0.901597	−	0.432578i	$-0.142396\pi$
$257$	28.9074	1.80319	0.901597	+	0.432578i	$0.142396\pi$
$258$	11.7775	0.733238
$259$	1.14680	0.0712585
$260$	0	0
$261$	−0.327567	−0.0202759
$262$	−14.3530	−0.886730
$263$	24.4338	1.50665	0.753327	−	0.657646i	$-0.228448\pi$
$263$	24.4338	1.50665	0.753327	+	0.657646i	$0.228448\pi$
$264$	22.4991	1.38472
$265$	0	0
$266$	−9.61910	−0.589785
$267$	5.50799	0.337083
$268$	−0.415613	−0.0253876
$269$	−18.7127	−1.14093	−0.570467	−	0.821320i	$-0.693238\pi$
$269$	−18.7127	−1.14093	−0.570467	+	0.821320i	$0.693238\pi$
$270$	0	0
$271$	−15.4865	−0.940735	−0.470368	−	0.882471i	$-0.655879\pi$
$271$	−15.4865	−0.940735	−0.470368	+	0.882471i	$0.655879\pi$
$272$	30.0941	1.82472
$273$	−15.4111	−0.932720
$274$	−33.1582	−2.00316
$275$	0	0
$276$	−0.366862	−0.0220825
$277$	4.59879	0.276315	0.138157	−	0.990410i	$-0.455882\pi$
$277$	4.59879	0.276315	0.138157	+	0.990410i	$0.455882\pi$
$278$	12.0476	0.722568
$279$	−5.82436	−0.348695
$280$	0	0
$281$	24.6065	1.46790	0.733951	−	0.679203i	$-0.237674\pi$
$281$	24.6065	1.46790	0.733951	+	0.679203i	$0.237674\pi$
$282$	19.4566	1.15862
$283$	16.9758	1.00910	0.504552	−	0.863381i	$-0.331658\pi$
$283$	16.9758	1.00910	0.504552	+	0.863381i	$0.331658\pi$
$284$	0.177133	0.0105109
$285$	0	0
$286$	41.4217	2.44931
$287$	16.2786	0.960897
$288$	0.391820	0.0230882
$289$	37.0131	2.17724
$290$	0	0
$291$	−16.2768	−0.954163
$292$	−0.412956	−0.0241664
$293$	−10.5453	−0.616064	−0.308032	−	0.951376i	$-0.599670\pi$
$293$	−10.5453	−0.616064	−0.308032	+	0.951376i	$0.599670\pi$
$294$	−0.771638	−0.0450029
$295$	0	0
$296$	−1.17511	−0.0683017
$297$	35.6554	2.06893
$298$	19.0557	1.10387
$299$	27.1338	1.56919
$300$	0	0
$301$	−17.8793	−1.03055
$302$	−20.2883	−1.16746
$303$	−10.9200	−0.627336
$304$	10.0961	0.579050
$305$	0	0
$306$	15.0029	0.857661
$307$	21.0573	1.20180	0.600902	−	0.799322i	$-0.294808\pi$
$307$	21.0573	1.20180	0.600902	+	0.799322i	$0.294808\pi$
$308$	0.850189	0.0484440
$309$	−7.60914	−0.432869
$310$	0	0
$311$	−13.1373	−0.744948	−0.372474	−	0.928043i	$-0.621490\pi$
$311$	−13.1373	−0.744948	−0.372474	+	0.928043i	$0.621490\pi$
$312$	15.7915	0.894017
$313$	13.0387	0.736992	0.368496	−	0.929629i	$-0.379873\pi$
$313$	13.0387	0.736992	0.368496	+	0.929629i	$0.379873\pi$
$314$	8.55253	0.482647
$315$	0	0
$316$	−0.170062	−0.00956672
$317$	17.8804	1.00426	0.502131	−	0.864792i	$-0.332550\pi$
$317$	17.8804	1.00426	0.502131	+	0.864792i	$0.332550\pi$
$318$	−4.48649	−0.251590
$319$	1.47476	0.0825707
$320$	0	0
$321$	−10.2515	−0.572185
$322$	23.4879	1.30893
$323$	18.1205	1.00825
$324$	−0.130517	−0.00725095
$325$	0	0
$326$	36.0036	1.99405
$327$	−18.8656	−1.04327
$328$	−16.6805	−0.921025
$329$	−29.5367	−1.62841
$330$	0	0
$331$	−29.0656	−1.59759	−0.798796	−	0.601602i	$-0.794529\pi$
$331$	−29.0656	−1.59759	−0.798796	+	0.601602i	$0.794529\pi$
$332$	−0.217368	−0.0119296
$333$	−0.600068	−0.0328835
$334$	23.8193	1.30333
$335$	0	0
$336$	14.0018	0.763862
$337$	25.4527	1.38650	0.693248	−	0.720699i	$-0.256179\pi$
$337$	25.4527	1.38650	0.693248	+	0.720699i	$0.256179\pi$
$338$	10.4660	0.569276
$339$	1.80754	0.0981722
$340$	0	0
$341$	26.2222	1.42001
$342$	5.03325	0.272167
$343$	−17.9089	−0.966989
$344$	18.3207	0.987785
$345$	0	0
$346$	3.43436	0.184632
$347$	−19.1091	−1.02583	−0.512914	−	0.858440i	$-0.671434\pi$
$347$	−19.1091	−1.02583	−0.512914	+	0.858440i	$0.671434\pi$
$348$	−0.0139949	−0.000750208 0
$349$	11.4331	0.611998	0.305999	−	0.952032i	$-0.401010\pi$
$349$	11.4331	0.611998	0.305999	+	0.952032i	$0.401010\pi$
$350$	0	0
$351$	25.0255	1.33576
$352$	−1.76404	−0.0940235
$353$	−19.0551	−1.01420	−0.507101	−	0.861887i	$-0.669283\pi$
$353$	−19.0551	−1.01420	−0.507101	+	0.861887i	$0.669283\pi$
$354$	−14.6147	−0.776762
$355$	0	0
$356$	−0.213272	−0.0113034
$357$	25.1306	1.33005
$358$	36.4517	1.92653
$359$	32.6313	1.72221	0.861106	−	0.508425i	$-0.169772\pi$
$359$	32.6313	1.72221	0.861106	+	0.508425i	$0.169772\pi$
$360$	0	0
$361$	−12.9209	−0.680045
$362$	11.4495	0.601774
$363$	−37.9267	−1.99064
$364$	0.596724	0.0312768
$365$	0	0
$366$	−20.0207	−1.04650
$367$	−25.9119	−1.35259	−0.676294	−	0.736631i	$-0.736415\pi$
$367$	−25.9119	−1.35259	−0.676294	+	0.736631i	$0.736415\pi$
$368$	−24.6526	−1.28511
$369$	−8.51788	−0.443423
$370$	0	0
$371$	6.81087	0.353603
$372$	−0.248839	−0.0129017
$373$	17.0376	0.882176	0.441088	−	0.897464i	$-0.354593\pi$
$373$	17.0376	0.882176	0.441088	+	0.897464i	$0.354593\pi$
$374$	−67.5456	−3.49270
$375$	0	0
$376$	30.2659	1.56084
$377$	1.03509	0.0533100
$378$	21.6629	1.11422
$379$	32.3546	1.66194	0.830972	−	0.556314i	$-0.187785\pi$
$379$	32.3546	1.66194	0.830972	+	0.556314i	$0.187785\pi$
$380$	0	0
$381$	12.0116	0.615374
$382$	19.3304	0.989030
$383$	12.2547	0.626183	0.313092	−	0.949723i	$-0.398635\pi$
$383$	12.2547	0.626183	0.313092	+	0.949723i	$0.398635\pi$
$384$	−14.6878	−0.749536
$385$	0	0
$386$	1.78082	0.0906413
$387$	9.35545	0.475564
$388$	0.630245	0.0319959
$389$	29.5698	1.49925	0.749624	−	0.661864i	$-0.230234\pi$
$389$	29.5698	1.49925	0.749624	+	0.661864i	$0.230234\pi$
$390$	0	0
$391$	−44.2467	−2.23765
$392$	−1.20033	−0.0606258
$393$	12.5800	0.634578
$394$	17.9235	0.902975
$395$	0	0
$396$	−0.444866	−0.0223553
$397$	24.4885	1.22904	0.614520	−	0.788901i	$-0.289350\pi$
$397$	24.4885	1.22904	0.614520	+	0.788901i	$0.289350\pi$
$398$	7.44575	0.373222
$399$	8.43090	0.422073
$400$	0	0
$401$	−1.96012	−0.0978838	−0.0489419	−	0.998802i	$-0.515585\pi$
$401$	−1.96012	−0.0978838	−0.0489419	+	0.998802i	$0.515585\pi$
$402$	15.3629	0.766233
$403$	18.4046	0.916799
$404$	0.422827	0.0210364
$405$	0	0
$406$	0.896010	0.0444682
$407$	2.70160	0.133913
$408$	−25.7509	−1.27486
$409$	−11.8558	−0.586234	−0.293117	−	0.956077i	$-0.594692\pi$
$409$	−11.8558	−0.586234	−0.293117	+	0.956077i	$0.594692\pi$
$410$	0	0
$411$	29.0624	1.43354
$412$	0.294629	0.0145153
$413$	22.1863	1.09172
$414$	−12.2902	−0.604029
$415$	0	0
$416$	−1.23813	−0.0607042
$417$	−10.5594	−0.517098
$418$	−22.6605	−1.10836
$419$	−11.3529	−0.554625	−0.277312	−	0.960780i	$-0.589444\pi$
$419$	−11.3529	−0.554625	−0.277312	+	0.960780i	$0.589444\pi$
$420$	0	0
$421$	−23.0831	−1.12500	−0.562500	−	0.826797i	$-0.690160\pi$
$421$	−23.0831	−1.12500	−0.562500	+	0.826797i	$0.690160\pi$
$422$	5.37024	0.261419
$423$	15.4553	0.751460
$424$	−6.97900	−0.338930
$425$	0	0
$426$	−6.54764	−0.317234
$427$	30.3932	1.47083
$428$	0.396945	0.0191870
$429$	−36.3051	−1.75282
$430$	0	0
$431$	−22.8580	−1.10103	−0.550516	−	0.834825i	$-0.685569\pi$
$431$	−22.8580	−1.10103	−0.550516	+	0.834825i	$0.685569\pi$
$432$	−22.7371	−1.09394
$433$	−40.5455	−1.94849	−0.974247	−	0.225483i	$-0.927604\pi$
$433$	−40.5455	−1.94849	−0.974247	+	0.225483i	$0.927604\pi$
$434$	15.9316	0.764743
$435$	0	0
$436$	0.730486	0.0349839
$437$	−14.8441	−0.710088
$438$	15.2647	0.729377
$439$	21.1447	1.00918	0.504591	−	0.863359i	$-0.331643\pi$
$439$	21.1447	1.00918	0.504591	+	0.863359i	$0.331643\pi$
$440$	0	0
$441$	−0.612948	−0.0291880
$442$	−47.4084	−2.25499
$443$	−21.1224	−1.00355	−0.501777	−	0.864997i	$-0.667320\pi$
$443$	−21.1224	−1.00355	−0.501777	+	0.864997i	$0.667320\pi$
$444$	−0.0256372	−0.00121669
$445$	0	0
$446$	−25.9992	−1.23110
$447$	−16.7019	−0.789971
$448$	21.2510	1.00402
$449$	−10.5759	−0.499108	−0.249554	−	0.968361i	$-0.580284\pi$
$449$	−10.5759	−0.499108	−0.249554	+	0.968361i	$0.580284\pi$
$450$	0	0
$451$	38.3489	1.80578
$452$	−0.0699889	−0.00329200
$453$	17.7822	0.835482
$454$	2.22390	0.104373
$455$	0	0
$456$	−8.63903	−0.404559
$457$	20.8957	0.977462	0.488731	−	0.872435i	$-0.337460\pi$
$457$	20.8957	0.977462	0.488731	+	0.872435i	$0.337460\pi$
$458$	−0.671739	−0.0313883
$459$	−40.8087	−1.90479
$460$	0	0
$461$	−12.3670	−0.575988	−0.287994	−	0.957632i	$-0.592988\pi$
$461$	−12.3670	−0.575988	−0.287994	+	0.957632i	$0.592988\pi$
$462$	−31.4268	−1.46211
$463$	−35.9887	−1.67254	−0.836268	−	0.548320i	$-0.815267\pi$
$463$	−35.9887	−1.67254	−0.836268	+	0.548320i	$0.815267\pi$
$464$	−0.940440	−0.0436588
$465$	0	0
$466$	−13.1998	−0.611468
$467$	−19.4423	−0.899684	−0.449842	−	0.893108i	$-0.648520\pi$
$467$	−19.4423	−0.899684	−0.449842	+	0.893108i	$0.648520\pi$
$468$	−0.312239	−0.0144332
$469$	−23.3222	−1.07692
$470$	0	0
$471$	−7.49608	−0.345401
$472$	−22.7340	−1.04642
$473$	−42.1197	−1.93667
$474$	6.28625	0.288737
$475$	0	0
$476$	−0.973067	−0.0446005
$477$	−3.56382	−0.163176
$478$	−0.323381	−0.0147911
$479$	5.74347	0.262426	0.131213	−	0.991354i	$-0.458113\pi$
$479$	5.74347	0.262426	0.131213	+	0.991354i	$0.458113\pi$
$480$	0	0
$481$	1.89618	0.0864583
$482$	1.43128	0.0651932
$483$	−20.5866	−0.936721
$484$	1.46854	0.0667518
$485$	0	0
$486$	−19.0179	−0.862670
$487$	−7.70331	−0.349070	−0.174535	−	0.984651i	$-0.555842\pi$
$487$	−7.70331	−0.349070	−0.174535	+	0.984651i	$0.555842\pi$
$488$	−31.1434	−1.40980
$489$	−31.5563	−1.42702
$490$	0	0
$491$	34.3071	1.54826	0.774128	−	0.633029i	$-0.218189\pi$
$491$	34.3071	1.54826	0.774128	+	0.633029i	$0.218189\pi$
$492$	−0.363917	−0.0164066
$493$	−1.68791	−0.0760196
$494$	−15.9048	−0.715589
$495$	0	0
$496$	−16.7216	−0.750823
$497$	9.93987	0.445864
$498$	8.03490	0.360053
$499$	4.47335	0.200255	0.100127	−	0.994975i	$-0.468075\pi$
$499$	4.47335	0.200255	0.100127	+	0.994975i	$0.468075\pi$
$500$	0	0
$501$	−20.8770	−0.932716
$502$	−16.0289	−0.715403
$503$	−19.9980	−0.891666	−0.445833	−	0.895116i	$-0.647092\pi$
$503$	−19.9980	−0.891666	−0.445833	+	0.895116i	$0.647092\pi$
$504$	10.8584	0.483672
$505$	0	0
$506$	55.3323	2.45982
$507$	−9.17320	−0.407396
$508$	−0.465096	−0.0206353
$509$	8.51666	0.377494	0.188747	−	0.982026i	$-0.439557\pi$
$509$	8.51666	0.377494	0.188747	+	0.982026i	$0.439557\pi$
$510$	0	0
$511$	−23.1731	−1.02512
$512$	−21.7489	−0.961177
$513$	−13.6907	−0.604458
$514$	41.3747	1.82496
$515$	0	0
$516$	0.399701	0.0175959
$517$	−69.5820	−3.06021
$518$	1.64139	0.0721186
$519$	−3.01013	−0.132130
$520$	0	0
$521$	−1.77481	−0.0777559	−0.0388779	−	0.999244i	$-0.512378\pi$
$521$	−1.77481	−0.0777559	−0.0388779	+	0.999244i	$0.512378\pi$
$522$	−0.468842	−0.0205207
$523$	11.2858	0.493492	0.246746	−	0.969080i	$-0.420639\pi$
$523$	11.2858	0.493492	0.246746	+	0.969080i	$0.420639\pi$
$524$	−0.487105	−0.0212793
$525$	0	0
$526$	34.9718	1.52484
$527$	−30.0121	−1.30735
$528$	32.9852	1.43550
$529$	13.2462	0.575922
$530$	0	0
$531$	−11.6091	−0.503793
$532$	−0.326449	−0.0141533
$533$	26.9160	1.16586
$534$	7.88349	0.341152
$535$	0	0
$536$	23.8979	1.03223
$537$	−31.9491	−1.37870
$538$	−26.7832	−1.15471
$539$	2.75959	0.118864
$540$	0	0
$541$	−36.1557	−1.55445	−0.777227	−	0.629220i	$-0.783374\pi$
$541$	−36.1557	−1.55445	−0.777227	+	0.629220i	$0.783374\pi$
$542$	−22.1655	−0.952090
$543$	−10.0352	−0.430653
$544$	2.01900	0.0865637
$545$	0	0
$546$	−22.0576	−0.943978
$547$	−16.6299	−0.711045	−0.355522	−	0.934668i	$-0.615697\pi$
$547$	−16.6299	−0.711045	−0.355522	+	0.934668i	$0.615697\pi$
$548$	−1.12531	−0.0480708
$549$	−15.9034	−0.678740
$550$	0	0
$551$	−0.566267	−0.0241238
$552$	21.0948	0.897853
$553$	−9.54306	−0.405812
$554$	6.58218	0.279650
$555$	0	0
$556$	0.408867	0.0173398
$557$	14.9409	0.633067	0.316534	−	0.948581i	$-0.397481\pi$
$557$	14.9409	0.633067	0.316534	+	0.948581i	$0.397481\pi$
$558$	−8.33631	−0.352904
$559$	−29.5626	−1.25037
$560$	0	0
$561$	59.2020	2.49951
$562$	35.2189	1.48562
$563$	21.4419	0.903669	0.451835	−	0.892102i	$-0.350770\pi$
$563$	21.4419	0.903669	0.451835	+	0.892102i	$0.350770\pi$
$564$	0.660309	0.0278040
$565$	0	0
$566$	24.2971	1.02128
$567$	−7.32400	−0.307579
$568$	−10.1852	−0.427363
$569$	−43.9351	−1.84186	−0.920928	−	0.389733i	$-0.872567\pi$
$569$	−43.9351	−1.84186	−0.920928	+	0.389733i	$0.872567\pi$
$570$	0	0
$571$	−5.17887	−0.216729	−0.108365	−	0.994111i	$-0.534561\pi$
$571$	−5.17887	−0.216729	−0.108365	+	0.994111i	$0.534561\pi$
$572$	1.40575	0.0587773
$573$	−16.9426	−0.707788
$574$	23.2993	0.972496
$575$	0	0
$576$	−11.1197	−0.463322
$577$	−28.5960	−1.19047	−0.595233	−	0.803553i	$-0.702940\pi$
$577$	−28.5960	−1.19047	−0.595233	+	0.803553i	$0.702940\pi$
$578$	52.9762	2.20352
$579$	−1.56084	−0.0648664
$580$	0	0
$581$	−12.1977	−0.506044
$582$	−23.2967	−0.965680
$583$	16.0449	0.664512
$584$	23.7452	0.982583
$585$	0	0
$586$	−15.0934	−0.623501
$587$	−37.0634	−1.52977	−0.764885	−	0.644166i	$-0.777204\pi$
$587$	−37.0634	−1.52977	−0.764885	+	0.644166i	$0.777204\pi$
$588$	−0.0261875	−0.00107995
$589$	−10.0686	−0.414869
$590$	0	0
$591$	−15.7095	−0.646204
$592$	−1.72278	−0.0708060
$593$	−10.3353	−0.424422	−0.212211	−	0.977224i	$-0.568066\pi$
$593$	−10.3353	−0.424422	−0.212211	+	0.977224i	$0.568066\pi$
$594$	51.0330	2.09391
$595$	0	0
$596$	0.646704	0.0264900
$597$	−6.52602	−0.267092
$598$	38.8362	1.58813
$599$	4.02899	0.164620	0.0823100	−	0.996607i	$-0.473770\pi$
$599$	4.02899	0.164620	0.0823100	+	0.996607i	$0.473770\pi$
$600$	0	0
$601$	−5.22632	−0.213186	−0.106593	−	0.994303i	$-0.533994\pi$
$601$	−5.22632	−0.213186	−0.106593	+	0.994303i	$0.533994\pi$
$602$	−25.5904	−1.04299
$603$	12.2035	0.496964
$604$	−0.688536	−0.0280161
$605$	0	0
$606$	−15.6296	−0.634909
$607$	−15.4091	−0.625438	−0.312719	−	0.949846i	$-0.601240\pi$
$607$	−15.4091	−0.625438	−0.312719	+	0.949846i	$0.601240\pi$
$608$	0.677341	0.0274698
$609$	−0.785330	−0.0318232
$610$	0	0
$611$	−48.8377	−1.97576
$612$	0.509163	0.0205817
$613$	1.06481	0.0430073	0.0215036	−	0.999769i	$-0.493155\pi$
$613$	1.06481	0.0430073	0.0215036	+	0.999769i	$0.493155\pi$
$614$	30.1390	1.21631
$615$	0	0
$616$	−48.8863	−1.96968
$617$	37.7359	1.51919	0.759594	−	0.650397i	$-0.225397\pi$
$617$	37.7359	1.51919	0.759594	+	0.650397i	$0.225397\pi$
$618$	−10.8908	−0.438094
$619$	7.53328	0.302788	0.151394	−	0.988473i	$-0.451624\pi$
$619$	7.53328	0.302788	0.151394	+	0.988473i	$0.451624\pi$
$620$	0	0
$621$	33.4298	1.34149
$622$	−18.8032	−0.753940
$623$	−11.9678	−0.479480
$624$	23.1514	0.926797
$625$	0	0
$626$	18.6621	0.745888
$627$	19.8613	0.793186
$628$	0.290252	0.0115823
$629$	−3.09207	−0.123289
$630$	0	0
$631$	−8.18895	−0.325997	−0.162998	−	0.986626i	$-0.552117\pi$
$631$	−8.18895	−0.325997	−0.162998	+	0.986626i	$0.552117\pi$
$632$	9.77864	0.388973
$633$	−4.70688	−0.187082
$634$	25.5919	1.01638
$635$	0	0
$636$	−0.152260	−0.00603752
$637$	1.93688	0.0767419
$638$	2.11080	0.0835674
$639$	−5.20109	−0.205752
$640$	0	0
$641$	5.68523	0.224553	0.112277	−	0.993677i	$-0.464186\pi$
$641$	5.68523	0.224553	0.112277	+	0.993677i	$0.464186\pi$
$642$	−14.6729	−0.579092
$643$	−37.7503	−1.48872	−0.744362	−	0.667776i	$-0.767246\pi$
$643$	−37.7503	−1.48872	−0.744362	+	0.667776i	$0.767246\pi$
$644$	0.797122	0.0314110
$645$	0	0
$646$	25.9356	1.02042
$647$	4.20432	0.165289	0.0826445	−	0.996579i	$-0.473663\pi$
$647$	4.20432	0.165289	0.0826445	+	0.996579i	$0.473663\pi$
$648$	7.50480	0.294816
$649$	52.2661	2.05163
$650$	0	0
$651$	−13.9637	−0.547280
$652$	1.22187	0.0478523
$653$	26.8425	1.05043	0.525214	−	0.850970i	$-0.323985\pi$
$653$	26.8425	1.05043	0.525214	+	0.850970i	$0.323985\pi$
$654$	−27.0020	−1.05586
$655$	0	0
$656$	−24.4547	−0.954795
$657$	12.1255	0.473060
$658$	−42.2755	−1.64807
$659$	8.37755	0.326343	0.163171	−	0.986598i	$-0.447828\pi$
$659$	8.37755	0.326343	0.163171	+	0.986598i	$0.447828\pi$
$660$	0	0
$661$	5.20204	0.202336	0.101168	−	0.994869i	$-0.467742\pi$
$661$	5.20204	0.202336	0.101168	+	0.994869i	$0.467742\pi$
$662$	−41.6012	−1.61688
$663$	41.5523	1.61376
$664$	12.4988	0.485046
$665$	0	0
$666$	−0.858867	−0.0332804
$667$	1.38271	0.0535387
$668$	0.808368	0.0312767
$669$	22.7877	0.881022
$670$	0	0
$671$	71.5996	2.76407
$672$	0.939374	0.0362371
$673$	−37.9105	−1.46134	−0.730672	−	0.682729i	$-0.760793\pi$
$673$	−37.9105	−1.46134	−0.730672	+	0.682729i	$0.760793\pi$
$674$	36.4300	1.40323
$675$	0	0
$676$	0.355191	0.0136612
$677$	−2.59729	−0.0998221	−0.0499110	−	0.998754i	$-0.515894\pi$
$677$	−2.59729	−0.0998221	−0.0499110	+	0.998754i	$0.515894\pi$
$678$	2.58711	0.0993572
$679$	35.3664	1.35724
$680$	0	0
$681$	−1.94919	−0.0746931
$682$	37.5314	1.43715
$683$	35.4303	1.35570	0.677852	−	0.735198i	$-0.262911\pi$
$683$	35.4303	1.35570	0.677852	+	0.735198i	$0.262911\pi$
$684$	0.170816	0.00653131
$685$	0	0
$686$	−25.6327	−0.978662
$687$	0.588763	0.0224627
$688$	26.8593	1.02400
$689$	11.2615	0.429028
$690$	0	0
$691$	7.68880	0.292496	0.146248	−	0.989248i	$-0.453280\pi$
$691$	7.68880	0.292496	0.146248	+	0.989248i	$0.453280\pi$
$692$	0.116554	0.00443071
$693$	−24.9638	−0.948295
$694$	−27.3505	−1.03821
$695$	0	0
$696$	0.804717	0.0305027
$697$	−43.8915	−1.66251
$698$	16.3640	0.619385
$699$	11.5693	0.437590
$700$	0	0
$701$	1.90080	0.0717923	0.0358962	−	0.999356i	$-0.488571\pi$
$701$	1.90080	0.0717923	0.0358962	+	0.999356i	$0.488571\pi$
$702$	35.8186	1.35189
$703$	−1.03734	−0.0391240
$704$	50.0628	1.88681
$705$	0	0
$706$	−27.2733	−1.02644
$707$	23.7270	0.892347
$708$	−0.495987	−0.0186403
$709$	−37.7635	−1.41824	−0.709118	−	0.705090i	$-0.750907\pi$
$709$	−37.7635	−1.41824	−0.709118	+	0.705090i	$0.750907\pi$
$710$	0	0
$711$	4.99346	0.187269
$712$	12.2632	0.459584
$713$	24.5855	0.920733
$714$	35.9690	1.34610
$715$	0	0
$716$	1.23708	0.0462320
$717$	0.283436	0.0105851
$718$	46.7046	1.74300
$719$	−14.2675	−0.532087	−0.266043	−	0.963961i	$-0.585716\pi$
$719$	−14.2675	−0.532087	−0.266043	+	0.963961i	$0.585716\pi$
$720$	0	0
$721$	16.5332	0.615729
$722$	−18.4934	−0.688253
$723$	−1.25448	−0.0466548
$724$	0.388569	0.0144410
$725$	0	0
$726$	−54.2839	−2.01466
$727$	−48.4790	−1.79799	−0.898994	−	0.437961i	$-0.855701\pi$
$727$	−48.4790	−1.79799	−0.898994	+	0.437961i	$0.855701\pi$
$728$	−34.3119	−1.27168
$729$	24.7296	0.915911
$730$	0	0
$731$	48.2073	1.78301
$732$	−0.679454	−0.0251134
$733$	−8.26234	−0.305176	−0.152588	−	0.988290i	$-0.548761\pi$
$733$	−8.26234	−0.305176	−0.152588	+	0.988290i	$0.548761\pi$
$734$	−37.0873	−1.36892
$735$	0	0
$736$	−1.65393	−0.0609647
$737$	−54.9420	−2.02382
$738$	−12.1915	−0.448776
$739$	−19.8239	−0.729235	−0.364618	−	0.931157i	$-0.618800\pi$
$739$	−19.8239	−0.729235	−0.364618	+	0.931157i	$0.618800\pi$
$740$	0	0
$741$	13.9401	0.512103
$742$	9.74829	0.357871
$743$	−6.46288	−0.237100	−0.118550	−	0.992948i	$-0.537825\pi$
$743$	−6.46288	−0.237100	−0.118550	+	0.992948i	$0.537825\pi$
$744$	14.3084	0.524571
$745$	0	0
$746$	24.3857	0.892824
$747$	6.38249	0.233523
$748$	−2.29233	−0.0838159
$749$	22.2747	0.813898
$750$	0	0
$751$	−10.3960	−0.379354	−0.189677	−	0.981846i	$-0.560744\pi$
$751$	−10.3960	−0.379354	−0.189677	+	0.981846i	$0.560744\pi$
$752$	44.3718	1.61807
$753$	14.0489	0.511970
$754$	1.48151	0.0539535
$755$	0	0
$756$	0.735185	0.0267384
$757$	−52.5543	−1.91012	−0.955060	−	0.296413i	$-0.904210\pi$
$757$	−52.5543	−1.91012	−0.955060	+	0.296413i	$0.904210\pi$
$758$	46.3086	1.68201
$759$	−48.4974	−1.76034
$760$	0	0
$761$	14.0555	0.509512	0.254756	−	0.967005i	$-0.418005\pi$
$761$	14.0555	0.509512	0.254756	+	0.967005i	$0.418005\pi$
$762$	17.1920	0.622802
$763$	40.9914	1.48399
$764$	0.656027	0.0237342
$765$	0	0
$766$	17.5399	0.633742
$767$	36.6841	1.32459
$768$	−1.46160	−0.0527410
$769$	12.0208	0.433480	0.216740	−	0.976229i	$-0.430458\pi$
$769$	12.0208	0.433480	0.216740	+	0.976229i	$0.430458\pi$
$770$	0	0
$771$	−36.2639	−1.30601
$772$	0.0604366	0.00217516
$773$	2.43858	0.0877097	0.0438549	−	0.999038i	$-0.486036\pi$
$773$	2.43858	0.0877097	0.0438549	+	0.999038i	$0.486036\pi$
$774$	13.3903	0.481305
$775$	0	0
$776$	−36.2394	−1.30092
$777$	−1.43864	−0.0516109
$778$	42.3228	1.51734
$779$	−14.7249	−0.527574
$780$	0	0
$781$	23.4161	0.837896
$782$	−63.3296	−2.26466
$783$	1.27527	0.0455745
$784$	−1.75976	−0.0628487
$785$	0	0
$786$	18.0056	0.642238
$787$	53.9723	1.92391	0.961953	−	0.273215i	$-0.0880870\pi$
$787$	53.9723	1.92391	0.961953	+	0.273215i	$0.0880870\pi$
$788$	0.608281	0.0216691
$789$	−30.6519	−1.09124
$790$	0	0
$791$	−3.92745	−0.139644
$792$	25.5800	0.908946
$793$	50.2537	1.78456
$794$	35.0499	1.24388
$795$	0	0
$796$	0.252691	0.00895638
$797$	20.8297	0.737827	0.368913	−	0.929464i	$-0.379730\pi$
$797$	20.8297	0.737827	0.368913	+	0.929464i	$0.379730\pi$
$798$	12.0670	0.427168
$799$	79.6388	2.81742
$800$	0	0
$801$	6.26222	0.221265
$802$	−2.80549	−0.0990653
$803$	−54.5908	−1.92647
$804$	0.521380	0.0183877
$805$	0	0
$806$	26.3422	0.927866
$807$	23.4748	0.826353
$808$	−24.3127	−0.855319
$809$	−23.6812	−0.832585	−0.416293	−	0.909231i	$-0.636671\pi$
$809$	−23.6812	−0.832585	−0.416293	+	0.909231i	$0.636671\pi$
$810$	0	0
$811$	41.0035	1.43983	0.719913	−	0.694064i	$-0.244182\pi$
$811$	41.0035	1.43983	0.719913	+	0.694064i	$0.244182\pi$
$812$	0.0304084	0.00106712
$813$	19.4275	0.681353
$814$	3.86676	0.135530
$815$	0	0
$816$	−37.7526	−1.32160
$817$	16.1728	0.565814
$818$	−16.9691	−0.593310
$819$	−17.5214	−0.612246
$820$	0	0
$821$	3.55405	0.124037	0.0620186	−	0.998075i	$-0.480246\pi$
$821$	3.55405	0.124037	0.0620186	+	0.998075i	$0.480246\pi$
$822$	41.5965	1.45084
$823$	−49.8185	−1.73657	−0.868283	−	0.496070i	$-0.834776\pi$
$823$	−49.8185	−1.73657	−0.868283	+	0.496070i	$0.834776\pi$
$824$	−16.9413	−0.590180
$825$	0	0
$826$	31.7550	1.10490
$827$	28.2275	0.981566	0.490783	−	0.871282i	$-0.336711\pi$
$827$	28.2275	0.981566	0.490783	+	0.871282i	$0.336711\pi$
$828$	−0.417098	−0.0144952
$829$	−27.2897	−0.947810	−0.473905	−	0.880576i	$-0.657156\pi$
$829$	−27.2897	−0.947810	−0.473905	+	0.880576i	$0.657156\pi$
$830$	0	0
$831$	−5.76912	−0.200128
$832$	35.1377	1.21818
$833$	−3.15843	−0.109433
$834$	−15.1136	−0.523340
$835$	0	0
$836$	−0.769041	−0.0265978
$837$	22.6752	0.783768
$838$	−16.2492	−0.561319
$839$	−32.4642	−1.12079	−0.560394	−	0.828226i	$-0.689350\pi$
$839$	−32.4642	−1.12079	−0.560394	+	0.828226i	$0.689350\pi$
$840$	0	0
$841$	−28.9473	−0.998181
$842$	−33.0384	−1.13858
$843$	−30.8685	−1.06317
$844$	0.182253	0.00627340
$845$	0	0
$846$	22.1209	0.760531
$847$	82.4075	2.83156
$848$	−10.2317	−0.351357
$849$	−21.2958	−0.730871
$850$	0	0
$851$	2.53297	0.0868292
$852$	−0.222211	−0.00761282
$853$	−29.3273	−1.00415	−0.502073	−	0.864825i	$-0.667429\pi$
$853$	−29.3273	−1.00415	−0.502073	+	0.864825i	$0.667429\pi$
$854$	43.5012	1.48858
$855$	0	0
$856$	−22.8245	−0.780126
$857$	−36.6965	−1.25353	−0.626764	−	0.779209i	$-0.715621\pi$
$857$	−36.6965	−1.25353	−0.626764	+	0.779209i	$0.715621\pi$
$858$	−51.9628	−1.77398
$859$	32.9541	1.12438	0.562190	−	0.827008i	$-0.309959\pi$
$859$	32.9541	1.12438	0.562190	+	0.827008i	$0.309959\pi$
$860$	0	0
$861$	−20.4213	−0.695956
$862$	−32.7163	−1.11432
$863$	−0.594484	−0.0202365	−0.0101182	−	0.999949i	$-0.503221\pi$
$863$	−0.594484	−0.0202365	−0.0101182	+	0.999949i	$0.503221\pi$
$864$	−1.52542	−0.0518958
$865$	0	0
$866$	−58.0322	−1.97201
$867$	−46.4323	−1.57692
$868$	0.540680	0.0183519
$869$	−22.4813	−0.762627
$870$	0	0
$871$	−38.5623	−1.30663
$872$	−42.0033	−1.42241
$873$	−18.5057	−0.626321
$874$	−21.2461	−0.718659
$875$	0	0
$876$	0.518047	0.0175032
$877$	6.05272	0.204386	0.102193	−	0.994765i	$-0.467414\pi$
$877$	6.05272	0.204386	0.102193	+	0.994765i	$0.467414\pi$
$878$	30.2641	1.02136
$879$	13.2290	0.446201
$880$	0	0
$881$	−12.3380	−0.415678	−0.207839	−	0.978163i	$-0.566643\pi$
$881$	−12.3380	−0.415678	−0.207839	+	0.978163i	$0.566643\pi$
$882$	−0.877302	−0.0295403
$883$	9.65216	0.324821	0.162411	−	0.986723i	$-0.448073\pi$
$883$	9.65216	0.324821	0.162411	+	0.986723i	$0.448073\pi$
$884$	−1.60892	−0.0541139
$885$	0	0
$886$	−30.2321	−1.01567
$887$	−2.95581	−0.0992463	−0.0496231	−	0.998768i	$-0.515802\pi$
$887$	−2.95581	−0.0992463	−0.0496231	+	0.998768i	$0.515802\pi$
$888$	1.47415	0.0494693
$889$	−26.0990	−0.875332
$890$	0	0
$891$	−17.2537	−0.578021
$892$	−0.882349	−0.0295432
$893$	26.7176	0.894069
$894$	−23.9051	−0.799506
$895$	0	0
$896$	31.9139	1.06617
$897$	−34.0390	−1.13653
$898$	−15.1371	−0.505133
$899$	0.937879	0.0312800
$900$	0	0
$901$	−18.3639	−0.611790
$902$	54.8881	1.82757
$903$	22.4293	0.746401
$904$	4.02440	0.133849
$905$	0	0
$906$	25.4514	0.845566
$907$	4.99717	0.165928	0.0829641	−	0.996553i	$-0.473561\pi$
$907$	4.99717	0.165928	0.0829641	+	0.996553i	$0.473561\pi$
$908$	0.0754736	0.00250468
$909$	−12.4153	−0.411789
$910$	0	0
$911$	22.8938	0.758505	0.379252	−	0.925293i	$-0.376181\pi$
$911$	22.8938	0.758505	0.379252	+	0.925293i	$0.376181\pi$
$912$	−12.6654	−0.419393
$913$	−28.7350	−0.950990
$914$	29.9078	0.989261
$915$	0	0
$916$	−0.0227972	−0.000753240 0
$917$	−27.3340	−0.902649
$918$	−58.4088	−1.92778
$919$	41.2946	1.36218	0.681092	−	0.732198i	$-0.261505\pi$
$919$	41.2946	1.36218	0.681092	+	0.732198i	$0.261505\pi$
$920$	0	0
$921$	−26.4161	−0.870440
$922$	−17.7007	−0.582940
$923$	16.4351	0.540969
$924$	−1.06655	−0.0350869
$925$	0	0
$926$	−51.5101	−1.69273
$927$	−8.65109	−0.284139
$928$	−0.0630936	−0.00207115
$929$	−25.0144	−0.820695	−0.410347	−	0.911929i	$-0.634593\pi$
$929$	−25.0144	−0.820695	−0.410347	+	0.911929i	$0.634593\pi$
$930$	0	0
$931$	−1.05960	−0.0347271
$932$	−0.447968	−0.0146737
$933$	16.4806	0.539549
$934$	−27.8275	−0.910544
$935$	0	0
$936$	17.9539	0.586841
$937$	23.0290	0.752326	0.376163	−	0.926554i	$-0.377243\pi$
$937$	23.0290	0.752326	0.376163	+	0.926554i	$0.377243\pi$
$938$	−33.3807	−1.08992
$939$	−16.3569	−0.533786
$940$	0	0
$941$	−37.9931	−1.23854	−0.619271	−	0.785178i	$-0.712572\pi$
$941$	−37.9931	−1.23854	−0.619271	+	0.785178i	$0.712572\pi$
$942$	−10.7290	−0.349570
$943$	35.9552	1.17086
$944$	−33.3296	−1.08479
$945$	0	0
$946$	−60.2853	−1.96004
$947$	−10.7536	−0.349446	−0.174723	−	0.984618i	$-0.555903\pi$
$947$	−10.7536	−0.349446	−0.174723	+	0.984618i	$0.555903\pi$
$948$	0.213340	0.00692896
$949$	−38.3158	−1.24378
$950$	0	0
$951$	−22.4306	−0.727364
$952$	55.9519	1.81341
$953$	26.7122	0.865294	0.432647	−	0.901563i	$-0.357580\pi$
$953$	26.7122	0.865294	0.432647	+	0.901563i	$0.357580\pi$
$954$	−5.10085	−0.165146
$955$	0	0
$956$	−0.0109748	−0.000354949 0
$957$	−1.85006	−0.0598041
$958$	8.22054	0.265594
$959$	−63.1470	−2.03912
$960$	0	0
$961$	−14.3239	−0.462062
$962$	2.71397	0.0875019
$963$	−11.6553	−0.375588
$964$	0.0485743	0.00156447
$965$	0	0
$966$	−29.4652	−0.948028
$967$	−60.3341	−1.94021	−0.970107	−	0.242678i	$-0.921974\pi$
$967$	−60.3341	−1.94021	−0.970107	+	0.242678i	$0.921974\pi$
$968$	−84.4418	−2.71406
$969$	−22.7319	−0.730255
$970$	0	0
$971$	−53.6051	−1.72027	−0.860135	−	0.510067i	$-0.829621\pi$
$971$	−53.6051	−1.72027	−0.860135	+	0.510067i	$0.829621\pi$
$972$	−0.645421	−0.0207019
$973$	22.9437	0.735540
$974$	−11.0256	−0.353284
$975$	0	0
$976$	−45.6583	−1.46149
$977$	8.77988	0.280893	0.140447	−	0.990088i	$-0.455146\pi$
$977$	8.77988	0.280893	0.140447	+	0.990088i	$0.455146\pi$
$978$	−45.1660	−1.44425
$979$	−28.1935	−0.901069
$980$	0	0
$981$	−21.4490	−0.684813
$982$	49.1032	1.56695
$983$	25.0304	0.798346	0.399173	−	0.916876i	$-0.369297\pi$
$983$	25.0304	0.798346	0.399173	+	0.916876i	$0.369297\pi$
$984$	20.9254	0.667078
$985$	0	0
$986$	−2.41588	−0.0769372
$987$	37.0534	1.17942
$988$	−0.539768	−0.0171723
$989$	−39.4907	−1.25573
$990$	0	0
$991$	28.6686	0.910690	0.455345	−	0.890315i	$-0.349516\pi$
$991$	28.6686	0.910690	0.455345	+	0.890315i	$0.349516\pi$
$992$	−1.12185	−0.0356186
$993$	36.4624	1.15710
$994$	14.2268	0.451246
$995$	0	0
$996$	0.272685	0.00864035
$997$	36.7733	1.16462	0.582312	−	0.812966i	$-0.302148\pi$
$997$	36.7733	1.16462	0.582312	+	0.812966i	$0.302148\pi$
$998$	6.40263	0.202672
$999$	2.33616	0.0739128

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.k.1.18		25
5.4	even	2		1205.2.a.d.1.8	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.8	✓	25	5.4	even	2
6025.2.a.k.1.18		25	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)

\(f(q)\)	\(=\)	\(q+1.43128 q^{2} -1.25448 q^{3} +0.0485743 q^{4} -1.79552 q^{6} +2.72576 q^{7} -2.79304 q^{8} -1.42627 q^{9} +O(q^{10})\)	\(q+1.43128 q^{2} -1.25448 q^{3} +0.0485743 q^{4} -1.79552 q^{6} +2.72576 q^{7} -2.79304 q^{8} -1.42627 q^{9} +6.42128 q^{11} -0.0609357 q^{12} +4.50692 q^{13} +3.90133 q^{14} -4.09479 q^{16} -7.34936 q^{17} -2.04139 q^{18} -2.46559 q^{19} -3.41942 q^{21} +9.19068 q^{22} +6.02048 q^{23} +3.50383 q^{24} +6.45068 q^{26} +5.55269 q^{27} +0.132402 q^{28} +0.229668 q^{29} +4.08364 q^{31} -0.274717 q^{32} -8.05540 q^{33} -10.5190 q^{34} -0.0692799 q^{36} +0.420726 q^{37} -3.52896 q^{38} -5.65386 q^{39} +5.97215 q^{41} -4.89416 q^{42} -6.55939 q^{43} +0.311909 q^{44} +8.61702 q^{46} -10.8362 q^{47} +5.13685 q^{48} +0.429757 q^{49} +9.21966 q^{51} +0.218920 q^{52} +2.49871 q^{53} +7.94747 q^{54} -7.61316 q^{56} +3.09305 q^{57} +0.328720 q^{58} +8.13951 q^{59} +11.1504 q^{61} +5.84484 q^{62} -3.88766 q^{63} +7.79638 q^{64} -11.5296 q^{66} -8.55624 q^{67} -0.356990 q^{68} -7.55260 q^{69} +3.64665 q^{71} +3.98363 q^{72} -8.50154 q^{73} +0.602178 q^{74} -0.119764 q^{76} +17.5029 q^{77} -8.09228 q^{78} -3.50107 q^{79} -2.68696 q^{81} +8.54784 q^{82} -4.47496 q^{83} -0.166096 q^{84} -9.38835 q^{86} -0.288114 q^{87} -17.9349 q^{88} -4.39063 q^{89} +12.2848 q^{91} +0.292440 q^{92} -5.12286 q^{93} -15.5096 q^{94} +0.344629 q^{96} +12.9749 q^{97} +0.615104 q^{98} -9.15847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9}+O(q^{10}) \) 25 * q + 4 * q^2 - 9 * q^3 + 36 * q^4 + 7 * q^6 - 7 * q^7 + 15 * q^8 + 36 * q^9	\( 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9} + 10 q^{11} - 22 q^{12} - 10 q^{13} + 13 q^{14} + 54 q^{16} - q^{17} + 13 q^{18} + 50 q^{19} + 9 q^{21} - 11 q^{22} + 31 q^{23} + 22 q^{24} + 8 q^{26} - 42 q^{27} - 14 q^{28} + 4 q^{29} + 34 q^{31} + 44 q^{32} - 28 q^{33} + 33 q^{34} + 83 q^{36} - 14 q^{37} + 10 q^{38} + 23 q^{39} + 11 q^{41} - 23 q^{42} - 49 q^{43} + 20 q^{44} + 27 q^{46} + 28 q^{47} - 30 q^{48} + 66 q^{49} + 49 q^{51} - 39 q^{52} + 16 q^{53} + 5 q^{54} + 51 q^{56} - 10 q^{57} + 8 q^{58} + 30 q^{59} + 35 q^{61} + 18 q^{62} + 73 q^{64} - 13 q^{66} - 37 q^{67} - 11 q^{68} - 4 q^{69} + 12 q^{71} + 90 q^{72} - 36 q^{73} - 12 q^{74} + 57 q^{76} + 31 q^{77} + 9 q^{78} + 16 q^{79} + 65 q^{81} + 11 q^{82} - 43 q^{83} - 62 q^{84} - 9 q^{86} + 22 q^{87} - 20 q^{88} + 38 q^{89} + 86 q^{91} + 119 q^{92} - 10 q^{93} - 18 q^{94} - 34 q^{96} - 17 q^{97} + 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q + 4 * q^2 - 9 * q^3 + 36 * q^4 + 7 * q^6 - 7 * q^7 + 15 * q^8 + 36 * q^9 + 10 * q^11 - 22 * q^12 - 10 * q^13 + 13 * q^14 + 54 * q^16 - q^17 + 13 * q^18 + 50 * q^19 + 9 * q^21 - 11 * q^22 + 31 * q^23 + 22 * q^24 + 8 * q^26 - 42 * q^27 - 14 * q^28 + 4 * q^29 + 34 * q^31 + 44 * q^32 - 28 * q^33 + 33 * q^34 + 83 * q^36 - 14 * q^37 + 10 * q^38 + 23 * q^39 + 11 * q^41 - 23 * q^42 - 49 * q^43 + 20 * q^44 + 27 * q^46 + 28 * q^47 - 30 * q^48 + 66 * q^49 + 49 * q^51 - 39 * q^52 + 16 * q^53 + 5 * q^54 + 51 * q^56 - 10 * q^57 + 8 * q^58 + 30 * q^59 + 35 * q^61 + 18 * q^62 + 73 * q^64 - 13 * q^66 - 37 * q^67 - 11 * q^68 - 4 * q^69 + 12 * q^71 + 90 * q^72 - 36 * q^73 - 12 * q^74 + 57 * q^76 + 31 * q^77 + 9 * q^78 + 16 * q^79 + 65 * q^81 + 11 * q^82 - 43 * q^83 - 62 * q^84 - 9 * q^86 + 22 * q^87 - 20 * q^88 + 38 * q^89 + 86 * q^91 + 119 * q^92 - 10 * q^93 - 18 * q^94 - 34 * q^96 - 17 * q^97 + 32 * q^98 + 26 * q^99

Introduction

L-functions

Modular forms

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Database

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