LMFDB - Embedded newform 8025.2.a.bc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8025,2,Mod(1,8025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8025 = 3 \cdot 5^{2} \cdot 107 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8025.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:	$64.0799476221$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 26x^{7} + 51x^{6} - 101x^{5} - 65x^{4} + 126x^{3} + 5x^{2} - 10x + 1 $ x^10 - 2x^9 - 13x^8 + 26x^7 + 51x^6 - 101x^5 - 65x^4 + 126x^3 + 5x^2 - 10*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1605)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.07812$ of defining polynomial
Character	$\chi$	$=$	8025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.07812 q^{2} +1.00000 q^{3} +2.31860 q^{4} -2.07812 q^{6} -0.151414 q^{7} -0.662092 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.07812 q^{2} +1.00000 q^{3} +2.31860 q^{4} -2.07812 q^{6} -0.151414 q^{7} -0.662092 q^{8} +1.00000 q^{9} -4.71510 q^{11} +2.31860 q^{12} +0.171560 q^{13} +0.314658 q^{14} -3.26129 q^{16} +2.52256 q^{17} -2.07812 q^{18} +7.60625 q^{19} -0.151414 q^{21} +9.79857 q^{22} +6.83195 q^{23} -0.662092 q^{24} -0.356522 q^{26} +1.00000 q^{27} -0.351069 q^{28} -9.08284 q^{29} -3.81654 q^{31} +8.10155 q^{32} -4.71510 q^{33} -5.24219 q^{34} +2.31860 q^{36} +0.510217 q^{37} -15.8067 q^{38} +0.171560 q^{39} -3.87101 q^{41} +0.314658 q^{42} -4.14916 q^{43} -10.9324 q^{44} -14.1976 q^{46} +0.851888 q^{47} -3.26129 q^{48} -6.97707 q^{49} +2.52256 q^{51} +0.397778 q^{52} -9.78792 q^{53} -2.07812 q^{54} +0.100250 q^{56} +7.60625 q^{57} +18.8753 q^{58} -11.9376 q^{59} +2.00565 q^{61} +7.93125 q^{62} -0.151414 q^{63} -10.3135 q^{64} +9.79857 q^{66} -1.67356 q^{67} +5.84881 q^{68} +6.83195 q^{69} -4.13888 q^{71} -0.662092 q^{72} +3.38266 q^{73} -1.06029 q^{74} +17.6359 q^{76} +0.713934 q^{77} -0.356522 q^{78} +11.8372 q^{79} +1.00000 q^{81} +8.04444 q^{82} +0.333192 q^{83} -0.351069 q^{84} +8.62247 q^{86} -9.08284 q^{87} +3.12183 q^{88} +16.9505 q^{89} -0.0259766 q^{91} +15.8406 q^{92} -3.81654 q^{93} -1.77033 q^{94} +8.10155 q^{96} +6.78735 q^{97} +14.4992 q^{98} -4.71510 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{6} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^6 + 10 * q^9	$ 10 q - 2 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{6} + 10 q^{9} - 14 q^{11} + 10 q^{12} + 3 q^{13} - 16 q^{14} + 10 q^{16} - 8 q^{17} - 2 q^{18} - 19 q^{19} - 5 q^{22} - 4 q^{23} - 22 q^{26} + 10 q^{27} - 25 q^{29} - 2 q^{31} + 13 q^{32} - 14 q^{33} - 37 q^{34} + 10 q^{36} + 10 q^{37} + 13 q^{38} + 3 q^{39} - 31 q^{41} - 16 q^{42} - 62 q^{44} + 2 q^{46} + q^{47} + 10 q^{48} + 26 q^{49} - 8 q^{51} + 30 q^{52} - 9 q^{53} - 2 q^{54} - 63 q^{56} - 19 q^{57} - 30 q^{58} - 65 q^{59} + 12 q^{61} + 39 q^{62} - 2 q^{64} - 5 q^{66} + 10 q^{67} - 22 q^{68} - 4 q^{69} - 45 q^{71} - q^{73} + 19 q^{74} - 39 q^{76} + q^{77} - 22 q^{78} - 47 q^{79} + 10 q^{81} + 23 q^{82} - q^{83} + 12 q^{86} - 25 q^{87} + 8 q^{88} - 34 q^{89} - 26 q^{91} - 14 q^{92} - 2 q^{93} - 64 q^{94} + 13 q^{96} - 5 q^{97} + 51 q^{98} - 14 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^6 + 10 * q^9 - 14 * q^11 + 10 * q^12 + 3 * q^13 - 16 * q^14 + 10 * q^16 - 8 * q^17 - 2 * q^18 - 19 * q^19 - 5 * q^22 - 4 * q^23 - 22 * q^26 + 10 * q^27 - 25 * q^29 - 2 * q^31 + 13 * q^32 - 14 * q^33 - 37 * q^34 + 10 * q^36 + 10 * q^37 + 13 * q^38 + 3 * q^39 - 31 * q^41 - 16 * q^42 - 62 * q^44 + 2 * q^46 + q^47 + 10 * q^48 + 26 * q^49 - 8 * q^51 + 30 * q^52 - 9 * q^53 - 2 * q^54 - 63 * q^56 - 19 * q^57 - 30 * q^58 - 65 * q^59 + 12 * q^61 + 39 * q^62 - 2 * q^64 - 5 * q^66 + 10 * q^67 - 22 * q^68 - 4 * q^69 - 45 * q^71 - q^73 + 19 * q^74 - 39 * q^76 + q^77 - 22 * q^78 - 47 * q^79 + 10 * q^81 + 23 * q^82 - q^83 + 12 * q^86 - 25 * q^87 + 8 * q^88 - 34 * q^89 - 26 * q^91 - 14 * q^92 - 2 * q^93 - 64 * q^94 + 13 * q^96 - 5 * q^97 + 51 * q^98 - 14 * 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 $

$2$	−2.07812	−1.46946	−0.734728	−	0.678362i	$-0.762690\pi$
$2$	−2.07812	−1.46946	−0.734728	+	0.678362i	$0.762690\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.31860	1.15930
$5$	0	0
$5$	0	0
$6$	−2.07812	−0.848391
$7$	−0.151414	−0.0572292	−0.0286146	−	0.999591i	$-0.509110\pi$
$7$	−0.151414	−0.0572292	−0.0286146	+	0.999591i	$0.509110\pi$
$8$	−0.662092	−0.234085
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.71510	−1.42166	−0.710829	−	0.703365i	$-0.751680\pi$
$11$	−4.71510	−1.42166	−0.710829	+	0.703365i	$0.751680\pi$
$12$	2.31860	0.669322
$13$	0.171560	0.0475821	0.0237910	−	0.999717i	$-0.492426\pi$
$13$	0.171560	0.0475821	0.0237910	+	0.999717i	$0.492426\pi$
$14$	0.314658	0.0840958
$15$	0	0
$16$	−3.26129	−0.815323
$17$	2.52256	0.611810	0.305905	−	0.952062i	$-0.401041\pi$
$17$	2.52256	0.611810	0.305905	+	0.952062i	$0.401041\pi$
$18$	−2.07812	−0.489819
$19$	7.60625	1.74499	0.872497	−	0.488620i	$-0.162500\pi$
$19$	7.60625	1.74499	0.872497	+	0.488620i	$0.162500\pi$
$20$	0	0
$21$	−0.151414	−0.0330413
$22$	9.79857	2.08906
$23$	6.83195	1.42456	0.712280	−	0.701895i	$-0.247663\pi$
$23$	6.83195	1.42456	0.712280	+	0.701895i	$0.247663\pi$
$24$	−0.662092	−0.135149
$25$	0	0
$26$	−0.356522	−0.0699198
$27$	1.00000	0.192450
$28$	−0.351069	−0.0663459
$29$	−9.08284	−1.68664	−0.843320	−	0.537411i	$-0.819402\pi$
$29$	−9.08284	−1.68664	−0.843320	+	0.537411i	$0.819402\pi$
$30$	0	0
$31$	−3.81654	−0.685471	−0.342736	−	0.939432i	$-0.611353\pi$
$31$	−3.81654	−0.685471	−0.342736	+	0.939432i	$0.611353\pi$
$32$	8.10155	1.43217
$33$	−4.71510	−0.820794
$34$	−5.24219	−0.899028
$35$	0	0
$36$	2.31860	0.386433
$37$	0.510217	0.0838791	0.0419395	−	0.999120i	$-0.486646\pi$
$37$	0.510217	0.0838791	0.0419395	+	0.999120i	$0.486646\pi$
$38$	−15.8067	−2.56419
$39$	0.171560	0.0274715
$40$	0	0
$41$	−3.87101	−0.604550	−0.302275	−	0.953221i	$-0.597746\pi$
$41$	−3.87101	−0.604550	−0.302275	+	0.953221i	$0.597746\pi$
$42$	0.314658	0.0485527
$43$	−4.14916	−0.632741	−0.316371	−	0.948636i	$-0.602464\pi$
$43$	−4.14916	−0.632741	−0.316371	+	0.948636i	$0.602464\pi$
$44$	−10.9324	−1.64813
$45$	0	0
$46$	−14.1976	−2.09333
$47$	0.851888	0.124261	0.0621303	−	0.998068i	$-0.480211\pi$
$47$	0.851888	0.124261	0.0621303	+	0.998068i	$0.480211\pi$
$48$	−3.26129	−0.470727
$49$	−6.97707	−0.996725
$50$	0	0
$51$	2.52256	0.353229
$52$	0.397778	0.0551619
$53$	−9.78792	−1.34447	−0.672237	−	0.740336i	$-0.734667\pi$
$53$	−9.78792	−1.34447	−0.672237	+	0.740336i	$0.734667\pi$
$54$	−2.07812	−0.282797
$55$	0	0
$56$	0.100250	0.0133965
$57$	7.60625	1.00747
$58$	18.8753	2.47844
$59$	−11.9376	−1.55415	−0.777074	−	0.629409i	$-0.783297\pi$
$59$	−11.9376	−1.55415	−0.777074	+	0.629409i	$0.783297\pi$
$60$	0	0
$61$	2.00565	0.256798	0.128399	−	0.991723i	$-0.459016\pi$
$61$	2.00565	0.256798	0.128399	+	0.991723i	$0.459016\pi$
$62$	7.93125	1.00727
$63$	−0.151414	−0.0190764
$64$	−10.3135	−1.28918
$65$	0	0
$66$	9.79857	1.20612
$67$	−1.67356	−0.204458	−0.102229	−	0.994761i	$-0.532597\pi$
$67$	−1.67356	−0.204458	−0.102229	+	0.994761i	$0.532597\pi$
$68$	5.84881	0.709272
$69$	6.83195	0.822470
$70$	0	0
$71$	−4.13888	−0.491195	−0.245598	−	0.969372i	$-0.578984\pi$
$71$	−4.13888	−0.491195	−0.245598	+	0.969372i	$0.578984\pi$
$72$	−0.662092	−0.0780282
$73$	3.38266	0.395910	0.197955	−	0.980211i	$-0.436570\pi$
$73$	3.38266	0.395910	0.197955	+	0.980211i	$0.436570\pi$
$74$	−1.06029	−0.123257
$75$	0	0
$76$	17.6359	2.02297
$77$	0.713934	0.0813603
$78$	−0.356522	−0.0403682
$79$	11.8372	1.33179	0.665894	−	0.746047i	$-0.268050\pi$
$79$	11.8372	1.33179	0.665894	+	0.746047i	$0.268050\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	8.04444	0.888360
$83$	0.333192	0.0365726	0.0182863	−	0.999833i	$-0.494179\pi$
$83$	0.333192	0.0365726	0.0182863	+	0.999833i	$0.494179\pi$
$84$	−0.351069	−0.0383048
$85$	0	0
$86$	8.62247	0.929785
$87$	−9.08284	−0.973783
$88$	3.12183	0.332788
$89$	16.9505	1.79675	0.898376	−	0.439227i	$-0.144748\pi$
$89$	16.9505	1.79675	0.898376	+	0.439227i	$0.144748\pi$
$90$	0	0
$91$	−0.0259766	−0.00272309
$92$	15.8406	1.65149
$93$	−3.81654	−0.395757
$94$	−1.77033	−0.182595
$95$	0	0
$96$	8.10155	0.826861
$97$	6.78735	0.689151	0.344576	−	0.938759i	$-0.388023\pi$
$97$	6.78735	0.689151	0.344576	+	0.938759i	$0.388023\pi$
$98$	14.4992	1.46464
$99$	−4.71510	−0.473886
$100$	0	0
$101$	3.12859	0.311307	0.155653	−	0.987812i	$-0.450252\pi$
$101$	3.12859	0.311307	0.155653	+	0.987812i	$0.450252\pi$
$102$	−5.24219	−0.519054
$103$	0.954318	0.0940318	0.0470159	−	0.998894i	$-0.485029\pi$
$103$	0.954318	0.0940318	0.0470159	+	0.998894i	$0.485029\pi$
$104$	−0.113588	−0.0111382
$105$	0	0
$106$	20.3405	1.97565
$107$	1.00000	0.0966736
$107$	1.00000	0.0966736
$108$	2.31860	0.223107
$109$	3.24487	0.310802	0.155401	−	0.987851i	$-0.450333\pi$
$109$	3.24487	0.310802	0.155401	+	0.987851i	$0.450333\pi$
$110$	0	0
$111$	0.510217	0.0484276
$112$	0.493806	0.0466603
$113$	−7.68556	−0.722997	−0.361498	−	0.932373i	$-0.617735\pi$
$113$	−7.68556	−0.722997	−0.361498	+	0.932373i	$0.617735\pi$
$114$	−15.8067	−1.48044
$115$	0	0
$116$	−21.0595	−1.95532
$117$	0.171560	0.0158607
$118$	24.8079	2.28375
$119$	−0.381952	−0.0350134
$120$	0	0
$121$	11.2322	1.02111
$122$	−4.16800	−0.377353
$123$	−3.87101	−0.349037
$124$	−8.84904	−0.794667
$125$	0	0
$126$	0.314658	0.0280319
$127$	−2.01094	−0.178442	−0.0892211	−	0.996012i	$-0.528438\pi$
$127$	−2.01094	−0.178442	−0.0892211	+	0.996012i	$0.528438\pi$
$128$	5.22953	0.462229
$129$	−4.14916	−0.365313
$130$	0	0
$131$	−10.2019	−0.891345	−0.445672	−	0.895196i	$-0.647035\pi$
$131$	−10.2019	−0.891345	−0.445672	+	0.895196i	$0.647035\pi$
$132$	−10.9324	−0.951547
$133$	−1.15169	−0.0998646
$134$	3.47787	0.300442
$135$	0	0
$136$	−1.67016	−0.143215
$137$	−12.6003	−1.07652	−0.538259	−	0.842780i	$-0.680918\pi$
$137$	−12.6003	−1.07652	−0.538259	+	0.842780i	$0.680918\pi$
$138$	−14.1976	−1.20858
$139$	−13.6774	−1.16010	−0.580051	−	0.814580i	$-0.696967\pi$
$139$	−13.6774	−1.16010	−0.580051	+	0.814580i	$0.696967\pi$
$140$	0	0
$141$	0.851888	0.0717419
$142$	8.60111	0.721789
$143$	−0.808922	−0.0676454
$144$	−3.26129	−0.271774
$145$	0	0
$146$	−7.02958	−0.581772
$147$	−6.97707	−0.575459
$148$	1.18299	0.0972411
$149$	−14.1457	−1.15886	−0.579432	−	0.815020i	$-0.696726\pi$
$149$	−14.1457	−1.15886	−0.579432	+	0.815020i	$0.696726\pi$
$150$	0	0
$151$	−5.55621	−0.452158	−0.226079	−	0.974109i	$-0.572591\pi$
$151$	−5.55621	−0.452158	−0.226079	+	0.974109i	$0.572591\pi$
$152$	−5.03603	−0.408476
$153$	2.52256	0.203937
$154$	−1.48364	−0.119555
$155$	0	0
$156$	0.397778	0.0318478
$157$	6.67965	0.533094	0.266547	−	0.963822i	$-0.414117\pi$
$157$	6.67965	0.533094	0.266547	+	0.963822i	$0.414117\pi$
$158$	−24.5991	−1.95700
$159$	−9.78792	−0.776233
$160$	0	0
$161$	−1.03446	−0.0815265
$162$	−2.07812	−0.163273
$163$	19.1478	1.49977	0.749885	−	0.661568i	$-0.230109\pi$
$163$	19.1478	1.49977	0.749885	+	0.661568i	$0.230109\pi$
$164$	−8.97533	−0.700855
$165$	0	0
$166$	−0.692414	−0.0537418
$167$	−3.07430	−0.237896	−0.118948	−	0.992900i	$-0.537952\pi$
$167$	−3.07430	−0.237896	−0.118948	+	0.992900i	$0.537952\pi$
$168$	0.100250	0.00773447
$169$	−12.9706	−0.997736
$170$	0	0
$171$	7.60625	0.581664
$172$	−9.62025	−0.733537
$173$	−7.01511	−0.533349	−0.266674	−	0.963787i	$-0.585925\pi$
$173$	−7.01511	−0.533349	−0.266674	+	0.963787i	$0.585925\pi$
$174$	18.8753	1.43093
$175$	0	0
$176$	15.3773	1.15911
$177$	−11.9376	−0.897288
$178$	−35.2253	−2.64025
$179$	2.87507	0.214893	0.107446	−	0.994211i	$-0.465733\pi$
$179$	2.87507	0.214893	0.107446	+	0.994211i	$0.465733\pi$
$180$	0	0
$181$	18.6355	1.38517	0.692583	−	0.721338i	$-0.256472\pi$
$181$	18.6355	1.38517	0.692583	+	0.721338i	$0.256472\pi$
$182$	0.0539826	0.00400146
$183$	2.00565	0.148262
$184$	−4.52338	−0.333468
$185$	0	0
$186$	7.93125	0.581547
$187$	−11.8941	−0.869785
$188$	1.97519	0.144055
$189$	−0.151414	−0.0110138
$190$	0	0
$191$	25.4002	1.83789	0.918946	−	0.394383i	$-0.129042\pi$
$191$	25.4002	1.83789	0.918946	+	0.394383i	$0.129042\pi$
$192$	−10.3135	−0.744309
$193$	−25.9410	−1.86727	−0.933636	−	0.358224i	$-0.883383\pi$
$193$	−25.9410	−1.86727	−0.933636	+	0.358224i	$0.883383\pi$
$194$	−14.1050	−1.01268
$195$	0	0
$196$	−16.1770	−1.15550
$197$	−0.287535	−0.0204860	−0.0102430	−	0.999948i	$-0.503261\pi$
$197$	−0.287535	−0.0204860	−0.0102430	+	0.999948i	$0.503261\pi$
$198$	9.79857	0.696354
$199$	−24.8529	−1.76178	−0.880889	−	0.473323i	$-0.843054\pi$
$199$	−24.8529	−1.76178	−0.880889	+	0.473323i	$0.843054\pi$
$200$	0	0
$201$	−1.67356	−0.118044
$202$	−6.50160	−0.457451
$203$	1.37527	0.0965252
$204$	5.84881	0.409498
$205$	0	0
$206$	−1.98319	−0.138176
$207$	6.83195	0.474853
$208$	−0.559506	−0.0387948
$209$	−35.8642	−2.48078
$210$	0	0
$211$	12.6353	0.869847	0.434924	−	0.900467i	$-0.356775\pi$
$211$	12.6353	0.869847	0.434924	+	0.900467i	$0.356775\pi$
$212$	−22.6943	−1.55865
$213$	−4.13888	−0.283592
$214$	−2.07812	−0.142058
$215$	0	0
$216$	−0.662092	−0.0450496
$217$	0.577879	0.0392290
$218$	−6.74324	−0.456710
$219$	3.38266	0.228579
$220$	0	0
$221$	0.432769	0.0291112
$222$	−1.06029	−0.0711622
$223$	21.4659	1.43746	0.718732	−	0.695288i	$-0.244723\pi$
$223$	21.4659	1.43746	0.718732	+	0.695288i	$0.244723\pi$
$224$	−1.22669	−0.0819618
$225$	0	0
$226$	15.9716	1.06241
$227$	−5.80226	−0.385109	−0.192555	−	0.981286i	$-0.561677\pi$
$227$	−5.80226	−0.385109	−0.192555	+	0.981286i	$0.561677\pi$
$228$	17.6359	1.16796
$229$	21.5873	1.42653	0.713264	−	0.700895i	$-0.247216\pi$
$229$	21.5873	1.42653	0.713264	+	0.700895i	$0.247216\pi$
$230$	0	0
$231$	0.713934	0.0469734
$232$	6.01367	0.394817
$233$	−10.9054	−0.714435	−0.357218	−	0.934021i	$-0.616275\pi$
$233$	−10.9054	−0.714435	−0.357218	+	0.934021i	$0.616275\pi$
$234$	−0.356522	−0.0233066
$235$	0	0
$236$	−27.6786	−1.80173
$237$	11.8372	0.768908
$238$	0.793743	0.0514507
$239$	1.28063	0.0828372	0.0414186	−	0.999142i	$-0.486812\pi$
$239$	1.28063	0.0828372	0.0414186	+	0.999142i	$0.486812\pi$
$240$	0	0
$241$	−16.8353	−1.08446	−0.542230	−	0.840230i	$-0.682420\pi$
$241$	−16.8353	−1.08446	−0.542230	+	0.840230i	$0.682420\pi$
$242$	−23.3419	−1.50047
$243$	1.00000	0.0641500
$244$	4.65031	0.297705
$245$	0	0
$246$	8.04444	0.512895
$247$	1.30493	0.0830304
$248$	2.52690	0.160458
$249$	0.333192	0.0211152
$250$	0	0
$251$	−4.30023	−0.271428	−0.135714	−	0.990748i	$-0.543333\pi$
$251$	−4.30023	−0.271428	−0.135714	+	0.990748i	$0.543333\pi$
$252$	−0.351069	−0.0221153
$253$	−32.2134	−2.02524
$254$	4.17899	0.262213
$255$	0	0
$256$	9.75930	0.609956
$257$	4.80475	0.299712	0.149856	−	0.988708i	$-0.452119\pi$
$257$	4.80475	0.299712	0.149856	+	0.988708i	$0.452119\pi$
$258$	8.62247	0.536812
$259$	−0.0772541	−0.00480034
$260$	0	0
$261$	−9.08284	−0.562214
$262$	21.2008	1.30979
$263$	−24.3580	−1.50198	−0.750990	−	0.660313i	$-0.770424\pi$
$263$	−24.3580	−1.50198	−0.750990	+	0.660313i	$0.770424\pi$
$264$	3.12183	0.192135
$265$	0	0
$266$	2.39337	0.146747
$267$	16.9505	1.03736
$268$	−3.88033	−0.237029
$269$	3.31969	0.202405	0.101202	−	0.994866i	$-0.467731\pi$
$269$	3.31969	0.202405	0.101202	+	0.994866i	$0.467731\pi$
$270$	0	0
$271$	8.89095	0.540087	0.270043	−	0.962848i	$-0.412962\pi$
$271$	8.89095	0.540087	0.270043	+	0.962848i	$0.412962\pi$
$272$	−8.22680	−0.498823
$273$	−0.0259766	−0.00157217
$274$	26.1850	1.58189
$275$	0	0
$276$	15.8406	0.953490
$277$	−2.38710	−0.143427	−0.0717135	−	0.997425i	$-0.522847\pi$
$277$	−2.38710	−0.143427	−0.0717135	+	0.997425i	$0.522847\pi$
$278$	28.4233	1.70472
$279$	−3.81654	−0.228490
$280$	0	0
$281$	−11.1209	−0.663420	−0.331710	−	0.943381i	$-0.607626\pi$
$281$	−11.1209	−0.663420	−0.331710	+	0.943381i	$0.607626\pi$
$282$	−1.77033	−0.105422
$283$	19.5637	1.16294	0.581469	−	0.813568i	$-0.302478\pi$
$283$	19.5637	1.16294	0.581469	+	0.813568i	$0.302478\pi$
$284$	−9.59642	−0.569443
$285$	0	0
$286$	1.68104	0.0994020
$287$	0.586126	0.0345980
$288$	8.10155	0.477389
$289$	−10.6367	−0.625688
$290$	0	0
$291$	6.78735	0.397882
$292$	7.84303	0.458978
$293$	−11.8245	−0.690795	−0.345398	−	0.938456i	$-0.612256\pi$
$293$	−11.8245	−0.690795	−0.345398	+	0.938456i	$0.612256\pi$
$294$	14.4992	0.845612
$295$	0	0
$296$	−0.337810	−0.0196348
$297$	−4.71510	−0.273598
$298$	29.3966	1.70290
$299$	1.17209	0.0677836
$300$	0	0
$301$	0.628242	0.0362113
$302$	11.5465	0.664426
$303$	3.12859	0.179733
$304$	−24.8062	−1.42273
$305$	0	0
$306$	−5.24219	−0.299676
$307$	8.14602	0.464918	0.232459	−	0.972606i	$-0.425323\pi$
$307$	8.14602	0.464918	0.232459	+	0.972606i	$0.425323\pi$
$308$	1.65533	0.0943211
$309$	0.954318	0.0542893
$310$	0	0
$311$	−3.55596	−0.201640	−0.100820	−	0.994905i	$-0.532147\pi$
$311$	−3.55596	−0.201640	−0.100820	+	0.994905i	$0.532147\pi$
$312$	−0.113588	−0.00643067
$313$	4.38944	0.248106	0.124053	−	0.992276i	$-0.460411\pi$
$313$	4.38944	0.248106	0.124053	+	0.992276i	$0.460411\pi$
$314$	−13.8811	−0.783358
$315$	0	0
$316$	27.4457	1.54394
$317$	−3.97176	−0.223076	−0.111538	−	0.993760i	$-0.535578\pi$
$317$	−3.97176	−0.223076	−0.111538	+	0.993760i	$0.535578\pi$
$318$	20.3405	1.14064
$319$	42.8265	2.39783
$320$	0	0
$321$	1.00000	0.0558146
$322$	2.14973	0.119800
$323$	19.1872	1.06760
$324$	2.31860	0.128811
$325$	0	0
$326$	−39.7915	−2.20385
$327$	3.24487	0.179442
$328$	2.56296	0.141516
$329$	−0.128988	−0.00711134
$330$	0	0
$331$	−26.1084	−1.43505	−0.717525	−	0.696533i	$-0.754725\pi$
$331$	−26.1084	−1.43505	−0.717525	+	0.696533i	$0.754725\pi$
$332$	0.772539	0.0423986
$333$	0.510217	0.0279597
$334$	6.38877	0.349578
$335$	0	0
$336$	0.493806	0.0269393
$337$	14.3885	0.783791	0.391896	−	0.920010i	$-0.371819\pi$
$337$	14.3885	0.783791	0.391896	+	0.920010i	$0.371819\pi$
$338$	26.9545	1.46613
$339$	−7.68556	−0.417422
$340$	0	0
$341$	17.9954	0.974505
$342$	−15.8067	−0.854730
$343$	2.11633	0.114271
$344$	2.74712	0.148115
$345$	0	0
$346$	14.5783	0.783733
$347$	31.6065	1.69673	0.848364	−	0.529414i	$-0.177588\pi$
$347$	31.6065	1.69673	0.848364	+	0.529414i	$0.177588\pi$
$348$	−21.0595	−1.12891
$349$	−28.5555	−1.52854	−0.764270	−	0.644896i	$-0.776900\pi$
$349$	−28.5555	−1.52854	−0.764270	+	0.644896i	$0.776900\pi$
$350$	0	0
$351$	0.171560	0.00915718
$352$	−38.1997	−2.03605
$353$	−20.1424	−1.07207	−0.536035	−	0.844196i	$-0.680079\pi$
$353$	−20.1424	−1.07207	−0.536035	+	0.844196i	$0.680079\pi$
$354$	24.8079	1.31853
$355$	0	0
$356$	39.3015	2.08298
$357$	−0.381952	−0.0202150
$358$	−5.97475	−0.315775
$359$	−18.5853	−0.980895	−0.490448	−	0.871471i	$-0.663167\pi$
$359$	−18.5853	−0.980895	−0.490448	+	0.871471i	$0.663167\pi$
$360$	0	0
$361$	38.8550	2.04500
$362$	−38.7269	−2.03544
$363$	11.2322	0.589538
$364$	−0.0602293	−0.00315688
$365$	0	0
$366$	−4.16800	−0.217865
$367$	−36.5752	−1.90921	−0.954604	−	0.297877i	$-0.903722\pi$
$367$	−36.5752	−1.90921	−0.954604	+	0.297877i	$0.903722\pi$
$368$	−22.2810	−1.16148
$369$	−3.87101	−0.201517
$370$	0	0
$371$	1.48203	0.0769433
$372$	−8.84904	−0.458801
$373$	−0.0320395	−0.00165894	−0.000829471	−	1.00000i	$-0.500264\pi$
$373$	−0.0320395	−0.00165894	−0.000829471		1.00000i	$0.500264\pi$
$374$	24.7175	1.27811
$375$	0	0
$376$	−0.564028	−0.0290875
$377$	−1.55825	−0.0802539
$378$	0.314658	0.0161842
$379$	−3.74974	−0.192611	−0.0963055	−	0.995352i	$-0.530703\pi$
$379$	−3.74974	−0.192611	−0.0963055	+	0.995352i	$0.530703\pi$
$380$	0	0
$381$	−2.01094	−0.103024
$382$	−52.7847	−2.70070
$383$	−9.42879	−0.481789	−0.240894	−	0.970551i	$-0.577441\pi$
$383$	−9.42879	−0.481789	−0.240894	+	0.970551i	$0.577441\pi$
$384$	5.22953	0.266868
$385$	0	0
$386$	53.9086	2.74387
$387$	−4.14916	−0.210914
$388$	15.7372	0.798933
$389$	−3.08788	−0.156562	−0.0782810	−	0.996931i	$-0.524943\pi$
$389$	−3.08788	−0.156562	−0.0782810	+	0.996931i	$0.524943\pi$
$390$	0	0
$391$	17.2340	0.871561
$392$	4.61946	0.233318
$393$	−10.2019	−0.514618
$394$	0.597534	0.0301033
$395$	0	0
$396$	−10.9324	−0.549376
$397$	18.6524	0.936139	0.468069	−	0.883692i	$-0.344950\pi$
$397$	18.6524	0.936139	0.468069	+	0.883692i	$0.344950\pi$
$398$	51.6475	2.58885
$399$	−1.15169	−0.0576569
$400$	0	0
$401$	−18.9724	−0.947437	−0.473719	−	0.880676i	$-0.657089\pi$
$401$	−18.9724	−0.947437	−0.473719	+	0.880676i	$0.657089\pi$
$402$	3.47787	0.173461
$403$	−0.654765	−0.0326161
$404$	7.25396	0.360898
$405$	0	0
$406$	−2.85799	−0.141839
$407$	−2.40572	−0.119247
$408$	−1.67016	−0.0826855
$409$	9.13452	0.451673	0.225837	−	0.974165i	$-0.427488\pi$
$409$	9.13452	0.451673	0.225837	+	0.974165i	$0.427488\pi$
$410$	0	0
$411$	−12.6003	−0.621528
$412$	2.21268	0.109011
$413$	1.80753	0.0889427
$414$	−14.1976	−0.697776
$415$	0	0
$416$	1.38990	0.0681455
$417$	−13.6774	−0.669785
$418$	74.5304	3.64540
$419$	−30.6592	−1.49780	−0.748900	−	0.662682i	$-0.769418\pi$
$419$	−30.6592	−1.49780	−0.748900	+	0.662682i	$0.769418\pi$
$420$	0	0
$421$	−5.73296	−0.279407	−0.139704	−	0.990193i	$-0.544615\pi$
$421$	−5.73296	−0.279407	−0.139704	+	0.990193i	$0.544615\pi$
$422$	−26.2576	−1.27820
$423$	0.851888	0.0414202
$424$	6.48050	0.314721
$425$	0	0
$426$	8.60111	0.416725
$427$	−0.303685	−0.0146963
$428$	2.31860	0.112074
$429$	−0.808922	−0.0390551
$430$	0	0
$431$	3.70782	0.178599	0.0892996	−	0.996005i	$-0.471537\pi$
$431$	3.70782	0.178599	0.0892996	+	0.996005i	$0.471537\pi$
$432$	−3.26129	−0.156909
$433$	−9.94747	−0.478045	−0.239023	−	0.971014i	$-0.576827\pi$
$433$	−9.94747	−0.478045	−0.239023	+	0.971014i	$0.576827\pi$
$434$	−1.20090	−0.0576453
$435$	0	0
$436$	7.52355	0.360313
$437$	51.9655	2.48585
$438$	−7.02958	−0.335886
$439$	−37.9041	−1.80906	−0.904531	−	0.426408i	$-0.859779\pi$
$439$	−37.9041	−1.80906	−0.904531	+	0.426408i	$0.859779\pi$
$440$	0	0
$441$	−6.97707	−0.332242
$442$	−0.899349	−0.0427776
$443$	1.71681	0.0815682	0.0407841	−	0.999168i	$-0.487014\pi$
$443$	1.71681	0.0815682	0.0407841	+	0.999168i	$0.487014\pi$
$444$	1.18299	0.0561422
$445$	0	0
$446$	−44.6088	−2.11229
$447$	−14.1457	−0.669071
$448$	1.56160	0.0737789
$449$	15.3151	0.722764	0.361382	−	0.932418i	$-0.382305\pi$
$449$	15.3151	0.722764	0.361382	+	0.932418i	$0.382305\pi$
$450$	0	0
$451$	18.2522	0.859463
$452$	−17.8198	−0.838171
$453$	−5.55621	−0.261054
$454$	12.0578	0.565901
$455$	0	0
$456$	−5.03603	−0.235834
$457$	−23.0509	−1.07827	−0.539137	−	0.842218i	$-0.681250\pi$
$457$	−23.0509	−1.07827	−0.539137	+	0.842218i	$0.681250\pi$
$458$	−44.8611	−2.09622
$459$	2.52256	0.117743
$460$	0	0
$461$	−16.2346	−0.756121	−0.378061	−	0.925781i	$-0.623409\pi$
$461$	−16.2346	−0.756121	−0.378061	+	0.925781i	$0.623409\pi$
$462$	−1.48364	−0.0690254
$463$	16.6745	0.774928	0.387464	−	0.921885i	$-0.373351\pi$
$463$	16.6745	0.774928	0.387464	+	0.921885i	$0.373351\pi$
$464$	29.6218	1.37516
$465$	0	0
$466$	22.6627	1.04983
$467$	39.7960	1.84154	0.920768	−	0.390109i	$-0.127563\pi$
$467$	39.7960	1.84154	0.920768	+	0.390109i	$0.127563\pi$
$468$	0.397778	0.0183873
$469$	0.253401	0.0117010
$470$	0	0
$471$	6.67965	0.307782
$472$	7.90381	0.363802
$473$	19.5637	0.899541
$474$	−24.5991	−1.12988
$475$	0	0
$476$	−0.885593	−0.0405911
$477$	−9.78792	−0.448158
$478$	−2.66131	−0.121726
$479$	−40.9086	−1.86916	−0.934581	−	0.355750i	$-0.884225\pi$
$479$	−40.9086	−1.86916	−0.934581	+	0.355750i	$0.884225\pi$
$480$	0	0
$481$	0.0875326	0.00399114
$482$	34.9859	1.59357
$483$	−1.03446	−0.0470693
$484$	26.0430	1.18377
$485$	0	0
$486$	−2.07812	−0.0942656
$487$	−32.6216	−1.47823	−0.739113	−	0.673581i	$-0.764755\pi$
$487$	−32.6216	−1.47823	−0.739113	+	0.673581i	$0.764755\pi$
$488$	−1.32793	−0.0601124
$489$	19.1478	0.865893
$490$	0	0
$491$	−37.9072	−1.71073	−0.855364	−	0.518028i	$-0.826666\pi$
$491$	−37.9072	−1.71073	−0.855364	+	0.518028i	$0.826666\pi$
$492$	−8.97533	−0.404639
$493$	−22.9120	−1.03190
$494$	−2.71180	−0.122010
$495$	0	0
$496$	12.4469	0.558880
$497$	0.626686	0.0281107
$498$	−0.692414	−0.0310278
$499$	23.0051	1.02985	0.514926	−	0.857235i	$-0.327819\pi$
$499$	23.0051	1.02985	0.514926	+	0.857235i	$0.327819\pi$
$500$	0	0
$501$	−3.07430	−0.137350
$502$	8.93642	0.398852
$503$	−33.4136	−1.48984	−0.744919	−	0.667155i	$-0.767512\pi$
$503$	−33.4136	−1.48984	−0.744919	+	0.667155i	$0.767512\pi$
$504$	0.100250	0.00446550
$505$	0	0
$506$	66.9434	2.97600
$507$	−12.9706	−0.576043
$508$	−4.66257	−0.206868
$509$	−32.8285	−1.45510	−0.727548	−	0.686057i	$-0.759340\pi$
$509$	−32.8285	−1.45510	−0.727548	+	0.686057i	$0.759340\pi$
$510$	0	0
$511$	−0.512182	−0.0226576
$512$	−30.7401	−1.35853
$513$	7.60625	0.335824
$514$	−9.98486	−0.440413
$515$	0	0
$516$	−9.62025	−0.423508
$517$	−4.01674	−0.176656
$518$	0.160544	0.00705388
$519$	−7.01511	−0.307929
$520$	0	0
$521$	−30.4328	−1.33328	−0.666642	−	0.745378i	$-0.732269\pi$
$521$	−30.4328	−1.33328	−0.666642	+	0.745378i	$0.732269\pi$
$522$	18.8753	0.826148
$523$	41.3730	1.80911	0.904556	−	0.426354i	$-0.140202\pi$
$523$	41.3730	1.80911	0.904556	+	0.426354i	$0.140202\pi$
$524$	−23.6541	−1.03334
$525$	0	0
$526$	50.6190	2.20709
$527$	−9.62745	−0.419378
$528$	15.3773	0.669212
$529$	23.6756	1.02937
$530$	0	0
$531$	−11.9376	−0.518050
$532$	−2.67032	−0.115773
$533$	−0.664109	−0.0287658
$534$	−35.2253	−1.52435
$535$	0	0
$536$	1.10805	0.0478606
$537$	2.87507	0.124068
$538$	−6.89873	−0.297425
$539$	32.8976	1.41700
$540$	0	0
$541$	2.86962	0.123375	0.0616873	−	0.998096i	$-0.480352\pi$
$541$	2.86962	0.123375	0.0616873	+	0.998096i	$0.480352\pi$
$542$	−18.4765	−0.793633
$543$	18.6355	0.799726
$544$	20.4366	0.876214
$545$	0	0
$546$	0.0539826	0.00231024
$547$	5.11885	0.218866	0.109433	−	0.993994i	$-0.465096\pi$
$547$	5.11885	0.218866	0.109433	+	0.993994i	$0.465096\pi$
$548$	−29.2151	−1.24801
$549$	2.00565	0.0855992
$550$	0	0
$551$	−69.0863	−2.94318
$552$	−4.52338	−0.192528
$553$	−1.79232	−0.0762172
$554$	4.96069	0.210760
$555$	0	0
$556$	−31.7124	−1.34491
$557$	40.6481	1.72232	0.861159	−	0.508336i	$-0.169739\pi$
$557$	40.6481	1.72232	0.861159	+	0.508336i	$0.169739\pi$
$558$	7.93125	0.335756
$559$	−0.711829	−0.0301071
$560$	0	0
$561$	−11.8941	−0.502170
$562$	23.1107	0.974866
$563$	−9.41401	−0.396753	−0.198377	−	0.980126i	$-0.563567\pi$
$563$	−9.41401	−0.396753	−0.198377	+	0.980126i	$0.563567\pi$
$564$	1.97519	0.0831704
$565$	0	0
$566$	−40.6557	−1.70889
$567$	−0.151414	−0.00635880
$568$	2.74032	0.114981
$569$	28.1780	1.18128	0.590641	−	0.806934i	$-0.298875\pi$
$569$	28.1780	1.18128	0.590641	+	0.806934i	$0.298875\pi$
$570$	0	0
$571$	−3.46608	−0.145051	−0.0725256	−	0.997367i	$-0.523106\pi$
$571$	−3.46608	−0.145051	−0.0725256	+	0.997367i	$0.523106\pi$
$572$	−1.87557	−0.0784214
$573$	25.4002	1.06111
$574$	−1.21804	−0.0508402
$575$	0	0
$576$	−10.3135	−0.429727
$577$	22.0413	0.917591	0.458795	−	0.888542i	$-0.348281\pi$
$577$	22.0413	0.917591	0.458795	+	0.888542i	$0.348281\pi$
$578$	22.1044	0.919421
$579$	−25.9410	−1.07807
$580$	0	0
$581$	−0.0504500	−0.00209302
$582$	−14.1050	−0.584670
$583$	46.1511	1.91138
$584$	−2.23963	−0.0926764
$585$	0	0
$586$	24.5728	1.01509
$587$	43.3902	1.79091	0.895453	−	0.445156i	$-0.146852\pi$
$587$	43.3902	1.79091	0.895453	+	0.445156i	$0.146852\pi$
$588$	−16.1770	−0.667130
$589$	−29.0296	−1.19614
$590$	0	0
$591$	−0.287535	−0.0118276
$592$	−1.66397	−0.0683886
$593$	−11.0380	−0.453277	−0.226638	−	0.973979i	$-0.572774\pi$
$593$	−11.0380	−0.453277	−0.226638	+	0.973979i	$0.572774\pi$
$594$	9.79857	0.402040
$595$	0	0
$596$	−32.7983	−1.34347
$597$	−24.8529	−1.01716
$598$	−2.43574	−0.0996049
$599$	−23.2629	−0.950495	−0.475247	−	0.879852i	$-0.657641\pi$
$599$	−23.2629	−0.950495	−0.475247	+	0.879852i	$0.657641\pi$
$600$	0	0
$601$	14.7298	0.600841	0.300420	−	0.953807i	$-0.402873\pi$
$601$	14.7298	0.600841	0.300420	+	0.953807i	$0.402873\pi$
$602$	−1.30557	−0.0532109
$603$	−1.67356	−0.0681528
$604$	−12.8826	−0.524187
$605$	0	0
$606$	−6.50160	−0.264110
$607$	−21.6008	−0.876748	−0.438374	−	0.898793i	$-0.644445\pi$
$607$	−21.6008	−0.876748	−0.438374	+	0.898793i	$0.644445\pi$
$608$	61.6224	2.49912
$609$	1.37527	0.0557288
$610$	0	0
$611$	0.146150	0.00591258
$612$	5.84881	0.236424
$613$	25.5369	1.03143	0.515713	−	0.856761i	$-0.327527\pi$
$613$	25.5369	1.03143	0.515713	+	0.856761i	$0.327527\pi$
$614$	−16.9284	−0.683176
$615$	0	0
$616$	−0.472690	−0.0190452
$617$	−10.1391	−0.408183	−0.204092	−	0.978952i	$-0.565424\pi$
$617$	−10.1391	−0.408183	−0.204092	+	0.978952i	$0.565424\pi$
$618$	−1.98319	−0.0797757
$619$	−20.4537	−0.822104	−0.411052	−	0.911612i	$-0.634839\pi$
$619$	−20.4537	−0.822104	−0.411052	+	0.911612i	$0.634839\pi$
$620$	0	0
$621$	6.83195	0.274157
$622$	7.38973	0.296301
$623$	−2.56655	−0.102827
$624$	−0.559506	−0.0223982
$625$	0	0
$626$	−9.12181	−0.364581
$627$	−35.8642	−1.43228
$628$	15.4874	0.618016
$629$	1.28705	0.0513181
$630$	0	0
$631$	−36.9254	−1.46998	−0.734989	−	0.678079i	$-0.762813\pi$
$631$	−36.9254	−1.46998	−0.734989	+	0.678079i	$0.762813\pi$
$632$	−7.83730	−0.311751
$633$	12.6353	0.502206
$634$	8.25381	0.327801
$635$	0	0
$636$	−22.6943	−0.899887
$637$	−1.19698	−0.0474263
$638$	−88.9988	−3.52350
$639$	−4.13888	−0.163732
$640$	0	0
$641$	−16.5953	−0.655476	−0.327738	−	0.944769i	$-0.606286\pi$
$641$	−16.5953	−0.655476	−0.327738	+	0.944769i	$0.606286\pi$
$642$	−2.07812	−0.0820170
$643$	−48.1076	−1.89718	−0.948589	−	0.316511i	$-0.897489\pi$
$643$	−48.1076	−1.89718	−0.948589	+	0.316511i	$0.897489\pi$
$644$	−2.39849	−0.0945137
$645$	0	0
$646$	−39.8734	−1.56880
$647$	−22.4486	−0.882545	−0.441272	−	0.897373i	$-0.645473\pi$
$647$	−22.4486	−0.882545	−0.441272	+	0.897373i	$0.645473\pi$
$648$	−0.662092	−0.0260094
$649$	56.2872	2.20947
$650$	0	0
$651$	0.577879	0.0226489
$652$	44.3961	1.73868
$653$	3.48746	0.136475	0.0682374	−	0.997669i	$-0.478262\pi$
$653$	3.48746	0.136475	0.0682374	+	0.997669i	$0.478262\pi$
$654$	−6.74324	−0.263682
$655$	0	0
$656$	12.6245	0.492904
$657$	3.38266	0.131970
$658$	0.268053	0.0104498
$659$	6.15625	0.239813	0.119907	−	0.992785i	$-0.461740\pi$
$659$	6.15625	0.239813	0.119907	+	0.992785i	$0.461740\pi$
$660$	0	0
$661$	−28.2065	−1.09711	−0.548553	−	0.836116i	$-0.684821\pi$
$661$	−28.2065	−1.09711	−0.548553	+	0.836116i	$0.684821\pi$
$662$	54.2566	2.10874
$663$	0.432769	0.0168074
$664$	−0.220604	−0.00856108
$665$	0	0
$666$	−1.06029	−0.0410855
$667$	−62.0535	−2.40272
$668$	−7.12807	−0.275793
$669$	21.4659	0.829920
$670$	0	0
$671$	−9.45686	−0.365078
$672$	−1.22669	−0.0473206
$673$	−12.0941	−0.466192	−0.233096	−	0.972454i	$-0.574886\pi$
$673$	−12.0941	−0.466192	−0.233096	+	0.972454i	$0.574886\pi$
$674$	−29.9011	−1.15175
$675$	0	0
$676$	−30.0736	−1.15668
$677$	8.74662	0.336160	0.168080	−	0.985773i	$-0.446243\pi$
$677$	8.74662	0.336160	0.168080	+	0.985773i	$0.446243\pi$
$678$	15.9716	0.613384
$679$	−1.02770	−0.0394396
$680$	0	0
$681$	−5.80226	−0.222343
$682$	−37.3967	−1.43199
$683$	14.7728	0.565266	0.282633	−	0.959228i	$-0.408792\pi$
$683$	14.7728	0.565266	0.282633	+	0.959228i	$0.408792\pi$
$684$	17.6359	0.674324
$685$	0	0
$686$	−4.39799	−0.167916
$687$	21.5873	0.823606
$688$	13.5316	0.515888
$689$	−1.67921	−0.0639729
$690$	0	0
$691$	5.16521	0.196494	0.0982469	−	0.995162i	$-0.468677\pi$
$691$	5.16521	0.196494	0.0982469	+	0.995162i	$0.468677\pi$
$692$	−16.2652	−0.618312
$693$	0.713934	0.0271201
$694$	−65.6823	−2.49327
$695$	0	0
$696$	6.01367	0.227948
$697$	−9.76485	−0.369870
$698$	59.3418	2.24612
$699$	−10.9054	−0.412480
$700$	0	0
$701$	9.54887	0.360656	0.180328	−	0.983607i	$-0.442284\pi$
$701$	9.54887	0.360656	0.180328	+	0.983607i	$0.442284\pi$
$702$	−0.356522	−0.0134561
$703$	3.88083	0.146368
$704$	48.6290	1.83277
$705$	0	0
$706$	41.8584	1.57536
$707$	−0.473714	−0.0178158
$708$	−27.6786	−1.04023
$709$	34.7154	1.30376	0.651882	−	0.758321i	$-0.273980\pi$
$709$	34.7154	1.30376	0.651882	+	0.758321i	$0.273980\pi$
$710$	0	0
$711$	11.8372	0.443929
$712$	−11.2228	−0.420592
$713$	−26.0744	−0.976495
$714$	0.793743	0.0297051
$715$	0	0
$716$	6.66613	0.249125
$717$	1.28063	0.0478261
$718$	38.6226	1.44138
$719$	5.97879	0.222971	0.111486	−	0.993766i	$-0.464439\pi$
$719$	5.97879	0.222971	0.111486	+	0.993766i	$0.464439\pi$
$720$	0	0
$721$	−0.144497	−0.00538137
$722$	−80.7455	−3.00504
$723$	−16.8353	−0.626113
$724$	43.2083	1.60582
$725$	0	0
$726$	−23.3419	−0.866299
$727$	4.67154	0.173258	0.0866290	−	0.996241i	$-0.472391\pi$
$727$	4.67154	0.173258	0.0866290	+	0.996241i	$0.472391\pi$
$728$	0.0171989	0.000637433 0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−10.4665	−0.387118
$732$	4.65031	0.171880
$733$	−28.8100	−1.06412	−0.532061	−	0.846706i	$-0.678582\pi$
$733$	−28.8100	−1.06412	−0.532061	+	0.846706i	$0.678582\pi$
$734$	76.0078	2.80550
$735$	0	0
$736$	55.3494	2.04021
$737$	7.89102	0.290670
$738$	8.04444	0.296120
$739$	54.1750	1.99286	0.996430	−	0.0844186i	$-0.0269033\pi$
$739$	54.1750	1.99286	0.996430	+	0.0844186i	$0.0269033\pi$
$740$	0	0
$741$	1.30493	0.0479376
$742$	−3.07985	−0.113065
$743$	−52.4137	−1.92287	−0.961436	−	0.275027i	$-0.911313\pi$
$743$	−52.4137	−1.92287	−0.961436	+	0.275027i	$0.911313\pi$
$744$	2.52690	0.0926406
$745$	0	0
$746$	0.0665821	0.00243774
$747$	0.333192	0.0121909
$748$	−27.5777	−1.00834
$749$	−0.151414	−0.00553256
$750$	0	0
$751$	−3.29692	−0.120306	−0.0601531	−	0.998189i	$-0.519159\pi$
$751$	−3.29692	−0.120306	−0.0601531	+	0.998189i	$0.519159\pi$
$752$	−2.77826	−0.101313
$753$	−4.30023	−0.156709
$754$	3.23823	0.117930
$755$	0	0
$756$	−0.351069	−0.0127683
$757$	−9.52491	−0.346189	−0.173094	−	0.984905i	$-0.555377\pi$
$757$	−9.52491	−0.346189	−0.173094	+	0.984905i	$0.555377\pi$
$758$	7.79242	0.283033
$759$	−32.2134	−1.16927
$760$	0	0
$761$	−16.1050	−0.583805	−0.291902	−	0.956448i	$-0.594288\pi$
$761$	−16.1050	−0.583805	−0.291902	+	0.956448i	$0.594288\pi$
$762$	4.17899	0.151389
$763$	−0.491319	−0.0177870
$764$	58.8929	2.13067
$765$	0	0
$766$	19.5942	0.707967
$767$	−2.04802	−0.0739497
$768$	9.75930	0.352158
$769$	−9.92943	−0.358064	−0.179032	−	0.983843i	$-0.557297\pi$
$769$	−9.92943	−0.358064	−0.179032	+	0.983843i	$0.557297\pi$
$770$	0	0
$771$	4.80475	0.173039
$772$	−60.1467	−2.16473
$773$	−5.32509	−0.191530	−0.0957651	−	0.995404i	$-0.530530\pi$
$773$	−5.32509	−0.191530	−0.0957651	+	0.995404i	$0.530530\pi$
$774$	8.62247	0.309928
$775$	0	0
$776$	−4.49385	−0.161320
$777$	−0.0772541	−0.00277148
$778$	6.41701	0.230061
$779$	−29.4439	−1.05494
$780$	0	0
$781$	19.5153	0.698311
$782$	−35.8144	−1.28072
$783$	−9.08284	−0.324594
$784$	22.7543	0.812653
$785$	0	0
$786$	21.2008	0.756208
$787$	44.0277	1.56942	0.784709	−	0.619864i	$-0.212812\pi$
$787$	44.0277	1.56942	0.784709	+	0.619864i	$0.212812\pi$
$788$	−0.666680	−0.0237495
$789$	−24.3580	−0.867169
$790$	0	0
$791$	1.16370	0.0413766
$792$	3.12183	0.110929
$793$	0.344089	0.0122190
$794$	−38.7621	−1.37561
$795$	0	0
$796$	−57.6240	−2.04243
$797$	−12.6257	−0.447226	−0.223613	−	0.974678i	$-0.571785\pi$
$797$	−12.6257	−0.447226	−0.223613	+	0.974678i	$0.571785\pi$
$798$	2.39337	0.0847242
$799$	2.14894	0.0760239
$800$	0	0
$801$	16.9505	0.598917
$802$	39.4270	1.39222
$803$	−15.9496	−0.562848
$804$	−3.88033	−0.136849
$805$	0	0
$806$	1.36068	0.0479280
$807$	3.31969	0.116859
$808$	−2.07141	−0.0728721
$809$	−33.1368	−1.16503	−0.582513	−	0.812821i	$-0.697931\pi$
$809$	−33.1368	−1.16503	−0.582513	+	0.812821i	$0.697931\pi$
$810$	0	0
$811$	−14.6411	−0.514118	−0.257059	−	0.966396i	$-0.582753\pi$
$811$	−14.6411	−0.514118	−0.257059	+	0.966396i	$0.582753\pi$
$812$	3.18871	0.111902
$813$	8.89095	0.311819
$814$	4.99939	0.175229
$815$	0	0
$816$	−8.22680	−0.287996
$817$	−31.5595	−1.10413
$818$	−18.9827	−0.663714
$819$	−0.0259766	−0.000907696 0
$820$	0	0
$821$	14.2169	0.496173	0.248086	−	0.968738i	$-0.420198\pi$
$821$	14.2169	0.496173	0.248086	+	0.968738i	$0.420198\pi$
$822$	26.1850	0.913307
$823$	−18.2599	−0.636499	−0.318249	−	0.948007i	$-0.603095\pi$
$823$	−18.2599	−0.636499	−0.318249	+	0.948007i	$0.603095\pi$
$824$	−0.631846	−0.0220114
$825$	0	0
$826$	−3.75627	−0.130697
$827$	27.2329	0.946981	0.473490	−	0.880799i	$-0.342994\pi$
$827$	27.2329	0.946981	0.473490	+	0.880799i	$0.342994\pi$
$828$	15.8406	0.550498
$829$	2.99457	0.104006	0.0520028	−	0.998647i	$-0.483440\pi$
$829$	2.99457	0.104006	0.0520028	+	0.998647i	$0.483440\pi$
$830$	0	0
$831$	−2.38710	−0.0828076
$832$	−1.76937	−0.0613420
$833$	−17.6001	−0.609807
$834$	28.4233	0.984219
$835$	0	0
$836$	−83.1549	−2.87597
$837$	−3.81654	−0.131919
$838$	63.7137	2.20095
$839$	43.3473	1.49651	0.748257	−	0.663409i	$-0.230891\pi$
$839$	43.3473	1.49651	0.748257	+	0.663409i	$0.230891\pi$
$840$	0	0
$841$	53.4980	1.84476
$842$	11.9138	0.410577
$843$	−11.1209	−0.383026
$844$	29.2961	1.00841
$845$	0	0
$846$	−1.77033	−0.0608652
$847$	−1.70072	−0.0584373
$848$	31.9213	1.09618
$849$	19.5637	0.671423
$850$	0	0
$851$	3.48577	0.119491
$852$	−9.59642	−0.328768
$853$	38.2318	1.30903	0.654515	−	0.756049i	$-0.272873\pi$
$853$	38.2318	1.30903	0.654515	+	0.756049i	$0.272873\pi$
$854$	0.631094	0.0215956
$855$	0	0
$856$	−0.662092	−0.0226298
$857$	10.8634	0.371086	0.185543	−	0.982636i	$-0.440596\pi$
$857$	10.8634	0.371086	0.185543	+	0.982636i	$0.440596\pi$
$858$	1.68104	0.0573897
$859$	21.8366	0.745054	0.372527	−	0.928021i	$-0.378491\pi$
$859$	21.8366	0.745054	0.372527	+	0.928021i	$0.378491\pi$
$860$	0	0
$861$	0.586126	0.0199751
$862$	−7.70530	−0.262444
$863$	−51.6079	−1.75675	−0.878376	−	0.477970i	$-0.841373\pi$
$863$	−51.6079	−1.75675	−0.878376	+	0.477970i	$0.841373\pi$
$864$	8.10155	0.275620
$865$	0	0
$866$	20.6721	0.702466
$867$	−10.6367	−0.361241
$868$	1.33987	0.0454782
$869$	−55.8136	−1.89335
$870$	0	0
$871$	−0.287116	−0.00972855
$872$	−2.14840	−0.0727540
$873$	6.78735	0.229717
$874$	−107.991	−3.65284
$875$	0	0
$876$	7.84303	0.264991
$877$	−0.618567	−0.0208875	−0.0104438	−	0.999945i	$-0.503324\pi$
$877$	−0.618567	−0.0208875	−0.0104438	+	0.999945i	$0.503324\pi$
$878$	78.7693	2.65834
$879$	−11.8245	−0.398831
$880$	0	0
$881$	40.9940	1.38112	0.690562	−	0.723273i	$-0.257363\pi$
$881$	40.9940	1.38112	0.690562	+	0.723273i	$0.257363\pi$
$882$	14.4992	0.488214
$883$	−32.9199	−1.10784	−0.553921	−	0.832569i	$-0.686869\pi$
$883$	−32.9199	−1.10784	−0.553921	+	0.832569i	$0.686869\pi$
$884$	1.00342	0.0337486
$885$	0	0
$886$	−3.56775	−0.119861
$887$	41.3141	1.38719	0.693596	−	0.720364i	$-0.256025\pi$
$887$	41.3141	1.38719	0.693596	+	0.720364i	$0.256025\pi$
$888$	−0.337810	−0.0113362
$889$	0.304485	0.0102121
$890$	0	0
$891$	−4.71510	−0.157962
$892$	49.7709	1.66645
$893$	6.47967	0.216834
$894$	29.3966	0.983170
$895$	0	0
$896$	−0.791825	−0.0264530
$897$	1.17209	0.0391349
$898$	−31.8267	−1.06207
$899$	34.6650	1.15614
$900$	0	0
$901$	−24.6906	−0.822564
$902$	−37.9304	−1.26294
$903$	0.628242	0.0209066
$904$	5.08855	0.169243
$905$	0	0
$906$	11.5465	0.383607
$907$	−7.83197	−0.260056	−0.130028	−	0.991510i	$-0.541507\pi$
$907$	−7.83197	−0.260056	−0.130028	+	0.991510i	$0.541507\pi$
$908$	−13.4531	−0.446457
$909$	3.12859	0.103769
$910$	0	0
$911$	−2.94713	−0.0976428	−0.0488214	−	0.998808i	$-0.515547\pi$
$911$	−2.94713	−0.0976428	−0.0488214	+	0.998808i	$0.515547\pi$
$912$	−24.8062	−0.821415
$913$	−1.57103	−0.0519937
$914$	47.9026	1.58448
$915$	0	0
$916$	50.0523	1.65377
$917$	1.54471	0.0510110
$918$	−5.24219	−0.173018
$919$	−43.4933	−1.43471	−0.717355	−	0.696708i	$-0.754647\pi$
$919$	−43.4933	−1.43471	−0.717355	+	0.696708i	$0.754647\pi$
$920$	0	0
$921$	8.14602	0.268420
$922$	33.7376	1.11109
$923$	−0.710065	−0.0233721
$924$	1.65533	0.0544563
$925$	0	0
$926$	−34.6516	−1.13872
$927$	0.954318	0.0313439
$928$	−73.5851	−2.41555
$929$	16.7165	0.548451	0.274225	−	0.961665i	$-0.411579\pi$
$929$	16.7165	0.548451	0.274225	+	0.961665i	$0.411579\pi$
$930$	0	0
$931$	−53.0694	−1.73928
$932$	−25.2852	−0.828245
$933$	−3.55596	−0.116417
$934$	−82.7009	−2.70606
$935$	0	0
$936$	−0.113588	−0.00371275
$937$	27.9950	0.914558	0.457279	−	0.889323i	$-0.348824\pi$
$937$	27.9950	0.914558	0.457279	+	0.889323i	$0.348824\pi$
$938$	−0.526600	−0.0171941
$939$	4.38944	0.143244
$940$	0	0
$941$	7.15724	0.233319	0.116660	−	0.993172i	$-0.462781\pi$
$941$	7.15724	0.233319	0.116660	+	0.993172i	$0.462781\pi$
$942$	−13.8811	−0.452272
$943$	−26.4466	−0.861218
$944$	38.9322	1.26713
$945$	0	0
$946$	−40.6558	−1.32184
$947$	−53.4069	−1.73549	−0.867745	−	0.497010i	$-0.834431\pi$
$947$	−53.4069	−1.73549	−0.867745	+	0.497010i	$0.834431\pi$
$948$	27.4457	0.891395
$949$	0.580327	0.0188382
$950$	0	0
$951$	−3.97176	−0.128793
$952$	0.252887	0.00819611
$953$	−32.2617	−1.04506	−0.522530	−	0.852621i	$-0.675012\pi$
$953$	−32.2617	−1.04506	−0.522530	+	0.852621i	$0.675012\pi$
$954$	20.3405	0.658549
$955$	0	0
$956$	2.96927	0.0960332
$957$	42.8265	1.38438
$958$	85.0132	2.74665
$959$	1.90787	0.0616083
$960$	0	0
$961$	−16.4340	−0.530129
$962$	−0.181904	−0.00586481
$963$	1.00000	0.0322245
$964$	−39.0344	−1.25721
$965$	0	0
$966$	2.14973	0.0691663
$967$	60.9149	1.95889	0.979445	−	0.201710i	$-0.0646499\pi$
$967$	60.9149	1.95889	0.979445	+	0.201710i	$0.0646499\pi$
$968$	−7.43674	−0.239026
$969$	19.1872	0.616382
$970$	0	0
$971$	−50.0845	−1.60729	−0.803645	−	0.595109i	$-0.797109\pi$
$971$	−50.0845	−1.60729	−0.803645	+	0.595109i	$0.797109\pi$
$972$	2.31860	0.0743691
$973$	2.07095	0.0663917
$974$	67.7918	2.17219
$975$	0	0
$976$	−6.54102	−0.209373
$977$	−39.7412	−1.27143	−0.635716	−	0.771923i	$-0.719295\pi$
$977$	−39.7412	−1.27143	−0.635716	+	0.771923i	$0.719295\pi$
$978$	−39.7915	−1.27239
$979$	−79.9235	−2.55437
$980$	0	0
$981$	3.24487	0.103601
$982$	78.7759	2.51384
$983$	−37.2333	−1.18756	−0.593779	−	0.804629i	$-0.702364\pi$
$983$	−37.2333	−1.18756	−0.593779	+	0.804629i	$0.702364\pi$
$984$	2.56296	0.0817043
$985$	0	0
$986$	47.6140	1.51634
$987$	−0.128988	−0.00410573
$988$	3.02560	0.0962572
$989$	−28.3469	−0.901378
$990$	0	0
$991$	−43.6651	−1.38707	−0.693534	−	0.720424i	$-0.743947\pi$
$991$	−43.6651	−1.38707	−0.693534	+	0.720424i	$0.743947\pi$
$992$	−30.9199	−0.981708
$993$	−26.1084	−0.828526
$994$	−1.30233	−0.0413075
$995$	0	0
$996$	0.772539	0.0244788
$997$	−40.6230	−1.28654	−0.643271	−	0.765638i	$-0.722423\pi$
$997$	−40.6230	−1.28654	−0.643271	+	0.765638i	$0.722423\pi$
$998$	−47.8076	−1.51332
$999$	0.510217	0.0161425

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8025.2.a.bc.1.2		10
5.4	even	2		1605.2.a.k.1.9	✓	10
15.14	odd	2		4815.2.a.p.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1605.2.a.k.1.9	✓	10	5.4	even	2
4815.2.a.p.1.2		10	15.14	odd	2
8025.2.a.bc.1.2		10	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:	\( N \)	\(=\)	\( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.07812 q^{2} +1.00000 q^{3} +2.31860 q^{4} -2.07812 q^{6} -0.151414 q^{7} -0.662092 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.07812 q^{2} +1.00000 q^{3} +2.31860 q^{4} -2.07812 q^{6} -0.151414 q^{7} -0.662092 q^{8} +1.00000 q^{9} -4.71510 q^{11} +2.31860 q^{12} +0.171560 q^{13} +0.314658 q^{14} -3.26129 q^{16} +2.52256 q^{17} -2.07812 q^{18} +7.60625 q^{19} -0.151414 q^{21} +9.79857 q^{22} +6.83195 q^{23} -0.662092 q^{24} -0.356522 q^{26} +1.00000 q^{27} -0.351069 q^{28} -9.08284 q^{29} -3.81654 q^{31} +8.10155 q^{32} -4.71510 q^{33} -5.24219 q^{34} +2.31860 q^{36} +0.510217 q^{37} -15.8067 q^{38} +0.171560 q^{39} -3.87101 q^{41} +0.314658 q^{42} -4.14916 q^{43} -10.9324 q^{44} -14.1976 q^{46} +0.851888 q^{47} -3.26129 q^{48} -6.97707 q^{49} +2.52256 q^{51} +0.397778 q^{52} -9.78792 q^{53} -2.07812 q^{54} +0.100250 q^{56} +7.60625 q^{57} +18.8753 q^{58} -11.9376 q^{59} +2.00565 q^{61} +7.93125 q^{62} -0.151414 q^{63} -10.3135 q^{64} +9.79857 q^{66} -1.67356 q^{67} +5.84881 q^{68} +6.83195 q^{69} -4.13888 q^{71} -0.662092 q^{72} +3.38266 q^{73} -1.06029 q^{74} +17.6359 q^{76} +0.713934 q^{77} -0.356522 q^{78} +11.8372 q^{79} +1.00000 q^{81} +8.04444 q^{82} +0.333192 q^{83} -0.351069 q^{84} +8.62247 q^{86} -9.08284 q^{87} +3.12183 q^{88} +16.9505 q^{89} -0.0259766 q^{91} +15.8406 q^{92} -3.81654 q^{93} -1.77033 q^{94} +8.10155 q^{96} +6.78735 q^{97} +14.4992 q^{98} -4.71510 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{6} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^6 + 10 * q^9	\( 10 q - 2 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{6} + 10 q^{9} - 14 q^{11} + 10 q^{12} + 3 q^{13} - 16 q^{14} + 10 q^{16} - 8 q^{17} - 2 q^{18} - 19 q^{19} - 5 q^{22} - 4 q^{23} - 22 q^{26} + 10 q^{27} - 25 q^{29} - 2 q^{31} + 13 q^{32} - 14 q^{33} - 37 q^{34} + 10 q^{36} + 10 q^{37} + 13 q^{38} + 3 q^{39} - 31 q^{41} - 16 q^{42} - 62 q^{44} + 2 q^{46} + q^{47} + 10 q^{48} + 26 q^{49} - 8 q^{51} + 30 q^{52} - 9 q^{53} - 2 q^{54} - 63 q^{56} - 19 q^{57} - 30 q^{58} - 65 q^{59} + 12 q^{61} + 39 q^{62} - 2 q^{64} - 5 q^{66} + 10 q^{67} - 22 q^{68} - 4 q^{69} - 45 q^{71} - q^{73} + 19 q^{74} - 39 q^{76} + q^{77} - 22 q^{78} - 47 q^{79} + 10 q^{81} + 23 q^{82} - q^{83} + 12 q^{86} - 25 q^{87} + 8 q^{88} - 34 q^{89} - 26 q^{91} - 14 q^{92} - 2 q^{93} - 64 q^{94} + 13 q^{96} - 5 q^{97} + 51 q^{98} - 14 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^6 + 10 * q^9 - 14 * q^11 + 10 * q^12 + 3 * q^13 - 16 * q^14 + 10 * q^16 - 8 * q^17 - 2 * q^18 - 19 * q^19 - 5 * q^22 - 4 * q^23 - 22 * q^26 + 10 * q^27 - 25 * q^29 - 2 * q^31 + 13 * q^32 - 14 * q^33 - 37 * q^34 + 10 * q^36 + 10 * q^37 + 13 * q^38 + 3 * q^39 - 31 * q^41 - 16 * q^42 - 62 * q^44 + 2 * q^46 + q^47 + 10 * q^48 + 26 * q^49 - 8 * q^51 + 30 * q^52 - 9 * q^53 - 2 * q^54 - 63 * q^56 - 19 * q^57 - 30 * q^58 - 65 * q^59 + 12 * q^61 + 39 * q^62 - 2 * q^64 - 5 * q^66 + 10 * q^67 - 22 * q^68 - 4 * q^69 - 45 * q^71 - q^73 + 19 * q^74 - 39 * q^76 + q^77 - 22 * q^78 - 47 * q^79 + 10 * q^81 + 23 * q^82 - q^83 + 12 * q^86 - 25 * q^87 + 8 * q^88 - 34 * q^89 - 26 * q^91 - 14 * q^92 - 2 * q^93 - 64 * q^94 + 13 * q^96 - 5 * q^97 + 51 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

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Database

Properties

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