LMFDB - Embedded newform 5225.2.a.y.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5225,2,Mod(1,5225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5225, 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("5225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5225 = 5^{2} \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5225.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:	$41.7218350561$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 5 x^{14} - 11 x^{13} + 87 x^{12} - 4 x^{11} - 545 x^{10} + 431 x^{9} + 1480 x^{8} - 1763 x^{7} + \cdots + 15 $ x^15 - 5x^14 - 11x^13 + 87x^12 - 4x^11 - 545x^10 + 431x^9 + 1480x^8 - 1763x^7 - 1609x^6 + 2516x^5 + 391x^4 - 1081x^3 - 45x^2 + 153x + 15
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$2.40444$ of defining polynomial
Character	$\chi$	$=$	5225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.40444 q^{2} +1.94792 q^{3} +3.78133 q^{4} +4.68365 q^{6} -0.665236 q^{7} +4.28310 q^{8} +0.794388 q^{9} +O(q^{10})$	\(q+2.40444 q^{2} +1.94792 q^{3} +3.78133 q^{4} +4.68365 q^{6} -0.665236 q^{7} +4.28310 q^{8} +0.794388 q^{9} +1.00000 q^{11} +7.36572 q^{12} +3.05467 q^{13} -1.59952 q^{14} +2.73579 q^{16} +4.49220 q^{17} +1.91006 q^{18} +1.00000 q^{19} -1.29583 q^{21} +2.40444 q^{22} +0.205258 q^{23} +8.34313 q^{24} +7.34478 q^{26} -4.29635 q^{27} -2.51548 q^{28} +0.0417920 q^{29} +6.76694 q^{31} -1.98815 q^{32} +1.94792 q^{33} +10.8012 q^{34} +3.00384 q^{36} +7.60762 q^{37} +2.40444 q^{38} +5.95026 q^{39} +5.90733 q^{41} -3.11574 q^{42} -1.77676 q^{43} +3.78133 q^{44} +0.493531 q^{46} -2.44032 q^{47} +5.32910 q^{48} -6.55746 q^{49} +8.75045 q^{51} +11.5507 q^{52} -3.34793 q^{53} -10.3303 q^{54} -2.84927 q^{56} +1.94792 q^{57} +0.100486 q^{58} +7.44003 q^{59} -11.7720 q^{61} +16.2707 q^{62} -0.528456 q^{63} -10.2520 q^{64} +4.68365 q^{66} -7.55329 q^{67} +16.9865 q^{68} +0.399826 q^{69} +2.36041 q^{71} +3.40244 q^{72} -1.57148 q^{73} +18.2921 q^{74} +3.78133 q^{76} -0.665236 q^{77} +14.3070 q^{78} -4.66885 q^{79} -10.7521 q^{81} +14.2038 q^{82} +12.5787 q^{83} -4.89995 q^{84} -4.27211 q^{86} +0.0814074 q^{87} +4.28310 q^{88} +6.06754 q^{89} -2.03208 q^{91} +0.776148 q^{92} +13.1815 q^{93} -5.86759 q^{94} -3.87276 q^{96} +8.44105 q^{97} -15.7670 q^{98} +0.794388 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 5 q^{2} + 4 q^{3} + 17 q^{4} - q^{6} + 21 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q + 5 * q^2 + 4 * q^3 + 17 * q^4 - q^6 + 21 * q^7 + 9 * q^8 + 15 * q^9	$ 15 q + 5 q^{2} + 4 q^{3} + 17 q^{4} - q^{6} + 21 q^{7} + 9 q^{8} + 15 q^{9} + 15 q^{11} + 11 q^{12} + 13 q^{13} + 9 q^{14} + 21 q^{16} + 17 q^{17} + 22 q^{18} + 15 q^{19} + 6 q^{21} + 5 q^{22} + 26 q^{23} + q^{24} + 3 q^{26} + q^{27} + 46 q^{28} + 9 q^{29} + 14 q^{31} + 18 q^{32} + 4 q^{33} - 13 q^{34} + 12 q^{36} + 9 q^{37} + 5 q^{38} - 22 q^{39} + 4 q^{41} - 6 q^{42} + 28 q^{43} + 17 q^{44} + 27 q^{46} + 14 q^{47} - 4 q^{48} + 32 q^{49} - 40 q^{51} + 14 q^{52} + 3 q^{53} - 39 q^{54} + 34 q^{56} + 4 q^{57} + 26 q^{58} + q^{59} + 2 q^{61} - 3 q^{62} + 45 q^{63} + 5 q^{64} - q^{66} + 37 q^{67} + 26 q^{68} - 7 q^{69} - 7 q^{71} + 16 q^{72} + 42 q^{73} - 43 q^{74} + 17 q^{76} + 21 q^{77} - 64 q^{78} - 10 q^{79} + 31 q^{81} + 22 q^{82} + 14 q^{83} - 32 q^{84} + 37 q^{86} + 29 q^{87} + 9 q^{88} + 15 q^{89} - 22 q^{91} + 26 q^{92} - 18 q^{93} - 44 q^{94} + 71 q^{96} + 8 q^{97} - 10 q^{98} + 15 q^{99}+O(q^{100}) $ 15 * q + 5 * q^2 + 4 * q^3 + 17 * q^4 - q^6 + 21 * q^7 + 9 * q^8 + 15 * q^9 + 15 * q^11 + 11 * q^12 + 13 * q^13 + 9 * q^14 + 21 * q^16 + 17 * q^17 + 22 * q^18 + 15 * q^19 + 6 * q^21 + 5 * q^22 + 26 * q^23 + q^24 + 3 * q^26 + q^27 + 46 * q^28 + 9 * q^29 + 14 * q^31 + 18 * q^32 + 4 * q^33 - 13 * q^34 + 12 * q^36 + 9 * q^37 + 5 * q^38 - 22 * q^39 + 4 * q^41 - 6 * q^42 + 28 * q^43 + 17 * q^44 + 27 * q^46 + 14 * q^47 - 4 * q^48 + 32 * q^49 - 40 * q^51 + 14 * q^52 + 3 * q^53 - 39 * q^54 + 34 * q^56 + 4 * q^57 + 26 * q^58 + q^59 + 2 * q^61 - 3 * q^62 + 45 * q^63 + 5 * q^64 - q^66 + 37 * q^67 + 26 * q^68 - 7 * q^69 - 7 * q^71 + 16 * q^72 + 42 * q^73 - 43 * q^74 + 17 * q^76 + 21 * q^77 - 64 * q^78 - 10 * q^79 + 31 * q^81 + 22 * q^82 + 14 * q^83 - 32 * q^84 + 37 * q^86 + 29 * q^87 + 9 * q^88 + 15 * q^89 - 22 * q^91 + 26 * q^92 - 18 * q^93 - 44 * q^94 + 71 * q^96 + 8 * q^97 - 10 * q^98 + 15 * 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 $

$2$	2.40444	1.70020	0.850098	−	0.526625i	$-0.176543\pi$
$2$	2.40444	1.70020	0.850098	+	0.526625i	$0.176543\pi$
$3$	1.94792	1.12463	0.562316	−	0.826923i	$-0.309911\pi$
$3$	1.94792	1.12463	0.562316	+	0.826923i	$0.309911\pi$
$4$	3.78133	1.89066
$5$	0	0
$5$	0	0
$6$	4.68365	1.91209
$7$	−0.665236	−0.251436	−0.125718	−	0.992066i	$-0.540123\pi$
$7$	−0.665236	−0.251436	−0.125718	+	0.992066i	$0.540123\pi$
$8$	4.28310	1.51430
$9$	0.794388	0.264796
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	7.36572	2.12630
$13$	3.05467	0.847214	0.423607	−	0.905846i	$-0.360764\pi$
$13$	3.05467	0.847214	0.423607	+	0.905846i	$0.360764\pi$
$14$	−1.59952	−0.427490
$15$	0	0
$16$	2.73579	0.683948
$17$	4.49220	1.08952	0.544759	−	0.838592i	$-0.316621\pi$
$17$	4.49220	1.08952	0.544759	+	0.838592i	$0.316621\pi$
$18$	1.91006	0.450205
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−1.29583	−0.282773
$22$	2.40444	0.512628
$23$	0.205258	0.0427993	0.0213996	−	0.999771i	$-0.493188\pi$
$23$	0.205258	0.0427993	0.0213996	+	0.999771i	$0.493188\pi$
$24$	8.34313	1.70303
$25$	0	0
$26$	7.34478	1.44043
$27$	−4.29635	−0.826833
$28$	−2.51548	−0.475381
$29$	0.0417920	0.00776057	0.00388029	−	0.999992i	$-0.498765\pi$
$29$	0.0417920	0.00776057	0.00388029	+	0.999992i	$0.498765\pi$
$30$	0	0
$31$	6.76694	1.21538	0.607690	−	0.794175i	$-0.292097\pi$
$31$	6.76694	1.21538	0.607690	+	0.794175i	$0.292097\pi$
$32$	−1.98815	−0.351459
$33$	1.94792	0.339089
$34$	10.8012	1.85240
$35$	0	0
$36$	3.00384	0.500641
$37$	7.60762	1.25069	0.625343	−	0.780350i	$-0.284959\pi$
$37$	7.60762	1.25069	0.625343	+	0.780350i	$0.284959\pi$
$38$	2.40444	0.390052
$39$	5.95026	0.952804
$40$	0	0
$41$	5.90733	0.922569	0.461285	−	0.887252i	$-0.347389\pi$
$41$	5.90733	0.922569	0.461285	+	0.887252i	$0.347389\pi$
$42$	−3.11574	−0.480769
$43$	−1.77676	−0.270953	−0.135477	−	0.990781i	$-0.543257\pi$
$43$	−1.77676	−0.270953	−0.135477	+	0.990781i	$0.543257\pi$
$44$	3.78133	0.570057
$45$	0	0
$46$	0.493531	0.0727671
$47$	−2.44032	−0.355957	−0.177978	−	0.984034i	$-0.556956\pi$
$47$	−2.44032	−0.355957	−0.177978	+	0.984034i	$0.556956\pi$
$48$	5.32910	0.769189
$49$	−6.55746	−0.936780
$50$	0	0
$51$	8.75045	1.22531
$52$	11.5507	1.60180
$53$	−3.34793	−0.459874	−0.229937	−	0.973205i	$-0.573852\pi$
$53$	−3.34793	−0.459874	−0.229937	+	0.973205i	$0.573852\pi$
$54$	−10.3303	−1.40578
$55$	0	0
$56$	−2.84927	−0.380750
$57$	1.94792	0.258008
$58$	0.100486	0.0131945
$59$	7.44003	0.968610	0.484305	−	0.874899i	$-0.339073\pi$
$59$	7.44003	0.968610	0.484305	+	0.874899i	$0.339073\pi$
$60$	0	0
$61$	−11.7720	−1.50725	−0.753623	−	0.657307i	$-0.771695\pi$
$61$	−11.7720	−1.50725	−0.753623	+	0.657307i	$0.771695\pi$
$62$	16.2707	2.06638
$63$	−0.528456	−0.0665792
$64$	−10.2520	−1.28150
$65$	0	0
$66$	4.68365	0.576518
$67$	−7.55329	−0.922781	−0.461390	−	0.887197i	$-0.652649\pi$
$67$	−7.55329	−0.922781	−0.461390	+	0.887197i	$0.652649\pi$
$68$	16.9865	2.05991
$69$	0.399826	0.0481334
$70$	0	0
$71$	2.36041	0.280129	0.140065	−	0.990142i	$-0.455269\pi$
$71$	2.36041	0.280129	0.140065	+	0.990142i	$0.455269\pi$
$72$	3.40244	0.400982
$73$	−1.57148	−0.183928	−0.0919639	−	0.995762i	$-0.529314\pi$
$73$	−1.57148	−0.183928	−0.0919639	+	0.995762i	$0.529314\pi$
$74$	18.2921	2.12641
$75$	0	0
$76$	3.78133	0.433748
$77$	−0.665236	−0.0758107
$78$	14.3070	1.61995
$79$	−4.66885	−0.525287	−0.262643	−	0.964893i	$-0.584594\pi$
$79$	−4.66885	−0.525287	−0.262643	+	0.964893i	$0.584594\pi$
$80$	0	0
$81$	−10.7521	−1.19468
$82$	14.2038	1.56855
$83$	12.5787	1.38069	0.690347	−	0.723478i	$-0.257458\pi$
$83$	12.5787	1.38069	0.690347	+	0.723478i	$0.257458\pi$
$84$	−4.89995	−0.534628
$85$	0	0
$86$	−4.27211	−0.460673
$87$	0.0814074	0.00872779
$88$	4.28310	0.456580
$89$	6.06754	0.643158	0.321579	−	0.946883i	$-0.395786\pi$
$89$	6.06754	0.643158	0.321579	+	0.946883i	$0.395786\pi$
$90$	0	0
$91$	−2.03208	−0.213020
$92$	0.776148	0.0809191
$93$	13.1815	1.36685
$94$	−5.86759	−0.605196
$95$	0	0
$96$	−3.87276	−0.395262
$97$	8.44105	0.857059	0.428529	−	0.903528i	$-0.359032\pi$
$97$	8.44105	0.857059	0.428529	+	0.903528i	$0.359032\pi$
$98$	−15.7670	−1.59271
$99$	0.794388	0.0798390
$100$	0	0
$101$	13.8688	1.37999	0.689997	−	0.723813i	$-0.257612\pi$
$101$	13.8688	1.37999	0.689997	+	0.723813i	$0.257612\pi$
$102$	21.0399	2.08326
$103$	4.43412	0.436906	0.218453	−	0.975847i	$-0.429899\pi$
$103$	4.43412	0.436906	0.218453	+	0.975847i	$0.429899\pi$
$104$	13.0835	1.28294
$105$	0	0
$106$	−8.04991	−0.781876
$107$	−16.9555	−1.63915	−0.819574	−	0.572973i	$-0.805790\pi$
$107$	−16.9555	−1.63915	−0.819574	+	0.572973i	$0.805790\pi$
$108$	−16.2459	−1.56326
$109$	−9.27495	−0.888379	−0.444189	−	0.895933i	$-0.646508\pi$
$109$	−9.27495	−0.888379	−0.444189	+	0.895933i	$0.646508\pi$
$110$	0	0
$111$	14.8190	1.40656
$112$	−1.81995	−0.171969
$113$	2.93718	0.276307	0.138153	−	0.990411i	$-0.455883\pi$
$113$	2.93718	0.276307	0.138153	+	0.990411i	$0.455883\pi$
$114$	4.68365	0.438664
$115$	0	0
$116$	0.158029	0.0146726
$117$	2.42660	0.224339
$118$	17.8891	1.64683
$119$	−2.98838	−0.273944
$120$	0	0
$121$	1.00000	0.0909091
$122$	−28.3050	−2.56261
$123$	11.5070	1.03755
$124$	25.5880	2.29787
$125$	0	0
$126$	−1.27064	−0.113198
$127$	−9.66723	−0.857828	−0.428914	−	0.903345i	$-0.641104\pi$
$127$	−9.66723	−0.857828	−0.428914	+	0.903345i	$0.641104\pi$
$128$	−20.6739	−1.82734
$129$	−3.46098	−0.304722
$130$	0	0
$131$	−9.82740	−0.858624	−0.429312	−	0.903156i	$-0.641244\pi$
$131$	−9.82740	−0.858624	−0.429312	+	0.903156i	$0.641244\pi$
$132$	7.36572	0.641104
$133$	−0.665236	−0.0576833
$134$	−18.1614	−1.56891
$135$	0	0
$136$	19.2405	1.64986
$137$	−5.19124	−0.443517	−0.221759	−	0.975102i	$-0.571180\pi$
$137$	−5.19124	−0.443517	−0.221759	+	0.975102i	$0.571180\pi$
$138$	0.961358	0.0818362
$139$	−12.5477	−1.06428	−0.532142	−	0.846655i	$-0.678613\pi$
$139$	−12.5477	−1.06428	−0.532142	+	0.846655i	$0.678613\pi$
$140$	0	0
$141$	−4.75354	−0.400320
$142$	5.67546	0.476274
$143$	3.05467	0.255445
$144$	2.17328	0.181107
$145$	0	0
$146$	−3.77853	−0.312713
$147$	−12.7734	−1.05353
$148$	28.7669	2.36463
$149$	−12.9080	−1.05746	−0.528731	−	0.848790i	$-0.677332\pi$
$149$	−12.9080	−1.05746	−0.528731	+	0.848790i	$0.677332\pi$
$150$	0	0
$151$	14.1347	1.15027	0.575134	−	0.818059i	$-0.304950\pi$
$151$	14.1347	1.15027	0.575134	+	0.818059i	$0.304950\pi$
$152$	4.28310	0.347405
$153$	3.56855	0.288500
$154$	−1.59952	−0.128893
$155$	0	0
$156$	22.4999	1.80143
$157$	−18.3892	−1.46762	−0.733810	−	0.679354i	$-0.762260\pi$
$157$	−18.3892	−1.46762	−0.733810	+	0.679354i	$0.762260\pi$
$158$	−11.2260	−0.893090
$159$	−6.52150	−0.517189
$160$	0	0
$161$	−0.136545	−0.0107613
$162$	−25.8528	−2.03119
$163$	−8.81855	−0.690722	−0.345361	−	0.938470i	$-0.612244\pi$
$163$	−8.81855	−0.690722	−0.345361	+	0.938470i	$0.612244\pi$
$164$	22.3375	1.74427
$165$	0	0
$166$	30.2448	2.34745
$167$	1.12696	0.0872065	0.0436033	−	0.999049i	$-0.486116\pi$
$167$	1.12696	0.0872065	0.0436033	+	0.999049i	$0.486116\pi$
$168$	−5.55015	−0.428203
$169$	−3.66897	−0.282228
$170$	0	0
$171$	0.794388	0.0607484
$172$	−6.71851	−0.512281
$173$	−10.7254	−0.815439	−0.407719	−	0.913107i	$-0.633676\pi$
$173$	−10.7254	−0.815439	−0.407719	+	0.913107i	$0.633676\pi$
$174$	0.195739	0.0148389
$175$	0	0
$176$	2.73579	0.206218
$177$	14.4926	1.08933
$178$	14.5890	1.09349
$179$	−7.65684	−0.572299	−0.286150	−	0.958185i	$-0.592375\pi$
$179$	−7.65684	−0.572299	−0.286150	+	0.958185i	$0.592375\pi$
$180$	0	0
$181$	18.9423	1.40797	0.703986	−	0.710213i	$-0.251402\pi$
$181$	18.9423	1.40797	0.703986	+	0.710213i	$0.251402\pi$
$182$	−4.88601	−0.362175
$183$	−22.9308	−1.69510
$184$	0.879140	0.0648111
$185$	0	0
$186$	31.6940	2.32392
$187$	4.49220	0.328502
$188$	−9.22763	−0.672994
$189$	2.85809	0.207895
$190$	0	0
$191$	−7.50113	−0.542763	−0.271382	−	0.962472i	$-0.587481\pi$
$191$	−7.50113	−0.542763	−0.271382	+	0.962472i	$0.587481\pi$
$192$	−19.9700	−1.44121
$193$	20.2215	1.45557	0.727786	−	0.685804i	$-0.240549\pi$
$193$	20.2215	1.45557	0.727786	+	0.685804i	$0.240549\pi$
$194$	20.2960	1.45717
$195$	0	0
$196$	−24.7959	−1.77114
$197$	−24.5070	−1.74605	−0.873024	−	0.487676i	$-0.837845\pi$
$197$	−24.5070	−1.74605	−0.873024	+	0.487676i	$0.837845\pi$
$198$	1.91006	0.135742
$199$	9.96226	0.706206	0.353103	−	0.935584i	$-0.385127\pi$
$199$	9.96226	0.706206	0.353103	+	0.935584i	$0.385127\pi$
$200$	0	0
$201$	−14.7132	−1.03779
$202$	33.3466	2.34626
$203$	−0.0278015	−0.00195129
$204$	33.0883	2.31665
$205$	0	0
$206$	10.6616	0.742826
$207$	0.163055	0.0113331
$208$	8.35695	0.579450
$209$	1.00000	0.0691714
$210$	0	0
$211$	7.15413	0.492511	0.246255	−	0.969205i	$-0.420800\pi$
$211$	7.15413	0.492511	0.246255	+	0.969205i	$0.420800\pi$
$212$	−12.6596	−0.869468
$213$	4.59789	0.315042
$214$	−40.7684	−2.78687
$215$	0	0
$216$	−18.4017	−1.25208
$217$	−4.50162	−0.305590
$218$	−22.3010	−1.51042
$219$	−3.06111	−0.206851
$220$	0	0
$221$	13.7222	0.923056
$222$	35.6315	2.39143
$223$	11.2847	0.755680	0.377840	−	0.925871i	$-0.376667\pi$
$223$	11.2847	0.755680	0.377840	+	0.925871i	$0.376667\pi$
$224$	1.32259	0.0883693
$225$	0	0
$226$	7.06228	0.469776
$227$	11.0481	0.733291	0.366646	−	0.930361i	$-0.380506\pi$
$227$	11.0481	0.733291	0.366646	+	0.930361i	$0.380506\pi$
$228$	7.36572	0.487807
$229$	−21.0370	−1.39016	−0.695081	−	0.718932i	$-0.744631\pi$
$229$	−21.0370	−1.39016	−0.695081	+	0.718932i	$0.744631\pi$
$230$	0	0
$231$	−1.29583	−0.0852591
$232$	0.178999	0.0117519
$233$	−4.59419	−0.300975	−0.150488	−	0.988612i	$-0.548084\pi$
$233$	−4.59419	−0.300975	−0.150488	+	0.988612i	$0.548084\pi$
$234$	5.83461	0.381420
$235$	0	0
$236$	28.1332	1.83132
$237$	−9.09454	−0.590754
$238$	−7.18537	−0.465758
$239$	10.8821	0.703904	0.351952	−	0.936018i	$-0.385518\pi$
$239$	10.8821	0.703904	0.351952	+	0.936018i	$0.385518\pi$
$240$	0	0
$241$	3.13644	0.202036	0.101018	−	0.994885i	$-0.467790\pi$
$241$	3.13644	0.202036	0.101018	+	0.994885i	$0.467790\pi$
$242$	2.40444	0.154563
$243$	−8.05519	−0.516740
$244$	−44.5137	−2.84970
$245$	0	0
$246$	27.6679	1.76404
$247$	3.05467	0.194364
$248$	28.9835	1.84045
$249$	24.5023	1.55277
$250$	0	0
$251$	12.9263	0.815899	0.407950	−	0.913004i	$-0.366244\pi$
$251$	12.9263	0.815899	0.407950	+	0.913004i	$0.366244\pi$
$252$	−1.99827	−0.125879
$253$	0.205258	0.0129045
$254$	−23.2443	−1.45848
$255$	0	0
$256$	−29.2053	−1.82533
$257$	−27.5153	−1.71635	−0.858177	−	0.513353i	$-0.828403\pi$
$257$	−27.5153	−1.71635	−0.858177	+	0.513353i	$0.828403\pi$
$258$	−8.32172	−0.518088
$259$	−5.06087	−0.314467
$260$	0	0
$261$	0.0331991	0.00205497
$262$	−23.6294	−1.45983
$263$	26.7289	1.64818	0.824088	−	0.566462i	$-0.191688\pi$
$263$	26.7289	1.64818	0.824088	+	0.566462i	$0.191688\pi$
$264$	8.34313	0.513484
$265$	0	0
$266$	−1.59952	−0.0980729
$267$	11.8191	0.723316
$268$	−28.5615	−1.74467
$269$	−10.8583	−0.662044	−0.331022	−	0.943623i	$-0.607393\pi$
$269$	−10.8583	−0.662044	−0.331022	+	0.943623i	$0.607393\pi$
$270$	0	0
$271$	−6.99688	−0.425030	−0.212515	−	0.977158i	$-0.568166\pi$
$271$	−6.99688	−0.425030	−0.212515	+	0.977158i	$0.568166\pi$
$272$	12.2897	0.745174
$273$	−3.95833	−0.239569
$274$	−12.4820	−0.754066
$275$	0	0
$276$	1.51187	0.0910041
$277$	−5.93902	−0.356841	−0.178420	−	0.983954i	$-0.557099\pi$
$277$	−5.93902	−0.356841	−0.178420	+	0.983954i	$0.557099\pi$
$278$	−30.1702	−1.80949
$279$	5.37558	0.321828
$280$	0	0
$281$	−9.12274	−0.544217	−0.272109	−	0.962267i	$-0.587721\pi$
$281$	−9.12274	−0.544217	−0.272109	+	0.962267i	$0.587721\pi$
$282$	−11.4296	−0.680622
$283$	−9.66343	−0.574431	−0.287216	−	0.957866i	$-0.592730\pi$
$283$	−9.66343	−0.574431	−0.287216	+	0.957866i	$0.592730\pi$
$284$	8.92549	0.529630
$285$	0	0
$286$	7.34478	0.434306
$287$	−3.92977	−0.231967
$288$	−1.57937	−0.0930650
$289$	3.17988	0.187052
$290$	0	0
$291$	16.4425	0.963876
$292$	−5.94228	−0.347746
$293$	8.88003	0.518777	0.259389	−	0.965773i	$-0.416479\pi$
$293$	8.88003	0.518777	0.259389	+	0.965773i	$0.416479\pi$
$294$	−30.7129	−1.79121
$295$	0	0
$296$	32.5842	1.89392
$297$	−4.29635	−0.249300
$298$	−31.0364	−1.79789
$299$	0.626996	0.0362601
$300$	0	0
$301$	1.18196	0.0681273
$302$	33.9861	1.95568
$303$	27.0152	1.55198
$304$	2.73579	0.156908
$305$	0	0
$306$	8.58037	0.490507
$307$	−5.48367	−0.312969	−0.156485	−	0.987680i	$-0.550016\pi$
$307$	−5.48367	−0.312969	−0.156485	+	0.987680i	$0.550016\pi$
$308$	−2.51548	−0.143333
$309$	8.63730	0.491359
$310$	0	0
$311$	−18.4687	−1.04726	−0.523632	−	0.851945i	$-0.675423\pi$
$311$	−18.4687	−1.04726	−0.523632	+	0.851945i	$0.675423\pi$
$312$	25.4855	1.44283
$313$	−19.9848	−1.12961	−0.564805	−	0.825225i	$-0.691049\pi$
$313$	−19.9848	−1.12961	−0.564805	+	0.825225i	$0.691049\pi$
$314$	−44.2158	−2.49524
$315$	0	0
$316$	−17.6545	−0.993141
$317$	7.52151	0.422450	0.211225	−	0.977437i	$-0.432255\pi$
$317$	7.52151	0.422450	0.211225	+	0.977437i	$0.432255\pi$
$318$	−15.6806	−0.879322
$319$	0.0417920	0.00233990
$320$	0	0
$321$	−33.0279	−1.84344
$322$	−0.328315	−0.0182963
$323$	4.49220	0.249953
$324$	−40.6573	−2.25874
$325$	0	0
$326$	−21.2037	−1.17436
$327$	−18.0668	−0.999099
$328$	25.3017	1.39705
$329$	1.62339	0.0895002
$330$	0	0
$331$	24.7743	1.36172	0.680860	−	0.732414i	$-0.261606\pi$
$331$	24.7743	1.36172	0.680860	+	0.732414i	$0.261606\pi$
$332$	47.5643	2.61043
$333$	6.04341	0.331177
$334$	2.70970	0.148268
$335$	0	0
$336$	−3.54511	−0.193402
$337$	20.7859	1.13228	0.566140	−	0.824309i	$-0.308436\pi$
$337$	20.7859	1.13228	0.566140	+	0.824309i	$0.308436\pi$
$338$	−8.82182	−0.479844
$339$	5.72139	0.310743
$340$	0	0
$341$	6.76694	0.366451
$342$	1.91006	0.103284
$343$	9.01891	0.486976
$344$	−7.61003	−0.410305
$345$	0	0
$346$	−25.7886	−1.38640
$347$	−5.29461	−0.284230	−0.142115	−	0.989850i	$-0.545390\pi$
$347$	−5.29461	−0.284230	−0.142115	+	0.989850i	$0.545390\pi$
$348$	0.307828	0.0165013
$349$	−5.79324	−0.310105	−0.155053	−	0.987906i	$-0.549555\pi$
$349$	−5.79324	−0.310105	−0.155053	+	0.987906i	$0.549555\pi$
$350$	0	0
$351$	−13.1240	−0.700505
$352$	−1.98815	−0.105969
$353$	−24.4881	−1.30337	−0.651686	−	0.758489i	$-0.725938\pi$
$353$	−24.4881	−1.30337	−0.651686	+	0.758489i	$0.725938\pi$
$354$	34.8465	1.85207
$355$	0	0
$356$	22.9434	1.21600
$357$	−5.82111	−0.308086
$358$	−18.4104	−0.973021
$359$	−1.29578	−0.0683884	−0.0341942	−	0.999415i	$-0.510886\pi$
$359$	−1.29578	−0.0683884	−0.0341942	+	0.999415i	$0.510886\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	45.5457	2.39383
$363$	1.94792	0.102239
$364$	−7.68396	−0.402749
$365$	0	0
$366$	−55.1358	−2.88199
$367$	−1.48217	−0.0773688	−0.0386844	−	0.999251i	$-0.512317\pi$
$367$	−1.48217	−0.0773688	−0.0386844	+	0.999251i	$0.512317\pi$
$368$	0.561543	0.0292725
$369$	4.69271	0.244293
$370$	0	0
$371$	2.22717	0.115629
$372$	49.8434	2.58426
$373$	−21.1434	−1.09477	−0.547383	−	0.836882i	$-0.684376\pi$
$373$	−21.1434	−1.09477	−0.547383	+	0.836882i	$0.684376\pi$
$374$	10.8012	0.558518
$375$	0	0
$376$	−10.4521	−0.539026
$377$	0.127661	0.00657487
$378$	6.87210	0.353463
$379$	−7.09981	−0.364693	−0.182346	−	0.983234i	$-0.558369\pi$
$379$	−7.09981	−0.364693	−0.182346	+	0.983234i	$0.558369\pi$
$380$	0	0
$381$	−18.8310	−0.964740
$382$	−18.0360	−0.922803
$383$	−0.626205	−0.0319976	−0.0159988	−	0.999872i	$-0.505093\pi$
$383$	−0.626205	−0.0319976	−0.0159988	+	0.999872i	$0.505093\pi$
$384$	−40.2712	−2.05508
$385$	0	0
$386$	48.6213	2.47476
$387$	−1.41144	−0.0717473
$388$	31.9184	1.62041
$389$	−0.689943	−0.0349815	−0.0174907	−	0.999847i	$-0.505568\pi$
$389$	−0.689943	−0.0349815	−0.0174907	+	0.999847i	$0.505568\pi$
$390$	0	0
$391$	0.922061	0.0466306
$392$	−28.0862	−1.41857
$393$	−19.1430	−0.965636
$394$	−58.9255	−2.96862
$395$	0	0
$396$	3.00384	0.150949
$397$	27.4815	1.37926	0.689628	−	0.724164i	$-0.257774\pi$
$397$	27.4815	1.37926	0.689628	+	0.724164i	$0.257774\pi$
$398$	23.9537	1.20069
$399$	−1.29583	−0.0648725
$400$	0	0
$401$	27.6174	1.37915	0.689574	−	0.724215i	$-0.257798\pi$
$401$	27.6174	1.37915	0.689574	+	0.724215i	$0.257798\pi$
$402$	−35.3770	−1.76444
$403$	20.6708	1.02969
$404$	52.4423	2.60910
$405$	0	0
$406$	−0.0668471	−0.00331757
$407$	7.60762	0.377096
$408$	37.4790	1.85549
$409$	−8.03757	−0.397432	−0.198716	−	0.980057i	$-0.563677\pi$
$409$	−8.03757	−0.397432	−0.198716	+	0.980057i	$0.563677\pi$
$410$	0	0
$411$	−10.1121	−0.498793
$412$	16.7669	0.826043
$413$	−4.94938	−0.243543
$414$	0.392055	0.0192685
$415$	0	0
$416$	−6.07316	−0.297761
$417$	−24.4419	−1.19693
$418$	2.40444	0.117605
$419$	−17.7286	−0.866101	−0.433050	−	0.901370i	$-0.642563\pi$
$419$	−17.7286	−0.866101	−0.433050	+	0.901370i	$0.642563\pi$
$420$	0	0
$421$	−15.5510	−0.757908	−0.378954	−	0.925416i	$-0.623716\pi$
$421$	−15.5510	−0.757908	−0.378954	+	0.925416i	$0.623716\pi$
$422$	17.2017	0.837364
$423$	−1.93856	−0.0942559
$424$	−14.3395	−0.696389
$425$	0	0
$426$	11.0553	0.535633
$427$	7.83114	0.378975
$428$	−64.1142	−3.09908
$429$	5.95026	0.287281
$430$	0	0
$431$	−34.1423	−1.64458	−0.822288	−	0.569072i	$-0.807303\pi$
$431$	−34.1423	−1.64458	−0.822288	+	0.569072i	$0.807303\pi$
$432$	−11.7539	−0.565511
$433$	5.06729	0.243519	0.121759	−	0.992560i	$-0.461146\pi$
$433$	5.06729	0.243519	0.121759	+	0.992560i	$0.461146\pi$
$434$	−10.8239	−0.519562
$435$	0	0
$436$	−35.0716	−1.67963
$437$	0.205258	0.00981883
$438$	−7.36027	−0.351687
$439$	−23.7809	−1.13500	−0.567500	−	0.823374i	$-0.692089\pi$
$439$	−23.7809	−1.13500	−0.567500	+	0.823374i	$0.692089\pi$
$440$	0	0
$441$	−5.20917	−0.248056
$442$	32.9942	1.56938
$443$	−13.0487	−0.619961	−0.309981	−	0.950743i	$-0.600323\pi$
$443$	−13.0487	−0.619961	−0.309981	+	0.950743i	$0.600323\pi$
$444$	56.0356	2.65933
$445$	0	0
$446$	27.1334	1.28480
$447$	−25.1437	−1.18925
$448$	6.81998	0.322214
$449$	−26.5900	−1.25486	−0.627430	−	0.778673i	$-0.715893\pi$
$449$	−26.5900	−1.25486	−0.627430	+	0.778673i	$0.715893\pi$
$450$	0	0
$451$	5.90733	0.278165
$452$	11.1064	0.522403
$453$	27.5333	1.29363
$454$	26.5646	1.24674
$455$	0	0
$456$	8.34313	0.390703
$457$	−0.764032	−0.0357399	−0.0178700	−	0.999840i	$-0.505688\pi$
$457$	−0.764032	−0.0357399	−0.0178700	+	0.999840i	$0.505688\pi$
$458$	−50.5821	−2.36355
$459$	−19.3001	−0.900851
$460$	0	0
$461$	−5.17462	−0.241006	−0.120503	−	0.992713i	$-0.538451\pi$
$461$	−5.17462	−0.241006	−0.120503	+	0.992713i	$0.538451\pi$
$462$	−3.11574	−0.144957
$463$	14.9993	0.697078	0.348539	−	0.937294i	$-0.386678\pi$
$463$	14.9993	0.697078	0.348539	+	0.937294i	$0.386678\pi$
$464$	0.114334	0.00530783
$465$	0	0
$466$	−11.0465	−0.511717
$467$	−8.46795	−0.391850	−0.195925	−	0.980619i	$-0.562771\pi$
$467$	−8.46795	−0.391850	−0.195925	+	0.980619i	$0.562771\pi$
$468$	9.17576	0.424150
$469$	5.02472	0.232020
$470$	0	0
$471$	−35.8207	−1.65053
$472$	31.8664	1.46677
$473$	−1.77676	−0.0816954
$474$	−21.8673	−1.00440
$475$	0	0
$476$	−11.3000	−0.517936
$477$	−2.65956	−0.121773
$478$	26.1653	1.19677
$479$	11.4343	0.522446	0.261223	−	0.965278i	$-0.415874\pi$
$479$	11.4343	0.522446	0.261223	+	0.965278i	$0.415874\pi$
$480$	0	0
$481$	23.2388	1.05960
$482$	7.54139	0.343501
$483$	−0.265979	−0.0121025
$484$	3.78133	0.171879
$485$	0	0
$486$	−19.3682	−0.878560
$487$	34.9001	1.58148	0.790738	−	0.612155i	$-0.209697\pi$
$487$	34.9001	1.58148	0.790738	+	0.612155i	$0.209697\pi$
$488$	−50.4205	−2.28243
$489$	−17.1778	−0.776808
$490$	0	0
$491$	15.5534	0.701917	0.350958	−	0.936391i	$-0.385856\pi$
$491$	15.5534	0.701917	0.350958	+	0.936391i	$0.385856\pi$
$492$	43.5117	1.96166
$493$	0.187738	0.00845529
$494$	7.34478	0.330457
$495$	0	0
$496$	18.5129	0.831256
$497$	−1.57023	−0.0704345
$498$	58.9144	2.64002
$499$	−29.1290	−1.30399	−0.651996	−	0.758222i	$-0.726068\pi$
$499$	−29.1290	−1.30399	−0.651996	+	0.758222i	$0.726068\pi$
$500$	0	0
$501$	2.19522	0.0980752
$502$	31.0804	1.38719
$503$	5.76237	0.256931	0.128466	−	0.991714i	$-0.458995\pi$
$503$	5.76237	0.256931	0.128466	+	0.991714i	$0.458995\pi$
$504$	−2.26343	−0.100821
$505$	0	0
$506$	0.493531	0.0219401
$507$	−7.14686	−0.317403
$508$	−36.5550	−1.62186
$509$	20.3839	0.903502	0.451751	−	0.892144i	$-0.350799\pi$
$509$	20.3839	0.903502	0.451751	+	0.892144i	$0.350799\pi$
$510$	0	0
$511$	1.04541	0.0462460
$512$	−28.8745	−1.27608
$513$	−4.29635	−0.189689
$514$	−66.1588	−2.91814
$515$	0	0
$516$	−13.0871	−0.576128
$517$	−2.44032	−0.107325
$518$	−12.1685	−0.534655
$519$	−20.8922	−0.917068
$520$	0	0
$521$	21.9184	0.960262	0.480131	−	0.877197i	$-0.340589\pi$
$521$	21.9184	0.960262	0.480131	+	0.877197i	$0.340589\pi$
$522$	0.0798251	0.00349385
$523$	3.65894	0.159994	0.0799972	−	0.996795i	$-0.474509\pi$
$523$	3.65894	0.159994	0.0799972	+	0.996795i	$0.474509\pi$
$524$	−37.1606	−1.62337
$525$	0	0
$526$	64.2681	2.80222
$527$	30.3985	1.32418
$528$	5.32910	0.231919
$529$	−22.9579	−0.998168
$530$	0	0
$531$	5.91027	0.256484
$532$	−2.51548	−0.109060
$533$	18.0450	0.781614
$534$	28.4182	1.22978
$535$	0	0
$536$	−32.3515	−1.39737
$537$	−14.9149	−0.643626
$538$	−26.1082	−1.12560
$539$	−6.55746	−0.282450
$540$	0	0
$541$	−29.6166	−1.27332	−0.636659	−	0.771145i	$-0.719684\pi$
$541$	−29.6166	−1.27332	−0.636659	+	0.771145i	$0.719684\pi$
$542$	−16.8236	−0.722635
$543$	36.8981	1.58345
$544$	−8.93118	−0.382921
$545$	0	0
$546$	−9.51756	−0.407314
$547$	0.893755	0.0382142	0.0191071	−	0.999817i	$-0.493918\pi$
$547$	0.893755	0.0382142	0.0191071	+	0.999817i	$0.493918\pi$
$548$	−19.6298	−0.838542
$549$	−9.35151	−0.399113
$550$	0	0
$551$	0.0417920	0.00178040
$552$	1.71249	0.0728886
$553$	3.10589	0.132076
$554$	−14.2800	−0.606699
$555$	0	0
$556$	−47.4470	−2.01220
$557$	−2.52940	−0.107174	−0.0535870	−	0.998563i	$-0.517065\pi$
$557$	−2.52940	−0.107174	−0.0535870	+	0.998563i	$0.517065\pi$
$558$	12.9253	0.547170
$559$	−5.42742	−0.229555
$560$	0	0
$561$	8.75045	0.369444
$562$	−21.9351	−0.925276
$563$	26.4031	1.11276	0.556379	−	0.830929i	$-0.312190\pi$
$563$	26.4031	1.11276	0.556379	+	0.830929i	$0.312190\pi$
$564$	−17.9747	−0.756871
$565$	0	0
$566$	−23.2351	−0.976645
$567$	7.15270	0.300385
$568$	10.1099	0.424201
$569$	25.7456	1.07931	0.539656	−	0.841886i	$-0.318554\pi$
$569$	25.7456	1.07931	0.539656	+	0.841886i	$0.318554\pi$
$570$	0	0
$571$	−32.1904	−1.34712	−0.673562	−	0.739131i	$-0.735237\pi$
$571$	−32.1904	−1.34712	−0.673562	+	0.739131i	$0.735237\pi$
$572$	11.5507	0.482960
$573$	−14.6116	−0.610408
$574$	−9.44889	−0.394389
$575$	0	0
$576$	−8.14405	−0.339335
$577$	44.7621	1.86347	0.931735	−	0.363138i	$-0.118295\pi$
$577$	44.7621	1.86347	0.931735	+	0.363138i	$0.118295\pi$
$578$	7.64582	0.318024
$579$	39.3898	1.63698
$580$	0	0
$581$	−8.36783	−0.347156
$582$	39.5350	1.63878
$583$	−3.34793	−0.138657
$584$	−6.73080	−0.278522
$585$	0	0
$586$	21.3515	0.882022
$587$	20.5841	0.849597	0.424799	−	0.905288i	$-0.360345\pi$
$587$	20.5841	0.849597	0.424799	+	0.905288i	$0.360345\pi$
$588$	−48.3004	−1.99188
$589$	6.76694	0.278827
$590$	0	0
$591$	−47.7376	−1.96366
$592$	20.8129	0.855403
$593$	37.6866	1.54760	0.773802	−	0.633428i	$-0.218353\pi$
$593$	37.6866	1.54760	0.773802	+	0.633428i	$0.218353\pi$
$594$	−10.3303	−0.423858
$595$	0	0
$596$	−48.8092	−1.99930
$597$	19.4057	0.794222
$598$	1.50758	0.0616493
$599$	−29.3217	−1.19805	−0.599027	−	0.800729i	$-0.704446\pi$
$599$	−29.3217	−1.19805	−0.599027	+	0.800729i	$0.704446\pi$
$600$	0	0
$601$	−17.4596	−0.712190	−0.356095	−	0.934450i	$-0.615892\pi$
$601$	−17.4596	−0.712190	−0.356095	+	0.934450i	$0.615892\pi$
$602$	2.84196	0.115830
$603$	−6.00024	−0.244349
$604$	53.4481	2.17477
$605$	0	0
$606$	64.9565	2.63868
$607$	39.4241	1.60017	0.800087	−	0.599884i	$-0.204787\pi$
$607$	39.4241	1.60017	0.800087	+	0.599884i	$0.204787\pi$
$608$	−1.98815	−0.0806302
$609$	−0.0541551	−0.00219448
$610$	0	0
$611$	−7.45437	−0.301571
$612$	13.4939	0.545457
$613$	24.8034	1.00180	0.500901	−	0.865505i	$-0.333002\pi$
$613$	24.8034	1.00180	0.500901	+	0.865505i	$0.333002\pi$
$614$	−13.1851	−0.532109
$615$	0	0
$616$	−2.84927	−0.114800
$617$	−44.9932	−1.81136	−0.905678	−	0.423966i	$-0.860638\pi$
$617$	−44.9932	−1.81136	−0.905678	+	0.423966i	$0.860638\pi$
$618$	20.7679	0.835406
$619$	4.48348	0.180206	0.0901031	−	0.995932i	$-0.471280\pi$
$619$	4.48348	0.180206	0.0901031	+	0.995932i	$0.471280\pi$
$620$	0	0
$621$	−0.881861	−0.0353879
$622$	−44.4069	−1.78055
$623$	−4.03635	−0.161713
$624$	16.2787	0.651668
$625$	0	0
$626$	−48.0523	−1.92056
$627$	1.94792	0.0777924
$628$	−69.5358	−2.77478
$629$	34.1750	1.36265
$630$	0	0
$631$	41.6458	1.65789	0.828947	−	0.559327i	$-0.188941\pi$
$631$	41.6458	1.65789	0.828947	+	0.559327i	$0.188941\pi$
$632$	−19.9971	−0.795444
$633$	13.9357	0.553893
$634$	18.0850	0.718247
$635$	0	0
$636$	−24.6600	−0.977831
$637$	−20.0309	−0.793653
$638$	0.100486	0.00397829
$639$	1.87508	0.0741771
$640$	0	0
$641$	−28.0569	−1.10818	−0.554090	−	0.832457i	$-0.686934\pi$
$641$	−28.0569	−1.10818	−0.554090	+	0.832457i	$0.686934\pi$
$642$	−79.4136	−3.13420
$643$	22.4021	0.883453	0.441727	−	0.897150i	$-0.354366\pi$
$643$	22.4021	0.883453	0.441727	+	0.897150i	$0.354366\pi$
$644$	−0.516322	−0.0203459
$645$	0	0
$646$	10.8012	0.424969
$647$	−25.5651	−1.00507	−0.502533	−	0.864558i	$-0.667599\pi$
$647$	−25.5651	−1.00507	−0.502533	+	0.864558i	$0.667599\pi$
$648$	−46.0523	−1.80911
$649$	7.44003	0.292047
$650$	0	0
$651$	−8.76879	−0.343676
$652$	−33.3458	−1.30592
$653$	11.9470	0.467523	0.233761	−	0.972294i	$-0.424897\pi$
$653$	11.9470	0.467523	0.233761	+	0.972294i	$0.424897\pi$
$654$	−43.4406	−1.69866
$655$	0	0
$656$	16.1612	0.630989
$657$	−1.24837	−0.0487034
$658$	3.90333	0.152168
$659$	17.3208	0.674724	0.337362	−	0.941375i	$-0.390465\pi$
$659$	17.3208	0.674724	0.337362	+	0.941375i	$0.390465\pi$
$660$	0	0
$661$	18.6524	0.725495	0.362748	−	0.931887i	$-0.381839\pi$
$661$	18.6524	0.725495	0.362748	+	0.931887i	$0.381839\pi$
$662$	59.5683	2.31519
$663$	26.7298	1.03810
$664$	53.8759	2.09079
$665$	0	0
$666$	14.5310	0.563065
$667$	0.00857814	0.000332147 0
$668$	4.26139	0.164878
$669$	21.9817	0.849862
$670$	0	0
$671$	−11.7720	−0.454452
$672$	2.57630	0.0993830
$673$	47.6707	1.83757	0.918785	−	0.394758i	$-0.129171\pi$
$673$	47.6707	1.83757	0.918785	+	0.394758i	$0.129171\pi$
$674$	49.9784	1.92510
$675$	0	0
$676$	−13.8736	−0.533599
$677$	4.64806	0.178639	0.0893197	−	0.996003i	$-0.471531\pi$
$677$	4.64806	0.178639	0.0893197	+	0.996003i	$0.471531\pi$
$678$	13.7567	0.528324
$679$	−5.61529	−0.215495
$680$	0	0
$681$	21.5209	0.824683
$682$	16.2707	0.623038
$683$	25.0058	0.956820	0.478410	−	0.878137i	$-0.341213\pi$
$683$	25.0058	0.956820	0.478410	+	0.878137i	$0.341213\pi$
$684$	3.00384	0.114855
$685$	0	0
$686$	21.6854	0.827954
$687$	−40.9783	−1.56342
$688$	−4.86084	−0.185318
$689$	−10.2268	−0.389612
$690$	0	0
$691$	−19.9866	−0.760328	−0.380164	−	0.924919i	$-0.624132\pi$
$691$	−19.9866	−0.760328	−0.380164	+	0.924919i	$0.624132\pi$
$692$	−40.5563	−1.54172
$693$	−0.528456	−0.0200744
$694$	−12.7306	−0.483246
$695$	0	0
$696$	0.348676	0.0132165
$697$	26.5369	1.00516
$698$	−13.9295	−0.527239
$699$	−8.94911	−0.338487
$700$	0	0
$701$	−28.2573	−1.06726	−0.533632	−	0.845717i	$-0.679173\pi$
$701$	−28.2573	−1.06726	−0.533632	+	0.845717i	$0.679173\pi$
$702$	−31.5558	−1.19100
$703$	7.60762	0.286927
$704$	−10.2520	−0.386386
$705$	0	0
$706$	−58.8803	−2.21599
$707$	−9.22600	−0.346980
$708$	54.8012	2.05956
$709$	−20.5903	−0.773287	−0.386643	−	0.922229i	$-0.626366\pi$
$709$	−20.5903	−0.773287	−0.386643	+	0.922229i	$0.626366\pi$
$710$	0	0
$711$	−3.70888	−0.139094
$712$	25.9879	0.973936
$713$	1.38897	0.0520173
$714$	−13.9965	−0.523806
$715$	0	0
$716$	−28.9530	−1.08203
$717$	21.1974	0.791632
$718$	−3.11561	−0.116274
$719$	36.7987	1.37236	0.686179	−	0.727433i	$-0.259287\pi$
$719$	36.7987	1.37236	0.686179	+	0.727433i	$0.259287\pi$
$720$	0	0
$721$	−2.94973	−0.109854
$722$	2.40444	0.0894840
$723$	6.10954	0.227216
$724$	71.6272	2.66200
$725$	0	0
$726$	4.68365	0.173827
$727$	7.19540	0.266862	0.133431	−	0.991058i	$-0.457400\pi$
$727$	7.19540	0.266862	0.133431	+	0.991058i	$0.457400\pi$
$728$	−8.70360	−0.322577
$729$	16.5655	0.613537
$730$	0	0
$731$	−7.98156	−0.295208
$732$	−86.7090	−3.20486
$733$	23.2371	0.858282	0.429141	−	0.903237i	$-0.358816\pi$
$733$	23.2371	0.858282	0.429141	+	0.903237i	$0.358816\pi$
$734$	−3.56379	−0.131542
$735$	0	0
$736$	−0.408084	−0.0150422
$737$	−7.55329	−0.278229
$738$	11.2833	0.415345
$739$	8.05244	0.296214	0.148107	−	0.988971i	$-0.452682\pi$
$739$	8.05244	0.296214	0.148107	+	0.988971i	$0.452682\pi$
$740$	0	0
$741$	5.95026	0.218588
$742$	5.35509	0.196592
$743$	28.2801	1.03750	0.518748	−	0.854927i	$-0.326398\pi$
$743$	28.2801	1.03750	0.518748	+	0.854927i	$0.326398\pi$
$744$	56.4575	2.06983
$745$	0	0
$746$	−50.8381	−1.86132
$747$	9.99239	0.365603
$748$	16.9865	0.621088
$749$	11.2794	0.412140
$750$	0	0
$751$	22.2029	0.810195	0.405098	−	0.914273i	$-0.367238\pi$
$751$	22.2029	0.810195	0.405098	+	0.914273i	$0.367238\pi$
$752$	−6.67619	−0.243456
$753$	25.1793	0.917586
$754$	0.306953	0.0111786
$755$	0	0
$756$	10.8074	0.393061
$757$	−8.75295	−0.318131	−0.159066	−	0.987268i	$-0.550848\pi$
$757$	−8.75295	−0.318131	−0.159066	+	0.987268i	$0.550848\pi$
$758$	−17.0711	−0.620049
$759$	0.399826	0.0145128
$760$	0	0
$761$	−13.4713	−0.488334	−0.244167	−	0.969733i	$-0.578514\pi$
$761$	−13.4713	−0.488334	−0.244167	+	0.969733i	$0.578514\pi$
$762$	−45.2780	−1.64025
$763$	6.17003	0.223370
$764$	−28.3643	−1.02618
$765$	0	0
$766$	−1.50567	−0.0544022
$767$	22.7269	0.820620
$768$	−56.8896	−2.05282
$769$	23.4526	0.845723	0.422862	−	0.906194i	$-0.361026\pi$
$769$	23.4526	0.845723	0.422862	+	0.906194i	$0.361026\pi$
$770$	0	0
$771$	−53.5975	−1.93027
$772$	76.4640	2.75200
$773$	−36.4566	−1.31125	−0.655626	−	0.755086i	$-0.727595\pi$
$773$	−36.4566	−1.31125	−0.655626	+	0.755086i	$0.727595\pi$
$774$	−3.39371	−0.121984
$775$	0	0
$776$	36.1538	1.29785
$777$	−9.85816	−0.353660
$778$	−1.65893	−0.0594754
$779$	5.90733	0.211652
$780$	0	0
$781$	2.36041	0.0844621
$782$	2.21704	0.0792812
$783$	−0.179553	−0.00641670
$784$	−17.9398	−0.640708
$785$	0	0
$786$	−46.0281	−1.64177
$787$	0.310043	0.0110519	0.00552593	−	0.999985i	$-0.498241\pi$
$787$	0.310043	0.0110519	0.00552593	+	0.999985i	$0.498241\pi$
$788$	−92.6689	−3.30119
$789$	52.0658	1.85359
$790$	0	0
$791$	−1.95392	−0.0694734
$792$	3.40244	0.120901
$793$	−35.9595	−1.27696
$794$	66.0775	2.34500
$795$	0	0
$796$	37.6706	1.33520
$797$	39.9134	1.41381	0.706903	−	0.707311i	$-0.250092\pi$
$797$	39.9134	1.41381	0.706903	+	0.707311i	$0.250092\pi$
$798$	−3.11574	−0.110296
$799$	−10.9624	−0.387821
$800$	0	0
$801$	4.81998	0.170306
$802$	66.4044	2.34482
$803$	−1.57148	−0.0554563
$804$	−55.6354	−1.96211
$805$	0	0
$806$	49.7017	1.75067
$807$	−21.1511	−0.744555
$808$	59.4012	2.08973
$809$	35.5265	1.24904	0.624522	−	0.781007i	$-0.285294\pi$
$809$	35.5265	1.24904	0.624522	+	0.781007i	$0.285294\pi$
$810$	0	0
$811$	−5.44459	−0.191185	−0.0955927	−	0.995421i	$-0.530475\pi$
$811$	−5.44459	−0.191185	−0.0955927	+	0.995421i	$0.530475\pi$
$812$	−0.105127	−0.00368923
$813$	−13.6294	−0.478003
$814$	18.2921	0.641137
$815$	0	0
$816$	23.9394	0.838046
$817$	−1.77676	−0.0621609
$818$	−19.3258	−0.675712
$819$	−1.61426	−0.0564068
$820$	0	0
$821$	−5.04790	−0.176173	−0.0880865	−	0.996113i	$-0.528075\pi$
$821$	−5.04790	−0.176173	−0.0880865	+	0.996113i	$0.528075\pi$
$822$	−24.3139	−0.848046
$823$	−43.4928	−1.51607	−0.758033	−	0.652217i	$-0.773839\pi$
$823$	−43.4928	−1.51607	−0.758033	+	0.652217i	$0.773839\pi$
$824$	18.9918	0.661609
$825$	0	0
$826$	−11.9005	−0.414071
$827$	−14.5718	−0.506711	−0.253356	−	0.967373i	$-0.581534\pi$
$827$	−14.5718	−0.506711	−0.253356	+	0.967373i	$0.581534\pi$
$828$	0.616563	0.0214271
$829$	42.0994	1.46217	0.731086	−	0.682285i	$-0.239014\pi$
$829$	42.0994	1.46217	0.731086	+	0.682285i	$0.239014\pi$
$830$	0	0
$831$	−11.5687	−0.401315
$832$	−31.3164	−1.08570
$833$	−29.4574	−1.02064
$834$	−58.7691	−2.03501
$835$	0	0
$836$	3.78133	0.130780
$837$	−29.0732	−1.00492
$838$	−42.6274	−1.47254
$839$	39.2894	1.35642	0.678211	−	0.734868i	$-0.262756\pi$
$839$	39.2894	1.35642	0.678211	+	0.734868i	$0.262756\pi$
$840$	0	0
$841$	−28.9983	−0.999940
$842$	−37.3914	−1.28859
$843$	−17.7704	−0.612044
$844$	27.0521	0.931172
$845$	0	0
$846$	−4.66115	−0.160253
$847$	−0.665236	−0.0228578
$848$	−9.15925	−0.314530
$849$	−18.8236	−0.646023
$850$	0	0
$851$	1.56153	0.0535284
$852$	17.3861	0.595639
$853$	40.0833	1.37243	0.686213	−	0.727401i	$-0.259272\pi$
$853$	40.0833	1.37243	0.686213	+	0.727401i	$0.259272\pi$
$854$	18.8295	0.644332
$855$	0	0
$856$	−72.6220	−2.48217
$857$	8.21405	0.280587	0.140293	−	0.990110i	$-0.455195\pi$
$857$	8.21405	0.280587	0.140293	+	0.990110i	$0.455195\pi$
$858$	14.3070	0.488434
$859$	−47.6682	−1.62642	−0.813210	−	0.581971i	$-0.802282\pi$
$859$	−47.6682	−1.62642	−0.813210	+	0.581971i	$0.802282\pi$
$860$	0	0
$861$	−7.65487	−0.260877
$862$	−82.0930	−2.79610
$863$	1.03040	0.0350752	0.0175376	−	0.999846i	$-0.494417\pi$
$863$	1.03040	0.0350752	0.0175376	+	0.999846i	$0.494417\pi$
$864$	8.54180	0.290598
$865$	0	0
$866$	12.1840	0.414029
$867$	6.19414	0.210364
$868$	−17.0221	−0.577768
$869$	−4.66885	−0.158380
$870$	0	0
$871$	−23.0728	−0.781793
$872$	−39.7255	−1.34528
$873$	6.70547	0.226946
$874$	0.493531	0.0166939
$875$	0	0
$876$	−11.5751	−0.391086
$877$	25.9529	0.876366	0.438183	−	0.898886i	$-0.355622\pi$
$877$	25.9529	0.876366	0.438183	+	0.898886i	$0.355622\pi$
$878$	−57.1797	−1.92972
$879$	17.2976	0.583433
$880$	0	0
$881$	−14.8144	−0.499109	−0.249554	−	0.968361i	$-0.580284\pi$
$881$	−14.8144	−0.499109	−0.249554	+	0.968361i	$0.580284\pi$
$882$	−12.5251	−0.421743
$883$	1.57133	0.0528794	0.0264397	−	0.999650i	$-0.491583\pi$
$883$	1.57133	0.0528794	0.0264397	+	0.999650i	$0.491583\pi$
$884$	51.8882	1.74519
$885$	0	0
$886$	−31.3748	−1.05406
$887$	39.1857	1.31573	0.657864	−	0.753137i	$-0.271460\pi$
$887$	39.1857	1.31573	0.657864	+	0.753137i	$0.271460\pi$
$888$	63.4714	2.12996
$889$	6.43099	0.215689
$890$	0	0
$891$	−10.7521	−0.360209
$892$	42.6712	1.42874
$893$	−2.44032	−0.0816620
$894$	−60.4564	−2.02196
$895$	0	0
$896$	13.7531	0.459457
$897$	1.22134	0.0407793
$898$	−63.9340	−2.13351
$899$	0.282804	0.00943204
$900$	0	0
$901$	−15.0396	−0.501042
$902$	14.2038	0.472935
$903$	2.30237	0.0766181
$904$	12.5802	0.418412
$905$	0	0
$906$	66.2022	2.19942
$907$	−51.6485	−1.71496	−0.857481	−	0.514516i	$-0.827972\pi$
$907$	−51.6485	−1.71496	−0.857481	+	0.514516i	$0.827972\pi$
$908$	41.7767	1.38641
$909$	11.0172	0.365417
$910$	0	0
$911$	20.7905	0.688822	0.344411	−	0.938819i	$-0.388079\pi$
$911$	20.7905	0.688822	0.344411	+	0.938819i	$0.388079\pi$
$912$	5.32910	0.176464
$913$	12.5787	0.416295
$914$	−1.83707	−0.0607649
$915$	0	0
$916$	−79.5477	−2.62833
$917$	6.53754	0.215889
$918$	−46.4059	−1.53162
$919$	11.0153	0.363363	0.181681	−	0.983357i	$-0.441846\pi$
$919$	11.0153	0.363363	0.181681	+	0.983357i	$0.441846\pi$
$920$	0	0
$921$	−10.6817	−0.351975
$922$	−12.4421	−0.409758
$923$	7.21028	0.237329
$924$	−4.89995	−0.161196
$925$	0	0
$926$	36.0650	1.18517
$927$	3.52241	0.115691
$928$	−0.0830888	−0.00272752
$929$	22.8406	0.749375	0.374687	−	0.927151i	$-0.377750\pi$
$929$	22.8406	0.749375	0.374687	+	0.927151i	$0.377750\pi$
$930$	0	0
$931$	−6.55746	−0.214912
$932$	−17.3721	−0.569044
$933$	−35.9755	−1.17779
$934$	−20.3607	−0.666221
$935$	0	0
$936$	10.3934	0.339717
$937$	13.4463	0.439270	0.219635	−	0.975582i	$-0.429513\pi$
$937$	13.4463	0.439270	0.219635	+	0.975582i	$0.429513\pi$
$938$	12.0816	0.394479
$939$	−38.9288	−1.27039
$940$	0	0
$941$	−15.2843	−0.498253	−0.249126	−	0.968471i	$-0.580143\pi$
$941$	−15.2843	−0.498253	−0.249126	+	0.968471i	$0.580143\pi$
$942$	−86.1288	−2.80623
$943$	1.21253	0.0394853
$944$	20.3544	0.662478
$945$	0	0
$946$	−4.27211	−0.138898
$947$	31.6259	1.02770	0.513852	−	0.857879i	$-0.328218\pi$
$947$	31.6259	1.02770	0.513852	+	0.857879i	$0.328218\pi$
$948$	−34.3895	−1.11692
$949$	−4.80036	−0.155826
$950$	0	0
$951$	14.6513	0.475100
$952$	−12.7995	−0.414834
$953$	−16.2564	−0.526596	−0.263298	−	0.964715i	$-0.584810\pi$
$953$	−16.2564	−0.526596	−0.263298	+	0.964715i	$0.584810\pi$
$954$	−6.39475	−0.207038
$955$	0	0
$956$	41.1488	1.33085
$957$	0.0814074	0.00263153
$958$	27.4931	0.888261
$959$	3.45340	0.111516
$960$	0	0
$961$	14.7915	0.477146
$962$	55.8763	1.80152
$963$	−13.4692	−0.434040
$964$	11.8599	0.381983
$965$	0	0
$966$	−0.639530	−0.0205765
$967$	43.6663	1.40421	0.702106	−	0.712072i	$-0.252243\pi$
$967$	43.6663	1.40421	0.702106	+	0.712072i	$0.252243\pi$
$968$	4.28310	0.137664
$969$	8.75045	0.281105
$970$	0	0
$971$	−32.5513	−1.04462	−0.522311	−	0.852755i	$-0.674930\pi$
$971$	−32.5513	−1.04462	−0.522311	+	0.852755i	$0.674930\pi$
$972$	−30.4593	−0.976983
$973$	8.34720	0.267599
$974$	83.9153	2.68882
$975$	0	0
$976$	−32.2056	−1.03088
$977$	37.0156	1.18423	0.592117	−	0.805852i	$-0.298292\pi$
$977$	37.0156	1.18423	0.592117	+	0.805852i	$0.298292\pi$
$978$	−41.3030	−1.32073
$979$	6.06754	0.193919
$980$	0	0
$981$	−7.36791	−0.235239
$982$	37.3973	1.19340
$983$	10.3708	0.330777	0.165389	−	0.986228i	$-0.447112\pi$
$983$	10.3708	0.330777	0.165389	+	0.986228i	$0.447112\pi$
$984$	49.2856	1.57117
$985$	0	0
$986$	0.451405	0.0143757
$987$	3.16223	0.100655
$988$	11.5507	0.367478
$989$	−0.364694	−0.0115966
$990$	0	0
$991$	−20.4472	−0.649525	−0.324763	−	0.945796i	$-0.605284\pi$
$991$	−20.4472	−0.649525	−0.324763	+	0.945796i	$0.605284\pi$
$992$	−13.4537	−0.427156
$993$	48.2583	1.53143
$994$	−3.77552	−0.119752
$995$	0	0
$996$	92.6514	2.93577
$997$	−51.6575	−1.63601	−0.818004	−	0.575212i	$-0.804920\pi$
$997$	−51.6575	−1.63601	−0.818004	+	0.575212i	$0.804920\pi$
$998$	−70.0389	−2.21704
$999$	−32.6850	−1.03411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5225.2.a.y.1.13	yes	15
5.4	even	2		5225.2.a.r.1.3	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5225.2.a.r.1.3	✓	15	5.4	even	2
5225.2.a.y.1.13	yes	15	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:	\( N \)	\(=\)	\( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5225.a (trivial)

\(f(q)\)	\(=\)	\(q+2.40444 q^{2} +1.94792 q^{3} +3.78133 q^{4} +4.68365 q^{6} -0.665236 q^{7} +4.28310 q^{8} +0.794388 q^{9} +O(q^{10})\)	\(q+2.40444 q^{2} +1.94792 q^{3} +3.78133 q^{4} +4.68365 q^{6} -0.665236 q^{7} +4.28310 q^{8} +0.794388 q^{9} +1.00000 q^{11} +7.36572 q^{12} +3.05467 q^{13} -1.59952 q^{14} +2.73579 q^{16} +4.49220 q^{17} +1.91006 q^{18} +1.00000 q^{19} -1.29583 q^{21} +2.40444 q^{22} +0.205258 q^{23} +8.34313 q^{24} +7.34478 q^{26} -4.29635 q^{27} -2.51548 q^{28} +0.0417920 q^{29} +6.76694 q^{31} -1.98815 q^{32} +1.94792 q^{33} +10.8012 q^{34} +3.00384 q^{36} +7.60762 q^{37} +2.40444 q^{38} +5.95026 q^{39} +5.90733 q^{41} -3.11574 q^{42} -1.77676 q^{43} +3.78133 q^{44} +0.493531 q^{46} -2.44032 q^{47} +5.32910 q^{48} -6.55746 q^{49} +8.75045 q^{51} +11.5507 q^{52} -3.34793 q^{53} -10.3303 q^{54} -2.84927 q^{56} +1.94792 q^{57} +0.100486 q^{58} +7.44003 q^{59} -11.7720 q^{61} +16.2707 q^{62} -0.528456 q^{63} -10.2520 q^{64} +4.68365 q^{66} -7.55329 q^{67} +16.9865 q^{68} +0.399826 q^{69} +2.36041 q^{71} +3.40244 q^{72} -1.57148 q^{73} +18.2921 q^{74} +3.78133 q^{76} -0.665236 q^{77} +14.3070 q^{78} -4.66885 q^{79} -10.7521 q^{81} +14.2038 q^{82} +12.5787 q^{83} -4.89995 q^{84} -4.27211 q^{86} +0.0814074 q^{87} +4.28310 q^{88} +6.06754 q^{89} -2.03208 q^{91} +0.776148 q^{92} +13.1815 q^{93} -5.86759 q^{94} -3.87276 q^{96} +8.44105 q^{97} -15.7670 q^{98} +0.794388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 5 q^{2} + 4 q^{3} + 17 q^{4} - q^{6} + 21 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q + 5 * q^2 + 4 * q^3 + 17 * q^4 - q^6 + 21 * q^7 + 9 * q^8 + 15 * q^9	\( 15 q + 5 q^{2} + 4 q^{3} + 17 q^{4} - q^{6} + 21 q^{7} + 9 q^{8} + 15 q^{9} + 15 q^{11} + 11 q^{12} + 13 q^{13} + 9 q^{14} + 21 q^{16} + 17 q^{17} + 22 q^{18} + 15 q^{19} + 6 q^{21} + 5 q^{22} + 26 q^{23} + q^{24} + 3 q^{26} + q^{27} + 46 q^{28} + 9 q^{29} + 14 q^{31} + 18 q^{32} + 4 q^{33} - 13 q^{34} + 12 q^{36} + 9 q^{37} + 5 q^{38} - 22 q^{39} + 4 q^{41} - 6 q^{42} + 28 q^{43} + 17 q^{44} + 27 q^{46} + 14 q^{47} - 4 q^{48} + 32 q^{49} - 40 q^{51} + 14 q^{52} + 3 q^{53} - 39 q^{54} + 34 q^{56} + 4 q^{57} + 26 q^{58} + q^{59} + 2 q^{61} - 3 q^{62} + 45 q^{63} + 5 q^{64} - q^{66} + 37 q^{67} + 26 q^{68} - 7 q^{69} - 7 q^{71} + 16 q^{72} + 42 q^{73} - 43 q^{74} + 17 q^{76} + 21 q^{77} - 64 q^{78} - 10 q^{79} + 31 q^{81} + 22 q^{82} + 14 q^{83} - 32 q^{84} + 37 q^{86} + 29 q^{87} + 9 q^{88} + 15 q^{89} - 22 q^{91} + 26 q^{92} - 18 q^{93} - 44 q^{94} + 71 q^{96} + 8 q^{97} - 10 q^{98} + 15 q^{99}+O(q^{100}) \) 15 * q + 5 * q^2 + 4 * q^3 + 17 * q^4 - q^6 + 21 * q^7 + 9 * q^8 + 15 * q^9 + 15 * q^11 + 11 * q^12 + 13 * q^13 + 9 * q^14 + 21 * q^16 + 17 * q^17 + 22 * q^18 + 15 * q^19 + 6 * q^21 + 5 * q^22 + 26 * q^23 + q^24 + 3 * q^26 + q^27 + 46 * q^28 + 9 * q^29 + 14 * q^31 + 18 * q^32 + 4 * q^33 - 13 * q^34 + 12 * q^36 + 9 * q^37 + 5 * q^38 - 22 * q^39 + 4 * q^41 - 6 * q^42 + 28 * q^43 + 17 * q^44 + 27 * q^46 + 14 * q^47 - 4 * q^48 + 32 * q^49 - 40 * q^51 + 14 * q^52 + 3 * q^53 - 39 * q^54 + 34 * q^56 + 4 * q^57 + 26 * q^58 + q^59 + 2 * q^61 - 3 * q^62 + 45 * q^63 + 5 * q^64 - q^66 + 37 * q^67 + 26 * q^68 - 7 * q^69 - 7 * q^71 + 16 * q^72 + 42 * q^73 - 43 * q^74 + 17 * q^76 + 21 * q^77 - 64 * q^78 - 10 * q^79 + 31 * q^81 + 22 * q^82 + 14 * q^83 - 32 * q^84 + 37 * q^86 + 29 * q^87 + 9 * q^88 + 15 * q^89 - 22 * q^91 + 26 * q^92 - 18 * q^93 - 44 * q^94 + 71 * q^96 + 8 * q^97 - 10 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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