LMFDB - Embedded newform 3525.2.a.y.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 9x^{5} + 6x^{4} + 20x^{3} - 9x^{2} - 12x + 3 $ x^7 - x^6 - 9x^5 + 6x^4 + 20x^3 - 9x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.74386$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74386 q^{2} +1.00000 q^{3} +5.52877 q^{4} -2.74386 q^{6} +1.02926 q^{7} -9.68245 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.74386 q^{2} +1.00000 q^{3} +5.52877 q^{4} -2.74386 q^{6} +1.02926 q^{7} -9.68245 q^{8} +1.00000 q^{9} -0.119464 q^{11} +5.52877 q^{12} -1.18268 q^{13} -2.82415 q^{14} +15.5097 q^{16} -3.82462 q^{17} -2.74386 q^{18} +0.0209452 q^{19} +1.02926 q^{21} +0.327794 q^{22} -1.16967 q^{23} -9.68245 q^{24} +3.24510 q^{26} +1.00000 q^{27} +5.69055 q^{28} -7.97830 q^{29} +8.11526 q^{31} -23.1917 q^{32} -0.119464 q^{33} +10.4942 q^{34} +5.52877 q^{36} -5.42971 q^{37} -0.0574706 q^{38} -1.18268 q^{39} +1.83931 q^{41} -2.82415 q^{42} -1.46685 q^{43} -0.660491 q^{44} +3.20942 q^{46} +1.00000 q^{47} +15.5097 q^{48} -5.94062 q^{49} -3.82462 q^{51} -6.53875 q^{52} +4.92741 q^{53} -2.74386 q^{54} -9.96578 q^{56} +0.0209452 q^{57} +21.8914 q^{58} +10.4035 q^{59} +2.94055 q^{61} -22.2671 q^{62} +1.02926 q^{63} +32.6152 q^{64} +0.327794 q^{66} -5.46626 q^{67} -21.1455 q^{68} -1.16967 q^{69} -7.27290 q^{71} -9.68245 q^{72} -13.6461 q^{73} +14.8984 q^{74} +0.115801 q^{76} -0.122960 q^{77} +3.24510 q^{78} -9.77166 q^{79} +1.00000 q^{81} -5.04681 q^{82} +2.67463 q^{83} +5.69055 q^{84} +4.02483 q^{86} -7.97830 q^{87} +1.15671 q^{88} +1.54211 q^{89} -1.21729 q^{91} -6.46685 q^{92} +8.11526 q^{93} -2.74386 q^{94} -23.1917 q^{96} +0.676142 q^{97} +16.3002 q^{98} -0.119464 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9} - 8 q^{11} + 5 q^{12} - 5 q^{13} - 3 q^{14} + 9 q^{16} - 10 q^{17} - q^{18} + 7 q^{19} - 11 q^{21} - 20 q^{22} - 4 q^{23} - 6 q^{24} + 7 q^{27} - 2 q^{28} - 11 q^{29} + 3 q^{31} - 28 q^{32} - 8 q^{33} + 8 q^{34} + 5 q^{36} - 11 q^{37} + 2 q^{38} - 5 q^{39} - 20 q^{41} - 3 q^{42} - 18 q^{43} + q^{44} - 19 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} - 10 q^{51} - 29 q^{52} - 12 q^{53} - q^{54} - 47 q^{56} + 7 q^{57} + 19 q^{58} + 18 q^{59} - 4 q^{61} - 12 q^{62} - 11 q^{63} + 42 q^{64} - 20 q^{66} - 22 q^{67} - 44 q^{68} - 4 q^{69} - 14 q^{71} - 6 q^{72} - 30 q^{73} + 31 q^{74} - 2 q^{76} + 8 q^{77} - q^{79} + 7 q^{81} - 29 q^{82} - 54 q^{83} - 2 q^{84} - 29 q^{86} - 11 q^{87} + 22 q^{88} - 14 q^{89} + 20 q^{91} + 5 q^{92} + 3 q^{93} - q^{94} - 28 q^{96} - 24 q^{97} + 26 q^{98} - 8 q^{99}+O(q^{100}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9 - 8 * q^11 + 5 * q^12 - 5 * q^13 - 3 * q^14 + 9 * q^16 - 10 * q^17 - q^18 + 7 * q^19 - 11 * q^21 - 20 * q^22 - 4 * q^23 - 6 * q^24 + 7 * q^27 - 2 * q^28 - 11 * q^29 + 3 * q^31 - 28 * q^32 - 8 * q^33 + 8 * q^34 + 5 * q^36 - 11 * q^37 + 2 * q^38 - 5 * q^39 - 20 * q^41 - 3 * q^42 - 18 * q^43 + q^44 - 19 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 - 10 * q^51 - 29 * q^52 - 12 * q^53 - q^54 - 47 * q^56 + 7 * q^57 + 19 * q^58 + 18 * q^59 - 4 * q^61 - 12 * q^62 - 11 * q^63 + 42 * q^64 - 20 * q^66 - 22 * q^67 - 44 * q^68 - 4 * q^69 - 14 * q^71 - 6 * q^72 - 30 * q^73 + 31 * q^74 - 2 * q^76 + 8 * q^77 - q^79 + 7 * q^81 - 29 * q^82 - 54 * q^83 - 2 * q^84 - 29 * q^86 - 11 * q^87 + 22 * q^88 - 14 * q^89 + 20 * q^91 + 5 * q^92 + 3 * q^93 - q^94 - 28 * q^96 - 24 * q^97 + 26 * q^98 - 8 * 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 $

$2$	−2.74386	−1.94020	−0.970101	−	0.242701i	$-0.921967\pi$
$2$	−2.74386	−1.94020	−0.970101	+	0.242701i	$0.921967\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.52877	2.76438
$5$	0	0
$5$	0	0
$6$	−2.74386	−1.12018
$7$	1.02926	0.389025	0.194512	−	0.980900i	$-0.437688\pi$
$7$	1.02926	0.389025	0.194512	+	0.980900i	$0.437688\pi$
$8$	−9.68245	−3.42326
$9$	1.00000	0.333333
$10$	0	0
$11$	−0.119464	−0.0360199	−0.0180099	−	0.999838i	$-0.505733\pi$
$11$	−0.119464	−0.0360199	−0.0180099	+	0.999838i	$0.505733\pi$
$12$	5.52877	1.59602
$13$	−1.18268	−0.328016	−0.164008	−	0.986459i	$-0.552442\pi$
$13$	−1.18268	−0.328016	−0.164008	+	0.986459i	$0.552442\pi$
$14$	−2.82415	−0.754786
$15$	0	0
$16$	15.5097	3.87744
$17$	−3.82462	−0.927607	−0.463804	−	0.885938i	$-0.653516\pi$
$17$	−3.82462	−0.927607	−0.463804	+	0.885938i	$0.653516\pi$
$18$	−2.74386	−0.646734
$19$	0.0209452	0.00480515	0.00240258	−	0.999997i	$-0.499235\pi$
$19$	0.0209452	0.00480515	0.00240258	+	0.999997i	$0.499235\pi$
$20$	0	0
$21$	1.02926	0.224603
$22$	0.327794	0.0698858
$23$	−1.16967	−0.243893	−0.121947	−	0.992537i	$-0.538914\pi$
$23$	−1.16967	−0.243893	−0.121947	+	0.992537i	$0.538914\pi$
$24$	−9.68245	−1.97642
$25$	0	0
$26$	3.24510	0.636417
$27$	1.00000	0.192450
$28$	5.69055	1.07541
$29$	−7.97830	−1.48153	−0.740767	−	0.671762i	$-0.765538\pi$
$29$	−7.97830	−1.48153	−0.740767	+	0.671762i	$0.765538\pi$
$30$	0	0
$31$	8.11526	1.45754	0.728771	−	0.684757i	$-0.240092\pi$
$31$	8.11526	1.45754	0.728771	+	0.684757i	$0.240092\pi$
$32$	−23.1917	−4.09975
$33$	−0.119464	−0.0207961
$34$	10.4942	1.79975
$35$	0	0
$36$	5.52877	0.921462
$37$	−5.42971	−0.892638	−0.446319	−	0.894874i	$-0.647265\pi$
$37$	−5.42971	−0.892638	−0.446319	+	0.894874i	$0.647265\pi$
$38$	−0.0574706	−0.00932297
$39$	−1.18268	−0.189380
$40$	0	0
$41$	1.83931	0.287252	0.143626	−	0.989632i	$-0.454124\pi$
$41$	1.83931	0.287252	0.143626	+	0.989632i	$0.454124\pi$
$42$	−2.82415	−0.435776
$43$	−1.46685	−0.223692	−0.111846	−	0.993726i	$-0.535676\pi$
$43$	−1.46685	−0.223692	−0.111846	+	0.993726i	$0.535676\pi$
$44$	−0.660491	−0.0995728
$45$	0	0
$46$	3.20942	0.473203
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	15.5097	2.23864
$49$	−5.94062	−0.848660
$50$	0	0
$51$	−3.82462	−0.535554
$52$	−6.53875	−0.906761
$53$	4.92741	0.676832	0.338416	−	0.940997i	$-0.390109\pi$
$53$	4.92741	0.676832	0.338416	+	0.940997i	$0.390109\pi$
$54$	−2.74386	−0.373392
$55$	0	0
$56$	−9.96578	−1.33173
$57$	0.0209452	0.00277426
$58$	21.8914	2.87448
$59$	10.4035	1.35442	0.677212	−	0.735788i	$-0.263188\pi$
$59$	10.4035	1.35442	0.677212	+	0.735788i	$0.263188\pi$
$60$	0	0
$61$	2.94055	0.376499	0.188249	−	0.982121i	$-0.439719\pi$
$61$	2.94055	0.376499	0.188249	+	0.982121i	$0.439719\pi$
$62$	−22.2671	−2.82793
$63$	1.02926	0.129675
$64$	32.6152	4.07691
$65$	0	0
$66$	0.327794	0.0403486
$67$	−5.46626	−0.667810	−0.333905	−	0.942607i	$-0.608367\pi$
$67$	−5.46626	−0.667810	−0.333905	+	0.942607i	$0.608367\pi$
$68$	−21.1455	−2.56426
$69$	−1.16967	−0.140812
$70$	0	0
$71$	−7.27290	−0.863134	−0.431567	−	0.902081i	$-0.642039\pi$
$71$	−7.27290	−0.863134	−0.431567	+	0.902081i	$0.642039\pi$
$72$	−9.68245	−1.14109
$73$	−13.6461	−1.59716	−0.798579	−	0.601890i	$-0.794415\pi$
$73$	−13.6461	−1.59716	−0.798579	+	0.601890i	$0.794415\pi$
$74$	14.8984	1.73190
$75$	0	0
$76$	0.115801	0.0132833
$77$	−0.122960	−0.0140126
$78$	3.24510	0.367435
$79$	−9.77166	−1.09940	−0.549699	−	0.835363i	$-0.685258\pi$
$79$	−9.77166	−1.09940	−0.549699	+	0.835363i	$0.685258\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−5.04681	−0.557327
$83$	2.67463	0.293579	0.146790	−	0.989168i	$-0.453106\pi$
$83$	2.67463	0.293579	0.146790	+	0.989168i	$0.453106\pi$
$84$	5.69055	0.620890
$85$	0	0
$86$	4.02483	0.434009
$87$	−7.97830	−0.855364
$88$	1.15671	0.123305
$89$	1.54211	0.163464	0.0817319	−	0.996654i	$-0.473955\pi$
$89$	1.54211	0.163464	0.0817319	+	0.996654i	$0.473955\pi$
$90$	0	0
$91$	−1.21729	−0.127606
$92$	−6.46685	−0.674215
$93$	8.11526	0.841513
$94$	−2.74386	−0.283008
$95$	0	0
$96$	−23.1917	−2.36699
$97$	0.676142	0.0686518	0.0343259	−	0.999411i	$-0.489072\pi$
$97$	0.676142	0.0686518	0.0343259	+	0.999411i	$0.489072\pi$
$98$	16.3002	1.64657
$99$	−0.119464	−0.0120066
$100$	0	0
$101$	−17.8048	−1.77164	−0.885820	−	0.464029i	$-0.846403\pi$
$101$	−17.8048	−1.77164	−0.885820	+	0.464029i	$0.846403\pi$
$102$	10.4942	1.03908
$103$	7.63174	0.751977	0.375989	−	0.926624i	$-0.377303\pi$
$103$	7.63174	0.751977	0.375989	+	0.926624i	$0.377303\pi$
$104$	11.4512	1.12288
$105$	0	0
$106$	−13.5201	−1.31319
$107$	−18.7845	−1.81596	−0.907982	−	0.419009i	$-0.862378\pi$
$107$	−18.7845	−1.81596	−0.907982	+	0.419009i	$0.862378\pi$
$108$	5.52877	0.532006
$109$	−3.80223	−0.364188	−0.182094	−	0.983281i	$-0.558287\pi$
$109$	−3.80223	−0.364188	−0.182094	+	0.983281i	$0.558287\pi$
$110$	0	0
$111$	−5.42971	−0.515365
$112$	15.9636	1.50842
$113$	−6.32238	−0.594759	−0.297380	−	0.954759i	$-0.596113\pi$
$113$	−6.32238	−0.594759	−0.297380	+	0.954759i	$0.596113\pi$
$114$	−0.0574706	−0.00538262
$115$	0	0
$116$	−44.1102	−4.09553
$117$	−1.18268	−0.109339
$118$	−28.5458	−2.62786
$119$	−3.93654	−0.360862
$120$	0	0
$121$	−10.9857	−0.998703
$122$	−8.06845	−0.730483
$123$	1.83931	0.165845
$124$	44.8674	4.02921
$125$	0	0
$126$	−2.82415	−0.251595
$127$	6.49751	0.576560	0.288280	−	0.957546i	$-0.406917\pi$
$127$	6.49751	0.576560	0.288280	+	0.957546i	$0.406917\pi$
$128$	−43.1083	−3.81027
$129$	−1.46685	−0.129149
$130$	0	0
$131$	9.16211	0.800497	0.400249	−	0.916407i	$-0.368924\pi$
$131$	9.16211	0.800497	0.400249	+	0.916407i	$0.368924\pi$
$132$	−0.660491	−0.0574884
$133$	0.0215581	0.00186932
$134$	14.9987	1.29569
$135$	0	0
$136$	37.0317	3.17544
$137$	−17.8989	−1.52920	−0.764602	−	0.644503i	$-0.777064\pi$
$137$	−17.8989	−1.52920	−0.764602	+	0.644503i	$0.777064\pi$
$138$	3.20942	0.273204
$139$	17.8190	1.51139	0.755693	−	0.654926i	$-0.227300\pi$
$139$	17.8190	1.51139	0.755693	+	0.654926i	$0.227300\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	19.9558	1.67465
$143$	0.141288	0.0118151
$144$	15.5097	1.29248
$145$	0	0
$146$	37.4431	3.09881
$147$	−5.94062	−0.489974
$148$	−30.0196	−2.46760
$149$	−21.3872	−1.75211	−0.876055	−	0.482210i	$-0.839834\pi$
$149$	−21.3872	−1.75211	−0.876055	+	0.482210i	$0.839834\pi$
$150$	0	0
$151$	−22.4370	−1.82590	−0.912948	−	0.408076i	$-0.866200\pi$
$151$	−22.4370	−1.82590	−0.912948	+	0.408076i	$0.866200\pi$
$152$	−0.202801	−0.0164493
$153$	−3.82462	−0.309202
$154$	0.337386	0.0271873
$155$	0	0
$156$	−6.53875	−0.523519
$157$	8.89749	0.710097	0.355048	−	0.934848i	$-0.384464\pi$
$157$	8.89749	0.710097	0.355048	+	0.934848i	$0.384464\pi$
$158$	26.8121	2.13305
$159$	4.92741	0.390769
$160$	0	0
$161$	−1.20390	−0.0948806
$162$	−2.74386	−0.215578
$163$	13.1961	1.03360	0.516799	−	0.856107i	$-0.327123\pi$
$163$	13.1961	1.03360	0.516799	+	0.856107i	$0.327123\pi$
$164$	10.1691	0.794075
$165$	0	0
$166$	−7.33882	−0.569603
$167$	1.84498	0.142769	0.0713846	−	0.997449i	$-0.477258\pi$
$167$	1.84498	0.142769	0.0713846	+	0.997449i	$0.477258\pi$
$168$	−9.96578	−0.768877
$169$	−11.6013	−0.892406
$170$	0	0
$171$	0.0209452	0.00160172
$172$	−8.10987	−0.618372
$173$	14.4845	1.10124	0.550619	−	0.834757i	$-0.314392\pi$
$173$	14.4845	1.10124	0.550619	+	0.834757i	$0.314392\pi$
$174$	21.8914	1.65958
$175$	0	0
$176$	−1.85286	−0.139665
$177$	10.4035	0.781977
$178$	−4.23134	−0.317153
$179$	−9.67242	−0.722950	−0.361475	−	0.932382i	$-0.617727\pi$
$179$	−9.67242	−0.722950	−0.361475	+	0.932382i	$0.617727\pi$
$180$	0	0
$181$	10.3164	0.766815	0.383407	−	0.923579i	$-0.374751\pi$
$181$	10.3164	0.766815	0.383407	+	0.923579i	$0.374751\pi$
$182$	3.34006	0.247582
$183$	2.94055	0.217372
$184$	11.3253	0.834911
$185$	0	0
$186$	−22.2671	−1.63270
$187$	0.456906	0.0334123
$188$	5.52877	0.403227
$189$	1.02926	0.0748678
$190$	0	0
$191$	13.6002	0.984076	0.492038	−	0.870574i	$-0.336252\pi$
$191$	13.6002	0.984076	0.492038	+	0.870574i	$0.336252\pi$
$192$	32.6152	2.35380
$193$	6.62965	0.477212	0.238606	−	0.971116i	$-0.423309\pi$
$193$	6.62965	0.477212	0.238606	+	0.971116i	$0.423309\pi$
$194$	−1.85524	−0.133198
$195$	0	0
$196$	−32.8443	−2.34602
$197$	−10.4131	−0.741903	−0.370951	−	0.928652i	$-0.620968\pi$
$197$	−10.4131	−0.741903	−0.370951	+	0.928652i	$0.620968\pi$
$198$	0.327794	0.0232953
$199$	−8.50826	−0.603135	−0.301567	−	0.953445i	$-0.597510\pi$
$199$	−8.50826	−0.603135	−0.301567	+	0.953445i	$0.597510\pi$
$200$	0	0
$201$	−5.46626	−0.385560
$202$	48.8538	3.43734
$203$	−8.21177	−0.576353
$204$	−21.1455	−1.48048
$205$	0	0
$206$	−20.9404	−1.45899
$207$	−1.16967	−0.0812978
$208$	−18.3430	−1.27186
$209$	−0.00250220	−0.000173081 0
$210$	0	0
$211$	24.2932	1.67241	0.836207	−	0.548413i	$-0.184768\pi$
$211$	24.2932	1.67241	0.836207	+	0.548413i	$0.184768\pi$
$212$	27.2425	1.87102
$213$	−7.27290	−0.498331
$214$	51.5420	3.52334
$215$	0	0
$216$	−9.68245	−0.658807
$217$	8.35273	0.567020
$218$	10.4328	0.706598
$219$	−13.6461	−0.922120
$220$	0	0
$221$	4.52330	0.304270
$222$	14.8984	0.999912
$223$	4.67537	0.313086	0.156543	−	0.987671i	$-0.449965\pi$
$223$	4.67537	0.313086	0.156543	+	0.987671i	$0.449965\pi$
$224$	−23.8703	−1.59490
$225$	0	0
$226$	17.3477	1.15395
$227$	6.34164	0.420909	0.210455	−	0.977604i	$-0.432506\pi$
$227$	6.34164	0.420909	0.210455	+	0.977604i	$0.432506\pi$
$228$	0.115801	0.00766911
$229$	−13.7153	−0.906334	−0.453167	−	0.891426i	$-0.649706\pi$
$229$	−13.7153	−0.906334	−0.453167	+	0.891426i	$0.649706\pi$
$230$	0	0
$231$	−0.122960	−0.00809019
$232$	77.2495	5.07168
$233$	15.9565	1.04535	0.522674	−	0.852533i	$-0.324934\pi$
$233$	15.9565	1.04535	0.522674	+	0.852533i	$0.324934\pi$
$234$	3.24510	0.212139
$235$	0	0
$236$	57.5187	3.74415
$237$	−9.77166	−0.634738
$238$	10.8013	0.700146
$239$	−10.4112	−0.673445	−0.336723	−	0.941604i	$-0.609318\pi$
$239$	−10.4112	−0.673445	−0.336723	+	0.941604i	$0.609318\pi$
$240$	0	0
$241$	−10.1087	−0.651159	−0.325579	−	0.945515i	$-0.605559\pi$
$241$	−10.1087	−0.651159	−0.325579	+	0.945515i	$0.605559\pi$
$242$	30.1433	1.93768
$243$	1.00000	0.0641500
$244$	16.2576	1.04079
$245$	0	0
$246$	−5.04681	−0.321773
$247$	−0.0247714	−0.00157617
$248$	−78.5756	−4.98955
$249$	2.67463	0.169498
$250$	0	0
$251$	−16.8366	−1.06272	−0.531360	−	0.847146i	$-0.678319\pi$
$251$	−16.8366	−1.06272	−0.531360	+	0.847146i	$0.678319\pi$
$252$	5.69055	0.358471
$253$	0.139734	0.00878501
$254$	−17.8283	−1.11864
$255$	0	0
$256$	53.0527	3.31579
$257$	10.9742	0.684554	0.342277	−	0.939599i	$-0.388802\pi$
$257$	10.9742	0.684554	0.342277	+	0.939599i	$0.388802\pi$
$258$	4.02483	0.250575
$259$	−5.58859	−0.347258
$260$	0	0
$261$	−7.97830	−0.493845
$262$	−25.1396	−1.55313
$263$	23.3186	1.43788	0.718942	−	0.695070i	$-0.244627\pi$
$263$	23.3186	1.43788	0.718942	+	0.695070i	$0.244627\pi$
$264$	1.15671	0.0711905
$265$	0	0
$266$	−0.0591524	−0.00362686
$267$	1.54211	0.0943758
$268$	−30.2217	−1.84608
$269$	−6.40443	−0.390485	−0.195243	−	0.980755i	$-0.562549\pi$
$269$	−6.40443	−0.390485	−0.195243	+	0.980755i	$0.562549\pi$
$270$	0	0
$271$	11.1005	0.674307	0.337154	−	0.941450i	$-0.390536\pi$
$271$	11.1005	0.674307	0.337154	+	0.941450i	$0.390536\pi$
$272$	−59.3190	−3.59674
$273$	−1.21729	−0.0736735
$274$	49.1120	2.96696
$275$	0	0
$276$	−6.46685	−0.389258
$277$	0.445143	0.0267461	0.0133730	−	0.999911i	$-0.495743\pi$
$277$	0.445143	0.0267461	0.0133730	+	0.999911i	$0.495743\pi$
$278$	−48.8928	−2.93239
$279$	8.11526	0.485848
$280$	0	0
$281$	1.29722	0.0773854	0.0386927	−	0.999251i	$-0.487681\pi$
$281$	1.29722	0.0773854	0.0386927	+	0.999251i	$0.487681\pi$
$282$	−2.74386	−0.163395
$283$	−15.0364	−0.893820	−0.446910	−	0.894579i	$-0.647476\pi$
$283$	−15.0364	−0.893820	−0.446910	+	0.894579i	$0.647476\pi$
$284$	−40.2102	−2.38603
$285$	0	0
$286$	−0.387674	−0.0229236
$287$	1.89313	0.111748
$288$	−23.1917	−1.36658
$289$	−2.37225	−0.139544
$290$	0	0
$291$	0.676142	0.0396362
$292$	−75.4463	−4.41516
$293$	30.8308	1.80116	0.900578	−	0.434695i	$-0.143144\pi$
$293$	30.8308	1.80116	0.900578	+	0.434695i	$0.143144\pi$
$294$	16.3002	0.950649
$295$	0	0
$296$	52.5729	3.05574
$297$	−0.119464	−0.00693203
$298$	58.6836	3.39945
$299$	1.38334	0.0800009
$300$	0	0
$301$	−1.50977	−0.0870219
$302$	61.5639	3.54261
$303$	−17.8048	−1.02286
$304$	0.324854	0.0186317
$305$	0	0
$306$	10.4942	0.599915
$307$	−33.4248	−1.90766	−0.953828	−	0.300353i	$-0.902896\pi$
$307$	−33.4248	−1.90766	−0.953828	+	0.300353i	$0.902896\pi$
$308$	−0.679819	−0.0387363
$309$	7.63174	0.434154
$310$	0	0
$311$	22.9768	1.30290	0.651448	−	0.758693i	$-0.274162\pi$
$311$	22.9768	1.30290	0.651448	+	0.758693i	$0.274162\pi$
$312$	11.4512	0.648297
$313$	3.86668	0.218558	0.109279	−	0.994011i	$-0.465146\pi$
$313$	3.86668	0.218558	0.109279	+	0.994011i	$0.465146\pi$
$314$	−24.4135	−1.37773
$315$	0	0
$316$	−54.0253	−3.03916
$317$	−8.18916	−0.459949	−0.229975	−	0.973197i	$-0.573864\pi$
$317$	−8.18916	−0.459949	−0.229975	+	0.973197i	$0.573864\pi$
$318$	−13.5201	−0.758171
$319$	0.953123	0.0533647
$320$	0	0
$321$	−18.7845	−1.04845
$322$	3.30333	0.184087
$323$	−0.0801074	−0.00445729
$324$	5.52877	0.307154
$325$	0	0
$326$	−36.2082	−2.00539
$327$	−3.80223	−0.210264
$328$	−17.8090	−0.983340
$329$	1.02926	0.0567451
$330$	0	0
$331$	−27.7818	−1.52703	−0.763513	−	0.645793i	$-0.776527\pi$
$331$	−27.7818	−1.52703	−0.763513	+	0.645793i	$0.776527\pi$
$332$	14.7874	0.811566
$333$	−5.42971	−0.297546
$334$	−5.06238	−0.277001
$335$	0	0
$336$	15.9636	0.870886
$337$	−14.2990	−0.778915	−0.389458	−	0.921044i	$-0.627338\pi$
$337$	−14.2990	−0.778915	−0.389458	+	0.921044i	$0.627338\pi$
$338$	31.8323	1.73145
$339$	−6.32238	−0.343384
$340$	0	0
$341$	−0.969484	−0.0525005
$342$	−0.0574706	−0.00310766
$343$	−13.3193	−0.719174
$344$	14.2027	0.765758
$345$	0	0
$346$	−39.7435	−2.13662
$347$	5.94837	0.319325	0.159663	−	0.987172i	$-0.448959\pi$
$347$	5.94837	0.319325	0.159663	+	0.987172i	$0.448959\pi$
$348$	−44.1102	−2.36455
$349$	14.7729	0.790777	0.395388	−	0.918514i	$-0.370610\pi$
$349$	14.7729	0.790777	0.395388	+	0.918514i	$0.370610\pi$
$350$	0	0
$351$	−1.18268	−0.0631266
$352$	2.77058	0.147672
$353$	25.9975	1.38371	0.691854	−	0.722037i	$-0.256794\pi$
$353$	25.9975	1.38371	0.691854	+	0.722037i	$0.256794\pi$
$354$	−28.5458	−1.51719
$355$	0	0
$356$	8.52599	0.451877
$357$	−3.93654	−0.208344
$358$	26.5398	1.40267
$359$	−23.3262	−1.23111	−0.615556	−	0.788093i	$-0.711068\pi$
$359$	−23.3262	−1.23111	−0.615556	+	0.788093i	$0.711068\pi$
$360$	0	0
$361$	−18.9996	−0.999977
$362$	−28.3069	−1.48778
$363$	−10.9857	−0.576601
$364$	−6.73009	−0.352753
$365$	0	0
$366$	−8.06845	−0.421745
$367$	−29.2782	−1.52831	−0.764155	−	0.645033i	$-0.776844\pi$
$367$	−29.2782	−1.52831	−0.764155	+	0.645033i	$0.776844\pi$
$368$	−18.1413	−0.945682
$369$	1.83931	0.0957507
$370$	0	0
$371$	5.07160	0.263304
$372$	44.8674	2.32626
$373$	−23.8764	−1.23627	−0.618137	−	0.786070i	$-0.712112\pi$
$373$	−23.8764	−1.23627	−0.618137	+	0.786070i	$0.712112\pi$
$374$	−1.25369	−0.0648266
$375$	0	0
$376$	−9.68245	−0.499334
$377$	9.43576	0.485966
$378$	−2.82415	−0.145259
$379$	−12.0075	−0.616785	−0.308392	−	0.951259i	$-0.599791\pi$
$379$	−12.0075	−0.616785	−0.308392	+	0.951259i	$0.599791\pi$
$380$	0	0
$381$	6.49751	0.332877
$382$	−37.3170	−1.90931
$383$	−22.1802	−1.13335	−0.566677	−	0.823940i	$-0.691771\pi$
$383$	−22.1802	−1.13335	−0.566677	+	0.823940i	$0.691771\pi$
$384$	−43.1083	−2.19986
$385$	0	0
$386$	−18.1908	−0.925889
$387$	−1.46685	−0.0745641
$388$	3.73823	0.189780
$389$	−18.6898	−0.947611	−0.473806	−	0.880629i	$-0.657120\pi$
$389$	−18.6898	−0.947611	−0.473806	+	0.880629i	$0.657120\pi$
$390$	0	0
$391$	4.47355	0.226237
$392$	57.5197	2.90519
$393$	9.16211	0.462167
$394$	28.5721	1.43944
$395$	0	0
$396$	−0.660491	−0.0331909
$397$	−34.0417	−1.70850	−0.854251	−	0.519861i	$-0.825984\pi$
$397$	−34.0417	−1.70850	−0.854251	+	0.519861i	$0.825984\pi$
$398$	23.3455	1.17020
$399$	0.0215581	0.00107925
$400$	0	0
$401$	−23.4122	−1.16915	−0.584576	−	0.811339i	$-0.698739\pi$
$401$	−23.4122	−1.16915	−0.584576	+	0.811339i	$0.698739\pi$
$402$	14.9987	0.748065
$403$	−9.59773	−0.478097
$404$	−98.4384	−4.89749
$405$	0	0
$406$	22.5319	1.11824
$407$	0.648657	0.0321527
$408$	37.0317	1.83334
$409$	−19.2139	−0.950065	−0.475033	−	0.879968i	$-0.657564\pi$
$409$	−19.2139	−0.950065	−0.475033	+	0.879968i	$0.657564\pi$
$410$	0	0
$411$	−17.8989	−0.882886
$412$	42.1941	2.07875
$413$	10.7080	0.526904
$414$	3.20942	0.157734
$415$	0	0
$416$	27.4283	1.34478
$417$	17.8190	0.872599
$418$	0.00686569	0.000335812 0
$419$	0.619132	0.0302466	0.0151233	−	0.999886i	$-0.495186\pi$
$419$	0.619132	0.0302466	0.0151233	+	0.999886i	$0.495186\pi$
$420$	0	0
$421$	−16.6146	−0.809744	−0.404872	−	0.914373i	$-0.632684\pi$
$421$	−16.6146	−0.809744	−0.404872	+	0.914373i	$0.632684\pi$
$422$	−66.6572	−3.24482
$423$	1.00000	0.0486217
$424$	−47.7094	−2.31697
$425$	0	0
$426$	19.9558	0.966862
$427$	3.02660	0.146467
$428$	−103.855	−5.02002
$429$	0.141288	0.00682144
$430$	0	0
$431$	−31.3125	−1.50827	−0.754135	−	0.656719i	$-0.771944\pi$
$431$	−31.3125	−1.50827	−0.754135	+	0.656719i	$0.771944\pi$
$432$	15.5097	0.746213
$433$	26.8103	1.28842	0.644210	−	0.764848i	$-0.277186\pi$
$433$	26.8103	1.28842	0.644210	+	0.764848i	$0.277186\pi$
$434$	−22.9187	−1.10013
$435$	0	0
$436$	−21.0217	−1.00675
$437$	−0.0244990	−0.00117195
$438$	37.4431	1.78910
$439$	19.8688	0.948286	0.474143	−	0.880448i	$-0.342758\pi$
$439$	19.8688	0.948286	0.474143	+	0.880448i	$0.342758\pi$
$440$	0	0
$441$	−5.94062	−0.282887
$442$	−12.4113	−0.590345
$443$	−13.0757	−0.621248	−0.310624	−	0.950533i	$-0.600538\pi$
$443$	−13.0757	−0.621248	−0.310624	+	0.950533i	$0.600538\pi$
$444$	−30.0196	−1.42467
$445$	0	0
$446$	−12.8286	−0.607450
$447$	−21.3872	−1.01158
$448$	33.5696	1.58602
$449$	19.5039	0.920447	0.460223	−	0.887803i	$-0.347769\pi$
$449$	19.5039	0.920447	0.460223	+	0.887803i	$0.347769\pi$
$450$	0	0
$451$	−0.219732	−0.0103468
$452$	−34.9550	−1.64414
$453$	−22.4370	−1.05418
$454$	−17.4006	−0.816649
$455$	0	0
$456$	−0.202801	−0.00949701
$457$	40.2483	1.88274	0.941369	−	0.337380i	$-0.109541\pi$
$457$	40.2483	1.88274	0.941369	+	0.337380i	$0.109541\pi$
$458$	37.6329	1.75847
$459$	−3.82462	−0.178518
$460$	0	0
$461$	27.1740	1.26562	0.632809	−	0.774308i	$-0.281902\pi$
$461$	27.1740	1.26562	0.632809	+	0.774308i	$0.281902\pi$
$462$	0.337386	0.0156966
$463$	−27.2565	−1.26672	−0.633358	−	0.773859i	$-0.718324\pi$
$463$	−27.2565	−1.26672	−0.633358	+	0.773859i	$0.718324\pi$
$464$	−123.741	−5.74455
$465$	0	0
$466$	−43.7825	−2.02819
$467$	12.3100	0.569638	0.284819	−	0.958581i	$-0.408066\pi$
$467$	12.3100	0.569638	0.284819	+	0.958581i	$0.408066\pi$
$468$	−6.53875	−0.302254
$469$	−5.62622	−0.259795
$470$	0	0
$471$	8.89749	0.409975
$472$	−100.732	−4.63655
$473$	0.175236	0.00805737
$474$	26.8121	1.23152
$475$	0	0
$476$	−21.7642	−0.997562
$477$	4.92741	0.225611
$478$	28.5669	1.30662
$479$	13.7400	0.627795	0.313898	−	0.949457i	$-0.398365\pi$
$479$	13.7400	0.627795	0.313898	+	0.949457i	$0.398365\pi$
$480$	0	0
$481$	6.42159	0.292799
$482$	27.7369	1.26338
$483$	−1.20390	−0.0547793
$484$	−60.7376	−2.76080
$485$	0	0
$486$	−2.74386	−0.124464
$487$	25.6917	1.16420	0.582101	−	0.813117i	$-0.302231\pi$
$487$	25.6917	1.16420	0.582101	+	0.813117i	$0.302231\pi$
$488$	−28.4717	−1.28885
$489$	13.1961	0.596748
$490$	0	0
$491$	17.3987	0.785192	0.392596	−	0.919711i	$-0.371577\pi$
$491$	17.3987	0.785192	0.392596	+	0.919711i	$0.371577\pi$
$492$	10.1691	0.458460
$493$	30.5140	1.37428
$494$	0.0679692	0.00305808
$495$	0	0
$496$	125.866	5.65153
$497$	−7.48572	−0.335780
$498$	−7.33882	−0.328860
$499$	−5.07529	−0.227201	−0.113600	−	0.993527i	$-0.536238\pi$
$499$	−5.07529	−0.227201	−0.113600	+	0.993527i	$0.536238\pi$
$500$	0	0
$501$	1.84498	0.0824278
$502$	46.1974	2.06189
$503$	38.4339	1.71368	0.856842	−	0.515578i	$-0.172423\pi$
$503$	38.4339	1.71368	0.856842	+	0.515578i	$0.172423\pi$
$504$	−9.96578	−0.443911
$505$	0	0
$506$	−0.383411	−0.0170447
$507$	−11.6013	−0.515231
$508$	35.9232	1.59383
$509$	−40.5514	−1.79741	−0.898705	−	0.438553i	$-0.855491\pi$
$509$	−40.5514	−1.79741	−0.898705	+	0.438553i	$0.855491\pi$
$510$	0	0
$511$	−14.0454	−0.621334
$512$	−59.3525	−2.62304
$513$	0.0209452	0.000924752 0
$514$	−30.1118	−1.32817
$515$	0	0
$516$	−8.10987	−0.357017
$517$	−0.119464	−0.00525404
$518$	15.3343	0.673751
$519$	14.4845	0.635800
$520$	0	0
$521$	39.3658	1.72465	0.862324	−	0.506356i	$-0.169008\pi$
$521$	39.3658	1.72465	0.862324	+	0.506356i	$0.169008\pi$
$522$	21.8914	0.958158
$523$	−33.9088	−1.48273	−0.741364	−	0.671104i	$-0.765821\pi$
$523$	−33.9088	−1.48273	−0.741364	+	0.671104i	$0.765821\pi$
$524$	50.6552	2.21288
$525$	0	0
$526$	−63.9829	−2.78979
$527$	−31.0378	−1.35203
$528$	−1.85286	−0.0806355
$529$	−21.6319	−0.940516
$530$	0	0
$531$	10.4035	0.451475
$532$	0.119190	0.00516753
$533$	−2.17531	−0.0942232
$534$	−4.23134	−0.183108
$535$	0	0
$536$	52.9268	2.28609
$537$	−9.67242	−0.417396
$538$	17.5729	0.757620
$539$	0.709692	0.0305686
$540$	0	0
$541$	12.9039	0.554781	0.277390	−	0.960757i	$-0.410530\pi$
$541$	12.9039	0.554781	0.277390	+	0.960757i	$0.410530\pi$
$542$	−30.4582	−1.30829
$543$	10.3164	0.442721
$544$	88.6995	3.80296
$545$	0	0
$546$	3.34006	0.142941
$547$	−3.89151	−0.166389	−0.0831945	−	0.996533i	$-0.526512\pi$
$547$	−3.89151	−0.166389	−0.0831945	+	0.996533i	$0.526512\pi$
$548$	−98.9587	−4.22731
$549$	2.94055	0.125500
$550$	0	0
$551$	−0.167107	−0.00711900
$552$	11.3253	0.482036
$553$	−10.0576	−0.427693
$554$	−1.22141	−0.0518928
$555$	0	0
$556$	98.5170	4.17805
$557$	−32.3464	−1.37056	−0.685280	−	0.728279i	$-0.740320\pi$
$557$	−32.3464	−1.37056	−0.685280	+	0.728279i	$0.740320\pi$
$558$	−22.2671	−0.942643
$559$	1.73481	0.0733746
$560$	0	0
$561$	0.456906	0.0192906
$562$	−3.55938	−0.150143
$563$	−26.4574	−1.11504	−0.557522	−	0.830162i	$-0.688248\pi$
$563$	−26.4574	−1.11504	−0.557522	+	0.830162i	$0.688248\pi$
$564$	5.52877	0.232803
$565$	0	0
$566$	41.2577	1.73419
$567$	1.02926	0.0432250
$568$	70.4195	2.95474
$569$	−33.4921	−1.40406	−0.702030	−	0.712147i	$-0.747723\pi$
$569$	−33.4921	−1.40406	−0.702030	+	0.712147i	$0.747723\pi$
$570$	0	0
$571$	−34.7609	−1.45470	−0.727349	−	0.686268i	$-0.759248\pi$
$571$	−34.7609	−1.45470	−0.727349	+	0.686268i	$0.759248\pi$
$572$	0.781148	0.0326614
$573$	13.6002	0.568156
$574$	−5.19449	−0.216814
$575$	0	0
$576$	32.6152	1.35897
$577$	−25.8358	−1.07556	−0.537779	−	0.843086i	$-0.680737\pi$
$577$	−25.8358	−1.07556	−0.537779	+	0.843086i	$0.680737\pi$
$578$	6.50914	0.270744
$579$	6.62965	0.275519
$580$	0	0
$581$	2.75290	0.114210
$582$	−1.85524	−0.0769022
$583$	−0.588650	−0.0243794
$584$	132.128	5.46749
$585$	0	0
$586$	−84.5955	−3.49461
$587$	13.4975	0.557102	0.278551	−	0.960421i	$-0.410146\pi$
$587$	13.4975	0.557102	0.278551	+	0.960421i	$0.410146\pi$
$588$	−32.8443	−1.35448
$589$	0.169975	0.00700372
$590$	0	0
$591$	−10.4131	−0.428338
$592$	−84.2134	−3.46115
$593$	−6.54000	−0.268566	−0.134283	−	0.990943i	$-0.542873\pi$
$593$	−6.54000	−0.268566	−0.134283	+	0.990943i	$0.542873\pi$
$594$	0.327794	0.0134495
$595$	0	0
$596$	−118.245	−4.84351
$597$	−8.50826	−0.348220
$598$	−3.79570	−0.155218
$599$	9.05655	0.370041	0.185020	−	0.982735i	$-0.440765\pi$
$599$	9.05655	0.370041	0.185020	+	0.982735i	$0.440765\pi$
$600$	0	0
$601$	7.79075	0.317791	0.158896	−	0.987295i	$-0.449207\pi$
$601$	7.79075	0.317791	0.158896	+	0.987295i	$0.449207\pi$
$602$	4.14261	0.168840
$603$	−5.46626	−0.222603
$604$	−124.049	−5.04748
$605$	0	0
$606$	48.8538	1.98455
$607$	31.9151	1.29539	0.647697	−	0.761898i	$-0.275732\pi$
$607$	31.9151	1.29539	0.647697	+	0.761898i	$0.275732\pi$
$608$	−0.485754	−0.0196999
$609$	−8.21177	−0.332758
$610$	0	0
$611$	−1.18268	−0.0478460
$612$	−21.1455	−0.854755
$613$	−8.31660	−0.335905	−0.167952	−	0.985795i	$-0.553715\pi$
$613$	−8.31660	−0.335905	−0.167952	+	0.985795i	$0.553715\pi$
$614$	91.7131	3.70124
$615$	0	0
$616$	1.19056	0.0479689
$617$	−8.50251	−0.342298	−0.171149	−	0.985245i	$-0.554748\pi$
$617$	−8.50251	−0.342298	−0.171149	+	0.985245i	$0.554748\pi$
$618$	−20.9404	−0.842347
$619$	5.12854	0.206133	0.103067	−	0.994674i	$-0.467134\pi$
$619$	5.12854	0.206133	0.103067	+	0.994674i	$0.467134\pi$
$620$	0	0
$621$	−1.16967	−0.0469373
$622$	−63.0452	−2.52788
$623$	1.58724	0.0635914
$624$	−18.3430	−0.734309
$625$	0	0
$626$	−10.6096	−0.424046
$627$	−0.00250220	−9.99283e−5 0
$628$	49.1922	1.96298
$629$	20.7666	0.828018
$630$	0	0
$631$	31.7926	1.26564	0.632822	−	0.774298i	$-0.281897\pi$
$631$	31.7926	1.26564	0.632822	+	0.774298i	$0.281897\pi$
$632$	94.6136	3.76353
$633$	24.2932	0.965569
$634$	22.4699	0.892394
$635$	0	0
$636$	27.2425	1.08024
$637$	7.02584	0.278374
$638$	−2.61524	−0.103538
$639$	−7.27290	−0.287711
$640$	0	0
$641$	19.7742	0.781035	0.390518	−	0.920595i	$-0.372296\pi$
$641$	19.7742	0.781035	0.390518	+	0.920595i	$0.372296\pi$
$642$	51.5420	2.03420
$643$	−6.37909	−0.251567	−0.125783	−	0.992058i	$-0.540144\pi$
$643$	−6.37909	−0.251567	−0.125783	+	0.992058i	$0.540144\pi$
$644$	−6.65608	−0.262286
$645$	0	0
$646$	0.219804	0.00864805
$647$	−23.1894	−0.911671	−0.455836	−	0.890064i	$-0.650660\pi$
$647$	−23.1894	−0.911671	−0.455836	+	0.890064i	$0.650660\pi$
$648$	−9.68245	−0.380363
$649$	−1.24285	−0.0487862
$650$	0	0
$651$	8.35273	0.327369
$652$	72.9582	2.85726
$653$	−20.8605	−0.816336	−0.408168	−	0.912907i	$-0.633832\pi$
$653$	−20.8605	−0.816336	−0.408168	+	0.912907i	$0.633832\pi$
$654$	10.4328	0.407954
$655$	0	0
$656$	28.5273	1.11380
$657$	−13.6461	−0.532386
$658$	−2.82415	−0.110097
$659$	39.4863	1.53817	0.769085	−	0.639147i	$-0.220712\pi$
$659$	39.4863	1.53817	0.769085	+	0.639147i	$0.220712\pi$
$660$	0	0
$661$	−13.0916	−0.509204	−0.254602	−	0.967046i	$-0.581945\pi$
$661$	−13.0916	−0.509204	−0.254602	+	0.967046i	$0.581945\pi$
$662$	76.2294	2.96274
$663$	4.52330	0.175670
$664$	−25.8970	−1.00500
$665$	0	0
$666$	14.8984	0.577300
$667$	9.33200	0.361336
$668$	10.2005	0.394669
$669$	4.67537	0.180760
$670$	0	0
$671$	−0.351291	−0.0135614
$672$	−23.8703	−0.920818
$673$	1.13751	0.0438477	0.0219238	−	0.999760i	$-0.493021\pi$
$673$	1.13751	0.0438477	0.0219238	+	0.999760i	$0.493021\pi$
$674$	39.2344	1.51125
$675$	0	0
$676$	−64.1408	−2.46695
$677$	40.4312	1.55390	0.776949	−	0.629563i	$-0.216766\pi$
$677$	40.4312	1.55390	0.776949	+	0.629563i	$0.216766\pi$
$678$	17.3477	0.666235
$679$	0.695928	0.0267073
$680$	0	0
$681$	6.34164	0.243012
$682$	2.66013	0.101862
$683$	20.1125	0.769584	0.384792	−	0.923003i	$-0.374273\pi$
$683$	20.1125	0.769584	0.384792	+	0.923003i	$0.374273\pi$
$684$	0.115801	0.00442776
$685$	0	0
$686$	36.5463	1.39534
$687$	−13.7153	−0.523272
$688$	−22.7505	−0.867353
$689$	−5.82754	−0.222011
$690$	0	0
$691$	−22.1262	−0.841722	−0.420861	−	0.907125i	$-0.638272\pi$
$691$	−22.1262	−0.841722	−0.420861	+	0.907125i	$0.638272\pi$
$692$	80.0815	3.04424
$693$	−0.122960	−0.00467087
$694$	−16.3215	−0.619556
$695$	0	0
$696$	77.2495	2.92814
$697$	−7.03467	−0.266457
$698$	−40.5348	−1.53427
$699$	15.9565	0.603532
$700$	0	0
$701$	−23.6697	−0.893992	−0.446996	−	0.894536i	$-0.647506\pi$
$701$	−23.6697	−0.893992	−0.446996	+	0.894536i	$0.647506\pi$
$702$	3.24510	0.122478
$703$	−0.113726	−0.00428926
$704$	−3.89636	−0.146850
$705$	0	0
$706$	−71.3336	−2.68468
$707$	−18.3258	−0.689212
$708$	57.5187	2.16169
$709$	45.9960	1.72742	0.863708	−	0.503992i	$-0.168136\pi$
$709$	45.9960	1.72742	0.863708	+	0.503992i	$0.168136\pi$
$710$	0	0
$711$	−9.77166	−0.366466
$712$	−14.9314	−0.559579
$713$	−9.49219	−0.355485
$714$	10.8013	0.404229
$715$	0	0
$716$	−53.4766	−1.99851
$717$	−10.4112	−0.388814
$718$	64.0039	2.38861
$719$	14.9980	0.559331	0.279665	−	0.960098i	$-0.409777\pi$
$719$	14.9980	0.559331	0.279665	+	0.960098i	$0.409777\pi$
$720$	0	0
$721$	7.85506	0.292538
$722$	52.1321	1.94016
$723$	−10.1087	−0.375947
$724$	57.0372	2.11977
$725$	0	0
$726$	30.1433	1.11872
$727$	10.3312	0.383164	0.191582	−	0.981477i	$-0.438638\pi$
$727$	10.3312	0.383164	0.191582	+	0.981477i	$0.438638\pi$
$728$	11.7863	0.436829
$729$	1.00000	0.0370370
$730$	0	0
$731$	5.61015	0.207499
$732$	16.2576	0.600899
$733$	−46.8761	−1.73141	−0.865705	−	0.500555i	$-0.833129\pi$
$733$	−46.8761	−1.73141	−0.865705	+	0.500555i	$0.833129\pi$
$734$	80.3353	2.96523
$735$	0	0
$736$	27.1267	0.999902
$737$	0.653024	0.0240544
$738$	−5.04681	−0.185776
$739$	0.576983	0.0212247	0.0106123	−	0.999944i	$-0.496622\pi$
$739$	0.576983	0.0212247	0.0106123	+	0.999944i	$0.496622\pi$
$740$	0	0
$741$	−0.0247714	−0.000909999 0
$742$	−13.9158	−0.510863
$743$	15.8374	0.581018	0.290509	−	0.956872i	$-0.406175\pi$
$743$	15.8374	0.581018	0.290509	+	0.956872i	$0.406175\pi$
$744$	−78.5756	−2.88072
$745$	0	0
$746$	65.5136	2.39862
$747$	2.67463	0.0978597
$748$	2.52613	0.0923644
$749$	−19.3342	−0.706455
$750$	0	0
$751$	35.8797	1.30927	0.654634	−	0.755946i	$-0.272823\pi$
$751$	35.8797	1.30927	0.654634	+	0.755946i	$0.272823\pi$
$752$	15.5097	0.565582
$753$	−16.8366	−0.613561
$754$	−25.8904	−0.942873
$755$	0	0
$756$	5.69055	0.206963
$757$	−15.2593	−0.554608	−0.277304	−	0.960782i	$-0.589441\pi$
$757$	−15.2593	−0.554608	−0.277304	+	0.960782i	$0.589441\pi$
$758$	32.9469	1.19669
$759$	0.139734	0.00507203
$760$	0	0
$761$	−33.1241	−1.20075	−0.600374	−	0.799719i	$-0.704982\pi$
$761$	−33.1241	−1.20075	−0.600374	+	0.799719i	$0.704982\pi$
$762$	−17.8283	−0.645849
$763$	−3.91349	−0.141678
$764$	75.1923	2.72036
$765$	0	0
$766$	60.8593	2.19894
$767$	−12.3040	−0.444272
$768$	53.0527	1.91437
$769$	−6.54347	−0.235963	−0.117982	−	0.993016i	$-0.537642\pi$
$769$	−6.54347	−0.235963	−0.117982	+	0.993016i	$0.537642\pi$
$770$	0	0
$771$	10.9742	0.395228
$772$	36.6538	1.31920
$773$	19.4626	0.700021	0.350011	−	0.936746i	$-0.386178\pi$
$773$	19.4626	0.700021	0.350011	+	0.936746i	$0.386178\pi$
$774$	4.02483	0.144670
$775$	0	0
$776$	−6.54671	−0.235013
$777$	−5.58859	−0.200490
$778$	51.2822	1.83856
$779$	0.0385247	0.00138029
$780$	0	0
$781$	0.868852	0.0310900
$782$	−12.2748	−0.438946
$783$	−7.97830	−0.285121
$784$	−92.1375	−3.29063
$785$	0	0
$786$	−25.1396	−0.896698
$787$	−11.2548	−0.401190	−0.200595	−	0.979674i	$-0.564288\pi$
$787$	−11.2548	−0.401190	−0.200595	+	0.979674i	$0.564288\pi$
$788$	−57.5716	−2.05090
$789$	23.3186	0.830163
$790$	0	0
$791$	−6.50739	−0.231376
$792$	1.15671	0.0411018
$793$	−3.47772	−0.123497
$794$	93.4055	3.31484
$795$	0	0
$796$	−47.0402	−1.66730
$797$	9.05408	0.320712	0.160356	−	0.987059i	$-0.448736\pi$
$797$	9.05408	0.320712	0.160356	+	0.987059i	$0.448736\pi$
$798$	−0.0591524	−0.00209397
$799$	−3.82462	−0.135305
$800$	0	0
$801$	1.54211	0.0544879
$802$	64.2399	2.26839
$803$	1.63023	0.0575294
$804$	−30.2217	−1.06584
$805$	0	0
$806$	26.3348	0.927605
$807$	−6.40443	−0.225447
$808$	172.394	6.06479
$809$	−2.18273	−0.0767408	−0.0383704	−	0.999264i	$-0.512217\pi$
$809$	−2.18273	−0.0767408	−0.0383704	+	0.999264i	$0.512217\pi$
$810$	0	0
$811$	1.95046	0.0684900	0.0342450	−	0.999413i	$-0.489097\pi$
$811$	1.95046	0.0684900	0.0342450	+	0.999413i	$0.489097\pi$
$812$	−45.4010	−1.59326
$813$	11.1005	0.389311
$814$	−1.77982	−0.0623828
$815$	0	0
$816$	−59.3190	−2.07658
$817$	−0.0307234	−0.00107488
$818$	52.7202	1.84332
$819$	−1.21729	−0.0425354
$820$	0	0
$821$	−30.6586	−1.06999	−0.534996	−	0.844855i	$-0.679687\pi$
$821$	−30.6586	−1.06999	−0.534996	+	0.844855i	$0.679687\pi$
$822$	49.1120	1.71298
$823$	22.4399	0.782207	0.391104	−	0.920347i	$-0.372093\pi$
$823$	22.4399	0.782207	0.391104	+	0.920347i	$0.372093\pi$
$824$	−73.8939	−2.57422
$825$	0	0
$826$	−29.3811	−1.02230
$827$	3.13513	0.109019	0.0545097	−	0.998513i	$-0.482640\pi$
$827$	3.13513	0.109019	0.0545097	+	0.998513i	$0.482640\pi$
$828$	−6.46685	−0.224738
$829$	52.0099	1.80638	0.903189	−	0.429242i	$-0.141219\pi$
$829$	52.0099	1.80638	0.903189	+	0.429242i	$0.141219\pi$
$830$	0	0
$831$	0.445143	0.0154418
$832$	−38.5733	−1.33729
$833$	22.7206	0.787223
$834$	−48.8928	−1.69302
$835$	0	0
$836$	−0.0138341	−0.000478462 0
$837$	8.11526	0.280504
$838$	−1.69881	−0.0586845
$839$	−55.3452	−1.91073	−0.955365	−	0.295429i	$-0.904538\pi$
$839$	−55.3452	−1.91073	−0.955365	+	0.295429i	$0.904538\pi$
$840$	0	0
$841$	34.6533	1.19494
$842$	45.5880	1.57107
$843$	1.29722	0.0446785
$844$	134.312	4.62320
$845$	0	0
$846$	−2.74386	−0.0943359
$847$	−11.3072	−0.388520
$848$	76.4229	2.62437
$849$	−15.0364	−0.516047
$850$	0	0
$851$	6.35098	0.217709
$852$	−40.2102	−1.37758
$853$	42.5632	1.45734	0.728668	−	0.684867i	$-0.240140\pi$
$853$	42.5632	1.45734	0.728668	+	0.684867i	$0.240140\pi$
$854$	−8.30456	−0.284176
$855$	0	0
$856$	181.880	6.21652
$857$	6.09064	0.208052	0.104026	−	0.994575i	$-0.466827\pi$
$857$	6.09064	0.208052	0.104026	+	0.994575i	$0.466827\pi$
$858$	−0.387674	−0.0132350
$859$	−39.3877	−1.34389	−0.671946	−	0.740600i	$-0.734541\pi$
$859$	−39.3877	−1.34389	−0.671946	+	0.740600i	$0.734541\pi$
$860$	0	0
$861$	1.89313	0.0645178
$862$	85.9172	2.92635
$863$	46.7512	1.59143	0.795715	−	0.605671i	$-0.207095\pi$
$863$	46.7512	1.59143	0.795715	+	0.605671i	$0.207095\pi$
$864$	−23.1917	−0.788997
$865$	0	0
$866$	−73.5637	−2.49980
$867$	−2.37225	−0.0805660
$868$	46.1803	1.56746
$869$	1.16737	0.0396002
$870$	0	0
$871$	6.46483	0.219052
$872$	36.8149	1.24671
$873$	0.676142	0.0228839
$874$	0.0672218	0.00227381
$875$	0	0
$876$	−75.4463	−2.54909
$877$	−36.5404	−1.23388	−0.616941	−	0.787009i	$-0.711628\pi$
$877$	−36.5404	−1.23388	−0.616941	+	0.787009i	$0.711628\pi$
$878$	−54.5172	−1.83987
$879$	30.8308	1.03990
$880$	0	0
$881$	−1.73909	−0.0585915	−0.0292957	−	0.999571i	$-0.509326\pi$
$881$	−1.73909	−0.0585915	−0.0292957	+	0.999571i	$0.509326\pi$
$882$	16.3002	0.548857
$883$	−35.6044	−1.19818	−0.599092	−	0.800680i	$-0.704472\pi$
$883$	−35.6044	−1.19818	−0.599092	+	0.800680i	$0.704472\pi$
$884$	25.0083	0.841119
$885$	0	0
$886$	35.8780	1.20535
$887$	2.66844	0.0895975	0.0447987	−	0.998996i	$-0.485735\pi$
$887$	2.66844	0.0895975	0.0447987	+	0.998996i	$0.485735\pi$
$888$	52.5729	1.76423
$889$	6.68764	0.224296
$890$	0	0
$891$	−0.119464	−0.00400221
$892$	25.8490	0.865490
$893$	0.0209452	0.000700903 0
$894$	58.6836	1.96267
$895$	0	0
$896$	−44.3698	−1.48229
$897$	1.38334	0.0461885
$898$	−53.5160	−1.78585
$899$	−64.7460	−2.15940
$900$	0	0
$901$	−18.8455	−0.627834
$902$	0.602914	0.0200749
$903$	−1.50977	−0.0502421
$904$	61.2161	2.03602
$905$	0	0
$906$	61.5639	2.04533
$907$	14.3274	0.475734	0.237867	−	0.971298i	$-0.423552\pi$
$907$	14.3274	0.475734	0.237867	+	0.971298i	$0.423552\pi$
$908$	35.0614	1.16355
$909$	−17.8048	−0.590547
$910$	0	0
$911$	−29.9782	−0.993222	−0.496611	−	0.867973i	$-0.665422\pi$
$911$	−29.9782	−0.993222	−0.496611	+	0.867973i	$0.665422\pi$
$912$	0.324854	0.0107570
$913$	−0.319523	−0.0105747
$914$	−110.436	−3.65289
$915$	0	0
$916$	−75.8288	−2.50546
$917$	9.43022	0.311413
$918$	10.4942	0.346361
$919$	25.8148	0.851552	0.425776	−	0.904829i	$-0.360001\pi$
$919$	25.8148	0.851552	0.425776	+	0.904829i	$0.360001\pi$
$920$	0	0
$921$	−33.4248	−1.10139
$922$	−74.5615	−2.45555
$923$	8.60149	0.283122
$924$	−0.679819	−0.0223644
$925$	0	0
$926$	74.7880	2.45769
$927$	7.63174	0.250659
$928$	185.030	6.07392
$929$	−9.39504	−0.308241	−0.154121	−	0.988052i	$-0.549254\pi$
$929$	−9.39504	−0.308241	−0.154121	+	0.988052i	$0.549254\pi$
$930$	0	0
$931$	−0.124427	−0.00407794
$932$	88.2201	2.88974
$933$	22.9768	0.752228
$934$	−33.7769	−1.10521
$935$	0	0
$936$	11.4512	0.374295
$937$	39.1292	1.27830	0.639148	−	0.769083i	$-0.279287\pi$
$937$	39.1292	1.27830	0.639148	+	0.769083i	$0.279287\pi$
$938$	15.4376	0.504054
$939$	3.86668	0.126184
$940$	0	0
$941$	48.7722	1.58993	0.794964	−	0.606657i	$-0.207490\pi$
$941$	48.7722	1.58993	0.794964	+	0.606657i	$0.207490\pi$
$942$	−24.4135	−0.795434
$943$	−2.15139	−0.0700589
$944$	161.356	5.25169
$945$	0	0
$946$	−0.480824	−0.0156329
$947$	26.1112	0.848500	0.424250	−	0.905545i	$-0.360538\pi$
$947$	26.1112	0.848500	0.424250	+	0.905545i	$0.360538\pi$
$948$	−54.0253	−1.75466
$949$	16.1390	0.523893
$950$	0	0
$951$	−8.18916	−0.265552
$952$	38.1154	1.23533
$953$	−43.9893	−1.42495	−0.712477	−	0.701696i	$-0.752427\pi$
$953$	−43.9893	−1.42495	−0.712477	+	0.701696i	$0.752427\pi$
$954$	−13.5201	−0.437730
$955$	0	0
$956$	−57.5612	−1.86166
$957$	0.953123	0.0308101
$958$	−37.7006	−1.21805
$959$	−18.4226	−0.594898
$960$	0	0
$961$	34.8574	1.12443
$962$	−17.6200	−0.568090
$963$	−18.7845	−0.605322
$964$	−55.8887	−1.80005
$965$	0	0
$966$	3.30333	0.106283
$967$	−46.8296	−1.50594	−0.752969	−	0.658056i	$-0.771379\pi$
$967$	−46.8296	−1.50594	−0.752969	+	0.658056i	$0.771379\pi$
$968$	106.369	3.41882
$969$	−0.0801074	−0.00257342
$970$	0	0
$971$	55.0347	1.76615	0.883074	−	0.469234i	$-0.155470\pi$
$971$	55.0347	1.76615	0.883074	+	0.469234i	$0.155470\pi$
$972$	5.52877	0.177335
$973$	18.3404	0.587966
$974$	−70.4944	−2.25879
$975$	0	0
$976$	45.6072	1.45985
$977$	−6.92519	−0.221556	−0.110778	−	0.993845i	$-0.535334\pi$
$977$	−6.92519	−0.221556	−0.110778	+	0.993845i	$0.535334\pi$
$978$	−36.2082	−1.15781
$979$	−0.184228	−0.00588794
$980$	0	0
$981$	−3.80223	−0.121396
$982$	−47.7396	−1.52343
$983$	−1.85143	−0.0590515	−0.0295258	−	0.999564i	$-0.509400\pi$
$983$	−1.85143	−0.0590515	−0.0295258	+	0.999564i	$0.509400\pi$
$984$	−17.8090	−0.567731
$985$	0	0
$986$	−83.7262	−2.66638
$987$	1.02926	0.0327618
$988$	−0.136955	−0.00435713
$989$	1.71573	0.0545571
$990$	0	0
$991$	−35.4387	−1.12575	−0.562874	−	0.826543i	$-0.690304\pi$
$991$	−35.4387	−1.12575	−0.562874	+	0.826543i	$0.690304\pi$
$992$	−188.206	−5.97556
$993$	−27.7818	−0.881629
$994$	20.5398	0.651482
$995$	0	0
$996$	14.7874	0.468558
$997$	−28.0155	−0.887261	−0.443630	−	0.896210i	$-0.646310\pi$
$997$	−28.0155	−0.887261	−0.443630	+	0.896210i	$0.646310\pi$
$998$	13.9259	0.440816
$999$	−5.42971	−0.171788

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.y.1.1	✓	7
5.4	even	2		3525.2.a.bb.1.7	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.y.1.1	✓	7	1.1	even	1	trivial
3525.2.a.bb.1.7	yes	7	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74386 q^{2} +1.00000 q^{3} +5.52877 q^{4} -2.74386 q^{6} +1.02926 q^{7} -9.68245 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.74386 q^{2} +1.00000 q^{3} +5.52877 q^{4} -2.74386 q^{6} +1.02926 q^{7} -9.68245 q^{8} +1.00000 q^{9} -0.119464 q^{11} +5.52877 q^{12} -1.18268 q^{13} -2.82415 q^{14} +15.5097 q^{16} -3.82462 q^{17} -2.74386 q^{18} +0.0209452 q^{19} +1.02926 q^{21} +0.327794 q^{22} -1.16967 q^{23} -9.68245 q^{24} +3.24510 q^{26} +1.00000 q^{27} +5.69055 q^{28} -7.97830 q^{29} +8.11526 q^{31} -23.1917 q^{32} -0.119464 q^{33} +10.4942 q^{34} +5.52877 q^{36} -5.42971 q^{37} -0.0574706 q^{38} -1.18268 q^{39} +1.83931 q^{41} -2.82415 q^{42} -1.46685 q^{43} -0.660491 q^{44} +3.20942 q^{46} +1.00000 q^{47} +15.5097 q^{48} -5.94062 q^{49} -3.82462 q^{51} -6.53875 q^{52} +4.92741 q^{53} -2.74386 q^{54} -9.96578 q^{56} +0.0209452 q^{57} +21.8914 q^{58} +10.4035 q^{59} +2.94055 q^{61} -22.2671 q^{62} +1.02926 q^{63} +32.6152 q^{64} +0.327794 q^{66} -5.46626 q^{67} -21.1455 q^{68} -1.16967 q^{69} -7.27290 q^{71} -9.68245 q^{72} -13.6461 q^{73} +14.8984 q^{74} +0.115801 q^{76} -0.122960 q^{77} +3.24510 q^{78} -9.77166 q^{79} +1.00000 q^{81} -5.04681 q^{82} +2.67463 q^{83} +5.69055 q^{84} +4.02483 q^{86} -7.97830 q^{87} +1.15671 q^{88} +1.54211 q^{89} -1.21729 q^{91} -6.46685 q^{92} +8.11526 q^{93} -2.74386 q^{94} -23.1917 q^{96} +0.676142 q^{97} +16.3002 q^{98} -0.119464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9} - 8 q^{11} + 5 q^{12} - 5 q^{13} - 3 q^{14} + 9 q^{16} - 10 q^{17} - q^{18} + 7 q^{19} - 11 q^{21} - 20 q^{22} - 4 q^{23} - 6 q^{24} + 7 q^{27} - 2 q^{28} - 11 q^{29} + 3 q^{31} - 28 q^{32} - 8 q^{33} + 8 q^{34} + 5 q^{36} - 11 q^{37} + 2 q^{38} - 5 q^{39} - 20 q^{41} - 3 q^{42} - 18 q^{43} + q^{44} - 19 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} - 10 q^{51} - 29 q^{52} - 12 q^{53} - q^{54} - 47 q^{56} + 7 q^{57} + 19 q^{58} + 18 q^{59} - 4 q^{61} - 12 q^{62} - 11 q^{63} + 42 q^{64} - 20 q^{66} - 22 q^{67} - 44 q^{68} - 4 q^{69} - 14 q^{71} - 6 q^{72} - 30 q^{73} + 31 q^{74} - 2 q^{76} + 8 q^{77} - q^{79} + 7 q^{81} - 29 q^{82} - 54 q^{83} - 2 q^{84} - 29 q^{86} - 11 q^{87} + 22 q^{88} - 14 q^{89} + 20 q^{91} + 5 q^{92} + 3 q^{93} - q^{94} - 28 q^{96} - 24 q^{97} + 26 q^{98} - 8 q^{99}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9 - 8 * q^11 + 5 * q^12 - 5 * q^13 - 3 * q^14 + 9 * q^16 - 10 * q^17 - q^18 + 7 * q^19 - 11 * q^21 - 20 * q^22 - 4 * q^23 - 6 * q^24 + 7 * q^27 - 2 * q^28 - 11 * q^29 + 3 * q^31 - 28 * q^32 - 8 * q^33 + 8 * q^34 + 5 * q^36 - 11 * q^37 + 2 * q^38 - 5 * q^39 - 20 * q^41 - 3 * q^42 - 18 * q^43 + q^44 - 19 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 - 10 * q^51 - 29 * q^52 - 12 * q^53 - q^54 - 47 * q^56 + 7 * q^57 + 19 * q^58 + 18 * q^59 - 4 * q^61 - 12 * q^62 - 11 * q^63 + 42 * q^64 - 20 * q^66 - 22 * q^67 - 44 * q^68 - 4 * q^69 - 14 * q^71 - 6 * q^72 - 30 * q^73 + 31 * q^74 - 2 * q^76 + 8 * q^77 - q^79 + 7 * q^81 - 29 * q^82 - 54 * q^83 - 2 * q^84 - 29 * q^86 - 11 * q^87 + 22 * q^88 - 14 * q^89 + 20 * q^91 + 5 * q^92 + 3 * q^93 - q^94 - 28 * q^96 - 24 * q^97 + 26 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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