LMFDB - Embedded newform 7595.2.a.bf.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7595,2,Mod(1,7595)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7595, 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("7595.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7595 = 5 \cdot 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7595.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:	$60.6463803352$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 1085)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64279 q^{2} -0.623799 q^{3} +4.98432 q^{4} +1.00000 q^{5} +1.64857 q^{6} -7.88694 q^{8} -2.61087 q^{9} +O(q^{10})$	\(q-2.64279 q^{2} -0.623799 q^{3} +4.98432 q^{4} +1.00000 q^{5} +1.64857 q^{6} -7.88694 q^{8} -2.61087 q^{9} -2.64279 q^{10} +0.198858 q^{11} -3.10922 q^{12} +1.91238 q^{13} -0.623799 q^{15} +10.8748 q^{16} +7.90045 q^{17} +6.89999 q^{18} +2.11143 q^{19} +4.98432 q^{20} -0.525540 q^{22} -2.30329 q^{23} +4.91987 q^{24} +1.00000 q^{25} -5.05401 q^{26} +3.50006 q^{27} +2.31694 q^{29} +1.64857 q^{30} -1.00000 q^{31} -12.9660 q^{32} -0.124048 q^{33} -20.8792 q^{34} -13.0134 q^{36} -10.1620 q^{37} -5.58007 q^{38} -1.19294 q^{39} -7.88694 q^{40} -0.137874 q^{41} -5.25805 q^{43} +0.991174 q^{44} -2.61087 q^{45} +6.08711 q^{46} -5.34146 q^{47} -6.78372 q^{48} -2.64279 q^{50} -4.92830 q^{51} +9.53191 q^{52} -8.88169 q^{53} -9.24991 q^{54} +0.198858 q^{55} -1.31711 q^{57} -6.12317 q^{58} +1.35852 q^{59} -3.10922 q^{60} +0.122888 q^{61} +2.64279 q^{62} +12.5168 q^{64} +1.91238 q^{65} +0.327832 q^{66} -0.513416 q^{67} +39.3784 q^{68} +1.43679 q^{69} -7.37652 q^{71} +20.5918 q^{72} -10.3602 q^{73} +26.8561 q^{74} -0.623799 q^{75} +10.5241 q^{76} +3.15269 q^{78} -4.36858 q^{79} +10.8748 q^{80} +5.64929 q^{81} +0.364371 q^{82} -2.63999 q^{83} +7.90045 q^{85} +13.8959 q^{86} -1.44530 q^{87} -1.56838 q^{88} +9.89183 q^{89} +6.89999 q^{90} -11.4803 q^{92} +0.623799 q^{93} +14.1163 q^{94} +2.11143 q^{95} +8.08820 q^{96} -13.1548 q^{97} -0.519194 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * 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 $

$2$	−2.64279	−1.86873	−0.934366	−	0.356314i	$-0.884033\pi$
$2$	−2.64279	−1.86873	−0.934366	+	0.356314i	$0.884033\pi$
$3$	−0.623799	−0.360151	−0.180075	−	0.983653i	$-0.557634\pi$
$3$	−0.623799	−0.360151	−0.180075	+	0.983653i	$0.557634\pi$
$4$	4.98432	2.49216
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.64857	0.673025
$7$	0	0
$7$	0	0
$8$	−7.88694	−2.78845
$9$	−2.61087	−0.870291
$10$	−2.64279	−0.835723
$11$	0.198858	0.0599580	0.0299790	−	0.999551i	$-0.490456\pi$
$11$	0.198858	0.0599580	0.0299790	+	0.999551i	$0.490456\pi$
$12$	−3.10922	−0.897554
$13$	1.91238	0.530398	0.265199	−	0.964194i	$-0.414562\pi$
$13$	1.91238	0.530398	0.265199	+	0.964194i	$0.414562\pi$
$14$	0	0
$15$	−0.623799	−0.161064
$16$	10.8748	2.71871
$17$	7.90045	1.91614	0.958071	−	0.286532i	$-0.0925026\pi$
$17$	7.90045	1.91614	0.958071	+	0.286532i	$0.0925026\pi$
$18$	6.89999	1.62634
$19$	2.11143	0.484396	0.242198	−	0.970227i	$-0.422132\pi$
$19$	2.11143	0.484396	0.242198	+	0.970227i	$0.422132\pi$
$20$	4.98432	1.11453
$21$	0	0
$22$	−0.525540	−0.112046
$23$	−2.30329	−0.480269	−0.240135	−	0.970740i	$-0.577192\pi$
$23$	−2.30329	−0.480269	−0.240135	+	0.970740i	$0.577192\pi$
$24$	4.91987	1.00426
$25$	1.00000	0.200000
$26$	−5.05401	−0.991173
$27$	3.50006	0.673587
$28$	0	0
$29$	2.31694	0.430244	0.215122	−	0.976587i	$-0.430985\pi$
$29$	2.31694	0.430244	0.215122	+	0.976587i	$0.430985\pi$
$30$	1.64857	0.300986
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−12.9660	−2.29209
$33$	−0.124048	−0.0215939
$34$	−20.8792	−3.58076
$35$	0	0
$36$	−13.0134	−2.16891
$37$	−10.1620	−1.67063	−0.835315	−	0.549771i	$-0.814715\pi$
$37$	−10.1620	−1.67063	−0.835315	+	0.549771i	$0.814715\pi$
$38$	−5.58007	−0.905207
$39$	−1.19294	−0.191023
$40$	−7.88694	−1.24703
$41$	−0.137874	−0.0215322	−0.0107661	−	0.999942i	$-0.503427\pi$
$41$	−0.137874	−0.0215322	−0.0107661	+	0.999942i	$0.503427\pi$
$42$	0	0
$43$	−5.25805	−0.801845	−0.400923	−	0.916112i	$-0.631310\pi$
$43$	−5.25805	−0.801845	−0.400923	+	0.916112i	$0.631310\pi$
$44$	0.991174	0.149425
$45$	−2.61087	−0.389206
$46$	6.08711	0.897495
$47$	−5.34146	−0.779132	−0.389566	−	0.920999i	$-0.627375\pi$
$47$	−5.34146	−0.779132	−0.389566	+	0.920999i	$0.627375\pi$
$48$	−6.78372	−0.979146
$49$	0	0
$50$	−2.64279	−0.373747
$51$	−4.92830	−0.690100
$52$	9.53191	1.32184
$53$	−8.88169	−1.21999	−0.609997	−	0.792404i	$-0.708829\pi$
$53$	−8.88169	−1.21999	−0.609997	+	0.792404i	$0.708829\pi$
$54$	−9.24991	−1.25875
$55$	0.198858	0.0268140
$56$	0	0
$57$	−1.31711	−0.174456
$58$	−6.12317	−0.804012
$59$	1.35852	0.176865	0.0884324	−	0.996082i	$-0.471814\pi$
$59$	1.35852	0.176865	0.0884324	+	0.996082i	$0.471814\pi$
$60$	−3.10922	−0.401398
$61$	0.122888	0.0157342	0.00786709	−	0.999969i	$-0.497496\pi$
$61$	0.122888	0.0157342	0.00786709	+	0.999969i	$0.497496\pi$
$62$	2.64279	0.335634
$63$	0	0
$64$	12.5168	1.56460
$65$	1.91238	0.237201
$66$	0.327832	0.0403533
$67$	−0.513416	−0.0627237	−0.0313619	−	0.999508i	$-0.509984\pi$
$67$	−0.513416	−0.0627237	−0.0313619	+	0.999508i	$0.509984\pi$
$68$	39.3784	4.77533
$69$	1.43679	0.172969
$70$	0	0
$71$	−7.37652	−0.875432	−0.437716	−	0.899113i	$-0.644212\pi$
$71$	−7.37652	−0.875432	−0.437716	+	0.899113i	$0.644212\pi$
$72$	20.5918	2.42677
$73$	−10.3602	−1.21257	−0.606286	−	0.795246i	$-0.707341\pi$
$73$	−10.3602	−1.21257	−0.606286	+	0.795246i	$0.707341\pi$
$74$	26.8561	3.12196
$75$	−0.623799	−0.0720301
$76$	10.5241	1.20719
$77$	0	0
$78$	3.15269	0.356972
$79$	−4.36858	−0.491504	−0.245752	−	0.969333i	$-0.579035\pi$
$79$	−4.36858	−0.491504	−0.245752	+	0.969333i	$0.579035\pi$
$80$	10.8748	1.21584
$81$	5.64929	0.627699
$82$	0.364371	0.0402380
$83$	−2.63999	−0.289776	−0.144888	−	0.989448i	$-0.546282\pi$
$83$	−2.63999	−0.289776	−0.144888	+	0.989448i	$0.546282\pi$
$84$	0	0
$85$	7.90045	0.856924
$86$	13.8959	1.49843
$87$	−1.44530	−0.154953
$88$	−1.56838	−0.167190
$89$	9.89183	1.04853	0.524266	−	0.851554i	$-0.324340\pi$
$89$	9.89183	1.04853	0.524266	+	0.851554i	$0.324340\pi$
$90$	6.89999	0.727322
$91$	0	0
$92$	−11.4803	−1.19691
$93$	0.623799	0.0646850
$94$	14.1163	1.45599
$95$	2.11143	0.216629
$96$	8.08820	0.825499
$97$	−13.1548	−1.33567	−0.667833	−	0.744311i	$-0.732778\pi$
$97$	−13.1548	−1.33567	−0.667833	+	0.744311i	$0.732778\pi$
$98$	0	0
$99$	−0.519194	−0.0521810
$100$	4.98432	0.498432
$101$	11.0935	1.10384	0.551922	−	0.833896i	$-0.313895\pi$
$101$	11.0935	1.10384	0.551922	+	0.833896i	$0.313895\pi$
$102$	13.0244	1.28961
$103$	8.09467	0.797592	0.398796	−	0.917040i	$-0.369428\pi$
$103$	8.09467	0.797592	0.398796	+	0.917040i	$0.369428\pi$
$104$	−15.0828	−1.47899
$105$	0	0
$106$	23.4724	2.27984
$107$	0.661700	0.0639690	0.0319845	−	0.999488i	$-0.489817\pi$
$107$	0.661700	0.0639690	0.0319845	+	0.999488i	$0.489817\pi$
$108$	17.4454	1.67869
$109$	13.6359	1.30608	0.653042	−	0.757322i	$-0.273493\pi$
$109$	13.6359	1.30608	0.653042	+	0.757322i	$0.273493\pi$
$110$	−0.525540	−0.0501083
$111$	6.33908	0.601679
$112$	0	0
$113$	−17.9266	−1.68639	−0.843196	−	0.537606i	$-0.819329\pi$
$113$	−17.9266	−1.68639	−0.843196	+	0.537606i	$0.819329\pi$
$114$	3.48084	0.326011
$115$	−2.30329	−0.214783
$116$	11.5484	1.07224
$117$	−4.99298	−0.461601
$118$	−3.59029	−0.330513
$119$	0	0
$120$	4.91987	0.449120
$121$	−10.9605	−0.996405
$122$	−0.324766	−0.0294030
$123$	0.0860055	0.00775485
$124$	−4.98432	−0.447606
$125$	1.00000	0.0894427
$126$	0	0
$127$	−2.11601	−0.187766	−0.0938828	−	0.995583i	$-0.529928\pi$
$127$	−2.11601	−0.187766	−0.0938828	+	0.995583i	$0.529928\pi$
$128$	−7.14710	−0.631721
$129$	3.27997	0.288785
$130$	−5.05401	−0.443266
$131$	16.3629	1.42964	0.714818	−	0.699310i	$-0.246509\pi$
$131$	16.3629	1.42964	0.714818	+	0.699310i	$0.246509\pi$
$132$	−0.618294	−0.0538156
$133$	0	0
$134$	1.35685	0.117214
$135$	3.50006	0.301237
$136$	−62.3104	−5.34307
$137$	−6.73968	−0.575809	−0.287905	−	0.957659i	$-0.592959\pi$
$137$	−6.73968	−0.575809	−0.287905	+	0.957659i	$0.592959\pi$
$138$	−3.79713	−0.323233
$139$	−12.1300	−1.02886	−0.514428	−	0.857533i	$-0.671996\pi$
$139$	−12.1300	−1.02886	−0.514428	+	0.857533i	$0.671996\pi$
$140$	0	0
$141$	3.33200	0.280605
$142$	19.4946	1.63595
$143$	0.380292	0.0318016
$144$	−28.3929	−2.36607
$145$	2.31694	0.192411
$146$	27.3799	2.26597
$147$	0	0
$148$	−50.6509	−4.16348
$149$	−8.88048	−0.727518	−0.363759	−	0.931493i	$-0.618507\pi$
$149$	−8.88048	−0.727518	−0.363759	+	0.931493i	$0.618507\pi$
$150$	1.64857	0.134605
$151$	16.6312	1.35343	0.676713	−	0.736247i	$-0.263404\pi$
$151$	16.6312	1.35343	0.676713	+	0.736247i	$0.263404\pi$
$152$	−16.6527	−1.35072
$153$	−20.6271	−1.66760
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	−5.94600	−0.476061
$157$	−5.25799	−0.419633	−0.209817	−	0.977741i	$-0.567287\pi$
$157$	−5.25799	−0.419633	−0.209817	+	0.977741i	$0.567287\pi$
$158$	11.5452	0.918490
$159$	5.54040	0.439382
$160$	−12.9660	−1.02505
$161$	0	0
$162$	−14.9299	−1.17300
$163$	20.1037	1.57464	0.787322	−	0.616542i	$-0.211467\pi$
$163$	20.1037	1.57464	0.787322	+	0.616542i	$0.211467\pi$
$164$	−0.687207	−0.0536618
$165$	−0.124048	−0.00965710
$166$	6.97693	0.541515
$167$	14.1436	1.09447	0.547234	−	0.836980i	$-0.315681\pi$
$167$	14.1436	1.09447	0.547234	+	0.836980i	$0.315681\pi$
$168$	0	0
$169$	−9.34281	−0.718678
$170$	−20.8792	−1.60136
$171$	−5.51269	−0.421566
$172$	−26.2078	−1.99833
$173$	−13.0608	−0.992991	−0.496495	−	0.868039i	$-0.665380\pi$
$173$	−13.0608	−0.992991	−0.496495	+	0.868039i	$0.665380\pi$
$174$	3.81963	0.289565
$175$	0	0
$176$	2.16255	0.163009
$177$	−0.847446	−0.0636980
$178$	−26.1420	−1.95943
$179$	13.6085	1.01714	0.508572	−	0.861019i	$-0.330173\pi$
$179$	13.6085	1.01714	0.508572	+	0.861019i	$0.330173\pi$
$180$	−13.0134	−0.969965
$181$	−10.4904	−0.779748	−0.389874	−	0.920868i	$-0.627481\pi$
$181$	−10.4904	−0.779748	−0.389874	+	0.920868i	$0.627481\pi$
$182$	0	0
$183$	−0.0766573	−0.00566667
$184$	18.1659	1.33921
$185$	−10.1620	−0.747129
$186$	−1.64857	−0.120879
$187$	1.57107	0.114888
$188$	−26.6236	−1.94172
$189$	0	0
$190$	−5.58007	−0.404821
$191$	−8.75418	−0.633430	−0.316715	−	0.948521i	$-0.602580\pi$
$191$	−8.75418	−0.633430	−0.316715	+	0.948521i	$0.602580\pi$
$192$	−7.80795	−0.563491
$193$	−17.8912	−1.28783	−0.643917	−	0.765095i	$-0.722692\pi$
$193$	−17.8912	−1.28783	−0.643917	+	0.765095i	$0.722692\pi$
$194$	34.7653	2.49600
$195$	−1.19294	−0.0854282
$196$	0	0
$197$	−1.65315	−0.117782	−0.0588909	−	0.998264i	$-0.518756\pi$
$197$	−1.65315	−0.117782	−0.0588909	+	0.998264i	$0.518756\pi$
$198$	1.37212	0.0975123
$199$	−12.0192	−0.852022	−0.426011	−	0.904718i	$-0.640082\pi$
$199$	−12.0192	−0.852022	−0.426011	+	0.904718i	$0.640082\pi$
$200$	−7.88694	−0.557691
$201$	0.320268	0.0225900
$202$	−29.3177	−2.06279
$203$	0	0
$204$	−24.5642	−1.71984
$205$	−0.137874	−0.00962951
$206$	−21.3925	−1.49049
$207$	6.01360	0.417974
$208$	20.7968	1.44200
$209$	0.419876	0.0290434
$210$	0	0
$211$	6.42922	0.442606	0.221303	−	0.975205i	$-0.428969\pi$
$211$	6.42922	0.442606	0.221303	+	0.975205i	$0.428969\pi$
$212$	−44.2693	−3.04042
$213$	4.60147	0.315287
$214$	−1.74873	−0.119541
$215$	−5.25805	−0.358596
$216$	−27.6047	−1.87827
$217$	0	0
$218$	−36.0368	−2.44072
$219$	6.46270	0.436709
$220$	0.991174	0.0668249
$221$	15.1087	1.01632
$222$	−16.7528	−1.12438
$223$	−23.4576	−1.57083	−0.785417	−	0.618967i	$-0.787551\pi$
$223$	−23.4576	−1.57083	−0.785417	+	0.618967i	$0.787551\pi$
$224$	0	0
$225$	−2.61087	−0.174058
$226$	47.3762	3.15142
$227$	26.3981	1.75210	0.876052	−	0.482217i	$-0.160168\pi$
$227$	26.3981	1.75210	0.876052	+	0.482217i	$0.160168\pi$
$228$	−6.56491	−0.434772
$229$	−18.2024	−1.20285	−0.601423	−	0.798931i	$-0.705399\pi$
$229$	−18.2024	−1.20285	−0.601423	+	0.798931i	$0.705399\pi$
$230$	6.08711	0.401372
$231$	0	0
$232$	−18.2735	−1.19972
$233$	4.83757	0.316920	0.158460	−	0.987365i	$-0.449347\pi$
$233$	4.83757	0.316920	0.158460	+	0.987365i	$0.449347\pi$
$234$	13.1954	0.862609
$235$	−5.34146	−0.348438
$236$	6.77132	0.440776
$237$	2.72512	0.177016
$238$	0	0
$239$	23.9266	1.54768	0.773841	−	0.633380i	$-0.218333\pi$
$239$	23.9266	1.54768	0.773841	+	0.633380i	$0.218333\pi$
$240$	−6.78372	−0.437887
$241$	10.6250	0.684414	0.342207	−	0.939625i	$-0.388826\pi$
$241$	10.6250	0.684414	0.342207	+	0.939625i	$0.388826\pi$
$242$	28.9662	1.86201
$243$	−14.0242	−0.899653
$244$	0.612513	0.0392121
$245$	0	0
$246$	−0.227294	−0.0144917
$247$	4.03786	0.256923
$248$	7.88694	0.500821
$249$	1.64682	0.104363
$250$	−2.64279	−0.167145
$251$	−23.7984	−1.50214	−0.751071	−	0.660222i	$-0.770462\pi$
$251$	−23.7984	−1.50214	−0.751071	+	0.660222i	$0.770462\pi$
$252$	0	0
$253$	−0.458028	−0.0287960
$254$	5.59216	0.350884
$255$	−4.92830	−0.308622
$256$	−6.14527	−0.384079
$257$	−3.11137	−0.194082	−0.0970408	−	0.995280i	$-0.530938\pi$
$257$	−3.11137	−0.194082	−0.0970408	+	0.995280i	$0.530938\pi$
$258$	−8.66826	−0.539662
$259$	0	0
$260$	9.53191	0.591144
$261$	−6.04923	−0.374438
$262$	−43.2438	−2.67161
$263$	19.5476	1.20536	0.602678	−	0.797985i	$-0.294101\pi$
$263$	19.5476	1.20536	0.602678	+	0.797985i	$0.294101\pi$
$264$	0.978356	0.0602136
$265$	−8.88169	−0.545598
$266$	0	0
$267$	−6.17052	−0.377630
$268$	−2.55903	−0.156318
$269$	17.6860	1.07833	0.539167	−	0.842199i	$-0.318739\pi$
$269$	17.6860	1.07833	0.539167	+	0.842199i	$0.318739\pi$
$270$	−9.24991	−0.562932
$271$	4.23099	0.257014	0.128507	−	0.991709i	$-0.458981\pi$
$271$	4.23099	0.257014	0.128507	+	0.991709i	$0.458981\pi$
$272$	85.9162	5.20943
$273$	0	0
$274$	17.8115	1.07603
$275$	0.198858	0.0119916
$276$	7.16143	0.431068
$277$	−22.3354	−1.34200	−0.671002	−	0.741456i	$-0.734136\pi$
$277$	−22.3354	−1.34200	−0.671002	+	0.741456i	$0.734136\pi$
$278$	32.0571	1.92266
$279$	2.61087	0.156309
$280$	0	0
$281$	29.3376	1.75013	0.875067	−	0.484002i	$-0.160817\pi$
$281$	29.3376	1.75013	0.875067	+	0.484002i	$0.160817\pi$
$282$	−8.80577	−0.524376
$283$	−20.1505	−1.19782	−0.598912	−	0.800815i	$-0.704400\pi$
$283$	−20.1505	−1.19782	−0.598912	+	0.800815i	$0.704400\pi$
$284$	−36.7670	−2.18172
$285$	−1.31711	−0.0780189
$286$	−1.00503	−0.0594288
$287$	0	0
$288$	33.8527	1.99479
$289$	45.4171	2.67160
$290$	−6.12317	−0.359565
$291$	8.20595	0.481041
$292$	−51.6387	−3.02193
$293$	13.2742	0.775490	0.387745	−	0.921767i	$-0.373254\pi$
$293$	13.2742	0.775490	0.387745	+	0.921767i	$0.373254\pi$
$294$	0	0
$295$	1.35852	0.0790963
$296$	80.1474	4.65847
$297$	0.696016	0.0403869
$298$	23.4692	1.35954
$299$	−4.40476	−0.254734
$300$	−3.10922	−0.179511
$301$	0	0
$302$	−43.9527	−2.52919
$303$	−6.92011	−0.397550
$304$	22.9615	1.31693
$305$	0.122888	0.00703654
$306$	54.5130	3.11630
$307$	0.519468	0.0296476	0.0148238	−	0.999890i	$-0.495281\pi$
$307$	0.519468	0.0296476	0.0148238	+	0.999890i	$0.495281\pi$
$308$	0	0
$309$	−5.04945	−0.287253
$310$	2.64279	0.150100
$311$	−30.5101	−1.73007	−0.865036	−	0.501711i	$-0.832704\pi$
$311$	−30.5101	−1.73007	−0.865036	+	0.501711i	$0.832704\pi$
$312$	9.40864	0.532660
$313$	−15.3130	−0.865541	−0.432770	−	0.901504i	$-0.642464\pi$
$313$	−15.3130	−0.865541	−0.432770	+	0.901504i	$0.642464\pi$
$314$	13.8957	0.784182
$315$	0	0
$316$	−21.7744	−1.22491
$317$	−32.1792	−1.80736	−0.903681	−	0.428205i	$-0.859146\pi$
$317$	−32.1792	−1.80736	−0.903681	+	0.428205i	$0.859146\pi$
$318$	−14.6421	−0.821087
$319$	0.460742	0.0257966
$320$	12.5168	0.699709
$321$	−0.412768	−0.0230385
$322$	0	0
$323$	16.6813	0.928171
$324$	28.1579	1.56433
$325$	1.91238	0.106080
$326$	−53.1298	−2.94259
$327$	−8.50607	−0.470387
$328$	1.08740	0.0600416
$329$	0	0
$330$	0.327832	0.0180465
$331$	3.37467	0.185489	0.0927443	−	0.995690i	$-0.470436\pi$
$331$	3.37467	0.185489	0.0927443	+	0.995690i	$0.470436\pi$
$332$	−13.1586	−0.722170
$333$	26.5318	1.45394
$334$	−37.3786	−2.04527
$335$	−0.513416	−0.0280509
$336$	0	0
$337$	12.3858	0.674697	0.337349	−	0.941380i	$-0.390470\pi$
$337$	12.3858	0.674697	0.337349	+	0.941380i	$0.390470\pi$
$338$	24.6911	1.34302
$339$	11.1826	0.607355
$340$	39.3784	2.13559
$341$	−0.198858	−0.0107688
$342$	14.5689	0.787794
$343$	0	0
$344$	41.4699	2.23591
$345$	1.43679	0.0773542
$346$	34.5168	1.85563
$347$	−17.8703	−0.959325	−0.479663	−	0.877453i	$-0.659241\pi$
$347$	−17.8703	−0.959325	−0.479663	+	0.877453i	$0.659241\pi$
$348$	−7.20386	−0.386168
$349$	3.80810	0.203843	0.101921	−	0.994792i	$-0.467501\pi$
$349$	3.80810	0.203843	0.101921	+	0.994792i	$0.467501\pi$
$350$	0	0
$351$	6.69344	0.357269
$352$	−2.57840	−0.137429
$353$	20.2634	1.07851	0.539256	−	0.842142i	$-0.318706\pi$
$353$	20.2634	1.07851	0.539256	+	0.842142i	$0.318706\pi$
$354$	2.23962	0.119034
$355$	−7.37652	−0.391505
$356$	49.3041	2.61311
$357$	0	0
$358$	−35.9643	−1.90077
$359$	8.64988	0.456523	0.228261	−	0.973600i	$-0.426696\pi$
$359$	8.64988	0.456523	0.228261	+	0.973600i	$0.426696\pi$
$360$	20.5918	1.08528
$361$	−14.5418	−0.765360
$362$	27.7240	1.45714
$363$	6.83712	0.358856
$364$	0	0
$365$	−10.3602	−0.542279
$366$	0.202589	0.0105895
$367$	19.2567	1.00519	0.502595	−	0.864522i	$-0.332379\pi$
$367$	19.2567	1.00519	0.502595	+	0.864522i	$0.332379\pi$
$368$	−25.0479	−1.30571
$369$	0.359971	0.0187393
$370$	26.8561	1.39618
$371$	0	0
$372$	3.10922	0.161205
$373$	−8.70218	−0.450582	−0.225291	−	0.974292i	$-0.572333\pi$
$373$	−8.70218	−0.450582	−0.225291	+	0.974292i	$0.572333\pi$
$374$	−4.15200	−0.214695
$375$	−0.623799	−0.0322129
$376$	42.1278	2.17257
$377$	4.43086	0.228201
$378$	0	0
$379$	−22.1167	−1.13606	−0.568029	−	0.823009i	$-0.692294\pi$
$379$	−22.1167	−1.13606	−0.568029	+	0.823009i	$0.692294\pi$
$380$	10.5241	0.539874
$381$	1.31997	0.0676239
$382$	23.1354	1.18371
$383$	30.9553	1.58174	0.790871	−	0.611983i	$-0.209628\pi$
$383$	30.9553	1.58174	0.790871	+	0.611983i	$0.209628\pi$
$384$	4.45836	0.227515
$385$	0	0
$386$	47.2826	2.40662
$387$	13.7281	0.697839
$388$	−65.5677	−3.32870
$389$	−0.361605	−0.0183341	−0.00916704	−	0.999958i	$-0.502918\pi$
$389$	−0.361605	−0.0183341	−0.00916704	+	0.999958i	$0.502918\pi$
$390$	3.15269	0.159643
$391$	−18.1970	−0.920264
$392$	0	0
$393$	−10.2072	−0.514885
$394$	4.36892	0.220103
$395$	−4.36858	−0.219807
$396$	−2.58783	−0.130043
$397$	35.4957	1.78148	0.890740	−	0.454514i	$-0.150187\pi$
$397$	35.4957	1.78148	0.890740	+	0.454514i	$0.150187\pi$
$398$	31.7643	1.59220
$399$	0	0
$400$	10.8748	0.543742
$401$	−36.9053	−1.84296	−0.921481	−	0.388422i	$-0.873020\pi$
$401$	−36.9053	−1.84296	−0.921481	+	0.388422i	$0.873020\pi$
$402$	−0.846401	−0.0422147
$403$	−1.91238	−0.0952623
$404$	55.2936	2.75096
$405$	5.64929	0.280715
$406$	0	0
$407$	−2.02081	−0.100168
$408$	38.8692	1.92431
$409$	−10.2251	−0.505600	−0.252800	−	0.967519i	$-0.581352\pi$
$409$	−10.2251	−0.505600	−0.252800	+	0.967519i	$0.581352\pi$
$410$	0.364371	0.0179950
$411$	4.20421	0.207378
$412$	40.3465	1.98773
$413$	0	0
$414$	−15.8927	−0.781082
$415$	−2.63999	−0.129592
$416$	−24.7960	−1.21572
$417$	7.56671	0.370544
$418$	−1.10964	−0.0542744
$419$	16.5460	0.808326	0.404163	−	0.914687i	$-0.367563\pi$
$419$	16.5460	0.808326	0.404163	+	0.914687i	$0.367563\pi$
$420$	0	0
$421$	25.3436	1.23517	0.617585	−	0.786504i	$-0.288111\pi$
$421$	25.3436	1.23517	0.617585	+	0.786504i	$0.288111\pi$
$422$	−16.9911	−0.827112
$423$	13.9459	0.678072
$424$	70.0494	3.40190
$425$	7.90045	0.383228
$426$	−12.1607	−0.589188
$427$	0	0
$428$	3.29813	0.159421
$429$	−0.237226	−0.0114534
$430$	13.8959	0.670120
$431$	−28.4612	−1.37093	−0.685463	−	0.728107i	$-0.740400\pi$
$431$	−28.4612	−1.37093	−0.685463	+	0.728107i	$0.740400\pi$
$432$	38.0626	1.83129
$433$	27.4071	1.31710	0.658550	−	0.752537i	$-0.271170\pi$
$433$	27.4071	1.31710	0.658550	+	0.752537i	$0.271170\pi$
$434$	0	0
$435$	−1.44530	−0.0692970
$436$	67.9658	3.25497
$437$	−4.86324	−0.232641
$438$	−17.0795	−0.816092
$439$	−21.3057	−1.01687	−0.508433	−	0.861102i	$-0.669775\pi$
$439$	−21.3057	−1.01687	−0.508433	+	0.861102i	$0.669775\pi$
$440$	−1.56838	−0.0747697
$441$	0	0
$442$	−39.9290	−1.89923
$443$	35.9341	1.70728	0.853640	−	0.520863i	$-0.174390\pi$
$443$	35.9341	1.70728	0.853640	+	0.520863i	$0.174390\pi$
$444$	31.5960	1.49948
$445$	9.89183	0.468918
$446$	61.9933	2.93547
$447$	5.53964	0.262016
$448$	0	0
$449$	38.4793	1.81595	0.907976	−	0.419022i	$-0.137627\pi$
$449$	38.4793	1.81595	0.907976	+	0.419022i	$0.137627\pi$
$450$	6.89999	0.325268
$451$	−0.0274173	−0.00129103
$452$	−89.3520	−4.20276
$453$	−10.3745	−0.487437
$454$	−69.7646	−3.27421
$455$	0	0
$456$	10.3880	0.486461
$457$	−34.7798	−1.62693	−0.813465	−	0.581614i	$-0.802421\pi$
$457$	−34.7798	−1.62693	−0.813465	+	0.581614i	$0.802421\pi$
$458$	48.1049	2.24780
$459$	27.6521	1.29069
$460$	−11.4803	−0.535274
$461$	−24.0282	−1.11911	−0.559553	−	0.828795i	$-0.689027\pi$
$461$	−24.0282	−1.11911	−0.559553	+	0.828795i	$0.689027\pi$
$462$	0	0
$463$	−29.2388	−1.35884	−0.679421	−	0.733749i	$-0.737769\pi$
$463$	−29.2388	−1.35884	−0.679421	+	0.733749i	$0.737769\pi$
$464$	25.1963	1.16971
$465$	0.623799	0.0289280
$466$	−12.7847	−0.592239
$467$	−26.6819	−1.23469	−0.617346	−	0.786692i	$-0.711792\pi$
$467$	−26.6819	−1.23469	−0.617346	+	0.786692i	$0.711792\pi$
$468$	−24.8866	−1.15038
$469$	0	0
$470$	14.1163	0.651138
$471$	3.27993	0.151131
$472$	−10.7146	−0.493179
$473$	−1.04561	−0.0480771
$474$	−7.20191	−0.330795
$475$	2.11143	0.0968792
$476$	0	0
$477$	23.1890	1.06175
$478$	−63.2329	−2.89220
$479$	−14.2571	−0.651423	−0.325712	−	0.945469i	$-0.605604\pi$
$479$	−14.2571	−0.651423	−0.325712	+	0.945469i	$0.605604\pi$
$480$	8.08820	0.369174
$481$	−19.4337	−0.886099
$482$	−28.0795	−1.27899
$483$	0	0
$484$	−54.6305	−2.48320
$485$	−13.1548	−0.597328
$486$	37.0630	1.68121
$487$	−21.0943	−0.955872	−0.477936	−	0.878395i	$-0.658615\pi$
$487$	−21.0943	−0.955872	−0.477936	+	0.878395i	$0.658615\pi$
$488$	−0.969208	−0.0438740
$489$	−12.5407	−0.567109
$490$	0	0
$491$	−12.1950	−0.550352	−0.275176	−	0.961394i	$-0.588736\pi$
$491$	−12.1950	−0.550352	−0.275176	+	0.961394i	$0.588736\pi$
$492$	0.428679	0.0193264
$493$	18.3048	0.824409
$494$	−10.6712	−0.480120
$495$	−0.519194	−0.0233360
$496$	−10.8748	−0.488295
$497$	0	0
$498$	−4.35220	−0.195027
$499$	−14.2877	−0.639607	−0.319803	−	0.947484i	$-0.603617\pi$
$499$	−14.2877	−0.639607	−0.319803	+	0.947484i	$0.603617\pi$
$500$	4.98432	0.222906
$501$	−8.82279	−0.394173
$502$	62.8941	2.80710
$503$	−36.8761	−1.64423	−0.822113	−	0.569325i	$-0.807205\pi$
$503$	−36.8761	−1.64423	−0.822113	+	0.569325i	$0.807205\pi$
$504$	0	0
$505$	11.0935	0.493654
$506$	1.21047	0.0538120
$507$	5.82804	0.258832
$508$	−10.5469	−0.467942
$509$	−20.0442	−0.888443	−0.444221	−	0.895917i	$-0.646520\pi$
$509$	−20.0442	−0.888443	−0.444221	+	0.895917i	$0.646520\pi$
$510$	13.0244	0.576732
$511$	0	0
$512$	30.5348	1.34946
$513$	7.39014	0.326283
$514$	8.22268	0.362687
$515$	8.09467	0.356694
$516$	16.3484	0.719700
$517$	−1.06219	−0.0467152
$518$	0	0
$519$	8.14729	0.357626
$520$	−15.0828	−0.661425
$521$	9.82681	0.430520	0.215260	−	0.976557i	$-0.430940\pi$
$521$	9.82681	0.430520	0.215260	+	0.976557i	$0.430940\pi$
$522$	15.9868	0.699724
$523$	−31.2206	−1.36518	−0.682592	−	0.730800i	$-0.739147\pi$
$523$	−31.2206	−1.36518	−0.682592	+	0.730800i	$0.739147\pi$
$524$	81.5582	3.56289
$525$	0	0
$526$	−51.6601	−2.25249
$527$	−7.90045	−0.344149
$528$	−1.34900	−0.0587076
$529$	−17.6949	−0.769341
$530$	23.4724	1.01958
$531$	−3.54694	−0.153924
$532$	0	0
$533$	−0.263667	−0.0114207
$534$	16.3074	0.705689
$535$	0.661700	0.0286078
$536$	4.04928	0.174902
$537$	−8.48895	−0.366325
$538$	−46.7403	−2.01512
$539$	0	0
$540$	17.4454	0.750732
$541$	−23.0717	−0.991929	−0.495965	−	0.868343i	$-0.665185\pi$
$541$	−23.0717	−0.991929	−0.495965	+	0.868343i	$0.665185\pi$
$542$	−11.1816	−0.480291
$543$	6.54393	0.280827
$544$	−102.437	−4.39197
$545$	13.6359	0.584098
$546$	0	0
$547$	20.0133	0.855708	0.427854	−	0.903848i	$-0.359270\pi$
$547$	20.0133	0.855708	0.427854	+	0.903848i	$0.359270\pi$
$548$	−33.5927	−1.43501
$549$	−0.320845	−0.0136933
$550$	−0.525540	−0.0224091
$551$	4.89206	0.208409
$552$	−11.3319	−0.482317
$553$	0	0
$554$	59.0277	2.50785
$555$	6.33908	0.269079
$556$	−60.4601	−2.56408
$557$	−4.99168	−0.211504	−0.105752	−	0.994393i	$-0.533725\pi$
$557$	−4.99168	−0.211504	−0.105752	+	0.994393i	$0.533725\pi$
$558$	−6.89999	−0.292100
$559$	−10.0554	−0.425297
$560$	0	0
$561$	−0.980033	−0.0413770
$562$	−77.5330	−3.27053
$563$	3.61812	0.152485	0.0762427	−	0.997089i	$-0.475708\pi$
$563$	3.61812	0.152485	0.0762427	+	0.997089i	$0.475708\pi$
$564$	16.6078	0.699313
$565$	−17.9266	−0.754177
$566$	53.2535	2.23841
$567$	0	0
$568$	58.1781	2.44110
$569$	9.83019	0.412103	0.206052	−	0.978541i	$-0.433939\pi$
$569$	9.83019	0.412103	0.206052	+	0.978541i	$0.433939\pi$
$570$	3.48084	0.145797
$571$	10.1360	0.424178	0.212089	−	0.977250i	$-0.431973\pi$
$571$	10.1360	0.424178	0.212089	+	0.977250i	$0.431973\pi$
$572$	1.89550	0.0792548
$573$	5.46085	0.228130
$574$	0	0
$575$	−2.30329	−0.0960538
$576$	−32.6797	−1.36165
$577$	−10.5654	−0.439844	−0.219922	−	0.975518i	$-0.570580\pi$
$577$	−10.5654	−0.439844	−0.219922	+	0.975518i	$0.570580\pi$
$578$	−120.028	−4.99250
$579$	11.1605	0.463815
$580$	11.5484	0.479520
$581$	0	0
$582$	−21.6866	−0.898938
$583$	−1.76620	−0.0731485
$584$	81.7104	3.38120
$585$	−4.99298	−0.206434
$586$	−35.0810	−1.44918
$587$	−14.8247	−0.611882	−0.305941	−	0.952051i	$-0.598971\pi$
$587$	−14.8247	−0.611882	−0.305941	+	0.952051i	$0.598971\pi$
$588$	0	0
$589$	−2.11143	−0.0870001
$590$	−3.59029	−0.147810
$591$	1.03123	0.0424192
$592$	−110.511	−4.54196
$593$	−22.6074	−0.928374	−0.464187	−	0.885737i	$-0.653653\pi$
$593$	−22.6074	−0.928374	−0.464187	+	0.885737i	$0.653653\pi$
$594$	−1.83942	−0.0754724
$595$	0	0
$596$	−44.2632	−1.81309
$597$	7.49760	0.306856
$598$	11.6408	0.476030
$599$	24.4161	0.997614	0.498807	−	0.866713i	$-0.333772\pi$
$599$	24.4161	0.997614	0.498807	+	0.866713i	$0.333772\pi$
$600$	4.91987	0.200853
$601$	17.8775	0.729237	0.364618	−	0.931157i	$-0.381199\pi$
$601$	17.8775	0.729237	0.364618	+	0.931157i	$0.381199\pi$
$602$	0	0
$603$	1.34046	0.0545879
$604$	82.8952	3.37296
$605$	−10.9605	−0.445606
$606$	18.2884	0.742915
$607$	9.79618	0.397615	0.198807	−	0.980039i	$-0.436293\pi$
$607$	9.79618	0.397615	0.198807	+	0.980039i	$0.436293\pi$
$608$	−27.3769	−1.11028
$609$	0	0
$610$	−0.324766	−0.0131494
$611$	−10.2149	−0.413250
$612$	−102.812	−4.15593
$613$	6.00423	0.242508	0.121254	−	0.992621i	$-0.461308\pi$
$613$	6.00423	0.242508	0.121254	+	0.992621i	$0.461308\pi$
$614$	−1.37284	−0.0554035
$615$	0.0860055	0.00346808
$616$	0	0
$617$	−1.19561	−0.0481333	−0.0240667	−	0.999710i	$-0.507661\pi$
$617$	−1.19561	−0.0481333	−0.0240667	+	0.999710i	$0.507661\pi$
$618$	13.3446	0.536800
$619$	34.4287	1.38381	0.691903	−	0.721991i	$-0.256773\pi$
$619$	34.4287	1.38381	0.691903	+	0.721991i	$0.256773\pi$
$620$	−4.98432	−0.200175
$621$	−8.06165	−0.323503
$622$	80.6318	3.23304
$623$	0	0
$624$	−12.9730	−0.519337
$625$	1.00000	0.0400000
$626$	40.4689	1.61746
$627$	−0.261918	−0.0104600
$628$	−26.2075	−1.04579
$629$	−80.2848	−3.20116
$630$	0	0
$631$	−10.6557	−0.424195	−0.212097	−	0.977249i	$-0.568029\pi$
$631$	−10.6557	−0.424195	−0.212097	+	0.977249i	$0.568029\pi$
$632$	34.4547	1.37054
$633$	−4.01054	−0.159405
$634$	85.0427	3.37748
$635$	−2.11601	−0.0839713
$636$	27.6151	1.09501
$637$	0	0
$638$	−1.21764	−0.0482069
$639$	19.2592	0.761881
$640$	−7.14710	−0.282514
$641$	−29.9800	−1.18414	−0.592069	−	0.805887i	$-0.701689\pi$
$641$	−29.9800	−1.18414	−0.592069	+	0.805887i	$0.701689\pi$
$642$	1.09086	0.0430528
$643$	35.0194	1.38103	0.690515	−	0.723318i	$-0.257384\pi$
$643$	35.0194	1.38103	0.690515	+	0.723318i	$0.257384\pi$
$644$	0	0
$645$	3.27997	0.129149
$646$	−44.0851	−1.73450
$647$	−8.10700	−0.318719	−0.159360	−	0.987221i	$-0.550943\pi$
$647$	−8.10700	−0.318719	−0.159360	+	0.987221i	$0.550943\pi$
$648$	−44.5556	−1.75031
$649$	0.270154	0.0106045
$650$	−5.05401	−0.198235
$651$	0	0
$652$	100.203	3.92427
$653$	−46.1737	−1.80691	−0.903457	−	0.428678i	$-0.858980\pi$
$653$	−46.1737	−1.80691	−0.903457	+	0.428678i	$0.858980\pi$
$654$	22.4797	0.879027
$655$	16.3629	0.639353
$656$	−1.49935	−0.0585399
$657$	27.0493	1.05529
$658$	0	0
$659$	44.1638	1.72038	0.860188	−	0.509977i	$-0.170346\pi$
$659$	44.1638	1.72038	0.860188	+	0.509977i	$0.170346\pi$
$660$	−0.618294	−0.0240671
$661$	1.91364	0.0744318	0.0372159	−	0.999307i	$-0.488151\pi$
$661$	1.91364	0.0744318	0.0372159	+	0.999307i	$0.488151\pi$
$662$	−8.91853	−0.346629
$663$	−9.42477	−0.366028
$664$	20.8214	0.808028
$665$	0	0
$666$	−70.1180	−2.71702
$667$	−5.33658	−0.206633
$668$	70.4965	2.72759
$669$	14.6328	0.565737
$670$	1.35685	0.0524196
$671$	0.0244373	0.000943390 0
$672$	0	0
$673$	3.85447	0.148579	0.0742894	−	0.997237i	$-0.476331\pi$
$673$	3.85447	0.148579	0.0742894	+	0.997237i	$0.476331\pi$
$674$	−32.7330	−1.26083
$675$	3.50006	0.134717
$676$	−46.5676	−1.79106
$677$	−29.3019	−1.12616	−0.563082	−	0.826401i	$-0.690384\pi$
$677$	−29.3019	−1.12616	−0.563082	+	0.826401i	$0.690384\pi$
$678$	−29.5532	−1.13498
$679$	0	0
$680$	−62.3104	−2.38949
$681$	−16.4671	−0.631021
$682$	0.525540	0.0201240
$683$	23.1003	0.883909	0.441954	−	0.897038i	$-0.354285\pi$
$683$	23.1003	0.883909	0.441954	+	0.897038i	$0.354285\pi$
$684$	−27.4770	−1.05061
$685$	−6.73968	−0.257510
$686$	0	0
$687$	11.3546	0.433206
$688$	−57.1805	−2.17999
$689$	−16.9852	−0.647083
$690$	−3.79713	−0.144554
$691$	−6.86815	−0.261277	−0.130638	−	0.991430i	$-0.541703\pi$
$691$	−6.86815	−0.261277	−0.130638	+	0.991430i	$0.541703\pi$
$692$	−65.0990	−2.47469
$693$	0	0
$694$	47.2273	1.79272
$695$	−12.1300	−0.460119
$696$	11.3990	0.432079
$697$	−1.08926	−0.0412588
$698$	−10.0640	−0.380928
$699$	−3.01767	−0.114139
$700$	0	0
$701$	−33.3225	−1.25857	−0.629287	−	0.777173i	$-0.716653\pi$
$701$	−33.3225	−1.25857	−0.629287	+	0.777173i	$0.716653\pi$
$702$	−17.6893	−0.667641
$703$	−21.4565	−0.809247
$704$	2.48906	0.0938101
$705$	3.33200	0.125490
$706$	−53.5518	−2.01545
$707$	0	0
$708$	−4.22395	−0.158746
$709$	44.9361	1.68761	0.843806	−	0.536649i	$-0.180310\pi$
$709$	44.9361	1.68761	0.843806	+	0.536649i	$0.180310\pi$
$710$	19.4946	0.731618
$711$	11.4058	0.427752
$712$	−78.0163	−2.92378
$713$	2.30329	0.0862589
$714$	0	0
$715$	0.380292	0.0142221
$716$	67.8290	2.53489
$717$	−14.9254	−0.557399
$718$	−22.8598	−0.853119
$719$	−13.0140	−0.485340	−0.242670	−	0.970109i	$-0.578023\pi$
$719$	−13.0140	−0.485340	−0.242670	+	0.970109i	$0.578023\pi$
$720$	−28.3929	−1.05814
$721$	0	0
$722$	38.4310	1.43025
$723$	−6.62785	−0.246492
$724$	−52.2878	−1.94326
$725$	2.31694	0.0860489
$726$	−18.0691	−0.670606
$727$	−21.6500	−0.802955	−0.401477	−	0.915869i	$-0.631503\pi$
$727$	−21.6500	−0.802955	−0.401477	+	0.915869i	$0.631503\pi$
$728$	0	0
$729$	−8.19958	−0.303688
$730$	27.3799	1.01337
$731$	−41.5410	−1.53645
$732$	−0.382085	−0.0141223
$733$	−35.9885	−1.32926	−0.664632	−	0.747170i	$-0.731412\pi$
$733$	−35.9885	−1.32926	−0.664632	+	0.747170i	$0.731412\pi$
$734$	−50.8913	−1.87843
$735$	0	0
$736$	29.8645	1.10082
$737$	−0.102097	−0.00376079
$738$	−0.951326	−0.0350188
$739$	−21.7701	−0.800825	−0.400413	−	0.916335i	$-0.631133\pi$
$739$	−21.7701	−0.800825	−0.400413	+	0.916335i	$0.631133\pi$
$740$	−50.6509	−1.86197
$741$	−2.51881	−0.0925310
$742$	0	0
$743$	41.7920	1.53320	0.766600	−	0.642125i	$-0.221947\pi$
$743$	41.7920	1.53320	0.766600	+	0.642125i	$0.221947\pi$
$744$	−4.91987	−0.180371
$745$	−8.88048	−0.325356
$746$	22.9980	0.842017
$747$	6.89268	0.252190
$748$	7.83072	0.286320
$749$	0	0
$750$	1.64857	0.0601972
$751$	−34.1905	−1.24763	−0.623814	−	0.781572i	$-0.714418\pi$
$751$	−34.1905	−1.24763	−0.623814	+	0.781572i	$0.714418\pi$
$752$	−58.0875	−2.11823
$753$	14.8454	0.540997
$754$	−11.7098	−0.426446
$755$	16.6312	0.605270
$756$	0	0
$757$	−39.1724	−1.42374	−0.711872	−	0.702309i	$-0.752153\pi$
$757$	−39.1724	−1.42374	−0.711872	+	0.702309i	$0.752153\pi$
$758$	58.4497	2.12299
$759$	0.285718	0.0103709
$760$	−16.6527	−0.604058
$761$	−32.9766	−1.19540	−0.597701	−	0.801719i	$-0.703919\pi$
$761$	−32.9766	−1.19540	−0.597701	+	0.801719i	$0.703919\pi$
$762$	−3.48839	−0.126371
$763$	0	0
$764$	−43.6337	−1.57861
$765$	−20.6271	−0.745774
$766$	−81.8083	−2.95585
$767$	2.59801	0.0938088
$768$	3.83341	0.138326
$769$	−2.44422	−0.0881408	−0.0440704	−	0.999028i	$-0.514033\pi$
$769$	−2.44422	−0.0881408	−0.0440704	+	0.999028i	$0.514033\pi$
$770$	0	0
$771$	1.94087	0.0698987
$772$	−89.1754	−3.20949
$773$	16.3178	0.586910	0.293455	−	0.955973i	$-0.405195\pi$
$773$	16.3178	0.586910	0.293455	+	0.955973i	$0.405195\pi$
$774$	−36.2805	−1.30408
$775$	−1.00000	−0.0359211
$776$	103.751	3.72444
$777$	0	0
$778$	0.955644	0.0342615
$779$	−0.291111	−0.0104301
$780$	−5.94600	−0.212901
$781$	−1.46688	−0.0524891
$782$	48.0909	1.71973
$783$	8.10942	0.289807
$784$	0	0
$785$	−5.25799	−0.187666
$786$	26.9754	0.962182
$787$	−18.1490	−0.646941	−0.323471	−	0.946238i	$-0.604850\pi$
$787$	−18.1490	−0.646941	−0.323471	+	0.946238i	$0.604850\pi$
$788$	−8.23982	−0.293531
$789$	−12.1938	−0.434110
$790$	11.5452	0.410761
$791$	0	0
$792$	4.09485	0.145504
$793$	0.235008	0.00834538
$794$	−93.8076	−3.32911
$795$	5.54040	0.196498
$796$	−59.9078	−2.12338
$797$	−32.5562	−1.15320	−0.576599	−	0.817027i	$-0.695621\pi$
$797$	−32.5562	−1.15320	−0.576599	+	0.817027i	$0.695621\pi$
$798$	0	0
$799$	−42.1999	−1.49293
$800$	−12.9660	−0.458418
$801$	−25.8263	−0.912529
$802$	97.5329	3.44401
$803$	−2.06022	−0.0727035
$804$	1.59632	0.0562979
$805$	0	0
$806$	5.05401	0.178020
$807$	−11.0325	−0.388363
$808$	−87.4937	−3.07802
$809$	17.8296	0.626857	0.313428	−	0.949612i	$-0.398522\pi$
$809$	17.8296	0.626857	0.313428	+	0.949612i	$0.398522\pi$
$810$	−14.9299	−0.524582
$811$	−34.6242	−1.21582	−0.607910	−	0.794006i	$-0.707992\pi$
$811$	−34.6242	−1.21582	−0.607910	+	0.794006i	$0.707992\pi$
$812$	0	0
$813$	−2.63929	−0.0925638
$814$	5.34056	0.187187
$815$	20.1037	0.704202
$816$	−53.5945	−1.87618
$817$	−11.1020	−0.388411
$818$	27.0229	0.944832
$819$	0	0
$820$	−0.687207	−0.0239983
$821$	−12.9060	−0.450422	−0.225211	−	0.974310i	$-0.572307\pi$
$821$	−12.9060	−0.450422	−0.225211	+	0.974310i	$0.572307\pi$
$822$	−11.1108	−0.387534
$823$	47.9220	1.67046	0.835228	−	0.549904i	$-0.185336\pi$
$823$	47.9220	1.67046	0.835228	+	0.549904i	$0.185336\pi$
$824$	−63.8422	−2.22405
$825$	−0.124048	−0.00431878
$826$	0	0
$827$	−15.9127	−0.553340	−0.276670	−	0.960965i	$-0.589231\pi$
$827$	−15.9127	−0.553340	−0.276670	+	0.960965i	$0.589231\pi$
$828$	29.9737	1.04166
$829$	−21.5720	−0.749227	−0.374613	−	0.927181i	$-0.622225\pi$
$829$	−21.5720	−0.749227	−0.374613	+	0.927181i	$0.622225\pi$
$830$	6.97693	0.242173
$831$	13.9328	0.483324
$832$	23.9368	0.829859
$833$	0	0
$834$	−19.9972	−0.692447
$835$	14.1436	0.489461
$836$	2.09280	0.0723810
$837$	−3.50006	−0.120980
$838$	−43.7276	−1.51054
$839$	56.1642	1.93900	0.969502	−	0.245083i	$-0.0788153\pi$
$839$	56.1642	1.93900	0.969502	+	0.245083i	$0.0788153\pi$
$840$	0	0
$841$	−23.6318	−0.814890
$842$	−66.9777	−2.30820
$843$	−18.3008	−0.630312
$844$	32.0453	1.10305
$845$	−9.34281	−0.321402
$846$	−36.8560	−1.26714
$847$	0	0
$848$	−96.5870	−3.31681
$849$	12.5699	0.431397
$850$	−20.8792	−0.716151
$851$	23.4061	0.802352
$852$	22.9352	0.785747
$853$	−36.9754	−1.26601	−0.633007	−	0.774146i	$-0.718180\pi$
$853$	−36.9754	−1.26601	−0.633007	+	0.774146i	$0.718180\pi$
$854$	0	0
$855$	−5.51269	−0.188530
$856$	−5.21879	−0.178375
$857$	48.3534	1.65172	0.825860	−	0.563875i	$-0.190690\pi$
$857$	48.3534	1.65172	0.825860	+	0.563875i	$0.190690\pi$
$858$	0.626938	0.0214033
$859$	−7.27950	−0.248373	−0.124187	−	0.992259i	$-0.539632\pi$
$859$	−7.27950	−0.248373	−0.124187	+	0.992259i	$0.539632\pi$
$860$	−26.2078	−0.893680
$861$	0	0
$862$	75.2168	2.56189
$863$	16.9863	0.578221	0.289111	−	0.957296i	$-0.406640\pi$
$863$	16.9863	0.578221	0.289111	+	0.957296i	$0.406640\pi$
$864$	−45.3819	−1.54392
$865$	−13.0608	−0.444079
$866$	−72.4310	−2.46131
$867$	−28.3312	−0.962177
$868$	0	0
$869$	−0.868729	−0.0294696
$870$	3.81963	0.129498
$871$	−0.981845	−0.0332686
$872$	−107.546	−3.64195
$873$	34.3455	1.16242
$874$	12.8525	0.434743
$875$	0	0
$876$	32.2122	1.08835
$877$	50.4524	1.70366	0.851829	−	0.523820i	$-0.175494\pi$
$877$	50.4524	1.70366	0.851829	+	0.523820i	$0.175494\pi$
$878$	56.3064	1.90025
$879$	−8.28047	−0.279293
$880$	2.16255	0.0728996
$881$	−27.7230	−0.934013	−0.467006	−	0.884254i	$-0.654668\pi$
$881$	−27.7230	−0.934013	−0.467006	+	0.884254i	$0.654668\pi$
$882$	0	0
$883$	−31.4096	−1.05702	−0.528508	−	0.848928i	$-0.677248\pi$
$883$	−31.4096	−1.05702	−0.528508	+	0.848928i	$0.677248\pi$
$884$	75.3064	2.53283
$885$	−0.847446	−0.0284866
$886$	−94.9662	−3.19045
$887$	−27.5908	−0.926407	−0.463204	−	0.886252i	$-0.653300\pi$
$887$	−27.5908	−0.926407	−0.463204	+	0.886252i	$0.653300\pi$
$888$	−49.9959	−1.67775
$889$	0	0
$890$	−26.1420	−0.876282
$891$	1.12341	0.0376356
$892$	−116.920	−3.91477
$893$	−11.2781	−0.377409
$894$	−14.6401	−0.489638
$895$	13.6085	0.454881
$896$	0	0
$897$	2.74769	0.0917426
$898$	−101.693	−3.39353
$899$	−2.31694	−0.0772742
$900$	−13.0134	−0.433782
$901$	−70.1694	−2.33768
$902$	0.0724581	0.00241259
$903$	0	0
$904$	141.386	4.70243
$905$	−10.4904	−0.348714
$906$	27.4176	0.910890
$907$	34.9391	1.16013	0.580067	−	0.814569i	$-0.303027\pi$
$907$	34.9391	1.16013	0.580067	+	0.814569i	$0.303027\pi$
$908$	131.577	4.36653
$909$	−28.9637	−0.960666
$910$	0	0
$911$	−1.51482	−0.0501883	−0.0250941	−	0.999685i	$-0.507989\pi$
$911$	−1.51482	−0.0501883	−0.0250941	+	0.999685i	$0.507989\pi$
$912$	−14.3234	−0.474294
$913$	−0.524983	−0.0173744
$914$	91.9155	3.04030
$915$	−0.0766573	−0.00253421
$916$	−90.7264	−2.99769
$917$	0	0
$918$	−73.0785	−2.41195
$919$	−11.0604	−0.364849	−0.182424	−	0.983220i	$-0.558394\pi$
$919$	−11.0604	−0.364849	−0.182424	+	0.983220i	$0.558394\pi$
$920$	18.1659	0.598912
$921$	−0.324044	−0.0106776
$922$	63.5015	2.09131
$923$	−14.1067	−0.464327
$924$	0	0
$925$	−10.1620	−0.334126
$926$	77.2719	2.53931
$927$	−21.1342	−0.694137
$928$	−30.0415	−0.986160
$929$	49.7295	1.63157	0.815786	−	0.578354i	$-0.196305\pi$
$929$	49.7295	1.63157	0.815786	+	0.578354i	$0.196305\pi$
$930$	−1.64857	−0.0540587
$931$	0	0
$932$	24.1120	0.789816
$933$	19.0322	0.623086
$934$	70.5146	2.30731
$935$	1.57107	0.0513795
$936$	39.3793	1.28715
$937$	−28.7618	−0.939607	−0.469804	−	0.882771i	$-0.655675\pi$
$937$	−28.7618	−0.939607	−0.469804	+	0.882771i	$0.655675\pi$
$938$	0	0
$939$	9.55223	0.311725
$940$	−26.6236	−0.868365
$941$	−4.83046	−0.157468	−0.0787342	−	0.996896i	$-0.525088\pi$
$941$	−4.83046	−0.157468	−0.0787342	+	0.996896i	$0.525088\pi$
$942$	−8.66815	−0.282424
$943$	0.317563	0.0103413
$944$	14.7737	0.480844
$945$	0	0
$946$	2.76332	0.0898432
$947$	10.7002	0.347709	0.173854	−	0.984771i	$-0.444378\pi$
$947$	10.7002	0.347709	0.173854	+	0.984771i	$0.444378\pi$
$948$	13.5829	0.441152
$949$	−19.8127	−0.643147
$950$	−5.58007	−0.181041
$951$	20.0734	0.650923
$952$	0	0
$953$	−15.1766	−0.491617	−0.245808	−	0.969318i	$-0.579053\pi$
$953$	−15.1766	−0.491617	−0.245808	+	0.969318i	$0.579053\pi$
$954$	−61.2836	−1.98413
$955$	−8.75418	−0.283278
$956$	119.258	3.85707
$957$	−0.287411	−0.00929066
$958$	37.6785	1.21734
$959$	0	0
$960$	−7.80795	−0.252001
$961$	1.00000	0.0322581
$962$	51.3591	1.65588
$963$	−1.72762	−0.0556717
$964$	52.9583	1.70567
$965$	−17.8912	−0.575937
$966$	0	0
$967$	−0.356978	−0.0114797	−0.00573983	−	0.999984i	$-0.501827\pi$
$967$	−0.356978	−0.0114797	−0.00573983	+	0.999984i	$0.501827\pi$
$968$	86.4444	2.77843
$969$	−10.4058	−0.334282
$970$	34.7653	1.11625
$971$	−58.0554	−1.86309	−0.931543	−	0.363632i	$-0.881537\pi$
$971$	−58.0554	−1.86309	−0.931543	+	0.363632i	$0.881537\pi$
$972$	−69.9012	−2.24208
$973$	0	0
$974$	55.7476	1.78627
$975$	−1.19294	−0.0382047
$976$	1.33639	0.0427767
$977$	55.7791	1.78453	0.892265	−	0.451511i	$-0.149115\pi$
$977$	55.7791	1.78453	0.892265	+	0.451511i	$0.149115\pi$
$978$	33.1424	1.05978
$979$	1.96707	0.0628679
$980$	0	0
$981$	−35.6016	−1.13667
$982$	32.2287	1.02846
$983$	−40.4759	−1.29098	−0.645490	−	0.763768i	$-0.723347\pi$
$983$	−40.4759	−1.29098	−0.645490	+	0.763768i	$0.723347\pi$
$984$	−0.678320	−0.0216240
$985$	−1.65315	−0.0526736
$986$	−48.3758	−1.54060
$987$	0	0
$988$	20.1260	0.640294
$989$	12.1108	0.385102
$990$	1.37212	0.0436088
$991$	−21.3031	−0.676714	−0.338357	−	0.941018i	$-0.609871\pi$
$991$	−21.3031	−0.676714	−0.338357	+	0.941018i	$0.609871\pi$
$992$	12.9660	0.411672
$993$	−2.10512	−0.0668038
$994$	0	0
$995$	−12.0192	−0.381036
$996$	8.20830	0.260090
$997$	15.2778	0.483852	0.241926	−	0.970295i	$-0.422221\pi$
$997$	15.2778	0.483852	0.241926	+	0.970295i	$0.422221\pi$
$998$	37.7594	1.19525
$999$	−35.5678	−1.12531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.bf.1.1		21
7.3	odd	6		1085.2.j.d.156.21	✓	42
7.5	odd	6		1085.2.j.d.466.21	yes	42
7.6	odd	2		7595.2.a.bg.1.1		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1085.2.j.d.156.21	✓	42	7.3	odd	6
1085.2.j.d.466.21	yes	42	7.5	odd	6
7595.2.a.bf.1.1		21	1.1	even	1	trivial
7595.2.a.bg.1.1		21	7.6	odd	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:	\( N \)	\(=\)	\( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7595.a (trivial)

\(f(q)\)	\(=\)	\(q-2.64279 q^{2} -0.623799 q^{3} +4.98432 q^{4} +1.00000 q^{5} +1.64857 q^{6} -7.88694 q^{8} -2.61087 q^{9} +O(q^{10})\)	\(q-2.64279 q^{2} -0.623799 q^{3} +4.98432 q^{4} +1.00000 q^{5} +1.64857 q^{6} -7.88694 q^{8} -2.61087 q^{9} -2.64279 q^{10} +0.198858 q^{11} -3.10922 q^{12} +1.91238 q^{13} -0.623799 q^{15} +10.8748 q^{16} +7.90045 q^{17} +6.89999 q^{18} +2.11143 q^{19} +4.98432 q^{20} -0.525540 q^{22} -2.30329 q^{23} +4.91987 q^{24} +1.00000 q^{25} -5.05401 q^{26} +3.50006 q^{27} +2.31694 q^{29} +1.64857 q^{30} -1.00000 q^{31} -12.9660 q^{32} -0.124048 q^{33} -20.8792 q^{34} -13.0134 q^{36} -10.1620 q^{37} -5.58007 q^{38} -1.19294 q^{39} -7.88694 q^{40} -0.137874 q^{41} -5.25805 q^{43} +0.991174 q^{44} -2.61087 q^{45} +6.08711 q^{46} -5.34146 q^{47} -6.78372 q^{48} -2.64279 q^{50} -4.92830 q^{51} +9.53191 q^{52} -8.88169 q^{53} -9.24991 q^{54} +0.198858 q^{55} -1.31711 q^{57} -6.12317 q^{58} +1.35852 q^{59} -3.10922 q^{60} +0.122888 q^{61} +2.64279 q^{62} +12.5168 q^{64} +1.91238 q^{65} +0.327832 q^{66} -0.513416 q^{67} +39.3784 q^{68} +1.43679 q^{69} -7.37652 q^{71} +20.5918 q^{72} -10.3602 q^{73} +26.8561 q^{74} -0.623799 q^{75} +10.5241 q^{76} +3.15269 q^{78} -4.36858 q^{79} +10.8748 q^{80} +5.64929 q^{81} +0.364371 q^{82} -2.63999 q^{83} +7.90045 q^{85} +13.8959 q^{86} -1.44530 q^{87} -1.56838 q^{88} +9.89183 q^{89} +6.89999 q^{90} -11.4803 q^{92} +0.623799 q^{93} +14.1163 q^{94} +2.11143 q^{95} +8.08820 q^{96} -13.1548 q^{97} -0.519194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more