LMFDB - Embedded newform 8085.2.a.bn.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8085,2,Mod(1,8085)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8085, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8085.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8085.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.5590500342$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.13448.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 7x^{2} + 2 $ x^4 - 7*x^2 + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1155)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.58874$ of defining polynomial
Character	$\chi$	$=$	8085.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58874 q^{2} -1.00000 q^{3} +4.70156 q^{4} +1.00000 q^{5} +2.58874 q^{6} -6.99364 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.58874 q^{2} -1.00000 q^{3} +4.70156 q^{4} +1.00000 q^{5} +2.58874 q^{6} -6.99364 q^{8} +1.00000 q^{9} -2.58874 q^{10} -1.00000 q^{11} -4.70156 q^{12} +2.40490 q^{13} -1.00000 q^{15} +8.70156 q^{16} +3.70156 q^{17} -2.58874 q^{18} -4.15641 q^{19} +4.70156 q^{20} +2.58874 q^{22} -0.0692417 q^{23} +6.99364 q^{24} +1.00000 q^{25} -6.22565 q^{26} -1.00000 q^{27} +0.703336 q^{29} +2.58874 q^{30} -5.22742 q^{31} -8.53879 q^{32} +1.00000 q^{33} -9.58237 q^{34} +4.70156 q^{36} +7.95005 q^{37} +10.7598 q^{38} -2.40490 q^{39} -6.99364 q^{40} -2.31773 q^{41} +4.24849 q^{43} -4.70156 q^{44} +1.00000 q^{45} +0.179249 q^{46} -13.3532 q^{47} -8.70156 q^{48} -2.58874 q^{50} -3.70156 q^{51} +11.3068 q^{52} -8.51136 q^{53} +2.58874 q^{54} -1.00000 q^{55} +4.15641 q^{57} -1.82075 q^{58} +4.47414 q^{59} -4.70156 q^{60} -5.02107 q^{61} +13.5324 q^{62} +4.70156 q^{64} +2.40490 q^{65} -2.58874 q^{66} +4.72263 q^{67} +17.4031 q^{68} +0.0692417 q^{69} +4.40490 q^{71} -6.99364 q^{72} +14.2129 q^{73} -20.5806 q^{74} -1.00000 q^{75} -19.5416 q^{76} +6.22565 q^{78} -4.40490 q^{79} +8.70156 q^{80} +1.00000 q^{81} +6.00000 q^{82} -5.56308 q^{83} +3.70156 q^{85} -10.9982 q^{86} -0.703336 q^{87} +6.99364 q^{88} -15.1968 q^{89} -2.58874 q^{90} -0.325544 q^{92} +5.22742 q^{93} +34.5679 q^{94} -4.15641 q^{95} +8.53879 q^{96} +8.24494 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 6 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 6 * q^4 + 4 * q^5 + 4 * q^9	$ 4 q - 4 q^{3} + 6 q^{4} + 4 q^{5} + 4 q^{9} - 4 q^{11} - 6 q^{12} - 8 q^{13} - 4 q^{15} + 22 q^{16} + 2 q^{17} - 10 q^{19} + 6 q^{20} - 2 q^{23} + 4 q^{25} - 20 q^{26} - 4 q^{27} - 2 q^{29} - 24 q^{31} + 4 q^{33} + 6 q^{36} + 8 q^{37} - 16 q^{38} + 8 q^{39} + 6 q^{43} - 6 q^{44} + 4 q^{45} - 12 q^{46} - 4 q^{47} - 22 q^{48} - 2 q^{51} - 12 q^{52} + 14 q^{53} - 4 q^{55} + 10 q^{57} - 20 q^{58} + 2 q^{59} - 6 q^{60} - 6 q^{61} - 8 q^{62} + 6 q^{64} - 8 q^{65} - 8 q^{67} + 44 q^{68} + 2 q^{69} - 4 q^{73} - 36 q^{74} - 4 q^{75} - 56 q^{76} + 20 q^{78} + 22 q^{80} + 4 q^{81} + 24 q^{82} - 6 q^{83} + 2 q^{85} - 36 q^{86} + 2 q^{87} - 18 q^{89} - 44 q^{92} + 24 q^{93} + 36 q^{94} - 10 q^{95} + 6 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 6 * q^4 + 4 * q^5 + 4 * q^9 - 4 * q^11 - 6 * q^12 - 8 * q^13 - 4 * q^15 + 22 * q^16 + 2 * q^17 - 10 * q^19 + 6 * q^20 - 2 * q^23 + 4 * q^25 - 20 * q^26 - 4 * q^27 - 2 * q^29 - 24 * q^31 + 4 * q^33 + 6 * q^36 + 8 * q^37 - 16 * q^38 + 8 * q^39 + 6 * q^43 - 6 * q^44 + 4 * q^45 - 12 * q^46 - 4 * q^47 - 22 * q^48 - 2 * q^51 - 12 * q^52 + 14 * q^53 - 4 * q^55 + 10 * q^57 - 20 * q^58 + 2 * q^59 - 6 * q^60 - 6 * q^61 - 8 * q^62 + 6 * q^64 - 8 * q^65 - 8 * q^67 + 44 * q^68 + 2 * q^69 - 4 * q^73 - 36 * q^74 - 4 * q^75 - 56 * q^76 + 20 * q^78 + 22 * q^80 + 4 * q^81 + 24 * q^82 - 6 * q^83 + 2 * q^85 - 36 * q^86 + 2 * q^87 - 18 * q^89 - 44 * q^92 + 24 * q^93 + 36 * q^94 - 10 * q^95 + 6 * q^97 - 4 * 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 $

$2$	−2.58874	−1.83051	−0.915257	−	0.402871i	$-0.868012\pi$
$2$	−2.58874	−1.83051	−0.915257	+	0.402871i	$0.868012\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.70156	2.35078
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.58874	1.05685
$7$	0	0
$7$	0	0
$8$	−6.99364	−2.47262
$9$	1.00000	0.333333
$10$	−2.58874	−0.818631
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.70156	−1.35722
$13$	2.40490	0.666999	0.333499	−	0.942750i	$-0.391771\pi$
$13$	2.40490	0.666999	0.333499	+	0.942750i	$0.391771\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	8.70156	2.17539
$17$	3.70156	0.897761	0.448880	−	0.893592i	$-0.351823\pi$
$17$	3.70156	0.897761	0.448880	+	0.893592i	$0.351823\pi$
$18$	−2.58874	−0.610171
$19$	−4.15641	−0.953545	−0.476773	−	0.879027i	$-0.658193\pi$
$19$	−4.15641	−0.953545	−0.476773	+	0.879027i	$0.658193\pi$
$20$	4.70156	1.05130
$21$	0	0
$22$	2.58874	0.551921
$23$	−0.0692417	−0.0144379	−0.00721895	−	0.999974i	$-0.502298\pi$
$23$	−0.0692417	−0.0144379	−0.00721895	+	0.999974i	$0.502298\pi$
$24$	6.99364	1.42757
$25$	1.00000	0.200000
$26$	−6.22565	−1.22095
$27$	−1.00000	−0.192450
$28$	0	0
$29$	0.703336	0.130606	0.0653031	−	0.997865i	$-0.479199\pi$
$29$	0.703336	0.130606	0.0653031	+	0.997865i	$0.479199\pi$
$30$	2.58874	0.472637
$31$	−5.22742	−0.938873	−0.469436	−	0.882966i	$-0.655543\pi$
$31$	−5.22742	−0.938873	−0.469436	+	0.882966i	$0.655543\pi$
$32$	−8.53879	−1.50946
$33$	1.00000	0.174078
$34$	−9.58237	−1.64336
$35$	0	0
$36$	4.70156	0.783594
$37$	7.95005	1.30698	0.653490	−	0.756935i	$-0.273304\pi$
$37$	7.95005	1.30698	0.653490	+	0.756935i	$0.273304\pi$
$38$	10.7598	1.74548
$39$	−2.40490	−0.385092
$40$	−6.99364	−1.10579
$41$	−2.31773	−0.361969	−0.180984	−	0.983486i	$-0.557928\pi$
$41$	−2.31773	−0.361969	−0.180984	+	0.983486i	$0.557928\pi$
$42$	0	0
$43$	4.24849	0.647889	0.323944	−	0.946076i	$-0.394991\pi$
$43$	4.24849	0.647889	0.323944	+	0.946076i	$0.394991\pi$
$44$	−4.70156	−0.708787
$45$	1.00000	0.149071
$46$	0.179249	0.0264288
$47$	−13.3532	−1.94776	−0.973881	−	0.227061i	$-0.927088\pi$
$47$	−13.3532	−1.94776	−0.973881	+	0.227061i	$0.927088\pi$
$48$	−8.70156	−1.25596
$49$	0	0
$50$	−2.58874	−0.366103
$51$	−3.70156	−0.518322
$52$	11.3068	1.56797
$53$	−8.51136	−1.16912	−0.584562	−	0.811349i	$-0.698734\pi$
$53$	−8.51136	−1.16912	−0.584562	+	0.811349i	$0.698734\pi$
$54$	2.58874	0.352283
$55$	−1.00000	−0.134840
$56$	0	0
$57$	4.15641	0.550530
$58$	−1.82075	−0.239076
$59$	4.47414	0.582483	0.291242	−	0.956650i	$-0.405932\pi$
$59$	4.47414	0.582483	0.291242	+	0.956650i	$0.405932\pi$
$60$	−4.70156	−0.606969
$61$	−5.02107	−0.642882	−0.321441	−	0.946930i	$-0.604167\pi$
$61$	−5.02107	−0.642882	−0.321441	+	0.946930i	$0.604167\pi$
$62$	13.5324	1.71862
$63$	0	0
$64$	4.70156	0.587695
$65$	2.40490	0.298291
$66$	−2.58874	−0.318652
$67$	4.72263	0.576961	0.288481	−	0.957486i	$-0.406850\pi$
$67$	4.72263	0.576961	0.288481	+	0.957486i	$0.406850\pi$
$68$	17.4031	2.11044
$69$	0.0692417	0.00833572
$70$	0	0
$71$	4.40490	0.522765	0.261383	−	0.965235i	$-0.415822\pi$
$71$	4.40490	0.522765	0.261383	+	0.965235i	$0.415822\pi$
$72$	−6.99364	−0.824208
$73$	14.2129	1.66350	0.831748	−	0.555153i	$-0.187340\pi$
$73$	14.2129	1.66350	0.831748	+	0.555153i	$0.187340\pi$
$74$	−20.5806	−2.39245
$75$	−1.00000	−0.115470
$76$	−19.5416	−2.24158
$77$	0	0
$78$	6.22565	0.704916
$79$	−4.40490	−0.495590	−0.247795	−	0.968813i	$-0.579706\pi$
$79$	−4.40490	−0.495590	−0.247795	+	0.968813i	$0.579706\pi$
$80$	8.70156	0.972864
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	−5.56308	−0.610627	−0.305314	−	0.952252i	$-0.598761\pi$
$83$	−5.56308	−0.610627	−0.305314	+	0.952252i	$0.598761\pi$
$84$	0	0
$85$	3.70156	0.401491
$86$	−10.9982	−1.18597
$87$	−0.703336	−0.0754055
$88$	6.99364	0.745524
$89$	−15.1968	−1.61085	−0.805427	−	0.592695i	$-0.798064\pi$
$89$	−15.1968	−1.61085	−0.805427	+	0.592695i	$0.798064\pi$
$90$	−2.58874	−0.272877
$91$	0	0
$92$	−0.325544	−0.0339403
$93$	5.22742	0.542058
$94$	34.5679	3.56540
$95$	−4.15641	−0.426438
$96$	8.53879	0.871487
$97$	8.24494	0.837147	0.418574	−	0.908183i	$-0.362530\pi$
$97$	8.24494	0.837147	0.418574	+	0.908183i	$0.362530\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	4.70156	0.470156
$101$	−11.0354	−1.09807	−0.549034	−	0.835800i	$-0.685004\pi$
$101$	−11.0354	−1.09807	−0.549034	+	0.835800i	$0.685004\pi$
$102$	9.58237	0.948796
$103$	2.84182	0.280013	0.140006	−	0.990151i	$-0.455288\pi$
$103$	2.84182	0.280013	0.140006	+	0.990151i	$0.455288\pi$
$104$	−16.8190	−1.64924
$105$	0	0
$106$	22.0337	2.14010
$107$	−15.3567	−1.48459	−0.742295	−	0.670073i	$-0.766263\pi$
$107$	−15.3567	−1.48459	−0.742295	+	0.670073i	$0.766263\pi$
$108$	−4.70156	−0.452408
$109$	12.8597	1.23174	0.615870	−	0.787848i	$-0.288805\pi$
$109$	12.8597	1.23174	0.615870	+	0.787848i	$0.288805\pi$
$110$	2.58874	0.246826
$111$	−7.95005	−0.754586
$112$	0	0
$113$	16.5114	1.55326	0.776629	−	0.629958i	$-0.216928\pi$
$113$	16.5114	1.55326	0.776629	+	0.629958i	$0.216928\pi$
$114$	−10.7598	−1.00775
$115$	−0.0692417	−0.00645682
$116$	3.30678	0.307026
$117$	2.40490	0.222333
$118$	−11.5824	−1.06624
$119$	0	0
$120$	6.99364	0.638429
$121$	1.00000	0.0909091
$122$	12.9982	1.17680
$123$	2.31773	0.208983
$124$	−24.5771	−2.20708
$125$	1.00000	0.0894427
$126$	0	0
$127$	−0.248490	−0.0220500	−0.0110250	−	0.999939i	$-0.503509\pi$
$127$	−0.248490	−0.0220500	−0.0110250	+	0.999939i	$0.503509\pi$
$128$	4.90647	0.433675
$129$	−4.24849	−0.374059
$130$	−6.22565	−0.546026
$131$	−12.6178	−1.10242	−0.551212	−	0.834365i	$-0.685834\pi$
$131$	−12.6178	−1.10242	−0.551212	+	0.834365i	$0.685834\pi$
$132$	4.70156	0.409218
$133$	0	0
$134$	−12.2256	−1.05614
$135$	−1.00000	−0.0860663
$136$	−25.8874	−2.21982
$137$	9.40312	0.803363	0.401682	−	0.915779i	$-0.368426\pi$
$137$	9.40312	0.803363	0.401682	+	0.915779i	$0.368426\pi$
$138$	−0.179249	−0.0152587
$139$	−22.4934	−1.90787	−0.953934	−	0.300016i	$-0.903008\pi$
$139$	−22.4934	−1.90787	−0.953934	+	0.300016i	$0.903008\pi$
$140$	0	0
$141$	13.3532	1.12454
$142$	−11.4031	−0.956929
$143$	−2.40490	−0.201108
$144$	8.70156	0.725130
$145$	0.703336	0.0584088
$146$	−36.7935	−3.04505
$147$	0	0
$148$	37.3777	3.07243
$149$	−13.9001	−1.13874	−0.569370	−	0.822081i	$-0.692813\pi$
$149$	−13.9001	−1.13874	−0.569370	+	0.822081i	$0.692813\pi$
$150$	2.58874	0.211370
$151$	2.95183	0.240216	0.120108	−	0.992761i	$-0.461676\pi$
$151$	2.95183	0.240216	0.120108	+	0.992761i	$0.461676\pi$
$152$	29.0684	2.35776
$153$	3.70156	0.299254
$154$	0	0
$155$	−5.22742	−0.419877
$156$	−11.3068	−0.905267
$157$	−5.15463	−0.411385	−0.205692	−	0.978617i	$-0.565945\pi$
$157$	−5.15463	−0.411385	−0.205692	+	0.978617i	$0.565945\pi$
$158$	11.4031	0.907184
$159$	8.51136	0.674995
$160$	−8.53879	−0.675051
$161$	0	0
$162$	−2.58874	−0.203390
$163$	2.32128	0.181817	0.0909083	−	0.995859i	$-0.471023\pi$
$163$	2.32128	0.181817	0.0909083	+	0.995859i	$0.471023\pi$
$164$	−10.8970	−0.850910
$165$	1.00000	0.0778499
$166$	14.4014	1.11776
$167$	−17.7581	−1.37416	−0.687081	−	0.726581i	$-0.741108\pi$
$167$	−17.7581	−1.37416	−0.687081	+	0.726581i	$0.741108\pi$
$168$	0	0
$169$	−7.21647	−0.555113
$170$	−9.58237	−0.734934
$171$	−4.15641	−0.317848
$172$	19.9745	1.52304
$173$	−20.2094	−1.53649	−0.768245	−	0.640156i	$-0.778870\pi$
$173$	−20.2094	−1.53649	−0.768245	+	0.640156i	$0.778870\pi$
$174$	1.82075	0.138031
$175$	0	0
$176$	−8.70156	−0.655905
$177$	−4.47414	−0.336297
$178$	39.3404	2.94869
$179$	−5.95005	−0.444728	−0.222364	−	0.974964i	$-0.571377\pi$
$179$	−5.95005	−0.444728	−0.222364	+	0.974964i	$0.571377\pi$
$180$	4.70156	0.350434
$181$	5.54161	0.411904	0.205952	−	0.978562i	$-0.433971\pi$
$181$	5.54161	0.411904	0.205952	+	0.978562i	$0.433971\pi$
$182$	0	0
$183$	5.02107	0.371168
$184$	0.484251	0.0356995
$185$	7.95005	0.584499
$186$	−13.5324	−0.992246
$187$	−3.70156	−0.270685
$188$	−62.7808	−4.57876
$189$	0	0
$190$	10.7598	0.780601
$191$	25.8966	1.87381	0.936905	−	0.349585i	$-0.113677\pi$
$191$	25.8966	1.87381	0.936905	+	0.349585i	$0.113677\pi$
$192$	−4.70156	−0.339306
$193$	−1.31596	−0.0947248	−0.0473624	−	0.998878i	$-0.515082\pi$
$193$	−1.31596	−0.0947248	−0.0473624	+	0.998878i	$0.515082\pi$
$194$	−21.3440	−1.53241
$195$	−2.40490	−0.172218
$196$	0	0
$197$	−4.44212	−0.316488	−0.158244	−	0.987400i	$-0.550583\pi$
$197$	−4.44212	−0.316488	−0.158244	+	0.987400i	$0.550583\pi$
$198$	2.58874	0.183974
$199$	25.7453	1.82504	0.912520	−	0.409033i	$-0.134134\pi$
$199$	25.7453	1.82504	0.912520	+	0.409033i	$0.134134\pi$
$200$	−6.99364	−0.494525
$201$	−4.72263	−0.333109
$202$	28.5679	2.01003
$203$	0	0
$204$	−17.4031	−1.21846
$205$	−2.31773	−0.161877
$206$	−7.35672	−0.512567
$207$	−0.0692417	−0.00481263
$208$	20.9264	1.45098
$209$	4.15641	0.287505
$210$	0	0
$211$	−24.2129	−1.66689	−0.833443	−	0.552605i	$-0.813634\pi$
$211$	−24.2129	−1.66689	−0.833443	+	0.552605i	$0.813634\pi$
$212$	−40.0167	−2.74836
$213$	−4.40490	−0.301819
$214$	39.7545	2.71756
$215$	4.24849	0.289745
$216$	6.99364	0.475857
$217$	0	0
$218$	−33.2905	−2.25472
$219$	−14.2129	−0.960420
$220$	−4.70156	−0.316979
$221$	8.90188	0.598805
$222$	20.5806	1.38128
$223$	−8.38697	−0.561633	−0.280817	−	0.959761i	$-0.590605\pi$
$223$	−8.38697	−0.561633	−0.280817	+	0.959761i	$0.590605\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−42.7436	−2.84326
$227$	−2.79542	−0.185538	−0.0927692	−	0.995688i	$-0.529572\pi$
$227$	−2.79542	−0.185538	−0.0927692	+	0.995688i	$0.529572\pi$
$228$	19.5416	1.29417
$229$	−9.95360	−0.657752	−0.328876	−	0.944373i	$-0.606670\pi$
$229$	−9.95360	−0.657752	−0.328876	+	0.944373i	$0.606670\pi$
$230$	0.179249	0.0118193
$231$	0	0
$232$	−4.91887	−0.322940
$233$	−2.77612	−0.181870	−0.0909350	−	0.995857i	$-0.528986\pi$
$233$	−2.77612	−0.181870	−0.0909350	+	0.995857i	$0.528986\pi$
$234$	−6.22565	−0.406983
$235$	−13.3532	−0.871065
$236$	21.0354	1.36929
$237$	4.40490	0.286129
$238$	0	0
$239$	−14.6034	−0.944618	−0.472309	−	0.881433i	$-0.656579\pi$
$239$	−14.6034	−0.944618	−0.472309	+	0.881433i	$0.656579\pi$
$240$	−8.70156	−0.561683
$241$	−10.5385	−0.678842	−0.339421	−	0.940635i	$-0.610231\pi$
$241$	−10.5385	−0.678842	−0.339421	+	0.940635i	$0.610231\pi$
$242$	−2.58874	−0.166410
$243$	−1.00000	−0.0641500
$244$	−23.6069	−1.51127
$245$	0	0
$246$	−6.00000	−0.382546
$247$	−9.99573	−0.636013
$248$	36.5587	2.32148
$249$	5.56308	0.352546
$250$	−2.58874	−0.163726
$251$	19.3904	1.22391	0.611955	−	0.790892i	$-0.290383\pi$
$251$	19.3904	1.22391	0.611955	+	0.790892i	$0.290383\pi$
$252$	0	0
$253$	0.0692417	0.00435319
$254$	0.643276	0.0403627
$255$	−3.70156	−0.231801
$256$	−22.1047	−1.38154
$257$	−2.71771	−0.169526	−0.0847631	−	0.996401i	$-0.527013\pi$
$257$	−2.71771	−0.169526	−0.0847631	+	0.996401i	$0.527013\pi$
$258$	10.9982	0.684720
$259$	0	0
$260$	11.3068	0.701216
$261$	0.703336	0.0435354
$262$	32.6642	2.01800
$263$	−14.4548	−0.891324	−0.445662	−	0.895201i	$-0.647032\pi$
$263$	−14.4548	−0.891324	−0.445662	+	0.895201i	$0.647032\pi$
$264$	−6.99364	−0.430428
$265$	−8.51136	−0.522849
$266$	0	0
$267$	15.1968	0.930027
$268$	22.2037	1.35631
$269$	17.2677	1.05283	0.526414	−	0.850228i	$-0.323536\pi$
$269$	17.2677	1.05283	0.526414	+	0.850228i	$0.323536\pi$
$270$	2.58874	0.157546
$271$	−15.7051	−0.954017	−0.477009	−	0.878899i	$-0.658279\pi$
$271$	−15.7051	−0.954017	−0.477009	+	0.878899i	$0.658279\pi$
$272$	32.2094	1.95298
$273$	0	0
$274$	−24.3422	−1.47057
$275$	−1.00000	−0.0603023
$276$	0.325544	0.0195955
$277$	15.9837	0.960369	0.480184	−	0.877168i	$-0.340570\pi$
$277$	15.9837	0.960369	0.480184	+	0.877168i	$0.340570\pi$
$278$	58.2296	3.49238
$279$	−5.22742	−0.312958
$280$	0	0
$281$	−5.50302	−0.328283	−0.164141	−	0.986437i	$-0.552485\pi$
$281$	−5.50302	−0.328283	−0.164141	+	0.986437i	$0.552485\pi$
$282$	−34.5679	−2.05849
$283$	8.09208	0.481024	0.240512	−	0.970646i	$-0.422685\pi$
$283$	8.09208	0.481024	0.240512	+	0.970646i	$0.422685\pi$
$284$	20.7099	1.22891
$285$	4.15641	0.246204
$286$	6.22565	0.368130
$287$	0	0
$288$	−8.53879	−0.503153
$289$	−3.29844	−0.194026
$290$	−1.82075	−0.106918
$291$	−8.24494	−0.483327
$292$	66.8229	3.91052
$293$	−6.51490	−0.380605	−0.190302	−	0.981726i	$-0.560947\pi$
$293$	−6.51490	−0.380605	−0.190302	+	0.981726i	$0.560947\pi$
$294$	0	0
$295$	4.47414	0.260494
$296$	−55.5998	−3.23167
$297$	1.00000	0.0580259
$298$	35.9837	2.08448
$299$	−0.166519	−0.00963006
$300$	−4.70156	−0.271445
$301$	0	0
$302$	−7.64150	−0.439719
$303$	11.0354	0.633970
$304$	−36.1672	−2.07433
$305$	−5.02107	−0.287505
$306$	−9.58237	−0.547788
$307$	22.5679	1.28802	0.644008	−	0.765019i	$-0.277270\pi$
$307$	22.5679	1.28802	0.644008	+	0.765019i	$0.277270\pi$
$308$	0	0
$309$	−2.84182	−0.161665
$310$	13.5324	0.768590
$311$	−0.0513177	−0.00290996	−0.00145498	−	0.999999i	$-0.500463\pi$
$311$	−0.0513177	−0.00290996	−0.00145498	+	0.999999i	$0.500463\pi$
$312$	16.8190	0.952187
$313$	3.44224	0.194567	0.0972835	−	0.995257i	$-0.468985\pi$
$313$	3.44224	0.194567	0.0972835	+	0.995257i	$0.468985\pi$
$314$	13.3440	0.753045
$315$	0	0
$316$	−20.7099	−1.16502
$317$	31.6582	1.77810	0.889050	−	0.457810i	$-0.151366\pi$
$317$	31.6582	1.77810	0.889050	+	0.457810i	$0.151366\pi$
$318$	−22.0337	−1.23559
$319$	−0.703336	−0.0393792
$320$	4.70156	0.262825
$321$	15.3567	0.857129
$322$	0	0
$323$	−15.3852	−0.856055
$324$	4.70156	0.261198
$325$	2.40490	0.133400
$326$	−6.00918	−0.332818
$327$	−12.8597	−0.711145
$328$	16.2094	0.895013
$329$	0	0
$330$	−2.58874	−0.142505
$331$	−3.55953	−0.195650	−0.0978248	−	0.995204i	$-0.531188\pi$
$331$	−3.55953	−0.195650	−0.0978248	+	0.995204i	$0.531188\pi$
$332$	−26.1552	−1.43545
$333$	7.95005	0.435660
$334$	45.9710	2.51542
$335$	4.72263	0.258025
$336$	0	0
$337$	4.23221	0.230543	0.115272	−	0.993334i	$-0.463226\pi$
$337$	4.23221	0.230543	0.115272	+	0.993334i	$0.463226\pi$
$338$	18.6815	1.01614
$339$	−16.5114	−0.896774
$340$	17.4031	0.943817
$341$	5.22742	0.283081
$342$	10.7598	0.581826
$343$	0	0
$344$	−29.7124	−1.60198
$345$	0.0692417	0.00372785
$346$	52.3168	2.81257
$347$	15.6160	0.838313	0.419157	−	0.907914i	$-0.362326\pi$
$347$	15.6160	0.838313	0.419157	+	0.907914i	$0.362326\pi$
$348$	−3.30678	−0.177262
$349$	−2.24357	−0.120096	−0.0600479	−	0.998195i	$-0.519125\pi$
$349$	−2.24357	−0.120096	−0.0600479	+	0.998195i	$0.519125\pi$
$350$	0	0
$351$	−2.40490	−0.128364
$352$	8.53879	0.455119
$353$	−11.9965	−0.638507	−0.319253	−	0.947669i	$-0.603432\pi$
$353$	−11.9965	−0.638507	−0.319253	+	0.947669i	$0.603432\pi$
$354$	11.5824	0.615596
$355$	4.40490	0.233788
$356$	−71.4486	−3.78677
$357$	0	0
$358$	15.4031	0.814080
$359$	24.6743	1.30226	0.651131	−	0.758966i	$-0.274295\pi$
$359$	24.6743	1.30226	0.651131	+	0.758966i	$0.274295\pi$
$360$	−6.99364	−0.368597
$361$	−1.72428	−0.0907514
$362$	−14.3458	−0.753997
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	14.2129	0.743938
$366$	−12.9982	−0.679428
$367$	−22.2808	−1.16305	−0.581524	−	0.813529i	$-0.697543\pi$
$367$	−22.2808	−1.16305	−0.581524	+	0.813529i	$0.697543\pi$
$368$	−0.602511	−0.0314081
$369$	−2.31773	−0.120656
$370$	−20.5806	−1.06993
$371$	0	0
$372$	24.5771	1.27426
$373$	13.6389	0.706195	0.353097	−	0.935587i	$-0.385128\pi$
$373$	13.6389	0.706195	0.353097	+	0.935587i	$0.385128\pi$
$374$	9.58237	0.495493
$375$	−1.00000	−0.0516398
$376$	93.3872	4.81608
$377$	1.69145	0.0871141
$378$	0	0
$379$	14.1985	0.729330	0.364665	−	0.931139i	$-0.381183\pi$
$379$	14.1985	0.729330	0.364665	+	0.931139i	$0.381183\pi$
$380$	−19.5416	−1.00246
$381$	0.248490	0.0127305
$382$	−67.0394	−3.43003
$383$	10.1244	0.517332	0.258666	−	0.965967i	$-0.416717\pi$
$383$	10.1244	0.517332	0.258666	+	0.965967i	$0.416717\pi$
$384$	−4.90647	−0.250382
$385$	0	0
$386$	3.40667	0.173395
$387$	4.24849	0.215963
$388$	38.7641	1.96795
$389$	−20.9342	−1.06141	−0.530703	−	0.847558i	$-0.678072\pi$
$389$	−20.9342	−1.06141	−0.530703	+	0.847558i	$0.678072\pi$
$390$	6.22565	0.315248
$391$	−0.256303	−0.0129618
$392$	0	0
$393$	12.6178	0.636485
$394$	11.4995	0.579335
$395$	−4.40490	−0.221634
$396$	−4.70156	−0.236262
$397$	24.5679	1.23303	0.616513	−	0.787345i	$-0.288545\pi$
$397$	24.5679	1.23303	0.616513	+	0.787345i	$0.288545\pi$
$398$	−66.6479	−3.34076
$399$	0	0
$400$	8.70156	0.435078
$401$	−38.4180	−1.91850	−0.959252	−	0.282551i	$-0.908819\pi$
$401$	−38.4180	−1.91850	−0.959252	+	0.282551i	$0.908819\pi$
$402$	12.2256	0.609760
$403$	−12.5714	−0.626227
$404$	−51.8838	−2.58132
$405$	1.00000	0.0496904
$406$	0	0
$407$	−7.95005	−0.394069
$408$	25.8874	1.28162
$409$	1.17748	0.0582224	0.0291112	−	0.999576i	$-0.490732\pi$
$409$	1.17748	0.0582224	0.0291112	+	0.999576i	$0.490732\pi$
$410$	6.00000	0.296319
$411$	−9.40312	−0.463822
$412$	13.3610	0.658249
$413$	0	0
$414$	0.179249	0.00880959
$415$	−5.56308	−0.273081
$416$	−20.5349	−1.00681
$417$	22.4934	1.10151
$418$	−10.7598	−0.526281
$419$	37.2585	1.82020	0.910098	−	0.414393i	$-0.136006\pi$
$419$	37.2585	1.82020	0.910098	+	0.414393i	$0.136006\pi$
$420$	0	0
$421$	3.10469	0.151313	0.0756566	−	0.997134i	$-0.475895\pi$
$421$	3.10469	0.151313	0.0756566	+	0.997134i	$0.475895\pi$
$422$	62.6809	3.05126
$423$	−13.3532	−0.649254
$424$	59.5253	2.89081
$425$	3.70156	0.179552
$426$	11.4031	0.552483
$427$	0	0
$428$	−72.2006	−3.48995
$429$	2.40490	0.116110
$430$	−10.9982	−0.530382
$431$	−13.5452	−0.652447	−0.326224	−	0.945293i	$-0.605776\pi$
$431$	−13.5452	−0.652447	−0.326224	+	0.945293i	$0.605776\pi$
$432$	−8.70156	−0.418654
$433$	33.7904	1.62386	0.811931	−	0.583754i	$-0.198417\pi$
$433$	33.7904	1.62386	0.811931	+	0.583754i	$0.198417\pi$
$434$	0	0
$435$	−0.703336	−0.0337224
$436$	60.4609	2.89555
$437$	0.287797	0.0137672
$438$	36.7935	1.75806
$439$	−11.6052	−0.553887	−0.276943	−	0.960886i	$-0.589321\pi$
$439$	−11.6052	−0.553887	−0.276943	+	0.960886i	$0.589321\pi$
$440$	6.99364	0.333408
$441$	0	0
$442$	−23.0446	−1.09612
$443$	−24.7226	−1.17461	−0.587304	−	0.809367i	$-0.699811\pi$
$443$	−24.7226	−1.17461	−0.587304	+	0.809367i	$0.699811\pi$
$444$	−37.3777	−1.77387
$445$	−15.1968	−0.720396
$446$	21.7117	1.02808
$447$	13.9001	0.657452
$448$	0	0
$449$	31.5275	1.48788	0.743938	−	0.668249i	$-0.232956\pi$
$449$	31.5275	1.48788	0.743938	+	0.668249i	$0.232956\pi$
$450$	−2.58874	−0.122034
$451$	2.31773	0.109138
$452$	77.6292	3.65137
$453$	−2.95183	−0.138689
$454$	7.23660	0.339631
$455$	0	0
$456$	−29.0684	−1.36125
$457$	−13.3874	−0.626235	−0.313118	−	0.949714i	$-0.601373\pi$
$457$	−13.3874	−0.626235	−0.313118	+	0.949714i	$0.601373\pi$
$458$	25.7673	1.20402
$459$	−3.70156	−0.172774
$460$	−0.325544	−0.0151786
$461$	−3.87070	−0.180276	−0.0901382	−	0.995929i	$-0.528731\pi$
$461$	−3.87070	−0.180276	−0.0901382	+	0.995929i	$0.528731\pi$
$462$	0	0
$463$	29.2484	1.35929	0.679643	−	0.733543i	$-0.262135\pi$
$463$	29.2484	1.35929	0.679643	+	0.733543i	$0.262135\pi$
$464$	6.12012	0.284119
$465$	5.22742	0.242416
$466$	7.18666	0.332915
$467$	−14.2551	−0.659645	−0.329823	−	0.944043i	$-0.606989\pi$
$467$	−14.2551	−0.659645	−0.329823	+	0.944043i	$0.606989\pi$
$468$	11.3068	0.522656
$469$	0	0
$470$	34.5679	1.59450
$471$	5.15463	0.237513
$472$	−31.2905	−1.44026
$473$	−4.24849	−0.195346
$474$	−11.4031	−0.523763
$475$	−4.15641	−0.190709
$476$	0	0
$477$	−8.51136	−0.389708
$478$	37.8045	1.72914
$479$	32.2339	1.47280	0.736401	−	0.676545i	$-0.236524\pi$
$479$	32.2339	1.47280	0.736401	+	0.676545i	$0.236524\pi$
$480$	8.53879	0.389741
$481$	19.1191	0.871754
$482$	27.2813	1.24263
$483$	0	0
$484$	4.70156	0.213707
$485$	8.24494	0.374384
$486$	2.58874	0.117428
$487$	5.27382	0.238980	0.119490	−	0.992835i	$-0.461874\pi$
$487$	5.27382	0.238980	0.119490	+	0.992835i	$0.461874\pi$
$488$	35.1155	1.58960
$489$	−2.32128	−0.104972
$490$	0	0
$491$	35.6647	1.60953	0.804764	−	0.593595i	$-0.202292\pi$
$491$	35.6647	1.60953	0.804764	+	0.593595i	$0.202292\pi$
$492$	10.8970	0.491273
$493$	2.60344	0.117253
$494$	25.8763	1.16423
$495$	−1.00000	−0.0449467
$496$	−45.4867	−2.04242
$497$	0	0
$498$	−14.4014	−0.645340
$499$	−39.0083	−1.74625	−0.873127	−	0.487494i	$-0.837911\pi$
$499$	−39.0083	−1.74625	−0.873127	+	0.487494i	$0.837911\pi$
$500$	4.70156	0.210260
$501$	17.7581	0.793372
$502$	−50.1966	−2.24039
$503$	32.6821	1.45722	0.728612	−	0.684926i	$-0.240166\pi$
$503$	32.6821	1.45722	0.728612	+	0.684926i	$0.240166\pi$
$504$	0	0
$505$	−11.0354	−0.491071
$506$	−0.179249	−0.00796857
$507$	7.21647	0.320495
$508$	−1.16829	−0.0518346
$509$	−3.25808	−0.144412	−0.0722058	−	0.997390i	$-0.523004\pi$
$509$	−3.25808	−0.144412	−0.0722058	+	0.997390i	$0.523004\pi$
$510$	9.58237	0.424315
$511$	0	0
$512$	47.4103	2.09526
$513$	4.15641	0.183510
$514$	7.03544	0.310320
$515$	2.84182	0.125226
$516$	−19.9745	−0.879330
$517$	13.3532	0.587272
$518$	0	0
$519$	20.2094	0.887093
$520$	−16.8190	−0.737561
$521$	−7.75506	−0.339755	−0.169878	−	0.985465i	$-0.554337\pi$
$521$	−7.75506	−0.339755	−0.169878	+	0.985465i	$0.554337\pi$
$522$	−1.82075	−0.0796921
$523$	−27.1647	−1.18783	−0.593916	−	0.804527i	$-0.702419\pi$
$523$	−27.1647	−1.18783	−0.593916	+	0.804527i	$0.702419\pi$
$524$	−59.3235	−2.59156
$525$	0	0
$526$	37.4198	1.63158
$527$	−19.3496	−0.842883
$528$	8.70156	0.378687
$529$	−22.9952	−0.999792
$530$	22.0337	0.957082
$531$	4.47414	0.194161
$532$	0	0
$533$	−5.57391	−0.241433
$534$	−39.3404	−1.70243
$535$	−15.3567	−0.663929
$536$	−33.0284	−1.42661
$537$	5.95005	0.256764
$538$	−44.7014	−1.92722
$539$	0	0
$540$	−4.70156	−0.202323
$541$	36.2087	1.55673	0.778366	−	0.627811i	$-0.216049\pi$
$541$	36.2087	1.55673	0.778366	+	0.627811i	$0.216049\pi$
$542$	40.6564	1.74634
$543$	−5.54161	−0.237813
$544$	−31.6069	−1.35513
$545$	12.8597	0.550851
$546$	0	0
$547$	−11.1160	−0.475288	−0.237644	−	0.971352i	$-0.576375\pi$
$547$	−11.1160	−0.475288	−0.237644	+	0.971352i	$0.576375\pi$
$548$	44.2094	1.88853
$549$	−5.02107	−0.214294
$550$	2.58874	0.110384
$551$	−2.92335	−0.124539
$552$	−0.484251	−0.0206111
$553$	0	0
$554$	−41.3777	−1.75797
$555$	−7.95005	−0.337461
$556$	−105.754	−4.48498
$557$	34.4772	1.46084	0.730422	−	0.682996i	$-0.239323\pi$
$557$	34.4772	1.46084	0.730422	+	0.682996i	$0.239323\pi$
$558$	13.5324	0.572873
$559$	10.2172	0.432141
$560$	0	0
$561$	3.70156	0.156280
$562$	14.2459	0.600926
$563$	−16.2129	−0.683293	−0.341647	−	0.939829i	$-0.610985\pi$
$563$	−16.2129	−0.683293	−0.341647	+	0.939829i	$0.610985\pi$
$564$	62.7808	2.64355
$565$	16.5114	0.694638
$566$	−20.9483	−0.880522
$567$	0	0
$568$	−30.8062	−1.29260
$569$	3.64807	0.152935	0.0764675	−	0.997072i	$-0.475636\pi$
$569$	3.64807	0.152935	0.0764675	+	0.997072i	$0.475636\pi$
$570$	−10.7598	−0.450680
$571$	−36.7563	−1.53820	−0.769102	−	0.639126i	$-0.779296\pi$
$571$	−36.7563	−1.53820	−0.769102	+	0.639126i	$0.779296\pi$
$572$	−11.3068	−0.472760
$573$	−25.8966	−1.08184
$574$	0	0
$575$	−0.0692417	−0.00288758
$576$	4.70156	0.195898
$577$	2.17433	0.0905186	0.0452593	−	0.998975i	$-0.485589\pi$
$577$	2.17433	0.0905186	0.0452593	+	0.998975i	$0.485589\pi$
$578$	8.53879	0.355167
$579$	1.31596	0.0546894
$580$	3.30678	0.137306
$581$	0	0
$582$	21.3440	0.884737
$583$	8.51136	0.352504
$584$	−99.4000	−4.11320
$585$	2.40490	0.0994303
$586$	16.8654	0.696702
$587$	−13.9501	−0.575780	−0.287890	−	0.957663i	$-0.592954\pi$
$587$	−13.9501	−0.575780	−0.287890	+	0.957663i	$0.592954\pi$
$588$	0	0
$589$	21.7273	0.895258
$590$	−11.5824	−0.476839
$591$	4.44212	0.182724
$592$	69.1779	2.84319
$593$	10.9483	0.449592	0.224796	−	0.974406i	$-0.427828\pi$
$593$	10.9483	0.449592	0.224796	+	0.974406i	$0.427828\pi$
$594$	−2.58874	−0.106217
$595$	0	0
$596$	−65.3522	−2.67693
$597$	−25.7453	−1.05369
$598$	0.431075	0.0176280
$599$	−41.1998	−1.68338	−0.841689	−	0.539963i	$-0.818438\pi$
$599$	−41.1998	−1.68338	−0.841689	+	0.539963i	$0.818438\pi$
$600$	6.99364	0.285514
$601$	−21.5110	−0.877450	−0.438725	−	0.898621i	$-0.644570\pi$
$601$	−21.5110	−0.877450	−0.438725	+	0.898621i	$0.644570\pi$
$602$	0	0
$603$	4.72263	0.192320
$604$	13.8782	0.564696
$605$	1.00000	0.0406558
$606$	−28.5679	−1.16049
$607$	13.8580	0.562478	0.281239	−	0.959638i	$-0.409255\pi$
$607$	13.8580	0.562478	0.281239	+	0.959638i	$0.409255\pi$
$608$	35.4907	1.43934
$609$	0	0
$610$	12.9982	0.526283
$611$	−32.1130	−1.29915
$612$	17.4031	0.703480
$613$	−32.0223	−1.29337	−0.646684	−	0.762758i	$-0.723845\pi$
$613$	−32.0223	−1.29337	−0.646684	+	0.762758i	$0.723845\pi$
$614$	−58.4223	−2.35773
$615$	2.31773	0.0934600
$616$	0	0
$617$	−3.39958	−0.136862	−0.0684309	−	0.997656i	$-0.521799\pi$
$617$	−3.39958	−0.136862	−0.0684309	+	0.997656i	$0.521799\pi$
$618$	7.35672	0.295931
$619$	1.91638	0.0770259	0.0385129	−	0.999258i	$-0.487738\pi$
$619$	1.91638	0.0770259	0.0385129	+	0.999258i	$0.487738\pi$
$620$	−24.5771	−0.987038
$621$	0.0692417	0.00277857
$622$	0.132848	0.00532672
$623$	0	0
$624$	−20.9264	−0.837725
$625$	1.00000	0.0400000
$626$	−8.91106	−0.356158
$627$	−4.15641	−0.165991
$628$	−24.2348	−0.967075
$629$	29.4276	1.17336
$630$	0	0
$631$	−37.4019	−1.48895	−0.744473	−	0.667653i	$-0.767299\pi$
$631$	−37.4019	−1.48895	−0.744473	+	0.667653i	$0.767299\pi$
$632$	30.8062	1.22541
$633$	24.2129	0.962377
$634$	−81.9547	−3.25484
$635$	−0.248490	−0.00986104
$636$	40.0167	1.58676
$637$	0	0
$638$	1.82075	0.0720842
$639$	4.40490	0.174255
$640$	4.90647	0.193945
$641$	8.52928	0.336886	0.168443	−	0.985711i	$-0.446126\pi$
$641$	8.52928	0.336886	0.168443	+	0.985711i	$0.446126\pi$
$642$	−39.7545	−1.56899
$643$	−36.3615	−1.43396	−0.716979	−	0.697095i	$-0.754476\pi$
$643$	−36.3615	−1.43396	−0.716979	+	0.697095i	$0.754476\pi$
$644$	0	0
$645$	−4.24849	−0.167284
$646$	39.8282	1.56702
$647$	−42.2551	−1.66122	−0.830609	−	0.556856i	$-0.812007\pi$
$647$	−42.2551	−1.66122	−0.830609	+	0.556856i	$0.812007\pi$
$648$	−6.99364	−0.274736
$649$	−4.47414	−0.175625
$650$	−6.22565	−0.244190
$651$	0	0
$652$	10.9136	0.427411
$653$	−21.8110	−0.853532	−0.426766	−	0.904362i	$-0.640347\pi$
$653$	−21.8110	−0.853532	−0.426766	+	0.904362i	$0.640347\pi$
$654$	33.2905	1.30176
$655$	−12.6178	−0.493019
$656$	−20.1679	−0.787424
$657$	14.2129	0.554499
$658$	0	0
$659$	−46.8164	−1.82371	−0.911853	−	0.410516i	$-0.865348\pi$
$659$	−46.8164	−1.82371	−0.911853	+	0.410516i	$0.865348\pi$
$660$	4.70156	0.183008
$661$	17.1113	0.665551	0.332775	−	0.943006i	$-0.392015\pi$
$661$	17.1113	0.665551	0.332775	+	0.943006i	$0.392015\pi$
$662$	9.21469	0.358139
$663$	−8.90188	−0.345720
$664$	38.9061	1.50985
$665$	0	0
$666$	−20.5806	−0.797482
$667$	−0.0487002	−0.00188568
$668$	−83.4907	−3.23035
$669$	8.38697	0.324259
$670$	−12.2256	−0.472318
$671$	5.02107	0.193836
$672$	0	0
$673$	−48.3707	−1.86455	−0.932277	−	0.361746i	$-0.882181\pi$
$673$	−48.3707	−1.86455	−0.932277	+	0.361746i	$0.882181\pi$
$674$	−10.9561	−0.422013
$675$	−1.00000	−0.0384900
$676$	−33.9287	−1.30495
$677$	−26.6463	−1.02410	−0.512050	−	0.858956i	$-0.671114\pi$
$677$	−26.6463	−1.02410	−0.512050	+	0.858956i	$0.671114\pi$
$678$	42.7436	1.64156
$679$	0	0
$680$	−25.8874	−0.992736
$681$	2.79542	0.107121
$682$	−13.5324	−0.518183
$683$	5.94514	0.227484	0.113742	−	0.993510i	$-0.463716\pi$
$683$	5.94514	0.227484	0.113742	+	0.993510i	$0.463716\pi$
$684$	−19.5416	−0.747192
$685$	9.40312	0.359275
$686$	0	0
$687$	9.95360	0.379754
$688$	36.9685	1.40941
$689$	−20.4689	−0.779805
$690$	−0.179249	−0.00682388
$691$	−7.72867	−0.294012	−0.147006	−	0.989136i	$-0.546964\pi$
$691$	−7.72867	−0.294012	−0.147006	+	0.989136i	$0.546964\pi$
$692$	−95.0156	−3.61195
$693$	0	0
$694$	−40.4258	−1.53454
$695$	−22.4934	−0.853225
$696$	4.91887	0.186449
$697$	−8.57923	−0.324961
$698$	5.80802	0.219837
$699$	2.77612	0.105003
$700$	0	0
$701$	−4.70334	−0.177643	−0.0888213	−	0.996048i	$-0.528310\pi$
$701$	−4.70334	−0.177643	−0.0888213	+	0.996048i	$0.528310\pi$
$702$	6.22565	0.234972
$703$	−33.0437	−1.24627
$704$	−4.70156	−0.177197
$705$	13.3532	0.502910
$706$	31.0557	1.16880
$707$	0	0
$708$	−21.0354	−0.790560
$709$	21.8822	0.821803	0.410901	−	0.911680i	$-0.365214\pi$
$709$	21.8822	0.821803	0.410901	+	0.911680i	$0.365214\pi$
$710$	−11.4031	−0.427952
$711$	−4.40490	−0.165197
$712$	106.281	3.98304
$713$	0.361956	0.0135553
$714$	0	0
$715$	−2.40490	−0.0899381
$716$	−27.9745	−1.04546
$717$	14.6034	0.545375
$718$	−63.8754	−2.38381
$719$	19.2875	0.719302	0.359651	−	0.933087i	$-0.382896\pi$
$719$	19.2875	0.719302	0.359651	+	0.933087i	$0.382896\pi$
$720$	8.70156	0.324288
$721$	0	0
$722$	4.46370	0.166122
$723$	10.5385	0.391930
$724$	26.0542	0.968297
$725$	0.703336	0.0261212
$726$	2.58874	0.0960771
$727$	−35.4877	−1.31616	−0.658082	−	0.752946i	$-0.728632\pi$
$727$	−35.4877	−1.31616	−0.658082	+	0.752946i	$0.728632\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−36.7935	−1.36179
$731$	15.7261	0.581649
$732$	23.6069	0.872535
$733$	−49.4163	−1.82523	−0.912615	−	0.408819i	$-0.865941\pi$
$733$	−49.4163	−1.82523	−0.912615	+	0.408819i	$0.865941\pi$
$734$	57.6791	2.12898
$735$	0	0
$736$	0.591240	0.0217934
$737$	−4.72263	−0.173960
$738$	6.00000	0.220863
$739$	18.1095	0.666168	0.333084	−	0.942897i	$-0.391911\pi$
$739$	18.1095	0.666168	0.333084	+	0.942897i	$0.391911\pi$
$740$	37.3777	1.37403
$741$	9.99573	0.367202
$742$	0	0
$743$	−45.0972	−1.65445	−0.827227	−	0.561868i	$-0.810083\pi$
$743$	−45.0972	−1.65445	−0.827227	+	0.561868i	$0.810083\pi$
$744$	−36.5587	−1.34031
$745$	−13.9001	−0.509260
$746$	−35.3075	−1.29270
$747$	−5.56308	−0.203542
$748$	−17.4031	−0.636321
$749$	0	0
$750$	2.58874	0.0945273
$751$	47.9495	1.74970	0.874851	−	0.484391i	$-0.160959\pi$
$751$	47.9495	1.74970	0.874851	+	0.484391i	$0.160959\pi$
$752$	−116.193	−4.23714
$753$	−19.3904	−0.706625
$754$	−4.37872	−0.159464
$755$	2.95183	0.107428
$756$	0	0
$757$	13.8158	0.502145	0.251073	−	0.967968i	$-0.419217\pi$
$757$	13.8158	0.502145	0.251073	+	0.967968i	$0.419217\pi$
$758$	−36.7563	−1.33505
$759$	−0.0692417	−0.00251331
$760$	29.0684	1.05442
$761$	−12.2221	−0.443051	−0.221525	−	0.975155i	$-0.571104\pi$
$761$	−12.2221	−0.443051	−0.221525	+	0.975155i	$0.571104\pi$
$762$	−0.643276	−0.0233034
$763$	0	0
$764$	121.754	4.40492
$765$	3.70156	0.133830
$766$	−26.2094	−0.946983
$767$	10.7598	0.388516
$768$	22.1047	0.797634
$769$	−29.3013	−1.05663	−0.528316	−	0.849048i	$-0.677177\pi$
$769$	−29.3013	−1.05663	−0.528316	+	0.849048i	$0.677177\pi$
$770$	0	0
$771$	2.71771	0.0978760
$772$	−6.18706	−0.222677
$773$	−43.2356	−1.55508	−0.777539	−	0.628835i	$-0.783532\pi$
$773$	−43.2356	−1.55508	−0.777539	+	0.628835i	$0.783532\pi$
$774$	−10.9982	−0.395323
$775$	−5.22742	−0.187775
$776$	−57.6621	−2.06995
$777$	0	0
$778$	54.1931	1.94292
$779$	9.63344	0.345154
$780$	−11.3068	−0.404848
$781$	−4.40490	−0.157620
$782$	0.663500	0.0237267
$783$	−0.703336	−0.0251352
$784$	0	0
$785$	−5.15463	−0.183977
$786$	−32.6642	−1.16509
$787$	20.1489	0.718230	0.359115	−	0.933293i	$-0.383079\pi$
$787$	20.1489	0.718230	0.359115	+	0.933293i	$0.383079\pi$
$788$	−20.8849	−0.743993
$789$	14.4548	0.514606
$790$	11.4031	0.405705
$791$	0	0
$792$	6.99364	0.248508
$793$	−12.0752	−0.428801
$794$	−63.5998	−2.25707
$795$	8.51136	0.301867
$796$	121.043	4.29027
$797$	7.08676	0.251026	0.125513	−	0.992092i	$-0.459942\pi$
$797$	7.08676	0.251026	0.125513	+	0.992092i	$0.459942\pi$
$798$	0	0
$799$	−49.4276	−1.74862
$800$	−8.53879	−0.301892
$801$	−15.1968	−0.536951
$802$	99.4542	3.51185
$803$	−14.2129	−0.501563
$804$	−22.2037	−0.783065
$805$	0	0
$806$	32.5441	1.14632
$807$	−17.2677	−0.607850
$808$	77.1779	2.71511
$809$	−12.5391	−0.440852	−0.220426	−	0.975404i	$-0.570745\pi$
$809$	−12.5391	−0.440852	−0.220426	+	0.975404i	$0.570745\pi$
$810$	−2.58874	−0.0909590
$811$	8.27697	0.290644	0.145322	−	0.989384i	$-0.453578\pi$
$811$	8.27697	0.290644	0.145322	+	0.989384i	$0.453578\pi$
$812$	0	0
$813$	15.7051	0.550802
$814$	20.5806	0.721350
$815$	2.32128	0.0813109
$816$	−32.2094	−1.12755
$817$	−17.6585	−0.617791
$818$	−3.04817	−0.106577
$819$	0	0
$820$	−10.8970	−0.380538
$821$	50.1133	1.74897	0.874483	−	0.485056i	$-0.161201\pi$
$821$	50.1133	1.74897	0.874483	+	0.485056i	$0.161201\pi$
$822$	24.3422	0.849032
$823$	−52.3851	−1.82603	−0.913014	−	0.407927i	$-0.866252\pi$
$823$	−52.3851	−1.82603	−0.913014	+	0.407927i	$0.866252\pi$
$824$	−19.8746	−0.692366
$825$	1.00000	0.0348155
$826$	0	0
$827$	27.7003	0.963234	0.481617	−	0.876382i	$-0.340050\pi$
$827$	27.7003	0.963234	0.481617	+	0.876382i	$0.340050\pi$
$828$	−0.325544	−0.0113134
$829$	7.51970	0.261170	0.130585	−	0.991437i	$-0.458314\pi$
$829$	7.51970	0.261170	0.130585	+	0.991437i	$0.458314\pi$
$830$	14.4014	0.499878
$831$	−15.9837	−0.554469
$832$	11.3068	0.391992
$833$	0	0
$834$	−58.2296	−2.01633
$835$	−17.7581	−0.614544
$836$	19.5416	0.675861
$837$	5.22742	0.180686
$838$	−96.4524	−3.33189
$839$	41.0385	1.41681	0.708403	−	0.705809i	$-0.249416\pi$
$839$	41.0385	1.41681	0.708403	+	0.705809i	$0.249416\pi$
$840$	0	0
$841$	−28.5053	−0.982942
$842$	−8.03722	−0.276981
$843$	5.50302	0.189534
$844$	−113.839	−3.91848
$845$	−7.21647	−0.248254
$846$	34.5679	1.18847
$847$	0	0
$848$	−74.0621	−2.54330
$849$	−8.09208	−0.277720
$850$	−9.58237	−0.328673
$851$	−0.550475	−0.0188700
$852$	−20.7099	−0.709509
$853$	−42.8693	−1.46782	−0.733909	−	0.679248i	$-0.762306\pi$
$853$	−42.8693	−1.46782	−0.733909	+	0.679248i	$0.762306\pi$
$854$	0	0
$855$	−4.15641	−0.142146
$856$	107.399	3.67083
$857$	−18.7354	−0.639988	−0.319994	−	0.947420i	$-0.603681\pi$
$857$	−18.7354	−0.639988	−0.319994	+	0.947420i	$0.603681\pi$
$858$	−6.22565	−0.212540
$859$	47.5569	1.62262	0.811310	−	0.584616i	$-0.198755\pi$
$859$	47.5569	1.62262	0.811310	+	0.584616i	$0.198755\pi$
$860$	19.9745	0.681126
$861$	0	0
$862$	35.0649	1.19431
$863$	−49.6177	−1.68901	−0.844503	−	0.535551i	$-0.820104\pi$
$863$	−49.6177	−1.68901	−0.844503	+	0.535551i	$0.820104\pi$
$864$	8.53879	0.290496
$865$	−20.2094	−0.687139
$866$	−87.4744	−2.97250
$867$	3.29844	0.112021
$868$	0	0
$869$	4.40490	0.149426
$870$	1.82075	0.0617293
$871$	11.3574	0.384832
$872$	−89.9364	−3.04563
$873$	8.24494	0.279049
$874$	−0.745030	−0.0252010
$875$	0	0
$876$	−66.8229	−2.25774
$877$	29.0962	0.982510	0.491255	−	0.871016i	$-0.336538\pi$
$877$	29.0962	0.982510	0.491255	+	0.871016i	$0.336538\pi$
$878$	30.0429	1.01390
$879$	6.51490	0.219742
$880$	−8.70156	−0.293330
$881$	−10.8454	−0.365390	−0.182695	−	0.983170i	$-0.558482\pi$
$881$	−10.8454	−0.365390	−0.182695	+	0.983170i	$0.558482\pi$
$882$	0	0
$883$	12.4000	0.417293	0.208646	−	0.977991i	$-0.433094\pi$
$883$	12.4000	0.417293	0.208646	+	0.977991i	$0.433094\pi$
$884$	41.8527	1.40766
$885$	−4.47414	−0.150397
$886$	64.0004	2.15014
$887$	−19.7823	−0.664224	−0.332112	−	0.943240i	$-0.607761\pi$
$887$	−19.7823	−0.664224	−0.332112	+	0.943240i	$0.607761\pi$
$888$	55.5998	1.86581
$889$	0	0
$890$	39.3404	1.31869
$891$	−1.00000	−0.0335013
$892$	−39.4319	−1.32028
$893$	55.5012	1.85728
$894$	−35.9837	−1.20348
$895$	−5.95005	−0.198888
$896$	0	0
$897$	0.166519	0.00555992
$898$	−81.6164	−2.72358
$899$	−3.67663	−0.122623
$900$	4.70156	0.156719
$901$	−31.5053	−1.04959
$902$	−6.00000	−0.199778
$903$	0	0
$904$	−115.474	−3.84062
$905$	5.54161	0.184209
$906$	7.64150	0.253872
$907$	−9.96278	−0.330809	−0.165404	−	0.986226i	$-0.552893\pi$
$907$	−9.96278	−0.330809	−0.165404	+	0.986226i	$0.552893\pi$
$908$	−13.1428	−0.436160
$909$	−11.0354	−0.366023
$910$	0	0
$911$	57.6869	1.91125	0.955627	−	0.294580i	$-0.0951799\pi$
$911$	57.6869	1.91125	0.955627	+	0.294580i	$0.0951799\pi$
$912$	36.1672	1.19762
$913$	5.56308	0.184111
$914$	34.6564	1.14633
$915$	5.02107	0.165991
$916$	−46.7975	−1.54623
$917$	0	0
$918$	9.58237	0.316265
$919$	19.2033	0.633460	0.316730	−	0.948516i	$-0.397415\pi$
$919$	19.2033	0.633460	0.316730	+	0.948516i	$0.397415\pi$
$920$	0.484251	0.0159653
$921$	−22.5679	−0.743637
$922$	10.0202	0.329998
$923$	10.5933	0.348684
$924$	0	0
$925$	7.95005	0.261396
$926$	−75.7163	−2.48819
$927$	2.84182	0.0933376
$928$	−6.00564	−0.197145
$929$	−39.9422	−1.31046	−0.655231	−	0.755428i	$-0.727429\pi$
$929$	−39.9422	−1.31046	−0.655231	+	0.755428i	$0.727429\pi$
$930$	−13.5324	−0.443746
$931$	0	0
$932$	−13.0521	−0.427536
$933$	0.0513177	0.00168007
$934$	36.9026	1.20749
$935$	−3.70156	−0.121054
$936$	−16.8190	−0.549745
$937$	−29.7826	−0.972954	−0.486477	−	0.873693i	$-0.661718\pi$
$937$	−29.7826	−0.972954	−0.486477	+	0.873693i	$0.661718\pi$
$938$	0	0
$939$	−3.44224	−0.112333
$940$	−62.7808	−2.04768
$941$	−26.5208	−0.864554	−0.432277	−	0.901741i	$-0.642290\pi$
$941$	−26.5208	−0.864554	−0.432277	+	0.901741i	$0.642290\pi$
$942$	−13.3440	−0.434771
$943$	0.160484	0.00522607
$944$	38.9320	1.26713
$945$	0	0
$946$	10.9982	0.357583
$947$	−34.6659	−1.12649	−0.563245	−	0.826290i	$-0.690447\pi$
$947$	−34.6659	−1.12649	−0.563245	+	0.826290i	$0.690447\pi$
$948$	20.7099	0.672626
$949$	34.1806	1.10955
$950$	10.7598	0.349096
$951$	−31.6582	−1.02659
$952$	0	0
$953$	−31.9451	−1.03480	−0.517402	−	0.855742i	$-0.673101\pi$
$953$	−31.9451	−1.03480	−0.517402	+	0.855742i	$0.673101\pi$
$954$	22.0337	0.713366
$955$	25.8966	0.837993
$956$	−68.6590	−2.22059
$957$	0.703336	0.0227356
$958$	−83.4450	−2.69599
$959$	0	0
$960$	−4.70156	−0.151742
$961$	−3.67405	−0.118518
$962$	−49.4942	−1.59576
$963$	−15.3567	−0.494864
$964$	−49.5472	−1.59581
$965$	−1.31596	−0.0423622
$966$	0	0
$967$	5.97781	0.192233	0.0961167	−	0.995370i	$-0.469358\pi$
$967$	5.97781	0.192233	0.0961167	+	0.995370i	$0.469358\pi$
$968$	−6.99364	−0.224784
$969$	15.3852	0.494244
$970$	−21.3440	−0.685314
$971$	6.61617	0.212323	0.106161	−	0.994349i	$-0.466144\pi$
$971$	6.61617	0.212323	0.106161	+	0.994349i	$0.466144\pi$
$972$	−4.70156	−0.150803
$973$	0	0
$974$	−13.6525	−0.437456
$975$	−2.40490	−0.0770184
$976$	−43.6911	−1.39852
$977$	14.9276	0.477577	0.238788	−	0.971072i	$-0.423250\pi$
$977$	14.9276	0.477577	0.238788	+	0.971072i	$0.423250\pi$
$978$	6.00918	0.192152
$979$	15.1968	0.485691
$980$	0	0
$981$	12.8597	0.410580
$982$	−92.3267	−2.94626
$983$	15.6774	0.500030	0.250015	−	0.968242i	$-0.419564\pi$
$983$	15.6774	0.500030	0.250015	+	0.968242i	$0.419564\pi$
$984$	−16.2094	−0.516736
$985$	−4.44212	−0.141538
$986$	−6.73962	−0.214633
$987$	0	0
$988$	−46.9956	−1.49513
$989$	−0.294173	−0.00935415
$990$	2.58874	0.0822755
$991$	−33.8504	−1.07529	−0.537647	−	0.843170i	$-0.680687\pi$
$991$	−33.8504	−1.07529	−0.537647	+	0.843170i	$0.680687\pi$
$992$	44.6359	1.41719
$993$	3.55953	0.112958
$994$	0	0
$995$	25.7453	0.816182
$996$	26.1552	0.828758
$997$	6.45130	0.204315	0.102157	−	0.994768i	$-0.467425\pi$
$997$	6.45130	0.204315	0.102157	+	0.994768i	$0.467425\pi$
$998$	100.982	3.19654
$999$	−7.95005	−0.251529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.bn.1.1		4
7.6	odd	2		1155.2.a.u.1.1	✓	4
21.20	even	2		3465.2.a.bl.1.4		4
35.34	odd	2		5775.2.a.bz.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.u.1.1	✓	4	7.6	odd	2
3465.2.a.bl.1.4		4	21.20	even	2
5775.2.a.bz.1.4		4	35.34	odd	2
8085.2.a.bn.1.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8085.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58874 q^{2} -1.00000 q^{3} +4.70156 q^{4} +1.00000 q^{5} +2.58874 q^{6} -6.99364 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.58874 q^{2} -1.00000 q^{3} +4.70156 q^{4} +1.00000 q^{5} +2.58874 q^{6} -6.99364 q^{8} +1.00000 q^{9} -2.58874 q^{10} -1.00000 q^{11} -4.70156 q^{12} +2.40490 q^{13} -1.00000 q^{15} +8.70156 q^{16} +3.70156 q^{17} -2.58874 q^{18} -4.15641 q^{19} +4.70156 q^{20} +2.58874 q^{22} -0.0692417 q^{23} +6.99364 q^{24} +1.00000 q^{25} -6.22565 q^{26} -1.00000 q^{27} +0.703336 q^{29} +2.58874 q^{30} -5.22742 q^{31} -8.53879 q^{32} +1.00000 q^{33} -9.58237 q^{34} +4.70156 q^{36} +7.95005 q^{37} +10.7598 q^{38} -2.40490 q^{39} -6.99364 q^{40} -2.31773 q^{41} +4.24849 q^{43} -4.70156 q^{44} +1.00000 q^{45} +0.179249 q^{46} -13.3532 q^{47} -8.70156 q^{48} -2.58874 q^{50} -3.70156 q^{51} +11.3068 q^{52} -8.51136 q^{53} +2.58874 q^{54} -1.00000 q^{55} +4.15641 q^{57} -1.82075 q^{58} +4.47414 q^{59} -4.70156 q^{60} -5.02107 q^{61} +13.5324 q^{62} +4.70156 q^{64} +2.40490 q^{65} -2.58874 q^{66} +4.72263 q^{67} +17.4031 q^{68} +0.0692417 q^{69} +4.40490 q^{71} -6.99364 q^{72} +14.2129 q^{73} -20.5806 q^{74} -1.00000 q^{75} -19.5416 q^{76} +6.22565 q^{78} -4.40490 q^{79} +8.70156 q^{80} +1.00000 q^{81} +6.00000 q^{82} -5.56308 q^{83} +3.70156 q^{85} -10.9982 q^{86} -0.703336 q^{87} +6.99364 q^{88} -15.1968 q^{89} -2.58874 q^{90} -0.325544 q^{92} +5.22742 q^{93} +34.5679 q^{94} -4.15641 q^{95} +8.53879 q^{96} +8.24494 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 6 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 6 * q^4 + 4 * q^5 + 4 * q^9	\( 4 q - 4 q^{3} + 6 q^{4} + 4 q^{5} + 4 q^{9} - 4 q^{11} - 6 q^{12} - 8 q^{13} - 4 q^{15} + 22 q^{16} + 2 q^{17} - 10 q^{19} + 6 q^{20} - 2 q^{23} + 4 q^{25} - 20 q^{26} - 4 q^{27} - 2 q^{29} - 24 q^{31} + 4 q^{33} + 6 q^{36} + 8 q^{37} - 16 q^{38} + 8 q^{39} + 6 q^{43} - 6 q^{44} + 4 q^{45} - 12 q^{46} - 4 q^{47} - 22 q^{48} - 2 q^{51} - 12 q^{52} + 14 q^{53} - 4 q^{55} + 10 q^{57} - 20 q^{58} + 2 q^{59} - 6 q^{60} - 6 q^{61} - 8 q^{62} + 6 q^{64} - 8 q^{65} - 8 q^{67} + 44 q^{68} + 2 q^{69} - 4 q^{73} - 36 q^{74} - 4 q^{75} - 56 q^{76} + 20 q^{78} + 22 q^{80} + 4 q^{81} + 24 q^{82} - 6 q^{83} + 2 q^{85} - 36 q^{86} + 2 q^{87} - 18 q^{89} - 44 q^{92} + 24 q^{93} + 36 q^{94} - 10 q^{95} + 6 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 6 * q^4 + 4 * q^5 + 4 * q^9 - 4 * q^11 - 6 * q^12 - 8 * q^13 - 4 * q^15 + 22 * q^16 + 2 * q^17 - 10 * q^19 + 6 * q^20 - 2 * q^23 + 4 * q^25 - 20 * q^26 - 4 * q^27 - 2 * q^29 - 24 * q^31 + 4 * q^33 + 6 * q^36 + 8 * q^37 - 16 * q^38 + 8 * q^39 + 6 * q^43 - 6 * q^44 + 4 * q^45 - 12 * q^46 - 4 * q^47 - 22 * q^48 - 2 * q^51 - 12 * q^52 + 14 * q^53 - 4 * q^55 + 10 * q^57 - 20 * q^58 + 2 * q^59 - 6 * q^60 - 6 * q^61 - 8 * q^62 + 6 * q^64 - 8 * q^65 - 8 * q^67 + 44 * q^68 + 2 * q^69 - 4 * q^73 - 36 * q^74 - 4 * q^75 - 56 * q^76 + 20 * q^78 + 22 * q^80 + 4 * q^81 + 24 * q^82 - 6 * q^83 + 2 * q^85 - 36 * q^86 + 2 * q^87 - 18 * q^89 - 44 * q^92 + 24 * q^93 + 36 * q^94 - 10 * q^95 + 6 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

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