LMFDB - Embedded newform 8085.2.a.ck.1.2

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 16x^{8} + 84x^{6} - 2x^{5} - 169x^{4} + 8x^{3} + 128x^{2} - 4x - 32 $ x^10 - 16x^8 + 84x^6 - 2x^5 - 169x^4 + 8x^3 + 128x^2 - 4*x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
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			1.2
Root			$2.20260$ 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)

$f(q)$	$=$	$q-2.20260 q^{2} -1.00000 q^{3} +2.85145 q^{4} -1.00000 q^{5} +2.20260 q^{6} -1.87541 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.20260 q^{2} -1.00000 q^{3} +2.85145 q^{4} -1.00000 q^{5} +2.20260 q^{6} -1.87541 q^{8} +1.00000 q^{9} +2.20260 q^{10} +1.00000 q^{11} -2.85145 q^{12} -5.14687 q^{13} +1.00000 q^{15} -1.57212 q^{16} -6.83758 q^{17} -2.20260 q^{18} +3.41007 q^{19} -2.85145 q^{20} -2.20260 q^{22} +1.95594 q^{23} +1.87541 q^{24} +1.00000 q^{25} +11.3365 q^{26} -1.00000 q^{27} -1.70712 q^{29} -2.20260 q^{30} -4.28403 q^{31} +7.21358 q^{32} -1.00000 q^{33} +15.0605 q^{34} +2.85145 q^{36} +6.69832 q^{37} -7.51102 q^{38} +5.14687 q^{39} +1.87541 q^{40} +1.76405 q^{41} +5.79224 q^{43} +2.85145 q^{44} -1.00000 q^{45} -4.30815 q^{46} -1.74269 q^{47} +1.57212 q^{48} -2.20260 q^{50} +6.83758 q^{51} -14.6761 q^{52} -8.55730 q^{53} +2.20260 q^{54} -1.00000 q^{55} -3.41007 q^{57} +3.76011 q^{58} +2.03973 q^{59} +2.85145 q^{60} +12.5501 q^{61} +9.43602 q^{62} -12.7444 q^{64} +5.14687 q^{65} +2.20260 q^{66} +2.81326 q^{67} -19.4970 q^{68} -1.95594 q^{69} +15.3624 q^{71} -1.87541 q^{72} -8.95105 q^{73} -14.7537 q^{74} -1.00000 q^{75} +9.72365 q^{76} -11.3365 q^{78} +11.8639 q^{79} +1.57212 q^{80} +1.00000 q^{81} -3.88550 q^{82} +9.70666 q^{83} +6.83758 q^{85} -12.7580 q^{86} +1.70712 q^{87} -1.87541 q^{88} -11.2120 q^{89} +2.20260 q^{90} +5.57726 q^{92} +4.28403 q^{93} +3.83846 q^{94} -3.41007 q^{95} -7.21358 q^{96} -8.13556 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^9	$ 10 q - 10 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{9} + 10 q^{11} - 12 q^{12} - 4 q^{13} + 10 q^{15} + 24 q^{16} - 12 q^{17} - 9 q^{19} - 12 q^{20} - q^{23} + 10 q^{25} - 6 q^{26} - 10 q^{27} + 3 q^{29} - 9 q^{31} - 10 q^{32} - 10 q^{33} - 6 q^{34} + 12 q^{36} + 3 q^{37} - 42 q^{38} + 4 q^{39} - 3 q^{41} + 12 q^{44} - 10 q^{45} - 22 q^{46} - 21 q^{47} - 24 q^{48} + 12 q^{51} - 24 q^{52} - 5 q^{53} - 10 q^{55} + 9 q^{57} - 26 q^{58} - 16 q^{59} + 12 q^{60} - 20 q^{61} + 18 q^{62} + 70 q^{64} + 4 q^{65} - q^{67} - 30 q^{68} + q^{69} + 22 q^{71} + q^{73} - 34 q^{74} - 10 q^{75} + 28 q^{76} + 6 q^{78} + 19 q^{79} - 24 q^{80} + 10 q^{81} - 32 q^{82} - 20 q^{83} + 12 q^{85} - 3 q^{87} - 18 q^{89} - 8 q^{92} + 9 q^{93} + 6 q^{94} + 9 q^{95} + 10 q^{96} - 6 q^{97} + 10 q^{99}+O(q^{100}) $ 10 * q - 10 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^9 + 10 * q^11 - 12 * q^12 - 4 * q^13 + 10 * q^15 + 24 * q^16 - 12 * q^17 - 9 * q^19 - 12 * q^20 - q^23 + 10 * q^25 - 6 * q^26 - 10 * q^27 + 3 * q^29 - 9 * q^31 - 10 * q^32 - 10 * q^33 - 6 * q^34 + 12 * q^36 + 3 * q^37 - 42 * q^38 + 4 * q^39 - 3 * q^41 + 12 * q^44 - 10 * q^45 - 22 * q^46 - 21 * q^47 - 24 * q^48 + 12 * q^51 - 24 * q^52 - 5 * q^53 - 10 * q^55 + 9 * q^57 - 26 * q^58 - 16 * q^59 + 12 * q^60 - 20 * q^61 + 18 * q^62 + 70 * q^64 + 4 * q^65 - q^67 - 30 * q^68 + q^69 + 22 * q^71 + q^73 - 34 * q^74 - 10 * q^75 + 28 * q^76 + 6 * q^78 + 19 * q^79 - 24 * q^80 + 10 * q^81 - 32 * q^82 - 20 * q^83 + 12 * q^85 - 3 * q^87 - 18 * q^89 - 8 * q^92 + 9 * q^93 + 6 * q^94 + 9 * q^95 + 10 * q^96 - 6 * q^97 + 10 * 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 $

$2$	−2.20260	−1.55747	−0.778737	−	0.627350i	$-0.784139\pi$
$2$	−2.20260	−1.55747	−0.778737	+	0.627350i	$0.784139\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.85145	1.42573
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.20260	0.899208
$7$	0	0
$7$	0	0
$8$	−1.87541	−0.663059
$9$	1.00000	0.333333
$10$	2.20260	0.696524
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.85145	−0.823144
$13$	−5.14687	−1.42749	−0.713743	−	0.700408i	$-0.753001\pi$
$13$	−5.14687	−1.42749	−0.713743	+	0.700408i	$0.753001\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	−1.57212	−0.393030
$17$	−6.83758	−1.65836	−0.829178	−	0.558984i	$-0.811191\pi$
$17$	−6.83758	−1.65836	−0.829178	+	0.558984i	$0.811191\pi$
$18$	−2.20260	−0.519158
$19$	3.41007	0.782323	0.391162	−	0.920322i	$-0.372073\pi$
$19$	3.41007	0.782323	0.391162	+	0.920322i	$0.372073\pi$
$20$	−2.85145	−0.637604
$21$	0	0
$22$	−2.20260	−0.469596
$23$	1.95594	0.407841	0.203921	−	0.978987i	$-0.434632\pi$
$23$	1.95594	0.407841	0.203921	+	0.978987i	$0.434632\pi$
$24$	1.87541	0.382817
$25$	1.00000	0.200000
$26$	11.3365	2.22327
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−1.70712	−0.317005	−0.158502	−	0.987359i	$-0.550667\pi$
$29$	−1.70712	−0.317005	−0.158502	+	0.987359i	$0.550667\pi$
$30$	−2.20260	−0.402138
$31$	−4.28403	−0.769435	−0.384718	−	0.923034i	$-0.625701\pi$
$31$	−4.28403	−0.769435	−0.384718	+	0.923034i	$0.625701\pi$
$32$	7.21358	1.27519
$33$	−1.00000	−0.174078
$34$	15.0605	2.58285
$35$	0	0
$36$	2.85145	0.475242
$37$	6.69832	1.10120	0.550599	−	0.834770i	$-0.314400\pi$
$37$	6.69832	1.10120	0.550599	+	0.834770i	$0.314400\pi$
$38$	−7.51102	−1.21845
$39$	5.14687	0.824159
$40$	1.87541	0.296529
$41$	1.76405	0.275499	0.137749	−	0.990467i	$-0.456013\pi$
$41$	1.76405	0.275499	0.137749	+	0.990467i	$0.456013\pi$
$42$	0	0
$43$	5.79224	0.883308	0.441654	−	0.897185i	$-0.354392\pi$
$43$	5.79224	0.883308	0.441654	+	0.897185i	$0.354392\pi$
$44$	2.85145	0.429873
$45$	−1.00000	−0.149071
$46$	−4.30815	−0.635202
$47$	−1.74269	−0.254198	−0.127099	−	0.991890i	$-0.540567\pi$
$47$	−1.74269	−0.254198	−0.127099	+	0.991890i	$0.540567\pi$
$48$	1.57212	0.226916
$49$	0	0
$50$	−2.20260	−0.311495
$51$	6.83758	0.957453
$52$	−14.6761	−2.03520
$53$	−8.55730	−1.17544	−0.587718	−	0.809066i	$-0.699973\pi$
$53$	−8.55730	−1.17544	−0.587718	+	0.809066i	$0.699973\pi$
$54$	2.20260	0.299736
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−3.41007	−0.451675
$58$	3.76011	0.493727
$59$	2.03973	0.265550	0.132775	−	0.991146i	$-0.457611\pi$
$59$	2.03973	0.265550	0.132775	+	0.991146i	$0.457611\pi$
$60$	2.85145	0.368121
$61$	12.5501	1.60687	0.803435	−	0.595393i	$-0.203004\pi$
$61$	12.5501	1.60687	0.803435	+	0.595393i	$0.203004\pi$
$62$	9.43602	1.19838
$63$	0	0
$64$	−12.7444	−1.59305
$65$	5.14687	0.638391
$66$	2.20260	0.271122
$67$	2.81326	0.343694	0.171847	−	0.985124i	$-0.445026\pi$
$67$	2.81326	0.343694	0.171847	+	0.985124i	$0.445026\pi$
$68$	−19.4970	−2.36436
$69$	−1.95594	−0.235467
$70$	0	0
$71$	15.3624	1.82318	0.911591	−	0.411098i	$-0.134855\pi$
$71$	15.3624	1.82318	0.911591	+	0.411098i	$0.134855\pi$
$72$	−1.87541	−0.221020
$73$	−8.95105	−1.04764	−0.523821	−	0.851829i	$-0.675494\pi$
$73$	−8.95105	−1.04764	−0.523821	+	0.851829i	$0.675494\pi$
$74$	−14.7537	−1.71509
$75$	−1.00000	−0.115470
$76$	9.72365	1.11538
$77$	0	0
$78$	−11.3365	−1.28361
$79$	11.8639	1.33479	0.667395	−	0.744704i	$-0.267409\pi$
$79$	11.8639	1.33479	0.667395	+	0.744704i	$0.267409\pi$
$80$	1.57212	0.175768
$81$	1.00000	0.111111
$82$	−3.88550	−0.429082
$83$	9.70666	1.06544	0.532722	−	0.846290i	$-0.321169\pi$
$83$	9.70666	1.06544	0.532722	+	0.846290i	$0.321169\pi$
$84$	0	0
$85$	6.83758	0.741640
$86$	−12.7580	−1.37573
$87$	1.70712	0.183023
$88$	−1.87541	−0.199920
$89$	−11.2120	−1.18847	−0.594236	−	0.804291i	$-0.702545\pi$
$89$	−11.2120	−1.18847	−0.594236	+	0.804291i	$0.702545\pi$
$90$	2.20260	0.232175
$91$	0	0
$92$	5.57726	0.581470
$93$	4.28403	0.444234
$94$	3.83846	0.395907
$95$	−3.41007	−0.349866
$96$	−7.21358	−0.736233
$97$	−8.13556	−0.826041	−0.413021	−	0.910722i	$-0.635526\pi$
$97$	−8.13556	−0.826041	−0.413021	+	0.910722i	$0.635526\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	2.85145	0.285145
$101$	−3.47572	−0.345847	−0.172923	−	0.984935i	$-0.555321\pi$
$101$	−3.47572	−0.345847	−0.172923	+	0.984935i	$0.555321\pi$
$102$	−15.0605	−1.49121
$103$	2.39012	0.235506	0.117753	−	0.993043i	$-0.462431\pi$
$103$	2.39012	0.235506	0.117753	+	0.993043i	$0.462431\pi$
$104$	9.65251	0.946507
$105$	0	0
$106$	18.8483	1.83071
$107$	−7.70291	−0.744668	−0.372334	−	0.928099i	$-0.621442\pi$
$107$	−7.70291	−0.744668	−0.372334	+	0.928099i	$0.621442\pi$
$108$	−2.85145	−0.274381
$109$	5.18856	0.496974	0.248487	−	0.968635i	$-0.420067\pi$
$109$	5.18856	0.496974	0.248487	+	0.968635i	$0.420067\pi$
$110$	2.20260	0.210010
$111$	−6.69832	−0.635776
$112$	0	0
$113$	−14.6864	−1.38158	−0.690788	−	0.723058i	$-0.742736\pi$
$113$	−14.6864	−1.38158	−0.690788	+	0.723058i	$0.742736\pi$
$114$	7.51102	0.703472
$115$	−1.95594	−0.182392
$116$	−4.86779	−0.451963
$117$	−5.14687	−0.475829
$118$	−4.49271	−0.413587
$119$	0	0
$120$	−1.87541	−0.171201
$121$	1.00000	0.0909091
$122$	−27.6428	−2.50266
$123$	−1.76405	−0.159059
$124$	−12.2157	−1.09700
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	1.74219	0.154594	0.0772972	−	0.997008i	$-0.475371\pi$
$127$	1.74219	0.154594	0.0772972	+	0.997008i	$0.475371\pi$
$128$	13.6437	1.20594
$129$	−5.79224	−0.509978
$130$	−11.3365	−0.994278
$131$	−3.23741	−0.282854	−0.141427	−	0.989949i	$-0.545169\pi$
$131$	−3.23741	−0.282854	−0.141427	+	0.989949i	$0.545169\pi$
$132$	−2.85145	−0.248187
$133$	0	0
$134$	−6.19649	−0.535295
$135$	1.00000	0.0860663
$136$	12.8233	1.09959
$137$	−18.8200	−1.60790	−0.803952	−	0.594694i	$-0.797273\pi$
$137$	−18.8200	−1.60790	−0.803952	+	0.594694i	$0.797273\pi$
$138$	4.30815	0.366734
$139$	12.0313	1.02048	0.510241	−	0.860032i	$-0.329556\pi$
$139$	12.0313	1.02048	0.510241	+	0.860032i	$0.329556\pi$
$140$	0	0
$141$	1.74269	0.146761
$142$	−33.8373	−2.83956
$143$	−5.14687	−0.430403
$144$	−1.57212	−0.131010
$145$	1.70712	0.141769
$146$	19.7156	1.63167
$147$	0	0
$148$	19.1000	1.57001
$149$	−6.08472	−0.498480	−0.249240	−	0.968442i	$-0.580181\pi$
$149$	−6.08472	−0.498480	−0.249240	+	0.968442i	$0.580181\pi$
$150$	2.20260	0.179842
$151$	−19.3411	−1.57395	−0.786977	−	0.616982i	$-0.788355\pi$
$151$	−19.3411	−1.57395	−0.786977	+	0.616982i	$0.788355\pi$
$152$	−6.39529	−0.518726
$153$	−6.83758	−0.552786
$154$	0	0
$155$	4.28403	0.344102
$156$	14.6761	1.17503
$157$	12.2637	0.978750	0.489375	−	0.872074i	$-0.337225\pi$
$157$	12.2637	0.978750	0.489375	+	0.872074i	$0.337225\pi$
$158$	−26.1314	−2.07890
$159$	8.55730	0.678638
$160$	−7.21358	−0.570283
$161$	0	0
$162$	−2.20260	−0.173053
$163$	20.3030	1.59025	0.795126	−	0.606445i	$-0.207405\pi$
$163$	20.3030	1.59025	0.795126	+	0.606445i	$0.207405\pi$
$164$	5.03011	0.392786
$165$	1.00000	0.0778499
$166$	−21.3799	−1.65940
$167$	12.1878	0.943123	0.471562	−	0.881833i	$-0.343690\pi$
$167$	12.1878	0.943123	0.471562	+	0.881833i	$0.343690\pi$
$168$	0	0
$169$	13.4903	1.03772
$170$	−15.0605	−1.15508
$171$	3.41007	0.260774
$172$	16.5163	1.25936
$173$	16.3652	1.24423	0.622113	−	0.782928i	$-0.286275\pi$
$173$	16.3652	1.24423	0.622113	+	0.782928i	$0.286275\pi$
$174$	−3.76011	−0.285054
$175$	0	0
$176$	−1.57212	−0.118503
$177$	−2.03973	−0.153315
$178$	24.6956	1.85101
$179$	−9.33484	−0.697718	−0.348859	−	0.937175i	$-0.613431\pi$
$179$	−9.33484	−0.697718	−0.348859	+	0.937175i	$0.613431\pi$
$180$	−2.85145	−0.212535
$181$	−12.7922	−0.950835	−0.475417	−	0.879760i	$-0.657703\pi$
$181$	−12.7922	−0.950835	−0.475417	+	0.879760i	$0.657703\pi$
$182$	0	0
$183$	−12.5501	−0.927727
$184$	−3.66819	−0.270423
$185$	−6.69832	−0.492470
$186$	−9.43602	−0.691883
$187$	−6.83758	−0.500013
$188$	−4.96921	−0.362417
$189$	0	0
$190$	7.51102	0.544907
$191$	13.7243	0.993055	0.496528	−	0.868021i	$-0.334608\pi$
$191$	13.7243	0.993055	0.496528	+	0.868021i	$0.334608\pi$
$192$	12.7444	0.919748
$193$	18.0809	1.30149	0.650744	−	0.759297i	$-0.274457\pi$
$193$	18.0809	1.30149	0.650744	+	0.759297i	$0.274457\pi$
$194$	17.9194	1.28654
$195$	−5.14687	−0.368575
$196$	0	0
$197$	−2.07444	−0.147798	−0.0738988	−	0.997266i	$-0.523544\pi$
$197$	−2.07444	−0.147798	−0.0738988	+	0.997266i	$0.523544\pi$
$198$	−2.20260	−0.156532
$199$	19.2986	1.36804	0.684020	−	0.729463i	$-0.260230\pi$
$199$	19.2986	1.36804	0.684020	+	0.729463i	$0.260230\pi$
$200$	−1.87541	−0.132612
$201$	−2.81326	−0.198432
$202$	7.65562	0.538647
$203$	0	0
$204$	19.4970	1.36507
$205$	−1.76405	−0.123207
$206$	−5.26448	−0.366794
$207$	1.95594	0.135947
$208$	8.09150	0.561044
$209$	3.41007	0.235879
$210$	0	0
$211$	23.3665	1.60862	0.804310	−	0.594210i	$-0.202535\pi$
$211$	23.3665	1.60862	0.804310	+	0.594210i	$0.202535\pi$
$212$	−24.4007	−1.67585
$213$	−15.3624	−1.05261
$214$	16.9664	1.15980
$215$	−5.79224	−0.395027
$216$	1.87541	0.127606
$217$	0	0
$218$	−11.4283	−0.774024
$219$	8.95105	0.604856
$220$	−2.85145	−0.192245
$221$	35.1922	2.36728
$222$	14.7537	0.990206
$223$	−26.2756	−1.75955	−0.879773	−	0.475395i	$-0.842305\pi$
$223$	−26.2756	−1.75955	−0.879773	+	0.475395i	$0.842305\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	32.3482	2.15177
$227$	9.51920	0.631812	0.315906	−	0.948791i	$-0.397692\pi$
$227$	9.51920	0.631812	0.315906	+	0.948791i	$0.397692\pi$
$228$	−9.72365	−0.643965
$229$	−25.5714	−1.68981	−0.844903	−	0.534919i	$-0.820342\pi$
$229$	−25.5714	−1.68981	−0.844903	+	0.534919i	$0.820342\pi$
$230$	4.30815	0.284071
$231$	0	0
$232$	3.20156	0.210193
$233$	−3.23954	−0.212229	−0.106115	−	0.994354i	$-0.533841\pi$
$233$	−3.23954	−0.212229	−0.106115	+	0.994354i	$0.533841\pi$
$234$	11.3365	0.741091
$235$	1.74269	0.113681
$236$	5.81619	0.378602
$237$	−11.8639	−0.770642
$238$	0	0
$239$	5.86555	0.379411	0.189705	−	0.981841i	$-0.439247\pi$
$239$	5.86555	0.379411	0.189705	+	0.981841i	$0.439247\pi$
$240$	−1.57212	−0.101480
$241$	16.1715	1.04170	0.520850	−	0.853648i	$-0.325615\pi$
$241$	16.1715	1.04170	0.520850	+	0.853648i	$0.325615\pi$
$242$	−2.20260	−0.141589
$243$	−1.00000	−0.0641500
$244$	35.7859	2.29096
$245$	0	0
$246$	3.88550	0.247731
$247$	−17.5512	−1.11676
$248$	8.03434	0.510181
$249$	−9.70666	−0.615134
$250$	2.20260	0.139305
$251$	−17.9970	−1.13596	−0.567980	−	0.823042i	$-0.692275\pi$
$251$	−17.9970	−1.13596	−0.567980	+	0.823042i	$0.692275\pi$
$252$	0	0
$253$	1.95594	0.122969
$254$	−3.83735	−0.240777
$255$	−6.83758	−0.428186
$256$	−4.56279	−0.285174
$257$	9.49758	0.592443	0.296221	−	0.955119i	$-0.404273\pi$
$257$	9.49758	0.592443	0.296221	+	0.955119i	$0.404273\pi$
$258$	12.7580	0.794278
$259$	0	0
$260$	14.6761	0.910171
$261$	−1.70712	−0.105668
$262$	7.13072	0.440537
$263$	−15.8693	−0.978543	−0.489272	−	0.872131i	$-0.662737\pi$
$263$	−15.8693	−0.978543	−0.489272	+	0.872131i	$0.662737\pi$
$264$	1.87541	0.115424
$265$	8.55730	0.525671
$266$	0	0
$267$	11.2120	0.686164
$268$	8.02188	0.490014
$269$	−10.2428	−0.624517	−0.312259	−	0.949997i	$-0.601086\pi$
$269$	−10.2428	−0.624517	−0.312259	+	0.949997i	$0.601086\pi$
$270$	−2.20260	−0.134046
$271$	−7.17237	−0.435690	−0.217845	−	0.975983i	$-0.569903\pi$
$271$	−7.17237	−0.435690	−0.217845	+	0.975983i	$0.569903\pi$
$272$	10.7495	0.651784
$273$	0	0
$274$	41.4530	2.50427
$275$	1.00000	0.0603023
$276$	−5.57726	−0.335712
$277$	−18.3909	−1.10500	−0.552501	−	0.833512i	$-0.686326\pi$
$277$	−18.3909	−1.10500	−0.552501	+	0.833512i	$0.686326\pi$
$278$	−26.5002	−1.58937
$279$	−4.28403	−0.256478
$280$	0	0
$281$	−13.3435	−0.796009	−0.398004	−	0.917384i	$-0.630297\pi$
$281$	−13.3435	−0.796009	−0.398004	+	0.917384i	$0.630297\pi$
$282$	−3.83846	−0.228577
$283$	−25.7154	−1.52862	−0.764312	−	0.644846i	$-0.776921\pi$
$283$	−25.7154	−1.52862	−0.764312	+	0.644846i	$0.776921\pi$
$284$	43.8052	2.59936
$285$	3.41007	0.201995
$286$	11.3365	0.670342
$287$	0	0
$288$	7.21358	0.425064
$289$	29.7525	1.75015
$290$	−3.76011	−0.220802
$291$	8.13556	0.476915
$292$	−25.5235	−1.49365
$293$	−0.328215	−0.0191745	−0.00958726	−	0.999954i	$-0.503052\pi$
$293$	−0.328215	−0.0191745	−0.00958726	+	0.999954i	$0.503052\pi$
$294$	0	0
$295$	−2.03973	−0.118758
$296$	−12.5621	−0.730158
$297$	−1.00000	−0.0580259
$298$	13.4022	0.776369
$299$	−10.0670	−0.582187
$300$	−2.85145	−0.164629
$301$	0	0
$302$	42.6007	2.45139
$303$	3.47572	0.199675
$304$	−5.36103	−0.307476
$305$	−12.5501	−0.718614
$306$	15.0605	0.860949
$307$	26.2832	1.50006	0.750031	−	0.661403i	$-0.230039\pi$
$307$	26.2832	1.50006	0.750031	+	0.661403i	$0.230039\pi$
$308$	0	0
$309$	−2.39012	−0.135969
$310$	−9.43602	−0.535930
$311$	2.91108	0.165072	0.0825361	−	0.996588i	$-0.473698\pi$
$311$	2.91108	0.165072	0.0825361	+	0.996588i	$0.473698\pi$
$312$	−9.65251	−0.546466
$313$	30.4036	1.71851	0.859256	−	0.511547i	$-0.170927\pi$
$313$	30.4036	1.71851	0.859256	+	0.511547i	$0.170927\pi$
$314$	−27.0120	−1.52438
$315$	0	0
$316$	33.8293	1.90305
$317$	−13.0618	−0.733621	−0.366811	−	0.930296i	$-0.619550\pi$
$317$	−13.0618	−0.733621	−0.366811	+	0.930296i	$0.619550\pi$
$318$	−18.8483	−1.05696
$319$	−1.70712	−0.0955806
$320$	12.7444	0.712434
$321$	7.70291	0.429934
$322$	0	0
$323$	−23.3166	−1.29737
$324$	2.85145	0.158414
$325$	−5.14687	−0.285497
$326$	−44.7194	−2.47678
$327$	−5.18856	−0.286928
$328$	−3.30833	−0.182672
$329$	0	0
$330$	−2.20260	−0.121249
$331$	34.1435	1.87670	0.938349	−	0.345688i	$-0.112355\pi$
$331$	34.1435	1.87670	0.938349	+	0.345688i	$0.112355\pi$
$332$	27.6781	1.51903
$333$	6.69832	0.367066
$334$	−26.8450	−1.46889
$335$	−2.81326	−0.153705
$336$	0	0
$337$	−1.66012	−0.0904325	−0.0452163	−	0.998977i	$-0.514398\pi$
$337$	−1.66012	−0.0904325	−0.0452163	+	0.998977i	$0.514398\pi$
$338$	−29.7138	−1.61622
$339$	14.6864	0.797653
$340$	19.4970	1.05738
$341$	−4.28403	−0.231993
$342$	−7.51102	−0.406150
$343$	0	0
$344$	−10.8628	−0.585685
$345$	1.95594	0.105304
$346$	−36.0461	−1.93785
$347$	5.75435	0.308910	0.154455	−	0.988000i	$-0.450638\pi$
$347$	5.75435	0.308910	0.154455	+	0.988000i	$0.450638\pi$
$348$	4.86779	0.260941
$349$	9.85776	0.527674	0.263837	−	0.964567i	$-0.415012\pi$
$349$	9.85776	0.527674	0.263837	+	0.964567i	$0.415012\pi$
$350$	0	0
$351$	5.14687	0.274720
$352$	7.21358	0.384485
$353$	−2.47383	−0.131669	−0.0658344	−	0.997831i	$-0.520971\pi$
$353$	−2.47383	−0.131669	−0.0658344	+	0.997831i	$0.520971\pi$
$354$	4.49271	0.238785
$355$	−15.3624	−0.815352
$356$	−31.9706	−1.69444
$357$	0	0
$358$	20.5609	1.08668
$359$	−5.26417	−0.277832	−0.138916	−	0.990304i	$-0.544362\pi$
$359$	−5.26417	−0.277832	−0.138916	+	0.990304i	$0.544362\pi$
$360$	1.87541	0.0988430
$361$	−7.37143	−0.387970
$362$	28.1761	1.48090
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	8.95105	0.468519
$366$	27.6428	1.44491
$367$	−5.91111	−0.308557	−0.154279	−	0.988027i	$-0.549305\pi$
$367$	−5.91111	−0.308557	−0.154279	+	0.988027i	$0.549305\pi$
$368$	−3.07497	−0.160294
$369$	1.76405	0.0918329
$370$	14.7537	0.767010
$371$	0	0
$372$	12.2157	0.633356
$373$	−2.00226	−0.103673	−0.0518366	−	0.998656i	$-0.516508\pi$
$373$	−2.00226	−0.103673	−0.0518366	+	0.998656i	$0.516508\pi$
$374$	15.0605	0.778758
$375$	1.00000	0.0516398
$376$	3.26827	0.168548
$377$	8.78635	0.452520
$378$	0	0
$379$	−13.8923	−0.713602	−0.356801	−	0.934180i	$-0.616133\pi$
$379$	−13.8923	−0.713602	−0.356801	+	0.934180i	$0.616133\pi$
$380$	−9.72365	−0.498813
$381$	−1.74219	−0.0892551
$382$	−30.2292	−1.54666
$383$	−3.05362	−0.156033	−0.0780164	−	0.996952i	$-0.524859\pi$
$383$	−3.05362	−0.156033	−0.0780164	+	0.996952i	$0.524859\pi$
$384$	−13.6437	−0.696251
$385$	0	0
$386$	−39.8249	−2.02703
$387$	5.79224	0.294436
$388$	−23.1982	−1.17771
$389$	−35.5082	−1.80034	−0.900169	−	0.435541i	$-0.856557\pi$
$389$	−35.5082	−1.80034	−0.900169	+	0.435541i	$0.856557\pi$
$390$	11.3365	0.574046
$391$	−13.3739	−0.676346
$392$	0	0
$393$	3.23741	0.163306
$394$	4.56916	0.230191
$395$	−11.8639	−0.596937
$396$	2.85145	0.143291
$397$	−15.8096	−0.793462	−0.396731	−	0.917935i	$-0.629855\pi$
$397$	−15.8096	−0.793462	−0.396731	+	0.917935i	$0.629855\pi$
$398$	−42.5071	−2.13069
$399$	0	0
$400$	−1.57212	−0.0786060
$401$	−38.9283	−1.94399	−0.971993	−	0.235008i	$-0.924488\pi$
$401$	−38.9283	−1.94399	−0.971993	+	0.235008i	$0.924488\pi$
$402$	6.19649	0.309053
$403$	22.0494	1.09836
$404$	−9.91084	−0.493083
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	6.69832	0.332023
$408$	−12.8233	−0.634847
$409$	28.3835	1.40348	0.701738	−	0.712435i	$-0.252408\pi$
$409$	28.3835	1.40348	0.701738	+	0.712435i	$0.252408\pi$
$410$	3.88550	0.191891
$411$	18.8200	0.928324
$412$	6.81532	0.335767
$413$	0	0
$414$	−4.30815	−0.211734
$415$	−9.70666	−0.476481
$416$	−37.1274	−1.82032
$417$	−12.0313	−0.589175
$418$	−7.51102	−0.367376
$419$	24.2406	1.18423	0.592116	−	0.805852i	$-0.298293\pi$
$419$	24.2406	1.18423	0.592116	+	0.805852i	$0.298293\pi$
$420$	0	0
$421$	29.0500	1.41581	0.707906	−	0.706307i	$-0.249640\pi$
$421$	29.0500	1.41581	0.707906	+	0.706307i	$0.249640\pi$
$422$	−51.4672	−2.50538
$423$	−1.74269	−0.0847327
$424$	16.0485	0.779383
$425$	−6.83758	−0.331671
$426$	33.8373	1.63942
$427$	0	0
$428$	−21.9645	−1.06169
$429$	5.14687	0.248493
$430$	12.7580	0.615245
$431$	2.93002	0.141134	0.0705671	−	0.997507i	$-0.477519\pi$
$431$	2.93002	0.141134	0.0705671	+	0.997507i	$0.477519\pi$
$432$	1.57212	0.0756386
$433$	25.5879	1.22968	0.614838	−	0.788653i	$-0.289221\pi$
$433$	25.5879	1.22968	0.614838	+	0.788653i	$0.289221\pi$
$434$	0	0
$435$	−1.70712	−0.0818503
$436$	14.7949	0.708549
$437$	6.66988	0.319064
$438$	−19.7156	−0.942048
$439$	20.2547	0.966706	0.483353	−	0.875425i	$-0.339419\pi$
$439$	20.2547	0.966706	0.483353	+	0.875425i	$0.339419\pi$
$440$	1.87541	0.0894068
$441$	0	0
$442$	−77.5143	−3.68698
$443$	36.4596	1.73225	0.866123	−	0.499830i	$-0.166604\pi$
$443$	36.4596	1.73225	0.866123	+	0.499830i	$0.166604\pi$
$444$	−19.1000	−0.906444
$445$	11.2120	0.531501
$446$	57.8747	2.74045
$447$	6.08472	0.287797
$448$	0	0
$449$	1.06754	0.0503803	0.0251901	−	0.999683i	$-0.491981\pi$
$449$	1.06754	0.0503803	0.0251901	+	0.999683i	$0.491981\pi$
$450$	−2.20260	−0.103832
$451$	1.76405	0.0830660
$452$	−41.8774	−1.96975
$453$	19.3411	0.908723
$454$	−20.9670	−0.984031
$455$	0	0
$456$	6.39529	0.299487
$457$	−29.7039	−1.38949	−0.694746	−	0.719256i	$-0.744483\pi$
$457$	−29.7039	−1.38949	−0.694746	+	0.719256i	$0.744483\pi$
$458$	56.3236	2.63183
$459$	6.83758	0.319151
$460$	−5.57726	−0.260041
$461$	0.0715235	0.00333118	0.00166559	−	0.999999i	$-0.499470\pi$
$461$	0.0715235	0.00333118	0.00166559	+	0.999999i	$0.499470\pi$
$462$	0	0
$463$	−11.6230	−0.540166	−0.270083	−	0.962837i	$-0.587051\pi$
$463$	−11.6230	−0.540166	−0.270083	+	0.962837i	$0.587051\pi$
$464$	2.68380	0.124592
$465$	−4.28403	−0.198667
$466$	7.13541	0.330541
$467$	−36.3151	−1.68046	−0.840232	−	0.542227i	$-0.817581\pi$
$467$	−36.3151	−1.68046	−0.840232	+	0.542227i	$0.817581\pi$
$468$	−14.6761	−0.678402
$469$	0	0
$470$	−3.83846	−0.177055
$471$	−12.2637	−0.565081
$472$	−3.82533	−0.176075
$473$	5.79224	0.266327
$474$	26.1314	1.20025
$475$	3.41007	0.156465
$476$	0	0
$477$	−8.55730	−0.391812
$478$	−12.9195	−0.590923
$479$	32.5372	1.48666	0.743332	−	0.668923i	$-0.233244\pi$
$479$	32.5372	1.48666	0.743332	+	0.668923i	$0.233244\pi$
$480$	7.21358	0.329253
$481$	−34.4754	−1.57194
$482$	−35.6194	−1.62242
$483$	0	0
$484$	2.85145	0.129612
$485$	8.13556	0.369417
$486$	2.20260	0.0999120
$487$	11.6139	0.526278	0.263139	−	0.964758i	$-0.415242\pi$
$487$	11.6139	0.526278	0.263139	+	0.964758i	$0.415242\pi$
$488$	−23.5365	−1.06545
$489$	−20.3030	−0.918132
$490$	0	0
$491$	4.53612	0.204712	0.102356	−	0.994748i	$-0.467362\pi$
$491$	4.53612	0.204712	0.102356	+	0.994748i	$0.467362\pi$
$492$	−5.03011	−0.226775
$493$	11.6726	0.525707
$494$	38.6583	1.73932
$495$	−1.00000	−0.0449467
$496$	6.73501	0.302411
$497$	0	0
$498$	21.3799	0.958056
$499$	20.4816	0.916883	0.458442	−	0.888725i	$-0.348408\pi$
$499$	20.4816	0.916883	0.458442	+	0.888725i	$0.348408\pi$
$500$	−2.85145	−0.127521
$501$	−12.1878	−0.544513
$502$	39.6402	1.76923
$503$	−32.1087	−1.43166	−0.715829	−	0.698276i	$-0.753951\pi$
$503$	−32.1087	−1.43166	−0.715829	+	0.698276i	$0.753951\pi$
$504$	0	0
$505$	3.47572	0.154667
$506$	−4.30815	−0.191521
$507$	−13.4903	−0.599125
$508$	4.96777	0.220409
$509$	9.85061	0.436621	0.218310	−	0.975879i	$-0.429945\pi$
$509$	9.85061	0.436621	0.218310	+	0.975879i	$0.429945\pi$
$510$	15.0605	0.666889
$511$	0	0
$512$	−17.2374	−0.761791
$513$	−3.41007	−0.150558
$514$	−20.9194	−0.922715
$515$	−2.39012	−0.105321
$516$	−16.5163	−0.727090
$517$	−1.74269	−0.0766436
$518$	0	0
$519$	−16.3652	−0.718354
$520$	−9.65251	−0.423291
$521$	−13.2825	−0.581917	−0.290959	−	0.956736i	$-0.593974\pi$
$521$	−13.2825	−0.581917	−0.290959	+	0.956736i	$0.593974\pi$
$522$	3.76011	0.164576
$523$	−30.8727	−1.34997	−0.674985	−	0.737831i	$-0.735850\pi$
$523$	−30.8727	−1.34997	−0.674985	+	0.737831i	$0.735850\pi$
$524$	−9.23132	−0.403272
$525$	0	0
$526$	34.9538	1.52406
$527$	29.2924	1.27600
$528$	1.57212	0.0684177
$529$	−19.1743	−0.833666
$530$	−18.8483	−0.818719
$531$	2.03973	0.0885167
$532$	0	0
$533$	−9.07935	−0.393270
$534$	−24.6956	−1.06868
$535$	7.70291	0.333026
$536$	−5.27602	−0.227890
$537$	9.33484	0.402828
$538$	22.5609	0.972669
$539$	0	0
$540$	2.85145	0.122707
$541$	−14.2860	−0.614202	−0.307101	−	0.951677i	$-0.599359\pi$
$541$	−14.2860	−0.614202	−0.307101	+	0.951677i	$0.599359\pi$
$542$	15.7979	0.678576
$543$	12.7922	0.548965
$544$	−49.3234	−2.11472
$545$	−5.18856	−0.222253
$546$	0	0
$547$	−20.9206	−0.894502	−0.447251	−	0.894408i	$-0.647597\pi$
$547$	−20.9206	−0.894502	−0.447251	+	0.894408i	$0.647597\pi$
$548$	−53.6645	−2.29243
$549$	12.5501	0.535623
$550$	−2.20260	−0.0939192
$551$	−5.82141	−0.248000
$552$	3.66819	0.156129
$553$	0	0
$554$	40.5078	1.72101
$555$	6.69832	0.284328
$556$	34.3067	1.45493
$557$	−5.27755	−0.223617	−0.111809	−	0.993730i	$-0.535664\pi$
$557$	−5.27755	−0.223617	−0.111809	+	0.993730i	$0.535664\pi$
$558$	9.43602	0.399459
$559$	−29.8119	−1.26091
$560$	0	0
$561$	6.83758	0.288683
$562$	29.3905	1.23976
$563$	−18.7191	−0.788917	−0.394459	−	0.918914i	$-0.629068\pi$
$563$	−18.7191	−0.788917	−0.394459	+	0.918914i	$0.629068\pi$
$564$	4.96921	0.209242
$565$	14.6864	0.617859
$566$	56.6409	2.38079
$567$	0	0
$568$	−28.8109	−1.20888
$569$	−4.44073	−0.186165	−0.0930825	−	0.995658i	$-0.529672\pi$
$569$	−4.44073	−0.186165	−0.0930825	+	0.995658i	$0.529672\pi$
$570$	−7.51102	−0.314602
$571$	2.24819	0.0940837	0.0470418	−	0.998893i	$-0.485021\pi$
$571$	2.24819	0.0940837	0.0470418	+	0.998893i	$0.485021\pi$
$572$	−14.6761	−0.613637
$573$	−13.7243	−0.573341
$574$	0	0
$575$	1.95594	0.0815682
$576$	−12.7444	−0.531017
$577$	4.41603	0.183842	0.0919208	−	0.995766i	$-0.470699\pi$
$577$	4.41603	0.183842	0.0919208	+	0.995766i	$0.470699\pi$
$578$	−65.5329	−2.72581
$579$	−18.0809	−0.751415
$580$	4.86779	0.202124
$581$	0	0
$582$	−17.9194	−0.742783
$583$	−8.55730	−0.354407
$584$	16.7869	0.694648
$585$	5.14687	0.212797
$586$	0.722927	0.0298638
$587$	21.3318	0.880456	0.440228	−	0.897886i	$-0.354898\pi$
$587$	21.3318	0.880456	0.440228	+	0.897886i	$0.354898\pi$
$588$	0	0
$589$	−14.6089	−0.601947
$590$	4.49271	0.184962
$591$	2.07444	0.0853310
$592$	−10.5306	−0.432803
$593$	30.5763	1.25562	0.627809	−	0.778367i	$-0.283952\pi$
$593$	30.5763	1.25562	0.627809	+	0.778367i	$0.283952\pi$
$594$	2.20260	0.0903738
$595$	0	0
$596$	−17.3503	−0.710696
$597$	−19.2986	−0.789839
$598$	22.1735	0.906742
$599$	16.0803	0.657025	0.328512	−	0.944500i	$-0.393453\pi$
$599$	16.0803	0.657025	0.328512	+	0.944500i	$0.393453\pi$
$600$	1.87541	0.0765634
$601$	−9.55135	−0.389608	−0.194804	−	0.980842i	$-0.562407\pi$
$601$	−9.55135	−0.389608	−0.194804	+	0.980842i	$0.562407\pi$
$602$	0	0
$603$	2.81326	0.114565
$604$	−55.1502	−2.24403
$605$	−1.00000	−0.0406558
$606$	−7.65562	−0.310988
$607$	−15.6921	−0.636925	−0.318462	−	0.947936i	$-0.603166\pi$
$607$	−15.6921	−0.636925	−0.318462	+	0.947936i	$0.603166\pi$
$608$	24.5988	0.997613
$609$	0	0
$610$	27.6428	1.11922
$611$	8.96942	0.362864
$612$	−19.4970	−0.788121
$613$	5.03194	0.203238	0.101619	−	0.994823i	$-0.467598\pi$
$613$	5.03194	0.203238	0.101619	+	0.994823i	$0.467598\pi$
$614$	−57.8914	−2.33631
$615$	1.76405	0.0711335
$616$	0	0
$617$	−42.6594	−1.71740	−0.858701	−	0.512478i	$-0.828728\pi$
$617$	−42.6594	−1.71740	−0.858701	+	0.512478i	$0.828728\pi$
$618$	5.26448	0.211769
$619$	−26.3779	−1.06022	−0.530108	−	0.847930i	$-0.677849\pi$
$619$	−26.3779	−1.06022	−0.530108	+	0.847930i	$0.677849\pi$
$620$	12.2157	0.490595
$621$	−1.95594	−0.0784891
$622$	−6.41195	−0.257096
$623$	0	0
$624$	−8.09150	−0.323919
$625$	1.00000	0.0400000
$626$	−66.9669	−2.67654
$627$	−3.41007	−0.136185
$628$	34.9694	1.39543
$629$	−45.8003	−1.82618
$630$	0	0
$631$	−33.7234	−1.34251	−0.671253	−	0.741228i	$-0.734244\pi$
$631$	−33.7234	−1.34251	−0.671253	+	0.741228i	$0.734244\pi$
$632$	−22.2497	−0.885045
$633$	−23.3665	−0.928737
$634$	28.7698	1.14260
$635$	−1.74219	−0.0691367
$636$	24.4007	0.967553
$637$	0	0
$638$	3.76011	0.148864
$639$	15.3624	0.607727
$640$	−13.6437	−0.539314
$641$	37.8053	1.49322	0.746610	−	0.665262i	$-0.231680\pi$
$641$	37.8053	1.49322	0.746610	+	0.665262i	$0.231680\pi$
$642$	−16.9664	−0.669612
$643$	9.42674	0.371754	0.185877	−	0.982573i	$-0.440487\pi$
$643$	9.42674	0.371754	0.185877	+	0.982573i	$0.440487\pi$
$644$	0	0
$645$	5.79224	0.228069
$646$	51.3572	2.02062
$647$	−10.1422	−0.398732	−0.199366	−	0.979925i	$-0.563888\pi$
$647$	−10.1422	−0.398732	−0.199366	+	0.979925i	$0.563888\pi$
$648$	−1.87541	−0.0736732
$649$	2.03973	0.0800663
$650$	11.3365	0.444654
$651$	0	0
$652$	57.8930	2.26726
$653$	47.8904	1.87410	0.937048	−	0.349200i	$-0.113546\pi$
$653$	47.8904	1.87410	0.937048	+	0.349200i	$0.113546\pi$
$654$	11.4283	0.446883
$655$	3.23741	0.126496
$656$	−2.77330	−0.108279
$657$	−8.95105	−0.349214
$658$	0	0
$659$	−19.8201	−0.772082	−0.386041	−	0.922482i	$-0.626158\pi$
$659$	−19.8201	−0.772082	−0.386041	+	0.922482i	$0.626158\pi$
$660$	2.85145	0.110993
$661$	−43.3206	−1.68498	−0.842488	−	0.538715i	$-0.818910\pi$
$661$	−43.3206	−1.68498	−0.842488	+	0.538715i	$0.818910\pi$
$662$	−75.2046	−2.92291
$663$	−35.1922	−1.36675
$664$	−18.2040	−0.706452
$665$	0	0
$666$	−14.7537	−0.571695
$667$	−3.33903	−0.129288
$668$	34.7531	1.34464
$669$	26.2756	1.01587
$670$	6.19649	0.239391
$671$	12.5501	0.484489
$672$	0	0
$673$	6.79446	0.261907	0.130954	−	0.991388i	$-0.458196\pi$
$673$	6.79446	0.261907	0.130954	+	0.991388i	$0.458196\pi$
$674$	3.65658	0.140846
$675$	−1.00000	−0.0384900
$676$	38.4670	1.47950
$677$	−19.5991	−0.753255	−0.376627	−	0.926365i	$-0.622916\pi$
$677$	−19.5991	−0.753255	−0.376627	+	0.926365i	$0.622916\pi$
$678$	−32.3482	−1.24232
$679$	0	0
$680$	−12.8233	−0.491751
$681$	−9.51920	−0.364777
$682$	9.43602	0.361324
$683$	28.9882	1.10920	0.554601	−	0.832116i	$-0.312871\pi$
$683$	28.9882	1.10920	0.554601	+	0.832116i	$0.312871\pi$
$684$	9.72365	0.371793
$685$	18.8200	0.719076
$686$	0	0
$687$	25.5714	0.975610
$688$	−9.10609	−0.347166
$689$	44.0433	1.67792
$690$	−4.30815	−0.164008
$691$	−47.3246	−1.80031	−0.900157	−	0.435565i	$-0.856548\pi$
$691$	−47.3246	−1.80031	−0.900157	+	0.435565i	$0.856548\pi$
$692$	46.6647	1.77393
$693$	0	0
$694$	−12.6745	−0.481119
$695$	−12.0313	−0.456373
$696$	−3.20156	−0.121355
$697$	−12.0618	−0.456875
$698$	−21.7127	−0.821838
$699$	3.23954	0.122531
$700$	0	0
$701$	−18.7012	−0.706336	−0.353168	−	0.935560i	$-0.614896\pi$
$701$	−18.7012	−0.706336	−0.353168	+	0.935560i	$0.614896\pi$
$702$	−11.3365	−0.427869
$703$	22.8417	0.861492
$704$	−12.7444	−0.480323
$705$	−1.74269	−0.0656336
$706$	5.44887	0.205071
$707$	0	0
$708$	−5.81619	−0.218586
$709$	−41.7840	−1.56923	−0.784616	−	0.619982i	$-0.787140\pi$
$709$	−41.7840	−1.56923	−0.784616	+	0.619982i	$0.787140\pi$
$710$	33.8373	1.26989
$711$	11.8639	0.444930
$712$	21.0272	0.788026
$713$	−8.37930	−0.313807
$714$	0	0
$715$	5.14687	0.192482
$716$	−26.6179	−0.994756
$717$	−5.86555	−0.219053
$718$	11.5949	0.432717
$719$	−15.1924	−0.566582	−0.283291	−	0.959034i	$-0.591426\pi$
$719$	−15.1924	−0.566582	−0.283291	+	0.959034i	$0.591426\pi$
$720$	1.57212	0.0585894
$721$	0	0
$722$	16.2363	0.604254
$723$	−16.1715	−0.601426
$724$	−36.4763	−1.35563
$725$	−1.70712	−0.0634010
$726$	2.20260	0.0817462
$727$	−32.2668	−1.19671	−0.598355	−	0.801231i	$-0.704179\pi$
$727$	−32.2668	−1.19671	−0.598355	+	0.801231i	$0.704179\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−19.7156	−0.729707
$731$	−39.6049	−1.46484
$732$	−35.7859	−1.32268
$733$	−43.2864	−1.59882	−0.799411	−	0.600785i	$-0.794855\pi$
$733$	−43.2864	−1.59882	−0.799411	+	0.600785i	$0.794855\pi$
$734$	13.0198	0.480570
$735$	0	0
$736$	14.1093	0.520076
$737$	2.81326	0.103628
$738$	−3.88550	−0.143027
$739$	23.8683	0.878010	0.439005	−	0.898485i	$-0.355331\pi$
$739$	23.8683	0.878010	0.439005	+	0.898485i	$0.355331\pi$
$740$	−19.1000	−0.702128
$741$	17.5512	0.644759
$742$	0	0
$743$	−35.0646	−1.28639	−0.643197	−	0.765701i	$-0.722392\pi$
$743$	−35.0646	−1.28639	−0.643197	+	0.765701i	$0.722392\pi$
$744$	−8.03434	−0.294553
$745$	6.08472	0.222927
$746$	4.41019	0.161468
$747$	9.70666	0.355148
$748$	−19.4970	−0.712882
$749$	0	0
$750$	−2.20260	−0.0804276
$751$	−0.406028	−0.0148162	−0.00740808	−	0.999973i	$-0.502358\pi$
$751$	−0.406028	−0.0148162	−0.00740808	+	0.999973i	$0.502358\pi$
$752$	2.73972	0.0999074
$753$	17.9970	0.655847
$754$	−19.3528	−0.704788
$755$	19.3411	0.703894
$756$	0	0
$757$	3.66428	0.133181	0.0665903	−	0.997780i	$-0.478788\pi$
$757$	3.66428	0.133181	0.0665903	+	0.997780i	$0.478788\pi$
$758$	30.5993	1.11142
$759$	−1.95594	−0.0709960
$760$	6.39529	0.231981
$761$	20.2128	0.732712	0.366356	−	0.930475i	$-0.380605\pi$
$761$	20.2128	0.732712	0.366356	+	0.930475i	$0.380605\pi$
$762$	3.83735	0.139012
$763$	0	0
$764$	39.1342	1.41583
$765$	6.83758	0.247213
$766$	6.72592	0.243017
$767$	−10.4982	−0.379069
$768$	4.56279	0.164646
$769$	−27.4566	−0.990109	−0.495054	−	0.868862i	$-0.664852\pi$
$769$	−27.4566	−0.990109	−0.495054	+	0.868862i	$0.664852\pi$
$770$	0	0
$771$	−9.49758	−0.342047
$772$	51.5567	1.85557
$773$	−43.4170	−1.56160	−0.780801	−	0.624780i	$-0.785189\pi$
$773$	−43.4170	−1.56160	−0.780801	+	0.624780i	$0.785189\pi$
$774$	−12.7580	−0.458577
$775$	−4.28403	−0.153887
$776$	15.2575	0.547714
$777$	0	0
$778$	78.2105	2.80398
$779$	6.01554	0.215529
$780$	−14.6761	−0.525488
$781$	15.3624	0.549710
$782$	29.4573	1.05339
$783$	1.70712	0.0610076
$784$	0	0
$785$	−12.2637	−0.437710
$786$	−7.13072	−0.254344
$787$	−9.49842	−0.338582	−0.169291	−	0.985566i	$-0.554148\pi$
$787$	−9.49842	−0.338582	−0.169291	+	0.985566i	$0.554148\pi$
$788$	−5.91517	−0.210719
$789$	15.8693	0.564962
$790$	26.1314	0.929713
$791$	0	0
$792$	−1.87541	−0.0666399
$793$	−64.5935	−2.29378
$794$	34.8223	1.23580
$795$	−8.55730	−0.303496
$796$	55.0290	1.95045
$797$	25.3838	0.899142	0.449571	−	0.893245i	$-0.351577\pi$
$797$	25.3838	0.899142	0.449571	+	0.893245i	$0.351577\pi$
$798$	0	0
$799$	11.9158	0.421551
$800$	7.21358	0.255039
$801$	−11.2120	−0.396157
$802$	85.7436	3.02771
$803$	−8.95105	−0.315876
$804$	−8.02188	−0.282910
$805$	0	0
$806$	−48.5660	−1.71066
$807$	10.2428	0.360565
$808$	6.51840	0.229317
$809$	22.5065	0.791285	0.395643	−	0.918405i	$-0.370522\pi$
$809$	22.5065	0.791285	0.395643	+	0.918405i	$0.370522\pi$
$810$	2.20260	0.0773915
$811$	−6.18538	−0.217198	−0.108599	−	0.994086i	$-0.534636\pi$
$811$	−6.18538	−0.217198	−0.108599	+	0.994086i	$0.534636\pi$
$812$	0	0
$813$	7.17237	0.251546
$814$	−14.7537	−0.517118
$815$	−20.3030	−0.711182
$816$	−10.7495	−0.376307
$817$	19.7519	0.691033
$818$	−62.5176	−2.18588
$819$	0	0
$820$	−5.03011	−0.175659
$821$	−32.9635	−1.15043	−0.575217	−	0.818001i	$-0.695083\pi$
$821$	−32.9635	−1.15043	−0.575217	+	0.818001i	$0.695083\pi$
$822$	−41.4530	−1.44584
$823$	24.7033	0.861102	0.430551	−	0.902566i	$-0.358319\pi$
$823$	24.7033	0.861102	0.430551	+	0.902566i	$0.358319\pi$
$824$	−4.48246	−0.156154
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	−16.9877	−0.590722	−0.295361	−	0.955386i	$-0.595440\pi$
$827$	−16.9877	−0.590722	−0.295361	+	0.955386i	$0.595440\pi$
$828$	5.57726	0.193823
$829$	−27.3622	−0.950327	−0.475164	−	0.879897i	$-0.657611\pi$
$829$	−27.3622	−0.950327	−0.475164	+	0.879897i	$0.657611\pi$
$830$	21.3799	0.742107
$831$	18.3909	0.637973
$832$	65.5938	2.27406
$833$	0	0
$834$	26.5002	0.917626
$835$	−12.1878	−0.421778
$836$	9.72365	0.336300
$837$	4.28403	0.148078
$838$	−53.3925	−1.84441
$839$	−13.6161	−0.470079	−0.235039	−	0.971986i	$-0.575522\pi$
$839$	−13.6161	−0.470079	−0.235039	+	0.971986i	$0.575522\pi$
$840$	0	0
$841$	−26.0857	−0.899508
$842$	−63.9856	−2.20509
$843$	13.3435	0.459576
$844$	66.6286	2.29345
$845$	−13.4903	−0.464080
$846$	3.83846	0.131969
$847$	0	0
$848$	13.4531	0.461981
$849$	25.7154	0.882552
$850$	15.0605	0.516570
$851$	13.1015	0.449113
$852$	−43.8052	−1.50074
$853$	40.8953	1.40023	0.700114	−	0.714031i	$-0.253133\pi$
$853$	40.8953	1.40023	0.700114	+	0.714031i	$0.253133\pi$
$854$	0	0
$855$	−3.41007	−0.116622
$856$	14.4461	0.493759
$857$	−7.75995	−0.265075	−0.132537	−	0.991178i	$-0.542312\pi$
$857$	−7.75995	−0.265075	−0.132537	+	0.991178i	$0.542312\pi$
$858$	−11.3365	−0.387022
$859$	39.8689	1.36031	0.680155	−	0.733068i	$-0.261912\pi$
$859$	39.8689	1.36031	0.680155	+	0.733068i	$0.261912\pi$
$860$	−16.5163	−0.563201
$861$	0	0
$862$	−6.45367	−0.219813
$863$	26.3459	0.896826	0.448413	−	0.893827i	$-0.351989\pi$
$863$	26.3459	0.896826	0.448413	+	0.893827i	$0.351989\pi$
$864$	−7.21358	−0.245411
$865$	−16.3652	−0.556435
$866$	−56.3600	−1.91519
$867$	−29.7525	−1.01045
$868$	0	0
$869$	11.8639	0.402455
$870$	3.76011	0.127480
$871$	−14.4795	−0.490619
$872$	−9.73069	−0.329523
$873$	−8.13556	−0.275347
$874$	−14.6911	−0.496933
$875$	0	0
$876$	25.5235	0.862359
$877$	−34.1562	−1.15337	−0.576687	−	0.816965i	$-0.695655\pi$
$877$	−34.1562	−1.15337	−0.576687	+	0.816965i	$0.695655\pi$
$878$	−44.6131	−1.50562
$879$	0.328215	0.0110704
$880$	1.57212	0.0529961
$881$	−55.0657	−1.85521	−0.927606	−	0.373560i	$-0.878137\pi$
$881$	−55.0657	−1.85521	−0.927606	+	0.373560i	$0.878137\pi$
$882$	0	0
$883$	6.48345	0.218185	0.109093	−	0.994032i	$-0.465205\pi$
$883$	6.48345	0.218185	0.109093	+	0.994032i	$0.465205\pi$
$884$	100.349	3.37510
$885$	2.03973	0.0685647
$886$	−80.3059	−2.69793
$887$	31.7048	1.06454	0.532271	−	0.846574i	$-0.321339\pi$
$887$	31.7048	1.06454	0.532271	+	0.846574i	$0.321339\pi$
$888$	12.5621	0.421557
$889$	0	0
$890$	−24.6956	−0.827799
$891$	1.00000	0.0335013
$892$	−74.9237	−2.50863
$893$	−5.94271	−0.198865
$894$	−13.4022	−0.448237
$895$	9.33484	0.312029
$896$	0	0
$897$	10.0670	0.336126
$898$	−2.35136	−0.0784660
$899$	7.31338	0.243915
$900$	2.85145	0.0950485
$901$	58.5112	1.94929
$902$	−3.88550	−0.129373
$903$	0	0
$904$	27.5430	0.916066
$905$	12.7922	0.425226
$906$	−42.6007	−1.41531
$907$	1.66281	0.0552128	0.0276064	−	0.999619i	$-0.491211\pi$
$907$	1.66281	0.0552128	0.0276064	+	0.999619i	$0.491211\pi$
$908$	27.1436	0.900791
$909$	−3.47572	−0.115282
$910$	0	0
$911$	43.8410	1.45252	0.726258	−	0.687422i	$-0.241258\pi$
$911$	43.8410	1.45252	0.726258	+	0.687422i	$0.241258\pi$
$912$	5.36103	0.177522
$913$	9.70666	0.321244
$914$	65.4259	2.16410
$915$	12.5501	0.414892
$916$	−72.9157	−2.40920
$917$	0	0
$918$	−15.0605	−0.497069
$919$	38.0855	1.25632	0.628162	−	0.778082i	$-0.283807\pi$
$919$	38.0855	1.25632	0.628162	+	0.778082i	$0.283807\pi$
$920$	3.66819	0.120937
$921$	−26.2832	−0.866061
$922$	−0.157538	−0.00518823
$923$	−79.0684	−2.60257
$924$	0	0
$925$	6.69832	0.220239
$926$	25.6008	0.841295
$927$	2.39012	0.0785019
$928$	−12.3145	−0.404242
$929$	8.08975	0.265416	0.132708	−	0.991155i	$-0.457633\pi$
$929$	8.08975	0.265416	0.132708	+	0.991155i	$0.457633\pi$
$930$	9.43602	0.309419
$931$	0	0
$932$	−9.23739	−0.302581
$933$	−2.91108	−0.0953045
$934$	79.9878	2.61728
$935$	6.83758	0.223613
$936$	9.65251	0.315502
$937$	−56.3898	−1.84217	−0.921087	−	0.389357i	$-0.872697\pi$
$937$	−56.3898	−1.84217	−0.921087	+	0.389357i	$0.872697\pi$
$938$	0	0
$939$	−30.4036	−0.992183
$940$	4.96921	0.162078
$941$	0.442558	0.0144270	0.00721349	−	0.999974i	$-0.497704\pi$
$941$	0.442558	0.0144270	0.00721349	+	0.999974i	$0.497704\pi$
$942$	27.0120	0.880100
$943$	3.45038	0.112360
$944$	−3.20670	−0.104369
$945$	0	0
$946$	−12.7580	−0.414798
$947$	−52.6800	−1.71187	−0.855935	−	0.517084i	$-0.827017\pi$
$947$	−52.6800	−1.71187	−0.855935	+	0.517084i	$0.827017\pi$
$948$	−33.8293	−1.09872
$949$	46.0699	1.49549
$950$	−7.51102	−0.243690
$951$	13.0618	0.423556
$952$	0	0
$953$	14.8893	0.482311	0.241156	−	0.970486i	$-0.422474\pi$
$953$	14.8893	0.482311	0.241156	+	0.970486i	$0.422474\pi$
$954$	18.8483	0.610237
$955$	−13.7243	−0.444108
$956$	16.7253	0.540936
$957$	1.70712	0.0551835
$958$	−71.6665	−2.31544
$959$	0	0
$960$	−12.7444	−0.411324
$961$	−12.6470	−0.407969
$962$	75.9356	2.44826
$963$	−7.70291	−0.248223
$964$	46.1124	1.48518
$965$	−18.0809	−0.582043
$966$	0	0
$967$	−15.2735	−0.491161	−0.245581	−	0.969376i	$-0.578979\pi$
$967$	−15.2735	−0.491161	−0.245581	+	0.969376i	$0.578979\pi$
$968$	−1.87541	−0.0602781
$969$	23.3166	0.749038
$970$	−17.9194	−0.575357
$971$	−41.5199	−1.33244	−0.666218	−	0.745757i	$-0.732088\pi$
$971$	−41.5199	−1.33244	−0.666218	+	0.745757i	$0.732088\pi$
$972$	−2.85145	−0.0914604
$973$	0	0
$974$	−25.5809	−0.819664
$975$	5.14687	0.164832
$976$	−19.7302	−0.631548
$977$	−52.7925	−1.68898	−0.844490	−	0.535571i	$-0.820096\pi$
$977$	−52.7925	−1.68898	−0.844490	+	0.535571i	$0.820096\pi$
$978$	44.7194	1.42997
$979$	−11.2120	−0.358338
$980$	0	0
$981$	5.18856	0.165658
$982$	−9.99127	−0.318834
$983$	−42.9809	−1.37088	−0.685439	−	0.728130i	$-0.740390\pi$
$983$	−42.9809	−1.37088	−0.685439	+	0.728130i	$0.740390\pi$
$984$	3.30833	0.105466
$985$	2.07444	0.0660971
$986$	−25.7101	−0.818776
$987$	0	0
$988$	−50.0464	−1.59219
$989$	11.3293	0.360249
$990$	2.20260	0.0700033
$991$	−20.4941	−0.651016	−0.325508	−	0.945539i	$-0.605535\pi$
$991$	−20.4941	−0.651016	−0.325508	+	0.945539i	$0.605535\pi$
$992$	−30.9032	−0.981178
$993$	−34.1435	−1.08351
$994$	0	0
$995$	−19.2986	−0.611806
$996$	−27.6781	−0.877014
$997$	−16.6550	−0.527470	−0.263735	−	0.964595i	$-0.584954\pi$
$997$	−16.6550	−0.527470	−0.263735	+	0.964595i	$0.584954\pi$
$998$	−45.1129	−1.42802
$999$	−6.69832	−0.211925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.ck.1.2		10
7.3	odd	6		1155.2.q.l.331.9	✓	20
7.5	odd	6		1155.2.q.l.991.9	yes	20
7.6	odd	2		8085.2.a.cn.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.l.331.9	✓	20	7.3	odd	6
1155.2.q.l.991.9	yes	20	7.5	odd	6
8085.2.a.ck.1.2		10	1.1	even	1	trivial
8085.2.a.cn.1.2		10	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:	\( N \)	\(=\)	\( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8085.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20260 q^{2} -1.00000 q^{3} +2.85145 q^{4} -1.00000 q^{5} +2.20260 q^{6} -1.87541 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.20260 q^{2} -1.00000 q^{3} +2.85145 q^{4} -1.00000 q^{5} +2.20260 q^{6} -1.87541 q^{8} +1.00000 q^{9} +2.20260 q^{10} +1.00000 q^{11} -2.85145 q^{12} -5.14687 q^{13} +1.00000 q^{15} -1.57212 q^{16} -6.83758 q^{17} -2.20260 q^{18} +3.41007 q^{19} -2.85145 q^{20} -2.20260 q^{22} +1.95594 q^{23} +1.87541 q^{24} +1.00000 q^{25} +11.3365 q^{26} -1.00000 q^{27} -1.70712 q^{29} -2.20260 q^{30} -4.28403 q^{31} +7.21358 q^{32} -1.00000 q^{33} +15.0605 q^{34} +2.85145 q^{36} +6.69832 q^{37} -7.51102 q^{38} +5.14687 q^{39} +1.87541 q^{40} +1.76405 q^{41} +5.79224 q^{43} +2.85145 q^{44} -1.00000 q^{45} -4.30815 q^{46} -1.74269 q^{47} +1.57212 q^{48} -2.20260 q^{50} +6.83758 q^{51} -14.6761 q^{52} -8.55730 q^{53} +2.20260 q^{54} -1.00000 q^{55} -3.41007 q^{57} +3.76011 q^{58} +2.03973 q^{59} +2.85145 q^{60} +12.5501 q^{61} +9.43602 q^{62} -12.7444 q^{64} +5.14687 q^{65} +2.20260 q^{66} +2.81326 q^{67} -19.4970 q^{68} -1.95594 q^{69} +15.3624 q^{71} -1.87541 q^{72} -8.95105 q^{73} -14.7537 q^{74} -1.00000 q^{75} +9.72365 q^{76} -11.3365 q^{78} +11.8639 q^{79} +1.57212 q^{80} +1.00000 q^{81} -3.88550 q^{82} +9.70666 q^{83} +6.83758 q^{85} -12.7580 q^{86} +1.70712 q^{87} -1.87541 q^{88} -11.2120 q^{89} +2.20260 q^{90} +5.57726 q^{92} +4.28403 q^{93} +3.83846 q^{94} -3.41007 q^{95} -7.21358 q^{96} -8.13556 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^9	\( 10 q - 10 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{9} + 10 q^{11} - 12 q^{12} - 4 q^{13} + 10 q^{15} + 24 q^{16} - 12 q^{17} - 9 q^{19} - 12 q^{20} - q^{23} + 10 q^{25} - 6 q^{26} - 10 q^{27} + 3 q^{29} - 9 q^{31} - 10 q^{32} - 10 q^{33} - 6 q^{34} + 12 q^{36} + 3 q^{37} - 42 q^{38} + 4 q^{39} - 3 q^{41} + 12 q^{44} - 10 q^{45} - 22 q^{46} - 21 q^{47} - 24 q^{48} + 12 q^{51} - 24 q^{52} - 5 q^{53} - 10 q^{55} + 9 q^{57} - 26 q^{58} - 16 q^{59} + 12 q^{60} - 20 q^{61} + 18 q^{62} + 70 q^{64} + 4 q^{65} - q^{67} - 30 q^{68} + q^{69} + 22 q^{71} + q^{73} - 34 q^{74} - 10 q^{75} + 28 q^{76} + 6 q^{78} + 19 q^{79} - 24 q^{80} + 10 q^{81} - 32 q^{82} - 20 q^{83} + 12 q^{85} - 3 q^{87} - 18 q^{89} - 8 q^{92} + 9 q^{93} + 6 q^{94} + 9 q^{95} + 10 q^{96} - 6 q^{97} + 10 q^{99}+O(q^{100}) \) 10 * q - 10 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^9 + 10 * q^11 - 12 * q^12 - 4 * q^13 + 10 * q^15 + 24 * q^16 - 12 * q^17 - 9 * q^19 - 12 * q^20 - q^23 + 10 * q^25 - 6 * q^26 - 10 * q^27 + 3 * q^29 - 9 * q^31 - 10 * q^32 - 10 * q^33 - 6 * q^34 + 12 * q^36 + 3 * q^37 - 42 * q^38 + 4 * q^39 - 3 * q^41 + 12 * q^44 - 10 * q^45 - 22 * q^46 - 21 * q^47 - 24 * q^48 + 12 * q^51 - 24 * q^52 - 5 * q^53 - 10 * q^55 + 9 * q^57 - 26 * q^58 - 16 * q^59 + 12 * q^60 - 20 * q^61 + 18 * q^62 + 70 * q^64 + 4 * q^65 - q^67 - 30 * q^68 + q^69 + 22 * q^71 + q^73 - 34 * q^74 - 10 * q^75 + 28 * q^76 + 6 * q^78 + 19 * q^79 - 24 * q^80 + 10 * q^81 - 32 * q^82 - 20 * q^83 + 12 * q^85 - 3 * q^87 - 18 * q^89 - 8 * q^92 + 9 * q^93 + 6 * q^94 + 9 * q^95 + 10 * q^96 - 6 * q^97 + 10 * q^99

Introduction

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