LMFDB - Embedded newform 8085.2.a.ce.1.6

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 13x^{6} + 53x^{4} - 72x^{2} - 6x + 24 $ x^8 - 13x^6 + 53x^4 - 72x^2 - 6x + 24
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1155)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.08995$ 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)

$f(q)$	$=$	$q+1.08995 q^{2} -1.00000 q^{3} -0.812006 q^{4} +1.00000 q^{5} -1.08995 q^{6} -3.06495 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.08995 q^{2} -1.00000 q^{3} -0.812006 q^{4} +1.00000 q^{5} -1.08995 q^{6} -3.06495 q^{8} +1.00000 q^{9} +1.08995 q^{10} -1.00000 q^{11} +0.812006 q^{12} -4.56615 q^{13} -1.00000 q^{15} -1.71663 q^{16} +3.62401 q^{17} +1.08995 q^{18} +4.55363 q^{19} -0.812006 q^{20} -1.08995 q^{22} +3.77098 q^{23} +3.06495 q^{24} +1.00000 q^{25} -4.97688 q^{26} -1.00000 q^{27} -9.80465 q^{29} -1.08995 q^{30} +0.564568 q^{31} +4.25885 q^{32} +1.00000 q^{33} +3.95000 q^{34} -0.812006 q^{36} +6.72107 q^{37} +4.96324 q^{38} +4.56615 q^{39} -3.06495 q^{40} -3.09471 q^{41} +8.41992 q^{43} +0.812006 q^{44} +1.00000 q^{45} +4.11018 q^{46} -8.51790 q^{47} +1.71663 q^{48} +1.08995 q^{50} -3.62401 q^{51} +3.70774 q^{52} -4.25808 q^{53} -1.08995 q^{54} -1.00000 q^{55} -4.55363 q^{57} -10.6866 q^{58} +3.30272 q^{59} +0.812006 q^{60} -1.90377 q^{61} +0.615352 q^{62} +8.07521 q^{64} -4.56615 q^{65} +1.08995 q^{66} -14.1880 q^{67} -2.94272 q^{68} -3.77098 q^{69} +6.05493 q^{71} -3.06495 q^{72} +2.70782 q^{73} +7.32564 q^{74} -1.00000 q^{75} -3.69758 q^{76} +4.97688 q^{78} +14.5515 q^{79} -1.71663 q^{80} +1.00000 q^{81} -3.37309 q^{82} +9.16676 q^{83} +3.62401 q^{85} +9.17730 q^{86} +9.80465 q^{87} +3.06495 q^{88} +1.12188 q^{89} +1.08995 q^{90} -3.06206 q^{92} -0.564568 q^{93} -9.28409 q^{94} +4.55363 q^{95} -4.25885 q^{96} -2.92803 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 10 q^{4} + 8 q^{5} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^3 + 10 * q^4 + 8 * q^5 + 8 * q^9	$ 8 q - 8 q^{3} + 10 q^{4} + 8 q^{5} + 8 q^{9} - 8 q^{11} - 10 q^{12} - 4 q^{13} - 8 q^{15} + 2 q^{16} - 4 q^{17} - 9 q^{19} + 10 q^{20} - 5 q^{23} + 8 q^{25} - 32 q^{26} - 8 q^{27} - 5 q^{29} - 5 q^{31} + 8 q^{33} + 10 q^{36} + 7 q^{37} + 8 q^{38} + 4 q^{39} - 9 q^{41} + 14 q^{43} - 10 q^{44} + 8 q^{45} + 18 q^{46} + 5 q^{47} - 2 q^{48} + 4 q^{51} - 8 q^{52} - q^{53} - 8 q^{55} + 9 q^{57} + 10 q^{58} - 16 q^{59} - 10 q^{60} - 26 q^{61} + 16 q^{62} - 8 q^{64} - 4 q^{65} + 3 q^{67} - 88 q^{68} + 5 q^{69} - 30 q^{71} - 15 q^{73} - 18 q^{74} - 8 q^{75} - 22 q^{76} + 32 q^{78} + 11 q^{79} + 2 q^{80} + 8 q^{81} - 42 q^{82} - 12 q^{83} - 4 q^{85} - 48 q^{86} + 5 q^{87} + 28 q^{92} + 5 q^{93} - 24 q^{94} - 9 q^{95} - 44 q^{97} - 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 10 * q^4 + 8 * q^5 + 8 * q^9 - 8 * q^11 - 10 * q^12 - 4 * q^13 - 8 * q^15 + 2 * q^16 - 4 * q^17 - 9 * q^19 + 10 * q^20 - 5 * q^23 + 8 * q^25 - 32 * q^26 - 8 * q^27 - 5 * q^29 - 5 * q^31 + 8 * q^33 + 10 * q^36 + 7 * q^37 + 8 * q^38 + 4 * q^39 - 9 * q^41 + 14 * q^43 - 10 * q^44 + 8 * q^45 + 18 * q^46 + 5 * q^47 - 2 * q^48 + 4 * q^51 - 8 * q^52 - q^53 - 8 * q^55 + 9 * q^57 + 10 * q^58 - 16 * q^59 - 10 * q^60 - 26 * q^61 + 16 * q^62 - 8 * q^64 - 4 * q^65 + 3 * q^67 - 88 * q^68 + 5 * q^69 - 30 * q^71 - 15 * q^73 - 18 * q^74 - 8 * q^75 - 22 * q^76 + 32 * q^78 + 11 * q^79 + 2 * q^80 + 8 * q^81 - 42 * q^82 - 12 * q^83 - 4 * q^85 - 48 * q^86 + 5 * q^87 + 28 * q^92 + 5 * q^93 - 24 * q^94 - 9 * q^95 - 44 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.08995	0.770712	0.385356	−	0.922768i	$-0.374079\pi$
$2$	1.08995	0.770712	0.385356	+	0.922768i	$0.374079\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.812006	−0.406003
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.08995	−0.444971
$7$	0	0
$7$	0	0
$8$	−3.06495	−1.08362
$9$	1.00000	0.333333
$10$	1.08995	0.344673
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.812006	0.234406
$13$	−4.56615	−1.26642	−0.633211	−	0.773979i	$-0.718263\pi$
$13$	−4.56615	−1.26642	−0.633211	+	0.773979i	$0.718263\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	−1.71663	−0.429158
$17$	3.62401	0.878952	0.439476	−	0.898254i	$-0.355164\pi$
$17$	3.62401	0.878952	0.439476	+	0.898254i	$0.355164\pi$
$18$	1.08995	0.256904
$19$	4.55363	1.04468	0.522338	−	0.852739i	$-0.325060\pi$
$19$	4.55363	1.04468	0.522338	+	0.852739i	$0.325060\pi$
$20$	−0.812006	−0.181570
$21$	0	0
$22$	−1.08995	−0.232378
$23$	3.77098	0.786303	0.393152	−	0.919474i	$-0.371385\pi$
$23$	3.77098	0.786303	0.393152	+	0.919474i	$0.371385\pi$
$24$	3.06495	0.625630
$25$	1.00000	0.200000
$26$	−4.97688	−0.976046
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−9.80465	−1.82068	−0.910339	−	0.413863i	$-0.864179\pi$
$29$	−9.80465	−1.82068	−0.910339	+	0.413863i	$0.864179\pi$
$30$	−1.08995	−0.198997
$31$	0.564568	0.101399	0.0506997	−	0.998714i	$-0.483855\pi$
$31$	0.564568	0.101399	0.0506997	+	0.998714i	$0.483855\pi$
$32$	4.25885	0.752866
$33$	1.00000	0.174078
$34$	3.95000	0.677419
$35$	0	0
$36$	−0.812006	−0.135334
$37$	6.72107	1.10494	0.552468	−	0.833534i	$-0.313686\pi$
$37$	6.72107	1.10494	0.552468	+	0.833534i	$0.313686\pi$
$38$	4.96324	0.805144
$39$	4.56615	0.731169
$40$	−3.06495	−0.484611
$41$	−3.09471	−0.483313	−0.241657	−	0.970362i	$-0.577691\pi$
$41$	−3.09471	−0.483313	−0.241657	+	0.970362i	$0.577691\pi$
$42$	0	0
$43$	8.41992	1.28403	0.642013	−	0.766694i	$-0.278100\pi$
$43$	8.41992	1.28403	0.642013	+	0.766694i	$0.278100\pi$
$44$	0.812006	0.122415
$45$	1.00000	0.149071
$46$	4.11018	0.606013
$47$	−8.51790	−1.24246	−0.621231	−	0.783627i	$-0.713367\pi$
$47$	−8.51790	−1.24246	−0.621231	+	0.783627i	$0.713367\pi$
$48$	1.71663	0.247775
$49$	0	0
$50$	1.08995	0.154142
$51$	−3.62401	−0.507463
$52$	3.70774	0.514171
$53$	−4.25808	−0.584892	−0.292446	−	0.956282i	$-0.594469\pi$
$53$	−4.25808	−0.584892	−0.292446	+	0.956282i	$0.594469\pi$
$54$	−1.08995	−0.148324
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−4.55363	−0.603144
$58$	−10.6866	−1.40322
$59$	3.30272	0.429977	0.214988	−	0.976617i	$-0.431029\pi$
$59$	3.30272	0.429977	0.214988	+	0.976617i	$0.431029\pi$
$60$	0.812006	0.104830
$61$	−1.90377	−0.243753	−0.121877	−	0.992545i	$-0.538891\pi$
$61$	−1.90377	−0.243753	−0.121877	+	0.992545i	$0.538891\pi$
$62$	0.615352	0.0781497
$63$	0	0
$64$	8.07521	1.00940
$65$	−4.56615	−0.566361
$66$	1.08995	0.134164
$67$	−14.1880	−1.73334	−0.866670	−	0.498881i	$-0.833744\pi$
$67$	−14.1880	−1.73334	−0.866670	+	0.498881i	$0.833744\pi$
$68$	−2.94272	−0.356857
$69$	−3.77098	−0.453973
$70$	0	0
$71$	6.05493	0.718588	0.359294	−	0.933224i	$-0.383017\pi$
$71$	6.05493	0.718588	0.359294	+	0.933224i	$0.383017\pi$
$72$	−3.06495	−0.361208
$73$	2.70782	0.316926	0.158463	−	0.987365i	$-0.449346\pi$
$73$	2.70782	0.316926	0.158463	+	0.987365i	$0.449346\pi$
$74$	7.32564	0.851588
$75$	−1.00000	−0.115470
$76$	−3.69758	−0.424141
$77$	0	0
$78$	4.97688	0.563521
$79$	14.5515	1.63717	0.818585	−	0.574385i	$-0.194759\pi$
$79$	14.5515	1.63717	0.818585	+	0.574385i	$0.194759\pi$
$80$	−1.71663	−0.191925
$81$	1.00000	0.111111
$82$	−3.37309	−0.372495
$83$	9.16676	1.00618	0.503091	−	0.864233i	$-0.332196\pi$
$83$	9.16676	1.00618	0.503091	+	0.864233i	$0.332196\pi$
$84$	0	0
$85$	3.62401	0.393079
$86$	9.17730	0.989614
$87$	9.80465	1.05117
$88$	3.06495	0.326725
$89$	1.12188	0.118919	0.0594596	−	0.998231i	$-0.481062\pi$
$89$	1.12188	0.118919	0.0594596	+	0.998231i	$0.481062\pi$
$90$	1.08995	0.114891
$91$	0	0
$92$	−3.06206	−0.319242
$93$	−0.564568	−0.0585430
$94$	−9.28409	−0.957581
$95$	4.55363	0.467193
$96$	−4.25885	−0.434667
$97$	−2.92803	−0.297296	−0.148648	−	0.988890i	$-0.547492\pi$
$97$	−2.92803	−0.297296	−0.148648	+	0.988890i	$0.547492\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	−0.812006	−0.0812006
$101$	−18.7736	−1.86805	−0.934024	−	0.357211i	$-0.883728\pi$
$101$	−18.7736	−1.86805	−0.934024	+	0.357211i	$0.883728\pi$
$102$	−3.95000	−0.391108
$103$	−19.3085	−1.90252	−0.951261	−	0.308387i	$-0.900211\pi$
$103$	−19.3085	−1.90252	−0.951261	+	0.308387i	$0.900211\pi$
$104$	13.9950	1.37232
$105$	0	0
$106$	−4.64110	−0.450784
$107$	−8.58725	−0.830161	−0.415080	−	0.909785i	$-0.636247\pi$
$107$	−8.58725	−0.830161	−0.415080	+	0.909785i	$0.636247\pi$
$108$	0.812006	0.0781353
$109$	6.65702	0.637627	0.318814	−	0.947817i	$-0.396716\pi$
$109$	6.65702	0.637627	0.318814	+	0.947817i	$0.396716\pi$
$110$	−1.08995	−0.103923
$111$	−6.72107	−0.637935
$112$	0	0
$113$	8.03060	0.755456	0.377728	−	0.925917i	$-0.376706\pi$
$113$	8.03060	0.755456	0.377728	+	0.925917i	$0.376706\pi$
$114$	−4.96324	−0.464850
$115$	3.77098	0.351646
$116$	7.96144	0.739201
$117$	−4.56615	−0.422141
$118$	3.59980	0.331388
$119$	0	0
$120$	3.06495	0.279790
$121$	1.00000	0.0909091
$122$	−2.07502	−0.187863
$123$	3.09471	0.279041
$124$	−0.458433	−0.0411685
$125$	1.00000	0.0894427
$126$	0	0
$127$	−8.66717	−0.769087	−0.384543	−	0.923107i	$-0.625641\pi$
$127$	−8.66717	−0.769087	−0.384543	+	0.923107i	$0.625641\pi$
$128$	0.283879	0.0250916
$129$	−8.41992	−0.741332
$130$	−4.97688	−0.436501
$131$	−13.4051	−1.17121	−0.585603	−	0.810598i	$-0.699142\pi$
$131$	−13.4051	−1.17121	−0.585603	+	0.810598i	$0.699142\pi$
$132$	−0.812006	−0.0706761
$133$	0	0
$134$	−15.4642	−1.33591
$135$	−1.00000	−0.0860663
$136$	−11.1074	−0.952453
$137$	−3.07894	−0.263052	−0.131526	−	0.991313i	$-0.541988\pi$
$137$	−3.07894	−0.263052	−0.131526	+	0.991313i	$0.541988\pi$
$138$	−4.11018	−0.349882
$139$	−19.9958	−1.69602	−0.848010	−	0.529981i	$-0.822199\pi$
$139$	−19.9958	−1.69602	−0.848010	+	0.529981i	$0.822199\pi$
$140$	0	0
$141$	8.51790	0.717336
$142$	6.59958	0.553825
$143$	4.56615	0.381841
$144$	−1.71663	−0.143053
$145$	−9.80465	−0.814232
$146$	2.95139	0.244259
$147$	0	0
$148$	−5.45755	−0.448608
$149$	−0.500540	−0.0410058	−0.0205029	−	0.999790i	$-0.506527\pi$
$149$	−0.500540	−0.0410058	−0.0205029	+	0.999790i	$0.506527\pi$
$150$	−1.08995	−0.0889941
$151$	5.97665	0.486373	0.243187	−	0.969980i	$-0.421807\pi$
$151$	5.97665	0.486373	0.243187	+	0.969980i	$0.421807\pi$
$152$	−13.9567	−1.13203
$153$	3.62401	0.292984
$154$	0	0
$155$	0.564568	0.0453472
$156$	−3.70774	−0.296857
$157$	−13.0079	−1.03815	−0.519073	−	0.854730i	$-0.673723\pi$
$157$	−13.0079	−1.03815	−0.519073	+	0.854730i	$0.673723\pi$
$158$	15.8604	1.26179
$159$	4.25808	0.337688
$160$	4.25885	0.336692
$161$	0	0
$162$	1.08995	0.0856347
$163$	−16.4515	−1.28858	−0.644291	−	0.764780i	$-0.722847\pi$
$163$	−16.4515	−1.28858	−0.644291	+	0.764780i	$0.722847\pi$
$164$	2.51293	0.196227
$165$	1.00000	0.0778499
$166$	9.99132	0.775477
$167$	−4.96417	−0.384139	−0.192070	−	0.981381i	$-0.561520\pi$
$167$	−4.96417	−0.384139	−0.192070	+	0.981381i	$0.561520\pi$
$168$	0	0
$169$	7.84972	0.603824
$170$	3.95000	0.302951
$171$	4.55363	0.348225
$172$	−6.83703	−0.521318
$173$	−2.12656	−0.161679	−0.0808397	−	0.996727i	$-0.525760\pi$
$173$	−2.12656	−0.161679	−0.0808397	+	0.996727i	$0.525760\pi$
$174$	10.6866	0.810148
$175$	0	0
$176$	1.71663	0.129396
$177$	−3.30272	−0.248247
$178$	1.22280	0.0916524
$179$	3.30434	0.246978	0.123489	−	0.992346i	$-0.460592\pi$
$179$	3.30434	0.246978	0.123489	+	0.992346i	$0.460592\pi$
$180$	−0.812006	−0.0605234
$181$	−15.8784	−1.18023	−0.590117	−	0.807317i	$-0.700919\pi$
$181$	−15.8784	−1.18023	−0.590117	+	0.807317i	$0.700919\pi$
$182$	0	0
$183$	1.90377	0.140731
$184$	−11.5579	−0.852057
$185$	6.72107	0.494143
$186$	−0.615352	−0.0451198
$187$	−3.62401	−0.265014
$188$	6.91658	0.504444
$189$	0	0
$190$	4.96324	0.360071
$191$	−21.8314	−1.57967	−0.789833	−	0.613321i	$-0.789833\pi$
$191$	−21.8314	−1.57967	−0.789833	+	0.613321i	$0.789833\pi$
$192$	−8.07521	−0.582778
$193$	5.63417	0.405556	0.202778	−	0.979225i	$-0.435003\pi$
$193$	5.63417	0.405556	0.202778	+	0.979225i	$0.435003\pi$
$194$	−3.19141	−0.229130
$195$	4.56615	0.326989
$196$	0	0
$197$	5.85298	0.417008	0.208504	−	0.978022i	$-0.433141\pi$
$197$	5.85298	0.417008	0.208504	+	0.978022i	$0.433141\pi$
$198$	−1.08995	−0.0774595
$199$	4.48365	0.317837	0.158919	−	0.987292i	$-0.449199\pi$
$199$	4.48365	0.317837	0.158919	+	0.987292i	$0.449199\pi$
$200$	−3.06495	−0.216725
$201$	14.1880	1.00074
$202$	−20.4624	−1.43973
$203$	0	0
$204$	2.94272	0.206032
$205$	−3.09471	−0.216144
$206$	−21.0453	−1.46630
$207$	3.77098	0.262101
$208$	7.83840	0.543496
$209$	−4.55363	−0.314981
$210$	0	0
$211$	13.6484	0.939593	0.469797	−	0.882775i	$-0.344327\pi$
$211$	13.6484	0.939593	0.469797	+	0.882775i	$0.344327\pi$
$212$	3.45759	0.237468
$213$	−6.05493	−0.414877
$214$	−9.35969	−0.639815
$215$	8.41992	0.574234
$216$	3.06495	0.208543
$217$	0	0
$218$	7.25583	0.491427
$219$	−2.70782	−0.182977
$220$	0.812006	0.0547454
$221$	−16.5478	−1.11312
$222$	−7.32564	−0.491664
$223$	18.9801	1.27100	0.635500	−	0.772101i	$-0.280794\pi$
$223$	18.9801	1.27100	0.635500	+	0.772101i	$0.280794\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	8.75297	0.582239
$227$	23.9200	1.58763	0.793814	−	0.608160i	$-0.208092\pi$
$227$	23.9200	1.58763	0.793814	+	0.608160i	$0.208092\pi$
$228$	3.69758	0.244878
$229$	10.4005	0.687286	0.343643	−	0.939100i	$-0.388339\pi$
$229$	10.4005	0.687286	0.343643	+	0.939100i	$0.388339\pi$
$230$	4.11018	0.271017
$231$	0	0
$232$	30.0508	1.97293
$233$	−11.2863	−0.739388	−0.369694	−	0.929154i	$-0.620538\pi$
$233$	−11.2863	−0.739388	−0.369694	+	0.929154i	$0.620538\pi$
$234$	−4.97688	−0.325349
$235$	−8.51790	−0.555646
$236$	−2.68183	−0.174572
$237$	−14.5515	−0.945221
$238$	0	0
$239$	13.2352	0.856114	0.428057	−	0.903752i	$-0.359198\pi$
$239$	13.2352	0.856114	0.428057	+	0.903752i	$0.359198\pi$
$240$	1.71663	0.110808
$241$	−23.3061	−1.50128	−0.750638	−	0.660714i	$-0.770254\pi$
$241$	−23.3061	−1.50128	−0.750638	+	0.660714i	$0.770254\pi$
$242$	1.08995	0.0700647
$243$	−1.00000	−0.0641500
$244$	1.54587	0.0989645
$245$	0	0
$246$	3.37309	0.215060
$247$	−20.7926	−1.32300
$248$	−1.73037	−0.109879
$249$	−9.16676	−0.580920
$250$	1.08995	0.0689346
$251$	−22.6632	−1.43049	−0.715244	−	0.698875i	$-0.753685\pi$
$251$	−22.6632	−1.43049	−0.715244	+	0.698875i	$0.753685\pi$
$252$	0	0
$253$	−3.77098	−0.237079
$254$	−9.44679	−0.592744
$255$	−3.62401	−0.226944
$256$	−15.8410	−0.990063
$257$	−15.2583	−0.951786	−0.475893	−	0.879503i	$-0.657875\pi$
$257$	−15.2583	−0.951786	−0.475893	+	0.879503i	$0.657875\pi$
$258$	−9.17730	−0.571354
$259$	0	0
$260$	3.70774	0.229944
$261$	−9.80465	−0.606893
$262$	−14.6109	−0.902663
$263$	25.4250	1.56777	0.783886	−	0.620905i	$-0.213235\pi$
$263$	25.4250	1.56777	0.783886	+	0.620905i	$0.213235\pi$
$264$	−3.06495	−0.188635
$265$	−4.25808	−0.261572
$266$	0	0
$267$	−1.12188	−0.0686580
$268$	11.5207	0.703742
$269$	−7.44969	−0.454216	−0.227108	−	0.973870i	$-0.572927\pi$
$269$	−7.44969	−0.454216	−0.227108	+	0.973870i	$0.572927\pi$
$270$	−1.08995	−0.0663323
$271$	−19.7180	−1.19779	−0.598893	−	0.800829i	$-0.704393\pi$
$271$	−19.7180	−1.19779	−0.598893	+	0.800829i	$0.704393\pi$
$272$	−6.22110	−0.377210
$273$	0	0
$274$	−3.35590	−0.202737
$275$	−1.00000	−0.0603023
$276$	3.06206	0.184314
$277$	16.0278	0.963016	0.481508	−	0.876442i	$-0.340089\pi$
$277$	16.0278	0.963016	0.481508	+	0.876442i	$0.340089\pi$
$278$	−21.7944	−1.30714
$279$	0.564568	0.0337998
$280$	0	0
$281$	−24.7348	−1.47555	−0.737777	−	0.675044i	$-0.764125\pi$
$281$	−24.7348	−1.47555	−0.737777	+	0.675044i	$0.764125\pi$
$282$	9.28409	0.552860
$283$	−11.9260	−0.708926	−0.354463	−	0.935070i	$-0.615336\pi$
$283$	−11.9260	−0.708926	−0.354463	+	0.935070i	$0.615336\pi$
$284$	−4.91664	−0.291749
$285$	−4.55363	−0.269734
$286$	4.97688	0.294289
$287$	0	0
$288$	4.25885	0.250955
$289$	−3.86653	−0.227443
$290$	−10.6866	−0.627538
$291$	2.92803	0.171644
$292$	−2.19876	−0.128673
$293$	−21.7379	−1.26994	−0.634970	−	0.772537i	$-0.718987\pi$
$293$	−21.7379	−1.26994	−0.634970	+	0.772537i	$0.718987\pi$
$294$	0	0
$295$	3.30272	0.192292
$296$	−20.5997	−1.19734
$297$	1.00000	0.0580259
$298$	−0.545564	−0.0316037
$299$	−17.2189	−0.995792
$300$	0.812006	0.0468812
$301$	0	0
$302$	6.51426	0.374854
$303$	18.7736	1.07852
$304$	−7.81692	−0.448331
$305$	−1.90377	−0.109010
$306$	3.95000	0.225806
$307$	−18.2233	−1.04006	−0.520029	−	0.854149i	$-0.674079\pi$
$307$	−18.2233	−1.04006	−0.520029	+	0.854149i	$0.674079\pi$
$308$	0	0
$309$	19.3085	1.09842
$310$	0.615352	0.0349496
$311$	17.4437	0.989140	0.494570	−	0.869138i	$-0.335326\pi$
$311$	17.4437	0.989140	0.494570	+	0.869138i	$0.335326\pi$
$312$	−13.9950	−0.792312
$313$	13.5001	0.763068	0.381534	−	0.924355i	$-0.375396\pi$
$313$	13.5001	0.763068	0.381534	+	0.924355i	$0.375396\pi$
$314$	−14.1780	−0.800111
$315$	0	0
$316$	−11.8159	−0.664696
$317$	4.94215	0.277579	0.138790	−	0.990322i	$-0.455679\pi$
$317$	4.94215	0.277579	0.138790	+	0.990322i	$0.455679\pi$
$318$	4.64110	0.260260
$319$	9.80465	0.548955
$320$	8.07521	0.451418
$321$	8.58725	0.479294
$322$	0	0
$323$	16.5024	0.918219
$324$	−0.812006	−0.0451115
$325$	−4.56615	−0.253284
$326$	−17.9313	−0.993126
$327$	−6.65702	−0.368134
$328$	9.48514	0.523729
$329$	0	0
$330$	1.08995	0.0599998
$331$	6.78152	0.372746	0.186373	−	0.982479i	$-0.440327\pi$
$331$	6.78152	0.372746	0.186373	+	0.982479i	$0.440327\pi$
$332$	−7.44346	−0.408513
$333$	6.72107	0.368312
$334$	−5.41070	−0.296061
$335$	−14.1880	−0.775174
$336$	0	0
$337$	20.7851	1.13224	0.566120	−	0.824323i	$-0.308444\pi$
$337$	20.7851	1.13224	0.566120	+	0.824323i	$0.308444\pi$
$338$	8.55581	0.465375
$339$	−8.03060	−0.436162
$340$	−2.94272	−0.159591
$341$	−0.564568	−0.0305731
$342$	4.96324	0.268381
$343$	0	0
$344$	−25.8066	−1.39140
$345$	−3.77098	−0.203023
$346$	−2.31785	−0.124608
$347$	−20.6691	−1.10958	−0.554788	−	0.831992i	$-0.687200\pi$
$347$	−20.6691	−1.10958	−0.554788	+	0.831992i	$0.687200\pi$
$348$	−7.96144	−0.426778
$349$	−28.4125	−1.52089	−0.760444	−	0.649404i	$-0.775018\pi$
$349$	−28.4125	−1.52089	−0.760444	+	0.649404i	$0.775018\pi$
$350$	0	0
$351$	4.56615	0.243723
$352$	−4.25885	−0.226998
$353$	16.8189	0.895180	0.447590	−	0.894239i	$-0.352282\pi$
$353$	16.8189	0.895180	0.447590	+	0.894239i	$0.352282\pi$
$354$	−3.59980	−0.191327
$355$	6.05493	0.321362
$356$	−0.910974	−0.0482816
$357$	0	0
$358$	3.60156	0.190349
$359$	−34.2289	−1.80653	−0.903266	−	0.429080i	$-0.858838\pi$
$359$	−34.2289	−1.80653	−0.903266	+	0.429080i	$0.858838\pi$
$360$	−3.06495	−0.161537
$361$	1.73558	0.0913463
$362$	−17.3067	−0.909621
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	2.70782	0.141734
$366$	2.07502	0.108463
$367$	−16.5486	−0.863827	−0.431914	−	0.901915i	$-0.642161\pi$
$367$	−16.5486	−0.863827	−0.431914	+	0.901915i	$0.642161\pi$
$368$	−6.47339	−0.337449
$369$	−3.09471	−0.161104
$370$	7.32564	0.380842
$371$	0	0
$372$	0.458433	0.0237686
$373$	5.73320	0.296854	0.148427	−	0.988923i	$-0.452579\pi$
$373$	5.73320	0.296854	0.148427	+	0.988923i	$0.452579\pi$
$374$	−3.95000	−0.204249
$375$	−1.00000	−0.0516398
$376$	26.1069	1.34636
$377$	44.7695	2.30575
$378$	0	0
$379$	1.31598	0.0675975	0.0337987	−	0.999429i	$-0.489239\pi$
$379$	1.31598	0.0675975	0.0337987	+	0.999429i	$0.489239\pi$
$380$	−3.69758	−0.189682
$381$	8.66717	0.444033
$382$	−23.7952	−1.21747
$383$	−4.38708	−0.224169	−0.112085	−	0.993699i	$-0.535753\pi$
$383$	−4.38708	−0.224169	−0.112085	+	0.993699i	$0.535753\pi$
$384$	−0.283879	−0.0144866
$385$	0	0
$386$	6.14097	0.312567
$387$	8.41992	0.428009
$388$	2.37758	0.120703
$389$	31.0100	1.57227	0.786134	−	0.618057i	$-0.212080\pi$
$389$	31.0100	1.57227	0.786134	+	0.618057i	$0.212080\pi$
$390$	4.97688	0.252014
$391$	13.6661	0.691123
$392$	0	0
$393$	13.4051	0.676197
$394$	6.37946	0.321393
$395$	14.5515	0.732165
$396$	0.812006	0.0408048
$397$	15.9494	0.800475	0.400238	−	0.916411i	$-0.368928\pi$
$397$	15.9494	0.800475	0.400238	+	0.916411i	$0.368928\pi$
$398$	4.88696	0.244961
$399$	0	0
$400$	−1.71663	−0.0858317
$401$	−6.15107	−0.307170	−0.153585	−	0.988135i	$-0.549082\pi$
$401$	−6.15107	−0.307170	−0.153585	+	0.988135i	$0.549082\pi$
$402$	15.4642	0.771286
$403$	−2.57790	−0.128414
$404$	15.2443	0.758433
$405$	1.00000	0.0496904
$406$	0	0
$407$	−6.72107	−0.333151
$408$	11.1074	0.549899
$409$	−22.3516	−1.10522	−0.552608	−	0.833442i	$-0.686367\pi$
$409$	−22.3516	−1.10522	−0.552608	+	0.833442i	$0.686367\pi$
$410$	−3.37309	−0.166585
$411$	3.07894	0.151873
$412$	15.6786	0.772430
$413$	0	0
$414$	4.11018	0.202004
$415$	9.16676	0.449978
$416$	−19.4466	−0.953446
$417$	19.9958	0.979197
$418$	−4.96324	−0.242760
$419$	−40.1788	−1.96286	−0.981431	−	0.191816i	$-0.938562\pi$
$419$	−40.1788	−1.96286	−0.981431	+	0.191816i	$0.938562\pi$
$420$	0	0
$421$	−3.98451	−0.194193	−0.0970966	−	0.995275i	$-0.530956\pi$
$421$	−3.98451	−0.194193	−0.0970966	+	0.995275i	$0.530956\pi$
$422$	14.8761	0.724156
$423$	−8.51790	−0.414154
$424$	13.0508	0.633803
$425$	3.62401	0.175790
$426$	−6.59958	−0.319751
$427$	0	0
$428$	6.97290	0.337048
$429$	−4.56615	−0.220456
$430$	9.17730	0.442569
$431$	24.3141	1.17117	0.585585	−	0.810611i	$-0.300865\pi$
$431$	24.3141	1.17117	0.585585	+	0.810611i	$0.300865\pi$
$432$	1.71663	0.0825916
$433$	14.7157	0.707190	0.353595	−	0.935399i	$-0.384959\pi$
$433$	14.7157	0.707190	0.353595	+	0.935399i	$0.384959\pi$
$434$	0	0
$435$	9.80465	0.470097
$436$	−5.40555	−0.258879
$437$	17.1717	0.821432
$438$	−2.95139	−0.141023
$439$	23.4424	1.11885	0.559423	−	0.828882i	$-0.311023\pi$
$439$	23.4424	1.11885	0.559423	+	0.828882i	$0.311023\pi$
$440$	3.06495	0.146116
$441$	0	0
$442$	−18.0363	−0.857898
$443$	25.4127	1.20740	0.603698	−	0.797213i	$-0.293693\pi$
$443$	25.4127	1.20740	0.603698	+	0.797213i	$0.293693\pi$
$444$	5.45755	0.259004
$445$	1.12188	0.0531823
$446$	20.6874	0.979575
$447$	0.500540	0.0236747
$448$	0	0
$449$	−10.1008	−0.476687	−0.238344	−	0.971181i	$-0.576604\pi$
$449$	−10.1008	−0.476687	−0.238344	+	0.971181i	$0.576604\pi$
$450$	1.08995	0.0513808
$451$	3.09471	0.145724
$452$	−6.52090	−0.306717
$453$	−5.97665	−0.280808
$454$	26.0717	1.22360
$455$	0	0
$456$	13.9567	0.653580
$457$	−39.0199	−1.82527	−0.912637	−	0.408771i	$-0.865958\pi$
$457$	−39.0199	−1.82527	−0.912637	+	0.408771i	$0.865958\pi$
$458$	11.3361	0.529699
$459$	−3.62401	−0.169154
$460$	−3.06206	−0.142769
$461$	−5.24439	−0.244256	−0.122128	−	0.992514i	$-0.538972\pi$
$461$	−5.24439	−0.244256	−0.122128	+	0.992514i	$0.538972\pi$
$462$	0	0
$463$	−2.16220	−0.100486	−0.0502429	−	0.998737i	$-0.516000\pi$
$463$	−2.16220	−0.100486	−0.0502429	+	0.998737i	$0.516000\pi$
$464$	16.8310	0.781359
$465$	−0.564568	−0.0261812
$466$	−12.3015	−0.569855
$467$	−18.4981	−0.855989	−0.427994	−	0.903781i	$-0.640780\pi$
$467$	−18.4981	−0.855989	−0.427994	+	0.903781i	$0.640780\pi$
$468$	3.70774	0.171390
$469$	0	0
$470$	−9.28409	−0.428243
$471$	13.0079	0.599374
$472$	−10.1227	−0.465933
$473$	−8.41992	−0.387148
$474$	−15.8604	−0.728493
$475$	4.55363	0.208935
$476$	0	0
$477$	−4.25808	−0.194964
$478$	14.4257	0.659818
$479$	10.7189	0.489758	0.244879	−	0.969554i	$-0.421252\pi$
$479$	10.7189	0.489758	0.244879	+	0.969554i	$0.421252\pi$
$480$	−4.25885	−0.194389
$481$	−30.6894	−1.39932
$482$	−25.4025	−1.15705
$483$	0	0
$484$	−0.812006	−0.0369094
$485$	−2.92803	−0.132955
$486$	−1.08995	−0.0494412
$487$	−31.3139	−1.41897	−0.709485	−	0.704721i	$-0.751072\pi$
$487$	−31.3139	−1.41897	−0.709485	+	0.704721i	$0.751072\pi$
$488$	5.83497	0.264137
$489$	16.4515	0.743963
$490$	0	0
$491$	−7.92758	−0.357766	−0.178883	−	0.983870i	$-0.557248\pi$
$491$	−7.92758	−0.357766	−0.178883	+	0.983870i	$0.557248\pi$
$492$	−2.51293	−0.113291
$493$	−35.5322	−1.60029
$494$	−22.6629	−1.01965
$495$	−1.00000	−0.0449467
$496$	−0.969156	−0.0435164
$497$	0	0
$498$	−9.99132	−0.447722
$499$	−12.3316	−0.552036	−0.276018	−	0.961152i	$-0.589015\pi$
$499$	−12.3316	−0.552036	−0.276018	+	0.961152i	$0.589015\pi$
$500$	−0.812006	−0.0363140
$501$	4.96417	0.221783
$502$	−24.7018	−1.10249
$503$	−43.4277	−1.93635	−0.968173	−	0.250280i	$-0.919477\pi$
$503$	−43.4277	−1.93635	−0.968173	+	0.250280i	$0.919477\pi$
$504$	0	0
$505$	−18.7736	−0.835416
$506$	−4.11018	−0.182720
$507$	−7.84972	−0.348618
$508$	7.03780	0.312252
$509$	5.69887	0.252598	0.126299	−	0.991992i	$-0.459690\pi$
$509$	5.69887	0.252598	0.126299	+	0.991992i	$0.459690\pi$
$510$	−3.95000	−0.174909
$511$	0	0
$512$	−17.8337	−0.788145
$513$	−4.55363	−0.201048
$514$	−16.6308	−0.733553
$515$	−19.3085	−0.850834
$516$	6.83703	0.300983
$517$	8.51790	0.374617
$518$	0	0
$519$	2.12656	0.0933456
$520$	13.9950	0.613722
$521$	15.5143	0.679695	0.339848	−	0.940480i	$-0.389624\pi$
$521$	15.5143	0.679695	0.339848	+	0.940480i	$0.389624\pi$
$522$	−10.6866	−0.467739
$523$	−11.9188	−0.521173	−0.260587	−	0.965450i	$-0.583916\pi$
$523$	−11.9188	−0.521173	−0.260587	+	0.965450i	$0.583916\pi$
$524$	10.8850	0.475514
$525$	0	0
$526$	27.7120	1.20830
$527$	2.04600	0.0891252
$528$	−1.71663	−0.0747069
$529$	−8.77972	−0.381727
$530$	−4.64110	−0.201597
$531$	3.30272	0.143326
$532$	0	0
$533$	14.1309	0.612078
$534$	−1.22280	−0.0529155
$535$	−8.58725	−0.371259
$536$	43.4855	1.87829
$537$	−3.30434	−0.142593
$538$	−8.11980	−0.350069
$539$	0	0
$540$	0.812006	0.0349432
$541$	33.4327	1.43738	0.718692	−	0.695329i	$-0.244741\pi$
$541$	33.4327	1.43738	0.718692	+	0.695329i	$0.244741\pi$
$542$	−21.4917	−0.923148
$543$	15.8784	0.681409
$544$	15.4341	0.661733
$545$	6.65702	0.285156
$546$	0	0
$547$	−5.49897	−0.235119	−0.117559	−	0.993066i	$-0.537507\pi$
$547$	−5.49897	−0.235119	−0.117559	+	0.993066i	$0.537507\pi$
$548$	2.50012	0.106800
$549$	−1.90377	−0.0812510
$550$	−1.08995	−0.0464757
$551$	−44.6468	−1.90202
$552$	11.5579	0.491935
$553$	0	0
$554$	17.4695	0.742208
$555$	−6.72107	−0.285293
$556$	16.2367	0.688589
$557$	0.0711065	0.00301288	0.00150644	−	0.999999i	$-0.499520\pi$
$557$	0.0711065	0.00301288	0.00150644	+	0.999999i	$0.499520\pi$
$558$	0.615352	0.0260499
$559$	−38.4466	−1.62612
$560$	0	0
$561$	3.62401	0.153006
$562$	−26.9597	−1.13723
$563$	−41.5211	−1.74991	−0.874953	−	0.484207i	$-0.839108\pi$
$563$	−41.5211	−1.74991	−0.874953	+	0.484207i	$0.839108\pi$
$564$	−6.91658	−0.291241
$565$	8.03060	0.337850
$566$	−12.9987	−0.546378
$567$	0	0
$568$	−18.5581	−0.778679
$569$	8.74127	0.366453	0.183227	−	0.983071i	$-0.441346\pi$
$569$	8.74127	0.366453	0.183227	+	0.983071i	$0.441346\pi$
$570$	−4.96324	−0.207887
$571$	−31.6879	−1.32610	−0.663049	−	0.748576i	$-0.730738\pi$
$571$	−31.6879	−1.32610	−0.663049	+	0.748576i	$0.730738\pi$
$572$	−3.70774	−0.155028
$573$	21.8314	0.912021
$574$	0	0
$575$	3.77098	0.157261
$576$	8.07521	0.336467
$577$	34.9975	1.45696	0.728482	−	0.685065i	$-0.240226\pi$
$577$	34.9975	1.45696	0.728482	+	0.685065i	$0.240226\pi$
$578$	−4.21433	−0.175293
$579$	−5.63417	−0.234148
$580$	7.96144	0.330581
$581$	0	0
$582$	3.19141	0.132288
$583$	4.25808	0.176352
$584$	−8.29932	−0.343428
$585$	−4.56615	−0.188787
$586$	−23.6932	−0.978757
$587$	14.2265	0.587190	0.293595	−	0.955930i	$-0.405148\pi$
$587$	14.2265	0.587190	0.293595	+	0.955930i	$0.405148\pi$
$588$	0	0
$589$	2.57084	0.105929
$590$	3.59980	0.148201
$591$	−5.85298	−0.240759
$592$	−11.5376	−0.474193
$593$	−3.69655	−0.151799	−0.0758996	−	0.997115i	$-0.524183\pi$
$593$	−3.69655	−0.151799	−0.0758996	+	0.997115i	$0.524183\pi$
$594$	1.08995	0.0447212
$595$	0	0
$596$	0.406442	0.0166485
$597$	−4.48365	−0.183504
$598$	−18.7677	−0.767469
$599$	−14.9366	−0.610295	−0.305147	−	0.952305i	$-0.598706\pi$
$599$	−14.9366	−0.610295	−0.305147	+	0.952305i	$0.598706\pi$
$600$	3.06495	0.125126
$601$	27.2425	1.11124	0.555622	−	0.831435i	$-0.312480\pi$
$601$	27.2425	1.11124	0.555622	+	0.831435i	$0.312480\pi$
$602$	0	0
$603$	−14.1880	−0.577780
$604$	−4.85308	−0.197469
$605$	1.00000	0.0406558
$606$	20.4624	0.831226
$607$	15.8512	0.643379	0.321690	−	0.946845i	$-0.395749\pi$
$607$	15.8512	0.643379	0.321690	+	0.946845i	$0.395749\pi$
$608$	19.3933	0.786500
$609$	0	0
$610$	−2.07502	−0.0840151
$611$	38.8940	1.57348
$612$	−2.94272	−0.118952
$613$	20.5994	0.832002	0.416001	−	0.909364i	$-0.363431\pi$
$613$	20.5994	0.832002	0.416001	+	0.909364i	$0.363431\pi$
$614$	−19.8625	−0.801584
$615$	3.09471	0.124791
$616$	0	0
$617$	−8.02829	−0.323207	−0.161603	−	0.986856i	$-0.551667\pi$
$617$	−8.02829	−0.323207	−0.161603	+	0.986856i	$0.551667\pi$
$618$	21.0453	0.846567
$619$	28.0680	1.12815	0.564074	−	0.825724i	$-0.309233\pi$
$619$	28.0680	1.12815	0.564074	+	0.825724i	$0.309233\pi$
$620$	−0.458433	−0.0184111
$621$	−3.77098	−0.151324
$622$	19.0127	0.762342
$623$	0	0
$624$	−7.83840	−0.313787
$625$	1.00000	0.0400000
$626$	14.7144	0.588106
$627$	4.55363	0.181855
$628$	10.5625	0.421490
$629$	24.3572	0.971186
$630$	0	0
$631$	−44.9940	−1.79118	−0.895592	−	0.444877i	$-0.853248\pi$
$631$	−44.9940	−1.79118	−0.895592	+	0.444877i	$0.853248\pi$
$632$	−44.5996	−1.77408
$633$	−13.6484	−0.542474
$634$	5.38671	0.213934
$635$	−8.66717	−0.343946
$636$	−3.45759	−0.137102
$637$	0	0
$638$	10.6866	0.423086
$639$	6.05493	0.239529
$640$	0.283879	0.0112213
$641$	14.0209	0.553794	0.276897	−	0.960900i	$-0.410694\pi$
$641$	14.0209	0.553794	0.276897	+	0.960900i	$0.410694\pi$
$642$	9.35969	0.369397
$643$	−1.75660	−0.0692736	−0.0346368	−	0.999400i	$-0.511027\pi$
$643$	−1.75660	−0.0692736	−0.0346368	+	0.999400i	$0.511027\pi$
$644$	0	0
$645$	−8.41992	−0.331534
$646$	17.9868	0.707683
$647$	6.03510	0.237264	0.118632	−	0.992938i	$-0.462149\pi$
$647$	6.03510	0.237264	0.118632	+	0.992938i	$0.462149\pi$
$648$	−3.06495	−0.120403
$649$	−3.30272	−0.129643
$650$	−4.97688	−0.195209
$651$	0	0
$652$	13.3587	0.523168
$653$	−18.2917	−0.715808	−0.357904	−	0.933758i	$-0.616508\pi$
$653$	−18.2917	−0.715808	−0.357904	+	0.933758i	$0.616508\pi$
$654$	−7.25583	−0.283726
$655$	−13.4051	−0.523780
$656$	5.31249	0.207418
$657$	2.70782	0.105642
$658$	0	0
$659$	−7.53407	−0.293486	−0.146743	−	0.989175i	$-0.546879\pi$
$659$	−7.53407	−0.293486	−0.146743	+	0.989175i	$0.546879\pi$
$660$	−0.812006	−0.0316073
$661$	−6.43101	−0.250137	−0.125069	−	0.992148i	$-0.539915\pi$
$661$	−6.43101	−0.250137	−0.125069	+	0.992148i	$0.539915\pi$
$662$	7.39153	0.287280
$663$	16.5478	0.642663
$664$	−28.0957	−1.09032
$665$	0	0
$666$	7.32564	0.283863
$667$	−36.9731	−1.43161
$668$	4.03094	0.155962
$669$	−18.9801	−0.733812
$670$	−15.4642	−0.597436
$671$	1.90377	0.0734943
$672$	0	0
$673$	−46.6969	−1.80004	−0.900018	−	0.435854i	$-0.856447\pi$
$673$	−46.6969	−1.80004	−0.900018	+	0.435854i	$0.856447\pi$
$674$	22.6548	0.872630
$675$	−1.00000	−0.0384900
$676$	−6.37402	−0.245155
$677$	16.8562	0.647838	0.323919	−	0.946085i	$-0.394999\pi$
$677$	16.8562	0.647838	0.323919	+	0.946085i	$0.394999\pi$
$678$	−8.75297	−0.336156
$679$	0	0
$680$	−11.1074	−0.425950
$681$	−23.9200	−0.916618
$682$	−0.615352	−0.0235630
$683$	−41.7048	−1.59579	−0.797895	−	0.602797i	$-0.794053\pi$
$683$	−41.7048	−1.59579	−0.797895	+	0.602797i	$0.794053\pi$
$684$	−3.69758	−0.141380
$685$	−3.07894	−0.117640
$686$	0	0
$687$	−10.4005	−0.396805
$688$	−14.4539	−0.551050
$689$	19.4430	0.740721
$690$	−4.11018	−0.156472
$691$	−15.2120	−0.578692	−0.289346	−	0.957225i	$-0.593438\pi$
$691$	−15.2120	−0.578692	−0.289346	+	0.957225i	$0.593438\pi$
$692$	1.72678	0.0656423
$693$	0	0
$694$	−22.5283	−0.855163
$695$	−19.9958	−0.758483
$696$	−30.0508	−1.13907
$697$	−11.2153	−0.424809
$698$	−30.9683	−1.17217
$699$	11.2863	0.426886
$700$	0	0
$701$	−27.3303	−1.03225	−0.516126	−	0.856513i	$-0.672626\pi$
$701$	−27.3303	−1.03225	−0.516126	+	0.856513i	$0.672626\pi$
$702$	4.97688	0.187840
$703$	30.6053	1.15430
$704$	−8.07521	−0.304346
$705$	8.51790	0.320803
$706$	18.3318	0.689926
$707$	0	0
$708$	2.68183	0.100789
$709$	9.37619	0.352130	0.176065	−	0.984379i	$-0.443663\pi$
$709$	9.37619	0.352130	0.176065	+	0.984379i	$0.443663\pi$
$710$	6.59958	0.247678
$711$	14.5515	0.545724
$712$	−3.43851	−0.128864
$713$	2.12897	0.0797307
$714$	0	0
$715$	4.56615	0.170764
$716$	−2.68314	−0.100274
$717$	−13.2352	−0.494278
$718$	−37.3078	−1.39232
$719$	28.1164	1.04857	0.524283	−	0.851544i	$-0.324333\pi$
$719$	28.1164	1.04857	0.524283	+	0.851544i	$0.324333\pi$
$720$	−1.71663	−0.0639752
$721$	0	0
$722$	1.89170	0.0704017
$723$	23.3061	0.866762
$724$	12.8934	0.479179
$725$	−9.80465	−0.364136
$726$	−1.08995	−0.0404519
$727$	−27.3955	−1.01604	−0.508021	−	0.861345i	$-0.669623\pi$
$727$	−27.3955	−1.01604	−0.508021	+	0.861345i	$0.669623\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.95139	0.109236
$731$	30.5139	1.12860
$732$	−1.54587	−0.0571372
$733$	23.6793	0.874615	0.437308	−	0.899312i	$-0.355932\pi$
$733$	23.6793	0.874615	0.437308	+	0.899312i	$0.355932\pi$
$734$	−18.0371	−0.665762
$735$	0	0
$736$	16.0600	0.591981
$737$	14.1880	0.522622
$738$	−3.37309	−0.124165
$739$	−27.9538	−1.02830	−0.514148	−	0.857702i	$-0.671892\pi$
$739$	−27.9538	−1.02830	−0.514148	+	0.857702i	$0.671892\pi$
$740$	−5.45755	−0.200623
$741$	20.7926	0.763834
$742$	0	0
$743$	20.8443	0.764705	0.382352	−	0.924017i	$-0.375114\pi$
$743$	20.8443	0.764705	0.382352	+	0.924017i	$0.375114\pi$
$744$	1.73037	0.0634385
$745$	−0.500540	−0.0183384
$746$	6.24891	0.228789
$747$	9.16676	0.335394
$748$	2.94272	0.107597
$749$	0	0
$750$	−1.08995	−0.0397994
$751$	28.0271	1.02272	0.511362	−	0.859365i	$-0.329141\pi$
$751$	28.0271	1.02272	0.511362	+	0.859365i	$0.329141\pi$
$752$	14.6221	0.533213
$753$	22.6632	0.825893
$754$	48.7966	1.77707
$755$	5.97665	0.217513
$756$	0	0
$757$	−2.91603	−0.105985	−0.0529925	−	0.998595i	$-0.516876\pi$
$757$	−2.91603	−0.105985	−0.0529925	+	0.998595i	$0.516876\pi$
$758$	1.43436	0.0520982
$759$	3.77098	0.136878
$760$	−13.9567	−0.506261
$761$	−19.2846	−0.699065	−0.349533	−	0.936924i	$-0.613660\pi$
$761$	−19.2846	−0.699065	−0.349533	+	0.936924i	$0.613660\pi$
$762$	9.44679	0.342221
$763$	0	0
$764$	17.7273	0.641350
$765$	3.62401	0.131026
$766$	−4.78170	−0.172770
$767$	−15.0807	−0.544532
$768$	15.8410	0.571613
$769$	−49.5688	−1.78750	−0.893748	−	0.448570i	$-0.851934\pi$
$769$	−49.5688	−1.78750	−0.893748	+	0.448570i	$0.851934\pi$
$770$	0	0
$771$	15.2583	0.549514
$772$	−4.57498	−0.164657
$773$	−20.2347	−0.727791	−0.363895	−	0.931440i	$-0.618553\pi$
$773$	−20.2347	−0.727791	−0.363895	+	0.931440i	$0.618553\pi$
$774$	9.17730	0.329871
$775$	0.564568	0.0202799
$776$	8.97427	0.322157
$777$	0	0
$778$	33.7993	1.21177
$779$	−14.0922	−0.504905
$780$	−3.70774	−0.132758
$781$	−6.05493	−0.216663
$782$	14.8954	0.532657
$783$	9.80465	0.350390
$784$	0	0
$785$	−13.0079	−0.464273
$786$	14.6109	0.521153
$787$	−47.1389	−1.68032	−0.840161	−	0.542337i	$-0.817540\pi$
$787$	−47.1389	−1.68032	−0.840161	+	0.542337i	$0.817540\pi$
$788$	−4.75266	−0.169306
$789$	−25.4250	−0.905153
$790$	15.8604	0.564288
$791$	0	0
$792$	3.06495	0.108908
$793$	8.69291	0.308694
$794$	17.3840	0.616936
$795$	4.25808	0.151019
$796$	−3.64075	−0.129043
$797$	39.1413	1.38646	0.693229	−	0.720718i	$-0.256188\pi$
$797$	39.1413	1.38646	0.693229	+	0.720718i	$0.256188\pi$
$798$	0	0
$799$	−30.8690	−1.09207
$800$	4.25885	0.150573
$801$	1.12188	0.0396397
$802$	−6.70436	−0.236739
$803$	−2.70782	−0.0955567
$804$	−11.5207	−0.406305
$805$	0	0
$806$	−2.80979	−0.0989705
$807$	7.44969	0.262242
$808$	57.5403	2.02426
$809$	−41.9891	−1.47626	−0.738128	−	0.674660i	$-0.764290\pi$
$809$	−41.9891	−1.47626	−0.738128	+	0.674660i	$0.764290\pi$
$810$	1.08995	0.0382970
$811$	35.5453	1.24817	0.624083	−	0.781358i	$-0.285473\pi$
$811$	35.5453	1.24817	0.624083	+	0.781358i	$0.285473\pi$
$812$	0	0
$813$	19.7180	0.691542
$814$	−7.32564	−0.256763
$815$	−16.4515	−0.576271
$816$	6.22110	0.217782
$817$	38.3412	1.34139
$818$	−24.3621	−0.851802
$819$	0	0
$820$	2.51293	0.0877552
$821$	−36.7888	−1.28394	−0.641970	−	0.766730i	$-0.721883\pi$
$821$	−36.7888	−1.28394	−0.641970	+	0.766730i	$0.721883\pi$
$822$	3.35590	0.117050
$823$	39.1748	1.36555	0.682774	−	0.730630i	$-0.260773\pi$
$823$	39.1748	1.36555	0.682774	+	0.730630i	$0.260773\pi$
$824$	59.1796	2.06162
$825$	1.00000	0.0348155
$826$	0	0
$827$	2.03711	0.0708372	0.0354186	−	0.999373i	$-0.488724\pi$
$827$	2.03711	0.0708372	0.0354186	+	0.999373i	$0.488724\pi$
$828$	−3.06206	−0.106414
$829$	−1.58002	−0.0548765	−0.0274382	−	0.999624i	$-0.508735\pi$
$829$	−1.58002	−0.0548765	−0.0274382	+	0.999624i	$0.508735\pi$
$830$	9.99132	0.346804
$831$	−16.0278	−0.555998
$832$	−36.8726	−1.27833
$833$	0	0
$834$	21.7944	0.754679
$835$	−4.96417	−0.171792
$836$	3.69758	0.127883
$837$	−0.564568	−0.0195143
$838$	−43.7929	−1.51280
$839$	26.0088	0.897923	0.448961	−	0.893551i	$-0.351794\pi$
$839$	26.0088	0.897923	0.448961	+	0.893551i	$0.351794\pi$
$840$	0	0
$841$	67.1312	2.31487
$842$	−4.34292	−0.149667
$843$	24.7348	0.851912
$844$	−11.0826	−0.381478
$845$	7.84972	0.270039
$846$	−9.28409	−0.319194
$847$	0	0
$848$	7.30957	0.251011
$849$	11.9260	0.409299
$850$	3.95000	0.135484
$851$	25.3450	0.868815
$852$	4.91664	0.168441
$853$	−3.98652	−0.136496	−0.0682479	−	0.997668i	$-0.521741\pi$
$853$	−3.98652	−0.136496	−0.0682479	+	0.997668i	$0.521741\pi$
$854$	0	0
$855$	4.55363	0.155731
$856$	26.3195	0.899582
$857$	46.8636	1.60083	0.800415	−	0.599446i	$-0.204612\pi$
$857$	46.8636	1.60083	0.800415	+	0.599446i	$0.204612\pi$
$858$	−4.97688	−0.169908
$859$	−5.88029	−0.200633	−0.100316	−	0.994956i	$-0.531986\pi$
$859$	−5.88029	−0.200633	−0.100316	+	0.994956i	$0.531986\pi$
$860$	−6.83703	−0.233141
$861$	0	0
$862$	26.5012	0.902635
$863$	46.2467	1.57426	0.787128	−	0.616790i	$-0.211567\pi$
$863$	46.2467	1.57426	0.787128	+	0.616790i	$0.211567\pi$
$864$	−4.25885	−0.144889
$865$	−2.12656	−0.0723052
$866$	16.0394	0.545040
$867$	3.86653	0.131314
$868$	0	0
$869$	−14.5515	−0.493626
$870$	10.6866	0.362309
$871$	64.7846	2.19514
$872$	−20.4034	−0.690948
$873$	−2.92803	−0.0990988
$874$	18.7163	0.633087
$875$	0	0
$876$	2.19876	0.0742893
$877$	30.2789	1.02245	0.511223	−	0.859448i	$-0.329193\pi$
$877$	30.2789	1.02245	0.511223	+	0.859448i	$0.329193\pi$
$878$	25.5511	0.862308
$879$	21.7379	0.733200
$880$	1.71663	0.0578677
$881$	−7.13297	−0.240316	−0.120158	−	0.992755i	$-0.538340\pi$
$881$	−7.13297	−0.240316	−0.120158	+	0.992755i	$0.538340\pi$
$882$	0	0
$883$	56.5578	1.90332	0.951660	−	0.307152i	$-0.0993760\pi$
$883$	56.5578	1.90332	0.951660	+	0.307152i	$0.0993760\pi$
$884$	13.4369	0.451932
$885$	−3.30272	−0.111020
$886$	27.6986	0.930554
$887$	12.5782	0.422334	0.211167	−	0.977450i	$-0.432274\pi$
$887$	12.5782	0.422334	0.211167	+	0.977450i	$0.432274\pi$
$888$	20.5997	0.691282
$889$	0	0
$890$	1.22280	0.0409882
$891$	−1.00000	−0.0335013
$892$	−15.4119	−0.516030
$893$	−38.7874	−1.29797
$894$	0.545564	0.0182464
$895$	3.30434	0.110452
$896$	0	0
$897$	17.2189	0.574921
$898$	−11.0094	−0.367389
$899$	−5.53539	−0.184616
$900$	−0.812006	−0.0270669
$901$	−15.4313	−0.514092
$902$	3.37309	0.112312
$903$	0	0
$904$	−24.6134	−0.818629
$905$	−15.8784	−0.527817
$906$	−6.51426	−0.216422
$907$	46.4602	1.54269	0.771344	−	0.636419i	$-0.219585\pi$
$907$	46.4602	1.54269	0.771344	+	0.636419i	$0.219585\pi$
$908$	−19.4232	−0.644582
$909$	−18.7736	−0.622682
$910$	0	0
$911$	47.8151	1.58418	0.792092	−	0.610401i	$-0.208992\pi$
$911$	47.8151	1.58418	0.792092	+	0.610401i	$0.208992\pi$
$912$	7.81692	0.258844
$913$	−9.16676	−0.303375
$914$	−42.5298	−1.40676
$915$	1.90377	0.0629368
$916$	−8.44529	−0.279040
$917$	0	0
$918$	−3.95000	−0.130369
$919$	27.7061	0.913940	0.456970	−	0.889482i	$-0.348935\pi$
$919$	27.7061	0.913940	0.456970	+	0.889482i	$0.348935\pi$
$920$	−11.5579	−0.381051
$921$	18.2233	0.600477
$922$	−5.71613	−0.188251
$923$	−27.6477	−0.910036
$924$	0	0
$925$	6.72107	0.220987
$926$	−2.35669	−0.0774457
$927$	−19.3085	−0.634174
$928$	−41.7566	−1.37073
$929$	20.8651	0.684561	0.342281	−	0.939598i	$-0.388801\pi$
$929$	20.8651	0.684561	0.342281	+	0.939598i	$0.388801\pi$
$930$	−0.615352	−0.0201782
$931$	0	0
$932$	9.16452	0.300194
$933$	−17.4437	−0.571080
$934$	−20.1620	−0.659721
$935$	−3.62401	−0.118518
$936$	13.9950	0.457441
$937$	27.1500	0.886951	0.443476	−	0.896286i	$-0.353745\pi$
$937$	27.1500	0.886951	0.443476	+	0.896286i	$0.353745\pi$
$938$	0	0
$939$	−13.5001	−0.440558
$940$	6.91658	0.225594
$941$	48.7306	1.58857	0.794286	−	0.607544i	$-0.207845\pi$
$941$	48.7306	1.58857	0.794286	+	0.607544i	$0.207845\pi$
$942$	14.1780	0.461944
$943$	−11.6701	−0.380031
$944$	−5.66955	−0.184528
$945$	0	0
$946$	−9.17730	−0.298380
$947$	−49.1014	−1.59558	−0.797791	−	0.602935i	$-0.793998\pi$
$947$	−49.1014	−1.59558	−0.797791	+	0.602935i	$0.793998\pi$
$948$	11.8159	0.383763
$949$	−12.3643	−0.401362
$950$	4.96324	0.161029
$951$	−4.94215	−0.160260
$952$	0	0
$953$	33.3622	1.08071	0.540353	−	0.841438i	$-0.318291\pi$
$953$	33.3622	1.08071	0.540353	+	0.841438i	$0.318291\pi$
$954$	−4.64110	−0.150261
$955$	−21.8314	−0.706449
$956$	−10.7471	−0.347585
$957$	−9.80465	−0.316939
$958$	11.6831	0.377463
$959$	0	0
$960$	−8.07521	−0.260626
$961$	−30.6813	−0.989718
$962$	−33.4499	−1.07847
$963$	−8.58725	−0.276720
$964$	18.9247	0.609522
$965$	5.63417	0.181370
$966$	0	0
$967$	−32.6247	−1.04914	−0.524569	−	0.851368i	$-0.675774\pi$
$967$	−32.6247	−1.04914	−0.524569	+	0.851368i	$0.675774\pi$
$968$	−3.06495	−0.0985112
$969$	−16.5024	−0.530134
$970$	−3.19141	−0.102470
$971$	−8.27383	−0.265520	−0.132760	−	0.991148i	$-0.542384\pi$
$971$	−8.27383	−0.265520	−0.132760	+	0.991148i	$0.542384\pi$
$972$	0.812006	0.0260451
$973$	0	0
$974$	−34.1307	−1.09362
$975$	4.56615	0.146234
$976$	3.26808	0.104609
$977$	11.6465	0.372606	0.186303	−	0.982492i	$-0.440349\pi$
$977$	11.6465	0.372606	0.186303	+	0.982492i	$0.440349\pi$
$978$	17.9313	0.573381
$979$	−1.12188	−0.0358555
$980$	0	0
$981$	6.65702	0.212542
$982$	−8.64067	−0.275735
$983$	−25.6481	−0.818047	−0.409023	−	0.912524i	$-0.634131\pi$
$983$	−25.6481	−0.818047	−0.409023	+	0.912524i	$0.634131\pi$
$984$	−9.48514	−0.302375
$985$	5.85298	0.186491
$986$	−38.7283	−1.23336
$987$	0	0
$988$	16.8837	0.537142
$989$	31.7513	1.00963
$990$	−1.08995	−0.0346409
$991$	−15.0252	−0.477292	−0.238646	−	0.971107i	$-0.576704\pi$
$991$	−15.0252	−0.477292	−0.238646	+	0.971107i	$0.576704\pi$
$992$	2.40441	0.0763401
$993$	−6.78152	−0.215205
$994$	0	0
$995$	4.48365	0.142141
$996$	7.44346	0.235855
$997$	−24.6383	−0.780302	−0.390151	−	0.920751i	$-0.627577\pi$
$997$	−24.6383	−0.780302	−0.390151	+	0.920751i	$0.627577\pi$
$998$	−13.4408	−0.425461
$999$	−6.72107	−0.212645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.ce.1.6		8
7.3	odd	6		1155.2.q.j.331.3	✓	16
7.5	odd	6		1155.2.q.j.991.3	yes	16
7.6	odd	2		8085.2.a.cf.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.j.331.3	✓	16	7.3	odd	6
1155.2.q.j.991.3	yes	16	7.5	odd	6
8085.2.a.ce.1.6		8	1.1	even	1	trivial
8085.2.a.cf.1.6		8	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)

\(f(q)\)	\(=\)	\(q+1.08995 q^{2} -1.00000 q^{3} -0.812006 q^{4} +1.00000 q^{5} -1.08995 q^{6} -3.06495 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.08995 q^{2} -1.00000 q^{3} -0.812006 q^{4} +1.00000 q^{5} -1.08995 q^{6} -3.06495 q^{8} +1.00000 q^{9} +1.08995 q^{10} -1.00000 q^{11} +0.812006 q^{12} -4.56615 q^{13} -1.00000 q^{15} -1.71663 q^{16} +3.62401 q^{17} +1.08995 q^{18} +4.55363 q^{19} -0.812006 q^{20} -1.08995 q^{22} +3.77098 q^{23} +3.06495 q^{24} +1.00000 q^{25} -4.97688 q^{26} -1.00000 q^{27} -9.80465 q^{29} -1.08995 q^{30} +0.564568 q^{31} +4.25885 q^{32} +1.00000 q^{33} +3.95000 q^{34} -0.812006 q^{36} +6.72107 q^{37} +4.96324 q^{38} +4.56615 q^{39} -3.06495 q^{40} -3.09471 q^{41} +8.41992 q^{43} +0.812006 q^{44} +1.00000 q^{45} +4.11018 q^{46} -8.51790 q^{47} +1.71663 q^{48} +1.08995 q^{50} -3.62401 q^{51} +3.70774 q^{52} -4.25808 q^{53} -1.08995 q^{54} -1.00000 q^{55} -4.55363 q^{57} -10.6866 q^{58} +3.30272 q^{59} +0.812006 q^{60} -1.90377 q^{61} +0.615352 q^{62} +8.07521 q^{64} -4.56615 q^{65} +1.08995 q^{66} -14.1880 q^{67} -2.94272 q^{68} -3.77098 q^{69} +6.05493 q^{71} -3.06495 q^{72} +2.70782 q^{73} +7.32564 q^{74} -1.00000 q^{75} -3.69758 q^{76} +4.97688 q^{78} +14.5515 q^{79} -1.71663 q^{80} +1.00000 q^{81} -3.37309 q^{82} +9.16676 q^{83} +3.62401 q^{85} +9.17730 q^{86} +9.80465 q^{87} +3.06495 q^{88} +1.12188 q^{89} +1.08995 q^{90} -3.06206 q^{92} -0.564568 q^{93} -9.28409 q^{94} +4.55363 q^{95} -4.25885 q^{96} -2.92803 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 10 q^{4} + 8 q^{5} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^3 + 10 * q^4 + 8 * q^5 + 8 * q^9	\( 8 q - 8 q^{3} + 10 q^{4} + 8 q^{5} + 8 q^{9} - 8 q^{11} - 10 q^{12} - 4 q^{13} - 8 q^{15} + 2 q^{16} - 4 q^{17} - 9 q^{19} + 10 q^{20} - 5 q^{23} + 8 q^{25} - 32 q^{26} - 8 q^{27} - 5 q^{29} - 5 q^{31} + 8 q^{33} + 10 q^{36} + 7 q^{37} + 8 q^{38} + 4 q^{39} - 9 q^{41} + 14 q^{43} - 10 q^{44} + 8 q^{45} + 18 q^{46} + 5 q^{47} - 2 q^{48} + 4 q^{51} - 8 q^{52} - q^{53} - 8 q^{55} + 9 q^{57} + 10 q^{58} - 16 q^{59} - 10 q^{60} - 26 q^{61} + 16 q^{62} - 8 q^{64} - 4 q^{65} + 3 q^{67} - 88 q^{68} + 5 q^{69} - 30 q^{71} - 15 q^{73} - 18 q^{74} - 8 q^{75} - 22 q^{76} + 32 q^{78} + 11 q^{79} + 2 q^{80} + 8 q^{81} - 42 q^{82} - 12 q^{83} - 4 q^{85} - 48 q^{86} + 5 q^{87} + 28 q^{92} + 5 q^{93} - 24 q^{94} - 9 q^{95} - 44 q^{97} - 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 10 * q^4 + 8 * q^5 + 8 * q^9 - 8 * q^11 - 10 * q^12 - 4 * q^13 - 8 * q^15 + 2 * q^16 - 4 * q^17 - 9 * q^19 + 10 * q^20 - 5 * q^23 + 8 * q^25 - 32 * q^26 - 8 * q^27 - 5 * q^29 - 5 * q^31 + 8 * q^33 + 10 * q^36 + 7 * q^37 + 8 * q^38 + 4 * q^39 - 9 * q^41 + 14 * q^43 - 10 * q^44 + 8 * q^45 + 18 * q^46 + 5 * q^47 - 2 * q^48 + 4 * q^51 - 8 * q^52 - q^53 - 8 * q^55 + 9 * q^57 + 10 * q^58 - 16 * q^59 - 10 * q^60 - 26 * q^61 + 16 * q^62 - 8 * q^64 - 4 * q^65 + 3 * q^67 - 88 * q^68 + 5 * q^69 - 30 * q^71 - 15 * q^73 - 18 * q^74 - 8 * q^75 - 22 * q^76 + 32 * q^78 + 11 * q^79 + 2 * q^80 + 8 * q^81 - 42 * q^82 - 12 * q^83 - 4 * q^85 - 48 * q^86 + 5 * q^87 + 28 * q^92 + 5 * q^93 - 24 * q^94 - 9 * q^95 - 44 * q^97 - 8 * q^99

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