LMFDB - Embedded newform 8085.2.a.ce.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:	$8$
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			1.2
Root			$1.93459$ 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)

$f(q)$	$=$	$q-1.93459 q^{2} -1.00000 q^{3} +1.74263 q^{4} +1.00000 q^{5} +1.93459 q^{6} +0.497910 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.93459 q^{2} -1.00000 q^{3} +1.74263 q^{4} +1.00000 q^{5} +1.93459 q^{6} +0.497910 q^{8} +1.00000 q^{9} -1.93459 q^{10} -1.00000 q^{11} -1.74263 q^{12} +6.71159 q^{13} -1.00000 q^{15} -4.44850 q^{16} -1.48525 q^{17} -1.93459 q^{18} +8.30518 q^{19} +1.74263 q^{20} +1.93459 q^{22} -4.08202 q^{23} -0.497910 q^{24} +1.00000 q^{25} -12.9842 q^{26} -1.00000 q^{27} -3.69187 q^{29} +1.93459 q^{30} -2.20934 q^{31} +7.61020 q^{32} +1.00000 q^{33} +2.87335 q^{34} +1.74263 q^{36} -4.21010 q^{37} -16.0671 q^{38} -6.71159 q^{39} +0.497910 q^{40} +3.16689 q^{41} +4.93147 q^{43} -1.74263 q^{44} +1.00000 q^{45} +7.89703 q^{46} +3.84028 q^{47} +4.44850 q^{48} -1.93459 q^{50} +1.48525 q^{51} +11.6958 q^{52} -12.2233 q^{53} +1.93459 q^{54} -1.00000 q^{55} -8.30518 q^{57} +7.14224 q^{58} -0.140745 q^{59} -1.74263 q^{60} -10.7697 q^{61} +4.27415 q^{62} -5.82558 q^{64} +6.71159 q^{65} -1.93459 q^{66} -10.4608 q^{67} -2.58824 q^{68} +4.08202 q^{69} -14.9677 q^{71} +0.497910 q^{72} +1.76038 q^{73} +8.14480 q^{74} -1.00000 q^{75} +14.4728 q^{76} +12.9842 q^{78} -6.56804 q^{79} -4.44850 q^{80} +1.00000 q^{81} -6.12663 q^{82} -9.32844 q^{83} -1.48525 q^{85} -9.54036 q^{86} +3.69187 q^{87} -0.497910 q^{88} -3.19464 q^{89} -1.93459 q^{90} -7.11344 q^{92} +2.20934 q^{93} -7.42935 q^{94} +8.30518 q^{95} -7.61020 q^{96} -10.3227 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.93459	−1.36796	−0.683980	−	0.729501i	$-0.739752\pi$
$2$	−1.93459	−1.36796	−0.683980	+	0.729501i	$0.739752\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.74263	0.871314
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.93459	0.789792
$7$	0	0
$7$	0	0
$8$	0.497910	0.176038
$9$	1.00000	0.333333
$10$	−1.93459	−0.611770
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.74263	−0.503053
$13$	6.71159	1.86146	0.930731	−	0.365706i	$-0.119172\pi$
$13$	6.71159	1.86146	0.930731	+	0.365706i	$0.119172\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	−4.44850	−1.11213
$17$	−1.48525	−0.360227	−0.180114	−	0.983646i	$-0.557647\pi$
$17$	−1.48525	−0.360227	−0.180114	+	0.983646i	$0.557647\pi$
$18$	−1.93459	−0.455987
$19$	8.30518	1.90534	0.952670	−	0.304006i	$-0.0983244\pi$
$19$	8.30518	1.90534	0.952670	+	0.304006i	$0.0983244\pi$
$20$	1.74263	0.389663
$21$	0	0
$22$	1.93459	0.412455
$23$	−4.08202	−0.851160	−0.425580	−	0.904921i	$-0.639930\pi$
$23$	−4.08202	−0.851160	−0.425580	+	0.904921i	$0.639930\pi$
$24$	−0.497910	−0.101635
$25$	1.00000	0.200000
$26$	−12.9842	−2.54640
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−3.69187	−0.685563	−0.342781	−	0.939415i	$-0.611369\pi$
$29$	−3.69187	−0.685563	−0.342781	+	0.939415i	$0.611369\pi$
$30$	1.93459	0.353206
$31$	−2.20934	−0.396809	−0.198404	−	0.980120i	$-0.563576\pi$
$31$	−2.20934	−0.396809	−0.198404	+	0.980120i	$0.563576\pi$
$32$	7.61020	1.34531
$33$	1.00000	0.174078
$34$	2.87335	0.492776
$35$	0	0
$36$	1.74263	0.290438
$37$	−4.21010	−0.692136	−0.346068	−	0.938209i	$-0.612483\pi$
$37$	−4.21010	−0.692136	−0.346068	+	0.938209i	$0.612483\pi$
$38$	−16.0671	−2.60643
$39$	−6.71159	−1.07472
$40$	0.497910	0.0787265
$41$	3.16689	0.494586	0.247293	−	0.968941i	$-0.420459\pi$
$41$	3.16689	0.494586	0.247293	+	0.968941i	$0.420459\pi$
$42$	0	0
$43$	4.93147	0.752042	0.376021	−	0.926611i	$-0.377292\pi$
$43$	4.93147	0.752042	0.376021	+	0.926611i	$0.377292\pi$
$44$	−1.74263	−0.262711
$45$	1.00000	0.149071
$46$	7.89703	1.16435
$47$	3.84028	0.560162	0.280081	−	0.959976i	$-0.409639\pi$
$47$	3.84028	0.560162	0.280081	+	0.959976i	$0.409639\pi$
$48$	4.44850	0.642086
$49$	0	0
$50$	−1.93459	−0.273592
$51$	1.48525	0.207977
$52$	11.6958	1.62192
$53$	−12.2233	−1.67900	−0.839502	−	0.543357i	$-0.817153\pi$
$53$	−12.2233	−1.67900	−0.839502	+	0.543357i	$0.817153\pi$
$54$	1.93459	0.263264
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−8.30518	−1.10005
$58$	7.14224	0.937822
$59$	−0.140745	−0.0183234	−0.00916171	−	0.999958i	$-0.502916\pi$
$59$	−0.140745	−0.0183234	−0.00916171	+	0.999958i	$0.502916\pi$
$60$	−1.74263	−0.224972
$61$	−10.7697	−1.37892	−0.689460	−	0.724324i	$-0.742152\pi$
$61$	−10.7697	−1.37892	−0.689460	+	0.724324i	$0.742152\pi$
$62$	4.27415	0.542818
$63$	0	0
$64$	−5.82558	−0.728198
$65$	6.71159	0.832471
$66$	−1.93459	−0.238131
$67$	−10.4608	−1.27799	−0.638995	−	0.769211i	$-0.720650\pi$
$67$	−10.4608	−1.27799	−0.638995	+	0.769211i	$0.720650\pi$
$68$	−2.58824	−0.313871
$69$	4.08202	0.491418
$70$	0	0
$71$	−14.9677	−1.77634	−0.888172	−	0.459511i	$-0.848025\pi$
$71$	−14.9677	−1.77634	−0.888172	+	0.459511i	$0.848025\pi$
$72$	0.497910	0.0586793
$73$	1.76038	0.206037	0.103019	−	0.994679i	$-0.467150\pi$
$73$	1.76038	0.206037	0.103019	+	0.994679i	$0.467150\pi$
$74$	8.14480	0.946814
$75$	−1.00000	−0.115470
$76$	14.4728	1.66015
$77$	0	0
$78$	12.9842	1.47017
$79$	−6.56804	−0.738962	−0.369481	−	0.929238i	$-0.620465\pi$
$79$	−6.56804	−0.738962	−0.369481	+	0.929238i	$0.620465\pi$
$80$	−4.44850	−0.497358
$81$	1.00000	0.111111
$82$	−6.12663	−0.676573
$83$	−9.32844	−1.02393	−0.511964	−	0.859007i	$-0.671082\pi$
$83$	−9.32844	−1.02393	−0.511964	+	0.859007i	$0.671082\pi$
$84$	0	0
$85$	−1.48525	−0.161098
$86$	−9.54036	−1.02876
$87$	3.69187	0.395810
$88$	−0.497910	−0.0530774
$89$	−3.19464	−0.338631	−0.169316	−	0.985562i	$-0.554156\pi$
$89$	−3.19464	−0.338631	−0.169316	+	0.985562i	$0.554156\pi$
$90$	−1.93459	−0.203923
$91$	0	0
$92$	−7.11344	−0.741628
$93$	2.20934	0.229098
$94$	−7.42935	−0.766279
$95$	8.30518	0.852094
$96$	−7.61020	−0.776713
$97$	−10.3227	−1.04811	−0.524057	−	0.851683i	$-0.675582\pi$
$97$	−10.3227	−1.04811	−0.524057	+	0.851683i	$0.675582\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	1.74263	0.174263
$101$	−8.57051	−0.852797	−0.426399	−	0.904535i	$-0.640218\pi$
$101$	−8.57051	−0.852797	−0.426399	+	0.904535i	$0.640218\pi$
$102$	−2.87335	−0.284504
$103$	−5.24410	−0.516717	−0.258358	−	0.966049i	$-0.583181\pi$
$103$	−5.24410	−0.516717	−0.258358	+	0.966049i	$0.583181\pi$
$104$	3.34177	0.327688
$105$	0	0
$106$	23.6471	2.29681
$107$	17.5524	1.69685	0.848425	−	0.529315i	$-0.177551\pi$
$107$	17.5524	1.69685	0.848425	+	0.529315i	$0.177551\pi$
$108$	−1.74263	−0.167684
$109$	2.31288	0.221533	0.110767	−	0.993846i	$-0.464669\pi$
$109$	2.31288	0.221533	0.110767	+	0.993846i	$0.464669\pi$
$110$	1.93459	0.184456
$111$	4.21010	0.399605
$112$	0	0
$113$	−1.08495	−0.102064	−0.0510319	−	0.998697i	$-0.516251\pi$
$113$	−1.08495	−0.102064	−0.0510319	+	0.998697i	$0.516251\pi$
$114$	16.0671	1.50482
$115$	−4.08202	−0.380650
$116$	−6.43355	−0.597340
$117$	6.71159	0.620487
$118$	0.272283	0.0250657
$119$	0	0
$120$	−0.497910	−0.0454528
$121$	1.00000	0.0909091
$122$	20.8349	1.88631
$123$	−3.16689	−0.285549
$124$	−3.85005	−0.345745
$125$	1.00000	0.0894427
$126$	0	0
$127$	19.8630	1.76255	0.881277	−	0.472600i	$-0.156684\pi$
$127$	19.8630	1.76255	0.881277	+	0.472600i	$0.156684\pi$
$128$	−3.95030	−0.349160
$129$	−4.93147	−0.434192
$130$	−12.9842	−1.13879
$131$	−12.0031	−1.04872	−0.524359	−	0.851497i	$-0.675695\pi$
$131$	−12.0031	−1.04872	−0.524359	+	0.851497i	$0.675695\pi$
$132$	1.74263	0.151676
$133$	0	0
$134$	20.2373	1.74824
$135$	−1.00000	−0.0860663
$136$	−0.739523	−0.0634136
$137$	−15.5154	−1.32557	−0.662783	−	0.748811i	$-0.730625\pi$
$137$	−15.5154	−1.32557	−0.662783	+	0.748811i	$0.730625\pi$
$138$	−7.89703	−0.672239
$139$	−22.8224	−1.93577	−0.967887	−	0.251386i	$-0.919114\pi$
$139$	−22.8224	−1.93577	−0.967887	+	0.251386i	$0.919114\pi$
$140$	0	0
$141$	−3.84028	−0.323410
$142$	28.9564	2.42997
$143$	−6.71159	−0.561252
$144$	−4.44850	−0.370709
$145$	−3.69187	−0.306593
$146$	−3.40561	−0.281850
$147$	0	0
$148$	−7.33663	−0.603068
$149$	8.18944	0.670905	0.335453	−	0.942057i	$-0.391111\pi$
$149$	8.18944	0.670905	0.335453	+	0.942057i	$0.391111\pi$
$150$	1.93459	0.157958
$151$	−12.0010	−0.976628	−0.488314	−	0.872668i	$-0.662388\pi$
$151$	−12.0010	−0.976628	−0.488314	+	0.872668i	$0.662388\pi$
$152$	4.13524	0.335412
$153$	−1.48525	−0.120076
$154$	0	0
$155$	−2.20934	−0.177458
$156$	−11.6958	−0.936414
$157$	−12.2003	−0.973686	−0.486843	−	0.873489i	$-0.661852\pi$
$157$	−12.2003	−0.973686	−0.486843	+	0.873489i	$0.661852\pi$
$158$	12.7064	1.01087
$159$	12.2233	0.969373
$160$	7.61020	0.601639
$161$	0	0
$162$	−1.93459	−0.151996
$163$	16.0673	1.25849	0.629244	−	0.777208i	$-0.283365\pi$
$163$	16.0673	1.25849	0.629244	+	0.777208i	$0.283365\pi$
$164$	5.51871	0.430939
$165$	1.00000	0.0778499
$166$	18.0467	1.40069
$167$	9.14403	0.707586	0.353793	−	0.935324i	$-0.384892\pi$
$167$	9.14403	0.707586	0.353793	+	0.935324i	$0.384892\pi$
$168$	0	0
$169$	32.0455	2.46504
$170$	2.87335	0.220376
$171$	8.30518	0.635113
$172$	8.59371	0.655265
$173$	6.46150	0.491259	0.245629	−	0.969364i	$-0.421005\pi$
$173$	6.46150	0.491259	0.245629	+	0.969364i	$0.421005\pi$
$174$	−7.14224	−0.541452
$175$	0	0
$176$	4.44850	0.335319
$177$	0.140745	0.0105790
$178$	6.18031	0.463234
$179$	−7.91900	−0.591894	−0.295947	−	0.955204i	$-0.595635\pi$
$179$	−7.91900	−0.591894	−0.295947	+	0.955204i	$0.595635\pi$
$180$	1.74263	0.129888
$181$	3.53233	0.262556	0.131278	−	0.991346i	$-0.458092\pi$
$181$	3.53233	0.262556	0.131278	+	0.991346i	$0.458092\pi$
$182$	0	0
$183$	10.7697	0.796120
$184$	−2.03248	−0.149836
$185$	−4.21010	−0.309533
$186$	−4.27415	−0.313396
$187$	1.48525	0.108613
$188$	6.69217	0.488077
$189$	0	0
$190$	−16.0671	−1.16563
$191$	−22.6357	−1.63786	−0.818930	−	0.573894i	$-0.805432\pi$
$191$	−22.6357	−1.63786	−0.818930	+	0.573894i	$0.805432\pi$
$192$	5.82558	0.420425
$193$	1.64934	0.118722	0.0593610	−	0.998237i	$-0.481094\pi$
$193$	1.64934	0.118722	0.0593610	+	0.998237i	$0.481094\pi$
$194$	19.9702	1.43378
$195$	−6.71159	−0.480627
$196$	0	0
$197$	11.3222	0.806674	0.403337	−	0.915052i	$-0.367850\pi$
$197$	11.3222	0.806674	0.403337	+	0.915052i	$0.367850\pi$
$198$	1.93459	0.137485
$199$	−5.45878	−0.386962	−0.193481	−	0.981104i	$-0.561978\pi$
$199$	−5.45878	−0.386962	−0.193481	+	0.981104i	$0.561978\pi$
$200$	0.497910	0.0352076
$201$	10.4608	0.737848
$202$	16.5804	1.16659
$203$	0	0
$204$	2.58824	0.181213
$205$	3.16689	0.221185
$206$	10.1452	0.706847
$207$	−4.08202	−0.283720
$208$	−29.8566	−2.07018
$209$	−8.30518	−0.574482
$210$	0	0
$211$	−15.3620	−1.05756	−0.528781	−	0.848758i	$-0.677351\pi$
$211$	−15.3620	−1.05756	−0.528781	+	0.848758i	$0.677351\pi$
$212$	−21.3007	−1.46294
$213$	14.9677	1.02557
$214$	−33.9566	−2.32122
$215$	4.93147	0.336324
$216$	−0.497910	−0.0338785
$217$	0	0
$218$	−4.47446	−0.303049
$219$	−1.76038	−0.118956
$220$	−1.74263	−0.117488
$221$	−9.96842	−0.670549
$222$	−8.14480	−0.546643
$223$	−17.4320	−1.16733	−0.583665	−	0.811994i	$-0.698382\pi$
$223$	−17.4320	−1.16733	−0.583665	+	0.811994i	$0.698382\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	2.09894	0.139619
$227$	−17.0312	−1.13040	−0.565202	−	0.824953i	$-0.691202\pi$
$227$	−17.0312	−1.13040	−0.565202	+	0.824953i	$0.691202\pi$
$228$	−14.4728	−0.958487
$229$	0.108739	0.00718570	0.00359285	−	0.999994i	$-0.498856\pi$
$229$	0.108739	0.00718570	0.00359285	+	0.999994i	$0.498856\pi$
$230$	7.89703	0.520714
$231$	0	0
$232$	−1.83822	−0.120685
$233$	−19.6861	−1.28968	−0.644840	−	0.764318i	$-0.723076\pi$
$233$	−19.6861	−1.28968	−0.644840	+	0.764318i	$0.723076\pi$
$234$	−12.9842	−0.848801
$235$	3.84028	0.250512
$236$	−0.245266	−0.0159655
$237$	6.56804	0.426640
$238$	0	0
$239$	−15.2615	−0.987187	−0.493593	−	0.869693i	$-0.664317\pi$
$239$	−15.2615	−0.987187	−0.493593	+	0.869693i	$0.664317\pi$
$240$	4.44850	0.287150
$241$	9.07335	0.584466	0.292233	−	0.956347i	$-0.405602\pi$
$241$	9.07335	0.584466	0.292233	+	0.956347i	$0.405602\pi$
$242$	−1.93459	−0.124360
$243$	−1.00000	−0.0641500
$244$	−18.7676	−1.20147
$245$	0	0
$246$	6.12663	0.390620
$247$	55.7410	3.54672
$248$	−1.10005	−0.0698533
$249$	9.32844	0.591166
$250$	−1.93459	−0.122354
$251$	19.4642	1.22857	0.614286	−	0.789084i	$-0.289444\pi$
$251$	19.4642	1.22857	0.614286	+	0.789084i	$0.289444\pi$
$252$	0	0
$253$	4.08202	0.256634
$254$	−38.4267	−2.41110
$255$	1.48525	0.0930102
$256$	19.2934	1.20584
$257$	−3.61118	−0.225259	−0.112630	−	0.993637i	$-0.535927\pi$
$257$	−3.61118	−0.225259	−0.112630	+	0.993637i	$0.535927\pi$
$258$	9.54036	0.593957
$259$	0	0
$260$	11.6958	0.725343
$261$	−3.69187	−0.228521
$262$	23.2211	1.43460
$263$	−11.9618	−0.737596	−0.368798	−	0.929510i	$-0.620231\pi$
$263$	−11.9618	−0.737596	−0.368798	+	0.929510i	$0.620231\pi$
$264$	0.497910	0.0306443
$265$	−12.2233	−0.750873
$266$	0	0
$267$	3.19464	0.195509
$268$	−18.2293	−1.11353
$269$	−2.32310	−0.141642	−0.0708211	−	0.997489i	$-0.522562\pi$
$269$	−2.32310	−0.141642	−0.0708211	+	0.997489i	$0.522562\pi$
$270$	1.93459	0.117735
$271$	−15.0562	−0.914596	−0.457298	−	0.889313i	$-0.651183\pi$
$271$	−15.0562	−0.914596	−0.457298	+	0.889313i	$0.651183\pi$
$272$	6.60716	0.400618
$273$	0	0
$274$	30.0158	1.81332
$275$	−1.00000	−0.0603023
$276$	7.11344	0.428179
$277$	4.09060	0.245780	0.122890	−	0.992420i	$-0.460784\pi$
$277$	4.09060	0.245780	0.122890	+	0.992420i	$0.460784\pi$
$278$	44.1520	2.64806
$279$	−2.20934	−0.132270
$280$	0	0
$281$	6.87097	0.409888	0.204944	−	0.978774i	$-0.434299\pi$
$281$	6.87097	0.409888	0.204944	+	0.978774i	$0.434299\pi$
$282$	7.42935	0.442411
$283$	22.6097	1.34401	0.672005	−	0.740547i	$-0.265433\pi$
$283$	22.6097	1.34401	0.672005	+	0.740547i	$0.265433\pi$
$284$	−26.0832	−1.54775
$285$	−8.30518	−0.491957
$286$	12.9842	0.767770
$287$	0	0
$288$	7.61020	0.448435
$289$	−14.7940	−0.870236
$290$	7.14224	0.419407
$291$	10.3227	0.605129
$292$	3.06769	0.179523
$293$	26.2364	1.53275	0.766374	−	0.642395i	$-0.222059\pi$
$293$	26.2364	1.53275	0.766374	+	0.642395i	$0.222059\pi$
$294$	0	0
$295$	−0.140745	−0.00819449
$296$	−2.09625	−0.121842
$297$	1.00000	0.0580259
$298$	−15.8432	−0.917772
$299$	−27.3969	−1.58440
$300$	−1.74263	−0.100611
$301$	0	0
$302$	23.2170	1.33599
$303$	8.57051	0.492363
$304$	−36.9457	−2.11898
$305$	−10.7697	−0.616672
$306$	2.87335	0.164259
$307$	14.4580	0.825160	0.412580	−	0.910921i	$-0.364628\pi$
$307$	14.4580	0.825160	0.412580	+	0.910921i	$0.364628\pi$
$308$	0	0
$309$	5.24410	0.298326
$310$	4.27415	0.242756
$311$	10.7404	0.609034	0.304517	−	0.952507i	$-0.401505\pi$
$311$	10.7404	0.609034	0.304517	+	0.952507i	$0.401505\pi$
$312$	−3.34177	−0.189191
$313$	−9.15391	−0.517410	−0.258705	−	0.965956i	$-0.583296\pi$
$313$	−9.15391	−0.517410	−0.258705	+	0.965956i	$0.583296\pi$
$314$	23.6025	1.33196
$315$	0	0
$316$	−11.4456	−0.643868
$317$	9.80425	0.550662	0.275331	−	0.961350i	$-0.411213\pi$
$317$	9.80425	0.550662	0.275331	+	0.961350i	$0.411213\pi$
$318$	−23.6471	−1.32606
$319$	3.69187	0.206705
$320$	−5.82558	−0.325660
$321$	−17.5524	−0.979677
$322$	0	0
$323$	−12.3353	−0.686355
$324$	1.74263	0.0968126
$325$	6.71159	0.372292
$326$	−31.0836	−1.72156
$327$	−2.31288	−0.127902
$328$	1.57683	0.0870658
$329$	0	0
$330$	−1.93459	−0.106496
$331$	4.50759	0.247760	0.123880	−	0.992297i	$-0.460466\pi$
$331$	4.50759	0.247760	0.123880	+	0.992297i	$0.460466\pi$
$332$	−16.2560	−0.892163
$333$	−4.21010	−0.230712
$334$	−17.6899	−0.967950
$335$	−10.4608	−0.571535
$336$	0	0
$337$	32.0610	1.74647	0.873236	−	0.487297i	$-0.162017\pi$
$337$	32.0610	1.74647	0.873236	+	0.487297i	$0.162017\pi$
$338$	−61.9948	−3.37207
$339$	1.08495	0.0589265
$340$	−2.58824	−0.140367
$341$	2.20934	0.119642
$342$	−16.0671	−0.868809
$343$	0	0
$344$	2.45543	0.132388
$345$	4.08202	0.219769
$346$	−12.5003	−0.672022
$347$	20.8537	1.11949	0.559743	−	0.828666i	$-0.310900\pi$
$347$	20.8537	1.11949	0.559743	+	0.828666i	$0.310900\pi$
$348$	6.43355	0.344875
$349$	33.6499	1.80124	0.900618	−	0.434612i	$-0.143115\pi$
$349$	33.6499	1.80124	0.900618	+	0.434612i	$0.143115\pi$
$350$	0	0
$351$	−6.71159	−0.358238
$352$	−7.61020	−0.405625
$353$	17.8635	0.950776	0.475388	−	0.879776i	$-0.342308\pi$
$353$	17.8635	0.950776	0.475388	+	0.879776i	$0.342308\pi$
$354$	−0.272283	−0.0144717
$355$	−14.9677	−0.794405
$356$	−5.56707	−0.295054
$357$	0	0
$358$	15.3200	0.809687
$359$	−4.63959	−0.244868	−0.122434	−	0.992477i	$-0.539070\pi$
$359$	−4.63959	−0.244868	−0.122434	+	0.992477i	$0.539070\pi$
$360$	0.497910	0.0262422
$361$	49.9761	2.63032
$362$	−6.83360	−0.359166
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	1.76038	0.0921426
$366$	−20.8349	−1.08906
$367$	−1.25869	−0.0657032	−0.0328516	−	0.999460i	$-0.510459\pi$
$367$	−1.25869	−0.0657032	−0.0328516	+	0.999460i	$0.510459\pi$
$368$	18.1589	0.946598
$369$	3.16689	0.164862
$370$	8.14480	0.423428
$371$	0	0
$372$	3.85005	0.199616
$373$	24.3256	1.25953	0.629766	−	0.776785i	$-0.283151\pi$
$373$	24.3256	1.25953	0.629766	+	0.776785i	$0.283151\pi$
$374$	−2.87335	−0.148578
$375$	−1.00000	−0.0516398
$376$	1.91211	0.0986097
$377$	−24.7783	−1.27615
$378$	0	0
$379$	−9.27384	−0.476365	−0.238182	−	0.971220i	$-0.576552\pi$
$379$	−9.27384	−0.476365	−0.238182	+	0.971220i	$0.576552\pi$
$380$	14.4728	0.742441
$381$	−19.8630	−1.01761
$382$	43.7907	2.24053
$383$	1.88789	0.0964668	0.0482334	−	0.998836i	$-0.484641\pi$
$383$	1.88789	0.0964668	0.0482334	+	0.998836i	$0.484641\pi$
$384$	3.95030	0.201588
$385$	0	0
$386$	−3.19079	−0.162407
$387$	4.93147	0.250681
$388$	−17.9887	−0.913235
$389$	−0.683875	−0.0346739	−0.0173369	−	0.999850i	$-0.505519\pi$
$389$	−0.683875	−0.0346739	−0.0173369	+	0.999850i	$0.505519\pi$
$390$	12.9842	0.657479
$391$	6.06284	0.306611
$392$	0	0
$393$	12.0031	0.605477
$394$	−21.9038	−1.10350
$395$	−6.56804	−0.330474
$396$	−1.74263	−0.0875703
$397$	11.7842	0.591432	0.295716	−	0.955276i	$-0.404442\pi$
$397$	11.7842	0.591432	0.295716	+	0.955276i	$0.404442\pi$
$398$	10.5605	0.529349
$399$	0	0
$400$	−4.44850	−0.222425
$401$	13.8108	0.689678	0.344839	−	0.938662i	$-0.387933\pi$
$401$	13.8108	0.689678	0.344839	+	0.938662i	$0.387933\pi$
$402$	−20.2373	−1.00935
$403$	−14.8282	−0.738644
$404$	−14.9352	−0.743054
$405$	1.00000	0.0496904
$406$	0	0
$407$	4.21010	0.208687
$408$	0.739523	0.0366119
$409$	−7.16690	−0.354381	−0.177190	−	0.984177i	$-0.556701\pi$
$409$	−7.16690	−0.354381	−0.177190	+	0.984177i	$0.556701\pi$
$410$	−6.12663	−0.302573
$411$	15.5154	0.765316
$412$	−9.13851	−0.450222
$413$	0	0
$414$	7.89703	0.388118
$415$	−9.32844	−0.457915
$416$	51.0766	2.50423
$417$	22.8224	1.11762
$418$	16.0671	0.785868
$419$	−30.6409	−1.49691	−0.748453	−	0.663188i	$-0.769203\pi$
$419$	−30.6409	−1.49691	−0.748453	+	0.663188i	$0.769203\pi$
$420$	0	0
$421$	4.81097	0.234472	0.117236	−	0.993104i	$-0.462597\pi$
$421$	4.81097	0.234472	0.117236	+	0.993104i	$0.462597\pi$
$422$	29.7191	1.44670
$423$	3.84028	0.186721
$424$	−6.08612	−0.295568
$425$	−1.48525	−0.0720454
$426$	−28.9564	−1.40294
$427$	0	0
$428$	30.5872	1.47849
$429$	6.71159	0.324039
$430$	−9.54036	−0.460077
$431$	−11.6861	−0.562901	−0.281451	−	0.959576i	$-0.590816\pi$
$431$	−11.6861	−0.562901	−0.281451	+	0.959576i	$0.590816\pi$
$432$	4.44850	0.214029
$433$	16.2375	0.780327	0.390163	−	0.920746i	$-0.372419\pi$
$433$	16.2375	0.780327	0.390163	+	0.920746i	$0.372419\pi$
$434$	0	0
$435$	3.69187	0.177012
$436$	4.03048	0.193025
$437$	−33.9019	−1.62175
$438$	3.40561	0.162726
$439$	10.7842	0.514703	0.257351	−	0.966318i	$-0.417150\pi$
$439$	10.7842	0.514703	0.257351	+	0.966318i	$0.417150\pi$
$440$	−0.497910	−0.0237369
$441$	0	0
$442$	19.2848	0.917284
$443$	25.1207	1.19352	0.596761	−	0.802419i	$-0.296454\pi$
$443$	25.1207	1.19352	0.596761	+	0.802419i	$0.296454\pi$
$444$	7.33663	0.348181
$445$	−3.19464	−0.151441
$446$	33.7236	1.59686
$447$	−8.18944	−0.387347
$448$	0	0
$449$	−25.0533	−1.18234	−0.591168	−	0.806548i	$-0.701333\pi$
$449$	−25.0533	−1.18234	−0.591168	+	0.806548i	$0.701333\pi$
$450$	−1.93459	−0.0911973
$451$	−3.16689	−0.149123
$452$	−1.89067	−0.0889295
$453$	12.0010	0.563856
$454$	32.9484	1.54635
$455$	0	0
$456$	−4.13524	−0.193650
$457$	−19.5264	−0.913408	−0.456704	−	0.889619i	$-0.650970\pi$
$457$	−19.5264	−0.913408	−0.456704	+	0.889619i	$0.650970\pi$
$458$	−0.210366	−0.00982975
$459$	1.48525	0.0693257
$460$	−7.11344	−0.331666
$461$	−24.0868	−1.12183	−0.560916	−	0.827873i	$-0.689551\pi$
$461$	−24.0868	−1.12183	−0.560916	+	0.827873i	$0.689551\pi$
$462$	0	0
$463$	36.8049	1.71047	0.855234	−	0.518242i	$-0.173413\pi$
$463$	36.8049	1.71047	0.855234	+	0.518242i	$0.173413\pi$
$464$	16.4233	0.762432
$465$	2.20934	0.102456
$466$	38.0845	1.76423
$467$	−41.2444	−1.90856	−0.954282	−	0.298909i	$-0.903377\pi$
$467$	−41.2444	−1.90856	−0.954282	+	0.298909i	$0.903377\pi$
$468$	11.6958	0.540639
$469$	0	0
$470$	−7.42935	−0.342690
$471$	12.2003	0.562158
$472$	−0.0700783	−0.00322562
$473$	−4.93147	−0.226749
$474$	−12.7064	−0.583626
$475$	8.30518	0.381068
$476$	0	0
$477$	−12.2233	−0.559668
$478$	29.5248	1.35043
$479$	−33.5808	−1.53435	−0.767173	−	0.641440i	$-0.778337\pi$
$479$	−33.5808	−1.53435	−0.767173	+	0.641440i	$0.778337\pi$
$480$	−7.61020	−0.347357
$481$	−28.2565	−1.28838
$482$	−17.5532	−0.799526
$483$	0	0
$484$	1.74263	0.0792103
$485$	−10.3227	−0.468731
$486$	1.93459	0.0877547
$487$	−31.2506	−1.41610	−0.708051	−	0.706162i	$-0.750425\pi$
$487$	−31.2506	−1.41610	−0.708051	+	0.706162i	$0.750425\pi$
$488$	−5.36235	−0.242742
$489$	−16.0673	−0.726588
$490$	0	0
$491$	−10.8532	−0.489800	−0.244900	−	0.969548i	$-0.578755\pi$
$491$	−10.8532	−0.489800	−0.244900	+	0.969548i	$0.578755\pi$
$492$	−5.51871	−0.248803
$493$	5.48336	0.246958
$494$	−107.836	−4.85177
$495$	−1.00000	−0.0449467
$496$	9.82825	0.441301
$497$	0	0
$498$	−18.0467	−0.808691
$499$	−22.8009	−1.02071	−0.510354	−	0.859965i	$-0.670485\pi$
$499$	−22.8009	−1.02071	−0.510354	+	0.859965i	$0.670485\pi$
$500$	1.74263	0.0779327
$501$	−9.14403	−0.408525
$502$	−37.6552	−1.68064
$503$	10.1945	0.454551	0.227275	−	0.973831i	$-0.427018\pi$
$503$	10.1945	0.454551	0.227275	+	0.973831i	$0.427018\pi$
$504$	0	0
$505$	−8.57051	−0.381383
$506$	−7.89703	−0.351066
$507$	−32.0455	−1.42319
$508$	34.6138	1.53574
$509$	30.4853	1.35124	0.675619	−	0.737251i	$-0.263877\pi$
$509$	30.4853	1.35124	0.675619	+	0.737251i	$0.263877\pi$
$510$	−2.87335	−0.127234
$511$	0	0
$512$	−29.4241	−1.30037
$513$	−8.30518	−0.366683
$514$	6.98614	0.308145
$515$	−5.24410	−0.231083
$516$	−8.59371	−0.378317
$517$	−3.84028	−0.168895
$518$	0	0
$519$	−6.46150	−0.283628
$520$	3.34177	0.146546
$521$	12.0377	0.527381	0.263690	−	0.964607i	$-0.415060\pi$
$521$	12.0377	0.527381	0.263690	+	0.964607i	$0.415060\pi$
$522$	7.14224	0.312607
$523$	−14.1437	−0.618462	−0.309231	−	0.950987i	$-0.600072\pi$
$523$	−14.1437	−0.618462	−0.309231	+	0.950987i	$0.600072\pi$
$524$	−20.9170	−0.913762
$525$	0	0
$526$	23.1411	1.00900
$527$	3.28143	0.142941
$528$	−4.44850	−0.193596
$529$	−6.33710	−0.275526
$530$	23.6471	1.02716
$531$	−0.140745	−0.00610781
$532$	0	0
$533$	21.2549	0.920652
$534$	−6.18031	−0.267448
$535$	17.5524	0.758855
$536$	−5.20854	−0.224975
$537$	7.91900	0.341730
$538$	4.49425	0.193761
$539$	0	0
$540$	−1.74263	−0.0749907
$541$	−21.1366	−0.908733	−0.454366	−	0.890815i	$-0.650134\pi$
$541$	−21.1366	−0.908733	−0.454366	+	0.890815i	$0.650134\pi$
$542$	29.1274	1.25113
$543$	−3.53233	−0.151587
$544$	−11.3031	−0.484616
$545$	2.31288	0.0990727
$546$	0	0
$547$	0.0576853	0.00246644	0.00123322	−	0.999999i	$-0.499607\pi$
$547$	0.0576853	0.00246644	0.00123322	+	0.999999i	$0.499607\pi$
$548$	−27.0375	−1.15498
$549$	−10.7697	−0.459640
$550$	1.93459	0.0824911
$551$	−30.6617	−1.30623
$552$	2.03248	0.0865081
$553$	0	0
$554$	−7.91362	−0.336217
$555$	4.21010	0.178709
$556$	−39.7710	−1.68667
$557$	39.3837	1.66874	0.834371	−	0.551204i	$-0.185831\pi$
$557$	39.3837	1.66874	0.834371	+	0.551204i	$0.185831\pi$
$558$	4.27415	0.180939
$559$	33.0980	1.39990
$560$	0	0
$561$	−1.48525	−0.0627075
$562$	−13.2925	−0.560710
$563$	−13.3884	−0.564252	−0.282126	−	0.959377i	$-0.591040\pi$
$563$	−13.3884	−0.564252	−0.282126	+	0.959377i	$0.591040\pi$
$564$	−6.69217	−0.281791
$565$	−1.08495	−0.0456443
$566$	−43.7405	−1.83855
$567$	0	0
$568$	−7.45259	−0.312704
$569$	−3.37309	−0.141407	−0.0707037	−	0.997497i	$-0.522524\pi$
$569$	−3.37309	−0.141407	−0.0707037	+	0.997497i	$0.522524\pi$
$570$	16.0671	0.672977
$571$	6.00819	0.251435	0.125717	−	0.992066i	$-0.459877\pi$
$571$	6.00819	0.251435	0.125717	+	0.992066i	$0.459877\pi$
$572$	−11.6958	−0.489026
$573$	22.6357	0.945619
$574$	0	0
$575$	−4.08202	−0.170232
$576$	−5.82558	−0.242733
$577$	14.6839	0.611299	0.305650	−	0.952144i	$-0.401126\pi$
$577$	14.6839	0.611299	0.305650	+	0.952144i	$0.401126\pi$
$578$	28.6203	1.19045
$579$	−1.64934	−0.0685442
$580$	−6.43355	−0.267139
$581$	0	0
$582$	−19.9702	−0.827791
$583$	12.2233	0.506239
$584$	0.876512	0.0362703
$585$	6.71159	0.277490
$586$	−50.7566	−2.09674
$587$	−47.2416	−1.94987	−0.974934	−	0.222495i	$-0.928580\pi$
$587$	−47.2416	−1.94987	−0.974934	+	0.222495i	$0.928580\pi$
$588$	0	0
$589$	−18.3489	−0.756055
$590$	0.272283	0.0112097
$591$	−11.3222	−0.465733
$592$	18.7286	0.769743
$593$	−19.1970	−0.788327	−0.394163	−	0.919040i	$-0.628966\pi$
$593$	−19.1970	−0.788327	−0.394163	+	0.919040i	$0.628966\pi$
$594$	−1.93459	−0.0793771
$595$	0	0
$596$	14.2711	0.584569
$597$	5.45878	0.223413
$598$	53.0016	2.16740
$599$	5.06216	0.206834	0.103417	−	0.994638i	$-0.467022\pi$
$599$	5.06216	0.206834	0.103417	+	0.994638i	$0.467022\pi$
$600$	−0.497910	−0.0203271
$601$	−23.9745	−0.977940	−0.488970	−	0.872301i	$-0.662627\pi$
$601$	−23.9745	−0.977940	−0.488970	+	0.872301i	$0.662627\pi$
$602$	0	0
$603$	−10.4608	−0.425997
$604$	−20.9133	−0.850949
$605$	1.00000	0.0406558
$606$	−16.5804	−0.673532
$607$	−18.8436	−0.764839	−0.382419	−	0.923989i	$-0.624909\pi$
$607$	−18.8436	−0.764839	−0.382419	+	0.923989i	$0.624909\pi$
$608$	63.2041	2.56327
$609$	0	0
$610$	20.8349	0.843582
$611$	25.7744	1.04272
$612$	−2.58824	−0.104624
$613$	25.2798	1.02104	0.510521	−	0.859865i	$-0.329453\pi$
$613$	25.2798	1.02104	0.510521	+	0.859865i	$0.329453\pi$
$614$	−27.9702	−1.12879
$615$	−3.16689	−0.127701
$616$	0	0
$617$	10.7730	0.433703	0.216852	−	0.976205i	$-0.430421\pi$
$617$	10.7730	0.433703	0.216852	+	0.976205i	$0.430421\pi$
$618$	−10.1452	−0.408099
$619$	−14.6044	−0.586999	−0.293500	−	0.955959i	$-0.594820\pi$
$619$	−14.6044	−0.586999	−0.293500	+	0.955959i	$0.594820\pi$
$620$	−3.85005	−0.154622
$621$	4.08202	0.163806
$622$	−20.7783	−0.833134
$623$	0	0
$624$	29.8566	1.19522
$625$	1.00000	0.0400000
$626$	17.7090	0.707796
$627$	8.30518	0.331677
$628$	−21.2605	−0.848386
$629$	6.25307	0.249326
$630$	0	0
$631$	−3.29278	−0.131083	−0.0655417	−	0.997850i	$-0.520878\pi$
$631$	−3.29278	−0.131083	−0.0655417	+	0.997850i	$0.520878\pi$
$632$	−3.27029	−0.130085
$633$	15.3620	0.610584
$634$	−18.9672	−0.753283
$635$	19.8630	0.788238
$636$	21.3007	0.844628
$637$	0	0
$638$	−7.14224	−0.282764
$639$	−14.9677	−0.592115
$640$	−3.95030	−0.156149
$641$	−20.6370	−0.815113	−0.407556	−	0.913180i	$-0.633619\pi$
$641$	−20.6370	−0.815113	−0.407556	+	0.913180i	$0.633619\pi$
$642$	33.9566	1.34016
$643$	−16.8602	−0.664901	−0.332451	−	0.943121i	$-0.607876\pi$
$643$	−16.8602	−0.664901	−0.332451	+	0.943121i	$0.607876\pi$
$644$	0	0
$645$	−4.93147	−0.194176
$646$	23.8637	0.938906
$647$	47.5408	1.86902	0.934510	−	0.355936i	$-0.115838\pi$
$647$	47.5408	1.86902	0.934510	+	0.355936i	$0.115838\pi$
$648$	0.497910	0.0195598
$649$	0.140745	0.00552472
$650$	−12.9842	−0.509281
$651$	0	0
$652$	27.9993	1.09654
$653$	−25.1796	−0.985355	−0.492678	−	0.870212i	$-0.663982\pi$
$653$	−25.1796	−0.985355	−0.492678	+	0.870212i	$0.663982\pi$
$654$	4.47446	0.174965
$655$	−12.0031	−0.469001
$656$	−14.0879	−0.550042
$657$	1.76038	0.0686790
$658$	0	0
$659$	−45.8239	−1.78504	−0.892522	−	0.451004i	$-0.851066\pi$
$659$	−45.8239	−1.78504	−0.892522	+	0.451004i	$0.851066\pi$
$660$	1.74263	0.0678317
$661$	30.9147	1.20244	0.601222	−	0.799082i	$-0.294681\pi$
$661$	30.9147	1.20244	0.601222	+	0.799082i	$0.294681\pi$
$662$	−8.72033	−0.338925
$663$	9.96842	0.387141
$664$	−4.64472	−0.180250
$665$	0	0
$666$	8.14480	0.315605
$667$	15.0703	0.583524
$668$	15.9346	0.616530
$669$	17.4320	0.673959
$670$	20.2373	0.781836
$671$	10.7697	0.415760
$672$	0	0
$673$	6.08146	0.234423	0.117212	−	0.993107i	$-0.462604\pi$
$673$	6.08146	0.234423	0.117212	+	0.993107i	$0.462604\pi$
$674$	−62.0247	−2.38910
$675$	−1.00000	−0.0384900
$676$	55.8433	2.14782
$677$	−20.6509	−0.793679	−0.396840	−	0.917888i	$-0.629893\pi$
$677$	−20.6509	−0.793679	−0.396840	+	0.917888i	$0.629893\pi$
$678$	−2.09894	−0.0806091
$679$	0	0
$680$	−0.739523	−0.0283594
$681$	17.0312	0.652639
$682$	−4.27415	−0.163666
$683$	−47.0872	−1.80174	−0.900871	−	0.434087i	$-0.857071\pi$
$683$	−47.0872	−1.80174	−0.900871	+	0.434087i	$0.857071\pi$
$684$	14.4728	0.553383
$685$	−15.5154	−0.592811
$686$	0	0
$687$	−0.108739	−0.00414867
$688$	−21.9377	−0.836366
$689$	−82.0380	−3.12540
$690$	−7.89703	−0.300635
$691$	33.1817	1.26229	0.631146	−	0.775664i	$-0.282585\pi$
$691$	33.1817	1.26229	0.631146	+	0.775664i	$0.282585\pi$
$692$	11.2600	0.428040
$693$	0	0
$694$	−40.3434	−1.53141
$695$	−22.8224	−0.865704
$696$	1.83822	0.0696775
$697$	−4.70364	−0.178163
$698$	−65.0986	−2.46402
$699$	19.6861	0.744597
$700$	0	0
$701$	−29.0289	−1.09641	−0.548203	−	0.836345i	$-0.684688\pi$
$701$	−29.0289	−1.09641	−0.548203	+	0.836345i	$0.684688\pi$
$702$	12.9842	0.490056
$703$	−34.9657	−1.31875
$704$	5.82558	0.219560
$705$	−3.84028	−0.144633
$706$	−34.5584	−1.30062
$707$	0	0
$708$	0.245266	0.00921766
$709$	28.2458	1.06079	0.530397	−	0.847749i	$-0.322043\pi$
$709$	28.2458	1.06079	0.530397	+	0.847749i	$0.322043\pi$
$710$	28.9564	1.08671
$711$	−6.56804	−0.246321
$712$	−1.59065	−0.0596120
$713$	9.01856	0.337748
$714$	0	0
$715$	−6.71159	−0.250999
$716$	−13.7999	−0.515725
$717$	15.2615	0.569953
$718$	8.97570	0.334970
$719$	4.99450	0.186263	0.0931317	−	0.995654i	$-0.470312\pi$
$719$	4.99450	0.186263	0.0931317	+	0.995654i	$0.470312\pi$
$720$	−4.44850	−0.165786
$721$	0	0
$722$	−96.6831	−3.59817
$723$	−9.07335	−0.337442
$724$	6.15553	0.228769
$725$	−3.69187	−0.137113
$726$	1.93459	0.0717993
$727$	19.7282	0.731679	0.365840	−	0.930678i	$-0.380782\pi$
$727$	19.7282	0.731679	0.365840	+	0.930678i	$0.380782\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−3.40561	−0.126047
$731$	−7.32449	−0.270906
$732$	18.7676	0.693670
$733$	5.45146	0.201354	0.100677	−	0.994919i	$-0.467899\pi$
$733$	5.45146	0.201354	0.100677	+	0.994919i	$0.467899\pi$
$734$	2.43505	0.0898793
$735$	0	0
$736$	−31.0650	−1.14507
$737$	10.4608	0.385329
$738$	−6.12663	−0.225524
$739$	44.6076	1.64092	0.820458	−	0.571707i	$-0.193719\pi$
$739$	44.6076	1.64092	0.820458	+	0.571707i	$0.193719\pi$
$740$	−7.33663	−0.269700
$741$	−55.7410	−2.04770
$742$	0	0
$743$	−44.4200	−1.62961	−0.814805	−	0.579735i	$-0.803156\pi$
$743$	−44.4200	−1.62961	−0.814805	+	0.579735i	$0.803156\pi$
$744$	1.10005	0.0403298
$745$	8.18944	0.300038
$746$	−47.0600	−1.72299
$747$	−9.32844	−0.341310
$748$	2.58824	0.0946356
$749$	0	0
$750$	1.93459	0.0706411
$751$	−37.8459	−1.38102	−0.690509	−	0.723324i	$-0.742613\pi$
$751$	−37.8459	−1.38102	−0.690509	+	0.723324i	$0.742613\pi$
$752$	−17.0835	−0.622971
$753$	−19.4642	−0.709316
$754$	47.9358	1.74572
$755$	−12.0010	−0.436761
$756$	0	0
$757$	35.1022	1.27581	0.637905	−	0.770115i	$-0.279801\pi$
$757$	35.1022	1.27581	0.637905	+	0.770115i	$0.279801\pi$
$758$	17.9410	0.651648
$759$	−4.08202	−0.148168
$760$	4.13524	0.150001
$761$	−32.5297	−1.17920	−0.589600	−	0.807695i	$-0.700715\pi$
$761$	−32.5297	−1.17920	−0.589600	+	0.807695i	$0.700715\pi$
$762$	38.4267	1.39205
$763$	0	0
$764$	−39.4455	−1.42709
$765$	−1.48525	−0.0536995
$766$	−3.65229	−0.131963
$767$	−0.944623	−0.0341083
$768$	−19.2934	−0.696189
$769$	−15.7130	−0.566626	−0.283313	−	0.959027i	$-0.591434\pi$
$769$	−15.7130	−0.566626	−0.283313	+	0.959027i	$0.591434\pi$
$770$	0	0
$771$	3.61118	0.130053
$772$	2.87418	0.103444
$773$	7.47248	0.268766	0.134383	−	0.990929i	$-0.457095\pi$
$773$	7.47248	0.268766	0.134383	+	0.990929i	$0.457095\pi$
$774$	−9.54036	−0.342921
$775$	−2.20934	−0.0793617
$776$	−5.13979	−0.184508
$777$	0	0
$778$	1.32302	0.0474324
$779$	26.3016	0.942354
$780$	−11.6958	−0.418777
$781$	14.9677	0.535588
$782$	−11.7291	−0.419431
$783$	3.69187	0.131937
$784$	0	0
$785$	−12.2003	−0.435446
$786$	−23.2211	−0.828268
$787$	−46.5029	−1.65765	−0.828825	−	0.559507i	$-0.810990\pi$
$787$	−46.5029	−1.65765	−0.828825	+	0.559507i	$0.810990\pi$
$788$	19.7304	0.702866
$789$	11.9618	0.425851
$790$	12.7064	0.452075
$791$	0	0
$792$	−0.497910	−0.0176925
$793$	−72.2819	−2.56681
$794$	−22.7976	−0.809056
$795$	12.2233	0.433517
$796$	−9.51261	−0.337166
$797$	−16.4790	−0.583717	−0.291859	−	0.956461i	$-0.594274\pi$
$797$	−16.4790	−0.583717	−0.291859	+	0.956461i	$0.594274\pi$
$798$	0	0
$799$	−5.70379	−0.201786
$800$	7.61020	0.269061
$801$	−3.19464	−0.112877
$802$	−26.7182	−0.943452
$803$	−1.76038	−0.0621225
$804$	18.2293	0.642897
$805$	0	0
$806$	28.6864	1.01043
$807$	2.32310	0.0817771
$808$	−4.26734	−0.150125
$809$	5.98715	0.210497	0.105249	−	0.994446i	$-0.466436\pi$
$809$	5.98715	0.210497	0.105249	+	0.994446i	$0.466436\pi$
$810$	−1.93459	−0.0679745
$811$	−13.7351	−0.482304	−0.241152	−	0.970487i	$-0.577525\pi$
$811$	−13.7351	−0.482304	−0.241152	+	0.970487i	$0.577525\pi$
$812$	0	0
$813$	15.0562	0.528042
$814$	−8.14480	−0.285475
$815$	16.0673	0.562813
$816$	−6.60716	−0.231297
$817$	40.9568	1.43290
$818$	13.8650	0.484778
$819$	0	0
$820$	5.51871	0.192722
$821$	45.1445	1.57555	0.787777	−	0.615960i	$-0.211232\pi$
$821$	45.1445	1.57555	0.787777	+	0.615960i	$0.211232\pi$
$822$	−30.0158	−1.04692
$823$	46.1553	1.60887	0.804436	−	0.594039i	$-0.202468\pi$
$823$	46.1553	1.60887	0.804436	+	0.594039i	$0.202468\pi$
$824$	−2.61109	−0.0909617
$825$	1.00000	0.0348155
$826$	0	0
$827$	−35.3533	−1.22936	−0.614678	−	0.788778i	$-0.710714\pi$
$827$	−35.3533	−1.22936	−0.614678	+	0.788778i	$0.710714\pi$
$828$	−7.11344	−0.247209
$829$	−14.9266	−0.518421	−0.259210	−	0.965821i	$-0.583462\pi$
$829$	−14.9266	−0.518421	−0.259210	+	0.965821i	$0.583462\pi$
$830$	18.0467	0.626409
$831$	−4.09060	−0.141901
$832$	−39.0990	−1.35551
$833$	0	0
$834$	−44.1520	−1.52886
$835$	9.14403	0.316442
$836$	−14.4728	−0.500554
$837$	2.20934	0.0763658
$838$	59.2775	2.04771
$839$	−47.9378	−1.65500	−0.827499	−	0.561468i	$-0.810237\pi$
$839$	−47.9378	−1.65500	−0.827499	+	0.561468i	$0.810237\pi$
$840$	0	0
$841$	−15.3701	−0.530004
$842$	−9.30725	−0.320749
$843$	−6.87097	−0.236649
$844$	−26.7702	−0.921469
$845$	32.0455	1.10240
$846$	−7.42935	−0.255426
$847$	0	0
$848$	54.3755	1.86726
$849$	−22.6097	−0.775965
$850$	2.87335	0.0985552
$851$	17.1857	0.589119
$852$	26.0832	0.893596
$853$	−39.3719	−1.34807	−0.674035	−	0.738700i	$-0.735440\pi$
$853$	−39.3719	−1.34807	−0.674035	+	0.738700i	$0.735440\pi$
$854$	0	0
$855$	8.30518	0.284031
$856$	8.73950	0.298710
$857$	−40.2125	−1.37363	−0.686816	−	0.726831i	$-0.740992\pi$
$857$	−40.2125	−1.37363	−0.686816	+	0.726831i	$0.740992\pi$
$858$	−12.9842	−0.443272
$859$	−49.6373	−1.69360	−0.846802	−	0.531909i	$-0.821475\pi$
$859$	−49.6373	−1.69360	−0.846802	+	0.531909i	$0.821475\pi$
$860$	8.59371	0.293043
$861$	0	0
$862$	22.6078	0.770026
$863$	−20.0952	−0.684047	−0.342024	−	0.939691i	$-0.611112\pi$
$863$	−20.0952	−0.684047	−0.342024	+	0.939691i	$0.611112\pi$
$864$	−7.61020	−0.258904
$865$	6.46150	0.219698
$866$	−31.4130	−1.06746
$867$	14.7940	0.502431
$868$	0	0
$869$	6.56804	0.222805
$870$	−7.14224	−0.242145
$871$	−70.2086	−2.37893
$872$	1.15160	0.0389982
$873$	−10.3227	−0.349371
$874$	65.5863	2.21849
$875$	0	0
$876$	−3.06769	−0.103648
$877$	9.37381	0.316531	0.158266	−	0.987397i	$-0.449410\pi$
$877$	9.37381	0.316531	0.158266	+	0.987397i	$0.449410\pi$
$878$	−20.8630	−0.704093
$879$	−26.2364	−0.884932
$880$	4.44850	0.149959
$881$	29.5052	0.994057	0.497028	−	0.867734i	$-0.334424\pi$
$881$	29.5052	0.994057	0.497028	+	0.867734i	$0.334424\pi$
$882$	0	0
$883$	−35.2052	−1.18475	−0.592374	−	0.805663i	$-0.701809\pi$
$883$	−35.2052	−1.18475	−0.592374	+	0.805663i	$0.701809\pi$
$884$	−17.3712	−0.584258
$885$	0.140745	0.00473109
$886$	−48.5982	−1.63269
$887$	37.8403	1.27055	0.635276	−	0.772285i	$-0.280886\pi$
$887$	37.8403	1.27055	0.635276	+	0.772285i	$0.280886\pi$
$888$	2.09625	0.0703456
$889$	0	0
$890$	6.18031	0.207165
$891$	−1.00000	−0.0335013
$892$	−30.3774	−1.01711
$893$	31.8942	1.06730
$894$	15.8432	0.529876
$895$	−7.91900	−0.264703
$896$	0	0
$897$	27.3969	0.914755
$898$	48.4677	1.61739
$899$	8.15658	0.272037
$900$	1.74263	0.0580876
$901$	18.1548	0.604823
$902$	6.12663	0.203994
$903$	0	0
$904$	−0.540209	−0.0179671
$905$	3.53233	0.117419
$906$	−23.2170	−0.771333
$907$	−3.76213	−0.124920	−0.0624598	−	0.998047i	$-0.519895\pi$
$907$	−3.76213	−0.124920	−0.0624598	+	0.998047i	$0.519895\pi$
$908$	−29.6791	−0.984936
$909$	−8.57051	−0.284266
$910$	0	0
$911$	22.8513	0.757097	0.378548	−	0.925582i	$-0.376423\pi$
$911$	22.8513	0.757097	0.378548	+	0.925582i	$0.376423\pi$
$912$	36.9457	1.22339
$913$	9.32844	0.308726
$914$	37.7756	1.24951
$915$	10.7697	0.356036
$916$	0.189492	0.00626100
$917$	0	0
$918$	−2.87335	−0.0948348
$919$	9.26268	0.305548	0.152774	−	0.988261i	$-0.451179\pi$
$919$	9.26268	0.305548	0.152774	+	0.988261i	$0.451179\pi$
$920$	−2.03248	−0.0670089
$921$	−14.4580	−0.476406
$922$	46.5979	1.53462
$923$	−100.457	−3.30660
$924$	0	0
$925$	−4.21010	−0.138427
$926$	−71.2023	−2.33985
$927$	−5.24410	−0.172239
$928$	−28.0959	−0.922292
$929$	15.3534	0.503729	0.251865	−	0.967762i	$-0.418956\pi$
$929$	15.3534	0.503729	0.251865	+	0.967762i	$0.418956\pi$
$930$	−4.27415	−0.140155
$931$	0	0
$932$	−34.3055	−1.12372
$933$	−10.7404	−0.351626
$934$	79.7909	2.61084
$935$	1.48525	0.0485730
$936$	3.34177	0.109229
$937$	−21.0242	−0.686831	−0.343416	−	0.939184i	$-0.611584\pi$
$937$	−21.0242	−0.686831	−0.343416	+	0.939184i	$0.611584\pi$
$938$	0	0
$939$	9.15391	0.298727
$940$	6.69217	0.218275
$941$	18.4574	0.601692	0.300846	−	0.953673i	$-0.402731\pi$
$941$	18.4574	0.601692	0.300846	+	0.953673i	$0.402731\pi$
$942$	−23.6025	−0.769009
$943$	−12.9273	−0.420972
$944$	0.626104	0.0203780
$945$	0	0
$946$	9.54036	0.310184
$947$	47.8334	1.55438	0.777188	−	0.629269i	$-0.216645\pi$
$947$	47.8334	1.55438	0.777188	+	0.629269i	$0.216645\pi$
$948$	11.4456	0.371737
$949$	11.8150	0.383530
$950$	−16.0671	−0.521286
$951$	−9.80425	−0.317925
$952$	0	0
$953$	−15.1716	−0.491456	−0.245728	−	0.969339i	$-0.579027\pi$
$953$	−15.1716	−0.491456	−0.245728	+	0.969339i	$0.579027\pi$
$954$	23.6471	0.765603
$955$	−22.6357	−0.732473
$956$	−26.5952	−0.860149
$957$	−3.69187	−0.119341
$958$	64.9650	2.09892
$959$	0	0
$960$	5.82558	0.188020
$961$	−26.1188	−0.842543
$962$	54.6646	1.76246
$963$	17.5524	0.565617
$964$	15.8115	0.509253
$965$	1.64934	0.0530941
$966$	0	0
$967$	33.0832	1.06388	0.531942	−	0.846781i	$-0.321463\pi$
$967$	33.0832	1.06388	0.531942	+	0.846781i	$0.321463\pi$
$968$	0.497910	0.0160034
$969$	12.3353	0.396267
$970$	19.9702	0.641205
$971$	−21.2934	−0.683337	−0.341669	−	0.939820i	$-0.610992\pi$
$971$	−21.2934	−0.683337	−0.341669	+	0.939820i	$0.610992\pi$
$972$	−1.74263	−0.0558948
$973$	0	0
$974$	60.4571	1.93717
$975$	−6.71159	−0.214943
$976$	47.9091	1.53353
$977$	48.5434	1.55304	0.776521	−	0.630092i	$-0.216983\pi$
$977$	48.5434	1.55304	0.776521	+	0.630092i	$0.216983\pi$
$978$	31.0836	0.993944
$979$	3.19464	0.102101
$980$	0	0
$981$	2.31288	0.0738444
$982$	20.9965	0.670026
$983$	12.0002	0.382748	0.191374	−	0.981517i	$-0.438706\pi$
$983$	12.0002	0.382748	0.191374	+	0.981517i	$0.438706\pi$
$984$	−1.57683	−0.0502675
$985$	11.3222	0.360755
$986$	−10.6080	−0.337829
$987$	0	0
$988$	97.1358	3.09030
$989$	−20.1304	−0.640108
$990$	1.93459	0.0614852
$991$	3.82770	0.121591	0.0607955	−	0.998150i	$-0.480636\pi$
$991$	3.82770	0.121591	0.0607955	+	0.998150i	$0.480636\pi$
$992$	−16.8135	−0.533829
$993$	−4.50759	−0.143044
$994$	0	0
$995$	−5.45878	−0.173055
$996$	16.2560	0.515091
$997$	−22.6591	−0.717621	−0.358811	−	0.933410i	$-0.616818\pi$
$997$	−22.6591	−0.717621	−0.358811	+	0.933410i	$0.616818\pi$
$998$	44.1103	1.39629
$999$	4.21010	0.133202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.ce.1.2		8
7.3	odd	6		1155.2.q.j.331.7	✓	16
7.5	odd	6		1155.2.q.j.991.7	yes	16
7.6	odd	2		8085.2.a.cf.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.j.331.7	✓	16	7.3	odd	6
1155.2.q.j.991.7	yes	16	7.5	odd	6
8085.2.a.ce.1.2		8	1.1	even	1	trivial
8085.2.a.cf.1.2		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)

\(f(q)\)	\(=\)	\(q-1.93459 q^{2} -1.00000 q^{3} +1.74263 q^{4} +1.00000 q^{5} +1.93459 q^{6} +0.497910 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.93459 q^{2} -1.00000 q^{3} +1.74263 q^{4} +1.00000 q^{5} +1.93459 q^{6} +0.497910 q^{8} +1.00000 q^{9} -1.93459 q^{10} -1.00000 q^{11} -1.74263 q^{12} +6.71159 q^{13} -1.00000 q^{15} -4.44850 q^{16} -1.48525 q^{17} -1.93459 q^{18} +8.30518 q^{19} +1.74263 q^{20} +1.93459 q^{22} -4.08202 q^{23} -0.497910 q^{24} +1.00000 q^{25} -12.9842 q^{26} -1.00000 q^{27} -3.69187 q^{29} +1.93459 q^{30} -2.20934 q^{31} +7.61020 q^{32} +1.00000 q^{33} +2.87335 q^{34} +1.74263 q^{36} -4.21010 q^{37} -16.0671 q^{38} -6.71159 q^{39} +0.497910 q^{40} +3.16689 q^{41} +4.93147 q^{43} -1.74263 q^{44} +1.00000 q^{45} +7.89703 q^{46} +3.84028 q^{47} +4.44850 q^{48} -1.93459 q^{50} +1.48525 q^{51} +11.6958 q^{52} -12.2233 q^{53} +1.93459 q^{54} -1.00000 q^{55} -8.30518 q^{57} +7.14224 q^{58} -0.140745 q^{59} -1.74263 q^{60} -10.7697 q^{61} +4.27415 q^{62} -5.82558 q^{64} +6.71159 q^{65} -1.93459 q^{66} -10.4608 q^{67} -2.58824 q^{68} +4.08202 q^{69} -14.9677 q^{71} +0.497910 q^{72} +1.76038 q^{73} +8.14480 q^{74} -1.00000 q^{75} +14.4728 q^{76} +12.9842 q^{78} -6.56804 q^{79} -4.44850 q^{80} +1.00000 q^{81} -6.12663 q^{82} -9.32844 q^{83} -1.48525 q^{85} -9.54036 q^{86} +3.69187 q^{87} -0.497910 q^{88} -3.19464 q^{89} -1.93459 q^{90} -7.11344 q^{92} +2.20934 q^{93} -7.42935 q^{94} +8.30518 q^{95} -7.61020 q^{96} -10.3227 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 10 q^{4} + 8 q^{5} + 8 q^{9}+O(q^{10}) \) 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

Introduction

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