LMFDB - Embedded newform 8085.2.a.ce.1.3

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			1.3
Root			$1.53073$ 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)

$f(q)$	$=$	$q-1.53073 q^{2} -1.00000 q^{3} +0.343144 q^{4} +1.00000 q^{5} +1.53073 q^{6} +2.53620 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.53073 q^{2} -1.00000 q^{3} +0.343144 q^{4} +1.00000 q^{5} +1.53073 q^{6} +2.53620 q^{8} +1.00000 q^{9} -1.53073 q^{10} -1.00000 q^{11} -0.343144 q^{12} -5.35786 q^{13} -1.00000 q^{15} -4.56854 q^{16} +1.31371 q^{17} -1.53073 q^{18} -5.88952 q^{19} +0.343144 q^{20} +1.53073 q^{22} -0.921735 q^{23} -2.53620 q^{24} +1.00000 q^{25} +8.20146 q^{26} -1.00000 q^{27} +8.16722 q^{29} +1.53073 q^{30} -3.50574 q^{31} +1.92081 q^{32} +1.00000 q^{33} -2.01094 q^{34} +0.343144 q^{36} +5.21301 q^{37} +9.01529 q^{38} +5.35786 q^{39} +2.53620 q^{40} +11.5873 q^{41} +1.17384 q^{43} -0.343144 q^{44} +1.00000 q^{45} +1.41093 q^{46} -1.95730 q^{47} +4.56854 q^{48} -1.53073 q^{50} -1.31371 q^{51} -1.83852 q^{52} +10.1387 q^{53} +1.53073 q^{54} -1.00000 q^{55} +5.88952 q^{57} -12.5018 q^{58} -10.6418 q^{59} -0.343144 q^{60} +0.173076 q^{61} +5.36636 q^{62} +6.19684 q^{64} -5.35786 q^{65} -1.53073 q^{66} -5.10460 q^{67} +0.450792 q^{68} +0.921735 q^{69} -9.02545 q^{71} +2.53620 q^{72} +0.385085 q^{73} -7.97972 q^{74} -1.00000 q^{75} -2.02096 q^{76} -8.20146 q^{78} +10.1107 q^{79} -4.56854 q^{80} +1.00000 q^{81} -17.7371 q^{82} +15.4518 q^{83} +1.31371 q^{85} -1.79684 q^{86} -8.16722 q^{87} -2.53620 q^{88} +1.73379 q^{89} -1.53073 q^{90} -0.316288 q^{92} +3.50574 q^{93} +2.99611 q^{94} -5.88952 q^{95} -1.92081 q^{96} +0.868531 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.53073	−1.08239	−0.541196	−	0.840897i	$-0.682028\pi$
$2$	−1.53073	−1.08239	−0.541196	+	0.840897i	$0.682028\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.343144	0.171572
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.53073	0.624919
$7$	0	0
$7$	0	0
$8$	2.53620	0.896684
$9$	1.00000	0.333333
$10$	−1.53073	−0.484060
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.343144	−0.0990572
$13$	−5.35786	−1.48600	−0.743002	−	0.669289i	$-0.766599\pi$
$13$	−5.35786	−1.48600	−0.743002	+	0.669289i	$0.766599\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	−4.56854	−1.14214
$17$	1.31371	0.318622	0.159311	−	0.987228i	$-0.449073\pi$
$17$	1.31371	0.318622	0.159311	+	0.987228i	$0.449073\pi$
$18$	−1.53073	−0.360797
$19$	−5.88952	−1.35115	−0.675575	−	0.737291i	$-0.736104\pi$
$19$	−5.88952	−1.35115	−0.675575	+	0.737291i	$0.736104\pi$
$20$	0.343144	0.0767293
$21$	0	0
$22$	1.53073	0.326353
$23$	−0.921735	−0.192195	−0.0960976	−	0.995372i	$-0.530636\pi$
$23$	−0.921735	−0.192195	−0.0960976	+	0.995372i	$0.530636\pi$
$24$	−2.53620	−0.517701
$25$	1.00000	0.200000
$26$	8.20146	1.60844
$27$	−1.00000	−0.192450
$28$	0	0
$29$	8.16722	1.51661	0.758307	−	0.651897i	$-0.226027\pi$
$29$	8.16722	1.51661	0.758307	+	0.651897i	$0.226027\pi$
$30$	1.53073	0.279472
$31$	−3.50574	−0.629650	−0.314825	−	0.949150i	$-0.601946\pi$
$31$	−3.50574	−0.629650	−0.314825	+	0.949150i	$0.601946\pi$
$32$	1.92081	0.339554
$33$	1.00000	0.174078
$34$	−2.01094	−0.344874
$35$	0	0
$36$	0.343144	0.0571907
$37$	5.21301	0.857013	0.428506	−	0.903539i	$-0.359040\pi$
$37$	5.21301	0.857013	0.428506	+	0.903539i	$0.359040\pi$
$38$	9.01529	1.46247
$39$	5.35786	0.857945
$40$	2.53620	0.401009
$41$	11.5873	1.80964	0.904818	−	0.425800i	$-0.140007\pi$
$41$	11.5873	1.80964	0.904818	+	0.425800i	$0.140007\pi$
$42$	0	0
$43$	1.17384	0.179010	0.0895048	−	0.995986i	$-0.471472\pi$
$43$	1.17384	0.179010	0.0895048	+	0.995986i	$0.471472\pi$
$44$	−0.343144	−0.0517309
$45$	1.00000	0.149071
$46$	1.41093	0.208030
$47$	−1.95730	−0.285502	−0.142751	−	0.989759i	$-0.545595\pi$
$47$	−1.95730	−0.285502	−0.142751	+	0.989759i	$0.545595\pi$
$48$	4.56854	0.659412
$49$	0	0
$50$	−1.53073	−0.216478
$51$	−1.31371	−0.183956
$52$	−1.83852	−0.254957
$53$	10.1387	1.39265	0.696326	−	0.717726i	$-0.254817\pi$
$53$	10.1387	1.39265	0.696326	+	0.717726i	$0.254817\pi$
$54$	1.53073	0.208306
$55$	−1.00000	−0.134840
$56$	0	0
$57$	5.88952	0.780087
$58$	−12.5018	−1.64157
$59$	−10.6418	−1.38545	−0.692724	−	0.721203i	$-0.743589\pi$
$59$	−10.6418	−1.38545	−0.692724	+	0.721203i	$0.743589\pi$
$60$	−0.343144	−0.0442997
$61$	0.173076	0.0221602	0.0110801	−	0.999939i	$-0.496473\pi$
$61$	0.173076	0.0221602	0.0110801	+	0.999939i	$0.496473\pi$
$62$	5.36636	0.681528
$63$	0	0
$64$	6.19684	0.774605
$65$	−5.35786	−0.664561
$66$	−1.53073	−0.188420
$67$	−5.10460	−0.623626	−0.311813	−	0.950143i	$-0.600936\pi$
$67$	−5.10460	−0.623626	−0.311813	+	0.950143i	$0.600936\pi$
$68$	0.450792	0.0546666
$69$	0.921735	0.110964
$70$	0	0
$71$	−9.02545	−1.07112	−0.535562	−	0.844496i	$-0.679900\pi$
$71$	−9.02545	−1.07112	−0.535562	+	0.844496i	$0.679900\pi$
$72$	2.53620	0.298895
$73$	0.385085	0.0450707	0.0225354	−	0.999746i	$-0.492826\pi$
$73$	0.385085	0.0450707	0.0225354	+	0.999746i	$0.492826\pi$
$74$	−7.97972	−0.927624
$75$	−1.00000	−0.115470
$76$	−2.02096	−0.231819
$77$	0	0
$78$	−8.20146	−0.928632
$79$	10.1107	1.13755	0.568773	−	0.822495i	$-0.307418\pi$
$79$	10.1107	1.13755	0.568773	+	0.822495i	$0.307418\pi$
$80$	−4.56854	−0.510778
$81$	1.00000	0.111111
$82$	−17.7371	−1.95873
$83$	15.4518	1.69605	0.848027	−	0.529953i	$-0.177790\pi$
$83$	15.4518	1.69605	0.848027	+	0.529953i	$0.177790\pi$
$84$	0	0
$85$	1.31371	0.142492
$86$	−1.79684	−0.193758
$87$	−8.16722	−0.875618
$88$	−2.53620	−0.270360
$89$	1.73379	0.183781	0.0918907	−	0.995769i	$-0.470709\pi$
$89$	1.73379	0.183781	0.0918907	+	0.995769i	$0.470709\pi$
$90$	−1.53073	−0.161353
$91$	0	0
$92$	−0.316288	−0.0329753
$93$	3.50574	0.363529
$94$	2.99611	0.309025
$95$	−5.88952	−0.604252
$96$	−1.92081	−0.196042
$97$	0.868531	0.0881859	0.0440930	−	0.999027i	$-0.485960\pi$
$97$	0.868531	0.0881859	0.0440930	+	0.999027i	$0.485960\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	0.343144	0.0343144
$101$	−5.70320	−0.567490	−0.283745	−	0.958900i	$-0.591577\pi$
$101$	−5.70320	−0.567490	−0.283745	+	0.958900i	$0.591577\pi$
$102$	2.01094	0.199113
$103$	−10.5822	−1.04270	−0.521349	−	0.853344i	$-0.674571\pi$
$103$	−10.5822	−1.04270	−0.521349	+	0.853344i	$0.674571\pi$
$104$	−13.5886	−1.33248
$105$	0	0
$106$	−15.5196	−1.50740
$107$	−10.3290	−0.998542	−0.499271	−	0.866446i	$-0.666399\pi$
$107$	−10.3290	−0.998542	−0.499271	+	0.866446i	$0.666399\pi$
$108$	−0.343144	−0.0330191
$109$	−19.6074	−1.87805	−0.939024	−	0.343850i	$-0.888269\pi$
$109$	−19.6074	−1.87805	−0.939024	+	0.343850i	$0.888269\pi$
$110$	1.53073	0.145950
$111$	−5.21301	−0.494797
$112$	0	0
$113$	13.0585	1.22844	0.614222	−	0.789133i	$-0.289470\pi$
$113$	13.0585	1.22844	0.614222	+	0.789133i	$0.289470\pi$
$114$	−9.01529	−0.844359
$115$	−0.921735	−0.0859523
$116$	2.80253	0.260209
$117$	−5.35786	−0.495335
$118$	16.2898	1.49960
$119$	0	0
$120$	−2.53620	−0.231523
$121$	1.00000	0.0909091
$122$	−0.264934	−0.0239860
$123$	−11.5873	−1.04479
$124$	−1.20297	−0.108030
$125$	1.00000	0.0894427
$126$	0	0
$127$	−3.36431	−0.298534	−0.149267	−	0.988797i	$-0.547691\pi$
$127$	−3.36431	−0.298534	−0.149267	+	0.988797i	$0.547691\pi$
$128$	−13.3273	−1.17798
$129$	−1.17384	−0.103351
$130$	8.20146	0.719316
$131$	−3.98443	−0.348122	−0.174061	−	0.984735i	$-0.555689\pi$
$131$	−3.98443	−0.348122	−0.174061	+	0.984735i	$0.555689\pi$
$132$	0.343144	0.0298669
$133$	0	0
$134$	7.81378	0.675008
$135$	−1.00000	−0.0860663
$136$	3.33184	0.285703
$137$	9.13812	0.780722	0.390361	−	0.920662i	$-0.372350\pi$
$137$	9.13812	0.780722	0.390361	+	0.920662i	$0.372350\pi$
$138$	−1.41093	−0.120106
$139$	−9.52612	−0.807995	−0.403997	−	0.914760i	$-0.632380\pi$
$139$	−9.52612	−0.807995	−0.403997	+	0.914760i	$0.632380\pi$
$140$	0	0
$141$	1.95730	0.164835
$142$	13.8156	1.15938
$143$	5.35786	0.448047
$144$	−4.56854	−0.380712
$145$	8.16722	0.678251
$146$	−0.589462	−0.0487842
$147$	0	0
$148$	1.78881	0.147039
$149$	3.78157	0.309798	0.154899	−	0.987930i	$-0.450495\pi$
$149$	3.78157	0.309798	0.154899	+	0.987930i	$0.450495\pi$
$150$	1.53073	0.124984
$151$	11.0817	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$151$	11.0817	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$152$	−14.9370	−1.21155
$153$	1.31371	0.106207
$154$	0	0
$155$	−3.50574	−0.281588
$156$	1.83852	0.147199
$157$	7.95188	0.634629	0.317315	−	0.948320i	$-0.397219\pi$
$157$	7.95188	0.634629	0.317315	+	0.948320i	$0.397219\pi$
$158$	−15.4768	−1.23127
$159$	−10.1387	−0.804048
$160$	1.92081	0.151853
$161$	0	0
$162$	−1.53073	−0.120266
$163$	9.96818	0.780768	0.390384	−	0.920652i	$-0.372342\pi$
$163$	9.96818	0.780768	0.390384	+	0.920652i	$0.372342\pi$
$164$	3.97612	0.310483
$165$	1.00000	0.0778499
$166$	−23.6526	−1.83580
$167$	0.298855	0.0231261	0.0115630	−	0.999933i	$-0.496319\pi$
$167$	0.298855	0.0231261	0.0115630	+	0.999933i	$0.496319\pi$
$168$	0	0
$169$	15.7067	1.20821
$170$	−2.01094	−0.154232
$171$	−5.88952	−0.450383
$172$	0.402798	0.0307130
$173$	3.34809	0.254550	0.127275	−	0.991867i	$-0.459377\pi$
$173$	3.34809	0.254550	0.127275	+	0.991867i	$0.459377\pi$
$174$	12.5018	0.947762
$175$	0	0
$176$	4.56854	0.344367
$177$	10.6418	0.799888
$178$	−2.65397	−0.198923
$179$	−25.0335	−1.87110	−0.935548	−	0.353201i	$-0.885093\pi$
$179$	−25.0335	−1.87110	−0.935548	+	0.353201i	$0.885093\pi$
$180$	0.343144	0.0255764
$181$	11.5851	0.861113	0.430557	−	0.902564i	$-0.358317\pi$
$181$	11.5851	0.861113	0.430557	+	0.902564i	$0.358317\pi$
$182$	0	0
$183$	−0.173076	−0.0127942
$184$	−2.33771	−0.172338
$185$	5.21301	0.383268
$186$	−5.36636	−0.393480
$187$	−1.31371	−0.0960681
$188$	−0.671637	−0.0489842
$189$	0	0
$190$	9.01529	0.654038
$191$	11.5115	0.832945	0.416472	−	0.909148i	$-0.363266\pi$
$191$	11.5115	0.832945	0.416472	+	0.909148i	$0.363266\pi$
$192$	−6.19684	−0.447218
$193$	−17.4824	−1.25841	−0.629204	−	0.777240i	$-0.716619\pi$
$193$	−17.4824	−1.25841	−0.629204	+	0.777240i	$0.716619\pi$
$194$	−1.32949	−0.0954517
$195$	5.35786	0.383685
$196$	0	0
$197$	−20.1656	−1.43674	−0.718369	−	0.695663i	$-0.755111\pi$
$197$	−20.1656	−1.43674	−0.718369	+	0.695663i	$0.755111\pi$
$198$	1.53073	0.108784
$199$	8.49942	0.602508	0.301254	−	0.953544i	$-0.402595\pi$
$199$	8.49942	0.602508	0.301254	+	0.953544i	$0.402595\pi$
$200$	2.53620	0.179337
$201$	5.10460	0.360051
$202$	8.73008	0.614246
$203$	0	0
$204$	−0.450792	−0.0315618
$205$	11.5873	0.809293
$206$	16.1986	1.12861
$207$	−0.921735	−0.0640650
$208$	24.4776	1.69722
$209$	5.88952	0.407387
$210$	0	0
$211$	21.9594	1.51175	0.755875	−	0.654716i	$-0.227212\pi$
$211$	21.9594	1.51175	0.755875	+	0.654716i	$0.227212\pi$
$212$	3.47902	0.238940
$213$	9.02545	0.618414
$214$	15.8109	1.08081
$215$	1.17384	0.0800555
$216$	−2.53620	−0.172567
$217$	0	0
$218$	30.0137	2.03278
$219$	−0.385085	−0.0260216
$220$	−0.343144	−0.0231348
$221$	−7.03869	−0.473473
$222$	7.97972	0.535564
$223$	15.3523	1.02807	0.514034	−	0.857770i	$-0.328151\pi$
$223$	15.3523	1.02807	0.514034	+	0.857770i	$0.328151\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−19.9891	−1.32966
$227$	−4.03956	−0.268115	−0.134058	−	0.990974i	$-0.542801\pi$
$227$	−4.03956	−0.268115	−0.134058	+	0.990974i	$0.542801\pi$
$228$	2.02096	0.133841
$229$	17.0788	1.12860	0.564299	−	0.825570i	$-0.309146\pi$
$229$	17.0788	1.12860	0.564299	+	0.825570i	$0.309146\pi$
$230$	1.41093	0.0930340
$231$	0	0
$232$	20.7137	1.35992
$233$	−6.31779	−0.413892	−0.206946	−	0.978352i	$-0.566352\pi$
$233$	−6.31779	−0.413892	−0.206946	+	0.978352i	$0.566352\pi$
$234$	8.20146	0.536146
$235$	−1.95730	−0.127680
$236$	−3.65168	−0.237704
$237$	−10.1107	−0.656762
$238$	0	0
$239$	5.44016	0.351895	0.175947	−	0.984400i	$-0.443701\pi$
$239$	5.44016	0.351895	0.175947	+	0.984400i	$0.443701\pi$
$240$	4.56854	0.294898
$241$	−16.0277	−1.03243	−0.516216	−	0.856458i	$-0.672660\pi$
$241$	−16.0277	−1.03243	−0.516216	+	0.856458i	$0.672660\pi$
$242$	−1.53073	−0.0983993
$243$	−1.00000	−0.0641500
$244$	0.0593901	0.00380206
$245$	0	0
$246$	17.7371	1.13088
$247$	31.5553	2.00781
$248$	−8.89128	−0.564597
$249$	−15.4518	−0.979217
$250$	−1.53073	−0.0968121
$251$	−13.2798	−0.838213	−0.419106	−	0.907937i	$-0.637657\pi$
$251$	−13.2798	−0.838213	−0.419106	+	0.907937i	$0.637657\pi$
$252$	0	0
$253$	0.921735	0.0579490
$254$	5.14986	0.323131
$255$	−1.31371	−0.0822678
$256$	8.00689	0.500431
$257$	23.9052	1.49117	0.745583	−	0.666413i	$-0.232171\pi$
$257$	23.9052	1.49117	0.745583	+	0.666413i	$0.232171\pi$
$258$	1.79684	0.111867
$259$	0	0
$260$	−1.83852	−0.114020
$261$	8.16722	0.505538
$262$	6.09911	0.376804
$263$	−26.6561	−1.64369	−0.821844	−	0.569713i	$-0.807054\pi$
$263$	−26.6561	−1.64369	−0.821844	+	0.569713i	$0.807054\pi$
$264$	2.53620	0.156093
$265$	10.1387	0.622813
$266$	0	0
$267$	−1.73379	−0.106106
$268$	−1.75161	−0.106997
$269$	−20.1901	−1.23101	−0.615506	−	0.788132i	$-0.711048\pi$
$269$	−20.1901	−1.23101	−0.615506	+	0.788132i	$0.711048\pi$
$270$	1.53073	0.0931575
$271$	−13.7596	−0.835835	−0.417918	−	0.908485i	$-0.637240\pi$
$271$	−13.7596	−0.835835	−0.417918	+	0.908485i	$0.637240\pi$
$272$	−6.00175	−0.363909
$273$	0	0
$274$	−13.9880	−0.845047
$275$	−1.00000	−0.0603023
$276$	0.316288	0.0190383
$277$	5.52250	0.331815	0.165907	−	0.986141i	$-0.446945\pi$
$277$	5.52250	0.331815	0.165907	+	0.986141i	$0.446945\pi$
$278$	14.5819	0.874567
$279$	−3.50574	−0.209883
$280$	0	0
$281$	2.57185	0.153424	0.0767119	−	0.997053i	$-0.475558\pi$
$281$	2.57185	0.153424	0.0767119	+	0.997053i	$0.475558\pi$
$282$	−2.99611	−0.178416
$283$	−3.10173	−0.184378	−0.0921892	−	0.995742i	$-0.529386\pi$
$283$	−3.10173	−0.184378	−0.0921892	+	0.995742i	$0.529386\pi$
$284$	−3.09703	−0.183775
$285$	5.88952	0.348865
$286$	−8.20146	−0.484962
$287$	0	0
$288$	1.92081	0.113185
$289$	−15.2742	−0.898480
$290$	−12.5018	−0.734133
$291$	−0.868531	−0.0509142
$292$	0.132139	0.00773288
$293$	−28.8157	−1.68343	−0.841717	−	0.539920i	$-0.818455\pi$
$293$	−28.8157	−1.68343	−0.841717	+	0.539920i	$0.818455\pi$
$294$	0	0
$295$	−10.6418	−0.619591
$296$	13.2212	0.768469
$297$	1.00000	0.0580259
$298$	−5.78857	−0.335323
$299$	4.93853	0.285603
$300$	−0.343144	−0.0198114
$301$	0	0
$302$	−16.9632	−0.976122
$303$	5.70320	0.327640
$304$	26.9065	1.54320
$305$	0.173076	0.00991033
$306$	−2.01094	−0.114958
$307$	18.2795	1.04327	0.521634	−	0.853169i	$-0.325323\pi$
$307$	18.2795	1.04327	0.521634	+	0.853169i	$0.325323\pi$
$308$	0	0
$309$	10.5822	0.602002
$310$	5.36636	0.304789
$311$	−6.12177	−0.347134	−0.173567	−	0.984822i	$-0.555529\pi$
$311$	−6.12177	−0.347134	−0.173567	+	0.984822i	$0.555529\pi$
$312$	13.5886	0.769305
$313$	−33.5823	−1.89818	−0.949092	−	0.315000i	$-0.897996\pi$
$313$	−33.5823	−1.89818	−0.949092	+	0.315000i	$0.897996\pi$
$314$	−12.1722	−0.686918
$315$	0	0
$316$	3.46944	0.195171
$317$	27.9132	1.56776	0.783881	−	0.620911i	$-0.213237\pi$
$317$	27.9132	1.56776	0.783881	+	0.620911i	$0.213237\pi$
$318$	15.5196	0.870295
$319$	−8.16722	−0.457277
$320$	6.19684	0.346414
$321$	10.3290	0.576509
$322$	0	0
$323$	−7.73714	−0.430506
$324$	0.343144	0.0190636
$325$	−5.35786	−0.297201
$326$	−15.2586	−0.845097
$327$	19.6074	1.08429
$328$	29.3878	1.62267
$329$	0	0
$330$	−1.53073	−0.0842641
$331$	−23.3768	−1.28490	−0.642452	−	0.766326i	$-0.722083\pi$
$331$	−23.3768	−1.28490	−0.642452	+	0.766326i	$0.722083\pi$
$332$	5.30219	0.290995
$333$	5.21301	0.285671
$334$	−0.457467	−0.0250315
$335$	−5.10460	−0.278894
$336$	0	0
$337$	26.5943	1.44868	0.724342	−	0.689441i	$-0.242144\pi$
$337$	26.5943	1.44868	0.724342	+	0.689441i	$0.242144\pi$
$338$	−24.0428	−1.30775
$339$	−13.0585	−0.709243
$340$	0.450792	0.0244477
$341$	3.50574	0.189847
$342$	9.01529	0.487491
$343$	0	0
$344$	2.97711	0.160515
$345$	0.921735	0.0496246
$346$	−5.12503	−0.275523
$347$	18.1504	0.974365	0.487182	−	0.873300i	$-0.338025\pi$
$347$	18.1504	0.974365	0.487182	+	0.873300i	$0.338025\pi$
$348$	−2.80253	−0.150232
$349$	−29.9470	−1.60302	−0.801512	−	0.597978i	$-0.795971\pi$
$349$	−29.9470	−1.60302	−0.801512	+	0.597978i	$0.795971\pi$
$350$	0	0
$351$	5.35786	0.285982
$352$	−1.92081	−0.102379
$353$	27.6928	1.47394	0.736970	−	0.675926i	$-0.236256\pi$
$353$	27.6928	1.47394	0.736970	+	0.675926i	$0.236256\pi$
$354$	−16.2898	−0.865793
$355$	−9.02545	−0.479021
$356$	0.594940	0.0315317
$357$	0	0
$358$	38.3197	2.02526
$359$	−15.8143	−0.834645	−0.417323	−	0.908758i	$-0.637031\pi$
$359$	−15.8143	−0.834645	−0.417323	+	0.908758i	$0.637031\pi$
$360$	2.53620	0.133670
$361$	15.6865	0.825605
$362$	−17.7337	−0.932062
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	0.385085	0.0201562
$366$	0.264934	0.0138483
$367$	−5.15118	−0.268890	−0.134445	−	0.990921i	$-0.542925\pi$
$367$	−5.15118	−0.268890	−0.134445	+	0.990921i	$0.542925\pi$
$368$	4.21099	0.219513
$369$	11.5873	0.603212
$370$	−7.97972	−0.414846
$371$	0	0
$372$	1.20297	0.0623713
$373$	24.9252	1.29058	0.645289	−	0.763938i	$-0.276737\pi$
$373$	24.9252	1.29058	0.645289	+	0.763938i	$0.276737\pi$
$374$	2.01094	0.103983
$375$	−1.00000	−0.0516398
$376$	−4.96412	−0.256005
$377$	−43.7588	−2.25370
$378$	0	0
$379$	−19.8388	−1.01905	−0.509525	−	0.860456i	$-0.670179\pi$
$379$	−19.8388	−1.01905	−0.509525	+	0.860456i	$0.670179\pi$
$380$	−2.02096	−0.103673
$381$	3.36431	0.172359
$382$	−17.6211	−0.901573
$383$	−1.15781	−0.0591614	−0.0295807	−	0.999562i	$-0.509417\pi$
$383$	−1.15781	−0.0591614	−0.0295807	+	0.999562i	$0.509417\pi$
$384$	13.3273	0.680107
$385$	0	0
$386$	26.7608	1.36209
$387$	1.17384	0.0596699
$388$	0.298031	0.0151302
$389$	−4.63367	−0.234936	−0.117468	−	0.993077i	$-0.537478\pi$
$389$	−4.63367	−0.234936	−0.117468	+	0.993077i	$0.537478\pi$
$390$	−8.20146	−0.415297
$391$	−1.21089	−0.0612376
$392$	0	0
$393$	3.98443	0.200988
$394$	30.8681	1.55511
$395$	10.1107	0.508726
$396$	−0.343144	−0.0172436
$397$	−11.9170	−0.598098	−0.299049	−	0.954238i	$-0.596669\pi$
$397$	−11.9170	−0.598098	−0.299049	+	0.954238i	$0.596669\pi$
$398$	−13.0103	−0.652150
$399$	0	0
$400$	−4.56854	−0.228427
$401$	−5.35104	−0.267218	−0.133609	−	0.991034i	$-0.542657\pi$
$401$	−5.35104	−0.267218	−0.133609	+	0.991034i	$0.542657\pi$
$402$	−7.81378	−0.389716
$403$	18.7833	0.935662
$404$	−1.95702	−0.0973654
$405$	1.00000	0.0496904
$406$	0	0
$407$	−5.21301	−0.258399
$408$	−3.33184	−0.164951
$409$	−19.0275	−0.940849	−0.470424	−	0.882440i	$-0.655899\pi$
$409$	−19.0275	−0.940849	−0.470424	+	0.882440i	$0.655899\pi$
$410$	−17.7371	−0.875973
$411$	−9.13812	−0.450750
$412$	−3.63123	−0.178898
$413$	0	0
$414$	1.41093	0.0693435
$415$	15.4518	0.758499
$416$	−10.2914	−0.504579
$417$	9.52612	0.466496
$418$	−9.01529	−0.440952
$419$	25.2455	1.23332	0.616661	−	0.787228i	$-0.288485\pi$
$419$	25.2455	1.23332	0.616661	+	0.787228i	$0.288485\pi$
$420$	0	0
$421$	−8.01438	−0.390597	−0.195298	−	0.980744i	$-0.562568\pi$
$421$	−8.01438	−0.390597	−0.195298	+	0.980744i	$0.562568\pi$
$422$	−33.6140	−1.63631
$423$	−1.95730	−0.0951674
$424$	25.7137	1.24877
$425$	1.31371	0.0637244
$426$	−13.8156	−0.669366
$427$	0	0
$428$	−3.54434	−0.171322
$429$	−5.35786	−0.258680
$430$	−1.79684	−0.0866514
$431$	22.6987	1.09336	0.546678	−	0.837343i	$-0.315892\pi$
$431$	22.6987	1.09336	0.546678	+	0.837343i	$0.315892\pi$
$432$	4.56854	0.219804
$433$	−14.0856	−0.676909	−0.338455	−	0.940983i	$-0.609904\pi$
$433$	−14.0856	−0.676909	−0.338455	+	0.940983i	$0.609904\pi$
$434$	0	0
$435$	−8.16722	−0.391588
$436$	−6.72816	−0.322221
$437$	5.42858	0.259684
$438$	0.589462	0.0281656
$439$	−34.1654	−1.63062	−0.815312	−	0.579022i	$-0.803435\pi$
$439$	−34.1654	−1.63062	−0.815312	+	0.579022i	$0.803435\pi$
$440$	−2.53620	−0.120909
$441$	0	0
$442$	10.7744	0.512484
$443$	−8.65025	−0.410986	−0.205493	−	0.978659i	$-0.565880\pi$
$443$	−8.65025	−0.410986	−0.205493	+	0.978659i	$0.565880\pi$
$444$	−1.78881	−0.0848933
$445$	1.73379	0.0821895
$446$	−23.5003	−1.11277
$447$	−3.78157	−0.178862
$448$	0	0
$449$	−36.9902	−1.74568	−0.872839	−	0.488009i	$-0.837723\pi$
$449$	−36.9902	−1.74568	−0.872839	+	0.488009i	$0.837723\pi$
$450$	−1.53073	−0.0721595
$451$	−11.5873	−0.545625
$452$	4.48096	0.210767
$453$	−11.0817	−0.520665
$454$	6.18349	0.290206
$455$	0	0
$456$	14.9370	0.699491
$457$	12.8337	0.600333	0.300167	−	0.953887i	$-0.402958\pi$
$457$	12.8337	0.600333	0.300167	+	0.953887i	$0.402958\pi$
$458$	−26.1431	−1.22159
$459$	−1.31371	−0.0613188
$460$	−0.316288	−0.0147470
$461$	16.2931	0.758844	0.379422	−	0.925224i	$-0.376123\pi$
$461$	16.2931	0.758844	0.379422	+	0.925224i	$0.376123\pi$
$462$	0	0
$463$	18.2051	0.846065	0.423033	−	0.906114i	$-0.360966\pi$
$463$	18.2051	0.846065	0.423033	+	0.906114i	$0.360966\pi$
$464$	−37.3123	−1.73218
$465$	3.50574	0.162575
$466$	9.67085	0.447994
$467$	−30.2972	−1.40199	−0.700994	−	0.713167i	$-0.747260\pi$
$467$	−30.2972	−1.40199	−0.700994	+	0.713167i	$0.747260\pi$
$468$	−1.83852	−0.0849856
$469$	0	0
$470$	2.99611	0.138200
$471$	−7.95188	−0.366403
$472$	−26.9898	−1.24231
$473$	−1.17384	−0.0539734
$474$	15.4768	0.710874
$475$	−5.88952	−0.270230
$476$	0	0
$477$	10.1387	0.464217
$478$	−8.32743	−0.380888
$479$	−20.0021	−0.913918	−0.456959	−	0.889488i	$-0.651061\pi$
$479$	−20.0021	−0.913918	−0.456959	+	0.889488i	$0.651061\pi$
$480$	−1.92081	−0.0876725
$481$	−27.9306	−1.27352
$482$	24.5341	1.11750
$483$	0	0
$484$	0.343144	0.0155975
$485$	0.868531	0.0394380
$486$	1.53073	0.0694355
$487$	37.7190	1.70921	0.854606	−	0.519276i	$-0.173798\pi$
$487$	37.7190	1.70921	0.854606	+	0.519276i	$0.173798\pi$
$488$	0.438957	0.0198707
$489$	−9.96818	−0.450777
$490$	0	0
$491$	−17.9323	−0.809275	−0.404637	−	0.914477i	$-0.632602\pi$
$491$	−17.9323	−0.809275	−0.404637	+	0.914477i	$0.632602\pi$
$492$	−3.97612	−0.179257
$493$	10.7294	0.483227
$494$	−48.3027	−2.17324
$495$	−1.00000	−0.0449467
$496$	16.0161	0.719145
$497$	0	0
$498$	23.6526	1.05990
$499$	6.05433	0.271029	0.135514	−	0.990775i	$-0.456731\pi$
$499$	6.05433	0.271029	0.135514	+	0.990775i	$0.456731\pi$
$500$	0.343144	0.0153459
$501$	−0.298855	−0.0133518
$502$	20.3278	0.907275
$503$	−12.2366	−0.545604	−0.272802	−	0.962070i	$-0.587950\pi$
$503$	−12.2366	−0.545604	−0.272802	+	0.962070i	$0.587950\pi$
$504$	0	0
$505$	−5.70320	−0.253789
$506$	−1.41093	−0.0627235
$507$	−15.7067	−0.697559
$508$	−1.15444	−0.0512201
$509$	−10.7706	−0.477399	−0.238700	−	0.971093i	$-0.576721\pi$
$509$	−10.7706	−0.477399	−0.238700	+	0.971093i	$0.576721\pi$
$510$	2.01094	0.0890460
$511$	0	0
$512$	14.3982	0.636317
$513$	5.88952	0.260029
$514$	−36.5925	−1.61403
$515$	−10.5822	−0.466308
$516$	−0.402798	−0.0177322
$517$	1.95730	0.0860822
$518$	0	0
$519$	−3.34809	−0.146965
$520$	−13.5886	−0.595901
$521$	41.7769	1.83028	0.915139	−	0.403138i	$-0.132081\pi$
$521$	41.7769	1.83028	0.915139	+	0.403138i	$0.132081\pi$
$522$	−12.5018	−0.547190
$523$	−7.42546	−0.324693	−0.162346	−	0.986734i	$-0.551906\pi$
$523$	−7.42546	−0.324693	−0.162346	+	0.986734i	$0.551906\pi$
$524$	−1.36723	−0.0597279
$525$	0	0
$526$	40.8034	1.77911
$527$	−4.60554	−0.200620
$528$	−4.56854	−0.198820
$529$	−22.1504	−0.963061
$530$	−15.5196	−0.674128
$531$	−10.6418	−0.461816
$532$	0	0
$533$	−62.0833	−2.68912
$534$	2.65397	0.114848
$535$	−10.3290	−0.446562
$536$	−12.9463	−0.559196
$537$	25.0335	1.08028
$538$	30.9057	1.33244
$539$	0	0
$540$	−0.343144	−0.0147666
$541$	−41.2506	−1.77350	−0.886751	−	0.462248i	$-0.847043\pi$
$541$	−41.2506	−1.77350	−0.886751	+	0.462248i	$0.847043\pi$
$542$	21.0622	0.904701
$543$	−11.5851	−0.497164
$544$	2.52339	0.108189
$545$	−19.6074	−0.839889
$546$	0	0
$547$	−19.7260	−0.843423	−0.421711	−	0.906730i	$-0.638570\pi$
$547$	−19.7260	−0.843423	−0.421711	+	0.906730i	$0.638570\pi$
$548$	3.13569	0.133950
$549$	0.173076	0.00738672
$550$	1.53073	0.0652707
$551$	−48.1010	−2.04917
$552$	2.33771	0.0994995
$553$	0	0
$554$	−8.45347	−0.359153
$555$	−5.21301	−0.221280
$556$	−3.26883	−0.138629
$557$	19.7757	0.837922	0.418961	−	0.908004i	$-0.362394\pi$
$557$	19.7757	0.837922	0.418961	+	0.908004i	$0.362394\pi$
$558$	5.36636	0.227176
$559$	−6.28930	−0.266009
$560$	0	0
$561$	1.31371	0.0554650
$562$	−3.93682	−0.166065
$563$	−31.6143	−1.33238	−0.666192	−	0.745780i	$-0.732077\pi$
$563$	−31.6143	−1.33238	−0.666192	+	0.745780i	$0.732077\pi$
$564$	0.671637	0.0282810
$565$	13.0585	0.549377
$566$	4.74791	0.199570
$567$	0	0
$568$	−22.8904	−0.960459
$569$	−27.8348	−1.16689	−0.583447	−	0.812151i	$-0.698297\pi$
$569$	−27.8348	−1.16689	−0.583447	+	0.812151i	$0.698297\pi$
$570$	−9.01529	−0.377609
$571$	22.5853	0.945165	0.472583	−	0.881286i	$-0.343322\pi$
$571$	22.5853	0.945165	0.472583	+	0.881286i	$0.343322\pi$
$572$	1.83852	0.0768723
$573$	−11.5115	−0.480901
$574$	0	0
$575$	−0.921735	−0.0384390
$576$	6.19684	0.258202
$577$	13.6210	0.567051	0.283526	−	0.958965i	$-0.408496\pi$
$577$	13.6210	0.567051	0.283526	+	0.958965i	$0.408496\pi$
$578$	23.3807	0.972507
$579$	17.4824	0.726542
$580$	2.80253	0.116369
$581$	0	0
$582$	1.32949	0.0551091
$583$	−10.1387	−0.419900
$584$	0.976653	0.0404142
$585$	−5.35786	−0.221520
$586$	44.1092	1.82213
$587$	−7.26307	−0.299779	−0.149889	−	0.988703i	$-0.547892\pi$
$587$	−7.26307	−0.299779	−0.149889	+	0.988703i	$0.547892\pi$
$588$	0	0
$589$	20.6472	0.850751
$590$	16.2898	0.670640
$591$	20.1656	0.829501
$592$	−23.8158	−0.978824
$593$	−17.6896	−0.726423	−0.363212	−	0.931707i	$-0.618320\pi$
$593$	−17.6896	−0.726423	−0.363212	+	0.931707i	$0.618320\pi$
$594$	−1.53073	−0.0628067
$595$	0	0
$596$	1.29762	0.0531527
$597$	−8.49942	−0.347858
$598$	−7.55958	−0.309134
$599$	−5.22413	−0.213452	−0.106726	−	0.994288i	$-0.534037\pi$
$599$	−5.22413	−0.213452	−0.106726	+	0.994288i	$0.534037\pi$
$600$	−2.53620	−0.103540
$601$	−15.1770	−0.619082	−0.309541	−	0.950886i	$-0.600175\pi$
$601$	−15.1770	−0.619082	−0.309541	+	0.950886i	$0.600175\pi$
$602$	0	0
$603$	−5.10460	−0.207875
$604$	3.80263	0.154727
$605$	1.00000	0.0406558
$606$	−8.73008	−0.354635
$607$	−3.48240	−0.141346	−0.0706732	−	0.997500i	$-0.522515\pi$
$607$	−3.48240	−0.141346	−0.0706732	+	0.997500i	$0.522515\pi$
$608$	−11.3126	−0.458788
$609$	0	0
$610$	−0.264934	−0.0107269
$611$	10.4870	0.424257
$612$	0.450792	0.0182222
$613$	−12.4960	−0.504709	−0.252355	−	0.967635i	$-0.581205\pi$
$613$	−12.4960	−0.504709	−0.252355	+	0.967635i	$0.581205\pi$
$614$	−27.9811	−1.12923
$615$	−11.5873	−0.467246
$616$	0	0
$617$	12.4851	0.502631	0.251315	−	0.967905i	$-0.419137\pi$
$617$	12.4851	0.502631	0.251315	+	0.967905i	$0.419137\pi$
$618$	−16.1986	−0.651602
$619$	−23.4859	−0.943980	−0.471990	−	0.881604i	$-0.656464\pi$
$619$	−23.4859	−0.943980	−0.471990	+	0.881604i	$0.656464\pi$
$620$	−1.20297	−0.0483126
$621$	0.921735	0.0369880
$622$	9.37079	0.375734
$623$	0	0
$624$	−24.4776	−0.979889
$625$	1.00000	0.0400000
$626$	51.4055	2.05458
$627$	−5.88952	−0.235205
$628$	2.72864	0.108885
$629$	6.84839	0.273063
$630$	0	0
$631$	7.42004	0.295387	0.147693	−	0.989033i	$-0.452815\pi$
$631$	7.42004	0.295387	0.147693	+	0.989033i	$0.452815\pi$
$632$	25.6429	1.02002
$633$	−21.9594	−0.872809
$634$	−42.7277	−1.69693
$635$	−3.36431	−0.133509
$636$	−3.47902	−0.137952
$637$	0	0
$638$	12.5018	0.494952
$639$	−9.02545	−0.357041
$640$	−13.3273	−0.526809
$641$	−42.5301	−1.67984	−0.839919	−	0.542712i	$-0.817398\pi$
$641$	−42.5301	−1.67984	−0.839919	+	0.542712i	$0.817398\pi$
$642$	−15.8109	−0.624008
$643$	22.4141	0.883927	0.441963	−	0.897033i	$-0.354282\pi$
$643$	22.4141	0.883927	0.441963	+	0.897033i	$0.354282\pi$
$644$	0	0
$645$	−1.17384	−0.0462201
$646$	11.8435	0.465976
$647$	−21.2229	−0.834358	−0.417179	−	0.908824i	$-0.636981\pi$
$647$	−21.2229	−0.834358	−0.417179	+	0.908824i	$0.636981\pi$
$648$	2.53620	0.0996315
$649$	10.6418	0.417728
$650$	8.20146	0.321688
$651$	0	0
$652$	3.42052	0.133958
$653$	−27.7236	−1.08491	−0.542454	−	0.840086i	$-0.682505\pi$
$653$	−27.7236	−1.08491	−0.542454	+	0.840086i	$0.682505\pi$
$654$	−30.0137	−1.17363
$655$	−3.98443	−0.155685
$656$	−52.9371	−2.06685
$657$	0.385085	0.0150236
$658$	0	0
$659$	7.78843	0.303394	0.151697	−	0.988427i	$-0.451526\pi$
$659$	7.78843	0.303394	0.151697	+	0.988427i	$0.451526\pi$
$660$	0.343144	0.0133569
$661$	−27.3883	−1.06528	−0.532640	−	0.846342i	$-0.678800\pi$
$661$	−27.3883	−1.06528	−0.532640	+	0.846342i	$0.678800\pi$
$662$	35.7836	1.39077
$663$	7.03869	0.273360
$664$	39.1889	1.52082
$665$	0	0
$666$	−7.97972	−0.309208
$667$	−7.52802	−0.291486
$668$	0.102550	0.00396779
$669$	−15.3523	−0.593555
$670$	7.81378	0.301873
$671$	−0.173076	−0.00668154
$672$	0	0
$673$	38.5804	1.48716	0.743582	−	0.668645i	$-0.233125\pi$
$673$	38.5804	1.48716	0.743582	+	0.668645i	$0.233125\pi$
$674$	−40.7088	−1.56804
$675$	−1.00000	−0.0384900
$676$	5.38966	0.207295
$677$	27.7973	1.06834	0.534169	−	0.845378i	$-0.320625\pi$
$677$	27.7973	1.06834	0.534169	+	0.845378i	$0.320625\pi$
$678$	19.9891	0.767678
$679$	0	0
$680$	3.33184	0.127770
$681$	4.03956	0.154796
$682$	−5.36636	−0.205488
$683$	27.5820	1.05540	0.527699	−	0.849432i	$-0.323055\pi$
$683$	27.5820	1.05540	0.527699	+	0.849432i	$0.323055\pi$
$684$	−2.02096	−0.0772732
$685$	9.13812	0.349150
$686$	0	0
$687$	−17.0788	−0.651596
$688$	−5.36275	−0.204453
$689$	−54.3216	−2.06949
$690$	−1.41093	−0.0537132
$691$	14.7790	0.562220	0.281110	−	0.959676i	$-0.409297\pi$
$691$	14.7790	0.562220	0.281110	+	0.959676i	$0.409297\pi$
$692$	1.14888	0.0436737
$693$	0	0
$694$	−27.7834	−1.05464
$695$	−9.52612	−0.361346
$696$	−20.7137	−0.785152
$697$	15.2224	0.576589
$698$	45.8408	1.73510
$699$	6.31779	0.238961
$700$	0	0
$701$	−42.9935	−1.62384	−0.811921	−	0.583767i	$-0.801578\pi$
$701$	−42.9935	−1.62384	−0.811921	+	0.583767i	$0.801578\pi$
$702$	−8.20146	−0.309544
$703$	−30.7021	−1.15795
$704$	−6.19684	−0.233552
$705$	1.95730	0.0737164
$706$	−42.3903	−1.59538
$707$	0	0
$708$	3.65168	0.137238
$709$	−7.33052	−0.275303	−0.137652	−	0.990481i	$-0.543955\pi$
$709$	−7.33052	−0.275303	−0.137652	+	0.990481i	$0.543955\pi$
$710$	13.8156	0.518489
$711$	10.1107	0.379182
$712$	4.39724	0.164794
$713$	3.23137	0.121016
$714$	0	0
$715$	5.35786	0.200373
$716$	−8.59011	−0.321028
$717$	−5.44016	−0.203166
$718$	24.2074	0.903413
$719$	−31.5369	−1.17613	−0.588064	−	0.808814i	$-0.700110\pi$
$719$	−31.5369	−1.17613	−0.588064	+	0.808814i	$0.700110\pi$
$720$	−4.56854	−0.170259
$721$	0	0
$722$	−24.0118	−0.893628
$723$	16.0277	0.596075
$724$	3.97536	0.147743
$725$	8.16722	0.303323
$726$	1.53073	0.0568108
$727$	−6.13585	−0.227566	−0.113783	−	0.993506i	$-0.536297\pi$
$727$	−6.13585	−0.227566	−0.113783	+	0.993506i	$0.536297\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.589462	−0.0218170
$731$	1.54209	0.0570364
$732$	−0.0593901	−0.00219512
$733$	−46.0271	−1.70005	−0.850024	−	0.526744i	$-0.823413\pi$
$733$	−46.0271	−1.70005	−0.850024	+	0.526744i	$0.823413\pi$
$734$	7.88509	0.291044
$735$	0	0
$736$	−1.77048	−0.0652606
$737$	5.10460	0.188030
$738$	−17.7371	−0.652911
$739$	31.4205	1.15582	0.577911	−	0.816100i	$-0.303868\pi$
$739$	31.4205	1.15582	0.577911	+	0.816100i	$0.303868\pi$
$740$	1.78881	0.0657580
$741$	−31.5553	−1.15921
$742$	0	0
$743$	22.7980	0.836379	0.418189	−	0.908360i	$-0.362665\pi$
$743$	22.7980	0.836379	0.418189	+	0.908360i	$0.362665\pi$
$744$	8.89128	0.325970
$745$	3.78157	0.138546
$746$	−38.1538	−1.39691
$747$	15.4518	0.565351
$748$	−0.450792	−0.0164826
$749$	0	0
$750$	1.53073	0.0558945
$751$	20.2217	0.737901	0.368951	−	0.929449i	$-0.379717\pi$
$751$	20.2217	0.737901	0.368951	+	0.929449i	$0.379717\pi$
$752$	8.94203	0.326082
$753$	13.2798	0.483942
$754$	66.9831	2.43938
$755$	11.0817	0.403306
$756$	0	0
$757$	53.3620	1.93948	0.969738	−	0.244147i	$-0.0785079\pi$
$757$	53.3620	1.93948	0.969738	+	0.244147i	$0.0785079\pi$
$758$	30.3679	1.10301
$759$	−0.921735	−0.0334569
$760$	−14.9370	−0.541823
$761$	42.9317	1.55627	0.778137	−	0.628095i	$-0.216165\pi$
$761$	42.9317	1.55627	0.778137	+	0.628095i	$0.216165\pi$
$762$	−5.14986	−0.186560
$763$	0	0
$764$	3.95011	0.142910
$765$	1.31371	0.0474974
$766$	1.77230	0.0640359
$767$	57.0174	2.05878
$768$	−8.00689	−0.288924
$769$	−28.8797	−1.04143	−0.520715	−	0.853731i	$-0.674335\pi$
$769$	−28.8797	−1.04143	−0.520715	+	0.853731i	$0.674335\pi$
$770$	0	0
$771$	−23.9052	−0.860925
$772$	−5.99897	−0.215908
$773$	17.5063	0.629657	0.314828	−	0.949149i	$-0.398053\pi$
$773$	17.5063	0.629657	0.314828	+	0.949149i	$0.398053\pi$
$774$	−1.79684	−0.0645862
$775$	−3.50574	−0.125930
$776$	2.20277	0.0790749
$777$	0	0
$778$	7.09291	0.254293
$779$	−68.2438	−2.44509
$780$	1.83852	0.0658295
$781$	9.02545	0.322956
$782$	1.85356	0.0662831
$783$	−8.16722	−0.291873
$784$	0	0
$785$	7.95188	0.283815
$786$	−6.09911	−0.217548
$787$	44.0950	1.57182	0.785909	−	0.618343i	$-0.212196\pi$
$787$	44.0950	1.57182	0.785909	+	0.618343i	$0.212196\pi$
$788$	−6.91969	−0.246504
$789$	26.6561	0.948983
$790$	−15.4768	−0.550641
$791$	0	0
$792$	−2.53620	−0.0901201
$793$	−0.927320	−0.0329301
$794$	18.2418	0.647376
$795$	−10.1387	−0.359581
$796$	2.91653	0.103374
$797$	−54.3564	−1.92540	−0.962701	−	0.270569i	$-0.912788\pi$
$797$	−54.3564	−1.92540	−0.962701	+	0.270569i	$0.912788\pi$
$798$	0	0
$799$	−2.57133	−0.0909673
$800$	1.92081	0.0679108
$801$	1.73379	0.0612604
$802$	8.19101	0.289235
$803$	−0.385085	−0.0135893
$804$	1.75161	0.0617746
$805$	0	0
$806$	−28.7522	−1.01275
$807$	20.1901	0.710725
$808$	−14.4645	−0.508859
$809$	−1.47876	−0.0519904	−0.0259952	−	0.999662i	$-0.508275\pi$
$809$	−1.47876	−0.0519904	−0.0259952	+	0.999662i	$0.508275\pi$
$810$	−1.53073	−0.0537845
$811$	33.6980	1.18330	0.591649	−	0.806196i	$-0.298477\pi$
$811$	33.6980	1.18330	0.591649	+	0.806196i	$0.298477\pi$
$812$	0	0
$813$	13.7596	0.482570
$814$	7.97972	0.279689
$815$	9.96818	0.349170
$816$	6.00175	0.210103
$817$	−6.91338	−0.241869
$818$	29.1260	1.01837
$819$	0	0
$820$	3.97612	0.138852
$821$	2.23068	0.0778512	0.0389256	−	0.999242i	$-0.487606\pi$
$821$	2.23068	0.0778512	0.0389256	+	0.999242i	$0.487606\pi$
$822$	13.9880	0.487888
$823$	10.0213	0.349322	0.174661	−	0.984629i	$-0.444117\pi$
$823$	10.0213	0.349322	0.174661	+	0.984629i	$0.444117\pi$
$824$	−26.8387	−0.934970
$825$	1.00000	0.0348155
$826$	0	0
$827$	−23.3243	−0.811064	−0.405532	−	0.914081i	$-0.632914\pi$
$827$	−23.3243	−0.811064	−0.405532	+	0.914081i	$0.632914\pi$
$828$	−0.316288	−0.0109918
$829$	20.7483	0.720617	0.360309	−	0.932833i	$-0.382671\pi$
$829$	20.7483	0.720617	0.360309	+	0.932833i	$0.382671\pi$
$830$	−23.6526	−0.820993
$831$	−5.52250	−0.191573
$832$	−33.2018	−1.15107
$833$	0	0
$834$	−14.5819	−0.504931
$835$	0.298855	0.0103423
$836$	2.02096	0.0698962
$837$	3.50574	0.121176
$838$	−38.6441	−1.33494
$839$	−43.1803	−1.49075	−0.745374	−	0.666646i	$-0.767729\pi$
$839$	−43.1803	−1.49075	−0.745374	+	0.666646i	$0.767729\pi$
$840$	0	0
$841$	37.7035	1.30012
$842$	12.2679	0.422779
$843$	−2.57185	−0.0885793
$844$	7.53525	0.259374
$845$	15.7067	0.540327
$846$	2.99611	0.103008
$847$	0	0
$848$	−46.3189	−1.59060
$849$	3.10173	0.106451
$850$	−2.01094	−0.0689748
$851$	−4.80501	−0.164714
$852$	3.09703	0.106102
$853$	−50.4430	−1.72714	−0.863568	−	0.504233i	$-0.831775\pi$
$853$	−50.4430	−1.72714	−0.863568	+	0.504233i	$0.831775\pi$
$854$	0	0
$855$	−5.88952	−0.201417
$856$	−26.1965	−0.895377
$857$	−24.0329	−0.820948	−0.410474	−	0.911872i	$-0.634637\pi$
$857$	−24.0329	−0.820948	−0.410474	+	0.911872i	$0.634637\pi$
$858$	8.20146	0.279993
$859$	−4.24051	−0.144684	−0.0723422	−	0.997380i	$-0.523047\pi$
$859$	−4.24051	−0.144684	−0.0723422	+	0.997380i	$0.523047\pi$
$860$	0.402798	0.0137353
$861$	0	0
$862$	−34.7456	−1.18344
$863$	37.7052	1.28350	0.641750	−	0.766914i	$-0.278209\pi$
$863$	37.7052	1.28350	0.641750	+	0.766914i	$0.278209\pi$
$864$	−1.92081	−0.0653472
$865$	3.34809	0.113838
$866$	21.5613	0.732681
$867$	15.2742	0.518738
$868$	0	0
$869$	−10.1107	−0.342983
$870$	12.5018	0.423852
$871$	27.3498	0.926711
$872$	−49.7284	−1.68402
$873$	0.868531	0.0293953
$874$	−8.30971	−0.281080
$875$	0	0
$876$	−0.132139	−0.00446458
$877$	−49.1481	−1.65961	−0.829807	−	0.558051i	$-0.811549\pi$
$877$	−49.1481	−1.65961	−0.829807	+	0.558051i	$0.811549\pi$
$878$	52.2981	1.76497
$879$	28.8157	0.971931
$880$	4.56854	0.154005
$881$	0.784318	0.0264243	0.0132122	−	0.999913i	$-0.495794\pi$
$881$	0.784318	0.0264243	0.0132122	+	0.999913i	$0.495794\pi$
$882$	0	0
$883$	−10.4881	−0.352952	−0.176476	−	0.984305i	$-0.556470\pi$
$883$	−10.4881	−0.352952	−0.176476	+	0.984305i	$0.556470\pi$
$884$	−2.41528	−0.0812348
$885$	10.6418	0.357721
$886$	13.2412	0.444848
$887$	−2.64178	−0.0887024	−0.0443512	−	0.999016i	$-0.514122\pi$
$887$	−2.64178	−0.0887024	−0.0443512	+	0.999016i	$0.514122\pi$
$888$	−13.2212	−0.443676
$889$	0	0
$890$	−2.65397	−0.0889612
$891$	−1.00000	−0.0335013
$892$	5.26806	0.176388
$893$	11.5276	0.385756
$894$	5.78857	0.193599
$895$	−25.0335	−0.836779
$896$	0	0
$897$	−4.93853	−0.164893
$898$	56.6222	1.88951
$899$	−28.6322	−0.954937
$900$	0.343144	0.0114381
$901$	13.3193	0.443730
$902$	17.7371	0.590581
$903$	0	0
$904$	33.1191	1.10153
$905$	11.5851	0.385102
$906$	16.9632	0.563564
$907$	16.2028	0.538004	0.269002	−	0.963140i	$-0.413306\pi$
$907$	16.2028	0.538004	0.269002	+	0.963140i	$0.413306\pi$
$908$	−1.38615	−0.0460010
$909$	−5.70320	−0.189163
$910$	0	0
$911$	−37.0892	−1.22882	−0.614410	−	0.788987i	$-0.710606\pi$
$911$	−37.0892	−1.22882	−0.614410	+	0.788987i	$0.710606\pi$
$912$	−26.9065	−0.890964
$913$	−15.4518	−0.511380
$914$	−19.6449	−0.649796
$915$	−0.173076	−0.00572173
$916$	5.86048	0.193636
$917$	0	0
$918$	2.01094	0.0663710
$919$	−56.1979	−1.85380	−0.926900	−	0.375310i	$-0.877536\pi$
$919$	−56.1979	−1.85380	−0.926900	+	0.375310i	$0.877536\pi$
$920$	−2.33771	−0.0770720
$921$	−18.2795	−0.602331
$922$	−24.9403	−0.821366
$923$	48.3571	1.59169
$924$	0	0
$925$	5.21301	0.171403
$926$	−27.8672	−0.915774
$927$	−10.5822	−0.347566
$928$	15.6877	0.514973
$929$	−27.4825	−0.901672	−0.450836	−	0.892607i	$-0.648874\pi$
$929$	−27.4825	−0.901672	−0.450836	+	0.892607i	$0.648874\pi$
$930$	−5.36636	−0.175970
$931$	0	0
$932$	−2.16791	−0.0710123
$933$	6.12177	0.200418
$934$	46.3770	1.51750
$935$	−1.31371	−0.0429630
$936$	−13.5886	−0.444158
$937$	−37.4890	−1.22471	−0.612356	−	0.790582i	$-0.709778\pi$
$937$	−37.4890	−1.22471	−0.612356	+	0.790582i	$0.709778\pi$
$938$	0	0
$939$	33.5823	1.09592
$940$	−0.671637	−0.0219064
$941$	−4.69863	−0.153171	−0.0765855	−	0.997063i	$-0.524402\pi$
$941$	−4.69863	−0.153171	−0.0765855	+	0.997063i	$0.524402\pi$
$942$	12.1722	0.396592
$943$	−10.6804	−0.347803
$944$	48.6176	1.58237
$945$	0	0
$946$	1.79684	0.0584204
$947$	17.6964	0.575055	0.287528	−	0.957772i	$-0.407167\pi$
$947$	17.6964	0.575055	0.287528	+	0.957772i	$0.407167\pi$
$948$	−3.46944	−0.112682
$949$	−2.06323	−0.0669753
$950$	9.01529	0.292495
$951$	−27.9132	−0.905148
$952$	0	0
$953$	−59.2504	−1.91931	−0.959654	−	0.281183i	$-0.909273\pi$
$953$	−59.2504	−1.91931	−0.959654	+	0.281183i	$0.909273\pi$
$954$	−15.5196	−0.502465
$955$	11.5115	0.372504
$956$	1.86676	0.0603753
$957$	8.16722	0.264009
$958$	30.6178	0.989218
$959$	0	0
$960$	−6.19684	−0.200002
$961$	−18.7098	−0.603541
$962$	42.7543	1.37845
$963$	−10.3290	−0.332847
$964$	−5.49980	−0.177137
$965$	−17.4824	−0.562777
$966$	0	0
$967$	54.4884	1.75223	0.876114	−	0.482104i	$-0.160127\pi$
$967$	54.4884	1.75223	0.876114	+	0.482104i	$0.160127\pi$
$968$	2.53620	0.0815167
$969$	7.73714	0.248553
$970$	−1.32949	−0.0426873
$971$	1.23740	0.0397102	0.0198551	−	0.999803i	$-0.493680\pi$
$971$	1.23740	0.0397102	0.0198551	+	0.999803i	$0.493680\pi$
$972$	−0.343144	−0.0110064
$973$	0	0
$974$	−57.7378	−1.85004
$975$	5.35786	0.171589
$976$	−0.790706	−0.0253099
$977$	−14.0643	−0.449956	−0.224978	−	0.974364i	$-0.572231\pi$
$977$	−14.0643	−0.449956	−0.224978	+	0.974364i	$0.572231\pi$
$978$	15.2586	0.487917
$979$	−1.73379	−0.0554122
$980$	0	0
$981$	−19.6074	−0.626016
$982$	27.4496	0.875952
$983$	55.3923	1.76674	0.883370	−	0.468676i	$-0.155269\pi$
$983$	55.3923	1.76674	0.883370	+	0.468676i	$0.155269\pi$
$984$	−29.3878	−0.936849
$985$	−20.1656	−0.642528
$986$	−16.4238	−0.523041
$987$	0	0
$988$	10.8280	0.344485
$989$	−1.08197	−0.0344048
$990$	1.53073	0.0486499
$991$	26.2423	0.833614	0.416807	−	0.908995i	$-0.363149\pi$
$991$	26.2423	0.833614	0.416807	+	0.908995i	$0.363149\pi$
$992$	−6.73386	−0.213800
$993$	23.3768	0.741840
$994$	0	0
$995$	8.49942	0.269450
$996$	−5.30219	−0.168006
$997$	−50.8671	−1.61098	−0.805489	−	0.592611i	$-0.798097\pi$
$997$	−50.8671	−1.61098	−0.805489	+	0.592611i	$0.798097\pi$
$998$	−9.26756	−0.293359
$999$	−5.21301	−0.164932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.ce.1.3		8
7.3	odd	6		1155.2.q.j.331.6	✓	16
7.5	odd	6		1155.2.q.j.991.6	yes	16
7.6	odd	2		8085.2.a.cf.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.j.331.6	✓	16	7.3	odd	6
1155.2.q.j.991.6	yes	16	7.5	odd	6
8085.2.a.ce.1.3		8	1.1	even	1	trivial
8085.2.a.cf.1.3		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)

\(f(q)\)	\(=\)	\(q-1.53073 q^{2} -1.00000 q^{3} +0.343144 q^{4} +1.00000 q^{5} +1.53073 q^{6} +2.53620 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.53073 q^{2} -1.00000 q^{3} +0.343144 q^{4} +1.00000 q^{5} +1.53073 q^{6} +2.53620 q^{8} +1.00000 q^{9} -1.53073 q^{10} -1.00000 q^{11} -0.343144 q^{12} -5.35786 q^{13} -1.00000 q^{15} -4.56854 q^{16} +1.31371 q^{17} -1.53073 q^{18} -5.88952 q^{19} +0.343144 q^{20} +1.53073 q^{22} -0.921735 q^{23} -2.53620 q^{24} +1.00000 q^{25} +8.20146 q^{26} -1.00000 q^{27} +8.16722 q^{29} +1.53073 q^{30} -3.50574 q^{31} +1.92081 q^{32} +1.00000 q^{33} -2.01094 q^{34} +0.343144 q^{36} +5.21301 q^{37} +9.01529 q^{38} +5.35786 q^{39} +2.53620 q^{40} +11.5873 q^{41} +1.17384 q^{43} -0.343144 q^{44} +1.00000 q^{45} +1.41093 q^{46} -1.95730 q^{47} +4.56854 q^{48} -1.53073 q^{50} -1.31371 q^{51} -1.83852 q^{52} +10.1387 q^{53} +1.53073 q^{54} -1.00000 q^{55} +5.88952 q^{57} -12.5018 q^{58} -10.6418 q^{59} -0.343144 q^{60} +0.173076 q^{61} +5.36636 q^{62} +6.19684 q^{64} -5.35786 q^{65} -1.53073 q^{66} -5.10460 q^{67} +0.450792 q^{68} +0.921735 q^{69} -9.02545 q^{71} +2.53620 q^{72} +0.385085 q^{73} -7.97972 q^{74} -1.00000 q^{75} -2.02096 q^{76} -8.20146 q^{78} +10.1107 q^{79} -4.56854 q^{80} +1.00000 q^{81} -17.7371 q^{82} +15.4518 q^{83} +1.31371 q^{85} -1.79684 q^{86} -8.16722 q^{87} -2.53620 q^{88} +1.73379 q^{89} -1.53073 q^{90} -0.316288 q^{92} +3.50574 q^{93} +2.99611 q^{94} -5.88952 q^{95} -1.92081 q^{96} +0.868531 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 10 q^{4} + 8 q^{5} + 8 q^{9}+O(q^{10}) \) 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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