LMFDB - Embedded newform 775.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(1,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.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:	$6.18840615665$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.144209.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 6x^{3} - x^{2} + 6x - 1 $ x^5 - 6x^3 - x^2 + 6x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.93413$ of defining polynomial
Character	$\chi$	$=$	775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23959 q^{2} +0.740841 q^{3} +3.01578 q^{4} -1.65918 q^{6} -3.67497 q^{7} -2.27494 q^{8} -2.45115 q^{9} +O(q^{10})$	\(q-2.23959 q^{2} +0.740841 q^{3} +3.01578 q^{4} -1.65918 q^{6} -3.67497 q^{7} -2.27494 q^{8} -2.45115 q^{9} +5.02619 q^{11} +2.23422 q^{12} +2.67247 q^{13} +8.23043 q^{14} -0.936618 q^{16} -3.30547 q^{17} +5.48959 q^{18} +2.88050 q^{19} -2.72256 q^{21} -11.2566 q^{22} -6.01040 q^{23} -1.68537 q^{24} -5.98526 q^{26} -4.03844 q^{27} -11.0829 q^{28} -5.13050 q^{29} -1.00000 q^{31} +6.64753 q^{32} +3.72360 q^{33} +7.40291 q^{34} -7.39215 q^{36} +7.90540 q^{37} -6.45115 q^{38} +1.97988 q^{39} -9.55651 q^{41} +6.09744 q^{42} -5.25000 q^{43} +15.1579 q^{44} +13.4609 q^{46} +1.06691 q^{47} -0.693885 q^{48} +6.50538 q^{49} -2.44883 q^{51} +8.05960 q^{52} +0.521408 q^{53} +9.04446 q^{54} +8.36034 q^{56} +2.13399 q^{57} +11.4902 q^{58} -8.09515 q^{59} +0.598687 q^{61} +2.23959 q^{62} +9.00791 q^{63} -13.0145 q^{64} -8.33936 q^{66} -12.4705 q^{67} -9.96858 q^{68} -4.45275 q^{69} -8.80048 q^{71} +5.57624 q^{72} -9.87423 q^{73} -17.7049 q^{74} +8.68697 q^{76} -18.4711 q^{77} -4.43412 q^{78} -2.40291 q^{79} +4.36163 q^{81} +21.4027 q^{82} +2.91400 q^{83} -8.21067 q^{84} +11.7579 q^{86} -3.80088 q^{87} -11.4343 q^{88} -7.65918 q^{89} -9.82125 q^{91} -18.1261 q^{92} -0.740841 q^{93} -2.38946 q^{94} +4.92476 q^{96} +14.5224 q^{97} -14.5694 q^{98} -12.3200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9}+O(q^{10}) $ 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9	$ 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9} - 2 q^{11} - 5 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 19 q^{17} - 5 q^{18} + 8 q^{19} - 15 q^{21} + 10 q^{22} - 12 q^{23} + 26 q^{24} - 16 q^{26} - 6 q^{27} - 6 q^{28} + 6 q^{29} - 5 q^{31} - 7 q^{32} - 3 q^{33} + 31 q^{34} - 13 q^{36} - 16 q^{37} - 14 q^{38} - 13 q^{39} - 2 q^{41} + 22 q^{42} - q^{43} - 4 q^{44} - 11 q^{46} - 8 q^{47} - 31 q^{48} - 9 q^{49} + 5 q^{51} + 26 q^{52} - 3 q^{53} + 10 q^{54} - 9 q^{56} - 14 q^{57} - 5 q^{58} - 4 q^{59} - 5 q^{61} + 4 q^{62} + 26 q^{63} - 5 q^{64} - 25 q^{66} - 13 q^{67} - 30 q^{68} + 10 q^{69} + 6 q^{71} - 2 q^{72} - 19 q^{73} + 4 q^{74} - 5 q^{76} - 23 q^{77} + 38 q^{78} - 6 q^{79} - 7 q^{81} + 27 q^{82} - 18 q^{83} - 15 q^{84} - 7 q^{86} + 5 q^{87} + q^{88} - 31 q^{89} + 8 q^{91} + 16 q^{92} + 3 q^{93} - 14 q^{94} + 10 q^{96} + q^{97} - 10 q^{98} - 33 q^{99}+O(q^{100}) $ 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9 - 2 * q^11 - 5 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 19 * q^17 - 5 * q^18 + 8 * q^19 - 15 * q^21 + 10 * q^22 - 12 * q^23 + 26 * q^24 - 16 * q^26 - 6 * q^27 - 6 * q^28 + 6 * q^29 - 5 * q^31 - 7 * q^32 - 3 * q^33 + 31 * q^34 - 13 * q^36 - 16 * q^37 - 14 * q^38 - 13 * q^39 - 2 * q^41 + 22 * q^42 - q^43 - 4 * q^44 - 11 * q^46 - 8 * q^47 - 31 * q^48 - 9 * q^49 + 5 * q^51 + 26 * q^52 - 3 * q^53 + 10 * q^54 - 9 * q^56 - 14 * q^57 - 5 * q^58 - 4 * q^59 - 5 * q^61 + 4 * q^62 + 26 * q^63 - 5 * q^64 - 25 * q^66 - 13 * q^67 - 30 * q^68 + 10 * q^69 + 6 * q^71 - 2 * q^72 - 19 * q^73 + 4 * q^74 - 5 * q^76 - 23 * q^77 + 38 * q^78 - 6 * q^79 - 7 * q^81 + 27 * q^82 - 18 * q^83 - 15 * q^84 - 7 * q^86 + 5 * q^87 + q^88 - 31 * q^89 + 8 * q^91 + 16 * q^92 + 3 * q^93 - 14 * q^94 + 10 * q^96 + q^97 - 10 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.23959	−1.58363	−0.791816	−	0.610759i	$-0.790864\pi$
$2$	−2.23959	−1.58363	−0.791816	+	0.610759i	$0.790864\pi$
$3$	0.740841	0.427725	0.213862	−	0.976864i	$-0.431396\pi$
$3$	0.740841	0.427725	0.213862	+	0.976864i	$0.431396\pi$
$4$	3.01578	1.50789
$5$	0	0
$5$	0	0
$6$	−1.65918	−0.677359
$7$	−3.67497	−1.38901	−0.694503	−	0.719489i	$-0.744376\pi$
$7$	−3.67497	−1.38901	−0.694503	+	0.719489i	$0.744376\pi$
$8$	−2.27494	−0.804314
$9$	−2.45115	−0.817052
$10$	0	0
$11$	5.02619	1.51545	0.757726	−	0.652573i	$-0.226310\pi$
$11$	5.02619	1.51545	0.757726	+	0.652573i	$0.226310\pi$
$12$	2.23422	0.644962
$13$	2.67247	0.741211	0.370605	−	0.928790i	$-0.379150\pi$
$13$	2.67247	0.741211	0.370605	+	0.928790i	$0.379150\pi$
$14$	8.23043	2.19968
$15$	0	0
$16$	−0.936618	−0.234155
$17$	−3.30547	−0.801694	−0.400847	−	0.916145i	$-0.631284\pi$
$17$	−3.30547	−0.801694	−0.400847	+	0.916145i	$0.631284\pi$
$18$	5.48959	1.29391
$19$	2.88050	0.660832	0.330416	−	0.943835i	$-0.392811\pi$
$19$	2.88050	0.660832	0.330416	+	0.943835i	$0.392811\pi$
$20$	0	0
$21$	−2.72256	−0.594112
$22$	−11.2566	−2.39992
$23$	−6.01040	−1.25326	−0.626628	−	0.779319i	$-0.715565\pi$
$23$	−6.01040	−1.25326	−0.626628	+	0.779319i	$0.715565\pi$
$24$	−1.68537	−0.344025
$25$	0	0
$26$	−5.98526	−1.17381
$27$	−4.03844	−0.777198
$28$	−11.0829	−2.09447
$29$	−5.13050	−0.952710	−0.476355	−	0.879253i	$-0.658042\pi$
$29$	−5.13050	−0.952710	−0.476355	+	0.879253i	$0.658042\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	6.64753	1.17513
$33$	3.72360	0.648196
$34$	7.40291	1.26959
$35$	0	0
$36$	−7.39215	−1.23203
$37$	7.90540	1.29964	0.649820	−	0.760088i	$-0.274844\pi$
$37$	7.90540	1.29964	0.649820	+	0.760088i	$0.274844\pi$
$38$	−6.45115	−1.04652
$39$	1.97988	0.317034
$40$	0	0
$41$	−9.55651	−1.49248	−0.746238	−	0.665679i	$-0.768142\pi$
$41$	−9.55651	−1.49248	−0.746238	+	0.665679i	$0.768142\pi$
$42$	6.09744	0.940856
$43$	−5.25000	−0.800617	−0.400309	−	0.916380i	$-0.631097\pi$
$43$	−5.25000	−0.800617	−0.400309	+	0.916380i	$0.631097\pi$
$44$	15.1579	2.28514
$45$	0	0
$46$	13.4609	1.98470
$47$	1.06691	0.155625	0.0778127	−	0.996968i	$-0.475206\pi$
$47$	1.06691	0.155625	0.0778127	+	0.996968i	$0.475206\pi$
$48$	−0.693885	−0.100154
$49$	6.50538	0.929339
$50$	0	0
$51$	−2.44883	−0.342904
$52$	8.05960	1.11767
$53$	0.521408	0.0716210	0.0358105	−	0.999359i	$-0.488599\pi$
$53$	0.521408	0.0716210	0.0358105	+	0.999359i	$0.488599\pi$
$54$	9.04446	1.23080
$55$	0	0
$56$	8.36034	1.11720
$57$	2.13399	0.282654
$58$	11.4902	1.50874
$59$	−8.09515	−1.05390	−0.526950	−	0.849897i	$-0.676664\pi$
$59$	−8.09515	−1.05390	−0.526950	+	0.849897i	$0.676664\pi$
$60$	0	0
$61$	0.598687	0.0766541	0.0383270	−	0.999265i	$-0.487797\pi$
$61$	0.598687	0.0766541	0.0383270	+	0.999265i	$0.487797\pi$
$62$	2.23959	0.284429
$63$	9.00791	1.13489
$64$	−13.0145	−1.62682
$65$	0	0
$66$	−8.33936	−1.02650
$67$	−12.4705	−1.52351	−0.761755	−	0.647865i	$-0.775662\pi$
$67$	−12.4705	−1.52351	−0.761755	+	0.647865i	$0.775662\pi$
$68$	−9.96858	−1.20887
$69$	−4.45275	−0.536048
$70$	0	0
$71$	−8.80048	−1.04442	−0.522212	−	0.852815i	$-0.674893\pi$
$71$	−8.80048	−1.04442	−0.522212	+	0.852815i	$0.674893\pi$
$72$	5.57624	0.657166
$73$	−9.87423	−1.15569	−0.577845	−	0.816146i	$-0.696106\pi$
$73$	−9.87423	−1.15569	−0.577845	+	0.816146i	$0.696106\pi$
$74$	−17.7049	−2.05815
$75$	0	0
$76$	8.68697	0.996464
$77$	−18.4711	−2.10497
$78$	−4.43412	−0.502065
$79$	−2.40291	−0.270349	−0.135174	−	0.990822i	$-0.543159\pi$
$79$	−2.40291	−0.270349	−0.135174	+	0.990822i	$0.543159\pi$
$80$	0	0
$81$	4.36163	0.484625
$82$	21.4027	2.36353
$83$	2.91400	0.319853	0.159927	−	0.987129i	$-0.448874\pi$
$83$	2.91400	0.319853	0.159927	+	0.987129i	$0.448874\pi$
$84$	−8.21067	−0.895857
$85$	0	0
$86$	11.7579	1.26788
$87$	−3.80088	−0.407497
$88$	−11.4343	−1.21890
$89$	−7.65918	−0.811872	−0.405936	−	0.913902i	$-0.633054\pi$
$89$	−7.65918	−0.811872	−0.405936	+	0.913902i	$0.633054\pi$
$90$	0	0
$91$	−9.82125	−1.02955
$92$	−18.1261	−1.88977
$93$	−0.740841	−0.0768216
$94$	−2.38946	−0.246454
$95$	0	0
$96$	4.92476	0.502631
$97$	14.5224	1.47452	0.737261	−	0.675608i	$-0.236119\pi$
$97$	14.5224	1.47452	0.737261	+	0.675608i	$0.236119\pi$
$98$	−14.5694	−1.47173
$99$	−12.3200	−1.23820
$100$	0	0
$101$	−14.6832	−1.46103	−0.730516	−	0.682896i	$-0.760720\pi$
$101$	−14.6832	−1.46103	−0.730516	+	0.682896i	$0.760720\pi$
$102$	5.48438	0.543034
$103$	16.2414	1.60031	0.800156	−	0.599792i	$-0.204750\pi$
$103$	16.2414	1.60031	0.800156	+	0.599792i	$0.204750\pi$
$104$	−6.07972	−0.596166
$105$	0	0
$106$	−1.16774	−0.113421
$107$	−7.72859	−0.747151	−0.373576	−	0.927600i	$-0.621868\pi$
$107$	−7.72859	−0.747151	−0.373576	+	0.927600i	$0.621868\pi$
$108$	−12.1791	−1.17193
$109$	−6.60865	−0.632994	−0.316497	−	0.948594i	$-0.602507\pi$
$109$	−6.60865	−0.632994	−0.316497	+	0.948594i	$0.602507\pi$
$110$	0	0
$111$	5.85664	0.555888
$112$	3.44204	0.325242
$113$	−11.3537	−1.06807	−0.534034	−	0.845463i	$-0.679324\pi$
$113$	−11.3537	−1.06807	−0.534034	+	0.845463i	$0.679324\pi$
$114$	−4.77928	−0.447620
$115$	0	0
$116$	−15.4725	−1.43658
$117$	−6.55065	−0.605607
$118$	18.1299	1.66899
$119$	12.1475	1.11356
$120$	0	0
$121$	14.2626	1.29660
$122$	−1.34082	−0.121392
$123$	−7.07985	−0.638369
$124$	−3.01578	−0.270825
$125$	0	0
$126$	−20.1741	−1.79725
$127$	11.1669	0.990901	0.495451	−	0.868636i	$-0.335003\pi$
$127$	11.1669	0.990901	0.495451	+	0.868636i	$0.335003\pi$
$128$	15.8522	1.40115
$129$	−3.88941	−0.342444
$130$	0	0
$131$	−1.93468	−0.169034	−0.0845170	−	0.996422i	$-0.526935\pi$
$131$	−1.93468	−0.169034	−0.0845170	+	0.996422i	$0.526935\pi$
$132$	11.2296	0.977410
$133$	−10.5857	−0.917901
$134$	27.9288	2.41268
$135$	0	0
$136$	7.51975	0.644813
$137$	−16.5372	−1.41287	−0.706434	−	0.707779i	$-0.749697\pi$
$137$	−16.5372	−1.41287	−0.706434	+	0.707779i	$0.749697\pi$
$138$	9.97236	0.848904
$139$	−22.3954	−1.89956	−0.949778	−	0.312924i	$-0.898691\pi$
$139$	−22.3954	−1.89956	−0.949778	+	0.312924i	$0.898691\pi$
$140$	0	0
$141$	0.790414	0.0665648
$142$	19.7095	1.65399
$143$	13.4324	1.12327
$144$	2.29580	0.191316
$145$	0	0
$146$	22.1143	1.83019
$147$	4.81945	0.397501
$148$	23.8410	1.95972
$149$	−4.86954	−0.398928	−0.199464	−	0.979905i	$-0.563920\pi$
$149$	−4.86954	−0.398928	−0.199464	+	0.979905i	$0.563920\pi$
$150$	0	0
$151$	19.5409	1.59022	0.795109	−	0.606466i	$-0.207414\pi$
$151$	19.5409	1.59022	0.795109	+	0.606466i	$0.207414\pi$
$152$	−6.55297	−0.531516
$153$	8.10222	0.655025
$154$	41.3677	3.33350
$155$	0	0
$156$	5.97088	0.478053
$157$	14.9019	1.18930	0.594649	−	0.803985i	$-0.297291\pi$
$157$	14.9019	1.18930	0.594649	+	0.803985i	$0.297291\pi$
$158$	5.38154	0.428133
$159$	0.386281	0.0306340
$160$	0	0
$161$	22.0880	1.74078
$162$	−9.76827	−0.767468
$163$	10.7995	0.845878	0.422939	−	0.906158i	$-0.360998\pi$
$163$	10.7995	0.845878	0.422939	+	0.906158i	$0.360998\pi$
$164$	−28.8204	−2.25049
$165$	0	0
$166$	−6.52618	−0.506530
$167$	−16.2405	−1.25673	−0.628364	−	0.777920i	$-0.716275\pi$
$167$	−16.2405	−1.25673	−0.628364	+	0.777920i	$0.716275\pi$
$168$	6.19368	0.477853
$169$	−5.85789	−0.450607
$170$	0	0
$171$	−7.06056	−0.539934
$172$	−15.8329	−1.20724
$173$	3.97252	0.302025	0.151013	−	0.988532i	$-0.451747\pi$
$173$	3.97252	0.302025	0.151013	+	0.988532i	$0.451747\pi$
$174$	8.51244	0.645326
$175$	0	0
$176$	−4.70762	−0.354850
$177$	−5.99722	−0.450779
$178$	17.1535	1.28571
$179$	24.8049	1.85401	0.927003	−	0.375053i	$-0.122376\pi$
$179$	24.8049	1.85401	0.927003	+	0.375053i	$0.122376\pi$
$180$	0	0
$181$	−15.9359	−1.18451	−0.592253	−	0.805752i	$-0.701761\pi$
$181$	−15.9359	−1.18451	−0.592253	+	0.805752i	$0.701761\pi$
$182$	21.9956	1.63042
$183$	0.443532	0.0327868
$184$	13.6733	1.00801
$185$	0	0
$186$	1.65918	0.121657
$187$	−16.6139	−1.21493
$188$	3.21758	0.234666
$189$	14.8411	1.07953
$190$	0	0
$191$	22.5120	1.62891	0.814456	−	0.580226i	$-0.197036\pi$
$191$	22.5120	1.62891	0.814456	+	0.580226i	$0.197036\pi$
$192$	−9.64170	−0.695830
$193$	−19.0305	−1.36984	−0.684922	−	0.728616i	$-0.740164\pi$
$193$	−19.0305	−1.36984	−0.684922	+	0.728616i	$0.740164\pi$
$194$	−32.5242	−2.33510
$195$	0	0
$196$	19.6188	1.40134
$197$	1.27674	0.0909642	0.0454821	−	0.998965i	$-0.485518\pi$
$197$	1.27674	0.0909642	0.0454821	+	0.998965i	$0.485518\pi$
$198$	27.5917	1.96086
$199$	9.21392	0.653157	0.326579	−	0.945170i	$-0.394104\pi$
$199$	9.21392	0.653157	0.326579	+	0.945170i	$0.394104\pi$
$200$	0	0
$201$	−9.23863	−0.651643
$202$	32.8844	2.31374
$203$	18.8544	1.32332
$204$	−7.38513	−0.517062
$205$	0	0
$206$	−36.3741	−2.53431
$207$	14.7324	1.02397
$208$	−2.50309	−0.173558
$209$	14.4779	1.00146
$210$	0	0
$211$	2.86821	0.197456	0.0987279	−	0.995114i	$-0.468523\pi$
$211$	2.86821	0.197456	0.0987279	+	0.995114i	$0.468523\pi$
$212$	1.57245	0.107997
$213$	−6.51976	−0.446726
$214$	17.3089	1.18321
$215$	0	0
$216$	9.18721	0.625111
$217$	3.67497	0.249473
$218$	14.8007	1.00243
$219$	−7.31523	−0.494317
$220$	0	0
$221$	−8.83378	−0.594224
$222$	−13.1165	−0.880322
$223$	−9.10462	−0.609691	−0.304845	−	0.952402i	$-0.598605\pi$
$223$	−9.10462	−0.609691	−0.304845	+	0.952402i	$0.598605\pi$
$224$	−24.4294	−1.63226
$225$	0	0
$226$	25.4277	1.69143
$227$	−4.62499	−0.306971	−0.153486	−	0.988151i	$-0.549050\pi$
$227$	−4.62499	−0.306971	−0.153486	+	0.988151i	$0.549050\pi$
$228$	6.43566	0.426212
$229$	26.1553	1.72839	0.864196	−	0.503156i	$-0.167828\pi$
$229$	26.1553	1.72839	0.864196	+	0.503156i	$0.167828\pi$
$230$	0	0
$231$	−13.6841	−0.900349
$232$	11.6716	0.766278
$233$	4.76330	0.312054	0.156027	−	0.987753i	$-0.450131\pi$
$233$	4.76330	0.312054	0.156027	+	0.987753i	$0.450131\pi$
$234$	14.6708	0.959060
$235$	0	0
$236$	−24.4132	−1.58917
$237$	−1.78017	−0.115635
$238$	−27.2054	−1.76347
$239$	0.674275	0.0436152	0.0218076	−	0.999762i	$-0.493058\pi$
$239$	0.674275	0.0436152	0.0218076	+	0.999762i	$0.493058\pi$
$240$	0	0
$241$	4.14684	0.267122	0.133561	−	0.991041i	$-0.457359\pi$
$241$	4.14684	0.267122	0.133561	+	0.991041i	$0.457359\pi$
$242$	−31.9423	−2.05333
$243$	15.3466	0.984484
$244$	1.80551	0.115586
$245$	0	0
$246$	15.8560	1.01094
$247$	7.69806	0.489816
$248$	2.27494	0.144459
$249$	2.15881	0.136809
$250$	0	0
$251$	23.0876	1.45728	0.728638	−	0.684899i	$-0.240154\pi$
$251$	23.0876	1.45728	0.728638	+	0.684899i	$0.240154\pi$
$252$	27.1659	1.71129
$253$	−30.2094	−1.89925
$254$	−25.0093	−1.56922
$255$	0	0
$256$	−9.47347	−0.592092
$257$	−27.3951	−1.70886	−0.854429	−	0.519568i	$-0.826093\pi$
$257$	−27.3951	−1.70886	−0.854429	+	0.519568i	$0.826093\pi$
$258$	8.71071	0.542305
$259$	−29.0521	−1.80521
$260$	0	0
$261$	12.5756	0.778413
$262$	4.33291	0.267688
$263$	13.1328	0.809802	0.404901	−	0.914361i	$-0.367306\pi$
$263$	13.1328	0.809802	0.404901	+	0.914361i	$0.367306\pi$
$264$	−8.47099	−0.521353
$265$	0	0
$266$	23.7078	1.45362
$267$	−5.67424	−0.347258
$268$	−37.6082	−2.29729
$269$	23.5415	1.43535	0.717676	−	0.696377i	$-0.245206\pi$
$269$	23.5415	1.43535	0.717676	+	0.696377i	$0.245206\pi$
$270$	0	0
$271$	21.2089	1.28835	0.644173	−	0.764880i	$-0.277202\pi$
$271$	21.2089	1.28835	0.644173	+	0.764880i	$0.277202\pi$
$272$	3.09596	0.187720
$273$	−7.27598	−0.440362
$274$	37.0366	2.23746
$275$	0	0
$276$	−13.4285	−0.808303
$277$	3.16271	0.190029	0.0950144	−	0.995476i	$-0.469710\pi$
$277$	3.16271	0.190029	0.0950144	+	0.995476i	$0.469710\pi$
$278$	50.1567	3.00820
$279$	2.45115	0.146747
$280$	0	0
$281$	21.9912	1.31189	0.655943	−	0.754810i	$-0.272271\pi$
$281$	21.9912	1.31189	0.655943	+	0.754810i	$0.272271\pi$
$282$	−1.77021	−0.105414
$283$	−15.6629	−0.931065	−0.465532	−	0.885031i	$-0.654137\pi$
$283$	−15.6629	−0.931065	−0.465532	+	0.885031i	$0.654137\pi$
$284$	−26.5403	−1.57488
$285$	0	0
$286$	−30.0830	−1.77885
$287$	35.1198	2.07306
$288$	−16.2941	−0.960140
$289$	−6.07387	−0.357287
$290$	0	0
$291$	10.7588	0.630690
$292$	−29.7785	−1.74266
$293$	−29.1815	−1.70480	−0.852401	−	0.522889i	$-0.824854\pi$
$293$	−29.1815	−1.70480	−0.852401	+	0.522889i	$0.824854\pi$
$294$	−10.7936	−0.629496
$295$	0	0
$296$	−17.9843	−1.04532
$297$	−20.2979	−1.17781
$298$	10.9058	0.631756
$299$	−16.0626	−0.928927
$300$	0	0
$301$	19.2936	1.11206
$302$	−43.7638	−2.51832
$303$	−10.8779	−0.624919
$304$	−2.69793	−0.154737
$305$	0	0
$306$	−18.1457	−1.03732
$307$	19.3160	1.10243	0.551213	−	0.834365i	$-0.314165\pi$
$307$	19.3160	1.10243	0.551213	+	0.834365i	$0.314165\pi$
$308$	−55.7047	−3.17407
$309$	12.0323	0.684493
$310$	0	0
$311$	6.15914	0.349253	0.174626	−	0.984635i	$-0.444128\pi$
$311$	6.15914	0.349253	0.174626	+	0.984635i	$0.444128\pi$
$312$	−4.50411	−0.254995
$313$	20.1839	1.14086	0.570430	−	0.821346i	$-0.306777\pi$
$313$	20.1839	1.14086	0.570430	+	0.821346i	$0.306777\pi$
$314$	−33.3741	−1.88341
$315$	0	0
$316$	−7.24666	−0.407656
$317$	25.2088	1.41587	0.707933	−	0.706280i	$-0.249628\pi$
$317$	25.2088	1.41587	0.707933	+	0.706280i	$0.249628\pi$
$318$	−0.865112	−0.0485131
$319$	−25.7869	−1.44379
$320$	0	0
$321$	−5.72565	−0.319575
$322$	−49.4682	−2.75676
$323$	−9.52141	−0.529785
$324$	13.1537	0.730762
$325$	0	0
$326$	−24.1864	−1.33956
$327$	−4.89596	−0.270747
$328$	21.7405	1.20042
$329$	−3.92087	−0.216165
$330$	0	0
$331$	−17.6922	−0.972454	−0.486227	−	0.873833i	$-0.661627\pi$
$331$	−17.6922	−0.972454	−0.486227	+	0.873833i	$0.661627\pi$
$332$	8.78800	0.482304
$333$	−19.3774	−1.06187
$334$	36.3721	1.99019
$335$	0	0
$336$	2.55000	0.139114
$337$	−2.89468	−0.157683	−0.0788415	−	0.996887i	$-0.525122\pi$
$337$	−2.89468	−0.157683	−0.0788415	+	0.996887i	$0.525122\pi$
$338$	13.1193	0.713595
$339$	−8.41129	−0.456839
$340$	0	0
$341$	−5.02619	−0.272183
$342$	15.8128	0.855057
$343$	1.81773	0.0981480
$344$	11.9434	0.643947
$345$	0	0
$346$	−8.89684	−0.478297
$347$	−6.89681	−0.370240	−0.185120	−	0.982716i	$-0.559267\pi$
$347$	−6.89681	−0.370240	−0.185120	+	0.982716i	$0.559267\pi$
$348$	−11.4626	−0.614462
$349$	−14.6691	−0.785220	−0.392610	−	0.919705i	$-0.628428\pi$
$349$	−14.6691	−0.785220	−0.392610	+	0.919705i	$0.628428\pi$
$350$	0	0
$351$	−10.7926	−0.576067
$352$	33.4117	1.78085
$353$	10.5568	0.561883	0.280942	−	0.959725i	$-0.409353\pi$
$353$	10.5568	0.561883	0.280942	+	0.959725i	$0.409353\pi$
$354$	13.4313	0.713868
$355$	0	0
$356$	−23.0984	−1.22421
$357$	8.99935	0.476296
$358$	−55.5530	−2.93607
$359$	20.4230	1.07788	0.538942	−	0.842343i	$-0.318824\pi$
$359$	20.4230	1.07788	0.538942	+	0.842343i	$0.318824\pi$
$360$	0	0
$361$	−10.7027	−0.563301
$362$	35.6899	1.87582
$363$	10.5663	0.554586
$364$	−29.6188	−1.55244
$365$	0	0
$366$	−0.993332	−0.0519223
$367$	15.0168	0.783872	0.391936	−	0.919993i	$-0.371806\pi$
$367$	15.0168	0.783872	0.391936	+	0.919993i	$0.371806\pi$
$368$	5.62945	0.293456
$369$	23.4245	1.21943
$370$	0	0
$371$	−1.91616	−0.0994820
$372$	−2.23422	−0.115839
$373$	−19.2471	−0.996578	−0.498289	−	0.867011i	$-0.666038\pi$
$373$	−19.2471	−0.996578	−0.498289	+	0.867011i	$0.666038\pi$
$374$	37.2084	1.92400
$375$	0	0
$376$	−2.42717	−0.125172
$377$	−13.7111	−0.706159
$378$	−33.2381	−1.70958
$379$	3.24968	0.166925	0.0834624	−	0.996511i	$-0.473402\pi$
$379$	3.24968	0.166925	0.0834624	+	0.996511i	$0.473402\pi$
$380$	0	0
$381$	8.27289	0.423833
$382$	−50.4177	−2.57960
$383$	2.01897	0.103164	0.0515822	−	0.998669i	$-0.483574\pi$
$383$	2.01897	0.103164	0.0515822	+	0.998669i	$0.483574\pi$
$384$	11.7440	0.599307
$385$	0	0
$386$	42.6206	2.16933
$387$	12.8686	0.654146
$388$	43.7963	2.22342
$389$	−15.2990	−0.775689	−0.387844	−	0.921725i	$-0.626780\pi$
$389$	−15.2990	−0.775689	−0.387844	+	0.921725i	$0.626780\pi$
$390$	0	0
$391$	19.8672	1.00473
$392$	−14.7994	−0.747480
$393$	−1.43329	−0.0723000
$394$	−2.85939	−0.144054
$395$	0	0
$396$	−37.1543	−1.86708
$397$	−14.1815	−0.711751	−0.355875	−	0.934533i	$-0.615817\pi$
$397$	−14.1815	−0.711751	−0.355875	+	0.934533i	$0.615817\pi$
$398$	−20.6354	−1.03436
$399$	−7.84235	−0.392609
$400$	0	0
$401$	−6.59958	−0.329567	−0.164784	−	0.986330i	$-0.552693\pi$
$401$	−6.59958	−0.329567	−0.164784	+	0.986330i	$0.552693\pi$
$402$	20.6908	1.03196
$403$	−2.67247	−0.133125
$404$	−44.2813	−2.20308
$405$	0	0
$406$	−42.2262	−2.09565
$407$	39.7340	1.96954
$408$	5.57094	0.275803
$409$	−29.1922	−1.44346	−0.721730	−	0.692175i	$-0.756653\pi$
$409$	−29.1922	−1.44346	−0.721730	+	0.692175i	$0.756653\pi$
$410$	0	0
$411$	−12.2514	−0.604318
$412$	48.9805	2.41310
$413$	29.7494	1.46387
$414$	−32.9947	−1.62160
$415$	0	0
$416$	17.7653	0.871018
$417$	−16.5915	−0.812487
$418$	−32.4247	−1.58594
$419$	−28.0209	−1.36891	−0.684454	−	0.729056i	$-0.739960\pi$
$419$	−28.0209	−1.36891	−0.684454	+	0.729056i	$0.739960\pi$
$420$	0	0
$421$	−30.7552	−1.49892	−0.749459	−	0.662051i	$-0.769686\pi$
$421$	−30.7552	−1.49892	−0.749459	+	0.662051i	$0.769686\pi$
$422$	−6.42363	−0.312697
$423$	−2.61517	−0.127154
$424$	−1.18617	−0.0576057
$425$	0	0
$426$	14.6016	0.707450
$427$	−2.20016	−0.106473
$428$	−23.3078	−1.12662
$429$	9.95123	0.480450
$430$	0	0
$431$	−26.9481	−1.29804	−0.649021	−	0.760770i	$-0.724821\pi$
$431$	−26.9481	−1.29804	−0.649021	+	0.760770i	$0.724821\pi$
$432$	3.78247	0.181984
$433$	9.45517	0.454386	0.227193	−	0.973850i	$-0.427045\pi$
$433$	9.45517	0.454386	0.227193	+	0.973850i	$0.427045\pi$
$434$	−8.23043	−0.395073
$435$	0	0
$436$	−19.9303	−0.954486
$437$	−17.3130	−0.828192
$438$	16.3831	0.782817
$439$	−20.3379	−0.970673	−0.485337	−	0.874327i	$-0.661303\pi$
$439$	−20.3379	−0.970673	−0.485337	+	0.874327i	$0.661303\pi$
$440$	0	0
$441$	−15.9457	−0.759318
$442$	19.7841	0.941033
$443$	−13.6821	−0.650056	−0.325028	−	0.945704i	$-0.605374\pi$
$443$	−13.6821	−0.650056	−0.325028	+	0.945704i	$0.605374\pi$
$444$	17.6624	0.838219
$445$	0	0
$446$	20.3907	0.965526
$447$	−3.60755	−0.170631
$448$	47.8280	2.25966
$449$	41.1092	1.94006	0.970031	−	0.242980i	$-0.0781250\pi$
$449$	41.1092	1.94006	0.970031	+	0.242980i	$0.0781250\pi$
$450$	0	0
$451$	−48.0328	−2.26178
$452$	−34.2403	−1.61053
$453$	14.4767	0.680175
$454$	10.3581	0.486130
$455$	0	0
$456$	−4.85471	−0.227343
$457$	16.6907	0.780760	0.390380	−	0.920654i	$-0.372344\pi$
$457$	16.6907	0.780760	0.390380	+	0.920654i	$0.372344\pi$
$458$	−58.5773	−2.73714
$459$	13.3489	0.623075
$460$	0	0
$461$	2.70160	0.125826	0.0629129	−	0.998019i	$-0.479961\pi$
$461$	2.70160	0.125826	0.0629129	+	0.998019i	$0.479961\pi$
$462$	30.6469	1.42582
$463$	−13.6205	−0.633000	−0.316500	−	0.948593i	$-0.602508\pi$
$463$	−13.6205	−0.633000	−0.316500	+	0.948593i	$0.602508\pi$
$464$	4.80532	0.223081
$465$	0	0
$466$	−10.6678	−0.494179
$467$	27.5703	1.27580	0.637901	−	0.770118i	$-0.279803\pi$
$467$	27.5703	1.27580	0.637901	+	0.770118i	$0.279803\pi$
$468$	−19.7553	−0.913190
$469$	45.8286	2.11617
$470$	0	0
$471$	11.0399	0.508692
$472$	18.4160	0.847665
$473$	−26.3875	−1.21330
$474$	3.98687	0.183123
$475$	0	0
$476$	36.6342	1.67913
$477$	−1.27805	−0.0585180
$478$	−1.51010	−0.0690704
$479$	5.41728	0.247522	0.123761	−	0.992312i	$-0.460504\pi$
$479$	5.41728	0.247522	0.123761	+	0.992312i	$0.460504\pi$
$480$	0	0
$481$	21.1270	0.963307
$482$	−9.28724	−0.423022
$483$	16.3637	0.744575
$484$	43.0128	1.95513
$485$	0	0
$486$	−34.3701	−1.55906
$487$	−1.23959	−0.0561714	−0.0280857	−	0.999606i	$-0.508941\pi$
$487$	−1.23959	−0.0561714	−0.0280857	+	0.999606i	$0.508941\pi$
$488$	−1.36198	−0.0616539
$489$	8.00067	0.361803
$490$	0	0
$491$	19.0450	0.859487	0.429743	−	0.902951i	$-0.358604\pi$
$491$	19.0450	0.859487	0.429743	+	0.902951i	$0.358604\pi$
$492$	−21.3513	−0.962591
$493$	16.9587	0.763782
$494$	−17.2405	−0.775689
$495$	0	0
$496$	0.936618	0.0420554
$497$	32.3415	1.45071
$498$	−4.83486	−0.216655
$499$	3.81671	0.170859	0.0854296	−	0.996344i	$-0.472774\pi$
$499$	3.81671	0.170859	0.0854296	+	0.996344i	$0.472774\pi$
$500$	0	0
$501$	−12.0316	−0.537533
$502$	−51.7068	−2.30779
$503$	−30.4237	−1.35653	−0.678263	−	0.734819i	$-0.737267\pi$
$503$	−30.4237	−1.35653	−0.678263	+	0.734819i	$0.737267\pi$
$504$	−20.4925	−0.912808
$505$	0	0
$506$	67.6568	3.00771
$507$	−4.33976	−0.192736
$508$	33.6769	1.49417
$509$	9.97990	0.442351	0.221176	−	0.975234i	$-0.429011\pi$
$509$	9.97990	0.442351	0.221176	+	0.975234i	$0.429011\pi$
$510$	0	0
$511$	36.2875	1.60526
$512$	−10.4877	−0.463495
$513$	−11.6327	−0.513597
$514$	61.3539	2.70620
$515$	0	0
$516$	−11.7296	−0.516368
$517$	5.36251	0.235843
$518$	65.0649	2.85879
$519$	2.94301	0.129184
$520$	0	0
$521$	8.27726	0.362633	0.181317	−	0.983425i	$-0.441964\pi$
$521$	8.27726	0.362633	0.181317	+	0.983425i	$0.441964\pi$
$522$	−28.1644	−1.23272
$523$	28.3888	1.24136	0.620678	−	0.784066i	$-0.286857\pi$
$523$	28.3888	1.24136	0.620678	+	0.784066i	$0.286857\pi$
$524$	−5.83459	−0.254885
$525$	0	0
$526$	−29.4121	−1.28243
$527$	3.30547	0.143988
$528$	−3.48760	−0.151778
$529$	13.1250	0.570650
$530$	0	0
$531$	19.8425	0.861090
$532$	−31.9243	−1.38409
$533$	−25.5395	−1.10624
$534$	12.7080	0.549928
$535$	0	0
$536$	28.3696	1.22538
$537$	18.3765	0.793004
$538$	−52.7235	−2.27307
$539$	32.6972	1.40837
$540$	0	0
$541$	−3.10137	−0.133338	−0.0666691	−	0.997775i	$-0.521237\pi$
$541$	−3.10137	−0.133338	−0.0666691	+	0.997775i	$0.521237\pi$
$542$	−47.4992	−2.04027
$543$	−11.8060	−0.506642
$544$	−21.9732	−0.942093
$545$	0	0
$546$	16.2952	0.697372
$547$	−35.4405	−1.51533	−0.757663	−	0.652646i	$-0.773659\pi$
$547$	−35.4405	−1.51533	−0.757663	+	0.652646i	$0.773659\pi$
$548$	−49.8726	−2.13045
$549$	−1.46748	−0.0626303
$550$	0	0
$551$	−14.7784	−0.629582
$552$	10.1298	0.431151
$553$	8.83061	0.375516
$554$	−7.08319	−0.300936
$555$	0	0
$556$	−67.5398	−2.86432
$557$	−11.6471	−0.493505	−0.246752	−	0.969079i	$-0.579363\pi$
$557$	−11.6471	−0.493505	−0.246752	+	0.969079i	$0.579363\pi$
$558$	−5.48959	−0.232393
$559$	−14.0305	−0.593426
$560$	0	0
$561$	−12.3083	−0.519655
$562$	−49.2514	−2.07755
$563$	31.6878	1.33548	0.667741	−	0.744394i	$-0.267261\pi$
$563$	31.6878	1.33548	0.667741	+	0.744394i	$0.267261\pi$
$564$	2.38372	0.100373
$565$	0	0
$566$	35.0786	1.47446
$567$	−16.0288	−0.673147
$568$	20.0206	0.840045
$569$	−29.7931	−1.24899	−0.624495	−	0.781028i	$-0.714695\pi$
$569$	−29.7931	−1.24899	−0.624495	+	0.781028i	$0.714695\pi$
$570$	0	0
$571$	35.6580	1.49224	0.746121	−	0.665810i	$-0.231914\pi$
$571$	35.6580	1.49224	0.746121	+	0.665810i	$0.231914\pi$
$572$	40.5091	1.69377
$573$	16.6778	0.696725
$574$	−78.6542	−3.28296
$575$	0	0
$576$	31.9006	1.32919
$577$	−6.76735	−0.281728	−0.140864	−	0.990029i	$-0.544988\pi$
$577$	−6.76735	−0.281728	−0.140864	+	0.990029i	$0.544988\pi$
$578$	13.6030	0.565811
$579$	−14.0986	−0.585916
$580$	0	0
$581$	−10.7089	−0.444278
$582$	−24.0953	−0.998781
$583$	2.62070	0.108538
$584$	22.4633	0.929538
$585$	0	0
$586$	65.3547	2.69978
$587$	−1.89702	−0.0782982	−0.0391491	−	0.999233i	$-0.512465\pi$
$587$	−1.89702	−0.0782982	−0.0391491	+	0.999233i	$0.512465\pi$
$588$	14.5344	0.599389
$589$	−2.88050	−0.118689
$590$	0	0
$591$	0.945864	0.0389076
$592$	−7.40434	−0.304317
$593$	−24.2080	−0.994103	−0.497051	−	0.867721i	$-0.665584\pi$
$593$	−24.2080	−0.994103	−0.497051	+	0.867721i	$0.665584\pi$
$594$	45.4592	1.86521
$595$	0	0
$596$	−14.6855	−0.601541
$597$	6.82605	0.279372
$598$	35.9738	1.47108
$599$	43.2713	1.76802	0.884009	−	0.467469i	$-0.154834\pi$
$599$	43.2713	1.76802	0.884009	+	0.467469i	$0.154834\pi$
$600$	0	0
$601$	4.08692	0.166709	0.0833545	−	0.996520i	$-0.473437\pi$
$601$	4.08692	0.166709	0.0833545	+	0.996520i	$0.473437\pi$
$602$	−43.2098	−1.76110
$603$	30.5671	1.24479
$604$	58.9312	2.39788
$605$	0	0
$606$	24.3621	0.989642
$607$	−0.641570	−0.0260405	−0.0130203	−	0.999915i	$-0.504145\pi$
$607$	−0.641570	−0.0260405	−0.0130203	+	0.999915i	$0.504145\pi$
$608$	19.1482	0.776563
$609$	13.9681	0.566017
$610$	0	0
$611$	2.85130	0.115351
$612$	24.4345	0.987707
$613$	16.9855	0.686038	0.343019	−	0.939328i	$-0.388550\pi$
$613$	16.9855	0.686038	0.343019	+	0.939328i	$0.388550\pi$
$614$	−43.2601	−1.74584
$615$	0	0
$616$	42.0206	1.69306
$617$	−12.1444	−0.488915	−0.244457	−	0.969660i	$-0.578610\pi$
$617$	−12.1444	−0.488915	−0.244457	+	0.969660i	$0.578610\pi$
$618$	−26.9474	−1.08399
$619$	7.09579	0.285204	0.142602	−	0.989780i	$-0.454453\pi$
$619$	7.09579	0.285204	0.142602	+	0.989780i	$0.454453\pi$
$620$	0	0
$621$	24.2726	0.974028
$622$	−13.7940	−0.553088
$623$	28.1472	1.12770
$624$	−1.85439	−0.0742350
$625$	0	0
$626$	−45.2037	−1.80670
$627$	10.7258	0.428349
$628$	44.9408	1.79333
$629$	−26.1311	−1.04191
$630$	0	0
$631$	−34.4872	−1.37291	−0.686457	−	0.727171i	$-0.740835\pi$
$631$	−34.4872	−1.37291	−0.686457	+	0.727171i	$0.740835\pi$
$632$	5.46648	0.217445
$633$	2.12489	0.0844567
$634$	−56.4574	−2.24221
$635$	0	0
$636$	1.16494	0.0461928
$637$	17.3854	0.688836
$638$	57.7521	2.28643
$639$	21.5713	0.853349
$640$	0	0
$641$	−20.5382	−0.811211	−0.405605	−	0.914048i	$-0.632939\pi$
$641$	−20.5382	−0.811211	−0.405605	+	0.914048i	$0.632939\pi$
$642$	12.8231	0.506089
$643$	32.3455	1.27558	0.637792	−	0.770209i	$-0.279848\pi$
$643$	32.3455	1.27558	0.637792	+	0.770209i	$0.279848\pi$
$644$	66.6127	2.62491
$645$	0	0
$646$	21.3241	0.838985
$647$	−23.1202	−0.908948	−0.454474	−	0.890760i	$-0.650173\pi$
$647$	−23.1202	−0.908948	−0.454474	+	0.890760i	$0.650173\pi$
$648$	−9.92245	−0.389790
$649$	−40.6877	−1.59713
$650$	0	0
$651$	2.72256	0.106706
$652$	32.5688	1.27549
$653$	7.05761	0.276186	0.138093	−	0.990419i	$-0.455903\pi$
$653$	7.05761	0.276186	0.138093	+	0.990419i	$0.455903\pi$
$654$	10.9650	0.428764
$655$	0	0
$656$	8.95080	0.349470
$657$	24.2033	0.944259
$658$	8.78117	0.342326
$659$	−13.8853	−0.540896	−0.270448	−	0.962735i	$-0.587172\pi$
$659$	−13.8853	−0.540896	−0.270448	+	0.962735i	$0.587172\pi$
$660$	0	0
$661$	−10.1962	−0.396584	−0.198292	−	0.980143i	$-0.563539\pi$
$661$	−10.1962	−0.396584	−0.198292	+	0.980143i	$0.563539\pi$
$662$	39.6234	1.54001
$663$	−6.54442	−0.254164
$664$	−6.62919	−0.257262
$665$	0	0
$666$	43.3974	1.68162
$667$	30.8364	1.19399
$668$	−48.9778	−1.89501
$669$	−6.74508	−0.260780
$670$	0	0
$671$	3.00912	0.116166
$672$	−18.0983	−0.698158
$673$	−23.9562	−0.923445	−0.461722	−	0.887025i	$-0.652768\pi$
$673$	−23.9562	−0.923445	−0.461722	+	0.887025i	$0.652768\pi$
$674$	6.48290	0.249712
$675$	0	0
$676$	−17.6661	−0.679466
$677$	−9.99786	−0.384249	−0.192124	−	0.981371i	$-0.561538\pi$
$677$	−9.99786	−0.384249	−0.192124	+	0.981371i	$0.561538\pi$
$678$	18.8379	0.723465
$679$	−53.3692	−2.04812
$680$	0	0
$681$	−3.42638	−0.131299
$682$	11.2566	0.431038
$683$	−37.6974	−1.44245	−0.721226	−	0.692700i	$-0.756421\pi$
$683$	−37.6974	−1.44245	−0.721226	+	0.692700i	$0.756421\pi$
$684$	−21.2931	−0.814162
$685$	0	0
$686$	−4.07097	−0.155430
$687$	19.3769	0.739275
$688$	4.91724	0.187468
$689$	1.39345	0.0530862
$690$	0	0
$691$	−32.1264	−1.22214	−0.611072	−	0.791575i	$-0.709261\pi$
$691$	−32.1264	−1.22214	−0.611072	+	0.791575i	$0.709261\pi$
$692$	11.9803	0.455422
$693$	45.2754	1.71987
$694$	15.4461	0.586324
$695$	0	0
$696$	8.64679	0.327756
$697$	31.5887	1.19651
$698$	32.8529	1.24350
$699$	3.52884	0.133473
$700$	0	0
$701$	−27.8813	−1.05306	−0.526530	−	0.850156i	$-0.676507\pi$
$701$	−27.8813	−1.05306	−0.526530	+	0.850156i	$0.676507\pi$
$702$	24.1711	0.912279
$703$	22.7715	0.858844
$704$	−65.4135	−2.46536
$705$	0	0
$706$	−23.6430	−0.889816
$707$	53.9602	2.02938
$708$	−18.0863	−0.679725
$709$	30.4246	1.14262	0.571310	−	0.820734i	$-0.306435\pi$
$709$	30.4246	1.14262	0.571310	+	0.820734i	$0.306435\pi$
$710$	0	0
$711$	5.88991	0.220889
$712$	17.4242	0.653000
$713$	6.01040	0.225091
$714$	−20.1549	−0.754278
$715$	0	0
$716$	74.8063	2.79564
$717$	0.499530	0.0186553
$718$	−45.7392	−1.70697
$719$	25.7714	0.961111	0.480556	−	0.876964i	$-0.340435\pi$
$719$	25.7714	0.961111	0.480556	+	0.876964i	$0.340435\pi$
$720$	0	0
$721$	−59.6866	−2.22284
$722$	23.9697	0.892061
$723$	3.07215	0.114254
$724$	−48.0592	−1.78611
$725$	0	0
$726$	−23.6642	−0.878261
$727$	−2.49622	−0.0925795	−0.0462898	−	0.998928i	$-0.514740\pi$
$727$	−2.49622	−0.0925795	−0.0462898	+	0.998928i	$0.514740\pi$
$728$	22.3428	0.828078
$729$	−1.71550	−0.0635370
$730$	0	0
$731$	17.3537	0.641850
$732$	1.33760	0.0494390
$733$	−45.2444	−1.67114	−0.835569	−	0.549385i	$-0.814862\pi$
$733$	−45.2444	−1.67114	−0.835569	+	0.549385i	$0.814862\pi$
$734$	−33.6316	−1.24136
$735$	0	0
$736$	−39.9543	−1.47274
$737$	−62.6789	−2.30881
$738$	−52.4613	−1.93113
$739$	8.57134	0.315302	0.157651	−	0.987495i	$-0.449608\pi$
$739$	8.57134	0.315302	0.157651	+	0.987495i	$0.449608\pi$
$740$	0	0
$741$	5.70304	0.209506
$742$	4.29142	0.157543
$743$	5.94817	0.218217	0.109109	−	0.994030i	$-0.465200\pi$
$743$	5.94817	0.218217	0.109109	+	0.994030i	$0.465200\pi$
$744$	1.68537	0.0617887
$745$	0	0
$746$	43.1057	1.57821
$747$	−7.14267	−0.261337
$748$	−50.1039	−1.83198
$749$	28.4023	1.03780
$750$	0	0
$751$	46.7694	1.70664	0.853319	−	0.521388i	$-0.174586\pi$
$751$	46.7694	1.70664	0.853319	+	0.521388i	$0.174586\pi$
$752$	−0.999291	−0.0364404
$753$	17.1042	0.623313
$754$	30.7074	1.11830
$755$	0	0
$756$	44.7576	1.62782
$757$	45.3088	1.64678	0.823388	−	0.567479i	$-0.192081\pi$
$757$	45.3088	1.64678	0.823388	+	0.567479i	$0.192081\pi$
$758$	−7.27796	−0.264348
$759$	−22.3804	−0.812356
$760$	0	0
$761$	−34.2873	−1.24291	−0.621457	−	0.783448i	$-0.713459\pi$
$761$	−34.2873	−1.24291	−0.621457	+	0.783448i	$0.713459\pi$
$762$	−18.5279	−0.671195
$763$	24.2866	0.879233
$764$	67.8913	2.45622
$765$	0	0
$766$	−4.52167	−0.163375
$767$	−21.6341	−0.781161
$768$	−7.01833	−0.253252
$769$	38.2808	1.38044	0.690220	−	0.723600i	$-0.257514\pi$
$769$	38.2808	1.38044	0.690220	+	0.723600i	$0.257514\pi$
$770$	0	0
$771$	−20.2954	−0.730921
$772$	−57.3918	−2.06558
$773$	3.17845	0.114321	0.0571604	−	0.998365i	$-0.481795\pi$
$773$	3.17845	0.114321	0.0571604	+	0.998365i	$0.481795\pi$
$774$	−28.8204	−1.03593
$775$	0	0
$776$	−33.0375	−1.18598
$777$	−21.5230	−0.772132
$778$	34.2635	1.22841
$779$	−27.5275	−0.986276
$780$	0	0
$781$	−44.2329	−1.58278
$782$	−44.4945	−1.59112
$783$	20.7192	0.740444
$784$	−6.09305	−0.217609
$785$	0	0
$786$	3.20999	0.114497
$787$	−9.42277	−0.335886	−0.167943	−	0.985797i	$-0.553712\pi$
$787$	−9.42277	−0.335886	−0.167943	+	0.985797i	$0.553712\pi$
$788$	3.85038	0.137164
$789$	9.72930	0.346372
$790$	0	0
$791$	41.7245	1.48355
$792$	28.0272	0.995903
$793$	1.59998	0.0568168
$794$	31.7609	1.12715
$795$	0	0
$796$	27.7872	0.984891
$797$	8.28600	0.293505	0.146753	−	0.989173i	$-0.453118\pi$
$797$	8.28600	0.293505	0.146753	+	0.989173i	$0.453118\pi$
$798$	17.5637	0.621748
$799$	−3.52665	−0.124764
$800$	0	0
$801$	18.7738	0.663341
$802$	14.7804	0.521914
$803$	−49.6297	−1.75139
$804$	−27.8617	−0.982607
$805$	0	0
$806$	5.98526	0.210822
$807$	17.4405	0.613936
$808$	33.4034	1.17513
$809$	−41.8918	−1.47284	−0.736418	−	0.676526i	$-0.763484\pi$
$809$	−41.8918	−1.47284	−0.736418	+	0.676526i	$0.763484\pi$
$810$	0	0
$811$	−33.5938	−1.17964	−0.589820	−	0.807535i	$-0.700801\pi$
$811$	−33.5938	−1.17964	−0.589820	+	0.807535i	$0.700801\pi$
$812$	56.8608	1.99542
$813$	15.7124	0.551057
$814$	−88.9881	−3.11903
$815$	0	0
$816$	2.29362	0.0802926
$817$	−15.1226	−0.529074
$818$	65.3786	2.28591
$819$	24.0734	0.841193
$820$	0	0
$821$	−30.9932	−1.08167	−0.540836	−	0.841128i	$-0.681892\pi$
$821$	−30.9932	−1.08167	−0.540836	+	0.841128i	$0.681892\pi$
$822$	27.4382	0.957018
$823$	−9.48741	−0.330710	−0.165355	−	0.986234i	$-0.552877\pi$
$823$	−9.48741	−0.330710	−0.165355	+	0.986234i	$0.552877\pi$
$824$	−36.9482	−1.28715
$825$	0	0
$826$	−66.6266	−2.31824
$827$	4.97893	0.173134	0.0865671	−	0.996246i	$-0.472410\pi$
$827$	4.97893	0.173134	0.0865671	+	0.996246i	$0.472410\pi$
$828$	44.4298	1.54404
$829$	−28.0734	−0.975030	−0.487515	−	0.873115i	$-0.662096\pi$
$829$	−28.0734	−0.975030	−0.487515	+	0.873115i	$0.662096\pi$
$830$	0	0
$831$	2.34306	0.0812800
$832$	−34.7810	−1.20581
$833$	−21.5033	−0.745046
$834$	37.1581	1.28668
$835$	0	0
$836$	43.6623	1.51009
$837$	4.03844	0.139589
$838$	62.7554	2.16785
$839$	0.672364	0.0232126	0.0116063	−	0.999933i	$-0.496306\pi$
$839$	0.672364	0.0232126	0.0116063	+	0.999933i	$0.496306\pi$
$840$	0	0
$841$	−2.67797	−0.0923438
$842$	68.8792	2.37373
$843$	16.2920	0.561126
$844$	8.64990	0.297742
$845$	0	0
$846$	5.85693	0.201365
$847$	−52.4144	−1.80098
$848$	−0.488361	−0.0167704
$849$	−11.6037	−0.398239
$850$	0	0
$851$	−47.5146	−1.62878
$852$	−19.6622	−0.673615
$853$	−22.9459	−0.785652	−0.392826	−	0.919613i	$-0.628502\pi$
$853$	−22.9459	−0.785652	−0.392826	+	0.919613i	$0.628502\pi$
$854$	4.92746	0.168614
$855$	0	0
$856$	17.5821	0.600944
$857$	30.7670	1.05098	0.525491	−	0.850799i	$-0.323882\pi$
$857$	30.7670	1.05098	0.525491	+	0.850799i	$0.323882\pi$
$858$	−22.2867	−0.760856
$859$	7.20222	0.245737	0.122868	−	0.992423i	$-0.460791\pi$
$859$	7.20222	0.245737	0.122868	+	0.992423i	$0.460791\pi$
$860$	0	0
$861$	26.0182	0.886698
$862$	60.3527	2.05562
$863$	−15.3436	−0.522303	−0.261152	−	0.965298i	$-0.584102\pi$
$863$	−15.3436	−0.522303	−0.261152	+	0.965298i	$0.584102\pi$
$864$	−26.8456	−0.913307
$865$	0	0
$866$	−21.1757	−0.719581
$867$	−4.49977	−0.152820
$868$	11.0829	0.376178
$869$	−12.0775	−0.409700
$870$	0	0
$871$	−33.3270	−1.12924
$872$	15.0343	0.509125
$873$	−35.5966	−1.20476
$874$	38.7740	1.31155
$875$	0	0
$876$	−22.0611	−0.745377
$877$	2.70184	0.0912348	0.0456174	−	0.998959i	$-0.485474\pi$
$877$	2.70184	0.0912348	0.0456174	+	0.998959i	$0.485474\pi$
$878$	45.5486	1.53719
$879$	−21.6188	−0.729186
$880$	0	0
$881$	21.5020	0.724420	0.362210	−	0.932097i	$-0.382022\pi$
$881$	21.5020	0.724420	0.362210	+	0.932097i	$0.382022\pi$
$882$	35.7119	1.20248
$883$	−15.4417	−0.519653	−0.259827	−	0.965655i	$-0.583665\pi$
$883$	−15.4417	−0.519653	−0.259827	+	0.965655i	$0.583665\pi$
$884$	−26.6408	−0.896026
$885$	0	0
$886$	30.6424	1.02945
$887$	−41.1908	−1.38305	−0.691526	−	0.722352i	$-0.743061\pi$
$887$	−41.1908	−1.38305	−0.691526	+	0.722352i	$0.743061\pi$
$888$	−13.3235	−0.447108
$889$	−41.0379	−1.37637
$890$	0	0
$891$	21.9223	0.734426
$892$	−27.4576	−0.919347
$893$	3.07325	0.102842
$894$	8.07946	0.270217
$895$	0	0
$896$	−58.2564	−1.94621
$897$	−11.8999	−0.397325
$898$	−92.0679	−3.07235
$899$	5.13050	0.171112
$900$	0	0
$901$	−1.72350	−0.0574181
$902$	107.574	3.58182
$903$	14.2935	0.475657
$904$	25.8290	0.859061
$905$	0	0
$906$	−32.4220	−1.07715
$907$	36.5292	1.21293	0.606466	−	0.795109i	$-0.292587\pi$
$907$	36.5292	1.21293	0.606466	+	0.795109i	$0.292587\pi$
$908$	−13.9480	−0.462880
$909$	35.9908	1.19374
$910$	0	0
$911$	−32.2943	−1.06996	−0.534979	−	0.844865i	$-0.679680\pi$
$911$	−32.2943	−1.06996	−0.534979	+	0.844865i	$0.679680\pi$
$912$	−1.99874	−0.0661848
$913$	14.6463	0.484723
$914$	−37.3805	−1.23644
$915$	0	0
$916$	78.8787	2.60623
$917$	7.10990	0.234789
$918$	−29.8962	−0.986721
$919$	9.06037	0.298874	0.149437	−	0.988771i	$-0.452254\pi$
$919$	9.06037	0.298874	0.149437	+	0.988771i	$0.452254\pi$
$920$	0	0
$921$	14.3101	0.471534
$922$	−6.05048	−0.199262
$923$	−23.5190	−0.774139
$924$	−41.2683	−1.35763
$925$	0	0
$926$	30.5045	1.00244
$927$	−39.8102	−1.30754
$928$	−34.1051	−1.11956
$929$	−23.6578	−0.776188	−0.388094	−	0.921620i	$-0.626866\pi$
$929$	−23.6578	−0.776188	−0.388094	+	0.921620i	$0.626866\pi$
$930$	0	0
$931$	18.7387	0.614138
$932$	14.3651	0.470543
$933$	4.56294	0.149384
$934$	−61.7463	−2.02040
$935$	0	0
$936$	14.9023	0.487098
$937$	−35.7122	−1.16667	−0.583334	−	0.812232i	$-0.698252\pi$
$937$	−35.7122	−1.16667	−0.583334	+	0.812232i	$0.698252\pi$
$938$	−102.637	−3.35123
$939$	14.9530	0.487974
$940$	0	0
$941$	−41.9221	−1.36662	−0.683311	−	0.730128i	$-0.739460\pi$
$941$	−41.9221	−1.36662	−0.683311	+	0.730128i	$0.739460\pi$
$942$	−24.7249	−0.805582
$943$	57.4385	1.87045
$944$	7.58207	0.246775
$945$	0	0
$946$	59.0972	1.92142
$947$	−42.0893	−1.36772	−0.683859	−	0.729614i	$-0.739700\pi$
$947$	−42.0893	−1.36772	−0.683859	+	0.729614i	$0.739700\pi$
$948$	−5.36862	−0.174365
$949$	−26.3886	−0.856611
$950$	0	0
$951$	18.6757	0.605600
$952$	−27.6348	−0.895650
$953$	−34.6630	−1.12284	−0.561422	−	0.827530i	$-0.689746\pi$
$953$	−34.6630	−1.12284	−0.561422	+	0.827530i	$0.689746\pi$
$954$	2.86232	0.0926710
$955$	0	0
$956$	2.03347	0.0657670
$957$	−19.1040	−0.617543
$958$	−12.1325	−0.391984
$959$	60.7736	1.96248
$960$	0	0
$961$	1.00000	0.0322581
$962$	−47.3158	−1.52552
$963$	18.9440	0.610461
$964$	12.5060	0.402790
$965$	0	0
$966$	−36.6481	−1.17913
$967$	25.6742	0.825628	0.412814	−	0.910815i	$-0.364546\pi$
$967$	25.6742	0.825628	0.412814	+	0.910815i	$0.364546\pi$
$968$	−32.4465	−1.04287
$969$	−7.05385	−0.226602
$970$	0	0
$971$	22.5664	0.724192	0.362096	−	0.932141i	$-0.382061\pi$
$971$	22.5664	0.724192	0.362096	+	0.932141i	$0.382061\pi$
$972$	46.2820	1.48449
$973$	82.3025	2.63850
$974$	2.77619	0.0889548
$975$	0	0
$976$	−0.560741	−0.0179489
$977$	−19.5130	−0.624275	−0.312138	−	0.950037i	$-0.601045\pi$
$977$	−19.5130	−0.624275	−0.312138	+	0.950037i	$0.601045\pi$
$978$	−17.9183	−0.572963
$979$	−38.4965	−1.23035
$980$	0	0
$981$	16.1988	0.517189
$982$	−42.6530	−1.36111
$983$	39.3717	1.25576	0.627882	−	0.778309i	$-0.283922\pi$
$983$	39.3717	1.25576	0.627882	+	0.778309i	$0.283922\pi$
$984$	16.1063	0.513449
$985$	0	0
$986$	−37.9806	−1.20955
$987$	−2.90474	−0.0924590
$988$	23.2157	0.738589
$989$	31.5546	1.00338
$990$	0	0
$991$	28.1540	0.894342	0.447171	−	0.894448i	$-0.352432\pi$
$991$	28.1540	0.894342	0.447171	+	0.894448i	$0.352432\pi$
$992$	−6.64753	−0.211059
$993$	−13.1071	−0.415942
$994$	−72.4318	−2.29740
$995$	0	0
$996$	6.51051	0.206293
$997$	38.7855	1.22835	0.614175	−	0.789170i	$-0.289489\pi$
$997$	38.7855	1.22835	0.614175	+	0.789170i	$0.289489\pi$
$998$	−8.54787	−0.270578
$999$	−31.9255	−1.01008

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.h.1.2	✓	5
3.2	odd	2		6975.2.a.by.1.4		5
5.2	odd	4		775.2.b.g.249.2		10
5.3	odd	4		775.2.b.g.249.9		10
5.4	even	2		775.2.a.k.1.4	yes	5
15.14	odd	2		6975.2.a.bp.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
775.2.a.h.1.2	✓	5	1.1	even	1	trivial
775.2.a.k.1.4	yes	5	5.4	even	2
775.2.b.g.249.2		10	5.2	odd	4
775.2.b.g.249.9		10	5.3	odd	4
6975.2.a.bp.1.2		5	15.14	odd	2
6975.2.a.by.1.4		5	3.2	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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23959 q^{2} +0.740841 q^{3} +3.01578 q^{4} -1.65918 q^{6} -3.67497 q^{7} -2.27494 q^{8} -2.45115 q^{9} +O(q^{10})\)	\(q-2.23959 q^{2} +0.740841 q^{3} +3.01578 q^{4} -1.65918 q^{6} -3.67497 q^{7} -2.27494 q^{8} -2.45115 q^{9} +5.02619 q^{11} +2.23422 q^{12} +2.67247 q^{13} +8.23043 q^{14} -0.936618 q^{16} -3.30547 q^{17} +5.48959 q^{18} +2.88050 q^{19} -2.72256 q^{21} -11.2566 q^{22} -6.01040 q^{23} -1.68537 q^{24} -5.98526 q^{26} -4.03844 q^{27} -11.0829 q^{28} -5.13050 q^{29} -1.00000 q^{31} +6.64753 q^{32} +3.72360 q^{33} +7.40291 q^{34} -7.39215 q^{36} +7.90540 q^{37} -6.45115 q^{38} +1.97988 q^{39} -9.55651 q^{41} +6.09744 q^{42} -5.25000 q^{43} +15.1579 q^{44} +13.4609 q^{46} +1.06691 q^{47} -0.693885 q^{48} +6.50538 q^{49} -2.44883 q^{51} +8.05960 q^{52} +0.521408 q^{53} +9.04446 q^{54} +8.36034 q^{56} +2.13399 q^{57} +11.4902 q^{58} -8.09515 q^{59} +0.598687 q^{61} +2.23959 q^{62} +9.00791 q^{63} -13.0145 q^{64} -8.33936 q^{66} -12.4705 q^{67} -9.96858 q^{68} -4.45275 q^{69} -8.80048 q^{71} +5.57624 q^{72} -9.87423 q^{73} -17.7049 q^{74} +8.68697 q^{76} -18.4711 q^{77} -4.43412 q^{78} -2.40291 q^{79} +4.36163 q^{81} +21.4027 q^{82} +2.91400 q^{83} -8.21067 q^{84} +11.7579 q^{86} -3.80088 q^{87} -11.4343 q^{88} -7.65918 q^{89} -9.82125 q^{91} -18.1261 q^{92} -0.740841 q^{93} -2.38946 q^{94} +4.92476 q^{96} +14.5224 q^{97} -14.5694 q^{98} -12.3200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9}+O(q^{10}) \) 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9	\( 5 q - 4 q^{2} - 3 q^{3} + 6 q^{4} - q^{6} - 2 q^{7} - 9 q^{8} + 6 q^{9} - 2 q^{11} - 5 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 19 q^{17} - 5 q^{18} + 8 q^{19} - 15 q^{21} + 10 q^{22} - 12 q^{23} + 26 q^{24} - 16 q^{26} - 6 q^{27} - 6 q^{28} + 6 q^{29} - 5 q^{31} - 7 q^{32} - 3 q^{33} + 31 q^{34} - 13 q^{36} - 16 q^{37} - 14 q^{38} - 13 q^{39} - 2 q^{41} + 22 q^{42} - q^{43} - 4 q^{44} - 11 q^{46} - 8 q^{47} - 31 q^{48} - 9 q^{49} + 5 q^{51} + 26 q^{52} - 3 q^{53} + 10 q^{54} - 9 q^{56} - 14 q^{57} - 5 q^{58} - 4 q^{59} - 5 q^{61} + 4 q^{62} + 26 q^{63} - 5 q^{64} - 25 q^{66} - 13 q^{67} - 30 q^{68} + 10 q^{69} + 6 q^{71} - 2 q^{72} - 19 q^{73} + 4 q^{74} - 5 q^{76} - 23 q^{77} + 38 q^{78} - 6 q^{79} - 7 q^{81} + 27 q^{82} - 18 q^{83} - 15 q^{84} - 7 q^{86} + 5 q^{87} + q^{88} - 31 q^{89} + 8 q^{91} + 16 q^{92} + 3 q^{93} - 14 q^{94} + 10 q^{96} + q^{97} - 10 q^{98} - 33 q^{99}+O(q^{100}) \) 5 * q - 4 * q^2 - 3 * q^3 + 6 * q^4 - q^6 - 2 * q^7 - 9 * q^8 + 6 * q^9 - 2 * q^11 - 5 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 19 * q^17 - 5 * q^18 + 8 * q^19 - 15 * q^21 + 10 * q^22 - 12 * q^23 + 26 * q^24 - 16 * q^26 - 6 * q^27 - 6 * q^28 + 6 * q^29 - 5 * q^31 - 7 * q^32 - 3 * q^33 + 31 * q^34 - 13 * q^36 - 16 * q^37 - 14 * q^38 - 13 * q^39 - 2 * q^41 + 22 * q^42 - q^43 - 4 * q^44 - 11 * q^46 - 8 * q^47 - 31 * q^48 - 9 * q^49 + 5 * q^51 + 26 * q^52 - 3 * q^53 + 10 * q^54 - 9 * q^56 - 14 * q^57 - 5 * q^58 - 4 * q^59 - 5 * q^61 + 4 * q^62 + 26 * q^63 - 5 * q^64 - 25 * q^66 - 13 * q^67 - 30 * q^68 + 10 * q^69 + 6 * q^71 - 2 * q^72 - 19 * q^73 + 4 * q^74 - 5 * q^76 - 23 * q^77 + 38 * q^78 - 6 * q^79 - 7 * q^81 + 27 * q^82 - 18 * q^83 - 15 * q^84 - 7 * q^86 + 5 * q^87 + q^88 - 31 * q^89 + 8 * q^91 + 16 * q^92 + 3 * q^93 - 14 * q^94 + 10 * q^96 + q^97 - 10 * q^98 - 33 * q^99

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