LMFDB - Embedded newform 8470.2.a.cn.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.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:	$67.6332905120$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.81361$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.10278 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.10278 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.62721 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.10278 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.10278 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.62721 q^{9} +1.00000 q^{10} +3.10278 q^{12} +1.00000 q^{14} +3.10278 q^{15} +1.00000 q^{16} +5.62721 q^{17} +6.62721 q^{18} -4.72999 q^{19} +1.00000 q^{20} +3.10278 q^{21} +4.52444 q^{23} +3.10278 q^{24} +1.00000 q^{25} +11.2544 q^{27} +1.00000 q^{28} -2.52444 q^{29} +3.10278 q^{30} -3.04888 q^{31} +1.00000 q^{32} +5.62721 q^{34} +1.00000 q^{35} +6.62721 q^{36} +4.52444 q^{37} -4.72999 q^{38} +1.00000 q^{40} -7.30833 q^{41} +3.10278 q^{42} +0.578337 q^{43} +6.62721 q^{45} +4.52444 q^{46} +11.8328 q^{47} +3.10278 q^{48} +1.00000 q^{49} +1.00000 q^{50} +17.4600 q^{51} -5.57331 q^{53} +11.2544 q^{54} +1.00000 q^{56} -14.6761 q^{57} -2.52444 q^{58} -7.62721 q^{59} +3.10278 q^{60} -9.83276 q^{61} -3.04888 q^{62} +6.62721 q^{63} +1.00000 q^{64} -13.2544 q^{67} +5.62721 q^{68} +14.0383 q^{69} +1.00000 q^{70} -8.41110 q^{71} +6.62721 q^{72} -4.57834 q^{73} +4.52444 q^{74} +3.10278 q^{75} -4.72999 q^{76} +9.77886 q^{79} +1.00000 q^{80} +15.0383 q^{81} -7.30833 q^{82} -7.25443 q^{83} +3.10278 q^{84} +5.62721 q^{85} +0.578337 q^{86} -7.83276 q^{87} +14.4111 q^{89} +6.62721 q^{90} +4.52444 q^{92} -9.45998 q^{93} +11.8328 q^{94} -4.72999 q^{95} +3.10278 q^{96} +16.5244 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} + 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 + 3 * q^7 + 3 * q^8 + 7 * q^9	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} + 3 q^{7} + 3 q^{8} + 7 q^{9} + 3 q^{10} + 2 q^{12} + 3 q^{14} + 2 q^{15} + 3 q^{16} + 4 q^{17} + 7 q^{18} + 6 q^{19} + 3 q^{20} + 2 q^{21} + 8 q^{23} + 2 q^{24} + 3 q^{25} + 8 q^{27} + 3 q^{28} - 2 q^{29} + 2 q^{30} + 2 q^{31} + 3 q^{32} + 4 q^{34} + 3 q^{35} + 7 q^{36} + 8 q^{37} + 6 q^{38} + 3 q^{40} + 2 q^{42} + 7 q^{45} + 8 q^{46} + 8 q^{47} + 2 q^{48} + 3 q^{49} + 3 q^{50} + 12 q^{51} + 8 q^{54} + 3 q^{56} - 20 q^{57} - 2 q^{58} - 10 q^{59} + 2 q^{60} - 2 q^{61} + 2 q^{62} + 7 q^{63} + 3 q^{64} - 14 q^{67} + 4 q^{68} + 3 q^{70} + 4 q^{71} + 7 q^{72} - 12 q^{73} + 8 q^{74} + 2 q^{75} + 6 q^{76} - 2 q^{79} + 3 q^{80} + 3 q^{81} + 4 q^{83} + 2 q^{84} + 4 q^{85} + 4 q^{87} + 14 q^{89} + 7 q^{90} + 8 q^{92} + 12 q^{93} + 8 q^{94} + 6 q^{95} + 2 q^{96} + 44 q^{97} + 3 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 + 3 * q^7 + 3 * q^8 + 7 * q^9 + 3 * q^10 + 2 * q^12 + 3 * q^14 + 2 * q^15 + 3 * q^16 + 4 * q^17 + 7 * q^18 + 6 * q^19 + 3 * q^20 + 2 * q^21 + 8 * q^23 + 2 * q^24 + 3 * q^25 + 8 * q^27 + 3 * q^28 - 2 * q^29 + 2 * q^30 + 2 * q^31 + 3 * q^32 + 4 * q^34 + 3 * q^35 + 7 * q^36 + 8 * q^37 + 6 * q^38 + 3 * q^40 + 2 * q^42 + 7 * q^45 + 8 * q^46 + 8 * q^47 + 2 * q^48 + 3 * q^49 + 3 * q^50 + 12 * q^51 + 8 * q^54 + 3 * q^56 - 20 * q^57 - 2 * q^58 - 10 * q^59 + 2 * q^60 - 2 * q^61 + 2 * q^62 + 7 * q^63 + 3 * q^64 - 14 * q^67 + 4 * q^68 + 3 * q^70 + 4 * q^71 + 7 * q^72 - 12 * q^73 + 8 * q^74 + 2 * q^75 + 6 * q^76 - 2 * q^79 + 3 * q^80 + 3 * q^81 + 4 * q^83 + 2 * q^84 + 4 * q^85 + 4 * q^87 + 14 * q^89 + 7 * q^90 + 8 * q^92 + 12 * q^93 + 8 * q^94 + 6 * q^95 + 2 * q^96 + 44 * q^97 + 3 * q^98

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	3.10278	1.79139	0.895694	−	0.444671i	$-0.146679\pi$
$3$	3.10278	1.79139	0.895694	+	0.444671i	$0.146679\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.10278	1.26670
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	6.62721	2.20907
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	3.10278	0.895694
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	1.00000	0.267261
$15$	3.10278	0.801133
$16$	1.00000	0.250000
$17$	5.62721	1.36480	0.682400	−	0.730979i	$-0.260936\pi$
$17$	5.62721	1.36480	0.682400	+	0.730979i	$0.260936\pi$
$18$	6.62721	1.56205
$19$	−4.72999	−1.08513	−0.542567	−	0.840013i	$-0.682547\pi$
$19$	−4.72999	−1.08513	−0.542567	+	0.840013i	$0.682547\pi$
$20$	1.00000	0.223607
$21$	3.10278	0.677081
$22$	0	0
$23$	4.52444	0.943411	0.471705	−	0.881756i	$-0.343639\pi$
$23$	4.52444	0.943411	0.471705	+	0.881756i	$0.343639\pi$
$24$	3.10278	0.633351
$25$	1.00000	0.200000
$26$	0	0
$27$	11.2544	2.16592
$28$	1.00000	0.188982
$29$	−2.52444	−0.468776	−0.234388	−	0.972143i	$-0.575309\pi$
$29$	−2.52444	−0.468776	−0.234388	+	0.972143i	$0.575309\pi$
$30$	3.10278	0.566487
$31$	−3.04888	−0.547594	−0.273797	−	0.961787i	$-0.588280\pi$
$31$	−3.04888	−0.547594	−0.273797	+	0.961787i	$0.588280\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	5.62721	0.965059
$35$	1.00000	0.169031
$36$	6.62721	1.10454
$37$	4.52444	0.743813	0.371907	−	0.928270i	$-0.378704\pi$
$37$	4.52444	0.743813	0.371907	+	0.928270i	$0.378704\pi$
$38$	−4.72999	−0.767305
$39$	0	0
$40$	1.00000	0.158114
$41$	−7.30833	−1.14137	−0.570684	−	0.821170i	$-0.693322\pi$
$41$	−7.30833	−1.14137	−0.570684	+	0.821170i	$0.693322\pi$
$42$	3.10278	0.478769
$43$	0.578337	0.0881956	0.0440978	−	0.999027i	$-0.485959\pi$
$43$	0.578337	0.0881956	0.0440978	+	0.999027i	$0.485959\pi$
$44$	0	0
$45$	6.62721	0.987927
$46$	4.52444	0.667092
$47$	11.8328	1.72599	0.862993	−	0.505216i	$-0.168587\pi$
$47$	11.8328	1.72599	0.862993	+	0.505216i	$0.168587\pi$
$48$	3.10278	0.447847
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	17.4600	2.44489
$52$	0	0
$53$	−5.57331	−0.765554	−0.382777	−	0.923841i	$-0.625032\pi$
$53$	−5.57331	−0.765554	−0.382777	+	0.923841i	$0.625032\pi$
$54$	11.2544	1.53153
$55$	0	0
$56$	1.00000	0.133631
$57$	−14.6761	−1.94390
$58$	−2.52444	−0.331475
$59$	−7.62721	−0.992979	−0.496489	−	0.868043i	$-0.665378\pi$
$59$	−7.62721	−0.992979	−0.496489	+	0.868043i	$0.665378\pi$
$60$	3.10278	0.400567
$61$	−9.83276	−1.25896	−0.629478	−	0.777018i	$-0.716731\pi$
$61$	−9.83276	−1.25896	−0.629478	+	0.777018i	$0.716731\pi$
$62$	−3.04888	−0.387208
$63$	6.62721	0.834950
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−13.2544	−1.61929	−0.809643	−	0.586923i	$-0.800339\pi$
$67$	−13.2544	−1.61929	−0.809643	+	0.586923i	$0.800339\pi$
$68$	5.62721	0.682400
$69$	14.0383	1.69001
$70$	1.00000	0.119523
$71$	−8.41110	−0.998214	−0.499107	−	0.866540i	$-0.666339\pi$
$71$	−8.41110	−0.998214	−0.499107	+	0.866540i	$0.666339\pi$
$72$	6.62721	0.781025
$73$	−4.57834	−0.535854	−0.267927	−	0.963439i	$-0.586339\pi$
$73$	−4.57834	−0.535854	−0.267927	+	0.963439i	$0.586339\pi$
$74$	4.52444	0.525955
$75$	3.10278	0.358278
$76$	−4.72999	−0.542567
$77$	0	0
$78$	0	0
$79$	9.77886	1.10021	0.550104	−	0.835096i	$-0.314588\pi$
$79$	9.77886	1.10021	0.550104	+	0.835096i	$0.314588\pi$
$80$	1.00000	0.111803
$81$	15.0383	1.67092
$82$	−7.30833	−0.807069
$83$	−7.25443	−0.796277	−0.398138	−	0.917325i	$-0.630344\pi$
$83$	−7.25443	−0.796277	−0.398138	+	0.917325i	$0.630344\pi$
$84$	3.10278	0.338541
$85$	5.62721	0.610357
$86$	0.578337	0.0623637
$87$	−7.83276	−0.839760
$88$	0	0
$89$	14.4111	1.52757	0.763787	−	0.645469i	$-0.223338\pi$
$89$	14.4111	1.52757	0.763787	+	0.645469i	$0.223338\pi$
$90$	6.62721	0.698570
$91$	0	0
$92$	4.52444	0.471705
$93$	−9.45998	−0.980954
$94$	11.8328	1.22046
$95$	−4.72999	−0.485287
$96$	3.10278	0.316676
$97$	16.5244	1.67780	0.838901	−	0.544284i	$-0.183198\pi$
$97$	16.5244	1.67780	0.838901	+	0.544284i	$0.183198\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−5.42166	−0.539476	−0.269738	−	0.962934i	$-0.586937\pi$
$101$	−5.42166	−0.539476	−0.269738	+	0.962934i	$0.586937\pi$
$102$	17.4600	1.72880
$103$	−5.62721	−0.554466	−0.277233	−	0.960803i	$-0.589417\pi$
$103$	−5.62721	−0.554466	−0.277233	+	0.960803i	$0.589417\pi$
$104$	0	0
$105$	3.10278	0.302800
$106$	−5.57331	−0.541328
$107$	−11.8328	−1.14392	−0.571958	−	0.820283i	$-0.693816\pi$
$107$	−11.8328	−1.14392	−0.571958	+	0.820283i	$0.693816\pi$
$108$	11.2544	1.08296
$109$	5.88666	0.563840	0.281920	−	0.959438i	$-0.409029\pi$
$109$	5.88666	0.563840	0.281920	+	0.959438i	$0.409029\pi$
$110$	0	0
$111$	14.0383	1.33246
$112$	1.00000	0.0944911
$113$	−5.25443	−0.494295	−0.247147	−	0.968978i	$-0.579493\pi$
$113$	−5.25443	−0.494295	−0.247147	+	0.968978i	$0.579493\pi$
$114$	−14.6761	−1.37454
$115$	4.52444	0.421906
$116$	−2.52444	−0.234388
$117$	0	0
$118$	−7.62721	−0.702142
$119$	5.62721	0.515846
$120$	3.10278	0.283243
$121$	0	0
$122$	−9.83276	−0.890217
$123$	−22.6761	−2.04463
$124$	−3.04888	−0.273797
$125$	1.00000	0.0894427
$126$	6.62721	0.590399
$127$	−20.7144	−1.83811	−0.919053	−	0.394134i	$-0.871045\pi$
$127$	−20.7144	−1.83811	−0.919053	+	0.394134i	$0.871045\pi$
$128$	1.00000	0.0883883
$129$	1.79445	0.157993
$130$	0	0
$131$	17.7789	1.55335	0.776673	−	0.629904i	$-0.216906\pi$
$131$	17.7789	1.55335	0.776673	+	0.629904i	$0.216906\pi$
$132$	0	0
$133$	−4.72999	−0.410142
$134$	−13.2544	−1.14501
$135$	11.2544	0.968627
$136$	5.62721	0.482530
$137$	−6.41110	−0.547737	−0.273869	−	0.961767i	$-0.588303\pi$
$137$	−6.41110	−0.547737	−0.273869	+	0.961767i	$0.588303\pi$
$138$	14.0383	1.19502
$139$	9.77886	0.829432	0.414716	−	0.909951i	$-0.363881\pi$
$139$	9.77886	0.829432	0.414716	+	0.909951i	$0.363881\pi$
$140$	1.00000	0.0845154
$141$	36.7144	3.09191
$142$	−8.41110	−0.705844
$143$	0	0
$144$	6.62721	0.552268
$145$	−2.52444	−0.209643
$146$	−4.57834	−0.378906
$147$	3.10278	0.255913
$148$	4.52444	0.371907
$149$	−1.88666	−0.154561	−0.0772807	−	0.997009i	$-0.524624\pi$
$149$	−1.88666	−0.154561	−0.0772807	+	0.997009i	$0.524624\pi$
$150$	3.10278	0.253341
$151$	19.9844	1.62631	0.813154	−	0.582048i	$-0.197749\pi$
$151$	19.9844	1.62631	0.813154	+	0.582048i	$0.197749\pi$
$152$	−4.72999	−0.383653
$153$	37.2927	3.01494
$154$	0	0
$155$	−3.04888	−0.244892
$156$	0	0
$157$	9.36222	0.747187	0.373593	−	0.927593i	$-0.378126\pi$
$157$	9.36222	0.747187	0.373593	+	0.927593i	$0.378126\pi$
$158$	9.77886	0.777965
$159$	−17.2927	−1.37140
$160$	1.00000	0.0790569
$161$	4.52444	0.356576
$162$	15.0383	1.18152
$163$	17.2544	1.35147	0.675735	−	0.737144i	$-0.263826\pi$
$163$	17.2544	1.35147	0.675735	+	0.737144i	$0.263826\pi$
$164$	−7.30833	−0.570684
$165$	0	0
$166$	−7.25443	−0.563053
$167$	−17.5678	−1.35944	−0.679718	−	0.733474i	$-0.737898\pi$
$167$	−17.5678	−1.35944	−0.679718	+	0.733474i	$0.737898\pi$
$168$	3.10278	0.239384
$169$	−13.0000	−1.00000
$170$	5.62721	0.431588
$171$	−31.3466	−2.39714
$172$	0.578337	0.0440978
$173$	−10.6761	−0.811688	−0.405844	−	0.913942i	$-0.633022\pi$
$173$	−10.6761	−0.811688	−0.405844	+	0.913942i	$0.633022\pi$
$174$	−7.83276	−0.593800
$175$	1.00000	0.0755929
$176$	0	0
$177$	−23.6655	−1.77881
$178$	14.4111	1.08016
$179$	−4.47054	−0.334144	−0.167072	−	0.985945i	$-0.553431\pi$
$179$	−4.47054	−0.334144	−0.167072	+	0.985945i	$0.553431\pi$
$180$	6.62721	0.493963
$181$	−10.4111	−0.773851	−0.386925	−	0.922111i	$-0.626463\pi$
$181$	−10.4111	−0.773851	−0.386925	+	0.922111i	$0.626463\pi$
$182$	0	0
$183$	−30.5089	−2.25528
$184$	4.52444	0.333546
$185$	4.52444	0.332643
$186$	−9.45998	−0.693639
$187$	0	0
$188$	11.8328	0.862993
$189$	11.2544	0.818639
$190$	−4.72999	−0.343149
$191$	14.6167	1.05762	0.528812	−	0.848739i	$-0.322638\pi$
$191$	14.6167	1.05762	0.528812	+	0.848739i	$0.322638\pi$
$192$	3.10278	0.223924
$193$	25.4983	1.83541	0.917704	−	0.397266i	$-0.130041\pi$
$193$	25.4983	1.83541	0.917704	+	0.397266i	$0.130041\pi$
$194$	16.5244	1.18639
$195$	0	0
$196$	1.00000	0.0714286
$197$	−5.89220	−0.419802	−0.209901	−	0.977723i	$-0.567314\pi$
$197$	−5.89220	−0.419802	−0.209901	+	0.977723i	$0.567314\pi$
$198$	0	0
$199$	15.9305	1.12928	0.564642	−	0.825336i	$-0.309014\pi$
$199$	15.9305	1.12928	0.564642	+	0.825336i	$0.309014\pi$
$200$	1.00000	0.0707107
$201$	−41.1255	−2.90077
$202$	−5.42166	−0.381467
$203$	−2.52444	−0.177181
$204$	17.4600	1.22244
$205$	−7.30833	−0.510436
$206$	−5.62721	−0.392067
$207$	29.9844	2.08406
$208$	0	0
$209$	0	0
$210$	3.10278	0.214112
$211$	−17.5678	−1.20942	−0.604708	−	0.796447i	$-0.706710\pi$
$211$	−17.5678	−1.20942	−0.604708	+	0.796447i	$0.706710\pi$
$212$	−5.57331	−0.382777
$213$	−26.0978	−1.78819
$214$	−11.8328	−0.808871
$215$	0.578337	0.0394423
$216$	11.2544	0.765767
$217$	−3.04888	−0.206971
$218$	5.88666	0.398695
$219$	−14.2056	−0.959922
$220$	0	0
$221$	0	0
$222$	14.0383	0.942190
$223$	9.62721	0.644686	0.322343	−	0.946623i	$-0.395530\pi$
$223$	9.62721	0.644686	0.322343	+	0.946623i	$0.395530\pi$
$224$	1.00000	0.0668153
$225$	6.62721	0.441814
$226$	−5.25443	−0.349519
$227$	−18.6167	−1.23563	−0.617815	−	0.786323i	$-0.711982\pi$
$227$	−18.6167	−1.23563	−0.617815	+	0.786323i	$0.711982\pi$
$228$	−14.6761	−0.971948
$229$	−10.8816	−0.719079	−0.359539	−	0.933130i	$-0.617066\pi$
$229$	−10.8816	−0.719079	−0.359539	+	0.933130i	$0.617066\pi$
$230$	4.52444	0.298333
$231$	0	0
$232$	−2.52444	−0.165737
$233$	−12.8433	−0.841394	−0.420697	−	0.907201i	$-0.638214\pi$
$233$	−12.8433	−0.841394	−0.420697	+	0.907201i	$0.638214\pi$
$234$	0	0
$235$	11.8328	0.771884
$236$	−7.62721	−0.496489
$237$	30.3416	1.97090
$238$	5.62721	0.364758
$239$	25.8867	1.67447	0.837234	−	0.546844i	$-0.184171\pi$
$239$	25.8867	1.67447	0.837234	+	0.546844i	$0.184171\pi$
$240$	3.10278	0.200283
$241$	−13.5139	−0.870505	−0.435253	−	0.900308i	$-0.643341\pi$
$241$	−13.5139	−0.870505	−0.435253	+	0.900308i	$0.643341\pi$
$242$	0	0
$243$	12.8972	0.827357
$244$	−9.83276	−0.629478
$245$	1.00000	0.0638877
$246$	−22.6761	−1.44577
$247$	0	0
$248$	−3.04888	−0.193604
$249$	−22.5089	−1.42644
$250$	1.00000	0.0632456
$251$	26.9894	1.70356	0.851779	−	0.523901i	$-0.175524\pi$
$251$	26.9894	1.70356	0.851779	+	0.523901i	$0.175524\pi$
$252$	6.62721	0.417475
$253$	0	0
$254$	−20.7144	−1.29974
$255$	17.4600	1.09339
$256$	1.00000	0.0625000
$257$	−2.83779	−0.177016	−0.0885081	−	0.996075i	$-0.528210\pi$
$257$	−2.83779	−0.177016	−0.0885081	+	0.996075i	$0.528210\pi$
$258$	1.79445	0.111718
$259$	4.52444	0.281135
$260$	0	0
$261$	−16.7300	−1.03556
$262$	17.7789	1.09838
$263$	2.95112	0.181974	0.0909871	−	0.995852i	$-0.470998\pi$
$263$	2.95112	0.181974	0.0909871	+	0.995852i	$0.470998\pi$
$264$	0	0
$265$	−5.57331	−0.342366
$266$	−4.72999	−0.290014
$267$	44.7144	2.73648
$268$	−13.2544	−0.809643
$269$	−2.88164	−0.175697	−0.0878483	−	0.996134i	$-0.527999\pi$
$269$	−2.88164	−0.175697	−0.0878483	+	0.996134i	$0.527999\pi$
$270$	11.2544	0.684923
$271$	16.3033	0.990355	0.495178	−	0.868792i	$-0.335103\pi$
$271$	16.3033	0.990355	0.495178	+	0.868792i	$0.335103\pi$
$272$	5.62721	0.341200
$273$	0	0
$274$	−6.41110	−0.387309
$275$	0	0
$276$	14.0383	0.845007
$277$	−13.3622	−0.802858	−0.401429	−	0.915890i	$-0.631486\pi$
$277$	−13.3622	−0.802858	−0.401429	+	0.915890i	$0.631486\pi$
$278$	9.77886	0.586497
$279$	−20.2056	−1.20967
$280$	1.00000	0.0597614
$281$	27.5577	1.64396	0.821978	−	0.569519i	$-0.192871\pi$
$281$	27.5577	1.64396	0.821978	+	0.569519i	$0.192871\pi$
$282$	36.7144	2.18631
$283$	11.8922	0.706918	0.353459	−	0.935450i	$-0.385005\pi$
$283$	11.8922	0.706918	0.353459	+	0.935450i	$0.385005\pi$
$284$	−8.41110	−0.499107
$285$	−14.6761	−0.869336
$286$	0	0
$287$	−7.30833	−0.431397
$288$	6.62721	0.390512
$289$	14.6655	0.862678
$290$	−2.52444	−0.148240
$291$	51.2716	3.00560
$292$	−4.57834	−0.267927
$293$	−14.3133	−0.836195	−0.418097	−	0.908402i	$-0.637303\pi$
$293$	−14.3133	−0.836195	−0.418097	+	0.908402i	$0.637303\pi$
$294$	3.10278	0.180958
$295$	−7.62721	−0.444074
$296$	4.52444	0.262978
$297$	0	0
$298$	−1.88666	−0.109291
$299$	0	0
$300$	3.10278	0.179139
$301$	0.578337	0.0333348
$302$	19.9844	1.14997
$303$	−16.8222	−0.966410
$304$	−4.72999	−0.271283
$305$	−9.83276	−0.563022
$306$	37.2927	2.13188
$307$	20.3033	1.15877	0.579385	−	0.815054i	$-0.303293\pi$
$307$	20.3033	1.15877	0.579385	+	0.815054i	$0.303293\pi$
$308$	0	0
$309$	−17.4600	−0.993263
$310$	−3.04888	−0.173165
$311$	−0.951124	−0.0539333	−0.0269666	−	0.999636i	$-0.508585\pi$
$311$	−0.951124	−0.0539333	−0.0269666	+	0.999636i	$0.508585\pi$
$312$	0	0
$313$	−10.0922	−0.570446	−0.285223	−	0.958461i	$-0.592068\pi$
$313$	−10.0922	−0.570446	−0.285223	+	0.958461i	$0.592068\pi$
$314$	9.36222	0.528341
$315$	6.62721	0.373401
$316$	9.77886	0.550104
$317$	−5.98441	−0.336118	−0.168059	−	0.985777i	$-0.553750\pi$
$317$	−5.98441	−0.336118	−0.168059	+	0.985777i	$0.553750\pi$
$318$	−17.2927	−0.969729
$319$	0	0
$320$	1.00000	0.0559017
$321$	−36.7144	−2.04920
$322$	4.52444	0.252137
$323$	−26.6167	−1.48099
$324$	15.0383	0.835462
$325$	0	0
$326$	17.2544	0.955634
$327$	18.2650	1.01006
$328$	−7.30833	−0.403535
$329$	11.8328	0.652361
$330$	0	0
$331$	17.2927	0.950495	0.475247	−	0.879852i	$-0.342359\pi$
$331$	17.2927	0.950495	0.475247	+	0.879852i	$0.342359\pi$
$332$	−7.25443	−0.398138
$333$	29.9844	1.64314
$334$	−17.5678	−0.961266
$335$	−13.2544	−0.724167
$336$	3.10278	0.169270
$337$	−27.1567	−1.47932	−0.739659	−	0.672982i	$-0.765013\pi$
$337$	−27.1567	−1.47932	−0.739659	+	0.672982i	$0.765013\pi$
$338$	−13.0000	−0.707107
$339$	−16.3033	−0.885474
$340$	5.62721	0.305178
$341$	0	0
$342$	−31.3466	−1.69503
$343$	1.00000	0.0539949
$344$	0.578337	0.0311818
$345$	14.0383	0.755797
$346$	−10.6761	−0.573950
$347$	−31.0872	−1.66885	−0.834424	−	0.551123i	$-0.814199\pi$
$347$	−31.0872	−1.66885	−0.834424	+	0.551123i	$0.814199\pi$
$348$	−7.83276	−0.419880
$349$	−21.7250	−1.16291	−0.581455	−	0.813578i	$-0.697516\pi$
$349$	−21.7250	−1.16291	−0.581455	+	0.813578i	$0.697516\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	0	0
$353$	8.22114	0.437567	0.218783	−	0.975773i	$-0.429791\pi$
$353$	8.22114	0.437567	0.218783	+	0.975773i	$0.429791\pi$
$354$	−23.6655	−1.25781
$355$	−8.41110	−0.446415
$356$	14.4111	0.763787
$357$	17.4600	0.924080
$358$	−4.47054	−0.236275
$359$	−14.8277	−0.782578	−0.391289	−	0.920268i	$-0.627971\pi$
$359$	−14.8277	−0.782578	−0.391289	+	0.920268i	$0.627971\pi$
$360$	6.62721	0.349285
$361$	3.37279	0.177515
$362$	−10.4111	−0.547195
$363$	0	0
$364$	0	0
$365$	−4.57834	−0.239641
$366$	−30.5089	−1.59472
$367$	−23.9406	−1.24969	−0.624844	−	0.780750i	$-0.714837\pi$
$367$	−23.9406	−1.24969	−0.624844	+	0.780750i	$0.714837\pi$
$368$	4.52444	0.235853
$369$	−48.4338	−2.52136
$370$	4.52444	0.235214
$371$	−5.57331	−0.289352
$372$	−9.45998	−0.490477
$373$	3.04888	0.157865	0.0789324	−	0.996880i	$-0.474849\pi$
$373$	3.04888	0.157865	0.0789324	+	0.996880i	$0.474849\pi$
$374$	0	0
$375$	3.10278	0.160227
$376$	11.8328	0.610228
$377$	0	0
$378$	11.2544	0.578865
$379$	−27.6655	−1.42108	−0.710541	−	0.703655i	$-0.751550\pi$
$379$	−27.6655	−1.42108	−0.710541	+	0.703655i	$0.751550\pi$
$380$	−4.72999	−0.242643
$381$	−64.2721	−3.29276
$382$	14.6167	0.747853
$383$	−7.52946	−0.384737	−0.192369	−	0.981323i	$-0.561617\pi$
$383$	−7.52946	−0.384737	−0.192369	+	0.981323i	$0.561617\pi$
$384$	3.10278	0.158338
$385$	0	0
$386$	25.4983	1.29783
$387$	3.83276	0.194830
$388$	16.5244	0.838901
$389$	−27.4600	−1.39228	−0.696138	−	0.717908i	$-0.745100\pi$
$389$	−27.4600	−1.39228	−0.696138	+	0.717908i	$0.745100\pi$
$390$	0	0
$391$	25.4600	1.28757
$392$	1.00000	0.0505076
$393$	55.1638	2.78265
$394$	−5.89220	−0.296845
$395$	9.77886	0.492028
$396$	0	0
$397$	27.4600	1.37818	0.689088	−	0.724677i	$-0.258011\pi$
$397$	27.4600	1.37818	0.689088	+	0.724677i	$0.258011\pi$
$398$	15.9305	0.798525
$399$	−14.6761	−0.734723
$400$	1.00000	0.0500000
$401$	1.52946	0.0763776	0.0381888	−	0.999271i	$-0.487841\pi$
$401$	1.52946	0.0763776	0.0381888	+	0.999271i	$0.487841\pi$
$402$	−41.1255	−2.05115
$403$	0	0
$404$	−5.42166	−0.269738
$405$	15.0383	0.747260
$406$	−2.52444	−0.125286
$407$	0	0
$408$	17.4600	0.864398
$409$	34.6705	1.71435	0.857174	−	0.515027i	$-0.172218\pi$
$409$	34.6705	1.71435	0.857174	+	0.515027i	$0.172218\pi$
$410$	−7.30833	−0.360932
$411$	−19.8922	−0.981210
$412$	−5.62721	−0.277233
$413$	−7.62721	−0.375311
$414$	29.9844	1.47365
$415$	−7.25443	−0.356106
$416$	0	0
$417$	30.3416	1.48584
$418$	0	0
$419$	25.4217	1.24193	0.620965	−	0.783838i	$-0.286741\pi$
$419$	25.4217	1.24193	0.620965	+	0.783838i	$0.286741\pi$
$420$	3.10278	0.151400
$421$	−13.7733	−0.671271	−0.335635	−	0.941992i	$-0.608951\pi$
$421$	−13.7733	−0.671271	−0.335635	+	0.941992i	$0.608951\pi$
$422$	−17.5678	−0.855186
$423$	78.4182	3.81283
$424$	−5.57331	−0.270664
$425$	5.62721	0.272960
$426$	−26.0978	−1.26444
$427$	−9.83276	−0.475841
$428$	−11.8328	−0.571958
$429$	0	0
$430$	0.578337	0.0278899
$431$	−29.2489	−1.40887	−0.704435	−	0.709769i	$-0.748799\pi$
$431$	−29.2489	−1.40887	−0.704435	+	0.709769i	$0.748799\pi$
$432$	11.2544	0.541479
$433$	−9.04334	−0.434595	−0.217298	−	0.976105i	$-0.569724\pi$
$433$	−9.04334	−0.434595	−0.217298	+	0.976105i	$0.569724\pi$
$434$	−3.04888	−0.146351
$435$	−7.83276	−0.375552
$436$	5.88666	0.281920
$437$	−21.4005	−1.02373
$438$	−14.2056	−0.678767
$439$	−36.7144	−1.75228	−0.876141	−	0.482054i	$-0.839891\pi$
$439$	−36.7144	−1.75228	−0.876141	+	0.482054i	$0.839891\pi$
$440$	0	0
$441$	6.62721	0.315582
$442$	0	0
$443$	−13.6655	−0.649269	−0.324634	−	0.945840i	$-0.605241\pi$
$443$	−13.6655	−0.649269	−0.324634	+	0.945840i	$0.605241\pi$
$444$	14.0383	0.666229
$445$	14.4111	0.683152
$446$	9.62721	0.455862
$447$	−5.85389	−0.276879
$448$	1.00000	0.0472456
$449$	−18.3517	−0.866068	−0.433034	−	0.901377i	$-0.642557\pi$
$449$	−18.3517	−0.866068	−0.433034	+	0.901377i	$0.642557\pi$
$450$	6.62721	0.312410
$451$	0	0
$452$	−5.25443	−0.247147
$453$	62.0071	2.91335
$454$	−18.6167	−0.873723
$455$	0	0
$456$	−14.6761	−0.687271
$457$	15.1567	0.708999	0.354500	−	0.935056i	$-0.384651\pi$
$457$	15.1567	0.708999	0.354500	+	0.935056i	$0.384651\pi$
$458$	−10.8816	−0.508466
$459$	63.3311	2.95604
$460$	4.52444	0.210953
$461$	9.52946	0.443831	0.221916	−	0.975066i	$-0.428769\pi$
$461$	9.52946	0.443831	0.221916	+	0.975066i	$0.428769\pi$
$462$	0	0
$463$	16.9355	0.787061	0.393531	−	0.919312i	$-0.371254\pi$
$463$	16.9355	0.787061	0.393531	+	0.919312i	$0.371254\pi$
$464$	−2.52444	−0.117194
$465$	−9.45998	−0.438696
$466$	−12.8433	−0.594956
$467$	16.0439	0.742421	0.371210	−	0.928549i	$-0.378943\pi$
$467$	16.0439	0.742421	0.371210	+	0.928549i	$0.378943\pi$
$468$	0	0
$469$	−13.2544	−0.612033
$470$	11.8328	0.545805
$471$	29.0489	1.33850
$472$	−7.62721	−0.351071
$473$	0	0
$474$	30.3416	1.39364
$475$	−4.72999	−0.217027
$476$	5.62721	0.257923
$477$	−36.9355	−1.69116
$478$	25.8867	1.18403
$479$	−12.4111	−0.567078	−0.283539	−	0.958961i	$-0.591508\pi$
$479$	−12.4111	−0.567078	−0.283539	+	0.958961i	$0.591508\pi$
$480$	3.10278	0.141622
$481$	0	0
$482$	−13.5139	−0.615540
$483$	14.0383	0.638765
$484$	0	0
$485$	16.5244	0.750336
$486$	12.8972	0.585030
$487$	1.37781	0.0624345	0.0312173	−	0.999513i	$-0.490062\pi$
$487$	1.37781	0.0624345	0.0312173	+	0.999513i	$0.490062\pi$
$488$	−9.83276	−0.445108
$489$	53.5366	2.42101
$490$	1.00000	0.0451754
$491$	6.31335	0.284917	0.142459	−	0.989801i	$-0.454499\pi$
$491$	6.31335	0.284917	0.142459	+	0.989801i	$0.454499\pi$
$492$	−22.6761	−1.02232
$493$	−14.2056	−0.639786
$494$	0	0
$495$	0	0
$496$	−3.04888	−0.136899
$497$	−8.41110	−0.377289
$498$	−22.5089	−1.00865
$499$	10.9794	0.491505	0.245753	−	0.969333i	$-0.420965\pi$
$499$	10.9794	0.491505	0.245753	+	0.969333i	$0.420965\pi$
$500$	1.00000	0.0447214
$501$	−54.5089	−2.43528
$502$	26.9894	1.20460
$503$	34.1744	1.52376	0.761880	−	0.647718i	$-0.224277\pi$
$503$	34.1744	1.52376	0.761880	+	0.647718i	$0.224277\pi$
$504$	6.62721	0.295200
$505$	−5.42166	−0.241261
$506$	0	0
$507$	−40.3361	−1.79139
$508$	−20.7144	−0.919053
$509$	−19.5678	−0.867326	−0.433663	−	0.901075i	$-0.642779\pi$
$509$	−19.5678	−0.867326	−0.433663	+	0.901075i	$0.642779\pi$
$510$	17.4600	0.773141
$511$	−4.57834	−0.202534
$512$	1.00000	0.0441942
$513$	−53.2333	−2.35031
$514$	−2.83779	−0.125169
$515$	−5.62721	−0.247965
$516$	1.79445	0.0789963
$517$	0	0
$518$	4.52444	0.198792
$519$	−33.1255	−1.45405
$520$	0	0
$521$	13.0278	0.570756	0.285378	−	0.958415i	$-0.407881\pi$
$521$	13.0278	0.570756	0.285378	+	0.958415i	$0.407881\pi$
$522$	−16.7300	−0.732252
$523$	33.6555	1.47165	0.735826	−	0.677171i	$-0.236794\pi$
$523$	33.6555	1.47165	0.735826	+	0.677171i	$0.236794\pi$
$524$	17.7789	0.776673
$525$	3.10278	0.135416
$526$	2.95112	0.128675
$527$	−17.1567	−0.747356
$528$	0	0
$529$	−2.52946	−0.109977
$530$	−5.57331	−0.242089
$531$	−50.5472	−2.19356
$532$	−4.72999	−0.205071
$533$	0	0
$534$	44.7144	1.93498
$535$	−11.8328	−0.511575
$536$	−13.2544	−0.572504
$537$	−13.8711	−0.598581
$538$	−2.88164	−0.124236
$539$	0	0
$540$	11.2544	0.484313
$541$	6.29776	0.270762	0.135381	−	0.990794i	$-0.456774\pi$
$541$	6.29776	0.270762	0.135381	+	0.990794i	$0.456774\pi$
$542$	16.3033	0.700287
$543$	−32.3033	−1.38627
$544$	5.62721	0.241265
$545$	5.88666	0.252157
$546$	0	0
$547$	17.6867	0.756227	0.378113	−	0.925759i	$-0.376573\pi$
$547$	17.6867	0.756227	0.378113	+	0.925759i	$0.376573\pi$
$548$	−6.41110	−0.273869
$549$	−65.1638	−2.78112
$550$	0	0
$551$	11.9406	0.508685
$552$	14.0383	0.597510
$553$	9.77886	0.415840
$554$	−13.3622	−0.567707
$555$	14.0383	0.595893
$556$	9.77886	0.414716
$557$	6.94108	0.294103	0.147051	−	0.989129i	$-0.453022\pi$
$557$	6.94108	0.294103	0.147051	+	0.989129i	$0.453022\pi$
$558$	−20.2056	−0.855369
$559$	0	0
$560$	1.00000	0.0422577
$561$	0	0
$562$	27.5577	1.16245
$563$	27.1355	1.14363	0.571814	−	0.820384i	$-0.306240\pi$
$563$	27.1355	1.14363	0.571814	+	0.820384i	$0.306240\pi$
$564$	36.7144	1.54596
$565$	−5.25443	−0.221055
$566$	11.8922	0.499867
$567$	15.0383	0.631550
$568$	−8.41110	−0.352922
$569$	−6.31335	−0.264669	−0.132335	−	0.991205i	$-0.542247\pi$
$569$	−6.31335	−0.264669	−0.132335	+	0.991205i	$0.542247\pi$
$570$	−14.6761	−0.614714
$571$	37.5366	1.57086	0.785429	−	0.618952i	$-0.212442\pi$
$571$	37.5366	1.57086	0.785429	+	0.618952i	$0.212442\pi$
$572$	0	0
$573$	45.3522	1.89461
$574$	−7.30833	−0.305044
$575$	4.52444	0.188682
$576$	6.62721	0.276134
$577$	−8.11334	−0.337763	−0.168881	−	0.985636i	$-0.554015\pi$
$577$	−8.11334	−0.337763	−0.168881	+	0.985636i	$0.554015\pi$
$578$	14.6655	0.610005
$579$	79.1155	3.28793
$580$	−2.52444	−0.104822
$581$	−7.25443	−0.300964
$582$	51.2716	2.12528
$583$	0	0
$584$	−4.57834	−0.189453
$585$	0	0
$586$	−14.3133	−0.591279
$587$	−45.7961	−1.89021	−0.945103	−	0.326774i	$-0.894039\pi$
$587$	−45.7961	−1.89021	−0.945103	+	0.326774i	$0.894039\pi$
$588$	3.10278	0.127956
$589$	14.4211	0.594213
$590$	−7.62721	−0.314007
$591$	−18.2822	−0.752028
$592$	4.52444	0.185953
$593$	46.3416	1.90302	0.951511	−	0.307615i	$-0.0995308\pi$
$593$	46.3416	1.90302	0.951511	+	0.307615i	$0.0995308\pi$
$594$	0	0
$595$	5.62721	0.230693
$596$	−1.88666	−0.0772807
$597$	49.4288	2.02299
$598$	0	0
$599$	15.5889	0.636945	0.318473	−	0.947932i	$-0.396830\pi$
$599$	15.5889	0.636945	0.318473	+	0.947932i	$0.396830\pi$
$600$	3.10278	0.126670
$601$	−23.9461	−0.976782	−0.488391	−	0.872625i	$-0.662416\pi$
$601$	−23.9461	−0.976782	−0.488391	+	0.872625i	$0.662416\pi$
$602$	0.578337	0.0235713
$603$	−87.8399	−3.57712
$604$	19.9844	0.813154
$605$	0	0
$606$	−16.8222	−0.683355
$607$	−8.24386	−0.334608	−0.167304	−	0.985905i	$-0.553506\pi$
$607$	−8.24386	−0.334608	−0.167304	+	0.985905i	$0.553506\pi$
$608$	−4.72999	−0.191826
$609$	−7.83276	−0.317400
$610$	−9.83276	−0.398117
$611$	0	0
$612$	37.2927	1.50747
$613$	−27.0177	−1.09123	−0.545617	−	0.838034i	$-0.683705\pi$
$613$	−27.0177	−1.09123	−0.545617	+	0.838034i	$0.683705\pi$
$614$	20.3033	0.819375
$615$	−22.6761	−0.914388
$616$	0	0
$617$	16.4011	0.660282	0.330141	−	0.943932i	$-0.392904\pi$
$617$	16.4011	0.660282	0.330141	+	0.943932i	$0.392904\pi$
$618$	−17.4600	−0.702343
$619$	−0.146111	−0.00587272	−0.00293636	−	0.999996i	$-0.500935\pi$
$619$	−0.146111	−0.00587272	−0.00293636	+	0.999996i	$0.500935\pi$
$620$	−3.04888	−0.122446
$621$	50.9200	2.04335
$622$	−0.951124	−0.0381366
$623$	14.4111	0.577369
$624$	0	0
$625$	1.00000	0.0400000
$626$	−10.0922	−0.403366
$627$	0	0
$628$	9.36222	0.373593
$629$	25.4600	1.01516
$630$	6.62721	0.264034
$631$	44.6832	1.77881	0.889406	−	0.457119i	$-0.151119\pi$
$631$	44.6832	1.77881	0.889406	+	0.457119i	$0.151119\pi$
$632$	9.77886	0.388982
$633$	−54.5089	−2.16653
$634$	−5.98441	−0.237671
$635$	−20.7144	−0.822026
$636$	−17.2927	−0.685702
$637$	0	0
$638$	0	0
$639$	−55.7422	−2.20513
$640$	1.00000	0.0395285
$641$	−37.1355	−1.46677	−0.733383	−	0.679816i	$-0.762060\pi$
$641$	−37.1355	−1.46677	−0.733383	+	0.679816i	$0.762060\pi$
$642$	−36.7144	−1.44900
$643$	−28.1205	−1.10896	−0.554482	−	0.832196i	$-0.687083\pi$
$643$	−28.1205	−1.10896	−0.554482	+	0.832196i	$0.687083\pi$
$644$	4.52444	0.178288
$645$	1.79445	0.0706564
$646$	−26.6167	−1.04722
$647$	−30.4494	−1.19709	−0.598545	−	0.801089i	$-0.704254\pi$
$647$	−30.4494	−1.19709	−0.598545	+	0.801089i	$0.704254\pi$
$648$	15.0383	0.590761
$649$	0	0
$650$	0	0
$651$	−9.45998	−0.370766
$652$	17.2544	0.675735
$653$	32.9355	1.28887	0.644434	−	0.764660i	$-0.277093\pi$
$653$	32.9355	1.28887	0.644434	+	0.764660i	$0.277093\pi$
$654$	18.2650	0.714218
$655$	17.7789	0.694678
$656$	−7.30833	−0.285342
$657$	−30.3416	−1.18374
$658$	11.8328	0.461289
$659$	−27.8922	−1.08653	−0.543263	−	0.839563i	$-0.682811\pi$
$659$	−27.8922	−1.08653	−0.543263	+	0.839563i	$0.682811\pi$
$660$	0	0
$661$	−29.0388	−1.12948	−0.564740	−	0.825269i	$-0.691023\pi$
$661$	−29.0388	−1.12948	−0.564740	+	0.825269i	$0.691023\pi$
$662$	17.2927	0.672101
$663$	0	0
$664$	−7.25443	−0.281526
$665$	−4.72999	−0.183421
$666$	29.9844	1.16187
$667$	−11.4217	−0.442249
$668$	−17.5678	−0.679718
$669$	29.8711	1.15488
$670$	−13.2544	−0.512063
$671$	0	0
$672$	3.10278	0.119692
$673$	11.6867	0.450487	0.225244	−	0.974302i	$-0.427682\pi$
$673$	11.6867	0.450487	0.225244	+	0.974302i	$0.427682\pi$
$674$	−27.1567	−1.04604
$675$	11.2544	0.433183
$676$	−13.0000	−0.500000
$677$	31.1638	1.19772	0.598861	−	0.800853i	$-0.295620\pi$
$677$	31.1638	1.19772	0.598861	+	0.800853i	$0.295620\pi$
$678$	−16.3033	−0.626125
$679$	16.5244	0.634150
$680$	5.62721	0.215794
$681$	−57.7633	−2.21349
$682$	0	0
$683$	12.5400	0.479831	0.239915	−	0.970794i	$-0.422880\pi$
$683$	12.5400	0.479831	0.239915	+	0.970794i	$0.422880\pi$
$684$	−31.3466	−1.19857
$685$	−6.41110	−0.244956
$686$	1.00000	0.0381802
$687$	−33.7633	−1.28815
$688$	0.578337	0.0220489
$689$	0	0
$690$	14.0383	0.534429
$691$	−25.1638	−0.957277	−0.478638	−	0.878012i	$-0.658869\pi$
$691$	−25.1638	−0.957277	−0.478638	+	0.878012i	$0.658869\pi$
$692$	−10.6761	−0.405844
$693$	0	0
$694$	−31.0872	−1.18005
$695$	9.77886	0.370933
$696$	−7.83276	−0.296900
$697$	−41.1255	−1.55774
$698$	−21.7250	−0.822302
$699$	−39.8500	−1.50726
$700$	1.00000	0.0377964
$701$	13.1411	0.496332	0.248166	−	0.968718i	$-0.420172\pi$
$701$	13.1411	0.496332	0.248166	+	0.968718i	$0.420172\pi$
$702$	0	0
$703$	−21.4005	−0.807137
$704$	0	0
$705$	36.7144	1.38274
$706$	8.22114	0.309407
$707$	−5.42166	−0.203903
$708$	−23.6655	−0.889405
$709$	25.3311	0.951328	0.475664	−	0.879627i	$-0.342208\pi$
$709$	25.3311	0.951328	0.475664	+	0.879627i	$0.342208\pi$
$710$	−8.41110	−0.315663
$711$	64.8066	2.43044
$712$	14.4111	0.540079
$713$	−13.7944	−0.516606
$714$	17.4600	0.653423
$715$	0	0
$716$	−4.47054	−0.167072
$717$	80.3205	2.99962
$718$	−14.8277	−0.553366
$719$	−43.2616	−1.61338	−0.806692	−	0.590972i	$-0.798744\pi$
$719$	−43.2616	−1.61338	−0.806692	+	0.590972i	$0.798744\pi$
$720$	6.62721	0.246982
$721$	−5.62721	−0.209568
$722$	3.37279	0.125522
$723$	−41.9305	−1.55941
$724$	−10.4111	−0.386925
$725$	−2.52444	−0.0937553
$726$	0	0
$727$	−47.6938	−1.76886	−0.884432	−	0.466668i	$-0.845454\pi$
$727$	−47.6938	−1.76886	−0.884432	+	0.466668i	$0.845454\pi$
$728$	0	0
$729$	−5.09775	−0.188806
$730$	−4.57834	−0.169452
$731$	3.25443	0.120369
$732$	−30.5089	−1.12764
$733$	−32.7738	−1.21053	−0.605265	−	0.796024i	$-0.706933\pi$
$733$	−32.7738	−1.21053	−0.605265	+	0.796024i	$0.706933\pi$
$734$	−23.9406	−0.883662
$735$	3.10278	0.114448
$736$	4.52444	0.166773
$737$	0	0
$738$	−48.4338	−1.78287
$739$	34.5089	1.26943	0.634714	−	0.772747i	$-0.281118\pi$
$739$	34.5089	1.26943	0.634714	+	0.772747i	$0.281118\pi$
$740$	4.52444	0.166322
$741$	0	0
$742$	−5.57331	−0.204603
$743$	34.2822	1.25769	0.628846	−	0.777530i	$-0.283528\pi$
$743$	34.2822	1.25769	0.628846	+	0.777530i	$0.283528\pi$
$744$	−9.45998	−0.346820
$745$	−1.88666	−0.0691220
$746$	3.04888	0.111627
$747$	−48.0766	−1.75903
$748$	0	0
$749$	−11.8328	−0.432360
$750$	3.10278	0.113297
$751$	−39.1355	−1.42808	−0.714038	−	0.700107i	$-0.753136\pi$
$751$	−39.1355	−1.42808	−0.714038	+	0.700107i	$0.753136\pi$
$752$	11.8328	0.431496
$753$	83.7422	3.05173
$754$	0	0
$755$	19.9844	0.727307
$756$	11.2544	0.409320
$757$	−25.7577	−0.936181	−0.468090	−	0.883681i	$-0.655058\pi$
$757$	−25.7577	−0.936181	−0.468090	+	0.883681i	$0.655058\pi$
$758$	−27.6655	−1.00486
$759$	0	0
$760$	−4.72999	−0.171575
$761$	−1.74055	−0.0630949	−0.0315475	−	0.999502i	$-0.510044\pi$
$761$	−1.74055	−0.0630949	−0.0315475	+	0.999502i	$0.510044\pi$
$762$	−64.2721	−2.32833
$763$	5.88666	0.213111
$764$	14.6167	0.528812
$765$	37.2927	1.34832
$766$	−7.52946	−0.272050
$767$	0	0
$768$	3.10278	0.111962
$769$	36.8449	1.32866	0.664331	−	0.747438i	$-0.268717\pi$
$769$	36.8449	1.32866	0.664331	+	0.747438i	$0.268717\pi$
$770$	0	0
$771$	−8.80501	−0.317105
$772$	25.4983	0.917704
$773$	−33.4499	−1.20311	−0.601555	−	0.798831i	$-0.705452\pi$
$773$	−33.4499	−1.20311	−0.601555	+	0.798831i	$0.705452\pi$
$774$	3.83276	0.137766
$775$	−3.04888	−0.109519
$776$	16.5244	0.593193
$777$	14.0383	0.503622
$778$	−27.4600	−0.984488
$779$	34.5683	1.23854
$780$	0	0
$781$	0	0
$782$	25.4600	0.910447
$783$	−28.4111	−1.01533
$784$	1.00000	0.0357143
$785$	9.36222	0.334152
$786$	55.1638	1.96763
$787$	−6.72445	−0.239701	−0.119850	−	0.992792i	$-0.538241\pi$
$787$	−6.72445	−0.239701	−0.119850	+	0.992792i	$0.538241\pi$
$788$	−5.89220	−0.209901
$789$	9.15667	0.325986
$790$	9.77886	0.347916
$791$	−5.25443	−0.186826
$792$	0	0
$793$	0	0
$794$	27.4600	0.974518
$795$	−17.2927	−0.613310
$796$	15.9305	0.564642
$797$	−31.2444	−1.10673	−0.553366	−	0.832938i	$-0.686657\pi$
$797$	−31.2444	−1.10673	−0.553366	+	0.832938i	$0.686657\pi$
$798$	−14.6761	−0.519528
$799$	66.5855	2.35562
$800$	1.00000	0.0353553
$801$	95.5054	3.37452
$802$	1.52946	0.0540072
$803$	0	0
$804$	−41.1255	−1.45038
$805$	4.52444	0.159465
$806$	0	0
$807$	−8.94108	−0.314741
$808$	−5.42166	−0.190733
$809$	44.7910	1.57477	0.787384	−	0.616462i	$-0.211435\pi$
$809$	44.7910	1.57477	0.787384	+	0.616462i	$0.211435\pi$
$810$	15.0383	0.528392
$811$	15.3466	0.538893	0.269447	−	0.963015i	$-0.413159\pi$
$811$	15.3466	0.538893	0.269447	+	0.963015i	$0.413159\pi$
$812$	−2.52444	−0.0885904
$813$	50.5855	1.77411
$814$	0	0
$815$	17.2544	0.604396
$816$	17.4600	0.611221
$817$	−2.73553	−0.0957040
$818$	34.6705	1.21223
$819$	0	0
$820$	−7.30833	−0.255218
$821$	10.0822	0.351870	0.175935	−	0.984402i	$-0.443705\pi$
$821$	10.0822	0.351870	0.175935	+	0.984402i	$0.443705\pi$
$822$	−19.8922	−0.693820
$823$	17.2388	0.600908	0.300454	−	0.953796i	$-0.402862\pi$
$823$	17.2388	0.600908	0.300454	+	0.953796i	$0.402862\pi$
$824$	−5.62721	−0.196033
$825$	0	0
$826$	−7.62721	−0.265385
$827$	−55.7422	−1.93834	−0.969172	−	0.246384i	$-0.920758\pi$
$827$	−55.7422	−1.93834	−0.969172	+	0.246384i	$0.920758\pi$
$828$	29.9844	1.04203
$829$	−32.8605	−1.14129	−0.570646	−	0.821196i	$-0.693307\pi$
$829$	−32.8605	−1.14129	−0.570646	+	0.821196i	$0.693307\pi$
$830$	−7.25443	−0.251805
$831$	−41.4600	−1.43823
$832$	0	0
$833$	5.62721	0.194971
$834$	30.3416	1.05064
$835$	−17.5678	−0.607958
$836$	0	0
$837$	−34.3133	−1.18604
$838$	25.4217	0.878177
$839$	6.71440	0.231807	0.115903	−	0.993260i	$-0.463024\pi$
$839$	6.71440	0.231807	0.115903	+	0.993260i	$0.463024\pi$
$840$	3.10278	0.107056
$841$	−22.6272	−0.780249
$842$	−13.7733	−0.474660
$843$	85.5054	2.94496
$844$	−17.5678	−0.604708
$845$	−13.0000	−0.447214
$846$	78.4182	2.69607
$847$	0	0
$848$	−5.57331	−0.191388
$849$	36.8988	1.26636
$850$	5.62721	0.193012
$851$	20.4705	0.701721
$852$	−26.0978	−0.894094
$853$	−3.01056	−0.103080	−0.0515399	−	0.998671i	$-0.516413\pi$
$853$	−3.01056	−0.103080	−0.0515399	+	0.998671i	$0.516413\pi$
$854$	−9.83276	−0.336470
$855$	−31.3466	−1.07203
$856$	−11.8328	−0.404436
$857$	−17.8116	−0.608434	−0.304217	−	0.952603i	$-0.598395\pi$
$857$	−17.8116	−0.608434	−0.304217	+	0.952603i	$0.598395\pi$
$858$	0	0
$859$	−44.3416	−1.51292	−0.756458	−	0.654042i	$-0.773072\pi$
$859$	−44.3416	−1.51292	−0.756458	+	0.654042i	$0.773072\pi$
$860$	0.578337	0.0197211
$861$	−22.6761	−0.772799
$862$	−29.2489	−0.996221
$863$	−27.1099	−0.922832	−0.461416	−	0.887184i	$-0.652658\pi$
$863$	−27.1099	−0.922832	−0.461416	+	0.887184i	$0.652658\pi$
$864$	11.2544	0.382883
$865$	−10.6761	−0.362998
$866$	−9.04334	−0.307305
$867$	45.5038	1.54539
$868$	−3.04888	−0.103486
$869$	0	0
$870$	−7.83276	−0.265556
$871$	0	0
$872$	5.88666	0.199348
$873$	109.511	3.70638
$874$	−21.4005	−0.723884
$875$	1.00000	0.0338062
$876$	−14.2056	−0.479961
$877$	−40.9511	−1.38282	−0.691411	−	0.722462i	$-0.743010\pi$
$877$	−40.9511	−1.38282	−0.691411	+	0.722462i	$0.743010\pi$
$878$	−36.7144	−1.23905
$879$	−44.4111	−1.49795
$880$	0	0
$881$	53.3311	1.79677	0.898384	−	0.439210i	$-0.144742\pi$
$881$	53.3311	1.79677	0.898384	+	0.439210i	$0.144742\pi$
$882$	6.62721	0.223150
$883$	27.7944	0.935358	0.467679	−	0.883898i	$-0.345090\pi$
$883$	27.7944	0.935358	0.467679	+	0.883898i	$0.345090\pi$
$884$	0	0
$885$	−23.6655	−0.795508
$886$	−13.6655	−0.459102
$887$	−30.2933	−1.01715	−0.508574	−	0.861018i	$-0.669827\pi$
$887$	−30.2933	−1.01715	−0.508574	+	0.861018i	$0.669827\pi$
$888$	14.0383	0.471095
$889$	−20.7144	−0.694739
$890$	14.4111	0.483061
$891$	0	0
$892$	9.62721	0.322343
$893$	−55.9688	−1.87293
$894$	−5.85389	−0.195783
$895$	−4.47054	−0.149434
$896$	1.00000	0.0334077
$897$	0	0
$898$	−18.3517	−0.612403
$899$	7.69670	0.256699
$900$	6.62721	0.220907
$901$	−31.3622	−1.04483
$902$	0	0
$903$	1.79445	0.0597156
$904$	−5.25443	−0.174760
$905$	−10.4111	−0.346077
$906$	62.0071	2.06005
$907$	−39.8711	−1.32390	−0.661949	−	0.749549i	$-0.730270\pi$
$907$	−39.8711	−1.32390	−0.661949	+	0.749549i	$0.730270\pi$
$908$	−18.6167	−0.617815
$909$	−35.9305	−1.19174
$910$	0	0
$911$	19.7733	0.655119	0.327560	−	0.944830i	$-0.393774\pi$
$911$	19.7733	0.655119	0.327560	+	0.944830i	$0.393774\pi$
$912$	−14.6761	−0.485974
$913$	0	0
$914$	15.1567	0.501338
$915$	−30.5089	−1.00859
$916$	−10.8816	−0.359539
$917$	17.7789	0.587110
$918$	63.3311	2.09024
$919$	17.8100	0.587499	0.293749	−	0.955882i	$-0.405097\pi$
$919$	17.8100	0.587499	0.293749	+	0.955882i	$0.405097\pi$
$920$	4.52444	0.149166
$921$	62.9966	2.07581
$922$	9.52946	0.313836
$923$	0	0
$924$	0	0
$925$	4.52444	0.148763
$926$	16.9355	0.556536
$927$	−37.2927	−1.22485
$928$	−2.52444	−0.0828687
$929$	24.7355	0.811546	0.405773	−	0.913974i	$-0.367002\pi$
$929$	24.7355	0.811546	0.405773	+	0.913974i	$0.367002\pi$
$930$	−9.45998	−0.310205
$931$	−4.72999	−0.155019
$932$	−12.8433	−0.420697
$933$	−2.95112	−0.0966155
$934$	16.0439	0.524971
$935$	0	0
$936$	0	0
$937$	3.52946	0.115302	0.0576512	−	0.998337i	$-0.481639\pi$
$937$	3.52946	0.115302	0.0576512	+	0.998337i	$0.481639\pi$
$938$	−13.2544	−0.432772
$939$	−31.3139	−1.02189
$940$	11.8328	0.385942
$941$	−49.4217	−1.61110	−0.805550	−	0.592528i	$-0.798130\pi$
$941$	−49.4217	−1.61110	−0.805550	+	0.592528i	$0.798130\pi$
$942$	29.0489	0.946464
$943$	−33.0661	−1.07678
$944$	−7.62721	−0.248245
$945$	11.2544	0.366107
$946$	0	0
$947$	30.7144	0.998084	0.499042	−	0.866578i	$-0.333685\pi$
$947$	30.7144	0.998084	0.499042	+	0.866578i	$0.333685\pi$
$948$	30.3416	0.985450
$949$	0	0
$950$	−4.72999	−0.153461
$951$	−18.5683	−0.602118
$952$	5.62721	0.182379
$953$	24.7527	0.801819	0.400910	−	0.916118i	$-0.368694\pi$
$953$	24.7527	0.801819	0.400910	+	0.916118i	$0.368694\pi$
$954$	−36.9355	−1.19583
$955$	14.6167	0.472984
$956$	25.8867	0.837234
$957$	0	0
$958$	−12.4111	−0.400984
$959$	−6.41110	−0.207025
$960$	3.10278	0.100142
$961$	−21.7044	−0.700141
$962$	0	0
$963$	−78.4182	−2.52699
$964$	−13.5139	−0.435253
$965$	25.4983	0.820819
$966$	14.0383	0.451675
$967$	34.2822	1.10244	0.551220	−	0.834360i	$-0.314162\pi$
$967$	34.2822	1.10244	0.551220	+	0.834360i	$0.314162\pi$
$968$	0	0
$969$	−82.5855	−2.65303
$970$	16.5244	0.530568
$971$	−48.0383	−1.54162	−0.770811	−	0.637063i	$-0.780149\pi$
$971$	−48.0383	−1.54162	−0.770811	+	0.637063i	$0.780149\pi$
$972$	12.8972	0.413679
$973$	9.77886	0.313496
$974$	1.37781	0.0441479
$975$	0	0
$976$	−9.83276	−0.314739
$977$	27.5678	0.881971	0.440986	−	0.897514i	$-0.354629\pi$
$977$	27.5678	0.881971	0.440986	+	0.897514i	$0.354629\pi$
$978$	53.5366	1.71191
$979$	0	0
$980$	1.00000	0.0319438
$981$	39.0122	1.24556
$982$	6.31335	0.201467
$983$	56.3316	1.79670	0.898349	−	0.439282i	$-0.144767\pi$
$983$	56.3316	1.79670	0.898349	+	0.439282i	$0.144767\pi$
$984$	−22.6761	−0.722887
$985$	−5.89220	−0.187741
$986$	−14.2056	−0.452397
$987$	36.7144	1.16863
$988$	0	0
$989$	2.61665	0.0832046
$990$	0	0
$991$	4.37993	0.139133	0.0695665	−	0.997577i	$-0.477838\pi$
$991$	4.37993	0.139133	0.0695665	+	0.997577i	$0.477838\pi$
$992$	−3.04888	−0.0968019
$993$	53.6555	1.70271
$994$	−8.41110	−0.266784
$995$	15.9305	0.505031
$996$	−22.5089	−0.713220
$997$	−27.7139	−0.877708	−0.438854	−	0.898558i	$-0.644615\pi$
$997$	−27.7139	−0.877708	−0.438854	+	0.898558i	$0.644615\pi$
$998$	10.9794	0.347547
$999$	50.9200	1.61104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cn.1.3	yes	3
11.10	odd	2		8470.2.a.ch.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.ch.1.3	✓	3	11.10	odd	2
8470.2.a.cn.1.3	yes	3	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.10278 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.10278 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.62721 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.10278 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.10278 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.62721 q^{9} +1.00000 q^{10} +3.10278 q^{12} +1.00000 q^{14} +3.10278 q^{15} +1.00000 q^{16} +5.62721 q^{17} +6.62721 q^{18} -4.72999 q^{19} +1.00000 q^{20} +3.10278 q^{21} +4.52444 q^{23} +3.10278 q^{24} +1.00000 q^{25} +11.2544 q^{27} +1.00000 q^{28} -2.52444 q^{29} +3.10278 q^{30} -3.04888 q^{31} +1.00000 q^{32} +5.62721 q^{34} +1.00000 q^{35} +6.62721 q^{36} +4.52444 q^{37} -4.72999 q^{38} +1.00000 q^{40} -7.30833 q^{41} +3.10278 q^{42} +0.578337 q^{43} +6.62721 q^{45} +4.52444 q^{46} +11.8328 q^{47} +3.10278 q^{48} +1.00000 q^{49} +1.00000 q^{50} +17.4600 q^{51} -5.57331 q^{53} +11.2544 q^{54} +1.00000 q^{56} -14.6761 q^{57} -2.52444 q^{58} -7.62721 q^{59} +3.10278 q^{60} -9.83276 q^{61} -3.04888 q^{62} +6.62721 q^{63} +1.00000 q^{64} -13.2544 q^{67} +5.62721 q^{68} +14.0383 q^{69} +1.00000 q^{70} -8.41110 q^{71} +6.62721 q^{72} -4.57834 q^{73} +4.52444 q^{74} +3.10278 q^{75} -4.72999 q^{76} +9.77886 q^{79} +1.00000 q^{80} +15.0383 q^{81} -7.30833 q^{82} -7.25443 q^{83} +3.10278 q^{84} +5.62721 q^{85} +0.578337 q^{86} -7.83276 q^{87} +14.4111 q^{89} +6.62721 q^{90} +4.52444 q^{92} -9.45998 q^{93} +11.8328 q^{94} -4.72999 q^{95} +3.10278 q^{96} +16.5244 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} + 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 + 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} + 3 q^{7} + 3 q^{8} + 7 q^{9} + 3 q^{10} + 2 q^{12} + 3 q^{14} + 2 q^{15} + 3 q^{16} + 4 q^{17} + 7 q^{18} + 6 q^{19} + 3 q^{20} + 2 q^{21} + 8 q^{23} + 2 q^{24} + 3 q^{25} + 8 q^{27} + 3 q^{28} - 2 q^{29} + 2 q^{30} + 2 q^{31} + 3 q^{32} + 4 q^{34} + 3 q^{35} + 7 q^{36} + 8 q^{37} + 6 q^{38} + 3 q^{40} + 2 q^{42} + 7 q^{45} + 8 q^{46} + 8 q^{47} + 2 q^{48} + 3 q^{49} + 3 q^{50} + 12 q^{51} + 8 q^{54} + 3 q^{56} - 20 q^{57} - 2 q^{58} - 10 q^{59} + 2 q^{60} - 2 q^{61} + 2 q^{62} + 7 q^{63} + 3 q^{64} - 14 q^{67} + 4 q^{68} + 3 q^{70} + 4 q^{71} + 7 q^{72} - 12 q^{73} + 8 q^{74} + 2 q^{75} + 6 q^{76} - 2 q^{79} + 3 q^{80} + 3 q^{81} + 4 q^{83} + 2 q^{84} + 4 q^{85} + 4 q^{87} + 14 q^{89} + 7 q^{90} + 8 q^{92} + 12 q^{93} + 8 q^{94} + 6 q^{95} + 2 q^{96} + 44 q^{97} + 3 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 + 3 * q^7 + 3 * q^8 + 7 * q^9 + 3 * q^10 + 2 * q^12 + 3 * q^14 + 2 * q^15 + 3 * q^16 + 4 * q^17 + 7 * q^18 + 6 * q^19 + 3 * q^20 + 2 * q^21 + 8 * q^23 + 2 * q^24 + 3 * q^25 + 8 * q^27 + 3 * q^28 - 2 * q^29 + 2 * q^30 + 2 * q^31 + 3 * q^32 + 4 * q^34 + 3 * q^35 + 7 * q^36 + 8 * q^37 + 6 * q^38 + 3 * q^40 + 2 * q^42 + 7 * q^45 + 8 * q^46 + 8 * q^47 + 2 * q^48 + 3 * q^49 + 3 * q^50 + 12 * q^51 + 8 * q^54 + 3 * q^56 - 20 * q^57 - 2 * q^58 - 10 * q^59 + 2 * q^60 - 2 * q^61 + 2 * q^62 + 7 * q^63 + 3 * q^64 - 14 * q^67 + 4 * q^68 + 3 * q^70 + 4 * q^71 + 7 * q^72 - 12 * q^73 + 8 * q^74 + 2 * q^75 + 6 * q^76 - 2 * q^79 + 3 * q^80 + 3 * q^81 + 4 * q^83 + 2 * q^84 + 4 * q^85 + 4 * q^87 + 14 * q^89 + 7 * q^90 + 8 * q^92 + 12 * q^93 + 8 * q^94 + 6 * q^95 + 2 * q^96 + 44 * q^97 + 3 * q^98

Introduction

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