LMFDB - Embedded newform 8450.2.a.bt.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8450,2,Mod(1,8450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8450, 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("8450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8450 = 2 \cdot 5^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8450.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:	$67.4735897080$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	8450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.21432 q^{3} +1.00000 q^{4} -2.21432 q^{6} +3.90321 q^{7} -1.00000 q^{8} +1.90321 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.21432 q^{3} +1.00000 q^{4} -2.21432 q^{6} +3.90321 q^{7} -1.00000 q^{8} +1.90321 q^{9} -1.06668 q^{11} +2.21432 q^{12} -3.90321 q^{14} +1.00000 q^{16} +1.31111 q^{17} -1.90321 q^{18} +6.59210 q^{19} +8.64296 q^{21} +1.06668 q^{22} +2.14764 q^{23} -2.21432 q^{24} -2.42864 q^{27} +3.90321 q^{28} -9.05086 q^{29} +6.92396 q^{31} -1.00000 q^{32} -2.36196 q^{33} -1.31111 q^{34} +1.90321 q^{36} -5.02074 q^{37} -6.59210 q^{38} +5.95407 q^{41} -8.64296 q^{42} +2.00000 q^{43} -1.06668 q^{44} -2.14764 q^{46} +0.0967881 q^{47} +2.21432 q^{48} +8.23506 q^{49} +2.90321 q^{51} -1.49532 q^{53} +2.42864 q^{54} -3.90321 q^{56} +14.5970 q^{57} +9.05086 q^{58} -7.18421 q^{59} +7.88739 q^{61} -6.92396 q^{62} +7.42864 q^{63} +1.00000 q^{64} +2.36196 q^{66} +8.42864 q^{67} +1.31111 q^{68} +4.75557 q^{69} +15.4795 q^{71} -1.90321 q^{72} +15.3526 q^{73} +5.02074 q^{74} +6.59210 q^{76} -4.16346 q^{77} +4.30174 q^{79} -11.0874 q^{81} -5.95407 q^{82} -9.69381 q^{83} +8.64296 q^{84} -2.00000 q^{86} -20.0415 q^{87} +1.06668 q^{88} -4.52543 q^{89} +2.14764 q^{92} +15.3319 q^{93} -0.0967881 q^{94} -2.21432 q^{96} +4.26025 q^{97} -8.23506 q^{98} -2.03011 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} + 5 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^4 + 5 * q^7 - 3 * q^8 - q^9	$ 3 q - 3 q^{2} + 3 q^{4} + 5 q^{7} - 3 q^{8} - q^{9} - 3 q^{11} - 5 q^{14} + 3 q^{16} + 4 q^{17} + q^{18} + 13 q^{19} + 6 q^{21} + 3 q^{22} + 6 q^{27} + 5 q^{28} - 14 q^{29} - 6 q^{31} - 3 q^{32} + 6 q^{33} - 4 q^{34} - q^{36} + 5 q^{37} - 13 q^{38} - 2 q^{41} - 6 q^{42} + 6 q^{43} - 3 q^{44} + 7 q^{47} - 2 q^{49} + 2 q^{51} + 9 q^{53} - 6 q^{54} - 5 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 4 q^{61} + 6 q^{62} + 9 q^{63} + 3 q^{64} - 6 q^{66} + 12 q^{67} + 4 q^{68} + 14 q^{69} + 20 q^{71} + q^{72} + 6 q^{73} - 5 q^{74} + 13 q^{76} - 19 q^{77} - 14 q^{79} - 13 q^{81} + 2 q^{82} + 4 q^{83} + 6 q^{84} - 6 q^{86} - 20 q^{87} + 3 q^{88} - 7 q^{89} + 26 q^{93} - 7 q^{94} + 26 q^{97} + 2 q^{98} - 13 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 + 5 * q^7 - 3 * q^8 - q^9 - 3 * q^11 - 5 * q^14 + 3 * q^16 + 4 * q^17 + q^18 + 13 * q^19 + 6 * q^21 + 3 * q^22 + 6 * q^27 + 5 * q^28 - 14 * q^29 - 6 * q^31 - 3 * q^32 + 6 * q^33 - 4 * q^34 - q^36 + 5 * q^37 - 13 * q^38 - 2 * q^41 - 6 * q^42 + 6 * q^43 - 3 * q^44 + 7 * q^47 - 2 * q^49 + 2 * q^51 + 9 * q^53 - 6 * q^54 - 5 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 4 * q^61 + 6 * q^62 + 9 * q^63 + 3 * q^64 - 6 * q^66 + 12 * q^67 + 4 * q^68 + 14 * q^69 + 20 * q^71 + q^72 + 6 * q^73 - 5 * q^74 + 13 * q^76 - 19 * q^77 - 14 * q^79 - 13 * q^81 + 2 * q^82 + 4 * q^83 + 6 * q^84 - 6 * q^86 - 20 * q^87 + 3 * q^88 - 7 * q^89 + 26 * q^93 - 7 * q^94 + 26 * q^97 + 2 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.21432	1.27844	0.639219	−	0.769025i	$-0.279258\pi$
$3$	2.21432	1.27844	0.639219	+	0.769025i	$0.279258\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−2.21432	−0.903992
$7$	3.90321	1.47528	0.737638	−	0.675197i	$-0.235941\pi$
$7$	3.90321	1.47528	0.737638	+	0.675197i	$0.235941\pi$
$8$	−1.00000	−0.353553
$9$	1.90321	0.634404
$10$	0	0
$11$	−1.06668	−0.321615	−0.160808	−	0.986986i	$-0.551410\pi$
$11$	−1.06668	−0.321615	−0.160808	+	0.986986i	$0.551410\pi$
$12$	2.21432	0.639219
$13$	0	0
$13$	0	0
$14$	−3.90321	−1.04318
$15$	0	0
$16$	1.00000	0.250000
$17$	1.31111	0.317990	0.158995	−	0.987279i	$-0.449175\pi$
$17$	1.31111	0.317990	0.158995	+	0.987279i	$0.449175\pi$
$18$	−1.90321	−0.448591
$19$	6.59210	1.51233	0.756166	−	0.654380i	$-0.227070\pi$
$19$	6.59210	1.51233	0.756166	+	0.654380i	$0.227070\pi$
$20$	0	0
$21$	8.64296	1.88605
$22$	1.06668	0.227416
$23$	2.14764	0.447815	0.223907	−	0.974610i	$-0.428119\pi$
$23$	2.14764	0.447815	0.223907	+	0.974610i	$0.428119\pi$
$24$	−2.21432	−0.451996
$25$	0	0
$26$	0	0
$27$	−2.42864	−0.467392
$28$	3.90321	0.737638
$29$	−9.05086	−1.68070	−0.840351	−	0.542043i	$-0.817651\pi$
$29$	−9.05086	−1.68070	−0.840351	+	0.542043i	$0.817651\pi$
$30$	0	0
$31$	6.92396	1.24358	0.621790	−	0.783184i	$-0.286406\pi$
$31$	6.92396	1.24358	0.621790	+	0.783184i	$0.286406\pi$
$32$	−1.00000	−0.176777
$33$	−2.36196	−0.411165
$34$	−1.31111	−0.224853
$35$	0	0
$36$	1.90321	0.317202
$37$	−5.02074	−0.825405	−0.412703	−	0.910866i	$-0.635415\pi$
$37$	−5.02074	−0.825405	−0.412703	+	0.910866i	$0.635415\pi$
$38$	−6.59210	−1.06938
$39$	0	0
$40$	0	0
$41$	5.95407	0.929869	0.464935	−	0.885345i	$-0.346078\pi$
$41$	5.95407	0.929869	0.464935	+	0.885345i	$0.346078\pi$
$42$	−8.64296	−1.33364
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	−1.06668	−0.160808
$45$	0	0
$46$	−2.14764	−0.316653
$47$	0.0967881	0.0141180	0.00705900	−	0.999975i	$-0.497753\pi$
$47$	0.0967881	0.0141180	0.00705900	+	0.999975i	$0.497753\pi$
$48$	2.21432	0.319610
$49$	8.23506	1.17644
$50$	0	0
$51$	2.90321	0.406531
$52$	0	0
$53$	−1.49532	−0.205397	−0.102699	−	0.994713i	$-0.532748\pi$
$53$	−1.49532	−0.205397	−0.102699	+	0.994713i	$0.532748\pi$
$54$	2.42864	0.330496
$55$	0	0
$56$	−3.90321	−0.521589
$57$	14.5970	1.93342
$58$	9.05086	1.18844
$59$	−7.18421	−0.935304	−0.467652	−	0.883913i	$-0.654900\pi$
$59$	−7.18421	−0.935304	−0.467652	+	0.883913i	$0.654900\pi$
$60$	0	0
$61$	7.88739	1.00988	0.504938	−	0.863155i	$-0.331515\pi$
$61$	7.88739	1.00988	0.504938	+	0.863155i	$0.331515\pi$
$62$	−6.92396	−0.879343
$63$	7.42864	0.935921
$64$	1.00000	0.125000
$65$	0	0
$66$	2.36196	0.290738
$67$	8.42864	1.02972	0.514861	−	0.857274i	$-0.327843\pi$
$67$	8.42864	1.02972	0.514861	+	0.857274i	$0.327843\pi$
$68$	1.31111	0.158995
$69$	4.75557	0.572503
$70$	0	0
$71$	15.4795	1.83708	0.918539	−	0.395330i	$-0.129370\pi$
$71$	15.4795	1.83708	0.918539	+	0.395330i	$0.129370\pi$
$72$	−1.90321	−0.224296
$73$	15.3526	1.79689	0.898443	−	0.439091i	$-0.144699\pi$
$73$	15.3526	1.79689	0.898443	+	0.439091i	$0.144699\pi$
$74$	5.02074	0.583650
$75$	0	0
$76$	6.59210	0.756166
$77$	−4.16346	−0.474471
$78$	0	0
$79$	4.30174	0.483984	0.241992	−	0.970278i	$-0.422199\pi$
$79$	4.30174	0.483984	0.241992	+	0.970278i	$0.422199\pi$
$80$	0	0
$81$	−11.0874	−1.23194
$82$	−5.95407	−0.657517
$83$	−9.69381	−1.06403	−0.532017	−	0.846734i	$-0.678566\pi$
$83$	−9.69381	−1.06403	−0.532017	+	0.846734i	$0.678566\pi$
$84$	8.64296	0.943024
$85$	0	0
$86$	−2.00000	−0.215666
$87$	−20.0415	−2.14867
$88$	1.06668	0.113708
$89$	−4.52543	−0.479694	−0.239847	−	0.970811i	$-0.577097\pi$
$89$	−4.52543	−0.479694	−0.239847	+	0.970811i	$0.577097\pi$
$90$	0	0
$91$	0	0
$92$	2.14764	0.223907
$93$	15.3319	1.58984
$94$	−0.0967881	−0.00998293
$95$	0	0
$96$	−2.21432	−0.225998
$97$	4.26025	0.432563	0.216282	−	0.976331i	$-0.430607\pi$
$97$	4.26025	0.432563	0.216282	+	0.976331i	$0.430607\pi$
$98$	−8.23506	−0.831867
$99$	−2.03011	−0.204034
$100$	0	0
$101$	1.45875	0.145151	0.0725756	−	0.997363i	$-0.476878\pi$
$101$	1.45875	0.145151	0.0725756	+	0.997363i	$0.476878\pi$
$102$	−2.90321	−0.287461
$103$	−10.2444	−1.00941	−0.504707	−	0.863291i	$-0.668399\pi$
$103$	−10.2444	−1.00941	−0.504707	+	0.863291i	$0.668399\pi$
$104$	0	0
$105$	0	0
$106$	1.49532	0.145238
$107$	−2.21432	−0.214066	−0.107033	−	0.994255i	$-0.534135\pi$
$107$	−2.21432	−0.214066	−0.107033	+	0.994255i	$0.534135\pi$
$108$	−2.42864	−0.233696
$109$	−0.133353	−0.0127729	−0.00638645	−	0.999980i	$-0.502033\pi$
$109$	−0.133353	−0.0127729	−0.00638645	+	0.999980i	$0.502033\pi$
$110$	0	0
$111$	−11.1175	−1.05523
$112$	3.90321	0.368819
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	−14.5970	−1.36714
$115$	0	0
$116$	−9.05086	−0.840351
$117$	0	0
$118$	7.18421	0.661360
$119$	5.11753	0.469123
$120$	0	0
$121$	−9.86220	−0.896564
$122$	−7.88739	−0.714091
$123$	13.1842	1.18878
$124$	6.92396	0.621790
$125$	0	0
$126$	−7.42864	−0.661796
$127$	9.99063	0.886525	0.443263	−	0.896392i	$-0.353821\pi$
$127$	9.99063	0.886525	0.443263	+	0.896392i	$0.353821\pi$
$128$	−1.00000	−0.0883883
$129$	4.42864	0.389920
$130$	0	0
$131$	9.25581	0.808684	0.404342	−	0.914608i	$-0.367501\pi$
$131$	9.25581	0.808684	0.404342	+	0.914608i	$0.367501\pi$
$132$	−2.36196	−0.205582
$133$	25.7304	2.23111
$134$	−8.42864	−0.728124
$135$	0	0
$136$	−1.31111	−0.112427
$137$	14.7906	1.26365	0.631823	−	0.775113i	$-0.282307\pi$
$137$	14.7906	1.26365	0.631823	+	0.775113i	$0.282307\pi$
$138$	−4.75557	−0.404821
$139$	−12.6938	−1.07668	−0.538338	−	0.842729i	$-0.680947\pi$
$139$	−12.6938	−1.07668	−0.538338	+	0.842729i	$0.680947\pi$
$140$	0	0
$141$	0.214320	0.0180490
$142$	−15.4795	−1.29901
$143$	0	0
$144$	1.90321	0.158601
$145$	0	0
$146$	−15.3526	−1.27059
$147$	18.2351	1.50400
$148$	−5.02074	−0.412703
$149$	−7.28592	−0.596886	−0.298443	−	0.954428i	$-0.596467\pi$
$149$	−7.28592	−0.596886	−0.298443	+	0.954428i	$0.596467\pi$
$150$	0	0
$151$	−20.1082	−1.63638	−0.818190	−	0.574949i	$-0.805022\pi$
$151$	−20.1082	−1.63638	−0.818190	+	0.574949i	$0.805022\pi$
$152$	−6.59210	−0.534690
$153$	2.49532	0.201734
$154$	4.16346	0.335502
$155$	0	0
$156$	0	0
$157$	−1.98418	−0.158355	−0.0791773	−	0.996861i	$-0.525229\pi$
$157$	−1.98418	−0.158355	−0.0791773	+	0.996861i	$0.525229\pi$
$158$	−4.30174	−0.342228
$159$	−3.31111	−0.262588
$160$	0	0
$161$	8.38271	0.660650
$162$	11.0874	0.871110
$163$	4.70318	0.368382	0.184191	−	0.982891i	$-0.441034\pi$
$163$	4.70318	0.368382	0.184191	+	0.982891i	$0.441034\pi$
$164$	5.95407	0.464935
$165$	0	0
$166$	9.69381	0.752386
$167$	9.69535	0.750248	0.375124	−	0.926975i	$-0.377600\pi$
$167$	9.69535	0.750248	0.375124	+	0.926975i	$0.377600\pi$
$168$	−8.64296	−0.666819
$169$	0	0
$170$	0	0
$171$	12.5462	0.959430
$172$	2.00000	0.152499
$173$	24.0716	1.83013	0.915065	−	0.403307i	$-0.132139\pi$
$173$	24.0716	1.83013	0.915065	+	0.403307i	$0.132139\pi$
$174$	20.0415	1.51934
$175$	0	0
$176$	−1.06668	−0.0804038
$177$	−15.9081	−1.19573
$178$	4.52543	0.339195
$179$	3.05086	0.228032	0.114016	−	0.993479i	$-0.463629\pi$
$179$	3.05086	0.228032	0.114016	+	0.993479i	$0.463629\pi$
$180$	0	0
$181$	10.6430	0.791085	0.395542	−	0.918448i	$-0.370557\pi$
$181$	10.6430	0.791085	0.395542	+	0.918448i	$0.370557\pi$
$182$	0	0
$183$	17.4652	1.29107
$184$	−2.14764	−0.158326
$185$	0	0
$186$	−15.3319	−1.12419
$187$	−1.39853	−0.102270
$188$	0.0967881	0.00705900
$189$	−9.47949	−0.689532
$190$	0	0
$191$	14.7304	1.06585	0.532926	−	0.846162i	$-0.321092\pi$
$191$	14.7304	1.06585	0.532926	+	0.846162i	$0.321092\pi$
$192$	2.21432	0.159805
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−4.26025	−0.305868
$195$	0	0
$196$	8.23506	0.588219
$197$	10.4128	0.741883	0.370941	−	0.928656i	$-0.379035\pi$
$197$	10.4128	0.741883	0.370941	+	0.928656i	$0.379035\pi$
$198$	2.03011	0.144274
$199$	−4.36842	−0.309669	−0.154834	−	0.987940i	$-0.549484\pi$
$199$	−4.36842	−0.309669	−0.154834	+	0.987940i	$0.549484\pi$
$200$	0	0
$201$	18.6637	1.31644
$202$	−1.45875	−0.102637
$203$	−35.3274	−2.47950
$204$	2.90321	0.203265
$205$	0	0
$206$	10.2444	0.713763
$207$	4.08742	0.284095
$208$	0	0
$209$	−7.03164	−0.486389
$210$	0	0
$211$	5.49532	0.378313	0.189157	−	0.981947i	$-0.439425\pi$
$211$	5.49532	0.378313	0.189157	+	0.981947i	$0.439425\pi$
$212$	−1.49532	−0.102699
$213$	34.2766	2.34859
$214$	2.21432	0.151368
$215$	0	0
$216$	2.42864	0.165248
$217$	27.0257	1.83462
$218$	0.133353	0.00903181
$219$	33.9956	2.29721
$220$	0	0
$221$	0	0
$222$	11.1175	0.746160
$223$	20.0968	1.34578	0.672890	−	0.739742i	$-0.265053\pi$
$223$	20.0968	1.34578	0.672890	+	0.739742i	$0.265053\pi$
$224$	−3.90321	−0.260794
$225$	0	0
$226$	14.0000	0.931266
$227$	−19.3590	−1.28491	−0.642453	−	0.766325i	$-0.722083\pi$
$227$	−19.3590	−1.28491	−0.642453	+	0.766325i	$0.722083\pi$
$228$	14.5970	0.966712
$229$	−15.7255	−1.03917	−0.519584	−	0.854420i	$-0.673913\pi$
$229$	−15.7255	−1.03917	−0.519584	+	0.854420i	$0.673913\pi$
$230$	0	0
$231$	−9.21924	−0.606582
$232$	9.05086	0.594218
$233$	−14.8825	−0.974983	−0.487491	−	0.873128i	$-0.662088\pi$
$233$	−14.8825	−0.974983	−0.487491	+	0.873128i	$0.662088\pi$
$234$	0	0
$235$	0	0
$236$	−7.18421	−0.467652
$237$	9.52543	0.618743
$238$	−5.11753	−0.331720
$239$	−4.42219	−0.286047	−0.143024	−	0.989719i	$-0.545683\pi$
$239$	−4.42219	−0.286047	−0.143024	+	0.989719i	$0.545683\pi$
$240$	0	0
$241$	11.2810	0.726673	0.363336	−	0.931658i	$-0.381638\pi$
$241$	11.2810	0.726673	0.363336	+	0.931658i	$0.381638\pi$
$242$	9.86220	0.633966
$243$	−17.2652	−1.10756
$244$	7.88739	0.504938
$245$	0	0
$246$	−13.1842	−0.840594
$247$	0	0
$248$	−6.92396	−0.439672
$249$	−21.4652	−1.36030
$250$	0	0
$251$	2.65233	0.167413	0.0837067	−	0.996490i	$-0.473324\pi$
$251$	2.65233	0.167413	0.0837067	+	0.996490i	$0.473324\pi$
$252$	7.42864	0.467960
$253$	−2.29084	−0.144024
$254$	−9.99063	−0.626868
$255$	0	0
$256$	1.00000	0.0625000
$257$	4.10171	0.255858	0.127929	−	0.991783i	$-0.459167\pi$
$257$	4.10171	0.255858	0.127929	+	0.991783i	$0.459167\pi$
$258$	−4.42864	−0.275715
$259$	−19.5970	−1.21770
$260$	0	0
$261$	−17.2257	−1.06624
$262$	−9.25581	−0.571826
$263$	−10.8020	−0.666079	−0.333039	−	0.942913i	$-0.608074\pi$
$263$	−10.8020	−0.666079	−0.333039	+	0.942913i	$0.608074\pi$
$264$	2.36196	0.145369
$265$	0	0
$266$	−25.7304	−1.57763
$267$	−10.0207	−0.613260
$268$	8.42864	0.514861
$269$	−18.5827	−1.13301	−0.566505	−	0.824059i	$-0.691705\pi$
$269$	−18.5827	−1.13301	−0.566505	+	0.824059i	$0.691705\pi$
$270$	0	0
$271$	−19.7748	−1.20123	−0.600616	−	0.799537i	$-0.705078\pi$
$271$	−19.7748	−1.20123	−0.600616	+	0.799537i	$0.705078\pi$
$272$	1.31111	0.0794976
$273$	0	0
$274$	−14.7906	−0.893533
$275$	0	0
$276$	4.75557	0.286252
$277$	0.204952	0.0123144	0.00615718	−	0.999981i	$-0.498040\pi$
$277$	0.204952	0.0123144	0.00615718	+	0.999981i	$0.498040\pi$
$278$	12.6938	0.761324
$279$	13.1778	0.788932
$280$	0	0
$281$	20.4558	1.22029	0.610146	−	0.792289i	$-0.291111\pi$
$281$	20.4558	1.22029	0.610146	+	0.792289i	$0.291111\pi$
$282$	−0.214320	−0.0127626
$283$	1.43801	0.0854807	0.0427403	−	0.999086i	$-0.486391\pi$
$283$	1.43801	0.0854807	0.0427403	+	0.999086i	$0.486391\pi$
$284$	15.4795	0.918539
$285$	0	0
$286$	0	0
$287$	23.2400	1.37181
$288$	−1.90321	−0.112148
$289$	−15.2810	−0.898882
$290$	0	0
$291$	9.43356	0.553005
$292$	15.3526	0.898443
$293$	20.9146	1.22184	0.610922	−	0.791691i	$-0.290799\pi$
$293$	20.9146	1.22184	0.610922	+	0.791691i	$0.290799\pi$
$294$	−18.2351	−1.06349
$295$	0	0
$296$	5.02074	0.291825
$297$	2.59057	0.150320
$298$	7.28592	0.422062
$299$	0	0
$300$	0	0
$301$	7.80642	0.449955
$302$	20.1082	1.15709
$303$	3.23014	0.185567
$304$	6.59210	0.378083
$305$	0	0
$306$	−2.49532	−0.142648
$307$	−12.5303	−0.715145	−0.357572	−	0.933885i	$-0.616395\pi$
$307$	−12.5303	−0.715145	−0.357572	+	0.933885i	$0.616395\pi$
$308$	−4.16346	−0.237235
$309$	−22.6844	−1.29047
$310$	0	0
$311$	−9.78123	−0.554643	−0.277321	−	0.960777i	$-0.589447\pi$
$311$	−9.78123	−0.554643	−0.277321	+	0.960777i	$0.589447\pi$
$312$	0	0
$313$	17.2128	0.972924	0.486462	−	0.873702i	$-0.338287\pi$
$313$	17.2128	0.972924	0.486462	+	0.873702i	$0.338287\pi$
$314$	1.98418	0.111974
$315$	0	0
$316$	4.30174	0.241992
$317$	−13.7447	−0.771978	−0.385989	−	0.922503i	$-0.626140\pi$
$317$	−13.7447	−0.771978	−0.385989	+	0.922503i	$0.626140\pi$
$318$	3.31111	0.185678
$319$	9.65433	0.540539
$320$	0	0
$321$	−4.90321	−0.273671
$322$	−8.38271	−0.467150
$323$	8.64296	0.480907
$324$	−11.0874	−0.615968
$325$	0	0
$326$	−4.70318	−0.260485
$327$	−0.295286	−0.0163294
$328$	−5.95407	−0.328758
$329$	0.377784	0.0208279
$330$	0	0
$331$	−19.3876	−1.06564	−0.532820	−	0.846228i	$-0.678868\pi$
$331$	−19.3876	−1.06564	−0.532820	+	0.846228i	$0.678868\pi$
$332$	−9.69381	−0.532017
$333$	−9.55554	−0.523640
$334$	−9.69535	−0.530506
$335$	0	0
$336$	8.64296	0.471512
$337$	0.555539	0.0302621	0.0151311	−	0.999886i	$-0.495183\pi$
$337$	0.555539	0.0302621	0.0151311	+	0.999886i	$0.495183\pi$
$338$	0	0
$339$	−31.0005	−1.68371
$340$	0	0
$341$	−7.38562	−0.399954
$342$	−12.5462	−0.678419
$343$	4.82071	0.260294
$344$	−2.00000	−0.107833
$345$	0	0
$346$	−24.0716	−1.29410
$347$	6.68445	0.358840	0.179420	−	0.983773i	$-0.442578\pi$
$347$	6.68445	0.358840	0.179420	+	0.983773i	$0.442578\pi$
$348$	−20.0415	−1.07434
$349$	−10.5827	−0.566481	−0.283240	−	0.959049i	$-0.591409\pi$
$349$	−10.5827	−0.566481	−0.283240	+	0.959049i	$0.591409\pi$
$350$	0	0
$351$	0	0
$352$	1.06668	0.0568541
$353$	9.20940	0.490167	0.245083	−	0.969502i	$-0.421185\pi$
$353$	9.20940	0.490167	0.245083	+	0.969502i	$0.421185\pi$
$354$	15.9081	0.845508
$355$	0	0
$356$	−4.52543	−0.239847
$357$	11.3319	0.599745
$358$	−3.05086	−0.161243
$359$	4.19358	0.221328	0.110664	−	0.993858i	$-0.464702\pi$
$359$	4.19358	0.221328	0.110664	+	0.993858i	$0.464702\pi$
$360$	0	0
$361$	24.4558	1.28715
$362$	−10.6430	−0.559382
$363$	−21.8381	−1.14620
$364$	0	0
$365$	0	0
$366$	−17.4652	−0.912921
$367$	13.9684	0.729142	0.364571	−	0.931176i	$-0.381216\pi$
$367$	13.9684	0.729142	0.364571	+	0.931176i	$0.381216\pi$
$368$	2.14764	0.111954
$369$	11.3319	0.589913
$370$	0	0
$371$	−5.83654	−0.303018
$372$	15.3319	0.794919
$373$	11.8479	0.613462	0.306731	−	0.951796i	$-0.400765\pi$
$373$	11.8479	0.613462	0.306731	+	0.951796i	$0.400765\pi$
$374$	1.39853	0.0723162
$375$	0	0
$376$	−0.0967881	−0.00499146
$377$	0	0
$378$	9.47949	0.487573
$379$	−0.606394	−0.0311484	−0.0155742	−	0.999879i	$-0.504958\pi$
$379$	−0.606394	−0.0311484	−0.0155742	+	0.999879i	$0.504958\pi$
$380$	0	0
$381$	22.1225	1.13337
$382$	−14.7304	−0.753672
$383$	34.7797	1.77716	0.888580	−	0.458722i	$-0.151693\pi$
$383$	34.7797	1.77716	0.888580	+	0.458722i	$0.151693\pi$
$384$	−2.21432	−0.112999
$385$	0	0
$386$	−14.0000	−0.712581
$387$	3.80642	0.193491
$388$	4.26025	0.216282
$389$	−18.6844	−0.947339	−0.473670	−	0.880703i	$-0.657071\pi$
$389$	−18.6844	−0.947339	−0.473670	+	0.880703i	$0.657071\pi$
$390$	0	0
$391$	2.81579	0.142401
$392$	−8.23506	−0.415934
$393$	20.4953	1.03385
$394$	−10.4128	−0.524590
$395$	0	0
$396$	−2.03011	−0.102017
$397$	−22.9748	−1.15307	−0.576536	−	0.817072i	$-0.695596\pi$
$397$	−22.9748	−1.15307	−0.576536	+	0.817072i	$0.695596\pi$
$398$	4.36842	0.218969
$399$	56.9753	2.85233
$400$	0	0
$401$	4.37334	0.218394	0.109197	−	0.994020i	$-0.465172\pi$
$401$	4.37334	0.218394	0.109197	+	0.994020i	$0.465172\pi$
$402$	−18.6637	−0.930861
$403$	0	0
$404$	1.45875	0.0725756
$405$	0	0
$406$	35.3274	1.75327
$407$	5.35551	0.265463
$408$	−2.90321	−0.143730
$409$	3.76986	0.186408	0.0932038	−	0.995647i	$-0.470289\pi$
$409$	3.76986	0.186408	0.0932038	+	0.995647i	$0.470289\pi$
$410$	0	0
$411$	32.7511	1.61549
$412$	−10.2444	−0.504707
$413$	−28.0415	−1.37983
$414$	−4.08742	−0.200886
$415$	0	0
$416$	0	0
$417$	−28.1082	−1.37646
$418$	7.03164	0.343929
$419$	7.45230	0.364069	0.182034	−	0.983292i	$-0.441732\pi$
$419$	7.45230	0.364069	0.182034	+	0.983292i	$0.441732\pi$
$420$	0	0
$421$	−27.6751	−1.34880	−0.674400	−	0.738366i	$-0.735598\pi$
$421$	−27.6751	−1.34880	−0.674400	+	0.738366i	$0.735598\pi$
$422$	−5.49532	−0.267508
$423$	0.184208	0.00895651
$424$	1.49532	0.0726190
$425$	0	0
$426$	−34.2766	−1.66070
$427$	30.7862	1.48985
$428$	−2.21432	−0.107033
$429$	0	0
$430$	0	0
$431$	−19.6894	−0.948404	−0.474202	−	0.880416i	$-0.657263\pi$
$431$	−19.6894	−0.948404	−0.474202	+	0.880416i	$0.657263\pi$
$432$	−2.42864	−0.116848
$433$	−13.7462	−0.660600	−0.330300	−	0.943876i	$-0.607150\pi$
$433$	−13.7462	−0.660600	−0.330300	+	0.943876i	$0.607150\pi$
$434$	−27.0257	−1.29727
$435$	0	0
$436$	−0.133353	−0.00638645
$437$	14.1575	0.677244
$438$	−33.9956	−1.62437
$439$	41.8227	1.99609	0.998045	−	0.0625026i	$-0.0199082\pi$
$439$	41.8227	1.99609	0.998045	+	0.0625026i	$0.0199082\pi$
$440$	0	0
$441$	15.6731	0.746337
$442$	0	0
$443$	−23.6829	−1.12521	−0.562605	−	0.826726i	$-0.690201\pi$
$443$	−23.6829	−1.12521	−0.562605	+	0.826726i	$0.690201\pi$
$444$	−11.1175	−0.527615
$445$	0	0
$446$	−20.0968	−0.951610
$447$	−16.1334	−0.763081
$448$	3.90321	0.184409
$449$	−7.05578	−0.332983	−0.166491	−	0.986043i	$-0.553244\pi$
$449$	−7.05578	−0.332983	−0.166491	+	0.986043i	$0.553244\pi$
$450$	0	0
$451$	−6.35106	−0.299060
$452$	−14.0000	−0.658505
$453$	−44.5259	−2.09201
$454$	19.3590	0.908565
$455$	0	0
$456$	−14.5970	−0.683568
$457$	35.6795	1.66902	0.834509	−	0.550995i	$-0.185751\pi$
$457$	35.6795	1.66902	0.834509	+	0.550995i	$0.185751\pi$
$458$	15.7255	0.734802
$459$	−3.18421	−0.148626
$460$	0	0
$461$	14.6015	0.680058	0.340029	−	0.940415i	$-0.389563\pi$
$461$	14.6015	0.680058	0.340029	+	0.940415i	$0.389563\pi$
$462$	9.21924	0.428918
$463$	−30.7511	−1.42913	−0.714563	−	0.699571i	$-0.753374\pi$
$463$	−30.7511	−1.42913	−0.714563	+	0.699571i	$0.753374\pi$
$464$	−9.05086	−0.420175
$465$	0	0
$466$	14.8825	0.689417
$467$	−20.5620	−0.951496	−0.475748	−	0.879582i	$-0.657822\pi$
$467$	−20.5620	−0.951496	−0.475748	+	0.879582i	$0.657822\pi$
$468$	0	0
$469$	32.8988	1.51912
$470$	0	0
$471$	−4.39361	−0.202447
$472$	7.18421	0.330680
$473$	−2.13335	−0.0980917
$474$	−9.52543	−0.437517
$475$	0	0
$476$	5.11753	0.234562
$477$	−2.84590	−0.130305
$478$	4.42219	0.202266
$479$	−11.9333	−0.545247	−0.272624	−	0.962121i	$-0.587891\pi$
$479$	−11.9333	−0.545247	−0.272624	+	0.962121i	$0.587891\pi$
$480$	0	0
$481$	0	0
$482$	−11.2810	−0.513835
$483$	18.5620	0.844600
$484$	−9.86220	−0.448282
$485$	0	0
$486$	17.2652	0.783164
$487$	27.9719	1.26753	0.633764	−	0.773527i	$-0.281509\pi$
$487$	27.9719	1.26753	0.633764	+	0.773527i	$0.281509\pi$
$488$	−7.88739	−0.357045
$489$	10.4143	0.470953
$490$	0	0
$491$	−20.7812	−0.937844	−0.468922	−	0.883240i	$-0.655357\pi$
$491$	−20.7812	−0.937844	−0.468922	+	0.883240i	$0.655357\pi$
$492$	13.1842	0.594390
$493$	−11.8666	−0.534447
$494$	0	0
$495$	0	0
$496$	6.92396	0.310895
$497$	60.4197	2.71020
$498$	21.4652	0.961879
$499$	−34.2908	−1.53507	−0.767534	−	0.641008i	$-0.778517\pi$
$499$	−34.2908	−1.53507	−0.767534	+	0.641008i	$0.778517\pi$
$500$	0	0
$501$	21.4686	0.959146
$502$	−2.65233	−0.118379
$503$	−20.2257	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$503$	−20.2257	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$504$	−7.42864	−0.330898
$505$	0	0
$506$	2.29084	0.101840
$507$	0	0
$508$	9.99063	0.443263
$509$	27.3778	1.21350	0.606749	−	0.794893i	$-0.292473\pi$
$509$	27.3778	1.21350	0.606749	+	0.794893i	$0.292473\pi$
$510$	0	0
$511$	59.9244	2.65090
$512$	−1.00000	−0.0441942
$513$	−16.0098	−0.706852
$514$	−4.10171	−0.180919
$515$	0	0
$516$	4.42864	0.194960
$517$	−0.103242	−0.00454056
$518$	19.5970	0.861044
$519$	53.3022	2.33971
$520$	0	0
$521$	−31.2034	−1.36705	−0.683523	−	0.729929i	$-0.739553\pi$
$521$	−31.2034	−1.36705	−0.683523	+	0.729929i	$0.739553\pi$
$522$	17.2257	0.753948
$523$	−9.84791	−0.430619	−0.215310	−	0.976546i	$-0.569076\pi$
$523$	−9.84791	−0.430619	−0.215310	+	0.976546i	$0.569076\pi$
$524$	9.25581	0.404342
$525$	0	0
$526$	10.8020	0.470989
$527$	9.07805	0.395446
$528$	−2.36196	−0.102791
$529$	−18.3876	−0.799462
$530$	0	0
$531$	−13.6731	−0.593361
$532$	25.7304	1.11555
$533$	0	0
$534$	10.0207	0.433640
$535$	0	0
$536$	−8.42864	−0.364062
$537$	6.75557	0.291524
$538$	18.5827	0.801159
$539$	−8.78415	−0.378360
$540$	0	0
$541$	−41.6149	−1.78916	−0.894581	−	0.446905i	$-0.852526\pi$
$541$	−41.6149	−1.78916	−0.894581	+	0.446905i	$0.852526\pi$
$542$	19.7748	0.849400
$543$	23.5669	1.01135
$544$	−1.31111	−0.0562133
$545$	0	0
$546$	0	0
$547$	6.77430	0.289648	0.144824	−	0.989457i	$-0.453738\pi$
$547$	6.77430	0.289648	0.144824	+	0.989457i	$0.453738\pi$
$548$	14.7906	0.631823
$549$	15.0114	0.640670
$550$	0	0
$551$	−59.6642	−2.54178
$552$	−4.75557	−0.202410
$553$	16.7906	0.714009
$554$	−0.204952	−0.00870757
$555$	0	0
$556$	−12.6938	−0.538338
$557$	−25.4449	−1.07814	−0.539068	−	0.842262i	$-0.681224\pi$
$557$	−25.4449	−1.07814	−0.539068	+	0.842262i	$0.681224\pi$
$558$	−13.1778	−0.557859
$559$	0	0
$560$	0	0
$561$	−3.09679	−0.130746
$562$	−20.4558	−0.862877
$563$	13.1842	0.555648	0.277824	−	0.960632i	$-0.410387\pi$
$563$	13.1842	0.555648	0.277824	+	0.960632i	$0.410387\pi$
$564$	0.214320	0.00902449
$565$	0	0
$566$	−1.43801	−0.0604440
$567$	−43.2766	−1.81744
$568$	−15.4795	−0.649505
$569$	−24.4608	−1.02545	−0.512724	−	0.858553i	$-0.671364\pi$
$569$	−24.4608	−1.02545	−0.512724	+	0.858553i	$0.671364\pi$
$570$	0	0
$571$	24.3526	1.01912	0.509562	−	0.860434i	$-0.329807\pi$
$571$	24.3526	1.01912	0.509562	+	0.860434i	$0.329807\pi$
$572$	0	0
$573$	32.6178	1.36263
$574$	−23.2400	−0.970018
$575$	0	0
$576$	1.90321	0.0793005
$577$	42.0479	1.75048	0.875239	−	0.483690i	$-0.160704\pi$
$577$	42.0479	1.75048	0.875239	+	0.483690i	$0.160704\pi$
$578$	15.2810	0.635606
$579$	31.0005	1.28834
$580$	0	0
$581$	−37.8370	−1.56974
$582$	−9.43356	−0.391034
$583$	1.59502	0.0660589
$584$	−15.3526	−0.635295
$585$	0	0
$586$	−20.9146	−0.863974
$587$	7.34614	0.303208	0.151604	−	0.988441i	$-0.451556\pi$
$587$	7.34614	0.303208	0.151604	+	0.988441i	$0.451556\pi$
$588$	18.2351	0.752001
$589$	45.6434	1.88071
$590$	0	0
$591$	23.0573	0.948451
$592$	−5.02074	−0.206351
$593$	−4.19358	−0.172210	−0.0861048	−	0.996286i	$-0.527442\pi$
$593$	−4.19358	−0.172210	−0.0861048	+	0.996286i	$0.527442\pi$
$594$	−2.59057	−0.106292
$595$	0	0
$596$	−7.28592	−0.298443
$597$	−9.67307	−0.395892
$598$	0	0
$599$	9.33630	0.381471	0.190735	−	0.981641i	$-0.438913\pi$
$599$	9.33630	0.381471	0.190735	+	0.981641i	$0.438913\pi$
$600$	0	0
$601$	−2.97142	−0.121207	−0.0606034	−	0.998162i	$-0.519302\pi$
$601$	−2.97142	−0.121207	−0.0606034	+	0.998162i	$0.519302\pi$
$602$	−7.80642	−0.318166
$603$	16.0415	0.653260
$604$	−20.1082	−0.818190
$605$	0	0
$606$	−3.23014	−0.131216
$607$	−17.1432	−0.695821	−0.347910	−	0.937528i	$-0.613109\pi$
$607$	−17.1432	−0.695821	−0.347910	+	0.937528i	$0.613109\pi$
$608$	−6.59210	−0.267345
$609$	−78.2262	−3.16988
$610$	0	0
$611$	0	0
$612$	2.49532	0.100867
$613$	29.2844	1.18279	0.591393	−	0.806384i	$-0.298578\pi$
$613$	29.2844	1.18279	0.591393	+	0.806384i	$0.298578\pi$
$614$	12.5303	0.505684
$615$	0	0
$616$	4.16346	0.167751
$617$	13.2159	0.532050	0.266025	−	0.963966i	$-0.414290\pi$
$617$	13.2159	0.532050	0.266025	+	0.963966i	$0.414290\pi$
$618$	22.6844	0.912502
$619$	18.9333	0.760995	0.380497	−	0.924782i	$-0.375753\pi$
$619$	18.9333	0.760995	0.380497	+	0.924782i	$0.375753\pi$
$620$	0	0
$621$	−5.21585	−0.209305
$622$	9.78123	0.392192
$623$	−17.6637	−0.707681
$624$	0	0
$625$	0	0
$626$	−17.2128	−0.687961
$627$	−15.5703	−0.621818
$628$	−1.98418	−0.0791773
$629$	−6.58274	−0.262471
$630$	0	0
$631$	−2.42864	−0.0966826	−0.0483413	−	0.998831i	$-0.515394\pi$
$631$	−2.42864	−0.0966826	−0.0483413	+	0.998831i	$0.515394\pi$
$632$	−4.30174	−0.171114
$633$	12.1684	0.483650
$634$	13.7447	0.545871
$635$	0	0
$636$	−3.31111	−0.131294
$637$	0	0
$638$	−9.65433	−0.382219
$639$	29.4608	1.16545
$640$	0	0
$641$	15.0874	0.595917	0.297959	−	0.954579i	$-0.403694\pi$
$641$	15.0874	0.595917	0.297959	+	0.954579i	$0.403694\pi$
$642$	4.90321	0.193514
$643$	6.70318	0.264348	0.132174	−	0.991227i	$-0.457804\pi$
$643$	6.70318	0.264348	0.132174	+	0.991227i	$0.457804\pi$
$644$	8.38271	0.330325
$645$	0	0
$646$	−8.64296	−0.340053
$647$	22.3733	0.879587	0.439793	−	0.898099i	$-0.355052\pi$
$647$	22.3733	0.879587	0.439793	+	0.898099i	$0.355052\pi$
$648$	11.0874	0.435555
$649$	7.66323	0.300808
$650$	0	0
$651$	59.8435	2.34545
$652$	4.70318	0.184191
$653$	16.4128	0.642283	0.321142	−	0.947031i	$-0.395933\pi$
$653$	16.4128	0.642283	0.321142	+	0.947031i	$0.395933\pi$
$654$	0.295286	0.0115466
$655$	0	0
$656$	5.95407	0.232467
$657$	29.2192	1.13995
$658$	−0.377784	−0.0147276
$659$	8.66815	0.337663	0.168832	−	0.985645i	$-0.446001\pi$
$659$	8.66815	0.337663	0.168832	+	0.985645i	$0.446001\pi$
$660$	0	0
$661$	−17.4302	−0.677955	−0.338978	−	0.940794i	$-0.610081\pi$
$661$	−17.4302	−0.677955	−0.338978	+	0.940794i	$0.610081\pi$
$662$	19.3876	0.753522
$663$	0	0
$664$	9.69381	0.376193
$665$	0	0
$666$	9.55554	0.370270
$667$	−19.4380	−0.752643
$668$	9.69535	0.375124
$669$	44.5007	1.72050
$670$	0	0
$671$	−8.41329	−0.324792
$672$	−8.64296	−0.333409
$673$	40.4830	1.56051	0.780253	−	0.625464i	$-0.215090\pi$
$673$	40.4830	1.56051	0.780253	+	0.625464i	$0.215090\pi$
$674$	−0.555539	−0.0213986
$675$	0	0
$676$	0	0
$677$	40.0228	1.53820	0.769100	−	0.639129i	$-0.220705\pi$
$677$	40.0228	1.53820	0.769100	+	0.639129i	$0.220705\pi$
$678$	31.0005	1.19057
$679$	16.6287	0.638150
$680$	0	0
$681$	−42.8671	−1.64267
$682$	7.38562	0.282810
$683$	−43.3087	−1.65716	−0.828580	−	0.559871i	$-0.810851\pi$
$683$	−43.3087	−1.65716	−0.828580	+	0.559871i	$0.810851\pi$
$684$	12.5462	0.479715
$685$	0	0
$686$	−4.82071	−0.184056
$687$	−34.8212	−1.32851
$688$	2.00000	0.0762493
$689$	0	0
$690$	0	0
$691$	−28.3481	−1.07841	−0.539207	−	0.842173i	$-0.681276\pi$
$691$	−28.3481	−1.07841	−0.539207	+	0.842173i	$0.681276\pi$
$692$	24.0716	0.915065
$693$	−7.92396	−0.301006
$694$	−6.68445	−0.253738
$695$	0	0
$696$	20.0415	0.759671
$697$	7.80642	0.295689
$698$	10.5827	0.400562
$699$	−32.9545	−1.24646
$700$	0	0
$701$	12.8080	0.483750	0.241875	−	0.970307i	$-0.422238\pi$
$701$	12.8080	0.483750	0.241875	+	0.970307i	$0.422238\pi$
$702$	0	0
$703$	−33.0973	−1.24829
$704$	−1.06668	−0.0402019
$705$	0	0
$706$	−9.20940	−0.346600
$707$	5.69381	0.214138
$708$	−15.9081	−0.597864
$709$	−2.52251	−0.0947350	−0.0473675	−	0.998878i	$-0.515083\pi$
$709$	−2.52251	−0.0947350	−0.0473675	+	0.998878i	$0.515083\pi$
$710$	0	0
$711$	8.18712	0.307041
$712$	4.52543	0.169598
$713$	14.8702	0.556893
$714$	−11.3319	−0.424084
$715$	0	0
$716$	3.05086	0.114016
$717$	−9.79213	−0.365694
$718$	−4.19358	−0.156503
$719$	17.0223	0.634824	0.317412	−	0.948288i	$-0.397186\pi$
$719$	17.0223	0.634824	0.317412	+	0.948288i	$0.397186\pi$
$720$	0	0
$721$	−39.9862	−1.48916
$722$	−24.4558	−0.910152
$723$	24.9797	0.929006
$724$	10.6430	0.395542
$725$	0	0
$726$	21.8381	0.810487
$727$	−30.5353	−1.13249	−0.566245	−	0.824237i	$-0.691605\pi$
$727$	−30.5353	−1.13249	−0.566245	+	0.824237i	$0.691605\pi$
$728$	0	0
$729$	−4.96836	−0.184013
$730$	0	0
$731$	2.62222	0.0969861
$732$	17.4652	0.645533
$733$	−24.4499	−0.903076	−0.451538	−	0.892252i	$-0.649124\pi$
$733$	−24.4499	−0.903076	−0.451538	+	0.892252i	$0.649124\pi$
$734$	−13.9684	−0.515581
$735$	0	0
$736$	−2.14764	−0.0791632
$737$	−8.99063	−0.331174
$738$	−11.3319	−0.417131
$739$	10.7955	0.397120	0.198560	−	0.980089i	$-0.436374\pi$
$739$	10.7955	0.397120	0.198560	+	0.980089i	$0.436374\pi$
$740$	0	0
$741$	0	0
$742$	5.83654	0.214266
$743$	−29.9353	−1.09822	−0.549110	−	0.835750i	$-0.685033\pi$
$743$	−29.9353	−1.09822	−0.549110	+	0.835750i	$0.685033\pi$
$744$	−15.3319	−0.562093
$745$	0	0
$746$	−11.8479	−0.433783
$747$	−18.4494	−0.675028
$748$	−1.39853	−0.0511352
$749$	−8.64296	−0.315807
$750$	0	0
$751$	26.9175	0.982234	0.491117	−	0.871094i	$-0.336589\pi$
$751$	26.9175	0.982234	0.491117	+	0.871094i	$0.336589\pi$
$752$	0.0967881	0.00352950
$753$	5.87310	0.214028
$754$	0	0
$755$	0	0
$756$	−9.47949	−0.344766
$757$	−35.9066	−1.30505	−0.652524	−	0.757768i	$-0.726290\pi$
$757$	−35.9066	−1.30505	−0.652524	+	0.757768i	$0.726290\pi$
$758$	0.606394	0.0220252
$759$	−5.07265	−0.184126
$760$	0	0
$761$	−22.5397	−0.817064	−0.408532	−	0.912744i	$-0.633959\pi$
$761$	−22.5397	−0.817064	−0.408532	+	0.912744i	$0.633959\pi$
$762$	−22.1225	−0.801412
$763$	−0.520505	−0.0188436
$764$	14.7304	0.532926
$765$	0	0
$766$	−34.7797	−1.25664
$767$	0	0
$768$	2.21432	0.0799024
$769$	−2.47457	−0.0892354	−0.0446177	−	0.999004i	$-0.514207\pi$
$769$	−2.47457	−0.0892354	−0.0446177	+	0.999004i	$0.514207\pi$
$770$	0	0
$771$	9.08250	0.327098
$772$	14.0000	0.503871
$773$	44.2005	1.58978	0.794891	−	0.606752i	$-0.207528\pi$
$773$	44.2005	1.58978	0.794891	+	0.606752i	$0.207528\pi$
$774$	−3.80642	−0.136819
$775$	0	0
$776$	−4.26025	−0.152934
$777$	−43.3941	−1.55675
$778$	18.6844	0.669870
$779$	39.2498	1.40627
$780$	0	0
$781$	−16.5116	−0.590832
$782$	−2.81579	−0.100693
$783$	21.9813	0.785546
$784$	8.23506	0.294109
$785$	0	0
$786$	−20.4953	−0.731044
$787$	−34.0306	−1.21306	−0.606530	−	0.795061i	$-0.707439\pi$
$787$	−34.0306	−1.21306	−0.606530	+	0.795061i	$0.707439\pi$
$788$	10.4128	0.370941
$789$	−23.9190	−0.851540
$790$	0	0
$791$	−54.6450	−1.94295
$792$	2.03011	0.0721369
$793$	0	0
$794$	22.9748	0.815346
$795$	0	0
$796$	−4.36842	−0.154834
$797$	8.13780	0.288256	0.144128	−	0.989559i	$-0.453962\pi$
$797$	8.13780	0.288256	0.144128	+	0.989559i	$0.453962\pi$
$798$	−56.9753	−2.01690
$799$	0.126900	0.00448939
$800$	0	0
$801$	−8.61285	−0.304320
$802$	−4.37334	−0.154428
$803$	−16.3763	−0.577905
$804$	18.6637	0.658218
$805$	0	0
$806$	0	0
$807$	−41.1481	−1.44848
$808$	−1.45875	−0.0513187
$809$	−7.85236	−0.276074	−0.138037	−	0.990427i	$-0.544079\pi$
$809$	−7.85236	−0.276074	−0.138037	+	0.990427i	$0.544079\pi$
$810$	0	0
$811$	−9.33477	−0.327788	−0.163894	−	0.986478i	$-0.552405\pi$
$811$	−9.33477	−0.327788	−0.163894	+	0.986478i	$0.552405\pi$
$812$	−35.3274	−1.23975
$813$	−43.7877	−1.53570
$814$	−5.35551	−0.187711
$815$	0	0
$816$	2.90321	0.101633
$817$	13.1842	0.461257
$818$	−3.76986	−0.131810
$819$	0	0
$820$	0	0
$821$	47.5319	1.65887	0.829437	−	0.558600i	$-0.188661\pi$
$821$	47.5319	1.65887	0.829437	+	0.558600i	$0.188661\pi$
$822$	−32.7511	−1.14233
$823$	−1.38715	−0.0483531	−0.0241765	−	0.999708i	$-0.507696\pi$
$823$	−1.38715	−0.0483531	−0.0241765	+	0.999708i	$0.507696\pi$
$824$	10.2444	0.356882
$825$	0	0
$826$	28.0415	0.975688
$827$	31.5131	1.09582	0.547910	−	0.836537i	$-0.315424\pi$
$827$	31.5131	1.09582	0.547910	+	0.836537i	$0.315424\pi$
$828$	4.08742	0.142048
$829$	−28.8256	−1.00116	−0.500578	−	0.865692i	$-0.666879\pi$
$829$	−28.8256	−1.00116	−0.500578	+	0.865692i	$0.666879\pi$
$830$	0	0
$831$	0.453829	0.0157431
$832$	0	0
$833$	10.7971	0.374096
$834$	28.1082	0.973306
$835$	0	0
$836$	−7.03164	−0.243194
$837$	−16.8158	−0.581239
$838$	−7.45230	−0.257435
$839$	−8.43509	−0.291212	−0.145606	−	0.989343i	$-0.546513\pi$
$839$	−8.43509	−0.291212	−0.145606	+	0.989343i	$0.546513\pi$
$840$	0	0
$841$	52.9180	1.82476
$842$	27.6751	0.953746
$843$	45.2958	1.56007
$844$	5.49532	0.189157
$845$	0	0
$846$	−0.184208	−0.00633321
$847$	−38.4943	−1.32268
$848$	−1.49532	−0.0513494
$849$	3.18421	0.109282
$850$	0	0
$851$	−10.7828	−0.369628
$852$	34.2766	1.17430
$853$	40.0656	1.37182	0.685910	−	0.727686i	$-0.259404\pi$
$853$	40.0656	1.37182	0.685910	+	0.727686i	$0.259404\pi$
$854$	−30.7862	−1.05348
$855$	0	0
$856$	2.21432	0.0756839
$857$	32.0479	1.09474	0.547368	−	0.836892i	$-0.315630\pi$
$857$	32.0479	1.09474	0.547368	+	0.836892i	$0.315630\pi$
$858$	0	0
$859$	−26.6894	−0.910630	−0.455315	−	0.890331i	$-0.650473\pi$
$859$	−26.6894	−0.910630	−0.455315	+	0.890331i	$0.650473\pi$
$860$	0	0
$861$	51.4608	1.75378
$862$	19.6894	0.670623
$863$	−30.6593	−1.04365	−0.521827	−	0.853052i	$-0.674749\pi$
$863$	−30.6593	−1.04365	−0.521827	+	0.853052i	$0.674749\pi$
$864$	2.42864	0.0826240
$865$	0	0
$866$	13.7462	0.467115
$867$	−33.8370	−1.14917
$868$	27.0257	0.917311
$869$	−4.58857	−0.155656
$870$	0	0
$871$	0	0
$872$	0.133353	0.00451591
$873$	8.10816	0.274420
$874$	−14.1575	−0.478884
$875$	0	0
$876$	33.9956	1.14860
$877$	−20.9304	−0.706770	−0.353385	−	0.935478i	$-0.614969\pi$
$877$	−20.9304	−0.706770	−0.353385	+	0.935478i	$0.614969\pi$
$878$	−41.8227	−1.41145
$879$	46.3116	1.56205
$880$	0	0
$881$	21.4701	0.723347	0.361673	−	0.932305i	$-0.382206\pi$
$881$	21.4701	0.723347	0.361673	+	0.932305i	$0.382206\pi$
$882$	−15.6731	−0.527740
$883$	−7.73530	−0.260314	−0.130157	−	0.991493i	$-0.541548\pi$
$883$	−7.73530	−0.260314	−0.130157	+	0.991493i	$0.541548\pi$
$884$	0	0
$885$	0	0
$886$	23.6829	0.795643
$887$	−48.4465	−1.62667	−0.813337	−	0.581793i	$-0.802351\pi$
$887$	−48.4465	−1.62667	−0.813337	+	0.581793i	$0.802351\pi$
$888$	11.1175	0.373080
$889$	38.9956	1.30787
$890$	0	0
$891$	11.8267	0.396209
$892$	20.0968	0.672890
$893$	0.638037	0.0213511
$894$	16.1334	0.539580
$895$	0	0
$896$	−3.90321	−0.130397
$897$	0	0
$898$	7.05578	0.235454
$899$	−62.6677	−2.09009
$900$	0	0
$901$	−1.96052	−0.0653144
$902$	6.35106	0.211467
$903$	17.2859	0.575239
$904$	14.0000	0.465633
$905$	0	0
$906$	44.5259	1.47927
$907$	12.0109	0.398815	0.199408	−	0.979917i	$-0.436098\pi$
$907$	12.0109	0.398815	0.199408	+	0.979917i	$0.436098\pi$
$908$	−19.3590	−0.642453
$909$	2.77631	0.0920845
$910$	0	0
$911$	−8.10171	−0.268422	−0.134211	−	0.990953i	$-0.542850\pi$
$911$	−8.10171	−0.268422	−0.134211	+	0.990953i	$0.542850\pi$
$912$	14.5970	0.483356
$913$	10.3402	0.342209
$914$	−35.6795	−1.18017
$915$	0	0
$916$	−15.7255	−0.519584
$917$	36.1274	1.19303
$918$	3.18421	0.105095
$919$	16.5936	0.547374	0.273687	−	0.961819i	$-0.411757\pi$
$919$	16.5936	0.547374	0.273687	+	0.961819i	$0.411757\pi$
$920$	0	0
$921$	−27.7462	−0.914268
$922$	−14.6015	−0.480874
$923$	0	0
$924$	−9.21924	−0.303291
$925$	0	0
$926$	30.7511	1.01054
$927$	−19.4973	−0.640376
$928$	9.05086	0.297109
$929$	−57.1209	−1.87408	−0.937038	−	0.349227i	$-0.886444\pi$
$929$	−57.1209	−1.87408	−0.937038	+	0.349227i	$0.886444\pi$
$930$	0	0
$931$	54.2864	1.77916
$932$	−14.8825	−0.487491
$933$	−21.6588	−0.709077
$934$	20.5620	0.672809
$935$	0	0
$936$	0	0
$937$	−11.1842	−0.365372	−0.182686	−	0.983171i	$-0.558479\pi$
$937$	−11.1842	−0.365372	−0.182686	+	0.983171i	$0.558479\pi$
$938$	−32.8988	−1.07418
$939$	38.1146	1.24382
$940$	0	0
$941$	7.68598	0.250556	0.125278	−	0.992122i	$-0.460018\pi$
$941$	7.68598	0.250556	0.125278	+	0.992122i	$0.460018\pi$
$942$	4.39361	0.143151
$943$	12.7872	0.416409
$944$	−7.18421	−0.233826
$945$	0	0
$946$	2.13335	0.0693613
$947$	−20.6746	−0.671834	−0.335917	−	0.941892i	$-0.609046\pi$
$947$	−20.6746	−0.671834	−0.335917	+	0.941892i	$0.609046\pi$
$948$	9.52543	0.309372
$949$	0	0
$950$	0	0
$951$	−30.4351	−0.986926
$952$	−5.11753	−0.165860
$953$	−30.9753	−1.00339	−0.501694	−	0.865045i	$-0.667290\pi$
$953$	−30.9753	−1.00339	−0.501694	+	0.865045i	$0.667290\pi$
$954$	2.84590	0.0921395
$955$	0	0
$956$	−4.42219	−0.143024
$957$	21.3778	0.691046
$958$	11.9333	0.385548
$959$	57.7309	1.86423
$960$	0	0
$961$	16.9412	0.546489
$962$	0	0
$963$	−4.21432	−0.135805
$964$	11.2810	0.363336
$965$	0	0
$966$	−18.5620	−0.597222
$967$	0.529873	0.0170396	0.00851979	−	0.999964i	$-0.497288\pi$
$967$	0.529873	0.0170396	0.00851979	+	0.999964i	$0.497288\pi$
$968$	9.86220	0.316983
$969$	19.1383	0.614810
$970$	0	0
$971$	−34.3240	−1.10151	−0.550755	−	0.834667i	$-0.685660\pi$
$971$	−34.3240	−1.10151	−0.550755	+	0.834667i	$0.685660\pi$
$972$	−17.2652	−0.553781
$973$	−49.5466	−1.58839
$974$	−27.9719	−0.896277
$975$	0	0
$976$	7.88739	0.252469
$977$	−19.9684	−0.638844	−0.319422	−	0.947613i	$-0.603489\pi$
$977$	−19.9684	−0.638844	−0.319422	+	0.947613i	$0.603489\pi$
$978$	−10.4143	−0.333014
$979$	4.82717	0.154277
$980$	0	0
$981$	−0.253799	−0.00810318
$982$	20.7812	0.663156
$983$	20.8524	0.665087	0.332543	−	0.943088i	$-0.392093\pi$
$983$	20.8524	0.665087	0.332543	+	0.943088i	$0.392093\pi$
$984$	−13.1842	−0.420297
$985$	0	0
$986$	11.8666	0.377911
$987$	0.836535	0.0266272
$988$	0	0
$989$	4.29529	0.136582
$990$	0	0
$991$	−2.95899	−0.0939954	−0.0469977	−	0.998895i	$-0.514965\pi$
$991$	−2.95899	−0.0939954	−0.0469977	+	0.998895i	$0.514965\pi$
$992$	−6.92396	−0.219836
$993$	−42.9304	−1.36236
$994$	−60.4197	−1.91640
$995$	0	0
$996$	−21.4652	−0.680151
$997$	−21.0479	−0.666595	−0.333297	−	0.942822i	$-0.608161\pi$
$997$	−21.0479	−0.666595	−0.333297	+	0.942822i	$0.608161\pi$
$998$	34.2908	1.08546
$999$	12.1936	0.385788

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8450.2.a.bt.1.3		3
5.2	odd	4		1690.2.b.b.339.1		6
5.3	odd	4		1690.2.b.b.339.6		6
5.4	even	2		8450.2.a.ca.1.1		3
13.4	even	6		650.2.e.j.601.1		6
13.10	even	6		650.2.e.j.451.1		6
13.12	even	2		8450.2.a.cb.1.3		3
65.4	even	6		650.2.e.k.601.3		6
65.8	even	4		1690.2.c.b.1689.6		6
65.12	odd	4		1690.2.b.c.339.4		6
65.17	odd	12		130.2.n.a.29.4	yes	12
65.18	even	4		1690.2.c.c.1689.6		6
65.23	odd	12		130.2.n.a.9.4	yes	12
65.38	odd	4		1690.2.b.c.339.3		6
65.43	odd	12		130.2.n.a.29.3	yes	12
65.47	even	4		1690.2.c.c.1689.1		6
65.49	even	6		650.2.e.k.451.3		6
65.57	even	4		1690.2.c.b.1689.1		6
65.62	odd	12		130.2.n.a.9.3	✓	12
65.64	even	2		8450.2.a.bu.1.1		3
195.17	even	12		1170.2.bp.h.289.1		12
195.23	even	12		1170.2.bp.h.919.1		12
195.62	even	12		1170.2.bp.h.919.4		12
195.173	even	12		1170.2.bp.h.289.4		12
260.23	even	12		1040.2.dh.b.529.6		12
260.43	even	12		1040.2.dh.b.289.1		12
260.127	even	12		1040.2.dh.b.529.1		12
260.147	even	12		1040.2.dh.b.289.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.3	✓	12	65.62	odd	12
130.2.n.a.9.4	yes	12	65.23	odd	12
130.2.n.a.29.3	yes	12	65.43	odd	12
130.2.n.a.29.4	yes	12	65.17	odd	12
650.2.e.j.451.1		6	13.10	even	6
650.2.e.j.601.1		6	13.4	even	6
650.2.e.k.451.3		6	65.49	even	6
650.2.e.k.601.3		6	65.4	even	6
1040.2.dh.b.289.1		12	260.43	even	12
1040.2.dh.b.289.6		12	260.147	even	12
1040.2.dh.b.529.1		12	260.127	even	12
1040.2.dh.b.529.6		12	260.23	even	12
1170.2.bp.h.289.1		12	195.17	even	12
1170.2.bp.h.289.4		12	195.173	even	12
1170.2.bp.h.919.1		12	195.23	even	12
1170.2.bp.h.919.4		12	195.62	even	12
1690.2.b.b.339.1		6	5.2	odd	4
1690.2.b.b.339.6		6	5.3	odd	4
1690.2.b.c.339.3		6	65.38	odd	4
1690.2.b.c.339.4		6	65.12	odd	4
1690.2.c.b.1689.1		6	65.57	even	4
1690.2.c.b.1689.6		6	65.8	even	4
1690.2.c.c.1689.1		6	65.47	even	4
1690.2.c.c.1689.6		6	65.18	even	4
8450.2.a.bt.1.3		3	1.1	even	1	trivial
8450.2.a.bu.1.1		3	65.64	even	2
8450.2.a.ca.1.1		3	5.4	even	2
8450.2.a.cb.1.3		3	13.12	even	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:	\( N \)	\(=\)	\( 8450 = 2 \cdot 5^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8450.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.21432 q^{3} +1.00000 q^{4} -2.21432 q^{6} +3.90321 q^{7} -1.00000 q^{8} +1.90321 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.21432 q^{3} +1.00000 q^{4} -2.21432 q^{6} +3.90321 q^{7} -1.00000 q^{8} +1.90321 q^{9} -1.06668 q^{11} +2.21432 q^{12} -3.90321 q^{14} +1.00000 q^{16} +1.31111 q^{17} -1.90321 q^{18} +6.59210 q^{19} +8.64296 q^{21} +1.06668 q^{22} +2.14764 q^{23} -2.21432 q^{24} -2.42864 q^{27} +3.90321 q^{28} -9.05086 q^{29} +6.92396 q^{31} -1.00000 q^{32} -2.36196 q^{33} -1.31111 q^{34} +1.90321 q^{36} -5.02074 q^{37} -6.59210 q^{38} +5.95407 q^{41} -8.64296 q^{42} +2.00000 q^{43} -1.06668 q^{44} -2.14764 q^{46} +0.0967881 q^{47} +2.21432 q^{48} +8.23506 q^{49} +2.90321 q^{51} -1.49532 q^{53} +2.42864 q^{54} -3.90321 q^{56} +14.5970 q^{57} +9.05086 q^{58} -7.18421 q^{59} +7.88739 q^{61} -6.92396 q^{62} +7.42864 q^{63} +1.00000 q^{64} +2.36196 q^{66} +8.42864 q^{67} +1.31111 q^{68} +4.75557 q^{69} +15.4795 q^{71} -1.90321 q^{72} +15.3526 q^{73} +5.02074 q^{74} +6.59210 q^{76} -4.16346 q^{77} +4.30174 q^{79} -11.0874 q^{81} -5.95407 q^{82} -9.69381 q^{83} +8.64296 q^{84} -2.00000 q^{86} -20.0415 q^{87} +1.06668 q^{88} -4.52543 q^{89} +2.14764 q^{92} +15.3319 q^{93} -0.0967881 q^{94} -2.21432 q^{96} +4.26025 q^{97} -8.23506 q^{98} -2.03011 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} + 5 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^4 + 5 * q^7 - 3 * q^8 - q^9	\( 3 q - 3 q^{2} + 3 q^{4} + 5 q^{7} - 3 q^{8} - q^{9} - 3 q^{11} - 5 q^{14} + 3 q^{16} + 4 q^{17} + q^{18} + 13 q^{19} + 6 q^{21} + 3 q^{22} + 6 q^{27} + 5 q^{28} - 14 q^{29} - 6 q^{31} - 3 q^{32} + 6 q^{33} - 4 q^{34} - q^{36} + 5 q^{37} - 13 q^{38} - 2 q^{41} - 6 q^{42} + 6 q^{43} - 3 q^{44} + 7 q^{47} - 2 q^{49} + 2 q^{51} + 9 q^{53} - 6 q^{54} - 5 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 4 q^{61} + 6 q^{62} + 9 q^{63} + 3 q^{64} - 6 q^{66} + 12 q^{67} + 4 q^{68} + 14 q^{69} + 20 q^{71} + q^{72} + 6 q^{73} - 5 q^{74} + 13 q^{76} - 19 q^{77} - 14 q^{79} - 13 q^{81} + 2 q^{82} + 4 q^{83} + 6 q^{84} - 6 q^{86} - 20 q^{87} + 3 q^{88} - 7 q^{89} + 26 q^{93} - 7 q^{94} + 26 q^{97} + 2 q^{98} - 13 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 + 5 * q^7 - 3 * q^8 - q^9 - 3 * q^11 - 5 * q^14 + 3 * q^16 + 4 * q^17 + q^18 + 13 * q^19 + 6 * q^21 + 3 * q^22 + 6 * q^27 + 5 * q^28 - 14 * q^29 - 6 * q^31 - 3 * q^32 + 6 * q^33 - 4 * q^34 - q^36 + 5 * q^37 - 13 * q^38 - 2 * q^41 - 6 * q^42 + 6 * q^43 - 3 * q^44 + 7 * q^47 - 2 * q^49 + 2 * q^51 + 9 * q^53 - 6 * q^54 - 5 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 4 * q^61 + 6 * q^62 + 9 * q^63 + 3 * q^64 - 6 * q^66 + 12 * q^67 + 4 * q^68 + 14 * q^69 + 20 * q^71 + q^72 + 6 * q^73 - 5 * q^74 + 13 * q^76 - 19 * q^77 - 14 * q^79 - 13 * q^81 + 2 * q^82 + 4 * q^83 + 6 * q^84 - 6 * q^86 - 20 * q^87 + 3 * q^88 - 7 * q^89 + 26 * q^93 - 7 * q^94 + 26 * q^97 + 2 * q^98 - 13 * q^99

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