LMFDB - Embedded newform 3525.2.a.bi.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 17 x^{11} + 51 x^{10} + 106 x^{9} - 316 x^{8} - 288 x^{7} + 852 x^{6} + 309 x^{5} + \cdots - 2 $ x^13 - 3x^12 - 17x^11 + 51x^10 + 106x^9 - 316x^8 - 288x^7 + 852x^6 + 309x^5 - 923x^4 - 107x^3 + 293x^2 + 12x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$2.74237$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.74237 q^{2} +1.00000 q^{3} +5.52059 q^{4} +2.74237 q^{6} +1.18262 q^{7} +9.65475 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.74237 q^{2} +1.00000 q^{3} +5.52059 q^{4} +2.74237 q^{6} +1.18262 q^{7} +9.65475 q^{8} +1.00000 q^{9} -3.47841 q^{11} +5.52059 q^{12} -5.63132 q^{13} +3.24317 q^{14} +15.4357 q^{16} +4.27384 q^{17} +2.74237 q^{18} +8.18104 q^{19} +1.18262 q^{21} -9.53909 q^{22} -6.05477 q^{23} +9.65475 q^{24} -15.4432 q^{26} +1.00000 q^{27} +6.52874 q^{28} +4.15942 q^{29} -2.98011 q^{31} +23.0209 q^{32} -3.47841 q^{33} +11.7204 q^{34} +5.52059 q^{36} +6.90639 q^{37} +22.4354 q^{38} -5.63132 q^{39} +7.34896 q^{41} +3.24317 q^{42} +2.62207 q^{43} -19.2029 q^{44} -16.6044 q^{46} +1.00000 q^{47} +15.4357 q^{48} -5.60142 q^{49} +4.27384 q^{51} -31.0882 q^{52} -1.77644 q^{53} +2.74237 q^{54} +11.4179 q^{56} +8.18104 q^{57} +11.4067 q^{58} +2.60332 q^{59} -9.07880 q^{61} -8.17257 q^{62} +1.18262 q^{63} +32.2604 q^{64} -9.53909 q^{66} -12.8586 q^{67} +23.5941 q^{68} -6.05477 q^{69} +1.83113 q^{71} +9.65475 q^{72} -1.43456 q^{73} +18.9399 q^{74} +45.1642 q^{76} -4.11362 q^{77} -15.4432 q^{78} -2.99071 q^{79} +1.00000 q^{81} +20.1536 q^{82} -6.78713 q^{83} +6.52874 q^{84} +7.19069 q^{86} +4.15942 q^{87} -33.5832 q^{88} -11.7281 q^{89} -6.65969 q^{91} -33.4259 q^{92} -2.98011 q^{93} +2.74237 q^{94} +23.0209 q^{96} -14.9476 q^{97} -15.3612 q^{98} -3.47841 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9	$ 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9} + 16 q^{11} + 17 q^{12} - 8 q^{13} - 4 q^{14} + 29 q^{16} + 12 q^{17} + 3 q^{18} + 28 q^{19} - 4 q^{21} + 6 q^{23} + 15 q^{24} + 4 q^{26} + 13 q^{27} - 20 q^{28} + 12 q^{29} + 26 q^{31} + 53 q^{32} + 16 q^{33} + 8 q^{34} + 17 q^{36} - 4 q^{37} + 2 q^{38} - 8 q^{39} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{44} + 16 q^{46} + 13 q^{47} + 29 q^{48} + 21 q^{49} + 12 q^{51} - 32 q^{52} + 6 q^{53} + 3 q^{54} + 28 q^{57} - 4 q^{58} + 34 q^{59} + 24 q^{61} + 30 q^{62} - 4 q^{63} + 13 q^{64} - 24 q^{67} + 44 q^{68} + 6 q^{69} + 20 q^{71} + 15 q^{72} - 6 q^{73} + 20 q^{74} + 66 q^{76} - 2 q^{77} + 4 q^{78} + 6 q^{79} + 13 q^{81} + 20 q^{82} + 14 q^{83} - 20 q^{84} + 48 q^{86} + 12 q^{87} - 22 q^{88} + 36 q^{89} + 4 q^{91} + 4 q^{92} + 26 q^{93} + 3 q^{94} + 53 q^{96} - 32 q^{97} - 39 q^{98} + 16 q^{99}+O(q^{100}) $ 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9 + 16 * q^11 + 17 * q^12 - 8 * q^13 - 4 * q^14 + 29 * q^16 + 12 * q^17 + 3 * q^18 + 28 * q^19 - 4 * q^21 + 6 * q^23 + 15 * q^24 + 4 * q^26 + 13 * q^27 - 20 * q^28 + 12 * q^29 + 26 * q^31 + 53 * q^32 + 16 * q^33 + 8 * q^34 + 17 * q^36 - 4 * q^37 + 2 * q^38 - 8 * q^39 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 4 * q^44 + 16 * q^46 + 13 * q^47 + 29 * q^48 + 21 * q^49 + 12 * q^51 - 32 * q^52 + 6 * q^53 + 3 * q^54 + 28 * q^57 - 4 * q^58 + 34 * q^59 + 24 * q^61 + 30 * q^62 - 4 * q^63 + 13 * q^64 - 24 * q^67 + 44 * q^68 + 6 * q^69 + 20 * q^71 + 15 * q^72 - 6 * q^73 + 20 * q^74 + 66 * q^76 - 2 * q^77 + 4 * q^78 + 6 * q^79 + 13 * q^81 + 20 * q^82 + 14 * q^83 - 20 * q^84 + 48 * q^86 + 12 * q^87 - 22 * q^88 + 36 * q^89 + 4 * q^91 + 4 * q^92 + 26 * q^93 + 3 * q^94 + 53 * q^96 - 32 * q^97 - 39 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.74237	1.93915	0.969574	−	0.244799i	$-0.0787219\pi$
$2$	2.74237	1.93915	0.969574	+	0.244799i	$0.0787219\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.52059	2.76029
$5$	0	0
$5$	0	0
$6$	2.74237	1.11957
$7$	1.18262	0.446987	0.223493	−	0.974705i	$-0.428254\pi$
$7$	1.18262	0.446987	0.223493	+	0.974705i	$0.428254\pi$
$8$	9.65475	3.41347
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.47841	−1.04878	−0.524390	−	0.851478i	$-0.675707\pi$
$11$	−3.47841	−1.04878	−0.524390	+	0.851478i	$0.675707\pi$
$12$	5.52059	1.59366
$13$	−5.63132	−1.56185	−0.780923	−	0.624627i	$-0.785251\pi$
$13$	−5.63132	−1.56185	−0.780923	+	0.624627i	$0.785251\pi$
$14$	3.24317	0.866773
$15$	0	0
$16$	15.4357	3.85893
$17$	4.27384	1.03656	0.518279	−	0.855212i	$-0.326573\pi$
$17$	4.27384	1.03656	0.518279	+	0.855212i	$0.326573\pi$
$18$	2.74237	0.646383
$19$	8.18104	1.87686	0.938430	−	0.345470i	$-0.112280\pi$
$19$	8.18104	1.87686	0.938430	+	0.345470i	$0.112280\pi$
$20$	0	0
$21$	1.18262	0.258068
$22$	−9.53909	−2.03374
$23$	−6.05477	−1.26251	−0.631253	−	0.775577i	$-0.717459\pi$
$23$	−6.05477	−1.26251	−0.631253	+	0.775577i	$0.717459\pi$
$24$	9.65475	1.97077
$25$	0	0
$26$	−15.4432	−3.02865
$27$	1.00000	0.192450
$28$	6.52874	1.23381
$29$	4.15942	0.772385	0.386193	−	0.922418i	$-0.373790\pi$
$29$	4.15942	0.772385	0.386193	+	0.922418i	$0.373790\pi$
$30$	0	0
$31$	−2.98011	−0.535244	−0.267622	−	0.963524i	$-0.586238\pi$
$31$	−2.98011	−0.535244	−0.267622	+	0.963524i	$0.586238\pi$
$32$	23.0209	4.06956
$33$	−3.47841	−0.605514
$34$	11.7204	2.01004
$35$	0	0
$36$	5.52059	0.920098
$37$	6.90639	1.13540	0.567702	−	0.823234i	$-0.307833\pi$
$37$	6.90639	1.13540	0.567702	+	0.823234i	$0.307833\pi$
$38$	22.4354	3.63951
$39$	−5.63132	−0.901732
$40$	0	0
$41$	7.34896	1.14772	0.573858	−	0.818955i	$-0.305446\pi$
$41$	7.34896	1.14772	0.573858	+	0.818955i	$0.305446\pi$
$42$	3.24317	0.500432
$43$	2.62207	0.399862	0.199931	−	0.979810i	$-0.435928\pi$
$43$	2.62207	0.399862	0.199931	+	0.979810i	$0.435928\pi$
$44$	−19.2029	−2.89494
$45$	0	0
$46$	−16.6044	−2.44819
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	15.4357	2.22795
$49$	−5.60142	−0.800203
$50$	0	0
$51$	4.27384	0.598457
$52$	−31.0882	−4.31116
$53$	−1.77644	−0.244013	−0.122006	−	0.992529i	$-0.538933\pi$
$53$	−1.77644	−0.244013	−0.122006	+	0.992529i	$0.538933\pi$
$54$	2.74237	0.373189
$55$	0	0
$56$	11.4179	1.52578
$57$	8.18104	1.08361
$58$	11.4067	1.49777
$59$	2.60332	0.338923	0.169462	−	0.985537i	$-0.445797\pi$
$59$	2.60332	0.338923	0.169462	+	0.985537i	$0.445797\pi$
$60$	0	0
$61$	−9.07880	−1.16242	−0.581211	−	0.813753i	$-0.697421\pi$
$61$	−9.07880	−1.16242	−0.581211	+	0.813753i	$0.697421\pi$
$62$	−8.17257	−1.03792
$63$	1.18262	0.148996
$64$	32.2604	4.03256
$65$	0	0
$66$	−9.53909	−1.17418
$67$	−12.8586	−1.57093	−0.785463	−	0.618908i	$-0.787575\pi$
$67$	−12.8586	−1.57093	−0.785463	+	0.618908i	$0.787575\pi$
$68$	23.5941	2.86120
$69$	−6.05477	−0.728908
$70$	0	0
$71$	1.83113	0.217315	0.108657	−	0.994079i	$-0.465345\pi$
$71$	1.83113	0.217315	0.108657	+	0.994079i	$0.465345\pi$
$72$	9.65475	1.13782
$73$	−1.43456	−0.167902	−0.0839510	−	0.996470i	$-0.526754\pi$
$73$	−1.43456	−0.167902	−0.0839510	+	0.996470i	$0.526754\pi$
$74$	18.9399	2.20172
$75$	0	0
$76$	45.1642	5.18068
$77$	−4.11362	−0.468791
$78$	−15.4432	−1.74859
$79$	−2.99071	−0.336481	−0.168241	−	0.985746i	$-0.553809\pi$
$79$	−2.99071	−0.336481	−0.168241	+	0.985746i	$0.553809\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	20.1536	2.22559
$83$	−6.78713	−0.744984	−0.372492	−	0.928035i	$-0.621497\pi$
$83$	−6.78713	−0.744984	−0.372492	+	0.928035i	$0.621497\pi$
$84$	6.52874	0.712343
$85$	0	0
$86$	7.19069	0.775392
$87$	4.15942	0.445937
$88$	−33.5832	−3.57998
$89$	−11.7281	−1.24318	−0.621590	−	0.783343i	$-0.713513\pi$
$89$	−11.7281	−1.24318	−0.621590	+	0.783343i	$0.713513\pi$
$90$	0	0
$91$	−6.65969	−0.698125
$92$	−33.4259	−3.48489
$93$	−2.98011	−0.309023
$94$	2.74237	0.282854
$95$	0	0
$96$	23.0209	2.34956
$97$	−14.9476	−1.51770	−0.758850	−	0.651266i	$-0.774238\pi$
$97$	−14.9476	−1.51770	−0.758850	+	0.651266i	$0.774238\pi$
$98$	−15.3612	−1.55171
$99$	−3.47841	−0.349593
$100$	0	0
$101$	−12.9891	−1.29246	−0.646230	−	0.763142i	$-0.723655\pi$
$101$	−12.9891	−1.29246	−0.646230	+	0.763142i	$0.723655\pi$
$102$	11.7204	1.16050
$103$	3.89453	0.383740	0.191870	−	0.981420i	$-0.438545\pi$
$103$	3.89453	0.383740	0.191870	+	0.981420i	$0.438545\pi$
$104$	−54.3690	−5.33132
$105$	0	0
$106$	−4.87166	−0.473177
$107$	10.4948	1.01457	0.507286	−	0.861778i	$-0.330649\pi$
$107$	10.4948	1.01457	0.507286	+	0.861778i	$0.330649\pi$
$108$	5.52059	0.531219
$109$	−5.81961	−0.557418	−0.278709	−	0.960376i	$-0.589906\pi$
$109$	−5.81961	−0.557418	−0.278709	+	0.960376i	$0.589906\pi$
$110$	0	0
$111$	6.90639	0.655526
$112$	18.2545	1.72489
$113$	−15.1609	−1.42621	−0.713107	−	0.701055i	$-0.752713\pi$
$113$	−15.1609	−1.42621	−0.713107	+	0.701055i	$0.752713\pi$
$114$	22.4354	2.10127
$115$	0	0
$116$	22.9625	2.13201
$117$	−5.63132	−0.520615
$118$	7.13926	0.657222
$119$	5.05431	0.463328
$120$	0	0
$121$	1.09934	0.0999399
$122$	−24.8974	−2.25411
$123$	7.34896	0.662634
$124$	−16.4520	−1.47743
$125$	0	0
$126$	3.24317	0.288924
$127$	−9.51162	−0.844020	−0.422010	−	0.906591i	$-0.638675\pi$
$127$	−9.51162	−0.844020	−0.422010	+	0.906591i	$0.638675\pi$
$128$	42.4282	3.75016
$129$	2.62207	0.230860
$130$	0	0
$131$	10.8032	0.943878	0.471939	−	0.881631i	$-0.343554\pi$
$131$	10.8032	0.943878	0.471939	+	0.881631i	$0.343554\pi$
$132$	−19.2029	−1.67140
$133$	9.67503	0.838931
$134$	−35.2630	−3.04626
$135$	0	0
$136$	41.2628	3.53826
$137$	−2.10628	−0.179952	−0.0899759	−	0.995944i	$-0.528679\pi$
$137$	−2.10628	−0.179952	−0.0899759	+	0.995944i	$0.528679\pi$
$138$	−16.6044	−1.41346
$139$	−1.89352	−0.160607	−0.0803033	−	0.996770i	$-0.525589\pi$
$139$	−1.89352	−0.160607	−0.0803033	+	0.996770i	$0.525589\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	5.02163	0.421405
$143$	19.5880	1.63803
$144$	15.4357	1.28631
$145$	0	0
$146$	−3.93408	−0.325587
$147$	−5.60142	−0.461997
$148$	38.1273	3.13405
$149$	6.21102	0.508827	0.254413	−	0.967096i	$-0.418118\pi$
$149$	6.21102	0.508827	0.254413	+	0.967096i	$0.418118\pi$
$150$	0	0
$151$	−15.8462	−1.28955	−0.644773	−	0.764374i	$-0.723048\pi$
$151$	−15.8462	−1.28955	−0.644773	+	0.764374i	$0.723048\pi$
$152$	78.9859	6.40660
$153$	4.27384	0.345519
$154$	−11.2811	−0.909055
$155$	0	0
$156$	−31.0882	−2.48905
$157$	13.7455	1.09701	0.548505	−	0.836147i	$-0.315197\pi$
$157$	13.7455	1.09701	0.548505	+	0.836147i	$0.315197\pi$
$158$	−8.20164	−0.652487
$159$	−1.77644	−0.140881
$160$	0	0
$161$	−7.16046	−0.564324
$162$	2.74237	0.215461
$163$	−5.87563	−0.460215	−0.230107	−	0.973165i	$-0.573908\pi$
$163$	−5.87563	−0.460215	−0.230107	+	0.973165i	$0.573908\pi$
$164$	40.5706	3.16803
$165$	0	0
$166$	−18.6128	−1.44463
$167$	−6.92563	−0.535921	−0.267961	−	0.963430i	$-0.586350\pi$
$167$	−6.92563	−0.535921	−0.267961	+	0.963430i	$0.586350\pi$
$168$	11.4179	0.880907
$169$	18.7117	1.43936
$170$	0	0
$171$	8.18104	0.625620
$172$	14.4754	1.10374
$173$	−5.58431	−0.424567	−0.212284	−	0.977208i	$-0.568090\pi$
$173$	−5.58431	−0.424567	−0.212284	+	0.977208i	$0.568090\pi$
$174$	11.4067	0.864737
$175$	0	0
$176$	−53.6918	−4.04717
$177$	2.60332	0.195678
$178$	−32.1629	−2.41071
$179$	−10.2242	−0.764191	−0.382096	−	0.924123i	$-0.624797\pi$
$179$	−10.2242	−0.764191	−0.382096	+	0.924123i	$0.624797\pi$
$180$	0	0
$181$	−7.13256	−0.530159	−0.265080	−	0.964227i	$-0.585398\pi$
$181$	−7.13256	−0.530159	−0.265080	+	0.964227i	$0.585398\pi$
$182$	−18.2633	−1.35377
$183$	−9.07880	−0.671124
$184$	−58.4573	−4.30953
$185$	0	0
$186$	−8.17257	−0.599242
$187$	−14.8662	−1.08712
$188$	5.52059	0.402630
$189$	1.18262	0.0860226
$190$	0	0
$191$	9.25306	0.669528	0.334764	−	0.942302i	$-0.391343\pi$
$191$	9.25306	0.669528	0.334764	+	0.942302i	$0.391343\pi$
$192$	32.2604	2.32820
$193$	−1.96214	−0.141238	−0.0706191	−	0.997503i	$-0.522497\pi$
$193$	−1.96214	−0.141238	−0.0706191	+	0.997503i	$0.522497\pi$
$194$	−40.9919	−2.94304
$195$	0	0
$196$	−30.9231	−2.20880
$197$	8.01414	0.570984	0.285492	−	0.958381i	$-0.407843\pi$
$197$	8.01414	0.570984	0.285492	+	0.958381i	$0.407843\pi$
$198$	−9.53909	−0.677913
$199$	19.8368	1.40619	0.703096	−	0.711095i	$-0.251800\pi$
$199$	19.8368	1.40619	0.703096	+	0.711095i	$0.251800\pi$
$200$	0	0
$201$	−12.8586	−0.906975
$202$	−35.6208	−2.50627
$203$	4.91900	0.345246
$204$	23.5941	1.65192
$205$	0	0
$206$	10.6803	0.744128
$207$	−6.05477	−0.420835
$208$	−86.9234	−6.02705
$209$	−28.4570	−1.96841
$210$	0	0
$211$	−2.65052	−0.182470	−0.0912348	−	0.995829i	$-0.529081\pi$
$211$	−2.65052	−0.182470	−0.0912348	+	0.995829i	$0.529081\pi$
$212$	−9.80700	−0.673547
$213$	1.83113	0.125467
$214$	28.7807	1.96741
$215$	0	0
$216$	9.65475	0.656923
$217$	−3.52433	−0.239247
$218$	−15.9595	−1.08091
$219$	−1.43456	−0.0969383
$220$	0	0
$221$	−24.0673	−1.61894
$222$	18.9399	1.27116
$223$	0.118378	0.00792715	0.00396358	−	0.999992i	$-0.498738\pi$
$223$	0.118378	0.00792715	0.00396358	+	0.999992i	$0.498738\pi$
$224$	27.2249	1.81904
$225$	0	0
$226$	−41.5767	−2.76564
$227$	1.63231	0.108340	0.0541702	−	0.998532i	$-0.482749\pi$
$227$	1.63231	0.108340	0.0541702	+	0.998532i	$0.482749\pi$
$228$	45.1642	2.99107
$229$	−15.2328	−1.00661	−0.503307	−	0.864107i	$-0.667884\pi$
$229$	−15.2328	−1.00661	−0.503307	+	0.864107i	$0.667884\pi$
$230$	0	0
$231$	−4.11362	−0.270657
$232$	40.1582	2.63651
$233$	16.1791	1.05993	0.529964	−	0.848020i	$-0.322205\pi$
$233$	16.1791	1.05993	0.529964	+	0.848020i	$0.322205\pi$
$234$	−15.4432	−1.00955
$235$	0	0
$236$	14.3719	0.935528
$237$	−2.99071	−0.194268
$238$	13.8608	0.898461
$239$	−11.7407	−0.759445	−0.379723	−	0.925100i	$-0.623981\pi$
$239$	−11.7407	−0.759445	−0.379723	+	0.925100i	$0.623981\pi$
$240$	0	0
$241$	29.5789	1.90534	0.952672	−	0.304002i	$-0.0983228\pi$
$241$	29.5789	1.90534	0.952672	+	0.304002i	$0.0983228\pi$
$242$	3.01479	0.193798
$243$	1.00000	0.0641500
$244$	−50.1203	−3.20862
$245$	0	0
$246$	20.1536	1.28494
$247$	−46.0700	−2.93137
$248$	−28.7723	−1.82704
$249$	−6.78713	−0.430117
$250$	0	0
$251$	16.6905	1.05349	0.526746	−	0.850023i	$-0.323412\pi$
$251$	16.6905	1.05349	0.526746	+	0.850023i	$0.323412\pi$
$252$	6.52874	0.411272
$253$	21.0610	1.32409
$254$	−26.0844	−1.63668
$255$	0	0
$256$	51.8329	3.23956
$257$	20.6039	1.28524	0.642618	−	0.766187i	$-0.277848\pi$
$257$	20.6039	1.28524	0.642618	+	0.766187i	$0.277848\pi$
$258$	7.19069	0.447673
$259$	8.16761	0.507510
$260$	0	0
$261$	4.15942	0.257462
$262$	29.6263	1.83032
$263$	−5.57321	−0.343659	−0.171829	−	0.985127i	$-0.554968\pi$
$263$	−5.57321	−0.343659	−0.171829	+	0.985127i	$0.554968\pi$
$264$	−33.5832	−2.06690
$265$	0	0
$266$	26.5325	1.62681
$267$	−11.7281	−0.717751
$268$	−70.9870	−4.33622
$269$	11.0853	0.675885	0.337943	−	0.941167i	$-0.390269\pi$
$269$	11.0853	0.675885	0.337943	+	0.941167i	$0.390269\pi$
$270$	0	0
$271$	8.20390	0.498352	0.249176	−	0.968458i	$-0.419840\pi$
$271$	8.20390	0.498352	0.249176	+	0.968458i	$0.419840\pi$
$272$	65.9697	4.00000
$273$	−6.65969	−0.403062
$274$	−5.77620	−0.348953
$275$	0	0
$276$	−33.4259	−2.01200
$277$	−12.0691	−0.725163	−0.362582	−	0.931952i	$-0.618105\pi$
$277$	−12.0691	−0.725163	−0.362582	+	0.931952i	$0.618105\pi$
$278$	−5.19274	−0.311440
$279$	−2.98011	−0.178415
$280$	0	0
$281$	24.3492	1.45255	0.726276	−	0.687403i	$-0.241249\pi$
$281$	24.3492	1.45255	0.726276	+	0.687403i	$0.241249\pi$
$282$	2.74237	0.163306
$283$	−23.0077	−1.36767	−0.683834	−	0.729638i	$-0.739689\pi$
$283$	−23.0077	−1.36767	−0.683834	+	0.729638i	$0.739689\pi$
$284$	10.1089	0.599853
$285$	0	0
$286$	53.7176	3.17639
$287$	8.69100	0.513013
$288$	23.0209	1.35652
$289$	1.26568	0.0744518
$290$	0	0
$291$	−14.9476	−0.876244
$292$	−7.91959	−0.463459
$293$	−24.7312	−1.44481	−0.722406	−	0.691469i	$-0.756964\pi$
$293$	−24.7312	−1.44481	−0.722406	+	0.691469i	$0.756964\pi$
$294$	−15.3612	−0.895881
$295$	0	0
$296$	66.6795	3.87567
$297$	−3.47841	−0.201838
$298$	17.0329	0.986690
$299$	34.0963	1.97184
$300$	0	0
$301$	3.10090	0.178733
$302$	−43.4562	−2.50062
$303$	−12.9891	−0.746202
$304$	126.280	7.24267
$305$	0	0
$306$	11.7204	0.670013
$307$	9.37703	0.535176	0.267588	−	0.963533i	$-0.413773\pi$
$307$	9.37703	0.535176	0.267588	+	0.963533i	$0.413773\pi$
$308$	−22.7096	−1.29400
$309$	3.89453	0.221552
$310$	0	0
$311$	24.1338	1.36850	0.684251	−	0.729246i	$-0.260129\pi$
$311$	24.1338	1.36850	0.684251	+	0.729246i	$0.260129\pi$
$312$	−54.3690	−3.07804
$313$	30.6656	1.73332	0.866660	−	0.498900i	$-0.166262\pi$
$313$	30.6656	1.73332	0.866660	+	0.498900i	$0.166262\pi$
$314$	37.6953	2.12727
$315$	0	0
$316$	−16.5105	−0.928787
$317$	12.2027	0.685372	0.342686	−	0.939450i	$-0.388663\pi$
$317$	12.2027	0.685372	0.342686	+	0.939450i	$0.388663\pi$
$318$	−4.87166	−0.273189
$319$	−14.4682	−0.810062
$320$	0	0
$321$	10.4948	0.585764
$322$	−19.6366	−1.09431
$323$	34.9644	1.94547
$324$	5.52059	0.306699
$325$	0	0
$326$	−16.1132	−0.892425
$327$	−5.81961	−0.321825
$328$	70.9524	3.91769
$329$	1.18262	0.0651997
$330$	0	0
$331$	2.92128	0.160568	0.0802841	−	0.996772i	$-0.474417\pi$
$331$	2.92128	0.160568	0.0802841	+	0.996772i	$0.474417\pi$
$332$	−37.4689	−2.05638
$333$	6.90639	0.378468
$334$	−18.9926	−1.03923
$335$	0	0
$336$	18.2545	0.995866
$337$	7.60845	0.414459	0.207229	−	0.978292i	$-0.433555\pi$
$337$	7.60845	0.414459	0.207229	+	0.978292i	$0.433555\pi$
$338$	51.3145	2.79114
$339$	−15.1609	−0.823425
$340$	0	0
$341$	10.3661	0.561354
$342$	22.4354	1.21317
$343$	−14.9026	−0.804667
$344$	25.3154	1.36492
$345$	0	0
$346$	−15.3142	−0.823298
$347$	11.8416	0.635691	0.317846	−	0.948142i	$-0.397041\pi$
$347$	11.8416	0.635691	0.317846	+	0.948142i	$0.397041\pi$
$348$	22.9625	1.23092
$349$	15.7616	0.843697	0.421848	−	0.906666i	$-0.361381\pi$
$349$	15.7616	0.843697	0.421848	+	0.906666i	$0.361381\pi$
$350$	0	0
$351$	−5.63132	−0.300577
$352$	−80.0762	−4.26808
$353$	16.7000	0.888851	0.444426	−	0.895816i	$-0.353408\pi$
$353$	16.7000	0.888851	0.444426	+	0.895816i	$0.353408\pi$
$354$	7.13926	0.379448
$355$	0	0
$356$	−64.7462	−3.43154
$357$	5.05431	0.267502
$358$	−28.0385	−1.48188
$359$	24.5406	1.29520	0.647602	−	0.761979i	$-0.275772\pi$
$359$	24.5406	1.29520	0.647602	+	0.761979i	$0.275772\pi$
$360$	0	0
$361$	47.9294	2.52260
$362$	−19.5601	−1.02806
$363$	1.09934	0.0577003
$364$	−36.7654	−1.92703
$365$	0	0
$366$	−24.8974	−1.30141
$367$	−17.9776	−0.938425	−0.469213	−	0.883085i	$-0.655462\pi$
$367$	−17.9776	−0.938425	−0.469213	+	0.883085i	$0.655462\pi$
$368$	−93.4597	−4.87192
$369$	7.34896	0.382572
$370$	0	0
$371$	−2.10085	−0.109071
$372$	−16.4520	−0.852996
$373$	−36.5447	−1.89221	−0.946105	−	0.323859i	$-0.895020\pi$
$373$	−36.5447	−1.89221	−0.946105	+	0.323859i	$0.895020\pi$
$374$	−40.7685	−2.10809
$375$	0	0
$376$	9.65475	0.497906
$377$	−23.4230	−1.20635
$378$	3.24317	0.166811
$379$	16.8696	0.866531	0.433265	−	0.901266i	$-0.357361\pi$
$379$	16.8696	0.866531	0.433265	+	0.901266i	$0.357361\pi$
$380$	0	0
$381$	−9.51162	−0.487295
$382$	25.3753	1.29831
$383$	−16.2560	−0.830645	−0.415322	−	0.909674i	$-0.636331\pi$
$383$	−16.2560	−0.830645	−0.415322	+	0.909674i	$0.636331\pi$
$384$	42.4282	2.16515
$385$	0	0
$386$	−5.38092	−0.273882
$387$	2.62207	0.133287
$388$	−82.5196	−4.18930
$389$	−14.3181	−0.725959	−0.362979	−	0.931797i	$-0.618240\pi$
$389$	−14.3181	−0.725959	−0.362979	+	0.931797i	$0.618240\pi$
$390$	0	0
$391$	−25.8771	−1.30866
$392$	−54.0803	−2.73147
$393$	10.8032	0.544948
$394$	21.9777	1.10722
$395$	0	0
$396$	−19.2029	−0.964981
$397$	11.6416	0.584275	0.292138	−	0.956376i	$-0.405633\pi$
$397$	11.6416	0.584275	0.292138	+	0.956376i	$0.405633\pi$
$398$	54.3998	2.72681
$399$	9.67503	0.484357
$400$	0	0
$401$	17.8760	0.892684	0.446342	−	0.894862i	$-0.352726\pi$
$401$	17.8760	0.892684	0.446342	+	0.894862i	$0.352726\pi$
$402$	−35.2630	−1.75876
$403$	16.7820	0.835969
$404$	−71.7073	−3.56757
$405$	0	0
$406$	13.4897	0.669483
$407$	−24.0233	−1.19079
$408$	41.2628	2.04281
$409$	1.48293	0.0733264	0.0366632	−	0.999328i	$-0.488327\pi$
$409$	1.48293	0.0733264	0.0366632	+	0.999328i	$0.488327\pi$
$410$	0	0
$411$	−2.10628	−0.103895
$412$	21.5001	1.05924
$413$	3.07873	0.151494
$414$	−16.6044	−0.816062
$415$	0	0
$416$	−129.638	−6.35603
$417$	−1.89352	−0.0927263
$418$	−78.0396	−3.81704
$419$	40.3031	1.96893	0.984467	−	0.175570i	$-0.0561767\pi$
$419$	40.3031	1.96893	0.984467	+	0.175570i	$0.0561767\pi$
$420$	0	0
$421$	8.56293	0.417332	0.208666	−	0.977987i	$-0.433088\pi$
$421$	8.56293	0.417332	0.208666	+	0.977987i	$0.433088\pi$
$422$	−7.26871	−0.353835
$423$	1.00000	0.0486217
$424$	−17.1511	−0.832931
$425$	0	0
$426$	5.02163	0.243299
$427$	−10.7367	−0.519587
$428$	57.9376	2.80052
$429$	19.5880	0.945719
$430$	0	0
$431$	1.03240	0.0497290	0.0248645	−	0.999691i	$-0.492085\pi$
$431$	1.03240	0.0497290	0.0248645	+	0.999691i	$0.492085\pi$
$432$	15.4357	0.742651
$433$	21.1914	1.01839	0.509196	−	0.860651i	$-0.329943\pi$
$433$	21.1914	1.01839	0.509196	+	0.860651i	$0.329943\pi$
$434$	−9.66502	−0.463936
$435$	0	0
$436$	−32.1277	−1.53864
$437$	−49.5343	−2.36955
$438$	−3.93408	−0.187978
$439$	7.72254	0.368577	0.184288	−	0.982872i	$-0.441002\pi$
$439$	7.72254	0.368577	0.184288	+	0.982872i	$0.441002\pi$
$440$	0	0
$441$	−5.60142	−0.266734
$442$	−66.0015	−3.13937
$443$	−30.0193	−1.42626	−0.713131	−	0.701031i	$-0.752724\pi$
$443$	−30.0193	−1.42626	−0.713131	+	0.701031i	$0.752724\pi$
$444$	38.1273	1.80944
$445$	0	0
$446$	0.324635	0.0153719
$447$	6.21102	0.293771
$448$	38.1517	1.80250
$449$	20.5004	0.967473	0.483736	−	0.875214i	$-0.339279\pi$
$449$	20.5004	0.967473	0.483736	+	0.875214i	$0.339279\pi$
$450$	0	0
$451$	−25.5627	−1.20370
$452$	−83.6969	−3.93677
$453$	−15.8462	−0.744520
$454$	4.47641	0.210088
$455$	0	0
$456$	78.9859	3.69885
$457$	−14.3886	−0.673073	−0.336536	−	0.941670i	$-0.609255\pi$
$457$	−14.3886	−0.673073	−0.336536	+	0.941670i	$0.609255\pi$
$458$	−41.7741	−1.95197
$459$	4.27384	0.199486
$460$	0	0
$461$	−4.15305	−0.193427	−0.0967135	−	0.995312i	$-0.530833\pi$
$461$	−4.15305	−0.193427	−0.0967135	+	0.995312i	$0.530833\pi$
$462$	−11.2811	−0.524843
$463$	14.6304	0.679930	0.339965	−	0.940438i	$-0.389585\pi$
$463$	14.6304	0.679930	0.339965	+	0.940438i	$0.389585\pi$
$464$	64.2036	2.98058
$465$	0	0
$466$	44.3691	2.05536
$467$	27.2159	1.25940	0.629701	−	0.776838i	$-0.283177\pi$
$467$	27.2159	1.25940	0.629701	+	0.776838i	$0.283177\pi$
$468$	−31.0882	−1.43705
$469$	−15.2068	−0.702184
$470$	0	0
$471$	13.7455	0.633359
$472$	25.1344	1.15690
$473$	−9.12064	−0.419367
$474$	−8.20164	−0.376714
$475$	0	0
$476$	27.9027	1.27892
$477$	−1.77644	−0.0813376
$478$	−32.1974	−1.47268
$479$	11.5282	0.526736	0.263368	−	0.964695i	$-0.415167\pi$
$479$	11.5282	0.526736	0.263368	+	0.964695i	$0.415167\pi$
$480$	0	0
$481$	−38.8921	−1.77333
$482$	81.1162	3.69474
$483$	−7.16046	−0.325812
$484$	6.06900	0.275863
$485$	0	0
$486$	2.74237	0.124396
$487$	−10.7084	−0.485243	−0.242621	−	0.970121i	$-0.578007\pi$
$487$	−10.7084	−0.485243	−0.242621	+	0.970121i	$0.578007\pi$
$488$	−87.6536	−3.96789
$489$	−5.87563	−0.265705
$490$	0	0
$491$	−23.6363	−1.06669	−0.533346	−	0.845897i	$-0.679066\pi$
$491$	−23.6363	−1.06669	−0.533346	+	0.845897i	$0.679066\pi$
$492$	40.5706	1.82906
$493$	17.7767	0.800622
$494$	−126.341	−5.68435
$495$	0	0
$496$	−46.0002	−2.06547
$497$	2.16552	0.0971368
$498$	−18.6128	−0.834060
$499$	20.8755	0.934514	0.467257	−	0.884121i	$-0.345242\pi$
$499$	20.8755	0.934514	0.467257	+	0.884121i	$0.345242\pi$
$500$	0	0
$501$	−6.92563	−0.309414
$502$	45.7714	2.04288
$503$	−25.7847	−1.14968	−0.574842	−	0.818264i	$-0.694937\pi$
$503$	−25.7847	−1.14968	−0.574842	+	0.818264i	$0.694937\pi$
$504$	11.4179	0.508592
$505$	0	0
$506$	57.7569	2.56761
$507$	18.7117	0.831017
$508$	−52.5098	−2.32974
$509$	−20.8904	−0.925951	−0.462976	−	0.886371i	$-0.653218\pi$
$509$	−20.8904	−0.925951	−0.462976	+	0.886371i	$0.653218\pi$
$510$	0	0
$511$	−1.69653	−0.0750500
$512$	57.2885	2.53182
$513$	8.18104	0.361202
$514$	56.5035	2.49226
$515$	0	0
$516$	14.4754	0.637243
$517$	−3.47841	−0.152980
$518$	22.3986	0.984138
$519$	−5.58431	−0.245124
$520$	0	0
$521$	16.8480	0.738124	0.369062	−	0.929405i	$-0.379679\pi$
$521$	16.8480	0.738124	0.369062	+	0.929405i	$0.379679\pi$
$522$	11.4067	0.499256
$523$	1.30328	0.0569885	0.0284942	−	0.999594i	$-0.490929\pi$
$523$	1.30328	0.0569885	0.0284942	+	0.999594i	$0.490929\pi$
$524$	59.6399	2.60538
$525$	0	0
$526$	−15.2838	−0.666405
$527$	−12.7365	−0.554812
$528$	−53.6918	−2.33663
$529$	13.6602	0.593922
$530$	0	0
$531$	2.60332	0.112974
$532$	53.4119	2.31570
$533$	−41.3843	−1.79255
$534$	−32.1629	−1.39182
$535$	0	0
$536$	−124.146	−5.36231
$537$	−10.2242	−0.441206
$538$	30.4001	1.31064
$539$	19.4840	0.839237
$540$	0	0
$541$	15.3500	0.659950	0.329975	−	0.943990i	$-0.392960\pi$
$541$	15.3500	0.659950	0.329975	+	0.943990i	$0.392960\pi$
$542$	22.4981	0.966377
$543$	−7.13256	−0.306087
$544$	98.3877	4.21834
$545$	0	0
$546$	−18.2633	−0.781598
$547$	−35.5735	−1.52101	−0.760507	−	0.649330i	$-0.775050\pi$
$547$	−35.5735	−1.52101	−0.760507	+	0.649330i	$0.775050\pi$
$548$	−11.6279	−0.496720
$549$	−9.07880	−0.387474
$550$	0	0
$551$	34.0284	1.44966
$552$	−58.4573	−2.48811
$553$	−3.53686	−0.150403
$554$	−33.0980	−1.40620
$555$	0	0
$556$	−10.4534	−0.443321
$557$	7.76343	0.328947	0.164474	−	0.986381i	$-0.447407\pi$
$557$	7.76343	0.328947	0.164474	+	0.986381i	$0.447407\pi$
$558$	−8.17257	−0.345973
$559$	−14.7657	−0.624523
$560$	0	0
$561$	−14.8662	−0.627650
$562$	66.7745	2.81671
$563$	18.1505	0.764954	0.382477	−	0.923965i	$-0.375071\pi$
$563$	18.1505	0.764954	0.382477	+	0.923965i	$0.375071\pi$
$564$	5.52059	0.232459
$565$	0	0
$566$	−63.0957	−2.65211
$567$	1.18262	0.0496652
$568$	17.6791	0.741797
$569$	−21.5551	−0.903635	−0.451818	−	0.892110i	$-0.649224\pi$
$569$	−21.5551	−0.903635	−0.451818	+	0.892110i	$0.649224\pi$
$570$	0	0
$571$	6.55294	0.274232	0.137116	−	0.990555i	$-0.456217\pi$
$571$	6.55294	0.274232	0.137116	+	0.990555i	$0.456217\pi$
$572$	108.137	4.52145
$573$	9.25306	0.386552
$574$	23.8339	0.994809
$575$	0	0
$576$	32.2604	1.34419
$577$	15.6852	0.652981	0.326491	−	0.945200i	$-0.394134\pi$
$577$	15.6852	0.652981	0.326491	+	0.945200i	$0.394134\pi$
$578$	3.47097	0.144373
$579$	−1.96214	−0.0815439
$580$	0	0
$581$	−8.02657	−0.332998
$582$	−40.9919	−1.69917
$583$	6.17919	0.255916
$584$	−13.8503	−0.573129
$585$	0	0
$586$	−67.8221	−2.80170
$587$	−19.0872	−0.787815	−0.393907	−	0.919150i	$-0.628877\pi$
$587$	−19.0872	−0.787815	−0.393907	+	0.919150i	$0.628877\pi$
$588$	−30.9231	−1.27525
$589$	−24.3804	−1.00458
$590$	0	0
$591$	8.01414	0.329657
$592$	106.605	4.38144
$593$	−9.57363	−0.393142	−0.196571	−	0.980490i	$-0.562981\pi$
$593$	−9.57363	−0.393142	−0.196571	+	0.980490i	$0.562981\pi$
$594$	−9.53909	−0.391393
$595$	0	0
$596$	34.2885	1.40451
$597$	19.8368	0.811865
$598$	93.5047	3.82369
$599$	31.9147	1.30400	0.652001	−	0.758218i	$-0.273930\pi$
$599$	31.9147	1.30400	0.652001	+	0.758218i	$0.273930\pi$
$600$	0	0
$601$	−28.1866	−1.14976	−0.574878	−	0.818239i	$-0.694950\pi$
$601$	−28.1866	−1.14976	−0.574878	+	0.818239i	$0.694950\pi$
$602$	8.50382	0.346590
$603$	−12.8586	−0.523642
$604$	−87.4804	−3.55953
$605$	0	0
$606$	−35.6208	−1.44700
$607$	24.3726	0.989253	0.494627	−	0.869106i	$-0.335305\pi$
$607$	24.3726	0.989253	0.494627	+	0.869106i	$0.335305\pi$
$608$	188.335	7.63800
$609$	4.91900	0.199328
$610$	0	0
$611$	−5.63132	−0.227819
$612$	23.5941	0.953735
$613$	−26.0517	−1.05222	−0.526109	−	0.850417i	$-0.676350\pi$
$613$	−26.0517	−1.05222	−0.526109	+	0.850417i	$0.676350\pi$
$614$	25.7153	1.03778
$615$	0	0
$616$	−39.7160	−1.60020
$617$	−41.6712	−1.67762	−0.838810	−	0.544424i	$-0.816748\pi$
$617$	−41.6712	−1.67762	−0.838810	+	0.544424i	$0.816748\pi$
$618$	10.6803	0.429623
$619$	−14.0162	−0.563358	−0.281679	−	0.959509i	$-0.590891\pi$
$619$	−14.0162	−0.563358	−0.281679	+	0.959509i	$0.590891\pi$
$620$	0	0
$621$	−6.05477	−0.242969
$622$	66.1838	2.65373
$623$	−13.8699	−0.555685
$624$	−86.9234	−3.47972
$625$	0	0
$626$	84.0963	3.36116
$627$	−28.4570	−1.13646
$628$	75.8833	3.02807
$629$	29.5168	1.17691
$630$	0	0
$631$	−13.8924	−0.553048	−0.276524	−	0.961007i	$-0.589183\pi$
$631$	−13.8924	−0.553048	−0.276524	+	0.961007i	$0.589183\pi$
$632$	−28.8746	−1.14857
$633$	−2.65052	−0.105349
$634$	33.4643	1.32904
$635$	0	0
$636$	−9.80700	−0.388873
$637$	31.5434	1.24979
$638$	−39.6771	−1.57083
$639$	1.83113	0.0724383
$640$	0	0
$641$	−39.7776	−1.57112	−0.785561	−	0.618785i	$-0.787625\pi$
$641$	−39.7776	−1.57112	−0.785561	+	0.618785i	$0.787625\pi$
$642$	28.7807	1.13588
$643$	28.8715	1.13858	0.569290	−	0.822137i	$-0.307218\pi$
$643$	28.8715	1.13858	0.569290	+	0.822137i	$0.307218\pi$
$644$	−39.5300	−1.55770
$645$	0	0
$646$	95.8854	3.77256
$647$	−26.7367	−1.05113	−0.525564	−	0.850754i	$-0.676146\pi$
$647$	−26.7367	−1.05113	−0.525564	+	0.850754i	$0.676146\pi$
$648$	9.65475	0.379274
$649$	−9.05541	−0.355456
$650$	0	0
$651$	−3.52433	−0.138129
$652$	−32.4369	−1.27033
$653$	6.84567	0.267892	0.133946	−	0.990989i	$-0.457235\pi$
$653$	6.84567	0.267892	0.133946	+	0.990989i	$0.457235\pi$
$654$	−15.9595	−0.624067
$655$	0	0
$656$	113.436	4.42895
$657$	−1.43456	−0.0559673
$658$	3.24317	0.126432
$659$	−4.14255	−0.161371	−0.0806854	−	0.996740i	$-0.525711\pi$
$659$	−4.14255	−0.161371	−0.0806854	+	0.996740i	$0.525711\pi$
$660$	0	0
$661$	−26.8061	−1.04264	−0.521319	−	0.853362i	$-0.674560\pi$
$661$	−26.8061	−1.04264	−0.521319	+	0.853362i	$0.674560\pi$
$662$	8.01124	0.311366
$663$	−24.0673	−0.934698
$664$	−65.5281	−2.54298
$665$	0	0
$666$	18.9399	0.733905
$667$	−25.1843	−0.975141
$668$	−38.2336	−1.47930
$669$	0.118378	0.00457674
$670$	0	0
$671$	31.5798	1.21912
$672$	27.2249	1.05022
$673$	−26.4223	−1.01850	−0.509252	−	0.860617i	$-0.670078\pi$
$673$	−26.4223	−1.01850	−0.509252	+	0.860617i	$0.670078\pi$
$674$	20.8652	0.803696
$675$	0	0
$676$	103.300	3.97307
$677$	1.48733	0.0571626	0.0285813	−	0.999591i	$-0.490901\pi$
$677$	1.48733	0.0571626	0.0285813	+	0.999591i	$0.490901\pi$
$678$	−41.5767	−1.59674
$679$	−17.6773	−0.678392
$680$	0	0
$681$	1.63231	0.0625504
$682$	28.4276	1.08855
$683$	1.53579	0.0587655	0.0293828	−	0.999568i	$-0.490646\pi$
$683$	1.53579	0.0587655	0.0293828	+	0.999568i	$0.490646\pi$
$684$	45.1642	1.72689
$685$	0	0
$686$	−40.8685	−1.56037
$687$	−15.2328	−0.581169
$688$	40.4735	1.54304
$689$	10.0037	0.381111
$690$	0	0
$691$	19.1681	0.729188	0.364594	−	0.931167i	$-0.381208\pi$
$691$	19.1681	0.729188	0.364594	+	0.931167i	$0.381208\pi$
$692$	−30.8287	−1.17193
$693$	−4.11362	−0.156264
$694$	32.4741	1.23270
$695$	0	0
$696$	40.1582	1.52219
$697$	31.4083	1.18967
$698$	43.2240	1.63605
$699$	16.1791	0.611950
$700$	0	0
$701$	−2.52069	−0.0952052	−0.0476026	−	0.998866i	$-0.515158\pi$
$701$	−2.52069	−0.0952052	−0.0476026	+	0.998866i	$0.515158\pi$
$702$	−15.4432	−0.582864
$703$	56.5015	2.13099
$704$	−112.215	−4.22926
$705$	0	0
$706$	45.7976	1.72361
$707$	−15.3611	−0.577713
$708$	14.3719	0.540127
$709$	36.8532	1.38405	0.692025	−	0.721873i	$-0.256719\pi$
$709$	36.8532	1.38405	0.692025	+	0.721873i	$0.256719\pi$
$710$	0	0
$711$	−2.99071	−0.112160
$712$	−113.232	−4.24356
$713$	18.0439	0.675749
$714$	13.8608	0.518727
$715$	0	0
$716$	−56.4435	−2.10939
$717$	−11.7407	−0.438466
$718$	67.2994	2.51159
$719$	35.6166	1.32828	0.664138	−	0.747610i	$-0.268799\pi$
$719$	35.6166	1.32828	0.664138	+	0.747610i	$0.268799\pi$
$720$	0	0
$721$	4.60574	0.171527
$722$	131.440	4.89170
$723$	29.5789	1.10005
$724$	−39.3759	−1.46339
$725$	0	0
$726$	3.01479	0.111889
$727$	4.53503	0.168195	0.0840975	−	0.996458i	$-0.473199\pi$
$727$	4.53503	0.168195	0.0840975	+	0.996458i	$0.473199\pi$
$728$	−64.2976	−2.38303
$729$	1.00000	0.0370370
$730$	0	0
$731$	11.2063	0.414480
$732$	−50.1203	−1.85250
$733$	−39.5305	−1.46009	−0.730047	−	0.683397i	$-0.760502\pi$
$733$	−39.5305	−1.46009	−0.730047	+	0.683397i	$0.760502\pi$
$734$	−49.3013	−1.81975
$735$	0	0
$736$	−139.386	−5.13785
$737$	44.7275	1.64756
$738$	20.1536	0.741863
$739$	−51.9928	−1.91259	−0.956293	−	0.292409i	$-0.905543\pi$
$739$	−51.9928	−1.91259	−0.956293	+	0.292409i	$0.905543\pi$
$740$	0	0
$741$	−46.0700	−1.69243
$742$	−5.76130	−0.211504
$743$	−35.8825	−1.31640	−0.658201	−	0.752842i	$-0.728682\pi$
$743$	−35.8825	−1.31640	−0.658201	+	0.752842i	$0.728682\pi$
$744$	−28.7723	−1.05484
$745$	0	0
$746$	−100.219	−3.66928
$747$	−6.78713	−0.248328
$748$	−82.0699	−3.00077
$749$	12.4113	0.453500
$750$	0	0
$751$	−30.8687	−1.12641	−0.563207	−	0.826316i	$-0.690433\pi$
$751$	−30.8687	−1.12641	−0.563207	+	0.826316i	$0.690433\pi$
$752$	15.4357	0.562883
$753$	16.6905	0.608234
$754$	−64.2346	−2.33929
$755$	0	0
$756$	6.52874	0.237448
$757$	3.12622	0.113625	0.0568123	−	0.998385i	$-0.481906\pi$
$757$	3.12622	0.113625	0.0568123	+	0.998385i	$0.481906\pi$
$758$	46.2626	1.68033
$759$	21.0610	0.764465
$760$	0	0
$761$	28.7431	1.04194	0.520968	−	0.853576i	$-0.325571\pi$
$761$	28.7431	1.04194	0.520968	+	0.853576i	$0.325571\pi$
$762$	−26.0844	−0.944937
$763$	−6.88236	−0.249158
$764$	51.0824	1.84809
$765$	0	0
$766$	−44.5801	−1.61074
$767$	−14.6601	−0.529346
$768$	51.8329	1.87036
$769$	43.3401	1.56288	0.781441	−	0.623979i	$-0.214485\pi$
$769$	43.3401	1.56288	0.781441	+	0.623979i	$0.214485\pi$
$770$	0	0
$771$	20.6039	0.742032
$772$	−10.8322	−0.389859
$773$	32.0671	1.15337	0.576686	−	0.816966i	$-0.304346\pi$
$773$	32.0671	1.15337	0.576686	+	0.816966i	$0.304346\pi$
$774$	7.19069	0.258464
$775$	0	0
$776$	−144.315	−5.18062
$777$	8.16761	0.293011
$778$	−39.2656	−1.40774
$779$	60.1222	2.15410
$780$	0	0
$781$	−6.36941	−0.227915
$782$	−70.9645	−2.53769
$783$	4.15942	0.148646
$784$	−86.4619	−3.08793
$785$	0	0
$786$	29.6263	1.05674
$787$	25.1775	0.897483	0.448741	−	0.893662i	$-0.351872\pi$
$787$	25.1775	0.897483	0.448741	+	0.893662i	$0.351872\pi$
$788$	44.2427	1.57608
$789$	−5.57321	−0.198411
$790$	0	0
$791$	−17.9295	−0.637499
$792$	−33.5832	−1.19333
$793$	51.1256	1.81552
$794$	31.9256	1.13300
$795$	0	0
$796$	109.511	3.88150
$797$	47.5905	1.68574	0.842871	−	0.538116i	$-0.180864\pi$
$797$	47.5905	1.68574	0.842871	+	0.538116i	$0.180864\pi$
$798$	26.5325	0.939240
$799$	4.27384	0.151197
$800$	0	0
$801$	−11.7281	−0.414393
$802$	49.0225	1.73105
$803$	4.98997	0.176092
$804$	−70.9870	−2.50352
$805$	0	0
$806$	46.0224	1.62107
$807$	11.0853	0.390222
$808$	−125.406	−4.41178
$809$	−7.72930	−0.271748	−0.135874	−	0.990726i	$-0.543384\pi$
$809$	−7.72930	−0.271748	−0.135874	+	0.990726i	$0.543384\pi$
$810$	0	0
$811$	45.0007	1.58019	0.790095	−	0.612985i	$-0.210031\pi$
$811$	45.0007	1.58019	0.790095	+	0.612985i	$0.210031\pi$
$812$	27.1558	0.952980
$813$	8.20390	0.287723
$814$	−65.8806	−2.30912
$815$	0	0
$816$	65.9697	2.30940
$817$	21.4513	0.750485
$818$	4.06675	0.142191
$819$	−6.65969	−0.232708
$820$	0	0
$821$	38.1851	1.33267	0.666335	−	0.745652i	$-0.267862\pi$
$821$	38.1851	1.33267	0.666335	+	0.745652i	$0.267862\pi$
$822$	−5.77620	−0.201468
$823$	−7.04124	−0.245442	−0.122721	−	0.992441i	$-0.539162\pi$
$823$	−7.04124	−0.245442	−0.122721	+	0.992441i	$0.539162\pi$
$824$	37.6008	1.30988
$825$	0	0
$826$	8.44301	0.293770
$827$	−2.26867	−0.0788895	−0.0394447	−	0.999222i	$-0.512559\pi$
$827$	−2.26867	−0.0788895	−0.0394447	+	0.999222i	$0.512559\pi$
$828$	−33.4259	−1.16163
$829$	−3.91186	−0.135864	−0.0679322	−	0.997690i	$-0.521640\pi$
$829$	−3.91186	−0.135864	−0.0679322	+	0.997690i	$0.521640\pi$
$830$	0	0
$831$	−12.0691	−0.418673
$832$	−181.669	−6.29823
$833$	−23.9396	−0.829456
$834$	−5.19274	−0.179810
$835$	0	0
$836$	−157.099	−5.43340
$837$	−2.98011	−0.103008
$838$	110.526	3.81805
$839$	29.5413	1.01988	0.509939	−	0.860210i	$-0.329668\pi$
$839$	29.5413	1.01988	0.509939	+	0.860210i	$0.329668\pi$
$840$	0	0
$841$	−11.6992	−0.403421
$842$	23.4827	0.809268
$843$	24.3492	0.838632
$844$	−14.6325	−0.503670
$845$	0	0
$846$	2.74237	0.0942846
$847$	1.30010	0.0446718
$848$	−27.4206	−0.941629
$849$	−23.0077	−0.789623
$850$	0	0
$851$	−41.8166	−1.43345
$852$	10.1089	0.346325
$853$	−34.1490	−1.16924	−0.584620	−	0.811308i	$-0.698756\pi$
$853$	−34.1490	−1.16924	−0.584620	+	0.811308i	$0.698756\pi$
$854$	−29.4441	−1.00756
$855$	0	0
$856$	101.325	3.46321
$857$	−13.1307	−0.448535	−0.224267	−	0.974528i	$-0.571999\pi$
$857$	−13.1307	−0.448535	−0.224267	+	0.974528i	$0.571999\pi$
$858$	53.7176	1.83389
$859$	22.8736	0.780437	0.390219	−	0.920722i	$-0.372399\pi$
$859$	22.8736	0.780437	0.390219	+	0.920722i	$0.372399\pi$
$860$	0	0
$861$	8.69100	0.296188
$862$	2.83123	0.0964319
$863$	−25.6058	−0.871630	−0.435815	−	0.900036i	$-0.643540\pi$
$863$	−25.6058	−0.871630	−0.435815	+	0.900036i	$0.643540\pi$
$864$	23.0209	0.783188
$865$	0	0
$866$	58.1145	1.97481
$867$	1.26568	0.0429848
$868$	−19.4564	−0.660393
$869$	10.4029	0.352895
$870$	0	0
$871$	72.4108	2.45355
$872$	−56.1869	−1.90273
$873$	−14.9476	−0.505900
$874$	−135.841	−4.59490
$875$	0	0
$876$	−7.91959	−0.267578
$877$	−23.2851	−0.786283	−0.393141	−	0.919478i	$-0.628612\pi$
$877$	−23.2851	−0.786283	−0.393141	+	0.919478i	$0.628612\pi$
$878$	21.1781	0.714725
$879$	−24.7312	−0.834162
$880$	0	0
$881$	−12.1682	−0.409959	−0.204979	−	0.978766i	$-0.565713\pi$
$881$	−12.1682	−0.409959	−0.204979	+	0.978766i	$0.565713\pi$
$882$	−15.3612	−0.517237
$883$	−19.9941	−0.672855	−0.336427	−	0.941709i	$-0.609219\pi$
$883$	−19.9941	−0.672855	−0.336427	+	0.941709i	$0.609219\pi$
$884$	−132.866	−4.46876
$885$	0	0
$886$	−82.3241	−2.76573
$887$	6.65494	0.223451	0.111726	−	0.993739i	$-0.464362\pi$
$887$	6.65494	0.223451	0.111726	+	0.993739i	$0.464362\pi$
$888$	66.6795	2.23762
$889$	−11.2486	−0.377266
$890$	0	0
$891$	−3.47841	−0.116531
$892$	0.653514	0.0218813
$893$	8.18104	0.273768
$894$	17.0329	0.569666
$895$	0	0
$896$	50.1763	1.67627
$897$	34.0963	1.13844
$898$	56.2196	1.87607
$899$	−12.3956	−0.413415
$900$	0	0
$901$	−7.59222	−0.252933
$902$	−70.1024	−2.33415
$903$	3.10090	0.103192
$904$	−146.374	−4.86834
$905$	0	0
$906$	−43.4562	−1.44373
$907$	0.194434	0.00645608	0.00322804	−	0.999995i	$-0.498972\pi$
$907$	0.194434	0.00645608	0.00322804	+	0.999995i	$0.498972\pi$
$908$	9.01133	0.299051
$909$	−12.9891	−0.430820
$910$	0	0
$911$	−23.6508	−0.783585	−0.391793	−	0.920054i	$-0.628145\pi$
$911$	−23.6508	−0.783585	−0.391793	+	0.920054i	$0.628145\pi$
$912$	126.280	4.18156
$913$	23.6084	0.781325
$914$	−39.4590	−1.30519
$915$	0	0
$916$	−84.0943	−2.77855
$917$	12.7760	0.421901
$918$	11.7204	0.386832
$919$	−4.37513	−0.144322	−0.0721612	−	0.997393i	$-0.522990\pi$
$919$	−4.37513	−0.144322	−0.0721612	+	0.997393i	$0.522990\pi$
$920$	0	0
$921$	9.37703	0.308984
$922$	−11.3892	−0.375083
$923$	−10.3117	−0.339412
$924$	−22.7096	−0.747092
$925$	0	0
$926$	40.1218	1.31849
$927$	3.89453	0.127913
$928$	95.7537	3.14327
$929$	−32.4233	−1.06377	−0.531886	−	0.846816i	$-0.678517\pi$
$929$	−32.4233	−1.06377	−0.531886	+	0.846816i	$0.678517\pi$
$930$	0	0
$931$	−45.8254	−1.50187
$932$	89.3182	2.92572
$933$	24.1338	0.790105
$934$	74.6361	2.44217
$935$	0	0
$936$	−54.3690	−1.77711
$937$	27.8464	0.909702	0.454851	−	0.890567i	$-0.349692\pi$
$937$	27.8464	0.909702	0.454851	+	0.890567i	$0.349692\pi$
$938$	−41.7026	−1.36164
$939$	30.6656	1.00073
$940$	0	0
$941$	27.0603	0.882141	0.441070	−	0.897473i	$-0.354599\pi$
$941$	27.0603	0.882141	0.441070	+	0.897473i	$0.354599\pi$
$942$	37.6953	1.22818
$943$	−44.4963	−1.44900
$944$	40.1841	1.30788
$945$	0	0
$946$	−25.0122	−0.813215
$947$	17.1707	0.557973	0.278986	−	0.960295i	$-0.410002\pi$
$947$	17.1707	0.557973	0.278986	+	0.960295i	$0.410002\pi$
$948$	−16.5105	−0.536236
$949$	8.07844	0.262237
$950$	0	0
$951$	12.2027	0.395700
$952$	48.7981	1.58155
$953$	13.1959	0.427459	0.213729	−	0.976893i	$-0.431439\pi$
$953$	13.1959	0.427459	0.213729	+	0.976893i	$0.431439\pi$
$954$	−4.87166	−0.157726
$955$	0	0
$956$	−64.8158	−2.09629
$957$	−14.4682	−0.467690
$958$	31.6145	1.02142
$959$	−2.49092	−0.0804361
$960$	0	0
$961$	−22.1189	−0.713513
$962$	−106.656	−3.43874
$963$	10.4948	0.338191
$964$	163.293	5.25931
$965$	0	0
$966$	−19.6366	−0.631798
$967$	−12.2492	−0.393906	−0.196953	−	0.980413i	$-0.563105\pi$
$967$	−12.2492	−0.393906	−0.196953	+	0.980413i	$0.563105\pi$
$968$	10.6138	0.341142
$969$	34.9644	1.12322
$970$	0	0
$971$	54.7498	1.75700	0.878502	−	0.477738i	$-0.158543\pi$
$971$	54.7498	1.75700	0.878502	+	0.477738i	$0.158543\pi$
$972$	5.52059	0.177073
$973$	−2.23931	−0.0717890
$974$	−29.3663	−0.940957
$975$	0	0
$976$	−140.138	−4.48570
$977$	−42.0218	−1.34440	−0.672198	−	0.740372i	$-0.734650\pi$
$977$	−42.0218	−1.34440	−0.672198	+	0.740372i	$0.734650\pi$
$978$	−16.1132	−0.515242
$979$	40.7953	1.30382
$980$	0	0
$981$	−5.81961	−0.185806
$982$	−64.8196	−2.06848
$983$	18.6630	0.595259	0.297629	−	0.954682i	$-0.403804\pi$
$983$	18.6630	0.595259	0.297629	+	0.954682i	$0.403804\pi$
$984$	70.9524	2.26188
$985$	0	0
$986$	48.7502	1.55252
$987$	1.18262	0.0376431
$988$	−254.334	−8.09143
$989$	−15.8760	−0.504828
$990$	0	0
$991$	16.9705	0.539085	0.269542	−	0.962989i	$-0.413128\pi$
$991$	16.9705	0.539085	0.269542	+	0.962989i	$0.413128\pi$
$992$	−68.6050	−2.17821
$993$	2.92128	0.0927041
$994$	5.93865	0.188363
$995$	0	0
$996$	−37.4689	−1.18725
$997$	38.4006	1.21616	0.608079	−	0.793876i	$-0.291940\pi$
$997$	38.4006	1.21616	0.608079	+	0.793876i	$0.291940\pi$
$998$	57.2482	1.81216
$999$	6.90639	0.218509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bi.1.13		13
5.2	odd	4		705.2.c.c.424.26	yes	26
5.3	odd	4		705.2.c.c.424.1	✓	26
5.4	even	2		3525.2.a.bh.1.1		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.c.424.1	✓	26	5.3	odd	4
705.2.c.c.424.26	yes	26	5.2	odd	4
3525.2.a.bh.1.1		13	5.4	even	2
3525.2.a.bi.1.13		13	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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+2.74237 q^{2} +1.00000 q^{3} +5.52059 q^{4} +2.74237 q^{6} +1.18262 q^{7} +9.65475 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.74237 q^{2} +1.00000 q^{3} +5.52059 q^{4} +2.74237 q^{6} +1.18262 q^{7} +9.65475 q^{8} +1.00000 q^{9} -3.47841 q^{11} +5.52059 q^{12} -5.63132 q^{13} +3.24317 q^{14} +15.4357 q^{16} +4.27384 q^{17} +2.74237 q^{18} +8.18104 q^{19} +1.18262 q^{21} -9.53909 q^{22} -6.05477 q^{23} +9.65475 q^{24} -15.4432 q^{26} +1.00000 q^{27} +6.52874 q^{28} +4.15942 q^{29} -2.98011 q^{31} +23.0209 q^{32} -3.47841 q^{33} +11.7204 q^{34} +5.52059 q^{36} +6.90639 q^{37} +22.4354 q^{38} -5.63132 q^{39} +7.34896 q^{41} +3.24317 q^{42} +2.62207 q^{43} -19.2029 q^{44} -16.6044 q^{46} +1.00000 q^{47} +15.4357 q^{48} -5.60142 q^{49} +4.27384 q^{51} -31.0882 q^{52} -1.77644 q^{53} +2.74237 q^{54} +11.4179 q^{56} +8.18104 q^{57} +11.4067 q^{58} +2.60332 q^{59} -9.07880 q^{61} -8.17257 q^{62} +1.18262 q^{63} +32.2604 q^{64} -9.53909 q^{66} -12.8586 q^{67} +23.5941 q^{68} -6.05477 q^{69} +1.83113 q^{71} +9.65475 q^{72} -1.43456 q^{73} +18.9399 q^{74} +45.1642 q^{76} -4.11362 q^{77} -15.4432 q^{78} -2.99071 q^{79} +1.00000 q^{81} +20.1536 q^{82} -6.78713 q^{83} +6.52874 q^{84} +7.19069 q^{86} +4.15942 q^{87} -33.5832 q^{88} -11.7281 q^{89} -6.65969 q^{91} -33.4259 q^{92} -2.98011 q^{93} +2.74237 q^{94} +23.0209 q^{96} -14.9476 q^{97} -15.3612 q^{98} -3.47841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9} + 16 q^{11} + 17 q^{12} - 8 q^{13} - 4 q^{14} + 29 q^{16} + 12 q^{17} + 3 q^{18} + 28 q^{19} - 4 q^{21} + 6 q^{23} + 15 q^{24} + 4 q^{26} + 13 q^{27} - 20 q^{28} + 12 q^{29} + 26 q^{31} + 53 q^{32} + 16 q^{33} + 8 q^{34} + 17 q^{36} - 4 q^{37} + 2 q^{38} - 8 q^{39} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{44} + 16 q^{46} + 13 q^{47} + 29 q^{48} + 21 q^{49} + 12 q^{51} - 32 q^{52} + 6 q^{53} + 3 q^{54} + 28 q^{57} - 4 q^{58} + 34 q^{59} + 24 q^{61} + 30 q^{62} - 4 q^{63} + 13 q^{64} - 24 q^{67} + 44 q^{68} + 6 q^{69} + 20 q^{71} + 15 q^{72} - 6 q^{73} + 20 q^{74} + 66 q^{76} - 2 q^{77} + 4 q^{78} + 6 q^{79} + 13 q^{81} + 20 q^{82} + 14 q^{83} - 20 q^{84} + 48 q^{86} + 12 q^{87} - 22 q^{88} + 36 q^{89} + 4 q^{91} + 4 q^{92} + 26 q^{93} + 3 q^{94} + 53 q^{96} - 32 q^{97} - 39 q^{98} + 16 q^{99}+O(q^{100}) \) 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9 + 16 * q^11 + 17 * q^12 - 8 * q^13 - 4 * q^14 + 29 * q^16 + 12 * q^17 + 3 * q^18 + 28 * q^19 - 4 * q^21 + 6 * q^23 + 15 * q^24 + 4 * q^26 + 13 * q^27 - 20 * q^28 + 12 * q^29 + 26 * q^31 + 53 * q^32 + 16 * q^33 + 8 * q^34 + 17 * q^36 - 4 * q^37 + 2 * q^38 - 8 * q^39 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 4 * q^44 + 16 * q^46 + 13 * q^47 + 29 * q^48 + 21 * q^49 + 12 * q^51 - 32 * q^52 + 6 * q^53 + 3 * q^54 + 28 * q^57 - 4 * q^58 + 34 * q^59 + 24 * q^61 + 30 * q^62 - 4 * q^63 + 13 * q^64 - 24 * q^67 + 44 * q^68 + 6 * q^69 + 20 * q^71 + 15 * q^72 - 6 * q^73 + 20 * q^74 + 66 * q^76 - 2 * q^77 + 4 * q^78 + 6 * q^79 + 13 * q^81 + 20 * q^82 + 14 * q^83 - 20 * q^84 + 48 * q^86 + 12 * q^87 - 22 * q^88 + 36 * q^89 + 4 * q^91 + 4 * q^92 + 26 * q^93 + 3 * q^94 + 53 * q^96 - 32 * q^97 - 39 * q^98 + 16 * q^99

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