LMFDB - Embedded newform 3525.2.a.bi.1.3

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			1.3
Root			$-2.12231$ 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)

$f(q)$	$=$	$q-2.12231 q^{2} +1.00000 q^{3} +2.50418 q^{4} -2.12231 q^{6} +4.63433 q^{7} -1.07002 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.12231 q^{2} +1.00000 q^{3} +2.50418 q^{4} -2.12231 q^{6} +4.63433 q^{7} -1.07002 q^{8} +1.00000 q^{9} +4.08582 q^{11} +2.50418 q^{12} -4.23600 q^{13} -9.83546 q^{14} -2.73744 q^{16} +7.20453 q^{17} -2.12231 q^{18} +7.38579 q^{19} +4.63433 q^{21} -8.67135 q^{22} +1.57065 q^{23} -1.07002 q^{24} +8.99009 q^{26} +1.00000 q^{27} +11.6052 q^{28} +2.66888 q^{29} +1.84722 q^{31} +7.94974 q^{32} +4.08582 q^{33} -15.2902 q^{34} +2.50418 q^{36} -9.46873 q^{37} -15.6749 q^{38} -4.23600 q^{39} +0.908892 q^{41} -9.83546 q^{42} -7.29082 q^{43} +10.2316 q^{44} -3.33339 q^{46} +1.00000 q^{47} -2.73744 q^{48} +14.4770 q^{49} +7.20453 q^{51} -10.6077 q^{52} +2.88718 q^{53} -2.12231 q^{54} -4.95884 q^{56} +7.38579 q^{57} -5.66418 q^{58} +9.12158 q^{59} +4.68426 q^{61} -3.92037 q^{62} +4.63433 q^{63} -11.3969 q^{64} -8.67135 q^{66} +7.73764 q^{67} +18.0414 q^{68} +1.57065 q^{69} +1.83932 q^{71} -1.07002 q^{72} -12.0602 q^{73} +20.0955 q^{74} +18.4954 q^{76} +18.9350 q^{77} +8.99009 q^{78} +1.60760 q^{79} +1.00000 q^{81} -1.92895 q^{82} -6.99249 q^{83} +11.6052 q^{84} +15.4733 q^{86} +2.66888 q^{87} -4.37193 q^{88} -7.65663 q^{89} -19.6310 q^{91} +3.93318 q^{92} +1.84722 q^{93} -2.12231 q^{94} +7.94974 q^{96} -5.64019 q^{97} -30.7246 q^{98} +4.08582 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.12231	−1.50070	−0.750348	−	0.661043i	$-0.770114\pi$
$2$	−2.12231	−1.50070	−0.750348	+	0.661043i	$0.770114\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.50418	1.25209
$5$	0	0
$5$	0	0
$6$	−2.12231	−0.866428
$7$	4.63433	1.75161	0.875806	−	0.482664i	$-0.160331\pi$
$7$	4.63433	1.75161	0.875806	+	0.482664i	$0.160331\pi$
$8$	−1.07002	−0.378311
$9$	1.00000	0.333333
$10$	0	0
$11$	4.08582	1.23192	0.615960	−	0.787777i	$-0.288768\pi$
$11$	4.08582	1.23192	0.615960	+	0.787777i	$0.288768\pi$
$12$	2.50418	0.722895
$13$	−4.23600	−1.17486	−0.587428	−	0.809277i	$-0.699859\pi$
$13$	−4.23600	−1.17486	−0.587428	+	0.809277i	$0.699859\pi$
$14$	−9.83546	−2.62864
$15$	0	0
$16$	−2.73744	−0.684360
$17$	7.20453	1.74736	0.873678	−	0.486505i	$-0.161729\pi$
$17$	7.20453	1.74736	0.873678	+	0.486505i	$0.161729\pi$
$18$	−2.12231	−0.500232
$19$	7.38579	1.69442	0.847208	−	0.531261i	$-0.178282\pi$
$19$	7.38579	1.69442	0.847208	+	0.531261i	$0.178282\pi$
$20$	0	0
$21$	4.63433	1.01129
$22$	−8.67135	−1.84874
$23$	1.57065	0.327503	0.163751	−	0.986502i	$-0.447641\pi$
$23$	1.57065	0.327503	0.163751	+	0.986502i	$0.447641\pi$
$24$	−1.07002	−0.218418
$25$	0	0
$26$	8.99009	1.76310
$27$	1.00000	0.192450
$28$	11.6052	2.19318
$29$	2.66888	0.495599	0.247799	−	0.968811i	$-0.420293\pi$
$29$	2.66888	0.495599	0.247799	+	0.968811i	$0.420293\pi$
$30$	0	0
$31$	1.84722	0.331771	0.165885	−	0.986145i	$-0.446952\pi$
$31$	1.84722	0.331771	0.165885	+	0.986145i	$0.446952\pi$
$32$	7.94974	1.40533
$33$	4.08582	0.711250
$34$	−15.2902	−2.62225
$35$	0	0
$36$	2.50418	0.417363
$37$	−9.46873	−1.55665	−0.778325	−	0.627862i	$-0.783930\pi$
$37$	−9.46873	−1.55665	−0.778325	+	0.627862i	$0.783930\pi$
$38$	−15.6749	−2.54281
$39$	−4.23600	−0.678303
$40$	0	0
$41$	0.908892	0.141945	0.0709725	−	0.997478i	$-0.477390\pi$
$41$	0.908892	0.141945	0.0709725	+	0.997478i	$0.477390\pi$
$42$	−9.83546	−1.51764
$43$	−7.29082	−1.11184	−0.555920	−	0.831236i	$-0.687634\pi$
$43$	−7.29082	−1.11184	−0.555920	+	0.831236i	$0.687634\pi$
$44$	10.2316	1.54248
$45$	0	0
$46$	−3.33339	−0.491482
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−2.73744	−0.395116
$49$	14.4770	2.06814
$50$	0	0
$51$	7.20453	1.00884
$52$	−10.6077	−1.47102
$53$	2.88718	0.396585	0.198293	−	0.980143i	$-0.436460\pi$
$53$	2.88718	0.396585	0.198293	+	0.980143i	$0.436460\pi$
$54$	−2.12231	−0.288809
$55$	0	0
$56$	−4.95884	−0.662654
$57$	7.38579	0.978272
$58$	−5.66418	−0.743744
$59$	9.12158	1.18753	0.593765	−	0.804639i	$-0.297641\pi$
$59$	9.12158	1.18753	0.593765	+	0.804639i	$0.297641\pi$
$60$	0	0
$61$	4.68426	0.599758	0.299879	−	0.953977i	$-0.403054\pi$
$61$	4.68426	0.599758	0.299879	+	0.953977i	$0.403054\pi$
$62$	−3.92037	−0.497887
$63$	4.63433	0.583871
$64$	−11.3969	−1.42461
$65$	0	0
$66$	−8.67135	−1.06737
$67$	7.73764	0.945303	0.472651	−	0.881249i	$-0.343297\pi$
$67$	7.73764	0.945303	0.472651	+	0.881249i	$0.343297\pi$
$68$	18.0414	2.18785
$69$	1.57065	0.189084
$70$	0	0
$71$	1.83932	0.218287	0.109144	−	0.994026i	$-0.465189\pi$
$71$	1.83932	0.218287	0.109144	+	0.994026i	$0.465189\pi$
$72$	−1.07002	−0.126104
$73$	−12.0602	−1.41154	−0.705768	−	0.708444i	$-0.749398\pi$
$73$	−12.0602	−1.41154	−0.705768	+	0.708444i	$0.749398\pi$
$74$	20.0955	2.33606
$75$	0	0
$76$	18.4954	2.12156
$77$	18.9350	2.15785
$78$	8.99009	1.01793
$79$	1.60760	0.180869	0.0904347	−	0.995902i	$-0.471174\pi$
$79$	1.60760	0.180869	0.0904347	+	0.995902i	$0.471174\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−1.92895	−0.213016
$83$	−6.99249	−0.767526	−0.383763	−	0.923432i	$-0.625372\pi$
$83$	−6.99249	−0.767526	−0.383763	+	0.923432i	$0.625372\pi$
$84$	11.6052	1.26623
$85$	0	0
$86$	15.4733	1.66853
$87$	2.66888	0.286134
$88$	−4.37193	−0.466049
$89$	−7.65663	−0.811601	−0.405801	−	0.913962i	$-0.633007\pi$
$89$	−7.65663	−0.811601	−0.405801	+	0.913962i	$0.633007\pi$
$90$	0	0
$91$	−19.6310	−2.05789
$92$	3.93318	0.410063
$93$	1.84722	0.191548
$94$	−2.12231	−0.218899
$95$	0	0
$96$	7.94974	0.811367
$97$	−5.64019	−0.572675	−0.286337	−	0.958129i	$-0.592438\pi$
$97$	−5.64019	−0.572675	−0.286337	+	0.958129i	$0.592438\pi$
$98$	−30.7246	−3.10366
$99$	4.08582	0.410640
$100$	0	0
$101$	−3.72733	−0.370884	−0.185442	−	0.982655i	$-0.559372\pi$
$101$	−3.72733	−0.370884	−0.185442	+	0.982655i	$0.559372\pi$
$102$	−15.2902	−1.51396
$103$	−17.8251	−1.75636	−0.878180	−	0.478329i	$-0.841242\pi$
$103$	−17.8251	−1.75636	−0.878180	+	0.478329i	$0.841242\pi$
$104$	4.53262	0.444460
$105$	0	0
$106$	−6.12748	−0.595154
$107$	−15.1309	−1.46276	−0.731381	−	0.681969i	$-0.761124\pi$
$107$	−15.1309	−1.46276	−0.731381	+	0.681969i	$0.761124\pi$
$108$	2.50418	0.240965
$109$	−0.0125636	−0.00120338	−0.000601689	−	1.00000i	$-0.500192\pi$
$109$	−0.0125636	−0.00120338	−0.000601689		1.00000i	$0.500192\pi$
$110$	0	0
$111$	−9.46873	−0.898732
$112$	−12.6862	−1.19873
$113$	−2.15722	−0.202934	−0.101467	−	0.994839i	$-0.532354\pi$
$113$	−2.15722	−0.202934	−0.101467	+	0.994839i	$0.532354\pi$
$114$	−15.6749	−1.46809
$115$	0	0
$116$	6.68336	0.620535
$117$	−4.23600	−0.391618
$118$	−19.3588	−1.78212
$119$	33.3882	3.06069
$120$	0	0
$121$	5.69391	0.517628
$122$	−9.94143	−0.900055
$123$	0.908892	0.0819520
$124$	4.62577	0.415407
$125$	0	0
$126$	−9.83546	−0.876213
$127$	−4.69699	−0.416790	−0.208395	−	0.978045i	$-0.566824\pi$
$127$	−4.69699	−0.416790	−0.208395	+	0.978045i	$0.566824\pi$
$128$	8.28820	0.732580
$129$	−7.29082	−0.641921
$130$	0	0
$131$	15.3128	1.33788	0.668941	−	0.743316i	$-0.266748\pi$
$131$	15.3128	1.33788	0.668941	+	0.743316i	$0.266748\pi$
$132$	10.2316	0.890549
$133$	34.2282	2.96796
$134$	−16.4216	−1.41861
$135$	0	0
$136$	−7.70902	−0.661043
$137$	7.97478	0.681332	0.340666	−	0.940184i	$-0.389348\pi$
$137$	7.97478	0.681332	0.340666	+	0.940184i	$0.389348\pi$
$138$	−3.33339	−0.283757
$139$	−16.7191	−1.41810	−0.709048	−	0.705161i	$-0.750875\pi$
$139$	−16.7191	−1.41810	−0.709048	+	0.705161i	$0.750875\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	−3.90360	−0.327583
$143$	−17.3075	−1.44733
$144$	−2.73744	−0.228120
$145$	0	0
$146$	25.5953	2.11829
$147$	14.4770	1.19404
$148$	−23.7114	−1.94907
$149$	−3.17686	−0.260259	−0.130129	−	0.991497i	$-0.541539\pi$
$149$	−3.17686	−0.260259	−0.130129	+	0.991497i	$0.541539\pi$
$150$	0	0
$151$	−8.59739	−0.699646	−0.349823	−	0.936816i	$-0.613758\pi$
$151$	−8.59739	−0.699646	−0.349823	+	0.936816i	$0.613758\pi$
$152$	−7.90298	−0.641016
$153$	7.20453	0.582452
$154$	−40.1859	−3.23827
$155$	0	0
$156$	−10.6077	−0.849296
$157$	7.74369	0.618014	0.309007	−	0.951060i	$-0.400003\pi$
$157$	7.74369	0.618014	0.309007	+	0.951060i	$0.400003\pi$
$158$	−3.41182	−0.271430
$159$	2.88718	0.228968
$160$	0	0
$161$	7.27890	0.573657
$162$	−2.12231	−0.166744
$163$	4.71986	0.369688	0.184844	−	0.982768i	$-0.440822\pi$
$163$	4.71986	0.369688	0.184844	+	0.982768i	$0.440822\pi$
$164$	2.27603	0.177728
$165$	0	0
$166$	14.8402	1.15182
$167$	−6.37944	−0.493656	−0.246828	−	0.969059i	$-0.579388\pi$
$167$	−6.37944	−0.493656	−0.246828	+	0.969059i	$0.579388\pi$
$168$	−4.95884	−0.382583
$169$	4.94370	0.380285
$170$	0	0
$171$	7.38579	0.564806
$172$	−18.2575	−1.39212
$173$	−0.327252	−0.0248805	−0.0124402	−	0.999923i	$-0.503960\pi$
$173$	−0.327252	−0.0248805	−0.0124402	+	0.999923i	$0.503960\pi$
$174$	−5.66418	−0.429401
$175$	0	0
$176$	−11.1847	−0.843078
$177$	9.12158	0.685620
$178$	16.2497	1.21797
$179$	−3.86814	−0.289118	−0.144559	−	0.989496i	$-0.546176\pi$
$179$	−3.86814	−0.289118	−0.144559	+	0.989496i	$0.546176\pi$
$180$	0	0
$181$	−25.0443	−1.86153	−0.930766	−	0.365616i	$-0.880858\pi$
$181$	−25.0443	−1.86153	−0.930766	+	0.365616i	$0.880858\pi$
$182$	41.6630	3.08827
$183$	4.68426	0.346271
$184$	−1.68063	−0.123898
$185$	0	0
$186$	−3.92037	−0.287455
$187$	29.4364	2.15260
$188$	2.50418	0.182636
$189$	4.63433	0.337098
$190$	0	0
$191$	−14.1460	−1.02357	−0.511784	−	0.859114i	$-0.671015\pi$
$191$	−14.1460	−1.02357	−0.511784	+	0.859114i	$0.671015\pi$
$192$	−11.3969	−0.822499
$193$	−13.0065	−0.936232	−0.468116	−	0.883667i	$-0.655067\pi$
$193$	−13.0065	−0.936232	−0.468116	+	0.883667i	$0.655067\pi$
$194$	11.9702	0.859411
$195$	0	0
$196$	36.2530	2.58950
$197$	−14.3116	−1.01966	−0.509829	−	0.860276i	$-0.670291\pi$
$197$	−14.3116	−1.01966	−0.509829	+	0.860276i	$0.670291\pi$
$198$	−8.67135	−0.616246
$199$	−8.03906	−0.569874	−0.284937	−	0.958546i	$-0.591973\pi$
$199$	−8.03906	−0.569874	−0.284937	+	0.958546i	$0.591973\pi$
$200$	0	0
$201$	7.73764	0.545771
$202$	7.91054	0.556584
$203$	12.3685	0.868097
$204$	18.0414	1.26315
$205$	0	0
$206$	37.8303	2.63576
$207$	1.57065	0.109168
$208$	11.5958	0.804024
$209$	30.1770	2.08739
$210$	0	0
$211$	−1.53701	−0.105812	−0.0529060	−	0.998599i	$-0.516848\pi$
$211$	−1.53701	−0.105812	−0.0529060	+	0.998599i	$0.516848\pi$
$212$	7.23003	0.496560
$213$	1.83932	0.126028
$214$	32.1125	2.19516
$215$	0	0
$216$	−1.07002	−0.0728059
$217$	8.56063	0.581133
$218$	0.0266639	0.00180591
$219$	−12.0602	−0.814950
$220$	0	0
$221$	−30.5184	−2.05289
$222$	20.0955	1.34872
$223$	−2.89282	−0.193718	−0.0968589	−	0.995298i	$-0.530880\pi$
$223$	−2.89282	−0.193718	−0.0968589	+	0.995298i	$0.530880\pi$
$224$	36.8417	2.46159
$225$	0	0
$226$	4.57827	0.304542
$227$	−17.8195	−1.18272	−0.591359	−	0.806408i	$-0.701408\pi$
$227$	−17.8195	−1.18272	−0.591359	+	0.806408i	$0.701408\pi$
$228$	18.4954	1.22488
$229$	26.4493	1.74782	0.873911	−	0.486086i	$-0.161576\pi$
$229$	26.4493	1.74782	0.873911	+	0.486086i	$0.161576\pi$
$230$	0	0
$231$	18.9350	1.24583
$232$	−2.85577	−0.187490
$233$	−9.98885	−0.654391	−0.327196	−	0.944957i	$-0.606104\pi$
$233$	−9.98885	−0.654391	−0.327196	+	0.944957i	$0.606104\pi$
$234$	8.99009	0.587700
$235$	0	0
$236$	22.8421	1.48689
$237$	1.60760	0.104425
$238$	−70.8599	−4.59316
$239$	−30.3880	−1.96564	−0.982820	−	0.184568i	$-0.940911\pi$
$239$	−30.3880	−1.96564	−0.982820	+	0.184568i	$0.940911\pi$
$240$	0	0
$241$	11.6159	0.748246	0.374123	−	0.927379i	$-0.377944\pi$
$241$	11.6159	0.748246	0.374123	+	0.927379i	$0.377944\pi$
$242$	−12.0842	−0.776803
$243$	1.00000	0.0641500
$244$	11.7302	0.750951
$245$	0	0
$246$	−1.92895	−0.122985
$247$	−31.2862	−1.99069
$248$	−1.97657	−0.125512
$249$	−6.99249	−0.443131
$250$	0	0
$251$	1.34801	0.0850854	0.0425427	−	0.999095i	$-0.486454\pi$
$251$	1.34801	0.0850854	0.0425427	+	0.999095i	$0.486454\pi$
$252$	11.6052	0.731059
$253$	6.41738	0.403457
$254$	9.96844	0.625476
$255$	0	0
$256$	5.20368	0.325230
$257$	13.3116	0.830355	0.415177	−	0.909740i	$-0.363720\pi$
$257$	13.3116	0.830355	0.415177	+	0.909740i	$0.363720\pi$
$258$	15.4733	0.963328
$259$	−43.8812	−2.72665
$260$	0	0
$261$	2.66888	0.165200
$262$	−32.4983	−2.00775
$263$	20.5469	1.26697	0.633487	−	0.773753i	$-0.281623\pi$
$263$	20.5469	1.26697	0.633487	+	0.773753i	$0.281623\pi$
$264$	−4.37193	−0.269073
$265$	0	0
$266$	−72.6427	−4.45401
$267$	−7.65663	−0.468578
$268$	19.3764	1.18360
$269$	−9.46285	−0.576960	−0.288480	−	0.957486i	$-0.593150\pi$
$269$	−9.46285	−0.576960	−0.288480	+	0.957486i	$0.593150\pi$
$270$	0	0
$271$	−8.94312	−0.543256	−0.271628	−	0.962402i	$-0.587562\pi$
$271$	−8.94312	−0.543256	−0.271628	+	0.962402i	$0.587562\pi$
$272$	−19.7220	−1.19582
$273$	−19.6310	−1.18812
$274$	−16.9249	−1.02247
$275$	0	0
$276$	3.93318	0.236750
$277$	22.1764	1.33245	0.666224	−	0.745752i	$-0.267909\pi$
$277$	22.1764	1.33245	0.666224	+	0.745752i	$0.267909\pi$
$278$	35.4830	2.12813
$279$	1.84722	0.110590
$280$	0	0
$281$	−16.5654	−0.988209	−0.494105	−	0.869402i	$-0.664504\pi$
$281$	−16.5654	−0.988209	−0.494105	+	0.869402i	$0.664504\pi$
$282$	−2.12231	−0.126381
$283$	6.90978	0.410744	0.205372	−	0.978684i	$-0.434160\pi$
$283$	6.90978	0.410744	0.205372	+	0.978684i	$0.434160\pi$
$284$	4.60599	0.273315
$285$	0	0
$286$	36.7319	2.17200
$287$	4.21210	0.248633
$288$	7.94974	0.468443
$289$	34.9053	2.05325
$290$	0	0
$291$	−5.64019	−0.330634
$292$	−30.2008	−1.76737
$293$	25.0690	1.46455	0.732273	−	0.681011i	$-0.238459\pi$
$293$	25.0690	1.46455	0.732273	+	0.681011i	$0.238459\pi$
$294$	−30.7246	−1.79190
$295$	0	0
$296$	10.1318	0.588897
$297$	4.08582	0.237083
$298$	6.74227	0.390569
$299$	−6.65326	−0.384768
$300$	0	0
$301$	−33.7881	−1.94751
$302$	18.2463	1.04996
$303$	−3.72733	−0.214130
$304$	−20.2182	−1.15959
$305$	0	0
$306$	−15.2902	−0.874083
$307$	−18.0924	−1.03259	−0.516293	−	0.856412i	$-0.672688\pi$
$307$	−18.0924	−1.03259	−0.516293	+	0.856412i	$0.672688\pi$
$308$	47.4167	2.70182
$309$	−17.8251	−1.01404
$310$	0	0
$311$	19.8040	1.12298	0.561490	−	0.827484i	$-0.310228\pi$
$311$	19.8040	1.12298	0.561490	+	0.827484i	$0.310228\pi$
$312$	4.53262	0.256609
$313$	5.66054	0.319952	0.159976	−	0.987121i	$-0.448858\pi$
$313$	5.66054	0.319952	0.159976	+	0.987121i	$0.448858\pi$
$314$	−16.4345	−0.927451
$315$	0	0
$316$	4.02573	0.226465
$317$	2.40002	0.134799	0.0673994	−	0.997726i	$-0.478530\pi$
$317$	2.40002	0.134799	0.0673994	+	0.997726i	$0.478530\pi$
$318$	−6.12748	−0.343612
$319$	10.9046	0.610539
$320$	0	0
$321$	−15.1309	−0.844526
$322$	−15.4480	−0.860886
$323$	53.2112	2.96075
$324$	2.50418	0.139121
$325$	0	0
$326$	−10.0170	−0.554790
$327$	−0.0125636	−0.000694771 0
$328$	−0.972536	−0.0536993
$329$	4.63433	0.255499
$330$	0	0
$331$	29.5097	1.62200	0.811000	−	0.585046i	$-0.198924\pi$
$331$	29.5097	1.62200	0.811000	+	0.585046i	$0.198924\pi$
$332$	−17.5105	−0.961012
$333$	−9.46873	−0.518883
$334$	13.5391	0.740828
$335$	0	0
$336$	−12.6862	−0.692089
$337$	16.1052	0.877307	0.438653	−	0.898656i	$-0.355456\pi$
$337$	16.1052	0.877307	0.438653	+	0.898656i	$0.355456\pi$
$338$	−10.4920	−0.570692
$339$	−2.15722	−0.117164
$340$	0	0
$341$	7.54741	0.408715
$342$	−15.6749	−0.847602
$343$	34.6509	1.87097
$344$	7.80136	0.420621
$345$	0	0
$346$	0.694528	0.0373381
$347$	26.6453	1.43039	0.715197	−	0.698923i	$-0.246337\pi$
$347$	26.6453	1.43039	0.715197	+	0.698923i	$0.246337\pi$
$348$	6.68336	0.358266
$349$	2.46209	0.131792	0.0658962	−	0.997826i	$-0.479009\pi$
$349$	2.46209	0.131792	0.0658962	+	0.997826i	$0.479009\pi$
$350$	0	0
$351$	−4.23600	−0.226101
$352$	32.4812	1.73125
$353$	13.4323	0.714931	0.357466	−	0.933926i	$-0.383641\pi$
$353$	13.4323	0.714931	0.357466	+	0.933926i	$0.383641\pi$
$354$	−19.3588	−1.02891
$355$	0	0
$356$	−19.1736	−1.01620
$357$	33.3882	1.76709
$358$	8.20937	0.433879
$359$	1.89990	0.100273	0.0501365	−	0.998742i	$-0.484034\pi$
$359$	1.89990	0.100273	0.0501365	+	0.998742i	$0.484034\pi$
$360$	0	0
$361$	35.5499	1.87105
$362$	53.1517	2.79359
$363$	5.69391	0.298853
$364$	−49.1596	−2.57666
$365$	0	0
$366$	−9.94143	−0.519647
$367$	−31.1705	−1.62709	−0.813543	−	0.581504i	$-0.802464\pi$
$367$	−31.1705	−1.62709	−0.813543	+	0.581504i	$0.802464\pi$
$368$	−4.29956	−0.224130
$369$	0.908892	0.0473150
$370$	0	0
$371$	13.3802	0.694663
$372$	4.62577	0.239835
$373$	23.7160	1.22797	0.613983	−	0.789319i	$-0.289566\pi$
$373$	23.7160	1.22797	0.613983	+	0.789319i	$0.289566\pi$
$374$	−62.4730	−3.23040
$375$	0	0
$376$	−1.07002	−0.0551823
$377$	−11.3054	−0.582257
$378$	−9.83546	−0.505882
$379$	0.123885	0.00636352	0.00318176	−	0.999995i	$-0.498987\pi$
$379$	0.123885	0.00636352	0.00318176	+	0.999995i	$0.498987\pi$
$380$	0	0
$381$	−4.69699	−0.240634
$382$	30.0221	1.53606
$383$	−13.2157	−0.675289	−0.337645	−	0.941274i	$-0.609630\pi$
$383$	−13.2157	−0.675289	−0.337645	+	0.941274i	$0.609630\pi$
$384$	8.28820	0.422955
$385$	0	0
$386$	27.6039	1.40500
$387$	−7.29082	−0.370613
$388$	−14.1241	−0.717040
$389$	30.3573	1.53918	0.769588	−	0.638541i	$-0.220462\pi$
$389$	30.3573	1.53918	0.769588	+	0.638541i	$0.220462\pi$
$390$	0	0
$391$	11.3158	0.572263
$392$	−15.4907	−0.782401
$393$	15.3128	0.772426
$394$	30.3735	1.53020
$395$	0	0
$396$	10.2316	0.514159
$397$	19.9262	1.00007	0.500034	−	0.866006i	$-0.333321\pi$
$397$	19.9262	1.00007	0.500034	+	0.866006i	$0.333321\pi$
$398$	17.0613	0.855207
$399$	34.2282	1.71355
$400$	0	0
$401$	1.99651	0.0997009	0.0498505	−	0.998757i	$-0.484126\pi$
$401$	1.99651	0.0997009	0.0498505	+	0.998757i	$0.484126\pi$
$402$	−16.4216	−0.819036
$403$	−7.82483	−0.389782
$404$	−9.33392	−0.464380
$405$	0	0
$406$	−26.2497	−1.30275
$407$	−38.6875	−1.91767
$408$	−7.70902	−0.381654
$409$	−22.6181	−1.11839	−0.559196	−	0.829036i	$-0.688890\pi$
$409$	−22.6181	−1.11839	−0.559196	+	0.829036i	$0.688890\pi$
$410$	0	0
$411$	7.97478	0.393367
$412$	−44.6373	−2.19912
$413$	42.2724	2.08009
$414$	−3.33339	−0.163827
$415$	0	0
$416$	−33.6751	−1.65106
$417$	−16.7191	−0.818738
$418$	−64.0448	−3.13253
$419$	15.7016	0.767075	0.383538	−	0.923525i	$-0.374706\pi$
$419$	15.7016	0.767075	0.383538	+	0.923525i	$0.374706\pi$
$420$	0	0
$421$	−13.4100	−0.653564	−0.326782	−	0.945100i	$-0.605964\pi$
$421$	−13.4100	−0.653564	−0.326782	+	0.945100i	$0.605964\pi$
$422$	3.26200	0.158792
$423$	1.00000	0.0486217
$424$	−3.08936	−0.150032
$425$	0	0
$426$	−3.90360	−0.189130
$427$	21.7084	1.05054
$428$	−37.8906	−1.83151
$429$	−17.3075	−0.835615
$430$	0	0
$431$	−0.754429	−0.0363395	−0.0181698	−	0.999835i	$-0.505784\pi$
$431$	−0.754429	−0.0363395	−0.0181698	+	0.999835i	$0.505784\pi$
$432$	−2.73744	−0.131705
$433$	−4.79029	−0.230207	−0.115103	−	0.993354i	$-0.536720\pi$
$433$	−4.79029	−0.230207	−0.115103	+	0.993354i	$0.536720\pi$
$434$	−18.1683	−0.872105
$435$	0	0
$436$	−0.0314616	−0.00150674
$437$	11.6005	0.554926
$438$	25.5953	1.22299
$439$	5.59869	0.267211	0.133605	−	0.991035i	$-0.457345\pi$
$439$	5.59869	0.267211	0.133605	+	0.991035i	$0.457345\pi$
$440$	0	0
$441$	14.4770	0.689381
$442$	64.7694	3.08076
$443$	22.5635	1.07203	0.536013	−	0.844210i	$-0.319930\pi$
$443$	22.5635	1.07203	0.536013	+	0.844210i	$0.319930\pi$
$444$	−23.7114	−1.12529
$445$	0	0
$446$	6.13945	0.290712
$447$	−3.17686	−0.150260
$448$	−52.8169	−2.49536
$449$	−16.1120	−0.760371	−0.380186	−	0.924910i	$-0.624140\pi$
$449$	−16.1120	−0.760371	−0.380186	+	0.924910i	$0.624140\pi$
$450$	0	0
$451$	3.71357	0.174865
$452$	−5.40206	−0.254091
$453$	−8.59739	−0.403941
$454$	37.8183	1.77490
$455$	0	0
$456$	−7.90298	−0.370091
$457$	27.8145	1.30111	0.650553	−	0.759461i	$-0.274537\pi$
$457$	27.8145	1.30111	0.650553	+	0.759461i	$0.274537\pi$
$458$	−56.1336	−2.62295
$459$	7.20453	0.336279
$460$	0	0
$461$	−2.56902	−0.119651	−0.0598256	−	0.998209i	$-0.519054\pi$
$461$	−2.56902	−0.119651	−0.0598256	+	0.998209i	$0.519054\pi$
$462$	−40.1859	−1.86962
$463$	−36.9412	−1.71680	−0.858402	−	0.512978i	$-0.828542\pi$
$463$	−36.9412	−1.71680	−0.858402	+	0.512978i	$0.828542\pi$
$464$	−7.30591	−0.339168
$465$	0	0
$466$	21.1994	0.982043
$467$	−24.3681	−1.12762	−0.563811	−	0.825904i	$-0.690665\pi$
$467$	−24.3681	−1.12762	−0.563811	+	0.825904i	$0.690665\pi$
$468$	−10.6077	−0.490341
$469$	35.8588	1.65580
$470$	0	0
$471$	7.74369	0.356810
$472$	−9.76032	−0.449255
$473$	−29.7890	−1.36970
$474$	−3.41182	−0.156710
$475$	0	0
$476$	83.6100	3.83226
$477$	2.88718	0.132195
$478$	64.4927	2.94983
$479$	−18.4022	−0.840818	−0.420409	−	0.907335i	$-0.638113\pi$
$479$	−18.4022	−0.840818	−0.420409	+	0.907335i	$0.638113\pi$
$480$	0	0
$481$	40.1095	1.82884
$482$	−24.6525	−1.12289
$483$	7.27890	0.331201
$484$	14.2586	0.648117
$485$	0	0
$486$	−2.12231	−0.0962697
$487$	−40.9123	−1.85391	−0.926956	−	0.375169i	$-0.877585\pi$
$487$	−40.9123	−1.85391	−0.926956	+	0.375169i	$0.877585\pi$
$488$	−5.01227	−0.226895
$489$	4.71986	0.213440
$490$	0	0
$491$	32.4435	1.46416	0.732078	−	0.681221i	$-0.238551\pi$
$491$	32.4435	1.46416	0.732078	+	0.681221i	$0.238551\pi$
$492$	2.27603	0.102611
$493$	19.2280	0.865987
$494$	66.3989	2.98743
$495$	0	0
$496$	−5.05666	−0.227051
$497$	8.52402	0.382355
$498$	14.8402	0.665006
$499$	−16.2578	−0.727801	−0.363901	−	0.931438i	$-0.618555\pi$
$499$	−16.2578	−0.727801	−0.363901	+	0.931438i	$0.618555\pi$
$500$	0	0
$501$	−6.37944	−0.285012
$502$	−2.86088	−0.127687
$503$	−43.7901	−1.95251	−0.976253	−	0.216633i	$-0.930492\pi$
$503$	−43.7901	−1.95251	−0.976253	+	0.216633i	$0.930492\pi$
$504$	−4.95884	−0.220885
$505$	0	0
$506$	−13.6196	−0.605467
$507$	4.94370	0.219557
$508$	−11.7621	−0.521859
$509$	−5.63451	−0.249745	−0.124873	−	0.992173i	$-0.539852\pi$
$509$	−5.63451	−0.249745	−0.124873	+	0.992173i	$0.539852\pi$
$510$	0	0
$511$	−55.8907	−2.47246
$512$	−27.6202	−1.22065
$513$	7.38579	0.326091
$514$	−28.2513	−1.24611
$515$	0	0
$516$	−18.2575	−0.803743
$517$	4.08582	0.179694
$518$	93.1293	4.09187
$519$	−0.327252	−0.0143648
$520$	0	0
$521$	3.88916	0.170387	0.0851936	−	0.996364i	$-0.472849\pi$
$521$	3.88916	0.170387	0.0851936	+	0.996364i	$0.472849\pi$
$522$	−5.66418	−0.247915
$523$	−21.0512	−0.920504	−0.460252	−	0.887788i	$-0.652241\pi$
$523$	−21.0512	−0.920504	−0.460252	+	0.887788i	$0.652241\pi$
$524$	38.3459	1.67515
$525$	0	0
$526$	−43.6067	−1.90134
$527$	13.3084	0.579721
$528$	−11.1847	−0.486751
$529$	−20.5331	−0.892742
$530$	0	0
$531$	9.12158	0.395843
$532$	85.7135	3.71615
$533$	−3.85006	−0.166765
$534$	16.2497	0.703194
$535$	0	0
$536$	−8.27946	−0.357618
$537$	−3.86814	−0.166922
$538$	20.0831	0.865842
$539$	59.1504	2.54779
$540$	0	0
$541$	−12.2832	−0.528097	−0.264049	−	0.964509i	$-0.585058\pi$
$541$	−12.2832	−0.528097	−0.264049	+	0.964509i	$0.585058\pi$
$542$	18.9800	0.815262
$543$	−25.0443	−1.07476
$544$	57.2741	2.45561
$545$	0	0
$546$	41.6630	1.78301
$547$	41.3740	1.76902	0.884512	−	0.466517i	$-0.154492\pi$
$547$	41.3740	1.76902	0.884512	+	0.466517i	$0.154492\pi$
$548$	19.9703	0.853089
$549$	4.68426	0.199919
$550$	0	0
$551$	19.7118	0.839751
$552$	−1.68063	−0.0715324
$553$	7.45016	0.316813
$554$	−47.0650	−1.99960
$555$	0	0
$556$	−41.8676	−1.77558
$557$	10.3976	0.440562	0.220281	−	0.975436i	$-0.429303\pi$
$557$	10.3976	0.440562	0.220281	+	0.975436i	$0.429303\pi$
$558$	−3.92037	−0.165962
$559$	30.8839	1.30625
$560$	0	0
$561$	29.4364	1.24281
$562$	35.1569	1.48300
$563$	4.92759	0.207673	0.103837	−	0.994594i	$-0.466888\pi$
$563$	4.92759	0.207673	0.103837	+	0.994594i	$0.466888\pi$
$564$	2.50418	0.105445
$565$	0	0
$566$	−14.6647	−0.616402
$567$	4.63433	0.194624
$568$	−1.96812	−0.0825804
$569$	44.1705	1.85173	0.925863	−	0.377860i	$-0.123340\pi$
$569$	44.1705	1.85173	0.925863	+	0.377860i	$0.123340\pi$
$570$	0	0
$571$	39.9298	1.67101	0.835505	−	0.549483i	$-0.185175\pi$
$571$	39.9298	1.67101	0.835505	+	0.549483i	$0.185175\pi$
$572$	−43.3412	−1.81219
$573$	−14.1460	−0.590957
$574$	−8.93937	−0.373122
$575$	0	0
$576$	−11.3969	−0.474870
$577$	−4.57511	−0.190464	−0.0952321	−	0.995455i	$-0.530359\pi$
$577$	−4.57511	−0.190464	−0.0952321	+	0.995455i	$0.530359\pi$
$578$	−74.0796	−3.08131
$579$	−13.0065	−0.540534
$580$	0	0
$581$	−32.4055	−1.34441
$582$	11.9702	0.496181
$583$	11.7965	0.488561
$584$	12.9047	0.533999
$585$	0	0
$586$	−53.2041	−2.19784
$587$	29.3530	1.21153	0.605764	−	0.795644i	$-0.292867\pi$
$587$	29.3530	1.21153	0.605764	+	0.795644i	$0.292867\pi$
$588$	36.2530	1.49505
$589$	13.6432	0.562158
$590$	0	0
$591$	−14.3116	−0.588700
$592$	25.9201	1.06531
$593$	16.4200	0.674290	0.337145	−	0.941453i	$-0.390539\pi$
$593$	16.4200	0.674290	0.337145	+	0.941453i	$0.390539\pi$
$594$	−8.67135	−0.355790
$595$	0	0
$596$	−7.95543	−0.325867
$597$	−8.03906	−0.329017
$598$	14.1203	0.577420
$599$	9.68042	0.395531	0.197766	−	0.980249i	$-0.436632\pi$
$599$	9.68042	0.395531	0.197766	+	0.980249i	$0.436632\pi$
$600$	0	0
$601$	8.54664	0.348625	0.174312	−	0.984690i	$-0.444230\pi$
$601$	8.54664	0.348625	0.174312	+	0.984690i	$0.444230\pi$
$602$	71.7086	2.92262
$603$	7.73764	0.315101
$604$	−21.5294	−0.876019
$605$	0	0
$606$	7.91054	0.321344
$607$	−17.5467	−0.712198	−0.356099	−	0.934448i	$-0.615893\pi$
$607$	−17.5467	−0.712198	−0.356099	+	0.934448i	$0.615893\pi$
$608$	58.7151	2.38121
$609$	12.3685	0.501196
$610$	0	0
$611$	−4.23600	−0.171370
$612$	18.0414	0.729282
$613$	−10.7360	−0.433625	−0.216812	−	0.976213i	$-0.569566\pi$
$613$	−10.7360	−0.433625	−0.216812	+	0.976213i	$0.569566\pi$
$614$	38.3975	1.54960
$615$	0	0
$616$	−20.2609	−0.816337
$617$	3.58248	0.144225	0.0721127	−	0.997396i	$-0.477026\pi$
$617$	3.58248	0.144225	0.0721127	+	0.997396i	$0.477026\pi$
$618$	37.8303	1.52176
$619$	27.1092	1.08961	0.544805	−	0.838563i	$-0.316604\pi$
$619$	27.1092	1.08961	0.544805	+	0.838563i	$0.316604\pi$
$620$	0	0
$621$	1.57065	0.0630279
$622$	−42.0300	−1.68525
$623$	−35.4833	−1.42161
$624$	11.5958	0.464204
$625$	0	0
$626$	−12.0134	−0.480152
$627$	30.1770	1.20515
$628$	19.3916	0.773809
$629$	−68.2178	−2.72002
$630$	0	0
$631$	24.2442	0.965146	0.482573	−	0.875856i	$-0.339702\pi$
$631$	24.2442	0.965146	0.482573	+	0.875856i	$0.339702\pi$
$632$	−1.72017	−0.0684248
$633$	−1.53701	−0.0610906
$634$	−5.09358	−0.202292
$635$	0	0
$636$	7.23003	0.286689
$637$	−61.3246	−2.42977
$638$	−23.1428	−0.916233
$639$	1.83932	0.0727624
$640$	0	0
$641$	11.8495	0.468028	0.234014	−	0.972233i	$-0.424814\pi$
$641$	11.8495	0.468028	0.234014	+	0.972233i	$0.424814\pi$
$642$	32.1125	1.26738
$643$	−20.5847	−0.811781	−0.405890	−	0.913922i	$-0.633038\pi$
$643$	−20.5847	−0.811781	−0.405890	+	0.913922i	$0.633038\pi$
$644$	18.2277	0.718271
$645$	0	0
$646$	−112.930	−4.44318
$647$	11.9443	0.469578	0.234789	−	0.972046i	$-0.424560\pi$
$647$	11.9443	0.469578	0.234789	+	0.972046i	$0.424560\pi$
$648$	−1.07002	−0.0420345
$649$	37.2691	1.46294
$650$	0	0
$651$	8.56063	0.335517
$652$	11.8194	0.462883
$653$	−19.7809	−0.774086	−0.387043	−	0.922062i	$-0.626503\pi$
$653$	−19.7809	−0.774086	−0.387043	+	0.922062i	$0.626503\pi$
$654$	0.0266639	0.00104264
$655$	0	0
$656$	−2.48804	−0.0971416
$657$	−12.0602	−0.470512
$658$	−9.83546	−0.383426
$659$	−24.2252	−0.943678	−0.471839	−	0.881685i	$-0.656410\pi$
$659$	−24.2252	−0.943678	−0.471839	+	0.881685i	$0.656410\pi$
$660$	0	0
$661$	36.7337	1.42877	0.714387	−	0.699750i	$-0.246705\pi$
$661$	36.7337	1.42877	0.714387	+	0.699750i	$0.246705\pi$
$662$	−62.6286	−2.43413
$663$	−30.5184	−1.18524
$664$	7.48214	0.290363
$665$	0	0
$666$	20.0955	0.778686
$667$	4.19187	0.162310
$668$	−15.9753	−0.618102
$669$	−2.89282	−0.111843
$670$	0	0
$671$	19.1390	0.738854
$672$	36.8417	1.42120
$673$	−22.2594	−0.858036	−0.429018	−	0.903296i	$-0.641140\pi$
$673$	−22.2594	−0.858036	−0.429018	+	0.903296i	$0.641140\pi$
$674$	−34.1802	−1.31657
$675$	0	0
$676$	12.3799	0.476150
$677$	−27.2505	−1.04732	−0.523661	−	0.851927i	$-0.675434\pi$
$677$	−27.2505	−1.04732	−0.523661	+	0.851927i	$0.675434\pi$
$678$	4.57827	0.175827
$679$	−26.1385	−1.00310
$680$	0	0
$681$	−17.8195	−0.682843
$682$	−16.0179	−0.613357
$683$	14.5708	0.557535	0.278767	−	0.960359i	$-0.410074\pi$
$683$	14.5708	0.557535	0.278767	+	0.960359i	$0.410074\pi$
$684$	18.4954	0.707187
$685$	0	0
$686$	−73.5398	−2.80776
$687$	26.4493	1.00911
$688$	19.9582	0.760899
$689$	−12.2301	−0.465930
$690$	0	0
$691$	36.0901	1.37293	0.686466	−	0.727162i	$-0.259161\pi$
$691$	36.0901	1.37293	0.686466	+	0.727162i	$0.259161\pi$
$692$	−0.819497	−0.0311526
$693$	18.9350	0.719282
$694$	−56.5494	−2.14659
$695$	0	0
$696$	−2.85577	−0.108248
$697$	6.54814	0.248028
$698$	−5.22530	−0.197780
$699$	−9.98885	−0.377813
$700$	0	0
$701$	−3.59794	−0.135892	−0.0679462	−	0.997689i	$-0.521645\pi$
$701$	−3.59794	−0.135892	−0.0679462	+	0.997689i	$0.521645\pi$
$702$	8.99009	0.339309
$703$	−69.9341	−2.63761
$704$	−46.5656	−1.75501
$705$	0	0
$706$	−28.5075	−1.07290
$707$	−17.2737	−0.649644
$708$	22.8421	0.858458
$709$	−40.3771	−1.51640	−0.758198	−	0.652025i	$-0.773920\pi$
$709$	−40.3771	−1.51640	−0.758198	+	0.652025i	$0.773920\pi$
$710$	0	0
$711$	1.60760	0.0602898
$712$	8.19278	0.307037
$713$	2.90133	0.108656
$714$	−70.8599	−2.65186
$715$	0	0
$716$	−9.68651	−0.362002
$717$	−30.3880	−1.13486
$718$	−4.03217	−0.150479
$719$	11.0091	0.410569	0.205284	−	0.978702i	$-0.434188\pi$
$719$	11.0091	0.410569	0.205284	+	0.978702i	$0.434188\pi$
$720$	0	0
$721$	−82.6075	−3.07646
$722$	−75.4478	−2.80788
$723$	11.6159	0.432000
$724$	−62.7155	−2.33081
$725$	0	0
$726$	−12.0842	−0.448488
$727$	9.24089	0.342726	0.171363	−	0.985208i	$-0.445183\pi$
$727$	9.24089	0.342726	0.171363	+	0.985208i	$0.445183\pi$
$728$	21.0057	0.778522
$729$	1.00000	0.0370370
$730$	0	0
$731$	−52.5269	−1.94278
$732$	11.7302	0.433562
$733$	21.6216	0.798613	0.399306	−	0.916818i	$-0.369251\pi$
$733$	21.6216	0.798613	0.399306	+	0.916818i	$0.369251\pi$
$734$	66.1533	2.44176
$735$	0	0
$736$	12.4862	0.460249
$737$	31.6146	1.16454
$738$	−1.92895	−0.0710055
$739$	−48.3012	−1.77679	−0.888393	−	0.459083i	$-0.848178\pi$
$739$	−48.3012	−1.77679	−0.888393	+	0.459083i	$0.848178\pi$
$740$	0	0
$741$	−31.2862	−1.14933
$742$	−28.3968	−1.04248
$743$	46.5382	1.70732	0.853660	−	0.520830i	$-0.174378\pi$
$743$	46.5382	1.70732	0.853660	+	0.520830i	$0.174378\pi$
$744$	−1.97657	−0.0724646
$745$	0	0
$746$	−50.3325	−1.84280
$747$	−6.99249	−0.255842
$748$	73.7141	2.69525
$749$	−70.1217	−2.56219
$750$	0	0
$751$	−1.62284	−0.0592182	−0.0296091	−	0.999562i	$-0.509426\pi$
$751$	−1.62284	−0.0592182	−0.0296091	+	0.999562i	$0.509426\pi$
$752$	−2.73744	−0.0998242
$753$	1.34801	0.0491241
$754$	23.9935	0.873791
$755$	0	0
$756$	11.6052	0.422077
$757$	35.6331	1.29511	0.647554	−	0.762020i	$-0.275792\pi$
$757$	35.6331	1.29511	0.647554	+	0.762020i	$0.275792\pi$
$758$	−0.262921	−0.00954972
$759$	6.41738	0.232936
$760$	0	0
$761$	−27.0065	−0.978983	−0.489492	−	0.872008i	$-0.662818\pi$
$761$	−27.0065	−0.978983	−0.489492	+	0.872008i	$0.662818\pi$
$762$	9.96844	0.361119
$763$	−0.0582240	−0.00210785
$764$	−35.4241	−1.28160
$765$	0	0
$766$	28.0477	1.01340
$767$	−38.6390	−1.39517
$768$	5.20368	0.187772
$769$	−0.409856	−0.0147798	−0.00738990	−	0.999973i	$-0.502352\pi$
$769$	−0.409856	−0.0147798	−0.00738990	+	0.999973i	$0.502352\pi$
$770$	0	0
$771$	13.3116	0.479406
$772$	−32.5707	−1.17225
$773$	18.1099	0.651366	0.325683	−	0.945479i	$-0.394406\pi$
$773$	18.1099	0.651366	0.325683	+	0.945479i	$0.394406\pi$
$774$	15.4733	0.556178
$775$	0	0
$776$	6.03514	0.216649
$777$	−43.8812	−1.57423
$778$	−64.4274	−2.30984
$779$	6.71288	0.240514
$780$	0	0
$781$	7.51513	0.268913
$782$	−24.0155	−0.858794
$783$	2.66888	0.0953781
$784$	−39.6300	−1.41536
$785$	0	0
$786$	−32.4983	−1.15918
$787$	6.00376	0.214011	0.107005	−	0.994258i	$-0.465874\pi$
$787$	6.00376	0.214011	0.107005	+	0.994258i	$0.465874\pi$
$788$	−35.8388	−1.27670
$789$	20.5469	0.731488
$790$	0	0
$791$	−9.99725	−0.355461
$792$	−4.37193	−0.155350
$793$	−19.8425	−0.704629
$794$	−42.2895	−1.50080
$795$	0	0
$796$	−20.1312	−0.713533
$797$	−39.5206	−1.39989	−0.699945	−	0.714196i	$-0.746792\pi$
$797$	−39.5206	−1.39989	−0.699945	+	0.714196i	$0.746792\pi$
$798$	−72.6427	−2.57152
$799$	7.20453	0.254878
$800$	0	0
$801$	−7.65663	−0.270534
$802$	−4.23720	−0.149621
$803$	−49.2756	−1.73890
$804$	19.3764	0.683354
$805$	0	0
$806$	16.6067	0.584945
$807$	−9.46285	−0.333108
$808$	3.98834	0.140309
$809$	46.2225	1.62510	0.812549	−	0.582893i	$-0.198079\pi$
$809$	46.2225	1.62510	0.812549	+	0.582893i	$0.198079\pi$
$810$	0	0
$811$	20.5428	0.721355	0.360677	−	0.932691i	$-0.382546\pi$
$811$	20.5428	0.721355	0.360677	+	0.932691i	$0.382546\pi$
$812$	30.9729	1.08694
$813$	−8.94312	−0.313649
$814$	82.1067	2.87784
$815$	0	0
$816$	−19.7220	−0.690408
$817$	−53.8485	−1.88392
$818$	48.0024	1.67837
$819$	−19.6310	−0.685963
$820$	0	0
$821$	−38.8345	−1.35533	−0.677667	−	0.735369i	$-0.737009\pi$
$821$	−38.8345	−1.35533	−0.677667	+	0.735369i	$0.737009\pi$
$822$	−16.9249	−0.590325
$823$	−0.0587025	−0.00204624	−0.00102312	−	0.999999i	$-0.500326\pi$
$823$	−0.0587025	−0.00204624	−0.00102312	+	0.999999i	$0.500326\pi$
$824$	19.0733	0.664450
$825$	0	0
$826$	−89.7150	−3.12158
$827$	−5.29081	−0.183979	−0.0919897	−	0.995760i	$-0.529323\pi$
$827$	−5.29081	−0.183979	−0.0919897	+	0.995760i	$0.529323\pi$
$828$	3.93318	0.136688
$829$	−12.9896	−0.451148	−0.225574	−	0.974226i	$-0.572426\pi$
$829$	−12.9896	−0.451148	−0.225574	+	0.974226i	$0.572426\pi$
$830$	0	0
$831$	22.1764	0.769289
$832$	48.2772	1.67371
$833$	104.300	3.61378
$834$	35.4830	1.22868
$835$	0	0
$836$	75.5687	2.61360
$837$	1.84722	0.0638493
$838$	−33.3237	−1.15115
$839$	21.7836	0.752053	0.376026	−	0.926609i	$-0.377290\pi$
$839$	21.7836	0.752053	0.376026	+	0.926609i	$0.377290\pi$
$840$	0	0
$841$	−21.8771	−0.754382
$842$	28.4602	0.980802
$843$	−16.5654	−0.570543
$844$	−3.84895	−0.132486
$845$	0	0
$846$	−2.12231	−0.0729664
$847$	26.3875	0.906684
$848$	−7.90349	−0.271407
$849$	6.90978	0.237143
$850$	0	0
$851$	−14.8720	−0.509807
$852$	4.60599	0.157799
$853$	−13.6786	−0.468345	−0.234173	−	0.972195i	$-0.575238\pi$
$853$	−13.6786	−0.468345	−0.234173	+	0.972195i	$0.575238\pi$
$854$	−46.0719	−1.57655
$855$	0	0
$856$	16.1905	0.553379
$857$	36.0713	1.23217	0.616086	−	0.787679i	$-0.288717\pi$
$857$	36.0713	1.23217	0.616086	+	0.787679i	$0.288717\pi$
$858$	36.7319	1.25401
$859$	−34.4691	−1.17607	−0.588035	−	0.808835i	$-0.700098\pi$
$859$	−34.4691	−1.17607	−0.588035	+	0.808835i	$0.700098\pi$
$860$	0	0
$861$	4.21210	0.143548
$862$	1.60113	0.0545346
$863$	−40.7815	−1.38822	−0.694109	−	0.719870i	$-0.744202\pi$
$863$	−40.7815	−1.38822	−0.694109	+	0.719870i	$0.744202\pi$
$864$	7.94974	0.270456
$865$	0	0
$866$	10.1665	0.345470
$867$	34.9053	1.18544
$868$	21.4374	0.727631
$869$	6.56837	0.222817
$870$	0	0
$871$	−32.7766	−1.11059
$872$	0.0134434	0.000455251 0
$873$	−5.64019	−0.190892
$874$	−24.6197	−0.832775
$875$	0	0
$876$	−30.2008	−1.02039
$877$	4.36362	0.147349	0.0736746	−	0.997282i	$-0.476527\pi$
$877$	4.36362	0.147349	0.0736746	+	0.997282i	$0.476527\pi$
$878$	−11.8821	−0.401003
$879$	25.0690	0.845557
$880$	0	0
$881$	−42.5856	−1.43475	−0.717373	−	0.696690i	$-0.754655\pi$
$881$	−42.5856	−1.43475	−0.717373	+	0.696690i	$0.754655\pi$
$882$	−30.7246	−1.03455
$883$	−41.5659	−1.39880	−0.699401	−	0.714729i	$-0.746550\pi$
$883$	−41.5659	−1.39880	−0.699401	+	0.714729i	$0.746550\pi$
$884$	−76.4236	−2.57040
$885$	0	0
$886$	−47.8867	−1.60879
$887$	28.1950	0.946697	0.473348	−	0.880875i	$-0.343045\pi$
$887$	28.1950	0.946697	0.473348	+	0.880875i	$0.343045\pi$
$888$	10.1318	0.340000
$889$	−21.7674	−0.730055
$890$	0	0
$891$	4.08582	0.136880
$892$	−7.24415	−0.242552
$893$	7.38579	0.247156
$894$	6.74227	0.225495
$895$	0	0
$896$	38.4102	1.28320
$897$	−6.65326	−0.222146
$898$	34.1945	1.14109
$899$	4.93001	0.164425
$900$	0	0
$901$	20.8008	0.692975
$902$	−7.88132	−0.262419
$903$	−33.7881	−1.12440
$904$	2.30827	0.0767720
$905$	0	0
$906$	18.2463	0.606192
$907$	−35.8544	−1.19052	−0.595262	−	0.803531i	$-0.702952\pi$
$907$	−35.8544	−1.19052	−0.595262	+	0.803531i	$0.702952\pi$
$908$	−44.6231	−1.48087
$909$	−3.72733	−0.123628
$910$	0	0
$911$	32.6228	1.08084	0.540420	−	0.841395i	$-0.318265\pi$
$911$	32.6228	1.08084	0.540420	+	0.841395i	$0.318265\pi$
$912$	−20.2182	−0.669491
$913$	−28.5701	−0.945531
$914$	−59.0308	−1.95257
$915$	0	0
$916$	66.2339	2.18843
$917$	70.9644	2.34345
$918$	−15.2902	−0.504652
$919$	−31.0958	−1.02576	−0.512878	−	0.858462i	$-0.671421\pi$
$919$	−31.0958	−1.02576	−0.512878	+	0.858462i	$0.671421\pi$
$920$	0	0
$921$	−18.0924	−0.596164
$922$	5.45225	0.179560
$923$	−7.79137	−0.256456
$924$	47.4167	1.55990
$925$	0	0
$926$	78.4005	2.57640
$927$	−17.8251	−0.585454
$928$	21.2169	0.696479
$929$	−21.8101	−0.715565	−0.357783	−	0.933805i	$-0.616467\pi$
$929$	−21.8101	−0.715565	−0.357783	+	0.933805i	$0.616467\pi$
$930$	0	0
$931$	106.924	3.50430
$932$	−25.0139	−0.819357
$933$	19.8040	0.648352
$934$	51.7166	1.69222
$935$	0	0
$936$	4.53262	0.148153
$937$	−14.9128	−0.487181	−0.243590	−	0.969878i	$-0.578325\pi$
$937$	−14.9128	−0.487181	−0.243590	+	0.969878i	$0.578325\pi$
$938$	−76.1032	−2.48486
$939$	5.66054	0.184725
$940$	0	0
$941$	−10.8049	−0.352230	−0.176115	−	0.984370i	$-0.556353\pi$
$941$	−10.8049	−0.352230	−0.176115	+	0.984370i	$0.556353\pi$
$942$	−16.4345	−0.535464
$943$	1.42755	0.0464874
$944$	−24.9698	−0.812698
$945$	0	0
$946$	63.2213	2.05550
$947$	−8.58759	−0.279059	−0.139530	−	0.990218i	$-0.544559\pi$
$947$	−8.58759	−0.279059	−0.139530	+	0.990218i	$0.544559\pi$
$948$	4.02573	0.130749
$949$	51.0868	1.65835
$950$	0	0
$951$	2.40002	0.0778261
$952$	−35.7261	−1.15789
$953$	44.3454	1.43649	0.718244	−	0.695792i	$-0.244946\pi$
$953$	44.3454	1.43649	0.718244	+	0.695792i	$0.244946\pi$
$954$	−6.12748	−0.198385
$955$	0	0
$956$	−76.0972	−2.46116
$957$	10.9046	0.352495
$958$	39.0551	1.26181
$959$	36.9578	1.19343
$960$	0	0
$961$	−27.5878	−0.889928
$962$	−85.1247	−2.74453
$963$	−15.1309	−0.487587
$964$	29.0883	0.936871
$965$	0	0
$966$	−15.4480	−0.497033
$967$	23.3060	0.749469	0.374734	−	0.927132i	$-0.377734\pi$
$967$	23.3060	0.749469	0.374734	+	0.927132i	$0.377734\pi$
$968$	−6.09263	−0.195824
$969$	53.2112	1.70939
$970$	0	0
$971$	−11.9879	−0.384709	−0.192354	−	0.981326i	$-0.561612\pi$
$971$	−11.9879	−0.384709	−0.192354	+	0.981326i	$0.561612\pi$
$972$	2.50418	0.0803216
$973$	−77.4818	−2.48395
$974$	86.8284	2.78216
$975$	0	0
$976$	−12.8229	−0.410451
$977$	5.50818	0.176222	0.0881112	−	0.996111i	$-0.471917\pi$
$977$	5.50818	0.176222	0.0881112	+	0.996111i	$0.471917\pi$
$978$	−10.0170	−0.320308
$979$	−31.2836	−0.999828
$980$	0	0
$981$	−0.0125636	−0.000401126 0
$982$	−68.8551	−2.19725
$983$	4.06279	0.129583	0.0647915	−	0.997899i	$-0.479362\pi$
$983$	4.06279	0.129583	0.0647915	+	0.997899i	$0.479362\pi$
$984$	−0.972536	−0.0310033
$985$	0	0
$986$	−40.8078	−1.29958
$987$	4.63433	0.147512
$988$	−78.3463	−2.49253
$989$	−11.4513	−0.364130
$990$	0	0
$991$	−14.0303	−0.445687	−0.222844	−	0.974854i	$-0.571534\pi$
$991$	−14.0303	−0.445687	−0.222844	+	0.974854i	$0.571534\pi$
$992$	14.6849	0.466247
$993$	29.5097	0.936462
$994$	−18.0906	−0.573798
$995$	0	0
$996$	−17.5105	−0.554840
$997$	13.6700	0.432933	0.216466	−	0.976290i	$-0.430547\pi$
$997$	13.6700	0.432933	0.216466	+	0.976290i	$0.430547\pi$
$998$	34.5041	1.09221
$999$	−9.46873	−0.299577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bi.1.3		13
5.2	odd	4		705.2.c.c.424.6	✓	26
5.3	odd	4		705.2.c.c.424.21	yes	26
5.4	even	2		3525.2.a.bh.1.11		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.c.424.6	✓	26	5.2	odd	4
705.2.c.c.424.21	yes	26	5.3	odd	4
3525.2.a.bh.1.11		13	5.4	even	2
3525.2.a.bi.1.3		13	1.1	even	1	trivial

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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)

\(f(q)\)	\(=\)	\(q-2.12231 q^{2} +1.00000 q^{3} +2.50418 q^{4} -2.12231 q^{6} +4.63433 q^{7} -1.07002 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.12231 q^{2} +1.00000 q^{3} +2.50418 q^{4} -2.12231 q^{6} +4.63433 q^{7} -1.07002 q^{8} +1.00000 q^{9} +4.08582 q^{11} +2.50418 q^{12} -4.23600 q^{13} -9.83546 q^{14} -2.73744 q^{16} +7.20453 q^{17} -2.12231 q^{18} +7.38579 q^{19} +4.63433 q^{21} -8.67135 q^{22} +1.57065 q^{23} -1.07002 q^{24} +8.99009 q^{26} +1.00000 q^{27} +11.6052 q^{28} +2.66888 q^{29} +1.84722 q^{31} +7.94974 q^{32} +4.08582 q^{33} -15.2902 q^{34} +2.50418 q^{36} -9.46873 q^{37} -15.6749 q^{38} -4.23600 q^{39} +0.908892 q^{41} -9.83546 q^{42} -7.29082 q^{43} +10.2316 q^{44} -3.33339 q^{46} +1.00000 q^{47} -2.73744 q^{48} +14.4770 q^{49} +7.20453 q^{51} -10.6077 q^{52} +2.88718 q^{53} -2.12231 q^{54} -4.95884 q^{56} +7.38579 q^{57} -5.66418 q^{58} +9.12158 q^{59} +4.68426 q^{61} -3.92037 q^{62} +4.63433 q^{63} -11.3969 q^{64} -8.67135 q^{66} +7.73764 q^{67} +18.0414 q^{68} +1.57065 q^{69} +1.83932 q^{71} -1.07002 q^{72} -12.0602 q^{73} +20.0955 q^{74} +18.4954 q^{76} +18.9350 q^{77} +8.99009 q^{78} +1.60760 q^{79} +1.00000 q^{81} -1.92895 q^{82} -6.99249 q^{83} +11.6052 q^{84} +15.4733 q^{86} +2.66888 q^{87} -4.37193 q^{88} -7.65663 q^{89} -19.6310 q^{91} +3.93318 q^{92} +1.84722 q^{93} -2.12231 q^{94} +7.94974 q^{96} -5.64019 q^{97} -30.7246 q^{98} +4.08582 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 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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