LMFDB - Embedded newform 3525.2.a.bh.1.11

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			1.11
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	$-0.229886\pi$
$2$	2.12231	1.50070	0.750348	+	0.661043i	$0.229886\pi$
$3$	−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	$-0.839669\pi$
$7$	−4.63433	−1.75161	−0.875806	+	0.482664i	$0.839669\pi$
$8$	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	$-0.300141\pi$
$13$	4.23600	1.17486	0.587428	+	0.809277i	$0.300141\pi$
$14$	−9.83546	−2.62864
$15$	0	0
$16$	−2.73744	−0.684360
$17$	−7.20453	−1.74736	−0.873678	−	0.486505i	$-0.838271\pi$
$17$	−7.20453	−1.74736	−0.873678	+	0.486505i	$0.838271\pi$
$18$	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	$-0.552359\pi$
$23$	−1.57065	−0.327503	−0.163751	+	0.986502i	$0.552359\pi$
$24$	−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	$-0.216070\pi$
$37$	9.46873	1.55665	0.778325	+	0.627862i	$0.216070\pi$
$38$	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	$-0.312366\pi$
$43$	7.29082	1.11184	0.555920	+	0.831236i	$0.312366\pi$
$44$	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	$-0.563540\pi$
$53$	−2.88718	−0.396585	−0.198293	+	0.980143i	$0.563540\pi$
$54$	−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	$-0.656703\pi$
$67$	−7.73764	−0.945303	−0.472651	+	0.881249i	$0.656703\pi$
$68$	−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	$-0.250602\pi$
$73$	12.0602	1.41154	0.705768	+	0.708444i	$0.250602\pi$
$74$	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	$-0.374628\pi$
$83$	6.99249	0.767526	0.383763	+	0.923432i	$0.374628\pi$
$84$	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	$-0.407562\pi$
$97$	5.64019	0.572675	0.286337	+	0.958129i	$0.407562\pi$
$98$	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	$-0.158758\pi$
$103$	17.8251	1.75636	0.878180	+	0.478329i	$0.158758\pi$
$104$	4.53262	0.444460
$105$	0	0
$106$	−6.12748	−0.595154
$107$	15.1309	1.46276	0.731381	−	0.681969i	$-0.238876\pi$
$107$	15.1309	1.46276	0.731381	+	0.681969i	$0.238876\pi$
$108$	−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	$-0.467646\pi$
$113$	2.15722	0.202934	0.101467	+	0.994839i	$0.467646\pi$
$114$	−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	$-0.433176\pi$
$127$	4.69699	0.416790	0.208395	+	0.978045i	$0.433176\pi$
$128$	−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	$-0.610652\pi$
$137$	−7.97478	−0.681332	−0.340666	+	0.940184i	$0.610652\pi$
$138$	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	$-0.599997\pi$
$157$	−7.74369	−0.618014	−0.309007	+	0.951060i	$0.599997\pi$
$158$	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	$-0.559178\pi$
$163$	−4.71986	−0.369688	−0.184844	+	0.982768i	$0.559178\pi$
$164$	2.27603	0.177728
$165$	0	0
$166$	14.8402	1.15182
$167$	6.37944	0.493656	0.246828	−	0.969059i	$-0.420612\pi$
$167$	6.37944	0.493656	0.246828	+	0.969059i	$0.420612\pi$
$168$	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	$-0.496040\pi$
$173$	0.327252	0.0248805	0.0124402	+	0.999923i	$0.496040\pi$
$174$	−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	$-0.344933\pi$
$193$	13.0065	0.936232	0.468116	+	0.883667i	$0.344933\pi$
$194$	11.9702	0.859411
$195$	0	0
$196$	36.2530	2.58950
$197$	14.3116	1.01966	0.509829	−	0.860276i	$-0.329709\pi$
$197$	14.3116	1.01966	0.509829	+	0.860276i	$0.329709\pi$
$198$	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	$-0.469120\pi$
$223$	2.89282	0.193718	0.0968589	+	0.995298i	$0.469120\pi$
$224$	36.8417	2.46159
$225$	0	0
$226$	4.57827	0.304542
$227$	17.8195	1.18272	0.591359	−	0.806408i	$-0.298592\pi$
$227$	17.8195	1.18272	0.591359	+	0.806408i	$0.298592\pi$
$228$	−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	$-0.393896\pi$
$233$	9.98885	0.654391	0.327196	+	0.944957i	$0.393896\pi$
$234$	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	$-0.636280\pi$
$257$	−13.3116	−0.830355	−0.415177	+	0.909740i	$0.636280\pi$
$258$	−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	$-0.718377\pi$
$263$	−20.5469	−1.26697	−0.633487	+	0.773753i	$0.718377\pi$
$264$	−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	$-0.732091\pi$
$277$	−22.1764	−1.33245	−0.666224	+	0.745752i	$0.732091\pi$
$278$	−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	$-0.565840\pi$
$283$	−6.90978	−0.410744	−0.205372	+	0.978684i	$0.565840\pi$
$284$	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	$-0.761541\pi$
$293$	−25.0690	−1.46455	−0.732273	+	0.681011i	$0.761541\pi$
$294$	−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	$-0.327312\pi$
$307$	18.0924	1.03259	0.516293	+	0.856412i	$0.327312\pi$
$308$	−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	$-0.551142\pi$
$313$	−5.66054	−0.319952	−0.159976	+	0.987121i	$0.551142\pi$
$314$	−16.4345	−0.927451
$315$	0	0
$316$	4.02573	0.226465
$317$	−2.40002	−0.134799	−0.0673994	−	0.997726i	$-0.521470\pi$
$317$	−2.40002	−0.134799	−0.0673994	+	0.997726i	$0.521470\pi$
$318$	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	$-0.644544\pi$
$337$	−16.1052	−0.877307	−0.438653	+	0.898656i	$0.644544\pi$
$338$	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	$-0.753663\pi$
$347$	−26.6453	−1.43039	−0.715197	+	0.698923i	$0.753663\pi$
$348$	−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	$-0.616359\pi$
$353$	−13.4323	−0.714931	−0.357466	+	0.933926i	$0.616359\pi$
$354$	−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	$-0.197536\pi$
$367$	31.1705	1.62709	0.813543	+	0.581504i	$0.197536\pi$
$368$	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	$-0.710434\pi$
$373$	−23.7160	−1.22797	−0.613983	+	0.789319i	$0.710434\pi$
$374$	−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	$-0.390370\pi$
$383$	13.2157	0.675289	0.337645	+	0.941274i	$0.390370\pi$
$384$	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	$-0.666679\pi$
$397$	−19.9262	−1.00007	−0.500034	+	0.866006i	$0.666679\pi$
$398$	−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	$-0.463280\pi$
$433$	4.79029	0.230207	0.115103	+	0.993354i	$0.463280\pi$
$434$	−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	$-0.680070\pi$
$443$	−22.5635	−1.07203	−0.536013	+	0.844210i	$0.680070\pi$
$444$	−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	$-0.725463\pi$
$457$	−27.8145	−1.30111	−0.650553	+	0.759461i	$0.725463\pi$
$458$	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	$-0.171458\pi$
$463$	36.9412	1.71680	0.858402	+	0.512978i	$0.171458\pi$
$464$	−7.30591	−0.339168
$465$	0	0
$466$	21.1994	0.982043
$467$	24.3681	1.12762	0.563811	−	0.825904i	$-0.309335\pi$
$467$	24.3681	1.12762	0.563811	+	0.825904i	$0.309335\pi$
$468$	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	$-0.122415\pi$
$487$	40.9123	1.85391	0.926956	+	0.375169i	$0.122415\pi$
$488$	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	$-0.0695075\pi$
$503$	43.7901	1.95251	0.976253	+	0.216633i	$0.0695075\pi$
$504$	−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	$-0.347759\pi$
$523$	21.0512	0.920504	0.460252	+	0.887788i	$0.347759\pi$
$524$	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	$-0.845508\pi$
$547$	−41.3740	−1.76902	−0.884512	+	0.466517i	$0.845508\pi$
$548$	−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	$-0.570697\pi$
$557$	−10.3976	−0.440562	−0.220281	+	0.975436i	$0.570697\pi$
$558$	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	$-0.533112\pi$
$563$	−4.92759	−0.207673	−0.103837	+	0.994594i	$0.533112\pi$
$564$	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	$-0.469641\pi$
$577$	4.57511	0.190464	0.0952321	+	0.995455i	$0.469641\pi$
$578$	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	$-0.707133\pi$
$587$	−29.3530	−1.21153	−0.605764	+	0.795644i	$0.707133\pi$
$588$	−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	$-0.609461\pi$
$593$	−16.4200	−0.674290	−0.337145	+	0.941453i	$0.609461\pi$
$594$	−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	$-0.384107\pi$
$607$	17.5467	0.712198	0.356099	+	0.934448i	$0.384107\pi$
$608$	−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	$-0.430434\pi$
$613$	10.7360	0.433625	0.216812	+	0.976213i	$0.430434\pi$
$614$	38.3975	1.54960
$615$	0	0
$616$	−20.2609	−0.816337
$617$	−3.58248	−0.144225	−0.0721127	−	0.997396i	$-0.522974\pi$
$617$	−3.58248	−0.144225	−0.0721127	+	0.997396i	$0.522974\pi$
$618$	−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	$-0.366962\pi$
$643$	20.5847	0.811781	0.405890	+	0.913922i	$0.366962\pi$
$644$	18.2277	0.718271
$645$	0	0
$646$	−112.930	−4.44318
$647$	−11.9443	−0.469578	−0.234789	−	0.972046i	$-0.575440\pi$
$647$	−11.9443	−0.469578	−0.234789	+	0.972046i	$0.575440\pi$
$648$	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	$-0.373497\pi$
$653$	19.7809	0.774086	0.387043	+	0.922062i	$0.373497\pi$
$654$	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	$-0.358860\pi$
$673$	22.2594	0.858036	0.429018	+	0.903296i	$0.358860\pi$
$674$	−34.1802	−1.31657
$675$	0	0
$676$	12.3799	0.476150
$677$	27.2505	1.04732	0.523661	−	0.851927i	$-0.324566\pi$
$677$	27.2505	1.04732	0.523661	+	0.851927i	$0.324566\pi$
$678$	−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	$-0.589926\pi$
$683$	−14.5708	−0.557535	−0.278767	+	0.960359i	$0.589926\pi$
$684$	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	$-0.554817\pi$
$727$	−9.24089	−0.342726	−0.171363	+	0.985208i	$0.554817\pi$
$728$	−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	$-0.630749\pi$
$733$	−21.6216	−0.798613	−0.399306	+	0.916818i	$0.630749\pi$
$734$	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	$-0.825622\pi$
$743$	−46.5382	−1.70732	−0.853660	+	0.520830i	$0.825622\pi$
$744$	−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	$-0.724208\pi$
$757$	−35.6331	−1.29511	−0.647554	+	0.762020i	$0.724208\pi$
$758$	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	$-0.605594\pi$
$773$	−18.1099	−0.651366	−0.325683	+	0.945479i	$0.605594\pi$
$774$	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	$-0.534126\pi$
$787$	−6.00376	−0.214011	−0.107005	+	0.994258i	$0.534126\pi$
$788$	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	$-0.253208\pi$
$797$	39.5206	1.39989	0.699945	+	0.714196i	$0.253208\pi$
$798$	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	$-0.499674\pi$
$823$	0.0587025	0.00204624	0.00102312	+	0.999999i	$0.499674\pi$
$824$	19.0733	0.664450
$825$	0	0
$826$	−89.7150	−3.12158
$827$	5.29081	0.183979	0.0919897	−	0.995760i	$-0.470677\pi$
$827$	5.29081	0.183979	0.0919897	+	0.995760i	$0.470677\pi$
$828$	−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	$-0.424762\pi$
$853$	13.6786	0.468345	0.234173	+	0.972195i	$0.424762\pi$
$854$	−46.0719	−1.57655
$855$	0	0
$856$	16.1905	0.553379
$857$	−36.0713	−1.23217	−0.616086	−	0.787679i	$-0.711283\pi$
$857$	−36.0713	−1.23217	−0.616086	+	0.787679i	$0.711283\pi$
$858$	−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	$-0.255798\pi$
$863$	40.7815	1.38822	0.694109	+	0.719870i	$0.255798\pi$
$864$	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	$-0.523473\pi$
$877$	−4.36362	−0.147349	−0.0736746	+	0.997282i	$0.523473\pi$
$878$	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	$-0.253450\pi$
$883$	41.5659	1.39880	0.699401	+	0.714729i	$0.253450\pi$
$884$	−76.4236	−2.57040
$885$	0	0
$886$	−47.8867	−1.60879
$887$	−28.1950	−0.946697	−0.473348	−	0.880875i	$-0.656955\pi$
$887$	−28.1950	−0.946697	−0.473348	+	0.880875i	$0.656955\pi$
$888$	−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	$-0.297048\pi$
$907$	35.8544	1.19052	0.595262	+	0.803531i	$0.297048\pi$
$908$	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	$-0.421675\pi$
$937$	14.9128	0.487181	0.243590	+	0.969878i	$0.421675\pi$
$938$	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	$-0.455441\pi$
$947$	8.58759	0.279059	0.139530	+	0.990218i	$0.455441\pi$
$948$	−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	$-0.755054\pi$
$953$	−44.3454	−1.43649	−0.718244	+	0.695792i	$0.755054\pi$
$954$	−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	$-0.622266\pi$
$967$	−23.3060	−0.749469	−0.374734	+	0.927132i	$0.622266\pi$
$968$	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	$-0.528083\pi$
$977$	−5.50818	−0.176222	−0.0881112	+	0.996111i	$0.528083\pi$
$978$	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	$-0.520638\pi$
$983$	−4.06279	−0.129583	−0.0647915	+	0.997899i	$0.520638\pi$
$984$	−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	$-0.569453\pi$
$997$	−13.6700	−0.432933	−0.216466	+	0.976290i	$0.569453\pi$
$998$	−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.bh.1.11		13
5.2	odd	4		705.2.c.c.424.21	yes	26
5.3	odd	4		705.2.c.c.424.6	✓	26
5.4	even	2		3525.2.a.bi.1.3		13

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

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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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