LMFDB - Embedded newform 1666.2.a.ba.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1666,2,Mod(1,1666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1666, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1666 = 2 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1666.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:	$13.3030769767$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.23949216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 13x^{3} - 2x^{2} + 24x - 4 $ x^5 - 13x^3 - 2x^2 + 24*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 238)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.171872$ of defining polynomial
Character	$\chi$	$=$	1666.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.171872 q^{3} +1.00000 q^{4} -3.68841 q^{5} +0.171872 q^{6} +1.00000 q^{8} -2.97046 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.171872 q^{3} +1.00000 q^{4} -3.68841 q^{5} +0.171872 q^{6} +1.00000 q^{8} -2.97046 q^{9} -3.68841 q^{10} +1.82813 q^{11} +0.171872 q^{12} +4.94814 q^{13} -0.633936 q^{15} +1.00000 q^{16} +1.00000 q^{17} -2.97046 q^{18} -5.94814 q^{19} -3.68841 q^{20} +1.82813 q^{22} +7.23019 q^{23} +0.171872 q^{24} +8.60440 q^{25} +4.94814 q^{26} -1.02616 q^{27} +10.3545 q^{29} -0.633936 q^{30} +1.02232 q^{31} +1.00000 q^{32} +0.314204 q^{33} +1.00000 q^{34} -2.97046 q^{36} +5.68841 q^{37} -5.94814 q^{38} +0.850448 q^{39} -3.68841 q^{40} -2.97768 q^{41} -2.06262 q^{43} +1.82813 q^{44} +10.9563 q^{45} +7.23019 q^{46} +8.01076 q^{47} +0.171872 q^{48} +8.60440 q^{50} +0.171872 q^{51} +4.94814 q^{52} -8.95890 q^{53} -1.02616 q^{54} -6.74289 q^{55} -1.02232 q^{57} +10.3545 q^{58} +12.0035 q^{59} -0.633936 q^{60} -3.70981 q^{61} +1.02232 q^{62} +1.00000 q^{64} -18.2508 q^{65} +0.314204 q^{66} +5.42869 q^{67} +1.00000 q^{68} +1.24267 q^{69} -5.40206 q^{71} -2.97046 q^{72} +6.97768 q^{73} +5.68841 q^{74} +1.47886 q^{75} -5.94814 q^{76} +0.850448 q^{78} +5.20496 q^{79} -3.68841 q^{80} +8.73501 q^{81} -2.97768 q^{82} +15.2731 q^{83} -3.68841 q^{85} -2.06262 q^{86} +1.77965 q^{87} +1.82813 q^{88} -2.93016 q^{89} +10.9563 q^{90} +7.23019 q^{92} +0.175708 q^{93} +8.01076 q^{94} +21.9392 q^{95} +0.171872 q^{96} -6.91860 q^{97} -5.43038 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 5 q^{4} + q^{5} + 5 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 5 * q^4 + q^5 + 5 * q^8 + 11 * q^9	$ 5 q + 5 q^{2} + 5 q^{4} + q^{5} + 5 q^{8} + 11 q^{9} + q^{10} + 10 q^{11} - 2 q^{13} - 4 q^{15} + 5 q^{16} + 5 q^{17} + 11 q^{18} - 3 q^{19} + q^{20} + 10 q^{22} + 3 q^{23} + 18 q^{25} - 2 q^{26} + 6 q^{27} + 12 q^{29} - 4 q^{30} + 6 q^{31} + 5 q^{32} - 26 q^{33} + 5 q^{34} + 11 q^{36} + 9 q^{37} - 3 q^{38} + 6 q^{39} + q^{40} - 14 q^{41} + q^{43} + 10 q^{44} + 37 q^{45} + 3 q^{46} + 2 q^{47} + 18 q^{50} - 2 q^{52} + 20 q^{53} + 6 q^{54} + 6 q^{55} - 6 q^{57} + 12 q^{58} - 3 q^{59} - 4 q^{60} - 16 q^{61} + 6 q^{62} + 5 q^{64} + 2 q^{65} - 26 q^{66} + 15 q^{67} + 5 q^{68} - 4 q^{69} + 7 q^{71} + 11 q^{72} + 34 q^{73} + 9 q^{74} - 46 q^{75} - 3 q^{76} + 6 q^{78} - 12 q^{79} + q^{80} + 53 q^{81} - 14 q^{82} - 16 q^{83} + q^{85} + q^{86} + 20 q^{87} + 10 q^{88} - q^{89} + 37 q^{90} + 3 q^{92} - 12 q^{93} + 2 q^{94} - 3 q^{95} + 18 q^{97} + 16 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 5 * q^4 + q^5 + 5 * q^8 + 11 * q^9 + q^10 + 10 * q^11 - 2 * q^13 - 4 * q^15 + 5 * q^16 + 5 * q^17 + 11 * q^18 - 3 * q^19 + q^20 + 10 * q^22 + 3 * q^23 + 18 * q^25 - 2 * q^26 + 6 * q^27 + 12 * q^29 - 4 * q^30 + 6 * q^31 + 5 * q^32 - 26 * q^33 + 5 * q^34 + 11 * q^36 + 9 * q^37 - 3 * q^38 + 6 * q^39 + q^40 - 14 * q^41 + q^43 + 10 * q^44 + 37 * q^45 + 3 * q^46 + 2 * q^47 + 18 * q^50 - 2 * q^52 + 20 * q^53 + 6 * q^54 + 6 * q^55 - 6 * q^57 + 12 * q^58 - 3 * q^59 - 4 * q^60 - 16 * q^61 + 6 * q^62 + 5 * q^64 + 2 * q^65 - 26 * q^66 + 15 * q^67 + 5 * q^68 - 4 * q^69 + 7 * q^71 + 11 * q^72 + 34 * q^73 + 9 * q^74 - 46 * q^75 - 3 * q^76 + 6 * q^78 - 12 * q^79 + q^80 + 53 * q^81 - 14 * q^82 - 16 * q^83 + q^85 + q^86 + 20 * q^87 + 10 * q^88 - q^89 + 37 * q^90 + 3 * q^92 - 12 * q^93 + 2 * q^94 - 3 * q^95 + 18 * q^97 + 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.171872	0.0992305	0.0496152	−	0.998768i	$-0.484200\pi$
$3$	0.171872	0.0992305	0.0496152	+	0.998768i	$0.484200\pi$
$4$	1.00000	0.500000
$5$	−3.68841	−1.64951	−0.824754	−	0.565491i	$-0.808687\pi$
$5$	−3.68841	−1.64951	−0.824754	+	0.565491i	$0.808687\pi$
$6$	0.171872	0.0701665
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.97046	−0.990153
$10$	−3.68841	−1.16638
$11$	1.82813	0.551201	0.275601	−	0.961272i	$-0.411123\pi$
$11$	1.82813	0.551201	0.275601	+	0.961272i	$0.411123\pi$
$12$	0.171872	0.0496152
$13$	4.94814	1.37237	0.686184	−	0.727428i	$-0.259285\pi$
$13$	4.94814	1.37237	0.686184	+	0.727428i	$0.259285\pi$
$14$	0	0
$15$	−0.633936	−0.163682
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.97046	−0.700144
$19$	−5.94814	−1.36460	−0.682298	−	0.731074i	$-0.739020\pi$
$19$	−5.94814	−1.36460	−0.682298	+	0.731074i	$0.739020\pi$
$20$	−3.68841	−0.824754
$21$	0	0
$22$	1.82813	0.389758
$23$	7.23019	1.50760	0.753799	−	0.657105i	$-0.228219\pi$
$23$	7.23019	1.50760	0.753799	+	0.657105i	$0.228219\pi$
$24$	0.171872	0.0350833
$25$	8.60440	1.72088
$26$	4.94814	0.970410
$27$	−1.02616	−0.197484
$28$	0	0
$29$	10.3545	1.92278	0.961392	−	0.275183i	$-0.0887384\pi$
$29$	10.3545	1.92278	0.961392	+	0.275183i	$0.0887384\pi$
$30$	−0.633936	−0.115740
$31$	1.02232	0.183614	0.0918070	−	0.995777i	$-0.470736\pi$
$31$	1.02232	0.183614	0.0918070	+	0.995777i	$0.470736\pi$
$32$	1.00000	0.176777
$33$	0.314204	0.0546960
$34$	1.00000	0.171499
$35$	0	0
$36$	−2.97046	−0.495077
$37$	5.68841	0.935169	0.467585	−	0.883948i	$-0.345124\pi$
$37$	5.68841	0.935169	0.467585	+	0.883948i	$0.345124\pi$
$38$	−5.94814	−0.964916
$39$	0.850448	0.136181
$40$	−3.68841	−0.583189
$41$	−2.97768	−0.465036	−0.232518	−	0.972592i	$-0.574696\pi$
$41$	−2.97768	−0.465036	−0.232518	+	0.972592i	$0.574696\pi$
$42$	0	0
$43$	−2.06262	−0.314547	−0.157274	−	0.987555i	$-0.550270\pi$
$43$	−2.06262	−0.314547	−0.157274	+	0.987555i	$0.550270\pi$
$44$	1.82813	0.275601
$45$	10.9563	1.63327
$46$	7.23019	1.06603
$47$	8.01076	1.16849	0.584245	−	0.811577i	$-0.301391\pi$
$47$	8.01076	1.16849	0.584245	+	0.811577i	$0.301391\pi$
$48$	0.171872	0.0248076
$49$	0	0
$50$	8.60440	1.21685
$51$	0.171872	0.0240669
$52$	4.94814	0.686184
$53$	−8.95890	−1.23060	−0.615300	−	0.788293i	$-0.710965\pi$
$53$	−8.95890	−1.23060	−0.615300	+	0.788293i	$0.710965\pi$
$54$	−1.02616	−0.139642
$55$	−6.74289	−0.909211
$56$	0	0
$57$	−1.02232	−0.135410
$58$	10.3545	1.35961
$59$	12.0035	1.56273	0.781364	−	0.624075i	$-0.214524\pi$
$59$	12.0035	1.56273	0.781364	+	0.624075i	$0.214524\pi$
$60$	−0.633936	−0.0818408
$61$	−3.70981	−0.474992	−0.237496	−	0.971388i	$-0.576327\pi$
$61$	−3.70981	−0.474992	−0.237496	+	0.971388i	$0.576327\pi$
$62$	1.02232	0.129835
$63$	0	0
$64$	1.00000	0.125000
$65$	−18.2508	−2.26373
$66$	0.314204	0.0386759
$67$	5.42869	0.663220	0.331610	−	0.943417i	$-0.392408\pi$
$67$	5.42869	0.663220	0.331610	+	0.943417i	$0.392408\pi$
$68$	1.00000	0.121268
$69$	1.24267	0.149600
$70$	0	0
$71$	−5.40206	−0.641106	−0.320553	−	0.947231i	$-0.603869\pi$
$71$	−5.40206	−0.641106	−0.320553	+	0.947231i	$0.603869\pi$
$72$	−2.97046	−0.350072
$73$	6.97768	0.816676	0.408338	−	0.912831i	$-0.366109\pi$
$73$	6.97768	0.816676	0.408338	+	0.912831i	$0.366109\pi$
$74$	5.68841	0.661265
$75$	1.47886	0.170764
$76$	−5.94814	−0.682298
$77$	0	0
$78$	0.850448	0.0962942
$79$	5.20496	0.585603	0.292802	−	0.956173i	$-0.405412\pi$
$79$	5.20496	0.585603	0.292802	+	0.956173i	$0.405412\pi$
$80$	−3.68841	−0.412377
$81$	8.73501	0.970557
$82$	−2.97768	−0.328830
$83$	15.2731	1.67644	0.838221	−	0.545331i	$-0.183596\pi$
$83$	15.2731	1.67644	0.838221	+	0.545331i	$0.183596\pi$
$84$	0	0
$85$	−3.68841	−0.400065
$86$	−2.06262	−0.222418
$87$	1.77965	0.190799
$88$	1.82813	0.194879
$89$	−2.93016	−0.310596	−0.155298	−	0.987868i	$-0.549634\pi$
$89$	−2.93016	−0.310596	−0.155298	+	0.987868i	$0.549634\pi$
$90$	10.9563	1.15489
$91$	0	0
$92$	7.23019	0.753799
$93$	0.175708	0.0182201
$94$	8.01076	0.826247
$95$	21.9392	2.25091
$96$	0.171872	0.0175416
$97$	−6.91860	−0.702477	−0.351239	−	0.936286i	$-0.614239\pi$
$97$	−6.91860	−0.702477	−0.351239	+	0.936286i	$0.614239\pi$
$98$	0	0
$99$	−5.43038	−0.545774
$100$	8.60440	0.860440
$101$	−7.33219	−0.729580	−0.364790	−	0.931090i	$-0.618859\pi$
$101$	−7.33219	−0.729580	−0.364790	+	0.931090i	$0.618859\pi$
$102$	0.171872	0.0170179
$103$	6.57486	0.647840	0.323920	−	0.946085i	$-0.394999\pi$
$103$	6.57486	0.647840	0.323920	+	0.946085i	$0.394999\pi$
$104$	4.94814	0.485205
$105$	0	0
$106$	−8.95890	−0.870166
$107$	1.26404	0.122199	0.0610995	−	0.998132i	$-0.480539\pi$
$107$	1.26404	0.122199	0.0610995	+	0.998132i	$0.480539\pi$
$108$	−1.02616	−0.0987419
$109$	−6.04292	−0.578807	−0.289403	−	0.957207i	$-0.593457\pi$
$109$	−6.04292	−0.578807	−0.289403	+	0.957207i	$0.593457\pi$
$110$	−6.74289	−0.642909
$111$	0.977680	0.0927973
$112$	0	0
$113$	7.37683	0.693954	0.346977	−	0.937874i	$-0.387208\pi$
$113$	7.37683	0.693954	0.346977	+	0.937874i	$0.387208\pi$
$114$	−1.02232	−0.0957490
$115$	−26.6679	−2.48680
$116$	10.3545	0.961392
$117$	−14.6983	−1.35885
$118$	12.0035	1.10502
$119$	0	0
$120$	−0.633936	−0.0578702
$121$	−7.65795	−0.696177
$122$	−3.70981	−0.335870
$123$	−0.511780	−0.0461457
$124$	1.02232	0.0918070
$125$	−13.2945	−1.18910
$126$	0	0
$127$	−19.3876	−1.72037	−0.860185	−	0.509982i	$-0.829652\pi$
$127$	−19.3876	−1.72037	−0.860185	+	0.509982i	$0.829652\pi$
$128$	1.00000	0.0883883
$129$	−0.354508	−0.0312126
$130$	−18.2508	−1.60070
$131$	−5.25158	−0.458833	−0.229416	−	0.973328i	$-0.573682\pi$
$131$	−5.25158	−0.458833	−0.229416	+	0.973328i	$0.573682\pi$
$132$	0.314204	0.0273480
$133$	0	0
$134$	5.42869	0.468967
$135$	3.78489	0.325751
$136$	1.00000	0.0857493
$137$	−9.34559	−0.798448	−0.399224	−	0.916853i	$-0.630720\pi$
$137$	−9.34559	−0.798448	−0.399224	+	0.916853i	$0.630720\pi$
$138$	1.24267	0.105783
$139$	2.28636	0.193926	0.0969631	−	0.995288i	$-0.469087\pi$
$139$	2.28636	0.193926	0.0969631	+	0.995288i	$0.469087\pi$
$140$	0	0
$141$	1.37683	0.115950
$142$	−5.40206	−0.453331
$143$	9.04583	0.756451
$144$	−2.97046	−0.247538
$145$	−38.1917	−3.17165
$146$	6.97768	0.577477
$147$	0	0
$148$	5.68841	0.467585
$149$	−4.04030	−0.330995	−0.165497	−	0.986210i	$-0.552923\pi$
$149$	−4.04030	−0.330995	−0.165497	+	0.986210i	$0.552923\pi$
$150$	1.47886	0.120748
$151$	−5.24267	−0.426642	−0.213321	−	0.976982i	$-0.568428\pi$
$151$	−5.24267	−0.426642	−0.213321	+	0.976982i	$0.568428\pi$
$152$	−5.94814	−0.482458
$153$	−2.97046	−0.240147
$154$	0	0
$155$	−3.77074	−0.302873
$156$	0.850448	0.0680903
$157$	2.60440	0.207853	0.103927	−	0.994585i	$-0.466859\pi$
$157$	2.60440	0.207853	0.103927	+	0.994585i	$0.466859\pi$
$158$	5.20496	0.414084
$159$	−1.53979	−0.122113
$160$	−3.68841	−0.291595
$161$	0	0
$162$	8.73501	0.686287
$163$	−6.97768	−0.546534	−0.273267	−	0.961938i	$-0.588104\pi$
$163$	−6.97768	−0.546534	−0.273267	+	0.961938i	$0.588104\pi$
$164$	−2.97768	−0.232518
$165$	−1.15892	−0.0902215
$166$	15.2731	1.18542
$167$	10.7681	0.833262	0.416631	−	0.909076i	$-0.363211\pi$
$167$	10.7681	0.833262	0.416631	+	0.909076i	$0.363211\pi$
$168$	0	0
$169$	11.4841	0.883392
$170$	−3.68841	−0.282888
$171$	17.6687	1.35116
$172$	−2.06262	−0.157274
$173$	19.8586	1.50982	0.754911	−	0.655828i	$-0.227680\pi$
$173$	19.8586	1.50982	0.754911	+	0.655828i	$0.227680\pi$
$174$	1.77965	0.134915
$175$	0	0
$176$	1.82813	0.137800
$177$	2.06308	0.155070
$178$	−2.93016	−0.219625
$179$	−14.4171	−1.07759	−0.538793	−	0.842438i	$-0.681120\pi$
$179$	−14.4171	−1.07759	−0.538793	+	0.842438i	$0.681120\pi$
$180$	10.9563	0.816633
$181$	12.5427	0.932291	0.466146	−	0.884708i	$-0.345642\pi$
$181$	12.5427	0.932291	0.466146	+	0.884708i	$0.345642\pi$
$182$	0	0
$183$	−0.637613	−0.0471337
$184$	7.23019	0.533016
$185$	−20.9812	−1.54257
$186$	0.175708	0.0128836
$187$	1.82813	0.133686
$188$	8.01076	0.584245
$189$	0	0
$190$	21.9392	1.59164
$191$	−16.4188	−1.18802	−0.594012	−	0.804456i	$-0.702457\pi$
$191$	−16.4188	−1.18802	−0.594012	+	0.804456i	$0.702457\pi$
$192$	0.171872	0.0124038
$193$	14.6284	1.05298	0.526488	−	0.850183i	$-0.323509\pi$
$193$	14.6284	1.05298	0.526488	+	0.850183i	$0.323509\pi$
$194$	−6.91860	−0.496727
$195$	−3.13680	−0.224631
$196$	0	0
$197$	15.7527	1.12234	0.561168	−	0.827702i	$-0.310352\pi$
$197$	15.7527	1.12234	0.561168	+	0.827702i	$0.310352\pi$
$198$	−5.43038	−0.385920
$199$	−9.90493	−0.702142	−0.351071	−	0.936349i	$-0.614182\pi$
$199$	−9.90493	−0.702142	−0.351071	+	0.936349i	$0.614182\pi$
$200$	8.60440	0.608423
$201$	0.933040	0.0658116
$202$	−7.33219	−0.515891
$203$	0	0
$204$	0.171872	0.0120335
$205$	10.9829	0.767080
$206$	6.57486	0.458092
$207$	−21.4770	−1.49275
$208$	4.94814	0.343092
$209$	−10.8740	−0.752168
$210$	0	0
$211$	−3.29622	−0.226921	−0.113461	−	0.993542i	$-0.536194\pi$
$211$	−3.29622	−0.226921	−0.113461	+	0.993542i	$0.536194\pi$
$212$	−8.95890	−0.615300
$213$	−0.928464	−0.0636173
$214$	1.26404	0.0864077
$215$	7.60781	0.518848
$216$	−1.02616	−0.0698211
$217$	0	0
$218$	−6.04292	−0.409278
$219$	1.19927	0.0810391
$220$	−6.74289	−0.454606
$221$	4.94814	0.332848
$222$	0.977680	0.0656176
$223$	−19.3340	−1.29470	−0.647351	−	0.762192i	$-0.724123\pi$
$223$	−19.3340	−1.29470	−0.647351	+	0.762192i	$0.724123\pi$
$224$	0	0
$225$	−25.5590	−1.70393
$226$	7.37683	0.490699
$227$	25.1120	1.66674	0.833371	−	0.552714i	$-0.186408\pi$
$227$	25.1120	1.66674	0.833371	+	0.552714i	$0.186408\pi$
$228$	−1.02232	−0.0677048
$229$	−19.1029	−1.26236	−0.631178	−	0.775638i	$-0.717428\pi$
$229$	−19.1029	−1.26236	−0.631178	+	0.775638i	$0.717428\pi$
$230$	−26.6679	−1.75843
$231$	0	0
$232$	10.3545	0.679807
$233$	27.5664	1.80593	0.902967	−	0.429710i	$-0.141384\pi$
$233$	27.5664	1.80593	0.902967	+	0.429710i	$0.141384\pi$
$234$	−14.6983	−0.960855
$235$	−29.5470	−1.92743
$236$	12.0035	0.781364
$237$	0.894587	0.0581097
$238$	0	0
$239$	9.49713	0.614318	0.307159	−	0.951658i	$-0.400622\pi$
$239$	9.49713	0.614318	0.307159	+	0.951658i	$0.400622\pi$
$240$	−0.633936	−0.0409204
$241$	−18.0858	−1.16501	−0.582506	−	0.812827i	$-0.697928\pi$
$241$	−18.0858	−1.16501	−0.582506	+	0.812827i	$0.697928\pi$
$242$	−7.65795	−0.492272
$243$	4.57977	0.293793
$244$	−3.70981	−0.237496
$245$	0	0
$246$	−0.511780	−0.0326299
$247$	−29.4322	−1.87273
$248$	1.02232	0.0649174
$249$	2.62502	0.166354
$250$	−13.2945	−0.840818
$251$	4.53331	0.286140	0.143070	−	0.989713i	$-0.454303\pi$
$251$	4.53331	0.286140	0.143070	+	0.989713i	$0.454303\pi$
$252$	0	0
$253$	13.2177	0.830990
$254$	−19.3876	−1.21649
$255$	−0.633936	−0.0396986
$256$	1.00000	0.0625000
$257$	7.96877	0.497078	0.248539	−	0.968622i	$-0.420050\pi$
$257$	7.96877	0.497078	0.248539	+	0.968622i	$0.420050\pi$
$258$	−0.354508	−0.0220707
$259$	0	0
$260$	−18.2508	−1.13187
$261$	−30.7576	−1.90385
$262$	−5.25158	−0.324444
$263$	−4.50869	−0.278018	−0.139009	−	0.990291i	$-0.544392\pi$
$263$	−4.50869	−0.278018	−0.139009	+	0.990291i	$0.544392\pi$
$264$	0.314204	0.0193379
$265$	33.0441	2.02989
$266$	0	0
$267$	−0.503612	−0.0308206
$268$	5.42869	0.331610
$269$	0.895060	0.0545728	0.0272864	−	0.999628i	$-0.491313\pi$
$269$	0.895060	0.0545728	0.0272864	+	0.999628i	$0.491313\pi$
$270$	3.78489	0.230341
$271$	−2.49978	−0.151851	−0.0759253	−	0.997114i	$-0.524191\pi$
$271$	−2.49978	−0.151851	−0.0759253	+	0.997114i	$0.524191\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	−9.34559	−0.564588
$275$	15.7299	0.948551
$276$	1.24267	0.0747998
$277$	−0.458227	−0.0275322	−0.0137661	−	0.999905i	$-0.504382\pi$
$277$	−0.458227	−0.0275322	−0.0137661	+	0.999905i	$0.504382\pi$
$278$	2.28636	0.137126
$279$	−3.03676	−0.181806
$280$	0	0
$281$	−10.5633	−0.630154	−0.315077	−	0.949066i	$-0.602030\pi$
$281$	−10.5633	−0.630154	−0.315077	+	0.949066i	$0.602030\pi$
$282$	1.37683	0.0819889
$283$	16.1826	0.961958	0.480979	−	0.876732i	$-0.340281\pi$
$283$	16.1826	0.961958	0.480979	+	0.876732i	$0.340281\pi$
$284$	−5.40206	−0.320553
$285$	3.77074	0.223359
$286$	9.04583	0.534891
$287$	0	0
$288$	−2.97046	−0.175036
$289$	1.00000	0.0588235
$290$	−38.1917	−2.24269
$291$	−1.18911	−0.0697072
$292$	6.97768	0.408338
$293$	−11.1685	−0.652470	−0.326235	−	0.945289i	$-0.605780\pi$
$293$	−11.1685	−0.652470	−0.326235	+	0.945289i	$0.605780\pi$
$294$	0	0
$295$	−44.2740	−2.57773
$296$	5.68841	0.330632
$297$	−1.87594	−0.108853
$298$	−4.04030	−0.234048
$299$	35.7760	2.06898
$300$	1.47886	0.0853818
$301$	0	0
$302$	−5.24267	−0.301682
$303$	−1.26020	−0.0723966
$304$	−5.94814	−0.341149
$305$	13.6833	0.783504
$306$	−2.97046	−0.169810
$307$	−4.86674	−0.277760	−0.138880	−	0.990309i	$-0.544350\pi$
$307$	−4.86674	−0.277760	−0.138880	+	0.990309i	$0.544350\pi$
$308$	0	0
$309$	1.13003	0.0642854
$310$	−3.77074	−0.214164
$311$	−12.6001	−0.714485	−0.357243	−	0.934012i	$-0.616283\pi$
$311$	−12.6001	−0.714485	−0.357243	+	0.934012i	$0.616283\pi$
$312$	0.850448	0.0481471
$313$	14.5410	0.821905	0.410952	−	0.911657i	$-0.365196\pi$
$313$	14.5410	0.821905	0.410952	+	0.911657i	$0.365196\pi$
$314$	2.60440	0.146975
$315$	0	0
$316$	5.20496	0.292802
$317$	29.3160	1.64655	0.823276	−	0.567641i	$-0.192144\pi$
$317$	29.3160	1.64655	0.823276	+	0.567641i	$0.192144\pi$
$318$	−1.53979	−0.0863469
$319$	18.9294	1.05984
$320$	−3.68841	−0.206189
$321$	0.217253	0.0121259
$322$	0	0
$323$	−5.94814	−0.330963
$324$	8.73501	0.485278
$325$	42.5758	2.36168
$326$	−6.97768	−0.386458
$327$	−1.03861	−0.0574353
$328$	−2.97768	−0.164415
$329$	0	0
$330$	−1.15892	−0.0637962
$331$	−16.5230	−0.908186	−0.454093	−	0.890954i	$-0.650037\pi$
$331$	−16.5230	−0.908186	−0.454093	+	0.890954i	$0.650037\pi$
$332$	15.2731	0.838221
$333$	−16.8972	−0.925961
$334$	10.7681	0.589205
$335$	−20.0232	−1.09399
$336$	0	0
$337$	−9.28940	−0.506026	−0.253013	−	0.967463i	$-0.581422\pi$
$337$	−9.28940	−0.506026	−0.253013	+	0.967463i	$0.581422\pi$
$338$	11.4841	0.624652
$339$	1.26787	0.0688613
$340$	−3.68841	−0.200032
$341$	1.86893	0.101208
$342$	17.6687	0.955415
$343$	0	0
$344$	−2.06262	−0.111209
$345$	−4.58347	−0.246766
$346$	19.8586	1.06760
$347$	−27.2928	−1.46515	−0.732577	−	0.680684i	$-0.761682\pi$
$347$	−27.2928	−1.46515	−0.732577	+	0.680684i	$0.761682\pi$
$348$	1.77965	0.0953994
$349$	0.0806064	0.00431476	0.00215738	−	0.999998i	$-0.499313\pi$
$349$	0.0806064	0.00431476	0.00215738	+	0.999998i	$0.499313\pi$
$350$	0	0
$351$	−5.07756	−0.271020
$352$	1.82813	0.0974395
$353$	25.1899	1.34072	0.670360	−	0.742036i	$-0.266140\pi$
$353$	25.1899	1.34072	0.670360	+	0.742036i	$0.266140\pi$
$354$	2.06308	0.109651
$355$	19.9250	1.05751
$356$	−2.93016	−0.155298
$357$	0	0
$358$	−14.4171	−0.761969
$359$	25.8516	1.36440	0.682199	−	0.731167i	$-0.261024\pi$
$359$	25.8516	1.36440	0.682199	+	0.731167i	$0.261024\pi$
$360$	10.9563	0.577447
$361$	16.3804	0.862125
$362$	12.5427	0.659230
$363$	−1.31619	−0.0690820
$364$	0	0
$365$	−25.7366	−1.34711
$366$	−0.637613	−0.0333286
$367$	−11.2623	−0.587888	−0.293944	−	0.955823i	$-0.594968\pi$
$367$	−11.2623	−0.587888	−0.293944	+	0.955823i	$0.594968\pi$
$368$	7.23019	0.376900
$369$	8.84508	0.460456
$370$	−20.9812	−1.09076
$371$	0	0
$372$	0.175708	0.00911005
$373$	−3.92397	−0.203175	−0.101588	−	0.994827i	$-0.532392\pi$
$373$	−3.92397	−0.203175	−0.101588	+	0.994827i	$0.532392\pi$
$374$	1.82813	0.0945302
$375$	−2.28496	−0.117995
$376$	8.01076	0.413124
$377$	51.2356	2.63877
$378$	0	0
$379$	22.8470	1.17357	0.586786	−	0.809742i	$-0.300393\pi$
$379$	22.8470	1.17357	0.586786	+	0.809742i	$0.300393\pi$
$380$	21.9392	1.12546
$381$	−3.33219	−0.170713
$382$	−16.4188	−0.840060
$383$	−0.812735	−0.0415288	−0.0207644	−	0.999784i	$-0.506610\pi$
$383$	−0.812735	−0.0415288	−0.0207644	+	0.999784i	$0.506610\pi$
$384$	0.171872	0.00877082
$385$	0	0
$386$	14.6284	0.744566
$387$	6.12694	0.311450
$388$	−6.91860	−0.351239
$389$	0.199721	0.0101263	0.00506314	−	0.999987i	$-0.498388\pi$
$389$	0.199721	0.0101263	0.00506314	+	0.999987i	$0.498388\pi$
$390$	−3.13680	−0.158838
$391$	7.23019	0.365646
$392$	0	0
$393$	−0.902601	−0.0455302
$394$	15.7527	0.793611
$395$	−19.1980	−0.965958
$396$	−5.43038	−0.272887
$397$	−3.99828	−0.200668	−0.100334	−	0.994954i	$-0.531991\pi$
$397$	−3.99828	−0.200668	−0.100334	+	0.994954i	$0.531991\pi$
$398$	−9.90493	−0.496489
$399$	0	0
$400$	8.60440	0.430220
$401$	13.9409	0.696176	0.348088	−	0.937462i	$-0.386831\pi$
$401$	13.9409	0.696176	0.348088	+	0.937462i	$0.386831\pi$
$402$	0.933040	0.0465358
$403$	5.05858	0.251986
$404$	−7.33219	−0.364790
$405$	−32.2183	−1.60094
$406$	0	0
$407$	10.3991	0.515467
$408$	0.171872	0.00850894
$409$	23.1913	1.14673	0.573367	−	0.819299i	$-0.305637\pi$
$409$	23.1913	1.14673	0.573367	+	0.819299i	$0.305637\pi$
$410$	10.9829	0.542408
$411$	−1.60625	−0.0792304
$412$	6.57486	0.323920
$413$	0	0
$414$	−21.4770	−1.05554
$415$	−56.3335	−2.76530
$416$	4.94814	0.242603
$417$	0.392961	0.0192434
$418$	−10.8740	−0.531863
$419$	−9.20496	−0.449691	−0.224846	−	0.974394i	$-0.572188\pi$
$419$	−9.20496	−0.449691	−0.224846	+	0.974394i	$0.572188\pi$
$420$	0	0
$421$	−34.3151	−1.67242	−0.836208	−	0.548413i	$-0.815232\pi$
$421$	−34.3151	−1.67242	−0.836208	+	0.548413i	$0.815232\pi$
$422$	−3.29622	−0.160458
$423$	−23.7957	−1.15698
$424$	−8.95890	−0.435083
$425$	8.60440	0.417374
$426$	−0.928464	−0.0449842
$427$	0	0
$428$	1.26404	0.0610995
$429$	1.55473	0.0750629
$430$	7.60781	0.366881
$431$	−20.8540	−1.00450	−0.502250	−	0.864722i	$-0.667494\pi$
$431$	−20.8540	−1.00450	−0.502250	+	0.864722i	$0.667494\pi$
$432$	−1.02616	−0.0493710
$433$	−30.8132	−1.48079	−0.740394	−	0.672174i	$-0.765361\pi$
$433$	−30.8132	−1.48079	−0.740394	+	0.672174i	$0.765361\pi$
$434$	0	0
$435$	−6.56409	−0.314724
$436$	−6.04292	−0.289403
$437$	−43.0062	−2.05726
$438$	1.19927	0.0573033
$439$	−10.0391	−0.479139	−0.239570	−	0.970879i	$-0.577006\pi$
$439$	−10.0391	−0.479139	−0.239570	+	0.970879i	$0.577006\pi$
$440$	−6.74289	−0.321455
$441$	0	0
$442$	4.94814	0.235359
$443$	−9.56499	−0.454446	−0.227223	−	0.973843i	$-0.572965\pi$
$443$	−9.56499	−0.454446	−0.227223	+	0.973843i	$0.572965\pi$
$444$	0.977680	0.0463986
$445$	10.8076	0.512331
$446$	−19.3340	−0.915493
$447$	−0.694416	−0.0328447
$448$	0	0
$449$	14.4582	0.682326	0.341163	−	0.940004i	$-0.389179\pi$
$449$	14.4582	0.682326	0.341163	+	0.940004i	$0.389179\pi$
$450$	−25.5590	−1.20486
$451$	−5.44358	−0.256328
$452$	7.37683	0.346977
$453$	−0.901069	−0.0423359
$454$	25.1120	1.17856
$455$	0	0
$456$	−1.02232	−0.0478745
$457$	−17.3979	−0.813840	−0.406920	−	0.913464i	$-0.633397\pi$
$457$	−17.3979	−0.813840	−0.406920	+	0.913464i	$0.633397\pi$
$458$	−19.1029	−0.892621
$459$	−1.02616	−0.0478969
$460$	−26.6679	−1.24340
$461$	−4.55976	−0.212369	−0.106185	−	0.994346i	$-0.533863\pi$
$461$	−4.55976	−0.212369	−0.106185	+	0.994346i	$0.533863\pi$
$462$	0	0
$463$	38.3920	1.78423	0.892115	−	0.451809i	$-0.149221\pi$
$463$	38.3920	1.78423	0.892115	+	0.451809i	$0.149221\pi$
$464$	10.3545	0.480696
$465$	−0.648085	−0.0300542
$466$	27.5664	1.27699
$467$	5.26065	0.243434	0.121717	−	0.992565i	$-0.461160\pi$
$467$	5.26065	0.243434	0.121717	+	0.992565i	$0.461160\pi$
$468$	−14.6983	−0.679427
$469$	0	0
$470$	−29.5470	−1.36290
$471$	0.447623	0.0206254
$472$	12.0035	0.552508
$473$	−3.77074	−0.173379
$474$	0.894587	0.0410897
$475$	−51.1802	−2.34831
$476$	0	0
$477$	26.6121	1.21848
$478$	9.49713	0.434389
$479$	−7.04371	−0.321836	−0.160918	−	0.986968i	$-0.551445\pi$
$479$	−7.04371	−0.321836	−0.160918	+	0.986968i	$0.551445\pi$
$480$	−0.633936	−0.0289351
$481$	28.1471	1.28340
$482$	−18.0858	−0.823788
$483$	0	0
$484$	−7.65795	−0.348089
$485$	25.5187	1.15874
$486$	4.57977	0.207743
$487$	−16.6699	−0.755387	−0.377693	−	0.925931i	$-0.623283\pi$
$487$	−16.6699	−0.755387	−0.377693	+	0.925931i	$0.623283\pi$
$488$	−3.70981	−0.167935
$489$	−1.19927	−0.0542328
$490$	0	0
$491$	14.7249	0.664526	0.332263	−	0.943187i	$-0.392188\pi$
$491$	14.7249	0.664526	0.332263	+	0.943187i	$0.392188\pi$
$492$	−0.511780	−0.0230728
$493$	10.3545	0.466344
$494$	−29.4322	−1.32422
$495$	20.0295	0.900259
$496$	1.02232	0.0459035
$497$	0	0
$498$	2.62502	0.117630
$499$	15.0874	0.675404	0.337702	−	0.941253i	$-0.390350\pi$
$499$	15.0874	0.675404	0.337702	+	0.941253i	$0.390350\pi$
$500$	−13.2945	−0.594548
$501$	1.85074	0.0826850
$502$	4.53331	0.202331
$503$	2.30775	0.102897	0.0514487	−	0.998676i	$-0.483616\pi$
$503$	2.30775	0.102897	0.0514487	+	0.998676i	$0.483616\pi$
$504$	0	0
$505$	27.0441	1.20345
$506$	13.2177	0.587599
$507$	1.97380	0.0876593
$508$	−19.3876	−0.860185
$509$	17.6421	0.781970	0.390985	−	0.920397i	$-0.372134\pi$
$509$	17.6421	0.781970	0.390985	+	0.920397i	$0.372134\pi$
$510$	−0.633936	−0.0280711
$511$	0	0
$512$	1.00000	0.0441942
$513$	6.10372	0.269486
$514$	7.96877	0.351487
$515$	−24.2508	−1.06862
$516$	−0.354508	−0.0156063
$517$	14.6447	0.644073
$518$	0	0
$519$	3.41314	0.149820
$520$	−18.2508	−0.800350
$521$	−2.03597	−0.0891973	−0.0445987	−	0.999005i	$-0.514201\pi$
$521$	−2.03597	−0.0891973	−0.0445987	+	0.999005i	$0.514201\pi$
$522$	−30.7576	−1.34623
$523$	−9.39650	−0.410880	−0.205440	−	0.978670i	$-0.565863\pi$
$523$	−9.39650	−0.410880	−0.205440	+	0.978670i	$0.565863\pi$
$524$	−5.25158	−0.229416
$525$	0	0
$526$	−4.50869	−0.196588
$527$	1.02232	0.0445330
$528$	0.314204	0.0136740
$529$	29.2756	1.27285
$530$	33.0441	1.43535
$531$	−35.6560	−1.54734
$532$	0	0
$533$	−14.7340	−0.638199
$534$	−0.503612	−0.0217934
$535$	−4.66229	−0.201568
$536$	5.42869	0.234484
$537$	−2.47790	−0.106929
$538$	0.895060	0.0385888
$539$	0	0
$540$	3.78489	0.162876
$541$	−1.67569	−0.0720436	−0.0360218	−	0.999351i	$-0.511469\pi$
$541$	−1.67569	−0.0720436	−0.0360218	+	0.999351i	$0.511469\pi$
$542$	−2.49978	−0.107375
$543$	2.15574	0.0925117
$544$	1.00000	0.0428746
$545$	22.2888	0.954747
$546$	0	0
$547$	−9.67792	−0.413798	−0.206899	−	0.978362i	$-0.566337\pi$
$547$	−9.67792	−0.413798	−0.206899	+	0.978362i	$0.566337\pi$
$548$	−9.34559	−0.399224
$549$	11.0198	0.470315
$550$	15.7299	0.670727
$551$	−61.5901	−2.62382
$552$	1.24267	0.0528915
$553$	0	0
$554$	−0.458227	−0.0194682
$555$	−3.60609	−0.153070
$556$	2.28636	0.0969631
$557$	15.2024	0.644145	0.322072	−	0.946715i	$-0.395621\pi$
$557$	15.2024	0.644145	0.322072	+	0.946715i	$0.395621\pi$
$558$	−3.03676	−0.128556
$559$	−10.2061	−0.431674
$560$	0	0
$561$	0.314204	0.0132657
$562$	−10.5633	−0.445586
$563$	−35.2483	−1.48554	−0.742769	−	0.669547i	$-0.766488\pi$
$563$	−35.2483	−1.48554	−0.742769	+	0.669547i	$0.766488\pi$
$564$	1.37683	0.0579749
$565$	−27.2088	−1.14468
$566$	16.1826	0.680207
$567$	0	0
$568$	−5.40206	−0.226665
$569$	9.15360	0.383739	0.191869	−	0.981420i	$-0.438545\pi$
$569$	9.15360	0.383739	0.191869	+	0.981420i	$0.438545\pi$
$570$	3.77074	0.157939
$571$	−25.1691	−1.05329	−0.526647	−	0.850084i	$-0.676551\pi$
$571$	−25.1691	−1.05329	−0.526647	+	0.850084i	$0.676551\pi$
$572$	9.04583	0.378225
$573$	−2.82194	−0.117888
$574$	0	0
$575$	62.2114	2.59439
$576$	−2.97046	−0.123769
$577$	−24.5346	−1.02139	−0.510693	−	0.859763i	$-0.670611\pi$
$577$	−24.5346	−1.02139	−0.510693	+	0.859763i	$0.670611\pi$
$578$	1.00000	0.0415945
$579$	2.51422	0.104487
$580$	−38.1917	−1.58582
$581$	0	0
$582$	−1.18911	−0.0492904
$583$	−16.3780	−0.678308
$584$	6.97768	0.288738
$585$	54.2132	2.24144
$586$	−11.1685	−0.461366
$587$	35.2231	1.45381	0.726906	−	0.686737i	$-0.240957\pi$
$587$	35.2231	1.45381	0.726906	+	0.686737i	$0.240957\pi$
$588$	0	0
$589$	−6.08090	−0.250559
$590$	−44.2740	−1.82273
$591$	2.70746	0.111370
$592$	5.68841	0.233792
$593$	−30.6871	−1.26017	−0.630085	−	0.776526i	$-0.716980\pi$
$593$	−30.6871	−1.26017	−0.630085	+	0.776526i	$0.716980\pi$
$594$	−1.87594	−0.0769709
$595$	0	0
$596$	−4.04030	−0.165497
$597$	−1.70238	−0.0696738
$598$	35.7760	1.46299
$599$	−28.5878	−1.16806	−0.584032	−	0.811731i	$-0.698526\pi$
$599$	−28.5878	−1.16806	−0.584032	+	0.811731i	$0.698526\pi$
$600$	1.47886	0.0603741
$601$	43.5436	1.77618	0.888090	−	0.459670i	$-0.152032\pi$
$601$	43.5436	1.77618	0.888090	+	0.459670i	$0.152032\pi$
$602$	0	0
$603$	−16.1257	−0.656689
$604$	−5.24267	−0.213321
$605$	28.2457	1.14835
$606$	−1.26020	−0.0511921
$607$	−15.4448	−0.626887	−0.313444	−	0.949607i	$-0.601483\pi$
$607$	−15.4448	−0.626887	−0.313444	+	0.949607i	$0.601483\pi$
$608$	−5.94814	−0.241229
$609$	0	0
$610$	13.6833	0.554021
$611$	39.6384	1.60360
$612$	−2.97046	−0.120074
$613$	−8.33079	−0.336477	−0.168239	−	0.985746i	$-0.553808\pi$
$613$	−8.33079	−0.336477	−0.168239	+	0.985746i	$0.553808\pi$
$614$	−4.86674	−0.196406
$615$	1.88766	0.0761177
$616$	0	0
$617$	25.8787	1.04184	0.520920	−	0.853606i	$-0.325589\pi$
$617$	25.8787	1.04184	0.520920	+	0.853606i	$0.325589\pi$
$618$	1.13003	0.0454567
$619$	−0.755641	−0.0303718	−0.0151859	−	0.999885i	$-0.504834\pi$
$619$	−0.755641	−0.0303718	−0.0151859	+	0.999885i	$0.504834\pi$
$620$	−3.77074	−0.151437
$621$	−7.41930	−0.297726
$622$	−12.6001	−0.505217
$623$	0	0
$624$	0.850448	0.0340452
$625$	6.01365	0.240546
$626$	14.5410	0.581174
$627$	−1.86893	−0.0746379
$628$	2.60440	0.103927
$629$	5.68841	0.226812
$630$	0	0
$631$	−43.5489	−1.73365	−0.866826	−	0.498610i	$-0.833844\pi$
$631$	−43.5489	−1.73365	−0.866826	+	0.498610i	$0.833844\pi$
$632$	5.20496	0.207042
$633$	−0.566529	−0.0225175
$634$	29.3160	1.16429
$635$	71.5095	2.83777
$636$	−1.53979	−0.0610565
$637$	0	0
$638$	18.9294	0.749421
$639$	16.0466	0.634794
$640$	−3.68841	−0.145797
$641$	−15.8372	−0.625532	−0.312766	−	0.949830i	$-0.601256\pi$
$641$	−15.8372	−0.625532	−0.312766	+	0.949830i	$0.601256\pi$
$642$	0.217253	0.00857427
$643$	32.6461	1.28744	0.643718	−	0.765263i	$-0.277391\pi$
$643$	32.6461	1.28744	0.643718	+	0.765263i	$0.277391\pi$
$644$	0	0
$645$	1.30757	0.0514855
$646$	−5.94814	−0.234026
$647$	−12.2933	−0.483299	−0.241649	−	0.970364i	$-0.577688\pi$
$647$	−12.2933	−0.483299	−0.241649	+	0.970364i	$0.577688\pi$
$648$	8.73501	0.343144
$649$	21.9440	0.861378
$650$	42.5758	1.66996
$651$	0	0
$652$	−6.97768	−0.273267
$653$	−32.5498	−1.27377	−0.636886	−	0.770958i	$-0.719778\pi$
$653$	−32.5498	−1.27377	−0.636886	+	0.770958i	$0.719778\pi$
$654$	−1.03861	−0.0406129
$655$	19.3700	0.756849
$656$	−2.97768	−0.116259
$657$	−20.7269	−0.808634
$658$	0	0
$659$	39.9358	1.55568	0.777839	−	0.628464i	$-0.216316\pi$
$659$	39.9358	1.55568	0.777839	+	0.628464i	$0.216316\pi$
$660$	−1.15892	−0.0451107
$661$	31.5685	1.22787	0.613937	−	0.789355i	$-0.289585\pi$
$661$	31.5685	1.22787	0.613937	+	0.789355i	$0.289585\pi$
$662$	−16.5230	−0.642184
$663$	0.850448	0.0330287
$664$	15.2731	0.592712
$665$	0	0
$666$	−16.8972	−0.654753
$667$	74.8650	2.89879
$668$	10.7681	0.416631
$669$	−3.32298	−0.128474
$670$	−20.0232	−0.773565
$671$	−6.78200	−0.261816
$672$	0	0
$673$	−21.9031	−0.844301	−0.422151	−	0.906526i	$-0.638725\pi$
$673$	−21.9031	−0.844301	−0.422151	+	0.906526i	$0.638725\pi$
$674$	−9.28940	−0.357814
$675$	−8.82945	−0.339846
$676$	11.4841	0.441696
$677$	−34.5878	−1.32932	−0.664658	−	0.747148i	$-0.731423\pi$
$677$	−34.5878	−1.32932	−0.664658	+	0.747148i	$0.731423\pi$
$678$	1.26787	0.0486923
$679$	0	0
$680$	−3.68841	−0.141444
$681$	4.31605	0.165392
$682$	1.86893	0.0715651
$683$	−15.6219	−0.597757	−0.298878	−	0.954291i	$-0.596612\pi$
$683$	−15.6219	−0.597757	−0.298878	+	0.954291i	$0.596612\pi$
$684$	17.6687	0.675580
$685$	34.4704	1.31705
$686$	0	0
$687$	−3.28326	−0.125264
$688$	−2.06262	−0.0786368
$689$	−44.3299	−1.68884
$690$	−4.58347	−0.174490
$691$	39.2140	1.49177	0.745886	−	0.666074i	$-0.232026\pi$
$691$	39.2140	1.49177	0.745886	+	0.666074i	$0.232026\pi$
$692$	19.8586	0.754911
$693$	0	0
$694$	−27.2928	−1.03602
$695$	−8.43302	−0.319883
$696$	1.77965	0.0674575
$697$	−2.97768	−0.112788
$698$	0.0806064	0.00305100
$699$	4.73790	0.179204
$700$	0	0
$701$	9.38669	0.354530	0.177265	−	0.984163i	$-0.443275\pi$
$701$	9.38669	0.354530	0.177265	+	0.984163i	$0.443275\pi$
$702$	−5.07756	−0.191640
$703$	−33.8355	−1.27613
$704$	1.82813	0.0689002
$705$	−5.07831	−0.191260
$706$	25.1899	0.948033
$707$	0	0
$708$	2.06308	0.0775351
$709$	33.0209	1.24013	0.620063	−	0.784552i	$-0.287107\pi$
$709$	33.0209	1.24013	0.620063	+	0.784552i	$0.287107\pi$
$710$	19.9250	0.747773
$711$	−15.4611	−0.579837
$712$	−2.93016	−0.109812
$713$	7.39156	0.276816
$714$	0	0
$715$	−33.3648	−1.24777
$716$	−14.4171	−0.538793
$717$	1.63229	0.0609591
$718$	25.8516	0.964775
$719$	7.93708	0.296003	0.148002	−	0.988987i	$-0.452716\pi$
$719$	7.93708	0.296003	0.148002	+	0.988987i	$0.452716\pi$
$720$	10.9563	0.408317
$721$	0	0
$722$	16.3804	0.609614
$723$	−3.10845	−0.115605
$724$	12.5427	0.466146
$725$	89.0943	3.30888
$726$	−1.31619	−0.0488483
$727$	2.87182	0.106510	0.0532549	−	0.998581i	$-0.483040\pi$
$727$	2.87182	0.106510	0.0532549	+	0.998581i	$0.483040\pi$
$728$	0	0
$729$	−25.4179	−0.941404
$730$	−25.7366	−0.952553
$731$	−2.06262	−0.0762889
$732$	−0.637613	−0.0235669
$733$	13.7785	0.508919	0.254460	−	0.967083i	$-0.418102\pi$
$733$	13.7785	0.508919	0.254460	+	0.967083i	$0.418102\pi$
$734$	−11.2623	−0.415700
$735$	0	0
$736$	7.23019	0.266508
$737$	9.92433	0.365568
$738$	8.84508	0.325592
$739$	10.2131	0.375696	0.187848	−	0.982198i	$-0.439849\pi$
$739$	10.2131	0.375696	0.187848	+	0.982198i	$0.439849\pi$
$740$	−20.9812	−0.771285
$741$	−5.05858	−0.185832
$742$	0	0
$743$	−7.70129	−0.282533	−0.141267	−	0.989972i	$-0.545117\pi$
$743$	−7.70129	−0.282533	−0.141267	+	0.989972i	$0.545117\pi$
$744$	0.175708	0.00644178
$745$	14.9023	0.545978
$746$	−3.92397	−0.143667
$747$	−45.3682	−1.65993
$748$	1.82813	0.0668430
$749$	0	0
$750$	−2.28496	−0.0834348
$751$	−1.97845	−0.0721945	−0.0360973	−	0.999348i	$-0.511493\pi$
$751$	−1.97845	−0.0721945	−0.0360973	+	0.999348i	$0.511493\pi$
$752$	8.01076	0.292122
$753$	0.779149	0.0283938
$754$	51.2356	1.86589
$755$	19.3371	0.703750
$756$	0	0
$757$	33.8969	1.23201	0.616003	−	0.787744i	$-0.288751\pi$
$757$	33.8969	1.23201	0.616003	+	0.787744i	$0.288751\pi$
$758$	22.8470	0.829841
$759$	2.27176	0.0824595
$760$	21.9392	0.795818
$761$	−23.0157	−0.834319	−0.417159	−	0.908833i	$-0.636974\pi$
$761$	−23.0157	−0.834319	−0.417159	+	0.908833i	$0.636974\pi$
$762$	−3.33219	−0.120712
$763$	0	0
$764$	−16.4188	−0.594012
$765$	10.9563	0.396125
$766$	−0.812735	−0.0293653
$767$	59.3952	2.14464
$768$	0.171872	0.00620190
$769$	−9.24002	−0.333204	−0.166602	−	0.986024i	$-0.553279\pi$
$769$	−9.24002	−0.333204	−0.166602	+	0.986024i	$0.553279\pi$
$770$	0	0
$771$	1.36961	0.0493253
$772$	14.6284	0.526488
$773$	−27.2864	−0.981422	−0.490711	−	0.871322i	$-0.663263\pi$
$773$	−27.2864	−0.981422	−0.490711	+	0.871322i	$0.663263\pi$
$774$	6.12694	0.220228
$775$	8.79644	0.315978
$776$	−6.91860	−0.248363
$777$	0	0
$778$	0.199721	0.00716036
$779$	17.7117	0.634586
$780$	−3.13680	−0.112316
$781$	−9.87565	−0.353379
$782$	7.23019	0.258551
$783$	−10.6253	−0.379719
$784$	0	0
$785$	−9.60609	−0.342856
$786$	−0.902601	−0.0321947
$787$	1.22632	0.0437137	0.0218568	−	0.999761i	$-0.493042\pi$
$787$	1.22632	0.0437137	0.0218568	+	0.999761i	$0.493042\pi$
$788$	15.7527	0.561168
$789$	−0.774918	−0.0275878
$790$	−19.1980	−0.683035
$791$	0	0
$792$	−5.43038	−0.192960
$793$	−18.3567	−0.651864
$794$	−3.99828	−0.141894
$795$	5.67937	0.201426
$796$	−9.90493	−0.351071
$797$	3.78457	0.134057	0.0670283	−	0.997751i	$-0.478648\pi$
$797$	3.78457	0.134057	0.0670283	+	0.997751i	$0.478648\pi$
$798$	0	0
$799$	8.01076	0.283400
$800$	8.60440	0.304211
$801$	8.70391	0.307538
$802$	13.9409	0.492271
$803$	12.7561	0.450153
$804$	0.933040	0.0329058
$805$	0	0
$806$	5.05858	0.178181
$807$	0.153836	0.00541528
$808$	−7.33219	−0.257945
$809$	−10.7275	−0.377157	−0.188579	−	0.982058i	$-0.560388\pi$
$809$	−10.7275	−0.377157	−0.188579	+	0.982058i	$0.560388\pi$
$810$	−32.2183	−1.13204
$811$	3.50621	0.123120	0.0615598	−	0.998103i	$-0.480393\pi$
$811$	3.50621	0.123120	0.0615598	+	0.998103i	$0.480393\pi$
$812$	0	0
$813$	−0.429642	−0.0150682
$814$	10.3991	0.364490
$815$	25.7366	0.901513
$816$	0.171872	0.00601673
$817$	12.2688	0.429230
$818$	23.1913	0.810863
$819$	0	0
$820$	10.9829	0.383540
$821$	44.4027	1.54966	0.774832	−	0.632167i	$-0.217835\pi$
$821$	44.4027	1.54966	0.774832	+	0.632167i	$0.217835\pi$
$822$	−1.60625	−0.0560243
$823$	2.17711	0.0758892	0.0379446	−	0.999280i	$-0.487919\pi$
$823$	2.17711	0.0758892	0.0379446	+	0.999280i	$0.487919\pi$
$824$	6.57486	0.229046
$825$	2.70354	0.0941251
$826$	0	0
$827$	−39.5327	−1.37469	−0.687343	−	0.726333i	$-0.741223\pi$
$827$	−39.5327	−1.37469	−0.687343	+	0.726333i	$0.741223\pi$
$828$	−21.4770	−0.746377
$829$	35.1516	1.22086	0.610432	−	0.792069i	$-0.290996\pi$
$829$	35.1516	1.22086	0.610432	+	0.792069i	$0.290996\pi$
$830$	−56.3335	−1.95537
$831$	−0.0787565	−0.00273203
$832$	4.94814	0.171546
$833$	0	0
$834$	0.392961	0.0136071
$835$	−39.7173	−1.37447
$836$	−10.8740	−0.376084
$837$	−1.04906	−0.0362608
$838$	−9.20496	−0.317980
$839$	−37.4610	−1.29330	−0.646648	−	0.762789i	$-0.723830\pi$
$839$	−37.4610	−1.29330	−0.646648	+	0.762789i	$0.723830\pi$
$840$	0	0
$841$	78.2158	2.69710
$842$	−34.3151	−1.18258
$843$	−1.81554	−0.0625304
$844$	−3.29622	−0.113461
$845$	−42.3581	−1.45716
$846$	−23.7957	−0.818111
$847$	0	0
$848$	−8.95890	−0.307650
$849$	2.78135	0.0954555
$850$	8.60440	0.295128
$851$	41.1283	1.40986
$852$	−0.928464	−0.0318086
$853$	32.1702	1.10149	0.550743	−	0.834675i	$-0.314344\pi$
$853$	32.1702	1.10149	0.550743	+	0.834675i	$0.314344\pi$
$854$	0	0
$855$	−65.1695	−2.22875
$856$	1.26404	0.0432038
$857$	−25.8837	−0.884170	−0.442085	−	0.896973i	$-0.645761\pi$
$857$	−25.8837	−0.884170	−0.442085	+	0.896973i	$0.645761\pi$
$858$	1.55473	0.0530775
$859$	−54.2882	−1.85229	−0.926145	−	0.377168i	$-0.876898\pi$
$859$	−54.2882	−1.85229	−0.926145	+	0.377168i	$0.876898\pi$
$860$	7.60781	0.259424
$861$	0	0
$862$	−20.8540	−0.710289
$863$	−44.6087	−1.51850	−0.759249	−	0.650801i	$-0.774433\pi$
$863$	−44.6087	−1.51850	−0.759249	+	0.650801i	$0.774433\pi$
$864$	−1.02616	−0.0349105
$865$	−73.2467	−2.49046
$866$	−30.8132	−1.04707
$867$	0.171872	0.00583709
$868$	0	0
$869$	9.51532	0.322785
$870$	−6.56409	−0.222544
$871$	26.8619	0.910181
$872$	−6.04292	−0.204639
$873$	20.5514	0.695560
$874$	−43.0062	−1.45471
$875$	0	0
$876$	1.19927	0.0405196
$877$	−47.6150	−1.60785	−0.803923	−	0.594734i	$-0.797257\pi$
$877$	−47.6150	−1.60785	−0.803923	+	0.594734i	$0.797257\pi$
$878$	−10.0391	−0.338803
$879$	−1.91955	−0.0647449
$880$	−6.74289	−0.227303
$881$	−4.68067	−0.157696	−0.0788478	−	0.996887i	$-0.525124\pi$
$881$	−4.68067	−0.157696	−0.0788478	+	0.996887i	$0.525124\pi$
$882$	0	0
$883$	51.7248	1.74068	0.870339	−	0.492453i	$-0.163900\pi$
$883$	51.7248	1.74068	0.870339	+	0.492453i	$0.163900\pi$
$884$	4.94814	0.166424
$885$	−7.60947	−0.255790
$886$	−9.56499	−0.321342
$887$	−32.9043	−1.10482	−0.552409	−	0.833574i	$-0.686291\pi$
$887$	−32.9043	−1.10482	−0.552409	+	0.833574i	$0.686291\pi$
$888$	0.977680	0.0328088
$889$	0	0
$890$	10.8076	0.362273
$891$	15.9687	0.534972
$892$	−19.3340	−0.647351
$893$	−47.6491	−1.59452
$894$	−0.694416	−0.0232247
$895$	53.1763	1.77749
$896$	0	0
$897$	6.14890	0.205306
$898$	14.4582	0.482477
$899$	10.5856	0.353050
$900$	−25.5590	−0.851967
$901$	−8.95890	−0.298464
$902$	−5.44358	−0.181251
$903$	0	0
$904$	7.37683	0.245350
$905$	−46.2627	−1.53782
$906$	−0.901069	−0.0299360
$907$	35.9769	1.19459	0.597296	−	0.802021i	$-0.296242\pi$
$907$	35.9769	1.19459	0.597296	+	0.802021i	$0.296242\pi$
$908$	25.1120	0.833371
$909$	21.7800	0.722396
$910$	0	0
$911$	5.89765	0.195398	0.0976990	−	0.995216i	$-0.468852\pi$
$911$	5.89765	0.195398	0.0976990	+	0.995216i	$0.468852\pi$
$912$	−1.02232	−0.0338524
$913$	27.9212	0.924057
$914$	−17.3979	−0.575471
$915$	2.35178	0.0777475
$916$	−19.1029	−0.631178
$917$	0	0
$918$	−1.02616	−0.0338682
$919$	−14.0982	−0.465056	−0.232528	−	0.972590i	$-0.574700\pi$
$919$	−14.0982	−0.465056	−0.232528	+	0.972590i	$0.574700\pi$
$920$	−26.6679	−0.879215
$921$	−0.836457	−0.0275622
$922$	−4.55976	−0.150168
$923$	−26.7301	−0.879833
$924$	0	0
$925$	48.9454	1.60931
$926$	38.3920	1.26164
$927$	−19.5303	−0.641461
$928$	10.3545	0.339903
$929$	39.1392	1.28412	0.642058	−	0.766656i	$-0.278081\pi$
$929$	39.1392	1.28412	0.642058	+	0.766656i	$0.278081\pi$
$930$	−0.648085	−0.0212515
$931$	0	0
$932$	27.5664	0.902967
$933$	−2.16560	−0.0708987
$934$	5.26065	0.172134
$935$	−6.74289	−0.220516
$936$	−14.6983	−0.480427
$937$	41.3628	1.35127	0.675633	−	0.737239i	$-0.263871\pi$
$937$	41.3628	1.35127	0.675633	+	0.737239i	$0.263871\pi$
$938$	0	0
$939$	2.49919	0.0815580
$940$	−29.5470	−0.963717
$941$	17.8980	0.583458	0.291729	−	0.956501i	$-0.405769\pi$
$941$	17.8980	0.583458	0.291729	+	0.956501i	$0.405769\pi$
$942$	0.447623	0.0145844
$943$	−21.5292	−0.701087
$944$	12.0035	0.390682
$945$	0	0
$946$	−3.77074	−0.122597
$947$	−40.6916	−1.32230	−0.661149	−	0.750254i	$-0.729931\pi$
$947$	−40.6916	−1.32230	−0.661149	+	0.750254i	$0.729931\pi$
$948$	0.894587	0.0290548
$949$	34.5265	1.12078
$950$	−51.1802	−1.66050
$951$	5.03861	0.163388
$952$	0	0
$953$	49.3942	1.60004	0.800018	−	0.599976i	$-0.204823\pi$
$953$	49.3942	1.60004	0.800018	+	0.599976i	$0.204823\pi$
$954$	26.6121	0.861597
$955$	60.5594	1.95966
$956$	9.49713	0.307159
$957$	3.25343	0.105168
$958$	−7.04371	−0.227572
$959$	0	0
$960$	−0.633936	−0.0204602
$961$	−29.9549	−0.966286
$962$	28.1471	0.907498
$963$	−3.75477	−0.120996
$964$	−18.0858	−0.582506
$965$	−53.9556	−1.73689
$966$	0	0
$967$	30.9906	0.996590	0.498295	−	0.867008i	$-0.333960\pi$
$967$	30.9906	0.996590	0.498295	+	0.867008i	$0.333960\pi$
$968$	−7.65795	−0.246136
$969$	−1.02232	−0.0328416
$970$	25.5187	0.819355
$971$	33.7688	1.08369	0.541845	−	0.840478i	$-0.317726\pi$
$971$	33.7688	1.08369	0.541845	+	0.840478i	$0.317726\pi$
$972$	4.57977	0.146896
$973$	0	0
$974$	−16.6699	−0.534139
$975$	7.31759	0.234350
$976$	−3.70981	−0.118748
$977$	23.4145	0.749096	0.374548	−	0.927208i	$-0.377798\pi$
$977$	23.4145	0.749096	0.374548	+	0.927208i	$0.377798\pi$
$978$	−1.19927	−0.0383484
$979$	−5.35670	−0.171201
$980$	0	0
$981$	17.9503	0.573108
$982$	14.7249	0.469891
$983$	−42.2225	−1.34669	−0.673344	−	0.739330i	$-0.735143\pi$
$983$	−42.2225	−1.34669	−0.673344	+	0.739330i	$0.735143\pi$
$984$	−0.511780	−0.0163150
$985$	−58.1026	−1.85130
$986$	10.3545	0.329755
$987$	0	0
$988$	−29.4322	−0.936364
$989$	−14.9131	−0.474211
$990$	20.0295	0.636579
$991$	−50.8256	−1.61453	−0.807264	−	0.590190i	$-0.799053\pi$
$991$	−50.8256	−1.61453	−0.807264	+	0.590190i	$0.799053\pi$
$992$	1.02232	0.0324587
$993$	−2.83984	−0.0901197
$994$	0	0
$995$	36.5335	1.15819
$996$	2.62502	0.0831770
$997$	−52.9222	−1.67606	−0.838032	−	0.545621i	$-0.816294\pi$
$997$	−52.9222	−1.67606	−0.838032	+	0.545621i	$0.816294\pi$
$998$	15.0874	0.477583
$999$	−5.83720	−0.184681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1666.2.a.ba.1.3		5
7.3	odd	6		238.2.e.f.205.3	yes	10
7.5	odd	6		238.2.e.f.137.3	✓	10
7.6	odd	2		1666.2.a.z.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.e.f.137.3	✓	10	7.5	odd	6
238.2.e.f.205.3	yes	10	7.3	odd	6
1666.2.a.z.1.3		5	7.6	odd	2
1666.2.a.ba.1.3		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1666.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.171872 q^{3} +1.00000 q^{4} -3.68841 q^{5} +0.171872 q^{6} +1.00000 q^{8} -2.97046 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.171872 q^{3} +1.00000 q^{4} -3.68841 q^{5} +0.171872 q^{6} +1.00000 q^{8} -2.97046 q^{9} -3.68841 q^{10} +1.82813 q^{11} +0.171872 q^{12} +4.94814 q^{13} -0.633936 q^{15} +1.00000 q^{16} +1.00000 q^{17} -2.97046 q^{18} -5.94814 q^{19} -3.68841 q^{20} +1.82813 q^{22} +7.23019 q^{23} +0.171872 q^{24} +8.60440 q^{25} +4.94814 q^{26} -1.02616 q^{27} +10.3545 q^{29} -0.633936 q^{30} +1.02232 q^{31} +1.00000 q^{32} +0.314204 q^{33} +1.00000 q^{34} -2.97046 q^{36} +5.68841 q^{37} -5.94814 q^{38} +0.850448 q^{39} -3.68841 q^{40} -2.97768 q^{41} -2.06262 q^{43} +1.82813 q^{44} +10.9563 q^{45} +7.23019 q^{46} +8.01076 q^{47} +0.171872 q^{48} +8.60440 q^{50} +0.171872 q^{51} +4.94814 q^{52} -8.95890 q^{53} -1.02616 q^{54} -6.74289 q^{55} -1.02232 q^{57} +10.3545 q^{58} +12.0035 q^{59} -0.633936 q^{60} -3.70981 q^{61} +1.02232 q^{62} +1.00000 q^{64} -18.2508 q^{65} +0.314204 q^{66} +5.42869 q^{67} +1.00000 q^{68} +1.24267 q^{69} -5.40206 q^{71} -2.97046 q^{72} +6.97768 q^{73} +5.68841 q^{74} +1.47886 q^{75} -5.94814 q^{76} +0.850448 q^{78} +5.20496 q^{79} -3.68841 q^{80} +8.73501 q^{81} -2.97768 q^{82} +15.2731 q^{83} -3.68841 q^{85} -2.06262 q^{86} +1.77965 q^{87} +1.82813 q^{88} -2.93016 q^{89} +10.9563 q^{90} +7.23019 q^{92} +0.175708 q^{93} +8.01076 q^{94} +21.9392 q^{95} +0.171872 q^{96} -6.91860 q^{97} -5.43038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 5 q^{4} + q^{5} + 5 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 5 * q^4 + q^5 + 5 * q^8 + 11 * q^9	\( 5 q + 5 q^{2} + 5 q^{4} + q^{5} + 5 q^{8} + 11 q^{9} + q^{10} + 10 q^{11} - 2 q^{13} - 4 q^{15} + 5 q^{16} + 5 q^{17} + 11 q^{18} - 3 q^{19} + q^{20} + 10 q^{22} + 3 q^{23} + 18 q^{25} - 2 q^{26} + 6 q^{27} + 12 q^{29} - 4 q^{30} + 6 q^{31} + 5 q^{32} - 26 q^{33} + 5 q^{34} + 11 q^{36} + 9 q^{37} - 3 q^{38} + 6 q^{39} + q^{40} - 14 q^{41} + q^{43} + 10 q^{44} + 37 q^{45} + 3 q^{46} + 2 q^{47} + 18 q^{50} - 2 q^{52} + 20 q^{53} + 6 q^{54} + 6 q^{55} - 6 q^{57} + 12 q^{58} - 3 q^{59} - 4 q^{60} - 16 q^{61} + 6 q^{62} + 5 q^{64} + 2 q^{65} - 26 q^{66} + 15 q^{67} + 5 q^{68} - 4 q^{69} + 7 q^{71} + 11 q^{72} + 34 q^{73} + 9 q^{74} - 46 q^{75} - 3 q^{76} + 6 q^{78} - 12 q^{79} + q^{80} + 53 q^{81} - 14 q^{82} - 16 q^{83} + q^{85} + q^{86} + 20 q^{87} + 10 q^{88} - q^{89} + 37 q^{90} + 3 q^{92} - 12 q^{93} + 2 q^{94} - 3 q^{95} + 18 q^{97} + 16 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 5 * q^4 + q^5 + 5 * q^8 + 11 * q^9 + q^10 + 10 * q^11 - 2 * q^13 - 4 * q^15 + 5 * q^16 + 5 * q^17 + 11 * q^18 - 3 * q^19 + q^20 + 10 * q^22 + 3 * q^23 + 18 * q^25 - 2 * q^26 + 6 * q^27 + 12 * q^29 - 4 * q^30 + 6 * q^31 + 5 * q^32 - 26 * q^33 + 5 * q^34 + 11 * q^36 + 9 * q^37 - 3 * q^38 + 6 * q^39 + q^40 - 14 * q^41 + q^43 + 10 * q^44 + 37 * q^45 + 3 * q^46 + 2 * q^47 + 18 * q^50 - 2 * q^52 + 20 * q^53 + 6 * q^54 + 6 * q^55 - 6 * q^57 + 12 * q^58 - 3 * q^59 - 4 * q^60 - 16 * q^61 + 6 * q^62 + 5 * q^64 + 2 * q^65 - 26 * q^66 + 15 * q^67 + 5 * q^68 - 4 * q^69 + 7 * q^71 + 11 * q^72 + 34 * q^73 + 9 * q^74 - 46 * q^75 - 3 * q^76 + 6 * q^78 - 12 * q^79 + q^80 + 53 * q^81 - 14 * q^82 - 16 * q^83 + q^85 + q^86 + 20 * q^87 + 10 * q^88 - q^89 + 37 * q^90 + 3 * q^92 - 12 * q^93 + 2 * q^94 - 3 * q^95 + 18 * q^97 + 16 * q^99

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