LMFDB - Embedded newform 931.2.a.m.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, 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("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.5744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} - 2x + 1 $ x^4 - 5x^2 - 2x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.37988$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.37988 q^{2} +0.579810 q^{3} +3.66382 q^{4} +3.67575 q^{5} +1.37988 q^{6} +3.95969 q^{8} -2.66382 q^{9} +O(q^{10})$	\(q+2.37988 q^{2} +0.579810 q^{3} +3.66382 q^{4} +3.67575 q^{5} +1.37988 q^{6} +3.95969 q^{8} -2.66382 q^{9} +8.74783 q^{10} -4.50420 q^{11} +2.12432 q^{12} +6.04370 q^{13} +2.13124 q^{15} +2.09594 q^{16} -5.29926 q^{17} -6.33957 q^{18} -1.00000 q^{19} +13.4673 q^{20} -10.7194 q^{22} -0.432116 q^{23} +2.29587 q^{24} +8.51111 q^{25} +14.3833 q^{26} -3.28394 q^{27} +1.82845 q^{29} +5.07208 q^{30} -5.46389 q^{31} -2.93130 q^{32} -2.61158 q^{33} -12.6116 q^{34} -9.75976 q^{36} -6.12771 q^{37} -2.37988 q^{38} +3.50420 q^{39} +14.5548 q^{40} -1.21525 q^{41} +2.24864 q^{43} -16.5026 q^{44} -9.79153 q^{45} -1.02838 q^{46} +9.90053 q^{47} +1.21525 q^{48} +20.2554 q^{50} -3.07256 q^{51} +22.1430 q^{52} +10.2993 q^{53} -7.81538 q^{54} -16.5563 q^{55} -0.579810 q^{57} +4.35149 q^{58} +1.30780 q^{59} +7.80847 q^{60} +7.92439 q^{61} -13.0034 q^{62} -11.1680 q^{64} +22.2151 q^{65} -6.21525 q^{66} -9.41856 q^{67} -19.4155 q^{68} -0.250546 q^{69} -10.6956 q^{71} -10.5479 q^{72} -3.45549 q^{73} -14.5832 q^{74} +4.93483 q^{75} -3.66382 q^{76} +8.33957 q^{78} -0.0567691 q^{79} +7.70413 q^{80} +6.08740 q^{81} -2.89214 q^{82} +13.5997 q^{83} -19.4787 q^{85} +5.35149 q^{86} +1.06016 q^{87} -17.8352 q^{88} +10.4873 q^{89} -23.3026 q^{90} -1.58320 q^{92} -3.16802 q^{93} +23.5621 q^{94} -3.67575 q^{95} -1.69960 q^{96} -1.74831 q^{97} +11.9984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^8 + 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{8} + 2 q^{9} + 10 q^{10} - 6 q^{11} + 6 q^{12} + 2 q^{13} + 4 q^{15} + 2 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} - 14 q^{22} - 8 q^{23} + 12 q^{24} + 20 q^{25} + 16 q^{26} - 10 q^{27} + 2 q^{29} + 2 q^{30} + 2 q^{32} + 18 q^{33} - 22 q^{34} - 20 q^{36} + 10 q^{37} + 2 q^{39} + 22 q^{40} + 12 q^{41} + 4 q^{43} - 14 q^{44} + 8 q^{45} - 8 q^{46} + 16 q^{47} - 12 q^{48} + 12 q^{50} - 10 q^{51} + 28 q^{52} + 12 q^{53} + 4 q^{54} - 8 q^{55} - 2 q^{57} + 4 q^{58} + 14 q^{59} - 2 q^{60} + 20 q^{61} - 20 q^{62} - 20 q^{64} + 10 q^{65} - 8 q^{66} + 2 q^{67} - 24 q^{68} + 14 q^{69} - 2 q^{71} - 8 q^{72} - 16 q^{73} - 26 q^{74} + 36 q^{75} - 2 q^{76} + 14 q^{78} - 8 q^{79} + 28 q^{80} - 20 q^{81} - 12 q^{82} + 20 q^{83} - 14 q^{85} + 8 q^{86} - 20 q^{87} - 2 q^{88} + 16 q^{89} - 32 q^{90} + 26 q^{92} + 12 q^{93} + 10 q^{94} - 8 q^{95} - 12 q^{96} + 2 q^{97} + 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^8 + 2 * q^9 + 10 * q^10 - 6 * q^11 + 6 * q^12 + 2 * q^13 + 4 * q^15 + 2 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 - 14 * q^22 - 8 * q^23 + 12 * q^24 + 20 * q^25 + 16 * q^26 - 10 * q^27 + 2 * q^29 + 2 * q^30 + 2 * q^32 + 18 * q^33 - 22 * q^34 - 20 * q^36 + 10 * q^37 + 2 * q^39 + 22 * q^40 + 12 * q^41 + 4 * q^43 - 14 * q^44 + 8 * q^45 - 8 * q^46 + 16 * q^47 - 12 * q^48 + 12 * q^50 - 10 * q^51 + 28 * q^52 + 12 * q^53 + 4 * q^54 - 8 * q^55 - 2 * q^57 + 4 * q^58 + 14 * q^59 - 2 * q^60 + 20 * q^61 - 20 * q^62 - 20 * q^64 + 10 * q^65 - 8 * q^66 + 2 * q^67 - 24 * q^68 + 14 * q^69 - 2 * q^71 - 8 * q^72 - 16 * q^73 - 26 * q^74 + 36 * q^75 - 2 * q^76 + 14 * q^78 - 8 * q^79 + 28 * q^80 - 20 * q^81 - 12 * q^82 + 20 * q^83 - 14 * q^85 + 8 * q^86 - 20 * q^87 - 2 * q^88 + 16 * q^89 - 32 * q^90 + 26 * q^92 + 12 * q^93 + 10 * q^94 - 8 * q^95 - 12 * q^96 + 2 * q^97 + 8 * 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 $

$2$	2.37988	1.68283	0.841414	−	0.540391i	$-0.181724\pi$
$2$	2.37988	1.68283	0.841414	+	0.540391i	$0.181724\pi$
$3$	0.579810	0.334754	0.167377	−	0.985893i	$-0.446470\pi$
$3$	0.579810	0.334754	0.167377	+	0.985893i	$0.446470\pi$
$4$	3.66382	1.83191
$5$	3.67575	1.64384	0.821922	−	0.569600i	$-0.192902\pi$
$5$	3.67575	1.64384	0.821922	+	0.569600i	$0.192902\pi$
$6$	1.37988	0.563333
$7$	0	0
$7$	0	0
$8$	3.95969	1.39996
$9$	−2.66382	−0.887940
$10$	8.74783	2.76631
$11$	−4.50420	−1.35807	−0.679034	−	0.734107i	$-0.737601\pi$
$11$	−4.50420	−1.35807	−0.679034	+	0.734107i	$0.737601\pi$
$12$	2.12432	0.613239
$13$	6.04370	1.67622	0.838110	−	0.545501i	$-0.183661\pi$
$13$	6.04370	1.67622	0.838110	+	0.545501i	$0.183661\pi$
$14$	0	0
$15$	2.13124	0.550283
$16$	2.09594	0.523984
$17$	−5.29926	−1.28526	−0.642629	−	0.766177i	$-0.722156\pi$
$17$	−5.29926	−1.28526	−0.642629	+	0.766177i	$0.722156\pi$
$18$	−6.33957	−1.49425
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	13.4673	3.01137
$21$	0	0
$22$	−10.7194	−2.28539
$23$	−0.432116	−0.0901025	−0.0450513	−	0.998985i	$-0.514345\pi$
$23$	−0.432116	−0.0901025	−0.0450513	+	0.998985i	$0.514345\pi$
$24$	2.29587	0.468642
$25$	8.51111	1.70222
$26$	14.3833	2.82079
$27$	−3.28394	−0.631995
$28$	0	0
$29$	1.82845	0.339535	0.169768	−	0.985484i	$-0.445698\pi$
$29$	1.82845	0.339535	0.169768	+	0.985484i	$0.445698\pi$
$30$	5.07208	0.926031
$31$	−5.46389	−0.981343	−0.490672	−	0.871345i	$-0.663249\pi$
$31$	−5.46389	−0.981343	−0.490672	+	0.871345i	$0.663249\pi$
$32$	−2.93130	−0.518186
$33$	−2.61158	−0.454618
$34$	−12.6116	−2.16287
$35$	0	0
$36$	−9.75976	−1.62663
$37$	−6.12771	−1.00739	−0.503694	−	0.863882i	$-0.668026\pi$
$37$	−6.12771	−1.00739	−0.503694	+	0.863882i	$0.668026\pi$
$38$	−2.37988	−0.386067
$39$	3.50420	0.561121
$40$	14.5548	2.30132
$41$	−1.21525	−0.189789	−0.0948947	−	0.995487i	$-0.530251\pi$
$41$	−1.21525	−0.189789	−0.0948947	+	0.995487i	$0.530251\pi$
$42$	0	0
$43$	2.24864	0.342915	0.171457	−	0.985192i	$-0.445152\pi$
$43$	2.24864	0.342915	0.171457	+	0.985192i	$0.445152\pi$
$44$	−16.5026	−2.48786
$45$	−9.79153	−1.45963
$46$	−1.02838	−0.151627
$47$	9.90053	1.44414	0.722071	−	0.691819i	$-0.243191\pi$
$47$	9.90053	1.44414	0.722071	+	0.691819i	$0.243191\pi$
$48$	1.21525	0.175406
$49$	0	0
$50$	20.2554	2.86455
$51$	−3.07256	−0.430245
$52$	22.1430	3.07068
$53$	10.2993	1.41471	0.707356	−	0.706858i	$-0.249888\pi$
$53$	10.2993	1.41471	0.707356	+	0.706858i	$0.249888\pi$
$54$	−7.81538	−1.06354
$55$	−16.5563	−2.23245
$56$	0	0
$57$	−0.579810	−0.0767978
$58$	4.35149	0.571379
$59$	1.30780	0.170260	0.0851302	−	0.996370i	$-0.472869\pi$
$59$	1.30780	0.170260	0.0851302	+	0.996370i	$0.472869\pi$
$60$	7.80847	1.00807
$61$	7.92439	1.01461	0.507307	−	0.861765i	$-0.330641\pi$
$61$	7.92439	1.01461	0.507307	+	0.861765i	$0.330641\pi$
$62$	−13.0034	−1.65143
$63$	0	0
$64$	−11.1680	−1.39600
$65$	22.2151	2.75544
$66$	−6.21525	−0.765044
$67$	−9.41856	−1.15066	−0.575330	−	0.817921i	$-0.695127\pi$
$67$	−9.41856	−1.15066	−0.575330	+	0.817921i	$0.695127\pi$
$68$	−19.4155	−2.35448
$69$	−0.250546	−0.0301622
$70$	0	0
$71$	−10.6956	−1.26933	−0.634667	−	0.772786i	$-0.718863\pi$
$71$	−10.6956	−1.26933	−0.634667	+	0.772786i	$0.718863\pi$
$72$	−10.5479	−1.24308
$73$	−3.45549	−0.404434	−0.202217	−	0.979341i	$-0.564815\pi$
$73$	−3.45549	−0.404434	−0.202217	+	0.979341i	$0.564815\pi$
$74$	−14.5832	−1.69526
$75$	4.93483	0.569825
$76$	−3.66382	−0.420269
$77$	0	0
$78$	8.33957	0.944270
$79$	−0.0567691	−0.00638703	−0.00319351	−	0.999995i	$-0.501017\pi$
$79$	−0.0567691	−0.00638703	−0.00319351	+	0.999995i	$0.501017\pi$
$80$	7.70413	0.861348
$81$	6.08740	0.676377
$82$	−2.89214	−0.319383
$83$	13.5997	1.49276	0.746378	−	0.665522i	$-0.231791\pi$
$83$	13.5997	1.49276	0.746378	+	0.665522i	$0.231791\pi$
$84$	0	0
$85$	−19.4787	−2.11276
$86$	5.35149	0.577066
$87$	1.06016	0.113661
$88$	−17.8352	−1.90124
$89$	10.4873	1.11165	0.555824	−	0.831300i	$-0.312403\pi$
$89$	10.4873	1.11165	0.555824	+	0.831300i	$0.312403\pi$
$90$	−23.3026	−2.45631
$91$	0	0
$92$	−1.58320	−0.165060
$93$	−3.16802	−0.328508
$94$	23.5621	2.43024
$95$	−3.67575	−0.377124
$96$	−1.69960	−0.173465
$97$	−1.74831	−0.177514	−0.0887570	−	0.996053i	$-0.528289\pi$
$97$	−1.74831	−0.177514	−0.0887570	+	0.996053i	$0.528289\pi$
$98$	0	0
$99$	11.9984	1.20588
$100$	31.1832	3.11832
$101$	8.64349	0.860060	0.430030	−	0.902815i	$-0.358503\pi$
$101$	8.64349	0.860060	0.430030	+	0.902815i	$0.358503\pi$
$102$	−7.31233	−0.724028
$103$	−3.77120	−0.371588	−0.185794	−	0.982589i	$-0.559486\pi$
$103$	−3.77120	−0.371588	−0.185794	+	0.982589i	$0.559486\pi$
$104$	23.9312	2.34664
$105$	0	0
$106$	24.5110	2.38072
$107$	0.688818	0.0665905	0.0332953	−	0.999446i	$-0.489400\pi$
$107$	0.688818	0.0665905	0.0332953	+	0.999446i	$0.489400\pi$
$108$	−12.0318	−1.15776
$109$	−1.31118	−0.125588	−0.0627942	−	0.998026i	$-0.520001\pi$
$109$	−1.31118	−0.125588	−0.0627942	+	0.998026i	$0.520001\pi$
$110$	−39.4020	−3.75683
$111$	−3.55291	−0.337227
$112$	0	0
$113$	−0.0199865	−0.00188017	−0.000940084	−	1.00000i	$-0.500299\pi$
$113$	−0.0199865	−0.00188017	−0.000940084		1.00000i	$0.500299\pi$
$114$	−1.37988	−0.129237
$115$	−1.58835	−0.148114
$116$	6.69912	0.621998
$117$	−16.0993	−1.48838
$118$	3.11239	0.286519
$119$	0	0
$120$	8.43903	0.770375
$121$	9.28781	0.844346
$122$	18.8591	1.70742
$123$	−0.704612	−0.0635327
$124$	−20.0187	−1.79773
$125$	12.9060	1.15434
$126$	0	0
$127$	21.2232	1.88325	0.941626	−	0.336662i	$-0.109298\pi$
$127$	21.2232	1.88325	0.941626	+	0.336662i	$0.109298\pi$
$128$	−20.7159	−1.83105
$129$	1.30379	0.114792
$130$	52.8692	4.63694
$131$	−2.49275	−0.217793	−0.108896	−	0.994053i	$-0.534732\pi$
$131$	−2.49275	−0.217793	−0.108896	+	0.994053i	$0.534732\pi$
$132$	−9.56836	−0.832819
$133$	0	0
$134$	−22.4150	−1.93636
$135$	−12.0709	−1.03890
$136$	−20.9834	−1.79931
$137$	3.91938	0.334855	0.167427	−	0.985884i	$-0.446454\pi$
$137$	3.91938	0.334855	0.167427	+	0.985884i	$0.446454\pi$
$138$	−0.596268	−0.0507577
$139$	−18.1936	−1.54316	−0.771582	−	0.636130i	$-0.780534\pi$
$139$	−18.1936	−1.54316	−0.771582	+	0.636130i	$0.780534\pi$
$140$	0	0
$141$	5.74043	0.483432
$142$	−25.4542	−2.13607
$143$	−27.2220	−2.27642
$144$	−5.58320	−0.465266
$145$	6.72093	0.558143
$146$	−8.22364	−0.680594
$147$	0	0
$148$	−22.4508	−1.84545
$149$	−0.959350	−0.0785930	−0.0392965	−	0.999228i	$-0.512512\pi$
$149$	−0.959350	−0.0785930	−0.0392965	+	0.999228i	$0.512512\pi$
$150$	11.7443	0.958918
$151$	−15.5398	−1.26461	−0.632307	−	0.774718i	$-0.717892\pi$
$151$	−15.5398	−1.26461	−0.632307	+	0.774718i	$0.717892\pi$
$152$	−3.95969	−0.321173
$153$	14.1163	1.14123
$154$	0	0
$155$	−20.0839	−1.61318
$156$	12.8388	1.02792
$157$	15.4105	1.22989	0.614946	−	0.788569i	$-0.289178\pi$
$157$	15.4105	1.22989	0.614946	+	0.788569i	$0.289178\pi$
$158$	−0.135104	−0.0107483
$159$	5.97162	0.473580
$160$	−10.7747	−0.851817
$161$	0	0
$162$	14.4873	1.13823
$163$	17.9108	1.40289	0.701443	−	0.712726i	$-0.252540\pi$
$163$	17.9108	1.40289	0.701443	+	0.712726i	$0.252540\pi$
$164$	−4.45244	−0.347677
$165$	−9.59951	−0.747321
$166$	32.3655	2.51205
$167$	17.2678	1.33622	0.668112	−	0.744061i	$-0.267103\pi$
$167$	17.2678	1.33622	0.668112	+	0.744061i	$0.267103\pi$
$168$	0	0
$169$	23.5263	1.80971
$170$	−46.3570	−3.55542
$171$	2.66382	0.203707
$172$	8.23862	0.628189
$173$	−7.82492	−0.594918	−0.297459	−	0.954735i	$-0.596139\pi$
$173$	−7.82492	−0.594918	−0.297459	+	0.954735i	$0.596139\pi$
$174$	2.52304	0.191271
$175$	0	0
$176$	−9.44051	−0.711606
$177$	0.758273	0.0569953
$178$	24.9584	1.87071
$179$	−17.1461	−1.28156	−0.640779	−	0.767726i	$-0.721388\pi$
$179$	−17.1461	−1.28156	−0.640779	+	0.767726i	$0.721388\pi$
$180$	−35.8744	−2.67392
$181$	−20.7983	−1.54593	−0.772963	−	0.634451i	$-0.781226\pi$
$181$	−20.7983	−1.54593	−0.772963	+	0.634451i	$0.781226\pi$
$182$	0	0
$183$	4.59464	0.339646
$184$	−1.71105	−0.126140
$185$	−22.5239	−1.65599
$186$	−7.53950	−0.552823
$187$	23.8689	1.74547
$188$	36.2738	2.64554
$189$	0	0
$190$	−8.74783	−0.634634
$191$	−22.5264	−1.62996	−0.814978	−	0.579493i	$-0.803251\pi$
$191$	−22.5264	−1.62996	−0.814978	+	0.579493i	$0.803251\pi$
$192$	−6.47533	−0.467317
$193$	−6.74945	−0.485836	−0.242918	−	0.970047i	$-0.578105\pi$
$193$	−6.74945	−0.485836	−0.242918	+	0.970047i	$0.578105\pi$
$194$	−4.16077	−0.298726
$195$	12.8805	0.922395
$196$	0	0
$197$	−27.4542	−1.95603	−0.978015	−	0.208532i	$-0.933131\pi$
$197$	−27.4542	−1.95603	−0.978015	+	0.208532i	$0.933131\pi$
$198$	28.5547	2.02929
$199$	−22.5161	−1.59613	−0.798063	−	0.602574i	$-0.794142\pi$
$199$	−22.5161	−1.59613	−0.798063	+	0.602574i	$0.794142\pi$
$200$	33.7014	2.38305
$201$	−5.46098	−0.385188
$202$	20.5705	1.44733
$203$	0	0
$204$	−11.2573	−0.788170
$205$	−4.46694	−0.311984
$206$	−8.97500	−0.625318
$207$	1.15108	0.0800056
$208$	12.6672	0.878313
$209$	4.50420	0.311562
$210$	0	0
$211$	−1.51565	−0.104341	−0.0521707	−	0.998638i	$-0.516614\pi$
$211$	−1.51565	−0.104341	−0.0521707	+	0.998638i	$0.516614\pi$
$212$	37.7346	2.59162
$213$	−6.20142	−0.424914
$214$	1.63930	0.112060
$215$	8.26544	0.563698
$216$	−13.0034	−0.884768
$217$	0	0
$218$	−3.12045	−0.211344
$219$	−2.00353	−0.135386
$220$	−60.6593	−4.08965
$221$	−32.0271	−2.15438
$222$	−8.45549	−0.567495
$223$	0.292340	0.0195765	0.00978826	−	0.999952i	$-0.496884\pi$
$223$	0.292340	0.0195765	0.00978826	+	0.999952i	$0.496884\pi$
$224$	0	0
$225$	−22.6721	−1.51147
$226$	−0.0475653	−0.00316400
$227$	7.39329	0.490710	0.245355	−	0.969433i	$-0.421096\pi$
$227$	7.39329	0.490710	0.245355	+	0.969433i	$0.421096\pi$
$228$	−2.12432	−0.140687
$229$	−8.99837	−0.594629	−0.297315	−	0.954780i	$-0.596091\pi$
$229$	−8.99837	−0.594629	−0.297315	+	0.954780i	$0.596091\pi$
$230$	−3.78008	−0.249251
$231$	0	0
$232$	7.24010	0.475336
$233$	17.1504	1.12356	0.561781	−	0.827286i	$-0.310117\pi$
$233$	17.1504	1.12356	0.561781	+	0.827286i	$0.310117\pi$
$234$	−38.3144	−2.50469
$235$	36.3919	2.37394
$236$	4.79153	0.311902
$237$	−0.0329153	−0.00213808
$238$	0	0
$239$	4.95229	0.320337	0.160169	−	0.987090i	$-0.448796\pi$
$239$	4.95229	0.320337	0.160169	+	0.987090i	$0.448796\pi$
$240$	4.46694	0.288339
$241$	−3.10285	−0.199872	−0.0999361	−	0.994994i	$-0.531864\pi$
$241$	−3.10285	−0.199872	−0.0999361	+	0.994994i	$0.531864\pi$
$242$	22.1039	1.42089
$243$	13.3814	0.858415
$244$	29.0335	1.85868
$245$	0	0
$246$	−1.67689	−0.106915
$247$	−6.04370	−0.384551
$248$	−21.6353	−1.37384
$249$	7.88522	0.499706
$250$	30.7146	1.94256
$251$	−13.0268	−0.822242	−0.411121	−	0.911581i	$-0.634863\pi$
$251$	−13.0268	−0.822242	−0.411121	+	0.911581i	$0.634863\pi$
$252$	0	0
$253$	1.94634	0.122365
$254$	50.5085	3.16919
$255$	−11.2940	−0.707256
$256$	−26.9653	−1.68533
$257$	13.1545	0.820553	0.410277	−	0.911961i	$-0.365432\pi$
$257$	13.1545	0.820553	0.410277	+	0.911961i	$0.365432\pi$
$258$	3.10285	0.193175
$259$	0	0
$260$	81.3921	5.04773
$261$	−4.87067	−0.301487
$262$	−5.93245	−0.366508
$263$	9.04757	0.557897	0.278948	−	0.960306i	$-0.410014\pi$
$263$	9.04757	0.557897	0.278948	+	0.960306i	$0.410014\pi$
$264$	−10.3410	−0.636448
$265$	37.8575	2.32556
$266$	0	0
$267$	6.08062	0.372128
$268$	−34.5079	−2.10791
$269$	23.8130	1.45190	0.725952	−	0.687745i	$-0.241399\pi$
$269$	23.8130	1.45190	0.725952	+	0.687745i	$0.241399\pi$
$270$	−28.7274	−1.74829
$271$	7.08449	0.430352	0.215176	−	0.976575i	$-0.430967\pi$
$271$	7.08449	0.430352	0.215176	+	0.976575i	$0.430967\pi$
$272$	−11.1069	−0.673455
$273$	0	0
$274$	9.32764	0.563503
$275$	−38.3358	−2.31173
$276$	−0.917954	−0.0552543
$277$	−7.39824	−0.444517	−0.222259	−	0.974988i	$-0.571343\pi$
$277$	−7.39824	−0.444517	−0.222259	+	0.974988i	$0.571343\pi$
$278$	−43.2986	−2.59688
$279$	14.5548	0.871374
$280$	0	0
$281$	7.51308	0.448193	0.224096	−	0.974567i	$-0.428057\pi$
$281$	7.51308	0.448193	0.224096	+	0.974567i	$0.428057\pi$
$282$	13.6615	0.813532
$283$	−19.0079	−1.12990	−0.564952	−	0.825124i	$-0.691105\pi$
$283$	−19.0079	−1.12990	−0.564952	+	0.825124i	$0.691105\pi$
$284$	−39.1867	−2.32530
$285$	−2.13124	−0.126244
$286$	−64.7851	−3.83082
$287$	0	0
$288$	7.80847	0.460118
$289$	11.0821	0.651889
$290$	15.9950	0.939258
$291$	−1.01369	−0.0594235
$292$	−12.6603	−0.740887
$293$	29.2440	1.70845	0.854225	−	0.519903i	$-0.174032\pi$
$293$	29.2440	1.70845	0.854225	+	0.519903i	$0.174032\pi$
$294$	0	0
$295$	4.80713	0.279882
$296$	−24.2638	−1.41031
$297$	14.7915	0.858291
$298$	−2.28314	−0.132259
$299$	−2.61158	−0.151032
$300$	18.0803	1.04387
$301$	0	0
$302$	−36.9829	−2.12813
$303$	5.01159	0.287908
$304$	−2.09594	−0.120210
$305$	29.1280	1.66787
$306$	33.5950	1.92050
$307$	23.8873	1.36332	0.681661	−	0.731668i	$-0.261258\pi$
$307$	23.8873	1.36332	0.681661	+	0.731668i	$0.261258\pi$
$308$	0	0
$309$	−2.18658	−0.124390
$310$	−47.7972	−2.71470
$311$	5.18801	0.294185	0.147092	−	0.989123i	$-0.453009\pi$
$311$	5.18801	0.294185	0.147092	+	0.989123i	$0.453009\pi$
$312$	13.8755	0.785548
$313$	−3.79430	−0.214466	−0.107233	−	0.994234i	$-0.534199\pi$
$313$	−3.79430	−0.214466	−0.107233	+	0.994234i	$0.534199\pi$
$314$	36.6751	2.06970
$315$	0	0
$316$	−0.207992	−0.0117005
$317$	3.43115	0.192713	0.0963564	−	0.995347i	$-0.469281\pi$
$317$	3.43115	0.192713	0.0963564	+	0.995347i	$0.469281\pi$
$318$	14.2117	0.796954
$319$	−8.23571	−0.461111
$320$	−41.0508	−2.29481
$321$	0.399384	0.0222914
$322$	0	0
$323$	5.29926	0.294858
$324$	22.3031	1.23906
$325$	51.4386	2.85330
$326$	42.6256	2.36081
$327$	−0.760237	−0.0420412
$328$	−4.81199	−0.265698
$329$	0	0
$330$	−22.8457	−1.25761
$331$	16.4573	0.904572	0.452286	−	0.891873i	$-0.350609\pi$
$331$	16.4573	0.904572	0.452286	+	0.891873i	$0.350609\pi$
$332$	49.8267	2.73459
$333$	16.3231	0.894501
$334$	41.0953	2.24864
$335$	−34.6203	−1.89151
$336$	0	0
$337$	18.7939	1.02377	0.511885	−	0.859054i	$-0.328947\pi$
$337$	18.7939	1.02377	0.511885	+	0.859054i	$0.328947\pi$
$338$	55.9897	3.04544
$339$	−0.0115884	−0.000629393 0
$340$	−71.3665	−3.87039
$341$	24.6104	1.33273
$342$	6.33957	0.342805
$343$	0	0
$344$	8.90392	0.480067
$345$	−0.920942	−0.0495819
$346$	−18.6224	−1.00114
$347$	12.3184	0.661288	0.330644	−	0.943756i	$-0.392734\pi$
$347$	12.3184	0.661288	0.330644	+	0.943756i	$0.392734\pi$
$348$	3.88422	0.208216
$349$	−33.1360	−1.77373	−0.886864	−	0.462031i	$-0.847121\pi$
$349$	−33.1360	−1.77373	−0.886864	+	0.462031i	$0.847121\pi$
$350$	0	0
$351$	−19.8472	−1.05936
$352$	13.2032	0.703732
$353$	33.5785	1.78720	0.893602	−	0.448860i	$-0.148170\pi$
$353$	33.5785	1.78720	0.893602	+	0.448860i	$0.148170\pi$
$354$	1.80460	0.0959133
$355$	−39.3143	−2.08659
$356$	38.4234	2.03644
$357$	0	0
$358$	−40.8056	−2.15664
$359$	15.4887	0.817465	0.408732	−	0.912654i	$-0.365971\pi$
$359$	15.4887	0.817465	0.408732	+	0.912654i	$0.365971\pi$
$360$	−38.7714	−2.04343
$361$	1.00000	0.0526316
$362$	−49.4974	−2.60153
$363$	5.38517	0.282648
$364$	0	0
$365$	−12.7015	−0.664827
$366$	10.9347	0.571565
$367$	25.5451	1.33344	0.666722	−	0.745306i	$-0.267697\pi$
$367$	25.5451	1.33344	0.666722	+	0.745306i	$0.267697\pi$
$368$	−0.905689	−0.0472123
$369$	3.23720	0.168522
$370$	−53.6041	−2.78675
$371$	0	0
$372$	−11.6071	−0.601798
$373$	−31.9071	−1.65209	−0.826044	−	0.563605i	$-0.809414\pi$
$373$	−31.9071	−1.65209	−0.826044	+	0.563605i	$0.809414\pi$
$374$	56.8051	2.93732
$375$	7.48301	0.386421
$376$	39.2030	2.02174
$377$	11.0506	0.569136
$378$	0	0
$379$	1.23056	0.0632096	0.0316048	−	0.999500i	$-0.489938\pi$
$379$	1.23056	0.0632096	0.0316048	+	0.999500i	$0.489938\pi$
$380$	−13.4673	−0.690857
$381$	12.3054	0.630425
$382$	−53.6102	−2.74293
$383$	−25.2646	−1.29096	−0.645480	−	0.763777i	$-0.723342\pi$
$383$	−25.2646	−1.29096	−0.645480	+	0.763777i	$0.723342\pi$
$384$	−12.0113	−0.612949
$385$	0	0
$386$	−16.0629	−0.817579
$387$	−5.98998	−0.304488
$388$	−6.40549	−0.325190
$389$	0.847295	0.0429595	0.0214798	−	0.999769i	$-0.493162\pi$
$389$	0.847295	0.0429595	0.0214798	+	0.999769i	$0.493162\pi$
$390$	30.6541	1.55223
$391$	2.28990	0.115805
$392$	0	0
$393$	−1.44532	−0.0729070
$394$	−65.3377	−3.29166
$395$	−0.208669	−0.0104993
$396$	43.9599	2.20907
$397$	3.85487	0.193471	0.0967353	−	0.995310i	$-0.469160\pi$
$397$	3.85487	0.193471	0.0967353	+	0.995310i	$0.469160\pi$
$398$	−53.5856	−2.68601
$399$	0	0
$400$	17.8388	0.891938
$401$	−2.15447	−0.107589	−0.0537945	−	0.998552i	$-0.517132\pi$
$401$	−2.15447	−0.107589	−0.0537945	+	0.998552i	$0.517132\pi$
$402$	−12.9965	−0.648205
$403$	−33.0221	−1.64495
$404$	31.6682	1.57555
$405$	22.3757	1.11186
$406$	0	0
$407$	27.6004	1.36810
$408$	−12.1664	−0.602326
$409$	14.1877	0.701536	0.350768	−	0.936462i	$-0.385921\pi$
$409$	14.1877	0.701536	0.350768	+	0.936462i	$0.385921\pi$
$410$	−10.6308	−0.525016
$411$	2.27250	0.112094
$412$	−13.8170	−0.680715
$413$	0	0
$414$	2.73943	0.134636
$415$	49.9889	2.45386
$416$	−17.7159	−0.868594
$417$	−10.5489	−0.516580
$418$	10.7194	0.524305
$419$	12.2981	0.600802	0.300401	−	0.953813i	$-0.402879\pi$
$419$	12.2981	0.600802	0.300401	+	0.953813i	$0.402879\pi$
$420$	0	0
$421$	−3.33504	−0.162540	−0.0812699	−	0.996692i	$-0.525898\pi$
$421$	−3.33504	−0.162540	−0.0812699	+	0.996692i	$0.525898\pi$
$422$	−3.60705	−0.175588
$423$	−26.3732	−1.28231
$424$	40.7818	1.98054
$425$	−45.1026	−2.18780
$426$	−14.7586	−0.715057
$427$	0	0
$428$	2.52370	0.121988
$429$	−15.7836	−0.762040
$430$	19.6707	0.948607
$431$	7.64011	0.368011	0.184006	−	0.982925i	$-0.441094\pi$
$431$	7.64011	0.368011	0.184006	+	0.982925i	$0.441094\pi$
$432$	−6.88293	−0.331155
$433$	17.5326	0.842562	0.421281	−	0.906930i	$-0.361581\pi$
$433$	17.5326	0.842562	0.421281	+	0.906930i	$0.361581\pi$
$434$	0	0
$435$	3.89686	0.186840
$436$	−4.80394	−0.230067
$437$	0.432116	0.0206709
$438$	−4.76815	−0.227831
$439$	3.36761	0.160727	0.0803637	−	0.996766i	$-0.474392\pi$
$439$	3.36761	0.160727	0.0803637	+	0.996766i	$0.474392\pi$
$440$	−65.5578	−3.12534
$441$	0	0
$442$	−76.2206	−3.62544
$443$	−9.92792	−0.471690	−0.235845	−	0.971791i	$-0.575786\pi$
$443$	−9.92792	−0.471690	−0.235845	+	0.971791i	$0.575786\pi$
$444$	−13.0172	−0.617770
$445$	38.5485	1.82737
$446$	0.695733	0.0329439
$447$	−0.556241	−0.0263093
$448$	0	0
$449$	14.6185	0.689890	0.344945	−	0.938623i	$-0.387898\pi$
$449$	14.6185	0.689890	0.344945	+	0.938623i	$0.387898\pi$
$450$	−53.9568	−2.54355
$451$	5.47371	0.257747
$452$	−0.0732268	−0.00344430
$453$	−9.01016	−0.423334
$454$	17.5951	0.825780
$455$	0	0
$456$	−2.29587	−0.107514
$457$	0.950146	0.0444460	0.0222230	−	0.999753i	$-0.492926\pi$
$457$	0.950146	0.0444460	0.0222230	+	0.999753i	$0.492926\pi$
$458$	−21.4150	−1.00066
$459$	17.4024	0.812277
$460$	−5.81943	−0.271332
$461$	−12.2549	−0.570769	−0.285385	−	0.958413i	$-0.592121\pi$
$461$	−12.2549	−0.570769	−0.285385	+	0.958413i	$0.592121\pi$
$462$	0	0
$463$	−4.61016	−0.214252	−0.107126	−	0.994245i	$-0.534165\pi$
$463$	−4.61016	−0.214252	−0.107126	+	0.994245i	$0.534165\pi$
$464$	3.83232	0.177911
$465$	−11.6448	−0.540016
$466$	40.8159	1.89076
$467$	−12.9273	−0.598204	−0.299102	−	0.954221i	$-0.596687\pi$
$467$	−12.9273	−0.598204	−0.299102	+	0.954221i	$0.596687\pi$
$468$	−58.9850	−2.72658
$469$	0	0
$470$	86.6082	3.99494
$471$	8.93517	0.411711
$472$	5.17846	0.238358
$473$	−10.1283	−0.465701
$474$	−0.0783345	−0.00359802
$475$	−8.51111	−0.390517
$476$	0	0
$477$	−27.4354	−1.25618
$478$	11.7859	0.539072
$479$	−1.90005	−0.0868157	−0.0434078	−	0.999057i	$-0.513821\pi$
$479$	−1.90005	−0.0868157	−0.0434078	+	0.999057i	$0.513821\pi$
$480$	−6.24730	−0.285149
$481$	−37.0340	−1.68861
$482$	−7.38441	−0.336351
$483$	0	0
$484$	34.0289	1.54677
$485$	−6.42635	−0.291805
$486$	31.8460	1.44456
$487$	21.6940	0.983047	0.491524	−	0.870864i	$-0.336440\pi$
$487$	21.6940	0.983047	0.491524	+	0.870864i	$0.336440\pi$
$488$	31.3781	1.42042
$489$	10.3849	0.469621
$490$	0	0
$491$	4.70528	0.212346	0.106173	−	0.994348i	$-0.466140\pi$
$491$	4.70528	0.212346	0.106173	+	0.994348i	$0.466140\pi$
$492$	−2.58157	−0.116386
$493$	−9.68944	−0.436390
$494$	−14.3833	−0.647134
$495$	44.1030	1.98228
$496$	−11.4520	−0.514208
$497$	0	0
$498$	18.7659	0.840919
$499$	19.2724	0.862749	0.431375	−	0.902173i	$-0.358029\pi$
$499$	19.2724	0.862749	0.431375	+	0.902173i	$0.358029\pi$
$500$	47.2851	2.11466
$501$	10.0121	0.447306
$502$	−31.0021	−1.38369
$503$	−22.6721	−1.01090	−0.505449	−	0.862857i	$-0.668673\pi$
$503$	−22.6721	−1.01090	−0.505449	+	0.862857i	$0.668673\pi$
$504$	0	0
$505$	31.7713	1.41380
$506$	4.63205	0.205920
$507$	13.6408	0.605809
$508$	77.7578	3.44995
$509$	22.7268	1.00735	0.503675	−	0.863893i	$-0.331981\pi$
$509$	22.7268	1.00735	0.503675	+	0.863893i	$0.331981\pi$
$510$	−26.8783	−1.19019
$511$	0	0
$512$	−22.7423	−1.00508
$513$	3.28394	0.144990
$514$	31.3060	1.38085
$515$	−13.8620	−0.610832
$516$	4.77684	0.210289
$517$	−44.5940	−1.96124
$518$	0	0
$519$	−4.53697	−0.199151
$520$	87.9649	3.85752
$521$	−4.76348	−0.208692	−0.104346	−	0.994541i	$-0.533275\pi$
$521$	−4.76348	−0.208692	−0.104346	+	0.994541i	$0.533275\pi$
$522$	−11.5916	−0.507350
$523$	−11.6745	−0.510489	−0.255244	−	0.966877i	$-0.582156\pi$
$523$	−11.6745	−0.510489	−0.255244	+	0.966877i	$0.582156\pi$
$524$	−9.13300	−0.398977
$525$	0	0
$526$	21.5321	0.938844
$527$	28.9545	1.26128
$528$	−5.47371	−0.238213
$529$	−22.8133	−0.991882
$530$	90.0961	3.91353
$531$	−3.48373	−0.151181
$532$	0	0
$533$	−7.34458	−0.318129
$534$	14.4711	0.626228
$535$	2.53192	0.109464
$536$	−37.2946	−1.61088
$537$	−9.94147	−0.429006
$538$	56.6720	2.44330
$539$	0	0
$540$	−44.2257	−1.90317
$541$	−41.0129	−1.76328	−0.881641	−	0.471921i	$-0.843561\pi$
$541$	−41.0129	−1.76328	−0.881641	+	0.471921i	$0.843561\pi$
$542$	16.8602	0.724209
$543$	−12.0591	−0.517504
$544$	15.5337	0.666003
$545$	−4.81957	−0.206448
$546$	0	0
$547$	10.2922	0.440063	0.220031	−	0.975493i	$-0.429384\pi$
$547$	10.2922	0.440063	0.220031	+	0.975493i	$0.429384\pi$
$548$	14.3599	0.613424
$549$	−21.1091	−0.900916
$550$	−91.2344	−3.89025
$551$	−1.82845	−0.0778947
$552$	−0.992083	−0.0422258
$553$	0	0
$554$	−17.6069	−0.748046
$555$	−13.0596	−0.554349
$556$	−66.6582	−2.82694
$557$	−17.1195	−0.725377	−0.362688	−	0.931910i	$-0.618141\pi$
$557$	−17.1195	−0.725377	−0.362688	+	0.931910i	$0.618141\pi$
$558$	34.6387	1.46637
$559$	13.5901	0.574801
$560$	0	0
$561$	13.8394	0.584301
$562$	17.8802	0.754231
$563$	−13.6132	−0.573728	−0.286864	−	0.957971i	$-0.592613\pi$
$563$	−13.6132	−0.573728	−0.286864	+	0.957971i	$0.592613\pi$
$564$	21.0319	0.885603
$565$	−0.0734652	−0.00309070
$566$	−45.2365	−1.90143
$567$	0	0
$568$	−42.3512	−1.77702
$569$	−23.3825	−0.980244	−0.490122	−	0.871654i	$-0.663048\pi$
$569$	−23.3825	−0.980244	−0.490122	+	0.871654i	$0.663048\pi$
$570$	−5.07208	−0.212446
$571$	−23.5747	−0.986569	−0.493284	−	0.869868i	$-0.664204\pi$
$571$	−23.5747	−0.986569	−0.493284	+	0.869868i	$0.664204\pi$
$572$	−99.7366	−4.17020
$573$	−13.0611	−0.545634
$574$	0	0
$575$	−3.67779	−0.153375
$576$	29.7496	1.23957
$577$	34.5413	1.43797	0.718986	−	0.695025i	$-0.244607\pi$
$577$	34.5413	1.43797	0.718986	+	0.695025i	$0.244607\pi$
$578$	26.3741	1.09702
$579$	−3.91340	−0.162636
$580$	24.6243	1.02247
$581$	0	0
$582$	−2.41245	−0.0999995
$583$	−46.3899	−1.92127
$584$	−13.6827	−0.566193
$585$	−59.1770	−2.44667
$586$	69.5971	2.87503
$587$	−11.7207	−0.483766	−0.241883	−	0.970305i	$-0.577765\pi$
$587$	−11.7207	−0.483766	−0.241883	+	0.970305i	$0.577765\pi$
$588$	0	0
$589$	5.46389	0.225136
$590$	11.4404	0.470993
$591$	−15.9182	−0.654789
$592$	−12.8433	−0.527856
$593$	−15.2897	−0.627873	−0.313937	−	0.949444i	$-0.601648\pi$
$593$	−15.2897	−0.627873	−0.313937	+	0.949444i	$0.601648\pi$
$594$	35.2020	1.44436
$595$	0	0
$596$	−3.51489	−0.143975
$597$	−13.0551	−0.534309
$598$	−6.21525	−0.254160
$599$	29.2938	1.19691	0.598457	−	0.801155i	$-0.295781\pi$
$599$	29.2938	1.19691	0.598457	+	0.801155i	$0.295781\pi$
$600$	19.5404	0.797734
$601$	20.8023	0.848544	0.424272	−	0.905535i	$-0.360530\pi$
$601$	20.8023	0.848544	0.424272	+	0.905535i	$0.360530\pi$
$602$	0	0
$603$	25.0894	1.02172
$604$	−56.9352	−2.31666
$605$	34.1396	1.38797
$606$	11.9270	0.484500
$607$	−27.8757	−1.13144	−0.565719	−	0.824598i	$-0.691401\pi$
$607$	−27.8757	−1.13144	−0.565719	+	0.824598i	$0.691401\pi$
$608$	2.93130	0.118880
$609$	0	0
$610$	69.3212	2.80673
$611$	59.8358	2.42070
$612$	51.7194	2.09063
$613$	20.7135	0.836612	0.418306	−	0.908306i	$-0.362624\pi$
$613$	20.7135	0.836612	0.418306	+	0.908306i	$0.362624\pi$
$614$	56.8489	2.29424
$615$	−2.58998	−0.104438
$616$	0	0
$617$	5.19945	0.209322	0.104661	−	0.994508i	$-0.466624\pi$
$617$	5.19945	0.209322	0.104661	+	0.994508i	$0.466624\pi$
$618$	−5.20380	−0.209328
$619$	11.2942	0.453954	0.226977	−	0.973900i	$-0.427116\pi$
$619$	11.2942	0.453954	0.226977	+	0.973900i	$0.427116\pi$
$620$	−73.5837	−2.95519
$621$	1.41905	0.0569443
$622$	12.3468	0.495062
$623$	0	0
$624$	7.34458	0.294018
$625$	4.88350	0.195340
$626$	−9.02996	−0.360910
$627$	2.61158	0.104297
$628$	56.4613	2.25305
$629$	32.4723	1.29475
$630$	0	0
$631$	−40.0390	−1.59393	−0.796964	−	0.604027i	$-0.793562\pi$
$631$	−40.0390	−1.59393	−0.796964	+	0.604027i	$0.793562\pi$
$632$	−0.224788	−0.00894159
$633$	−0.878787	−0.0349286
$634$	8.16573	0.324303
$635$	78.0110	3.09577
$636$	21.8789	0.867556
$637$	0	0
$638$	−19.6000	−0.775971
$639$	28.4911	1.12709
$640$	−76.1465	−3.00995
$641$	−28.2257	−1.11485	−0.557425	−	0.830227i	$-0.688211\pi$
$641$	−28.2257	−1.11485	−0.557425	+	0.830227i	$0.688211\pi$
$642$	0.950485	0.0375126
$643$	−25.4806	−1.00486	−0.502429	−	0.864619i	$-0.667560\pi$
$643$	−25.4806	−1.00486	−0.502429	+	0.864619i	$0.667560\pi$
$644$	0	0
$645$	4.79239	0.188700
$646$	12.6116	0.496196
$647$	−7.39619	−0.290774	−0.145387	−	0.989375i	$-0.546443\pi$
$647$	−7.39619	−0.290774	−0.145387	+	0.989375i	$0.546443\pi$
$648$	24.1042	0.946902
$649$	−5.89057	−0.231225
$650$	122.418	4.80161
$651$	0	0
$652$	65.6221	2.56996
$653$	−24.1603	−0.945466	−0.472733	−	0.881206i	$-0.656732\pi$
$653$	−24.1603	−0.945466	−0.472733	+	0.881206i	$0.656732\pi$
$654$	−1.80927	−0.0707481
$655$	−9.16273	−0.358017
$656$	−2.54708	−0.0994467
$657$	9.20480	0.359114
$658$	0	0
$659$	−35.2732	−1.37405	−0.687023	−	0.726635i	$-0.741083\pi$
$659$	−35.2732	−1.37405	−0.687023	+	0.726635i	$0.741083\pi$
$660$	−35.1709	−1.36902
$661$	−14.5686	−0.566651	−0.283326	−	0.959024i	$-0.591438\pi$
$661$	−14.5686	−0.566651	−0.283326	+	0.959024i	$0.591438\pi$
$662$	39.1663	1.52224
$663$	−18.5696	−0.721185
$664$	53.8504	2.08980
$665$	0	0
$666$	38.8470	1.50529
$667$	−0.790104	−0.0305930
$668$	63.2662	2.44784
$669$	0.169502	0.00655331
$670$	−82.3920	−3.18308
$671$	−35.6930	−1.37791
$672$	0	0
$673$	−14.8265	−0.571519	−0.285760	−	0.958301i	$-0.592246\pi$
$673$	−14.8265	−0.571519	−0.285760	+	0.958301i	$0.592246\pi$
$674$	44.7272	1.72283
$675$	−27.9500	−1.07580
$676$	86.1961	3.31523
$677$	−14.1561	−0.544063	−0.272031	−	0.962288i	$-0.587695\pi$
$677$	−14.1561	−0.544063	−0.272031	+	0.962288i	$0.587695\pi$
$678$	−0.0275789	−0.00105916
$679$	0	0
$680$	−77.1297	−2.95779
$681$	4.28671	0.164267
$682$	58.5698	2.24276
$683$	25.9197	0.991790	0.495895	−	0.868382i	$-0.334840\pi$
$683$	25.9197	0.991790	0.495895	+	0.868382i	$0.334840\pi$
$684$	9.75976	0.373174
$685$	14.4066	0.550449
$686$	0	0
$687$	−5.21735	−0.199054
$688$	4.71301	0.179682
$689$	62.2456	2.37137
$690$	−2.19173	−0.0834378
$691$	−0.606530	−0.0230735	−0.0115367	−	0.999933i	$-0.503672\pi$
$691$	−0.606530	−0.0230735	−0.0115367	+	0.999933i	$0.503672\pi$
$692$	−28.6691	−1.08984
$693$	0	0
$694$	29.3164	1.11283
$695$	−66.8752	−2.53672
$696$	4.19789	0.159120
$697$	6.43990	0.243929
$698$	−78.8596	−2.98488
$699$	9.94399	0.376116
$700$	0	0
$701$	10.1080	0.381774	0.190887	−	0.981612i	$-0.438864\pi$
$701$	10.1080	0.381774	0.190887	+	0.981612i	$0.438864\pi$
$702$	−47.2338	−1.78273
$703$	6.12771	0.231111
$704$	50.3030	1.89586
$705$	21.1004	0.794686
$706$	79.9128	3.00756
$707$	0	0
$708$	2.77818	0.104410
$709$	−6.48660	−0.243609	−0.121805	−	0.992554i	$-0.538868\pi$
$709$	−6.48660	−0.243609	−0.121805	+	0.992554i	$0.538868\pi$
$710$	−93.5632	−3.51136
$711$	0.151223	0.00567130
$712$	41.5263	1.55626
$713$	2.36104	0.0884215
$714$	0	0
$715$	−100.061	−3.74208
$716$	−62.8201	−2.34770
$717$	2.87139	0.107234
$718$	36.8613	1.37565
$719$	42.0919	1.56976	0.784881	−	0.619646i	$-0.212724\pi$
$719$	42.0919	1.56976	0.784881	+	0.619646i	$0.212724\pi$
$720$	−20.5224	−0.764825
$721$	0	0
$722$	2.37988	0.0885699
$723$	−1.79907	−0.0669080
$724$	−76.2012	−2.83200
$725$	15.5622	0.577964
$726$	12.8160	0.475648
$727$	−19.0511	−0.706566	−0.353283	−	0.935517i	$-0.614935\pi$
$727$	−19.0511	−0.706566	−0.353283	+	0.935517i	$0.614935\pi$
$728$	0	0
$729$	−10.5035	−0.389020
$730$	−30.2280	−1.11879
$731$	−11.9161	−0.440734
$732$	16.8339	0.622200
$733$	−10.5669	−0.390298	−0.195149	−	0.980774i	$-0.562519\pi$
$733$	−10.5669	−0.390298	−0.195149	+	0.980774i	$0.562519\pi$
$734$	60.7943	2.24396
$735$	0	0
$736$	1.26666	0.0466899
$737$	42.4231	1.56267
$738$	7.70413	0.283593
$739$	−45.7665	−1.68355	−0.841774	−	0.539829i	$-0.818489\pi$
$739$	−45.7665	−1.68355	−0.841774	+	0.539829i	$0.818489\pi$
$740$	−82.5235	−3.03362
$741$	−3.50420	−0.128730
$742$	0	0
$743$	−3.60657	−0.132312	−0.0661561	−	0.997809i	$-0.521074\pi$
$743$	−3.60657	−0.132312	−0.0661561	+	0.997809i	$0.521074\pi$
$744$	−12.5444	−0.459899
$745$	−3.52633	−0.129195
$746$	−75.9351	−2.78018
$747$	−36.2270	−1.32548
$748$	87.4514	3.19754
$749$	0	0
$750$	17.8087	0.650280
$751$	40.7543	1.48714	0.743572	−	0.668655i	$-0.233130\pi$
$751$	40.7543	1.48714	0.743572	+	0.668655i	$0.233130\pi$
$752$	20.7509	0.756707
$753$	−7.55305	−0.275248
$754$	26.2991	0.957757
$755$	−57.1205	−2.07883
$756$	0	0
$757$	49.8317	1.81116	0.905582	−	0.424171i	$-0.139435\pi$
$757$	49.8317	1.81116	0.905582	+	0.424171i	$0.139435\pi$
$758$	2.92858	0.106371
$759$	1.12851	0.0409622
$760$	−14.5548	−0.527959
$761$	−5.73155	−0.207769	−0.103884	−	0.994589i	$-0.533127\pi$
$761$	−5.73155	−0.207769	−0.103884	+	0.994589i	$0.533127\pi$
$762$	29.2854	1.06090
$763$	0	0
$764$	−82.5328	−2.98593
$765$	51.8878	1.87601
$766$	−60.1266	−2.17246
$767$	7.90392	0.285394
$768$	−15.6348	−0.564171
$769$	32.1203	1.15829	0.579144	−	0.815225i	$-0.303387\pi$
$769$	32.1203	1.15829	0.579144	+	0.815225i	$0.303387\pi$
$770$	0	0
$771$	7.62710	0.274683
$772$	−24.7288	−0.890008
$773$	−30.2461	−1.08788	−0.543938	−	0.839126i	$-0.683067\pi$
$773$	−30.2461	−1.08788	−0.543938	+	0.839126i	$0.683067\pi$
$774$	−14.2554	−0.512400
$775$	−46.5038	−1.67046
$776$	−6.92276	−0.248513
$777$	0	0
$778$	2.01646	0.0722935
$779$	1.21525	0.0435407
$780$	47.1920	1.68974
$781$	48.1751	1.72384
$782$	5.44967	0.194880
$783$	−6.00453	−0.214584
$784$	0	0
$785$	56.6451	2.02175
$786$	−3.43970	−0.122690
$787$	−24.7813	−0.883359	−0.441679	−	0.897173i	$-0.645617\pi$
$787$	−24.7813	−0.883359	−0.441679	+	0.897173i	$0.645617\pi$
$788$	−100.587	−3.58327
$789$	5.24587	0.186758
$790$	−0.496607	−0.0176685
$791$	0	0
$792$	47.5098	1.68819
$793$	47.8926	1.70072
$794$	9.17413	0.325578
$795$	21.9501	0.778491
$796$	−82.4950	−2.92396
$797$	36.1269	1.27968	0.639840	−	0.768508i	$-0.279001\pi$
$797$	36.1269	1.27968	0.639840	+	0.768508i	$0.279001\pi$
$798$	0	0
$799$	−52.4655	−1.85609
$800$	−24.9487	−0.882068
$801$	−27.9362	−0.987076
$802$	−5.12737	−0.181054
$803$	15.5642	0.549249
$804$	−20.0081	−0.705630
$805$	0	0
$806$	−78.5885	−2.76816
$807$	13.8070	0.486030
$808$	34.2255	1.20405
$809$	−40.7511	−1.43273	−0.716366	−	0.697725i	$-0.754196\pi$
$809$	−40.7511	−1.43273	−0.716366	+	0.697725i	$0.754196\pi$
$810$	53.2515	1.87107
$811$	−21.9161	−0.769579	−0.384790	−	0.923004i	$-0.625726\pi$
$811$	−21.9161	−0.769579	−0.384790	+	0.923004i	$0.625726\pi$
$812$	0	0
$813$	4.10766	0.144062
$814$	65.6856	2.30228
$815$	65.8357	2.30612
$816$	−6.43990	−0.225441
$817$	−2.24864	−0.0786700
$818$	33.7650	1.18056
$819$	0	0
$820$	−16.3660	−0.571527
$821$	19.5286	0.681552	0.340776	−	0.940145i	$-0.389310\pi$
$821$	19.5286	0.681552	0.340776	+	0.940145i	$0.389310\pi$
$822$	5.40826	0.188635
$823$	−5.54240	−0.193196	−0.0965980	−	0.995323i	$-0.530796\pi$
$823$	−5.54240	−0.193196	−0.0965980	+	0.995323i	$0.530796\pi$
$824$	−14.9328	−0.520208
$825$	−22.2275	−0.773861
$826$	0	0
$827$	11.4463	0.398026	0.199013	−	0.979997i	$-0.436226\pi$
$827$	11.4463	0.398026	0.199013	+	0.979997i	$0.436226\pi$
$828$	4.21735	0.146563
$829$	26.5666	0.922695	0.461347	−	0.887220i	$-0.347366\pi$
$829$	26.5666	0.922695	0.461347	+	0.887220i	$0.347366\pi$
$830$	118.967	4.12942
$831$	−4.28958	−0.148804
$832$	−67.4961	−2.34001
$833$	0	0
$834$	−25.1050	−0.869315
$835$	63.4721	2.19654
$836$	16.5026	0.570753
$837$	17.9431	0.620204
$838$	29.2680	1.01105
$839$	9.43889	0.325867	0.162933	−	0.986637i	$-0.447904\pi$
$839$	9.43889	0.325867	0.162933	+	0.986637i	$0.447904\pi$
$840$	0	0
$841$	−25.6568	−0.884716
$842$	−7.93698	−0.273526
$843$	4.35616	0.150034
$844$	−5.55305	−0.191144
$845$	86.4767	2.97489
$846$	−62.7651	−2.15791
$847$	0	0
$848$	21.5866	0.741286
$849$	−11.0210	−0.378239
$850$	−107.339	−3.68168
$851$	2.64788	0.0907683
$852$	−22.7209	−0.778404
$853$	−10.2552	−0.351132	−0.175566	−	0.984468i	$-0.556176\pi$
$853$	−10.2552	−0.351132	−0.175566	+	0.984468i	$0.556176\pi$
$854$	0	0
$855$	9.79153	0.334863
$856$	2.72750	0.0932242
$857$	−50.9286	−1.73969	−0.869845	−	0.493326i	$-0.835781\pi$
$857$	−50.9286	−1.73969	−0.869845	+	0.493326i	$0.835781\pi$
$858$	−37.5631	−1.28238
$859$	−25.4105	−0.866995	−0.433498	−	0.901155i	$-0.642721\pi$
$859$	−25.4105	−0.866995	−0.433498	+	0.901155i	$0.642721\pi$
$860$	30.2831	1.03264
$861$	0	0
$862$	18.1825	0.619299
$863$	2.37082	0.0807035	0.0403518	−	0.999186i	$-0.487152\pi$
$863$	2.37082	0.0807035	0.0403518	+	0.999186i	$0.487152\pi$
$864$	9.62623	0.327491
$865$	−28.7624	−0.977952
$866$	41.7254	1.41789
$867$	6.42552	0.218222
$868$	0	0
$869$	0.255699	0.00867401
$870$	9.27406	0.314420
$871$	−56.9230	−1.92876
$872$	−5.19187	−0.175819
$873$	4.65718	0.157622
$874$	1.02838	0.0347856
$875$	0	0
$876$	−7.34057	−0.248015
$877$	−36.7436	−1.24074	−0.620372	−	0.784308i	$-0.713018\pi$
$877$	−36.7436	−1.24074	−0.620372	+	0.784308i	$0.713018\pi$
$878$	8.01451	0.270477
$879$	16.9560	0.571910
$880$	−34.7009	−1.16977
$881$	15.5620	0.524296	0.262148	−	0.965028i	$-0.415569\pi$
$881$	15.5620	0.524296	0.262148	+	0.965028i	$0.415569\pi$
$882$	0	0
$883$	44.6059	1.50111	0.750555	−	0.660808i	$-0.229786\pi$
$883$	44.6059	1.50111	0.750555	+	0.660808i	$0.229786\pi$
$884$	−117.342	−3.94662
$885$	2.78722	0.0936914
$886$	−23.6272	−0.793772
$887$	43.6097	1.46427	0.732135	−	0.681160i	$-0.238524\pi$
$887$	43.6097	1.46427	0.732135	+	0.681160i	$0.238524\pi$
$888$	−14.0684	−0.472105
$889$	0	0
$890$	91.7408	3.07516
$891$	−27.4188	−0.918566
$892$	1.07108	0.0358624
$893$	−9.90053	−0.331309
$894$	−1.32379	−0.0442740
$895$	−63.0246	−2.10668
$896$	0	0
$897$	−1.51422	−0.0505584
$898$	34.7902	1.16097
$899$	−9.99046	−0.333200
$900$	−83.0664	−2.76888
$901$	−54.5784	−1.81827
$902$	13.0268	0.433744
$903$	0	0
$904$	−0.0791402	−0.00263216
$905$	−76.4493	−2.54126
$906$	−21.4431	−0.712399
$907$	14.4173	0.478718	0.239359	−	0.970931i	$-0.423063\pi$
$907$	14.4173	0.478718	0.239359	+	0.970931i	$0.423063\pi$
$908$	27.0877	0.898936
$909$	−23.0247	−0.763682
$910$	0	0
$911$	39.6275	1.31292	0.656459	−	0.754362i	$-0.272053\pi$
$911$	39.6275	1.31292	0.656459	+	0.754362i	$0.272053\pi$
$912$	−1.21525	−0.0402408
$913$	−61.2556	−2.02726
$914$	2.26123	0.0747949
$915$	16.8887	0.558325
$916$	−32.9684	−1.08931
$917$	0	0
$918$	41.4157	1.36692
$919$	2.33795	0.0771218	0.0385609	−	0.999256i	$-0.487723\pi$
$919$	2.33795	0.0771218	0.0385609	+	0.999256i	$0.487723\pi$
$920$	−6.28937	−0.207355
$921$	13.8501	0.456377
$922$	−29.1652	−0.960506
$923$	−64.6409	−2.12768
$924$	0	0
$925$	−52.1536	−1.71480
$926$	−10.9716	−0.360550
$927$	10.0458	0.329947
$928$	−5.35975	−0.175942
$929$	−29.6203	−0.971809	−0.485905	−	0.874012i	$-0.661510\pi$
$929$	−29.6203	−0.971809	−0.485905	+	0.874012i	$0.661510\pi$
$930$	−27.7133	−0.908755
$931$	0	0
$932$	62.8360	2.05826
$933$	3.00806	0.0984794
$934$	−30.7654	−1.00667
$935$	87.7360	2.86928
$936$	−63.7483	−2.08368
$937$	−17.8133	−0.581936	−0.290968	−	0.956733i	$-0.593977\pi$
$937$	−17.8133	−0.581936	−0.290968	+	0.956733i	$0.593977\pi$
$938$	0	0
$939$	−2.19997	−0.0717934
$940$	133.333	4.34885
$941$	41.0626	1.33860	0.669301	−	0.742991i	$-0.266594\pi$
$941$	41.0626	1.33860	0.669301	+	0.742991i	$0.266594\pi$
$942$	21.2646	0.692839
$943$	0.525128	0.0171005
$944$	2.74106	0.0892138
$945$	0	0
$946$	−24.1042	−0.783695
$947$	−43.3894	−1.40997	−0.704983	−	0.709224i	$-0.749046\pi$
$947$	−43.3894	−1.40997	−0.704983	+	0.709224i	$0.749046\pi$
$948$	−0.120596	−0.00391677
$949$	−20.8839	−0.677921
$950$	−20.2554	−0.657172
$951$	1.98942	0.0645113
$952$	0	0
$953$	24.8507	0.804993	0.402496	−	0.915422i	$-0.368143\pi$
$953$	24.8507	0.804993	0.402496	+	0.915422i	$0.368143\pi$
$954$	−65.2928	−2.11393
$955$	−82.8014	−2.67939
$956$	18.1443	0.586829
$957$	−4.77515	−0.154359
$958$	−4.52190	−0.146096
$959$	0	0
$960$	−23.8017	−0.768196
$961$	−1.14593	−0.0369656
$962$	−88.1364	−2.84163
$963$	−1.83489	−0.0591284
$964$	−11.3683	−0.366148
$965$	−24.8093	−0.798639
$966$	0	0
$967$	12.6790	0.407729	0.203864	−	0.978999i	$-0.434650\pi$
$967$	12.6790	0.407729	0.203864	+	0.978999i	$0.434650\pi$
$968$	36.7768	1.18205
$969$	3.07256	0.0987050
$970$	−15.2939	−0.491058
$971$	−42.6022	−1.36717	−0.683585	−	0.729871i	$-0.739580\pi$
$971$	−42.6022	−1.36717	−0.683585	+	0.729871i	$0.739580\pi$
$972$	49.0269	1.57254
$973$	0	0
$974$	51.6290	1.65430
$975$	29.8246	0.955153
$976$	16.6090	0.531642
$977$	−5.87740	−0.188035	−0.0940173	−	0.995571i	$-0.529971\pi$
$977$	−5.87740	−0.188035	−0.0940173	+	0.995571i	$0.529971\pi$
$978$	24.7148	0.790291
$979$	−47.2367	−1.50969
$980$	0	0
$981$	3.49275	0.111515
$982$	11.1980	0.357342
$983$	11.8280	0.377254	0.188627	−	0.982049i	$-0.439596\pi$
$983$	11.8280	0.377254	0.188627	+	0.982049i	$0.439596\pi$
$984$	−2.79004	−0.0889434
$985$	−100.915	−3.21541
$986$	−23.0597	−0.734370
$987$	0	0
$988$	−22.1430	−0.704463
$989$	−0.971675	−0.0308975
$990$	104.960	3.33584
$991$	−37.3818	−1.18747	−0.593737	−	0.804659i	$-0.702348\pi$
$991$	−37.3818	−1.18747	−0.593737	+	0.804659i	$0.702348\pi$
$992$	16.0163	0.508519
$993$	9.54209	0.302809
$994$	0	0
$995$	−82.7636	−2.62378
$996$	28.8900	0.915416
$997$	38.8366	1.22997	0.614984	−	0.788539i	$-0.289162\pi$
$997$	38.8366	1.22997	0.614984	+	0.788539i	$0.289162\pi$
$998$	45.8659	1.45186
$999$	20.1230	0.636665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.m.1.4	yes	4
3.2	odd	2		8379.2.a.bu.1.1		4
7.2	even	3		931.2.f.n.704.1		8
7.3	odd	6		931.2.f.o.324.1		8
7.4	even	3		931.2.f.n.324.1		8
7.5	odd	6		931.2.f.o.704.1		8
7.6	odd	2		931.2.a.l.1.4	✓	4
21.20	even	2		8379.2.a.bv.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.l.1.4	✓	4	7.6	odd	2
931.2.a.m.1.4	yes	4	1.1	even	1	trivial
931.2.f.n.324.1		8	7.4	even	3
931.2.f.n.704.1		8	7.2	even	3
931.2.f.o.324.1		8	7.3	odd	6
931.2.f.o.704.1		8	7.5	odd	6
8379.2.a.bu.1.1		4	3.2	odd	2
8379.2.a.bv.1.1		4	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q+2.37988 q^{2} +0.579810 q^{3} +3.66382 q^{4} +3.67575 q^{5} +1.37988 q^{6} +3.95969 q^{8} -2.66382 q^{9} +O(q^{10})\)	\(q+2.37988 q^{2} +0.579810 q^{3} +3.66382 q^{4} +3.67575 q^{5} +1.37988 q^{6} +3.95969 q^{8} -2.66382 q^{9} +8.74783 q^{10} -4.50420 q^{11} +2.12432 q^{12} +6.04370 q^{13} +2.13124 q^{15} +2.09594 q^{16} -5.29926 q^{17} -6.33957 q^{18} -1.00000 q^{19} +13.4673 q^{20} -10.7194 q^{22} -0.432116 q^{23} +2.29587 q^{24} +8.51111 q^{25} +14.3833 q^{26} -3.28394 q^{27} +1.82845 q^{29} +5.07208 q^{30} -5.46389 q^{31} -2.93130 q^{32} -2.61158 q^{33} -12.6116 q^{34} -9.75976 q^{36} -6.12771 q^{37} -2.37988 q^{38} +3.50420 q^{39} +14.5548 q^{40} -1.21525 q^{41} +2.24864 q^{43} -16.5026 q^{44} -9.79153 q^{45} -1.02838 q^{46} +9.90053 q^{47} +1.21525 q^{48} +20.2554 q^{50} -3.07256 q^{51} +22.1430 q^{52} +10.2993 q^{53} -7.81538 q^{54} -16.5563 q^{55} -0.579810 q^{57} +4.35149 q^{58} +1.30780 q^{59} +7.80847 q^{60} +7.92439 q^{61} -13.0034 q^{62} -11.1680 q^{64} +22.2151 q^{65} -6.21525 q^{66} -9.41856 q^{67} -19.4155 q^{68} -0.250546 q^{69} -10.6956 q^{71} -10.5479 q^{72} -3.45549 q^{73} -14.5832 q^{74} +4.93483 q^{75} -3.66382 q^{76} +8.33957 q^{78} -0.0567691 q^{79} +7.70413 q^{80} +6.08740 q^{81} -2.89214 q^{82} +13.5997 q^{83} -19.4787 q^{85} +5.35149 q^{86} +1.06016 q^{87} -17.8352 q^{88} +10.4873 q^{89} -23.3026 q^{90} -1.58320 q^{92} -3.16802 q^{93} +23.5621 q^{94} -3.67575 q^{95} -1.69960 q^{96} -1.74831 q^{97} +11.9984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^8 + 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{8} + 2 q^{9} + 10 q^{10} - 6 q^{11} + 6 q^{12} + 2 q^{13} + 4 q^{15} + 2 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} - 14 q^{22} - 8 q^{23} + 12 q^{24} + 20 q^{25} + 16 q^{26} - 10 q^{27} + 2 q^{29} + 2 q^{30} + 2 q^{32} + 18 q^{33} - 22 q^{34} - 20 q^{36} + 10 q^{37} + 2 q^{39} + 22 q^{40} + 12 q^{41} + 4 q^{43} - 14 q^{44} + 8 q^{45} - 8 q^{46} + 16 q^{47} - 12 q^{48} + 12 q^{50} - 10 q^{51} + 28 q^{52} + 12 q^{53} + 4 q^{54} - 8 q^{55} - 2 q^{57} + 4 q^{58} + 14 q^{59} - 2 q^{60} + 20 q^{61} - 20 q^{62} - 20 q^{64} + 10 q^{65} - 8 q^{66} + 2 q^{67} - 24 q^{68} + 14 q^{69} - 2 q^{71} - 8 q^{72} - 16 q^{73} - 26 q^{74} + 36 q^{75} - 2 q^{76} + 14 q^{78} - 8 q^{79} + 28 q^{80} - 20 q^{81} - 12 q^{82} + 20 q^{83} - 14 q^{85} + 8 q^{86} - 20 q^{87} - 2 q^{88} + 16 q^{89} - 32 q^{90} + 26 q^{92} + 12 q^{93} + 10 q^{94} - 8 q^{95} - 12 q^{96} + 2 q^{97} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^8 + 2 * q^9 + 10 * q^10 - 6 * q^11 + 6 * q^12 + 2 * q^13 + 4 * q^15 + 2 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 - 14 * q^22 - 8 * q^23 + 12 * q^24 + 20 * q^25 + 16 * q^26 - 10 * q^27 + 2 * q^29 + 2 * q^30 + 2 * q^32 + 18 * q^33 - 22 * q^34 - 20 * q^36 + 10 * q^37 + 2 * q^39 + 22 * q^40 + 12 * q^41 + 4 * q^43 - 14 * q^44 + 8 * q^45 - 8 * q^46 + 16 * q^47 - 12 * q^48 + 12 * q^50 - 10 * q^51 + 28 * q^52 + 12 * q^53 + 4 * q^54 - 8 * q^55 - 2 * q^57 + 4 * q^58 + 14 * q^59 - 2 * q^60 + 20 * q^61 - 20 * q^62 - 20 * q^64 + 10 * q^65 - 8 * q^66 + 2 * q^67 - 24 * q^68 + 14 * q^69 - 2 * q^71 - 8 * q^72 - 16 * q^73 - 26 * q^74 + 36 * q^75 - 2 * q^76 + 14 * q^78 - 8 * q^79 + 28 * q^80 - 20 * q^81 - 12 * q^82 + 20 * q^83 - 14 * q^85 + 8 * q^86 - 20 * q^87 - 2 * q^88 + 16 * q^89 - 32 * q^90 + 26 * q^92 + 12 * q^93 + 10 * q^94 - 8 * q^95 - 12 * q^96 + 2 * q^97 + 8 * q^99

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