LMFDB - Embedded newform 1175.2.a.j.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1175,2,Mod(1,1175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, 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("1175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1175 = 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1175.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:	$9.38242223750$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 8x^{9} + 44x^{8} + 8x^{7} - 156x^{6} + 48x^{5} + 208x^{4} - 96x^{3} - 86x^{2} + 41x + 4 $ x^11 - 4x^10 - 8x^9 + 44x^8 + 8x^7 - 156x^6 + 48x^5 + 208x^4 - 96x^3 - 86x^2 + 41x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 235)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.719688$ of defining polynomial
Character	$\chi$	$=$	1175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.719688 q^{2} -0.189045 q^{3} -1.48205 q^{4} -0.136054 q^{6} +1.87262 q^{7} -2.50599 q^{8} -2.96426 q^{9} +O(q^{10})$	\(q+0.719688 q^{2} -0.189045 q^{3} -1.48205 q^{4} -0.136054 q^{6} +1.87262 q^{7} -2.50599 q^{8} -2.96426 q^{9} +3.72364 q^{11} +0.280174 q^{12} -2.09265 q^{13} +1.34770 q^{14} +1.16057 q^{16} -0.359855 q^{17} -2.13334 q^{18} +2.77894 q^{19} -0.354010 q^{21} +2.67986 q^{22} +8.53731 q^{23} +0.473745 q^{24} -1.50605 q^{26} +1.12752 q^{27} -2.77532 q^{28} +6.08232 q^{29} -1.14155 q^{31} +5.84723 q^{32} -0.703936 q^{33} -0.258983 q^{34} +4.39318 q^{36} +3.17523 q^{37} +1.99997 q^{38} +0.395605 q^{39} -9.70789 q^{41} -0.254777 q^{42} +8.96725 q^{43} -5.51862 q^{44} +6.14420 q^{46} -1.00000 q^{47} -0.219400 q^{48} -3.49329 q^{49} +0.0680288 q^{51} +3.10141 q^{52} +13.7551 q^{53} +0.811459 q^{54} -4.69277 q^{56} -0.525344 q^{57} +4.37737 q^{58} +6.52974 q^{59} -3.29397 q^{61} -0.821560 q^{62} -5.55094 q^{63} +1.88704 q^{64} -0.506614 q^{66} +2.82523 q^{67} +0.533323 q^{68} -1.61394 q^{69} +1.66645 q^{71} +7.42841 q^{72} -7.80026 q^{73} +2.28518 q^{74} -4.11852 q^{76} +6.97297 q^{77} +0.284712 q^{78} +10.0962 q^{79} +8.67963 q^{81} -6.98665 q^{82} +7.67806 q^{83} +0.524661 q^{84} +6.45362 q^{86} -1.14983 q^{87} -9.33140 q^{88} -15.7015 q^{89} -3.91874 q^{91} -12.6527 q^{92} +0.215805 q^{93} -0.719688 q^{94} -1.10539 q^{96} +11.2020 q^{97} -2.51408 q^{98} -11.0378 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 4 q^{2} + 4 q^{3} + 10 q^{4} - 2 q^{6} + 12 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 11 * q + 4 * q^2 + 4 * q^3 + 10 * q^4 - 2 * q^6 + 12 * q^7 + 12 * q^8 + 9 * q^9	$ 11 q + 4 q^{2} + 4 q^{3} + 10 q^{4} - 2 q^{6} + 12 q^{7} + 12 q^{8} + 9 q^{9} + 12 q^{12} + 19 q^{13} + 12 q^{16} + 16 q^{17} - 10 q^{18} - 6 q^{21} + 22 q^{22} + 3 q^{23} - 12 q^{24} + 6 q^{26} + 16 q^{27} + 18 q^{28} + 4 q^{29} + 2 q^{31} + 28 q^{32} + 18 q^{33} - 16 q^{34} - 8 q^{36} + 40 q^{37} - 14 q^{38} - 10 q^{39} + 4 q^{41} + 16 q^{42} + 23 q^{43} + 24 q^{44} - 16 q^{46} - 11 q^{47} - 18 q^{48} + 5 q^{49} + 12 q^{51} + 46 q^{52} + 16 q^{53} + 26 q^{56} + 42 q^{57} + 16 q^{58} + 7 q^{59} - 7 q^{61} + 14 q^{63} + 24 q^{64} + 12 q^{66} + 32 q^{67} - 58 q^{68} - 2 q^{69} - 17 q^{71} + 57 q^{73} - 16 q^{74} - 10 q^{76} + 8 q^{77} - 22 q^{78} - 13 q^{79} - 25 q^{81} + 12 q^{82} + 8 q^{83} - 4 q^{84} - 6 q^{86} - 10 q^{87} + 26 q^{88} - 37 q^{89} + 32 q^{91} + 4 q^{92} - 10 q^{93} - 4 q^{94} - 6 q^{96} + 32 q^{97} - 20 q^{98} - 8 q^{99}+O(q^{100}) $ 11 * q + 4 * q^2 + 4 * q^3 + 10 * q^4 - 2 * q^6 + 12 * q^7 + 12 * q^8 + 9 * q^9 + 12 * q^12 + 19 * q^13 + 12 * q^16 + 16 * q^17 - 10 * q^18 - 6 * q^21 + 22 * q^22 + 3 * q^23 - 12 * q^24 + 6 * q^26 + 16 * q^27 + 18 * q^28 + 4 * q^29 + 2 * q^31 + 28 * q^32 + 18 * q^33 - 16 * q^34 - 8 * q^36 + 40 * q^37 - 14 * q^38 - 10 * q^39 + 4 * q^41 + 16 * q^42 + 23 * q^43 + 24 * q^44 - 16 * q^46 - 11 * q^47 - 18 * q^48 + 5 * q^49 + 12 * q^51 + 46 * q^52 + 16 * q^53 + 26 * q^56 + 42 * q^57 + 16 * q^58 + 7 * q^59 - 7 * q^61 + 14 * q^63 + 24 * q^64 + 12 * q^66 + 32 * q^67 - 58 * q^68 - 2 * q^69 - 17 * q^71 + 57 * q^73 - 16 * q^74 - 10 * q^76 + 8 * q^77 - 22 * q^78 - 13 * q^79 - 25 * q^81 + 12 * q^82 + 8 * q^83 - 4 * q^84 - 6 * q^86 - 10 * q^87 + 26 * q^88 - 37 * q^89 + 32 * q^91 + 4 * q^92 - 10 * q^93 - 4 * q^94 - 6 * q^96 + 32 * q^97 - 20 * q^98 - 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 $

$2$	0.719688	0.508896	0.254448	−	0.967086i	$-0.418106\pi$
$2$	0.719688	0.508896	0.254448	+	0.967086i	$0.418106\pi$
$3$	−0.189045	−0.109145	−0.0545727	−	0.998510i	$-0.517380\pi$
$3$	−0.189045	−0.109145	−0.0545727	+	0.998510i	$0.517380\pi$
$4$	−1.48205	−0.741025
$5$	0	0
$5$	0	0
$6$	−0.136054	−0.0555436
$7$	1.87262	0.707785	0.353892	−	0.935286i	$-0.384858\pi$
$7$	1.87262	0.707785	0.353892	+	0.935286i	$0.384858\pi$
$8$	−2.50599	−0.886001
$9$	−2.96426	−0.988087
$10$	0	0
$11$	3.72364	1.12272	0.561360	−	0.827572i	$-0.310278\pi$
$11$	3.72364	1.12272	0.561360	+	0.827572i	$0.310278\pi$
$12$	0.280174	0.0808794
$13$	−2.09265	−0.580396	−0.290198	−	0.956967i	$-0.593721\pi$
$13$	−2.09265	−0.580396	−0.290198	+	0.956967i	$0.593721\pi$
$14$	1.34770	0.360189
$15$	0	0
$16$	1.16057	0.290142
$17$	−0.359855	−0.0872776	−0.0436388	−	0.999047i	$-0.513895\pi$
$17$	−0.359855	−0.0872776	−0.0436388	+	0.999047i	$0.513895\pi$
$18$	−2.13334	−0.502834
$19$	2.77894	0.637531	0.318766	−	0.947834i	$-0.396732\pi$
$19$	2.77894	0.637531	0.318766	+	0.947834i	$0.396732\pi$
$20$	0	0
$21$	−0.354010	−0.0772514
$22$	2.67986	0.571348
$23$	8.53731	1.78015	0.890076	−	0.455812i	$-0.150651\pi$
$23$	8.53731	1.78015	0.890076	+	0.455812i	$0.150651\pi$
$24$	0.473745	0.0967029
$25$	0	0
$26$	−1.50605	−0.295361
$27$	1.12752	0.216990
$28$	−2.77532	−0.524486
$29$	6.08232	1.12946	0.564729	−	0.825276i	$-0.308981\pi$
$29$	6.08232	1.12946	0.564729	+	0.825276i	$0.308981\pi$
$30$	0	0
$31$	−1.14155	−0.205028	−0.102514	−	0.994732i	$-0.532689\pi$
$31$	−1.14155	−0.205028	−0.102514	+	0.994732i	$0.532689\pi$
$32$	5.84723	1.03365
$33$	−0.703936	−0.122540
$34$	−0.258983	−0.0444153
$35$	0	0
$36$	4.39318	0.732197
$37$	3.17523	0.522005	0.261003	−	0.965338i	$-0.415947\pi$
$37$	3.17523	0.522005	0.261003	+	0.965338i	$0.415947\pi$
$38$	1.99997	0.324437
$39$	0.395605	0.0633475
$40$	0	0
$41$	−9.70789	−1.51612	−0.758059	−	0.652187i	$-0.773852\pi$
$41$	−9.70789	−1.51612	−0.758059	+	0.652187i	$0.773852\pi$
$42$	−0.254777	−0.0393129
$43$	8.96725	1.36749	0.683747	−	0.729719i	$-0.260349\pi$
$43$	8.96725	1.36749	0.683747	+	0.729719i	$0.260349\pi$
$44$	−5.51862	−0.831963
$45$	0	0
$46$	6.14420	0.905913
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−0.219400	−0.0316676
$49$	−3.49329	−0.499041
$50$	0	0
$51$	0.0680288	0.00952594
$52$	3.10141	0.430088
$53$	13.7551	1.88940	0.944701	−	0.327933i	$-0.106352\pi$
$53$	13.7551	1.88940	0.944701	+	0.327933i	$0.106352\pi$
$54$	0.811459	0.110426
$55$	0	0
$56$	−4.69277	−0.627098
$57$	−0.525344	−0.0695836
$58$	4.37737	0.574777
$59$	6.52974	0.850099	0.425050	−	0.905170i	$-0.360257\pi$
$59$	6.52974	0.850099	0.425050	+	0.905170i	$0.360257\pi$
$60$	0	0
$61$	−3.29397	−0.421750	−0.210875	−	0.977513i	$-0.567631\pi$
$61$	−3.29397	−0.421750	−0.210875	+	0.977513i	$0.567631\pi$
$62$	−0.821560	−0.104338
$63$	−5.55094	−0.699353
$64$	1.88704	0.235880
$65$	0	0
$66$	−0.506614	−0.0623599
$67$	2.82523	0.345157	0.172579	−	0.984996i	$-0.444790\pi$
$67$	2.82523	0.345157	0.172579	+	0.984996i	$0.444790\pi$
$68$	0.533323	0.0646749
$69$	−1.61394	−0.194295
$70$	0	0
$71$	1.66645	0.197771	0.0988854	−	0.995099i	$-0.468472\pi$
$71$	1.66645	0.197771	0.0988854	+	0.995099i	$0.468472\pi$
$72$	7.42841	0.875446
$73$	−7.80026	−0.912951	−0.456476	−	0.889736i	$-0.650888\pi$
$73$	−7.80026	−0.912951	−0.456476	+	0.889736i	$0.650888\pi$
$74$	2.28518	0.265647
$75$	0	0
$76$	−4.11852	−0.472426
$77$	6.97297	0.794644
$78$	0.284712	0.0322373
$79$	10.0962	1.13592	0.567958	−	0.823058i	$-0.307734\pi$
$79$	10.0962	1.13592	0.567958	+	0.823058i	$0.307734\pi$
$80$	0	0
$81$	8.67963	0.964404
$82$	−6.98665	−0.771546
$83$	7.67806	0.842776	0.421388	−	0.906880i	$-0.361543\pi$
$83$	7.67806	0.842776	0.421388	+	0.906880i	$0.361543\pi$
$84$	0.524661	0.0572452
$85$	0	0
$86$	6.45362	0.695912
$87$	−1.14983	−0.123275
$88$	−9.33140	−0.994731
$89$	−15.7015	−1.66436	−0.832178	−	0.554509i	$-0.812906\pi$
$89$	−15.7015	−1.66436	−0.832178	+	0.554509i	$0.812906\pi$
$90$	0	0
$91$	−3.91874	−0.410796
$92$	−12.6527	−1.31914
$93$	0.215805	0.0223779
$94$	−0.719688	−0.0742302
$95$	0	0
$96$	−1.10539	−0.112818
$97$	11.2020	1.13739	0.568695	−	0.822548i	$-0.307448\pi$
$97$	11.2020	1.13739	0.568695	+	0.822548i	$0.307448\pi$
$98$	−2.51408	−0.253960
$99$	−11.0378	−1.10934
$100$	0	0
$101$	−1.57057	−0.156277	−0.0781387	−	0.996942i	$-0.524898\pi$
$101$	−1.57057	−0.156277	−0.0781387	+	0.996942i	$0.524898\pi$
$102$	0.0489595	0.00484772
$103$	11.8195	1.16461	0.582307	−	0.812969i	$-0.302150\pi$
$103$	11.8195	1.16461	0.582307	+	0.812969i	$0.302150\pi$
$104$	5.24415	0.514232
$105$	0	0
$106$	9.89935	0.961510
$107$	15.2839	1.47755	0.738775	−	0.673952i	$-0.235405\pi$
$107$	15.2839	1.47755	0.738775	+	0.673952i	$0.235405\pi$
$108$	−1.67103	−0.160795
$109$	−4.38991	−0.420477	−0.210238	−	0.977650i	$-0.567424\pi$
$109$	−4.38991	−0.420477	−0.210238	+	0.977650i	$0.567424\pi$
$110$	0	0
$111$	−0.600263	−0.0569744
$112$	2.17331	0.205358
$113$	−14.8434	−1.39635	−0.698176	−	0.715926i	$-0.746005\pi$
$113$	−14.8434	−1.39635	−0.698176	+	0.715926i	$0.746005\pi$
$114$	−0.378084	−0.0354108
$115$	0	0
$116$	−9.01430	−0.836957
$117$	6.20316	0.573482
$118$	4.69937	0.432612
$119$	−0.673872	−0.0617738
$120$	0	0
$121$	2.86549	0.260499
$122$	−2.37063	−0.214627
$123$	1.83523	0.165477
$124$	1.69183	0.151931
$125$	0	0
$126$	−3.99495	−0.355898
$127$	−9.08048	−0.805762	−0.402881	−	0.915252i	$-0.631991\pi$
$127$	−9.08048	−0.805762	−0.402881	+	0.915252i	$0.631991\pi$
$128$	−10.3364	−0.913615
$129$	−1.69522	−0.149255
$130$	0	0
$131$	−12.9046	−1.12748	−0.563741	−	0.825952i	$-0.690638\pi$
$131$	−12.9046	−1.12748	−0.563741	+	0.825952i	$0.690638\pi$
$132$	1.04327	0.0908048
$133$	5.20390	0.451235
$134$	2.03329	0.175649
$135$	0	0
$136$	0.901792	0.0773281
$137$	−6.04331	−0.516315	−0.258158	−	0.966103i	$-0.583115\pi$
$137$	−6.04331	−0.516315	−0.258158	+	0.966103i	$0.583115\pi$
$138$	−1.16153	−0.0988762
$139$	1.81245	0.153730	0.0768651	−	0.997042i	$-0.475509\pi$
$139$	1.81245	0.153730	0.0768651	+	0.997042i	$0.475509\pi$
$140$	0	0
$141$	0.189045	0.0159205
$142$	1.19932	0.100645
$143$	−7.79227	−0.651622
$144$	−3.44023	−0.286686
$145$	0	0
$146$	−5.61375	−0.464597
$147$	0.660389	0.0544680
$148$	−4.70585	−0.386819
$149$	7.12063	0.583345	0.291672	−	0.956518i	$-0.405788\pi$
$149$	7.12063	0.583345	0.291672	+	0.956518i	$0.405788\pi$
$150$	0	0
$151$	8.20340	0.667583	0.333792	−	0.942647i	$-0.391672\pi$
$151$	8.20340	0.667583	0.333792	+	0.942647i	$0.391672\pi$
$152$	−6.96398	−0.564853
$153$	1.06670	0.0862379
$154$	5.01836	0.404391
$155$	0	0
$156$	−0.586306	−0.0469421
$157$	1.27885	0.102063	0.0510316	−	0.998697i	$-0.483749\pi$
$157$	1.27885	0.102063	0.0510316	+	0.998697i	$0.483749\pi$
$158$	7.26614	0.578063
$159$	−2.60033	−0.206219
$160$	0	0
$161$	15.9872	1.25996
$162$	6.24663	0.490782
$163$	1.12747	0.0883103	0.0441551	−	0.999025i	$-0.485940\pi$
$163$	1.12747	0.0883103	0.0441551	+	0.999025i	$0.485940\pi$
$164$	14.3876	1.12348
$165$	0	0
$166$	5.52580	0.428886
$167$	−1.00253	−0.0775781	−0.0387890	−	0.999247i	$-0.512350\pi$
$167$	−1.00253	−0.0775781	−0.0387890	+	0.999247i	$0.512350\pi$
$168$	0.887146	0.0684448
$169$	−8.62082	−0.663140
$170$	0	0
$171$	−8.23749	−0.629937
$172$	−13.2899	−1.01335
$173$	−18.6315	−1.41653	−0.708264	−	0.705947i	$-0.750521\pi$
$173$	−18.6315	−1.41653	−0.708264	+	0.705947i	$0.750521\pi$
$174$	−0.827522	−0.0627343
$175$	0	0
$176$	4.32154	0.325748
$177$	−1.23442	−0.0927843
$178$	−11.3002	−0.846984
$179$	−11.5646	−0.864381	−0.432190	−	0.901782i	$-0.642259\pi$
$179$	−11.5646	−0.864381	−0.432190	+	0.901782i	$0.642259\pi$
$180$	0	0
$181$	−17.0785	−1.26943	−0.634717	−	0.772745i	$-0.718883\pi$
$181$	−17.0785	−1.26943	−0.634717	+	0.772745i	$0.718883\pi$
$182$	−2.82027	−0.209052
$183$	0.622709	0.0460320
$184$	−21.3944	−1.57722
$185$	0	0
$186$	0.155312	0.0113880
$187$	−1.33997	−0.0979883
$188$	1.48205	0.108090
$189$	2.11141	0.153583
$190$	0	0
$191$	−8.26692	−0.598174	−0.299087	−	0.954226i	$-0.596682\pi$
$191$	−8.26692	−0.598174	−0.299087	+	0.954226i	$0.596682\pi$
$192$	−0.356736	−0.0257452
$193$	11.8348	0.851888	0.425944	−	0.904749i	$-0.359942\pi$
$193$	11.8348	0.851888	0.425944	+	0.904749i	$0.359942\pi$
$194$	8.06195	0.578814
$195$	0	0
$196$	5.17722	0.369801
$197$	−2.30681	−0.164353	−0.0821766	−	0.996618i	$-0.526187\pi$
$197$	−2.30681	−0.164353	−0.0821766	+	0.996618i	$0.526187\pi$
$198$	−7.94380	−0.564541
$199$	−17.1512	−1.21582	−0.607908	−	0.794007i	$-0.707991\pi$
$199$	−17.1512	−1.21582	−0.607908	+	0.794007i	$0.707991\pi$
$200$	0	0
$201$	−0.534097	−0.0376723
$202$	−1.13032	−0.0795290
$203$	11.3899	0.799414
$204$	−0.100822	−0.00705896
$205$	0	0
$206$	8.50638	0.592668
$207$	−25.3068	−1.75895
$208$	−2.42866	−0.168397
$209$	10.3478	0.715769
$210$	0	0
$211$	−21.3945	−1.47286	−0.736429	−	0.676515i	$-0.763489\pi$
$211$	−21.3945	−1.47286	−0.736429	+	0.676515i	$0.763489\pi$
$212$	−20.3857	−1.40009
$213$	−0.315034	−0.0215858
$214$	10.9996	0.751920
$215$	0	0
$216$	−2.82554	−0.192254
$217$	−2.13769	−0.145116
$218$	−3.15936	−0.213979
$219$	1.47460	0.0996443
$220$	0	0
$221$	0.753050	0.0506556
$222$	−0.432002	−0.0289941
$223$	4.58013	0.306708	0.153354	−	0.988171i	$-0.450992\pi$
$223$	4.58013	0.306708	0.153354	+	0.988171i	$0.450992\pi$
$224$	10.9496	0.731604
$225$	0	0
$226$	−10.6826	−0.710598
$227$	−13.9190	−0.923839	−0.461920	−	0.886922i	$-0.652839\pi$
$227$	−13.9190	−0.923839	−0.461920	+	0.886922i	$0.652839\pi$
$228$	0.778586	0.0515631
$229$	−13.2321	−0.874401	−0.437200	−	0.899364i	$-0.644030\pi$
$229$	−13.2321	−0.874401	−0.437200	+	0.899364i	$0.644030\pi$
$230$	0	0
$231$	−1.31821	−0.0867316
$232$	−15.2422	−1.00070
$233$	−4.65252	−0.304797	−0.152398	−	0.988319i	$-0.548700\pi$
$233$	−4.65252	−0.304797	−0.152398	+	0.988319i	$0.548700\pi$
$234$	4.46434	0.291843
$235$	0	0
$236$	−9.67739	−0.629944
$237$	−1.90865	−0.123980
$238$	−0.484978	−0.0314364
$239$	27.2088	1.75999	0.879996	−	0.474982i	$-0.157545\pi$
$239$	27.2088	1.75999	0.879996	+	0.474982i	$0.157545\pi$
$240$	0	0
$241$	27.8445	1.79362	0.896810	−	0.442416i	$-0.145879\pi$
$241$	27.8445	1.79362	0.896810	+	0.442416i	$0.145879\pi$
$242$	2.06226	0.132567
$243$	−5.02339	−0.322251
$244$	4.88183	0.312527
$245$	0	0
$246$	1.32079	0.0842107
$247$	−5.81533	−0.370021
$248$	2.86071	0.181655
$249$	−1.45150	−0.0919851
$250$	0	0
$251$	11.6307	0.734126	0.367063	−	0.930196i	$-0.380363\pi$
$251$	11.6307	0.734126	0.367063	+	0.930196i	$0.380363\pi$
$252$	8.22677	0.518238
$253$	31.7899	1.99861
$254$	−6.53511	−0.410049
$255$	0	0
$256$	−11.2130	−0.700815
$257$	12.3725	0.771773	0.385886	−	0.922546i	$-0.373896\pi$
$257$	12.3725	0.771773	0.385886	+	0.922546i	$0.373896\pi$
$258$	−1.22003	−0.0759556
$259$	5.94601	0.369467
$260$	0	0
$261$	−18.0296	−1.11600
$262$	−9.28730	−0.573771
$263$	−16.4725	−1.01574	−0.507869	−	0.861434i	$-0.669567\pi$
$263$	−16.4725	−1.01574	−0.507869	+	0.861434i	$0.669567\pi$
$264$	1.76406	0.108570
$265$	0	0
$266$	3.74518	0.229632
$267$	2.96829	0.181657
$268$	−4.18713	−0.255770
$269$	11.4078	0.695546	0.347773	−	0.937579i	$-0.386938\pi$
$269$	11.4078	0.695546	0.347773	+	0.937579i	$0.386938\pi$
$270$	0	0
$271$	25.3623	1.54065	0.770325	−	0.637651i	$-0.220094\pi$
$271$	25.3623	1.54065	0.770325	+	0.637651i	$0.220094\pi$
$272$	−0.417636	−0.0253229
$273$	0.740819	0.0448364
$274$	−4.34930	−0.262751
$275$	0	0
$276$	2.39194	0.143978
$277$	3.14505	0.188968	0.0944838	−	0.995526i	$-0.469880\pi$
$277$	3.14505	0.188968	0.0944838	+	0.995526i	$0.469880\pi$
$278$	1.30440	0.0782327
$279$	3.38385	0.202586
$280$	0	0
$281$	29.1289	1.73768	0.868841	−	0.495091i	$-0.164865\pi$
$281$	29.1289	1.73768	0.868841	+	0.495091i	$0.164865\pi$
$282$	0.136054	0.00810187
$283$	17.9149	1.06493	0.532466	−	0.846451i	$-0.321265\pi$
$283$	17.9149	1.06493	0.532466	+	0.846451i	$0.321265\pi$
$284$	−2.46976	−0.146553
$285$	0	0
$286$	−5.60800	−0.331608
$287$	−18.1792	−1.07308
$288$	−17.3327	−1.02134
$289$	−16.8705	−0.992383
$290$	0	0
$291$	−2.11768	−0.124141
$292$	11.5604	0.676519
$293$	−0.963286	−0.0562758	−0.0281379	−	0.999604i	$-0.508958\pi$
$293$	−0.963286	−0.0562758	−0.0281379	+	0.999604i	$0.508958\pi$
$294$	0.475274	0.0277185
$295$	0	0
$296$	−7.95710	−0.462497
$297$	4.19846	0.243619
$298$	5.12463	0.296862
$299$	−17.8656	−1.03319
$300$	0	0
$301$	16.7923	0.967891
$302$	5.90389	0.339731
$303$	0.296909	0.0170569
$304$	3.22514	0.184975
$305$	0	0
$306$	0.767694	0.0438862
$307$	−25.2767	−1.44262	−0.721308	−	0.692614i	$-0.756459\pi$
$307$	−25.2767	−1.44262	−0.721308	+	0.692614i	$0.756459\pi$
$308$	−10.3343	−0.588850
$309$	−2.23443	−0.127112
$310$	0	0
$311$	19.0720	1.08148	0.540738	−	0.841191i	$-0.318145\pi$
$311$	19.0720	1.08148	0.540738	+	0.841191i	$0.318145\pi$
$312$	−0.991382	−0.0561260
$313$	19.0759	1.07824	0.539118	−	0.842231i	$-0.318758\pi$
$313$	19.0759	1.07824	0.539118	+	0.842231i	$0.318758\pi$
$314$	0.920373	0.0519396
$315$	0	0
$316$	−14.9631	−0.841742
$317$	26.2139	1.47232	0.736158	−	0.676809i	$-0.236638\pi$
$317$	26.2139	1.47232	0.736158	+	0.676809i	$0.236638\pi$
$318$	−1.87142	−0.104944
$319$	22.6484	1.26807
$320$	0	0
$321$	−2.88935	−0.161268
$322$	11.5058	0.641191
$323$	−1.00001	−0.0556422
$324$	−12.8636	−0.714647
$325$	0	0
$326$	0.811427	0.0449408
$327$	0.829891	0.0458931
$328$	24.3279	1.34328
$329$	−1.87262	−0.103241
$330$	0	0
$331$	−2.80256	−0.154042	−0.0770212	−	0.997029i	$-0.524541\pi$
$331$	−2.80256	−0.154042	−0.0770212	+	0.997029i	$0.524541\pi$
$332$	−11.3793	−0.624518
$333$	−9.41223	−0.515787
$334$	−0.721509	−0.0394792
$335$	0	0
$336$	−0.410853	−0.0224139
$337$	22.8677	1.24568	0.622840	−	0.782349i	$-0.285979\pi$
$337$	22.8677	1.24568	0.622840	+	0.782349i	$0.285979\pi$
$338$	−6.20430	−0.337470
$339$	2.80608	0.152405
$340$	0	0
$341$	−4.25072	−0.230189
$342$	−5.92842	−0.320572
$343$	−19.6500	−1.06100
$344$	−22.4718	−1.21160
$345$	0	0
$346$	−13.4089	−0.720866
$347$	−32.9161	−1.76703	−0.883516	−	0.468402i	$-0.844830\pi$
$347$	−32.9161	−1.76703	−0.883516	+	0.468402i	$0.844830\pi$
$348$	1.70411	0.0913499
$349$	3.84654	0.205901	0.102950	−	0.994686i	$-0.467172\pi$
$349$	3.84654	0.205901	0.102950	+	0.994686i	$0.467172\pi$
$350$	0	0
$351$	−2.35949	−0.125940
$352$	21.7730	1.16050
$353$	−15.2984	−0.814252	−0.407126	−	0.913372i	$-0.633469\pi$
$353$	−15.2984	−0.814252	−0.407126	+	0.913372i	$0.633469\pi$
$354$	−0.888394	−0.0472176
$355$	0	0
$356$	23.2704	1.23333
$357$	0.127392	0.00674232
$358$	−8.32292	−0.439880
$359$	−9.35813	−0.493903	−0.246952	−	0.969028i	$-0.579429\pi$
$359$	−9.35813	−0.493903	−0.246952	+	0.969028i	$0.579429\pi$
$360$	0	0
$361$	−11.2775	−0.593554
$362$	−12.2912	−0.646010
$363$	−0.541707	−0.0284322
$364$	5.80777	0.304410
$365$	0	0
$366$	0.448156	0.0234255
$367$	22.7106	1.18548	0.592741	−	0.805393i	$-0.298046\pi$
$367$	22.7106	1.18548	0.592741	+	0.805393i	$0.298046\pi$
$368$	9.90813	0.516497
$369$	28.7767	1.49806
$370$	0	0
$371$	25.7580	1.33729
$372$	−0.319833	−0.0165826
$373$	−7.91647	−0.409899	−0.204950	−	0.978773i	$-0.565703\pi$
$373$	−7.91647	−0.409899	−0.204950	+	0.978773i	$0.565703\pi$
$374$	−0.964360	−0.0498659
$375$	0	0
$376$	2.50599	0.129237
$377$	−12.7282	−0.655534
$378$	1.51956	0.0781576
$379$	7.78093	0.399680	0.199840	−	0.979829i	$-0.435958\pi$
$379$	7.78093	0.399680	0.199840	+	0.979829i	$0.435958\pi$
$380$	0	0
$381$	1.71662	0.0879452
$382$	−5.94961	−0.304408
$383$	−30.6300	−1.56512	−0.782560	−	0.622575i	$-0.786087\pi$
$383$	−30.6300	−1.56512	−0.782560	+	0.622575i	$0.786087\pi$
$384$	1.95404	0.0997167
$385$	0	0
$386$	8.51737	0.433523
$387$	−26.5813	−1.35120
$388$	−16.6019	−0.842835
$389$	18.5796	0.942022	0.471011	−	0.882127i	$-0.343889\pi$
$389$	18.5796	0.942022	0.471011	+	0.882127i	$0.343889\pi$
$390$	0	0
$391$	−3.07219	−0.155367
$392$	8.75414	0.442151
$393$	2.43956	0.123059
$394$	−1.66018	−0.0836387
$395$	0	0
$396$	16.3586	0.822052
$397$	0.836302	0.0419728	0.0209864	−	0.999780i	$-0.493319\pi$
$397$	0.836302	0.0419728	0.0209864	+	0.999780i	$0.493319\pi$
$398$	−12.3435	−0.618724
$399$	−0.983772	−0.0492502
$400$	0	0
$401$	−16.6318	−0.830550	−0.415275	−	0.909696i	$-0.636315\pi$
$401$	−16.6318	−0.830550	−0.415275	+	0.909696i	$0.636315\pi$
$402$	−0.384383	−0.0191713
$403$	2.38886	0.118998
$404$	2.32766	0.115805
$405$	0	0
$406$	8.19717	0.406819
$407$	11.8234	0.586065
$408$	−0.170480	−0.00844000
$409$	−4.36898	−0.216032	−0.108016	−	0.994149i	$-0.534450\pi$
$409$	−4.36898	−0.216032	−0.108016	+	0.994149i	$0.534450\pi$
$410$	0	0
$411$	1.14246	0.0563534
$412$	−17.5171	−0.863008
$413$	12.2277	0.601687
$414$	−18.2130	−0.895121
$415$	0	0
$416$	−12.2362	−0.599928
$417$	−0.342635	−0.0167789
$418$	7.44715	0.364252
$419$	−24.7322	−1.20824	−0.604122	−	0.796891i	$-0.706476\pi$
$419$	−24.7322	−1.20824	−0.604122	+	0.796891i	$0.706476\pi$
$420$	0	0
$421$	−2.61372	−0.127385	−0.0636924	−	0.997970i	$-0.520288\pi$
$421$	−2.61372	−0.127385	−0.0636924	+	0.997970i	$0.520288\pi$
$422$	−15.3974	−0.749532
$423$	2.96426	0.144127
$424$	−34.4700	−1.67401
$425$	0	0
$426$	−0.226726	−0.0109849
$427$	−6.16836	−0.298508
$428$	−22.6515	−1.09490
$429$	1.47309	0.0711215
$430$	0	0
$431$	−18.0881	−0.871271	−0.435635	−	0.900123i	$-0.643476\pi$
$431$	−18.0881	−0.871271	−0.435635	+	0.900123i	$0.643476\pi$
$432$	1.30856	0.0629580
$433$	38.9940	1.87393	0.936965	−	0.349423i	$-0.113622\pi$
$433$	38.9940	1.87393	0.936965	+	0.349423i	$0.113622\pi$
$434$	−1.53847	−0.0738490
$435$	0	0
$436$	6.50606	0.311584
$437$	23.7246	1.13490
$438$	1.06125	0.0507086
$439$	−4.72110	−0.225326	−0.112663	−	0.993633i	$-0.535938\pi$
$439$	−4.72110	−0.225326	−0.112663	+	0.993633i	$0.535938\pi$
$440$	0	0
$441$	10.3550	0.493096
$442$	0.541961	0.0257784
$443$	−21.4026	−1.01687	−0.508435	−	0.861100i	$-0.669776\pi$
$443$	−21.4026	−1.01687	−0.508435	+	0.861100i	$0.669776\pi$
$444$	0.889619	0.0422195
$445$	0	0
$446$	3.29626	0.156083
$447$	−1.34612	−0.0636694
$448$	3.53372	0.166952
$449$	4.35064	0.205319	0.102660	−	0.994717i	$-0.467265\pi$
$449$	4.35064	0.205319	0.102660	+	0.994717i	$0.467265\pi$
$450$	0	0
$451$	−36.1487	−1.70217
$452$	21.9987	1.03473
$453$	−1.55081	−0.0728636
$454$	−10.0174	−0.470138
$455$	0	0
$456$	1.31651	0.0616511
$457$	36.5080	1.70777	0.853887	−	0.520459i	$-0.174239\pi$
$457$	36.5080	1.70777	0.853887	+	0.520459i	$0.174239\pi$
$458$	−9.52297	−0.444979
$459$	−0.405742	−0.0189384
$460$	0	0
$461$	−29.7005	−1.38329	−0.691645	−	0.722238i	$-0.743114\pi$
$461$	−29.7005	−1.38329	−0.691645	+	0.722238i	$0.743114\pi$
$462$	−0.948698	−0.0441374
$463$	−15.7692	−0.732859	−0.366429	−	0.930446i	$-0.619420\pi$
$463$	−15.7692	−0.732859	−0.366429	+	0.930446i	$0.619420\pi$
$464$	7.05895	0.327703
$465$	0	0
$466$	−3.34836	−0.155110
$467$	27.5499	1.27486	0.637428	−	0.770510i	$-0.279998\pi$
$467$	27.5499	1.27486	0.637428	+	0.770510i	$0.279998\pi$
$468$	−9.19338	−0.424964
$469$	5.29059	0.244297
$470$	0	0
$471$	−0.241760	−0.0111397
$472$	−16.3634	−0.753189
$473$	33.3908	1.53531
$474$	−1.37363	−0.0630929
$475$	0	0
$476$	0.998712	0.0457759
$477$	−40.7736	−1.86689
$478$	19.5819	0.895653
$479$	15.3034	0.699230	0.349615	−	0.936893i	$-0.386312\pi$
$479$	15.3034	0.699230	0.349615	+	0.936893i	$0.386312\pi$
$480$	0	0
$481$	−6.64465	−0.302970
$482$	20.0393	0.912766
$483$	−3.02230	−0.137519
$484$	−4.24680	−0.193036
$485$	0	0
$486$	−3.61527	−0.163992
$487$	−17.3084	−0.784318	−0.392159	−	0.919898i	$-0.628272\pi$
$487$	−17.3084	−0.784318	−0.392159	+	0.919898i	$0.628272\pi$
$488$	8.25465	0.373671
$489$	−0.213143	−0.00963865
$490$	0	0
$491$	14.3728	0.648633	0.324317	−	0.945949i	$-0.394866\pi$
$491$	14.3728	0.648633	0.324317	+	0.945949i	$0.394866\pi$
$492$	−2.71990	−0.122623
$493$	−2.18875	−0.0985765
$494$	−4.18523	−0.188302
$495$	0	0
$496$	−1.32485	−0.0594873
$497$	3.12063	0.139979
$498$	−1.04463	−0.0468109
$499$	42.9302	1.92182	0.960909	−	0.276864i	$-0.0892950\pi$
$499$	42.9302	1.92182	0.960909	+	0.276864i	$0.0892950\pi$
$500$	0	0
$501$	0.189523	0.00846728
$502$	8.37051	0.373594
$503$	9.02257	0.402297	0.201148	−	0.979561i	$-0.435533\pi$
$503$	9.02257	0.402297	0.201148	+	0.979561i	$0.435533\pi$
$504$	13.9106	0.619628
$505$	0	0
$506$	22.8788	1.01709
$507$	1.62973	0.0723787
$508$	13.4577	0.597090
$509$	−23.8927	−1.05902	−0.529512	−	0.848303i	$-0.677625\pi$
$509$	−23.8927	−1.05902	−0.529512	+	0.848303i	$0.677625\pi$
$510$	0	0
$511$	−14.6069	−0.646173
$512$	12.6028	0.556972
$513$	3.13329	0.138338
$514$	8.90431	0.392752
$515$	0	0
$516$	2.51239	0.110602
$517$	−3.72364	−0.163765
$518$	4.27928	0.188021
$519$	3.52220	0.154607
$520$	0	0
$521$	−22.7964	−0.998728	−0.499364	−	0.866392i	$-0.666433\pi$
$521$	−22.7964	−0.998728	−0.499364	+	0.866392i	$0.666433\pi$
$522$	−12.9757	−0.567930
$523$	−0.344765	−0.0150755	−0.00753775	−	0.999972i	$-0.502399\pi$
$523$	−0.344765	−0.0150755	−0.00753775	+	0.999972i	$0.502399\pi$
$524$	19.1253	0.835492
$525$	0	0
$526$	−11.8551	−0.516905
$527$	0.410792	0.0178944
$528$	−0.816966	−0.0355539
$529$	49.8857	2.16894
$530$	0	0
$531$	−19.3558	−0.839972
$532$	−7.71243	−0.334376
$533$	20.3152	0.879949
$534$	2.13624	0.0924444
$535$	0	0
$536$	−7.08000	−0.305809
$537$	2.18624	0.0943431
$538$	8.21006	0.353961
$539$	−13.0077	−0.560283
$540$	0	0
$541$	13.9244	0.598658	0.299329	−	0.954150i	$-0.403237\pi$
$541$	13.9244	0.598658	0.299329	+	0.954150i	$0.403237\pi$
$542$	18.2529	0.784031
$543$	3.22861	0.138553
$544$	−2.10415	−0.0902148
$545$	0	0
$546$	0.533159	0.0228171
$547$	13.3587	0.571175	0.285587	−	0.958353i	$-0.407811\pi$
$547$	13.3587	0.571175	0.285587	+	0.958353i	$0.407811\pi$
$548$	8.95649	0.382602
$549$	9.76419	0.416726
$550$	0	0
$551$	16.9024	0.720065
$552$	4.04451	0.172146
$553$	18.9064	0.803984
$554$	2.26345	0.0961649
$555$	0	0
$556$	−2.68614	−0.113918
$557$	4.50151	0.190735	0.0953677	−	0.995442i	$-0.469597\pi$
$557$	4.50151	0.190735	0.0953677	+	0.995442i	$0.469597\pi$
$558$	2.43532	0.103095
$559$	−18.7653	−0.793688
$560$	0	0
$561$	0.253315	0.0106950
$562$	20.9637	0.884300
$563$	28.6470	1.20733	0.603663	−	0.797239i	$-0.293707\pi$
$563$	28.6470	1.20733	0.603663	+	0.797239i	$0.293707\pi$
$564$	−0.280174	−0.0117975
$565$	0	0
$566$	12.8932	0.541940
$567$	16.2537	0.682590
$568$	−4.17610	−0.175225
$569$	−30.5740	−1.28173	−0.640865	−	0.767654i	$-0.721424\pi$
$569$	−30.5740	−1.28173	−0.640865	+	0.767654i	$0.721424\pi$
$570$	0	0
$571$	18.6563	0.780740	0.390370	−	0.920658i	$-0.372347\pi$
$571$	18.6563	0.780740	0.390370	+	0.920658i	$0.372347\pi$
$572$	11.5485	0.482868
$573$	1.56282	0.0652878
$574$	−13.0834	−0.546089
$575$	0	0
$576$	−5.59369	−0.233070
$577$	27.1717	1.13117	0.565587	−	0.824689i	$-0.308650\pi$
$577$	27.1717	1.13117	0.565587	+	0.824689i	$0.308650\pi$
$578$	−12.1415	−0.505020
$579$	−2.23731	−0.0929796
$580$	0	0
$581$	14.3781	0.596504
$582$	−1.52407	−0.0631748
$583$	51.2189	2.12127
$584$	19.5474	0.808876
$585$	0	0
$586$	−0.693265	−0.0286385
$587$	−1.09014	−0.0449950	−0.0224975	−	0.999747i	$-0.507162\pi$
$587$	−1.09014	−0.0449950	−0.0224975	+	0.999747i	$0.507162\pi$
$588$	−0.978729	−0.0403621
$589$	−3.17229	−0.130712
$590$	0	0
$591$	0.436091	0.0179384
$592$	3.68507	0.151456
$593$	−45.0873	−1.85151	−0.925757	−	0.378120i	$-0.876571\pi$
$593$	−45.0873	−1.85151	−0.925757	+	0.378120i	$0.876571\pi$
$594$	3.02158	0.123977
$595$	0	0
$596$	−10.5531	−0.432273
$597$	3.24235	0.132701
$598$	−12.8577	−0.525788
$599$	9.88679	0.403963	0.201982	−	0.979389i	$-0.435262\pi$
$599$	9.88679	0.403963	0.201982	+	0.979389i	$0.435262\pi$
$600$	0	0
$601$	1.16954	0.0477065	0.0238532	−	0.999715i	$-0.492407\pi$
$601$	1.16954	0.0477065	0.0238532	+	0.999715i	$0.492407\pi$
$602$	12.0852	0.492556
$603$	−8.37473	−0.341045
$604$	−12.1578	−0.494696
$605$	0	0
$606$	0.213682	0.00868022
$607$	−28.2105	−1.14503	−0.572514	−	0.819895i	$-0.694032\pi$
$607$	−28.2105	−1.14503	−0.572514	+	0.819895i	$0.694032\pi$
$608$	16.2491	0.658986
$609$	−2.15320	−0.0872523
$610$	0	0
$611$	2.09265	0.0846595
$612$	−1.58091	−0.0639044
$613$	−7.36475	−0.297460	−0.148730	−	0.988878i	$-0.547518\pi$
$613$	−7.36475	−0.297460	−0.148730	+	0.988878i	$0.547518\pi$
$614$	−18.1913	−0.734142
$615$	0	0
$616$	−17.4742	−0.704055
$617$	9.44071	0.380069	0.190034	−	0.981777i	$-0.439140\pi$
$617$	9.44071	0.380069	0.190034	+	0.981777i	$0.439140\pi$
$618$	−1.60809	−0.0646869
$619$	−37.9981	−1.52727	−0.763636	−	0.645647i	$-0.776588\pi$
$619$	−37.9981	−1.52727	−0.763636	+	0.645647i	$0.776588\pi$
$620$	0	0
$621$	9.62595	0.386276
$622$	13.7259	0.550359
$623$	−29.4030	−1.17801
$624$	0.459127	0.0183798
$625$	0	0
$626$	13.7287	0.548710
$627$	−1.95619	−0.0781228
$628$	−1.89532	−0.0756314
$629$	−1.14262	−0.0455594
$630$	0	0
$631$	−38.1884	−1.52026	−0.760128	−	0.649774i	$-0.774864\pi$
$631$	−38.1884	−1.52026	−0.760128	+	0.649774i	$0.774864\pi$
$632$	−25.3011	−1.00642
$633$	4.04453	0.160756
$634$	18.8658	0.749257
$635$	0	0
$636$	3.85381	0.152814
$637$	7.31022	0.289641
$638$	16.2998	0.645314
$639$	−4.93978	−0.195415
$640$	0	0
$641$	−13.5805	−0.536398	−0.268199	−	0.963364i	$-0.586428\pi$
$641$	−13.5805	−0.536398	−0.268199	+	0.963364i	$0.586428\pi$
$642$	−2.07943	−0.0820685
$643$	14.2258	0.561011	0.280505	−	0.959852i	$-0.409498\pi$
$643$	14.2258	0.561011	0.280505	+	0.959852i	$0.409498\pi$
$644$	−23.6938	−0.933665
$645$	0	0
$646$	−0.719698	−0.0283161
$647$	−28.8921	−1.13586	−0.567932	−	0.823075i	$-0.692256\pi$
$647$	−28.8921	−1.13586	−0.567932	+	0.823075i	$0.692256\pi$
$648$	−21.7511	−0.854463
$649$	24.3144	0.954423
$650$	0	0
$651$	0.404120	0.0158387
$652$	−1.67097	−0.0654401
$653$	33.6034	1.31500	0.657501	−	0.753454i	$-0.271614\pi$
$653$	33.6034	1.31500	0.657501	+	0.753454i	$0.271614\pi$
$654$	0.597262	0.0233548
$655$	0	0
$656$	−11.2667	−0.439889
$657$	23.1220	0.902076
$658$	−1.34770	−0.0525390
$659$	−16.1787	−0.630232	−0.315116	−	0.949053i	$-0.602043\pi$
$659$	−16.1787	−0.630232	−0.315116	+	0.949053i	$0.602043\pi$
$660$	0	0
$661$	−5.41423	−0.210589	−0.105295	−	0.994441i	$-0.533579\pi$
$661$	−5.41423	−0.210589	−0.105295	+	0.994441i	$0.533579\pi$
$662$	−2.01697	−0.0783917
$663$	−0.142360	−0.00552882
$664$	−19.2411	−0.746700
$665$	0	0
$666$	−6.77387	−0.262482
$667$	51.9267	2.01061
$668$	1.48580	0.0574873
$669$	−0.865852	−0.0334758
$670$	0	0
$671$	−12.2656	−0.473507
$672$	−2.06998	−0.0798511
$673$	−10.7477	−0.414295	−0.207148	−	0.978310i	$-0.566418\pi$
$673$	−10.7477	−0.414295	−0.207148	+	0.978310i	$0.566418\pi$
$674$	16.4576	0.633922
$675$	0	0
$676$	12.7765	0.491403
$677$	−10.6388	−0.408882	−0.204441	−	0.978879i	$-0.565538\pi$
$677$	−10.6388	−0.408882	−0.204441	+	0.978879i	$0.565538\pi$
$678$	2.01950	0.0775585
$679$	20.9771	0.805028
$680$	0	0
$681$	2.63133	0.100833
$682$	−3.05919	−0.117142
$683$	−39.8465	−1.52468	−0.762342	−	0.647174i	$-0.775951\pi$
$683$	−39.8465	−1.52468	−0.762342	+	0.647174i	$0.775951\pi$
$684$	12.2084	0.466799
$685$	0	0
$686$	−14.1418	−0.539938
$687$	2.50146	0.0954368
$688$	10.4071	0.396767
$689$	−28.7845	−1.09660
$690$	0	0
$691$	30.4621	1.15883	0.579417	−	0.815032i	$-0.303280\pi$
$691$	30.4621	1.15883	0.579417	+	0.815032i	$0.303280\pi$
$692$	27.6128	1.04968
$693$	−20.6697	−0.785177
$694$	−23.6894	−0.899236
$695$	0	0
$696$	2.88147	0.109222
$697$	3.49343	0.132323
$698$	2.76831	0.104782
$699$	0.879537	0.0332671
$700$	0	0
$701$	2.34227	0.0884662	0.0442331	−	0.999021i	$-0.485916\pi$
$701$	2.34227	0.0884662	0.0442331	+	0.999021i	$0.485916\pi$
$702$	−1.69810	−0.0640906
$703$	8.82377	0.332795
$704$	7.02666	0.264827
$705$	0	0
$706$	−11.0101	−0.414370
$707$	−2.94108	−0.110611
$708$	1.82946	0.0687555
$709$	−24.6853	−0.927074	−0.463537	−	0.886078i	$-0.653420\pi$
$709$	−24.6853	−0.927074	−0.463537	+	0.886078i	$0.653420\pi$
$710$	0	0
$711$	−29.9279	−1.12238
$712$	39.3478	1.47462
$713$	−9.74576	−0.364982
$714$	0.0916827	0.00343114
$715$	0	0
$716$	17.1393	0.640527
$717$	−5.14369	−0.192095
$718$	−6.73494	−0.251346
$719$	−18.0594	−0.673503	−0.336751	−	0.941594i	$-0.609328\pi$
$719$	−18.0594	−0.673503	−0.336751	+	0.941594i	$0.609328\pi$
$720$	0	0
$721$	22.1335	0.824296
$722$	−8.11630	−0.302057
$723$	−5.26386	−0.195765
$724$	25.3112	0.940682
$725$	0	0
$726$	−0.389860	−0.0144691
$727$	51.1538	1.89719	0.948594	−	0.316495i	$-0.102506\pi$
$727$	51.1538	1.89719	0.948594	+	0.316495i	$0.102506\pi$
$728$	9.82032	0.363965
$729$	−25.0893	−0.929232
$730$	0	0
$731$	−3.22691	−0.119352
$732$	−0.922886	−0.0341108
$733$	15.5141	0.573027	0.286514	−	0.958076i	$-0.407504\pi$
$733$	15.5141	0.573027	0.286514	+	0.958076i	$0.407504\pi$
$734$	16.3445	0.603287
$735$	0	0
$736$	49.9196	1.84006
$737$	10.5201	0.387515
$738$	20.7103	0.762355
$739$	21.5641	0.793246	0.396623	−	0.917981i	$-0.370182\pi$
$739$	21.5641	0.793246	0.396623	+	0.917981i	$0.370182\pi$
$740$	0	0
$741$	1.09936	0.0403860
$742$	18.5377	0.680542
$743$	−8.78438	−0.322268	−0.161134	−	0.986933i	$-0.551515\pi$
$743$	−8.78438	−0.322268	−0.161134	+	0.986933i	$0.551515\pi$
$744$	−0.540804	−0.0198268
$745$	0	0
$746$	−5.69739	−0.208596
$747$	−22.7598	−0.832736
$748$	1.98590	0.0726117
$749$	28.6210	1.04579
$750$	0	0
$751$	36.9634	1.34881	0.674407	−	0.738360i	$-0.264399\pi$
$751$	36.9634	1.34881	0.674407	+	0.738360i	$0.264399\pi$
$752$	−1.16057	−0.0423216
$753$	−2.19874	−0.0801264
$754$	−9.16030	−0.333599
$755$	0	0
$756$	−3.12921	−0.113808
$757$	27.2840	0.991655	0.495827	−	0.868421i	$-0.334865\pi$
$757$	27.2840	0.991655	0.495827	+	0.868421i	$0.334865\pi$
$758$	5.59984	0.203396
$759$	−6.00972	−0.218139
$760$	0	0
$761$	−4.88123	−0.176945	−0.0884723	−	0.996079i	$-0.528198\pi$
$761$	−4.88123	−0.176945	−0.0884723	+	0.996079i	$0.528198\pi$
$762$	1.23543	0.0447550
$763$	−8.22063	−0.297607
$764$	12.2520	0.443261
$765$	0	0
$766$	−22.0440	−0.796484
$767$	−13.6644	−0.493394
$768$	2.11977	0.0764907
$769$	17.0881	0.616212	0.308106	−	0.951352i	$-0.400305\pi$
$769$	17.0881	0.616212	0.308106	+	0.951352i	$0.400305\pi$
$770$	0	0
$771$	−2.33895	−0.0842354
$772$	−17.5398	−0.631270
$773$	−27.3759	−0.984644	−0.492322	−	0.870413i	$-0.663852\pi$
$773$	−27.3759	−0.984644	−0.492322	+	0.870413i	$0.663852\pi$
$774$	−19.1302	−0.687622
$775$	0	0
$776$	−28.0721	−1.00773
$777$	−1.12407	−0.0403256
$778$	13.3715	0.479391
$779$	−26.9776	−0.966572
$780$	0	0
$781$	6.20525	0.222041
$782$	−2.21102	−0.0790659
$783$	6.85791	0.245082
$784$	−4.05419	−0.144793
$785$	0	0
$786$	1.75572	0.0626245
$787$	−12.0081	−0.428044	−0.214022	−	0.976829i	$-0.568656\pi$
$787$	−12.0081	−0.428044	−0.214022	+	0.976829i	$0.568656\pi$
$788$	3.41880	0.121790
$789$	3.11405	0.110863
$790$	0	0
$791$	−27.7961	−0.988316
$792$	27.6607	0.982881
$793$	6.89312	0.244782
$794$	0.601876	0.0213598
$795$	0	0
$796$	25.4189	0.900950
$797$	−46.7484	−1.65591	−0.827957	−	0.560791i	$-0.810497\pi$
$797$	−46.7484	−1.65591	−0.827957	+	0.560791i	$0.810497\pi$
$798$	−0.708009	−0.0250632
$799$	0.359855	0.0127308
$800$	0	0
$801$	46.5433	1.64453
$802$	−11.9697	−0.422664
$803$	−29.0453	−1.02499
$804$	0.791557	0.0279161
$805$	0	0
$806$	1.71924	0.0605575
$807$	−2.15659	−0.0759156
$808$	3.93583	0.138462
$809$	−43.2865	−1.52187	−0.760935	−	0.648828i	$-0.775260\pi$
$809$	−43.2865	−1.52187	−0.760935	+	0.648828i	$0.775260\pi$
$810$	0	0
$811$	39.8126	1.39801	0.699004	−	0.715118i	$-0.253627\pi$
$811$	39.8126	1.39801	0.699004	+	0.715118i	$0.253627\pi$
$812$	−16.8804	−0.592385
$813$	−4.79462	−0.168155
$814$	8.50918	0.298247
$815$	0	0
$816$	0.0789521	0.00276388
$817$	24.9194	0.871820
$818$	−3.14430	−0.109938
$819$	11.6162	0.405902
$820$	0	0
$821$	−12.9070	−0.450456	−0.225228	−	0.974306i	$-0.572313\pi$
$821$	−12.9070	−0.450456	−0.225228	+	0.974306i	$0.572313\pi$
$822$	0.822215	0.0286780
$823$	−8.64502	−0.301346	−0.150673	−	0.988584i	$-0.548144\pi$
$823$	−8.64502	−0.301346	−0.150673	+	0.988584i	$0.548144\pi$
$824$	−29.6196	−1.03185
$825$	0	0
$826$	8.80015	0.306196
$827$	39.8780	1.38669	0.693347	−	0.720604i	$-0.256135\pi$
$827$	39.8780	1.38669	0.693347	+	0.720604i	$0.256135\pi$
$828$	37.5060	1.30342
$829$	32.6073	1.13250	0.566249	−	0.824234i	$-0.308394\pi$
$829$	32.6073	1.13250	0.566249	+	0.824234i	$0.308394\pi$
$830$	0	0
$831$	−0.594556	−0.0206249
$832$	−3.94892	−0.136904
$833$	1.25708	0.0435551
$834$	−0.246591	−0.00853874
$835$	0	0
$836$	−15.3359	−0.530402
$837$	−1.28711	−0.0444892
$838$	−17.7994	−0.614871
$839$	27.3433	0.943997	0.471998	−	0.881599i	$-0.343533\pi$
$839$	27.3433	0.943997	0.471998	+	0.881599i	$0.343533\pi$
$840$	0	0
$841$	7.99464	0.275677
$842$	−1.88106	−0.0648257
$843$	−5.50667	−0.189660
$844$	31.7077	1.09142
$845$	0	0
$846$	2.13334	0.0733459
$847$	5.36598	0.184377
$848$	15.9637	0.548195
$849$	−3.38673	−0.116232
$850$	0	0
$851$	27.1080	0.929249
$852$	0.466896	0.0159956
$853$	49.2999	1.68800	0.843998	−	0.536346i	$-0.180196\pi$
$853$	49.2999	1.68800	0.843998	+	0.536346i	$0.180196\pi$
$854$	−4.43930	−0.151910
$855$	0	0
$856$	−38.3013	−1.30911
$857$	−26.6376	−0.909923	−0.454961	−	0.890511i	$-0.650347\pi$
$857$	−26.6376	−0.909923	−0.454961	+	0.890511i	$0.650347\pi$
$858$	1.06017	0.0361935
$859$	35.1483	1.19924	0.599622	−	0.800283i	$-0.295318\pi$
$859$	35.1483	1.19924	0.599622	+	0.800283i	$0.295318\pi$
$860$	0	0
$861$	3.43669	0.117122
$862$	−13.0178	−0.443387
$863$	1.90888	0.0649789	0.0324894	−	0.999472i	$-0.489656\pi$
$863$	1.90888	0.0649789	0.0324894	+	0.999472i	$0.489656\pi$
$864$	6.59284	0.224293
$865$	0	0
$866$	28.0635	0.953636
$867$	3.18929	0.108314
$868$	3.16816	0.107534
$869$	37.5948	1.27531
$870$	0	0
$871$	−5.91222	−0.200328
$872$	11.0011	0.372543
$873$	−33.2057	−1.12384
$874$	17.0743	0.577548
$875$	0	0
$876$	−2.18543	−0.0738389
$877$	−16.5919	−0.560270	−0.280135	−	0.959961i	$-0.590379\pi$
$877$	−16.5919	−0.560270	−0.280135	+	0.959961i	$0.590379\pi$
$878$	−3.39772	−0.114667
$879$	0.182105	0.00614223
$880$	0	0
$881$	−40.9693	−1.38029	−0.690145	−	0.723671i	$-0.742453\pi$
$881$	−40.9693	−1.38029	−0.690145	+	0.723671i	$0.742453\pi$
$882$	7.45238	0.250935
$883$	−20.5269	−0.690786	−0.345393	−	0.938458i	$-0.612254\pi$
$883$	−20.5269	−0.690786	−0.345393	+	0.938458i	$0.612254\pi$
$884$	−1.11606	−0.0375370
$885$	0	0
$886$	−15.4032	−0.517482
$887$	−17.8524	−0.599425	−0.299712	−	0.954030i	$-0.596891\pi$
$887$	−17.8524	−0.599425	−0.299712	+	0.954030i	$0.596891\pi$
$888$	1.50425	0.0504794
$889$	−17.0043	−0.570306
$890$	0	0
$891$	32.3198	1.08275
$892$	−6.78798	−0.227278
$893$	−2.77894	−0.0929935
$894$	−0.968788	−0.0324011
$895$	0	0
$896$	−19.3561	−0.646642
$897$	3.37740	0.112768
$898$	3.13110	0.104486
$899$	−6.94327	−0.231571
$900$	0	0
$901$	−4.94982	−0.164903
$902$	−26.0158	−0.866230
$903$	−3.17450	−0.105641
$904$	37.1974	1.23717
$905$	0	0
$906$	−1.11610	−0.0370800
$907$	−46.0647	−1.52955	−0.764777	−	0.644295i	$-0.777151\pi$
$907$	−46.0647	−1.52955	−0.764777	+	0.644295i	$0.777151\pi$
$908$	20.6287	0.684588
$909$	4.65558	0.154416
$910$	0	0
$911$	42.4215	1.40549	0.702744	−	0.711443i	$-0.251958\pi$
$911$	42.4215	1.40549	0.702744	+	0.711443i	$0.251958\pi$
$912$	−0.609698	−0.0201891
$913$	28.5903	0.946201
$914$	26.2744	0.869080
$915$	0	0
$916$	19.6106	0.647952
$917$	−24.1655	−0.798015
$918$	−0.292008	−0.00963769
$919$	−52.5913	−1.73483	−0.867414	−	0.497587i	$-0.834220\pi$
$919$	−52.5913	−1.73483	−0.867414	+	0.497587i	$0.834220\pi$
$920$	0	0
$921$	4.77844	0.157455
$922$	−21.3751	−0.703951
$923$	−3.48729	−0.114785
$924$	1.95365	0.0642703
$925$	0	0
$926$	−11.3489	−0.372949
$927$	−35.0362	−1.15074
$928$	35.5647	1.16747
$929$	23.7026	0.777658	0.388829	−	0.921310i	$-0.372880\pi$
$929$	23.7026	0.777658	0.388829	+	0.921310i	$0.372880\pi$
$930$	0	0
$931$	−9.70761	−0.318154
$932$	6.89526	0.225862
$933$	−3.60548	−0.118038
$934$	19.8273	0.648770
$935$	0	0
$936$	−15.5450	−0.508106
$937$	−31.8280	−1.03978	−0.519888	−	0.854234i	$-0.674026\pi$
$937$	−31.8280	−1.03978	−0.519888	+	0.854234i	$0.674026\pi$
$938$	3.80758	0.124322
$939$	−3.60621	−0.117684
$940$	0	0
$941$	17.3201	0.564618	0.282309	−	0.959324i	$-0.408900\pi$
$941$	17.3201	0.564618	0.282309	+	0.959324i	$0.408900\pi$
$942$	−0.173992	−0.00566897
$943$	−82.8792	−2.69892
$944$	7.57820	0.246649
$945$	0	0
$946$	24.0310	0.781314
$947$	−44.0661	−1.43196	−0.715978	−	0.698123i	$-0.754019\pi$
$947$	−44.0661	−1.43196	−0.715978	+	0.698123i	$0.754019\pi$
$948$	2.82871	0.0918721
$949$	16.3232	0.529873
$950$	0	0
$951$	−4.95560	−0.160696
$952$	1.68872	0.0547316
$953$	−7.26720	−0.235408	−0.117704	−	0.993049i	$-0.537553\pi$
$953$	−7.26720	−0.235408	−0.117704	+	0.993049i	$0.537553\pi$
$954$	−29.3443	−0.950055
$955$	0	0
$956$	−40.3248	−1.30420
$957$	−4.28157	−0.138403
$958$	11.0137	0.355835
$959$	−11.3168	−0.365440
$960$	0	0
$961$	−29.6969	−0.957963
$962$	−4.78207	−0.154180
$963$	−45.3055	−1.45995
$964$	−41.2669	−1.32912
$965$	0	0
$966$	−2.17511	−0.0699830
$967$	−13.5129	−0.434545	−0.217273	−	0.976111i	$-0.569716\pi$
$967$	−13.5129	−0.434545	−0.217273	+	0.976111i	$0.569716\pi$
$968$	−7.18088	−0.230802
$969$	0.189048	0.00607309
$970$	0	0
$971$	1.73747	0.0557582	0.0278791	−	0.999611i	$-0.491125\pi$
$971$	1.73747	0.0557582	0.0278791	+	0.999611i	$0.491125\pi$
$972$	7.44491	0.238796
$973$	3.39404	0.108808
$974$	−12.4566	−0.399136
$975$	0	0
$976$	−3.82288	−0.122367
$977$	−22.9040	−0.732764	−0.366382	−	0.930465i	$-0.619404\pi$
$977$	−22.9040	−0.732764	−0.366382	+	0.930465i	$0.619404\pi$
$978$	−0.153396	−0.00490507
$979$	−58.4667	−1.86860
$980$	0	0
$981$	13.0128	0.415468
$982$	10.3439	0.330087
$983$	−21.0051	−0.669957	−0.334979	−	0.942226i	$-0.608729\pi$
$983$	−21.0051	−0.669957	−0.334979	+	0.942226i	$0.608729\pi$
$984$	−4.59907	−0.146613
$985$	0	0
$986$	−1.57522	−0.0501652
$987$	0.354010	0.0112683
$988$	8.61861	0.274195
$989$	76.5562	2.43435
$990$	0	0
$991$	0.429196	0.0136339	0.00681693	−	0.999977i	$-0.497830\pi$
$991$	0.429196	0.0136339	0.00681693	+	0.999977i	$0.497830\pi$
$992$	−6.67490	−0.211928
$993$	0.529810	0.0168130
$994$	2.24588	0.0712349
$995$	0	0
$996$	2.15119	0.0681632
$997$	−4.99449	−0.158177	−0.0790885	−	0.996868i	$-0.525201\pi$
$997$	−4.99449	−0.158177	−0.0790885	+	0.996868i	$0.525201\pi$
$998$	30.8963	0.978006
$999$	3.58012	0.113270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.j.1.6		11
5.2	odd	4		235.2.c.a.189.13	yes	22
5.3	odd	4		235.2.c.a.189.10	✓	22
5.4	even	2		1175.2.a.i.1.6		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.2.c.a.189.10	✓	22	5.3	odd	4
235.2.c.a.189.13	yes	22	5.2	odd	4
1175.2.a.i.1.6		11	5.4	even	2
1175.2.a.j.1.6		11	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:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q+0.719688 q^{2} -0.189045 q^{3} -1.48205 q^{4} -0.136054 q^{6} +1.87262 q^{7} -2.50599 q^{8} -2.96426 q^{9} +O(q^{10})\)	\(q+0.719688 q^{2} -0.189045 q^{3} -1.48205 q^{4} -0.136054 q^{6} +1.87262 q^{7} -2.50599 q^{8} -2.96426 q^{9} +3.72364 q^{11} +0.280174 q^{12} -2.09265 q^{13} +1.34770 q^{14} +1.16057 q^{16} -0.359855 q^{17} -2.13334 q^{18} +2.77894 q^{19} -0.354010 q^{21} +2.67986 q^{22} +8.53731 q^{23} +0.473745 q^{24} -1.50605 q^{26} +1.12752 q^{27} -2.77532 q^{28} +6.08232 q^{29} -1.14155 q^{31} +5.84723 q^{32} -0.703936 q^{33} -0.258983 q^{34} +4.39318 q^{36} +3.17523 q^{37} +1.99997 q^{38} +0.395605 q^{39} -9.70789 q^{41} -0.254777 q^{42} +8.96725 q^{43} -5.51862 q^{44} +6.14420 q^{46} -1.00000 q^{47} -0.219400 q^{48} -3.49329 q^{49} +0.0680288 q^{51} +3.10141 q^{52} +13.7551 q^{53} +0.811459 q^{54} -4.69277 q^{56} -0.525344 q^{57} +4.37737 q^{58} +6.52974 q^{59} -3.29397 q^{61} -0.821560 q^{62} -5.55094 q^{63} +1.88704 q^{64} -0.506614 q^{66} +2.82523 q^{67} +0.533323 q^{68} -1.61394 q^{69} +1.66645 q^{71} +7.42841 q^{72} -7.80026 q^{73} +2.28518 q^{74} -4.11852 q^{76} +6.97297 q^{77} +0.284712 q^{78} +10.0962 q^{79} +8.67963 q^{81} -6.98665 q^{82} +7.67806 q^{83} +0.524661 q^{84} +6.45362 q^{86} -1.14983 q^{87} -9.33140 q^{88} -15.7015 q^{89} -3.91874 q^{91} -12.6527 q^{92} +0.215805 q^{93} -0.719688 q^{94} -1.10539 q^{96} +11.2020 q^{97} -2.51408 q^{98} -11.0378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{2} + 4 q^{3} + 10 q^{4} - 2 q^{6} + 12 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 11 * q + 4 * q^2 + 4 * q^3 + 10 * q^4 - 2 * q^6 + 12 * q^7 + 12 * q^8 + 9 * q^9	\( 11 q + 4 q^{2} + 4 q^{3} + 10 q^{4} - 2 q^{6} + 12 q^{7} + 12 q^{8} + 9 q^{9} + 12 q^{12} + 19 q^{13} + 12 q^{16} + 16 q^{17} - 10 q^{18} - 6 q^{21} + 22 q^{22} + 3 q^{23} - 12 q^{24} + 6 q^{26} + 16 q^{27} + 18 q^{28} + 4 q^{29} + 2 q^{31} + 28 q^{32} + 18 q^{33} - 16 q^{34} - 8 q^{36} + 40 q^{37} - 14 q^{38} - 10 q^{39} + 4 q^{41} + 16 q^{42} + 23 q^{43} + 24 q^{44} - 16 q^{46} - 11 q^{47} - 18 q^{48} + 5 q^{49} + 12 q^{51} + 46 q^{52} + 16 q^{53} + 26 q^{56} + 42 q^{57} + 16 q^{58} + 7 q^{59} - 7 q^{61} + 14 q^{63} + 24 q^{64} + 12 q^{66} + 32 q^{67} - 58 q^{68} - 2 q^{69} - 17 q^{71} + 57 q^{73} - 16 q^{74} - 10 q^{76} + 8 q^{77} - 22 q^{78} - 13 q^{79} - 25 q^{81} + 12 q^{82} + 8 q^{83} - 4 q^{84} - 6 q^{86} - 10 q^{87} + 26 q^{88} - 37 q^{89} + 32 q^{91} + 4 q^{92} - 10 q^{93} - 4 q^{94} - 6 q^{96} + 32 q^{97} - 20 q^{98} - 8 q^{99}+O(q^{100}) \) 11 * q + 4 * q^2 + 4 * q^3 + 10 * q^4 - 2 * q^6 + 12 * q^7 + 12 * q^8 + 9 * q^9 + 12 * q^12 + 19 * q^13 + 12 * q^16 + 16 * q^17 - 10 * q^18 - 6 * q^21 + 22 * q^22 + 3 * q^23 - 12 * q^24 + 6 * q^26 + 16 * q^27 + 18 * q^28 + 4 * q^29 + 2 * q^31 + 28 * q^32 + 18 * q^33 - 16 * q^34 - 8 * q^36 + 40 * q^37 - 14 * q^38 - 10 * q^39 + 4 * q^41 + 16 * q^42 + 23 * q^43 + 24 * q^44 - 16 * q^46 - 11 * q^47 - 18 * q^48 + 5 * q^49 + 12 * q^51 + 46 * q^52 + 16 * q^53 + 26 * q^56 + 42 * q^57 + 16 * q^58 + 7 * q^59 - 7 * q^61 + 14 * q^63 + 24 * q^64 + 12 * q^66 + 32 * q^67 - 58 * q^68 - 2 * q^69 - 17 * q^71 + 57 * q^73 - 16 * q^74 - 10 * q^76 + 8 * q^77 - 22 * q^78 - 13 * q^79 - 25 * q^81 + 12 * q^82 + 8 * q^83 - 4 * q^84 - 6 * q^86 - 10 * q^87 + 26 * q^88 - 37 * q^89 + 32 * q^91 + 4 * q^92 - 10 * q^93 - 4 * q^94 - 6 * q^96 + 32 * q^97 - 20 * q^98 - 8 * q^99

Introduction

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