LMFDB - Embedded newform 1175.2.a.j.1.7

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			1.7
Root			$0.748750$ 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)

$f(q)$	$=$	$q+0.748750 q^{2} +2.80944 q^{3} -1.43937 q^{4} +2.10357 q^{6} +1.97691 q^{7} -2.57523 q^{8} +4.89297 q^{9} +O(q^{10})$	\(q+0.748750 q^{2} +2.80944 q^{3} -1.43937 q^{4} +2.10357 q^{6} +1.97691 q^{7} -2.57523 q^{8} +4.89297 q^{9} -0.683196 q^{11} -4.04384 q^{12} +3.13202 q^{13} +1.48021 q^{14} +0.950545 q^{16} +1.72800 q^{17} +3.66361 q^{18} +4.21437 q^{19} +5.55401 q^{21} -0.511543 q^{22} -6.32383 q^{23} -7.23496 q^{24} +2.34510 q^{26} +5.31818 q^{27} -2.84551 q^{28} +4.62266 q^{29} +9.24789 q^{31} +5.86218 q^{32} -1.91940 q^{33} +1.29384 q^{34} -7.04281 q^{36} +0.820682 q^{37} +3.15551 q^{38} +8.79922 q^{39} -9.85369 q^{41} +4.15857 q^{42} -5.29702 q^{43} +0.983375 q^{44} -4.73497 q^{46} -1.00000 q^{47} +2.67050 q^{48} -3.09183 q^{49} +4.85471 q^{51} -4.50814 q^{52} +4.43246 q^{53} +3.98198 q^{54} -5.09100 q^{56} +11.8400 q^{57} +3.46122 q^{58} -7.94529 q^{59} +6.03056 q^{61} +6.92436 q^{62} +9.67295 q^{63} +2.48822 q^{64} -1.43715 q^{66} +11.6410 q^{67} -2.48724 q^{68} -17.7664 q^{69} -16.7985 q^{71} -12.6005 q^{72} +5.86850 q^{73} +0.614485 q^{74} -6.06606 q^{76} -1.35062 q^{77} +6.58842 q^{78} -7.36295 q^{79} +0.262216 q^{81} -7.37795 q^{82} -15.3880 q^{83} -7.99430 q^{84} -3.96614 q^{86} +12.9871 q^{87} +1.75939 q^{88} +9.21820 q^{89} +6.19172 q^{91} +9.10236 q^{92} +25.9814 q^{93} -0.748750 q^{94} +16.4695 q^{96} -2.30654 q^{97} -2.31500 q^{98} -3.34286 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.748750	0.529446	0.264723	−	0.964324i	$-0.414719\pi$
$2$	0.748750	0.529446	0.264723	+	0.964324i	$0.414719\pi$
$3$	2.80944	1.62203	0.811016	−	0.585024i	$-0.198915\pi$
$3$	2.80944	1.62203	0.811016	+	0.585024i	$0.198915\pi$
$4$	−1.43937	−0.719687
$5$	0	0
$5$	0	0
$6$	2.10357	0.858779
$7$	1.97691	0.747202	0.373601	−	0.927590i	$-0.378123\pi$
$7$	1.97691	0.747202	0.373601	+	0.927590i	$0.378123\pi$
$8$	−2.57523	−0.910481
$9$	4.89297	1.63099
$10$	0	0
$11$	−0.683196	−0.205991	−0.102996	−	0.994682i	$-0.532843\pi$
$11$	−0.683196	−0.205991	−0.102996	+	0.994682i	$0.532843\pi$
$12$	−4.04384	−1.16736
$13$	3.13202	0.868665	0.434333	−	0.900753i	$-0.356984\pi$
$13$	3.13202	0.868665	0.434333	+	0.900753i	$0.356984\pi$
$14$	1.48021	0.395603
$15$	0	0
$16$	0.950545	0.237636
$17$	1.72800	0.419101	0.209551	−	0.977798i	$-0.432800\pi$
$17$	1.72800	0.419101	0.209551	+	0.977798i	$0.432800\pi$
$18$	3.66361	0.863520
$19$	4.21437	0.966843	0.483422	−	0.875388i	$-0.339394\pi$
$19$	4.21437	0.966843	0.483422	+	0.875388i	$0.339394\pi$
$20$	0	0
$21$	5.55401	1.21199
$22$	−0.511543	−0.109061
$23$	−6.32383	−1.31861	−0.659305	−	0.751876i	$-0.729149\pi$
$23$	−6.32383	−1.31861	−0.659305	+	0.751876i	$0.729149\pi$
$24$	−7.23496	−1.47683
$25$	0	0
$26$	2.34510	0.459911
$27$	5.31818	1.02348
$28$	−2.84551	−0.537751
$29$	4.62266	0.858406	0.429203	−	0.903208i	$-0.358794\pi$
$29$	4.62266	0.858406	0.429203	+	0.903208i	$0.358794\pi$
$30$	0	0
$31$	9.24789	1.66097	0.830485	−	0.557041i	$-0.188063\pi$
$31$	9.24789	1.66097	0.830485	+	0.557041i	$0.188063\pi$
$32$	5.86218	1.03630
$33$	−1.91940	−0.334125
$34$	1.29384	0.221891
$35$	0	0
$36$	−7.04281	−1.17380
$37$	0.820682	0.134919	0.0674596	−	0.997722i	$-0.478511\pi$
$37$	0.820682	0.134919	0.0674596	+	0.997722i	$0.478511\pi$
$38$	3.15551	0.511891
$39$	8.79922	1.40900
$40$	0	0
$41$	−9.85369	−1.53889	−0.769444	−	0.638714i	$-0.779467\pi$
$41$	−9.85369	−1.53889	−0.769444	+	0.638714i	$0.779467\pi$
$42$	4.15857	0.641681
$43$	−5.29702	−0.807788	−0.403894	−	0.914806i	$-0.632344\pi$
$43$	−5.29702	−0.807788	−0.403894	+	0.914806i	$0.632344\pi$
$44$	0.983375	0.148249
$45$	0	0
$46$	−4.73497	−0.698133
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	2.67050	0.385453
$49$	−3.09183	−0.441690
$50$	0	0
$51$	4.85471	0.679796
$52$	−4.50814	−0.625167
$53$	4.43246	0.608845	0.304422	−	0.952537i	$-0.401537\pi$
$53$	4.43246	0.608845	0.304422	+	0.952537i	$0.401537\pi$
$54$	3.98198	0.541879
$55$	0	0
$56$	−5.09100	−0.680313
$57$	11.8400	1.56825
$58$	3.46122	0.454480
$59$	−7.94529	−1.03439	−0.517194	−	0.855868i	$-0.673023\pi$
$59$	−7.94529	−1.03439	−0.517194	+	0.855868i	$0.673023\pi$
$60$	0	0
$61$	6.03056	0.772134	0.386067	−	0.922471i	$-0.373833\pi$
$61$	6.03056	0.772134	0.386067	+	0.922471i	$0.373833\pi$
$62$	6.92436	0.879394
$63$	9.67295	1.21868
$64$	2.48822	0.311027
$65$	0	0
$66$	−1.43715	−0.176901
$67$	11.6410	1.42218	0.711090	−	0.703101i	$-0.248202\pi$
$67$	11.6410	1.42218	0.711090	+	0.703101i	$0.248202\pi$
$68$	−2.48724	−0.301622
$69$	−17.7664	−2.13883
$70$	0	0
$71$	−16.7985	−1.99361	−0.996807	−	0.0798465i	$-0.974557\pi$
$71$	−16.7985	−1.99361	−0.996807	+	0.0798465i	$0.974557\pi$
$72$	−12.6005	−1.48498
$73$	5.86850	0.686856	0.343428	−	0.939179i	$-0.388412\pi$
$73$	5.86850	0.686856	0.343428	+	0.939179i	$0.388412\pi$
$74$	0.614485	0.0714325
$75$	0	0
$76$	−6.06606	−0.695824
$77$	−1.35062	−0.153917
$78$	6.58842	0.745991
$79$	−7.36295	−0.828397	−0.414198	−	0.910187i	$-0.635938\pi$
$79$	−7.36295	−0.828397	−0.414198	+	0.910187i	$0.635938\pi$
$80$	0	0
$81$	0.262216	0.0291351
$82$	−7.37795	−0.814758
$83$	−15.3880	−1.68905	−0.844524	−	0.535518i	$-0.820117\pi$
$83$	−15.3880	−1.68905	−0.844524	+	0.535518i	$0.820117\pi$
$84$	−7.99430	−0.872250
$85$	0	0
$86$	−3.96614	−0.427680
$87$	12.9871	1.39236
$88$	1.75939	0.187551
$89$	9.21820	0.977128	0.488564	−	0.872528i	$-0.337521\pi$
$89$	9.21820	0.977128	0.488564	+	0.872528i	$0.337521\pi$
$90$	0	0
$91$	6.19172	0.649068
$92$	9.10236	0.948986
$93$	25.9814	2.69415
$94$	−0.748750	−0.0772276
$95$	0	0
$96$	16.4695	1.68091
$97$	−2.30654	−0.234193	−0.117097	−	0.993121i	$-0.537359\pi$
$97$	−2.30654	−0.234193	−0.117097	+	0.993121i	$0.537359\pi$
$98$	−2.31500	−0.233851
$99$	−3.34286	−0.335970
$100$	0	0
$101$	4.38984	0.436805	0.218402	−	0.975859i	$-0.429915\pi$
$101$	4.38984	0.436805	0.218402	+	0.975859i	$0.429915\pi$
$102$	3.63496	0.359915
$103$	−0.930698	−0.0917044	−0.0458522	−	0.998948i	$-0.514600\pi$
$103$	−0.930698	−0.0917044	−0.0458522	+	0.998948i	$0.514600\pi$
$104$	−8.06567	−0.790904
$105$	0	0
$106$	3.31880	0.322351
$107$	−11.3328	−1.09558	−0.547789	−	0.836616i	$-0.684530\pi$
$107$	−11.3328	−1.09558	−0.547789	+	0.836616i	$0.684530\pi$
$108$	−7.65485	−0.736588
$109$	−11.2292	−1.07556	−0.537779	−	0.843086i	$-0.680736\pi$
$109$	−11.2292	−1.07556	−0.537779	+	0.843086i	$0.680736\pi$
$110$	0	0
$111$	2.30566	0.218843
$112$	1.87914	0.177562
$113$	12.4798	1.17400	0.587002	−	0.809586i	$-0.300308\pi$
$113$	12.4798	1.17400	0.587002	+	0.809586i	$0.300308\pi$
$114$	8.86522	0.830304
$115$	0	0
$116$	−6.65374	−0.617784
$117$	15.3249	1.41678
$118$	−5.94903	−0.547653
$119$	3.41610	0.313153
$120$	0	0
$121$	−10.5332	−0.957568
$122$	4.51538	0.408803
$123$	−27.6834	−2.49613
$124$	−13.3112	−1.19538
$125$	0	0
$126$	7.24262	0.645224
$127$	−13.1841	−1.16990	−0.584948	−	0.811071i	$-0.698885\pi$
$127$	−13.1841	−1.16990	−0.584948	+	0.811071i	$0.698885\pi$
$128$	−9.86131	−0.871625
$129$	−14.8817	−1.31026
$130$	0	0
$131$	16.9113	1.47755	0.738774	−	0.673954i	$-0.235405\pi$
$131$	16.9113	1.47755	0.738774	+	0.673954i	$0.235405\pi$
$132$	2.76274	0.240465
$133$	8.33143	0.722427
$134$	8.71623	0.752967
$135$	0	0
$136$	−4.44999	−0.381584
$137$	−6.16669	−0.526856	−0.263428	−	0.964679i	$-0.584853\pi$
$137$	−6.16669	−0.526856	−0.263428	+	0.964679i	$0.584853\pi$
$138$	−13.3026	−1.13239
$139$	11.3125	0.959514	0.479757	−	0.877401i	$-0.340725\pi$
$139$	11.3125	0.959514	0.479757	+	0.877401i	$0.340725\pi$
$140$	0	0
$141$	−2.80944	−0.236598
$142$	−12.5779	−1.05551
$143$	−2.13978	−0.178938
$144$	4.65098	0.387582
$145$	0	0
$146$	4.39404	0.363653
$147$	−8.68631	−0.716435
$148$	−1.18127	−0.0970996
$149$	−15.4251	−1.26368	−0.631838	−	0.775100i	$-0.717699\pi$
$149$	−15.4251	−1.26368	−0.631838	+	0.775100i	$0.717699\pi$
$150$	0	0
$151$	−21.0300	−1.71140	−0.855699	−	0.517475i	$-0.826872\pi$
$151$	−21.0300	−1.71140	−0.855699	+	0.517475i	$0.826872\pi$
$152$	−10.8530	−0.880293
$153$	8.45504	0.683549
$154$	−1.01127	−0.0814909
$155$	0	0
$156$	−12.6654	−1.01404
$157$	−15.3462	−1.22476	−0.612381	−	0.790563i	$-0.709788\pi$
$157$	−15.3462	−1.22476	−0.612381	+	0.790563i	$0.709788\pi$
$158$	−5.51301	−0.438591
$159$	12.4527	0.987566
$160$	0	0
$161$	−12.5016	−0.985268
$162$	0.196334	0.0154255
$163$	16.9593	1.32836	0.664179	−	0.747574i	$-0.268781\pi$
$163$	16.9593	1.32836	0.664179	+	0.747574i	$0.268781\pi$
$164$	14.1832	1.10752
$165$	0	0
$166$	−11.5217	−0.894260
$167$	−5.65697	−0.437749	−0.218875	−	0.975753i	$-0.570239\pi$
$167$	−5.65697	−0.437749	−0.218875	+	0.975753i	$0.570239\pi$
$168$	−14.3029	−1.10349
$169$	−3.19046	−0.245420
$170$	0	0
$171$	20.6208	1.57691
$172$	7.62440	0.581355
$173$	4.11982	0.313224	0.156612	−	0.987660i	$-0.449943\pi$
$173$	4.11982	0.313224	0.156612	+	0.987660i	$0.449943\pi$
$174$	9.72409	0.737181
$175$	0	0
$176$	−0.649409	−0.0489510
$177$	−22.3218	−1.67781
$178$	6.90213	0.517336
$179$	10.2012	0.762471	0.381236	−	0.924478i	$-0.375499\pi$
$179$	10.2012	0.762471	0.381236	+	0.924478i	$0.375499\pi$
$180$	0	0
$181$	−24.9208	−1.85235	−0.926176	−	0.377093i	$-0.876924\pi$
$181$	−24.9208	−1.85235	−0.926176	+	0.377093i	$0.876924\pi$
$182$	4.63605	0.343647
$183$	16.9425	1.25243
$184$	16.2853	1.20057
$185$	0	0
$186$	19.4536	1.42641
$187$	−1.18056	−0.0863313
$188$	1.43937	0.104977
$189$	10.5136	0.764749
$190$	0	0
$191$	−13.2172	−0.956366	−0.478183	−	0.878260i	$-0.658704\pi$
$191$	−13.2172	−0.956366	−0.478183	+	0.878260i	$0.658704\pi$
$192$	6.99050	0.504496
$193$	−1.62104	−0.116685	−0.0583426	−	0.998297i	$-0.518582\pi$
$193$	−1.62104	−0.116685	−0.0583426	+	0.998297i	$0.518582\pi$
$194$	−1.72702	−0.123993
$195$	0	0
$196$	4.45029	0.317878
$197$	21.6483	1.54238	0.771189	−	0.636606i	$-0.219662\pi$
$197$	21.6483	1.54238	0.771189	+	0.636606i	$0.219662\pi$
$198$	−2.50296	−0.177878
$199$	3.81022	0.270099	0.135050	−	0.990839i	$-0.456881\pi$
$199$	3.81022	0.270099	0.135050	+	0.990839i	$0.456881\pi$
$200$	0	0
$201$	32.7048	2.30682
$202$	3.28689	0.231265
$203$	9.13858	0.641403
$204$	−6.98775	−0.489240
$205$	0	0
$206$	−0.696860	−0.0485525
$207$	−30.9423	−2.15064
$208$	2.97712	0.206426
$209$	−2.87924	−0.199161
$210$	0	0
$211$	14.4047	0.991658	0.495829	−	0.868420i	$-0.334864\pi$
$211$	14.4047	0.991658	0.495829	+	0.868420i	$0.334864\pi$
$212$	−6.37996	−0.438178
$213$	−47.1944	−3.23371
$214$	−8.48540	−0.580050
$215$	0	0
$216$	−13.6955	−0.931863
$217$	18.2823	1.24108
$218$	−8.40782	−0.569450
$219$	16.4872	1.11410
$220$	0	0
$221$	5.41212	0.364059
$222$	1.72636	0.115866
$223$	25.4589	1.70485	0.852426	−	0.522848i	$-0.175131\pi$
$223$	25.4589	1.70485	0.852426	+	0.522848i	$0.175131\pi$
$224$	11.5890	0.774323
$225$	0	0
$226$	9.34427	0.621572
$227$	12.6614	0.840366	0.420183	−	0.907439i	$-0.361966\pi$
$227$	12.6614	0.840366	0.420183	+	0.907439i	$0.361966\pi$
$228$	−17.0422	−1.12865
$229$	9.14714	0.604460	0.302230	−	0.953235i	$-0.402269\pi$
$229$	9.14714	0.604460	0.302230	+	0.953235i	$0.402269\pi$
$230$	0	0
$231$	−3.79448	−0.249659
$232$	−11.9044	−0.781563
$233$	0.902354	0.0591152	0.0295576	−	0.999563i	$-0.490590\pi$
$233$	0.902354	0.0591152	0.0295576	+	0.999563i	$0.490590\pi$
$234$	11.4745	0.750110
$235$	0	0
$236$	11.4362	0.744436
$237$	−20.6858	−1.34369
$238$	2.55780	0.165798
$239$	8.18082	0.529173	0.264587	−	0.964362i	$-0.414764\pi$
$239$	8.18082	0.529173	0.264587	+	0.964362i	$0.414764\pi$
$240$	0	0
$241$	14.5360	0.936343	0.468171	−	0.883638i	$-0.344913\pi$
$241$	14.5360	0.936343	0.468171	+	0.883638i	$0.344913\pi$
$242$	−7.88676	−0.506980
$243$	−15.2179	−0.976226
$244$	−8.68023	−0.555695
$245$	0	0
$246$	−20.7279	−1.32156
$247$	13.1995	0.839863
$248$	−23.8155	−1.51228
$249$	−43.2316	−2.73969
$250$	0	0
$251$	2.85075	0.179938	0.0899689	−	0.995945i	$-0.471323\pi$
$251$	2.85075	0.179938	0.0899689	+	0.995945i	$0.471323\pi$
$252$	−13.9230	−0.877066
$253$	4.32042	0.271622
$254$	−9.87156	−0.619397
$255$	0	0
$256$	−12.3601	−0.772505
$257$	4.98269	0.310812	0.155406	−	0.987851i	$-0.450331\pi$
$257$	4.98269	0.310812	0.155406	+	0.987851i	$0.450331\pi$
$258$	−11.1427	−0.693711
$259$	1.62241	0.100812
$260$	0	0
$261$	22.6185	1.40005
$262$	12.6623	0.782282
$263$	−6.57236	−0.405269	−0.202635	−	0.979254i	$-0.564950\pi$
$263$	−6.57236	−0.405269	−0.202635	+	0.979254i	$0.564950\pi$
$264$	4.94290	0.304214
$265$	0	0
$266$	6.23816	0.382486
$267$	25.8980	1.58493
$268$	−16.7558	−1.02352
$269$	0.492290	0.0300154	0.0150077	−	0.999887i	$-0.495223\pi$
$269$	0.492290	0.0300154	0.0150077	+	0.999887i	$0.495223\pi$
$270$	0	0
$271$	−29.3003	−1.77987	−0.889933	−	0.456092i	$-0.849249\pi$
$271$	−29.3003	−1.77987	−0.889933	+	0.456092i	$0.849249\pi$
$272$	1.64254	0.0995936
$273$	17.3953	1.05281
$274$	−4.61731	−0.278942
$275$	0	0
$276$	25.5725	1.53929
$277$	−0.337290	−0.0202658	−0.0101329	−	0.999949i	$-0.503225\pi$
$277$	−0.337290	−0.0202658	−0.0101329	+	0.999949i	$0.503225\pi$
$278$	8.47024	0.508011
$279$	45.2496	2.70902
$280$	0	0
$281$	−5.54902	−0.331027	−0.165513	−	0.986208i	$-0.552928\pi$
$281$	−5.54902	−0.331027	−0.165513	+	0.986208i	$0.552928\pi$
$282$	−2.10357	−0.125266
$283$	3.43506	0.204193	0.102097	−	0.994774i	$-0.467445\pi$
$283$	3.43506	0.204193	0.102097	+	0.994774i	$0.467445\pi$
$284$	24.1793	1.43478
$285$	0	0
$286$	−1.60216	−0.0947379
$287$	−19.4799	−1.14986
$288$	28.6834	1.69019
$289$	−14.0140	−0.824354
$290$	0	0
$291$	−6.48008	−0.379869
$292$	−8.44696	−0.494321
$293$	7.30273	0.426630	0.213315	−	0.976983i	$-0.431574\pi$
$293$	7.30273	0.426630	0.213315	+	0.976983i	$0.431574\pi$
$294$	−6.50387	−0.379313
$295$	0	0
$296$	−2.11344	−0.122841
$297$	−3.63336	−0.210829
$298$	−11.5496	−0.669049
$299$	−19.8064	−1.14543
$300$	0	0
$301$	−10.4717	−0.603581
$302$	−15.7462	−0.906092
$303$	12.3330	0.708512
$304$	4.00595	0.229757
$305$	0	0
$306$	6.33071	0.361902
$307$	8.41895	0.480495	0.240247	−	0.970712i	$-0.422771\pi$
$307$	8.41895	0.480495	0.240247	+	0.970712i	$0.422771\pi$
$308$	1.94404	0.110772
$309$	−2.61474	−0.148748
$310$	0	0
$311$	15.1569	0.859468	0.429734	−	0.902956i	$-0.358607\pi$
$311$	15.1569	0.859468	0.429734	+	0.902956i	$0.358607\pi$
$312$	−22.6600	−1.28287
$313$	19.2947	1.09060	0.545299	−	0.838241i	$-0.316416\pi$
$313$	19.2947	1.09060	0.545299	+	0.838241i	$0.316416\pi$
$314$	−11.4905	−0.648445
$315$	0	0
$316$	10.5980	0.596186
$317$	−15.6412	−0.878497	−0.439248	−	0.898366i	$-0.644755\pi$
$317$	−15.6412	−0.878497	−0.439248	+	0.898366i	$0.644755\pi$
$318$	9.32398	0.522863
$319$	−3.15819	−0.176824
$320$	0	0
$321$	−31.8387	−1.77706
$322$	−9.36060	−0.521646
$323$	7.28243	0.405205
$324$	−0.377427	−0.0209682
$325$	0	0
$326$	12.6983	0.703294
$327$	−31.5477	−1.74459
$328$	25.3755	1.40113
$329$	−1.97691	−0.108991
$330$	0	0
$331$	2.38310	0.130987	0.0654936	−	0.997853i	$-0.479138\pi$
$331$	2.38310	0.130987	0.0654936	+	0.997853i	$0.479138\pi$
$332$	22.1490	1.21559
$333$	4.01557	0.220052
$334$	−4.23565	−0.231765
$335$	0	0
$336$	5.27934	0.288012
$337$	2.74008	0.149262	0.0746308	−	0.997211i	$-0.476222\pi$
$337$	2.74008	0.149262	0.0746308	+	0.997211i	$0.476222\pi$
$338$	−2.38886	−0.129937
$339$	35.0614	1.90427
$340$	0	0
$341$	−6.31813	−0.342146
$342$	15.4398	0.834889
$343$	−19.9506	−1.07723
$344$	13.6411	0.735476
$345$	0	0
$346$	3.08471	0.165835
$347$	−5.91877	−0.317736	−0.158868	−	0.987300i	$-0.550784\pi$
$347$	−5.91877	−0.317736	−0.158868	+	0.987300i	$0.550784\pi$
$348$	−18.6933	−1.00207
$349$	−16.5244	−0.884530	−0.442265	−	0.896884i	$-0.645825\pi$
$349$	−16.5244	−0.884530	−0.442265	+	0.896884i	$0.645825\pi$
$350$	0	0
$351$	16.6566	0.889065
$352$	−4.00502	−0.213468
$353$	−30.5888	−1.62808	−0.814038	−	0.580811i	$-0.802735\pi$
$353$	−30.5888	−1.62808	−0.814038	+	0.580811i	$0.802735\pi$
$354$	−16.7135	−0.888310
$355$	0	0
$356$	−13.2684	−0.703226
$357$	9.59733	0.507945
$358$	7.63813	0.403688
$359$	−22.1287	−1.16791	−0.583954	−	0.811786i	$-0.698495\pi$
$359$	−22.1287	−1.16791	−0.583954	+	0.811786i	$0.698495\pi$
$360$	0	0
$361$	−1.23907	−0.0652141
$362$	−18.6595	−0.980720
$363$	−29.5925	−1.55321
$364$	−8.91220	−0.467126
$365$	0	0
$366$	12.6857	0.663092
$367$	26.8601	1.40209	0.701044	−	0.713118i	$-0.252718\pi$
$367$	26.8601	1.40209	0.701044	+	0.713118i	$0.252718\pi$
$368$	−6.01108	−0.313349
$369$	−48.2138	−2.50991
$370$	0	0
$371$	8.76257	0.454930
$372$	−37.3970	−1.93894
$373$	−19.6742	−1.01869	−0.509346	−	0.860562i	$-0.670113\pi$
$373$	−19.6742	−1.01869	−0.509346	+	0.860562i	$0.670113\pi$
$374$	−0.883946	−0.0457078
$375$	0	0
$376$	2.57523	0.132807
$377$	14.4783	0.745668
$378$	7.87202	0.404893
$379$	−31.7644	−1.63163	−0.815814	−	0.578315i	$-0.803711\pi$
$379$	−31.7644	−1.63163	−0.815814	+	0.578315i	$0.803711\pi$
$380$	0	0
$381$	−37.0398	−1.89761
$382$	−9.89641	−0.506344
$383$	17.6040	0.899520	0.449760	−	0.893149i	$-0.351509\pi$
$383$	17.6040	0.899520	0.449760	+	0.893149i	$0.351509\pi$
$384$	−27.7048	−1.41380
$385$	0	0
$386$	−1.21375	−0.0617785
$387$	−25.9182	−1.31749
$388$	3.31997	0.168546
$389$	3.17068	0.160760	0.0803800	−	0.996764i	$-0.474387\pi$
$389$	3.17068	0.160760	0.0803800	+	0.996764i	$0.474387\pi$
$390$	0	0
$391$	−10.9276	−0.552631
$392$	7.96217	0.402150
$393$	47.5113	2.39663
$394$	16.2092	0.816606
$395$	0	0
$396$	4.81162	0.241793
$397$	16.5434	0.830288	0.415144	−	0.909756i	$-0.363731\pi$
$397$	16.5434	0.830288	0.415144	+	0.909756i	$0.363731\pi$
$398$	2.85290	0.143003
$399$	23.4067	1.17180
$400$	0	0
$401$	29.2083	1.45859	0.729296	−	0.684198i	$-0.239848\pi$
$401$	29.2083	1.45859	0.729296	+	0.684198i	$0.239848\pi$
$402$	24.4877	1.22134
$403$	28.9646	1.44283
$404$	−6.31861	−0.314363
$405$	0	0
$406$	6.84251	0.339588
$407$	−0.560687	−0.0277922
$408$	−12.5020	−0.618941
$409$	−16.5232	−0.817017	−0.408509	−	0.912754i	$-0.633951\pi$
$409$	−16.5232	−0.817017	−0.408509	+	0.912754i	$0.633951\pi$
$410$	0	0
$411$	−17.3250	−0.854577
$412$	1.33962	0.0659985
$413$	−15.7071	−0.772897
$414$	−23.1680	−1.13865
$415$	0	0
$416$	18.3605	0.900195
$417$	31.7818	1.55636
$418$	−2.15583	−0.105445
$419$	−0.431769	−0.0210933	−0.0105467	−	0.999944i	$-0.503357\pi$
$419$	−0.431769	−0.0210933	−0.0105467	+	0.999944i	$0.503357\pi$
$420$	0	0
$421$	20.8738	1.01733	0.508663	−	0.860966i	$-0.330140\pi$
$421$	20.8738	1.01733	0.508663	+	0.860966i	$0.330140\pi$
$422$	10.7855	0.525029
$423$	−4.89297	−0.237904
$424$	−11.4146	−0.554342
$425$	0	0
$426$	−35.3368	−1.71207
$427$	11.9219	0.576940
$428$	16.3121	0.788474
$429$	−6.01160	−0.290243
$430$	0	0
$431$	−23.2391	−1.11939	−0.559695	−	0.828699i	$-0.689082\pi$
$431$	−23.2391	−1.11939	−0.559695	+	0.828699i	$0.689082\pi$
$432$	5.05516	0.243217
$433$	11.2027	0.538368	0.269184	−	0.963089i	$-0.413246\pi$
$433$	11.2027	0.538368	0.269184	+	0.963089i	$0.413246\pi$
$434$	13.6888	0.657085
$435$	0	0
$436$	16.1629	0.774065
$437$	−26.6510	−1.27489
$438$	12.3448	0.589857
$439$	24.2970	1.15963	0.579817	−	0.814747i	$-0.303124\pi$
$439$	24.2970	1.15963	0.579817	+	0.814747i	$0.303124\pi$
$440$	0	0
$441$	−15.1282	−0.720391
$442$	4.05233	0.192749
$443$	11.0069	0.522953	0.261477	−	0.965210i	$-0.415791\pi$
$443$	11.0069	0.522953	0.261477	+	0.965210i	$0.415791\pi$
$444$	−3.31870	−0.157499
$445$	0	0
$446$	19.0623	0.902627
$447$	−43.3360	−2.04972
$448$	4.91898	0.232400
$449$	−3.08314	−0.145502	−0.0727512	−	0.997350i	$-0.523178\pi$
$449$	−3.08314	−0.145502	−0.0727512	+	0.997350i	$0.523178\pi$
$450$	0	0
$451$	6.73201	0.316998
$452$	−17.9631	−0.844915
$453$	−59.0826	−2.77594
$454$	9.48021	0.444928
$455$	0	0
$456$	−30.4908	−1.42786
$457$	15.9199	0.744703	0.372352	−	0.928092i	$-0.378552\pi$
$457$	15.9199	0.744703	0.372352	+	0.928092i	$0.378552\pi$
$458$	6.84892	0.320029
$459$	9.18980	0.428943
$460$	0	0
$461$	16.5425	0.770461	0.385231	−	0.922820i	$-0.374122\pi$
$461$	16.5425	0.770461	0.385231	+	0.922820i	$0.374122\pi$
$462$	−2.84112	−0.132181
$463$	−18.5890	−0.863904	−0.431952	−	0.901897i	$-0.642175\pi$
$463$	−18.5890	−0.863904	−0.431952	+	0.901897i	$0.642175\pi$
$464$	4.39404	0.203988
$465$	0	0
$466$	0.675638	0.0312983
$467$	−26.4830	−1.22549	−0.612743	−	0.790282i	$-0.709934\pi$
$467$	−26.4830	−1.22549	−0.612743	+	0.790282i	$0.709934\pi$
$468$	−22.0582	−1.01964
$469$	23.0133	1.06265
$470$	0	0
$471$	−43.1143	−1.98660
$472$	20.4609	0.941791
$473$	3.61891	0.166398
$474$	−15.4885	−0.711409
$475$	0	0
$476$	−4.91704	−0.225372
$477$	21.6879	0.993019
$478$	6.12539	0.280169
$479$	8.56769	0.391468	0.195734	−	0.980657i	$-0.437291\pi$
$479$	8.56769	0.391468	0.195734	+	0.980657i	$0.437291\pi$
$480$	0	0
$481$	2.57039	0.117200
$482$	10.8838	0.495743
$483$	−35.1226	−1.59814
$484$	15.1613	0.689149
$485$	0	0
$486$	−11.3944	−0.516859
$487$	4.14697	0.187917	0.0939585	−	0.995576i	$-0.470048\pi$
$487$	4.14697	0.187917	0.0939585	+	0.995576i	$0.470048\pi$
$488$	−15.5301	−0.703014
$489$	47.6463	2.15464
$490$	0	0
$491$	3.28381	0.148196	0.0740982	−	0.997251i	$-0.476392\pi$
$491$	3.28381	0.148196	0.0740982	+	0.997251i	$0.476392\pi$
$492$	39.8467	1.79643
$493$	7.98795	0.359759
$494$	9.88311	0.444662
$495$	0	0
$496$	8.79053	0.394707
$497$	−33.2091	−1.48963
$498$	−32.3696	−1.45052
$499$	−5.43554	−0.243328	−0.121664	−	0.992571i	$-0.538823\pi$
$499$	−5.43554	−0.243328	−0.121664	+	0.992571i	$0.538823\pi$
$500$	0	0
$501$	−15.8929	−0.710043
$502$	2.13450	0.0952673
$503$	−5.44837	−0.242931	−0.121465	−	0.992596i	$-0.538759\pi$
$503$	−5.44837	−0.242931	−0.121465	+	0.992596i	$0.538759\pi$
$504$	−24.9101	−1.10958
$505$	0	0
$506$	3.23491	0.143809
$507$	−8.96342	−0.398080
$508$	18.9768	0.841959
$509$	−4.78776	−0.212214	−0.106107	−	0.994355i	$-0.533839\pi$
$509$	−4.78776	−0.212214	−0.106107	+	0.994355i	$0.533839\pi$
$510$	0	0
$511$	11.6015	0.513220
$512$	10.4680	0.462625
$513$	22.4128	0.989548
$514$	3.73079	0.164558
$515$	0	0
$516$	21.4203	0.942976
$517$	0.683196	0.0300469
$518$	1.21478	0.0533745
$519$	11.5744	0.508059
$520$	0	0
$521$	40.1879	1.76066	0.880332	−	0.474358i	$-0.157320\pi$
$521$	40.1879	1.76066	0.880332	+	0.474358i	$0.157320\pi$
$522$	16.9356	0.741252
$523$	37.6921	1.64816	0.824081	−	0.566472i	$-0.191692\pi$
$523$	37.6921	1.64816	0.824081	+	0.566472i	$0.191692\pi$
$524$	−24.3417	−1.06337
$525$	0	0
$526$	−4.92105	−0.214568
$527$	15.9803	0.696115
$528$	−1.82448	−0.0794001
$529$	16.9908	0.738732
$530$	0	0
$531$	−38.8760	−1.68708
$532$	−11.9920	−0.519921
$533$	−30.8619	−1.33678
$534$	19.3911	0.839136
$535$	0	0
$536$	−29.9784	−1.29487
$537$	28.6596	1.23675
$538$	0.368602	0.0158915
$539$	2.11233	0.0909843
$540$	0	0
$541$	−26.2912	−1.13035	−0.565173	−	0.824972i	$-0.691191\pi$
$541$	−26.2912	−1.13035	−0.565173	+	0.824972i	$0.691191\pi$
$542$	−21.9386	−0.942343
$543$	−70.0136	−3.00457
$544$	10.1298	0.434313
$545$	0	0
$546$	13.0247	0.557406
$547$	17.5817	0.751739	0.375869	−	0.926673i	$-0.377344\pi$
$547$	17.5817	0.751739	0.375869	+	0.926673i	$0.377344\pi$
$548$	8.87617	0.379171
$549$	29.5073	1.25934
$550$	0	0
$551$	19.4816	0.829945
$552$	45.7527	1.94736
$553$	−14.5559	−0.618979
$554$	−0.252546	−0.0107297
$555$	0	0
$556$	−16.2829	−0.690550
$557$	5.68003	0.240671	0.120335	−	0.992733i	$-0.461603\pi$
$557$	5.68003	0.240671	0.120335	+	0.992733i	$0.461603\pi$
$558$	33.8806	1.43428
$559$	−16.5904	−0.701698
$560$	0	0
$561$	−3.31672	−0.140032
$562$	−4.15483	−0.175261
$563$	23.9665	1.01007	0.505033	−	0.863100i	$-0.331480\pi$
$563$	23.9665	1.01007	0.505033	+	0.863100i	$0.331480\pi$
$564$	4.04384	0.170276
$565$	0	0
$566$	2.57200	0.108109
$567$	0.518378	0.0217698
$568$	43.2600	1.81515
$569$	15.9562	0.668919	0.334459	−	0.942410i	$-0.391446\pi$
$569$	15.9562	0.668919	0.334459	+	0.942410i	$0.391446\pi$
$570$	0	0
$571$	1.44799	0.0605964	0.0302982	−	0.999541i	$-0.490354\pi$
$571$	1.44799	0.0605964	0.0302982	+	0.999541i	$0.490354\pi$
$572$	3.07995	0.128779
$573$	−37.1331	−1.55126
$574$	−14.5855	−0.608789
$575$	0	0
$576$	12.1748	0.507282
$577$	27.0861	1.12761	0.563804	−	0.825909i	$-0.309337\pi$
$577$	27.0861	1.12761	0.563804	+	0.825909i	$0.309337\pi$
$578$	−10.4930	−0.436451
$579$	−4.55422	−0.189267
$580$	0	0
$581$	−30.4206	−1.26206
$582$	−4.85196	−0.201120
$583$	−3.02824	−0.125417
$584$	−15.1127	−0.625369
$585$	0	0
$586$	5.46792	0.225878
$587$	25.0175	1.03258	0.516292	−	0.856413i	$-0.327312\pi$
$587$	25.0175	1.03258	0.516292	+	0.856413i	$0.327312\pi$
$588$	12.5028	0.515609
$589$	38.9741	1.60590
$590$	0	0
$591$	60.8197	2.50179
$592$	0.780095	0.0320617
$593$	45.5416	1.87017	0.935085	−	0.354424i	$-0.115323\pi$
$593$	45.5416	1.87017	0.935085	+	0.354424i	$0.115323\pi$
$594$	−2.72048	−0.111623
$595$	0	0
$596$	22.2025	0.909452
$597$	10.7046	0.438110
$598$	−14.8300	−0.606444
$599$	−1.43737	−0.0587294	−0.0293647	−	0.999569i	$-0.509348\pi$
$599$	−1.43737	−0.0587294	−0.0293647	+	0.999569i	$0.509348\pi$
$600$	0	0
$601$	1.94408	0.0793008	0.0396504	−	0.999214i	$-0.487376\pi$
$601$	1.94408	0.0793008	0.0396504	+	0.999214i	$0.487376\pi$
$602$	−7.84071	−0.319564
$603$	56.9592	2.31956
$604$	30.2700	1.23167
$605$	0	0
$606$	9.23432	0.375119
$607$	46.4934	1.88711	0.943555	−	0.331215i	$-0.107459\pi$
$607$	46.4934	1.88711	0.943555	+	0.331215i	$0.107459\pi$
$608$	24.7054	1.00194
$609$	25.6743	1.04038
$610$	0	0
$611$	−3.13202	−0.126708
$612$	−12.1700	−0.491941
$613$	−17.1954	−0.694515	−0.347258	−	0.937770i	$-0.612887\pi$
$613$	−17.1954	−0.694515	−0.347258	+	0.937770i	$0.612887\pi$
$614$	6.30368	0.254396
$615$	0	0
$616$	3.47815	0.140139
$617$	42.5107	1.71142	0.855708	−	0.517459i	$-0.173122\pi$
$617$	42.5107	1.71142	0.855708	+	0.517459i	$0.173122\pi$
$618$	−1.95779	−0.0787538
$619$	2.71314	0.109050	0.0545251	−	0.998512i	$-0.482636\pi$
$619$	2.71314	0.109050	0.0545251	+	0.998512i	$0.482636\pi$
$620$	0	0
$621$	−33.6313	−1.34958
$622$	11.3487	0.455042
$623$	18.2236	0.730112
$624$	8.36405	0.334830
$625$	0	0
$626$	14.4469	0.577413
$627$	−8.08907	−0.323046
$628$	22.0889	0.881445
$629$	1.41814	0.0565448
$630$	0	0
$631$	−6.94580	−0.276508	−0.138254	−	0.990397i	$-0.544149\pi$
$631$	−6.94580	−0.276508	−0.138254	+	0.990397i	$0.544149\pi$
$632$	18.9613	0.754240
$633$	40.4691	1.60850
$634$	−11.7113	−0.465117
$635$	0	0
$636$	−17.9241	−0.710738
$637$	−9.68366	−0.383680
$638$	−2.36469	−0.0936190
$639$	−82.1945	−3.25156
$640$	0	0
$641$	−32.1269	−1.26894	−0.634468	−	0.772949i	$-0.718781\pi$
$641$	−32.1269	−1.26894	−0.634468	+	0.772949i	$0.718781\pi$
$642$	−23.8392	−0.940860
$643$	−19.8992	−0.784747	−0.392373	−	0.919806i	$-0.628346\pi$
$643$	−19.8992	−0.784747	−0.392373	+	0.919806i	$0.628346\pi$
$644$	17.9945	0.709084
$645$	0	0
$646$	5.45272	0.214534
$647$	−33.8197	−1.32959	−0.664794	−	0.747027i	$-0.731481\pi$
$647$	−33.8197	−1.32959	−0.664794	+	0.747027i	$0.731481\pi$
$648$	−0.675267	−0.0265270
$649$	5.42819	0.213075
$650$	0	0
$651$	51.3629	2.01307
$652$	−24.4108	−0.956001
$653$	13.8854	0.543377	0.271689	−	0.962385i	$-0.412418\pi$
$653$	13.8854	0.543377	0.271689	+	0.962385i	$0.412418\pi$
$654$	−23.6213	−0.923666
$655$	0	0
$656$	−9.36638	−0.365696
$657$	28.7144	1.12025
$658$	−1.48021	−0.0577046
$659$	−21.9217	−0.853950	−0.426975	−	0.904263i	$-0.640421\pi$
$659$	−21.9217	−0.853950	−0.426975	+	0.904263i	$0.640421\pi$
$660$	0	0
$661$	34.4901	1.34151	0.670755	−	0.741679i	$-0.265970\pi$
$661$	34.4901	1.34151	0.670755	+	0.741679i	$0.265970\pi$
$662$	1.78435	0.0693507
$663$	15.2050	0.590515
$664$	39.6275	1.53785
$665$	0	0
$666$	3.00666	0.116506
$667$	−29.2329	−1.13190
$668$	8.14249	0.315042
$669$	71.5252	2.76532
$670$	0	0
$671$	−4.12006	−0.159053
$672$	32.5586	1.25598
$673$	30.0617	1.15879	0.579397	−	0.815046i	$-0.303288\pi$
$673$	30.0617	1.15879	0.579397	+	0.815046i	$0.303288\pi$
$674$	2.05163	0.0790259
$675$	0	0
$676$	4.59227	0.176626
$677$	−22.3311	−0.858256	−0.429128	−	0.903244i	$-0.641179\pi$
$677$	−22.3311	−0.858256	−0.429128	+	0.903244i	$0.641179\pi$
$678$	26.2522	1.00821
$679$	−4.55981	−0.174990
$680$	0	0
$681$	35.5714	1.36310
$682$	−4.73070	−0.181148
$683$	6.66867	0.255169	0.127585	−	0.991828i	$-0.459278\pi$
$683$	6.66867	0.255169	0.127585	+	0.991828i	$0.459278\pi$
$684$	−29.6810	−1.13488
$685$	0	0
$686$	−14.9380	−0.570337
$687$	25.6984	0.980453
$688$	−5.03506	−0.191960
$689$	13.8825	0.528883
$690$	0	0
$691$	31.6587	1.20435	0.602176	−	0.798363i	$-0.294300\pi$
$691$	31.6587	1.20435	0.602176	+	0.798363i	$0.294300\pi$
$692$	−5.92996	−0.225423
$693$	−6.60853	−0.251037
$694$	−4.43168	−0.168224
$695$	0	0
$696$	−33.4448	−1.26772
$697$	−17.0272	−0.644950
$698$	−12.3726	−0.468311
$699$	2.53511	0.0958867
$700$	0	0
$701$	−11.4406	−0.432107	−0.216054	−	0.976381i	$-0.569319\pi$
$701$	−11.4406	−0.432107	−0.216054	+	0.976381i	$0.569319\pi$
$702$	12.4716	0.470712
$703$	3.45866	0.130446
$704$	−1.69994	−0.0640689
$705$	0	0
$706$	−22.9033	−0.861979
$707$	8.67831	0.326381
$708$	32.1294	1.20750
$709$	−36.0783	−1.35495	−0.677474	−	0.735547i	$-0.736925\pi$
$709$	−36.0783	−1.35495	−0.677474	+	0.735547i	$0.736925\pi$
$710$	0	0
$711$	−36.0267	−1.35111
$712$	−23.7390	−0.889657
$713$	−58.4821	−2.19017
$714$	7.18600	0.268929
$715$	0	0
$716$	−14.6833	−0.548741
$717$	22.9836	0.858336
$718$	−16.5689	−0.618345
$719$	−43.8728	−1.63618	−0.818090	−	0.575090i	$-0.804967\pi$
$719$	−43.8728	−1.63618	−0.818090	+	0.575090i	$0.804967\pi$
$720$	0	0
$721$	−1.83991	−0.0685217
$722$	−0.927752	−0.0345274
$723$	40.8379	1.51878
$724$	35.8704	1.33311
$725$	0	0
$726$	−22.1574	−0.822338
$727$	45.8479	1.70040	0.850202	−	0.526456i	$-0.176479\pi$
$727$	45.8479	1.70040	0.850202	+	0.526456i	$0.176479\pi$
$728$	−15.9451	−0.590965
$729$	−43.5403	−1.61260
$730$	0	0
$731$	−9.15325	−0.338545
$732$	−24.3866	−0.901355
$733$	24.0847	0.889588	0.444794	−	0.895633i	$-0.353277\pi$
$733$	24.0847	0.889588	0.444794	+	0.895633i	$0.353277\pi$
$734$	20.1115	0.742330
$735$	0	0
$736$	−37.0714	−1.36647
$737$	−7.95312	−0.292957
$738$	−36.1001	−1.32886
$739$	−13.5864	−0.499782	−0.249891	−	0.968274i	$-0.580395\pi$
$739$	−13.5864	−0.499782	−0.249891	+	0.968274i	$0.580395\pi$
$740$	0	0
$741$	37.0832	1.36229
$742$	6.56097	0.240861
$743$	−10.3030	−0.377982	−0.188991	−	0.981979i	$-0.560522\pi$
$743$	−10.3030	−0.377982	−0.188991	+	0.981979i	$0.560522\pi$
$744$	−66.9081	−2.45297
$745$	0	0
$746$	−14.7311	−0.539342
$747$	−75.2928	−2.75482
$748$	1.69927	0.0621315
$749$	−22.4038	−0.818618
$750$	0	0
$751$	14.8677	0.542532	0.271266	−	0.962504i	$-0.412558\pi$
$751$	14.8677	0.542532	0.271266	+	0.962504i	$0.412558\pi$
$752$	−0.950545	−0.0346628
$753$	8.00902	0.291865
$754$	10.8406	0.394791
$755$	0	0
$756$	−15.1329	−0.550380
$757$	8.77657	0.318990	0.159495	−	0.987199i	$-0.449013\pi$
$757$	8.77657	0.318990	0.159495	+	0.987199i	$0.449013\pi$
$758$	−23.7836	−0.863859
$759$	12.1380	0.440580
$760$	0	0
$761$	−15.6051	−0.565683	−0.282842	−	0.959167i	$-0.591277\pi$
$761$	−15.6051	−0.565683	−0.282842	+	0.959167i	$0.591277\pi$
$762$	−27.7336	−1.00468
$763$	−22.1990	−0.803659
$764$	19.0246	0.688284
$765$	0	0
$766$	13.1810	0.476247
$767$	−24.8848	−0.898537
$768$	−34.7250	−1.25303
$769$	13.4781	0.486032	0.243016	−	0.970022i	$-0.421863\pi$
$769$	13.4781	0.486032	0.243016	+	0.970022i	$0.421863\pi$
$770$	0	0
$771$	13.9986	0.504147
$772$	2.33329	0.0839768
$773$	7.27907	0.261810	0.130905	−	0.991395i	$-0.458212\pi$
$773$	7.27907	0.261810	0.130905	+	0.991395i	$0.458212\pi$
$774$	−19.4062	−0.697542
$775$	0	0
$776$	5.93986	0.213229
$777$	4.55808	0.163520
$778$	2.37405	0.0851137
$779$	−41.5271	−1.48786
$780$	0	0
$781$	11.4767	0.410668
$782$	−8.18202	−0.292588
$783$	24.5841	0.878565
$784$	−2.93892	−0.104961
$785$	0	0
$786$	35.5741	1.26889
$787$	45.4996	1.62189	0.810943	−	0.585125i	$-0.198954\pi$
$787$	45.4996	1.62189	0.810943	+	0.585125i	$0.198954\pi$
$788$	−31.1600	−1.11003
$789$	−18.4647	−0.657359
$790$	0	0
$791$	24.6715	0.877218
$792$	8.60863	0.305894
$793$	18.8878	0.670726
$794$	12.3868	0.439593
$795$	0	0
$796$	−5.48433	−0.194387
$797$	−12.4843	−0.442218	−0.221109	−	0.975249i	$-0.570968\pi$
$797$	−12.4843	−0.442218	−0.221109	+	0.975249i	$0.570968\pi$
$798$	17.5257	0.620405
$799$	−1.72800	−0.0611322
$800$	0	0
$801$	45.1044	1.59368
$802$	21.8697	0.772246
$803$	−4.00934	−0.141486
$804$	−47.0745	−1.66019
$805$	0	0
$806$	21.6872	0.763899
$807$	1.38306	0.0486860
$808$	−11.3048	−0.397703
$809$	−16.4111	−0.576985	−0.288492	−	0.957482i	$-0.593154\pi$
$809$	−16.4111	−0.576985	−0.288492	+	0.957482i	$0.593154\pi$
$810$	0	0
$811$	16.4277	0.576854	0.288427	−	0.957502i	$-0.406868\pi$
$811$	16.4277	0.576854	0.288427	+	0.957502i	$0.406868\pi$
$812$	−13.1538	−0.461609
$813$	−82.3174	−2.88700
$814$	−0.419814	−0.0147145
$815$	0	0
$816$	4.61462	0.161544
$817$	−22.3236	−0.781005
$818$	−12.3717	−0.432567
$819$	30.2959	1.05862
$820$	0	0
$821$	−19.1719	−0.669102	−0.334551	−	0.942378i	$-0.608585\pi$
$821$	−19.1719	−0.669102	−0.334551	+	0.942378i	$0.608585\pi$
$822$	−12.9721	−0.452453
$823$	−16.6275	−0.579599	−0.289800	−	0.957087i	$-0.593589\pi$
$823$	−16.6275	−0.579599	−0.289800	+	0.957087i	$0.593589\pi$
$824$	2.39676	0.0834952
$825$	0	0
$826$	−11.7607	−0.409207
$827$	−4.38493	−0.152479	−0.0762394	−	0.997090i	$-0.524291\pi$
$827$	−4.38493	−0.152479	−0.0762394	+	0.997090i	$0.524291\pi$
$828$	44.5375	1.54779
$829$	7.24562	0.251651	0.125825	−	0.992052i	$-0.459842\pi$
$829$	7.24562	0.251651	0.125825	+	0.992052i	$0.459842\pi$
$830$	0	0
$831$	−0.947598	−0.0328718
$832$	7.79314	0.270179
$833$	−5.34267	−0.185113
$834$	23.7966	0.824010
$835$	0	0
$836$	4.14431	0.143334
$837$	49.1819	1.69998
$838$	−0.323287	−0.0111678
$839$	−24.7609	−0.854841	−0.427420	−	0.904053i	$-0.640578\pi$
$839$	−24.7609	−0.854841	−0.427420	+	0.904053i	$0.640578\pi$
$840$	0	0
$841$	−7.63101	−0.263138
$842$	15.6292	0.538619
$843$	−15.5897	−0.536936
$844$	−20.7337	−0.713683
$845$	0	0
$846$	−3.66361	−0.125957
$847$	−20.8233	−0.715496
$848$	4.21325	0.144684
$849$	9.65061	0.331208
$850$	0	0
$851$	−5.18985	−0.177906
$852$	67.9304	2.32726
$853$	39.8734	1.36524	0.682620	−	0.730773i	$-0.260840\pi$
$853$	39.8734	1.36524	0.682620	+	0.730773i	$0.260840\pi$
$854$	8.92650	0.305459
$855$	0	0
$856$	29.1845	0.997504
$857$	−31.7357	−1.08407	−0.542035	−	0.840356i	$-0.682346\pi$
$857$	−31.7357	−1.08407	−0.542035	+	0.840356i	$0.682346\pi$
$858$	−4.50118	−0.153668
$859$	8.31812	0.283811	0.141905	−	0.989880i	$-0.454677\pi$
$859$	8.31812	0.283811	0.141905	+	0.989880i	$0.454677\pi$
$860$	0	0
$861$	−54.7276	−1.86511
$862$	−17.4003	−0.592656
$863$	−15.5640	−0.529803	−0.264902	−	0.964275i	$-0.585339\pi$
$863$	−15.5640	−0.529803	−0.264902	+	0.964275i	$0.585339\pi$
$864$	31.1761	1.06063
$865$	0	0
$866$	8.38803	0.285037
$867$	−39.3716	−1.33713
$868$	−26.3150	−0.893189
$869$	5.03034	0.170643
$870$	0	0
$871$	36.4599	1.23540
$872$	28.9177	0.979275
$873$	−11.2858	−0.381967
$874$	−19.9549	−0.674985
$875$	0	0
$876$	−23.7313	−0.801805
$877$	36.3553	1.22763	0.613816	−	0.789449i	$-0.289634\pi$
$877$	36.3553	1.22763	0.613816	+	0.789449i	$0.289634\pi$
$878$	18.1924	0.613964
$879$	20.5166	0.692008
$880$	0	0
$881$	17.3559	0.584734	0.292367	−	0.956306i	$-0.405557\pi$
$881$	17.3559	0.584734	0.292367	+	0.956306i	$0.405557\pi$
$882$	−11.3272	−0.381408
$883$	−24.3049	−0.817924	−0.408962	−	0.912551i	$-0.634109\pi$
$883$	−24.3049	−0.817924	−0.408962	+	0.912551i	$0.634109\pi$
$884$	−7.79007	−0.262008
$885$	0	0
$886$	8.24141	0.276875
$887$	−17.1376	−0.575425	−0.287713	−	0.957717i	$-0.592895\pi$
$887$	−17.1376	−0.575425	−0.287713	+	0.957717i	$0.592895\pi$
$888$	−5.93760	−0.199253
$889$	−26.0637	−0.874148
$890$	0	0
$891$	−0.179145	−0.00600159
$892$	−36.6448	−1.22696
$893$	−4.21437	−0.141029
$894$	−32.4479	−1.08522
$895$	0	0
$896$	−19.4949	−0.651280
$897$	−55.6448	−1.85793
$898$	−2.30850	−0.0770357
$899$	42.7499	1.42579
$900$	0	0
$901$	7.65928	0.255168
$902$	5.04059	0.167833
$903$	−29.4197	−0.979028
$904$	−32.1384	−1.06891
$905$	0	0
$906$	−44.2381	−1.46971
$907$	−44.7807	−1.48692	−0.743459	−	0.668781i	$-0.766816\pi$
$907$	−44.7807	−1.48692	−0.743459	+	0.668781i	$0.766816\pi$
$908$	−18.2245	−0.604800
$909$	21.4793	0.712424
$910$	0	0
$911$	20.4872	0.678771	0.339385	−	0.940647i	$-0.389781\pi$
$911$	20.4872	0.678771	0.339385	+	0.940647i	$0.389781\pi$
$912$	11.2545	0.372673
$913$	10.5130	0.347930
$914$	11.9200	0.394280
$915$	0	0
$916$	−13.1661	−0.435022
$917$	33.4321	1.10403
$918$	6.88086	0.227102
$919$	37.4338	1.23483	0.617413	−	0.786639i	$-0.288181\pi$
$919$	37.4338	1.23483	0.617413	+	0.786639i	$0.288181\pi$
$920$	0	0
$921$	23.6525	0.779378
$922$	12.3862	0.407918
$923$	−52.6132	−1.73178
$924$	5.46168	0.179676
$925$	0	0
$926$	−13.9185	−0.457390
$927$	−4.55388	−0.149569
$928$	27.0989	0.889564
$929$	37.7113	1.23727	0.618633	−	0.785680i	$-0.287687\pi$
$929$	37.7113	1.23727	0.618633	+	0.785680i	$0.287687\pi$
$930$	0	0
$931$	−13.0301	−0.427045
$932$	−1.29883	−0.0425444
$933$	42.5824	1.39408
$934$	−19.8291	−0.648828
$935$	0	0
$936$	−39.4650	−1.28995
$937$	33.1293	1.08229	0.541144	−	0.840930i	$-0.317991\pi$
$937$	33.1293	1.08229	0.541144	+	0.840930i	$0.317991\pi$
$938$	17.2312	0.562618
$939$	54.2072	1.76899
$940$	0	0
$941$	14.0037	0.456507	0.228254	−	0.973602i	$-0.426698\pi$
$941$	14.0037	0.456507	0.228254	+	0.973602i	$0.426698\pi$
$942$	−32.2818	−1.05180
$943$	62.3131	2.02919
$944$	−7.55235	−0.245808
$945$	0	0
$946$	2.70966	0.0880985
$947$	−43.5062	−1.41376	−0.706881	−	0.707332i	$-0.749898\pi$
$947$	−43.5062	−1.41376	−0.706881	+	0.707332i	$0.749898\pi$
$948$	29.7746	0.967033
$949$	18.3802	0.596648
$950$	0	0
$951$	−43.9430	−1.42495
$952$	−8.79724	−0.285120
$953$	−43.7414	−1.41692	−0.708461	−	0.705750i	$-0.750610\pi$
$953$	−43.7414	−1.41692	−0.708461	+	0.705750i	$0.750610\pi$
$954$	16.2388	0.525750
$955$	0	0
$956$	−11.7753	−0.380839
$957$	−8.87274	−0.286815
$958$	6.41505	0.207261
$959$	−12.1910	−0.393668
$960$	0	0
$961$	54.5235	1.75882
$962$	1.92458	0.0620509
$963$	−55.4508	−1.78688
$964$	−20.9227	−0.673874
$965$	0	0
$966$	−26.2981	−0.846127
$967$	−6.63558	−0.213386	−0.106693	−	0.994292i	$-0.534026\pi$
$967$	−6.63558	−0.213386	−0.106693	+	0.994292i	$0.534026\pi$
$968$	27.1255	0.871847
$969$	20.4596	0.657256
$970$	0	0
$971$	−18.0134	−0.578078	−0.289039	−	0.957317i	$-0.593336\pi$
$971$	−18.0134	−0.578078	−0.289039	+	0.957317i	$0.593336\pi$
$972$	21.9042	0.702577
$973$	22.3638	0.716951
$974$	3.10504	0.0994919
$975$	0	0
$976$	5.73232	0.183487
$977$	55.9193	1.78902	0.894509	−	0.447051i	$-0.147526\pi$
$977$	55.9193	1.78902	0.894509	+	0.447051i	$0.147526\pi$
$978$	35.6751	1.14076
$979$	−6.29785	−0.201280
$980$	0	0
$981$	−54.9439	−1.75422
$982$	2.45875	0.0784620
$983$	−11.8397	−0.377627	−0.188813	−	0.982013i	$-0.560464\pi$
$983$	−11.8397	−0.377627	−0.188813	+	0.982013i	$0.560464\pi$
$984$	71.2911	2.27268
$985$	0	0
$986$	5.98098	0.190473
$987$	−5.55401	−0.176786
$988$	−18.9990	−0.604439
$989$	33.4975	1.06516
$990$	0	0
$991$	−53.7886	−1.70865	−0.854326	−	0.519738i	$-0.826029\pi$
$991$	−53.7886	−1.70865	−0.854326	+	0.519738i	$0.826029\pi$
$992$	54.2128	1.72126
$993$	6.69520	0.212466
$994$	−24.8653	−0.788680
$995$	0	0
$996$	62.2264	1.97172
$997$	−31.2731	−0.990429	−0.495215	−	0.868771i	$-0.664911\pi$
$997$	−31.2731	−0.990429	−0.495215	+	0.868771i	$0.664911\pi$
$998$	−4.06986	−0.128829
$999$	4.36453	0.138088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.j.1.7		11
5.2	odd	4		235.2.c.a.189.14	yes	22
5.3	odd	4		235.2.c.a.189.9	✓	22
5.4	even	2		1175.2.a.i.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.2.c.a.189.9	✓	22	5.3	odd	4
235.2.c.a.189.14	yes	22	5.2	odd	4
1175.2.a.i.1.5		11	5.4	even	2
1175.2.a.j.1.7		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)

\(f(q)\)	\(=\)	\(q+0.748750 q^{2} +2.80944 q^{3} -1.43937 q^{4} +2.10357 q^{6} +1.97691 q^{7} -2.57523 q^{8} +4.89297 q^{9} +O(q^{10})\)	\(q+0.748750 q^{2} +2.80944 q^{3} -1.43937 q^{4} +2.10357 q^{6} +1.97691 q^{7} -2.57523 q^{8} +4.89297 q^{9} -0.683196 q^{11} -4.04384 q^{12} +3.13202 q^{13} +1.48021 q^{14} +0.950545 q^{16} +1.72800 q^{17} +3.66361 q^{18} +4.21437 q^{19} +5.55401 q^{21} -0.511543 q^{22} -6.32383 q^{23} -7.23496 q^{24} +2.34510 q^{26} +5.31818 q^{27} -2.84551 q^{28} +4.62266 q^{29} +9.24789 q^{31} +5.86218 q^{32} -1.91940 q^{33} +1.29384 q^{34} -7.04281 q^{36} +0.820682 q^{37} +3.15551 q^{38} +8.79922 q^{39} -9.85369 q^{41} +4.15857 q^{42} -5.29702 q^{43} +0.983375 q^{44} -4.73497 q^{46} -1.00000 q^{47} +2.67050 q^{48} -3.09183 q^{49} +4.85471 q^{51} -4.50814 q^{52} +4.43246 q^{53} +3.98198 q^{54} -5.09100 q^{56} +11.8400 q^{57} +3.46122 q^{58} -7.94529 q^{59} +6.03056 q^{61} +6.92436 q^{62} +9.67295 q^{63} +2.48822 q^{64} -1.43715 q^{66} +11.6410 q^{67} -2.48724 q^{68} -17.7664 q^{69} -16.7985 q^{71} -12.6005 q^{72} +5.86850 q^{73} +0.614485 q^{74} -6.06606 q^{76} -1.35062 q^{77} +6.58842 q^{78} -7.36295 q^{79} +0.262216 q^{81} -7.37795 q^{82} -15.3880 q^{83} -7.99430 q^{84} -3.96614 q^{86} +12.9871 q^{87} +1.75939 q^{88} +9.21820 q^{89} +6.19172 q^{91} +9.10236 q^{92} +25.9814 q^{93} -0.748750 q^{94} +16.4695 q^{96} -2.30654 q^{97} -2.31500 q^{98} -3.34286 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{2} + 4 q^{3} + 10 q^{4} - 2 q^{6} + 12 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 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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