LMFDB - Embedded newform 1075.6.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,6,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("1075.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1075.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:	$172.412606299$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.3914 q^{2} +10.7135 q^{3} +75.9819 q^{4} -111.328 q^{6} +32.3758 q^{7} -457.035 q^{8} -128.222 q^{9} +O(q^{10})$	\(q-10.3914 q^{2} +10.7135 q^{3} +75.9819 q^{4} -111.328 q^{6} +32.3758 q^{7} -457.035 q^{8} -128.222 q^{9} -479.766 q^{11} +814.029 q^{12} -1007.59 q^{13} -336.431 q^{14} +2317.83 q^{16} -198.861 q^{17} +1332.41 q^{18} +96.0573 q^{19} +346.857 q^{21} +4985.46 q^{22} -3306.75 q^{23} -4896.43 q^{24} +10470.3 q^{26} -3977.07 q^{27} +2459.98 q^{28} -5468.12 q^{29} -6813.16 q^{31} -9460.46 q^{32} -5139.96 q^{33} +2066.45 q^{34} -9742.54 q^{36} -8331.89 q^{37} -998.174 q^{38} -10794.8 q^{39} +11546.9 q^{41} -3604.34 q^{42} -1849.00 q^{43} -36453.6 q^{44} +34361.8 q^{46} -7858.43 q^{47} +24832.0 q^{48} -15758.8 q^{49} -2130.49 q^{51} -76558.9 q^{52} -28601.0 q^{53} +41327.5 q^{54} -14796.9 q^{56} +1029.11 q^{57} +56821.6 q^{58} +34498.4 q^{59} -46059.6 q^{61} +70798.5 q^{62} -4151.29 q^{63} +24137.2 q^{64} +53411.5 q^{66} -56049.4 q^{67} -15109.8 q^{68} -35426.7 q^{69} +72455.3 q^{71} +58601.9 q^{72} -31223.2 q^{73} +86580.3 q^{74} +7298.62 q^{76} -15532.8 q^{77} +112174. q^{78} +94916.2 q^{79} -11450.3 q^{81} -119989. q^{82} +90420.3 q^{83} +26354.9 q^{84} +19213.8 q^{86} -58582.5 q^{87} +219270. q^{88} +7482.85 q^{89} -32621.7 q^{91} -251253. q^{92} -72992.5 q^{93} +81660.3 q^{94} -101354. q^{96} -47189.8 q^{97} +163757. q^{98} +61516.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9}+O(q^{10}) $ 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9} + 675 q^{11} + 4446 q^{12} - 1241 q^{13} + 2375 q^{14} + 10518 q^{16} - 1153 q^{17} + 6680 q^{18} + 4065 q^{19} + 9953 q^{21} - 9283 q^{22} + 360 q^{23} + 2265 q^{24} + 23695 q^{26} - 1323 q^{27} + 30375 q^{28} + 19290 q^{29} + 23291 q^{31} - 8166 q^{32} + 10388 q^{33} - 13153 q^{34} + 148705 q^{36} - 13501 q^{37} + 8127 q^{38} - 1327 q^{39} + 38345 q^{41} + 21835 q^{42} - 68413 q^{43} + 47768 q^{44} + 48755 q^{46} - 84859 q^{47} + 208720 q^{48} + 107255 q^{49} + 62027 q^{51} - 128320 q^{52} + 53559 q^{53} + 44158 q^{54} + 107538 q^{56} - 104239 q^{57} + 85186 q^{58} + 48186 q^{59} + 82364 q^{61} - 206506 q^{62} + 75269 q^{63} + 161467 q^{64} + 91969 q^{66} - 38168 q^{67} - 95991 q^{68} + 287103 q^{69} + 155302 q^{71} - 9979 q^{72} - 31927 q^{73} + 59946 q^{74} + 225407 q^{76} + 80007 q^{77} + 67815 q^{78} + 150174 q^{79} + 417489 q^{81} - 60603 q^{82} - 266568 q^{83} + 586273 q^{84} + 57554 q^{87} - 323054 q^{88} + 334356 q^{89} + 51747 q^{91} + 258529 q^{92} + 285287 q^{93} + 302744 q^{94} + 287282 q^{96} + 78640 q^{97} + 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9 + 675 * q^11 + 4446 * q^12 - 1241 * q^13 + 2375 * q^14 + 10518 * q^16 - 1153 * q^17 + 6680 * q^18 + 4065 * q^19 + 9953 * q^21 - 9283 * q^22 + 360 * q^23 + 2265 * q^24 + 23695 * q^26 - 1323 * q^27 + 30375 * q^28 + 19290 * q^29 + 23291 * q^31 - 8166 * q^32 + 10388 * q^33 - 13153 * q^34 + 148705 * q^36 - 13501 * q^37 + 8127 * q^38 - 1327 * q^39 + 38345 * q^41 + 21835 * q^42 - 68413 * q^43 + 47768 * q^44 + 48755 * q^46 - 84859 * q^47 + 208720 * q^48 + 107255 * q^49 + 62027 * q^51 - 128320 * q^52 + 53559 * q^53 + 44158 * q^54 + 107538 * q^56 - 104239 * q^57 + 85186 * q^58 + 48186 * q^59 + 82364 * q^61 - 206506 * q^62 + 75269 * q^63 + 161467 * q^64 + 91969 * q^66 - 38168 * q^67 - 95991 * q^68 + 287103 * q^69 + 155302 * q^71 - 9979 * q^72 - 31927 * q^73 + 59946 * q^74 + 225407 * q^76 + 80007 * q^77 + 67815 * q^78 + 150174 * q^79 + 417489 * q^81 - 60603 * q^82 - 266568 * q^83 + 586273 * q^84 + 57554 * q^87 - 323054 * q^88 + 334356 * q^89 + 51747 * q^91 + 258529 * q^92 + 285287 * q^93 + 302744 * q^94 + 287282 * q^96 + 78640 * q^97 + 397117 * q^98 + 362152 * 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 $

$2$	−10.3914	−1.83696	−0.918482	−	0.395463i	$-0.870584\pi$
$2$	−10.3914	−1.83696	−0.918482	+	0.395463i	$0.870584\pi$
$3$	10.7135	0.687269	0.343634	−	0.939103i	$-0.388342\pi$
$3$	10.7135	0.687269	0.343634	+	0.939103i	$0.388342\pi$
$4$	75.9819	2.37444
$5$	0	0
$5$	0	0
$6$	−111.328	−1.26249
$7$	32.3758	0.249733	0.124866	−	0.992174i	$-0.460150\pi$
$7$	32.3758	0.249733	0.124866	+	0.992174i	$0.460150\pi$
$8$	−457.035	−2.52479
$9$	−128.222	−0.527662
$10$	0	0
$11$	−479.766	−1.19550	−0.597748	−	0.801684i	$-0.703938\pi$
$11$	−479.766	−1.19550	−0.597748	+	0.801684i	$0.703938\pi$
$12$	814.029	1.63188
$13$	−1007.59	−1.65359	−0.826793	−	0.562506i	$-0.809837\pi$
$13$	−1007.59	−1.65359	−0.826793	+	0.562506i	$0.809837\pi$
$14$	−336.431	−0.458750
$15$	0	0
$16$	2317.83	2.26351
$17$	−198.861	−0.166889	−0.0834444	−	0.996512i	$-0.526592\pi$
$17$	−198.861	−0.166889	−0.0834444	+	0.996512i	$0.526592\pi$
$18$	1332.41	0.969295
$19$	96.0573	0.0610445	0.0305223	−	0.999534i	$-0.490283\pi$
$19$	96.0573	0.0610445	0.0305223	+	0.999534i	$0.490283\pi$
$20$	0	0
$21$	346.857	0.171634
$22$	4985.46	2.19608
$23$	−3306.75	−1.30341	−0.651705	−	0.758472i	$-0.725946\pi$
$23$	−3306.75	−1.30341	−0.651705	+	0.758472i	$0.725946\pi$
$24$	−4896.43	−1.73521
$25$	0	0
$26$	10470.3	3.03758
$27$	−3977.07	−1.04991
$28$	2459.98	0.592975
$29$	−5468.12	−1.20738	−0.603688	−	0.797220i	$-0.706303\pi$
$29$	−5468.12	−1.20738	−0.603688	+	0.797220i	$0.706303\pi$
$30$	0	0
$31$	−6813.16	−1.27334	−0.636670	−	0.771136i	$-0.719689\pi$
$31$	−6813.16	−1.27334	−0.636670	+	0.771136i	$0.719689\pi$
$32$	−9460.46	−1.63319
$33$	−5139.96	−0.821627
$34$	2066.45	0.306568
$35$	0	0
$36$	−9742.54	−1.25290
$37$	−8331.89	−1.00055	−0.500275	−	0.865866i	$-0.666768\pi$
$37$	−8331.89	−1.00055	−0.500275	+	0.865866i	$0.666768\pi$
$38$	−998.174	−0.112137
$39$	−10794.8	−1.13646
$40$	0	0
$41$	11546.9	1.07277	0.536384	−	0.843974i	$-0.319790\pi$
$41$	11546.9	1.07277	0.536384	+	0.843974i	$0.319790\pi$
$42$	−3604.34	−0.315285
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	−36453.6	−2.83863
$45$	0	0
$46$	34361.8	2.39432
$47$	−7858.43	−0.518909	−0.259454	−	0.965755i	$-0.583543\pi$
$47$	−7858.43	−0.518909	−0.259454	+	0.965755i	$0.583543\pi$
$48$	24832.0	1.55564
$49$	−15758.8	−0.937633
$50$	0	0
$51$	−2130.49	−0.114697
$52$	−76558.9	−3.92633
$53$	−28601.0	−1.39859	−0.699297	−	0.714831i	$-0.746503\pi$
$53$	−28601.0	−1.39859	−0.699297	+	0.714831i	$0.746503\pi$
$54$	41327.5	1.92865
$55$	0	0
$56$	−14796.9	−0.630523
$57$	1029.11	0.0419540
$58$	56821.6	2.21791
$59$	34498.4	1.29024	0.645118	−	0.764083i	$-0.276808\pi$
$59$	34498.4	1.29024	0.645118	+	0.764083i	$0.276808\pi$
$60$	0	0
$61$	−46059.6	−1.58488	−0.792439	−	0.609951i	$-0.791189\pi$
$61$	−46059.6	−1.58488	−0.792439	+	0.609951i	$0.791189\pi$
$62$	70798.5	2.33908
$63$	−4151.29	−0.131774
$64$	24137.2	0.736609
$65$	0	0
$66$	53411.5	1.50930
$67$	−56049.4	−1.52540	−0.762700	−	0.646752i	$-0.776127\pi$
$67$	−56049.4	−1.52540	−0.762700	+	0.646752i	$0.776127\pi$
$68$	−15109.8	−0.396266
$69$	−35426.7	−0.895794
$70$	0	0
$71$	72455.3	1.70579	0.852893	−	0.522086i	$-0.174846\pi$
$71$	72455.3	1.70579	0.852893	+	0.522086i	$0.174846\pi$
$72$	58601.9	1.33223
$73$	−31223.2	−0.685757	−0.342878	−	0.939380i	$-0.611402\pi$
$73$	−31223.2	−0.685757	−0.342878	+	0.939380i	$0.611402\pi$
$74$	86580.3	1.83798
$75$	0	0
$76$	7298.62	0.144946
$77$	−15532.8	−0.298555
$78$	112174.	2.08763
$79$	94916.2	1.71109	0.855545	−	0.517729i	$-0.173222\pi$
$79$	94916.2	1.71109	0.855545	+	0.517729i	$0.173222\pi$
$80$	0	0
$81$	−11450.3	−0.193912
$82$	−119989.	−1.97064
$83$	90420.3	1.44069	0.720345	−	0.693616i	$-0.243983\pi$
$83$	90420.3	1.44069	0.720345	+	0.693616i	$0.243983\pi$
$84$	26354.9	0.407533
$85$	0	0
$86$	19213.8	0.280134
$87$	−58582.5	−0.829792
$88$	219270.	3.01837
$89$	7482.85	0.100136	0.0500682	−	0.998746i	$-0.484056\pi$
$89$	7482.85	0.100136	0.0500682	+	0.998746i	$0.484056\pi$
$90$	0	0
$91$	−32621.7	−0.412955
$92$	−251253.	−3.09486
$93$	−72992.5	−0.875127
$94$	81660.3	0.953216
$95$	0	0
$96$	−101354.	−1.12244
$97$	−47189.8	−0.509236	−0.254618	−	0.967042i	$-0.581950\pi$
$97$	−47189.8	−0.509236	−0.254618	+	0.967042i	$0.581950\pi$
$98$	163757.	1.72240
$99$	61516.5	0.630817
$100$	0	0
$101$	18074.2	0.176301	0.0881507	−	0.996107i	$-0.471904\pi$
$101$	18074.2	0.176301	0.0881507	+	0.996107i	$0.471904\pi$
$102$	22138.8	0.210695
$103$	−53603.2	−0.497849	−0.248924	−	0.968523i	$-0.580077\pi$
$103$	−53603.2	−0.497849	−0.248924	+	0.968523i	$0.580077\pi$
$104$	460506.	4.17495
$105$	0	0
$106$	297205.	2.56917
$107$	−36003.9	−0.304011	−0.152006	−	0.988380i	$-0.548573\pi$
$107$	−36003.9	−0.304011	−0.152006	+	0.988380i	$0.548573\pi$
$108$	−302185.	−2.49295
$109$	180156.	1.45238	0.726192	−	0.687492i	$-0.241288\pi$
$109$	180156.	1.45238	0.726192	+	0.687492i	$0.241288\pi$
$110$	0	0
$111$	−89263.4	−0.687648
$112$	75041.7	0.565272
$113$	171363.	1.26247	0.631236	−	0.775591i	$-0.282548\pi$
$113$	171363.	1.26247	0.631236	+	0.775591i	$0.282548\pi$
$114$	−10693.9	−0.0770679
$115$	0	0
$116$	−415478.	−2.86684
$117$	129195.	0.872534
$118$	−358488.	−2.37012
$119$	−6438.28	−0.0416776
$120$	0	0
$121$	69124.8	0.429210
$122$	478626.	2.91136
$123$	123707.	0.737280
$124$	−517677.	−3.02346
$125$	0	0
$126$	43137.8	0.242065
$127$	40101.8	0.220625	0.110312	−	0.993897i	$-0.464815\pi$
$127$	40101.8	0.220625	0.110312	+	0.993897i	$0.464815\pi$
$128$	51914.7	0.280069
$129$	−19809.2	−0.104808
$130$	0	0
$131$	51282.9	0.261093	0.130546	−	0.991442i	$-0.458327\pi$
$131$	51282.9	0.261093	0.130546	+	0.991442i	$0.458327\pi$
$132$	−390544.	−1.95090
$133$	3109.94	0.0152448
$134$	582434.	2.80211
$135$	0	0
$136$	90886.4	0.421359
$137$	−90718.8	−0.412948	−0.206474	−	0.978452i	$-0.566199\pi$
$137$	−90718.8	−0.412948	−0.206474	+	0.978452i	$0.566199\pi$
$138$	368134.	1.64554
$139$	−17644.5	−0.0774590	−0.0387295	−	0.999250i	$-0.512331\pi$
$139$	−17644.5	−0.0774590	−0.0387295	+	0.999250i	$0.512331\pi$
$140$	0	0
$141$	−84190.9	−0.356630
$142$	−752915.	−3.13347
$143$	483409.	1.97686
$144$	−297196.	−1.19437
$145$	0	0
$146$	324454.	1.25971
$147$	−168831.	−0.644406
$148$	−633073.	−2.37574
$149$	−23722.0	−0.0875357	−0.0437679	−	0.999042i	$-0.513936\pi$
$149$	−23722.0	−0.0875357	−0.0437679	+	0.999042i	$0.513936\pi$
$150$	0	0
$151$	−14478.0	−0.0516731	−0.0258366	−	0.999666i	$-0.508225\pi$
$151$	−14478.0	−0.0516731	−0.0258366	+	0.999666i	$0.508225\pi$
$152$	−43901.6	−0.154124
$153$	25498.3	0.0880608
$154$	161408.	0.548434
$155$	0	0
$156$	−820210.	−2.69845
$157$	−86363.8	−0.279629	−0.139815	−	0.990178i	$-0.544651\pi$
$157$	−86363.8	−0.279629	−0.139815	+	0.990178i	$0.544651\pi$
$158$	−986316.	−3.14321
$159$	−306416.	−0.961210
$160$	0	0
$161$	−107059.	−0.325505
$162$	118985.	0.356209
$163$	−25449.7	−0.0750262	−0.0375131	−	0.999296i	$-0.511944\pi$
$163$	−25449.7	−0.0750262	−0.0375131	+	0.999296i	$0.511944\pi$
$164$	877356.	2.54722
$165$	0	0
$166$	−939596.	−2.64650
$167$	−272167.	−0.755169	−0.377584	−	0.925975i	$-0.623245\pi$
$167$	−272167.	−0.755169	−0.377584	+	0.925975i	$0.623245\pi$
$168$	−158526.	−0.433339
$169$	643951.	1.73435
$170$	0	0
$171$	−12316.6	−0.0322108
$172$	−140491.	−0.362098
$173$	−206190.	−0.523784	−0.261892	−	0.965097i	$-0.584346\pi$
$173$	−206190.	−0.523784	−0.261892	+	0.965097i	$0.584346\pi$
$174$	608756.	1.52430
$175$	0	0
$176$	−1.11202e6	−2.70601
$177$	369598.	0.886740
$178$	−77757.5	−0.183947
$179$	−447277.	−1.04338	−0.521692	−	0.853134i	$-0.674699\pi$
$179$	−447277.	−1.04338	−0.521692	+	0.853134i	$0.674699\pi$
$180$	0	0
$181$	737155.	1.67248	0.836242	−	0.548360i	$-0.184748\pi$
$181$	737155.	1.67248	0.836242	+	0.548360i	$0.184748\pi$
$182$	338986.	0.758583
$183$	−493458.	−1.08924
$184$	1.51130e6	3.29084
$185$	0	0
$186$	758497.	1.60758
$187$	95406.7	0.199515
$188$	−597098.	−1.23211
$189$	−128761.	−0.262198
$190$	0	0
$191$	−293031.	−0.581206	−0.290603	−	0.956844i	$-0.593856\pi$
$191$	−293031.	−0.581206	−0.290603	+	0.956844i	$0.593856\pi$
$192$	258593.	0.506248
$193$	−818655.	−1.58200	−0.791002	−	0.611813i	$-0.790440\pi$
$193$	−818655.	−1.58200	−0.791002	+	0.611813i	$0.790440\pi$
$194$	490370.	0.935448
$195$	0	0
$196$	−1.19738e6	−2.22635
$197$	38352.2	0.0704085	0.0352043	−	0.999380i	$-0.488792\pi$
$197$	38352.2	0.0704085	0.0352043	+	0.999380i	$0.488792\pi$
$198$	−639245.	−1.15879
$199$	−394032.	−0.705340	−0.352670	−	0.935748i	$-0.614726\pi$
$199$	−394032.	−0.705340	−0.352670	+	0.935748i	$0.614726\pi$
$200$	0	0
$201$	−600483.	−1.04836
$202$	−187817.	−0.323859
$203$	−177035.	−0.301522
$204$	−161879.	−0.272342
$205$	0	0
$206$	557014.	0.914530
$207$	423997.	0.687760
$208$	−2.33543e6	−3.74290
$209$	−46085.1	−0.0729784
$210$	0	0
$211$	−1.07695e6	−1.66529	−0.832646	−	0.553806i	$-0.813175\pi$
$211$	−1.07695e6	−1.66529	−0.832646	+	0.553806i	$0.813175\pi$
$212$	−2.17316e6	−3.32087
$213$	776247.	1.17233
$214$	374132.	0.558458
$215$	0	0
$216$	1.81766e6	2.65081
$217$	−220582.	−0.317995
$218$	−1.87208e6	−2.66798
$219$	−334508.	−0.471299
$220$	0	0
$221$	200371.	0.275965
$222$	927575.	1.26318
$223$	213985.	0.288151	0.144076	−	0.989567i	$-0.453979\pi$
$223$	213985.	0.288151	0.144076	+	0.989567i	$0.453979\pi$
$224$	−306290.	−0.407862
$225$	0	0
$226$	−1.78071e6	−2.31911
$227$	−955063.	−1.23018	−0.615088	−	0.788458i	$-0.710880\pi$
$227$	−955063.	−1.23018	−0.615088	+	0.788458i	$0.710880\pi$
$228$	78193.5	0.0996170
$229$	374184.	0.471516	0.235758	−	0.971812i	$-0.424243\pi$
$229$	374184.	0.471516	0.235758	+	0.971812i	$0.424243\pi$
$230$	0	0
$231$	−166410.	−0.205187
$232$	2.49912e6	3.04837
$233$	−284638.	−0.343481	−0.171740	−	0.985142i	$-0.554939\pi$
$233$	−284638.	−0.343481	−0.171740	+	0.985142i	$0.554939\pi$
$234$	−1.34253e6	−1.60281
$235$	0	0
$236$	2.62126e6	3.06358
$237$	1.01688e6	1.17598
$238$	66903.0	0.0765602
$239$	−1.15869e6	−1.31212	−0.656058	−	0.754710i	$-0.727778\pi$
$239$	−1.15869e6	−1.31212	−0.656058	+	0.754710i	$0.727778\pi$
$240$	0	0
$241$	−1.48261e6	−1.64432	−0.822159	−	0.569258i	$-0.807230\pi$
$241$	−1.48261e6	−1.64432	−0.822159	+	0.569258i	$0.807230\pi$
$242$	−718305.	−0.788444
$243$	843756.	0.916645
$244$	−3.49970e6	−3.76319
$245$	0	0
$246$	−1.28550e6	−1.35436
$247$	−96786.7	−0.100942
$248$	3.11386e6	3.21491
$249$	968714.	0.990141
$250$	0	0
$251$	877029.	0.878678	0.439339	−	0.898321i	$-0.355213\pi$
$251$	877029.	0.878678	0.439339	+	0.898321i	$0.355213\pi$
$252$	−315423.	−0.312890
$253$	1.58647e6	1.55822
$254$	−416715.	−0.405280
$255$	0	0
$256$	−1.31186e6	−1.25109
$257$	−186867.	−0.176482	−0.0882410	−	0.996099i	$-0.528125\pi$
$257$	−186867.	−0.176482	−0.0882410	+	0.996099i	$0.528125\pi$
$258$	205846.	0.192528
$259$	−269752.	−0.249871
$260$	0	0
$261$	701131.	0.637086
$262$	−532903.	−0.479617
$263$	1.38916e6	1.23840	0.619202	−	0.785232i	$-0.287456\pi$
$263$	1.38916e6	1.23840	0.619202	+	0.785232i	$0.287456\pi$
$264$	2.34914e6	2.07443
$265$	0	0
$266$	−32316.7	−0.0280042
$267$	80167.2	0.0688206
$268$	−4.25874e6	−3.62196
$269$	−268441.	−0.226187	−0.113094	−	0.993584i	$-0.536076\pi$
$269$	−268441.	−0.226187	−0.113094	+	0.993584i	$0.536076\pi$
$270$	0	0
$271$	2.20077e6	1.82034	0.910169	−	0.414236i	$-0.135951\pi$
$271$	2.20077e6	1.82034	0.910169	+	0.414236i	$0.135951\pi$
$272$	−460926.	−0.377754
$273$	−349491.	−0.283811
$274$	942698.	0.758571
$275$	0	0
$276$	−2.69179e6	−2.12700
$277$	312338.	0.244583	0.122291	−	0.992494i	$-0.460976\pi$
$277$	312338.	0.244583	0.122291	+	0.992494i	$0.460976\pi$
$278$	183352.	0.142289
$279$	873595.	0.671893
$280$	0	0
$281$	2.59307e6	1.95906	0.979530	−	0.201299i	$-0.0645164\pi$
$281$	2.59307e6	1.95906	0.979530	+	0.201299i	$0.0645164\pi$
$282$	874865.	0.655116
$283$	2.46875e6	1.83236	0.916179	−	0.400769i	$-0.131257\pi$
$283$	2.46875e6	1.83236	0.916179	+	0.400769i	$0.131257\pi$
$284$	5.50530e6	4.05028
$285$	0	0
$286$	−5.02332e6	−3.63141
$287$	373841.	0.267906
$288$	1.21304e6	0.861773
$289$	−1.38031e6	−0.972148
$290$	0	0
$291$	−505566.	−0.349982
$292$	−2.37240e6	−1.62828
$293$	−653907.	−0.444987	−0.222493	−	0.974934i	$-0.571420\pi$
$293$	−653907.	−0.444987	−0.222493	+	0.974934i	$0.571420\pi$
$294$	1.75440e6	1.18375
$295$	0	0
$296$	3.80797e6	2.52618
$297$	1.90806e6	1.25517
$298$	246505.	0.160800
$299$	3.33185e6	2.15530
$300$	0	0
$301$	−59862.9	−0.0380839
$302$	150447.	0.0949217
$303$	193637.	0.121166
$304$	222645.	0.138175
$305$	0	0
$306$	−264964.	−0.161764
$307$	−1.75714e6	−1.06405	−0.532024	−	0.846729i	$-0.678569\pi$
$307$	−1.75714e6	−1.06405	−0.532024	+	0.846729i	$0.678569\pi$
$308$	−1.18021e6	−0.708899
$309$	−574275.	−0.342156
$310$	0	0
$311$	−1.34652e6	−0.789425	−0.394713	−	0.918805i	$-0.629156\pi$
$311$	−1.34652e6	−0.789425	−0.394713	+	0.918805i	$0.629156\pi$
$312$	4.93361e6	2.86932
$313$	−32160.2	−0.0185549	−0.00927744	−	0.999957i	$-0.502953\pi$
$313$	−32160.2	−0.0185549	−0.00927744	+	0.999957i	$0.502953\pi$
$314$	897443.	0.513669
$315$	0	0
$316$	7.21192e6	4.06287
$317$	−2.00141e6	−1.11863	−0.559316	−	0.828955i	$-0.688936\pi$
$317$	−2.00141e6	−1.11863	−0.559316	+	0.828955i	$0.688936\pi$
$318$	3.18410e6	1.76571
$319$	2.62342e6	1.44341
$320$	0	0
$321$	−385726.	−0.208937
$322$	1.11249e6	0.597940
$323$	−19102.0	−0.0101876
$324$	−870016.	−0.460431
$325$	0	0
$326$	264458.	0.137820
$327$	1.93009e6	0.998178
$328$	−5.27734e6	−2.70851
$329$	−254423.	−0.129589
$330$	0	0
$331$	2.96497e6	1.48748	0.743739	−	0.668470i	$-0.233051\pi$
$331$	2.96497e6	1.48748	0.743739	+	0.668470i	$0.233051\pi$
$332$	6.87031e6	3.42083
$333$	1.06833e6	0.527952
$334$	2.82820e6	1.38722
$335$	0	0
$336$	803957.	0.388494
$337$	−3.61827e6	−1.73551	−0.867753	−	0.496995i	$-0.834437\pi$
$337$	−3.61827e6	−1.73551	−0.867753	+	0.496995i	$0.834437\pi$
$338$	−6.69157e6	−3.18593
$339$	1.83589e6	0.867658
$340$	0	0
$341$	3.26873e6	1.52227
$342$	127988.	0.0591701
$343$	−1.05435e6	−0.483891
$344$	845058.	0.385026
$345$	0	0
$346$	2.14261e6	0.962171
$347$	−356137.	−0.158779	−0.0793896	−	0.996844i	$-0.525297\pi$
$347$	−356137.	−0.158779	−0.0793896	+	0.996844i	$0.525297\pi$
$348$	−4.45121e6	−1.97029
$349$	−1.41157e6	−0.620353	−0.310177	−	0.950679i	$-0.600388\pi$
$349$	−1.41157e6	−0.620353	−0.310177	+	0.950679i	$0.600388\pi$
$350$	0	0
$351$	4.00727e6	1.73612
$352$	4.53881e6	1.95248
$353$	1.58980e6	0.679056	0.339528	−	0.940596i	$-0.389733\pi$
$353$	1.58980e6	0.679056	0.339528	+	0.940596i	$0.389733\pi$
$354$	−3.84065e6	−1.62891
$355$	0	0
$356$	568561.	0.237767
$357$	−68976.3	−0.0286437
$358$	4.64785e6	1.91666
$359$	−294348.	−0.120538	−0.0602691	−	0.998182i	$-0.519196\pi$
$359$	−294348.	−0.120538	−0.0602691	+	0.998182i	$0.519196\pi$
$360$	0	0
$361$	−2.46687e6	−0.996274
$362$	−7.66009e6	−3.07229
$363$	740565.	0.294983
$364$	−2.47866e6	−0.980535
$365$	0	0
$366$	5.12774e6	2.00089
$367$	−932852.	−0.361533	−0.180766	−	0.983526i	$-0.557858\pi$
$367$	−932852.	−0.361533	−0.180766	+	0.983526i	$0.557858\pi$
$368$	−7.66448e6	−2.95028
$369$	−1.48056e6	−0.566058
$370$	0	0
$371$	−925981.	−0.349275
$372$	−5.54611e6	−2.07793
$373$	332058.	0.123578	0.0617891	−	0.998089i	$-0.480319\pi$
$373$	332058.	0.123578	0.0617891	+	0.998089i	$0.480319\pi$
$374$	−991413.	−0.366501
$375$	0	0
$376$	3.59158e6	1.31013
$377$	5.50964e6	1.99650
$378$	1.33801e6	0.481648
$379$	633497.	0.226541	0.113270	−	0.993564i	$-0.463867\pi$
$379$	633497.	0.226541	0.113270	+	0.993564i	$0.463867\pi$
$380$	0	0
$381$	429629.	0.151629
$382$	3.04501e6	1.06765
$383$	2.40610e6	0.838141	0.419071	−	0.907954i	$-0.362356\pi$
$383$	2.40610e6	0.838141	0.419071	+	0.907954i	$0.362356\pi$
$384$	556186.	0.192483
$385$	0	0
$386$	8.50700e6	2.90608
$387$	237082.	0.0804676
$388$	−3.58557e6	−1.20915
$389$	3.66374e6	1.22758	0.613791	−	0.789469i	$-0.289644\pi$
$389$	3.66374e6	1.22758	0.613791	+	0.789469i	$0.289644\pi$
$390$	0	0
$391$	657582.	0.217525
$392$	7.20233e6	2.36733
$393$	549417.	0.179441
$394$	−398535.	−0.129338
$395$	0	0
$396$	4.67414e6	1.49783
$397$	850882.	0.270952	0.135476	−	0.990781i	$-0.456744\pi$
$397$	850882.	0.270952	0.135476	+	0.990781i	$0.456744\pi$
$398$	4.09456e6	1.29568
$399$	33318.2	0.0104773
$400$	0	0
$401$	−3.22950e6	−1.00294	−0.501469	−	0.865176i	$-0.667207\pi$
$401$	−3.22950e6	−1.00294	−0.501469	+	0.865176i	$0.667207\pi$
$402$	6.23988e6	1.92580
$403$	6.86489e6	2.10558
$404$	1.37331e6	0.418616
$405$	0	0
$406$	1.83965e6	0.553884
$407$	3.99736e6	1.19615
$408$	973708.	0.289587
$409$	−3.54783e6	−1.04871	−0.524354	−	0.851500i	$-0.675693\pi$
$409$	−3.54783e6	−1.04871	−0.524354	+	0.851500i	$0.675693\pi$
$410$	0	0
$411$	−971912.	−0.283806
$412$	−4.07287e6	−1.18211
$413$	1.11692e6	0.322215
$414$	−4.40594e6	−1.26339
$415$	0	0
$416$	9.53230e6	2.70063
$417$	−189034.	−0.0532352
$418$	478890.	0.134059
$419$	−4.20207e6	−1.16931	−0.584653	−	0.811283i	$-0.698769\pi$
$419$	−4.20207e6	−1.16931	−0.584653	+	0.811283i	$0.698769\pi$
$420$	0	0
$421$	−1.54441e6	−0.424675	−0.212337	−	0.977196i	$-0.568108\pi$
$421$	−1.54441e6	−0.424675	−0.212337	+	0.977196i	$0.568108\pi$
$422$	1.11911e7	3.05908
$423$	1.00762e6	0.273808
$424$	1.30717e7	3.53115
$425$	0	0
$426$	−8.06632e6	−2.15353
$427$	−1.49122e6	−0.395796
$428$	−2.73564e6	−0.721855
$429$	5.17899e6	1.35863
$430$	0	0
$431$	−6.57620e6	−1.70523	−0.852613	−	0.522543i	$-0.824983\pi$
$431$	−6.57620e6	−1.70523	−0.852613	+	0.522543i	$0.824983\pi$
$432$	−9.21818e6	−2.37649
$433$	−6.90213e6	−1.76914	−0.884572	−	0.466403i	$-0.845549\pi$
$433$	−6.90213e6	−1.76914	−0.884572	+	0.466403i	$0.845549\pi$
$434$	2.29216e6	0.584145
$435$	0	0
$436$	1.36886e7	3.44859
$437$	−317637.	−0.0795661
$438$	3.47602e6	0.865759
$439$	−3.13570e6	−0.776557	−0.388279	−	0.921542i	$-0.626930\pi$
$439$	−3.13570e6	−0.776557	−0.388279	+	0.921542i	$0.626930\pi$
$440$	0	0
$441$	2.02062e6	0.494753
$442$	−2.08214e6	−0.506937
$443$	237630.	0.0575296	0.0287648	−	0.999586i	$-0.490843\pi$
$443$	237630.	0.0575296	0.0287648	+	0.999586i	$0.490843\pi$
$444$	−6.78240e6	−1.63277
$445$	0	0
$446$	−2.22361e6	−0.529323
$447$	−254145.	−0.0601606
$448$	781462.	0.183956
$449$	−563998.	−0.132027	−0.0660133	−	0.997819i	$-0.521028\pi$
$449$	−563998.	−0.132027	−0.0660133	+	0.997819i	$0.521028\pi$
$450$	0	0
$451$	−5.53981e6	−1.28249
$452$	1.30205e7	2.99766
$453$	−155109.	−0.0355133
$454$	9.92447e6	2.25979
$455$	0	0
$456$	−470338.	−0.105925
$457$	939287.	0.210382	0.105191	−	0.994452i	$-0.466455\pi$
$457$	939287.	0.210382	0.105191	+	0.994452i	$0.466455\pi$
$458$	−3.88831e6	−0.866158
$459$	790883.	0.175219
$460$	0	0
$461$	−2.50431e6	−0.548828	−0.274414	−	0.961612i	$-0.588484\pi$
$461$	−2.50431e6	−0.548828	−0.274414	+	0.961612i	$0.588484\pi$
$462$	1.72924e6	0.376922
$463$	−1.08762e6	−0.235790	−0.117895	−	0.993026i	$-0.537615\pi$
$463$	−1.08762e6	−0.235790	−0.117895	+	0.993026i	$0.537615\pi$
$464$	−1.26742e7	−2.73291
$465$	0	0
$466$	2.95779e6	0.630962
$467$	4.25181e6	0.902156	0.451078	−	0.892485i	$-0.351040\pi$
$467$	4.25181e6	0.902156	0.451078	+	0.892485i	$0.351040\pi$
$468$	9.81651e6	2.07177
$469$	−1.81465e6	−0.380943
$470$	0	0
$471$	−925255.	−0.192180
$472$	−1.57670e7	−3.25757
$473$	887088.	0.182311
$474$	−1.05669e7	−2.16023
$475$	0	0
$476$	−489193.	−0.0989608
$477$	3.66727e6	0.737984
$478$	1.20405e7	2.41031
$479$	2.07539e6	0.413296	0.206648	−	0.978415i	$-0.433745\pi$
$479$	2.07539e6	0.413296	0.206648	+	0.978415i	$0.433745\pi$
$480$	0	0
$481$	8.39515e6	1.65450
$482$	1.54065e7	3.02055
$483$	−1.14697e6	−0.223709
$484$	5.25223e6	1.01913
$485$	0	0
$486$	−8.76783e6	−1.68384
$487$	6.93900e6	1.32579	0.662894	−	0.748713i	$-0.269328\pi$
$487$	6.93900e6	1.32579	0.662894	+	0.748713i	$0.269328\pi$
$488$	2.10509e7	4.00148
$489$	−272654.	−0.0515632
$490$	0	0
$491$	−4.12534e6	−0.772246	−0.386123	−	0.922447i	$-0.626186\pi$
$491$	−4.12534e6	−0.772246	−0.386123	+	0.922447i	$0.626186\pi$
$492$	9.39952e6	1.75062
$493$	1.08739e6	0.201498
$494$	1.00575e6	0.185427
$495$	0	0
$496$	−1.57918e7	−2.88221
$497$	2.34580e6	0.425991
$498$	−1.00663e7	−1.81885
$499$	−9.05615e6	−1.62814	−0.814071	−	0.580766i	$-0.802753\pi$
$499$	−9.05615e6	−1.62814	−0.814071	+	0.580766i	$0.802753\pi$
$500$	0	0
$501$	−2.91585e6	−0.519004
$502$	−9.11359e6	−1.61410
$503$	−629503.	−0.110937	−0.0554687	−	0.998460i	$-0.517665\pi$
$503$	−629503.	−0.110937	−0.0554687	+	0.998460i	$0.517665\pi$
$504$	1.89728e6	0.332703
$505$	0	0
$506$	−1.64857e7	−2.86240
$507$	6.89894e6	1.19196
$508$	3.04701e6	0.523860
$509$	4.74912e6	0.812491	0.406245	−	0.913764i	$-0.366838\pi$
$509$	4.74912e6	0.812491	0.406245	+	0.913764i	$0.366838\pi$
$510$	0	0
$511$	−1.01088e6	−0.171256
$512$	1.19708e7	2.01813
$513$	−382027.	−0.0640915
$514$	1.94182e6	0.324191
$515$	0	0
$516$	−1.50514e6	−0.248859
$517$	3.77021e6	0.620353
$518$	2.80311e6	0.459003
$519$	−2.20901e6	−0.359980
$520$	0	0
$521$	207720.	0.0335261	0.0167631	−	0.999859i	$-0.494664\pi$
$521$	207720.	0.0335261	0.0167631	+	0.999859i	$0.494664\pi$
$522$	−7.28576e6	−1.17030
$523$	6.29406e6	1.00618	0.503092	−	0.864233i	$-0.332196\pi$
$523$	6.29406e6	1.00618	0.503092	+	0.864233i	$0.332196\pi$
$524$	3.89657e6	0.619947
$525$	0	0
$526$	−1.44353e7	−2.27490
$527$	1.35487e6	0.212506
$528$	−1.19136e7	−1.85976
$529$	4.49823e6	0.698880
$530$	0	0
$531$	−4.42345e6	−0.680808
$532$	236299.	0.0361978
$533$	−1.16346e7	−1.77391
$534$	−833052.	−0.126421
$535$	0	0
$536$	2.56166e7	3.85131
$537$	−4.79189e6	−0.717085
$538$	2.78949e6	0.415498
$539$	7.56054e6	1.12094
$540$	0	0
$541$	−5.07003e6	−0.744762	−0.372381	−	0.928080i	$-0.621458\pi$
$541$	−5.07003e6	−0.744762	−0.372381	+	0.928080i	$0.621458\pi$
$542$	−2.28692e7	−3.34390
$543$	7.89748e6	1.14945
$544$	1.88132e6	0.272561
$545$	0	0
$546$	3.63171e6	0.521351
$547$	2.41264e6	0.344765	0.172383	−	0.985030i	$-0.444853\pi$
$547$	2.41264e6	0.344765	0.172383	+	0.985030i	$0.444853\pi$
$548$	−6.89299e6	−0.980519
$549$	5.90585e6	0.836279
$550$	0	0
$551$	−525253.	−0.0737037
$552$	1.61913e7	2.26169
$553$	3.07299e6	0.427315
$554$	−3.24564e6	−0.449289
$555$	0	0
$556$	−1.34066e6	−0.183921
$557$	−2.87671e6	−0.392878	−0.196439	−	0.980516i	$-0.562938\pi$
$557$	−2.87671e6	−0.392878	−0.196439	+	0.980516i	$0.562938\pi$
$558$	−9.07791e6	−1.23424
$559$	1.86304e6	0.252169
$560$	0	0
$561$	1.02214e6	0.137120
$562$	−2.69457e7	−3.59872
$563$	8.95145e6	1.19021	0.595104	−	0.803649i	$-0.297111\pi$
$563$	8.95145e6	1.19021	0.595104	+	0.803649i	$0.297111\pi$
$564$	−6.39699e6	−0.846794
$565$	0	0
$566$	−2.56538e7	−3.36598
$567$	−370713.	−0.0484262
$568$	−3.31146e7	−4.30675
$569$	−4.16298e6	−0.539044	−0.269522	−	0.962994i	$-0.586866\pi$
$569$	−4.16298e6	−0.539044	−0.269522	+	0.962994i	$0.586866\pi$
$570$	0	0
$571$	−1.38745e7	−1.78084	−0.890422	−	0.455136i	$-0.849591\pi$
$571$	−1.38745e7	−1.78084	−0.890422	+	0.455136i	$0.849591\pi$
$572$	3.67304e7	4.69391
$573$	−3.13938e6	−0.399445
$574$	−3.88474e6	−0.492133
$575$	0	0
$576$	−3.09491e6	−0.388680
$577$	−1.32504e7	−1.65688	−0.828439	−	0.560079i	$-0.810771\pi$
$577$	−1.32504e7	−1.65688	−0.828439	+	0.560079i	$0.810771\pi$
$578$	1.43434e7	1.78580
$579$	−8.77063e6	−1.08726
$580$	0	0
$581$	2.92743e6	0.359788
$582$	5.25356e6	0.642904
$583$	1.37218e7	1.67201
$584$	1.42701e7	1.73139
$585$	0	0
$586$	6.79503e6	0.817424
$587$	−5.64994e6	−0.676782	−0.338391	−	0.941006i	$-0.609883\pi$
$587$	−5.64994e6	−0.676782	−0.338391	+	0.941006i	$0.609883\pi$
$588$	−1.28281e7	−1.53010
$589$	−654454.	−0.0777304
$590$	0	0
$591$	410885.	0.0483896
$592$	−1.93119e7	−2.26475
$593$	−1.46018e7	−1.70517	−0.852586	−	0.522586i	$-0.824967\pi$
$593$	−1.46018e7	−1.70517	−0.852586	+	0.522586i	$0.824967\pi$
$594$	−1.98275e7	−2.30570
$595$	0	0
$596$	−1.80244e6	−0.207848
$597$	−4.22145e6	−0.484758
$598$	−3.46228e7	−3.95921
$599$	1.72437e7	1.96364	0.981821	−	0.189810i	$-0.0607872\pi$
$599$	1.72437e7	1.96364	0.981821	+	0.189810i	$0.0607872\pi$
$600$	0	0
$601$	−9.56962e6	−1.08071	−0.540354	−	0.841438i	$-0.681710\pi$
$601$	−9.56962e6	−1.08071	−0.540354	+	0.841438i	$0.681710\pi$
$602$	622062.	0.0699588
$603$	7.18675e6	0.804895
$604$	−1.10006e6	−0.122695
$605$	0	0
$606$	−2.01217e6	−0.222578
$607$	−1.17150e7	−1.29053	−0.645267	−	0.763957i	$-0.723254\pi$
$607$	−1.17150e7	−1.29053	−0.645267	+	0.763957i	$0.723254\pi$
$608$	−908747.	−0.0996975
$609$	−1.89666e6	−0.207226
$610$	0	0
$611$	7.91809e6	0.858060
$612$	1.93741e6	0.209095
$613$	8.98079e6	0.965302	0.482651	−	0.875813i	$-0.339674\pi$
$613$	8.98079e6	0.965302	0.482651	+	0.875813i	$0.339674\pi$
$614$	1.82593e7	1.95462
$615$	0	0
$616$	7.09905e6	0.753787
$617$	3.56818e6	0.377341	0.188670	−	0.982040i	$-0.439582\pi$
$617$	3.56818e6	0.377341	0.188670	+	0.982040i	$0.439582\pi$
$618$	5.96755e6	0.628528
$619$	−1.25223e7	−1.31359	−0.656793	−	0.754071i	$-0.728088\pi$
$619$	−1.25223e7	−1.31359	−0.656793	+	0.754071i	$0.728088\pi$
$620$	0	0
$621$	1.31512e7	1.36847
$622$	1.39923e7	1.45015
$623$	242263.	0.0250074
$624$	−2.50205e7	−2.57238
$625$	0	0
$626$	334191.	0.0340847
$627$	−493731.	−0.0501558
$628$	−6.56208e6	−0.663961
$629$	1.65689e6	0.166981
$630$	0	0
$631$	2.66773e6	0.266727	0.133364	−	0.991067i	$-0.457422\pi$
$631$	2.66773e6	0.266727	0.133364	+	0.991067i	$0.457422\pi$
$632$	−4.33801e7	−4.32014
$633$	−1.15379e7	−1.14450
$634$	2.07975e7	2.05489
$635$	0	0
$636$	−2.32821e7	−2.28233
$637$	1.58785e7	1.55046
$638$	−2.72611e7	−2.65150
$639$	−9.29035e6	−0.900078
$640$	0	0
$641$	−1.31555e7	−1.26463	−0.632315	−	0.774712i	$-0.717895\pi$
$641$	−1.31555e7	−1.26463	−0.632315	+	0.774712i	$0.717895\pi$
$642$	4.00825e6	0.383811
$643$	1.69141e7	1.61332	0.806660	−	0.591015i	$-0.201273\pi$
$643$	1.69141e7	1.61332	0.806660	+	0.591015i	$0.201273\pi$
$644$	−8.13452e6	−0.772890
$645$	0	0
$646$	198498.	0.0187143
$647$	8.12500e6	0.763067	0.381534	−	0.924355i	$-0.375396\pi$
$647$	8.12500e6	0.763067	0.381534	+	0.924355i	$0.375396\pi$
$648$	5.23319e6	0.489586
$649$	−1.65512e7	−1.54247
$650$	0	0
$651$	−2.36319e6	−0.218548
$652$	−1.93371e6	−0.178145
$653$	1.68339e7	1.54490	0.772452	−	0.635073i	$-0.219030\pi$
$653$	1.68339e7	1.54490	0.772452	+	0.635073i	$0.219030\pi$
$654$	−2.00564e7	−1.83362
$655$	0	0
$656$	2.67638e7	2.42822
$657$	4.00349e6	0.361847
$658$	2.64382e6	0.238049
$659$	9.72824e6	0.872611	0.436306	−	0.899799i	$-0.356287\pi$
$659$	9.72824e6	0.872611	0.436306	+	0.899799i	$0.356287\pi$
$660$	0	0
$661$	1.52695e7	1.35932	0.679658	−	0.733529i	$-0.262128\pi$
$661$	1.52695e7	1.35932	0.679658	+	0.733529i	$0.262128\pi$
$662$	−3.08103e7	−2.73244
$663$	2.14666e6	0.189662
$664$	−4.13253e7	−3.63744
$665$	0	0
$666$	−1.11015e7	−0.969829
$667$	1.80817e7	1.57371
$668$	−2.06798e7	−1.79310
$669$	2.29252e6	0.198037
$670$	0	0
$671$	2.20979e7	1.89472
$672$	−3.28143e6	−0.280311
$673$	−8.10372e6	−0.689679	−0.344839	−	0.938662i	$-0.612067\pi$
$673$	−8.10372e6	−0.689679	−0.344839	+	0.938662i	$0.612067\pi$
$674$	3.75990e7	3.18806
$675$	0	0
$676$	4.89286e7	4.11809
$677$	7.00789e6	0.587646	0.293823	−	0.955860i	$-0.405072\pi$
$677$	7.00789e6	0.587646	0.293823	+	0.955860i	$0.405072\pi$
$678$	−1.90776e7	−1.59386
$679$	−1.52781e6	−0.127173
$680$	0	0
$681$	−1.02320e7	−0.845462
$682$	−3.39667e7	−2.79636
$683$	−4.81971e6	−0.395339	−0.197669	−	0.980269i	$-0.563337\pi$
$683$	−4.81971e6	−0.395339	−0.197669	+	0.980269i	$0.563337\pi$
$684$	−935842.	−0.0764825
$685$	0	0
$686$	1.09562e7	0.888890
$687$	4.00881e6	0.324058
$688$	−4.28567e6	−0.345182
$689$	2.88182e7	2.31269
$690$	0	0
$691$	−1.47553e7	−1.17558	−0.587792	−	0.809012i	$-0.700003\pi$
$691$	−1.47553e7	−1.17558	−0.587792	+	0.809012i	$0.700003\pi$
$692$	−1.56667e7	−1.24369
$693$	1.99165e6	0.157536
$694$	3.70078e6	0.291672
$695$	0	0
$696$	2.67743e7	2.09505
$697$	−2.29623e6	−0.179033
$698$	1.46682e7	1.13957
$699$	−3.04946e6	−0.236064
$700$	0	0
$701$	4.26269e6	0.327634	0.163817	−	0.986491i	$-0.447619\pi$
$701$	4.26269e6	0.327634	0.163817	+	0.986491i	$0.447619\pi$
$702$	−4.16413e7	−3.18920
$703$	−800339.	−0.0610781
$704$	−1.15802e7	−0.880613
$705$	0	0
$706$	−1.65203e7	−1.24740
$707$	585167.	0.0440283
$708$	2.80827e7	2.10551
$709$	4.49950e6	0.336162	0.168081	−	0.985773i	$-0.446243\pi$
$709$	4.49950e6	0.336162	0.168081	+	0.985773i	$0.446243\pi$
$710$	0	0
$711$	−1.21703e7	−0.902876
$712$	−3.41993e6	−0.252823
$713$	2.25294e7	1.65969
$714$	716763.	0.0526175
$715$	0	0
$716$	−3.39850e7	−2.47745
$717$	−1.24136e7	−0.901777
$718$	3.05870e6	0.221424
$719$	2.12391e7	1.53220	0.766098	−	0.642724i	$-0.222196\pi$
$719$	2.12391e7	1.53220	0.766098	+	0.642724i	$0.222196\pi$
$720$	0	0
$721$	−1.73545e6	−0.124329
$722$	2.56343e7	1.83012
$723$	−1.58839e7	−1.13009
$724$	5.60104e7	3.97121
$725$	0	0
$726$	−7.69554e6	−0.541873
$727$	4.84102e6	0.339704	0.169852	−	0.985470i	$-0.445671\pi$
$727$	4.84102e6	0.339704	0.169852	+	0.985470i	$0.445671\pi$
$728$	1.49093e7	1.04262
$729$	1.18220e7	0.823893
$730$	0	0
$731$	367694.	0.0254503
$732$	−3.74939e7	−2.58632
$733$	1.64050e7	1.12776	0.563880	−	0.825856i	$-0.309308\pi$
$733$	1.64050e7	1.12776	0.563880	+	0.825856i	$0.309308\pi$
$734$	9.69367e6	0.664122
$735$	0	0
$736$	3.12834e7	2.12872
$737$	2.68906e7	1.82361
$738$	1.53852e7	1.03983
$739$	1.30199e7	0.876993	0.438497	−	0.898733i	$-0.355511\pi$
$739$	1.30199e7	0.876993	0.438497	+	0.898733i	$0.355511\pi$
$740$	0	0
$741$	−1.03692e6	−0.0693745
$742$	9.62227e6	0.641605
$743$	930526.	0.0618381	0.0309191	−	0.999522i	$-0.490157\pi$
$743$	930526.	0.0618381	0.0309191	+	0.999522i	$0.490157\pi$
$744$	3.33602e7	2.20951
$745$	0	0
$746$	−3.45056e6	−0.227009
$747$	−1.15938e7	−0.760197
$748$	7.24919e6	0.473735
$749$	−1.16566e6	−0.0759216
$750$	0	0
$751$	1.69601e7	1.09731	0.548653	−	0.836050i	$-0.315141\pi$
$751$	1.69601e7	1.09731	0.548653	+	0.836050i	$0.315141\pi$
$752$	−1.82145e7	−1.17455
$753$	9.39602e6	0.603888
$754$	−5.72530e7	−3.66750
$755$	0	0
$756$	−9.78350e6	−0.622573
$757$	−1.51869e7	−0.963231	−0.481616	−	0.876382i	$-0.659950\pi$
$757$	−1.51869e7	−0.963231	−0.481616	+	0.876382i	$0.659950\pi$
$758$	−6.58295e6	−0.416148
$759$	1.69965e7	1.07092
$760$	0	0
$761$	2.34732e7	1.46930	0.734650	−	0.678447i	$-0.237347\pi$
$761$	2.34732e7	1.46930	0.734650	+	0.678447i	$0.237347\pi$
$762$	−4.46446e6	−0.278536
$763$	5.83269e6	0.362708
$764$	−2.22651e7	−1.38004
$765$	0	0
$766$	−2.50029e7	−1.53963
$767$	−3.47604e7	−2.13352
$768$	−1.40545e7	−0.859832
$769$	−5.62917e6	−0.343264	−0.171632	−	0.985161i	$-0.554904\pi$
$769$	−5.62917e6	−0.343264	−0.171632	+	0.985161i	$0.554904\pi$
$770$	0	0
$771$	−2.00200e6	−0.121291
$772$	−6.22030e7	−3.75637
$773$	−2.04324e7	−1.22990	−0.614952	−	0.788565i	$-0.710824\pi$
$773$	−2.04324e7	−1.22990	−0.614952	+	0.788565i	$0.710824\pi$
$774$	−2.46362e6	−0.147816
$775$	0	0
$776$	2.15674e7	1.28571
$777$	−2.88998e6	−0.171728
$778$	−3.80715e7	−2.25502
$779$	1.10916e6	0.0654866
$780$	0	0
$781$	−3.47616e7	−2.03926
$782$	−6.83323e6	−0.399585
$783$	2.17471e7	1.26764
$784$	−3.65263e7	−2.12234
$785$	0	0
$786$	−5.70924e6	−0.329626
$787$	−1.75378e7	−1.00934	−0.504671	−	0.863312i	$-0.668386\pi$
$787$	−1.75378e7	−1.00934	−0.504671	+	0.863312i	$0.668386\pi$
$788$	2.91408e6	0.167180
$789$	1.48827e7	0.851116
$790$	0	0
$791$	5.54803e6	0.315281
$792$	−2.81152e7	−1.59268
$793$	4.64094e7	2.62073
$794$	−8.84189e6	−0.497730
$795$	0	0
$796$	−2.99393e7	−1.67478
$797$	−1.30369e6	−0.0726991	−0.0363495	−	0.999339i	$-0.511573\pi$
$797$	−1.30369e6	−0.0726991	−0.0363495	+	0.999339i	$0.511573\pi$
$798$	−346224.	−0.0192464
$799$	1.56273e6	0.0866000
$800$	0	0
$801$	−959464.	−0.0528381
$802$	3.35591e7	1.84236
$803$	1.49798e7	0.819819
$804$	−4.56259e7	−2.48926
$805$	0	0
$806$	−7.13361e7	−3.86787
$807$	−2.87593e6	−0.155452
$808$	−8.26055e6	−0.445123
$809$	5.89454e6	0.316649	0.158325	−	0.987387i	$-0.449391\pi$
$809$	5.89454e6	0.316649	0.158325	+	0.987387i	$0.449391\pi$
$810$	0	0
$811$	−2.23254e7	−1.19192	−0.595959	−	0.803015i	$-0.703228\pi$
$811$	−2.23254e7	−1.19192	−0.595959	+	0.803015i	$0.703228\pi$
$812$	−1.34514e7	−0.715944
$813$	2.35779e7	1.25106
$814$	−4.15383e7	−2.19729
$815$	0	0
$816$	−4.93811e6	−0.259618
$817$	−177610.	−0.00930920
$818$	3.68671e7	1.92644
$819$	4.18281e6	0.217900
$820$	0	0
$821$	−1.06013e7	−0.548910	−0.274455	−	0.961600i	$-0.588497\pi$
$821$	−1.06013e7	−0.548910	−0.274455	+	0.961600i	$0.588497\pi$
$822$	1.00996e7	0.521342
$823$	4.17124e6	0.214667	0.107334	−	0.994223i	$-0.465769\pi$
$823$	4.17124e6	0.214667	0.107334	+	0.994223i	$0.465769\pi$
$824$	2.44985e7	1.25696
$825$	0	0
$826$	−1.16064e7	−0.591897
$827$	−2.08490e7	−1.06004	−0.530019	−	0.847986i	$-0.677815\pi$
$827$	−2.08490e7	−1.06004	−0.530019	+	0.847986i	$0.677815\pi$
$828$	3.22161e7	1.63304
$829$	−3.64863e6	−0.184392	−0.0921962	−	0.995741i	$-0.529389\pi$
$829$	−3.64863e6	−0.184392	−0.0921962	+	0.995741i	$0.529389\pi$
$830$	0	0
$831$	3.34622e6	0.168094
$832$	−2.43205e7	−1.21805
$833$	3.13381e6	0.156480
$834$	1.96433e6	0.0977911
$835$	0	0
$836$	−3.50163e6	−0.173283
$837$	2.70964e7	1.33690
$838$	4.36656e7	2.14797
$839$	−1.57078e7	−0.770392	−0.385196	−	0.922835i	$-0.625866\pi$
$839$	−1.57078e7	−0.770392	−0.385196	+	0.922835i	$0.625866\pi$
$840$	0	0
$841$	9.38915e6	0.457758
$842$	1.60486e7	0.780112
$843$	2.77807e7	1.34640
$844$	−8.18289e7	−3.95413
$845$	0	0
$846$	−1.04706e7	−0.502976
$847$	2.23797e6	0.107188
$848$	−6.62923e7	−3.16573
$849$	2.64488e7	1.25932
$850$	0	0
$851$	2.75515e7	1.30413
$852$	5.89808e7	2.78363
$853$	−1.62995e7	−0.767010	−0.383505	−	0.923539i	$-0.625283\pi$
$853$	−1.62995e7	−0.767010	−0.383505	+	0.923539i	$0.625283\pi$
$854$	1.54959e7	0.727064
$855$	0	0
$856$	1.64550e7	0.767564
$857$	−3.36620e7	−1.56563	−0.782813	−	0.622257i	$-0.786216\pi$
$857$	−3.36620e7	−1.56563	−0.782813	+	0.622257i	$0.786216\pi$
$858$	−5.38171e7	−2.49576
$859$	2.90319e7	1.34243	0.671216	−	0.741262i	$-0.265773\pi$
$859$	2.90319e7	1.34243	0.671216	+	0.741262i	$0.265773\pi$
$860$	0	0
$861$	4.00513e6	0.184123
$862$	6.83362e7	3.13244
$863$	1.76205e7	0.805360	0.402680	−	0.915341i	$-0.368079\pi$
$863$	1.76205e7	0.805360	0.402680	+	0.915341i	$0.368079\pi$
$864$	3.76249e7	1.71471
$865$	0	0
$866$	7.17230e7	3.24985
$867$	−1.47879e7	−0.668127
$868$	−1.67602e7	−0.755058
$869$	−4.55376e7	−2.04560
$870$	0	0
$871$	5.64750e7	2.52238
$872$	−8.23375e7	−3.66696
$873$	6.05076e6	0.268704
$874$	3.30071e6	0.146160
$875$	0	0
$876$	−2.54166e7	−1.11907
$877$	−1.58023e7	−0.693779	−0.346889	−	0.937906i	$-0.612762\pi$
$877$	−1.58023e7	−0.693779	−0.346889	+	0.937906i	$0.612762\pi$
$878$	3.25844e7	1.42651
$879$	−7.00561e6	−0.305825
$880$	0	0
$881$	−6.13164e6	−0.266157	−0.133078	−	0.991106i	$-0.542486\pi$
$881$	−6.13164e6	−0.266157	−0.133078	+	0.991106i	$0.542486\pi$
$882$	−2.09972e7	−0.908843
$883$	1.40336e7	0.605714	0.302857	−	0.953036i	$-0.402060\pi$
$883$	1.40336e7	0.605714	0.302857	+	0.953036i	$0.402060\pi$
$884$	1.52246e7	0.655261
$885$	0	0
$886$	−2.46931e6	−0.105680
$887$	2.67408e7	1.14121	0.570604	−	0.821225i	$-0.306709\pi$
$887$	2.67408e7	1.14121	0.570604	+	0.821225i	$0.306709\pi$
$888$	4.07965e7	1.73616
$889$	1.29833e6	0.0550973
$890$	0	0
$891$	5.49347e6	0.231821
$892$	1.62590e7	0.684196
$893$	−754859.	−0.0316765
$894$	2.64093e6	0.110513
$895$	0	0
$896$	1.68078e6	0.0699425
$897$	3.56957e7	1.48127
$898$	5.86075e6	0.242528
$899$	3.72552e7	1.53740
$900$	0	0
$901$	5.68762e6	0.233409
$902$	5.75666e7	2.35589
$903$	−641339.	−0.0261739
$904$	−7.83191e7	−3.18747
$905$	0	0
$906$	1.61181e6	0.0652367
$907$	1.32108e7	0.533226	0.266613	−	0.963804i	$-0.414095\pi$
$907$	1.32108e7	0.533226	0.266613	+	0.963804i	$0.414095\pi$
$908$	−7.25675e7	−2.92097
$909$	−2.31751e6	−0.0930274
$910$	0	0
$911$	−8.31567e6	−0.331972	−0.165986	−	0.986128i	$-0.553081\pi$
$911$	−8.31567e6	−0.331972	−0.165986	+	0.986128i	$0.553081\pi$
$912$	2.38530e6	0.0949631
$913$	−4.33806e7	−1.72234
$914$	−9.76054e6	−0.386463
$915$	0	0
$916$	2.84312e7	1.11958
$917$	1.66033e6	0.0652034
$918$	−8.21841e6	−0.321871
$919$	−1.18529e6	−0.0462952	−0.0231476	−	0.999732i	$-0.507369\pi$
$919$	−1.18529e6	−0.0462952	−0.0231476	+	0.999732i	$0.507369\pi$
$920$	0	0
$921$	−1.88251e7	−0.731287
$922$	2.60234e7	1.00818
$923$	−7.30055e7	−2.82066
$924$	−1.26442e7	−0.487204
$925$	0	0
$926$	1.13020e7	0.433138
$927$	6.87309e6	0.262696
$928$	5.17309e7	1.97188
$929$	3.62565e7	1.37831	0.689155	−	0.724614i	$-0.257982\pi$
$929$	3.62565e7	1.37831	0.689155	+	0.724614i	$0.257982\pi$
$930$	0	0
$931$	−1.51375e6	−0.0572374
$932$	−2.16273e7	−0.815573
$933$	−1.44259e7	−0.542547
$934$	−4.41824e7	−1.65723
$935$	0	0
$936$	−5.90468e7	−2.20296
$937$	−3.36065e7	−1.25047	−0.625237	−	0.780435i	$-0.714998\pi$
$937$	−3.36065e7	−1.25047	−0.625237	+	0.780435i	$0.714998\pi$
$938$	1.88568e7	0.699778
$939$	−344547.	−0.0127522
$940$	0	0
$941$	1.25843e6	0.0463292	0.0231646	−	0.999732i	$-0.492626\pi$
$941$	1.25843e6	0.0463292	0.0231646	+	0.999732i	$0.492626\pi$
$942$	9.61472e6	0.353028
$943$	−3.81827e7	−1.39826
$944$	7.99616e7	2.92046
$945$	0	0
$946$	−9.21812e6	−0.334899
$947$	7.90621e6	0.286479	0.143240	−	0.989688i	$-0.454248\pi$
$947$	7.90621e6	0.286479	0.143240	+	0.989688i	$0.454248\pi$
$948$	7.72646e7	2.79229
$949$	3.14603e7	1.13396
$950$	0	0
$951$	−2.14420e7	−0.768801
$952$	2.94252e6	0.105227
$953$	−5.10670e6	−0.182141	−0.0910706	−	0.995844i	$-0.529029\pi$
$953$	−5.10670e6	−0.182141	−0.0910706	+	0.995844i	$0.529029\pi$
$954$	−3.81082e7	−1.35565
$955$	0	0
$956$	−8.80395e7	−3.11554
$957$	2.81059e7	0.992013
$958$	−2.15663e7	−0.759210
$959$	−2.93710e6	−0.103127
$960$	0	0
$961$	1.77900e7	0.621395
$962$	−8.72377e7	−3.03925
$963$	4.61648e6	0.160415
$964$	−1.12652e8	−3.90433
$965$	0	0
$966$	1.19187e7	0.410946
$967$	−2.82239e7	−0.970625	−0.485312	−	0.874341i	$-0.661294\pi$
$967$	−2.82239e7	−0.970625	−0.485312	+	0.874341i	$0.661294\pi$
$968$	−3.15925e7	−1.08366
$969$	−204649.	−0.00700165
$970$	0	0
$971$	2.81394e7	0.957783	0.478891	−	0.877874i	$-0.341039\pi$
$971$	2.81394e7	0.957783	0.478891	+	0.877874i	$0.341039\pi$
$972$	6.41102e7	2.17651
$973$	−571255.	−0.0193441
$974$	−7.21061e7	−2.43543
$975$	0	0
$976$	−1.06758e8	−3.58738
$977$	−2.87981e7	−0.965224	−0.482612	−	0.875834i	$-0.660312\pi$
$977$	−2.87981e7	−0.965224	−0.482612	+	0.875834i	$0.660312\pi$
$978$	2.83327e6	0.0947197
$979$	−3.59002e6	−0.119713
$980$	0	0
$981$	−2.30999e7	−0.766367
$982$	4.28682e7	1.41859
$983$	1.20486e7	0.397698	0.198849	−	0.980030i	$-0.436280\pi$
$983$	1.20486e7	0.397698	0.198849	+	0.980030i	$0.436280\pi$
$984$	−5.65386e7	−1.86148
$985$	0	0
$986$	−1.12996e7	−0.370144
$987$	−2.72575e6	−0.0890622
$988$	−7.35404e6	−0.239681
$989$	6.11417e6	0.198768
$990$	0	0
$991$	4.07918e7	1.31944	0.659718	−	0.751513i	$-0.270676\pi$
$991$	4.07918e7	1.31944	0.659718	+	0.751513i	$0.270676\pi$
$992$	6.44557e7	2.07961
$993$	3.17651e7	1.02230
$994$	−2.43762e7	−0.782530
$995$	0	0
$996$	7.36048e7	2.35103
$997$	5.27117e7	1.67946	0.839728	−	0.543006i	$-0.182714\pi$
$997$	5.27117e7	1.67946	0.839728	+	0.543006i	$0.182714\pi$
$998$	9.41064e7	2.99084
$999$	3.31365e7	1.05049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.i.1.3	✓	37
5.4	even	2		1075.6.a.j.1.35	yes	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1075.6.a.i.1.3	✓	37	1.1	even	1	trivial
1075.6.a.j.1.35	yes	37	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-10.3914 q^{2} +10.7135 q^{3} +75.9819 q^{4} -111.328 q^{6} +32.3758 q^{7} -457.035 q^{8} -128.222 q^{9} +O(q^{10})\)	\(q-10.3914 q^{2} +10.7135 q^{3} +75.9819 q^{4} -111.328 q^{6} +32.3758 q^{7} -457.035 q^{8} -128.222 q^{9} -479.766 q^{11} +814.029 q^{12} -1007.59 q^{13} -336.431 q^{14} +2317.83 q^{16} -198.861 q^{17} +1332.41 q^{18} +96.0573 q^{19} +346.857 q^{21} +4985.46 q^{22} -3306.75 q^{23} -4896.43 q^{24} +10470.3 q^{26} -3977.07 q^{27} +2459.98 q^{28} -5468.12 q^{29} -6813.16 q^{31} -9460.46 q^{32} -5139.96 q^{33} +2066.45 q^{34} -9742.54 q^{36} -8331.89 q^{37} -998.174 q^{38} -10794.8 q^{39} +11546.9 q^{41} -3604.34 q^{42} -1849.00 q^{43} -36453.6 q^{44} +34361.8 q^{46} -7858.43 q^{47} +24832.0 q^{48} -15758.8 q^{49} -2130.49 q^{51} -76558.9 q^{52} -28601.0 q^{53} +41327.5 q^{54} -14796.9 q^{56} +1029.11 q^{57} +56821.6 q^{58} +34498.4 q^{59} -46059.6 q^{61} +70798.5 q^{62} -4151.29 q^{63} +24137.2 q^{64} +53411.5 q^{66} -56049.4 q^{67} -15109.8 q^{68} -35426.7 q^{69} +72455.3 q^{71} +58601.9 q^{72} -31223.2 q^{73} +86580.3 q^{74} +7298.62 q^{76} -15532.8 q^{77} +112174. q^{78} +94916.2 q^{79} -11450.3 q^{81} -119989. q^{82} +90420.3 q^{83} +26354.9 q^{84} +19213.8 q^{86} -58582.5 q^{87} +219270. q^{88} +7482.85 q^{89} -32621.7 q^{91} -251253. q^{92} -72992.5 q^{93} +81660.3 q^{94} -101354. q^{96} -47189.8 q^{97} +163757. q^{98} +61516.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9}+O(q^{10}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9} + 675 q^{11} + 4446 q^{12} - 1241 q^{13} + 2375 q^{14} + 10518 q^{16} - 1153 q^{17} + 6680 q^{18} + 4065 q^{19} + 9953 q^{21} - 9283 q^{22} + 360 q^{23} + 2265 q^{24} + 23695 q^{26} - 1323 q^{27} + 30375 q^{28} + 19290 q^{29} + 23291 q^{31} - 8166 q^{32} + 10388 q^{33} - 13153 q^{34} + 148705 q^{36} - 13501 q^{37} + 8127 q^{38} - 1327 q^{39} + 38345 q^{41} + 21835 q^{42} - 68413 q^{43} + 47768 q^{44} + 48755 q^{46} - 84859 q^{47} + 208720 q^{48} + 107255 q^{49} + 62027 q^{51} - 128320 q^{52} + 53559 q^{53} + 44158 q^{54} + 107538 q^{56} - 104239 q^{57} + 85186 q^{58} + 48186 q^{59} + 82364 q^{61} - 206506 q^{62} + 75269 q^{63} + 161467 q^{64} + 91969 q^{66} - 38168 q^{67} - 95991 q^{68} + 287103 q^{69} + 155302 q^{71} - 9979 q^{72} - 31927 q^{73} + 59946 q^{74} + 225407 q^{76} + 80007 q^{77} + 67815 q^{78} + 150174 q^{79} + 417489 q^{81} - 60603 q^{82} - 266568 q^{83} + 586273 q^{84} + 57554 q^{87} - 323054 q^{88} + 334356 q^{89} + 51747 q^{91} + 258529 q^{92} + 285287 q^{93} + 302744 q^{94} + 287282 q^{96} + 78640 q^{97} + 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9 + 675 * q^11 + 4446 * q^12 - 1241 * q^13 + 2375 * q^14 + 10518 * q^16 - 1153 * q^17 + 6680 * q^18 + 4065 * q^19 + 9953 * q^21 - 9283 * q^22 + 360 * q^23 + 2265 * q^24 + 23695 * q^26 - 1323 * q^27 + 30375 * q^28 + 19290 * q^29 + 23291 * q^31 - 8166 * q^32 + 10388 * q^33 - 13153 * q^34 + 148705 * q^36 - 13501 * q^37 + 8127 * q^38 - 1327 * q^39 + 38345 * q^41 + 21835 * q^42 - 68413 * q^43 + 47768 * q^44 + 48755 * q^46 - 84859 * q^47 + 208720 * q^48 + 107255 * q^49 + 62027 * q^51 - 128320 * q^52 + 53559 * q^53 + 44158 * q^54 + 107538 * q^56 - 104239 * q^57 + 85186 * q^58 + 48186 * q^59 + 82364 * q^61 - 206506 * q^62 + 75269 * q^63 + 161467 * q^64 + 91969 * q^66 - 38168 * q^67 - 95991 * q^68 + 287103 * q^69 + 155302 * q^71 - 9979 * q^72 - 31927 * q^73 + 59946 * q^74 + 225407 * q^76 + 80007 * q^77 + 67815 * q^78 + 150174 * q^79 + 417489 * q^81 - 60603 * q^82 - 266568 * q^83 + 586273 * q^84 + 57554 * q^87 - 323054 * q^88 + 334356 * q^89 + 51747 * q^91 + 258529 * q^92 + 285287 * q^93 + 302744 * q^94 + 287282 * q^96 + 78640 * q^97 + 397117 * q^98 + 362152 * q^99

Introduction

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