LMFDB - Embedded newform 1250.4.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1250,4,Mod(1,1250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1250, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1250.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1250 = 2 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1250.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:	$73.7523875072$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} - 125 x^{14} + 990 x^{13} + 6166 x^{12} - 47880 x^{11} - 151199 x^{10} + \cdots - 45086320 $ x^16 - 8x^15 - 125x^14 + 990x^13 + 6166x^12 - 47880x^11 - 151199x^10 + 1143340x^9 + 1899751x^8 - 14035110x^7 - 11070230x^6 + 83435508x^5 + 14900696x^4 - 193725880x^3 + 78433160x^2 + 82757040*x - 45086320
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 5^{15} $
Twist minimal:	no (minimal twist has level 50)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.06650$ of defining polynomial
Character	$\chi$	$=$	1250.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -9.35299 q^{3} +4.00000 q^{4} -18.7060 q^{6} -11.0064 q^{7} +8.00000 q^{8} +60.4783 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -9.35299 q^{3} +4.00000 q^{4} -18.7060 q^{6} -11.0064 q^{7} +8.00000 q^{8} +60.4783 q^{9} -66.8790 q^{11} -37.4119 q^{12} +43.8216 q^{13} -22.0127 q^{14} +16.0000 q^{16} -8.69369 q^{17} +120.957 q^{18} -97.4041 q^{19} +102.942 q^{21} -133.758 q^{22} +21.5350 q^{23} -74.8239 q^{24} +87.6431 q^{26} -313.122 q^{27} -44.0255 q^{28} -20.6776 q^{29} -196.840 q^{31} +32.0000 q^{32} +625.519 q^{33} -17.3874 q^{34} +241.913 q^{36} +182.957 q^{37} -194.808 q^{38} -409.863 q^{39} -261.444 q^{41} +205.885 q^{42} -77.2928 q^{43} -267.516 q^{44} +43.0700 q^{46} +55.3619 q^{47} -149.648 q^{48} -221.860 q^{49} +81.3120 q^{51} +175.286 q^{52} -447.016 q^{53} -626.245 q^{54} -88.0510 q^{56} +911.019 q^{57} -41.3553 q^{58} -273.156 q^{59} +657.412 q^{61} -393.679 q^{62} -665.647 q^{63} +64.0000 q^{64} +1251.04 q^{66} +295.909 q^{67} -34.7748 q^{68} -201.417 q^{69} -186.813 q^{71} +483.827 q^{72} +161.573 q^{73} +365.914 q^{74} -389.616 q^{76} +736.095 q^{77} -819.725 q^{78} -977.315 q^{79} +1295.71 q^{81} -522.889 q^{82} +817.151 q^{83} +411.770 q^{84} -154.586 q^{86} +193.398 q^{87} -535.032 q^{88} +927.195 q^{89} -482.316 q^{91} +86.1400 q^{92} +1841.04 q^{93} +110.724 q^{94} -299.296 q^{96} -273.371 q^{97} -443.720 q^{98} -4044.73 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9}+O(q^{10}) $ 16 * q + 32 * q^2 + 12 * q^3 + 64 * q^4 + 24 * q^6 + 56 * q^7 + 128 * q^8 + 212 * q^9	\( 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9} + 72 q^{11} + 48 q^{12} + 202 q^{13} + 112 q^{14} + 256 q^{16} + 216 q^{17} + 424 q^{18} + 100 q^{19} + 192 q^{21} + 144 q^{22} + 292 q^{23} + 96 q^{24} + 404 q^{26} + 570 q^{27} + 224 q^{28} + 400 q^{29} + 102 q^{31} + 512 q^{32} + 664 q^{33} + 432 q^{34} + 848 q^{36} + 646 q^{37} + 200 q^{38} + 104 q^{39} + 532 q^{41} + 384 q^{42} + 902 q^{43} + 288 q^{44} + 584 q^{46} + 776 q^{47} + 192 q^{48} + 1038 q^{49} + 442 q^{51} + 808 q^{52} + 632 q^{53} + 1140 q^{54} + 448 q^{56} + 1400 q^{57} + 800 q^{58} + 1000 q^{59} + 662 q^{61} + 204 q^{62} + 932 q^{63} + 1024 q^{64} + 1328 q^{66} + 1326 q^{67} + 864 q^{68} + 1854 q^{69} + 1292 q^{71} + 1696 q^{72} + 2272 q^{73} + 1292 q^{74} + 400 q^{76} + 2582 q^{77} + 208 q^{78} + 320 q^{79} + 2956 q^{81} + 1064 q^{82} + 2842 q^{83} + 768 q^{84} + 1804 q^{86} + 2920 q^{87} + 576 q^{88} + 2780 q^{89} + 812 q^{91} + 1168 q^{92} + 2824 q^{93} + 1552 q^{94} + 384 q^{96} + 3796 q^{97} + 2076 q^{98} + 1054 q^{99}+O(q^{100}) \) 16 * q + 32 * q^2 + 12 * q^3 + 64 * q^4 + 24 * q^6 + 56 * q^7 + 128 * q^8 + 212 * q^9 + 72 * q^11 + 48 * q^12 + 202 * q^13 + 112 * q^14 + 256 * q^16 + 216 * q^17 + 424 * q^18 + 100 * q^19 + 192 * q^21 + 144 * q^22 + 292 * q^23 + 96 * q^24 + 404 * q^26 + 570 * q^27 + 224 * q^28 + 400 * q^29 + 102 * q^31 + 512 * q^32 + 664 * q^33 + 432 * q^34 + 848 * q^36 + 646 * q^37 + 200 * q^38 + 104 * q^39 + 532 * q^41 + 384 * q^42 + 902 * q^43 + 288 * q^44 + 584 * q^46 + 776 * q^47 + 192 * q^48 + 1038 * q^49 + 442 * q^51 + 808 * q^52 + 632 * q^53 + 1140 * q^54 + 448 * q^56 + 1400 * q^57 + 800 * q^58 + 1000 * q^59 + 662 * q^61 + 204 * q^62 + 932 * q^63 + 1024 * q^64 + 1328 * q^66 + 1326 * q^67 + 864 * q^68 + 1854 * q^69 + 1292 * q^71 + 1696 * q^72 + 2272 * q^73 + 1292 * q^74 + 400 * q^76 + 2582 * q^77 + 208 * q^78 + 320 * q^79 + 2956 * q^81 + 1064 * q^82 + 2842 * q^83 + 768 * q^84 + 1804 * q^86 + 2920 * q^87 + 576 * q^88 + 2780 * q^89 + 812 * q^91 + 1168 * q^92 + 2824 * q^93 + 1552 * q^94 + 384 * q^96 + 3796 * q^97 + 2076 * q^98 + 1054 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−9.35299	−1.79998	−0.899991	−	0.435908i	$-0.856427\pi$
$3$	−9.35299	−1.79998	−0.899991	+	0.435908i	$0.856427\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−18.7060	−1.27278
$7$	−11.0064	−0.594288	−0.297144	−	0.954833i	$-0.596034\pi$
$7$	−11.0064	−0.594288	−0.297144	+	0.954833i	$0.596034\pi$
$8$	8.00000	0.353553
$9$	60.4783	2.23994
$10$	0	0
$11$	−66.8790	−1.83316	−0.916581	−	0.399849i	$-0.869063\pi$
$11$	−66.8790	−1.83316	−0.916581	+	0.399849i	$0.869063\pi$
$12$	−37.4119	−0.899991
$13$	43.8216	0.934917	0.467458	−	0.884015i	$-0.345170\pi$
$13$	43.8216	0.934917	0.467458	+	0.884015i	$0.345170\pi$
$14$	−22.0127	−0.420225
$15$	0	0
$16$	16.0000	0.250000
$17$	−8.69369	−0.124031	−0.0620156	−	0.998075i	$-0.519753\pi$
$17$	−8.69369	−0.124031	−0.0620156	+	0.998075i	$0.519753\pi$
$18$	120.957	1.58388
$19$	−97.4041	−1.17611	−0.588053	−	0.808822i	$-0.700105\pi$
$19$	−97.4041	−1.17611	−0.588053	+	0.808822i	$0.700105\pi$
$20$	0	0
$21$	102.942	1.06971
$22$	−133.758	−1.29624
$23$	21.5350	0.195233	0.0976165	−	0.995224i	$-0.468878\pi$
$23$	21.5350	0.195233	0.0976165	+	0.995224i	$0.468878\pi$
$24$	−74.8239	−0.636390
$25$	0	0
$26$	87.6431	0.661086
$27$	−313.122	−2.23187
$28$	−44.0255	−0.297144
$29$	−20.6776	−0.132405	−0.0662024	−	0.997806i	$-0.521088\pi$
$29$	−20.6776	−0.132405	−0.0662024	+	0.997806i	$0.521088\pi$
$30$	0	0
$31$	−196.840	−1.14043	−0.570217	−	0.821494i	$-0.693141\pi$
$31$	−196.840	−1.14043	−0.570217	+	0.821494i	$0.693141\pi$
$32$	32.0000	0.176777
$33$	625.519	3.29966
$34$	−17.3874	−0.0877033
$35$	0	0
$36$	241.913	1.11997
$37$	182.957	0.812918	0.406459	−	0.913669i	$-0.366763\pi$
$37$	182.957	0.812918	0.406459	+	0.913669i	$0.366763\pi$
$38$	−194.808	−0.831633
$39$	−409.863	−1.68283
$40$	0	0
$41$	−261.444	−0.995872	−0.497936	−	0.867214i	$-0.665908\pi$
$41$	−261.444	−0.995872	−0.497936	+	0.867214i	$0.665908\pi$
$42$	205.885	0.756398
$43$	−77.2928	−0.274117	−0.137059	−	0.990563i	$-0.543765\pi$
$43$	−77.2928	−0.274117	−0.137059	+	0.990563i	$0.543765\pi$
$44$	−267.516	−0.916581
$45$	0	0
$46$	43.0700	0.138051
$47$	55.3619	0.171816	0.0859080	−	0.996303i	$-0.472621\pi$
$47$	55.3619	0.171816	0.0859080	+	0.996303i	$0.472621\pi$
$48$	−149.648	−0.449996
$49$	−221.860	−0.646822
$50$	0	0
$51$	81.3120	0.223254
$52$	175.286	0.467458
$53$	−447.016	−1.15854	−0.579268	−	0.815137i	$-0.696662\pi$
$53$	−447.016	−1.15854	−0.579268	+	0.815137i	$0.696662\pi$
$54$	−626.245	−1.57817
$55$	0	0
$56$	−88.0510	−0.210113
$57$	911.019	2.11697
$58$	−41.3553	−0.0936244
$59$	−273.156	−0.602743	−0.301372	−	0.953507i	$-0.597444\pi$
$59$	−273.156	−0.602743	−0.301372	+	0.953507i	$0.597444\pi$
$60$	0	0
$61$	657.412	1.37989	0.689943	−	0.723864i	$-0.257636\pi$
$61$	657.412	1.37989	0.689943	+	0.723864i	$0.257636\pi$
$62$	−393.679	−0.806409
$63$	−665.647	−1.33117
$64$	64.0000	0.125000
$65$	0	0
$66$	1251.04	2.33321
$67$	295.909	0.539567	0.269783	−	0.962921i	$-0.413048\pi$
$67$	295.909	0.539567	0.269783	+	0.962921i	$0.413048\pi$
$68$	−34.7748	−0.0620156
$69$	−201.417	−0.351416
$70$	0	0
$71$	−186.813	−0.312262	−0.156131	−	0.987736i	$-0.549902\pi$
$71$	−186.813	−0.312262	−0.156131	+	0.987736i	$0.549902\pi$
$72$	483.827	0.791938
$73$	161.573	0.259050	0.129525	−	0.991576i	$-0.458655\pi$
$73$	161.573	0.259050	0.129525	+	0.991576i	$0.458655\pi$
$74$	365.914	0.574820
$75$	0	0
$76$	−389.616	−0.588053
$77$	736.095	1.08943
$78$	−819.725	−1.18994
$79$	−977.315	−1.39186	−0.695928	−	0.718112i	$-0.745007\pi$
$79$	−977.315	−1.39186	−0.695928	+	0.718112i	$0.745007\pi$
$80$	0	0
$81$	1295.71	1.77739
$82$	−522.889	−0.704188
$83$	817.151	1.08065	0.540325	−	0.841456i	$-0.318301\pi$
$83$	817.151	1.08065	0.540325	+	0.841456i	$0.318301\pi$
$84$	411.770	0.534854
$85$	0	0
$86$	−154.586	−0.193830
$87$	193.398	0.238326
$88$	−535.032	−0.648121
$89$	927.195	1.10430	0.552149	−	0.833746i	$-0.313808\pi$
$89$	927.195	1.10430	0.552149	+	0.833746i	$0.313808\pi$
$90$	0	0
$91$	−482.316	−0.555610
$92$	86.1400	0.0976165
$93$	1841.04	2.05276
$94$	110.724	0.121492
$95$	0	0
$96$	−299.296	−0.318195
$97$	−273.371	−0.286151	−0.143075	−	0.989712i	$-0.545699\pi$
$97$	−273.371	−0.286151	−0.143075	+	0.989712i	$0.545699\pi$
$98$	−443.720	−0.457372
$99$	−4044.73	−4.10617
$100$	0	0
$101$	1126.42	1.10974	0.554868	−	0.831939i	$-0.312769\pi$
$101$	1126.42	1.10974	0.554868	+	0.831939i	$0.312769\pi$
$102$	162.624	0.157864
$103$	1326.65	1.26911	0.634555	−	0.772877i	$-0.281183\pi$
$103$	1326.65	1.26911	0.634555	+	0.772877i	$0.281183\pi$
$104$	350.573	0.330543
$105$	0	0
$106$	−894.033	−0.819209
$107$	493.813	0.446157	0.223078	−	0.974801i	$-0.428389\pi$
$107$	493.813	0.446157	0.223078	+	0.974801i	$0.428389\pi$
$108$	−1252.49	−1.11593
$109$	−850.293	−0.747186	−0.373593	−	0.927593i	$-0.621874\pi$
$109$	−850.293	−0.747186	−0.373593	+	0.927593i	$0.621874\pi$
$110$	0	0
$111$	−1711.20	−1.46324
$112$	−176.102	−0.148572
$113$	114.023	0.0949233	0.0474617	−	0.998873i	$-0.484887\pi$
$113$	114.023	0.0949233	0.0474617	+	0.998873i	$0.484887\pi$
$114$	1822.04	1.49692
$115$	0	0
$116$	−82.7105	−0.0662024
$117$	2650.26	2.09416
$118$	−546.312	−0.426204
$119$	95.6860	0.0737103
$120$	0	0
$121$	3141.80	2.36048
$122$	1314.82	0.975726
$123$	2445.28	1.79255
$124$	−787.359	−0.570217
$125$	0	0
$126$	−1331.29	−0.941278
$127$	266.163	0.185970	0.0929849	−	0.995668i	$-0.470359\pi$
$127$	266.163	0.185970	0.0929849	+	0.995668i	$0.470359\pi$
$128$	128.000	0.0883883
$129$	722.919	0.493407
$130$	0	0
$131$	2832.71	1.88927	0.944637	−	0.328118i	$-0.106414\pi$
$131$	2832.71	1.88927	0.944637	+	0.328118i	$0.106414\pi$
$132$	2502.07	1.64983
$133$	1072.06	0.698946
$134$	591.817	0.381531
$135$	0	0
$136$	−69.5495	−0.0438516
$137$	−1449.34	−0.903833	−0.451917	−	0.892060i	$-0.649260\pi$
$137$	−1449.34	−0.903833	−0.451917	+	0.892060i	$0.649260\pi$
$138$	−402.833	−0.248489
$139$	1886.53	1.15117	0.575587	−	0.817740i	$-0.304773\pi$
$139$	1886.53	1.15117	0.575587	+	0.817740i	$0.304773\pi$
$140$	0	0
$141$	−517.799	−0.309266
$142$	−373.626	−0.220803
$143$	−2930.74	−1.71385
$144$	967.653	0.559985
$145$	0	0
$146$	323.146	0.183176
$147$	2075.05	1.16427
$148$	731.829	0.406459
$149$	2804.20	1.54181	0.770903	−	0.636953i	$-0.219806\pi$
$149$	2804.20	1.54181	0.770903	+	0.636953i	$0.219806\pi$
$150$	0	0
$151$	2908.13	1.56729	0.783644	−	0.621210i	$-0.213358\pi$
$151$	2908.13	1.56729	0.783644	+	0.621210i	$0.213358\pi$
$152$	−779.232	−0.415816
$153$	−525.780	−0.277822
$154$	1472.19	0.770341
$155$	0	0
$156$	−1639.45	−0.841417
$157$	1144.83	0.581956	0.290978	−	0.956730i	$-0.406019\pi$
$157$	1144.83	0.581956	0.290978	+	0.956730i	$0.406019\pi$
$158$	−1954.63	−0.984190
$159$	4180.94	2.08535
$160$	0	0
$161$	−237.022	−0.116025
$162$	2591.43	1.25680
$163$	4025.11	1.93418	0.967089	−	0.254440i	$-0.0818912\pi$
$163$	4025.11	1.93418	0.967089	+	0.254440i	$0.0818912\pi$
$164$	−1045.78	−0.497936
$165$	0	0
$166$	1634.30	0.764135
$167$	−859.949	−0.398472	−0.199236	−	0.979952i	$-0.563846\pi$
$167$	−859.949	−0.398472	−0.199236	+	0.979952i	$0.563846\pi$
$168$	823.539	0.378199
$169$	−276.670	−0.125931
$170$	0	0
$171$	−5890.84	−2.63441
$172$	−309.171	−0.137059
$173$	−2183.50	−0.959587	−0.479794	−	0.877381i	$-0.659288\pi$
$173$	−2183.50	−0.959587	−0.479794	+	0.877381i	$0.659288\pi$
$174$	386.795	0.168522
$175$	0	0
$176$	−1070.06	−0.458291
$177$	2554.82	1.08493
$178$	1854.39	0.780856
$179$	−3684.79	−1.53862	−0.769312	−	0.638873i	$-0.779401\pi$
$179$	−3684.79	−1.53862	−0.769312	+	0.638873i	$0.779401\pi$
$180$	0	0
$181$	−1099.70	−0.451601	−0.225801	−	0.974174i	$-0.572500\pi$
$181$	−1099.70	−0.451601	−0.225801	+	0.974174i	$0.572500\pi$
$182$	−964.633	−0.392875
$183$	−6148.77	−2.48377
$184$	172.280	0.0690253
$185$	0	0
$186$	3682.08	1.45152
$187$	581.426	0.227369
$188$	221.447	0.0859080
$189$	3446.34	1.32637
$190$	0	0
$191$	−1085.35	−0.411168	−0.205584	−	0.978639i	$-0.565909\pi$
$191$	−1085.35	−0.411168	−0.205584	+	0.978639i	$0.565909\pi$
$192$	−598.591	−0.224998
$193$	−1043.82	−0.389305	−0.194653	−	0.980872i	$-0.562358\pi$
$193$	−1043.82	−0.389305	−0.194653	+	0.980872i	$0.562358\pi$
$194$	−546.742	−0.202339
$195$	0	0
$196$	−887.439	−0.323411
$197$	1189.51	0.430200	0.215100	−	0.976592i	$-0.430992\pi$
$197$	1189.51	0.430200	0.215100	+	0.976592i	$0.430992\pi$
$198$	−8089.46	−2.90350
$199$	−1232.23	−0.438947	−0.219473	−	0.975619i	$-0.570434\pi$
$199$	−1232.23	−0.438947	−0.219473	+	0.975619i	$0.570434\pi$
$200$	0	0
$201$	−2767.63	−0.971211
$202$	2252.85	0.784701
$203$	227.586	0.0786866
$204$	325.248	0.111627
$205$	0	0
$206$	2653.29	0.897397
$207$	1302.40	0.437310
$208$	701.145	0.233729
$209$	6514.29	2.15599
$210$	0	0
$211$	2658.19	0.867287	0.433644	−	0.901084i	$-0.357228\pi$
$211$	2658.19	0.867287	0.433644	+	0.901084i	$0.357228\pi$
$212$	−1788.07	−0.579268
$213$	1747.26	0.562067
$214$	987.627	0.315480
$215$	0	0
$216$	−2504.98	−0.789085
$217$	2166.49	0.677746
$218$	−1700.59	−0.528340
$219$	−1511.19	−0.466286
$220$	0	0
$221$	−380.971	−0.115959
$222$	−3422.39	−1.03467
$223$	4080.96	1.22548	0.612738	−	0.790286i	$-0.290068\pi$
$223$	4080.96	1.22548	0.612738	+	0.790286i	$0.290068\pi$
$224$	−352.204	−0.105056
$225$	0	0
$226$	228.045	0.0671209
$227$	−3311.57	−0.968267	−0.484133	−	0.874994i	$-0.660865\pi$
$227$	−3311.57	−0.968267	−0.484133	+	0.874994i	$0.660865\pi$
$228$	3644.07	1.05849
$229$	3652.99	1.05413	0.527066	−	0.849824i	$-0.323292\pi$
$229$	3652.99	1.05413	0.527066	+	0.849824i	$0.323292\pi$
$230$	0	0
$231$	−6884.69	−1.96095
$232$	−165.421	−0.0468122
$233$	1713.47	0.481775	0.240887	−	0.970553i	$-0.422562\pi$
$233$	1713.47	0.481775	0.240887	+	0.970553i	$0.422562\pi$
$234$	5300.51	1.48079
$235$	0	0
$236$	−1092.62	−0.301372
$237$	9140.82	2.50532
$238$	191.372	0.0521210
$239$	2641.74	0.714979	0.357490	−	0.933917i	$-0.383633\pi$
$239$	2641.74	0.714979	0.357490	+	0.933917i	$0.383633\pi$
$240$	0	0
$241$	−2003.54	−0.535516	−0.267758	−	0.963486i	$-0.586283\pi$
$241$	−2003.54	−0.535516	−0.267758	+	0.963486i	$0.586283\pi$
$242$	6283.61	1.66911
$243$	−3664.49	−0.967396
$244$	2629.65	0.689943
$245$	0	0
$246$	4890.57	1.26753
$247$	−4268.40	−1.09956
$248$	−1574.72	−0.403204
$249$	−7642.80	−1.94515
$250$	0	0
$251$	561.737	0.141261	0.0706305	−	0.997503i	$-0.477499\pi$
$251$	561.737	0.141261	0.0706305	+	0.997503i	$0.477499\pi$
$252$	−2662.59	−0.665584
$253$	−1440.24	−0.357894
$254$	532.327	0.131501
$255$	0	0
$256$	256.000	0.0625000
$257$	−6131.77	−1.48829	−0.744143	−	0.668020i	$-0.767142\pi$
$257$	−6131.77	−1.48829	−0.744143	+	0.668020i	$0.767142\pi$
$258$	1445.84	0.348891
$259$	−2013.69	−0.483108
$260$	0	0
$261$	−1250.55	−0.296579
$262$	5665.42	1.33592
$263$	4032.36	0.945422	0.472711	−	0.881217i	$-0.343275\pi$
$263$	4032.36	0.945422	0.472711	+	0.881217i	$0.343275\pi$
$264$	5004.15	1.16661
$265$	0	0
$266$	2144.13	0.494229
$267$	−8672.04	−1.98772
$268$	1183.63	0.269783
$269$	−1288.44	−0.292036	−0.146018	−	0.989282i	$-0.546646\pi$
$269$	−1288.44	−0.292036	−0.146018	+	0.989282i	$0.546646\pi$
$270$	0	0
$271$	3002.93	0.673118	0.336559	−	0.941662i	$-0.390737\pi$
$271$	3002.93	0.673118	0.336559	+	0.941662i	$0.390737\pi$
$272$	−139.099	−0.0310078
$273$	4511.10	1.00009
$274$	−2898.67	−0.639107
$275$	0	0
$276$	−805.667	−0.175708
$277$	5330.59	1.15626	0.578130	−	0.815944i	$-0.303783\pi$
$277$	5330.59	1.15626	0.578130	+	0.815944i	$0.303783\pi$
$278$	3773.06	0.814003
$279$	−11904.5	−2.55450
$280$	0	0
$281$	−1304.27	−0.276891	−0.138445	−	0.990370i	$-0.544211\pi$
$281$	−1304.27	−0.276891	−0.138445	+	0.990370i	$0.544211\pi$
$282$	−1035.60	−0.218684
$283$	1339.95	0.281456	0.140728	−	0.990048i	$-0.455056\pi$
$283$	1339.95	0.281456	0.140728	+	0.990048i	$0.455056\pi$
$284$	−747.252	−0.156131
$285$	0	0
$286$	−5861.49	−1.21188
$287$	2877.55	0.591835
$288$	1935.31	0.395969
$289$	−4837.42	−0.984616
$290$	0	0
$291$	2556.84	0.515066
$292$	646.291	0.129525
$293$	6330.65	1.26225	0.631127	−	0.775680i	$-0.282593\pi$
$293$	6330.65	1.26225	0.631127	+	0.775680i	$0.282593\pi$
$294$	4150.10	0.823262
$295$	0	0
$296$	1463.66	0.287410
$297$	20941.3	4.09138
$298$	5608.40	1.09022
$299$	943.698	0.182527
$300$	0	0
$301$	850.713	0.162905
$302$	5816.27	1.10824
$303$	−10535.4	−1.99750
$304$	−1558.46	−0.294027
$305$	0	0
$306$	−1051.56	−0.196450
$307$	6554.21	1.21846	0.609232	−	0.792992i	$-0.291478\pi$
$307$	6554.21	1.21846	0.609232	+	0.792992i	$0.291478\pi$
$308$	2944.38	0.544713
$309$	−12408.1	−2.28438
$310$	0	0
$311$	−8244.49	−1.50322	−0.751611	−	0.659607i	$-0.770723\pi$
$311$	−8244.49	−1.50322	−0.751611	+	0.659607i	$0.770723\pi$
$312$	−3278.90	−0.594972
$313$	−4871.21	−0.879670	−0.439835	−	0.898078i	$-0.644963\pi$
$313$	−4871.21	−0.879670	−0.439835	+	0.898078i	$0.644963\pi$
$314$	2289.65	0.411505
$315$	0	0
$316$	−3909.26	−0.695928
$317$	6900.91	1.22269	0.611347	−	0.791363i	$-0.290628\pi$
$317$	6900.91	1.22269	0.611347	+	0.791363i	$0.290628\pi$
$318$	8361.88	1.47456
$319$	1382.90	0.242720
$320$	0	0
$321$	−4618.63	−0.803074
$322$	−474.045	−0.0820418
$323$	846.801	0.145874
$324$	5182.86	0.888693
$325$	0	0
$326$	8050.22	1.36767
$327$	7952.78	1.34492
$328$	−2091.55	−0.352094
$329$	−609.333	−0.102108
$330$	0	0
$331$	1913.28	0.317715	0.158857	−	0.987302i	$-0.449219\pi$
$331$	1913.28	0.317715	0.158857	+	0.987302i	$0.449219\pi$
$332$	3268.60	0.540325
$333$	11064.9	1.82089
$334$	−1719.90	−0.281763
$335$	0	0
$336$	1647.08	0.267427
$337$	−5209.46	−0.842070	−0.421035	−	0.907044i	$-0.638333\pi$
$337$	−5209.46	−0.842070	−0.421035	+	0.907044i	$0.638333\pi$
$338$	−553.340	−0.0890465
$339$	−1066.45	−0.170860
$340$	0	0
$341$	13164.4	2.09060
$342$	−11781.7	−1.86281
$343$	6217.06	0.978686
$344$	−618.343	−0.0969151
$345$	0	0
$346$	−4367.01	−0.678531
$347$	−10733.1	−1.66047	−0.830234	−	0.557416i	$-0.811793\pi$
$347$	−10733.1	−1.66047	−0.830234	+	0.557416i	$0.811793\pi$
$348$	773.591	0.119163
$349$	−2715.52	−0.416500	−0.208250	−	0.978076i	$-0.566777\pi$
$349$	−2715.52	−0.416500	−0.208250	+	0.978076i	$0.566777\pi$
$350$	0	0
$351$	−13721.5	−2.08661
$352$	−2140.13	−0.324060
$353$	654.628	0.0987034	0.0493517	−	0.998781i	$-0.484284\pi$
$353$	654.628	0.0987034	0.0493517	+	0.998781i	$0.484284\pi$
$354$	5109.64	0.767160
$355$	0	0
$356$	3708.78	0.552149
$357$	−894.950	−0.132677
$358$	−7369.57	−1.08797
$359$	330.377	0.0485700	0.0242850	−	0.999705i	$-0.492269\pi$
$359$	330.377	0.0485700	0.0242850	+	0.999705i	$0.492269\pi$
$360$	0	0
$361$	2628.55	0.383226
$362$	−2199.39	−0.319330
$363$	−29385.2	−4.24883
$364$	−1929.27	−0.277805
$365$	0	0
$366$	−12297.5	−1.75629
$367$	9666.23	1.37486	0.687429	−	0.726252i	$-0.258739\pi$
$367$	9666.23	1.37486	0.687429	+	0.726252i	$0.258739\pi$
$368$	344.560	0.0488083
$369$	−15811.7	−2.23069
$370$	0	0
$371$	4920.03	0.688504
$372$	7364.16	1.02638
$373$	−3847.53	−0.534095	−0.267047	−	0.963683i	$-0.586048\pi$
$373$	−3847.53	−0.534095	−0.267047	+	0.963683i	$0.586048\pi$
$374$	1162.85	0.160774
$375$	0	0
$376$	442.895	0.0607462
$377$	−906.126	−0.123787
$378$	6892.68	0.937887
$379$	−8782.00	−1.19024	−0.595120	−	0.803637i	$-0.702895\pi$
$379$	−8782.00	−1.19024	−0.595120	+	0.803637i	$0.702895\pi$
$380$	0	0
$381$	−2489.42	−0.334743
$382$	−2170.70	−0.290740
$383$	4832.78	0.644761	0.322380	−	0.946610i	$-0.395517\pi$
$383$	4832.78	0.644761	0.322380	+	0.946610i	$0.395517\pi$
$384$	−1197.18	−0.159098
$385$	0	0
$386$	−2087.64	−0.275280
$387$	−4674.54	−0.614006
$388$	−1093.48	−0.143075
$389$	−12312.8	−1.60484	−0.802420	−	0.596759i	$-0.796455\pi$
$389$	−12312.8	−1.60484	−0.802420	+	0.596759i	$0.796455\pi$
$390$	0	0
$391$	−187.219	−0.0242150
$392$	−1774.88	−0.228686
$393$	−26494.3	−3.40066
$394$	2379.03	0.304197
$395$	0	0
$396$	−16178.9	−2.05309
$397$	−5799.22	−0.733134	−0.366567	−	0.930392i	$-0.619467\pi$
$397$	−5799.22	−0.733134	−0.366567	+	0.930392i	$0.619467\pi$
$398$	−2464.46	−0.310382
$399$	−10027.0	−1.25809
$400$	0	0
$401$	−15149.2	−1.88657	−0.943284	−	0.331987i	$-0.892281\pi$
$401$	−15149.2	−1.88657	−0.943284	+	0.331987i	$0.892281\pi$
$402$	−5535.26	−0.686750
$403$	−8625.83	−1.06621
$404$	4505.69	0.554868
$405$	0	0
$406$	455.171	0.0556398
$407$	−12236.0	−1.49021
$408$	650.496	0.0789322
$409$	−14161.4	−1.71207	−0.856034	−	0.516920i	$-0.827078\pi$
$409$	−14161.4	−1.71207	−0.856034	+	0.516920i	$0.827078\pi$
$410$	0	0
$411$	13555.6	1.62688
$412$	5306.59	0.634555
$413$	3006.45	0.358203
$414$	2604.80	0.309225
$415$	0	0
$416$	1402.29	0.165271
$417$	−17644.7	−2.07209
$418$	13028.6	1.52452
$419$	2055.41	0.239650	0.119825	−	0.992795i	$-0.461767\pi$
$419$	2055.41	0.239650	0.119825	+	0.992795i	$0.461767\pi$
$420$	0	0
$421$	5567.99	0.644577	0.322289	−	0.946641i	$-0.395548\pi$
$421$	5567.99	0.644577	0.322289	+	0.946641i	$0.395548\pi$
$422$	5316.39	0.613265
$423$	3348.19	0.384857
$424$	−3576.13	−0.409605
$425$	0	0
$426$	3494.52	0.397441
$427$	−7235.72	−0.820050
$428$	1975.25	0.223078
$429$	27411.2	3.08491
$430$	0	0
$431$	4336.97	0.484697	0.242348	−	0.970189i	$-0.422082\pi$
$431$	4336.97	0.484697	0.242348	+	0.970189i	$0.422082\pi$
$432$	−5009.96	−0.557967
$433$	−7566.71	−0.839799	−0.419899	−	0.907571i	$-0.637935\pi$
$433$	−7566.71	−0.839799	−0.419899	+	0.907571i	$0.637935\pi$
$434$	4332.98	0.479239
$435$	0	0
$436$	−3401.17	−0.373593
$437$	−2097.60	−0.229615
$438$	−3022.38	−0.329714
$439$	2850.83	0.309938	0.154969	−	0.987919i	$-0.450472\pi$
$439$	2850.83	0.309938	0.154969	+	0.987919i	$0.450472\pi$
$440$	0	0
$441$	−13417.7	−1.44884
$442$	−761.943	−0.0819953
$443$	−4745.22	−0.508922	−0.254461	−	0.967083i	$-0.581898\pi$
$443$	−4745.22	−0.508922	−0.254461	+	0.967083i	$0.581898\pi$
$444$	−6844.78	−0.731619
$445$	0	0
$446$	8161.92	0.866543
$447$	−26227.6	−2.77522
$448$	−704.408	−0.0742860
$449$	3614.47	0.379905	0.189953	−	0.981793i	$-0.439167\pi$
$449$	3614.47	0.379905	0.189953	+	0.981793i	$0.439167\pi$
$450$	0	0
$451$	17485.1	1.82559
$452$	456.090	0.0474617
$453$	−27199.7	−2.82109
$454$	−6623.14	−0.684668
$455$	0	0
$456$	7288.15	0.748462
$457$	5105.92	0.522637	0.261318	−	0.965253i	$-0.415843\pi$
$457$	5105.92	0.522637	0.261318	+	0.965253i	$0.415843\pi$
$458$	7305.98	0.745384
$459$	2722.19	0.276821
$460$	0	0
$461$	7523.41	0.760088	0.380044	−	0.924969i	$-0.375909\pi$
$461$	7523.41	0.760088	0.380044	+	0.924969i	$0.375909\pi$
$462$	−13769.4	−1.38660
$463$	4700.44	0.471810	0.235905	−	0.971776i	$-0.424195\pi$
$463$	4700.44	0.471810	0.235905	+	0.971776i	$0.424195\pi$
$464$	−330.842	−0.0331012
$465$	0	0
$466$	3426.95	0.340666
$467$	4186.73	0.414858	0.207429	−	0.978250i	$-0.433490\pi$
$467$	4186.73	0.414858	0.207429	+	0.978250i	$0.433490\pi$
$468$	10601.0	1.04708
$469$	−3256.88	−0.320658
$470$	0	0
$471$	−10707.5	−1.04751
$472$	−2185.25	−0.213102
$473$	5169.27	0.502502
$474$	18281.6	1.77153
$475$	0	0
$476$	382.744	0.0368551
$477$	−27034.8	−2.59505
$478$	5283.48	0.505567
$479$	−1921.76	−0.183314	−0.0916572	−	0.995791i	$-0.529216\pi$
$479$	−1921.76	−0.183314	−0.0916572	+	0.995791i	$0.529216\pi$
$480$	0	0
$481$	8017.47	0.760011
$482$	−4007.08	−0.378667
$483$	2216.87	0.208842
$484$	12567.2	1.18024
$485$	0	0
$486$	−7328.98	−0.684052
$487$	−20195.8	−1.87918	−0.939590	−	0.342301i	$-0.888794\pi$
$487$	−20195.8	−1.87918	−0.939590	+	0.342301i	$0.888794\pi$
$488$	5259.30	0.487863
$489$	−37646.8	−3.48149
$490$	0	0
$491$	17699.6	1.62683	0.813414	−	0.581685i	$-0.197606\pi$
$491$	17699.6	1.62683	0.813414	+	0.581685i	$0.197606\pi$
$492$	9781.14	0.896276
$493$	179.765	0.0164223
$494$	−8536.80	−0.777507
$495$	0	0
$496$	−3149.44	−0.285109
$497$	2056.13	0.185574
$498$	−15285.6	−1.37543
$499$	−1132.59	−0.101606	−0.0508032	−	0.998709i	$-0.516178\pi$
$499$	−1132.59	−0.101606	−0.0508032	+	0.998709i	$0.516178\pi$
$500$	0	0
$501$	8043.09	0.717243
$502$	1123.47	0.0998867
$503$	17378.2	1.54047	0.770236	−	0.637759i	$-0.220139\pi$
$503$	17378.2	1.54047	0.770236	+	0.637759i	$0.220139\pi$
$504$	−5325.18	−0.470639
$505$	0	0
$506$	−2880.48	−0.253069
$507$	2587.69	0.226673
$508$	1064.65	0.0929849
$509$	1253.52	0.109158	0.0545788	−	0.998509i	$-0.482618\pi$
$509$	1253.52	0.109158	0.0545788	+	0.998509i	$0.482618\pi$
$510$	0	0
$511$	−1778.33	−0.153950
$512$	512.000	0.0441942
$513$	30499.4	2.62491
$514$	−12263.5	−1.05238
$515$	0	0
$516$	2891.67	0.246703
$517$	−3702.55	−0.314967
$518$	−4027.39	−0.341609
$519$	20422.3	1.72724
$520$	0	0
$521$	22017.2	1.85142	0.925712	−	0.378230i	$-0.123467\pi$
$521$	22017.2	1.85142	0.925712	+	0.378230i	$0.123467\pi$
$522$	−2501.10	−0.209713
$523$	−2463.41	−0.205961	−0.102980	−	0.994683i	$-0.532838\pi$
$523$	−2463.41	−0.205961	−0.102980	+	0.994683i	$0.532838\pi$
$524$	11330.8	0.944637
$525$	0	0
$526$	8064.72	0.668515
$527$	1711.26	0.141449
$528$	10008.3	0.824915
$529$	−11703.2	−0.961884
$530$	0	0
$531$	−16520.0	−1.35011
$532$	4288.26	0.349473
$533$	−11456.9	−0.931057
$534$	−17344.1	−1.40553
$535$	0	0
$536$	2367.27	0.190766
$537$	34463.8	2.76950
$538$	−2576.89	−0.206501
$539$	14837.8	1.18573
$540$	0	0
$541$	−6760.27	−0.537240	−0.268620	−	0.963246i	$-0.586568\pi$
$541$	−6760.27	−0.537240	−0.268620	+	0.963246i	$0.586568\pi$
$542$	6005.86	0.475966
$543$	10285.4	0.812875
$544$	−278.198	−0.0219258
$545$	0	0
$546$	9022.20	0.707169
$547$	6639.10	0.518953	0.259477	−	0.965749i	$-0.416450\pi$
$547$	6639.10	0.518953	0.259477	+	0.965749i	$0.416450\pi$
$548$	−5797.35	−0.451917
$549$	39759.2	3.09086
$550$	0	0
$551$	2014.09	0.155722
$552$	−1611.33	−0.124244
$553$	10756.7	0.827163
$554$	10661.2	0.817600
$555$	0	0
$556$	7546.11	0.575587
$557$	13052.1	0.992880	0.496440	−	0.868071i	$-0.334640\pi$
$557$	13052.1	0.992880	0.496440	+	0.868071i	$0.334640\pi$
$558$	−23809.1	−1.80631
$559$	−3387.09	−0.256277
$560$	0	0
$561$	−5438.07	−0.409261
$562$	−2608.54	−0.195791
$563$	8951.44	0.670086	0.335043	−	0.942203i	$-0.391249\pi$
$563$	8951.44	0.670086	0.335043	+	0.942203i	$0.391249\pi$
$564$	−2071.19	−0.154633
$565$	0	0
$566$	2679.91	0.199019
$567$	−14261.1	−1.05628
$568$	−1494.50	−0.110401
$569$	8552.22	0.630101	0.315051	−	0.949075i	$-0.397979\pi$
$569$	8552.22	0.630101	0.315051	+	0.949075i	$0.397979\pi$
$570$	0	0
$571$	5148.40	0.377327	0.188664	−	0.982042i	$-0.439584\pi$
$571$	5148.40	0.377327	0.188664	+	0.982042i	$0.439584\pi$
$572$	−11723.0	−0.856927
$573$	10151.2	0.740095
$574$	5755.10	0.418490
$575$	0	0
$576$	3870.61	0.279992
$577$	22589.2	1.62981	0.814905	−	0.579595i	$-0.196789\pi$
$577$	22589.2	1.62981	0.814905	+	0.579595i	$0.196789\pi$
$578$	−9674.84	−0.696229
$579$	9762.84	0.700743
$580$	0	0
$581$	−8993.86	−0.642217
$582$	5113.67	0.364207
$583$	29896.0	2.12379
$584$	1292.58	0.0915881
$585$	0	0
$586$	12661.3	0.892548
$587$	−19307.4	−1.35759	−0.678793	−	0.734329i	$-0.737497\pi$
$587$	−19307.4	−1.35759	−0.678793	+	0.734329i	$0.737497\pi$
$588$	8300.21	0.582134
$589$	19173.0	1.34127
$590$	0	0
$591$	−11125.5	−0.774353
$592$	2927.31	0.203230
$593$	−23184.3	−1.60551	−0.802753	−	0.596311i	$-0.796632\pi$
$593$	−23184.3	−1.60551	−0.802753	+	0.596311i	$0.796632\pi$
$594$	41882.6	2.89304
$595$	0	0
$596$	11216.8	0.770903
$597$	11525.0	0.790096
$598$	1887.40	0.129066
$599$	13668.4	0.932345	0.466173	−	0.884694i	$-0.345633\pi$
$599$	13668.4	0.932345	0.466173	+	0.884694i	$0.345633\pi$
$600$	0	0
$601$	10686.9	0.725337	0.362668	−	0.931918i	$-0.381866\pi$
$601$	10686.9	0.725337	0.362668	+	0.931918i	$0.381866\pi$
$602$	1701.43	0.115191
$603$	17896.1	1.20860
$604$	11632.5	0.783644
$605$	0	0
$606$	−21070.8	−1.41245
$607$	−18467.8	−1.23490	−0.617449	−	0.786611i	$-0.711834\pi$
$607$	−18467.8	−1.23490	−0.617449	+	0.786611i	$0.711834\pi$
$608$	−3116.93	−0.207908
$609$	−2128.61	−0.141635
$610$	0	0
$611$	2426.04	0.160634
$612$	−2103.12	−0.138911
$613$	−1676.39	−0.110455	−0.0552275	−	0.998474i	$-0.517588\pi$
$613$	−1676.39	−0.110455	−0.0552275	+	0.998474i	$0.517588\pi$
$614$	13108.4	0.861585
$615$	0	0
$616$	5888.76	0.385170
$617$	21066.8	1.37458	0.687290	−	0.726383i	$-0.258800\pi$
$617$	21066.8	1.37458	0.687290	+	0.726383i	$0.258800\pi$
$618$	−24816.2	−1.61530
$619$	18074.0	1.17359	0.586797	−	0.809734i	$-0.300389\pi$
$619$	18074.0	1.17359	0.586797	+	0.809734i	$0.300389\pi$
$620$	0	0
$621$	−6743.10	−0.435734
$622$	−16489.0	−1.06294
$623$	−10205.1	−0.656271
$624$	−6557.80	−0.420709
$625$	0	0
$626$	−9742.41	−0.622021
$627$	−60928.0	−3.88075
$628$	4579.30	0.290978
$629$	−1590.57	−0.100827
$630$	0	0
$631$	13169.6	0.830860	0.415430	−	0.909625i	$-0.363631\pi$
$631$	13169.6	0.830860	0.415430	+	0.909625i	$0.363631\pi$
$632$	−7818.52	−0.492095
$633$	−24862.1	−1.56110
$634$	13801.8	0.864575
$635$	0	0
$636$	16723.8	1.04267
$637$	−9722.25	−0.604724
$638$	2765.80	0.171629
$639$	−11298.1	−0.699448
$640$	0	0
$641$	−5660.52	−0.348794	−0.174397	−	0.984675i	$-0.555798\pi$
$641$	−5660.52	−0.348794	−0.174397	+	0.984675i	$0.555798\pi$
$642$	−9237.26	−0.567859
$643$	−9823.57	−0.602494	−0.301247	−	0.953546i	$-0.597403\pi$
$643$	−9823.57	−0.602494	−0.301247	+	0.953546i	$0.597403\pi$
$644$	−948.089	−0.0580123
$645$	0	0
$646$	1693.60	0.103148
$647$	−17234.6	−1.04724	−0.523620	−	0.851952i	$-0.675419\pi$
$647$	−17234.6	−1.04724	−0.523620	+	0.851952i	$0.675419\pi$
$648$	10365.7	0.628401
$649$	18268.4	1.10493
$650$	0	0
$651$	−20263.2	−1.21993
$652$	16100.4	0.967089
$653$	16159.5	0.968410	0.484205	−	0.874955i	$-0.339109\pi$
$653$	16159.5	0.968410	0.484205	+	0.874955i	$0.339109\pi$
$654$	15905.6	0.951004
$655$	0	0
$656$	−4183.11	−0.248968
$657$	9771.65	0.580257
$658$	−1218.67	−0.0722014
$659$	−8090.84	−0.478261	−0.239131	−	0.970987i	$-0.576862\pi$
$659$	−8090.84	−0.478261	−0.239131	+	0.970987i	$0.576862\pi$
$660$	0	0
$661$	6076.79	0.357579	0.178790	−	0.983887i	$-0.442782\pi$
$661$	6076.79	0.357579	0.178790	+	0.983887i	$0.442782\pi$
$662$	3826.57	0.224658
$663$	3563.22	0.208724
$664$	6537.20	0.382067
$665$	0	0
$666$	22129.9	1.28756
$667$	−445.293	−0.0258498
$668$	−3439.80	−0.199236
$669$	−38169.1	−2.20584
$670$	0	0
$671$	−43967.1	−2.52955
$672$	3294.16	0.189100
$673$	−1758.61	−0.100727	−0.0503637	−	0.998731i	$-0.516038\pi$
$673$	−1758.61	−0.100727	−0.0503637	+	0.998731i	$0.516038\pi$
$674$	−10418.9	−0.595433
$675$	0	0
$676$	−1106.68	−0.0629654
$677$	22048.6	1.25169	0.625846	−	0.779946i	$-0.284754\pi$
$677$	22048.6	1.25169	0.625846	+	0.779946i	$0.284754\pi$
$678$	−2132.90	−0.120817
$679$	3008.82	0.170056
$680$	0	0
$681$	30973.1	1.74286
$682$	26328.9	1.47828
$683$	−35559.3	−1.99215	−0.996074	−	0.0885221i	$-0.971786\pi$
$683$	−35559.3	−1.99215	−0.996074	+	0.0885221i	$0.971786\pi$
$684$	−23563.3	−1.31720
$685$	0	0
$686$	12434.1	0.692036
$687$	−34166.3	−1.89742
$688$	−1236.69	−0.0685293
$689$	−19589.0	−1.08314
$690$	0	0
$691$	−7850.85	−0.432215	−0.216107	−	0.976370i	$-0.569336\pi$
$691$	−7850.85	−0.432215	−0.216107	+	0.976370i	$0.569336\pi$
$692$	−8734.01	−0.479794
$693$	44517.8	2.44025
$694$	−21466.2	−1.17413
$695$	0	0
$696$	1547.18	0.0842611
$697$	2272.92	0.123519
$698$	−5431.04	−0.294510
$699$	−16026.1	−0.867186
$700$	0	0
$701$	6401.45	0.344906	0.172453	−	0.985018i	$-0.444831\pi$
$701$	6401.45	0.344906	0.172453	+	0.985018i	$0.444831\pi$
$702$	−27443.0	−1.47546
$703$	−17820.8	−0.956078
$704$	−4280.26	−0.229145
$705$	0	0
$706$	1309.26	0.0697939
$707$	−12397.8	−0.659503
$708$	10219.3	0.542464
$709$	−7311.77	−0.387305	−0.193653	−	0.981070i	$-0.562033\pi$
$709$	−7311.77	−0.387305	−0.193653	+	0.981070i	$0.562033\pi$
$710$	0	0
$711$	−59106.4	−3.11767
$712$	7417.56	0.390428
$713$	−4238.95	−0.222650
$714$	−1789.90	−0.0938169
$715$	0	0
$716$	−14739.1	−0.769312
$717$	−24708.2	−1.28695
$718$	660.754	0.0343442
$719$	−4328.70	−0.224525	−0.112262	−	0.993679i	$-0.535810\pi$
$719$	−4328.70	−0.224525	−0.112262	+	0.993679i	$0.535810\pi$
$720$	0	0
$721$	−14601.6	−0.754217
$722$	5257.10	0.270982
$723$	18739.1	0.963920
$724$	−4398.79	−0.225801
$725$	0	0
$726$	−58770.5	−3.00438
$727$	30326.4	1.54710	0.773552	−	0.633733i	$-0.218478\pi$
$727$	30326.4	1.54710	0.773552	+	0.633733i	$0.218478\pi$
$728$	−3858.53	−0.196438
$729$	−710.343	−0.0360892
$730$	0	0
$731$	671.960	0.0339991
$732$	−24595.1	−1.24189
$733$	17885.3	0.901241	0.450620	−	0.892716i	$-0.351203\pi$
$733$	17885.3	0.901241	0.450620	+	0.892716i	$0.351203\pi$
$734$	19332.5	0.972172
$735$	0	0
$736$	689.120	0.0345127
$737$	−19790.1	−0.989114
$738$	−31623.4	−1.57734
$739$	13831.4	0.688495	0.344247	−	0.938879i	$-0.388134\pi$
$739$	13831.4	0.688495	0.344247	+	0.938879i	$0.388134\pi$
$740$	0	0
$741$	39922.3	1.97919
$742$	9840.06	0.486846
$743$	8682.92	0.428729	0.214364	−	0.976754i	$-0.431232\pi$
$743$	8682.92	0.428729	0.214364	+	0.976754i	$0.431232\pi$
$744$	14728.3	0.725761
$745$	0	0
$746$	−7695.05	−0.377662
$747$	49419.9	2.42059
$748$	2325.70	0.113685
$749$	−5435.09	−0.265146
$750$	0	0
$751$	4892.32	0.237714	0.118857	−	0.992911i	$-0.462077\pi$
$751$	4892.32	0.237714	0.118857	+	0.992911i	$0.462077\pi$
$752$	885.790	0.0429540
$753$	−5253.92	−0.254268
$754$	−1812.25	−0.0875310
$755$	0	0
$756$	13785.4	0.663186
$757$	−35983.3	−1.72765	−0.863827	−	0.503789i	$-0.831939\pi$
$757$	−35983.3	−1.72765	−0.863827	+	0.503789i	$0.831939\pi$
$758$	−17564.0	−0.841627
$759$	13470.6	0.644203
$760$	0	0
$761$	21839.0	1.04029	0.520147	−	0.854077i	$-0.325877\pi$
$761$	21839.0	1.04029	0.520147	+	0.854077i	$0.325877\pi$
$762$	−4978.84	−0.236699
$763$	9358.64	0.444044
$764$	−4341.39	−0.205584
$765$	0	0
$766$	9665.56	0.455915
$767$	−11970.1	−0.563515
$768$	−2394.36	−0.112499
$769$	507.176	0.0237831	0.0118916	−	0.999929i	$-0.496215\pi$
$769$	507.176	0.0237831	0.0118916	+	0.999929i	$0.496215\pi$
$770$	0	0
$771$	57350.4	2.67889
$772$	−4175.28	−0.194653
$773$	15102.0	0.702693	0.351347	−	0.936245i	$-0.385724\pi$
$773$	15102.0	0.702693	0.351347	+	0.936245i	$0.385724\pi$
$774$	−9349.08	−0.434168
$775$	0	0
$776$	−2186.97	−0.101170
$777$	18834.1	0.869585
$778$	−24625.6	−1.13479
$779$	25465.7	1.17125
$780$	0	0
$781$	12493.9	0.572428
$782$	−374.438	−0.0171226
$783$	6474.63	0.295510
$784$	−3549.76	−0.161705
$785$	0	0
$786$	−52988.5	−2.40463
$787$	313.653	0.0142065	0.00710325	−	0.999975i	$-0.497739\pi$
$787$	313.653	0.0142065	0.00710325	+	0.999975i	$0.497739\pi$
$788$	4758.06	0.215100
$789$	−37714.6	−1.70174
$790$	0	0
$791$	−1254.97	−0.0564118
$792$	−32357.9	−1.45175
$793$	28808.8	1.29008
$794$	−11598.4	−0.518404
$795$	0	0
$796$	−4928.91	−0.219473
$797$	−31356.2	−1.39359	−0.696797	−	0.717269i	$-0.745392\pi$
$797$	−31356.2	−1.39359	−0.696797	+	0.717269i	$0.745392\pi$
$798$	−20054.0	−0.889605
$799$	−481.299	−0.0213106
$800$	0	0
$801$	56075.2	2.47356
$802$	−30298.3	−1.33400
$803$	−10805.8	−0.474881
$804$	−11070.5	−0.485606
$805$	0	0
$806$	−17251.7	−0.753925
$807$	12050.8	0.525661
$808$	9011.38	0.392351
$809$	−22951.4	−0.997438	−0.498719	−	0.866764i	$-0.666196\pi$
$809$	−22951.4	−0.997438	−0.498719	+	0.866764i	$0.666196\pi$
$810$	0	0
$811$	10690.9	0.462895	0.231448	−	0.972847i	$-0.425654\pi$
$811$	10690.9	0.462895	0.231448	+	0.972847i	$0.425654\pi$
$812$	910.343	0.0393433
$813$	−28086.3	−1.21160
$814$	−24472.0	−1.05374
$815$	0	0
$816$	1300.99	0.0558135
$817$	7528.63	0.322391
$818$	−28322.8	−1.21061
$819$	−29169.7	−1.24453
$820$	0	0
$821$	7037.75	0.299171	0.149585	−	0.988749i	$-0.452206\pi$
$821$	7037.75	0.299171	0.149585	+	0.988749i	$0.452206\pi$
$822$	27111.2	1.15038
$823$	20265.4	0.858331	0.429165	−	0.903226i	$-0.358808\pi$
$823$	20265.4	0.858331	0.429165	+	0.903226i	$0.358808\pi$
$824$	10613.2	0.448698
$825$	0	0
$826$	6012.91	0.253288
$827$	−17999.1	−0.756821	−0.378410	−	0.925638i	$-0.623529\pi$
$827$	−17999.1	−0.756821	−0.378410	+	0.925638i	$0.623529\pi$
$828$	5209.61	0.218655
$829$	34154.7	1.43093	0.715465	−	0.698648i	$-0.246215\pi$
$829$	34154.7	1.43093	0.715465	+	0.698648i	$0.246215\pi$
$830$	0	0
$831$	−49856.9	−2.08125
$832$	2804.58	0.116865
$833$	1928.78	0.0802261
$834$	−35289.4	−1.46519
$835$	0	0
$836$	26057.2	1.07800
$837$	61634.9	2.54530
$838$	4110.83	0.169458
$839$	25544.6	1.05113	0.525565	−	0.850753i	$-0.323854\pi$
$839$	25544.6	1.05113	0.525565	+	0.850753i	$0.323854\pi$
$840$	0	0
$841$	−23961.4	−0.982469
$842$	11136.0	0.455785
$843$	12198.8	0.498399
$844$	10632.8	0.433644
$845$	0	0
$846$	6696.39	0.272135
$847$	−34579.9	−1.40281
$848$	−7152.26	−0.289634
$849$	−12532.6	−0.506616
$850$	0	0
$851$	3939.98	0.158708
$852$	6989.04	0.281033
$853$	34916.4	1.40154	0.700771	−	0.713387i	$-0.252840\pi$
$853$	34916.4	1.40154	0.700771	+	0.713387i	$0.252840\pi$
$854$	−14471.4	−0.579863
$855$	0	0
$856$	3950.51	0.157740
$857$	24807.3	0.988801	0.494400	−	0.869234i	$-0.335388\pi$
$857$	24807.3	0.988801	0.494400	+	0.869234i	$0.335388\pi$
$858$	54822.4	2.18136
$859$	−28730.1	−1.14116	−0.570581	−	0.821241i	$-0.693282\pi$
$859$	−28730.1	−1.14116	−0.570581	+	0.821241i	$0.693282\pi$
$860$	0	0
$861$	−26913.7	−1.06529
$862$	8673.93	0.342732
$863$	7964.19	0.314142	0.157071	−	0.987587i	$-0.449795\pi$
$863$	7964.19	0.314142	0.157071	+	0.987587i	$0.449795\pi$
$864$	−10019.9	−0.394542
$865$	0	0
$866$	−15133.4	−0.593827
$867$	45244.3	1.77229
$868$	8665.96	0.338873
$869$	65361.9	2.55150
$870$	0	0
$871$	12967.2	0.504450
$872$	−6802.34	−0.264170
$873$	−16533.0	−0.640960
$874$	−4195.19	−0.162362
$875$	0	0
$876$	−6044.75	−0.233143
$877$	−7735.73	−0.297853	−0.148927	−	0.988848i	$-0.547582\pi$
$877$	−7735.73	−0.297853	−0.148927	+	0.988848i	$0.547582\pi$
$878$	5701.67	0.219159
$879$	−59210.5	−2.27204
$880$	0	0
$881$	33924.0	1.29731	0.648654	−	0.761083i	$-0.275332\pi$
$881$	33924.0	1.29731	0.648654	+	0.761083i	$0.275332\pi$
$882$	−26835.4	−1.02449
$883$	43587.1	1.66118	0.830591	−	0.556883i	$-0.188003\pi$
$883$	43587.1	1.66118	0.830591	+	0.556883i	$0.188003\pi$
$884$	−1523.89	−0.0579794
$885$	0	0
$886$	−9490.44	−0.359862
$887$	24919.1	0.943294	0.471647	−	0.881788i	$-0.343660\pi$
$887$	24919.1	0.943294	0.471647	+	0.881788i	$0.343660\pi$
$888$	−13689.6	−0.517333
$889$	−2929.49	−0.110520
$890$	0	0
$891$	−86656.1	−3.25824
$892$	16323.8	0.612738
$893$	−5392.47	−0.202074
$894$	−52455.3	−1.96238
$895$	0	0
$896$	−1408.82	−0.0525281
$897$	−8826.39	−0.328545
$898$	7228.94	0.268633
$899$	4070.18	0.150999
$900$	0	0
$901$	3886.22	0.143695
$902$	34970.3	1.29089
$903$	−7956.71	−0.293226
$904$	912.180	0.0335605
$905$	0	0
$906$	−54399.5	−1.99481
$907$	−22241.5	−0.814241	−0.407120	−	0.913375i	$-0.633467\pi$
$907$	−22241.5	−0.814241	−0.407120	+	0.913375i	$0.633467\pi$
$908$	−13246.3	−0.484133
$909$	68124.2	2.48574
$910$	0	0
$911$	10150.7	0.369162	0.184581	−	0.982817i	$-0.440907\pi$
$911$	10150.7	0.369162	0.184581	+	0.982817i	$0.440907\pi$
$912$	14576.3	0.529243
$913$	−54650.2	−1.98101
$914$	10211.8	0.369560
$915$	0	0
$916$	14612.0	0.527066
$917$	−31177.8	−1.12277
$918$	5444.38	0.195742
$919$	−52423.9	−1.88173	−0.940863	−	0.338788i	$-0.889983\pi$
$919$	−52423.9	−1.88173	−0.940863	+	0.338788i	$0.889983\pi$
$920$	0	0
$921$	−61301.4	−2.19322
$922$	15046.8	0.537463
$923$	−8186.44	−0.291939
$924$	−27538.8	−0.980475
$925$	0	0
$926$	9400.89	0.333620
$927$	80233.4	2.84273
$928$	−661.684	−0.0234061
$929$	8747.04	0.308914	0.154457	−	0.988000i	$-0.450637\pi$
$929$	8747.04	0.308914	0.154457	+	0.988000i	$0.450637\pi$
$930$	0	0
$931$	21610.0	0.760731
$932$	6853.90	0.240887
$933$	77110.6	2.70577
$934$	8373.46	0.293349
$935$	0	0
$936$	21202.0	0.740396
$937$	21245.4	0.740723	0.370361	−	0.928888i	$-0.379234\pi$
$937$	21245.4	0.740723	0.370361	+	0.928888i	$0.379234\pi$
$938$	−6513.76	−0.226740
$939$	45560.3	1.58339
$940$	0	0
$941$	21178.7	0.733693	0.366847	−	0.930281i	$-0.380437\pi$
$941$	21178.7	0.733693	0.366847	+	0.930281i	$0.380437\pi$
$942$	−21415.1	−0.740702
$943$	−5630.21	−0.194427
$944$	−4370.49	−0.150686
$945$	0	0
$946$	10338.5	0.355322
$947$	−1342.36	−0.0460623	−0.0230311	−	0.999735i	$-0.507332\pi$
$947$	−1342.36	−0.0460623	−0.0230311	+	0.999735i	$0.507332\pi$
$948$	36563.3	1.25266
$949$	7080.37	0.242190
$950$	0	0
$951$	−64544.1	−2.20083
$952$	765.488	0.0260605
$953$	−46781.5	−1.59014	−0.795069	−	0.606519i	$-0.792565\pi$
$953$	−46781.5	−1.59014	−0.795069	+	0.606519i	$0.792565\pi$
$954$	−54069.6	−1.83498
$955$	0	0
$956$	10567.0	0.357490
$957$	−12934.2	−0.436891
$958$	−3843.53	−0.129623
$959$	15951.9	0.537137
$960$	0	0
$961$	8954.87	0.300590
$962$	16034.9	0.537409
$963$	29865.0	0.999363
$964$	−8014.16	−0.267758
$965$	0	0
$966$	4433.73	0.147674
$967$	990.729	0.0329470	0.0164735	−	0.999864i	$-0.494756\pi$
$967$	990.729	0.0329470	0.0164735	+	0.999864i	$0.494756\pi$
$968$	25134.4	0.834557
$969$	−7920.12	−0.262570
$970$	0	0
$971$	−46565.4	−1.53898	−0.769492	−	0.638656i	$-0.779491\pi$
$971$	−46565.4	−1.53898	−0.769492	+	0.638656i	$0.779491\pi$
$972$	−14658.0	−0.483698
$973$	−20763.8	−0.684129
$974$	−40391.7	−1.32878
$975$	0	0
$976$	10518.6	0.344971
$977$	−32716.6	−1.07134	−0.535668	−	0.844429i	$-0.679940\pi$
$977$	−32716.6	−1.07134	−0.535668	+	0.844429i	$0.679940\pi$
$978$	−75293.6	−2.46178
$979$	−62009.9	−2.02436
$980$	0	0
$981$	−51424.3	−1.67365
$982$	35399.2	1.15034
$983$	−50510.7	−1.63890	−0.819451	−	0.573150i	$-0.805721\pi$
$983$	−50510.7	−1.63890	−0.819451	+	0.573150i	$0.805721\pi$
$984$	19562.3	0.633763
$985$	0	0
$986$	359.530	0.0116123
$987$	5699.08	0.183793
$988$	−17073.6	−0.549781
$989$	−1664.50	−0.0535168
$990$	0	0
$991$	−25892.3	−0.829964	−0.414982	−	0.909830i	$-0.636212\pi$
$991$	−25892.3	−0.829964	−0.414982	+	0.909830i	$0.636212\pi$
$992$	−6298.87	−0.201602
$993$	−17894.9	−0.571881
$994$	4112.27	0.131220
$995$	0	0
$996$	−30571.2	−0.972576
$997$	58375.0	1.85432	0.927158	−	0.374670i	$-0.122244\pi$
$997$	58375.0	1.85432	0.927158	+	0.374670i	$0.122244\pi$
$998$	−2265.18	−0.0718466
$999$	−57288.0	−1.81433

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1250.4.a.n.1.1		16
5.4	even	2		1250.4.a.m.1.16		16
25.2	odd	20		50.4.e.a.29.8	yes	32
25.9	even	10		250.4.d.d.151.1		32
25.11	even	5		250.4.d.c.101.8		32
25.12	odd	20		250.4.e.b.99.1		32
25.13	odd	20		50.4.e.a.19.8	✓	32
25.14	even	10		250.4.d.d.101.1		32
25.16	even	5		250.4.d.c.151.8		32
25.23	odd	20		250.4.e.b.149.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.19.8	✓	32	25.13	odd	20
50.4.e.a.29.8	yes	32	25.2	odd	20
250.4.d.c.101.8		32	25.11	even	5
250.4.d.c.151.8		32	25.16	even	5
250.4.d.d.101.1		32	25.14	even	10
250.4.d.d.151.1		32	25.9	even	10
250.4.e.b.99.1		32	25.12	odd	20
250.4.e.b.149.1		32	25.23	odd	20
1250.4.a.m.1.16		16	5.4	even	2
1250.4.a.n.1.1		16	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:	\( N \)	\(=\)	\( 1250 = 2 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1250.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -9.35299 q^{3} +4.00000 q^{4} -18.7060 q^{6} -11.0064 q^{7} +8.00000 q^{8} +60.4783 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -9.35299 q^{3} +4.00000 q^{4} -18.7060 q^{6} -11.0064 q^{7} +8.00000 q^{8} +60.4783 q^{9} -66.8790 q^{11} -37.4119 q^{12} +43.8216 q^{13} -22.0127 q^{14} +16.0000 q^{16} -8.69369 q^{17} +120.957 q^{18} -97.4041 q^{19} +102.942 q^{21} -133.758 q^{22} +21.5350 q^{23} -74.8239 q^{24} +87.6431 q^{26} -313.122 q^{27} -44.0255 q^{28} -20.6776 q^{29} -196.840 q^{31} +32.0000 q^{32} +625.519 q^{33} -17.3874 q^{34} +241.913 q^{36} +182.957 q^{37} -194.808 q^{38} -409.863 q^{39} -261.444 q^{41} +205.885 q^{42} -77.2928 q^{43} -267.516 q^{44} +43.0700 q^{46} +55.3619 q^{47} -149.648 q^{48} -221.860 q^{49} +81.3120 q^{51} +175.286 q^{52} -447.016 q^{53} -626.245 q^{54} -88.0510 q^{56} +911.019 q^{57} -41.3553 q^{58} -273.156 q^{59} +657.412 q^{61} -393.679 q^{62} -665.647 q^{63} +64.0000 q^{64} +1251.04 q^{66} +295.909 q^{67} -34.7748 q^{68} -201.417 q^{69} -186.813 q^{71} +483.827 q^{72} +161.573 q^{73} +365.914 q^{74} -389.616 q^{76} +736.095 q^{77} -819.725 q^{78} -977.315 q^{79} +1295.71 q^{81} -522.889 q^{82} +817.151 q^{83} +411.770 q^{84} -154.586 q^{86} +193.398 q^{87} -535.032 q^{88} +927.195 q^{89} -482.316 q^{91} +86.1400 q^{92} +1841.04 q^{93} +110.724 q^{94} -299.296 q^{96} -273.371 q^{97} -443.720 q^{98} -4044.73 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9}+O(q^{10}) \) 16 * q + 32 * q^2 + 12 * q^3 + 64 * q^4 + 24 * q^6 + 56 * q^7 + 128 * q^8 + 212 * q^9	\( 16 q + 32 q^{2} + 12 q^{3} + 64 q^{4} + 24 q^{6} + 56 q^{7} + 128 q^{8} + 212 q^{9} + 72 q^{11} + 48 q^{12} + 202 q^{13} + 112 q^{14} + 256 q^{16} + 216 q^{17} + 424 q^{18} + 100 q^{19} + 192 q^{21} + 144 q^{22} + 292 q^{23} + 96 q^{24} + 404 q^{26} + 570 q^{27} + 224 q^{28} + 400 q^{29} + 102 q^{31} + 512 q^{32} + 664 q^{33} + 432 q^{34} + 848 q^{36} + 646 q^{37} + 200 q^{38} + 104 q^{39} + 532 q^{41} + 384 q^{42} + 902 q^{43} + 288 q^{44} + 584 q^{46} + 776 q^{47} + 192 q^{48} + 1038 q^{49} + 442 q^{51} + 808 q^{52} + 632 q^{53} + 1140 q^{54} + 448 q^{56} + 1400 q^{57} + 800 q^{58} + 1000 q^{59} + 662 q^{61} + 204 q^{62} + 932 q^{63} + 1024 q^{64} + 1328 q^{66} + 1326 q^{67} + 864 q^{68} + 1854 q^{69} + 1292 q^{71} + 1696 q^{72} + 2272 q^{73} + 1292 q^{74} + 400 q^{76} + 2582 q^{77} + 208 q^{78} + 320 q^{79} + 2956 q^{81} + 1064 q^{82} + 2842 q^{83} + 768 q^{84} + 1804 q^{86} + 2920 q^{87} + 576 q^{88} + 2780 q^{89} + 812 q^{91} + 1168 q^{92} + 2824 q^{93} + 1552 q^{94} + 384 q^{96} + 3796 q^{97} + 2076 q^{98} + 1054 q^{99}+O(q^{100}) \) 16 * q + 32 * q^2 + 12 * q^3 + 64 * q^4 + 24 * q^6 + 56 * q^7 + 128 * q^8 + 212 * q^9 + 72 * q^11 + 48 * q^12 + 202 * q^13 + 112 * q^14 + 256 * q^16 + 216 * q^17 + 424 * q^18 + 100 * q^19 + 192 * q^21 + 144 * q^22 + 292 * q^23 + 96 * q^24 + 404 * q^26 + 570 * q^27 + 224 * q^28 + 400 * q^29 + 102 * q^31 + 512 * q^32 + 664 * q^33 + 432 * q^34 + 848 * q^36 + 646 * q^37 + 200 * q^38 + 104 * q^39 + 532 * q^41 + 384 * q^42 + 902 * q^43 + 288 * q^44 + 584 * q^46 + 776 * q^47 + 192 * q^48 + 1038 * q^49 + 442 * q^51 + 808 * q^52 + 632 * q^53 + 1140 * q^54 + 448 * q^56 + 1400 * q^57 + 800 * q^58 + 1000 * q^59 + 662 * q^61 + 204 * q^62 + 932 * q^63 + 1024 * q^64 + 1328 * q^66 + 1326 * q^67 + 864 * q^68 + 1854 * q^69 + 1292 * q^71 + 1696 * q^72 + 2272 * q^73 + 1292 * q^74 + 400 * q^76 + 2582 * q^77 + 208 * q^78 + 320 * q^79 + 2956 * q^81 + 1064 * q^82 + 2842 * q^83 + 768 * q^84 + 1804 * q^86 + 2920 * q^87 + 576 * q^88 + 2780 * q^89 + 812 * q^91 + 1168 * q^92 + 2824 * q^93 + 1552 * q^94 + 384 * q^96 + 3796 * q^97 + 2076 * q^98 + 1054 * q^99

Introduction

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