LMFDB - Embedded newform 2013.4.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.35127 q^{2} -3.00000 q^{3} +3.23102 q^{4} -13.0308 q^{5} +10.0538 q^{6} +23.8563 q^{7} +15.9822 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.35127 q^{2} -3.00000 q^{3} +3.23102 q^{4} -13.0308 q^{5} +10.0538 q^{6} +23.8563 q^{7} +15.9822 q^{8} +9.00000 q^{9} +43.6697 q^{10} -11.0000 q^{11} -9.69305 q^{12} -69.7329 q^{13} -79.9489 q^{14} +39.0924 q^{15} -79.4087 q^{16} -53.5524 q^{17} -30.1614 q^{18} +153.842 q^{19} -42.1027 q^{20} -71.5689 q^{21} +36.8640 q^{22} +62.5038 q^{23} -47.9465 q^{24} +44.8018 q^{25} +233.694 q^{26} -27.0000 q^{27} +77.0800 q^{28} -232.532 q^{29} -131.009 q^{30} +257.591 q^{31} +138.263 q^{32} +33.0000 q^{33} +179.469 q^{34} -310.867 q^{35} +29.0791 q^{36} +349.559 q^{37} -515.567 q^{38} +209.199 q^{39} -208.260 q^{40} -99.5601 q^{41} +239.847 q^{42} -493.672 q^{43} -35.5412 q^{44} -117.277 q^{45} -209.467 q^{46} +386.133 q^{47} +238.226 q^{48} +226.122 q^{49} -150.143 q^{50} +160.657 q^{51} -225.308 q^{52} +300.133 q^{53} +90.4843 q^{54} +143.339 q^{55} +381.275 q^{56} -461.527 q^{57} +779.277 q^{58} +477.661 q^{59} +126.308 q^{60} -61.0000 q^{61} -863.258 q^{62} +214.707 q^{63} +171.914 q^{64} +908.675 q^{65} -110.592 q^{66} +535.876 q^{67} -173.029 q^{68} -187.511 q^{69} +1041.80 q^{70} -858.075 q^{71} +143.839 q^{72} -499.616 q^{73} -1171.47 q^{74} -134.405 q^{75} +497.067 q^{76} -262.419 q^{77} -701.081 q^{78} +234.094 q^{79} +1034.76 q^{80} +81.0000 q^{81} +333.653 q^{82} -363.007 q^{83} -231.240 q^{84} +697.831 q^{85} +1654.43 q^{86} +697.595 q^{87} -175.804 q^{88} -1530.45 q^{89} +393.028 q^{90} -1663.57 q^{91} +201.951 q^{92} -772.774 q^{93} -1294.04 q^{94} -2004.69 q^{95} -414.788 q^{96} +199.409 q^{97} -757.797 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) $ 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9} + 95 q^{10} - 418 q^{11} - 426 q^{12} + 13 q^{13} + 26 q^{14} - 45 q^{15} + 486 q^{16} - 224 q^{17} - 18 q^{18} + 367 q^{19} + 18 q^{20} - 189 q^{21} + 22 q^{22} + 51 q^{23} + 135 q^{24} + 773 q^{25} - 439 q^{26} - 1026 q^{27} + 22 q^{28} - 462 q^{29} - 285 q^{30} + 234 q^{31} - 597 q^{32} + 1254 q^{33} + 956 q^{34} - 522 q^{35} + 1278 q^{36} + 954 q^{37} + 705 q^{38} - 39 q^{39} + 1495 q^{40} - 740 q^{41} - 78 q^{42} + 1441 q^{43} - 1562 q^{44} + 135 q^{45} + 581 q^{46} + 1003 q^{47} - 1458 q^{48} + 2707 q^{49} + 388 q^{50} + 672 q^{51} + 788 q^{52} + 735 q^{53} + 54 q^{54} - 165 q^{55} + 1059 q^{56} - 1101 q^{57} + 177 q^{58} + 261 q^{59} - 54 q^{60} - 2318 q^{61} + 1251 q^{62} + 567 q^{63} + 5571 q^{64} - 1354 q^{65} - 66 q^{66} + 3495 q^{67} - 1856 q^{68} - 153 q^{69} + 542 q^{70} - 873 q^{71} - 405 q^{72} + 989 q^{73} - 3406 q^{74} - 2319 q^{75} + 1712 q^{76} - 693 q^{77} + 1317 q^{78} + 2313 q^{79} + 1593 q^{80} + 3078 q^{81} + 5170 q^{82} + 569 q^{83} - 66 q^{84} - 1271 q^{85} + 3065 q^{86} + 1386 q^{87} + 495 q^{88} - 2917 q^{89} + 855 q^{90} + 2740 q^{91} + 1083 q^{92} - 702 q^{93} + 3272 q^{94} + 2696 q^{95} + 1791 q^{96} + 4250 q^{97} + 5952 q^{98} - 3762 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9 + 95 * q^10 - 418 * q^11 - 426 * q^12 + 13 * q^13 + 26 * q^14 - 45 * q^15 + 486 * q^16 - 224 * q^17 - 18 * q^18 + 367 * q^19 + 18 * q^20 - 189 * q^21 + 22 * q^22 + 51 * q^23 + 135 * q^24 + 773 * q^25 - 439 * q^26 - 1026 * q^27 + 22 * q^28 - 462 * q^29 - 285 * q^30 + 234 * q^31 - 597 * q^32 + 1254 * q^33 + 956 * q^34 - 522 * q^35 + 1278 * q^36 + 954 * q^37 + 705 * q^38 - 39 * q^39 + 1495 * q^40 - 740 * q^41 - 78 * q^42 + 1441 * q^43 - 1562 * q^44 + 135 * q^45 + 581 * q^46 + 1003 * q^47 - 1458 * q^48 + 2707 * q^49 + 388 * q^50 + 672 * q^51 + 788 * q^52 + 735 * q^53 + 54 * q^54 - 165 * q^55 + 1059 * q^56 - 1101 * q^57 + 177 * q^58 + 261 * q^59 - 54 * q^60 - 2318 * q^61 + 1251 * q^62 + 567 * q^63 + 5571 * q^64 - 1354 * q^65 - 66 * q^66 + 3495 * q^67 - 1856 * q^68 - 153 * q^69 + 542 * q^70 - 873 * q^71 - 405 * q^72 + 989 * q^73 - 3406 * q^74 - 2319 * q^75 + 1712 * q^76 - 693 * q^77 + 1317 * q^78 + 2313 * q^79 + 1593 * q^80 + 3078 * q^81 + 5170 * q^82 + 569 * q^83 - 66 * q^84 - 1271 * q^85 + 3065 * q^86 + 1386 * q^87 + 495 * q^88 - 2917 * q^89 + 855 * q^90 + 2740 * q^91 + 1083 * q^92 - 702 * q^93 + 3272 * q^94 + 2696 * q^95 + 1791 * q^96 + 4250 * q^97 + 5952 * q^98 - 3762 * 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 $

$2$	−3.35127	−1.18485	−0.592427	−	0.805624i	$-0.701830\pi$
$2$	−3.35127	−1.18485	−0.592427	+	0.805624i	$0.701830\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	3.23102	0.403877
$5$	−13.0308	−1.16551	−0.582755	−	0.812648i	$-0.698025\pi$
$5$	−13.0308	−1.16551	−0.582755	+	0.812648i	$0.698025\pi$
$6$	10.0538	0.684075
$7$	23.8563	1.28812	0.644059	−	0.764976i	$-0.277249\pi$
$7$	23.8563	1.28812	0.644059	+	0.764976i	$0.277249\pi$
$8$	15.9822	0.706318
$9$	9.00000	0.333333
$10$	43.6697	1.38096
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−9.69305	−0.233179
$13$	−69.7329	−1.48772	−0.743862	−	0.668333i	$-0.767008\pi$
$13$	−69.7329	−1.48772	−0.743862	+	0.668333i	$0.767008\pi$
$14$	−79.9489	−1.52623
$15$	39.0924	0.672908
$16$	−79.4087	−1.24076
$17$	−53.5524	−0.764022	−0.382011	−	0.924158i	$-0.624768\pi$
$17$	−53.5524	−0.764022	−0.382011	+	0.924158i	$0.624768\pi$
$18$	−30.1614	−0.394951
$19$	153.842	1.85757	0.928785	−	0.370619i	$-0.120854\pi$
$19$	153.842	1.85757	0.928785	+	0.370619i	$0.120854\pi$
$20$	−42.1027	−0.470723
$21$	−71.5689	−0.743695
$22$	36.8640	0.357247
$23$	62.5038	0.566650	0.283325	−	0.959024i	$-0.408562\pi$
$23$	62.5038	0.566650	0.283325	+	0.959024i	$0.408562\pi$
$24$	−47.9465	−0.407793
$25$	44.8018	0.358414
$26$	233.694	1.76274
$27$	−27.0000	−0.192450
$28$	77.0800	0.520241
$29$	−232.532	−1.48897	−0.744484	−	0.667641i	$-0.767304\pi$
$29$	−232.532	−1.48897	−0.744484	+	0.667641i	$0.767304\pi$
$30$	−131.009	−0.797297
$31$	257.591	1.49241	0.746206	−	0.665715i	$-0.231874\pi$
$31$	257.591	1.49241	0.746206	+	0.665715i	$0.231874\pi$
$32$	138.263	0.763801
$33$	33.0000	0.174078
$34$	179.469	0.905253
$35$	−310.867	−1.50132
$36$	29.0791	0.134626
$37$	349.559	1.55317	0.776583	−	0.630015i	$-0.216951\pi$
$37$	349.559	1.55317	0.776583	+	0.630015i	$0.216951\pi$
$38$	−515.567	−2.20095
$39$	209.199	0.858938
$40$	−208.260	−0.823221
$41$	−99.5601	−0.379236	−0.189618	−	0.981858i	$-0.560725\pi$
$41$	−99.5601	−0.379236	−0.189618	+	0.981858i	$0.560725\pi$
$42$	239.847	0.881170
$43$	−493.672	−1.75080	−0.875399	−	0.483401i	$-0.839401\pi$
$43$	−493.672	−1.75080	−0.875399	+	0.483401i	$0.839401\pi$
$44$	−35.5412	−0.121774
$45$	−117.277	−0.388503
$46$	−209.467	−0.671397
$47$	386.133	1.19837	0.599183	−	0.800612i	$-0.295492\pi$
$47$	386.133	1.19837	0.599183	+	0.800612i	$0.295492\pi$
$48$	238.226	0.716353
$49$	226.122	0.659249
$50$	−150.143	−0.424668
$51$	160.657	0.441108
$52$	−225.308	−0.600858
$53$	300.133	0.777858	0.388929	−	0.921268i	$-0.372845\pi$
$53$	300.133	0.777858	0.388929	+	0.921268i	$0.372845\pi$
$54$	90.4843	0.228025
$55$	143.339	0.351415
$56$	381.275	0.909821
$57$	−461.527	−1.07247
$58$	779.277	1.76421
$59$	477.661	1.05400	0.527001	−	0.849864i	$-0.323316\pi$
$59$	477.661	1.05400	0.527001	+	0.849864i	$0.323316\pi$
$60$	126.308	0.271772
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−863.258	−1.76829
$63$	214.707	0.429373
$64$	171.914	0.335769
$65$	908.675	1.73396
$66$	−110.592	−0.206256
$67$	535.876	0.977129	0.488564	−	0.872528i	$-0.337521\pi$
$67$	535.876	0.977129	0.488564	+	0.872528i	$0.337521\pi$
$68$	−173.029	−0.308571
$69$	−187.511	−0.327156
$70$	1041.80	1.77884
$71$	−858.075	−1.43429	−0.717146	−	0.696923i	$-0.754552\pi$
$71$	−858.075	−1.43429	−0.717146	+	0.696923i	$0.754552\pi$
$72$	143.839	0.235439
$73$	−499.616	−0.801037	−0.400518	−	0.916289i	$-0.631170\pi$
$73$	−499.616	−0.801037	−0.400518	+	0.916289i	$0.631170\pi$
$74$	−1171.47	−1.84027
$75$	−134.405	−0.206931
$76$	497.067	0.750230
$77$	−262.419	−0.388382
$78$	−701.081	−1.01772
$79$	234.094	0.333387	0.166694	−	0.986009i	$-0.446691\pi$
$79$	234.094	0.333387	0.166694	+	0.986009i	$0.446691\pi$
$80$	1034.76	1.44612
$81$	81.0000	0.111111
$82$	333.653	0.449339
$83$	−363.007	−0.480062	−0.240031	−	0.970765i	$-0.577158\pi$
$83$	−363.007	−0.480062	−0.240031	+	0.970765i	$0.577158\pi$
$84$	−231.240	−0.300362
$85$	697.831	0.890475
$86$	1654.43	2.07444
$87$	697.595	0.859656
$88$	−175.804	−0.212963
$89$	−1530.45	−1.82278	−0.911390	−	0.411545i	$-0.864989\pi$
$89$	−1530.45	−1.82278	−0.911390	+	0.411545i	$0.864989\pi$
$90$	393.028	0.460320
$91$	−1663.57	−1.91637
$92$	201.951	0.228857
$93$	−772.774	−0.861644
$94$	−1294.04	−1.41989
$95$	−2004.69	−2.16502
$96$	−414.788	−0.440981
$97$	199.409	0.208731	0.104366	−	0.994539i	$-0.466719\pi$
$97$	199.409	0.208731	0.104366	+	0.994539i	$0.466719\pi$
$98$	−757.797	−0.781113
$99$	−99.0000	−0.100504
$100$	144.755	0.144755
$101$	505.186	0.497701	0.248851	−	0.968542i	$-0.419947\pi$
$101$	505.186	0.497701	0.248851	+	0.968542i	$0.419947\pi$
$102$	−538.406	−0.522648
$103$	−1985.91	−1.89978	−0.949892	−	0.312579i	$-0.898807\pi$
$103$	−1985.91	−1.89978	−0.949892	+	0.312579i	$0.898807\pi$
$104$	−1114.48	−1.05081
$105$	932.600	0.866785
$106$	−1005.83	−0.921647
$107$	327.156	0.295583	0.147791	−	0.989019i	$-0.452784\pi$
$107$	327.156	0.295583	0.147791	+	0.989019i	$0.452784\pi$
$108$	−87.2374	−0.0777262
$109$	882.112	0.775147	0.387573	−	0.921839i	$-0.373313\pi$
$109$	882.112	0.775147	0.387573	+	0.921839i	$0.373313\pi$
$110$	−480.367	−0.416375
$111$	−1048.68	−0.896721
$112$	−1894.40	−1.59825
$113$	−586.100	−0.487926	−0.243963	−	0.969785i	$-0.578448\pi$
$113$	−586.100	−0.487926	−0.243963	+	0.969785i	$0.578448\pi$
$114$	1546.70	1.27072
$115$	−814.475	−0.660436
$116$	−751.314	−0.601360
$117$	−627.596	−0.495908
$118$	−1600.77	−1.24884
$119$	−1277.56	−0.984150
$120$	624.781	0.475287
$121$	121.000	0.0909091
$122$	204.428	0.151705
$123$	298.680	0.218952
$124$	832.282	0.602751
$125$	1045.05	0.747775
$126$	−719.540	−0.508744
$127$	−1636.01	−1.14309	−0.571545	−	0.820570i	$-0.693656\pi$
$127$	−1636.01	−1.14309	−0.571545	+	0.820570i	$0.693656\pi$
$128$	−1682.23	−1.16164
$129$	1481.02	1.01082
$130$	−3045.22	−2.05449
$131$	−2194.69	−1.46375	−0.731874	−	0.681440i	$-0.761354\pi$
$131$	−2194.69	−1.46375	−0.731874	+	0.681440i	$0.761354\pi$
$132$	106.624	0.0703060
$133$	3670.10	2.39277
$134$	−1795.86	−1.15775
$135$	351.832	0.224303
$136$	−855.883	−0.539642
$137$	−359.062	−0.223918	−0.111959	−	0.993713i	$-0.535713\pi$
$137$	−359.062	−0.223918	−0.111959	+	0.993713i	$0.535713\pi$
$138$	628.402	0.387631
$139$	−404.259	−0.246682	−0.123341	−	0.992364i	$-0.539361\pi$
$139$	−404.259	−0.246682	−0.123341	+	0.992364i	$0.539361\pi$
$140$	−1004.41	−0.606347
$141$	−1158.40	−0.691877
$142$	2875.64	1.69943
$143$	767.062	0.448566
$144$	−714.678	−0.413587
$145$	3030.08	1.73541
$146$	1674.35	0.949111
$147$	−678.367	−0.380617
$148$	1129.43	0.627288
$149$	−1770.03	−0.973200	−0.486600	−	0.873625i	$-0.661763\pi$
$149$	−1770.03	−0.973200	−0.486600	+	0.873625i	$0.661763\pi$
$150$	450.429	0.245182
$151$	−767.056	−0.413391	−0.206696	−	0.978405i	$-0.566271\pi$
$151$	−767.056	−0.413391	−0.206696	+	0.978405i	$0.566271\pi$
$152$	2458.73	1.31204
$153$	−481.972	−0.254674
$154$	879.438	0.460176
$155$	−3356.62	−1.73942
$156$	675.924	0.346905
$157$	2665.82	1.35513	0.677566	−	0.735462i	$-0.263035\pi$
$157$	2665.82	1.35513	0.677566	+	0.735462i	$0.263035\pi$
$158$	−784.511	−0.395015
$159$	−900.400	−0.449096
$160$	−1801.67	−0.890218
$161$	1491.11	0.729912
$162$	−271.453	−0.131650
$163$	1862.64	0.895052	0.447526	−	0.894271i	$-0.352305\pi$
$163$	1862.64	0.895052	0.447526	+	0.894271i	$0.352305\pi$
$164$	−321.680	−0.153165
$165$	−430.016	−0.202889
$166$	1216.53	0.568803
$167$	−498.513	−0.230994	−0.115497	−	0.993308i	$-0.536846\pi$
$167$	−498.513	−0.230994	−0.115497	+	0.993308i	$0.536846\pi$
$168$	−1143.82	−0.525286
$169$	2665.68	1.21333
$170$	−2338.62	−1.05508
$171$	1384.58	0.619190
$172$	−1595.06	−0.707107
$173$	−3064.60	−1.34681	−0.673403	−	0.739276i	$-0.735168\pi$
$173$	−3064.60	−1.34681	−0.673403	+	0.739276i	$0.735168\pi$
$174$	−2337.83	−1.01857
$175$	1068.80	0.461680
$176$	873.495	0.374103
$177$	−1432.98	−0.608529
$178$	5128.95	2.15973
$179$	−1882.10	−0.785891	−0.392945	−	0.919562i	$-0.628544\pi$
$179$	−1882.10	−0.785891	−0.392945	+	0.919562i	$0.628544\pi$
$180$	−378.925	−0.156908
$181$	−1336.84	−0.548987	−0.274494	−	0.961589i	$-0.588510\pi$
$181$	−1336.84	−0.548987	−0.274494	+	0.961589i	$0.588510\pi$
$182$	5575.07	2.27061
$183$	183.000	0.0739221
$184$	998.946	0.400235
$185$	−4555.03	−1.81023
$186$	2589.77	1.02092
$187$	589.077	0.230361
$188$	1247.60	0.483993
$189$	−644.120	−0.247898
$190$	6718.25	2.56523
$191$	778.549	0.294942	0.147471	−	0.989066i	$-0.452887\pi$
$191$	778.549	0.294942	0.147471	+	0.989066i	$0.452887\pi$
$192$	−515.741	−0.193856
$193$	−592.359	−0.220927	−0.110464	−	0.993880i	$-0.535234\pi$
$193$	−592.359	−0.220927	−0.110464	+	0.993880i	$0.535234\pi$
$194$	−668.275	−0.247316
$195$	−2726.03	−1.00110
$196$	730.605	0.266255
$197$	2094.13	0.757364	0.378682	−	0.925527i	$-0.376377\pi$
$197$	2094.13	0.757364	0.378682	+	0.925527i	$0.376377\pi$
$198$	331.776	0.119082
$199$	232.369	0.0827748	0.0413874	−	0.999143i	$-0.486822\pi$
$199$	232.369	0.0827748	0.0413874	+	0.999143i	$0.486822\pi$
$200$	716.029	0.253155
$201$	−1607.63	−0.564146
$202$	−1693.01	−0.589703
$203$	−5547.34	−1.91797
$204$	519.086	0.178153
$205$	1297.35	0.442003
$206$	6655.33	2.25096
$207$	562.534	0.188883
$208$	5537.40	1.84591
$209$	−1692.26	−0.560078
$210$	−3125.39	−1.02701
$211$	5210.07	1.69988	0.849942	−	0.526876i	$-0.176637\pi$
$211$	5210.07	1.69988	0.849942	+	0.526876i	$0.176637\pi$
$212$	969.735	0.314159
$213$	2574.23	0.828089
$214$	−1096.39	−0.350222
$215$	6432.94	2.04057
$216$	−431.518	−0.135931
$217$	6145.17	1.92240
$218$	−2956.20	−0.918435
$219$	1498.85	0.462479
$220$	463.130	0.141928
$221$	3734.36	1.13665
$222$	3514.40	1.06248
$223$	−1463.74	−0.439547	−0.219774	−	0.975551i	$-0.570532\pi$
$223$	−1463.74	−0.439547	−0.219774	+	0.975551i	$0.570532\pi$
$224$	3298.43	0.983866
$225$	403.216	0.119471
$226$	1964.18	0.578120
$227$	2051.04	0.599703	0.299851	−	0.953986i	$-0.403063\pi$
$227$	2051.04	0.599703	0.299851	+	0.953986i	$0.403063\pi$
$228$	−1491.20	−0.433145
$229$	2835.96	0.818364	0.409182	−	0.912453i	$-0.365814\pi$
$229$	2835.96	0.818364	0.409182	+	0.912453i	$0.365814\pi$
$230$	2729.53	0.782520
$231$	787.257	0.224233
$232$	−3716.36	−1.05168
$233$	3560.33	1.00105	0.500526	−	0.865722i	$-0.333140\pi$
$233$	3560.33	1.00105	0.500526	+	0.865722i	$0.333140\pi$
$234$	2103.24	0.587579
$235$	−5031.62	−1.39671
$236$	1543.33	0.425688
$237$	−702.281	−0.192481
$238$	4281.45	1.16607
$239$	478.510	0.129507	0.0647536	−	0.997901i	$-0.479374\pi$
$239$	478.510	0.129507	0.0647536	+	0.997901i	$0.479374\pi$
$240$	−3104.28	−0.834917
$241$	−6812.36	−1.82084	−0.910421	−	0.413683i	$-0.864242\pi$
$241$	−6812.36	−1.82084	−0.910421	+	0.413683i	$0.864242\pi$
$242$	−405.504	−0.107714
$243$	−243.000	−0.0641500
$244$	−197.092	−0.0517112
$245$	−2946.55	−0.768361
$246$	−1000.96	−0.259426
$247$	−10727.9	−2.76355
$248$	4116.86	1.05412
$249$	1089.02	0.277164
$250$	−3502.24	−0.886003
$251$	−3969.19	−0.998141	−0.499070	−	0.866561i	$-0.666325\pi$
$251$	−3969.19	−0.998141	−0.499070	+	0.866561i	$0.666325\pi$
$252$	693.720	0.173414
$253$	−687.542	−0.170851
$254$	5482.72	1.35439
$255$	−2093.49	−0.514116
$256$	4262.30	1.04060
$257$	3799.18	0.922127	0.461064	−	0.887367i	$-0.347468\pi$
$257$	3799.18	0.922127	0.461064	+	0.887367i	$0.347468\pi$
$258$	−4963.29	−1.19768
$259$	8339.18	2.00066
$260$	2935.95	0.700306
$261$	−2092.79	−0.496323
$262$	7355.00	1.73433
$263$	−7515.29	−1.76203	−0.881013	−	0.473092i	$-0.843138\pi$
$263$	−7515.29	−1.76203	−0.881013	+	0.473092i	$0.843138\pi$
$264$	527.411	0.122954
$265$	−3910.98	−0.906601
$266$	−12299.5	−2.83508
$267$	4591.35	1.05238
$268$	1731.42	0.394640
$269$	5206.80	1.18016	0.590082	−	0.807343i	$-0.299095\pi$
$269$	5206.80	1.18016	0.590082	+	0.807343i	$0.299095\pi$
$270$	−1179.08	−0.265766
$271$	7335.97	1.64438	0.822192	−	0.569210i	$-0.192751\pi$
$271$	7335.97	1.64438	0.822192	+	0.569210i	$0.192751\pi$
$272$	4252.53	0.947968
$273$	4990.70	1.10641
$274$	1203.31	0.265310
$275$	−492.820	−0.108066
$276$	−605.853	−0.132131
$277$	6341.19	1.37547	0.687734	−	0.725962i	$-0.258605\pi$
$277$	6341.19	1.37547	0.687734	+	0.725962i	$0.258605\pi$
$278$	1354.78	0.292282
$279$	2318.32	0.497470
$280$	−4968.32	−1.06041
$281$	−7537.13	−1.60010	−0.800049	−	0.599934i	$-0.795193\pi$
$281$	−7537.13	−1.60010	−0.800049	+	0.599934i	$0.795193\pi$
$282$	3882.11	0.819773
$283$	2122.41	0.445810	0.222905	−	0.974840i	$-0.428446\pi$
$283$	2122.41	0.445810	0.222905	+	0.974840i	$0.428446\pi$
$284$	−2772.46	−0.579278
$285$	6014.06	1.24997
$286$	−2570.63	−0.531485
$287$	−2375.13	−0.488501
$288$	1244.36	0.254600
$289$	−2045.14	−0.416271
$290$	−10154.6	−2.05620
$291$	−598.228	−0.120511
$292$	−1614.27	−0.323520
$293$	3456.41	0.689165	0.344583	−	0.938756i	$-0.388020\pi$
$293$	3456.41	0.689165	0.344583	+	0.938756i	$0.388020\pi$
$294$	2273.39	0.450976
$295$	−6224.31	−1.22845
$296$	5586.70	1.09703
$297$	297.000	0.0580259
$298$	5931.86	1.15310
$299$	−4358.57	−0.843019
$300$	−434.266	−0.0835745
$301$	−11777.2	−2.25523
$302$	2570.61	0.489808
$303$	−1515.56	−0.287348
$304$	−12216.4	−2.30480
$305$	794.879	0.149228
$306$	1615.22	0.301751
$307$	−2021.60	−0.375828	−0.187914	−	0.982186i	$-0.560173\pi$
$307$	−2021.60	−0.375828	−0.187914	+	0.982186i	$0.560173\pi$
$308$	−847.881	−0.156859
$309$	5957.74	1.09684
$310$	11248.9	2.06096
$311$	9710.85	1.77058	0.885292	−	0.465035i	$-0.153958\pi$
$311$	9710.85	1.77058	0.885292	+	0.465035i	$0.153958\pi$
$312$	3343.45	0.606684
$313$	−779.453	−0.140758	−0.0703791	−	0.997520i	$-0.522421\pi$
$313$	−779.453	−0.140758	−0.0703791	+	0.997520i	$0.522421\pi$
$314$	−8933.88	−1.60563
$315$	−2797.80	−0.500438
$316$	756.360	0.134647
$317$	2514.67	0.445545	0.222773	−	0.974870i	$-0.428489\pi$
$317$	2514.67	0.445545	0.222773	+	0.974870i	$0.428489\pi$
$318$	3017.48	0.532113
$319$	2557.85	0.448941
$320$	−2240.17	−0.391342
$321$	−981.468	−0.170655
$322$	−4997.11	−0.864839
$323$	−8238.62	−1.41922
$324$	261.712	0.0448752
$325$	−3124.16	−0.533222
$326$	−6242.22	−1.06051
$327$	−2646.34	−0.447531
$328$	−1591.18	−0.267861
$329$	9211.69	1.54364
$330$	1441.10	0.240394
$331$	10068.3	1.67192	0.835961	−	0.548789i	$-0.184911\pi$
$331$	10068.3	1.67192	0.835961	+	0.548789i	$0.184911\pi$
$332$	−1172.88	−0.193886
$333$	3146.03	0.517722
$334$	1670.65	0.273695
$335$	−6982.89	−1.13885
$336$	5683.19	0.922748
$337$	−430.761	−0.0696292	−0.0348146	−	0.999394i	$-0.511084\pi$
$337$	−430.761	−0.0696292	−0.0348146	+	0.999394i	$0.511084\pi$
$338$	−8933.40	−1.43761
$339$	1758.30	0.281704
$340$	2254.70	0.359642
$341$	−2833.50	−0.449979
$342$	−4640.10	−0.733649
$343$	−2788.27	−0.438928
$344$	−7889.95	−1.23662
$345$	2443.43	0.381303
$346$	10270.3	1.59577
$347$	−8761.97	−1.35552	−0.677762	−	0.735281i	$-0.737050\pi$
$347$	−8761.97	−1.35552	−0.677762	+	0.735281i	$0.737050\pi$
$348$	2253.94	0.347195
$349$	4347.15	0.666755	0.333377	−	0.942793i	$-0.391812\pi$
$349$	4347.15	0.666755	0.333377	+	0.942793i	$0.391812\pi$
$350$	−3581.85	−0.547023
$351$	1882.79	0.286313
$352$	−1520.89	−0.230295
$353$	−8065.95	−1.21617	−0.608084	−	0.793873i	$-0.708062\pi$
$353$	−8065.95	−1.21617	−0.608084	+	0.793873i	$0.708062\pi$
$354$	4802.31	0.721017
$355$	11181.4	1.67168
$356$	−4944.91	−0.736179
$357$	3832.68	0.568199
$358$	6307.41	0.931165
$359$	−5424.02	−0.797406	−0.398703	−	0.917080i	$-0.630540\pi$
$359$	−5424.02	−0.797406	−0.398703	+	0.917080i	$0.630540\pi$
$360$	−1874.34	−0.274407
$361$	16808.4	2.45057
$362$	4480.12	0.650469
$363$	−363.000	−0.0524864
$364$	−5375.01	−0.773976
$365$	6510.40	0.933616
$366$	−613.283	−0.0875869
$367$	−5881.03	−0.836478	−0.418239	−	0.908337i	$-0.637353\pi$
$367$	−5881.03	−0.836478	−0.418239	+	0.908337i	$0.637353\pi$
$368$	−4963.35	−0.703077
$369$	−896.040	−0.126412
$370$	15265.1	2.14486
$371$	7160.06	1.00197
$372$	−2496.84	−0.347998
$373$	−2427.50	−0.336973	−0.168487	−	0.985704i	$-0.553888\pi$
$373$	−2427.50	−0.336973	−0.168487	+	0.985704i	$0.553888\pi$
$374$	−1974.15	−0.272944
$375$	−3135.14	−0.431728
$376$	6171.23	0.846428
$377$	16215.1	2.21517
$378$	2158.62	0.293723
$379$	−9097.72	−1.23303	−0.616515	−	0.787343i	$-0.711456\pi$
$379$	−9097.72	−1.23303	−0.616515	+	0.787343i	$0.711456\pi$
$380$	−6477.18	−0.874401
$381$	4908.03	0.659964
$382$	−2609.13	−0.349462
$383$	10438.6	1.39265	0.696327	−	0.717725i	$-0.254817\pi$
$383$	10438.6	1.39265	0.696327	+	0.717725i	$0.254817\pi$
$384$	5046.69	0.670672
$385$	3419.53	0.452664
$386$	1985.16	0.261766
$387$	−4443.05	−0.583599
$388$	644.295	0.0843019
$389$	8070.12	1.05185	0.525927	−	0.850530i	$-0.323719\pi$
$389$	8070.12	1.05185	0.525927	+	0.850530i	$0.323719\pi$
$390$	9135.65	1.18616
$391$	−3347.23	−0.432933
$392$	3613.92	0.465639
$393$	6584.07	0.845095
$394$	−7018.00	−0.897365
$395$	−3050.43	−0.388566
$396$	−319.871	−0.0405912
$397$	9123.23	1.15335	0.576677	−	0.816972i	$-0.304349\pi$
$397$	9123.23	1.15335	0.576677	+	0.816972i	$0.304349\pi$
$398$	−778.731	−0.0980760
$399$	−11010.3	−1.38147
$400$	−3557.65	−0.444706
$401$	1392.34	0.173392	0.0866959	−	0.996235i	$-0.472369\pi$
$401$	1392.34	0.173392	0.0866959	+	0.996235i	$0.472369\pi$
$402$	5387.59	0.668430
$403$	−17962.6	−2.22030
$404$	1632.26	0.201010
$405$	−1055.49	−0.129501
$406$	18590.6	2.27251
$407$	−3845.15	−0.468297
$408$	2567.65	0.311563
$409$	−7678.30	−0.928283	−0.464141	−	0.885761i	$-0.653637\pi$
$409$	−7678.30	−0.928283	−0.464141	+	0.885761i	$0.653637\pi$
$410$	−4347.76	−0.523709
$411$	1077.19	0.129279
$412$	−6416.51	−0.767279
$413$	11395.2	1.35768
$414$	−1885.21	−0.223799
$415$	4730.27	0.559517
$416$	−9641.46	−1.13633
$417$	1212.78	0.142422
$418$	5671.24	0.663611
$419$	4345.66	0.506681	0.253340	−	0.967377i	$-0.418471\pi$
$419$	4345.66	0.506681	0.253340	+	0.967377i	$0.418471\pi$
$420$	3013.24	0.350074
$421$	8094.47	0.937056	0.468528	−	0.883449i	$-0.344785\pi$
$421$	8094.47	0.937056	0.468528	+	0.883449i	$0.344785\pi$
$422$	−17460.3	−2.01411
$423$	3475.19	0.399456
$424$	4796.78	0.549415
$425$	−2399.24	−0.273836
$426$	−8626.93	−0.981164
$427$	−1455.23	−0.164927
$428$	1057.05	0.119379
$429$	−2301.19	−0.258980
$430$	−21558.5	−2.41778
$431$	9219.60	1.03038	0.515189	−	0.857077i	$-0.327722\pi$
$431$	9219.60	1.03038	0.515189	+	0.857077i	$0.327722\pi$
$432$	2144.03	0.238784
$433$	5608.32	0.622445	0.311222	−	0.950337i	$-0.399262\pi$
$433$	5608.32	0.622445	0.311222	+	0.950337i	$0.399262\pi$
$434$	−20594.1	−2.27776
$435$	−9090.23	−1.00194
$436$	2850.12	0.313064
$437$	9615.73	1.05259
$438$	−5023.05	−0.547969
$439$	8699.92	0.945842	0.472921	−	0.881105i	$-0.343200\pi$
$439$	8699.92	0.945842	0.472921	+	0.881105i	$0.343200\pi$
$440$	2290.86	0.248211
$441$	2035.10	0.219750
$442$	−12514.9	−1.34677
$443$	3422.22	0.367031	0.183515	−	0.983017i	$-0.441252\pi$
$443$	3422.22	0.367031	0.183515	+	0.983017i	$0.441252\pi$
$444$	−3388.29	−0.362165
$445$	19943.0	2.12447
$446$	4905.38	0.520799
$447$	5310.10	0.561877
$448$	4101.22	0.432510
$449$	4456.92	0.468453	0.234226	−	0.972182i	$-0.424744\pi$
$449$	4456.92	0.468453	0.234226	+	0.972182i	$0.424744\pi$
$450$	−1351.29	−0.141556
$451$	1095.16	0.114344
$452$	−1893.70	−0.197062
$453$	2301.17	0.238672
$454$	−6873.60	−0.710560
$455$	21677.6	2.23354
$456$	−7376.19	−0.757504
$457$	9901.25	1.01348	0.506741	−	0.862099i	$-0.330850\pi$
$457$	9901.25	1.01348	0.506741	+	0.862099i	$0.330850\pi$
$458$	−9504.06	−0.969641
$459$	1445.92	0.147036
$460$	−2631.58	−0.266735
$461$	−5582.22	−0.563970	−0.281985	−	0.959419i	$-0.590993\pi$
$461$	−5582.22	−0.563970	−0.281985	+	0.959419i	$0.590993\pi$
$462$	−2638.31	−0.265683
$463$	−6725.22	−0.675048	−0.337524	−	0.941317i	$-0.609589\pi$
$463$	−6725.22	−0.675048	−0.337524	+	0.941317i	$0.609589\pi$
$464$	18465.0	1.84745
$465$	10069.9	1.00426
$466$	−11931.6	−1.18610
$467$	9801.00	0.971169	0.485585	−	0.874190i	$-0.338607\pi$
$467$	9801.00	0.971169	0.485585	+	0.874190i	$0.338607\pi$
$468$	−2027.77	−0.200286
$469$	12784.0	1.25866
$470$	16862.3	1.65490
$471$	−7997.46	−0.782385
$472$	7634.05	0.744461
$473$	5430.39	0.527885
$474$	2353.53	0.228062
$475$	6892.41	0.665780
$476$	−4127.82	−0.397476
$477$	2701.20	0.259286
$478$	−1603.62	−0.153447
$479$	−6375.33	−0.608134	−0.304067	−	0.952651i	$-0.598345\pi$
$479$	−6375.33	−0.608134	−0.304067	+	0.952651i	$0.598345\pi$
$480$	5405.02	0.513967
$481$	−24375.8	−2.31068
$482$	22830.1	2.15743
$483$	−4473.33	−0.421415
$484$	390.953	0.0367161
$485$	−2598.46	−0.243279
$486$	814.359	0.0760084
$487$	17549.5	1.63294	0.816472	−	0.577385i	$-0.195927\pi$
$487$	17549.5	1.63294	0.816472	+	0.577385i	$0.195927\pi$
$488$	−974.911	−0.0904348
$489$	−5587.93	−0.516759
$490$	9874.70	0.910395
$491$	17821.6	1.63804	0.819021	−	0.573763i	$-0.194517\pi$
$491$	17821.6	1.63804	0.819021	+	0.573763i	$0.194517\pi$
$492$	965.041	0.0884296
$493$	12452.6	1.13760
$494$	35952.0	3.27440
$495$	1290.05	0.117138
$496$	−20455.0	−1.85172
$497$	−20470.5	−1.84754
$498$	−3649.60	−0.328399
$499$	9900.74	0.888213	0.444106	−	0.895974i	$-0.353521\pi$
$499$	9900.74	0.888213	0.444106	+	0.895974i	$0.353521\pi$
$500$	3376.56	0.302009
$501$	1495.54	0.133365
$502$	13301.8	1.18265
$503$	−1936.99	−0.171702	−0.0858512	−	0.996308i	$-0.527361\pi$
$503$	−1936.99	−0.171702	−0.0858512	+	0.996308i	$0.527361\pi$
$504$	3431.47	0.303274
$505$	−6582.97	−0.580076
$506$	2304.14	0.202434
$507$	−7997.03	−0.700514
$508$	−5285.98	−0.461668
$509$	−15067.2	−1.31207	−0.656033	−	0.754732i	$-0.727767\pi$
$509$	−15067.2	−1.31207	−0.656033	+	0.754732i	$0.727767\pi$
$510$	7015.86	0.609152
$511$	−11919.0	−1.03183
$512$	−826.283	−0.0713221
$513$	−4153.74	−0.357490
$514$	−12732.1	−1.09259
$515$	25878.0	2.21422
$516$	4785.19	0.408248
$517$	−4247.46	−0.361321
$518$	−27946.8	−2.37049
$519$	9193.81	0.777579
$520$	14522.6	1.22473
$521$	−6779.25	−0.570066	−0.285033	−	0.958518i	$-0.592004\pi$
$521$	−6779.25	−0.570066	−0.285033	+	0.958518i	$0.592004\pi$
$522$	7013.49	0.588069
$523$	10481.5	0.876337	0.438169	−	0.898893i	$-0.355627\pi$
$523$	10481.5	0.876337	0.438169	+	0.898893i	$0.355627\pi$
$524$	−7091.08	−0.591174
$525$	−3206.41	−0.266551
$526$	25185.8	2.08774
$527$	−13794.6	−1.14023
$528$	−2620.49	−0.215989
$529$	−8260.27	−0.678908
$530$	13106.7	1.07419
$531$	4298.95	0.351334
$532$	11858.2	0.966385
$533$	6942.61	0.564199
$534$	−15386.9	−1.24692
$535$	−4263.10	−0.344505
$536$	8564.45	0.690164
$537$	5646.29	0.453734
$538$	−17449.4	−1.39832
$539$	−2487.34	−0.198771
$540$	1136.77	0.0905907
$541$	−10836.1	−0.861144	−0.430572	−	0.902556i	$-0.641688\pi$
$541$	−10836.1	−0.861144	−0.430572	+	0.902556i	$0.641688\pi$
$542$	−24584.8	−1.94835
$543$	4010.53	0.316958
$544$	−7404.30	−0.583560
$545$	−11494.6	−0.903441
$546$	−16725.2	−1.31094
$547$	−17642.6	−1.37905	−0.689526	−	0.724261i	$-0.742181\pi$
$547$	−17642.6	−1.37905	−0.689526	+	0.724261i	$0.742181\pi$
$548$	−1160.14	−0.0904353
$549$	−549.000	−0.0426790
$550$	1651.57	0.128042
$551$	−35773.2	−2.76586
$552$	−2996.84	−0.231076
$553$	5584.60	0.429442
$554$	−21251.0	−1.62973
$555$	13665.1	1.04514
$556$	−1306.17	−0.0996292
$557$	24472.5	1.86164	0.930821	−	0.365475i	$-0.119093\pi$
$557$	24472.5	1.86164	0.930821	+	0.365475i	$0.119093\pi$
$558$	−7769.32	−0.589429
$559$	34425.2	2.60471
$560$	24685.5	1.86277
$561$	−1767.23	−0.132999
$562$	25259.0	1.89588
$563$	3679.15	0.275413	0.137707	−	0.990473i	$-0.456027\pi$
$563$	3679.15	0.275413	0.137707	+	0.990473i	$0.456027\pi$
$564$	−3742.80	−0.279433
$565$	7637.35	0.568683
$566$	−7112.77	−0.528219
$567$	1932.36	0.143124
$568$	−13713.9	−1.01307
$569$	5964.36	0.439436	0.219718	−	0.975563i	$-0.429486\pi$
$569$	5964.36	0.439436	0.219718	+	0.975563i	$0.429486\pi$
$570$	−20154.8	−1.48103
$571$	−9067.38	−0.664550	−0.332275	−	0.943183i	$-0.607816\pi$
$571$	−9067.38	−0.664550	−0.332275	+	0.943183i	$0.607816\pi$
$572$	2478.39	0.181165
$573$	−2335.65	−0.170285
$574$	7959.71	0.578801
$575$	2800.28	0.203096
$576$	1547.22	0.111923
$577$	−14101.5	−1.01742	−0.508712	−	0.860937i	$-0.669878\pi$
$577$	−14101.5	−1.01742	−0.508712	+	0.860937i	$0.669878\pi$
$578$	6853.82	0.493220
$579$	1777.08	0.127552
$580$	9790.22	0.700891
$581$	−8659.99	−0.618377
$582$	2004.82	0.142788
$583$	−3301.46	−0.234533
$584$	−7984.95	−0.565787
$585$	8178.08	0.577986
$586$	−11583.4	−0.816559
$587$	−10527.2	−0.740212	−0.370106	−	0.928990i	$-0.620679\pi$
$587$	−10527.2	−0.740212	−0.370106	+	0.928990i	$0.620679\pi$
$588$	−2191.81	−0.153723
$589$	39628.4	2.77226
$590$	20859.3	1.45553
$591$	−6282.40	−0.437264
$592$	−27758.0	−1.92711
$593$	−4729.41	−0.327510	−0.163755	−	0.986501i	$-0.552361\pi$
$593$	−4729.41	−0.327510	−0.163755	+	0.986501i	$0.552361\pi$
$594$	−995.327	−0.0687522
$595$	16647.7	1.14704
$596$	−5719.01	−0.393053
$597$	−697.107	−0.0477901
$598$	14606.8	0.998854
$599$	−726.396	−0.0495488	−0.0247744	−	0.999693i	$-0.507887\pi$
$599$	−726.396	−0.0495488	−0.0247744	+	0.999693i	$0.507887\pi$
$600$	−2148.09	−0.146159
$601$	17491.2	1.18715	0.593577	−	0.804777i	$-0.297715\pi$
$601$	17491.2	1.18715	0.593577	+	0.804777i	$0.297715\pi$
$602$	39468.5	2.67212
$603$	4822.88	0.325710
$604$	−2478.37	−0.166959
$605$	−1576.73	−0.105955
$606$	5079.04	0.340465
$607$	−6087.79	−0.407077	−0.203539	−	0.979067i	$-0.565244\pi$
$607$	−6087.79	−0.407077	−0.203539	+	0.979067i	$0.565244\pi$
$608$	21270.6	1.41881
$609$	16642.0	1.10734
$610$	−2663.85	−0.176814
$611$	−26926.1	−1.78284
$612$	−1557.26	−0.102857
$613$	18608.1	1.22606	0.613030	−	0.790060i	$-0.289951\pi$
$613$	18608.1	1.22606	0.613030	+	0.790060i	$0.289951\pi$
$614$	6774.94	0.445300
$615$	−3892.04	−0.255191
$616$	−4194.02	−0.274321
$617$	−13454.6	−0.877895	−0.438948	−	0.898513i	$-0.644649\pi$
$617$	−13454.6	−0.877895	−0.438948	+	0.898513i	$0.644649\pi$
$618$	−19966.0	−1.29960
$619$	−4291.52	−0.278660	−0.139330	−	0.990246i	$-0.544495\pi$
$619$	−4291.52	−0.278660	−0.139330	+	0.990246i	$0.544495\pi$
$620$	−10845.3	−0.702512
$621$	−1687.60	−0.109052
$622$	−32543.7	−2.09788
$623$	−36510.8	−2.34796
$624$	−16612.2	−1.06574
$625$	−19218.0	−1.22995
$626$	2612.16	0.166778
$627$	5076.79	0.323361
$628$	8613.31	0.547306
$629$	−18719.7	−1.18665
$630$	9376.18	0.592946
$631$	18959.8	1.19616	0.598082	−	0.801435i	$-0.295930\pi$
$631$	18959.8	1.19616	0.598082	+	0.801435i	$0.295930\pi$
$632$	3741.32	0.235477
$633$	−15630.2	−0.981429
$634$	−8427.33	−0.527906
$635$	21318.5	1.33228
$636$	−2909.21	−0.181380
$637$	−15768.2	−0.980781
$638$	−8572.05	−0.531929
$639$	−7722.68	−0.478098
$640$	21920.8	1.35390
$641$	−6073.73	−0.374256	−0.187128	−	0.982336i	$-0.559918\pi$
$641$	−6073.73	−0.374256	−0.187128	+	0.982336i	$0.559918\pi$
$642$	3289.16	0.202201
$643$	11588.8	0.710760	0.355380	−	0.934722i	$-0.384352\pi$
$643$	11588.8	0.710760	0.355380	+	0.934722i	$0.384352\pi$
$644$	4817.80	0.294795
$645$	−19298.8	−1.17813
$646$	27609.9	1.68157
$647$	−682.726	−0.0414849	−0.0207424	−	0.999785i	$-0.506603\pi$
$647$	−682.726	−0.0414849	−0.0207424	+	0.999785i	$0.506603\pi$
$648$	1294.55	0.0784798
$649$	−5254.27	−0.317794
$650$	10469.9	0.631790
$651$	−18435.5	−1.10990
$652$	6018.23	0.361491
$653$	−13876.2	−0.831571	−0.415786	−	0.909463i	$-0.636493\pi$
$653$	−13876.2	−0.831571	−0.415786	+	0.909463i	$0.636493\pi$
$654$	8868.59	0.530259
$655$	28598.6	1.70601
$656$	7905.93	0.470541
$657$	−4496.55	−0.267012
$658$	−30870.9	−1.82898
$659$	14928.1	0.882422	0.441211	−	0.897403i	$-0.354549\pi$
$659$	14928.1	0.882422	0.441211	+	0.897403i	$0.354549\pi$
$660$	−1389.39	−0.0819423
$661$	8688.29	0.511249	0.255624	−	0.966776i	$-0.417719\pi$
$661$	8688.29	0.511249	0.255624	+	0.966776i	$0.417719\pi$
$662$	−33741.7	−1.98098
$663$	−11203.1	−0.656247
$664$	−5801.63	−0.339077
$665$	−47824.4	−2.78880
$666$	−10543.2	−0.613424
$667$	−14534.1	−0.843723
$668$	−1610.70	−0.0932934
$669$	4391.21	0.253773
$670$	23401.6	1.34937
$671$	671.000	0.0386046
$672$	−9895.30	−0.568035
$673$	−2640.51	−0.151239	−0.0756197	−	0.997137i	$-0.524093\pi$
$673$	−2640.51	−0.151239	−0.0756197	+	0.997137i	$0.524093\pi$
$674$	1443.60	0.0825004
$675$	−1209.65	−0.0689769
$676$	8612.84	0.490034
$677$	25842.3	1.46706	0.733531	−	0.679656i	$-0.237871\pi$
$677$	25842.3	1.46706	0.733531	+	0.679656i	$0.237871\pi$
$678$	−5892.54	−0.333778
$679$	4757.17	0.268871
$680$	11152.8	0.628959
$681$	−6153.13	−0.346238
$682$	9495.84	0.533159
$683$	−4546.04	−0.254684	−0.127342	−	0.991859i	$-0.540645\pi$
$683$	−4546.04	−0.254684	−0.127342	+	0.991859i	$0.540645\pi$
$684$	4473.60	0.250077
$685$	4678.87	0.260979
$686$	9344.24	0.520065
$687$	−8507.87	−0.472483
$688$	39201.9	2.17232
$689$	−20929.2	−1.15724
$690$	−8188.58	−0.451788
$691$	21732.0	1.19642	0.598208	−	0.801341i	$-0.295880\pi$
$691$	21732.0	1.19642	0.598208	+	0.801341i	$0.295880\pi$
$692$	−9901.78	−0.543944
$693$	−2361.77	−0.129461
$694$	29363.7	1.60610
$695$	5267.82	0.287511
$696$	11149.1	0.607191
$697$	5331.68	0.289744
$698$	−14568.5	−0.790007
$699$	−10681.0	−0.577958
$700$	3453.33	0.186462
$701$	31407.2	1.69220	0.846100	−	0.533024i	$-0.178944\pi$
$701$	31407.2	1.69220	0.846100	+	0.533024i	$0.178944\pi$
$702$	−6309.73	−0.339239
$703$	53776.9	2.88511
$704$	−1891.05	−0.101238
$705$	15094.9	0.806390
$706$	27031.2	1.44098
$707$	12051.8	0.641098
$708$	−4629.99	−0.245771
$709$	1459.63	0.0773165	0.0386583	−	0.999252i	$-0.487692\pi$
$709$	1459.63	0.0773165	0.0386583	+	0.999252i	$0.487692\pi$
$710$	−37471.9	−1.98070
$711$	2106.84	0.111129
$712$	−24459.9	−1.28746
$713$	16100.4	0.845675
$714$	−12844.4	−0.673233
$715$	−9995.43	−0.522808
$716$	−6081.08	−0.317403
$717$	−1435.53	−0.0747710
$718$	18177.4	0.944809
$719$	−7127.91	−0.369717	−0.184858	−	0.982765i	$-0.559183\pi$
$719$	−7127.91	−0.369717	−0.184858	+	0.982765i	$0.559183\pi$
$720$	9312.83	0.482040
$721$	−47376.5	−2.44715
$722$	−56329.6	−2.90356
$723$	20437.1	1.05126
$724$	−4319.36	−0.221723
$725$	−10417.8	−0.533667
$726$	1216.51	0.0621887
$727$	−14695.2	−0.749677	−0.374839	−	0.927090i	$-0.622302\pi$
$727$	−14695.2	−0.749677	−0.374839	+	0.927090i	$0.622302\pi$
$728$	−26587.4	−1.35356
$729$	729.000	0.0370370
$730$	−21818.1	−1.10620
$731$	26437.3	1.33765
$732$	591.276	0.0298555
$733$	16977.1	0.855478	0.427739	−	0.903902i	$-0.359310\pi$
$733$	16977.1	0.855478	0.427739	+	0.903902i	$0.359310\pi$
$734$	19708.9	0.991104
$735$	8839.66	0.443613
$736$	8641.95	0.432808
$737$	−5894.63	−0.294615
$738$	3002.87	0.149780
$739$	−6300.88	−0.313642	−0.156821	−	0.987627i	$-0.550125\pi$
$739$	−6300.88	−0.313642	−0.156821	+	0.987627i	$0.550125\pi$
$740$	−14717.4	−0.731111
$741$	32183.6	1.59554
$742$	−23995.3	−1.18719
$743$	−17676.2	−0.872782	−0.436391	−	0.899757i	$-0.643743\pi$
$743$	−17676.2	−0.872782	−0.436391	+	0.899757i	$0.643743\pi$
$744$	−12350.6	−0.608595
$745$	23065.0	1.13427
$746$	8135.20	0.399264
$747$	−3267.06	−0.160021
$748$	1903.32	0.0930376
$749$	7804.72	0.380745
$750$	10506.7	0.511534
$751$	−5350.10	−0.259957	−0.129979	−	0.991517i	$-0.541491\pi$
$751$	−5350.10	−0.259957	−0.129979	+	0.991517i	$0.541491\pi$
$752$	−30662.3	−1.48689
$753$	11907.6	0.576277
$754$	−54341.2	−2.62466
$755$	9995.35	0.481812
$756$	−2081.16	−0.100121
$757$	28813.8	1.38343	0.691714	−	0.722171i	$-0.256856\pi$
$757$	28813.8	1.38343	0.691714	+	0.722171i	$0.256856\pi$
$758$	30488.9	1.46096
$759$	2062.63	0.0986411
$760$	−32039.2	−1.52919
$761$	19183.9	0.913819	0.456909	−	0.889513i	$-0.348956\pi$
$761$	19183.9	0.913819	0.456909	+	0.889513i	$0.348956\pi$
$762$	−16448.2	−0.781960
$763$	21043.9	0.998480
$764$	2515.51	0.119120
$765$	6280.48	0.296825
$766$	−34982.5	−1.65009
$767$	−33308.7	−1.56807
$768$	−12786.9	−0.600791
$769$	−12631.3	−0.592325	−0.296162	−	0.955138i	$-0.595707\pi$
$769$	−12631.3	−0.592325	−0.296162	+	0.955138i	$0.595707\pi$
$770$	−11459.8	−0.536340
$771$	−11397.6	−0.532390
$772$	−1913.92	−0.0892274
$773$	−18580.5	−0.864548	−0.432274	−	0.901742i	$-0.642289\pi$
$773$	−18580.5	−0.864548	−0.432274	+	0.901742i	$0.642289\pi$
$774$	14889.9	0.691479
$775$	11540.6	0.534902
$776$	3186.99	0.147431
$777$	−25017.5	−1.15508
$778$	−27045.1	−1.24629
$779$	−15316.5	−0.704457
$780$	−8807.84	−0.404322
$781$	9438.83	0.432456
$782$	11217.5	0.512962
$783$	6278.36	0.286552
$784$	−17956.1	−0.817970
$785$	−34737.8	−1.57942
$786$	−22065.0	−1.00131
$787$	37392.3	1.69364	0.846818	−	0.531883i	$-0.178515\pi$
$787$	37392.3	1.69364	0.846818	+	0.531883i	$0.178515\pi$
$788$	6766.18	0.305882
$789$	22545.9	1.01731
$790$	10222.8	0.460394
$791$	−13982.2	−0.628506
$792$	−1582.23	−0.0709876
$793$	4253.71	0.190484
$794$	−30574.4	−1.36656
$795$	11732.9	0.523427
$796$	750.788	0.0334309
$797$	23328.0	1.03679	0.518394	−	0.855142i	$-0.326530\pi$
$797$	23328.0	1.03679	0.518394	+	0.855142i	$0.326530\pi$
$798$	36898.5	1.63683
$799$	−20678.3	−0.915578
$800$	6194.42	0.273757
$801$	−13774.0	−0.607593
$802$	−4666.11	−0.205444
$803$	5495.78	0.241522
$804$	−5194.27	−0.227845
$805$	−19430.3	−0.850720
$806$	60197.5	2.63073
$807$	−15620.4	−0.681368
$808$	8073.95	0.351536
$809$	−5328.20	−0.231557	−0.115779	−	0.993275i	$-0.536936\pi$
$809$	−5328.20	−0.231557	−0.115779	+	0.993275i	$0.536936\pi$
$810$	3537.25	0.153440
$811$	−19296.1	−0.835484	−0.417742	−	0.908566i	$-0.637178\pi$
$811$	−19296.1	−0.835484	−0.417742	+	0.908566i	$0.637178\pi$
$812$	−17923.6	−0.774623
$813$	−22007.9	−0.949386
$814$	12886.1	0.554863
$815$	−24271.7	−1.04319
$816$	−12757.6	−0.547309
$817$	−75947.6	−3.25223
$818$	25732.1	1.09988
$819$	−14972.1	−0.638788
$820$	4191.75	0.178515
$821$	−38697.1	−1.64499	−0.822495	−	0.568772i	$-0.807419\pi$
$821$	−38697.1	−1.64499	−0.822495	+	0.568772i	$0.807419\pi$
$822$	−3609.94	−0.153177
$823$	−27358.2	−1.15875	−0.579373	−	0.815062i	$-0.696703\pi$
$823$	−27358.2	−1.15875	−0.579373	+	0.815062i	$0.696703\pi$
$824$	−31739.2	−1.34185
$825$	1478.46	0.0623919
$826$	−38188.5	−1.60865
$827$	41268.2	1.73523	0.867615	−	0.497236i	$-0.165652\pi$
$827$	41268.2	1.73523	0.867615	+	0.497236i	$0.165652\pi$
$828$	1817.56	0.0762856
$829$	−8301.79	−0.347808	−0.173904	−	0.984763i	$-0.555638\pi$
$829$	−8301.79	−0.347808	−0.173904	+	0.984763i	$0.555638\pi$
$830$	−15852.4	−0.662946
$831$	−19023.6	−0.794127
$832$	−11988.0	−0.499531
$833$	−12109.4	−0.503680
$834$	−4064.35	−0.168749
$835$	6496.02	0.269226
$836$	−5467.74	−0.226203
$837$	−6954.96	−0.287215
$838$	−14563.5	−0.600342
$839$	1553.47	0.0639232	0.0319616	−	0.999489i	$-0.489825\pi$
$839$	1553.47	0.0639232	0.0319616	+	0.999489i	$0.489825\pi$
$840$	14905.0	0.612226
$841$	29682.0	1.21702
$842$	−27126.8	−1.11027
$843$	22611.4	0.923817
$844$	16833.8	0.686544
$845$	−34735.9	−1.41414
$846$	−11646.3	−0.473296
$847$	2886.61	0.117102
$848$	−23833.2	−0.965135
$849$	−6367.23	−0.257388
$850$	8040.52	0.324456
$851$	21848.8	0.880101
$852$	8317.37	0.334446
$853$	−39074.2	−1.56844	−0.784218	−	0.620485i	$-0.786936\pi$
$853$	−39074.2	−1.56844	−0.784218	+	0.620485i	$0.786936\pi$
$854$	4876.88	0.195414
$855$	−18042.2	−0.721672
$856$	5228.66	0.208775
$857$	17698.0	0.705427	0.352713	−	0.935731i	$-0.385259\pi$
$857$	17698.0	0.705427	0.352713	+	0.935731i	$0.385259\pi$
$858$	7711.90	0.306853
$859$	36254.9	1.44005	0.720024	−	0.693949i	$-0.244131\pi$
$859$	36254.9	1.44005	0.720024	+	0.693949i	$0.244131\pi$
$860$	20785.0	0.824141
$861$	7125.40	0.282036
$862$	−30897.4	−1.22085
$863$	36448.5	1.43768	0.718841	−	0.695174i	$-0.244673\pi$
$863$	36448.5	1.43768	0.718841	+	0.695174i	$0.244673\pi$
$864$	−3733.09	−0.146994
$865$	39934.2	1.56972
$866$	−18795.0	−0.737505
$867$	6135.42	0.240334
$868$	19855.1	0.776414
$869$	−2575.03	−0.100520
$870$	30463.8	1.18715
$871$	−37368.2	−1.45370
$872$	14098.0	0.547500
$873$	1794.68	0.0695772
$874$	−32224.9	−1.24717
$875$	24930.9	0.963222
$876$	4842.81	0.186785
$877$	−22166.6	−0.853493	−0.426746	−	0.904371i	$-0.640340\pi$
$877$	−22166.6	−0.853493	−0.426746	+	0.904371i	$0.640340\pi$
$878$	−29155.8	−1.12068
$879$	−10369.2	−0.397890
$880$	−11382.3	−0.436021
$881$	25032.2	0.957272	0.478636	−	0.878013i	$-0.341131\pi$
$881$	25032.2	0.957272	0.478636	+	0.878013i	$0.341131\pi$
$882$	−6820.17	−0.260371
$883$	−26167.7	−0.997296	−0.498648	−	0.866804i	$-0.666170\pi$
$883$	−26167.7	−0.997296	−0.498648	+	0.866804i	$0.666170\pi$
$884$	12065.8	0.459068
$885$	18672.9	0.709247
$886$	−11468.8	−0.434877
$887$	37536.5	1.42092	0.710459	−	0.703739i	$-0.248487\pi$
$887$	37536.5	1.42092	0.710459	+	0.703739i	$0.248487\pi$
$888$	−16760.1	−0.633370
$889$	−39029.1	−1.47244
$890$	−66834.4	−2.51718
$891$	−891.000	−0.0335013
$892$	−4729.36	−0.177523
$893$	59403.5	2.22605
$894$	−17795.6	−0.665742
$895$	24525.2	0.915964
$896$	−40131.8	−1.49633
$897$	13075.7	0.486717
$898$	−14936.4	−0.555048
$899$	−59898.1	−2.22215
$900$	1302.80	0.0482518
$901$	−16072.9	−0.594300
$902$	−3670.18	−0.135481
$903$	35331.6	1.30206
$904$	−9367.14	−0.344631
$905$	17420.1	0.639850
$906$	−7711.83	−0.282791
$907$	20230.9	0.740637	0.370318	−	0.928905i	$-0.379249\pi$
$907$	20230.9	0.740637	0.370318	+	0.928905i	$0.379249\pi$
$908$	6626.95	0.242206
$909$	4546.67	0.165900
$910$	−72647.6	−2.64642
$911$	4559.04	0.165804	0.0829022	−	0.996558i	$-0.473581\pi$
$911$	4559.04	0.165804	0.0829022	+	0.996558i	$0.473581\pi$
$912$	36649.2	1.33068
$913$	3993.07	0.144744
$914$	−33181.8	−1.20083
$915$	−2384.64	−0.0861570
$916$	9163.02	0.330518
$917$	−52357.1	−1.88548
$918$	−4845.65	−0.174216
$919$	17680.9	0.634644	0.317322	−	0.948318i	$-0.397216\pi$
$919$	17680.9	0.634644	0.317322	+	0.948318i	$0.397216\pi$
$920$	−13017.1	−0.466478
$921$	6064.81	0.216984
$922$	18707.5	0.668221
$923$	59836.1	2.13383
$924$	2543.64	0.0905624
$925$	15660.9	0.556677
$926$	22538.0	0.799833
$927$	−17873.2	−0.633261
$928$	−32150.5	−1.13727
$929$	−24482.1	−0.864621	−0.432311	−	0.901725i	$-0.642302\pi$
$929$	−24482.1	−0.864621	−0.432311	+	0.901725i	$0.642302\pi$
$930$	−33746.8	−1.18989
$931$	34787.2	1.22460
$932$	11503.5	0.404302
$933$	−29132.5	−1.02225
$934$	−32845.8	−1.15069
$935$	−7676.14	−0.268488
$936$	−10030.3	−0.350269
$937$	43623.2	1.52092	0.760462	−	0.649382i	$-0.224972\pi$
$937$	43623.2	1.52092	0.760462	+	0.649382i	$0.224972\pi$
$938$	−42842.7	−1.49132
$939$	2338.36	0.0812667
$940$	−16257.2	−0.564099
$941$	−20152.6	−0.698146	−0.349073	−	0.937095i	$-0.613504\pi$
$941$	−20152.6	−0.698146	−0.349073	+	0.937095i	$0.613504\pi$
$942$	26801.7	0.927012
$943$	−6222.88	−0.214894
$944$	−37930.4	−1.30777
$945$	8393.40	0.288928
$946$	−18198.7	−0.625467
$947$	−10974.9	−0.376597	−0.188298	−	0.982112i	$-0.560297\pi$
$947$	−10974.9	−0.376597	−0.188298	+	0.982112i	$0.560297\pi$
$948$	−2269.08	−0.0777387
$949$	34839.7	1.19172
$950$	−23098.3	−0.788851
$951$	−7544.00	−0.257236
$952$	−20418.2	−0.695123
$953$	40656.7	1.38195	0.690976	−	0.722878i	$-0.257181\pi$
$953$	40656.7	1.38195	0.690976	+	0.722878i	$0.257181\pi$
$954$	−9052.45	−0.307216
$955$	−10145.1	−0.343757
$956$	1546.07	0.0523050
$957$	−7673.55	−0.259196
$958$	21365.5	0.720550
$959$	−8565.89	−0.288433
$960$	6720.51	0.225941
$961$	36562.2	1.22729
$962$	81689.7	2.73782
$963$	2944.40	0.0985276
$964$	−22010.9	−0.735396
$965$	7718.92	0.257493
$966$	14991.3	0.499315
$967$	16971.0	0.564375	0.282187	−	0.959359i	$-0.408940\pi$
$967$	16971.0	0.564375	0.282187	+	0.959359i	$0.408940\pi$
$968$	1933.84	0.0642107
$969$	24715.9	0.819389
$970$	8708.16	0.288250
$971$	−33427.5	−1.10478	−0.552388	−	0.833587i	$-0.686283\pi$
$971$	−33427.5	−1.10478	−0.552388	+	0.833587i	$0.686283\pi$
$972$	−785.137	−0.0259087
$973$	−9644.12	−0.317756
$974$	−58813.1	−1.93480
$975$	9372.48	0.307856
$976$	4843.93	0.158863
$977$	32934.0	1.07846	0.539228	−	0.842160i	$-0.318716\pi$
$977$	32934.0	1.07846	0.539228	+	0.842160i	$0.318716\pi$
$978$	18726.7	0.612283
$979$	16834.9	0.549589
$980$	−9520.37	−0.310323
$981$	7939.01	0.258382
$982$	−59725.1	−1.94084
$983$	−46150.4	−1.49743	−0.748713	−	0.662895i	$-0.769328\pi$
$983$	−46150.4	−1.49743	−0.748713	+	0.662895i	$0.769328\pi$
$984$	4773.55	0.154650
$985$	−27288.2	−0.882716
$986$	−41732.2	−1.34789
$987$	−27635.1	−0.891220
$988$	−34661.9	−1.11614
$989$	−30856.4	−0.992090
$990$	−4323.31	−0.138792
$991$	14370.2	0.460632	0.230316	−	0.973116i	$-0.426024\pi$
$991$	14370.2	0.460632	0.230316	+	0.973116i	$0.426024\pi$
$992$	35615.3	1.13990
$993$	−30205.0	−0.965284
$994$	68602.1	2.18906
$995$	−3027.95	−0.0964749
$996$	3518.64	0.111940
$997$	−38356.1	−1.21840	−0.609202	−	0.793015i	$-0.708510\pi$
$997$	−38356.1	−1.21840	−0.609202	+	0.793015i	$0.708510\pi$
$998$	−33180.1	−1.05240
$999$	−9438.09	−0.298907

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.e.1.8	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.e.1.8	✓	38	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-3.35127 q^{2} -3.00000 q^{3} +3.23102 q^{4} -13.0308 q^{5} +10.0538 q^{6} +23.8563 q^{7} +15.9822 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.35127 q^{2} -3.00000 q^{3} +3.23102 q^{4} -13.0308 q^{5} +10.0538 q^{6} +23.8563 q^{7} +15.9822 q^{8} +9.00000 q^{9} +43.6697 q^{10} -11.0000 q^{11} -9.69305 q^{12} -69.7329 q^{13} -79.9489 q^{14} +39.0924 q^{15} -79.4087 q^{16} -53.5524 q^{17} -30.1614 q^{18} +153.842 q^{19} -42.1027 q^{20} -71.5689 q^{21} +36.8640 q^{22} +62.5038 q^{23} -47.9465 q^{24} +44.8018 q^{25} +233.694 q^{26} -27.0000 q^{27} +77.0800 q^{28} -232.532 q^{29} -131.009 q^{30} +257.591 q^{31} +138.263 q^{32} +33.0000 q^{33} +179.469 q^{34} -310.867 q^{35} +29.0791 q^{36} +349.559 q^{37} -515.567 q^{38} +209.199 q^{39} -208.260 q^{40} -99.5601 q^{41} +239.847 q^{42} -493.672 q^{43} -35.5412 q^{44} -117.277 q^{45} -209.467 q^{46} +386.133 q^{47} +238.226 q^{48} +226.122 q^{49} -150.143 q^{50} +160.657 q^{51} -225.308 q^{52} +300.133 q^{53} +90.4843 q^{54} +143.339 q^{55} +381.275 q^{56} -461.527 q^{57} +779.277 q^{58} +477.661 q^{59} +126.308 q^{60} -61.0000 q^{61} -863.258 q^{62} +214.707 q^{63} +171.914 q^{64} +908.675 q^{65} -110.592 q^{66} +535.876 q^{67} -173.029 q^{68} -187.511 q^{69} +1041.80 q^{70} -858.075 q^{71} +143.839 q^{72} -499.616 q^{73} -1171.47 q^{74} -134.405 q^{75} +497.067 q^{76} -262.419 q^{77} -701.081 q^{78} +234.094 q^{79} +1034.76 q^{80} +81.0000 q^{81} +333.653 q^{82} -363.007 q^{83} -231.240 q^{84} +697.831 q^{85} +1654.43 q^{86} +697.595 q^{87} -175.804 q^{88} -1530.45 q^{89} +393.028 q^{90} -1663.57 q^{91} +201.951 q^{92} -772.774 q^{93} -1294.04 q^{94} -2004.69 q^{95} -414.788 q^{96} +199.409 q^{97} -757.797 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9} + 95 q^{10} - 418 q^{11} - 426 q^{12} + 13 q^{13} + 26 q^{14} - 45 q^{15} + 486 q^{16} - 224 q^{17} - 18 q^{18} + 367 q^{19} + 18 q^{20} - 189 q^{21} + 22 q^{22} + 51 q^{23} + 135 q^{24} + 773 q^{25} - 439 q^{26} - 1026 q^{27} + 22 q^{28} - 462 q^{29} - 285 q^{30} + 234 q^{31} - 597 q^{32} + 1254 q^{33} + 956 q^{34} - 522 q^{35} + 1278 q^{36} + 954 q^{37} + 705 q^{38} - 39 q^{39} + 1495 q^{40} - 740 q^{41} - 78 q^{42} + 1441 q^{43} - 1562 q^{44} + 135 q^{45} + 581 q^{46} + 1003 q^{47} - 1458 q^{48} + 2707 q^{49} + 388 q^{50} + 672 q^{51} + 788 q^{52} + 735 q^{53} + 54 q^{54} - 165 q^{55} + 1059 q^{56} - 1101 q^{57} + 177 q^{58} + 261 q^{59} - 54 q^{60} - 2318 q^{61} + 1251 q^{62} + 567 q^{63} + 5571 q^{64} - 1354 q^{65} - 66 q^{66} + 3495 q^{67} - 1856 q^{68} - 153 q^{69} + 542 q^{70} - 873 q^{71} - 405 q^{72} + 989 q^{73} - 3406 q^{74} - 2319 q^{75} + 1712 q^{76} - 693 q^{77} + 1317 q^{78} + 2313 q^{79} + 1593 q^{80} + 3078 q^{81} + 5170 q^{82} + 569 q^{83} - 66 q^{84} - 1271 q^{85} + 3065 q^{86} + 1386 q^{87} + 495 q^{88} - 2917 q^{89} + 855 q^{90} + 2740 q^{91} + 1083 q^{92} - 702 q^{93} + 3272 q^{94} + 2696 q^{95} + 1791 q^{96} + 4250 q^{97} + 5952 q^{98} - 3762 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9 + 95 * q^10 - 418 * q^11 - 426 * q^12 + 13 * q^13 + 26 * q^14 - 45 * q^15 + 486 * q^16 - 224 * q^17 - 18 * q^18 + 367 * q^19 + 18 * q^20 - 189 * q^21 + 22 * q^22 + 51 * q^23 + 135 * q^24 + 773 * q^25 - 439 * q^26 - 1026 * q^27 + 22 * q^28 - 462 * q^29 - 285 * q^30 + 234 * q^31 - 597 * q^32 + 1254 * q^33 + 956 * q^34 - 522 * q^35 + 1278 * q^36 + 954 * q^37 + 705 * q^38 - 39 * q^39 + 1495 * q^40 - 740 * q^41 - 78 * q^42 + 1441 * q^43 - 1562 * q^44 + 135 * q^45 + 581 * q^46 + 1003 * q^47 - 1458 * q^48 + 2707 * q^49 + 388 * q^50 + 672 * q^51 + 788 * q^52 + 735 * q^53 + 54 * q^54 - 165 * q^55 + 1059 * q^56 - 1101 * q^57 + 177 * q^58 + 261 * q^59 - 54 * q^60 - 2318 * q^61 + 1251 * q^62 + 567 * q^63 + 5571 * q^64 - 1354 * q^65 - 66 * q^66 + 3495 * q^67 - 1856 * q^68 - 153 * q^69 + 542 * q^70 - 873 * q^71 - 405 * q^72 + 989 * q^73 - 3406 * q^74 - 2319 * q^75 + 1712 * q^76 - 693 * q^77 + 1317 * q^78 + 2313 * q^79 + 1593 * q^80 + 3078 * q^81 + 5170 * q^82 + 569 * q^83 - 66 * q^84 - 1271 * q^85 + 3065 * q^86 + 1386 * q^87 + 495 * q^88 - 2917 * q^89 + 855 * q^90 + 2740 * q^91 + 1083 * q^92 - 702 * q^93 + 3272 * q^94 + 2696 * q^95 + 1791 * q^96 + 4250 * q^97 + 5952 * q^98 - 3762 * q^99

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