LMFDB - Embedded newform 983.4.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,4,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, 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("983.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	983.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:	$57.9988775356$
Analytic rank:	$0$
Dimension:	$136$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.51197 q^{2} -7.25700 q^{3} +12.3578 q^{4} +17.5119 q^{5} +32.7433 q^{6} -15.6407 q^{7} -19.6624 q^{8} +25.6640 q^{9} +O(q^{10})$	\(q-4.51197 q^{2} -7.25700 q^{3} +12.3578 q^{4} +17.5119 q^{5} +32.7433 q^{6} -15.6407 q^{7} -19.6624 q^{8} +25.6640 q^{9} -79.0132 q^{10} -22.3859 q^{11} -89.6807 q^{12} +73.4493 q^{13} +70.5702 q^{14} -127.084 q^{15} -10.1467 q^{16} +23.1083 q^{17} -115.795 q^{18} -132.790 q^{19} +216.409 q^{20} +113.504 q^{21} +101.004 q^{22} -135.543 q^{23} +142.690 q^{24} +181.668 q^{25} -331.400 q^{26} +9.69516 q^{27} -193.285 q^{28} +295.434 q^{29} +573.399 q^{30} +324.586 q^{31} +203.081 q^{32} +162.455 q^{33} -104.264 q^{34} -273.899 q^{35} +317.152 q^{36} -204.821 q^{37} +599.145 q^{38} -533.021 q^{39} -344.326 q^{40} -19.5668 q^{41} -512.128 q^{42} +118.432 q^{43} -276.641 q^{44} +449.427 q^{45} +611.565 q^{46} +176.388 q^{47} +73.6346 q^{48} -98.3690 q^{49} -819.679 q^{50} -167.697 q^{51} +907.673 q^{52} -66.8746 q^{53} -43.7442 q^{54} -392.021 q^{55} +307.533 q^{56} +963.658 q^{57} -1332.99 q^{58} +303.294 q^{59} -1570.48 q^{60} -38.7667 q^{61} -1464.52 q^{62} -401.403 q^{63} -835.119 q^{64} +1286.24 q^{65} -732.989 q^{66} -470.326 q^{67} +285.568 q^{68} +983.635 q^{69} +1235.82 q^{70} -532.538 q^{71} -504.616 q^{72} -608.820 q^{73} +924.147 q^{74} -1318.36 q^{75} -1641.00 q^{76} +350.131 q^{77} +2404.97 q^{78} -408.349 q^{79} -177.688 q^{80} -763.286 q^{81} +88.2848 q^{82} +240.168 q^{83} +1402.67 q^{84} +404.671 q^{85} -534.359 q^{86} -2143.96 q^{87} +440.160 q^{88} -368.978 q^{89} -2027.80 q^{90} -1148.80 q^{91} -1675.02 q^{92} -2355.52 q^{93} -795.858 q^{94} -2325.41 q^{95} -1473.75 q^{96} +372.288 q^{97} +443.837 q^{98} -574.513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) $ 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9} + 257 q^{10} + 204 q^{11} + 296 q^{12} + 530 q^{13} + 103 q^{14} + 226 q^{15} + 2737 q^{16} + 664 q^{17} + 949 q^{18} + 421 q^{19} + 500 q^{20} + 684 q^{21} + 905 q^{22} + 617 q^{23} + 917 q^{24} + 5430 q^{25} + 572 q^{26} + 886 q^{27} + 2728 q^{28} + 688 q^{29} + 712 q^{30} + 1019 q^{31} + 2363 q^{32} + 1764 q^{33} + 1260 q^{34} + 834 q^{35} + 7190 q^{36} + 3303 q^{37} + 384 q^{38} + 1950 q^{39} + 2766 q^{40} + 1975 q^{41} + 448 q^{42} + 3021 q^{43} + 2038 q^{44} + 2266 q^{45} + 2742 q^{46} + 1293 q^{47} + 2589 q^{48} + 10447 q^{49} + 2191 q^{50} + 1032 q^{51} + 4983 q^{52} + 2415 q^{53} + 1878 q^{54} + 2612 q^{55} + 1540 q^{56} + 7908 q^{57} + 5743 q^{58} + 1059 q^{59} + 2611 q^{60} + 4312 q^{61} + 3258 q^{62} + 5605 q^{63} + 13735 q^{64} + 3554 q^{65} + 433 q^{66} + 5715 q^{67} + 5881 q^{68} + 1398 q^{69} + 4287 q^{70} + 2530 q^{71} + 9891 q^{72} + 14106 q^{73} + 2318 q^{74} + 2621 q^{75} + 4651 q^{76} + 4750 q^{77} + 6639 q^{78} + 4791 q^{79} + 4812 q^{80} + 19932 q^{81} + 5380 q^{82} + 4284 q^{83} + 9282 q^{84} + 12058 q^{85} + 2451 q^{86} + 6984 q^{87} + 11197 q^{88} + 5313 q^{89} + 5405 q^{90} + 6298 q^{91} + 6588 q^{92} + 5700 q^{93} + 4743 q^{94} + 5778 q^{95} + 9613 q^{96} + 15382 q^{97} + 6640 q^{98} + 8542 q^{99}+O(q^{100}) \) 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9 + 257 * q^10 + 204 * q^11 + 296 * q^12 + 530 * q^13 + 103 * q^14 + 226 * q^15 + 2737 * q^16 + 664 * q^17 + 949 * q^18 + 421 * q^19 + 500 * q^20 + 684 * q^21 + 905 * q^22 + 617 * q^23 + 917 * q^24 + 5430 * q^25 + 572 * q^26 + 886 * q^27 + 2728 * q^28 + 688 * q^29 + 712 * q^30 + 1019 * q^31 + 2363 * q^32 + 1764 * q^33 + 1260 * q^34 + 834 * q^35 + 7190 * q^36 + 3303 * q^37 + 384 * q^38 + 1950 * q^39 + 2766 * q^40 + 1975 * q^41 + 448 * q^42 + 3021 * q^43 + 2038 * q^44 + 2266 * q^45 + 2742 * q^46 + 1293 * q^47 + 2589 * q^48 + 10447 * q^49 + 2191 * q^50 + 1032 * q^51 + 4983 * q^52 + 2415 * q^53 + 1878 * q^54 + 2612 * q^55 + 1540 * q^56 + 7908 * q^57 + 5743 * q^58 + 1059 * q^59 + 2611 * q^60 + 4312 * q^61 + 3258 * q^62 + 5605 * q^63 + 13735 * q^64 + 3554 * q^65 + 433 * q^66 + 5715 * q^67 + 5881 * q^68 + 1398 * q^69 + 4287 * q^70 + 2530 * q^71 + 9891 * q^72 + 14106 * q^73 + 2318 * q^74 + 2621 * q^75 + 4651 * q^76 + 4750 * q^77 + 6639 * q^78 + 4791 * q^79 + 4812 * q^80 + 19932 * q^81 + 5380 * q^82 + 4284 * q^83 + 9282 * q^84 + 12058 * q^85 + 2451 * q^86 + 6984 * q^87 + 11197 * q^88 + 5313 * q^89 + 5405 * q^90 + 6298 * q^91 + 6588 * q^92 + 5700 * q^93 + 4743 * q^94 + 5778 * q^95 + 9613 * q^96 + 15382 * q^97 + 6640 * q^98 + 8542 * 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 $

$2$	−4.51197	−1.59522	−0.797610	−	0.603173i	$-0.793903\pi$
$2$	−4.51197	−1.59522	−0.797610	+	0.603173i	$0.793903\pi$
$3$	−7.25700	−1.39661	−0.698305	−	0.715800i	$-0.746062\pi$
$3$	−7.25700	−1.39661	−0.698305	+	0.715800i	$0.746062\pi$
$4$	12.3578	1.54473
$5$	17.5119	1.56632	0.783158	−	0.621823i	$-0.213608\pi$
$5$	17.5119	1.56632	0.783158	+	0.621823i	$0.213608\pi$
$6$	32.7433	2.22790
$7$	−15.6407	−0.844518	−0.422259	−	0.906475i	$-0.638763\pi$
$7$	−15.6407	−0.844518	−0.422259	+	0.906475i	$0.638763\pi$
$8$	−19.6624	−0.868962
$9$	25.6640	0.950519
$10$	−79.0132	−2.49862
$11$	−22.3859	−0.613601	−0.306800	−	0.951774i	$-0.599258\pi$
$11$	−22.3859	−0.613601	−0.306800	+	0.951774i	$0.599258\pi$
$12$	−89.6807	−2.15738
$13$	73.4493	1.56701	0.783506	−	0.621384i	$-0.213429\pi$
$13$	73.4493	1.56701	0.783506	+	0.621384i	$0.213429\pi$
$14$	70.5702	1.34719
$15$	−127.084	−2.18753
$16$	−10.1467	−0.158542
$17$	23.1083	0.329681	0.164841	−	0.986320i	$-0.447289\pi$
$17$	23.1083	0.329681	0.164841	+	0.986320i	$0.447289\pi$
$18$	−115.795	−1.51629
$19$	−132.790	−1.60338	−0.801688	−	0.597742i	$-0.796065\pi$
$19$	−132.790	−1.60338	−0.801688	+	0.597742i	$0.796065\pi$
$20$	216.409	2.41953
$21$	113.504	1.17946
$22$	101.004	0.978828
$23$	−135.543	−1.22881	−0.614405	−	0.788991i	$-0.710604\pi$
$23$	−135.543	−1.22881	−0.614405	+	0.788991i	$0.710604\pi$
$24$	142.690	1.21360
$25$	181.668	1.45334
$26$	−331.400	−2.49973
$27$	9.69516	0.0691050
$28$	−193.285	−1.30455
$29$	295.434	1.89175	0.945874	−	0.324535i	$-0.105208\pi$
$29$	295.434	1.89175	0.945874	+	0.324535i	$0.105208\pi$
$30$	573.399	3.48959
$31$	324.586	1.88056	0.940281	−	0.340399i	$-0.110562\pi$
$31$	324.586	1.88056	0.940281	+	0.340399i	$0.110562\pi$
$32$	203.081	1.12187
$33$	162.455	0.856961
$34$	−104.264	−0.525914
$35$	−273.899	−1.32278
$36$	317.152	1.46829
$37$	−204.821	−0.910066	−0.455033	−	0.890475i	$-0.650372\pi$
$37$	−204.821	−0.910066	−0.455033	+	0.890475i	$0.650372\pi$
$38$	599.145	2.55774
$39$	−533.021	−2.18850
$40$	−344.326	−1.36107
$41$	−19.5668	−0.0745322	−0.0372661	−	0.999305i	$-0.511865\pi$
$41$	−19.5668	−0.0745322	−0.0372661	+	0.999305i	$0.511865\pi$
$42$	−512.128	−1.88150
$43$	118.432	0.420015	0.210008	−	0.977700i	$-0.432651\pi$
$43$	118.432	0.420015	0.210008	+	0.977700i	$0.432651\pi$
$44$	−276.641	−0.947846
$45$	449.427	1.48881
$46$	611.565	1.96022
$47$	176.388	0.547423	0.273711	−	0.961812i	$-0.411749\pi$
$47$	176.388	0.547423	0.273711	+	0.961812i	$0.411749\pi$
$48$	73.6346	0.221422
$49$	−98.3690	−0.286790
$50$	−819.679	−2.31840
$51$	−167.697	−0.460436
$52$	907.673	2.42061
$53$	−66.8746	−0.173320	−0.0866598	−	0.996238i	$-0.527619\pi$
$53$	−66.8746	−0.173320	−0.0866598	+	0.996238i	$0.527619\pi$
$54$	−43.7442	−0.110238
$55$	−392.021	−0.961092
$56$	307.533	0.733854
$57$	963.658	2.23929
$58$	−1332.99	−3.01775
$59$	303.294	0.669245	0.334623	−	0.942352i	$-0.391391\pi$
$59$	303.294	0.669245	0.334623	+	0.942352i	$0.391391\pi$
$60$	−1570.48	−3.37914
$61$	−38.7667	−0.0813700	−0.0406850	−	0.999172i	$-0.512954\pi$
$61$	−38.7667	−0.0813700	−0.0406850	+	0.999172i	$0.512954\pi$
$62$	−1464.52	−2.99991
$63$	−401.403	−0.802730
$64$	−835.119	−1.63109
$65$	1286.24	2.45443
$66$	−732.989	−1.36704
$67$	−470.326	−0.857603	−0.428802	−	0.903399i	$-0.641064\pi$
$67$	−470.326	−0.857603	−0.428802	+	0.903399i	$0.641064\pi$
$68$	285.568	0.509268
$69$	983.635	1.71617
$70$	1235.82	2.11013
$71$	−532.538	−0.890150	−0.445075	−	0.895493i	$-0.646823\pi$
$71$	−532.538	−0.890150	−0.445075	+	0.895493i	$0.646823\pi$
$72$	−504.616	−0.825966
$73$	−608.820	−0.976124	−0.488062	−	0.872809i	$-0.662296\pi$
$73$	−608.820	−0.976124	−0.488062	+	0.872809i	$0.662296\pi$
$74$	924.147	1.45176
$75$	−1318.36	−2.02975
$76$	−1641.00	−2.47678
$77$	350.131	0.518197
$78$	2404.97	3.49115
$79$	−408.349	−0.581555	−0.290777	−	0.956791i	$-0.593914\pi$
$79$	−408.349	−0.581555	−0.290777	+	0.956791i	$0.593914\pi$
$80$	−177.688	−0.248327
$81$	−763.286	−1.04703
$82$	88.2848	0.118895
$83$	240.168	0.317612	0.158806	−	0.987310i	$-0.449236\pi$
$83$	240.168	0.317612	0.158806	+	0.987310i	$0.449236\pi$
$84$	1402.67	1.82195
$85$	404.671	0.516385
$86$	−534.359	−0.670017
$87$	−2143.96	−2.64203
$88$	440.160	0.533196
$89$	−368.978	−0.439457	−0.219728	−	0.975561i	$-0.570517\pi$
$89$	−368.978	−0.439457	−0.219728	+	0.975561i	$0.570517\pi$
$90$	−2027.80	−2.37499
$91$	−1148.80	−1.32337
$92$	−1675.02	−1.89818
$93$	−2355.52	−2.62641
$94$	−795.858	−0.873260
$95$	−2325.41	−2.51139
$96$	−1473.75	−1.56682
$97$	372.288	0.389692	0.194846	−	0.980834i	$-0.437579\pi$
$97$	372.288	0.389692	0.194846	+	0.980834i	$0.437579\pi$
$98$	443.837	0.457493
$99$	−574.513	−0.583239
$100$	2245.02	2.24502
$101$	−1207.57	−1.18968	−0.594841	−	0.803843i	$-0.702785\pi$
$101$	−1207.57	−1.18968	−0.594841	+	0.803843i	$0.702785\pi$
$102$	756.642	0.734497
$103$	949.720	0.908531	0.454266	−	0.890866i	$-0.349902\pi$
$103$	949.720	0.908531	0.454266	+	0.890866i	$0.349902\pi$
$104$	−1444.19	−1.36167
$105$	1987.68	1.84741
$106$	301.736	0.276483
$107$	1697.43	1.53362	0.766809	−	0.641875i	$-0.221843\pi$
$107$	1697.43	1.53362	0.766809	+	0.641875i	$0.221843\pi$
$108$	119.811	0.106748
$109$	15.4714	0.0135953	0.00679766	−	0.999977i	$-0.497836\pi$
$109$	15.4714	0.0135953	0.00679766	+	0.999977i	$0.497836\pi$
$110$	1768.78	1.53315
$111$	1486.39	1.27101
$112$	158.701	0.133892
$113$	1212.73	1.00959	0.504797	−	0.863238i	$-0.331567\pi$
$113$	1212.73	1.00959	0.504797	+	0.863238i	$0.331567\pi$
$114$	−4347.99	−3.57216
$115$	−2373.62	−1.92470
$116$	3650.92	2.92224
$117$	1885.00	1.48948
$118$	−1368.45	−1.06759
$119$	−361.429	−0.278422
$120$	2498.77	1.90088
$121$	−829.871	−0.623494
$122$	174.914	0.129803
$123$	141.996	0.104092
$124$	4011.18	2.90496
$125$	992.364	0.710078
$126$	1811.12	1.28053
$127$	1030.98	0.720349	0.360175	−	0.932885i	$-0.382717\pi$
$127$	1030.98	0.720349	0.360175	+	0.932885i	$0.382717\pi$
$128$	2143.38	1.48008
$129$	−859.458	−0.586597
$130$	−5803.46	−3.91536
$131$	658.109	0.438926	0.219463	−	0.975621i	$-0.429570\pi$
$131$	658.109	0.438926	0.219463	+	0.975621i	$0.429570\pi$
$132$	2007.59	1.32377
$133$	2076.93	1.35408
$134$	2122.09	1.36807
$135$	169.781	0.108240
$136$	−454.363	−0.286480
$137$	1635.52	1.01994	0.509972	−	0.860191i	$-0.329656\pi$
$137$	1635.52	1.01994	0.509972	+	0.860191i	$0.329656\pi$
$138$	−4438.12	−2.73767
$139$	−2127.24	−1.29806	−0.649031	−	0.760762i	$-0.724825\pi$
$139$	−2127.24	−1.29806	−0.649031	+	0.760762i	$0.724825\pi$
$140$	−3384.79	−2.04334
$141$	−1280.05	−0.764536
$142$	2402.79	1.41998
$143$	−1644.23	−0.961520
$144$	−260.405	−0.150697
$145$	5173.62	2.96307
$146$	2746.98	1.55713
$147$	713.863	0.400534
$148$	−2531.15	−1.40580
$149$	−338.510	−0.186120	−0.0930598	−	0.995661i	$-0.529665\pi$
$149$	−338.510	−0.186120	−0.0930598	+	0.995661i	$0.529665\pi$
$150$	5948.41	3.23790
$151$	−509.362	−0.274512	−0.137256	−	0.990536i	$-0.543828\pi$
$151$	−509.362	−0.274512	−0.137256	+	0.990536i	$0.543828\pi$
$152$	2610.97	1.39327
$153$	593.051	0.313368
$154$	−1579.78	−0.826638
$155$	5684.13	2.94555
$156$	−6586.98	−3.38065
$157$	1414.37	0.718974	0.359487	−	0.933150i	$-0.382952\pi$
$157$	1414.37	0.718974	0.359487	+	0.933150i	$0.382952\pi$
$158$	1842.46	0.927708
$159$	485.309	0.242060
$160$	3556.33	1.75720
$161$	2119.98	1.03775
$162$	3443.92	1.67025
$163$	1008.11	0.484424	0.242212	−	0.970223i	$-0.422127\pi$
$163$	1008.11	0.484424	0.242212	+	0.970223i	$0.422127\pi$
$164$	−241.803	−0.115132
$165$	2844.89	1.34227
$166$	−1083.63	−0.506661
$167$	−3566.97	−1.65282	−0.826409	−	0.563070i	$-0.809620\pi$
$167$	−3566.97	−1.65282	−0.826409	+	0.563070i	$0.809620\pi$
$168$	−2231.77	−1.02491
$169$	3197.79	1.45553
$170$	−1825.86	−0.823747
$171$	−3407.93	−1.52404
$172$	1463.56	0.648809
$173$	1526.21	0.670728	0.335364	−	0.942089i	$-0.391141\pi$
$173$	1526.21	0.670728	0.335364	+	0.942089i	$0.391141\pi$
$174$	9673.48	4.21463
$175$	−2841.41	−1.22737
$176$	227.143	0.0972816
$177$	−2201.00	−0.934675
$178$	1664.82	0.701030
$179$	−1757.71	−0.733953	−0.366976	−	0.930230i	$-0.619607\pi$
$179$	−1757.71	−0.733953	−0.366976	+	0.930230i	$0.619607\pi$
$180$	5553.94	2.29981
$181$	4804.86	1.97316	0.986582	−	0.163267i	$-0.0522034\pi$
$181$	4804.86	1.97316	0.986582	+	0.163267i	$0.0522034\pi$
$182$	5183.33	2.11107
$183$	281.330	0.113642
$184$	2665.09	1.06779
$185$	−3586.82	−1.42545
$186$	10628.0	4.18971
$187$	−517.300	−0.202293
$188$	2179.78	0.845620
$189$	−151.639	−0.0583604
$190$	10492.2	4.00623
$191$	−3276.87	−1.24139	−0.620697	−	0.784050i	$-0.713150\pi$
$191$	−3276.87	−1.24139	−0.620697	+	0.784050i	$0.713150\pi$
$192$	6060.45	2.27800
$193$	2399.17	0.894797	0.447399	−	0.894335i	$-0.352351\pi$
$193$	2399.17	0.894797	0.447399	+	0.894335i	$0.352351\pi$
$194$	−1679.75	−0.621645
$195$	−9334.23	−3.42789
$196$	−1215.63	−0.443013
$197$	−2426.29	−0.877492	−0.438746	−	0.898611i	$-0.644577\pi$
$197$	−2426.29	−0.877492	−0.438746	+	0.898611i	$0.644577\pi$
$198$	2592.18	0.930395
$199$	2654.06	0.945436	0.472718	−	0.881214i	$-0.343273\pi$
$199$	2654.06	0.945436	0.472718	+	0.881214i	$0.343273\pi$
$200$	−3572.02	−1.26290
$201$	3413.15	1.19774
$202$	5448.52	1.89781
$203$	−4620.79	−1.59761
$204$	−2072.37	−0.711249
$205$	−342.653	−0.116741
$206$	−4285.11	−1.44931
$207$	−3478.58	−1.16801
$208$	−745.267	−0.248437
$209$	2972.63	0.983833
$210$	−8968.35	−2.94702
$211$	−4322.46	−1.41028	−0.705142	−	0.709066i	$-0.749117\pi$
$211$	−4322.46	−1.41028	−0.705142	+	0.709066i	$0.749117\pi$
$212$	−826.425	−0.267732
$213$	3864.63	1.24319
$214$	−7658.76	−2.44646
$215$	2073.97	0.657876
$216$	−190.630	−0.0600496
$217$	−5076.75	−1.58817
$218$	−69.8063	−0.0216875
$219$	4418.21	1.36326
$220$	−4844.52	−1.48463
$221$	1697.29	0.516614
$222$	−6706.53	−2.02754
$223$	5982.18	1.79640	0.898199	−	0.439590i	$-0.144876\pi$
$223$	5982.18	1.79640	0.898199	+	0.439590i	$0.144876\pi$
$224$	−3176.32	−0.947441
$225$	4662.33	1.38143
$226$	−5471.80	−1.61053
$227$	108.455	0.0317110	0.0158555	−	0.999874i	$-0.494953\pi$
$227$	108.455	0.0317110	0.0158555	+	0.999874i	$0.494953\pi$
$228$	11908.7	3.45910
$229$	1522.08	0.439222	0.219611	−	0.975587i	$-0.429521\pi$
$229$	1522.08	0.439222	0.219611	+	0.975587i	$0.429521\pi$
$230$	10709.7	3.07033
$231$	−2540.90	−0.723719
$232$	−5808.93	−1.64386
$233$	−3884.47	−1.09219	−0.546095	−	0.837723i	$-0.683886\pi$
$233$	−3884.47	−1.09219	−0.546095	+	0.837723i	$0.683886\pi$
$234$	−8505.07	−2.37604
$235$	3088.90	0.857437
$236$	3748.05	1.03380
$237$	2963.39	0.812206
$238$	1630.76	0.444144
$239$	−3844.55	−1.04052	−0.520258	−	0.854009i	$-0.674164\pi$
$239$	−3844.55	−1.04052	−0.520258	+	0.854009i	$0.674164\pi$
$240$	1289.48	0.346816
$241$	−1539.74	−0.411549	−0.205774	−	0.978599i	$-0.565971\pi$
$241$	−1539.74	−0.411549	−0.205774	+	0.978599i	$0.565971\pi$
$242$	3744.35	0.994611
$243$	5277.40	1.39319
$244$	−479.072	−0.125695
$245$	−1722.63	−0.449203
$246$	−640.682	−0.166050
$247$	−9753.34	−2.51251
$248$	−6382.14	−1.63414
$249$	−1742.90	−0.443580
$250$	−4477.51	−1.13273
$251$	2101.12	0.528373	0.264187	−	0.964472i	$-0.414897\pi$
$251$	2101.12	0.528373	0.264187	+	0.964472i	$0.414897\pi$
$252$	−4960.47	−1.24000
$253$	3034.25	0.753999
$254$	−4651.73	−1.14912
$255$	−2936.69	−0.721188
$256$	−2989.92	−0.729960
$257$	1193.33	0.289643	0.144821	−	0.989458i	$-0.453739\pi$
$257$	1193.33	0.289643	0.144821	+	0.989458i	$0.453739\pi$
$258$	3877.84	0.935752
$259$	3203.55	0.768566
$260$	15895.1	3.79144
$261$	7582.02	1.79814
$262$	−2969.36	−0.700183
$263$	−1963.58	−0.460379	−0.230189	−	0.973146i	$-0.573935\pi$
$263$	−1963.58	−0.460379	−0.230189	+	0.973146i	$0.573935\pi$
$264$	−3194.24	−0.744667
$265$	−1171.10	−0.271473
$266$	−9371.03	−2.16006
$267$	2677.68	0.613749
$268$	−5812.20	−1.32476
$269$	−7005.82	−1.58793	−0.793964	−	0.607965i	$-0.791986\pi$
$269$	−7005.82	−1.58793	−0.793964	+	0.607965i	$0.791986\pi$
$270$	−766.046	−0.172667
$271$	7872.98	1.76476	0.882379	−	0.470540i	$-0.155941\pi$
$271$	7872.98	1.76476	0.882379	+	0.470540i	$0.155941\pi$
$272$	−234.473	−0.0522684
$273$	8336.82	1.84823
$274$	−7379.43	−1.62703
$275$	−4066.80	−0.891772
$276$	12155.6	2.65102
$277$	3677.01	0.797581	0.398790	−	0.917042i	$-0.369430\pi$
$277$	3677.01	0.797581	0.398790	+	0.917042i	$0.369430\pi$
$278$	9598.05	2.07069
$279$	8330.19	1.78751
$280$	5385.50	1.14945
$281$	3082.97	0.654500	0.327250	−	0.944938i	$-0.393878\pi$
$281$	3082.97	0.654500	0.327250	+	0.944938i	$0.393878\pi$
$282$	5775.54	1.21960
$283$	9216.03	1.93582	0.967909	−	0.251302i	$-0.0808586\pi$
$283$	9216.03	1.93582	0.967909	+	0.251302i	$0.0808586\pi$
$284$	−6581.01	−1.37504
$285$	16875.5	3.50744
$286$	7418.70	1.53384
$287$	306.038	0.0629438
$288$	5211.86	1.06636
$289$	−4379.01	−0.891310
$290$	−23343.2	−4.72675
$291$	−2701.70	−0.544248
$292$	−7523.70	−1.50785
$293$	5981.73	1.19268	0.596342	−	0.802730i	$-0.296620\pi$
$293$	5981.73	1.19268	0.596342	+	0.802730i	$0.296620\pi$
$294$	−3220.93	−0.638940
$295$	5311.26	1.04825
$296$	4027.27	0.790813
$297$	−217.035	−0.0424029
$298$	1527.35	0.296902
$299$	−9955.52	−1.92556
$300$	−16292.1	−3.13542
$301$	−1852.35	−0.354710
$302$	2298.22	0.437907
$303$	8763.35	1.66152
$304$	1347.38	0.254203
$305$	−678.880	−0.127451
$306$	−2675.83	−0.499892
$307$	3894.51	0.724011	0.362005	−	0.932176i	$-0.382092\pi$
$307$	3894.51	0.724011	0.362005	+	0.932176i	$0.382092\pi$
$308$	4326.86	0.800473
$309$	−6892.12	−1.26886
$310$	−25646.6	−4.69881
$311$	4121.41	0.751460	0.375730	−	0.926729i	$-0.377392\pi$
$311$	4121.41	0.751460	0.375730	+	0.926729i	$0.377392\pi$
$312$	10480.5	1.90173
$313$	−5180.66	−0.935554	−0.467777	−	0.883846i	$-0.654945\pi$
$313$	−5180.66	−0.935554	−0.467777	+	0.883846i	$0.654945\pi$
$314$	−6381.58	−1.14692
$315$	−7029.34	−1.25733
$316$	−5046.31	−0.898345
$317$	−2899.76	−0.513775	−0.256888	−	0.966441i	$-0.582697\pi$
$317$	−2899.76	−0.513775	−0.256888	+	0.966441i	$0.582697\pi$
$318$	−2189.70	−0.386139
$319$	−6613.55	−1.16078
$320$	−14624.5	−2.55480
$321$	−12318.3	−2.14187
$322$	−9565.29	−1.65544
$323$	−3068.55	−0.528603
$324$	−9432.56	−1.61738
$325$	13343.4	2.27741
$326$	−4548.55	−0.772763
$327$	−112.276	−0.0189874
$328$	384.730	0.0647657
$329$	−2758.83	−0.462308
$330$	−12836.1	−2.14122
$331$	8683.42	1.44195	0.720973	−	0.692964i	$-0.243695\pi$
$331$	8683.42	1.44195	0.720973	+	0.692964i	$0.243695\pi$
$332$	2967.95	0.490625
$333$	−5256.54	−0.865035
$334$	16094.1	2.63661
$335$	−8236.31	−1.34328
$336$	−1151.70	−0.186994
$337$	−4307.31	−0.696244	−0.348122	−	0.937449i	$-0.613180\pi$
$337$	−4307.31	−0.696244	−0.348122	+	0.937449i	$0.613180\pi$
$338$	−14428.3	−2.32189
$339$	−8800.79	−1.41001
$340$	5000.85	0.797674
$341$	−7266.16	−1.15391
$342$	15376.5	2.43118
$343$	6903.31	1.08672
$344$	−2328.65	−0.364977
$345$	17225.3	2.68806
$346$	−6886.23	−1.06996
$347$	9437.19	1.45999	0.729993	−	0.683455i	$-0.239523\pi$
$347$	9437.19	1.45999	0.729993	+	0.683455i	$0.239523\pi$
$348$	−26494.7	−4.08122
$349$	−92.2954	−0.0141560	−0.00707802	−	0.999975i	$-0.502253\pi$
$349$	−92.2954	−0.0141560	−0.00707802	+	0.999975i	$0.502253\pi$
$350$	12820.3	1.95793
$351$	712.102	0.108288
$352$	−4546.14	−0.688381
$353$	5329.21	0.803528	0.401764	−	0.915743i	$-0.368397\pi$
$353$	5329.21	0.803528	0.401764	+	0.915743i	$0.368397\pi$
$354$	9930.84	1.49101
$355$	−9325.77	−1.39425
$356$	−4559.77	−0.678841
$357$	2622.89	0.388846
$358$	7930.73	1.17082
$359$	2295.60	0.337486	0.168743	−	0.985660i	$-0.446029\pi$
$359$	2295.60	0.337486	0.168743	+	0.985660i	$0.446029\pi$
$360$	−8836.80	−1.29372
$361$	10774.2	1.57082
$362$	−21679.4	−3.14763
$363$	6022.37	0.870778
$364$	−14196.6	−2.04425
$365$	−10661.6	−1.52892
$366$	−1269.35	−0.181284
$367$	8450.07	1.20188	0.600940	−	0.799294i	$-0.294793\pi$
$367$	8450.07	1.20188	0.600940	+	0.799294i	$0.294793\pi$
$368$	1375.31	0.194818
$369$	−502.163	−0.0708444
$370$	16183.6	2.27391
$371$	1045.97	0.146371
$372$	−29109.1	−4.05709
$373$	8958.02	1.24351	0.621754	−	0.783212i	$-0.286420\pi$
$373$	8958.02	1.24351	0.621754	+	0.783212i	$0.286420\pi$
$374$	2334.04	0.322701
$375$	−7201.58	−0.991702
$376$	−3468.21	−0.475690
$377$	21699.4	2.96439
$378$	684.190	0.0930977
$379$	10912.9	1.47905	0.739525	−	0.673129i	$-0.235050\pi$
$379$	10912.9	1.47905	0.739525	+	0.673129i	$0.235050\pi$
$380$	−28737.1	−3.87942
$381$	−7481.79	−1.00605
$382$	14785.1	1.98030
$383$	1641.61	0.219014	0.109507	−	0.993986i	$-0.465073\pi$
$383$	1641.61	0.219014	0.109507	+	0.993986i	$0.465073\pi$
$384$	−15554.5	−2.06709
$385$	6131.47	0.811659
$386$	−10825.0	−1.42740
$387$	3039.43	0.399233
$388$	4600.67	0.601969
$389$	3209.96	0.418384	0.209192	−	0.977875i	$-0.432917\pi$
$389$	3209.96	0.418384	0.209192	+	0.977875i	$0.432917\pi$
$390$	42115.7	5.46824
$391$	−3132.16	−0.405116
$392$	1934.17	0.249210
$393$	−4775.90	−0.613008
$394$	10947.3	1.39979
$395$	−7150.98	−0.910898
$396$	−7099.73	−0.900947
$397$	−5410.32	−0.683970	−0.341985	−	0.939705i	$-0.611099\pi$
$397$	−5410.32	−0.683970	−0.341985	+	0.939705i	$0.611099\pi$
$398$	−11975.0	−1.50818
$399$	−15072.3	−1.89112
$400$	−1843.33	−0.230416
$401$	−7788.68	−0.969946	−0.484973	−	0.874529i	$-0.661171\pi$
$401$	−7788.68	−0.969946	−0.484973	+	0.874529i	$0.661171\pi$
$402$	−15400.0	−1.91066
$403$	23840.6	2.94686
$404$	−14923.0	−1.83774
$405$	−13366.6	−1.63998
$406$	20848.8	2.54855
$407$	4585.11	0.558417
$408$	3297.31	0.400101
$409$	−3236.67	−0.391303	−0.195652	−	0.980673i	$-0.562682\pi$
$409$	−3236.67	−0.391303	−0.195652	+	0.980673i	$0.562682\pi$
$410$	1546.04	0.186228
$411$	−11869.0	−1.42446
$412$	11736.5	1.40343
$413$	−4743.72	−0.565189
$414$	15695.2	1.86323
$415$	4205.80	0.497481
$416$	14916.1	1.75799
$417$	15437.4	1.81289
$418$	−13412.4	−1.56943
$419$	14487.5	1.68917	0.844583	−	0.535424i	$-0.179848\pi$
$419$	14487.5	1.68917	0.844583	+	0.535424i	$0.179848\pi$
$420$	24563.4	2.85375
$421$	−12293.7	−1.42318	−0.711588	−	0.702597i	$-0.752024\pi$
$421$	−12293.7	−1.42318	−0.711588	+	0.702597i	$0.752024\pi$
$422$	19502.8	2.24972
$423$	4526.83	0.520336
$424$	1314.91	0.150608
$425$	4198.03	0.479140
$426$	−17437.1	−1.98317
$427$	606.338	0.0687184
$428$	20976.6	2.36902
$429$	11932.2	1.34287
$430$	−9357.67	−1.04946
$431$	6958.06	0.777629	0.388815	−	0.921316i	$-0.372885\pi$
$431$	6958.06	0.777629	0.388815	+	0.921316i	$0.372885\pi$
$432$	−98.3738	−0.0109561
$433$	2066.73	0.229378	0.114689	−	0.993401i	$-0.463413\pi$
$433$	2066.73	0.229378	0.114689	+	0.993401i	$0.463413\pi$
$434$	22906.1	2.53348
$435$	−37544.9	−4.13826
$436$	191.193	0.0210011
$437$	17998.8	1.97025
$438$	−19934.8	−2.17471
$439$	2754.45	0.299459	0.149730	−	0.988727i	$-0.452160\pi$
$439$	2754.45	0.299459	0.149730	+	0.988727i	$0.452160\pi$
$440$	7708.06	0.835153
$441$	−2524.54	−0.272599
$442$	−7658.09	−0.824114
$443$	−5897.77	−0.632532	−0.316266	−	0.948671i	$-0.602429\pi$
$443$	−5897.77	−0.632532	−0.316266	+	0.948671i	$0.602429\pi$
$444$	18368.5	1.96336
$445$	−6461.53	−0.688327
$446$	−26991.4	−2.86565
$447$	2456.57	0.259937
$448$	13061.8	1.37749
$449$	−4557.85	−0.479061	−0.239530	−	0.970889i	$-0.576993\pi$
$449$	−4557.85	−0.479061	−0.239530	+	0.970889i	$0.576993\pi$
$450$	−21036.3	−2.20369
$451$	438.021	0.0457330
$452$	14986.7	1.55955
$453$	3696.44	0.383386
$454$	−489.345	−0.0505861
$455$	−20117.7	−2.07281
$456$	−18947.8	−1.94586
$457$	1886.42	0.193092	0.0965461	−	0.995329i	$-0.469220\pi$
$457$	1886.42	0.193092	0.0965461	+	0.995329i	$0.469220\pi$
$458$	−6867.57	−0.700656
$459$	224.038	0.0227826
$460$	−29332.8	−2.97315
$461$	15813.1	1.59759	0.798797	−	0.601600i	$-0.205470\pi$
$461$	15813.1	1.59759	0.798797	+	0.601600i	$0.205470\pi$
$462$	11464.5	1.15449
$463$	3215.31	0.322739	0.161370	−	0.986894i	$-0.448409\pi$
$463$	3215.31	0.322739	0.161370	+	0.986894i	$0.448409\pi$
$464$	−2997.68	−0.299922
$465$	−41249.8	−4.11379
$466$	17526.6	1.74228
$467$	8367.77	0.829152	0.414576	−	0.910015i	$-0.363930\pi$
$467$	8367.77	0.829152	0.414576	+	0.910015i	$0.363930\pi$
$468$	23294.6	2.30084
$469$	7356.21	0.724261
$470$	−13937.0	−1.36780
$471$	−10264.1	−1.00413
$472$	−5963.47	−0.581549
$473$	−2651.20	−0.257722
$474$	−13370.7	−1.29565
$475$	−24123.7	−2.33026
$476$	−4466.48	−0.430086
$477$	−1716.27	−0.164744
$478$	17346.5	1.65985
$479$	9813.36	0.936083	0.468041	−	0.883707i	$-0.344960\pi$
$479$	9813.36	0.936083	0.468041	+	0.883707i	$0.344960\pi$
$480$	−25808.3	−2.45413
$481$	−15044.0	−1.42608
$482$	6947.25	0.656511
$483$	−15384.7	−1.44934
$484$	−10255.4	−0.963129
$485$	6519.49	0.610381
$486$	−23811.4	−2.22245
$487$	−213.391	−0.0198556	−0.00992778	−	0.999951i	$-0.503160\pi$
$487$	−213.391	−0.0198556	−0.00992778	+	0.999951i	$0.503160\pi$
$488$	762.246	0.0707074
$489$	−7315.84	−0.676551
$490$	7772.45	0.716579
$491$	−9982.42	−0.917516	−0.458758	−	0.888561i	$-0.651706\pi$
$491$	−9982.42	−0.917516	−0.458758	+	0.888561i	$0.651706\pi$
$492$	1754.77	0.160795
$493$	6826.96	0.623673
$494$	44006.7	4.00801
$495$	−10060.8	−0.913537
$496$	−3293.48	−0.298148
$497$	8329.26	0.751747
$498$	7863.88	0.707608
$499$	18963.4	1.70124	0.850619	−	0.525783i	$-0.176228\pi$
$499$	18963.4	1.70124	0.850619	+	0.525783i	$0.176228\pi$
$500$	12263.5	1.09688
$501$	25885.5	2.30834
$502$	−9480.19	−0.842872
$503$	−5727.46	−0.507703	−0.253852	−	0.967243i	$-0.581698\pi$
$503$	−5727.46	−0.507703	−0.253852	+	0.967243i	$0.581698\pi$
$504$	7892.53	0.697542
$505$	−21146.9	−1.86342
$506$	−13690.4	−1.20279
$507$	−23206.4	−2.03280
$508$	12740.6	1.11274
$509$	14507.3	1.26331	0.631653	−	0.775251i	$-0.282377\pi$
$509$	14507.3	1.26331	0.631653	+	0.775251i	$0.282377\pi$
$510$	13250.3	1.15045
$511$	9522.37	0.824354
$512$	−3656.66	−0.315631
$513$	−1287.42	−0.110801
$514$	−5384.28	−0.462044
$515$	16631.4	1.42305
$516$	−10621.0	−0.906134
$517$	−3948.61	−0.335899
$518$	−14454.3	−1.22603
$519$	−11075.7	−0.936746
$520$	−25290.5	−2.13281
$521$	12119.9	1.01916	0.509580	−	0.860423i	$-0.329801\pi$
$521$	12119.9	1.01916	0.509580	+	0.860423i	$0.329801\pi$
$522$	−34209.8	−2.86843
$523$	−10388.7	−0.868581	−0.434291	−	0.900773i	$-0.643001\pi$
$523$	−10388.7	−0.868581	−0.434291	+	0.900773i	$0.643001\pi$
$524$	8132.80	0.678021
$525$	20620.1	1.71416
$526$	8859.61	0.734406
$527$	7500.63	0.619986
$528$	−1648.38	−0.135864
$529$	6204.87	0.509976
$530$	5283.98	0.433059
$531$	7783.74	0.636131
$532$	25666.3	2.09169
$533$	−1437.17	−0.116793
$534$	−12081.6	−0.979066
$535$	29725.4	2.40213
$536$	9247.72	0.745225
$537$	12755.7	1.02505
$538$	31610.0	2.53310
$539$	2202.08	0.175975
$540$	2098.12	0.167202
$541$	14534.3	1.15505	0.577523	−	0.816374i	$-0.304019\pi$
$541$	14534.3	1.15505	0.577523	+	0.816374i	$0.304019\pi$
$542$	−35522.6	−2.81518
$543$	−34868.9	−2.75574
$544$	4692.84	0.369860
$545$	270.934	0.0212945
$546$	−37615.4	−2.94834
$547$	11229.2	0.877743	0.438871	−	0.898550i	$-0.355378\pi$
$547$	11229.2	0.877743	0.438871	+	0.898550i	$0.355378\pi$
$548$	20211.5	1.57554
$549$	−994.910	−0.0773438
$550$	18349.3	1.42257
$551$	−39230.7	−3.03318
$552$	−19340.6	−1.49129
$553$	6386.86	0.491133
$554$	−16590.5	−1.27232
$555$	26029.5	1.99080
$556$	−26288.1	−2.00515
$557$	609.590	0.0463719	0.0231860	−	0.999731i	$-0.492619\pi$
$557$	609.590	0.0463719	0.0231860	+	0.999731i	$0.492619\pi$
$558$	−37585.5	−2.85147
$559$	8698.71	0.658169
$560$	2779.17	0.209717
$561$	3754.04	0.282524
$562$	−13910.2	−1.04407
$563$	23035.4	1.72438	0.862190	−	0.506585i	$-0.169092\pi$
$563$	23035.4	1.72438	0.862190	+	0.506585i	$0.169092\pi$
$564$	−15818.6	−1.18100
$565$	21237.3	1.58134
$566$	−41582.4	−3.08806
$567$	11938.3	0.884237
$568$	10471.0	0.773506
$569$	−21487.0	−1.58309	−0.791547	−	0.611108i	$-0.790724\pi$
$569$	−21487.0	−1.58309	−0.791547	+	0.611108i	$0.790724\pi$
$570$	−76141.7	−5.59513
$571$	−10160.7	−0.744681	−0.372340	−	0.928096i	$-0.621445\pi$
$571$	−10160.7	−0.744681	−0.372340	+	0.928096i	$0.621445\pi$
$572$	−20319.1	−1.48529
$573$	23780.3	1.73374
$574$	−1380.83	−0.100409
$575$	−24623.8	−1.78588
$576$	−21432.5	−1.55038
$577$	−14891.4	−1.07441	−0.537206	−	0.843451i	$-0.680520\pi$
$577$	−14891.4	−1.07441	−0.537206	+	0.843451i	$0.680520\pi$
$578$	19757.9	1.42184
$579$	−17410.8	−1.24968
$580$	63934.7	4.57714
$581$	−3756.38	−0.268229
$582$	12190.0	0.868196
$583$	1497.05	0.106349
$584$	11970.8	0.848215
$585$	33010.1	2.33299
$586$	−26989.4	−1.90259
$587$	2160.59	0.151920	0.0759599	−	0.997111i	$-0.475798\pi$
$587$	2160.59	0.151920	0.0759599	+	0.997111i	$0.475798\pi$
$588$	8821.80	0.618716
$589$	−43101.9	−3.01525
$590$	−23964.2	−1.67219
$591$	17607.6	1.22551
$592$	2078.26	0.144284
$593$	1075.72	0.0744934	0.0372467	−	0.999306i	$-0.488141\pi$
$593$	1075.72	0.0744934	0.0372467	+	0.999306i	$0.488141\pi$
$594$	979.254	0.0676419
$595$	−6329.33	−0.436096
$596$	−4183.25	−0.287504
$597$	−19260.5	−1.32040
$598$	44919.0	3.07169
$599$	12553.5	0.856300	0.428150	−	0.903708i	$-0.359166\pi$
$599$	12553.5	0.856300	0.428150	+	0.903708i	$0.359166\pi$
$600$	25922.2	1.76378
$601$	15790.9	1.07175	0.535877	−	0.844296i	$-0.319981\pi$
$601$	15790.9	1.07175	0.535877	+	0.844296i	$0.319981\pi$
$602$	8357.75	0.565841
$603$	−12070.4	−0.815169
$604$	−6294.61	−0.424046
$605$	−14532.6	−0.976588
$606$	−39539.9	−2.65049
$607$	14497.2	0.969396	0.484698	−	0.874682i	$-0.338930\pi$
$607$	14497.2	0.969396	0.484698	+	0.874682i	$0.338930\pi$
$608$	−26967.1	−1.79878
$609$	33533.0	2.23124
$610$	3063.08	0.203313
$611$	12955.6	0.857818
$612$	7328.83	0.484069
$613$	−25347.7	−1.67012	−0.835059	−	0.550161i	$-0.814566\pi$
$613$	−25347.7	−1.67012	−0.835059	+	0.550161i	$0.814566\pi$
$614$	−17571.9	−1.15496
$615$	2486.63	0.163042
$616$	−6884.41	−0.450293
$617$	−17887.7	−1.16715	−0.583574	−	0.812060i	$-0.698346\pi$
$617$	−17887.7	−1.16715	−0.583574	+	0.812060i	$0.698346\pi$
$618$	31097.0	2.02412
$619$	−16665.8	−1.08216	−0.541079	−	0.840972i	$-0.681984\pi$
$619$	−16665.8	−1.08216	−0.541079	+	0.840972i	$0.681984\pi$
$620$	70243.6	4.55008
$621$	−1314.11	−0.0849169
$622$	−18595.7	−1.19874
$623$	5771.07	0.371129
$624$	5408.40	0.346970
$625$	−5330.27	−0.341137
$626$	23375.0	1.49242
$627$	−21572.4	−1.37403
$628$	17478.5	1.11062
$629$	−4733.07	−0.300031
$630$	31716.1	2.00572
$631$	16797.5	1.05974	0.529872	−	0.848078i	$-0.322240\pi$
$631$	16797.5	1.05974	0.529872	+	0.848078i	$0.322240\pi$
$632$	8029.11	0.505349
$633$	31368.1	1.96962
$634$	13083.6	0.819585
$635$	18054.4	1.12829
$636$	5997.37	0.373917
$637$	−7225.13	−0.449403
$638$	29840.1	1.85170
$639$	−13667.1	−0.846105
$640$	37534.8	2.31827
$641$	21189.2	1.30565	0.652825	−	0.757509i	$-0.273584\pi$
$641$	21189.2	1.30565	0.652825	+	0.757509i	$0.273584\pi$
$642$	55579.6	3.41675
$643$	18859.1	1.15666	0.578330	−	0.815803i	$-0.303705\pi$
$643$	18859.1	1.15666	0.578330	+	0.815803i	$0.303705\pi$
$644$	26198.4	1.60305
$645$	−15050.8	−0.918796
$646$	13845.2	0.843238
$647$	−28759.8	−1.74755	−0.873774	−	0.486333i	$-0.838334\pi$
$647$	−28759.8	−1.74755	−0.873774	+	0.486333i	$0.838334\pi$
$648$	15008.0	0.909831
$649$	−6789.51	−0.410649
$650$	−60204.8	−3.63296
$651$	36842.0	2.21805
$652$	12458.0	0.748304
$653$	−25107.0	−1.50461	−0.752306	−	0.658813i	$-0.771059\pi$
$653$	−25107.0	−1.50461	−0.752306	+	0.658813i	$0.771059\pi$
$654$	506.584	0.0302890
$655$	11524.8	0.687496
$656$	198.539	0.0118165
$657$	−15624.8	−0.927824
$658$	12447.8	0.737484
$659$	−23055.3	−1.36283	−0.681417	−	0.731895i	$-0.738636\pi$
$659$	−23055.3	−1.36283	−0.681417	+	0.731895i	$0.738636\pi$
$660$	35156.7	2.07344
$661$	18640.2	1.09685	0.548425	−	0.836200i	$-0.315228\pi$
$661$	18640.2	1.09685	0.548425	+	0.836200i	$0.315228\pi$
$662$	−39179.3	−2.30022
$663$	−12317.2	−0.721509
$664$	−4722.26	−0.275993
$665$	36371.0	2.12092
$666$	23717.3	1.37992
$667$	−40043.9	−2.32460
$668$	−44080.0	−2.55316
$669$	−43412.7	−2.50887
$670$	37161.9	2.14282
$671$	867.828	0.0499287
$672$	23050.5	1.32321
$673$	29032.4	1.66288	0.831440	−	0.555615i	$-0.187517\pi$
$673$	29032.4	1.66288	0.831440	+	0.555615i	$0.187517\pi$
$674$	19434.4	1.11066
$675$	1761.30	0.100433
$676$	39517.8	2.24839
$677$	24064.3	1.36613	0.683063	−	0.730359i	$-0.260647\pi$
$677$	24064.3	1.36613	0.683063	+	0.730359i	$0.260647\pi$
$678$	39708.8	2.24928
$679$	−5822.84	−0.329102
$680$	−7956.78	−0.448719
$681$	−787.057	−0.0442879
$682$	32784.7	1.84075
$683$	−2454.24	−0.137494	−0.0687472	−	0.997634i	$-0.521900\pi$
$683$	−2454.24	−0.137494	−0.0687472	+	0.997634i	$0.521900\pi$
$684$	−42114.6	−2.35423
$685$	28641.2	1.59755
$686$	−31147.5	−1.73355
$687$	−11045.7	−0.613422
$688$	−1201.69	−0.0665901
$689$	−4911.89	−0.271594
$690$	−77720.2	−4.28805
$691$	−24749.5	−1.36254	−0.681270	−	0.732032i	$-0.738572\pi$
$691$	−24749.5	−1.36254	−0.681270	+	0.732032i	$0.738572\pi$
$692$	18860.7	1.03609
$693$	8985.77	0.492556
$694$	−42580.3	−2.32900
$695$	−37252.2	−2.03317
$696$	42155.4	2.29583
$697$	−452.155	−0.0245719
$698$	416.434	0.0225820
$699$	28189.6	1.52536
$700$	−35113.7	−1.89596
$701$	−20860.1	−1.12393	−0.561965	−	0.827161i	$-0.689954\pi$
$701$	−20860.1	−1.12393	−0.561965	+	0.827161i	$0.689954\pi$
$702$	−3212.98	−0.172744
$703$	27198.3	1.45918
$704$	18694.9	1.00084
$705$	−22416.1	−1.19750
$706$	−24045.2	−1.28180
$707$	18887.3	1.00471
$708$	−27199.6	−1.44382
$709$	21768.2	1.15306	0.576532	−	0.817074i	$-0.304405\pi$
$709$	21768.2	1.15306	0.576532	+	0.817074i	$0.304405\pi$
$710$	42077.5	2.22414
$711$	−10479.9	−0.552779
$712$	7254.99	0.381871
$713$	−43995.4	−2.31085
$714$	−11834.4	−0.620296
$715$	−28793.6	−1.50604
$716$	−21721.5	−1.13376
$717$	27899.9	1.45319
$718$	−10357.7	−0.538364
$719$	−32034.1	−1.66157	−0.830786	−	0.556591i	$-0.812109\pi$
$719$	−32034.1	−1.66157	−0.830786	+	0.556591i	$0.812109\pi$
$720$	−4560.20	−0.236040
$721$	−14854.3	−0.767271
$722$	−48612.9	−2.50580
$723$	11173.9	0.574773
$724$	59377.7	3.04800
$725$	53670.8	2.74936
$726$	−27172.7	−1.38908
$727$	9656.20	0.492611	0.246306	−	0.969192i	$-0.420783\pi$
$727$	9656.20	0.492611	0.246306	+	0.969192i	$0.420783\pi$
$728$	22588.1	1.14996
$729$	−17689.3	−0.898712
$730$	48104.9	2.43896
$731$	2736.75	0.138471
$732$	3476.63	0.175546
$733$	28013.4	1.41159	0.705796	−	0.708415i	$-0.250590\pi$
$733$	28013.4	1.41159	0.705796	+	0.708415i	$0.250590\pi$
$734$	−38126.4	−1.91726
$735$	12501.1	0.627362
$736$	−27526.1	−1.37857
$737$	10528.7	0.526226
$738$	2265.74	0.113012
$739$	39095.9	1.94610	0.973048	−	0.230601i	$-0.0740693\pi$
$739$	39095.9	1.94610	0.973048	+	0.230601i	$0.0740693\pi$
$740$	−44325.3	−2.20193
$741$	70780.0	3.50900
$742$	−4719.36	−0.233495
$743$	10905.8	0.538488	0.269244	−	0.963072i	$-0.413226\pi$
$743$	10905.8	0.538488	0.269244	+	0.963072i	$0.413226\pi$
$744$	46315.2	2.28225
$745$	−5927.97	−0.291522
$746$	−40418.3	−1.98367
$747$	6163.67	0.301897
$748$	−6392.70	−0.312487
$749$	−26549.0	−1.29517
$750$	32493.3	1.58198
$751$	−35261.3	−1.71332	−0.856661	−	0.515880i	$-0.827465\pi$
$751$	−35261.3	−1.71332	−0.856661	+	0.515880i	$0.827465\pi$
$752$	−1789.76	−0.0867896
$753$	−15247.8	−0.737931
$754$	−97906.9	−4.72886
$755$	−8919.91	−0.429972
$756$	−1873.93	−0.0901509
$757$	22545.5	1.08247	0.541235	−	0.840871i	$-0.317957\pi$
$757$	22545.5	1.08247	0.541235	+	0.840871i	$0.317957\pi$
$758$	−49238.8	−2.35941
$759$	−22019.6	−1.05304
$760$	45723.1	2.18231
$761$	−14102.9	−0.671786	−0.335893	−	0.941900i	$-0.609038\pi$
$761$	−14102.9	−0.671786	−0.335893	+	0.941900i	$0.609038\pi$
$762$	33757.6	1.60487
$763$	−241.983	−0.0114815
$764$	−40495.1	−1.91762
$765$	10385.5	0.490834
$766$	−7406.89	−0.349376
$767$	22276.7	1.04872
$768$	21697.8	1.01947
$769$	28975.8	1.35877	0.679384	−	0.733783i	$-0.262247\pi$
$769$	28975.8	1.35877	0.679384	+	0.733783i	$0.262247\pi$
$770$	−27665.0	−1.29478
$771$	−8660.02	−0.404518
$772$	29648.5	1.38222
$773$	28917.2	1.34551	0.672755	−	0.739865i	$-0.265111\pi$
$773$	28917.2	1.34551	0.672755	+	0.739865i	$0.265111\pi$
$774$	−13713.8	−0.636864
$775$	58966.9	2.73310
$776$	−7320.07	−0.338628
$777$	−23248.1	−1.07339
$778$	−14483.2	−0.667415
$779$	2598.28	0.119503
$780$	−115351.	−5.29516
$781$	11921.3	0.546196
$782$	14132.2	0.646249
$783$	2864.28	0.130729
$784$	998.120	0.0454683
$785$	24768.3	1.12614
$786$	21548.7	0.977883
$787$	−12032.8	−0.545010	−0.272505	−	0.962154i	$-0.587852\pi$
$787$	−12032.8	−0.545010	−0.272505	+	0.962154i	$0.587852\pi$
$788$	−29983.7	−1.35549
$789$	14249.7	0.642970
$790$	32265.0	1.45308
$791$	−18967.9	−0.852620
$792$	11296.3	0.506813
$793$	−2847.39	−0.127508
$794$	24411.2	1.09108
$795$	8498.70	0.379142
$796$	32798.5	1.46044
$797$	17589.6	0.781749	0.390875	−	0.920444i	$-0.372173\pi$
$797$	17589.6	0.781749	0.390875	+	0.920444i	$0.372173\pi$
$798$	68005.6	3.01676
$799$	4076.03	0.180475
$800$	36893.2	1.63046
$801$	−9469.47	−0.417712
$802$	35142.3	1.54728
$803$	13629.0	0.598950
$804$	42179.1	1.85018
$805$	37125.0	1.62545
$806$	−107568.	−4.70090
$807$	50841.3	2.21772
$808$	23743.7	1.03379
$809$	−24063.1	−1.04575	−0.522877	−	0.852408i	$-0.675141\pi$
$809$	−24063.1	−1.04575	−0.522877	+	0.852408i	$0.675141\pi$
$810$	60309.7	2.61613
$811$	−3527.56	−0.152737	−0.0763684	−	0.997080i	$-0.524333\pi$
$811$	−3527.56	−0.152737	−0.0763684	+	0.997080i	$0.524333\pi$
$812$	−57102.9	−2.46788
$813$	−57134.2	−2.46468
$814$	−20687.9	−0.890798
$815$	17653.9	0.758761
$816$	1701.57	0.0729985
$817$	−15726.6	−0.673442
$818$	14603.7	0.624215
$819$	−29482.7	−1.25789
$820$	−4234.44	−0.180333
$821$	−33506.6	−1.42435	−0.712174	−	0.702003i	$-0.752289\pi$
$821$	−33506.6	−1.42435	−0.712174	+	0.702003i	$0.752289\pi$
$822$	53552.5	2.27233
$823$	24545.1	1.03960	0.519799	−	0.854289i	$-0.326007\pi$
$823$	24545.1	1.03960	0.519799	+	0.854289i	$0.326007\pi$
$824$	−18673.8	−0.789479
$825$	29512.8	1.24546
$826$	21403.5	0.901602
$827$	23884.4	1.00428	0.502142	−	0.864785i	$-0.332545\pi$
$827$	23884.4	1.00428	0.502142	+	0.864785i	$0.332545\pi$
$828$	−42987.7	−1.80426
$829$	−33675.5	−1.41086	−0.705428	−	0.708782i	$-0.749245\pi$
$829$	−33675.5	−1.41086	−0.705428	+	0.708782i	$0.749245\pi$
$830$	−18976.4	−0.793592
$831$	−26684.0	−1.11391
$832$	−61338.8	−2.55594
$833$	−2273.14	−0.0945492
$834$	−69653.0	−2.89195
$835$	−62464.6	−2.58883
$836$	36735.2	1.51975
$837$	3146.92	0.129956
$838$	−65367.1	−2.69459
$839$	−2984.24	−0.122798	−0.0613989	−	0.998113i	$-0.519556\pi$
$839$	−2984.24	−0.122798	−0.0613989	+	0.998113i	$0.519556\pi$
$840$	−39082.5	−1.60533
$841$	62892.1	2.57871
$842$	55468.6	2.27028
$843$	−22373.1	−0.914081
$844$	−53416.2	−2.17851
$845$	55999.5	2.27981
$846$	−20424.9	−0.830051
$847$	12979.7	0.526552
$848$	678.557	0.0274785
$849$	−66880.7	−2.70358
$850$	−18941.4	−0.764334
$851$	27762.1	1.11830
$852$	47758.4	1.92039
$853$	46355.2	1.86069	0.930346	−	0.366683i	$-0.119507\pi$
$853$	46355.2	1.86069	0.930346	+	0.366683i	$0.119507\pi$
$854$	−2735.78	−0.109621
$855$	−59679.5	−2.38713
$856$	−33375.6	−1.33266
$857$	−10144.1	−0.404334	−0.202167	−	0.979351i	$-0.564798\pi$
$857$	−10144.1	−0.404334	−0.202167	+	0.979351i	$0.564798\pi$
$858$	−53837.5	−2.14217
$859$	34358.6	1.36473	0.682363	−	0.731013i	$-0.260952\pi$
$859$	34358.6	1.36473	0.682363	+	0.731013i	$0.260952\pi$
$860$	25629.7	1.01624
$861$	−2220.92	−0.0879079
$862$	−31394.5	−1.24049
$863$	−40800.6	−1.60935	−0.804675	−	0.593716i	$-0.797660\pi$
$863$	−40800.6	−1.60935	−0.804675	+	0.593716i	$0.797660\pi$
$864$	1968.90	0.0775269
$865$	26727.0	1.05057
$866$	−9325.01	−0.365909
$867$	31778.5	1.24481
$868$	−62737.6	−2.45329
$869$	9141.26	0.356843
$870$	169401.	6.60143
$871$	−34545.1	−1.34387
$872$	−304.204	−0.0118138
$873$	9554.41	0.370410
$874$	−81209.8	−3.14298
$875$	−15521.3	−0.599673
$876$	54599.5	2.10587
$877$	35138.5	1.35296	0.676478	−	0.736463i	$-0.263505\pi$
$877$	35138.5	1.35296	0.676478	+	0.736463i	$0.263505\pi$
$878$	−12428.0	−0.477704
$879$	−43409.4	−1.66571
$880$	3977.72	0.152374
$881$	30568.2	1.16898	0.584489	−	0.811402i	$-0.301295\pi$
$881$	30568.2	1.16898	0.584489	+	0.811402i	$0.301295\pi$
$882$	11390.7	0.434856
$883$	−13913.0	−0.530248	−0.265124	−	0.964214i	$-0.585413\pi$
$883$	−13913.0	−0.530248	−0.265124	+	0.964214i	$0.585413\pi$
$884$	20974.8	0.798029
$885$	−38543.8	−1.46399
$886$	26610.5	1.00903
$887$	39686.1	1.50229	0.751143	−	0.660139i	$-0.229503\pi$
$887$	39686.1	1.50229	0.751143	+	0.660139i	$0.229503\pi$
$888$	−29225.9	−1.10446
$889$	−16125.2	−0.608348
$890$	29154.2	1.09803
$891$	17086.9	0.642460
$892$	73926.8	2.77495
$893$	−23422.6	−0.877725
$894$	−11083.9	−0.414656
$895$	−30780.9	−1.14960
$896$	−33524.0	−1.24995
$897$	72247.2	2.68926
$898$	20564.9	0.764208
$899$	95893.7	3.55755
$900$	57616.3	2.13394
$901$	−1545.36	−0.0571402
$902$	−1976.34	−0.0729543
$903$	13442.5	0.495392
$904$	−23845.2	−0.877299
$905$	84142.4	3.09060
$906$	−16678.2	−0.611585
$907$	−28167.0	−1.03117	−0.515585	−	0.856838i	$-0.672425\pi$
$907$	−28167.0	−1.03117	−0.515585	+	0.856838i	$0.672425\pi$
$908$	1340.27	0.0489849
$909$	−30991.2	−1.13082
$910$	90770.1	3.30659
$911$	−26406.7	−0.960366	−0.480183	−	0.877168i	$-0.659430\pi$
$911$	−26406.7	−0.960366	−0.480183	+	0.877168i	$0.659430\pi$
$912$	−9777.95	−0.355022
$913$	−5376.37	−0.194887
$914$	−8511.47	−0.308025
$915$	4926.63	0.177999
$916$	18809.6	0.678479
$917$	−10293.3	−0.370680
$918$	−1010.85	−0.0363433
$919$	16790.7	0.602692	0.301346	−	0.953515i	$-0.402564\pi$
$919$	16790.7	0.602692	0.301346	+	0.953515i	$0.402564\pi$
$920$	46671.0	1.67250
$921$	−28262.4	−1.01116
$922$	−71348.3	−2.54852
$923$	−39114.5	−1.39488
$924$	−31400.0	−1.11795
$925$	−37209.5	−1.32264
$926$	−14507.4	−0.514840
$927$	24373.7	0.863577
$928$	59996.8	2.12230
$929$	11643.6	0.411211	0.205605	−	0.978635i	$-0.434084\pi$
$929$	11643.6	0.411211	0.205605	+	0.978635i	$0.434084\pi$
$930$	186117.	6.56240
$931$	13062.4	0.459832
$932$	−48003.6	−1.68714
$933$	−29909.1	−1.04950
$934$	−37755.1	−1.32268
$935$	−9058.92	−0.316854
$936$	−37063.6	−1.29430
$937$	−5715.02	−0.199255	−0.0996273	−	0.995025i	$-0.531765\pi$
$937$	−5715.02	−0.199255	−0.0996273	+	0.995025i	$0.531765\pi$
$938$	−33191.0	−1.15536
$939$	37596.1	1.30660
$940$	38172.1	1.32451
$941$	28546.0	0.988919	0.494460	−	0.869201i	$-0.335366\pi$
$941$	28546.0	0.988919	0.494460	+	0.869201i	$0.335366\pi$
$942$	46311.1	1.60180
$943$	2652.14	0.0915860
$944$	−3077.43	−0.106104
$945$	−2655.49	−0.0914107
$946$	11962.1	0.411123
$947$	−15766.0	−0.540999	−0.270500	−	0.962720i	$-0.587189\pi$
$947$	−15766.0	−0.540999	−0.270500	+	0.962720i	$0.587189\pi$
$948$	36621.0	1.25464
$949$	−44717.4	−1.52960
$950$	108845.	3.71727
$951$	21043.5	0.717543
$952$	7106.56	0.241938
$953$	−11143.6	−0.378779	−0.189390	−	0.981902i	$-0.560651\pi$
$953$	−11143.6	−0.378779	−0.189390	+	0.981902i	$0.560651\pi$
$954$	7743.76	0.262802
$955$	−57384.4	−1.94441
$956$	−47510.3	−1.60731
$957$	47994.6	1.62115
$958$	−44277.5	−1.49326
$959$	−25580.7	−0.861360
$960$	106130.	3.56806
$961$	75565.3	2.53651
$962$	67877.9	2.27492
$963$	43563.0	1.45773
$964$	−19027.8	−0.635731
$965$	42014.1	1.40153
$966$	69415.3	2.31201
$967$	44154.2	1.46836	0.734179	−	0.678956i	$-0.237567\pi$
$967$	44154.2	1.46836	0.734179	+	0.678956i	$0.237567\pi$
$968$	16317.2	0.541793
$969$	22268.5	0.738252
$970$	−29415.7	−0.973692
$971$	−46059.9	−1.52228	−0.761139	−	0.648589i	$-0.775360\pi$
$971$	−46059.9	−1.52228	−0.761139	+	0.648589i	$0.775360\pi$
$972$	65217.2	2.15210
$973$	33271.6	1.09624
$974$	962.811	0.0316740
$975$	−96832.8	−3.18065
$976$	393.354	0.0129006
$977$	−43869.9	−1.43656	−0.718281	−	0.695753i	$-0.755071\pi$
$977$	−43869.9	−1.43656	−0.718281	+	0.695753i	$0.755071\pi$
$978$	33008.8	1.07925
$979$	8259.92	0.269651
$980$	−21288.0	−0.693897
$981$	397.058	0.0129226
$982$	45040.3	1.46364
$983$	−983.000	−0.0318950
$983$	−983.000	−0.0318950
$984$	−2791.98	−0.0904524
$985$	−42489.0	−1.37443
$986$	−30803.0	−0.994897
$987$	20020.8	0.645664
$988$	−120530.	−3.88115
$989$	−16052.6	−0.516119
$990$	45394.1	1.45729
$991$	1265.63	0.0405691	0.0202845	−	0.999794i	$-0.493543\pi$
$991$	1265.63	0.0405691	0.0202845	+	0.999794i	$0.493543\pi$
$992$	65917.2	2.10975
$993$	−63015.6	−2.01384
$994$	−37581.3	−1.19920
$995$	46477.8	1.48085
$996$	−21538.4	−0.685211
$997$	−33845.3	−1.07512	−0.537558	−	0.843227i	$-0.680653\pi$
$997$	−33845.3	−1.07512	−0.537558	+	0.843227i	$0.680653\pi$
$998$	−85562.1	−2.71385
$999$	−1985.78	−0.0628901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.b.1.15	✓	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.b.1.15	✓	136	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-4.51197 q^{2} -7.25700 q^{3} +12.3578 q^{4} +17.5119 q^{5} +32.7433 q^{6} -15.6407 q^{7} -19.6624 q^{8} +25.6640 q^{9} +O(q^{10})\)	\(q-4.51197 q^{2} -7.25700 q^{3} +12.3578 q^{4} +17.5119 q^{5} +32.7433 q^{6} -15.6407 q^{7} -19.6624 q^{8} +25.6640 q^{9} -79.0132 q^{10} -22.3859 q^{11} -89.6807 q^{12} +73.4493 q^{13} +70.5702 q^{14} -127.084 q^{15} -10.1467 q^{16} +23.1083 q^{17} -115.795 q^{18} -132.790 q^{19} +216.409 q^{20} +113.504 q^{21} +101.004 q^{22} -135.543 q^{23} +142.690 q^{24} +181.668 q^{25} -331.400 q^{26} +9.69516 q^{27} -193.285 q^{28} +295.434 q^{29} +573.399 q^{30} +324.586 q^{31} +203.081 q^{32} +162.455 q^{33} -104.264 q^{34} -273.899 q^{35} +317.152 q^{36} -204.821 q^{37} +599.145 q^{38} -533.021 q^{39} -344.326 q^{40} -19.5668 q^{41} -512.128 q^{42} +118.432 q^{43} -276.641 q^{44} +449.427 q^{45} +611.565 q^{46} +176.388 q^{47} +73.6346 q^{48} -98.3690 q^{49} -819.679 q^{50} -167.697 q^{51} +907.673 q^{52} -66.8746 q^{53} -43.7442 q^{54} -392.021 q^{55} +307.533 q^{56} +963.658 q^{57} -1332.99 q^{58} +303.294 q^{59} -1570.48 q^{60} -38.7667 q^{61} -1464.52 q^{62} -401.403 q^{63} -835.119 q^{64} +1286.24 q^{65} -732.989 q^{66} -470.326 q^{67} +285.568 q^{68} +983.635 q^{69} +1235.82 q^{70} -532.538 q^{71} -504.616 q^{72} -608.820 q^{73} +924.147 q^{74} -1318.36 q^{75} -1641.00 q^{76} +350.131 q^{77} +2404.97 q^{78} -408.349 q^{79} -177.688 q^{80} -763.286 q^{81} +88.2848 q^{82} +240.168 q^{83} +1402.67 q^{84} +404.671 q^{85} -534.359 q^{86} -2143.96 q^{87} +440.160 q^{88} -368.978 q^{89} -2027.80 q^{90} -1148.80 q^{91} -1675.02 q^{92} -2355.52 q^{93} -795.858 q^{94} -2325.41 q^{95} -1473.75 q^{96} +372.288 q^{97} +443.837 q^{98} -574.513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) \) 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9} + 257 q^{10} + 204 q^{11} + 296 q^{12} + 530 q^{13} + 103 q^{14} + 226 q^{15} + 2737 q^{16} + 664 q^{17} + 949 q^{18} + 421 q^{19} + 500 q^{20} + 684 q^{21} + 905 q^{22} + 617 q^{23} + 917 q^{24} + 5430 q^{25} + 572 q^{26} + 886 q^{27} + 2728 q^{28} + 688 q^{29} + 712 q^{30} + 1019 q^{31} + 2363 q^{32} + 1764 q^{33} + 1260 q^{34} + 834 q^{35} + 7190 q^{36} + 3303 q^{37} + 384 q^{38} + 1950 q^{39} + 2766 q^{40} + 1975 q^{41} + 448 q^{42} + 3021 q^{43} + 2038 q^{44} + 2266 q^{45} + 2742 q^{46} + 1293 q^{47} + 2589 q^{48} + 10447 q^{49} + 2191 q^{50} + 1032 q^{51} + 4983 q^{52} + 2415 q^{53} + 1878 q^{54} + 2612 q^{55} + 1540 q^{56} + 7908 q^{57} + 5743 q^{58} + 1059 q^{59} + 2611 q^{60} + 4312 q^{61} + 3258 q^{62} + 5605 q^{63} + 13735 q^{64} + 3554 q^{65} + 433 q^{66} + 5715 q^{67} + 5881 q^{68} + 1398 q^{69} + 4287 q^{70} + 2530 q^{71} + 9891 q^{72} + 14106 q^{73} + 2318 q^{74} + 2621 q^{75} + 4651 q^{76} + 4750 q^{77} + 6639 q^{78} + 4791 q^{79} + 4812 q^{80} + 19932 q^{81} + 5380 q^{82} + 4284 q^{83} + 9282 q^{84} + 12058 q^{85} + 2451 q^{86} + 6984 q^{87} + 11197 q^{88} + 5313 q^{89} + 5405 q^{90} + 6298 q^{91} + 6588 q^{92} + 5700 q^{93} + 4743 q^{94} + 5778 q^{95} + 9613 q^{96} + 15382 q^{97} + 6640 q^{98} + 8542 q^{99}+O(q^{100}) \) 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9 + 257 * q^10 + 204 * q^11 + 296 * q^12 + 530 * q^13 + 103 * q^14 + 226 * q^15 + 2737 * q^16 + 664 * q^17 + 949 * q^18 + 421 * q^19 + 500 * q^20 + 684 * q^21 + 905 * q^22 + 617 * q^23 + 917 * q^24 + 5430 * q^25 + 572 * q^26 + 886 * q^27 + 2728 * q^28 + 688 * q^29 + 712 * q^30 + 1019 * q^31 + 2363 * q^32 + 1764 * q^33 + 1260 * q^34 + 834 * q^35 + 7190 * q^36 + 3303 * q^37 + 384 * q^38 + 1950 * q^39 + 2766 * q^40 + 1975 * q^41 + 448 * q^42 + 3021 * q^43 + 2038 * q^44 + 2266 * q^45 + 2742 * q^46 + 1293 * q^47 + 2589 * q^48 + 10447 * q^49 + 2191 * q^50 + 1032 * q^51 + 4983 * q^52 + 2415 * q^53 + 1878 * q^54 + 2612 * q^55 + 1540 * q^56 + 7908 * q^57 + 5743 * q^58 + 1059 * q^59 + 2611 * q^60 + 4312 * q^61 + 3258 * q^62 + 5605 * q^63 + 13735 * q^64 + 3554 * q^65 + 433 * q^66 + 5715 * q^67 + 5881 * q^68 + 1398 * q^69 + 4287 * q^70 + 2530 * q^71 + 9891 * q^72 + 14106 * q^73 + 2318 * q^74 + 2621 * q^75 + 4651 * q^76 + 4750 * q^77 + 6639 * q^78 + 4791 * q^79 + 4812 * q^80 + 19932 * q^81 + 5380 * q^82 + 4284 * q^83 + 9282 * q^84 + 12058 * q^85 + 2451 * q^86 + 6984 * q^87 + 11197 * q^88 + 5313 * q^89 + 5405 * q^90 + 6298 * q^91 + 6588 * q^92 + 5700 * q^93 + 4743 * q^94 + 5778 * q^95 + 9613 * q^96 + 15382 * q^97 + 6640 * q^98 + 8542 * q^99

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