LMFDB - Embedded newform 2013.4.a.g.1.5

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:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-4.64624 q^{2} -3.00000 q^{3} +13.5875 q^{4} -15.1595 q^{5} +13.9387 q^{6} +14.1108 q^{7} -25.9610 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.64624 q^{2} -3.00000 q^{3} +13.5875 q^{4} -15.1595 q^{5} +13.9387 q^{6} +14.1108 q^{7} -25.9610 q^{8} +9.00000 q^{9} +70.4347 q^{10} +11.0000 q^{11} -40.7626 q^{12} -52.0870 q^{13} -65.5624 q^{14} +45.4785 q^{15} +11.9209 q^{16} -7.88117 q^{17} -41.8162 q^{18} -50.5955 q^{19} -205.980 q^{20} -42.3325 q^{21} -51.1086 q^{22} -220.348 q^{23} +77.8831 q^{24} +104.811 q^{25} +242.009 q^{26} -27.0000 q^{27} +191.732 q^{28} -176.319 q^{29} -211.304 q^{30} +94.4411 q^{31} +152.301 q^{32} -33.0000 q^{33} +36.6178 q^{34} -213.913 q^{35} +122.288 q^{36} +64.7744 q^{37} +235.079 q^{38} +156.261 q^{39} +393.556 q^{40} -68.8274 q^{41} +196.687 q^{42} +316.210 q^{43} +149.463 q^{44} -136.436 q^{45} +1023.79 q^{46} +80.9936 q^{47} -35.7626 q^{48} -143.884 q^{49} -486.975 q^{50} +23.6435 q^{51} -707.734 q^{52} -140.348 q^{53} +125.448 q^{54} -166.755 q^{55} -366.332 q^{56} +151.787 q^{57} +819.220 q^{58} -21.6994 q^{59} +617.941 q^{60} +61.0000 q^{61} -438.796 q^{62} +126.998 q^{63} -802.994 q^{64} +789.613 q^{65} +153.326 q^{66} +50.3343 q^{67} -107.086 q^{68} +661.043 q^{69} +993.893 q^{70} -569.991 q^{71} -233.649 q^{72} -9.87488 q^{73} -300.957 q^{74} -314.432 q^{75} -687.469 q^{76} +155.219 q^{77} -726.026 q^{78} -365.679 q^{79} -180.714 q^{80} +81.0000 q^{81} +319.789 q^{82} -1430.32 q^{83} -575.195 q^{84} +119.475 q^{85} -1469.19 q^{86} +528.957 q^{87} -285.571 q^{88} +595.602 q^{89} +633.912 q^{90} -734.992 q^{91} -2993.98 q^{92} -283.323 q^{93} -376.316 q^{94} +767.003 q^{95} -456.903 q^{96} -1444.56 q^{97} +668.519 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * 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 $

$2$	−4.64624	−1.64269	−0.821347	−	0.570429i	$-0.806777\pi$
$2$	−4.64624	−1.64269	−0.821347	+	0.570429i	$0.806777\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	13.5875	1.69844
$5$	−15.1595	−1.35591	−0.677954	−	0.735105i	$-0.737133\pi$
$5$	−15.1595	−1.35591	−0.677954	+	0.735105i	$0.737133\pi$
$6$	13.9387	0.948410
$7$	14.1108	0.761914	0.380957	−	0.924593i	$-0.375595\pi$
$7$	14.1108	0.761914	0.380957	+	0.924593i	$0.375595\pi$
$8$	−25.9610	−1.14733
$9$	9.00000	0.333333
$10$	70.4347	2.22734
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−40.7626	−0.980596
$13$	−52.0870	−1.11126	−0.555628	−	0.831431i	$-0.687522\pi$
$13$	−52.0870	−1.11126	−0.555628	+	0.831431i	$0.687522\pi$
$14$	−65.5624	−1.25159
$15$	45.4785	0.782833
$16$	11.9209	0.186263
$17$	−7.88117	−0.112439	−0.0562196	−	0.998418i	$-0.517905\pi$
$17$	−7.88117	−0.112439	−0.0562196	+	0.998418i	$0.517905\pi$
$18$	−41.8162	−0.547565
$19$	−50.5955	−0.610916	−0.305458	−	0.952206i	$-0.598810\pi$
$19$	−50.5955	−0.610916	−0.305458	+	0.952206i	$0.598810\pi$
$20$	−205.980	−2.30293
$21$	−42.3325	−0.439891
$22$	−51.1086	−0.495291
$23$	−220.348	−1.99764	−0.998818	−	0.0486038i	$-0.984523\pi$
$23$	−220.348	−1.99764	−0.998818	+	0.0486038i	$0.984523\pi$
$24$	77.8831	0.662409
$25$	104.811	0.838484
$26$	242.009	1.82545
$27$	−27.0000	−0.192450
$28$	191.732	1.29407
$29$	−176.319	−1.12902	−0.564511	−	0.825426i	$-0.690935\pi$
$29$	−176.319	−1.12902	−0.564511	+	0.825426i	$0.690935\pi$
$30$	−211.304	−1.28596
$31$	94.4411	0.547165	0.273583	−	0.961848i	$-0.411791\pi$
$31$	94.4411	0.547165	0.273583	+	0.961848i	$0.411791\pi$
$32$	152.301	0.841353
$33$	−33.0000	−0.174078
$34$	36.6178	0.184703
$35$	−213.913	−1.03308
$36$	122.288	0.566147
$37$	64.7744	0.287807	0.143903	−	0.989592i	$-0.454035\pi$
$37$	64.7744	0.287807	0.143903	+	0.989592i	$0.454035\pi$
$38$	235.079	1.00355
$39$	156.261	0.641584
$40$	393.556	1.55567
$41$	−68.8274	−0.262172	−0.131086	−	0.991371i	$-0.541846\pi$
$41$	−68.8274	−0.262172	−0.131086	+	0.991371i	$0.541846\pi$
$42$	196.687	0.722607
$43$	316.210	1.12143	0.560717	−	0.828008i	$-0.310526\pi$
$43$	316.210	1.12143	0.560717	+	0.828008i	$0.310526\pi$
$44$	149.463	0.512100
$45$	−136.436	−0.451969
$46$	1023.79	3.28150
$47$	80.9936	0.251365	0.125682	−	0.992071i	$-0.459888\pi$
$47$	80.9936	0.251365	0.125682	+	0.992071i	$0.459888\pi$
$48$	−35.7626	−0.107539
$49$	−143.884	−0.419487
$50$	−486.975	−1.37737
$51$	23.6435	0.0649168
$52$	−707.734	−1.88740
$53$	−140.348	−0.363742	−0.181871	−	0.983322i	$-0.558215\pi$
$53$	−140.348	−0.363742	−0.181871	+	0.983322i	$0.558215\pi$
$54$	125.448	0.316137
$55$	−166.755	−0.408821
$56$	−366.332	−0.874164
$57$	151.787	0.352713
$58$	819.220	1.85464
$59$	−21.6994	−0.0478818	−0.0239409	−	0.999713i	$-0.507621\pi$
$59$	−21.6994	−0.0478818	−0.0239409	+	0.999713i	$0.507621\pi$
$60$	617.941	1.32960
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−438.796	−0.898825
$63$	126.998	0.253971
$64$	−802.994	−1.56835
$65$	789.613	1.50676
$66$	153.326	0.285956
$67$	50.3343	0.0917808	0.0458904	−	0.998946i	$-0.485387\pi$
$67$	50.3343	0.0917808	0.0458904	+	0.998946i	$0.485387\pi$
$68$	−107.086	−0.190971
$69$	661.043	1.15334
$70$	993.893	1.69704
$71$	−569.991	−0.952753	−0.476377	−	0.879241i	$-0.658050\pi$
$71$	−569.991	−0.952753	−0.476377	+	0.879241i	$0.658050\pi$
$72$	−233.649	−0.382442
$73$	−9.87488	−0.0158324	−0.00791622	−	0.999969i	$-0.502520\pi$
$73$	−9.87488	−0.0158324	−0.00791622	+	0.999969i	$0.502520\pi$
$74$	−300.957	−0.472778
$75$	−314.432	−0.484099
$76$	−687.469	−1.03761
$77$	155.219	0.229726
$78$	−726.026	−1.05393
$79$	−365.679	−0.520787	−0.260393	−	0.965503i	$-0.583852\pi$
$79$	−365.679	−0.520787	−0.260393	+	0.965503i	$0.583852\pi$
$80$	−180.714	−0.252556
$81$	81.0000	0.111111
$82$	319.789	0.430668
$83$	−1430.32	−1.89154	−0.945771	−	0.324835i	$-0.894691\pi$
$83$	−1430.32	−1.89154	−0.945771	+	0.324835i	$0.894691\pi$
$84$	−575.195	−0.747130
$85$	119.475	0.152457
$86$	−1469.19	−1.84217
$87$	528.957	0.651841
$88$	−285.571	−0.345932
$89$	595.602	0.709367	0.354683	−	0.934986i	$-0.384589\pi$
$89$	595.602	0.709367	0.354683	+	0.934986i	$0.384589\pi$
$90$	633.912	0.742447
$91$	−734.992	−0.846682
$92$	−2993.98	−3.39287
$93$	−283.323	−0.315906
$94$	−376.316	−0.412915
$95$	767.003	0.828346
$96$	−456.903	−0.485755
$97$	−1444.56	−1.51209	−0.756045	−	0.654520i	$-0.772871\pi$
$97$	−1444.56	−1.51209	−0.756045	+	0.654520i	$0.772871\pi$
$98$	668.519	0.689088
$99$	99.0000	0.100504
$100$	1424.12	1.42412
$101$	−1727.80	−1.70221	−0.851104	−	0.524998i	$-0.824066\pi$
$101$	−1727.80	−1.70221	−0.851104	+	0.524998i	$0.824066\pi$
$102$	−109.853	−0.106638
$103$	1449.08	1.38624	0.693119	−	0.720823i	$-0.256236\pi$
$103$	1449.08	1.38624	0.693119	+	0.720823i	$0.256236\pi$
$104$	1352.23	1.27497
$105$	641.740	0.596452
$106$	652.092	0.597517
$107$	−771.055	−0.696642	−0.348321	−	0.937375i	$-0.613248\pi$
$107$	−771.055	−0.696642	−0.348321	+	0.937375i	$0.613248\pi$
$108$	−366.863	−0.326865
$109$	−200.176	−0.175902	−0.0879512	−	0.996125i	$-0.528032\pi$
$109$	−200.176	−0.175902	−0.0879512	+	0.996125i	$0.528032\pi$
$110$	774.781	0.671568
$111$	−194.323	−0.166165
$112$	168.213	0.141917
$113$	−466.485	−0.388347	−0.194174	−	0.980967i	$-0.562203\pi$
$113$	−466.485	−0.388347	−0.194174	+	0.980967i	$0.562203\pi$
$114$	−705.237	−0.579399
$115$	3340.36	2.70861
$116$	−2395.74	−1.91758
$117$	−468.783	−0.370419
$118$	100.821	0.0786551
$119$	−111.210	−0.0856690
$120$	−1180.67	−0.898165
$121$	121.000	0.0909091
$122$	−283.421	−0.210325
$123$	206.482	0.151365
$124$	1283.22	0.929329
$125$	306.062	0.219000
$126$	−590.061	−0.417197
$127$	2708.38	1.89236	0.946180	−	0.323640i	$-0.104907\pi$
$127$	2708.38	1.89236	0.946180	+	0.323640i	$0.104907\pi$
$128$	2512.49	1.73496
$129$	−948.631	−0.647460
$130$	−3668.73	−2.47515
$131$	−1320.86	−0.880948	−0.440474	−	0.897765i	$-0.645190\pi$
$131$	−1320.86	−0.880948	−0.440474	+	0.897765i	$0.645190\pi$
$132$	−448.389	−0.295661
$133$	−713.946	−0.465466
$134$	−233.865	−0.150768
$135$	409.307	0.260944
$136$	204.603	0.129004
$137$	−2977.86	−1.85705	−0.928525	−	0.371269i	$-0.878923\pi$
$137$	−2977.86	−1.85705	−0.928525	+	0.371269i	$0.878923\pi$
$138$	−3071.36	−1.89458
$139$	−1169.21	−0.713460	−0.356730	−	0.934208i	$-0.616108\pi$
$139$	−1169.21	−0.713460	−0.356730	+	0.934208i	$0.616108\pi$
$140$	−2906.56	−1.75463
$141$	−242.981	−0.145125
$142$	2648.31	1.56508
$143$	−572.957	−0.335056
$144$	107.288	0.0620878
$145$	2672.91	1.53085
$146$	45.8811	0.0260078
$147$	431.652	0.242191
$148$	880.125	0.488823
$149$	−284.010	−0.156154	−0.0780772	−	0.996947i	$-0.524878\pi$
$149$	−284.010	−0.156154	−0.0780772	+	0.996947i	$0.524878\pi$
$150$	1460.92	0.795226
$151$	−2172.62	−1.17089	−0.585447	−	0.810711i	$-0.699081\pi$
$151$	−2172.62	−1.17089	−0.585447	+	0.810711i	$0.699081\pi$
$152$	1313.51	0.700920
$153$	−70.9306	−0.0374797
$154$	−721.186	−0.377369
$155$	−1431.68	−0.741906
$156$	2123.20	1.08969
$157$	−1234.54	−0.627562	−0.313781	−	0.949495i	$-0.601596\pi$
$157$	−1234.54	−0.627562	−0.313781	+	0.949495i	$0.601596\pi$
$158$	1699.03	0.855493
$159$	421.045	0.210007
$160$	−2308.81	−1.14080
$161$	−3109.29	−1.52203
$162$	−376.345	−0.182522
$163$	2141.25	1.02893	0.514464	−	0.857512i	$-0.327991\pi$
$163$	2141.25	1.02893	0.514464	+	0.857512i	$0.327991\pi$
$164$	−935.195	−0.445283
$165$	500.264	0.236033
$166$	6645.61	3.10722
$167$	−3204.89	−1.48504	−0.742520	−	0.669824i	$-0.766370\pi$
$167$	−3204.89	−1.48504	−0.742520	+	0.669824i	$0.766370\pi$
$168$	1099.00	0.504699
$169$	516.055	0.234891
$170$	−555.108	−0.250440
$171$	−455.360	−0.203639
$172$	4296.52	1.90469
$173$	2592.11	1.13916	0.569579	−	0.821937i	$-0.307106\pi$
$173$	2592.11	1.13916	0.569579	+	0.821937i	$0.307106\pi$
$174$	−2457.66	−1.07077
$175$	1478.97	0.638853
$176$	131.129	0.0561605
$177$	65.0983	0.0276446
$178$	−2767.31	−1.16527
$179$	140.843	0.0588108	0.0294054	−	0.999568i	$-0.490639\pi$
$179$	140.843	0.0588108	0.0294054	+	0.999568i	$0.490639\pi$
$180$	−1853.82	−0.767643
$181$	2594.04	1.06527	0.532634	−	0.846346i	$-0.321202\pi$
$181$	2594.04	1.06527	0.532634	+	0.846346i	$0.321202\pi$
$182$	3414.95	1.39084
$183$	−183.000	−0.0739221
$184$	5720.45	2.29194
$185$	−981.948	−0.390239
$186$	1316.39	0.518937
$187$	−86.6929	−0.0339017
$188$	1100.50	0.426928
$189$	−380.993	−0.146630
$190$	−3563.68	−1.36072
$191$	−1826.74	−0.692034	−0.346017	−	0.938228i	$-0.612466\pi$
$191$	−1826.74	−0.692034	−0.346017	+	0.938228i	$0.612466\pi$
$192$	2408.98	0.905486
$193$	−3097.96	−1.15542	−0.577709	−	0.816242i	$-0.696053\pi$
$193$	−3097.96	−1.15542	−0.577709	+	0.816242i	$0.696053\pi$
$194$	6711.76	2.48390
$195$	−2368.84	−0.869929
$196$	−1955.03	−0.712474
$197$	4146.25	1.49953	0.749767	−	0.661702i	$-0.230166\pi$
$197$	4146.25	1.49953	0.749767	+	0.661702i	$0.230166\pi$
$198$	−459.978	−0.165097
$199$	−3943.91	−1.40491	−0.702453	−	0.711730i	$-0.747912\pi$
$199$	−3943.91	−1.40491	−0.702453	+	0.711730i	$0.747912\pi$
$200$	−2720.99	−0.962015
$201$	−151.003	−0.0529897
$202$	8027.79	2.79621
$203$	−2488.01	−0.860217
$204$	321.257	0.110257
$205$	1043.39	0.355480
$206$	−6732.79	−2.27716
$207$	−1983.13	−0.665879
$208$	−620.921	−0.206986
$209$	−556.551	−0.184198
$210$	−2981.68	−0.979788
$211$	−629.657	−0.205438	−0.102719	−	0.994710i	$-0.532754\pi$
$211$	−629.657	−0.205438	−0.102719	+	0.994710i	$0.532754\pi$
$212$	−1906.99	−0.617795
$213$	1709.97	0.550072
$214$	3582.51	1.14437
$215$	−4793.59	−1.52056
$216$	700.948	0.220803
$217$	1332.64	0.416893
$218$	930.064	0.288954
$219$	29.6246	0.00914086
$220$	−2265.78	−0.694359
$221$	410.507	0.124949
$222$	902.872	0.272959
$223$	−4651.21	−1.39672	−0.698360	−	0.715747i	$-0.746086\pi$
$223$	−4651.21	−1.39672	−0.698360	+	0.715747i	$0.746086\pi$
$224$	2149.10	0.641039
$225$	943.295	0.279495
$226$	2167.40	0.637936
$227$	−506.977	−0.148235	−0.0741173	−	0.997250i	$-0.523614\pi$
$227$	−506.977	−0.148235	−0.0741173	+	0.997250i	$0.523614\pi$
$228$	2062.41	0.599062
$229$	1576.14	0.454822	0.227411	−	0.973799i	$-0.426974\pi$
$229$	1576.14	0.454822	0.227411	+	0.973799i	$0.426974\pi$
$230$	−15520.1	−4.44942
$231$	−465.658	−0.132632
$232$	4577.42	1.29536
$233$	−3508.16	−0.986384	−0.493192	−	0.869920i	$-0.664170\pi$
$233$	−3508.16	−0.986384	−0.493192	+	0.869920i	$0.664170\pi$
$234$	2178.08	0.608485
$235$	−1227.82	−0.340827
$236$	−294.842	−0.0813244
$237$	1097.04	0.300676
$238$	516.708	0.140728
$239$	−2727.16	−0.738098	−0.369049	−	0.929410i	$-0.620317\pi$
$239$	−2727.16	−0.738098	−0.369049	+	0.929410i	$0.620317\pi$
$240$	542.143	0.145813
$241$	−5489.96	−1.46738	−0.733692	−	0.679483i	$-0.762204\pi$
$241$	−5489.96	−1.46738	−0.733692	+	0.679483i	$0.762204\pi$
$242$	−562.195	−0.149336
$243$	−243.000	−0.0641500
$244$	828.840	0.217463
$245$	2181.21	0.568785
$246$	−959.366	−0.248646
$247$	2635.37	0.678885
$248$	−2451.79	−0.627777
$249$	4290.96	1.09208
$250$	−1422.04	−0.359750
$251$	−517.258	−0.130076	−0.0650379	−	0.997883i	$-0.520717\pi$
$251$	−517.258	−0.130076	−0.0650379	+	0.997883i	$0.520717\pi$
$252$	1725.58	0.431356
$253$	−2423.82	−0.602310
$254$	−12583.8	−3.10857
$255$	−358.424	−0.0880211
$256$	−5249.69	−1.28166
$257$	3797.76	0.921781	0.460890	−	0.887457i	$-0.347530\pi$
$257$	3797.76	0.921781	0.460890	+	0.887457i	$0.347530\pi$
$258$	4407.57	1.06358
$259$	914.022	0.219284
$260$	10728.9	2.55915
$261$	−1586.87	−0.376340
$262$	6137.04	1.44713
$263$	−1215.76	−0.285045	−0.142523	−	0.989792i	$-0.545521\pi$
$263$	−1215.76	−0.285045	−0.142523	+	0.989792i	$0.545521\pi$
$264$	856.714	0.199724
$265$	2127.61	0.493200
$266$	3317.16	0.764618
$267$	−1786.80	−0.409553
$268$	683.919	0.155884
$269$	8214.46	1.86188	0.930938	−	0.365177i	$-0.118991\pi$
$269$	8214.46	1.86188	0.930938	+	0.365177i	$0.118991\pi$
$270$	−1901.74	−0.428652
$271$	−5778.63	−1.29530	−0.647651	−	0.761937i	$-0.724248\pi$
$271$	−5778.63	−1.29530	−0.647651	+	0.761937i	$0.724248\pi$
$272$	−93.9503	−0.0209433
$273$	2204.97	0.488832
$274$	13835.9	3.05057
$275$	1152.92	0.252813
$276$	8981.94	1.95887
$277$	4876.60	1.05779	0.528893	−	0.848689i	$-0.322607\pi$
$277$	4876.60	1.05779	0.528893	+	0.848689i	$0.322607\pi$
$278$	5432.42	1.17200
$279$	849.970	0.182388
$280$	5553.41	1.18529
$281$	−2263.07	−0.480438	−0.240219	−	0.970719i	$-0.577219\pi$
$281$	−2263.07	−0.480438	−0.240219	+	0.970719i	$0.577219\pi$
$282$	1128.95	0.238397
$283$	−403.076	−0.0846657	−0.0423328	−	0.999104i	$-0.513479\pi$
$283$	−403.076	−0.0846657	−0.0423328	+	0.999104i	$0.513479\pi$
$284$	−7744.77	−1.61820
$285$	−2301.01	−0.478246
$286$	2662.09	0.550395
$287$	−971.213	−0.199752
$288$	1370.71	0.280451
$289$	−4850.89	−0.987357
$290$	−12419.0	−2.51471
$291$	4333.67	0.873005
$292$	−134.175	−0.0268905
$293$	−3957.27	−0.789031	−0.394515	−	0.918889i	$-0.629088\pi$
$293$	−3957.27	−0.789031	−0.394515	+	0.918889i	$0.629088\pi$
$294$	−2005.56	−0.397845
$295$	328.953	0.0649233
$296$	−1681.61	−0.330208
$297$	−297.000	−0.0580259
$298$	1319.58	0.256514
$299$	11477.2	2.21989
$300$	−4272.35	−0.822214
$301$	4462.00	0.854436
$302$	10094.5	1.92342
$303$	5183.41	0.982770
$304$	−603.142	−0.113791
$305$	−924.730	−0.173606
$306$	329.560	0.0615677
$307$	9340.08	1.73637	0.868186	−	0.496239i	$-0.165286\pi$
$307$	9340.08	1.73637	0.868186	+	0.496239i	$0.165286\pi$
$308$	2109.05	0.390176
$309$	−4347.25	−0.800345
$310$	6651.93	1.21872
$311$	1649.22	0.300702	0.150351	−	0.988633i	$-0.451960\pi$
$311$	1649.22	0.300702	0.150351	+	0.988633i	$0.451960\pi$
$312$	−4056.70	−0.736106
$313$	−1248.05	−0.225380	−0.112690	−	0.993630i	$-0.535947\pi$
$313$	−1248.05	−0.225380	−0.112690	+	0.993630i	$0.535947\pi$
$314$	5735.98	1.03089
$315$	−1925.22	−0.344362
$316$	−4968.68	−0.884526
$317$	−5954.80	−1.05506	−0.527531	−	0.849536i	$-0.676882\pi$
$317$	−5954.80	−1.05506	−0.527531	+	0.849536i	$0.676882\pi$
$318$	−1956.28	−0.344976
$319$	−1939.51	−0.340413
$320$	12173.0	2.12653
$321$	2313.17	0.402207
$322$	14446.5	2.50022
$323$	398.752	0.0686909
$324$	1100.59	0.188716
$325$	−5459.27	−0.931771
$326$	−9948.74	−1.69021
$327$	600.527	0.101557
$328$	1786.83	0.300796
$329$	1142.89	0.191518
$330$	−2324.34	−0.387730
$331$	−6932.58	−1.15121	−0.575603	−	0.817730i	$-0.695232\pi$
$331$	−6932.58	−1.15121	−0.575603	+	0.817730i	$0.695232\pi$
$332$	−19434.5	−3.21267
$333$	582.970	0.0959355
$334$	14890.7	2.43947
$335$	−763.043	−0.124446
$336$	−504.640	−0.0819356
$337$	−3850.81	−0.622454	−0.311227	−	0.950336i	$-0.600740\pi$
$337$	−3850.81	−0.622454	−0.311227	+	0.950336i	$0.600740\pi$
$338$	−2397.71	−0.385853
$339$	1399.46	0.224212
$340$	1623.37	0.258939
$341$	1038.85	0.164977
$342$	2115.71	0.334516
$343$	−6870.35	−1.08153
$344$	−8209.15	−1.28665
$345$	−10021.1	−1.56382
$346$	−12043.5	−1.87129
$347$	5226.18	0.808518	0.404259	−	0.914644i	$-0.367529\pi$
$347$	5226.18	0.808518	0.404259	+	0.914644i	$0.367529\pi$
$348$	7187.22	1.10711
$349$	−1836.96	−0.281749	−0.140874	−	0.990027i	$-0.544991\pi$
$349$	−1836.96	−0.281749	−0.140874	+	0.990027i	$0.544991\pi$
$350$	−6871.63	−1.04944
$351$	1406.35	0.213861
$352$	1675.31	0.253677
$353$	7037.53	1.06110	0.530552	−	0.847652i	$-0.321985\pi$
$353$	7037.53	1.06110	0.530552	+	0.847652i	$0.321985\pi$
$354$	−302.462	−0.0454115
$355$	8640.78	1.29184
$356$	8092.76	1.20482
$357$	333.630	0.0494610
$358$	−654.392	−0.0966081
$359$	4474.86	0.657867	0.328934	−	0.944353i	$-0.393311\pi$
$359$	4474.86	0.657867	0.328934	+	0.944353i	$0.393311\pi$
$360$	3542.01	0.518556
$361$	−4299.09	−0.626781
$362$	−12052.5	−1.74991
$363$	−363.000	−0.0524864
$364$	−9986.73	−1.43804
$365$	149.698	0.0214673
$366$	850.262	0.121431
$367$	−12680.2	−1.80355	−0.901775	−	0.432206i	$-0.857735\pi$
$367$	−12680.2	−1.80355	−0.901775	+	0.432206i	$0.857735\pi$
$368$	−2626.73	−0.372086
$369$	−619.447	−0.0873906
$370$	4562.36	0.641043
$371$	−1980.43	−0.277140
$372$	−3849.67	−0.536548
$373$	6523.10	0.905504	0.452752	−	0.891636i	$-0.350442\pi$
$373$	6523.10	0.905504	0.452752	+	0.891636i	$0.350442\pi$
$374$	402.796	0.0556901
$375$	−918.187	−0.126440
$376$	−2102.68	−0.288397
$377$	9183.93	1.25463
$378$	1770.18	0.240869
$379$	8167.79	1.10700	0.553498	−	0.832851i	$-0.313293\pi$
$379$	8167.79	1.10700	0.553498	+	0.832851i	$0.313293\pi$
$380$	10421.7	1.40690
$381$	−8125.14	−1.09255
$382$	8487.49	1.13680
$383$	4170.56	0.556411	0.278206	−	0.960522i	$-0.410260\pi$
$383$	4170.56	0.556411	0.278206	+	0.960522i	$0.410260\pi$
$384$	−7537.48	−1.00168
$385$	−2353.05	−0.311487
$386$	14393.9	1.89800
$387$	2845.89	0.373811
$388$	−19628.0	−2.56820
$389$	1955.08	0.254824	0.127412	−	0.991850i	$-0.459333\pi$
$389$	1955.08	0.254824	0.127412	+	0.991850i	$0.459333\pi$
$390$	11006.2	1.42903
$391$	1736.60	0.224613
$392$	3735.38	0.481288
$393$	3962.58	0.508616
$394$	−19264.5	−2.46327
$395$	5543.52	0.706138
$396$	1345.17	0.170700
$397$	11771.0	1.48808	0.744040	−	0.668135i	$-0.232907\pi$
$397$	11771.0	1.48808	0.744040	+	0.668135i	$0.232907\pi$
$398$	18324.3	2.30783
$399$	2141.84	0.268737
$400$	1249.43	0.156179
$401$	9933.15	1.23700	0.618501	−	0.785784i	$-0.287740\pi$
$401$	9933.15	1.23700	0.618501	+	0.785784i	$0.287740\pi$
$402$	701.596	0.0870458
$403$	−4919.15	−0.608041
$404$	−23476.6	−2.89110
$405$	−1227.92	−0.150656
$406$	11559.9	1.41307
$407$	712.518	0.0867770
$408$	−613.810	−0.0744807
$409$	2420.07	0.292579	0.146290	−	0.989242i	$-0.453267\pi$
$409$	2420.07	0.292579	0.146290	+	0.989242i	$0.453267\pi$
$410$	−4847.84	−0.583945
$411$	8933.59	1.07217
$412$	19689.5	2.35444
$413$	−306.197	−0.0364818
$414$	9214.09	1.09383
$415$	21682.9	2.56475
$416$	−7932.91	−0.934959
$417$	3507.62	0.411916
$418$	2585.87	0.302581
$419$	12571.8	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$419$	12571.8	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$420$	8719.67	1.01304
$421$	−6219.36	−0.719984	−0.359992	−	0.932955i	$-0.617221\pi$
$421$	−6219.36	−0.719984	−0.359992	+	0.932955i	$0.617221\pi$
$422$	2925.54	0.337472
$423$	728.943	0.0837882
$424$	3643.59	0.417331
$425$	−826.030	−0.0942785
$426$	−7944.94	−0.903600
$427$	860.762	0.0975531
$428$	−10476.7	−1.18321
$429$	1718.87	0.193445
$430$	22272.2	2.49781
$431$	−3702.08	−0.413742	−0.206871	−	0.978368i	$-0.566328\pi$
$431$	−3702.08	−0.413742	−0.206871	+	0.978368i	$0.566328\pi$
$432$	−321.863	−0.0358464
$433$	14047.4	1.55906	0.779531	−	0.626364i	$-0.215458\pi$
$433$	14047.4	1.55906	0.779531	+	0.626364i	$0.215458\pi$
$434$	−6191.78	−0.684828
$435$	−8018.72	−0.883835
$436$	−2719.89	−0.298760
$437$	11148.6	1.22039
$438$	−137.643	−0.0150156
$439$	−1392.72	−0.151414	−0.0757070	−	0.997130i	$-0.524121\pi$
$439$	−1392.72	−0.151414	−0.0757070	+	0.997130i	$0.524121\pi$
$440$	4329.12	0.469051
$441$	−1294.96	−0.139829
$442$	−1907.31	−0.205252
$443$	−13413.4	−1.43858	−0.719290	−	0.694710i	$-0.755533\pi$
$443$	−13413.4	−1.43858	−0.719290	+	0.694710i	$0.755533\pi$
$444$	−2640.37	−0.282222
$445$	−9029.02	−0.961835
$446$	21610.7	2.29438
$447$	852.030	0.0901558
$448$	−11330.9	−1.19495
$449$	1434.47	0.150773	0.0753863	−	0.997154i	$-0.475981\pi$
$449$	1434.47	0.150773	0.0753863	+	0.997154i	$0.475981\pi$
$450$	−4382.77	−0.459124
$451$	−757.102	−0.0790477
$452$	−6338.39	−0.659585
$453$	6517.85	0.676016
$454$	2355.54	0.243504
$455$	11142.1	1.14802
$456$	−3940.54	−0.404677
$457$	−949.223	−0.0971615	−0.0485807	−	0.998819i	$-0.515470\pi$
$457$	−949.223	−0.0971615	−0.0485807	+	0.998819i	$0.515470\pi$
$458$	−7323.13	−0.747134
$459$	212.792	0.0216389
$460$	45387.2	4.60042
$461$	9179.14	0.927365	0.463683	−	0.886001i	$-0.346528\pi$
$461$	9179.14	0.927365	0.463683	+	0.886001i	$0.346528\pi$
$462$	2163.56	0.217874
$463$	12561.4	1.26086	0.630428	−	0.776248i	$-0.282880\pi$
$463$	12561.4	1.26086	0.630428	+	0.776248i	$0.282880\pi$
$464$	−2101.87	−0.210295
$465$	4295.04	0.428339
$466$	16299.8	1.62033
$467$	11981.9	1.18727	0.593636	−	0.804734i	$-0.297692\pi$
$467$	11981.9	1.18727	0.593636	+	0.804734i	$0.297692\pi$
$468$	−6369.61	−0.629135
$469$	710.260	0.0699291
$470$	5704.76	0.559874
$471$	3703.63	0.362323
$472$	563.340	0.0549360
$473$	3478.31	0.338125
$474$	−5097.10	−0.493919
$475$	−5302.94	−0.512244
$476$	−1511.07	−0.145504
$477$	−1263.13	−0.121247
$478$	12671.0	1.21247
$479$	7208.81	0.687639	0.343819	−	0.939036i	$-0.388279\pi$
$479$	7208.81	0.687639	0.343819	+	0.939036i	$0.388279\pi$
$480$	6926.43	0.658639
$481$	−3373.90	−0.319827
$482$	25507.7	2.41046
$483$	9327.87	0.878743
$484$	1644.09	0.154404
$485$	21898.8	2.05025
$486$	1129.04	0.105379
$487$	−12089.9	−1.12494	−0.562469	−	0.826819i	$-0.690148\pi$
$487$	−12089.9	−1.12494	−0.562469	+	0.826819i	$0.690148\pi$
$488$	−1583.62	−0.146900
$489$	−6423.74	−0.594052
$490$	−10134.4	−0.934340
$491$	47.1953	0.00433787	0.00216893	−	0.999998i	$-0.499310\pi$
$491$	47.1953	0.00433787	0.00216893	+	0.999998i	$0.499310\pi$
$492$	2805.59	0.257084
$493$	1389.60	0.126946
$494$	−12244.6	−1.11520
$495$	−1500.79	−0.136274
$496$	1125.82	0.101917
$497$	−8043.05	−0.725916
$498$	−19936.8	−1.79396
$499$	−1508.60	−0.135340	−0.0676698	−	0.997708i	$-0.521556\pi$
$499$	−1508.60	−0.135340	−0.0676698	+	0.997708i	$0.521556\pi$
$500$	4158.63	0.371959
$501$	9614.67	0.857389
$502$	2403.31	0.213675
$503$	2086.97	0.184997	0.0924984	−	0.995713i	$-0.470515\pi$
$503$	2086.97	0.184997	0.0924984	+	0.995713i	$0.470515\pi$
$504$	−3296.99	−0.291388
$505$	26192.7	2.30804
$506$	11261.7	0.989411
$507$	−1548.16	−0.135614
$508$	36800.2	3.21406
$509$	−16421.8	−1.43003	−0.715015	−	0.699109i	$-0.753580\pi$
$509$	−16421.8	−1.43003	−0.715015	+	0.699109i	$0.753580\pi$
$510$	1665.32	0.144592
$511$	−139.343	−0.0120630
$512$	4291.38	0.370418
$513$	1366.08	0.117571
$514$	−17645.3	−1.51420
$515$	−21967.4	−1.87961
$516$	−12889.6	−1.09967
$517$	890.930	0.0757893
$518$	−4246.76	−0.360216
$519$	−7776.32	−0.657693
$520$	−20499.2	−1.72875
$521$	2353.01	0.197864	0.0989322	−	0.995094i	$-0.468457\pi$
$521$	2353.01	0.197864	0.0989322	+	0.995094i	$0.468457\pi$
$522$	7372.98	0.618212
$523$	11423.8	0.955118	0.477559	−	0.878600i	$-0.341522\pi$
$523$	11423.8	0.955118	0.477559	+	0.878600i	$0.341522\pi$
$524$	−17947.3	−1.49624
$525$	−4436.90	−0.368842
$526$	5648.71	0.468242
$527$	−744.307	−0.0615228
$528$	−393.388	−0.0324243
$529$	36386.0	2.99055
$530$	−9885.39	−0.810177
$531$	−195.295	−0.0159606
$532$	−9700.76	−0.790567
$533$	3585.01	0.291340
$534$	8301.92	0.672770
$535$	11688.8	0.944582
$536$	−1306.73	−0.105303
$537$	−422.530	−0.0339544
$538$	−38166.4	−3.05849
$539$	−1582.72	−0.126480
$540$	5561.47	0.443199
$541$	1887.25	0.149980	0.0749901	−	0.997184i	$-0.476107\pi$
$541$	1887.25	0.149980	0.0749901	+	0.997184i	$0.476107\pi$
$542$	26848.9	2.12778
$543$	−7782.12	−0.615033
$544$	−1200.31	−0.0946010
$545$	3034.56	0.238507
$546$	−10244.8	−0.803001
$547$	16353.1	1.27826	0.639129	−	0.769100i	$-0.279295\pi$
$547$	16353.1	1.27826	0.639129	+	0.769100i	$0.279295\pi$
$548$	−40461.8	−3.15409
$549$	549.000	0.0426790
$550$	−5356.72	−0.415293
$551$	8920.95	0.689737
$552$	−17161.3	−1.32325
$553$	−5160.05	−0.396795
$554$	−22657.9	−1.73762
$555$	2945.84	0.225305
$556$	−15886.7	−1.21177
$557$	3049.32	0.231964	0.115982	−	0.993251i	$-0.462999\pi$
$557$	3049.32	0.231964	0.115982	+	0.993251i	$0.462999\pi$
$558$	−3949.16	−0.299608
$559$	−16470.4	−1.24620
$560$	−2550.03	−0.192426
$561$	260.079	0.0195731
$562$	10514.7	0.789213
$563$	22013.2	1.64786	0.823931	−	0.566691i	$-0.191777\pi$
$563$	22013.2	1.64786	0.823931	+	0.566691i	$0.191777\pi$
$564$	−3301.51	−0.246487
$565$	7071.68	0.526563
$566$	1872.79	0.139080
$567$	1142.98	0.0846571
$568$	14797.5	1.09312
$569$	10172.6	0.749489	0.374745	−	0.927128i	$-0.377730\pi$
$569$	10172.6	0.749489	0.374745	+	0.927128i	$0.377730\pi$
$570$	10691.0	0.785611
$571$	−25684.6	−1.88243	−0.941215	−	0.337809i	$-0.890314\pi$
$571$	−25684.6	−1.88243	−0.941215	+	0.337809i	$0.890314\pi$
$572$	−7785.07	−0.569074
$573$	5480.23	0.399546
$574$	4512.49	0.328132
$575$	−23094.7	−1.67499
$576$	−7226.95	−0.522783
$577$	12649.6	0.912668	0.456334	−	0.889808i	$-0.349162\pi$
$577$	12649.6	0.912668	0.456334	+	0.889808i	$0.349162\pi$
$578$	22538.4	1.62193
$579$	9293.87	0.667081
$580$	36318.2	2.60006
$581$	−20183.0	−1.44119
$582$	−20135.3	−1.43408
$583$	−1543.83	−0.109672
$584$	256.362	0.0181650
$585$	7106.52	0.502253
$586$	18386.4	1.29614
$587$	−23086.0	−1.62327	−0.811637	−	0.584162i	$-0.801423\pi$
$587$	−23086.0	−1.62327	−0.811637	+	0.584162i	$0.801423\pi$
$588$	5865.09	0.411347
$589$	−4778.30	−0.334272
$590$	−1528.39	−0.106649
$591$	−12438.8	−0.865756
$592$	772.166	0.0536078
$593$	23604.4	1.63460	0.817298	−	0.576215i	$-0.195471\pi$
$593$	23604.4	1.63460	0.817298	+	0.576215i	$0.195471\pi$
$594$	1379.93	0.0953187
$595$	1685.89	0.116159
$596$	−3859.00	−0.265219
$597$	11831.7	0.811123
$598$	−53326.0	−3.64659
$599$	−17707.1	−1.20783	−0.603916	−	0.797048i	$-0.706394\pi$
$599$	−17707.1	−1.20783	−0.603916	+	0.797048i	$0.706394\pi$
$600$	8162.97	0.555420
$601$	7508.66	0.509625	0.254813	−	0.966990i	$-0.417986\pi$
$601$	7508.66	0.509625	0.254813	+	0.966990i	$0.417986\pi$
$602$	−20731.5	−1.40358
$603$	453.009	0.0305936
$604$	−29520.5	−1.98870
$605$	−1834.30	−0.123264
$606$	−24083.4	−1.61439
$607$	−25084.7	−1.67736	−0.838680	−	0.544625i	$-0.816672\pi$
$607$	−25084.7	−1.67736	−0.838680	+	0.544625i	$0.816672\pi$
$608$	−7705.75	−0.513996
$609$	7464.03	0.496647
$610$	4296.52	0.285182
$611$	−4218.72	−0.279331
$612$	−963.772	−0.0636571
$613$	−11291.9	−0.744005	−0.372002	−	0.928232i	$-0.621329\pi$
$613$	−11291.9	−0.744005	−0.372002	+	0.928232i	$0.621329\pi$
$614$	−43396.2	−2.85233
$615$	−3130.17	−0.205237
$616$	−4029.65	−0.263570
$617$	−16208.4	−1.05758	−0.528790	−	0.848753i	$-0.677354\pi$
$617$	−16208.4	−1.05758	−0.528790	+	0.848753i	$0.677354\pi$
$618$	20198.4	1.31472
$619$	−3721.30	−0.241635	−0.120817	−	0.992675i	$-0.538552\pi$
$619$	−3721.30	−0.241635	−0.120817	+	0.992675i	$0.538552\pi$
$620$	−19453.0	−1.26008
$621$	5949.38	0.384445
$622$	−7662.65	−0.493962
$623$	8404.44	0.540477
$624$	1862.76	0.119504
$625$	−17741.1	−1.13543
$626$	5798.74	0.370231
$627$	1669.65	0.106347
$628$	−16774.4	−1.06588
$629$	−510.498	−0.0323607
$630$	8945.04	0.565681
$631$	−13484.8	−0.850745	−0.425373	−	0.905018i	$-0.639857\pi$
$631$	−13484.8	−0.850745	−0.425373	+	0.905018i	$0.639857\pi$
$632$	9493.41	0.597512
$633$	1888.97	0.118610
$634$	27667.4	1.73314
$635$	−41057.7	−2.56587
$636$	5720.96	0.356684
$637$	7494.48	0.466157
$638$	9011.42	0.559194
$639$	−5129.92	−0.317584
$640$	−38088.2	−2.35245
$641$	−19058.4	−1.17435	−0.587176	−	0.809459i	$-0.699760\pi$
$641$	−19058.4	−1.17435	−0.587176	+	0.809459i	$0.699760\pi$
$642$	−10747.5	−0.660702
$643$	−12311.9	−0.755104	−0.377552	−	0.925988i	$-0.623234\pi$
$643$	−12311.9	−0.755104	−0.377552	+	0.925988i	$0.623234\pi$
$644$	−42247.6	−2.58508
$645$	14380.8	0.877895
$646$	−1852.70	−0.112838
$647$	88.1931	0.00535893	0.00267946	−	0.999996i	$-0.499147\pi$
$647$	88.1931	0.00535893	0.00267946	+	0.999996i	$0.499147\pi$
$648$	−2102.84	−0.127481
$649$	−238.694	−0.0144369
$650$	25365.1	1.53061
$651$	−3997.93	−0.240693
$652$	29094.3	1.74758
$653$	11916.9	0.714155	0.357077	−	0.934075i	$-0.383773\pi$
$653$	11916.9	0.714155	0.357077	+	0.934075i	$0.383773\pi$
$654$	−2790.19	−0.166827
$655$	20023.6	1.19448
$656$	−820.482	−0.0488330
$657$	−88.8739	−0.00527748
$658$	−5310.14	−0.314606
$659$	−15123.6	−0.893977	−0.446988	−	0.894540i	$-0.647503\pi$
$659$	−15123.6	−0.893977	−0.446988	+	0.894540i	$0.647503\pi$
$660$	6797.35	0.400889
$661$	10818.7	0.636609	0.318304	−	0.947989i	$-0.396887\pi$
$661$	10818.7	0.636609	0.318304	+	0.947989i	$0.396887\pi$
$662$	32210.4	1.89108
$663$	−1231.52	−0.0721392
$664$	37132.6	2.17022
$665$	10823.1	0.631128
$666$	−2708.62	−0.157593
$667$	38851.5	2.25537
$668$	−43546.5	−2.52226
$669$	13953.6	0.806396
$670$	3545.28	0.204427
$671$	671.000	0.0386046
$672$	−6447.29	−0.370104
$673$	−408.382	−0.0233908	−0.0116954	−	0.999932i	$-0.503723\pi$
$673$	−408.382	−0.0233908	−0.0116954	+	0.999932i	$0.503723\pi$
$674$	17891.8	1.02250
$675$	−2829.88	−0.161366
$676$	7011.91	0.398948
$677$	14925.3	0.847303	0.423652	−	0.905825i	$-0.360748\pi$
$677$	14925.3	0.847303	0.423652	+	0.905825i	$0.360748\pi$
$678$	−6502.21	−0.368312
$679$	−20383.9	−1.15208
$680$	−3101.69	−0.174918
$681$	1520.93	0.0855833
$682$	−4826.76	−0.271006
$683$	−3880.73	−0.217412	−0.108706	−	0.994074i	$-0.534671\pi$
$683$	−3880.73	−0.217412	−0.108706	+	0.994074i	$0.534671\pi$
$684$	−6187.22	−0.345869
$685$	45142.9	2.51799
$686$	31921.3	1.77662
$687$	−4728.42	−0.262592
$688$	3769.50	0.208882
$689$	7310.32	0.404211
$690$	46560.3	2.56887
$691$	−24832.6	−1.36712	−0.683558	−	0.729896i	$-0.739568\pi$
$691$	−24832.6	−1.36712	−0.683558	+	0.729896i	$0.739568\pi$
$692$	35220.3	1.93479
$693$	1396.97	0.0765753
$694$	−24282.1	−1.32815
$695$	17724.6	0.967385
$696$	−13732.3	−0.747874
$697$	542.441	0.0294784
$698$	8534.96	0.462827
$699$	10524.5	0.569489
$700$	20095.5	1.08505
$701$	1245.88	0.0671274	0.0335637	−	0.999437i	$-0.489314\pi$
$701$	1245.88	0.0671274	0.0335637	+	0.999437i	$0.489314\pi$
$702$	−6534.23	−0.351309
$703$	−3277.29	−0.175826
$704$	−8832.94	−0.472875
$705$	3683.47	0.196777
$706$	−32698.0	−1.74307
$707$	−24380.8	−1.29694
$708$	884.525	0.0469527
$709$	18029.1	0.955002	0.477501	−	0.878631i	$-0.341543\pi$
$709$	18029.1	0.955002	0.477501	+	0.878631i	$0.341543\pi$
$710$	−40147.1	−2.12210
$711$	−3291.11	−0.173596
$712$	−15462.4	−0.813875
$713$	−20809.9	−1.09304
$714$	−1550.13	−0.0812493
$715$	8685.74	0.454305
$716$	1913.72	0.0998867
$717$	8181.48	0.426141
$718$	−20791.3	−1.08067
$719$	−1888.34	−0.0979460	−0.0489730	−	0.998800i	$-0.515595\pi$
$719$	−1888.34	−0.0979460	−0.0489730	+	0.998800i	$0.515595\pi$
$720$	−1626.43	−0.0841852
$721$	20447.8	1.05619
$722$	19974.6	1.02961
$723$	16469.9	0.847194
$724$	35246.6	1.80930
$725$	−18480.1	−0.946667
$726$	1686.58	0.0862191
$727$	13600.3	0.693818	0.346909	−	0.937899i	$-0.387231\pi$
$727$	13600.3	0.693818	0.346909	+	0.937899i	$0.387231\pi$
$728$	19081.1	0.971420
$729$	729.000	0.0370370
$730$	−695.534	−0.0352642
$731$	−2492.11	−0.126093
$732$	−2486.52	−0.125552
$733$	13691.2	0.689899	0.344949	−	0.938621i	$-0.387896\pi$
$733$	13691.2	0.689899	0.344949	+	0.938621i	$0.387896\pi$
$734$	58915.4	2.96268
$735$	−6543.63	−0.328388
$736$	−33559.2	−1.68072
$737$	553.677	0.0276730
$738$	2878.10	0.143556
$739$	12997.3	0.646975	0.323487	−	0.946233i	$-0.395145\pi$
$739$	12997.3	0.646975	0.323487	+	0.946233i	$0.395145\pi$
$740$	−13342.3	−0.662798
$741$	−7906.11	−0.391954
$742$	9201.57	0.455256
$743$	−9883.52	−0.488010	−0.244005	−	0.969774i	$-0.578461\pi$
$743$	−9883.52	−0.488010	−0.244005	+	0.969774i	$0.578461\pi$
$744$	7355.37	0.362447
$745$	4305.45	0.211731
$746$	−30307.9	−1.48747
$747$	−12872.9	−0.630514
$748$	−1177.94	−0.0575800
$749$	−10880.2	−0.530782
$750$	4266.12	0.207702
$751$	30966.5	1.50464	0.752319	−	0.658799i	$-0.228935\pi$
$751$	30966.5	1.50464	0.752319	+	0.658799i	$0.228935\pi$
$752$	965.513	0.0468200
$753$	1551.77	0.0750994
$754$	−42670.7	−2.06098
$755$	32935.8	1.58762
$756$	−5176.75	−0.249043
$757$	−33073.4	−1.58795	−0.793973	−	0.607954i	$-0.791991\pi$
$757$	−33073.4	−1.58795	−0.793973	+	0.607954i	$0.791991\pi$
$758$	−37949.5	−1.81845
$759$	7271.47	0.347744
$760$	−19912.2	−0.950383
$761$	3511.60	0.167274	0.0836368	−	0.996496i	$-0.473346\pi$
$761$	3511.60	0.167274	0.0836368	+	0.996496i	$0.473346\pi$
$762$	37751.3	1.79473
$763$	−2824.65	−0.134022
$764$	−24820.9	−1.17538
$765$	1075.27	0.0508190
$766$	−19377.4	−0.914013
$767$	1130.26	0.0532089
$768$	15749.1	0.739969
$769$	16061.0	0.753153	0.376576	−	0.926386i	$-0.377101\pi$
$769$	16061.0	0.753153	0.376576	+	0.926386i	$0.377101\pi$
$770$	10932.8	0.511677
$771$	−11393.3	−0.532190
$772$	−42093.6	−1.96241
$773$	−41485.2	−1.93030	−0.965149	−	0.261702i	$-0.915716\pi$
$773$	−41485.2	−1.93030	−0.965149	+	0.261702i	$0.915716\pi$
$774$	−13222.7	−0.614057
$775$	9898.43	0.458790
$776$	37502.2	1.73486
$777$	−2742.07	−0.126604
$778$	−9083.79	−0.418598
$779$	3482.36	0.160165
$780$	−32186.7	−1.47752
$781$	−6269.90	−0.287266
$782$	−8068.65	−0.368970
$783$	4760.61	0.217280
$784$	−1715.22	−0.0781350
$785$	18715.1	0.850916
$786$	−18411.1	−0.835500
$787$	13764.6	0.623450	0.311725	−	0.950172i	$-0.399093\pi$
$787$	13764.6	0.623450	0.311725	+	0.950172i	$0.399093\pi$
$788$	56337.3	2.54687
$789$	3647.28	0.164571
$790$	−25756.5	−1.15997
$791$	−6582.50	−0.295887
$792$	−2570.14	−0.115311
$793$	−3177.31	−0.142282
$794$	−54690.7	−2.44446
$795$	−6382.83	−0.284749
$796$	−53588.0	−2.38615
$797$	−38287.3	−1.70164	−0.850819	−	0.525459i	$-0.823894\pi$
$797$	−38287.3	−1.70164	−0.850819	+	0.525459i	$0.823894\pi$
$798$	−9951.49	−0.441452
$799$	−638.325	−0.0282632
$800$	15962.8	0.705461
$801$	5360.41	0.236456
$802$	−46151.8	−2.03201
$803$	−108.624	−0.00477366
$804$	−2051.76	−0.0899999
$805$	47135.3	2.06373
$806$	22855.6	0.998825
$807$	−24643.4	−1.07495
$808$	44855.6	1.95299
$809$	22490.1	0.977391	0.488695	−	0.872454i	$-0.337473\pi$
$809$	22490.1	0.977391	0.488695	+	0.872454i	$0.337473\pi$
$810$	5705.21	0.247482
$811$	−7070.74	−0.306150	−0.153075	−	0.988215i	$-0.548918\pi$
$811$	−7070.74	−0.306150	−0.153075	+	0.988215i	$0.548918\pi$
$812$	−33805.9	−1.46103
$813$	17335.9	0.747843
$814$	−3310.53	−0.142548
$815$	−32460.2	−1.39513
$816$	281.851	0.0120916
$817$	−15998.8	−0.685102
$818$	−11244.2	−0.480618
$819$	−6614.92	−0.282227
$820$	14177.1	0.603763
$821$	30563.5	1.29924	0.649618	−	0.760260i	$-0.274929\pi$
$821$	30563.5	1.29924	0.649618	+	0.760260i	$0.274929\pi$
$822$	−41507.6	−1.76124
$823$	22853.9	0.967969	0.483984	−	0.875077i	$-0.339189\pi$
$823$	22853.9	0.967969	0.483984	+	0.875077i	$0.339189\pi$
$824$	−37619.7	−1.59047
$825$	−3458.75	−0.145961
$826$	1422.67	0.0599284
$827$	41852.6	1.75980	0.879902	−	0.475155i	$-0.157608\pi$
$827$	41852.6	1.75980	0.879902	+	0.475155i	$0.157608\pi$
$828$	−26945.8	−1.13096
$829$	−36868.4	−1.54462	−0.772310	−	0.635245i	$-0.780899\pi$
$829$	−36868.4	−1.54462	−0.772310	+	0.635245i	$0.780899\pi$
$830$	−100744.	−4.21311
$831$	−14629.8	−0.610713
$832$	41825.5	1.74284
$833$	1133.97	0.0471667
$834$	−16297.3	−0.676652
$835$	48584.5	2.01358
$836$	−7562.15	−0.312850
$837$	−2549.91	−0.105302
$838$	−58411.8	−2.40788
$839$	13010.6	0.535370	0.267685	−	0.963507i	$-0.413741\pi$
$839$	13010.6	0.535370	0.267685	+	0.963507i	$0.413741\pi$
$840$	−16660.2	−0.684325
$841$	6699.39	0.274689
$842$	28896.6	1.18271
$843$	6789.20	0.277381
$844$	−8555.49	−0.348924
$845$	−7823.13	−0.318490
$846$	−3386.84	−0.137638
$847$	1707.41	0.0692649
$848$	−1673.07	−0.0677518
$849$	1209.23	0.0488818
$850$	3837.93	0.154871
$851$	−14272.9	−0.574933
$852$	23234.3	0.934266
$853$	−27101.4	−1.08785	−0.543923	−	0.839135i	$-0.683062\pi$
$853$	−27101.4	−1.08785	−0.543923	+	0.839135i	$0.683062\pi$
$854$	−3999.30	−0.160250
$855$	6903.03	0.276115
$856$	20017.4	0.799276
$857$	35862.5	1.42945	0.714726	−	0.699404i	$-0.246551\pi$
$857$	35862.5	1.42945	0.714726	+	0.699404i	$0.246551\pi$
$858$	−7986.28	−0.317771
$859$	−7310.25	−0.290364	−0.145182	−	0.989405i	$-0.546377\pi$
$859$	−7310.25	−0.290364	−0.145182	+	0.989405i	$0.546377\pi$
$860$	−65133.1	−2.58258
$861$	2913.64	0.115327
$862$	17200.8	0.679652
$863$	−13079.1	−0.515895	−0.257947	−	0.966159i	$-0.583046\pi$
$863$	−13079.1	−0.515895	−0.257947	+	0.966159i	$0.583046\pi$
$864$	−4112.13	−0.161918
$865$	−39295.0	−1.54459
$866$	−65267.4	−2.56106
$867$	14552.7	0.570051
$868$	18107.4	0.708069
$869$	−4022.47	−0.157023
$870$	37256.9	1.45187
$871$	−2621.76	−0.101992
$872$	5196.77	0.201817
$873$	−13001.0	−0.504030
$874$	−51799.1	−2.00472
$875$	4318.80	0.166859
$876$	402.526	0.0155252
$877$	10469.4	0.403110	0.201555	−	0.979477i	$-0.435401\pi$
$877$	10469.4	0.403110	0.201555	+	0.979477i	$0.435401\pi$
$878$	6470.90	0.248727
$879$	11871.8	0.455547
$880$	−1987.86	−0.0761484
$881$	−11466.8	−0.438510	−0.219255	−	0.975668i	$-0.570363\pi$
$881$	−11466.8	−0.438510	−0.219255	+	0.975668i	$0.570363\pi$
$882$	6016.67	0.229696
$883$	45581.2	1.73718	0.868589	−	0.495533i	$-0.165027\pi$
$883$	45581.2	1.73718	0.868589	+	0.495533i	$0.165027\pi$
$884$	5577.77	0.212218
$885$	−986.858	−0.0374835
$886$	62321.9	2.36315
$887$	−14096.4	−0.533609	−0.266804	−	0.963751i	$-0.585968\pi$
$887$	−14096.4	−0.533609	−0.266804	+	0.963751i	$0.585968\pi$
$888$	5044.83	0.190646
$889$	38217.5	1.44182
$890$	41951.0	1.58000
$891$	891.000	0.0335013
$892$	−63198.5	−2.37225
$893$	−4097.92	−0.153563
$894$	−3958.74	−0.148098
$895$	−2135.12	−0.0797420
$896$	35453.4	1.32189
$897$	−34431.7	−1.28165
$898$	−6664.90	−0.247673
$899$	−16651.8	−0.617761
$900$	12817.1	0.474706
$901$	1106.11	0.0408988
$902$	3517.68	0.129851
$903$	−13386.0	−0.493309
$904$	12110.4	0.445561
$905$	−39324.4	−1.44440
$906$	−30283.5	−1.11049
$907$	−1180.77	−0.0432269	−0.0216135	−	0.999766i	$-0.506880\pi$
$907$	−1180.77	−0.0432269	−0.0216135	+	0.999766i	$0.506880\pi$
$908$	−6888.57	−0.251768
$909$	−15550.2	−0.567402
$910$	−51768.9	−1.88585
$911$	−26459.4	−0.962283	−0.481141	−	0.876643i	$-0.659778\pi$
$911$	−26459.4	−0.962283	−0.481141	+	0.876643i	$0.659778\pi$
$912$	1809.43	0.0656974
$913$	−15733.5	−0.570321
$914$	4410.32	0.159606
$915$	2774.19	0.100232
$916$	21415.9	0.772489
$917$	−18638.5	−0.671207
$918$	−988.681	−0.0355461
$919$	−42134.5	−1.51239	−0.756196	−	0.654346i	$-0.772944\pi$
$919$	−42134.5	−1.51239	−0.756196	+	0.654346i	$0.772944\pi$
$920$	−86719.2	−3.10766
$921$	−28020.2	−1.00249
$922$	−42648.5	−1.52338
$923$	29689.1	1.05875
$924$	−6327.14	−0.225268
$925$	6789.04	0.241321
$926$	−58363.1	−2.07120
$927$	13041.8	0.462079
$928$	−26853.6	−0.949905
$929$	28164.8	0.994678	0.497339	−	0.867556i	$-0.334311\pi$
$929$	28164.8	0.994678	0.497339	+	0.867556i	$0.334311\pi$
$930$	−19955.8	−0.703630
$931$	7279.89	0.256271
$932$	−47667.3	−1.67532
$933$	−4947.65	−0.173611
$934$	−55670.8	−1.95032
$935$	1314.22	0.0459675
$936$	12170.1	0.424991
$937$	195.738	0.00682442	0.00341221	−	0.999994i	$-0.498914\pi$
$937$	195.738	0.00682442	0.00341221	+	0.999994i	$0.498914\pi$
$938$	−3300.04	−0.114872
$939$	3744.15	0.130123
$940$	−16683.1	−0.578875
$941$	19349.4	0.670322	0.335161	−	0.942161i	$-0.391209\pi$
$941$	19349.4	0.670322	0.335161	+	0.942161i	$0.391209\pi$
$942$	−17207.9	−0.595186
$943$	15166.0	0.523724
$944$	−258.676	−0.00891862
$945$	5775.66	0.198817
$946$	−16161.1	−0.555435
$947$	33528.2	1.15050	0.575248	−	0.817979i	$-0.304905\pi$
$947$	33528.2	1.15050	0.575248	+	0.817979i	$0.304905\pi$
$948$	14906.0	0.510681
$949$	514.353	0.0175939
$950$	24638.7	0.841459
$951$	17864.4	0.609140
$952$	2887.13	0.0982903
$953$	34206.5	1.16270	0.581352	−	0.813652i	$-0.302524\pi$
$953$	34206.5	1.16270	0.581352	+	0.813652i	$0.302524\pi$
$954$	5868.83	0.199172
$955$	27692.5	0.938334
$956$	−37055.4	−1.25362
$957$	5818.53	0.196537
$958$	−33493.8	−1.12958
$959$	−42020.2	−1.41491
$960$	−36519.0	−1.22776
$961$	−20871.9	−0.700610
$962$	15676.0	0.525378
$963$	−6939.50	−0.232214
$964$	−74595.0	−2.49227
$965$	46963.5	1.56664
$966$	−43339.5	−1.44351
$967$	−27848.6	−0.926111	−0.463056	−	0.886329i	$-0.653247\pi$
$967$	−27848.6	−0.926111	−0.463056	+	0.886329i	$0.653247\pi$
$968$	−3141.28	−0.104302
$969$	−1196.26	−0.0396587
$970$	−101747.	−3.36794
$971$	25773.5	0.851814	0.425907	−	0.904767i	$-0.359955\pi$
$971$	25773.5	0.851814	0.425907	+	0.904767i	$0.359955\pi$
$972$	−3301.77	−0.108955
$973$	−16498.5	−0.543595
$974$	56172.5	1.84793
$975$	16377.8	0.537958
$976$	727.172	0.0238486
$977$	31039.6	1.01642	0.508212	−	0.861232i	$-0.330307\pi$
$977$	31039.6	1.01642	0.508212	+	0.861232i	$0.330307\pi$
$978$	29846.2	0.975846
$979$	6551.62	0.213882
$980$	29637.3	0.966049
$981$	−1801.58	−0.0586341
$982$	−219.281	−0.00712579
$983$	719.504	0.0233455	0.0116727	−	0.999932i	$-0.496284\pi$
$983$	719.504	0.0233455	0.0116727	+	0.999932i	$0.496284\pi$
$984$	−5360.49	−0.173665
$985$	−62855.1	−2.03323
$986$	−6456.42	−0.208534
$987$	−3428.67	−0.110573
$988$	35808.2	1.15305
$989$	−69676.2	−2.24022
$990$	6973.03	0.223856
$991$	−31544.7	−1.01115	−0.505575	−	0.862783i	$-0.668720\pi$
$991$	−31544.7	−1.01115	−0.505575	+	0.862783i	$0.668720\pi$
$992$	14383.5	0.460359
$993$	20797.7	0.664649
$994$	37370.0	1.19246
$995$	59787.7	1.90492
$996$	58303.6	1.85484
$997$	38155.1	1.21202	0.606010	−	0.795457i	$-0.292769\pi$
$997$	38155.1	1.21202	0.606010	+	0.795457i	$0.292769\pi$
$998$	7009.34	0.222321
$999$	−1748.91	−0.0553884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.g.1.5	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.g.1.5	✓	39	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)

\(f(q)\)	\(=\)	\(q-4.64624 q^{2} -3.00000 q^{3} +13.5875 q^{4} -15.1595 q^{5} +13.9387 q^{6} +14.1108 q^{7} -25.9610 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.64624 q^{2} -3.00000 q^{3} +13.5875 q^{4} -15.1595 q^{5} +13.9387 q^{6} +14.1108 q^{7} -25.9610 q^{8} +9.00000 q^{9} +70.4347 q^{10} +11.0000 q^{11} -40.7626 q^{12} -52.0870 q^{13} -65.5624 q^{14} +45.4785 q^{15} +11.9209 q^{16} -7.88117 q^{17} -41.8162 q^{18} -50.5955 q^{19} -205.980 q^{20} -42.3325 q^{21} -51.1086 q^{22} -220.348 q^{23} +77.8831 q^{24} +104.811 q^{25} +242.009 q^{26} -27.0000 q^{27} +191.732 q^{28} -176.319 q^{29} -211.304 q^{30} +94.4411 q^{31} +152.301 q^{32} -33.0000 q^{33} +36.6178 q^{34} -213.913 q^{35} +122.288 q^{36} +64.7744 q^{37} +235.079 q^{38} +156.261 q^{39} +393.556 q^{40} -68.8274 q^{41} +196.687 q^{42} +316.210 q^{43} +149.463 q^{44} -136.436 q^{45} +1023.79 q^{46} +80.9936 q^{47} -35.7626 q^{48} -143.884 q^{49} -486.975 q^{50} +23.6435 q^{51} -707.734 q^{52} -140.348 q^{53} +125.448 q^{54} -166.755 q^{55} -366.332 q^{56} +151.787 q^{57} +819.220 q^{58} -21.6994 q^{59} +617.941 q^{60} +61.0000 q^{61} -438.796 q^{62} +126.998 q^{63} -802.994 q^{64} +789.613 q^{65} +153.326 q^{66} +50.3343 q^{67} -107.086 q^{68} +661.043 q^{69} +993.893 q^{70} -569.991 q^{71} -233.649 q^{72} -9.87488 q^{73} -300.957 q^{74} -314.432 q^{75} -687.469 q^{76} +155.219 q^{77} -726.026 q^{78} -365.679 q^{79} -180.714 q^{80} +81.0000 q^{81} +319.789 q^{82} -1430.32 q^{83} -575.195 q^{84} +119.475 q^{85} -1469.19 q^{86} +528.957 q^{87} -285.571 q^{88} +595.602 q^{89} +633.912 q^{90} -734.992 q^{91} -2993.98 q^{92} -283.323 q^{93} -376.316 q^{94} +767.003 q^{95} -456.903 q^{96} -1444.56 q^{97} +668.519 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * q^99

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