LMFDB - Embedded newform 2015.4.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2015,4,Mod(1,2015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2015, 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("2015.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2015 = 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2015.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:	$118.888848662$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	2015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.33607 q^{2} -8.60031 q^{3} +10.8015 q^{4} -5.00000 q^{5} +37.2915 q^{6} +8.52424 q^{7} -12.1475 q^{8} +46.9653 q^{9} +O(q^{10})$	\(q-4.33607 q^{2} -8.60031 q^{3} +10.8015 q^{4} -5.00000 q^{5} +37.2915 q^{6} +8.52424 q^{7} -12.1475 q^{8} +46.9653 q^{9} +21.6803 q^{10} -37.5402 q^{11} -92.8962 q^{12} -13.0000 q^{13} -36.9617 q^{14} +43.0015 q^{15} -33.7396 q^{16} +78.3025 q^{17} -203.645 q^{18} +132.947 q^{19} -54.0075 q^{20} -73.3111 q^{21} +162.777 q^{22} -68.7553 q^{23} +104.472 q^{24} +25.0000 q^{25} +56.3689 q^{26} -171.708 q^{27} +92.0746 q^{28} +76.6627 q^{29} -186.458 q^{30} +31.0000 q^{31} +243.477 q^{32} +322.857 q^{33} -339.525 q^{34} -42.6212 q^{35} +507.296 q^{36} -306.627 q^{37} -576.468 q^{38} +111.804 q^{39} +60.7375 q^{40} +146.903 q^{41} +317.882 q^{42} -117.303 q^{43} -405.490 q^{44} -234.827 q^{45} +298.128 q^{46} -560.950 q^{47} +290.171 q^{48} -270.337 q^{49} -108.402 q^{50} -673.425 q^{51} -140.420 q^{52} +161.500 q^{53} +744.537 q^{54} +187.701 q^{55} -103.548 q^{56} -1143.39 q^{57} -332.415 q^{58} +191.897 q^{59} +464.481 q^{60} -733.679 q^{61} -134.418 q^{62} +400.344 q^{63} -785.818 q^{64} +65.0000 q^{65} -1399.93 q^{66} -482.288 q^{67} +845.784 q^{68} +591.317 q^{69} +184.809 q^{70} +170.624 q^{71} -570.511 q^{72} -728.195 q^{73} +1329.56 q^{74} -215.008 q^{75} +1436.03 q^{76} -320.002 q^{77} -484.790 q^{78} +1042.02 q^{79} +168.698 q^{80} +208.677 q^{81} -636.980 q^{82} +684.801 q^{83} -791.870 q^{84} -391.512 q^{85} +508.634 q^{86} -659.322 q^{87} +456.019 q^{88} +896.013 q^{89} +1018.22 q^{90} -110.815 q^{91} -742.660 q^{92} -266.610 q^{93} +2432.32 q^{94} -664.736 q^{95} -2093.98 q^{96} -117.098 q^{97} +1172.20 q^{98} -1763.09 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9} + 25 q^{10} + 127 q^{11} - 76 q^{12} - 520 q^{13} + 138 q^{14} + 85 q^{15} + 413 q^{16} - 264 q^{17} - 126 q^{18} - q^{19} - 745 q^{20} + 176 q^{21} - 191 q^{22} - 106 q^{23} + 31 q^{24} + 1000 q^{25} + 65 q^{26} - 344 q^{27} + 255 q^{28} + 107 q^{29} + 175 q^{30} + 1240 q^{31} - 372 q^{32} - 386 q^{33} - 6 q^{34} + 100 q^{35} + 790 q^{36} - 741 q^{37} - 318 q^{38} + 221 q^{39} + 195 q^{40} + 1232 q^{41} - 1180 q^{42} - 615 q^{43} - 152 q^{44} - 1235 q^{45} - 329 q^{46} - 784 q^{47} - 1089 q^{48} - 516 q^{49} - 125 q^{50} - 200 q^{51} - 1937 q^{52} - 1503 q^{53} + 1658 q^{54} - 635 q^{55} + 1518 q^{56} - 1704 q^{57} - 1035 q^{58} - 107 q^{59} + 380 q^{60} - 857 q^{61} - 155 q^{62} - 2636 q^{63} - 215 q^{64} + 2600 q^{65} - 1785 q^{66} - 2689 q^{67} - 2639 q^{68} + 2544 q^{69} - 690 q^{70} + 1554 q^{71} - 420 q^{72} - 1968 q^{73} - 27 q^{74} - 425 q^{75} - 110 q^{76} - 1040 q^{77} + 455 q^{78} - 3182 q^{79} - 2065 q^{80} - 1576 q^{81} - 386 q^{82} + 317 q^{83} - 617 q^{84} + 1320 q^{85} + 347 q^{86} - 216 q^{87} - 4081 q^{88} + 3610 q^{89} + 630 q^{90} + 260 q^{91} - 4965 q^{92} - 527 q^{93} - 2942 q^{94} + 5 q^{95} + 1002 q^{96} - 3318 q^{97} + 1659 q^{98} + 5943 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9 + 25 * q^10 + 127 * q^11 - 76 * q^12 - 520 * q^13 + 138 * q^14 + 85 * q^15 + 413 * q^16 - 264 * q^17 - 126 * q^18 - q^19 - 745 * q^20 + 176 * q^21 - 191 * q^22 - 106 * q^23 + 31 * q^24 + 1000 * q^25 + 65 * q^26 - 344 * q^27 + 255 * q^28 + 107 * q^29 + 175 * q^30 + 1240 * q^31 - 372 * q^32 - 386 * q^33 - 6 * q^34 + 100 * q^35 + 790 * q^36 - 741 * q^37 - 318 * q^38 + 221 * q^39 + 195 * q^40 + 1232 * q^41 - 1180 * q^42 - 615 * q^43 - 152 * q^44 - 1235 * q^45 - 329 * q^46 - 784 * q^47 - 1089 * q^48 - 516 * q^49 - 125 * q^50 - 200 * q^51 - 1937 * q^52 - 1503 * q^53 + 1658 * q^54 - 635 * q^55 + 1518 * q^56 - 1704 * q^57 - 1035 * q^58 - 107 * q^59 + 380 * q^60 - 857 * q^61 - 155 * q^62 - 2636 * q^63 - 215 * q^64 + 2600 * q^65 - 1785 * q^66 - 2689 * q^67 - 2639 * q^68 + 2544 * q^69 - 690 * q^70 + 1554 * q^71 - 420 * q^72 - 1968 * q^73 - 27 * q^74 - 425 * q^75 - 110 * q^76 - 1040 * q^77 + 455 * q^78 - 3182 * q^79 - 2065 * q^80 - 1576 * q^81 - 386 * q^82 + 317 * q^83 - 617 * q^84 + 1320 * q^85 + 347 * q^86 - 216 * q^87 - 4081 * q^88 + 3610 * q^89 + 630 * q^90 + 260 * q^91 - 4965 * q^92 - 527 * q^93 - 2942 * q^94 + 5 * q^95 + 1002 * q^96 - 3318 * q^97 + 1659 * q^98 + 5943 * 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 $

$2$	−4.33607	−1.53303	−0.766516	−	0.642225i	$-0.778011\pi$
$2$	−4.33607	−1.53303	−0.766516	+	0.642225i	$0.778011\pi$
$3$	−8.60031	−1.65513	−0.827565	−	0.561370i	$-0.810275\pi$
$3$	−8.60031	−1.65513	−0.827565	+	0.561370i	$0.810275\pi$
$4$	10.8015	1.35019
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	37.2915	2.53737
$7$	8.52424	0.460266	0.230133	−	0.973159i	$-0.426084\pi$
$7$	8.52424	0.460266	0.230133	+	0.973159i	$0.426084\pi$
$8$	−12.1475	−0.536849
$9$	46.9653	1.73946
$10$	21.6803	0.685593
$11$	−37.5402	−1.02898	−0.514491	−	0.857496i	$-0.672019\pi$
$11$	−37.5402	−1.02898	−0.514491	+	0.857496i	$0.672019\pi$
$12$	−92.8962	−2.23474
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−36.9617	−0.705602
$15$	43.0015	0.740197
$16$	−33.7396	−0.527181
$17$	78.3025	1.11713	0.558563	−	0.829462i	$-0.311353\pi$
$17$	78.3025	1.11713	0.558563	+	0.829462i	$0.311353\pi$
$18$	−203.645	−2.66664
$19$	132.947	1.60527	0.802636	−	0.596469i	$-0.203430\pi$
$19$	132.947	1.60527	0.802636	+	0.596469i	$0.203430\pi$
$20$	−54.0075	−0.603822
$21$	−73.3111	−0.761800
$22$	162.777	1.57746
$23$	−68.7553	−0.623325	−0.311662	−	0.950193i	$-0.600886\pi$
$23$	−68.7553	−0.623325	−0.311662	+	0.950193i	$0.600886\pi$
$24$	104.472	0.888555
$25$	25.0000	0.200000
$26$	56.3689	0.425187
$27$	−171.708	−1.22390
$28$	92.0746	0.621445
$29$	76.6627	0.490893	0.245447	−	0.969410i	$-0.421065\pi$
$29$	76.6627	0.490893	0.245447	+	0.969410i	$0.421065\pi$
$30$	−186.458	−1.13475
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	243.477	1.34503
$33$	322.857	1.70310
$34$	−339.525	−1.71259
$35$	−42.6212	−0.205837
$36$	507.296	2.34859
$37$	−306.627	−1.36241	−0.681205	−	0.732092i	$-0.738544\pi$
$37$	−306.627	−1.36241	−0.681205	+	0.732092i	$0.738544\pi$
$38$	−576.468	−2.46093
$39$	111.804	0.459051
$40$	60.7375	0.240086
$41$	146.903	0.559569	0.279784	−	0.960063i	$-0.409737\pi$
$41$	146.903	0.559569	0.279784	+	0.960063i	$0.409737\pi$
$42$	317.882	1.16786
$43$	−117.303	−0.416012	−0.208006	−	0.978128i	$-0.566697\pi$
$43$	−117.303	−0.416012	−0.208006	+	0.978128i	$0.566697\pi$
$44$	−405.490	−1.38932
$45$	−234.827	−0.777908
$46$	298.128	0.955577
$47$	−560.950	−1.74091	−0.870457	−	0.492245i	$-0.836177\pi$
$47$	−560.950	−1.74091	−0.870457	+	0.492245i	$0.836177\pi$
$48$	290.171	0.872553
$49$	−270.337	−0.788155
$50$	−108.402	−0.306606
$51$	−673.425	−1.84899
$52$	−140.420	−0.374475
$53$	161.500	0.418560	0.209280	−	0.977856i	$-0.432888\pi$
$53$	161.500	0.418560	0.209280	+	0.977856i	$0.432888\pi$
$54$	744.537	1.87627
$55$	187.701	0.460174
$56$	−103.548	−0.247093
$57$	−1143.39	−2.65693
$58$	−332.415	−0.752555
$59$	191.897	0.423438	0.211719	−	0.977331i	$-0.432094\pi$
$59$	191.897	0.423438	0.211719	+	0.977331i	$0.432094\pi$
$60$	464.481	0.999404
$61$	−733.679	−1.53997	−0.769984	−	0.638064i	$-0.779736\pi$
$61$	−733.679	−1.53997	−0.769984	+	0.638064i	$0.779736\pi$
$62$	−134.418	−0.275341
$63$	400.344	0.800612
$64$	−785.818	−1.53480
$65$	65.0000	0.124035
$66$	−1399.93	−2.61090
$67$	−482.288	−0.879416	−0.439708	−	0.898141i	$-0.644918\pi$
$67$	−482.288	−0.879416	−0.439708	+	0.898141i	$0.644918\pi$
$68$	845.784	1.50833
$69$	591.317	1.03168
$70$	184.809	0.315555
$71$	170.624	0.285203	0.142601	−	0.989780i	$-0.454453\pi$
$71$	170.624	0.285203	0.142601	+	0.989780i	$0.454453\pi$
$72$	−570.511	−0.933825
$73$	−728.195	−1.16752	−0.583759	−	0.811927i	$-0.698419\pi$
$73$	−728.195	−1.16752	−0.583759	+	0.811927i	$0.698419\pi$
$74$	1329.56	2.08862
$75$	−215.008	−0.331026
$76$	1436.03	2.16742
$77$	−320.002	−0.473605
$78$	−484.790	−0.703739
$79$	1042.02	1.48400	0.742001	−	0.670399i	$-0.233877\pi$
$79$	1042.02	1.48400	0.742001	+	0.670399i	$0.233877\pi$
$80$	168.698	0.235763
$81$	208.677	0.286251
$82$	−636.980	−0.857837
$83$	684.801	0.905622	0.452811	−	0.891606i	$-0.350421\pi$
$83$	684.801	0.905622	0.452811	+	0.891606i	$0.350421\pi$
$84$	−791.870	−1.02857
$85$	−391.512	−0.499594
$86$	508.634	0.637760
$87$	−659.322	−0.812492
$88$	456.019	0.552407
$89$	896.013	1.06716	0.533580	−	0.845750i	$-0.320846\pi$
$89$	896.013	1.06716	0.533580	+	0.845750i	$0.320846\pi$
$90$	1018.22	1.19256
$91$	−110.815	−0.127655
$92$	−742.660	−0.841605
$93$	−266.610	−0.297270
$94$	2432.32	2.66888
$95$	−664.736	−0.717899
$96$	−2093.98	−2.22621
$97$	−117.098	−0.122573	−0.0612863	−	0.998120i	$-0.519520\pi$
$97$	−117.098	−0.122573	−0.0612863	+	0.998120i	$0.519520\pi$
$98$	1172.20	1.20827
$99$	−1763.09	−1.78987
$100$	270.038	0.270038
$101$	441.485	0.434945	0.217472	−	0.976066i	$-0.430219\pi$
$101$	441.485	0.434945	0.217472	+	0.976066i	$0.430219\pi$
$102$	2920.02	2.83456
$103$	−252.600	−0.241645	−0.120823	−	0.992674i	$-0.538553\pi$
$103$	−252.600	−0.241645	−0.120823	+	0.992674i	$0.538553\pi$
$104$	157.918	0.148895
$105$	366.555	0.340687
$106$	−700.274	−0.641666
$107$	685.685	0.619511	0.309755	−	0.950816i	$-0.399753\pi$
$107$	685.685	0.619511	0.309755	+	0.950816i	$0.399753\pi$
$108$	−1854.70	−1.65249
$109$	1092.70	0.960203	0.480102	−	0.877213i	$-0.340600\pi$
$109$	1092.70	0.960203	0.480102	+	0.877213i	$0.340600\pi$
$110$	−813.884	−0.705462
$111$	2637.09	2.25497
$112$	−287.604	−0.242643
$113$	180.112	0.149942	0.0749712	−	0.997186i	$-0.476114\pi$
$113$	180.112	0.149942	0.0749712	+	0.997186i	$0.476114\pi$
$114$	4957.80	4.07317
$115$	343.776	0.278759
$116$	828.072	0.662798
$117$	−610.549	−0.482438
$118$	−832.077	−0.649143
$119$	667.469	0.514175
$120$	−522.361	−0.397374
$121$	78.2655	0.0588020
$122$	3181.28	2.36082
$123$	−1263.41	−0.926159
$124$	334.847	0.242501
$125$	−125.000	−0.0894427
$126$	−1735.92	−1.22736
$127$	−433.705	−0.303032	−0.151516	−	0.988455i	$-0.548416\pi$
$127$	−433.705	−0.303032	−0.151516	+	0.988455i	$0.548416\pi$
$128$	1459.54	1.00786
$129$	1008.84	0.688554
$130$	−281.845	−0.190149
$131$	447.724	0.298609	0.149305	−	0.988791i	$-0.452297\pi$
$131$	447.724	0.298609	0.149305	+	0.988791i	$0.452297\pi$
$132$	3487.34	2.29950
$133$	1133.27	0.738852
$134$	2091.24	1.34817
$135$	858.539	0.547343
$136$	−951.179	−0.599728
$137$	−758.828	−0.473220	−0.236610	−	0.971605i	$-0.576036\pi$
$137$	−758.828	−0.473220	−0.236610	+	0.971605i	$0.576036\pi$
$138$	−2563.99	−1.58160
$139$	1204.71	0.735126	0.367563	−	0.929999i	$-0.380192\pi$
$139$	1204.71	0.735126	0.367563	+	0.929999i	$0.380192\pi$
$140$	−460.373	−0.277919
$141$	4824.34	2.88144
$142$	−739.839	−0.437225
$143$	488.022	0.285388
$144$	−1584.59	−0.917008
$145$	−383.313	−0.219534
$146$	3157.51	1.78984
$147$	2324.98	1.30450
$148$	−3312.03	−1.83951
$149$	2162.77	1.18913	0.594567	−	0.804046i	$-0.297324\pi$
$149$	2162.77	1.18913	0.594567	+	0.804046i	$0.297324\pi$
$150$	932.288	0.507474
$151$	−6.60700	−0.00356073	−0.00178036	−	0.999998i	$-0.500567\pi$
$151$	−6.60700	−0.00356073	−0.00178036	+	0.999998i	$0.500567\pi$
$152$	−1614.98	−0.861788
$153$	3677.50	1.94319
$154$	1387.55	0.726051
$155$	−155.000	−0.0803219
$156$	1207.65	0.619804
$157$	271.920	0.138227	0.0691133	−	0.997609i	$-0.477983\pi$
$157$	271.920	0.138227	0.0691133	+	0.997609i	$0.477983\pi$
$158$	−4518.26	−2.27502
$159$	−1388.95	−0.692772
$160$	−1217.39	−0.601518
$161$	−586.087	−0.286895
$162$	−904.837	−0.438831
$163$	2231.44	1.07227	0.536134	−	0.844133i	$-0.319884\pi$
$163$	2231.44	1.07227	0.536134	+	0.844133i	$0.319884\pi$
$164$	1586.77	0.755523
$165$	−1614.29	−0.761648
$166$	−2969.34	−1.38835
$167$	−2015.56	−0.933943	−0.466972	−	0.884272i	$-0.654655\pi$
$167$	−2015.56	−0.933943	−0.466972	+	0.884272i	$0.654655\pi$
$168$	890.547	0.408971
$169$	169.000	0.0769231
$170$	1697.62	0.765893
$171$	6243.90	2.79230
$172$	−1267.05	−0.561695
$173$	1276.98	0.561196	0.280598	−	0.959825i	$-0.409467\pi$
$173$	1276.98	0.561196	0.280598	+	0.959825i	$0.409467\pi$
$174$	2858.87	1.24558
$175$	213.106	0.0920531
$176$	1266.59	0.542459
$177$	−1650.37	−0.700844
$178$	−3885.17	−1.63599
$179$	3912.36	1.63365	0.816825	−	0.576885i	$-0.195732\pi$
$179$	3912.36	1.63365	0.816825	+	0.576885i	$0.195732\pi$
$180$	−2536.48	−1.05032
$181$	−2979.87	−1.22371	−0.611857	−	0.790968i	$-0.709577\pi$
$181$	−2979.87	−1.22371	−0.611857	+	0.790968i	$0.709577\pi$
$182$	480.502	0.195699
$183$	6309.87	2.54885
$184$	835.205	0.334631
$185$	1533.14	0.609289
$186$	1156.04	0.455725
$187$	−2939.49	−1.14950
$188$	−6059.10	−2.35056
$189$	−1463.68	−0.563317
$190$	2882.34	1.10056
$191$	−1990.39	−0.754029	−0.377015	−	0.926207i	$-0.623049\pi$
$191$	−1990.39	−0.754029	−0.377015	+	0.926207i	$0.623049\pi$
$192$	6758.27	2.54029
$193$	−681.251	−0.254080	−0.127040	−	0.991898i	$-0.540548\pi$
$193$	−681.251	−0.254080	−0.127040	+	0.991898i	$0.540548\pi$
$194$	507.747	0.187908
$195$	−559.020	−0.205294
$196$	−2920.05	−1.06416
$197$	445.120	0.160982	0.0804911	−	0.996755i	$-0.474351\pi$
$197$	445.120	0.160982	0.0804911	+	0.996755i	$0.474351\pi$
$198$	7644.86	2.74392
$199$	−2198.13	−0.783021	−0.391510	−	0.920174i	$-0.628047\pi$
$199$	−2198.13	−0.783021	−0.391510	+	0.920174i	$0.628047\pi$
$200$	−303.688	−0.107370
$201$	4147.83	1.45555
$202$	−1914.31	−0.666784
$203$	653.491	0.225941
$204$	−7274.00	−2.49648
$205$	−734.513	−0.250247
$206$	1095.29	0.370450
$207$	−3229.11	−1.08425
$208$	438.615	0.146214
$209$	−4990.86	−1.65179
$210$	−1589.41	−0.522284
$211$	3243.53	1.05826	0.529132	−	0.848539i	$-0.322518\pi$
$211$	3243.53	1.05826	0.529132	+	0.848539i	$0.322518\pi$
$212$	1744.44	0.565135
$213$	−1467.42	−0.472047
$214$	−2973.18	−0.949730
$215$	586.515	0.186046
$216$	2085.82	0.657047
$217$	264.251	0.0826662
$218$	−4738.04	−1.47202
$219$	6262.70	1.93239
$220$	2027.45	0.621322
$221$	−1017.93	−0.309835
$222$	−11434.6	−3.45694
$223$	−464.373	−0.139447	−0.0697236	−	0.997566i	$-0.522212\pi$
$223$	−464.373	−0.139447	−0.0697236	+	0.997566i	$0.522212\pi$
$224$	2075.46	0.619073
$225$	1174.13	0.347891
$226$	−780.977	−0.229866
$227$	720.690	0.210722	0.105361	−	0.994434i	$-0.466400\pi$
$227$	720.690	0.210722	0.105361	+	0.994434i	$0.466400\pi$
$228$	−12350.3	−3.58736
$229$	−3206.16	−0.925193	−0.462597	−	0.886569i	$-0.653082\pi$
$229$	−3206.16	−0.925193	−0.462597	+	0.886569i	$0.653082\pi$
$230$	−1490.64	−0.427347
$231$	2752.11	0.783877
$232$	−931.260	−0.263535
$233$	−3936.38	−1.10678	−0.553392	−	0.832921i	$-0.686667\pi$
$233$	−3936.38	−1.10678	−0.553392	+	0.832921i	$0.686667\pi$
$234$	2647.38	0.739593
$235$	2804.75	0.778560
$236$	2072.77	0.571720
$237$	−8961.67	−2.45622
$238$	−2894.19	−0.788246
$239$	−1776.18	−0.480717	−0.240358	−	0.970684i	$-0.577265\pi$
$239$	−1776.18	−0.480717	−0.240358	+	0.970684i	$0.577265\pi$
$240$	−1450.85	−0.390218
$241$	3736.13	0.998610	0.499305	−	0.866426i	$-0.333589\pi$
$241$	3736.13	0.998610	0.499305	+	0.866426i	$0.333589\pi$
$242$	−339.365	−0.0901454
$243$	2841.43	0.750114
$244$	−7924.84	−2.07924
$245$	1351.69	0.352474
$246$	5478.22	1.41983
$247$	−1728.31	−0.445222
$248$	−376.573	−0.0964209
$249$	−5889.50	−1.49892
$250$	542.009	0.137119
$251$	5019.17	1.26218	0.631090	−	0.775710i	$-0.282608\pi$
$251$	5019.17	1.26218	0.631090	+	0.775710i	$0.282608\pi$
$252$	4324.31	1.08098
$253$	2581.09	0.641389
$254$	1880.58	0.464558
$255$	3367.13	0.826893
$256$	−42.1345	−0.0102867
$257$	−6609.47	−1.60423	−0.802116	−	0.597169i	$-0.796292\pi$
$257$	−6609.47	−1.60423	−0.802116	+	0.597169i	$0.796292\pi$
$258$	−4374.41	−1.05558
$259$	−2613.76	−0.627071
$260$	702.098	0.167470
$261$	3600.49	0.853887
$262$	−1941.36	−0.457777
$263$	2453.84	0.575324	0.287662	−	0.957732i	$-0.407122\pi$
$263$	2453.84	0.575324	0.287662	+	0.957732i	$0.407122\pi$
$264$	−3921.91	−0.914306
$265$	−807.499	−0.187186
$266$	−4913.95	−1.13268
$267$	−7705.99	−1.76629
$268$	−5209.44	−1.18738
$269$	3665.92	0.830912	0.415456	−	0.909613i	$-0.363622\pi$
$269$	3665.92	0.830912	0.415456	+	0.909613i	$0.363622\pi$
$270$	−3722.68	−0.839094
$271$	3275.30	0.734171	0.367086	−	0.930187i	$-0.380356\pi$
$271$	3275.30	0.734171	0.367086	+	0.930187i	$0.380356\pi$
$272$	−2641.89	−0.588928
$273$	953.044	0.211285
$274$	3290.33	0.725461
$275$	−938.505	−0.205796
$276$	6387.11	1.39297
$277$	4963.30	1.07659	0.538295	−	0.842756i	$-0.319068\pi$
$277$	4963.30	1.07659	0.538295	+	0.842756i	$0.319068\pi$
$278$	−5223.72	−1.12697
$279$	1455.92	0.312415
$280$	517.741	0.110503
$281$	2693.22	0.571758	0.285879	−	0.958266i	$-0.407715\pi$
$281$	2693.22	0.571758	0.285879	+	0.958266i	$0.407715\pi$
$282$	−20918.7	−4.41734
$283$	−3704.81	−0.778192	−0.389096	−	0.921197i	$-0.627213\pi$
$283$	−3704.81	−0.778192	−0.389096	+	0.921197i	$0.627213\pi$
$284$	1843.00	0.385077
$285$	5716.93	1.18822
$286$	−2116.10	−0.437509
$287$	1252.23	0.257550
$288$	11435.0	2.33963
$289$	1218.28	0.247970
$290$	1662.07	0.336553
$291$	1007.08	0.202874
$292$	−7865.60	−1.57637
$293$	−3576.56	−0.713123	−0.356561	−	0.934272i	$-0.616051\pi$
$293$	−3576.56	−0.713123	−0.356561	+	0.934272i	$0.616051\pi$
$294$	−10081.3	−1.99984
$295$	−959.483	−0.189367
$296$	3724.75	0.731409
$297$	6445.94	1.25937
$298$	−9377.91	−1.82298
$299$	893.819	0.172879
$300$	−2322.41	−0.446947
$301$	−999.918	−0.191476
$302$	28.6484	0.00545871
$303$	−3796.91	−0.719890
$304$	−4485.58	−0.846269
$305$	3668.40	0.688694
$306$	−15945.9	−2.97897
$307$	8401.10	1.56181	0.780906	−	0.624649i	$-0.214758\pi$
$307$	8401.10	1.56181	0.780906	+	0.624649i	$0.214758\pi$
$308$	−3456.50	−0.639455
$309$	2172.44	0.399954
$310$	672.091	0.123136
$311$	−5378.40	−0.980646	−0.490323	−	0.871541i	$-0.663121\pi$
$311$	−5378.40	−0.980646	−0.490323	+	0.871541i	$0.663121\pi$
$312$	−1358.14	−0.246441
$313$	−2100.89	−0.379390	−0.189695	−	0.981843i	$-0.560750\pi$
$313$	−2100.89	−0.379390	−0.189695	+	0.981843i	$0.560750\pi$
$314$	−1179.06	−0.211906
$315$	−2001.72	−0.358045
$316$	11255.4	2.00368
$317$	5628.90	0.997321	0.498660	−	0.866797i	$-0.333826\pi$
$317$	5628.90	0.997321	0.498660	+	0.866797i	$0.333826\pi$
$318$	6022.57	1.06204
$319$	−2877.93	−0.505120
$320$	3929.09	0.686383
$321$	−5897.10	−1.02537
$322$	2541.31	0.439819
$323$	10410.1	1.79329
$324$	2254.02	0.386492
$325$	−325.000	−0.0554700
$326$	−9675.68	−1.64382
$327$	−9397.60	−1.58926
$328$	−1784.50	−0.300404
$329$	−4781.67	−0.801283
$330$	6999.66	1.16763
$331$	−6042.84	−1.00346	−0.501729	−	0.865025i	$-0.667303\pi$
$331$	−6042.84	−1.00346	−0.501729	+	0.865025i	$0.667303\pi$
$332$	7396.88	1.22276
$333$	−14400.8	−2.36985
$334$	8739.60	1.43177
$335$	2411.44	0.393287
$336$	2473.49	0.401606
$337$	−2321.22	−0.375208	−0.187604	−	0.982245i	$-0.560072\pi$
$337$	−2321.22	−0.375208	−0.187604	+	0.982245i	$0.560072\pi$
$338$	−732.796	−0.117926
$339$	−1549.02	−0.248174
$340$	−4228.92	−0.674545
$341$	−1163.75	−0.184810
$342$	−27074.0	−4.28068
$343$	−5228.23	−0.823027
$344$	1424.94	0.223336
$345$	−2956.58	−0.461383
$346$	−5537.07	−0.860332
$347$	5907.49	0.913921	0.456960	−	0.889487i	$-0.348938\pi$
$347$	5907.49	0.913921	0.456960	+	0.889487i	$0.348938\pi$
$348$	−7121.67	−1.09702
$349$	10703.2	1.64163	0.820815	−	0.571194i	$-0.193520\pi$
$349$	10703.2	1.64163	0.820815	+	0.571194i	$0.193520\pi$
$350$	−924.043	−0.141120
$351$	2232.20	0.339448
$352$	−9140.18	−1.38401
$353$	59.3664	0.00895115	0.00447557	−	0.999990i	$-0.498575\pi$
$353$	59.3664	0.00895115	0.00447557	+	0.999990i	$0.498575\pi$
$354$	7156.12	1.07442
$355$	−853.122	−0.127546
$356$	9678.28	1.44087
$357$	−5740.44	−0.851026
$358$	−16964.3	−2.50444
$359$	2248.18	0.330513	0.165257	−	0.986251i	$-0.447155\pi$
$359$	2248.18	0.330513	0.165257	+	0.986251i	$0.447155\pi$
$360$	2852.56	0.417619
$361$	10815.9	1.57690
$362$	12920.9	1.87599
$363$	−673.107	−0.0973250
$364$	−1196.97	−0.172358
$365$	3640.98	0.522130
$366$	−27360.0	−3.90746
$367$	3510.94	0.499373	0.249686	−	0.968327i	$-0.419672\pi$
$367$	3510.94	0.499373	0.249686	+	0.968327i	$0.419672\pi$
$368$	2319.78	0.328605
$369$	6899.32	0.973345
$370$	−6647.78	−0.934059
$371$	1376.66	0.192649
$372$	−2879.78	−0.401370
$373$	2310.40	0.320719	0.160359	−	0.987059i	$-0.448735\pi$
$373$	2310.40	0.320719	0.160359	+	0.987059i	$0.448735\pi$
$374$	12745.8	1.76222
$375$	1075.04	0.148039
$376$	6814.14	0.934608
$377$	−996.615	−0.136149
$378$	6346.61	0.863583
$379$	1958.42	0.265428	0.132714	−	0.991154i	$-0.457631\pi$
$379$	1958.42	0.265428	0.132714	+	0.991154i	$0.457631\pi$
$380$	−7180.14	−0.969299
$381$	3730.00	0.501558
$382$	8630.47	1.15595
$383$	−34.1893	−0.00456134	−0.00228067	−	0.999997i	$-0.500726\pi$
$383$	−34.1893	−0.00456134	−0.00228067	+	0.999997i	$0.500726\pi$
$384$	−12552.5	−1.66814
$385$	1600.01	0.211802
$386$	2953.95	0.389513
$387$	−5509.17	−0.723635
$388$	−1264.84	−0.165496
$389$	3300.01	0.430121	0.215061	−	0.976601i	$-0.431005\pi$
$389$	3300.01	0.430121	0.215061	+	0.976601i	$0.431005\pi$
$390$	2423.95	0.314722
$391$	−5383.71	−0.696332
$392$	3283.92	0.423120
$393$	−3850.56	−0.494237
$394$	−1930.07	−0.246791
$395$	−5210.09	−0.663666
$396$	−19044.0	−2.41666
$397$	734.140	0.0928096	0.0464048	−	0.998923i	$-0.485224\pi$
$397$	734.140	0.0928096	0.0464048	+	0.998923i	$0.485224\pi$
$398$	9531.24	1.20040
$399$	−9746.50	−1.22290
$400$	−843.490	−0.105436
$401$	−3594.58	−0.447642	−0.223821	−	0.974630i	$-0.571853\pi$
$401$	−3594.58	−0.447642	−0.223821	+	0.974630i	$0.571853\pi$
$402$	−17985.3	−2.23140
$403$	−403.000	−0.0498135
$404$	4768.70	0.587257
$405$	−1043.38	−0.128015
$406$	−2833.58	−0.346375
$407$	11510.8	1.40189
$408$	8180.44	0.992627
$409$	−9424.62	−1.13941	−0.569703	−	0.821850i	$-0.692942\pi$
$409$	−9424.62	−1.13941	−0.569703	+	0.821850i	$0.692942\pi$
$410$	3184.90	0.383636
$411$	6526.16	0.783240
$412$	−2728.46	−0.326266
$413$	1635.77	0.194894
$414$	14001.7	1.66218
$415$	−3424.00	−0.405007
$416$	−3165.20	−0.373045
$417$	−10360.9	−1.21673
$418$	21640.7	2.53225
$419$	−2192.47	−0.255631	−0.127815	−	0.991798i	$-0.540797\pi$
$419$	−2192.47	−0.255631	−0.127815	+	0.991798i	$0.540797\pi$
$420$	3959.35	0.459992
$421$	−2516.00	−0.291265	−0.145632	−	0.989339i	$-0.546522\pi$
$421$	−2516.00	−0.291265	−0.145632	+	0.989339i	$0.546522\pi$
$422$	−14064.2	−1.62235
$423$	−26345.2	−3.02824
$424$	−1961.82	−0.224704
$425$	1957.56	0.223425
$426$	6362.84	0.723664
$427$	−6254.06	−0.708794
$428$	7406.42	0.836456
$429$	−4197.14	−0.472354
$430$	−2543.17	−0.285215
$431$	4974.33	0.555928	0.277964	−	0.960592i	$-0.410340\pi$
$431$	4974.33	0.555928	0.277964	+	0.960592i	$0.410340\pi$
$432$	5793.35	0.645215
$433$	−15789.2	−1.75238	−0.876189	−	0.481969i	$-0.839922\pi$
$433$	−15789.2	−1.75238	−0.876189	+	0.481969i	$0.839922\pi$
$434$	−1145.81	−0.126730
$435$	3296.61	0.363357
$436$	11802.9	1.29645
$437$	−9140.82	−1.00061
$438$	−27155.5	−2.96242
$439$	−7614.94	−0.827885	−0.413942	−	0.910303i	$-0.635849\pi$
$439$	−7614.94	−0.827885	−0.413942	+	0.910303i	$0.635849\pi$
$440$	−2280.10	−0.247044
$441$	−12696.5	−1.37096
$442$	4413.82	0.474987
$443$	13501.1	1.44799	0.723994	−	0.689806i	$-0.242304\pi$
$443$	13501.1	1.44799	0.723994	+	0.689806i	$0.242304\pi$
$444$	28484.5	3.04463
$445$	−4480.06	−0.477248
$446$	2013.55	0.213777
$447$	−18600.5	−1.96817
$448$	−6698.50	−0.706416
$449$	553.192	0.0581442	0.0290721	−	0.999577i	$-0.490745\pi$
$449$	553.192	0.0581442	0.0290721	+	0.999577i	$0.490745\pi$
$450$	−5091.12	−0.533328
$451$	−5514.75	−0.575786
$452$	1945.48	0.202450
$453$	56.8222	0.00589347
$454$	−3124.96	−0.323043
$455$	554.076	0.0570889
$456$	13889.3	1.42637
$457$	−10451.2	−1.06978	−0.534888	−	0.844923i	$-0.679646\pi$
$457$	−10451.2	−1.06978	−0.534888	+	0.844923i	$0.679646\pi$
$458$	13902.1	1.41835
$459$	−13445.1	−1.36725
$460$	3713.30	0.376377
$461$	−14855.3	−1.50082	−0.750411	−	0.660971i	$-0.770145\pi$
$461$	−14855.3	−1.50082	−0.750411	+	0.660971i	$0.770145\pi$
$462$	−11933.4	−1.20171
$463$	−16158.2	−1.62189	−0.810947	−	0.585119i	$-0.801048\pi$
$463$	−16158.2	−1.62189	−0.810947	+	0.585119i	$0.801048\pi$
$464$	−2586.57	−0.258790
$465$	1333.05	0.132943
$466$	17068.4	1.69674
$467$	−400.958	−0.0397305	−0.0198653	−	0.999803i	$-0.506324\pi$
$467$	−400.958	−0.0397305	−0.0198653	+	0.999803i	$0.506324\pi$
$468$	−6594.85	−0.651382
$469$	−4111.14	−0.404765
$470$	−12161.6	−1.19356
$471$	−2338.59	−0.228783
$472$	−2331.06	−0.227322
$473$	4403.57	0.428069
$474$	38858.4	3.76546
$475$	3323.68	0.321054
$476$	7209.67	0.694232
$477$	7584.88	0.728067
$478$	7701.62	0.736954
$479$	727.013	0.0693488	0.0346744	−	0.999399i	$-0.488961\pi$
$479$	727.013	0.0693488	0.0346744	+	0.999399i	$0.488961\pi$
$480$	10469.9	0.995590
$481$	3986.15	0.377865
$482$	−16200.1	−1.53090
$483$	5040.53	0.474849
$484$	845.385	0.0793938
$485$	585.492	0.0548161
$486$	−12320.6	−1.14995
$487$	1556.49	0.144828	0.0724142	−	0.997375i	$-0.476930\pi$
$487$	1556.49	0.144828	0.0724142	+	0.997375i	$0.476930\pi$
$488$	8912.37	0.826730
$489$	−19191.1	−1.77474
$490$	−5861.01	−0.540354
$491$	−5659.45	−0.520178	−0.260089	−	0.965585i	$-0.583752\pi$
$491$	−5659.45	−0.520178	−0.260089	+	0.965585i	$0.583752\pi$
$492$	−13646.7	−1.25049
$493$	6002.88	0.548389
$494$	7494.08	0.682540
$495$	8815.43	0.800453
$496$	−1045.93	−0.0946845
$497$	1454.44	0.131269
$498$	25537.3	2.29790
$499$	−6411.75	−0.575209	−0.287605	−	0.957749i	$-0.592859\pi$
$499$	−6411.75	−0.575209	−0.287605	+	0.957749i	$0.592859\pi$
$500$	−1350.19	−0.120764
$501$	17334.4	1.54580
$502$	−21763.5	−1.93496
$503$	−9027.95	−0.800271	−0.400136	−	0.916456i	$-0.631037\pi$
$503$	−9027.95	−0.800271	−0.400136	+	0.916456i	$0.631037\pi$
$504$	−4863.17	−0.429808
$505$	−2207.43	−0.194513
$506$	−11191.8	−0.983271
$507$	−1453.45	−0.127318
$508$	−4684.67	−0.409150
$509$	−1553.02	−0.135239	−0.0676194	−	0.997711i	$-0.521540\pi$
$509$	−1553.02	−0.135239	−0.0676194	+	0.997711i	$0.521540\pi$
$510$	−14600.1	−1.26765
$511$	−6207.31	−0.537369
$512$	−11493.6	−0.992093
$513$	−22828.1	−1.96469
$514$	28659.1	2.45934
$515$	1263.00	0.108067
$516$	10897.0	0.929678
$517$	21058.2	1.79137
$518$	11333.5	0.961320
$519$	−10982.4	−0.928853
$520$	−789.588	−0.0665879
$521$	8024.45	0.674775	0.337387	−	0.941366i	$-0.390457\pi$
$521$	8024.45	0.674775	0.337387	+	0.941366i	$0.390457\pi$
$522$	−15612.0	−1.30904
$523$	−8153.27	−0.681678	−0.340839	−	0.940122i	$-0.610711\pi$
$523$	−8153.27	−0.681678	−0.340839	+	0.940122i	$0.610711\pi$
$524$	4836.09	0.403178
$525$	−1832.78	−0.152360
$526$	−10640.0	−0.881991
$527$	2427.38	0.200642
$528$	−10893.1	−0.897841
$529$	−7439.71	−0.611466
$530$	3501.37	0.286962
$531$	9012.48	0.736551
$532$	12241.1	0.997588
$533$	−1909.73	−0.155197
$534$	33413.7	2.70778
$535$	−3428.42	−0.277054
$536$	5858.60	0.472114
$537$	−33647.5	−2.70390
$538$	−15895.7	−1.27382
$539$	10148.5	0.810997
$540$	9273.51	0.739015
$541$	−3237.57	−0.257290	−0.128645	−	0.991691i	$-0.541063\pi$
$541$	−3237.57	−0.257290	−0.128645	+	0.991691i	$0.541063\pi$
$542$	−14201.9	−1.12551
$543$	25627.8	2.02541
$544$	19064.9	1.50257
$545$	−5463.52	−0.429416
$546$	−4132.47	−0.323907
$547$	−14716.4	−1.15032	−0.575161	−	0.818040i	$-0.695061\pi$
$547$	−14716.4	−1.15032	−0.575161	+	0.818040i	$0.695061\pi$
$548$	−8196.48	−0.638935
$549$	−34457.5	−2.67870
$550$	4069.42	0.315492
$551$	10192.1	0.788017
$552$	−7183.02	−0.553858
$553$	8882.41	0.683035
$554$	−21521.2	−1.65045
$555$	−13185.4	−1.00845
$556$	13012.7	0.992557
$557$	−18958.6	−1.44219	−0.721096	−	0.692835i	$-0.756361\pi$
$557$	−18958.6	−1.44219	−0.721096	+	0.692835i	$0.756361\pi$
$558$	−6312.99	−0.478943
$559$	1524.94	0.115381
$560$	1438.02	0.108513
$561$	25280.5	1.90257
$562$	−11678.0	−0.876523
$563$	−16319.9	−1.22167	−0.610835	−	0.791758i	$-0.709166\pi$
$563$	−16319.9	−1.22167	−0.610835	+	0.791758i	$0.709166\pi$
$564$	52110.1	3.89048
$565$	−900.559	−0.0670563
$566$	16064.3	1.19299
$567$	1778.81	0.131751
$568$	−2072.66	−0.153111
$569$	−21777.2	−1.60447	−0.802237	−	0.597006i	$-0.796357\pi$
$569$	−21777.2	−1.60447	−0.802237	+	0.597006i	$0.796357\pi$
$570$	−24789.0	−1.82157
$571$	−2739.63	−0.200788	−0.100394	−	0.994948i	$-0.532010\pi$
$571$	−2739.63	−0.200788	−0.100394	+	0.994948i	$0.532010\pi$
$572$	5271.37	0.385327
$573$	17118.0	1.24802
$574$	−5429.77	−0.394833
$575$	−1718.88	−0.124665
$576$	−36906.2	−2.66972
$577$	18712.2	1.35008	0.675042	−	0.737780i	$-0.264126\pi$
$577$	18712.2	1.35008	0.675042	+	0.737780i	$0.264126\pi$
$578$	−5282.53	−0.380146
$579$	5858.97	0.420536
$580$	−4140.36	−0.296412
$581$	5837.41	0.416827
$582$	−4366.78	−0.311012
$583$	−6062.73	−0.430691
$584$	8845.75	0.626781
$585$	3052.74	0.215753
$586$	15508.2	1.09324
$587$	−22923.6	−1.61186	−0.805928	−	0.592013i	$-0.798333\pi$
$587$	−22923.6	−1.61186	−0.805928	+	0.592013i	$0.798333\pi$
$588$	25113.3	1.76132
$589$	4121.36	0.288315
$590$	4160.39	0.290306
$591$	−3828.17	−0.266446
$592$	10345.5	0.718237
$593$	24452.0	1.69329	0.846646	−	0.532156i	$-0.178618\pi$
$593$	24452.0	1.69329	0.846646	+	0.532156i	$0.178618\pi$
$594$	−27950.1	−1.93065
$595$	−3337.35	−0.229946
$596$	23361.1	1.60555
$597$	18904.6	1.29600
$598$	−3875.66	−0.265029
$599$	20401.6	1.39163	0.695816	−	0.718220i	$-0.255043\pi$
$599$	20401.6	1.39163	0.695816	+	0.718220i	$0.255043\pi$
$600$	2611.81	0.177711
$601$	2639.98	0.179180	0.0895899	−	0.995979i	$-0.471444\pi$
$601$	2639.98	0.179180	0.0895899	+	0.995979i	$0.471444\pi$
$602$	4335.72	0.293539
$603$	−22650.8	−1.52971
$604$	−71.3655	−0.00480765
$605$	−391.327	−0.0262971
$606$	16463.7	1.10361
$607$	16681.4	1.11545	0.557723	−	0.830027i	$-0.311675\pi$
$607$	16681.4	1.11545	0.557723	+	0.830027i	$0.311675\pi$
$608$	32369.6	2.15915
$609$	−5620.22	−0.373962
$610$	−15906.4	−1.05579
$611$	7292.35	0.482843
$612$	39722.5	2.62367
$613$	25930.7	1.70853	0.854267	−	0.519834i	$-0.174006\pi$
$613$	25930.7	1.70853	0.854267	+	0.519834i	$0.174006\pi$
$614$	−36427.8	−2.39431
$615$	6317.04	0.414191
$616$	3887.22	0.254254
$617$	17376.9	1.13382	0.566910	−	0.823780i	$-0.308139\pi$
$617$	17376.9	1.13382	0.566910	+	0.823780i	$0.308139\pi$
$618$	−9419.86	−0.613143
$619$	29614.0	1.92292	0.961458	−	0.274951i	$-0.0886618\pi$
$619$	29614.0	1.92292	0.961458	+	0.274951i	$0.0886618\pi$
$620$	−1674.23	−0.108450
$621$	11805.8	0.762884
$622$	23321.1	1.50336
$623$	7637.83	0.491177
$624$	−3772.22	−0.242003
$625$	625.000	0.0400000
$626$	9109.60	0.581618
$627$	42922.9	2.73393
$628$	2937.14	0.186632
$629$	−24009.7	−1.52198
$630$	8679.59	0.548894
$631$	13576.4	0.856523	0.428262	−	0.903655i	$-0.359126\pi$
$631$	13576.4	0.856523	0.428262	+	0.903655i	$0.359126\pi$
$632$	−12657.9	−0.796684
$633$	−27895.4	−1.75157
$634$	−24407.3	−1.52892
$635$	2168.53	0.135520
$636$	−15002.7	−0.935372
$637$	3514.39	0.218595
$638$	12478.9	0.774365
$639$	8013.42	0.496097
$640$	−7297.71	−0.450730
$641$	−18468.0	−1.13798	−0.568988	−	0.822346i	$-0.692665\pi$
$641$	−18468.0	−1.13798	−0.568988	+	0.822346i	$0.692665\pi$
$642$	25570.2	1.57193
$643$	14022.5	0.860020	0.430010	−	0.902824i	$-0.358510\pi$
$643$	14022.5	0.860020	0.430010	+	0.902824i	$0.358510\pi$
$644$	−6330.62	−0.387362
$645$	−5044.21	−0.307931
$646$	−45138.9	−2.74917
$647$	28693.6	1.74353	0.871764	−	0.489925i	$-0.162976\pi$
$647$	28693.6	1.74353	0.871764	+	0.489925i	$0.162976\pi$
$648$	−2534.90	−0.153673
$649$	−7203.84	−0.435709
$650$	1409.22	0.0850373
$651$	−2272.64	−0.136823
$652$	24102.9	1.44776
$653$	21032.2	1.26042	0.630210	−	0.776425i	$-0.282969\pi$
$653$	21032.2	1.26042	0.630210	+	0.776425i	$0.282969\pi$
$654$	40748.6	2.43639
$655$	−2238.62	−0.133542
$656$	−4956.43	−0.294994
$657$	−34199.9	−2.03085
$658$	20733.7	1.22839
$659$	−9626.06	−0.569011	−0.284505	−	0.958674i	$-0.591829\pi$
$659$	−9626.06	−0.569011	−0.284505	+	0.958674i	$0.591829\pi$
$660$	−17436.7	−1.02837
$661$	−5940.13	−0.349537	−0.174769	−	0.984610i	$-0.555918\pi$
$661$	−5940.13	−0.349537	−0.174769	+	0.984610i	$0.555918\pi$
$662$	26202.2	1.53833
$663$	8754.53	0.512817
$664$	−8318.62	−0.486182
$665$	−5666.37	−0.330424
$666$	62443.0	3.63306
$667$	−5270.96	−0.305986
$668$	−21771.1	−1.26100
$669$	3993.75	0.230803
$670$	−10456.2	−0.602922
$671$	27542.5	1.58460
$672$	−17849.6	−1.02465
$673$	−9953.41	−0.570098	−0.285049	−	0.958513i	$-0.592010\pi$
$673$	−9953.41	−0.570098	−0.285049	+	0.958513i	$0.592010\pi$
$674$	10065.0	0.575206
$675$	−4292.69	−0.244779
$676$	1825.45	0.103861
$677$	34769.8	1.97388	0.986938	−	0.161103i	$-0.0515050\pi$
$677$	34769.8	1.97388	0.986938	+	0.161103i	$0.0515050\pi$
$678$	6716.64	0.380459
$679$	−998.175	−0.0564160
$680$	4755.90	0.268206
$681$	−6198.16	−0.348772
$682$	5046.08	0.283320
$683$	−6831.22	−0.382708	−0.191354	−	0.981521i	$-0.561288\pi$
$683$	−6831.22	−0.382708	−0.191354	+	0.981521i	$0.561288\pi$
$684$	67443.5	3.77013
$685$	3794.14	0.211630
$686$	22670.0	1.26173
$687$	27574.0	1.53132
$688$	3957.75	0.219314
$689$	−2099.50	−0.116088
$690$	12820.0	0.707315
$691$	−32219.3	−1.77378	−0.886889	−	0.461982i	$-0.847139\pi$
$691$	−32219.3	−1.77378	−0.886889	+	0.461982i	$0.847139\pi$
$692$	13793.3	0.757720
$693$	−15029.0	−0.823814
$694$	−25615.3	−1.40107
$695$	−6023.57	−0.328758
$696$	8009.12	0.436185
$697$	11502.8	0.625109
$698$	−46409.8	−2.51667
$699$	33854.1	1.83187
$700$	2301.86	0.124289
$701$	2307.21	0.124311	0.0621555	−	0.998066i	$-0.480203\pi$
$701$	2307.21	0.124311	0.0621555	+	0.998066i	$0.480203\pi$
$702$	−9678.98	−0.520384
$703$	−40765.2	−2.18704
$704$	29499.7	1.57928
$705$	−24121.7	−1.28862
$706$	−257.417	−0.0137224
$707$	3763.33	0.200190
$708$	−17826.5	−0.946271
$709$	−790.646	−0.0418806	−0.0209403	−	0.999781i	$-0.506666\pi$
$709$	−790.646	−0.0418806	−0.0209403	+	0.999781i	$0.506666\pi$
$710$	3699.19	0.195533
$711$	48938.7	2.58135
$712$	−10884.3	−0.572903
$713$	−2131.41	−0.111952
$714$	24890.9	1.30465
$715$	−2440.11	−0.127629
$716$	42259.3	2.20573
$717$	15275.7	0.795649
$718$	−9748.26	−0.506688
$719$	29782.1	1.54476	0.772382	−	0.635158i	$-0.219065\pi$
$719$	29782.1	1.54476	0.772382	+	0.635158i	$0.219065\pi$
$720$	7922.95	0.410099
$721$	−2153.23	−0.111221
$722$	−46898.7	−2.41744
$723$	−32131.8	−1.65283
$724$	−32187.1	−1.65224
$725$	1916.57	0.0981786
$726$	2918.64	0.149202
$727$	17417.1	0.888536	0.444268	−	0.895894i	$-0.353464\pi$
$727$	17417.1	0.888536	0.444268	+	0.895894i	$0.353464\pi$
$728$	1346.13	0.0685313
$729$	−30071.4	−1.52779
$730$	−15787.5	−0.800442
$731$	−9185.11	−0.464738
$732$	68156.0	3.44142
$733$	−31103.3	−1.56729	−0.783646	−	0.621208i	$-0.786642\pi$
$733$	−31103.3	−1.56729	−0.783646	+	0.621208i	$0.786642\pi$
$734$	−15223.7	−0.765555
$735$	−11624.9	−0.583390
$736$	−16740.3	−0.838393
$737$	18105.2	0.904903
$738$	−29916.0	−1.49217
$739$	−33138.5	−1.64955	−0.824777	−	0.565458i	$-0.808700\pi$
$739$	−33138.5	−1.64955	−0.824777	+	0.565458i	$0.808700\pi$
$740$	16560.2	0.822654
$741$	14864.0	0.736901
$742$	−5969.30	−0.295337
$743$	−9415.45	−0.464898	−0.232449	−	0.972609i	$-0.574674\pi$
$743$	−9415.45	−0.464898	−0.232449	+	0.972609i	$0.574674\pi$
$744$	3238.64	0.159589
$745$	−10813.8	−0.531797
$746$	−10018.1	−0.491672
$747$	32161.9	1.57529
$748$	−31750.9	−1.55204
$749$	5844.94	0.285140
$750$	−4661.44	−0.226949
$751$	5963.68	0.289771	0.144885	−	0.989448i	$-0.453719\pi$
$751$	5963.68	0.289771	0.144885	+	0.989448i	$0.453719\pi$
$752$	18926.2	0.917777
$753$	−43166.4	−2.08907
$754$	4321.39	0.208721
$755$	33.0350	0.00159241
$756$	−15809.9	−0.760584
$757$	−23993.3	−1.15198	−0.575990	−	0.817456i	$-0.695383\pi$
$757$	−23993.3	−1.15198	−0.575990	+	0.817456i	$0.695383\pi$
$758$	−8491.83	−0.406909
$759$	−22198.1	−1.06158
$760$	8074.88	0.385403
$761$	−14506.5	−0.691013	−0.345506	−	0.938416i	$-0.612293\pi$
$761$	−14506.5	−0.691013	−0.345506	+	0.938416i	$0.612293\pi$
$762$	−16173.5	−0.768904
$763$	9314.48	0.441949
$764$	−21499.2	−1.01808
$765$	−18387.5	−0.869021
$766$	148.247	0.00699268
$767$	−2494.66	−0.117440
$768$	362.369	0.0170259
$769$	−21002.6	−0.984880	−0.492440	−	0.870346i	$-0.663895\pi$
$769$	−21002.6	−0.984880	−0.492440	+	0.870346i	$0.663895\pi$
$770$	−6937.75	−0.324700
$771$	56843.5	2.65521
$772$	−7358.53	−0.343056
$773$	28563.3	1.32904	0.664521	−	0.747269i	$-0.268636\pi$
$773$	28563.3	1.32904	0.664521	+	0.747269i	$0.268636\pi$
$774$	23888.1	1.10936
$775$	775.000	0.0359211
$776$	1422.45	0.0658030
$777$	22479.2	1.03788
$778$	−14309.1	−0.659390
$779$	19530.3	0.898260
$780$	−6038.26	−0.277185
$781$	−6405.27	−0.293468
$782$	23344.1	1.06750
$783$	−13163.6	−0.600802
$784$	9121.07	0.415501
$785$	−1359.60	−0.0618168
$786$	16696.3	0.757681
$787$	−26543.7	−1.20226	−0.601131	−	0.799150i	$-0.705283\pi$
$787$	−26543.7	−1.20226	−0.601131	+	0.799150i	$0.705283\pi$
$788$	4807.96	0.217356
$789$	−21103.8	−0.952237
$790$	22591.3	1.01742
$791$	1535.32	0.0690133
$792$	21417.1	0.960888
$793$	9537.83	0.427110
$794$	−3183.28	−0.142280
$795$	6944.74	0.309817
$796$	−23743.1	−1.05723
$797$	−14478.7	−0.643490	−0.321745	−	0.946826i	$-0.604269\pi$
$797$	−14478.7	−0.643490	−0.321745	+	0.946826i	$0.604269\pi$
$798$	42261.5	1.87474
$799$	−43923.8	−1.94482
$800$	6086.93	0.269007
$801$	42081.5	1.85628
$802$	15586.3	0.686250
$803$	27336.6	1.20135
$804$	44802.8	1.96526
$805$	2930.43	0.128303
$806$	1747.44	0.0763658
$807$	−31528.1	−1.37527
$808$	−5362.94	−0.233500
$809$	−10500.6	−0.456344	−0.228172	−	0.973621i	$-0.573275\pi$
$809$	−10500.6	−0.456344	−0.228172	+	0.973621i	$0.573275\pi$
$810$	4524.18	0.196251
$811$	5571.15	0.241220	0.120610	−	0.992700i	$-0.461515\pi$
$811$	5571.15	0.241220	0.120610	+	0.992700i	$0.461515\pi$
$812$	7058.68	0.305063
$813$	−28168.6	−1.21515
$814$	−49911.8	−2.14915
$815$	−11157.2	−0.479533
$816$	22721.1	0.974752
$817$	−15595.1	−0.667813
$818$	40865.8	1.74675
$819$	−5204.47	−0.222050
$820$	−7933.84	−0.337880
$821$	−20157.5	−0.856884	−0.428442	−	0.903569i	$-0.640937\pi$
$821$	−20157.5	−0.856884	−0.428442	+	0.903569i	$0.640937\pi$
$822$	−28297.9	−1.20073
$823$	−2188.48	−0.0926921	−0.0463461	−	0.998925i	$-0.514758\pi$
$823$	−2188.48	−0.0926921	−0.0463461	+	0.998925i	$0.514758\pi$
$824$	3068.46	0.129727
$825$	8071.43	0.340620
$826$	−7092.83	−0.298778
$827$	9871.65	0.415080	0.207540	−	0.978227i	$-0.433454\pi$
$827$	9871.65	0.415080	0.207540	+	0.978227i	$0.433454\pi$
$828$	−34879.3	−1.46394
$829$	−2129.29	−0.0892077	−0.0446038	−	0.999005i	$-0.514203\pi$
$829$	−2129.29	−0.0892077	−0.0446038	+	0.999005i	$0.514203\pi$
$830$	14846.7	0.620888
$831$	−42685.9	−1.78190
$832$	10215.6	0.425677
$833$	−21168.1	−0.880469
$834$	44925.6	1.86528
$835$	10077.8	0.417672
$836$	−53908.8	−2.23023
$837$	−5322.94	−0.219818
$838$	9506.72	0.391890
$839$	−5763.19	−0.237148	−0.118574	−	0.992945i	$-0.537832\pi$
$839$	−5763.19	−0.237148	−0.118574	+	0.992945i	$0.537832\pi$
$840$	−4452.73	−0.182897
$841$	−18511.8	−0.759024
$842$	10909.6	0.446518
$843$	−23162.5	−0.946333
$844$	35035.0	1.42886
$845$	−845.000	−0.0344010
$846$	114235.	4.64239
$847$	667.154	0.0270646
$848$	−5448.93	−0.220657
$849$	31862.5	1.28801
$850$	−8488.12	−0.342518
$851$	21082.2	0.849224
$852$	−15850.4	−0.637352
$853$	−8878.99	−0.356402	−0.178201	−	0.983994i	$-0.557028\pi$
$853$	−8878.99	−0.356402	−0.178201	+	0.983994i	$0.557028\pi$
$854$	27118.0	1.08660
$855$	−31219.5	−1.24875
$856$	−8329.36	−0.332584
$857$	−478.423	−0.0190696	−0.00953479	−	0.999955i	$-0.503035\pi$
$857$	−478.423	−0.0190696	−0.00953479	+	0.999955i	$0.503035\pi$
$858$	18199.1	0.724134
$859$	13957.5	0.554393	0.277196	−	0.960813i	$-0.410595\pi$
$859$	13957.5	0.554393	0.277196	+	0.960813i	$0.410595\pi$
$860$	6335.24	0.251197
$861$	−10769.6	−0.426279
$862$	−21569.0	−0.852255
$863$	3663.12	0.144489	0.0722445	−	0.997387i	$-0.476984\pi$
$863$	3663.12	0.144489	0.0722445	+	0.997387i	$0.476984\pi$
$864$	−41806.9	−1.64618
$865$	−6384.90	−0.250975
$866$	68463.0	2.68645
$867$	−10477.6	−0.410423
$868$	2854.31	0.111615
$869$	−39117.5	−1.52701
$870$	−14294.3	−0.557039
$871$	6269.75	0.243906
$872$	−13273.6	−0.515484
$873$	−5499.56	−0.213210
$874$	39635.2	1.53396
$875$	−1065.53	−0.0411674
$876$	67646.6	2.60909
$877$	49595.6	1.90961	0.954803	−	0.297240i	$-0.0960662\pi$
$877$	49595.6	1.90961	0.954803	+	0.297240i	$0.0960662\pi$
$878$	33018.9	1.26917
$879$	30759.5	1.18031
$880$	−6332.95	−0.242595
$881$	−45396.9	−1.73605	−0.868025	−	0.496521i	$-0.834611\pi$
$881$	−45396.9	−1.73605	−0.868025	+	0.496521i	$0.834611\pi$
$882$	55052.8	2.10173
$883$	24268.7	0.924923	0.462461	−	0.886639i	$-0.346966\pi$
$883$	24268.7	0.924923	0.462461	+	0.886639i	$0.346966\pi$
$884$	−10995.2	−0.418335
$885$	8251.85	0.313427
$886$	−58541.9	−2.21981
$887$	38313.5	1.45033	0.725164	−	0.688576i	$-0.241764\pi$
$887$	38313.5	1.45033	0.725164	+	0.688576i	$0.241764\pi$
$888$	−32034.0	−1.21058
$889$	−3697.01	−0.139475
$890$	19425.9	0.731637
$891$	−7833.76	−0.294546
$892$	−5015.93	−0.188280
$893$	−74576.7	−2.79464
$894$	80652.9	3.01727
$895$	−19561.8	−0.730591
$896$	12441.5	0.463885
$897$	−7687.12	−0.286138
$898$	−2398.68	−0.0891370
$899$	2376.54	0.0881670
$900$	12682.4	0.469718
$901$	12645.8	0.467584
$902$	23912.3	0.882698
$903$	8599.61	0.316918
$904$	−2187.91	−0.0804964
$905$	14899.4	0.547262
$906$	−246.385	−0.00903488
$907$	−27513.4	−1.00724	−0.503620	−	0.863926i	$-0.667999\pi$
$907$	−27513.4	−1.00724	−0.503620	+	0.863926i	$0.667999\pi$
$908$	7784.53	0.284514
$909$	20734.5	0.756567
$910$	−2402.51	−0.0875192
$911$	21880.2	0.795743	0.397872	−	0.917441i	$-0.369749\pi$
$911$	21880.2	0.795743	0.397872	+	0.917441i	$0.369749\pi$
$912$	38577.4	1.40069
$913$	−25707.5	−0.931868
$914$	45317.3	1.64000
$915$	−31549.3	−1.13988
$916$	−34631.4	−1.24918
$917$	3816.50	0.137440
$918$	58299.1	2.09603
$919$	−14603.8	−0.524194	−0.262097	−	0.965042i	$-0.584414\pi$
$919$	−14603.8	−0.524194	−0.262097	+	0.965042i	$0.584414\pi$
$920$	−4176.03	−0.149652
$921$	−72252.1	−2.58500
$922$	64413.5	2.30081
$923$	−2218.12	−0.0791010
$924$	29726.9	1.05838
$925$	−7665.68	−0.272482
$926$	70063.3	2.48642
$927$	−11863.5	−0.420331
$928$	18665.6	0.660268
$929$	−46967.4	−1.65872	−0.829359	−	0.558716i	$-0.811294\pi$
$929$	−46967.4	−1.65872	−0.829359	+	0.558716i	$0.811294\pi$
$930$	−5780.19	−0.203806
$931$	−35940.6	−1.26520
$932$	−42518.8	−1.49437
$933$	46255.9	1.62310
$934$	1738.58	0.0609081
$935$	14697.4	0.514073
$936$	7416.64	0.258996
$937$	7918.62	0.276083	0.138042	−	0.990426i	$-0.455919\pi$
$937$	7918.62	0.276083	0.138042	+	0.990426i	$0.455919\pi$
$938$	17826.2	0.620518
$939$	18068.3	0.627941
$940$	30295.5	1.05120
$941$	43117.6	1.49372	0.746861	−	0.664980i	$-0.231560\pi$
$941$	43117.6	1.49372	0.746861	+	0.664980i	$0.231560\pi$
$942$	10140.3	0.350732
$943$	−10100.3	−0.348793
$944$	−6474.51	−0.223228
$945$	7318.39	0.251923
$946$	−19094.2	−0.656243
$947$	−55225.8	−1.89504	−0.947518	−	0.319703i	$-0.896417\pi$
$947$	−55225.8	−1.89504	−0.947518	+	0.319703i	$0.896417\pi$
$948$	−96799.5	−3.31635
$949$	9466.54	0.323811
$950$	−14411.7	−0.492187
$951$	−48410.3	−1.65070
$952$	−8108.08	−0.276034
$953$	225.875	0.00767767	0.00383883	−	0.999993i	$-0.498778\pi$
$953$	225.875	0.00767767	0.00383883	+	0.999993i	$0.498778\pi$
$954$	−32888.6	−1.11615
$955$	9951.95	0.337212
$956$	−19185.4	−0.649058
$957$	24751.1	0.836039
$958$	−3152.38	−0.106314
$959$	−6468.43	−0.217807
$960$	−33791.4	−1.13605
$961$	961.000	0.0322581
$962$	−17284.2	−0.579279
$963$	32203.4	1.07761
$964$	40355.8	1.34831
$965$	3406.25	0.113628
$966$	−21856.1	−0.727958
$967$	32610.5	1.08447	0.542235	−	0.840227i	$-0.317578\pi$
$967$	32610.5	1.08447	0.542235	+	0.840227i	$0.317578\pi$
$968$	−950.730	−0.0315678
$969$	−89530.0	−2.96813
$970$	−2538.73	−0.0840349
$971$	−6472.91	−0.213930	−0.106965	−	0.994263i	$-0.534113\pi$
$971$	−6472.91	−0.213930	−0.106965	+	0.994263i	$0.534113\pi$
$972$	30691.7	1.01279
$973$	10269.3	0.338353
$974$	−6749.06	−0.222027
$975$	2795.10	0.0918101
$976$	24754.0	0.811842
$977$	6839.07	0.223952	0.111976	−	0.993711i	$-0.464282\pi$
$977$	6839.07	0.223952	0.111976	+	0.993711i	$0.464282\pi$
$978$	83213.8	2.72074
$979$	−33636.5	−1.09809
$980$	14600.2	0.475906
$981$	51319.2	1.67023
$982$	24539.7	0.797449
$983$	18501.7	0.600319	0.300159	−	0.953889i	$-0.402960\pi$
$983$	18501.7	0.600319	0.300159	+	0.953889i	$0.402960\pi$
$984$	15347.2	0.497208
$985$	−2225.60	−0.0719934
$986$	−26028.9	−0.840698
$987$	41123.9	1.32623
$988$	−18668.4	−0.601134
$989$	8065.20	0.259311
$990$	−38224.3	−1.22712
$991$	4081.82	0.130841	0.0654204	−	0.997858i	$-0.479161\pi$
$991$	4081.82	0.130841	0.0654204	+	0.997858i	$0.479161\pi$
$992$	7547.79	0.241575
$993$	51970.3	1.66085
$994$	−6306.56	−0.201240
$995$	10990.6	0.350178
$996$	−63615.4	−2.02383
$997$	3424.69	0.108787	0.0543937	−	0.998520i	$-0.482677\pi$
$997$	3424.69	0.108787	0.0543937	+	0.998520i	$0.482677\pi$
$998$	27801.8	0.881815
$999$	52650.3	1.66745

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2015.4.a.d.1.6	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2015.4.a.d.1.6	✓	40	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:	\( N \)	\(=\)	\( 2015 = 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2015.a (trivial)

\(f(q)\)	\(=\)	\(q-4.33607 q^{2} -8.60031 q^{3} +10.8015 q^{4} -5.00000 q^{5} +37.2915 q^{6} +8.52424 q^{7} -12.1475 q^{8} +46.9653 q^{9} +O(q^{10})\)	\(q-4.33607 q^{2} -8.60031 q^{3} +10.8015 q^{4} -5.00000 q^{5} +37.2915 q^{6} +8.52424 q^{7} -12.1475 q^{8} +46.9653 q^{9} +21.6803 q^{10} -37.5402 q^{11} -92.8962 q^{12} -13.0000 q^{13} -36.9617 q^{14} +43.0015 q^{15} -33.7396 q^{16} +78.3025 q^{17} -203.645 q^{18} +132.947 q^{19} -54.0075 q^{20} -73.3111 q^{21} +162.777 q^{22} -68.7553 q^{23} +104.472 q^{24} +25.0000 q^{25} +56.3689 q^{26} -171.708 q^{27} +92.0746 q^{28} +76.6627 q^{29} -186.458 q^{30} +31.0000 q^{31} +243.477 q^{32} +322.857 q^{33} -339.525 q^{34} -42.6212 q^{35} +507.296 q^{36} -306.627 q^{37} -576.468 q^{38} +111.804 q^{39} +60.7375 q^{40} +146.903 q^{41} +317.882 q^{42} -117.303 q^{43} -405.490 q^{44} -234.827 q^{45} +298.128 q^{46} -560.950 q^{47} +290.171 q^{48} -270.337 q^{49} -108.402 q^{50} -673.425 q^{51} -140.420 q^{52} +161.500 q^{53} +744.537 q^{54} +187.701 q^{55} -103.548 q^{56} -1143.39 q^{57} -332.415 q^{58} +191.897 q^{59} +464.481 q^{60} -733.679 q^{61} -134.418 q^{62} +400.344 q^{63} -785.818 q^{64} +65.0000 q^{65} -1399.93 q^{66} -482.288 q^{67} +845.784 q^{68} +591.317 q^{69} +184.809 q^{70} +170.624 q^{71} -570.511 q^{72} -728.195 q^{73} +1329.56 q^{74} -215.008 q^{75} +1436.03 q^{76} -320.002 q^{77} -484.790 q^{78} +1042.02 q^{79} +168.698 q^{80} +208.677 q^{81} -636.980 q^{82} +684.801 q^{83} -791.870 q^{84} -391.512 q^{85} +508.634 q^{86} -659.322 q^{87} +456.019 q^{88} +896.013 q^{89} +1018.22 q^{90} -110.815 q^{91} -742.660 q^{92} -266.610 q^{93} +2432.32 q^{94} -664.736 q^{95} -2093.98 q^{96} -117.098 q^{97} +1172.20 q^{98} -1763.09 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9} + 25 q^{10} + 127 q^{11} - 76 q^{12} - 520 q^{13} + 138 q^{14} + 85 q^{15} + 413 q^{16} - 264 q^{17} - 126 q^{18} - q^{19} - 745 q^{20} + 176 q^{21} - 191 q^{22} - 106 q^{23} + 31 q^{24} + 1000 q^{25} + 65 q^{26} - 344 q^{27} + 255 q^{28} + 107 q^{29} + 175 q^{30} + 1240 q^{31} - 372 q^{32} - 386 q^{33} - 6 q^{34} + 100 q^{35} + 790 q^{36} - 741 q^{37} - 318 q^{38} + 221 q^{39} + 195 q^{40} + 1232 q^{41} - 1180 q^{42} - 615 q^{43} - 152 q^{44} - 1235 q^{45} - 329 q^{46} - 784 q^{47} - 1089 q^{48} - 516 q^{49} - 125 q^{50} - 200 q^{51} - 1937 q^{52} - 1503 q^{53} + 1658 q^{54} - 635 q^{55} + 1518 q^{56} - 1704 q^{57} - 1035 q^{58} - 107 q^{59} + 380 q^{60} - 857 q^{61} - 155 q^{62} - 2636 q^{63} - 215 q^{64} + 2600 q^{65} - 1785 q^{66} - 2689 q^{67} - 2639 q^{68} + 2544 q^{69} - 690 q^{70} + 1554 q^{71} - 420 q^{72} - 1968 q^{73} - 27 q^{74} - 425 q^{75} - 110 q^{76} - 1040 q^{77} + 455 q^{78} - 3182 q^{79} - 2065 q^{80} - 1576 q^{81} - 386 q^{82} + 317 q^{83} - 617 q^{84} + 1320 q^{85} + 347 q^{86} - 216 q^{87} - 4081 q^{88} + 3610 q^{89} + 630 q^{90} + 260 q^{91} - 4965 q^{92} - 527 q^{93} - 2942 q^{94} + 5 q^{95} + 1002 q^{96} - 3318 q^{97} + 1659 q^{98} + 5943 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9 + 25 * q^10 + 127 * q^11 - 76 * q^12 - 520 * q^13 + 138 * q^14 + 85 * q^15 + 413 * q^16 - 264 * q^17 - 126 * q^18 - q^19 - 745 * q^20 + 176 * q^21 - 191 * q^22 - 106 * q^23 + 31 * q^24 + 1000 * q^25 + 65 * q^26 - 344 * q^27 + 255 * q^28 + 107 * q^29 + 175 * q^30 + 1240 * q^31 - 372 * q^32 - 386 * q^33 - 6 * q^34 + 100 * q^35 + 790 * q^36 - 741 * q^37 - 318 * q^38 + 221 * q^39 + 195 * q^40 + 1232 * q^41 - 1180 * q^42 - 615 * q^43 - 152 * q^44 - 1235 * q^45 - 329 * q^46 - 784 * q^47 - 1089 * q^48 - 516 * q^49 - 125 * q^50 - 200 * q^51 - 1937 * q^52 - 1503 * q^53 + 1658 * q^54 - 635 * q^55 + 1518 * q^56 - 1704 * q^57 - 1035 * q^58 - 107 * q^59 + 380 * q^60 - 857 * q^61 - 155 * q^62 - 2636 * q^63 - 215 * q^64 + 2600 * q^65 - 1785 * q^66 - 2689 * q^67 - 2639 * q^68 + 2544 * q^69 - 690 * q^70 + 1554 * q^71 - 420 * q^72 - 1968 * q^73 - 27 * q^74 - 425 * q^75 - 110 * q^76 - 1040 * q^77 + 455 * q^78 - 3182 * q^79 - 2065 * q^80 - 1576 * q^81 - 386 * q^82 + 317 * q^83 - 617 * q^84 + 1320 * q^85 + 347 * q^86 - 216 * q^87 - 4081 * q^88 + 3610 * q^89 + 630 * q^90 + 260 * q^91 - 4965 * q^92 - 527 * q^93 - 2942 * q^94 + 5 * q^95 + 1002 * q^96 - 3318 * q^97 + 1659 * q^98 + 5943 * q^99

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