LMFDB - Embedded newform 2015.4.a.d.1.9

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			1.9
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)

$f(q)$	$=$	$q-3.76849 q^{2} +3.72438 q^{3} +6.20150 q^{4} -5.00000 q^{5} -14.0353 q^{6} -30.0034 q^{7} +6.77763 q^{8} -13.1290 q^{9} +O(q^{10})$	\(q-3.76849 q^{2} +3.72438 q^{3} +6.20150 q^{4} -5.00000 q^{5} -14.0353 q^{6} -30.0034 q^{7} +6.77763 q^{8} -13.1290 q^{9} +18.8424 q^{10} +7.58960 q^{11} +23.0967 q^{12} -13.0000 q^{13} +113.067 q^{14} -18.6219 q^{15} -75.1534 q^{16} +49.1398 q^{17} +49.4765 q^{18} +31.8346 q^{19} -31.0075 q^{20} -111.744 q^{21} -28.6013 q^{22} +96.1237 q^{23} +25.2425 q^{24} +25.0000 q^{25} +48.9903 q^{26} -149.456 q^{27} -186.066 q^{28} -181.561 q^{29} +70.1764 q^{30} +31.0000 q^{31} +228.994 q^{32} +28.2666 q^{33} -185.183 q^{34} +150.017 q^{35} -81.4195 q^{36} +136.681 q^{37} -119.968 q^{38} -48.4169 q^{39} -33.8881 q^{40} -222.172 q^{41} +421.106 q^{42} +299.839 q^{43} +47.0669 q^{44} +65.6450 q^{45} -362.241 q^{46} +239.078 q^{47} -279.900 q^{48} +557.202 q^{49} -94.2122 q^{50} +183.015 q^{51} -80.6195 q^{52} -338.422 q^{53} +563.222 q^{54} -37.9480 q^{55} -203.352 q^{56} +118.564 q^{57} +684.212 q^{58} +433.586 q^{59} -115.484 q^{60} +379.531 q^{61} -116.823 q^{62} +393.914 q^{63} -261.732 q^{64} +65.0000 q^{65} -106.522 q^{66} -198.810 q^{67} +304.741 q^{68} +358.001 q^{69} -565.337 q^{70} +26.0919 q^{71} -88.9835 q^{72} +909.013 q^{73} -515.080 q^{74} +93.1095 q^{75} +197.423 q^{76} -227.714 q^{77} +182.459 q^{78} +387.026 q^{79} +375.767 q^{80} -202.146 q^{81} +837.253 q^{82} -1062.40 q^{83} -692.980 q^{84} -245.699 q^{85} -1129.94 q^{86} -676.203 q^{87} +51.4395 q^{88} +1613.80 q^{89} -247.382 q^{90} +390.044 q^{91} +596.111 q^{92} +115.456 q^{93} -900.964 q^{94} -159.173 q^{95} +852.859 q^{96} +344.813 q^{97} -2099.81 q^{98} -99.6439 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.76849	−1.33236	−0.666181	−	0.745790i	$-0.732072\pi$
$2$	−3.76849	−1.33236	−0.666181	+	0.745790i	$0.732072\pi$
$3$	3.72438	0.716757	0.358379	−	0.933576i	$-0.383330\pi$
$3$	3.72438	0.716757	0.358379	+	0.933576i	$0.383330\pi$
$4$	6.20150	0.775187
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−14.0353	−0.954980
$7$	−30.0034	−1.62003	−0.810015	−	0.586409i	$-0.800541\pi$
$7$	−30.0034	−1.62003	−0.810015	+	0.586409i	$0.800541\pi$
$8$	6.77763	0.299532
$9$	−13.1290	−0.486259
$10$	18.8424	0.595850
$11$	7.58960	0.208032	0.104016	−	0.994576i	$-0.466831\pi$
$11$	7.58960	0.208032	0.104016	+	0.994576i	$0.466831\pi$
$12$	23.0967	0.555621
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	113.067	2.15847
$15$	−18.6219	−0.320544
$16$	−75.1534	−1.17427
$17$	49.1398	0.701068	0.350534	−	0.936550i	$-0.386000\pi$
$17$	49.1398	0.701068	0.350534	+	0.936550i	$0.386000\pi$
$18$	49.4765	0.647873
$19$	31.8346	0.384388	0.192194	−	0.981357i	$-0.438440\pi$
$19$	31.8346	0.384388	0.192194	+	0.981357i	$0.438440\pi$
$20$	−31.0075	−0.346674
$21$	−111.744	−1.16117
$22$	−28.6013	−0.277174
$23$	96.1237	0.871442	0.435721	−	0.900082i	$-0.356493\pi$
$23$	96.1237	0.871442	0.435721	+	0.900082i	$0.356493\pi$
$24$	25.2425	0.214691
$25$	25.0000	0.200000
$26$	48.9903	0.369531
$27$	−149.456	−1.06529
$28$	−186.066	−1.25583
$29$	−181.561	−1.16259	−0.581295	−	0.813693i	$-0.697454\pi$
$29$	−181.561	−1.16259	−0.581295	+	0.813693i	$0.697454\pi$
$30$	70.1764	0.427080
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	228.994	1.26502
$33$	28.2666	0.149108
$34$	−185.183	−0.934076
$35$	150.017	0.724499
$36$	−81.4195	−0.376942
$37$	136.681	0.607303	0.303651	−	0.952783i	$-0.401794\pi$
$37$	136.681	0.607303	0.303651	+	0.952783i	$0.401794\pi$
$38$	−119.968	−0.512144
$39$	−48.4169	−0.198793
$40$	−33.8881	−0.133955
$41$	−222.172	−0.846280	−0.423140	−	0.906064i	$-0.639072\pi$
$41$	−222.172	−0.846280	−0.423140	+	0.906064i	$0.639072\pi$
$42$	421.106	1.54710
$43$	299.839	1.06337	0.531686	−	0.846942i	$-0.321559\pi$
$43$	299.839	1.06337	0.531686	+	0.846942i	$0.321559\pi$
$44$	47.0669	0.161264
$45$	65.6450	0.217462
$46$	−362.241	−1.16108
$47$	239.078	0.741982	0.370991	−	0.928636i	$-0.379018\pi$
$47$	239.078	0.741982	0.370991	+	0.928636i	$0.379018\pi$
$48$	−279.900	−0.841668
$49$	557.202	1.62450
$50$	−94.2122	−0.266472
$51$	183.015	0.502496
$52$	−80.6195	−0.214998
$53$	−338.422	−0.877091	−0.438545	−	0.898709i	$-0.644506\pi$
$53$	−338.422	−0.877091	−0.438545	+	0.898709i	$0.644506\pi$
$54$	563.222	1.41935
$55$	−37.9480	−0.0930347
$56$	−203.352	−0.485250
$57$	118.564	0.275513
$58$	684.212	1.54899
$59$	433.586	0.956747	0.478374	−	0.878156i	$-0.341226\pi$
$59$	433.586	0.956747	0.478374	+	0.878156i	$0.341226\pi$
$60$	−115.484	−0.248481
$61$	379.531	0.796623	0.398311	−	0.917250i	$-0.369596\pi$
$61$	379.531	0.796623	0.398311	+	0.917250i	$0.369596\pi$
$62$	−116.823	−0.239299
$63$	393.914	0.787754
$64$	−261.732	−0.511196
$65$	65.0000	0.124035
$66$	−106.522	−0.198666
$67$	−198.810	−0.362514	−0.181257	−	0.983436i	$-0.558017\pi$
$67$	−198.810	−0.362514	−0.181257	+	0.983436i	$0.558017\pi$
$68$	304.741	0.543459
$69$	358.001	0.624613
$70$	−565.337	−0.965295
$71$	26.0919	0.0436131	0.0218066	−	0.999762i	$-0.493058\pi$
$71$	26.0919	0.0436131	0.0218066	+	0.999762i	$0.493058\pi$
$72$	−88.9835	−0.145650
$73$	909.013	1.45742	0.728711	−	0.684821i	$-0.240120\pi$
$73$	909.013	1.45742	0.728711	+	0.684821i	$0.240120\pi$
$74$	−515.080	−0.809147
$75$	93.1095	0.143351
$76$	197.423	0.297973
$77$	−227.714	−0.337018
$78$	182.459	0.264864
$79$	387.026	0.551188	0.275594	−	0.961274i	$-0.411126\pi$
$79$	387.026	0.551188	0.275594	+	0.961274i	$0.411126\pi$
$80$	375.767	0.525150
$81$	−202.146	−0.277293
$82$	837.253	1.12755
$83$	−1062.40	−1.40499	−0.702495	−	0.711689i	$-0.747930\pi$
$83$	−1062.40	−1.40499	−0.702495	+	0.711689i	$0.747930\pi$
$84$	−692.980	−0.900122
$85$	−245.699	−0.313527
$86$	−1129.94	−1.41680
$87$	−676.203	−0.833294
$88$	51.4395	0.0623122
$89$	1613.80	1.92205	0.961026	−	0.276457i	$-0.0891604\pi$
$89$	1613.80	1.92205	0.961026	+	0.276457i	$0.0891604\pi$
$90$	−247.382	−0.289738
$91$	390.044	0.449315
$92$	596.111	0.675531
$93$	115.456	0.128733
$94$	−900.964	−0.988589
$95$	−159.173	−0.171903
$96$	852.859	0.906714
$97$	344.813	0.360932	0.180466	−	0.983581i	$-0.442239\pi$
$97$	344.813	0.360932	0.180466	+	0.983581i	$0.442239\pi$
$98$	−2099.81	−2.16442
$99$	−99.6439	−0.101157
$100$	155.037	0.155037
$101$	−196.423	−0.193513	−0.0967566	−	0.995308i	$-0.530847\pi$
$101$	−196.423	−0.193513	−0.0967566	+	0.995308i	$0.530847\pi$
$102$	−689.691	−0.669506
$103$	91.4789	0.0875115	0.0437558	−	0.999042i	$-0.486068\pi$
$103$	91.4789	0.0875115	0.0437558	+	0.999042i	$0.486068\pi$
$104$	−88.1092	−0.0830751
$105$	558.720	0.519290
$106$	1275.34	1.16860
$107$	300.327	0.271343	0.135672	−	0.990754i	$-0.456681\pi$
$107$	300.327	0.271343	0.135672	+	0.990754i	$0.456681\pi$
$108$	−926.849	−0.825797
$109$	103.452	0.0909071	0.0454536	−	0.998966i	$-0.485527\pi$
$109$	103.452	0.0909071	0.0454536	+	0.998966i	$0.485527\pi$
$110$	143.007	0.123956
$111$	509.052	0.435289
$112$	2254.86	1.90236
$113$	−2059.61	−1.71462	−0.857308	−	0.514804i	$-0.827865\pi$
$113$	−2059.61	−1.71462	−0.857308	+	0.514804i	$0.827865\pi$
$114$	−446.808	−0.367083
$115$	−480.618	−0.389721
$116$	−1125.95	−0.901225
$117$	170.677	0.134864
$118$	−1633.96	−1.27473
$119$	−1474.36	−1.13575
$120$	−126.212	−0.0960129
$121$	−1273.40	−0.956723
$122$	−1430.26	−1.06139
$123$	−827.454	−0.606577
$124$	192.246	0.139228
$125$	−125.000	−0.0894427
$126$	−1484.46	−1.04957
$127$	182.823	0.127740	0.0638698	−	0.997958i	$-0.479656\pi$
$127$	182.823	0.127740	0.0638698	+	0.997958i	$0.479656\pi$
$128$	−845.614	−0.583925
$129$	1116.71	0.762179
$130$	−244.952	−0.165259
$131$	−546.866	−0.364732	−0.182366	−	0.983231i	$-0.558376\pi$
$131$	−546.866	−0.364732	−0.182366	+	0.983231i	$0.558376\pi$
$132$	175.295	0.115587
$133$	−955.147	−0.622720
$134$	749.212	0.483000
$135$	747.278	0.476411
$136$	333.052	0.209992
$137$	435.241	0.271424	0.135712	−	0.990748i	$-0.456668\pi$
$137$	435.241	0.271424	0.135712	+	0.990748i	$0.456668\pi$
$138$	−1349.12	−0.832210
$139$	−1565.25	−0.955125	−0.477563	−	0.878598i	$-0.658480\pi$
$139$	−1565.25	−0.955125	−0.477563	+	0.878598i	$0.658480\pi$
$140$	930.329	0.561623
$141$	890.419	0.531821
$142$	−98.3268	−0.0581085
$143$	−98.6649	−0.0576977
$144$	986.689	0.571001
$145$	907.807	0.519926
$146$	−3425.60	−1.94181
$147$	2075.23	1.16437
$148$	847.627	0.470773
$149$	1923.66	1.05767	0.528833	−	0.848726i	$-0.322630\pi$
$149$	1923.66	1.05767	0.528833	+	0.848726i	$0.322630\pi$
$150$	−350.882	−0.190996
$151$	1386.42	0.747187	0.373593	−	0.927593i	$-0.378126\pi$
$151$	1386.42	0.747187	0.373593	+	0.927593i	$0.378126\pi$
$152$	215.763	0.115136
$153$	−645.157	−0.340901
$154$	858.136	0.449030
$155$	−155.000	−0.0803219
$156$	−300.258	−0.154102
$157$	−388.268	−0.197370	−0.0986851	−	0.995119i	$-0.531464\pi$
$157$	−388.268	−0.197370	−0.0986851	+	0.995119i	$0.531464\pi$
$158$	−1458.50	−0.734381
$159$	−1260.41	−0.628661
$160$	−1144.97	−0.565736
$161$	−2884.03	−1.41176
$162$	761.786	0.369454
$163$	−3241.59	−1.55767	−0.778837	−	0.627226i	$-0.784190\pi$
$163$	−3241.59	−1.55767	−0.778837	+	0.627226i	$0.784190\pi$
$164$	−1377.80	−0.656025
$165$	−141.333	−0.0666833
$166$	4003.66	1.87195
$167$	−2289.27	−1.06077	−0.530386	−	0.847756i	$-0.677953\pi$
$167$	−2289.27	−1.06077	−0.530386	+	0.847756i	$0.677953\pi$
$168$	−757.359	−0.347807
$169$	169.000	0.0769231
$170$	925.914	0.417732
$171$	−417.957	−0.186912
$172$	1859.45	0.824312
$173$	2376.40	1.04436	0.522180	−	0.852835i	$-0.325119\pi$
$173$	2376.40	1.04436	0.522180	+	0.852835i	$0.325119\pi$
$174$	2548.26	1.11025
$175$	−750.084	−0.324006
$176$	−570.385	−0.244286
$177$	1614.84	0.685755
$178$	−6081.59	−2.56087
$179$	−938.983	−0.392083	−0.196042	−	0.980596i	$-0.562809\pi$
$179$	−938.983	−0.392083	−0.196042	+	0.980596i	$0.562809\pi$
$180$	407.097	0.168574
$181$	−935.891	−0.384333	−0.192166	−	0.981362i	$-0.561551\pi$
$181$	−935.891	−0.384333	−0.192166	+	0.981362i	$0.561551\pi$
$182$	−1469.88	−0.598651
$183$	1413.52	0.570985
$184$	651.491	0.261025
$185$	−683.405	−0.271594
$186$	−435.094	−0.171519
$187$	372.952	0.145845
$188$	1482.64	0.575175
$189$	4484.17	1.72580
$190$	599.842	0.229038
$191$	−872.484	−0.330527	−0.165264	−	0.986249i	$-0.552848\pi$
$191$	−872.484	−0.330527	−0.165264	+	0.986249i	$0.552848\pi$
$192$	−974.791	−0.366404
$193$	−520.332	−0.194064	−0.0970320	−	0.995281i	$-0.530935\pi$
$193$	−520.332	−0.194064	−0.0970320	+	0.995281i	$0.530935\pi$
$194$	−1299.42	−0.480892
$195$	242.085	0.0889028
$196$	3455.49	1.25929
$197$	811.530	0.293498	0.146749	−	0.989174i	$-0.453119\pi$
$197$	811.530	0.293498	0.146749	+	0.989174i	$0.453119\pi$
$198$	375.507	0.134778
$199$	1359.63	0.484328	0.242164	−	0.970235i	$-0.422143\pi$
$199$	1359.63	0.484328	0.242164	+	0.970235i	$0.422143\pi$
$200$	169.441	0.0599063
$201$	−740.443	−0.259835
$202$	740.218	0.257830
$203$	5447.45	1.88343
$204$	1134.97	0.389528
$205$	1110.86	0.378468
$206$	−344.737	−0.116597
$207$	−1262.01	−0.423747
$208$	976.994	0.325684
$209$	241.612	0.0799650
$210$	−2105.53	−0.691882
$211$	−604.286	−0.197160	−0.0985800	−	0.995129i	$-0.531430\pi$
$211$	−604.286	−0.197160	−0.0985800	+	0.995129i	$0.531430\pi$
$212$	−2098.72	−0.679910
$213$	97.1759	0.0312600
$214$	−1131.78	−0.361527
$215$	−1499.19	−0.475554
$216$	−1012.95	−0.319087
$217$	−930.104	−0.290966
$218$	−389.856	−0.121121
$219$	3385.51	1.04462
$220$	−235.335	−0.0721194
$221$	−638.818	−0.194441
$222$	−1918.35	−0.579962
$223$	−2695.24	−0.809356	−0.404678	−	0.914459i	$-0.632616\pi$
$223$	−2695.24	−0.809356	−0.404678	+	0.914459i	$0.632616\pi$
$224$	−6870.58	−2.04937
$225$	−328.225	−0.0972519
$226$	7761.60	2.28449
$227$	−610.006	−0.178359	−0.0891796	−	0.996016i	$-0.528425\pi$
$227$	−610.006	−0.178359	−0.0891796	+	0.996016i	$0.528425\pi$
$228$	735.276	0.213574
$229$	2829.46	0.816490	0.408245	−	0.912872i	$-0.366141\pi$
$229$	2829.46	0.816490	0.408245	+	0.912872i	$0.366141\pi$
$230$	1811.20	0.519249
$231$	−848.092	−0.241560
$232$	−1230.56	−0.348232
$233$	1215.22	0.341680	0.170840	−	0.985299i	$-0.445352\pi$
$233$	1215.22	0.341680	0.170840	+	0.985299i	$0.445352\pi$
$234$	−643.194	−0.179688
$235$	−1195.39	−0.331825
$236$	2688.88	0.741658
$237$	1441.43	0.395068
$238$	5556.11	1.51323
$239$	1909.22	0.516726	0.258363	−	0.966048i	$-0.416817\pi$
$239$	1909.22	0.516726	0.258363	+	0.966048i	$0.416817\pi$
$240$	1399.50	0.376405
$241$	−3460.29	−0.924883	−0.462442	−	0.886650i	$-0.653027\pi$
$241$	−3460.29	−0.924883	−0.462442	+	0.886650i	$0.653027\pi$
$242$	4798.78	1.27470
$243$	3282.43	0.866535
$244$	2353.66	0.617532
$245$	−2786.01	−0.726497
$246$	3118.25	0.808180
$247$	−413.850	−0.106610
$248$	210.106	0.0537975
$249$	−3956.80	−1.00704
$250$	471.061	0.119170
$251$	−2025.14	−0.509266	−0.254633	−	0.967038i	$-0.581955\pi$
$251$	−2025.14	−0.509266	−0.254633	+	0.967038i	$0.581955\pi$
$252$	2442.86	0.610657
$253$	729.541	0.181288
$254$	−688.967	−0.170195
$255$	−915.077	−0.224723
$256$	5280.54	1.28920
$257$	3.49864	0.000849179 0	0.000424590	−	1.00000i	$-0.499865\pi$
$257$	3.49864	0.000849179 0	0.000424590		1.00000i	$0.499865\pi$
$258$	−4208.32	−1.01550
$259$	−4100.89	−0.983849
$260$	403.097	0.0961502
$261$	2383.72	0.565320
$262$	2060.86	0.485955
$263$	−2492.07	−0.584288	−0.292144	−	0.956374i	$-0.594369\pi$
$263$	−2492.07	−0.584288	−0.292144	+	0.956374i	$0.594369\pi$
$264$	191.580	0.0446627
$265$	1692.11	0.392247
$266$	3599.46	0.829688
$267$	6010.41	1.37764
$268$	−1232.92	−0.281017
$269$	676.822	0.153407	0.0767037	−	0.997054i	$-0.475560\pi$
$269$	676.822	0.153407	0.0767037	+	0.997054i	$0.475560\pi$
$270$	−2816.11	−0.634751
$271$	2089.33	0.468332	0.234166	−	0.972197i	$-0.424764\pi$
$271$	2089.33	0.468332	0.234166	+	0.972197i	$0.424764\pi$
$272$	−3693.03	−0.823245
$273$	1452.67	0.322050
$274$	−1640.20	−0.361636
$275$	189.740	0.0416064
$276$	2220.14	0.484192
$277$	5934.11	1.28717	0.643585	−	0.765374i	$-0.277446\pi$
$277$	5934.11	1.28717	0.643585	+	0.765374i	$0.277446\pi$
$278$	5898.61	1.27257
$279$	−406.999	−0.0873347
$280$	1016.76	0.217010
$281$	6642.90	1.41026	0.705128	−	0.709080i	$-0.250889\pi$
$281$	6642.90	1.41026	0.705128	+	0.709080i	$0.250889\pi$
$282$	−3355.53	−0.708578
$283$	−2823.48	−0.593069	−0.296535	−	0.955022i	$-0.595831\pi$
$283$	−2823.48	−0.593069	−0.296535	+	0.955022i	$0.595831\pi$
$284$	161.809	0.0338084
$285$	−592.821	−0.123213
$286$	371.817	0.0768742
$287$	6665.92	1.37100
$288$	−3006.46	−0.615129
$289$	−2498.28	−0.508503
$290$	−3421.06	−0.692729
$291$	1284.21	0.258701
$292$	5637.24	1.12978
$293$	310.152	0.0618405	0.0309203	−	0.999522i	$-0.490156\pi$
$293$	310.152	0.0618405	0.0309203	+	0.999522i	$0.490156\pi$
$294$	−7820.48	−1.55136
$295$	−2167.93	−0.427870
$296$	926.373	0.181906
$297$	−1134.31	−0.221614
$298$	−7249.28	−1.40919
$299$	−1249.61	−0.241695
$300$	577.418	0.111124
$301$	−8996.17	−1.72269
$302$	−5224.71	−0.995523
$303$	−731.554	−0.138702
$304$	−2392.48	−0.451376
$305$	−1897.66	−0.356261
$306$	2431.27	0.454203
$307$	2480.49	0.461137	0.230569	−	0.973056i	$-0.425941\pi$
$307$	2480.49	0.461137	0.230569	+	0.973056i	$0.425941\pi$
$308$	−1412.17	−0.261252
$309$	340.702	0.0627245
$310$	584.116	0.107018
$311$	−4053.00	−0.738987	−0.369493	−	0.929233i	$-0.620469\pi$
$311$	−4053.00	−0.738987	−0.369493	+	0.929233i	$0.620469\pi$
$312$	−328.152	−0.0595447
$313$	−9682.74	−1.74857	−0.874283	−	0.485417i	$-0.838668\pi$
$313$	−9682.74	−1.74857	−0.874283	+	0.485417i	$0.838668\pi$
$314$	1463.18	0.262968
$315$	−1969.57	−0.352294
$316$	2400.14	0.427274
$317$	7813.56	1.38440	0.692198	−	0.721708i	$-0.256643\pi$
$317$	7813.56	1.38440	0.692198	+	0.721708i	$0.256643\pi$
$318$	4749.84	0.837604
$319$	−1377.98	−0.241856
$320$	1308.66	0.228614
$321$	1118.53	0.194487
$322$	10868.4	1.88098
$323$	1564.35	0.269482
$324$	−1253.61	−0.214954
$325$	−325.000	−0.0554700
$326$	12215.9	2.07539
$327$	385.293	0.0651583
$328$	−1505.80	−0.253488
$329$	−7173.16	−1.20203
$330$	532.611	0.0888463
$331$	3985.03	0.661743	0.330872	−	0.943676i	$-0.392657\pi$
$331$	3985.03	0.661743	0.330872	+	0.943676i	$0.392657\pi$
$332$	−6588.50	−1.08913
$333$	−1794.48	−0.295307
$334$	8627.08	1.41333
$335$	994.048	0.162121
$336$	8397.93	1.36353
$337$	−11605.8	−1.87599	−0.937994	−	0.346650i	$-0.887319\pi$
$337$	−11605.8	−1.87599	−0.937994	+	0.346650i	$0.887319\pi$
$338$	−636.874	−0.102489
$339$	−7670.76	−1.22896
$340$	−1523.70	−0.243042
$341$	235.278	0.0373636
$342$	1575.07	0.249035
$343$	−6426.78	−1.01170
$344$	2032.20	0.318514
$345$	−1790.01	−0.279335
$346$	−8955.43	−1.39146
$347$	−12034.1	−1.86174	−0.930870	−	0.365350i	$-0.880949\pi$
$347$	−12034.1	−1.86174	−0.930870	+	0.365350i	$0.880949\pi$
$348$	−4193.47	−0.645959
$349$	−5876.42	−0.901312	−0.450656	−	0.892698i	$-0.648810\pi$
$349$	−5876.42	−0.901312	−0.450656	+	0.892698i	$0.648810\pi$
$350$	2826.68	0.431693
$351$	1942.92	0.295457
$352$	1737.97	0.263165
$353$	−7357.81	−1.10940	−0.554698	−	0.832052i	$-0.687166\pi$
$353$	−7357.81	−1.10940	−0.554698	+	0.832052i	$0.687166\pi$
$354$	−6085.50	−0.913674
$355$	−130.459	−0.0195044
$356$	10008.0	1.48995
$357$	−5491.08	−0.814058
$358$	3538.55	0.522396
$359$	−25.7016	−0.00377849	−0.00188925	−	0.999998i	$-0.500601\pi$
$359$	−25.7016	−0.00377849	−0.00188925	+	0.999998i	$0.500601\pi$
$360$	444.917	0.0651367
$361$	−5845.56	−0.852246
$362$	3526.89	0.512070
$363$	−4742.62	−0.685738
$364$	2418.86	0.348304
$365$	−4545.06	−0.651779
$366$	−5326.83	−0.760759
$367$	−544.275	−0.0774140	−0.0387070	−	0.999251i	$-0.512324\pi$
$367$	−544.275	−0.0774140	−0.0387070	+	0.999251i	$0.512324\pi$
$368$	−7224.02	−1.02331
$369$	2916.90	0.411511
$370$	2575.40	0.361862
$371$	10153.8	1.42091
$372$	715.999	0.0997925
$373$	1809.38	0.251170	0.125585	−	0.992083i	$-0.459919\pi$
$373$	1809.38	0.251170	0.125585	+	0.992083i	$0.459919\pi$
$374$	−1405.46	−0.194318
$375$	−465.547	−0.0641087
$376$	1620.38	0.222247
$377$	2360.30	0.322444
$378$	−16898.5	−2.29938
$379$	−3299.86	−0.447236	−0.223618	−	0.974677i	$-0.571787\pi$
$379$	−3299.86	−0.447236	−0.223618	+	0.974677i	$0.571787\pi$
$380$	−987.113	−0.133257
$381$	680.903	0.0915583
$382$	3287.95	0.440382
$383$	−7650.30	−1.02066	−0.510329	−	0.859979i	$-0.670476\pi$
$383$	−7650.30	−1.02066	−0.510329	+	0.859979i	$0.670476\pi$
$384$	−3149.39	−0.418532
$385$	1138.57	0.150719
$386$	1960.87	0.258563
$387$	−3936.58	−0.517074
$388$	2138.36	0.279790
$389$	13100.5	1.70752	0.853758	−	0.520670i	$-0.174318\pi$
$389$	13100.5	1.70752	0.853758	+	0.520670i	$0.174318\pi$
$390$	−912.293	−0.118451
$391$	4723.50	0.610941
$392$	3776.51	0.486588
$393$	−2036.73	−0.261424
$394$	−3058.24	−0.391045
$395$	−1935.13	−0.246499
$396$	−617.942	−0.0784160
$397$	−6657.39	−0.841625	−0.420812	−	0.907148i	$-0.638255\pi$
$397$	−6657.39	−0.841625	−0.420812	+	0.907148i	$0.638255\pi$
$398$	−5123.73	−0.645300
$399$	−3557.33	−0.446339
$400$	−1878.84	−0.234854
$401$	−12566.3	−1.56491	−0.782457	−	0.622705i	$-0.786034\pi$
$401$	−12566.3	−1.56491	−0.782457	+	0.622705i	$0.786034\pi$
$402$	2790.35	0.346194
$403$	−403.000	−0.0498135
$404$	−1218.12	−0.150009
$405$	1010.73	0.124009
$406$	−20528.7	−2.50941
$407$	1037.35	0.126338
$408$	1240.41	0.150513
$409$	−3672.62	−0.444008	−0.222004	−	0.975046i	$-0.571260\pi$
$409$	−3672.62	−0.444008	−0.222004	+	0.975046i	$0.571260\pi$
$410$	−4186.27	−0.504256
$411$	1621.00	0.194545
$412$	567.307	0.0678378
$413$	−13009.0	−1.54996
$414$	4755.86	0.564584
$415$	5312.02	0.628330
$416$	−2976.92	−0.350854
$417$	−5829.57	−0.684593
$418$	−910.513	−0.106542
$419$	9432.37	1.09976	0.549882	−	0.835242i	$-0.314673\pi$
$419$	9432.37	1.09976	0.549882	+	0.835242i	$0.314673\pi$
$420$	3464.90	0.402547
$421$	−12520.4	−1.44942	−0.724709	−	0.689056i	$-0.758026\pi$
$421$	−12520.4	−1.44942	−0.724709	+	0.689056i	$0.758026\pi$
$422$	2277.24	0.262688
$423$	−3138.86	−0.360796
$424$	−2293.70	−0.262716
$425$	1228.50	0.140214
$426$	−366.206	−0.0416497
$427$	−11387.2	−1.29055
$428$	1862.48	0.210342
$429$	−367.465	−0.0413552
$430$	5649.69	0.633610
$431$	2887.41	0.322695	0.161347	−	0.986898i	$-0.448416\pi$
$431$	2887.41	0.322695	0.161347	+	0.986898i	$0.448416\pi$
$432$	11232.1	1.25094
$433$	−5900.31	−0.654851	−0.327426	−	0.944877i	$-0.606181\pi$
$433$	−5900.31	−0.654851	−0.327426	+	0.944877i	$0.606181\pi$
$434$	3505.09	0.387672
$435$	3381.02	0.372660
$436$	641.556	0.0704700
$437$	3060.06	0.334972
$438$	−12758.2	−1.39181
$439$	−9996.21	−1.08677	−0.543386	−	0.839483i	$-0.682858\pi$
$439$	−9996.21	−1.08677	−0.543386	+	0.839483i	$0.682858\pi$
$440$	−257.198	−0.0278669
$441$	−7315.51	−0.789926
$442$	2407.38	0.259066
$443$	−18205.3	−1.95250	−0.976252	−	0.216638i	$-0.930491\pi$
$443$	−18205.3	−1.95250	−0.976252	+	0.216638i	$0.930491\pi$
$444$	3156.88	0.337430
$445$	−8069.01	−0.859568
$446$	10157.0	1.07836
$447$	7164.43	0.758090
$448$	7852.86	0.828153
$449$	8105.95	0.851990	0.425995	−	0.904725i	$-0.359924\pi$
$449$	8105.95	0.851990	0.425995	+	0.904725i	$0.359924\pi$
$450$	1236.91	0.129575
$451$	−1686.20	−0.176053
$452$	−12772.7	−1.32915
$453$	5163.55	0.535552
$454$	2298.80	0.237639
$455$	−1950.22	−0.200940
$456$	803.585	0.0825248
$457$	−6106.39	−0.625044	−0.312522	−	0.949911i	$-0.601174\pi$
$457$	−6106.39	−0.625044	−0.312522	+	0.949911i	$0.601174\pi$
$458$	−10662.8	−1.08786
$459$	−7344.22	−0.746839
$460$	−2980.55	−0.302107
$461$	−3459.45	−0.349507	−0.174753	−	0.984612i	$-0.555913\pi$
$461$	−3459.45	−0.349507	−0.174753	+	0.984612i	$0.555913\pi$
$462$	3196.02	0.321845
$463$	−6408.07	−0.643215	−0.321607	−	0.946873i	$-0.604223\pi$
$463$	−6408.07	−0.643215	−0.321607	+	0.946873i	$0.604223\pi$
$464$	13645.0	1.36520
$465$	−577.279	−0.0575713
$466$	−4579.53	−0.455241
$467$	1608.85	0.159419	0.0797097	−	0.996818i	$-0.474601\pi$
$467$	1608.85	0.159419	0.0797097	+	0.996818i	$0.474601\pi$
$468$	1058.45	0.104545
$469$	5964.96	0.587284
$470$	4504.82	0.442110
$471$	−1446.06	−0.141466
$472$	2938.69	0.286576
$473$	2275.66	0.221215
$474$	−5432.02	−0.526373
$475$	795.866	0.0768776
$476$	−9143.24	−0.880420
$477$	4443.14	0.426493
$478$	−7194.89	−0.688466
$479$	6903.46	0.658512	0.329256	−	0.944241i	$-0.393202\pi$
$479$	6903.46	0.658512	0.329256	+	0.944241i	$0.393202\pi$
$480$	−4264.30	−0.405495
$481$	−1776.85	−0.168436
$482$	13040.1	1.23228
$483$	−10741.2	−1.01189
$484$	−7896.98	−0.741639
$485$	−1724.06	−0.161414
$486$	−12369.8	−1.15454
$487$	9950.27	0.925852	0.462926	−	0.886397i	$-0.346800\pi$
$487$	9950.27	0.925852	0.462926	+	0.886397i	$0.346800\pi$
$488$	2572.32	0.238614
$489$	−12072.9	−1.11647
$490$	10499.0	0.967956
$491$	−19053.3	−1.75125	−0.875624	−	0.482993i	$-0.839550\pi$
$491$	−19053.3	−1.75125	−0.875624	+	0.482993i	$0.839550\pi$
$492$	−5131.45	−0.470211
$493$	−8921.89	−0.815054
$494$	1559.59	0.142043
$495$	498.220	0.0452390
$496$	−2329.76	−0.210905
$497$	−782.843	−0.0706546
$498$	14911.1	1.34174
$499$	10244.0	0.919011	0.459506	−	0.888175i	$-0.348027\pi$
$499$	10244.0	0.919011	0.459506	+	0.888175i	$0.348027\pi$
$500$	−775.187	−0.0693349
$501$	−8526.11	−0.760316
$502$	7631.72	0.678527
$503$	9873.80	0.875251	0.437625	−	0.899157i	$-0.355820\pi$
$503$	9873.80	0.875251	0.437625	+	0.899157i	$0.355820\pi$
$504$	2669.80	0.235957
$505$	982.116	0.0865417
$506$	−2749.27	−0.241541
$507$	629.420	0.0551352
$508$	1133.78	0.0990221
$509$	−14675.8	−1.27799	−0.638993	−	0.769213i	$-0.720649\pi$
$509$	−14675.8	−1.27799	−0.638993	+	0.769213i	$0.720649\pi$
$510$	3448.46	0.299412
$511$	−27273.4	−2.36107
$512$	−13134.8	−1.13375
$513$	−4757.87	−0.409483
$514$	−13.1846	−0.00113141
$515$	−457.395	−0.0391363
$516$	6925.30	0.590832
$517$	1814.51	0.154356
$518$	15454.1	1.31084
$519$	8850.61	0.748552
$520$	440.546	0.0371523
$521$	2911.81	0.244854	0.122427	−	0.992478i	$-0.460932\pi$
$521$	2911.81	0.244854	0.122427	+	0.992478i	$0.460932\pi$
$522$	−8983.01	−0.753210
$523$	−16433.4	−1.37396	−0.686982	−	0.726675i	$-0.741065\pi$
$523$	−16433.4	−1.37396	−0.686982	+	0.726675i	$0.741065\pi$
$524$	−3391.39	−0.282736
$525$	−2793.60	−0.232234
$526$	9391.34	0.778482
$527$	1523.33	0.125916
$528$	−2124.33	−0.175094
$529$	−2927.24	−0.240588
$530$	−6376.69	−0.522615
$531$	−5692.55	−0.465227
$532$	−5923.34	−0.482724
$533$	2888.24	0.234716
$534$	−22650.2	−1.83552
$535$	−1501.64	−0.121348
$536$	−1347.46	−0.108585
$537$	−3497.13	−0.281028
$538$	−2550.60	−0.204394
$539$	4228.94	0.337947
$540$	4634.24	0.369308
$541$	7657.21	0.608520	0.304260	−	0.952589i	$-0.401591\pi$
$541$	7657.21	0.608520	0.304260	+	0.952589i	$0.401591\pi$
$542$	−7873.63	−0.623988
$543$	−3485.61	−0.275473
$544$	11252.7	0.886867
$545$	−517.258	−0.0406549
$546$	−5474.37	−0.429087
$547$	521.382	0.0407545	0.0203772	−	0.999792i	$-0.493513\pi$
$547$	521.382	0.0407545	0.0203772	+	0.999792i	$0.493513\pi$
$548$	2699.15	0.210405
$549$	−4982.87	−0.387365
$550$	−715.033	−0.0554348
$551$	−5779.94	−0.446885
$552$	2426.40	0.187091
$553$	−11612.1	−0.892940
$554$	−22362.6	−1.71498
$555$	−2545.26	−0.194667
$556$	−9706.87	−0.740401
$557$	−4123.19	−0.313654	−0.156827	−	0.987626i	$-0.550127\pi$
$557$	−4123.19	−0.313654	−0.156827	+	0.987626i	$0.550127\pi$
$558$	1533.77	0.116361
$559$	−3897.90	−0.294926
$560$	−11274.3	−0.850759
$561$	1389.01	0.104535
$562$	−25033.7	−1.87897
$563$	−20642.4	−1.54525	−0.772624	−	0.634864i	$-0.781056\pi$
$563$	−20642.4	−1.54525	−0.772624	+	0.634864i	$0.781056\pi$
$564$	5521.93	0.412261
$565$	10298.0	0.766799
$566$	10640.3	0.790182
$567$	6065.07	0.449222
$568$	176.841	0.0130635
$569$	−7852.24	−0.578529	−0.289264	−	0.957249i	$-0.593411\pi$
$569$	−7852.24	−0.578529	−0.289264	+	0.957249i	$0.593411\pi$
$570$	2234.04	0.164164
$571$	−562.218	−0.0412050	−0.0206025	−	0.999788i	$-0.506558\pi$
$571$	−562.218	−0.0412050	−0.0206025	+	0.999788i	$0.506558\pi$
$572$	−611.870	−0.0447265
$573$	−3249.46	−0.236908
$574$	−25120.4	−1.82667
$575$	2403.09	0.174288
$576$	3436.29	0.248574
$577$	11234.8	0.810591	0.405296	−	0.914186i	$-0.367169\pi$
$577$	11234.8	0.810591	0.405296	+	0.914186i	$0.367169\pi$
$578$	9414.73	0.677510
$579$	−1937.91	−0.139097
$580$	5629.76	0.403040
$581$	31875.7	2.27612
$582$	−4839.54	−0.344683
$583$	−2568.49	−0.182463
$584$	6160.95	0.436544
$585$	−853.385	−0.0603130
$586$	−1168.80	−0.0823940
$587$	9120.06	0.641269	0.320635	−	0.947203i	$-0.396104\pi$
$587$	9120.06	0.641269	0.320635	+	0.947203i	$0.396104\pi$
$588$	12869.5	0.902604
$589$	986.874	0.0690381
$590$	8169.82	0.570078
$591$	3022.44	0.210367
$592$	−10272.0	−0.713139
$593$	19536.2	1.35288	0.676440	−	0.736498i	$-0.263522\pi$
$593$	19536.2	1.35288	0.676440	+	0.736498i	$0.263522\pi$
$594$	4274.63	0.295270
$595$	7371.80	0.507923
$596$	11929.6	0.819889
$597$	5063.76	0.347146
$598$	4709.13	0.322025
$599$	1670.02	0.113915	0.0569576	−	0.998377i	$-0.481860\pi$
$599$	1670.02	0.113915	0.0569576	+	0.998377i	$0.481860\pi$
$600$	631.061	0.0429383
$601$	−4798.35	−0.325672	−0.162836	−	0.986653i	$-0.552064\pi$
$601$	−4798.35	−0.325672	−0.162836	+	0.986653i	$0.552064\pi$
$602$	33902.0	2.29525
$603$	2610.17	0.176276
$604$	8597.88	0.579210
$605$	6366.99	0.427859
$606$	2756.85	0.184801
$607$	−9606.48	−0.642364	−0.321182	−	0.947017i	$-0.604080\pi$
$607$	−9606.48	−0.642364	−0.321182	+	0.947017i	$0.604080\pi$
$608$	7289.93	0.486259
$609$	20288.4	1.34996
$610$	7151.29	0.474668
$611$	−3108.02	−0.205789
$612$	−4000.94	−0.264262
$613$	14296.6	0.941979	0.470989	−	0.882139i	$-0.343897\pi$
$613$	14296.6	0.941979	0.470989	+	0.882139i	$0.343897\pi$
$614$	−9347.70	−0.614401
$615$	4137.27	0.271270
$616$	−1543.36	−0.100948
$617$	−2611.04	−0.170367	−0.0851837	−	0.996365i	$-0.527148\pi$
$617$	−2611.04	−0.170367	−0.0851837	+	0.996365i	$0.527148\pi$
$618$	−1283.93	−0.0835717
$619$	26835.0	1.74247	0.871235	−	0.490866i	$-0.163320\pi$
$619$	26835.0	1.74247	0.871235	+	0.490866i	$0.163320\pi$
$620$	−961.232	−0.0622645
$621$	−14366.2	−0.928336
$622$	15273.7	0.984597
$623$	−48419.5	−3.11378
$624$	3638.70	0.233437
$625$	625.000	0.0400000
$626$	36489.3	2.32972
$627$	899.856	0.0573155
$628$	−2407.84	−0.152999
$629$	6716.48	0.425761
$630$	7422.30	0.469384
$631$	18611.0	1.17416	0.587078	−	0.809530i	$-0.300278\pi$
$631$	18611.0	1.17416	0.587078	+	0.809530i	$0.300278\pi$
$632$	2623.12	0.165098
$633$	−2250.59	−0.141316
$634$	−29445.3	−1.84452
$635$	−914.116	−0.0571269
$636$	−7816.44	−0.487330
$637$	−7243.63	−0.450554
$638$	5192.90	0.322239
$639$	−342.560	−0.0212073
$640$	4228.07	0.261139
$641$	2108.40	0.129917	0.0649586	−	0.997888i	$-0.479308\pi$
$641$	2108.40	0.129917	0.0649586	+	0.997888i	$0.479308\pi$
$642$	−4215.18	−0.259127
$643$	13406.3	0.822226	0.411113	−	0.911584i	$-0.365140\pi$
$643$	13406.3	0.822226	0.411113	+	0.911584i	$0.365140\pi$
$644$	−17885.3	−1.09438
$645$	−5583.57	−0.340857
$646$	−5895.23	−0.359048
$647$	22982.9	1.39652	0.698261	−	0.715843i	$-0.253958\pi$
$647$	22982.9	1.39652	0.698261	+	0.715843i	$0.253958\pi$
$648$	−1370.07	−0.0830579
$649$	3290.75	0.199034
$650$	1224.76	0.0739061
$651$	−3464.06	−0.208552
$652$	−20102.7	−1.20749
$653$	1899.86	0.113855	0.0569274	−	0.998378i	$-0.481870\pi$
$653$	1899.86	0.113855	0.0569274	+	0.998378i	$0.481870\pi$
$654$	−1451.97	−0.0868144
$655$	2734.33	0.163113
$656$	16697.0	0.993763
$657$	−11934.4	−0.708685
$658$	27032.0	1.60154
$659$	29582.5	1.74867	0.874333	−	0.485326i	$-0.161299\pi$
$659$	29582.5	1.74867	0.874333	+	0.485326i	$0.161299\pi$
$660$	−876.475	−0.0516921
$661$	−12703.5	−0.747516	−0.373758	−	0.927526i	$-0.621931\pi$
$661$	−12703.5	−0.747516	−0.373758	+	0.927526i	$0.621931\pi$
$662$	−15017.5	−0.881681
$663$	−2379.20	−0.139367
$664$	−7200.59	−0.420839
$665$	4775.73	0.278489
$666$	6762.49	0.393455
$667$	−17452.3	−1.01313
$668$	−14196.9	−0.822297
$669$	−10038.1	−0.580112
$670$	−3746.06	−0.216004
$671$	2880.49	0.165723
$672$	−25588.6	−1.46890
$673$	−17952.9	−1.02828	−0.514140	−	0.857706i	$-0.671889\pi$
$673$	−17952.9	−1.02828	−0.514140	+	0.857706i	$0.671889\pi$
$674$	43736.3	2.49950
$675$	−3736.39	−0.213057
$676$	1048.05	0.0596298
$677$	−14603.7	−0.829046	−0.414523	−	0.910039i	$-0.636052\pi$
$677$	−14603.7	−0.829046	−0.414523	+	0.910039i	$0.636052\pi$
$678$	28907.2	1.63742
$679$	−10345.5	−0.584721
$680$	−1665.26	−0.0939113
$681$	−2271.89	−0.127840
$682$	−886.641	−0.0497819
$683$	−28071.9	−1.57268	−0.786342	−	0.617792i	$-0.788027\pi$
$683$	−28071.9	−1.57268	−0.786342	+	0.617792i	$0.788027\pi$
$684$	−2591.96	−0.144892
$685$	−2176.21	−0.121385
$686$	24219.2	1.34795
$687$	10538.0	0.585225
$688$	−22533.9	−1.24869
$689$	4399.48	0.243261
$690$	6745.61	0.372175
$691$	7609.43	0.418924	0.209462	−	0.977817i	$-0.432829\pi$
$691$	7609.43	0.418924	0.209462	+	0.977817i	$0.432829\pi$
$692$	14737.2	0.809574
$693$	2989.65	0.163878
$694$	45350.3	2.48051
$695$	7826.23	0.427145
$696$	−4583.05	−0.249598
$697$	−10917.5	−0.593300
$698$	22145.2	1.20087
$699$	4525.93	0.244902
$700$	−4651.65	−0.251165
$701$	31781.1	1.71235	0.856174	−	0.516687i	$-0.172835\pi$
$701$	31781.1	1.71235	0.856174	+	0.516687i	$0.172835\pi$
$702$	−7321.88	−0.393656
$703$	4351.19	0.233440
$704$	−1986.45	−0.106345
$705$	−4452.09	−0.237838
$706$	27727.8	1.47812
$707$	5893.36	0.313497
$708$	10014.4	0.531589
$709$	−23433.5	−1.24128	−0.620638	−	0.784097i	$-0.713126\pi$
$709$	−23433.5	−1.24128	−0.620638	+	0.784097i	$0.713126\pi$
$710$	491.634	0.0259869
$711$	−5081.26	−0.268020
$712$	10937.8	0.575716
$713$	2979.83	0.156516
$714$	20693.1	1.08462
$715$	493.324	0.0258032
$716$	−5823.10	−0.303938
$717$	7110.68	0.370367
$718$	96.8562	0.00503432
$719$	8831.45	0.458077	0.229039	−	0.973417i	$-0.426442\pi$
$719$	8831.45	0.458077	0.229039	+	0.973417i	$0.426442\pi$
$720$	−4933.45	−0.255359
$721$	−2744.68	−0.141771
$722$	22028.9	1.13550
$723$	−12887.4	−0.662917
$724$	−5803.93	−0.297930
$725$	−4539.03	−0.232518
$726$	17872.5	0.913651
$727$	−26472.2	−1.35048	−0.675239	−	0.737599i	$-0.735960\pi$
$727$	−26472.2	−1.35048	−0.675239	+	0.737599i	$0.735960\pi$
$728$	2643.57	0.134584
$729$	17683.0	0.898388
$730$	17128.0	0.868406
$731$	14734.0	0.745496
$732$	8765.93	0.442620
$733$	−10582.2	−0.533236	−0.266618	−	0.963802i	$-0.585906\pi$
$733$	−10582.2	−0.533236	−0.266618	+	0.963802i	$0.585906\pi$
$734$	2051.09	0.103143
$735$	−10376.2	−0.520722
$736$	22011.7	1.10239
$737$	−1508.89	−0.0754146
$738$	−10992.3	−0.548282
$739$	−18880.7	−0.939835	−0.469917	−	0.882710i	$-0.655716\pi$
$739$	−18880.7	−0.939835	−0.469917	+	0.882710i	$0.655716\pi$
$740$	−4238.13	−0.210536
$741$	−1541.34	−0.0764135
$742$	−38264.4	−1.89317
$743$	−2997.86	−0.148023	−0.0740113	−	0.997257i	$-0.523580\pi$
$743$	−2997.86	−0.148023	−0.0740113	+	0.997257i	$0.523580\pi$
$744$	782.516	0.0385597
$745$	−9618.29	−0.473003
$746$	−6818.64	−0.334649
$747$	13948.3	0.683189
$748$	2312.86	0.113057
$749$	−9010.83	−0.439584
$750$	1754.41	0.0854160
$751$	6059.57	0.294430	0.147215	−	0.989105i	$-0.452969\pi$
$751$	6059.57	0.294430	0.147215	+	0.989105i	$0.452969\pi$
$752$	−17967.6	−0.871289
$753$	−7542.39	−0.365020
$754$	−8894.75	−0.429612
$755$	−6932.10	−0.334152
$756$	27808.6	1.33782
$757$	−7076.21	−0.339748	−0.169874	−	0.985466i	$-0.554336\pi$
$757$	−7076.21	−0.339748	−0.169874	+	0.985466i	$0.554336\pi$
$758$	12435.5	0.595880
$759$	2717.09	0.129939
$760$	−1078.82	−0.0514905
$761$	−37954.1	−1.80793	−0.903966	−	0.427604i	$-0.859358\pi$
$761$	−37954.1	−1.80793	−0.903966	+	0.427604i	$0.859358\pi$
$762$	−2565.97	−0.121989
$763$	−3103.90	−0.147272
$764$	−5410.71	−0.256221
$765$	3225.78	0.152456
$766$	28830.1	1.35989
$767$	−5636.62	−0.265354
$768$	19666.7	0.924040
$769$	40495.3	1.89896	0.949479	−	0.313830i	$-0.101612\pi$
$769$	40495.3	1.89896	0.949479	+	0.313830i	$0.101612\pi$
$770$	−4290.68	−0.200812
$771$	13.0303	0.000608655 0
$772$	−3226.84	−0.150436
$773$	25307.4	1.17755	0.588774	−	0.808298i	$-0.299611\pi$
$773$	25307.4	1.17755	0.588774	+	0.808298i	$0.299611\pi$
$774$	14835.0	0.688930
$775$	775.000	0.0359211
$776$	2337.01	0.108111
$777$	−15273.3	−0.705180
$778$	−49369.2	−2.27503
$779$	−7072.77	−0.325300
$780$	1501.29	0.0689163
$781$	198.027	0.00907293
$782$	−17800.5	−0.813994
$783$	27135.4	1.23849
$784$	−41875.6	−1.90760
$785$	1941.34	0.0882666
$786$	7675.41	0.348311
$787$	−15810.6	−0.716119	−0.358059	−	0.933699i	$-0.616561\pi$
$787$	−15810.6	−0.716119	−0.358059	+	0.933699i	$0.616561\pi$
$788$	5032.70	0.227516
$789$	−9281.42	−0.418792
$790$	7292.51	0.328425
$791$	61795.2	2.77773
$792$	−675.350	−0.0302999
$793$	−4933.91	−0.220943
$794$	25088.3	1.12135
$795$	6302.05	0.281146
$796$	8431.72	0.375445
$797$	−29999.0	−1.33327	−0.666637	−	0.745383i	$-0.732267\pi$
$797$	−29999.0	−1.33327	−0.666637	+	0.745383i	$0.732267\pi$
$798$	13405.7	0.594685
$799$	11748.3	0.520180
$800$	5724.84	0.253005
$801$	−21187.6	−0.934616
$802$	47355.9	2.08503
$803$	6899.05	0.303191
$804$	−4591.85	−0.201421
$805$	14420.2	0.631359
$806$	1518.70	0.0663697
$807$	2520.74	0.109956
$808$	−1331.28	−0.0579633
$809$	33617.9	1.46099	0.730496	−	0.682917i	$-0.239289\pi$
$809$	33617.9	1.46099	0.730496	+	0.682917i	$0.239289\pi$
$810$	−3808.93	−0.165225
$811$	7989.11	0.345913	0.172956	−	0.984929i	$-0.444668\pi$
$811$	7989.11	0.345913	0.172956	+	0.984929i	$0.444668\pi$
$812$	33782.4	1.46001
$813$	7781.47	0.335680
$814$	−3909.26	−0.168328
$815$	16208.0	0.696613
$816$	−13754.2	−0.590066
$817$	9545.26	0.408747
$818$	13840.2	0.591580
$819$	−5120.89	−0.218484
$820$	6889.00	0.293384
$821$	1290.51	0.0548589	0.0274295	−	0.999624i	$-0.491268\pi$
$821$	1290.51	0.0548589	0.0274295	+	0.999624i	$0.491268\pi$
$822$	−6108.73	−0.259205
$823$	−11573.7	−0.490201	−0.245100	−	0.969498i	$-0.578821\pi$
$823$	−11573.7	−0.490201	−0.245100	+	0.969498i	$0.578821\pi$
$824$	620.010	0.0262125
$825$	706.664	0.0298217
$826$	49024.4	2.06511
$827$	−14923.4	−0.627493	−0.313746	−	0.949507i	$-0.601584\pi$
$827$	−14923.4	−0.627493	−0.313746	+	0.949507i	$0.601584\pi$
$828$	−7826.34	−0.328483
$829$	3412.23	0.142957	0.0714787	−	0.997442i	$-0.477228\pi$
$829$	3412.23	0.142957	0.0714787	+	0.997442i	$0.477228\pi$
$830$	−20018.3	−0.837163
$831$	22100.9	0.922589
$832$	3402.52	0.141780
$833$	27380.8	1.13888
$834$	21968.7	0.912125
$835$	11446.3	0.474392
$836$	1498.36	0.0619878
$837$	−4633.12	−0.191331
$838$	−35545.8	−1.46528
$839$	−46696.7	−1.92151	−0.960756	−	0.277394i	$-0.910529\pi$
$839$	−46696.7	−1.92151	−0.960756	+	0.277394i	$0.910529\pi$
$840$	3786.79	0.155544
$841$	8575.51	0.351614
$842$	47182.8	1.93115
$843$	24740.7	1.01081
$844$	−3747.48	−0.152836
$845$	−845.000	−0.0344010
$846$	11828.8	0.480710
$847$	38206.2	1.54992
$848$	25433.5	1.02994
$849$	−10515.7	−0.425086
$850$	−4629.57	−0.186815
$851$	13138.3	0.529229
$852$	602.637	0.0242324
$853$	−12827.6	−0.514899	−0.257449	−	0.966292i	$-0.582882\pi$
$853$	−12827.6	−0.514899	−0.257449	+	0.966292i	$0.582882\pi$
$854$	42912.6	1.71948
$855$	2089.79	0.0835897
$856$	2035.51	0.0812759
$857$	20232.9	0.806468	0.403234	−	0.915097i	$-0.367886\pi$
$857$	20232.9	0.806468	0.403234	+	0.915097i	$0.367886\pi$
$858$	1384.79	0.0551001
$859$	8313.72	0.330222	0.165111	−	0.986275i	$-0.447202\pi$
$859$	8313.72	0.330222	0.165111	+	0.986275i	$0.447202\pi$
$860$	−9297.25	−0.368644
$861$	24826.4	0.982673
$862$	−10881.2	−0.429946
$863$	−38242.4	−1.50844	−0.754221	−	0.656620i	$-0.771985\pi$
$863$	−38242.4	−1.50844	−0.754221	+	0.656620i	$0.771985\pi$
$864$	−34224.4	−1.34761
$865$	−11882.0	−0.467052
$866$	22235.2	0.872499
$867$	−9304.53	−0.364473
$868$	−5768.04	−0.225553
$869$	2937.37	0.114665
$870$	−12741.3	−0.496518
$871$	2584.53	0.100543
$872$	701.157	0.0272296
$873$	−4527.05	−0.175507
$874$	−11531.8	−0.446304
$875$	3750.42	0.144900
$876$	20995.2	0.809775
$877$	8366.77	0.322150	0.161075	−	0.986942i	$-0.448504\pi$
$877$	8366.77	0.322150	0.161075	+	0.986942i	$0.448504\pi$
$878$	37670.6	1.44797
$879$	1155.12	0.0443246
$880$	2851.92	0.109248
$881$	−12125.2	−0.463688	−0.231844	−	0.972753i	$-0.574476\pi$
$881$	−12125.2	−0.463688	−0.231844	+	0.972753i	$0.574476\pi$
$882$	27568.4	1.05247
$883$	44646.7	1.70156	0.850781	−	0.525520i	$-0.176129\pi$
$883$	44646.7	1.70156	0.850781	+	0.525520i	$0.176129\pi$
$884$	−3961.63	−0.150728
$885$	−8074.19	−0.306679
$886$	68606.4	2.60144
$887$	−26404.8	−0.999534	−0.499767	−	0.866160i	$-0.666581\pi$
$887$	−26404.8	−0.999534	−0.499767	+	0.866160i	$0.666581\pi$
$888$	3450.16	0.130383
$889$	−5485.31	−0.206942
$890$	30408.0	1.14526
$891$	−1534.21	−0.0576857
$892$	−16714.5	−0.627403
$893$	7610.98	0.285209
$894$	−26999.1	−1.01005
$895$	4694.91	0.175345
$896$	25371.3	0.945976
$897$	−4654.01	−0.173236
$898$	−30547.2	−1.13516
$899$	−5628.40	−0.208807
$900$	−2035.49	−0.0753884
$901$	−16630.0	−0.614900
$902$	6354.42	0.234567
$903$	−33505.2	−1.23475
$904$	−13959.3	−0.513582
$905$	4679.45	0.171879
$906$	−19458.8	−0.713548
$907$	5910.75	0.216387	0.108194	−	0.994130i	$-0.465493\pi$
$907$	5910.75	0.216387	0.108194	+	0.994130i	$0.465493\pi$
$908$	−3782.95	−0.138262
$909$	2578.84	0.0940976
$910$	7349.38	0.267725
$911$	28753.8	1.04572	0.522862	−	0.852417i	$-0.324864\pi$
$911$	28753.8	1.04572	0.522862	+	0.852417i	$0.324864\pi$
$912$	−8910.51	−0.323527
$913$	−8063.23	−0.292283
$914$	23011.9	0.832784
$915$	−7067.59	−0.255352
$916$	17546.9	0.632933
$917$	16407.8	0.590876
$918$	27676.6	0.995059
$919$	−8568.20	−0.307550	−0.153775	−	0.988106i	$-0.549143\pi$
$919$	−8568.20	−0.307550	−0.153775	+	0.988106i	$0.549143\pi$
$920$	−3257.45	−0.116734
$921$	9238.29	0.330523
$922$	13036.9	0.465669
$923$	−339.194	−0.0120961
$924$	−5259.44	−0.187254
$925$	3417.02	0.121461
$926$	24148.7	0.856994
$927$	−1201.03	−0.0425533
$928$	−41576.4	−1.47070
$929$	16102.5	0.568683	0.284342	−	0.958723i	$-0.408225\pi$
$929$	16102.5	0.568683	0.284342	+	0.958723i	$0.408225\pi$
$930$	2175.47	0.0767058
$931$	17738.3	0.624436
$932$	7536.16	0.264866
$933$	−15094.9	−0.529674
$934$	−6062.94	−0.212404
$935$	−1864.76	−0.0652237
$936$	1156.79	0.0403961
$937$	−34157.6	−1.19091	−0.595454	−	0.803390i	$-0.703028\pi$
$937$	−34157.6	−1.19091	−0.595454	+	0.803390i	$0.703028\pi$
$938$	−22478.9	−0.782475
$939$	−36062.2	−1.25330
$940$	−7413.22	−0.257226
$941$	−5202.60	−0.180234	−0.0901169	−	0.995931i	$-0.528724\pi$
$941$	−5202.60	−0.180234	−0.0901169	+	0.995931i	$0.528724\pi$
$942$	5449.44	0.188485
$943$	−21356.0	−0.737484
$944$	−32585.5	−1.12348
$945$	−22420.9	−0.771800
$946$	−8575.79	−0.294739
$947$	−1520.43	−0.0521724	−0.0260862	−	0.999660i	$-0.508304\pi$
$947$	−1520.43	−0.0521724	−0.0260862	+	0.999660i	$0.508304\pi$
$948$	8939.04	0.306251
$949$	−11817.2	−0.404216
$950$	−2999.21	−0.102429
$951$	29100.7	0.992275
$952$	−9992.67	−0.340193
$953$	9008.32	0.306200	0.153100	−	0.988211i	$-0.451074\pi$
$953$	9008.32	0.306200	0.153100	+	0.988211i	$0.451074\pi$
$954$	−16743.9	−0.568244
$955$	4362.42	0.147816
$956$	11840.1	0.400559
$957$	−5132.11	−0.173352
$958$	−26015.6	−0.877376
$959$	−13058.7	−0.439716
$960$	4873.95	0.163861
$961$	961.000	0.0322581
$962$	6696.04	0.224417
$963$	−3943.00	−0.131943
$964$	−21459.0	−0.716958
$965$	2601.66	0.0867880
$966$	40478.2	1.34820
$967$	−12999.4	−0.432300	−0.216150	−	0.976360i	$-0.569350\pi$
$967$	−12999.4	−0.432300	−0.216150	+	0.976360i	$0.569350\pi$
$968$	−8630.62	−0.286569
$969$	5826.23	0.193153
$970$	6497.11	0.215062
$971$	−11764.9	−0.388831	−0.194415	−	0.980919i	$-0.562281\pi$
$971$	−11764.9	−0.388831	−0.194415	+	0.980919i	$0.562281\pi$
$972$	20356.0	0.671727
$973$	46962.6	1.54733
$974$	−37497.5	−1.23357
$975$	−1210.42	−0.0397585
$976$	−28523.1	−0.935452
$977$	−10918.1	−0.357525	−0.178763	−	0.983892i	$-0.557209\pi$
$977$	−10918.1	−0.357525	−0.178763	+	0.983892i	$0.557209\pi$
$978$	45496.6	1.48755
$979$	12248.1	0.399848
$980$	−17277.4	−0.563171
$981$	−1358.22	−0.0442044
$982$	71802.1	2.33330
$983$	−10464.6	−0.339540	−0.169770	−	0.985484i	$-0.554302\pi$
$983$	−10464.6	−0.339540	−0.169770	+	0.985484i	$0.554302\pi$
$984$	−5608.17	−0.181689
$985$	−4057.65	−0.131256
$986$	33622.0	1.08595
$987$	−26715.6	−0.861566
$988$	−2566.49	−0.0826427
$989$	28821.6	0.926667
$990$	−1877.53	−0.0602747
$991$	−24589.6	−0.788209	−0.394104	−	0.919066i	$-0.628945\pi$
$991$	−24589.6	−0.788209	−0.394104	+	0.919066i	$0.628945\pi$
$992$	7098.80	0.227205
$993$	14841.8	0.474309
$994$	2950.14	0.0941374
$995$	−6798.13	−0.216598
$996$	−24538.1	−0.780641
$997$	−12471.9	−0.396178	−0.198089	−	0.980184i	$-0.563474\pi$
$997$	−12471.9	−0.396178	−0.198089	+	0.980184i	$0.563474\pi$
$998$	−38604.6	−1.22446
$999$	−20427.7	−0.646952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2015.4.a.d.1.9	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2015.4.a.d.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-3.76849 q^{2} +3.72438 q^{3} +6.20150 q^{4} -5.00000 q^{5} -14.0353 q^{6} -30.0034 q^{7} +6.77763 q^{8} -13.1290 q^{9} +O(q^{10})\)	\(q-3.76849 q^{2} +3.72438 q^{3} +6.20150 q^{4} -5.00000 q^{5} -14.0353 q^{6} -30.0034 q^{7} +6.77763 q^{8} -13.1290 q^{9} +18.8424 q^{10} +7.58960 q^{11} +23.0967 q^{12} -13.0000 q^{13} +113.067 q^{14} -18.6219 q^{15} -75.1534 q^{16} +49.1398 q^{17} +49.4765 q^{18} +31.8346 q^{19} -31.0075 q^{20} -111.744 q^{21} -28.6013 q^{22} +96.1237 q^{23} +25.2425 q^{24} +25.0000 q^{25} +48.9903 q^{26} -149.456 q^{27} -186.066 q^{28} -181.561 q^{29} +70.1764 q^{30} +31.0000 q^{31} +228.994 q^{32} +28.2666 q^{33} -185.183 q^{34} +150.017 q^{35} -81.4195 q^{36} +136.681 q^{37} -119.968 q^{38} -48.4169 q^{39} -33.8881 q^{40} -222.172 q^{41} +421.106 q^{42} +299.839 q^{43} +47.0669 q^{44} +65.6450 q^{45} -362.241 q^{46} +239.078 q^{47} -279.900 q^{48} +557.202 q^{49} -94.2122 q^{50} +183.015 q^{51} -80.6195 q^{52} -338.422 q^{53} +563.222 q^{54} -37.9480 q^{55} -203.352 q^{56} +118.564 q^{57} +684.212 q^{58} +433.586 q^{59} -115.484 q^{60} +379.531 q^{61} -116.823 q^{62} +393.914 q^{63} -261.732 q^{64} +65.0000 q^{65} -106.522 q^{66} -198.810 q^{67} +304.741 q^{68} +358.001 q^{69} -565.337 q^{70} +26.0919 q^{71} -88.9835 q^{72} +909.013 q^{73} -515.080 q^{74} +93.1095 q^{75} +197.423 q^{76} -227.714 q^{77} +182.459 q^{78} +387.026 q^{79} +375.767 q^{80} -202.146 q^{81} +837.253 q^{82} -1062.40 q^{83} -692.980 q^{84} -245.699 q^{85} -1129.94 q^{86} -676.203 q^{87} +51.4395 q^{88} +1613.80 q^{89} -247.382 q^{90} +390.044 q^{91} +596.111 q^{92} +115.456 q^{93} -900.964 q^{94} -159.173 q^{95} +852.859 q^{96} +344.813 q^{97} -2099.81 q^{98} -99.6439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) \) 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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