LMFDB - Embedded newform 2015.4.a.d.1.20

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			1.20
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)

$f(q)$	$=$	$q-0.497250 q^{2} +4.81569 q^{3} -7.75274 q^{4} -5.00000 q^{5} -2.39460 q^{6} +27.1189 q^{7} +7.83306 q^{8} -3.80913 q^{9} +O(q^{10})$	\(q-0.497250 q^{2} +4.81569 q^{3} -7.75274 q^{4} -5.00000 q^{5} -2.39460 q^{6} +27.1189 q^{7} +7.83306 q^{8} -3.80913 q^{9} +2.48625 q^{10} -8.68997 q^{11} -37.3348 q^{12} -13.0000 q^{13} -13.4849 q^{14} -24.0785 q^{15} +58.1269 q^{16} +43.4115 q^{17} +1.89409 q^{18} +31.1346 q^{19} +38.7637 q^{20} +130.596 q^{21} +4.32109 q^{22} -88.0392 q^{23} +37.7216 q^{24} +25.0000 q^{25} +6.46426 q^{26} -148.367 q^{27} -210.246 q^{28} -270.705 q^{29} +11.9730 q^{30} +31.0000 q^{31} -91.5681 q^{32} -41.8482 q^{33} -21.5864 q^{34} -135.594 q^{35} +29.5312 q^{36} -102.467 q^{37} -15.4817 q^{38} -62.6040 q^{39} -39.1653 q^{40} +389.256 q^{41} -64.9390 q^{42} +45.4478 q^{43} +67.3711 q^{44} +19.0456 q^{45} +43.7775 q^{46} -429.600 q^{47} +279.921 q^{48} +392.433 q^{49} -12.4313 q^{50} +209.056 q^{51} +100.786 q^{52} +477.888 q^{53} +73.7757 q^{54} +43.4498 q^{55} +212.424 q^{56} +149.935 q^{57} +134.608 q^{58} +130.177 q^{59} +186.674 q^{60} -1.15196 q^{61} -15.4148 q^{62} -103.299 q^{63} -419.483 q^{64} +65.0000 q^{65} +20.8090 q^{66} -63.5091 q^{67} -336.558 q^{68} -423.970 q^{69} +67.4244 q^{70} +239.449 q^{71} -29.8371 q^{72} -665.284 q^{73} +50.9519 q^{74} +120.392 q^{75} -241.379 q^{76} -235.662 q^{77} +31.1298 q^{78} +505.551 q^{79} -290.635 q^{80} -611.644 q^{81} -193.558 q^{82} +708.005 q^{83} -1012.48 q^{84} -217.057 q^{85} -22.5989 q^{86} -1303.63 q^{87} -68.0690 q^{88} -118.984 q^{89} -9.47046 q^{90} -352.545 q^{91} +682.545 q^{92} +149.286 q^{93} +213.619 q^{94} -155.673 q^{95} -440.964 q^{96} -1753.46 q^{97} -195.138 q^{98} +33.1012 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.497250	−0.175805	−0.0879023	−	0.996129i	$-0.528016\pi$
$2$	−0.497250	−0.175805	−0.0879023	+	0.996129i	$0.528016\pi$
$3$	4.81569	0.926780	0.463390	−	0.886154i	$-0.346633\pi$
$3$	4.81569	0.926780	0.463390	+	0.886154i	$0.346633\pi$
$4$	−7.75274	−0.969093
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−2.39460	−0.162932
$7$	27.1189	1.46428	0.732141	−	0.681153i	$-0.238521\pi$
$7$	27.1189	1.46428	0.732141	+	0.681153i	$0.238521\pi$
$8$	7.83306	0.346175
$9$	−3.80913	−0.141079
$10$	2.48625	0.0786222
$11$	−8.68997	−0.238193	−0.119097	−	0.992883i	$-0.538000\pi$
$11$	−8.68997	−0.238193	−0.119097	+	0.992883i	$0.538000\pi$
$12$	−37.3348	−0.898136
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−13.4849	−0.257427
$15$	−24.0785	−0.414469
$16$	58.1269	0.908234
$17$	43.4115	0.619343	0.309671	−	0.950844i	$-0.399781\pi$
$17$	43.4115	0.619343	0.309671	+	0.950844i	$0.399781\pi$
$18$	1.89409	0.0248023
$19$	31.1346	0.375935	0.187968	−	0.982175i	$-0.439810\pi$
$19$	31.1346	0.375935	0.187968	+	0.982175i	$0.439810\pi$
$20$	38.7637	0.433391
$21$	130.596	1.35707
$22$	4.32109	0.0418754
$23$	−88.0392	−0.798150	−0.399075	−	0.916918i	$-0.630669\pi$
$23$	−88.0392	−0.798150	−0.399075	+	0.916918i	$0.630669\pi$
$24$	37.7216	0.320829
$25$	25.0000	0.200000
$26$	6.46426	0.0487594
$27$	−148.367	−1.05753
$28$	−210.246	−1.41902
$29$	−270.705	−1.73340	−0.866701	−	0.498828i	$-0.833764\pi$
$29$	−270.705	−1.73340	−0.866701	+	0.498828i	$0.833764\pi$
$30$	11.9730	0.0728655
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	−91.5681	−0.505847
$33$	−41.8482	−0.220753
$34$	−21.5864	−0.108883
$35$	−135.594	−0.654847
$36$	29.5312	0.136719
$37$	−102.467	−0.455284	−0.227642	−	0.973745i	$-0.573102\pi$
$37$	−102.467	−0.455284	−0.227642	+	0.973745i	$0.573102\pi$
$38$	−15.4817	−0.0660912
$39$	−62.6040	−0.257043
$40$	−39.1653	−0.154814
$41$	389.256	1.48272	0.741361	−	0.671107i	$-0.234181\pi$
$41$	389.256	1.48272	0.741361	+	0.671107i	$0.234181\pi$
$42$	−64.9390	−0.238579
$43$	45.4478	0.161180	0.0805898	−	0.996747i	$-0.474320\pi$
$43$	45.4478	0.161180	0.0805898	+	0.996747i	$0.474320\pi$
$44$	67.3711	0.230831
$45$	19.0456	0.0630924
$46$	43.7775	0.140318
$47$	−429.600	−1.33327	−0.666634	−	0.745385i	$-0.732266\pi$
$47$	−429.600	−1.33327	−0.666634	+	0.745385i	$0.732266\pi$
$48$	279.921	0.841733
$49$	392.433	1.14412
$50$	−12.4313	−0.0351609
$51$	209.056	0.573994
$52$	100.786	0.268778
$53$	477.888	1.23855	0.619274	−	0.785175i	$-0.287427\pi$
$53$	477.888	1.23855	0.619274	+	0.785175i	$0.287427\pi$
$54$	73.7757	0.185918
$55$	43.4498	0.106523
$56$	212.424	0.506898
$57$	149.935	0.348409
$58$	134.608	0.304740
$59$	130.177	0.287248	0.143624	−	0.989632i	$-0.454124\pi$
$59$	130.177	0.287248	0.143624	+	0.989632i	$0.454124\pi$
$60$	186.674	0.401659
$61$	−1.15196	−0.00241793	−0.00120897	−	0.999999i	$-0.500385\pi$
$61$	−1.15196	−0.00241793	−0.00120897	+	0.999999i	$0.500385\pi$
$62$	−15.4148	−0.0315754
$63$	−103.299	−0.206579
$64$	−419.483	−0.819303
$65$	65.0000	0.124035
$66$	20.8090	0.0388093
$67$	−63.5091	−0.115804	−0.0579020	−	0.998322i	$-0.518441\pi$
$67$	−63.5091	−0.115804	−0.0579020	+	0.998322i	$0.518441\pi$
$68$	−336.558	−0.600201
$69$	−423.970	−0.739709
$70$	67.4244	0.115125
$71$	239.449	0.400244	0.200122	−	0.979771i	$-0.435866\pi$
$71$	239.449	0.400244	0.200122	+	0.979771i	$0.435866\pi$
$72$	−29.8371	−0.0488380
$73$	−665.284	−1.06665	−0.533326	−	0.845910i	$-0.679058\pi$
$73$	−665.284	−1.06665	−0.533326	+	0.845910i	$0.679058\pi$
$74$	50.9519	0.0800410
$75$	120.392	0.185356
$76$	−241.379	−0.364316
$77$	−235.662	−0.348782
$78$	31.1298	0.0451892
$79$	505.551	0.719986	0.359993	−	0.932955i	$-0.382779\pi$
$79$	505.551	0.719986	0.359993	+	0.932955i	$0.382779\pi$
$80$	−290.635	−0.406174
$81$	−611.644	−0.839018
$82$	−193.558	−0.260669
$83$	708.005	0.936310	0.468155	−	0.883646i	$-0.344919\pi$
$83$	708.005	0.936310	0.468155	+	0.883646i	$0.344919\pi$
$84$	−1012.48	−1.31512
$85$	−217.057	−0.276978
$86$	−22.5989	−0.0283361
$87$	−1303.63	−1.60648
$88$	−68.0690	−0.0824566
$89$	−118.984	−0.141711	−0.0708553	−	0.997487i	$-0.522573\pi$
$89$	−118.984	−0.141711	−0.0708553	+	0.997487i	$0.522573\pi$
$90$	−9.47046	−0.0110919
$91$	−352.545	−0.406119
$92$	682.545	0.773481
$93$	149.286	0.166455
$94$	213.619	0.234395
$95$	−155.673	−0.168123
$96$	−440.964	−0.468809
$97$	−1753.46	−1.83544	−0.917718	−	0.397233i	$-0.869970\pi$
$97$	−1753.46	−1.83544	−0.917718	+	0.397233i	$0.869970\pi$
$98$	−195.138	−0.201142
$99$	33.1012	0.0336040
$100$	−193.819	−0.193819
$101$	696.272	0.685957	0.342979	−	0.939343i	$-0.388564\pi$
$101$	696.272	0.685957	0.342979	+	0.939343i	$0.388564\pi$
$102$	−103.953	−0.100911
$103$	−412.022	−0.394153	−0.197076	−	0.980388i	$-0.563145\pi$
$103$	−412.022	−0.394153	−0.197076	+	0.980388i	$0.563145\pi$
$104$	−101.830	−0.0960118
$105$	−652.980	−0.606899
$106$	−237.630	−0.217742
$107$	718.363	0.649035	0.324518	−	0.945880i	$-0.394798\pi$
$107$	718.363	0.649035	0.324518	+	0.945880i	$0.394798\pi$
$108$	1150.25	1.02484
$109$	−1544.47	−1.35719	−0.678593	−	0.734514i	$-0.737410\pi$
$109$	−1544.47	−1.35719	−0.678593	+	0.734514i	$0.737410\pi$
$110$	−21.6055	−0.0187273
$111$	−493.450	−0.421948
$112$	1576.34	1.32991
$113$	−565.929	−0.471134	−0.235567	−	0.971858i	$-0.575695\pi$
$113$	−565.929	−0.471134	−0.235567	+	0.971858i	$0.575695\pi$
$114$	−74.5551	−0.0612520
$115$	440.196	0.356943
$116$	2098.71	1.67983
$117$	49.5187	0.0391282
$118$	−64.7306	−0.0504994
$119$	1177.27	0.906892
$120$	−188.608	−0.143479
$121$	−1255.48	−0.943264
$122$	0.572814	0.000425083 0
$123$	1874.54	1.37416
$124$	−240.335	−0.174054
$125$	−125.000	−0.0894427
$126$	51.3656	0.0363176
$127$	−496.360	−0.346809	−0.173405	−	0.984851i	$-0.555477\pi$
$127$	−496.360	−0.346809	−0.173405	+	0.984851i	$0.555477\pi$
$128$	941.133	0.649884
$129$	218.863	0.149378
$130$	−32.3213	−0.0218059
$131$	−999.330	−0.666503	−0.333251	−	0.942838i	$-0.608146\pi$
$131$	−999.330	−0.666503	−0.333251	+	0.942838i	$0.608146\pi$
$132$	324.438	0.213930
$133$	844.336	0.550475
$134$	31.5799	0.0203589
$135$	741.836	0.472941
$136$	340.044	0.214401
$137$	−1120.85	−0.698983	−0.349491	−	0.936940i	$-0.613646\pi$
$137$	−1120.85	−0.698983	−0.349491	+	0.936940i	$0.613646\pi$
$138$	210.819	0.130044
$139$	1619.71	0.988358	0.494179	−	0.869360i	$-0.335469\pi$
$139$	1619.71	0.988358	0.494179	+	0.869360i	$0.335469\pi$
$140$	1051.23	0.634607
$141$	−2068.82	−1.23565
$142$	−119.066	−0.0703648
$143$	112.970	0.0660629
$144$	−221.413	−0.128133
$145$	1353.52	0.775201
$146$	330.813	0.187522
$147$	1889.84	1.06035
$148$	794.402	0.441212
$149$	−2067.81	−1.13693	−0.568463	−	0.822709i	$-0.692462\pi$
$149$	−2067.81	−1.13693	−0.568463	+	0.822709i	$0.692462\pi$
$150$	−59.8651	−0.0325864
$151$	−592.162	−0.319135	−0.159568	−	0.987187i	$-0.551010\pi$
$151$	−592.162	−0.319135	−0.159568	+	0.987187i	$0.551010\pi$
$152$	243.879	0.130140
$153$	−165.360	−0.0873762
$154$	117.183	0.0613174
$155$	−155.000	−0.0803219
$156$	485.352	0.249098
$157$	1483.43	0.754082	0.377041	−	0.926197i	$-0.376942\pi$
$157$	1483.43	0.754082	0.377041	+	0.926197i	$0.376942\pi$
$158$	−251.385	−0.126577
$159$	2301.36	1.14786
$160$	457.841	0.226222
$161$	−2387.52	−1.16872
$162$	304.140	0.147503
$163$	−2492.61	−1.19777	−0.598884	−	0.800835i	$-0.704389\pi$
$163$	−2492.61	−1.19777	−0.598884	+	0.800835i	$0.704389\pi$
$164$	−3017.80	−1.43689
$165$	209.241	0.0987236
$166$	−352.056	−0.164608
$167$	2845.66	1.31858	0.659292	−	0.751887i	$-0.270856\pi$
$167$	2845.66	1.31858	0.659292	+	0.751887i	$0.270856\pi$
$168$	1022.97	0.469783
$169$	169.000	0.0769231
$170$	107.932	0.0486941
$171$	−118.596	−0.0530365
$172$	−352.345	−0.156198
$173$	−2909.04	−1.27844	−0.639221	−	0.769023i	$-0.720743\pi$
$173$	−2909.04	−1.27844	−0.639221	+	0.769023i	$0.720743\pi$
$174$	648.231	0.282427
$175$	677.972	0.292856
$176$	−505.121	−0.216335
$177$	626.892	0.266215
$178$	59.1647	0.0249134
$179$	−3452.13	−1.44148	−0.720738	−	0.693208i	$-0.756197\pi$
$179$	−3452.13	−1.44148	−0.720738	+	0.693208i	$0.756197\pi$
$180$	−147.656	−0.0611424
$181$	1123.85	0.461519	0.230760	−	0.973011i	$-0.425879\pi$
$181$	1123.85	0.461519	0.230760	+	0.973011i	$0.425879\pi$
$182$	175.303	0.0713975
$183$	−5.54750	−0.00224089
$184$	−689.616	−0.276300
$185$	512.336	0.203609
$186$	−74.2327	−0.0292635
$187$	−377.244	−0.147523
$188$	3330.58	1.29206
$189$	−4023.55	−1.54852
$190$	77.4085	0.0295569
$191$	2013.60	0.762821	0.381411	−	0.924406i	$-0.375438\pi$
$191$	2013.60	0.762821	0.381411	+	0.924406i	$0.375438\pi$
$192$	−2020.10	−0.759314
$193$	−642.091	−0.239475	−0.119738	−	0.992806i	$-0.538205\pi$
$193$	−642.091	−0.239475	−0.119738	+	0.992806i	$0.538205\pi$
$194$	871.910	0.322678
$195$	313.020	0.114953
$196$	−3042.43	−1.10876
$197$	975.534	0.352812	0.176406	−	0.984317i	$-0.443553\pi$
$197$	975.534	0.352812	0.176406	+	0.984317i	$0.443553\pi$
$198$	−16.4596	−0.00590774
$199$	−3548.12	−1.26392	−0.631960	−	0.775001i	$-0.717749\pi$
$199$	−3548.12	−1.26392	−0.631960	+	0.775001i	$0.717749\pi$
$200$	195.826	0.0692351
$201$	−305.840	−0.107325
$202$	−346.222	−0.120594
$203$	−7341.21	−2.53819
$204$	−1620.76	−0.556254
$205$	−1946.28	−0.663093
$206$	204.878	0.0692938
$207$	335.353	0.112602
$208$	−755.650	−0.251899
$209$	−270.559	−0.0895452
$210$	324.695	0.106696
$211$	−5377.42	−1.75449	−0.877244	−	0.480044i	$-0.840621\pi$
$211$	−5377.42	−1.75449	−0.877244	+	0.480044i	$0.840621\pi$
$212$	−3704.95	−1.20027
$213$	1153.11	0.370938
$214$	−357.206	−0.114103
$215$	−227.239	−0.0720817
$216$	−1162.17	−0.366091
$217$	840.685	0.262993
$218$	767.988	0.238600
$219$	−3203.80	−0.988552
$220$	−336.855	−0.103231
$221$	−564.349	−0.171775
$222$	245.368	0.0741804
$223$	−2172.07	−0.652254	−0.326127	−	0.945326i	$-0.605744\pi$
$223$	−2172.07	−0.652254	−0.326127	+	0.945326i	$0.605744\pi$
$224$	−2483.22	−0.740703
$225$	−95.2282	−0.0282158
$226$	281.409	0.0828275
$227$	−2430.40	−0.710623	−0.355311	−	0.934748i	$-0.615625\pi$
$227$	−2430.40	−0.710623	−0.355311	+	0.934748i	$0.615625\pi$
$228$	−1162.41	−0.337641
$229$	−4015.20	−1.15866	−0.579328	−	0.815095i	$-0.696685\pi$
$229$	−4015.20	−1.15866	−0.579328	+	0.815095i	$0.696685\pi$
$230$	−218.888	−0.0627523
$231$	−1134.88	−0.323244
$232$	−2120.45	−0.600061
$233$	1879.58	0.528478	0.264239	−	0.964457i	$-0.414879\pi$
$233$	1879.58	0.528478	0.264239	+	0.964457i	$0.414879\pi$
$234$	−24.6232	−0.00687892
$235$	2148.00	0.596256
$236$	−1009.23	−0.278369
$237$	2434.57	0.667268
$238$	−585.398	−0.159436
$239$	−711.335	−0.192521	−0.0962603	−	0.995356i	$-0.530688\pi$
$239$	−711.335	−0.192521	−0.0962603	+	0.995356i	$0.530688\pi$
$240$	−1399.61	−0.376434
$241$	−4577.47	−1.22349	−0.611745	−	0.791055i	$-0.709532\pi$
$241$	−4577.47	−1.22349	−0.611745	+	0.791055i	$0.709532\pi$
$242$	624.290	0.165830
$243$	1060.43	0.279944
$244$	8.93087	0.00234320
$245$	−1962.17	−0.511666
$246$	−932.114	−0.241583
$247$	−404.750	−0.104266
$248$	242.825	0.0621750
$249$	3409.54	0.867753
$250$	62.1563	0.0157244
$251$	−344.837	−0.0867169	−0.0433585	−	0.999060i	$-0.513806\pi$
$251$	−344.837	−0.0867169	−0.0433585	+	0.999060i	$0.513806\pi$
$252$	800.853	0.200194
$253$	765.058	0.190114
$254$	246.815	0.0609707
$255$	−1045.28	−0.256698
$256$	2887.89	0.705051
$257$	−924.531	−0.224400	−0.112200	−	0.993686i	$-0.535790\pi$
$257$	−924.531	−0.224400	−0.112200	+	0.993686i	$0.535790\pi$
$258$	−108.829	−0.0262614
$259$	−2778.80	−0.666664
$260$	−503.928	−0.120201
$261$	1031.15	0.244546
$262$	496.917	0.117174
$263$	1010.20	0.236851	0.118426	−	0.992963i	$-0.462215\pi$
$263$	1010.20	0.236851	0.118426	+	0.992963i	$0.462215\pi$
$264$	−327.799	−0.0764191
$265$	−2389.44	−0.553895
$266$	−419.846	−0.0967761
$267$	−572.988	−0.131335
$268$	492.370	0.112225
$269$	−322.022	−0.0729889	−0.0364944	−	0.999334i	$-0.511619\pi$
$269$	−322.022	−0.0729889	−0.0364944	+	0.999334i	$0.511619\pi$
$270$	−368.878	−0.0831453
$271$	123.739	0.0277367	0.0138683	−	0.999904i	$-0.495585\pi$
$271$	123.739	0.0277367	0.0138683	+	0.999904i	$0.495585\pi$
$272$	2523.38	0.562508
$273$	−1697.75	−0.376383
$274$	557.343	0.122884
$275$	−217.249	−0.0476386
$276$	3286.93	0.716847
$277$	−3729.07	−0.808874	−0.404437	−	0.914566i	$-0.632532\pi$
$277$	−3729.07	−0.808874	−0.404437	+	0.914566i	$0.632532\pi$
$278$	−805.400	−0.173758
$279$	−118.083	−0.0253385
$280$	−1062.12	−0.226692
$281$	4124.32	0.875573	0.437787	−	0.899079i	$-0.355763\pi$
$281$	4124.32	0.875573	0.437787	+	0.899079i	$0.355763\pi$
$282$	1028.72	0.217232
$283$	−457.822	−0.0961650	−0.0480825	−	0.998843i	$-0.515311\pi$
$283$	−457.822	−0.0961650	−0.0480825	+	0.998843i	$0.515311\pi$
$284$	−1856.38	−0.387874
$285$	−749.674	−0.155813
$286$	−56.1742	−0.0116142
$287$	10556.2	2.17112
$288$	348.795	0.0713643
$289$	−3028.45	−0.616415
$290$	−673.041	−0.136284
$291$	−8444.14	−1.70104
$292$	5157.77	1.03368
$293$	4891.28	0.975262	0.487631	−	0.873050i	$-0.337861\pi$
$293$	4891.28	0.975262	0.487631	+	0.873050i	$0.337861\pi$
$294$	−939.722	−0.186414
$295$	−650.885	−0.128461
$296$	−802.631	−0.157608
$297$	1289.31	0.251896
$298$	1028.22	0.199877
$299$	1144.51	0.221367
$300$	−933.370	−0.179627
$301$	1232.49	0.236012
$302$	294.453	0.0561055
$303$	3353.03	0.635731
$304$	1809.76	0.341437
$305$	5.75982	0.00108133
$306$	82.2253	0.0153611
$307$	−5980.45	−1.11180	−0.555900	−	0.831249i	$-0.687626\pi$
$307$	−5980.45	−1.11180	−0.555900	+	0.831249i	$0.687626\pi$
$308$	1827.03	0.338002
$309$	−1984.17	−0.365293
$310$	77.0738	0.0141210
$311$	−4091.52	−0.746010	−0.373005	−	0.927829i	$-0.621673\pi$
$311$	−4091.52	−0.746010	−0.373005	+	0.927829i	$0.621673\pi$
$312$	−490.380	−0.0889818
$313$	7554.47	1.36423	0.682115	−	0.731245i	$-0.261060\pi$
$313$	7554.47	1.36423	0.682115	+	0.731245i	$0.261060\pi$
$314$	−737.638	−0.132571
$315$	516.496	0.0923850
$316$	−3919.40	−0.697733
$317$	−2839.91	−0.503170	−0.251585	−	0.967835i	$-0.580952\pi$
$317$	−2839.91	−0.503170	−0.251585	+	0.967835i	$0.580952\pi$
$318$	−1144.35	−0.201799
$319$	2352.42	0.412884
$320$	2097.42	0.366404
$321$	3459.41	0.601513
$322$	1187.20	0.205466
$323$	1351.60	0.232833
$324$	4741.92	0.813086
$325$	−325.000	−0.0554700
$326$	1239.45	0.210573
$327$	−7437.69	−1.25781
$328$	3049.06	0.513282
$329$	−11650.3	−1.95228
$330$	−104.045	−0.0173561
$331$	1750.24	0.290640	0.145320	−	0.989385i	$-0.453579\pi$
$331$	1750.24	0.290640	0.145320	+	0.989385i	$0.453579\pi$
$332$	−5488.98	−0.907371
$333$	390.311	0.0642309
$334$	−1415.00	−0.231813
$335$	317.546	0.0517892
$336$	7591.15	1.23253
$337$	−6863.66	−1.10946	−0.554729	−	0.832031i	$-0.687178\pi$
$337$	−6863.66	−1.10946	−0.554729	+	0.832031i	$0.687178\pi$
$338$	−84.0353	−0.0135234
$339$	−2725.34	−0.436638
$340$	1682.79	0.268418
$341$	−269.389	−0.0427807
$342$	58.9718	0.00932407
$343$	1340.58	0.211033
$344$	355.995	0.0557965
$345$	2119.85	0.330808
$346$	1446.52	0.224756
$347$	−3809.73	−0.589386	−0.294693	−	0.955592i	$-0.595217\pi$
$347$	−3809.73	−0.589386	−0.294693	+	0.955592i	$0.595217\pi$
$348$	10106.7	1.55683
$349$	−377.959	−0.0579704	−0.0289852	−	0.999580i	$-0.509228\pi$
$349$	−377.959	−0.0579704	−0.0289852	+	0.999580i	$0.509228\pi$
$350$	−337.122	−0.0514855
$351$	1928.77	0.293306
$352$	795.724	0.120489
$353$	4004.65	0.603812	0.301906	−	0.953338i	$-0.402377\pi$
$353$	4004.65	0.603812	0.301906	+	0.953338i	$0.402377\pi$
$354$	−311.722	−0.0468019
$355$	−1197.24	−0.178995
$356$	922.450	0.137331
$357$	5669.37	0.840489
$358$	1716.57	0.253418
$359$	−6938.85	−1.02011	−0.510054	−	0.860142i	$-0.670375\pi$
$359$	−6938.85	−1.02011	−0.510054	+	0.860142i	$0.670375\pi$
$360$	149.186	0.0218410
$361$	−5889.64	−0.858673
$362$	−558.834	−0.0811372
$363$	−6046.02	−0.874198
$364$	2733.19	0.393567
$365$	3326.42	0.477021
$366$	2.75850	0.000393959 0
$367$	12430.1	1.76797	0.883987	−	0.467511i	$-0.154849\pi$
$367$	12430.1	1.76797	0.883987	+	0.467511i	$0.154849\pi$
$368$	−5117.45	−0.724906
$369$	−1482.73	−0.209181
$370$	−254.759	−0.0357954
$371$	12959.8	1.81358
$372$	−1157.38	−0.161310
$373$	4270.00	0.592740	0.296370	−	0.955073i	$-0.404224\pi$
$373$	4270.00	0.592740	0.296370	+	0.955073i	$0.404224\pi$
$374$	187.585	0.0259352
$375$	−601.961	−0.0828937
$376$	−3365.08	−0.461545
$377$	3519.16	0.480759
$378$	2000.71	0.272237
$379$	−1636.98	−0.221863	−0.110931	−	0.993828i	$-0.535383\pi$
$379$	−1636.98	−0.221863	−0.110931	+	0.993828i	$0.535383\pi$
$380$	1206.89	0.162927
$381$	−2390.31	−0.321416
$382$	−1001.26	−0.134107
$383$	−13026.7	−1.73795	−0.868973	−	0.494859i	$-0.835220\pi$
$383$	−13026.7	−1.73795	−0.868973	+	0.494859i	$0.835220\pi$
$384$	4532.21	0.602300
$385$	1178.31	0.155980
$386$	319.280	0.0421009
$387$	−173.117	−0.0227390
$388$	13594.1	1.77871
$389$	10457.0	1.36296	0.681478	−	0.731838i	$-0.261337\pi$
$389$	10457.0	1.36296	0.681478	+	0.731838i	$0.261337\pi$
$390$	−155.649	−0.0202092
$391$	−3821.91	−0.494328
$392$	3073.95	0.396066
$393$	−4812.46	−0.617701
$394$	−485.085	−0.0620259
$395$	−2527.75	−0.321987
$396$	−256.625	−0.0325654
$397$	−5071.98	−0.641197	−0.320599	−	0.947215i	$-0.603884\pi$
$397$	−5071.98	−0.641197	−0.320599	+	0.947215i	$0.603884\pi$
$398$	1764.31	0.222203
$399$	4066.06	0.510169
$400$	1453.17	0.181647
$401$	−528.809	−0.0658540	−0.0329270	−	0.999458i	$-0.510483\pi$
$401$	−528.809	−0.0658540	−0.0329270	+	0.999458i	$0.510483\pi$
$402$	152.079	0.0188682
$403$	−403.000	−0.0498135
$404$	−5398.02	−0.664756
$405$	3058.22	0.375220
$406$	3650.42	0.446225
$407$	890.437	0.108445
$408$	1637.55	0.198703
$409$	−9530.07	−1.15216	−0.576078	−	0.817395i	$-0.695418\pi$
$409$	−9530.07	−1.15216	−0.576078	+	0.817395i	$0.695418\pi$
$410$	967.788	0.116575
$411$	−5397.66	−0.647803
$412$	3194.30	0.381970
$413$	3530.25	0.420611
$414$	−166.754	−0.0197960
$415$	−3540.03	−0.418730
$416$	1190.39	0.140297
$417$	7800.01	0.915991
$418$	134.536	0.0157425
$419$	−2609.02	−0.304198	−0.152099	−	0.988365i	$-0.548603\pi$
$419$	−2609.02	−0.304198	−0.152099	+	0.988365i	$0.548603\pi$
$420$	5062.39	0.588141
$421$	−2113.38	−0.244656	−0.122328	−	0.992490i	$-0.539036\pi$
$421$	−2113.38	−0.244656	−0.122328	+	0.992490i	$0.539036\pi$
$422$	2673.93	0.308447
$423$	1636.40	0.188096
$424$	3743.33	0.428755
$425$	1085.29	0.123869
$426$	−573.385	−0.0652127
$427$	−31.2399	−0.00354053
$428$	−5569.28	−0.628976
$429$	544.027	0.0612258
$430$	112.995	0.0126723
$431$	−1039.53	−0.116178	−0.0580888	−	0.998311i	$-0.518501\pi$
$431$	−1039.53	−0.116178	−0.0580888	+	0.998311i	$0.518501\pi$
$432$	−8624.13	−0.960483
$433$	−9514.85	−1.05602	−0.528008	−	0.849240i	$-0.677061\pi$
$433$	−9514.85	−1.05602	−0.528008	+	0.849240i	$0.677061\pi$
$434$	−418.031	−0.0462353
$435$	6518.16	0.718441
$436$	11973.9	1.31524
$437$	−2741.07	−0.300053
$438$	1593.09	0.173792
$439$	−13729.1	−1.49261	−0.746304	−	0.665605i	$-0.768173\pi$
$439$	−13729.1	−1.49261	−0.746304	+	0.665605i	$0.768173\pi$
$440$	340.345	0.0368757
$441$	−1494.83	−0.161411
$442$	280.623	0.0301988
$443$	−8932.92	−0.958049	−0.479024	−	0.877802i	$-0.659009\pi$
$443$	−8932.92	−0.958049	−0.479024	+	0.877802i	$0.659009\pi$
$444$	3825.59	0.408907
$445$	594.918	0.0633749
$446$	1080.06	0.114669
$447$	−9957.95	−1.05368
$448$	−11375.9	−1.19969
$449$	12420.3	1.30545	0.652727	−	0.757593i	$-0.273625\pi$
$449$	12420.3	1.30545	0.652727	+	0.757593i	$0.273625\pi$
$450$	47.3523	0.00496046
$451$	−3382.62	−0.353174
$452$	4387.50	0.456572
$453$	−2851.67	−0.295768
$454$	1208.52	0.124931
$455$	1762.73	0.181622
$456$	1174.45	0.120611
$457$	11607.1	1.18809	0.594043	−	0.804433i	$-0.297531\pi$
$457$	11607.1	1.18809	0.594043	+	0.804433i	$0.297531\pi$
$458$	1996.56	0.203697
$459$	−6440.84	−0.654973
$460$	−3412.73	−0.345911
$461$	18644.7	1.88367	0.941836	−	0.336074i	$-0.109099\pi$
$461$	18644.7	1.88367	0.941836	+	0.336074i	$0.109099\pi$
$462$	564.317	0.0568278
$463$	−10357.2	−1.03961	−0.519804	−	0.854286i	$-0.673995\pi$
$463$	−10357.2	−1.03961	−0.519804	+	0.854286i	$0.673995\pi$
$464$	−15735.3	−1.57433
$465$	−746.432	−0.0744408
$466$	−934.623	−0.0929089
$467$	14186.7	1.40574	0.702869	−	0.711319i	$-0.251902\pi$
$467$	14186.7	1.40574	0.702869	+	0.711319i	$0.251902\pi$
$468$	−383.906	−0.0379189
$469$	−1722.30	−0.169570
$470$	−1068.09	−0.104825
$471$	7143.75	0.698868
$472$	1019.68	0.0994380
$473$	−394.940	−0.0383919
$474$	−1210.59	−0.117309
$475$	778.366	0.0751871
$476$	−9127.07	−0.878863
$477$	−1820.34	−0.174733
$478$	353.711	0.0338460
$479$	2442.81	0.233017	0.116508	−	0.993190i	$-0.462830\pi$
$479$	2442.81	0.233017	0.116508	+	0.993190i	$0.462830\pi$
$480$	2204.82	0.209658
$481$	1332.07	0.126273
$482$	2276.15	0.215095
$483$	−11497.6	−1.08314
$484$	9733.45	0.914110
$485$	8767.32	0.820832
$486$	−527.298	−0.0492154
$487$	125.463	0.0116740	0.00583701	−	0.999983i	$-0.498142\pi$
$487$	125.463	0.0116740	0.00583701	+	0.999983i	$0.498142\pi$
$488$	−9.02339	−0.000837028 0
$489$	−12003.6	−1.11007
$490$	975.688	0.0899533
$491$	16775.1	1.54185	0.770926	−	0.636925i	$-0.219794\pi$
$491$	16775.1	1.54185	0.770926	+	0.636925i	$0.219794\pi$
$492$	−14532.8	−1.33168
$493$	−11751.7	−1.07357
$494$	201.262	0.0183304
$495$	−165.506	−0.0150282
$496$	1801.94	0.163124
$497$	6493.58	0.586070
$498$	−1695.39	−0.152555
$499$	1802.33	0.161690	0.0808450	−	0.996727i	$-0.474238\pi$
$499$	1802.33	0.161690	0.0808450	+	0.996727i	$0.474238\pi$
$500$	969.093	0.0866783
$501$	13703.8	1.22204
$502$	171.471	0.0152452
$503$	5215.31	0.462304	0.231152	−	0.972918i	$-0.425751\pi$
$503$	5215.31	0.462304	0.231152	+	0.972918i	$0.425751\pi$
$504$	−809.149	−0.0715126
$505$	−3481.36	−0.306769
$506$	−380.425	−0.0334229
$507$	813.852	0.0712908
$508$	3848.15	0.336091
$509$	−16167.9	−1.40792	−0.703960	−	0.710239i	$-0.748587\pi$
$509$	−16167.9	−1.40792	−0.703960	+	0.710239i	$0.748587\pi$
$510$	519.766	0.0451287
$511$	−18041.7	−1.56188
$512$	−8965.07	−0.773835
$513$	−4619.36	−0.397563
$514$	459.724	0.0394505
$515$	2060.11	0.176270
$516$	−1696.79	−0.144761
$517$	3733.21	0.317575
$518$	1381.76	0.117203
$519$	−14009.1	−1.18483
$520$	509.149	0.0429378
$521$	−23019.2	−1.93568	−0.967838	−	0.251572i	$-0.919052\pi$
$521$	−23019.2	−1.93568	−0.967838	+	0.251572i	$0.919052\pi$
$522$	−512.740	−0.0429924
$523$	776.692	0.0649376	0.0324688	−	0.999473i	$-0.489663\pi$
$523$	776.692	0.0649376	0.0324688	+	0.999473i	$0.489663\pi$
$524$	7747.55	0.645903
$525$	3264.90	0.271413
$526$	−502.324	−0.0416395
$527$	1345.76	0.111237
$528$	−2432.51	−0.200495
$529$	−4416.09	−0.362957
$530$	1188.15	0.0973773
$531$	−495.861	−0.0405246
$532$	−6545.92	−0.533462
$533$	−5060.33	−0.411233
$534$	284.919	0.0230892
$535$	−3591.82	−0.290257
$536$	−497.471	−0.0400885
$537$	−16624.4	−1.33593
$538$	160.125	0.0128318
$539$	−3410.23	−0.272522
$540$	−5751.26	−0.458324
$541$	21862.3	1.73740	0.868698	−	0.495341i	$-0.164957\pi$
$541$	21862.3	1.73740	0.868698	+	0.495341i	$0.164957\pi$
$542$	−61.5295	−0.00487623
$543$	5412.10	0.427727
$544$	−3975.11	−0.313293
$545$	7722.35	0.606952
$546$	844.206	0.0661698
$547$	−4741.81	−0.370649	−0.185325	−	0.982677i	$-0.559334\pi$
$547$	−4741.81	−0.370649	−0.185325	+	0.982677i	$0.559334\pi$
$548$	8689.65	0.677379
$549$	4.38798	0.000341119 0
$550$	108.027	0.00837509
$551$	−8428.30	−0.651647
$552$	−3320.98	−0.256069
$553$	13710.0	1.05426
$554$	1854.28	0.142204
$555$	2467.25	0.188701
$556$	−12557.2	−0.957811
$557$	−19634.3	−1.49359	−0.746796	−	0.665054i	$-0.768409\pi$
$557$	−19634.3	−1.49359	−0.746796	+	0.665054i	$0.768409\pi$
$558$	58.7168	0.00445463
$559$	−590.822	−0.0447032
$560$	−7881.69	−0.594754
$561$	−1816.69	−0.136722
$562$	−2050.82	−0.153930
$563$	−994.133	−0.0744187	−0.0372093	−	0.999307i	$-0.511847\pi$
$563$	−994.133	−0.0744187	−0.0372093	+	0.999307i	$0.511847\pi$
$564$	16039.0	1.19746
$565$	2829.65	0.210698
$566$	227.652	0.0169063
$567$	−16587.1	−1.22856
$568$	1875.62	0.138555
$569$	−22590.0	−1.66436	−0.832180	−	0.554506i	$-0.812907\pi$
$569$	−22590.0	−1.66436	−0.832180	+	0.554506i	$0.812907\pi$
$570$	372.775	0.0273927
$571$	5702.61	0.417945	0.208973	−	0.977921i	$-0.432988\pi$
$571$	5702.61	0.417945	0.208973	+	0.977921i	$0.432988\pi$
$572$	−875.824	−0.0640211
$573$	9696.87	0.706968
$574$	−5249.07	−0.381693
$575$	−2200.98	−0.159630
$576$	1597.87	0.115586
$577$	11765.5	0.848877	0.424439	−	0.905457i	$-0.360471\pi$
$577$	11765.5	0.848877	0.424439	+	0.905457i	$0.360471\pi$
$578$	1505.90	0.108369
$579$	−3092.11	−0.221941
$580$	−10493.5	−0.751241
$581$	19200.3	1.37102
$582$	4198.85	0.299051
$583$	−4152.83	−0.295013
$584$	−5211.21	−0.369249
$585$	−247.593	−0.0174987
$586$	−2432.19	−0.171455
$587$	−9751.25	−0.685651	−0.342825	−	0.939399i	$-0.611384\pi$
$587$	−9751.25	−0.685651	−0.342825	+	0.939399i	$0.611384\pi$
$588$	−14651.4	−1.02758
$589$	965.173	0.0675200
$590$	323.653	0.0225840
$591$	4697.87	0.326979
$592$	−5956.11	−0.413504
$593$	−10427.7	−0.722112	−0.361056	−	0.932544i	$-0.617584\pi$
$593$	−10427.7	−0.722112	−0.361056	+	0.932544i	$0.617584\pi$
$594$	−641.108	−0.0442845
$595$	−5886.35	−0.405574
$596$	16031.2	1.10179
$597$	−17086.7	−1.17137
$598$	−569.108	−0.0389173
$599$	4581.23	0.312494	0.156247	−	0.987718i	$-0.450060\pi$
$599$	4581.23	0.312494	0.156247	+	0.987718i	$0.450060\pi$
$600$	943.039	0.0641657
$601$	−486.581	−0.0330250	−0.0165125	−	0.999864i	$-0.505256\pi$
$601$	−486.581	−0.0330250	−0.0165125	+	0.999864i	$0.505256\pi$
$602$	−612.858	−0.0414921
$603$	241.914	0.0163375
$604$	4590.88	0.309272
$605$	6277.42	0.421841
$606$	−1667.30	−0.111764
$607$	22296.0	1.49088	0.745442	−	0.666571i	$-0.232238\pi$
$607$	22296.0	1.49088	0.745442	+	0.666571i	$0.232238\pi$
$608$	−2850.94	−0.190166
$609$	−35353.0	−2.35234
$610$	−2.86407	−0.000190103 0
$611$	5584.80	0.369782
$612$	1281.99	0.0846756
$613$	26294.0	1.73247	0.866236	−	0.499635i	$-0.166533\pi$
$613$	26294.0	1.73247	0.866236	+	0.499635i	$0.166533\pi$
$614$	2973.78	0.195459
$615$	−9372.68	−0.614541
$616$	−1845.96	−0.120740
$617$	14720.7	0.960506	0.480253	−	0.877130i	$-0.340545\pi$
$617$	14720.7	0.960506	0.480253	+	0.877130i	$0.340545\pi$
$618$	986.629	0.0642201
$619$	−9228.08	−0.599205	−0.299602	−	0.954064i	$-0.596854\pi$
$619$	−9228.08	−0.599205	−0.299602	+	0.954064i	$0.596854\pi$
$620$	1201.68	0.0778394
$621$	13062.1	0.844067
$622$	2034.51	0.131152
$623$	−3226.70	−0.207504
$624$	−3638.98	−0.233455
$625$	625.000	0.0400000
$626$	−3756.46	−0.239838
$627$	−1302.93	−0.0829887
$628$	−11500.7	−0.730775
$629$	−4448.25	−0.281977
$630$	−256.828	−0.0162417
$631$	25999.7	1.64030	0.820152	−	0.572146i	$-0.193889\pi$
$631$	25999.7	1.64030	0.820152	+	0.572146i	$0.193889\pi$
$632$	3960.01	0.249241
$633$	−25896.0	−1.62603
$634$	1412.14	0.0884596
$635$	2481.80	0.155098
$636$	−17841.9	−1.11238
$637$	−5101.63	−0.317322
$638$	−1169.74	−0.0725869
$639$	−912.091	−0.0564660
$640$	−4705.67	−0.290637
$641$	−9264.29	−0.570854	−0.285427	−	0.958400i	$-0.592135\pi$
$641$	−9264.29	−0.570854	−0.285427	+	0.958400i	$0.592135\pi$
$642$	−1720.20	−0.105749
$643$	−22501.4	−1.38004	−0.690022	−	0.723788i	$-0.742399\pi$
$643$	−22501.4	−1.38004	−0.690022	+	0.723788i	$0.742399\pi$
$644$	18509.9	1.13259
$645$	−1094.31	−0.0668039
$646$	−672.083	−0.0409331
$647$	4308.88	0.261823	0.130912	−	0.991394i	$-0.458210\pi$
$647$	4308.88	0.261823	0.130912	+	0.991394i	$0.458210\pi$
$648$	−4791.04	−0.290447
$649$	−1131.23	−0.0684204
$650$	161.606	0.00975188
$651$	4048.48	0.243736
$652$	19324.6	1.16075
$653$	−6029.96	−0.361364	−0.180682	−	0.983542i	$-0.557830\pi$
$653$	−6029.96	−0.361364	−0.180682	+	0.983542i	$0.557830\pi$
$654$	3698.39	0.221129
$655$	4996.65	0.298069
$656$	22626.3	1.34666
$657$	2534.15	0.150482
$658$	5793.10	0.343220
$659$	18902.7	1.11737	0.558684	−	0.829380i	$-0.311306\pi$
$659$	18902.7	1.11737	0.558684	+	0.829380i	$0.311306\pi$
$660$	−1622.19	−0.0956723
$661$	7677.77	0.451786	0.225893	−	0.974152i	$-0.427470\pi$
$661$	7677.77	0.451786	0.225893	+	0.974152i	$0.427470\pi$
$662$	−870.307	−0.0510958
$663$	−2717.73	−0.159197
$664$	5545.85	0.324127
$665$	−4221.68	−0.246180
$666$	−194.082	−0.0112921
$667$	23832.7	1.38351
$668$	−22061.6	−1.27783
$669$	−10460.0	−0.604496
$670$	−157.900	−0.00910477
$671$	10.0105	0.000575934 0
$672$	−11958.4	−0.686468
$673$	12557.6	0.719256	0.359628	−	0.933096i	$-0.382904\pi$
$673$	12557.6	0.719256	0.359628	+	0.933096i	$0.382904\pi$
$674$	3412.96	0.195048
$675$	−3709.18	−0.211506
$676$	−1310.21	−0.0745456
$677$	8731.25	0.495671	0.247836	−	0.968802i	$-0.420281\pi$
$677$	8731.25	0.495671	0.247836	+	0.968802i	$0.420281\pi$
$678$	1355.18	0.0767629
$679$	−47551.9	−2.68759
$680$	−1700.22	−0.0958832
$681$	−11704.1	−0.658591
$682$	133.954	0.00752105
$683$	21118.6	1.18313	0.591567	−	0.806256i	$-0.298509\pi$
$683$	21118.6	1.18313	0.591567	+	0.806256i	$0.298509\pi$
$684$	919.443	0.0513973
$685$	5604.25	0.312594
$686$	−666.602	−0.0371006
$687$	−19336.0	−1.07382
$688$	2641.74	0.146389
$689$	−6212.55	−0.343511
$690$	−1054.10	−0.0581576
$691$	−9856.48	−0.542631	−0.271316	−	0.962490i	$-0.587459\pi$
$691$	−9856.48	−0.542631	−0.271316	+	0.962490i	$0.587459\pi$
$692$	22553.1	1.23893
$693$	897.668	0.0492057
$694$	1894.39	0.103617
$695$	−8098.54	−0.442007
$696$	−10211.4	−0.556125
$697$	16898.2	0.918312
$698$	187.940	0.0101915
$699$	9051.48	0.489783
$700$	−5256.14	−0.283805
$701$	25622.6	1.38053	0.690266	−	0.723556i	$-0.257493\pi$
$701$	25622.6	1.38053	0.690266	+	0.723556i	$0.257493\pi$
$702$	−959.084	−0.0515645
$703$	−3190.28	−0.171157
$704$	3645.30	0.195152
$705$	10344.1	0.552598
$706$	−1991.31	−0.106153
$707$	18882.1	1.00443
$708$	−4860.13	−0.257987
$709$	1209.97	0.0640923	0.0320461	−	0.999486i	$-0.489798\pi$
$709$	1209.97	0.0640923	0.0320461	+	0.999486i	$0.489798\pi$
$710$	595.330	0.0314681
$711$	−1925.71	−0.101575
$712$	−932.006	−0.0490567
$713$	−2729.22	−0.143352
$714$	−2819.10	−0.147762
$715$	−564.848	−0.0295442
$716$	26763.5	1.39692
$717$	−3425.57	−0.178424
$718$	3450.35	0.179340
$719$	−6659.75	−0.345434	−0.172717	−	0.984972i	$-0.555255\pi$
$719$	−6659.75	−0.345434	−0.172717	+	0.984972i	$0.555255\pi$
$720$	1107.07	0.0573026
$721$	−11173.6	−0.577150
$722$	2928.62	0.150959
$723$	−22043.7	−1.13391
$724$	−8712.90	−0.447255
$725$	−6767.62	−0.346680
$726$	3006.39	0.153688
$727$	9667.48	0.493187	0.246593	−	0.969119i	$-0.420689\pi$
$727$	9667.48	0.493187	0.246593	+	0.969119i	$0.420689\pi$
$728$	−2761.51	−0.140588
$729$	21621.1	1.09846
$730$	−1654.06	−0.0838625
$731$	1972.96	0.0998255
$732$	43.0083	0.00217163
$733$	8603.91	0.433551	0.216775	−	0.976222i	$-0.430446\pi$
$733$	8603.91	0.433551	0.216775	+	0.976222i	$0.430446\pi$
$734$	−6180.88	−0.310818
$735$	−9449.19	−0.474202
$736$	8061.59	0.403742
$737$	551.892	0.0275837
$738$	737.286	0.0367749
$739$	−23928.7	−1.19111	−0.595555	−	0.803315i	$-0.703068\pi$
$739$	−23928.7	−1.19111	−0.595555	+	0.803315i	$0.703068\pi$
$740$	−3972.01	−0.197316
$741$	−1949.15	−0.0966314
$742$	−6444.26	−0.318836
$743$	−36687.6	−1.81149	−0.905746	−	0.423821i	$-0.860689\pi$
$743$	−36687.6	−1.81149	−0.905746	+	0.423821i	$0.860689\pi$
$744$	1169.37	0.0576225
$745$	10339.1	0.508449
$746$	−2123.26	−0.104206
$747$	−2696.88	−0.132093
$748$	2924.68	0.142964
$749$	19481.2	0.950371
$750$	299.325	0.0145731
$751$	12486.5	0.606708	0.303354	−	0.952878i	$-0.401894\pi$
$751$	12486.5	0.606708	0.303354	+	0.952878i	$0.401894\pi$
$752$	−24971.3	−1.21092
$753$	−1660.63	−0.0803675
$754$	−1749.91	−0.0845197
$755$	2960.81	0.142722
$756$	31193.6	1.50066
$757$	10030.3	0.481583	0.240792	−	0.970577i	$-0.422593\pi$
$757$	10030.3	0.481583	0.240792	+	0.970577i	$0.422593\pi$
$758$	813.989	0.0390045
$759$	3684.28	0.176194
$760$	−1219.40	−0.0582002
$761$	−8430.99	−0.401607	−0.200804	−	0.979632i	$-0.564355\pi$
$761$	−8430.99	−0.401607	−0.200804	+	0.979632i	$0.564355\pi$
$762$	1188.58	0.0565064
$763$	−41884.3	−1.98730
$764$	−15610.9	−0.739245
$765$	826.799	0.0390758
$766$	6477.53	0.305539
$767$	−1692.30	−0.0796681
$768$	13907.2	0.653427
$769$	27324.3	1.28133	0.640664	−	0.767821i	$-0.278659\pi$
$769$	27324.3	1.28133	0.640664	+	0.767821i	$0.278659\pi$
$770$	−585.915	−0.0274220
$771$	−4452.26	−0.207969
$772$	4977.97	0.232074
$773$	−16517.0	−0.768532	−0.384266	−	0.923222i	$-0.625546\pi$
$773$	−16517.0	−0.768532	−0.384266	+	0.923222i	$0.625546\pi$
$774$	86.0823	0.00399763
$775$	775.000	0.0359211
$776$	−13735.0	−0.635383
$777$	−13381.8	−0.617851
$778$	−5199.74	−0.239614
$779$	12119.3	0.557407
$780$	−2426.76	−0.111400
$781$	−2080.80	−0.0953354
$782$	1900.45	0.0869052
$783$	40163.7	1.83312
$784$	22811.0	1.03913
$785$	−7417.17	−0.337236
$786$	2393.00	0.108595
$787$	−17057.2	−0.772582	−0.386291	−	0.922377i	$-0.626244\pi$
$787$	−17057.2	−0.772582	−0.386291	+	0.922377i	$0.626244\pi$
$788$	−7563.07	−0.341907
$789$	4864.83	0.219509
$790$	1256.93	0.0566069
$791$	−15347.4	−0.689873
$792$	259.284	0.0116329
$793$	14.9755	0.000670613 0
$794$	2522.04	0.112725
$795$	−11506.8	−0.513339
$796$	27507.7	1.22485
$797$	14883.4	0.661478	0.330739	−	0.943722i	$-0.392702\pi$
$797$	14883.4	0.661478	0.330739	+	0.943722i	$0.392702\pi$
$798$	−2021.85	−0.0896901
$799$	−18649.6	−0.825750
$800$	−2289.20	−0.101169
$801$	453.224	0.0199924
$802$	262.950	0.0115774
$803$	5781.30	0.254069
$804$	2371.10	0.104008
$805$	11937.6	0.522666
$806$	200.392	0.00875745
$807$	−1550.76	−0.0676446
$808$	5453.94	0.237462
$809$	25774.3	1.12012	0.560060	−	0.828452i	$-0.310778\pi$
$809$	25774.3	1.12012	0.560060	+	0.828452i	$0.310778\pi$
$810$	−1520.70	−0.0659654
$811$	11789.7	0.510473	0.255236	−	0.966879i	$-0.417847\pi$
$811$	11789.7	0.510473	0.255236	+	0.966879i	$0.417847\pi$
$812$	56914.5	2.45974
$813$	595.891	0.0257058
$814$	−442.770	−0.0190652
$815$	12463.1	0.535658
$816$	12151.8	0.521321
$817$	1415.00	0.0605931
$818$	4738.83	0.202554
$819$	1342.89	0.0572948
$820$	15089.0	0.642599
$821$	−1138.03	−0.0483772	−0.0241886	−	0.999707i	$-0.507700\pi$
$821$	−1138.03	−0.0483772	−0.0241886	+	0.999707i	$0.507700\pi$
$822$	2683.99	0.113887
$823$	−23462.5	−0.993743	−0.496872	−	0.867824i	$-0.665518\pi$
$823$	−23462.5	−0.993743	−0.496872	+	0.867824i	$0.665518\pi$
$824$	−3227.39	−0.136446
$825$	−1046.20	−0.0441505
$826$	−1755.42	−0.0739454
$827$	−15142.8	−0.636721	−0.318361	−	0.947970i	$-0.603132\pi$
$827$	−15142.8	−0.636721	−0.318361	+	0.947970i	$0.603132\pi$
$828$	−2599.90	−0.109122
$829$	−19686.7	−0.824787	−0.412393	−	0.911006i	$-0.635307\pi$
$829$	−19686.7	−0.824787	−0.412393	+	0.911006i	$0.635307\pi$
$830$	1760.28	0.0736147
$831$	−17958.0	−0.749648
$832$	5453.28	0.227234
$833$	17036.1	0.708603
$834$	−3878.56	−0.161035
$835$	−14228.3	−0.589689
$836$	2097.57	0.0867776
$837$	−4599.38	−0.189938
$838$	1297.33	0.0534793
$839$	8010.45	0.329620	0.164810	−	0.986325i	$-0.447299\pi$
$839$	8010.45	0.329620	0.164810	+	0.986325i	$0.447299\pi$
$840$	−5114.83	−0.210093
$841$	48892.2	2.00468
$842$	1050.88	0.0430116
$843$	19861.4	0.811464
$844$	41689.8	1.70026
$845$	−845.000	−0.0344010
$846$	−813.702	−0.0330681
$847$	−34047.3	−1.38120
$848$	27778.2	1.12489
$849$	−2204.73	−0.0891238
$850$	−539.659	−0.0217767
$851$	9021.13	0.363385
$852$	−8939.77	−0.359474
$853$	−1762.75	−0.0707568	−0.0353784	−	0.999374i	$-0.511264\pi$
$853$	−1762.75	−0.0707568	−0.0353784	+	0.999374i	$0.511264\pi$
$854$	15.5341	0.000622442 0
$855$	592.979	0.0237187
$856$	5626.98	0.224680
$857$	38146.0	1.52047	0.760234	−	0.649649i	$-0.225084\pi$
$857$	38146.0	1.52047	0.760234	+	0.649649i	$0.225084\pi$
$858$	−270.517	−0.0107638
$859$	24886.6	0.988497	0.494248	−	0.869321i	$-0.335443\pi$
$859$	24886.6	0.988497	0.494248	+	0.869321i	$0.335443\pi$
$860$	1761.73	0.0698539
$861$	50835.3	2.01215
$862$	516.909	0.0204246
$863$	−19514.8	−0.769747	−0.384874	−	0.922969i	$-0.625755\pi$
$863$	−19514.8	−0.769747	−0.384874	+	0.922969i	$0.625755\pi$
$864$	13585.7	0.534948
$865$	14545.2	0.571737
$866$	4731.26	0.185652
$867$	−14584.1	−0.571281
$868$	−6517.61	−0.254864
$869$	−4393.22	−0.171496
$870$	−3241.16	−0.126305
$871$	825.618	0.0321183
$872$	−12097.9	−0.469825
$873$	6679.17	0.258941
$874$	1363.00	0.0527507
$875$	−3389.86	−0.130969
$876$	24838.2	0.957998
$877$	23572.1	0.907608	0.453804	−	0.891102i	$-0.350067\pi$
$877$	23572.1	0.907608	0.453804	+	0.891102i	$0.350067\pi$
$878$	6826.81	0.262407
$879$	23554.9	0.903853
$880$	2525.61	0.0967479
$881$	−2816.98	−0.107726	−0.0538629	−	0.998548i	$-0.517153\pi$
$881$	−2816.98	−0.107726	−0.0538629	+	0.998548i	$0.517153\pi$
$882$	743.304	0.0283768
$883$	6537.10	0.249140	0.124570	−	0.992211i	$-0.460245\pi$
$883$	6537.10	0.249140	0.124570	+	0.992211i	$0.460245\pi$
$884$	4375.25	0.166466
$885$	−3134.46	−0.119055
$886$	4441.90	0.168429
$887$	35863.8	1.35760	0.678799	−	0.734324i	$-0.262501\pi$
$887$	35863.8	1.35760	0.678799	+	0.734324i	$0.262501\pi$
$888$	−3865.22	−0.146068
$889$	−13460.7	−0.507827
$890$	−295.823	−0.0111416
$891$	5315.17	0.199848
$892$	16839.5	0.632095
$893$	−13375.4	−0.501223
$894$	4951.60	0.185242
$895$	17260.6	0.644648
$896$	25522.5	0.951614
$897$	5511.61	0.205158
$898$	−6175.99	−0.229505
$899$	−8391.85	−0.311328
$900$	738.280	0.0273437
$901$	20745.8	0.767085
$902$	1682.01	0.0620896
$903$	5935.31	0.218732
$904$	−4432.96	−0.163095
$905$	−5619.24	−0.206398
$906$	1417.99	0.0519974
$907$	−21938.5	−0.803147	−0.401574	−	0.915827i	$-0.631537\pi$
$907$	−21938.5	−0.803147	−0.401574	+	0.915827i	$0.631537\pi$
$908$	18842.3	0.688659
$909$	−2652.19	−0.0967741
$910$	−876.517	−0.0319299
$911$	17964.8	0.653349	0.326674	−	0.945137i	$-0.394072\pi$
$911$	17964.8	0.653349	0.326674	+	0.945137i	$0.394072\pi$
$912$	8715.25	0.316437
$913$	−6152.55	−0.223022
$914$	−5771.62	−0.208871
$915$	27.7375	0.00100216
$916$	31128.8	1.12285
$917$	−27100.7	−0.975948
$918$	3202.71	0.115147
$919$	4269.44	0.153249	0.0766245	−	0.997060i	$-0.475586\pi$
$919$	4269.44	0.153249	0.0766245	+	0.997060i	$0.475586\pi$
$920$	3448.08	0.123565
$921$	−28800.0	−1.03039
$922$	−9271.11	−0.331158
$923$	−3112.83	−0.111008
$924$	8798.40	0.313253
$925$	−2561.68	−0.0910568
$926$	5150.10	0.182768
$927$	1569.44	0.0556066
$928$	24787.9	0.876836
$929$	51216.8	1.80879	0.904396	−	0.426694i	$-0.140322\pi$
$929$	51216.8	1.80879	0.904396	+	0.426694i	$0.140322\pi$
$930$	371.164	0.0130870
$931$	12218.3	0.430115
$932$	−14571.9	−0.512145
$933$	−19703.5	−0.691387
$934$	−7054.32	−0.247135
$935$	1886.22	0.0659744
$936$	387.883	0.0135452
$937$	4990.42	0.173991	0.0869957	−	0.996209i	$-0.472273\pi$
$937$	4990.42	0.173991	0.0869957	+	0.996209i	$0.472273\pi$
$938$	856.412	0.0298111
$939$	36380.0	1.26434
$940$	−16652.9	−0.577827
$941$	−1615.99	−0.0559828	−0.0279914	−	0.999608i	$-0.508911\pi$
$941$	−1615.99	−0.0559828	−0.0279914	+	0.999608i	$0.508911\pi$
$942$	−3552.23	−0.122864
$943$	−34269.8	−1.18343
$944$	7566.79	0.260888
$945$	20117.8	0.692519
$946$	196.384	0.00674947
$947$	−49501.9	−1.69862	−0.849311	−	0.527893i	$-0.822982\pi$
$947$	−49501.9	−1.69862	−0.849311	+	0.527893i	$0.822982\pi$
$948$	−18874.6	−0.646645
$949$	8648.69	0.295836
$950$	−387.043	−0.0132182
$951$	−13676.1	−0.466328
$952$	9221.62	0.313944
$953$	−22515.5	−0.765318	−0.382659	−	0.923890i	$-0.624992\pi$
$953$	−22515.5	−0.765318	−0.382659	+	0.923890i	$0.624992\pi$
$954$	905.164	0.0307188
$955$	−10068.0	−0.341144
$956$	5514.79	0.186570
$957$	11328.5	0.382653
$958$	−1214.69	−0.0409654
$959$	−30396.2	−1.02351
$960$	10100.5	0.339575
$961$	961.000	0.0322581
$962$	−662.374	−0.0221994
$963$	−2736.34	−0.0915652
$964$	35488.0	1.18568
$965$	3210.46	0.107097
$966$	5717.18	0.190421
$967$	28192.5	0.937549	0.468775	−	0.883318i	$-0.344696\pi$
$967$	28192.5	0.937549	0.468775	+	0.883318i	$0.344696\pi$
$968$	−9834.28	−0.326535
$969$	6508.88	0.215785
$970$	−4359.55	−0.144306
$971$	30797.1	1.01785	0.508923	−	0.860812i	$-0.330044\pi$
$971$	30797.1	1.01785	0.508923	+	0.860812i	$0.330044\pi$
$972$	−8221.21	−0.271292
$973$	43924.6	1.44723
$974$	−62.3863	−0.00205235
$975$	−1565.10	−0.0514085
$976$	−66.9601	−0.00219605
$977$	1070.49	0.0350542	0.0175271	−	0.999846i	$-0.494421\pi$
$977$	1070.49	0.0350542	0.0175271	+	0.999846i	$0.494421\pi$
$978$	5968.81	0.195155
$979$	1033.96	0.0337545
$980$	15212.2	0.495852
$981$	5883.08	0.191470
$982$	−8341.42	−0.271065
$983$	−16211.2	−0.525999	−0.262999	−	0.964796i	$-0.584712\pi$
$983$	−16211.2	−0.525999	−0.262999	+	0.964796i	$0.584712\pi$
$984$	14683.3	0.475699
$985$	−4877.67	−0.157782
$986$	5843.54	0.188738
$987$	−56104.1	−1.80933
$988$	3137.92	0.101043
$989$	−4001.19	−0.128646
$990$	82.2980	0.00264202
$991$	−42951.2	−1.37678	−0.688390	−	0.725341i	$-0.741682\pi$
$991$	−42951.2	−1.37678	−0.688390	+	0.725341i	$0.741682\pi$
$992$	−2838.61	−0.0908528
$993$	8428.61	0.269359
$994$	−3228.94	−0.103034
$995$	17740.6	0.565242
$996$	−26433.2	−0.840933
$997$	34324.9	1.09035	0.545176	−	0.838322i	$-0.316463\pi$
$997$	34324.9	1.09035	0.545176	+	0.838322i	$0.316463\pi$
$998$	−896.209	−0.0284258
$999$	15202.8	0.481476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2015.4.a.d.1.20	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2015.4.a.d.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-0.497250 q^{2} +4.81569 q^{3} -7.75274 q^{4} -5.00000 q^{5} -2.39460 q^{6} +27.1189 q^{7} +7.83306 q^{8} -3.80913 q^{9} +O(q^{10})\)	\(q-0.497250 q^{2} +4.81569 q^{3} -7.75274 q^{4} -5.00000 q^{5} -2.39460 q^{6} +27.1189 q^{7} +7.83306 q^{8} -3.80913 q^{9} +2.48625 q^{10} -8.68997 q^{11} -37.3348 q^{12} -13.0000 q^{13} -13.4849 q^{14} -24.0785 q^{15} +58.1269 q^{16} +43.4115 q^{17} +1.89409 q^{18} +31.1346 q^{19} +38.7637 q^{20} +130.596 q^{21} +4.32109 q^{22} -88.0392 q^{23} +37.7216 q^{24} +25.0000 q^{25} +6.46426 q^{26} -148.367 q^{27} -210.246 q^{28} -270.705 q^{29} +11.9730 q^{30} +31.0000 q^{31} -91.5681 q^{32} -41.8482 q^{33} -21.5864 q^{34} -135.594 q^{35} +29.5312 q^{36} -102.467 q^{37} -15.4817 q^{38} -62.6040 q^{39} -39.1653 q^{40} +389.256 q^{41} -64.9390 q^{42} +45.4478 q^{43} +67.3711 q^{44} +19.0456 q^{45} +43.7775 q^{46} -429.600 q^{47} +279.921 q^{48} +392.433 q^{49} -12.4313 q^{50} +209.056 q^{51} +100.786 q^{52} +477.888 q^{53} +73.7757 q^{54} +43.4498 q^{55} +212.424 q^{56} +149.935 q^{57} +134.608 q^{58} +130.177 q^{59} +186.674 q^{60} -1.15196 q^{61} -15.4148 q^{62} -103.299 q^{63} -419.483 q^{64} +65.0000 q^{65} +20.8090 q^{66} -63.5091 q^{67} -336.558 q^{68} -423.970 q^{69} +67.4244 q^{70} +239.449 q^{71} -29.8371 q^{72} -665.284 q^{73} +50.9519 q^{74} +120.392 q^{75} -241.379 q^{76} -235.662 q^{77} +31.1298 q^{78} +505.551 q^{79} -290.635 q^{80} -611.644 q^{81} -193.558 q^{82} +708.005 q^{83} -1012.48 q^{84} -217.057 q^{85} -22.5989 q^{86} -1303.63 q^{87} -68.0690 q^{88} -118.984 q^{89} -9.47046 q^{90} -352.545 q^{91} +682.545 q^{92} +149.286 q^{93} +213.619 q^{94} -155.673 q^{95} -440.964 q^{96} -1753.46 q^{97} -195.138 q^{98} +33.1012 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) \) 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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