LMFDB - Embedded newform 2015.4.a.d.1.10

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			1.10
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)

$f(q)$	$=$	$q-3.41025 q^{2} -3.08447 q^{3} +3.62984 q^{4} -5.00000 q^{5} +10.5188 q^{6} -22.1095 q^{7} +14.9034 q^{8} -17.4860 q^{9} +O(q^{10})$	\(q-3.41025 q^{2} -3.08447 q^{3} +3.62984 q^{4} -5.00000 q^{5} +10.5188 q^{6} -22.1095 q^{7} +14.9034 q^{8} -17.4860 q^{9} +17.0513 q^{10} -32.6844 q^{11} -11.1961 q^{12} -13.0000 q^{13} +75.3990 q^{14} +15.4224 q^{15} -79.8630 q^{16} -26.8331 q^{17} +59.6318 q^{18} -73.2550 q^{19} -18.1492 q^{20} +68.1961 q^{21} +111.462 q^{22} -81.4570 q^{23} -45.9690 q^{24} +25.0000 q^{25} +44.3333 q^{26} +137.216 q^{27} -80.2538 q^{28} +217.870 q^{29} -52.5942 q^{30} +31.0000 q^{31} +153.126 q^{32} +100.814 q^{33} +91.5076 q^{34} +110.547 q^{35} -63.4715 q^{36} +60.0184 q^{37} +249.818 q^{38} +40.0981 q^{39} -74.5168 q^{40} -79.4624 q^{41} -232.566 q^{42} -9.73651 q^{43} -118.639 q^{44} +87.4302 q^{45} +277.789 q^{46} -343.299 q^{47} +246.335 q^{48} +145.829 q^{49} -85.2564 q^{50} +82.7659 q^{51} -47.1879 q^{52} -270.464 q^{53} -467.941 q^{54} +163.422 q^{55} -329.506 q^{56} +225.953 q^{57} -742.992 q^{58} -179.222 q^{59} +55.9807 q^{60} -232.168 q^{61} -105.718 q^{62} +386.607 q^{63} +116.705 q^{64} +65.0000 q^{65} -343.802 q^{66} +647.205 q^{67} -97.3997 q^{68} +251.252 q^{69} -376.995 q^{70} +600.693 q^{71} -260.601 q^{72} +593.018 q^{73} -204.678 q^{74} -77.1118 q^{75} -265.904 q^{76} +722.635 q^{77} -136.745 q^{78} +873.603 q^{79} +399.315 q^{80} +48.8841 q^{81} +270.987 q^{82} +1074.26 q^{83} +247.541 q^{84} +134.165 q^{85} +33.2040 q^{86} -672.014 q^{87} -487.108 q^{88} -310.240 q^{89} -298.159 q^{90} +287.423 q^{91} -295.676 q^{92} -95.6186 q^{93} +1170.74 q^{94} +366.275 q^{95} -472.313 q^{96} +76.4673 q^{97} -497.315 q^{98} +571.521 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.41025	−1.20571	−0.602854	−	0.797852i	$-0.705970\pi$
$2$	−3.41025	−1.20571	−0.602854	+	0.797852i	$0.705970\pi$
$3$	−3.08447	−0.593607	−0.296803	−	0.954939i	$-0.595921\pi$
$3$	−3.08447	−0.593607	−0.296803	+	0.954939i	$0.595921\pi$
$4$	3.62984	0.453730
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	10.5188	0.715716
$7$	−22.1095	−1.19380	−0.596900	−	0.802316i	$-0.703601\pi$
$7$	−22.1095	−1.19380	−0.596900	+	0.802316i	$0.703601\pi$
$8$	14.9034	0.658642
$9$	−17.4860	−0.647631
$10$	17.0513	0.539209
$11$	−32.6844	−0.895884	−0.447942	−	0.894063i	$-0.647843\pi$
$11$	−32.6844	−0.895884	−0.447942	+	0.894063i	$0.647843\pi$
$12$	−11.1961	−0.269337
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	75.3990	1.43937
$15$	15.4224	0.265469
$16$	−79.8630	−1.24786
$17$	−26.8331	−0.382822	−0.191411	−	0.981510i	$-0.561306\pi$
$17$	−26.8331	−0.382822	−0.191411	+	0.981510i	$0.561306\pi$
$18$	59.6318	0.780853
$19$	−73.2550	−0.884519	−0.442259	−	0.896887i	$-0.645823\pi$
$19$	−73.2550	−0.884519	−0.442259	+	0.896887i	$0.645823\pi$
$20$	−18.1492	−0.202914
$21$	68.1961	0.708648
$22$	111.462	1.08017
$23$	−81.4570	−0.738477	−0.369238	−	0.929335i	$-0.620381\pi$
$23$	−81.4570	−0.738477	−0.369238	+	0.929335i	$0.620381\pi$
$24$	−45.9690	−0.390974
$25$	25.0000	0.200000
$26$	44.3333	0.334403
$27$	137.216	0.978045
$28$	−80.2538	−0.541663
$29$	217.870	1.39508	0.697542	−	0.716544i	$-0.254277\pi$
$29$	217.870	1.39508	0.697542	+	0.716544i	$0.254277\pi$
$30$	−52.5942	−0.320078
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	153.126	0.845911
$33$	100.814	0.531803
$34$	91.5076	0.461572
$35$	110.547	0.533884
$36$	−63.4715	−0.293849
$37$	60.0184	0.266675	0.133337	−	0.991071i	$-0.457431\pi$
$37$	60.0184	0.266675	0.133337	+	0.991071i	$0.457431\pi$
$38$	249.818	1.06647
$39$	40.0981	0.164637
$40$	−74.5168	−0.294554
$41$	−79.4624	−0.302682	−0.151341	−	0.988482i	$-0.548359\pi$
$41$	−79.4624	−0.302682	−0.151341	+	0.988482i	$0.548359\pi$
$42$	−232.566	−0.854422
$43$	−9.73651	−0.0345303	−0.0172652	−	0.999851i	$-0.505496\pi$
$43$	−9.73651	−0.0345303	−0.0172652	+	0.999851i	$0.505496\pi$
$44$	−118.639	−0.406489
$45$	87.4302	0.289629
$46$	277.789	0.890386
$47$	−343.299	−1.06543	−0.532717	−	0.846294i	$-0.678829\pi$
$47$	−343.299	−1.06543	−0.532717	+	0.846294i	$0.678829\pi$
$48$	246.335	0.740738
$49$	145.829	0.425158
$50$	−85.2564	−0.241141
$51$	82.7659	0.227246
$52$	−47.1879	−0.125842
$53$	−270.464	−0.700965	−0.350483	−	0.936569i	$-0.613982\pi$
$53$	−270.464	−0.700965	−0.350483	+	0.936569i	$0.613982\pi$
$54$	−467.941	−1.17924
$55$	163.422	0.400651
$56$	−329.506	−0.786287
$57$	225.953	0.525056
$58$	−742.992	−1.68206
$59$	−179.222	−0.395469	−0.197734	−	0.980256i	$-0.563358\pi$
$59$	−179.222	−0.395469	−0.197734	+	0.980256i	$0.563358\pi$
$60$	55.9807	0.120451
$61$	−232.168	−0.487313	−0.243656	−	0.969862i	$-0.578347\pi$
$61$	−232.168	−0.487313	−0.243656	+	0.969862i	$0.578347\pi$
$62$	−105.718	−0.216551
$63$	386.607	0.773142
$64$	116.705	0.227939
$65$	65.0000	0.124035
$66$	−343.802	−0.641198
$67$	647.205	1.18013	0.590065	−	0.807356i	$-0.299102\pi$
$67$	647.205	1.18013	0.590065	+	0.807356i	$0.299102\pi$
$68$	−97.3997	−0.173698
$69$	251.252	0.438365
$70$	−376.995	−0.643707
$71$	600.693	1.00407	0.502036	−	0.864846i	$-0.332584\pi$
$71$	600.693	1.00407	0.502036	+	0.864846i	$0.332584\pi$
$72$	−260.601	−0.426557
$73$	593.018	0.950788	0.475394	−	0.879773i	$-0.342306\pi$
$73$	593.018	0.950788	0.475394	+	0.879773i	$0.342306\pi$
$74$	−204.678	−0.321531
$75$	−77.1118	−0.118721
$76$	−265.904	−0.401332
$77$	722.635	1.06951
$78$	−136.745	−0.198504
$79$	873.603	1.24415	0.622076	−	0.782957i	$-0.286290\pi$
$79$	873.603	1.24415	0.622076	+	0.782957i	$0.286290\pi$
$80$	399.315	0.558060
$81$	48.8841	0.0670564
$82$	270.987	0.364945
$83$	1074.26	1.42066	0.710332	−	0.703866i	$-0.248545\pi$
$83$	1074.26	1.42066	0.710332	+	0.703866i	$0.248545\pi$
$84$	247.541	0.321535
$85$	134.165	0.171203
$86$	33.2040	0.0416334
$87$	−672.014	−0.828131
$88$	−487.108	−0.590067
$89$	−310.240	−0.369499	−0.184749	−	0.982786i	$-0.559147\pi$
$89$	−310.240	−0.369499	−0.184749	+	0.982786i	$0.559147\pi$
$90$	−298.159	−0.349208
$91$	287.423	0.331101
$92$	−295.676	−0.335069
$93$	−95.6186	−0.106615
$94$	1170.74	1.28460
$95$	366.275	0.395569
$96$	−472.313	−0.502138
$97$	76.4673	0.0800421	0.0400210	−	0.999199i	$-0.487258\pi$
$97$	76.4673	0.0800421	0.0400210	+	0.999199i	$0.487258\pi$
$98$	−497.315	−0.512617
$99$	571.521	0.580202
$100$	90.7459	0.0907459
$101$	−527.057	−0.519249	−0.259625	−	0.965710i	$-0.583599\pi$
$101$	−527.057	−0.519249	−0.259625	+	0.965710i	$0.583599\pi$
$102$	−282.253	−0.273992
$103$	−1508.67	−1.44324	−0.721620	−	0.692290i	$-0.756602\pi$
$103$	−1508.67	−1.44324	−0.721620	+	0.692290i	$0.756602\pi$
$104$	−193.744	−0.182674
$105$	−340.980	−0.316917
$106$	922.353	0.845159
$107$	−535.623	−0.483931	−0.241966	−	0.970285i	$-0.577792\pi$
$107$	−535.623	−0.483931	−0.241966	+	0.970285i	$0.577792\pi$
$108$	498.072	0.443768
$109$	240.368	0.211221	0.105610	−	0.994408i	$-0.466320\pi$
$109$	240.368	0.211221	0.105610	+	0.994408i	$0.466320\pi$
$110$	−557.311	−0.483068
$111$	−185.125	−0.158300
$112$	1765.73	1.48969
$113$	−776.527	−0.646456	−0.323228	−	0.946321i	$-0.604768\pi$
$113$	−776.527	−0.646456	−0.323228	+	0.946321i	$0.604768\pi$
$114$	−770.558	−0.633064
$115$	407.285	0.330257
$116$	790.832	0.632991
$117$	227.318	0.179620
$118$	611.191	0.476820
$119$	593.266	0.457013
$120$	229.845	0.174849
$121$	−262.729	−0.197393
$122$	791.752	0.587556
$123$	245.100	0.179674
$124$	112.525	0.0814923
$125$	−125.000	−0.0894427
$126$	−1318.43	−0.932182
$127$	319.318	0.223109	0.111555	−	0.993758i	$-0.464417\pi$
$127$	319.318	0.223109	0.111555	+	0.993758i	$0.464417\pi$
$128$	−1623.00	−1.12074
$129$	30.0320	0.0204974
$130$	−221.667	−0.149550
$131$	1947.41	1.29882	0.649412	−	0.760437i	$-0.275015\pi$
$131$	1947.41	1.29882	0.649412	+	0.760437i	$0.275015\pi$
$132$	365.939	0.241295
$133$	1619.63	1.05594
$134$	−2207.14	−1.42289
$135$	−686.080	−0.437395
$136$	−399.903	−0.252143
$137$	2483.02	1.54846	0.774228	−	0.632907i	$-0.218138\pi$
$137$	2483.02	1.54846	0.774228	+	0.632907i	$0.218138\pi$
$138$	−856.833	−0.528540
$139$	1063.51	0.648963	0.324482	−	0.945892i	$-0.394810\pi$
$139$	1063.51	0.648963	0.324482	+	0.945892i	$0.394810\pi$
$140$	401.269	0.242239
$141$	1058.90	0.632449
$142$	−2048.52	−1.21062
$143$	424.897	0.248473
$144$	1396.49	0.808152
$145$	−1089.35	−0.623900
$146$	−2022.34	−1.14637
$147$	−449.807	−0.252377
$148$	217.857	0.120998
$149$	−983.535	−0.540767	−0.270384	−	0.962753i	$-0.587151\pi$
$149$	−983.535	−0.540767	−0.270384	+	0.962753i	$0.587151\pi$
$150$	262.971	0.143143
$151$	2240.38	1.20741	0.603706	−	0.797207i	$-0.293690\pi$
$151$	2240.38	1.20741	0.603706	+	0.797207i	$0.293690\pi$
$152$	−1091.75	−0.582581
$153$	469.204	0.247927
$154$	−2464.37	−1.28951
$155$	−155.000	−0.0803219
$156$	145.550	0.0747007
$157$	2134.91	1.08525	0.542626	−	0.839975i	$-0.317430\pi$
$157$	2134.91	1.08525	0.542626	+	0.839975i	$0.317430\pi$
$158$	−2979.21	−1.50008
$159$	834.240	0.416098
$160$	−765.631	−0.378303
$161$	1800.97	0.881593
$162$	−166.707	−0.0808504
$163$	−145.980	−0.0701476	−0.0350738	−	0.999385i	$-0.511167\pi$
$163$	−145.980	−0.0701476	−0.0350738	+	0.999385i	$0.511167\pi$
$164$	−288.436	−0.137336
$165$	−504.071	−0.237829
$166$	−3663.49	−1.71291
$167$	3123.42	1.44729	0.723645	−	0.690173i	$-0.242465\pi$
$167$	3123.42	1.44729	0.723645	+	0.690173i	$0.242465\pi$
$168$	1016.35	0.466745
$169$	169.000	0.0769231
$170$	−457.538	−0.206421
$171$	1280.94	0.572841
$172$	−35.3419	−0.0156674
$173$	−1995.88	−0.877131	−0.438565	−	0.898699i	$-0.644513\pi$
$173$	−1995.88	−0.877131	−0.438565	+	0.898699i	$0.644513\pi$
$174$	2291.74	0.998484
$175$	−552.737	−0.238760
$176$	2610.27	1.11794
$177$	552.804	0.234753
$178$	1058.00	0.445507
$179$	229.491	0.0958264	0.0479132	−	0.998852i	$-0.484743\pi$
$179$	229.491	0.0958264	0.0479132	+	0.998852i	$0.484743\pi$
$180$	317.357	0.131413
$181$	1840.27	0.755726	0.377863	−	0.925861i	$-0.376659\pi$
$181$	1840.27	0.755726	0.377863	+	0.925861i	$0.376659\pi$
$182$	−980.187	−0.399210
$183$	716.116	0.289272
$184$	−1213.98	−0.486392
$185$	−300.092	−0.119261
$186$	326.084	0.128546
$187$	877.023	0.342964
$188$	−1246.12	−0.483419
$189$	−3033.77	−1.16759
$190$	−1249.09	−0.476940
$191$	3002.71	1.13753	0.568766	−	0.822499i	$-0.307421\pi$
$191$	3002.71	1.13753	0.568766	+	0.822499i	$0.307421\pi$
$192$	−359.972	−0.135306
$193$	−359.343	−0.134021	−0.0670106	−	0.997752i	$-0.521346\pi$
$193$	−359.343	−0.134021	−0.0670106	+	0.997752i	$0.521346\pi$
$194$	−260.773	−0.0965073
$195$	−200.491	−0.0736279
$196$	529.337	0.192907
$197$	−2255.59	−0.815758	−0.407879	−	0.913036i	$-0.633731\pi$
$197$	−2255.59	−0.815758	−0.407879	+	0.913036i	$0.633731\pi$
$198$	−1949.03	−0.699553
$199$	4854.87	1.72941	0.864705	−	0.502280i	$-0.167505\pi$
$199$	4854.87	1.72941	0.864705	+	0.502280i	$0.167505\pi$
$200$	372.584	0.131728
$201$	−1996.29	−0.700534
$202$	1797.40	0.626062
$203$	−4816.99	−1.66545
$204$	300.427	0.103108
$205$	397.312	0.135363
$206$	5144.95	1.74012
$207$	1424.36	0.478260
$208$	1038.22	0.346094
$209$	2394.30	0.792426
$210$	1162.83	0.382109
$211$	983.487	0.320882	0.160441	−	0.987045i	$-0.448708\pi$
$211$	983.487	0.320882	0.160441	+	0.987045i	$0.448708\pi$
$212$	−981.742	−0.318049
$213$	−1852.82	−0.596025
$214$	1826.61	0.583479
$215$	48.6825	0.0154424
$216$	2044.98	0.644182
$217$	−685.394	−0.214413
$218$	−819.716	−0.254670
$219$	−1829.15	−0.564394
$220$	593.195	0.181787
$221$	348.830	0.106176
$222$	631.323	0.190863
$223$	−4975.48	−1.49409	−0.747046	−	0.664772i	$-0.768529\pi$
$223$	−4975.48	−1.49409	−0.747046	+	0.664772i	$0.768529\pi$
$224$	−3385.54	−1.00985
$225$	−437.151	−0.129526
$226$	2648.16	0.779437
$227$	−1472.54	−0.430554	−0.215277	−	0.976553i	$-0.569065\pi$
$227$	−1472.54	−0.430554	−0.215277	+	0.976553i	$0.569065\pi$
$228$	820.173	0.238234
$229$	287.386	0.0829302	0.0414651	−	0.999140i	$-0.486797\pi$
$229$	287.386	0.0829302	0.0414651	+	0.999140i	$0.486797\pi$
$230$	−1388.95	−0.398193
$231$	−2228.95	−0.634866
$232$	3247.00	0.918861
$233$	−2097.74	−0.589817	−0.294908	−	0.955526i	$-0.595289\pi$
$233$	−2097.74	−0.589817	−0.294908	+	0.955526i	$0.595289\pi$
$234$	−775.214	−0.216570
$235$	1716.50	0.476476
$236$	−650.545	−0.179436
$237$	−2694.60	−0.738537
$238$	−2023.19	−0.551024
$239$	3018.76	0.817019	0.408509	−	0.912754i	$-0.366049\pi$
$239$	3018.76	0.817019	0.408509	+	0.912754i	$0.366049\pi$
$240$	−1231.68	−0.331268
$241$	−4145.79	−1.10811	−0.554054	−	0.832481i	$-0.686920\pi$
$241$	−4145.79	−1.10811	−0.554054	+	0.832481i	$0.686920\pi$
$242$	895.974	0.237998
$243$	−3855.61	−1.01785
$244$	−842.732	−0.221108
$245$	−729.147	−0.190137
$246$	−835.852	−0.216634
$247$	952.315	0.245321
$248$	462.004	0.118296
$249$	−3313.52	−0.843316
$250$	426.282	0.107842
$251$	3762.70	0.946214	0.473107	−	0.881005i	$-0.343132\pi$
$251$	3762.70	0.946214	0.473107	+	0.881005i	$0.343132\pi$
$252$	1403.32	0.350797
$253$	2662.37	0.661589
$254$	−1088.96	−0.269005
$255$	−413.829	−0.101627
$256$	4601.21	1.12334
$257$	4310.18	1.04615	0.523077	−	0.852285i	$-0.324784\pi$
$257$	4310.18	1.04615	0.523077	+	0.852285i	$0.324784\pi$
$258$	−102.417	−0.0247139
$259$	−1326.98	−0.318356
$260$	235.939	0.0562782
$261$	−3809.68	−0.903499
$262$	−6641.16	−1.56600
$263$	−3840.31	−0.900393	−0.450196	−	0.892930i	$-0.648646\pi$
$263$	−3840.31	−0.900393	−0.450196	+	0.892930i	$0.648646\pi$
$264$	1502.47	0.350268
$265$	1352.32	0.313481
$266$	−5523.35	−1.27315
$267$	956.928	0.219337
$268$	2349.25	0.535460
$269$	3680.53	0.834223	0.417112	−	0.908855i	$-0.363042\pi$
$269$	3680.53	0.834223	0.417112	+	0.908855i	$0.363042\pi$
$270$	2339.71	0.527370
$271$	5876.53	1.31725	0.658623	−	0.752473i	$-0.271139\pi$
$271$	5876.53	1.31725	0.658623	+	0.752473i	$0.271139\pi$
$272$	2142.97	0.477708
$273$	−886.549	−0.196544
$274$	−8467.72	−1.86698
$275$	−817.110	−0.179177
$276$	912.004	0.198899
$277$	−8657.52	−1.87791	−0.938953	−	0.344046i	$-0.888202\pi$
$277$	−8657.52	−1.87791	−0.938953	+	0.344046i	$0.888202\pi$
$278$	−3626.85	−0.782459
$279$	−542.067	−0.116318
$280$	1647.53	0.351638
$281$	−2080.35	−0.441649	−0.220824	−	0.975314i	$-0.570875\pi$
$281$	−2080.35	−0.441649	−0.220824	+	0.975314i	$0.570875\pi$
$282$	−3611.11	−0.762548
$283$	−4786.11	−1.00532	−0.502658	−	0.864485i	$-0.667645\pi$
$283$	−4786.11	−1.00532	−0.502658	+	0.864485i	$0.667645\pi$
$284$	2180.42	0.455578
$285$	−1129.77	−0.234812
$286$	−1449.01	−0.299586
$287$	1756.87	0.361341
$288$	−2677.57	−0.547838
$289$	−4192.99	−0.853447
$290$	3714.96	0.752241
$291$	−235.861	−0.0475135
$292$	2152.56	0.431401
$293$	−603.083	−0.120247	−0.0601237	−	0.998191i	$-0.519150\pi$
$293$	−603.083	−0.120247	−0.0601237	+	0.998191i	$0.519150\pi$
$294$	1533.95	0.304293
$295$	896.108	0.176859
$296$	894.476	0.175643
$297$	−4484.82	−0.876215
$298$	3354.10	0.652007
$299$	1058.94	0.204817
$300$	−279.903	−0.0538674
$301$	215.269	0.0412223
$302$	−7640.26	−1.45579
$303$	1625.69	0.308230
$304$	5850.36	1.10375
$305$	1160.84	0.217933
$306$	−1600.11	−0.298928
$307$	−2359.98	−0.438733	−0.219366	−	0.975643i	$-0.570399\pi$
$307$	−2359.98	−0.438733	−0.219366	+	0.975643i	$0.570399\pi$
$308$	2623.05	0.485267
$309$	4653.45	0.856717
$310$	528.589	0.0968447
$311$	1902.44	0.346872	0.173436	−	0.984845i	$-0.444513\pi$
$311$	1902.44	0.346872	0.173436	+	0.984845i	$0.444513\pi$
$312$	597.597	0.108437
$313$	4227.22	0.763375	0.381688	−	0.924291i	$-0.375343\pi$
$313$	4227.22	0.763375	0.381688	+	0.924291i	$0.375343\pi$
$314$	−7280.59	−1.30849
$315$	−1933.04	−0.345759
$316$	3171.04	0.564509
$317$	2752.36	0.487660	0.243830	−	0.969818i	$-0.421596\pi$
$317$	2752.36	0.487660	0.243830	+	0.969818i	$0.421596\pi$
$318$	−2844.97	−0.501692
$319$	−7120.95	−1.24983
$320$	−583.523	−0.101937
$321$	1652.11	0.287265
$322$	−6141.77	−1.06294
$323$	1965.66	0.338613
$324$	177.441	0.0304255
$325$	−325.000	−0.0554700
$326$	497.830	0.0845775
$327$	−741.408	−0.125382
$328$	−1184.26	−0.199359
$329$	7590.17	1.27191
$330$	1719.01	0.286753
$331$	−5249.10	−0.871652	−0.435826	−	0.900031i	$-0.643544\pi$
$331$	−5249.10	−0.871652	−0.435826	+	0.900031i	$0.643544\pi$
$332$	3899.38	0.644598
$333$	−1049.48	−0.172707
$334$	−10651.7	−1.74501
$335$	−3236.03	−0.527770
$336$	−5446.34	−0.884293
$337$	−10537.1	−1.70324	−0.851618	−	0.524163i	$-0.824378\pi$
$337$	−10537.1	−1.70324	−0.851618	+	0.524163i	$0.824378\pi$
$338$	−576.333	−0.0927467
$339$	2395.18	0.383741
$340$	486.999	0.0776800
$341$	−1013.22	−0.160905
$342$	−4368.33	−0.690679
$343$	4359.34	0.686246
$344$	−145.107	−0.0227431
$345$	−1256.26	−0.196043
$346$	6806.44	1.05756
$347$	−4361.66	−0.674772	−0.337386	−	0.941366i	$-0.609543\pi$
$347$	−4361.66	−0.674772	−0.337386	+	0.941366i	$0.609543\pi$
$348$	−2439.30	−0.375748
$349$	−2158.57	−0.331077	−0.165538	−	0.986203i	$-0.552936\pi$
$349$	−2158.57	−0.331077	−0.165538	+	0.986203i	$0.552936\pi$
$350$	1884.97	0.287875
$351$	−1783.81	−0.271261
$352$	−5004.84	−0.757837
$353$	1004.91	0.151518	0.0757590	−	0.997126i	$-0.475862\pi$
$353$	1004.91	0.151518	0.0757590	+	0.997126i	$0.475862\pi$
$354$	−1885.20	−0.283044
$355$	−3003.47	−0.449035
$356$	−1126.12	−0.167653
$357$	−1829.91	−0.271286
$358$	−782.621	−0.115539
$359$	−6652.84	−0.978060	−0.489030	−	0.872267i	$-0.662649\pi$
$359$	−6652.84	−0.978060	−0.489030	+	0.872267i	$0.662649\pi$
$360$	1303.00	0.190762
$361$	−1492.70	−0.217627
$362$	−6275.80	−0.911185
$363$	810.382	0.117174
$364$	1043.30	0.150230
$365$	−2965.09	−0.425205
$366$	−2442.14	−0.348777
$367$	−6052.64	−0.860887	−0.430443	−	0.902618i	$-0.641643\pi$
$367$	−6052.64	−0.860887	−0.430443	+	0.902618i	$0.641643\pi$
$368$	6505.40	0.921515
$369$	1389.48	0.196026
$370$	1023.39	0.143793
$371$	5979.83	0.836812
$372$	−347.080	−0.0483744
$373$	−9118.99	−1.26585	−0.632927	−	0.774211i	$-0.718147\pi$
$373$	−9118.99	−1.26585	−0.632927	+	0.774211i	$0.718147\pi$
$374$	−2990.87	−0.413514
$375$	385.559	0.0530938
$376$	−5116.32	−0.701739
$377$	−2832.31	−0.386927
$378$	10345.9	1.40777
$379$	−2073.09	−0.280970	−0.140485	−	0.990083i	$-0.544866\pi$
$379$	−2073.09	−0.280970	−0.140485	+	0.990083i	$0.544866\pi$
$380$	1329.52	0.179481
$381$	−984.928	−0.132439
$382$	−10240.0	−1.37153
$383$	755.387	0.100779	0.0503897	−	0.998730i	$-0.483954\pi$
$383$	755.387	0.100779	0.0503897	+	0.998730i	$0.483954\pi$
$384$	5006.10	0.665278
$385$	−3613.18	−0.478298
$386$	1225.45	0.161590
$387$	170.253	0.0223629
$388$	277.564	0.0363175
$389$	287.630	0.0374895	0.0187447	−	0.999824i	$-0.494033\pi$
$389$	287.630	0.0374895	0.0187447	+	0.999824i	$0.494033\pi$
$390$	683.724	0.0887737
$391$	2185.74	0.282705
$392$	2173.35	0.280027
$393$	−6006.73	−0.770991
$394$	7692.14	0.983565
$395$	−4368.01	−0.556401
$396$	2074.53	0.263255
$397$	−8466.97	−1.07039	−0.535195	−	0.844728i	$-0.679762\pi$
$397$	−8466.97	−1.07039	−0.535195	+	0.844728i	$0.679762\pi$
$398$	−16556.3	−2.08516
$399$	−4995.71	−0.626812
$400$	−1996.57	−0.249572
$401$	6077.40	0.756835	0.378418	−	0.925635i	$-0.376468\pi$
$401$	6077.40	0.756835	0.378418	+	0.925635i	$0.376468\pi$
$402$	6807.85	0.844638
$403$	−403.000	−0.0498135
$404$	−1913.13	−0.235599
$405$	−244.420	−0.0299885
$406$	16427.2	2.00805
$407$	−1961.67	−0.238909
$408$	1233.49	0.149674
$409$	14957.9	1.80836	0.904182	−	0.427147i	$-0.140481\pi$
$409$	14957.9	1.80836	0.904182	+	0.427147i	$0.140481\pi$
$410$	−1354.94	−0.163209
$411$	−7658.80	−0.919174
$412$	−5476.23	−0.654841
$413$	3962.50	0.472111
$414$	−4857.43	−0.576642
$415$	−5371.29	−0.635341
$416$	−1990.64	−0.234613
$417$	−3280.37	−0.385229
$418$	−8165.16	−0.955433
$419$	−5625.31	−0.655881	−0.327941	−	0.944698i	$-0.606355\pi$
$419$	−5625.31	−0.655881	−0.327941	+	0.944698i	$0.606355\pi$
$420$	−1237.70	−0.143795
$421$	10304.2	1.19287	0.596434	−	0.802662i	$-0.296584\pi$
$421$	10304.2	1.19287	0.596434	+	0.802662i	$0.296584\pi$
$422$	−3353.94	−0.386890
$423$	6002.94	0.690007
$424$	−4030.83	−0.461685
$425$	−670.827	−0.0765645
$426$	6318.59	0.718631
$427$	5133.12	0.581754
$428$	−1944.22	−0.219574
$429$	−1310.58	−0.147496
$430$	−166.020	−0.0186190
$431$	1961.97	0.219269	0.109634	−	0.993972i	$-0.465032\pi$
$431$	1961.97	0.219269	0.109634	+	0.993972i	$0.465032\pi$
$432$	−10958.5	−1.22046
$433$	−9819.13	−1.08979	−0.544893	−	0.838505i	$-0.683430\pi$
$433$	−9819.13	−1.08979	−0.544893	+	0.838505i	$0.683430\pi$
$434$	2337.37	0.258519
$435$	3360.07	0.370352
$436$	872.496	0.0958371
$437$	5967.13	0.653196
$438$	6237.86	0.680494
$439$	10816.6	1.17597	0.587984	−	0.808873i	$-0.299922\pi$
$439$	10816.6	1.17597	0.587984	+	0.808873i	$0.299922\pi$
$440$	2435.54	0.263886
$441$	−2549.98	−0.275346
$442$	−1189.60	−0.128017
$443$	−4839.98	−0.519084	−0.259542	−	0.965732i	$-0.583572\pi$
$443$	−4839.98	−0.519084	−0.259542	+	0.965732i	$0.583572\pi$
$444$	−671.974	−0.0718254
$445$	1551.20	0.165245
$446$	16967.6	1.80144
$447$	3033.69	0.321003
$448$	−2580.28	−0.272113
$449$	−3333.15	−0.350336	−0.175168	−	0.984539i	$-0.556047\pi$
$449$	−3333.15	−0.350336	−0.175168	+	0.984539i	$0.556047\pi$
$450$	1490.80	0.156171
$451$	2597.18	0.271167
$452$	−2818.67	−0.293316
$453$	−6910.38	−0.716729
$454$	5021.73	0.519122
$455$	−1437.12	−0.148073
$456$	3367.46	0.345824
$457$	4133.17	0.423066	0.211533	−	0.977371i	$-0.432154\pi$
$457$	4133.17	0.423066	0.211533	+	0.977371i	$0.432154\pi$
$458$	−980.060	−0.0999895
$459$	−3681.93	−0.374417
$460$	1478.38	0.149847
$461$	−7199.08	−0.727320	−0.363660	−	0.931532i	$-0.618473\pi$
$461$	−7199.08	−0.727320	−0.363660	+	0.931532i	$0.618473\pi$
$462$	7601.28	0.765463
$463$	−1189.22	−0.119369	−0.0596844	−	0.998217i	$-0.519009\pi$
$463$	−1189.22	−0.119369	−0.0596844	+	0.998217i	$0.519009\pi$
$464$	−17399.7	−1.74087
$465$	478.093	0.0476797
$466$	7153.81	0.711146
$467$	−5857.68	−0.580431	−0.290215	−	0.956961i	$-0.593727\pi$
$467$	−5857.68	−0.580431	−0.290215	+	0.956961i	$0.593727\pi$
$468$	825.129	0.0814991
$469$	−14309.4	−1.40884
$470$	−5853.69	−0.574491
$471$	−6585.07	−0.644213
$472$	−2671.01	−0.260472
$473$	318.232	0.0309351
$474$	9189.28	0.890459
$475$	−1831.38	−0.176904
$476$	2153.46	0.207360
$477$	4729.35	0.453967
$478$	−10294.7	−0.985085
$479$	−2902.20	−0.276837	−0.138418	−	0.990374i	$-0.544202\pi$
$479$	−2902.20	−0.276837	−0.138418	+	0.990374i	$0.544202\pi$
$480$	2361.57	0.224563
$481$	−780.239	−0.0739622
$482$	14138.2	1.33605
$483$	−5555.05	−0.523320
$484$	−953.665	−0.0895628
$485$	−382.337	−0.0357959
$486$	13148.6	1.22723
$487$	−1580.66	−0.147077	−0.0735384	−	0.997292i	$-0.523429\pi$
$487$	−1580.66	−0.147077	−0.0735384	+	0.997292i	$0.523429\pi$
$488$	−3460.08	−0.320965
$489$	450.272	0.0416401
$490$	2486.58	0.229249
$491$	−3463.75	−0.318364	−0.159182	−	0.987249i	$-0.550886\pi$
$491$	−3463.75	−0.318364	−0.159182	+	0.987249i	$0.550886\pi$
$492$	889.672	0.0815234
$493$	−5846.12	−0.534069
$494$	−3247.64	−0.295786
$495$	−2857.60	−0.259474
$496$	−2475.75	−0.224122
$497$	−13281.0	−1.19866
$498$	11299.9	1.01679
$499$	−8553.78	−0.767374	−0.383687	−	0.923463i	$-0.625346\pi$
$499$	−8553.78	−0.767374	−0.383687	+	0.923463i	$0.625346\pi$
$500$	−453.730	−0.0405828
$501$	−9634.10	−0.859121
$502$	−12831.8	−1.14086
$503$	−13801.6	−1.22342	−0.611711	−	0.791081i	$-0.709519\pi$
$503$	−13801.6	−1.22342	−0.611711	+	0.791081i	$0.709519\pi$
$504$	5761.75	0.509224
$505$	2635.29	0.232215
$506$	−9079.37	−0.797683
$507$	−521.276	−0.0456621
$508$	1159.07	0.101231
$509$	−1672.70	−0.145661	−0.0728303	−	0.997344i	$-0.523203\pi$
$509$	−1672.70	−0.145661	−0.0728303	+	0.997344i	$0.523203\pi$
$510$	1411.26	0.122533
$511$	−13111.3	−1.13505
$512$	−2707.29	−0.233685
$513$	−10051.8	−0.865099
$514$	−14698.8	−1.26136
$515$	7543.35	0.645436
$516$	109.011	0.00930029
$517$	11220.5	0.954504
$518$	4525.32	0.383844
$519$	6156.22	0.520671
$520$	968.719	0.0816945
$521$	−9868.31	−0.829825	−0.414912	−	0.909861i	$-0.636188\pi$
$521$	−9868.31	−0.829825	−0.414912	+	0.909861i	$0.636188\pi$
$522$	12992.0	1.08936
$523$	6876.53	0.574933	0.287466	−	0.957791i	$-0.407187\pi$
$523$	6876.53	0.574933	0.287466	+	0.957791i	$0.407187\pi$
$524$	7068.78	0.589315
$525$	1704.90	0.141730
$526$	13096.4	1.08561
$527$	−831.826	−0.0687569
$528$	−8051.32	−0.663615
$529$	−5531.76	−0.454652
$530$	−4611.76	−0.377966
$531$	3133.87	0.256118
$532$	5879.00	0.479111
$533$	1033.01	0.0839488
$534$	−3263.37	−0.264456
$535$	2678.11	0.216421
$536$	9645.54	0.777283
$537$	−707.857	−0.0568832
$538$	−12551.6	−1.00583
$539$	−4766.35	−0.380892
$540$	−2490.36	−0.198459
$541$	−13675.1	−1.08676	−0.543381	−	0.839486i	$-0.682856\pi$
$541$	−13675.1	−1.08676	−0.543381	+	0.839486i	$0.682856\pi$
$542$	−20040.5	−1.58821
$543$	−5676.27	−0.448604
$544$	−4108.85	−0.323833
$545$	−1201.84	−0.0944608
$546$	3023.36	0.236974
$547$	−7542.08	−0.589536	−0.294768	−	0.955569i	$-0.595242\pi$
$547$	−7542.08	−0.589536	−0.294768	+	0.955569i	$0.595242\pi$
$548$	9012.95	0.702580
$549$	4059.70	0.315599
$550$	2786.55	0.216035
$551$	−15960.1	−1.23398
$552$	3744.50	0.288725
$553$	−19314.9	−1.48527
$554$	29524.3	2.26420
$555$	925.625	0.0707939
$556$	3860.37	0.294454
$557$	14253.7	1.08429	0.542143	−	0.840286i	$-0.317613\pi$
$557$	14253.7	1.08429	0.542143	+	0.840286i	$0.317613\pi$
$558$	1848.59	0.140245
$559$	126.575	0.00957698
$560$	−8828.65	−0.666211
$561$	−2705.15	−0.203586
$562$	7094.53	0.532499
$563$	5052.76	0.378239	0.189119	−	0.981954i	$-0.439437\pi$
$563$	5052.76	0.378239	0.189119	+	0.981954i	$0.439437\pi$
$564$	3843.63	0.286961
$565$	3882.64	0.289104
$566$	16321.8	1.21212
$567$	−1080.80	−0.0800519
$568$	8952.35	0.661325
$569$	14405.1	1.06132	0.530660	−	0.847584i	$-0.321944\pi$
$569$	14405.1	1.06132	0.530660	+	0.847584i	$0.321944\pi$
$570$	3852.79	0.283115
$571$	17454.1	1.27922	0.639608	−	0.768701i	$-0.279097\pi$
$571$	17454.1	1.27922	0.639608	+	0.768701i	$0.279097\pi$
$572$	1542.31	0.112740
$573$	−9261.78	−0.675247
$574$	−5991.39	−0.435672
$575$	−2036.43	−0.147695
$576$	−2040.70	−0.147620
$577$	14055.1	1.01408	0.507039	−	0.861923i	$-0.330740\pi$
$577$	14055.1	1.01408	0.507039	+	0.861923i	$0.330740\pi$
$578$	14299.1	1.02901
$579$	1108.38	0.0795559
$580$	−3954.16	−0.283082
$581$	−23751.3	−1.69599
$582$	804.348	0.0572874
$583$	8839.97	0.627983
$584$	8837.96	0.626229
$585$	−1136.59	−0.0803287
$586$	2056.67	0.144983
$587$	10913.6	0.767383	0.383691	−	0.923461i	$-0.374653\pi$
$587$	10913.6	0.767383	0.383691	+	0.923461i	$0.374653\pi$
$588$	−1632.72	−0.114511
$589$	−2270.91	−0.158864
$590$	−3055.96	−0.213240
$591$	6957.31	0.484240
$592$	−4793.25	−0.332772
$593$	−17173.6	−1.18927	−0.594633	−	0.803997i	$-0.702703\pi$
$593$	−17173.6	−1.18927	−0.594633	+	0.803997i	$0.702703\pi$
$594$	15294.4	1.05646
$595$	−2966.33	−0.204383
$596$	−3570.07	−0.245362
$597$	−14974.7	−1.02659
$598$	−3611.26	−0.246949
$599$	−6523.72	−0.444995	−0.222497	−	0.974933i	$-0.571421\pi$
$599$	−6523.72	−0.444995	−0.222497	+	0.974933i	$0.571421\pi$
$600$	−1149.23	−0.0781949
$601$	6325.26	0.429306	0.214653	−	0.976690i	$-0.431138\pi$
$601$	6325.26	0.429306	0.214653	+	0.976690i	$0.431138\pi$
$602$	−734.123	−0.0497020
$603$	−11317.1	−0.764289
$604$	8132.21	0.547839
$605$	1313.65	0.0882766
$606$	−5544.03	−0.371635
$607$	−16480.9	−1.10204	−0.551019	−	0.834493i	$-0.685761\pi$
$607$	−16480.9	−1.10204	−0.551019	+	0.834493i	$0.685761\pi$
$608$	−11217.3	−0.748224
$609$	14857.9	0.988623
$610$	−3958.76	−0.262763
$611$	4462.89	0.295498
$612$	1703.13	0.112492
$613$	−6610.20	−0.435536	−0.217768	−	0.976001i	$-0.569878\pi$
$613$	−6610.20	−0.435536	−0.217768	+	0.976001i	$0.569878\pi$
$614$	8048.12	0.528983
$615$	−1225.50	−0.0803526
$616$	10769.7	0.704421
$617$	4812.57	0.314014	0.157007	−	0.987597i	$-0.449815\pi$
$617$	4812.57	0.314014	0.157007	+	0.987597i	$0.449815\pi$
$618$	−15869.5	−1.03295
$619$	11845.2	0.769143	0.384571	−	0.923095i	$-0.374349\pi$
$619$	11845.2	0.769143	0.384571	+	0.923095i	$0.374349\pi$
$620$	−562.625	−0.0364444
$621$	−11177.2	−0.722263
$622$	−6487.79	−0.418226
$623$	6859.25	0.441108
$624$	−3202.36	−0.205444
$625$	625.000	0.0400000
$626$	−14415.9	−0.920407
$627$	−7385.14	−0.470389
$628$	7749.38	0.492411
$629$	−1610.48	−0.102089
$630$	6592.14	0.416885
$631$	−13507.0	−0.852146	−0.426073	−	0.904689i	$-0.640103\pi$
$631$	−13507.0	−0.852146	−0.426073	+	0.904689i	$0.640103\pi$
$632$	13019.6	0.819450
$633$	−3033.54	−0.190478
$634$	−9386.26	−0.587975
$635$	−1596.59	−0.0997776
$636$	3028.16	0.188796
$637$	−1895.78	−0.117918
$638$	24284.3	1.50693
$639$	−10503.7	−0.650269
$640$	8115.01	0.501209
$641$	−19954.1	−1.22955	−0.614774	−	0.788703i	$-0.710753\pi$
$641$	−19954.1	−1.22955	−0.614774	+	0.788703i	$0.710753\pi$
$642$	−5634.13	−0.346357
$643$	−10721.1	−0.657543	−0.328772	−	0.944409i	$-0.606635\pi$
$643$	−10721.1	−0.657543	−0.328772	+	0.944409i	$0.606635\pi$
$644$	6537.24	0.400005
$645$	−150.160	−0.00916673
$646$	−6703.39	−0.408269
$647$	19853.6	1.20637	0.603187	−	0.797600i	$-0.293897\pi$
$647$	19853.6	1.20637	0.603187	+	0.797600i	$0.293897\pi$
$648$	728.538	0.0441661
$649$	5857.75	0.354294
$650$	1108.33	0.0668806
$651$	2114.08	0.127277
$652$	−529.885	−0.0318281
$653$	821.674	0.0492413	0.0246207	−	0.999697i	$-0.492162\pi$
$653$	821.674	0.0492413	0.0246207	+	0.999697i	$0.492162\pi$
$654$	2528.39	0.151174
$655$	−9737.05	−0.580852
$656$	6346.11	0.377704
$657$	−10369.5	−0.615759
$658$	−25884.4	−1.53356
$659$	13165.2	0.778213	0.389106	−	0.921193i	$-0.372784\pi$
$659$	13165.2	0.778213	0.389106	+	0.921193i	$0.372784\pi$
$660$	−1829.70	−0.107910
$661$	24158.4	1.42156	0.710780	−	0.703414i	$-0.248342\pi$
$661$	24158.4	1.42156	0.710780	+	0.703414i	$0.248342\pi$
$662$	17900.8	1.05096
$663$	−1075.96	−0.0630267
$664$	16010.1	0.935709
$665$	−8098.15	−0.472230
$666$	3579.00	0.208234
$667$	−17747.0	−1.03024
$668$	11337.5	0.656678
$669$	15346.7	0.886904
$670$	11035.7	0.636336
$671$	7588.27	0.436575
$672$	10442.6	0.599453
$673$	32068.2	1.83676	0.918379	−	0.395702i	$-0.129499\pi$
$673$	32068.2	1.83676	0.918379	+	0.395702i	$0.129499\pi$
$674$	35934.1	2.05360
$675$	3430.40	0.195609
$676$	613.443	0.0349023
$677$	25375.4	1.44055	0.720276	−	0.693687i	$-0.244015\pi$
$677$	25375.4	1.44055	0.720276	+	0.693687i	$0.244015\pi$
$678$	−8168.16	−0.462679
$679$	−1690.65	−0.0955542
$680$	1999.52	0.112762
$681$	4542.00	0.255580
$682$	3455.33	0.194005
$683$	13929.9	0.780401	0.390200	−	0.920730i	$-0.372406\pi$
$683$	13929.9	0.780401	0.390200	+	0.920730i	$0.372406\pi$
$684$	4649.60	0.259915
$685$	−12415.1	−0.692491
$686$	−14866.5	−0.827412
$687$	−886.435	−0.0492280
$688$	777.586	0.0430890
$689$	3516.04	0.194413
$690$	4284.16	0.236370
$691$	3855.16	0.212239	0.106120	−	0.994353i	$-0.466157\pi$
$691$	3855.16	0.212239	0.106120	+	0.994353i	$0.466157\pi$
$692$	−7244.70	−0.397980
$693$	−12636.0	−0.692645
$694$	14874.4	0.813578
$695$	−5317.56	−0.290225
$696$	−10015.3	−0.545442
$697$	2132.22	0.115873
$698$	7361.29	0.399182
$699$	6470.41	0.350119
$700$	−2006.35	−0.108333
$701$	27465.6	1.47983	0.739916	−	0.672699i	$-0.234865\pi$
$701$	27465.6	1.47983	0.739916	+	0.672699i	$0.234865\pi$
$702$	6083.24	0.327061
$703$	−4396.65	−0.235879
$704$	−3814.42	−0.204206
$705$	−5294.49	−0.282840
$706$	−3426.99	−0.182686
$707$	11653.0	0.619880
$708$	2006.59	0.106514
$709$	−23635.1	−1.25195	−0.625976	−	0.779842i	$-0.715299\pi$
$709$	−23635.1	−1.25195	−0.625976	+	0.779842i	$0.715299\pi$
$710$	10242.6	0.541405
$711$	−15275.8	−0.805751
$712$	−4623.62	−0.243368
$713$	−2525.17	−0.132634
$714$	6240.46	0.327092
$715$	−2124.49	−0.111121
$716$	833.013	0.0434793
$717$	−9311.29	−0.484988
$718$	22687.9	1.17925
$719$	24819.3	1.28735	0.643673	−	0.765300i	$-0.277410\pi$
$719$	24819.3	1.28735	0.643673	+	0.765300i	$0.277410\pi$
$720$	−6982.43	−0.361417
$721$	33355.9	1.72294
$722$	5090.49	0.262394
$723$	12787.6	0.657780
$724$	6679.90	0.342896
$725$	5446.75	0.279017
$726$	−2763.61	−0.141277
$727$	−1065.05	−0.0543337	−0.0271669	−	0.999631i	$-0.508649\pi$
$727$	−1065.05	−0.0543337	−0.0271669	+	0.999631i	$0.508649\pi$
$728$	4283.58	0.218077
$729$	10572.7	0.537147
$730$	10111.7	0.512673
$731$	261.260	0.0132190
$732$	2599.38	0.131251
$733$	−13676.3	−0.689146	−0.344573	−	0.938760i	$-0.611976\pi$
$733$	−13676.3	−0.689146	−0.344573	+	0.938760i	$0.611976\pi$
$734$	20641.1	1.03798
$735$	2249.03	0.112866
$736$	−12473.2	−0.624685
$737$	−21153.5	−1.05726
$738$	−4738.49	−0.236350
$739$	3384.36	0.168465	0.0842325	−	0.996446i	$-0.473156\pi$
$739$	3384.36	0.168465	0.0842325	+	0.996446i	$0.473156\pi$
$740$	−1089.28	−0.0541120
$741$	−2937.39	−0.145624
$742$	−20392.7	−1.00895
$743$	15351.9	0.758018	0.379009	−	0.925393i	$-0.376265\pi$
$743$	15351.9	0.758018	0.379009	+	0.925393i	$0.376265\pi$
$744$	−1425.04	−0.0702211
$745$	4917.67	0.241838
$746$	31098.1	1.52625
$747$	−18784.5	−0.920066
$748$	3183.45	0.155613
$749$	11842.3	0.577717
$750$	−1314.85	−0.0640156
$751$	2897.72	0.140798	0.0703989	−	0.997519i	$-0.477573\pi$
$751$	2897.72	0.140798	0.0703989	+	0.997519i	$0.477573\pi$
$752$	27416.9	1.32951
$753$	−11606.0	−0.561679
$754$	9658.90	0.466520
$755$	−11201.9	−0.539971
$756$	−11012.1	−0.529770
$757$	−7213.36	−0.346333	−0.173166	−	0.984893i	$-0.555400\pi$
$757$	−7213.36	−0.346333	−0.173166	+	0.984893i	$0.555400\pi$
$758$	7069.77	0.338767
$759$	−8212.02	−0.392724
$760$	5458.73	0.260538
$761$	29912.5	1.42487	0.712437	−	0.701736i	$-0.247592\pi$
$761$	29912.5	1.42487	0.712437	+	0.701736i	$0.247592\pi$
$762$	3358.85	0.159683
$763$	−5314.41	−0.252155
$764$	10899.4	0.516132
$765$	−2346.02	−0.110877
$766$	−2576.06	−0.121510
$767$	2329.88	0.109683
$768$	−14192.3	−0.666824
$769$	−33224.1	−1.55798	−0.778992	−	0.627033i	$-0.784269\pi$
$769$	−33224.1	−1.55798	−0.778992	+	0.627033i	$0.784269\pi$
$770$	12321.9	0.576687
$771$	−13294.6	−0.621004
$772$	−1304.36	−0.0608094
$773$	37365.6	1.73861	0.869306	−	0.494273i	$-0.164566\pi$
$773$	37365.6	1.73861	0.869306	+	0.494273i	$0.164566\pi$
$774$	−580.606	−0.0269631
$775$	775.000	0.0359211
$776$	1139.62	0.0527191
$777$	4093.02	0.188978
$778$	−980.890	−0.0452013
$779$	5821.02	0.267728
$780$	−727.749	−0.0334072
$781$	−19633.3	−0.899533
$782$	−7453.94	−0.340860
$783$	29895.2	1.36445
$784$	−11646.4	−0.530538
$785$	−10674.6	−0.485339
$786$	20484.5	0.929589
$787$	4935.75	0.223558	0.111779	−	0.993733i	$-0.464345\pi$
$787$	4935.75	0.223558	0.111779	+	0.993733i	$0.464345\pi$
$788$	−8187.43	−0.370134
$789$	11845.3	0.534480
$790$	14896.0	0.670857
$791$	17168.6	0.771739
$792$	8517.58	0.382145
$793$	3018.18	0.135156
$794$	28874.5	1.29058
$795$	−4171.20	−0.186085
$796$	17622.4	0.784685
$797$	−7663.11	−0.340579	−0.170289	−	0.985394i	$-0.554470\pi$
$797$	−7663.11	−0.340579	−0.170289	+	0.985394i	$0.554470\pi$
$798$	17036.6	0.755752
$799$	9211.78	0.407872
$800$	3828.15	0.169182
$801$	5424.87	0.239299
$802$	−20725.5	−0.912522
$803$	−19382.4	−0.851795
$804$	−7246.20	−0.317853
$805$	−9004.86	−0.394260
$806$	1374.33	0.0600606
$807$	−11352.5	−0.495201
$808$	−7854.93	−0.341999
$809$	−21989.6	−0.955640	−0.477820	−	0.878458i	$-0.658573\pi$
$809$	−21989.6	−0.955640	−0.477820	+	0.878458i	$0.658573\pi$
$810$	833.536	0.0361574
$811$	19590.6	0.848236	0.424118	−	0.905607i	$-0.360584\pi$
$811$	19590.6	0.848236	0.424118	+	0.905607i	$0.360584\pi$
$812$	−17484.9	−0.755665
$813$	−18126.0	−0.781927
$814$	6689.78	0.288055
$815$	729.902	0.0313710
$816$	−6609.93	−0.283571
$817$	713.248	0.0305427
$818$	−51010.3	−2.18036
$819$	−5025.89	−0.214431
$820$	1442.18	0.0614184
$821$	29835.5	1.26829	0.634146	−	0.773213i	$-0.281352\pi$
$821$	29835.5	1.26829	0.634146	+	0.773213i	$0.281352\pi$
$822$	26118.5	1.10825
$823$	−2826.77	−0.119727	−0.0598633	−	0.998207i	$-0.519066\pi$
$823$	−2826.77	−0.119727	−0.0598633	+	0.998207i	$0.519066\pi$
$824$	−22484.3	−0.950578
$825$	2520.35	0.106361
$826$	−13513.1	−0.569227
$827$	30190.0	1.26942	0.634710	−	0.772750i	$-0.281119\pi$
$827$	30190.0	1.26942	0.634710	+	0.772750i	$0.281119\pi$
$828$	5170.19	0.217001
$829$	2248.87	0.0942179	0.0471089	−	0.998890i	$-0.484999\pi$
$829$	2248.87	0.0942179	0.0471089	+	0.998890i	$0.484999\pi$
$830$	18317.5	0.766035
$831$	26703.9	1.11474
$832$	−1517.16	−0.0632188
$833$	−3913.05	−0.162760
$834$	11186.9	0.464473
$835$	−15617.1	−0.647248
$836$	8690.91	0.359547
$837$	4253.69	0.175662
$838$	19183.7	0.790801
$839$	−15191.3	−0.625102	−0.312551	−	0.949901i	$-0.601183\pi$
$839$	−15191.3	−0.625102	−0.312551	+	0.949901i	$0.601183\pi$
$840$	−5081.76	−0.208735
$841$	23078.3	0.946259
$842$	−35140.0	−1.43825
$843$	6416.78	0.262166
$844$	3569.90	0.145594
$845$	−845.000	−0.0344010
$846$	−20471.6	−0.831947
$847$	5808.81	0.235647
$848$	21600.1	0.874706
$849$	14762.6	0.596763
$850$	2287.69	0.0923143
$851$	−4888.92	−0.196933
$852$	−6725.44	−0.270434
$853$	−31642.9	−1.27014	−0.635072	−	0.772453i	$-0.719030\pi$
$853$	−31642.9	−1.27014	−0.635072	+	0.772453i	$0.719030\pi$
$854$	−17505.2	−0.701425
$855$	−6404.70	−0.256182
$856$	−7982.59	−0.318737
$857$	−1347.75	−0.0537202	−0.0268601	−	0.999639i	$-0.508551\pi$
$857$	−1347.75	−0.0537202	−0.0268601	+	0.999639i	$0.508551\pi$
$858$	4469.43	0.177836
$859$	−25502.3	−1.01295	−0.506476	−	0.862254i	$-0.669052\pi$
$859$	−25502.3	−1.01295	−0.506476	+	0.862254i	$0.669052\pi$
$860$	176.710	0.00700669
$861$	−5419.03	−0.214495
$862$	−6690.82	−0.264374
$863$	−739.828	−0.0291820	−0.0145910	−	0.999894i	$-0.504645\pi$
$863$	−739.828	−0.0291820	−0.0145910	+	0.999894i	$0.504645\pi$
$864$	21011.4	0.827339
$865$	9979.38	0.392265
$866$	33485.7	1.31396
$867$	12933.1	0.506612
$868$	−2487.87	−0.0972855
$869$	−28553.2	−1.11462
$870$	−11458.7	−0.446536
$871$	−8413.67	−0.327309
$872$	3582.29	0.139119
$873$	−1337.11	−0.0518377
$874$	−20349.4	−0.787563
$875$	2763.69	0.106777
$876$	−6639.51	−0.256082
$877$	−30364.0	−1.16912	−0.584560	−	0.811350i	$-0.698733\pi$
$877$	−30364.0	−1.16912	−0.584560	+	0.811350i	$0.698733\pi$
$878$	−36887.5	−1.41787
$879$	1860.19	0.0713797
$880$	−13051.4	−0.499956
$881$	12231.2	0.467739	0.233870	−	0.972268i	$-0.424861\pi$
$881$	12231.2	0.467739	0.233870	+	0.972268i	$0.424861\pi$
$882$	8696.07	0.331986
$883$	8931.78	0.340406	0.170203	−	0.985409i	$-0.445558\pi$
$883$	8931.78	0.340406	0.170203	+	0.985409i	$0.445558\pi$
$884$	1266.20	0.0481751
$885$	−2764.02	−0.104985
$886$	16505.6	0.625864
$887$	36931.1	1.39800	0.699000	−	0.715122i	$-0.253629\pi$
$887$	36931.1	1.39800	0.699000	+	0.715122i	$0.253629\pi$
$888$	−2758.99	−0.104263
$889$	−7059.96	−0.266348
$890$	−5289.99	−0.199237
$891$	−1597.75	−0.0600747
$892$	−18060.2	−0.677914
$893$	25148.4	0.942396
$894$	−10345.6	−0.387036
$895$	−1147.45	−0.0428549
$896$	35883.7	1.33794
$897$	−3266.27	−0.121581
$898$	11366.9	0.422403
$899$	6753.97	0.250564
$900$	−1586.79	−0.0587699
$901$	7257.40	0.268345
$902$	−8857.05	−0.326949
$903$	−663.992	−0.0244698
$904$	−11572.9	−0.425783
$905$	−9201.37	−0.337971
$906$	23566.2	0.864165
$907$	−39397.5	−1.44231	−0.721153	−	0.692776i	$-0.756388\pi$
$907$	−39397.5	−1.44231	−0.721153	+	0.692776i	$0.756388\pi$
$908$	−5345.07	−0.195355
$909$	9216.14	0.336282
$910$	4900.93	0.178532
$911$	17917.3	0.651623	0.325811	−	0.945435i	$-0.394363\pi$
$911$	17917.3	0.651623	0.325811	+	0.945435i	$0.394363\pi$
$912$	−18045.3	−0.655196
$913$	−35111.5	−1.27275
$914$	−14095.2	−0.510094
$915$	−3580.58	−0.129366
$916$	1043.17	0.0376279
$917$	−43056.2	−1.55054
$918$	12556.3	0.451438
$919$	31400.2	1.12709	0.563546	−	0.826085i	$-0.309437\pi$
$919$	31400.2	1.12709	0.563546	+	0.826085i	$0.309437\pi$
$920$	6069.92	0.217521
$921$	7279.28	0.260435
$922$	24550.7	0.876935
$923$	−7809.01	−0.278480
$924$	−8090.72	−0.288058
$925$	1500.46	0.0533349
$926$	4055.54	0.143924
$927$	26380.6	0.934686
$928$	33361.6	1.18012
$929$	−4493.75	−0.158703	−0.0793515	−	0.996847i	$-0.525285\pi$
$929$	−4493.75	−0.158703	−0.0793515	+	0.996847i	$0.525285\pi$
$930$	−1630.42	−0.0574877
$931$	−10682.7	−0.376061
$932$	−7614.44	−0.267617
$933$	−5868.01	−0.205906
$934$	19976.2	0.699829
$935$	−4385.12	−0.153378
$936$	3387.81	0.118306
$937$	24166.1	0.842554	0.421277	−	0.906932i	$-0.361582\pi$
$937$	24166.1	0.842554	0.421277	+	0.906932i	$0.361582\pi$
$938$	48798.6	1.69865
$939$	−13038.7	−0.453145
$940$	6230.61	0.216191
$941$	−10667.9	−0.369567	−0.184783	−	0.982779i	$-0.559158\pi$
$941$	−10667.9	−0.369567	−0.184783	+	0.982779i	$0.559158\pi$
$942$	22456.8	0.776732
$943$	6472.77	0.223523
$944$	14313.2	0.493489
$945$	15168.9	0.522162
$946$	−1085.25	−0.0372987
$947$	31697.1	1.08766	0.543832	−	0.839194i	$-0.316973\pi$
$947$	31697.1	1.08766	0.543832	+	0.839194i	$0.316973\pi$
$948$	−9780.97	−0.335096
$949$	−7709.23	−0.263701
$950$	6245.46	0.213294
$951$	−8489.59	−0.289478
$952$	8841.66	0.301008
$953$	10317.8	0.350709	0.175354	−	0.984505i	$-0.443893\pi$
$953$	10317.8	0.350709	0.175354	+	0.984505i	$0.443893\pi$
$954$	−16128.3	−0.547351
$955$	−15013.6	−0.508720
$956$	10957.6	0.370706
$957$	21964.4	0.741909
$958$	9897.23	0.333784
$959$	−54898.2	−1.84855
$960$	1799.86	0.0605107
$961$	961.000	0.0322581
$962$	2660.81	0.0891768
$963$	9365.92	0.313409
$964$	−15048.5	−0.502781
$965$	1796.72	0.0599361
$966$	18944.1	0.630971
$967$	3584.56	0.119205	0.0596027	−	0.998222i	$-0.481017\pi$
$967$	3584.56	0.119205	0.0596027	+	0.998222i	$0.481017\pi$
$968$	−3915.55	−0.130011
$969$	−6063.02	−0.201003
$970$	1303.87	0.0431594
$971$	47389.2	1.56621	0.783105	−	0.621889i	$-0.213634\pi$
$971$	47389.2	1.56621	0.783105	+	0.621889i	$0.213634\pi$
$972$	−13995.2	−0.461829
$973$	−23513.7	−0.774732
$974$	5390.44	0.177331
$975$	1002.45	0.0329274
$976$	18541.6	0.608097
$977$	35197.1	1.15256	0.576282	−	0.817251i	$-0.304503\pi$
$977$	35197.1	1.15256	0.576282	+	0.817251i	$0.304503\pi$
$978$	−1535.54	−0.0502058
$979$	10140.0	0.331028
$980$	−2646.68	−0.0862706
$981$	−4203.08	−0.136793
$982$	11812.3	0.383854
$983$	36630.2	1.18853	0.594264	−	0.804270i	$-0.297444\pi$
$983$	36630.2	1.18853	0.594264	+	0.804270i	$0.297444\pi$
$984$	3652.81	0.118341
$985$	11278.0	0.364818
$986$	19936.8	0.643931
$987$	−23411.7	−0.755017
$988$	3456.75	0.111310
$989$	793.107	0.0254998
$990$	9745.15	0.312850
$991$	−20062.8	−0.643102	−0.321551	−	0.946892i	$-0.604204\pi$
$991$	−20062.8	−0.643102	−0.321551	+	0.946892i	$0.604204\pi$
$992$	4746.91	0.151930
$993$	16190.7	0.517419
$994$	45291.7	1.44524
$995$	−24274.3	−0.773415
$996$	−12027.5	−0.382638
$997$	−44751.2	−1.42155	−0.710774	−	0.703420i	$-0.751655\pi$
$997$	−44751.2	−1.42155	−0.710774	+	0.703420i	$0.751655\pi$
$998$	29170.6	0.925229
$999$	8235.48	0.260820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2015.4.a.d.1.10	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2015.4.a.d.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-3.41025 q^{2} -3.08447 q^{3} +3.62984 q^{4} -5.00000 q^{5} +10.5188 q^{6} -22.1095 q^{7} +14.9034 q^{8} -17.4860 q^{9} +O(q^{10})\)	\(q-3.41025 q^{2} -3.08447 q^{3} +3.62984 q^{4} -5.00000 q^{5} +10.5188 q^{6} -22.1095 q^{7} +14.9034 q^{8} -17.4860 q^{9} +17.0513 q^{10} -32.6844 q^{11} -11.1961 q^{12} -13.0000 q^{13} +75.3990 q^{14} +15.4224 q^{15} -79.8630 q^{16} -26.8331 q^{17} +59.6318 q^{18} -73.2550 q^{19} -18.1492 q^{20} +68.1961 q^{21} +111.462 q^{22} -81.4570 q^{23} -45.9690 q^{24} +25.0000 q^{25} +44.3333 q^{26} +137.216 q^{27} -80.2538 q^{28} +217.870 q^{29} -52.5942 q^{30} +31.0000 q^{31} +153.126 q^{32} +100.814 q^{33} +91.5076 q^{34} +110.547 q^{35} -63.4715 q^{36} +60.0184 q^{37} +249.818 q^{38} +40.0981 q^{39} -74.5168 q^{40} -79.4624 q^{41} -232.566 q^{42} -9.73651 q^{43} -118.639 q^{44} +87.4302 q^{45} +277.789 q^{46} -343.299 q^{47} +246.335 q^{48} +145.829 q^{49} -85.2564 q^{50} +82.7659 q^{51} -47.1879 q^{52} -270.464 q^{53} -467.941 q^{54} +163.422 q^{55} -329.506 q^{56} +225.953 q^{57} -742.992 q^{58} -179.222 q^{59} +55.9807 q^{60} -232.168 q^{61} -105.718 q^{62} +386.607 q^{63} +116.705 q^{64} +65.0000 q^{65} -343.802 q^{66} +647.205 q^{67} -97.3997 q^{68} +251.252 q^{69} -376.995 q^{70} +600.693 q^{71} -260.601 q^{72} +593.018 q^{73} -204.678 q^{74} -77.1118 q^{75} -265.904 q^{76} +722.635 q^{77} -136.745 q^{78} +873.603 q^{79} +399.315 q^{80} +48.8841 q^{81} +270.987 q^{82} +1074.26 q^{83} +247.541 q^{84} +134.165 q^{85} +33.2040 q^{86} -672.014 q^{87} -487.108 q^{88} -310.240 q^{89} -298.159 q^{90} +287.423 q^{91} -295.676 q^{92} -95.6186 q^{93} +1170.74 q^{94} +366.275 q^{95} -472.313 q^{96} +76.4673 q^{97} -497.315 q^{98} +571.521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) \) 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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