LMFDB - Embedded newform 2013.4.a.a.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$118.770844842$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.439845 q^{2} +3.00000 q^{3} -7.80654 q^{4} -18.8775 q^{5} +1.31954 q^{6} -35.5540 q^{7} -6.95243 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.439845 q^{2} +3.00000 q^{3} -7.80654 q^{4} -18.8775 q^{5} +1.31954 q^{6} -35.5540 q^{7} -6.95243 q^{8} +9.00000 q^{9} -8.30317 q^{10} +11.0000 q^{11} -23.4196 q^{12} +49.3645 q^{13} -15.6382 q^{14} -56.6325 q^{15} +59.3943 q^{16} -110.226 q^{17} +3.95861 q^{18} +71.2154 q^{19} +147.368 q^{20} -106.662 q^{21} +4.83830 q^{22} -66.5654 q^{23} -20.8573 q^{24} +231.360 q^{25} +21.7127 q^{26} +27.0000 q^{27} +277.553 q^{28} +275.282 q^{29} -24.9095 q^{30} +188.291 q^{31} +81.7437 q^{32} +33.0000 q^{33} -48.4823 q^{34} +671.170 q^{35} -70.2588 q^{36} +337.078 q^{37} +31.3237 q^{38} +148.093 q^{39} +131.244 q^{40} -146.766 q^{41} -46.9147 q^{42} -535.786 q^{43} -85.8719 q^{44} -169.897 q^{45} -29.2785 q^{46} -220.964 q^{47} +178.183 q^{48} +921.085 q^{49} +101.763 q^{50} -330.678 q^{51} -385.365 q^{52} -574.934 q^{53} +11.8758 q^{54} -207.652 q^{55} +247.186 q^{56} +213.646 q^{57} +121.082 q^{58} -305.680 q^{59} +442.104 q^{60} +61.0000 q^{61} +82.8187 q^{62} -319.986 q^{63} -439.200 q^{64} -931.877 q^{65} +14.5149 q^{66} +110.133 q^{67} +860.482 q^{68} -199.696 q^{69} +295.211 q^{70} +281.565 q^{71} -62.5718 q^{72} +548.668 q^{73} +148.262 q^{74} +694.080 q^{75} -555.945 q^{76} -391.094 q^{77} +65.1381 q^{78} +428.207 q^{79} -1121.22 q^{80} +81.0000 q^{81} -64.5544 q^{82} -335.082 q^{83} +832.660 q^{84} +2080.79 q^{85} -235.663 q^{86} +825.847 q^{87} -76.4767 q^{88} +1085.22 q^{89} -74.7286 q^{90} -1755.10 q^{91} +519.645 q^{92} +564.872 q^{93} -97.1898 q^{94} -1344.37 q^{95} +245.231 q^{96} +1549.50 q^{97} +405.135 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9} - 161 q^{10} + 396 q^{11} + 438 q^{12} - 233 q^{13} - 264 q^{14} - 195 q^{15} + 574 q^{16} - 556 q^{17} - 126 q^{18} - 615 q^{19} - 136 q^{20} - 315 q^{21} - 154 q^{22} - 457 q^{23} - 567 q^{24} + 863 q^{25} + 115 q^{26} + 972 q^{27} - 424 q^{28} - 754 q^{29} - 483 q^{30} - 508 q^{31} - 1511 q^{32} + 1188 q^{33} - 860 q^{34} - 826 q^{35} + 1314 q^{36} - 412 q^{37} - 599 q^{38} - 699 q^{39} - 2791 q^{40} - 2066 q^{41} - 792 q^{42} - 2063 q^{43} + 1606 q^{44} - 585 q^{45} - 787 q^{46} - 1815 q^{47} + 1722 q^{48} + 2825 q^{49} + 808 q^{50} - 1668 q^{51} - 2882 q^{52} - 759 q^{53} - 378 q^{54} - 715 q^{55} - 1749 q^{56} - 1845 q^{57} - 335 q^{58} - 2337 q^{59} - 408 q^{60} + 2196 q^{61} - 1689 q^{62} - 945 q^{63} + 4723 q^{64} - 3550 q^{65} - 462 q^{66} - 1331 q^{67} - 6166 q^{68} - 1371 q^{69} - 1750 q^{70} - 361 q^{71} - 1701 q^{72} - 4627 q^{73} - 3394 q^{74} + 2589 q^{75} - 7214 q^{76} - 1155 q^{77} + 345 q^{78} - 2583 q^{79} - 2643 q^{80} + 2916 q^{81} + 1090 q^{82} - 6123 q^{83} - 1272 q^{84} + 295 q^{85} + 613 q^{86} - 2262 q^{87} - 2079 q^{88} - 2485 q^{89} - 1449 q^{90} - 3156 q^{91} - 6291 q^{92} - 1524 q^{93} - 1744 q^{94} - 5572 q^{95} - 4533 q^{96} - 2558 q^{97} - 2314 q^{98} + 3564 q^{99}+O(q^{100}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9 - 161 * q^10 + 396 * q^11 + 438 * q^12 - 233 * q^13 - 264 * q^14 - 195 * q^15 + 574 * q^16 - 556 * q^17 - 126 * q^18 - 615 * q^19 - 136 * q^20 - 315 * q^21 - 154 * q^22 - 457 * q^23 - 567 * q^24 + 863 * q^25 + 115 * q^26 + 972 * q^27 - 424 * q^28 - 754 * q^29 - 483 * q^30 - 508 * q^31 - 1511 * q^32 + 1188 * q^33 - 860 * q^34 - 826 * q^35 + 1314 * q^36 - 412 * q^37 - 599 * q^38 - 699 * q^39 - 2791 * q^40 - 2066 * q^41 - 792 * q^42 - 2063 * q^43 + 1606 * q^44 - 585 * q^45 - 787 * q^46 - 1815 * q^47 + 1722 * q^48 + 2825 * q^49 + 808 * q^50 - 1668 * q^51 - 2882 * q^52 - 759 * q^53 - 378 * q^54 - 715 * q^55 - 1749 * q^56 - 1845 * q^57 - 335 * q^58 - 2337 * q^59 - 408 * q^60 + 2196 * q^61 - 1689 * q^62 - 945 * q^63 + 4723 * q^64 - 3550 * q^65 - 462 * q^66 - 1331 * q^67 - 6166 * q^68 - 1371 * q^69 - 1750 * q^70 - 361 * q^71 - 1701 * q^72 - 4627 * q^73 - 3394 * q^74 + 2589 * q^75 - 7214 * q^76 - 1155 * q^77 + 345 * q^78 - 2583 * q^79 - 2643 * q^80 + 2916 * q^81 + 1090 * q^82 - 6123 * q^83 - 1272 * q^84 + 295 * q^85 + 613 * q^86 - 2262 * q^87 - 2079 * q^88 - 2485 * q^89 - 1449 * q^90 - 3156 * q^91 - 6291 * q^92 - 1524 * q^93 - 1744 * q^94 - 5572 * q^95 - 4533 * q^96 - 2558 * q^97 - 2314 * q^98 + 3564 * 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 $

$2$	0.439845	0.155509	0.0777544	−	0.996973i	$-0.475225\pi$
$2$	0.439845	0.155509	0.0777544	+	0.996973i	$0.475225\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.80654	−0.975817
$5$	−18.8775	−1.68845	−0.844227	−	0.535985i	$-0.819940\pi$
$5$	−18.8775	−1.68845	−0.844227	+	0.535985i	$0.819940\pi$
$6$	1.31954	0.0897830
$7$	−35.5540	−1.91973	−0.959867	−	0.280455i	$-0.909515\pi$
$7$	−35.5540	−1.91973	−0.959867	+	0.280455i	$0.909515\pi$
$8$	−6.95243	−0.307257
$9$	9.00000	0.333333
$10$	−8.30317	−0.262569
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−23.4196	−0.563388
$13$	49.3645	1.05317	0.526586	−	0.850122i	$-0.323472\pi$
$13$	49.3645	1.05317	0.526586	+	0.850122i	$0.323472\pi$
$14$	−15.6382	−0.298535
$15$	−56.6325	−0.974830
$16$	59.3943	0.928036
$17$	−110.226	−1.57257	−0.786286	−	0.617863i	$-0.787998\pi$
$17$	−110.226	−1.57257	−0.786286	+	0.617863i	$0.787998\pi$
$18$	3.95861	0.0518362
$19$	71.2154	0.859891	0.429945	−	0.902855i	$-0.358533\pi$
$19$	71.2154	0.859891	0.429945	+	0.902855i	$0.358533\pi$
$20$	147.368	1.64762
$21$	−106.662	−1.10836
$22$	4.83830	0.0468876
$23$	−66.5654	−0.603471	−0.301736	−	0.953392i	$-0.597566\pi$
$23$	−66.5654	−0.603471	−0.301736	+	0.953392i	$0.597566\pi$
$24$	−20.8573	−0.177395
$25$	231.360	1.85088
$26$	21.7127	0.163777
$27$	27.0000	0.192450
$28$	277.553	1.87331
$29$	275.282	1.76271	0.881356	−	0.472454i	$-0.156632\pi$
$29$	275.282	1.76271	0.881356	+	0.472454i	$0.156632\pi$
$30$	−24.9095	−0.151595
$31$	188.291	1.09090	0.545451	−	0.838143i	$-0.316358\pi$
$31$	188.291	1.09090	0.545451	+	0.838143i	$0.316358\pi$
$32$	81.7437	0.451574
$33$	33.0000	0.174078
$34$	−48.4823	−0.244549
$35$	671.170	3.24138
$36$	−70.2588	−0.325272
$37$	337.078	1.49771	0.748855	−	0.662734i	$-0.230604\pi$
$37$	337.078	1.49771	0.748855	+	0.662734i	$0.230604\pi$
$38$	31.3237	0.133721
$39$	148.093	0.608049
$40$	131.244	0.518789
$41$	−146.766	−0.559050	−0.279525	−	0.960138i	$-0.590177\pi$
$41$	−146.766	−0.559050	−0.279525	+	0.960138i	$0.590177\pi$
$42$	−46.9147	−0.172360
$43$	−535.786	−1.90015	−0.950077	−	0.312016i	$-0.898996\pi$
$43$	−535.786	−1.90015	−0.950077	+	0.312016i	$0.898996\pi$
$44$	−85.8719	−0.294220
$45$	−169.897	−0.562818
$46$	−29.2785	−0.0938451
$47$	−220.964	−0.685763	−0.342882	−	0.939379i	$-0.611403\pi$
$47$	−220.964	−0.685763	−0.342882	+	0.939379i	$0.611403\pi$
$48$	178.183	0.535802
$49$	921.085	2.68538
$50$	101.763	0.287828
$51$	−330.678	−0.907924
$52$	−385.365	−1.02770
$53$	−574.934	−1.49006	−0.745030	−	0.667031i	$-0.767565\pi$
$53$	−574.934	−1.49006	−0.745030	+	0.667031i	$0.767565\pi$
$54$	11.8758	0.0299277
$55$	−207.652	−0.509088
$56$	247.186	0.589851
$57$	213.646	0.496458
$58$	121.082	0.274117
$59$	−305.680	−0.674511	−0.337255	−	0.941413i	$-0.609499\pi$
$59$	−305.680	−0.674511	−0.337255	+	0.941413i	$0.609499\pi$
$60$	442.104	0.951255
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	82.8187	0.169645
$63$	−319.986	−0.639911
$64$	−439.200	−0.857812
$65$	−931.877	−1.77823
$66$	14.5149	0.0270706
$67$	110.133	0.200818	0.100409	−	0.994946i	$-0.467985\pi$
$67$	110.133	0.200818	0.100409	+	0.994946i	$0.467985\pi$
$68$	860.482	1.53454
$69$	−199.696	−0.348414
$70$	295.211	0.504064
$71$	281.565	0.470642	0.235321	−	0.971918i	$-0.424386\pi$
$71$	281.565	0.470642	0.235321	+	0.971918i	$0.424386\pi$
$72$	−62.5718	−0.102419
$73$	548.668	0.879682	0.439841	−	0.898076i	$-0.355035\pi$
$73$	548.668	0.879682	0.439841	+	0.898076i	$0.355035\pi$
$74$	148.262	0.232907
$75$	694.080	1.06861
$76$	−555.945	−0.839096
$77$	−391.094	−0.578822
$78$	65.1381	0.0945570
$79$	428.207	0.609836	0.304918	−	0.952379i	$-0.401371\pi$
$79$	428.207	0.609836	0.304918	+	0.952379i	$0.401371\pi$
$80$	−1121.22	−1.56695
$81$	81.0000	0.111111
$82$	−64.5544	−0.0869371
$83$	−335.082	−0.443133	−0.221566	−	0.975145i	$-0.571117\pi$
$83$	−335.082	−0.443133	−0.221566	+	0.975145i	$0.571117\pi$
$84$	832.660	1.08156
$85$	2080.79	2.65521
$86$	−235.663	−0.295490
$87$	825.847	1.01770
$88$	−76.4767	−0.0926414
$89$	1085.22	1.29251	0.646255	−	0.763121i	$-0.276334\pi$
$89$	1085.22	1.29251	0.646255	+	0.763121i	$0.276334\pi$
$90$	−74.7286	−0.0875231
$91$	−1755.10	−2.02181
$92$	519.645	0.588878
$93$	564.872	0.629833
$94$	−97.1898	−0.106642
$95$	−1344.37	−1.45189
$96$	245.231	0.260717
$97$	1549.50	1.62193	0.810966	−	0.585093i	$-0.198942\pi$
$97$	1549.50	1.62193	0.810966	+	0.585093i	$0.198942\pi$
$98$	405.135	0.417600
$99$	99.0000	0.100504
$100$	−1806.12	−1.80612
$101$	1116.57	1.10002	0.550012	−	0.835157i	$-0.314623\pi$
$101$	1116.57	1.10002	0.550012	+	0.835157i	$0.314623\pi$
$102$	−145.447	−0.141190
$103$	−1411.24	−1.35003	−0.675017	−	0.737803i	$-0.735864\pi$
$103$	−1411.24	−1.35003	−0.675017	+	0.737803i	$0.735864\pi$
$104$	−343.203	−0.323594
$105$	2013.51	1.87141
$106$	−252.882	−0.231717
$107$	−984.424	−0.889420	−0.444710	−	0.895675i	$-0.646693\pi$
$107$	−984.424	−0.889420	−0.444710	+	0.895675i	$0.646693\pi$
$108$	−210.776	−0.187796
$109$	−1581.61	−1.38983	−0.694913	−	0.719093i	$-0.744557\pi$
$109$	−1581.61	−1.38983	−0.694913	+	0.719093i	$0.744557\pi$
$110$	−91.3349	−0.0791677
$111$	1011.23	0.864703
$112$	−2111.70	−1.78158
$113$	−859.504	−0.715534	−0.357767	−	0.933811i	$-0.616462\pi$
$113$	−859.504	−0.715534	−0.357767	+	0.933811i	$0.616462\pi$
$114$	93.9712	0.0772036
$115$	1256.59	1.01893
$116$	−2149.00	−1.72008
$117$	444.280	0.351057
$118$	−134.452	−0.104892
$119$	3918.97	3.01892
$120$	393.733	0.299523
$121$	121.000	0.0909091
$122$	26.8306	0.0199109
$123$	−440.299	−0.322768
$124$	−1469.90	−1.06452
$125$	−2007.81	−1.43667
$126$	−140.744	−0.0995118
$127$	−1637.12	−1.14386	−0.571932	−	0.820301i	$-0.693806\pi$
$127$	−1637.12	−1.14386	−0.571932	+	0.820301i	$0.693806\pi$
$128$	−847.130	−0.584972
$129$	−1607.36	−1.09705
$130$	−409.882	−0.276531
$131$	1649.22	1.09995	0.549974	−	0.835182i	$-0.314637\pi$
$131$	1649.22	1.09995	0.549974	+	0.835182i	$0.314637\pi$
$132$	−257.616	−0.169868
$133$	−2531.99	−1.65076
$134$	48.4412	0.0312290
$135$	−509.692	−0.324943
$136$	766.338	0.483183
$137$	−339.920	−0.211980	−0.105990	−	0.994367i	$-0.533801\pi$
$137$	−339.920	−0.211980	−0.105990	+	0.994367i	$0.533801\pi$
$138$	−87.8354	−0.0541815
$139$	1273.59	0.777152	0.388576	−	0.921417i	$-0.372967\pi$
$139$	1273.59	0.777152	0.388576	+	0.921417i	$0.372967\pi$
$140$	−5239.51	−3.16300
$141$	−662.891	−0.395926
$142$	123.845	0.0731890
$143$	543.009	0.317543
$144$	534.549	0.309345
$145$	−5196.64	−2.97626
$146$	241.329	0.136798
$147$	2763.26	1.55040
$148$	−2631.41	−1.46149
$149$	456.783	0.251148	0.125574	−	0.992084i	$-0.459923\pi$
$149$	456.783	0.251148	0.125574	+	0.992084i	$0.459923\pi$
$150$	305.288	0.166177
$151$	−3078.53	−1.65912	−0.829560	−	0.558418i	$-0.811409\pi$
$151$	−3078.53	−1.65912	−0.829560	+	0.558418i	$0.811409\pi$
$152$	−495.120	−0.264207
$153$	−992.033	−0.524190
$154$	−172.021	−0.0900118
$155$	−3554.45	−1.84194
$156$	−1156.10	−0.593345
$157$	1455.87	0.740070	0.370035	−	0.929018i	$-0.379346\pi$
$157$	1455.87	0.740070	0.370035	+	0.929018i	$0.379346\pi$
$158$	188.345	0.0948348
$159$	−1724.80	−0.860287
$160$	−1543.12	−0.762463
$161$	2366.66	1.15850
$162$	35.6275	0.0172787
$163$	2920.39	1.40333	0.701665	−	0.712507i	$-0.252440\pi$
$163$	2920.39	1.40333	0.701665	+	0.712507i	$0.252440\pi$
$164$	1145.74	0.545530
$165$	−622.957	−0.293922
$166$	−147.384	−0.0689110
$167$	−486.208	−0.225293	−0.112646	−	0.993635i	$-0.535933\pi$
$167$	−486.208	−0.225293	−0.112646	+	0.993635i	$0.535933\pi$
$168$	741.559	0.340551
$169$	239.849	0.109171
$170$	915.225	0.412909
$171$	640.938	0.286630
$172$	4182.63	1.85420
$173$	1215.30	0.534088	0.267044	−	0.963684i	$-0.413953\pi$
$173$	1215.30	0.534088	0.267044	+	0.963684i	$0.413953\pi$
$174$	363.245	0.158261
$175$	−8225.76	−3.55320
$176$	653.337	0.279813
$177$	−917.040	−0.389429
$178$	477.330	0.200997
$179$	−470.460	−0.196446	−0.0982229	−	0.995164i	$-0.531316\pi$
$179$	−470.460	−0.196446	−0.0982229	+	0.995164i	$0.531316\pi$
$180$	1326.31	0.549208
$181$	2347.50	0.964022	0.482011	−	0.876165i	$-0.339907\pi$
$181$	2347.50	0.964022	0.482011	+	0.876165i	$0.339907\pi$
$182$	−771.973	−0.314409
$183$	183.000	0.0739221
$184$	462.791	0.185421
$185$	−6363.18	−2.52881
$186$	248.456	0.0979445
$187$	−1212.48	−0.474148
$188$	1724.96	0.669179
$189$	−959.957	−0.369453
$190$	−591.314	−0.225781
$191$	2324.25	0.880507	0.440253	−	0.897874i	$-0.354889\pi$
$191$	2324.25	0.880507	0.440253	+	0.897874i	$0.354889\pi$
$192$	−1317.60	−0.495258
$193$	−308.526	−0.115068	−0.0575341	−	0.998344i	$-0.518324\pi$
$193$	−308.526	−0.115068	−0.0575341	+	0.998344i	$0.518324\pi$
$194$	681.538	0.252225
$195$	−2795.63	−1.02666
$196$	−7190.49	−2.62044
$197$	2957.89	1.06975	0.534875	−	0.844931i	$-0.320359\pi$
$197$	2957.89	1.06975	0.534875	+	0.844931i	$0.320359\pi$
$198$	43.5447	0.0156292
$199$	−127.856	−0.0455451	−0.0227725	−	0.999741i	$-0.507249\pi$
$199$	−127.856	−0.0455451	−0.0227725	+	0.999741i	$0.507249\pi$
$200$	−1608.51	−0.568695
$201$	330.398	0.115943
$202$	491.116	0.171063
$203$	−9787.38	−3.38394
$204$	2581.45	0.885968
$205$	2770.58	0.943930
$206$	−620.726	−0.209942
$207$	−599.088	−0.201157
$208$	2931.97	0.977381
$209$	783.369	0.259267
$210$	885.633	0.291021
$211$	−621.210	−0.202682	−0.101341	−	0.994852i	$-0.532313\pi$
$211$	−621.210	−0.202682	−0.101341	+	0.994852i	$0.532313\pi$
$212$	4488.24	1.45403
$213$	844.695	0.271725
$214$	−432.994	−0.138312
$215$	10114.3	3.20832
$216$	−187.716	−0.0591316
$217$	−6694.48	−2.09424
$218$	−695.665	−0.216130
$219$	1646.01	0.507885
$220$	1621.05	0.496777
$221$	−5441.24	−1.65619
$222$	444.786	0.134469
$223$	−860.033	−0.258260	−0.129130	−	0.991628i	$-0.541218\pi$
$223$	−860.033	−0.258260	−0.129130	+	0.991628i	$0.541218\pi$
$224$	−2906.31	−0.866903
$225$	2082.24	0.616960
$226$	−378.049	−0.111272
$227$	−5154.32	−1.50707	−0.753534	−	0.657409i	$-0.771653\pi$
$227$	−5154.32	−1.50707	−0.753534	+	0.657409i	$0.771653\pi$
$228$	−1667.84	−0.484452
$229$	−4853.04	−1.40043	−0.700214	−	0.713933i	$-0.746912\pi$
$229$	−4853.04	−1.40043	−0.700214	+	0.713933i	$0.746912\pi$
$230$	552.704	0.158453
$231$	−1173.28	−0.334183
$232$	−1913.88	−0.541605
$233$	−5137.46	−1.44449	−0.722245	−	0.691638i	$-0.756889\pi$
$233$	−5137.46	−1.44449	−0.722245	+	0.691638i	$0.756889\pi$
$234$	195.414	0.0545925
$235$	4171.24	1.15788
$236$	2386.30	0.658199
$237$	1284.62	0.352089
$238$	1723.74	0.469468
$239$	4197.62	1.13607	0.568037	−	0.823003i	$-0.307703\pi$
$239$	4197.62	1.13607	0.568037	+	0.823003i	$0.307703\pi$
$240$	−3363.65	−0.904677
$241$	5762.56	1.54025	0.770123	−	0.637896i	$-0.220195\pi$
$241$	5762.56	1.54025	0.770123	+	0.637896i	$0.220195\pi$
$242$	53.2213	0.0141372
$243$	243.000	0.0641500
$244$	−476.199	−0.124941
$245$	−17387.8	−4.53414
$246$	−193.663	−0.0501932
$247$	3515.51	0.905613
$248$	−1309.08	−0.335187
$249$	−1005.25	−0.255843
$250$	−883.125	−0.223415
$251$	2873.45	0.722591	0.361296	−	0.932451i	$-0.382334\pi$
$251$	2873.45	0.722591	0.361296	+	0.932451i	$0.382334\pi$
$252$	2497.98	0.624437
$253$	−732.219	−0.181953
$254$	−720.078	−0.177881
$255$	6242.37	1.53299
$256$	3140.99	0.766844
$257$	−611.104	−0.148325	−0.0741626	−	0.997246i	$-0.523628\pi$
$257$	−611.104	−0.148325	−0.0741626	+	0.997246i	$0.523628\pi$
$258$	−706.989	−0.170601
$259$	−11984.5	−2.87520
$260$	7274.73	1.73523
$261$	2477.54	0.587570
$262$	725.403	0.171052
$263$	317.771	0.0745041	0.0372520	−	0.999306i	$-0.488140\pi$
$263$	317.771	0.0745041	0.0372520	+	0.999306i	$0.488140\pi$
$264$	−229.430	−0.0534865
$265$	10853.3	2.51590
$266$	−1113.68	−0.256708
$267$	3255.67	0.746231
$268$	−859.753	−0.195962
$269$	3471.07	0.786746	0.393373	−	0.919379i	$-0.371308\pi$
$269$	3471.07	0.786746	0.393373	+	0.919379i	$0.371308\pi$
$270$	−224.186	−0.0505315
$271$	−5828.86	−1.30656	−0.653281	−	0.757116i	$-0.726608\pi$
$271$	−5828.86	−1.30656	−0.653281	+	0.757116i	$0.726608\pi$
$272$	−6546.79	−1.45940
$273$	−5265.31	−1.16729
$274$	−149.512	−0.0329648
$275$	2544.96	0.558061
$276$	1558.93	0.339989
$277$	6022.65	1.30638	0.653188	−	0.757196i	$-0.273431\pi$
$277$	6022.65	1.30638	0.653188	+	0.757196i	$0.273431\pi$
$278$	560.180	0.120854
$279$	1694.61	0.363634
$280$	−4666.26	−0.995937
$281$	−7620.24	−1.61774	−0.808871	−	0.587986i	$-0.799921\pi$
$281$	−7620.24	−1.61774	−0.808871	+	0.587986i	$0.799921\pi$
$282$	−291.569	−0.0615699
$283$	3905.10	0.820262	0.410131	−	0.912027i	$-0.365483\pi$
$283$	3905.10	0.820262	0.410131	+	0.912027i	$0.365483\pi$
$284$	−2198.05	−0.459261
$285$	−4033.10	−0.838247
$286$	238.840	0.0493808
$287$	5218.13	1.07323
$288$	735.693	0.150525
$289$	7236.75	1.47298
$290$	−2285.72	−0.462834
$291$	4648.49	0.936423
$292$	−4283.20	−0.858409
$293$	591.079	0.117854	0.0589270	−	0.998262i	$-0.481232\pi$
$293$	591.079	0.117854	0.0589270	+	0.998262i	$0.481232\pi$
$294$	1215.40	0.241102
$295$	5770.47	1.13888
$296$	−2343.51	−0.460181
$297$	297.000	0.0580259
$298$	200.914	0.0390558
$299$	−3285.96	−0.635559
$300$	−5418.36	−1.04276
$301$	19049.3	3.64779
$302$	−1354.08	−0.258008
$303$	3349.70	0.635099
$304$	4229.79	0.798010
$305$	−1151.53	−0.216184
$306$	−436.341	−0.0815162
$307$	−8805.57	−1.63700	−0.818502	−	0.574503i	$-0.805195\pi$
$307$	−8805.57	−1.63700	−0.818502	+	0.574503i	$0.805195\pi$
$308$	3053.09	0.564824
$309$	−4233.71	−0.779442
$310$	−1563.41	−0.286438
$311$	562.025	0.102474	0.0512371	−	0.998687i	$-0.483684\pi$
$311$	562.025	0.102474	0.0512371	+	0.998687i	$0.483684\pi$
$312$	−1029.61	−0.186827
$313$	878.732	0.158686	0.0793432	−	0.996847i	$-0.474718\pi$
$313$	878.732	0.158686	0.0793432	+	0.996847i	$0.474718\pi$
$314$	640.356	0.115087
$315$	6040.53	1.08046
$316$	−3342.81	−0.595088
$317$	−890.110	−0.157708	−0.0788542	−	0.996886i	$-0.525126\pi$
$317$	−890.110	−0.157708	−0.0788542	+	0.996886i	$0.525126\pi$
$318$	−758.645	−0.133782
$319$	3028.10	0.531477
$320$	8290.99	1.44838
$321$	−2953.27	−0.513507
$322$	1040.97	0.180158
$323$	−7849.78	−1.35224
$324$	−632.329	−0.108424
$325$	11421.0	1.94929
$326$	1284.52	0.218230
$327$	−4744.84	−0.802417
$328$	1020.38	0.171772
$329$	7856.14	1.31648
$330$	−274.005	−0.0457075
$331$	−2969.30	−0.493074	−0.246537	−	0.969133i	$-0.579293\pi$
$331$	−2969.30	−0.493074	−0.246537	+	0.969133i	$0.579293\pi$
$332$	2615.83	0.432417
$333$	3033.70	0.499236
$334$	−213.856	−0.0350350
$335$	−2079.03	−0.339073
$336$	−6335.11	−1.02860
$337$	−1163.98	−0.188149	−0.0940744	−	0.995565i	$-0.529989\pi$
$337$	−1163.98	−0.188149	−0.0940744	+	0.995565i	$0.529989\pi$
$338$	105.497	0.0169771
$339$	−2578.51	−0.413114
$340$	−16243.8	−2.59100
$341$	2071.20	0.328919
$342$	281.914	0.0445735
$343$	−20553.2	−3.23548
$344$	3725.01	0.583835
$345$	3769.76	0.588282
$346$	534.542	0.0830554
$347$	250.050	0.0386842	0.0193421	−	0.999813i	$-0.493843\pi$
$347$	250.050	0.0386842	0.0193421	+	0.999813i	$0.493843\pi$
$348$	−6447.00	−0.993091
$349$	8083.00	1.23975	0.619876	−	0.784700i	$-0.287183\pi$
$349$	8083.00	1.23975	0.619876	+	0.784700i	$0.287183\pi$
$350$	−3618.06	−0.552553
$351$	1332.84	0.202683
$352$	899.181	0.136155
$353$	−5218.17	−0.786785	−0.393392	−	0.919371i	$-0.628699\pi$
$353$	−5218.17	−0.786785	−0.393392	+	0.919371i	$0.628699\pi$
$354$	−403.356	−0.0605596
$355$	−5315.24	−0.794658
$356$	−8471.83	−1.26125
$357$	11756.9	1.74297
$358$	−206.929	−0.0305490
$359$	187.989	0.0276371	0.0138185	−	0.999905i	$-0.495601\pi$
$359$	187.989	0.0276371	0.0138185	+	0.999905i	$0.495601\pi$
$360$	1181.20	0.172930
$361$	−1787.37	−0.260588
$362$	1032.53	0.149914
$363$	363.000	0.0524864
$364$	13701.3	1.97292
$365$	−10357.5	−1.48530
$366$	80.4917	0.0114955
$367$	−694.306	−0.0987533	−0.0493767	−	0.998780i	$-0.515723\pi$
$367$	−694.306	−0.0987533	−0.0493767	+	0.998780i	$0.515723\pi$
$368$	−3953.60	−0.560043
$369$	−1320.90	−0.186350
$370$	−2798.82	−0.393253
$371$	20441.2	2.86052
$372$	−4409.69	−0.614602
$373$	−1713.39	−0.237844	−0.118922	−	0.992904i	$-0.537944\pi$
$373$	−1713.39	−0.237844	−0.118922	+	0.992904i	$0.537944\pi$
$374$	−533.306	−0.0737342
$375$	−6023.43	−0.829462
$376$	1536.23	0.210705
$377$	13589.2	1.85644
$378$	−422.233	−0.0574532
$379$	3048.40	0.413155	0.206577	−	0.978430i	$-0.433767\pi$
$379$	3048.40	0.413155	0.206577	+	0.978430i	$0.433767\pi$
$380$	10494.9	1.41678
$381$	−4911.35	−0.660410
$382$	1022.31	0.136926
$383$	53.4348	0.00712896	0.00356448	−	0.999994i	$-0.498865\pi$
$383$	53.4348	0.00712896	0.00356448	+	0.999994i	$0.498865\pi$
$384$	−2541.39	−0.337734
$385$	7382.87	0.977314
$386$	−135.704	−0.0178941
$387$	−4822.07	−0.633384
$388$	−12096.2	−1.58271
$389$	−2541.23	−0.331222	−0.165611	−	0.986191i	$-0.552960\pi$
$389$	−2541.23	−0.331222	−0.165611	+	0.986191i	$0.552960\pi$
$390$	−1229.65	−0.159655
$391$	7337.23	0.949001
$392$	−6403.78	−0.825101
$393$	4947.67	0.635056
$394$	1301.01	0.166356
$395$	−8083.47	−1.02968
$396$	−772.847	−0.0980733
$397$	−11689.2	−1.47775	−0.738874	−	0.673843i	$-0.764642\pi$
$397$	−11689.2	−1.47775	−0.738874	+	0.673843i	$0.764642\pi$
$398$	−56.2368	−0.00708265
$399$	−7595.97	−0.953068
$400$	13741.5	1.71768
$401$	6265.77	0.780294	0.390147	−	0.920753i	$-0.372424\pi$
$401$	6265.77	0.780294	0.390147	+	0.920753i	$0.372424\pi$
$402$	145.324	0.0180301
$403$	9294.86	1.14891
$404$	−8716.51	−1.07342
$405$	−1529.08	−0.187606
$406$	−4304.93	−0.526232
$407$	3707.86	0.451576
$408$	2299.01	0.278966
$409$	−562.103	−0.0679564	−0.0339782	−	0.999423i	$-0.510818\pi$
$409$	−562.103	−0.0679564	−0.0339782	+	0.999423i	$0.510818\pi$
$410$	1218.63	0.146789
$411$	−1019.76	−0.122387
$412$	11016.9	1.31739
$413$	10868.1	1.29488
$414$	−263.506	−0.0312817
$415$	6325.51	0.748210
$416$	4035.23	0.475586
$417$	3820.76	0.448689
$418$	344.561	0.0403183
$419$	−12277.7	−1.43152	−0.715759	−	0.698348i	$-0.753919\pi$
$419$	−12277.7	−1.43152	−0.715759	+	0.698348i	$0.753919\pi$
$420$	−15718.5	−1.82616
$421$	7952.42	0.920611	0.460305	−	0.887761i	$-0.347740\pi$
$421$	7952.42	0.920611	0.460305	+	0.887761i	$0.347740\pi$
$422$	−273.236	−0.0315188
$423$	−1988.67	−0.228588
$424$	3997.18	0.457831
$425$	−25501.9	−2.91064
$426$	371.535	0.0422557
$427$	−2168.79	−0.245797
$428$	7684.94	0.867911
$429$	1629.03	0.183334
$430$	4448.72	0.498922
$431$	1217.89	0.136111	0.0680553	−	0.997682i	$-0.478321\pi$
$431$	1217.89	0.136111	0.0680553	+	0.997682i	$0.478321\pi$
$432$	1603.65	0.178601
$433$	4188.48	0.464863	0.232431	−	0.972613i	$-0.425332\pi$
$433$	4188.48	0.464863	0.232431	+	0.972613i	$0.425332\pi$
$434$	−2944.53	−0.325673
$435$	−15589.9	−1.71834
$436$	12346.9	1.35622
$437$	−4740.48	−0.518919
$438$	723.987	0.0789805
$439$	−16016.8	−1.74132	−0.870660	−	0.491885i	$-0.836308\pi$
$439$	−16016.8	−1.74132	−0.870660	+	0.491885i	$0.836308\pi$
$440$	1443.69	0.156421
$441$	8289.77	0.895127
$442$	−2393.30	−0.257552
$443$	−15206.5	−1.63089	−0.815444	−	0.578835i	$-0.803507\pi$
$443$	−15206.5	−1.63089	−0.815444	+	0.578835i	$0.803507\pi$
$444$	−7894.23	−0.843792
$445$	−20486.3	−2.18235
$446$	−378.281	−0.0401617
$447$	1370.35	0.145001
$448$	15615.3	1.64677
$449$	−16537.7	−1.73822	−0.869111	−	0.494617i	$-0.835308\pi$
$449$	−16537.7	−1.73822	−0.869111	+	0.494617i	$0.835308\pi$
$450$	915.863	0.0959426
$451$	−1614.43	−0.168560
$452$	6709.75	0.698230
$453$	−9235.58	−0.957893
$454$	−2267.10	−0.234362
$455$	33131.9	3.41374
$456$	−1485.36	−0.152540
$457$	12415.1	1.27079	0.635396	−	0.772186i	$-0.280837\pi$
$457$	12415.1	1.27079	0.635396	+	0.772186i	$0.280837\pi$
$458$	−2134.59	−0.217779
$459$	−2976.10	−0.302641
$460$	−9809.60	−0.994293
$461$	18623.0	1.88147	0.940736	−	0.339141i	$-0.110136\pi$
$461$	18623.0	1.88147	0.940736	+	0.339141i	$0.110136\pi$
$462$	−516.062	−0.0519684
$463$	−6129.33	−0.615236	−0.307618	−	0.951510i	$-0.599532\pi$
$463$	−6129.33	−0.615236	−0.307618	+	0.951510i	$0.599532\pi$
$464$	16350.2	1.63586
$465$	−10663.4	−1.06344
$466$	−2259.69	−0.224631
$467$	1763.10	0.174703	0.0873516	−	0.996178i	$-0.472160\pi$
$467$	1763.10	0.174703	0.0873516	+	0.996178i	$0.472160\pi$
$468$	−3468.29	−0.342568
$469$	−3915.65	−0.385518
$470$	1834.70	0.180060
$471$	4367.60	0.427279
$472$	2125.22	0.207248
$473$	−5893.65	−0.572918
$474$	565.034	0.0547529
$475$	16476.4	1.59155
$476$	−30593.6	−2.94591
$477$	−5174.40	−0.496687
$478$	1846.30	0.176669
$479$	−12235.3	−1.16711	−0.583554	−	0.812074i	$-0.698338\pi$
$479$	−12235.3	−1.16711	−0.583554	+	0.812074i	$0.698338\pi$
$480$	−4629.35	−0.440208
$481$	16639.7	1.57735
$482$	2534.63	0.239522
$483$	7099.99	0.668863
$484$	−944.591	−0.0887106
$485$	−29250.6	−2.73856
$486$	106.882	0.00997589
$487$	19113.7	1.77849	0.889246	−	0.457429i	$-0.151230\pi$
$487$	19113.7	1.77849	0.889246	+	0.457429i	$0.151230\pi$
$488$	−424.098	−0.0393402
$489$	8761.18	0.810213
$490$	−7647.93	−0.705099
$491$	−2631.72	−0.241890	−0.120945	−	0.992659i	$-0.538592\pi$
$491$	−2631.72	−0.241890	−0.120945	+	0.992659i	$0.538592\pi$
$492$	3437.21	0.314962
$493$	−30343.2	−2.77199
$494$	1546.28	0.140831
$495$	−1868.87	−0.169696
$496$	11183.4	1.01240
$497$	−10010.8	−0.903508
$498$	−442.152	−0.0397858
$499$	21875.5	1.96249	0.981245	−	0.192766i	$-0.0617458\pi$
$499$	21875.5	1.96249	0.981245	+	0.192766i	$0.0617458\pi$
$500$	15674.0	1.40193
$501$	−1458.62	−0.130073
$502$	1263.87	0.112369
$503$	−6543.47	−0.580038	−0.290019	−	0.957021i	$-0.593662\pi$
$503$	−6543.47	−0.580038	−0.290019	+	0.957021i	$0.593662\pi$
$504$	2224.68	0.196617
$505$	−21078.0	−1.85734
$506$	−322.063	−0.0282953
$507$	719.548	0.0630301
$508$	12780.2	1.11620
$509$	10802.4	0.940683	0.470342	−	0.882484i	$-0.344131\pi$
$509$	10802.4	0.940683	0.470342	+	0.882484i	$0.344131\pi$
$510$	2745.67	0.238393
$511$	−19507.3	−1.68876
$512$	8158.59	0.704223
$513$	1922.82	0.165486
$514$	−268.791	−0.0230659
$515$	26640.6	2.27947
$516$	12547.9	1.07052
$517$	−2430.60	−0.206765
$518$	−5271.30	−0.447119
$519$	3645.89	0.308356
$520$	6478.81	0.546374
$521$	−9327.51	−0.784349	−0.392175	−	0.919891i	$-0.628277\pi$
$521$	−9327.51	−0.784349	−0.392175	+	0.919891i	$0.628277\pi$
$522$	1089.73	0.0913723
$523$	1791.37	0.149773	0.0748864	−	0.997192i	$-0.476141\pi$
$523$	1791.37	0.149773	0.0748864	+	0.997192i	$0.476141\pi$
$524$	−12874.7	−1.07335
$525$	−24677.3	−2.05144
$526$	139.770	0.0115860
$527$	−20754.5	−1.71552
$528$	1960.01	0.161550
$529$	−7736.05	−0.635822
$530$	4773.77	0.391244
$531$	−2751.12	−0.224837
$532$	19766.1	1.61084
$533$	−7245.04	−0.588776
$534$	1431.99	0.116045
$535$	18583.5	1.50174
$536$	−765.688	−0.0617028
$537$	−1411.38	−0.113418
$538$	1526.73	0.122346
$539$	10131.9	0.809673
$540$	3978.93	0.317085
$541$	−10294.3	−0.818093	−0.409047	−	0.912513i	$-0.634139\pi$
$541$	−10294.3	−0.818093	−0.409047	+	0.912513i	$0.634139\pi$
$542$	−2563.80	−0.203182
$543$	7042.49	0.556578
$544$	−9010.27	−0.710133
$545$	29856.9	2.34666
$546$	−2315.92	−0.181524
$547$	3813.75	0.298106	0.149053	−	0.988829i	$-0.452377\pi$
$547$	3813.75	0.298106	0.149053	+	0.988829i	$0.452377\pi$
$548$	2653.60	0.206854
$549$	549.000	0.0426790
$550$	1119.39	0.0867834
$551$	19604.3	1.51574
$552$	1388.37	0.107053
$553$	−15224.5	−1.17072
$554$	2649.03	0.203153
$555$	−19089.6	−1.46001
$556$	−9942.29	−0.758358
$557$	21538.6	1.63846	0.819228	−	0.573468i	$-0.194402\pi$
$557$	21538.6	1.63846	0.819228	+	0.573468i	$0.194402\pi$
$558$	745.368	0.0565483
$559$	−26448.8	−2.00119
$560$	39863.7	3.00812
$561$	−3637.45	−0.273749
$562$	−3351.73	−0.251573
$563$	−9557.42	−0.715448	−0.357724	−	0.933827i	$-0.616447\pi$
$563$	−9557.42	−0.715448	−0.357724	+	0.933827i	$0.616447\pi$
$564$	5174.88	0.386351
$565$	16225.3	1.20815
$566$	1717.64	0.127558
$567$	−2879.87	−0.213304
$568$	−1957.56	−0.144608
$569$	8654.54	0.637640	0.318820	−	0.947815i	$-0.396713\pi$
$569$	8654.54	0.637640	0.318820	+	0.947815i	$0.396713\pi$
$570$	−1773.94	−0.130355
$571$	17675.5	1.29544	0.647721	−	0.761877i	$-0.275722\pi$
$571$	17675.5	1.29544	0.647721	+	0.761877i	$0.275722\pi$
$572$	−4239.02	−0.309864
$573$	6972.75	0.508361
$574$	2295.17	0.166896
$575$	−15400.6	−1.11695
$576$	−3952.80	−0.285937
$577$	−20493.2	−1.47858	−0.739291	−	0.673386i	$-0.764839\pi$
$577$	−20493.2	−1.47858	−0.739291	+	0.673386i	$0.764839\pi$
$578$	3183.05	0.229061
$579$	−925.577	−0.0664347
$580$	40567.7	2.90428
$581$	11913.5	0.850697
$582$	2044.61	0.145622
$583$	−6324.27	−0.449270
$584$	−3814.58	−0.270288
$585$	−8386.90	−0.592744
$586$	259.983	0.0183273
$587$	−7550.86	−0.530933	−0.265466	−	0.964120i	$-0.585526\pi$
$587$	−7550.86	−0.530933	−0.265466	+	0.964120i	$0.585526\pi$
$588$	−21571.5	−1.51291
$589$	13409.2	0.938057
$590$	2538.11	0.177106
$591$	8873.66	0.617621
$592$	20020.5	1.38993
$593$	−18688.0	−1.29414	−0.647070	−	0.762431i	$-0.724006\pi$
$593$	−18688.0	−1.29414	−0.647070	+	0.762431i	$0.724006\pi$
$594$	130.634	0.00902353
$595$	−73980.3	−5.09731
$596$	−3565.89	−0.245075
$597$	−383.568	−0.0262954
$598$	−1445.31	−0.0988350
$599$	2348.31	0.160183	0.0800914	−	0.996788i	$-0.474479\pi$
$599$	2348.31	0.160183	0.0800914	+	0.996788i	$0.474479\pi$
$600$	−4825.54	−0.328336
$601$	−18037.2	−1.22422	−0.612109	−	0.790774i	$-0.709678\pi$
$601$	−18037.2	−1.22422	−0.612109	+	0.790774i	$0.709678\pi$
$602$	8378.75	0.567263
$603$	991.193	0.0669394
$604$	24032.6	1.61900
$605$	−2284.18	−0.153496
$606$	1473.35	0.0987635
$607$	5805.01	0.388168	0.194084	−	0.980985i	$-0.437827\pi$
$607$	5805.01	0.388168	0.194084	+	0.980985i	$0.437827\pi$
$608$	5821.41	0.388305
$609$	−29362.1	−1.95372
$610$	−506.494	−0.0336186
$611$	−10907.8	−0.722227
$612$	7744.34	0.511514
$613$	1519.23	0.100099	0.0500497	−	0.998747i	$-0.484062\pi$
$613$	1519.23	0.100099	0.0500497	+	0.998747i	$0.484062\pi$
$614$	−3873.09	−0.254568
$615$	8311.74	0.544979
$616$	2719.05	0.177847
$617$	−22344.6	−1.45796	−0.728979	−	0.684536i	$-0.760005\pi$
$617$	−22344.6	−1.45796	−0.728979	+	0.684536i	$0.760005\pi$
$618$	−1862.18	−0.121210
$619$	−22541.9	−1.46371	−0.731856	−	0.681460i	$-0.761345\pi$
$619$	−22541.9	−1.46371	−0.731856	+	0.681460i	$0.761345\pi$
$620$	27748.0	1.79740
$621$	−1797.26	−0.116138
$622$	247.204	0.0159356
$623$	−38584.0	−2.48128
$624$	8795.90	0.564291
$625$	8982.41	0.574874
$626$	386.506	0.0246771
$627$	2350.11	0.149688
$628$	−11365.3	−0.722173
$629$	−37154.7	−2.35525
$630$	2656.90	0.168021
$631$	−2919.40	−0.184183	−0.0920915	−	0.995751i	$-0.529355\pi$
$631$	−2919.40	−0.184183	−0.0920915	+	0.995751i	$0.529355\pi$
$632$	−2977.08	−0.187376
$633$	−1863.63	−0.117018
$634$	−391.510	−0.0245250
$635$	30904.7	1.93136
$636$	13464.7	0.839483
$637$	45468.9	2.82817
$638$	1331.90	0.0826494
$639$	2534.08	0.156881
$640$	15991.7	0.987698
$641$	259.043	0.0159619	0.00798095	−	0.999968i	$-0.497460\pi$
$641$	259.043	0.0159619	0.00798095	+	0.999968i	$0.497460\pi$
$642$	−1298.98	−0.0798548
$643$	−18436.2	−1.13072	−0.565358	−	0.824845i	$-0.691262\pi$
$643$	−18436.2	−1.13072	−0.565358	+	0.824845i	$0.691262\pi$
$644$	−18475.4	−1.13049
$645$	30342.9	1.85233
$646$	−3452.69	−0.210285
$647$	29531.4	1.79443	0.897216	−	0.441592i	$-0.145586\pi$
$647$	29531.4	1.79443	0.897216	+	0.441592i	$0.145586\pi$
$648$	−563.147	−0.0341396
$649$	−3362.48	−0.203373
$650$	5023.45	0.303132
$651$	−20083.4	−1.20911
$652$	−22798.2	−1.36939
$653$	28787.5	1.72518	0.862590	−	0.505904i	$-0.168841\pi$
$653$	28787.5	1.72518	0.862590	+	0.505904i	$0.168841\pi$
$654$	−2087.00	−0.124783
$655$	−31133.2	−1.85721
$656$	−8717.08	−0.518818
$657$	4938.02	0.293227
$658$	3455.48	0.204725
$659$	−18148.4	−1.07278	−0.536390	−	0.843970i	$-0.680212\pi$
$659$	−18148.4	−1.07278	−0.536390	+	0.843970i	$0.680212\pi$
$660$	4863.14	0.286814
$661$	2493.67	0.146736	0.0733681	−	0.997305i	$-0.476625\pi$
$661$	2493.67	0.146736	0.0733681	+	0.997305i	$0.476625\pi$
$662$	−1306.03	−0.0766773
$663$	−16323.7	−0.956200
$664$	2329.63	0.136156
$665$	47797.6	2.78724
$666$	1334.36	0.0776356
$667$	−18324.3	−1.06375
$668$	3795.60	0.219844
$669$	−2580.10	−0.149107
$670$	−914.450	−0.0527288
$671$	671.000	0.0386046
$672$	−8718.94	−0.500507
$673$	−31627.3	−1.81150	−0.905752	−	0.423809i	$-0.860693\pi$
$673$	−31627.3	−1.81150	−0.905752	+	0.423809i	$0.860693\pi$
$674$	−511.972	−0.0292588
$675$	6246.72	0.356202
$676$	−1872.39	−0.106531
$677$	−20977.3	−1.19087	−0.595437	−	0.803402i	$-0.703021\pi$
$677$	−20977.3	−1.19087	−0.595437	+	0.803402i	$0.703021\pi$
$678$	−1134.15	−0.0642428
$679$	−55090.7	−3.11368
$680$	−14466.5	−0.815833
$681$	−15463.0	−0.870106
$682$	911.005	0.0511499
$683$	−9651.79	−0.540725	−0.270363	−	0.962759i	$-0.587144\pi$
$683$	−9651.79	−0.540725	−0.270363	+	0.962759i	$0.587144\pi$
$684$	−5003.51	−0.279699
$685$	6416.83	0.357919
$686$	−9040.24	−0.503146
$687$	−14559.1	−0.808537
$688$	−31822.6	−1.76341
$689$	−28381.3	−1.56929
$690$	1658.11	0.0914829
$691$	10999.4	0.605550	0.302775	−	0.953062i	$-0.402087\pi$
$691$	10999.4	0.605550	0.302775	+	0.953062i	$0.402087\pi$
$692$	−9487.25	−0.521172
$693$	−3519.84	−0.192941
$694$	109.983	0.00601573
$695$	−24042.1	−1.31219
$696$	−5741.64	−0.312696
$697$	16177.4	0.879146
$698$	3555.27	0.192792
$699$	−15412.4	−0.833976
$700$	64214.7	3.46727
$701$	27466.7	1.47989	0.739945	−	0.672668i	$-0.234852\pi$
$701$	27466.7	1.47989	0.739945	+	0.672668i	$0.234852\pi$
$702$	586.243	0.0315190
$703$	24005.1	1.28787
$704$	−4831.20	−0.258640
$705$	12513.7	0.668502
$706$	−2295.18	−0.122352
$707$	−39698.4	−2.11175
$708$	7158.91	0.380012
$709$	6331.53	0.335382	0.167691	−	0.985840i	$-0.446369\pi$
$709$	6331.53	0.335382	0.167691	+	0.985840i	$0.446369\pi$
$710$	−2337.88	−0.123576
$711$	3853.86	0.203279
$712$	−7544.94	−0.397133
$713$	−12533.6	−0.658328
$714$	5171.22	0.271048
$715$	−10250.7	−0.536157
$716$	3672.66	0.191695
$717$	12592.9	0.655913
$718$	82.6862	0.00429780
$719$	−17001.7	−0.881857	−0.440929	−	0.897542i	$-0.645351\pi$
$719$	−17001.7	−0.881857	−0.440929	+	0.897542i	$0.645351\pi$
$720$	−10090.9	−0.522316
$721$	50175.1	2.59171
$722$	−786.166	−0.0405237
$723$	17287.7	0.889261
$724$	−18325.8	−0.940709
$725$	63689.3	3.26257
$726$	159.664	0.00816209
$727$	22943.6	1.17047	0.585235	−	0.810864i	$-0.301002\pi$
$727$	22943.6	1.17047	0.585235	+	0.810864i	$0.301002\pi$
$728$	12202.2	0.621215
$729$	729.000	0.0370370
$730$	−4555.69	−0.230978
$731$	59057.5	2.98813
$732$	−1428.60	−0.0721345
$733$	14880.3	0.749819	0.374910	−	0.927061i	$-0.377674\pi$
$733$	14880.3	0.749819	0.374910	+	0.927061i	$0.377674\pi$
$734$	−305.387	−0.0153570
$735$	−52163.4	−2.61779
$736$	−5441.30	−0.272512
$737$	1211.46	0.0605490
$738$	−580.990	−0.0289790
$739$	5816.94	0.289553	0.144776	−	0.989464i	$-0.453754\pi$
$739$	5816.94	0.289553	0.144776	+	0.989464i	$0.453754\pi$
$740$	49674.4	2.46766
$741$	10546.5	0.522856
$742$	8990.95	0.444836
$743$	−15201.4	−0.750587	−0.375294	−	0.926906i	$-0.622458\pi$
$743$	−15201.4	−0.750587	−0.375294	+	0.926906i	$0.622458\pi$
$744$	−3927.23	−0.193520
$745$	−8622.92	−0.424053
$746$	−753.624	−0.0369868
$747$	−3015.74	−0.147711
$748$	9465.31	0.462682
$749$	35000.2	1.70745
$750$	−2649.37	−0.128989
$751$	−14000.5	−0.680272	−0.340136	−	0.940376i	$-0.610473\pi$
$751$	−14000.5	−0.680272	−0.340136	+	0.940376i	$0.610473\pi$
$752$	−13124.0	−0.636413
$753$	8620.35	0.417188
$754$	5977.12	0.288692
$755$	58114.9	2.80135
$756$	7493.94	0.360519
$757$	−2401.50	−0.115302	−0.0576512	−	0.998337i	$-0.518361\pi$
$757$	−2401.50	−0.115302	−0.0576512	+	0.998337i	$0.518361\pi$
$758$	1340.82	0.0642492
$759$	−2196.66	−0.105051
$760$	9346.62	0.446102
$761$	11700.0	0.557324	0.278662	−	0.960389i	$-0.410109\pi$
$761$	11700.0	0.557324	0.278662	+	0.960389i	$0.410109\pi$
$762$	−2160.23	−0.102700
$763$	56232.7	2.66810
$764$	−18144.3	−0.859213
$765$	18727.1	0.885072
$766$	23.5030	0.00110862
$767$	−15089.7	−0.710376
$768$	9422.98	0.442738
$769$	25345.0	1.18851	0.594254	−	0.804277i	$-0.297447\pi$
$769$	25345.0	1.18851	0.594254	+	0.804277i	$0.297447\pi$
$770$	3247.32	0.151981
$771$	−1833.31	−0.0856356
$772$	2408.52	0.112286
$773$	−13320.8	−0.619813	−0.309906	−	0.950767i	$-0.600298\pi$
$773$	−13320.8	−0.619813	−0.309906	+	0.950767i	$0.600298\pi$
$774$	−2120.97	−0.0984968
$775$	43562.9	2.01913
$776$	−10772.8	−0.498350
$777$	−35953.4	−1.66000
$778$	−1117.75	−0.0515079
$779$	−10452.0	−0.480722
$780$	21824.2	1.00184
$781$	3097.21	0.141904
$782$	3227.24	0.147578
$783$	7432.62	0.339234
$784$	54707.2	2.49213
$785$	−27483.1	−1.24957
$786$	2176.21	0.0987567
$787$	8184.82	0.370721	0.185360	−	0.982671i	$-0.440655\pi$
$787$	8184.82	0.370721	0.185360	+	0.982671i	$0.440655\pi$
$788$	−23090.9	−1.04388
$789$	953.312	0.0430149
$790$	−3555.48	−0.160124
$791$	30558.8	1.37364
$792$	−688.290	−0.0308805
$793$	3011.23	0.134845
$794$	−5141.46	−0.229803
$795$	32559.9	1.45256
$796$	998.112	0.0444436
$797$	23764.3	1.05618	0.528090	−	0.849188i	$-0.322908\pi$
$797$	23764.3	1.05618	0.528090	+	0.849188i	$0.322908\pi$
$798$	−3341.05	−0.148210
$799$	24355.9	1.07841
$800$	18912.2	0.835810
$801$	9767.01	0.430837
$802$	2755.97	0.121342
$803$	6035.35	0.265234
$804$	−2579.26	−0.113139
$805$	−44676.7	−1.95608
$806$	4088.30	0.178665
$807$	10413.2	0.454228
$808$	−7762.84	−0.337990
$809$	−25078.8	−1.08989	−0.544946	−	0.838471i	$-0.683450\pi$
$809$	−25078.8	−1.08989	−0.544946	+	0.838471i	$0.683450\pi$
$810$	−672.557	−0.0291744
$811$	2348.62	0.101691	0.0508454	−	0.998707i	$-0.483808\pi$
$811$	2348.62	0.101691	0.0508454	+	0.998707i	$0.483808\pi$
$812$	76405.5	3.30210
$813$	−17486.6	−0.754343
$814$	1630.88	0.0702241
$815$	−55129.7	−2.36946
$816$	−19640.4	−0.842586
$817$	−38156.2	−1.63392
$818$	−247.238	−0.0105678
$819$	−15795.9	−0.673937
$820$	−21628.6	−0.921103
$821$	−2730.86	−0.116087	−0.0580436	−	0.998314i	$-0.518486\pi$
$821$	−2730.86	−0.116087	−0.0580436	+	0.998314i	$0.518486\pi$
$822$	−448.536	−0.0190322
$823$	−19329.5	−0.818692	−0.409346	−	0.912379i	$-0.634243\pi$
$823$	−19329.5	−0.818692	−0.409346	+	0.912379i	$0.634243\pi$
$824$	9811.53	0.414807
$825$	7634.88	0.322197
$826$	4780.30	0.201365
$827$	−37899.5	−1.59359	−0.796793	−	0.604252i	$-0.793472\pi$
$827$	−37899.5	−1.59359	−0.796793	+	0.604252i	$0.793472\pi$
$828$	4676.80	0.196293
$829$	−31492.6	−1.31940	−0.659700	−	0.751529i	$-0.729317\pi$
$829$	−31492.6	−1.31940	−0.659700	+	0.751529i	$0.729317\pi$
$830$	2782.24	0.116353
$831$	18067.9	0.754236
$832$	−21680.9	−0.903424
$833$	−101527.	−4.22295
$834$	1680.54	0.0697750
$835$	9178.39	0.380397
$836$	−6115.40	−0.252997
$837$	5083.84	0.209944
$838$	−5400.30	−0.222613
$839$	−28706.1	−1.18122	−0.590611	−	0.806956i	$-0.701113\pi$
$839$	−28706.1	−1.18122	−0.590611	+	0.806956i	$0.701113\pi$
$840$	−13998.8	−0.575005
$841$	51391.3	2.10715
$842$	3497.83	0.143163
$843$	−22860.7	−0.934004
$844$	4849.50	0.197780
$845$	−4527.76	−0.184331
$846$	−874.708	−0.0355474
$847$	−4302.03	−0.174521
$848$	−34147.8	−1.38283
$849$	11715.3	0.473579
$850$	−11216.9	−0.452630
$851$	−22437.7	−0.903825
$852$	−6594.14	−0.265154
$853$	−7840.18	−0.314704	−0.157352	−	0.987543i	$-0.550296\pi$
$853$	−7840.18	−0.314704	−0.157352	+	0.987543i	$0.550296\pi$
$854$	−953.933	−0.0382235
$855$	−12099.3	−0.483962
$856$	6844.14	0.273280
$857$	−45292.4	−1.80532	−0.902660	−	0.430354i	$-0.858389\pi$
$857$	−45292.4	−1.80532	−0.902660	+	0.430354i	$0.858389\pi$
$858$	716.520	0.0285100
$859$	20487.9	0.813780	0.406890	−	0.913477i	$-0.366613\pi$
$859$	20487.9	0.813780	0.406890	+	0.913477i	$0.366613\pi$
$860$	−78957.6	−3.13074
$861$	15654.4	0.619628
$862$	535.683	0.0211664
$863$	−11989.2	−0.472907	−0.236453	−	0.971643i	$-0.575985\pi$
$863$	−11989.2	−0.472907	−0.236453	+	0.971643i	$0.575985\pi$
$864$	2207.08	0.0869056
$865$	−22941.8	−0.901784
$866$	1842.28	0.0722902
$867$	21710.2	0.850425
$868$	52260.7	2.04360
$869$	4710.27	0.183872
$870$	−6857.15	−0.267217
$871$	5436.63	0.211496
$872$	10996.1	0.427034
$873$	13945.5	0.540644
$874$	−2085.08	−0.0806965
$875$	71385.6	2.75803
$876$	−12849.6	−0.495602
$877$	14961.1	0.576056	0.288028	−	0.957622i	$-0.407000\pi$
$877$	14961.1	0.576056	0.288028	+	0.957622i	$0.407000\pi$
$878$	−7044.90	−0.270790
$879$	1773.24	0.0680430
$880$	−12333.4	−0.472452
$881$	−40856.0	−1.56240	−0.781200	−	0.624280i	$-0.785392\pi$
$881$	−40856.0	−1.56240	−0.781200	+	0.624280i	$0.785392\pi$
$882$	3646.21	0.139200
$883$	−20593.8	−0.784865	−0.392432	−	0.919781i	$-0.628366\pi$
$883$	−20593.8	−0.784865	−0.392432	+	0.919781i	$0.628366\pi$
$884$	42477.2	1.61614
$885$	17311.4	0.657533
$886$	−6688.51	−0.253617
$887$	−28515.4	−1.07943	−0.539715	−	0.841848i	$-0.681468\pi$
$887$	−28515.4	−1.07943	−0.539715	+	0.841848i	$0.681468\pi$
$888$	−7030.53	−0.265686
$889$	58206.0	2.19591
$890$	−9010.80	−0.339374
$891$	891.000	0.0335013
$892$	6713.87	0.252015
$893$	−15736.0	−0.589682
$894$	602.741	0.0225489
$895$	8881.10	0.331690
$896$	30118.8	1.12299
$897$	−9857.89	−0.366940
$898$	−7274.02	−0.270309
$899$	51833.0	1.92295
$900$	−16255.1	−0.602040
$901$	63372.6	2.34323
$902$	−710.099	−0.0262125
$903$	57148.0	2.10605
$904$	5975.64	0.219853
$905$	−44314.8	−1.62771
$906$	−4062.23	−0.148961
$907$	−23052.9	−0.843944	−0.421972	−	0.906609i	$-0.638662\pi$
$907$	−23052.9	−0.843944	−0.421972	+	0.906609i	$0.638662\pi$
$908$	40237.4	1.47062
$909$	10049.1	0.366675
$910$	14572.9	0.530866
$911$	−16942.7	−0.616178	−0.308089	−	0.951358i	$-0.599689\pi$
$911$	−16942.7	−0.616178	−0.308089	+	0.951358i	$0.599689\pi$
$912$	12689.4	0.460731
$913$	−3685.90	−0.133610
$914$	5460.70	0.197619
$915$	−3454.58	−0.124814
$916$	37885.4	1.36656
$917$	−58636.4	−2.11161
$918$	−1309.02	−0.0470634
$919$	43284.8	1.55368	0.776840	−	0.629698i	$-0.216821\pi$
$919$	43284.8	1.55368	0.776840	+	0.629698i	$0.216821\pi$
$920$	−8736.33	−0.313074
$921$	−26416.7	−0.945125
$922$	8191.22	0.292585
$923$	13899.3	0.495667
$924$	9159.26	0.326101
$925$	77986.3	2.77208
$926$	−2695.96	−0.0956746
$927$	−12701.1	−0.450011
$928$	22502.6	0.795995
$929$	−944.718	−0.0333640	−0.0166820	−	0.999861i	$-0.505310\pi$
$929$	−944.718	−0.0333640	−0.0166820	+	0.999861i	$0.505310\pi$
$930$	−4690.23	−0.165375
$931$	65595.4	2.30913
$932$	40105.7	1.40956
$933$	1686.07	0.0591636
$934$	775.489	0.0271679
$935$	22888.7	0.800577
$936$	−3088.83	−0.107865
$937$	−20433.3	−0.712407	−0.356204	−	0.934408i	$-0.615929\pi$
$937$	−20433.3	−0.712407	−0.356204	+	0.934408i	$0.615929\pi$
$938$	−1722.28	−0.0599514
$939$	2636.20	0.0916177
$940$	−32563.0	−1.12988
$941$	−33442.1	−1.15854	−0.579268	−	0.815137i	$-0.696661\pi$
$941$	−33442.1	−1.15854	−0.579268	+	0.815137i	$0.696661\pi$
$942$	1921.07	0.0664457
$943$	9769.55	0.337371
$944$	−18155.7	−0.625970
$945$	18121.6	0.623805
$946$	−2592.29	−0.0890937
$947$	−10696.6	−0.367048	−0.183524	−	0.983015i	$-0.558750\pi$
$947$	−10696.6	−0.367048	−0.183524	+	0.983015i	$0.558750\pi$
$948$	−10028.4	−0.343574
$949$	27084.7	0.926456
$950$	7247.06	0.247501
$951$	−2670.33	−0.0910530
$952$	−27246.4	−0.927583
$953$	13667.1	0.464553	0.232277	−	0.972650i	$-0.425382\pi$
$953$	13667.1	0.464553	0.232277	+	0.972650i	$0.425382\pi$
$954$	−2275.94	−0.0772391
$955$	−43876.0	−1.48670
$956$	−32768.9	−1.10860
$957$	9084.31	0.306849
$958$	−5381.64	−0.181496
$959$	12085.5	0.406946
$960$	24873.0	0.836221
$961$	5662.33	0.190068
$962$	7318.87	0.245291
$963$	−8859.82	−0.296473
$964$	−44985.6	−1.50300
$965$	5824.19	0.194287
$966$	3122.90	0.104014
$967$	55402.8	1.84243	0.921217	−	0.389049i	$-0.127196\pi$
$967$	55402.8	1.84243	0.921217	+	0.389049i	$0.127196\pi$
$968$	−841.244	−0.0279324
$969$	−23549.3	−0.780716
$970$	−12865.7	−0.425870
$971$	48178.0	1.59228	0.796140	−	0.605112i	$-0.206872\pi$
$971$	48178.0	1.59228	0.796140	+	0.605112i	$0.206872\pi$
$972$	−1896.99	−0.0625987
$973$	−45281.0	−1.49193
$974$	8407.08	0.276571
$975$	34262.9	1.12543
$976$	3623.05	0.118823
$977$	−24723.6	−0.809597	−0.404799	−	0.914406i	$-0.632658\pi$
$977$	−24723.6	−0.809597	−0.404799	+	0.914406i	$0.632658\pi$
$978$	3853.56	0.125995
$979$	11937.5	0.389707
$980$	135738.	4.42449
$981$	−14234.5	−0.463276
$982$	−1157.55	−0.0376159
$983$	17286.3	0.560883	0.280441	−	0.959871i	$-0.409519\pi$
$983$	17286.3	0.560883	0.280441	+	0.959871i	$0.409519\pi$
$984$	3061.15	0.0991725
$985$	−55837.5	−1.80622
$986$	−13346.3	−0.431068
$987$	23568.4	0.760072
$988$	−27443.9	−0.883713
$989$	35664.8	1.14669
$990$	−822.014	−0.0263892
$991$	−21473.0	−0.688308	−0.344154	−	0.938913i	$-0.611834\pi$
$991$	−21473.0	−0.688308	−0.344154	+	0.938913i	$0.611834\pi$
$992$	15391.6	0.492624
$993$	−8907.90	−0.284676
$994$	−4403.18	−0.140503
$995$	2413.60	0.0769008
$996$	7847.49	0.249656
$997$	23027.4	0.731478	0.365739	−	0.930717i	$-0.380816\pi$
$997$	23027.4	0.731478	0.365739	+	0.930717i	$0.380816\pi$
$998$	9621.84	0.305184
$999$	9101.10	0.288234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.a.1.20	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.a.1.20	✓	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q+0.439845 q^{2} +3.00000 q^{3} -7.80654 q^{4} -18.8775 q^{5} +1.31954 q^{6} -35.5540 q^{7} -6.95243 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.439845 q^{2} +3.00000 q^{3} -7.80654 q^{4} -18.8775 q^{5} +1.31954 q^{6} -35.5540 q^{7} -6.95243 q^{8} +9.00000 q^{9} -8.30317 q^{10} +11.0000 q^{11} -23.4196 q^{12} +49.3645 q^{13} -15.6382 q^{14} -56.6325 q^{15} +59.3943 q^{16} -110.226 q^{17} +3.95861 q^{18} +71.2154 q^{19} +147.368 q^{20} -106.662 q^{21} +4.83830 q^{22} -66.5654 q^{23} -20.8573 q^{24} +231.360 q^{25} +21.7127 q^{26} +27.0000 q^{27} +277.553 q^{28} +275.282 q^{29} -24.9095 q^{30} +188.291 q^{31} +81.7437 q^{32} +33.0000 q^{33} -48.4823 q^{34} +671.170 q^{35} -70.2588 q^{36} +337.078 q^{37} +31.3237 q^{38} +148.093 q^{39} +131.244 q^{40} -146.766 q^{41} -46.9147 q^{42} -535.786 q^{43} -85.8719 q^{44} -169.897 q^{45} -29.2785 q^{46} -220.964 q^{47} +178.183 q^{48} +921.085 q^{49} +101.763 q^{50} -330.678 q^{51} -385.365 q^{52} -574.934 q^{53} +11.8758 q^{54} -207.652 q^{55} +247.186 q^{56} +213.646 q^{57} +121.082 q^{58} -305.680 q^{59} +442.104 q^{60} +61.0000 q^{61} +82.8187 q^{62} -319.986 q^{63} -439.200 q^{64} -931.877 q^{65} +14.5149 q^{66} +110.133 q^{67} +860.482 q^{68} -199.696 q^{69} +295.211 q^{70} +281.565 q^{71} -62.5718 q^{72} +548.668 q^{73} +148.262 q^{74} +694.080 q^{75} -555.945 q^{76} -391.094 q^{77} +65.1381 q^{78} +428.207 q^{79} -1121.22 q^{80} +81.0000 q^{81} -64.5544 q^{82} -335.082 q^{83} +832.660 q^{84} +2080.79 q^{85} -235.663 q^{86} +825.847 q^{87} -76.4767 q^{88} +1085.22 q^{89} -74.7286 q^{90} -1755.10 q^{91} +519.645 q^{92} +564.872 q^{93} -97.1898 q^{94} -1344.37 q^{95} +245.231 q^{96} +1549.50 q^{97} +405.135 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9} - 161 q^{10} + 396 q^{11} + 438 q^{12} - 233 q^{13} - 264 q^{14} - 195 q^{15} + 574 q^{16} - 556 q^{17} - 126 q^{18} - 615 q^{19} - 136 q^{20} - 315 q^{21} - 154 q^{22} - 457 q^{23} - 567 q^{24} + 863 q^{25} + 115 q^{26} + 972 q^{27} - 424 q^{28} - 754 q^{29} - 483 q^{30} - 508 q^{31} - 1511 q^{32} + 1188 q^{33} - 860 q^{34} - 826 q^{35} + 1314 q^{36} - 412 q^{37} - 599 q^{38} - 699 q^{39} - 2791 q^{40} - 2066 q^{41} - 792 q^{42} - 2063 q^{43} + 1606 q^{44} - 585 q^{45} - 787 q^{46} - 1815 q^{47} + 1722 q^{48} + 2825 q^{49} + 808 q^{50} - 1668 q^{51} - 2882 q^{52} - 759 q^{53} - 378 q^{54} - 715 q^{55} - 1749 q^{56} - 1845 q^{57} - 335 q^{58} - 2337 q^{59} - 408 q^{60} + 2196 q^{61} - 1689 q^{62} - 945 q^{63} + 4723 q^{64} - 3550 q^{65} - 462 q^{66} - 1331 q^{67} - 6166 q^{68} - 1371 q^{69} - 1750 q^{70} - 361 q^{71} - 1701 q^{72} - 4627 q^{73} - 3394 q^{74} + 2589 q^{75} - 7214 q^{76} - 1155 q^{77} + 345 q^{78} - 2583 q^{79} - 2643 q^{80} + 2916 q^{81} + 1090 q^{82} - 6123 q^{83} - 1272 q^{84} + 295 q^{85} + 613 q^{86} - 2262 q^{87} - 2079 q^{88} - 2485 q^{89} - 1449 q^{90} - 3156 q^{91} - 6291 q^{92} - 1524 q^{93} - 1744 q^{94} - 5572 q^{95} - 4533 q^{96} - 2558 q^{97} - 2314 q^{98} + 3564 q^{99}+O(q^{100}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9 - 161 * q^10 + 396 * q^11 + 438 * q^12 - 233 * q^13 - 264 * q^14 - 195 * q^15 + 574 * q^16 - 556 * q^17 - 126 * q^18 - 615 * q^19 - 136 * q^20 - 315 * q^21 - 154 * q^22 - 457 * q^23 - 567 * q^24 + 863 * q^25 + 115 * q^26 + 972 * q^27 - 424 * q^28 - 754 * q^29 - 483 * q^30 - 508 * q^31 - 1511 * q^32 + 1188 * q^33 - 860 * q^34 - 826 * q^35 + 1314 * q^36 - 412 * q^37 - 599 * q^38 - 699 * q^39 - 2791 * q^40 - 2066 * q^41 - 792 * q^42 - 2063 * q^43 + 1606 * q^44 - 585 * q^45 - 787 * q^46 - 1815 * q^47 + 1722 * q^48 + 2825 * q^49 + 808 * q^50 - 1668 * q^51 - 2882 * q^52 - 759 * q^53 - 378 * q^54 - 715 * q^55 - 1749 * q^56 - 1845 * q^57 - 335 * q^58 - 2337 * q^59 - 408 * q^60 + 2196 * q^61 - 1689 * q^62 - 945 * q^63 + 4723 * q^64 - 3550 * q^65 - 462 * q^66 - 1331 * q^67 - 6166 * q^68 - 1371 * q^69 - 1750 * q^70 - 361 * q^71 - 1701 * q^72 - 4627 * q^73 - 3394 * q^74 + 2589 * q^75 - 7214 * q^76 - 1155 * q^77 + 345 * q^78 - 2583 * q^79 - 2643 * q^80 + 2916 * q^81 + 1090 * q^82 - 6123 * q^83 - 1272 * q^84 + 295 * q^85 + 613 * q^86 - 2262 * q^87 - 2079 * q^88 - 2485 * q^89 - 1449 * q^90 - 3156 * q^91 - 6291 * q^92 - 1524 * q^93 - 1744 * q^94 - 5572 * q^95 - 4533 * q^96 - 2558 * q^97 - 2314 * q^98 + 3564 * q^99

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