LMFDB - Embedded newform 2013.4.a.h.1.37

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:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.37
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)

$f(q)$	$=$	$q+5.32917 q^{2} +3.00000 q^{3} +20.4001 q^{4} -19.7812 q^{5} +15.9875 q^{6} +5.38201 q^{7} +66.0823 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+5.32917 q^{2} +3.00000 q^{3} +20.4001 q^{4} -19.7812 q^{5} +15.9875 q^{6} +5.38201 q^{7} +66.0823 q^{8} +9.00000 q^{9} -105.417 q^{10} -11.0000 q^{11} +61.2003 q^{12} -16.9545 q^{13} +28.6817 q^{14} -59.3435 q^{15} +188.963 q^{16} +20.3181 q^{17} +47.9626 q^{18} +90.6060 q^{19} -403.538 q^{20} +16.1460 q^{21} -58.6209 q^{22} -41.7664 q^{23} +198.247 q^{24} +266.295 q^{25} -90.3537 q^{26} +27.0000 q^{27} +109.794 q^{28} +103.403 q^{29} -316.252 q^{30} +122.004 q^{31} +478.360 q^{32} -33.0000 q^{33} +108.279 q^{34} -106.462 q^{35} +183.601 q^{36} +424.911 q^{37} +482.855 q^{38} -50.8636 q^{39} -1307.19 q^{40} +435.959 q^{41} +86.0450 q^{42} -211.345 q^{43} -224.401 q^{44} -178.031 q^{45} -222.580 q^{46} +72.6837 q^{47} +566.890 q^{48} -314.034 q^{49} +1419.13 q^{50} +60.9544 q^{51} -345.874 q^{52} +172.808 q^{53} +143.888 q^{54} +217.593 q^{55} +355.656 q^{56} +271.818 q^{57} +551.054 q^{58} +495.894 q^{59} -1210.61 q^{60} +61.0000 q^{61} +650.178 q^{62} +48.4381 q^{63} +1037.56 q^{64} +335.381 q^{65} -175.863 q^{66} -237.894 q^{67} +414.492 q^{68} -125.299 q^{69} -567.357 q^{70} +571.601 q^{71} +594.741 q^{72} -444.724 q^{73} +2264.43 q^{74} +798.884 q^{75} +1848.37 q^{76} -59.2021 q^{77} -271.061 q^{78} -544.122 q^{79} -3737.91 q^{80} +81.0000 q^{81} +2323.30 q^{82} +969.339 q^{83} +329.381 q^{84} -401.916 q^{85} -1126.29 q^{86} +310.210 q^{87} -726.905 q^{88} +621.256 q^{89} -948.756 q^{90} -91.2495 q^{91} -852.038 q^{92} +366.011 q^{93} +387.344 q^{94} -1792.29 q^{95} +1435.08 q^{96} -1381.72 q^{97} -1673.54 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * 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 $

$2$	5.32917	1.88415	0.942074	−	0.335406i	$-0.108873\pi$
$2$	5.32917	1.88415	0.942074	+	0.335406i	$0.108873\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	20.4001	2.55001
$5$	−19.7812	−1.76928	−0.884641	−	0.466273i	$-0.845596\pi$
$5$	−19.7812	−1.76928	−0.884641	+	0.466273i	$0.845596\pi$
$6$	15.9875	1.08781
$7$	5.38201	0.290601	0.145301	−	0.989388i	$-0.453585\pi$
$7$	5.38201	0.290601	0.145301	+	0.989388i	$0.453585\pi$
$8$	66.0823	2.92045
$9$	9.00000	0.333333
$10$	−105.417	−3.33359
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	61.2003	1.47225
$13$	−16.9545	−0.361719	−0.180859	−	0.983509i	$-0.557888\pi$
$13$	−16.9545	−0.361719	−0.180859	+	0.983509i	$0.557888\pi$
$14$	28.6817	0.547536
$15$	−59.3435	−1.02150
$16$	188.963	2.95255
$17$	20.3181	0.289875	0.144937	−	0.989441i	$-0.453702\pi$
$17$	20.3181	0.289875	0.144937	+	0.989441i	$0.453702\pi$
$18$	47.9626	0.628049
$19$	90.6060	1.09402	0.547012	−	0.837125i	$-0.315765\pi$
$19$	90.6060	1.09402	0.547012	+	0.837125i	$0.315765\pi$
$20$	−403.538	−4.51169
$21$	16.1460	0.167779
$22$	−58.6209	−0.568092
$23$	−41.7664	−0.378647	−0.189324	−	0.981915i	$-0.560630\pi$
$23$	−41.7664	−0.378647	−0.189324	+	0.981915i	$0.560630\pi$
$24$	198.247	1.68612
$25$	266.295	2.13036
$26$	−90.3537	−0.681531
$27$	27.0000	0.192450
$28$	109.794	0.741037
$29$	103.403	0.662121	0.331060	−	0.943610i	$-0.392594\pi$
$29$	103.403	0.662121	0.331060	+	0.943610i	$0.392594\pi$
$30$	−316.252	−1.92465
$31$	122.004	0.706855	0.353427	−	0.935462i	$-0.385016\pi$
$31$	122.004	0.706855	0.353427	+	0.935462i	$0.385016\pi$
$32$	478.360	2.64259
$33$	−33.0000	−0.174078
$34$	108.279	0.546167
$35$	−106.462	−0.514156
$36$	183.601	0.850004
$37$	424.911	1.88797	0.943987	−	0.329984i	$-0.107043\pi$
$37$	424.911	1.88797	0.943987	+	0.329984i	$0.107043\pi$
$38$	482.855	2.06130
$39$	−50.8636	−0.208838
$40$	−1307.19	−5.16710
$41$	435.959	1.66062	0.830310	−	0.557302i	$-0.188163\pi$
$41$	435.959	1.66062	0.830310	+	0.557302i	$0.188163\pi$
$42$	86.0450	0.316120
$43$	−211.345	−0.749529	−0.374765	−	0.927120i	$-0.622276\pi$
$43$	−211.345	−0.749529	−0.374765	+	0.927120i	$0.622276\pi$
$44$	−224.401	−0.768858
$45$	−178.031	−0.589761
$46$	−222.580	−0.713427
$47$	72.6837	0.225575	0.112787	−	0.993619i	$-0.464022\pi$
$47$	72.6837	0.225575	0.112787	+	0.993619i	$0.464022\pi$
$48$	566.890	1.70466
$49$	−314.034	−0.915551
$50$	1419.13	4.01391
$51$	60.9544	0.167359
$52$	−345.874	−0.922387
$53$	172.808	0.447869	0.223934	−	0.974604i	$-0.428110\pi$
$53$	172.808	0.447869	0.223934	+	0.974604i	$0.428110\pi$
$54$	143.888	0.362604
$55$	217.593	0.533459
$56$	355.656	0.848687
$57$	271.818	0.631635
$58$	551.054	1.24753
$59$	495.894	1.09424	0.547118	−	0.837056i	$-0.315725\pi$
$59$	495.894	1.09424	0.547118	+	0.837056i	$0.315725\pi$
$60$	−1210.61	−2.60483
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	650.178	1.33182
$63$	48.4381	0.0968671
$64$	1037.56	2.02648
$65$	335.381	0.639982
$66$	−175.863	−0.327988
$67$	−237.894	−0.433782	−0.216891	−	0.976196i	$-0.569592\pi$
$67$	−237.894	−0.433782	−0.216891	+	0.976196i	$0.569592\pi$
$68$	414.492	0.739184
$69$	−125.299	−0.218612
$70$	−567.357	−0.968745
$71$	571.601	0.955445	0.477722	−	0.878511i	$-0.341463\pi$
$71$	571.601	0.955445	0.477722	+	0.878511i	$0.341463\pi$
$72$	594.741	0.973484
$73$	−444.724	−0.713027	−0.356514	−	0.934290i	$-0.616035\pi$
$73$	−444.724	−0.713027	−0.356514	+	0.934290i	$0.616035\pi$
$74$	2264.43	3.55722
$75$	798.884	1.22996
$76$	1848.37	2.78977
$77$	−59.2021	−0.0876196
$78$	−271.061	−0.393482
$79$	−544.122	−0.774918	−0.387459	−	0.921887i	$-0.626647\pi$
$79$	−544.122	−0.774918	−0.387459	+	0.921887i	$0.626647\pi$
$80$	−3737.91	−5.22389
$81$	81.0000	0.111111
$82$	2323.30	3.12885
$83$	969.339	1.28191	0.640956	−	0.767577i	$-0.278538\pi$
$83$	969.339	1.28191	0.640956	+	0.767577i	$0.278538\pi$
$84$	329.381	0.427838
$85$	−401.916	−0.512870
$86$	−1126.29	−1.41222
$87$	310.210	0.382276
$88$	−726.905	−0.880549
$89$	621.256	0.739922	0.369961	−	0.929047i	$-0.379371\pi$
$89$	621.256	0.739922	0.369961	+	0.929047i	$0.379371\pi$
$90$	−948.756	−1.11120
$91$	−91.2495	−0.105116
$92$	−852.038	−0.965555
$93$	366.011	0.408103
$94$	387.344	0.425016
$95$	−1792.29	−1.93564
$96$	1435.08	1.52570
$97$	−1381.72	−1.44632	−0.723158	−	0.690683i	$-0.757310\pi$
$97$	−1381.72	−1.44632	−0.723158	+	0.690683i	$0.757310\pi$
$98$	−1673.54	−1.72503
$99$	−99.0000	−0.100504
$100$	5432.44	5.43244
$101$	−581.724	−0.573106	−0.286553	−	0.958064i	$-0.592509\pi$
$101$	−581.724	−0.573106	−0.286553	+	0.958064i	$0.592509\pi$
$102$	324.836	0.315329
$103$	1028.37	0.983772	0.491886	−	0.870660i	$-0.336308\pi$
$103$	1028.37	0.983772	0.491886	+	0.870660i	$0.336308\pi$
$104$	−1120.39	−1.05638
$105$	−319.387	−0.296848
$106$	920.926	0.843851
$107$	405.157	0.366056	0.183028	−	0.983108i	$-0.441410\pi$
$107$	405.157	0.366056	0.183028	+	0.983108i	$0.441410\pi$
$108$	550.803	0.490750
$109$	−1290.37	−1.13390	−0.566948	−	0.823754i	$-0.691876\pi$
$109$	−1290.37	−1.13390	−0.566948	+	0.823754i	$0.691876\pi$
$110$	1159.59	1.00511
$111$	1274.73	1.09002
$112$	1017.00	0.858015
$113$	−435.937	−0.362916	−0.181458	−	0.983399i	$-0.558082\pi$
$113$	−435.937	−0.362916	−0.181458	+	0.983399i	$0.558082\pi$
$114$	1448.57	1.19009
$115$	826.188	0.669934
$116$	2109.44	1.68842
$117$	−152.591	−0.120573
$118$	2642.70	2.06170
$119$	109.352	0.0842379
$120$	−3921.56	−2.98323
$121$	121.000	0.0909091
$122$	325.080	0.241240
$123$	1307.88	0.958759
$124$	2488.89	1.80249
$125$	−2794.98	−1.99992
$126$	258.135	0.182512
$127$	−951.620	−0.664903	−0.332451	−	0.943120i	$-0.607876\pi$
$127$	−951.620	−0.664903	−0.332451	+	0.943120i	$0.607876\pi$
$128$	1702.44	1.17559
$129$	−634.034	−0.432741
$130$	1787.30	1.20582
$131$	208.543	0.139088	0.0695440	−	0.997579i	$-0.477846\pi$
$131$	208.543	0.139088	0.0695440	+	0.997579i	$0.477846\pi$
$132$	−673.203	−0.443900
$133$	487.642	0.317925
$134$	−1267.78	−0.817308
$135$	−534.092	−0.340498
$136$	1342.67	0.846565
$137$	2138.95	1.33389	0.666946	−	0.745106i	$-0.267601\pi$
$137$	2138.95	1.33389	0.666946	+	0.745106i	$0.267601\pi$
$138$	−667.741	−0.411898
$139$	20.8115	0.0126993	0.00634966	−	0.999980i	$-0.497979\pi$
$139$	20.8115	0.0126993	0.00634966	+	0.999980i	$0.497979\pi$
$140$	−2171.85	−1.31110
$141$	218.051	0.130236
$142$	3046.16	1.80020
$143$	186.500	0.109062
$144$	1700.67	0.984183
$145$	−2045.44	−1.17148
$146$	−2370.01	−1.34345
$147$	−942.102	−0.528594
$148$	8668.23	4.81435
$149$	−57.5280	−0.0316300	−0.0158150	−	0.999875i	$-0.505034\pi$
$149$	−57.5280	−0.0316300	−0.0158150	+	0.999875i	$0.505034\pi$
$150$	4257.39	2.31743
$151$	−2190.16	−1.18035	−0.590173	−	0.807277i	$-0.700941\pi$
$151$	−2190.16	−1.18035	−0.590173	+	0.807277i	$0.700941\pi$
$152$	5987.45	3.19504
$153$	182.863	0.0966249
$154$	−315.498	−0.165088
$155$	−2413.37	−1.25062
$156$	−1037.62	−0.532540
$157$	1158.35	0.588832	0.294416	−	0.955677i	$-0.404875\pi$
$157$	1158.35	0.588832	0.294416	+	0.955677i	$0.404875\pi$
$158$	−2899.72	−1.46006
$159$	518.425	0.258577
$160$	−9462.52	−4.67548
$161$	−224.787	−0.110035
$162$	431.663	0.209350
$163$	−3797.70	−1.82490	−0.912450	−	0.409188i	$-0.865812\pi$
$163$	−3797.70	−1.82490	−0.912450	+	0.409188i	$0.865812\pi$
$164$	8893.61	4.23460
$165$	652.779	0.307992
$166$	5165.78	2.41531
$167$	2089.60	0.968252	0.484126	−	0.874998i	$-0.339138\pi$
$167$	2089.60	0.968252	0.484126	+	0.874998i	$0.339138\pi$
$168$	1066.97	0.489990
$169$	−1909.54	−0.869160
$170$	−2141.88	−0.966323
$171$	815.454	0.364674
$172$	−4311.45	−1.91131
$173$	−1494.58	−0.656825	−0.328413	−	0.944534i	$-0.606514\pi$
$173$	−1494.58	−0.656825	−0.328413	+	0.944534i	$0.606514\pi$
$174$	1653.16	0.720263
$175$	1433.20	0.619085
$176$	−2078.60	−0.890227
$177$	1487.68	0.631757
$178$	3310.78	1.39412
$179$	1445.48	0.603577	0.301788	−	0.953375i	$-0.402416\pi$
$179$	1445.48	0.603577	0.301788	+	0.953375i	$0.402416\pi$
$180$	−3631.84	−1.50390
$181$	2877.22	1.18156	0.590779	−	0.806834i	$-0.298821\pi$
$181$	2877.22	1.18156	0.590779	+	0.806834i	$0.298821\pi$
$182$	−486.285	−0.198054
$183$	183.000	0.0739221
$184$	−2760.02	−1.10582
$185$	−8405.25	−3.34036
$186$	1950.54	0.768926
$187$	−223.499	−0.0874005
$188$	1482.75	0.575218
$189$	145.314	0.0559262
$190$	−9551.44	−3.64702
$191$	−812.123	−0.307660	−0.153830	−	0.988097i	$-0.549161\pi$
$191$	−812.123	−0.307660	−0.153830	+	0.988097i	$0.549161\pi$
$192$	3112.67	1.16999
$193$	−1491.16	−0.556144	−0.278072	−	0.960560i	$-0.589695\pi$
$193$	−1491.16	−0.556144	−0.278072	+	0.960560i	$0.589695\pi$
$194$	−7363.44	−2.72507
$195$	1006.14	0.369494
$196$	−6406.32	−2.33467
$197$	−4553.97	−1.64699	−0.823495	−	0.567323i	$-0.807979\pi$
$197$	−4553.97	−1.64699	−0.823495	+	0.567323i	$0.807979\pi$
$198$	−527.588	−0.189364
$199$	4371.11	1.55708	0.778541	−	0.627593i	$-0.215960\pi$
$199$	4371.11	1.55708	0.778541	+	0.627593i	$0.215960\pi$
$200$	17597.4	6.22161
$201$	−713.682	−0.250444
$202$	−3100.11	−1.07982
$203$	556.517	0.192413
$204$	1243.48	0.426768
$205$	−8623.79	−2.93810
$206$	5480.38	1.85357
$207$	−375.897	−0.126216
$208$	−3203.78	−1.06799
$209$	−996.666	−0.329860
$210$	−1702.07	−0.559305
$211$	1161.54	0.378974	0.189487	−	0.981883i	$-0.439318\pi$
$211$	1161.54	0.378974	0.189487	+	0.981883i	$0.439318\pi$
$212$	3525.31	1.14207
$213$	1714.80	0.551626
$214$	2159.15	0.689704
$215$	4180.64	1.32613
$216$	1784.22	0.562041
$217$	656.625	0.205413
$218$	−6876.59	−2.13643
$219$	−1334.17	−0.411666
$220$	4438.92	1.36033
$221$	−344.484	−0.104853
$222$	6793.28	2.05376
$223$	−5017.44	−1.50669	−0.753347	−	0.657623i	$-0.771562\pi$
$223$	−5017.44	−1.50669	−0.753347	+	0.657623i	$0.771562\pi$
$224$	2574.54	0.767940
$225$	2396.65	0.710119
$226$	−2323.18	−0.683787
$227$	4462.17	1.30469	0.652345	−	0.757922i	$-0.273785\pi$
$227$	4462.17	1.30469	0.652345	+	0.757922i	$0.273785\pi$
$228$	5545.11	1.61068
$229$	−4627.91	−1.33546	−0.667731	−	0.744403i	$-0.732734\pi$
$229$	−4627.91	−1.33546	−0.667731	+	0.744403i	$0.732734\pi$
$230$	4402.90	1.26225
$231$	−177.606	−0.0505872
$232$	6833.12	1.93369
$233$	4562.66	1.28287	0.641437	−	0.767176i	$-0.278339\pi$
$233$	4562.66	1.28287	0.641437	+	0.767176i	$0.278339\pi$
$234$	−813.183	−0.227177
$235$	−1437.77	−0.399105
$236$	10116.3	2.79031
$237$	−1632.37	−0.447399
$238$	582.758	0.158717
$239$	2181.57	0.590435	0.295218	−	0.955430i	$-0.404608\pi$
$239$	2181.57	0.590435	0.295218	+	0.955430i	$0.404608\pi$
$240$	−11213.7	−3.01602
$241$	2968.89	0.793541	0.396770	−	0.917918i	$-0.370131\pi$
$241$	2968.89	0.793541	0.396770	+	0.917918i	$0.370131\pi$
$242$	644.830	0.171286
$243$	243.000	0.0641500
$244$	1244.41	0.326496
$245$	6211.96	1.61987
$246$	6969.91	1.80644
$247$	−1536.18	−0.395729
$248$	8062.28	2.06433
$249$	2908.02	0.740113
$250$	−14894.9	−3.76815
$251$	2481.16	0.623943	0.311972	−	0.950091i	$-0.399011\pi$
$251$	2481.16	0.623943	0.311972	+	0.950091i	$0.399011\pi$
$252$	988.142	0.247012
$253$	459.430	0.114166
$254$	−5071.35	−1.25278
$255$	−1205.75	−0.296106
$256$	772.154	0.188514
$257$	1771.99	0.430092	0.215046	−	0.976604i	$-0.431010\pi$
$257$	1771.99	0.430092	0.215046	+	0.976604i	$0.431010\pi$
$258$	−3378.88	−0.815348
$259$	2286.88	0.548647
$260$	6841.80	1.63196
$261$	930.629	0.220707
$262$	1111.36	0.262062
$263$	−2389.65	−0.560273	−0.280137	−	0.959960i	$-0.590380\pi$
$263$	−2389.65	−0.560273	−0.280137	+	0.959960i	$0.590380\pi$
$264$	−2180.72	−0.508385
$265$	−3418.35	−0.792406
$266$	2598.73	0.599017
$267$	1863.77	0.427194
$268$	−4853.06	−1.10615
$269$	2805.65	0.635923	0.317961	−	0.948104i	$-0.397002\pi$
$269$	2805.65	0.635923	0.317961	+	0.948104i	$0.397002\pi$
$270$	−2846.27	−0.641549
$271$	−1049.02	−0.235141	−0.117571	−	0.993065i	$-0.537511\pi$
$271$	−1049.02	−0.235141	−0.117571	+	0.993065i	$0.537511\pi$
$272$	3839.38	0.855869
$273$	−273.749	−0.0606887
$274$	11398.9	2.51325
$275$	−2929.24	−0.642327
$276$	−2556.11	−0.557464
$277$	1808.97	0.392385	0.196193	−	0.980565i	$-0.437142\pi$
$277$	1808.97	0.392385	0.196193	+	0.980565i	$0.437142\pi$
$278$	110.908	0.0239274
$279$	1098.03	0.235618
$280$	−7035.28	−1.50157
$281$	1585.43	0.336579	0.168290	−	0.985738i	$-0.446176\pi$
$281$	1585.43	0.336579	0.168290	+	0.985738i	$0.446176\pi$
$282$	1162.03	0.245383
$283$	1533.41	0.322091	0.161046	−	0.986947i	$-0.448513\pi$
$283$	1533.41	0.322091	0.161046	+	0.986947i	$0.448513\pi$
$284$	11660.7	2.43640
$285$	−5376.88	−1.11754
$286$	993.891	0.205489
$287$	2346.34	0.482578
$288$	4305.24	0.880863
$289$	−4500.17	−0.915973
$290$	−10900.5	−2.20724
$291$	−4145.17	−0.835031
$292$	−9072.41	−1.81823
$293$	4640.84	0.925326	0.462663	−	0.886534i	$-0.346894\pi$
$293$	4640.84	0.925326	0.462663	+	0.886534i	$0.346894\pi$
$294$	−5020.63	−0.995948
$295$	−9809.36	−1.93601
$296$	28079.1	5.51373
$297$	−297.000	−0.0580259
$298$	−306.577	−0.0595957
$299$	708.129	0.136964
$300$	16297.3	3.13642
$301$	−1137.46	−0.217814
$302$	−11671.7	−2.22395
$303$	−1745.17	−0.330883
$304$	17121.2	3.23016
$305$	−1206.65	−0.226533
$306$	974.509	0.182056
$307$	−6875.77	−1.27824	−0.639122	−	0.769106i	$-0.720702\pi$
$307$	−6875.77	−1.27824	−0.639122	+	0.769106i	$0.720702\pi$
$308$	−1207.73	−0.223431
$309$	3085.12	0.567981
$310$	−12861.3	−2.35636
$311$	−2726.38	−0.497103	−0.248551	−	0.968619i	$-0.579955\pi$
$311$	−2726.38	−0.497103	−0.248551	+	0.968619i	$0.579955\pi$
$312$	−3361.18	−0.609902
$313$	10505.0	1.89705	0.948527	−	0.316696i	$-0.102574\pi$
$313$	10505.0	1.89705	0.948527	+	0.316696i	$0.102574\pi$
$314$	6173.07	1.10945
$315$	−958.162	−0.171385
$316$	−11100.2	−1.97605
$317$	−3544.69	−0.628043	−0.314021	−	0.949416i	$-0.601676\pi$
$317$	−3544.69	−0.628043	−0.314021	+	0.949416i	$0.601676\pi$
$318$	2762.78	0.487198
$319$	−1137.44	−0.199637
$320$	−20524.1	−3.58541
$321$	1215.47	0.211343
$322$	−1197.93	−0.207323
$323$	1840.94	0.317130
$324$	1652.41	0.283335
$325$	−4514.91	−0.770590
$326$	−20238.6	−3.43838
$327$	−3871.10	−0.654655
$328$	28809.2	4.84976
$329$	391.184	0.0655523
$330$	3478.77	0.580303
$331$	7059.26	1.17224	0.586121	−	0.810224i	$-0.300654\pi$
$331$	7059.26	1.17224	0.586121	+	0.810224i	$0.300654\pi$
$332$	19774.6	3.26889
$333$	3824.20	0.629324
$334$	11135.8	1.82433
$335$	4705.82	0.767482
$336$	3051.01	0.495375
$337$	3835.18	0.619928	0.309964	−	0.950748i	$-0.399683\pi$
$337$	3835.18	0.619928	0.309964	+	0.950748i	$0.399683\pi$
$338$	−10176.3	−1.63762
$339$	−1307.81	−0.209530
$340$	−8199.13	−1.30782
$341$	−1342.04	−0.213125
$342$	4345.70	0.687100
$343$	−3536.16	−0.556661
$344$	−13966.1	−2.18896
$345$	2478.56	0.386787
$346$	−7964.87	−1.23756
$347$	−10512.3	−1.62632	−0.813158	−	0.582043i	$-0.802253\pi$
$347$	−10512.3	−1.62632	−0.813158	+	0.582043i	$0.802253\pi$
$348$	6328.31	0.974807
$349$	−9708.75	−1.48910	−0.744552	−	0.667564i	$-0.767337\pi$
$349$	−9708.75	−1.48910	−0.744552	+	0.667564i	$0.767337\pi$
$350$	7637.78	1.16645
$351$	−457.773	−0.0696128
$352$	−5261.96	−0.796771
$353$	−10946.1	−1.65043	−0.825217	−	0.564815i	$-0.808947\pi$
$353$	−10946.1	−1.65043	−0.825217	+	0.564815i	$0.808947\pi$
$354$	7928.11	1.19032
$355$	−11306.9	−1.69045
$356$	12673.7	1.88681
$357$	328.057	0.0486348
$358$	7703.21	1.13723
$359$	−5114.40	−0.751888	−0.375944	−	0.926642i	$-0.622681\pi$
$359$	−5114.40	−0.751888	−0.375944	+	0.926642i	$0.622681\pi$
$360$	−11764.7	−1.72237
$361$	1350.45	0.196887
$362$	15333.2	2.22623
$363$	363.000	0.0524864
$364$	−1861.50	−0.268047
$365$	8797.16	1.26155
$366$	975.239	0.139280
$367$	4128.59	0.587222	0.293611	−	0.955925i	$-0.405143\pi$
$367$	4128.59	0.587222	0.293611	+	0.955925i	$0.405143\pi$
$368$	−7892.31	−1.11798
$369$	3923.63	0.553540
$370$	−44793.0	−6.29372
$371$	930.056	0.130151
$372$	7466.66	1.04067
$373$	−3180.52	−0.441504	−0.220752	−	0.975330i	$-0.570851\pi$
$373$	−3180.52	−0.441504	−0.220752	+	0.975330i	$0.570851\pi$
$374$	−1191.07	−0.164675
$375$	−8384.93	−1.15466
$376$	4803.10	0.658780
$377$	−1753.15	−0.239501
$378$	774.405	0.105373
$379$	−9067.68	−1.22896	−0.614480	−	0.788933i	$-0.710634\pi$
$379$	−9067.68	−1.22896	−0.614480	+	0.788933i	$0.710634\pi$
$380$	−36562.9	−4.93589
$381$	−2854.86	−0.383882
$382$	−4327.94	−0.579678
$383$	−3691.26	−0.492466	−0.246233	−	0.969211i	$-0.579193\pi$
$383$	−3691.26	−0.492466	−0.246233	+	0.969211i	$0.579193\pi$
$384$	5107.32	0.678729
$385$	1171.09	0.155024
$386$	−7946.63	−1.04786
$387$	−1902.10	−0.249843
$388$	−28187.3	−3.68812
$389$	2101.65	0.273927	0.136964	−	0.990576i	$-0.456266\pi$
$389$	2101.65	0.273927	0.136964	+	0.990576i	$0.456266\pi$
$390$	5361.91	0.696181
$391$	−848.614	−0.109760
$392$	−20752.1	−2.67382
$393$	625.630	0.0803025
$394$	−24268.9	−3.10317
$395$	10763.4	1.37105
$396$	−2019.61	−0.256286
$397$	−4546.19	−0.574727	−0.287363	−	0.957822i	$-0.592779\pi$
$397$	−4546.19	−0.574727	−0.287363	+	0.957822i	$0.592779\pi$
$398$	23294.4	2.93377
$399$	1462.93	0.183554
$400$	50319.9	6.28999
$401$	3616.69	0.450396	0.225198	−	0.974313i	$-0.427697\pi$
$401$	3616.69	0.450396	0.225198	+	0.974313i	$0.427697\pi$
$402$	−3803.33	−0.471873
$403$	−2068.51	−0.255683
$404$	−11867.2	−1.46143
$405$	−1602.27	−0.196587
$406$	2965.78	0.362535
$407$	−4674.03	−0.569245
$408$	4028.00	0.488764
$409$	−14260.5	−1.72405	−0.862023	−	0.506869i	$-0.830803\pi$
$409$	−14260.5	−1.72405	−0.862023	+	0.506869i	$0.830803\pi$
$410$	−45957.7	−5.53582
$411$	6416.86	0.770123
$412$	20978.9	2.50863
$413$	2668.91	0.317986
$414$	−2003.22	−0.237809
$415$	−19174.7	−2.26807
$416$	−8110.37	−0.955874
$417$	62.4344	0.00733195
$418$	−5311.41	−0.621506
$419$	−8049.91	−0.938577	−0.469288	−	0.883045i	$-0.655490\pi$
$419$	−8049.91	−0.938577	−0.469288	+	0.883045i	$0.655490\pi$
$420$	−6515.54	−0.756966
$421$	−5664.62	−0.655764	−0.327882	−	0.944719i	$-0.606335\pi$
$421$	−5664.62	−0.655764	−0.327882	+	0.944719i	$0.606335\pi$
$422$	6190.03	0.714042
$423$	654.153	0.0751915
$424$	11419.6	1.30798
$425$	5410.61	0.617537
$426$	9138.48	1.03935
$427$	328.303	0.0372077
$428$	8265.25	0.933448
$429$	559.500	0.0629671
$430$	22279.4	2.49862
$431$	−7211.17	−0.805916	−0.402958	−	0.915218i	$-0.632018\pi$
$431$	−7211.17	−0.805916	−0.402958	+	0.915218i	$0.632018\pi$
$432$	5102.01	0.568219
$433$	11971.0	1.32861	0.664304	−	0.747462i	$-0.268728\pi$
$433$	11971.0	1.32861	0.664304	+	0.747462i	$0.268728\pi$
$434$	3499.27	0.387028
$435$	−6136.31	−0.676353
$436$	−26323.6	−2.89145
$437$	−3784.28	−0.414249
$438$	−7110.03	−0.775640
$439$	−15000.0	−1.63077	−0.815387	−	0.578916i	$-0.803476\pi$
$439$	−15000.0	−1.63077	−0.815387	+	0.578916i	$0.803476\pi$
$440$	14379.0	1.55794
$441$	−2826.31	−0.305184
$442$	−1835.82	−0.197559
$443$	3156.17	0.338496	0.169248	−	0.985573i	$-0.445866\pi$
$443$	3156.17	0.338496	0.169248	+	0.985573i	$0.445866\pi$
$444$	26004.7	2.77957
$445$	−12289.2	−1.30913
$446$	−26738.8	−2.83884
$447$	−172.584	−0.0182616
$448$	5584.14	0.588897
$449$	−16896.0	−1.77588	−0.887940	−	0.459958i	$-0.847864\pi$
$449$	−16896.0	−1.77588	−0.887940	+	0.459958i	$0.847864\pi$
$450$	12772.2	1.33797
$451$	−4795.55	−0.500696
$452$	−8893.16	−0.925440
$453$	−6570.47	−0.681473
$454$	23779.7	2.45823
$455$	1805.02	0.185980
$456$	17962.4	1.84466
$457$	4702.48	0.481341	0.240670	−	0.970607i	$-0.422633\pi$
$457$	4702.48	0.481341	0.240670	+	0.970607i	$0.422633\pi$
$458$	−24662.9	−2.51621
$459$	548.589	0.0557864
$460$	16854.3	1.70834
$461$	−9188.88	−0.928349	−0.464174	−	0.885744i	$-0.653649\pi$
$461$	−9188.88	−0.928349	−0.464174	+	0.885744i	$0.653649\pi$
$462$	−946.495	−0.0953137
$463$	−1994.20	−0.200169	−0.100085	−	0.994979i	$-0.531911\pi$
$463$	−1994.20	−0.200169	−0.100085	+	0.994979i	$0.531911\pi$
$464$	19539.4	1.95494
$465$	−7240.12	−0.722049
$466$	24315.2	2.41712
$467$	−3493.88	−0.346205	−0.173102	−	0.984904i	$-0.555379\pi$
$467$	−3493.88	−0.346205	−0.173102	+	0.984904i	$0.555379\pi$
$468$	−3112.87	−0.307462
$469$	−1280.35	−0.126057
$470$	−7662.12	−0.751973
$471$	3475.06	0.339963
$472$	32769.8	3.19566
$473$	2324.79	0.225992
$474$	−8699.17	−0.842967
$475$	24127.9	2.33066
$476$	2230.80	0.214808
$477$	1555.28	0.149290
$478$	11626.0	1.11247
$479$	6855.31	0.653919	0.326959	−	0.945038i	$-0.393976\pi$
$479$	6855.31	0.653919	0.326959	+	0.945038i	$0.393976\pi$
$480$	−28387.5	−2.69939
$481$	−7204.18	−0.682915
$482$	15821.8	1.49515
$483$	−674.361	−0.0635290
$484$	2468.41	0.231819
$485$	27332.1	2.55894
$486$	1294.99	0.120868
$487$	14440.9	1.34370	0.671850	−	0.740687i	$-0.265500\pi$
$487$	14440.9	1.34370	0.671850	+	0.740687i	$0.265500\pi$
$488$	4031.02	0.373926
$489$	−11393.1	−1.05361
$490$	33104.6	3.05207
$491$	8150.66	0.749153	0.374577	−	0.927196i	$-0.377788\pi$
$491$	8150.66	0.749153	0.374577	+	0.927196i	$0.377788\pi$
$492$	26680.8	2.44485
$493$	2100.96	0.191932
$494$	−8186.59	−0.745611
$495$	1958.34	0.177820
$496$	23054.2	2.08702
$497$	3076.36	0.277653
$498$	15497.3	1.39448
$499$	16654.1	1.49407	0.747033	−	0.664787i	$-0.231478\pi$
$499$	16654.1	1.49407	0.747033	+	0.664787i	$0.231478\pi$
$500$	−57017.8	−5.09983
$501$	6268.80	0.559021
$502$	13222.6	1.17560
$503$	15686.4	1.39050	0.695252	−	0.718766i	$-0.255293\pi$
$503$	15686.4	1.39050	0.695252	+	0.718766i	$0.255293\pi$
$504$	3200.90	0.282896
$505$	11507.2	1.01399
$506$	2448.38	0.215106
$507$	−5728.63	−0.501810
$508$	−19413.2	−1.69551
$509$	16295.7	1.41904	0.709521	−	0.704684i	$-0.248911\pi$
$509$	16295.7	1.41904	0.709521	+	0.704684i	$0.248911\pi$
$510$	−6425.65	−0.557907
$511$	−2393.51	−0.207207
$512$	−9504.59	−0.820405
$513$	2446.36	0.210545
$514$	9443.24	0.810357
$515$	−20342.4	−1.74057
$516$	−12934.4	−1.10349
$517$	−799.521	−0.0680133
$518$	12187.2	1.03373
$519$	−4483.74	−0.379218
$520$	22162.7	1.86904
$521$	10667.6	0.897038	0.448519	−	0.893773i	$-0.351952\pi$
$521$	10667.6	0.897038	0.448519	+	0.893773i	$0.351952\pi$
$522$	4959.48	0.415844
$523$	2167.16	0.181192	0.0905958	−	0.995888i	$-0.471123\pi$
$523$	2167.16	0.181192	0.0905958	+	0.995888i	$0.471123\pi$
$524$	4254.31	0.354676
$525$	4299.60	0.357429
$526$	−12734.8	−1.05564
$527$	2478.88	0.204899
$528$	−6235.79	−0.513973
$529$	−10422.6	−0.856626
$530$	−18217.0	−1.49301
$531$	4463.04	0.364745
$532$	9947.95	0.810711
$533$	−7391.49	−0.600677
$534$	9932.35	0.804897
$535$	−8014.48	−0.647657
$536$	−15720.6	−1.26684
$537$	4336.44	0.348475
$538$	14951.8	1.19817
$539$	3454.37	0.276049
$540$	−10895.5	−0.868275
$541$	7691.98	0.611283	0.305642	−	0.952147i	$-0.401129\pi$
$541$	7691.98	0.611283	0.305642	+	0.952147i	$0.401129\pi$
$542$	−5590.40	−0.443041
$543$	8631.65	0.682172
$544$	9719.37	0.766019
$545$	25525.0	2.00618
$546$	−1458.85	−0.114346
$547$	7538.10	0.589225	0.294612	−	0.955617i	$-0.404809\pi$
$547$	7538.10	0.589225	0.294612	+	0.955617i	$0.404809\pi$
$548$	43634.9	3.40144
$549$	549.000	0.0426790
$550$	−15610.4	−1.21024
$551$	9368.95	0.724375
$552$	−8280.05	−0.638446
$553$	−2928.47	−0.225192
$554$	9640.34	0.739312
$555$	−25215.7	−1.92856
$556$	424.556	0.0323834
$557$	4961.05	0.377391	0.188695	−	0.982036i	$-0.439574\pi$
$557$	4961.05	0.377391	0.188695	+	0.982036i	$0.439574\pi$
$558$	5851.61	0.443939
$559$	3583.25	0.271119
$560$	−20117.5	−1.51807
$561$	−670.498	−0.0504607
$562$	8449.02	0.634165
$563$	−15554.2	−1.16435	−0.582177	−	0.813062i	$-0.697799\pi$
$563$	−15554.2	−1.16435	−0.582177	+	0.813062i	$0.697799\pi$
$564$	4448.26	0.332102
$565$	8623.35	0.642101
$566$	8171.81	0.606867
$567$	435.943	0.0322890
$568$	37772.7	2.79033
$569$	−15438.4	−1.13745	−0.568726	−	0.822527i	$-0.692564\pi$
$569$	−15438.4	−1.13745	−0.568726	+	0.822527i	$0.692564\pi$
$570$	−28654.3	−2.10561
$571$	−7383.04	−0.541104	−0.270552	−	0.962705i	$-0.587206\pi$
$571$	−7383.04	−0.541104	−0.270552	+	0.962705i	$0.587206\pi$
$572$	3804.62	0.278110
$573$	−2436.37	−0.177628
$574$	12504.0	0.909249
$575$	−11122.2	−0.806654
$576$	9338.01	0.675492
$577$	−5799.15	−0.418408	−0.209204	−	0.977872i	$-0.567087\pi$
$577$	−5799.15	−0.418408	−0.209204	+	0.977872i	$0.567087\pi$
$578$	−23982.2	−1.72583
$579$	−4473.47	−0.321090
$580$	−41727.1	−2.98728
$581$	5216.99	0.372525
$582$	−22090.3	−1.57332
$583$	−1900.89	−0.135038
$584$	−29388.4	−2.08236
$585$	3018.43	0.213327
$586$	24731.8	1.74345
$587$	−24300.5	−1.70867	−0.854335	−	0.519723i	$-0.826035\pi$
$587$	−24300.5	−1.70867	−0.854335	+	0.519723i	$0.826035\pi$
$588$	−19219.0	−1.34792
$589$	11054.3	0.773315
$590$	−52275.8	−3.64773
$591$	−13661.9	−0.950890
$592$	80292.6	5.57434
$593$	−13329.6	−0.923072	−0.461536	−	0.887121i	$-0.652702\pi$
$593$	−13329.6	−0.923072	−0.461536	+	0.887121i	$0.652702\pi$
$594$	−1582.76	−0.109329
$595$	−2163.12	−0.149041
$596$	−1173.58	−0.0806570
$597$	13113.3	0.898982
$598$	3773.75	0.258060
$599$	−14025.9	−0.956729	−0.478365	−	0.878161i	$-0.658770\pi$
$599$	−14025.9	−0.956729	−0.478365	+	0.878161i	$0.658770\pi$
$600$	52792.1	3.59205
$601$	21938.1	1.48898	0.744488	−	0.667635i	$-0.232693\pi$
$601$	21938.1	1.48898	0.744488	+	0.667635i	$0.232693\pi$
$602$	−6061.72	−0.410394
$603$	−2141.04	−0.144594
$604$	−44679.4	−3.00990
$605$	−2393.52	−0.160844
$606$	−9300.33	−0.623432
$607$	10371.2	0.693499	0.346750	−	0.937958i	$-0.387285\pi$
$607$	10371.2	0.693499	0.346750	+	0.937958i	$0.387285\pi$
$608$	43342.3	2.89105
$609$	1669.55	0.111090
$610$	−6430.46	−0.426822
$611$	−1232.32	−0.0815946
$612$	3730.43	0.246395
$613$	12761.8	0.840853	0.420427	−	0.907327i	$-0.361880\pi$
$613$	12761.8	0.840853	0.420427	+	0.907327i	$0.361880\pi$
$614$	−36642.2	−2.40840
$615$	−25871.4	−1.69632
$616$	−3912.21	−0.255889
$617$	−2661.26	−0.173644	−0.0868219	−	0.996224i	$-0.527671\pi$
$617$	−2661.26	−0.173644	−0.0868219	+	0.996224i	$0.527671\pi$
$618$	16441.1	1.07016
$619$	−28969.7	−1.88108	−0.940542	−	0.339677i	$-0.889682\pi$
$619$	−28969.7	−1.88108	−0.940542	+	0.339677i	$0.889682\pi$
$620$	−49233.1	−3.18911
$621$	−1127.69	−0.0728707
$622$	−14529.4	−0.936615
$623$	3343.61	0.215022
$624$	−9611.35	−0.616606
$625$	22001.1	1.40807
$626$	55983.0	3.57433
$627$	−2990.00	−0.190445
$628$	23630.5	1.50153
$629$	8633.40	0.547275
$630$	−5106.21	−0.322915
$631$	−10977.3	−0.692549	−0.346275	−	0.938133i	$-0.612553\pi$
$631$	−10977.3	−0.692549	−0.346275	+	0.938133i	$0.612553\pi$
$632$	−35956.9	−2.26311
$633$	3484.61	0.218801
$634$	−18890.3	−1.18333
$635$	18824.2	1.17640
$636$	10575.9	0.659375
$637$	5324.30	0.331172
$638$	−6061.59	−0.376145
$639$	5144.41	0.318482
$640$	−33676.3	−2.07996
$641$	−15147.5	−0.933371	−0.466686	−	0.884423i	$-0.654552\pi$
$641$	−15147.5	−0.933371	−0.466686	+	0.884423i	$0.654552\pi$
$642$	6477.46	0.398201
$643$	30528.6	1.87237	0.936183	−	0.351512i	$-0.114333\pi$
$643$	30528.6	1.87237	0.936183	+	0.351512i	$0.114333\pi$
$644$	−4585.68	−0.280592
$645$	12541.9	0.765641
$646$	9810.71	0.597519
$647$	−4376.74	−0.265947	−0.132973	−	0.991120i	$-0.542452\pi$
$647$	−4376.74	−0.265947	−0.132973	+	0.991120i	$0.542452\pi$
$648$	5352.67	0.324495
$649$	−5454.83	−0.329924
$650$	−24060.7	−1.45191
$651$	1969.87	0.118595
$652$	−77473.4	−4.65352
$653$	13543.6	0.811639	0.405819	−	0.913953i	$-0.366986\pi$
$653$	13543.6	0.811639	0.405819	+	0.913953i	$0.366986\pi$
$654$	−20629.8	−1.23347
$655$	−4125.23	−0.246086
$656$	82380.3	4.90306
$657$	−4002.51	−0.237676
$658$	2084.69	0.123510
$659$	11308.0	0.668432	0.334216	−	0.942496i	$-0.391528\pi$
$659$	11308.0	0.668432	0.334216	+	0.942496i	$0.391528\pi$
$660$	13316.7	0.785385
$661$	−8799.30	−0.517781	−0.258890	−	0.965907i	$-0.583357\pi$
$661$	−8799.30	−0.517781	−0.258890	+	0.965907i	$0.583357\pi$
$662$	37620.0	2.20868
$663$	−1033.45	−0.0605369
$664$	64056.1	3.74377
$665$	−9646.14	−0.562498
$666$	20379.8	1.18574
$667$	−4318.78	−0.250710
$668$	42628.0	2.46905
$669$	−15052.3	−0.869891
$670$	25078.1	1.44605
$671$	−671.000	−0.0386046
$672$	7723.61	0.443370
$673$	26894.0	1.54040	0.770199	−	0.637804i	$-0.220157\pi$
$673$	26894.0	1.54040	0.770199	+	0.637804i	$0.220157\pi$
$674$	20438.4	1.16804
$675$	7189.96	0.409988
$676$	−38954.9	−2.21637
$677$	16433.7	0.932938	0.466469	−	0.884538i	$-0.345526\pi$
$677$	16433.7	0.932938	0.466469	+	0.884538i	$0.345526\pi$
$678$	−6969.55	−0.394785
$679$	−7436.44	−0.420301
$680$	−26559.5	−1.49781
$681$	13386.5	0.753263
$682$	−7151.96	−0.401558
$683$	10471.5	0.586651	0.293325	−	0.956013i	$-0.405238\pi$
$683$	10471.5	0.586651	0.293325	+	0.956013i	$0.405238\pi$
$684$	16635.3	0.929924
$685$	−42311.0	−2.36003
$686$	−18844.8	−1.04883
$687$	−13883.7	−0.771029
$688$	−39936.4	−2.21302
$689$	−2929.89	−0.162003
$690$	13208.7	0.728763
$691$	1498.98	0.0825238	0.0412619	−	0.999148i	$-0.486862\pi$
$691$	1498.98	0.0825238	0.0412619	+	0.999148i	$0.486862\pi$
$692$	−30489.6	−1.67491
$693$	−532.819	−0.0292065
$694$	−56022.0	−3.06422
$695$	−411.675	−0.0224687
$696$	20499.4	1.11642
$697$	8857.87	0.481371
$698$	−51739.6	−2.80569
$699$	13688.0	0.740668
$700$	29237.4	1.57867
$701$	−13273.9	−0.715188	−0.357594	−	0.933877i	$-0.616403\pi$
$701$	−13273.9	−0.715188	−0.357594	+	0.933877i	$0.616403\pi$
$702$	−2439.55	−0.131161
$703$	38499.5	2.06549
$704$	−11413.1	−0.611006
$705$	−4313.31	−0.230423
$706$	−58333.8	−3.10966
$707$	−3130.84	−0.166545
$708$	30348.9	1.61099
$709$	10552.3	0.558956	0.279478	−	0.960152i	$-0.409839\pi$
$709$	10552.3	0.558956	0.279478	+	0.960152i	$0.409839\pi$
$710$	−60256.6	−3.18506
$711$	−4897.10	−0.258306
$712$	41054.0	2.16091
$713$	−5095.65	−0.267649
$714$	1748.27	0.0916351
$715$	−3689.19	−0.192962
$716$	29487.9	1.53913
$717$	6544.71	0.340888
$718$	−27255.5	−1.41667
$719$	22483.5	1.16619	0.583097	−	0.812403i	$-0.301841\pi$
$719$	22483.5	1.16619	0.583097	+	0.812403i	$0.301841\pi$
$720$	−33641.2	−1.74130
$721$	5534.71	0.285885
$722$	7196.76	0.370964
$723$	8906.68	0.458151
$724$	58695.5	3.01299
$725$	27535.7	1.41055
$726$	1934.49	0.0988921
$727$	−24412.8	−1.24542	−0.622709	−	0.782453i	$-0.713968\pi$
$727$	−24412.8	−1.24542	−0.622709	+	0.782453i	$0.713968\pi$
$728$	−6029.98	−0.306986
$729$	729.000	0.0370370
$730$	46881.6	2.37694
$731$	−4294.13	−0.217269
$732$	3733.22	0.188502
$733$	17447.5	0.879178	0.439589	−	0.898199i	$-0.355124\pi$
$733$	17447.5	0.879178	0.439589	+	0.898199i	$0.355124\pi$
$734$	22002.0	1.10641
$735$	18635.9	0.935231
$736$	−19979.3	−1.00061
$737$	2616.83	0.130790
$738$	20909.7	1.04295
$739$	17572.4	0.874713	0.437356	−	0.899288i	$-0.355915\pi$
$739$	17572.4	0.874713	0.437356	+	0.899288i	$0.355915\pi$
$740$	−171468.	−8.51795
$741$	−4608.55	−0.228474
$742$	4956.43	0.245224
$743$	−13026.4	−0.643192	−0.321596	−	0.946877i	$-0.604219\pi$
$743$	−13026.4	−0.643192	−0.321596	+	0.946877i	$0.604219\pi$
$744$	24186.8	1.19184
$745$	1137.97	0.0559625
$746$	−16949.5	−0.831859
$747$	8724.05	0.427304
$748$	−4559.41	−0.222872
$749$	2180.56	0.106376
$750$	−44684.8	−2.17554
$751$	−18118.4	−0.880361	−0.440181	−	0.897909i	$-0.645086\pi$
$751$	−18118.4	−0.880361	−0.440181	+	0.897909i	$0.645086\pi$
$752$	13734.5	0.666020
$753$	7443.49	0.360234
$754$	−9342.86	−0.451256
$755$	43323.8	2.08837
$756$	2964.43	0.142613
$757$	−15517.2	−0.745024	−0.372512	−	0.928027i	$-0.621504\pi$
$757$	−15517.2	−0.745024	−0.372512	+	0.928027i	$0.621504\pi$
$758$	−48323.3	−2.31554
$759$	1378.29	0.0659140
$760$	−118439.	−5.65293
$761$	15546.5	0.740551	0.370276	−	0.928922i	$-0.379263\pi$
$761$	15546.5	0.740551	0.370276	+	0.928922i	$0.379263\pi$
$762$	−15214.1	−0.723290
$763$	−6944.76	−0.329512
$764$	−16567.4	−0.784538
$765$	−3617.25	−0.170957
$766$	−19671.4	−0.927879
$767$	−8407.65	−0.395805
$768$	2316.46	0.108839
$769$	22894.5	1.07360	0.536800	−	0.843709i	$-0.319633\pi$
$769$	22894.5	1.07360	0.536800	+	0.843709i	$0.319633\pi$
$770$	6240.93	0.292088
$771$	5315.97	0.248314
$772$	−30419.7	−1.41817
$773$	32270.1	1.50152	0.750759	−	0.660576i	$-0.229688\pi$
$773$	32270.1	1.50152	0.750759	+	0.660576i	$0.229688\pi$
$774$	−10136.6	−0.470741
$775$	32488.9	1.50585
$776$	−91307.4	−4.22390
$777$	6860.63	0.316762
$778$	11200.0	0.516120
$779$	39500.5	1.81676
$780$	20525.4	0.942214
$781$	−6287.61	−0.288077
$782$	−4522.41	−0.206805
$783$	2791.89	0.127425
$784$	−59340.9	−2.70321
$785$	−22913.6	−1.04181
$786$	3334.09	0.151302
$787$	−21216.7	−0.960983	−0.480491	−	0.877000i	$-0.659542\pi$
$787$	−21216.7	−0.960983	−0.480491	+	0.877000i	$0.659542\pi$
$788$	−92901.5	−4.19985
$789$	−7168.94	−0.323474
$790$	57359.9	2.58326
$791$	−2346.22	−0.105464
$792$	−6542.15	−0.293516
$793$	−1034.23	−0.0463133
$794$	−24227.4	−1.08287
$795$	−10255.1	−0.457496
$796$	89171.0	3.97058
$797$	−36920.9	−1.64091	−0.820454	−	0.571712i	$-0.806279\pi$
$797$	−36920.9	−1.64091	−0.820454	+	0.571712i	$0.806279\pi$
$798$	7796.19	0.345842
$799$	1476.80	0.0653884
$800$	127385.	5.62966
$801$	5591.31	0.246641
$802$	19274.0	0.848612
$803$	4891.96	0.214986
$804$	−14559.2	−0.638635
$805$	4446.55	0.194684
$806$	−11023.5	−0.481744
$807$	8416.94	0.367150
$808$	−38441.7	−1.67373
$809$	−10039.7	−0.436314	−0.218157	−	0.975914i	$-0.570004\pi$
$809$	−10039.7	−0.436314	−0.218157	+	0.975914i	$0.570004\pi$
$810$	−8538.80	−0.370399
$811$	−11408.1	−0.493948	−0.246974	−	0.969022i	$-0.579436\pi$
$811$	−11408.1	−0.493948	−0.246974	+	0.969022i	$0.579436\pi$
$812$	11353.0	0.490656
$813$	−3147.05	−0.135759
$814$	−24908.7	−1.07254
$815$	75122.9	3.22876
$816$	11518.1	0.494136
$817$	−19149.1	−0.820002
$818$	−75996.6	−3.24836
$819$	−821.246	−0.0350386
$820$	−175926.	−7.49220
$821$	6479.73	0.275450	0.137725	−	0.990471i	$-0.456021\pi$
$821$	6479.73	0.275450	0.137725	+	0.990471i	$0.456021\pi$
$822$	34196.6	1.45103
$823$	−11460.8	−0.485417	−0.242708	−	0.970099i	$-0.578036\pi$
$823$	−11460.8	−0.485417	−0.242708	+	0.970099i	$0.578036\pi$
$824$	67957.2	2.87306
$825$	−8787.73	−0.370848
$826$	14223.1	0.599133
$827$	17376.3	0.730634	0.365317	−	0.930883i	$-0.380961\pi$
$827$	17376.3	0.730634	0.365317	+	0.930883i	$0.380961\pi$
$828$	−7668.34	−0.321852
$829$	−31755.0	−1.33040	−0.665198	−	0.746667i	$-0.731653\pi$
$829$	−31755.0	−1.33040	−0.665198	+	0.746667i	$0.731653\pi$
$830$	−102185.	−4.27337
$831$	5426.92	0.226544
$832$	−17591.3	−0.733015
$833$	−6380.58	−0.265395
$834$	332.724	0.0138145
$835$	−41334.7	−1.71311
$836$	−20332.1	−0.841148
$837$	3294.10	0.136034
$838$	−42899.4	−1.76842
$839$	36153.1	1.48766	0.743829	−	0.668370i	$-0.233008\pi$
$839$	36153.1	1.48766	0.743829	+	0.668370i	$0.233008\pi$
$840$	−21105.9	−0.866930
$841$	−13696.8	−0.561596
$842$	−30187.7	−1.23556
$843$	4756.29	0.194324
$844$	23695.5	0.966388
$845$	37773.0	1.53779
$846$	3486.10	0.141672
$847$	651.223	0.0264183
$848$	32654.4	1.32236
$849$	4600.23	0.185959
$850$	28834.1	1.16353
$851$	−17747.0	−0.714876
$852$	34982.2	1.40665
$853$	30839.9	1.23791	0.618956	−	0.785426i	$-0.287556\pi$
$853$	30839.9	1.23791	0.618956	+	0.785426i	$0.287556\pi$
$854$	1749.58	0.0701048
$855$	−16130.6	−0.645212
$856$	26773.7	1.06905
$857$	−11999.5	−0.478292	−0.239146	−	0.970984i	$-0.576867\pi$
$857$	−11999.5	−0.478292	−0.239146	+	0.970984i	$0.576867\pi$
$858$	2981.67	0.118639
$859$	12507.2	0.496786	0.248393	−	0.968659i	$-0.420098\pi$
$859$	12507.2	0.496786	0.248393	+	0.968659i	$0.420098\pi$
$860$	85285.6	3.38164
$861$	7039.01	0.278617
$862$	−38429.6	−1.51847
$863$	5253.21	0.207209	0.103605	−	0.994619i	$-0.466962\pi$
$863$	5253.21	0.207209	0.103605	+	0.994619i	$0.466962\pi$
$864$	12915.7	0.508566
$865$	29564.5	1.16211
$866$	63795.3	2.50330
$867$	−13500.5	−0.528837
$868$	13395.2	0.523805
$869$	5985.35	0.233647
$870$	−32701.5	−1.27435
$871$	4033.38	0.156907
$872$	−85270.3	−3.31149
$873$	−12435.5	−0.482105
$874$	−20167.1	−0.780506
$875$	−15042.6	−0.581180
$876$	−27217.2	−1.04975
$877$	−28682.5	−1.10438	−0.552189	−	0.833719i	$-0.686207\pi$
$877$	−28682.5	−1.10438	−0.552189	+	0.833719i	$0.686207\pi$
$878$	−79937.5	−3.07262
$879$	13922.5	0.534237
$880$	41117.1	1.57506
$881$	9535.44	0.364651	0.182325	−	0.983238i	$-0.441638\pi$
$881$	9535.44	0.364651	0.182325	+	0.983238i	$0.441638\pi$
$882$	−15061.9	−0.575011
$883$	46195.9	1.76061	0.880303	−	0.474413i	$-0.157340\pi$
$883$	46195.9	1.76061	0.880303	+	0.474413i	$0.157340\pi$
$884$	−7027.52	−0.267377
$885$	−29428.1	−1.11776
$886$	16819.8	0.637777
$887$	−16228.8	−0.614331	−0.307165	−	0.951656i	$-0.599380\pi$
$887$	−16228.8	−0.614331	−0.307165	+	0.951656i	$0.599380\pi$
$888$	84237.3	3.18336
$889$	−5121.63	−0.193222
$890$	−65491.2	−2.46659
$891$	−891.000	−0.0335013
$892$	−102356.	−3.84209
$893$	6585.58	0.246784
$894$	−919.730	−0.0344076
$895$	−28593.3	−1.06790
$896$	9162.55	0.341629
$897$	2124.39	0.0790761
$898$	−90041.6	−3.34602
$899$	12615.6	0.468023
$900$	48892.0	1.81081
$901$	3511.14	0.129826
$902$	−25556.3	−0.943385
$903$	−3412.38	−0.125755
$904$	−28807.7	−1.05988
$905$	−56914.7	−2.09051
$906$	−35015.2	−1.28400
$907$	33999.6	1.24469	0.622347	−	0.782741i	$-0.286179\pi$
$907$	33999.6	1.24469	0.622347	+	0.782741i	$0.286179\pi$
$908$	91028.7	3.32698
$909$	−5235.52	−0.191035
$910$	9619.28	0.350413
$911$	−45722.2	−1.66284	−0.831419	−	0.555647i	$-0.812471\pi$
$911$	−45722.2	−1.66284	−0.831419	+	0.555647i	$0.812471\pi$
$912$	51363.6	1.86493
$913$	−10662.7	−0.386511
$914$	25060.3	0.906917
$915$	−3619.95	−0.130789
$916$	−94409.8	−3.40545
$917$	1122.38	0.0404191
$918$	2923.53	0.105110
$919$	−27180.2	−0.975617	−0.487808	−	0.872951i	$-0.662203\pi$
$919$	−27180.2	−0.975617	−0.487808	+	0.872951i	$0.662203\pi$
$920$	54596.4	1.95651
$921$	−20627.3	−0.737994
$922$	−48969.1	−1.74915
$923$	−9691.23	−0.345602
$924$	−3623.19	−0.128998
$925$	113152.	4.02206
$926$	−10627.5	−0.377149
$927$	9255.35	0.327924
$928$	49463.9	1.74971
$929$	45366.5	1.60218	0.801090	−	0.598544i	$-0.204254\pi$
$929$	45366.5	1.60218	0.801090	+	0.598544i	$0.204254\pi$
$930$	−38583.9	−1.36045
$931$	−28453.4	−1.00163
$932$	93078.7	3.27135
$933$	−8179.15	−0.287003
$934$	−18619.5	−0.652301
$935$	4421.08	0.154636
$936$	−10083.6	−0.352127
$937$	−16458.4	−0.573824	−0.286912	−	0.957957i	$-0.592629\pi$
$937$	−16458.4	−0.573824	−0.286912	+	0.957957i	$0.592629\pi$
$938$	−6823.19	−0.237511
$939$	31515.0	1.09526
$940$	−29330.6	−1.01772
$941$	−47985.6	−1.66236	−0.831182	−	0.556000i	$-0.812335\pi$
$941$	−47985.6	−1.66236	−0.831182	+	0.556000i	$0.812335\pi$
$942$	18519.2	0.640540
$943$	−18208.4	−0.628789
$944$	93705.7	3.23078
$945$	−2874.49	−0.0989493
$946$	12389.2	0.425801
$947$	−32695.7	−1.12193	−0.560965	−	0.827840i	$-0.689570\pi$
$947$	−32695.7	−1.12193	−0.560965	+	0.827840i	$0.689570\pi$
$948$	−33300.5	−1.14087
$949$	7540.09	0.257915
$950$	128582.	4.39131
$951$	−10634.1	−0.362601
$952$	7226.25	0.246013
$953$	48321.0	1.64247	0.821233	−	0.570593i	$-0.193287\pi$
$953$	48321.0	1.64247	0.821233	+	0.570593i	$0.193287\pi$
$954$	8288.33	0.281284
$955$	16064.7	0.544338
$956$	44504.2	1.50562
$957$	−3412.31	−0.115260
$958$	36533.1	1.23208
$959$	11511.9	0.387631
$960$	−61572.2	−2.07004
$961$	−14906.1	−0.500357
$962$	−38392.3	−1.28671
$963$	3646.41	0.122019
$964$	60565.7	2.02354
$965$	29496.8	0.983975
$966$	−3593.79	−0.119698
$967$	13098.5	0.435592	0.217796	−	0.975994i	$-0.430113\pi$
$967$	13098.5	0.435592	0.217796	+	0.975994i	$0.430113\pi$
$968$	7995.96	0.265496
$969$	5522.83	0.183095
$970$	145657.	4.82142
$971$	38653.5	1.27750	0.638749	−	0.769415i	$-0.279452\pi$
$971$	38653.5	1.27750	0.638749	+	0.769415i	$0.279452\pi$
$972$	4957.22	0.163583
$973$	112.007	0.00369044
$974$	76958.3	2.53173
$975$	−13544.7	−0.444901
$976$	11526.8	0.378035
$977$	40998.1	1.34252	0.671262	−	0.741221i	$-0.265753\pi$
$977$	40998.1	1.34252	0.671262	+	0.741221i	$0.265753\pi$
$978$	−60715.8	−1.98515
$979$	−6833.82	−0.223095
$980$	126725.	4.13068
$981$	−11613.3	−0.377965
$982$	43436.3	1.41152
$983$	−35616.2	−1.15562	−0.577812	−	0.816170i	$-0.696093\pi$
$983$	−35616.2	−1.15562	−0.577812	+	0.816170i	$0.696093\pi$
$984$	86427.6	2.80001
$985$	90082.9	2.91399
$986$	11196.4	0.361628
$987$	1173.55	0.0378466
$988$	−31338.3	−1.00911
$989$	8827.10	0.283807
$990$	10436.3	0.335038
$991$	−24547.6	−0.786862	−0.393431	−	0.919354i	$-0.628712\pi$
$991$	−24547.6	−0.786862	−0.393431	+	0.919354i	$0.628712\pi$
$992$	58361.6	1.86793
$993$	21177.8	0.676794
$994$	16394.5	0.523140
$995$	−86465.6	−2.75492
$996$	59323.8	1.88730
$997$	−48321.4	−1.53496	−0.767479	−	0.641074i	$-0.778489\pi$
$997$	−48321.4	−1.53496	−0.767479	+	0.641074i	$0.778489\pi$
$998$	88752.5	2.81504
$999$	11472.6	0.363341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.h.1.37	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.h.1.37	✓	39	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)

\(f(q)\)	\(=\)	\(q+5.32917 q^{2} +3.00000 q^{3} +20.4001 q^{4} -19.7812 q^{5} +15.9875 q^{6} +5.38201 q^{7} +66.0823 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+5.32917 q^{2} +3.00000 q^{3} +20.4001 q^{4} -19.7812 q^{5} +15.9875 q^{6} +5.38201 q^{7} +66.0823 q^{8} +9.00000 q^{9} -105.417 q^{10} -11.0000 q^{11} +61.2003 q^{12} -16.9545 q^{13} +28.6817 q^{14} -59.3435 q^{15} +188.963 q^{16} +20.3181 q^{17} +47.9626 q^{18} +90.6060 q^{19} -403.538 q^{20} +16.1460 q^{21} -58.6209 q^{22} -41.7664 q^{23} +198.247 q^{24} +266.295 q^{25} -90.3537 q^{26} +27.0000 q^{27} +109.794 q^{28} +103.403 q^{29} -316.252 q^{30} +122.004 q^{31} +478.360 q^{32} -33.0000 q^{33} +108.279 q^{34} -106.462 q^{35} +183.601 q^{36} +424.911 q^{37} +482.855 q^{38} -50.8636 q^{39} -1307.19 q^{40} +435.959 q^{41} +86.0450 q^{42} -211.345 q^{43} -224.401 q^{44} -178.031 q^{45} -222.580 q^{46} +72.6837 q^{47} +566.890 q^{48} -314.034 q^{49} +1419.13 q^{50} +60.9544 q^{51} -345.874 q^{52} +172.808 q^{53} +143.888 q^{54} +217.593 q^{55} +355.656 q^{56} +271.818 q^{57} +551.054 q^{58} +495.894 q^{59} -1210.61 q^{60} +61.0000 q^{61} +650.178 q^{62} +48.4381 q^{63} +1037.56 q^{64} +335.381 q^{65} -175.863 q^{66} -237.894 q^{67} +414.492 q^{68} -125.299 q^{69} -567.357 q^{70} +571.601 q^{71} +594.741 q^{72} -444.724 q^{73} +2264.43 q^{74} +798.884 q^{75} +1848.37 q^{76} -59.2021 q^{77} -271.061 q^{78} -544.122 q^{79} -3737.91 q^{80} +81.0000 q^{81} +2323.30 q^{82} +969.339 q^{83} +329.381 q^{84} -401.916 q^{85} -1126.29 q^{86} +310.210 q^{87} -726.905 q^{88} +621.256 q^{89} -948.756 q^{90} -91.2495 q^{91} -852.038 q^{92} +366.011 q^{93} +387.344 q^{94} -1792.29 q^{95} +1435.08 q^{96} -1381.72 q^{97} -1673.54 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * q^99

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