LMFDB - Embedded newform 2013.4.a.d.1.2

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:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-5.34535 q^{2} -3.00000 q^{3} +20.5728 q^{4} +5.60041 q^{5} +16.0360 q^{6} +11.9095 q^{7} -67.2058 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.34535 q^{2} -3.00000 q^{3} +20.5728 q^{4} +5.60041 q^{5} +16.0360 q^{6} +11.9095 q^{7} -67.2058 q^{8} +9.00000 q^{9} -29.9362 q^{10} +11.0000 q^{11} -61.7183 q^{12} -65.0588 q^{13} -63.6604 q^{14} -16.8012 q^{15} +194.656 q^{16} -36.6620 q^{17} -48.1081 q^{18} -88.0693 q^{19} +115.216 q^{20} -35.7285 q^{21} -58.7988 q^{22} +213.521 q^{23} +201.617 q^{24} -93.6354 q^{25} +347.762 q^{26} -27.0000 q^{27} +245.011 q^{28} -157.646 q^{29} +89.8085 q^{30} +324.346 q^{31} -502.860 q^{32} -33.0000 q^{33} +195.971 q^{34} +66.6980 q^{35} +185.155 q^{36} +245.123 q^{37} +470.761 q^{38} +195.176 q^{39} -376.380 q^{40} +69.5872 q^{41} +190.981 q^{42} -128.825 q^{43} +226.300 q^{44} +50.4037 q^{45} -1141.34 q^{46} -52.0562 q^{47} -583.969 q^{48} -201.164 q^{49} +500.514 q^{50} +109.986 q^{51} -1338.44 q^{52} -157.329 q^{53} +144.324 q^{54} +61.6045 q^{55} -800.387 q^{56} +264.208 q^{57} +842.671 q^{58} +569.443 q^{59} -345.648 q^{60} -61.0000 q^{61} -1733.74 q^{62} +107.185 q^{63} +1130.71 q^{64} -364.356 q^{65} +176.397 q^{66} -61.1289 q^{67} -754.238 q^{68} -640.563 q^{69} -356.524 q^{70} +1159.94 q^{71} -604.852 q^{72} -239.455 q^{73} -1310.27 q^{74} +280.906 q^{75} -1811.83 q^{76} +131.004 q^{77} -1043.29 q^{78} -380.622 q^{79} +1090.16 q^{80} +81.0000 q^{81} -371.968 q^{82} -460.439 q^{83} -735.033 q^{84} -205.322 q^{85} +688.617 q^{86} +472.937 q^{87} -739.264 q^{88} -176.098 q^{89} -269.425 q^{90} -774.817 q^{91} +4392.71 q^{92} -973.038 q^{93} +278.259 q^{94} -493.224 q^{95} +1508.58 q^{96} -1351.41 q^{97} +1075.29 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9 - 45 * q^10 + 407 * q^11 - 474 * q^12 - 169 * q^13 + 102 * q^14 + 45 * q^15 + 598 * q^16 - 338 * q^17 - 36 * q^18 - 235 * q^19 - 550 * q^20 + 231 * q^21 - 44 * q^22 - 53 * q^23 + 207 * q^24 + 750 * q^25 - 75 * q^26 - 999 * q^27 - 1378 * q^28 - 30 * q^29 + 135 * q^30 - 506 * q^31 - 841 * q^32 - 1221 * q^33 - 316 * q^34 - 822 * q^35 + 1422 * q^36 - 830 * q^37 - 371 * q^38 + 507 * q^39 - 613 * q^40 + 16 * q^41 - 306 * q^42 - 1137 * q^43 + 1738 * q^44 - 135 * q^45 - 659 * q^46 - 489 * q^47 - 1794 * q^48 + 2214 * q^49 + 1066 * q^50 + 1014 * q^51 - 2342 * q^52 + 731 * q^53 + 108 * q^54 - 165 * q^55 + 3051 * q^56 + 705 * q^57 - 611 * q^58 - 425 * q^59 + 1650 * q^60 - 2257 * q^61 + 453 * q^62 - 693 * q^63 + 4919 * q^64 + 1346 * q^65 + 132 * q^66 - 1907 * q^67 - 3236 * q^68 + 159 * q^69 - 1050 * q^70 - 561 * q^71 - 621 * q^72 - 2397 * q^73 - 1840 * q^74 - 2250 * q^75 - 3868 * q^76 - 847 * q^77 + 225 * q^78 + 393 * q^79 - 4031 * q^80 + 2997 * q^81 - 1946 * q^82 - 4191 * q^83 + 4134 * q^84 - 2667 * q^85 + 2405 * q^86 + 90 * q^87 - 759 * q^88 + 1437 * q^89 - 405 * q^90 - 5192 * q^91 - 737 * q^92 + 1518 * q^93 - 1960 * q^94 + 1356 * q^95 + 2523 * q^96 - 2368 * q^97 - 3014 * q^98 + 3663 * 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 $

$2$	−5.34535	−1.88987	−0.944933	−	0.327263i	$-0.893874\pi$
$2$	−5.34535	−1.88987	−0.944933	+	0.327263i	$0.893874\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	20.5728	2.57160
$5$	5.60041	0.500916	0.250458	−	0.968127i	$-0.419419\pi$
$5$	5.60041	0.500916	0.250458	+	0.968127i	$0.419419\pi$
$6$	16.0360	1.09111
$7$	11.9095	0.643052	0.321526	−	0.946901i	$-0.395804\pi$
$7$	11.9095	0.643052	0.321526	+	0.946901i	$0.395804\pi$
$8$	−67.2058	−2.97010
$9$	9.00000	0.333333
$10$	−29.9362	−0.946664
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−61.7183	−1.48471
$13$	−65.0588	−1.38800	−0.694002	−	0.719973i	$-0.744154\pi$
$13$	−65.0588	−1.38800	−0.694002	+	0.719973i	$0.744154\pi$
$14$	−63.6604	−1.21528
$15$	−16.8012	−0.289204
$16$	194.656	3.04151
$17$	−36.6620	−0.523049	−0.261524	−	0.965197i	$-0.584225\pi$
$17$	−36.6620	−0.523049	−0.261524	+	0.965197i	$0.584225\pi$
$18$	−48.1081	−0.629955
$19$	−88.0693	−1.06339	−0.531697	−	0.846935i	$-0.678446\pi$
$19$	−88.0693	−1.06339	−0.531697	+	0.846935i	$0.678446\pi$
$20$	115.216	1.28815
$21$	−35.7285	−0.371266
$22$	−58.7988	−0.569816
$23$	213.521	1.93575	0.967873	−	0.251438i	$-0.0809034\pi$
$23$	213.521	1.93575	0.967873	+	0.251438i	$0.0809034\pi$
$24$	201.617	1.71479
$25$	−93.6354	−0.749083
$26$	347.762	2.62314
$27$	−27.0000	−0.192450
$28$	245.011	1.65367
$29$	−157.646	−1.00945	−0.504725	−	0.863280i	$-0.668406\pi$
$29$	−157.646	−1.00945	−0.504725	+	0.863280i	$0.668406\pi$
$30$	89.8085	0.546557
$31$	324.346	1.87917	0.939585	−	0.342316i	$-0.111211\pi$
$31$	324.346	1.87917	0.939585	+	0.342316i	$0.111211\pi$
$32$	−502.860	−2.77794
$33$	−33.0000	−0.174078
$34$	195.971	0.988493
$35$	66.6980	0.322115
$36$	185.155	0.857198
$37$	245.123	1.08913	0.544567	−	0.838717i	$-0.316694\pi$
$37$	245.123	1.08913	0.544567	+	0.838717i	$0.316694\pi$
$38$	470.761	2.00967
$39$	195.176	0.801365
$40$	−376.380	−1.48777
$41$	69.5872	0.265066	0.132533	−	0.991179i	$-0.457689\pi$
$41$	69.5872	0.265066	0.132533	+	0.991179i	$0.457689\pi$
$42$	190.981	0.701643
$43$	−128.825	−0.456877	−0.228438	−	0.973558i	$-0.573362\pi$
$43$	−128.825	−0.456877	−0.228438	+	0.973558i	$0.573362\pi$
$44$	226.300	0.775365
$45$	50.4037	0.166972
$46$	−1141.34	−3.65830
$47$	−52.0562	−0.161557	−0.0807785	−	0.996732i	$-0.525741\pi$
$47$	−52.0562	−0.161557	−0.0807785	+	0.996732i	$0.525741\pi$
$48$	−583.969	−1.75601
$49$	−201.164	−0.586484
$50$	500.514	1.41567
$51$	109.986	0.301982
$52$	−1338.44	−3.56939
$53$	−157.329	−0.407752	−0.203876	−	0.978997i	$-0.565354\pi$
$53$	−157.329	−0.407752	−0.203876	+	0.978997i	$0.565354\pi$
$54$	144.324	0.363705
$55$	61.6045	0.151032
$56$	−800.387	−1.90993
$57$	264.208	0.613951
$58$	842.671	1.90773
$59$	569.443	1.25653	0.628265	−	0.778000i	$-0.283766\pi$
$59$	569.443	1.25653	0.628265	+	0.778000i	$0.283766\pi$
$60$	−345.648	−0.743715
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−1733.74	−3.55138
$63$	107.185	0.214351
$64$	1130.71	2.20842
$65$	−364.356	−0.695274
$66$	176.397	0.328984
$67$	−61.1289	−0.111464	−0.0557320	−	0.998446i	$-0.517749\pi$
$67$	−61.1289	−0.111464	−0.0557320	+	0.998446i	$0.517749\pi$
$68$	−754.238	−1.34507
$69$	−640.563	−1.11760
$70$	−356.524	−0.608754
$71$	1159.94	1.93887	0.969435	−	0.245348i	$-0.0789021\pi$
$71$	1159.94	1.93887	0.969435	+	0.245348i	$0.0789021\pi$
$72$	−604.852	−0.990035
$73$	−239.455	−0.383919	−0.191960	−	0.981403i	$-0.561484\pi$
$73$	−239.455	−0.383919	−0.191960	+	0.981403i	$0.561484\pi$
$74$	−1310.27	−2.05832
$75$	280.906	0.432483
$76$	−1811.83	−2.73462
$77$	131.004	0.193887
$78$	−1043.29	−1.51447
$79$	−380.622	−0.542067	−0.271034	−	0.962570i	$-0.587365\pi$
$79$	−380.622	−0.542067	−0.271034	+	0.962570i	$0.587365\pi$
$80$	1090.16	1.52354
$81$	81.0000	0.111111
$82$	−371.968	−0.500939
$83$	−460.439	−0.608913	−0.304456	−	0.952526i	$-0.598475\pi$
$83$	−460.439	−0.608913	−0.304456	+	0.952526i	$0.598475\pi$
$84$	−735.033	−0.954746
$85$	−205.322	−0.262004
$86$	688.617	0.863436
$87$	472.937	0.582806
$88$	−739.264	−0.895520
$89$	−176.098	−0.209734	−0.104867	−	0.994486i	$-0.533442\pi$
$89$	−176.098	−0.209734	−0.104867	+	0.994486i	$0.533442\pi$
$90$	−269.425	−0.315555
$91$	−774.817	−0.892559
$92$	4392.71	4.97796
$93$	−973.038	−1.08494
$94$	278.259	0.305321
$95$	−493.224	−0.532671
$96$	1508.58	1.60384
$97$	−1351.41	−1.41459	−0.707294	−	0.706920i	$-0.750084\pi$
$97$	−1351.41	−1.41459	−0.707294	+	0.706920i	$0.750084\pi$
$98$	1075.29	1.10838
$99$	99.0000	0.100504
$100$	−1926.34	−1.92634
$101$	371.331	0.365830	0.182915	−	0.983129i	$-0.441447\pi$
$101$	371.331	0.365830	0.182915	+	0.983129i	$0.441447\pi$
$102$	−587.913	−0.570707
$103$	−1439.17	−1.37675	−0.688375	−	0.725355i	$-0.741675\pi$
$103$	−1439.17	−1.37675	−0.688375	+	0.725355i	$0.741675\pi$
$104$	4372.33	4.12252
$105$	−200.094	−0.185973
$106$	840.980	0.770597
$107$	2094.80	1.89263	0.946317	−	0.323240i	$-0.104772\pi$
$107$	2094.80	1.89263	0.946317	+	0.323240i	$0.104772\pi$
$108$	−555.465	−0.494904
$109$	−1203.50	−1.05756	−0.528781	−	0.848758i	$-0.677351\pi$
$109$	−1203.50	−1.05756	−0.528781	+	0.848758i	$0.677351\pi$
$110$	−329.298	−0.285430
$111$	−735.368	−0.628812
$112$	2318.26	1.95585
$113$	−1797.18	−1.49615	−0.748073	−	0.663616i	$-0.769021\pi$
$113$	−1797.18	−1.49615	−0.748073	+	0.663616i	$0.769021\pi$
$114$	−1412.28	−1.16029
$115$	1195.80	0.969646
$116$	−3243.21	−2.59590
$117$	−585.529	−0.462668
$118$	−3043.87	−2.37467
$119$	−436.625	−0.336348
$120$	1129.14	0.858966
$121$	121.000	0.0909091
$122$	326.066	0.241973
$123$	−208.762	−0.153036
$124$	6672.69	4.83246
$125$	−1224.45	−0.876144
$126$	−572.943	−0.405094
$127$	1765.29	1.23342	0.616711	−	0.787190i	$-0.288465\pi$
$127$	1765.29	1.23342	0.616711	+	0.787190i	$0.288465\pi$
$128$	−2021.17	−1.39569
$129$	386.476	0.263778
$130$	1947.61	1.31397
$131$	−1950.54	−1.30091	−0.650455	−	0.759545i	$-0.725422\pi$
$131$	−1950.54	−1.30091	−0.650455	+	0.759545i	$0.725422\pi$
$132$	−678.901	−0.447657
$133$	−1048.86	−0.683818
$134$	326.755	0.210652
$135$	−151.211	−0.0964013
$136$	2463.90	1.55351
$137$	605.311	0.377483	0.188742	−	0.982027i	$-0.439559\pi$
$137$	605.311	0.377483	0.188742	+	0.982027i	$0.439559\pi$
$138$	3424.03	2.11212
$139$	−1538.60	−0.938863	−0.469431	−	0.882969i	$-0.655541\pi$
$139$	−1538.60	−0.938863	−0.469431	+	0.882969i	$0.655541\pi$
$140$	1372.16	0.828349
$141$	156.169	0.0932750
$142$	−6200.30	−3.66421
$143$	−715.647	−0.418499
$144$	1751.91	1.01384
$145$	−882.880	−0.505650
$146$	1279.97	0.725557
$147$	603.492	0.338607
$148$	5042.85	2.80081
$149$	3506.82	1.92812	0.964060	−	0.265684i	$-0.0855979\pi$
$149$	3506.82	1.92812	0.964060	+	0.265684i	$0.0855979\pi$
$150$	−1501.54	−0.817336
$151$	1768.32	0.953004	0.476502	−	0.879173i	$-0.341905\pi$
$151$	1768.32	0.953004	0.476502	+	0.879173i	$0.341905\pi$
$152$	5918.77	3.15839
$153$	−329.958	−0.174350
$154$	−700.264	−0.366421
$155$	1816.47	0.941306
$156$	4015.32	2.06079
$157$	−2101.06	−1.06804	−0.534022	−	0.845471i	$-0.679320\pi$
$157$	−2101.06	−1.06804	−0.534022	+	0.845471i	$0.679320\pi$
$158$	2034.56	1.02443
$159$	471.988	0.235416
$160$	−2816.22	−1.39151
$161$	2542.92	1.24479
$162$	−432.973	−0.209985
$163$	125.648	0.0603772	0.0301886	−	0.999544i	$-0.490389\pi$
$163$	125.648	0.0603772	0.0301886	+	0.999544i	$0.490389\pi$
$164$	1431.60	0.681642
$165$	−184.814	−0.0871983
$166$	2461.21	1.15076
$167$	2150.26	0.996358	0.498179	−	0.867074i	$-0.334002\pi$
$167$	2150.26	0.996358	0.498179	+	0.867074i	$0.334002\pi$
$168$	2401.16	1.10270
$169$	2035.64	0.926557
$170$	1097.52	0.495152
$171$	−792.624	−0.354465
$172$	−2650.29	−1.17490
$173$	1144.64	0.503035	0.251517	−	0.967853i	$-0.419070\pi$
$173$	1144.64	0.503035	0.251517	+	0.967853i	$0.419070\pi$
$174$	−2528.01	−1.10143
$175$	−1115.15	−0.481699
$176$	2141.22	0.917049
$177$	−1708.33	−0.725457
$178$	941.306	0.396370
$179$	1157.19	0.483199	0.241599	−	0.970376i	$-0.422328\pi$
$179$	1157.19	0.483199	0.241599	+	0.970376i	$0.422328\pi$
$180$	1036.94	0.429384
$181$	1703.66	0.699626	0.349813	−	0.936820i	$-0.386245\pi$
$181$	1703.66	0.699626	0.349813	+	0.936820i	$0.386245\pi$
$182$	4141.67	1.68682
$183$	183.000	0.0739221
$184$	−14349.8	−5.74937
$185$	1372.79	0.545564
$186$	5201.23	2.05039
$187$	−403.282	−0.157705
$188$	−1070.94	−0.415459
$189$	−321.556	−0.123755
$190$	2636.46	1.00668
$191$	−888.543	−0.336611	−0.168306	−	0.985735i	$-0.553830\pi$
$191$	−888.543	−0.336611	−0.168306	+	0.985735i	$0.553830\pi$
$192$	−3392.14	−1.27503
$193$	−3145.14	−1.17302	−0.586509	−	0.809943i	$-0.699498\pi$
$193$	−3145.14	−1.17302	−0.586509	+	0.809943i	$0.699498\pi$
$194$	7223.76	2.67338
$195$	1093.07	0.401416
$196$	−4138.50	−1.50820
$197$	−698.747	−0.252709	−0.126354	−	0.991985i	$-0.540328\pi$
$197$	−698.747	−0.252709	−0.126354	+	0.991985i	$0.540328\pi$
$198$	−529.190	−0.189939
$199$	−907.165	−0.323152	−0.161576	−	0.986860i	$-0.551658\pi$
$199$	−907.165	−0.323152	−0.161576	+	0.986860i	$0.551658\pi$
$200$	6292.84	2.22486
$201$	183.387	0.0643537
$202$	−1984.90	−0.691370
$203$	−1877.48	−0.649129
$204$	2262.71	0.776577
$205$	389.717	0.132776
$206$	7692.84	2.60187
$207$	1921.69	0.645249
$208$	−12664.1	−4.22162
$209$	−968.763	−0.320625
$210$	1069.57	0.351464
$211$	4586.84	1.49655	0.748273	−	0.663391i	$-0.230883\pi$
$211$	4586.84	1.49655	0.748273	+	0.663391i	$0.230883\pi$
$212$	−3236.70	−1.04857
$213$	−3479.83	−1.11941
$214$	−11197.4	−3.57683
$215$	−721.475	−0.228857
$216$	1814.56	0.571597
$217$	3862.79	1.20840
$218$	6433.12	1.99865
$219$	718.366	0.221656
$220$	1267.37	0.388393
$221$	2385.18	0.725994
$222$	3930.80	1.18837
$223$	2654.35	0.797077	0.398539	−	0.917152i	$-0.369517\pi$
$223$	2654.35	0.797077	0.398539	+	0.917152i	$0.369517\pi$
$224$	−5988.81	−1.78636
$225$	−842.719	−0.249694
$226$	9606.56	2.82752
$227$	−2944.69	−0.860996	−0.430498	−	0.902592i	$-0.641662\pi$
$227$	−2944.69	−0.860996	−0.430498	+	0.902592i	$0.641662\pi$
$228$	5435.49	1.57883
$229$	−4005.37	−1.15582	−0.577909	−	0.816101i	$-0.696131\pi$
$229$	−4005.37	−1.15582	−0.577909	+	0.816101i	$0.696131\pi$
$230$	−6391.99	−1.83250
$231$	−393.013	−0.111941
$232$	10594.7	2.99817
$233$	−545.142	−0.153276	−0.0766382	−	0.997059i	$-0.524419\pi$
$233$	−545.142	−0.153276	−0.0766382	+	0.997059i	$0.524419\pi$
$234$	3129.86	0.874381
$235$	−291.536	−0.0809265
$236$	11715.0	3.23128
$237$	1141.87	0.312963
$238$	2333.91	0.635652
$239$	96.4368	0.0261003	0.0130502	−	0.999915i	$-0.495846\pi$
$239$	96.4368	0.0261003	0.0130502	+	0.999915i	$0.495846\pi$
$240$	−3270.47	−0.879616
$241$	2447.68	0.654228	0.327114	−	0.944985i	$-0.393924\pi$
$241$	2447.68	0.654228	0.327114	+	0.944985i	$0.393924\pi$
$242$	−646.787	−0.171806
$243$	−243.000	−0.0641500
$244$	−1254.94	−0.329259
$245$	−1126.60	−0.293779
$246$	1115.90	0.289217
$247$	5729.68	1.47600
$248$	−21797.9	−5.58133
$249$	1381.32	0.351556
$250$	6545.10	1.65579
$251$	4972.05	1.25033	0.625166	−	0.780492i	$-0.285031\pi$
$251$	4972.05	1.25033	0.625166	+	0.780492i	$0.285031\pi$
$252$	2205.10	0.551223
$253$	2348.73	0.583650
$254$	−9436.11	−2.33100
$255$	615.966	0.151268
$256$	1758.16	0.429238
$257$	−2282.02	−0.553884	−0.276942	−	0.960887i	$-0.589321\pi$
$257$	−2282.02	−0.553884	−0.276942	+	0.960887i	$0.589321\pi$
$258$	−2065.85	−0.498505
$259$	2919.29	0.700369
$260$	−7495.81	−1.78796
$261$	−1418.81	−0.336483
$262$	10426.3	2.45854
$263$	−6484.06	−1.52024	−0.760122	−	0.649781i	$-0.774861\pi$
$263$	−6484.06	−1.52024	−0.760122	+	0.649781i	$0.774861\pi$
$264$	2217.79	0.517029
$265$	−881.109	−0.204249
$266$	5606.53	1.29232
$267$	528.294	0.121090
$268$	−1257.59	−0.286640
$269$	−7210.76	−1.63438	−0.817189	−	0.576370i	$-0.804469\pi$
$269$	−7210.76	−1.63438	−0.817189	+	0.576370i	$0.804469\pi$
$270$	808.276	0.182186
$271$	2635.52	0.590762	0.295381	−	0.955379i	$-0.404553\pi$
$271$	2635.52	0.590762	0.295381	+	0.955379i	$0.404553\pi$
$272$	−7136.49	−1.59086
$273$	2324.45	0.515319
$274$	−3235.60	−0.713393
$275$	−1029.99	−0.225857
$276$	−13178.1	−2.87403
$277$	−6923.25	−1.50173	−0.750863	−	0.660458i	$-0.770362\pi$
$277$	−6923.25	−1.50173	−0.750863	+	0.660458i	$0.770362\pi$
$278$	8224.33	1.77433
$279$	2919.11	0.626390
$280$	−4482.49	−0.956715
$281$	6692.69	1.42083	0.710413	−	0.703785i	$-0.248508\pi$
$281$	6692.69	1.42083	0.710413	+	0.703785i	$0.248508\pi$
$282$	−834.776	−0.176277
$283$	−4429.41	−0.930392	−0.465196	−	0.885208i	$-0.654016\pi$
$283$	−4429.41	−0.930392	−0.465196	+	0.885208i	$0.654016\pi$
$284$	23863.2	4.98599
$285$	1479.67	0.307538
$286$	3825.38	0.790907
$287$	828.748	0.170451
$288$	−4525.74	−0.925979
$289$	−3568.90	−0.726420
$290$	4719.30	0.955610
$291$	4054.23	0.816712
$292$	−4926.26	−0.987286
$293$	−6177.77	−1.23177	−0.615886	−	0.787835i	$-0.711202\pi$
$293$	−6177.77	−1.23177	−0.615886	+	0.787835i	$0.711202\pi$
$294$	−3225.88	−0.639922
$295$	3189.12	0.629415
$296$	−16473.7	−3.23484
$297$	−297.000	−0.0580259
$298$	−18745.2	−3.64389
$299$	−13891.4	−2.68683
$300$	5779.02	1.11217
$301$	−1534.24	−0.293795
$302$	−9452.27	−1.80105
$303$	−1113.99	−0.211212
$304$	−17143.3	−3.23432
$305$	−341.625	−0.0641357
$306$	1763.74	0.329498
$307$	5299.64	0.985232	0.492616	−	0.870247i	$-0.336041\pi$
$307$	5299.64	0.985232	0.492616	+	0.870247i	$0.336041\pi$
$308$	2695.12	0.498600
$309$	4317.50	0.794866
$310$	−9709.67	−1.77894
$311$	−4158.54	−0.758229	−0.379115	−	0.925350i	$-0.623771\pi$
$311$	−4158.54	−0.758229	−0.379115	+	0.925350i	$0.623771\pi$
$312$	−13117.0	−2.38014
$313$	−358.313	−0.0647062	−0.0323531	−	0.999477i	$-0.510300\pi$
$313$	−358.313	−0.0647062	−0.0323531	+	0.999477i	$0.510300\pi$
$314$	11230.9	2.01846
$315$	600.282	0.107372
$316$	−7830.44	−1.39398
$317$	671.518	0.118979	0.0594893	−	0.998229i	$-0.481053\pi$
$317$	671.518	0.118979	0.0594893	+	0.998229i	$0.481053\pi$
$318$	−2522.94	−0.444904
$319$	−1734.10	−0.304361
$320$	6332.45	1.10623
$321$	−6284.40	−1.09271
$322$	−13592.8	−2.35248
$323$	3228.79	0.556207
$324$	1666.39	0.285733
$325$	6091.81	1.03973
$326$	−671.631	−0.114105
$327$	3610.49	0.610584
$328$	−4676.67	−0.787273
$329$	−619.963	−0.103890
$330$	987.893	0.164793
$331$	4839.99	0.803716	0.401858	−	0.915702i	$-0.368364\pi$
$331$	4839.99	0.803716	0.401858	+	0.915702i	$0.368364\pi$
$332$	−9472.50	−1.56588
$333$	2206.11	0.363045
$334$	−11493.9	−1.88298
$335$	−342.347	−0.0558340
$336$	−6954.77	−1.12921
$337$	1730.41	0.279708	0.139854	−	0.990172i	$-0.455337\pi$
$337$	1730.41	0.279708	0.139854	+	0.990172i	$0.455337\pi$
$338$	−10881.2	−1.75107
$339$	5391.54	0.863801
$340$	−4224.04	−0.673767
$341$	3567.81	0.566591
$342$	4236.85	0.669891
$343$	−6480.72	−1.02019
$344$	8657.82	1.35697
$345$	−3587.41	−0.559826
$346$	−6118.47	−0.950668
$347$	381.564	0.0590300	0.0295150	−	0.999564i	$-0.490604\pi$
$347$	381.564	0.0590300	0.0295150	+	0.999564i	$0.490604\pi$
$348$	9729.62	1.49874
$349$	5554.13	0.851879	0.425940	−	0.904752i	$-0.359944\pi$
$349$	5554.13	0.851879	0.425940	+	0.904752i	$0.359944\pi$
$350$	5960.86	0.910348
$351$	1756.59	0.267122
$352$	−5531.46	−0.837579
$353$	−11958.6	−1.80309	−0.901547	−	0.432681i	$-0.857568\pi$
$353$	−11958.6	−1.80309	−0.901547	+	0.432681i	$0.857568\pi$
$354$	9131.62	1.37102
$355$	6496.15	0.971211
$356$	−3622.82	−0.539352
$357$	1309.88	0.194190
$358$	−6185.60	−0.913181
$359$	6568.88	0.965717	0.482858	−	0.875698i	$-0.339599\pi$
$359$	6568.88	0.965717	0.482858	+	0.875698i	$0.339599\pi$
$360$	−3387.42	−0.495924
$361$	897.206	0.130807
$362$	−9106.67	−1.32220
$363$	−363.000	−0.0524864
$364$	−15940.1	−2.29530
$365$	−1341.05	−0.192311
$366$	−978.199	−0.139703
$367$	−7502.45	−1.06710	−0.533549	−	0.845769i	$-0.679142\pi$
$367$	−7502.45	−1.06710	−0.533549	+	0.845769i	$0.679142\pi$
$368$	41563.2	5.88759
$369$	626.285	0.0883553
$370$	−7338.03	−1.03104
$371$	−1873.71	−0.262206
$372$	−20018.1	−2.79002
$373$	−3130.70	−0.434588	−0.217294	−	0.976106i	$-0.569723\pi$
$373$	−3130.70	−0.434588	−0.217294	+	0.976106i	$0.569723\pi$
$374$	2155.68	0.298042
$375$	3673.34	0.505842
$376$	3498.48	0.479841
$377$	10256.2	1.40112
$378$	1718.83	0.233881
$379$	7575.01	1.02666	0.513328	−	0.858193i	$-0.328413\pi$
$379$	7575.01	1.02666	0.513328	+	0.858193i	$0.328413\pi$
$380$	−10147.0	−1.36981
$381$	−5295.88	−0.712116
$382$	4749.57	0.636150
$383$	−8679.74	−1.15800	−0.579000	−	0.815327i	$-0.696557\pi$
$383$	−8679.74	−1.15800	−0.579000	+	0.815327i	$0.696557\pi$
$384$	6063.51	0.805800
$385$	733.678	0.0971213
$386$	16811.9	2.21685
$387$	−1159.43	−0.152292
$388$	−27802.3	−3.63775
$389$	−12722.8	−1.65828	−0.829141	−	0.559040i	$-0.811170\pi$
$389$	−12722.8	−1.65828	−0.829141	+	0.559040i	$0.811170\pi$
$390$	−5842.83	−0.758623
$391$	−7828.09	−1.01249
$392$	13519.4	1.74192
$393$	5851.61	0.751080
$394$	3735.05	0.477586
$395$	−2131.64	−0.271530
$396$	2036.70	0.258455
$397$	−370.499	−0.0468384	−0.0234192	−	0.999726i	$-0.507455\pi$
$397$	−370.499	−0.0468384	−0.0234192	+	0.999726i	$0.507455\pi$
$398$	4849.12	0.610714
$399$	3146.58	0.394802
$400$	−18226.7	−2.27834
$401$	7488.12	0.932516	0.466258	−	0.884649i	$-0.345602\pi$
$401$	7488.12	0.932516	0.466258	+	0.884649i	$0.345602\pi$
$402$	−980.266	−0.121620
$403$	−21101.6	−2.60830
$404$	7639.31	0.940767
$405$	453.633	0.0556573
$406$	10035.8	1.22677
$407$	2696.35	0.328386
$408$	−7391.69	−0.896920
$409$	−6620.06	−0.800344	−0.400172	−	0.916440i	$-0.631050\pi$
$409$	−6620.06	−0.800344	−0.400172	+	0.916440i	$0.631050\pi$
$410$	−2083.17	−0.250928
$411$	−1815.93	−0.217940
$412$	−29607.6	−3.54044
$413$	6781.78	0.808013
$414$	−10272.1	−1.21943
$415$	−2578.65	−0.305014
$416$	32715.5	3.85579
$417$	4615.79	0.542053
$418$	5178.37	0.605939
$419$	−16084.2	−1.87533	−0.937664	−	0.347544i	$-0.887016\pi$
$419$	−16084.2	−1.87533	−0.937664	+	0.347544i	$0.887016\pi$
$420$	−4116.49	−0.478248
$421$	−13808.3	−1.59852	−0.799260	−	0.600985i	$-0.794775\pi$
$421$	−13808.3	−1.59852	−0.799260	+	0.600985i	$0.794775\pi$
$422$	−24518.3	−2.82827
$423$	−468.506	−0.0538523
$424$	10573.4	1.21107
$425$	3432.86	0.391807
$426$	18600.9	2.11553
$427$	−726.479	−0.0823344
$428$	43095.8	4.86709
$429$	2146.94	0.241621
$430$	3856.54	0.432509
$431$	3894.78	0.435279	0.217639	−	0.976029i	$-0.430164\pi$
$431$	3894.78	0.435279	0.217639	+	0.976029i	$0.430164\pi$
$432$	−5255.72	−0.585338
$433$	−2176.70	−0.241583	−0.120792	−	0.992678i	$-0.538543\pi$
$433$	−2176.70	−0.241583	−0.120792	+	0.992678i	$0.538543\pi$
$434$	−20648.0	−2.28372
$435$	2648.64	0.291937
$436$	−24759.3	−2.71962
$437$	−18804.6	−2.05846
$438$	−3839.92	−0.418900
$439$	−8234.84	−0.895279	−0.447640	−	0.894214i	$-0.647735\pi$
$439$	−8234.84	−0.895279	−0.447640	+	0.894214i	$0.647735\pi$
$440$	−4140.18	−0.448580
$441$	−1810.48	−0.195495
$442$	−12749.6	−1.37203
$443$	13478.1	1.44552	0.722760	−	0.691099i	$-0.242873\pi$
$443$	13478.1	1.44552	0.722760	+	0.691099i	$0.242873\pi$
$444$	−15128.6	−1.61705
$445$	−986.222	−0.105059
$446$	−14188.4	−1.50637
$447$	−10520.5	−1.11320
$448$	13466.2	1.42013
$449$	10209.1	1.07304	0.536520	−	0.843888i	$-0.319739\pi$
$449$	10209.1	1.07304	0.536520	+	0.843888i	$0.319739\pi$
$450$	4504.63	0.471889
$451$	765.459	0.0799204
$452$	−36973.0	−3.84748
$453$	−5304.95	−0.550217
$454$	15740.4	1.62717
$455$	−4339.29	−0.447097
$456$	−17756.3	−1.82350
$457$	−463.835	−0.0474776	−0.0237388	−	0.999718i	$-0.507557\pi$
$457$	−463.835	−0.0474776	−0.0237388	+	0.999718i	$0.507557\pi$
$458$	21410.1	2.18434
$459$	989.873	0.100661
$460$	24601.0	2.49354
$461$	−9677.48	−0.977712	−0.488856	−	0.872364i	$-0.662586\pi$
$461$	−9677.48	−0.977712	−0.488856	+	0.872364i	$0.662586\pi$
$462$	2100.79	0.211553
$463$	−8472.55	−0.850437	−0.425219	−	0.905091i	$-0.639803\pi$
$463$	−8472.55	−0.850437	−0.425219	+	0.905091i	$0.639803\pi$
$464$	−30686.7	−3.07025
$465$	−5449.41	−0.543463
$466$	2913.97	0.289672
$467$	−10374.5	−1.02800	−0.514000	−	0.857790i	$-0.671837\pi$
$467$	−10374.5	−1.02800	−0.514000	+	0.857790i	$0.671837\pi$
$468$	−12045.9	−1.18980
$469$	−728.014	−0.0716771
$470$	1558.36	0.152940
$471$	6303.18	0.616635
$472$	−38269.9	−3.73202
$473$	−1417.08	−0.137753
$474$	−6103.67	−0.591457
$475$	8246.41	0.796571
$476$	−8982.59	−0.864950
$477$	−1415.96	−0.135917
$478$	−515.488	−0.0493261
$479$	9103.72	0.868392	0.434196	−	0.900818i	$-0.357033\pi$
$479$	9103.72	0.868392	0.434196	+	0.900818i	$0.357033\pi$
$480$	8448.67	0.803390
$481$	−15947.4	−1.51172
$482$	−13083.7	−1.23640
$483$	−7628.77	−0.718677
$484$	2489.30	0.233781
$485$	−7568.46	−0.708589
$486$	1298.92	0.121235
$487$	342.102	0.0318319	0.0159160	−	0.999873i	$-0.494934\pi$
$487$	342.102	0.0318319	0.0159160	+	0.999873i	$0.494934\pi$
$488$	4099.55	0.380283
$489$	−376.943	−0.0348588
$490$	6022.08	0.555204
$491$	−11969.5	−1.10016	−0.550078	−	0.835113i	$-0.685402\pi$
$491$	−11969.5	−1.10016	−0.550078	+	0.835113i	$0.685402\pi$
$492$	−4294.80	−0.393546
$493$	5779.60	0.527992
$494$	−30627.2	−2.78944
$495$	554.441	0.0503439
$496$	63136.0	5.71551
$497$	13814.3	1.24679
$498$	−7383.62	−0.664394
$499$	−6166.77	−0.553232	−0.276616	−	0.960981i	$-0.589213\pi$
$499$	−6166.77	−0.553232	−0.276616	+	0.960981i	$0.589213\pi$
$500$	−25190.3	−2.25309
$501$	−6450.77	−0.575247
$502$	−26577.4	−2.36296
$503$	17734.4	1.57204	0.786022	−	0.618199i	$-0.212137\pi$
$503$	17734.4	1.57204	0.786022	+	0.618199i	$0.212137\pi$
$504$	−7203.48	−0.636644
$505$	2079.61	0.183250
$506$	−12554.8	−1.10302
$507$	−6106.93	−0.534948
$508$	36317.0	3.17186
$509$	8779.14	0.764496	0.382248	−	0.924060i	$-0.375150\pi$
$509$	8779.14	0.764496	0.382248	+	0.924060i	$0.375150\pi$
$510$	−3292.55	−0.285876
$511$	−2851.79	−0.246880
$512$	6771.38	0.584483
$513$	2377.87	0.204650
$514$	12198.2	1.04677
$515$	−8059.92	−0.689636
$516$	7950.88	0.678330
$517$	−572.618	−0.0487113
$518$	−15604.6	−1.32360
$519$	−3433.91	−0.290427
$520$	24486.8	2.06504
$521$	21583.9	1.81499	0.907495	−	0.420064i	$-0.137992\pi$
$521$	21583.9	1.81499	0.907495	+	0.420064i	$0.137992\pi$
$522$	7584.04	0.635909
$523$	11072.3	0.925736	0.462868	−	0.886427i	$-0.346820\pi$
$523$	11072.3	0.925736	0.462868	+	0.886427i	$0.346820\pi$
$524$	−40127.9	−3.34541
$525$	3345.45	0.278109
$526$	34659.5	2.87306
$527$	−11891.2	−0.982898
$528$	−6423.66	−0.529458
$529$	33424.2	2.74712
$530$	4709.83	0.386004
$531$	5124.99	0.418843
$532$	−21578.0	−1.75850
$533$	−4527.26	−0.367913
$534$	−2823.92	−0.228844
$535$	11731.7	0.948051
$536$	4108.22	0.331060
$537$	−3471.58	−0.278975
$538$	38544.0	3.08876
$539$	−2212.81	−0.176832
$540$	−3110.83	−0.247905
$541$	6634.56	0.527249	0.263625	−	0.964625i	$-0.415082\pi$
$541$	6634.56	0.527249	0.263625	+	0.964625i	$0.415082\pi$
$542$	−14087.8	−1.11646
$543$	−5110.99	−0.403929
$544$	18435.8	1.45300
$545$	−6740.08	−0.529749
$546$	−12425.0	−0.973884
$547$	−15503.6	−1.21186	−0.605929	−	0.795519i	$-0.707198\pi$
$547$	−15503.6	−1.21186	−0.605929	+	0.795519i	$0.707198\pi$
$548$	12452.9	0.970734
$549$	−549.000	−0.0426790
$550$	5505.65	0.426840
$551$	13883.7	1.07344
$552$	43049.5	3.31940
$553$	−4533.01	−0.348577
$554$	37007.2	2.83806
$555$	−4118.36	−0.314982
$556$	−31653.1	−2.41438
$557$	6127.36	0.466113	0.233056	−	0.972463i	$-0.425127\pi$
$557$	6127.36	0.466113	0.233056	+	0.972463i	$0.425127\pi$
$558$	−15603.7	−1.18379
$559$	8381.23	0.634147
$560$	12983.2	0.979715
$561$	1209.84	0.0910511
$562$	−35774.8	−2.68517
$563$	−6641.62	−0.497177	−0.248589	−	0.968609i	$-0.579967\pi$
$563$	−6641.62	−0.497177	−0.248589	+	0.968609i	$0.579967\pi$
$564$	3212.82	0.239865
$565$	−10065.0	−0.749444
$566$	23676.7	1.75832
$567$	964.668	0.0714502
$568$	−77954.8	−5.75865
$569$	−4928.27	−0.363100	−0.181550	−	0.983382i	$-0.558111\pi$
$569$	−4928.27	−0.363100	−0.181550	+	0.983382i	$0.558111\pi$
$570$	−7909.37	−0.581205
$571$	15329.0	1.12347	0.561734	−	0.827318i	$-0.310135\pi$
$571$	15329.0	1.12347	0.561734	+	0.827318i	$0.310135\pi$
$572$	−14722.8	−1.07621
$573$	2665.63	0.194342
$574$	−4429.95	−0.322130
$575$	−19993.1	−1.45004
$576$	10176.4	0.736140
$577$	20415.8	1.47300	0.736501	−	0.676436i	$-0.236477\pi$
$577$	20415.8	1.47300	0.736501	+	0.676436i	$0.236477\pi$
$578$	19077.0	1.37284
$579$	9435.43	0.677242
$580$	−18163.3	−1.30033
$581$	−5483.59	−0.391562
$582$	−21671.3	−1.54348
$583$	−1730.62	−0.122942
$584$	16092.8	1.14028
$585$	−3279.20	−0.231758
$586$	33022.3	2.32788
$587$	8942.95	0.628816	0.314408	−	0.949288i	$-0.398194\pi$
$587$	8942.95	0.628816	0.314408	+	0.949288i	$0.398194\pi$
$588$	12415.5	0.870760
$589$	−28564.9	−1.99830
$590$	−17046.9	−1.18951
$591$	2096.24	0.145902
$592$	47714.7	3.31261
$593$	14381.4	0.995907	0.497953	−	0.867204i	$-0.334085\pi$
$593$	14381.4	0.995907	0.497953	+	0.867204i	$0.334085\pi$
$594$	1587.57	0.109661
$595$	−2445.28	−0.168482
$596$	72145.0	4.95834
$597$	2721.50	0.186572
$598$	74254.4	5.07774
$599$	−8220.64	−0.560745	−0.280372	−	0.959891i	$-0.590458\pi$
$599$	−8220.64	−0.560745	−0.280372	+	0.959891i	$0.590458\pi$
$600$	−18878.5	−1.28452
$601$	6778.69	0.460081	0.230040	−	0.973181i	$-0.426114\pi$
$601$	6778.69	0.460081	0.230040	+	0.973181i	$0.426114\pi$
$602$	8201.08	0.555234
$603$	−550.160	−0.0371546
$604$	36379.2	2.45074
$605$	677.650	0.0455378
$606$	5954.69	0.399163
$607$	−1019.21	−0.0681520	−0.0340760	−	0.999419i	$-0.510849\pi$
$607$	−1019.21	−0.0681520	−0.0340760	+	0.999419i	$0.510849\pi$
$608$	44286.6	2.95404
$609$	5632.44	0.374775
$610$	1826.11	0.121208
$611$	3386.71	0.224242
$612$	−6788.14	−0.448357
$613$	−29331.5	−1.93261	−0.966304	−	0.257403i	$-0.917133\pi$
$613$	−29331.5	−1.93261	−0.966304	+	0.257403i	$0.917133\pi$
$614$	−28328.4	−1.86196
$615$	−1169.15	−0.0766581
$616$	−8804.25	−0.575866
$617$	−9651.69	−0.629761	−0.314880	−	0.949131i	$-0.601964\pi$
$617$	−9651.69	−0.629761	−0.314880	+	0.949131i	$0.601964\pi$
$618$	−23078.5	−1.50219
$619$	−26321.3	−1.70912	−0.854558	−	0.519357i	$-0.826172\pi$
$619$	−26321.3	−1.70912	−0.854558	+	0.519357i	$0.826172\pi$
$620$	37369.8	2.42066
$621$	−5765.06	−0.372535
$622$	22228.9	1.43295
$623$	−2097.24	−0.134870
$624$	37992.3	2.43736
$625$	4847.01	0.310209
$626$	1915.31	0.122286
$627$	2906.29	0.185113
$628$	−43224.6	−2.74657
$629$	−8986.68	−0.569670
$630$	−3208.72	−0.202918
$631$	−8089.97	−0.510391	−0.255195	−	0.966889i	$-0.582140\pi$
$631$	−8089.97	−0.510391	−0.255195	+	0.966889i	$0.582140\pi$
$632$	25580.0	1.61000
$633$	−13760.5	−0.864031
$634$	−3589.50	−0.224854
$635$	9886.37	0.617840
$636$	9710.10	0.605394
$637$	13087.5	0.814043
$638$	9269.38	0.575201
$639$	10439.5	0.646290
$640$	−11319.4	−0.699121
$641$	−29213.3	−1.80009	−0.900044	−	0.435799i	$-0.856466\pi$
$641$	−29213.3	−1.80009	−0.900044	+	0.435799i	$0.856466\pi$
$642$	33592.3	2.06508
$643$	−11967.3	−0.733972	−0.366986	−	0.930227i	$-0.619610\pi$
$643$	−11967.3	−0.733972	−0.366986	+	0.930227i	$0.619610\pi$
$644$	52315.0	3.20108
$645$	2164.43	0.132131
$646$	−17259.0	−1.05116
$647$	−3262.45	−0.198238	−0.0991191	−	0.995076i	$-0.531602\pi$
$647$	−3262.45	−0.198238	−0.0991191	+	0.995076i	$0.531602\pi$
$648$	−5443.67	−0.330012
$649$	6263.88	0.378858
$650$	−32562.8	−1.96495
$651$	−11588.4	−0.697672
$652$	2584.92	0.155266
$653$	10795.6	0.646957	0.323479	−	0.946235i	$-0.395148\pi$
$653$	10795.6	0.646957	0.323479	+	0.946235i	$0.395148\pi$
$654$	−19299.4	−1.15392
$655$	−10923.8	−0.651646
$656$	13545.6	0.806199
$657$	−2155.10	−0.127973
$658$	3313.92	0.196337
$659$	2760.90	0.163201	0.0816003	−	0.996665i	$-0.473997\pi$
$659$	2760.90	0.163201	0.0816003	+	0.996665i	$0.473997\pi$
$660$	−3802.12	−0.224239
$661$	10965.5	0.645250	0.322625	−	0.946527i	$-0.395435\pi$
$661$	10965.5	0.645250	0.322625	+	0.946527i	$0.395435\pi$
$662$	−25871.5	−1.51892
$663$	−7155.55	−0.419153
$664$	30944.2	1.80853
$665$	−5874.05	−0.342535
$666$	−11792.4	−0.686106
$667$	−33660.6	−1.95404
$668$	44236.7	2.56223
$669$	−7963.04	−0.460193
$670$	1829.96	0.105519
$671$	−671.000	−0.0386046
$672$	17966.4	1.03135
$673$	11292.3	0.646786	0.323393	−	0.946265i	$-0.395176\pi$
$673$	11292.3	0.646786	0.323393	+	0.946265i	$0.395176\pi$
$674$	−9249.67	−0.528611
$675$	2528.16	0.144161
$676$	41878.8	2.38273
$677$	1361.78	0.0773078	0.0386539	−	0.999253i	$-0.487693\pi$
$677$	1361.78	0.0773078	0.0386539	+	0.999253i	$0.487693\pi$
$678$	−28819.7	−1.63247
$679$	−16094.6	−0.909653
$680$	13798.8	0.778178
$681$	8834.07	0.497096
$682$	−19071.2	−1.07078
$683$	−29251.8	−1.63878	−0.819391	−	0.573235i	$-0.805688\pi$
$683$	−29251.8	−1.63878	−0.819391	+	0.573235i	$0.805688\pi$
$684$	−16306.5	−0.911540
$685$	3389.99	0.189087
$686$	34641.7	1.92803
$687$	12016.1	0.667312
$688$	−25076.7	−1.38959
$689$	10235.7	0.565961
$690$	19176.0	1.05800
$691$	6444.03	0.354765	0.177382	−	0.984142i	$-0.443237\pi$
$691$	6444.03	0.354765	0.177382	+	0.984142i	$0.443237\pi$
$692$	23548.3	1.29360
$693$	1179.04	0.0646291
$694$	−2039.59	−0.111559
$695$	−8616.76	−0.470291
$696$	−31784.1	−1.73100
$697$	−2551.20	−0.138642
$698$	−29688.8	−1.60994
$699$	1635.42	0.0884942
$700$	−22941.7	−1.23874
$701$	−29690.6	−1.59971	−0.799857	−	0.600191i	$-0.795091\pi$
$701$	−29690.6	−1.59971	−0.799857	+	0.600191i	$0.795091\pi$
$702$	−9389.57	−0.504824
$703$	−21587.8	−1.15818
$704$	12437.8	0.665864
$705$	874.608	0.0467229
$706$	63922.9	3.40761
$707$	4422.37	0.235248
$708$	−35145.1	−1.86558
$709$	−12050.0	−0.638287	−0.319143	−	0.947706i	$-0.603395\pi$
$709$	−12050.0	−0.638287	−0.319143	+	0.947706i	$0.603395\pi$
$710$	−34724.2	−1.83546
$711$	−3425.60	−0.180689
$712$	11834.8	0.622933
$713$	69254.6	3.63760
$714$	−7001.74	−0.366994
$715$	−4007.91	−0.209633
$716$	23806.6	1.24259
$717$	−289.310	−0.0150690
$718$	−35113.0	−1.82508
$719$	27701.7	1.43685	0.718427	−	0.695602i	$-0.244862\pi$
$719$	27701.7	1.43685	0.718427	+	0.695602i	$0.244862\pi$
$720$	9811.40	0.507846
$721$	−17139.7	−0.885321
$722$	−4795.88	−0.247208
$723$	−7343.04	−0.377719
$724$	35049.0	1.79915
$725$	14761.2	0.756162
$726$	1940.36	0.0991923
$727$	−4178.99	−0.213192	−0.106596	−	0.994302i	$-0.533995\pi$
$727$	−4178.99	−0.213192	−0.106596	+	0.994302i	$0.533995\pi$
$728$	52072.2	2.65099
$729$	729.000	0.0370370
$730$	7168.37	0.363443
$731$	4722.99	0.238969
$732$	3764.82	0.190098
$733$	3472.68	0.174988	0.0874942	−	0.996165i	$-0.472114\pi$
$733$	3472.68	0.174988	0.0874942	+	0.996165i	$0.472114\pi$
$734$	40103.2	2.01667
$735$	3379.80	0.169614
$736$	−107371.	−5.37738
$737$	−672.418	−0.0336076
$738$	−3347.71	−0.166980
$739$	20105.9	1.00082	0.500410	−	0.865788i	$-0.333183\pi$
$739$	20105.9	1.00082	0.500410	+	0.865788i	$0.333183\pi$
$740$	28242.0	1.40297
$741$	−17189.0	−0.852167
$742$	10015.6	0.495534
$743$	−33903.7	−1.67403	−0.837016	−	0.547178i	$-0.815702\pi$
$743$	−33903.7	−1.67403	−0.837016	+	0.547178i	$0.815702\pi$
$744$	65393.8	3.22238
$745$	19639.6	0.965826
$746$	16734.7	0.821314
$747$	−4143.95	−0.202971
$748$	−8296.62	−0.405554
$749$	24948.0	1.21706
$750$	−19635.3	−0.955973
$751$	−3819.07	−0.185566	−0.0927829	−	0.995686i	$-0.529576\pi$
$751$	−3819.07	−0.185566	−0.0927829	+	0.995686i	$0.529576\pi$
$752$	−10133.1	−0.491377
$753$	−14916.2	−0.721879
$754$	−54823.1	−2.64793
$755$	9903.30	0.477375
$756$	−6615.30	−0.318249
$757$	−3192.91	−0.153300	−0.0766502	−	0.997058i	$-0.524422\pi$
$757$	−3192.91	−0.153300	−0.0766502	+	0.997058i	$0.524422\pi$
$758$	−40491.1	−1.94024
$759$	−7046.19	−0.336970
$760$	33147.5	1.58209
$761$	−35937.6	−1.71188	−0.855939	−	0.517077i	$-0.827020\pi$
$761$	−35937.6	−1.71188	−0.855939	+	0.517077i	$0.827020\pi$
$762$	28308.3	1.34580
$763$	−14333.0	−0.680067
$764$	−18279.8	−0.865627
$765$	−1847.90	−0.0873345
$766$	46396.3	2.18847
$767$	−37047.3	−1.74407
$768$	−5274.48	−0.247821
$769$	−2005.99	−0.0940676	−0.0470338	−	0.998893i	$-0.514977\pi$
$769$	−2005.99	−0.0940676	−0.0470338	+	0.998893i	$0.514977\pi$
$770$	−3921.77	−0.183546
$771$	6846.05	0.319785
$772$	−64704.3	−3.01653
$773$	−16645.6	−0.774515	−0.387258	−	0.921972i	$-0.626578\pi$
$773$	−16645.6	−0.774515	−0.387258	+	0.921972i	$0.626578\pi$
$774$	6197.55	0.287812
$775$	−30370.3	−1.40765
$776$	90822.7	4.20147
$777$	−8757.86	−0.404358
$778$	68007.8	3.13393
$779$	−6128.50	−0.281869
$780$	22487.4	1.03228
$781$	12759.4	0.584591
$782$	41843.9	1.91347
$783$	4256.43	0.194269
$784$	−39157.9	−1.78380
$785$	−11766.8	−0.535000
$786$	−31278.9	−1.41944
$787$	−10171.8	−0.460720	−0.230360	−	0.973105i	$-0.573990\pi$
$787$	−10171.8	−0.460720	−0.230360	+	0.973105i	$0.573990\pi$
$788$	−14375.2	−0.649865
$789$	19452.2	0.877713
$790$	11394.4	0.513155
$791$	−21403.5	−0.962100
$792$	−6653.37	−0.298507
$793$	3968.59	0.177716
$794$	1980.45	0.0885183
$795$	2643.33	0.117923
$796$	−18662.9	−0.831016
$797$	−22409.9	−0.995985	−0.497993	−	0.867181i	$-0.665929\pi$
$797$	−22409.9	−0.995985	−0.497993	+	0.867181i	$0.665929\pi$
$798$	−16819.6	−0.746124
$799$	1908.48	0.0845022
$800$	47085.5	2.08091
$801$	−1584.88	−0.0699115
$802$	−40026.6	−1.76233
$803$	−2634.01	−0.115756
$804$	3772.77	0.165492
$805$	14241.4	0.623533
$806$	112795.	4.92933
$807$	21632.3	0.943609
$808$	−24955.6	−1.08655
$809$	26373.4	1.14616	0.573078	−	0.819501i	$-0.305749\pi$
$809$	26373.4	1.14616	0.573078	+	0.819501i	$0.305749\pi$
$810$	−2424.83	−0.105185
$811$	−13945.0	−0.603791	−0.301895	−	0.953341i	$-0.597619\pi$
$811$	−13945.0	−0.603791	−0.301895	+	0.953341i	$0.597619\pi$
$812$	−38624.9	−1.66930
$813$	−7906.57	−0.341077
$814$	−14412.9	−0.620606
$815$	703.679	0.0302439
$816$	21409.5	0.918482
$817$	11345.6	0.485840
$818$	35386.5	1.51254
$819$	−6973.35	−0.297520
$820$	8017.55	0.341445
$821$	−41648.8	−1.77047	−0.885234	−	0.465146i	$-0.846002\pi$
$821$	−41648.8	−1.77047	−0.885234	+	0.465146i	$0.846002\pi$
$822$	9706.80	0.411878
$823$	−5874.90	−0.248829	−0.124414	−	0.992230i	$-0.539705\pi$
$823$	−5874.90	−0.248829	−0.124414	+	0.992230i	$0.539705\pi$
$824$	96720.2	4.08909
$825$	3089.97	0.130399
$826$	−36251.0	−1.52704
$827$	−20518.9	−0.862770	−0.431385	−	0.902168i	$-0.641975\pi$
$827$	−20518.9	−0.862770	−0.431385	+	0.902168i	$0.641975\pi$
$828$	39534.4	1.65932
$829$	−16402.1	−0.687174	−0.343587	−	0.939121i	$-0.611642\pi$
$829$	−16402.1	−0.687174	−0.343587	+	0.939121i	$0.611642\pi$
$830$	13783.8	0.576436
$831$	20769.8	0.867021
$832$	−73562.7	−3.06530
$833$	7375.07	0.306760
$834$	−24673.0	−1.02441
$835$	12042.3	0.499091
$836$	−19930.1	−0.824519
$837$	−8757.34	−0.361646
$838$	85975.4	3.54412
$839$	11459.0	0.471525	0.235763	−	0.971811i	$-0.424241\pi$
$839$	11459.0	0.471525	0.235763	+	0.971811i	$0.424241\pi$
$840$	13447.5	0.552360
$841$	463.140	0.0189897
$842$	73810.4	3.02099
$843$	−20078.1	−0.820315
$844$	94364.0	3.84851
$845$	11400.4	0.464127
$846$	2504.33	0.101774
$847$	1441.05	0.0584593
$848$	−30625.2	−1.24018
$849$	13288.2	0.537162
$850$	−18349.8	−0.740463
$851$	52338.8	2.10829
$852$	−71589.6	−2.87866
$853$	−6039.58	−0.242428	−0.121214	−	0.992626i	$-0.538679\pi$
$853$	−6039.58	−0.242428	−0.121214	+	0.992626i	$0.538679\pi$
$854$	3883.28	0.155601
$855$	−4439.02	−0.177557
$856$	−140783.	−5.62132
$857$	−35333.3	−1.40836	−0.704178	−	0.710023i	$-0.748684\pi$
$857$	−35333.3	−1.40836	−0.704178	+	0.710023i	$0.748684\pi$
$858$	−11476.1	−0.456631
$859$	32379.6	1.28612	0.643061	−	0.765815i	$-0.277664\pi$
$859$	32379.6	1.28612	0.643061	+	0.765815i	$0.277664\pi$
$860$	−14842.7	−0.588527
$861$	−2486.24	−0.0984100
$862$	−20819.0	−0.822619
$863$	−22505.1	−0.887696	−0.443848	−	0.896102i	$-0.646387\pi$
$863$	−22505.1	−0.887696	−0.443848	+	0.896102i	$0.646387\pi$
$864$	13577.2	0.534614
$865$	6410.43	0.251978
$866$	11635.2	0.456560
$867$	10706.7	0.419399
$868$	79468.4	3.10753
$869$	−4186.84	−0.163439
$870$	−14157.9	−0.551722
$871$	3976.97	0.154712
$872$	80882.1	3.14107
$873$	−12162.7	−0.471529
$874$	100517.	3.89022
$875$	−14582.5	−0.563406
$876$	14778.8	0.570010
$877$	−21946.1	−0.845001	−0.422500	−	0.906363i	$-0.638847\pi$
$877$	−21946.1	−0.845001	−0.422500	+	0.906363i	$0.638847\pi$
$878$	44018.1	1.69196
$879$	18533.3	0.711164
$880$	11991.7	0.459364
$881$	−27817.9	−1.06380	−0.531902	−	0.846806i	$-0.678522\pi$
$881$	−27817.9	−1.06380	−0.531902	+	0.846806i	$0.678522\pi$
$882$	9677.63	0.369459
$883$	−3522.54	−0.134250	−0.0671250	−	0.997745i	$-0.521383\pi$
$883$	−3522.54	−0.134250	−0.0671250	+	0.997745i	$0.521383\pi$
$884$	49069.8	1.86696
$885$	−9567.35	−0.363393
$886$	−72045.3	−2.73184
$887$	−24494.4	−0.927217	−0.463608	−	0.886040i	$-0.653446\pi$
$887$	−24494.4	−0.927217	−0.463608	+	0.886040i	$0.653446\pi$
$888$	49421.0	1.86764
$889$	21023.7	0.793154
$890$	5271.70	0.198548
$891$	891.000	0.0335013
$892$	54607.2	2.04976
$893$	4584.56	0.171799
$894$	56235.5	2.10380
$895$	6480.75	0.242042
$896$	−24071.1	−0.897498
$897$	41674.2	1.55124
$898$	−54571.0	−2.02790
$899$	−51131.7	−1.89693
$900$	−17337.0	−0.642113
$901$	5768.00	0.213274
$902$	−4091.65	−0.151039
$903$	4602.73	0.169623
$904$	120781.	4.44371
$905$	9541.21	0.350454
$906$	28356.8	1.03984
$907$	−12652.9	−0.463211	−0.231605	−	0.972810i	$-0.574398\pi$
$907$	−12652.9	−0.463211	−0.231605	+	0.972810i	$0.574398\pi$
$908$	−60580.4	−2.21413
$909$	3341.98	0.121943
$910$	23195.0	0.844954
$911$	−30466.6	−1.10802	−0.554009	−	0.832510i	$-0.686903\pi$
$911$	−30466.6	−1.10802	−0.554009	+	0.832510i	$0.686903\pi$
$912$	51429.8	1.86734
$913$	−5064.83	−0.183594
$914$	2479.36	0.0897263
$915$	1024.88	0.0370288
$916$	−82401.6	−2.97230
$917$	−23229.9	−0.836552
$918$	−5291.22	−0.190236
$919$	−13657.8	−0.490239	−0.245119	−	0.969493i	$-0.578827\pi$
$919$	−13657.8	−0.490239	−0.245119	+	0.969493i	$0.578827\pi$
$920$	−80365.0	−2.87995
$921$	−15898.9	−0.568824
$922$	51729.5	1.84775
$923$	−75464.4	−2.69116
$924$	−8085.36	−0.287867
$925$	−22952.2	−0.815852
$926$	45288.7	1.60721
$927$	−12952.5	−0.458916
$928$	79273.7	2.80419
$929$	−27600.4	−0.974748	−0.487374	−	0.873193i	$-0.662045\pi$
$929$	−27600.4	−0.974748	−0.487374	+	0.873193i	$0.662045\pi$
$930$	29129.0	1.02707
$931$	17716.4	0.623664
$932$	−11215.1	−0.394165
$933$	12475.6	0.437764
$934$	55455.5	1.94278
$935$	−2258.54	−0.0789970
$936$	39350.9	1.37417
$937$	−37424.1	−1.30479	−0.652397	−	0.757877i	$-0.726237\pi$
$937$	−37424.1	−1.30479	−0.652397	+	0.757877i	$0.726237\pi$
$938$	3891.49	0.135460
$939$	1074.94	0.0373582
$940$	−5997.70	−0.208110
$941$	55759.4	1.93167	0.965837	−	0.259150i	$-0.0834425\pi$
$941$	55759.4	1.93167	0.965837	+	0.259150i	$0.0834425\pi$
$942$	−33692.7	−1.16536
$943$	14858.3	0.513100
$944$	110846.	3.82174
$945$	−1800.85	−0.0619910
$946$	7574.79	0.260336
$947$	38570.9	1.32353	0.661767	−	0.749710i	$-0.269807\pi$
$947$	38570.9	1.32353	0.661767	+	0.749710i	$0.269807\pi$
$948$	23491.3	0.804813
$949$	15578.7	0.532882
$950$	−44079.9	−1.50541
$951$	−2014.55	−0.0686923
$952$	29343.7	0.998988
$953$	44095.6	1.49884	0.749421	−	0.662094i	$-0.230332\pi$
$953$	44095.6	1.49884	0.749421	+	0.662094i	$0.230332\pi$
$954$	7568.82	0.256866
$955$	−4976.20	−0.168614
$956$	1983.97	0.0671195
$957$	5202.31	0.175723
$958$	−48662.6	−1.64114
$959$	7208.94	0.242741
$960$	−18997.3	−0.638684
$961$	75409.3	2.53128
$962$	85244.4	2.85695
$963$	18853.2	0.630878
$964$	50355.5	1.68241
$965$	−17614.1	−0.587583
$966$	40778.5	1.35820
$967$	58254.2	1.93726	0.968629	−	0.248512i	$-0.0799417\pi$
$967$	58254.2	1.93726	0.968629	+	0.248512i	$0.0799417\pi$
$968$	−8131.90	−0.270010
$969$	−9686.38	−0.321126
$970$	40456.0	1.33914
$971$	3085.07	0.101962	0.0509808	−	0.998700i	$-0.483765\pi$
$971$	3085.07	0.101962	0.0509808	+	0.998700i	$0.483765\pi$
$972$	−4999.18	−0.164968
$973$	−18323.9	−0.603737
$974$	−1828.66	−0.0601580
$975$	−18275.4	−0.600289
$976$	−11874.0	−0.389425
$977$	16675.0	0.546041	0.273020	−	0.962008i	$-0.411977\pi$
$977$	16675.0	0.546041	0.273020	+	0.962008i	$0.411977\pi$
$978$	2014.89	0.0658785
$979$	−1937.08	−0.0632373
$980$	−23177.3	−0.755481
$981$	−10831.5	−0.352521
$982$	63981.2	2.07915
$983$	15933.0	0.516973	0.258486	−	0.966015i	$-0.416776\pi$
$983$	15933.0	0.516973	0.258486	+	0.966015i	$0.416776\pi$
$984$	14030.0	0.454532
$985$	−3913.27	−0.126586
$986$	−30894.0	−0.997834
$987$	1859.89	0.0599807
$988$	117875.	3.79566
$989$	−27506.9	−0.884398
$990$	−2963.68	−0.0951433
$991$	48229.4	1.54597	0.772986	−	0.634423i	$-0.218762\pi$
$991$	48229.4	1.54597	0.772986	+	0.634423i	$0.218762\pi$
$992$	−163101.	−5.22021
$993$	−14520.0	−0.464026
$994$	−73842.3	−2.35627
$995$	−5080.50	−0.161872
$996$	28417.5	0.904059
$997$	−40145.0	−1.27523	−0.637616	−	0.770355i	$-0.720079\pi$
$997$	−40145.0	−1.27523	−0.637616	+	0.770355i	$0.720079\pi$
$998$	32963.6	1.04553
$999$	−6618.32	−0.209604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.d.1.2	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.d.1.2	✓	37	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)

\(f(q)\)	\(=\)	\(q-5.34535 q^{2} -3.00000 q^{3} +20.5728 q^{4} +5.60041 q^{5} +16.0360 q^{6} +11.9095 q^{7} -67.2058 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.34535 q^{2} -3.00000 q^{3} +20.5728 q^{4} +5.60041 q^{5} +16.0360 q^{6} +11.9095 q^{7} -67.2058 q^{8} +9.00000 q^{9} -29.9362 q^{10} +11.0000 q^{11} -61.7183 q^{12} -65.0588 q^{13} -63.6604 q^{14} -16.8012 q^{15} +194.656 q^{16} -36.6620 q^{17} -48.1081 q^{18} -88.0693 q^{19} +115.216 q^{20} -35.7285 q^{21} -58.7988 q^{22} +213.521 q^{23} +201.617 q^{24} -93.6354 q^{25} +347.762 q^{26} -27.0000 q^{27} +245.011 q^{28} -157.646 q^{29} +89.8085 q^{30} +324.346 q^{31} -502.860 q^{32} -33.0000 q^{33} +195.971 q^{34} +66.6980 q^{35} +185.155 q^{36} +245.123 q^{37} +470.761 q^{38} +195.176 q^{39} -376.380 q^{40} +69.5872 q^{41} +190.981 q^{42} -128.825 q^{43} +226.300 q^{44} +50.4037 q^{45} -1141.34 q^{46} -52.0562 q^{47} -583.969 q^{48} -201.164 q^{49} +500.514 q^{50} +109.986 q^{51} -1338.44 q^{52} -157.329 q^{53} +144.324 q^{54} +61.6045 q^{55} -800.387 q^{56} +264.208 q^{57} +842.671 q^{58} +569.443 q^{59} -345.648 q^{60} -61.0000 q^{61} -1733.74 q^{62} +107.185 q^{63} +1130.71 q^{64} -364.356 q^{65} +176.397 q^{66} -61.1289 q^{67} -754.238 q^{68} -640.563 q^{69} -356.524 q^{70} +1159.94 q^{71} -604.852 q^{72} -239.455 q^{73} -1310.27 q^{74} +280.906 q^{75} -1811.83 q^{76} +131.004 q^{77} -1043.29 q^{78} -380.622 q^{79} +1090.16 q^{80} +81.0000 q^{81} -371.968 q^{82} -460.439 q^{83} -735.033 q^{84} -205.322 q^{85} +688.617 q^{86} +472.937 q^{87} -739.264 q^{88} -176.098 q^{89} -269.425 q^{90} -774.817 q^{91} +4392.71 q^{92} -973.038 q^{93} +278.259 q^{94} -493.224 q^{95} +1508.58 q^{96} -1351.41 q^{97} +1075.29 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9 - 45 * q^10 + 407 * q^11 - 474 * q^12 - 169 * q^13 + 102 * q^14 + 45 * q^15 + 598 * q^16 - 338 * q^17 - 36 * q^18 - 235 * q^19 - 550 * q^20 + 231 * q^21 - 44 * q^22 - 53 * q^23 + 207 * q^24 + 750 * q^25 - 75 * q^26 - 999 * q^27 - 1378 * q^28 - 30 * q^29 + 135 * q^30 - 506 * q^31 - 841 * q^32 - 1221 * q^33 - 316 * q^34 - 822 * q^35 + 1422 * q^36 - 830 * q^37 - 371 * q^38 + 507 * q^39 - 613 * q^40 + 16 * q^41 - 306 * q^42 - 1137 * q^43 + 1738 * q^44 - 135 * q^45 - 659 * q^46 - 489 * q^47 - 1794 * q^48 + 2214 * q^49 + 1066 * q^50 + 1014 * q^51 - 2342 * q^52 + 731 * q^53 + 108 * q^54 - 165 * q^55 + 3051 * q^56 + 705 * q^57 - 611 * q^58 - 425 * q^59 + 1650 * q^60 - 2257 * q^61 + 453 * q^62 - 693 * q^63 + 4919 * q^64 + 1346 * q^65 + 132 * q^66 - 1907 * q^67 - 3236 * q^68 + 159 * q^69 - 1050 * q^70 - 561 * q^71 - 621 * q^72 - 2397 * q^73 - 1840 * q^74 - 2250 * q^75 - 3868 * q^76 - 847 * q^77 + 225 * q^78 + 393 * q^79 - 4031 * q^80 + 2997 * q^81 - 1946 * q^82 - 4191 * q^83 + 4134 * q^84 - 2667 * q^85 + 2405 * q^86 + 90 * q^87 - 759 * q^88 + 1437 * q^89 - 405 * q^90 - 5192 * q^91 - 737 * q^92 + 1518 * q^93 - 1960 * q^94 + 1356 * q^95 + 2523 * q^96 - 2368 * q^97 - 3014 * q^98 + 3663 * q^99

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