LMFDB - Embedded newform 2013.4.a.e.1.15

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:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-1.82980 q^{2} -3.00000 q^{3} -4.65183 q^{4} +19.9990 q^{5} +5.48940 q^{6} +32.4689 q^{7} +23.1503 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.82980 q^{2} -3.00000 q^{3} -4.65183 q^{4} +19.9990 q^{5} +5.48940 q^{6} +32.4689 q^{7} +23.1503 q^{8} +9.00000 q^{9} -36.5943 q^{10} -11.0000 q^{11} +13.9555 q^{12} +23.8590 q^{13} -59.4116 q^{14} -59.9971 q^{15} -5.14590 q^{16} -128.890 q^{17} -16.4682 q^{18} +98.1013 q^{19} -93.0320 q^{20} -97.4067 q^{21} +20.1278 q^{22} -133.120 q^{23} -69.4510 q^{24} +274.961 q^{25} -43.6572 q^{26} -27.0000 q^{27} -151.040 q^{28} +95.6042 q^{29} +109.783 q^{30} +77.7336 q^{31} -175.787 q^{32} +33.0000 q^{33} +235.844 q^{34} +649.346 q^{35} -41.8664 q^{36} +216.217 q^{37} -179.506 q^{38} -71.5770 q^{39} +462.984 q^{40} -231.976 q^{41} +178.235 q^{42} +222.113 q^{43} +51.1701 q^{44} +179.991 q^{45} +243.584 q^{46} -141.920 q^{47} +15.4377 q^{48} +711.229 q^{49} -503.124 q^{50} +386.671 q^{51} -110.988 q^{52} +566.865 q^{53} +49.4046 q^{54} -219.989 q^{55} +751.666 q^{56} -294.304 q^{57} -174.937 q^{58} -207.078 q^{59} +279.096 q^{60} -61.0000 q^{61} -142.237 q^{62} +292.220 q^{63} +362.822 q^{64} +477.157 q^{65} -60.3835 q^{66} +0.102142 q^{67} +599.575 q^{68} +399.361 q^{69} -1188.17 q^{70} +410.272 q^{71} +208.353 q^{72} +1042.57 q^{73} -395.634 q^{74} -824.883 q^{75} -456.350 q^{76} -357.158 q^{77} +130.972 q^{78} +185.498 q^{79} -102.913 q^{80} +81.0000 q^{81} +424.470 q^{82} -1011.50 q^{83} +453.119 q^{84} -2577.68 q^{85} -406.423 q^{86} -286.813 q^{87} -254.654 q^{88} -926.119 q^{89} -329.348 q^{90} +774.675 q^{91} +619.253 q^{92} -233.201 q^{93} +259.685 q^{94} +1961.93 q^{95} +527.360 q^{96} -921.861 q^{97} -1301.41 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) $ 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9} + 95 q^{10} - 418 q^{11} - 426 q^{12} + 13 q^{13} + 26 q^{14} - 45 q^{15} + 486 q^{16} - 224 q^{17} - 18 q^{18} + 367 q^{19} + 18 q^{20} - 189 q^{21} + 22 q^{22} + 51 q^{23} + 135 q^{24} + 773 q^{25} - 439 q^{26} - 1026 q^{27} + 22 q^{28} - 462 q^{29} - 285 q^{30} + 234 q^{31} - 597 q^{32} + 1254 q^{33} + 956 q^{34} - 522 q^{35} + 1278 q^{36} + 954 q^{37} + 705 q^{38} - 39 q^{39} + 1495 q^{40} - 740 q^{41} - 78 q^{42} + 1441 q^{43} - 1562 q^{44} + 135 q^{45} + 581 q^{46} + 1003 q^{47} - 1458 q^{48} + 2707 q^{49} + 388 q^{50} + 672 q^{51} + 788 q^{52} + 735 q^{53} + 54 q^{54} - 165 q^{55} + 1059 q^{56} - 1101 q^{57} + 177 q^{58} + 261 q^{59} - 54 q^{60} - 2318 q^{61} + 1251 q^{62} + 567 q^{63} + 5571 q^{64} - 1354 q^{65} - 66 q^{66} + 3495 q^{67} - 1856 q^{68} - 153 q^{69} + 542 q^{70} - 873 q^{71} - 405 q^{72} + 989 q^{73} - 3406 q^{74} - 2319 q^{75} + 1712 q^{76} - 693 q^{77} + 1317 q^{78} + 2313 q^{79} + 1593 q^{80} + 3078 q^{81} + 5170 q^{82} + 569 q^{83} - 66 q^{84} - 1271 q^{85} + 3065 q^{86} + 1386 q^{87} + 495 q^{88} - 2917 q^{89} + 855 q^{90} + 2740 q^{91} + 1083 q^{92} - 702 q^{93} + 3272 q^{94} + 2696 q^{95} + 1791 q^{96} + 4250 q^{97} + 5952 q^{98} - 3762 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9 + 95 * q^10 - 418 * q^11 - 426 * q^12 + 13 * q^13 + 26 * q^14 - 45 * q^15 + 486 * q^16 - 224 * q^17 - 18 * q^18 + 367 * q^19 + 18 * q^20 - 189 * q^21 + 22 * q^22 + 51 * q^23 + 135 * q^24 + 773 * q^25 - 439 * q^26 - 1026 * q^27 + 22 * q^28 - 462 * q^29 - 285 * q^30 + 234 * q^31 - 597 * q^32 + 1254 * q^33 + 956 * q^34 - 522 * q^35 + 1278 * q^36 + 954 * q^37 + 705 * q^38 - 39 * q^39 + 1495 * q^40 - 740 * q^41 - 78 * q^42 + 1441 * q^43 - 1562 * q^44 + 135 * q^45 + 581 * q^46 + 1003 * q^47 - 1458 * q^48 + 2707 * q^49 + 388 * q^50 + 672 * q^51 + 788 * q^52 + 735 * q^53 + 54 * q^54 - 165 * q^55 + 1059 * q^56 - 1101 * q^57 + 177 * q^58 + 261 * q^59 - 54 * q^60 - 2318 * q^61 + 1251 * q^62 + 567 * q^63 + 5571 * q^64 - 1354 * q^65 - 66 * q^66 + 3495 * q^67 - 1856 * q^68 - 153 * q^69 + 542 * q^70 - 873 * q^71 - 405 * q^72 + 989 * q^73 - 3406 * q^74 - 2319 * q^75 + 1712 * q^76 - 693 * q^77 + 1317 * q^78 + 2313 * q^79 + 1593 * q^80 + 3078 * q^81 + 5170 * q^82 + 569 * q^83 - 66 * q^84 - 1271 * q^85 + 3065 * q^86 + 1386 * q^87 + 495 * q^88 - 2917 * q^89 + 855 * q^90 + 2740 * q^91 + 1083 * q^92 - 702 * q^93 + 3272 * q^94 + 2696 * q^95 + 1791 * q^96 + 4250 * q^97 + 5952 * q^98 - 3762 * 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 $

$2$	−1.82980	−0.646933	−0.323466	−	0.946240i	$-0.604848\pi$
$2$	−1.82980	−0.646933	−0.323466	+	0.946240i	$0.604848\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−4.65183	−0.581478
$5$	19.9990	1.78877	0.894384	−	0.447301i	$-0.147615\pi$
$5$	19.9990	1.78877	0.894384	+	0.447301i	$0.147615\pi$
$6$	5.48940	0.373507
$7$	32.4689	1.75316	0.876578	−	0.481261i	$-0.159821\pi$
$7$	32.4689	1.75316	0.876578	+	0.481261i	$0.159821\pi$
$8$	23.1503	1.02311
$9$	9.00000	0.333333
$10$	−36.5943	−1.15721
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	13.9555	0.335717
$13$	23.8590	0.509023	0.254511	−	0.967070i	$-0.418085\pi$
$13$	23.8590	0.509023	0.254511	+	0.967070i	$0.418085\pi$
$14$	−59.4116	−1.13417
$15$	−59.9971	−1.03275
$16$	−5.14590	−0.0804047
$17$	−128.890	−1.83885	−0.919426	−	0.393262i	$-0.871346\pi$
$17$	−128.890	−1.83885	−0.919426	+	0.393262i	$0.871346\pi$
$18$	−16.4682	−0.215644
$19$	98.1013	1.18453	0.592263	−	0.805745i	$-0.298235\pi$
$19$	98.1013	1.18453	0.592263	+	0.805745i	$0.298235\pi$
$20$	−93.0320	−1.04013
$21$	−97.4067	−1.01218
$22$	20.1278	0.195057
$23$	−133.120	−1.20685	−0.603425	−	0.797420i	$-0.706198\pi$
$23$	−133.120	−1.20685	−0.603425	+	0.797420i	$0.706198\pi$
$24$	−69.4510	−0.590693
$25$	274.961	2.19969
$26$	−43.6572	−0.329303
$27$	−27.0000	−0.192450
$28$	−151.040	−1.01942
$29$	95.6042	0.612181	0.306091	−	0.952002i	$-0.400979\pi$
$29$	95.6042	0.612181	0.306091	+	0.952002i	$0.400979\pi$
$30$	109.783	0.668117
$31$	77.7336	0.450367	0.225183	−	0.974316i	$-0.427702\pi$
$31$	77.7336	0.450367	0.225183	+	0.974316i	$0.427702\pi$
$32$	−175.787	−0.971093
$33$	33.0000	0.174078
$34$	235.844	1.18961
$35$	649.346	3.13599
$36$	−41.8664	−0.193826
$37$	216.217	0.960699	0.480349	−	0.877077i	$-0.340510\pi$
$37$	216.217	0.960699	0.480349	+	0.877077i	$0.340510\pi$
$38$	−179.506	−0.766308
$39$	−71.5770	−0.293884
$40$	462.984	1.83011
$41$	−231.976	−0.883623	−0.441811	−	0.897108i	$-0.645664\pi$
$41$	−231.976	−0.883623	−0.441811	+	0.897108i	$0.645664\pi$
$42$	178.235	0.654815
$43$	222.113	0.787720	0.393860	−	0.919170i	$-0.371139\pi$
$43$	222.113	0.787720	0.393860	+	0.919170i	$0.371139\pi$
$44$	51.1701	0.175322
$45$	179.991	0.596256
$46$	243.584	0.780750
$47$	−141.920	−0.440450	−0.220225	−	0.975449i	$-0.570679\pi$
$47$	−141.920	−0.440450	−0.220225	+	0.975449i	$0.570679\pi$
$48$	15.4377	0.0464217
$49$	711.229	2.07355
$50$	−503.124	−1.42305
$51$	386.671	1.06166
$52$	−110.988	−0.295986
$53$	566.865	1.46915	0.734574	−	0.678528i	$-0.237382\pi$
$53$	566.865	1.46915	0.734574	+	0.678528i	$0.237382\pi$
$54$	49.4046	0.124502
$55$	−219.989	−0.539334
$56$	751.666	1.79367
$57$	−294.304	−0.683886
$58$	−174.937	−0.396040
$59$	−207.078	−0.456937	−0.228468	−	0.973551i	$-0.573372\pi$
$59$	−207.078	−0.456937	−0.228468	+	0.973551i	$0.573372\pi$
$60$	279.096	0.600519
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−142.237	−0.291357
$63$	292.220	0.584385
$64$	362.822	0.708637
$65$	477.157	0.910523
$66$	−60.3835	−0.112616
$67$	0.102142	0.000186249 0	9.31244e−5	−	1.00000i	$-0.499970\pi$
$67$	0.102142	0.000186249 0	9.31244e−5		1.00000i	$0.499970\pi$
$68$	599.575	1.06925
$69$	399.361	0.696775
$70$	−1188.17	−2.02877
$71$	410.272	0.685779	0.342890	−	0.939376i	$-0.388594\pi$
$71$	410.272	0.685779	0.342890	+	0.939376i	$0.388594\pi$
$72$	208.353	0.341037
$73$	1042.57	1.67156	0.835778	−	0.549067i	$-0.185017\pi$
$73$	1042.57	1.67156	0.835778	+	0.549067i	$0.185017\pi$
$74$	−395.634	−0.621507
$75$	−824.883	−1.26999
$76$	−456.350	−0.688776
$77$	−357.158	−0.528596
$78$	130.972	0.190123
$79$	185.498	0.264180	0.132090	−	0.991238i	$-0.457831\pi$
$79$	185.498	0.264180	0.132090	+	0.991238i	$0.457831\pi$
$80$	−102.913	−0.143825
$81$	81.0000	0.111111
$82$	424.470	0.571644
$83$	−1011.50	−1.33767	−0.668836	−	0.743410i	$-0.733207\pi$
$83$	−1011.50	−1.33767	−0.668836	+	0.743410i	$0.733207\pi$
$84$	453.119	0.588563
$85$	−2577.68	−3.28928
$86$	−406.423	−0.509602
$87$	−286.813	−0.353443
$88$	−254.654	−0.308479
$89$	−926.119	−1.10302	−0.551508	−	0.834170i	$-0.685947\pi$
$89$	−926.119	−1.10302	−0.551508	+	0.834170i	$0.685947\pi$
$90$	−329.348	−0.385737
$91$	774.675	0.892396
$92$	619.253	0.701757
$93$	−233.201	−0.260019
$94$	259.685	0.284941
$95$	1961.93	2.11884
$96$	527.360	0.560661
$97$	−921.861	−0.964957	−0.482479	−	0.875908i	$-0.660263\pi$
$97$	−921.861	−0.964957	−0.482479	+	0.875908i	$0.660263\pi$
$98$	−1301.41	−1.34145
$99$	−99.0000	−0.100504
$100$	−1279.07	−1.27907
$101$	−317.809	−0.313100	−0.156550	−	0.987670i	$-0.550037\pi$
$101$	−317.809	−0.313100	−0.156550	+	0.987670i	$0.550037\pi$
$102$	−707.531	−0.686824
$103$	1689.02	1.61577	0.807884	−	0.589341i	$-0.200613\pi$
$103$	1689.02	1.61577	0.807884	+	0.589341i	$0.200613\pi$
$104$	552.344	0.520786
$105$	−1948.04	−1.81056
$106$	−1037.25	−0.950440
$107$	1424.32	1.28686	0.643429	−	0.765505i	$-0.277511\pi$
$107$	1424.32	1.28686	0.643429	+	0.765505i	$0.277511\pi$
$108$	125.599	0.111906
$109$	−325.317	−0.285869	−0.142934	−	0.989732i	$-0.545654\pi$
$109$	−325.317	−0.285869	−0.142934	+	0.989732i	$0.545654\pi$
$110$	402.537	0.348912
$111$	−648.651	−0.554660
$112$	−167.082	−0.140962
$113$	71.4672	0.0594962	0.0297481	−	0.999557i	$-0.490529\pi$
$113$	71.4672	0.0594962	0.0297481	+	0.999557i	$0.490529\pi$
$114$	538.518	0.442428
$115$	−2662.28	−2.15877
$116$	−444.734	−0.355970
$117$	214.731	0.169674
$118$	378.912	0.295607
$119$	−4184.93	−3.22379
$120$	−1388.95	−1.05661
$121$	121.000	0.0909091
$122$	111.618	0.0828312
$123$	695.927	0.510160
$124$	−361.603	−0.261879
$125$	2999.08	2.14596
$126$	−534.705	−0.378058
$127$	1236.35	0.863848	0.431924	−	0.901910i	$-0.357835\pi$
$127$	1236.35	0.863848	0.431924	+	0.901910i	$0.357835\pi$
$128$	742.401	0.512653
$129$	−666.340	−0.454790
$130$	−873.102	−0.589047
$131$	2622.72	1.74922	0.874610	−	0.484827i	$-0.161118\pi$
$131$	2622.72	1.74922	0.874610	+	0.484827i	$0.161118\pi$
$132$	−153.510	−0.101222
$133$	3185.24	2.07666
$134$	−0.186900	−0.000120490 0
$135$	−539.974	−0.344248
$136$	−2983.85	−1.88135
$137$	374.025	0.233249	0.116625	−	0.993176i	$-0.462793\pi$
$137$	374.025	0.233249	0.116625	+	0.993176i	$0.462793\pi$
$138$	−730.752	−0.450766
$139$	−1102.73	−0.672892	−0.336446	−	0.941703i	$-0.609225\pi$
$139$	−1102.73	−0.672892	−0.336446	+	0.941703i	$0.609225\pi$
$140$	−3020.65	−1.82351
$141$	425.760	0.254294
$142$	−750.716	−0.443653
$143$	−262.449	−0.153476
$144$	−46.3131	−0.0268016
$145$	1911.99	1.09505
$146$	−1907.70	−1.08138
$147$	−2133.69	−1.19717
$148$	−1005.80	−0.558625
$149$	−60.4713	−0.0332483	−0.0166242	−	0.999862i	$-0.505292\pi$
$149$	−60.4713	−0.0332483	−0.0166242	+	0.999862i	$0.505292\pi$
$150$	1509.37	0.821598
$151$	−2532.40	−1.36479	−0.682396	−	0.730982i	$-0.739062\pi$
$151$	−2532.40	−1.36479	−0.682396	+	0.730982i	$0.739062\pi$
$152$	2271.08	1.21190
$153$	−1160.01	−0.612951
$154$	653.528	0.341966
$155$	1554.60	0.805602
$156$	332.964	0.170887
$157$	−1328.91	−0.675533	−0.337767	−	0.941230i	$-0.609671\pi$
$157$	−1328.91	−0.675533	−0.337767	+	0.941230i	$0.609671\pi$
$158$	−339.425	−0.170906
$159$	−1700.59	−0.848213
$160$	−3515.56	−1.73706
$161$	−4322.27	−2.11579
$162$	−148.214	−0.0718814
$163$	−2180.55	−1.04781	−0.523907	−	0.851776i	$-0.675526\pi$
$163$	−2180.55	−1.04781	−0.523907	+	0.851776i	$0.675526\pi$
$164$	1079.11	0.513807
$165$	659.968	0.311384
$166$	1850.85	0.865384
$167$	−62.7972	−0.0290982	−0.0145491	−	0.999894i	$-0.504631\pi$
$167$	−62.7972	−0.0290982	−0.0145491	+	0.999894i	$0.504631\pi$
$168$	−2255.00	−1.03558
$169$	−1627.75	−0.740896
$170$	4716.64	2.12794
$171$	882.912	0.394842
$172$	−1033.23	−0.458042
$173$	1566.21	0.688305	0.344153	−	0.938914i	$-0.388166\pi$
$173$	1566.21	0.688305	0.344153	+	0.938914i	$0.388166\pi$
$174$	524.810	0.228654
$175$	8927.68	3.85640
$176$	56.6049	0.0242429
$177$	621.234	0.263812
$178$	1694.61	0.713577
$179$	−619.266	−0.258582	−0.129291	−	0.991607i	$-0.541270\pi$
$179$	−619.266	−0.258582	−0.129291	+	0.991607i	$0.541270\pi$
$180$	−837.288	−0.346710
$181$	−1401.28	−0.575451	−0.287725	−	0.957713i	$-0.592899\pi$
$181$	−1401.28	−0.575451	−0.287725	+	0.957713i	$0.592899\pi$
$182$	−1417.50	−0.577320
$183$	183.000	0.0739221
$184$	−3081.78	−1.23474
$185$	4324.13	1.71847
$186$	426.711	0.168215
$187$	1417.79	0.554435
$188$	660.187	0.256112
$189$	−876.660	−0.337395
$190$	−3589.94	−1.37075
$191$	3641.46	1.37951	0.689755	−	0.724042i	$-0.257718\pi$
$191$	3641.46	1.37951	0.689755	+	0.724042i	$0.257718\pi$
$192$	−1088.47	−0.409132
$193$	1733.07	0.646367	0.323183	−	0.946336i	$-0.395247\pi$
$193$	1733.07	0.646367	0.323183	+	0.946336i	$0.395247\pi$
$194$	1686.82	0.624262
$195$	−1431.47	−0.525691
$196$	−3308.51	−1.20573
$197$	−1901.55	−0.687714	−0.343857	−	0.939022i	$-0.611734\pi$
$197$	−1901.55	−0.687714	−0.343857	+	0.939022i	$0.611734\pi$
$198$	181.150	0.0650192
$199$	442.716	0.157705	0.0788526	−	0.996886i	$-0.474874\pi$
$199$	442.716	0.157705	0.0788526	+	0.996886i	$0.474874\pi$
$200$	6365.44	2.25052
$201$	−0.306427	−0.000107531 0
$202$	581.527	0.202555
$203$	3104.16	1.07325
$204$	−1798.73	−0.617333
$205$	−4639.29	−1.58060
$206$	−3090.57	−1.04529
$207$	−1198.08	−0.402283
$208$	−122.776	−0.0409278
$209$	−1079.11	−0.357148
$210$	3564.52	1.17131
$211$	5006.25	1.63339	0.816693	−	0.577073i	$-0.195805\pi$
$211$	5006.25	1.63339	0.816693	+	0.577073i	$0.195805\pi$
$212$	−2636.96	−0.854278
$213$	−1230.82	−0.395935
$214$	−2606.22	−0.832511
$215$	4442.05	1.40905
$216$	−625.059	−0.196898
$217$	2523.92	0.789563
$218$	595.265	0.184938
$219$	−3127.71	−0.965074
$220$	1023.35	0.313611
$221$	−3075.19	−0.936018
$222$	1186.90	0.358827
$223$	−2000.22	−0.600650	−0.300325	−	0.953837i	$-0.597095\pi$
$223$	−2000.22	−0.600650	−0.300325	+	0.953837i	$0.597095\pi$
$224$	−5707.60	−1.70248
$225$	2474.65	0.733230
$226$	−130.771	−0.0384900
$227$	4459.77	1.30399	0.651995	−	0.758224i	$-0.273932\pi$
$227$	4459.77	1.30399	0.651995	+	0.758224i	$0.273932\pi$
$228$	1369.05	0.397665
$229$	4673.92	1.34874	0.674369	−	0.738395i	$-0.264416\pi$
$229$	4673.92	1.34874	0.674369	+	0.738395i	$0.264416\pi$
$230$	4871.44	1.39658
$231$	1071.47	0.305185
$232$	2213.27	0.626329
$233$	−1992.90	−0.560340	−0.280170	−	0.959950i	$-0.590391\pi$
$233$	−1992.90	−0.560340	−0.280170	+	0.959950i	$0.590391\pi$
$234$	−392.915	−0.109768
$235$	−2838.26	−0.787862
$236$	963.291	0.265699
$237$	−556.495	−0.152524
$238$	7657.58	2.08558
$239$	−2232.01	−0.604087	−0.302043	−	0.953294i	$-0.597669\pi$
$239$	−2232.01	−0.604087	−0.302043	+	0.953294i	$0.597669\pi$
$240$	308.739	0.0830376
$241$	5220.21	1.39528	0.697641	−	0.716447i	$-0.254233\pi$
$241$	5220.21	1.39528	0.697641	+	0.716447i	$0.254233\pi$
$242$	−221.406	−0.0588120
$243$	−243.000	−0.0641500
$244$	283.761	0.0744507
$245$	14223.9	3.70910
$246$	−1273.41	−0.330039
$247$	2340.60	0.602951
$248$	1799.56	0.460775
$249$	3034.51	0.772306
$250$	−5487.71	−1.38829
$251$	−434.075	−0.109158	−0.0545788	−	0.998509i	$-0.517382\pi$
$251$	−434.075	−0.109158	−0.0545788	+	0.998509i	$0.517382\pi$
$252$	−1359.36	−0.339807
$253$	1464.33	0.363879
$254$	−2262.28	−0.558852
$255$	7733.04	1.89907
$256$	−4261.02	−1.04029
$257$	−1473.59	−0.357665	−0.178832	−	0.983880i	$-0.557232\pi$
$257$	−1473.59	−0.357665	−0.178832	+	0.983880i	$0.557232\pi$
$258$	1219.27	0.294219
$259$	7020.32	1.68425
$260$	−2219.65	−0.529450
$261$	860.438	0.204060
$262$	−4799.05	−1.13163
$263$	−4031.38	−0.945192	−0.472596	−	0.881279i	$-0.656683\pi$
$263$	−4031.38	−0.945192	−0.472596	+	0.881279i	$0.656683\pi$
$264$	763.961	0.178101
$265$	11336.7	2.62797
$266$	−5828.36	−1.34346
$267$	2778.36	0.636826
$268$	−0.475148	−0.000108300 0
$269$	−4494.20	−1.01865	−0.509324	−	0.860575i	$-0.670105\pi$
$269$	−4494.20	−1.01865	−0.509324	+	0.860575i	$0.670105\pi$
$270$	988.045	0.222706
$271$	6398.73	1.43430	0.717150	−	0.696919i	$-0.245446\pi$
$271$	6398.73	1.43430	0.717150	+	0.696919i	$0.245446\pi$
$272$	663.257	0.147852
$273$	−2324.03	−0.515225
$274$	−684.392	−0.150896
$275$	−3024.57	−0.663231
$276$	−1857.76	−0.405159
$277$	−187.639	−0.0407008	−0.0203504	−	0.999793i	$-0.506478\pi$
$277$	−187.639	−0.0407008	−0.0203504	+	0.999793i	$0.506478\pi$
$278$	2017.77	0.435316
$279$	699.603	0.150122
$280$	15032.6	3.20846
$281$	6057.52	1.28598	0.642992	−	0.765873i	$-0.277693\pi$
$281$	6057.52	1.28598	0.642992	+	0.765873i	$0.277693\pi$
$282$	−779.056	−0.164511
$283$	−2206.71	−0.463517	−0.231758	−	0.972773i	$-0.574448\pi$
$283$	−2206.71	−0.463517	−0.231758	+	0.972773i	$0.574448\pi$
$284$	−1908.51	−0.398766
$285$	−5885.79	−1.22331
$286$	480.230	0.0992887
$287$	−7532.00	−1.54913
$288$	−1582.08	−0.323698
$289$	11699.7	2.38138
$290$	−3498.57	−0.708424
$291$	2765.58	0.557118
$292$	−4849.86	−0.971974
$293$	−9290.47	−1.85241	−0.926203	−	0.377025i	$-0.876947\pi$
$293$	−9290.47	−1.85241	−0.926203	+	0.377025i	$0.876947\pi$
$294$	3904.22	0.774486
$295$	−4141.36	−0.817353
$296$	5005.49	0.982900
$297$	297.000	0.0580259
$298$	110.651	0.0215094
$299$	−3176.12	−0.614314
$300$	3837.21	0.738472
$301$	7211.77	1.38100
$302$	4633.79	0.882929
$303$	953.426	0.180769
$304$	−504.820	−0.0952414
$305$	−1219.94	−0.229028
$306$	2122.59	0.396538
$307$	985.997	0.183302	0.0916512	−	0.995791i	$-0.470786\pi$
$307$	985.997	0.183302	0.0916512	+	0.995791i	$0.470786\pi$
$308$	1661.44	0.307367
$309$	−5067.06	−0.932864
$310$	−2844.60	−0.521170
$311$	5791.24	1.05592	0.527960	−	0.849269i	$-0.322957\pi$
$311$	5791.24	1.05592	0.527960	+	0.849269i	$0.322957\pi$
$312$	−1657.03	−0.300676
$313$	8323.64	1.50313	0.751565	−	0.659659i	$-0.229299\pi$
$313$	8323.64	1.50313	0.751565	+	0.659659i	$0.229299\pi$
$314$	2431.65	0.437024
$315$	5844.12	1.04533
$316$	−862.906	−0.153615
$317$	4844.52	0.858344	0.429172	−	0.903223i	$-0.358805\pi$
$317$	4844.52	0.858344	0.429172	+	0.903223i	$0.358805\pi$
$318$	3111.75	0.548737
$319$	−1051.65	−0.184580
$320$	7256.09	1.26759
$321$	−4272.95	−0.742968
$322$	7908.90	1.36878
$323$	−12644.3	−2.17817
$324$	−376.798	−0.0646087
$325$	6560.30	1.11969
$326$	3989.97	0.677865
$327$	975.950	0.165046
$328$	−5370.32	−0.904043
$329$	−4607.98	−0.772177
$330$	−1207.61	−0.201445
$331$	−8208.19	−1.36303	−0.681515	−	0.731804i	$-0.738679\pi$
$331$	−8208.19	−1.36303	−0.681515	+	0.731804i	$0.738679\pi$
$332$	4705.33	0.777827
$333$	1945.95	0.320233
$334$	114.906	0.0188245
$335$	2.04275	0.000333156 0
$336$	501.245	0.0813844
$337$	7977.87	1.28956	0.644781	−	0.764367i	$-0.276949\pi$
$337$	7977.87	1.28956	0.644781	+	0.764367i	$0.276949\pi$
$338$	2978.46	0.479310
$339$	−214.402	−0.0343501
$340$	11990.9	1.91264
$341$	−855.070	−0.135791
$342$	−1615.55	−0.255436
$343$	11956.0	1.88211
$344$	5142.00	0.805924
$345$	7986.84	1.24637
$346$	−2865.86	−0.445287
$347$	−7769.50	−1.20198	−0.600992	−	0.799255i	$-0.705228\pi$
$347$	−7769.50	−1.20198	−0.600992	+	0.799255i	$0.705228\pi$
$348$	1334.20	0.205519
$349$	−6267.56	−0.961303	−0.480652	−	0.876912i	$-0.659600\pi$
$349$	−6267.56	−0.961303	−0.480652	+	0.876912i	$0.659600\pi$
$350$	−16335.9	−2.49483
$351$	−644.193	−0.0979615
$352$	1933.65	0.292796
$353$	−3838.34	−0.578737	−0.289369	−	0.957218i	$-0.593445\pi$
$353$	−3838.34	−0.578737	−0.289369	+	0.957218i	$0.593445\pi$
$354$	−1136.74	−0.170669
$355$	8205.04	1.22670
$356$	4308.14	0.641380
$357$	12554.8	1.86126
$358$	1133.13	0.167285
$359$	2620.75	0.385287	0.192644	−	0.981269i	$-0.438294\pi$
$359$	2620.75	0.385287	0.192644	+	0.981269i	$0.438294\pi$
$360$	4166.86	0.610035
$361$	2764.87	0.403101
$362$	2564.07	0.372278
$363$	−363.000	−0.0524864
$364$	−3603.65	−0.518909
$365$	20850.4	2.99003
$366$	−334.854	−0.0478226
$367$	−11771.3	−1.67428	−0.837138	−	0.546992i	$-0.815773\pi$
$367$	−11771.3	−1.67428	−0.837138	+	0.546992i	$0.815773\pi$
$368$	685.025	0.0970364
$369$	−2087.78	−0.294541
$370$	−7912.30	−1.11173
$371$	18405.5	2.57565
$372$	1084.81	0.151196
$373$	−8630.94	−1.19810	−0.599052	−	0.800710i	$-0.704456\pi$
$373$	−8630.94	−1.19810	−0.599052	+	0.800710i	$0.704456\pi$
$374$	−2594.28	−0.358682
$375$	−8997.23	−1.23897
$376$	−3285.49	−0.450628
$377$	2281.02	0.311614
$378$	1604.11	0.218272
$379$	−5668.93	−0.768320	−0.384160	−	0.923267i	$-0.625509\pi$
$379$	−5668.93	−0.768320	−0.384160	+	0.923267i	$0.625509\pi$
$380$	−9126.56	−1.23206
$381$	−3709.06	−0.498743
$382$	−6663.14	−0.892450
$383$	−3212.56	−0.428600	−0.214300	−	0.976768i	$-0.568747\pi$
$383$	−3212.56	−0.428600	−0.214300	+	0.976768i	$0.568747\pi$
$384$	−2227.20	−0.295981
$385$	−7142.81	−0.945536
$386$	−3171.17	−0.418156
$387$	1999.02	0.262573
$388$	4288.34	0.561102
$389$	4092.78	0.533450	0.266725	−	0.963773i	$-0.414058\pi$
$389$	4092.78	0.533450	0.266725	+	0.963773i	$0.414058\pi$
$390$	2619.31	0.340087
$391$	17157.9	2.21922
$392$	16465.2	2.12147
$393$	−7868.15	−1.00991
$394$	3479.46	0.444905
$395$	3709.79	0.472556
$396$	460.531	0.0584408
$397$	−3246.87	−0.410468	−0.205234	−	0.978713i	$-0.565796\pi$
$397$	−3246.87	−0.410468	−0.205234	+	0.978713i	$0.565796\pi$
$398$	−810.083	−0.102025
$399$	−9555.72	−1.19896
$400$	−1414.92	−0.176865
$401$	452.745	0.0563815	0.0281908	−	0.999603i	$-0.491025\pi$
$401$	452.745	0.0563815	0.0281908	+	0.999603i	$0.491025\pi$
$402$	0.560701	6.95652e−5 0
$403$	1854.65	0.229247
$404$	1478.39	0.182061
$405$	1619.92	0.198752
$406$	−5680.00	−0.694320
$407$	−2378.39	−0.289662
$408$	8951.56	1.08620
$409$	13157.2	1.59066	0.795332	−	0.606174i	$-0.207297\pi$
$409$	13157.2	1.59066	0.795332	+	0.606174i	$0.207297\pi$
$410$	8488.98	1.02254
$411$	−1122.08	−0.134666
$412$	−7857.03	−0.939534
$413$	−6723.59	−0.801081
$414$	2192.26	0.260250
$415$	−20229.1	−2.39278
$416$	−4194.09	−0.494309
$417$	3308.18	0.388495
$418$	1974.57	0.231051
$419$	13850.6	1.61491	0.807455	−	0.589929i	$-0.200844\pi$
$419$	13850.6	1.61491	0.807455	+	0.589929i	$0.200844\pi$
$420$	9061.94	1.05280
$421$	2371.40	0.274525	0.137263	−	0.990535i	$-0.456170\pi$
$421$	2371.40	0.274525	0.137263	+	0.990535i	$0.456170\pi$
$422$	−9160.44	−1.05669
$423$	−1277.28	−0.146817
$424$	13123.1	1.50310
$425$	−35439.8	−4.04490
$426$	2252.15	0.256143
$427$	−1980.60	−0.224469
$428$	−6625.67	−0.748281
$429$	787.347	0.0886095
$430$	−8128.07	−0.911559
$431$	−9874.29	−1.10355	−0.551773	−	0.833995i	$-0.686048\pi$
$431$	−9874.29	−1.10355	−0.551773	+	0.833995i	$0.686048\pi$
$432$	138.939	0.0154739
$433$	−3009.81	−0.334046	−0.167023	−	0.985953i	$-0.553415\pi$
$433$	−3009.81	−0.334046	−0.167023	+	0.985953i	$0.553415\pi$
$434$	−4618.28	−0.510794
$435$	−5735.98	−0.632227
$436$	1513.32	0.166226
$437$	−13059.3	−1.42954
$438$	5723.09	0.624338
$439$	924.470	0.100507	0.0502535	−	0.998736i	$-0.483997\pi$
$439$	924.470	0.100507	0.0502535	+	0.998736i	$0.483997\pi$
$440$	−5092.83	−0.551798
$441$	6401.06	0.691184
$442$	5627.00	0.605540
$443$	5848.32	0.627228	0.313614	−	0.949551i	$-0.398460\pi$
$443$	5848.32	0.627228	0.313614	+	0.949551i	$0.398460\pi$
$444$	3017.41	0.322523
$445$	−18521.5	−1.97304
$446$	3660.01	0.388580
$447$	181.414	0.0191959
$448$	11780.4	1.24235
$449$	4369.24	0.459236	0.229618	−	0.973281i	$-0.426252\pi$
$449$	4369.24	0.459236	0.229618	+	0.973281i	$0.426252\pi$
$450$	−4528.12	−0.474350
$451$	2551.73	0.266422
$452$	−332.453	−0.0345957
$453$	7597.20	0.787963
$454$	−8160.50	−0.843593
$455$	15492.8	1.59629
$456$	−6813.23	−0.699691
$457$	−1824.60	−0.186764	−0.0933820	−	0.995630i	$-0.529768\pi$
$457$	−1824.60	−0.186764	−0.0933820	+	0.995630i	$0.529768\pi$
$458$	−8552.34	−0.872543
$459$	3480.04	0.353887
$460$	12384.5	1.25528
$461$	−18348.8	−1.85377	−0.926887	−	0.375341i	$-0.877526\pi$
$461$	−18348.8	−1.85377	−0.926887	+	0.375341i	$0.877526\pi$
$462$	−1960.58	−0.197434
$463$	−15932.2	−1.59921	−0.799605	−	0.600527i	$-0.794958\pi$
$463$	−15932.2	−1.59921	−0.799605	+	0.600527i	$0.794958\pi$
$464$	−491.970	−0.0492223
$465$	−4663.79	−0.465114
$466$	3646.61	0.362502
$467$	13867.2	1.37409	0.687044	−	0.726616i	$-0.258908\pi$
$467$	13867.2	1.37409	0.687044	+	0.726616i	$0.258908\pi$
$468$	−998.891	−0.0986619
$469$	3.31645	0.000326523 0
$470$	5193.45	0.509694
$471$	3986.74	0.390019
$472$	−4793.92	−0.467496
$473$	−2443.25	−0.237507
$474$	1018.28	0.0986728
$475$	26974.0	2.60559
$476$	19467.5	1.87457
$477$	5101.78	0.489716
$478$	4084.14	0.390803
$479$	2141.43	0.204269	0.102134	−	0.994771i	$-0.467433\pi$
$479$	2141.43	0.204269	0.102134	+	0.994771i	$0.467433\pi$
$480$	10546.7	1.00289
$481$	5158.72	0.489018
$482$	−9551.94	−0.902654
$483$	12966.8	1.22155
$484$	−562.871	−0.0528617
$485$	−18436.3	−1.72608
$486$	444.642	0.0415007
$487$	5704.93	0.530832	0.265416	−	0.964134i	$-0.414491\pi$
$487$	5704.93	0.530832	0.265416	+	0.964134i	$0.414491\pi$
$488$	−1412.17	−0.130996
$489$	6541.64	0.604956
$490$	−26026.9	−2.39954
$491$	−8122.06	−0.746524	−0.373262	−	0.927726i	$-0.621761\pi$
$491$	−8122.06	−0.746524	−0.373262	+	0.927726i	$0.621761\pi$
$492$	−3237.33	−0.296647
$493$	−12322.5	−1.12571
$494$	−4282.83	−0.390068
$495$	−1979.90	−0.179778
$496$	−400.010	−0.0362116
$497$	13321.1	1.20228
$498$	−5552.55	−0.499630
$499$	−16899.7	−1.51610	−0.758050	−	0.652197i	$-0.773848\pi$
$499$	−16899.7	−1.51610	−0.758050	+	0.652197i	$0.773848\pi$
$500$	−13951.2	−1.24783
$501$	188.392	0.0167998
$502$	794.270	0.0706176
$503$	−1065.04	−0.0944095	−0.0472047	−	0.998885i	$-0.515031\pi$
$503$	−1065.04	−0.0944095	−0.0472047	+	0.998885i	$0.515031\pi$
$504$	6764.99	0.597890
$505$	−6355.86	−0.560064
$506$	−2679.42	−0.235405
$507$	4883.24	0.427756
$508$	−5751.31	−0.502309
$509$	1445.07	0.125838	0.0629190	−	0.998019i	$-0.479959\pi$
$509$	1445.07	0.125838	0.0629190	+	0.998019i	$0.479959\pi$
$510$	−14149.9	−1.22857
$511$	33851.1	2.93050
$512$	1857.62	0.160343
$513$	−2648.74	−0.227962
$514$	2696.37	0.231385
$515$	33778.8	2.89023
$516$	3099.70	0.264451
$517$	1561.12	0.132801
$518$	−12845.8	−1.08960
$519$	−4698.63	−0.397393
$520$	11046.3	0.931565
$521$	−16703.8	−1.40462	−0.702308	−	0.711873i	$-0.747847\pi$
$521$	−16703.8	−1.40462	−0.702308	+	0.711873i	$0.747847\pi$
$522$	−1574.43	−0.132013
$523$	13162.2	1.10046	0.550232	−	0.835012i	$-0.314539\pi$
$523$	13162.2	1.10046	0.550232	+	0.835012i	$0.314539\pi$
$524$	−12200.4	−1.01713
$525$	−26783.0	−2.22649
$526$	7376.63	0.611476
$527$	−10019.1	−0.828158
$528$	−169.815	−0.0139967
$529$	5554.06	0.456486
$530$	−20744.0	−1.70012
$531$	−1863.70	−0.152312
$532$	−14817.2	−1.20753
$533$	−5534.71	−0.449784
$534$	−5083.84	−0.411984
$535$	28485.0	2.30189
$536$	2.36463	0.000190553 0
$537$	1857.80	0.149292
$538$	8223.50	0.658997
$539$	−7823.52	−0.625200
$540$	2511.86	0.200173
$541$	−10604.7	−0.842757	−0.421378	−	0.906885i	$-0.638454\pi$
$541$	−10604.7	−0.842757	−0.421378	+	0.906885i	$0.638454\pi$
$542$	−11708.4	−0.927895
$543$	4203.85	0.332237
$544$	22657.2	1.78570
$545$	−6506.01	−0.511352
$546$	4252.51	0.333316
$547$	18504.6	1.44643	0.723216	−	0.690622i	$-0.242663\pi$
$547$	18504.6	1.44643	0.723216	+	0.690622i	$0.242663\pi$
$548$	−1739.90	−0.135629
$549$	−549.000	−0.0426790
$550$	5534.37	0.429066
$551$	9378.90	0.725145
$552$	9245.35	0.712877
$553$	6022.92	0.463148
$554$	343.341	0.0263306
$555$	−12972.4	−0.992157
$556$	5129.69	0.391272
$557$	22725.9	1.72877	0.864386	−	0.502829i	$-0.167707\pi$
$557$	22725.9	1.72877	0.864386	+	0.502829i	$0.167707\pi$
$558$	−1280.13	−0.0971190
$559$	5299.40	0.400968
$560$	−3341.47	−0.252148
$561$	−4253.38	−0.320103
$562$	−11084.1	−0.831945
$563$	21634.1	1.61948	0.809742	−	0.586787i	$-0.199607\pi$
$563$	21634.1	1.61948	0.809742	+	0.586787i	$0.199607\pi$
$564$	−1980.56	−0.147866
$565$	1429.27	0.106425
$566$	4037.84	0.299864
$567$	2629.98	0.194795
$568$	9497.93	0.701627
$569$	19293.4	1.42148	0.710738	−	0.703457i	$-0.248361\pi$
$569$	19293.4	1.42148	0.710738	+	0.703457i	$0.248361\pi$
$570$	10769.8	0.791401
$571$	−22121.8	−1.62131	−0.810654	−	0.585525i	$-0.800888\pi$
$571$	−22121.8	−1.62131	−0.810654	+	0.585525i	$0.800888\pi$
$572$	1220.87	0.0892431
$573$	−10924.4	−0.796461
$574$	13782.1	1.00218
$575$	−36603.0	−2.65469
$576$	3265.40	0.236212
$577$	−5962.13	−0.430167	−0.215084	−	0.976596i	$-0.569002\pi$
$577$	−5962.13	−0.430167	−0.215084	+	0.976596i	$0.569002\pi$
$578$	−21408.2	−1.54059
$579$	−5199.20	−0.373180
$580$	−8894.25	−0.636748
$581$	−32842.4	−2.34515
$582$	−5060.47	−0.360418
$583$	−6235.51	−0.442965
$584$	24135.9	1.71019
$585$	4294.41	0.303508
$586$	16999.7	1.19838
$587$	−12462.3	−0.876276	−0.438138	−	0.898908i	$-0.644362\pi$
$587$	−12462.3	−0.876276	−0.438138	+	0.898908i	$0.644362\pi$
$588$	9925.54	0.696126
$589$	7625.77	0.533471
$590$	7577.86	0.528772
$591$	5704.64	0.397052
$592$	−1112.63	−0.0772447
$593$	18416.1	1.27531	0.637654	−	0.770323i	$-0.279905\pi$
$593$	18416.1	1.27531	0.637654	+	0.770323i	$0.279905\pi$
$594$	−543.451	−0.0375388
$595$	−83694.4	−5.76662
$596$	281.302	0.0193332
$597$	−1328.15	−0.0910511
$598$	5811.67	0.397420
$599$	19950.4	1.36085	0.680425	−	0.732818i	$-0.261795\pi$
$599$	19950.4	1.36085	0.680425	+	0.732818i	$0.261795\pi$
$600$	−19096.3	−1.29934
$601$	18857.9	1.27991	0.639957	−	0.768411i	$-0.278952\pi$
$601$	18857.9	1.27991	0.639957	+	0.768411i	$0.278952\pi$
$602$	−13196.1	−0.893411
$603$	0.919281	6.20829e−5 0
$604$	11780.3	0.793597
$605$	2419.88	0.162615
$606$	−1744.58	−0.116945
$607$	−20080.4	−1.34273	−0.671367	−	0.741125i	$-0.734293\pi$
$607$	−20080.4	−1.34273	−0.671367	+	0.741125i	$0.734293\pi$
$608$	−17244.9	−1.15029
$609$	−9312.49	−0.619641
$610$	2232.25	0.148166
$611$	−3386.07	−0.224199
$612$	5396.18	0.356418
$613$	7575.51	0.499139	0.249569	−	0.968357i	$-0.419711\pi$
$613$	7575.51	0.499139	0.249569	+	0.968357i	$0.419711\pi$
$614$	−1804.18	−0.118584
$615$	13917.9	0.912557
$616$	−8268.32	−0.540812
$617$	14962.4	0.976280	0.488140	−	0.872765i	$-0.337676\pi$
$617$	14962.4	0.976280	0.488140	+	0.872765i	$0.337676\pi$
$618$	9271.72	0.603500
$619$	19688.0	1.27840	0.639199	−	0.769041i	$-0.279266\pi$
$619$	19688.0	1.27840	0.639199	+	0.769041i	$0.279266\pi$
$620$	−7231.72	−0.468440
$621$	3594.25	0.232258
$622$	−10596.8	−0.683109
$623$	−30070.0	−1.93376
$624$	368.328	0.0236297
$625$	25608.5	1.63894
$626$	−15230.6	−0.972424
$627$	3237.34	0.206199
$628$	6181.87	0.392808
$629$	−27868.3	−1.76658
$630$	−10693.6	−0.676257
$631$	−7268.46	−0.458563	−0.229281	−	0.973360i	$-0.573638\pi$
$631$	−7268.46	−0.458563	−0.229281	+	0.973360i	$0.573638\pi$
$632$	4294.35	0.270285
$633$	−15018.7	−0.943036
$634$	−8864.50	−0.555291
$635$	24725.9	1.54522
$636$	7910.87	0.493218
$637$	16969.2	1.05549
$638$	1924.30	0.119411
$639$	3692.45	0.228593
$640$	14847.3	0.917017
$641$	−1883.78	−0.116076	−0.0580382	−	0.998314i	$-0.518485\pi$
$641$	−1883.78	−0.116076	−0.0580382	+	0.998314i	$0.518485\pi$
$642$	7818.65	0.480650
$643$	20230.5	1.24077	0.620384	−	0.784298i	$-0.286977\pi$
$643$	20230.5	1.24077	0.620384	+	0.784298i	$0.286977\pi$
$644$	20106.5	1.23029
$645$	−13326.2	−0.813514
$646$	23136.6	1.40913
$647$	6513.17	0.395764	0.197882	−	0.980226i	$-0.436594\pi$
$647$	6513.17	0.395764	0.197882	+	0.980226i	$0.436594\pi$
$648$	1875.18	0.113679
$649$	2277.86	0.137772
$650$	−12004.0	−0.724365
$651$	−7571.77	−0.455854
$652$	10143.5	0.609281
$653$	11743.6	0.703773	0.351887	−	0.936043i	$-0.385540\pi$
$653$	11743.6	0.703773	0.351887	+	0.936043i	$0.385540\pi$
$654$	−1785.79	−0.106774
$655$	52451.8	3.12895
$656$	1193.72	0.0710474
$657$	9383.13	0.557186
$658$	8431.69	0.499546
$659$	13520.7	0.799231	0.399615	−	0.916683i	$-0.369144\pi$
$659$	13520.7	0.799231	0.399615	+	0.916683i	$0.369144\pi$
$660$	−3070.06	−0.181063
$661$	5584.55	0.328614	0.164307	−	0.986409i	$-0.447461\pi$
$661$	5584.55	0.328614	0.164307	+	0.986409i	$0.447461\pi$
$662$	15019.4	0.881789
$663$	9225.58	0.540410
$664$	−23416.6	−1.36859
$665$	63701.7	3.71466
$666$	−3560.71	−0.207169
$667$	−12726.9	−0.738811
$668$	292.122	0.0169199
$669$	6000.67	0.346785
$670$	−3.73782	−0.000215529 0
$671$	671.000	0.0386046
$672$	17122.8	0.982926
$673$	−21903.4	−1.25455	−0.627277	−	0.778796i	$-0.715831\pi$
$673$	−21903.4	−1.25455	−0.627277	+	0.778796i	$0.715831\pi$
$674$	−14597.9	−0.834260
$675$	−7423.95	−0.423330
$676$	7572.00	0.430815
$677$	−21675.3	−1.23050	−0.615251	−	0.788331i	$-0.710945\pi$
$677$	−21675.3	−1.23050	−0.615251	+	0.788331i	$0.710945\pi$
$678$	392.312	0.0222222
$679$	−29931.8	−1.69172
$680$	−59674.2	−3.36529
$681$	−13379.3	−0.752858
$682$	1564.61	0.0878474
$683$	−9286.03	−0.520235	−0.260117	−	0.965577i	$-0.583761\pi$
$683$	−9286.03	−0.520235	−0.260117	+	0.965577i	$0.583761\pi$
$684$	−4107.15	−0.229592
$685$	7480.14	0.417228
$686$	−21877.1	−1.21760
$687$	−14021.7	−0.778694
$688$	−1142.97	−0.0633364
$689$	13524.8	0.747830
$690$	−14614.3	−0.806316
$691$	3222.17	0.177391	0.0886954	−	0.996059i	$-0.471730\pi$
$691$	3222.17	0.177391	0.0886954	+	0.996059i	$0.471730\pi$
$692$	−7285.74	−0.400235
$693$	−3214.42	−0.176199
$694$	14216.6	0.777603
$695$	−22053.5	−1.20365
$696$	−6639.81	−0.361611
$697$	29899.4	1.62485
$698$	11468.4	0.621898
$699$	5978.70	0.323513
$700$	−41530.0	−2.24241
$701$	−11779.9	−0.634696	−0.317348	−	0.948309i	$-0.602792\pi$
$701$	−11779.9	−0.634696	−0.317348	+	0.948309i	$0.602792\pi$
$702$	1178.75	0.0633745
$703$	21211.2	1.13797
$704$	−3991.04	−0.213662
$705$	8514.78	0.454872
$706$	7023.40	0.374404
$707$	−10318.9	−0.548913
$708$	−2889.87	−0.153401
$709$	−30466.8	−1.61383	−0.806916	−	0.590667i	$-0.798865\pi$
$709$	−30466.8	−1.61383	−0.806916	+	0.590667i	$0.798865\pi$
$710$	−15013.6	−0.793592
$711$	1669.48	0.0880599
$712$	−21440.0	−1.12851
$713$	−10347.9	−0.543525
$714$	−22972.7	−1.20411
$715$	−5248.73	−0.274533
$716$	2880.72	0.150360
$717$	6696.03	0.348770
$718$	−4795.46	−0.249255
$719$	17209.8	0.892650	0.446325	−	0.894871i	$-0.352733\pi$
$719$	17209.8	0.892650	0.446325	+	0.894871i	$0.352733\pi$
$720$	−926.217	−0.0479418
$721$	54840.6	2.83269
$722$	−5059.16	−0.260779
$723$	−15660.6	−0.805567
$724$	6518.53	0.334612
$725$	26287.4	1.34661
$726$	664.218	0.0339552
$727$	12695.9	0.647682	0.323841	−	0.946112i	$-0.395026\pi$
$727$	12695.9	0.647682	0.323841	+	0.946112i	$0.395026\pi$
$728$	17934.0	0.913019
$729$	729.000	0.0370370
$730$	−38152.1	−1.93435
$731$	−28628.3	−1.44850
$732$	−851.284	−0.0429841
$733$	21703.2	1.09363	0.546813	−	0.837255i	$-0.315841\pi$
$733$	21703.2	1.09363	0.546813	+	0.837255i	$0.315841\pi$
$734$	21539.2	1.08314
$735$	−42671.6	−2.14145
$736$	23400.8	1.17196
$737$	−1.12357	−5.61561e−5 0
$738$	3820.23	0.190548
$739$	2952.01	0.146944	0.0734718	−	0.997297i	$-0.476592\pi$
$739$	2952.01	0.146944	0.0734718	+	0.997297i	$0.476592\pi$
$740$	−20115.1	−0.999251
$741$	−7021.80	−0.348114
$742$	−33678.4	−1.66627
$743$	38931.9	1.92231	0.961153	−	0.276016i	$-0.0890141\pi$
$743$	38931.9	1.92231	0.961153	+	0.276016i	$0.0890141\pi$
$744$	−5398.68	−0.266028
$745$	−1209.37	−0.0594736
$746$	15792.9	0.775093
$747$	−9103.52	−0.445891
$748$	−6595.33	−0.322392
$749$	46246.0	2.25606
$750$	16463.1	0.801532
$751$	−7254.22	−0.352477	−0.176239	−	0.984347i	$-0.556393\pi$
$751$	−7254.22	−0.352477	−0.176239	+	0.984347i	$0.556393\pi$
$752$	730.306	0.0354142
$753$	1302.22	0.0630221
$754$	−4173.82	−0.201593
$755$	−50645.5	−2.44130
$756$	4078.07	0.196188
$757$	13704.2	0.657977	0.328988	−	0.944334i	$-0.393292\pi$
$757$	13704.2	0.657977	0.328988	+	0.944334i	$0.393292\pi$
$758$	10373.0	0.497051
$759$	−4392.98	−0.210086
$760$	45419.4	2.16781
$761$	−14192.9	−0.676076	−0.338038	−	0.941132i	$-0.609763\pi$
$761$	−14192.9	−0.676076	−0.338038	+	0.941132i	$0.609763\pi$
$762$	6786.85	0.322653
$763$	−10562.7	−0.501172
$764$	−16939.4	−0.802156
$765$	−23199.1	−1.09643
$766$	5878.34	0.277276
$767$	−4940.67	−0.232591
$768$	12783.1	0.600611
$769$	8532.17	0.400101	0.200051	−	0.979786i	$-0.435889\pi$
$769$	8532.17	0.400101	0.200051	+	0.979786i	$0.435889\pi$
$770$	13069.9	0.611698
$771$	4420.76	0.206498
$772$	−8061.92	−0.375848
$773$	34830.3	1.62065	0.810324	−	0.585983i	$-0.199291\pi$
$773$	34830.3	1.62065	0.810324	+	0.585983i	$0.199291\pi$
$774$	−3657.81	−0.169867
$775$	21373.7	0.990667
$776$	−21341.4	−0.987257
$777$	−21061.0	−0.972404
$778$	−7488.98	−0.345106
$779$	−22757.1	−1.04667
$780$	6658.95	0.305678
$781$	−4512.99	−0.206770
$782$	−31395.6	−1.43568
$783$	−2581.31	−0.117814
$784$	−3659.91	−0.166723
$785$	−26576.9	−1.20837
$786$	14397.2	0.653345
$787$	−24047.9	−1.08922	−0.544608	−	0.838691i	$-0.683322\pi$
$787$	−24047.9	−1.08922	−0.544608	+	0.838691i	$0.683322\pi$
$788$	8845.67	0.399891
$789$	12094.1	0.545707
$790$	−6788.17	−0.305712
$791$	2320.46	0.104306
$792$	−2291.88	−0.102826
$793$	−1455.40	−0.0651737
$794$	5941.13	0.265545
$795$	−34010.2	−1.51726
$796$	−2059.44	−0.0917021
$797$	−39350.2	−1.74888	−0.874440	−	0.485134i	$-0.838771\pi$
$797$	−39350.2	−1.74888	−0.874440	+	0.485134i	$0.838771\pi$
$798$	17485.1	0.775645
$799$	18292.1	0.809922
$800$	−48334.5	−2.13610
$801$	−8335.07	−0.367672
$802$	−828.433	−0.0364751
$803$	−11468.3	−0.503993
$804$	1.42544	6.25268e−5 0
$805$	−86441.3	−3.78466
$806$	−3393.64	−0.148307
$807$	13482.6	0.588117
$808$	−7357.37	−0.320336
$809$	16073.5	0.698535	0.349268	−	0.937023i	$-0.386430\pi$
$809$	16073.5	0.698535	0.349268	+	0.937023i	$0.386430\pi$
$810$	−2964.13	−0.128579
$811$	−32982.0	−1.42806	−0.714028	−	0.700117i	$-0.753131\pi$
$811$	−32982.0	−1.42806	−0.714028	+	0.700117i	$0.753131\pi$
$812$	−14440.0	−0.624071
$813$	−19196.2	−0.828093
$814$	4351.98	0.187391
$815$	−43608.8	−1.87430
$816$	−1989.77	−0.0853626
$817$	21789.6	0.933075
$818$	−24075.1	−1.02905
$819$	6972.08	0.297465
$820$	21581.2	0.919082
$821$	−42874.7	−1.82258	−0.911289	−	0.411767i	$-0.864912\pi$
$821$	−42874.7	−1.82258	−0.911289	+	0.411767i	$0.864912\pi$
$822$	2053.18	0.0871201
$823$	20236.8	0.857123	0.428561	−	0.903513i	$-0.359021\pi$
$823$	20236.8	0.857123	0.428561	+	0.903513i	$0.359021\pi$
$824$	39101.4	1.65311
$825$	9073.72	0.382917
$826$	12302.8	0.518245
$827$	−28999.5	−1.21936	−0.609680	−	0.792648i	$-0.708702\pi$
$827$	−28999.5	−1.21936	−0.609680	+	0.792648i	$0.708702\pi$
$828$	5573.28	0.233919
$829$	−18359.4	−0.769179	−0.384590	−	0.923088i	$-0.625657\pi$
$829$	−18359.4	−0.769179	−0.384590	+	0.923088i	$0.625657\pi$
$830$	37015.2	1.54797
$831$	562.916	0.0234986
$832$	8656.57	0.360712
$833$	−91670.5	−3.81296
$834$	−6053.31	−0.251330
$835$	−1255.88	−0.0520498
$836$	5019.85	0.207674
$837$	−2098.81	−0.0866731
$838$	−25343.9	−1.04474
$839$	47873.3	1.96993	0.984964	−	0.172762i	$-0.0552691\pi$
$839$	47873.3	1.96993	0.984964	+	0.172762i	$0.0552691\pi$
$840$	−45097.7	−1.85240
$841$	−15248.8	−0.625234
$842$	−4339.20	−0.177599
$843$	−18172.6	−0.742463
$844$	−23288.2	−0.949778
$845$	−32553.4	−1.32529
$846$	2337.17	0.0949804
$847$	3928.74	0.159378
$848$	−2917.03	−0.118126
$849$	6620.13	0.267612
$850$	64847.8	2.61678
$851$	−28782.9	−1.15942
$852$	5725.54	0.230228
$853$	−40676.1	−1.63273	−0.816367	−	0.577533i	$-0.804015\pi$
$853$	−40676.1	−1.63273	−0.816367	+	0.577533i	$0.804015\pi$
$854$	3624.11	0.145216
$855$	17657.4	0.706280
$856$	32973.4	1.31660
$857$	−28869.9	−1.15073	−0.575367	−	0.817896i	$-0.695141\pi$
$857$	−28869.9	−1.15073	−0.575367	+	0.817896i	$0.695141\pi$
$858$	−1440.69	−0.0573244
$859$	39479.1	1.56811	0.784057	−	0.620689i	$-0.213147\pi$
$859$	39479.1	1.56811	0.784057	+	0.620689i	$0.213147\pi$
$860$	−20663.6	−0.819331
$861$	22596.0	0.894389
$862$	18068.0	0.713919
$863$	−42034.9	−1.65803	−0.829017	−	0.559223i	$-0.811100\pi$
$863$	−42034.9	−1.65803	−0.829017	+	0.559223i	$0.811100\pi$
$864$	4746.24	0.186887
$865$	31322.7	1.23122
$866$	5507.35	0.216105
$867$	−35099.1	−1.37489
$868$	−11740.9	−0.459114
$869$	−2040.48	−0.0796531
$870$	10495.7	0.409009
$871$	2.43701	9.48049e−5 0
$872$	−7531.18	−0.292475
$873$	−8296.75	−0.321652
$874$	23895.9	0.924819
$875$	97376.7	3.76221
$876$	14549.6	0.561169
$877$	−32205.1	−1.24001	−0.620005	−	0.784598i	$-0.712870\pi$
$877$	−32205.1	−1.24001	−0.620005	+	0.784598i	$0.712870\pi$
$878$	−1691.60	−0.0650212
$879$	27871.4	1.06949
$880$	1132.04	0.0433650
$881$	8038.39	0.307401	0.153701	−	0.988117i	$-0.450881\pi$
$881$	8038.39	0.307401	0.153701	+	0.988117i	$0.450881\pi$
$882$	−11712.7	−0.447150
$883$	49507.1	1.88680	0.943400	−	0.331656i	$-0.107607\pi$
$883$	49507.1	1.88680	0.943400	+	0.331656i	$0.107607\pi$
$884$	14305.3	0.544274
$885$	12424.1	0.471899
$886$	−10701.3	−0.405774
$887$	11845.6	0.448405	0.224203	−	0.974543i	$-0.428022\pi$
$887$	11845.6	0.448405	0.224203	+	0.974543i	$0.428022\pi$
$888$	−15016.5	−0.567478
$889$	40143.1	1.51446
$890$	33890.6	1.27642
$891$	−891.000	−0.0335013
$892$	9304.69	0.349265
$893$	−13922.5	−0.521724
$894$	−331.952	−0.0124185
$895$	−12384.7	−0.462543
$896$	24104.9	0.898761
$897$	9528.37	0.354674
$898$	−7994.83	−0.297095
$899$	7431.67	0.275706
$900$	−11511.6	−0.426357
$901$	−73063.4	−2.70155
$902$	−4669.17	−0.172357
$903$	−21635.3	−0.797318
$904$	1654.49	0.0608711
$905$	−28024.3	−1.02935
$906$	−13901.4	−0.509759
$907$	33966.6	1.24349	0.621744	−	0.783221i	$-0.286425\pi$
$907$	33966.6	1.24349	0.621744	+	0.783221i	$0.286425\pi$
$908$	−20746.1	−0.758241
$909$	−2860.28	−0.104367
$910$	−28348.7	−1.03269
$911$	41893.9	1.52361	0.761804	−	0.647807i	$-0.224314\pi$
$911$	41893.9	1.52361	0.761804	+	0.647807i	$0.224314\pi$
$912$	1514.46	0.0549877
$913$	11126.5	0.403323
$914$	3338.65	0.120824
$915$	3659.82	0.132229
$916$	−21742.2	−0.784262
$917$	85156.7	3.06665
$918$	−6367.78	−0.228941
$919$	27264.7	0.978648	0.489324	−	0.872102i	$-0.337243\pi$
$919$	27264.7	0.978648	0.489324	+	0.872102i	$0.337243\pi$
$920$	−61632.7	−2.20866
$921$	−2957.99	−0.105830
$922$	33574.7	1.19927
$923$	9788.68	0.349077
$924$	−4984.31	−0.177459
$925$	59451.2	2.11324
$926$	29152.8	1.03458
$927$	15201.2	0.538590
$928$	−16806.0	−0.594485
$929$	39197.5	1.38432	0.692158	−	0.721746i	$-0.256660\pi$
$929$	39197.5	1.38432	0.692158	+	0.721746i	$0.256660\pi$
$930$	8533.81	0.300898
$931$	69772.5	2.45618
$932$	9270.63	0.325826
$933$	−17373.7	−0.609636
$934$	−25374.3	−0.888942
$935$	28354.5	0.991755
$936$	4971.09	0.173595
$937$	42253.1	1.47316	0.736579	−	0.676352i	$-0.236440\pi$
$937$	42253.1	1.47316	0.736579	+	0.676352i	$0.236440\pi$
$938$	−6.06844	−0.000211238 0
$939$	−24970.9	−0.867833
$940$	13203.1	0.458125
$941$	51819.2	1.79517	0.897586	−	0.440839i	$-0.145319\pi$
$941$	51819.2	1.79517	0.897586	+	0.440839i	$0.145319\pi$
$942$	−7294.94	−0.252316
$943$	30880.7	1.06640
$944$	1065.60	0.0367399
$945$	−17532.3	−0.603521
$946$	4470.66	0.153651
$947$	20160.1	0.691778	0.345889	−	0.938275i	$-0.387577\pi$
$947$	20160.1	0.691778	0.345889	+	0.938275i	$0.387577\pi$
$948$	2588.72	0.0886895
$949$	24874.7	0.850860
$950$	−49357.2	−1.68564
$951$	−14533.5	−0.495565
$952$	−96882.4	−3.29830
$953$	−8082.44	−0.274728	−0.137364	−	0.990521i	$-0.543863\pi$
$953$	−8082.44	−0.274728	−0.137364	+	0.990521i	$0.543863\pi$
$954$	−9335.25	−0.316813
$955$	72825.6	2.46762
$956$	10382.9	0.351263
$957$	3154.94	0.106567
$958$	−3918.40	−0.132148
$959$	12144.2	0.408922
$960$	−21768.3	−0.731841
$961$	−23748.5	−0.797170
$962$	−9439.44	−0.316361
$963$	12818.9	0.428953
$964$	−24283.5	−0.811326
$965$	34659.6	1.15620
$966$	−23726.7	−0.790263
$967$	−53091.8	−1.76558	−0.882790	−	0.469767i	$-0.844338\pi$
$967$	−53091.8	−1.76558	−0.882790	+	0.469767i	$0.844338\pi$
$968$	2801.19	0.0930100
$969$	37932.9	1.25757
$970$	33734.8	1.11666
$971$	−35539.7	−1.17458	−0.587292	−	0.809375i	$-0.699806\pi$
$971$	−35539.7	−1.17458	−0.587292	+	0.809375i	$0.699806\pi$
$972$	1130.39	0.0373018
$973$	−35804.3	−1.17968
$974$	−10438.9	−0.343412
$975$	−19680.9	−0.646454
$976$	313.900	0.0102948
$977$	−24597.1	−0.805456	−0.402728	−	0.915320i	$-0.631938\pi$
$977$	−24597.1	−0.805456	−0.402728	+	0.915320i	$0.631938\pi$
$978$	−11969.9	−0.391365
$979$	10187.3	0.332572
$980$	−66167.0	−2.15676
$981$	−2927.85	−0.0952895
$982$	14861.8	0.482951
$983$	−925.303	−0.0300230	−0.0150115	−	0.999887i	$-0.504778\pi$
$983$	−925.303	−0.0300230	−0.0150115	+	0.999887i	$0.504778\pi$
$984$	16111.0	0.521950
$985$	−38029.1	−1.23016
$986$	22547.7	0.728259
$987$	13823.9	0.445816
$988$	−10888.1	−0.350603
$989$	−29567.8	−0.950660
$990$	3622.83	0.116304
$991$	−34289.6	−1.09914	−0.549569	−	0.835448i	$-0.685208\pi$
$991$	−34289.6	−1.09914	−0.549569	+	0.835448i	$0.685208\pi$
$992$	−13664.5	−0.437348
$993$	24624.6	0.786946
$994$	−24374.9	−0.777792
$995$	8853.89	0.282098
$996$	−14116.0	−0.449079
$997$	−11977.8	−0.380481	−0.190241	−	0.981738i	$-0.560927\pi$
$997$	−11977.8	−0.380481	−0.190241	+	0.981738i	$0.560927\pi$
$998$	30923.1	0.980814
$999$	−5837.86	−0.184887

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.e.1.15	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.e.1.15	✓	38	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)

\(f(q)\)	\(=\)	\(q-1.82980 q^{2} -3.00000 q^{3} -4.65183 q^{4} +19.9990 q^{5} +5.48940 q^{6} +32.4689 q^{7} +23.1503 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.82980 q^{2} -3.00000 q^{3} -4.65183 q^{4} +19.9990 q^{5} +5.48940 q^{6} +32.4689 q^{7} +23.1503 q^{8} +9.00000 q^{9} -36.5943 q^{10} -11.0000 q^{11} +13.9555 q^{12} +23.8590 q^{13} -59.4116 q^{14} -59.9971 q^{15} -5.14590 q^{16} -128.890 q^{17} -16.4682 q^{18} +98.1013 q^{19} -93.0320 q^{20} -97.4067 q^{21} +20.1278 q^{22} -133.120 q^{23} -69.4510 q^{24} +274.961 q^{25} -43.6572 q^{26} -27.0000 q^{27} -151.040 q^{28} +95.6042 q^{29} +109.783 q^{30} +77.7336 q^{31} -175.787 q^{32} +33.0000 q^{33} +235.844 q^{34} +649.346 q^{35} -41.8664 q^{36} +216.217 q^{37} -179.506 q^{38} -71.5770 q^{39} +462.984 q^{40} -231.976 q^{41} +178.235 q^{42} +222.113 q^{43} +51.1701 q^{44} +179.991 q^{45} +243.584 q^{46} -141.920 q^{47} +15.4377 q^{48} +711.229 q^{49} -503.124 q^{50} +386.671 q^{51} -110.988 q^{52} +566.865 q^{53} +49.4046 q^{54} -219.989 q^{55} +751.666 q^{56} -294.304 q^{57} -174.937 q^{58} -207.078 q^{59} +279.096 q^{60} -61.0000 q^{61} -142.237 q^{62} +292.220 q^{63} +362.822 q^{64} +477.157 q^{65} -60.3835 q^{66} +0.102142 q^{67} +599.575 q^{68} +399.361 q^{69} -1188.17 q^{70} +410.272 q^{71} +208.353 q^{72} +1042.57 q^{73} -395.634 q^{74} -824.883 q^{75} -456.350 q^{76} -357.158 q^{77} +130.972 q^{78} +185.498 q^{79} -102.913 q^{80} +81.0000 q^{81} +424.470 q^{82} -1011.50 q^{83} +453.119 q^{84} -2577.68 q^{85} -406.423 q^{86} -286.813 q^{87} -254.654 q^{88} -926.119 q^{89} -329.348 q^{90} +774.675 q^{91} +619.253 q^{92} -233.201 q^{93} +259.685 q^{94} +1961.93 q^{95} +527.360 q^{96} -921.861 q^{97} -1301.41 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9} + 95 q^{10} - 418 q^{11} - 426 q^{12} + 13 q^{13} + 26 q^{14} - 45 q^{15} + 486 q^{16} - 224 q^{17} - 18 q^{18} + 367 q^{19} + 18 q^{20} - 189 q^{21} + 22 q^{22} + 51 q^{23} + 135 q^{24} + 773 q^{25} - 439 q^{26} - 1026 q^{27} + 22 q^{28} - 462 q^{29} - 285 q^{30} + 234 q^{31} - 597 q^{32} + 1254 q^{33} + 956 q^{34} - 522 q^{35} + 1278 q^{36} + 954 q^{37} + 705 q^{38} - 39 q^{39} + 1495 q^{40} - 740 q^{41} - 78 q^{42} + 1441 q^{43} - 1562 q^{44} + 135 q^{45} + 581 q^{46} + 1003 q^{47} - 1458 q^{48} + 2707 q^{49} + 388 q^{50} + 672 q^{51} + 788 q^{52} + 735 q^{53} + 54 q^{54} - 165 q^{55} + 1059 q^{56} - 1101 q^{57} + 177 q^{58} + 261 q^{59} - 54 q^{60} - 2318 q^{61} + 1251 q^{62} + 567 q^{63} + 5571 q^{64} - 1354 q^{65} - 66 q^{66} + 3495 q^{67} - 1856 q^{68} - 153 q^{69} + 542 q^{70} - 873 q^{71} - 405 q^{72} + 989 q^{73} - 3406 q^{74} - 2319 q^{75} + 1712 q^{76} - 693 q^{77} + 1317 q^{78} + 2313 q^{79} + 1593 q^{80} + 3078 q^{81} + 5170 q^{82} + 569 q^{83} - 66 q^{84} - 1271 q^{85} + 3065 q^{86} + 1386 q^{87} + 495 q^{88} - 2917 q^{89} + 855 q^{90} + 2740 q^{91} + 1083 q^{92} - 702 q^{93} + 3272 q^{94} + 2696 q^{95} + 1791 q^{96} + 4250 q^{97} + 5952 q^{98} - 3762 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9 + 95 * q^10 - 418 * q^11 - 426 * q^12 + 13 * q^13 + 26 * q^14 - 45 * q^15 + 486 * q^16 - 224 * q^17 - 18 * q^18 + 367 * q^19 + 18 * q^20 - 189 * q^21 + 22 * q^22 + 51 * q^23 + 135 * q^24 + 773 * q^25 - 439 * q^26 - 1026 * q^27 + 22 * q^28 - 462 * q^29 - 285 * q^30 + 234 * q^31 - 597 * q^32 + 1254 * q^33 + 956 * q^34 - 522 * q^35 + 1278 * q^36 + 954 * q^37 + 705 * q^38 - 39 * q^39 + 1495 * q^40 - 740 * q^41 - 78 * q^42 + 1441 * q^43 - 1562 * q^44 + 135 * q^45 + 581 * q^46 + 1003 * q^47 - 1458 * q^48 + 2707 * q^49 + 388 * q^50 + 672 * q^51 + 788 * q^52 + 735 * q^53 + 54 * q^54 - 165 * q^55 + 1059 * q^56 - 1101 * q^57 + 177 * q^58 + 261 * q^59 - 54 * q^60 - 2318 * q^61 + 1251 * q^62 + 567 * q^63 + 5571 * q^64 - 1354 * q^65 - 66 * q^66 + 3495 * q^67 - 1856 * q^68 - 153 * q^69 + 542 * q^70 - 873 * q^71 - 405 * q^72 + 989 * q^73 - 3406 * q^74 - 2319 * q^75 + 1712 * q^76 - 693 * q^77 + 1317 * q^78 + 2313 * q^79 + 1593 * q^80 + 3078 * q^81 + 5170 * q^82 + 569 * q^83 - 66 * q^84 - 1271 * q^85 + 3065 * q^86 + 1386 * q^87 + 495 * q^88 - 2917 * q^89 + 855 * q^90 + 2740 * q^91 + 1083 * q^92 - 702 * q^93 + 3272 * q^94 + 2696 * q^95 + 1791 * q^96 + 4250 * q^97 + 5952 * q^98 - 3762 * q^99

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