LMFDB - Embedded newform 2013.4.a.d.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.84685 q^{2} -3.00000 q^{3} +0.104547 q^{4} -9.28768 q^{5} +8.54055 q^{6} +6.39681 q^{7} +22.4772 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.84685 q^{2} -3.00000 q^{3} +0.104547 q^{4} -9.28768 q^{5} +8.54055 q^{6} +6.39681 q^{7} +22.4772 q^{8} +9.00000 q^{9} +26.4406 q^{10} +11.0000 q^{11} -0.313642 q^{12} -1.06140 q^{13} -18.2108 q^{14} +27.8630 q^{15} -64.8254 q^{16} -2.24914 q^{17} -25.6216 q^{18} +21.5309 q^{19} -0.971001 q^{20} -19.1904 q^{21} -31.3153 q^{22} +83.1186 q^{23} -67.4315 q^{24} -38.7390 q^{25} +3.02166 q^{26} -27.0000 q^{27} +0.668769 q^{28} -291.840 q^{29} -79.3219 q^{30} -16.0307 q^{31} +4.73096 q^{32} -33.0000 q^{33} +6.40296 q^{34} -59.4116 q^{35} +0.940925 q^{36} +17.6911 q^{37} -61.2951 q^{38} +3.18421 q^{39} -208.761 q^{40} +355.441 q^{41} +54.6323 q^{42} +279.184 q^{43} +1.15002 q^{44} -83.5891 q^{45} -236.626 q^{46} -250.134 q^{47} +194.476 q^{48} -302.081 q^{49} +110.284 q^{50} +6.74742 q^{51} -0.110967 q^{52} -565.078 q^{53} +76.8649 q^{54} -102.164 q^{55} +143.782 q^{56} -64.5926 q^{57} +830.824 q^{58} +388.172 q^{59} +2.91300 q^{60} -61.0000 q^{61} +45.6371 q^{62} +57.5713 q^{63} +505.135 q^{64} +9.85798 q^{65} +93.9460 q^{66} +20.4835 q^{67} -0.235141 q^{68} -249.356 q^{69} +169.136 q^{70} +358.355 q^{71} +202.294 q^{72} -400.605 q^{73} -50.3638 q^{74} +116.217 q^{75} +2.25099 q^{76} +70.3649 q^{77} -9.06497 q^{78} +355.286 q^{79} +602.078 q^{80} +81.0000 q^{81} -1011.89 q^{82} +312.307 q^{83} -2.00631 q^{84} +20.8893 q^{85} -794.795 q^{86} +875.520 q^{87} +247.249 q^{88} +1096.70 q^{89} +237.966 q^{90} -6.78960 q^{91} +8.68982 q^{92} +48.0922 q^{93} +712.094 q^{94} -199.972 q^{95} -14.1929 q^{96} +9.45031 q^{97} +859.978 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.84685	−1.00651	−0.503256	−	0.864137i	$-0.667865\pi$
$2$	−2.84685	−1.00651	−0.503256	+	0.864137i	$0.667865\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	0.104547	0.0130684
$5$	−9.28768	−0.830715	−0.415358	−	0.909658i	$-0.636344\pi$
$5$	−9.28768	−0.830715	−0.415358	+	0.909658i	$0.636344\pi$
$6$	8.54055	0.581111
$7$	6.39681	0.345395	0.172698	−	0.984975i	$-0.444752\pi$
$7$	6.39681	0.345395	0.172698	+	0.984975i	$0.444752\pi$
$8$	22.4772	0.993359
$9$	9.00000	0.333333
$10$	26.4406	0.836126
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−0.313642	−0.00754504
$13$	−1.06140	−0.0226446	−0.0113223	−	0.999936i	$-0.503604\pi$
$13$	−1.06140	−0.0226446	−0.0113223	+	0.999936i	$0.503604\pi$
$14$	−18.2108	−0.347645
$15$	27.8630	0.479614
$16$	−64.8254	−1.01290
$17$	−2.24914	−0.0320880	−0.0160440	−	0.999871i	$-0.505107\pi$
$17$	−2.24914	−0.0320880	−0.0160440	+	0.999871i	$0.505107\pi$
$18$	−25.6216	−0.335504
$19$	21.5309	0.259975	0.129987	−	0.991516i	$-0.458506\pi$
$19$	21.5309	0.259975	0.129987	+	0.991516i	$0.458506\pi$
$20$	−0.971001	−0.0108561
$21$	−19.1904	−0.199414
$22$	−31.3153	−0.303475
$23$	83.1186	0.753541	0.376770	−	0.926307i	$-0.377035\pi$
$23$	83.1186	0.753541	0.376770	+	0.926307i	$0.377035\pi$
$24$	−67.4315	−0.573516
$25$	−38.7390	−0.309912
$26$	3.02166	0.0227921
$27$	−27.0000	−0.192450
$28$	0.668769	0.00451377
$29$	−291.840	−1.86874	−0.934368	−	0.356310i	$-0.884035\pi$
$29$	−291.840	−1.86874	−0.934368	+	0.356310i	$0.884035\pi$
$30$	−79.3219	−0.482737
$31$	−16.0307	−0.0928777	−0.0464388	−	0.998921i	$-0.514787\pi$
$31$	−16.0307	−0.0928777	−0.0464388	+	0.998921i	$0.514787\pi$
$32$	4.73096	0.0261351
$33$	−33.0000	−0.174078
$34$	6.40296	0.0322970
$35$	−59.4116	−0.286925
$36$	0.940925	0.00435613
$37$	17.6911	0.0786052	0.0393026	−	0.999227i	$-0.487486\pi$
$37$	17.6911	0.0786052	0.0393026	+	0.999227i	$0.487486\pi$
$38$	−61.2951	−0.261668
$39$	3.18421	0.0130739
$40$	−208.761	−0.825199
$41$	355.441	1.35391	0.676957	−	0.736022i	$-0.263298\pi$
$41$	355.441	1.35391	0.676957	+	0.736022i	$0.263298\pi$
$42$	54.6323	0.200713
$43$	279.184	0.990121	0.495061	−	0.868858i	$-0.335146\pi$
$43$	279.184	0.990121	0.495061	+	0.868858i	$0.335146\pi$
$44$	1.15002	0.00394027
$45$	−83.5891	−0.276905
$46$	−236.626	−0.758448
$47$	−250.134	−0.776294	−0.388147	−	0.921597i	$-0.626885\pi$
$47$	−250.134	−0.776294	−0.388147	+	0.921597i	$0.626885\pi$
$48$	194.476	0.584797
$49$	−302.081	−0.880702
$50$	110.284	0.311930
$51$	6.74742	0.0185260
$52$	−0.110967	−0.000295929 0
$53$	−565.078	−1.46452	−0.732259	−	0.681027i	$-0.761534\pi$
$53$	−565.078	−1.46452	−0.732259	+	0.681027i	$0.761534\pi$
$54$	76.8649	0.193704
$55$	−102.164	−0.250470
$56$	143.782	0.343102
$57$	−64.5926	−0.150097
$58$	830.824	1.88091
$59$	388.172	0.856538	0.428269	−	0.903651i	$-0.359124\pi$
$59$	388.172	0.856538	0.428269	+	0.903651i	$0.359124\pi$
$60$	2.91300	0.00626778
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	45.6371	0.0934826
$63$	57.5713	0.115132
$64$	505.135	0.986592
$65$	9.85798	0.0188113
$66$	93.9460	0.175211
$67$	20.4835	0.0373501	0.0186750	−	0.999826i	$-0.494055\pi$
$67$	20.4835	0.0373501	0.0186750	+	0.999826i	$0.494055\pi$
$68$	−0.235141	−0.000419339 0
$69$	−249.356	−0.435057
$70$	169.136	0.288794
$71$	358.355	0.598999	0.299500	−	0.954096i	$-0.403180\pi$
$71$	358.355	0.598999	0.299500	+	0.954096i	$0.403180\pi$
$72$	202.294	0.331120
$73$	−400.605	−0.642292	−0.321146	−	0.947030i	$-0.604068\pi$
$73$	−400.605	−0.642292	−0.321146	+	0.947030i	$0.604068\pi$
$74$	−50.3638	−0.0791172
$75$	116.217	0.178928
$76$	2.25099	0.00339745
$77$	70.3649	0.104141
$78$	−9.06497	−0.0131590
$79$	355.286	0.505985	0.252993	−	0.967468i	$-0.418585\pi$
$79$	355.286	0.505985	0.252993	+	0.967468i	$0.418585\pi$
$80$	602.078	0.841430
$81$	81.0000	0.111111
$82$	−1011.89	−1.36273
$83$	312.307	0.413013	0.206507	−	0.978445i	$-0.433790\pi$
$83$	312.307	0.413013	0.206507	+	0.978445i	$0.433790\pi$
$84$	−2.00631	−0.00260602
$85$	20.8893	0.0266560
$86$	−794.795	−0.996570
$87$	875.520	1.07891
$88$	247.249	0.299509
$89$	1096.70	1.30618	0.653092	−	0.757279i	$-0.273471\pi$
$89$	1096.70	1.30618	0.653092	+	0.757279i	$0.273471\pi$
$90$	237.966	0.278709
$91$	−6.78960	−0.00782136
$92$	8.68982	0.00984757
$93$	48.0922	0.0536229
$94$	712.094	0.781350
$95$	−199.972	−0.215965
$96$	−14.1929	−0.0150891
$97$	9.45031	0.00989210	0.00494605	−	0.999988i	$-0.498426\pi$
$97$	9.45031	0.00989210	0.00494605	+	0.999988i	$0.498426\pi$
$98$	859.978	0.886438
$99$	99.0000	0.100504
$100$	−4.05005	−0.00405005
$101$	−622.691	−0.613466	−0.306733	−	0.951796i	$-0.599236\pi$
$101$	−622.691	−0.613466	−0.306733	+	0.951796i	$0.599236\pi$
$102$	−19.2089	−0.0186467
$103$	1540.84	1.47402	0.737008	−	0.675885i	$-0.236238\pi$
$103$	1540.84	1.47402	0.737008	+	0.675885i	$0.236238\pi$
$104$	−23.8573	−0.0224943
$105$	178.235	0.165656
$106$	1608.69	1.47406
$107$	1496.32	1.35191	0.675957	−	0.736941i	$-0.263731\pi$
$107$	1496.32	1.35191	0.675957	+	0.736941i	$0.263731\pi$
$108$	−2.82277	−0.00251501
$109$	−1533.40	−1.34746	−0.673732	−	0.738976i	$-0.735310\pi$
$109$	−1533.40	−1.34746	−0.673732	+	0.738976i	$0.735310\pi$
$110$	290.847	0.252101
$111$	−53.0732	−0.0453828
$112$	−414.676	−0.349850
$113$	−322.176	−0.268211	−0.134105	−	0.990967i	$-0.542816\pi$
$113$	−322.176	−0.268211	−0.134105	+	0.990967i	$0.542816\pi$
$114$	183.885	0.151074
$115$	−771.979	−0.625978
$116$	−30.5111	−0.0244214
$117$	−9.55263	−0.00754822
$118$	−1105.07	−0.862116
$119$	−14.3873	−0.0110831
$120$	626.282	0.476429
$121$	121.000	0.0909091
$122$	173.658	0.128871
$123$	−1066.32	−0.781683
$124$	−1.67597	−0.00121376
$125$	1520.76	1.08816
$126$	−163.897	−0.115882
$127$	1268.23	0.886121	0.443061	−	0.896492i	$-0.353893\pi$
$127$	1268.23	0.886121	0.443061	+	0.896492i	$0.353893\pi$
$128$	−1475.89	−1.01915
$129$	−837.553	−0.571647
$130$	−28.0642	−0.0189338
$131$	1890.43	1.26082	0.630412	−	0.776260i	$-0.282886\pi$
$131$	1890.43	1.26082	0.630412	+	0.776260i	$0.282886\pi$
$132$	−3.45006	−0.00227492
$133$	137.729	0.0897941
$134$	−58.3134	−0.0375933
$135$	250.767	0.159871
$136$	−50.5542	−0.0318749
$137$	1623.90	1.01270	0.506349	−	0.862329i	$-0.330995\pi$
$137$	1623.90	1.01270	0.506349	+	0.862329i	$0.330995\pi$
$138$	709.879	0.437890
$139$	−1297.94	−0.792014	−0.396007	−	0.918247i	$-0.629604\pi$
$139$	−1297.94	−0.792014	−0.396007	+	0.918247i	$0.629604\pi$
$140$	−6.21131	−0.00374965
$141$	750.402	0.448194
$142$	−1020.18	−0.602901
$143$	−11.6754	−0.00682762
$144$	−583.429	−0.337633
$145$	2710.52	1.55239
$146$	1140.46	0.646475
$147$	906.242	0.508474
$148$	1.84955	0.00102724
$149$	−1168.81	−0.642634	−0.321317	−	0.946972i	$-0.604126\pi$
$149$	−1168.81	−0.642634	−0.321317	+	0.946972i	$0.604126\pi$
$150$	−330.852	−0.180093
$151$	956.149	0.515300	0.257650	−	0.966238i	$-0.417052\pi$
$151$	956.149	0.515300	0.257650	+	0.966238i	$0.417052\pi$
$152$	483.953	0.258248
$153$	−20.2422	−0.0106960
$154$	−200.318	−0.104819
$155$	148.888	0.0771549
$156$	0.332900	0.000170855 0
$157$	3060.58	1.55580	0.777902	−	0.628386i	$-0.216284\pi$
$157$	3060.58	1.55580	0.777902	+	0.628386i	$0.216284\pi$
$158$	−1011.45	−0.509281
$159$	1695.23	0.845540
$160$	−43.9397	−0.0217109
$161$	531.694	0.260269
$162$	−230.595	−0.111835
$163$	−3534.94	−1.69864	−0.849318	−	0.527881i	$-0.822987\pi$
$163$	−3534.94	−1.69864	−0.849318	+	0.527881i	$0.822987\pi$
$164$	37.1603	0.0176935
$165$	306.493	0.144609
$166$	−889.090	−0.415703
$167$	1921.05	0.890152	0.445076	−	0.895493i	$-0.353177\pi$
$167$	1921.05	0.890152	0.445076	+	0.895493i	$0.353177\pi$
$168$	−431.347	−0.198090
$169$	−2195.87	−0.999487
$170$	−59.4686	−0.0268296
$171$	193.778	0.0866583
$172$	29.1879	0.0129393
$173$	275.607	0.121121	0.0605607	−	0.998165i	$-0.480711\pi$
$173$	275.607	0.121121	0.0605607	+	0.998165i	$0.480711\pi$
$174$	−2492.47	−1.08594
$175$	−247.806	−0.107042
$176$	−713.080	−0.305400
$177$	−1164.52	−0.494522
$178$	−3122.15	−1.31469
$179$	−1710.11	−0.714075	−0.357037	−	0.934090i	$-0.616213\pi$
$179$	−1710.11	−0.714075	−0.357037	+	0.934090i	$0.616213\pi$
$180$	−8.73901	−0.00361871
$181$	−4408.56	−1.81042	−0.905209	−	0.424966i	$-0.860286\pi$
$181$	−4408.56	−1.81042	−0.905209	+	0.424966i	$0.860286\pi$
$182$	19.3290	0.00787230
$183$	183.000	0.0739221
$184$	1868.27	0.748537
$185$	−164.309	−0.0652986
$186$	−136.911	−0.0539722
$187$	−24.7405	−0.00967490
$188$	−26.1508	−0.0101449
$189$	−172.714	−0.0664714
$190$	569.290	0.217372
$191$	1751.39	0.663487	0.331743	−	0.943370i	$-0.392363\pi$
$191$	1751.39	0.663487	0.331743	+	0.943370i	$0.392363\pi$
$192$	−1515.41	−0.569609
$193$	−1723.45	−0.642782	−0.321391	−	0.946947i	$-0.604150\pi$
$193$	−1723.45	−0.642782	−0.321391	+	0.946947i	$0.604150\pi$
$194$	−26.9036	−0.00995653
$195$	−29.5739	−0.0108607
$196$	−31.5817	−0.0115094
$197$	−1211.77	−0.438250	−0.219125	−	0.975697i	$-0.570320\pi$
$197$	−1211.77	−0.438250	−0.219125	+	0.975697i	$0.570320\pi$
$198$	−281.838	−0.101158
$199$	−2826.40	−1.00683	−0.503413	−	0.864046i	$-0.667923\pi$
$199$	−2826.40	−1.00683	−0.503413	+	0.864046i	$0.667923\pi$
$200$	−870.743	−0.307854
$201$	−61.4504	−0.0215641
$202$	1772.71	0.617461
$203$	−1866.85	−0.645453
$204$	0.705423	0.000242105 0
$205$	−3301.22	−1.12472
$206$	−4386.54	−1.48362
$207$	748.068	0.251180
$208$	68.8060	0.0229367
$209$	236.840	0.0783854
$210$	−507.407	−0.166735
$211$	−1584.93	−0.517115	−0.258558	−	0.965996i	$-0.583247\pi$
$211$	−1584.93	−0.517115	−0.258558	+	0.965996i	$0.583247\pi$
$212$	−59.0773	−0.0191389
$213$	−1075.07	−0.345832
$214$	−4259.80	−1.36072
$215$	−2592.97	−0.822509
$216$	−606.883	−0.191172
$217$	−102.546	−0.0320795
$218$	4365.37	1.35624
$219$	1201.82	0.370827
$220$	−10.6810	−0.00327324
$221$	2.38724	0.000726622 0
$222$	151.091	0.0456783
$223$	−3235.97	−0.971733	−0.485867	−	0.874033i	$-0.661496\pi$
$223$	−3235.97	−0.971733	−0.485867	+	0.874033i	$0.661496\pi$
$224$	30.2631	0.00902696
$225$	−348.651	−0.103304
$226$	917.188	0.269958
$227$	727.742	0.212784	0.106392	−	0.994324i	$-0.466070\pi$
$227$	727.742	0.212784	0.106392	+	0.994324i	$0.466070\pi$
$228$	−6.75298	−0.00196152
$229$	2749.50	0.793415	0.396707	−	0.917945i	$-0.370153\pi$
$229$	2749.50	0.793415	0.396707	+	0.917945i	$0.370153\pi$
$230$	2197.71	0.630055
$231$	−211.095	−0.0601256
$232$	−6559.73	−1.85633
$233$	2083.46	0.585803	0.292901	−	0.956143i	$-0.405379\pi$
$233$	2083.46	0.585803	0.292901	+	0.956143i	$0.405379\pi$
$234$	27.1949	0.00759738
$235$	2323.17	0.644879
$236$	40.5823	0.0111936
$237$	−1065.86	−0.292131
$238$	40.9585	0.0111552
$239$	6701.61	1.81377	0.906885	−	0.421377i	$-0.138453\pi$
$239$	6701.61	1.81377	0.906885	+	0.421377i	$0.138453\pi$
$240$	−1806.23	−0.485800
$241$	2324.89	0.621409	0.310704	−	0.950507i	$-0.399435\pi$
$241$	2324.89	0.621409	0.310704	+	0.950507i	$0.399435\pi$
$242$	−344.469	−0.0915012
$243$	−243.000	−0.0641500
$244$	−6.37738	−0.00167324
$245$	2805.63	0.731613
$246$	3035.66	0.786774
$247$	−22.8529	−0.00588704
$248$	−360.326	−0.0922609
$249$	−936.920	−0.238453
$250$	−4329.36	−1.09525
$251$	−4431.87	−1.11449	−0.557245	−	0.830348i	$-0.688142\pi$
$251$	−4431.87	−1.11449	−0.557245	+	0.830348i	$0.688142\pi$
$252$	6.01892	0.00150459
$253$	914.305	0.227201
$254$	−3610.47	−0.891893
$255$	−62.6678	−0.0153899
$256$	160.557	0.0391985
$257$	−4461.52	−1.08289	−0.541443	−	0.840737i	$-0.682122\pi$
$257$	−4461.52	−1.08289	−0.541443	+	0.840737i	$0.682122\pi$
$258$	2384.39	0.575370
$259$	113.166	0.0271499
$260$	1.03062	0.000245833 0
$261$	−2626.56	−0.622912
$262$	−5381.78	−1.26904
$263$	6482.40	1.51986	0.759928	−	0.650007i	$-0.225234\pi$
$263$	6482.40	1.51986	0.759928	+	0.650007i	$0.225234\pi$
$264$	−741.746	−0.172922
$265$	5248.26	1.21660
$266$	−392.094	−0.0903789
$267$	−3290.11	−0.754126
$268$	2.14149	0.000488106 0
$269$	1197.61	0.271449	0.135724	−	0.990747i	$-0.456664\pi$
$269$	1197.61	0.271449	0.135724	+	0.990747i	$0.456664\pi$
$270$	−713.897	−0.160912
$271$	7050.16	1.58032	0.790160	−	0.612900i	$-0.209997\pi$
$271$	7050.16	1.58032	0.790160	+	0.612900i	$0.209997\pi$
$272$	145.801	0.0325019
$273$	20.3688	0.00451566
$274$	−4623.01	−1.01929
$275$	−426.129	−0.0934420
$276$	−26.0695	−0.00568550
$277$	4154.15	0.901079	0.450539	−	0.892757i	$-0.351232\pi$
$277$	4154.15	0.901079	0.450539	+	0.892757i	$0.351232\pi$
$278$	3695.04	0.797173
$279$	−144.277	−0.0309592
$280$	−1335.40	−0.285020
$281$	−2868.73	−0.609019	−0.304509	−	0.952509i	$-0.598493\pi$
$281$	−2868.73	−0.609019	−0.304509	+	0.952509i	$0.598493\pi$
$282$	−2136.28	−0.451113
$283$	1591.84	0.334364	0.167182	−	0.985926i	$-0.446533\pi$
$283$	1591.84	0.334364	0.167182	+	0.985926i	$0.446533\pi$
$284$	37.4651	0.00782796
$285$	599.916	0.124687
$286$	33.2382	0.00687209
$287$	2273.69	0.467636
$288$	42.5787	0.00871171
$289$	−4907.94	−0.998970
$290$	−7716.43	−1.56250
$291$	−28.3509	−0.00571121
$292$	−41.8822	−0.00839373
$293$	713.807	0.142324	0.0711622	−	0.997465i	$-0.477329\pi$
$293$	713.807	0.142324	0.0711622	+	0.997465i	$0.477329\pi$
$294$	−2579.93	−0.511785
$295$	−3605.22	−0.711539
$296$	397.645	0.0780833
$297$	−297.000	−0.0580259
$298$	3327.42	0.646820
$299$	−88.2224	−0.0170637
$300$	12.1502	0.00233830
$301$	1785.89	0.341983
$302$	−2722.01	−0.518656
$303$	1868.07	0.354185
$304$	−1395.75	−0.263328
$305$	566.549	0.106362
$306$	57.6266	0.0107657
$307$	678.337	0.126107	0.0630533	−	0.998010i	$-0.479916\pi$
$307$	678.337	0.126107	0.0630533	+	0.998010i	$0.479916\pi$
$308$	7.35646	0.00136095
$309$	−4622.52	−0.851023
$310$	−423.863	−0.0776574
$311$	−7545.50	−1.37578	−0.687888	−	0.725817i	$-0.741462\pi$
$311$	−7545.50	−1.37578	−0.687888	+	0.725817i	$0.741462\pi$
$312$	71.5720	0.0129871
$313$	−585.489	−0.105731	−0.0528655	−	0.998602i	$-0.516835\pi$
$313$	−585.489	−0.105731	−0.0528655	+	0.998602i	$0.516835\pi$
$314$	−8713.02	−1.56594
$315$	−534.704	−0.0956418
$316$	37.1442	0.00661242
$317$	1088.34	0.192830	0.0964152	−	0.995341i	$-0.469262\pi$
$317$	1088.34	0.192830	0.0964152	+	0.995341i	$0.469262\pi$
$318$	−4826.07	−0.851047
$319$	−3210.24	−0.563445
$320$	−4691.53	−0.819577
$321$	−4488.96	−0.780528
$322$	−1513.65	−0.261965
$323$	−48.4259	−0.00834207
$324$	8.46832	0.00145204
$325$	41.1177	0.00701785
$326$	10063.4	1.70970
$327$	4600.21	0.777958
$328$	7989.30	1.34492
$329$	−1600.06	−0.268128
$330$	−872.540	−0.145551
$331$	8500.89	1.41163	0.705817	−	0.708394i	$-0.250580\pi$
$331$	8500.89	1.41163	0.705817	+	0.708394i	$0.250580\pi$
$332$	32.6508	0.00539742
$333$	159.220	0.0262017
$334$	−5468.94	−0.895950
$335$	−190.244	−0.0310273
$336$	1244.03	0.201986
$337$	−7380.34	−1.19298	−0.596488	−	0.802622i	$-0.703438\pi$
$337$	−7380.34	−1.19298	−0.596488	+	0.802622i	$0.703438\pi$
$338$	6251.32	1.00600
$339$	966.529	0.154852
$340$	2.18392	0.000348351 0
$341$	−176.338	−0.0280037
$342$	−551.656	−0.0872227
$343$	−4126.46	−0.649586
$344$	6275.27	0.983546
$345$	2315.94	0.361408
$346$	−784.611	−0.121910
$347$	6933.42	1.07264	0.536319	−	0.844015i	$-0.319814\pi$
$347$	6933.42	1.07264	0.536319	+	0.844015i	$0.319814\pi$
$348$	91.5332	0.0140997
$349$	−7512.73	−1.15228	−0.576142	−	0.817349i	$-0.695443\pi$
$349$	−7512.73	−1.15228	−0.576142	+	0.817349i	$0.695443\pi$
$350$	705.466	0.107739
$351$	28.6579	0.00435796
$352$	52.0406	0.00788004
$353$	−5176.06	−0.780436	−0.390218	−	0.920722i	$-0.627600\pi$
$353$	−5176.06	−0.780436	−0.390218	+	0.920722i	$0.627600\pi$
$354$	3315.20	0.497743
$355$	−3328.29	−0.497598
$356$	114.657	0.0170697
$357$	43.1620	0.00639880
$358$	4868.41	0.718725
$359$	−1603.58	−0.235748	−0.117874	−	0.993029i	$-0.537608\pi$
$359$	−1603.58	−0.235748	−0.117874	+	0.993029i	$0.537608\pi$
$360$	−1878.85	−0.275066
$361$	−6395.42	−0.932413
$362$	12550.5	1.82221
$363$	−363.000	−0.0524864
$364$	−0.709834	−0.000102213 0
$365$	3720.70	0.533562
$366$	−520.973	−0.0744036
$367$	−5449.65	−0.775121	−0.387560	−	0.921844i	$-0.626682\pi$
$367$	−5449.65	−0.775121	−0.387560	+	0.921844i	$0.626682\pi$
$368$	−5388.20	−0.763259
$369$	3198.97	0.451305
$370$	467.763	0.0657239
$371$	−3614.70	−0.505838
$372$	5.02791	0.000700766 0
$373$	−4378.53	−0.607806	−0.303903	−	0.952703i	$-0.598290\pi$
$373$	−4378.53	−0.607806	−0.303903	+	0.952703i	$0.598290\pi$
$374$	70.4325	0.00973791
$375$	−4562.27	−0.628252
$376$	−5622.31	−0.771139
$377$	309.760	0.0423169
$378$	491.691	0.0669043
$379$	−13280.3	−1.79990	−0.899951	−	0.435991i	$-0.856398\pi$
$379$	−13280.3	−1.79990	−0.899951	+	0.435991i	$0.856398\pi$
$380$	−20.9065	−0.00282232
$381$	−3804.70	−0.511602
$382$	−4985.94	−0.667808
$383$	7002.07	0.934176	0.467088	−	0.884211i	$-0.345303\pi$
$383$	7002.07	0.934176	0.467088	+	0.884211i	$0.345303\pi$
$384$	4427.67	0.588408
$385$	−653.527	−0.0865112
$386$	4906.41	0.646968
$387$	2512.66	0.330040
$388$	0.988004	0.000129274 0
$389$	6989.34	0.910987	0.455493	−	0.890239i	$-0.349463\pi$
$389$	6989.34	0.910987	0.455493	+	0.890239i	$0.349463\pi$
$390$	84.1925	0.0109314
$391$	−186.945	−0.0241796
$392$	−6789.92	−0.874854
$393$	−5671.30	−0.727937
$394$	3449.73	0.441104
$395$	−3299.79	−0.420330
$396$	10.3502	0.00131342
$397$	−11789.1	−1.49037	−0.745186	−	0.666857i	$-0.767639\pi$
$397$	−11789.1	−1.49037	−0.745186	+	0.666857i	$0.767639\pi$
$398$	8046.34	1.01338
$399$	−413.187	−0.0518427
$400$	2511.27	0.313909
$401$	−14810.4	−1.84438	−0.922189	−	0.386739i	$-0.873601\pi$
$401$	−14810.4	−1.84438	−0.922189	+	0.386739i	$0.873601\pi$
$402$	174.940	0.0217045
$403$	17.0151	0.00210318
$404$	−65.1006	−0.00801702
$405$	−752.302	−0.0923017
$406$	5314.63	0.649657
$407$	194.602	0.0237004
$408$	151.663	0.0184030
$409$	−2953.47	−0.357066	−0.178533	−	0.983934i	$-0.557135\pi$
$409$	−2953.47	−0.357066	−0.178533	+	0.983934i	$0.557135\pi$
$410$	9398.07	1.13204
$411$	−4871.71	−0.584681
$412$	161.091	0.0192630
$413$	2483.07	0.295844
$414$	−2129.64	−0.252816
$415$	−2900.60	−0.343097
$416$	−5.02146	−0.000591821 0
$417$	3893.83	0.457270
$418$	−674.247	−0.0788959
$419$	−11335.8	−1.32169	−0.660845	−	0.750523i	$-0.729802\pi$
$419$	−11335.8	−1.32169	−0.660845	+	0.750523i	$0.729802\pi$
$420$	18.6339	0.00216486
$421$	9018.78	1.04406	0.522029	−	0.852928i	$-0.325175\pi$
$421$	9018.78	1.04406	0.522029	+	0.852928i	$0.325175\pi$
$422$	4512.06	0.520483
$423$	−2251.21	−0.258765
$424$	−12701.3	−1.45479
$425$	87.1294	0.00994446
$426$	3060.55	0.348085
$427$	−390.206	−0.0442234
$428$	156.436	0.0176673
$429$	35.0263	0.00394193
$430$	7381.81	0.827866
$431$	947.421	0.105883	0.0529416	−	0.998598i	$-0.483140\pi$
$431$	947.421	0.105883	0.0529416	+	0.998598i	$0.483140\pi$
$432$	1750.29	0.194932
$433$	−11201.1	−1.24317	−0.621584	−	0.783348i	$-0.713510\pi$
$433$	−11201.1	−1.24317	−0.621584	+	0.783348i	$0.713510\pi$
$434$	291.932	0.0322885
$435$	−8131.55	−0.896271
$436$	−160.313	−0.0176092
$437$	1789.62	0.195902
$438$	−3421.39	−0.373243
$439$	9982.41	1.08527	0.542636	−	0.839968i	$-0.317426\pi$
$439$	9982.41	1.08527	0.542636	+	0.839968i	$0.317426\pi$
$440$	−2296.37	−0.248807
$441$	−2718.73	−0.293567
$442$	−6.79612	−0.000731354 0
$443$	−7422.54	−0.796062	−0.398031	−	0.917372i	$-0.630306\pi$
$443$	−7422.54	−0.796062	−0.398031	+	0.917372i	$0.630306\pi$
$444$	−5.54866	−0.000593080 0
$445$	−10185.8	−1.08507
$446$	9212.31	0.978062
$447$	3506.43	0.371025
$448$	3231.26	0.340764
$449$	−4482.40	−0.471131	−0.235565	−	0.971859i	$-0.575694\pi$
$449$	−4482.40	−0.471131	−0.235565	+	0.971859i	$0.575694\pi$
$450$	992.556	0.103977
$451$	3909.85	0.408221
$452$	−33.6826	−0.00350508
$453$	−2868.45	−0.297509
$454$	−2071.77	−0.214170
$455$	63.0596	0.00649732
$456$	−1451.86	−0.149100
$457$	788.238	0.0806832	0.0403416	−	0.999186i	$-0.487155\pi$
$457$	788.238	0.0806832	0.0403416	+	0.999186i	$0.487155\pi$
$458$	−7827.41	−0.798582
$459$	60.7267	0.00617534
$460$	−80.7083	−0.00818053
$461$	11147.8	1.12626	0.563130	−	0.826368i	$-0.309597\pi$
$461$	11147.8	1.12626	0.563130	+	0.826368i	$0.309597\pi$
$462$	600.955	0.0605172
$463$	−9054.95	−0.908897	−0.454449	−	0.890773i	$-0.650164\pi$
$463$	−9054.95	−0.908897	−0.454449	+	0.890773i	$0.650164\pi$
$464$	18918.7	1.89284
$465$	−446.665	−0.0445454
$466$	−5931.29	−0.589618
$467$	3272.26	0.324244	0.162122	−	0.986771i	$-0.448166\pi$
$467$	3272.26	0.324244	0.162122	+	0.986771i	$0.448166\pi$
$468$	−0.998701	−9.86431e−5 0
$469$	131.029	0.0129005
$470$	−6613.70	−0.649079
$471$	−9181.75	−0.898243
$472$	8725.01	0.850850
$473$	3071.03	0.298533
$474$	3034.34	0.294033
$475$	−834.084	−0.0805693
$476$	−1.50415	−0.000144838 0
$477$	−5085.70	−0.488173
$478$	−19078.5	−1.82558
$479$	9750.51	0.930088	0.465044	−	0.885288i	$-0.346038\pi$
$479$	9750.51	0.930088	0.465044	+	0.885288i	$0.346038\pi$
$480$	131.819	0.0125348
$481$	−18.7774	−0.00177999
$482$	−6618.62	−0.625456
$483$	−1595.08	−0.150267
$484$	12.6502	0.00118804
$485$	−87.7715	−0.00821752
$486$	691.784	0.0645678
$487$	930.371	0.0865691	0.0432845	−	0.999063i	$-0.486218\pi$
$487$	930.371	0.0865691	0.0432845	+	0.999063i	$0.486218\pi$
$488$	−1371.11	−0.127187
$489$	10604.8	0.980708
$490$	−7987.20	−0.736378
$491$	−4039.68	−0.371299	−0.185650	−	0.982616i	$-0.559439\pi$
$491$	−4039.68	−0.371299	−0.185650	+	0.982616i	$0.559439\pi$
$492$	−111.481	−0.0102153
$493$	656.389	0.0599640
$494$	65.0589	0.00592538
$495$	−919.480	−0.0834900
$496$	1039.20	0.0940756
$497$	2292.33	0.206892
$498$	2667.27	0.240006
$499$	−5510.56	−0.494362	−0.247181	−	0.968969i	$-0.579504\pi$
$499$	−5510.56	−0.494362	−0.247181	+	0.968969i	$0.579504\pi$
$500$	158.991	0.0142206
$501$	−5763.15	−0.513930
$502$	12616.9	1.12175
$503$	1488.52	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$503$	1488.52	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$504$	1294.04	0.114367
$505$	5783.35	0.509616
$506$	−2602.89	−0.228681
$507$	6587.62	0.577054
$508$	132.590	0.0115802
$509$	−3244.94	−0.282572	−0.141286	−	0.989969i	$-0.545124\pi$
$509$	−3244.94	−0.282572	−0.141286	+	0.989969i	$0.545124\pi$
$510$	178.406	0.0154901
$511$	−2562.60	−0.221845
$512$	11350.0	0.979699
$513$	−581.334	−0.0500322
$514$	12701.3	1.08994
$515$	−14310.8	−1.22449
$516$	−87.5638	−0.00747051
$517$	−2751.48	−0.234061
$518$	−322.168	−0.0273267
$519$	−826.820	−0.0699294
$520$	221.579	0.0186863
$521$	−10520.6	−0.884676	−0.442338	−	0.896848i	$-0.645851\pi$
$521$	−10520.6	−0.884676	−0.442338	+	0.896848i	$0.645851\pi$
$522$	7477.42	0.626969
$523$	−15043.7	−1.25777	−0.628886	−	0.777497i	$-0.716489\pi$
$523$	−15043.7	−1.25777	−0.628886	+	0.777497i	$0.716489\pi$
$524$	197.640	0.0164770
$525$	743.418	0.0618008
$526$	−18454.4	−1.52975
$527$	36.0554	0.00298026
$528$	2139.24	0.176323
$529$	−5258.29	−0.432177
$530$	−14941.0	−1.22452
$531$	3493.55	0.285513
$532$	14.3992	0.00117347
$533$	−377.266	−0.0306589
$534$	9366.45	0.759037
$535$	−13897.3	−1.12306
$536$	460.410	0.0371021
$537$	5130.32	0.412271
$538$	−3409.42	−0.273217
$539$	−3322.89	−0.265542
$540$	26.2170	0.00208926
$541$	−5209.69	−0.414015	−0.207008	−	0.978339i	$-0.566372\pi$
$541$	−5209.69	−0.414015	−0.207008	+	0.978339i	$0.566372\pi$
$542$	−20070.7	−1.59061
$543$	13225.7	1.04525
$544$	−10.6406	−0.000838624 0
$545$	14241.8	1.11936
$546$	−57.9869	−0.00454507
$547$	8767.00	0.685283	0.342642	−	0.939466i	$-0.388678\pi$
$547$	8767.00	0.685283	0.342642	+	0.939466i	$0.388678\pi$
$548$	169.775	0.0132343
$549$	−549.000	−0.0426790
$550$	1213.12	0.0940506
$551$	−6283.57	−0.485824
$552$	−5604.81	−0.432168
$553$	2272.70	0.174765
$554$	−11826.2	−0.906947
$555$	492.927	0.0377002
$556$	−135.696	−0.0103504
$557$	−2544.36	−0.193551	−0.0967756	−	0.995306i	$-0.530853\pi$
$557$	−2544.36	−0.193551	−0.0967756	+	0.995306i	$0.530853\pi$
$558$	410.734	0.0311609
$559$	−296.327	−0.0224209
$560$	3851.38	0.290626
$561$	74.2216	0.00558581
$562$	8166.85	0.612985
$563$	1238.15	0.0926854	0.0463427	−	0.998926i	$-0.485243\pi$
$563$	1238.15	0.0926854	0.0463427	+	0.998926i	$0.485243\pi$
$564$	78.4525	0.00585717
$565$	2992.27	0.222807
$566$	−4531.73	−0.336542
$567$	518.142	0.0383773
$568$	8054.81	0.595022
$569$	−1495.68	−0.110197	−0.0550985	−	0.998481i	$-0.517547\pi$
$569$	−1495.68	−0.110197	−0.0550985	+	0.998481i	$0.517547\pi$
$570$	−1707.87	−0.125500
$571$	−24740.8	−1.81326	−0.906629	−	0.421929i	$-0.861353\pi$
$571$	−24740.8	−1.81326	−0.906629	+	0.421929i	$0.861353\pi$
$572$	−1.22063	−8.92260e−5 0
$573$	−5254.16	−0.383064
$574$	−6472.84	−0.470682
$575$	−3219.93	−0.233531
$576$	4546.22	0.328864
$577$	−1322.75	−0.0954365	−0.0477183	−	0.998861i	$-0.515195\pi$
$577$	−1322.75	−0.0954365	−0.0477183	+	0.998861i	$0.515195\pi$
$578$	13972.2	1.00548
$579$	5170.36	0.371110
$580$	283.377	0.0202872
$581$	1997.77	0.142653
$582$	80.7108	0.00574840
$583$	−6215.86	−0.441569
$584$	−9004.47	−0.638027
$585$	88.7218	0.00627042
$586$	−2032.10	−0.143251
$587$	−3929.19	−0.276277	−0.138139	−	0.990413i	$-0.544112\pi$
$587$	−3929.19	−0.276277	−0.138139	+	0.990413i	$0.544112\pi$
$588$	94.7451	0.00664494
$589$	−345.156	−0.0241459
$590$	10263.5	0.716173
$591$	3635.32	0.253024
$592$	−1146.83	−0.0796191
$593$	−573.882	−0.0397412	−0.0198706	−	0.999803i	$-0.506325\pi$
$593$	−573.882	−0.0397412	−0.0198706	+	0.999803i	$0.506325\pi$
$594$	845.514	0.0584038
$595$	133.625	0.00920686
$596$	−122.196	−0.00839820
$597$	8479.21	0.581291
$598$	251.156	0.0171748
$599$	26226.9	1.78898	0.894491	−	0.447085i	$-0.147538\pi$
$599$	26226.9	1.78898	0.894491	+	0.447085i	$0.147538\pi$
$600$	2612.23	0.177740
$601$	2614.25	0.177433	0.0887167	−	0.996057i	$-0.471723\pi$
$601$	2614.25	0.177433	0.0887167	+	0.996057i	$0.471723\pi$
$602$	−5084.16	−0.344211
$603$	184.351	0.0124500
$604$	99.9627	0.00673415
$605$	−1123.81	−0.0755196
$606$	−5318.12	−0.356491
$607$	−23678.4	−1.58332	−0.791660	−	0.610961i	$-0.790783\pi$
$607$	−23678.4	−1.58332	−0.791660	+	0.610961i	$0.790783\pi$
$608$	101.862	0.00679448
$609$	5600.54	0.372652
$610$	−1612.88	−0.107055
$611$	265.493	0.0175789
$612$	−2.11627	−0.000139780 0
$613$	−27614.1	−1.81945	−0.909724	−	0.415213i	$-0.863707\pi$
$613$	−27614.1	−1.81945	−0.909724	+	0.415213i	$0.863707\pi$
$614$	−1931.12	−0.126928
$615$	9903.66	0.649356
$616$	1581.60	0.103449
$617$	−3826.43	−0.249670	−0.124835	−	0.992178i	$-0.539840\pi$
$617$	−3826.43	−0.249670	−0.124835	+	0.992178i	$0.539840\pi$
$618$	13159.6	0.856566
$619$	29307.3	1.90301	0.951503	−	0.307638i	$-0.0995386\pi$
$619$	29307.3	1.90301	0.951503	+	0.307638i	$0.0995386\pi$
$620$	15.5659	0.00100829
$621$	−2244.20	−0.145019
$622$	21480.9	1.38474
$623$	7015.41	0.451150
$624$	−206.418	−0.0132425
$625$	−9281.92	−0.594043
$626$	1666.80	0.106420
$627$	−710.519	−0.0452558
$628$	319.975	0.0203319
$629$	−39.7897	−0.00252229
$630$	1522.22	0.0962647
$631$	30118.8	1.90017	0.950087	−	0.311985i	$-0.100994\pi$
$631$	30118.8	1.90017	0.950087	+	0.311985i	$0.100994\pi$
$632$	7985.83	0.502625
$633$	4754.80	0.298557
$634$	−3098.34	−0.194086
$635$	−11778.9	−0.736115
$636$	177.232	0.0110498
$637$	320.630	0.0199432
$638$	9139.07	0.567115
$639$	3225.20	0.199666
$640$	13707.6	0.846626
$641$	1969.56	0.121362	0.0606809	−	0.998157i	$-0.480673\pi$
$641$	1969.56	0.121362	0.0606809	+	0.998157i	$0.480673\pi$
$642$	12779.4	0.785611
$643$	5872.09	0.360144	0.180072	−	0.983653i	$-0.442367\pi$
$643$	5872.09	0.360144	0.180072	+	0.983653i	$0.442367\pi$
$644$	55.5872	0.00340131
$645$	7778.92	0.474876
$646$	137.861	0.00839641
$647$	11530.7	0.700649	0.350324	−	0.936628i	$-0.386071\pi$
$647$	11530.7	0.700649	0.350324	+	0.936628i	$0.386071\pi$
$648$	1820.65	0.110373
$649$	4269.90	0.258256
$650$	−117.056	−0.00706355
$651$	307.637	0.0185211
$652$	−369.568	−0.0221985
$653$	20127.7	1.20621	0.603107	−	0.797661i	$-0.293929\pi$
$653$	20127.7	1.20621	0.603107	+	0.797661i	$0.293929\pi$
$654$	−13096.1	−0.783025
$655$	−17557.8	−1.04739
$656$	−23041.6	−1.37138
$657$	−3605.45	−0.214097
$658$	4555.13	0.269875
$659$	−17742.9	−1.04881	−0.524405	−	0.851469i	$-0.675712\pi$
$659$	−17742.9	−1.04881	−0.524405	+	0.851469i	$0.675712\pi$
$660$	32.0430	0.00188981
$661$	−4032.42	−0.237281	−0.118641	−	0.992937i	$-0.537854\pi$
$661$	−4032.42	−0.237281	−0.118641	+	0.992937i	$0.537854\pi$
$662$	−24200.7	−1.42083
$663$	−7.16173	−0.000419515 0
$664$	7019.77	0.410271
$665$	−1279.18	−0.0745934
$666$	−453.274	−0.0263724
$667$	−24257.3	−1.40817
$668$	200.841	0.0116329
$669$	9707.91	0.561030
$670$	541.596	0.0312294
$671$	−671.000	−0.0386046
$672$	−90.7893	−0.00521172
$673$	−18019.4	−1.03209	−0.516045	−	0.856562i	$-0.672596\pi$
$673$	−18019.4	−1.03209	−0.516045	+	0.856562i	$0.672596\pi$
$674$	21010.7	1.20075
$675$	1045.95	0.0596426
$676$	−229.572	−0.0130617
$677$	−8069.67	−0.458113	−0.229057	−	0.973413i	$-0.573564\pi$
$677$	−8069.67	−0.458113	−0.229057	+	0.973413i	$0.573564\pi$
$678$	−2751.56	−0.155860
$679$	60.4519	0.00341669
$680$	469.532	0.0264790
$681$	−2183.23	−0.122851
$682$	502.008	0.0281861
$683$	619.600	0.0347121	0.0173560	−	0.999849i	$-0.494475\pi$
$683$	619.600	0.0347121	0.0173560	+	0.999849i	$0.494475\pi$
$684$	20.2589	0.00113248
$685$	−15082.3	−0.841263
$686$	11747.4	0.653817
$687$	−8248.50	−0.458078
$688$	−18098.2	−1.00289
$689$	599.776	0.0331635
$690$	−6593.12	−0.363762
$691$	28436.6	1.56553	0.782764	−	0.622319i	$-0.213809\pi$
$691$	28436.6	1.56553	0.782764	+	0.622319i	$0.213809\pi$
$692$	28.8139	0.00158286
$693$	633.285	0.0347135
$694$	−19738.4	−1.07962
$695$	12054.9	0.657938
$696$	19679.2	1.07175
$697$	−799.435	−0.0434444
$698$	21387.6	1.15979
$699$	−6250.38	−0.338213
$700$	−25.9074	−0.00139887
$701$	24189.6	1.30332	0.651660	−	0.758511i	$-0.274073\pi$
$701$	24189.6	1.30332	0.651660	+	0.758511i	$0.274073\pi$
$702$	−81.5847	−0.00438635
$703$	380.904	0.0204354
$704$	5556.49	0.297469
$705$	−6969.50	−0.372321
$706$	14735.5	0.785519
$707$	−3983.24	−0.211888
$708$	−121.747	−0.00646262
$709$	21407.3	1.13395	0.566973	−	0.823736i	$-0.308114\pi$
$709$	21407.3	1.13395	0.566973	+	0.823736i	$0.308114\pi$
$710$	9475.14	0.500839
$711$	3197.58	0.168662
$712$	24650.8	1.29751
$713$	−1332.45	−0.0699871
$714$	−122.876	−0.00644048
$715$	108.438	0.00567181
$716$	−178.787	−0.00933181
$717$	−20104.8	−1.04718
$718$	4565.15	0.237284
$719$	−35131.0	−1.82221	−0.911103	−	0.412178i	$-0.864768\pi$
$719$	−35131.0	−1.82221	−0.911103	+	0.412178i	$0.864768\pi$
$720$	5418.70	0.280477
$721$	9856.47	0.509118
$722$	18206.8	0.938486
$723$	−6974.68	−0.358770
$724$	−460.903	−0.0236593
$725$	11305.6	0.579143
$726$	1033.41	0.0528282
$727$	9059.51	0.462172	0.231086	−	0.972933i	$-0.425772\pi$
$727$	9059.51	0.462172	0.231086	+	0.972933i	$0.425772\pi$
$728$	−152.611	−0.00776942
$729$	729.000	0.0370370
$730$	−10592.3	−0.537037
$731$	−627.924	−0.0317710
$732$	19.1321	0.000966044 0
$733$	−28221.9	−1.42210	−0.711050	−	0.703142i	$-0.751780\pi$
$733$	−28221.9	−1.42210	−0.711050	+	0.703142i	$0.751780\pi$
$734$	15514.3	0.780169
$735$	−8416.89	−0.422397
$736$	393.231	0.0196939
$737$	225.318	0.0112615
$738$	−9106.97	−0.454244
$739$	12093.9	0.602005	0.301003	−	0.953623i	$-0.402679\pi$
$739$	12093.9	0.602005	0.301003	+	0.953623i	$0.402679\pi$
$740$	−17.1780	−0.000853348 0
$741$	68.5588	0.00339888
$742$	10290.5	0.509132
$743$	−21617.3	−1.06738	−0.533688	−	0.845681i	$-0.679194\pi$
$743$	−21617.3	−1.06738	−0.533688	+	0.845681i	$0.679194\pi$
$744$	1080.98	0.0532669
$745$	10855.5	0.533846
$746$	12465.0	0.611765
$747$	2810.76	0.137671
$748$	−2.58655	−0.000126435 0
$749$	9571.68	0.466945
$750$	12988.1	0.632344
$751$	−26656.2	−1.29521	−0.647603	−	0.761978i	$-0.724228\pi$
$751$	−26656.2	−1.29521	−0.647603	+	0.761978i	$0.724228\pi$
$752$	16215.1	0.786306
$753$	13295.6	0.643451
$754$	−881.840	−0.0425925
$755$	−8880.40	−0.428068
$756$	−18.0568	−0.000868675 0
$757$	−19329.7	−0.928073	−0.464037	−	0.885816i	$-0.653599\pi$
$757$	−19329.7	−0.928073	−0.464037	+	0.885816i	$0.653599\pi$
$758$	37807.0	1.81162
$759$	−2742.91	−0.131175
$760$	−4494.80	−0.214531
$761$	14675.9	0.699079	0.349540	−	0.936922i	$-0.386338\pi$
$761$	14675.9	0.699079	0.349540	+	0.936922i	$0.386338\pi$
$762$	10831.4	0.514935
$763$	−9808.90	−0.465408
$764$	183.103	0.00867071
$765$	188.004	0.00888533
$766$	−19933.8	−0.940260
$767$	−412.007	−0.0193960
$768$	−481.672	−0.0226313
$769$	5632.92	0.264146	0.132073	−	0.991240i	$-0.457837\pi$
$769$	5632.92	0.264146	0.132073	+	0.991240i	$0.457837\pi$
$770$	1860.49	0.0870747
$771$	13384.5	0.625205
$772$	−180.182	−0.00840013
$773$	38271.6	1.78077	0.890383	−	0.455212i	$-0.150437\pi$
$773$	38271.6	1.78077	0.890383	+	0.455212i	$0.150437\pi$
$774$	−7153.16	−0.332190
$775$	621.015	0.0287839
$776$	212.416	0.00982641
$777$	−339.499	−0.0156750
$778$	−19897.6	−0.916920
$779$	7652.95	0.351984
$780$	−3.09187	−0.000141932 0
$781$	3941.91	0.180605
$782$	532.205	0.0243371
$783$	7879.68	0.359638
$784$	19582.5	0.892061
$785$	−28425.7	−1.29243
$786$	16145.3	0.732678
$787$	25879.1	1.17216	0.586080	−	0.810254i	$-0.300671\pi$
$787$	25879.1	1.17216	0.586080	+	0.810254i	$0.300671\pi$
$788$	−126.687	−0.00572722
$789$	−19447.2	−0.877489
$790$	9393.99	0.423067
$791$	−2060.90	−0.0926388
$792$	2225.24	0.0998364
$793$	64.7456	0.00289935
$794$	33561.8	1.50008
$795$	−15744.8	−0.702403
$796$	−295.492	−0.0131576
$797$	−20842.1	−0.926303	−0.463152	−	0.886279i	$-0.653281\pi$
$797$	−20842.1	−0.926303	−0.463152	+	0.886279i	$0.653281\pi$
$798$	1176.28	0.0521803
$799$	562.586	0.0249097
$800$	−183.273	−0.00809959
$801$	9870.34	0.435395
$802$	42162.9	1.85639
$803$	−4406.66	−0.193658
$804$	−6.42447	−0.000281808 0
$805$	−4938.21	−0.216210
$806$	−48.4394	−0.00211688
$807$	−3592.84	−0.156721
$808$	−13996.3	−0.609392
$809$	−20600.4	−0.895269	−0.447634	−	0.894217i	$-0.647733\pi$
$809$	−20600.4	−0.895269	−0.447634	+	0.894217i	$0.647733\pi$
$810$	2141.69	0.0929029
$811$	−29829.8	−1.29157	−0.645786	−	0.763519i	$-0.723470\pi$
$811$	−29829.8	−1.29157	−0.645786	+	0.763519i	$0.723470\pi$
$812$	−195.174	−0.00843504
$813$	−21150.5	−0.912398
$814$	−554.002	−0.0238547
$815$	32831.4	1.41108
$816$	−437.404	−0.0187650
$817$	6011.08	0.257407
$818$	8408.09	0.359391
$819$	−61.1064	−0.00260712
$820$	−345.133	−0.0146983
$821$	−1399.05	−0.0594729	−0.0297364	−	0.999558i	$-0.509467\pi$
$821$	−1399.05	−0.0594729	−0.0297364	+	0.999558i	$0.509467\pi$
$822$	13869.0	0.588489
$823$	−14204.5	−0.601624	−0.300812	−	0.953683i	$-0.597258\pi$
$823$	−14204.5	−0.601624	−0.300812	+	0.953683i	$0.597258\pi$
$824$	34633.7	1.46423
$825$	1278.39	0.0539487
$826$	−7068.91	−0.297771
$827$	−2757.57	−0.115949	−0.0579747	−	0.998318i	$-0.518464\pi$
$827$	−2757.57	−0.115949	−0.0579747	+	0.998318i	$0.518464\pi$
$828$	78.2084	0.00328252
$829$	20594.8	0.862833	0.431416	−	0.902153i	$-0.358014\pi$
$829$	20594.8	0.862833	0.431416	+	0.902153i	$0.358014\pi$
$830$	8257.58	0.345331
$831$	−12462.5	−0.520238
$832$	−536.152	−0.0223410
$833$	679.421	0.0282600
$834$	−11085.1	−0.460248
$835$	−17842.1	−0.739463
$836$	24.7609	0.00102437
$837$	432.830	0.0178743
$838$	32271.2	1.33030
$839$	39340.9	1.61883	0.809416	−	0.587236i	$-0.199784\pi$
$839$	39340.9	1.61883	0.809416	+	0.587236i	$0.199784\pi$
$840$	4006.21	0.164556
$841$	60781.6	2.49217
$842$	−25675.1	−1.05086
$843$	8606.20	0.351617
$844$	−165.700	−0.00675787
$845$	20394.6	0.830289
$846$	6408.85	0.260450
$847$	774.014	0.0313996
$848$	36631.4	1.48341
$849$	−4775.52	−0.193045
$850$	−248.044	−0.0100092
$851$	1470.46	0.0592322
$852$	−112.395	−0.00451948
$853$	−8443.51	−0.338922	−0.169461	−	0.985537i	$-0.554203\pi$
$853$	−8443.51	−0.338922	−0.169461	+	0.985537i	$0.554203\pi$
$854$	1110.86	0.0445114
$855$	−1799.75	−0.0719884
$856$	33633.0	1.34294
$857$	4865.24	0.193925	0.0969623	−	0.995288i	$-0.469087\pi$
$857$	4865.24	0.193925	0.0969623	+	0.995288i	$0.469087\pi$
$858$	−99.7146	−0.00396760
$859$	−20818.6	−0.826916	−0.413458	−	0.910523i	$-0.635679\pi$
$859$	−20818.6	−0.826916	−0.413458	+	0.910523i	$0.635679\pi$
$860$	−271.088	−0.0107489
$861$	−6821.06	−0.269990
$862$	−2697.16	−0.106573
$863$	−25056.9	−0.988353	−0.494176	−	0.869362i	$-0.664530\pi$
$863$	−25056.9	−0.988353	−0.494176	+	0.869362i	$0.664530\pi$
$864$	−127.736	−0.00502971
$865$	−2559.75	−0.100617
$866$	31887.9	1.25126
$867$	14723.8	0.576756
$868$	−10.7209	−0.000419228 0
$869$	3908.15	0.152560
$870$	23149.3	0.902109
$871$	−21.7412	−0.000845779 0
$872$	−34466.6	−1.33852
$873$	85.0528	0.00329737
$874$	−5094.77	−0.197177
$875$	9727.99	0.375847
$876$	125.647	0.00484612
$877$	20794.4	0.800657	0.400328	−	0.916372i	$-0.368896\pi$
$877$	20794.4	0.800657	0.400328	+	0.916372i	$0.368896\pi$
$878$	−28418.4	−1.09234
$879$	−2141.42	−0.0821710
$880$	6622.86	0.253701
$881$	−15721.2	−0.601202	−0.300601	−	0.953750i	$-0.597187\pi$
$881$	−15721.2	−0.601202	−0.300601	+	0.953750i	$0.597187\pi$
$882$	7739.80	0.295479
$883$	8224.28	0.313442	0.156721	−	0.987643i	$-0.449908\pi$
$883$	8224.28	0.313442	0.156721	+	0.987643i	$0.449908\pi$
$884$	0.249580	9.49578e−6 0
$885$	10815.7	0.410807
$886$	21130.8	0.801247
$887$	−4195.50	−0.158818	−0.0794088	−	0.996842i	$-0.525303\pi$
$887$	−4195.50	−0.158818	−0.0794088	+	0.996842i	$0.525303\pi$
$888$	−1192.94	−0.0450814
$889$	8112.65	0.306062
$890$	28997.5	1.09213
$891$	891.000	0.0335013
$892$	−338.311	−0.0126990
$893$	−5385.61	−0.201817
$894$	−9982.26	−0.373442
$895$	15882.9	0.593193
$896$	−9441.00	−0.352011
$897$	264.667	0.00985171
$898$	12760.7	0.474199
$899$	4678.41	0.173564
$900$	−36.4505	−0.00135002
$901$	1270.94	0.0469935
$902$	−11130.7	−0.410879
$903$	−5357.67	−0.197444
$904$	−7241.61	−0.266430
$905$	40945.3	1.50394
$906$	8166.03	0.299446
$907$	−20890.7	−0.764788	−0.382394	−	0.923999i	$-0.624900\pi$
$907$	−20890.7	−0.764788	−0.382394	+	0.923999i	$0.624900\pi$
$908$	76.0834	0.00278074
$909$	−5604.22	−0.204489
$910$	−179.521	−0.00653964
$911$	−1297.14	−0.0471749	−0.0235874	−	0.999722i	$-0.507509\pi$
$911$	−1297.14	−0.0471749	−0.0235874	+	0.999722i	$0.507509\pi$
$912$	4187.25	0.152032
$913$	3435.37	0.124528
$914$	−2244.00	−0.0812087
$915$	−1699.65	−0.0614082
$916$	287.452	0.0103687
$917$	12092.8	0.435483
$918$	−172.880	−0.00621556
$919$	−22784.1	−0.817822	−0.408911	−	0.912574i	$-0.634091\pi$
$919$	−22784.1	−0.817822	−0.408911	+	0.912574i	$0.634091\pi$
$920$	−17351.9	−0.621821
$921$	−2035.01	−0.0728077
$922$	−31736.2	−1.13360
$923$	−380.360	−0.0135641
$924$	−22.0694	−0.000785746 0
$925$	−685.334	−0.0243607
$926$	25778.1	0.914817
$927$	13867.6	0.491338
$928$	−1380.68	−0.0488397
$929$	43270.1	1.52814	0.764071	−	0.645132i	$-0.223198\pi$
$929$	43270.1	1.52814	0.764071	+	0.645132i	$0.223198\pi$
$930$	1271.59	0.0448355
$931$	−6504.06	−0.228960
$932$	217.820	0.00765550
$933$	22636.5	0.794304
$934$	−9315.62	−0.326356
$935$	229.782	0.00803709
$936$	−214.716	−0.00749809
$937$	−26470.7	−0.922904	−0.461452	−	0.887165i	$-0.652671\pi$
$937$	−26470.7	−0.922904	−0.461452	+	0.887165i	$0.652671\pi$
$938$	−373.020	−0.0129846
$939$	1756.47	0.0610438
$940$	242.881	0.00842754
$941$	−42815.2	−1.48325	−0.741623	−	0.670817i	$-0.765944\pi$
$941$	−42815.2	−1.48325	−0.741623	+	0.670817i	$0.765944\pi$
$942$	26139.0	0.904094
$943$	29543.7	1.02023
$944$	−25163.4	−0.867585
$945$	1604.11	0.0552188
$946$	−8742.75	−0.300477
$947$	−54151.4	−1.85817	−0.929083	−	0.369872i	$-0.879402\pi$
$947$	−54151.4	−1.85817	−0.929083	+	0.369872i	$0.879402\pi$
$948$	−111.433	−0.00381768
$949$	425.204	0.0145445
$950$	2374.51	0.0810940
$951$	−3265.02	−0.111331
$952$	−323.386	−0.0110095
$953$	−14129.5	−0.480271	−0.240136	−	0.970739i	$-0.577192\pi$
$953$	−14129.5	−0.480271	−0.240136	+	0.970739i	$0.577192\pi$
$954$	14478.2	0.491352
$955$	−16266.3	−0.551169
$956$	700.635	0.0237031
$957$	9630.72	0.325305
$958$	−27758.2	−0.936146
$959$	10387.8	0.349781
$960$	14074.6	0.473183
$961$	−29534.0	−0.991374
$962$	53.4563	0.00179158
$963$	13466.9	0.450638
$964$	243.061	0.00812082
$965$	16006.9	0.533969
$966$	4540.96	0.151245
$967$	4217.27	0.140246	0.0701232	−	0.997538i	$-0.477661\pi$
$967$	4217.27	0.140246	0.0701232	+	0.997538i	$0.477661\pi$
$968$	2719.74	0.0903054
$969$	145.278	0.00481630
$970$	249.872	0.00827104
$971$	14296.1	0.472486	0.236243	−	0.971694i	$-0.424084\pi$
$971$	14296.1	0.472486	0.236243	+	0.971694i	$0.424084\pi$
$972$	−25.4050	−0.000838338 0
$973$	−8302.69	−0.273558
$974$	−2648.63	−0.0871329
$975$	−123.353	−0.00405176
$976$	3954.35	0.129688
$977$	46199.6	1.51285	0.756425	−	0.654080i	$-0.226944\pi$
$977$	46199.6	1.51285	0.756425	+	0.654080i	$0.226944\pi$
$978$	−30190.3	−0.987096
$979$	12063.7	0.393829
$980$	293.321	0.00956101
$981$	−13800.6	−0.449154
$982$	11500.3	0.373718
$983$	51474.9	1.67019	0.835094	−	0.550108i	$-0.185413\pi$
$983$	51474.9	1.67019	0.835094	+	0.550108i	$0.185413\pi$
$984$	−23967.9	−0.776492
$985$	11254.6	0.364061
$986$	−1868.64	−0.0603546
$987$	4800.18	0.154804
$988$	−2.38921	−7.69342e−5 0
$989$	23205.4	0.746096
$990$	2617.62	0.0840338
$991$	37532.1	1.20307	0.601537	−	0.798845i	$-0.294555\pi$
$991$	37532.1	1.20307	0.601537	+	0.798845i	$0.294555\pi$
$992$	−75.8409	−0.00242737
$993$	−25502.7	−0.815008
$994$	−6525.92	−0.208239
$995$	26250.7	0.836386
$996$	−97.9524	−0.00311620
$997$	−56558.3	−1.79661	−0.898305	−	0.439373i	$-0.855201\pi$
$997$	−56558.3	−1.79661	−0.898305	+	0.439373i	$0.855201\pi$
$998$	15687.7	0.497582
$999$	−477.659	−0.0151276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.d.1.10	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.d.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.84685 q^{2} -3.00000 q^{3} +0.104547 q^{4} -9.28768 q^{5} +8.54055 q^{6} +6.39681 q^{7} +22.4772 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.84685 q^{2} -3.00000 q^{3} +0.104547 q^{4} -9.28768 q^{5} +8.54055 q^{6} +6.39681 q^{7} +22.4772 q^{8} +9.00000 q^{9} +26.4406 q^{10} +11.0000 q^{11} -0.313642 q^{12} -1.06140 q^{13} -18.2108 q^{14} +27.8630 q^{15} -64.8254 q^{16} -2.24914 q^{17} -25.6216 q^{18} +21.5309 q^{19} -0.971001 q^{20} -19.1904 q^{21} -31.3153 q^{22} +83.1186 q^{23} -67.4315 q^{24} -38.7390 q^{25} +3.02166 q^{26} -27.0000 q^{27} +0.668769 q^{28} -291.840 q^{29} -79.3219 q^{30} -16.0307 q^{31} +4.73096 q^{32} -33.0000 q^{33} +6.40296 q^{34} -59.4116 q^{35} +0.940925 q^{36} +17.6911 q^{37} -61.2951 q^{38} +3.18421 q^{39} -208.761 q^{40} +355.441 q^{41} +54.6323 q^{42} +279.184 q^{43} +1.15002 q^{44} -83.5891 q^{45} -236.626 q^{46} -250.134 q^{47} +194.476 q^{48} -302.081 q^{49} +110.284 q^{50} +6.74742 q^{51} -0.110967 q^{52} -565.078 q^{53} +76.8649 q^{54} -102.164 q^{55} +143.782 q^{56} -64.5926 q^{57} +830.824 q^{58} +388.172 q^{59} +2.91300 q^{60} -61.0000 q^{61} +45.6371 q^{62} +57.5713 q^{63} +505.135 q^{64} +9.85798 q^{65} +93.9460 q^{66} +20.4835 q^{67} -0.235141 q^{68} -249.356 q^{69} +169.136 q^{70} +358.355 q^{71} +202.294 q^{72} -400.605 q^{73} -50.3638 q^{74} +116.217 q^{75} +2.25099 q^{76} +70.3649 q^{77} -9.06497 q^{78} +355.286 q^{79} +602.078 q^{80} +81.0000 q^{81} -1011.89 q^{82} +312.307 q^{83} -2.00631 q^{84} +20.8893 q^{85} -794.795 q^{86} +875.520 q^{87} +247.249 q^{88} +1096.70 q^{89} +237.966 q^{90} -6.78960 q^{91} +8.68982 q^{92} +48.0922 q^{93} +712.094 q^{94} -199.972 q^{95} -14.1929 q^{96} +9.45031 q^{97} +859.978 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) \) 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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