LMFDB - Embedded newform 2013.4.a.d.1.8

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			1.8
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)

$f(q)$	$=$	$q-3.99170 q^{2} -3.00000 q^{3} +7.93363 q^{4} +2.24192 q^{5} +11.9751 q^{6} +2.67076 q^{7} +0.264912 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.99170 q^{2} -3.00000 q^{3} +7.93363 q^{4} +2.24192 q^{5} +11.9751 q^{6} +2.67076 q^{7} +0.264912 q^{8} +9.00000 q^{9} -8.94905 q^{10} +11.0000 q^{11} -23.8009 q^{12} +67.0862 q^{13} -10.6608 q^{14} -6.72575 q^{15} -64.5265 q^{16} -40.8746 q^{17} -35.9253 q^{18} +109.209 q^{19} +17.7865 q^{20} -8.01227 q^{21} -43.9087 q^{22} +175.390 q^{23} -0.794737 q^{24} -119.974 q^{25} -267.788 q^{26} -27.0000 q^{27} +21.1888 q^{28} -109.835 q^{29} +26.8471 q^{30} -258.630 q^{31} +255.451 q^{32} -33.0000 q^{33} +163.159 q^{34} +5.98761 q^{35} +71.4027 q^{36} -18.8963 q^{37} -435.928 q^{38} -201.259 q^{39} +0.593911 q^{40} -294.905 q^{41} +31.9825 q^{42} +120.524 q^{43} +87.2700 q^{44} +20.1772 q^{45} -700.104 q^{46} +546.321 q^{47} +193.580 q^{48} -335.867 q^{49} +478.899 q^{50} +122.624 q^{51} +532.237 q^{52} +47.7726 q^{53} +107.776 q^{54} +24.6611 q^{55} +0.707516 q^{56} -327.626 q^{57} +438.427 q^{58} -813.600 q^{59} -53.3596 q^{60} -61.0000 q^{61} +1032.37 q^{62} +24.0368 q^{63} -503.470 q^{64} +150.402 q^{65} +131.726 q^{66} -441.614 q^{67} -324.284 q^{68} -526.170 q^{69} -23.9007 q^{70} -295.111 q^{71} +2.38421 q^{72} -930.124 q^{73} +75.4284 q^{74} +359.921 q^{75} +866.422 q^{76} +29.3783 q^{77} +803.363 q^{78} -100.760 q^{79} -144.663 q^{80} +81.0000 q^{81} +1177.17 q^{82} -100.458 q^{83} -63.5664 q^{84} -91.6375 q^{85} -481.097 q^{86} +329.505 q^{87} +2.91404 q^{88} -1429.55 q^{89} -80.5414 q^{90} +179.171 q^{91} +1391.48 q^{92} +775.889 q^{93} -2180.75 q^{94} +244.837 q^{95} -766.353 q^{96} -1342.63 q^{97} +1340.68 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.99170	−1.41128	−0.705639	−	0.708572i	$-0.749340\pi$
$2$	−3.99170	−1.41128	−0.705639	+	0.708572i	$0.749340\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	7.93363	0.991704
$5$	2.24192	0.200523	0.100262	−	0.994961i	$-0.468032\pi$
$5$	2.24192	0.200523	0.100262	+	0.994961i	$0.468032\pi$
$6$	11.9751	0.814801
$7$	2.67076	0.144207	0.0721036	−	0.997397i	$-0.477029\pi$
$7$	2.67076	0.144207	0.0721036	+	0.997397i	$0.477029\pi$
$8$	0.264912	0.0117076
$9$	9.00000	0.333333
$10$	−8.94905	−0.282994
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−23.8009	−0.572561
$13$	67.0862	1.43126	0.715630	−	0.698480i	$-0.246140\pi$
$13$	67.0862	1.43126	0.715630	+	0.698480i	$0.246140\pi$
$14$	−10.6608	−0.203516
$15$	−6.72575	−0.115772
$16$	−64.5265	−1.00823
$17$	−40.8746	−0.583150	−0.291575	−	0.956548i	$-0.594179\pi$
$17$	−40.8746	−0.583150	−0.291575	+	0.956548i	$0.594179\pi$
$18$	−35.9253	−0.470426
$19$	109.209	1.31864	0.659321	−	0.751862i	$-0.270844\pi$
$19$	109.209	1.31864	0.659321	+	0.751862i	$0.270844\pi$
$20$	17.7865	0.198860
$21$	−8.01227	−0.0832581
$22$	−43.9087	−0.425516
$23$	175.390	1.59006	0.795029	−	0.606571i	$-0.207455\pi$
$23$	175.390	1.59006	0.795029	+	0.606571i	$0.207455\pi$
$24$	−0.794737	−0.00675938
$25$	−119.974	−0.959790
$26$	−267.788	−2.01990
$27$	−27.0000	−0.192450
$28$	21.1888	0.143011
$29$	−109.835	−0.703304	−0.351652	−	0.936131i	$-0.614380\pi$
$29$	−109.835	−0.703304	−0.351652	+	0.936131i	$0.614380\pi$
$30$	26.8471	0.163387
$31$	−258.630	−1.49843	−0.749214	−	0.662328i	$-0.769568\pi$
$31$	−258.630	−1.49843	−0.749214	+	0.662328i	$0.769568\pi$
$32$	255.451	1.41118
$33$	−33.0000	−0.174078
$34$	163.159	0.822987
$35$	5.98761	0.0289169
$36$	71.4027	0.330568
$37$	−18.8963	−0.0839605	−0.0419803	−	0.999118i	$-0.513367\pi$
$37$	−18.8963	−0.0839605	−0.0419803	+	0.999118i	$0.513367\pi$
$38$	−435.928	−1.86097
$39$	−201.259	−0.826338
$40$	0.593911	0.00234764
$41$	−294.905	−1.12333	−0.561663	−	0.827366i	$-0.689838\pi$
$41$	−294.905	−1.12333	−0.561663	+	0.827366i	$0.689838\pi$
$42$	31.9825	0.117500
$43$	120.524	0.427437	0.213719	−	0.976895i	$-0.431442\pi$
$43$	120.524	0.427437	0.213719	+	0.976895i	$0.431442\pi$
$44$	87.2700	0.299010
$45$	20.1772	0.0668410
$46$	−700.104	−2.24401
$47$	546.321	1.69551	0.847756	−	0.530387i	$-0.177953\pi$
$47$	546.321	1.69551	0.847756	+	0.530387i	$0.177953\pi$
$48$	193.580	0.582100
$49$	−335.867	−0.979204
$50$	478.899	1.35453
$51$	122.624	0.336682
$52$	532.237	1.41939
$53$	47.7726	0.123813	0.0619063	−	0.998082i	$-0.480282\pi$
$53$	47.7726	0.123813	0.0619063	+	0.998082i	$0.480282\pi$
$54$	107.776	0.271600
$55$	24.6611	0.0604600
$56$	0.707516	0.00168832
$57$	−327.626	−0.761318
$58$	438.427	0.992558
$59$	−813.600	−1.79528	−0.897641	−	0.440727i	$-0.854721\pi$
$59$	−813.600	−1.79528	−0.897641	+	0.440727i	$0.854721\pi$
$60$	−53.3596	−0.114812
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	1032.37	2.11470
$63$	24.0368	0.0480691
$64$	−503.470	−0.983340
$65$	150.402	0.287001
$66$	131.726	0.245672
$67$	−441.614	−0.805250	−0.402625	−	0.915365i	$-0.631902\pi$
$67$	−441.614	−0.805250	−0.402625	+	0.915365i	$0.631902\pi$
$68$	−324.284	−0.578313
$69$	−526.170	−0.918021
$70$	−23.9007	−0.0408097
$71$	−295.111	−0.493285	−0.246642	−	0.969107i	$-0.579327\pi$
$71$	−295.111	−0.493285	−0.246642	+	0.969107i	$0.579327\pi$
$72$	2.38421	0.00390253
$73$	−930.124	−1.49127	−0.745636	−	0.666354i	$-0.767854\pi$
$73$	−930.124	−1.49127	−0.745636	+	0.666354i	$0.767854\pi$
$74$	75.4284	0.118492
$75$	359.921	0.554135
$76$	866.422	1.30770
$77$	29.3783	0.0434801
$78$	803.363	1.16619
$79$	−100.760	−0.143498	−0.0717489	−	0.997423i	$-0.522858\pi$
$79$	−100.760	−0.143498	−0.0717489	+	0.997423i	$0.522858\pi$
$80$	−144.663	−0.202173
$81$	81.0000	0.111111
$82$	1177.17	1.58532
$83$	−100.458	−0.132852	−0.0664260	−	0.997791i	$-0.521160\pi$
$83$	−100.458	−0.132852	−0.0664260	+	0.997791i	$0.521160\pi$
$84$	−63.5664	−0.0825674
$85$	−91.6375	−0.116935
$86$	−481.097	−0.603233
$87$	329.505	0.406053
$88$	2.91404	0.00352997
$89$	−1429.55	−1.70260	−0.851302	−	0.524676i	$-0.824186\pi$
$89$	−1429.55	−1.70260	−0.851302	+	0.524676i	$0.824186\pi$
$90$	−80.5414	−0.0943312
$91$	179.171	0.206398
$92$	1391.48	1.57687
$93$	775.889	0.865117
$94$	−2180.75	−2.39284
$95$	244.837	0.264418
$96$	−766.353	−0.814745
$97$	−1342.63	−1.40540	−0.702700	−	0.711486i	$-0.748022\pi$
$97$	−1342.63	−1.40540	−0.702700	+	0.711486i	$0.748022\pi$
$98$	1340.68	1.38193
$99$	99.0000	0.100504
$100$	−951.828	−0.951828
$101$	−173.566	−0.170995	−0.0854973	−	0.996338i	$-0.527248\pi$
$101$	−173.566	−0.170995	−0.0854973	+	0.996338i	$0.527248\pi$
$102$	−489.477	−0.475152
$103$	1017.48	0.973348	0.486674	−	0.873584i	$-0.338210\pi$
$103$	1017.48	0.973348	0.486674	+	0.873584i	$0.338210\pi$
$104$	17.7720	0.0167566
$105$	−17.9628	−0.0166952
$106$	−190.694	−0.174734
$107$	1555.50	1.40538	0.702690	−	0.711496i	$-0.251982\pi$
$107$	1555.50	1.40538	0.702690	+	0.711496i	$0.251982\pi$
$108$	−214.208	−0.190854
$109$	2058.04	1.80848	0.904240	−	0.427025i	$-0.140439\pi$
$109$	2058.04	1.80848	0.904240	+	0.427025i	$0.140439\pi$
$110$	−98.4395	−0.0853258
$111$	56.6890	0.0484746
$112$	−172.335	−0.145394
$113$	748.711	0.623299	0.311650	−	0.950197i	$-0.399118\pi$
$113$	748.711	0.623299	0.311650	+	0.950197i	$0.399118\pi$
$114$	1307.78	1.07443
$115$	393.210	0.318844
$116$	−871.390	−0.697470
$117$	603.776	0.477086
$118$	3247.64	2.53364
$119$	−109.166	−0.0840945
$120$	−1.78173	−0.00135541
$121$	121.000	0.0909091
$122$	243.493	0.180696
$123$	884.714	0.648552
$124$	−2051.87	−1.48600
$125$	−549.211	−0.392983
$126$	−95.9476	−0.0678388
$127$	−463.434	−0.323804	−0.161902	−	0.986807i	$-0.551763\pi$
$127$	−463.434	−0.323804	−0.161902	+	0.986807i	$0.551763\pi$
$128$	−33.9076	−0.0234144
$129$	−361.573	−0.246781
$130$	−600.358	−0.405037
$131$	−1307.14	−0.871794	−0.435897	−	0.899997i	$-0.643569\pi$
$131$	−1307.14	−0.871794	−0.435897	+	0.899997i	$0.643569\pi$
$132$	−261.810	−0.172634
$133$	291.670	0.190158
$134$	1762.79	1.13643
$135$	−60.5317	−0.0385907
$136$	−10.8282	−0.00682728
$137$	−445.612	−0.277892	−0.138946	−	0.990300i	$-0.544371\pi$
$137$	−445.612	−0.277892	−0.138946	+	0.990300i	$0.544371\pi$
$138$	2100.31	1.29558
$139$	1680.60	1.02551	0.512757	−	0.858534i	$-0.328624\pi$
$139$	1680.60	1.02551	0.512757	+	0.858534i	$0.328624\pi$
$140$	47.5035	0.0286770
$141$	−1638.96	−0.978904
$142$	1177.99	0.696162
$143$	737.948	0.431541
$144$	−580.739	−0.336076
$145$	−246.241	−0.141029
$146$	3712.77	2.10460
$147$	1007.60	0.565344
$148$	−149.917	−0.0832640
$149$	1773.96	0.975359	0.487679	−	0.873023i	$-0.337844\pi$
$149$	1773.96	0.975359	0.487679	+	0.873023i	$0.337844\pi$
$150$	−1436.70	−0.782039
$151$	−2289.22	−1.23373	−0.616867	−	0.787068i	$-0.711598\pi$
$151$	−2289.22	−1.23373	−0.616867	+	0.787068i	$0.711598\pi$
$152$	28.9307	0.0154381
$153$	−367.872	−0.194383
$154$	−117.269	−0.0613625
$155$	−579.826	−0.300469
$156$	−1596.71	−0.819483
$157$	−3759.96	−1.91132	−0.955662	−	0.294466i	$-0.904858\pi$
$157$	−3759.96	−1.91132	−0.955662	+	0.294466i	$0.904858\pi$
$158$	402.201	0.202515
$159$	−143.318	−0.0714833
$160$	572.700	0.282974
$161$	468.424	0.229298
$162$	−323.327	−0.156809
$163$	−1024.17	−0.492142	−0.246071	−	0.969252i	$-0.579140\pi$
$163$	−1024.17	−0.492142	−0.246071	+	0.969252i	$0.579140\pi$
$164$	−2339.66	−1.11401
$165$	−73.9832	−0.0349066
$166$	400.998	0.187491
$167$	−844.133	−0.391144	−0.195572	−	0.980689i	$-0.562656\pi$
$167$	−844.133	−0.391144	−0.195572	+	0.980689i	$0.562656\pi$
$168$	−2.12255	−0.000974751 0
$169$	2303.56	1.04850
$170$	365.789	0.165028
$171$	982.878	0.439547
$172$	956.197	0.423891
$173$	3389.52	1.48960	0.744799	−	0.667289i	$-0.232546\pi$
$173$	3389.52	1.48960	0.744799	+	0.667289i	$0.232546\pi$
$174$	−1315.28	−0.573053
$175$	−320.421	−0.138409
$176$	−709.792	−0.303992
$177$	2440.80	1.03651
$178$	5706.32	2.40285
$179$	4365.13	1.82271	0.911355	−	0.411622i	$-0.135038\pi$
$179$	4365.13	1.82271	0.911355	+	0.411622i	$0.135038\pi$
$180$	160.079	0.0662865
$181$	−1511.96	−0.620902	−0.310451	−	0.950589i	$-0.600480\pi$
$181$	−1511.96	−0.620902	−0.310451	+	0.950589i	$0.600480\pi$
$182$	−715.196	−0.291285
$183$	183.000	0.0739221
$184$	46.4630	0.0186157
$185$	−42.3640	−0.0168360
$186$	−3097.11	−1.22092
$187$	−449.621	−0.175826
$188$	4334.31	1.68145
$189$	−72.1104	−0.0277527
$190$	−977.314	−0.373167
$191$	1053.18	0.398979	0.199490	−	0.979900i	$-0.436072\pi$
$191$	1053.18	0.398979	0.199490	+	0.979900i	$0.436072\pi$
$192$	1510.41	0.567732
$193$	2253.70	0.840544	0.420272	−	0.907398i	$-0.361935\pi$
$193$	2253.70	0.840544	0.420272	+	0.907398i	$0.361935\pi$
$194$	5359.39	1.98341
$195$	−451.205	−0.165700
$196$	−2664.65	−0.971081
$197$	−1848.96	−0.668697	−0.334348	−	0.942450i	$-0.608516\pi$
$197$	−1848.96	−0.668697	−0.334348	+	0.942450i	$0.608516\pi$
$198$	−395.178	−0.141839
$199$	−1951.91	−0.695313	−0.347656	−	0.937622i	$-0.613022\pi$
$199$	−1951.91	−0.695313	−0.347656	+	0.937622i	$0.613022\pi$
$200$	−31.7825	−0.0112368
$201$	1324.84	0.464911
$202$	692.823	0.241321
$203$	−293.342	−0.101422
$204$	972.853	0.333889
$205$	−661.151	−0.225253
$206$	−4061.45	−1.37366
$207$	1578.51	0.530020
$208$	−4328.84	−1.44303
$209$	1201.30	0.397586
$210$	71.7022	0.0235615
$211$	5704.16	1.86109	0.930547	−	0.366173i	$-0.119332\pi$
$211$	5704.16	1.86109	0.930547	+	0.366173i	$0.119332\pi$
$212$	379.010	0.122786
$213$	885.333	0.284798
$214$	−6209.08	−1.98338
$215$	270.206	0.0857110
$216$	−7.15263	−0.00225313
$217$	−690.736	−0.216084
$218$	−8215.06	−2.55227
$219$	2790.37	0.860986
$220$	195.652	0.0599584
$221$	−2742.13	−0.834639
$222$	−226.285	−0.0684111
$223$	−5584.71	−1.67704	−0.838520	−	0.544871i	$-0.816578\pi$
$223$	−5584.71	−1.67704	−0.838520	+	0.544871i	$0.816578\pi$
$224$	682.247	0.203502
$225$	−1079.76	−0.319930
$226$	−2988.63	−0.879648
$227$	−2667.31	−0.779893	−0.389946	−	0.920838i	$-0.627506\pi$
$227$	−2667.31	−0.779893	−0.389946	+	0.920838i	$0.627506\pi$
$228$	−2599.27	−0.755003
$229$	1342.31	0.387346	0.193673	−	0.981066i	$-0.437960\pi$
$229$	1342.31	0.387346	0.193673	+	0.981066i	$0.437960\pi$
$230$	−1569.57	−0.449977
$231$	−88.1349	−0.0251033
$232$	−29.0966	−0.00823400
$233$	1278.88	0.359579	0.179790	−	0.983705i	$-0.442458\pi$
$233$	1278.88	0.359579	0.179790	+	0.983705i	$0.442458\pi$
$234$	−2410.09	−0.673301
$235$	1224.81	0.339989
$236$	−6454.80	−1.78039
$237$	302.279	0.0828485
$238$	435.758	0.118681
$239$	4266.39	1.15469	0.577343	−	0.816502i	$-0.304090\pi$
$239$	4266.39	1.15469	0.577343	+	0.816502i	$0.304090\pi$
$240$	433.989	0.116725
$241$	−2907.71	−0.777186	−0.388593	−	0.921409i	$-0.627039\pi$
$241$	−2907.71	−0.777186	−0.388593	+	0.921409i	$0.627039\pi$
$242$	−482.995	−0.128298
$243$	−243.000	−0.0641500
$244$	−483.952	−0.126975
$245$	−752.986	−0.196353
$246$	−3531.51	−0.915287
$247$	7326.40	1.88732
$248$	−68.5142	−0.0175430
$249$	301.374	0.0767021
$250$	2192.28	0.554608
$251$	6253.33	1.57254	0.786268	−	0.617885i	$-0.212010\pi$
$251$	6253.33	1.57254	0.786268	+	0.617885i	$0.212010\pi$
$252$	190.699	0.0476703
$253$	1929.29	0.479421
$254$	1849.89	0.456978
$255$	274.913	0.0675125
$256$	4163.11	1.01638
$257$	4501.11	1.09250	0.546248	−	0.837623i	$-0.316056\pi$
$257$	4501.11	1.09250	0.546248	+	0.837623i	$0.316056\pi$
$258$	1443.29	0.348276
$259$	−50.4675	−0.0121077
$260$	1193.23	0.284620
$261$	−988.514	−0.234435
$262$	5217.69	1.23034
$263$	−6667.74	−1.56331	−0.781655	−	0.623711i	$-0.785624\pi$
$263$	−6667.74	−1.56331	−0.781655	+	0.623711i	$0.785624\pi$
$264$	−8.74211	−0.00203803
$265$	107.102	0.0248273
$266$	−1164.26	−0.268365
$267$	4288.64	0.982999
$268$	−3503.61	−0.798570
$269$	3321.01	0.752735	0.376367	−	0.926471i	$-0.377173\pi$
$269$	3321.01	0.752735	0.376367	+	0.926471i	$0.377173\pi$
$270$	241.624	0.0544622
$271$	−5905.76	−1.32380	−0.661900	−	0.749592i	$-0.730250\pi$
$271$	−5905.76	−1.32380	−0.661900	+	0.749592i	$0.730250\pi$
$272$	2637.50	0.587948
$273$	−537.513	−0.119164
$274$	1778.75	0.392183
$275$	−1319.71	−0.289388
$276$	−4174.44	−0.910405
$277$	−5094.03	−1.10495	−0.552474	−	0.833530i	$-0.686316\pi$
$277$	−5094.03	−1.10495	−0.552474	+	0.833530i	$0.686316\pi$
$278$	−6708.44	−1.44728
$279$	−2327.67	−0.499476
$280$	1.58619	0.000338547 0
$281$	7481.11	1.58821	0.794103	−	0.607784i	$-0.207941\pi$
$281$	7481.11	1.58821	0.794103	+	0.607784i	$0.207941\pi$
$282$	6542.24	1.38151
$283$	−7206.27	−1.51367	−0.756835	−	0.653606i	$-0.773255\pi$
$283$	−7206.27	−1.51367	−0.756835	+	0.653606i	$0.773255\pi$
$284$	−2341.30	−0.489193
$285$	−734.510	−0.152662
$286$	−2945.67	−0.609024
$287$	−787.618	−0.161992
$288$	2299.06	0.470393
$289$	−3242.26	−0.659936
$290$	982.918	0.199031
$291$	4027.90	0.811408
$292$	−7379.27	−1.47890
$293$	−2913.02	−0.580820	−0.290410	−	0.956902i	$-0.593792\pi$
$293$	−2913.02	−0.580820	−0.290410	+	0.956902i	$0.593792\pi$
$294$	−4022.04	−0.797857
$295$	−1824.02	−0.359996
$296$	−5.00587	−0.000982975 0
$297$	−297.000	−0.0580259
$298$	−7081.11	−1.37650
$299$	11766.3	2.27579
$300$	2855.48	0.549538
$301$	321.891	0.0616395
$302$	9137.85	1.74114
$303$	520.698	0.0987238
$304$	−7046.86	−1.32949
$305$	−136.757	−0.0256744
$306$	1468.43	0.274329
$307$	7775.77	1.44556	0.722780	−	0.691078i	$-0.242864\pi$
$307$	7775.77	1.44556	0.722780	+	0.691078i	$0.242864\pi$
$308$	233.077	0.0431194
$309$	−3052.43	−0.561963
$310$	2314.49	0.424046
$311$	−8046.28	−1.46708	−0.733542	−	0.679645i	$-0.762134\pi$
$311$	−8046.28	−1.46708	−0.733542	+	0.679645i	$0.762134\pi$
$312$	−53.3159	−0.00967442
$313$	295.432	0.0533508	0.0266754	−	0.999644i	$-0.491508\pi$
$313$	295.432	0.0533508	0.0266754	+	0.999644i	$0.491508\pi$
$314$	15008.6	2.69741
$315$	53.8885	0.00963896
$316$	−799.389	−0.142307
$317$	1289.69	0.228505	0.114253	−	0.993452i	$-0.463553\pi$
$317$	1289.69	0.228505	0.114253	+	0.993452i	$0.463553\pi$
$318$	572.081	0.100883
$319$	−1208.18	−0.212054
$320$	−1128.74	−0.197182
$321$	−4666.50	−0.811397
$322$	−1869.81	−0.323603
$323$	−4463.87	−0.768967
$324$	642.624	0.110189
$325$	−8048.59	−1.37371
$326$	4088.17	0.694548
$327$	−6174.11	−1.04413
$328$	−78.1239	−0.0131514
$329$	1459.09	0.244505
$330$	295.319	0.0492629
$331$	−6123.95	−1.01693	−0.508463	−	0.861084i	$-0.669786\pi$
$331$	−6123.95	−1.01693	−0.508463	+	0.861084i	$0.669786\pi$
$332$	−796.998	−0.131750
$333$	−170.067	−0.0279868
$334$	3369.52	0.552012
$335$	−990.062	−0.161471
$336$	517.004	0.0839430
$337$	−6824.24	−1.10309	−0.551543	−	0.834146i	$-0.685961\pi$
$337$	−6824.24	−1.10309	−0.551543	+	0.834146i	$0.685961\pi$
$338$	−9195.11	−1.47973
$339$	−2246.13	−0.359862
$340$	−727.019	−0.115965
$341$	−2844.93	−0.451793
$342$	−3923.35	−0.620323
$343$	−1813.09	−0.285416
$344$	31.9284	0.00500426
$345$	−1179.63	−0.184084
$346$	−13529.9	−2.10224
$347$	6039.69	0.934373	0.467187	−	0.884159i	$-0.345268\pi$
$347$	6039.69	0.934373	0.467187	+	0.884159i	$0.345268\pi$
$348$	2614.17	0.402684
$349$	−8066.34	−1.23720	−0.618598	−	0.785708i	$-0.712299\pi$
$349$	−8066.34	−1.23720	−0.618598	+	0.785708i	$0.712299\pi$
$350$	1279.02	0.195333
$351$	−1811.33	−0.275446
$352$	2809.96	0.425487
$353$	−3512.75	−0.529645	−0.264823	−	0.964297i	$-0.585313\pi$
$353$	−3512.75	−0.529645	−0.264823	+	0.964297i	$0.585313\pi$
$354$	−9742.93	−1.46280
$355$	−661.614	−0.0989150
$356$	−11341.5	−1.68848
$357$	327.499	0.0485520
$358$	−17424.3	−2.57235
$359$	−11407.4	−1.67705	−0.838524	−	0.544864i	$-0.816581\pi$
$359$	−11407.4	−1.67705	−0.838524	+	0.544864i	$0.816581\pi$
$360$	5.34520	0.000782547 0
$361$	5067.54	0.738817
$362$	6035.29	0.876265
$363$	−363.000	−0.0524864
$364$	1421.48	0.204686
$365$	−2085.26	−0.299034
$366$	−730.480	−0.104325
$367$	−900.420	−0.128070	−0.0640348	−	0.997948i	$-0.520397\pi$
$367$	−900.420	−0.128070	−0.0640348	+	0.997948i	$0.520397\pi$
$368$	−11317.3	−1.60314
$369$	−2654.14	−0.374442
$370$	169.104	0.0237603
$371$	127.589	0.0178547
$372$	6155.62	0.857941
$373$	4846.74	0.672800	0.336400	−	0.941719i	$-0.390791\pi$
$373$	4846.74	0.672800	0.336400	+	0.941719i	$0.390791\pi$
$374$	1794.75	0.248140
$375$	1647.63	0.226889
$376$	144.727	0.0198503
$377$	−7368.41	−1.00661
$378$	287.843	0.0391668
$379$	−14352.1	−1.94517	−0.972585	−	0.232549i	$-0.925294\pi$
$379$	−14352.1	−1.94517	−0.972585	+	0.232549i	$0.925294\pi$
$380$	1942.45	0.262225
$381$	1390.30	0.186949
$382$	−4203.95	−0.563071
$383$	−5901.76	−0.787378	−0.393689	−	0.919244i	$-0.628801\pi$
$383$	−5901.76	−0.787378	−0.393689	+	0.919244i	$0.628801\pi$
$384$	101.723	0.0135183
$385$	65.8637	0.00871877
$386$	−8996.10	−1.18624
$387$	1084.72	0.142479
$388$	−10652.0	−1.39374
$389$	12187.1	1.58845	0.794226	−	0.607622i	$-0.207876\pi$
$389$	12187.1	1.58845	0.794226	+	0.607622i	$0.207876\pi$
$390$	1801.07	0.233848
$391$	−7169.01	−0.927244
$392$	−88.9753	−0.0114641
$393$	3921.41	0.503330
$394$	7380.51	0.943717
$395$	−225.894	−0.0287746
$396$	785.430	0.0996700
$397$	−8268.63	−1.04532	−0.522658	−	0.852542i	$-0.675060\pi$
$397$	−8268.63	−1.04532	−0.522658	+	0.852542i	$0.675060\pi$
$398$	7791.43	0.981279
$399$	−875.009	−0.109788
$400$	7741.49	0.967687
$401$	−7799.16	−0.971251	−0.485626	−	0.874167i	$-0.661408\pi$
$401$	−7799.16	−0.971251	−0.485626	+	0.874167i	$0.661408\pi$
$402$	−5288.37	−0.656119
$403$	−17350.5	−2.14464
$404$	−1377.01	−0.169576
$405$	181.595	0.0222803
$406$	1170.93	0.143134
$407$	−207.860	−0.0253150
$408$	32.4846	0.00394173
$409$	−6821.09	−0.824649	−0.412324	−	0.911037i	$-0.635283\pi$
$409$	−6821.09	−0.824649	−0.412324	+	0.911037i	$0.635283\pi$
$410$	2639.11	0.317894
$411$	1336.84	0.160441
$412$	8072.28	0.965273
$413$	−2172.93	−0.258893
$414$	−6300.93	−0.748005
$415$	−225.219	−0.0266399
$416$	17137.2	2.01976
$417$	−5041.79	−0.592081
$418$	−4795.21	−0.561103
$419$	13676.3	1.59458	0.797290	−	0.603596i	$-0.206266\pi$
$419$	13676.3	1.59458	0.797290	+	0.603596i	$0.206266\pi$
$420$	−142.511	−0.0165567
$421$	−8428.78	−0.975757	−0.487879	−	0.872911i	$-0.662229\pi$
$421$	−8428.78	−0.975757	−0.487879	+	0.872911i	$0.662229\pi$
$422$	−22769.3	−2.62652
$423$	4916.89	0.565171
$424$	12.6556	0.00144955
$425$	4903.89	0.559702
$426$	−3533.98	−0.401929
$427$	−162.916	−0.0184638
$428$	12340.8	1.39372
$429$	−2213.85	−0.249150
$430$	−1078.58	−0.120962
$431$	−4529.29	−0.506191	−0.253096	−	0.967441i	$-0.581449\pi$
$431$	−4529.29	−0.506191	−0.253096	+	0.967441i	$0.581449\pi$
$432$	1742.22	0.194033
$433$	−3706.69	−0.411391	−0.205696	−	0.978616i	$-0.565946\pi$
$433$	−3706.69	−0.411391	−0.205696	+	0.978616i	$0.565946\pi$
$434$	2757.21	0.304955
$435$	738.722	0.0814230
$436$	16327.7	1.79348
$437$	19154.1	2.09672
$438$	−11138.3	−1.21509
$439$	−12906.1	−1.40313	−0.701567	−	0.712603i	$-0.747516\pi$
$439$	−12906.1	−1.40313	−0.701567	+	0.712603i	$0.747516\pi$
$440$	6.53303	0.000707840 0
$441$	−3022.80	−0.326401
$442$	10945.7	1.17791
$443$	−9858.29	−1.05730	−0.528648	−	0.848841i	$-0.677301\pi$
$443$	−9858.29	−1.05730	−0.528648	+	0.848841i	$0.677301\pi$
$444$	449.750	0.0480725
$445$	−3204.93	−0.341411
$446$	22292.5	2.36677
$447$	−5321.88	−0.563124
$448$	−1344.65	−0.141805
$449$	12701.1	1.33497	0.667484	−	0.744624i	$-0.267371\pi$
$449$	12701.1	1.33497	0.667484	+	0.744624i	$0.267371\pi$
$450$	4310.09	0.451510
$451$	−3243.95	−0.338695
$452$	5940.00	0.618129
$453$	6867.65	0.712296
$454$	10647.1	1.10065
$455$	401.686	0.0413876
$456$	−86.7922	−0.00891320
$457$	−5788.98	−0.592554	−0.296277	−	0.955102i	$-0.595745\pi$
$457$	−5788.98	−0.592554	−0.296277	+	0.955102i	$0.595745\pi$
$458$	−5358.09	−0.546653
$459$	1103.62	0.112227
$460$	3119.58	0.316199
$461$	2120.81	0.214265	0.107132	−	0.994245i	$-0.465833\pi$
$461$	2120.81	0.214265	0.107132	+	0.994245i	$0.465833\pi$
$462$	351.808	0.0354277
$463$	13567.7	1.36187	0.680933	−	0.732346i	$-0.261575\pi$
$463$	13567.7	1.36187	0.680933	+	0.732346i	$0.261575\pi$
$464$	7087.26	0.709090
$465$	1739.48	0.173476
$466$	−5104.89	−0.507466
$467$	2315.82	0.229472	0.114736	−	0.993396i	$-0.463398\pi$
$467$	2315.82	0.229472	0.114736	+	0.993396i	$0.463398\pi$
$468$	4790.14	0.473129
$469$	−1179.44	−0.116123
$470$	−4889.05	−0.479819
$471$	11279.9	1.10350
$472$	−215.533	−0.0210184
$473$	1325.77	0.128877
$474$	−1206.60	−0.116922
$475$	−13102.2	−1.26562
$476$	−866.085	−0.0833969
$477$	429.953	0.0412709
$478$	−17030.1	−1.62958
$479$	−7486.16	−0.714094	−0.357047	−	0.934086i	$-0.616216\pi$
$479$	−7486.16	−0.714094	−0.357047	+	0.934086i	$0.616216\pi$
$480$	−1718.10	−0.163375
$481$	−1267.68	−0.120169
$482$	11606.7	1.09683
$483$	−1405.27	−0.132385
$484$	959.970	0.0901549
$485$	−3010.07	−0.281815
$486$	969.982	0.0905335
$487$	13430.0	1.24964	0.624818	−	0.780771i	$-0.285173\pi$
$487$	13430.0	1.24964	0.624818	+	0.780771i	$0.285173\pi$
$488$	−16.1597	−0.00149900
$489$	3072.51	0.284138
$490$	3005.69	0.277109
$491$	−16271.7	−1.49559	−0.747793	−	0.663932i	$-0.768886\pi$
$491$	−16271.7	−1.49559	−0.747793	+	0.663932i	$0.768886\pi$
$492$	7018.99	0.643172
$493$	4489.46	0.410132
$494$	−29244.8	−2.66353
$495$	221.950	0.0201533
$496$	16688.5	1.51075
$497$	−788.169	−0.0711352
$498$	−1203.00	−0.108248
$499$	5012.15	0.449648	0.224824	−	0.974399i	$-0.427819\pi$
$499$	5012.15	0.449648	0.224824	+	0.974399i	$0.427819\pi$
$500$	−4357.24	−0.389723
$501$	2532.40	0.225827
$502$	−24961.4	−2.21929
$503$	−5118.34	−0.453709	−0.226854	−	0.973929i	$-0.572844\pi$
$503$	−5118.34	−0.453709	−0.226854	+	0.973929i	$0.572844\pi$
$504$	6.36765	0.000562773 0
$505$	−389.120	−0.0342884
$506$	−7701.14	−0.676596
$507$	−6910.68	−0.605353
$508$	−3676.72	−0.321118
$509$	16458.7	1.43324	0.716619	−	0.697464i	$-0.245688\pi$
$509$	16458.7	1.43324	0.716619	+	0.697464i	$0.245688\pi$
$510$	−1097.37	−0.0952789
$511$	−2484.13	−0.215052
$512$	−16346.6	−1.41099
$513$	−2948.64	−0.253773
$514$	−17967.1	−1.54182
$515$	2281.10	0.195179
$516$	−2868.59	−0.244734
$517$	6009.53	0.511216
$518$	201.451	0.0170873
$519$	−10168.6	−0.860019
$520$	39.8433	0.00336008
$521$	−3408.90	−0.286654	−0.143327	−	0.989675i	$-0.545780\pi$
$521$	−3408.90	−0.286654	−0.143327	+	0.989675i	$0.545780\pi$
$522$	3945.85	0.330853
$523$	2755.28	0.230363	0.115182	−	0.993344i	$-0.463255\pi$
$523$	2755.28	0.230363	0.115182	+	0.993344i	$0.463255\pi$
$524$	−10370.3	−0.864562
$525$	961.262	0.0799103
$526$	26615.6	2.20626
$527$	10571.4	0.873809
$528$	2129.38	0.175510
$529$	18594.7	1.52829
$530$	−427.519	−0.0350382
$531$	−7322.40	−0.598427
$532$	2314.00	0.188580
$533$	−19784.0	−1.60777
$534$	−17119.0	−1.38728
$535$	3487.30	0.281811
$536$	−116.989	−0.00942753
$537$	−13095.4	−1.05234
$538$	−13256.5	−1.06232
$539$	−3694.54	−0.295241
$540$	−480.237	−0.0382705
$541$	−16902.5	−1.34325	−0.671624	−	0.740892i	$-0.734403\pi$
$541$	−16902.5	−1.34325	−0.671624	+	0.740892i	$0.734403\pi$
$542$	23574.0	1.86825
$543$	4535.89	0.358478
$544$	−10441.5	−0.822930
$545$	4613.95	0.362642
$546$	2145.59	0.168173
$547$	7298.36	0.570485	0.285243	−	0.958455i	$-0.407926\pi$
$547$	7298.36	0.570485	0.285243	+	0.958455i	$0.407926\pi$
$548$	−3535.33	−0.275587
$549$	−549.000	−0.0426790
$550$	5267.89	0.408406
$551$	−11994.9	−0.927407
$552$	−139.389	−0.0107478
$553$	−269.104	−0.0206934
$554$	20333.8	1.55939
$555$	127.092	0.00972028
$556$	13333.2	1.01701
$557$	−10198.5	−0.775807	−0.387904	−	0.921700i	$-0.626801\pi$
$557$	−10198.5	−0.775807	−0.387904	+	0.921700i	$0.626801\pi$
$558$	9291.34	0.704899
$559$	8085.53	0.611773
$560$	−386.360	−0.0291548
$561$	1348.86	0.101513
$562$	−29862.3	−2.24140
$563$	−26648.5	−1.99485	−0.997426	−	0.0717064i	$-0.977156\pi$
$563$	−26648.5	−1.99485	−0.997426	+	0.0717064i	$0.977156\pi$
$564$	−13002.9	−0.970783
$565$	1678.55	0.124986
$566$	28765.2	2.13621
$567$	216.331	0.0160230
$568$	−78.1785	−0.00577517
$569$	22863.4	1.68451	0.842254	−	0.539080i	$-0.181228\pi$
$569$	22863.4	1.68451	0.842254	+	0.539080i	$0.181228\pi$
$570$	2931.94	0.215448
$571$	6252.57	0.458252	0.229126	−	0.973397i	$-0.426413\pi$
$571$	6252.57	0.458252	0.229126	+	0.973397i	$0.426413\pi$
$572$	5854.61	0.427961
$573$	−3159.53	−0.230351
$574$	3143.93	0.228615
$575$	−21042.2	−1.52612
$576$	−4531.23	−0.327780
$577$	10199.7	0.735906	0.367953	−	0.929844i	$-0.380059\pi$
$577$	10199.7	0.735906	0.367953	+	0.929844i	$0.380059\pi$
$578$	12942.1	0.931352
$579$	−6761.11	−0.485289
$580$	−1953.58	−0.139859
$581$	−268.299	−0.0191582
$582$	−16078.2	−1.14512
$583$	525.499	0.0373309
$584$	−246.401	−0.0174592
$585$	1353.62	0.0956668
$586$	11627.9	0.819698
$587$	−1668.87	−0.117345	−0.0586724	−	0.998277i	$-0.518687\pi$
$587$	−1668.87	−0.117345	−0.0586724	+	0.998277i	$0.518687\pi$
$588$	7993.94	0.560654
$589$	−28244.6	−1.97589
$590$	7280.94	0.508054
$591$	5546.89	0.386072
$592$	1219.32	0.0846512
$593$	10622.3	0.735594	0.367797	−	0.929906i	$-0.380112\pi$
$593$	10622.3	0.735594	0.367797	+	0.929906i	$0.380112\pi$
$594$	1185.53	0.0818906
$595$	−244.741	−0.0168629
$596$	14073.9	0.967267
$597$	5855.73	0.401439
$598$	−46967.3	−3.21177
$599$	−9284.75	−0.633330	−0.316665	−	0.948538i	$-0.602563\pi$
$599$	−9284.75	−0.633330	−0.316665	+	0.948538i	$0.602563\pi$
$600$	95.3476	0.00648759
$601$	−15104.7	−1.02518	−0.512589	−	0.858634i	$-0.671313\pi$
$601$	−15104.7	−1.02518	−0.512589	+	0.858634i	$0.671313\pi$
$602$	−1284.89	−0.0869905
$603$	−3974.53	−0.268417
$604$	−18161.8	−1.22350
$605$	271.272	0.0182294
$606$	−2078.47	−0.139327
$607$	2067.69	0.138262	0.0691310	−	0.997608i	$-0.477977\pi$
$607$	2067.69	0.138262	0.0691310	+	0.997608i	$0.477977\pi$
$608$	27897.5	1.86084
$609$	880.026	0.0585558
$610$	545.892	0.0362336
$611$	36650.6	2.42672
$612$	−2918.56	−0.192771
$613$	27466.8	1.80975	0.904873	−	0.425682i	$-0.139966\pi$
$613$	27466.8	1.80975	0.904873	+	0.425682i	$0.139966\pi$
$614$	−31038.5	−2.04009
$615$	1983.45	0.130050
$616$	7.78268	0.000509047 0
$617$	−5072.67	−0.330985	−0.165493	−	0.986211i	$-0.552921\pi$
$617$	−5072.67	−0.330985	−0.165493	+	0.986211i	$0.552921\pi$
$618$	12184.4	0.793085
$619$	17665.2	1.14705	0.573525	−	0.819188i	$-0.305575\pi$
$619$	17665.2	1.14705	0.573525	+	0.819188i	$0.305575\pi$
$620$	−4600.13	−0.297977
$621$	−4735.53	−0.306007
$622$	32118.3	2.07046
$623$	−3817.97	−0.245528
$624$	12986.5	0.833136
$625$	13765.4	0.880988
$626$	−1179.27	−0.0752928
$627$	−3603.89	−0.229546
$628$	−29830.2	−1.89547
$629$	772.381	0.0489616
$630$	−215.106	−0.0136032
$631$	−18056.7	−1.13918	−0.569592	−	0.821927i	$-0.692899\pi$
$631$	−18056.7	−1.13918	−0.569592	+	0.821927i	$0.692899\pi$
$632$	−26.6924	−0.00168001
$633$	−17112.5	−1.07450
$634$	−5148.05	−0.322484
$635$	−1038.98	−0.0649302
$636$	−1137.03	−0.0708903
$637$	−22532.1	−1.40150
$638$	4822.70	0.299267
$639$	−2656.00	−0.164428
$640$	−76.0180	−0.00469512
$641$	−6459.28	−0.398013	−0.199006	−	0.979998i	$-0.563771\pi$
$641$	−6459.28	−0.398013	−0.199006	+	0.979998i	$0.563771\pi$
$642$	18627.2	1.14511
$643$	−20371.7	−1.24943	−0.624713	−	0.780854i	$-0.714784\pi$
$643$	−20371.7	−1.24943	−0.624713	+	0.780854i	$0.714784\pi$
$644$	3716.30	0.227396
$645$	−810.617	−0.0494853
$646$	17818.4	1.08523
$647$	−16697.8	−1.01462	−0.507309	−	0.861764i	$-0.669360\pi$
$647$	−16697.8	−1.01462	−0.507309	+	0.861764i	$0.669360\pi$
$648$	21.4579	0.00130084
$649$	−8949.60	−0.541298
$650$	32127.5	1.93868
$651$	2072.21	0.124756
$652$	−8125.38	−0.488059
$653$	5762.13	0.345313	0.172657	−	0.984982i	$-0.444765\pi$
$653$	5762.13	0.345313	0.172657	+	0.984982i	$0.444765\pi$
$654$	24645.2	1.47355
$655$	−2930.49	−0.174815
$656$	19029.2	1.13257
$657$	−8371.12	−0.497091
$658$	−5824.24	−0.345065
$659$	−5279.50	−0.312079	−0.156040	−	0.987751i	$-0.549873\pi$
$659$	−5279.50	−0.312079	−0.156040	+	0.987751i	$0.549873\pi$
$660$	−586.956	−0.0346170
$661$	3845.20	0.226265	0.113132	−	0.993580i	$-0.463912\pi$
$661$	3845.20	0.226265	0.113132	+	0.993580i	$0.463912\pi$
$662$	24444.9	1.43517
$663$	8226.38	0.481879
$664$	−26.6126	−0.00155538
$665$	653.899	0.0381310
$666$	678.856	0.0394972
$667$	−19263.9	−1.11830
$668$	−6697.05	−0.387899
$669$	16754.1	0.968239
$670$	3952.03	0.227881
$671$	−671.000	−0.0386046
$672$	−2046.74	−0.117492
$673$	−1717.40	−0.0983668	−0.0491834	−	0.998790i	$-0.515662\pi$
$673$	−1717.40	−0.0983668	−0.0491834	+	0.998790i	$0.515662\pi$
$674$	27240.3	1.55676
$675$	3239.29	0.184712
$676$	18275.6	1.03980
$677$	−4018.17	−0.228110	−0.114055	−	0.993474i	$-0.536384\pi$
$677$	−4018.17	−0.228110	−0.114055	+	0.993474i	$0.536384\pi$
$678$	8965.88	0.507865
$679$	−3585.85	−0.202669
$680$	−24.2759	−0.00136903
$681$	8001.93	0.450271
$682$	11356.1	0.637605
$683$	−6488.05	−0.363482	−0.181741	−	0.983346i	$-0.558173\pi$
$683$	−6488.05	−0.363482	−0.181741	+	0.983346i	$0.558173\pi$
$684$	7797.80	0.435901
$685$	−999.026	−0.0557238
$686$	7237.30	0.402801
$687$	−4026.93	−0.223634
$688$	−7777.02	−0.430954
$689$	3204.88	0.177208
$690$	4708.72	0.259794
$691$	−6253.37	−0.344268	−0.172134	−	0.985074i	$-0.555066\pi$
$691$	−6253.37	−0.344268	−0.172134	+	0.985074i	$0.555066\pi$
$692$	26891.2	1.47724
$693$	264.405	0.0144934
$694$	−24108.6	−1.31866
$695$	3767.76	0.205639
$696$	87.2899	0.00475390
$697$	12054.1	0.655068
$698$	32198.4	1.74603
$699$	−3836.63	−0.207603
$700$	−2542.10	−0.137261
$701$	14074.9	0.758350	0.379175	−	0.925325i	$-0.376208\pi$
$701$	14074.9	0.758350	0.379175	+	0.925325i	$0.376208\pi$
$702$	7230.27	0.388731
$703$	−2063.64	−0.110714
$704$	−5538.17	−0.296488
$705$	−3674.42	−0.196293
$706$	14021.8	0.747476
$707$	−463.552	−0.0246587
$708$	19364.4	1.02791
$709$	27959.7	1.48103	0.740513	−	0.672042i	$-0.234583\pi$
$709$	27959.7	1.48103	0.740513	+	0.672042i	$0.234583\pi$
$710$	2640.96	0.139596
$711$	−906.836	−0.0478326
$712$	−378.705	−0.0199334
$713$	−45361.1	−2.38259
$714$	−1307.27	−0.0685203
$715$	1654.42	0.0865339
$716$	34631.3	1.80759
$717$	−12799.2	−0.666658
$718$	45534.9	2.36678
$719$	−7188.98	−0.372884	−0.186442	−	0.982466i	$-0.559696\pi$
$719$	−7188.98	−0.372884	−0.186442	+	0.982466i	$0.559696\pi$
$720$	−1301.97	−0.0673909
$721$	2717.43	0.140364
$722$	−20228.1	−1.04268
$723$	8723.12	0.448709
$724$	−11995.4	−0.615751
$725$	13177.3	0.675025
$726$	1448.99	0.0740729
$727$	−17217.9	−0.878375	−0.439187	−	0.898396i	$-0.644734\pi$
$727$	−17217.9	−0.878375	−0.439187	+	0.898396i	$0.644734\pi$
$728$	47.4646	0.00241642
$729$	729.000	0.0370370
$730$	8323.73	0.422021
$731$	−4926.39	−0.249260
$732$	1451.86	0.0733089
$733$	13280.9	0.669226	0.334613	−	0.942356i	$-0.391394\pi$
$733$	13280.9	0.669226	0.334613	+	0.942356i	$0.391394\pi$
$734$	3594.20	0.180742
$735$	2258.96	0.113364
$736$	44803.6	2.24386
$737$	−4857.76	−0.242792
$738$	10594.5	0.528441
$739$	4521.30	0.225059	0.112530	−	0.993648i	$-0.464105\pi$
$739$	4521.30	0.225059	0.112530	+	0.993648i	$0.464105\pi$
$740$	−336.101	−0.0166964
$741$	−21979.2	−1.08964
$742$	−509.296	−0.0251979
$743$	−14399.9	−0.711013	−0.355506	−	0.934674i	$-0.615692\pi$
$743$	−14399.9	−0.711013	−0.355506	+	0.934674i	$0.615692\pi$
$744$	205.543	0.0101284
$745$	3977.07	0.195582
$746$	−19346.7	−0.949508
$747$	−904.123	−0.0442840
$748$	−3567.13	−0.174368
$749$	4154.36	0.202666
$750$	−6576.85	−0.320203
$751$	30878.8	1.50038	0.750190	−	0.661223i	$-0.229962\pi$
$751$	30878.8	1.50038	0.750190	+	0.661223i	$0.229962\pi$
$752$	−35252.2	−1.70946
$753$	−18760.0	−0.907904
$754$	29412.4	1.42061
$755$	−5132.23	−0.247392
$756$	−572.098	−0.0275225
$757$	26375.7	1.26637	0.633183	−	0.774002i	$-0.281748\pi$
$757$	26375.7	1.26637	0.633183	+	0.774002i	$0.281748\pi$
$758$	57289.3	2.74517
$759$	−5787.87	−0.276794
$760$	64.8603	0.00309570
$761$	9667.12	0.460490	0.230245	−	0.973133i	$-0.426047\pi$
$761$	9667.12	0.460490	0.230245	+	0.973133i	$0.426047\pi$
$762$	−5549.67	−0.263836
$763$	5496.51	0.260796
$764$	8355.51	0.395670
$765$	−824.738	−0.0389784
$766$	23558.0	1.11121
$767$	−54581.3	−2.56951
$768$	−12489.3	−0.586810
$769$	−12188.5	−0.571559	−0.285780	−	0.958295i	$-0.592253\pi$
$769$	−12188.5	−0.571559	−0.285780	+	0.958295i	$0.592253\pi$
$770$	−262.908	−0.0123046
$771$	−13503.3	−0.630753
$772$	17880.1	0.833572
$773$	3407.30	0.158541	0.0792704	−	0.996853i	$-0.474741\pi$
$773$	3407.30	0.158541	0.0792704	+	0.996853i	$0.474741\pi$
$774$	−4329.87	−0.201078
$775$	31028.8	1.43818
$776$	−355.680	−0.0164538
$777$	151.402	0.00699039
$778$	−48647.0	−2.24175
$779$	−32206.1	−1.48126
$780$	−3579.70	−0.164325
$781$	−3246.22	−0.148731
$782$	28616.5	1.30860
$783$	2965.54	0.135351
$784$	21672.3	0.987260
$785$	−8429.53	−0.383265
$786$	−15653.1	−0.710339
$787$	7104.30	0.321780	0.160890	−	0.986972i	$-0.448564\pi$
$787$	7104.30	0.321780	0.160890	+	0.986972i	$0.448564\pi$
$788$	−14669.0	−0.663150
$789$	20003.2	0.902577
$790$	901.702	0.0406090
$791$	1999.62	0.0898843
$792$	26.2263	0.00117666
$793$	−4092.26	−0.183254
$794$	33005.9	1.47523
$795$	−321.307	−0.0143341
$796$	−15485.7	−0.689544
$797$	−6283.40	−0.279259	−0.139629	−	0.990204i	$-0.544591\pi$
$797$	−6283.40	−0.279259	−0.139629	+	0.990204i	$0.544591\pi$
$798$	3492.77	0.154941
$799$	−22330.7	−0.988738
$800$	−30647.4	−1.35444
$801$	−12865.9	−0.567535
$802$	31131.9	1.37070
$803$	−10231.4	−0.449635
$804$	10510.8	0.461055
$805$	1050.17	0.0459795
$806$	69257.8	3.02668
$807$	−9963.03	−0.434591
$808$	−45.9798	−0.00200193
$809$	−6692.10	−0.290830	−0.145415	−	0.989371i	$-0.546452\pi$
$809$	−6692.10	−0.290830	−0.145415	+	0.989371i	$0.546452\pi$
$810$	−724.873	−0.0314437
$811$	19507.5	0.844637	0.422318	−	0.906448i	$-0.361216\pi$
$811$	19507.5	0.844637	0.422318	+	0.906448i	$0.361216\pi$
$812$	−2327.27	−0.100580
$813$	17717.3	0.764296
$814$	829.713	0.0357266
$815$	−2296.10	−0.0986858
$816$	−7912.50	−0.339452
$817$	13162.3	0.563637
$818$	27227.7	1.16381
$819$	1612.54	0.0687993
$820$	−5245.33	−0.223384
$821$	−23775.2	−1.01067	−0.505336	−	0.862923i	$-0.668631\pi$
$821$	−23775.2	−1.01067	−0.505336	+	0.862923i	$0.668631\pi$
$822$	−5336.25	−0.226427
$823$	35936.2	1.52206	0.761031	−	0.648716i	$-0.224694\pi$
$823$	35936.2	1.52206	0.761031	+	0.648716i	$0.224694\pi$
$824$	269.542	0.0113956
$825$	3959.14	0.167078
$826$	8673.66	0.365369
$827$	25096.8	1.05526	0.527631	−	0.849474i	$-0.323080\pi$
$827$	25096.8	1.05526	0.527631	+	0.849474i	$0.323080\pi$
$828$	12523.3	0.525623
$829$	8329.67	0.348976	0.174488	−	0.984659i	$-0.444173\pi$
$829$	8329.67	0.348976	0.174488	+	0.984659i	$0.444173\pi$
$830$	899.005	0.0375963
$831$	15282.1	0.637942
$832$	−33775.9	−1.40741
$833$	13728.4	0.571023
$834$	20125.3	0.835590
$835$	−1892.48	−0.0784334
$836$	9530.64	0.394287
$837$	6983.00	0.288372
$838$	−54591.5	−2.25040
$839$	7103.90	0.292317	0.146158	−	0.989261i	$-0.453309\pi$
$839$	7103.90	0.292317	0.146158	+	0.989261i	$0.453309\pi$
$840$	−4.75858	−0.000195460 0
$841$	−12325.3	−0.505363
$842$	33645.1	1.37706
$843$	−22443.3	−0.916951
$844$	45254.7	1.84565
$845$	5164.39	0.210249
$846$	−19626.7	−0.797613
$847$	323.161	0.0131097
$848$	−3082.60	−0.124831
$849$	21618.8	0.873917
$850$	−19574.8	−0.789895
$851$	−3314.23	−0.133502
$852$	7023.90	0.282435
$853$	12516.6	0.502414	0.251207	−	0.967933i	$-0.419173\pi$
$853$	12516.6	0.502414	0.251207	+	0.967933i	$0.419173\pi$
$854$	650.311	0.0260576
$855$	2203.53	0.0881394
$856$	412.071	0.0164536
$857$	3228.70	0.128693	0.0643467	−	0.997928i	$-0.479504\pi$
$857$	3228.70	0.128693	0.0643467	+	0.997928i	$0.479504\pi$
$858$	8837.00	0.351620
$859$	4995.43	0.198419	0.0992095	−	0.995067i	$-0.468369\pi$
$859$	4995.43	0.198419	0.0992095	+	0.995067i	$0.468369\pi$
$860$	2143.71	0.0850000
$861$	2362.85	0.0935259
$862$	18079.6	0.714376
$863$	34594.5	1.36456	0.682278	−	0.731093i	$-0.260989\pi$
$863$	34594.5	1.36456	0.682278	+	0.731093i	$0.260989\pi$
$864$	−6897.18	−0.271582
$865$	7599.02	0.298699
$866$	14796.0	0.580587
$867$	9726.79	0.381014
$868$	−5480.05	−0.214291
$869$	−1108.35	−0.0432662
$870$	−2948.75	−0.114910
$871$	−29626.2	−1.15252
$872$	545.200	0.0211729
$873$	−12083.7	−0.468467
$874$	−76457.4	−2.95905
$875$	−1466.81	−0.0566710
$876$	22137.8	0.853844
$877$	−22394.1	−0.862253	−0.431126	−	0.902291i	$-0.641884\pi$
$877$	−22394.1	−0.862253	−0.431126	+	0.902291i	$0.641884\pi$
$878$	51517.3	1.98021
$879$	8739.05	0.335337
$880$	−1591.29	−0.0609574
$881$	50195.6	1.91956	0.959781	−	0.280750i	$-0.0905831\pi$
$881$	50195.6	1.91956	0.959781	+	0.280750i	$0.0905831\pi$
$882$	12066.1	0.460643
$883$	644.524	0.0245640	0.0122820	−	0.999925i	$-0.496090\pi$
$883$	644.524	0.0245640	0.0122820	+	0.999925i	$0.496090\pi$
$884$	−21755.0	−0.827715
$885$	5472.07	0.207844
$886$	39351.3	1.49214
$887$	34884.1	1.32051	0.660256	−	0.751041i	$-0.270448\pi$
$887$	34884.1	1.32051	0.660256	+	0.751041i	$0.270448\pi$
$888$	15.0176	0.000567521 0
$889$	−1237.72	−0.0466949
$890$	12793.1	0.481826
$891$	891.000	0.0335013
$892$	−44307.0	−1.66313
$893$	59663.0	2.23577
$894$	21243.3	0.794724
$895$	9786.25	0.365495
$896$	−90.5590	−0.00337652
$897$	−35298.8	−1.31393
$898$	−50698.8	−1.88401
$899$	28406.6	1.05385
$900$	−8566.45	−0.317276
$901$	−1952.69	−0.0722014
$902$	12948.9	0.477993
$903$	−965.674	−0.0355876
$904$	198.343	0.00729733
$905$	−3389.69	−0.124505
$906$	−27413.6	−1.00525
$907$	26682.9	0.976839	0.488419	−	0.872609i	$-0.337574\pi$
$907$	26682.9	0.976839	0.488419	+	0.872609i	$0.337574\pi$
$908$	−21161.5	−0.773423
$909$	−1562.09	−0.0569982
$910$	−1603.41	−0.0584093
$911$	−48632.5	−1.76868	−0.884339	−	0.466846i	$-0.845390\pi$
$911$	−48632.5	−1.76868	−0.884339	+	0.466846i	$0.845390\pi$
$912$	21140.6	0.767582
$913$	−1105.04	−0.0400564
$914$	23107.8	0.836258
$915$	410.271	0.0148231
$916$	10649.4	0.384133
$917$	−3491.04	−0.125719
$918$	−4405.30	−0.158384
$919$	18165.4	0.652038	0.326019	−	0.945363i	$-0.394293\pi$
$919$	18165.4	0.652038	0.326019	+	0.945363i	$0.394293\pi$
$920$	104.166	0.00373289
$921$	−23327.3	−0.834594
$922$	−8465.63	−0.302387
$923$	−19797.9	−0.706018
$924$	−699.230	−0.0248950
$925$	2267.07	0.0805845
$926$	−54158.1	−1.92197
$927$	9157.28	0.324449
$928$	−28057.4	−0.992489
$929$	−18526.4	−0.654286	−0.327143	−	0.944975i	$-0.606086\pi$
$929$	−18526.4	−0.654286	−0.327143	+	0.944975i	$0.606086\pi$
$930$	−6943.47	−0.244823
$931$	−36679.6	−1.29122
$932$	10146.1	0.356596
$933$	24138.9	0.847021
$934$	−9244.06	−0.323849
$935$	−1008.01	−0.0352573
$936$	159.948	0.00558553
$937$	−32603.9	−1.13674	−0.568369	−	0.822774i	$-0.692425\pi$
$937$	−32603.9	−1.13674	−0.568369	+	0.822774i	$0.692425\pi$
$938$	4707.98	0.163882
$939$	−886.296	−0.0308021
$940$	9717.16	0.337169
$941$	10872.5	0.376657	0.188329	−	0.982106i	$-0.439693\pi$
$941$	10872.5	0.376657	0.188329	+	0.982106i	$0.439693\pi$
$942$	−45025.9	−1.55735
$943$	−51723.3	−1.78615
$944$	52498.8	1.81005
$945$	−161.665	−0.00556506
$946$	−5292.06	−0.181881
$947$	−41316.9	−1.41776	−0.708881	−	0.705329i	$-0.750799\pi$
$947$	−41316.9	−1.41776	−0.708881	+	0.705329i	$0.750799\pi$
$948$	2398.17	0.0821613
$949$	−62398.5	−2.13440
$950$	52299.9	1.78614
$951$	−3869.07	−0.131928
$952$	−28.9195	−0.000984544 0
$953$	−51658.4	−1.75591	−0.877953	−	0.478746i	$-0.841091\pi$
$953$	−51658.4	−1.75591	−0.877953	+	0.478746i	$0.841091\pi$
$954$	−1716.24	−0.0582447
$955$	2361.13	0.0800046
$956$	33848.0	1.14511
$957$	3624.55	0.122430
$958$	29882.5	1.00779
$959$	−1190.12	−0.0400741
$960$	3386.21	0.113843
$961$	37098.3	1.24528
$962$	5060.21	0.169592
$963$	13999.5	0.468460
$964$	−23068.7	−0.770739
$965$	5052.61	0.168549
$966$	5609.42	0.186832
$967$	−10619.6	−0.353156	−0.176578	−	0.984287i	$-0.556503\pi$
$967$	−10619.6	−0.353156	−0.176578	+	0.984287i	$0.556503\pi$
$968$	32.0544	0.00106433
$969$	13391.6	0.443963
$970$	12015.3	0.397719
$971$	12318.6	0.407129	0.203564	−	0.979062i	$-0.434747\pi$
$971$	12318.6	0.407129	0.203564	+	0.979062i	$0.434747\pi$
$972$	−1927.87	−0.0636179
$973$	4488.47	0.147887
$974$	−53608.6	−1.76358
$975$	24145.8	0.793111
$976$	3936.12	0.129090
$977$	34480.4	1.12910	0.564548	−	0.825400i	$-0.309051\pi$
$977$	34480.4	1.12910	0.564548	+	0.825400i	$0.309051\pi$
$978$	−12264.5	−0.400998
$979$	−15725.0	−0.513354
$980$	−5973.91	−0.194724
$981$	18522.3	0.602826
$982$	64951.8	2.11069
$983$	−41959.7	−1.36145	−0.680726	−	0.732538i	$-0.738335\pi$
$983$	−41959.7	−1.36145	−0.680726	+	0.732538i	$0.738335\pi$
$984$	234.372	0.00759298
$985$	−4145.22	−0.134089
$986$	−17920.6	−0.578810
$987$	−4377.27	−0.141165
$988$	58125.0	1.87166
$989$	21138.8	0.679650
$990$	−885.956	−0.0284419
$991$	−38529.0	−1.23503	−0.617514	−	0.786560i	$-0.711860\pi$
$991$	−38529.0	−1.23503	−0.617514	+	0.786560i	$0.711860\pi$
$992$	−66067.2	−2.11455
$993$	18371.8	0.587123
$994$	3146.13	0.100392
$995$	−4376.02	−0.139426
$996$	2390.99	0.0760658
$997$	38875.5	1.23490	0.617452	−	0.786609i	$-0.288165\pi$
$997$	38875.5	1.23490	0.617452	+	0.786609i	$0.288165\pi$
$998$	−20007.0	−0.634578
$999$	510.201	0.0161582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.d.1.8	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.d.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-3.99170 q^{2} -3.00000 q^{3} +7.93363 q^{4} +2.24192 q^{5} +11.9751 q^{6} +2.67076 q^{7} +0.264912 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.99170 q^{2} -3.00000 q^{3} +7.93363 q^{4} +2.24192 q^{5} +11.9751 q^{6} +2.67076 q^{7} +0.264912 q^{8} +9.00000 q^{9} -8.94905 q^{10} +11.0000 q^{11} -23.8009 q^{12} +67.0862 q^{13} -10.6608 q^{14} -6.72575 q^{15} -64.5265 q^{16} -40.8746 q^{17} -35.9253 q^{18} +109.209 q^{19} +17.7865 q^{20} -8.01227 q^{21} -43.9087 q^{22} +175.390 q^{23} -0.794737 q^{24} -119.974 q^{25} -267.788 q^{26} -27.0000 q^{27} +21.1888 q^{28} -109.835 q^{29} +26.8471 q^{30} -258.630 q^{31} +255.451 q^{32} -33.0000 q^{33} +163.159 q^{34} +5.98761 q^{35} +71.4027 q^{36} -18.8963 q^{37} -435.928 q^{38} -201.259 q^{39} +0.593911 q^{40} -294.905 q^{41} +31.9825 q^{42} +120.524 q^{43} +87.2700 q^{44} +20.1772 q^{45} -700.104 q^{46} +546.321 q^{47} +193.580 q^{48} -335.867 q^{49} +478.899 q^{50} +122.624 q^{51} +532.237 q^{52} +47.7726 q^{53} +107.776 q^{54} +24.6611 q^{55} +0.707516 q^{56} -327.626 q^{57} +438.427 q^{58} -813.600 q^{59} -53.3596 q^{60} -61.0000 q^{61} +1032.37 q^{62} +24.0368 q^{63} -503.470 q^{64} +150.402 q^{65} +131.726 q^{66} -441.614 q^{67} -324.284 q^{68} -526.170 q^{69} -23.9007 q^{70} -295.111 q^{71} +2.38421 q^{72} -930.124 q^{73} +75.4284 q^{74} +359.921 q^{75} +866.422 q^{76} +29.3783 q^{77} +803.363 q^{78} -100.760 q^{79} -144.663 q^{80} +81.0000 q^{81} +1177.17 q^{82} -100.458 q^{83} -63.5664 q^{84} -91.6375 q^{85} -481.097 q^{86} +329.505 q^{87} +2.91404 q^{88} -1429.55 q^{89} -80.5414 q^{90} +179.171 q^{91} +1391.48 q^{92} +775.889 q^{93} -2180.75 q^{94} +244.837 q^{95} -766.353 q^{96} -1342.63 q^{97} +1340.68 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) \) 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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