LMFDB - Embedded newform 2013.4.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$118.770844842$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-3.95658 q^{2} -3.00000 q^{3} +7.65452 q^{4} +8.88627 q^{5} +11.8697 q^{6} -1.22023 q^{7} +1.36690 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.95658 q^{2} -3.00000 q^{3} +7.65452 q^{4} +8.88627 q^{5} +11.8697 q^{6} -1.22023 q^{7} +1.36690 q^{8} +9.00000 q^{9} -35.1592 q^{10} -11.0000 q^{11} -22.9636 q^{12} +57.8958 q^{13} +4.82796 q^{14} -26.6588 q^{15} -66.6445 q^{16} +37.1350 q^{17} -35.6092 q^{18} +150.112 q^{19} +68.0202 q^{20} +3.66070 q^{21} +43.5224 q^{22} -96.0837 q^{23} -4.10071 q^{24} -46.0342 q^{25} -229.069 q^{26} -27.0000 q^{27} -9.34032 q^{28} +160.616 q^{29} +105.478 q^{30} +12.7986 q^{31} +252.749 q^{32} +33.0000 q^{33} -146.928 q^{34} -10.8433 q^{35} +68.8907 q^{36} +122.096 q^{37} -593.929 q^{38} -173.687 q^{39} +12.1467 q^{40} +313.799 q^{41} -14.4839 q^{42} +379.382 q^{43} -84.1998 q^{44} +79.9765 q^{45} +380.163 q^{46} +50.3672 q^{47} +199.933 q^{48} -341.511 q^{49} +182.138 q^{50} -111.405 q^{51} +443.165 q^{52} -302.198 q^{53} +106.828 q^{54} -97.7490 q^{55} -1.66794 q^{56} -450.336 q^{57} -635.490 q^{58} +716.111 q^{59} -204.061 q^{60} -61.0000 q^{61} -50.6388 q^{62} -10.9821 q^{63} -466.865 q^{64} +514.478 q^{65} -130.567 q^{66} +107.662 q^{67} +284.251 q^{68} +288.251 q^{69} +42.9025 q^{70} -233.502 q^{71} +12.3021 q^{72} +518.786 q^{73} -483.082 q^{74} +138.102 q^{75} +1149.03 q^{76} +13.4226 q^{77} +687.208 q^{78} +172.905 q^{79} -592.221 q^{80} +81.0000 q^{81} -1241.57 q^{82} +1320.18 q^{83} +28.0209 q^{84} +329.992 q^{85} -1501.05 q^{86} -481.848 q^{87} -15.0359 q^{88} -141.881 q^{89} -316.433 q^{90} -70.6464 q^{91} -735.475 q^{92} -38.3959 q^{93} -199.282 q^{94} +1333.93 q^{95} -758.247 q^{96} +785.651 q^{97} +1351.22 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) $ 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9} + 95 q^{10} - 418 q^{11} - 426 q^{12} + 13 q^{13} + 26 q^{14} - 45 q^{15} + 486 q^{16} - 224 q^{17} - 18 q^{18} + 367 q^{19} + 18 q^{20} - 189 q^{21} + 22 q^{22} + 51 q^{23} + 135 q^{24} + 773 q^{25} - 439 q^{26} - 1026 q^{27} + 22 q^{28} - 462 q^{29} - 285 q^{30} + 234 q^{31} - 597 q^{32} + 1254 q^{33} + 956 q^{34} - 522 q^{35} + 1278 q^{36} + 954 q^{37} + 705 q^{38} - 39 q^{39} + 1495 q^{40} - 740 q^{41} - 78 q^{42} + 1441 q^{43} - 1562 q^{44} + 135 q^{45} + 581 q^{46} + 1003 q^{47} - 1458 q^{48} + 2707 q^{49} + 388 q^{50} + 672 q^{51} + 788 q^{52} + 735 q^{53} + 54 q^{54} - 165 q^{55} + 1059 q^{56} - 1101 q^{57} + 177 q^{58} + 261 q^{59} - 54 q^{60} - 2318 q^{61} + 1251 q^{62} + 567 q^{63} + 5571 q^{64} - 1354 q^{65} - 66 q^{66} + 3495 q^{67} - 1856 q^{68} - 153 q^{69} + 542 q^{70} - 873 q^{71} - 405 q^{72} + 989 q^{73} - 3406 q^{74} - 2319 q^{75} + 1712 q^{76} - 693 q^{77} + 1317 q^{78} + 2313 q^{79} + 1593 q^{80} + 3078 q^{81} + 5170 q^{82} + 569 q^{83} - 66 q^{84} - 1271 q^{85} + 3065 q^{86} + 1386 q^{87} + 495 q^{88} - 2917 q^{89} + 855 q^{90} + 2740 q^{91} + 1083 q^{92} - 702 q^{93} + 3272 q^{94} + 2696 q^{95} + 1791 q^{96} + 4250 q^{97} + 5952 q^{98} - 3762 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9 + 95 * q^10 - 418 * q^11 - 426 * q^12 + 13 * q^13 + 26 * q^14 - 45 * q^15 + 486 * q^16 - 224 * q^17 - 18 * q^18 + 367 * q^19 + 18 * q^20 - 189 * q^21 + 22 * q^22 + 51 * q^23 + 135 * q^24 + 773 * q^25 - 439 * q^26 - 1026 * q^27 + 22 * q^28 - 462 * q^29 - 285 * q^30 + 234 * q^31 - 597 * q^32 + 1254 * q^33 + 956 * q^34 - 522 * q^35 + 1278 * q^36 + 954 * q^37 + 705 * q^38 - 39 * q^39 + 1495 * q^40 - 740 * q^41 - 78 * q^42 + 1441 * q^43 - 1562 * q^44 + 135 * q^45 + 581 * q^46 + 1003 * q^47 - 1458 * q^48 + 2707 * q^49 + 388 * q^50 + 672 * q^51 + 788 * q^52 + 735 * q^53 + 54 * q^54 - 165 * q^55 + 1059 * q^56 - 1101 * q^57 + 177 * q^58 + 261 * q^59 - 54 * q^60 - 2318 * q^61 + 1251 * q^62 + 567 * q^63 + 5571 * q^64 - 1354 * q^65 - 66 * q^66 + 3495 * q^67 - 1856 * q^68 - 153 * q^69 + 542 * q^70 - 873 * q^71 - 405 * q^72 + 989 * q^73 - 3406 * q^74 - 2319 * q^75 + 1712 * q^76 - 693 * q^77 + 1317 * q^78 + 2313 * q^79 + 1593 * q^80 + 3078 * q^81 + 5170 * q^82 + 569 * q^83 - 66 * q^84 - 1271 * q^85 + 3065 * q^86 + 1386 * q^87 + 495 * q^88 - 2917 * q^89 + 855 * q^90 + 2740 * q^91 + 1083 * q^92 - 702 * q^93 + 3272 * q^94 + 2696 * q^95 + 1791 * q^96 + 4250 * q^97 + 5952 * q^98 - 3762 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−3.95658	−1.39886	−0.699431	−	0.714700i	$-0.746563\pi$
$2$	−3.95658	−1.39886	−0.699431	+	0.714700i	$0.746563\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	7.65452	0.956815
$5$	8.88627	0.794812	0.397406	−	0.917643i	$-0.369910\pi$
$5$	8.88627	0.794812	0.397406	+	0.917643i	$0.369910\pi$
$6$	11.8697	0.807633
$7$	−1.22023	−0.0658865	−0.0329432	−	0.999457i	$-0.510488\pi$
$7$	−1.22023	−0.0658865	−0.0329432	+	0.999457i	$0.510488\pi$
$8$	1.36690	0.0604092
$9$	9.00000	0.333333
$10$	−35.1592	−1.11183
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−22.9636	−0.552418
$13$	57.8958	1.23518	0.617592	−	0.786498i	$-0.288108\pi$
$13$	57.8958	1.23518	0.617592	+	0.786498i	$0.288108\pi$
$14$	4.82796	0.0921661
$15$	−26.6588	−0.458885
$16$	−66.6445	−1.04132
$17$	37.1350	0.529798	0.264899	−	0.964276i	$-0.414661\pi$
$17$	37.1350	0.529798	0.264899	+	0.964276i	$0.414661\pi$
$18$	−35.6092	−0.466287
$19$	150.112	1.81253	0.906264	−	0.422713i	$-0.138922\pi$
$19$	150.112	1.81253	0.906264	+	0.422713i	$0.138922\pi$
$20$	68.0202	0.760489
$21$	3.66070	0.0380396
$22$	43.5224	0.421773
$23$	−96.0837	−0.871080	−0.435540	−	0.900169i	$-0.643443\pi$
$23$	−96.0837	−0.871080	−0.435540	+	0.900169i	$0.643443\pi$
$24$	−4.10071	−0.0348773
$25$	−46.0342	−0.368273
$26$	−229.069	−1.72785
$27$	−27.0000	−0.192450
$28$	−9.34032	−0.0630412
$29$	160.616	1.02847	0.514235	−	0.857649i	$-0.328076\pi$
$29$	160.616	1.02847	0.514235	+	0.857649i	$0.328076\pi$
$30$	105.478	0.641917
$31$	12.7986	0.0741517	0.0370759	−	0.999312i	$-0.488196\pi$
$31$	12.7986	0.0741517	0.0370759	+	0.999312i	$0.488196\pi$
$32$	252.749	1.39625
$33$	33.0000	0.174078
$34$	−146.928	−0.741115
$35$	−10.8433	−0.0523674
$36$	68.8907	0.318938
$37$	122.096	0.542499	0.271249	−	0.962509i	$-0.412563\pi$
$37$	122.096	0.542499	0.271249	+	0.962509i	$0.412563\pi$
$38$	−593.929	−2.53548
$39$	−173.687	−0.713134
$40$	12.1467	0.0480140
$41$	313.799	1.19530	0.597649	−	0.801758i	$-0.296102\pi$
$41$	313.799	1.19530	0.597649	+	0.801758i	$0.296102\pi$
$42$	−14.4839	−0.0532121
$43$	379.382	1.34547	0.672735	−	0.739884i	$-0.265120\pi$
$43$	379.382	1.34547	0.672735	+	0.739884i	$0.265120\pi$
$44$	−84.1998	−0.288491
$45$	79.9765	0.264937
$46$	380.163	1.21852
$47$	50.3672	0.156315	0.0781576	−	0.996941i	$-0.475096\pi$
$47$	50.3672	0.156315	0.0781576	+	0.996941i	$0.475096\pi$
$48$	199.933	0.601206
$49$	−341.511	−0.995659
$50$	182.138	0.515164
$51$	−111.405	−0.305879
$52$	443.165	1.18184
$53$	−302.198	−0.783208	−0.391604	−	0.920134i	$-0.628080\pi$
$53$	−302.198	−0.783208	−0.391604	+	0.920134i	$0.628080\pi$
$54$	106.828	0.269211
$55$	−97.7490	−0.239645
$56$	−1.66794	−0.00398015
$57$	−450.336	−1.04646
$58$	−635.490	−1.43869
$59$	716.111	1.58016	0.790082	−	0.613001i	$-0.210038\pi$
$59$	716.111	1.58016	0.790082	+	0.613001i	$0.210038\pi$
$60$	−204.061	−0.439068
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−50.6388	−0.103728
$63$	−10.9821	−0.0219622
$64$	−466.865	−0.911847
$65$	514.478	0.981740
$66$	−130.567	−0.243511
$67$	107.662	0.196314	0.0981572	−	0.995171i	$-0.468705\pi$
$67$	107.662	0.196314	0.0981572	+	0.995171i	$0.468705\pi$
$68$	284.251	0.506919
$69$	288.251	0.502918
$70$	42.9025	0.0732548
$71$	−233.502	−0.390304	−0.195152	−	0.980773i	$-0.562520\pi$
$71$	−233.502	−0.390304	−0.195152	+	0.980773i	$0.562520\pi$
$72$	12.3021	0.0201364
$73$	518.786	0.831771	0.415885	−	0.909417i	$-0.363472\pi$
$73$	518.786	0.831771	0.415885	+	0.909417i	$0.363472\pi$
$74$	−483.082	−0.758881
$75$	138.102	0.212623
$76$	1149.03	1.73425
$77$	13.4226	0.0198655
$78$	687.208	0.997576
$79$	172.905	0.246244	0.123122	−	0.992392i	$-0.460709\pi$
$79$	172.905	0.246244	0.123122	+	0.992392i	$0.460709\pi$
$80$	−592.221	−0.827654
$81$	81.0000	0.111111
$82$	−1241.57	−1.67206
$83$	1320.18	1.74588	0.872941	−	0.487826i	$-0.162210\pi$
$83$	1320.18	1.74588	0.872941	+	0.487826i	$0.162210\pi$
$84$	28.0209	0.0363969
$85$	329.992	0.421090
$86$	−1501.05	−1.88213
$87$	−481.848	−0.593787
$88$	−15.0359	−0.0182141
$89$	−141.881	−0.168982	−0.0844908	−	0.996424i	$-0.526926\pi$
$89$	−141.881	−0.168982	−0.0844908	+	0.996424i	$0.526926\pi$
$90$	−316.433	−0.370611
$91$	−70.6464	−0.0813820
$92$	−735.475	−0.833463
$93$	−38.3959	−0.0428115
$94$	−199.282	−0.218663
$95$	1333.93	1.44062
$96$	−758.247	−0.806127
$97$	785.651	0.822379	0.411190	−	0.911550i	$-0.365113\pi$
$97$	785.651	0.822379	0.411190	+	0.911550i	$0.365113\pi$
$98$	1351.22	1.39279
$99$	−99.0000	−0.100504
$100$	−352.370	−0.352370
$101$	802.996	0.791100	0.395550	−	0.918444i	$-0.370554\pi$
$101$	802.996	0.791100	0.395550	+	0.918444i	$0.370554\pi$
$102$	440.783	0.427883
$103$	277.171	0.265150	0.132575	−	0.991173i	$-0.457675\pi$
$103$	277.171	0.265150	0.132575	+	0.991173i	$0.457675\pi$
$104$	79.1380	0.0746165
$105$	32.5300	0.0302343
$106$	1195.67	1.09560
$107$	−464.799	−0.419942	−0.209971	−	0.977708i	$-0.567337\pi$
$107$	−464.799	−0.419942	−0.209971	+	0.977708i	$0.567337\pi$
$108$	−206.672	−0.184139
$109$	−641.753	−0.563934	−0.281967	−	0.959424i	$-0.590987\pi$
$109$	−641.753	−0.563934	−0.281967	+	0.959424i	$0.590987\pi$
$110$	386.752	0.335230
$111$	−366.288	−0.313212
$112$	81.3219	0.0686089
$113$	−939.339	−0.781997	−0.390998	−	0.920391i	$-0.627870\pi$
$113$	−939.339	−0.781997	−0.390998	+	0.920391i	$0.627870\pi$
$114$	1781.79	1.46386
$115$	−853.826	−0.692345
$116$	1229.44	0.984056
$117$	521.062	0.411728
$118$	−2833.35	−2.21043
$119$	−45.3135	−0.0349065
$120$	−36.4400	−0.0277209
$121$	121.000	0.0909091
$122$	241.351	0.179106
$123$	−941.398	−0.690106
$124$	97.9675	0.0709495
$125$	−1519.86	−1.08752
$126$	43.4516	0.0307220
$127$	1711.48	1.19582	0.597910	−	0.801563i	$-0.295998\pi$
$127$	1711.48	1.19582	0.597910	+	0.801563i	$0.295998\pi$
$128$	−174.801	−0.120706
$129$	−1138.15	−0.776807
$130$	−2035.57	−1.37332
$131$	−1601.88	−1.06837	−0.534185	−	0.845367i	$-0.679382\pi$
$131$	−1601.88	−1.06837	−0.534185	+	0.845367i	$0.679382\pi$
$132$	252.599	0.166560
$133$	−183.172	−0.119421
$134$	−425.975	−0.274617
$135$	−239.929	−0.152962
$136$	50.7600	0.0320047
$137$	−1004.82	−0.626624	−0.313312	−	0.949650i	$-0.601439\pi$
$137$	−1004.82	−0.626624	−0.313312	+	0.949650i	$0.601439\pi$
$138$	−1140.49	−0.703514
$139$	−1246.15	−0.760411	−0.380206	−	0.924902i	$-0.624147\pi$
$139$	−1246.15	−0.760411	−0.380206	+	0.924902i	$0.624147\pi$
$140$	−83.0006	−0.0501059
$141$	−151.102	−0.0902486
$142$	923.870	0.545982
$143$	−636.853	−0.372422
$144$	−599.800	−0.347107
$145$	1427.28	0.817440
$146$	−2052.62	−1.16353
$147$	1024.53	0.574844
$148$	934.586	0.519071
$149$	−2688.96	−1.47845	−0.739223	−	0.673461i	$-0.764807\pi$
$149$	−2688.96	−1.47845	−0.739223	+	0.673461i	$0.764807\pi$
$150$	−546.413	−0.297430
$151$	904.171	0.487287	0.243644	−	0.969865i	$-0.421657\pi$
$151$	904.171	0.487287	0.243644	+	0.969865i	$0.421657\pi$
$152$	205.188	0.109493
$153$	334.215	0.176599
$154$	−53.1075	−0.0277891
$155$	113.732	0.0589367
$156$	−1329.49	−0.682338
$157$	−3023.43	−1.53692	−0.768460	−	0.639898i	$-0.778977\pi$
$157$	−3023.43	−1.53692	−0.768460	+	0.639898i	$0.778977\pi$
$158$	−684.111	−0.344462
$159$	906.593	0.452185
$160$	2246.00	1.10976
$161$	117.245	0.0573924
$162$	−320.483	−0.155429
$163$	−766.187	−0.368174	−0.184087	−	0.982910i	$-0.558933\pi$
$163$	−766.187	−0.368174	−0.184087	+	0.982910i	$0.558933\pi$
$164$	2401.99	1.14368
$165$	293.247	0.138359
$166$	−5223.38	−2.44225
$167$	−2063.58	−0.956197	−0.478098	−	0.878306i	$-0.658674\pi$
$167$	−2063.58	−0.956197	−0.478098	+	0.878306i	$0.658674\pi$
$168$	5.00383	0.00229794
$169$	1154.92	0.525681
$170$	−1305.64	−0.589047
$171$	1351.01	0.604176
$172$	2903.99	1.28737
$173$	−3544.55	−1.55773	−0.778865	−	0.627191i	$-0.784204\pi$
$173$	−3544.55	−1.55773	−0.778865	+	0.627191i	$0.784204\pi$
$174$	1906.47	0.830627
$175$	56.1725	0.0242642
$176$	733.089	0.313970
$177$	−2148.33	−0.912308
$178$	561.364	0.236382
$179$	2882.63	1.20368	0.601839	−	0.798618i	$-0.294435\pi$
$179$	2882.63	1.20368	0.601839	+	0.798618i	$0.294435\pi$
$180$	612.182	0.253496
$181$	3518.33	1.44483	0.722417	−	0.691457i	$-0.243031\pi$
$181$	3518.33	1.44483	0.722417	+	0.691457i	$0.243031\pi$
$182$	279.518	0.113842
$183$	183.000	0.0739221
$184$	−131.337	−0.0526213
$185$	1084.98	0.431185
$186$	151.917	0.0598874
$187$	−408.485	−0.159740
$188$	385.537	0.149565
$189$	32.9463	0.0126799
$190$	−5277.82	−2.01523
$191$	−3846.64	−1.45724	−0.728620	−	0.684918i	$-0.759838\pi$
$191$	−3846.64	−1.45724	−0.728620	+	0.684918i	$0.759838\pi$
$192$	1400.60	0.526455
$193$	−4468.26	−1.66649	−0.833244	−	0.552905i	$-0.813519\pi$
$193$	−4468.26	−1.66649	−0.833244	+	0.552905i	$0.813519\pi$
$194$	−3108.49	−1.15040
$195$	−1543.43	−0.566808
$196$	−2614.10	−0.952662
$197$	−880.900	−0.318586	−0.159293	−	0.987231i	$-0.550922\pi$
$197$	−880.900	−0.318586	−0.159293	+	0.987231i	$0.550922\pi$
$198$	391.701	0.140591
$199$	−891.087	−0.317424	−0.158712	−	0.987325i	$-0.550734\pi$
$199$	−891.087	−0.317424	−0.158712	+	0.987325i	$0.550734\pi$
$200$	−62.9243	−0.0222471
$201$	−322.987	−0.113342
$202$	−3177.12	−1.10664
$203$	−195.989	−0.0677623
$204$	−852.753	−0.292670
$205$	2788.51	0.950038
$206$	−1096.65	−0.370909
$207$	−864.754	−0.290360
$208$	−3858.43	−1.28622
$209$	−1651.23	−0.546498
$210$	−128.708	−0.0422937
$211$	3530.73	1.15197	0.575984	−	0.817461i	$-0.304619\pi$
$211$	3530.73	1.15197	0.575984	+	0.817461i	$0.304619\pi$
$212$	−2313.18	−0.749386
$213$	700.506	0.225342
$214$	1839.01	0.587441
$215$	3371.29	1.06940
$216$	−36.9064	−0.0116258
$217$	−15.6173	−0.00488560
$218$	2539.15	0.788866
$219$	−1556.36	−0.480223
$220$	−748.222	−0.229296
$221$	2149.96	0.654398
$222$	1449.25	0.438140
$223$	4996.92	1.50053	0.750265	−	0.661137i	$-0.229926\pi$
$223$	4996.92	1.50053	0.750265	+	0.661137i	$0.229926\pi$
$224$	−308.413	−0.0919942
$225$	−414.307	−0.122758
$226$	3716.57	1.09391
$227$	2068.70	0.604867	0.302433	−	0.953171i	$-0.402201\pi$
$227$	2068.70	0.604867	0.302433	+	0.953171i	$0.402201\pi$
$228$	−3447.10	−1.00127
$229$	−1596.84	−0.460795	−0.230398	−	0.973097i	$-0.574003\pi$
$229$	−1596.84	−0.460795	−0.230398	+	0.973097i	$0.574003\pi$
$230$	3378.23	0.968496
$231$	−40.2677	−0.0114694
$232$	219.547	0.0621290
$233$	1880.67	0.528783	0.264392	−	0.964415i	$-0.414829\pi$
$233$	1880.67	0.528783	0.264392	+	0.964415i	$0.414829\pi$
$234$	−2061.62	−0.575951
$235$	447.577	0.124241
$236$	5481.49	1.51193
$237$	−518.714	−0.142169
$238$	179.286	0.0488294
$239$	1744.24	0.472073	0.236037	−	0.971744i	$-0.424152\pi$
$239$	1744.24	0.472073	0.236037	+	0.971744i	$0.424152\pi$
$240$	1776.66	0.477846
$241$	2440.26	0.652244	0.326122	−	0.945328i	$-0.394258\pi$
$241$	2440.26	0.652244	0.326122	+	0.945328i	$0.394258\pi$
$242$	−478.746	−0.127169
$243$	−243.000	−0.0641500
$244$	−466.926	−0.122508
$245$	−3034.76	−0.791362
$246$	3724.72	0.965363
$247$	8690.84	2.23881
$248$	17.4945	0.00447945
$249$	−3960.53	−1.00799
$250$	6013.43	1.52129
$251$	−4988.62	−1.25450	−0.627249	−	0.778819i	$-0.715819\pi$
$251$	−4988.62	−1.25450	−0.627249	+	0.778819i	$0.715819\pi$
$252$	−84.0628	−0.0210137
$253$	1056.92	0.262641
$254$	−6771.60	−1.67279
$255$	−989.976	−0.243116
$256$	4426.54	1.08070
$257$	6872.00	1.66795	0.833975	−	0.551801i	$-0.186059\pi$
$257$	6872.00	1.66795	0.833975	+	0.551801i	$0.186059\pi$
$258$	4503.16	1.08665
$259$	−148.986	−0.0357433
$260$	3938.08	0.939344
$261$	1445.54	0.342823
$262$	6337.95	1.49450
$263$	−5753.81	−1.34903	−0.674516	−	0.738261i	$-0.735648\pi$
$263$	−5753.81	−1.34903	−0.674516	+	0.738261i	$0.735648\pi$
$264$	45.1078	0.0105159
$265$	−2685.41	−0.622504
$266$	724.733	0.167054
$267$	425.643	0.0975616
$268$	824.105	0.187837
$269$	−6804.09	−1.54220	−0.771102	−	0.636711i	$-0.780294\pi$
$269$	−6804.09	−1.54220	−0.771102	+	0.636711i	$0.780294\pi$
$270$	949.300	0.213972
$271$	−524.716	−0.117617	−0.0588086	−	0.998269i	$-0.518730\pi$
$271$	−524.716	−0.117617	−0.0588086	+	0.998269i	$0.518730\pi$
$272$	−2474.84	−0.551689
$273$	211.939	0.0469859
$274$	3975.65	0.876561
$275$	506.376	0.111039
$276$	2206.43	0.481200
$277$	4089.40	0.887034	0.443517	−	0.896266i	$-0.353731\pi$
$277$	4089.40	0.887034	0.443517	+	0.896266i	$0.353731\pi$
$278$	4930.50	1.06371
$279$	115.188	0.0247172
$280$	−14.8218	−0.00316347
$281$	2049.20	0.435036	0.217518	−	0.976056i	$-0.430204\pi$
$281$	2049.20	0.435036	0.217518	+	0.976056i	$0.430204\pi$
$282$	597.846	0.126245
$283$	4174.12	0.876769	0.438385	−	0.898787i	$-0.355551\pi$
$283$	4174.12	0.876769	0.438385	+	0.898787i	$0.355551\pi$
$284$	−1787.35	−0.373449
$285$	−4001.80	−0.831742
$286$	2519.76	0.520967
$287$	−382.909	−0.0787540
$288$	2274.74	0.465418
$289$	−3533.99	−0.719314
$290$	−5647.13	−1.14349
$291$	−2356.95	−0.474801
$292$	3971.06	0.795851
$293$	−6634.20	−1.32278	−0.661389	−	0.750043i	$-0.730033\pi$
$293$	−6634.20	−1.32278	−0.661389	+	0.750043i	$0.730033\pi$
$294$	−4053.65	−0.804128
$295$	6363.56	1.25593
$296$	166.893	0.0327719
$297$	297.000	0.0580259
$298$	10639.1	2.06814
$299$	−5562.84	−1.07594
$300$	1057.11	0.203441
$301$	−462.935	−0.0886482
$302$	−3577.42	−0.681648
$303$	−2408.99	−0.456742
$304$	−10004.1	−1.88742
$305$	−542.063	−0.101765
$306$	−1322.35	−0.247038
$307$	7715.59	1.43437	0.717186	−	0.696882i	$-0.245430\pi$
$307$	7715.59	1.43437	0.717186	+	0.696882i	$0.245430\pi$
$308$	102.743	0.0190076
$309$	−831.513	−0.153085
$310$	−449.991	−0.0824444
$311$	275.200	0.0501774	0.0250887	−	0.999685i	$-0.492013\pi$
$311$	275.200	0.0501774	0.0250887	+	0.999685i	$0.492013\pi$
$312$	−237.414	−0.0430799
$313$	−3371.09	−0.608772	−0.304386	−	0.952549i	$-0.598451\pi$
$313$	−3371.09	−0.608772	−0.304386	+	0.952549i	$0.598451\pi$
$314$	11962.5	2.14994
$315$	−97.5900	−0.0174558
$316$	1323.50	0.235610
$317$	−8104.19	−1.43589	−0.717944	−	0.696101i	$-0.754917\pi$
$317$	−8104.19	−1.43589	−0.717944	+	0.696101i	$0.754917\pi$
$318$	−3587.01	−0.632545
$319$	−1766.77	−0.310095
$320$	−4148.69	−0.724747
$321$	1394.40	0.242454
$322$	−463.888	−0.0802841
$323$	5574.41	0.960274
$324$	620.016	0.106313
$325$	−2665.18	−0.454885
$326$	3031.48	0.515025
$327$	1925.26	0.325588
$328$	428.934	0.0722070
$329$	−61.4598	−0.0102991
$330$	−1160.26	−0.193545
$331$	11628.0	1.93092	0.965459	−	0.260554i	$-0.0839052\pi$
$331$	11628.0	1.93092	0.965459	+	0.260554i	$0.0839052\pi$
$332$	10105.3	1.67049
$333$	1098.86	0.180833
$334$	8164.73	1.33759
$335$	956.718	0.156033
$336$	−243.966	−0.0396114
$337$	−311.172	−0.0502985	−0.0251493	−	0.999684i	$-0.508006\pi$
$337$	−311.172	−0.0502985	−0.0251493	+	0.999684i	$0.508006\pi$
$338$	−4569.53	−0.735355
$339$	2818.02	0.451486
$340$	2525.93	0.402906
$341$	−140.785	−0.0223576
$342$	−5345.37	−0.845159
$343$	835.264	0.131487
$344$	518.578	0.0812787
$345$	2561.48	0.399726
$346$	14024.3	2.17905
$347$	7082.26	1.09566	0.547832	−	0.836588i	$-0.315453\pi$
$347$	7082.26	1.09566	0.547832	+	0.836588i	$0.315453\pi$
$348$	−3688.31	−0.568145
$349$	−3507.94	−0.538039	−0.269019	−	0.963135i	$-0.586700\pi$
$349$	−3507.94	−0.538039	−0.269019	+	0.963135i	$0.586700\pi$
$350$	−222.251	−0.0339423
$351$	−1563.19	−0.237711
$352$	−2780.24	−0.420986
$353$	5400.53	0.814281	0.407141	−	0.913365i	$-0.366526\pi$
$353$	5400.53	0.814281	0.407141	+	0.913365i	$0.366526\pi$
$354$	8500.05	1.27619
$355$	−2074.96	−0.310219
$356$	−1086.03	−0.161684
$357$	135.940	0.0201533
$358$	−11405.4	−1.68378
$359$	−10607.3	−1.55942	−0.779710	−	0.626141i	$-0.784633\pi$
$359$	−10607.3	−1.55942	−0.779710	+	0.626141i	$0.784633\pi$
$360$	109.320	0.0160047
$361$	15674.6	2.28526
$362$	−13920.5	−2.02112
$363$	−363.000	−0.0524864
$364$	−540.765	−0.0778675
$365$	4610.07	0.661102
$366$	−724.054	−0.103407
$367$	13998.3	1.99102	0.995508	−	0.0946744i	$-0.0301810\pi$
$367$	13998.3	1.99102	0.995508	+	0.0946744i	$0.0301810\pi$
$368$	6403.45	0.907073
$369$	2824.20	0.398433
$370$	−4292.80	−0.603168
$371$	368.752	0.0516028
$372$	−293.903	−0.0409627
$373$	−3783.13	−0.525156	−0.262578	−	0.964911i	$-0.584573\pi$
$373$	−3783.13	−0.525156	−0.262578	+	0.964911i	$0.584573\pi$
$374$	1616.20	0.223454
$375$	4559.57	0.627880
$376$	68.8472	0.00944287
$377$	9298.98	1.27035
$378$	−130.355	−0.0177374
$379$	−1546.32	−0.209575	−0.104787	−	0.994495i	$-0.533416\pi$
$379$	−1546.32	−0.209575	−0.104787	+	0.994495i	$0.533416\pi$
$380$	10210.6	1.37841
$381$	−5134.43	−0.690407
$382$	15219.5	2.03848
$383$	−1741.68	−0.232365	−0.116183	−	0.993228i	$-0.537066\pi$
$383$	−1741.68	−0.232365	−0.116183	+	0.993228i	$0.537066\pi$
$384$	524.402	0.0696895
$385$	119.277	0.0157894
$386$	17679.0	2.33119
$387$	3414.44	0.448490
$388$	6013.79	0.786865
$389$	14585.5	1.90107	0.950535	−	0.310617i	$-0.100536\pi$
$389$	14585.5	1.90107	0.950535	+	0.310617i	$0.100536\pi$
$390$	6106.72	0.792886
$391$	−3568.07	−0.461497
$392$	−466.813	−0.0601470
$393$	4805.63	0.616824
$394$	3485.35	0.445659
$395$	1536.48	0.195718
$396$	−757.798	−0.0961636
$397$	−5572.44	−0.704466	−0.352233	−	0.935912i	$-0.614577\pi$
$397$	−5572.44	−0.704466	−0.352233	+	0.935912i	$0.614577\pi$
$398$	3525.66	0.444033
$399$	549.515	0.0689478
$400$	3067.92	0.383490
$401$	9822.44	1.22322	0.611608	−	0.791161i	$-0.290523\pi$
$401$	9822.44	1.22322	0.611608	+	0.791161i	$0.290523\pi$
$402$	1277.93	0.158550
$403$	740.987	0.0915911
$404$	6146.55	0.756937
$405$	719.788	0.0883125
$406$	775.446	0.0947901
$407$	−1343.06	−0.163570
$408$	−152.280	−0.0184779
$409$	13040.4	1.57654	0.788270	−	0.615330i	$-0.210977\pi$
$409$	13040.4	1.57654	0.788270	+	0.615330i	$0.210977\pi$
$410$	−11033.0	−1.32897
$411$	3014.46	0.361782
$412$	2121.61	0.253700
$413$	−873.823	−0.104111
$414$	3421.47	0.406174
$415$	11731.4	1.38765
$416$	14633.1	1.72463
$417$	3738.45	0.439024
$418$	6533.22	0.764475
$419$	346.262	0.0403723	0.0201861	−	0.999796i	$-0.493574\pi$
$419$	346.262	0.0403723	0.0201861	+	0.999796i	$0.493574\pi$
$420$	249.002	0.0289287
$421$	−1469.65	−0.170134	−0.0850669	−	0.996375i	$-0.527110\pi$
$421$	−1469.65	−0.170134	−0.0850669	+	0.996375i	$0.527110\pi$
$422$	−13969.6	−1.61145
$423$	453.305	0.0521051
$424$	−413.075	−0.0473130
$425$	−1709.48	−0.195110
$426$	−2771.61	−0.315223
$427$	74.4343	0.00843590
$428$	−3557.81	−0.401807
$429$	1910.56	0.215018
$430$	−13338.8	−1.49594
$431$	−735.674	−0.0822185	−0.0411092	−	0.999155i	$-0.513089\pi$
$431$	−735.674	−0.0822185	−0.0411092	+	0.999155i	$0.513089\pi$
$432$	1799.40	0.200402
$433$	1517.72	0.168446	0.0842231	−	0.996447i	$-0.473159\pi$
$433$	1517.72	0.168446	0.0842231	+	0.996447i	$0.473159\pi$
$434$	61.7913	0.00683428
$435$	−4281.83	−0.471949
$436$	−4912.32	−0.539581
$437$	−14423.3	−1.57886
$438$	6157.85	0.671766
$439$	13654.1	1.48445	0.742227	−	0.670149i	$-0.233770\pi$
$439$	13654.1	1.48445	0.742227	+	0.670149i	$0.233770\pi$
$440$	−133.614	−0.0144768
$441$	−3073.60	−0.331886
$442$	−8506.49	−0.915413
$443$	8705.48	0.933656	0.466828	−	0.884348i	$-0.345397\pi$
$443$	8705.48	0.933656	0.466828	+	0.884348i	$0.345397\pi$
$444$	−2803.76	−0.299686
$445$	−1260.79	−0.134309
$446$	−19770.7	−2.09904
$447$	8066.89	0.853581
$448$	569.685	0.0600784
$449$	−45.7536	−0.00480902	−0.00240451	−	0.999997i	$-0.500765\pi$
$449$	−45.7536	−0.00480902	−0.00240451	+	0.999997i	$0.500765\pi$
$450$	1639.24	0.171721
$451$	−3451.79	−0.360396
$452$	−7190.20	−0.748227
$453$	−2712.51	−0.281335
$454$	−8185.00	−0.846125
$455$	−627.783	−0.0646834
$456$	−615.565	−0.0632160
$457$	232.748	0.0238238	0.0119119	−	0.999929i	$-0.496208\pi$
$457$	232.748	0.0238238	0.0119119	+	0.999929i	$0.496208\pi$
$458$	6318.02	0.644589
$459$	−1002.65	−0.101960
$460$	−6535.63	−0.662447
$461$	8054.12	0.813705	0.406852	−	0.913494i	$-0.366626\pi$
$461$	8054.12	0.813705	0.406852	+	0.913494i	$0.366626\pi$
$462$	159.323	0.0160441
$463$	3902.93	0.391760	0.195880	−	0.980628i	$-0.437244\pi$
$463$	3902.93	0.391760	0.195880	+	0.980628i	$0.437244\pi$
$464$	−10704.2	−1.07097
$465$	−341.197	−0.0340271
$466$	−7441.00	−0.739695
$467$	−15255.7	−1.51167	−0.755837	−	0.654760i	$-0.772770\pi$
$467$	−15255.7	−1.51167	−0.755837	+	0.654760i	$0.772770\pi$
$468$	3988.48	0.393948
$469$	−131.373	−0.0129345
$470$	−1770.87	−0.173796
$471$	9070.30	0.887341
$472$	978.855	0.0954565
$473$	−4173.20	−0.405674
$474$	2052.33	0.198875
$475$	−6910.27	−0.667505
$476$	−346.853	−0.0333991
$477$	−2719.78	−0.261069
$478$	−6901.22	−0.660365
$479$	1716.71	0.163755	0.0818775	−	0.996642i	$-0.473908\pi$
$479$	1716.71	0.163755	0.0818775	+	0.996642i	$0.473908\pi$
$480$	−6737.99	−0.640720
$481$	7068.84	0.670086
$482$	−9655.07	−0.912399
$483$	−351.734	−0.0331355
$484$	926.197	0.0869832
$485$	6981.51	0.653637
$486$	961.449	0.0897371
$487$	5924.92	0.551301	0.275651	−	0.961258i	$-0.411107\pi$
$487$	5924.92	0.551301	0.275651	+	0.961258i	$0.411107\pi$
$488$	−83.3811	−0.00773460
$489$	2298.56	0.212565
$490$	12007.3	1.10701
$491$	−17891.6	−1.64447	−0.822237	−	0.569145i	$-0.807274\pi$
$491$	−17891.6	−1.64447	−0.822237	+	0.569145i	$0.807274\pi$
$492$	−7205.96	−0.660304
$493$	5964.48	0.544881
$494$	−34386.0	−3.13178
$495$	−879.741	−0.0798817
$496$	−852.959	−0.0772157
$497$	284.927	0.0257158
$498$	15670.1	1.41003
$499$	312.453	0.0280307	0.0140153	−	0.999902i	$-0.495539\pi$
$499$	312.453	0.0280307	0.0140153	+	0.999902i	$0.495539\pi$
$500$	−11633.8	−1.04056
$501$	6190.75	0.552060
$502$	19737.9	1.75487
$503$	5792.47	0.513467	0.256733	−	0.966482i	$-0.417354\pi$
$503$	5792.47	0.513467	0.256733	+	0.966482i	$0.417354\pi$
$504$	−15.0115	−0.00132672
$505$	7135.64	0.628776
$506$	−4181.79	−0.367398
$507$	−3464.76	−0.303502
$508$	13100.5	1.14418
$509$	−18782.1	−1.63557	−0.817784	−	0.575525i	$-0.804798\pi$
$509$	−18782.1	−1.63557	−0.817784	+	0.575525i	$0.804798\pi$
$510$	3916.92	0.340086
$511$	−633.040	−0.0548024
$512$	−16115.5	−1.39104
$513$	−4053.02	−0.348821
$514$	−27189.6	−2.33323
$515$	2463.02	0.210745
$516$	−8711.96	−0.743261
$517$	−554.039	−0.0471308
$518$	589.474	0.0500000
$519$	10633.7	0.899356
$520$	703.242	0.0593061
$521$	15784.1	1.32728	0.663640	−	0.748052i	$-0.269011\pi$
$521$	15784.1	1.32728	0.663640	+	0.748052i	$0.269011\pi$
$522$	−5719.41	−0.479562
$523$	21999.8	1.83936	0.919678	−	0.392673i	$-0.128450\pi$
$523$	21999.8	1.83936	0.919678	+	0.392673i	$0.128450\pi$
$524$	−12261.6	−1.02223
$525$	−168.517	−0.0140090
$526$	22765.4	1.88711
$527$	475.278	0.0392855
$528$	−2199.27	−0.181270
$529$	−2934.91	−0.241219
$530$	10625.0	0.870797
$531$	6445.00	0.526721
$532$	−1402.09	−0.114264
$533$	18167.7	1.47641
$534$	−1684.09	−0.136475
$535$	−4130.33	−0.333775
$536$	147.164	0.0118592
$537$	−8647.90	−0.694943
$538$	26920.9	2.15733
$539$	3756.62	0.300202
$540$	−1836.55	−0.146356
$541$	−7662.26	−0.608921	−0.304460	−	0.952525i	$-0.598476\pi$
$541$	−7662.26	−0.608921	−0.304460	+	0.952525i	$0.598476\pi$
$542$	2076.08	0.164530
$543$	−10555.0	−0.834176
$544$	9385.84	0.739732
$545$	−5702.80	−0.448222
$546$	−838.555	−0.0657268
$547$	8399.38	0.656548	0.328274	−	0.944583i	$-0.393533\pi$
$547$	8399.38	0.656548	0.328274	+	0.944583i	$0.393533\pi$
$548$	−7691.42	−0.599564
$549$	−549.000	−0.0426790
$550$	−2003.52	−0.155328
$551$	24110.3	1.86413
$552$	394.012	0.0303809
$553$	−210.984	−0.0162242
$554$	−16180.1	−1.24084
$555$	−3254.93	−0.248945
$556$	−9538.69	−0.727573
$557$	2454.16	0.186690	0.0933448	−	0.995634i	$-0.470244\pi$
$557$	2454.16	0.186690	0.0933448	+	0.995634i	$0.470244\pi$
$558$	−455.750	−0.0345760
$559$	21964.6	1.66190
$560$	722.648	0.0545312
$561$	1225.46	0.0922260
$562$	−8107.83	−0.608556
$563$	−1701.43	−0.127365	−0.0636827	−	0.997970i	$-0.520285\pi$
$563$	−1701.43	−0.127365	−0.0636827	+	0.997970i	$0.520285\pi$
$564$	−1156.61	−0.0863513
$565$	−8347.23	−0.621541
$566$	−16515.2	−1.22648
$567$	−98.8390	−0.00732072
$568$	−319.175	−0.0235780
$569$	21311.2	1.57014	0.785071	−	0.619406i	$-0.212627\pi$
$569$	21311.2	1.57014	0.785071	+	0.619406i	$0.212627\pi$
$570$	15833.5	1.16349
$571$	−17715.4	−1.29836	−0.649182	−	0.760633i	$-0.724888\pi$
$571$	−17715.4	−1.29836	−0.649182	+	0.760633i	$0.724888\pi$
$572$	−4874.81	−0.356339
$573$	11539.9	0.841338
$574$	1515.01	0.110166
$575$	4423.13	0.320796
$576$	−4201.79	−0.303949
$577$	−9057.97	−0.653532	−0.326766	−	0.945105i	$-0.605959\pi$
$577$	−9057.97	−0.653532	−0.326766	+	0.945105i	$0.605959\pi$
$578$	13982.5	1.00622
$579$	13404.8	0.962148
$580$	10925.1	0.782140
$581$	−1610.92	−0.115030
$582$	9325.48	0.664181
$583$	3324.17	0.236146
$584$	709.130	0.0502466
$585$	4630.30	0.327247
$586$	26248.7	1.85039
$587$	−18991.4	−1.33537	−0.667683	−	0.744445i	$-0.732714\pi$
$587$	−18991.4	−1.33537	−0.667683	+	0.744445i	$0.732714\pi$
$588$	7842.31	0.550020
$589$	1921.23	0.134402
$590$	−25177.9	−1.75688
$591$	2642.70	0.183936
$592$	−8137.02	−0.564915
$593$	8153.72	0.564643	0.282321	−	0.959320i	$-0.408896\pi$
$593$	8153.72	0.564643	0.282321	+	0.959320i	$0.408896\pi$
$594$	−1175.10	−0.0811702
$595$	−402.668	−0.0277441
$596$	−20582.7	−1.41460
$597$	2673.26	0.183265
$598$	22009.8	1.50510
$599$	−687.708	−0.0469098	−0.0234549	−	0.999725i	$-0.507467\pi$
$599$	−687.708	−0.0469098	−0.0234549	+	0.999725i	$0.507467\pi$
$600$	188.773	0.0128444
$601$	−5557.55	−0.377200	−0.188600	−	0.982054i	$-0.560395\pi$
$601$	−5557.55	−0.377200	−0.188600	+	0.982054i	$0.560395\pi$
$602$	1831.64	0.124007
$603$	968.962	0.0654381
$604$	6921.00	0.466244
$605$	1075.24	0.0722557
$606$	9531.35	0.638919
$607$	−2693.79	−0.180128	−0.0900640	−	0.995936i	$-0.528707\pi$
$607$	−2693.79	−0.180128	−0.0900640	+	0.995936i	$0.528707\pi$
$608$	37940.6	2.53075
$609$	587.967	0.0391226
$610$	2144.71	0.142356
$611$	2916.05	0.193078
$612$	2558.26	0.168973
$613$	−865.669	−0.0570376	−0.0285188	−	0.999593i	$-0.509079\pi$
$613$	−865.669	−0.0570376	−0.0285188	+	0.999593i	$0.509079\pi$
$614$	−30527.4	−2.00649
$615$	−8365.52	−0.548505
$616$	18.3474	0.00120006
$617$	−13832.3	−0.902540	−0.451270	−	0.892387i	$-0.649029\pi$
$617$	−13832.3	−0.902540	−0.451270	+	0.892387i	$0.649029\pi$
$618$	3289.95	0.214144
$619$	−9661.22	−0.627330	−0.313665	−	0.949534i	$-0.601557\pi$
$619$	−9661.22	−0.627330	−0.313665	+	0.949534i	$0.601557\pi$
$620$	870.566	0.0563916
$621$	2594.26	0.167639
$622$	−1088.85	−0.0701912
$623$	173.128	0.0111336
$624$	11575.3	0.742601
$625$	−7751.59	−0.496102
$626$	13338.0	0.851588
$627$	4953.69	0.315521
$628$	−23143.0	−1.47055
$629$	4534.04	0.287415
$630$	386.123	0.0244183
$631$	−10442.3	−0.658797	−0.329399	−	0.944191i	$-0.606846\pi$
$631$	−10442.3	−0.658797	−0.329399	+	0.944191i	$0.606846\pi$
$632$	236.344	0.0148754
$633$	−10592.2	−0.665089
$634$	32064.9	2.00861
$635$	15208.7	0.950452
$636$	6939.54	0.432658
$637$	−19772.0	−1.22982
$638$	6990.39	0.433781
$639$	−2101.52	−0.130101
$640$	−1553.33	−0.0959384
$641$	22567.5	1.39058	0.695290	−	0.718729i	$-0.255276\pi$
$641$	22567.5	1.39058	0.695290	+	0.718729i	$0.255276\pi$
$642$	−5517.04	−0.339159
$643$	20778.9	1.27440	0.637199	−	0.770699i	$-0.280093\pi$
$643$	20778.9	1.27440	0.637199	+	0.770699i	$0.280093\pi$
$644$	897.452	0.0549139
$645$	−10113.9	−0.617416
$646$	−22055.6	−1.34329
$647$	−2742.07	−0.166618	−0.0833089	−	0.996524i	$-0.526549\pi$
$647$	−2742.07	−0.166618	−0.0833089	+	0.996524i	$0.526549\pi$
$648$	110.719	0.00671213
$649$	−7877.22	−0.476437
$650$	10545.0	0.636322
$651$	46.8520	0.00282070
$652$	−5864.80	−0.352275
$653$	−19852.7	−1.18974	−0.594868	−	0.803824i	$-0.702796\pi$
$653$	−19852.7	−1.18974	−0.594868	+	0.803824i	$0.702796\pi$
$654$	−7617.45	−0.455452
$655$	−14234.7	−0.849154
$656$	−20913.0	−1.24469
$657$	4669.07	0.277257
$658$	243.171	0.0144070
$659$	−1428.34	−0.0844315	−0.0422158	−	0.999109i	$-0.513442\pi$
$659$	−1428.34	−0.0844315	−0.0422158	+	0.999109i	$0.513442\pi$
$660$	2244.67	0.132384
$661$	−11431.6	−0.672674	−0.336337	−	0.941742i	$-0.609188\pi$
$661$	−11431.6	−0.672674	−0.336337	+	0.941742i	$0.609188\pi$
$662$	−46007.2	−2.70109
$663$	−6449.88	−0.377817
$664$	1804.55	0.105467
$665$	−1627.71	−0.0949173
$666$	−4347.74	−0.252960
$667$	−15432.6	−0.895880
$668$	−15795.7	−0.914904
$669$	−14990.8	−0.866332
$670$	−3785.33	−0.218269
$671$	671.000	0.0386046
$672$	925.239	0.0531129
$673$	29445.8	1.68656	0.843278	−	0.537477i	$-0.180623\pi$
$673$	29445.8	1.68656	0.843278	+	0.537477i	$0.180623\pi$
$674$	1231.18	0.0703607
$675$	1242.92	0.0708742
$676$	8840.37	0.502979
$677$	7101.91	0.403173	0.201587	−	0.979471i	$-0.435390\pi$
$677$	7101.91	0.403173	0.201587	+	0.979471i	$0.435390\pi$
$678$	−11149.7	−0.631567
$679$	−958.679	−0.0541837
$680$	451.067	0.0254377
$681$	−6206.11	−0.349220
$682$	557.027	0.0312752
$683$	−16337.0	−0.915255	−0.457627	−	0.889144i	$-0.651301\pi$
$683$	−16337.0	−0.915255	−0.457627	+	0.889144i	$0.651301\pi$
$684$	10341.3	0.578085
$685$	−8929.10	−0.498049
$686$	−3304.79	−0.183932
$687$	4790.52	0.266040
$688$	−25283.7	−1.40106
$689$	−17496.0	−0.967407
$690$	−10134.7	−0.559161
$691$	8058.72	0.443659	0.221829	−	0.975086i	$-0.428797\pi$
$691$	8058.72	0.443659	0.221829	+	0.975086i	$0.428797\pi$
$692$	−27131.9	−1.49046
$693$	120.803	0.00662184
$694$	−28021.5	−1.53268
$695$	−11073.6	−0.604384
$696$	−658.640	−0.0358702
$697$	11653.0	0.633267
$698$	13879.4	0.752642
$699$	−5642.00	−0.305293
$700$	429.974	0.0232164
$701$	23318.3	1.25638	0.628189	−	0.778060i	$-0.283796\pi$
$701$	23318.3	1.25638	0.628189	+	0.778060i	$0.283796\pi$
$702$	6184.87	0.332525
$703$	18328.0	0.983294
$704$	5135.52	0.274932
$705$	−1342.73	−0.0717307
$706$	−21367.6	−1.13907
$707$	−979.844	−0.0521228
$708$	−16444.5	−0.872911
$709$	−21814.2	−1.15550	−0.577749	−	0.816215i	$-0.696069\pi$
$709$	−21814.2	−1.15550	−0.577749	+	0.816215i	$0.696069\pi$
$710$	8209.76	0.433953
$711$	1556.14	0.0820814
$712$	−193.938	−0.0102080
$713$	−1229.74	−0.0645921
$714$	−537.859	−0.0281917
$715$	−5659.25	−0.296006
$716$	22065.2	1.15170
$717$	−5232.72	−0.272551
$718$	41968.6	2.18141
$719$	−15950.6	−0.827341	−0.413671	−	0.910427i	$-0.635753\pi$
$719$	−15950.6	−0.827341	−0.413671	+	0.910427i	$0.635753\pi$
$720$	−5329.99	−0.275885
$721$	−338.214	−0.0174698
$722$	−62017.7	−3.19676
$723$	−7320.77	−0.376573
$724$	26931.1	1.38244
$725$	−7393.82	−0.378758
$726$	1436.24	0.0734212
$727$	23518.9	1.19982	0.599909	−	0.800068i	$-0.295203\pi$
$727$	23518.9	1.19982	0.599909	+	0.800068i	$0.295203\pi$
$728$	−96.5669	−0.00491622
$729$	729.000	0.0370370
$730$	−18240.1	−0.924790
$731$	14088.4	0.712827
$732$	1400.78	0.0707298
$733$	−21643.0	−1.09059	−0.545294	−	0.838245i	$-0.683582\pi$
$733$	−21643.0	−1.09059	−0.545294	+	0.838245i	$0.683582\pi$
$734$	−55385.2	−2.78516
$735$	9104.28	0.456893
$736$	−24285.1	−1.21625
$737$	−1184.29	−0.0591910
$738$	−11174.2	−0.557353
$739$	37234.6	1.85344	0.926722	−	0.375747i	$-0.122614\pi$
$739$	37234.6	1.85344	0.926722	+	0.375747i	$0.122614\pi$
$740$	8304.99	0.412564
$741$	−26072.5	−1.29258
$742$	−1459.00	−0.0721852
$743$	18726.4	0.924637	0.462318	−	0.886714i	$-0.347018\pi$
$743$	18726.4	0.924637	0.462318	+	0.886714i	$0.347018\pi$
$744$	−52.4835	−0.00258621
$745$	−23894.9	−1.17509
$746$	14968.3	0.734621
$747$	11881.6	0.581960
$748$	−3126.76	−0.152842
$749$	567.164	0.0276685
$750$	−18040.3	−0.878318
$751$	−21216.4	−1.03089	−0.515443	−	0.856924i	$-0.672373\pi$
$751$	−21216.4	−1.03089	−0.515443	+	0.856924i	$0.672373\pi$
$752$	−3356.70	−0.162774
$753$	14965.9	0.724285
$754$	−36792.2	−1.77704
$755$	8034.71	0.387302
$756$	252.189	0.0121323
$757$	−2187.59	−0.105032	−0.0525161	−	0.998620i	$-0.516724\pi$
$757$	−2187.59	−0.105032	−0.0525161	+	0.998620i	$0.516724\pi$
$758$	6118.12	0.293166
$759$	−3170.76	−0.151636
$760$	1823.36	0.0870266
$761$	2717.87	0.129465	0.0647325	−	0.997903i	$-0.479381\pi$
$761$	2717.87	0.129465	0.0647325	+	0.997903i	$0.479381\pi$
$762$	20314.8	0.965784
$763$	783.090	0.0371556
$764$	−29444.2	−1.39431
$765$	2969.93	0.140363
$766$	6891.11	0.325047
$767$	41459.8	1.95179
$768$	−13279.6	−0.623941
$769$	−17775.7	−0.833558	−0.416779	−	0.909008i	$-0.636841\pi$
$769$	−17775.7	−0.833558	−0.416779	+	0.909008i	$0.636841\pi$
$770$	−471.928	−0.0220871
$771$	−20616.0	−0.962992
$772$	−34202.4	−1.59452
$773$	11953.1	0.556177	0.278088	−	0.960555i	$-0.410299\pi$
$773$	11953.1	0.556177	0.278088	+	0.960555i	$0.410299\pi$
$774$	−13509.5	−0.627375
$775$	−589.175	−0.0273081
$776$	1073.91	0.0496793
$777$	446.957	0.0206364
$778$	−57708.9	−2.65934
$779$	47105.0	2.16651
$780$	−11814.2	−0.542330
$781$	2568.52	0.117681
$782$	14117.4	0.645570
$783$	−4336.63	−0.197929
$784$	22759.8	1.03680
$785$	−26867.1	−1.22156
$786$	−19013.9	−0.862852
$787$	36541.5	1.65510	0.827549	−	0.561393i	$-0.189734\pi$
$787$	36541.5	1.65510	0.827549	+	0.561393i	$0.189734\pi$
$788$	−6742.87	−0.304828
$789$	17261.4	0.778864
$790$	−6079.19	−0.273782
$791$	1146.21	0.0515230
$792$	−135.324	−0.00607135
$793$	−3531.64	−0.158149
$794$	22047.8	0.985450
$795$	8056.23	0.359403
$796$	−6820.85	−0.303717
$797$	−9624.05	−0.427731	−0.213865	−	0.976863i	$-0.568605\pi$
$797$	−9624.05	−0.427731	−0.213865	+	0.976863i	$0.568605\pi$
$798$	−2174.20	−0.0964484
$799$	1870.39	0.0828155
$800$	−11635.1	−0.514203
$801$	−1276.93	−0.0563272
$802$	−38863.3	−1.71111
$803$	−5706.64	−0.250788
$804$	−2472.31	−0.108448
$805$	1041.87	0.0456162
$806$	−2931.78	−0.128123
$807$	20412.3	0.890392
$808$	1097.62	0.0477897
$809$	41591.3	1.80751	0.903753	−	0.428053i	$-0.140800\pi$
$809$	41591.3	1.80751	0.903753	+	0.428053i	$0.140800\pi$
$810$	−2847.90	−0.123537
$811$	−23089.7	−0.999739	−0.499869	−	0.866101i	$-0.666619\pi$
$811$	−23089.7	−0.999739	−0.499869	+	0.866101i	$0.666619\pi$
$812$	−1500.20	−0.0648360
$813$	1574.15	0.0679063
$814$	5313.91	0.228811
$815$	−6808.55	−0.292629
$816$	7424.53	0.318518
$817$	56949.7	2.43870
$818$	−51595.2	−2.20536
$819$	−635.818	−0.0271273
$820$	21344.7	0.909011
$821$	−21681.1	−0.921651	−0.460825	−	0.887491i	$-0.652447\pi$
$821$	−21681.1	−0.921651	−0.460825	+	0.887491i	$0.652447\pi$
$822$	−11926.9	−0.506083
$823$	5714.31	0.242027	0.121014	−	0.992651i	$-0.461386\pi$
$823$	5714.31	0.242027	0.121014	+	0.992651i	$0.461386\pi$
$824$	378.866	0.0160175
$825$	−1519.13	−0.0641081
$826$	3457.35	0.145638
$827$	8492.11	0.357073	0.178537	−	0.983933i	$-0.442864\pi$
$827$	8492.11	0.357073	0.178537	+	0.983933i	$0.442864\pi$
$828$	−6619.28	−0.277821
$829$	−32895.5	−1.37818	−0.689088	−	0.724678i	$-0.741988\pi$
$829$	−32895.5	−1.37818	−0.689088	+	0.724678i	$0.741988\pi$
$830$	−46416.4	−1.94113
$831$	−12268.2	−0.512130
$832$	−27029.5	−1.12630
$833$	−12682.0	−0.527498
$834$	−14791.5	−0.614133
$835$	−18337.6	−0.759997
$836$	−12639.4	−0.522897
$837$	−345.563	−0.0142705
$838$	−1370.01	−0.0564753
$839$	3105.36	0.127782	0.0638909	−	0.997957i	$-0.479649\pi$
$839$	3105.36	0.127782	0.0638909	+	0.997957i	$0.479649\pi$
$840$	44.4654	0.00182643
$841$	1408.46	0.0577500
$842$	5814.78	0.237994
$843$	−6147.61	−0.251168
$844$	27026.0	1.10222
$845$	10262.9	0.417818
$846$	−1793.54	−0.0728878
$847$	−147.648	−0.00598968
$848$	20139.8	0.815570
$849$	−12522.4	−0.506203
$850$	6763.69	0.272933
$851$	−11731.4	−0.472560
$852$	5362.04	0.215611
$853$	21889.8	0.878655	0.439327	−	0.898327i	$-0.355217\pi$
$853$	21889.8	0.878655	0.439327	+	0.898327i	$0.355217\pi$
$854$	−294.505	−0.0118007
$855$	12005.4	0.480206
$856$	−635.335	−0.0253684
$857$	28871.6	1.15080	0.575400	−	0.817872i	$-0.304846\pi$
$857$	28871.6	1.15080	0.575400	+	0.817872i	$0.304846\pi$
$858$	−7559.29	−0.300781
$859$	−35016.7	−1.39087	−0.695434	−	0.718590i	$-0.744788\pi$
$859$	−35016.7	−1.39087	−0.695434	+	0.718590i	$0.744788\pi$
$860$	25805.6	1.02321
$861$	1148.73	0.0454687
$862$	2910.75	0.115012
$863$	−31645.8	−1.24825	−0.624123	−	0.781326i	$-0.714544\pi$
$863$	−31645.8	−1.24825	−0.624123	+	0.781326i	$0.714544\pi$
$864$	−6824.22	−0.268709
$865$	−31497.9	−1.23810
$866$	−6005.00	−0.235633
$867$	10602.0	0.415296
$868$	−119.543	−0.00467461
$869$	−1901.95	−0.0742454
$870$	16941.4	0.660192
$871$	6233.20	0.242484
$872$	−877.215	−0.0340668
$873$	7070.86	0.274126
$874$	57067.0	2.20860
$875$	1854.58	0.0716529
$876$	−11913.2	−0.459485
$877$	2387.89	0.0919423	0.0459712	−	0.998943i	$-0.485362\pi$
$877$	2387.89	0.0919423	0.0459712	+	0.998943i	$0.485362\pi$
$878$	−54023.6	−2.07655
$879$	19902.6	0.763707
$880$	6514.43	0.249547
$881$	−31806.4	−1.21633	−0.608164	−	0.793812i	$-0.708094\pi$
$881$	−31806.4	−1.21633	−0.608164	+	0.793812i	$0.708094\pi$
$882$	12160.9	0.464263
$883$	30784.0	1.17323	0.586616	−	0.809865i	$-0.300460\pi$
$883$	30784.0	1.17323	0.586616	+	0.809865i	$0.300460\pi$
$884$	16456.9	0.626139
$885$	−19090.7	−0.725114
$886$	−34443.9	−1.30606
$887$	2141.01	0.0810465	0.0405232	−	0.999179i	$-0.487098\pi$
$887$	2141.01	0.0810465	0.0405232	+	0.999179i	$0.487098\pi$
$888$	−500.680	−0.0189209
$889$	−2088.40	−0.0787884
$890$	4988.43	0.187879
$891$	−891.000	−0.0335013
$892$	38249.0	1.43573
$893$	7560.72	0.283326
$894$	−31917.3	−1.19404
$895$	25615.9	0.956697
$896$	213.298	0.00795288
$897$	16688.5	0.621197
$898$	181.028	0.00672715
$899$	2055.67	0.0762628
$900$	−3171.33	−0.117457
$901$	−11222.1	−0.414942
$902$	13657.3	0.504144
$903$	1388.80	0.0511811
$904$	−1283.99	−0.0472398
$905$	31264.8	1.14837
$906$	10732.3	0.393550
$907$	40062.9	1.46667	0.733334	−	0.679869i	$-0.237963\pi$
$907$	40062.9	1.46667	0.733334	+	0.679869i	$0.237963\pi$
$908$	15835.0	0.578746
$909$	7226.97	0.263700
$910$	2483.88	0.0904831
$911$	−27900.6	−1.01470	−0.507348	−	0.861741i	$-0.669374\pi$
$911$	−27900.6	−1.01470	−0.507348	+	0.861741i	$0.669374\pi$
$912$	30012.4	1.08970
$913$	−14521.9	−0.526403
$914$	−920.885	−0.0333262
$915$	1626.19	0.0587542
$916$	−12223.0	−0.440896
$917$	1954.67	0.0703912
$918$	3967.05	0.142628
$919$	−29645.5	−1.06411	−0.532054	−	0.846710i	$-0.678580\pi$
$919$	−29645.5	−1.06411	−0.532054	+	0.846710i	$0.678580\pi$
$920$	−1167.10	−0.0418240
$921$	−23146.8	−0.828135
$922$	−31866.8	−1.13826
$923$	−13518.8	−0.482098
$924$	−308.230	−0.0109741
$925$	−5620.58	−0.199788
$926$	−15442.3	−0.548018
$927$	2494.54	0.0883834
$928$	40595.5	1.43600
$929$	−16873.4	−0.595908	−0.297954	−	0.954580i	$-0.596304\pi$
$929$	−16873.4	−0.595908	−0.297954	+	0.954580i	$0.596304\pi$
$930$	1349.97	0.0475993
$931$	−51264.8	−1.80466
$932$	14395.6	0.505948
$933$	−825.600	−0.0289699
$934$	60360.6	2.11462
$935$	−3629.91	−0.126963
$936$	712.242	0.0248722
$937$	−1946.08	−0.0678502	−0.0339251	−	0.999424i	$-0.510801\pi$
$937$	−1946.08	−0.0678502	−0.0339251	+	0.999424i	$0.510801\pi$
$938$	519.789	0.0180935
$939$	10113.3	0.351475
$940$	3425.99	0.118876
$941$	49889.3	1.72832	0.864158	−	0.503221i	$-0.167852\pi$
$941$	49889.3	1.72832	0.864158	+	0.503221i	$0.167852\pi$
$942$	−35887.4	−1.24127
$943$	−30151.0	−1.04120
$944$	−47724.8	−1.64546
$945$	292.770	0.0100781
$946$	16511.6	0.567482
$947$	40166.7	1.37829	0.689145	−	0.724623i	$-0.257986\pi$
$947$	40166.7	1.37829	0.689145	+	0.724623i	$0.257986\pi$
$948$	−3970.51	−0.136030
$949$	30035.5	1.02739
$950$	27341.0	0.933748
$951$	24312.6	0.829010
$952$	−61.9391	−0.00210868
$953$	13957.2	0.474416	0.237208	−	0.971459i	$-0.423768\pi$
$953$	13957.2	0.474416	0.237208	+	0.971459i	$0.423768\pi$
$954$	10761.0	0.365200
$955$	−34182.3	−1.15823
$956$	13351.3	0.451687
$957$	5300.32	0.179034
$958$	−6792.32	−0.229071
$959$	1226.12	0.0412861
$960$	12446.1	0.418433
$961$	−29627.2	−0.994502
$962$	−27968.4	−0.937358
$963$	−4183.19	−0.139981
$964$	18679.0	0.624077
$965$	−39706.2	−1.32455
$966$	1391.66	0.0463520
$967$	49717.1	1.65336	0.826678	−	0.562676i	$-0.190228\pi$
$967$	49717.1	1.65336	0.826678	+	0.562676i	$0.190228\pi$
$968$	165.395	0.00549175
$969$	−16723.2	−0.554414
$970$	−27622.9	−0.914349
$971$	−3314.77	−0.109553	−0.0547765	−	0.998499i	$-0.517445\pi$
$971$	−3314.77	−0.109553	−0.0547765	+	0.998499i	$0.517445\pi$
$972$	−1860.05	−0.0613797
$973$	1520.60	0.0501008
$974$	−23442.4	−0.771194
$975$	7995.55	0.262628
$976$	4065.31	0.133327
$977$	−43980.7	−1.44019	−0.720097	−	0.693874i	$-0.755903\pi$
$977$	−43980.7	−1.44019	−0.720097	+	0.693874i	$0.755903\pi$
$978$	−9094.44	−0.297350
$979$	1560.69	0.0509499
$980$	−23229.6	−0.757187
$981$	−5775.78	−0.187978
$982$	70789.6	2.30039
$983$	40133.8	1.30221	0.651104	−	0.758989i	$-0.274306\pi$
$983$	40133.8	1.30221	0.651104	+	0.758989i	$0.274306\pi$
$984$	−1286.80	−0.0416887
$985$	−7827.92	−0.253216
$986$	−23598.9	−0.762214
$987$	184.379	0.00594616
$988$	66524.3	2.14212
$989$	−36452.4	−1.17201
$990$	3480.77	0.111743
$991$	26378.4	0.845548	0.422774	−	0.906235i	$-0.361056\pi$
$991$	26378.4	0.845548	0.422774	+	0.906235i	$0.361056\pi$
$992$	3234.84	0.103535
$993$	−34884.1	−1.11482
$994$	−1127.34	−0.0359728
$995$	−7918.44	−0.252293
$996$	−30316.0	−0.964456
$997$	16507.6	0.524374	0.262187	−	0.965017i	$-0.415556\pi$
$997$	16507.6	0.524374	0.262187	+	0.965017i	$0.415556\pi$
$998$	−1236.25	−0.0392111
$999$	−3296.59	−0.104404

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.e.1.7	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.e.1.7	✓	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-3.95658 q^{2} -3.00000 q^{3} +7.65452 q^{4} +8.88627 q^{5} +11.8697 q^{6} -1.22023 q^{7} +1.36690 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.95658 q^{2} -3.00000 q^{3} +7.65452 q^{4} +8.88627 q^{5} +11.8697 q^{6} -1.22023 q^{7} +1.36690 q^{8} +9.00000 q^{9} -35.1592 q^{10} -11.0000 q^{11} -22.9636 q^{12} +57.8958 q^{13} +4.82796 q^{14} -26.6588 q^{15} -66.6445 q^{16} +37.1350 q^{17} -35.6092 q^{18} +150.112 q^{19} +68.0202 q^{20} +3.66070 q^{21} +43.5224 q^{22} -96.0837 q^{23} -4.10071 q^{24} -46.0342 q^{25} -229.069 q^{26} -27.0000 q^{27} -9.34032 q^{28} +160.616 q^{29} +105.478 q^{30} +12.7986 q^{31} +252.749 q^{32} +33.0000 q^{33} -146.928 q^{34} -10.8433 q^{35} +68.8907 q^{36} +122.096 q^{37} -593.929 q^{38} -173.687 q^{39} +12.1467 q^{40} +313.799 q^{41} -14.4839 q^{42} +379.382 q^{43} -84.1998 q^{44} +79.9765 q^{45} +380.163 q^{46} +50.3672 q^{47} +199.933 q^{48} -341.511 q^{49} +182.138 q^{50} -111.405 q^{51} +443.165 q^{52} -302.198 q^{53} +106.828 q^{54} -97.7490 q^{55} -1.66794 q^{56} -450.336 q^{57} -635.490 q^{58} +716.111 q^{59} -204.061 q^{60} -61.0000 q^{61} -50.6388 q^{62} -10.9821 q^{63} -466.865 q^{64} +514.478 q^{65} -130.567 q^{66} +107.662 q^{67} +284.251 q^{68} +288.251 q^{69} +42.9025 q^{70} -233.502 q^{71} +12.3021 q^{72} +518.786 q^{73} -483.082 q^{74} +138.102 q^{75} +1149.03 q^{76} +13.4226 q^{77} +687.208 q^{78} +172.905 q^{79} -592.221 q^{80} +81.0000 q^{81} -1241.57 q^{82} +1320.18 q^{83} +28.0209 q^{84} +329.992 q^{85} -1501.05 q^{86} -481.848 q^{87} -15.0359 q^{88} -141.881 q^{89} -316.433 q^{90} -70.6464 q^{91} -735.475 q^{92} -38.3959 q^{93} -199.282 q^{94} +1333.93 q^{95} -758.247 q^{96} +785.651 q^{97} +1351.22 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9} + 95 q^{10} - 418 q^{11} - 426 q^{12} + 13 q^{13} + 26 q^{14} - 45 q^{15} + 486 q^{16} - 224 q^{17} - 18 q^{18} + 367 q^{19} + 18 q^{20} - 189 q^{21} + 22 q^{22} + 51 q^{23} + 135 q^{24} + 773 q^{25} - 439 q^{26} - 1026 q^{27} + 22 q^{28} - 462 q^{29} - 285 q^{30} + 234 q^{31} - 597 q^{32} + 1254 q^{33} + 956 q^{34} - 522 q^{35} + 1278 q^{36} + 954 q^{37} + 705 q^{38} - 39 q^{39} + 1495 q^{40} - 740 q^{41} - 78 q^{42} + 1441 q^{43} - 1562 q^{44} + 135 q^{45} + 581 q^{46} + 1003 q^{47} - 1458 q^{48} + 2707 q^{49} + 388 q^{50} + 672 q^{51} + 788 q^{52} + 735 q^{53} + 54 q^{54} - 165 q^{55} + 1059 q^{56} - 1101 q^{57} + 177 q^{58} + 261 q^{59} - 54 q^{60} - 2318 q^{61} + 1251 q^{62} + 567 q^{63} + 5571 q^{64} - 1354 q^{65} - 66 q^{66} + 3495 q^{67} - 1856 q^{68} - 153 q^{69} + 542 q^{70} - 873 q^{71} - 405 q^{72} + 989 q^{73} - 3406 q^{74} - 2319 q^{75} + 1712 q^{76} - 693 q^{77} + 1317 q^{78} + 2313 q^{79} + 1593 q^{80} + 3078 q^{81} + 5170 q^{82} + 569 q^{83} - 66 q^{84} - 1271 q^{85} + 3065 q^{86} + 1386 q^{87} + 495 q^{88} - 2917 q^{89} + 855 q^{90} + 2740 q^{91} + 1083 q^{92} - 702 q^{93} + 3272 q^{94} + 2696 q^{95} + 1791 q^{96} + 4250 q^{97} + 5952 q^{98} - 3762 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9 + 95 * q^10 - 418 * q^11 - 426 * q^12 + 13 * q^13 + 26 * q^14 - 45 * q^15 + 486 * q^16 - 224 * q^17 - 18 * q^18 + 367 * q^19 + 18 * q^20 - 189 * q^21 + 22 * q^22 + 51 * q^23 + 135 * q^24 + 773 * q^25 - 439 * q^26 - 1026 * q^27 + 22 * q^28 - 462 * q^29 - 285 * q^30 + 234 * q^31 - 597 * q^32 + 1254 * q^33 + 956 * q^34 - 522 * q^35 + 1278 * q^36 + 954 * q^37 + 705 * q^38 - 39 * q^39 + 1495 * q^40 - 740 * q^41 - 78 * q^42 + 1441 * q^43 - 1562 * q^44 + 135 * q^45 + 581 * q^46 + 1003 * q^47 - 1458 * q^48 + 2707 * q^49 + 388 * q^50 + 672 * q^51 + 788 * q^52 + 735 * q^53 + 54 * q^54 - 165 * q^55 + 1059 * q^56 - 1101 * q^57 + 177 * q^58 + 261 * q^59 - 54 * q^60 - 2318 * q^61 + 1251 * q^62 + 567 * q^63 + 5571 * q^64 - 1354 * q^65 - 66 * q^66 + 3495 * q^67 - 1856 * q^68 - 153 * q^69 + 542 * q^70 - 873 * q^71 - 405 * q^72 + 989 * q^73 - 3406 * q^74 - 2319 * q^75 + 1712 * q^76 - 693 * q^77 + 1317 * q^78 + 2313 * q^79 + 1593 * q^80 + 3078 * q^81 + 5170 * q^82 + 569 * q^83 - 66 * q^84 - 1271 * q^85 + 3065 * q^86 + 1386 * q^87 + 495 * q^88 - 2917 * q^89 + 855 * q^90 + 2740 * q^91 + 1083 * q^92 - 702 * q^93 + 3272 * q^94 + 2696 * q^95 + 1791 * q^96 + 4250 * q^97 + 5952 * q^98 - 3762 * q^99

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