LMFDB - Embedded newform 2013.4.a.c.1.19

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			1.19
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)

$f(q)$	$=$	$q-0.169683 q^{2} +3.00000 q^{3} -7.97121 q^{4} +0.479910 q^{5} -0.509049 q^{6} +32.7035 q^{7} +2.71004 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.169683 q^{2} +3.00000 q^{3} -7.97121 q^{4} +0.479910 q^{5} -0.509049 q^{6} +32.7035 q^{7} +2.71004 q^{8} +9.00000 q^{9} -0.0814325 q^{10} -11.0000 q^{11} -23.9136 q^{12} -42.6739 q^{13} -5.54922 q^{14} +1.43973 q^{15} +63.3098 q^{16} +48.6110 q^{17} -1.52715 q^{18} -11.4307 q^{19} -3.82546 q^{20} +98.1105 q^{21} +1.86651 q^{22} -68.1724 q^{23} +8.13012 q^{24} -124.770 q^{25} +7.24103 q^{26} +27.0000 q^{27} -260.686 q^{28} +5.67219 q^{29} -0.244297 q^{30} -132.946 q^{31} -32.4229 q^{32} -33.0000 q^{33} -8.24845 q^{34} +15.6947 q^{35} -71.7409 q^{36} -304.191 q^{37} +1.93959 q^{38} -128.022 q^{39} +1.30058 q^{40} -431.568 q^{41} -16.6477 q^{42} +131.433 q^{43} +87.6833 q^{44} +4.31919 q^{45} +11.5677 q^{46} +64.2321 q^{47} +189.929 q^{48} +726.518 q^{49} +21.1713 q^{50} +145.833 q^{51} +340.162 q^{52} +123.322 q^{53} -4.58144 q^{54} -5.27901 q^{55} +88.6278 q^{56} -34.2921 q^{57} -0.962474 q^{58} +780.239 q^{59} -11.4764 q^{60} -61.0000 q^{61} +22.5586 q^{62} +294.331 q^{63} -500.977 q^{64} -20.4796 q^{65} +5.59953 q^{66} -133.497 q^{67} -387.488 q^{68} -204.517 q^{69} -2.66313 q^{70} -1069.39 q^{71} +24.3904 q^{72} -142.461 q^{73} +51.6160 q^{74} -374.309 q^{75} +91.1165 q^{76} -359.738 q^{77} +21.7231 q^{78} -763.123 q^{79} +30.3830 q^{80} +81.0000 q^{81} +73.2297 q^{82} +661.350 q^{83} -782.059 q^{84} +23.3289 q^{85} -22.3019 q^{86} +17.0166 q^{87} -29.8104 q^{88} -1539.28 q^{89} -0.732892 q^{90} -1395.58 q^{91} +543.416 q^{92} -398.837 q^{93} -10.8991 q^{94} -5.48571 q^{95} -97.2687 q^{96} +1129.11 q^{97} -123.278 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9} - 41 q^{10} - 407 q^{11} + 390 q^{12} + 51 q^{13} - 228 q^{14} - 105 q^{15} + 462 q^{16} - 190 q^{17} - 72 q^{18} - 51 q^{19} - 720 q^{20} - 105 q^{21} + 88 q^{22} - 583 q^{23} - 351 q^{24} + 598 q^{25} - 1019 q^{26} + 999 q^{27} - 498 q^{28} - 566 q^{29} - 123 q^{30} - 696 q^{31} - 859 q^{32} - 1221 q^{33} - 348 q^{34} - 1102 q^{35} + 1170 q^{36} - 1022 q^{37} - 455 q^{38} + 153 q^{39} - 503 q^{40} - 790 q^{41} - 684 q^{42} - 87 q^{43} - 1430 q^{44} - 315 q^{45} - 303 q^{46} - 1603 q^{47} + 1386 q^{48} + 110 q^{49} - 1926 q^{50} - 570 q^{51} + 736 q^{52} - 2619 q^{53} - 216 q^{54} + 385 q^{55} - 4937 q^{56} - 153 q^{57} - 1099 q^{58} - 2471 q^{59} - 2160 q^{60} - 2257 q^{61} - 2909 q^{62} - 315 q^{63} - 265 q^{64} - 1970 q^{65} + 264 q^{66} - 3033 q^{67} - 1956 q^{68} - 1749 q^{69} + 2410 q^{70} - 3891 q^{71} - 1053 q^{72} + 391 q^{73} - 532 q^{74} + 1794 q^{75} + 1554 q^{76} + 385 q^{77} - 3057 q^{78} + 67 q^{79} - 5111 q^{80} + 2997 q^{81} - 4818 q^{82} - 5315 q^{83} - 1494 q^{84} - 2747 q^{85} - 5195 q^{86} - 1698 q^{87} + 1287 q^{88} - 8945 q^{89} - 369 q^{90} - 4432 q^{91} - 4701 q^{92} - 2088 q^{93} - 372 q^{94} - 3388 q^{95} - 2577 q^{96} - 3784 q^{97} - 4502 q^{98} - 3663 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9 - 41 * q^10 - 407 * q^11 + 390 * q^12 + 51 * q^13 - 228 * q^14 - 105 * q^15 + 462 * q^16 - 190 * q^17 - 72 * q^18 - 51 * q^19 - 720 * q^20 - 105 * q^21 + 88 * q^22 - 583 * q^23 - 351 * q^24 + 598 * q^25 - 1019 * q^26 + 999 * q^27 - 498 * q^28 - 566 * q^29 - 123 * q^30 - 696 * q^31 - 859 * q^32 - 1221 * q^33 - 348 * q^34 - 1102 * q^35 + 1170 * q^36 - 1022 * q^37 - 455 * q^38 + 153 * q^39 - 503 * q^40 - 790 * q^41 - 684 * q^42 - 87 * q^43 - 1430 * q^44 - 315 * q^45 - 303 * q^46 - 1603 * q^47 + 1386 * q^48 + 110 * q^49 - 1926 * q^50 - 570 * q^51 + 736 * q^52 - 2619 * q^53 - 216 * q^54 + 385 * q^55 - 4937 * q^56 - 153 * q^57 - 1099 * q^58 - 2471 * q^59 - 2160 * q^60 - 2257 * q^61 - 2909 * q^62 - 315 * q^63 - 265 * q^64 - 1970 * q^65 + 264 * q^66 - 3033 * q^67 - 1956 * q^68 - 1749 * q^69 + 2410 * q^70 - 3891 * q^71 - 1053 * q^72 + 391 * q^73 - 532 * q^74 + 1794 * q^75 + 1554 * q^76 + 385 * q^77 - 3057 * q^78 + 67 * q^79 - 5111 * q^80 + 2997 * q^81 - 4818 * q^82 - 5315 * q^83 - 1494 * q^84 - 2747 * q^85 - 5195 * q^86 - 1698 * q^87 + 1287 * q^88 - 8945 * q^89 - 369 * q^90 - 4432 * q^91 - 4701 * q^92 - 2088 * q^93 - 372 * q^94 - 3388 * q^95 - 2577 * q^96 - 3784 * q^97 - 4502 * 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 $

$2$	−0.169683	−0.0599919	−0.0299960	−	0.999550i	$-0.509549\pi$
$2$	−0.169683	−0.0599919	−0.0299960	+	0.999550i	$0.509549\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.97121	−0.996401
$5$	0.479910	0.0429244	0.0214622	−	0.999770i	$-0.493168\pi$
$5$	0.479910	0.0429244	0.0214622	+	0.999770i	$0.493168\pi$
$6$	−0.509049	−0.0346364
$7$	32.7035	1.76582	0.882911	−	0.469540i	$-0.155580\pi$
$7$	32.7035	1.76582	0.882911	+	0.469540i	$0.155580\pi$
$8$	2.71004	0.119768
$9$	9.00000	0.333333
$10$	−0.0814325	−0.00257512
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−23.9136	−0.575272
$13$	−42.6739	−0.910431	−0.455216	−	0.890381i	$-0.650438\pi$
$13$	−42.6739	−0.910431	−0.455216	+	0.890381i	$0.650438\pi$
$14$	−5.54922	−0.105935
$15$	1.43973	0.0247824
$16$	63.3098	0.989216
$17$	48.6110	0.693523	0.346761	−	0.937953i	$-0.387281\pi$
$17$	48.6110	0.693523	0.346761	+	0.937953i	$0.387281\pi$
$18$	−1.52715	−0.0199973
$19$	−11.4307	−0.138020	−0.0690101	−	0.997616i	$-0.521984\pi$
$19$	−11.4307	−0.138020	−0.0690101	+	0.997616i	$0.521984\pi$
$20$	−3.82546	−0.0427700
$21$	98.1105	1.01950
$22$	1.86651	0.0180883
$23$	−68.1724	−0.618040	−0.309020	−	0.951056i	$-0.600001\pi$
$23$	−68.1724	−0.618040	−0.309020	+	0.951056i	$0.600001\pi$
$24$	8.13012	0.0691481
$25$	−124.770	−0.998157
$26$	7.24103	0.0546185
$27$	27.0000	0.192450
$28$	−260.686	−1.75947
$29$	5.67219	0.0363207	0.0181603	−	0.999835i	$-0.494219\pi$
$29$	5.67219	0.0363207	0.0181603	+	0.999835i	$0.494219\pi$
$30$	−0.244297	−0.00148675
$31$	−132.946	−0.770250	−0.385125	−	0.922864i	$-0.625842\pi$
$31$	−132.946	−0.770250	−0.385125	+	0.922864i	$0.625842\pi$
$32$	−32.4229	−0.179113
$33$	−33.0000	−0.174078
$34$	−8.24845	−0.0416058
$35$	15.6947	0.0757969
$36$	−71.7409	−0.332134
$37$	−304.191	−1.35159	−0.675794	−	0.737091i	$-0.736199\pi$
$37$	−304.191	−1.35159	−0.675794	+	0.737091i	$0.736199\pi$
$38$	1.93959	0.00828010
$39$	−128.022	−0.525638
$40$	1.30058	0.00514097
$41$	−431.568	−1.64389	−0.821947	−	0.569565i	$-0.807112\pi$
$41$	−431.568	−1.64389	−0.821947	+	0.569565i	$0.807112\pi$
$42$	−16.6477	−0.0611617
$43$	131.433	0.466124	0.233062	−	0.972462i	$-0.425126\pi$
$43$	131.433	0.466124	0.233062	+	0.972462i	$0.425126\pi$
$44$	87.6833	0.300426
$45$	4.31919	0.0143081
$46$	11.5677	0.0370774
$47$	64.2321	0.199345	0.0996725	−	0.995020i	$-0.468220\pi$
$47$	64.2321	0.199345	0.0996725	+	0.995020i	$0.468220\pi$
$48$	189.929	0.571124
$49$	726.518	2.11813
$50$	21.1713	0.0598814
$51$	145.833	0.400406
$52$	340.162	0.907154
$53$	123.322	0.319615	0.159808	−	0.987148i	$-0.448913\pi$
$53$	123.322	0.319615	0.159808	+	0.987148i	$0.448913\pi$
$54$	−4.58144	−0.0115455
$55$	−5.27901	−0.0129422
$56$	88.6278	0.211489
$57$	−34.2921	−0.0796860
$58$	−0.962474	−0.00217895
$59$	780.239	1.72167	0.860834	−	0.508885i	$-0.169942\pi$
$59$	780.239	1.72167	0.860834	+	0.508885i	$0.169942\pi$
$60$	−11.4764	−0.0246932
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	22.5586	0.0462088
$63$	294.331	0.588607
$64$	−500.977	−0.978471
$65$	−20.4796	−0.0390798
$66$	5.59953	0.0104433
$67$	−133.497	−0.243421	−0.121711	−	0.992566i	$-0.538838\pi$
$67$	−133.497	−0.243421	−0.121711	+	0.992566i	$0.538838\pi$
$68$	−387.488	−0.691027
$69$	−204.517	−0.356826
$70$	−2.66313	−0.00454721
$71$	−1069.39	−1.78752	−0.893759	−	0.448547i	$-0.851942\pi$
$71$	−1069.39	−1.78752	−0.893759	+	0.448547i	$0.851942\pi$
$72$	24.3904	0.0399227
$73$	−142.461	−0.228408	−0.114204	−	0.993457i	$-0.536432\pi$
$73$	−142.461	−0.228408	−0.114204	+	0.993457i	$0.536432\pi$
$74$	51.6160	0.0810843
$75$	−374.309	−0.576286
$76$	91.1165	0.137523
$77$	−359.738	−0.532415
$78$	21.7231	0.0315340
$79$	−763.123	−1.08681	−0.543406	−	0.839470i	$-0.682865\pi$
$79$	−763.123	−1.08681	−0.543406	+	0.839470i	$0.682865\pi$
$80$	30.3830	0.0424615
$81$	81.0000	0.111111
$82$	73.2297	0.0986203
$83$	661.350	0.874609	0.437304	−	0.899314i	$-0.355933\pi$
$83$	661.350	0.874609	0.437304	+	0.899314i	$0.355933\pi$
$84$	−782.059	−1.01583
$85$	23.3289	0.0297691
$86$	−22.3019	−0.0279637
$87$	17.0166	0.0209697
$88$	−29.8104	−0.0361114
$89$	−1539.28	−1.83330	−0.916648	−	0.399695i	$-0.869116\pi$
$89$	−1539.28	−1.83330	−0.916648	+	0.399695i	$0.869116\pi$
$90$	−0.732892	−0.000858374 0
$91$	−1395.58	−1.60766
$92$	543.416	0.615816
$93$	−398.837	−0.444704
$94$	−10.8991	−0.0119591
$95$	−5.48571	−0.00592444
$96$	−97.2687	−0.103411
$97$	1129.11	1.18189	0.590947	−	0.806710i	$-0.298754\pi$
$97$	1129.11	1.18189	0.590947	+	0.806710i	$0.298754\pi$
$98$	−123.278	−0.127071
$99$	−99.0000	−0.100504
$100$	994.565	0.994565
$101$	184.836	0.182098	0.0910489	−	0.995846i	$-0.470978\pi$
$101$	184.836	0.182098	0.0910489	+	0.995846i	$0.470978\pi$
$102$	−24.7453	−0.0240211
$103$	1751.75	1.67578	0.837889	−	0.545840i	$-0.183789\pi$
$103$	1751.75	1.67578	0.837889	+	0.545840i	$0.183789\pi$
$104$	−115.648	−0.109040
$105$	47.0842	0.0437614
$106$	−20.9257	−0.0191744
$107$	−987.704	−0.892383	−0.446191	−	0.894938i	$-0.647220\pi$
$107$	−987.704	−0.892383	−0.446191	+	0.894938i	$0.647220\pi$
$108$	−215.223	−0.191757
$109$	1232.34	1.08291	0.541455	−	0.840730i	$-0.317874\pi$
$109$	1232.34	1.08291	0.541455	+	0.840730i	$0.317874\pi$
$110$	0.895757	0.000776428 0
$111$	−912.574	−0.780339
$112$	2070.45	1.74678
$113$	−548.217	−0.456389	−0.228194	−	0.973616i	$-0.573282\pi$
$113$	−548.217	−0.456389	−0.228194	+	0.973616i	$0.573282\pi$
$114$	5.81878	0.00478052
$115$	−32.7166	−0.0265290
$116$	−45.2142	−0.0361900
$117$	−384.065	−0.303477
$118$	−132.393	−0.103286
$119$	1589.75	1.22464
$120$	3.90173	0.00296814
$121$	121.000	0.0909091
$122$	10.3507	0.00768118
$123$	−1294.70	−0.949102
$124$	1059.74	0.767478
$125$	−119.867	−0.0857698
$126$	−49.9430	−0.0353117
$127$	−50.5652	−0.0353302	−0.0176651	−	0.999844i	$-0.505623\pi$
$127$	−50.5652	−0.0353302	−0.0176651	+	0.999844i	$0.505623\pi$
$128$	344.390	0.237813
$129$	394.299	0.269117
$130$	3.47504	0.00234447
$131$	1313.78	0.876225	0.438113	−	0.898920i	$-0.355647\pi$
$131$	1313.78	0.876225	0.438113	+	0.898920i	$0.355647\pi$
$132$	263.050	0.173451
$133$	−373.824	−0.243719
$134$	22.6521	0.0146033
$135$	12.9576	0.00826081
$136$	131.738	0.0830618
$137$	−1196.60	−0.746225	−0.373112	−	0.927786i	$-0.621709\pi$
$137$	−1196.60	−0.746225	−0.373112	+	0.927786i	$0.621709\pi$
$138$	34.7030	0.0214067
$139$	−2232.73	−1.36243	−0.681215	−	0.732083i	$-0.738548\pi$
$139$	−2232.73	−1.36243	−0.681215	+	0.732083i	$0.738548\pi$
$140$	−125.106	−0.0755242
$141$	192.696	0.115092
$142$	181.458	0.107237
$143$	469.413	0.274505
$144$	569.788	0.329739
$145$	2.72214	0.00155904
$146$	24.1731	0.0137026
$147$	2179.55	1.22290
$148$	2424.77	1.34672
$149$	−2648.65	−1.45628	−0.728139	−	0.685429i	$-0.759615\pi$
$149$	−2648.65	−1.45628	−0.728139	+	0.685429i	$0.759615\pi$
$150$	63.5138	0.0345725
$151$	1624.63	0.875564	0.437782	−	0.899081i	$-0.355764\pi$
$151$	1624.63	0.875564	0.437782	+	0.899081i	$0.355764\pi$
$152$	−30.9777	−0.0165304
$153$	437.499	0.231174
$154$	61.0414	0.0319406
$155$	−63.8019	−0.0330626
$156$	1020.49	0.523746
$157$	−3846.63	−1.95538	−0.977690	−	0.210054i	$-0.932636\pi$
$157$	−3846.63	−1.95538	−0.977690	+	0.210054i	$0.932636\pi$
$158$	129.489	0.0651999
$159$	369.967	0.184530
$160$	−15.5601	−0.00768833
$161$	−2229.47	−1.09135
$162$	−13.7443	−0.00666577
$163$	−3047.74	−1.46453	−0.732263	−	0.681022i	$-0.761536\pi$
$163$	−3047.74	−1.46453	−0.732263	+	0.681022i	$0.761536\pi$
$164$	3440.12	1.63798
$165$	−15.8370	−0.00747219
$166$	−112.220	−0.0524695
$167$	−1204.85	−0.558289	−0.279144	−	0.960249i	$-0.590051\pi$
$167$	−1204.85	−0.558289	−0.279144	+	0.960249i	$0.590051\pi$
$168$	265.883	0.122103
$169$	−375.940	−0.171115
$170$	−3.95851	−0.00178591
$171$	−102.876	−0.0460067
$172$	−1047.68	−0.464446
$173$	1896.73	0.833560	0.416780	−	0.909007i	$-0.363159\pi$
$173$	1896.73	0.833560	0.416780	+	0.909007i	$0.363159\pi$
$174$	−2.88742	−0.00125802
$175$	−4080.40	−1.76257
$176$	−696.408	−0.298260
$177$	2340.72	0.994006
$178$	261.189	0.109983
$179$	2425.82	1.01293	0.506464	−	0.862261i	$-0.330952\pi$
$179$	2425.82	1.01293	0.506464	+	0.862261i	$0.330952\pi$
$180$	−34.4292	−0.0142567
$181$	2548.64	1.04662	0.523311	−	0.852142i	$-0.324696\pi$
$181$	2548.64	1.04662	0.523311	+	0.852142i	$0.324696\pi$
$182$	236.807	0.0964466
$183$	−183.000	−0.0739221
$184$	−184.750	−0.0740214
$185$	−145.984	−0.0580161
$186$	67.6758	0.0266787
$187$	−534.721	−0.209105
$188$	−512.008	−0.198628
$189$	882.994	0.339833
$190$	0.930830	0.000355419 0
$191$	783.374	0.296770	0.148385	−	0.988930i	$-0.452593\pi$
$191$	783.374	0.296770	0.148385	+	0.988930i	$0.452593\pi$
$192$	−1502.93	−0.564920
$193$	241.506	0.0900725	0.0450362	−	0.998985i	$-0.485660\pi$
$193$	241.506	0.0900725	0.0450362	+	0.998985i	$0.485660\pi$
$194$	−191.591	−0.0709041
$195$	−61.4389	−0.0225627
$196$	−5791.23	−2.11050
$197$	−1795.13	−0.649228	−0.324614	−	0.945846i	$-0.605234\pi$
$197$	−1795.13	−0.649228	−0.324614	+	0.945846i	$0.605234\pi$
$198$	16.7986	0.00602942
$199$	5081.10	1.81000	0.904998	−	0.425415i	$-0.139872\pi$
$199$	5081.10	1.81000	0.904998	+	0.425415i	$0.139872\pi$
$200$	−338.131	−0.119547
$201$	−400.490	−0.140539
$202$	−31.3635	−0.0109244
$203$	185.500	0.0641359
$204$	−1162.46	−0.398965
$205$	−207.114	−0.0705632
$206$	−297.242	−0.100533
$207$	−613.551	−0.206013
$208$	−2701.68	−0.900613
$209$	125.738	0.0416146
$210$	−7.98938	−0.00262533
$211$	−1584.95	−0.517119	−0.258560	−	0.965995i	$-0.583248\pi$
$211$	−1584.95	−0.517119	−0.258560	+	0.965995i	$0.583248\pi$
$212$	−983.028	−0.318465
$213$	−3208.18	−1.03202
$214$	167.596	0.0535358
$215$	63.0759	0.0200081
$216$	73.1711	0.0230494
$217$	−4347.79	−1.36012
$218$	−209.108	−0.0649659
$219$	−427.382	−0.131871
$220$	42.0801	0.0128956
$221$	−2074.42	−0.631405
$222$	154.848	0.0468141
$223$	−5097.09	−1.53061	−0.765306	−	0.643666i	$-0.777412\pi$
$223$	−5097.09	−1.53061	−0.765306	+	0.643666i	$0.777412\pi$
$224$	−1060.34	−0.316282
$225$	−1122.93	−0.332719
$226$	93.0230	0.0273796
$227$	−826.329	−0.241609	−0.120805	−	0.992676i	$-0.538547\pi$
$227$	−826.329	−0.241609	−0.120805	+	0.992676i	$0.538547\pi$
$228$	273.349	0.0793992
$229$	824.073	0.237800	0.118900	−	0.992906i	$-0.462063\pi$
$229$	824.073	0.237800	0.118900	+	0.992906i	$0.462063\pi$
$230$	5.55144	0.00159153
$231$	−1079.22	−0.307390
$232$	15.3719	0.00435005
$233$	−6511.76	−1.83090	−0.915450	−	0.402432i	$-0.868165\pi$
$233$	−6511.76	−1.83090	−0.915450	+	0.402432i	$0.868165\pi$
$234$	65.1692	0.0182062
$235$	30.8256	0.00855678
$236$	−6219.45	−1.71547
$237$	−2289.37	−0.627471
$238$	−269.753	−0.0734684
$239$	−4321.37	−1.16957	−0.584783	−	0.811190i	$-0.698820\pi$
$239$	−4321.37	−1.16957	−0.584783	+	0.811190i	$0.698820\pi$
$240$	91.1490	0.0245152
$241$	−4921.72	−1.31550	−0.657750	−	0.753236i	$-0.728492\pi$
$241$	−4921.72	−1.31550	−0.657750	+	0.753236i	$0.728492\pi$
$242$	−20.5316	−0.00545381
$243$	243.000	0.0641500
$244$	486.244	0.127576
$245$	348.663	0.0909195
$246$	219.689	0.0569385
$247$	487.792	0.125658
$248$	−360.288	−0.0922513
$249$	1984.05	0.504956
$250$	20.3394	0.00514550
$251$	−1727.62	−0.434449	−0.217224	−	0.976122i	$-0.569700\pi$
$251$	−1727.62	−0.434449	−0.217224	+	0.976122i	$0.569700\pi$
$252$	−2346.18	−0.586489
$253$	749.896	0.186346
$254$	8.58004	0.00211953
$255$	69.9867	0.0171872
$256$	3949.38	0.964204
$257$	5959.28	1.44642	0.723210	−	0.690628i	$-0.242666\pi$
$257$	5959.28	1.44642	0.723210	+	0.690628i	$0.242666\pi$
$258$	−66.9057	−0.0161448
$259$	−9948.11	−2.38666
$260$	163.247	0.0389391
$261$	51.0497	0.0121069
$262$	−222.926	−0.0525665
$263$	−7657.85	−1.79545	−0.897724	−	0.440557i	$-0.854781\pi$
$263$	−7657.85	−1.79545	−0.897724	+	0.440557i	$0.854781\pi$
$264$	−89.4313	−0.0208489
$265$	59.1836	0.0137193
$266$	63.4315	0.0146212
$267$	−4617.84	−1.05845
$268$	1064.13	0.242545
$269$	−81.5884	−0.0184927	−0.00924634	−	0.999957i	$-0.502943\pi$
$269$	−81.5884	−0.0184927	−0.00924634	+	0.999957i	$0.502943\pi$
$270$	−2.19868	−0.000495582 0
$271$	4842.83	1.08554	0.542769	−	0.839882i	$-0.317376\pi$
$271$	4842.83	1.08554	0.542769	+	0.839882i	$0.317376\pi$
$272$	3077.55	0.686044
$273$	−4186.75	−0.928183
$274$	203.043	0.0447675
$275$	1372.47	0.300956
$276$	1630.25	0.355541
$277$	−4864.24	−1.05510	−0.527552	−	0.849523i	$-0.676890\pi$
$277$	−4864.24	−1.05510	−0.527552	+	0.849523i	$0.676890\pi$
$278$	378.856	0.0817349
$279$	−1196.51	−0.256750
$280$	42.5333	0.00907805
$281$	−1218.28	−0.258635	−0.129317	−	0.991603i	$-0.541279\pi$
$281$	−1218.28	−0.258635	−0.129317	+	0.991603i	$0.541279\pi$
$282$	−32.6973	−0.00690459
$283$	4460.16	0.936852	0.468426	−	0.883503i	$-0.344821\pi$
$283$	4460.16	0.936852	0.468426	+	0.883503i	$0.344821\pi$
$284$	8524.37	1.78109
$285$	−16.4571	−0.00342048
$286$	−79.6513	−0.0164681
$287$	−14113.8	−2.90282
$288$	−291.806	−0.0597043
$289$	−2549.97	−0.519026
$290$	−0.461901	−9.35301e−5 0
$291$	3387.33	0.682367
$292$	1135.58	0.227586
$293$	3043.05	0.606746	0.303373	−	0.952872i	$-0.401887\pi$
$293$	3043.05	0.606746	0.303373	+	0.952872i	$0.401887\pi$
$294$	−369.833	−0.0733643
$295$	374.444	0.0739017
$296$	−824.370	−0.161877
$297$	−297.000	−0.0580259
$298$	449.430	0.0873650
$299$	2909.18	0.562683
$300$	2983.70	0.574212
$301$	4298.31	0.823092
$302$	−275.671	−0.0525268
$303$	554.508	0.105134
$304$	−723.676	−0.136532
$305$	−29.2745	−0.00549591
$306$	−74.2360	−0.0138686
$307$	−6426.30	−1.19469	−0.597343	−	0.801986i	$-0.703777\pi$
$307$	−6426.30	−1.19469	−0.597343	+	0.801986i	$0.703777\pi$
$308$	2867.55	0.530499
$309$	5255.26	0.967511
$310$	10.8261	0.00198349
$311$	1866.06	0.340240	0.170120	−	0.985423i	$-0.445584\pi$
$311$	1866.06	0.340240	0.170120	+	0.985423i	$0.445584\pi$
$312$	−346.944	−0.0629546
$313$	1103.81	0.199332	0.0996661	−	0.995021i	$-0.468223\pi$
$313$	1103.81	0.199332	0.0996661	+	0.995021i	$0.468223\pi$
$314$	652.707	0.117307
$315$	141.253	0.0252656
$316$	6083.01	1.08290
$317$	−8116.27	−1.43803	−0.719015	−	0.694995i	$-0.755407\pi$
$317$	−8116.27	−1.43803	−0.719015	+	0.694995i	$0.755407\pi$
$318$	−62.7770	−0.0110703
$319$	−62.3941	−0.0109511
$320$	−240.424	−0.0420003
$321$	−2963.11	−0.515217
$322$	378.303	0.0654721
$323$	−555.657	−0.0957201
$324$	−645.668	−0.110711
$325$	5324.41	0.908754
$326$	517.150	0.0878597
$327$	3697.03	0.625218
$328$	−1169.57	−0.196886
$329$	2100.61	0.352008
$330$	2.68727	0.000448271 0
$331$	−4115.75	−0.683451	−0.341725	−	0.939800i	$-0.611011\pi$
$331$	−4115.75	−0.683451	−0.341725	+	0.939800i	$0.611011\pi$
$332$	−5271.75	−0.871461
$333$	−2737.72	−0.450529
$334$	204.443	0.0334928
$335$	−64.0664	−0.0104487
$336$	6211.35	1.00850
$337$	−3897.65	−0.630026	−0.315013	−	0.949087i	$-0.602009\pi$
$337$	−3897.65	−0.630026	−0.315013	+	0.949087i	$0.602009\pi$
$338$	63.7906	0.0102655
$339$	−1644.65	−0.263496
$340$	−185.959	−0.0296620
$341$	1462.40	0.232239
$342$	17.4563	0.00276003
$343$	12542.4	1.97442
$344$	356.188	0.0558267
$345$	−98.1498	−0.0153165
$346$	−321.843	−0.0500069
$347$	2756.46	0.426439	0.213220	−	0.977004i	$-0.431605\pi$
$347$	2756.46	0.426439	0.213220	+	0.977004i	$0.431605\pi$
$348$	−135.643	−0.0208943
$349$	−2580.95	−0.395860	−0.197930	−	0.980216i	$-0.563422\pi$
$349$	−2580.95	−0.395860	−0.197930	+	0.980216i	$0.563422\pi$
$350$	692.375	0.105740
$351$	−1152.19	−0.175213
$352$	356.652	0.0540046
$353$	5885.14	0.887349	0.443674	−	0.896188i	$-0.353675\pi$
$353$	5885.14	0.887349	0.443674	+	0.896188i	$0.353675\pi$
$354$	−397.180	−0.0596324
$355$	−513.213	−0.0767282
$356$	12269.9	1.82670
$357$	4769.24	0.707045
$358$	−411.619	−0.0607675
$359$	−6512.78	−0.957469	−0.478734	−	0.877960i	$-0.658904\pi$
$359$	−6512.78	−0.957469	−0.478734	+	0.877960i	$0.658904\pi$
$360$	11.7052	0.00171366
$361$	−6728.34	−0.980950
$362$	−432.460	−0.0627889
$363$	363.000	0.0524864
$364$	11124.5	1.60187
$365$	−68.3683	−0.00980428
$366$	31.0520	0.00443473
$367$	3537.24	0.503113	0.251556	−	0.967843i	$-0.419058\pi$
$367$	3537.24	0.503113	0.251556	+	0.967843i	$0.419058\pi$
$368$	−4315.98	−0.611375
$369$	−3884.11	−0.547964
$370$	24.7710	0.00348050
$371$	4033.07	0.564384
$372$	3179.21	0.443103
$373$	−3376.10	−0.468654	−0.234327	−	0.972158i	$-0.575289\pi$
$373$	−3376.10	−0.468654	−0.234327	+	0.972158i	$0.575289\pi$
$374$	90.7329	0.0125446
$375$	−359.601	−0.0495192
$376$	174.072	0.0238752
$377$	−242.054	−0.0330675
$378$	−149.829	−0.0203872
$379$	−5078.12	−0.688246	−0.344123	−	0.938925i	$-0.611824\pi$
$379$	−5078.12	−0.688246	−0.344123	+	0.938925i	$0.611824\pi$
$380$	43.7277	0.00590312
$381$	−151.696	−0.0203979
$382$	−132.925	−0.0178038
$383$	−3390.07	−0.452284	−0.226142	−	0.974094i	$-0.572611\pi$
$383$	−3390.07	−0.452284	−0.226142	+	0.974094i	$0.572611\pi$
$384$	1033.17	0.137302
$385$	−172.642	−0.0228536
$386$	−40.9794	−0.00540362
$387$	1182.90	0.155375
$388$	−9000.37	−1.17764
$389$	1848.87	0.240981	0.120490	−	0.992714i	$-0.461553\pi$
$389$	1848.87	0.240981	0.120490	+	0.992714i	$0.461553\pi$
$390$	10.4251	0.00135358
$391$	−3313.92	−0.428625
$392$	1968.89	0.253684
$393$	3941.34	0.505889
$394$	304.603	0.0389485
$395$	−366.230	−0.0466508
$396$	789.150	0.100142
$397$	−5123.50	−0.647711	−0.323855	−	0.946107i	$-0.604979\pi$
$397$	−5123.50	−0.647711	−0.323855	+	0.946107i	$0.604979\pi$
$398$	−862.175	−0.108585
$399$	−1121.47	−0.140711
$400$	−7899.15	−0.987393
$401$	−5130.28	−0.638888	−0.319444	−	0.947605i	$-0.603496\pi$
$401$	−5130.28	−0.638888	−0.319444	+	0.947605i	$0.603496\pi$
$402$	67.9563	0.00843122
$403$	5673.31	0.701259
$404$	−1473.37	−0.181442
$405$	38.8727	0.00476938
$406$	−31.4762	−0.00384763
$407$	3346.10	0.407519
$408$	395.213	0.0479558
$409$	−10113.8	−1.22273	−0.611364	−	0.791349i	$-0.709379\pi$
$409$	−10113.8	−1.22273	−0.611364	+	0.791349i	$0.709379\pi$
$410$	35.1437	0.00423322
$411$	−3589.81	−0.430833
$412$	−13963.6	−1.66975
$413$	25516.5	3.04016
$414$	104.109	0.0123591
$415$	317.388	0.0375421
$416$	1383.61	0.163070
$417$	−6698.20	−0.786600
$418$	−21.3355	−0.00249654
$419$	1230.04	0.143416	0.0717082	−	0.997426i	$-0.477155\pi$
$419$	1230.04	0.143416	0.0717082	+	0.997426i	$0.477155\pi$
$420$	−375.318	−0.0436039
$421$	9894.77	1.14547	0.572733	−	0.819742i	$-0.305883\pi$
$421$	9894.77	1.14547	0.572733	+	0.819742i	$0.305883\pi$
$422$	268.938	0.0310230
$423$	578.089	0.0664483
$424$	334.208	0.0382797
$425$	−6065.17	−0.692245
$426$	544.374	0.0619131
$427$	−1994.91	−0.226090
$428$	7873.20	0.889171
$429$	1408.24	0.158486
$430$	−10.7029	−0.00120033
$431$	15027.5	1.67946	0.839730	−	0.543004i	$-0.182713\pi$
$431$	15027.5	1.67946	0.839730	+	0.543004i	$0.182713\pi$
$432$	1709.36	0.190375
$433$	13898.6	1.54255	0.771276	−	0.636501i	$-0.219619\pi$
$433$	13898.6	1.54255	0.771276	+	0.636501i	$0.219619\pi$
$434$	737.745	0.0815965
$435$	8.16642	0.000900115 0
$436$	−9823.27	−1.07901
$437$	779.258	0.0853020
$438$	72.5194	0.00791122
$439$	8662.62	0.941786	0.470893	−	0.882190i	$-0.343932\pi$
$439$	8662.62	0.941786	0.470893	+	0.882190i	$0.343932\pi$
$440$	−14.3063	−0.00155006
$441$	6538.66	0.706043
$442$	351.993	0.0378792
$443$	12406.2	1.33056	0.665279	−	0.746595i	$-0.268313\pi$
$443$	12406.2	1.33056	0.665279	+	0.746595i	$0.268313\pi$
$444$	7274.31	0.777531
$445$	−738.716	−0.0786932
$446$	864.889	0.0918244
$447$	−7945.94	−0.840783
$448$	−16383.7	−1.72780
$449$	−2231.68	−0.234565	−0.117282	−	0.993099i	$-0.537418\pi$
$449$	−2231.68	−0.234565	−0.117282	+	0.993099i	$0.537418\pi$
$450$	190.541	0.0199605
$451$	4747.25	0.495652
$452$	4369.95	0.454746
$453$	4873.88	0.505507
$454$	140.214	0.0144946
$455$	−669.755	−0.0690079
$456$	−92.9330	−0.00954383
$457$	2378.16	0.243425	0.121713	−	0.992565i	$-0.461161\pi$
$457$	2378.16	0.243425	0.121713	+	0.992565i	$0.461161\pi$
$458$	−139.831	−0.0142661
$459$	1312.50	0.133469
$460$	260.791	0.0264335
$461$	−4789.37	−0.483868	−0.241934	−	0.970293i	$-0.577782\pi$
$461$	−4789.37	−0.483868	−0.241934	+	0.970293i	$0.577782\pi$
$462$	183.124	0.0184409
$463$	10673.0	1.07131	0.535656	−	0.844436i	$-0.320064\pi$
$463$	10673.0	1.07131	0.535656	+	0.844436i	$0.320064\pi$
$464$	359.105	0.0359290
$465$	−191.406	−0.0190887
$466$	1104.93	0.109839
$467$	−16998.7	−1.68438	−0.842192	−	0.539178i	$-0.818735\pi$
$467$	−16998.7	−1.68438	−0.842192	+	0.539178i	$0.818735\pi$
$468$	3061.46	0.302385
$469$	−4365.81	−0.429838
$470$	−5.23058	−0.000513338 0
$471$	−11539.9	−1.12894
$472$	2114.48	0.206201
$473$	−1445.76	−0.140542
$474$	388.467	0.0376432
$475$	1426.21	0.137766
$476$	−12672.2	−1.22023
$477$	1109.90	0.106538
$478$	733.262	0.0701645
$479$	−9821.14	−0.936826	−0.468413	−	0.883510i	$-0.655174\pi$
$479$	−9821.14	−0.936826	−0.468413	+	0.883510i	$0.655174\pi$
$480$	−46.6802	−0.00443886
$481$	12981.0	1.23053
$482$	835.131	0.0789195
$483$	−6688.42	−0.630090
$484$	−964.516	−0.0905819
$485$	541.871	0.0507322
$486$	−41.2329	−0.00384849
$487$	362.824	0.0337600	0.0168800	−	0.999858i	$-0.494627\pi$
$487$	362.824	0.0337600	0.0168800	+	0.999858i	$0.494627\pi$
$488$	−165.312	−0.0153347
$489$	−9143.23	−0.845544
$490$	−59.1622	−0.00545444
$491$	−15927.6	−1.46396	−0.731980	−	0.681326i	$-0.761403\pi$
$491$	−15927.6	−1.46396	−0.731980	+	0.681326i	$0.761403\pi$
$492$	10320.4	0.945686
$493$	275.731	0.0251892
$494$	−82.7700	−0.00753846
$495$	−47.5111	−0.00431407
$496$	−8416.77	−0.761943
$497$	−34972.9	−3.15644
$498$	−336.659	−0.0302933
$499$	12778.6	1.14639	0.573195	−	0.819419i	$-0.305704\pi$
$499$	12778.6	1.14639	0.573195	+	0.819419i	$0.305704\pi$
$500$	955.484	0.0854611
$501$	−3614.55	−0.322328
$502$	293.148	0.0260634
$503$	3537.48	0.313575	0.156788	−	0.987632i	$-0.449886\pi$
$503$	3537.48	0.313575	0.156788	+	0.987632i	$0.449886\pi$
$504$	797.650	0.0704963
$505$	88.7047	0.00781645
$506$	−127.244	−0.0111793
$507$	−1127.82	−0.0987934
$508$	403.066	0.0352030
$509$	−7450.99	−0.648840	−0.324420	−	0.945913i	$-0.605169\pi$
$509$	−7450.99	−0.648840	−0.324420	+	0.945913i	$0.605169\pi$
$510$	−11.8755	−0.00103109
$511$	−4658.96	−0.403328
$512$	−3425.27	−0.295658
$513$	−308.629	−0.0265620
$514$	−1011.19	−0.0867735
$515$	840.683	0.0719319
$516$	−3143.04	−0.268148
$517$	−706.553	−0.0601048
$518$	1688.02	0.143181
$519$	5690.19	0.481256
$520$	−55.5006	−0.00468050
$521$	−22858.6	−1.92218	−0.961088	−	0.276243i	$-0.910911\pi$
$521$	−22858.6	−1.92218	−0.961088	+	0.276243i	$0.910911\pi$
$522$	−8.66226	−0.000726316 0
$523$	22864.0	1.91161	0.955806	−	0.293997i	$-0.0949855\pi$
$523$	22864.0	1.91161	0.955806	+	0.293997i	$0.0949855\pi$
$524$	−10472.4	−0.873072
$525$	−12241.2	−1.01762
$526$	1299.41	0.107712
$527$	−6462.62	−0.534186
$528$	−2089.22	−0.172200
$529$	−7519.53	−0.618027
$530$	−10.0424	−0.000823049 0
$531$	7022.15	0.573890
$532$	2979.83	0.242842
$533$	18416.7	1.49665
$534$	783.568	0.0634987
$535$	−474.009	−0.0383050
$536$	−361.781	−0.0291540
$537$	7277.45	0.584814
$538$	13.8442	0.00110941
$539$	−7991.70	−0.638640
$540$	−103.287	−0.00823108
$541$	−7890.39	−0.627050	−0.313525	−	0.949580i	$-0.601510\pi$
$541$	−7890.39	−0.627050	−0.313525	+	0.949580i	$0.601510\pi$
$542$	−821.745	−0.0651235
$543$	7645.91	0.604268
$544$	−1576.11	−0.124219
$545$	591.414	0.0464833
$546$	710.420	0.0556835
$547$	12900.5	1.00838	0.504192	−	0.863591i	$-0.331790\pi$
$547$	12900.5	1.00838	0.504192	+	0.863591i	$0.331790\pi$
$548$	9538.38	0.743539
$549$	−549.000	−0.0426790
$550$	−232.884	−0.0180549
$551$	−64.8371	−0.00501298
$552$	−554.249	−0.0427363
$553$	−24956.8	−1.91912
$554$	825.378	0.0632978
$555$	−437.953	−0.0334956
$556$	17797.6	1.35753
$557$	−11635.7	−0.885133	−0.442566	−	0.896736i	$-0.645932\pi$
$557$	−11635.7	−0.885133	−0.442566	+	0.896736i	$0.645932\pi$
$558$	203.027	0.0154029
$559$	−5608.75	−0.424374
$560$	993.630	0.0749795
$561$	−1604.16	−0.120727
$562$	206.721	0.0155160
$563$	12089.2	0.904968	0.452484	−	0.891772i	$-0.350538\pi$
$563$	12089.2	0.904968	0.452484	+	0.891772i	$0.350538\pi$
$564$	−1536.02	−0.114678
$565$	−263.095	−0.0195902
$566$	−756.813	−0.0562036
$567$	2648.98	0.196202
$568$	−2898.10	−0.214087
$569$	−19091.0	−1.40657	−0.703284	−	0.710909i	$-0.748284\pi$
$569$	−19091.0	−1.40657	−0.703284	+	0.710909i	$0.748284\pi$
$570$	2.79249	0.000205201 0
$571$	162.537	0.0119124	0.00595618	−	0.999982i	$-0.498104\pi$
$571$	162.537	0.0119124	0.00595618	+	0.999982i	$0.498104\pi$
$572$	−3741.79	−0.273517
$573$	2350.12	0.171340
$574$	2394.87	0.174146
$575$	8505.84	0.616901
$576$	−4508.79	−0.326157
$577$	3258.79	0.235122	0.117561	−	0.993066i	$-0.462492\pi$
$577$	3258.79	0.235122	0.117561	+	0.993066i	$0.462492\pi$
$578$	432.687	0.0311374
$579$	724.518	0.0520034
$580$	−21.6988	−0.00155343
$581$	21628.4	1.54440
$582$	−574.772	−0.0409365
$583$	−1356.55	−0.0963677
$584$	−386.074	−0.0273559
$585$	−184.317	−0.0130266
$586$	−516.353	−0.0363999
$587$	−7496.62	−0.527118	−0.263559	−	0.964643i	$-0.584896\pi$
$587$	−7496.62	−0.527118	−0.263559	+	0.964643i	$0.584896\pi$
$588$	−17373.7	−1.21850
$589$	1519.66	0.106310
$590$	−63.5368	−0.00443351
$591$	−5385.40	−0.374832
$592$	−19258.3	−1.33701
$593$	−2068.14	−0.143218	−0.0716091	−	0.997433i	$-0.522813\pi$
$593$	−2068.14	−0.143218	−0.0716091	+	0.997433i	$0.522813\pi$
$594$	50.3958	0.00348109
$595$	762.936	0.0525669
$596$	21112.9	1.45104
$597$	15243.3	1.04500
$598$	−493.638	−0.0337564
$599$	9952.66	0.678889	0.339445	−	0.940626i	$-0.389761\pi$
$599$	9952.66	0.678889	0.339445	+	0.940626i	$0.389761\pi$
$600$	−1014.39	−0.0690207
$601$	23357.7	1.58533	0.792664	−	0.609659i	$-0.208694\pi$
$601$	23357.7	1.58533	0.792664	+	0.609659i	$0.208694\pi$
$602$	−729.350	−0.0493789
$603$	−1201.47	−0.0811403
$604$	−12950.2	−0.872413
$605$	58.0691	0.00390222
$606$	−94.0906	−0.00630721
$607$	13840.5	0.925483	0.462741	−	0.886493i	$-0.346866\pi$
$607$	13840.5	0.925483	0.462741	+	0.886493i	$0.346866\pi$
$608$	370.617	0.0247212
$609$	556.501	0.0370289
$610$	4.96738	0.000329710 0
$611$	−2741.03	−0.181490
$612$	−3487.39	−0.230342
$613$	−9076.86	−0.598060	−0.299030	−	0.954244i	$-0.596663\pi$
$613$	−9076.86	−0.598060	−0.299030	+	0.954244i	$0.596663\pi$
$614$	1090.43	0.0716715
$615$	−621.341	−0.0407397
$616$	−974.905	−0.0637663
$617$	5666.98	0.369763	0.184882	−	0.982761i	$-0.440810\pi$
$617$	5666.98	0.369763	0.184882	+	0.982761i	$0.440810\pi$
$618$	−891.727	−0.0580429
$619$	15609.6	1.01358	0.506788	−	0.862071i	$-0.330833\pi$
$619$	15609.6	1.01358	0.506788	+	0.862071i	$0.330833\pi$
$620$	508.579	0.0329436
$621$	−1840.65	−0.118942
$622$	−316.639	−0.0204117
$623$	−50339.8	−3.23728
$624$	−8105.03	−0.519969
$625$	15538.7	0.994476
$626$	−187.298	−0.0119583
$627$	377.213	0.0240262
$628$	30662.3	1.94834
$629$	−14787.0	−0.937357
$630$	−23.9681	−0.00151574
$631$	27707.9	1.74807	0.874037	−	0.485860i	$-0.161493\pi$
$631$	27707.9	1.74807	0.874037	+	0.485860i	$0.161493\pi$
$632$	−2068.09	−0.130165
$633$	−4754.84	−0.298559
$634$	1377.19	0.0862702
$635$	−24.2667	−0.00151653
$636$	−2949.08	−0.183866
$637$	−31003.3	−1.92841
$638$	10.5872	0.000656977 0
$639$	−9624.55	−0.595839
$640$	165.276	0.0102080
$641$	−26276.9	−1.61915	−0.809575	−	0.587017i	$-0.800302\pi$
$641$	−26276.9	−1.61915	−0.809575	+	0.587017i	$0.800302\pi$
$642$	502.789	0.0309089
$643$	−765.746	−0.0469643	−0.0234822	−	0.999724i	$-0.507475\pi$
$643$	−765.746	−0.0469643	−0.0234822	+	0.999724i	$0.507475\pi$
$644$	17771.6	1.08742
$645$	189.228	0.0115517
$646$	94.2855	0.00574244
$647$	24815.2	1.50786	0.753932	−	0.656953i	$-0.228155\pi$
$647$	24815.2	1.50786	0.753932	+	0.656953i	$0.228155\pi$
$648$	219.513	0.0133076
$649$	−8582.63	−0.519103
$650$	−903.460	−0.0545179
$651$	−13043.4	−0.785268
$652$	24294.2	1.45925
$653$	22357.8	1.33986	0.669931	−	0.742423i	$-0.266324\pi$
$653$	22357.8	1.33986	0.669931	+	0.742423i	$0.266324\pi$
$654$	−627.323	−0.0375081
$655$	630.496	0.0376115
$656$	−27322.5	−1.62617
$657$	−1282.15	−0.0761359
$658$	−356.438	−0.0211176
$659$	−29455.8	−1.74118	−0.870588	−	0.492013i	$-0.836261\pi$
$659$	−29455.8	−1.74118	−0.870588	+	0.492013i	$0.836261\pi$
$660$	126.240	0.00744529
$661$	1884.54	0.110893	0.0554464	−	0.998462i	$-0.482342\pi$
$661$	1884.54	0.110893	0.0554464	+	0.998462i	$0.482342\pi$
$662$	698.372	0.0410015
$663$	−6223.25	−0.364542
$664$	1792.28	0.104750
$665$	−179.402	−0.0104615
$666$	464.544	0.0270281
$667$	−386.687	−0.0224476
$668$	9604.12	0.556279
$669$	−15291.3	−0.883700
$670$	10.8710	0.000626839 0
$671$	671.000	0.0386046
$672$	−3181.03	−0.182605
$673$	11405.1	0.653247	0.326623	−	0.945155i	$-0.394089\pi$
$673$	11405.1	0.653247	0.326623	+	0.945155i	$0.394089\pi$
$674$	661.365	0.0377965
$675$	−3368.78	−0.192095
$676$	2996.70	0.170499
$677$	21647.0	1.22889	0.614446	−	0.788959i	$-0.289379\pi$
$677$	21647.0	1.22889	0.614446	+	0.788959i	$0.289379\pi$
$678$	279.069	0.0158076
$679$	36925.8	2.08702
$680$	63.2222	0.00356538
$681$	−2478.99	−0.139493
$682$	−248.145	−0.0139325
$683$	−11197.0	−0.627294	−0.313647	−	0.949540i	$-0.601551\pi$
$683$	−11197.0	−0.627294	−0.313647	+	0.949540i	$0.601551\pi$
$684$	820.048	0.0458411
$685$	−574.262	−0.0320313
$686$	−2128.23	−0.118449
$687$	2472.22	0.137294
$688$	8320.99	0.461097
$689$	−5262.64	−0.290988
$690$	16.6543	0.000918869 0
$691$	21545.7	1.18616	0.593081	−	0.805143i	$-0.297911\pi$
$691$	21545.7	1.18616	0.593081	+	0.805143i	$0.297911\pi$
$692$	−15119.2	−0.830560
$693$	−3237.65	−0.177472
$694$	−467.724	−0.0255829
$695$	−1071.51	−0.0584816
$696$	46.1156	0.00251150
$697$	−20978.9	−1.14008
$698$	437.943	0.0237484
$699$	−19535.3	−1.05707
$700$	32525.7	1.75623
$701$	321.570	0.0173260	0.00866301	−	0.999962i	$-0.497242\pi$
$701$	321.570	0.0173260	0.00866301	+	0.999962i	$0.497242\pi$
$702$	195.508	0.0105113
$703$	3477.12	0.186546
$704$	5510.75	0.295020
$705$	92.4769	0.00494026
$706$	−998.606	−0.0532338
$707$	6044.79	0.321552
$708$	−18658.3	−0.990429
$709$	2109.43	0.111737	0.0558684	−	0.998438i	$-0.482207\pi$
$709$	2109.43	0.111737	0.0558684	+	0.998438i	$0.482207\pi$
$710$	87.0835	0.00460308
$711$	−6868.11	−0.362270
$712$	−4171.51	−0.219570
$713$	9063.22	0.476045
$714$	−809.259	−0.0424170
$715$	225.276	0.0117830
$716$	−19336.7	−1.00928
$717$	−12964.1	−0.675249
$718$	1105.11	0.0574404
$719$	−9640.15	−0.500024	−0.250012	−	0.968243i	$-0.580435\pi$
$719$	−9640.15	−0.500024	−0.250012	+	0.968243i	$0.580435\pi$
$720$	273.447	0.0141538
$721$	57288.4	2.95913
$722$	1141.68	0.0588491
$723$	−14765.2	−0.759505
$724$	−20315.7	−1.04286
$725$	−707.718	−0.0362538
$726$	−61.5949	−0.00314876
$727$	−13080.8	−0.667320	−0.333660	−	0.942694i	$-0.608284\pi$
$727$	−13080.8	−0.667320	−0.333660	+	0.942694i	$0.608284\pi$
$728$	−3782.09	−0.192546
$729$	729.000	0.0370370
$730$	11.6009	0.000588178 0
$731$	6389.08	0.323267
$732$	1458.73	0.0736561
$733$	−27649.4	−1.39325	−0.696625	−	0.717435i	$-0.745316\pi$
$733$	−27649.4	−1.39325	−0.696625	+	0.717435i	$0.745316\pi$
$734$	−600.209	−0.0301827
$735$	1045.99	0.0524924
$736$	2210.35	0.110699
$737$	1468.46	0.0733942
$738$	659.067	0.0328734
$739$	−2432.26	−0.121072	−0.0605360	−	0.998166i	$-0.519281\pi$
$739$	−2432.26	−0.121072	−0.0605360	+	0.998166i	$0.519281\pi$
$740$	1163.67	0.0578073
$741$	1463.38	0.0725486
$742$	−684.343	−0.0338585
$743$	27047.7	1.33551	0.667755	−	0.744381i	$-0.267255\pi$
$743$	27047.7	1.33551	0.667755	+	0.744381i	$0.267255\pi$
$744$	−1080.86	−0.0532613
$745$	−1271.11	−0.0625100
$746$	572.867	0.0281155
$747$	5952.15	0.291536
$748$	4262.37	0.208352
$749$	−32301.4	−1.57579
$750$	61.0181	0.00297075
$751$	14865.6	0.722309	0.361155	−	0.932506i	$-0.382383\pi$
$751$	14865.6	0.722309	0.361155	+	0.932506i	$0.382383\pi$
$752$	4066.52	0.197195
$753$	−5182.87	−0.250829
$754$	41.0725	0.00198378
$755$	779.674	0.0375831
$756$	−7038.53	−0.338610
$757$	21654.0	1.03967	0.519833	−	0.854268i	$-0.325994\pi$
$757$	21654.0	1.03967	0.519833	+	0.854268i	$0.325994\pi$
$758$	861.669	0.0412892
$759$	2249.69	0.107587
$760$	−14.8665	−0.000709558 0
$761$	−10653.6	−0.507481	−0.253741	−	0.967272i	$-0.581661\pi$
$761$	−10653.6	−0.507481	−0.253741	+	0.967272i	$0.581661\pi$
$762$	25.7401	0.00122371
$763$	40302.0	1.91223
$764$	−6244.44	−0.295701
$765$	209.960	0.00992303
$766$	575.237	0.0271334
$767$	−33295.8	−1.56746
$768$	11848.1	0.556683
$769$	31632.1	1.48333	0.741666	−	0.670769i	$-0.234036\pi$
$769$	31632.1	1.48333	0.741666	+	0.670769i	$0.234036\pi$
$770$	29.2944	0.00137103
$771$	17877.8	0.835091
$772$	−1925.10	−0.0897483
$773$	−30897.7	−1.43766	−0.718831	−	0.695185i	$-0.755322\pi$
$773$	−30897.7	−1.43766	−0.718831	+	0.695185i	$0.755322\pi$
$774$	−200.717	−0.00932122
$775$	16587.6	0.768831
$776$	3059.93	0.141553
$777$	−29844.3	−1.37794
$778$	−313.722	−0.0144569
$779$	4933.13	0.226890
$780$	489.742	0.0224815
$781$	11763.3	0.538957
$782$	562.316	0.0257140
$783$	153.149	0.00698992
$784$	45995.7	2.09529
$785$	−1846.04	−0.0839336
$786$	−668.778	−0.0303493
$787$	−5299.80	−0.240048	−0.120024	−	0.992771i	$-0.538297\pi$
$787$	−5299.80	−0.240048	−0.120024	+	0.992771i	$0.538297\pi$
$788$	14309.4	0.646892
$789$	−22973.5	−1.03660
$790$	62.1430	0.00279867
$791$	−17928.6	−0.805901
$792$	−268.294	−0.0120371
$793$	2603.11	0.116569
$794$	869.371	0.0388574
$795$	177.551	0.00792085
$796$	−40502.5	−1.80348
$797$	19789.8	0.879535	0.439768	−	0.898112i	$-0.355061\pi$
$797$	19789.8	0.879535	0.439768	+	0.898112i	$0.355061\pi$
$798$	190.294	0.00844154
$799$	3122.38	0.138250
$800$	4045.40	0.178783
$801$	−13853.5	−0.611099
$802$	870.521	0.0383281
$803$	1567.07	0.0688676
$804$	3192.39	0.140033
$805$	−1069.95	−0.0468455
$806$	−962.663	−0.0420699
$807$	−244.765	−0.0106768
$808$	500.913	0.0218095
$809$	7250.07	0.315079	0.157540	−	0.987513i	$-0.449644\pi$
$809$	7250.07	0.315079	0.157540	+	0.987513i	$0.449644\pi$
$810$	−6.59603	−0.000286125 0
$811$	21728.6	0.940808	0.470404	−	0.882451i	$-0.344108\pi$
$811$	21728.6	0.940808	0.470404	+	0.882451i	$0.344108\pi$
$812$	−1478.66	−0.0639050
$813$	14528.5	0.626736
$814$	−567.776	−0.0244479
$815$	−1462.64	−0.0628639
$816$	9232.65	0.396088
$817$	−1502.37	−0.0643345
$818$	1716.14	0.0733539
$819$	−12560.3	−0.535886
$820$	1650.95	0.0703092
$821$	8330.57	0.354128	0.177064	−	0.984199i	$-0.443340\pi$
$821$	8330.57	0.354128	0.177064	+	0.984199i	$0.443340\pi$
$822$	609.130	0.0258465
$823$	27158.4	1.15028	0.575141	−	0.818054i	$-0.304947\pi$
$823$	27158.4	1.15028	0.575141	+	0.818054i	$0.304947\pi$
$824$	4747.32	0.200705
$825$	4117.40	0.173757
$826$	−4329.72	−0.182385
$827$	−6719.75	−0.282550	−0.141275	−	0.989970i	$-0.545120\pi$
$827$	−6719.75	−0.282550	−0.141275	+	0.989970i	$0.545120\pi$
$828$	4890.74	0.205272
$829$	−12884.1	−0.539786	−0.269893	−	0.962890i	$-0.586988\pi$
$829$	−12884.1	−0.539786	−0.269893	+	0.962890i	$0.586988\pi$
$830$	−53.8553	−0.00225222
$831$	−14592.7	−0.609165
$832$	21378.6	0.890830
$833$	35316.7	1.46897
$834$	1136.57	0.0471896
$835$	−578.220	−0.0239642
$836$	−1002.28	−0.0414649
$837$	−3589.53	−0.148235
$838$	−208.717	−0.00860383
$839$	6552.87	0.269643	0.134821	−	0.990870i	$-0.456954\pi$
$839$	6552.87	0.269643	0.134821	+	0.990870i	$0.456954\pi$
$840$	127.600	0.00524121
$841$	−24356.8	−0.998681
$842$	−1678.97	−0.0687188
$843$	−3654.84	−0.149323
$844$	12633.9	0.515258
$845$	−180.417	−0.00734503
$846$	−98.0918	−0.00398637
$847$	3957.12	0.160529
$848$	7807.51	0.316169
$849$	13380.5	0.540892
$850$	1029.16	0.0415291
$851$	20737.4	0.835335
$852$	25573.1	1.02831
$853$	−48530.5	−1.94801	−0.974005	−	0.226525i	$-0.927264\pi$
$853$	−48530.5	−1.94801	−0.974005	+	0.226525i	$0.927264\pi$
$854$	338.502	0.0135636
$855$	−49.3714	−0.00197481
$856$	−2676.72	−0.106879
$857$	−1746.80	−0.0696261	−0.0348130	−	0.999394i	$-0.511084\pi$
$857$	−1746.80	−0.0696261	−0.0348130	+	0.999394i	$0.511084\pi$
$858$	−238.954	−0.00950787
$859$	26716.7	1.06119	0.530596	−	0.847625i	$-0.321968\pi$
$859$	26716.7	1.06119	0.530596	+	0.847625i	$0.321968\pi$
$860$	−502.791	−0.0199361
$861$	−42341.3	−1.67595
$862$	−2549.90	−0.100754
$863$	−4165.20	−0.164293	−0.0821466	−	0.996620i	$-0.526178\pi$
$863$	−4165.20	−0.164293	−0.0821466	+	0.996620i	$0.526178\pi$
$864$	−875.419	−0.0344703
$865$	910.260	0.0357801
$866$	−2358.36	−0.0925407
$867$	−7649.92	−0.299660
$868$	34657.1	1.35523
$869$	8394.36	0.327686
$870$	−1.38570	−5.39996e−5 0
$871$	5696.82	0.221618
$872$	3339.70	0.129698
$873$	10162.0	0.393965
$874$	−132.227	−0.00511743
$875$	−3920.07	−0.151454
$876$	3406.75	0.131397
$877$	−13273.8	−0.511087	−0.255543	−	0.966798i	$-0.582254\pi$
$877$	−13273.8	−0.511087	−0.255543	+	0.966798i	$0.582254\pi$
$878$	−1469.90	−0.0564996
$879$	9129.14	0.350305
$880$	−334.213	−0.0128026
$881$	−36131.1	−1.38171	−0.690855	−	0.722994i	$-0.742766\pi$
$881$	−36131.1	−1.38171	−0.690855	+	0.722994i	$0.742766\pi$
$882$	−1109.50	−0.0423569
$883$	−18945.1	−0.722031	−0.361016	−	0.932560i	$-0.617570\pi$
$883$	−18945.1	−0.722031	−0.361016	+	0.932560i	$0.617570\pi$
$884$	16535.6	0.629132
$885$	1123.33	0.0426672
$886$	−2105.12	−0.0798228
$887$	8670.90	0.328230	0.164115	−	0.986441i	$-0.447523\pi$
$887$	8670.90	0.328230	0.164115	+	0.986441i	$0.447523\pi$
$888$	−2473.11	−0.0934597
$889$	−1653.66	−0.0623868
$890$	125.347	0.00472096
$891$	−891.000	−0.0335013
$892$	40630.0	1.52510
$893$	−734.218	−0.0275136
$894$	1348.29	0.0504402
$895$	1164.17	0.0434793
$896$	11262.8	0.419936
$897$	8727.54	0.324865
$898$	378.678	0.0140720
$899$	−754.093	−0.0279760
$900$	8951.09	0.331522
$901$	5994.82	0.221661
$902$	−805.527	−0.0297352
$903$	12894.9	0.475212
$904$	−1485.69	−0.0546607
$905$	1223.12	0.0449257
$906$	−827.013	−0.0303263
$907$	41015.6	1.50154	0.750772	−	0.660562i	$-0.229682\pi$
$907$	41015.6	1.50154	0.750772	+	0.660562i	$0.229682\pi$
$908$	6586.84	0.240740
$909$	1663.53	0.0606993
$910$	113.646	0.00413992
$911$	17419.3	0.633508	0.316754	−	0.948508i	$-0.397407\pi$
$911$	17419.3	0.633508	0.316754	+	0.948508i	$0.397407\pi$
$912$	−2171.03	−0.0788266
$913$	−7274.84	−0.263705
$914$	−403.532	−0.0146036
$915$	−87.8235	−0.00317307
$916$	−6568.86	−0.236944
$917$	42965.2	1.54726
$918$	−222.708	−0.00800704
$919$	47151.6	1.69248	0.846238	−	0.532804i	$-0.178862\pi$
$919$	47151.6	1.69248	0.846238	+	0.532804i	$0.178862\pi$
$920$	−88.6633	−0.00317733
$921$	−19278.9	−0.689752
$922$	812.675	0.0290282
$923$	45635.2	1.62741
$924$	8602.65	0.306284
$925$	37953.8	1.34910
$926$	−1811.03	−0.0642701
$927$	15765.8	0.558593
$928$	−183.909	−0.00650550
$929$	25209.1	0.890296	0.445148	−	0.895457i	$-0.353151\pi$
$929$	25209.1	0.890296	0.445148	+	0.895457i	$0.353151\pi$
$930$	32.4783	0.00114517
$931$	−8304.61	−0.292344
$932$	51906.6	1.82431
$933$	5598.19	0.196438
$934$	2884.39	0.101049
$935$	−256.618	−0.00897572
$936$	−1040.83	−0.0363468
$937$	36132.7	1.25977	0.629885	−	0.776689i	$-0.283102\pi$
$937$	36132.7	1.25977	0.629885	+	0.776689i	$0.283102\pi$
$938$	740.802	0.0257868
$939$	3311.43	0.115085
$940$	−245.717	−0.00852598
$941$	−39631.9	−1.37297	−0.686484	−	0.727145i	$-0.740847\pi$
$941$	−39631.9	−1.37297	−0.686484	+	0.727145i	$0.740847\pi$
$942$	1958.12	0.0677272
$943$	29421.0	1.01599
$944$	49396.8	1.70310
$945$	423.758	0.0145871
$946$	245.321	0.00843136
$947$	−46191.6	−1.58503	−0.792516	−	0.609851i	$-0.791229\pi$
$947$	−46191.6	−1.58503	−0.792516	+	0.609851i	$0.791229\pi$
$948$	18249.0	0.625212
$949$	6079.35	0.207950
$950$	−242.003	−0.00826484
$951$	−24348.8	−0.830246
$952$	4308.28	0.146672
$953$	−39408.4	−1.33952	−0.669760	−	0.742578i	$-0.733603\pi$
$953$	−39408.4	−1.33952	−0.669760	+	0.742578i	$0.733603\pi$
$954$	−188.331	−0.00639145
$955$	375.949	0.0127387
$956$	34446.5	1.16536
$957$	−187.182	−0.00632262
$958$	1666.48	0.0562020
$959$	−39133.1	−1.31770
$960$	−721.271	−0.0242489
$961$	−12116.4	−0.406715
$962$	−2202.66	−0.0738217
$963$	−8889.34	−0.297461
$964$	39232.0	1.31077
$965$	115.901	0.00386631
$966$	1134.91	0.0378004
$967$	−20689.0	−0.688018	−0.344009	−	0.938966i	$-0.611785\pi$
$967$	−20689.0	−0.688018	−0.344009	+	0.938966i	$0.611785\pi$
$968$	327.915	0.0108880
$969$	−1666.97	−0.0552640
$970$	−91.9462	−0.00304352
$971$	7801.35	0.257834	0.128917	−	0.991655i	$-0.458850\pi$
$971$	7801.35	0.257834	0.128917	+	0.991655i	$0.458850\pi$
$972$	−1937.00	−0.0639192
$973$	−73018.1	−2.40581
$974$	−61.5650	−0.00202533
$975$	15973.2	0.524669
$976$	−3861.90	−0.126656
$977$	2361.07	0.0773157	0.0386579	−	0.999253i	$-0.487692\pi$
$977$	2361.07	0.0773157	0.0386579	+	0.999253i	$0.487692\pi$
$978$	1551.45	0.0507258
$979$	16932.1	0.552760
$980$	−2779.27	−0.0905923
$981$	11091.1	0.360970
$982$	2702.65	0.0878258
$983$	−24531.8	−0.795974	−0.397987	−	0.917391i	$-0.630291\pi$
$983$	−24531.8	−0.795974	−0.397987	+	0.917391i	$0.630291\pi$
$984$	−3508.70	−0.113672
$985$	−861.503	−0.0278678
$986$	−46.7868	−0.00151115
$987$	6301.84	0.203232
$988$	−3888.29	−0.125206
$989$	−8960.09	−0.288083
$990$	8.06182	0.000258809 0
$991$	20500.6	0.657138	0.328569	−	0.944480i	$-0.393434\pi$
$991$	20500.6	0.657138	0.328569	+	0.944480i	$0.393434\pi$
$992$	4310.49	0.137962
$993$	−12347.3	−0.394590
$994$	5934.31	0.189361
$995$	2438.47	0.0776931
$996$	−15815.3	−0.503138
$997$	−27185.7	−0.863569	−0.431784	−	0.901977i	$-0.642116\pi$
$997$	−27185.7	−0.863569	−0.431784	+	0.901977i	$0.642116\pi$
$998$	−2168.31	−0.0687741
$999$	−8213.16	−0.260113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.c.1.19	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.c.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-0.169683 q^{2} +3.00000 q^{3} -7.97121 q^{4} +0.479910 q^{5} -0.509049 q^{6} +32.7035 q^{7} +2.71004 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.169683 q^{2} +3.00000 q^{3} -7.97121 q^{4} +0.479910 q^{5} -0.509049 q^{6} +32.7035 q^{7} +2.71004 q^{8} +9.00000 q^{9} -0.0814325 q^{10} -11.0000 q^{11} -23.9136 q^{12} -42.6739 q^{13} -5.54922 q^{14} +1.43973 q^{15} +63.3098 q^{16} +48.6110 q^{17} -1.52715 q^{18} -11.4307 q^{19} -3.82546 q^{20} +98.1105 q^{21} +1.86651 q^{22} -68.1724 q^{23} +8.13012 q^{24} -124.770 q^{25} +7.24103 q^{26} +27.0000 q^{27} -260.686 q^{28} +5.67219 q^{29} -0.244297 q^{30} -132.946 q^{31} -32.4229 q^{32} -33.0000 q^{33} -8.24845 q^{34} +15.6947 q^{35} -71.7409 q^{36} -304.191 q^{37} +1.93959 q^{38} -128.022 q^{39} +1.30058 q^{40} -431.568 q^{41} -16.6477 q^{42} +131.433 q^{43} +87.6833 q^{44} +4.31919 q^{45} +11.5677 q^{46} +64.2321 q^{47} +189.929 q^{48} +726.518 q^{49} +21.1713 q^{50} +145.833 q^{51} +340.162 q^{52} +123.322 q^{53} -4.58144 q^{54} -5.27901 q^{55} +88.6278 q^{56} -34.2921 q^{57} -0.962474 q^{58} +780.239 q^{59} -11.4764 q^{60} -61.0000 q^{61} +22.5586 q^{62} +294.331 q^{63} -500.977 q^{64} -20.4796 q^{65} +5.59953 q^{66} -133.497 q^{67} -387.488 q^{68} -204.517 q^{69} -2.66313 q^{70} -1069.39 q^{71} +24.3904 q^{72} -142.461 q^{73} +51.6160 q^{74} -374.309 q^{75} +91.1165 q^{76} -359.738 q^{77} +21.7231 q^{78} -763.123 q^{79} +30.3830 q^{80} +81.0000 q^{81} +73.2297 q^{82} +661.350 q^{83} -782.059 q^{84} +23.3289 q^{85} -22.3019 q^{86} +17.0166 q^{87} -29.8104 q^{88} -1539.28 q^{89} -0.732892 q^{90} -1395.58 q^{91} +543.416 q^{92} -398.837 q^{93} -10.8991 q^{94} -5.48571 q^{95} -97.2687 q^{96} +1129.11 q^{97} -123.278 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9} - 41 q^{10} - 407 q^{11} + 390 q^{12} + 51 q^{13} - 228 q^{14} - 105 q^{15} + 462 q^{16} - 190 q^{17} - 72 q^{18} - 51 q^{19} - 720 q^{20} - 105 q^{21} + 88 q^{22} - 583 q^{23} - 351 q^{24} + 598 q^{25} - 1019 q^{26} + 999 q^{27} - 498 q^{28} - 566 q^{29} - 123 q^{30} - 696 q^{31} - 859 q^{32} - 1221 q^{33} - 348 q^{34} - 1102 q^{35} + 1170 q^{36} - 1022 q^{37} - 455 q^{38} + 153 q^{39} - 503 q^{40} - 790 q^{41} - 684 q^{42} - 87 q^{43} - 1430 q^{44} - 315 q^{45} - 303 q^{46} - 1603 q^{47} + 1386 q^{48} + 110 q^{49} - 1926 q^{50} - 570 q^{51} + 736 q^{52} - 2619 q^{53} - 216 q^{54} + 385 q^{55} - 4937 q^{56} - 153 q^{57} - 1099 q^{58} - 2471 q^{59} - 2160 q^{60} - 2257 q^{61} - 2909 q^{62} - 315 q^{63} - 265 q^{64} - 1970 q^{65} + 264 q^{66} - 3033 q^{67} - 1956 q^{68} - 1749 q^{69} + 2410 q^{70} - 3891 q^{71} - 1053 q^{72} + 391 q^{73} - 532 q^{74} + 1794 q^{75} + 1554 q^{76} + 385 q^{77} - 3057 q^{78} + 67 q^{79} - 5111 q^{80} + 2997 q^{81} - 4818 q^{82} - 5315 q^{83} - 1494 q^{84} - 2747 q^{85} - 5195 q^{86} - 1698 q^{87} + 1287 q^{88} - 8945 q^{89} - 369 q^{90} - 4432 q^{91} - 4701 q^{92} - 2088 q^{93} - 372 q^{94} - 3388 q^{95} - 2577 q^{96} - 3784 q^{97} - 4502 q^{98} - 3663 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9 - 41 * q^10 - 407 * q^11 + 390 * q^12 + 51 * q^13 - 228 * q^14 - 105 * q^15 + 462 * q^16 - 190 * q^17 - 72 * q^18 - 51 * q^19 - 720 * q^20 - 105 * q^21 + 88 * q^22 - 583 * q^23 - 351 * q^24 + 598 * q^25 - 1019 * q^26 + 999 * q^27 - 498 * q^28 - 566 * q^29 - 123 * q^30 - 696 * q^31 - 859 * q^32 - 1221 * q^33 - 348 * q^34 - 1102 * q^35 + 1170 * q^36 - 1022 * q^37 - 455 * q^38 + 153 * q^39 - 503 * q^40 - 790 * q^41 - 684 * q^42 - 87 * q^43 - 1430 * q^44 - 315 * q^45 - 303 * q^46 - 1603 * q^47 + 1386 * q^48 + 110 * q^49 - 1926 * q^50 - 570 * q^51 + 736 * q^52 - 2619 * q^53 - 216 * q^54 + 385 * q^55 - 4937 * q^56 - 153 * q^57 - 1099 * q^58 - 2471 * q^59 - 2160 * q^60 - 2257 * q^61 - 2909 * q^62 - 315 * q^63 - 265 * q^64 - 1970 * q^65 + 264 * q^66 - 3033 * q^67 - 1956 * q^68 - 1749 * q^69 + 2410 * q^70 - 3891 * q^71 - 1053 * q^72 + 391 * q^73 - 532 * q^74 + 1794 * q^75 + 1554 * q^76 + 385 * q^77 - 3057 * q^78 + 67 * q^79 - 5111 * q^80 + 2997 * q^81 - 4818 * q^82 - 5315 * q^83 - 1494 * q^84 - 2747 * q^85 - 5195 * q^86 - 1698 * q^87 + 1287 * q^88 - 8945 * q^89 - 369 * q^90 - 4432 * q^91 - 4701 * q^92 - 2088 * q^93 - 372 * q^94 - 3388 * q^95 - 2577 * q^96 - 3784 * q^97 - 4502 * q^98 - 3663 * q^99

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