LMFDB - Embedded newform 2013.4.a.g.1.12

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:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.91984 q^{2} -3.00000 q^{3} +0.525437 q^{4} +16.8265 q^{5} +8.75951 q^{6} +26.0578 q^{7} +21.8245 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.91984 q^{2} -3.00000 q^{3} +0.525437 q^{4} +16.8265 q^{5} +8.75951 q^{6} +26.0578 q^{7} +21.8245 q^{8} +9.00000 q^{9} -49.1305 q^{10} +11.0000 q^{11} -1.57631 q^{12} +31.7710 q^{13} -76.0844 q^{14} -50.4794 q^{15} -67.9274 q^{16} +83.9304 q^{17} -26.2785 q^{18} -2.09966 q^{19} +8.84126 q^{20} -78.1733 q^{21} -32.1182 q^{22} +114.946 q^{23} -65.4735 q^{24} +158.130 q^{25} -92.7659 q^{26} -27.0000 q^{27} +13.6917 q^{28} -140.940 q^{29} +147.392 q^{30} +156.611 q^{31} +23.7409 q^{32} -33.0000 q^{33} -245.063 q^{34} +438.460 q^{35} +4.72894 q^{36} +15.7859 q^{37} +6.13065 q^{38} -95.3129 q^{39} +367.229 q^{40} +330.591 q^{41} +228.253 q^{42} +54.2345 q^{43} +5.77981 q^{44} +151.438 q^{45} -335.622 q^{46} +140.031 q^{47} +203.782 q^{48} +336.007 q^{49} -461.714 q^{50} -251.791 q^{51} +16.6936 q^{52} +755.694 q^{53} +78.8355 q^{54} +185.091 q^{55} +568.697 q^{56} +6.29897 q^{57} +411.523 q^{58} -196.487 q^{59} -26.5238 q^{60} +61.0000 q^{61} -457.277 q^{62} +234.520 q^{63} +474.100 q^{64} +534.593 q^{65} +96.3546 q^{66} -476.005 q^{67} +44.1001 q^{68} -344.837 q^{69} -1280.23 q^{70} -90.4329 q^{71} +196.420 q^{72} -186.879 q^{73} -46.0922 q^{74} -474.391 q^{75} -1.10324 q^{76} +286.635 q^{77} +278.298 q^{78} +1370.06 q^{79} -1142.98 q^{80} +81.0000 q^{81} -965.271 q^{82} +1142.58 q^{83} -41.0752 q^{84} +1412.25 q^{85} -158.356 q^{86} +422.821 q^{87} +240.069 q^{88} +749.671 q^{89} -442.175 q^{90} +827.880 q^{91} +60.3967 q^{92} -469.832 q^{93} -408.867 q^{94} -35.3298 q^{95} -71.2228 q^{96} -1436.96 q^{97} -981.085 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.91984	−1.03232	−0.516159	−	0.856493i	$-0.672639\pi$
$2$	−2.91984	−1.03232	−0.516159	+	0.856493i	$0.672639\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	0.525437	0.0656797
$5$	16.8265	1.50501	0.752503	−	0.658589i	$-0.228846\pi$
$5$	16.8265	1.50501	0.752503	+	0.658589i	$0.228846\pi$
$6$	8.75951	0.596009
$7$	26.0578	1.40699	0.703494	−	0.710702i	$-0.251622\pi$
$7$	26.0578	1.40699	0.703494	+	0.710702i	$0.251622\pi$
$8$	21.8245	0.964515
$9$	9.00000	0.333333
$10$	−49.1305	−1.55364
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−1.57631	−0.0379202
$13$	31.7710	0.677821	0.338911	−	0.940819i	$-0.389942\pi$
$13$	31.7710	0.677821	0.338911	+	0.940819i	$0.389942\pi$
$14$	−76.0844	−1.45246
$15$	−50.4794	−0.868915
$16$	−67.9274	−1.06137
$17$	83.9304	1.19742	0.598709	−	0.800967i	$-0.295681\pi$
$17$	83.9304	1.19742	0.598709	+	0.800967i	$0.295681\pi$
$18$	−26.2785	−0.344106
$19$	−2.09966	−0.0253523	−0.0126762	−	0.999920i	$-0.504035\pi$
$19$	−2.09966	−0.0253523	−0.0126762	+	0.999920i	$0.504035\pi$
$20$	8.84126	0.0988483
$21$	−78.1733	−0.812324
$22$	−32.1182	−0.311255
$23$	114.946	1.04208	0.521040	−	0.853533i	$-0.325544\pi$
$23$	114.946	1.04208	0.521040	+	0.853533i	$0.325544\pi$
$24$	−65.4735	−0.556863
$25$	158.130	1.26504
$26$	−92.7659	−0.699727
$27$	−27.0000	−0.192450
$28$	13.6917	0.0924104
$29$	−140.940	−0.902482	−0.451241	−	0.892402i	$-0.649018\pi$
$29$	−140.940	−0.902482	−0.451241	+	0.892402i	$0.649018\pi$
$30$	147.392	0.896997
$31$	156.611	0.907358	0.453679	−	0.891165i	$-0.350111\pi$
$31$	156.611	0.907358	0.453679	+	0.891165i	$0.350111\pi$
$32$	23.7409	0.131151
$33$	−33.0000	−0.174078
$34$	−245.063	−1.23612
$35$	438.460	2.11752
$36$	4.72894	0.0218932
$37$	15.7859	0.0701401	0.0350700	−	0.999385i	$-0.488835\pi$
$37$	15.7859	0.0701401	0.0350700	+	0.999385i	$0.488835\pi$
$38$	6.13065	0.0261717
$39$	−95.3129	−0.391340
$40$	367.229	1.45160
$41$	330.591	1.25926	0.629630	−	0.776895i	$-0.283207\pi$
$41$	330.591	1.25926	0.629630	+	0.776895i	$0.283207\pi$
$42$	228.253	0.838577
$43$	54.2345	0.192341	0.0961707	−	0.995365i	$-0.469341\pi$
$43$	54.2345	0.192341	0.0961707	+	0.995365i	$0.469341\pi$
$44$	5.77981	0.0198032
$45$	151.438	0.501668
$46$	−335.622	−1.07576
$47$	140.031	0.434587	0.217293	−	0.976106i	$-0.430277\pi$
$47$	140.031	0.434587	0.217293	+	0.976106i	$0.430277\pi$
$48$	203.782	0.612780
$49$	336.007	0.979612
$50$	−461.714	−1.30592
$51$	−251.791	−0.691329
$52$	16.6936	0.0445191
$53$	755.694	1.95854	0.979270	−	0.202562i	$-0.0649266\pi$
$53$	755.694	1.95854	0.979270	+	0.202562i	$0.0649266\pi$
$54$	78.8355	0.198670
$55$	185.091	0.453776
$56$	568.697	1.35706
$57$	6.29897	0.0146372
$58$	411.523	0.931648
$59$	−196.487	−0.433567	−0.216783	−	0.976220i	$-0.569556\pi$
$59$	−196.487	−0.433567	−0.216783	+	0.976220i	$0.569556\pi$
$60$	−26.5238	−0.0570701
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−457.277	−0.936682
$63$	234.520	0.468996
$64$	474.100	0.925976
$65$	534.593	1.02012
$66$	96.3546	0.179703
$67$	−476.005	−0.867960	−0.433980	−	0.900923i	$-0.642891\pi$
$67$	−476.005	−0.867960	−0.433980	+	0.900923i	$0.642891\pi$
$68$	44.1001	0.0786460
$69$	−344.837	−0.601645
$70$	−1280.23	−2.18596
$71$	−90.4329	−0.151161	−0.0755804	−	0.997140i	$-0.524081\pi$
$71$	−90.4329	−0.151161	−0.0755804	+	0.997140i	$0.524081\pi$
$72$	196.420	0.321505
$73$	−186.879	−0.299624	−0.149812	−	0.988714i	$-0.547867\pi$
$73$	−186.879	−0.299624	−0.149812	+	0.988714i	$0.547867\pi$
$74$	−46.0922	−0.0724068
$75$	−474.391	−0.730372
$76$	−1.10324	−0.00166513
$77$	286.635	0.424223
$78$	278.298	0.403987
$79$	1370.06	1.95119	0.975597	−	0.219568i	$-0.0704648\pi$
$79$	1370.06	1.95119	0.975597	+	0.219568i	$0.0704648\pi$
$80$	−1142.98	−1.59736
$81$	81.0000	0.111111
$82$	−965.271	−1.29996
$83$	1142.58	1.51101	0.755507	−	0.655140i	$-0.227391\pi$
$83$	1142.58	1.51101	0.755507	+	0.655140i	$0.227391\pi$
$84$	−41.0752	−0.0533532
$85$	1412.25	1.80212
$86$	−158.356	−0.198557
$87$	422.821	0.521048
$88$	240.069	0.290812
$89$	749.671	0.892865	0.446432	−	0.894817i	$-0.352694\pi$
$89$	749.671	0.892865	0.446432	+	0.894817i	$0.352694\pi$
$90$	−442.175	−0.517881
$91$	827.880	0.953686
$92$	60.3967	0.0684434
$93$	−469.832	−0.523863
$94$	−408.867	−0.448632
$95$	−35.3298	−0.0381554
$96$	−71.2228	−0.0757203
$97$	−1436.96	−1.50413	−0.752065	−	0.659088i	$-0.770942\pi$
$97$	−1436.96	−1.50413	−0.752065	+	0.659088i	$0.770942\pi$
$98$	−981.085	−1.01127
$99$	99.0000	0.100504
$100$	83.0875	0.0830875
$101$	46.9626	0.0462669	0.0231335	−	0.999732i	$-0.492636\pi$
$101$	46.9626	0.0462669	0.0231335	+	0.999732i	$0.492636\pi$
$102$	735.188	0.713672
$103$	−303.254	−0.290102	−0.145051	−	0.989424i	$-0.546335\pi$
$103$	−303.254	−0.290102	−0.145051	+	0.989424i	$0.546335\pi$
$104$	693.385	0.653769
$105$	−1315.38	−1.22255
$106$	−2206.50	−2.02183
$107$	−705.363	−0.637290	−0.318645	−	0.947874i	$-0.603228\pi$
$107$	−705.363	−0.637290	−0.318645	+	0.947874i	$0.603228\pi$
$108$	−14.1868	−0.0126401
$109$	−2122.89	−1.86547	−0.932733	−	0.360567i	$-0.882583\pi$
$109$	−2122.89	−1.86547	−0.932733	+	0.360567i	$0.882583\pi$
$110$	−540.436	−0.468441
$111$	−47.3577	−0.0404954
$112$	−1770.04	−1.49333
$113$	−900.522	−0.749681	−0.374841	−	0.927089i	$-0.622303\pi$
$113$	−900.522	−0.749681	−0.374841	+	0.927089i	$0.622303\pi$
$114$	−18.3920	−0.0151102
$115$	1934.13	1.56833
$116$	−74.0554	−0.0592747
$117$	285.939	0.225940
$118$	573.710	0.447578
$119$	2187.04	1.68475
$120$	−1101.69	−0.838082
$121$	121.000	0.0909091
$122$	−178.110	−0.132175
$123$	−991.773	−0.727034
$124$	82.2891	0.0595950
$125$	557.464	0.398889
$126$	−684.759	−0.484152
$127$	−905.684	−0.632806	−0.316403	−	0.948625i	$-0.602475\pi$
$127$	−905.684	−0.632806	−0.316403	+	0.948625i	$0.602475\pi$
$128$	−1574.22	−1.08705
$129$	−162.703	−0.111048
$130$	−1560.92	−1.05309
$131$	−2579.26	−1.72024	−0.860118	−	0.510095i	$-0.829610\pi$
$131$	−2579.26	−1.72024	−0.860118	+	0.510095i	$0.829610\pi$
$132$	−17.3394	−0.0114334
$133$	−54.7124	−0.0356704
$134$	1389.86	0.896010
$135$	−454.315	−0.289638
$136$	1831.74	1.15493
$137$	−2623.13	−1.63583	−0.817915	−	0.575338i	$-0.804870\pi$
$137$	−2623.13	−1.63583	−0.817915	+	0.575338i	$0.804870\pi$
$138$	1006.87	0.621088
$139$	325.164	0.198418	0.0992089	−	0.995067i	$-0.468369\pi$
$139$	325.164	0.198418	0.0992089	+	0.995067i	$0.468369\pi$
$140$	230.383	0.139078
$141$	−420.092	−0.250909
$142$	264.049	0.156046
$143$	349.480	0.204371
$144$	−611.347	−0.353789
$145$	−2371.53	−1.35824
$146$	545.657	0.309307
$147$	−1008.02	−0.565579
$148$	8.29449	0.00460678
$149$	568.052	0.312326	0.156163	−	0.987731i	$-0.450087\pi$
$149$	568.052	0.312326	0.156163	+	0.987731i	$0.450087\pi$
$150$	1385.14	0.753976
$151$	51.2473	0.0276189	0.0138094	−	0.999905i	$-0.495604\pi$
$151$	51.2473	0.0276189	0.0138094	+	0.999905i	$0.495604\pi$
$152$	−45.8239	−0.0244527
$153$	755.373	0.399139
$154$	−836.928	−0.437932
$155$	2635.20	1.36558
$156$	−50.0809	−0.0257031
$157$	737.318	0.374805	0.187402	−	0.982283i	$-0.439993\pi$
$157$	737.318	0.374805	0.187402	+	0.982283i	$0.439993\pi$
$158$	−4000.36	−2.01425
$159$	−2267.08	−1.13076
$160$	399.476	0.197383
$161$	2995.23	1.46619
$162$	−236.507	−0.114702
$163$	−518.318	−0.249066	−0.124533	−	0.992215i	$-0.539743\pi$
$163$	−518.318	−0.249066	−0.124533	+	0.992215i	$0.539743\pi$
$164$	173.705	0.0827077
$165$	−555.274	−0.261988
$166$	−3336.14	−1.55985
$167$	−4193.28	−1.94303	−0.971513	−	0.236986i	$-0.923841\pi$
$167$	−4193.28	−1.94303	−0.971513	+	0.236986i	$0.923841\pi$
$168$	−1706.09	−0.783499
$169$	−1187.61	−0.540558
$170$	−4123.54	−1.86036
$171$	−18.8969	−0.00845078
$172$	28.4968	0.0126329
$173$	−825.496	−0.362782	−0.181391	−	0.983411i	$-0.558060\pi$
$173$	−825.496	−0.362782	−0.181391	+	0.983411i	$0.558060\pi$
$174$	−1234.57	−0.537887
$175$	4120.52	1.77990
$176$	−747.202	−0.320014
$177$	589.461	0.250320
$178$	−2188.92	−0.921720
$179$	3869.28	1.61566	0.807831	−	0.589414i	$-0.200641\pi$
$179$	3869.28	1.61566	0.807831	+	0.589414i	$0.200641\pi$
$180$	79.5713	0.0329494
$181$	−27.5660	−0.0113202	−0.00566012	−	0.999984i	$-0.501802\pi$
$181$	−27.5660	−0.0113202	−0.00566012	+	0.999984i	$0.501802\pi$
$182$	−2417.27	−0.984507
$183$	−183.000	−0.0739221
$184$	2508.63	1.00510
$185$	265.621	0.105561
$186$	1371.83	0.540793
$187$	923.234	0.361035
$188$	73.5774	0.0285435
$189$	−703.560	−0.270775
$190$	103.157	0.0393885
$191$	−228.700	−0.0866396	−0.0433198	−	0.999061i	$-0.513793\pi$
$191$	−228.700	−0.0866396	−0.0433198	+	0.999061i	$0.513793\pi$
$192$	−1422.30	−0.534613
$193$	−31.0506	−0.0115807	−0.00579034	−	0.999983i	$-0.501843\pi$
$193$	−31.0506	−0.0115807	−0.00579034	+	0.999983i	$0.501843\pi$
$194$	4195.67	1.55274
$195$	−1603.78	−0.588969
$196$	176.551	0.0643406
$197$	−611.827	−0.221273	−0.110637	−	0.993861i	$-0.535289\pi$
$197$	−611.827	−0.221273	−0.110637	+	0.993861i	$0.535289\pi$
$198$	−289.064	−0.103752
$199$	4347.03	1.54851	0.774253	−	0.632876i	$-0.218126\pi$
$199$	4347.03	1.54851	0.774253	+	0.632876i	$0.218126\pi$
$200$	3451.11	1.22015
$201$	1428.02	0.501117
$202$	−137.123	−0.0477621
$203$	−3672.59	−1.26978
$204$	−132.300	−0.0454063
$205$	5562.68	1.89519
$206$	885.450	0.299477
$207$	1034.51	0.347360
$208$	−2158.12	−0.719416
$209$	−23.0962	−0.00764401
$210$	3840.69	1.26206
$211$	−1984.88	−0.647605	−0.323802	−	0.946125i	$-0.604961\pi$
$211$	−1984.88	−0.647605	−0.323802	+	0.946125i	$0.604961\pi$
$212$	397.070	0.128636
$213$	271.299	0.0872727
$214$	2059.54	0.657886
$215$	912.575	0.289475
$216$	−589.261	−0.185621
$217$	4080.92	1.27664
$218$	6198.48	1.92575
$219$	560.638	0.172988
$220$	97.2538	0.0298039
$221$	2666.55	0.811635
$222$	138.277	0.0418041
$223$	−121.434	−0.0364654	−0.0182327	−	0.999834i	$-0.505804\pi$
$223$	−121.434	−0.0364654	−0.0182327	+	0.999834i	$0.505804\pi$
$224$	618.635	0.184528
$225$	1423.17	0.421680
$226$	2629.37	0.773909
$227$	−453.560	−0.132616	−0.0663080	−	0.997799i	$-0.521122\pi$
$227$	−453.560	−0.132616	−0.0663080	+	0.997799i	$0.521122\pi$
$228$	3.30971	0.000961365 0
$229$	3428.74	0.989421	0.494711	−	0.869058i	$-0.335274\pi$
$229$	3428.74	0.989421	0.494711	+	0.869058i	$0.335274\pi$
$230$	−5647.34	−1.61902
$231$	−859.906	−0.244925
$232$	−3075.95	−0.870458
$233$	−3939.11	−1.10755	−0.553776	−	0.832666i	$-0.686814\pi$
$233$	−3939.11	−1.10755	−0.553776	+	0.832666i	$0.686814\pi$
$234$	−834.893	−0.233242
$235$	2356.22	0.654055
$236$	−103.242	−0.0284765
$237$	−4110.19	−1.12652
$238$	−6385.79	−1.73920
$239$	−3676.50	−0.995032	−0.497516	−	0.867455i	$-0.665755\pi$
$239$	−3676.50	−0.995032	−0.497516	+	0.867455i	$0.665755\pi$
$240$	3428.94	0.922237
$241$	−6093.58	−1.62872	−0.814362	−	0.580358i	$-0.802913\pi$
$241$	−6093.58	−1.62872	−0.814362	+	0.580358i	$0.802913\pi$
$242$	−353.300	−0.0938471
$243$	−243.000	−0.0641500
$244$	32.0517	0.00840942
$245$	5653.81	1.47432
$246$	2895.81	0.750530
$247$	−66.7081	−0.0171843
$248$	3417.95	0.875161
$249$	−3427.73	−0.872385
$250$	−1627.70	−0.411780
$251$	655.711	0.164893	0.0824464	−	0.996595i	$-0.473727\pi$
$251$	655.711	0.164893	0.0824464	+	0.996595i	$0.473727\pi$
$252$	123.226	0.0308035
$253$	1264.40	0.314199
$254$	2644.45	0.653257
$255$	−4236.76	−1.04045
$256$	803.666	0.196208
$257$	4385.24	1.06437	0.532186	−	0.846627i	$-0.321371\pi$
$257$	4385.24	1.06437	0.532186	+	0.846627i	$0.321371\pi$
$258$	475.067	0.114637
$259$	411.345	0.0986862
$260$	280.895	0.0670015
$261$	−1268.46	−0.300827
$262$	7531.01	1.77583
$263$	−1334.27	−0.312832	−0.156416	−	0.987691i	$-0.549994\pi$
$263$	−1334.27	−0.312832	−0.156416	+	0.987691i	$0.549994\pi$
$264$	−720.208	−0.167901
$265$	12715.7	2.94761
$266$	159.751	0.0368232
$267$	−2249.01	−0.515496
$268$	−250.111	−0.0570073
$269$	−5731.67	−1.29913	−0.649565	−	0.760306i	$-0.725049\pi$
$269$	−5731.67	−1.29913	−0.649565	+	0.760306i	$0.725049\pi$
$270$	1326.52	0.298999
$271$	5336.24	1.19614	0.598069	−	0.801445i	$-0.295935\pi$
$271$	5336.24	1.19614	0.598069	+	0.801445i	$0.295935\pi$
$272$	−5701.17	−1.27090
$273$	−2483.64	−0.550611
$274$	7659.10	1.68870
$275$	1739.43	0.381424
$276$	−181.190	−0.0395158
$277$	4639.10	1.00627	0.503134	−	0.864208i	$-0.332180\pi$
$277$	4639.10	1.00627	0.503134	+	0.864208i	$0.332180\pi$
$278$	−949.426	−0.204830
$279$	1409.50	0.302453
$280$	9569.17	2.04238
$281$	−2468.69	−0.524092	−0.262046	−	0.965055i	$-0.584397\pi$
$281$	−2468.69	−0.524092	−0.262046	+	0.965055i	$0.584397\pi$
$282$	1226.60	0.259018
$283$	−3429.72	−0.720408	−0.360204	−	0.932874i	$-0.617293\pi$
$283$	−3429.72	−0.720408	−0.360204	+	0.932874i	$0.617293\pi$
$284$	−47.5168	−0.00992819
$285$	105.989	0.0220290
$286$	−1020.43	−0.210976
$287$	8614.46	1.77176
$288$	213.668	0.0437171
$289$	2131.31	0.433809
$290$	6924.48	1.40214
$291$	4310.87	0.868410
$292$	−98.1934	−0.0196792
$293$	91.5594	0.0182558	0.00912791	−	0.999958i	$-0.497094\pi$
$293$	91.5594	0.0182558	0.00912791	+	0.999958i	$0.497094\pi$
$294$	2943.26	0.583858
$295$	−3306.18	−0.652520
$296$	344.519	0.0676512
$297$	−297.000	−0.0580259
$298$	−1658.62	−0.322420
$299$	3651.93	0.706343
$300$	−249.263	−0.0479706
$301$	1413.23	0.270622
$302$	−149.634	−0.0285114
$303$	−140.888	−0.0267122
$304$	142.624	0.0269081
$305$	1026.41	0.192696
$306$	−2205.57	−0.412038
$307$	−5042.24	−0.937380	−0.468690	−	0.883363i	$-0.655274\pi$
$307$	−5042.24	−0.937380	−0.468690	+	0.883363i	$0.655274\pi$
$308$	150.609	0.0278628
$309$	909.761	0.167490
$310$	−7694.36	−1.40971
$311$	−2088.79	−0.380850	−0.190425	−	0.981702i	$-0.560987\pi$
$311$	−2088.79	−0.380850	−0.190425	+	0.981702i	$0.560987\pi$
$312$	−2080.15	−0.377454
$313$	−994.519	−0.179596	−0.0897980	−	0.995960i	$-0.528622\pi$
$313$	−994.519	−0.179596	−0.0897980	+	0.995960i	$0.528622\pi$
$314$	−2152.85	−0.386918
$315$	3946.14	0.705841
$316$	719.883	0.128154
$317$	6877.68	1.21858	0.609288	−	0.792949i	$-0.291455\pi$
$317$	6877.68	1.21858	0.609288	+	0.792949i	$0.291455\pi$
$318$	6619.51	1.16731
$319$	−1550.34	−0.272109
$320$	7977.43	1.39360
$321$	2116.09	0.367940
$322$	−8745.57	−1.51358
$323$	−176.225	−0.0303573
$324$	42.5604	0.00729774
$325$	5023.95	0.857472
$326$	1513.40	0.257116
$327$	6368.67	1.07703
$328$	7214.98	1.21457
$329$	3648.89	0.611458
$330$	1621.31	0.270455
$331$	−590.667	−0.0980847	−0.0490423	−	0.998797i	$-0.515617\pi$
$331$	−590.667	−0.0980847	−0.0490423	+	0.998797i	$0.515617\pi$
$332$	600.353	0.0992429
$333$	142.073	0.0233800
$334$	12243.7	2.00582
$335$	−8009.49	−1.30628
$336$	5310.11	0.862173
$337$	3351.28	0.541709	0.270854	−	0.962620i	$-0.412694\pi$
$337$	3351.28	0.541709	0.270854	+	0.962620i	$0.412694\pi$
$338$	3467.62	0.558028
$339$	2701.57	0.432829
$340$	742.050	0.118363
$341$	1722.72	0.273579
$342$	55.1759	0.00872388
$343$	−182.220	−0.0286851
$344$	1183.64	0.185516
$345$	−5802.39	−0.905478
$346$	2410.31	0.374506
$347$	1309.75	0.202626	0.101313	−	0.994855i	$-0.467696\pi$
$347$	1309.75	0.202626	0.101313	+	0.994855i	$0.467696\pi$
$348$	222.166	0.0342223
$349$	7825.14	1.20020	0.600100	−	0.799925i	$-0.295127\pi$
$349$	7825.14	1.20020	0.600100	+	0.799925i	$0.295127\pi$
$350$	−12031.2	−1.83742
$351$	−857.816	−0.130447
$352$	261.150	0.0395436
$353$	1872.64	0.282353	0.141176	−	0.989984i	$-0.454912\pi$
$353$	1872.64	0.282353	0.141176	+	0.989984i	$0.454912\pi$
$354$	−1721.13	−0.258410
$355$	−1521.67	−0.227498
$356$	393.905	0.0586431
$357$	−6561.11	−0.972692
$358$	−11297.7	−1.66788
$359$	−1517.06	−0.223029	−0.111514	−	0.993763i	$-0.535570\pi$
$359$	−1517.06	−0.223029	−0.111514	+	0.993763i	$0.535570\pi$
$360$	3305.06	0.483867
$361$	−6854.59	−0.999357
$362$	80.4882	0.0116861
$363$	−363.000	−0.0524864
$364$	434.999	0.0626378
$365$	−3144.52	−0.450936
$366$	534.330	0.0763111
$367$	−2843.89	−0.404496	−0.202248	−	0.979334i	$-0.564825\pi$
$367$	−2843.89	−0.404496	−0.202248	+	0.979334i	$0.564825\pi$
$368$	−7807.96	−1.10603
$369$	2975.32	0.419753
$370$	−775.569	−0.108973
$371$	19691.7	2.75564
$372$	−246.867	−0.0344072
$373$	−5380.57	−0.746904	−0.373452	−	0.927650i	$-0.621826\pi$
$373$	−5380.57	−0.746904	−0.373452	+	0.927650i	$0.621826\pi$
$374$	−2695.69	−0.372703
$375$	−1672.39	−0.230298
$376$	3056.10	0.419166
$377$	−4477.81	−0.611721
$378$	2054.28	0.279526
$379$	11677.7	1.58270	0.791351	−	0.611362i	$-0.209378\pi$
$379$	11677.7	1.58270	0.791351	+	0.611362i	$0.209378\pi$
$380$	−18.5636	−0.00250603
$381$	2717.05	0.365351
$382$	667.767	0.0894396
$383$	−3270.02	−0.436267	−0.218134	−	0.975919i	$-0.569997\pi$
$383$	−3270.02	−0.436267	−0.218134	+	0.975919i	$0.569997\pi$
$384$	4722.66	0.627610
$385$	4823.06	0.638457
$386$	90.6626	0.0119549
$387$	488.110	0.0641138
$388$	−755.030	−0.0987908
$389$	−3773.54	−0.491841	−0.245921	−	0.969290i	$-0.579090\pi$
$389$	−3773.54	−0.491841	−0.245921	+	0.969290i	$0.579090\pi$
$390$	4682.77	0.608003
$391$	9647.43	1.24780
$392$	7333.18	0.944851
$393$	7737.78	0.993179
$394$	1786.43	0.228424
$395$	23053.4	2.93656
$396$	52.0183	0.00660106
$397$	1316.27	0.166402	0.0832009	−	0.996533i	$-0.473486\pi$
$397$	1316.27	0.166402	0.0832009	+	0.996533i	$0.473486\pi$
$398$	−12692.6	−1.59855
$399$	164.137	0.0205943
$400$	−10741.4	−1.34267
$401$	−12433.8	−1.54841	−0.774207	−	0.632932i	$-0.781851\pi$
$401$	−12433.8	−1.54841	−0.774207	+	0.632932i	$0.781851\pi$
$402$	−4169.57	−0.517312
$403$	4975.67	0.615027
$404$	24.6759	0.00303880
$405$	1362.94	0.167223
$406$	10723.4	1.31082
$407$	173.645	0.0211480
$408$	−5495.21	−0.666798
$409$	−11514.6	−1.39208	−0.696039	−	0.718004i	$-0.745056\pi$
$409$	−11514.6	−1.39208	−0.696039	+	0.718004i	$0.745056\pi$
$410$	−16242.1	−1.95644
$411$	7869.38	0.944447
$412$	−159.341	−0.0190538
$413$	−5120.01	−0.610023
$414$	−3020.60	−0.358586
$415$	19225.6	2.27408
$416$	754.272	0.0888972
$417$	−975.493	−0.114557
$418$	67.4372	0.00789105
$419$	−14544.1	−1.69577	−0.847883	−	0.530184i	$-0.822123\pi$
$419$	−14544.1	−1.69577	−0.847883	+	0.530184i	$0.822123\pi$
$420$	−691.150	−0.0802969
$421$	9173.68	1.06199	0.530995	−	0.847375i	$-0.321818\pi$
$421$	9173.68	1.06199	0.530995	+	0.847375i	$0.321818\pi$
$422$	5795.52	0.668534
$423$	1260.28	0.144862
$424$	16492.6	1.88904
$425$	13271.9	1.51478
$426$	−792.148	−0.0900931
$427$	1589.52	0.180146
$428$	−370.624	−0.0418570
$429$	−1048.44	−0.117994
$430$	−2664.57	−0.298830
$431$	−13812.3	−1.54365	−0.771825	−	0.635835i	$-0.780656\pi$
$431$	−13812.3	−1.54365	−0.771825	+	0.635835i	$0.780656\pi$
$432$	1834.04	0.204260
$433$	3171.39	0.351980	0.175990	−	0.984392i	$-0.443687\pi$
$433$	3171.39	0.351980	0.175990	+	0.984392i	$0.443687\pi$
$434$	−11915.6	−1.31790
$435$	7114.59	0.784180
$436$	−1115.44	−0.122523
$437$	−241.346	−0.0264191
$438$	−1636.97	−0.178579
$439$	13318.9	1.44801	0.724007	−	0.689792i	$-0.242298\pi$
$439$	13318.9	1.44801	0.724007	+	0.689792i	$0.242298\pi$
$440$	4039.52	0.437674
$441$	3024.06	0.326537
$442$	−7785.88	−0.837865
$443$	−9276.75	−0.994925	−0.497462	−	0.867486i	$-0.665735\pi$
$443$	−9276.75	−0.994925	−0.497462	+	0.867486i	$0.665735\pi$
$444$	−24.8835	−0.00265972
$445$	12614.3	1.34377
$446$	354.566	0.0376439
$447$	−1704.16	−0.180322
$448$	12354.0	1.30284
$449$	−16243.7	−1.70733	−0.853663	−	0.520825i	$-0.825624\pi$
$449$	−16243.7	−1.70733	−0.853663	+	0.520825i	$0.825624\pi$
$450$	−4155.43	−0.435308
$451$	3636.50	0.379681
$452$	−473.168	−0.0492388
$453$	−153.742	−0.0159458
$454$	1324.32	0.136902
$455$	13930.3	1.43530
$456$	137.472	0.0141178
$457$	−4400.00	−0.450379	−0.225189	−	0.974315i	$-0.572300\pi$
$457$	−4400.00	−0.450379	−0.225189	+	0.974315i	$0.572300\pi$
$458$	−10011.4	−1.02140
$459$	−2266.12	−0.230443
$460$	1016.26	0.103008
$461$	−17549.2	−1.77299	−0.886496	−	0.462736i	$-0.846868\pi$
$461$	−17549.2	−1.77299	−0.886496	+	0.462736i	$0.846868\pi$
$462$	2510.78	0.252840
$463$	−3147.26	−0.315909	−0.157954	−	0.987446i	$-0.550490\pi$
$463$	−3147.26	−0.315909	−0.157954	+	0.987446i	$0.550490\pi$
$464$	9573.72	0.957863
$465$	−7905.61	−0.788417
$466$	11501.5	1.14335
$467$	−2104.15	−0.208497	−0.104249	−	0.994551i	$-0.533244\pi$
$467$	−2104.15	−0.208497	−0.104249	+	0.994551i	$0.533244\pi$
$468$	150.243	0.0148397
$469$	−12403.6	−1.22121
$470$	−6879.78	−0.675193
$471$	−2211.95	−0.216394
$472$	−4288.23	−0.418182
$473$	596.579	0.0579931
$474$	12001.1	1.16293
$475$	−332.019	−0.0320717
$476$	1149.15	0.110654
$477$	6801.25	0.652846
$478$	10734.8	1.02719
$479$	4754.56	0.453531	0.226766	−	0.973949i	$-0.427185\pi$
$479$	4754.56	0.453531	0.226766	+	0.973949i	$0.427185\pi$
$480$	−1198.43	−0.113959
$481$	501.533	0.0475424
$482$	17792.3	1.68136
$483$	−8985.68	−0.846506
$484$	63.5779	0.00597088
$485$	−24178.9	−2.26373
$486$	709.520	0.0662232
$487$	−17565.1	−1.63439	−0.817196	−	0.576360i	$-0.804473\pi$
$487$	−17565.1	−1.63439	−0.817196	+	0.576360i	$0.804473\pi$
$488$	1331.29	0.123494
$489$	1554.95	0.143798
$490$	−16508.2	−1.52197
$491$	948.851	0.0872120	0.0436060	−	0.999049i	$-0.486115\pi$
$491$	948.851	0.0872120	0.0436060	+	0.999049i	$0.486115\pi$
$492$	−521.115	−0.0477513
$493$	−11829.2	−1.08065
$494$	194.777	0.0177397
$495$	1665.82	0.151259
$496$	−10638.2	−0.963039
$497$	−2356.48	−0.212681
$498$	10008.4	0.900578
$499$	21063.0	1.88960	0.944798	−	0.327654i	$-0.106258\pi$
$499$	21063.0	1.88960	0.944798	+	0.327654i	$0.106258\pi$
$500$	292.912	0.0261989
$501$	12579.8	1.12181
$502$	−1914.57	−0.170222
$503$	1130.57	0.100218	0.0501089	−	0.998744i	$-0.484043\pi$
$503$	1130.57	0.100218	0.0501089	+	0.998744i	$0.484043\pi$
$504$	5118.28	0.452354
$505$	790.216	0.0696319
$506$	−3691.84	−0.324353
$507$	3562.82	0.312091
$508$	−475.880	−0.0415625
$509$	−3192.96	−0.278046	−0.139023	−	0.990289i	$-0.544396\pi$
$509$	−3192.96	−0.278046	−0.139023	+	0.990289i	$0.544396\pi$
$510$	12370.6	1.07408
$511$	−4869.66	−0.421567
$512$	10247.2	0.884504
$513$	56.6907	0.00487906
$514$	−12804.2	−1.09877
$515$	−5102.69	−0.436604
$516$	−85.4904	−0.00729362
$517$	1540.34	0.131033
$518$	−1201.06	−0.101875
$519$	2476.49	0.209452
$520$	11667.2	0.983926
$521$	1511.96	0.127140	0.0635701	−	0.997977i	$-0.479751\pi$
$521$	1511.96	0.127140	0.0635701	+	0.997977i	$0.479751\pi$
$522$	3703.70	0.310549
$523$	−6728.83	−0.562584	−0.281292	−	0.959622i	$-0.590763\pi$
$523$	−6728.83	−0.562584	−0.281292	+	0.959622i	$0.590763\pi$
$524$	−1355.24	−0.112985
$525$	−12361.6	−1.02762
$526$	3895.86	0.322942
$527$	13144.4	1.08649
$528$	2241.60	0.184760
$529$	1045.50	0.0859288
$530$	−37127.6	−3.04287
$531$	−1768.38	−0.144522
$532$	−28.7479	−0.00234282
$533$	10503.2	0.853553
$534$	6566.75	0.532155
$535$	−11868.8	−0.959125
$536$	−10388.6	−0.837161
$537$	−11607.8	−0.932803
$538$	16735.5	1.34111
$539$	3696.08	0.295364
$540$	−238.714	−0.0190234
$541$	7197.44	0.571982	0.285991	−	0.958232i	$-0.407677\pi$
$541$	7197.44	0.571982	0.285991	+	0.958232i	$0.407677\pi$
$542$	−15580.9	−1.23479
$543$	82.6980	0.00653575
$544$	1992.58	0.157043
$545$	−35720.7	−2.80754
$546$	7251.82	0.568405
$547$	23462.9	1.83400	0.917002	−	0.398883i	$-0.130602\pi$
$547$	23462.9	1.83400	0.917002	+	0.398883i	$0.130602\pi$
$548$	−1378.29	−0.107441
$549$	549.000	0.0426790
$550$	−5078.85	−0.393751
$551$	295.926	0.0228800
$552$	−7525.89	−0.580295
$553$	35700.8	2.74531
$554$	−13545.4	−1.03879
$555$	−796.862	−0.0609458
$556$	170.854	0.0130320
$557$	16365.2	1.24491	0.622455	−	0.782655i	$-0.286135\pi$
$557$	16365.2	1.24491	0.622455	+	0.782655i	$0.286135\pi$
$558$	−4115.50	−0.312227
$559$	1723.08	0.130373
$560$	−29783.5	−2.24747
$561$	−2769.70	−0.208444
$562$	7208.18	0.541030
$563$	8646.41	0.647251	0.323626	−	0.946185i	$-0.395098\pi$
$563$	8646.41	0.647251	0.323626	+	0.946185i	$0.395098\pi$
$564$	−220.732	−0.0164796
$565$	−15152.6	−1.12827
$566$	10014.2	0.743690
$567$	2110.68	0.156332
$568$	−1973.65	−0.145797
$569$	13004.8	0.958154	0.479077	−	0.877773i	$-0.340971\pi$
$569$	13004.8	0.958154	0.479077	+	0.877773i	$0.340971\pi$
$570$	−309.472	−0.0227410
$571$	7898.99	0.578918	0.289459	−	0.957190i	$-0.406525\pi$
$571$	7898.99	0.578918	0.289459	+	0.957190i	$0.406525\pi$
$572$	183.630	0.0134230
$573$	686.101	0.0500214
$574$	−25152.8	−1.82902
$575$	18176.4	1.31827
$576$	4266.90	0.308659
$577$	−22841.1	−1.64799	−0.823994	−	0.566599i	$-0.808259\pi$
$577$	−22841.1	−1.64799	−0.823994	+	0.566599i	$0.808259\pi$
$578$	−6223.06	−0.447829
$579$	93.1518	0.00668611
$580$	−1246.09	−0.0892088
$581$	29773.0	2.12598
$582$	−12587.0	−0.896475
$583$	8312.64	0.590522
$584$	−4078.55	−0.288992
$585$	4811.34	0.340042
$586$	−267.338	−0.0188458
$587$	22823.0	1.60478	0.802391	−	0.596798i	$-0.203561\pi$
$587$	22823.0	1.60478	0.802391	+	0.596798i	$0.203561\pi$
$588$	−529.652	−0.0371471
$589$	−328.829	−0.0230036
$590$	9653.51	0.673608
$591$	1835.48	0.127752
$592$	−1072.29	−0.0744443
$593$	−6448.36	−0.446547	−0.223273	−	0.974756i	$-0.571674\pi$
$593$	−6448.36	−0.446547	−0.223273	+	0.974756i	$0.571674\pi$
$594$	867.191	0.0599011
$595$	36800.1	2.53556
$596$	298.476	0.0205135
$597$	−13041.1	−0.894030
$598$	−10663.0	−0.729171
$599$	−6927.14	−0.472513	−0.236257	−	0.971691i	$-0.575921\pi$
$599$	−6927.14	−0.472513	−0.236257	+	0.971691i	$0.575921\pi$
$600$	−10353.3	−0.704455
$601$	−12369.6	−0.839543	−0.419772	−	0.907630i	$-0.637890\pi$
$601$	−12369.6	−0.839543	−0.419772	+	0.907630i	$0.637890\pi$
$602$	−4126.40	−0.279368
$603$	−4284.05	−0.289320
$604$	26.9273	0.00181400
$605$	2036.00	0.136819
$606$	411.370	0.0275755
$607$	−8310.23	−0.555687	−0.277843	−	0.960626i	$-0.589620\pi$
$607$	−8310.23	−0.555687	−0.277843	+	0.960626i	$0.589620\pi$
$608$	−49.8478	−0.00332499
$609$	11017.8	0.733108
$610$	−2996.96	−0.198924
$611$	4448.91	0.294572
$612$	396.901	0.0262153
$613$	22706.2	1.49608	0.748039	−	0.663655i	$-0.230996\pi$
$613$	22706.2	1.49608	0.748039	+	0.663655i	$0.230996\pi$
$614$	14722.5	0.967674
$615$	−16688.0	−1.09419
$616$	6255.67	0.409169
$617$	−9540.26	−0.622490	−0.311245	−	0.950330i	$-0.600746\pi$
$617$	−9540.26	−0.622490	−0.311245	+	0.950330i	$0.600746\pi$
$618$	−2656.35	−0.172903
$619$	26840.7	1.74284	0.871422	−	0.490534i	$-0.163198\pi$
$619$	26840.7	1.74284	0.871422	+	0.490534i	$0.163198\pi$
$620$	1384.64	0.0896908
$621$	−3103.53	−0.200548
$622$	6098.91	0.393158
$623$	19534.8	1.25625
$624$	6474.36	0.415355
$625$	−10386.1	−0.664712
$626$	2903.83	0.185400
$627$	69.2887	0.00441327
$628$	387.414	0.0246171
$629$	1324.91	0.0839870
$630$	−11522.1	−0.728652
$631$	19645.1	1.23939	0.619697	−	0.784841i	$-0.287256\pi$
$631$	19645.1	1.23939	0.619697	+	0.784841i	$0.287256\pi$
$632$	29901.0	1.88196
$633$	5954.63	0.373895
$634$	−20081.7	−1.25796
$635$	−15239.5	−0.952377
$636$	−1191.21	−0.0742681
$637$	10675.3	0.664002
$638$	4526.75	0.280902
$639$	−813.896	−0.0503869
$640$	−26488.6	−1.63602
$641$	−6179.63	−0.380781	−0.190391	−	0.981708i	$-0.560975\pi$
$641$	−6179.63	−0.380781	−0.190391	+	0.981708i	$0.560975\pi$
$642$	−6178.63	−0.379831
$643$	10341.9	0.634284	0.317142	−	0.948378i	$-0.397277\pi$
$643$	10341.9	0.634284	0.317142	+	0.948378i	$0.397277\pi$
$644$	1573.80	0.0962990
$645$	−2737.72	−0.167128
$646$	514.548	0.0313384
$647$	−16037.6	−0.974502	−0.487251	−	0.873262i	$-0.662000\pi$
$647$	−16037.6	−0.974502	−0.487251	+	0.873262i	$0.662000\pi$
$648$	1767.78	0.107168
$649$	−2161.36	−0.130725
$650$	−14669.1	−0.885183
$651$	−12242.8	−0.737069
$652$	−272.344	−0.0163586
$653$	−16258.9	−0.974362	−0.487181	−	0.873301i	$-0.661975\pi$
$653$	−16258.9	−0.974362	−0.487181	+	0.873301i	$0.661975\pi$
$654$	−18595.5	−1.11183
$655$	−43399.8	−2.58896
$656$	−22456.2	−1.33653
$657$	−1681.91	−0.0998747
$658$	−10654.1	−0.631219
$659$	11739.2	0.693920	0.346960	−	0.937880i	$-0.387214\pi$
$659$	11739.2	0.693920	0.346960	+	0.937880i	$0.387214\pi$
$660$	−291.762	−0.0172073
$661$	30822.0	1.81367	0.906837	−	0.421482i	$-0.138490\pi$
$661$	30822.0	1.81367	0.906837	+	0.421482i	$0.138490\pi$
$662$	1724.65	0.101255
$663$	−7999.64	−0.468598
$664$	24936.2	1.45740
$665$	−920.616	−0.0536841
$666$	−414.830	−0.0241356
$667$	−16200.5	−0.940457
$668$	−2203.30	−0.127617
$669$	364.301	0.0210533
$670$	23386.4	1.34850
$671$	671.000	0.0386046
$672$	−1855.91	−0.106537
$673$	33007.5	1.89056	0.945280	−	0.326261i	$-0.105789\pi$
$673$	33007.5	1.89056	0.945280	+	0.326261i	$0.105789\pi$
$674$	−9785.18	−0.559215
$675$	−4269.51	−0.243457
$676$	−624.013	−0.0355037
$677$	−6370.92	−0.361675	−0.180838	−	0.983513i	$-0.557881\pi$
$677$	−6370.92	−0.361675	−0.180838	+	0.983513i	$0.557881\pi$
$678$	−7888.12	−0.446817
$679$	−37443.8	−2.11629
$680$	30821.7	1.73817
$681$	1360.68	0.0765658
$682$	−5030.05	−0.282420
$683$	−33642.4	−1.88476	−0.942380	−	0.334544i	$-0.891418\pi$
$683$	−33642.4	−1.88476	−0.942380	+	0.334544i	$0.891418\pi$
$684$	−9.92914	−0.000555044 0
$685$	−44138.0	−2.46193
$686$	532.053	0.0296121
$687$	−10286.2	−0.571243
$688$	−3684.01	−0.204145
$689$	24009.1	1.32754
$690$	16942.0	0.934741
$691$	−18136.2	−0.998458	−0.499229	−	0.866470i	$-0.666383\pi$
$691$	−18136.2	−0.998458	−0.499229	+	0.866470i	$0.666383\pi$
$692$	−433.746	−0.0238274
$693$	2579.72	0.141408
$694$	−3824.26	−0.209174
$695$	5471.37	0.298620
$696$	9227.86	0.502559
$697$	27746.6	1.50786
$698$	−22848.1	−1.23899
$699$	11817.3	0.639445
$700$	2165.07	0.116903
$701$	−17637.7	−0.950308	−0.475154	−	0.879903i	$-0.657608\pi$
$701$	−17637.7	−0.950308	−0.475154	+	0.879903i	$0.657608\pi$
$702$	2504.68	0.134662
$703$	−33.1449	−0.00177821
$704$	5215.10	0.279192
$705$	−7068.67	−0.377619
$706$	−5467.80	−0.291478
$707$	1223.74	0.0650969
$708$	309.725	0.0164409
$709$	7973.21	0.422341	0.211171	−	0.977449i	$-0.432272\pi$
$709$	7973.21	0.422341	0.211171	+	0.977449i	$0.432272\pi$
$710$	4443.02	0.234850
$711$	12330.6	0.650398
$712$	16361.2	0.861182
$713$	18001.7	0.945539
$714$	19157.4	1.00413
$715$	5880.52	0.307579
$716$	2033.06	0.106116
$717$	11029.5	0.574482
$718$	4429.56	0.230236
$719$	−2170.97	−0.112606	−0.0563028	−	0.998414i	$-0.517931\pi$
$719$	−2170.97	−0.112606	−0.0563028	+	0.998414i	$0.517931\pi$
$720$	−10286.8	−0.532454
$721$	−7902.11	−0.408169
$722$	20014.3	1.03165
$723$	18280.8	0.940344
$724$	−14.4842	−0.000743510 0
$725$	−22286.9	−1.14168
$726$	1059.90	0.0541826
$727$	−13192.5	−0.673017	−0.336509	−	0.941680i	$-0.609246\pi$
$727$	−13192.5	−0.673017	−0.336509	+	0.941680i	$0.609246\pi$
$728$	18068.1	0.919845
$729$	729.000	0.0370370
$730$	9181.48	0.465509
$731$	4551.92	0.230313
$732$	−96.1550	−0.00485518
$733$	140.406	0.00707506	0.00353753	−	0.999994i	$-0.498874\pi$
$733$	140.406	0.00707506	0.00353753	+	0.999994i	$0.498874\pi$
$734$	8303.69	0.417568
$735$	−16961.4	−0.851200
$736$	2728.92	0.136670
$737$	−5236.06	−0.261700
$738$	−8687.44	−0.433319
$739$	29891.0	1.48790	0.743949	−	0.668236i	$-0.232950\pi$
$739$	29891.0	1.48790	0.743949	+	0.668236i	$0.232950\pi$
$740$	139.567	0.00693323
$741$	200.124	0.00992139
$742$	−57496.5	−2.84469
$743$	−8947.48	−0.441792	−0.220896	−	0.975297i	$-0.570898\pi$
$743$	−8947.48	−0.441792	−0.220896	+	0.975297i	$0.570898\pi$
$744$	−10253.8	−0.505274
$745$	9558.31	0.470053
$746$	15710.4	0.771042
$747$	10283.2	0.503671
$748$	485.102	0.0237127
$749$	−18380.2	−0.896659
$750$	4883.11	0.237741
$751$	−11085.1	−0.538616	−0.269308	−	0.963054i	$-0.586795\pi$
$751$	−11085.1	−0.538616	−0.269308	+	0.963054i	$0.586795\pi$
$752$	−9511.92	−0.461256
$753$	−1967.13	−0.0952009
$754$	13074.5	0.631491
$755$	862.311	0.0415665
$756$	−369.677	−0.0177844
$757$	−33498.9	−1.60837	−0.804186	−	0.594378i	$-0.797398\pi$
$757$	−33498.9	−1.60837	−0.804186	+	0.594378i	$0.797398\pi$
$758$	−34097.0	−1.63385
$759$	−3793.21	−0.181403
$760$	−771.055	−0.0368015
$761$	57.7508	0.00275094	0.00137547	−	0.999999i	$-0.499562\pi$
$761$	57.7508	0.00275094	0.00137547	+	0.999999i	$0.499562\pi$
$762$	−7933.34	−0.377158
$763$	−55317.7	−2.62469
$764$	−120.168	−0.00569046
$765$	12710.3	0.600707
$766$	9547.93	0.450366
$767$	−6242.58	−0.293881
$768$	−2411.00	−0.113281
$769$	35340.9	1.65725	0.828625	−	0.559803i	$-0.189123\pi$
$769$	35340.9	1.65725	0.828625	+	0.559803i	$0.189123\pi$
$770$	−14082.5	−0.659091
$771$	−13155.7	−0.614516
$772$	−16.3151	−0.000760615 0
$773$	−16080.6	−0.748226	−0.374113	−	0.927383i	$-0.622053\pi$
$773$	−16080.6	−0.748226	−0.374113	+	0.927383i	$0.622053\pi$
$774$	−1425.20	−0.0661858
$775$	24764.9	1.14785
$776$	−31360.8	−1.45076
$777$	−1234.03	−0.0569765
$778$	11018.1	0.507737
$779$	−694.127	−0.0319252
$780$	−842.686	−0.0386833
$781$	−994.762	−0.0455767
$782$	−28168.9	−1.28813
$783$	3805.39	0.173683
$784$	−22824.1	−1.03973
$785$	12406.5	0.564083
$786$	−22593.0	−1.02528
$787$	34091.1	1.54411	0.772057	−	0.635553i	$-0.219228\pi$
$787$	34091.1	1.54411	0.772057	+	0.635553i	$0.219228\pi$
$788$	−321.477	−0.0145332
$789$	4002.82	0.180614
$790$	−67312.0	−3.03146
$791$	−23465.6	−1.05479
$792$	2160.62	0.0969374
$793$	1938.03	0.0867861
$794$	−3843.28	−0.171780
$795$	−38147.0	−1.70180
$796$	2284.09	0.101705
$797$	−11506.1	−0.511375	−0.255687	−	0.966760i	$-0.582302\pi$
$797$	−11506.1	−0.511375	−0.255687	+	0.966760i	$0.582302\pi$
$798$	−479.253	−0.0212599
$799$	11752.8	0.520382
$800$	3754.16	0.165912
$801$	6747.04	0.297622
$802$	36304.6	1.59846
$803$	−2055.67	−0.0903401
$804$	750.333	0.0329132
$805$	50399.1	2.20663
$806$	−14528.1	−0.634903
$807$	17195.0	0.750053
$808$	1024.94	0.0446251
$809$	−27248.8	−1.18420	−0.592100	−	0.805864i	$-0.701701\pi$
$809$	−27248.8	−1.18420	−0.592100	+	0.805864i	$0.701701\pi$
$810$	−3979.57	−0.172627
$811$	12667.8	0.548491	0.274245	−	0.961660i	$-0.411572\pi$
$811$	12667.8	0.548491	0.274245	+	0.961660i	$0.411572\pi$
$812$	−1929.72	−0.0833988
$813$	−16008.7	−0.690591
$814$	−507.014	−0.0218315
$815$	−8721.47	−0.374846
$816$	17103.5	0.733754
$817$	−113.874	−0.00487630
$818$	33620.7	1.43707
$819$	7450.92	0.317895
$820$	2922.84	0.124476
$821$	29630.3	1.25957	0.629783	−	0.776771i	$-0.283144\pi$
$821$	29630.3	1.25957	0.629783	+	0.776771i	$0.283144\pi$
$822$	−22977.3	−0.974970
$823$	36000.1	1.52477	0.762384	−	0.647125i	$-0.224029\pi$
$823$	36000.1	1.52477	0.762384	+	0.647125i	$0.224029\pi$
$824$	−6618.36	−0.279807
$825$	−5218.30	−0.220215
$826$	14949.6	0.629737
$827$	34347.5	1.44423	0.722116	−	0.691772i	$-0.243170\pi$
$827$	34347.5	1.44423	0.722116	+	0.691772i	$0.243170\pi$
$828$	543.571	0.0228145
$829$	−17768.5	−0.744421	−0.372210	−	0.928148i	$-0.621400\pi$
$829$	−17768.5	−0.744421	−0.372210	+	0.928148i	$0.621400\pi$
$830$	−56135.4	−2.34758
$831$	−13917.3	−0.580969
$832$	15062.6	0.627646
$833$	28201.2	1.17301
$834$	2848.28	0.118259
$835$	−70558.0	−2.92427
$836$	−12.1356	−0.000502056 0
$837$	−4228.49	−0.174621
$838$	42466.4	1.75057
$839$	−44979.6	−1.85086	−0.925428	−	0.378922i	$-0.876295\pi$
$839$	−44979.6	−1.85086	−0.925428	+	0.378922i	$0.876295\pi$
$840$	−28707.5	−1.17917
$841$	−4524.81	−0.185527
$842$	−26785.6	−1.09631
$843$	7406.08	0.302585
$844$	−1042.93	−0.0425345
$845$	−19983.2	−0.813543
$846$	−3679.80	−0.149544
$847$	3152.99	0.127908
$848$	−51332.3	−2.07873
$849$	10289.1	0.415928
$850$	−38751.8	−1.56374
$851$	1814.52	0.0730915
$852$	142.551	0.00573204
$853$	−26285.4	−1.05509	−0.527547	−	0.849526i	$-0.676888\pi$
$853$	−26285.4	−1.05509	−0.527547	+	0.849526i	$0.676888\pi$
$854$	−4641.15	−0.185968
$855$	−317.968	−0.0127185
$856$	−15394.2	−0.614676
$857$	−11636.0	−0.463801	−0.231901	−	0.972739i	$-0.574494\pi$
$857$	−11636.0	−0.463801	−0.231901	+	0.972739i	$0.574494\pi$
$858$	3061.28	0.121807
$859$	−19.5558	−0.000776760 0	−0.000388380	−	1.00000i	$-0.500124\pi$
$859$	−19.5558	−0.000776760 0	−0.000388380		1.00000i	$0.500124\pi$
$860$	479.501	0.0190126
$861$	−25843.4	−1.02293
$862$	40329.5	1.59354
$863$	−16311.6	−0.643399	−0.321699	−	0.946842i	$-0.604254\pi$
$863$	−16311.6	−0.643399	−0.321699	+	0.946842i	$0.604254\pi$
$864$	−641.005	−0.0252401
$865$	−13890.2	−0.545989
$866$	−9259.94	−0.363355
$867$	−6393.92	−0.250460
$868$	2144.27	0.0838494
$869$	15070.7	0.588307
$870$	−20773.4	−0.809523
$871$	−15123.1	−0.588322
$872$	−46331.0	−1.79927
$873$	−12932.6	−0.501377
$874$	704.691	0.0272729
$875$	14526.3	0.561231
$876$	294.580	0.0113618
$877$	−10651.9	−0.410135	−0.205067	−	0.978748i	$-0.565741\pi$
$877$	−10651.9	−0.410135	−0.205067	+	0.978748i	$0.565741\pi$
$878$	−38889.1	−1.49481
$879$	−274.678	−0.0105400
$880$	−12572.8	−0.481623
$881$	−7078.62	−0.270698	−0.135349	−	0.990798i	$-0.543216\pi$
$881$	−7078.62	−0.270698	−0.135349	+	0.990798i	$0.543216\pi$
$882$	−8829.77	−0.337090
$883$	−3503.55	−0.133527	−0.0667633	−	0.997769i	$-0.521267\pi$
$883$	−3503.55	−0.133527	−0.0667633	+	0.997769i	$0.521267\pi$
$884$	1401.10	0.0533079
$885$	9918.55	0.376733
$886$	27086.6	1.02708
$887$	210.584	0.00797150	0.00398575	−	0.999992i	$-0.498731\pi$
$887$	210.584	0.00797150	0.00398575	+	0.999992i	$0.498731\pi$
$888$	−1033.56	−0.0390584
$889$	−23600.1	−0.890351
$890$	−36831.7	−1.38719
$891$	891.000	0.0335013
$892$	−63.8057	−0.00239504
$893$	−294.016	−0.0110178
$894$	4975.85	0.186149
$895$	65106.3	2.43158
$896$	−41020.7	−1.52947
$897$	−10955.8	−0.407808
$898$	47429.1	1.76250
$899$	−22072.8	−0.818874
$900$	747.788	0.0276958
$901$	63425.7	2.34519
$902$	−10618.0	−0.391951
$903$	−4239.69	−0.156244
$904$	−19653.4	−0.723079
$905$	−463.839	−0.0170370
$906$	448.901	0.0164611
$907$	−2785.00	−0.101956	−0.0509782	−	0.998700i	$-0.516234\pi$
$907$	−2785.00	−0.101956	−0.0509782	+	0.998700i	$0.516234\pi$
$908$	−238.317	−0.00871017
$909$	422.664	0.0154223
$910$	−40674.2	−1.48169
$911$	16991.7	0.617959	0.308980	−	0.951069i	$-0.400013\pi$
$911$	16991.7	0.617959	0.308980	+	0.951069i	$0.400013\pi$
$912$	−427.873	−0.0155354
$913$	12568.4	0.455588
$914$	12847.3	0.464934
$915$	−3079.24	−0.111253
$916$	1801.59	0.0649849
$917$	−67209.7	−2.42035
$918$	6616.70	0.237891
$919$	26362.6	0.946271	0.473136	−	0.880990i	$-0.343122\pi$
$919$	26362.6	0.946271	0.473136	+	0.880990i	$0.343122\pi$
$920$	42211.4	1.51268
$921$	15126.7	0.541196
$922$	51240.9	1.83029
$923$	−2873.14	−0.102460
$924$	−451.827	−0.0160866
$925$	2496.22	0.0887301
$926$	9189.49	0.326118
$927$	−2729.28	−0.0967005
$928$	−3346.06	−0.118362
$929$	17819.9	0.629336	0.314668	−	0.949202i	$-0.398107\pi$
$929$	17819.9	0.629336	0.314668	+	0.949202i	$0.398107\pi$
$930$	23083.1	0.813897
$931$	−705.499	−0.0248355
$932$	−2069.75	−0.0727436
$933$	6266.36	0.219884
$934$	6143.76	0.215236
$935$	15534.8	0.543360
$936$	6240.46	0.217923
$937$	−3748.54	−0.130693	−0.0653465	−	0.997863i	$-0.520815\pi$
$937$	−3748.54	−0.130693	−0.0653465	+	0.997863i	$0.520815\pi$
$938$	36216.6	1.26067
$939$	2983.56	0.103690
$940$	1238.05	0.0429581
$941$	52310.3	1.81218	0.906092	−	0.423080i	$-0.139051\pi$
$941$	52310.3	1.81218	0.906092	+	0.423080i	$0.139051\pi$
$942$	6458.54	0.223387
$943$	38000.0	1.31225
$944$	13346.9	0.460173
$945$	−11838.4	−0.407518
$946$	−1741.91	−0.0598673
$947$	11731.2	0.402546	0.201273	−	0.979535i	$-0.435492\pi$
$947$	11731.2	0.402546	0.201273	+	0.979535i	$0.435492\pi$
$948$	−2159.65	−0.0739896
$949$	−5937.33	−0.203092
$950$	969.441	0.0331082
$951$	−20633.0	−0.703546
$952$	47731.0	1.62497
$953$	11772.7	0.400162	0.200081	−	0.979779i	$-0.435879\pi$
$953$	11772.7	0.400162	0.200081	+	0.979779i	$0.435879\pi$
$954$	−19858.5	−0.673945
$955$	−3848.22	−0.130393
$956$	−1931.77	−0.0653534
$957$	4651.03	0.157102
$958$	−13882.5	−0.468188
$959$	−68352.8	−2.30159
$960$	−23932.3	−0.804595
$961$	−5264.11	−0.176701
$962$	−1464.39	−0.0490789
$963$	−6348.27	−0.212430
$964$	−3201.80	−0.106974
$965$	−522.472	−0.0174290
$966$	26236.7	0.873863
$967$	−18737.7	−0.623127	−0.311564	−	0.950225i	$-0.600853\pi$
$967$	−18737.7	−0.623127	−0.311564	+	0.950225i	$0.600853\pi$
$968$	2640.76	0.0876832
$969$	528.675	0.0175268
$970$	70598.4	2.33688
$971$	−4427.40	−0.146325	−0.0731627	−	0.997320i	$-0.523309\pi$
$971$	−4427.40	−0.146325	−0.0731627	+	0.997320i	$0.523309\pi$
$972$	−127.681	−0.00421335
$973$	8473.06	0.279171
$974$	51287.1	1.68721
$975$	−15071.8	−0.495062
$976$	−4143.57	−0.135894
$977$	46984.2	1.53855	0.769273	−	0.638921i	$-0.220619\pi$
$977$	46984.2	1.53855	0.769273	+	0.638921i	$0.220619\pi$
$978$	−4540.21	−0.148446
$979$	8246.38	0.269209
$980$	2970.72	0.0968330
$981$	−19106.0	−0.621822
$982$	−2770.49	−0.0900304
$983$	4779.73	0.155086	0.0775430	−	0.996989i	$-0.475292\pi$
$983$	4779.73	0.155086	0.0775430	+	0.996989i	$0.475292\pi$
$984$	−21644.9	−0.701235
$985$	−10294.9	−0.333018
$986$	34539.2	1.11557
$987$	−10946.7	−0.353025
$988$	−35.0509	−0.00112866
$989$	6234.01	0.200435
$990$	−4863.92	−0.156147
$991$	22314.0	0.715265	0.357633	−	0.933862i	$-0.383584\pi$
$991$	22314.0	0.715265	0.357633	+	0.933862i	$0.383584\pi$
$992$	3718.08	0.119001
$993$	1772.00	0.0566292
$994$	6880.53	0.219555
$995$	73145.1	2.33051
$996$	−1801.06	−0.0572979
$997$	43404.3	1.37877	0.689383	−	0.724397i	$-0.257882\pi$
$997$	43404.3	1.37877	0.689383	+	0.724397i	$0.257882\pi$
$998$	−61500.4	−1.95066
$999$	−426.219	−0.0134985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.g.1.12	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.g.1.12	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.91984 q^{2} -3.00000 q^{3} +0.525437 q^{4} +16.8265 q^{5} +8.75951 q^{6} +26.0578 q^{7} +21.8245 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.91984 q^{2} -3.00000 q^{3} +0.525437 q^{4} +16.8265 q^{5} +8.75951 q^{6} +26.0578 q^{7} +21.8245 q^{8} +9.00000 q^{9} -49.1305 q^{10} +11.0000 q^{11} -1.57631 q^{12} +31.7710 q^{13} -76.0844 q^{14} -50.4794 q^{15} -67.9274 q^{16} +83.9304 q^{17} -26.2785 q^{18} -2.09966 q^{19} +8.84126 q^{20} -78.1733 q^{21} -32.1182 q^{22} +114.946 q^{23} -65.4735 q^{24} +158.130 q^{25} -92.7659 q^{26} -27.0000 q^{27} +13.6917 q^{28} -140.940 q^{29} +147.392 q^{30} +156.611 q^{31} +23.7409 q^{32} -33.0000 q^{33} -245.063 q^{34} +438.460 q^{35} +4.72894 q^{36} +15.7859 q^{37} +6.13065 q^{38} -95.3129 q^{39} +367.229 q^{40} +330.591 q^{41} +228.253 q^{42} +54.2345 q^{43} +5.77981 q^{44} +151.438 q^{45} -335.622 q^{46} +140.031 q^{47} +203.782 q^{48} +336.007 q^{49} -461.714 q^{50} -251.791 q^{51} +16.6936 q^{52} +755.694 q^{53} +78.8355 q^{54} +185.091 q^{55} +568.697 q^{56} +6.29897 q^{57} +411.523 q^{58} -196.487 q^{59} -26.5238 q^{60} +61.0000 q^{61} -457.277 q^{62} +234.520 q^{63} +474.100 q^{64} +534.593 q^{65} +96.3546 q^{66} -476.005 q^{67} +44.1001 q^{68} -344.837 q^{69} -1280.23 q^{70} -90.4329 q^{71} +196.420 q^{72} -186.879 q^{73} -46.0922 q^{74} -474.391 q^{75} -1.10324 q^{76} +286.635 q^{77} +278.298 q^{78} +1370.06 q^{79} -1142.98 q^{80} +81.0000 q^{81} -965.271 q^{82} +1142.58 q^{83} -41.0752 q^{84} +1412.25 q^{85} -158.356 q^{86} +422.821 q^{87} +240.069 q^{88} +749.671 q^{89} -442.175 q^{90} +827.880 q^{91} +60.3967 q^{92} -469.832 q^{93} -408.867 q^{94} -35.3298 q^{95} -71.2228 q^{96} -1436.96 q^{97} -981.085 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * q^99

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