LMFDB - Embedded newform 2013.4.a.h.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)

$f(q)$	$=$	$q-2.16141 q^{2} +3.00000 q^{3} -3.32830 q^{4} +7.38660 q^{5} -6.48423 q^{6} -25.4500 q^{7} +24.4851 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.16141 q^{2} +3.00000 q^{3} -3.32830 q^{4} +7.38660 q^{5} -6.48423 q^{6} -25.4500 q^{7} +24.4851 q^{8} +9.00000 q^{9} -15.9655 q^{10} -11.0000 q^{11} -9.98490 q^{12} -88.8923 q^{13} +55.0079 q^{14} +22.1598 q^{15} -26.2960 q^{16} -27.5502 q^{17} -19.4527 q^{18} -90.6570 q^{19} -24.5848 q^{20} -76.3500 q^{21} +23.7755 q^{22} +5.00950 q^{23} +73.4554 q^{24} -70.4382 q^{25} +192.133 q^{26} +27.0000 q^{27} +84.7052 q^{28} -298.548 q^{29} -47.8964 q^{30} +54.0675 q^{31} -139.044 q^{32} -33.0000 q^{33} +59.5473 q^{34} -187.989 q^{35} -29.9547 q^{36} +349.435 q^{37} +195.947 q^{38} -266.677 q^{39} +180.862 q^{40} -200.616 q^{41} +165.024 q^{42} +124.039 q^{43} +36.6113 q^{44} +66.4794 q^{45} -10.8276 q^{46} -549.341 q^{47} -78.8880 q^{48} +304.702 q^{49} +152.246 q^{50} -82.6506 q^{51} +295.860 q^{52} +625.714 q^{53} -58.3581 q^{54} -81.2526 q^{55} -623.146 q^{56} -271.971 q^{57} +645.285 q^{58} +244.947 q^{59} -73.7545 q^{60} +61.0000 q^{61} -116.862 q^{62} -229.050 q^{63} +510.900 q^{64} -656.612 q^{65} +71.3266 q^{66} -36.2603 q^{67} +91.6954 q^{68} +15.0285 q^{69} +406.321 q^{70} -384.394 q^{71} +220.366 q^{72} -880.519 q^{73} -755.273 q^{74} -211.315 q^{75} +301.734 q^{76} +279.950 q^{77} +576.399 q^{78} +955.144 q^{79} -194.238 q^{80} +81.0000 q^{81} +433.614 q^{82} +266.848 q^{83} +254.116 q^{84} -203.502 q^{85} -268.100 q^{86} -895.644 q^{87} -269.336 q^{88} +86.8500 q^{89} -143.689 q^{90} +2262.31 q^{91} -16.6731 q^{92} +162.202 q^{93} +1187.35 q^{94} -669.647 q^{95} -417.133 q^{96} +1200.36 q^{97} -658.586 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * 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 $

$2$	−2.16141	−0.764174	−0.382087	−	0.924126i	$-0.624795\pi$
$2$	−2.16141	−0.764174	−0.382087	+	0.924126i	$0.624795\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−3.32830	−0.416038
$5$	7.38660	0.660677	0.330339	−	0.943862i	$-0.392837\pi$
$5$	7.38660	0.660677	0.330339	+	0.943862i	$0.392837\pi$
$6$	−6.48423	−0.441196
$7$	−25.4500	−1.37417	−0.687085	−	0.726577i	$-0.741110\pi$
$7$	−25.4500	−1.37417	−0.687085	+	0.726577i	$0.741110\pi$
$8$	24.4851	1.08210
$9$	9.00000	0.333333
$10$	−15.9655	−0.504873
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−9.98490	−0.240199
$13$	−88.8923	−1.89648	−0.948242	−	0.317548i	$-0.897141\pi$
$13$	−88.8923	−1.89648	−0.948242	+	0.317548i	$0.897141\pi$
$14$	55.0079	1.05011
$15$	22.1598	0.381442
$16$	−26.2960	−0.410875
$17$	−27.5502	−0.393053	−0.196527	−	0.980498i	$-0.562966\pi$
$17$	−27.5502	−0.393053	−0.196527	+	0.980498i	$0.562966\pi$
$18$	−19.4527	−0.254725
$19$	−90.6570	−1.09464	−0.547319	−	0.836924i	$-0.684352\pi$
$19$	−90.6570	−1.09464	−0.547319	+	0.836924i	$0.684352\pi$
$20$	−24.5848	−0.274867
$21$	−76.3500	−0.793377
$22$	23.7755	0.230407
$23$	5.00950	0.0454153	0.0227077	−	0.999742i	$-0.492771\pi$
$23$	5.00950	0.0454153	0.0227077	+	0.999742i	$0.492771\pi$
$24$	73.4554	0.624750
$25$	−70.4382	−0.563505
$26$	192.133	1.44924
$27$	27.0000	0.192450
$28$	84.7052	0.571706
$29$	−298.548	−1.91169	−0.955844	−	0.293873i	$-0.905056\pi$
$29$	−298.548	−1.91169	−0.955844	+	0.293873i	$0.905056\pi$
$30$	−47.8964	−0.291488
$31$	54.0675	0.313252	0.156626	−	0.987658i	$-0.449938\pi$
$31$	54.0675	0.313252	0.156626	+	0.987658i	$0.449938\pi$
$32$	−139.044	−0.768119
$33$	−33.0000	−0.174078
$34$	59.5473	0.300361
$35$	−187.989	−0.907883
$36$	−29.9547	−0.138679
$37$	349.435	1.55261	0.776307	−	0.630354i	$-0.217090\pi$
$37$	349.435	1.55261	0.776307	+	0.630354i	$0.217090\pi$
$38$	195.947	0.836495
$39$	−266.677	−1.09494
$40$	180.862	0.714919
$41$	−200.616	−0.764170	−0.382085	−	0.924127i	$-0.624794\pi$
$41$	−200.616	−0.764170	−0.382085	+	0.924127i	$0.624794\pi$
$42$	165.024	0.606279
$43$	124.039	0.439903	0.219952	−	0.975511i	$-0.429410\pi$
$43$	124.039	0.439903	0.219952	+	0.975511i	$0.429410\pi$
$44$	36.6113	0.125440
$45$	66.4794	0.220226
$46$	−10.8276	−0.0347052
$47$	−549.341	−1.70489	−0.852443	−	0.522820i	$-0.824880\pi$
$47$	−549.341	−1.70489	−0.852443	+	0.522820i	$0.824880\pi$
$48$	−78.8880	−0.237219
$49$	304.702	0.888343
$50$	152.246	0.430616
$51$	−82.6506	−0.226929
$52$	295.860	0.789009
$53$	625.714	1.62167	0.810834	−	0.585276i	$-0.199014\pi$
$53$	625.714	1.62167	0.810834	+	0.585276i	$0.199014\pi$
$54$	−58.3581	−0.147065
$55$	−81.2526	−0.199202
$56$	−623.146	−1.48699
$57$	−271.971	−0.631990
$58$	645.285	1.46086
$59$	244.947	0.540498	0.270249	−	0.962790i	$-0.412894\pi$
$59$	244.947	0.540498	0.270249	+	0.962790i	$0.412894\pi$
$60$	−73.7545	−0.158694
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−116.862	−0.239379
$63$	−229.050	−0.458057
$64$	510.900	0.997852
$65$	−656.612	−1.25296
$66$	71.3266	0.133026
$67$	−36.2603	−0.0661179	−0.0330590	−	0.999453i	$-0.510525\pi$
$67$	−36.2603	−0.0661179	−0.0330590	+	0.999453i	$0.510525\pi$
$68$	91.6954	0.163525
$69$	15.0285	0.0262205
$70$	406.321	0.693781
$71$	−384.394	−0.642523	−0.321261	−	0.946991i	$-0.604107\pi$
$71$	−384.394	−0.642523	−0.321261	+	0.946991i	$0.604107\pi$
$72$	220.366	0.360700
$73$	−880.519	−1.41174	−0.705870	−	0.708342i	$-0.749444\pi$
$73$	−880.519	−1.41174	−0.705870	+	0.708342i	$0.749444\pi$
$74$	−755.273	−1.18647
$75$	−211.315	−0.325340
$76$	301.734	0.455411
$77$	279.950	0.414328
$78$	576.399	0.836722
$79$	955.144	1.36028	0.680140	−	0.733082i	$-0.261919\pi$
$79$	955.144	1.36028	0.680140	+	0.733082i	$0.261919\pi$
$80$	−194.238	−0.271456
$81$	81.0000	0.111111
$82$	433.614	0.583959
$83$	266.848	0.352896	0.176448	−	0.984310i	$-0.443539\pi$
$83$	266.848	0.352896	0.176448	+	0.984310i	$0.443539\pi$
$84$	254.116	0.330075
$85$	−203.502	−0.259681
$86$	−268.100	−0.336163
$87$	−895.644	−1.10371
$88$	−269.336	−0.326265
$89$	86.8500	0.103439	0.0517196	−	0.998662i	$-0.483530\pi$
$89$	86.8500	0.103439	0.0517196	+	0.998662i	$0.483530\pi$
$90$	−143.689	−0.168291
$91$	2262.31	2.60609
$92$	−16.6731	−0.0188945
$93$	162.202	0.180856
$94$	1187.35	1.30283
$95$	−669.647	−0.723203
$96$	−417.133	−0.443474
$97$	1200.36	1.25647	0.628236	−	0.778023i	$-0.283777\pi$
$97$	1200.36	1.25647	0.628236	+	0.778023i	$0.283777\pi$
$98$	−658.586	−0.678849
$99$	−99.0000	−0.100504
$100$	234.439	0.234439
$101$	122.997	0.121175	0.0605876	−	0.998163i	$-0.480703\pi$
$101$	122.997	0.121175	0.0605876	+	0.998163i	$0.480703\pi$
$102$	178.642	0.173414
$103$	164.742	0.157597	0.0787985	−	0.996891i	$-0.474892\pi$
$103$	164.742	0.157597	0.0787985	+	0.996891i	$0.474892\pi$
$104$	−2176.54	−2.05218
$105$	−563.966	−0.524166
$106$	−1352.42	−1.23924
$107$	−376.239	−0.339929	−0.169964	−	0.985450i	$-0.554365\pi$
$107$	−376.239	−0.339929	−0.169964	+	0.985450i	$0.554365\pi$
$108$	−89.8641	−0.0800665
$109$	−1606.37	−1.41158	−0.705789	−	0.708422i	$-0.749407\pi$
$109$	−1606.37	−1.41158	−0.705789	+	0.708422i	$0.749407\pi$
$110$	175.620	0.152225
$111$	1048.30	0.896403
$112$	669.233	0.564612
$113$	−392.048	−0.326379	−0.163189	−	0.986595i	$-0.552178\pi$
$113$	−392.048	−0.326379	−0.163189	+	0.986595i	$0.552178\pi$
$114$	587.841	0.482951
$115$	37.0031	0.0300049
$116$	993.658	0.795334
$117$	−800.031	−0.632161
$118$	−529.432	−0.413035
$119$	701.152	0.540122
$120$	542.585	0.412758
$121$	121.000	0.0909091
$122$	−131.846	−0.0978425
$123$	−601.848	−0.441194
$124$	−179.953	−0.130325
$125$	−1443.62	−1.03297
$126$	495.071	0.350035
$127$	−2818.46	−1.96928	−0.984638	−	0.174606i	$-0.944135\pi$
$127$	−2818.46	−1.96928	−0.984638	+	0.174606i	$0.944135\pi$
$128$	8.08989	0.00558634
$129$	372.118	0.253978
$130$	1419.21	0.957483
$131$	1665.49	1.11080	0.555398	−	0.831585i	$-0.312566\pi$
$131$	1665.49	1.11080	0.555398	+	0.831585i	$0.312566\pi$
$132$	109.834	0.0724229
$133$	2307.22	1.50422
$134$	78.3734	0.0505256
$135$	199.438	0.127147
$136$	−674.570	−0.425323
$137$	510.331	0.318252	0.159126	−	0.987258i	$-0.449132\pi$
$137$	510.331	0.318252	0.159126	+	0.987258i	$0.449132\pi$
$138$	−32.4828	−0.0200371
$139$	−176.180	−0.107507	−0.0537533	−	0.998554i	$-0.517118\pi$
$139$	−176.180	−0.107507	−0.0537533	+	0.998554i	$0.517118\pi$
$140$	625.683	0.377713
$141$	−1648.02	−0.984317
$142$	830.833	0.491000
$143$	977.816	0.571812
$144$	−236.664	−0.136958
$145$	−2205.25	−1.26301
$146$	1903.16	1.07881
$147$	914.105	0.512885
$148$	−1163.02	−0.645946
$149$	2187.96	1.20299	0.601493	−	0.798878i	$-0.294573\pi$
$149$	2187.96	1.20299	0.601493	+	0.798878i	$0.294573\pi$
$150$	456.738	0.248617
$151$	1198.40	0.645860	0.322930	−	0.946423i	$-0.395332\pi$
$151$	1198.40	0.645860	0.322930	+	0.946423i	$0.395332\pi$
$152$	−2219.75	−1.18451
$153$	−247.952	−0.131018
$154$	−605.087	−0.316619
$155$	399.375	0.206958
$156$	887.581	0.455534
$157$	910.614	0.462898	0.231449	−	0.972847i	$-0.425653\pi$
$157$	910.614	0.462898	0.231449	+	0.972847i	$0.425653\pi$
$158$	−2064.46	−1.03949
$159$	1877.14	0.936270
$160$	−1027.07	−0.507479
$161$	−127.492	−0.0624084
$162$	−175.074	−0.0849083
$163$	−2338.28	−1.12361	−0.561805	−	0.827269i	$-0.689893\pi$
$163$	−2338.28	−1.12361	−0.561805	+	0.827269i	$0.689893\pi$
$164$	667.711	0.317924
$165$	−243.758	−0.115009
$166$	−576.768	−0.269674
$167$	502.954	0.233052	0.116526	−	0.993188i	$-0.462824\pi$
$167$	502.954	0.233052	0.116526	+	0.993188i	$0.462824\pi$
$168$	−1869.44	−0.858513
$169$	5704.85	2.59665
$170$	439.852	0.198442
$171$	−815.913	−0.364880
$172$	−412.841	−0.183016
$173$	448.172	0.196959	0.0984794	−	0.995139i	$-0.468602\pi$
$173$	448.172	0.196959	0.0984794	+	0.995139i	$0.468602\pi$
$174$	1935.86	0.843430
$175$	1792.65	0.774352
$176$	289.256	0.123884
$177$	734.841	0.312057
$178$	−187.719	−0.0790455
$179$	−2025.60	−0.845814	−0.422907	−	0.906173i	$-0.638990\pi$
$179$	−2025.60	−0.845814	−0.422907	+	0.906173i	$0.638990\pi$
$180$	−221.263	−0.0916222
$181$	−2941.60	−1.20800	−0.603999	−	0.796985i	$-0.706427\pi$
$181$	−2941.60	−1.20800	−0.603999	+	0.796985i	$0.706427\pi$
$182$	−4889.78	−1.99151
$183$	183.000	0.0739221
$184$	122.658	0.0491439
$185$	2581.14	1.02578
$186$	−350.586	−0.138206
$187$	303.052	0.118510
$188$	1828.37	0.709297
$189$	−687.150	−0.264459
$190$	1447.38	0.552653
$191$	4634.17	1.75559	0.877793	−	0.479039i	$-0.159015\pi$
$191$	4634.17	1.75559	0.877793	+	0.479039i	$0.159015\pi$
$192$	1532.70	0.576110
$193$	3418.86	1.27510	0.637552	−	0.770407i	$-0.279947\pi$
$193$	3418.86	1.27510	0.637552	+	0.770407i	$0.279947\pi$
$194$	−2594.47	−0.960164
$195$	−1969.84	−0.723399
$196$	−1014.14	−0.369584
$197$	−1103.45	−0.399073	−0.199537	−	0.979890i	$-0.563944\pi$
$197$	−1103.45	−0.399073	−0.199537	+	0.979890i	$0.563944\pi$
$198$	213.980	0.0768024
$199$	602.822	0.214738	0.107369	−	0.994219i	$-0.465757\pi$
$199$	602.822	0.214738	0.107369	+	0.994219i	$0.465757\pi$
$200$	−1724.69	−0.609769
$201$	−108.781	−0.0381732
$202$	−265.848	−0.0925990
$203$	7598.04	2.62699
$204$	275.086	0.0944112
$205$	−1481.87	−0.504870
$206$	−356.075	−0.120432
$207$	45.0855	0.0151384
$208$	2337.51	0.779218
$209$	997.227	0.330046
$210$	1218.96	0.400555
$211$	−1383.22	−0.451302	−0.225651	−	0.974208i	$-0.572451\pi$
$211$	−1383.22	−0.451302	−0.225651	+	0.974208i	$0.572451\pi$
$212$	−2082.56	−0.674675
$213$	−1153.18	−0.370961
$214$	813.207	0.259765
$215$	916.230	0.290634
$216$	661.098	0.208250
$217$	−1376.02	−0.430461
$218$	3472.02	1.07869
$219$	−2641.56	−0.815068
$220$	270.433	0.0828754
$221$	2449.00	0.745420
$222$	−2265.82	−0.685008
$223$	−5062.26	−1.52015	−0.760076	−	0.649834i	$-0.774838\pi$
$223$	−5062.26	−1.52015	−0.760076	+	0.649834i	$0.774838\pi$
$224$	3538.68	1.05553
$225$	−633.944	−0.187835
$226$	847.378	0.249410
$227$	−6006.54	−1.75625	−0.878123	−	0.478435i	$-0.841204\pi$
$227$	−6006.54	−1.75625	−0.878123	+	0.478435i	$0.841204\pi$
$228$	905.201	0.262932
$229$	2280.76	0.658153	0.329076	−	0.944303i	$-0.393263\pi$
$229$	2280.76	0.658153	0.329076	+	0.944303i	$0.393263\pi$
$230$	−79.9790	−0.0229290
$231$	839.850	0.239212
$232$	−7309.98	−2.06864
$233$	−3483.93	−0.979569	−0.489785	−	0.871843i	$-0.662925\pi$
$233$	−3483.93	−0.979569	−0.489785	+	0.871843i	$0.662925\pi$
$234$	1729.20	0.483082
$235$	−4057.76	−1.12638
$236$	−815.258	−0.224868
$237$	2865.43	0.785358
$238$	−1515.48	−0.412747
$239$	−2997.07	−0.811148	−0.405574	−	0.914062i	$-0.632928\pi$
$239$	−2997.07	−0.811148	−0.405574	+	0.914062i	$0.632928\pi$
$240$	−582.714	−0.156725
$241$	6448.00	1.72345	0.861727	−	0.507372i	$-0.169383\pi$
$241$	6448.00	1.72345	0.861727	+	0.507372i	$0.169383\pi$
$242$	−261.531	−0.0694704
$243$	243.000	0.0641500
$244$	−203.026	−0.0532682
$245$	2250.71	0.586908
$246$	1300.84	0.337149
$247$	8058.71	2.07597
$248$	1323.85	0.338970
$249$	800.544	0.203745
$250$	3120.26	0.789371
$251$	−3736.35	−0.939587	−0.469793	−	0.882776i	$-0.655672\pi$
$251$	−3736.35	−0.939587	−0.469793	+	0.882776i	$0.655672\pi$
$252$	762.347	0.190569
$253$	−55.1045	−0.0136932
$254$	6091.86	1.50487
$255$	−610.507	−0.149927
$256$	−4104.69	−1.00212
$257$	−478.492	−0.116138	−0.0580691	−	0.998313i	$-0.518494\pi$
$257$	−478.492	−0.116138	−0.0580691	+	0.998313i	$0.518494\pi$
$258$	−804.301	−0.194084
$259$	−8893.11	−2.13356
$260$	2185.40	0.521280
$261$	−2686.93	−0.637230
$262$	−3599.80	−0.848841
$263$	−2145.52	−0.503037	−0.251518	−	0.967852i	$-0.580930\pi$
$263$	−2145.52	−0.503037	−0.251518	+	0.967852i	$0.580930\pi$
$264$	−808.009	−0.188369
$265$	4621.89	1.07140
$266$	−4986.85	−1.14949
$267$	260.550	0.0597206
$268$	120.685	0.0275075
$269$	−5401.44	−1.22428	−0.612141	−	0.790749i	$-0.709691\pi$
$269$	−5401.44	−1.22428	−0.612141	+	0.790749i	$0.709691\pi$
$270$	−431.068	−0.0971628
$271$	−2008.55	−0.450224	−0.225112	−	0.974333i	$-0.572275\pi$
$271$	−2008.55	−0.450224	−0.225112	+	0.974333i	$0.572275\pi$
$272$	724.460	0.161496
$273$	6786.93	1.50463
$274$	−1103.03	−0.243200
$275$	774.820	0.169903
$276$	−50.0193	−0.0109087
$277$	9136.66	1.98184	0.990919	−	0.134464i	$-0.0429312\pi$
$277$	9136.66	1.98184	0.990919	+	0.134464i	$0.0429312\pi$
$278$	380.798	0.0821538
$279$	486.607	0.104417
$280$	−4602.93	−0.982420
$281$	2745.54	0.582865	0.291432	−	0.956591i	$-0.405868\pi$
$281$	2745.54	0.582865	0.291432	+	0.956591i	$0.405868\pi$
$282$	3562.06	0.752189
$283$	4985.87	1.04728	0.523638	−	0.851941i	$-0.324574\pi$
$283$	4985.87	1.04728	0.523638	+	0.851941i	$0.324574\pi$
$284$	1279.38	0.267314
$285$	−2008.94	−0.417541
$286$	−2113.46	−0.436964
$287$	5105.68	1.05010
$288$	−1251.40	−0.256040
$289$	−4153.99	−0.845509
$290$	4766.46	0.965159
$291$	3601.07	0.725425
$292$	2930.63	0.587337
$293$	2752.42	0.548799	0.274399	−	0.961616i	$-0.411521\pi$
$293$	2752.42	0.548799	0.274399	+	0.961616i	$0.411521\pi$
$294$	−1975.76	−0.391934
$295$	1809.33	0.357095
$296$	8555.96	1.68008
$297$	−297.000	−0.0580259
$298$	−4729.09	−0.919291
$299$	−445.306	−0.0861294
$300$	703.318	0.135354
$301$	−3156.80	−0.604502
$302$	−2590.25	−0.493549
$303$	368.992	0.0699606
$304$	2383.92	0.449760
$305$	450.582	0.0845911
$306$	535.926	0.100120
$307$	8543.55	1.58829	0.794147	−	0.607726i	$-0.207918\pi$
$307$	8543.55	1.58829	0.794147	+	0.607726i	$0.207918\pi$
$308$	−931.757	−0.172376
$309$	494.225	0.0909887
$310$	−863.213	−0.158152
$311$	2941.87	0.536393	0.268197	−	0.963364i	$-0.413572\pi$
$311$	2941.87	0.536393	0.268197	+	0.963364i	$0.413572\pi$
$312$	−6529.62	−1.18483
$313$	1249.72	0.225681	0.112840	−	0.993613i	$-0.464005\pi$
$313$	1249.72	0.225681	0.112840	+	0.993613i	$0.464005\pi$
$314$	−1968.21	−0.353734
$315$	−1691.90	−0.302628
$316$	−3179.01	−0.565927
$317$	−3164.93	−0.560758	−0.280379	−	0.959889i	$-0.590460\pi$
$317$	−3164.93	−0.560758	−0.280379	+	0.959889i	$0.590460\pi$
$318$	−4057.27	−0.715474
$319$	3284.03	0.576396
$320$	3773.81	0.659258
$321$	−1128.72	−0.196258
$322$	275.562	0.0476909
$323$	2497.62	0.430251
$324$	−269.592	−0.0462264
$325$	6261.41	1.06868
$326$	5053.99	0.858635
$327$	−4819.10	−0.814975
$328$	−4912.11	−0.826908
$329$	13980.7	2.34280
$330$	526.861	0.0878870
$331$	8235.26	1.36753	0.683763	−	0.729704i	$-0.260342\pi$
$331$	8235.26	1.36753	0.683763	+	0.729704i	$0.260342\pi$
$332$	−888.150	−0.146818
$333$	3144.91	0.517538
$334$	−1087.09	−0.178093
$335$	−267.840	−0.0436826
$336$	2007.70	0.325979
$337$	−1813.91	−0.293205	−0.146602	−	0.989195i	$-0.546834\pi$
$337$	−1813.91	−0.293205	−0.146602	+	0.989195i	$0.546834\pi$
$338$	−12330.5	−1.98430
$339$	−1176.14	−0.188435
$340$	677.317	0.108037
$341$	−594.742	−0.0944490
$342$	1763.52	0.278832
$343$	974.690	0.153435
$344$	3037.12	0.476019
$345$	111.009	0.0173233
$346$	−968.683	−0.150511
$347$	5537.51	0.856683	0.428341	−	0.903617i	$-0.359098\pi$
$347$	5537.51	0.856683	0.428341	+	0.903617i	$0.359098\pi$
$348$	2980.97	0.459187
$349$	−670.347	−0.102816	−0.0514081	−	0.998678i	$-0.516371\pi$
$349$	−670.347	−0.102816	−0.0514081	+	0.998678i	$0.516371\pi$
$350$	−3874.66	−0.591740
$351$	−2400.09	−0.364979
$352$	1529.49	0.231597
$353$	7391.32	1.11445	0.557225	−	0.830362i	$-0.311866\pi$
$353$	7391.32	1.11445	0.557225	+	0.830362i	$0.311866\pi$
$354$	−1588.29	−0.238466
$355$	−2839.36	−0.424500
$356$	−289.063	−0.0430346
$357$	2103.46	0.311840
$358$	4378.16	0.646350
$359$	12745.0	1.87369	0.936846	−	0.349743i	$-0.113731\pi$
$359$	12745.0	1.87369	0.936846	+	0.349743i	$0.113731\pi$
$360$	1627.76	0.238306
$361$	1359.69	0.198234
$362$	6358.01	0.923121
$363$	363.000	0.0524864
$364$	−7529.64	−1.08423
$365$	−6504.04	−0.932704
$366$	−395.538	−0.0564894
$367$	−12203.2	−1.73570	−0.867851	−	0.496824i	$-0.834500\pi$
$367$	−12203.2	−1.73570	−0.867851	+	0.496824i	$0.834500\pi$
$368$	−131.730	−0.0186600
$369$	−1805.55	−0.254723
$370$	−5578.90	−0.783873
$371$	−15924.4	−2.22845
$372$	−539.859	−0.0752429
$373$	−5664.20	−0.786277	−0.393138	−	0.919479i	$-0.628611\pi$
$373$	−5664.20	−0.786277	−0.393138	+	0.919479i	$0.628611\pi$
$374$	−655.021	−0.0905623
$375$	−4330.87	−0.596387
$376$	−13450.7	−1.84486
$377$	26538.6	3.62549
$378$	1485.21	0.202093
$379$	−246.432	−0.0333994	−0.0166997	−	0.999861i	$-0.505316\pi$
$379$	−246.432	−0.0333994	−0.0166997	+	0.999861i	$0.505316\pi$
$380$	2228.79	0.300880
$381$	−8455.39	−1.13696
$382$	−10016.4	−1.34157
$383$	−10457.0	−1.39511	−0.697555	−	0.716532i	$-0.745729\pi$
$383$	−10457.0	−1.39511	−0.697555	+	0.716532i	$0.745729\pi$
$384$	24.2697	0.00322528
$385$	2067.88	0.273737
$386$	−7389.57	−0.974402
$387$	1116.36	0.146634
$388$	−3995.15	−0.522740
$389$	−5349.34	−0.697229	−0.348615	−	0.937266i	$-0.613348\pi$
$389$	−5349.34	−0.697229	−0.348615	+	0.937266i	$0.613348\pi$
$390$	4257.62	0.552803
$391$	−138.013	−0.0178506
$392$	7460.66	0.961276
$393$	4996.46	0.641318
$394$	2385.01	0.304962
$395$	7055.26	0.898706
$396$	329.502	0.0418134
$397$	13369.4	1.69015	0.845077	−	0.534645i	$-0.179555\pi$
$397$	13369.4	1.69015	0.845077	+	0.534645i	$0.179555\pi$
$398$	−1302.95	−0.164098
$399$	6921.66	0.868462
$400$	1852.24	0.231530
$401$	6593.84	0.821149	0.410575	−	0.911827i	$-0.365328\pi$
$401$	6593.84	0.821149	0.410575	+	0.911827i	$0.365328\pi$
$402$	235.120	0.0291710
$403$	−4806.18	−0.594077
$404$	−409.373	−0.0504135
$405$	598.314	0.0734086
$406$	−16422.5	−2.00747
$407$	−3843.78	−0.468131
$408$	−2023.71	−0.245560
$409$	−3752.97	−0.453723	−0.226861	−	0.973927i	$-0.572846\pi$
$409$	−3752.97	−0.453723	−0.226861	+	0.973927i	$0.572846\pi$
$410$	3202.93	0.385809
$411$	1530.99	0.183743
$412$	−548.310	−0.0655663
$413$	−6233.90	−0.742737
$414$	−97.4483	−0.0115684
$415$	1971.10	0.233150
$416$	12360.0	1.45673
$417$	−528.541	−0.0620690
$418$	−2155.42	−0.252213
$419$	−4390.95	−0.511961	−0.255981	−	0.966682i	$-0.582398\pi$
$419$	−4390.95	−0.511961	−0.255981	+	0.966682i	$0.582398\pi$
$420$	1877.05	0.218073
$421$	−8115.75	−0.939519	−0.469759	−	0.882794i	$-0.655659\pi$
$421$	−8115.75	−0.939519	−0.469759	+	0.882794i	$0.655659\pi$
$422$	2989.71	0.344874
$423$	−4944.07	−0.568295
$424$	15320.7	1.75481
$425$	1940.59	0.221488
$426$	2492.50	0.283479
$427$	−1552.45	−0.175944
$428$	1252.24	0.141423
$429$	2933.45	0.330136
$430$	−1980.35	−0.222095
$431$	9803.79	1.09567	0.547833	−	0.836588i	$-0.315453\pi$
$431$	9803.79	1.09567	0.547833	+	0.836588i	$0.315453\pi$
$432$	−709.992	−0.0790730
$433$	7594.16	0.842845	0.421423	−	0.906864i	$-0.361531\pi$
$433$	7594.16	0.842845	0.421423	+	0.906864i	$0.361531\pi$
$434$	2974.14	0.328947
$435$	−6615.76	−0.729199
$436$	5346.47	0.587270
$437$	−454.146	−0.0497134
$438$	5709.49	0.622854
$439$	13594.0	1.47791	0.738957	−	0.673752i	$-0.235319\pi$
$439$	13594.0	1.47791	0.738957	+	0.673752i	$0.235319\pi$
$440$	−1989.48	−0.215556
$441$	2742.32	0.296114
$442$	−5293.30	−0.569630
$443$	6318.39	0.677643	0.338822	−	0.940851i	$-0.389972\pi$
$443$	6318.39	0.677643	0.338822	+	0.940851i	$0.389972\pi$
$444$	−3489.07	−0.372937
$445$	641.526	0.0683399
$446$	10941.6	1.16166
$447$	6563.89	0.694544
$448$	−13002.4	−1.37122
$449$	−12073.0	−1.26895	−0.634477	−	0.772942i	$-0.718784\pi$
$449$	−12073.0	−1.26895	−0.634477	+	0.772942i	$0.718784\pi$
$450$	1370.21	0.143539
$451$	2206.78	0.230406
$452$	1304.85	0.135786
$453$	3595.21	0.372887
$454$	12982.6	1.34208
$455$	16710.8	1.72179
$456$	−6659.24	−0.683876
$457$	1888.98	0.193354	0.0966771	−	0.995316i	$-0.469179\pi$
$457$	1888.98	0.193354	0.0966771	+	0.995316i	$0.469179\pi$
$458$	−4929.67	−0.502944
$459$	−743.856	−0.0756432
$460$	−123.158	−0.0124832
$461$	9364.33	0.946074	0.473037	−	0.881043i	$-0.343158\pi$
$461$	9364.33	0.946074	0.473037	+	0.881043i	$0.343158\pi$
$462$	−1815.26	−0.182800
$463$	15741.1	1.58002	0.790011	−	0.613093i	$-0.210075\pi$
$463$	15741.1	1.58002	0.790011	+	0.613093i	$0.210075\pi$
$464$	7850.62	0.785465
$465$	1198.12	0.119487
$466$	7530.20	0.748562
$467$	−6918.15	−0.685512	−0.342756	−	0.939425i	$-0.611360\pi$
$467$	−6918.15	−0.685512	−0.342756	+	0.939425i	$0.611360\pi$
$468$	2662.74	0.263003
$469$	922.824	0.0908573
$470$	8770.49	0.860750
$471$	2731.84	0.267254
$472$	5997.56	0.584873
$473$	−1364.43	−0.132636
$474$	−6193.38	−0.600150
$475$	6385.71	0.616835
$476$	−2333.65	−0.224711
$477$	5631.42	0.540556
$478$	6477.90	0.619858
$479$	−1520.86	−0.145072	−0.0725362	−	0.997366i	$-0.523109\pi$
$479$	−1520.86	−0.145072	−0.0725362	+	0.997366i	$0.523109\pi$
$480$	−3081.20	−0.292993
$481$	−31062.1	−2.94451
$482$	−13936.8	−1.31702
$483$	−382.475	−0.0360315
$484$	−402.724	−0.0378216
$485$	8866.55	0.830123
$486$	−525.223	−0.0490218
$487$	13205.7	1.22876	0.614380	−	0.789010i	$-0.289406\pi$
$487$	13205.7	1.22876	0.614380	+	0.789010i	$0.289406\pi$
$488$	1493.59	0.138549
$489$	−7014.85	−0.648717
$490$	−4864.71	−0.448500
$491$	14581.5	1.34023	0.670116	−	0.742256i	$-0.266244\pi$
$491$	14581.5	1.34023	0.670116	+	0.742256i	$0.266244\pi$
$492$	2003.13	0.183553
$493$	8225.06	0.751396
$494$	−17418.2	−1.58640
$495$	−731.273	−0.0664006
$496$	−1421.76	−0.128707
$497$	9782.81	0.882936
$498$	−1730.30	−0.155696
$499$	5124.27	0.459707	0.229853	−	0.973225i	$-0.426175\pi$
$499$	5124.27	0.459707	0.229853	+	0.973225i	$0.426175\pi$
$500$	4804.81	0.429755
$501$	1508.86	0.134553
$502$	8075.79	0.718008
$503$	16964.6	1.50381	0.751903	−	0.659274i	$-0.229136\pi$
$503$	16964.6	1.50381	0.751903	+	0.659274i	$0.229136\pi$
$504$	−5608.31	−0.495663
$505$	908.533	0.0800578
$506$	119.103	0.0104640
$507$	17114.5	1.49918
$508$	9380.69	0.819293
$509$	16949.2	1.47596	0.737978	−	0.674825i	$-0.235781\pi$
$509$	16949.2	1.47596	0.737978	+	0.674825i	$0.235781\pi$
$510$	1319.56	0.114570
$511$	22409.2	1.93997
$512$	8807.20	0.760209
$513$	−2447.74	−0.210663
$514$	1034.22	0.0887499
$515$	1216.88	0.104121
$516$	−1238.52	−0.105665
$517$	6042.75	0.514043
$518$	19221.7	1.63041
$519$	1344.52	0.113714
$520$	−16077.2	−1.35583
$521$	−2837.25	−0.238584	−0.119292	−	0.992859i	$-0.538062\pi$
$521$	−2837.25	−0.238584	−0.119292	+	0.992859i	$0.538062\pi$
$522$	5807.57	0.486954
$523$	−487.625	−0.0407693	−0.0203847	−	0.999792i	$-0.506489\pi$
$523$	−487.625	−0.0407693	−0.0203847	+	0.999792i	$0.506489\pi$
$524$	−5543.24	−0.462133
$525$	5377.95	0.447073
$526$	4637.36	0.384408
$527$	−1489.57	−0.123125
$528$	867.768	0.0715242
$529$	−12141.9	−0.997937
$530$	−9989.82	−0.818736
$531$	2204.52	0.180166
$532$	−7679.12	−0.625812
$533$	17833.2	1.44924
$534$	−563.156	−0.0456370
$535$	−2779.12	−0.224583
$536$	−887.838	−0.0715462
$537$	−6076.81	−0.488331
$538$	11674.7	0.935565
$539$	−3351.72	−0.267846
$540$	−663.790	−0.0528981
$541$	−23498.2	−1.86741	−0.933703	−	0.358049i	$-0.883442\pi$
$541$	−23498.2	−1.86741	−0.933703	+	0.358049i	$0.883442\pi$
$542$	4341.31	0.344050
$543$	−8824.81	−0.697438
$544$	3830.70	0.301912
$545$	−11865.6	−0.932598
$546$	−14669.3	−1.14980
$547$	286.117	0.0223647	0.0111823	−	0.999937i	$-0.496440\pi$
$547$	286.117	0.0223647	0.0111823	+	0.999937i	$0.496440\pi$
$548$	−1698.53	−0.132405
$549$	549.000	0.0426790
$550$	−1674.70	−0.129836
$551$	27065.5	2.09261
$552$	367.974	0.0283732
$553$	−24308.4	−1.86926
$554$	−19748.1	−1.51447
$555$	7743.41	0.592233
$556$	586.381	0.0447268
$557$	−11150.9	−0.848258	−0.424129	−	0.905602i	$-0.639420\pi$
$557$	−11150.9	−0.848258	−0.424129	+	0.905602i	$0.639420\pi$
$558$	−1051.76	−0.0797930
$559$	−11026.2	−0.834270
$560$	4943.35	0.373027
$561$	909.157	0.0684218
$562$	−5934.23	−0.445410
$563$	14165.1	1.06037	0.530184	−	0.847883i	$-0.322123\pi$
$563$	14165.1	1.06037	0.530184	+	0.847883i	$0.322123\pi$
$564$	5485.12	0.409513
$565$	−2895.90	−0.215631
$566$	−10776.5	−0.800302
$567$	−2061.45	−0.152686
$568$	−9411.92	−0.695274
$569$	19416.0	1.43051	0.715254	−	0.698864i	$-0.246311\pi$
$569$	19416.0	1.43051	0.715254	+	0.698864i	$0.246311\pi$
$570$	4342.14	0.319074
$571$	−10112.2	−0.741123	−0.370562	−	0.928808i	$-0.620835\pi$
$571$	−10112.2	−0.741123	−0.370562	+	0.928808i	$0.620835\pi$
$572$	−3254.46	−0.237895
$573$	13902.5	1.01359
$574$	−11035.5	−0.802459
$575$	−352.860	−0.0255918
$576$	4598.10	0.332617
$577$	−12908.4	−0.931344	−0.465672	−	0.884957i	$-0.654187\pi$
$577$	−12908.4	−0.931344	−0.465672	+	0.884957i	$0.654187\pi$
$578$	8978.47	0.646116
$579$	10256.6	0.736182
$580$	7339.75	0.525459
$581$	−6791.27	−0.484939
$582$	−7783.40	−0.554351
$583$	−6882.85	−0.488951
$584$	−21559.6	−1.52764
$585$	−5909.51	−0.417655
$586$	−5949.11	−0.419378
$587$	−14839.3	−1.04341	−0.521707	−	0.853125i	$-0.674705\pi$
$587$	−14839.3	−1.04341	−0.521707	+	0.853125i	$0.674705\pi$
$588$	−3042.42	−0.213380
$589$	−4901.59	−0.342898
$590$	−3910.70	−0.272883
$591$	−3310.34	−0.230405
$592$	−9188.74	−0.637931
$593$	−630.776	−0.0436811	−0.0218405	−	0.999761i	$-0.506953\pi$
$593$	−630.776	−0.0436811	−0.0218405	+	0.999761i	$0.506953\pi$
$594$	641.939	0.0443419
$595$	5179.13	0.356846
$596$	−7282.20	−0.500487
$597$	1808.47	0.123979
$598$	962.489	0.0658179
$599$	−22822.1	−1.55674	−0.778369	−	0.627807i	$-0.783953\pi$
$599$	−22822.1	−1.55674	−0.778369	+	0.627807i	$0.783953\pi$
$600$	−5174.06	−0.352050
$601$	−10474.2	−0.710903	−0.355451	−	0.934695i	$-0.615673\pi$
$601$	−10474.2	−0.710903	−0.355451	+	0.934695i	$0.615673\pi$
$602$	6823.15	0.461945
$603$	−326.343	−0.0220393
$604$	−3988.65	−0.268702
$605$	893.778	0.0600616
$606$	−797.544	−0.0534621
$607$	14539.0	0.972192	0.486096	−	0.873905i	$-0.338421\pi$
$607$	14539.0	0.972192	0.486096	+	0.873905i	$0.338421\pi$
$608$	12605.4	0.840813
$609$	22794.1	1.51669
$610$	−973.894	−0.0646423
$611$	48832.2	3.23329
$612$	825.258	0.0545083
$613$	9320.93	0.614142	0.307071	−	0.951687i	$-0.400651\pi$
$613$	9320.93	0.614142	0.307071	+	0.951687i	$0.400651\pi$
$614$	−18466.1	−1.21373
$615$	−4445.61	−0.291487
$616$	6854.60	0.448344
$617$	−9827.22	−0.641214	−0.320607	−	0.947212i	$-0.603887\pi$
$617$	−9827.22	−0.641214	−0.320607	+	0.947212i	$0.603887\pi$
$618$	−1068.22	−0.0695312
$619$	−21651.2	−1.40587	−0.702937	−	0.711252i	$-0.748129\pi$
$619$	−21651.2	−1.40587	−0.702937	+	0.711252i	$0.748129\pi$
$620$	−1329.24	−0.0861025
$621$	135.256	0.00874018
$622$	−6358.60	−0.409898
$623$	−2210.33	−0.142143
$624$	7012.54	0.449882
$625$	−1858.69	−0.118956
$626$	−2701.15	−0.172460
$627$	2991.68	0.190552
$628$	−3030.80	−0.192583
$629$	−9627.01	−0.610261
$630$	3656.89	0.231260
$631$	−3688.53	−0.232707	−0.116353	−	0.993208i	$-0.537121\pi$
$631$	−3688.53	−0.232707	−0.116353	+	0.993208i	$0.537121\pi$
$632$	23386.8	1.47196
$633$	−4149.66	−0.260560
$634$	6840.72	0.428517
$635$	−20818.9	−1.30106
$636$	−6247.69	−0.389524
$637$	−27085.6	−1.68473
$638$	−7098.14	−0.440467
$639$	−3459.54	−0.214174
$640$	59.7567	0.00369077
$641$	22569.3	1.39069	0.695346	−	0.718675i	$-0.255251\pi$
$641$	22569.3	1.39069	0.695346	+	0.718675i	$0.255251\pi$
$642$	2439.62	0.149975
$643$	16105.0	0.987745	0.493872	−	0.869534i	$-0.335581\pi$
$643$	16105.0	0.987745	0.493872	+	0.869534i	$0.335581\pi$
$644$	424.331	0.0259642
$645$	2748.69	0.167798
$646$	−5398.38	−0.328787
$647$	−4216.23	−0.256193	−0.128097	−	0.991762i	$-0.540887\pi$
$647$	−4216.23	−0.256193	−0.128097	+	0.991762i	$0.540887\pi$
$648$	1983.29	0.120233
$649$	−2694.42	−0.162966
$650$	−13533.5	−0.816657
$651$	−4128.05	−0.248527
$652$	7782.51	0.467464
$653$	11997.8	0.719006	0.359503	−	0.933144i	$-0.382946\pi$
$653$	11997.8	0.719006	0.359503	+	0.933144i	$0.382946\pi$
$654$	10416.1	0.622783
$655$	12302.3	0.733877
$656$	5275.40	0.313979
$657$	−7924.67	−0.470580
$658$	−30218.1	−1.79031
$659$	−6677.36	−0.394709	−0.197354	−	0.980332i	$-0.563235\pi$
$659$	−6677.36	−0.394709	−0.197354	+	0.980332i	$0.563235\pi$
$660$	811.299	0.0478481
$661$	26058.0	1.53334	0.766672	−	0.642040i	$-0.221912\pi$
$661$	26058.0	1.53334	0.766672	+	0.642040i	$0.221912\pi$
$662$	−17799.8	−1.04503
$663$	7347.01	0.430368
$664$	6533.80	0.381868
$665$	17042.5	0.993804
$666$	−6797.45	−0.395489
$667$	−1495.58	−0.0868200
$668$	−1673.98	−0.0969585
$669$	−15186.8	−0.877660
$670$	578.913	0.0333811
$671$	−671.000	−0.0386046
$672$	10616.0	0.609409
$673$	−17635.6	−1.01011	−0.505054	−	0.863088i	$-0.668527\pi$
$673$	−17635.6	−1.01011	−0.505054	+	0.863088i	$0.668527\pi$
$674$	3920.61	0.224060
$675$	−1901.83	−0.108447
$676$	−18987.4	−1.08031
$677$	−20177.3	−1.14546	−0.572731	−	0.819744i	$-0.694116\pi$
$677$	−20177.3	−1.14546	−0.572731	+	0.819744i	$0.694116\pi$
$678$	2542.13	0.143997
$679$	−30549.1	−1.72661
$680$	−4982.78	−0.281001
$681$	−18019.6	−1.01397
$682$	1285.48	0.0721755
$683$	10328.8	0.578655	0.289327	−	0.957230i	$-0.406568\pi$
$683$	10328.8	0.578655	0.289327	+	0.957230i	$0.406568\pi$
$684$	2715.60	0.151804
$685$	3769.61	0.210262
$686$	−2106.71	−0.117251
$687$	6842.29	0.379985
$688$	−3261.74	−0.180745
$689$	−55621.1	−3.07547
$690$	−239.937	−0.0132380
$691$	22361.3	1.23106	0.615530	−	0.788113i	$-0.288942\pi$
$691$	22361.3	1.23106	0.615530	+	0.788113i	$0.288942\pi$
$692$	−1491.65	−0.0819422
$693$	2519.55	0.138109
$694$	−11968.8	−0.654655
$695$	−1301.37	−0.0710272
$696$	−21930.0	−1.19433
$697$	5527.02	0.300360
$698$	1448.90	0.0785695
$699$	−10451.8	−0.565555
$700$	−5966.48	−0.322160
$701$	−23307.2	−1.25578	−0.627889	−	0.778303i	$-0.716081\pi$
$701$	−23307.2	−1.25578	−0.627889	+	0.778303i	$0.716081\pi$
$702$	5187.59	0.278907
$703$	−31678.7	−1.69955
$704$	−5619.90	−0.300864
$705$	−12173.3	−0.650316
$706$	−15975.7	−0.851633
$707$	−3130.28	−0.166515
$708$	−2445.77	−0.129827
$709$	−33592.8	−1.77942	−0.889708	−	0.456530i	$-0.849092\pi$
$709$	−33592.8	−1.77942	−0.889708	+	0.456530i	$0.849092\pi$
$710$	6137.03	0.324392
$711$	8596.30	0.453427
$712$	2126.53	0.111931
$713$	270.851	0.0142264
$714$	−4546.44	−0.238300
$715$	7222.73	0.377783
$716$	6741.82	0.351891
$717$	−8991.21	−0.468317
$718$	−27547.2	−1.43183
$719$	11333.3	0.587843	0.293921	−	0.955830i	$-0.405040\pi$
$719$	11333.3	0.587843	0.293921	+	0.955830i	$0.405040\pi$
$720$	−1748.14	−0.0904853
$721$	−4192.68	−0.216565
$722$	−2938.84	−0.151485
$723$	19344.0	0.995037
$724$	9790.54	0.502573
$725$	21029.2	1.07725
$726$	−784.592	−0.0401088
$727$	−9592.61	−0.489368	−0.244684	−	0.969603i	$-0.578684\pi$
$727$	−9592.61	−0.489368	−0.244684	+	0.969603i	$0.578684\pi$
$728$	55392.9	2.82005
$729$	729.000	0.0370370
$730$	14057.9	0.712748
$731$	−3417.31	−0.172906
$732$	−609.079	−0.0307544
$733$	22793.5	1.14857	0.574283	−	0.818657i	$-0.305281\pi$
$733$	22793.5	1.14857	0.574283	+	0.818657i	$0.305281\pi$
$734$	26376.2	1.32638
$735$	6752.13	0.338852
$736$	−696.543	−0.0348844
$737$	398.863	0.0199353
$738$	3902.53	0.194653
$739$	32100.8	1.59790	0.798949	−	0.601399i	$-0.205390\pi$
$739$	32100.8	1.59790	0.798949	+	0.601399i	$0.205390\pi$
$740$	−8590.79	−0.426762
$741$	24176.1	1.19856
$742$	34419.2	1.70292
$743$	20116.8	0.993288	0.496644	−	0.867954i	$-0.334566\pi$
$743$	20116.8	0.993288	0.496644	+	0.867954i	$0.334566\pi$
$744$	3971.55	0.195704
$745$	16161.6	0.794785
$746$	12242.7	0.600853
$747$	2401.63	0.117632
$748$	−1008.65	−0.0493046
$749$	9575.27	0.467120
$750$	9360.79	0.455744
$751$	−26692.0	−1.29694	−0.648471	−	0.761239i	$-0.724591\pi$
$751$	−26692.0	−1.29694	−0.648471	+	0.761239i	$0.724591\pi$
$752$	14445.5	0.700495
$753$	−11209.0	−0.542471
$754$	−57360.9	−2.77050
$755$	8852.13	0.426705
$756$	2287.04	0.110025
$757$	−36802.3	−1.76698	−0.883489	−	0.468452i	$-0.844812\pi$
$757$	−36802.3	−1.76698	−0.883489	+	0.468452i	$0.844812\pi$
$758$	532.642	0.0255230
$759$	−165.313	−0.00790579
$760$	−16396.4	−0.782578
$761$	−26460.1	−1.26042	−0.630210	−	0.776425i	$-0.717031\pi$
$761$	−26460.1	−1.26042	−0.630210	+	0.776425i	$0.717031\pi$
$762$	18275.6	0.868838
$763$	40882.0	1.93975
$764$	−15423.9	−0.730390
$765$	−1831.52	−0.0865605
$766$	22601.8	1.06611
$767$	−21773.9	−1.02505
$768$	−12314.1	−0.578575
$769$	−19920.9	−0.934158	−0.467079	−	0.884216i	$-0.654694\pi$
$769$	−19920.9	−0.934158	−0.467079	+	0.884216i	$0.654694\pi$
$770$	−4469.53	−0.209183
$771$	−1435.48	−0.0670525
$772$	−11379.0	−0.530491
$773$	1829.40	0.0851215	0.0425607	−	0.999094i	$-0.486448\pi$
$773$	1829.40	0.0851215	0.0425607	+	0.999094i	$0.486448\pi$
$774$	−2412.90	−0.112054
$775$	−3808.42	−0.176519
$776$	29390.9	1.35963
$777$	−26679.3	−1.23181
$778$	11562.1	0.532805
$779$	18187.3	0.836490
$780$	6556.20	0.300961
$781$	4228.33	0.193728
$782$	298.302	0.0136410
$783$	−8060.80	−0.367905
$784$	−8012.44	−0.364998
$785$	6726.34	0.305826
$786$	−10799.4	−0.490079
$787$	24012.4	1.08761	0.543804	−	0.839212i	$-0.316983\pi$
$787$	24012.4	1.08761	0.543804	+	0.839212i	$0.316983\pi$
$788$	3672.61	0.166029
$789$	−6436.57	−0.290429
$790$	−15249.3	−0.686768
$791$	9977.62	0.448500
$792$	−2424.03	−0.108755
$793$	−5422.43	−0.242820
$794$	−28896.8	−1.29157
$795$	13865.7	0.618573
$796$	−2006.37	−0.0893392
$797$	−14945.6	−0.664243	−0.332122	−	0.943237i	$-0.607764\pi$
$797$	−14945.6	−0.664243	−0.332122	+	0.943237i	$0.607764\pi$
$798$	−14960.5	−0.663656
$799$	15134.5	0.670111
$800$	9794.04	0.432839
$801$	781.650	0.0344797
$802$	−14252.0	−0.627501
$803$	9685.71	0.425655
$804$	362.056	0.0158815
$805$	−941.729	−0.0412318
$806$	10388.1	0.453979
$807$	−16204.3	−0.706839
$808$	3011.61	0.131124
$809$	2034.05	0.0883972	0.0441986	−	0.999023i	$-0.485927\pi$
$809$	2034.05	0.0883972	0.0441986	+	0.999023i	$0.485927\pi$
$810$	−1293.20	−0.0560970
$811$	−9883.49	−0.427936	−0.213968	−	0.976841i	$-0.568639\pi$
$811$	−9883.49	−0.427936	−0.213968	+	0.976841i	$0.568639\pi$
$812$	−25288.6	−1.09292
$813$	−6025.65	−0.259937
$814$	8308.00	0.357734
$815$	−17272.0	−0.742344
$816$	2173.38	0.0932397
$817$	−11245.0	−0.481535
$818$	8111.72	0.346723
$819$	20360.8	0.868697
$820$	4932.11	0.210045
$821$	−24315.0	−1.03362	−0.516808	−	0.856102i	$-0.672880\pi$
$821$	−24315.0	−1.03362	−0.516808	+	0.856102i	$0.672880\pi$
$822$	−3309.10	−0.140412
$823$	8209.96	0.347729	0.173865	−	0.984770i	$-0.444374\pi$
$823$	8209.96	0.347729	0.173865	+	0.984770i	$0.444374\pi$
$824$	4033.72	0.170536
$825$	2324.46	0.0980937
$826$	13474.0	0.567580
$827$	−32617.7	−1.37150	−0.685749	−	0.727838i	$-0.740525\pi$
$827$	−32617.7	−1.37150	−0.685749	+	0.727838i	$0.740525\pi$
$828$	−150.058	−0.00629816
$829$	−27714.9	−1.16113	−0.580565	−	0.814214i	$-0.697168\pi$
$829$	−27714.9	−1.16113	−0.580565	+	0.814214i	$0.697168\pi$
$830$	−4260.35	−0.178167
$831$	27410.0	1.14421
$832$	−45415.1	−1.89241
$833$	−8394.60	−0.349166
$834$	1142.39	0.0474315
$835$	3715.12	0.153972
$836$	−3319.07	−0.137312
$837$	1459.82	0.0602853
$838$	9490.65	0.391228
$839$	−31193.9	−1.28359	−0.641795	−	0.766876i	$-0.721810\pi$
$839$	−31193.9	−1.28359	−0.641795	+	0.766876i	$0.721810\pi$
$840$	−13808.8	−0.567200
$841$	64741.9	2.65455
$842$	17541.5	0.717956
$843$	8236.61	0.336517
$844$	4603.77	0.187759
$845$	42139.4	1.71555
$846$	10686.2	0.434277
$847$	−3079.45	−0.124925
$848$	−16453.8	−0.666303
$849$	14957.6	0.604645
$850$	−4194.41	−0.169255
$851$	1750.49	0.0705125
$852$	3838.13	0.154334
$853$	−11051.9	−0.443622	−0.221811	−	0.975090i	$-0.571197\pi$
$853$	−11051.9	−0.443622	−0.221811	+	0.975090i	$0.571197\pi$
$854$	3355.48	0.134452
$855$	−6026.82	−0.241068
$856$	−9212.25	−0.367837
$857$	2911.54	0.116052	0.0580259	−	0.998315i	$-0.481519\pi$
$857$	2911.54	0.116052	0.0580259	+	0.998315i	$0.481519\pi$
$858$	−6340.39	−0.252281
$859$	29231.4	1.16107	0.580537	−	0.814234i	$-0.302842\pi$
$859$	29231.4	1.16107	0.580537	+	0.814234i	$0.302842\pi$
$860$	−3049.49	−0.120915
$861$	15317.0	0.606275
$862$	−21190.0	−0.837280
$863$	−77.7632	−0.00306731	−0.00153366	−	0.999999i	$-0.500488\pi$
$863$	−77.7632	−0.00306731	−0.00153366	+	0.999999i	$0.500488\pi$
$864$	−3754.20	−0.147825
$865$	3310.46	0.130126
$866$	−16414.1	−0.644081
$867$	−12462.0	−0.488155
$868$	4579.80	0.179088
$869$	−10506.6	−0.410140
$870$	14299.4	0.557235
$871$	3223.26	0.125392
$872$	−39332.1	−1.52747
$873$	10803.2	0.418824
$874$	981.596	0.0379897
$875$	36740.2	1.41948
$876$	8791.90	0.339099
$877$	−6325.58	−0.243557	−0.121779	−	0.992557i	$-0.538860\pi$
$877$	−6325.58	−0.243557	−0.121779	+	0.992557i	$0.538860\pi$
$878$	−29382.1	−1.12938
$879$	8257.26	0.316849
$880$	2136.62	0.0818470
$881$	−35867.5	−1.37163	−0.685815	−	0.727776i	$-0.740554\pi$
$881$	−35867.5	−1.37163	−0.685815	+	0.727776i	$0.740554\pi$
$882$	−5927.27	−0.226283
$883$	−14792.9	−0.563784	−0.281892	−	0.959446i	$-0.590962\pi$
$883$	−14792.9	−0.563784	−0.281892	+	0.959446i	$0.590962\pi$
$884$	−8151.02	−0.310123
$885$	5427.98	0.206169
$886$	−13656.6	−0.517838
$887$	36802.6	1.39313	0.696567	−	0.717491i	$-0.254710\pi$
$887$	36802.6	1.39313	0.696567	+	0.717491i	$0.254710\pi$
$888$	25667.9	0.969997
$889$	71729.8	2.70612
$890$	−1386.60	−0.0522236
$891$	−891.000	−0.0335013
$892$	16848.7	0.632440
$893$	49801.6	1.86623
$894$	−14187.3	−0.530753
$895$	−14962.3	−0.558810
$896$	−205.887	−0.00767658
$897$	−1335.92	−0.0497269
$898$	26094.7	0.969701
$899$	−16141.7	−0.598840
$900$	2109.96	0.0781465
$901$	−17238.5	−0.637402
$902$	−4769.75	−0.176070
$903$	−9470.41	−0.349009
$904$	−9599.35	−0.353174
$905$	−21728.4	−0.798097
$906$	−7770.74	−0.284951
$907$	−37471.2	−1.37179	−0.685894	−	0.727702i	$-0.740589\pi$
$907$	−37471.2	−1.37179	−0.685894	+	0.727702i	$0.740589\pi$
$908$	19991.6	0.730664
$909$	1106.98	0.0403918
$910$	−36118.8	−1.31574
$911$	−46301.1	−1.68389	−0.841945	−	0.539564i	$-0.818589\pi$
$911$	−46301.1	−1.68389	−0.841945	+	0.539564i	$0.818589\pi$
$912$	7151.75	0.259669
$913$	−2935.33	−0.106402
$914$	−4082.87	−0.147756
$915$	1351.75	0.0488387
$916$	−7591.06	−0.273816
$917$	−42386.6	−1.52642
$918$	1607.78	0.0578046
$919$	−24003.9	−0.861606	−0.430803	−	0.902446i	$-0.641770\pi$
$919$	−24003.9	−0.861606	−0.430803	+	0.902446i	$0.641770\pi$
$920$	906.026	0.0324683
$921$	25630.7	0.917002
$922$	−20240.2	−0.722966
$923$	34169.6	1.21853
$924$	−2795.27	−0.0995213
$925$	−24613.6	−0.874907
$926$	−34022.9	−1.20741
$927$	1482.68	0.0525323
$928$	41511.4	1.46841
$929$	41240.3	1.45646	0.728229	−	0.685334i	$-0.240344\pi$
$929$	41240.3	1.45646	0.728229	+	0.685334i	$0.240344\pi$
$930$	−2589.64	−0.0913093
$931$	−27623.3	−0.972415
$932$	11595.6	0.407538
$933$	8825.62	0.309687
$934$	14953.0	0.523850
$935$	2238.53	0.0782969
$936$	−19588.9	−0.684062
$937$	−5749.94	−0.200472	−0.100236	−	0.994964i	$-0.531960\pi$
$937$	−5749.94	−0.200472	−0.100236	+	0.994964i	$0.531960\pi$
$938$	−1994.60	−0.0694308
$939$	3749.15	0.130297
$940$	13505.5	0.468616
$941$	−37475.1	−1.29825	−0.649125	−	0.760682i	$-0.724865\pi$
$941$	−37475.1	−1.29825	−0.649125	+	0.760682i	$0.724865\pi$
$942$	−5904.63	−0.204229
$943$	−1004.99	−0.0347050
$944$	−6441.13	−0.222077
$945$	−5075.70	−0.174722
$946$	2949.10	0.101357
$947$	−16416.9	−0.563335	−0.281667	−	0.959512i	$-0.590887\pi$
$947$	−16416.9	−0.563335	−0.281667	+	0.959512i	$0.590887\pi$
$948$	−9537.02	−0.326738
$949$	78271.4	2.67734
$950$	−13802.2	−0.471369
$951$	−9494.80	−0.323754
$952$	17167.8	0.584466
$953$	19169.7	0.651593	0.325797	−	0.945440i	$-0.394368\pi$
$953$	19169.7	0.651593	0.325797	+	0.945440i	$0.394368\pi$
$954$	−12171.8	−0.413079
$955$	34230.8	1.15988
$956$	9975.15	0.337468
$957$	9852.08	0.332782
$958$	3287.20	0.110861
$959$	−12987.9	−0.437332
$960$	11321.4	0.380623
$961$	−26867.7	−0.901873
$962$	67137.9	2.25012
$963$	−3386.15	−0.113310
$964$	−21460.9	−0.717022
$965$	25253.8	0.842432
$966$	826.686	0.0275343
$967$	−22199.8	−0.738261	−0.369131	−	0.929377i	$-0.620345\pi$
$967$	−22199.8	−0.738261	−0.369131	+	0.929377i	$0.620345\pi$
$968$	2962.70	0.0983727
$969$	7492.86	0.248406
$970$	−19164.3	−0.634358
$971$	−23817.3	−0.787163	−0.393581	−	0.919290i	$-0.628764\pi$
$971$	−23817.3	−0.787163	−0.393581	+	0.919290i	$0.628764\pi$
$972$	−808.777	−0.0266888
$973$	4483.79	0.147732
$974$	−28542.9	−0.938987
$975$	18784.2	0.617002
$976$	−1604.06	−0.0526072
$977$	−36731.9	−1.20282	−0.601411	−	0.798940i	$-0.705395\pi$
$977$	−36731.9	−1.20282	−0.601411	+	0.798940i	$0.705395\pi$
$978$	15162.0	0.495733
$979$	−955.350	−0.0311881
$980$	−7491.04	−0.244176
$981$	−14457.3	−0.470526
$982$	−31516.6	−1.02417
$983$	−25347.8	−0.822451	−0.411226	−	0.911534i	$-0.634899\pi$
$983$	−25347.8	−0.822451	−0.411226	+	0.911534i	$0.634899\pi$
$984$	−14736.3	−0.477416
$985$	−8150.73	−0.263659
$986$	−17777.7	−0.574197
$987$	41942.2	1.35262
$988$	−26821.8	−0.863680
$989$	621.376	0.0199784
$990$	1580.58	0.0507416
$991$	30315.2	0.971739	0.485870	−	0.874031i	$-0.338503\pi$
$991$	30315.2	0.971739	0.485870	+	0.874031i	$0.338503\pi$
$992$	−7517.78	−0.240615
$993$	24705.8	0.789541
$994$	−21144.7	−0.674717
$995$	4452.80	0.141873
$996$	−2664.45	−0.0847654
$997$	15977.5	0.507534	0.253767	−	0.967265i	$-0.418330\pi$
$997$	15977.5	0.507534	0.253767	+	0.967265i	$0.418330\pi$
$998$	−11075.6	−0.351296
$999$	9434.74	0.298801

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.h.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)

\(f(q)\)	\(=\)	\(q-2.16141 q^{2} +3.00000 q^{3} -3.32830 q^{4} +7.38660 q^{5} -6.48423 q^{6} -25.4500 q^{7} +24.4851 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.16141 q^{2} +3.00000 q^{3} -3.32830 q^{4} +7.38660 q^{5} -6.48423 q^{6} -25.4500 q^{7} +24.4851 q^{8} +9.00000 q^{9} -15.9655 q^{10} -11.0000 q^{11} -9.98490 q^{12} -88.8923 q^{13} +55.0079 q^{14} +22.1598 q^{15} -26.2960 q^{16} -27.5502 q^{17} -19.4527 q^{18} -90.6570 q^{19} -24.5848 q^{20} -76.3500 q^{21} +23.7755 q^{22} +5.00950 q^{23} +73.4554 q^{24} -70.4382 q^{25} +192.133 q^{26} +27.0000 q^{27} +84.7052 q^{28} -298.548 q^{29} -47.8964 q^{30} +54.0675 q^{31} -139.044 q^{32} -33.0000 q^{33} +59.5473 q^{34} -187.989 q^{35} -29.9547 q^{36} +349.435 q^{37} +195.947 q^{38} -266.677 q^{39} +180.862 q^{40} -200.616 q^{41} +165.024 q^{42} +124.039 q^{43} +36.6113 q^{44} +66.4794 q^{45} -10.8276 q^{46} -549.341 q^{47} -78.8880 q^{48} +304.702 q^{49} +152.246 q^{50} -82.6506 q^{51} +295.860 q^{52} +625.714 q^{53} -58.3581 q^{54} -81.2526 q^{55} -623.146 q^{56} -271.971 q^{57} +645.285 q^{58} +244.947 q^{59} -73.7545 q^{60} +61.0000 q^{61} -116.862 q^{62} -229.050 q^{63} +510.900 q^{64} -656.612 q^{65} +71.3266 q^{66} -36.2603 q^{67} +91.6954 q^{68} +15.0285 q^{69} +406.321 q^{70} -384.394 q^{71} +220.366 q^{72} -880.519 q^{73} -755.273 q^{74} -211.315 q^{75} +301.734 q^{76} +279.950 q^{77} +576.399 q^{78} +955.144 q^{79} -194.238 q^{80} +81.0000 q^{81} +433.614 q^{82} +266.848 q^{83} +254.116 q^{84} -203.502 q^{85} -268.100 q^{86} -895.644 q^{87} -269.336 q^{88} +86.8500 q^{89} -143.689 q^{90} +2262.31 q^{91} -16.6731 q^{92} +162.202 q^{93} +1187.35 q^{94} -669.647 q^{95} -417.133 q^{96} +1200.36 q^{97} -658.586 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * q^99

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