LMFDB - Embedded newform 2013.4.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.789172 q^{2} -3.00000 q^{3} -7.37721 q^{4} +13.9316 q^{5} +2.36752 q^{6} -21.1583 q^{7} +12.1353 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.789172 q^{2} -3.00000 q^{3} -7.37721 q^{4} +13.9316 q^{5} +2.36752 q^{6} -21.1583 q^{7} +12.1353 q^{8} +9.00000 q^{9} -10.9944 q^{10} -11.0000 q^{11} +22.1316 q^{12} +41.9615 q^{13} +16.6975 q^{14} -41.7948 q^{15} +49.4408 q^{16} +53.5444 q^{17} -7.10255 q^{18} +133.990 q^{19} -102.776 q^{20} +63.4749 q^{21} +8.68090 q^{22} -11.7942 q^{23} -36.4058 q^{24} +69.0892 q^{25} -33.1149 q^{26} -27.0000 q^{27} +156.089 q^{28} +42.0514 q^{29} +32.9833 q^{30} +184.113 q^{31} -136.099 q^{32} +33.0000 q^{33} -42.2558 q^{34} -294.769 q^{35} -66.3949 q^{36} -330.326 q^{37} -105.741 q^{38} -125.885 q^{39} +169.064 q^{40} -449.893 q^{41} -50.0926 q^{42} +384.881 q^{43} +81.1493 q^{44} +125.384 q^{45} +9.30762 q^{46} +324.914 q^{47} -148.323 q^{48} +104.673 q^{49} -54.5233 q^{50} -160.633 q^{51} -309.559 q^{52} +406.836 q^{53} +21.3077 q^{54} -153.248 q^{55} -256.761 q^{56} -401.970 q^{57} -33.1858 q^{58} -528.883 q^{59} +308.329 q^{60} -61.0000 q^{61} -145.297 q^{62} -190.425 q^{63} -288.121 q^{64} +584.591 q^{65} -26.0427 q^{66} -455.513 q^{67} -395.008 q^{68} +35.3825 q^{69} +232.623 q^{70} +991.343 q^{71} +109.217 q^{72} -574.694 q^{73} +260.684 q^{74} -207.268 q^{75} -988.471 q^{76} +232.741 q^{77} +99.3446 q^{78} -317.940 q^{79} +688.790 q^{80} +81.0000 q^{81} +355.043 q^{82} +1491.67 q^{83} -468.267 q^{84} +745.959 q^{85} -303.737 q^{86} -126.154 q^{87} -133.488 q^{88} +346.107 q^{89} -98.9498 q^{90} -887.834 q^{91} +87.0079 q^{92} -552.339 q^{93} -256.413 q^{94} +1866.69 q^{95} +408.298 q^{96} -317.692 q^{97} -82.6051 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) $ 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9} + 95 q^{10} - 418 q^{11} - 426 q^{12} + 13 q^{13} + 26 q^{14} - 45 q^{15} + 486 q^{16} - 224 q^{17} - 18 q^{18} + 367 q^{19} + 18 q^{20} - 189 q^{21} + 22 q^{22} + 51 q^{23} + 135 q^{24} + 773 q^{25} - 439 q^{26} - 1026 q^{27} + 22 q^{28} - 462 q^{29} - 285 q^{30} + 234 q^{31} - 597 q^{32} + 1254 q^{33} + 956 q^{34} - 522 q^{35} + 1278 q^{36} + 954 q^{37} + 705 q^{38} - 39 q^{39} + 1495 q^{40} - 740 q^{41} - 78 q^{42} + 1441 q^{43} - 1562 q^{44} + 135 q^{45} + 581 q^{46} + 1003 q^{47} - 1458 q^{48} + 2707 q^{49} + 388 q^{50} + 672 q^{51} + 788 q^{52} + 735 q^{53} + 54 q^{54} - 165 q^{55} + 1059 q^{56} - 1101 q^{57} + 177 q^{58} + 261 q^{59} - 54 q^{60} - 2318 q^{61} + 1251 q^{62} + 567 q^{63} + 5571 q^{64} - 1354 q^{65} - 66 q^{66} + 3495 q^{67} - 1856 q^{68} - 153 q^{69} + 542 q^{70} - 873 q^{71} - 405 q^{72} + 989 q^{73} - 3406 q^{74} - 2319 q^{75} + 1712 q^{76} - 693 q^{77} + 1317 q^{78} + 2313 q^{79} + 1593 q^{80} + 3078 q^{81} + 5170 q^{82} + 569 q^{83} - 66 q^{84} - 1271 q^{85} + 3065 q^{86} + 1386 q^{87} + 495 q^{88} - 2917 q^{89} + 855 q^{90} + 2740 q^{91} + 1083 q^{92} - 702 q^{93} + 3272 q^{94} + 2696 q^{95} + 1791 q^{96} + 4250 q^{97} + 5952 q^{98} - 3762 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9 + 95 * q^10 - 418 * q^11 - 426 * q^12 + 13 * q^13 + 26 * q^14 - 45 * q^15 + 486 * q^16 - 224 * q^17 - 18 * q^18 + 367 * q^19 + 18 * q^20 - 189 * q^21 + 22 * q^22 + 51 * q^23 + 135 * q^24 + 773 * q^25 - 439 * q^26 - 1026 * q^27 + 22 * q^28 - 462 * q^29 - 285 * q^30 + 234 * q^31 - 597 * q^32 + 1254 * q^33 + 956 * q^34 - 522 * q^35 + 1278 * q^36 + 954 * q^37 + 705 * q^38 - 39 * q^39 + 1495 * q^40 - 740 * q^41 - 78 * q^42 + 1441 * q^43 - 1562 * q^44 + 135 * q^45 + 581 * q^46 + 1003 * q^47 - 1458 * q^48 + 2707 * q^49 + 388 * q^50 + 672 * q^51 + 788 * q^52 + 735 * q^53 + 54 * q^54 - 165 * q^55 + 1059 * q^56 - 1101 * q^57 + 177 * q^58 + 261 * q^59 - 54 * q^60 - 2318 * q^61 + 1251 * q^62 + 567 * q^63 + 5571 * q^64 - 1354 * q^65 - 66 * q^66 + 3495 * q^67 - 1856 * q^68 - 153 * q^69 + 542 * q^70 - 873 * q^71 - 405 * q^72 + 989 * q^73 - 3406 * q^74 - 2319 * q^75 + 1712 * q^76 - 693 * q^77 + 1317 * q^78 + 2313 * q^79 + 1593 * q^80 + 3078 * q^81 + 5170 * q^82 + 569 * q^83 - 66 * q^84 - 1271 * q^85 + 3065 * q^86 + 1386 * q^87 + 495 * q^88 - 2917 * q^89 + 855 * q^90 + 2740 * q^91 + 1083 * q^92 - 702 * q^93 + 3272 * q^94 + 2696 * q^95 + 1791 * q^96 + 4250 * q^97 + 5952 * q^98 - 3762 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.789172	−0.279015	−0.139507	−	0.990221i	$-0.544552\pi$
$2$	−0.789172	−0.279015	−0.139507	+	0.990221i	$0.544552\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.37721	−0.922151
$5$	13.9316	1.24608	0.623040	−	0.782190i	$-0.285897\pi$
$5$	13.9316	1.24608	0.623040	+	0.782190i	$0.285897\pi$
$6$	2.36752	0.161089
$7$	−21.1583	−1.14244	−0.571220	−	0.820797i	$-0.693530\pi$
$7$	−21.1583	−1.14244	−0.571220	+	0.820797i	$0.693530\pi$
$8$	12.1353	0.536308
$9$	9.00000	0.333333
$10$	−10.9944	−0.347674
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	22.1316	0.532404
$13$	41.9615	0.895233	0.447617	−	0.894226i	$-0.352273\pi$
$13$	41.9615	0.895233	0.447617	+	0.894226i	$0.352273\pi$
$14$	16.6975	0.318757
$15$	−41.7948	−0.719424
$16$	49.4408	0.772513
$17$	53.5444	0.763908	0.381954	−	0.924181i	$-0.375251\pi$
$17$	53.5444	0.763908	0.381954	+	0.924181i	$0.375251\pi$
$18$	−7.10255	−0.0930049
$19$	133.990	1.61786	0.808931	−	0.587903i	$-0.200046\pi$
$19$	133.990	1.61786	0.808931	+	0.587903i	$0.200046\pi$
$20$	−102.776	−1.14907
$21$	63.4749	0.659588
$22$	8.68090	0.0841261
$23$	−11.7942	−0.106924	−0.0534620	−	0.998570i	$-0.517026\pi$
$23$	−11.7942	−0.106924	−0.0534620	+	0.998570i	$0.517026\pi$
$24$	−36.4058	−0.309638
$25$	69.0892	0.552714
$26$	−33.1149	−0.249783
$27$	−27.0000	−0.192450
$28$	156.089	1.05350
$29$	42.0514	0.269267	0.134634	−	0.990895i	$-0.457014\pi$
$29$	42.0514	0.269267	0.134634	+	0.990895i	$0.457014\pi$
$30$	32.9833	0.200730
$31$	184.113	1.06670	0.533349	−	0.845895i	$-0.320933\pi$
$31$	184.113	1.06670	0.533349	+	0.845895i	$0.320933\pi$
$32$	−136.099	−0.751851
$33$	33.0000	0.174078
$34$	−42.2558	−0.213141
$35$	−294.769	−1.42357
$36$	−66.3949	−0.307384
$37$	−330.326	−1.46771	−0.733854	−	0.679307i	$-0.762280\pi$
$37$	−330.326	−1.46771	−0.733854	+	0.679307i	$0.762280\pi$
$38$	−105.741	−0.451407
$39$	−125.885	−0.516863
$40$	169.064	0.668282
$41$	−449.893	−1.71369	−0.856847	−	0.515571i	$-0.827580\pi$
$41$	−449.893	−1.71369	−0.856847	+	0.515571i	$0.827580\pi$
$42$	−50.0926	−0.184035
$43$	384.881	1.36497	0.682485	−	0.730899i	$-0.260899\pi$
$43$	384.881	1.36497	0.682485	+	0.730899i	$0.260899\pi$
$44$	81.1493	0.278039
$45$	125.384	0.415360
$46$	9.30762	0.0298334
$47$	324.914	1.00837	0.504187	−	0.863594i	$-0.331792\pi$
$47$	324.914	1.00837	0.504187	+	0.863594i	$0.331792\pi$
$48$	−148.323	−0.446011
$49$	104.673	0.305169
$50$	−54.5233	−0.154215
$51$	−160.633	−0.441042
$52$	−309.559	−0.825540
$53$	406.836	1.05440	0.527200	−	0.849741i	$-0.323242\pi$
$53$	406.836	1.05440	0.527200	+	0.849741i	$0.323242\pi$
$54$	21.3077	0.0536964
$55$	−153.248	−0.375707
$56$	−256.761	−0.612700
$57$	−401.970	−0.934073
$58$	−33.1858	−0.0751295
$59$	−528.883	−1.16703	−0.583514	−	0.812103i	$-0.698323\pi$
$59$	−528.883	−1.16703	−0.583514	+	0.812103i	$0.698323\pi$
$60$	308.329	0.663418
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−145.297	−0.297625
$63$	−190.425	−0.380813
$64$	−288.121	−0.562736
$65$	584.591	1.11553
$66$	−26.0427	−0.0485702
$67$	−455.513	−0.830594	−0.415297	−	0.909686i	$-0.636322\pi$
$67$	−455.513	−0.830594	−0.415297	+	0.909686i	$0.636322\pi$
$68$	−395.008	−0.704438
$69$	35.3825	0.0617326
$70$	232.623	0.397197
$71$	991.343	1.65705	0.828526	−	0.559950i	$-0.189180\pi$
$71$	991.343	1.65705	0.828526	+	0.559950i	$0.189180\pi$
$72$	109.217	0.178769
$73$	−574.694	−0.921410	−0.460705	−	0.887553i	$-0.652403\pi$
$73$	−574.694	−0.921410	−0.460705	+	0.887553i	$0.652403\pi$
$74$	260.684	0.409512
$75$	−207.268	−0.319110
$76$	−988.471	−1.49191
$77$	232.741	0.344459
$78$	99.3446	0.144212
$79$	−317.940	−0.452799	−0.226399	−	0.974035i	$-0.572695\pi$
$79$	−317.940	−0.452799	−0.226399	+	0.974035i	$0.572695\pi$
$80$	688.790	0.962613
$81$	81.0000	0.111111
$82$	355.043	0.478145
$83$	1491.67	1.97267	0.986334	−	0.164756i	$-0.0526836\pi$
$83$	1491.67	1.97267	0.986334	+	0.164756i	$0.0526836\pi$
$84$	−468.267	−0.608240
$85$	745.959	0.951889
$86$	−303.737	−0.380847
$87$	−126.154	−0.155462
$88$	−133.488	−0.161703
$89$	346.107	0.412216	0.206108	−	0.978529i	$-0.433920\pi$
$89$	346.107	0.412216	0.206108	+	0.978529i	$0.433920\pi$
$90$	−98.9498	−0.115891
$91$	−887.834	−1.02275
$92$	87.0079	0.0986000
$93$	−552.339	−0.615859
$94$	−256.413	−0.281351
$95$	1866.69	2.01599
$96$	408.298	0.434081
$97$	−317.692	−0.332544	−0.166272	−	0.986080i	$-0.553173\pi$
$97$	−317.692	−0.332544	−0.166272	+	0.986080i	$0.553173\pi$
$98$	−82.6051	−0.0851466
$99$	−99.0000	−0.100504
$100$	−509.686	−0.509686
$101$	−1334.36	−1.31459	−0.657297	−	0.753631i	$-0.728300\pi$
$101$	−1334.36	−1.31459	−0.657297	+	0.753631i	$0.728300\pi$
$102$	126.767	0.123057
$103$	−182.166	−0.174266	−0.0871329	−	0.996197i	$-0.527770\pi$
$103$	−182.166	−0.174266	−0.0871329	+	0.996197i	$0.527770\pi$
$104$	509.214	0.480121
$105$	884.306	0.821899
$106$	−321.064	−0.294193
$107$	−1628.09	−1.47097	−0.735485	−	0.677541i	$-0.763046\pi$
$107$	−1628.09	−1.47097	−0.735485	+	0.677541i	$0.763046\pi$
$108$	199.185	0.177468
$109$	1534.50	1.34842	0.674211	−	0.738539i	$-0.264484\pi$
$109$	1534.50	1.34842	0.674211	+	0.738539i	$0.264484\pi$
$110$	120.939	0.104828
$111$	990.977	0.847382
$112$	−1046.08	−0.882550
$113$	−5.80472	−0.00483241	−0.00241621	−	0.999997i	$-0.500769\pi$
$113$	−5.80472	−0.00483241	−0.00241621	+	0.999997i	$0.500769\pi$
$114$	317.223	0.260620
$115$	−164.311	−0.133236
$116$	−310.222	−0.248305
$117$	377.654	0.298411
$118$	417.380	0.325618
$119$	−1132.91	−0.872719
$120$	−507.191	−0.385833
$121$	121.000	0.0909091
$122$	48.1395	0.0357242
$123$	1349.68	0.989401
$124$	−1358.24	−0.983657
$125$	−778.926	−0.557354
$126$	150.278	0.106252
$127$	−2126.07	−1.48550	−0.742750	−	0.669569i	$-0.766479\pi$
$127$	−2126.07	−1.48550	−0.742750	+	0.669569i	$0.766479\pi$
$128$	1316.17	0.908862
$129$	−1154.64	−0.788066
$130$	−461.343	−0.311250
$131$	1850.09	1.23391	0.616957	−	0.786997i	$-0.288365\pi$
$131$	1850.09	1.23391	0.616957	+	0.786997i	$0.288365\pi$
$132$	−243.448	−0.160526
$133$	−2835.00	−1.84831
$134$	359.478	0.231748
$135$	−376.153	−0.239808
$136$	649.776	0.409690
$137$	−1986.77	−1.23899	−0.619493	−	0.785002i	$-0.712662\pi$
$137$	−1986.77	−1.23899	−0.619493	+	0.785002i	$0.712662\pi$
$138$	−27.9229	−0.0172243
$139$	1895.47	1.15663	0.578317	−	0.815812i	$-0.303710\pi$
$139$	1895.47	1.15663	0.578317	+	0.815812i	$0.303710\pi$
$140$	2174.57	1.31275
$141$	−974.742	−0.582185
$142$	−782.340	−0.462342
$143$	−461.577	−0.269923
$144$	444.968	0.257504
$145$	585.843	0.335528
$146$	453.533	0.257087
$147$	−314.019	−0.176190
$148$	2436.88	1.35345
$149$	712.448	0.391718	0.195859	−	0.980632i	$-0.437251\pi$
$149$	712.448	0.391718	0.195859	+	0.980632i	$0.437251\pi$
$150$	163.570	0.0890362
$151$	−741.768	−0.399763	−0.199882	−	0.979820i	$-0.564056\pi$
$151$	−741.768	−0.399763	−0.199882	+	0.979820i	$0.564056\pi$
$152$	1626.00	0.867673
$153$	481.900	0.254636
$154$	−183.673	−0.0961090
$155$	2564.99	1.32919
$156$	928.676	0.476626
$157$	1921.15	0.976589	0.488294	−	0.872679i	$-0.337619\pi$
$157$	1921.15	0.976589	0.488294	+	0.872679i	$0.337619\pi$
$158$	250.910	0.126337
$159$	−1220.51	−0.608759
$160$	−1896.08	−0.936865
$161$	249.544	0.122154
$162$	−63.9230	−0.0310016
$163$	−1903.61	−0.914737	−0.457368	−	0.889277i	$-0.651208\pi$
$163$	−1903.61	−0.914737	−0.457368	+	0.889277i	$0.651208\pi$
$164$	3318.95	1.58028
$165$	459.743	0.216915
$166$	−1177.18	−0.550403
$167$	3283.61	1.52152	0.760759	−	0.649035i	$-0.224827\pi$
$167$	3283.61	1.52152	0.760759	+	0.649035i	$0.224827\pi$
$168$	770.284	0.353742
$169$	−436.231	−0.198558
$170$	−588.690	−0.265591
$171$	1205.91	0.539287
$172$	−2839.34	−1.25871
$173$	2116.66	0.930212	0.465106	−	0.885255i	$-0.346016\pi$
$173$	2116.66	0.930212	0.465106	+	0.885255i	$0.346016\pi$
$174$	99.5574	0.0433760
$175$	−1461.81	−0.631442
$176$	−543.849	−0.232921
$177$	1586.65	0.673784
$178$	−273.138	−0.115014
$179$	−2417.26	−1.00936	−0.504678	−	0.863308i	$-0.668389\pi$
$179$	−2417.26	−1.00936	−0.504678	+	0.863308i	$0.668389\pi$
$180$	−924.986	−0.383024
$181$	2254.09	0.925663	0.462832	−	0.886446i	$-0.346833\pi$
$181$	2254.09	0.925663	0.462832	+	0.886446i	$0.346833\pi$
$182$	700.654	0.285362
$183$	183.000	0.0739221
$184$	−143.125	−0.0573442
$185$	−4601.96	−1.82888
$186$	435.891	0.171834
$187$	−588.989	−0.230327
$188$	−2396.96	−0.929873
$189$	571.274	0.219863
$190$	−1473.14	−0.562489
$191$	−499.675	−0.189294	−0.0946472	−	0.995511i	$-0.530172\pi$
$191$	−499.675	−0.189294	−0.0946472	+	0.995511i	$0.530172\pi$
$192$	864.362	0.324896
$193$	2459.35	0.917243	0.458622	−	0.888632i	$-0.348343\pi$
$193$	2459.35	0.917243	0.458622	+	0.888632i	$0.348343\pi$
$194$	250.714	0.0927846
$195$	−1753.77	−0.644052
$196$	−772.195	−0.281412
$197$	−1227.08	−0.443784	−0.221892	−	0.975071i	$-0.571223\pi$
$197$	−1227.08	−0.443784	−0.221892	+	0.975071i	$0.571223\pi$
$198$	78.1281	0.0280420
$199$	2105.17	0.749907	0.374954	−	0.927044i	$-0.377659\pi$
$199$	2105.17	0.749907	0.374954	+	0.927044i	$0.377659\pi$
$200$	838.416	0.296425
$201$	1366.54	0.479544
$202$	1053.04	0.366791
$203$	−889.736	−0.307622
$204$	1185.02	0.406707
$205$	−6267.72	−2.13540
$206$	143.761	0.0486227
$207$	−106.147	−0.0356413
$208$	2074.61	0.691579
$209$	−1473.89	−0.487804
$210$	−697.870	−0.229322
$211$	−814.699	−0.265811	−0.132906	−	0.991129i	$-0.542431\pi$
$211$	−814.699	−0.265811	−0.132906	+	0.991129i	$0.542431\pi$
$212$	−3001.31	−0.972317
$213$	−2974.03	−0.956700
$214$	1284.85	0.410422
$215$	5362.00	1.70086
$216$	−327.652	−0.103213
$217$	−3895.52	−1.21864
$218$	−1210.98	−0.376229
$219$	1724.08	0.531976
$220$	1130.54	0.346459
$221$	2246.81	0.683875
$222$	−782.051	−0.236432
$223$	288.910	0.0867572	0.0433786	−	0.999059i	$-0.486188\pi$
$223$	288.910	0.0867572	0.0433786	+	0.999059i	$0.486188\pi$
$224$	2879.63	0.858944
$225$	621.803	0.184238
$226$	4.58093	0.00134831
$227$	−2988.14	−0.873701	−0.436850	−	0.899534i	$-0.643906\pi$
$227$	−2988.14	−0.873701	−0.436850	+	0.899534i	$0.643906\pi$
$228$	2965.41	0.861357
$229$	−1279.32	−0.369171	−0.184585	−	0.982816i	$-0.559094\pi$
$229$	−1279.32	−0.369171	−0.184585	+	0.982816i	$0.559094\pi$
$230$	129.670	0.0371747
$231$	−698.223	−0.198873
$232$	510.305	0.144410
$233$	3584.65	1.00789	0.503945	−	0.863736i	$-0.331882\pi$
$233$	3584.65	1.00789	0.503945	+	0.863736i	$0.331882\pi$
$234$	−298.034	−0.0832610
$235$	4526.57	1.25651
$236$	3901.68	1.07618
$237$	953.821	0.261423
$238$	894.060	0.243501
$239$	−2741.05	−0.741858	−0.370929	−	0.928661i	$-0.620961\pi$
$239$	−2741.05	−0.741858	−0.370929	+	0.928661i	$0.620961\pi$
$240$	−2066.37	−0.555765
$241$	−5902.64	−1.57769	−0.788843	−	0.614595i	$-0.789320\pi$
$241$	−5902.64	−1.57769	−0.788843	+	0.614595i	$0.789320\pi$
$242$	−95.4899	−0.0253650
$243$	−243.000	−0.0641500
$244$	450.010	0.118069
$245$	1458.26	0.380265
$246$	−1065.13	−0.276057
$247$	5622.42	1.44836
$248$	2234.26	0.572079
$249$	−4475.00	−1.13892
$250$	614.707	0.155510
$251$	−620.926	−0.156145	−0.0780727	−	0.996948i	$-0.524877\pi$
$251$	−620.926	−0.156145	−0.0780727	+	0.996948i	$0.524877\pi$
$252$	1404.80	0.351167
$253$	129.736	0.0322388
$254$	1677.84	0.414476
$255$	−2237.88	−0.549574
$256$	1266.28	0.309150
$257$	4317.83	1.04801	0.524005	−	0.851715i	$-0.324437\pi$
$257$	4317.83	1.04801	0.524005	+	0.851715i	$0.324437\pi$
$258$	911.211	0.219882
$259$	6989.12	1.67677
$260$	−4312.65	−1.02869
$261$	378.463	0.0897557
$262$	−1460.04	−0.344280
$263$	6002.34	1.40730	0.703650	−	0.710547i	$-0.251552\pi$
$263$	6002.34	1.40730	0.703650	+	0.710547i	$0.251552\pi$
$264$	400.464	0.0933593
$265$	5667.87	1.31387
$266$	2237.30	0.515706
$267$	−1038.32	−0.237993
$268$	3360.42	0.765933
$269$	8072.17	1.82962	0.914812	−	0.403879i	$-0.132338\pi$
$269$	8072.17	1.82962	0.914812	+	0.403879i	$0.132338\pi$
$270$	296.850	0.0669100
$271$	8016.90	1.79702	0.898509	−	0.438955i	$-0.144651\pi$
$271$	8016.90	1.79702	0.898509	+	0.438955i	$0.144651\pi$
$272$	2647.28	0.590129
$273$	2663.50	0.590485
$274$	1567.90	0.345695
$275$	−759.982	−0.166650
$276$	−261.024	−0.0569268
$277$	6689.57	1.45104	0.725519	−	0.688202i	$-0.241600\pi$
$277$	6689.57	1.45104	0.725519	+	0.688202i	$0.241600\pi$
$278$	−1495.86	−0.322718
$279$	1657.02	0.355566
$280$	−3577.10	−0.763473
$281$	−1433.51	−0.304328	−0.152164	−	0.988355i	$-0.548624\pi$
$281$	−1433.51	−0.304328	−0.152164	+	0.988355i	$0.548624\pi$
$282$	769.240	0.162438
$283$	656.582	0.137914	0.0689571	−	0.997620i	$-0.478033\pi$
$283$	656.582	0.137914	0.0689571	+	0.997620i	$0.478033\pi$
$284$	−7313.34	−1.52805
$285$	−5600.08	−1.16393
$286$	364.264	0.0753124
$287$	9518.96	1.95779
$288$	−1224.90	−0.250617
$289$	−2046.00	−0.416445
$290$	−462.331	−0.0936173
$291$	953.077	0.191994
$292$	4239.64	0.849679
$293$	7426.76	1.48081	0.740403	−	0.672163i	$-0.234635\pi$
$293$	7426.76	1.48081	0.740403	+	0.672163i	$0.234635\pi$
$294$	247.815	0.0491594
$295$	−7368.18	−1.45421
$296$	−4008.59	−0.787144
$297$	297.000	0.0580259
$298$	−562.244	−0.109295
$299$	−494.901	−0.0957219
$300$	1529.06	0.294267
$301$	−8143.41	−1.55940
$302$	585.383	0.111540
$303$	4003.09	0.758982
$304$	6624.57	1.24982
$305$	−849.827	−0.159544
$306$	−380.302	−0.0710471
$307$	1172.47	0.217969	0.108984	−	0.994043i	$-0.465240\pi$
$307$	1172.47	0.217969	0.108984	+	0.994043i	$0.465240\pi$
$308$	−1716.98	−0.317643
$309$	546.499	0.100612
$310$	−2024.22	−0.370864
$311$	−2843.40	−0.518438	−0.259219	−	0.965819i	$-0.583465\pi$
$311$	−2843.40	−0.518438	−0.259219	+	0.965819i	$0.583465\pi$
$312$	−1527.64	−0.277198
$313$	7847.41	1.41713	0.708565	−	0.705645i	$-0.249343\pi$
$313$	7847.41	1.41713	0.708565	+	0.705645i	$0.249343\pi$
$314$	−1516.12	−0.272483
$315$	−2652.92	−0.474524
$316$	2345.51	0.417549
$317$	2870.11	0.508522	0.254261	−	0.967136i	$-0.418168\pi$
$317$	2870.11	0.508522	0.254261	+	0.967136i	$0.418168\pi$
$318$	963.192	0.169853
$319$	−462.565	−0.0811871
$320$	−4013.98	−0.701214
$321$	4884.28	0.849265
$322$	−196.933	−0.0340828
$323$	7174.41	1.23590
$324$	−597.554	−0.102461
$325$	2899.09	0.494808
$326$	1502.27	0.255225
$327$	−4603.49	−0.778512
$328$	−5459.57	−0.919068
$329$	−6874.63	−1.15201
$330$	−362.816	−0.0605223
$331$	9127.62	1.51571	0.757854	−	0.652424i	$-0.226248\pi$
$331$	9127.62	1.51571	0.757854	+	0.652424i	$0.226248\pi$
$332$	−11004.3	−1.81910
$333$	−2972.93	−0.489236
$334$	−2591.34	−0.424526
$335$	−6346.02	−1.03499
$336$	3138.25	0.509540
$337$	−10645.6	−1.72078	−0.860388	−	0.509639i	$-0.829779\pi$
$337$	−10645.6	−1.72078	−0.860388	+	0.509639i	$0.829779\pi$
$338$	344.261	0.0554005
$339$	17.4142	0.00278999
$340$	−5503.09	−0.877786
$341$	−2025.24	−0.321622
$342$	−951.670	−0.150469
$343$	5042.59	0.793803
$344$	4670.63	0.732045
$345$	492.934	0.0769237
$346$	−1670.41	−0.259543
$347$	2797.12	0.432730	0.216365	−	0.976312i	$-0.430580\pi$
$347$	2797.12	0.432730	0.216365	+	0.976312i	$0.430580\pi$
$348$	930.666	0.143359
$349$	1223.09	0.187595	0.0937973	−	0.995591i	$-0.470099\pi$
$349$	1223.09	0.187595	0.0937973	+	0.995591i	$0.470099\pi$
$350$	1153.62	0.176182
$351$	−1132.96	−0.172288
$352$	1497.09	0.226691
$353$	1176.02	0.177318	0.0886589	−	0.996062i	$-0.471742\pi$
$353$	1176.02	0.177318	0.0886589	+	0.996062i	$0.471742\pi$
$354$	−1252.14	−0.187996
$355$	13811.0	2.06482
$356$	−2553.30	−0.380126
$357$	3398.72	0.503864
$358$	1907.64	0.281625
$359$	13550.1	1.99206	0.996030	−	0.0890186i	$-0.0283731\pi$
$359$	13550.1	1.99206	0.996030	+	0.0890186i	$0.0283731\pi$
$360$	1521.57	0.222761
$361$	11094.3	1.61748
$362$	−1778.86	−0.258274
$363$	−363.000	−0.0524864
$364$	6549.73	0.943130
$365$	−8006.41	−1.14815
$366$	−144.419	−0.0206254
$367$	13433.4	1.91067	0.955337	−	0.295517i	$-0.0954920\pi$
$367$	13433.4	1.91067	0.955337	+	0.295517i	$0.0954920\pi$
$368$	−583.113	−0.0826002
$369$	−4049.03	−0.571231
$370$	3631.74	0.510284
$371$	−8607.95	−1.20459
$372$	4074.72	0.567915
$373$	−8374.15	−1.16246	−0.581229	−	0.813740i	$-0.697428\pi$
$373$	−8374.15	−1.16246	−0.581229	+	0.813740i	$0.697428\pi$
$374$	464.814	0.0642645
$375$	2336.78	0.321788
$376$	3942.92	0.540799
$377$	1764.54	0.241057
$378$	−450.833	−0.0613449
$379$	8617.29	1.16792	0.583958	−	0.811784i	$-0.301503\pi$
$379$	8617.29	1.16792	0.583958	+	0.811784i	$0.301503\pi$
$380$	−13771.0	−1.85904
$381$	6378.22	0.857654
$382$	394.330	0.0528159
$383$	4835.06	0.645065	0.322533	−	0.946558i	$-0.395466\pi$
$383$	4835.06	0.645065	0.322533	+	0.946558i	$0.395466\pi$
$384$	−3948.52	−0.524732
$385$	3242.45	0.429223
$386$	−1940.85	−0.255924
$387$	3463.93	0.454990
$388$	2343.68	0.306656
$389$	5457.72	0.711355	0.355678	−	0.934609i	$-0.384250\pi$
$389$	5457.72	0.711355	0.355678	+	0.934609i	$0.384250\pi$
$390$	1384.03	0.179700
$391$	−631.511	−0.0816800
$392$	1270.24	0.163665
$393$	−5550.26	−0.712401
$394$	968.374	0.123822
$395$	−4429.42	−0.564223
$396$	730.343	0.0926796
$397$	−5026.71	−0.635474	−0.317737	−	0.948179i	$-0.602923\pi$
$397$	−5026.71	−0.635474	−0.317737	+	0.948179i	$0.602923\pi$
$398$	−1661.34	−0.209235
$399$	8504.99	1.06712
$400$	3415.83	0.426979
$401$	807.614	0.100574	0.0502872	−	0.998735i	$-0.483986\pi$
$401$	807.614	0.100574	0.0502872	+	0.998735i	$0.483986\pi$
$402$	−1078.44	−0.133800
$403$	7725.66	0.954944
$404$	9843.87	1.21225
$405$	1128.46	0.138453
$406$	702.155	0.0858309
$407$	3633.58	0.442531
$408$	−1949.33	−0.236535
$409$	−14198.4	−1.71654	−0.858268	−	0.513202i	$-0.828459\pi$
$409$	−14198.4	−1.71654	−0.858268	+	0.513202i	$0.828459\pi$
$410$	4946.31	0.595807
$411$	5960.31	0.715329
$412$	1343.88	0.160699
$413$	11190.3	1.33326
$414$	83.7686	0.00994445
$415$	20781.3	2.45810
$416$	−5710.94	−0.673082
$417$	−5686.42	−0.667782
$418$	1163.15	0.136104
$419$	−9946.15	−1.15967	−0.579835	−	0.814734i	$-0.696883\pi$
$419$	−9946.15	−1.15967	−0.579835	+	0.814734i	$0.696883\pi$
$420$	−6523.71	−0.757915
$421$	−3592.46	−0.415881	−0.207941	−	0.978141i	$-0.566676\pi$
$421$	−3592.46	−0.415881	−0.207941	+	0.978141i	$0.566676\pi$
$422$	642.938	0.0741652
$423$	2924.23	0.336125
$424$	4937.07	0.565484
$425$	3699.34	0.422222
$426$	2347.02	0.266933
$427$	1290.66	0.146274
$428$	12010.8	1.35646
$429$	1384.73	0.155840
$430$	−4231.54	−0.474565
$431$	2492.37	0.278546	0.139273	−	0.990254i	$-0.455523\pi$
$431$	2492.37	0.278546	0.139273	+	0.990254i	$0.455523\pi$
$432$	−1334.90	−0.148670
$433$	−13232.9	−1.46867	−0.734334	−	0.678788i	$-0.762505\pi$
$433$	−13232.9	−1.46867	−0.734334	+	0.678788i	$0.762505\pi$
$434$	3074.23	0.340018
$435$	−1757.53	−0.193717
$436$	−11320.3	−1.24345
$437$	−1580.30	−0.172988
$438$	−1360.60	−0.148429
$439$	3468.66	0.377108	0.188554	−	0.982063i	$-0.439620\pi$
$439$	3468.66	0.377108	0.188554	+	0.982063i	$0.439620\pi$
$440$	−1859.70	−0.201495
$441$	942.057	0.101723
$442$	−1773.12	−0.190811
$443$	10348.5	1.10987	0.554936	−	0.831893i	$-0.312743\pi$
$443$	10348.5	1.10987	0.554936	+	0.831893i	$0.312743\pi$
$444$	−7310.64	−0.781414
$445$	4821.82	0.513654
$446$	−228.000	−0.0242065
$447$	−2137.34	−0.226159
$448$	6096.14	0.642892
$449$	−16960.2	−1.78263	−0.891316	−	0.453383i	$-0.850217\pi$
$449$	−16960.2	−1.78263	−0.891316	+	0.453383i	$0.850217\pi$
$450$	−490.710	−0.0514051
$451$	4948.82	0.516698
$452$	42.8226	0.00445621
$453$	2225.30	0.230803
$454$	2358.16	0.243775
$455$	−12368.9	−1.27443
$456$	−4878.01	−0.500951
$457$	11803.7	1.20822	0.604109	−	0.796902i	$-0.293529\pi$
$457$	11803.7	1.20822	0.604109	+	0.796902i	$0.293529\pi$
$458$	1009.61	0.103004
$459$	−1445.70	−0.147014
$460$	1212.16	0.122863
$461$	5599.23	0.565687	0.282844	−	0.959166i	$-0.408722\pi$
$461$	5599.23	0.565687	0.282844	+	0.959166i	$0.408722\pi$
$462$	551.019	0.0554885
$463$	−14047.6	−1.41004	−0.705018	−	0.709189i	$-0.749061\pi$
$463$	−14047.6	−1.41004	−0.705018	+	0.709189i	$0.749061\pi$
$464$	2079.06	0.208012
$465$	−7694.96	−0.767409
$466$	−2828.91	−0.281216
$467$	−4712.43	−0.466950	−0.233475	−	0.972363i	$-0.575010\pi$
$467$	−4712.43	−0.466950	−0.233475	+	0.972363i	$0.575010\pi$
$468$	−2786.03	−0.275180
$469$	9637.88	0.948904
$470$	−3572.24	−0.350586
$471$	−5763.45	−0.563834
$472$	−6418.14	−0.625887
$473$	−4233.69	−0.411554
$474$	−752.729	−0.0729409
$475$	9257.26	0.894215
$476$	8357.70	0.804778
$477$	3661.53	0.351467
$478$	2163.16	0.206989
$479$	−14781.5	−1.40998	−0.704992	−	0.709216i	$-0.749049\pi$
$479$	−14781.5	−1.40998	−0.704992	+	0.709216i	$0.749049\pi$
$480$	5688.25	0.540900
$481$	−13861.0	−1.31394
$482$	4658.20	0.440197
$483$	−748.632	−0.0705258
$484$	−892.642	−0.0838319
$485$	−4425.96	−0.414376
$486$	191.769	0.0178988
$487$	17305.2	1.61021	0.805104	−	0.593133i	$-0.202109\pi$
$487$	17305.2	1.61021	0.805104	+	0.593133i	$0.202109\pi$
$488$	−740.251	−0.0686672
$489$	5710.82	0.528124
$490$	−1150.82	−0.106099
$491$	−607.950	−0.0558786	−0.0279393	−	0.999610i	$-0.508895\pi$
$491$	−607.950	−0.0558786	−0.0279393	+	0.999610i	$0.508895\pi$
$492$	−9956.85	−0.912377
$493$	2251.62	0.205695
$494$	−4437.06	−0.404115
$495$	−1379.23	−0.125236
$496$	9102.70	0.824039
$497$	−20975.1	−1.89308
$498$	3531.54	0.317776
$499$	12407.3	1.11308	0.556541	−	0.830820i	$-0.312128\pi$
$499$	12407.3	1.11308	0.556541	+	0.830820i	$0.312128\pi$
$500$	5746.30	0.513964
$501$	−9850.83	−0.878449
$502$	490.017	0.0435668
$503$	−3144.33	−0.278725	−0.139362	−	0.990241i	$-0.544505\pi$
$503$	−3144.33	−0.278725	−0.139362	+	0.990241i	$0.544505\pi$
$504$	−2310.85	−0.204233
$505$	−18589.8	−1.63809
$506$	−102.384	−0.00899509
$507$	1308.69	0.114637
$508$	15684.5	1.36985
$509$	−13454.3	−1.17161	−0.585805	−	0.810452i	$-0.699222\pi$
$509$	−13454.3	−1.17161	−0.585805	+	0.810452i	$0.699222\pi$
$510$	1766.07	0.153339
$511$	12159.5	1.05266
$512$	−11528.7	−0.995119
$513$	−3617.73	−0.311358
$514$	−3407.51	−0.292410
$515$	−2537.87	−0.217149
$516$	8518.03	0.726716
$517$	−3574.06	−0.304036
$518$	−5515.62	−0.467843
$519$	−6349.98	−0.537058
$520$	7094.16	0.598269
$521$	14131.1	1.18828	0.594141	−	0.804361i	$-0.297492\pi$
$521$	14131.1	1.18828	0.594141	+	0.804361i	$0.297492\pi$
$522$	−298.672	−0.0250432
$523$	−11677.1	−0.976297	−0.488148	−	0.872761i	$-0.662328\pi$
$523$	−11677.1	−0.976297	−0.488148	+	0.872761i	$0.662328\pi$
$524$	−13648.5	−1.13786
$525$	4385.43	0.364563
$526$	−4736.88	−0.392657
$527$	9858.22	0.814859
$528$	1631.55	0.134477
$529$	−12027.9	−0.988567
$530$	−4472.93	−0.366588
$531$	−4759.95	−0.389010
$532$	20914.4	1.70442
$533$	−18878.2	−1.53416
$534$	819.414	0.0664036
$535$	−22681.9	−1.83295
$536$	−5527.78	−0.445454
$537$	7251.79	0.582752
$538$	−6370.33	−0.510492
$539$	−1151.40	−0.0920120
$540$	2774.96	0.221139
$541$	772.283	0.0613734	0.0306867	−	0.999529i	$-0.490231\pi$
$541$	772.283	0.0613734	0.0306867	+	0.999529i	$0.490231\pi$
$542$	−6326.72	−0.501394
$543$	−6762.26	−0.534432
$544$	−7287.37	−0.574344
$545$	21378.0	1.68024
$546$	−2101.96	−0.164754
$547$	−12518.9	−0.978555	−0.489277	−	0.872128i	$-0.662739\pi$
$547$	−12518.9	−0.978555	−0.489277	+	0.872128i	$0.662739\pi$
$548$	14656.8	1.14253
$549$	−549.000	−0.0426790
$550$	599.756	0.0464976
$551$	5634.46	0.435637
$552$	429.376	0.0331077
$553$	6727.07	0.517295
$554$	−5279.23	−0.404861
$555$	13805.9	1.05590
$556$	−13983.3	−1.06659
$557$	7943.82	0.604291	0.302146	−	0.953262i	$-0.402297\pi$
$557$	7943.82	0.604291	0.302146	+	0.953262i	$0.402297\pi$
$558$	−1307.67	−0.0992082
$559$	16150.2	1.22197
$560$	−14573.6	−1.09973
$561$	1766.97	0.132979
$562$	1131.29	0.0849120
$563$	−6978.45	−0.522392	−0.261196	−	0.965286i	$-0.584117\pi$
$563$	−6978.45	−0.522392	−0.261196	+	0.965286i	$0.584117\pi$
$564$	7190.88	0.536863
$565$	−80.8690	−0.00602157
$566$	−518.156	−0.0384801
$567$	−1713.82	−0.126938
$568$	12030.2	0.888691
$569$	−1240.77	−0.0914161	−0.0457081	−	0.998955i	$-0.514554\pi$
$569$	−1240.77	−0.0914161	−0.0457081	+	0.998955i	$0.514554\pi$
$570$	4419.43	0.324753
$571$	8934.04	0.654778	0.327389	−	0.944890i	$-0.393831\pi$
$571$	8934.04	0.654778	0.327389	+	0.944890i	$0.393831\pi$
$572$	3405.15	0.248910
$573$	1499.03	0.109289
$574$	−7512.10	−0.546252
$575$	−814.849	−0.0590984
$576$	−2593.09	−0.187579
$577$	24080.3	1.73739	0.868695	−	0.495347i	$-0.164959\pi$
$577$	24080.3	1.73739	0.868695	+	0.495347i	$0.164959\pi$
$578$	1614.64	0.116194
$579$	−7378.05	−0.529571
$580$	−4321.88	−0.309408
$581$	−31561.1	−2.25366
$582$	−752.142	−0.0535692
$583$	−4475.20	−0.317914
$584$	−6974.07	−0.494159
$585$	5261.32	0.371844
$586$	−5861.00	−0.413166
$587$	−8438.64	−0.593356	−0.296678	−	0.954978i	$-0.595879\pi$
$587$	−8438.64	−0.593356	−0.296678	+	0.954978i	$0.595879\pi$
$588$	2316.58	0.162473
$589$	24669.3	1.72577
$590$	5814.77	0.405746
$591$	3681.23	0.256219
$592$	−16331.6	−1.13382
$593$	−5819.60	−0.403005	−0.201503	−	0.979488i	$-0.564582\pi$
$593$	−5819.60	−0.403005	−0.201503	+	0.979488i	$0.564582\pi$
$594$	−234.384	−0.0161901
$595$	−15783.2	−1.08748
$596$	−5255.87	−0.361223
$597$	−6315.51	−0.432959
$598$	390.562	0.0267078
$599$	12606.9	0.859941	0.429971	−	0.902843i	$-0.358524\pi$
$599$	12606.9	0.859941	0.429971	+	0.902843i	$0.358524\pi$
$600$	−2515.25	−0.171141
$601$	−1649.74	−0.111971	−0.0559853	−	0.998432i	$-0.517830\pi$
$601$	−1649.74	−0.111971	−0.0559853	+	0.998432i	$0.517830\pi$
$602$	6426.56	0.435094
$603$	−4099.62	−0.276865
$604$	5472.18	0.368642
$605$	1685.72	0.113280
$606$	−3159.13	−0.211767
$607$	18976.1	1.26889	0.634446	−	0.772967i	$-0.281228\pi$
$607$	18976.1	1.26889	0.634446	+	0.772967i	$0.281228\pi$
$608$	−18236.0	−1.21639
$609$	2669.21	0.177605
$610$	670.660	0.0445151
$611$	13633.9	0.902730
$612$	−3555.07	−0.234813
$613$	−6824.37	−0.449647	−0.224824	−	0.974399i	$-0.572181\pi$
$613$	−6824.37	−0.449647	−0.224824	+	0.974399i	$0.572181\pi$
$614$	−925.280	−0.0608164
$615$	18803.2	1.23287
$616$	2824.38	0.184736
$617$	15965.5	1.04173	0.520864	−	0.853640i	$-0.325610\pi$
$617$	15965.5	1.04173	0.520864	+	0.853640i	$0.325610\pi$
$618$	−431.282	−0.0280723
$619$	13474.7	0.874952	0.437476	−	0.899230i	$-0.355872\pi$
$619$	13474.7	0.874952	0.437476	+	0.899230i	$0.355872\pi$
$620$	−18922.4	−1.22572
$621$	318.442	0.0205775
$622$	2243.93	0.144652
$623$	−7323.03	−0.470932
$624$	−6223.84	−0.399284
$625$	−19487.8	−1.24722
$626$	−6192.96	−0.395400
$627$	4421.67	0.281634
$628$	−14172.7	−0.900562
$629$	−17687.1	−1.12119
$630$	2093.61	0.132399
$631$	4552.77	0.287231	0.143616	−	0.989634i	$-0.454127\pi$
$631$	4552.77	0.287231	0.143616	+	0.989634i	$0.454127\pi$
$632$	−3858.29	−0.242840
$633$	2444.10	0.153466
$634$	−2265.01	−0.141885
$635$	−29619.6	−1.85105
$636$	9003.94	0.561367
$637$	4392.24	0.273198
$638$	365.044	0.0226524
$639$	8922.09	0.552351
$640$	18336.4	1.13251
$641$	16307.7	1.00486	0.502429	−	0.864619i	$-0.332440\pi$
$641$	16307.7	1.00486	0.502429	+	0.864619i	$0.332440\pi$
$642$	−3854.54	−0.236957
$643$	−4590.73	−0.281556	−0.140778	−	0.990041i	$-0.544960\pi$
$643$	−4590.73	−0.281556	−0.140778	+	0.990041i	$0.544960\pi$
$644$	−1840.94	−0.112645
$645$	−16086.0	−0.981993
$646$	−5661.85	−0.344833
$647$	862.973	0.0524374	0.0262187	−	0.999656i	$-0.491653\pi$
$647$	862.973	0.0524374	0.0262187	+	0.999656i	$0.491653\pi$
$648$	982.957	0.0595898
$649$	5817.71	0.351872
$650$	−2287.88	−0.138059
$651$	11686.5	0.703582
$652$	14043.3	0.843525
$653$	−1847.24	−0.110701	−0.0553507	−	0.998467i	$-0.517628\pi$
$653$	−1847.24	−0.110701	−0.0553507	+	0.998467i	$0.517628\pi$
$654$	3632.94	0.217216
$655$	25774.7	1.53756
$656$	−22243.1	−1.32385
$657$	−5172.25	−0.307137
$658$	5425.26	0.321427
$659$	−15467.7	−0.914320	−0.457160	−	0.889384i	$-0.651133\pi$
$659$	−15467.7	−0.914320	−0.457160	+	0.889384i	$0.651133\pi$
$660$	−3391.62	−0.200028
$661$	−20271.8	−1.19286	−0.596430	−	0.802665i	$-0.703415\pi$
$661$	−20271.8	−1.19286	−0.596430	+	0.802665i	$0.703415\pi$
$662$	−7203.27	−0.422905
$663$	−6740.42	−0.394836
$664$	18101.8	1.05796
$665$	−39496.0	−2.30314
$666$	2346.15	0.136504
$667$	−495.961	−0.0287911
$668$	−24223.9	−1.40307
$669$	−866.730	−0.0500893
$670$	5008.11	0.288776
$671$	671.000	0.0386046
$672$	−8638.89	−0.495912
$673$	−4366.89	−0.250121	−0.125060	−	0.992149i	$-0.539912\pi$
$673$	−4366.89	−0.250121	−0.125060	+	0.992149i	$0.539912\pi$
$674$	8401.20	0.480122
$675$	−1865.41	−0.106370
$676$	3218.17	0.183100
$677$	−25108.2	−1.42539	−0.712693	−	0.701476i	$-0.752525\pi$
$677$	−25108.2	−1.42539	−0.712693	+	0.701476i	$0.752525\pi$
$678$	−13.7428	−0.000778449 0
$679$	6721.82	0.379912
$680$	9052.41	0.510506
$681$	8964.43	0.504431
$682$	1598.27	0.0897372
$683$	27447.0	1.53767	0.768836	−	0.639446i	$-0.220836\pi$
$683$	27447.0	1.53767	0.768836	+	0.639446i	$0.220836\pi$
$684$	−8896.24	−0.497304
$685$	−27678.9	−1.54388
$686$	−3979.47	−0.221482
$687$	3837.97	0.213141
$688$	19028.8	1.05446
$689$	17071.5	0.943935
$690$	−389.010	−0.0214628
$691$	5045.97	0.277797	0.138898	−	0.990307i	$-0.455644\pi$
$691$	5045.97	0.277797	0.138898	+	0.990307i	$0.455644\pi$
$692$	−15615.0	−0.857796
$693$	2094.67	0.114820
$694$	−2207.41	−0.120738
$695$	26407.0	1.44126
$696$	−1530.92	−0.0833753
$697$	−24089.2	−1.30910
$698$	−965.229	−0.0523416
$699$	−10753.9	−0.581905
$700$	10784.1	0.582285
$701$	16140.0	0.869616	0.434808	−	0.900523i	$-0.356816\pi$
$701$	16140.0	0.869616	0.434808	+	0.900523i	$0.356816\pi$
$702$	894.102	0.0480708
$703$	−44260.3	−2.37455
$704$	3169.33	0.169671
$705$	−13579.7	−0.725449
$706$	−928.082	−0.0494743
$707$	28232.8	1.50185
$708$	−11705.0	−0.621331
$709$	3480.93	0.184385	0.0921927	−	0.995741i	$-0.470612\pi$
$709$	3480.93	0.184385	0.0921927	+	0.995741i	$0.470612\pi$
$710$	−10899.2	−0.576115
$711$	−2861.46	−0.150933
$712$	4200.10	0.221075
$713$	−2171.46	−0.114056
$714$	−2682.18	−0.140585
$715$	−6430.50	−0.336345
$716$	17832.7	0.930779
$717$	8223.16	0.428312
$718$	−10693.4	−0.555814
$719$	−1816.35	−0.0942122	−0.0471061	−	0.998890i	$-0.515000\pi$
$719$	−1816.35	−0.0942122	−0.0471061	+	0.998890i	$0.515000\pi$
$720$	6199.11	0.320871
$721$	3854.33	0.199088
$722$	−8755.31	−0.451300
$723$	17707.9	0.910878
$724$	−16628.9	−0.853601
$725$	2905.30	0.148828
$726$	286.470	0.0146445
$727$	−25804.0	−1.31639	−0.658197	−	0.752846i	$-0.728681\pi$
$727$	−25804.0	−1.31639	−0.658197	+	0.752846i	$0.728681\pi$
$728$	−10774.1	−0.548509
$729$	729.000	0.0370370
$730$	6318.44	0.320350
$731$	20608.2	1.04271
$732$	−1350.03	−0.0681674
$733$	12679.5	0.638919	0.319459	−	0.947600i	$-0.396499\pi$
$733$	12679.5	0.638919	0.319459	+	0.947600i	$0.396499\pi$
$734$	−10601.3	−0.533106
$735$	−4374.79	−0.219546
$736$	1605.18	0.0803909
$737$	5010.65	0.250434
$738$	3195.39	0.159382
$739$	−13937.4	−0.693772	−0.346886	−	0.937907i	$-0.612761\pi$
$739$	−13937.4	−0.693772	−0.346886	+	0.937907i	$0.612761\pi$
$740$	33949.6	1.68650
$741$	−16867.3	−0.836213
$742$	6793.16	0.336098
$743$	27948.7	1.38000	0.689999	−	0.723810i	$-0.257611\pi$
$743$	27948.7	1.38000	0.689999	+	0.723810i	$0.257611\pi$
$744$	−6702.78	−0.330290
$745$	9925.53	0.488112
$746$	6608.65	0.324343
$747$	13425.0	0.657556
$748$	4345.09	0.212396
$749$	34447.7	1.68050
$750$	−1844.12	−0.0897837
$751$	8539.72	0.414938	0.207469	−	0.978242i	$-0.433477\pi$
$751$	8539.72	0.414938	0.207469	+	0.978242i	$0.433477\pi$
$752$	16064.0	0.778982
$753$	1862.78	0.0901505
$754$	−1392.53	−0.0672584
$755$	−10334.0	−0.498137
$756$	−4214.40	−0.202747
$757$	14007.0	0.672515	0.336258	−	0.941770i	$-0.390839\pi$
$757$	14007.0	0.672515	0.336258	+	0.941770i	$0.390839\pi$
$758$	−6800.53	−0.325866
$759$	−389.207	−0.0186131
$760$	22652.8	1.08119
$761$	−15218.9	−0.724945	−0.362473	−	0.931994i	$-0.618067\pi$
$761$	−15218.9	−0.724945	−0.362473	+	0.931994i	$0.618067\pi$
$762$	−5033.51	−0.239298
$763$	−32467.3	−1.54049
$764$	3686.21	0.174558
$765$	6713.63	0.317296
$766$	−3815.70	−0.179983
$767$	−22192.7	−1.04476
$768$	−3798.84	−0.178488
$769$	4542.72	0.213023	0.106512	−	0.994311i	$-0.466032\pi$
$769$	4542.72	0.213023	0.106512	+	0.994311i	$0.466032\pi$
$770$	−2558.86	−0.119759
$771$	−12953.5	−0.605069
$772$	−18143.1	−0.845837
$773$	8115.86	0.377629	0.188815	−	0.982013i	$-0.439535\pi$
$773$	8115.86	0.377629	0.188815	+	0.982013i	$0.439535\pi$
$774$	−2733.63	−0.126949
$775$	12720.2	0.589579
$776$	−3855.28	−0.178346
$777$	−20967.4	−0.968083
$778$	−4307.08	−0.198478
$779$	−60281.1	−2.77252
$780$	12937.9	0.593914
$781$	−10904.8	−0.499620
$782$	498.371	0.0227899
$783$	−1135.39	−0.0518205
$784$	5175.12	0.235747
$785$	26764.7	1.21691
$786$	4380.11	0.198770
$787$	27303.2	1.23666	0.618331	−	0.785918i	$-0.287809\pi$
$787$	27303.2	1.23666	0.618331	+	0.785918i	$0.287809\pi$
$788$	9052.39	0.409236
$789$	−18007.0	−0.812505
$790$	3495.57	0.157426
$791$	122.818	0.00552074
$792$	−1201.39	−0.0539010
$793$	−2559.65	−0.114623
$794$	3966.94	0.177306
$795$	−17003.6	−0.758562
$796$	−15530.3	−0.691527
$797$	−24993.5	−1.11081	−0.555405	−	0.831580i	$-0.687437\pi$
$797$	−24993.5	−1.11081	−0.555405	+	0.831580i	$0.687437\pi$
$798$	−6711.90	−0.297743
$799$	17397.3	0.770305
$800$	−9403.01	−0.415558
$801$	3114.96	0.137405
$802$	−637.346	−0.0280617
$803$	6321.64	0.277815
$804$	−10081.2	−0.442212
$805$	3476.55	0.152214
$806$	−6096.88	−0.266443
$807$	−24216.5	−1.05633
$808$	−16192.9	−0.705028
$809$	37774.1	1.64161	0.820807	−	0.571205i	$-0.193524\pi$
$809$	37774.1	1.64161	0.820807	+	0.571205i	$0.193524\pi$
$810$	−890.549	−0.0386305
$811$	30732.6	1.33066	0.665331	−	0.746548i	$-0.268290\pi$
$811$	30732.6	1.33066	0.665331	+	0.746548i	$0.268290\pi$
$812$	6563.76	0.283674
$813$	−24050.7	−1.03751
$814$	−2867.52	−0.123472
$815$	−26520.3	−1.13983
$816$	−7941.84	−0.340711
$817$	51570.1	2.20833
$818$	11204.9	0.478939
$819$	−7990.50	−0.340917
$820$	46238.3	1.96916
$821$	−26756.1	−1.13738	−0.568692	−	0.822550i	$-0.692551\pi$
$821$	−26756.1	−1.13738	−0.568692	+	0.822550i	$0.692551\pi$
$822$	−4703.71	−0.199587
$823$	7630.75	0.323197	0.161599	−	0.986857i	$-0.448335\pi$
$823$	7630.75	0.323197	0.161599	+	0.986857i	$0.448335\pi$
$824$	−2210.64	−0.0934602
$825$	2279.94	0.0962151
$826$	−8831.04	−0.371999
$827$	−6628.52	−0.278714	−0.139357	−	0.990242i	$-0.544503\pi$
$827$	−6628.52	−0.278714	−0.139357	+	0.990242i	$0.544503\pi$
$828$	783.071	0.0328667
$829$	18693.7	0.783184	0.391592	−	0.920139i	$-0.371924\pi$
$829$	18693.7	0.783184	0.391592	+	0.920139i	$0.371924\pi$
$830$	−16400.0	−0.685846
$831$	−20068.7	−0.837757
$832$	−12090.0	−0.503780
$833$	5604.66	0.233121
$834$	4487.57	0.186321
$835$	45745.9	1.89593
$836$	10873.2	0.449829
$837$	−4971.05	−0.205286
$838$	7849.23	0.323565
$839$	−18882.7	−0.777000	−0.388500	−	0.921449i	$-0.627007\pi$
$839$	−18882.7	−0.777000	−0.388500	+	0.921449i	$0.627007\pi$
$840$	10731.3	0.440791
$841$	−22620.7	−0.927495
$842$	2835.07	0.116037
$843$	4300.54	0.175704
$844$	6010.20	0.245118
$845$	−6077.39	−0.247419
$846$	−2307.72	−0.0937837
$847$	−2560.15	−0.103858
$848$	20114.3	0.814538
$849$	−1969.75	−0.0796248
$850$	−2919.42	−0.117806
$851$	3895.91	0.156933
$852$	21940.0	0.882222
$853$	−49044.1	−1.96863	−0.984313	−	0.176431i	$-0.943545\pi$
$853$	−49044.1	−1.96863	−0.984313	+	0.176431i	$0.943545\pi$
$854$	−1018.55	−0.0408127
$855$	16800.2	0.671995
$856$	−19757.4	−0.788893
$857$	−28161.6	−1.12250	−0.561249	−	0.827647i	$-0.689679\pi$
$857$	−28161.6	−1.12250	−0.561249	+	0.827647i	$0.689679\pi$
$858$	−1092.79	−0.0434817
$859$	33813.1	1.34306	0.671530	−	0.740978i	$-0.265638\pi$
$859$	33813.1	1.34306	0.671530	+	0.740978i	$0.265638\pi$
$860$	−39556.6	−1.56845
$861$	−28556.9	−1.13033
$862$	−1966.91	−0.0777184
$863$	35921.4	1.41689	0.708447	−	0.705764i	$-0.249396\pi$
$863$	35921.4	1.41689	0.708447	+	0.705764i	$0.249396\pi$
$864$	3674.69	0.144694
$865$	29488.4	1.15912
$866$	10443.0	0.409780
$867$	6137.99	0.240435
$868$	28738.0	1.12377
$869$	3497.34	0.136524
$870$	1386.99	0.0540500
$871$	−19114.0	−0.743575
$872$	18621.5	0.723170
$873$	−2859.23	−0.110848
$874$	1247.13	0.0482663
$875$	16480.7	0.636744
$876$	−12718.9	−0.490562
$877$	−23530.4	−0.906002	−0.453001	−	0.891510i	$-0.649647\pi$
$877$	−23530.4	−0.906002	−0.453001	+	0.891510i	$0.649647\pi$
$878$	−2737.37	−0.105218
$879$	−22280.3	−0.854944
$880$	−7576.69	−0.290239
$881$	7544.76	0.288524	0.144262	−	0.989540i	$-0.453919\pi$
$881$	7544.76	0.288524	0.144262	+	0.989540i	$0.453919\pi$
$882$	−743.446	−0.0283822
$883$	36835.1	1.40385	0.701925	−	0.712250i	$-0.252324\pi$
$883$	36835.1	1.40385	0.701925	+	0.712250i	$0.252324\pi$
$884$	−16575.1	−0.630636
$885$	22104.5	0.839589
$886$	−8166.77	−0.309671
$887$	−490.903	−0.0185828	−0.00929139	−	0.999957i	$-0.502958\pi$
$887$	−490.903	−0.0185828	−0.00929139	+	0.999957i	$0.502958\pi$
$888$	12025.8	0.454458
$889$	44984.1	1.69709
$890$	−3805.25	−0.143317
$891$	−891.000	−0.0335013
$892$	−2131.35	−0.0800032
$893$	43535.2	1.63141
$894$	1686.73	0.0631015
$895$	−33676.3	−1.25774
$896$	−27848.0	−1.03832
$897$	1484.70	0.0552651
$898$	13384.5	0.497380
$899$	7742.21	0.287227
$900$	−4587.17	−0.169895
$901$	21783.8	0.805465
$902$	−3905.47	−0.144166
$903$	24430.2	0.900318
$904$	−70.4419	−0.00259166
$905$	31403.0	1.15345
$906$	−1756.15	−0.0643975
$907$	1359.91	0.0497851	0.0248925	−	0.999690i	$-0.492076\pi$
$907$	1359.91	0.0497851	0.0248925	+	0.999690i	$0.492076\pi$
$908$	22044.2	0.805684
$909$	−12009.3	−0.438198
$910$	9761.22	0.355584
$911$	−35960.2	−1.30781	−0.653905	−	0.756576i	$-0.726871\pi$
$911$	−35960.2	−1.30781	−0.653905	+	0.756576i	$0.726871\pi$
$912$	−19873.7	−0.721584
$913$	−16408.3	−0.594782
$914$	−9315.18	−0.337110
$915$	2549.48	0.0921128
$916$	9437.83	0.340431
$917$	−39144.7	−1.40967
$918$	1140.91	0.0410191
$919$	−30817.4	−1.10617	−0.553085	−	0.833125i	$-0.686550\pi$
$919$	−30817.4	−1.10617	−0.553085	+	0.833125i	$0.686550\pi$
$920$	−1993.96	−0.0714554
$921$	−3517.41	−0.125844
$922$	−4418.75	−0.157835
$923$	41598.2	1.48345
$924$	5150.94	0.183391
$925$	−22821.9	−0.811223
$926$	11086.0	0.393421
$927$	−1639.50	−0.0580886
$928$	−5723.17	−0.202449
$929$	35138.9	1.24098	0.620489	−	0.784215i	$-0.286934\pi$
$929$	35138.9	1.24098	0.620489	+	0.784215i	$0.286934\pi$
$930$	6072.65	0.214118
$931$	14025.1	0.493722
$932$	−26444.7	−0.929426
$933$	8530.19	0.299320
$934$	3718.92	0.130286
$935$	−8205.55	−0.287005
$936$	4582.93	0.160040
$937$	40548.3	1.41372	0.706860	−	0.707353i	$-0.250111\pi$
$937$	40548.3	1.41372	0.706860	+	0.707353i	$0.250111\pi$
$938$	−7605.95	−0.264758
$939$	−23542.2	−0.818181
$940$	−33393.4	−1.15870
$941$	−37338.2	−1.29351	−0.646754	−	0.762699i	$-0.723874\pi$
$941$	−37338.2	−1.29351	−0.646754	+	0.762699i	$0.723874\pi$
$942$	4548.35	0.157318
$943$	5306.10	0.183235
$944$	−26148.4	−0.901545
$945$	7958.75	0.273966
$946$	3341.11	0.114830
$947$	−46901.1	−1.60938	−0.804689	−	0.593697i	$-0.797668\pi$
$947$	−46901.1	−1.60938	−0.804689	+	0.593697i	$0.797668\pi$
$948$	−7036.54	−0.241072
$949$	−24115.1	−0.824876
$950$	−7305.57	−0.249499
$951$	−8610.34	−0.293595
$952$	−13748.1	−0.468046
$953$	31640.9	1.07550	0.537748	−	0.843106i	$-0.319275\pi$
$953$	31640.9	1.07550	0.537748	+	0.843106i	$0.319275\pi$
$954$	−2889.57	−0.0980644
$955$	−6961.27	−0.235876
$956$	20221.3	0.684105
$957$	1387.70	0.0468734
$958$	11665.1	0.393406
$959$	42036.6	1.41547
$960$	12041.9	0.404846
$961$	4106.59	0.137847
$962$	10938.7	0.366609
$963$	−14652.8	−0.490323
$964$	43545.0	1.45486
$965$	34262.7	1.14296
$966$	590.800	0.0196777
$967$	−25689.8	−0.854319	−0.427160	−	0.904176i	$-0.640486\pi$
$967$	−25689.8	−0.854319	−0.427160	+	0.904176i	$0.640486\pi$
$968$	1468.37	0.0487553
$969$	−21523.2	−0.713546
$970$	3492.85	0.115617
$971$	−22419.5	−0.740965	−0.370482	−	0.928840i	$-0.620808\pi$
$971$	−22419.5	−0.740965	−0.370482	+	0.928840i	$0.620808\pi$
$972$	1792.66	0.0591560
$973$	−40105.0	−1.32138
$974$	−13656.8	−0.449272
$975$	−8697.27	−0.285677
$976$	−3015.89	−0.0989102
$977$	508.276	0.0166440	0.00832200	−	0.999965i	$-0.497351\pi$
$977$	508.276	0.0166440	0.00832200	+	0.999965i	$0.497351\pi$
$978$	−4506.82	−0.147354
$979$	−3807.17	−0.124288
$980$	−10757.9	−0.350662
$981$	13810.5	0.449474
$982$	479.777	0.0155909
$983$	23872.8	0.774591	0.387295	−	0.921956i	$-0.373409\pi$
$983$	23872.8	0.774591	0.387295	+	0.921956i	$0.373409\pi$
$984$	16378.7	0.530624
$985$	−17095.1	−0.552990
$986$	−1776.91	−0.0573920
$987$	20623.9	0.665112
$988$	−41477.7	−1.33561
$989$	−4539.34	−0.145948
$990$	1088.45	0.0349426
$991$	19143.3	0.613629	0.306814	−	0.951769i	$-0.400737\pi$
$991$	19143.3	0.613629	0.306814	+	0.951769i	$0.400737\pi$
$992$	−25057.7	−0.801998
$993$	−27382.9	−0.875095
$994$	16553.0	0.528198
$995$	29328.4	0.934444
$996$	33013.0	1.05026
$997$	−15581.5	−0.494956	−0.247478	−	0.968893i	$-0.579602\pi$
$997$	−15581.5	−0.494956	−0.247478	+	0.968893i	$0.579602\pi$
$998$	−9791.52	−0.310566
$999$	8918.79	0.282461

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.e.1.16	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.e.1.16	✓	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.789172 q^{2} -3.00000 q^{3} -7.37721 q^{4} +13.9316 q^{5} +2.36752 q^{6} -21.1583 q^{7} +12.1353 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.789172 q^{2} -3.00000 q^{3} -7.37721 q^{4} +13.9316 q^{5} +2.36752 q^{6} -21.1583 q^{7} +12.1353 q^{8} +9.00000 q^{9} -10.9944 q^{10} -11.0000 q^{11} +22.1316 q^{12} +41.9615 q^{13} +16.6975 q^{14} -41.7948 q^{15} +49.4408 q^{16} +53.5444 q^{17} -7.10255 q^{18} +133.990 q^{19} -102.776 q^{20} +63.4749 q^{21} +8.68090 q^{22} -11.7942 q^{23} -36.4058 q^{24} +69.0892 q^{25} -33.1149 q^{26} -27.0000 q^{27} +156.089 q^{28} +42.0514 q^{29} +32.9833 q^{30} +184.113 q^{31} -136.099 q^{32} +33.0000 q^{33} -42.2558 q^{34} -294.769 q^{35} -66.3949 q^{36} -330.326 q^{37} -105.741 q^{38} -125.885 q^{39} +169.064 q^{40} -449.893 q^{41} -50.0926 q^{42} +384.881 q^{43} +81.1493 q^{44} +125.384 q^{45} +9.30762 q^{46} +324.914 q^{47} -148.323 q^{48} +104.673 q^{49} -54.5233 q^{50} -160.633 q^{51} -309.559 q^{52} +406.836 q^{53} +21.3077 q^{54} -153.248 q^{55} -256.761 q^{56} -401.970 q^{57} -33.1858 q^{58} -528.883 q^{59} +308.329 q^{60} -61.0000 q^{61} -145.297 q^{62} -190.425 q^{63} -288.121 q^{64} +584.591 q^{65} -26.0427 q^{66} -455.513 q^{67} -395.008 q^{68} +35.3825 q^{69} +232.623 q^{70} +991.343 q^{71} +109.217 q^{72} -574.694 q^{73} +260.684 q^{74} -207.268 q^{75} -988.471 q^{76} +232.741 q^{77} +99.3446 q^{78} -317.940 q^{79} +688.790 q^{80} +81.0000 q^{81} +355.043 q^{82} +1491.67 q^{83} -468.267 q^{84} +745.959 q^{85} -303.737 q^{86} -126.154 q^{87} -133.488 q^{88} +346.107 q^{89} -98.9498 q^{90} -887.834 q^{91} +87.0079 q^{92} -552.339 q^{93} -256.413 q^{94} +1866.69 q^{95} +408.298 q^{96} -317.692 q^{97} -82.6051 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9} + 95 q^{10} - 418 q^{11} - 426 q^{12} + 13 q^{13} + 26 q^{14} - 45 q^{15} + 486 q^{16} - 224 q^{17} - 18 q^{18} + 367 q^{19} + 18 q^{20} - 189 q^{21} + 22 q^{22} + 51 q^{23} + 135 q^{24} + 773 q^{25} - 439 q^{26} - 1026 q^{27} + 22 q^{28} - 462 q^{29} - 285 q^{30} + 234 q^{31} - 597 q^{32} + 1254 q^{33} + 956 q^{34} - 522 q^{35} + 1278 q^{36} + 954 q^{37} + 705 q^{38} - 39 q^{39} + 1495 q^{40} - 740 q^{41} - 78 q^{42} + 1441 q^{43} - 1562 q^{44} + 135 q^{45} + 581 q^{46} + 1003 q^{47} - 1458 q^{48} + 2707 q^{49} + 388 q^{50} + 672 q^{51} + 788 q^{52} + 735 q^{53} + 54 q^{54} - 165 q^{55} + 1059 q^{56} - 1101 q^{57} + 177 q^{58} + 261 q^{59} - 54 q^{60} - 2318 q^{61} + 1251 q^{62} + 567 q^{63} + 5571 q^{64} - 1354 q^{65} - 66 q^{66} + 3495 q^{67} - 1856 q^{68} - 153 q^{69} + 542 q^{70} - 873 q^{71} - 405 q^{72} + 989 q^{73} - 3406 q^{74} - 2319 q^{75} + 1712 q^{76} - 693 q^{77} + 1317 q^{78} + 2313 q^{79} + 1593 q^{80} + 3078 q^{81} + 5170 q^{82} + 569 q^{83} - 66 q^{84} - 1271 q^{85} + 3065 q^{86} + 1386 q^{87} + 495 q^{88} - 2917 q^{89} + 855 q^{90} + 2740 q^{91} + 1083 q^{92} - 702 q^{93} + 3272 q^{94} + 2696 q^{95} + 1791 q^{96} + 4250 q^{97} + 5952 q^{98} - 3762 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9 + 95 * q^10 - 418 * q^11 - 426 * q^12 + 13 * q^13 + 26 * q^14 - 45 * q^15 + 486 * q^16 - 224 * q^17 - 18 * q^18 + 367 * q^19 + 18 * q^20 - 189 * q^21 + 22 * q^22 + 51 * q^23 + 135 * q^24 + 773 * q^25 - 439 * q^26 - 1026 * q^27 + 22 * q^28 - 462 * q^29 - 285 * q^30 + 234 * q^31 - 597 * q^32 + 1254 * q^33 + 956 * q^34 - 522 * q^35 + 1278 * q^36 + 954 * q^37 + 705 * q^38 - 39 * q^39 + 1495 * q^40 - 740 * q^41 - 78 * q^42 + 1441 * q^43 - 1562 * q^44 + 135 * q^45 + 581 * q^46 + 1003 * q^47 - 1458 * q^48 + 2707 * q^49 + 388 * q^50 + 672 * q^51 + 788 * q^52 + 735 * q^53 + 54 * q^54 - 165 * q^55 + 1059 * q^56 - 1101 * q^57 + 177 * q^58 + 261 * q^59 - 54 * q^60 - 2318 * q^61 + 1251 * q^62 + 567 * q^63 + 5571 * q^64 - 1354 * q^65 - 66 * q^66 + 3495 * q^67 - 1856 * q^68 - 153 * q^69 + 542 * q^70 - 873 * q^71 - 405 * q^72 + 989 * q^73 - 3406 * q^74 - 2319 * q^75 + 1712 * q^76 - 693 * q^77 + 1317 * q^78 + 2313 * q^79 + 1593 * q^80 + 3078 * q^81 + 5170 * q^82 + 569 * q^83 - 66 * q^84 - 1271 * q^85 + 3065 * q^86 + 1386 * q^87 + 495 * q^88 - 2917 * q^89 + 855 * q^90 + 2740 * q^91 + 1083 * q^92 - 702 * q^93 + 3272 * q^94 + 2696 * q^95 + 1791 * q^96 + 4250 * q^97 + 5952 * q^98 - 3762 * q^99

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