LMFDB - Embedded newform 1045.4.a.e.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,4,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.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:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.07818 q^{2} -9.17350 q^{3} +17.7879 q^{4} +5.00000 q^{5} -46.5847 q^{6} +27.6942 q^{7} +49.7048 q^{8} +57.1531 q^{9} +O(q^{10})$	\(q+5.07818 q^{2} -9.17350 q^{3} +17.7879 q^{4} +5.00000 q^{5} -46.5847 q^{6} +27.6942 q^{7} +49.7048 q^{8} +57.1531 q^{9} +25.3909 q^{10} +11.0000 q^{11} -163.178 q^{12} +61.8970 q^{13} +140.636 q^{14} -45.8675 q^{15} +110.107 q^{16} -32.8467 q^{17} +290.234 q^{18} -19.0000 q^{19} +88.9396 q^{20} -254.053 q^{21} +55.8600 q^{22} +45.2387 q^{23} -455.967 q^{24} +25.0000 q^{25} +314.324 q^{26} -276.610 q^{27} +492.622 q^{28} -246.380 q^{29} -232.924 q^{30} +143.117 q^{31} +161.503 q^{32} -100.909 q^{33} -166.802 q^{34} +138.471 q^{35} +1016.64 q^{36} +134.058 q^{37} -96.4854 q^{38} -567.812 q^{39} +248.524 q^{40} +163.145 q^{41} -1290.13 q^{42} -404.994 q^{43} +195.667 q^{44} +285.766 q^{45} +229.730 q^{46} -171.646 q^{47} -1010.06 q^{48} +423.968 q^{49} +126.955 q^{50} +301.319 q^{51} +1101.02 q^{52} +123.660 q^{53} -1404.67 q^{54} +55.0000 q^{55} +1376.53 q^{56} +174.297 q^{57} -1251.16 q^{58} +866.750 q^{59} -815.888 q^{60} +674.622 q^{61} +726.774 q^{62} +1582.81 q^{63} -60.7113 q^{64} +309.485 q^{65} -512.432 q^{66} -120.926 q^{67} -584.275 q^{68} -414.997 q^{69} +703.181 q^{70} +210.190 q^{71} +2840.79 q^{72} -627.397 q^{73} +680.770 q^{74} -229.338 q^{75} -337.970 q^{76} +304.636 q^{77} -2883.45 q^{78} +91.2577 q^{79} +550.534 q^{80} +994.346 q^{81} +828.481 q^{82} +570.479 q^{83} -4519.07 q^{84} -164.234 q^{85} -2056.63 q^{86} +2260.16 q^{87} +546.753 q^{88} -1212.13 q^{89} +1451.17 q^{90} +1714.19 q^{91} +804.702 q^{92} -1312.88 q^{93} -871.649 q^{94} -95.0000 q^{95} -1481.55 q^{96} -1274.56 q^{97} +2152.99 q^{98} +628.685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9}+O(q^{10}) $ 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9} + 60 q^{10} + 242 q^{11} + 164 q^{12} + 207 q^{13} + 129 q^{14} + 105 q^{15} + 604 q^{16} + 209 q^{17} + 869 q^{18} - 418 q^{19} + 480 q^{20} + 45 q^{21} + 132 q^{22} + 191 q^{23} + 458 q^{24} + 550 q^{25} + 363 q^{26} + 45 q^{27} + 577 q^{28} + 389 q^{29} + 135 q^{30} + 198 q^{31} + 1149 q^{32} + 231 q^{33} + 467 q^{34} + 465 q^{35} + 1315 q^{36} + 312 q^{37} - 228 q^{38} + 137 q^{39} + 570 q^{40} + 632 q^{41} - 1794 q^{42} + 1584 q^{43} + 1056 q^{44} + 1045 q^{45} + 681 q^{46} - 54 q^{47} + 2491 q^{48} + 1063 q^{49} + 300 q^{50} + 37 q^{51} + 1246 q^{52} + 343 q^{53} + 1078 q^{54} + 1210 q^{55} - 87 q^{56} - 399 q^{57} - 1424 q^{58} + 2787 q^{59} + 820 q^{60} + 2070 q^{61} - 446 q^{62} + 1696 q^{63} + 1758 q^{64} + 1035 q^{65} + 297 q^{66} + 2423 q^{67} - 524 q^{68} - 997 q^{69} + 645 q^{70} + 2538 q^{71} + 6010 q^{72} + 1397 q^{73} - 1977 q^{74} + 525 q^{75} - 1824 q^{76} + 1023 q^{77} + 202 q^{78} + 878 q^{79} + 3020 q^{80} + 2030 q^{81} - 190 q^{82} + 4932 q^{83} - 4580 q^{84} + 1045 q^{85} - 3394 q^{86} + 6009 q^{87} + 1254 q^{88} + 1812 q^{89} + 4345 q^{90} + 4349 q^{91} - 788 q^{92} - 4848 q^{93} - 2152 q^{94} - 2090 q^{95} + 4032 q^{96} + 988 q^{97} + 1366 q^{98} + 2299 q^{99}+O(q^{100}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9 + 60 * q^10 + 242 * q^11 + 164 * q^12 + 207 * q^13 + 129 * q^14 + 105 * q^15 + 604 * q^16 + 209 * q^17 + 869 * q^18 - 418 * q^19 + 480 * q^20 + 45 * q^21 + 132 * q^22 + 191 * q^23 + 458 * q^24 + 550 * q^25 + 363 * q^26 + 45 * q^27 + 577 * q^28 + 389 * q^29 + 135 * q^30 + 198 * q^31 + 1149 * q^32 + 231 * q^33 + 467 * q^34 + 465 * q^35 + 1315 * q^36 + 312 * q^37 - 228 * q^38 + 137 * q^39 + 570 * q^40 + 632 * q^41 - 1794 * q^42 + 1584 * q^43 + 1056 * q^44 + 1045 * q^45 + 681 * q^46 - 54 * q^47 + 2491 * q^48 + 1063 * q^49 + 300 * q^50 + 37 * q^51 + 1246 * q^52 + 343 * q^53 + 1078 * q^54 + 1210 * q^55 - 87 * q^56 - 399 * q^57 - 1424 * q^58 + 2787 * q^59 + 820 * q^60 + 2070 * q^61 - 446 * q^62 + 1696 * q^63 + 1758 * q^64 + 1035 * q^65 + 297 * q^66 + 2423 * q^67 - 524 * q^68 - 997 * q^69 + 645 * q^70 + 2538 * q^71 + 6010 * q^72 + 1397 * q^73 - 1977 * q^74 + 525 * q^75 - 1824 * q^76 + 1023 * q^77 + 202 * q^78 + 878 * q^79 + 3020 * q^80 + 2030 * q^81 - 190 * q^82 + 4932 * q^83 - 4580 * q^84 + 1045 * q^85 - 3394 * q^86 + 6009 * q^87 + 1254 * q^88 + 1812 * q^89 + 4345 * q^90 + 4349 * q^91 - 788 * q^92 - 4848 * q^93 - 2152 * q^94 - 2090 * q^95 + 4032 * q^96 + 988 * q^97 + 1366 * q^98 + 2299 * 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 $

$2$	5.07818	1.79541	0.897704	−	0.440599i	$-0.145234\pi$
$2$	5.07818	1.79541	0.897704	+	0.440599i	$0.145234\pi$
$3$	−9.17350	−1.76544	−0.882721	−	0.469898i	$-0.844291\pi$
$3$	−9.17350	−1.76544	−0.882721	+	0.469898i	$0.844291\pi$
$4$	17.7879	2.22349
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−46.5847	−3.16969
$7$	27.6942	1.49535	0.747673	−	0.664067i	$-0.231171\pi$
$7$	27.6942	1.49535	0.747673	+	0.664067i	$0.231171\pi$
$8$	49.7048	2.19666
$9$	57.1531	2.11678
$10$	25.3909	0.802931
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−163.178	−3.92544
$13$	61.8970	1.32055	0.660274	−	0.751025i	$-0.270440\pi$
$13$	61.8970	1.32055	0.660274	+	0.751025i	$0.270440\pi$
$14$	140.636	2.68476
$15$	−45.8675	−0.789529
$16$	110.107	1.72042
$17$	−32.8467	−0.468618	−0.234309	−	0.972162i	$-0.575283\pi$
$17$	−32.8467	−0.468618	−0.234309	+	0.972162i	$0.575283\pi$
$18$	290.234	3.80049
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	88.9396	0.994375
$21$	−254.053	−2.63995
$22$	55.8600	0.541336
$23$	45.2387	0.410127	0.205063	−	0.978749i	$-0.434260\pi$
$23$	45.2387	0.410127	0.205063	+	0.978749i	$0.434260\pi$
$24$	−455.967	−3.87808
$25$	25.0000	0.200000
$26$	314.324	2.37092
$27$	−276.610	−1.97161
$28$	492.622	3.32489
$29$	−246.380	−1.57764	−0.788820	−	0.614625i	$-0.789307\pi$
$29$	−246.380	−1.57764	−0.788820	+	0.614625i	$0.789307\pi$
$30$	−232.924	−1.41753
$31$	143.117	0.829180	0.414590	−	0.910008i	$-0.363925\pi$
$31$	143.117	0.829180	0.414590	+	0.910008i	$0.363925\pi$
$32$	161.503	0.892187
$33$	−100.909	−0.532301
$34$	−166.802	−0.841360
$35$	138.471	0.668739
$36$	1016.64	4.70665
$37$	134.058	0.595648	0.297824	−	0.954621i	$-0.403739\pi$
$37$	134.058	0.595648	0.297824	+	0.954621i	$0.403739\pi$
$38$	−96.4854	−0.411895
$39$	−567.812	−2.33135
$40$	248.524	0.982378
$41$	163.145	0.621439	0.310719	−	0.950502i	$-0.399430\pi$
$41$	163.145	0.621439	0.310719	+	0.950502i	$0.399430\pi$
$42$	−1290.13	−4.73978
$43$	−404.994	−1.43630	−0.718150	−	0.695888i	$-0.755011\pi$
$43$	−404.994	−1.43630	−0.718150	+	0.695888i	$0.755011\pi$
$44$	195.667	0.670407
$45$	285.766	0.946654
$46$	229.730	0.736345
$47$	−171.646	−0.532705	−0.266352	−	0.963876i	$-0.585818\pi$
$47$	−171.646	−0.532705	−0.266352	+	0.963876i	$0.585818\pi$
$48$	−1010.06	−3.03730
$49$	423.968	1.23606
$50$	126.955	0.359082
$51$	301.319	0.827317
$52$	1101.02	2.93623
$53$	123.660	0.320490	0.160245	−	0.987077i	$-0.448772\pi$
$53$	123.660	0.320490	0.160245	+	0.987077i	$0.448772\pi$
$54$	−1404.67	−3.53985
$55$	55.0000	0.134840
$56$	1376.53	3.28477
$57$	174.297	0.405020
$58$	−1251.16	−2.83251
$59$	866.750	1.91256	0.956281	−	0.292448i	$-0.0944699\pi$
$59$	866.750	1.91256	0.956281	+	0.292448i	$0.0944699\pi$
$60$	−815.888	−1.75551
$61$	674.622	1.41601	0.708004	−	0.706209i	$-0.249596\pi$
$61$	674.622	1.41601	0.708004	+	0.706209i	$0.249596\pi$
$62$	726.774	1.48872
$63$	1582.81	3.16532
$64$	−60.7113	−0.118577
$65$	309.485	0.590567
$66$	−512.432	−0.955697
$67$	−120.926	−0.220499	−0.110250	−	0.993904i	$-0.535165\pi$
$67$	−120.926	−0.220499	−0.110250	+	0.993904i	$0.535165\pi$
$68$	−584.275	−1.04197
$69$	−414.997	−0.724055
$70$	703.181	1.20066
$71$	210.190	0.351338	0.175669	−	0.984449i	$-0.443791\pi$
$71$	210.190	0.351338	0.175669	+	0.984449i	$0.443791\pi$
$72$	2840.79	4.64986
$73$	−627.397	−1.00591	−0.502954	−	0.864313i	$-0.667754\pi$
$73$	−627.397	−1.00591	−0.502954	+	0.864313i	$0.667754\pi$
$74$	680.770	1.06943
$75$	−229.338	−0.353088
$76$	−337.970	−0.510104
$77$	304.636	0.450864
$78$	−2883.45	−4.18572
$79$	91.2577	0.129966	0.0649829	−	0.997886i	$-0.479301\pi$
$79$	91.2577	0.129966	0.0649829	+	0.997886i	$0.479301\pi$
$80$	550.534	0.769394
$81$	994.346	1.36399
$82$	828.481	1.11574
$83$	570.479	0.754436	0.377218	−	0.926125i	$-0.376881\pi$
$83$	570.479	0.754436	0.377218	+	0.926125i	$0.376881\pi$
$84$	−4519.07	−5.86989
$85$	−164.234	−0.209572
$86$	−2056.63	−2.57875
$87$	2260.16	2.78523
$88$	546.753	0.662319
$89$	−1212.13	−1.44366	−0.721828	−	0.692073i	$-0.756698\pi$
$89$	−1212.13	−1.44366	−0.721828	+	0.692073i	$0.756698\pi$
$90$	1451.17	1.69963
$91$	1714.19	1.97468
$92$	804.702	0.911912
$93$	−1312.88	−1.46387
$94$	−871.649	−0.956422
$95$	−95.0000	−0.102598
$96$	−1481.55	−1.57510
$97$	−1274.56	−1.33414	−0.667070	−	0.744995i	$-0.732452\pi$
$97$	−1274.56	−1.33414	−0.667070	+	0.744995i	$0.732452\pi$
$98$	2152.99	2.21923
$99$	628.685	0.638234
$100$	444.698	0.444698
$101$	689.118	0.678909	0.339455	−	0.940622i	$-0.389757\pi$
$101$	689.118	0.678909	0.339455	+	0.940622i	$0.389757\pi$
$102$	1530.15	1.48537
$103$	1294.12	1.23800	0.618999	−	0.785392i	$-0.287539\pi$
$103$	1294.12	1.23800	0.618999	+	0.785392i	$0.287539\pi$
$104$	3076.58	2.90080
$105$	−1270.26	−1.18062
$106$	627.966	0.575410
$107$	900.931	0.813984	0.406992	−	0.913432i	$-0.366578\pi$
$107$	900.931	0.813984	0.406992	+	0.913432i	$0.366578\pi$
$108$	−4920.31	−4.38387
$109$	195.324	0.171639	0.0858196	−	0.996311i	$-0.472649\pi$
$109$	195.324	0.171639	0.0858196	+	0.996311i	$0.472649\pi$
$110$	279.300	0.242093
$111$	−1229.78	−1.05158
$112$	3049.32	2.57262
$113$	2109.46	1.75612	0.878058	−	0.478555i	$-0.158839\pi$
$113$	2109.46	1.75612	0.878058	+	0.478555i	$0.158839\pi$
$114$	885.109	0.727176
$115$	226.193	0.183414
$116$	−4382.58	−3.50786
$117$	3537.60	2.79531
$118$	4401.51	3.43383
$119$	−909.664	−0.700746
$120$	−2279.84	−1.73433
$121$	121.000	0.0909091
$122$	3425.85	2.54231
$123$	−1496.61	−1.09711
$124$	2545.75	1.84367
$125$	125.000	0.0894427
$126$	8037.80	5.68305
$127$	724.242	0.506032	0.253016	−	0.967462i	$-0.418577\pi$
$127$	724.242	0.506032	0.253016	+	0.967462i	$0.418577\pi$
$128$	−1600.33	−1.10508
$129$	3715.21	2.53571
$130$	1571.62	1.06031
$131$	2391.46	1.59498	0.797491	−	0.603331i	$-0.206160\pi$
$131$	2391.46	1.59498	0.797491	+	0.603331i	$0.206160\pi$
$132$	−1794.95	−1.18356
$133$	−526.190	−0.343056
$134$	−614.083	−0.395886
$135$	−1383.05	−0.881733
$136$	−1632.64	−1.02940
$137$	−2723.35	−1.69833	−0.849166	−	0.528125i	$-0.822895\pi$
$137$	−2723.35	−1.69833	−0.849166	+	0.528125i	$0.822895\pi$
$138$	−2107.43	−1.29997
$139$	−2452.77	−1.49670	−0.748349	−	0.663305i	$-0.769153\pi$
$139$	−2452.77	−1.49670	−0.748349	+	0.663305i	$0.769153\pi$
$140$	2463.11	1.48693
$141$	1574.59	0.940459
$142$	1067.38	0.630795
$143$	680.866	0.398160
$144$	6292.94	3.64175
$145$	−1231.90	−0.705542
$146$	−3186.04	−1.80602
$147$	−3889.27	−2.18219
$148$	2384.61	1.32442
$149$	−2460.10	−1.35261	−0.676306	−	0.736621i	$-0.736420\pi$
$149$	−2460.10	−1.35261	−0.676306	+	0.736621i	$0.736420\pi$
$150$	−1164.62	−0.633937
$151$	−1427.13	−0.769127	−0.384563	−	0.923099i	$-0.625648\pi$
$151$	−1427.13	−0.769127	−0.384563	+	0.923099i	$0.625648\pi$
$152$	−944.392	−0.503949
$153$	−1877.29	−0.991962
$154$	1547.00	0.809484
$155$	715.585	0.370820
$156$	−10100.2	−5.18373
$157$	284.575	0.144659	0.0723297	−	0.997381i	$-0.476957\pi$
$157$	284.575	0.144659	0.0723297	+	0.997381i	$0.476957\pi$
$158$	463.423	0.233342
$159$	−1134.39	−0.565806
$160$	807.516	0.398998
$161$	1252.85	0.613281
$162$	5049.47	2.44891
$163$	−2788.37	−1.33989	−0.669945	−	0.742411i	$-0.733682\pi$
$163$	−2788.37	−1.33989	−0.669945	+	0.742411i	$0.733682\pi$
$164$	2902.01	1.38176
$165$	−504.543	−0.238052
$166$	2896.99	1.35452
$167$	693.952	0.321555	0.160777	−	0.986991i	$-0.448600\pi$
$167$	693.952	0.321555	0.160777	+	0.986991i	$0.448600\pi$
$168$	−12627.6	−5.79907
$169$	1634.23	0.743847
$170$	−834.008	−0.376268
$171$	−1085.91	−0.485623
$172$	−7203.99	−3.19360
$173$	2364.83	1.03928	0.519638	−	0.854387i	$-0.326067\pi$
$173$	2364.83	1.03928	0.519638	+	0.854387i	$0.326067\pi$
$174$	11477.5	5.00062
$175$	692.355	0.299069
$176$	1211.17	0.518725
$177$	−7951.13	−3.37652
$178$	−6155.41	−2.59195
$179$	3930.37	1.64117	0.820585	−	0.571525i	$-0.193648\pi$
$179$	3930.37	1.64117	0.820585	+	0.571525i	$0.193648\pi$
$180$	5083.18	2.10488
$181$	1528.09	0.627524	0.313762	−	0.949502i	$-0.398411\pi$
$181$	1528.09	0.627524	0.313762	+	0.949502i	$0.398411\pi$
$182$	8704.95	3.54535
$183$	−6188.64	−2.49988
$184$	2248.58	0.900910
$185$	670.290	0.266382
$186$	−6667.06	−2.62824
$187$	−361.314	−0.141294
$188$	−3053.22	−1.18446
$189$	−7660.49	−2.94825
$190$	−482.427	−0.184205
$191$	−2324.06	−0.880434	−0.440217	−	0.897892i	$-0.645098\pi$
$191$	−2324.06	−0.880434	−0.440217	+	0.897892i	$0.645098\pi$
$192$	556.935	0.209340
$193$	−1881.16	−0.701601	−0.350801	−	0.936450i	$-0.614091\pi$
$193$	−1881.16	−0.701601	−0.350801	+	0.936450i	$0.614091\pi$
$194$	−6472.43	−2.39533
$195$	−2839.06	−1.04261
$196$	7541.52	2.74837
$197$	−1016.11	−0.367487	−0.183744	−	0.982974i	$-0.558822\pi$
$197$	−1016.11	−0.367487	−0.183744	+	0.982974i	$0.558822\pi$
$198$	3192.57	1.14589
$199$	−4340.82	−1.54629	−0.773146	−	0.634228i	$-0.781318\pi$
$199$	−4340.82	−1.54629	−0.773146	+	0.634228i	$0.781318\pi$
$200$	1242.62	0.439333
$201$	1109.31	0.389278
$202$	3499.47	1.21892
$203$	−6823.28	−2.35912
$204$	5359.85	1.83953
$205$	815.726	0.277916
$206$	6571.79	2.22271
$207$	2585.53	0.868149
$208$	6815.27	2.27189
$209$	−209.000	−0.0691714
$210$	−6450.63	−2.11969
$211$	−4392.86	−1.43326	−0.716628	−	0.697455i	$-0.754316\pi$
$211$	−4392.86	−1.43326	−0.716628	+	0.697455i	$0.754316\pi$
$212$	2199.65	0.712606
$213$	−1928.18	−0.620267
$214$	4575.09	1.46143
$215$	−2024.97	−0.642333
$216$	−13748.8	−4.33097
$217$	3963.51	1.23991
$218$	991.891	0.308162
$219$	5755.43	1.77587
$220$	978.336	0.299815
$221$	−2033.11	−0.618832
$222$	−6245.05	−1.88802
$223$	294.408	0.0884082	0.0442041	−	0.999023i	$-0.485925\pi$
$223$	294.408	0.0884082	0.0442041	+	0.999023i	$0.485925\pi$
$224$	4472.70	1.33413
$225$	1428.83	0.423357
$226$	10712.2	3.15294
$227$	4281.82	1.25196	0.625979	−	0.779840i	$-0.284699\pi$
$227$	4281.82	1.25196	0.625979	+	0.779840i	$0.284699\pi$
$228$	3100.37	0.900558
$229$	222.643	0.0642475	0.0321238	−	0.999484i	$-0.489773\pi$
$229$	222.643	0.0642475	0.0321238	+	0.999484i	$0.489773\pi$
$230$	1148.65	0.329303
$231$	−2794.58	−0.795973
$232$	−12246.3	−3.46554
$233$	1533.04	0.431042	0.215521	−	0.976499i	$-0.430855\pi$
$233$	1533.04	0.431042	0.215521	+	0.976499i	$0.430855\pi$
$234$	17964.6	5.01873
$235$	−858.229	−0.238233
$236$	15417.7	4.25256
$237$	−837.153	−0.229447
$238$	−4619.44	−1.25812
$239$	−2821.85	−0.763724	−0.381862	−	0.924219i	$-0.624717\pi$
$239$	−2821.85	−0.763724	−0.381862	+	0.924219i	$0.624717\pi$
$240$	−5050.32	−1.35832
$241$	−438.744	−0.117270	−0.0586349	−	0.998279i	$-0.518675\pi$
$241$	−438.744	−0.117270	−0.0586349	+	0.998279i	$0.518675\pi$
$242$	614.460	0.163219
$243$	−1653.17	−0.436424
$244$	12000.1	3.14848
$245$	2119.84	0.552783
$246$	−7600.07	−1.96977
$247$	−1176.04	−0.302955
$248$	7113.60	1.82143
$249$	−5233.29	−1.33191
$250$	634.773	0.160586
$251$	2340.11	0.588473	0.294236	−	0.955733i	$-0.404935\pi$
$251$	2340.11	0.588473	0.294236	+	0.955733i	$0.404935\pi$
$252$	28154.9	7.03806
$253$	497.625	0.123658
$254$	3677.83	0.908534
$255$	1506.60	0.369987
$256$	−7641.07	−1.86549
$257$	2943.11	0.714343	0.357172	−	0.934039i	$-0.383741\pi$
$257$	2943.11	0.714343	0.357172	+	0.934039i	$0.383741\pi$
$258$	18866.5	4.55263
$259$	3712.63	0.890700
$260$	5505.09	1.31312
$261$	−14081.4	−3.33952
$262$	12144.3	2.86364
$263$	5241.40	1.22889	0.614445	−	0.788959i	$-0.289380\pi$
$263$	5241.40	1.22889	0.614445	+	0.788959i	$0.289380\pi$
$264$	−5015.64	−1.16929
$265$	618.298	0.143327
$266$	−2672.09	−0.615925
$267$	11119.5	2.54869
$268$	−2151.02	−0.490277
$269$	−7033.57	−1.59422	−0.797108	−	0.603837i	$-0.793638\pi$
$269$	−7033.57	−1.59422	−0.797108	+	0.603837i	$0.793638\pi$
$270$	−7023.37	−1.58307
$271$	−6400.53	−1.43470	−0.717352	−	0.696711i	$-0.754646\pi$
$271$	−6400.53	−1.43470	−0.717352	+	0.696711i	$0.754646\pi$
$272$	−3616.64	−0.806218
$273$	−15725.1	−3.48617
$274$	−13829.7	−3.04920
$275$	275.000	0.0603023
$276$	−7381.93	−1.60993
$277$	5198.15	1.12753	0.563767	−	0.825934i	$-0.309352\pi$
$277$	5198.15	1.12753	0.563767	+	0.825934i	$0.309352\pi$
$278$	−12455.6	−2.68718
$279$	8179.59	1.75519
$280$	6882.67	1.46899
$281$	−5716.01	−1.21348	−0.606742	−	0.794899i	$-0.707524\pi$
$281$	−5716.01	−1.21348	−0.606742	+	0.794899i	$0.707524\pi$
$282$	7996.07	1.68851
$283$	935.968	0.196599	0.0982995	−	0.995157i	$-0.468660\pi$
$283$	935.968	0.196599	0.0982995	+	0.995157i	$0.468660\pi$
$284$	3738.85	0.781197
$285$	871.483	0.181130
$286$	3457.56	0.714860
$287$	4518.17	0.929266
$288$	9230.41	1.88857
$289$	−3834.09	−0.780397
$290$	−6255.80	−1.26674
$291$	11692.1	2.35535
$292$	−11160.1	−2.23663
$293$	6780.68	1.35198	0.675992	−	0.736909i	$-0.263715\pi$
$293$	6780.68	1.35198	0.675992	+	0.736909i	$0.263715\pi$
$294$	−19750.4	−3.91792
$295$	4333.75	0.855324
$296$	6663.33	1.30844
$297$	−3042.71	−0.594464
$298$	−12492.8	−2.42849
$299$	2800.14	0.541592
$300$	−4079.44	−0.785088
$301$	−11216.0	−2.14777
$302$	−7247.22	−1.38090
$303$	−6321.63	−1.19857
$304$	−2092.03	−0.394691
$305$	3373.11	0.633258
$306$	−9533.24	−1.78098
$307$	5388.61	1.00177	0.500886	−	0.865513i	$-0.333008\pi$
$307$	5388.61	1.00177	0.500886	+	0.865513i	$0.333008\pi$
$308$	5418.84	1.00249
$309$	−11871.6	−2.18561
$310$	3633.87	0.665774
$311$	−3917.97	−0.714366	−0.357183	−	0.934034i	$-0.616263\pi$
$311$	−3917.97	−0.714366	−0.357183	+	0.934034i	$0.616263\pi$
$312$	−28223.0	−5.12119
$313$	−6584.88	−1.18914	−0.594568	−	0.804045i	$-0.702677\pi$
$313$	−6584.88	−1.18914	−0.594568	+	0.804045i	$0.702677\pi$
$314$	1445.12	0.259723
$315$	7914.05	1.41558
$316$	1623.29	0.288978
$317$	−4853.07	−0.859859	−0.429930	−	0.902862i	$-0.641462\pi$
$317$	−4853.07	−0.859859	−0.429930	+	0.902862i	$0.641462\pi$
$318$	−5760.65	−1.01585
$319$	−2710.18	−0.475676
$320$	−303.557	−0.0530292
$321$	−8264.69	−1.43704
$322$	6362.19	1.10109
$323$	624.088	0.107508
$324$	17687.4	3.03281
$325$	1547.42	0.264110
$326$	−14159.8	−2.40565
$327$	−1791.81	−0.303019
$328$	8109.10	1.36509
$329$	−4753.59	−0.796578
$330$	−2562.16	−0.427401
$331$	8061.37	1.33865	0.669324	−	0.742970i	$-0.266584\pi$
$331$	8061.37	1.33865	0.669324	+	0.742970i	$0.266584\pi$
$332$	10147.6	1.67748
$333$	7661.83	1.26086
$334$	3524.01	0.577322
$335$	−604.629	−0.0986102
$336$	−27972.9	−4.54181
$337$	−8748.79	−1.41417	−0.707087	−	0.707126i	$-0.749991\pi$
$337$	−8748.79	−1.41417	−0.707087	+	0.707126i	$0.749991\pi$
$338$	8298.93	1.33551
$339$	−19351.1	−3.10032
$340$	−2921.37	−0.465982
$341$	1574.29	0.250007
$342$	−5514.45	−0.871892
$343$	2242.35	0.352991
$344$	−20130.1	−3.15507
$345$	−2074.98	−0.323807
$346$	12009.0	1.86592
$347$	−4799.56	−0.742518	−0.371259	−	0.928529i	$-0.621074\pi$
$347$	−4799.56	−0.742518	−0.371259	+	0.928529i	$0.621074\pi$
$348$	40203.6	6.19293
$349$	−4945.32	−0.758501	−0.379250	−	0.925294i	$-0.623818\pi$
$349$	−4945.32	−0.758501	−0.379250	+	0.925294i	$0.623818\pi$
$350$	3515.90	0.536951
$351$	−17121.3	−2.60361
$352$	1776.53	0.269005
$353$	9855.75	1.48603	0.743015	−	0.669275i	$-0.233395\pi$
$353$	9855.75	1.48603	0.743015	+	0.669275i	$0.233395\pi$
$354$	−40377.3	−6.06223
$355$	1050.95	0.157123
$356$	−21561.2	−3.20995
$357$	8344.80	1.23713
$358$	19959.1	2.94657
$359$	8066.59	1.18590	0.592951	−	0.805239i	$-0.297963\pi$
$359$	8066.59	1.18590	0.592951	+	0.805239i	$0.297963\pi$
$360$	14203.9	2.07948
$361$	361.000	0.0526316
$362$	7759.90	1.12666
$363$	−1109.99	−0.160495
$364$	30491.8	4.39067
$365$	−3136.99	−0.449856
$366$	−31427.0	−4.48830
$367$	−7835.28	−1.11444	−0.557218	−	0.830366i	$-0.688131\pi$
$367$	−7835.28	−1.11444	−0.557218	+	0.830366i	$0.688131\pi$
$368$	4981.08	0.705589
$369$	9324.26	1.31545
$370$	3403.85	0.478264
$371$	3424.65	0.479243
$372$	−23353.5	−3.25490
$373$	−1145.86	−0.159063	−0.0795314	−	0.996832i	$-0.525342\pi$
$373$	−1145.86	−0.159063	−0.0795314	+	0.996832i	$0.525342\pi$
$374$	−1834.82	−0.253680
$375$	−1146.69	−0.157906
$376$	−8531.63	−1.17017
$377$	−15250.1	−2.08335
$378$	−38901.3	−5.29330
$379$	−11261.7	−1.52632	−0.763159	−	0.646211i	$-0.776353\pi$
$379$	−11261.7	−1.52632	−0.763159	+	0.646211i	$0.776353\pi$
$380$	−1689.85	−0.228125
$381$	−6643.83	−0.893370
$382$	−11802.0	−1.58074
$383$	5644.60	0.753069	0.376535	−	0.926403i	$-0.377116\pi$
$383$	5644.60	0.753069	0.376535	+	0.926403i	$0.377116\pi$
$384$	14680.6	1.95096
$385$	1523.18	0.201632
$386$	−9552.88	−1.25966
$387$	−23146.7	−3.04034
$388$	−22671.7	−2.96645
$389$	7001.90	0.912623	0.456311	−	0.889820i	$-0.349170\pi$
$389$	7001.90	0.912623	0.456311	+	0.889820i	$0.349170\pi$
$390$	−14417.3	−1.87191
$391$	−1485.94	−0.192193
$392$	21073.3	2.71521
$393$	−21938.0	−2.81585
$394$	−5160.00	−0.659790
$395$	456.289	0.0581225
$396$	11183.0	1.41911
$397$	−4921.84	−0.622217	−0.311109	−	0.950374i	$-0.600700\pi$
$397$	−4921.84	−0.622217	−0.311109	+	0.950374i	$0.600700\pi$
$398$	−22043.4	−2.77623
$399$	4827.00	0.605645
$400$	2752.67	0.344083
$401$	−3360.81	−0.418531	−0.209266	−	0.977859i	$-0.567107\pi$
$401$	−3360.81	−0.418531	−0.209266	+	0.977859i	$0.567107\pi$
$402$	5633.29	0.698913
$403$	8858.51	1.09497
$404$	12258.0	1.50955
$405$	4971.73	0.609993
$406$	−34649.9	−4.23558
$407$	1474.64	0.179595
$408$	14977.0	1.81734
$409$	−10213.8	−1.23482	−0.617411	−	0.786641i	$-0.711818\pi$
$409$	−10213.8	−1.23482	−0.617411	+	0.786641i	$0.711818\pi$
$410$	4142.40	0.498972
$411$	24982.7	2.99831
$412$	23019.8	2.75268
$413$	24003.9	2.85994
$414$	13129.8	1.55868
$415$	2852.39	0.337394
$416$	9996.55	1.17818
$417$	22500.5	2.64233
$418$	−1061.34	−0.124191
$419$	−8666.68	−1.01049	−0.505244	−	0.862976i	$-0.668598\pi$
$419$	−8666.68	−1.01049	−0.505244	+	0.862976i	$0.668598\pi$
$420$	−22595.3	−2.62510
$421$	−11813.6	−1.36760	−0.683800	−	0.729669i	$-0.739674\pi$
$421$	−11813.6	−1.36760	−0.683800	+	0.729669i	$0.739674\pi$
$422$	−22307.7	−2.57328
$423$	−9810.10	−1.12762
$424$	6146.48	0.704008
$425$	−821.168	−0.0937235
$426$	−9791.65	−1.11363
$427$	18683.1	2.11742
$428$	16025.7	1.80988
$429$	−6245.93	−0.702929
$430$	−10283.2	−1.15325
$431$	13066.5	1.46030	0.730150	−	0.683287i	$-0.239450\pi$
$431$	13066.5	1.46030	0.730150	+	0.683287i	$0.239450\pi$
$432$	−30456.6	−3.39200
$433$	8779.94	0.974450	0.487225	−	0.873276i	$-0.338009\pi$
$433$	8779.94	0.974450	0.487225	+	0.873276i	$0.338009\pi$
$434$	20127.4	2.22615
$435$	11300.8	1.24559
$436$	3474.41	0.381638
$437$	−859.535	−0.0940895
$438$	29227.1	3.18841
$439$	−8887.53	−0.966238	−0.483119	−	0.875555i	$-0.660496\pi$
$439$	−8887.53	−0.966238	−0.483119	+	0.875555i	$0.660496\pi$
$440$	2733.77	0.296198
$441$	24231.1	2.61647
$442$	−10324.5	−1.11106
$443$	−4362.66	−0.467892	−0.233946	−	0.972250i	$-0.575164\pi$
$443$	−4362.66	−0.467892	−0.233946	+	0.972250i	$0.575164\pi$
$444$	−21875.2	−2.33818
$445$	−6060.64	−0.645622
$446$	1495.06	0.158729
$447$	22567.7	2.38796
$448$	−1681.35	−0.177313
$449$	−11623.3	−1.22168	−0.610841	−	0.791753i	$-0.709169\pi$
$449$	−11623.3	−1.22168	−0.610841	+	0.791753i	$0.709169\pi$
$450$	7255.85	0.760098
$451$	1794.60	0.187371
$452$	37522.9	3.90470
$453$	13091.8	1.35785
$454$	21743.9	2.24778
$455$	8570.93	0.883102
$456$	8663.38	0.889693
$457$	10246.9	1.04886	0.524429	−	0.851454i	$-0.324279\pi$
$457$	10246.9	1.04886	0.524429	+	0.851454i	$0.324279\pi$
$458$	1130.62	0.115351
$459$	9085.73	0.923934
$460$	4023.51	0.407820
$461$	7167.63	0.724143	0.362071	−	0.932150i	$-0.382070\pi$
$461$	7167.63	0.724143	0.362071	+	0.932150i	$0.382070\pi$
$462$	−14191.4	−1.42910
$463$	7642.01	0.767072	0.383536	−	0.923526i	$-0.374706\pi$
$463$	7642.01	0.767072	0.383536	+	0.923526i	$0.374706\pi$
$464$	−27128.0	−2.71420
$465$	−6564.42	−0.654662
$466$	7785.05	0.773896
$467$	6540.68	0.648108	0.324054	−	0.946039i	$-0.394954\pi$
$467$	6540.68	0.648108	0.324054	+	0.946039i	$0.394954\pi$
$468$	62926.6	6.21535
$469$	−3348.94	−0.329722
$470$	−4358.24	−0.427725
$471$	−2610.55	−0.255388
$472$	43081.6	4.20126
$473$	−4454.93	−0.433061
$474$	−4251.21	−0.411951
$475$	−475.000	−0.0458831
$476$	−16181.0	−1.55810
$477$	7067.54	0.678407
$478$	−14329.8	−1.37120
$479$	19520.5	1.86203	0.931017	−	0.364975i	$-0.118922\pi$
$479$	19520.5	1.86203	0.931017	+	0.364975i	$0.118922\pi$
$480$	−7407.75	−0.704408
$481$	8297.78	0.786582
$482$	−2228.02	−0.210547
$483$	−11493.0	−1.08271
$484$	2152.34	0.202135
$485$	−6372.78	−0.596645
$486$	−8395.11	−0.783559
$487$	4044.40	0.376323	0.188162	−	0.982138i	$-0.439747\pi$
$487$	4044.40	0.376323	0.188162	+	0.982138i	$0.439747\pi$
$488$	33532.0	3.11049
$489$	25579.1	2.36550
$490$	10764.9	0.992470
$491$	11987.1	1.10177	0.550885	−	0.834581i	$-0.314290\pi$
$491$	11987.1	1.10177	0.550885	+	0.834581i	$0.314290\pi$
$492$	−26621.6	−2.43942
$493$	8092.76	0.739310
$494$	−5972.15	−0.543927
$495$	3143.42	0.285427
$496$	15758.1	1.42654
$497$	5821.05	0.525372
$498$	−26575.6	−2.39133
$499$	−21698.2	−1.94659	−0.973293	−	0.229568i	$-0.926269\pi$
$499$	−21698.2	−1.94659	−0.973293	+	0.229568i	$0.926269\pi$
$500$	2223.49	0.198875
$501$	−6365.97	−0.567686
$502$	11883.5	1.05655
$503$	−7574.76	−0.671455	−0.335727	−	0.941959i	$-0.608982\pi$
$503$	−7574.76	−0.671455	−0.335727	+	0.941959i	$0.608982\pi$
$504$	78673.3	6.95315
$505$	3445.59	0.303618
$506$	2527.03	0.222016
$507$	−14991.6	−1.31322
$508$	12882.8	1.12516
$509$	−10611.4	−0.924048	−0.462024	−	0.886867i	$-0.652877\pi$
$509$	−10611.4	−0.924048	−0.462024	+	0.886867i	$0.652877\pi$
$510$	7650.77	0.664278
$511$	−17375.3	−1.50418
$512$	−26000.1	−2.24424
$513$	5255.59	0.452319
$514$	14945.6	1.28254
$515$	6470.62	0.553649
$516$	66085.8	5.63811
$517$	−1888.10	−0.160617
$518$	18853.4	1.59917
$519$	−21693.8	−1.83478
$520$	15382.9	1.29728
$521$	−9386.93	−0.789345	−0.394673	−	0.918822i	$-0.629142\pi$
$521$	−9386.93	−0.789345	−0.394673	+	0.918822i	$0.629142\pi$
$522$	−71507.7	−5.99580
$523$	−17893.6	−1.49605	−0.748025	−	0.663670i	$-0.768998\pi$
$523$	−17893.6	−1.49605	−0.748025	+	0.663670i	$0.768998\pi$
$524$	42539.0	3.54643
$525$	−6351.32	−0.527989
$526$	26616.8	2.20636
$527$	−4700.92	−0.388568
$528$	−11110.7	−0.915779
$529$	−10120.5	−0.831796
$530$	3139.83	0.257331
$531$	49537.5	4.04848
$532$	−9359.82	−0.762781
$533$	10098.2	0.820640
$534$	56466.6	4.57594
$535$	4504.65	0.364025
$536$	−6010.59	−0.484362
$537$	−36055.2	−2.89739
$538$	−35717.7	−2.86227
$539$	4663.65	0.372686
$540$	−24601.6	−1.96052
$541$	−13161.7	−1.04596	−0.522982	−	0.852344i	$-0.675181\pi$
$541$	−13161.7	−1.04596	−0.522982	+	0.852344i	$0.675181\pi$
$542$	−32503.1	−2.57588
$543$	−14017.9	−1.10786
$544$	−5304.85	−0.418095
$545$	976.621	0.0767593
$546$	−79854.8	−6.25911
$547$	16729.6	1.30769	0.653844	−	0.756629i	$-0.273155\pi$
$547$	16729.6	1.30769	0.653844	+	0.756629i	$0.273155\pi$
$548$	−48442.8	−3.77623
$549$	38556.7	2.99738
$550$	1396.50	0.108267
$551$	4681.21	0.361935
$552$	−20627.3	−1.59050
$553$	2527.31	0.194344
$554$	26397.2	2.02438
$555$	−6148.90	−0.470282
$556$	−43629.6	−3.32789
$557$	−25367.6	−1.92973	−0.964866	−	0.262743i	$-0.915373\pi$
$557$	−25367.6	−1.92973	−0.964866	+	0.262743i	$0.915373\pi$
$558$	41537.4	3.15129
$559$	−25067.9	−1.89670
$560$	15246.6	1.15051
$561$	3314.51	0.249445
$562$	−29026.9	−2.17870
$563$	−1168.64	−0.0874820	−0.0437410	−	0.999043i	$-0.513928\pi$
$563$	−1168.64	−0.0874820	−0.0437410	+	0.999043i	$0.513928\pi$
$564$	28008.7	2.09110
$565$	10547.3	0.785359
$566$	4753.02	0.352976
$567$	27537.6	2.03963
$568$	10447.5	0.771771
$569$	−4699.76	−0.346264	−0.173132	−	0.984899i	$-0.555389\pi$
$569$	−4699.76	−0.346264	−0.173132	+	0.984899i	$0.555389\pi$
$570$	4425.55	0.325203
$571$	12589.2	0.922666	0.461333	−	0.887227i	$-0.347371\pi$
$571$	12589.2	0.922666	0.461333	+	0.887227i	$0.347371\pi$
$572$	12111.2	0.885305
$573$	21319.7	1.55435
$574$	22944.1	1.66841
$575$	1130.97	0.0820253
$576$	−3469.84	−0.251001
$577$	12295.5	0.887123	0.443561	−	0.896244i	$-0.353715\pi$
$577$	12295.5	0.887123	0.443561	+	0.896244i	$0.353715\pi$
$578$	−19470.2	−1.40113
$579$	17256.9	1.23864
$580$	−21912.9	−1.56876
$581$	15798.9	1.12814
$582$	59374.8	4.22881
$583$	1360.26	0.0966313
$584$	−31184.7	−2.20964
$585$	17688.0	1.25010
$586$	34433.5	2.42736
$587$	23297.3	1.63813	0.819065	−	0.573701i	$-0.194493\pi$
$587$	23297.3	1.63813	0.819065	+	0.573701i	$0.194493\pi$
$588$	−69182.1	−4.85208
$589$	−2719.22	−0.190227
$590$	22007.6	1.53566
$591$	9321.31	0.648777
$592$	14760.7	1.02476
$593$	−23591.6	−1.63371	−0.816855	−	0.576844i	$-0.804284\pi$
$593$	−23591.6	−1.63371	−0.816855	+	0.576844i	$0.804284\pi$
$594$	−15451.4	−1.06731
$595$	−4548.32	−0.313383
$596$	−43760.0	−3.00752
$597$	39820.5	2.72989
$598$	14219.6	0.972379
$599$	19944.3	1.36044	0.680220	−	0.733008i	$-0.261884\pi$
$599$	19944.3	1.36044	0.680220	+	0.733008i	$0.261884\pi$
$600$	−11399.2	−0.775616
$601$	11964.3	0.812037	0.406018	−	0.913865i	$-0.366917\pi$
$601$	11964.3	0.812037	0.406018	+	0.913865i	$0.366917\pi$
$602$	−56956.7	−3.85612
$603$	−6911.29	−0.466749
$604$	−25385.7	−1.71015
$605$	605.000	0.0406558
$606$	−32102.4	−2.15193
$607$	−12604.6	−0.842844	−0.421422	−	0.906865i	$-0.638469\pi$
$607$	−12604.6	−0.842844	−0.421422	+	0.906865i	$0.638469\pi$
$608$	−3068.56	−0.204682
$609$	62593.4	4.16488
$610$	17129.3	1.13696
$611$	−10624.4	−0.703462
$612$	−33393.1	−2.20562
$613$	11422.6	0.752617	0.376308	−	0.926494i	$-0.377193\pi$
$613$	11422.6	0.752617	0.376308	+	0.926494i	$0.377193\pi$
$614$	27364.3	1.79859
$615$	−7483.06	−0.490644
$616$	15141.9	0.990396
$617$	−11356.2	−0.740978	−0.370489	−	0.928837i	$-0.620810\pi$
$617$	−11356.2	−0.740978	−0.370489	+	0.928837i	$0.620810\pi$
$618$	−60286.3	−3.92407
$619$	14328.6	0.930396	0.465198	−	0.885207i	$-0.345983\pi$
$619$	14328.6	0.930396	0.465198	+	0.885207i	$0.345983\pi$
$620$	12728.8	0.824516
$621$	−12513.5	−0.808612
$622$	−19896.2	−1.28258
$623$	−33568.9	−2.15876
$624$	−62519.9	−4.01089
$625$	625.000	0.0400000
$626$	−33439.2	−2.13498
$627$	1917.26	0.122118
$628$	5061.99	0.321649
$629$	−4403.36	−0.279131
$630$	40189.0	2.54154
$631$	15770.3	0.994938	0.497469	−	0.867482i	$-0.334263\pi$
$631$	15770.3	0.994938	0.497469	+	0.867482i	$0.334263\pi$
$632$	4535.95	0.285491
$633$	40297.9	2.53033
$634$	−24644.7	−1.54380
$635$	3621.21	0.226304
$636$	−20178.5	−1.25806
$637$	26242.4	1.63228
$638$	−13762.8	−0.854033
$639$	12013.0	0.743706
$640$	−8001.64	−0.494207
$641$	−18392.5	−1.13332	−0.566662	−	0.823951i	$-0.691765\pi$
$641$	−18392.5	−1.13332	−0.566662	+	0.823951i	$0.691765\pi$
$642$	−41969.6	−2.58007
$643$	−724.894	−0.0444588	−0.0222294	−	0.999753i	$-0.507076\pi$
$643$	−724.894	−0.0444588	−0.0222294	+	0.999753i	$0.507076\pi$
$644$	22285.6	1.36362
$645$	18576.0	1.13400
$646$	3169.23	0.193021
$647$	−9388.34	−0.570469	−0.285235	−	0.958458i	$-0.592072\pi$
$647$	−9388.34	−0.570469	−0.285235	+	0.958458i	$0.592072\pi$
$648$	49423.8	2.99622
$649$	9534.25	0.576659
$650$	7858.10	0.474185
$651$	−36359.3	−2.18899
$652$	−49599.3	−2.97923
$653$	−12136.3	−0.727302	−0.363651	−	0.931535i	$-0.618470\pi$
$653$	−12136.3	−0.727302	−0.363651	+	0.931535i	$0.618470\pi$
$654$	−9099.12	−0.544042
$655$	11957.3	0.713297
$656$	17963.4	1.06913
$657$	−35857.7	−2.12929
$658$	−24139.6	−1.43018
$659$	1334.33	0.0788740	0.0394370	−	0.999222i	$-0.487444\pi$
$659$	1334.33	0.0788740	0.0394370	+	0.999222i	$0.487444\pi$
$660$	−8974.76	−0.529306
$661$	−13987.1	−0.823049	−0.411524	−	0.911399i	$-0.635004\pi$
$661$	−13987.1	−0.823049	−0.411524	+	0.911399i	$0.635004\pi$
$662$	40937.1	2.40342
$663$	18650.8	1.09251
$664$	28355.5	1.65724
$665$	−2630.95	−0.153419
$666$	38908.2	2.26375
$667$	−11145.9	−0.647032
$668$	12344.0	0.714973
$669$	−2700.75	−0.156080
$670$	−3070.41	−0.177045
$671$	7420.84	0.426942
$672$	−41030.3	−2.35533
$673$	−4759.06	−0.272583	−0.136292	−	0.990669i	$-0.543518\pi$
$673$	−4759.06	−0.272583	−0.136292	+	0.990669i	$0.543518\pi$
$674$	−44427.9	−2.53902
$675$	−6915.25	−0.394323
$676$	29069.6	1.65394
$677$	30290.5	1.71959	0.859793	−	0.510643i	$-0.170593\pi$
$677$	30290.5	1.71959	0.859793	+	0.510643i	$0.170593\pi$
$678$	−98268.4	−5.56634
$679$	−35297.8	−1.99500
$680$	−8163.20	−0.460360
$681$	−39279.3	−2.21026
$682$	7994.51	0.448865
$683$	26727.5	1.49736	0.748682	−	0.662929i	$-0.230687\pi$
$683$	26727.5	1.49736	0.748682	+	0.662929i	$0.230687\pi$
$684$	−19316.1	−1.07978
$685$	−13616.8	−0.759518
$686$	11387.1	0.633762
$687$	−2042.42	−0.113425
$688$	−44592.5	−2.47104
$689$	7654.16	0.423222
$690$	−10537.1	−0.581366
$691$	8252.13	0.454307	0.227153	−	0.973859i	$-0.427058\pi$
$691$	8252.13	0.454307	0.227153	+	0.973859i	$0.427058\pi$
$692$	42065.4	2.31082
$693$	17410.9	0.954381
$694$	−24373.0	−1.33312
$695$	−12263.8	−0.669344
$696$	112341.	6.11821
$697$	−5358.78	−0.291217
$698$	−25113.2	−1.36182
$699$	−14063.3	−0.760979
$700$	12315.6	0.664977
$701$	−18646.8	−1.00468	−0.502340	−	0.864670i	$-0.667527\pi$
$701$	−18646.8	−1.00468	−0.502340	+	0.864670i	$0.667527\pi$
$702$	−86945.1	−4.67455
$703$	−2547.10	−0.136651
$704$	−667.824	−0.0357522
$705$	7872.97	0.420586
$706$	50049.3	2.66803
$707$	19084.6	1.01520
$708$	−141434.	−7.50765
$709$	−14383.8	−0.761910	−0.380955	−	0.924594i	$-0.624405\pi$
$709$	−14383.8	−0.761910	−0.380955	+	0.924594i	$0.624405\pi$
$710$	5336.92	0.282100
$711$	5215.67	0.275109
$712$	−60248.6	−3.17123
$713$	6474.42	0.340069
$714$	42376.4	2.22114
$715$	3404.33	0.178063
$716$	69913.0	3.64912
$717$	25886.2	1.34831
$718$	40963.6	2.12918
$719$	29880.1	1.54984	0.774922	−	0.632057i	$-0.217789\pi$
$719$	29880.1	1.54984	0.774922	+	0.632057i	$0.217789\pi$
$720$	31464.7	1.62864
$721$	35839.7	1.85123
$722$	1833.22	0.0944952
$723$	4024.82	0.207033
$724$	27181.5	1.39529
$725$	−6159.49	−0.315528
$726$	−5636.75	−0.288153
$727$	−27443.1	−1.40001	−0.700005	−	0.714138i	$-0.746819\pi$
$727$	−27443.1	−1.40001	−0.700005	+	0.714138i	$0.746819\pi$
$728$	85203.3	4.33770
$729$	−11682.0	−0.593506
$730$	−15930.2	−0.807675
$731$	13302.7	0.673076
$732$	−110083.	−5.55845
$733$	−888.442	−0.0447686	−0.0223843	−	0.999749i	$-0.507126\pi$
$733$	−888.442	−0.0447686	−0.0223843	+	0.999749i	$0.507126\pi$
$734$	−39789.0	−2.00087
$735$	−19446.4	−0.975905
$736$	7306.19	0.365910
$737$	−1330.18	−0.0664830
$738$	47350.3	2.36177
$739$	−8759.65	−0.436034	−0.218017	−	0.975945i	$-0.569959\pi$
$739$	−8759.65	−0.436034	−0.218017	+	0.975945i	$0.569959\pi$
$740$	11923.1	0.592298
$741$	10788.4	0.534848
$742$	17391.0	0.860437
$743$	−32312.5	−1.59546	−0.797732	−	0.603012i	$-0.793967\pi$
$743$	−32312.5	−1.59546	−0.797732	+	0.603012i	$0.793967\pi$
$744$	−65256.7	−3.21563
$745$	−12300.5	−0.604906
$746$	−5818.89	−0.285583
$747$	32604.6	1.59698
$748$	−6427.02	−0.314165
$749$	24950.5	1.21719
$750$	−5823.09	−0.283505
$751$	−21551.7	−1.04718	−0.523591	−	0.851969i	$-0.675408\pi$
$751$	−21551.7	−1.04718	−0.523591	+	0.851969i	$0.675408\pi$
$752$	−18899.4	−0.916474
$753$	−21467.0	−1.03891
$754$	−77443.0	−3.74046
$755$	−7135.64	−0.343964
$756$	−136264.	−6.55539
$757$	22014.7	1.05699	0.528493	−	0.848938i	$-0.322757\pi$
$757$	22014.7	1.05699	0.528493	+	0.848938i	$0.322757\pi$
$758$	−57188.9	−2.74036
$759$	−4564.97	−0.218311
$760$	−4721.96	−0.225373
$761$	−783.337	−0.0373140	−0.0186570	−	0.999826i	$-0.505939\pi$
$761$	−783.337	−0.0373140	−0.0186570	+	0.999826i	$0.505939\pi$
$762$	−33738.6	−1.60396
$763$	5409.35	0.256660
$764$	−41340.1	−1.95763
$765$	−9386.47	−0.443619
$766$	28664.3	1.35207
$767$	53649.2	2.52563
$768$	70095.3	3.29342
$769$	10848.3	0.508713	0.254356	−	0.967111i	$-0.418136\pi$
$769$	10848.3	0.508713	0.254356	+	0.967111i	$0.418136\pi$
$770$	7734.99	0.362012
$771$	−26998.6	−1.26113
$772$	−33462.0	−1.56000
$773$	−993.052	−0.0462065	−0.0231032	−	0.999733i	$-0.507355\pi$
$773$	−993.052	−0.0462065	−0.0231032	+	0.999733i	$0.507355\pi$
$774$	−117543.	−5.45865
$775$	3577.93	0.165836
$776$	−63351.6	−2.93066
$777$	−34057.8	−1.57248
$778$	35556.9	1.63853
$779$	−3099.76	−0.142568
$780$	−50501.0	−2.31824
$781$	2312.09	0.105932
$782$	−7545.88	−0.345064
$783$	68151.0	3.11050
$784$	46681.8	2.12654
$785$	1422.87	0.0646937
$786$	−111405.	−5.05559
$787$	−8868.75	−0.401698	−0.200849	−	0.979622i	$-0.564370\pi$
$787$	−8868.75	−0.401698	−0.200849	+	0.979622i	$0.564370\pi$
$788$	−18074.5	−0.817104
$789$	−48082.0	−2.16953
$790$	2317.12	0.104354
$791$	58419.7	2.62600
$792$	31248.7	1.40199
$793$	41757.0	1.86991
$794$	−24994.0	−1.11713
$795$	−5671.96	−0.253036
$796$	−77214.1	−3.43817
$797$	−2987.82	−0.132790	−0.0663952	−	0.997793i	$-0.521150\pi$
$797$	−2987.82	−0.132790	−0.0663952	+	0.997793i	$0.521150\pi$
$798$	24512.4	1.08738
$799$	5638.00	0.249635
$800$	4037.58	0.178437
$801$	−69276.9	−3.05591
$802$	−17066.8	−0.751435
$803$	−6901.37	−0.303293
$804$	19732.4	0.865556
$805$	6264.24	0.274268
$806$	44985.1	1.96592
$807$	64522.4	2.81450
$808$	34252.5	1.49134
$809$	−33614.5	−1.46084	−0.730421	−	0.682997i	$-0.760676\pi$
$809$	−33614.5	−1.46084	−0.730421	+	0.682997i	$0.760676\pi$
$810$	25247.4	1.09519
$811$	21537.0	0.932510	0.466255	−	0.884650i	$-0.345603\pi$
$811$	21537.0	0.932510	0.466255	+	0.884650i	$0.345603\pi$
$812$	−121372.	−5.24547
$813$	58715.3	2.53289
$814$	7488.47	0.322446
$815$	−13941.8	−0.599217
$816$	33177.3	1.42333
$817$	7694.88	0.329510
$818$	−51867.7	−2.21701
$819$	97971.1	4.17996
$820$	14510.1	0.617943
$821$	−8700.10	−0.369836	−0.184918	−	0.982754i	$-0.559202\pi$
$821$	−8700.10	−0.369836	−0.184918	+	0.982754i	$0.559202\pi$
$822$	126866.	5.38318
$823$	35386.4	1.49878	0.749388	−	0.662131i	$-0.230348\pi$
$823$	35386.4	1.49878	0.749388	+	0.662131i	$0.230348\pi$
$824$	64324.2	2.71946
$825$	−2522.71	−0.106460
$826$	121896.	5.13476
$827$	−21666.0	−0.911005	−0.455502	−	0.890235i	$-0.650540\pi$
$827$	−21666.0	−0.911005	−0.455502	+	0.890235i	$0.650540\pi$
$828$	45991.2	1.93032
$829$	6307.29	0.264247	0.132124	−	0.991233i	$-0.457820\pi$
$829$	6307.29	0.264247	0.132124	+	0.991233i	$0.457820\pi$
$830$	14485.0	0.605760
$831$	−47685.3	−1.99059
$832$	−3757.85	−0.156586
$833$	−13926.0	−0.579239
$834$	114261.	4.74406
$835$	3469.76	0.143804
$836$	−3717.68	−0.153802
$837$	−39587.6	−1.63482
$838$	−44010.9	−1.81424
$839$	−565.263	−0.0232599	−0.0116299	−	0.999932i	$-0.503702\pi$
$839$	−565.263	−0.0232599	−0.0116299	+	0.999932i	$0.503702\pi$
$840$	−63138.2	−2.59342
$841$	36313.9	1.48895
$842$	−59991.6	−2.45540
$843$	52435.9	2.14233
$844$	−78139.9	−3.18683
$845$	8171.16	0.332659
$846$	−49817.5	−2.02454
$847$	3351.00	0.135941
$848$	13615.8	0.551376
$849$	−8586.11	−0.347084
$850$	−4170.04	−0.168272
$851$	6064.60	0.244291
$852$	−34298.3	−1.37916
$853$	−39369.1	−1.58027	−0.790135	−	0.612932i	$-0.789990\pi$
$853$	−39369.1	−1.58027	−0.790135	+	0.612932i	$0.789990\pi$
$854$	94876.2	3.80163
$855$	−5429.55	−0.217177
$856$	44780.6	1.78805
$857$	15962.0	0.636232	0.318116	−	0.948052i	$-0.396950\pi$
$857$	15962.0	0.636232	0.318116	+	0.948052i	$0.396950\pi$
$858$	−31718.0	−1.26204
$859$	−45241.9	−1.79701	−0.898507	−	0.438960i	$-0.855347\pi$
$859$	−45241.9	−1.79701	−0.898507	+	0.438960i	$0.855347\pi$
$860$	−36020.0	−1.42822
$861$	−41447.5	−1.64056
$862$	66353.9	2.62183
$863$	−9253.55	−0.364999	−0.182500	−	0.983206i	$-0.558419\pi$
$863$	−9253.55	−0.364999	−0.182500	+	0.983206i	$0.558419\pi$
$864$	−44673.4	−1.75905
$865$	11824.1	0.464778
$866$	44586.1	1.74954
$867$	35172.1	1.37775
$868$	70502.6	2.75693
$869$	1003.84	0.0391862
$870$	57387.6	2.23635
$871$	−7484.94	−0.291180
$872$	9708.55	0.377033
$873$	−72844.9	−2.82408
$874$	−4364.87	−0.168929
$875$	3461.77	0.133748
$876$	102377.	3.94863
$877$	−28207.8	−1.08610	−0.543050	−	0.839700i	$-0.682731\pi$
$877$	−28207.8	−1.08610	−0.543050	+	0.839700i	$0.682731\pi$
$878$	−45132.5	−1.73479
$879$	−62202.6	−2.38685
$880$	6055.87	0.231981
$881$	−40546.2	−1.55055	−0.775276	−	0.631623i	$-0.782389\pi$
$881$	−40546.2	−1.55055	−0.775276	+	0.631623i	$0.782389\pi$
$882$	123050.	4.69763
$883$	31988.2	1.21913	0.609563	−	0.792738i	$-0.291345\pi$
$883$	31988.2	1.21913	0.609563	+	0.792738i	$0.291345\pi$
$884$	−36164.8	−1.37597
$885$	−39755.6	−1.51002
$886$	−22154.4	−0.840057
$887$	−39560.9	−1.49755	−0.748774	−	0.662825i	$-0.769357\pi$
$887$	−39560.9	−1.49755	−0.748774	+	0.662825i	$0.769357\pi$
$888$	−61126.0	−2.30997
$889$	20057.3	0.756693
$890$	−30777.0	−1.15916
$891$	10937.8	0.411258
$892$	5236.91	0.196575
$893$	3261.27	0.122211
$894$	114603.	4.28736
$895$	19651.8	0.733953
$896$	−44319.8	−1.65248
$897$	−25687.0	−0.956149
$898$	−59025.0	−2.19342
$899$	−35261.1	−1.30815
$900$	25415.9	0.941329
$901$	−4061.81	−0.150187
$902$	9113.29	0.336407
$903$	102890.	3.79176
$904$	104850.	3.85759
$905$	7640.43	0.280637
$906$	66482.4	2.43789
$907$	16706.1	0.611594	0.305797	−	0.952097i	$-0.401077\pi$
$907$	16706.1	0.611594	0.305797	+	0.952097i	$0.401077\pi$
$908$	76164.7	2.78372
$909$	39385.3	1.43710
$910$	43524.7	1.58553
$911$	39778.4	1.44667	0.723335	−	0.690497i	$-0.242608\pi$
$911$	39778.4	1.44667	0.723335	+	0.690497i	$0.242608\pi$
$912$	19191.2	0.696803
$913$	6275.26	0.227471
$914$	52035.5	1.88313
$915$	−30943.2	−1.11798
$916$	3960.36	0.142854
$917$	66229.5	2.38505
$918$	46139.0	1.65884
$919$	−13891.0	−0.498610	−0.249305	−	0.968425i	$-0.580202\pi$
$919$	−13891.0	−0.498610	−0.249305	+	0.968425i	$0.580202\pi$
$920$	11242.9	0.402899
$921$	−49432.4	−1.76857
$922$	36398.5	1.30013
$923$	13010.1	0.463959
$924$	−49709.8	−1.76984
$925$	3351.45	0.119130
$926$	38807.5	1.37721
$927$	73963.2	2.62057
$928$	−39791.1	−1.40755
$929$	−19939.5	−0.704193	−0.352096	−	0.935964i	$-0.614531\pi$
$929$	−19939.5	−0.704193	−0.352096	+	0.935964i	$0.614531\pi$
$930$	−33335.3	−1.17538
$931$	−8055.40	−0.283571
$932$	27269.6	0.958417
$933$	35941.5	1.26117
$934$	33214.7	1.16362
$935$	−1806.57	−0.0631884
$936$	175836.	6.14036
$937$	40507.9	1.41231	0.706156	−	0.708056i	$-0.250428\pi$
$937$	40507.9	1.41231	0.706156	+	0.708056i	$0.250428\pi$
$938$	−17006.5	−0.591986
$939$	60406.4	2.09935
$940$	−15266.1	−0.529708
$941$	−9851.09	−0.341271	−0.170636	−	0.985334i	$-0.554582\pi$
$941$	−9851.09	−0.341271	−0.170636	+	0.985334i	$0.554582\pi$
$942$	−13256.8	−0.458525
$943$	7380.47	0.254869
$944$	95435.0	3.29041
$945$	−38302.4	−1.31850
$946$	−22622.9	−0.777521
$947$	−41810.9	−1.43471	−0.717356	−	0.696707i	$-0.754648\pi$
$947$	−41810.9	−1.43471	−0.717356	+	0.696707i	$0.754648\pi$
$948$	−14891.2	−0.510173
$949$	−38834.0	−1.32835
$950$	−2412.14	−0.0823790
$951$	44519.6	1.51803
$952$	−45214.7	−1.53930
$953$	−11864.0	−0.403265	−0.201632	−	0.979461i	$-0.564625\pi$
$953$	−11864.0	−0.403265	−0.201632	+	0.979461i	$0.564625\pi$
$954$	35890.2	1.21802
$955$	−11620.3	−0.393742
$956$	−50194.8	−1.69813
$957$	24861.8	0.839778
$958$	99128.6	3.34311
$959$	−75421.0	−2.53960
$960$	2784.68	0.0936199
$961$	−9308.52	−0.312461
$962$	42137.6	1.41224
$963$	51491.0	1.72303
$964$	−7804.35	−0.260748
$965$	−9405.81	−0.313766
$966$	−58363.6	−1.94391
$967$	−37112.0	−1.23417	−0.617085	−	0.786896i	$-0.711687\pi$
$967$	−37112.0	−1.23417	−0.617085	+	0.786896i	$0.711687\pi$
$968$	6014.28	0.199697
$969$	−5725.07	−0.189800
$970$	−32362.1	−1.07122
$971$	−17510.0	−0.578706	−0.289353	−	0.957223i	$-0.593440\pi$
$971$	−17510.0	−0.578706	−0.289353	+	0.957223i	$0.593440\pi$
$972$	−29406.5	−0.970385
$973$	−67927.4	−2.23808
$974$	20538.2	0.675653
$975$	−14195.3	−0.466270
$976$	74280.4	2.43612
$977$	−36616.4	−1.19904	−0.599519	−	0.800360i	$-0.704642\pi$
$977$	−36616.4	−1.19904	−0.599519	+	0.800360i	$0.704642\pi$
$978$	129895.	4.24703
$979$	−13333.4	−0.435279
$980$	37707.6	1.22911
$981$	11163.4	0.363323
$982$	60872.5	1.97813
$983$	−5787.95	−0.187800	−0.0938998	−	0.995582i	$-0.529933\pi$
$983$	−5787.95	−0.187800	−0.0938998	+	0.995582i	$0.529933\pi$
$984$	−74388.9	−2.40999
$985$	−5080.56	−0.164345
$986$	41096.5	1.32736
$987$	43607.1	1.40631
$988$	−20919.3	−0.673616
$989$	−18321.4	−0.589065
$990$	15962.9	0.512458
$991$	33231.2	1.06521	0.532605	−	0.846364i	$-0.321213\pi$
$991$	33231.2	1.06521	0.532605	+	0.846364i	$0.321213\pi$
$992$	23113.9	0.739784
$993$	−73951.0	−2.36331
$994$	29560.4	0.943257
$995$	−21704.1	−0.691523
$996$	−93089.3	−2.96149
$997$	23199.8	0.736955	0.368477	−	0.929637i	$-0.379879\pi$
$997$	23199.8	0.736955	0.368477	+	0.929637i	$0.379879\pi$
$998$	−110188.	−3.49491
$999$	−37081.7	−1.17439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.e.1.20	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.e.1.20	✓	22	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q+5.07818 q^{2} -9.17350 q^{3} +17.7879 q^{4} +5.00000 q^{5} -46.5847 q^{6} +27.6942 q^{7} +49.7048 q^{8} +57.1531 q^{9} +O(q^{10})\)	\(q+5.07818 q^{2} -9.17350 q^{3} +17.7879 q^{4} +5.00000 q^{5} -46.5847 q^{6} +27.6942 q^{7} +49.7048 q^{8} +57.1531 q^{9} +25.3909 q^{10} +11.0000 q^{11} -163.178 q^{12} +61.8970 q^{13} +140.636 q^{14} -45.8675 q^{15} +110.107 q^{16} -32.8467 q^{17} +290.234 q^{18} -19.0000 q^{19} +88.9396 q^{20} -254.053 q^{21} +55.8600 q^{22} +45.2387 q^{23} -455.967 q^{24} +25.0000 q^{25} +314.324 q^{26} -276.610 q^{27} +492.622 q^{28} -246.380 q^{29} -232.924 q^{30} +143.117 q^{31} +161.503 q^{32} -100.909 q^{33} -166.802 q^{34} +138.471 q^{35} +1016.64 q^{36} +134.058 q^{37} -96.4854 q^{38} -567.812 q^{39} +248.524 q^{40} +163.145 q^{41} -1290.13 q^{42} -404.994 q^{43} +195.667 q^{44} +285.766 q^{45} +229.730 q^{46} -171.646 q^{47} -1010.06 q^{48} +423.968 q^{49} +126.955 q^{50} +301.319 q^{51} +1101.02 q^{52} +123.660 q^{53} -1404.67 q^{54} +55.0000 q^{55} +1376.53 q^{56} +174.297 q^{57} -1251.16 q^{58} +866.750 q^{59} -815.888 q^{60} +674.622 q^{61} +726.774 q^{62} +1582.81 q^{63} -60.7113 q^{64} +309.485 q^{65} -512.432 q^{66} -120.926 q^{67} -584.275 q^{68} -414.997 q^{69} +703.181 q^{70} +210.190 q^{71} +2840.79 q^{72} -627.397 q^{73} +680.770 q^{74} -229.338 q^{75} -337.970 q^{76} +304.636 q^{77} -2883.45 q^{78} +91.2577 q^{79} +550.534 q^{80} +994.346 q^{81} +828.481 q^{82} +570.479 q^{83} -4519.07 q^{84} -164.234 q^{85} -2056.63 q^{86} +2260.16 q^{87} +546.753 q^{88} -1212.13 q^{89} +1451.17 q^{90} +1714.19 q^{91} +804.702 q^{92} -1312.88 q^{93} -871.649 q^{94} -95.0000 q^{95} -1481.55 q^{96} -1274.56 q^{97} +2152.99 q^{98} +628.685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9}+O(q^{10}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9} + 60 q^{10} + 242 q^{11} + 164 q^{12} + 207 q^{13} + 129 q^{14} + 105 q^{15} + 604 q^{16} + 209 q^{17} + 869 q^{18} - 418 q^{19} + 480 q^{20} + 45 q^{21} + 132 q^{22} + 191 q^{23} + 458 q^{24} + 550 q^{25} + 363 q^{26} + 45 q^{27} + 577 q^{28} + 389 q^{29} + 135 q^{30} + 198 q^{31} + 1149 q^{32} + 231 q^{33} + 467 q^{34} + 465 q^{35} + 1315 q^{36} + 312 q^{37} - 228 q^{38} + 137 q^{39} + 570 q^{40} + 632 q^{41} - 1794 q^{42} + 1584 q^{43} + 1056 q^{44} + 1045 q^{45} + 681 q^{46} - 54 q^{47} + 2491 q^{48} + 1063 q^{49} + 300 q^{50} + 37 q^{51} + 1246 q^{52} + 343 q^{53} + 1078 q^{54} + 1210 q^{55} - 87 q^{56} - 399 q^{57} - 1424 q^{58} + 2787 q^{59} + 820 q^{60} + 2070 q^{61} - 446 q^{62} + 1696 q^{63} + 1758 q^{64} + 1035 q^{65} + 297 q^{66} + 2423 q^{67} - 524 q^{68} - 997 q^{69} + 645 q^{70} + 2538 q^{71} + 6010 q^{72} + 1397 q^{73} - 1977 q^{74} + 525 q^{75} - 1824 q^{76} + 1023 q^{77} + 202 q^{78} + 878 q^{79} + 3020 q^{80} + 2030 q^{81} - 190 q^{82} + 4932 q^{83} - 4580 q^{84} + 1045 q^{85} - 3394 q^{86} + 6009 q^{87} + 1254 q^{88} + 1812 q^{89} + 4345 q^{90} + 4349 q^{91} - 788 q^{92} - 4848 q^{93} - 2152 q^{94} - 2090 q^{95} + 4032 q^{96} + 988 q^{97} + 1366 q^{98} + 2299 q^{99}+O(q^{100}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9 + 60 * q^10 + 242 * q^11 + 164 * q^12 + 207 * q^13 + 129 * q^14 + 105 * q^15 + 604 * q^16 + 209 * q^17 + 869 * q^18 - 418 * q^19 + 480 * q^20 + 45 * q^21 + 132 * q^22 + 191 * q^23 + 458 * q^24 + 550 * q^25 + 363 * q^26 + 45 * q^27 + 577 * q^28 + 389 * q^29 + 135 * q^30 + 198 * q^31 + 1149 * q^32 + 231 * q^33 + 467 * q^34 + 465 * q^35 + 1315 * q^36 + 312 * q^37 - 228 * q^38 + 137 * q^39 + 570 * q^40 + 632 * q^41 - 1794 * q^42 + 1584 * q^43 + 1056 * q^44 + 1045 * q^45 + 681 * q^46 - 54 * q^47 + 2491 * q^48 + 1063 * q^49 + 300 * q^50 + 37 * q^51 + 1246 * q^52 + 343 * q^53 + 1078 * q^54 + 1210 * q^55 - 87 * q^56 - 399 * q^57 - 1424 * q^58 + 2787 * q^59 + 820 * q^60 + 2070 * q^61 - 446 * q^62 + 1696 * q^63 + 1758 * q^64 + 1035 * q^65 + 297 * q^66 + 2423 * q^67 - 524 * q^68 - 997 * q^69 + 645 * q^70 + 2538 * q^71 + 6010 * q^72 + 1397 * q^73 - 1977 * q^74 + 525 * q^75 - 1824 * q^76 + 1023 * q^77 + 202 * q^78 + 878 * q^79 + 3020 * q^80 + 2030 * q^81 - 190 * q^82 + 4932 * q^83 - 4580 * q^84 + 1045 * q^85 - 3394 * q^86 + 6009 * q^87 + 1254 * q^88 + 1812 * q^89 + 4345 * q^90 + 4349 * q^91 - 788 * q^92 - 4848 * q^93 - 2152 * q^94 - 2090 * q^95 + 4032 * q^96 + 988 * q^97 + 1366 * q^98 + 2299 * q^99

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