LMFDB - Embedded newform 1045.4.a.e.1.19

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			1.19
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)

$f(q)$	$=$	$q+4.50809 q^{2} +6.83061 q^{3} +12.3229 q^{4} +5.00000 q^{5} +30.7930 q^{6} +25.7280 q^{7} +19.4881 q^{8} +19.6572 q^{9} +O(q^{10})$	\(q+4.50809 q^{2} +6.83061 q^{3} +12.3229 q^{4} +5.00000 q^{5} +30.7930 q^{6} +25.7280 q^{7} +19.4881 q^{8} +19.6572 q^{9} +22.5405 q^{10} +11.0000 q^{11} +84.1730 q^{12} +18.7292 q^{13} +115.984 q^{14} +34.1530 q^{15} -10.7291 q^{16} -81.5050 q^{17} +88.6164 q^{18} -19.0000 q^{19} +61.6146 q^{20} +175.738 q^{21} +49.5890 q^{22} +162.296 q^{23} +133.116 q^{24} +25.0000 q^{25} +84.4331 q^{26} -50.1559 q^{27} +317.044 q^{28} -30.4718 q^{29} +153.965 q^{30} -26.1964 q^{31} -204.273 q^{32} +75.1367 q^{33} -367.432 q^{34} +128.640 q^{35} +242.234 q^{36} -135.372 q^{37} -85.6538 q^{38} +127.932 q^{39} +97.4406 q^{40} +111.683 q^{41} +792.242 q^{42} +8.70135 q^{43} +135.552 q^{44} +98.2859 q^{45} +731.647 q^{46} +346.950 q^{47} -73.2860 q^{48} +318.929 q^{49} +112.702 q^{50} -556.729 q^{51} +230.799 q^{52} -206.885 q^{53} -226.108 q^{54} +55.0000 q^{55} +501.390 q^{56} -129.782 q^{57} -137.370 q^{58} -651.486 q^{59} +420.865 q^{60} -320.001 q^{61} -118.096 q^{62} +505.739 q^{63} -835.047 q^{64} +93.6461 q^{65} +338.723 q^{66} -57.5798 q^{67} -1004.38 q^{68} +1108.58 q^{69} +579.921 q^{70} -435.008 q^{71} +383.081 q^{72} -284.437 q^{73} -610.270 q^{74} +170.765 q^{75} -234.135 q^{76} +283.008 q^{77} +576.729 q^{78} +800.973 q^{79} -53.6453 q^{80} -873.339 q^{81} +503.476 q^{82} -202.203 q^{83} +2165.60 q^{84} -407.525 q^{85} +39.2265 q^{86} -208.141 q^{87} +214.369 q^{88} +783.866 q^{89} +443.082 q^{90} +481.865 q^{91} +1999.96 q^{92} -178.937 q^{93} +1564.08 q^{94} -95.0000 q^{95} -1395.31 q^{96} +395.737 q^{97} +1437.76 q^{98} +216.229 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.50809	1.59385	0.796926	−	0.604077i	$-0.206458\pi$
$2$	4.50809	1.59385	0.796926	+	0.604077i	$0.206458\pi$
$3$	6.83061	1.31455	0.657275	−	0.753650i	$-0.271709\pi$
$3$	6.83061	1.31455	0.657275	+	0.753650i	$0.271709\pi$
$4$	12.3229	1.54036
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	30.7930	2.09520
$7$	25.7280	1.38918	0.694590	−	0.719406i	$-0.255586\pi$
$7$	25.7280	1.38918	0.694590	+	0.719406i	$0.255586\pi$
$8$	19.4881	0.861261
$9$	19.6572	0.728044
$10$	22.5405	0.712792
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	84.1730	2.02489
$13$	18.7292	0.399581	0.199790	−	0.979839i	$-0.435974\pi$
$13$	18.7292	0.399581	0.199790	+	0.979839i	$0.435974\pi$
$14$	115.984	2.21415
$15$	34.1530	0.587885
$16$	−10.7291	−0.167642
$17$	−81.5050	−1.16282	−0.581408	−	0.813612i	$-0.697498\pi$
$17$	−81.5050	−1.16282	−0.581408	+	0.813612i	$0.697498\pi$
$18$	88.6164	1.16039
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	61.6146	0.688872
$21$	175.738	1.82615
$22$	49.5890	0.480564
$23$	162.296	1.47135	0.735677	−	0.677333i	$-0.236864\pi$
$23$	162.296	1.47135	0.735677	+	0.677333i	$0.236864\pi$
$24$	133.116	1.13217
$25$	25.0000	0.200000
$26$	84.4331	0.636873
$27$	−50.1559	−0.357500
$28$	317.044	2.13984
$29$	−30.4718	−0.195120	−0.0975599	−	0.995230i	$-0.531104\pi$
$29$	−30.4718	−0.195120	−0.0975599	+	0.995230i	$0.531104\pi$
$30$	153.965	0.937002
$31$	−26.1964	−0.151774	−0.0758872	−	0.997116i	$-0.524179\pi$
$31$	−26.1964	−0.151774	−0.0758872	+	0.997116i	$0.524179\pi$
$32$	−204.273	−1.12846
$33$	75.1367	0.396352
$34$	−367.432	−1.85336
$35$	128.640	0.621260
$36$	242.234	1.12145
$37$	−135.372	−0.601487	−0.300744	−	0.953705i	$-0.597235\pi$
$37$	−135.372	−0.601487	−0.300744	+	0.953705i	$0.597235\pi$
$38$	−85.6538	−0.365655
$39$	127.932	0.525269
$40$	97.4406	0.385168
$41$	111.683	0.425413	0.212706	−	0.977116i	$-0.431772\pi$
$41$	111.683	0.425413	0.212706	+	0.977116i	$0.431772\pi$
$42$	792.242	2.91061
$43$	8.70135	0.0308591	0.0154296	−	0.999881i	$-0.495088\pi$
$43$	8.70135	0.0308591	0.0154296	+	0.999881i	$0.495088\pi$
$44$	135.552	0.464437
$45$	98.2859	0.325591
$46$	731.647	2.34512
$47$	346.950	1.07676	0.538382	−	0.842701i	$-0.319036\pi$
$47$	346.950	1.07676	0.538382	+	0.842701i	$0.319036\pi$
$48$	−73.2860	−0.220373
$49$	318.929	0.929821
$50$	112.702	0.318770
$51$	−556.729	−1.52858
$52$	230.799	0.615500
$53$	−206.885	−0.536187	−0.268093	−	0.963393i	$-0.586394\pi$
$53$	−206.885	−0.536187	−0.268093	+	0.963393i	$0.586394\pi$
$54$	−226.108	−0.569803
$55$	55.0000	0.134840
$56$	501.390	1.19645
$57$	−129.782	−0.301579
$58$	−137.370	−0.310992
$59$	−651.486	−1.43756	−0.718781	−	0.695236i	$-0.755300\pi$
$59$	−651.486	−1.43756	−0.718781	+	0.695236i	$0.755300\pi$
$60$	420.865	0.905557
$61$	−320.001	−0.671671	−0.335835	−	0.941921i	$-0.609019\pi$
$61$	−320.001	−0.671671	−0.335835	+	0.941921i	$0.609019\pi$
$62$	−118.096	−0.241906
$63$	505.739	1.01138
$64$	−835.047	−1.63095
$65$	93.6461	0.178698
$66$	338.723	0.631726
$67$	−57.5798	−0.104992	−0.0524962	−	0.998621i	$-0.516718\pi$
$67$	−57.5798	−0.104992	−0.0524962	+	0.998621i	$0.516718\pi$
$68$	−1004.38	−1.79116
$69$	1108.58	1.93417
$70$	579.921	0.990197
$71$	−435.008	−0.727125	−0.363563	−	0.931570i	$-0.618440\pi$
$71$	−435.008	−0.727125	−0.363563	+	0.931570i	$0.618440\pi$
$72$	383.081	0.627036
$73$	−284.437	−0.456040	−0.228020	−	0.973656i	$-0.573225\pi$
$73$	−284.437	−0.456040	−0.228020	+	0.973656i	$0.573225\pi$
$74$	−610.270	−0.958682
$75$	170.765	0.262910
$76$	−234.135	−0.353384
$77$	283.008	0.418854
$78$	576.729	0.837202
$79$	800.973	1.14072	0.570358	−	0.821397i	$-0.306805\pi$
$79$	800.973	1.14072	0.570358	+	0.821397i	$0.306805\pi$
$80$	−53.6453	−0.0749716
$81$	−873.339	−1.19800
$82$	503.476	0.678045
$83$	−202.203	−0.267405	−0.133703	−	0.991021i	$-0.542687\pi$
$83$	−202.203	−0.267405	−0.133703	+	0.991021i	$0.542687\pi$
$84$	2165.60	2.81293
$85$	−407.525	−0.520027
$86$	39.2265	0.0491849
$87$	−208.141	−0.256495
$88$	214.369	0.259680
$89$	783.866	0.933592	0.466796	−	0.884365i	$-0.345408\pi$
$89$	783.866	0.933592	0.466796	+	0.884365i	$0.345408\pi$
$90$	443.082	0.518944
$91$	481.865	0.555090
$92$	1999.96	2.26642
$93$	−178.937	−0.199515
$94$	1564.08	1.71620
$95$	−95.0000	−0.102598
$96$	−1395.31	−1.48341
$97$	395.737	0.414238	0.207119	−	0.978316i	$-0.433591\pi$
$97$	395.737	0.414238	0.207119	+	0.978316i	$0.433591\pi$
$98$	1437.76	1.48200
$99$	216.229	0.219513
$100$	308.073	0.308073
$101$	317.631	0.312925	0.156463	−	0.987684i	$-0.449991\pi$
$101$	317.631	0.312925	0.156463	+	0.987684i	$0.449991\pi$
$102$	−2509.79	−2.43633
$103$	31.9401	0.0305548	0.0152774	−	0.999883i	$-0.495137\pi$
$103$	31.9401	0.0305548	0.0152774	+	0.999883i	$0.495137\pi$
$104$	364.997	0.344143
$105$	878.688	0.816678
$106$	−932.659	−0.854602
$107$	579.594	0.523658	0.261829	−	0.965114i	$-0.415674\pi$
$107$	579.594	0.523658	0.261829	+	0.965114i	$0.415674\pi$
$108$	−618.067	−0.550681
$109$	−811.366	−0.712980	−0.356490	−	0.934299i	$-0.616027\pi$
$109$	−811.366	−0.712980	−0.356490	+	0.934299i	$0.616027\pi$
$110$	247.945	0.214915
$111$	−924.673	−0.790686
$112$	−276.037	−0.232884
$113$	−417.634	−0.347679	−0.173840	−	0.984774i	$-0.555617\pi$
$113$	−417.634	−0.347679	−0.173840	+	0.984774i	$0.555617\pi$
$114$	−585.067	−0.480672
$115$	811.482	0.658009
$116$	−375.502	−0.300556
$117$	368.164	0.290912
$118$	−2936.96	−2.29126
$119$	−2096.96	−1.61536
$120$	665.578	0.506322
$121$	121.000	0.0909091
$122$	−1442.59	−1.07054
$123$	762.861	0.559227
$124$	−322.816	−0.233788
$125$	125.000	0.0894427
$126$	2279.92	1.61200
$127$	1332.36	0.930927	0.465463	−	0.885067i	$-0.345888\pi$
$127$	1332.36	0.930927	0.465463	+	0.885067i	$0.345888\pi$
$128$	−2130.29	−1.47104
$129$	59.4355	0.0405659
$130$	422.166	0.284818
$131$	−2281.89	−1.52190	−0.760952	−	0.648808i	$-0.775268\pi$
$131$	−2281.89	−1.52190	−0.760952	+	0.648808i	$0.775268\pi$
$132$	925.903	0.610527
$133$	−488.832	−0.318700
$134$	−259.575	−0.167342
$135$	−250.779	−0.159879
$136$	−1588.38	−1.00149
$137$	−163.403	−0.101901	−0.0509506	−	0.998701i	$-0.516225\pi$
$137$	−163.403	−0.101901	−0.0509506	+	0.998701i	$0.516225\pi$
$138$	4997.60	3.08278
$139$	1658.54	1.01206	0.506028	−	0.862517i	$-0.331113\pi$
$139$	1658.54	1.01206	0.506028	+	0.862517i	$0.331113\pi$
$140$	1585.22	0.956967
$141$	2369.88	1.41546
$142$	−1961.06	−1.15893
$143$	206.021	0.120478
$144$	−210.903	−0.122050
$145$	−152.359	−0.0872602
$146$	−1282.27	−0.726860
$147$	2178.48	1.22230
$148$	−1668.18	−0.926510
$149$	2390.01	1.31408	0.657039	−	0.753857i	$-0.271809\pi$
$149$	2390.01	1.31408	0.657039	+	0.753857i	$0.271809\pi$
$150$	769.825	0.419040
$151$	31.3205	0.0168796	0.00843981	−	0.999964i	$-0.497313\pi$
$151$	31.3205	0.0168796	0.00843981	+	0.999964i	$0.497313\pi$
$152$	−370.274	−0.197587
$153$	−1602.16	−0.846581
$154$	1275.83	0.667591
$155$	−130.982	−0.0678756
$156$	1576.49	0.809106
$157$	457.781	0.232707	0.116353	−	0.993208i	$-0.462880\pi$
$157$	457.781	0.232707	0.116353	+	0.993208i	$0.462880\pi$
$158$	3610.86	1.81813
$159$	−1413.15	−0.704845
$160$	−1021.36	−0.504661
$161$	4175.56	2.04398
$162$	−3937.10	−1.90943
$163$	−326.905	−0.157087	−0.0785434	−	0.996911i	$-0.525027\pi$
$163$	−326.905	−0.157087	−0.0785434	+	0.996911i	$0.525027\pi$
$164$	1376.26	0.655291
$165$	375.683	0.177254
$166$	−911.550	−0.426205
$167$	−1098.65	−0.509081	−0.254540	−	0.967062i	$-0.581924\pi$
$167$	−1098.65	−0.509081	−0.254540	+	0.967062i	$0.581924\pi$
$168$	3424.80	1.57279
$169$	−1846.22	−0.840335
$170$	−1837.16	−0.828846
$171$	−373.486	−0.167025
$172$	107.226	0.0475343
$173$	2936.03	1.29030	0.645152	−	0.764054i	$-0.276794\pi$
$173$	2936.03	1.29030	0.645152	+	0.764054i	$0.276794\pi$
$174$	−938.319	−0.408815
$175$	643.199	0.277836
$176$	−118.020	−0.0505459
$177$	−4450.04	−1.88975
$178$	3533.74	1.48801
$179$	−1431.03	−0.597544	−0.298772	−	0.954325i	$-0.596577\pi$
$179$	−1431.03	−0.597544	−0.298772	+	0.954325i	$0.596577\pi$
$180$	1211.17	0.501529
$181$	2924.11	1.20081	0.600406	−	0.799695i	$-0.295006\pi$
$181$	2924.11	1.20081	0.600406	+	0.799695i	$0.295006\pi$
$182$	2172.29	0.884731
$183$	−2185.80	−0.882945
$184$	3162.85	1.26722
$185$	−676.860	−0.268993
$186$	−806.665	−0.317998
$187$	−896.555	−0.350602
$188$	4275.44	1.65861
$189$	−1290.41	−0.496632
$190$	−428.269	−0.163526
$191$	−2615.21	−0.990734	−0.495367	−	0.868684i	$-0.664966\pi$
$191$	−2615.21	−0.990734	−0.495367	+	0.868684i	$0.664966\pi$
$192$	−5703.88	−2.14397
$193$	−4539.29	−1.69298	−0.846490	−	0.532404i	$-0.821289\pi$
$193$	−4539.29	−1.69298	−0.846490	+	0.532404i	$0.821289\pi$
$194$	1784.02	0.660233
$195$	639.660	0.234908
$196$	3930.13	1.43226
$197$	1866.90	0.675183	0.337592	−	0.941293i	$-0.390388\pi$
$197$	1866.90	0.675183	0.337592	+	0.941293i	$0.390388\pi$
$198$	974.781	0.349872
$199$	−1473.96	−0.525056	−0.262528	−	0.964924i	$-0.584556\pi$
$199$	−1473.96	−0.525056	−0.262528	+	0.964924i	$0.584556\pi$
$200$	487.203	0.172252
$201$	−393.305	−0.138018
$202$	1431.91	0.498756
$203$	−783.978	−0.271057
$204$	−6860.52	−2.35457
$205$	558.414	0.190250
$206$	143.989	0.0486999
$207$	3190.29	1.07121
$208$	−200.947	−0.0669864
$209$	−209.000	−0.0691714
$210$	3961.21	1.30166
$211$	1065.45	0.347623	0.173812	−	0.984779i	$-0.444392\pi$
$211$	1065.45	0.347623	0.173812	+	0.984779i	$0.444392\pi$
$212$	−2549.43	−0.825923
$213$	−2971.37	−0.955843
$214$	2612.86	0.834634
$215$	43.5068	0.0138006
$216$	−977.444	−0.307901
$217$	−673.979	−0.210842
$218$	−3657.72	−1.13638
$219$	−1942.88	−0.599487
$220$	677.760	0.207703
$221$	−1526.53	−0.464639
$222$	−4168.51	−1.26024
$223$	4257.86	1.27860	0.639300	−	0.768958i	$-0.279224\pi$
$223$	4257.86	1.27860	0.639300	+	0.768958i	$0.279224\pi$
$224$	−5255.52	−1.56763
$225$	491.430	0.145609
$226$	−1882.74	−0.554149
$227$	2109.72	0.616859	0.308430	−	0.951247i	$-0.400197\pi$
$227$	2109.72	0.616859	0.308430	+	0.951247i	$0.400197\pi$
$228$	−1599.29	−0.464541
$229$	−405.164	−0.116917	−0.0584585	−	0.998290i	$-0.518619\pi$
$229$	−405.164	−0.116917	−0.0584585	+	0.998290i	$0.518619\pi$
$230$	3658.24	1.04877
$231$	1933.11	0.550604
$232$	−593.838	−0.168049
$233$	434.192	0.122081	0.0610405	−	0.998135i	$-0.480558\pi$
$233$	434.192	0.122081	0.0610405	+	0.998135i	$0.480558\pi$
$234$	1659.72	0.463671
$235$	1734.75	0.481543
$236$	−8028.20	−2.21437
$237$	5471.13	1.49953
$238$	−9453.29	−2.57465
$239$	740.332	0.200368	0.100184	−	0.994969i	$-0.468057\pi$
$239$	740.332	0.200368	0.100184	+	0.994969i	$0.468057\pi$
$240$	−366.430	−0.0985540
$241$	−5552.21	−1.48402	−0.742011	−	0.670387i	$-0.766128\pi$
$241$	−5552.21	−1.48402	−0.742011	+	0.670387i	$0.766128\pi$
$242$	545.479	0.144896
$243$	−4611.23	−1.21733
$244$	−3943.34	−1.03462
$245$	1594.64	0.415829
$246$	3439.05	0.891324
$247$	−355.855	−0.0916701
$248$	−510.518	−0.130717
$249$	−1381.17	−0.351518
$250$	563.512	0.142558
$251$	−2812.74	−0.707326	−0.353663	−	0.935373i	$-0.615064\pi$
$251$	−2812.74	−0.707326	−0.353663	+	0.935373i	$0.615064\pi$
$252$	6232.19	1.55790
$253$	1785.26	0.443630
$254$	6006.40	1.48376
$255$	−2783.64	−0.683602
$256$	−2923.18	−0.713667
$257$	−3179.43	−0.771702	−0.385851	−	0.922561i	$-0.626092\pi$
$257$	−3179.43	−0.771702	−0.385851	+	0.922561i	$0.626092\pi$
$258$	267.941	0.0646561
$259$	−3482.85	−0.835574
$260$	1153.99	0.275260
$261$	−598.990	−0.142056
$262$	−10287.0	−2.42569
$263$	−3316.28	−0.777532	−0.388766	−	0.921337i	$-0.627098\pi$
$263$	−3316.28	−0.777532	−0.388766	+	0.921337i	$0.627098\pi$
$264$	1464.27	0.341363
$265$	−1034.43	−0.239790
$266$	−2203.70	−0.507960
$267$	5354.28	1.22725
$268$	−709.551	−0.161727
$269$	4912.83	1.11353	0.556767	−	0.830669i	$-0.312042\pi$
$269$	4912.83	1.11353	0.556767	+	0.830669i	$0.312042\pi$
$270$	−1130.54	−0.254823
$271$	758.892	0.170108	0.0850542	−	0.996376i	$-0.472894\pi$
$271$	758.892	0.170108	0.0850542	+	0.996376i	$0.472894\pi$
$272$	874.473	0.194936
$273$	3291.43	0.729694
$274$	−736.636	−0.162415
$275$	275.000	0.0603023
$276$	13661.0	2.97933
$277$	−2644.49	−0.573617	−0.286809	−	0.957988i	$-0.592594\pi$
$277$	−2644.49	−0.573617	−0.286809	+	0.957988i	$0.592594\pi$
$278$	7476.87	1.61307
$279$	−514.947	−0.110498
$280$	2506.95	0.535067
$281$	−5557.99	−1.17993	−0.589967	−	0.807427i	$-0.700859\pi$
$281$	−5557.99	−1.17993	−0.589967	+	0.807427i	$0.700859\pi$
$282$	10683.6	2.25603
$283$	−8190.24	−1.72035	−0.860176	−	0.509998i	$-0.829646\pi$
$283$	−8190.24	−1.72035	−0.860176	+	0.509998i	$0.829646\pi$
$284$	−5360.56	−1.12004
$285$	−648.908	−0.134870
$286$	928.764	0.192024
$287$	2873.37	0.590975
$288$	−4015.42	−0.821566
$289$	1730.07	0.352141
$290$	−686.849	−0.139080
$291$	2703.13	0.544536
$292$	−3505.10	−0.702467
$293$	8749.93	1.74463	0.872314	−	0.488946i	$-0.162618\pi$
$293$	8749.93	1.74463	0.872314	+	0.488946i	$0.162618\pi$
$294$	9820.78	1.94816
$295$	−3257.43	−0.642898
$296$	−2638.15	−0.518038
$297$	−551.715	−0.107790
$298$	10774.4	2.09445
$299$	3039.69	0.587925
$300$	2104.32	0.404977
$301$	223.868	0.0428689
$302$	141.196	0.0269036
$303$	2169.61	0.411356
$304$	203.852	0.0384596
$305$	−1600.00	−0.300380
$306$	−7222.68	−1.34932
$307$	−10107.5	−1.87904	−0.939520	−	0.342495i	$-0.888728\pi$
$307$	−10107.5	−1.87904	−0.939520	+	0.342495i	$0.888728\pi$
$308$	3487.48	0.645187
$309$	218.170	0.0401659
$310$	−590.478	−0.108184
$311$	6877.96	1.25406	0.627031	−	0.778995i	$-0.284270\pi$
$311$	6877.96	1.25406	0.627031	+	0.778995i	$0.284270\pi$
$312$	2493.15	0.452394
$313$	−7408.18	−1.33781	−0.668906	−	0.743347i	$-0.733237\pi$
$313$	−7408.18	−1.33781	−0.668906	+	0.743347i	$0.733237\pi$
$314$	2063.72	0.370900
$315$	2528.70	0.452305
$316$	9870.32	1.75712
$317$	1526.52	0.270467	0.135233	−	0.990814i	$-0.456822\pi$
$317$	1526.52	0.270467	0.135233	+	0.990814i	$0.456822\pi$
$318$	−6370.63	−1.12342
$319$	−335.190	−0.0588308
$320$	−4175.24	−0.729384
$321$	3958.98	0.688376
$322$	18823.8	3.25779
$323$	1548.60	0.266768
$324$	−10762.1	−1.84535
$325$	468.231	0.0799162
$326$	−1473.72	−0.250373
$327$	−5542.12	−0.937248
$328$	2176.49	0.366391
$329$	8926.32	1.49582
$330$	1693.62	0.282517
$331$	3705.81	0.615377	0.307689	−	0.951487i	$-0.400444\pi$
$331$	3705.81	0.615377	0.307689	+	0.951487i	$0.400444\pi$
$332$	−2491.73	−0.411902
$333$	−2661.03	−0.437909
$334$	−4952.84	−0.811399
$335$	−287.899	−0.0469541
$336$	−1885.50	−0.306138
$337$	2043.47	0.330312	0.165156	−	0.986267i	$-0.447187\pi$
$337$	2043.47	0.330312	0.165156	+	0.986267i	$0.447187\pi$
$338$	−8322.92	−1.33937
$339$	−2852.70	−0.457042
$340$	−5021.90	−0.801031
$341$	−288.160	−0.0457617
$342$	−1683.71	−0.266213
$343$	−619.306	−0.0974909
$344$	169.573	0.0265778
$345$	5542.91	0.864987
$346$	13235.9	2.05655
$347$	−6628.87	−1.02552	−0.512761	−	0.858531i	$-0.671377\pi$
$347$	−6628.87	−1.02552	−0.512761	+	0.858531i	$0.671377\pi$
$348$	−2564.90	−0.395096
$349$	11392.5	1.74735	0.873674	−	0.486512i	$-0.161731\pi$
$349$	11392.5	1.74735	0.873674	+	0.486512i	$0.161731\pi$
$350$	2899.60	0.442830
$351$	−939.381	−0.142850
$352$	−2247.00	−0.340243
$353$	−7143.32	−1.07706	−0.538528	−	0.842608i	$-0.681019\pi$
$353$	−7143.32	−1.07706	−0.538528	+	0.842608i	$0.681019\pi$
$354$	−20061.2	−3.01198
$355$	−2175.04	−0.325180
$356$	9659.52	1.43807
$357$	−14323.5	−2.12347
$358$	−6451.22	−0.952396
$359$	11206.2	1.64746	0.823731	−	0.566981i	$-0.191889\pi$
$359$	11206.2	1.64746	0.823731	+	0.566981i	$0.191889\pi$
$360$	1915.41	0.280419
$361$	361.000	0.0526316
$362$	13182.1	1.91392
$363$	826.503	0.119505
$364$	5937.98	0.855041
$365$	−1422.19	−0.203947
$366$	−9853.79	−1.40728
$367$	3086.27	0.438970	0.219485	−	0.975616i	$-0.429562\pi$
$367$	3086.27	0.438970	0.219485	+	0.975616i	$0.429562\pi$
$368$	−1741.29	−0.246660
$369$	2195.37	0.309719
$370$	−3051.35	−0.428736
$371$	−5322.74	−0.744860
$372$	−2205.03	−0.307326
$373$	−57.5096	−0.00798321	−0.00399160	−	0.999992i	$-0.501271\pi$
$373$	−57.5096	−0.00798321	−0.00399160	+	0.999992i	$0.501271\pi$
$374$	−4041.76	−0.558808
$375$	853.826	0.117577
$376$	6761.40	0.927374
$377$	−570.713	−0.0779661
$378$	−5817.29	−0.791558
$379$	2353.27	0.318943	0.159471	−	0.987203i	$-0.449021\pi$
$379$	2353.27	0.318943	0.159471	+	0.987203i	$0.449021\pi$
$380$	−1170.68	−0.158038
$381$	9100.82	1.22375
$382$	−11789.6	−1.57908
$383$	8847.69	1.18041	0.590203	−	0.807255i	$-0.299048\pi$
$383$	8847.69	1.18041	0.590203	+	0.807255i	$0.299048\pi$
$384$	−14551.2	−1.93376
$385$	1415.04	0.187317
$386$	−20463.6	−2.69836
$387$	171.044	0.0224668
$388$	4876.64	0.638077
$389$	2221.56	0.289556	0.144778	−	0.989464i	$-0.453753\pi$
$389$	2221.56	0.289556	0.144778	+	0.989464i	$0.453753\pi$
$390$	2883.65	0.374408
$391$	−13228.0	−1.71091
$392$	6215.32	0.800819
$393$	−15586.7	−2.00062
$394$	8416.16	1.07614
$395$	4004.86	0.510143
$396$	2664.57	0.338131
$397$	1324.60	0.167455	0.0837274	−	0.996489i	$-0.473317\pi$
$397$	1324.60	0.167455	0.0837274	+	0.996489i	$0.473317\pi$
$398$	−6644.75	−0.836862
$399$	−3339.02	−0.418947
$400$	−268.227	−0.0335283
$401$	9877.29	1.23005	0.615023	−	0.788509i	$-0.289147\pi$
$401$	9877.29	1.23005	0.615023	+	0.788509i	$0.289147\pi$
$402$	−1773.06	−0.219980
$403$	−490.637	−0.0606461
$404$	3914.14	0.482019
$405$	−4366.70	−0.535760
$406$	−3534.25	−0.432024
$407$	−1489.09	−0.181355
$408$	−10849.6	−1.31651
$409$	8221.33	0.993933	0.496967	−	0.867770i	$-0.334447\pi$
$409$	8221.33	0.993933	0.496967	+	0.867770i	$0.334447\pi$
$410$	2517.38	0.303231
$411$	−1116.14	−0.133954
$412$	393.595	0.0470656
$413$	−16761.4	−1.99703
$414$	14382.1	1.70735
$415$	−1011.01	−0.119587
$416$	−3825.87	−0.450910
$417$	11328.9	1.33040
$418$	−942.192	−0.110249
$419$	5181.85	0.604176	0.302088	−	0.953280i	$-0.402316\pi$
$419$	5181.85	0.604176	0.302088	+	0.953280i	$0.402316\pi$
$420$	10828.0	1.25798
$421$	15500.6	1.79443	0.897213	−	0.441597i	$-0.145588\pi$
$421$	15500.6	1.79443	0.897213	+	0.441597i	$0.145588\pi$
$422$	4803.15	0.554060
$423$	6820.06	0.783931
$424$	−4031.81	−0.461797
$425$	−2037.63	−0.232563
$426$	−13395.2	−1.52347
$427$	−8232.98	−0.933072
$428$	7142.29	0.806625
$429$	1407.25	0.158375
$430$	196.133	0.0219962
$431$	−15250.0	−1.70433	−0.852166	−	0.523272i	$-0.824711\pi$
$431$	−15250.0	−1.70433	−0.852166	+	0.523272i	$0.824711\pi$
$432$	538.126	0.0599319
$433$	−7742.44	−0.859302	−0.429651	−	0.902995i	$-0.641363\pi$
$433$	−7742.44	−0.859302	−0.429651	+	0.902995i	$0.641363\pi$
$434$	−3038.36	−0.336051
$435$	−1040.70	−0.114708
$436$	−9998.40	−1.09825
$437$	−3083.63	−0.337552
$438$	−8758.69	−0.955494
$439$	−3048.78	−0.331459	−0.165729	−	0.986171i	$-0.552998\pi$
$439$	−3048.78	−0.331459	−0.165729	+	0.986171i	$0.552998\pi$
$440$	1071.85	0.116132
$441$	6269.24	0.676951
$442$	−6881.72	−0.740566
$443$	6213.30	0.666372	0.333186	−	0.942861i	$-0.391876\pi$
$443$	6213.30	0.666372	0.333186	+	0.942861i	$0.391876\pi$
$444$	−11394.7	−1.21794
$445$	3919.33	0.417515
$446$	19194.9	2.03790
$447$	16325.3	1.72742
$448$	−21484.1	−2.26569
$449$	11438.1	1.20222	0.601110	−	0.799167i	$-0.294725\pi$
$449$	11438.1	1.20222	0.601110	+	0.799167i	$0.294725\pi$
$450$	2215.41	0.232079
$451$	1228.51	0.128267
$452$	−5146.47	−0.535553
$453$	213.938	0.0221891
$454$	9510.82	0.983182
$455$	2409.32	0.248244
$456$	−2529.20	−0.259738
$457$	10720.8	1.09737	0.548684	−	0.836030i	$-0.315129\pi$
$457$	10720.8	1.09737	0.548684	+	0.836030i	$0.315129\pi$
$458$	−1826.52	−0.186348
$459$	4087.96	0.415707
$460$	9999.82	1.01357
$461$	14350.0	1.44978	0.724889	−	0.688866i	$-0.241891\pi$
$461$	14350.0	1.44978	0.724889	+	0.688866i	$0.241891\pi$
$462$	8714.66	0.877582
$463$	−5837.03	−0.585896	−0.292948	−	0.956128i	$-0.594636\pi$
$463$	−5837.03	−0.585896	−0.292948	+	0.956128i	$0.594636\pi$
$464$	326.934	0.0327102
$465$	−894.685	−0.0892259
$466$	1957.38	0.194579
$467$	−11977.3	−1.18681	−0.593407	−	0.804902i	$-0.702218\pi$
$467$	−11977.3	−1.18681	−0.593407	+	0.804902i	$0.702218\pi$
$468$	4536.85	0.448111
$469$	−1481.41	−0.145853
$470$	7820.42	0.767509
$471$	3126.93	0.305905
$472$	−12696.2	−1.23812
$473$	95.7149	0.00930438
$474$	24664.4	2.39003
$475$	−475.000	−0.0458831
$476$	−25840.7	−2.48824
$477$	−4066.78	−0.390367
$478$	3337.48	0.319358
$479$	6229.38	0.594212	0.297106	−	0.954844i	$-0.403978\pi$
$479$	6229.38	0.594212	0.297106	+	0.954844i	$0.403978\pi$
$480$	−6976.53	−0.663403
$481$	−2535.41	−0.240343
$482$	−25029.9	−2.36531
$483$	28521.6	2.68691
$484$	1491.07	0.140033
$485$	1978.69	0.185253
$486$	−20787.8	−1.94024
$487$	−12422.7	−1.15591	−0.577955	−	0.816069i	$-0.696149\pi$
$487$	−12422.7	−1.15591	−0.577955	+	0.816069i	$0.696149\pi$
$488$	−6236.21	−0.578484
$489$	−2232.96	−0.206499
$490$	7188.80	0.662769
$491$	−8664.81	−0.796410	−0.398205	−	0.917296i	$-0.630367\pi$
$491$	−8664.81	−0.796410	−0.398205	+	0.917296i	$0.630367\pi$
$492$	9400.67	0.861413
$493$	2483.61	0.226888
$494$	−1604.23	−0.146109
$495$	1081.15	0.0981694
$496$	281.063	0.0254437
$497$	−11191.9	−1.01011
$498$	−6226.44	−0.560268
$499$	−12850.1	−1.15281	−0.576404	−	0.817165i	$-0.695545\pi$
$499$	−12850.1	−1.15281	−0.576404	+	0.817165i	$0.695545\pi$
$500$	1540.36	0.137774
$501$	−7504.48	−0.669212
$502$	−12680.1	−1.12737
$503$	−11654.7	−1.03312	−0.516560	−	0.856251i	$-0.672788\pi$
$503$	−11654.7	−1.03312	−0.516560	+	0.856251i	$0.672788\pi$
$504$	9855.91	0.871066
$505$	1588.15	0.139944
$506$	8048.12	0.707080
$507$	−12610.8	−1.10466
$508$	16418.5	1.43397
$509$	15719.1	1.36883	0.684417	−	0.729090i	$-0.260057\pi$
$509$	15719.1	1.36883	0.684417	+	0.729090i	$0.260057\pi$
$510$	−12548.9	−1.08956
$511$	−7318.00	−0.633521
$512$	3864.37	0.333560
$513$	952.962	0.0820162
$514$	−14333.2	−1.22998
$515$	159.700	0.0136645
$516$	732.419	0.0624863
$517$	3816.45	0.324656
$518$	−15701.0	−1.33178
$519$	20054.9	1.69617
$520$	1824.99	0.153906
$521$	−9541.85	−0.802373	−0.401186	−	0.915996i	$-0.631402\pi$
$521$	−9541.85	−0.802373	−0.401186	+	0.915996i	$0.631402\pi$
$522$	−2700.30	−0.226416
$523$	481.954	0.0402952	0.0201476	−	0.999797i	$-0.493586\pi$
$523$	481.954	0.0402952	0.0201476	+	0.999797i	$0.493586\pi$
$524$	−28119.5	−2.34429
$525$	4393.44	0.365230
$526$	−14950.1	−1.23927
$527$	2135.14	0.176486
$528$	−806.146	−0.0664451
$529$	14173.1	1.16488
$530$	−4663.30	−0.382190
$531$	−12806.4	−1.04661
$532$	−6023.83	−0.490914
$533$	2091.73	0.169987
$534$	24137.6	1.95606
$535$	2897.97	0.234187
$536$	−1122.12	−0.0904259
$537$	−9774.81	−0.785501
$538$	22147.5	1.77481
$539$	3508.22	0.280352
$540$	−3090.33	−0.246272
$541$	−15988.0	−1.27057	−0.635283	−	0.772280i	$-0.719116\pi$
$541$	−15988.0	−1.27057	−0.635283	+	0.772280i	$0.719116\pi$
$542$	3421.15	0.271128
$543$	19973.4	1.57853
$544$	16649.2	1.31219
$545$	−4056.83	−0.318854
$546$	14838.1	1.16302
$547$	4908.68	0.383693	0.191846	−	0.981425i	$-0.438552\pi$
$547$	4908.68	0.383693	0.191846	+	0.981425i	$0.438552\pi$
$548$	−2013.60	−0.156965
$549$	−6290.32	−0.489006
$550$	1239.73	0.0961129
$551$	578.965	0.0447636
$552$	21604.2	1.66582
$553$	20607.4	1.58466
$554$	−11921.6	−0.914261
$555$	−4623.37	−0.353605
$556$	20438.1	1.55894
$557$	−10130.5	−0.770636	−0.385318	−	0.922784i	$-0.625908\pi$
$557$	−10130.5	−0.770636	−0.385318	+	0.922784i	$0.625908\pi$
$558$	−2321.43	−0.176118
$559$	162.970	0.0123307
$560$	−1380.19	−0.104149
$561$	−6124.02	−0.460884
$562$	−25055.9	−1.88064
$563$	5963.41	0.446408	0.223204	−	0.974772i	$-0.428348\pi$
$563$	5963.41	0.446408	0.223204	+	0.974772i	$0.428348\pi$
$564$	29203.8	2.18032
$565$	−2088.17	−0.155487
$566$	−36922.4	−2.74199
$567$	−22469.2	−1.66423
$568$	−8477.48	−0.626245
$569$	3447.54	0.254004	0.127002	−	0.991902i	$-0.459465\pi$
$569$	3447.54	0.254004	0.127002	+	0.991902i	$0.459465\pi$
$570$	−2925.34	−0.214963
$571$	13361.3	0.979249	0.489625	−	0.871933i	$-0.337134\pi$
$571$	13361.3	0.979249	0.489625	+	0.871933i	$0.337134\pi$
$572$	2538.79	0.185580
$573$	−17863.5	−1.30237
$574$	12953.4	0.941926
$575$	4057.41	0.294271
$576$	−16414.7	−1.18740
$577$	−10154.8	−0.732668	−0.366334	−	0.930484i	$-0.619387\pi$
$577$	−10154.8	−0.732668	−0.366334	+	0.930484i	$0.619387\pi$
$578$	7799.31	0.561261
$579$	−31006.1	−2.22551
$580$	−1877.51	−0.134413
$581$	−5202.27	−0.371474
$582$	12185.9	0.867910
$583$	−2275.74	−0.161666
$584$	−5543.15	−0.392769
$585$	1840.82	0.130100
$586$	39445.5	2.78068
$587$	−4929.58	−0.346619	−0.173310	−	0.984867i	$-0.555446\pi$
$587$	−4929.58	−0.346619	−0.173310	+	0.984867i	$0.555446\pi$
$588$	26845.2	1.88278
$589$	497.731	0.0348194
$590$	−14684.8	−1.02468
$591$	12752.1	0.887562
$592$	1452.42	0.100834
$593$	16488.8	1.14184	0.570921	−	0.821005i	$-0.306586\pi$
$593$	16488.8	1.14184	0.570921	+	0.821005i	$0.306586\pi$
$594$	−2487.18	−0.171802
$595$	−10484.8	−0.722411
$596$	29452.0	2.02416
$597$	−10068.0	−0.690213
$598$	13703.2	0.937065
$599$	23451.4	1.59967	0.799833	−	0.600223i	$-0.204922\pi$
$599$	23451.4	1.59967	0.799833	+	0.600223i	$0.204922\pi$
$600$	3327.89	0.226434
$601$	3863.58	0.262228	0.131114	−	0.991367i	$-0.458145\pi$
$601$	3863.58	0.262228	0.131114	+	0.991367i	$0.458145\pi$
$602$	1009.22	0.0683267
$603$	−1131.86	−0.0764391
$604$	385.959	0.0260008
$605$	605.000	0.0406558
$606$	9780.81	0.655641
$607$	−13988.2	−0.935361	−0.467681	−	0.883897i	$-0.654910\pi$
$607$	−13988.2	−0.935361	−0.467681	+	0.883897i	$0.654910\pi$
$608$	3881.18	0.258886
$609$	−5355.05	−0.356318
$610$	−7212.97	−0.478762
$611$	6498.11	0.430254
$612$	−19743.3	−1.30404
$613$	−19872.8	−1.30939	−0.654695	−	0.755893i	$-0.727203\pi$
$613$	−19872.8	−1.30939	−0.654695	+	0.755893i	$0.727203\pi$
$614$	−45565.5	−2.99491
$615$	3814.31	0.250094
$616$	5515.29	0.360742
$617$	−28617.2	−1.86724	−0.933620	−	0.358266i	$-0.883368\pi$
$617$	−28617.2	−1.86724	−0.933620	+	0.358266i	$0.883368\pi$
$618$	983.531	0.0640185
$619$	−3519.19	−0.228511	−0.114255	−	0.993451i	$-0.536448\pi$
$619$	−3519.19	−0.228511	−0.114255	+	0.993451i	$0.536448\pi$
$620$	−1614.08	−0.104553
$621$	−8140.12	−0.526009
$622$	31006.5	1.99879
$623$	20167.3	1.29693
$624$	−1372.59	−0.0880570
$625$	625.000	0.0400000
$626$	−33396.8	−2.13227
$627$	−1427.60	−0.0909294
$628$	5641.20	0.358453
$629$	11033.5	0.699419
$630$	11399.6	0.720907
$631$	−2792.10	−0.176152	−0.0880759	−	0.996114i	$-0.528072\pi$
$631$	−2792.10	−0.176152	−0.0880759	+	0.996114i	$0.528072\pi$
$632$	15609.5	0.982454
$633$	7277.67	0.456969
$634$	6881.70	0.431084
$635$	6661.79	0.416323
$636$	−17414.2	−1.08572
$637$	5973.29	0.371539
$638$	−1511.07	−0.0937677
$639$	−8551.02	−0.529379
$640$	−10651.5	−0.657869
$641$	−5934.17	−0.365656	−0.182828	−	0.983145i	$-0.558525\pi$
$641$	−5934.17	−0.365656	−0.182828	+	0.983145i	$0.558525\pi$
$642$	17847.4	1.09717
$643$	15826.7	0.970677	0.485339	−	0.874326i	$-0.338696\pi$
$643$	15826.7	0.970677	0.485339	+	0.874326i	$0.338696\pi$
$644$	51455.0	3.14847
$645$	297.177	0.0181416
$646$	6981.21	0.425189
$647$	−31093.1	−1.88933	−0.944665	−	0.328037i	$-0.893613\pi$
$647$	−31093.1	−1.88933	−0.944665	+	0.328037i	$0.893613\pi$
$648$	−17019.7	−1.03179
$649$	−7166.34	−0.433442
$650$	2110.83	0.127375
$651$	−4603.69	−0.277162
$652$	−4028.42	−0.241971
$653$	−96.3696	−0.00577524	−0.00288762	−	0.999996i	$-0.500919\pi$
$653$	−96.3696	−0.00577524	−0.00288762	+	0.999996i	$0.500919\pi$
$654$	−24984.4	−1.49383
$655$	−11409.4	−0.680616
$656$	−1198.25	−0.0713169
$657$	−5591.24	−0.332017
$658$	40240.7	2.38411
$659$	26865.9	1.58808	0.794042	−	0.607863i	$-0.207973\pi$
$659$	26865.9	1.58808	0.794042	+	0.607863i	$0.207973\pi$
$660$	4629.51	0.273036
$661$	−17431.2	−1.02571	−0.512857	−	0.858474i	$-0.671413\pi$
$661$	−17431.2	−1.02571	−0.512857	+	0.858474i	$0.671413\pi$
$662$	16706.2	0.980820
$663$	−10427.1	−0.610792
$664$	−3940.55	−0.230306
$665$	−2444.16	−0.142527
$666$	−11996.2	−0.697962
$667$	−4945.47	−0.287090
$668$	−13538.6	−0.784170
$669$	29083.8	1.68078
$670$	−1297.88	−0.0748378
$671$	−3520.01	−0.202516
$672$	−35898.4	−2.06073
$673$	24112.0	1.38106	0.690528	−	0.723306i	$-0.257378\pi$
$673$	24112.0	1.38106	0.690528	+	0.723306i	$0.257378\pi$
$674$	9212.18	0.526468
$675$	−1253.90	−0.0715001
$676$	−22750.8	−1.29442
$677$	26780.6	1.52033	0.760164	−	0.649731i	$-0.225118\pi$
$677$	26780.6	1.52033	0.760164	+	0.649731i	$0.225118\pi$
$678$	−12860.2	−0.728457
$679$	10181.5	0.575451
$680$	−7941.90	−0.447879
$681$	14410.7	0.810893
$682$	−1299.05	−0.0729374
$683$	−6606.91	−0.370141	−0.185070	−	0.982725i	$-0.559251\pi$
$683$	−6606.91	−0.370141	−0.185070	+	0.982725i	$0.559251\pi$
$684$	−4602.44	−0.257279
$685$	−817.015	−0.0455716
$686$	−2791.89	−0.155386
$687$	−2767.52	−0.153693
$688$	−93.3574	−0.00517328
$689$	−3874.80	−0.214250
$690$	24988.0	1.37866
$691$	−18136.8	−0.998490	−0.499245	−	0.866461i	$-0.666389\pi$
$691$	−18136.8	−0.998490	−0.499245	+	0.866461i	$0.666389\pi$
$692$	36180.5	1.98754
$693$	5563.13	0.304944
$694$	−29883.6	−1.63453
$695$	8292.72	0.452605
$696$	−4056.28	−0.220909
$697$	−9102.71	−0.494677
$698$	51358.3	2.78501
$699$	2965.80	0.160482
$700$	7926.09	0.427969
$701$	−835.314	−0.0450062	−0.0225031	−	0.999747i	$-0.507164\pi$
$701$	−835.314	−0.0450062	−0.0225031	+	0.999747i	$0.507164\pi$
$702$	−4234.82	−0.227682
$703$	2572.07	0.137991
$704$	−9185.52	−0.491751
$705$	11849.4	0.633013
$706$	−32202.8	−1.71667
$707$	8172.00	0.434709
$708$	−54837.5	−2.91090
$709$	8349.31	0.442263	0.221132	−	0.975244i	$-0.429025\pi$
$709$	8349.31	0.442263	0.221132	+	0.975244i	$0.429025\pi$
$710$	−9805.28	−0.518289
$711$	15744.9	0.830491
$712$	15276.1	0.804066
$713$	−4251.58	−0.223314
$714$	−64571.7	−3.38450
$715$	1030.11	0.0538795
$716$	−17634.5	−0.920435
$717$	5056.91	0.263395
$718$	50518.5	2.62581
$719$	−13348.3	−0.692360	−0.346180	−	0.938168i	$-0.612521\pi$
$719$	−13348.3	−0.692360	−0.346180	+	0.938168i	$0.612521\pi$
$720$	−1054.52	−0.0545826
$721$	821.753	0.0424462
$722$	1627.42	0.0838870
$723$	−37925.0	−1.95082
$724$	36033.5	1.84969
$725$	−761.795	−0.0390240
$726$	3725.96	0.190473
$727$	13428.2	0.685039	0.342519	−	0.939511i	$-0.388720\pi$
$727$	13428.2	0.685039	0.342519	+	0.939511i	$0.388720\pi$
$728$	9390.64	0.478077
$729$	−7917.32	−0.402241
$730$	−6411.36	−0.325062
$731$	−709.204	−0.0358835
$732$	−26935.4	−1.36006
$733$	21874.5	1.10225	0.551126	−	0.834422i	$-0.314198\pi$
$733$	21874.5	1.10225	0.551126	+	0.834422i	$0.314198\pi$
$734$	13913.2	0.699653
$735$	10892.4	0.546628
$736$	−33152.7	−1.66036
$737$	−633.378	−0.0316564
$738$	9896.93	0.493646
$739$	15345.9	0.763882	0.381941	−	0.924187i	$-0.375256\pi$
$739$	15345.9	0.763882	0.381941	+	0.924187i	$0.375256\pi$
$740$	−8340.89	−0.414348
$741$	−2430.71	−0.120505
$742$	−23995.4	−1.18720
$743$	24834.9	1.22625	0.613125	−	0.789986i	$-0.289912\pi$
$743$	24834.9	1.22625	0.613125	+	0.789986i	$0.289912\pi$
$744$	−3487.15	−0.171835
$745$	11950.1	0.587674
$746$	−259.259	−0.0127240
$747$	−3974.74	−0.194683
$748$	−11048.2	−0.540055
$749$	14911.8	0.727456
$750$	3849.13	0.187400
$751$	39459.1	1.91729	0.958644	−	0.284609i	$-0.0918637\pi$
$751$	39459.1	1.91729	0.958644	+	0.284609i	$0.0918637\pi$
$752$	−3722.45	−0.180510
$753$	−19212.7	−0.929816
$754$	−2572.83	−0.124267
$755$	156.602	0.00754879
$756$	−15901.6	−0.764995
$757$	34845.9	1.67305	0.836524	−	0.547930i	$-0.184584\pi$
$757$	34845.9	1.67305	0.836524	+	0.547930i	$0.184584\pi$
$758$	10608.8	0.508348
$759$	12194.4	0.583174
$760$	−1851.37	−0.0883635
$761$	−5593.80	−0.266459	−0.133229	−	0.991085i	$-0.542535\pi$
$761$	−5593.80	−0.266459	−0.133229	+	0.991085i	$0.542535\pi$
$762$	41027.3	1.95048
$763$	−20874.8	−0.990457
$764$	−32227.1	−1.52609
$765$	−8010.80	−0.378602
$766$	39886.2	1.88139
$767$	−12201.8	−0.574423
$768$	−19967.1	−0.938152
$769$	13138.7	0.616117	0.308058	−	0.951367i	$-0.400321\pi$
$769$	13138.7	0.616117	0.308058	+	0.951367i	$0.400321\pi$
$770$	6379.13	0.298556
$771$	−21717.4	−1.01444
$772$	−55937.3	−2.60781
$773$	−17549.0	−0.816552	−0.408276	−	0.912859i	$-0.633870\pi$
$773$	−17549.0	−0.816552	−0.408276	+	0.912859i	$0.633870\pi$
$774$	771.083	0.0358088
$775$	−654.909	−0.0303549
$776$	7712.18	0.356767
$777$	−23790.0	−1.09840
$778$	10015.0	0.461510
$779$	−2121.97	−0.0975964
$780$	7882.47	0.361843
$781$	−4785.08	−0.219237
$782$	−59632.9	−2.72694
$783$	1528.34	0.0697554
$784$	−3421.81	−0.155877
$785$	2288.91	0.104070
$786$	−70266.2	−3.18869
$787$	11717.9	0.530748	0.265374	−	0.964145i	$-0.414504\pi$
$787$	11717.9	0.530748	0.265374	+	0.964145i	$0.414504\pi$
$788$	23005.6	1.04003
$789$	−22652.2	−1.02210
$790$	18054.3	0.813093
$791$	−10744.9	−0.482989
$792$	4213.90	0.189058
$793$	−5993.37	−0.268387
$794$	5971.40	0.266898
$795$	−7065.76	−0.315216
$796$	−18163.5	−0.808778
$797$	−9356.33	−0.415832	−0.207916	−	0.978147i	$-0.566668\pi$
$797$	−9356.33	−0.415832	−0.207916	+	0.978147i	$0.566668\pi$
$798$	−15052.6	−0.667740
$799$	−28278.2	−1.25208
$800$	−5106.81	−0.225691
$801$	15408.6	0.679696
$802$	44527.8	1.96051
$803$	−3128.81	−0.137501
$804$	−4846.67	−0.212598
$805$	20877.8	0.914094
$806$	−2211.84	−0.0966610
$807$	33557.6	1.46380
$808$	6190.02	0.269510
$809$	25157.6	1.09332	0.546659	−	0.837356i	$-0.315900\pi$
$809$	25157.6	1.09332	0.546659	+	0.837356i	$0.315900\pi$
$810$	−19685.5	−0.853922
$811$	−37477.3	−1.62270	−0.811348	−	0.584563i	$-0.801266\pi$
$811$	−37477.3	−1.62270	−0.811348	+	0.584563i	$0.801266\pi$
$812$	−9660.90	−0.417526
$813$	5183.69	0.223616
$814$	−6712.97	−0.289053
$815$	−1634.52	−0.0702514
$816$	5973.18	0.256254
$817$	−165.326	−0.00707957
$818$	37062.6	1.58418
$819$	9472.11	0.404130
$820$	6881.29	0.293055
$821$	10529.7	0.447610	0.223805	−	0.974634i	$-0.428152\pi$
$821$	10529.7	0.447610	0.223805	+	0.974634i	$0.428152\pi$
$822$	−5031.67	−0.213503
$823$	10954.6	0.463979	0.231989	−	0.972718i	$-0.425477\pi$
$823$	10954.6	0.463979	0.231989	+	0.972718i	$0.425477\pi$
$824$	622.452	0.0263157
$825$	1878.42	0.0792704
$826$	−75562.0	−3.18298
$827$	43236.4	1.81799	0.908995	−	0.416807i	$-0.136851\pi$
$827$	43236.4	1.81799	0.908995	+	0.416807i	$0.136851\pi$
$828$	39313.7	1.65005
$829$	−23418.7	−0.981140	−0.490570	−	0.871402i	$-0.663211\pi$
$829$	−23418.7	−0.981140	−0.490570	+	0.871402i	$0.663211\pi$
$830$	−4557.75	−0.190605
$831$	−18063.5	−0.754049
$832$	−15639.8	−0.651697
$833$	−25994.3	−1.08121
$834$	51071.6	2.12046
$835$	−5493.27	−0.227668
$836$	−2575.49	−0.106549
$837$	1313.90	0.0542594
$838$	23360.3	0.962968
$839$	−19524.0	−0.803388	−0.401694	−	0.915774i	$-0.631579\pi$
$839$	−19524.0	−0.803388	−0.401694	+	0.915774i	$0.631579\pi$
$840$	17124.0	0.703373
$841$	−23460.5	−0.961928
$842$	69878.2	2.86005
$843$	−37964.4	−1.55108
$844$	13129.4	0.535467
$845$	−9231.08	−0.375809
$846$	30745.5	1.24947
$847$	3113.08	0.126289
$848$	2219.69	0.0898872
$849$	−55944.3	−2.26149
$850$	−9185.81	−0.370671
$851$	−21970.4	−0.885001
$852$	−36615.9	−1.47235
$853$	29508.9	1.18448	0.592241	−	0.805761i	$-0.298243\pi$
$853$	29508.9	1.18448	0.592241	+	0.805761i	$0.298243\pi$
$854$	−37115.0	−1.48718
$855$	−1867.43	−0.0746957
$856$	11295.2	0.451007
$857$	19515.9	0.777889	0.388945	−	0.921261i	$-0.372840\pi$
$857$	19515.9	0.777889	0.388945	+	0.921261i	$0.372840\pi$
$858$	6344.02	0.252426
$859$	−11313.4	−0.449370	−0.224685	−	0.974431i	$-0.572135\pi$
$859$	−11313.4	−0.449370	−0.224685	+	0.974431i	$0.572135\pi$
$860$	536.130	0.0212580
$861$	19626.9	0.776866
$862$	−68748.5	−2.71645
$863$	42075.4	1.65963	0.829816	−	0.558037i	$-0.188445\pi$
$863$	42075.4	1.65963	0.829816	+	0.558037i	$0.188445\pi$
$864$	10245.5	0.403424
$865$	14680.2	0.577042
$866$	−34903.6	−1.36960
$867$	11817.4	0.462907
$868$	−8305.39	−0.324773
$869$	8810.70	0.343939
$870$	−4691.60	−0.182828
$871$	−1078.43	−0.0419530
$872$	−15812.0	−0.614062
$873$	7779.08	0.301583
$874$	−13901.3	−0.538008
$875$	3216.00	0.124252
$876$	−23942.0	−0.923429
$877$	28616.0	1.10182	0.550908	−	0.834566i	$-0.314281\pi$
$877$	28616.0	1.10182	0.550908	+	0.834566i	$0.314281\pi$
$878$	−13744.2	−0.528296
$879$	59767.3	2.29340
$880$	−590.099	−0.0226048
$881$	2410.08	0.0921652	0.0460826	−	0.998938i	$-0.485326\pi$
$881$	2410.08	0.0921652	0.0460826	+	0.998938i	$0.485326\pi$
$882$	28262.3	1.07896
$883$	−19264.0	−0.734186	−0.367093	−	0.930184i	$-0.619647\pi$
$883$	−19264.0	−0.734186	−0.367093	+	0.930184i	$0.619647\pi$
$884$	−18811.2	−0.715714
$885$	−22250.2	−0.845122
$886$	28010.1	1.06210
$887$	2917.03	0.110422	0.0552110	−	0.998475i	$-0.482417\pi$
$887$	2917.03	0.110422	0.0552110	+	0.998475i	$0.482417\pi$
$888$	−18020.1	−0.680987
$889$	34278.9	1.29323
$890$	17668.7	0.665457
$891$	−9606.73	−0.361209
$892$	52469.3	1.96951
$893$	−6592.05	−0.247026
$894$	73595.8	2.75326
$895$	−7155.16	−0.267230
$896$	−54808.1	−2.04354
$897$	20762.9	0.772857
$898$	51564.0	1.91616
$899$	798.251	0.0296142
$900$	6055.85	0.224291
$901$	16862.2	0.623487
$902$	5538.24	0.204438
$903$	1529.15	0.0563534
$904$	−8138.91	−0.299442
$905$	14620.5	0.537020
$906$	964.451	0.0353662
$907$	11014.5	0.403233	0.201616	−	0.979465i	$-0.435381\pi$
$907$	11014.5	0.403233	0.201616	+	0.979465i	$0.435381\pi$
$908$	25997.9	0.950188
$909$	6243.72	0.227823
$910$	10861.5	0.395664
$911$	−31623.5	−1.15009	−0.575046	−	0.818121i	$-0.695016\pi$
$911$	−31623.5	−1.15009	−0.575046	+	0.818121i	$0.695016\pi$
$912$	1392.43	0.0505571
$913$	−2224.23	−0.0806258
$914$	48330.3	1.74904
$915$	−10929.0	−0.394865
$916$	−4992.80	−0.180095
$917$	−58708.4	−2.11420
$918$	18428.9	0.662576
$919$	1729.37	0.0620746	0.0310373	−	0.999518i	$-0.490119\pi$
$919$	1729.37	0.0620746	0.0310373	+	0.999518i	$0.490119\pi$
$920$	15814.3	0.566718
$921$	−69040.3	−2.47009
$922$	64691.3	2.31073
$923$	−8147.35	−0.290545
$924$	23821.6	0.848131
$925$	−3384.30	−0.120297
$926$	−26313.9	−0.933832
$927$	627.852	0.0222453
$928$	6224.56	0.220184
$929$	40885.2	1.44392	0.721959	−	0.691935i	$-0.243242\pi$
$929$	40885.2	1.44392	0.721959	+	0.691935i	$0.243242\pi$
$930$	−4033.33	−0.142213
$931$	−6059.65	−0.213316
$932$	5350.52	0.188049
$933$	46980.6	1.64853
$934$	−53994.7	−1.89161
$935$	−4482.78	−0.156794
$936$	7174.82	0.250552
$937$	35123.2	1.22457	0.612287	−	0.790636i	$-0.290250\pi$
$937$	35123.2	1.22457	0.612287	+	0.790636i	$0.290250\pi$
$938$	−6678.35	−0.232469
$939$	−50602.3	−1.75862
$940$	21377.2	0.741752
$941$	9308.08	0.322460	0.161230	−	0.986917i	$-0.448454\pi$
$941$	9308.08	0.322460	0.161230	+	0.986917i	$0.448454\pi$
$942$	14096.5	0.487567
$943$	18125.7	0.625933
$944$	6989.83	0.240995
$945$	−6452.05	−0.222101
$946$	431.492	0.0148298
$947$	−19090.8	−0.655087	−0.327543	−	0.944836i	$-0.606221\pi$
$947$	−19090.8	−0.655087	−0.327543	+	0.944836i	$0.606221\pi$
$948$	67420.3	2.30982
$949$	−5327.29	−0.182225
$950$	−2141.34	−0.0731309
$951$	10427.1	0.355542
$952$	−40865.8	−1.39125
$953$	−21383.5	−0.726841	−0.363420	−	0.931625i	$-0.618391\pi$
$953$	−21383.5	−0.726841	−0.363420	+	0.931625i	$0.618391\pi$
$954$	−18333.4	−0.622188
$955$	−13076.1	−0.443070
$956$	9123.04	0.308641
$957$	−2289.55	−0.0773361
$958$	28082.6	0.947087
$959$	−4204.03	−0.141559
$960$	−28519.4	−0.958812
$961$	−29104.8	−0.976965
$962$	−11429.9	−0.383071
$963$	11393.2	0.381246
$964$	−68419.5	−2.28594
$965$	−22696.5	−0.757124
$966$	128578.	4.28254
$967$	32808.3	1.09105	0.545524	−	0.838095i	$-0.316331\pi$
$967$	32808.3	1.09105	0.545524	+	0.838095i	$0.316331\pi$
$968$	2358.06	0.0782965
$969$	10577.8	0.350680
$970$	8920.11	0.295265
$971$	1942.94	0.0642142	0.0321071	−	0.999484i	$-0.489778\pi$
$971$	1942.94	0.0642142	0.0321071	+	0.999484i	$0.489778\pi$
$972$	−56823.8	−1.87513
$973$	42671.0	1.40593
$974$	−56002.9	−1.84235
$975$	3198.30	0.105054
$976$	3433.31	0.112600
$977$	−5348.19	−0.175132	−0.0875658	−	0.996159i	$-0.527909\pi$
$977$	−5348.19	−0.175132	−0.0875658	+	0.996159i	$0.527909\pi$
$978$	−10066.4	−0.329128
$979$	8622.53	0.281488
$980$	19650.7	0.640528
$981$	−15949.2	−0.519080
$982$	−39061.8	−1.26936
$983$	−40360.3	−1.30955	−0.654777	−	0.755822i	$-0.727238\pi$
$983$	−40360.3	−1.30955	−0.654777	+	0.755822i	$0.727238\pi$
$984$	14866.7	0.481640
$985$	9334.50	0.301951
$986$	11196.3	0.361627
$987$	60972.2	1.96633
$988$	−4385.17	−0.141205
$989$	1412.20	0.0454047
$990$	4873.90	0.156468
$991$	19458.6	0.623735	0.311868	−	0.950126i	$-0.399045\pi$
$991$	19458.6	0.623735	0.311868	+	0.950126i	$0.399045\pi$
$992$	5351.20	0.171271
$993$	25312.9	0.808945
$994$	−50454.0	−1.60996
$995$	−7369.80	−0.234812
$996$	−17020.0	−0.541466
$997$	52125.3	1.65579	0.827896	−	0.560882i	$-0.189538\pi$
$997$	52125.3	1.65579	0.827896	+	0.560882i	$0.189538\pi$
$998$	−57929.6	−1.83741
$999$	6789.71	0.215032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.e.1.19	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.e.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+4.50809 q^{2} +6.83061 q^{3} +12.3229 q^{4} +5.00000 q^{5} +30.7930 q^{6} +25.7280 q^{7} +19.4881 q^{8} +19.6572 q^{9} +O(q^{10})\)	\(q+4.50809 q^{2} +6.83061 q^{3} +12.3229 q^{4} +5.00000 q^{5} +30.7930 q^{6} +25.7280 q^{7} +19.4881 q^{8} +19.6572 q^{9} +22.5405 q^{10} +11.0000 q^{11} +84.1730 q^{12} +18.7292 q^{13} +115.984 q^{14} +34.1530 q^{15} -10.7291 q^{16} -81.5050 q^{17} +88.6164 q^{18} -19.0000 q^{19} +61.6146 q^{20} +175.738 q^{21} +49.5890 q^{22} +162.296 q^{23} +133.116 q^{24} +25.0000 q^{25} +84.4331 q^{26} -50.1559 q^{27} +317.044 q^{28} -30.4718 q^{29} +153.965 q^{30} -26.1964 q^{31} -204.273 q^{32} +75.1367 q^{33} -367.432 q^{34} +128.640 q^{35} +242.234 q^{36} -135.372 q^{37} -85.6538 q^{38} +127.932 q^{39} +97.4406 q^{40} +111.683 q^{41} +792.242 q^{42} +8.70135 q^{43} +135.552 q^{44} +98.2859 q^{45} +731.647 q^{46} +346.950 q^{47} -73.2860 q^{48} +318.929 q^{49} +112.702 q^{50} -556.729 q^{51} +230.799 q^{52} -206.885 q^{53} -226.108 q^{54} +55.0000 q^{55} +501.390 q^{56} -129.782 q^{57} -137.370 q^{58} -651.486 q^{59} +420.865 q^{60} -320.001 q^{61} -118.096 q^{62} +505.739 q^{63} -835.047 q^{64} +93.6461 q^{65} +338.723 q^{66} -57.5798 q^{67} -1004.38 q^{68} +1108.58 q^{69} +579.921 q^{70} -435.008 q^{71} +383.081 q^{72} -284.437 q^{73} -610.270 q^{74} +170.765 q^{75} -234.135 q^{76} +283.008 q^{77} +576.729 q^{78} +800.973 q^{79} -53.6453 q^{80} -873.339 q^{81} +503.476 q^{82} -202.203 q^{83} +2165.60 q^{84} -407.525 q^{85} +39.2265 q^{86} -208.141 q^{87} +214.369 q^{88} +783.866 q^{89} +443.082 q^{90} +481.865 q^{91} +1999.96 q^{92} -178.937 q^{93} +1564.08 q^{94} -95.0000 q^{95} -1395.31 q^{96} +395.737 q^{97} +1437.76 q^{98} +216.229 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9}+O(q^{10}) \) 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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