LMFDB - Embedded newform 1045.4.a.e.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.53824 q^{2} -3.76357 q^{3} -1.55736 q^{4} +5.00000 q^{5} +9.55282 q^{6} -9.64472 q^{7} +24.2588 q^{8} -12.8356 q^{9} +O(q^{10})$	\(q-2.53824 q^{2} -3.76357 q^{3} -1.55736 q^{4} +5.00000 q^{5} +9.55282 q^{6} -9.64472 q^{7} +24.2588 q^{8} -12.8356 q^{9} -12.6912 q^{10} +11.0000 q^{11} +5.86123 q^{12} -46.9286 q^{13} +24.4806 q^{14} -18.8178 q^{15} -49.1157 q^{16} -31.6738 q^{17} +32.5797 q^{18} -19.0000 q^{19} -7.78681 q^{20} +36.2986 q^{21} -27.9206 q^{22} +36.7068 q^{23} -91.2997 q^{24} +25.0000 q^{25} +119.116 q^{26} +149.924 q^{27} +15.0203 q^{28} +27.8119 q^{29} +47.7641 q^{30} -85.5751 q^{31} -69.4034 q^{32} -41.3992 q^{33} +80.3956 q^{34} -48.2236 q^{35} +19.9896 q^{36} +86.9037 q^{37} +48.2265 q^{38} +176.619 q^{39} +121.294 q^{40} -186.340 q^{41} -92.1343 q^{42} +8.86049 q^{43} -17.1310 q^{44} -64.1778 q^{45} -93.1706 q^{46} -614.878 q^{47} +184.850 q^{48} -249.979 q^{49} -63.4559 q^{50} +119.206 q^{51} +73.0848 q^{52} -185.341 q^{53} -380.542 q^{54} +55.0000 q^{55} -233.970 q^{56} +71.5078 q^{57} -70.5931 q^{58} -347.392 q^{59} +29.3062 q^{60} +32.5523 q^{61} +217.210 q^{62} +123.795 q^{63} +569.088 q^{64} -234.643 q^{65} +105.081 q^{66} -327.931 q^{67} +49.3276 q^{68} -138.149 q^{69} +122.403 q^{70} -567.966 q^{71} -311.376 q^{72} +606.994 q^{73} -220.582 q^{74} -94.0892 q^{75} +29.5899 q^{76} -106.092 q^{77} -448.301 q^{78} -248.679 q^{79} -245.579 q^{80} -217.688 q^{81} +472.974 q^{82} -669.920 q^{83} -56.5300 q^{84} -158.369 q^{85} -22.4900 q^{86} -104.672 q^{87} +266.847 q^{88} -248.601 q^{89} +162.898 q^{90} +452.614 q^{91} -57.1658 q^{92} +322.068 q^{93} +1560.70 q^{94} -95.0000 q^{95} +261.204 q^{96} -319.427 q^{97} +634.506 q^{98} -141.191 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.53824	−0.897402	−0.448701	−	0.893682i	$-0.648113\pi$
$2$	−2.53824	−0.897402	−0.448701	+	0.893682i	$0.648113\pi$
$3$	−3.76357	−0.724299	−0.362149	−	0.932120i	$-0.617957\pi$
$3$	−3.76357	−0.724299	−0.362149	+	0.932120i	$0.617957\pi$
$4$	−1.55736	−0.194670
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	9.55282	0.649987
$7$	−9.64472	−0.520766	−0.260383	−	0.965505i	$-0.583849\pi$
$7$	−9.64472	−0.520766	−0.260383	+	0.965505i	$0.583849\pi$
$8$	24.2588	1.07210
$9$	−12.8356	−0.475391
$10$	−12.6912	−0.401330
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	5.86123	0.140999
$13$	−46.9286	−1.00120	−0.500602	−	0.865677i	$-0.666888\pi$
$13$	−46.9286	−1.00120	−0.500602	+	0.865677i	$0.666888\pi$
$14$	24.4806	0.467336
$15$	−18.8178	−0.323916
$16$	−49.1157	−0.767433
$17$	−31.6738	−0.451884	−0.225942	−	0.974141i	$-0.572546\pi$
$17$	−31.6738	−0.451884	−0.225942	+	0.974141i	$0.572546\pi$
$18$	32.5797	0.426617
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−7.78681	−0.0870592
$21$	36.2986	0.377190
$22$	−27.9206	−0.270577
$23$	36.7068	0.332779	0.166389	−	0.986060i	$-0.446789\pi$
$23$	36.7068	0.332779	0.166389	+	0.986060i	$0.446789\pi$
$24$	−91.2997	−0.776520
$25$	25.0000	0.200000
$26$	119.116	0.898483
$27$	149.924	1.06862
$28$	15.0203	0.101378
$29$	27.8119	0.178088	0.0890438	−	0.996028i	$-0.471619\pi$
$29$	27.8119	0.178088	0.0890438	+	0.996028i	$0.471619\pi$
$30$	47.7641	0.290683
$31$	−85.5751	−0.495798	−0.247899	−	0.968786i	$-0.579740\pi$
$31$	−85.5751	−0.495798	−0.247899	+	0.968786i	$0.579740\pi$
$32$	−69.4034	−0.383403
$33$	−41.3992	−0.218384
$34$	80.3956	0.405521
$35$	−48.2236	−0.232894
$36$	19.9896	0.0925445
$37$	86.9037	0.386132	0.193066	−	0.981186i	$-0.438157\pi$
$37$	86.9037	0.386132	0.193066	+	0.981186i	$0.438157\pi$
$38$	48.2265	0.205878
$39$	176.619	0.725171
$40$	121.294	0.479457
$41$	−186.340	−0.709789	−0.354895	−	0.934906i	$-0.615483\pi$
$41$	−186.340	−0.709789	−0.354895	+	0.934906i	$0.615483\pi$
$42$	−92.1343	−0.338491
$43$	8.86049	0.0314235	0.0157118	−	0.999877i	$-0.494999\pi$
$43$	8.86049	0.0314235	0.0157118	+	0.999877i	$0.494999\pi$
$44$	−17.1310	−0.0586953
$45$	−64.1778	−0.212601
$46$	−93.1706	−0.298636
$47$	−614.878	−1.90828	−0.954140	−	0.299362i	$-0.903226\pi$
$47$	−614.878	−1.90828	−0.954140	+	0.299362i	$0.903226\pi$
$48$	184.850	0.555851
$49$	−249.979	−0.728803
$50$	−63.4559	−0.179480
$51$	119.206	0.327299
$52$	73.0848	0.194905
$53$	−185.341	−0.480350	−0.240175	−	0.970730i	$-0.577205\pi$
$53$	−185.341	−0.480350	−0.240175	+	0.970730i	$0.577205\pi$
$54$	−380.542	−0.958985
$55$	55.0000	0.134840
$56$	−233.970	−0.558313
$57$	71.5078	0.166166
$58$	−70.5931	−0.159816
$59$	−347.392	−0.766553	−0.383276	−	0.923634i	$-0.625204\pi$
$59$	−347.392	−0.766553	−0.383276	+	0.923634i	$0.625204\pi$
$60$	29.3062	0.0630568
$61$	32.5523	0.0683262	0.0341631	−	0.999416i	$-0.489123\pi$
$61$	32.5523	0.0683262	0.0341631	+	0.999416i	$0.489123\pi$
$62$	217.210	0.444930
$63$	123.795	0.247568
$64$	569.088	1.11150
$65$	−234.643	−0.447752
$66$	105.081	0.195978
$67$	−327.931	−0.597958	−0.298979	−	0.954260i	$-0.596646\pi$
$67$	−327.931	−0.597958	−0.298979	+	0.954260i	$0.596646\pi$
$68$	49.3276	0.0879683
$69$	−138.149	−0.241031
$70$	122.403	0.208999
$71$	−567.966	−0.949369	−0.474685	−	0.880156i	$-0.657438\pi$
$71$	−567.966	−0.949369	−0.474685	+	0.880156i	$0.657438\pi$
$72$	−311.376	−0.509666
$73$	606.994	0.973196	0.486598	−	0.873626i	$-0.338238\pi$
$73$	606.994	0.973196	0.486598	+	0.873626i	$0.338238\pi$
$74$	−220.582	−0.346515
$75$	−94.0892	−0.144860
$76$	29.5899	0.0446604
$77$	−106.092	−0.157017
$78$	−448.301	−0.650770
$79$	−248.679	−0.354159	−0.177079	−	0.984197i	$-0.556665\pi$
$79$	−248.679	−0.354159	−0.177079	+	0.984197i	$0.556665\pi$
$80$	−245.579	−0.343207
$81$	−217.688	−0.298612
$82$	472.974	0.636966
$83$	−669.920	−0.885943	−0.442972	−	0.896536i	$-0.646076\pi$
$83$	−669.920	−0.885943	−0.442972	+	0.896536i	$0.646076\pi$
$84$	−56.5300	−0.0734277
$85$	−158.369	−0.202089
$86$	−22.4900	−0.0281995
$87$	−104.672	−0.128989
$88$	266.847	0.323250
$89$	−248.601	−0.296086	−0.148043	−	0.988981i	$-0.547297\pi$
$89$	−248.601	−0.296086	−0.148043	+	0.988981i	$0.547297\pi$
$90$	162.898	0.190789
$91$	452.614	0.521393
$92$	−57.1658	−0.0647821
$93$	322.068	0.359106
$94$	1560.70	1.71249
$95$	−95.0000	−0.102598
$96$	261.204	0.277698
$97$	−319.427	−0.334359	−0.167180	−	0.985926i	$-0.553466\pi$
$97$	−319.427	−0.334359	−0.167180	+	0.985926i	$0.553466\pi$
$98$	634.506	0.654029
$99$	−141.191	−0.143336
$100$	−38.9340	−0.0389340
$101$	949.121	0.935060	0.467530	−	0.883977i	$-0.345144\pi$
$101$	949.121	0.935060	0.467530	+	0.883977i	$0.345144\pi$
$102$	−302.574	−0.293719
$103$	1444.65	1.38200	0.691000	−	0.722854i	$-0.257170\pi$
$103$	1444.65	1.38200	0.691000	+	0.722854i	$0.257170\pi$
$104$	−1138.43	−1.07339
$105$	181.493	0.168685
$106$	470.439	0.431067
$107$	−221.421	−0.200052	−0.100026	−	0.994985i	$-0.531893\pi$
$107$	−221.421	−0.200052	−0.100026	+	0.994985i	$0.531893\pi$
$108$	−233.486	−0.208029
$109$	−1623.07	−1.42625	−0.713127	−	0.701035i	$-0.752722\pi$
$109$	−1623.07	−1.42625	−0.713127	+	0.701035i	$0.752722\pi$
$110$	−139.603	−0.121006
$111$	−327.068	−0.279675
$112$	473.708	0.399653
$113$	928.651	0.773099	0.386549	−	0.922269i	$-0.373667\pi$
$113$	928.651	0.773099	0.386549	+	0.922269i	$0.373667\pi$
$114$	−181.504	−0.149117
$115$	183.534	0.148823
$116$	−43.3132	−0.0346683
$117$	602.355	0.475964
$118$	881.763	0.687906
$119$	305.485	0.235326
$120$	−456.499	−0.347270
$121$	121.000	0.0909091
$122$	−82.6255	−0.0613161
$123$	701.302	0.514099
$124$	133.271	0.0965171
$125$	125.000	0.0894427
$126$	−314.222	−0.222168
$127$	−826.682	−0.577608	−0.288804	−	0.957388i	$-0.593258\pi$
$127$	−826.682	−0.577608	−0.288804	+	0.957388i	$0.593258\pi$
$128$	−889.252	−0.614059
$129$	−33.3470	−0.0227600
$130$	595.580	0.401814
$131$	−1883.18	−1.25598	−0.627992	−	0.778220i	$-0.716123\pi$
$131$	−1883.18	−1.25598	−0.627992	+	0.778220i	$0.716123\pi$
$132$	64.4736	0.0425129
$133$	183.250	0.119472
$134$	832.367	0.536608
$135$	749.619	0.477903
$136$	−768.369	−0.484464
$137$	2842.07	1.77237	0.886185	−	0.463331i	$-0.153346\pi$
$137$	2842.07	1.77237	0.886185	+	0.463331i	$0.153346\pi$
$138$	350.654	0.216302
$139$	770.648	0.470256	0.235128	−	0.971964i	$-0.424449\pi$
$139$	770.648	0.470256	0.235128	+	0.971964i	$0.424449\pi$
$140$	75.1016	0.0453375
$141$	2314.13	1.38216
$142$	1441.63	0.851965
$143$	−516.215	−0.301875
$144$	630.428	0.364831
$145$	139.059	0.0796432
$146$	−1540.69	−0.873348
$147$	940.814	0.527871
$148$	−135.340	−0.0751684
$149$	419.544	0.230674	0.115337	−	0.993326i	$-0.463205\pi$
$149$	419.544	0.230674	0.115337	+	0.993326i	$0.463205\pi$
$150$	238.820	0.129997
$151$	2794.38	1.50598	0.752991	−	0.658031i	$-0.228610\pi$
$151$	2794.38	1.50598	0.752991	+	0.658031i	$0.228610\pi$
$152$	−460.918	−0.245956
$153$	406.551	0.214822
$154$	269.286	0.140907
$155$	−427.875	−0.221728
$156$	−275.060	−0.141169
$157$	−1553.13	−0.789511	−0.394756	−	0.918786i	$-0.629171\pi$
$157$	−1553.13	−0.789511	−0.394756	+	0.918786i	$0.629171\pi$
$158$	631.205	0.317823
$159$	697.543	0.347917
$160$	−347.017	−0.171463
$161$	−354.027	−0.173300
$162$	552.544	0.267975
$163$	3006.69	1.44480	0.722399	−	0.691477i	$-0.243039\pi$
$163$	3006.69	1.44480	0.722399	+	0.691477i	$0.243039\pi$
$164$	290.198	0.138175
$165$	−206.996	−0.0976644
$166$	1700.41	0.795047
$167$	−318.377	−0.147526	−0.0737628	−	0.997276i	$-0.523501\pi$
$167$	−318.377	−0.147526	−0.0737628	+	0.997276i	$0.523501\pi$
$168$	880.561	0.404385
$169$	5.29674	0.00241090
$170$	401.978	0.181355
$171$	243.876	0.109062
$172$	−13.7990	−0.00611722
$173$	2886.01	1.26832	0.634160	−	0.773202i	$-0.281346\pi$
$173$	2886.01	1.26832	0.634160	+	0.773202i	$0.281346\pi$
$174$	265.682	0.115755
$175$	−241.118	−0.104153
$176$	−540.273	−0.231390
$177$	1307.43	0.555213
$178$	631.008	0.265708
$179$	1872.31	0.781803	0.390901	−	0.920433i	$-0.372163\pi$
$179$	1872.31	0.781803	0.390901	+	0.920433i	$0.372163\pi$
$180$	99.9480	0.0413872
$181$	20.6358	0.00847430	0.00423715	−	0.999991i	$-0.498651\pi$
$181$	20.6358	0.00847430	0.00423715	+	0.999991i	$0.498651\pi$
$182$	−1148.84	−0.467899
$183$	−122.513	−0.0494886
$184$	890.465	0.356772
$185$	434.518	0.172683
$186$	−817.483	−0.322262
$187$	−348.412	−0.136248
$188$	957.587	0.371485
$189$	−1445.97	−0.556503
$190$	241.132	0.0920715
$191$	1140.42	0.432033	0.216016	−	0.976390i	$-0.430694\pi$
$191$	1140.42	0.432033	0.216016	+	0.976390i	$0.430694\pi$
$192$	−2141.80	−0.805058
$193$	1375.39	0.512968	0.256484	−	0.966549i	$-0.417436\pi$
$193$	1375.39	0.512968	0.256484	+	0.966549i	$0.417436\pi$
$194$	810.780	0.300055
$195$	883.095	0.324307
$196$	389.308	0.141876
$197$	−1424.28	−0.515107	−0.257553	−	0.966264i	$-0.582916\pi$
$197$	−1424.28	−0.515107	−0.257553	+	0.966264i	$0.582916\pi$
$198$	358.376	0.128630
$199$	1823.69	0.649638	0.324819	−	0.945776i	$-0.394697\pi$
$199$	1823.69	0.649638	0.324819	+	0.945776i	$0.394697\pi$
$200$	606.471	0.214420
$201$	1234.19	0.433100
$202$	−2409.09	−0.839124
$203$	−268.238	−0.0927420
$204$	−185.648	−0.0637153
$205$	−931.698	−0.317427
$206$	−3666.87	−1.24021
$207$	−471.153	−0.158200
$208$	2304.93	0.768358
$209$	−209.000	−0.0691714
$210$	−460.671	−0.151378
$211$	−2673.76	−0.872367	−0.436184	−	0.899858i	$-0.643670\pi$
$211$	−2673.76	−0.872367	−0.436184	+	0.899858i	$0.643670\pi$
$212$	288.643	0.0935097
$213$	2137.58	0.687627
$214$	562.019	0.179527
$215$	44.3024	0.0140530
$216$	3636.98	1.14567
$217$	825.348	0.258195
$218$	4119.73	1.27992
$219$	−2284.46	−0.704885
$220$	−85.6549	−0.0262493
$221$	1486.41	0.452428
$222$	830.175	0.250981
$223$	4969.37	1.49226	0.746130	−	0.665801i	$-0.231910\pi$
$223$	4969.37	1.49226	0.746130	+	0.665801i	$0.231910\pi$
$224$	669.376	0.199663
$225$	−320.889	−0.0950782
$226$	−2357.13	−0.693780
$227$	6630.28	1.93862	0.969311	−	0.245839i	$-0.0790633\pi$
$227$	6630.28	1.93862	0.969311	+	0.245839i	$0.0790633\pi$
$228$	−111.363	−0.0323475
$229$	920.237	0.265550	0.132775	−	0.991146i	$-0.457611\pi$
$229$	920.237	0.265550	0.132775	+	0.991146i	$0.457611\pi$
$230$	−465.853	−0.133554
$231$	399.284	0.113727
$232$	674.684	0.190928
$233$	−470.867	−0.132393	−0.0661963	−	0.997807i	$-0.521086\pi$
$233$	−470.867	−0.132393	−0.0661963	+	0.997807i	$0.521086\pi$
$234$	−1528.92	−0.427131
$235$	−3074.39	−0.853408
$236$	541.015	0.149225
$237$	935.919	0.256517
$238$	−775.393	−0.211182
$239$	−2552.74	−0.690890	−0.345445	−	0.938439i	$-0.612272\pi$
$239$	−2552.74	−0.690890	−0.345445	+	0.938439i	$0.612272\pi$
$240$	924.252	0.248584
$241$	1782.61	0.476465	0.238233	−	0.971208i	$-0.423432\pi$
$241$	1782.61	0.476465	0.238233	+	0.971208i	$0.423432\pi$
$242$	−307.126	−0.0815820
$243$	−3228.66	−0.852340
$244$	−50.6958	−0.0133011
$245$	−1249.90	−0.325930
$246$	−1780.07	−0.461354
$247$	891.644	0.229692
$248$	−2075.95	−0.531545
$249$	2521.29	0.641688
$250$	−317.279	−0.0802660
$251$	168.725	0.0424296	0.0212148	−	0.999775i	$-0.493247\pi$
$251$	168.725	0.0424296	0.0212148	+	0.999775i	$0.493247\pi$
$252$	−192.794	−0.0481940
$253$	403.775	0.100337
$254$	2098.31	0.518346
$255$	596.032	0.146373
$256$	−2295.57	−0.560442
$257$	4050.96	0.983238	0.491619	−	0.870810i	$-0.336405\pi$
$257$	4050.96	0.983238	0.491619	+	0.870810i	$0.336405\pi$
$258$	84.6426	0.0204249
$259$	−838.162	−0.201084
$260$	365.424	0.0871640
$261$	−356.981	−0.0846613
$262$	4779.94	1.12712
$263$	3237.52	0.759064	0.379532	−	0.925179i	$-0.376085\pi$
$263$	3237.52	0.759064	0.379532	+	0.925179i	$0.376085\pi$
$264$	−1004.30	−0.234130
$265$	−926.704	−0.214819
$266$	−465.131	−0.107214
$267$	935.626	0.214455
$268$	510.707	0.116405
$269$	−3161.09	−0.716487	−0.358243	−	0.933628i	$-0.616624\pi$
$269$	−3161.09	−0.716487	−0.358243	+	0.933628i	$0.616624\pi$
$270$	−1902.71	−0.428871
$271$	6969.12	1.56215	0.781077	−	0.624435i	$-0.214671\pi$
$271$	6969.12	1.56215	0.781077	+	0.624435i	$0.214671\pi$
$272$	1555.68	0.346791
$273$	−1703.44	−0.377645
$274$	−7213.85	−1.59053
$275$	275.000	0.0603023
$276$	215.147	0.0469216
$277$	−4920.99	−1.06741	−0.533707	−	0.845669i	$-0.679201\pi$
$277$	−4920.99	−1.06741	−0.533707	+	0.845669i	$0.679201\pi$
$278$	−1956.09	−0.422008
$279$	1098.40	0.235698
$280$	−1169.85	−0.249685
$281$	−8999.18	−1.91048	−0.955242	−	0.295825i	$-0.904405\pi$
$281$	−8999.18	−1.91048	−0.955242	+	0.295825i	$0.904405\pi$
$282$	−5873.81	−1.24036
$283$	−1274.82	−0.267775	−0.133888	−	0.990997i	$-0.542746\pi$
$283$	−1274.82	−0.267775	−0.133888	+	0.990997i	$0.542746\pi$
$284$	884.529	0.184814
$285$	357.539	0.0743115
$286$	1310.28	0.270903
$287$	1797.19	0.369634
$288$	890.831	0.182266
$289$	−3909.77	−0.795801
$290$	−352.966	−0.0714719
$291$	1202.18	0.242176
$292$	−945.309	−0.189452
$293$	4097.19	0.816929	0.408465	−	0.912774i	$-0.366064\pi$
$293$	4097.19	0.816929	0.408465	+	0.912774i	$0.366064\pi$
$294$	−2388.01	−0.473712
$295$	−1736.96	−0.342813
$296$	2108.18	0.413972
$297$	1649.16	0.322202
$298$	−1064.90	−0.207007
$299$	−1722.60	−0.333179
$300$	146.531	0.0281999
$301$	−85.4569	−0.0163643
$302$	−7092.79	−1.35147
$303$	−3572.08	−0.677263
$304$	933.199	0.176061
$305$	162.762	0.0305564
$306$	−1031.92	−0.192781
$307$	9283.94	1.72594	0.862968	−	0.505259i	$-0.168603\pi$
$307$	9283.94	1.72594	0.862968	+	0.505259i	$0.168603\pi$
$308$	165.224	0.0305665
$309$	−5437.06	−1.00098
$310$	1086.05	0.198979
$311$	−6824.43	−1.24430	−0.622151	−	0.782897i	$-0.713741\pi$
$311$	−6824.43	−1.24430	−0.622151	+	0.782897i	$0.713741\pi$
$312$	4284.57	0.777456
$313$	3810.56	0.688132	0.344066	−	0.938945i	$-0.388196\pi$
$313$	3810.56	0.688132	0.344066	+	0.938945i	$0.388196\pi$
$314$	3942.21	0.708509
$315$	618.977	0.110716
$316$	387.283	0.0689442
$317$	9657.55	1.71111	0.855556	−	0.517711i	$-0.173216\pi$
$317$	9657.55	1.71111	0.855556	+	0.517711i	$0.173216\pi$
$318$	−1770.53	−0.312221
$319$	305.931	0.0536954
$320$	2845.44	0.497078
$321$	833.333	0.144898
$322$	898.605	0.155520
$323$	601.802	0.103669
$324$	339.019	0.0581309
$325$	−1173.22	−0.200241
$326$	−7631.68	−1.29656
$327$	6108.52	1.03303
$328$	−4520.38	−0.760964
$329$	5930.32	0.993767
$330$	525.405	0.0876442
$331$	−468.734	−0.0778367	−0.0389184	−	0.999242i	$-0.512391\pi$
$331$	−468.734	−0.0778367	−0.0389184	+	0.999242i	$0.512391\pi$
$332$	1043.31	0.172467
$333$	−1115.46	−0.183564
$334$	808.116	0.132390
$335$	−1639.66	−0.267415
$336$	−1782.83	−0.289468
$337$	6262.07	1.01222	0.506108	−	0.862470i	$-0.331084\pi$
$337$	6262.07	1.01222	0.506108	+	0.862470i	$0.331084\pi$
$338$	−13.4444	−0.00216354
$339$	−3495.04	−0.559954
$340$	246.638	0.0393406
$341$	−941.326	−0.149489
$342$	−619.014	−0.0978726
$343$	5719.12	0.900302
$344$	214.945	0.0336891
$345$	−690.743	−0.107792
$346$	−7325.37	−1.13819
$347$	2630.18	0.406904	0.203452	−	0.979085i	$-0.434784\pi$
$347$	2630.18	0.406904	0.203452	+	0.979085i	$0.434784\pi$
$348$	163.012	0.0251102
$349$	3083.94	0.473007	0.236503	−	0.971631i	$-0.423999\pi$
$349$	3083.94	0.473007	0.236503	+	0.971631i	$0.423999\pi$
$350$	612.014	0.0934673
$351$	−7035.72	−1.06991
$352$	−763.437	−0.115600
$353$	76.4696	0.0115299	0.00576496	−	0.999983i	$-0.498165\pi$
$353$	76.4696	0.0115299	0.00576496	+	0.999983i	$0.498165\pi$
$354$	−3318.58	−0.498249
$355$	−2839.83	−0.424571
$356$	387.161	0.0576391
$357$	−1149.71	−0.170446
$358$	−4752.35	−0.701591
$359$	1549.60	0.227813	0.113906	−	0.993491i	$-0.463664\pi$
$359$	1549.60	0.227813	0.113906	+	0.993491i	$0.463664\pi$
$360$	−1556.88	−0.227930
$361$	361.000	0.0526316
$362$	−52.3786	−0.00760485
$363$	−455.392	−0.0658454
$364$	−704.883	−0.101500
$365$	3034.97	0.435226
$366$	310.967	0.0444112
$367$	−3940.66	−0.560493	−0.280246	−	0.959928i	$-0.590416\pi$
$367$	−3940.66	−0.560493	−0.280246	+	0.959928i	$0.590416\pi$
$368$	−1802.88	−0.255385
$369$	2391.77	0.337427
$370$	−1102.91	−0.154966
$371$	1787.56	0.250150
$372$	−501.576	−0.0699072
$373$	−5964.92	−0.828021	−0.414010	−	0.910272i	$-0.635872\pi$
$373$	−5964.92	−0.828021	−0.414010	+	0.910272i	$0.635872\pi$
$374$	884.351	0.122269
$375$	−470.446	−0.0647833
$376$	−14916.2	−2.04586
$377$	−1305.17	−0.178302
$378$	3670.22	0.499407
$379$	−2641.10	−0.357954	−0.178977	−	0.983853i	$-0.557279\pi$
$379$	−2641.10	−0.357954	−0.178977	+	0.983853i	$0.557279\pi$
$380$	147.949	0.0199727
$381$	3111.27	0.418361
$382$	−2894.67	−0.387707
$383$	−790.735	−0.105495	−0.0527476	−	0.998608i	$-0.516798\pi$
$383$	−790.735	−0.105495	−0.0527476	+	0.998608i	$0.516798\pi$
$384$	3346.76	0.444762
$385$	−530.460	−0.0702201
$386$	−3491.06	−0.460338
$387$	−113.729	−0.0149385
$388$	497.463	0.0650898
$389$	−10365.8	−1.35107	−0.675537	−	0.737326i	$-0.736088\pi$
$389$	−10365.8	−1.35107	−0.675537	+	0.737326i	$0.736088\pi$
$390$	−2241.50	−0.291033
$391$	−1162.65	−0.150377
$392$	−6064.21	−0.781349
$393$	7087.46	0.909707
$394$	3615.17	0.462258
$395$	−1243.39	−0.158385
$396$	219.886	0.0279032
$397$	−8725.97	−1.10313	−0.551567	−	0.834131i	$-0.685970\pi$
$397$	−8725.97	−1.10313	−0.551567	+	0.834131i	$0.685970\pi$
$398$	−4628.95	−0.582986
$399$	−689.673	−0.0865334
$400$	−1227.89	−0.153487
$401$	1406.39	0.175142	0.0875708	−	0.996158i	$-0.472090\pi$
$401$	1406.39	0.175142	0.0875708	+	0.996158i	$0.472090\pi$
$402$	−3132.67	−0.388665
$403$	4015.92	0.496395
$404$	−1478.12	−0.182028
$405$	−1088.44	−0.133543
$406$	680.851	0.0832268
$407$	955.940	0.116423
$408$	2891.81	0.350897
$409$	−1362.03	−0.164665	−0.0823327	−	0.996605i	$-0.526237\pi$
$409$	−1362.03	−0.164665	−0.0823327	+	0.996605i	$0.526237\pi$
$410$	2364.87	0.284860
$411$	−10696.3	−1.28373
$412$	−2249.85	−0.269034
$413$	3350.50	0.399195
$414$	1195.90	0.141969
$415$	−3349.60	−0.396206
$416$	3257.01	0.383865
$417$	−2900.39	−0.340606
$418$	530.491	0.0620746
$419$	7765.60	0.905428	0.452714	−	0.891656i	$-0.350456\pi$
$419$	7765.60	0.905428	0.452714	+	0.891656i	$0.350456\pi$
$420$	−282.650	−0.0328379
$421$	−10567.7	−1.22337	−0.611687	−	0.791100i	$-0.709509\pi$
$421$	−10567.7	−1.22337	−0.611687	+	0.791100i	$0.709509\pi$
$422$	6786.64	0.782864
$423$	7892.30	0.907179
$424$	−4496.15	−0.514982
$425$	−791.845	−0.0903768
$426$	−5425.68	−0.617078
$427$	−313.958	−0.0355820
$428$	344.833	0.0389442
$429$	1942.81	0.218647
$430$	−112.450	−0.0126112
$431$	9650.99	1.07859	0.539295	−	0.842117i	$-0.318691\pi$
$431$	9650.99	1.07859	0.539295	+	0.842117i	$0.318691\pi$
$432$	−7363.62	−0.820098
$433$	6748.94	0.749038	0.374519	−	0.927219i	$-0.377808\pi$
$433$	6748.94	0.749038	0.374519	+	0.927219i	$0.377808\pi$
$434$	−2094.93	−0.231704
$435$	−523.360	−0.0576855
$436$	2527.70	0.277649
$437$	−697.430	−0.0763446
$438$	5798.51	0.632565
$439$	5097.94	0.554240	0.277120	−	0.960835i	$-0.410620\pi$
$439$	5097.94	0.554240	0.277120	+	0.960835i	$0.410620\pi$
$440$	1334.24	0.144562
$441$	3208.63	0.346466
$442$	−3772.85	−0.406010
$443$	8379.42	0.898687	0.449343	−	0.893359i	$-0.351658\pi$
$443$	8379.42	0.898687	0.449343	+	0.893359i	$0.351658\pi$
$444$	509.363	0.0544444
$445$	−1243.00	−0.132414
$446$	−12613.4	−1.33916
$447$	−1578.98	−0.167077
$448$	−5488.70	−0.578831
$449$	−11500.8	−1.20881	−0.604407	−	0.796675i	$-0.706590\pi$
$449$	−11500.8	−1.20881	−0.604407	+	0.796675i	$0.706590\pi$
$450$	814.492	0.0853234
$451$	−2049.74	−0.214009
$452$	−1446.25	−0.150499
$453$	−10516.8	−1.09078
$454$	−16829.2	−1.73972
$455$	2263.07	0.233174
$456$	1734.70	0.178146
$457$	−10701.8	−1.09543	−0.547713	−	0.836667i	$-0.684501\pi$
$457$	−10701.8	−1.09543	−0.547713	+	0.836667i	$0.684501\pi$
$458$	−2335.78	−0.238305
$459$	−4748.66	−0.482894
$460$	−285.829	−0.0289714
$461$	6872.88	0.694365	0.347182	−	0.937798i	$-0.387138\pi$
$461$	6872.88	0.694365	0.347182	+	0.937798i	$0.387138\pi$
$462$	−1013.48	−0.102059
$463$	15817.6	1.58771	0.793853	−	0.608109i	$-0.208072\pi$
$463$	15817.6	1.58771	0.793853	+	0.608109i	$0.208072\pi$
$464$	−1366.00	−0.136670
$465$	1610.34	0.160597
$466$	1195.17	0.118809
$467$	7964.67	0.789210	0.394605	−	0.918851i	$-0.370881\pi$
$467$	7964.67	0.789210	0.394605	+	0.918851i	$0.370881\pi$
$468$	−938.085	−0.0926560
$469$	3162.81	0.311396
$470$	7803.52	0.765850
$471$	5845.31	0.571842
$472$	−8427.33	−0.821821
$473$	97.4654	0.00947455
$474$	−2375.58	−0.230199
$475$	−475.000	−0.0458831
$476$	−475.751	−0.0458109
$477$	2378.95	0.228354
$478$	6479.45	0.620006
$479$	7588.63	0.723870	0.361935	−	0.932203i	$-0.382116\pi$
$479$	7588.63	0.723870	0.361935	+	0.932203i	$0.382116\pi$
$480$	1306.02	0.124191
$481$	−4078.27	−0.386597
$482$	−4524.69	−0.427581
$483$	1332.41	0.125521
$484$	−188.441	−0.0176973
$485$	−1597.13	−0.149530
$486$	8195.10	0.764891
$487$	−12207.6	−1.13589	−0.567947	−	0.823065i	$-0.692262\pi$
$487$	−12207.6	−1.13589	−0.567947	+	0.823065i	$0.692262\pi$
$488$	789.682	0.0732525
$489$	−11315.9	−1.04647
$490$	3172.53	0.292491
$491$	4211.15	0.387060	0.193530	−	0.981094i	$-0.438006\pi$
$491$	4211.15	0.387060	0.193530	+	0.981094i	$0.438006\pi$
$492$	−1092.18	−0.100080
$493$	−880.908	−0.0804749
$494$	−2263.20	−0.206126
$495$	−705.956	−0.0641017
$496$	4203.08	0.380492
$497$	5477.88	0.494399
$498$	−6399.62	−0.575851
$499$	1403.47	0.125907	0.0629537	−	0.998016i	$-0.479948\pi$
$499$	1403.47	0.125907	0.0629537	+	0.998016i	$0.479948\pi$
$500$	−194.670	−0.0174118
$501$	1198.23	0.106853
$502$	−428.264	−0.0380764
$503$	862.836	0.0764850	0.0382425	−	0.999268i	$-0.487824\pi$
$503$	862.836	0.0764850	0.0382425	+	0.999268i	$0.487824\pi$
$504$	3003.13	0.265417
$505$	4745.60	0.418172
$506$	−1024.88	−0.0900422
$507$	−19.9346	−0.00174621
$508$	1287.44	0.112443
$509$	−12586.1	−1.09601	−0.548006	−	0.836474i	$-0.684613\pi$
$509$	−12586.1	−1.09601	−0.548006	+	0.836474i	$0.684613\pi$
$510$	−1512.87	−0.131355
$511$	−5854.29	−0.506807
$512$	12940.7	1.11700
$513$	−2848.55	−0.245159
$514$	−10282.3	−0.882359
$515$	7223.27	0.618050
$516$	51.9334	0.00443070
$517$	−6763.65	−0.575368
$518$	2127.45	0.180453
$519$	−10861.7	−0.918642
$520$	−5692.17	−0.480035
$521$	−7666.99	−0.644716	−0.322358	−	0.946618i	$-0.604475\pi$
$521$	−7666.99	−0.644716	−0.322358	+	0.946618i	$0.604475\pi$
$522$	906.102	0.0759752
$523$	211.286	0.0176652	0.00883261	−	0.999961i	$-0.497188\pi$
$523$	211.286	0.0176652	0.00883261	+	0.999961i	$0.497188\pi$
$524$	2932.78	0.244502
$525$	907.464	0.0754381
$526$	−8217.58	−0.681185
$527$	2710.49	0.224043
$528$	2033.35	0.167595
$529$	−10819.6	−0.889258
$530$	2352.19	0.192779
$531$	4458.98	0.364412
$532$	−285.386	−0.0232576
$533$	8744.66	0.710644
$534$	−2374.84	−0.192452
$535$	−1107.11	−0.0894661
$536$	−7955.23	−0.641070
$537$	−7046.55	−0.566259
$538$	8023.59	0.642977
$539$	−2749.77	−0.219742
$540$	−1167.43	−0.0930335
$541$	−2185.47	−0.173680	−0.0868400	−	0.996222i	$-0.527677\pi$
$541$	−2185.47	−0.173680	−0.0868400	+	0.996222i	$0.527677\pi$
$542$	−17689.3	−1.40188
$543$	−77.6643	−0.00613793
$544$	2198.27	0.173254
$545$	−8115.34	−0.637840
$546$	4323.74	0.338899
$547$	−15718.0	−1.22862	−0.614310	−	0.789065i	$-0.710566\pi$
$547$	−15718.0	−1.22862	−0.614310	+	0.789065i	$0.710566\pi$
$548$	−4426.14	−0.345028
$549$	−417.828	−0.0324817
$550$	−698.015	−0.0541154
$551$	−528.426	−0.0408561
$552$	−3351.33	−0.258409
$553$	2398.44	0.184434
$554$	12490.6	0.957899
$555$	−1635.34	−0.125074
$556$	−1200.18	−0.0915448
$557$	−20876.3	−1.58807	−0.794036	−	0.607871i	$-0.792024\pi$
$557$	−20876.3	−1.58807	−0.794036	+	0.607871i	$0.792024\pi$
$558$	−2788.01	−0.211516
$559$	−415.811	−0.0314614
$560$	2368.54	0.178730
$561$	1311.27	0.0986843
$562$	22842.0	1.71447
$563$	17942.0	1.34310	0.671551	−	0.740959i	$-0.265629\pi$
$563$	17942.0	1.34310	0.671551	+	0.740959i	$0.265629\pi$
$564$	−3603.94	−0.269066
$565$	4643.25	0.345740
$566$	3235.80	0.240302
$567$	2099.54	0.155507
$568$	−13778.2	−1.01782
$569$	16518.3	1.21702	0.608511	−	0.793546i	$-0.291767\pi$
$569$	16518.3	1.21702	0.608511	+	0.793546i	$0.291767\pi$
$570$	−907.518	−0.0666873
$571$	−12774.5	−0.936243	−0.468122	−	0.883664i	$-0.655069\pi$
$571$	−12774.5	−0.936243	−0.468122	+	0.883664i	$0.655069\pi$
$572$	803.933	0.0587660
$573$	−4292.06	−0.312921
$574$	−4561.70	−0.331710
$575$	917.671	0.0665557
$576$	−7304.56	−0.528397
$577$	−14279.8	−1.03028	−0.515142	−	0.857105i	$-0.672261\pi$
$577$	−14279.8	−1.03028	−0.515142	+	0.857105i	$0.672261\pi$
$578$	9923.92	0.714153
$579$	−5176.37	−0.371542
$580$	−216.566	−0.0155042
$581$	6461.19	0.461369
$582$	−3051.42	−0.217329
$583$	−2038.75	−0.144831
$584$	14725.0	1.04336
$585$	3011.78	0.212858
$586$	−10399.6	−0.733114
$587$	−8740.25	−0.614564	−0.307282	−	0.951619i	$-0.599419\pi$
$587$	−8740.25	−0.614564	−0.307282	+	0.951619i	$0.599419\pi$
$588$	−1465.19	−0.102761
$589$	1625.93	0.113744
$590$	4408.82	0.307641
$591$	5360.39	0.373091
$592$	−4268.34	−0.296330
$593$	−11038.1	−0.764386	−0.382193	−	0.924083i	$-0.624831\pi$
$593$	−11038.1	−0.764386	−0.382193	+	0.924083i	$0.624831\pi$
$594$	−4185.96	−0.289145
$595$	1527.42	0.105241
$596$	−653.381	−0.0449053
$597$	−6863.58	−0.470532
$598$	4372.37	0.298996
$599$	18728.6	1.27751	0.638755	−	0.769410i	$-0.279450\pi$
$599$	18728.6	1.27751	0.638755	+	0.769410i	$0.279450\pi$
$600$	−2282.49	−0.155304
$601$	16968.6	1.15169	0.575843	−	0.817560i	$-0.304674\pi$
$601$	16968.6	1.15169	0.575843	+	0.817560i	$0.304674\pi$
$602$	216.910	0.0146854
$603$	4209.18	0.284264
$604$	−4351.86	−0.293170
$605$	605.000	0.0406558
$606$	9066.78	0.607777
$607$	−3121.03	−0.208697	−0.104348	−	0.994541i	$-0.533276\pi$
$607$	−3121.03	−0.208697	−0.104348	+	0.994541i	$0.533276\pi$
$608$	1318.66	0.0879587
$609$	1009.53	0.0671729
$610$	−413.128	−0.0274214
$611$	28855.4	1.91058
$612$	−633.147	−0.0418194
$613$	1523.97	0.100412	0.0502059	−	0.998739i	$-0.484012\pi$
$613$	1523.97	0.100412	0.0502059	+	0.998739i	$0.484012\pi$
$614$	−23564.8	−1.54886
$615$	3506.51	0.229912
$616$	−2573.67	−0.168338
$617$	−26142.2	−1.70575	−0.852874	−	0.522116i	$-0.825143\pi$
$617$	−26142.2	−1.70575	−0.852874	+	0.522116i	$0.825143\pi$
$618$	13800.5	0.898283
$619$	−21184.8	−1.37559	−0.687796	−	0.725904i	$-0.741421\pi$
$619$	−21184.8	−1.37559	−0.687796	+	0.725904i	$0.741421\pi$
$620$	666.357	0.0431638
$621$	5503.23	0.355615
$622$	17322.0	1.11664
$623$	2397.69	0.154191
$624$	−8674.78	−0.556521
$625$	625.000	0.0400000
$626$	−9672.09	−0.617531
$627$	786.586	0.0501008
$628$	2418.78	0.153694
$629$	−2752.57	−0.174487
$630$	−1571.11	−0.0993563
$631$	4220.51	0.266269	0.133135	−	0.991098i	$-0.457496\pi$
$631$	4220.51	0.266269	0.133135	+	0.991098i	$0.457496\pi$
$632$	−6032.66	−0.379693
$633$	10062.9	0.631855
$634$	−24513.1	−1.53555
$635$	−4133.41	−0.258314
$636$	−1086.33	−0.0677290
$637$	11731.2	0.729681
$638$	−776.524	−0.0481864
$639$	7290.17	0.451322
$640$	−4446.26	−0.274615
$641$	6959.90	0.428860	0.214430	−	0.976739i	$-0.431211\pi$
$641$	6959.90	0.428860	0.214430	+	0.976739i	$0.431211\pi$
$642$	−2115.20	−0.130031
$643$	26805.9	1.64405	0.822024	−	0.569453i	$-0.192845\pi$
$643$	26805.9	1.64405	0.822024	+	0.569453i	$0.192845\pi$
$644$	551.349	0.0337363
$645$	−166.735	−0.0101786
$646$	−1527.52	−0.0930330
$647$	3817.96	0.231993	0.115996	−	0.993250i	$-0.462994\pi$
$647$	3817.96	0.231993	0.115996	+	0.993250i	$0.462994\pi$
$648$	−5280.86	−0.320142
$649$	−3821.32	−0.231124
$650$	2977.90	0.179697
$651$	−3106.25	−0.187010
$652$	−4682.50	−0.281259
$653$	13444.6	0.805709	0.402854	−	0.915264i	$-0.368018\pi$
$653$	13444.6	0.805709	0.402854	+	0.915264i	$0.368018\pi$
$654$	−15504.9	−0.927046
$655$	−9415.88	−0.561693
$656$	9152.21	0.544716
$657$	−7791.11	−0.462649
$658$	−15052.6	−0.891808
$659$	−8003.10	−0.473075	−0.236537	−	0.971622i	$-0.576013\pi$
$659$	−8003.10	−0.473075	−0.236537	+	0.971622i	$0.576013\pi$
$660$	322.368	0.0190124
$661$	15330.5	0.902097	0.451049	−	0.892499i	$-0.351050\pi$
$661$	15330.5	0.902097	0.451049	+	0.892499i	$0.351050\pi$
$662$	1189.76	0.0698508
$663$	−5594.20	−0.327693
$664$	−16251.5	−0.949819
$665$	916.249	0.0534295
$666$	2831.29	0.164730
$667$	1020.89	0.0592637
$668$	495.829	0.0287188
$669$	−18702.6	−1.08084
$670$	4161.83	0.239979
$671$	358.076	0.0206011
$672$	−2519.24	−0.144616
$673$	1236.03	0.0707957	0.0353979	−	0.999373i	$-0.488730\pi$
$673$	1236.03	0.0707957	0.0353979	+	0.999373i	$0.488730\pi$
$674$	−15894.6	−0.908365
$675$	3748.10	0.213725
$676$	−8.24894	−0.000469330 0
$677$	11752.4	0.667181	0.333590	−	0.942718i	$-0.391740\pi$
$677$	11752.4	0.667181	0.333590	+	0.942718i	$0.391740\pi$
$678$	8871.24	0.502504
$679$	3080.78	0.174123
$680$	−3841.85	−0.216659
$681$	−24953.5	−1.40414
$682$	2389.31	0.134151
$683$	32961.3	1.84660	0.923302	−	0.384076i	$-0.125480\pi$
$683$	32961.3	1.84660	0.923302	+	0.384076i	$0.125480\pi$
$684$	−379.803	−0.0212312
$685$	14210.4	0.792628
$686$	−14516.5	−0.807932
$687$	−3463.37	−0.192338
$688$	−435.189	−0.0241155
$689$	8697.79	0.480928
$690$	1753.27	0.0967331
$691$	24735.7	1.36178	0.680889	−	0.732386i	$-0.261593\pi$
$691$	24735.7	1.36178	0.680889	+	0.732386i	$0.261593\pi$
$692$	−4494.56	−0.246904
$693$	1361.75	0.0746444
$694$	−6676.02	−0.365156
$695$	3853.24	0.210305
$696$	−2539.22	−0.138289
$697$	5902.08	0.320742
$698$	−7827.76	−0.424477
$699$	1772.14	0.0958919
$700$	375.508	0.0202755
$701$	4483.24	0.241555	0.120777	−	0.992680i	$-0.461461\pi$
$701$	4483.24	0.241555	0.120777	+	0.992680i	$0.461461\pi$
$702$	17858.3	0.960140
$703$	−1651.17	−0.0885847
$704$	6259.97	0.335130
$705$	11570.7	0.618123
$706$	−194.098	−0.0103470
$707$	−9154.01	−0.486947
$708$	−2036.15	−0.108084
$709$	−8323.72	−0.440908	−0.220454	−	0.975397i	$-0.570754\pi$
$709$	−8323.72	−0.440908	−0.220454	+	0.975397i	$0.570754\pi$
$710$	7208.16	0.381011
$711$	3191.93	0.168364
$712$	−6030.77	−0.317433
$713$	−3141.19	−0.164991
$714$	2918.24	0.152959
$715$	−2581.07	−0.135002
$716$	−2915.86	−0.152194
$717$	9607.40	0.500411
$718$	−3933.25	−0.204440
$719$	9996.13	0.518488	0.259244	−	0.965812i	$-0.416527\pi$
$719$	9996.13	0.518488	0.259244	+	0.965812i	$0.416527\pi$
$720$	3152.14	0.163157
$721$	−13933.3	−0.719699
$722$	−916.303	−0.0472317
$723$	−6708.98	−0.345103
$724$	−32.1374	−0.00164969
$725$	695.297	0.0356175
$726$	1155.89	0.0590897
$727$	−4411.76	−0.225066	−0.112533	−	0.993648i	$-0.535896\pi$
$727$	−4411.76	−0.225066	−0.112533	+	0.993648i	$0.535896\pi$
$728$	10979.9	0.558985
$729$	18028.9	0.915961
$730$	−7703.47	−0.390573
$731$	−280.645	−0.0141998
$732$	190.797	0.00963396
$733$	−5024.56	−0.253187	−0.126594	−	0.991955i	$-0.540404\pi$
$733$	−5024.56	−0.253187	−0.126594	+	0.991955i	$0.540404\pi$
$734$	10002.3	0.502987
$735$	4704.07	0.236071
$736$	−2547.58	−0.127588
$737$	−3607.24	−0.180291
$738$	−6070.88	−0.302808
$739$	15185.1	0.755877	0.377938	−	0.925831i	$-0.376633\pi$
$739$	15185.1	0.755877	0.377938	+	0.925831i	$0.376633\pi$
$740$	−676.702	−0.0336163
$741$	−3355.76	−0.166366
$742$	−4537.25	−0.224485
$743$	3691.45	0.182269	0.0911346	−	0.995839i	$-0.470951\pi$
$743$	3691.45	0.182269	0.0911346	+	0.995839i	$0.470951\pi$
$744$	7812.98	0.384997
$745$	2097.72	0.103160
$746$	15140.4	0.743067
$747$	8598.80	0.421169
$748$	542.603	0.0265234
$749$	2135.55	0.104180
$750$	1194.10	0.0581366
$751$	−25261.9	−1.22746	−0.613729	−	0.789517i	$-0.710331\pi$
$751$	−25261.9	−1.22746	−0.613729	+	0.789517i	$0.710331\pi$
$752$	30200.2	1.46448
$753$	−635.008	−0.0307317
$754$	3312.84	0.160009
$755$	13971.9	0.673496
$756$	2251.90	0.108335
$757$	−15801.7	−0.758683	−0.379341	−	0.925257i	$-0.623849\pi$
$757$	−15801.7	−0.758683	−0.379341	+	0.925257i	$0.623849\pi$
$758$	6703.74	0.321228
$759$	−1519.64	−0.0726736
$760$	−2304.59	−0.109995
$761$	15024.1	0.715668	0.357834	−	0.933785i	$-0.383515\pi$
$761$	15024.1	0.715668	0.357834	+	0.933785i	$0.383515\pi$
$762$	−7897.15	−0.375438
$763$	15654.0	0.742744
$764$	−1776.05	−0.0841039
$765$	2032.75	0.0960711
$766$	2007.07	0.0946716
$767$	16302.6	0.767476
$768$	8639.54	0.405928
$769$	9529.71	0.446879	0.223440	−	0.974718i	$-0.428271\pi$
$769$	9529.71	0.446879	0.223440	+	0.974718i	$0.428271\pi$
$770$	1346.43	0.0630156
$771$	−15246.1	−0.712158
$772$	−2141.98	−0.0998595
$773$	−10697.9	−0.497771	−0.248886	−	0.968533i	$-0.580064\pi$
$773$	−10697.9	−0.497771	−0.248886	+	0.968533i	$0.580064\pi$
$774$	288.672	0.0134058
$775$	−2139.38	−0.0991596
$776$	−7748.91	−0.358466
$777$	3154.48	0.145645
$778$	26310.9	1.21246
$779$	3540.45	0.162837
$780$	−1375.30	−0.0631328
$781$	−6247.63	−0.286246
$782$	2951.07	0.134949
$783$	4169.67	0.190309
$784$	12277.9	0.559308
$785$	−7765.65	−0.353080
$786$	−17989.6	−0.816373
$787$	41312.5	1.87120	0.935598	−	0.353068i	$-0.114862\pi$
$787$	41312.5	1.87120	0.935598	+	0.353068i	$0.114862\pi$
$788$	2218.13	0.100276
$789$	−12184.6	−0.549789
$790$	3156.03	0.142135
$791$	−8956.58	−0.402603
$792$	−3425.13	−0.153670
$793$	−1527.64	−0.0684086
$794$	22148.6	0.989954
$795$	3487.71	0.155593
$796$	−2840.14	−0.126465
$797$	−25830.6	−1.14801	−0.574006	−	0.818851i	$-0.694611\pi$
$797$	−25830.6	−1.14801	−0.574006	+	0.818851i	$0.694611\pi$
$798$	1750.55	0.0776552
$799$	19475.5	0.862320
$800$	−1735.08	−0.0766806
$801$	3190.93	0.140757
$802$	−3569.75	−0.157172
$803$	6676.94	0.293430
$804$	−1922.08	−0.0843117
$805$	−1770.14	−0.0775020
$806$	−10193.4	−0.445466
$807$	11897.0	0.518951
$808$	23024.6	1.00248
$809$	28881.1	1.25513	0.627567	−	0.778562i	$-0.284051\pi$
$809$	28881.1	1.25513	0.627567	+	0.778562i	$0.284051\pi$
$810$	2762.72	0.119842
$811$	21660.1	0.937839	0.468920	−	0.883241i	$-0.344643\pi$
$811$	21660.1	0.937839	0.468920	+	0.883241i	$0.344643\pi$
$812$	417.744	0.0180541
$813$	−26228.7	−1.13147
$814$	−2426.40	−0.104478
$815$	15033.4	0.646133
$816$	−5854.91	−0.251180
$817$	−168.349	−0.00720905
$818$	3457.16	0.147771
$819$	−5809.55	−0.247866
$820$	1450.99	0.0617936
$821$	6867.81	0.291947	0.145973	−	0.989289i	$-0.453369\pi$
$821$	6867.81	0.291947	0.145973	+	0.989289i	$0.453369\pi$
$822$	27149.8	1.15202
$823$	33170.6	1.40493	0.702463	−	0.711721i	$-0.252084\pi$
$823$	33170.6	1.40493	0.702463	+	0.711721i	$0.252084\pi$
$824$	35045.6	1.48164
$825$	−1034.98	−0.0436769
$826$	−8504.36	−0.358238
$827$	−21827.2	−0.917784	−0.458892	−	0.888492i	$-0.651754\pi$
$827$	−21827.2	−0.917784	−0.458892	+	0.888492i	$0.651754\pi$
$828$	733.756	0.0307968
$829$	2672.99	0.111986	0.0559932	−	0.998431i	$-0.482167\pi$
$829$	2672.99	0.111986	0.0559932	+	0.998431i	$0.482167\pi$
$830$	8502.07	0.355556
$831$	18520.5	0.773127
$832$	−26706.5	−1.11284
$833$	7917.80	0.329334
$834$	7361.86	0.305660
$835$	−1591.89	−0.0659754
$836$	325.489	0.0134656
$837$	−12829.7	−0.529822
$838$	−19710.9	−0.812533
$839$	−2678.80	−0.110229	−0.0551147	−	0.998480i	$-0.517552\pi$
$839$	−2678.80	−0.110229	−0.0551147	+	0.998480i	$0.517552\pi$
$840$	4402.80	0.180847
$841$	−23615.5	−0.968285
$842$	26823.4	1.09786
$843$	33869.0	1.38376
$844$	4164.02	0.169824
$845$	26.4837	0.00107819
$846$	−20032.5	−0.814104
$847$	−1167.01	−0.0473424
$848$	9103.15	0.368636
$849$	4797.89	0.193949
$850$	2009.89	0.0811043
$851$	3189.96	0.128496
$852$	−3328.98	−0.133860
$853$	2254.54	0.0904970	0.0452485	−	0.998976i	$-0.485592\pi$
$853$	2254.54	0.0904970	0.0452485	+	0.998976i	$0.485592\pi$
$854$	796.900	0.0319313
$855$	1219.38	0.0487741
$856$	−5371.42	−0.214476
$857$	15546.6	0.619674	0.309837	−	0.950790i	$-0.399725\pi$
$857$	15546.6	0.619674	0.309837	+	0.950790i	$0.399725\pi$
$858$	−4931.31	−0.196215
$859$	−40490.1	−1.60827	−0.804135	−	0.594447i	$-0.797371\pi$
$859$	−40490.1	−1.60827	−0.804135	+	0.594447i	$0.797371\pi$
$860$	−68.9949	−0.00273571
$861$	−6763.86	−0.267726
$862$	−24496.5	−0.967928
$863$	39455.1	1.55628	0.778139	−	0.628092i	$-0.216164\pi$
$863$	39455.1	1.55628	0.778139	+	0.628092i	$0.216164\pi$
$864$	−10405.2	−0.409714
$865$	14430.0	0.567210
$866$	−17130.4	−0.672188
$867$	14714.7	0.576398
$868$	−1285.36	−0.0502628
$869$	−2735.47	−0.106783
$870$	1328.41	0.0517670
$871$	15389.4	0.598678
$872$	−39373.7	−1.52908
$873$	4100.02	0.158951
$874$	1770.24	0.0685118
$875$	−1205.59	−0.0465787
$876$	3557.74	0.137220
$877$	39062.1	1.50403	0.752014	−	0.659147i	$-0.229083\pi$
$877$	39062.1	1.50403	0.752014	+	0.659147i	$0.229083\pi$
$878$	−12939.8	−0.497376
$879$	−15420.0	−0.591701
$880$	−2701.37	−0.103481
$881$	−12324.6	−0.471313	−0.235657	−	0.971836i	$-0.575724\pi$
$881$	−12324.6	−0.471313	−0.235657	+	0.971836i	$0.575724\pi$
$882$	−8144.25	−0.310920
$883$	−36817.0	−1.40316	−0.701581	−	0.712590i	$-0.747522\pi$
$883$	−36817.0	−1.40316	−0.701581	+	0.712590i	$0.747522\pi$
$884$	−2314.87	−0.0880743
$885$	6537.17	0.248299
$886$	−21268.9	−0.806483
$887$	38257.1	1.44819	0.724096	−	0.689699i	$-0.242257\pi$
$887$	38257.1	1.44819	0.724096	+	0.689699i	$0.242257\pi$
$888$	−7934.28	−0.299839
$889$	7973.12	0.300799
$890$	3155.04	0.118828
$891$	−2394.57	−0.0900349
$892$	−7739.11	−0.290498
$893$	11682.7	0.437789
$894$	4007.83	0.149935
$895$	9361.53	0.349633
$896$	8576.59	0.319781
$897$	6483.13	0.241322
$898$	29191.8	1.08479
$899$	−2380.01	−0.0882955
$900$	499.740	0.0185089
$901$	5870.45	0.217062
$902$	5202.71	0.192052
$903$	321.623	0.0118526
$904$	22528.0	0.828838
$905$	103.179	0.00378982
$906$	26694.2	0.978869
$907$	16843.3	0.616617	0.308308	−	0.951286i	$-0.400237\pi$
$907$	16843.3	0.616617	0.308308	+	0.951286i	$0.400237\pi$
$908$	−10325.7	−0.377392
$909$	−12182.5	−0.444519
$910$	−5744.20	−0.209251
$911$	−35356.3	−1.28585	−0.642924	−	0.765930i	$-0.722279\pi$
$911$	−35356.3	−1.28585	−0.642924	+	0.765930i	$0.722279\pi$
$912$	−3512.16	−0.127521
$913$	−7369.12	−0.267122
$914$	27163.7	0.983036
$915$	−612.565	−0.0221320
$916$	−1433.14	−0.0516947
$917$	18162.7	0.654073
$918$	12053.2	0.433350
$919$	21525.9	0.772660	0.386330	−	0.922361i	$-0.373743\pi$
$919$	21525.9	0.772660	0.386330	+	0.922361i	$0.373743\pi$
$920$	4452.33	0.159553
$921$	−34940.7	−1.25009
$922$	−17445.0	−0.623124
$923$	26653.9	0.950513
$924$	−621.830	−0.0221393
$925$	2172.59	0.0772264
$926$	−40148.9	−1.42481
$927$	−18543.0	−0.656991
$928$	−1930.24	−0.0682793
$929$	41045.0	1.44956	0.724781	−	0.688980i	$-0.241941\pi$
$929$	41045.0	1.44956	0.724781	+	0.688980i	$0.241941\pi$
$930$	−4087.42	−0.144120
$931$	4749.61	0.167199
$932$	733.310	0.0257729
$933$	25684.2	0.901246
$934$	−20216.2	−0.708238
$935$	−1742.06	−0.0609320
$936$	14612.4	0.510280
$937$	−43219.0	−1.50683	−0.753416	−	0.657544i	$-0.771595\pi$
$937$	−43219.0	−1.50683	−0.753416	+	0.657544i	$0.771595\pi$
$938$	−8027.94	−0.279447
$939$	−14341.3	−0.498413
$940$	4787.93	0.166133
$941$	12690.2	0.439625	0.219813	−	0.975542i	$-0.429455\pi$
$941$	12690.2	0.439625	0.219813	+	0.975542i	$0.429455\pi$
$942$	−14836.8	−0.513172
$943$	−6839.94	−0.236203
$944$	17062.4	0.588278
$945$	−7229.87	−0.248876
$946$	−247.390	−0.00850248
$947$	13705.2	0.470283	0.235141	−	0.971961i	$-0.424445\pi$
$947$	13705.2	0.470283	0.235141	+	0.971961i	$0.424445\pi$
$948$	−1457.56	−0.0499362
$949$	−28485.4	−0.974368
$950$	1205.66	0.0411756
$951$	−36346.9	−1.23936
$952$	7410.71	0.252293
$953$	33982.8	1.15510	0.577550	−	0.816355i	$-0.304009\pi$
$953$	33982.8	1.15510	0.577550	+	0.816355i	$0.304009\pi$
$954$	−6038.35	−0.204925
$955$	5702.12	0.193211
$956$	3975.53	0.134496
$957$	−1151.39	−0.0388915
$958$	−19261.7	−0.649602
$959$	−27411.0	−0.922990
$960$	−10709.0	−0.360033
$961$	−22467.9	−0.754184
$962$	10351.6	0.346933
$963$	2842.06	0.0951031
$964$	−2776.17	−0.0927535
$965$	6876.95	0.229406
$966$	−3381.96	−0.112643
$967$	−41198.8	−1.37008	−0.685039	−	0.728507i	$-0.740215\pi$
$967$	−41198.8	−1.37008	−0.685039	+	0.728507i	$0.740215\pi$
$968$	2935.32	0.0974636
$969$	−2264.92	−0.0750875
$970$	4053.90	0.134188
$971$	1462.97	0.0483511	0.0241756	−	0.999708i	$-0.492304\pi$
$971$	1462.97	0.0483511	0.0241756	+	0.999708i	$0.492304\pi$
$972$	5028.19	0.165925
$973$	−7432.69	−0.244893
$974$	30985.8	1.01935
$975$	4415.48	0.145034
$976$	−1598.83	−0.0524358
$977$	−2373.49	−0.0777222	−0.0388611	−	0.999245i	$-0.512373\pi$
$977$	−2373.49	−0.0777222	−0.0388611	+	0.999245i	$0.512373\pi$
$978$	28722.4	0.939100
$979$	−2734.61	−0.0892732
$980$	1946.54	0.0634490
$981$	20833.0	0.678028
$982$	−10688.9	−0.347348
$983$	−12162.2	−0.394621	−0.197311	−	0.980341i	$-0.563221\pi$
$983$	−12162.2	−0.394621	−0.197311	+	0.980341i	$0.563221\pi$
$984$	17012.8	0.551166
$985$	−7121.42	−0.230363
$986$	2235.95	0.0722183
$987$	−22319.2	−0.719784
$988$	−1388.61	−0.0447142
$989$	325.241	0.0104571
$990$	1791.88	0.0575250
$991$	28586.5	0.916327	0.458163	−	0.888868i	$-0.348507\pi$
$991$	28586.5	0.916327	0.458163	+	0.888868i	$0.348507\pi$
$992$	5939.20	0.190090
$993$	1764.11	0.0563771
$994$	−13904.1	−0.443675
$995$	9118.45	0.290527
$996$	−3926.56	−0.124917
$997$	41375.6	1.31432	0.657161	−	0.753750i	$-0.271757\pi$
$997$	41375.6	1.31432	0.657161	+	0.753750i	$0.271757\pi$
$998$	−3562.33	−0.112989
$999$	13028.9	0.412630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.e.1.6	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.e.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.53824 q^{2} -3.76357 q^{3} -1.55736 q^{4} +5.00000 q^{5} +9.55282 q^{6} -9.64472 q^{7} +24.2588 q^{8} -12.8356 q^{9} +O(q^{10})\)	\(q-2.53824 q^{2} -3.76357 q^{3} -1.55736 q^{4} +5.00000 q^{5} +9.55282 q^{6} -9.64472 q^{7} +24.2588 q^{8} -12.8356 q^{9} -12.6912 q^{10} +11.0000 q^{11} +5.86123 q^{12} -46.9286 q^{13} +24.4806 q^{14} -18.8178 q^{15} -49.1157 q^{16} -31.6738 q^{17} +32.5797 q^{18} -19.0000 q^{19} -7.78681 q^{20} +36.2986 q^{21} -27.9206 q^{22} +36.7068 q^{23} -91.2997 q^{24} +25.0000 q^{25} +119.116 q^{26} +149.924 q^{27} +15.0203 q^{28} +27.8119 q^{29} +47.7641 q^{30} -85.5751 q^{31} -69.4034 q^{32} -41.3992 q^{33} +80.3956 q^{34} -48.2236 q^{35} +19.9896 q^{36} +86.9037 q^{37} +48.2265 q^{38} +176.619 q^{39} +121.294 q^{40} -186.340 q^{41} -92.1343 q^{42} +8.86049 q^{43} -17.1310 q^{44} -64.1778 q^{45} -93.1706 q^{46} -614.878 q^{47} +184.850 q^{48} -249.979 q^{49} -63.4559 q^{50} +119.206 q^{51} +73.0848 q^{52} -185.341 q^{53} -380.542 q^{54} +55.0000 q^{55} -233.970 q^{56} +71.5078 q^{57} -70.5931 q^{58} -347.392 q^{59} +29.3062 q^{60} +32.5523 q^{61} +217.210 q^{62} +123.795 q^{63} +569.088 q^{64} -234.643 q^{65} +105.081 q^{66} -327.931 q^{67} +49.3276 q^{68} -138.149 q^{69} +122.403 q^{70} -567.966 q^{71} -311.376 q^{72} +606.994 q^{73} -220.582 q^{74} -94.0892 q^{75} +29.5899 q^{76} -106.092 q^{77} -448.301 q^{78} -248.679 q^{79} -245.579 q^{80} -217.688 q^{81} +472.974 q^{82} -669.920 q^{83} -56.5300 q^{84} -158.369 q^{85} -22.4900 q^{86} -104.672 q^{87} +266.847 q^{88} -248.601 q^{89} +162.898 q^{90} +452.614 q^{91} -57.1658 q^{92} +322.068 q^{93} +1560.70 q^{94} -95.0000 q^{95} +261.204 q^{96} -319.427 q^{97} +634.506 q^{98} -141.191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9}+O(q^{10}) \) 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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