LMFDB - Embedded newform 1849.4.a.i.1.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$1$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.44
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.20684 q^{2} +4.82832 q^{3} +9.69750 q^{4} -7.01067 q^{5} +20.3120 q^{6} +27.8882 q^{7} +7.14112 q^{8} -3.68734 q^{9} +O(q^{10})$	\(q+4.20684 q^{2} +4.82832 q^{3} +9.69750 q^{4} -7.01067 q^{5} +20.3120 q^{6} +27.8882 q^{7} +7.14112 q^{8} -3.68734 q^{9} -29.4928 q^{10} -14.8584 q^{11} +46.8226 q^{12} -60.1508 q^{13} +117.321 q^{14} -33.8498 q^{15} -47.5385 q^{16} -53.5705 q^{17} -15.5121 q^{18} -77.3824 q^{19} -67.9860 q^{20} +134.653 q^{21} -62.5069 q^{22} +61.7129 q^{23} +34.4796 q^{24} -75.8505 q^{25} -253.045 q^{26} -148.168 q^{27} +270.446 q^{28} +53.9349 q^{29} -142.401 q^{30} -191.801 q^{31} -257.116 q^{32} -71.7411 q^{33} -225.363 q^{34} -195.515 q^{35} -35.7580 q^{36} -366.299 q^{37} -325.536 q^{38} -290.427 q^{39} -50.0641 q^{40} +5.32390 q^{41} +566.465 q^{42} -144.089 q^{44} +25.8508 q^{45} +259.616 q^{46} +559.264 q^{47} -229.531 q^{48} +434.753 q^{49} -319.091 q^{50} -258.655 q^{51} -583.312 q^{52} +97.6988 q^{53} -623.320 q^{54} +104.167 q^{55} +199.153 q^{56} -373.627 q^{57} +226.896 q^{58} +873.184 q^{59} -328.258 q^{60} +723.179 q^{61} -806.878 q^{62} -102.833 q^{63} -701.337 q^{64} +421.697 q^{65} -301.803 q^{66} -982.993 q^{67} -519.500 q^{68} +297.970 q^{69} -822.501 q^{70} +417.795 q^{71} -26.3318 q^{72} +219.278 q^{73} -1540.96 q^{74} -366.230 q^{75} -750.416 q^{76} -414.374 q^{77} -1221.78 q^{78} -801.309 q^{79} +333.277 q^{80} -615.845 q^{81} +22.3968 q^{82} -792.865 q^{83} +1305.80 q^{84} +375.565 q^{85} +260.415 q^{87} -106.106 q^{88} -1205.01 q^{89} +108.750 q^{90} -1677.50 q^{91} +598.461 q^{92} -926.078 q^{93} +2352.73 q^{94} +542.503 q^{95} -1241.44 q^{96} +577.561 q^{97} +1828.94 q^{98} +54.7880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) $ 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * 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 $

$2$	4.20684	1.48734	0.743671	−	0.668545i	$-0.233083\pi$
$2$	4.20684	1.48734	0.743671	+	0.668545i	$0.233083\pi$
$3$	4.82832	0.929210	0.464605	−	0.885518i	$-0.346196\pi$
$3$	4.82832	0.929210	0.464605	+	0.885518i	$0.346196\pi$
$4$	9.69750	1.21219
$5$	−7.01067	−0.627054	−0.313527	−	0.949579i	$-0.601511\pi$
$5$	−7.01067	−0.627054	−0.313527	+	0.949579i	$0.601511\pi$
$6$	20.3120	1.38205
$7$	27.8882	1.50582	0.752911	−	0.658122i	$-0.228649\pi$
$7$	27.8882	1.50582	0.752911	+	0.658122i	$0.228649\pi$
$8$	7.14112	0.315596
$9$	−3.68734	−0.136568
$10$	−29.4928	−0.932644
$11$	−14.8584	−0.407270	−0.203635	−	0.979047i	$-0.565276\pi$
$11$	−14.8584	−0.407270	−0.203635	+	0.979047i	$0.565276\pi$
$12$	46.8226	1.12638
$13$	−60.1508	−1.28329	−0.641647	−	0.767000i	$-0.721749\pi$
$13$	−60.1508	−1.28329	−0.641647	+	0.767000i	$0.721749\pi$
$14$	117.321	2.23967
$15$	−33.8498	−0.582665
$16$	−47.5385	−0.742789
$17$	−53.5705	−0.764280	−0.382140	−	0.924104i	$-0.624813\pi$
$17$	−53.5705	−0.764280	−0.382140	+	0.924104i	$0.624813\pi$
$18$	−15.5121	−0.203124
$19$	−77.3824	−0.934355	−0.467178	−	0.884163i	$-0.654729\pi$
$19$	−77.3824	−0.934355	−0.467178	+	0.884163i	$0.654729\pi$
$20$	−67.9860	−0.760107
$21$	134.653	1.39923
$22$	−62.5069	−0.605751
$23$	61.7129	0.559480	0.279740	−	0.960076i	$-0.409752\pi$
$23$	61.7129	0.559480	0.279740	+	0.960076i	$0.409752\pi$
$24$	34.4796	0.293255
$25$	−75.8505	−0.606804
$26$	−253.045	−1.90870
$27$	−148.168	−1.05611
$28$	270.446	1.82534
$29$	53.9349	0.345361	0.172680	−	0.984978i	$-0.444757\pi$
$29$	53.9349	0.345361	0.172680	+	0.984978i	$0.444757\pi$
$30$	−142.401	−0.866622
$31$	−191.801	−1.11124	−0.555622	−	0.831435i	$-0.687520\pi$
$31$	−191.801	−1.11124	−0.555622	+	0.831435i	$0.687520\pi$
$32$	−257.116	−1.42038
$33$	−71.7411	−0.378440
$34$	−225.363	−1.13675
$35$	−195.515	−0.944231
$36$	−35.7580	−0.165546
$37$	−366.299	−1.62755	−0.813774	−	0.581182i	$-0.802590\pi$
$37$	−366.299	−1.62755	−0.813774	+	0.581182i	$0.802590\pi$
$38$	−325.536	−1.38971
$39$	−290.427	−1.19245
$40$	−50.0641	−0.197896
$41$	5.32390	0.0202793	0.0101397	−	0.999949i	$-0.496772\pi$
$41$	5.32390	0.0202793	0.0101397	+	0.999949i	$0.496772\pi$
$42$	566.465	2.08113
$43$	0	0
$43$	0	0
$44$	−144.089	−0.493688
$45$	25.8508	0.0856356
$46$	259.616	0.832138
$47$	559.264	1.73568	0.867841	−	0.496843i	$-0.165507\pi$
$47$	559.264	1.73568	0.867841	+	0.496843i	$0.165507\pi$
$48$	−229.531	−0.690207
$49$	434.753	1.26750
$50$	−319.091	−0.902525
$51$	−258.655	−0.710177
$52$	−583.312	−1.55559
$53$	97.6988	0.253207	0.126603	−	0.991953i	$-0.459592\pi$
$53$	97.6988	0.253207	0.126603	+	0.991953i	$0.459592\pi$
$54$	−623.320	−1.57080
$55$	104.167	0.255380
$56$	199.153	0.475231
$57$	−373.627	−0.868212
$58$	226.896	0.513670
$59$	873.184	1.92676	0.963380	−	0.268139i	$-0.0864086\pi$
$59$	873.184	1.92676	0.963380	+	0.268139i	$0.0864086\pi$
$60$	−328.258	−0.706299
$61$	723.179	1.51793	0.758964	−	0.651133i	$-0.225706\pi$
$61$	723.179	1.51793	0.758964	+	0.651133i	$0.225706\pi$
$62$	−806.878	−1.65280
$63$	−102.833	−0.205648
$64$	−701.337	−1.36980
$65$	421.697	0.804694
$66$	−301.803	−0.562870
$67$	−982.993	−1.79241	−0.896207	−	0.443637i	$-0.853688\pi$
$67$	−982.993	−1.79241	−0.896207	+	0.443637i	$0.853688\pi$
$68$	−519.500	−0.926451
$69$	297.970	0.519874
$70$	−822.501	−1.40440
$71$	417.795	0.698354	0.349177	−	0.937057i	$-0.386461\pi$
$71$	417.795	0.698354	0.349177	+	0.937057i	$0.386461\pi$
$72$	−26.3318	−0.0431004
$73$	219.278	0.351569	0.175784	−	0.984429i	$-0.443754\pi$
$73$	219.278	0.351569	0.175784	+	0.984429i	$0.443754\pi$
$74$	−1540.96	−2.42072
$75$	−366.230	−0.563848
$76$	−750.416	−1.13261
$77$	−414.374	−0.613277
$78$	−1221.78	−1.77358
$79$	−801.309	−1.14119	−0.570597	−	0.821230i	$-0.693288\pi$
$79$	−801.309	−1.14119	−0.570597	+	0.821230i	$0.693288\pi$
$80$	333.277	0.465768
$81$	−615.845	−0.844781
$82$	22.3968	0.0301623
$83$	−792.865	−1.04853	−0.524266	−	0.851554i	$-0.675660\pi$
$83$	−792.865	−1.04853	−0.524266	+	0.851554i	$0.675660\pi$
$84$	1305.80	1.69612
$85$	375.565	0.479244
$86$	0	0
$87$	260.415	0.320913
$88$	−106.106	−0.128533
$89$	−1205.01	−1.43518	−0.717589	−	0.696467i	$-0.754754\pi$
$89$	−1205.01	−1.43518	−0.717589	+	0.696467i	$0.754754\pi$
$90$	108.750	0.127370
$91$	−1677.50	−1.93241
$92$	598.461	0.678194
$93$	−926.078	−1.03258
$94$	2352.73	2.58155
$95$	542.503	0.585891
$96$	−1241.44	−1.31983
$97$	577.561	0.604561	0.302281	−	0.953219i	$-0.402252\pi$
$97$	577.561	0.604561	0.302281	+	0.953219i	$0.402252\pi$
$98$	1828.94	1.88521
$99$	54.7880	0.0556202
$100$	−735.560	−0.735560
$101$	1590.84	1.56727	0.783635	−	0.621221i	$-0.213363\pi$
$101$	1590.84	1.56727	0.783635	+	0.621221i	$0.213363\pi$
$102$	−1088.12	−1.05628
$103$	1356.26	1.29744	0.648718	−	0.761029i	$-0.275305\pi$
$103$	1356.26	1.29744	0.648718	+	0.761029i	$0.275305\pi$
$104$	−429.544	−0.405002
$105$	−944.010	−0.877390
$106$	411.003	0.376605
$107$	615.442	0.556047	0.278023	−	0.960574i	$-0.410321\pi$
$107$	615.442	0.556047	0.278023	+	0.960574i	$0.410321\pi$
$108$	−1436.86	−1.28020
$109$	1400.49	1.23067	0.615333	−	0.788267i	$-0.289022\pi$
$109$	1400.49	1.23067	0.615333	+	0.788267i	$0.289022\pi$
$110$	438.215	0.379838
$111$	−1768.61	−1.51233
$112$	−1325.76	−1.11851
$113$	−1104.14	−0.919193	−0.459597	−	0.888128i	$-0.652006\pi$
$113$	−1104.14	−0.919193	−0.459597	+	0.888128i	$0.652006\pi$
$114$	−1571.79	−1.29133
$115$	−432.649	−0.350824
$116$	523.034	0.418642
$117$	221.797	0.175257
$118$	3673.35	2.86575
$119$	−1493.99	−1.15087
$120$	−241.725	−0.183887
$121$	−1110.23	−0.834131
$122$	3042.30	2.25768
$123$	25.7055	0.0188438
$124$	−1859.99	−1.34704
$125$	1408.10	1.00755
$126$	−432.604	−0.305868
$127$	561.803	0.392535	0.196268	−	0.980550i	$-0.437118\pi$
$127$	561.803	0.392535	0.196268	+	0.980550i	$0.437118\pi$
$128$	−893.486	−0.616983
$129$	0	0
$130$	1774.01	1.19686
$131$	−255.265	−0.170249	−0.0851245	−	0.996370i	$-0.527129\pi$
$131$	−255.265	−0.170249	−0.0851245	+	0.996370i	$0.527129\pi$
$132$	−695.709	−0.458740
$133$	−2158.06	−1.40697
$134$	−4135.29	−2.66593
$135$	1038.76	0.662238
$136$	−382.553	−0.241204
$137$	−1067.47	−0.665692	−0.332846	−	0.942981i	$-0.608009\pi$
$137$	−1067.47	−0.665692	−0.332846	+	0.942981i	$0.608009\pi$
$138$	1253.51	0.773231
$139$	−476.139	−0.290544	−0.145272	−	0.989392i	$-0.546406\pi$
$139$	−476.139	−0.290544	−0.145272	+	0.989392i	$0.546406\pi$
$140$	−1896.01	−1.14459
$141$	2700.30	1.61281
$142$	1757.60	1.03869
$143$	893.744	0.522648
$144$	175.291	0.101441
$145$	−378.120	−0.216560
$146$	922.466	0.522903
$147$	2099.13	1.17778
$148$	−3552.19	−1.97289
$149$	−517.779	−0.284685	−0.142343	−	0.989817i	$-0.545463\pi$
$149$	−517.779	−0.284685	−0.142343	+	0.989817i	$0.545463\pi$
$150$	−1540.67	−0.838636
$151$	1364.45	0.735347	0.367674	−	0.929955i	$-0.380154\pi$
$151$	1364.45	0.735347	0.367674	+	0.929955i	$0.380154\pi$
$152$	−552.597	−0.294879
$153$	197.533	0.104376
$154$	−1743.21	−0.912153
$155$	1344.66	0.696809
$156$	−2816.42	−1.44547
$157$	−2848.68	−1.44808	−0.724042	−	0.689756i	$-0.757718\pi$
$157$	−2848.68	−1.44808	−0.724042	+	0.689756i	$0.757718\pi$
$158$	−3370.98	−1.69735
$159$	471.721	0.235282
$160$	1802.55	0.890653
$161$	1721.06	0.842477
$162$	−2590.76	−1.25648
$163$	−2047.22	−0.983745	−0.491873	−	0.870667i	$-0.663687\pi$
$163$	−2047.22	−0.983745	−0.491873	+	0.870667i	$0.663687\pi$
$164$	51.6285	0.0245824
$165$	502.953	0.237302
$166$	−3335.45	−1.55953
$167$	−900.176	−0.417112	−0.208556	−	0.978010i	$-0.566876\pi$
$167$	−900.176	−0.417112	−0.208556	+	0.978010i	$0.566876\pi$
$168$	961.575	0.441590
$169$	1421.12	0.646845
$170$	1579.94	0.712801
$171$	285.336	0.127603
$172$	0	0
$173$	1843.61	0.810215	0.405108	−	0.914269i	$-0.367234\pi$
$173$	1843.61	0.810215	0.405108	+	0.914269i	$0.367234\pi$
$174$	1095.52	0.477307
$175$	−2115.33	−0.913739
$176$	706.345	0.302516
$177$	4216.01	1.79037
$178$	−5069.29	−2.13460
$179$	−4436.88	−1.85267	−0.926335	−	0.376701i	$-0.877058\pi$
$179$	−4436.88	−1.85267	−0.926335	+	0.376701i	$0.877058\pi$
$180$	250.688	0.103806
$181$	−3254.36	−1.33643	−0.668217	−	0.743966i	$-0.732942\pi$
$181$	−3254.36	−1.33643	−0.668217	+	0.743966i	$0.732942\pi$
$182$	−7056.97	−2.87416
$183$	3491.74	1.41047
$184$	440.699	0.176569
$185$	2568.00	1.02056
$186$	−3895.86	−1.53580
$187$	795.972	0.311269
$188$	5423.46	2.10397
$189$	−4132.15	−1.59032
$190$	2282.22	0.871420
$191$	2246.48	0.851043	0.425522	−	0.904948i	$-0.360091\pi$
$191$	2246.48	0.851043	0.425522	+	0.904948i	$0.360091\pi$
$192$	−3386.28	−1.27283
$193$	−1020.49	−0.380605	−0.190302	−	0.981726i	$-0.560947\pi$
$193$	−1020.49	−0.380605	−0.190302	+	0.981726i	$0.560947\pi$
$194$	2429.71	0.899190
$195$	2036.09	0.747730
$196$	4216.02	1.53645
$197$	2025.70	0.732614	0.366307	−	0.930494i	$-0.380622\pi$
$197$	2025.70	0.732614	0.366307	+	0.930494i	$0.380622\pi$
$198$	230.484	0.0827263
$199$	−2340.03	−0.833569	−0.416784	−	0.909005i	$-0.636843\pi$
$199$	−2340.03	−0.833569	−0.416784	+	0.909005i	$0.636843\pi$
$200$	−541.657	−0.191505
$201$	−4746.20	−1.66553
$202$	6692.40	2.33107
$203$	1504.15	0.520052
$204$	−2508.31	−0.860868
$205$	−37.3241	−0.0127162
$206$	5705.56	1.92973
$207$	−227.557	−0.0764072
$208$	2859.48	0.953216
$209$	1149.78	0.380535
$210$	−3971.30	−1.30498
$211$	3911.57	1.27622	0.638112	−	0.769943i	$-0.279716\pi$
$211$	3911.57	1.27622	0.638112	+	0.769943i	$0.279716\pi$
$212$	947.435	0.306934
$213$	2017.25	0.648918
$214$	2589.07	0.827032
$215$	0	0
$216$	−1058.09	−0.333304
$217$	−5349.00	−1.67333
$218$	5891.64	1.83042
$219$	1058.74	0.326681
$220$	1010.16	0.309569
$221$	3222.31	0.980796
$222$	−7440.26	−2.24936
$223$	1.96080	0.000588811 0	0.000294406	−	1.00000i	$-0.499906\pi$
$223$	1.96080	0.000588811 0	0.000294406		1.00000i	$0.499906\pi$
$224$	−7170.50	−2.13884
$225$	279.687	0.0828701
$226$	−4644.94	−1.36715
$227$	49.4069	0.0144461	0.00722303	−	0.999974i	$-0.497701\pi$
$227$	49.4069	0.0144461	0.00722303	+	0.999974i	$0.497701\pi$
$228$	−3623.25	−1.05244
$229$	1697.91	0.489960	0.244980	−	0.969528i	$-0.421219\pi$
$229$	1697.91	0.489960	0.244980	+	0.969528i	$0.421219\pi$
$230$	−1820.09	−0.521795
$231$	−2000.73	−0.569863
$232$	385.156	0.108995
$233$	3795.60	1.06720	0.533601	−	0.845736i	$-0.320838\pi$
$233$	3795.60	1.06720	0.533601	+	0.845736i	$0.320838\pi$
$234$	933.063	0.260668
$235$	−3920.82	−1.08837
$236$	8467.70	2.33560
$237$	−3868.97	−1.06041
$238$	−6284.96	−1.71174
$239$	−2950.09	−0.798433	−0.399216	−	0.916857i	$-0.630718\pi$
$239$	−2950.09	−0.798433	−0.399216	+	0.916857i	$0.630718\pi$
$240$	1609.17	0.432797
$241$	−4078.25	−1.09005	−0.545027	−	0.838418i	$-0.683481\pi$
$241$	−4078.25	−1.09005	−0.545027	+	0.838418i	$0.683481\pi$
$242$	−4670.55	−1.24064
$243$	1027.05	0.271132
$244$	7013.03	1.84001
$245$	−3047.91	−0.794791
$246$	108.139	0.0280271
$247$	4654.61	1.19905
$248$	−1369.68	−0.350704
$249$	−3828.20	−0.974307
$250$	5923.64	1.49858
$251$	−3528.89	−0.887417	−0.443708	−	0.896171i	$-0.646337\pi$
$251$	−3528.89	−0.887417	−0.443708	+	0.896171i	$0.646337\pi$
$252$	−997.228	−0.249284
$253$	−916.955	−0.227860
$254$	2363.42	0.583835
$255$	1813.35	0.445319
$256$	1851.94	0.452134
$257$	−6455.09	−1.56676	−0.783380	−	0.621543i	$-0.786506\pi$
$257$	−6455.09	−1.56676	−0.783380	+	0.621543i	$0.786506\pi$
$258$	0	0
$259$	−10215.4	−2.45080
$260$	4089.41	0.975441
$261$	−198.877	−0.0471654
$262$	−1073.86	−0.253219
$263$	−3618.65	−0.848424	−0.424212	−	0.905563i	$-0.639449\pi$
$263$	−3618.65	−0.848424	−0.424212	+	0.905563i	$0.639449\pi$
$264$	−512.312	−0.119434
$265$	−684.935	−0.158774
$266$	−9078.61	−2.09265
$267$	−5818.17	−1.33358
$268$	−9532.58	−2.17274
$269$	1258.66	0.285286	0.142643	−	0.989774i	$-0.454440\pi$
$269$	1258.66	0.285286	0.142643	+	0.989774i	$0.454440\pi$
$270$	4369.89	0.984975
$271$	−4808.76	−1.07790	−0.538951	−	0.842337i	$-0.681179\pi$
$271$	−4808.76	−1.07790	−0.538951	+	0.842337i	$0.681179\pi$
$272$	2546.66	0.567698
$273$	−8099.50	−1.79562
$274$	−4490.66	−0.990112
$275$	1127.02	0.247133
$276$	2889.56	0.630185
$277$	6487.98	1.40731	0.703655	−	0.710542i	$-0.251550\pi$
$277$	6487.98	1.40731	0.703655	+	0.710542i	$0.251550\pi$
$278$	−2003.04	−0.432138
$279$	707.237	0.151761
$280$	−1396.20	−0.297996
$281$	−1896.75	−0.402672	−0.201336	−	0.979522i	$-0.564528\pi$
$281$	−1896.75	−0.402672	−0.201336	+	0.979522i	$0.564528\pi$
$282$	11359.7	2.39880
$283$	448.018	0.0941057	0.0470528	−	0.998892i	$-0.485017\pi$
$283$	448.018	0.0941057	0.0470528	+	0.998892i	$0.485017\pi$
$284$	4051.57	0.846536
$285$	2619.38	0.544416
$286$	3759.84	0.777357
$287$	148.474	0.0305371
$288$	948.074	0.193978
$289$	−2043.20	−0.415876
$290$	−1590.69	−0.322099
$291$	2788.65	0.561765
$292$	2126.44	0.426167
$293$	−2086.41	−0.416005	−0.208002	−	0.978128i	$-0.566696\pi$
$293$	−2086.41	−0.416005	−0.208002	+	0.978128i	$0.566696\pi$
$294$	8830.69	1.75176
$295$	−6121.61	−1.20818
$296$	−2615.79	−0.513647
$297$	2201.54	0.430123
$298$	−2178.21	−0.423425
$299$	−3712.08	−0.717977
$300$	−3551.52	−0.683490
$301$	0	0
$302$	5740.03	1.09371
$303$	7681.08	1.45632
$304$	3678.64	0.694028
$305$	−5069.97	−0.951822
$306$	830.989	0.155243
$307$	393.588	0.0731702	0.0365851	−	0.999331i	$-0.488352\pi$
$307$	393.588	0.0731702	0.0365851	+	0.999331i	$0.488352\pi$
$308$	−4018.40	−0.743407
$309$	6548.44	1.20559
$310$	5656.75	1.03639
$311$	2153.14	0.392583	0.196292	−	0.980546i	$-0.437110\pi$
$311$	2153.14	0.392583	0.196292	+	0.980546i	$0.437110\pi$
$312$	−2073.98	−0.376332
$313$	−6023.57	−1.08777	−0.543886	−	0.839159i	$-0.683047\pi$
$313$	−6023.57	−1.08777	−0.543886	+	0.839159i	$0.683047\pi$
$314$	−11983.9	−2.15380
$315$	720.932	0.128952
$316$	−7770.69	−1.38334
$317$	−6359.98	−1.12685	−0.563426	−	0.826166i	$-0.690517\pi$
$317$	−6359.98	−1.12685	−0.563426	+	0.826166i	$0.690517\pi$
$318$	1984.46	0.349946
$319$	−801.387	−0.140655
$320$	4916.84	0.858937
$321$	2971.55	0.516684
$322$	7240.24	1.25305
$323$	4145.42	0.714109
$324$	−5972.16	−1.02403
$325$	4562.47	0.778708
$326$	−8612.32	−1.46317
$327$	6762.01	1.14355
$328$	38.0186	0.00640008
$329$	15596.9	2.61363
$330$	2115.84	0.352950
$331$	6984.33	1.15980	0.579900	−	0.814688i	$-0.303092\pi$
$331$	6984.33	1.15980	0.579900	+	0.814688i	$0.303092\pi$
$332$	−7688.81	−1.27102
$333$	1350.67	0.222271
$334$	−3786.90	−0.620389
$335$	6891.44	1.12394
$336$	−6401.21	−1.03933
$337$	428.803	0.0693128	0.0346564	−	0.999399i	$-0.488966\pi$
$337$	428.803	0.0693128	0.0346564	+	0.999399i	$0.488966\pi$
$338$	5978.41	0.962079
$339$	−5331.14	−0.854124
$340$	3642.05	0.580934
$341$	2849.86	0.452577
$342$	1200.36	0.189790
$343$	2558.83	0.402810
$344$	0	0
$345$	−2088.97	−0.325989
$346$	7755.78	1.20507
$347$	871.352	0.134803	0.0674015	−	0.997726i	$-0.478529\pi$
$347$	871.352	0.134803	0.0674015	+	0.997726i	$0.478529\pi$
$348$	2525.38	0.389007
$349$	2954.05	0.453085	0.226543	−	0.974001i	$-0.427258\pi$
$349$	2954.05	0.453085	0.226543	+	0.974001i	$0.427258\pi$
$350$	−8898.87	−1.35904
$351$	8912.44	1.35530
$352$	3820.33	0.578478
$353$	−1760.46	−0.265438	−0.132719	−	0.991154i	$-0.542371\pi$
$353$	−1760.46	−0.265438	−0.132719	+	0.991154i	$0.542371\pi$
$354$	17736.1	2.66289
$355$	−2929.02	−0.437905
$356$	−11685.6	−1.73971
$357$	−7213.44	−1.06940
$358$	−18665.2	−2.75555
$359$	9960.60	1.46435	0.732173	−	0.681119i	$-0.238506\pi$
$359$	9960.60	1.46435	0.732173	+	0.681119i	$0.238506\pi$
$360$	184.603	0.0270263
$361$	−870.958	−0.126980
$362$	−13690.6	−1.98774
$363$	−5360.53	−0.775083
$364$	−16267.5	−2.34245
$365$	−1537.28	−0.220452
$366$	14689.2	2.09786
$367$	1291.52	0.183697	0.0918485	−	0.995773i	$-0.470722\pi$
$367$	1291.52	0.183697	0.0918485	+	0.995773i	$0.470722\pi$
$368$	−2933.74	−0.415575
$369$	−19.6310	−0.00276951
$370$	10803.2	1.51792
$371$	2724.65	0.381285
$372$	−8980.64	−1.25168
$373$	−7010.88	−0.973216	−0.486608	−	0.873620i	$-0.661766\pi$
$373$	−7010.88	−0.973216	−0.486608	+	0.873620i	$0.661766\pi$
$374$	3348.53	0.462963
$375$	6798.74	0.936228
$376$	3993.77	0.547774
$377$	−3244.23	−0.443200
$378$	−17383.3	−2.36534
$379$	2688.90	0.364431	0.182216	−	0.983259i	$-0.441673\pi$
$379$	2688.90	0.364431	0.182216	+	0.983259i	$0.441673\pi$
$380$	5260.92	0.710210
$381$	2712.57	0.364748
$382$	9450.56	1.26579
$383$	−5518.96	−0.736307	−0.368153	−	0.929765i	$-0.620010\pi$
$383$	−5518.96	−0.736307	−0.368153	+	0.929765i	$0.620010\pi$
$384$	−4314.04	−0.573307
$385$	2905.04	0.384558
$386$	−4293.05	−0.566089
$387$	0	0
$388$	5600.90	0.732842
$389$	6817.59	0.888601	0.444300	−	0.895878i	$-0.353452\pi$
$389$	6817.59	0.888601	0.444300	+	0.895878i	$0.353452\pi$
$390$	8565.50	1.11213
$391$	−3305.99	−0.427599
$392$	3104.62	0.400018
$393$	−1232.50	−0.158197
$394$	8521.78	1.08965
$395$	5617.71	0.715589
$396$	531.307	0.0674222
$397$	5351.01	0.676472	0.338236	−	0.941061i	$-0.390170\pi$
$397$	5351.01	0.676472	0.338236	+	0.941061i	$0.390170\pi$
$398$	−9844.12	−1.23980
$399$	−10419.8	−1.30737
$400$	3605.82	0.450727
$401$	−6590.42	−0.820723	−0.410362	−	0.911923i	$-0.634597\pi$
$401$	−6590.42	−0.820723	−0.410362	+	0.911923i	$0.634597\pi$
$402$	−19966.5	−2.47721
$403$	11537.0	1.42605
$404$	15427.2	1.89983
$405$	4317.49	0.529723
$406$	6327.72	0.773496
$407$	5442.62	0.662852
$408$	−1847.09	−0.224129
$409$	4132.15	0.499564	0.249782	−	0.968302i	$-0.419641\pi$
$409$	4132.15	0.499564	0.249782	+	0.968302i	$0.419641\pi$
$410$	−157.017	−0.0189134
$411$	−5154.07	−0.618568
$412$	13152.3	1.57274
$413$	24351.6	2.90136
$414$	−957.295	−0.113644
$415$	5558.51	0.657486
$416$	15465.7	1.82276
$417$	−2298.95	−0.269976
$418$	4836.94	0.565986
$419$	5101.36	0.594792	0.297396	−	0.954754i	$-0.403882\pi$
$419$	5101.36	0.594792	0.297396	+	0.954754i	$0.403882\pi$
$420$	−9154.54	−1.06356
$421$	−3542.08	−0.410048	−0.205024	−	0.978757i	$-0.565727\pi$
$421$	−3542.08	−0.410048	−0.205024	+	0.978757i	$0.565727\pi$
$422$	16455.3	1.89818
$423$	−2062.20	−0.237039
$424$	697.679	0.0799111
$425$	4063.35	0.463768
$426$	8486.23	0.965163
$427$	20168.2	2.28573
$428$	5968.25	0.674033
$429$	4315.28	0.485650
$430$	0	0
$431$	−8499.53	−0.949903	−0.474951	−	0.880012i	$-0.657534\pi$
$431$	−8499.53	−0.949903	−0.474951	+	0.880012i	$0.657534\pi$
$432$	7043.69	0.784467
$433$	−7919.12	−0.878911	−0.439456	−	0.898264i	$-0.644829\pi$
$433$	−7919.12	−0.878911	−0.439456	+	0.898264i	$0.644829\pi$
$434$	−22502.4	−2.48882
$435$	−1825.68	−0.201230
$436$	13581.3	1.49180
$437$	−4775.50	−0.522753
$438$	4453.96	0.485887
$439$	13630.2	1.48186	0.740929	−	0.671583i	$-0.234385\pi$
$439$	13630.2	1.48186	0.740929	+	0.671583i	$0.234385\pi$
$440$	743.872	0.0805970
$441$	−1603.08	−0.173101
$442$	13555.7	1.45878
$443$	−15066.5	−1.61587	−0.807936	−	0.589270i	$-0.799416\pi$
$443$	−15066.5	−1.61587	−0.807936	+	0.589270i	$0.799416\pi$
$444$	−17151.1	−1.83323
$445$	8447.94	0.899934
$446$	8.24877	0.000875764 0
$447$	−2500.00	−0.264533
$448$	−19559.0	−2.06267
$449$	−4920.86	−0.517215	−0.258608	−	0.965982i	$-0.583264\pi$
$449$	−4920.86	−0.517215	−0.258608	+	0.965982i	$0.583264\pi$
$450$	1176.60	0.123256
$451$	−79.1046	−0.00825918
$452$	−10707.4	−1.11423
$453$	6588.00	0.683292
$454$	207.847	0.0214862
$455$	11760.4	1.21173
$456$	−2668.12	−0.274004
$457$	8415.53	0.861404	0.430702	−	0.902494i	$-0.358266\pi$
$457$	8415.53	0.861404	0.430702	+	0.902494i	$0.358266\pi$
$458$	7142.82	0.728738
$459$	7937.45	0.807164
$460$	−4195.62	−0.425264
$461$	−17706.4	−1.78887	−0.894437	−	0.447194i	$-0.852423\pi$
$461$	−17706.4	−1.78887	−0.894437	+	0.447194i	$0.852423\pi$
$462$	−8416.76	−0.847582
$463$	9891.44	0.992860	0.496430	−	0.868077i	$-0.334644\pi$
$463$	9891.44	0.992860	0.496430	+	0.868077i	$0.334644\pi$
$464$	−2563.98	−0.256530
$465$	6492.43	0.647482
$466$	15967.5	1.58730
$467$	5637.96	0.558659	0.279330	−	0.960195i	$-0.409888\pi$
$467$	5637.96	0.558659	0.279330	+	0.960195i	$0.409888\pi$
$468$	2150.87	0.212445
$469$	−27413.9	−2.69906
$470$	−16494.2	−1.61877
$471$	−13754.3	−1.34557
$472$	6235.51	0.608078
$473$	0	0
$474$	−16276.1	−1.57719
$475$	5869.49	0.566970
$476$	−14487.9	−1.39507
$477$	−360.249	−0.0345800
$478$	−12410.6	−1.18754
$479$	−16670.3	−1.59015	−0.795077	−	0.606508i	$-0.792570\pi$
$479$	−16670.3	−1.59015	−0.795077	+	0.606508i	$0.792570\pi$
$480$	8703.30	0.827603
$481$	22033.2	2.08862
$482$	−17156.5	−1.62128
$483$	8309.84	0.782838
$484$	−10766.4	−1.01112
$485$	−4049.09	−0.379092
$486$	4320.62	0.403266
$487$	16410.3	1.52694	0.763470	−	0.645843i	$-0.223494\pi$
$487$	16410.3	1.52694	0.763470	+	0.645843i	$0.223494\pi$
$488$	5164.31	0.479052
$489$	−9884.62	−0.914106
$490$	−12822.1	−1.18213
$491$	3171.88	0.291538	0.145769	−	0.989319i	$-0.453434\pi$
$491$	3171.88	0.291538	0.145769	+	0.989319i	$0.453434\pi$
$492$	249.279	0.0228422
$493$	−2889.32	−0.263952
$494$	19581.2	1.78340
$495$	−384.101	−0.0348769
$496$	9117.94	0.825419
$497$	11651.6	1.05160
$498$	−16104.6	−1.44913
$499$	10898.7	0.977737	0.488869	−	0.872357i	$-0.337410\pi$
$499$	10898.7	0.977737	0.488869	+	0.872357i	$0.337410\pi$
$500$	13655.0	1.22134
$501$	−4346.34	−0.387585
$502$	−14845.5	−1.31989
$503$	932.683	0.0826765	0.0413383	−	0.999145i	$-0.486838\pi$
$503$	932.683	0.0826765	0.0413383	+	0.999145i	$0.486838\pi$
$504$	−734.346	−0.0649015
$505$	−11152.8	−0.982763
$506$	−3857.48	−0.338905
$507$	6861.61	0.601055
$508$	5448.09	0.475827
$509$	−18569.3	−1.61703	−0.808517	−	0.588473i	$-0.799729\pi$
$509$	−18569.3	−1.61703	−0.808517	+	0.588473i	$0.799729\pi$
$510$	7628.47	0.662342
$511$	6115.26	0.529400
$512$	14938.7	1.28946
$513$	11465.6	0.986783
$514$	−27155.5	−2.33031
$515$	−9508.27	−0.813562
$516$	0	0
$517$	−8309.76	−0.706892
$518$	−42974.7	−3.64517
$519$	8901.54	0.752860
$520$	3011.39	0.253958
$521$	−21616.7	−1.81774	−0.908872	−	0.417075i	$-0.863055\pi$
$521$	−21616.7	−1.81774	−0.908872	+	0.417075i	$0.863055\pi$
$522$	−836.642	−0.0701510
$523$	7553.08	0.631498	0.315749	−	0.948843i	$-0.397744\pi$
$523$	7553.08	0.631498	0.315749	+	0.948843i	$0.397744\pi$
$524$	−2475.43	−0.206374
$525$	−10213.5	−0.849055
$526$	−15223.1	−1.26190
$527$	10274.9	0.849301
$528$	3410.46	0.281101
$529$	−8358.52	−0.686983
$530$	−2881.41	−0.236152
$531$	−3219.73	−0.263134
$532$	−20927.8	−1.70552
$533$	−320.237	−0.0260244
$534$	−24476.1	−1.98349
$535$	−4314.66	−0.348671
$536$	−7019.67	−0.565678
$537$	−21422.7	−1.72152
$538$	5294.98	0.424317
$539$	−6459.73	−0.516216
$540$	10073.4	0.802757
$541$	17662.3	1.40363	0.701814	−	0.712360i	$-0.252374\pi$
$541$	17662.3	1.40363	0.701814	+	0.712360i	$0.252374\pi$
$542$	−20229.7	−1.60321
$543$	−15713.1	−1.24183
$544$	13773.8	1.08557
$545$	−9818.38	−0.771694
$546$	−34073.3	−2.67070
$547$	19855.5	1.55203	0.776016	−	0.630714i	$-0.217238\pi$
$547$	19855.5	1.55203	0.776016	+	0.630714i	$0.217238\pi$
$548$	−10351.8	−0.806944
$549$	−2666.61	−0.207301
$550$	4741.18	0.367572
$551$	−4173.62	−0.322690
$552$	2127.84	0.164070
$553$	−22347.1	−1.71843
$554$	27293.9	2.09315
$555$	12399.1	0.948314
$556$	−4617.36	−0.352194
$557$	4237.59	0.322356	0.161178	−	0.986925i	$-0.448471\pi$
$557$	4237.59	0.322356	0.161178	+	0.986925i	$0.448471\pi$
$558$	2975.23	0.225720
$559$	0	0
$560$	9294.49	0.701364
$561$	3843.21	0.289234
$562$	−7979.33	−0.598911
$563$	12500.8	0.935781	0.467890	−	0.883787i	$-0.345014\pi$
$563$	12500.8	0.935781	0.467890	+	0.883787i	$0.345014\pi$
$564$	26186.2	1.95503
$565$	7740.77	0.576383
$566$	1884.74	0.139967
$567$	−17174.8	−1.27209
$568$	2983.52	0.220398
$569$	102.851	0.00757777	0.00378889	−	0.999993i	$-0.498794\pi$
$569$	102.851	0.00757777	0.00378889	+	0.999993i	$0.498794\pi$
$570$	11019.3	0.809733
$571$	16482.6	1.20801	0.604006	−	0.796979i	$-0.293570\pi$
$571$	16482.6	1.20801	0.604006	+	0.796979i	$0.293570\pi$
$572$	8667.09	0.633547
$573$	10846.7	0.790798
$574$	624.606	0.0454191
$575$	−4680.95	−0.339494
$576$	2586.07	0.187071
$577$	12994.4	0.937547	0.468774	−	0.883318i	$-0.344696\pi$
$577$	12994.4	0.937547	0.468774	+	0.883318i	$0.344696\pi$
$578$	−8595.42	−0.618550
$579$	−4927.26	−0.353662
$580$	−3666.82	−0.262511
$581$	−22111.6	−1.57890
$582$	11731.4	0.835536
$583$	−1451.65	−0.103124
$584$	1565.89	0.110954
$585$	−1554.94	−0.109896
$586$	−8777.20	−0.618742
$587$	3247.27	0.228329	0.114165	−	0.993462i	$-0.463581\pi$
$587$	3247.27	0.228329	0.114165	+	0.993462i	$0.463581\pi$
$588$	20356.3	1.42768
$589$	14842.1	1.03830
$590$	−25752.6	−1.79698
$591$	9780.71	0.680752
$592$	17413.3	1.20892
$593$	6784.90	0.469852	0.234926	−	0.972013i	$-0.424515\pi$
$593$	6784.90	0.469852	0.234926	+	0.972013i	$0.424515\pi$
$594$	9261.54	0.639740
$595$	10473.8	0.721657
$596$	−5021.16	−0.345092
$597$	−11298.4	−0.774560
$598$	−15616.1	−1.06788
$599$	−14622.2	−0.997408	−0.498704	−	0.866772i	$-0.666190\pi$
$599$	−14622.2	−0.997408	−0.498704	+	0.866772i	$0.666190\pi$
$600$	−2615.29	−0.177948
$601$	−18858.5	−1.27995	−0.639977	−	0.768394i	$-0.721056\pi$
$601$	−18858.5	−1.27995	−0.639977	+	0.768394i	$0.721056\pi$
$602$	0	0
$603$	3624.63	0.244787
$604$	13231.8	0.891379
$605$	7783.45	0.523045
$606$	32313.1	2.16605
$607$	22932.4	1.53344	0.766718	−	0.641984i	$-0.221888\pi$
$607$	22932.4	1.53344	0.766718	+	0.641984i	$0.221888\pi$
$608$	19896.2	1.32714
$609$	7262.51	0.483238
$610$	−21328.6	−1.41569
$611$	−33640.2	−2.22739
$612$	1915.58	0.126524
$613$	−15582.9	−1.02673	−0.513367	−	0.858169i	$-0.671602\pi$
$613$	−15582.9	−1.02673	−0.513367	+	0.858169i	$0.671602\pi$
$614$	1655.76	0.108829
$615$	−180.213	−0.0118161
$616$	−2959.10	−0.193548
$617$	9064.42	0.591442	0.295721	−	0.955274i	$-0.404440\pi$
$617$	9064.42	0.591442	0.295721	+	0.955274i	$0.404440\pi$
$618$	27548.2	1.79313
$619$	−8539.07	−0.554466	−0.277233	−	0.960803i	$-0.589417\pi$
$619$	−8539.07	−0.554466	−0.277233	+	0.960803i	$0.589417\pi$
$620$	13039.8	0.844663
$621$	−9143.90	−0.590873
$622$	9057.92	0.583906
$623$	−33605.6	−2.16112
$624$	13806.5	0.885738
$625$	−390.398	−0.0249855
$626$	−25340.2	−1.61789
$627$	5551.50	0.353597
$628$	−27625.0	−1.75535
$629$	19622.8	1.24390
$630$	3032.84	0.191796
$631$	−15078.5	−0.951294	−0.475647	−	0.879636i	$-0.657786\pi$
$631$	−15078.5	−0.951294	−0.475647	+	0.879636i	$0.657786\pi$
$632$	−5722.24	−0.360156
$633$	18886.3	1.18588
$634$	−26755.4	−1.67602
$635$	−3938.62	−0.246141
$636$	4574.52	0.285207
$637$	−26150.7	−1.62658
$638$	−3371.31	−0.209203
$639$	−1540.55	−0.0953730
$640$	6263.94	0.386881
$641$	−22253.5	−1.37123	−0.685616	−	0.727963i	$-0.740467\pi$
$641$	−22253.5	−1.37123	−0.685616	+	0.727963i	$0.740467\pi$
$642$	12500.8	0.768487
$643$	6114.37	0.375003	0.187502	−	0.982264i	$-0.439961\pi$
$643$	6114.37	0.375003	0.187502	+	0.982264i	$0.439961\pi$
$644$	16690.0	1.02124
$645$	0	0
$646$	17439.1	1.06212
$647$	−4947.98	−0.300657	−0.150329	−	0.988636i	$-0.548033\pi$
$647$	−4947.98	−0.300657	−0.150329	+	0.988636i	$0.548033\pi$
$648$	−4397.82	−0.266609
$649$	−12974.1	−0.784713
$650$	19193.6	1.15821
$651$	−25826.7	−1.55488
$652$	−19852.9	−1.19248
$653$	−21153.5	−1.26769	−0.633845	−	0.773460i	$-0.718524\pi$
$653$	−21153.5	−1.26769	−0.633845	+	0.773460i	$0.718524\pi$
$654$	28446.7	1.70085
$655$	1789.58	0.106755
$656$	−253.090	−0.0150633
$657$	−808.552	−0.0480131
$658$	65613.6	3.88736
$659$	15358.2	0.907843	0.453922	−	0.891042i	$-0.350025\pi$
$659$	15358.2	0.907843	0.453922	+	0.891042i	$0.350025\pi$
$660$	4877.39	0.287655
$661$	−11989.6	−0.705511	−0.352755	−	0.935716i	$-0.614755\pi$
$661$	−11989.6	−0.705511	−0.352755	+	0.935716i	$0.614755\pi$
$662$	29382.0	1.72502
$663$	15558.3	0.911366
$664$	−5661.94	−0.330913
$665$	15129.4	0.882248
$666$	5682.06	0.330594
$667$	3328.48	0.193222
$668$	−8729.46	−0.505618
$669$	9.46737	0.000547129 0
$670$	28991.2	1.67168
$671$	−10745.3	−0.618207
$672$	−34621.5	−1.98743
$673$	−19868.3	−1.13799	−0.568994	−	0.822342i	$-0.692667\pi$
$673$	−19868.3	−1.13799	−0.568994	+	0.822342i	$0.692667\pi$
$674$	1803.91	0.103092
$675$	11238.6	0.640852
$676$	13781.3	0.784097
$677$	−11011.1	−0.625098	−0.312549	−	0.949902i	$-0.601183\pi$
$677$	−11011.1	−0.625098	−0.312549	+	0.949902i	$0.601183\pi$
$678$	−22427.3	−1.27037
$679$	16107.2	0.910362
$680$	2681.96	0.151248
$681$	238.552	0.0134234
$682$	11988.9	0.673136
$683$	−21704.9	−1.21598	−0.607989	−	0.793945i	$-0.708024\pi$
$683$	−21704.9	−1.21598	−0.607989	+	0.793945i	$0.708024\pi$
$684$	2767.04	0.154679
$685$	7483.66	0.417425
$686$	10764.6	0.599116
$687$	8198.03	0.455276
$688$	0	0
$689$	−5876.66	−0.324939
$690$	−8787.95	−0.484857
$691$	−4124.20	−0.227051	−0.113525	−	0.993535i	$-0.536214\pi$
$691$	−4124.20	−0.227051	−0.113525	+	0.993535i	$0.536214\pi$
$692$	17878.4	0.982133
$693$	1527.94	0.0837542
$694$	3665.64	0.200498
$695$	3338.06	0.182187
$696$	1859.66	0.101279
$697$	−285.204	−0.0154991
$698$	12427.2	0.673893
$699$	18326.4	0.991655
$700$	−20513.5	−1.10762
$701$	27363.8	1.47435	0.737173	−	0.675704i	$-0.236160\pi$
$701$	27363.8	1.47435	0.737173	+	0.675704i	$0.236160\pi$
$702$	37493.2	2.01580
$703$	28345.1	1.52071
$704$	10420.7	0.557878
$705$	−18930.9	−1.01132
$706$	−7405.96	−0.394797
$707$	44365.7	2.36003
$708$	40884.8	2.17026
$709$	17078.7	0.904658	0.452329	−	0.891851i	$-0.350593\pi$
$709$	17078.7	0.904658	0.452329	+	0.891851i	$0.350593\pi$
$710$	−12321.9	−0.651315
$711$	2954.70	0.155851
$712$	−8605.13	−0.452936
$713$	−11836.6	−0.621718
$714$	−30345.8	−1.59056
$715$	−6265.75	−0.327728
$716$	−43026.6	−2.24578
$717$	−14244.0	−0.741912
$718$	41902.6	2.17798
$719$	−14080.8	−0.730356	−0.365178	−	0.930938i	$-0.618992\pi$
$719$	−14080.8	−0.730356	−0.365178	+	0.930938i	$0.618992\pi$
$720$	−1228.91	−0.0636092
$721$	37823.6	1.95371
$722$	−3663.98	−0.188863
$723$	−19691.1	−1.01289
$724$	−31559.2	−1.62001
$725$	−4090.99	−0.209566
$726$	−22550.9	−1.15281
$727$	29786.3	1.51955	0.759775	−	0.650186i	$-0.225309\pi$
$727$	29786.3	1.51955	0.759775	+	0.650186i	$0.225309\pi$
$728$	−11979.2	−0.609862
$729$	21586.7	1.09672
$730$	−6467.11	−0.327888
$731$	0	0
$732$	33861.1	1.70976
$733$	−15924.8	−0.802452	−0.401226	−	0.915979i	$-0.631416\pi$
$733$	−15924.8	−0.802452	−0.401226	+	0.915979i	$0.631416\pi$
$734$	5433.22	0.273220
$735$	−14716.3	−0.738528
$736$	−15867.4	−0.794672
$737$	14605.7	0.729997
$738$	−82.5846	−0.00411922
$739$	37584.1	1.87084	0.935421	−	0.353536i	$-0.115021\pi$
$739$	37584.1	1.87084	0.935421	+	0.353536i	$0.115021\pi$
$740$	24903.2	1.23711
$741$	22474.0	1.11417
$742$	11462.2	0.567101
$743$	17948.3	0.886219	0.443110	−	0.896467i	$-0.353875\pi$
$743$	17948.3	0.886219	0.443110	+	0.896467i	$0.353875\pi$
$744$	−6613.23	−0.325878
$745$	3629.98	0.178513
$746$	−29493.7	−1.44751
$747$	2923.56	0.143196
$748$	7718.94	0.377316
$749$	17163.6	0.837308
$750$	28601.2	1.39249
$751$	2386.72	0.115969	0.0579844	−	0.998317i	$-0.481533\pi$
$751$	2386.72	0.115969	0.0579844	+	0.998317i	$0.481533\pi$
$752$	−26586.5	−1.28924
$753$	−17038.6	−0.824597
$754$	−13648.0	−0.659190
$755$	−9565.72	−0.461102
$756$	−40071.5	−1.92776
$757$	−20527.4	−0.985574	−0.492787	−	0.870150i	$-0.664022\pi$
$757$	−20527.4	−0.985574	−0.492787	+	0.870150i	$0.664022\pi$
$758$	11311.8	0.542034
$759$	−4427.35	−0.211729
$760$	3874.08	0.184905
$761$	−21708.9	−1.03410	−0.517048	−	0.855957i	$-0.672969\pi$
$761$	−21708.9	−1.03410	−0.517048	+	0.855957i	$0.672969\pi$
$762$	11411.3	0.542505
$763$	39057.2	1.85316
$764$	21785.2	1.03162
$765$	−1384.84	−0.0654496
$766$	−23217.4	−1.09514
$767$	−52522.7	−2.47260
$768$	8941.76	0.420128
$769$	−3194.65	−0.149807	−0.0749037	−	0.997191i	$-0.523865\pi$
$769$	−3194.65	−0.149807	−0.0749037	+	0.997191i	$0.523865\pi$
$770$	12221.0	0.571969
$771$	−31167.2	−1.45585
$772$	−9896.23	−0.461364
$773$	9743.41	0.453359	0.226679	−	0.973969i	$-0.427213\pi$
$773$	9743.41	0.453359	0.226679	+	0.973969i	$0.427213\pi$
$774$	0	0
$775$	14548.2	0.674306
$776$	4124.43	0.190797
$777$	−49323.4	−2.27731
$778$	28680.5	1.32165
$779$	−411.976	−0.0189481
$780$	19745.0	0.906390
$781$	−6207.76	−0.284419
$782$	−13907.8	−0.635986
$783$	−7991.45	−0.364739
$784$	−20667.5	−0.941486
$785$	19971.1	0.908026
$786$	−5184.93	−0.235293
$787$	−10035.8	−0.454561	−0.227280	−	0.973829i	$-0.572983\pi$
$787$	−10035.8	−0.454561	−0.227280	+	0.973829i	$0.572983\pi$
$788$	19644.2	0.888066
$789$	−17472.0	−0.788364
$790$	23632.8	1.06433
$791$	−30792.5	−1.38414
$792$	391.248	0.0175535
$793$	−43499.8	−1.94795
$794$	22510.8	1.00615
$795$	−3307.08	−0.147535
$796$	−22692.4	−1.01044
$797$	23138.7	1.02837	0.514187	−	0.857678i	$-0.328094\pi$
$797$	23138.7	1.02837	0.514187	+	0.857678i	$0.328094\pi$
$798$	−43834.4	−1.94451
$799$	−29960.1	−1.32655
$800$	19502.3	0.861890
$801$	4443.29	0.196000
$802$	−27724.9	−1.22070
$803$	−3258.11	−0.143183
$804$	−46026.3	−2.01893
$805$	−12065.8	−0.528278
$806$	48534.3	2.12103
$807$	6077.21	0.265090
$808$	11360.4	0.494624
$809$	−2919.61	−0.126883	−0.0634413	−	0.997986i	$-0.520208\pi$
$809$	−2919.61	−0.126883	−0.0634413	+	0.997986i	$0.520208\pi$
$810$	18163.0	0.787879
$811$	−16208.2	−0.701784	−0.350892	−	0.936416i	$-0.614122\pi$
$811$	−16208.2	−0.701784	−0.350892	+	0.936416i	$0.614122\pi$
$812$	14586.5	0.630401
$813$	−23218.2	−1.00160
$814$	22896.2	0.985888
$815$	14352.4	0.616861
$816$	12296.1	0.527511
$817$	0	0
$818$	17383.3	0.743022
$819$	6185.51	0.263906
$820$	−361.951	−0.0154145
$821$	−17404.8	−0.739867	−0.369934	−	0.929058i	$-0.620620\pi$
$821$	−17404.8	−0.739867	−0.369934	+	0.929058i	$0.620620\pi$
$822$	−21682.3	−0.920022
$823$	9581.39	0.405816	0.202908	−	0.979198i	$-0.434961\pi$
$823$	9581.39	0.405816	0.202908	+	0.979198i	$0.434961\pi$
$824$	9685.20	0.409466
$825$	5441.59	0.229639
$826$	102443.	4.31532
$827$	−36359.4	−1.52883	−0.764414	−	0.644726i	$-0.776972\pi$
$827$	−36359.4	−1.52883	−0.764414	+	0.644726i	$0.776972\pi$
$828$	−2206.73	−0.0926198
$829$	21898.1	0.917435	0.458717	−	0.888582i	$-0.348309\pi$
$829$	21898.1	0.917435	0.458717	+	0.888582i	$0.348309\pi$
$830$	23383.8	0.977907
$831$	31326.0	1.30769
$832$	42186.0	1.75785
$833$	−23289.9	−0.968726
$834$	−9671.32	−0.401547
$835$	6310.84	0.261552
$836$	11150.0	0.461280
$837$	28418.9	1.17360
$838$	21460.6	0.884659
$839$	−5384.09	−0.221549	−0.110774	−	0.993846i	$-0.535333\pi$
$839$	−5384.09	−0.221549	−0.110774	+	0.993846i	$0.535333\pi$
$840$	−6741.29	−0.276901
$841$	−21480.0	−0.880726
$842$	−14900.9	−0.609882
$843$	−9158.12	−0.374167
$844$	37932.4	1.54702
$845$	−9962.99	−0.405606
$846$	−8675.34	−0.352558
$847$	−30962.3	−1.25605
$848$	−4644.45	−0.188079
$849$	2163.17	0.0874440
$850$	17093.9	0.689782
$851$	−22605.4	−0.910579
$852$	19562.3	0.786610
$853$	3558.83	0.142851	0.0714255	−	0.997446i	$-0.477245\pi$
$853$	3558.83	0.142851	0.0714255	+	0.997446i	$0.477245\pi$
$854$	84844.3	3.39966
$855$	−2000.39	−0.0800141
$856$	4394.94	0.175486
$857$	−38994.7	−1.55430	−0.777149	−	0.629317i	$-0.783335\pi$
$857$	−38994.7	−1.55430	−0.777149	+	0.629317i	$0.783335\pi$
$858$	18153.7	0.722328
$859$	−10894.1	−0.432715	−0.216358	−	0.976314i	$-0.569418\pi$
$859$	−10894.1	−0.432715	−0.216358	+	0.976314i	$0.569418\pi$
$860$	0	0
$861$	716.880	0.0283754
$862$	−35756.2	−1.41283
$863$	48209.7	1.90160	0.950798	−	0.309811i	$-0.100266\pi$
$863$	48209.7	1.90160	0.950798	+	0.309811i	$0.100266\pi$
$864$	38096.4	1.50008
$865$	−12925.0	−0.508048
$866$	−33314.5	−1.30724
$867$	−9865.22	−0.386436
$868$	−51871.9	−2.02840
$869$	11906.2	0.464774
$870$	−7680.36	−0.299297
$871$	59127.8	2.30019
$872$	10001.1	0.388393
$873$	−2129.67	−0.0825639
$874$	−20089.7	−0.777512
$875$	39269.3	1.51719
$876$	10267.2	0.395999
$877$	14792.4	0.569558	0.284779	−	0.958593i	$-0.408080\pi$
$877$	14792.4	0.569558	0.284779	+	0.958593i	$0.408080\pi$
$878$	57340.2	2.20403
$879$	−10073.9	−0.386556
$880$	−4951.96	−0.189694
$881$	9682.56	0.370277	0.185138	−	0.982712i	$-0.440727\pi$
$881$	9682.56	0.370277	0.185138	+	0.982712i	$0.440727\pi$
$882$	−6743.92	−0.257460
$883$	−19920.4	−0.759201	−0.379601	−	0.925150i	$-0.623939\pi$
$883$	−19920.4	−0.759201	−0.379601	+	0.925150i	$0.623939\pi$
$884$	31248.3	1.18891
$885$	−29557.1	−1.12266
$886$	−63382.4	−2.40336
$887$	41838.2	1.58375	0.791876	−	0.610682i	$-0.209105\pi$
$887$	41838.2	1.58375	0.791876	+	0.610682i	$0.209105\pi$
$888$	−12629.9	−0.477286
$889$	15667.7	0.591089
$890$	35539.1	1.33851
$891$	9150.47	0.344054
$892$	19.0149	0.000713750 0
$893$	−43277.2	−1.62174
$894$	−10517.1	−0.393451
$895$	31105.5	1.16172
$896$	−24917.7	−0.929066
$897$	−17923.1	−0.667152
$898$	−20701.3	−0.769276
$899$	−10344.8	−0.383780
$900$	2712.26	0.100454
$901$	−5233.78	−0.193521
$902$	−332.780	−0.0122842
$903$	0	0
$904$	−7884.80	−0.290094
$905$	22815.2	0.838016
$906$	27714.7	1.01629
$907$	−35318.6	−1.29298	−0.646492	−	0.762921i	$-0.723765\pi$
$907$	−35318.6	−1.29298	−0.646492	+	0.762921i	$0.723765\pi$
$908$	479.124	0.0175113
$909$	−5865.97	−0.214040
$910$	49474.1	1.80225
$911$	1355.47	0.0492959	0.0246480	−	0.999696i	$-0.492154\pi$
$911$	1355.47	0.0492959	0.0246480	+	0.999696i	$0.492154\pi$
$912$	17761.7	0.644898
$913$	11780.7	0.427036
$914$	35402.8	1.28120
$915$	−24479.4	−0.884443
$916$	16465.5	0.593924
$917$	−7118.89	−0.256365
$918$	33391.6	1.20053
$919$	10499.0	0.376854	0.188427	−	0.982087i	$-0.439661\pi$
$919$	10499.0	0.376854	0.188427	+	0.982087i	$0.439661\pi$
$920$	−3089.60	−0.110719
$921$	1900.37	0.0679905
$922$	−74488.2	−2.66067
$923$	−25130.7	−0.896194
$924$	−19402.1	−0.690781
$925$	27784.0	0.987602
$926$	41611.7	1.47672
$927$	−5000.99	−0.177189
$928$	−13867.5	−0.490543
$929$	31511.5	1.11287	0.556436	−	0.830890i	$-0.312168\pi$
$929$	31511.5	1.11287	0.556436	+	0.830890i	$0.312168\pi$
$930$	27312.6	0.963028
$931$	−33642.2	−1.18430
$932$	36807.9	1.29365
$933$	10396.1	0.364793
$934$	23718.0	0.830918
$935$	−5580.30	−0.195182
$936$	1583.88	0.0553105
$937$	−5299.66	−0.184773	−0.0923864	−	0.995723i	$-0.529450\pi$
$937$	−5299.66	−0.184773	−0.0923864	+	0.995723i	$0.529450\pi$
$938$	−115326.	−4.01442
$939$	−29083.7	−1.01077
$940$	−38022.1	−1.31930
$941$	34588.6	1.19825	0.599126	−	0.800655i	$-0.295515\pi$
$941$	34588.6	1.19825	0.599126	+	0.800655i	$0.295515\pi$
$942$	−57862.2	−2.00133
$943$	328.553	0.0113459
$944$	−41509.8	−1.43118
$945$	28969.1	0.997213
$946$	0	0
$947$	−17342.1	−0.595083	−0.297541	−	0.954709i	$-0.596167\pi$
$947$	−17342.1	−0.595083	−0.297541	+	0.954709i	$0.596167\pi$
$948$	−37519.4	−1.28541
$949$	−13189.7	−0.451166
$950$	24692.0	0.843279
$951$	−30708.0	−1.04708
$952$	−10668.7	−0.363210
$953$	−53043.0	−1.80297	−0.901485	−	0.432810i	$-0.857522\pi$
$953$	−53043.0	−1.80297	−0.901485	+	0.432810i	$0.857522\pi$
$954$	−1515.51	−0.0514324
$955$	−15749.3	−0.533650
$956$	−28608.5	−0.967850
$957$	−3869.35	−0.130698
$958$	−70129.1	−2.36510
$959$	−29769.7	−1.00241
$960$	23740.1	0.798133
$961$	6996.75	0.234861
$962$	92690.1	3.10650
$963$	−2269.35	−0.0759384
$964$	−39548.8	−1.32135
$965$	7154.34	0.238659
$966$	34958.2	1.16435
$967$	4560.36	0.151656	0.0758280	−	0.997121i	$-0.475840\pi$
$967$	4560.36	0.151656	0.0758280	+	0.997121i	$0.475840\pi$
$968$	−7928.27	−0.263248
$969$	20015.4	0.663557
$970$	−17033.9	−0.563840
$971$	−27229.5	−0.899934	−0.449967	−	0.893045i	$-0.648564\pi$
$971$	−27229.5	−0.899934	−0.449967	+	0.893045i	$0.648564\pi$
$972$	9959.78	0.328663
$973$	−13278.7	−0.437508
$974$	69035.3	2.27108
$975$	22029.0	0.723583
$976$	−34378.8	−1.12750
$977$	31182.6	1.02110	0.510552	−	0.859847i	$-0.329441\pi$
$977$	31182.6	1.02110	0.510552	+	0.859847i	$0.329441\pi$
$978$	−41583.0	−1.35959
$979$	17904.5	0.584506
$980$	−29557.1	−0.963436
$981$	−5164.09	−0.168070
$982$	13343.6	0.433617
$983$	−28454.7	−0.923259	−0.461630	−	0.887073i	$-0.652735\pi$
$983$	−28454.7	−0.923259	−0.461630	+	0.887073i	$0.652735\pi$
$984$	183.566	0.00594702
$985$	−14201.5	−0.459388
$986$	−12154.9	−0.392588
$987$	75306.7	2.42861
$988$	45138.1	1.45348
$989$	0	0
$990$	−1615.85	−0.0518739
$991$	−40487.4	−1.29781	−0.648903	−	0.760871i	$-0.724772\pi$
$991$	−40487.4	−1.29781	−0.648903	+	0.760871i	$0.724772\pi$
$992$	49315.1	1.57838
$993$	33722.6	1.07770
$994$	49016.2	1.56409
$995$	16405.2	0.522692
$996$	−37124.0	−1.18104
$997$	−3912.73	−0.124290	−0.0621451	−	0.998067i	$-0.519794\pi$
$997$	−3912.73	−0.124290	−0.0621451	+	0.998067i	$0.519794\pi$
$998$	45848.9	1.45423
$999$	54273.9	1.71887

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.44	✓	50
43.42	odd	2		1849.4.a.j.1.7	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.44	✓	50	1.1	even	1	trivial
1849.4.a.j.1.7	yes	50	43.42	odd	2

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+4.20684 q^{2} +4.82832 q^{3} +9.69750 q^{4} -7.01067 q^{5} +20.3120 q^{6} +27.8882 q^{7} +7.14112 q^{8} -3.68734 q^{9} +O(q^{10})\)	\(q+4.20684 q^{2} +4.82832 q^{3} +9.69750 q^{4} -7.01067 q^{5} +20.3120 q^{6} +27.8882 q^{7} +7.14112 q^{8} -3.68734 q^{9} -29.4928 q^{10} -14.8584 q^{11} +46.8226 q^{12} -60.1508 q^{13} +117.321 q^{14} -33.8498 q^{15} -47.5385 q^{16} -53.5705 q^{17} -15.5121 q^{18} -77.3824 q^{19} -67.9860 q^{20} +134.653 q^{21} -62.5069 q^{22} +61.7129 q^{23} +34.4796 q^{24} -75.8505 q^{25} -253.045 q^{26} -148.168 q^{27} +270.446 q^{28} +53.9349 q^{29} -142.401 q^{30} -191.801 q^{31} -257.116 q^{32} -71.7411 q^{33} -225.363 q^{34} -195.515 q^{35} -35.7580 q^{36} -366.299 q^{37} -325.536 q^{38} -290.427 q^{39} -50.0641 q^{40} +5.32390 q^{41} +566.465 q^{42} -144.089 q^{44} +25.8508 q^{45} +259.616 q^{46} +559.264 q^{47} -229.531 q^{48} +434.753 q^{49} -319.091 q^{50} -258.655 q^{51} -583.312 q^{52} +97.6988 q^{53} -623.320 q^{54} +104.167 q^{55} +199.153 q^{56} -373.627 q^{57} +226.896 q^{58} +873.184 q^{59} -328.258 q^{60} +723.179 q^{61} -806.878 q^{62} -102.833 q^{63} -701.337 q^{64} +421.697 q^{65} -301.803 q^{66} -982.993 q^{67} -519.500 q^{68} +297.970 q^{69} -822.501 q^{70} +417.795 q^{71} -26.3318 q^{72} +219.278 q^{73} -1540.96 q^{74} -366.230 q^{75} -750.416 q^{76} -414.374 q^{77} -1221.78 q^{78} -801.309 q^{79} +333.277 q^{80} -615.845 q^{81} +22.3968 q^{82} -792.865 q^{83} +1305.80 q^{84} +375.565 q^{85} +260.415 q^{87} -106.106 q^{88} -1205.01 q^{89} +108.750 q^{90} -1677.50 q^{91} +598.461 q^{92} -926.078 q^{93} +2352.73 q^{94} +542.503 q^{95} -1241.44 q^{96} +577.561 q^{97} +1828.94 q^{98} +54.7880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * q^99

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