LMFDB - Embedded newform 1849.4.a.g.1.4

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:	$30$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-4.74823 q^{2} -6.58177 q^{3} +14.5457 q^{4} -7.24018 q^{5} +31.2517 q^{6} -6.49418 q^{7} -31.0804 q^{8} +16.3197 q^{9} +O(q^{10})$	\(q-4.74823 q^{2} -6.58177 q^{3} +14.5457 q^{4} -7.24018 q^{5} +31.2517 q^{6} -6.49418 q^{7} -31.0804 q^{8} +16.3197 q^{9} +34.3780 q^{10} +63.8849 q^{11} -95.7363 q^{12} +67.6680 q^{13} +30.8358 q^{14} +47.6532 q^{15} +31.2114 q^{16} -4.27273 q^{17} -77.4895 q^{18} +112.723 q^{19} -105.313 q^{20} +42.7432 q^{21} -303.340 q^{22} -98.2257 q^{23} +204.564 q^{24} -72.5798 q^{25} -321.303 q^{26} +70.2955 q^{27} -94.4623 q^{28} -287.907 q^{29} -226.268 q^{30} -91.1434 q^{31} +100.444 q^{32} -420.475 q^{33} +20.2879 q^{34} +47.0190 q^{35} +237.381 q^{36} +207.629 q^{37} -535.234 q^{38} -445.375 q^{39} +225.028 q^{40} +243.390 q^{41} -202.954 q^{42} +929.249 q^{44} -118.157 q^{45} +466.398 q^{46} -75.5686 q^{47} -205.426 q^{48} -300.826 q^{49} +344.626 q^{50} +28.1221 q^{51} +984.277 q^{52} +144.812 q^{53} -333.779 q^{54} -462.538 q^{55} +201.842 q^{56} -741.915 q^{57} +1367.05 q^{58} -180.475 q^{59} +693.148 q^{60} -566.438 q^{61} +432.770 q^{62} -105.983 q^{63} -726.623 q^{64} -489.928 q^{65} +1996.51 q^{66} +67.9387 q^{67} -62.1498 q^{68} +646.499 q^{69} -223.257 q^{70} +81.1601 q^{71} -507.222 q^{72} +592.386 q^{73} -985.871 q^{74} +477.703 q^{75} +1639.63 q^{76} -414.880 q^{77} +2114.74 q^{78} -646.997 q^{79} -225.976 q^{80} -903.300 q^{81} -1155.67 q^{82} -528.693 q^{83} +621.729 q^{84} +30.9353 q^{85} +1894.94 q^{87} -1985.57 q^{88} -493.314 q^{89} +561.038 q^{90} -439.448 q^{91} -1428.76 q^{92} +599.884 q^{93} +358.817 q^{94} -816.133 q^{95} -661.100 q^{96} +211.431 q^{97} +1428.39 q^{98} +1042.58 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} + 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} - 80 q^{18} - 254 q^{19} - 312 q^{20} - 548 q^{21} - 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} - 549 q^{26} + 10 q^{27} - 578 q^{28} - 793 q^{29} - 1560 q^{30} - 359 q^{31} - 676 q^{32} - 208 q^{33} - 1007 q^{34} - 514 q^{35} + 776 q^{36} - 510 q^{37} - 2066 q^{38} - 898 q^{39} - 1248 q^{40} - 270 q^{41} + 915 q^{42} + 3256 q^{44} - 807 q^{45} - 1960 q^{46} + 1421 q^{47} + 632 q^{48} + 386 q^{49} + 141 q^{50} - 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} - 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} - 1759 q^{61} - 395 q^{62} - 2204 q^{63} + 222 q^{64} - 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} - 1660 q^{69} - 1597 q^{70} - 727 q^{71} - 9100 q^{72} - 4623 q^{73} - 2649 q^{74} - 1027 q^{75} - 874 q^{76} - 3556 q^{77} - 4979 q^{78} + 546 q^{79} - 5809 q^{80} - 410 q^{81} + 4397 q^{82} - 492 q^{83} - 10611 q^{84} + 1723 q^{85} + 5937 q^{87} - 3974 q^{88} - 5218 q^{89} + 10492 q^{90} - 1104 q^{91} + 1060 q^{92} - 1997 q^{93} + 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} - 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 + 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 - 80 * q^18 - 254 * q^19 - 312 * q^20 - 548 * q^21 - 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 - 549 * q^26 + 10 * q^27 - 578 * q^28 - 793 * q^29 - 1560 * q^30 - 359 * q^31 - 676 * q^32 - 208 * q^33 - 1007 * q^34 - 514 * q^35 + 776 * q^36 - 510 * q^37 - 2066 * q^38 - 898 * q^39 - 1248 * q^40 - 270 * q^41 + 915 * q^42 + 3256 * q^44 - 807 * q^45 - 1960 * q^46 + 1421 * q^47 + 632 * q^48 + 386 * q^49 + 141 * q^50 - 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 - 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 - 1759 * q^61 - 395 * q^62 - 2204 * q^63 + 222 * q^64 - 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 - 1660 * q^69 - 1597 * q^70 - 727 * q^71 - 9100 * q^72 - 4623 * q^73 - 2649 * q^74 - 1027 * q^75 - 874 * q^76 - 3556 * q^77 - 4979 * q^78 + 546 * q^79 - 5809 * q^80 - 410 * q^81 + 4397 * q^82 - 492 * q^83 - 10611 * q^84 + 1723 * q^85 + 5937 * q^87 - 3974 * q^88 - 5218 * q^89 + 10492 * q^90 - 1104 * q^91 + 1060 * q^92 - 1997 * q^93 + 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 - 6270 * q^98 - 2693 * 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 $

$2$	−4.74823	−1.67875	−0.839376	−	0.543551i	$-0.817080\pi$
$2$	−4.74823	−1.67875	−0.839376	+	0.543551i	$0.817080\pi$
$3$	−6.58177	−1.26666	−0.633331	−	0.773881i	$-0.718313\pi$
$3$	−6.58177	−1.26666	−0.633331	+	0.773881i	$0.718313\pi$
$4$	14.5457	1.81821
$5$	−7.24018	−0.647581	−0.323791	−	0.946129i	$-0.604957\pi$
$5$	−7.24018	−0.647581	−0.323791	+	0.946129i	$0.604957\pi$
$6$	31.2517	2.12641
$7$	−6.49418	−0.350653	−0.175326	−	0.984510i	$-0.556098\pi$
$7$	−6.49418	−0.350653	−0.175326	+	0.984510i	$0.556098\pi$
$8$	−31.0804	−1.37357
$9$	16.3197	0.604432
$10$	34.3780	1.08713
$11$	63.8849	1.75109	0.875546	−	0.483134i	$-0.160502\pi$
$11$	63.8849	1.75109	0.875546	+	0.483134i	$0.160502\pi$
$12$	−95.7363	−2.30306
$13$	67.6680	1.44367	0.721835	−	0.692065i	$-0.243299\pi$
$13$	67.6680	1.44367	0.721835	+	0.692065i	$0.243299\pi$
$14$	30.8358	0.588659
$15$	47.6532	0.820266
$16$	31.2114	0.487679
$17$	−4.27273	−0.0609582	−0.0304791	−	0.999535i	$-0.509703\pi$
$17$	−4.27273	−0.0609582	−0.0304791	+	0.999535i	$0.509703\pi$
$18$	−77.4895	−1.01469
$19$	112.723	1.36107	0.680536	−	0.732715i	$-0.261747\pi$
$19$	112.723	1.36107	0.680536	+	0.732715i	$0.261747\pi$
$20$	−105.313	−1.17744
$21$	42.7432	0.444158
$22$	−303.340	−2.93965
$23$	−98.2257	−0.890499	−0.445250	−	0.895407i	$-0.646885\pi$
$23$	−98.2257	−0.890499	−0.445250	+	0.895407i	$0.646885\pi$
$24$	204.564	1.73985
$25$	−72.5798	−0.580639
$26$	−321.303	−2.42357
$27$	70.2955	0.501051
$28$	−94.4623	−0.637560
$29$	−287.907	−1.84355	−0.921776	−	0.387722i	$-0.873262\pi$
$29$	−287.907	−1.84355	−0.921776	+	0.387722i	$0.873262\pi$
$30$	−226.268	−1.37702
$31$	−91.1434	−0.528059	−0.264030	−	0.964515i	$-0.585052\pi$
$31$	−91.1434	−0.528059	−0.264030	+	0.964515i	$0.585052\pi$
$32$	100.444	0.554881
$33$	−420.475	−2.21804
$34$	20.2879	0.102334
$35$	47.0190	0.227076
$36$	237.381	1.09898
$37$	207.629	0.922542	0.461271	−	0.887259i	$-0.347394\pi$
$37$	207.629	0.922542	0.461271	+	0.887259i	$0.347394\pi$
$38$	−535.234	−2.28490
$39$	−445.375	−1.82864
$40$	225.028	0.889500
$41$	243.390	0.927102	0.463551	−	0.886070i	$-0.346575\pi$
$41$	243.390	0.927102	0.463551	+	0.886070i	$0.346575\pi$
$42$	−202.954	−0.745632
$43$	0	0
$43$	0	0
$44$	929.249	3.18385
$45$	−118.157	−0.391419
$46$	466.398	1.49493
$47$	−75.5686	−0.234528	−0.117264	−	0.993101i	$-0.537412\pi$
$47$	−75.5686	−0.234528	−0.117264	+	0.993101i	$0.537412\pi$
$48$	−205.426	−0.617724
$49$	−300.826	−0.877043
$50$	344.626	0.974748
$51$	28.1221	0.0772134
$52$	984.277	2.62490
$53$	144.812	0.375309	0.187655	−	0.982235i	$-0.439911\pi$
$53$	144.812	0.375309	0.187655	+	0.982235i	$0.439911\pi$
$54$	−333.779	−0.841141
$55$	−462.538	−1.13397
$56$	201.842	0.481647
$57$	−741.915	−1.72402
$58$	1367.05	3.09487
$59$	−180.475	−0.398235	−0.199118	−	0.979976i	$-0.563808\pi$
$59$	−180.475	−0.398235	−0.199118	+	0.979976i	$0.563808\pi$
$60$	693.148	1.49142
$61$	−566.438	−1.18893	−0.594466	−	0.804120i	$-0.702637\pi$
$61$	−566.438	−1.18893	−0.594466	+	0.804120i	$0.702637\pi$
$62$	432.770	0.886481
$63$	−105.983	−0.211946
$64$	−726.623	−1.41919
$65$	−489.928	−0.934894
$66$	1996.51	3.72354
$67$	67.9387	0.123881	0.0619406	−	0.998080i	$-0.480271\pi$
$67$	67.9387	0.123881	0.0619406	+	0.998080i	$0.480271\pi$
$68$	−62.1498	−0.110835
$69$	646.499	1.12796
$70$	−223.257	−0.381205
$71$	81.1601	0.135661	0.0678305	−	0.997697i	$-0.478392\pi$
$71$	81.1601	0.135661	0.0678305	+	0.997697i	$0.478392\pi$
$72$	−507.222	−0.830231
$73$	592.386	0.949775	0.474887	−	0.880047i	$-0.342489\pi$
$73$	592.386	0.949775	0.474887	+	0.880047i	$0.342489\pi$
$74$	−985.871	−1.54872
$75$	477.703	0.735473
$76$	1639.63	2.47472
$77$	−414.880	−0.614025
$78$	2114.74	3.06984
$79$	−646.997	−0.921429	−0.460715	−	0.887548i	$-0.652407\pi$
$79$	−646.997	−0.921429	−0.460715	+	0.887548i	$0.652407\pi$
$80$	−225.976	−0.315812
$81$	−903.300	−1.23909
$82$	−1155.67	−1.55637
$83$	−528.693	−0.699176	−0.349588	−	0.936904i	$-0.613678\pi$
$83$	−528.693	−0.699176	−0.349588	+	0.936904i	$0.613678\pi$
$84$	621.729	0.807573
$85$	30.9353	0.0394754
$86$	0	0
$87$	1894.94	2.33516
$88$	−1985.57	−2.40525
$89$	−493.314	−0.587542	−0.293771	−	0.955876i	$-0.594910\pi$
$89$	−493.314	−0.587542	−0.293771	+	0.955876i	$0.594910\pi$
$90$	561.038	0.657095
$91$	−439.448	−0.506227
$92$	−1428.76	−1.61911
$93$	599.884	0.668872
$94$	358.817	0.393715
$95$	−816.133	−0.881405
$96$	−661.100	−0.702846
$97$	211.431	0.221315	0.110657	−	0.993859i	$-0.464704\pi$
$97$	211.431	0.221315	0.110657	+	0.993859i	$0.464704\pi$
$98$	1428.39	1.47234
$99$	1042.58	1.05842
$100$	−1055.72	−1.05572
$101$	−1669.39	−1.64465	−0.822327	−	0.569015i	$-0.807324\pi$
$101$	−1669.39	−1.64465	−0.822327	+	0.569015i	$0.807324\pi$
$102$	−133.530	−0.129622
$103$	1218.81	1.16595	0.582977	−	0.812488i	$-0.301888\pi$
$103$	1218.81	1.16595	0.582977	+	0.812488i	$0.301888\pi$
$104$	−2103.15	−1.98299
$105$	−309.468	−0.287629
$106$	−687.598	−0.630052
$107$	35.7551	0.0323044	0.0161522	−	0.999870i	$-0.494858\pi$
$107$	35.7551	0.0323044	0.0161522	+	0.999870i	$0.494858\pi$
$108$	1022.50	0.911016
$109$	−258.041	−0.226751	−0.113375	−	0.993552i	$-0.536166\pi$
$109$	−258.041	−0.226751	−0.113375	+	0.993552i	$0.536166\pi$
$110$	2196.24	1.90366
$111$	−1366.57	−1.16855
$112$	−202.693	−0.171006
$113$	1259.75	1.04874	0.524369	−	0.851491i	$-0.324301\pi$
$113$	1259.75	1.04874	0.524369	+	0.851491i	$0.324301\pi$
$114$	3522.78	2.89420
$115$	711.172	0.576670
$116$	−4187.81	−3.35197
$117$	1104.32	0.872601
$118$	856.938	0.668539
$119$	27.7479	0.0213751
$120$	−1481.08	−1.12670
$121$	2750.28	2.06633
$122$	2689.58	1.99592
$123$	−1601.94	−1.17432
$124$	−1325.74	−0.960123
$125$	1430.51	1.02359
$126$	503.231	0.355804
$127$	2322.04	1.62242	0.811210	−	0.584755i	$-0.198809\pi$
$127$	2322.04	1.62242	0.811210	+	0.584755i	$0.198809\pi$
$128$	2646.62	1.82758
$129$	0	0
$130$	2326.29	1.56946
$131$	309.265	0.206264	0.103132	−	0.994668i	$-0.467114\pi$
$131$	309.265	0.206264	0.103132	+	0.994668i	$0.467114\pi$
$132$	−6116.10	−4.03287
$133$	−732.042	−0.477264
$134$	−322.589	−0.207966
$135$	−508.952	−0.324471
$136$	132.798	0.0837305
$137$	−2618.68	−1.63306	−0.816531	−	0.577302i	$-0.804105\pi$
$137$	−2618.68	−1.63306	−0.816531	+	0.577302i	$0.804105\pi$
$138$	−3069.72	−1.89357
$139$	2572.53	1.56978	0.784888	−	0.619638i	$-0.212721\pi$
$139$	2572.53	1.56978	0.784888	+	0.619638i	$0.212721\pi$
$140$	683.924	0.412872
$141$	497.375	0.297068
$142$	−385.367	−0.227741
$143$	4322.96	2.52800
$144$	509.360	0.294769
$145$	2084.50	1.19385
$146$	−2812.79	−1.59444
$147$	1979.96	1.11092
$148$	3020.11	1.67738
$149$	820.215	0.450971	0.225485	−	0.974247i	$-0.427603\pi$
$149$	820.215	0.450971	0.225485	+	0.974247i	$0.427603\pi$
$150$	−2268.25	−1.23468
$151$	−16.1628	−0.00871065	−0.00435533	−	0.999991i	$-0.501386\pi$
$151$	−16.1628	−0.00871065	−0.00435533	+	0.999991i	$0.501386\pi$
$152$	−3503.47	−1.86953
$153$	−69.7295	−0.0368451
$154$	1969.94	1.03080
$155$	659.894	0.341961
$156$	−6478.28	−3.32486
$157$	554.588	0.281917	0.140958	−	0.990016i	$-0.454982\pi$
$157$	554.588	0.281917	0.140958	+	0.990016i	$0.454982\pi$
$158$	3072.09	1.54685
$159$	−953.116	−0.475390
$160$	−727.234	−0.359330
$161$	637.895	0.312256
$162$	4289.07	2.08013
$163$	−3179.80	−1.52798	−0.763992	−	0.645226i	$-0.776763\pi$
$163$	−3179.80	−1.52798	−0.763992	+	0.645226i	$0.776763\pi$
$164$	3540.28	1.68567
$165$	3044.32	1.43636
$166$	2510.36	1.17374
$167$	440.782	0.204244	0.102122	−	0.994772i	$-0.467437\pi$
$167$	440.782	0.204244	0.102122	+	0.994772i	$0.467437\pi$
$168$	−1328.48	−0.610084
$169$	2381.96	1.08419
$170$	−146.888	−0.0662694
$171$	1839.60	0.822675
$172$	0	0
$173$	282.197	0.124018	0.0620088	−	0.998076i	$-0.480249\pi$
$173$	282.197	0.124018	0.0620088	+	0.998076i	$0.480249\pi$
$174$	−8997.60	−3.92015
$175$	471.346	0.203602
$176$	1993.94	0.853971
$177$	1187.85	0.504429
$178$	2342.37	0.986337
$179$	−2784.23	−1.16259	−0.581294	−	0.813694i	$-0.697453\pi$
$179$	−2784.23	−1.16259	−0.581294	+	0.813694i	$0.697453\pi$
$180$	−1718.68	−0.711682
$181$	−2484.38	−1.02024	−0.510118	−	0.860104i	$-0.670398\pi$
$181$	−2484.38	−1.02024	−0.510118	+	0.860104i	$0.670398\pi$
$182$	2086.60	0.849830
$183$	3728.16	1.50598
$184$	3052.90	1.22317
$185$	−1503.27	−0.597421
$186$	−2848.39	−1.12287
$187$	−272.963	−0.106743
$188$	−1099.20	−0.426421
$189$	−456.512	−0.175695
$190$	3875.19	1.47966
$191$	31.0465	0.0117615	0.00588076	−	0.999983i	$-0.498128\pi$
$191$	31.0465	0.0117615	0.00588076	+	0.999983i	$0.498128\pi$
$192$	4782.47	1.79763
$193$	1186.28	0.442436	0.221218	−	0.975224i	$-0.428997\pi$
$193$	1186.28	0.442436	0.221218	+	0.975224i	$0.428997\pi$
$194$	−1003.92	−0.371533
$195$	3224.59	1.18419
$196$	−4375.71	−1.59465
$197$	−3163.67	−1.14417	−0.572087	−	0.820193i	$-0.693866\pi$
$197$	−3163.67	−1.14417	−0.572087	+	0.820193i	$0.693866\pi$
$198$	−4950.41	−1.77682
$199$	1772.71	0.631479	0.315739	−	0.948846i	$-0.397747\pi$
$199$	1772.71	0.631479	0.315739	+	0.948846i	$0.397747\pi$
$200$	2255.81	0.797549
$201$	−447.157	−0.156915
$202$	7926.62	2.76097
$203$	1869.72	0.646447
$204$	409.055	0.140390
$205$	−1762.19	−0.600374
$206$	−5787.21	−1.95735
$207$	−1603.01	−0.538246
$208$	2112.02	0.704048
$209$	7201.28	2.38336
$210$	1469.43	0.482857
$211$	−2020.89	−0.659354	−0.329677	−	0.944094i	$-0.606940\pi$
$211$	−2020.89	−0.659354	−0.329677	+	0.944094i	$0.606940\pi$
$212$	2106.38	0.682391
$213$	−534.177	−0.171837
$214$	−169.773	−0.0542312
$215$	0	0
$216$	−2184.81	−0.688230
$217$	591.901	0.185165
$218$	1225.24	0.380659
$219$	−3898.95	−1.20304
$220$	−6727.93	−2.06180
$221$	−289.127	−0.0880035
$222$	6488.78	1.96170
$223$	4291.97	1.28884	0.644421	−	0.764671i	$-0.277098\pi$
$223$	4291.97	1.28884	0.644421	+	0.764671i	$0.277098\pi$
$224$	−652.302	−0.194570
$225$	−1184.48	−0.350956
$226$	−5981.59	−1.76057
$227$	569.427	0.166494	0.0832472	−	0.996529i	$-0.473471\pi$
$227$	569.427	0.166494	0.0832472	+	0.996529i	$0.473471\pi$
$228$	−10791.7	−3.13463
$229$	1652.86	0.476961	0.238480	−	0.971147i	$-0.423351\pi$
$229$	1652.86	0.476961	0.238480	+	0.971147i	$0.423351\pi$
$230$	−3376.81	−0.968087
$231$	2730.64	0.777762
$232$	8948.27	2.53225
$233$	6231.43	1.75208	0.876040	−	0.482239i	$-0.160176\pi$
$233$	6231.43	1.75208	0.876040	+	0.482239i	$0.160176\pi$
$234$	−5243.56	−1.46488
$235$	547.130	0.151876
$236$	−2625.14	−0.724076
$237$	4258.39	1.16714
$238$	−131.753	−0.0358836
$239$	−4606.82	−1.24682	−0.623411	−	0.781895i	$-0.714254\pi$
$239$	−4606.82	−1.24682	−0.623411	+	0.781895i	$0.714254\pi$
$240$	1487.32	0.400027
$241$	−2896.25	−0.774125	−0.387062	−	0.922053i	$-0.626510\pi$
$241$	−2896.25	−0.774125	−0.387062	+	0.922053i	$0.626510\pi$
$242$	−13059.0	−3.46885
$243$	4047.33	1.06846
$244$	−8239.22	−2.16173
$245$	2178.03	0.567956
$246$	7606.37	1.97140
$247$	7627.72	1.96494
$248$	2832.77	0.725328
$249$	3479.73	0.885619
$250$	−6792.40	−1.71836
$251$	5056.33	1.27153	0.635763	−	0.771885i	$-0.280686\pi$
$251$	5056.33	1.27153	0.635763	+	0.771885i	$0.280686\pi$
$252$	−1541.59	−0.385362
$253$	−6275.14	−1.55935
$254$	−11025.6	−2.72364
$255$	−203.609	−0.0500019
$256$	−6753.78	−1.64887
$257$	−4682.42	−1.13650	−0.568251	−	0.822855i	$-0.692380\pi$
$257$	−4682.42	−1.13650	−0.568251	+	0.822855i	$0.692380\pi$
$258$	0	0
$259$	−1348.38	−0.323492
$260$	−7126.34	−1.69983
$261$	−4698.55	−1.11430
$262$	−1468.46	−0.346267
$263$	−642.893	−0.150732	−0.0753659	−	0.997156i	$-0.524012\pi$
$263$	−642.893	−0.150732	−0.0753659	+	0.997156i	$0.524012\pi$
$264$	13068.5	3.04664
$265$	−1048.46	−0.243043
$266$	3475.90	0.801208
$267$	3246.88	0.744216
$268$	988.215	0.225242
$269$	−543.876	−0.123274	−0.0616370	−	0.998099i	$-0.519632\pi$
$269$	−543.876	−0.123274	−0.0616370	+	0.998099i	$0.519632\pi$
$270$	2416.62	0.544707
$271$	6641.35	1.48868	0.744342	−	0.667799i	$-0.232763\pi$
$271$	6641.35	1.48868	0.744342	+	0.667799i	$0.232763\pi$
$272$	−133.358	−0.0297280
$273$	2892.34	0.641218
$274$	12434.1	2.74151
$275$	−4636.75	−1.01675
$276$	9403.77	2.05087
$277$	−4025.89	−0.873257	−0.436629	−	0.899642i	$-0.643828\pi$
$277$	−4025.89	−0.873257	−0.436629	+	0.899642i	$0.643828\pi$
$278$	−12214.9	−2.63526
$279$	−1487.43	−0.319176
$280$	−1461.37	−0.311906
$281$	−3681.56	−0.781578	−0.390789	−	0.920480i	$-0.627798\pi$
$281$	−3681.56	−0.781578	−0.390789	+	0.920480i	$0.627798\pi$
$282$	−2361.65	−0.498703
$283$	−6040.04	−1.26870	−0.634352	−	0.773044i	$-0.718733\pi$
$283$	−6040.04	−1.26870	−0.634352	+	0.773044i	$0.718733\pi$
$284$	1180.53	0.246660
$285$	5371.60	1.11644
$286$	−20526.4	−4.24389
$287$	−1580.62	−0.325091
$288$	1639.21	0.335388
$289$	−4894.74	−0.996284
$290$	−9897.68	−2.00418
$291$	−1391.59	−0.280331
$292$	8616.66	1.72689
$293$	−2862.10	−0.570669	−0.285334	−	0.958428i	$-0.592105\pi$
$293$	−2862.10	−0.570669	−0.285334	+	0.958428i	$0.592105\pi$
$294$	−9401.33	−1.86495
$295$	1306.67	0.257890
$296$	−6453.20	−1.26718
$297$	4490.82	0.877387
$298$	−3894.57	−0.757069
$299$	−6646.74	−1.28559
$300$	6948.52	1.33724
$301$	0	0
$302$	76.7446	0.0146230
$303$	10987.5	2.08322
$304$	3518.24	0.663766
$305$	4101.11	0.769931
$306$	331.092	0.0618538
$307$	2900.09	0.539143	0.269572	−	0.962980i	$-0.413118\pi$
$307$	2900.09	0.539143	0.269572	+	0.962980i	$0.413118\pi$
$308$	−6034.71	−1.11643
$309$	−8021.95	−1.47687
$310$	−3133.33	−0.574068
$311$	4730.83	0.862574	0.431287	−	0.902215i	$-0.358060\pi$
$311$	4730.83	0.862574	0.431287	+	0.902215i	$0.358060\pi$
$312$	13842.4	2.51177
$313$	−3318.29	−0.599236	−0.299618	−	0.954059i	$-0.596859\pi$
$313$	−3318.29	−0.599236	−0.299618	+	0.954059i	$0.596859\pi$
$314$	−2633.31	−0.473268
$315$	767.334	0.137252
$316$	−9411.02	−1.67535
$317$	−3347.86	−0.593169	−0.296584	−	0.955007i	$-0.595848\pi$
$317$	−3347.86	−0.593169	−0.296584	+	0.955007i	$0.595848\pi$
$318$	4525.61	0.798062
$319$	−18392.9	−3.22823
$320$	5260.88	0.919039
$321$	−235.332	−0.0409188
$322$	−3028.87	−0.524200
$323$	−481.634	−0.0829685
$324$	−13139.1	−2.25293
$325$	−4911.33	−0.838251
$326$	15098.4	2.56511
$327$	1698.37	0.287217
$328$	−7564.67	−1.27344
$329$	490.756	0.0822379
$330$	−14455.1	−2.41130
$331$	−5076.71	−0.843025	−0.421512	−	0.906823i	$-0.638501\pi$
$331$	−5076.71	−0.843025	−0.421512	+	0.906823i	$0.638501\pi$
$332$	−7690.20	−1.27125
$333$	3388.44	0.557614
$334$	−2092.93	−0.342875
$335$	−491.888	−0.0802231
$336$	1334.08	0.216607
$337$	9191.45	1.48573	0.742863	−	0.669443i	$-0.233467\pi$
$337$	9191.45	1.48573	0.742863	+	0.669443i	$0.233467\pi$
$338$	−11310.1	−1.82008
$339$	−8291.39	−1.32840
$340$	449.975	0.0717745
$341$	−5822.68	−0.924680
$342$	−8734.83	−1.38107
$343$	4181.12	0.658190
$344$	0	0
$345$	−4680.77	−0.730446
$346$	−1339.94	−0.208195
$347$	8691.55	1.34463	0.672315	−	0.740265i	$-0.265300\pi$
$347$	8691.55	1.34463	0.672315	+	0.740265i	$0.265300\pi$
$348$	27563.2	4.24581
$349$	767.904	0.117779	0.0588896	−	0.998265i	$-0.481244\pi$
$349$	767.904	0.117779	0.0588896	+	0.998265i	$0.481244\pi$
$350$	−2238.06	−0.341798
$351$	4756.76	0.723353
$352$	6416.86	0.971648
$353$	2423.53	0.365415	0.182708	−	0.983167i	$-0.441514\pi$
$353$	2423.53	0.365415	0.182708	+	0.983167i	$0.441514\pi$
$354$	−5640.17	−0.846812
$355$	−587.614	−0.0878515
$356$	−7175.59	−1.06827
$357$	−182.630	−0.0270751
$358$	13220.2	1.95170
$359$	−12942.6	−1.90274	−0.951370	−	0.308049i	$-0.900324\pi$
$359$	−12942.6	−1.90274	−0.951370	+	0.308049i	$0.900324\pi$
$360$	3672.38	0.537642
$361$	5847.42	0.852518
$362$	11796.4	1.71272
$363$	−18101.7	−2.61733
$364$	−6392.07	−0.920427
$365$	−4288.98	−0.615056
$366$	−17702.2	−2.52816
$367$	−2315.29	−0.329311	−0.164656	−	0.986351i	$-0.552651\pi$
$367$	−2315.29	−0.329311	−0.164656	+	0.986351i	$0.552651\pi$
$368$	−3065.77	−0.434278
$369$	3972.05	0.560370
$370$	7137.89	1.00292
$371$	−940.432	−0.131603
$372$	8725.73	1.21615
$373$	6372.81	0.884643	0.442321	−	0.896857i	$-0.354155\pi$
$373$	6372.81	0.884643	0.442321	+	0.896857i	$0.354155\pi$
$374$	1296.09	0.179196
$375$	−9415.30	−1.29654
$376$	2348.70	0.322141
$377$	−19482.1	−2.66148
$378$	2167.62	0.294948
$379$	−4188.97	−0.567739	−0.283870	−	0.958863i	$-0.591618\pi$
$379$	−4188.97	−0.567739	−0.283870	+	0.958863i	$0.591618\pi$
$380$	−11871.2	−1.60258
$381$	−15283.1	−2.05506
$382$	−147.416	−0.0197447
$383$	−8286.83	−1.10558	−0.552790	−	0.833321i	$-0.686437\pi$
$383$	−8286.83	−1.10558	−0.552790	+	0.833321i	$0.686437\pi$
$384$	−17419.4	−2.31493
$385$	3003.80	0.397631
$386$	−5632.72	−0.742741
$387$	0	0
$388$	3075.40	0.402397
$389$	4363.81	0.568776	0.284388	−	0.958709i	$-0.408210\pi$
$389$	4363.81	0.568776	0.284388	+	0.958709i	$0.408210\pi$
$390$	−15311.1	−1.98797
$391$	419.692	0.0542832
$392$	9349.78	1.20468
$393$	−2035.51	−0.261267
$394$	15021.8	1.92079
$395$	4684.38	0.596700
$396$	15165.0	1.92442
$397$	−9604.63	−1.21421	−0.607107	−	0.794620i	$-0.707670\pi$
$397$	−9604.63	−1.21421	−0.607107	+	0.794620i	$0.707670\pi$
$398$	−8417.25	−1.06010
$399$	4818.13	0.604532
$400$	−2265.32	−0.283165
$401$	1601.76	0.199471	0.0997357	−	0.995014i	$-0.468200\pi$
$401$	1601.76	0.199471	0.0997357	+	0.995014i	$0.468200\pi$
$402$	2123.20	0.263422
$403$	−6167.49	−0.762344
$404$	−24282.3	−2.99033
$405$	6540.05	0.802414
$406$	−8877.86	−1.08522
$407$	13264.4	1.61546
$408$	−874.047	−0.106058
$409$	12589.9	1.52208	0.761038	−	0.648707i	$-0.224690\pi$
$409$	12589.9	1.52208	0.761038	+	0.648707i	$0.224690\pi$
$410$	8367.28	1.00788
$411$	17235.6	2.06854
$412$	17728.5	2.11995
$413$	1172.04	0.139642
$414$	7611.46	0.903582
$415$	3827.83	0.452773
$416$	6796.85	0.801065
$417$	−16931.8	−1.98837
$418$	−34193.3	−4.00108
$419$	−6913.96	−0.806131	−0.403066	−	0.915171i	$-0.632055\pi$
$419$	−6913.96	−0.806131	−0.403066	+	0.915171i	$0.632055\pi$
$420$	−4501.43	−0.522969
$421$	1405.50	0.162708	0.0813540	−	0.996685i	$-0.474076\pi$
$421$	1405.50	0.162708	0.0813540	+	0.996685i	$0.474076\pi$
$422$	9595.64	1.10689
$423$	−1233.25	−0.141756
$424$	−4500.80	−0.515515
$425$	310.114	0.0353947
$426$	2536.39	0.288471
$427$	3678.55	0.416902
$428$	520.082	0.0587363
$429$	−28452.7	−3.20212
$430$	0	0
$431$	4118.99	0.460336	0.230168	−	0.973151i	$-0.426072\pi$
$431$	4118.99	0.460336	0.230168	+	0.973151i	$0.426072\pi$
$432$	2194.02	0.244352
$433$	4335.08	0.481133	0.240567	−	0.970633i	$-0.422667\pi$
$433$	4335.08	0.481133	0.240567	+	0.970633i	$0.422667\pi$
$434$	−2810.48	−0.310847
$435$	−13719.7	−1.51220
$436$	−3753.38	−0.412281
$437$	−11072.3	−1.21203
$438$	18513.1	2.01961
$439$	8430.37	0.916537	0.458269	−	0.888814i	$-0.348470\pi$
$439$	8430.37	0.916537	0.458269	+	0.888814i	$0.348470\pi$
$440$	14375.9	1.55760
$441$	−4909.37	−0.530113
$442$	1372.84	0.147736
$443$	−10373.8	−1.11258	−0.556291	−	0.830988i	$-0.687776\pi$
$443$	−10373.8	−1.11258	−0.556291	+	0.830988i	$0.687776\pi$
$444$	−19877.7	−2.12467
$445$	3571.68	0.380481
$446$	−20379.3	−2.16365
$447$	−5398.47	−0.571228
$448$	4718.82	0.497642
$449$	4314.17	0.453449	0.226724	−	0.973959i	$-0.427198\pi$
$449$	4314.17	0.453449	0.226724	+	0.973959i	$0.427198\pi$
$450$	5624.17	0.589169
$451$	15549.0	1.62344
$452$	18323.9	1.90683
$453$	106.380	0.0110335
$454$	−2703.77	−0.279503
$455$	3181.68	0.327823
$456$	23059.0	2.36806
$457$	−8985.13	−0.919708	−0.459854	−	0.887995i	$-0.652098\pi$
$457$	−8985.13	−0.919708	−0.459854	+	0.887995i	$0.652098\pi$
$458$	−7848.16	−0.800699
$459$	−300.354	−0.0305432
$460$	10344.5	1.04851
$461$	−5953.29	−0.601458	−0.300729	−	0.953710i	$-0.597230\pi$
$461$	−5953.29	−0.601458	−0.300729	+	0.953710i	$0.597230\pi$
$462$	−12965.7	−1.30567
$463$	345.099	0.0346395	0.0173198	−	0.999850i	$-0.494487\pi$
$463$	345.099	0.0346395	0.0173198	+	0.999850i	$0.494487\pi$
$464$	−8986.00	−0.899062
$465$	−4343.27	−0.433149
$466$	−29588.3	−2.94131
$467$	−14107.1	−1.39786	−0.698930	−	0.715190i	$-0.746340\pi$
$467$	−14107.1	−1.39786	−0.698930	+	0.715190i	$0.746340\pi$
$468$	16063.1	1.58657
$469$	−441.206	−0.0434393
$470$	−2597.90	−0.254962
$471$	−3650.17	−0.357093
$472$	5609.25	0.547005
$473$	0	0
$474$	−20219.8	−1.95934
$475$	−8181.40	−0.790291
$476$	403.612	0.0388645
$477$	2363.27	0.226849
$478$	21874.2	2.09310
$479$	−20351.8	−1.94133	−0.970665	−	0.240437i	$-0.922709\pi$
$479$	−20351.8	−1.94133	−0.970665	+	0.240437i	$0.922709\pi$
$480$	4786.48	0.455150
$481$	14049.9	1.33185
$482$	13752.1	1.29956
$483$	−4198.48	−0.395523
$484$	40004.7	3.75701
$485$	−1530.80	−0.143319
$486$	−19217.6	−1.79368
$487$	−2038.26	−0.189655	−0.0948277	−	0.995494i	$-0.530230\pi$
$487$	−2038.26	−0.189655	−0.0948277	+	0.995494i	$0.530230\pi$
$488$	17605.1	1.63309
$489$	20928.7	1.93544
$490$	−10341.8	−0.953458
$491$	640.439	0.0588648	0.0294324	−	0.999567i	$-0.490630\pi$
$491$	640.439	0.0588648	0.0294324	+	0.999567i	$0.490630\pi$
$492$	−23301.3	−2.13517
$493$	1230.15	0.112380
$494$	−36218.2	−3.29865
$495$	−7548.46	−0.685410
$496$	−2844.72	−0.257523
$497$	−527.068	−0.0475699
$498$	−16522.6	−1.48674
$499$	−2228.98	−0.199966	−0.0999830	−	0.994989i	$-0.531879\pi$
$499$	−2228.98	−0.199966	−0.0999830	+	0.994989i	$0.531879\pi$
$500$	20807.8	1.86111
$501$	−2901.12	−0.258708
$502$	−24008.6	−2.13458
$503$	−5212.32	−0.462039	−0.231020	−	0.972949i	$-0.574206\pi$
$503$	−5212.32	−0.462039	−0.231020	+	0.972949i	$0.574206\pi$
$504$	3293.99	0.291123
$505$	12086.6	1.06505
$506$	29795.8	2.61776
$507$	−15677.5	−1.37330
$508$	33775.6	2.94990
$509$	14963.8	1.30306	0.651530	−	0.758623i	$-0.274127\pi$
$509$	14963.8	1.30306	0.651530	+	0.758623i	$0.274127\pi$
$510$	966.783	0.0839409
$511$	−3847.06	−0.333041
$512$	10895.5	0.940466
$513$	7923.90	0.681967
$514$	22233.2	1.90791
$515$	−8824.43	−0.755050
$516$	0	0
$517$	−4827.69	−0.410680
$518$	6402.43	0.543063
$519$	−1857.35	−0.157088
$520$	15227.2	1.28415
$521$	67.1640	0.00564781	0.00282391	−	0.999996i	$-0.499101\pi$
$521$	67.1640	0.00564781	0.00282391	+	0.999996i	$0.499101\pi$
$522$	22309.8	1.87064
$523$	17636.9	1.47458	0.737291	−	0.675576i	$-0.236105\pi$
$523$	17636.9	1.47458	0.737291	+	0.675576i	$0.236105\pi$
$524$	4498.47	0.375032
$525$	−3102.29	−0.257895
$526$	3052.60	0.253042
$527$	389.431	0.0321895
$528$	−13123.6	−1.08169
$529$	−2518.71	−0.207012
$530$	4978.34	0.408010
$531$	−2945.30	−0.240706
$532$	−10648.0	−0.867766
$533$	16469.7	1.33843
$534$	−15416.9	−1.24936
$535$	−258.873	−0.0209197
$536$	−2111.56	−0.170160
$537$	18325.2	1.47261
$538$	2582.45	0.206947
$539$	−19218.2	−1.53578
$540$	−7403.06	−0.589957
$541$	19780.6	1.57197	0.785984	−	0.618246i	$-0.212157\pi$
$541$	19780.6	1.57197	0.785984	+	0.618246i	$0.212157\pi$
$542$	−31534.6	−2.49913
$543$	16351.6	1.29229
$544$	−429.171	−0.0338245
$545$	1868.26	0.146840
$546$	−13733.5	−1.07645
$547$	22001.4	1.71977	0.859883	−	0.510491i	$-0.170536\pi$
$547$	22001.4	1.71977	0.859883	+	0.510491i	$0.170536\pi$
$548$	−38090.6	−2.96925
$549$	−9244.07	−0.718629
$550$	22016.4	1.70687
$551$	−32453.7	−2.50921
$552$	−20093.4	−1.54934
$553$	4201.72	0.323102
$554$	19115.8	1.46598
$555$	9894.19	0.756730
$556$	37419.2	2.85418
$557$	6514.58	0.495569	0.247784	−	0.968815i	$-0.420298\pi$
$557$	6514.58	0.495569	0.247784	+	0.968815i	$0.420298\pi$
$558$	7062.65	0.535817
$559$	0	0
$560$	1467.53	0.110740
$561$	1796.58	0.135208
$562$	17480.9	1.31208
$563$	−7032.80	−0.526460	−0.263230	−	0.964733i	$-0.584788\pi$
$563$	−7032.80	−0.526460	−0.263230	+	0.964733i	$0.584788\pi$
$564$	7234.66	0.540132
$565$	−9120.82	−0.679143
$566$	28679.5	2.12984
$567$	5866.19	0.434492
$568$	−2522.49	−0.186340
$569$	9441.10	0.695591	0.347796	−	0.937570i	$-0.386930\pi$
$569$	9441.10	0.695591	0.347796	+	0.937570i	$0.386930\pi$
$570$	−25505.6	−1.87423
$571$	1305.28	0.0956641	0.0478321	−	0.998855i	$-0.484769\pi$
$571$	1305.28	0.0956641	0.0478321	+	0.998855i	$0.484769\pi$
$572$	62880.4	4.59644
$573$	−204.341	−0.0148979
$574$	7505.15	0.545747
$575$	7129.20	0.517058
$576$	−11858.2	−0.857801
$577$	−5550.58	−0.400475	−0.200237	−	0.979747i	$-0.564171\pi$
$577$	−5550.58	−0.400475	−0.200237	+	0.979747i	$0.564171\pi$
$578$	23241.4	1.67251
$579$	−7807.81	−0.560417
$580$	30320.5	2.17067
$581$	3433.43	0.245168
$582$	6607.57	0.470606
$583$	9251.27	0.657201
$584$	−18411.6	−1.30458
$585$	−7995.46	−0.565080
$586$	13589.9	0.958011
$587$	9223.44	0.648539	0.324269	−	0.945965i	$-0.394882\pi$
$587$	9223.44	0.648539	0.324269	+	0.945965i	$0.394882\pi$
$588$	28799.9	2.01988
$589$	−10273.9	−0.718727
$590$	−6204.39	−0.432933
$591$	20822.6	1.44928
$592$	6480.41	0.449904
$593$	3764.33	0.260679	0.130339	−	0.991469i	$-0.458393\pi$
$593$	3764.33	0.260679	0.130339	+	0.991469i	$0.458393\pi$
$594$	−21323.4	−1.47292
$595$	−200.900	−0.0138421
$596$	11930.6	0.819960
$597$	−11667.6	−0.799870
$598$	31560.2	2.15818
$599$	−23710.7	−1.61735	−0.808675	−	0.588255i	$-0.799815\pi$
$599$	−23710.7	−1.61735	−0.808675	+	0.588255i	$0.799815\pi$
$600$	−14847.2	−1.01023
$601$	21266.2	1.44337	0.721685	−	0.692222i	$-0.243368\pi$
$601$	21266.2	1.44337	0.721685	+	0.692222i	$0.243368\pi$
$602$	0	0
$603$	1108.74	0.0748777
$604$	−235.099	−0.0158378
$605$	−19912.5	−1.33811
$606$	−52171.2	−3.49721
$607$	−18432.9	−1.23257	−0.616285	−	0.787523i	$-0.711363\pi$
$607$	−18432.9	−1.23257	−0.616285	+	0.787523i	$0.711363\pi$
$608$	11322.3	0.755233
$609$	−12306.1	−0.818829
$610$	−19473.0	−1.29252
$611$	−5113.58	−0.338581
$612$	−1014.26	−0.0669921
$613$	−23073.4	−1.52027	−0.760134	−	0.649766i	$-0.774867\pi$
$613$	−23073.4	−1.52027	−0.760134	+	0.649766i	$0.774867\pi$
$614$	−13770.3	−0.905089
$615$	11598.3	0.760470
$616$	12894.6	0.843409
$617$	−12367.5	−0.806962	−0.403481	−	0.914988i	$-0.632200\pi$
$617$	−12367.5	−0.806962	−0.403481	+	0.914988i	$0.632200\pi$
$618$	38090.1	2.47930
$619$	3347.45	0.217359	0.108680	−	0.994077i	$-0.465338\pi$
$619$	3347.45	0.217359	0.108680	+	0.994077i	$0.465338\pi$
$620$	9598.61	0.621757
$621$	−6904.83	−0.446185
$622$	−22463.0	−1.44805
$623$	3203.67	0.206023
$624$	−13900.8	−0.891790
$625$	−1284.69	−0.0822204
$626$	15756.0	1.00597
$627$	−47397.2	−3.01892
$628$	8066.86	0.512584
$629$	−887.144	−0.0562365
$630$	−3643.48	−0.230412
$631$	3670.98	0.231600	0.115800	−	0.993273i	$-0.463057\pi$
$631$	3670.98	0.231600	0.115800	+	0.993273i	$0.463057\pi$
$632$	20108.9	1.26565
$633$	13301.0	0.835178
$634$	15896.4	0.995784
$635$	−16812.0	−1.05065
$636$	−13863.7	−0.864359
$637$	−20356.3	−1.26616
$638$	87333.8	5.41940
$639$	1324.50	0.0819978
$640$	−19162.0	−1.18351
$641$	−25091.3	−1.54610	−0.773049	−	0.634346i	$-0.781269\pi$
$641$	−25091.3	−1.54610	−0.773049	+	0.634346i	$0.781269\pi$
$642$	1117.41	0.0686925
$643$	−15567.4	−0.954769	−0.477385	−	0.878694i	$-0.658415\pi$
$643$	−15567.4	−0.954769	−0.477385	+	0.878694i	$0.658415\pi$
$644$	9278.62	0.567747
$645$	0	0
$646$	2286.91	0.139284
$647$	−9506.90	−0.577674	−0.288837	−	0.957378i	$-0.593269\pi$
$647$	−9506.90	−0.577674	−0.288837	+	0.957378i	$0.593269\pi$
$648$	28074.9	1.70199
$649$	−11529.6	−0.697347
$650$	23320.1	1.40722
$651$	−3895.76	−0.234542
$652$	−46252.4	−2.77820
$653$	−18453.6	−1.10589	−0.552946	−	0.833217i	$-0.686496\pi$
$653$	−18453.6	−1.10589	−0.552946	+	0.833217i	$0.686496\pi$
$654$	−8064.23	−0.482166
$655$	−2239.13	−0.133573
$656$	7596.56	0.452128
$657$	9667.54	0.574074
$658$	−2330.22	−0.138057
$659$	10596.8	0.626390	0.313195	−	0.949689i	$-0.398601\pi$
$659$	10596.8	0.626390	0.313195	+	0.949689i	$0.398601\pi$
$660$	44281.7	2.61161
$661$	8247.27	0.485297	0.242649	−	0.970114i	$-0.421984\pi$
$661$	8247.27	0.485297	0.242649	+	0.970114i	$0.421984\pi$
$662$	24105.4	1.41523
$663$	1902.97	0.111471
$664$	16432.0	0.960369
$665$	5300.11	0.309067
$666$	−16089.1	−0.936095
$667$	28279.9	1.64168
$668$	6411.47	0.371358
$669$	−28248.8	−1.63253
$670$	2335.60	0.134675
$671$	−36186.8	−2.08193
$672$	4293.30	0.246455
$673$	19322.9	1.10675	0.553376	−	0.832931i	$-0.313339\pi$
$673$	19322.9	1.10675	0.553376	+	0.832931i	$0.313339\pi$
$674$	−43643.1	−2.49417
$675$	−5102.04	−0.290930
$676$	34647.2	1.97128
$677$	−17905.7	−1.01650	−0.508251	−	0.861209i	$-0.669708\pi$
$677$	−17905.7	−1.01650	−0.508251	+	0.861209i	$0.669708\pi$
$678$	39369.4	2.23005
$679$	−1373.07	−0.0776046
$680$	−961.483	−0.0542223
$681$	−3747.84	−0.210892
$682$	27647.4	1.55231
$683$	−21734.2	−1.21762	−0.608811	−	0.793315i	$-0.708353\pi$
$683$	−21734.2	−1.21762	−0.608811	+	0.793315i	$0.708353\pi$
$684$	26758.2	1.49580
$685$	18959.7	1.05754
$686$	−19852.9	−1.10494
$687$	−10878.7	−0.604148
$688$	0	0
$689$	9799.10	0.541823
$690$	22225.4	1.22624
$691$	−6021.45	−0.331500	−0.165750	−	0.986168i	$-0.553005\pi$
$691$	−6021.45	−0.331500	−0.165750	+	0.986168i	$0.553005\pi$
$692$	4104.75	0.225490
$693$	−6770.70	−0.371136
$694$	−41269.5	−2.25730
$695$	−18625.5	−1.01656
$696$	−58895.4	−3.20751
$697$	−1039.94	−0.0565144
$698$	−3646.18	−0.197722
$699$	−41013.8	−2.21929
$700$	6856.05	0.370192
$701$	18652.9	1.00501	0.502505	−	0.864574i	$-0.332412\pi$
$701$	18652.9	1.00501	0.502505	+	0.864574i	$0.332412\pi$
$702$	−22586.2	−1.21433
$703$	23404.5	1.25565
$704$	−46420.3	−2.48513
$705$	−3601.09	−0.192375
$706$	−11507.5	−0.613441
$707$	10841.3	0.576702
$708$	17278.0	0.917159
$709$	10478.4	0.555042	0.277521	−	0.960720i	$-0.410487\pi$
$709$	10478.4	0.555042	0.277521	+	0.960720i	$0.410487\pi$
$710$	2790.12	0.147481
$711$	−10558.8	−0.556941
$712$	15332.4	0.807031
$713$	8952.62	0.470236
$714$	867.169	0.0454524
$715$	−31299.0	−1.63709
$716$	−40498.6	−2.11383
$717$	30321.0	1.57930
$718$	61454.4	3.19423
$719$	13693.3	0.710256	0.355128	−	0.934818i	$-0.384437\pi$
$719$	13693.3	0.710256	0.355128	+	0.934818i	$0.384437\pi$
$720$	−3687.86	−0.190887
$721$	−7915.20	−0.408845
$722$	−27764.9	−1.43117
$723$	19062.5	0.980554
$724$	−36137.1	−1.85500
$725$	20896.2	1.07044
$726$	85951.0	4.39386
$727$	5502.74	0.280723	0.140361	−	0.990100i	$-0.455174\pi$
$727$	5502.74	0.280723	0.140361	+	0.990100i	$0.455174\pi$
$728$	13658.2	0.695340
$729$	−2249.48	−0.114286
$730$	20365.1	1.03253
$731$	0	0
$732$	54228.6	2.73818
$733$	4607.00	0.232146	0.116073	−	0.993241i	$-0.462969\pi$
$733$	4607.00	0.232146	0.116073	+	0.993241i	$0.462969\pi$
$734$	10993.5	0.552832
$735$	−14335.3	−0.719409
$736$	−9866.20	−0.494121
$737$	4340.26	0.216927
$738$	−18860.2	−0.940722
$739$	−13068.6	−0.650522	−0.325261	−	0.945624i	$-0.605452\pi$
$739$	−13068.6	−0.650522	−0.325261	+	0.945624i	$0.605452\pi$
$740$	−21866.1	−1.08624
$741$	−50203.9	−2.48891
$742$	4465.39	0.220929
$743$	−8692.14	−0.429184	−0.214592	−	0.976704i	$-0.568842\pi$
$743$	−8692.14	−0.429184	−0.214592	+	0.976704i	$0.568842\pi$
$744$	−18644.7	−0.918745
$745$	−5938.51	−0.292040
$746$	−30259.6	−1.48510
$747$	−8628.09	−0.422604
$748$	−3970.43	−0.194082
$749$	−232.200	−0.0113276
$750$	44706.0	2.17658
$751$	−3244.62	−0.157654	−0.0788269	−	0.996888i	$-0.525117\pi$
$751$	−3244.62	−0.157654	−0.0788269	+	0.996888i	$0.525117\pi$
$752$	−2358.61	−0.114374
$753$	−33279.6	−1.61059
$754$	92505.5	4.46797
$755$	117.021	0.00564086
$756$	−6640.27	−0.319450
$757$	6586.93	0.316256	0.158128	−	0.987419i	$-0.449454\pi$
$757$	6586.93	0.316256	0.158128	+	0.987419i	$0.449454\pi$
$758$	19890.2	0.953094
$759$	41301.5	1.97516
$760$	25365.7	1.21067
$761$	11201.2	0.533567	0.266783	−	0.963757i	$-0.414039\pi$
$761$	11201.2	0.533567	0.266783	+	0.963757i	$0.414039\pi$
$762$	72567.6	3.44993
$763$	1675.77	0.0795108
$764$	451.593	0.0213849
$765$	504.854	0.0238602
$766$	39347.8	1.85600
$767$	−12212.4	−0.574921
$768$	44451.8	2.08856
$769$	−12780.1	−0.599300	−0.299650	−	0.954049i	$-0.596870\pi$
$769$	−12780.1	−0.599300	−0.299650	+	0.954049i	$0.596870\pi$
$770$	−14262.8	−0.667525
$771$	30818.6	1.43956
$772$	17255.2	0.804442
$773$	31109.7	1.44753	0.723764	−	0.690048i	$-0.242410\pi$
$773$	31109.7	1.44753	0.723764	+	0.690048i	$0.242410\pi$
$774$	0	0
$775$	6615.17	0.306611
$776$	−6571.35	−0.303992
$777$	8874.73	0.409755
$778$	−20720.4	−0.954834
$779$	27435.6	1.26185
$780$	46903.9	2.15312
$781$	5184.90	0.237555
$782$	−1992.79	−0.0911281
$783$	−20238.6	−0.923714
$784$	−9389.20	−0.427715
$785$	−4015.32	−0.182564
$786$	9665.07	0.438603
$787$	−22971.4	−1.04046	−0.520231	−	0.854026i	$-0.674154\pi$
$787$	−22971.4	−1.04046	−0.520231	+	0.854026i	$0.674154\pi$
$788$	−46017.8	−2.08035
$789$	4231.37	0.190926
$790$	−22242.5	−1.00171
$791$	−8181.05	−0.367743
$792$	−32403.8	−1.45381
$793$	−38329.7	−1.71643
$794$	45605.0	2.03836
$795$	6900.73	0.307854
$796$	25785.3	1.14816
$797$	−16610.9	−0.738254	−0.369127	−	0.929379i	$-0.620343\pi$
$797$	−16610.9	−0.738254	−0.369127	+	0.929379i	$0.620343\pi$
$798$	−22877.6	−1.01486
$799$	322.884	0.0142964
$800$	−7290.22	−0.322185
$801$	−8050.72	−0.355129
$802$	−7605.52	−0.334863
$803$	37844.5	1.66314
$804$	−6504.20	−0.285305
$805$	−4618.48	−0.202211
$806$	29284.6	1.27979
$807$	3579.67	0.156146
$808$	51885.2	2.25905
$809$	8141.77	0.353831	0.176916	−	0.984226i	$-0.443388\pi$
$809$	8141.77	0.353831	0.176916	+	0.984226i	$0.443388\pi$
$810$	−31053.7	−1.34705
$811$	−13994.0	−0.605914	−0.302957	−	0.953004i	$-0.597974\pi$
$811$	−13994.0	−0.605914	−0.302957	+	0.953004i	$0.597974\pi$
$812$	27196.4	1.17538
$813$	−43711.8	−1.88566
$814$	−62982.3	−2.71195
$815$	23022.3	0.989493
$816$	877.732	0.0376553
$817$	0	0
$818$	−59779.6	−2.55519
$819$	−7171.64	−0.305980
$820$	−25632.2	−1.09161
$821$	−24401.3	−1.03728	−0.518642	−	0.854992i	$-0.673562\pi$
$821$	−24401.3	−1.03728	−0.518642	+	0.854992i	$0.673562\pi$
$822$	−81838.5	−3.47256
$823$	−9375.31	−0.397087	−0.198544	−	0.980092i	$-0.563621\pi$
$823$	−9375.31	−0.397087	−0.198544	+	0.980092i	$0.563621\pi$
$824$	−37881.2	−1.60152
$825$	30518.0	1.28788
$826$	−5565.11	−0.234425
$827$	26212.7	1.10218	0.551091	−	0.834445i	$-0.314212\pi$
$827$	26212.7	1.10218	0.551091	+	0.834445i	$0.314212\pi$
$828$	−23316.9	−0.978644
$829$	28984.2	1.21431	0.607156	−	0.794583i	$-0.292310\pi$
$829$	28984.2	1.21431	0.607156	+	0.794583i	$0.292310\pi$
$830$	−18175.4	−0.760094
$831$	26497.5	1.10612
$832$	−49169.1	−2.04884
$833$	1285.35	0.0534629
$834$	80395.9	3.33799
$835$	−3191.34	−0.132264
$836$	104748.	4.33346
$837$	−6406.97	−0.264585
$838$	32829.1	1.35329
$839$	−31470.6	−1.29498	−0.647489	−	0.762075i	$-0.724181\pi$
$839$	−31470.6	−1.29498	−0.647489	+	0.762075i	$0.724181\pi$
$840$	9618.40	0.395079
$841$	58501.5	2.39869
$842$	−6673.65	−0.273146
$843$	24231.2	0.989995
$844$	−29395.2	−1.19884
$845$	−17245.8	−0.702098
$846$	5855.78	0.237974
$847$	−17860.8	−0.724562
$848$	4519.78	0.183030
$849$	39754.2	1.60702
$850$	−1472.49	−0.0594189
$851$	−20394.5	−0.821522
$852$	−7769.97	−0.312435
$853$	46234.0	1.85583	0.927915	−	0.372793i	$-0.121600\pi$
$853$	46234.0	1.85583	0.927915	+	0.372793i	$0.121600\pi$
$854$	−17466.6	−0.699876
$855$	−13319.0	−0.532749
$856$	−1111.28	−0.0443725
$857$	27028.8	1.07735	0.538674	−	0.842515i	$-0.318926\pi$
$857$	27028.8	1.07735	0.538674	+	0.842515i	$0.318926\pi$
$858$	135100.	5.37557
$859$	−19051.6	−0.756730	−0.378365	−	0.925656i	$-0.623514\pi$
$859$	−19051.6	−0.756730	−0.378365	+	0.925656i	$0.623514\pi$
$860$	0	0
$861$	10403.3	0.411780
$862$	−19557.9	−0.772791
$863$	−28038.8	−1.10597	−0.552985	−	0.833191i	$-0.686511\pi$
$863$	−28038.8	−1.10597	−0.552985	+	0.833191i	$0.686511\pi$
$864$	7060.77	0.278024
$865$	−2043.16	−0.0803115
$866$	−20584.0	−0.807703
$867$	32216.1	1.26195
$868$	8609.61	0.336670
$869$	−41333.4	−1.61351
$870$	65144.2	2.53862
$871$	4597.28	0.178844
$872$	8020.02	0.311459
$873$	3450.48	0.133770
$874$	52573.7	2.03470
$875$	−9290.01	−0.358925
$876$	−56712.9	−2.18739
$877$	−34554.2	−1.33046	−0.665229	−	0.746639i	$-0.731666\pi$
$877$	−34554.2	−1.33046	−0.665229	+	0.746639i	$0.731666\pi$
$878$	−40029.4	−1.53864
$879$	18837.7	0.722844
$880$	−14436.5	−0.553016
$881$	−30894.5	−1.18145	−0.590727	−	0.806872i	$-0.701159\pi$
$881$	−30894.5	−1.18145	−0.590727	+	0.806872i	$0.701159\pi$
$882$	23310.8	0.889928
$883$	47950.9	1.82749	0.913747	−	0.406283i	$-0.133175\pi$
$883$	47950.9	1.82749	0.913747	+	0.406283i	$0.133175\pi$
$884$	−4205.55	−0.160009
$885$	−8600.22	−0.326659
$886$	49257.1	1.86775
$887$	24322.7	0.920718	0.460359	−	0.887733i	$-0.347721\pi$
$887$	24322.7	0.920718	0.460359	+	0.887733i	$0.347721\pi$
$888$	42473.5	1.60509
$889$	−15079.7	−0.568906
$890$	−16959.2	−0.638733
$891$	−57707.2	−2.16977
$892$	62429.7	2.34339
$893$	−8518.31	−0.319210
$894$	25633.2	0.958950
$895$	20158.3	0.752870
$896$	−17187.6	−0.640847
$897$	43747.3	1.62840
$898$	−20484.7	−0.761228
$899$	26240.8	0.973505
$900$	−17229.0	−0.638113
$901$	−618.741	−0.0228782
$902$	−73830.0	−2.72536
$903$	0	0
$904$	−39153.6	−1.44052
$905$	17987.4	0.660686
$906$	−505.115	−0.0185224
$907$	15503.6	0.567573	0.283787	−	0.958887i	$-0.408409\pi$
$907$	15503.6	0.567573	0.283787	+	0.958887i	$0.408409\pi$
$908$	8282.71	0.302722
$909$	−27243.8	−0.994081
$910$	−15107.4	−0.550334
$911$	−37717.3	−1.37171	−0.685857	−	0.727737i	$-0.740572\pi$
$911$	−37717.3	−1.37171	−0.685857	+	0.727737i	$0.740572\pi$
$912$	−23156.2	−0.840767
$913$	−33775.5	−1.22432
$914$	42663.5	1.54396
$915$	−26992.5	−0.975242
$916$	24042.0	0.867215
$917$	−2008.42	−0.0723271
$918$	1426.15	0.0512744
$919$	12828.0	0.460454	0.230227	−	0.973137i	$-0.426053\pi$
$919$	12828.0	0.460454	0.230227	+	0.973137i	$0.426053\pi$
$920$	−22103.5	−0.792099
$921$	−19087.7	−0.682912
$922$	28267.6	1.00970
$923$	5491.94	0.195850
$924$	39719.1	1.41414
$925$	−15069.7	−0.535663
$926$	−1638.61	−0.0581512
$927$	19890.6	0.704740
$928$	−28918.6	−1.02295
$929$	24681.0	0.871643	0.435821	−	0.900033i	$-0.356458\pi$
$929$	24681.0	0.871643	0.435821	+	0.900033i	$0.356458\pi$
$930$	20622.8	0.727150
$931$	−33909.9	−1.19372
$932$	90640.4	3.18565
$933$	−31137.2	−1.09259
$934$	66984.0	2.34666
$935$	1976.30	0.0691250
$936$	−34322.7	−1.19858
$937$	55836.5	1.94674	0.973372	−	0.229230i	$-0.0736207\pi$
$937$	55836.5	1.94674	0.973372	+	0.229230i	$0.0736207\pi$
$938$	2094.95	0.0729238
$939$	21840.2	0.759030
$940$	7958.39	0.276143
$941$	49564.3	1.71706	0.858528	−	0.512767i	$-0.171380\pi$
$941$	49564.3	1.71706	0.858528	+	0.512767i	$0.171380\pi$
$942$	17331.8	0.599471
$943$	−23907.2	−0.825583
$944$	−5632.90	−0.194211
$945$	3305.23	0.113777
$946$	0	0
$947$	19299.3	0.662242	0.331121	−	0.943588i	$-0.392573\pi$
$947$	19299.3	0.662242	0.331121	+	0.943588i	$0.392573\pi$
$948$	61941.1	2.12210
$949$	40085.6	1.37116
$950$	38847.1	1.32670
$951$	22034.8	0.751344
$952$	−862.415	−0.0293603
$953$	−31138.6	−1.05842	−0.529212	−	0.848490i	$-0.677512\pi$
$953$	−31138.6	−1.05842	−0.529212	+	0.848490i	$0.677512\pi$
$954$	−11221.4	−0.380823
$955$	−224.783	−0.00761654
$956$	−67009.3	−2.26698
$957$	121058.	4.08908
$958$	96635.0	3.25901
$959$	17006.2	0.572637
$960$	−34625.9	−1.16411
$961$	−21483.9	−0.721154
$962$	−66711.9	−2.23584
$963$	583.511	0.0195258
$964$	−42128.0	−1.40752
$965$	−8588.87	−0.286513
$966$	19935.3	0.663984
$967$	30007.9	0.997921	0.498960	−	0.866625i	$-0.333715\pi$
$967$	30007.9	0.997921	0.498960	+	0.866625i	$0.333715\pi$
$968$	−85479.8	−2.83825
$969$	3170.00	0.105093
$970$	7268.57	0.240598
$971$	−1715.92	−0.0567111	−0.0283555	−	0.999598i	$-0.509027\pi$
$971$	−1715.92	−0.0567111	−0.0283555	+	0.999598i	$0.509027\pi$
$972$	58871.2	1.94269
$973$	−16706.4	−0.550446
$974$	9678.10	0.318384
$975$	32325.2	1.06178
$976$	−17679.3	−0.579817
$977$	−17093.8	−0.559754	−0.279877	−	0.960036i	$-0.590294\pi$
$977$	−17093.8	−0.559754	−0.279877	+	0.960036i	$0.590294\pi$
$978$	−99374.3	−3.24912
$979$	−31515.3	−1.02884
$980$	31681.0	1.03266
$981$	−4211.14	−0.137056
$982$	−3040.95	−0.0988194
$983$	1878.63	0.0609552	0.0304776	−	0.999535i	$-0.490297\pi$
$983$	1878.63	0.0609552	0.0304776	+	0.999535i	$0.490297\pi$
$984$	49788.9	1.61302
$985$	22905.6	0.740946
$986$	−5841.03	−0.188658
$987$	−3230.04	−0.104168
$988$	110950.	3.57268
$989$	0	0
$990$	35841.8	1.15063
$991$	−32633.9	−1.04606	−0.523032	−	0.852313i	$-0.675199\pi$
$991$	−32633.9	−1.04606	−0.523032	+	0.852313i	$0.675199\pi$
$992$	−9154.82	−0.293010
$993$	33413.7	1.06783
$994$	2502.64	0.0798581
$995$	−12834.8	−0.408934
$996$	50615.1	1.61024
$997$	−12726.6	−0.404269	−0.202135	−	0.979358i	$-0.564788\pi$
$997$	−12726.6	−0.404269	−0.202135	+	0.979358i	$0.564788\pi$
$998$	10583.7	0.335693
$999$	14595.4	0.462241

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.g.1.4		30
43.2	odd	14		43.4.e.a.4.10	✓	60
43.22	odd	14		43.4.e.a.11.10	yes	60
43.42	odd	2		1849.4.a.h.1.27		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.4.10	✓	60	43.2	odd	14
43.4.e.a.11.10	yes	60	43.22	odd	14
1849.4.a.g.1.4		30	1.1	even	1	trivial
1849.4.a.h.1.27		30	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)

\(f(q)\)	\(=\)	\(q-4.74823 q^{2} -6.58177 q^{3} +14.5457 q^{4} -7.24018 q^{5} +31.2517 q^{6} -6.49418 q^{7} -31.0804 q^{8} +16.3197 q^{9} +O(q^{10})\)	\(q-4.74823 q^{2} -6.58177 q^{3} +14.5457 q^{4} -7.24018 q^{5} +31.2517 q^{6} -6.49418 q^{7} -31.0804 q^{8} +16.3197 q^{9} +34.3780 q^{10} +63.8849 q^{11} -95.7363 q^{12} +67.6680 q^{13} +30.8358 q^{14} +47.6532 q^{15} +31.2114 q^{16} -4.27273 q^{17} -77.4895 q^{18} +112.723 q^{19} -105.313 q^{20} +42.7432 q^{21} -303.340 q^{22} -98.2257 q^{23} +204.564 q^{24} -72.5798 q^{25} -321.303 q^{26} +70.2955 q^{27} -94.4623 q^{28} -287.907 q^{29} -226.268 q^{30} -91.1434 q^{31} +100.444 q^{32} -420.475 q^{33} +20.2879 q^{34} +47.0190 q^{35} +237.381 q^{36} +207.629 q^{37} -535.234 q^{38} -445.375 q^{39} +225.028 q^{40} +243.390 q^{41} -202.954 q^{42} +929.249 q^{44} -118.157 q^{45} +466.398 q^{46} -75.5686 q^{47} -205.426 q^{48} -300.826 q^{49} +344.626 q^{50} +28.1221 q^{51} +984.277 q^{52} +144.812 q^{53} -333.779 q^{54} -462.538 q^{55} +201.842 q^{56} -741.915 q^{57} +1367.05 q^{58} -180.475 q^{59} +693.148 q^{60} -566.438 q^{61} +432.770 q^{62} -105.983 q^{63} -726.623 q^{64} -489.928 q^{65} +1996.51 q^{66} +67.9387 q^{67} -62.1498 q^{68} +646.499 q^{69} -223.257 q^{70} +81.1601 q^{71} -507.222 q^{72} +592.386 q^{73} -985.871 q^{74} +477.703 q^{75} +1639.63 q^{76} -414.880 q^{77} +2114.74 q^{78} -646.997 q^{79} -225.976 q^{80} -903.300 q^{81} -1155.67 q^{82} -528.693 q^{83} +621.729 q^{84} +30.9353 q^{85} +1894.94 q^{87} -1985.57 q^{88} -493.314 q^{89} +561.038 q^{90} -439.448 q^{91} -1428.76 q^{92} +599.884 q^{93} +358.817 q^{94} -816.133 q^{95} -661.100 q^{96} +211.431 q^{97} +1428.39 q^{98} +1042.58 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} + 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} - 80 q^{18} - 254 q^{19} - 312 q^{20} - 548 q^{21} - 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} - 549 q^{26} + 10 q^{27} - 578 q^{28} - 793 q^{29} - 1560 q^{30} - 359 q^{31} - 676 q^{32} - 208 q^{33} - 1007 q^{34} - 514 q^{35} + 776 q^{36} - 510 q^{37} - 2066 q^{38} - 898 q^{39} - 1248 q^{40} - 270 q^{41} + 915 q^{42} + 3256 q^{44} - 807 q^{45} - 1960 q^{46} + 1421 q^{47} + 632 q^{48} + 386 q^{49} + 141 q^{50} - 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} - 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} - 1759 q^{61} - 395 q^{62} - 2204 q^{63} + 222 q^{64} - 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} - 1660 q^{69} - 1597 q^{70} - 727 q^{71} - 9100 q^{72} - 4623 q^{73} - 2649 q^{74} - 1027 q^{75} - 874 q^{76} - 3556 q^{77} - 4979 q^{78} + 546 q^{79} - 5809 q^{80} - 410 q^{81} + 4397 q^{82} - 492 q^{83} - 10611 q^{84} + 1723 q^{85} + 5937 q^{87} - 3974 q^{88} - 5218 q^{89} + 10492 q^{90} - 1104 q^{91} + 1060 q^{92} - 1997 q^{93} + 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} - 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 + 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 - 80 * q^18 - 254 * q^19 - 312 * q^20 - 548 * q^21 - 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 - 549 * q^26 + 10 * q^27 - 578 * q^28 - 793 * q^29 - 1560 * q^30 - 359 * q^31 - 676 * q^32 - 208 * q^33 - 1007 * q^34 - 514 * q^35 + 776 * q^36 - 510 * q^37 - 2066 * q^38 - 898 * q^39 - 1248 * q^40 - 270 * q^41 + 915 * q^42 + 3256 * q^44 - 807 * q^45 - 1960 * q^46 + 1421 * q^47 + 632 * q^48 + 386 * q^49 + 141 * q^50 - 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 - 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 - 1759 * q^61 - 395 * q^62 - 2204 * q^63 + 222 * q^64 - 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 - 1660 * q^69 - 1597 * q^70 - 727 * q^71 - 9100 * q^72 - 4623 * q^73 - 2649 * q^74 - 1027 * q^75 - 874 * q^76 - 3556 * q^77 - 4979 * q^78 + 546 * q^79 - 5809 * q^80 - 410 * q^81 + 4397 * q^82 - 492 * q^83 - 10611 * q^84 + 1723 * q^85 + 5937 * q^87 - 3974 * q^88 - 5218 * q^89 + 10492 * q^90 - 1104 * q^91 + 1060 * q^92 - 1997 * q^93 + 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 - 6270 * q^98 - 2693 * q^99

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