LMFDB - Embedded newform 1849.4.a.g.1.5

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			1.5
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)

$f(q)$	$=$	$q-4.39566 q^{2} -7.85436 q^{3} +11.3218 q^{4} -5.85216 q^{5} +34.5251 q^{6} -12.3980 q^{7} -14.6016 q^{8} +34.6910 q^{9} +O(q^{10})$	\(q-4.39566 q^{2} -7.85436 q^{3} +11.3218 q^{4} -5.85216 q^{5} +34.5251 q^{6} -12.3980 q^{7} -14.6016 q^{8} +34.6910 q^{9} +25.7241 q^{10} +50.9011 q^{11} -88.9257 q^{12} -72.3797 q^{13} +54.4973 q^{14} +45.9650 q^{15} -26.3910 q^{16} +72.1180 q^{17} -152.490 q^{18} -47.7505 q^{19} -66.2570 q^{20} +97.3782 q^{21} -223.744 q^{22} +194.454 q^{23} +114.686 q^{24} -90.7523 q^{25} +318.156 q^{26} -60.4081 q^{27} -140.368 q^{28} -114.570 q^{29} -202.046 q^{30} -108.300 q^{31} +232.818 q^{32} -399.795 q^{33} -317.006 q^{34} +72.5549 q^{35} +392.765 q^{36} -19.4210 q^{37} +209.895 q^{38} +568.496 q^{39} +85.4507 q^{40} -485.191 q^{41} -428.041 q^{42} +576.293 q^{44} -203.017 q^{45} -854.753 q^{46} -20.2520 q^{47} +207.284 q^{48} -189.290 q^{49} +398.916 q^{50} -566.441 q^{51} -819.469 q^{52} +276.032 q^{53} +265.533 q^{54} -297.881 q^{55} +181.030 q^{56} +375.050 q^{57} +503.612 q^{58} -65.3849 q^{59} +520.407 q^{60} +330.113 q^{61} +476.051 q^{62} -430.098 q^{63} -812.262 q^{64} +423.577 q^{65} +1757.36 q^{66} -522.685 q^{67} +816.506 q^{68} -1527.31 q^{69} -318.927 q^{70} -155.769 q^{71} -506.544 q^{72} -543.223 q^{73} +85.3682 q^{74} +712.801 q^{75} -540.622 q^{76} -631.070 q^{77} -2498.91 q^{78} +1153.53 q^{79} +154.444 q^{80} -462.190 q^{81} +2132.73 q^{82} +781.141 q^{83} +1102.50 q^{84} -422.046 q^{85} +899.877 q^{87} -743.236 q^{88} -515.449 q^{89} +892.395 q^{90} +897.361 q^{91} +2201.57 q^{92} +850.630 q^{93} +89.0210 q^{94} +279.443 q^{95} -1828.64 q^{96} +901.767 q^{97} +832.055 q^{98} +1765.81 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.39566	−1.55410	−0.777050	−	0.629439i	$-0.783285\pi$
$2$	−4.39566	−1.55410	−0.777050	+	0.629439i	$0.783285\pi$
$3$	−7.85436	−1.51157	−0.755786	−	0.654818i	$-0.772745\pi$
$3$	−7.85436	−1.51157	−0.755786	+	0.654818i	$0.772745\pi$
$4$	11.3218	1.41523
$5$	−5.85216	−0.523433	−0.261716	−	0.965145i	$-0.584288\pi$
$5$	−5.85216	−0.523433	−0.261716	+	0.965145i	$0.584288\pi$
$6$	34.5251	2.34914
$7$	−12.3980	−0.669428	−0.334714	−	0.942320i	$-0.608640\pi$
$7$	−12.3980	−0.669428	−0.334714	+	0.942320i	$0.608640\pi$
$8$	−14.6016	−0.645305
$9$	34.6910	1.28485
$10$	25.7241	0.813467
$11$	50.9011	1.39520	0.697602	−	0.716485i	$-0.254250\pi$
$11$	50.9011	1.39520	0.697602	+	0.716485i	$0.254250\pi$
$12$	−88.9257	−2.13922
$13$	−72.3797	−1.54419	−0.772096	−	0.635506i	$-0.780792\pi$
$13$	−72.3797	−1.54419	−0.772096	+	0.635506i	$0.780792\pi$
$14$	54.4973	1.04036
$15$	45.9650	0.791207
$16$	−26.3910	−0.412359
$17$	72.1180	1.02889	0.514446	−	0.857523i	$-0.327997\pi$
$17$	72.1180	1.02889	0.514446	+	0.857523i	$0.327997\pi$
$18$	−152.490	−1.99679
$19$	−47.7505	−0.576564	−0.288282	−	0.957546i	$-0.593084\pi$
$19$	−47.7505	−0.576564	−0.288282	+	0.957546i	$0.593084\pi$
$20$	−66.2570	−0.740776
$21$	97.3782	1.01189
$22$	−223.744	−2.16829
$23$	194.454	1.76289	0.881444	−	0.472289i	$-0.156572\pi$
$23$	194.454	1.76289	0.881444	+	0.472289i	$0.156572\pi$
$24$	114.686	0.975425
$25$	−90.7523	−0.726018
$26$	318.156	2.39983
$27$	−60.4081	−0.430576
$28$	−140.368	−0.947392
$29$	−114.570	−0.733627	−0.366813	−	0.930295i	$-0.619551\pi$
$29$	−114.570	−0.733627	−0.366813	+	0.930295i	$0.619551\pi$
$30$	−202.046	−1.22961
$31$	−108.300	−0.627461	−0.313731	−	0.949512i	$-0.601579\pi$
$31$	−108.300	−0.627461	−0.313731	+	0.949512i	$0.601579\pi$
$32$	232.818	1.28615
$33$	−399.795	−2.10895
$34$	−317.006	−1.59900
$35$	72.5549	0.350400
$36$	392.765	1.81836
$37$	−19.4210	−0.0862918	−0.0431459	−	0.999069i	$-0.513738\pi$
$37$	−19.4210	−0.0862918	−0.0431459	+	0.999069i	$0.513738\pi$
$38$	209.895	0.896038
$39$	568.496	2.33416
$40$	85.4507	0.337774
$41$	−485.191	−1.84815	−0.924074	−	0.382214i	$-0.875162\pi$
$41$	−485.191	−1.84815	−0.924074	+	0.382214i	$0.875162\pi$
$42$	−428.041	−1.57258
$43$	0	0
$43$	0	0
$44$	576.293	1.97453
$45$	−203.017	−0.672534
$46$	−854.753	−2.73970
$47$	−20.2520	−0.0628523	−0.0314262	−	0.999506i	$-0.510005\pi$
$47$	−20.2520	−0.0628523	−0.0314262	+	0.999506i	$0.510005\pi$
$48$	207.284	0.623311
$49$	−189.290	−0.551866
$50$	398.916	1.12830
$51$	−566.441	−1.55525
$52$	−819.469	−2.18538
$53$	276.032	0.715396	0.357698	−	0.933837i	$-0.383562\pi$
$53$	276.032	0.715396	0.357698	+	0.933837i	$0.383562\pi$
$54$	265.533	0.669158
$55$	−297.881	−0.730296
$56$	181.030	0.431985
$57$	375.050	0.871519
$58$	503.612	1.14013
$59$	−65.3849	−0.144278	−0.0721389	−	0.997395i	$-0.522982\pi$
$59$	−65.3849	−0.144278	−0.0721389	+	0.997395i	$0.522982\pi$
$60$	520.407	1.11974
$61$	330.113	0.692896	0.346448	−	0.938069i	$-0.387388\pi$
$61$	330.113	0.692896	0.346448	+	0.938069i	$0.387388\pi$
$62$	476.051	0.975138
$63$	−430.098	−0.860116
$64$	−812.262	−1.58645
$65$	423.577	0.808281
$66$	1757.36	3.27752
$67$	−522.685	−0.953077	−0.476538	−	0.879154i	$-0.658109\pi$
$67$	−522.685	−0.953077	−0.476538	+	0.879154i	$0.658109\pi$
$68$	816.506	1.45612
$69$	−1527.31	−2.66473
$70$	−318.927	−0.544557
$71$	−155.769	−0.260371	−0.130185	−	0.991490i	$-0.541557\pi$
$71$	−155.769	−0.260371	−0.130185	+	0.991490i	$0.541557\pi$
$72$	−506.544	−0.829122
$73$	−543.223	−0.870951	−0.435476	−	0.900201i	$-0.643420\pi$
$73$	−543.223	−0.870951	−0.435476	+	0.900201i	$0.643420\pi$
$74$	85.3682	0.134106
$75$	712.801	1.09743
$76$	−540.622	−0.815969
$77$	−631.070	−0.933988
$78$	−2498.91	−3.62752
$79$	1153.53	1.64281	0.821407	−	0.570342i	$-0.193189\pi$
$79$	1153.53	1.64281	0.821407	+	0.570342i	$0.193189\pi$
$80$	154.444	0.215842
$81$	−462.190	−0.634006
$82$	2132.73	2.87221
$83$	781.141	1.03303	0.516514	−	0.856279i	$-0.327229\pi$
$83$	781.141	1.03303	0.516514	+	0.856279i	$0.327229\pi$
$84$	1102.50	1.43205
$85$	−422.046	−0.538556
$86$	0	0
$87$	899.877	1.10893
$88$	−743.236	−0.900332
$89$	−515.449	−0.613904	−0.306952	−	0.951725i	$-0.599309\pi$
$89$	−515.449	−0.613904	−0.306952	+	0.951725i	$0.599309\pi$
$90$	892.395	1.04519
$91$	897.361	1.03373
$92$	2201.57	2.49489
$93$	850.630	0.948454
$94$	89.0210	0.0976788
$95$	279.443	0.301792
$96$	−1828.64	−1.94411
$97$	901.767	0.943924	0.471962	−	0.881619i	$-0.343546\pi$
$97$	901.767	0.943924	0.471962	+	0.881619i	$0.343546\pi$
$98$	832.055	0.857656
$99$	1765.81	1.79263
$100$	−1027.48	−1.02748
$101$	−199.561	−0.196605	−0.0983024	−	0.995157i	$-0.531341\pi$
$101$	−199.561	−0.196605	−0.0983024	+	0.995157i	$0.531341\pi$
$102$	2489.88	2.41701
$103$	−881.273	−0.843052	−0.421526	−	0.906816i	$-0.638505\pi$
$103$	−881.273	−0.843052	−0.421526	+	0.906816i	$0.638505\pi$
$104$	1056.86	0.996475
$105$	−569.872	−0.529656
$106$	−1213.34	−1.11180
$107$	1495.28	1.35098	0.675488	−	0.737371i	$-0.263933\pi$
$107$	1495.28	1.35098	0.675488	+	0.737371i	$0.263933\pi$
$108$	−683.930	−0.609363
$109$	−760.930	−0.668660	−0.334330	−	0.942456i	$-0.608510\pi$
$109$	−760.930	−0.668660	−0.334330	+	0.942456i	$0.608510\pi$
$110$	1309.38	1.13495
$111$	152.540	0.130436
$112$	327.195	0.276045
$113$	1352.82	1.12621	0.563107	−	0.826384i	$-0.309606\pi$
$113$	1352.82	1.12621	0.563107	+	0.826384i	$0.309606\pi$
$114$	−1648.59	−1.35443
$115$	−1137.97	−0.922753
$116$	−1297.14	−1.03825
$117$	−2510.92	−1.98406
$118$	287.410	0.224222
$119$	−894.117	−0.688769
$120$	−671.161	−0.510570
$121$	1259.92	0.946595
$122$	−1451.06	−1.07683
$123$	3810.86	2.79361
$124$	−1226.16	−0.888000
$125$	1262.62	0.903454
$126$	1890.57	1.33671
$127$	229.260	0.160185	0.0800926	−	0.996787i	$-0.474478\pi$
$127$	229.260	0.160185	0.0800926	+	0.996787i	$0.474478\pi$
$128$	1707.88	1.17935
$129$	0	0
$130$	−1861.90	−1.25615
$131$	1670.22	1.11396	0.556978	−	0.830527i	$-0.311961\pi$
$131$	1670.22	1.11396	0.556978	+	0.830527i	$0.311961\pi$
$132$	−4526.41	−2.98465
$133$	592.010	0.385968
$134$	2297.55	1.48118
$135$	353.518	0.225377
$136$	−1053.04	−0.663949
$137$	2120.54	1.32241	0.661203	−	0.750207i	$-0.270046\pi$
$137$	2120.54	1.32241	0.661203	+	0.750207i	$0.270046\pi$
$138$	6713.54	4.14126
$139$	−546.720	−0.333613	−0.166806	−	0.985990i	$-0.553346\pi$
$139$	−546.720	−0.333613	−0.166806	+	0.985990i	$0.553346\pi$
$140$	821.453	0.495896
$141$	159.067	0.0950059
$142$	684.706	0.404642
$143$	−3684.20	−2.15446
$144$	−915.530	−0.529821
$145$	670.483	0.384004
$146$	2387.82	1.35355
$147$	1486.75	0.834186
$148$	−219.881	−0.122123
$149$	3202.06	1.76056	0.880280	−	0.474455i	$-0.157355\pi$
$149$	3202.06	1.76056	0.880280	+	0.474455i	$0.157355\pi$
$150$	−3133.23	−1.70552
$151$	1219.91	0.657452	0.328726	−	0.944425i	$-0.393381\pi$
$151$	1219.91	0.657452	0.328726	+	0.944425i	$0.393381\pi$
$152$	697.233	0.372060
$153$	2501.85	1.32198
$154$	2773.97	1.45151
$155$	633.790	0.328434
$156$	6436.41	3.30337
$157$	−1934.69	−0.983472	−0.491736	−	0.870744i	$-0.663637\pi$
$157$	−1934.69	−0.983472	−0.491736	+	0.870744i	$0.663637\pi$
$158$	−5070.53	−2.55310
$159$	−2168.06	−1.08137
$160$	−1362.49	−0.673214
$161$	−2410.83	−1.18013
$162$	2031.63	0.985309
$163$	−1091.52	−0.524505	−0.262253	−	0.964999i	$-0.584465\pi$
$163$	−1091.52	−0.524505	−0.262253	+	0.964999i	$0.584465\pi$
$164$	−5493.24	−2.61555
$165$	2339.67	1.10390
$166$	−3433.63	−1.60543
$167$	2286.50	1.05949	0.529744	−	0.848157i	$-0.322288\pi$
$167$	2286.50	1.05949	0.529744	+	0.848157i	$0.322288\pi$
$168$	−1421.88	−0.652977
$169$	3041.81	1.38453
$170$	1855.17	0.836970
$171$	−1656.51	−0.740800
$172$	0	0
$173$	−1171.22	−0.514720	−0.257360	−	0.966316i	$-0.582853\pi$
$173$	−1171.22	−0.514720	−0.257360	+	0.966316i	$0.582853\pi$
$174$	−3955.55	−1.72339
$175$	1125.14	0.486017
$176$	−1343.33	−0.575325
$177$	513.557	0.218087
$178$	2265.74	0.954069
$179$	−931.735	−0.389057	−0.194528	−	0.980897i	$-0.562318\pi$
$179$	−931.735	−0.389057	−0.194528	+	0.980897i	$0.562318\pi$
$180$	−2298.52	−0.951788
$181$	−305.691	−0.125535	−0.0627675	−	0.998028i	$-0.519993\pi$
$181$	−305.691	−0.125535	−0.0627675	+	0.998028i	$0.519993\pi$
$182$	−3944.49	−1.60651
$183$	−2592.83	−1.04736
$184$	−2839.33	−1.13760
$185$	113.655	0.0451680
$186$	−3739.08	−1.47399
$187$	3670.88	1.43552
$188$	−229.290	−0.0889503
$189$	748.938	0.288239
$190$	−1228.34	−0.469016
$191$	−302.996	−0.114786	−0.0573928	−	0.998352i	$-0.518279\pi$
$191$	−302.996	−0.114786	−0.0573928	+	0.998352i	$0.518279\pi$
$192$	6379.80	2.39803
$193$	3593.56	1.34026	0.670130	−	0.742244i	$-0.266239\pi$
$193$	3593.56	1.34026	0.670130	+	0.742244i	$0.266239\pi$
$194$	−3963.86	−1.46695
$195$	−3326.93	−1.22178
$196$	−2143.11	−0.781017
$197$	−2255.81	−0.815838	−0.407919	−	0.913018i	$-0.633745\pi$
$197$	−2255.81	−0.815838	−0.407919	+	0.913018i	$0.633745\pi$
$198$	−7761.90	−2.78593
$199$	533.234	0.189950	0.0949748	−	0.995480i	$-0.469723\pi$
$199$	533.234	0.189950	0.0949748	+	0.995480i	$0.469723\pi$
$200$	1325.13	0.468503
$201$	4105.36	1.44065
$202$	877.203	0.305543
$203$	1420.44	0.491110
$204$	−6413.14	−2.20103
$205$	2839.41	0.967381
$206$	3873.78	1.31019
$207$	6745.80	2.26505
$208$	1910.17	0.636762
$209$	−2430.55	−0.804425
$210$	2504.96	0.823138
$211$	4938.57	1.61130	0.805651	−	0.592390i	$-0.201816\pi$
$211$	4938.57	1.61130	0.805651	+	0.592390i	$0.201816\pi$
$212$	3125.19	1.01245
$213$	1223.46	0.393570
$214$	−6572.75	−2.09955
$215$	0	0
$216$	882.054	0.277853
$217$	1342.70	0.420040
$218$	3344.79	1.03916
$219$	4266.67	1.31651
$220$	−3372.55	−1.03353
$221$	−5219.87	−1.58881
$222$	−670.513	−0.202711
$223$	1407.81	0.422752	0.211376	−	0.977405i	$-0.432206\pi$
$223$	1407.81	0.422752	0.211376	+	0.977405i	$0.432206\pi$
$224$	−2886.48	−0.860986
$225$	−3148.29	−0.932827
$226$	−5946.52	−1.75025
$227$	297.127	0.0868766	0.0434383	−	0.999056i	$-0.486169\pi$
$227$	297.127	0.0868766	0.0434383	+	0.999056i	$0.486169\pi$
$228$	4246.25	1.23340
$229$	3885.00	1.12108	0.560542	−	0.828126i	$-0.310593\pi$
$229$	3885.00	1.12108	0.560542	+	0.828126i	$0.310593\pi$
$230$	5002.15	1.43405
$231$	4956.65	1.41179
$232$	1672.91	0.473413
$233$	5538.50	1.55725	0.778625	−	0.627489i	$-0.215917\pi$
$233$	5538.50	1.55725	0.778625	+	0.627489i	$0.215917\pi$
$234$	11037.2	3.08343
$235$	118.518	0.0328990
$236$	−740.276	−0.204186
$237$	−9060.25	−2.48323
$238$	3930.23	1.07042
$239$	−2719.79	−0.736103	−0.368052	−	0.929805i	$-0.619975\pi$
$239$	−2719.79	−0.736103	−0.368052	+	0.929805i	$0.619975\pi$
$240$	−1213.06	−0.326261
$241$	−1477.37	−0.394878	−0.197439	−	0.980315i	$-0.563262\pi$
$241$	−1477.37	−0.394878	−0.197439	+	0.980315i	$0.563262\pi$
$242$	−5538.17	−1.47110
$243$	5261.23	1.38892
$244$	3737.48	0.980605
$245$	1107.76	0.288865
$246$	−16751.3	−4.34155
$247$	3456.16	0.890326
$248$	1581.35	0.404904
$249$	−6135.36	−1.56150
$250$	−5550.03	−1.40406
$251$	−3405.07	−0.856280	−0.428140	−	0.903712i	$-0.640831\pi$
$251$	−3405.07	−0.856280	−0.428140	+	0.903712i	$0.640831\pi$
$252$	−4869.50	−1.21726
$253$	9897.90	2.45959
$254$	−1007.75	−0.248944
$255$	3314.90	0.814067
$256$	−1009.17	−0.246378
$257$	−2338.70	−0.567642	−0.283821	−	0.958877i	$-0.591602\pi$
$257$	−2338.70	−0.567642	−0.283821	+	0.958877i	$0.591602\pi$
$258$	0	0
$259$	240.781	0.0577661
$260$	4795.66	1.14390
$261$	−3974.56	−0.942602
$262$	−7341.74	−1.73120
$263$	2652.29	0.621854	0.310927	−	0.950434i	$-0.399361\pi$
$263$	2652.29	0.621854	0.310927	+	0.950434i	$0.399361\pi$
$264$	5837.65	1.36092
$265$	−1615.38	−0.374462
$266$	−2602.27	−0.599833
$267$	4048.52	0.927961
$268$	−5917.75	−1.34882
$269$	−3751.84	−0.850387	−0.425193	−	0.905103i	$-0.639794\pi$
$269$	−3751.84	−0.850387	−0.425193	+	0.905103i	$0.639794\pi$
$270$	−1553.94	−0.350259
$271$	−6834.16	−1.53190	−0.765952	−	0.642898i	$-0.777732\pi$
$271$	−6834.16	−1.53190	−0.765952	+	0.642898i	$0.777732\pi$
$272$	−1903.26	−0.424273
$273$	−7048.20	−1.56255
$274$	−9321.16	−2.05515
$275$	−4619.39	−1.01294
$276$	−17291.9	−3.77120
$277$	−3328.70	−0.722029	−0.361015	−	0.932560i	$-0.617570\pi$
$277$	−3328.70	−0.722029	−0.361015	+	0.932560i	$0.617570\pi$
$278$	2403.20	0.518468
$279$	−3757.05	−0.806195
$280$	−1059.42	−0.226115
$281$	−273.014	−0.0579596	−0.0289798	−	0.999580i	$-0.509226\pi$
$281$	−273.014	−0.0579596	−0.0289798	+	0.999580i	$0.509226\pi$
$282$	−699.203	−0.147649
$283$	4738.49	0.995314	0.497657	−	0.867374i	$-0.334194\pi$
$283$	4738.49	0.995314	0.497657	+	0.867374i	$0.334194\pi$
$284$	−1763.58	−0.368484
$285$	−2194.85	−0.456181
$286$	16194.5	3.34825
$287$	6015.38	1.23720
$288$	8076.71	1.65252
$289$	287.999	0.0586199
$290$	−2947.22	−0.596781
$291$	−7082.81	−1.42681
$292$	−6150.27	−1.23259
$293$	6636.13	1.32316	0.661581	−	0.749873i	$-0.269886\pi$
$293$	6636.13	1.32316	0.661581	+	0.749873i	$0.269886\pi$
$294$	−6535.26	−1.29641
$295$	382.643	0.0755198
$296$	283.578	0.0556845
$297$	−3074.84	−0.600741
$298$	−14075.2	−2.73609
$299$	−14074.5	−2.72224
$300$	8070.21	1.55311
$301$	0	0
$302$	−5362.33	−1.02175
$303$	1567.43	0.297182
$304$	1260.18	0.237751
$305$	−1931.87	−0.362684
$306$	−10997.3	−2.05448
$307$	6964.04	1.29465	0.647327	−	0.762212i	$-0.275887\pi$
$307$	6964.04	1.29465	0.647327	+	0.762212i	$0.275887\pi$
$308$	−7144.86	−1.32181
$309$	6921.84	1.27434
$310$	−2785.92	−0.510419
$311$	−1532.20	−0.279366	−0.139683	−	0.990196i	$-0.544608\pi$
$311$	−1532.20	−0.279366	−0.139683	+	0.990196i	$0.544608\pi$
$312$	−8300.94	−1.50624
$313$	−7971.39	−1.43952	−0.719760	−	0.694223i	$-0.755748\pi$
$313$	−7971.39	−1.43952	−0.719760	+	0.694223i	$0.755748\pi$
$314$	8504.24	1.52841
$315$	2517.00	0.450213
$316$	13060.1	2.32496
$317$	−3644.45	−0.645719	−0.322860	−	0.946447i	$-0.604644\pi$
$317$	−3644.45	−0.645719	−0.322860	+	0.946447i	$0.604644\pi$
$318$	9530.05	1.68056
$319$	−5831.75	−1.02356
$320$	4753.49	0.830400
$321$	−11744.5	−2.04210
$322$	10597.2	1.83403
$323$	−3443.67	−0.593222
$324$	−5232.84	−0.897263
$325$	6568.62	1.12111
$326$	4797.94	0.815133
$327$	5976.62	1.01073
$328$	7084.55	1.19262
$329$	251.084	0.0420751
$330$	−10284.4	−1.71556
$331$	−5229.57	−0.868409	−0.434204	−	0.900814i	$-0.642970\pi$
$331$	−5229.57	−0.868409	−0.434204	+	0.900814i	$0.642970\pi$
$332$	8843.93	1.46197
$333$	−673.735	−0.110872
$334$	−10050.7	−1.64655
$335$	3058.83	0.498872
$336$	−2569.91	−0.417261
$337$	−4729.01	−0.764408	−0.382204	−	0.924078i	$-0.624835\pi$
$337$	−4729.01	−0.764408	−0.382204	+	0.924078i	$0.624835\pi$
$338$	−13370.8	−2.15170
$339$	−10625.5	−1.70236
$340$	−4778.32	−0.762179
$341$	−5512.60	−0.875437
$342$	7281.47	1.15128
$343$	6599.32	1.03886
$344$	0	0
$345$	8938.06	1.39481
$346$	5148.31	0.799927
$347$	−10045.8	−1.55415	−0.777074	−	0.629409i	$-0.783297\pi$
$347$	−10045.8	−1.55415	−0.777074	+	0.629409i	$0.783297\pi$
$348$	10188.2	1.56939
$349$	−2985.23	−0.457867	−0.228933	−	0.973442i	$-0.573524\pi$
$349$	−2985.23	−0.457867	−0.228933	+	0.973442i	$0.573524\pi$
$350$	−4945.75	−0.755319
$351$	4372.32	0.664892
$352$	11850.7	1.79444
$353$	4066.23	0.613098	0.306549	−	0.951855i	$-0.400826\pi$
$353$	4066.23	0.613098	0.306549	+	0.951855i	$0.400826\pi$
$354$	−2257.42	−0.338928
$355$	911.582	0.136287
$356$	−5835.82	−0.868814
$357$	7022.72	1.04112
$358$	4095.59	0.604633
$359$	−5734.13	−0.842996	−0.421498	−	0.906829i	$-0.638496\pi$
$359$	−5734.13	−0.842996	−0.421498	+	0.906829i	$0.638496\pi$
$360$	2964.37	0.433989
$361$	−4578.89	−0.667574
$362$	1343.71	0.195094
$363$	−9895.85	−1.43085
$364$	10159.8	1.46296
$365$	3179.02	0.455884
$366$	11397.2	1.62771
$367$	−7460.30	−1.06110	−0.530551	−	0.847653i	$-0.678015\pi$
$367$	−7460.30	−1.06110	−0.530551	+	0.847653i	$0.678015\pi$
$368$	−5131.83	−0.726943
$369$	−16831.8	−2.37460
$370$	−499.588	−0.0701955
$371$	−3422.24	−0.478906
$372$	9630.67	1.34228
$373$	−5646.39	−0.783805	−0.391902	−	0.920007i	$-0.628183\pi$
$373$	−5646.39	−0.783805	−0.391902	+	0.920007i	$0.628183\pi$
$374$	−16135.9	−2.23093
$375$	−9917.04	−1.36564
$376$	295.711	0.0405589
$377$	8292.56	1.13286
$378$	−3292.08	−0.447953
$379$	−3098.26	−0.419912	−0.209956	−	0.977711i	$-0.567332\pi$
$379$	−3098.26	−0.419912	−0.209956	+	0.977711i	$0.567332\pi$
$380$	3163.81	0.427105
$381$	−1800.69	−0.242132
$382$	1331.87	0.178388
$383$	−4625.15	−0.617060	−0.308530	−	0.951215i	$-0.599837\pi$
$383$	−4625.15	−0.617060	−0.308530	+	0.951215i	$0.599837\pi$
$384$	−13414.3	−1.78267
$385$	3693.12	0.488880
$386$	−15796.1	−2.08290
$387$	0	0
$388$	10209.6	1.33587
$389$	13403.3	1.74698	0.873488	−	0.486845i	$-0.161852\pi$
$389$	13403.3	1.74698	0.873488	+	0.486845i	$0.161852\pi$
$390$	14624.0	1.89876
$391$	14023.6	1.81382
$392$	2763.94	0.356122
$393$	−13118.6	−1.68383
$394$	9915.79	1.26789
$395$	−6750.64	−0.859903
$396$	19992.2	2.53698
$397$	8906.42	1.12595	0.562973	−	0.826475i	$-0.309657\pi$
$397$	8906.42	1.12595	0.562973	+	0.826475i	$0.309657\pi$
$398$	−2343.92	−0.295201
$399$	−4649.86	−0.583419
$400$	2395.04	0.299380
$401$	−10.3507	−0.00128900	−0.000644499	−	1.00000i	$-0.500205\pi$
$401$	−10.3507	−0.00128900	−0.000644499		1.00000i	$0.500205\pi$
$402$	−18045.8	−2.23891
$403$	7838.73	0.968921
$404$	−2259.40	−0.278240
$405$	2704.81	0.331860
$406$	−6243.77	−0.763234
$407$	−988.551	−0.120395
$408$	8270.93	1.00361
$409$	7522.58	0.909456	0.454728	−	0.890630i	$-0.349736\pi$
$409$	7522.58	0.909456	0.454728	+	0.890630i	$0.349736\pi$
$410$	−12481.1	−1.50341
$411$	−16655.5	−1.99891
$412$	−9977.61	−1.19311
$413$	810.641	0.0965836
$414$	−29652.2	−3.52012
$415$	−4571.36	−0.540721
$416$	−16851.3	−1.98607
$417$	4294.14	0.504280
$418$	10683.9	1.25016
$419$	109.458	0.0127622	0.00638110	−	0.999980i	$-0.497969\pi$
$419$	109.458	0.0127622	0.00638110	+	0.999980i	$0.497969\pi$
$420$	−6451.99	−0.749583
$421$	8920.89	1.03273	0.516363	−	0.856370i	$-0.327286\pi$
$421$	8920.89	1.03273	0.516363	+	0.856370i	$0.327286\pi$
$422$	−21708.3	−2.50413
$423$	−702.563	−0.0807560
$424$	−4030.51	−0.461648
$425$	−6544.87	−0.746995
$426$	−5377.93	−0.611647
$427$	−4092.73	−0.463844
$428$	16929.3	1.91194
$429$	28937.1	3.25663
$430$	0	0
$431$	−16280.0	−1.81944	−0.909720	−	0.415223i	$-0.863703\pi$
$431$	−16280.0	−1.81944	−0.909720	+	0.415223i	$0.863703\pi$
$432$	1594.23	0.177552
$433$	−12363.2	−1.37214	−0.686070	−	0.727535i	$-0.740666\pi$
$433$	−12363.2	−1.37214	−0.686070	+	0.727535i	$0.740666\pi$
$434$	−5902.07	−0.652784
$435$	−5266.22	−0.580450
$436$	−8615.12	−0.946306
$437$	−9285.27	−1.01642
$438$	−18754.8	−2.04598
$439$	−15673.1	−1.70396	−0.851979	−	0.523576i	$-0.824598\pi$
$439$	−15673.1	−1.70396	−0.851979	+	0.523576i	$0.824598\pi$
$440$	4349.53	0.471263
$441$	−6566.67	−0.709067
$442$	22944.8	2.46917
$443$	8049.79	0.863335	0.431667	−	0.902033i	$-0.357925\pi$
$443$	8049.79	0.863335	0.431667	+	0.902033i	$0.357925\pi$
$444$	1727.03	0.184597
$445$	3016.49	0.321338
$446$	−6188.23	−0.656999
$447$	−25150.2	−2.66121
$448$	10070.4	1.06201
$449$	−7655.72	−0.804668	−0.402334	−	0.915493i	$-0.631801\pi$
$449$	−7655.72	−0.804668	−0.402334	+	0.915493i	$0.631801\pi$
$450$	13838.8	1.44971
$451$	−24696.7	−2.57854
$452$	15316.3	1.59385
$453$	−9581.65	−0.993787
$454$	−1306.07	−0.135015
$455$	−5251.50	−0.541086
$456$	−5476.32	−0.562395
$457$	5935.62	0.607563	0.303782	−	0.952742i	$-0.401751\pi$
$457$	5935.62	0.607563	0.303782	+	0.952742i	$0.401751\pi$
$458$	−17077.1	−1.74228
$459$	−4356.51	−0.443016
$460$	−12883.9	−1.30591
$461$	14649.8	1.48007	0.740033	−	0.672571i	$-0.234810\pi$
$461$	14649.8	1.48007	0.740033	+	0.672571i	$0.234810\pi$
$462$	−21787.8	−2.19407
$463$	8724.18	0.875695	0.437848	−	0.899049i	$-0.355741\pi$
$463$	8724.18	0.875695	0.437848	+	0.899049i	$0.355741\pi$
$464$	3023.62	0.302518
$465$	−4978.02	−0.496452
$466$	−24345.4	−2.42012
$467$	−211.747	−0.0209818	−0.0104909	−	0.999945i	$-0.503339\pi$
$467$	−211.747	−0.0209818	−0.0104909	+	0.999945i	$0.503339\pi$
$468$	−28428.2	−2.80790
$469$	6480.24	0.638016
$470$	−520.964	−0.0511283
$471$	15195.8	1.48659
$472$	954.724	0.0931032
$473$	0	0
$474$	39825.8	3.85919
$475$	4333.47	0.418596
$476$	−10123.0	−0.974765
$477$	9575.85	0.919178
$478$	11955.3	1.14398
$479$	8169.97	0.779323	0.389661	−	0.920958i	$-0.372592\pi$
$479$	8169.97	0.779323	0.389661	+	0.920958i	$0.372592\pi$
$480$	10701.5	1.01761
$481$	1405.69	0.133251
$482$	6494.00	0.613679
$483$	18935.6	1.78385
$484$	14264.6	1.33965
$485$	−5277.28	−0.494080
$486$	−23126.6	−2.15852
$487$	8646.83	0.804570	0.402285	−	0.915515i	$-0.368216\pi$
$487$	8646.83	0.804570	0.402285	+	0.915515i	$0.368216\pi$
$488$	−4820.17	−0.447129
$489$	8573.18	0.792828
$490$	−4869.32	−0.448925
$491$	7773.64	0.714500	0.357250	−	0.934009i	$-0.383714\pi$
$491$	7773.64	0.714500	0.357250	+	0.934009i	$0.383714\pi$
$492$	43145.9	3.95359
$493$	−8262.58	−0.754823
$494$	−15192.1	−1.38366
$495$	−10333.8	−0.938322
$496$	2858.15	0.258739
$497$	1931.22	0.174299
$498$	26969.0	2.42672
$499$	17480.8	1.56823	0.784114	−	0.620617i	$-0.213118\pi$
$499$	17480.8	1.56823	0.784114	+	0.620617i	$0.213118\pi$
$500$	14295.1	1.27859
$501$	−17959.0	−1.60149
$502$	14967.5	1.33075
$503$	−10065.2	−0.892218	−0.446109	−	0.894979i	$-0.647191\pi$
$503$	−10065.2	−0.892218	−0.446109	+	0.894979i	$0.647191\pi$
$504$	6280.12	0.555037
$505$	1167.86	0.102909
$506$	−43507.8	−3.82245
$507$	−23891.5	−2.09282
$508$	2595.64	0.226698
$509$	5106.23	0.444656	0.222328	−	0.974972i	$-0.428634\pi$
$509$	5106.23	0.444656	0.222328	+	0.974972i	$0.428634\pi$
$510$	−14571.2	−1.26514
$511$	6734.86	0.583039
$512$	−9227.10	−0.796454
$513$	2884.52	0.248255
$514$	10280.1	0.882172
$515$	5157.35	0.441281
$516$	0	0
$517$	−1030.85	−0.0876919
$518$	−1058.39	−0.0897743
$519$	9199.23	0.778037
$520$	−6184.89	−0.521588
$521$	−7651.54	−0.643416	−0.321708	−	0.946839i	$-0.604257\pi$
$521$	−7651.54	−0.643416	−0.321708	+	0.946839i	$0.604257\pi$
$522$	17470.8	1.46490
$523$	−3318.37	−0.277442	−0.138721	−	0.990331i	$-0.544299\pi$
$523$	−3318.37	−0.277442	−0.138721	+	0.990331i	$0.544299\pi$
$524$	18910.0	1.57650
$525$	−8837.29	−0.734650
$526$	−11658.6	−0.966423
$527$	−7810.39	−0.645590
$528$	10551.0	0.869646
$529$	25645.3	2.10777
$530$	7100.68	0.581951
$531$	−2268.27	−0.185376
$532$	6702.62	0.546232
$533$	35117.9	2.85390
$534$	−17795.9	−1.44214
$535$	−8750.63	−0.707145
$536$	7632.03	0.615025
$537$	7318.18	0.588087
$538$	16491.8	1.32159
$539$	−9635.07	−0.769966
$540$	4002.46	0.318960
$541$	3001.86	0.238558	0.119279	−	0.992861i	$-0.461942\pi$
$541$	3001.86	0.238558	0.119279	+	0.992861i	$0.461942\pi$
$542$	30040.7	2.38073
$543$	2401.01	0.189755
$544$	16790.4	1.32331
$545$	4453.08	0.349998
$546$	30981.5	2.42836
$547$	−7159.56	−0.559636	−0.279818	−	0.960053i	$-0.590274\pi$
$547$	−7159.56	−0.559636	−0.279818	+	0.960053i	$0.590274\pi$
$548$	24008.3	1.87151
$549$	11452.0	0.890269
$550$	20305.3	1.57422
$551$	5470.79	0.422983
$552$	22301.2	1.71957
$553$	−14301.4	−1.09975
$554$	14631.8	1.12211
$555$	−892.687	−0.0682747
$556$	−6189.87	−0.472138
$557$	−8290.11	−0.630634	−0.315317	−	0.948986i	$-0.602111\pi$
$557$	−8290.11	−0.630634	−0.315317	+	0.948986i	$0.602111\pi$
$558$	16514.7	1.25291
$559$	0	0
$560$	−1914.79	−0.144491
$561$	−28832.4	−2.16989
$562$	1200.08	0.0900751
$563$	11830.8	0.885630	0.442815	−	0.896613i	$-0.353980\pi$
$563$	11830.8	0.885630	0.442815	+	0.896613i	$0.353980\pi$
$564$	1800.92	0.134455
$565$	−7916.89	−0.589498
$566$	−20828.8	−1.54682
$567$	5730.23	0.424421
$568$	2274.47	0.168019
$569$	−661.208	−0.0487158	−0.0243579	−	0.999703i	$-0.507754\pi$
$569$	−661.208	−0.0487158	−0.0243579	+	0.999703i	$0.507754\pi$
$570$	9647.81	0.708951
$571$	13866.7	1.01629	0.508146	−	0.861271i	$-0.330331\pi$
$571$	13866.7	1.01629	0.508146	+	0.861271i	$0.330331\pi$
$572$	−41711.9	−3.04906
$573$	2379.84	0.173507
$574$	−26441.6	−1.92273
$575$	−17647.1	−1.27989
$576$	−28178.2	−2.03835
$577$	15498.6	1.11822	0.559112	−	0.829092i	$-0.311142\pi$
$577$	15498.6	1.11822	0.559112	+	0.829092i	$0.311142\pi$
$578$	−1265.95	−0.0911011
$579$	−28225.1	−2.02590
$580$	7591.09	0.543453
$581$	−9684.56	−0.691538
$582$	31133.6	2.21740
$583$	14050.3	0.998123
$584$	7931.91	0.562029
$585$	14694.3	1.03852
$586$	−29170.2	−2.05633
$587$	21748.6	1.52923	0.764617	−	0.644485i	$-0.222928\pi$
$587$	21748.6	1.52923	0.764617	+	0.644485i	$0.222928\pi$
$588$	16832.8	1.18056
$589$	5171.39	0.361772
$590$	−1681.97	−0.117365
$591$	17718.0	1.23320
$592$	512.540	0.0355832
$593$	22274.2	1.54248	0.771240	−	0.636545i	$-0.219637\pi$
$593$	22274.2	1.54248	0.771240	+	0.636545i	$0.219637\pi$
$594$	13515.9	0.933612
$595$	5232.51	0.360524
$596$	36253.2	2.49159
$597$	−4188.22	−0.287123
$598$	61866.7	4.23063
$599$	22572.5	1.53971	0.769856	−	0.638217i	$-0.220328\pi$
$599$	22572.5	1.53971	0.769856	+	0.638217i	$0.220328\pi$
$600$	−10408.0	−0.708176
$601$	−22982.2	−1.55984	−0.779918	−	0.625881i	$-0.784739\pi$
$601$	−22982.2	−1.55984	−0.779918	+	0.625881i	$0.784739\pi$
$602$	0	0
$603$	−18132.5	−1.22456
$604$	13811.7	0.930444
$605$	−7373.24	−0.495479
$606$	−6889.87	−0.461851
$607$	−9708.39	−0.649178	−0.324589	−	0.945855i	$-0.605226\pi$
$607$	−9708.39	−0.649178	−0.324589	+	0.945855i	$0.605226\pi$
$608$	−11117.2	−0.741549
$609$	−11156.7	−0.742349
$610$	8491.86	0.563648
$611$	1465.83	0.0970561
$612$	28325.4	1.87090
$613$	13924.3	0.917450	0.458725	−	0.888578i	$-0.348306\pi$
$613$	13924.3	0.917450	0.458725	+	0.888578i	$0.348306\pi$
$614$	−30611.5	−2.01202
$615$	−22301.8	−1.46227
$616$	9214.62	0.602707
$617$	7924.09	0.517037	0.258519	−	0.966006i	$-0.416766\pi$
$617$	7924.09	0.517037	0.258519	+	0.966006i	$0.416766\pi$
$618$	−30426.0	−1.98044
$619$	−7645.23	−0.496426	−0.248213	−	0.968705i	$-0.579843\pi$
$619$	−7645.23	−0.496426	−0.248213	+	0.968705i	$0.579843\pi$
$620$	7175.66	0.464808
$621$	−11746.6	−0.759057
$622$	6735.02	0.434163
$623$	6390.53	0.410965
$624$	−15003.2	−0.962512
$625$	3955.01	0.253121
$626$	35039.5	2.23716
$627$	19090.4	1.21595
$628$	−21904.2	−1.39184
$629$	−1400.60	−0.0887850
$630$	−11063.9	−0.699676
$631$	−10857.9	−0.685020	−0.342510	−	0.939514i	$-0.611277\pi$
$631$	−10857.9	−0.685020	−0.342510	+	0.939514i	$0.611277\pi$
$632$	−16843.4	−1.06012
$633$	−38789.3	−2.43560
$634$	16019.8	1.00351
$635$	−1341.66	−0.0838461
$636$	−24546.4	−1.53039
$637$	13700.8	0.852188
$638$	25634.4	1.59071
$639$	−5403.77	−0.334538
$640$	−9994.79	−0.617310
$641$	−9993.21	−0.615769	−0.307885	−	0.951424i	$-0.599621\pi$
$641$	−9993.21	−0.615769	−0.307885	+	0.951424i	$0.599621\pi$
$642$	51624.8	3.17363
$643$	4952.30	0.303732	0.151866	−	0.988401i	$-0.451472\pi$
$643$	4952.30	0.303732	0.151866	+	0.988401i	$0.451472\pi$
$644$	−27295.0	−1.67015
$645$	0	0
$646$	15137.2	0.921927
$647$	−12682.7	−0.770644	−0.385322	−	0.922782i	$-0.625910\pi$
$647$	−12682.7	−0.770644	−0.385322	+	0.922782i	$0.625910\pi$
$648$	6748.71	0.409127
$649$	−3328.16	−0.201297
$650$	−28873.4	−1.74232
$651$	−10546.1	−0.634921
$652$	−12358.0	−0.742294
$653$	−599.654	−0.0359361	−0.0179681	−	0.999839i	$-0.505720\pi$
$653$	−599.654	−0.0359361	−0.0179681	+	0.999839i	$0.505720\pi$
$654$	−26271.2	−1.57077
$655$	−9774.42	−0.583081
$656$	12804.7	0.762100
$657$	−18845.0	−1.11904
$658$	−1103.68	−0.0653889
$659$	−19082.8	−1.12801	−0.564007	−	0.825770i	$-0.690741\pi$
$659$	−19082.8	−1.12801	−0.564007	+	0.825770i	$0.690741\pi$
$660$	26489.3	1.56226
$661$	30565.8	1.79860	0.899298	−	0.437336i	$-0.144078\pi$
$661$	30565.8	1.79860	0.899298	+	0.437336i	$0.144078\pi$
$662$	22987.4	1.34959
$663$	40998.8	2.40160
$664$	−11405.9	−0.666618
$665$	−3464.53	−0.202028
$666$	2961.51	0.172307
$667$	−22278.6	−1.29330
$668$	25887.3	1.49942
$669$	−11057.4	−0.639020
$670$	−13445.6	−0.775296
$671$	16803.1	0.966732
$672$	22671.4	1.30144
$673$	16705.8	0.956850	0.478425	−	0.878128i	$-0.341208\pi$
$673$	16705.8	0.956850	0.478425	+	0.878128i	$0.341208\pi$
$674$	20787.1	1.18797
$675$	5482.17	0.312606
$676$	34438.9	1.95943
$677$	11786.3	0.669105	0.334553	−	0.942377i	$-0.391415\pi$
$677$	11786.3	0.669105	0.334553	+	0.942377i	$0.391415\pi$
$678$	46706.1	2.64563
$679$	−11180.1	−0.631889
$680$	6162.53	0.347533
$681$	−2333.74	−0.131320
$682$	24231.5	1.36052
$683$	−2424.38	−0.135822	−0.0679110	−	0.997691i	$-0.521633\pi$
$683$	−2424.38	−0.135822	−0.0679110	+	0.997691i	$0.521633\pi$
$684$	−18754.7	−1.04840
$685$	−12409.7	−0.692191
$686$	−29008.4	−1.61450
$687$	−30514.2	−1.69460
$688$	0	0
$689$	−19979.1	−1.10471
$690$	−39288.7	−2.16767
$691$	−3786.01	−0.208432	−0.104216	−	0.994555i	$-0.533233\pi$
$691$	−3786.01	−0.208432	−0.104216	+	0.994555i	$0.533233\pi$
$692$	−13260.4	−0.728446
$693$	−21892.5	−1.20004
$694$	44158.1	2.41530
$695$	3199.49	0.174624
$696$	−13139.6	−0.715598
$697$	−34991.0	−1.90155
$698$	13122.0	0.711571
$699$	−43501.4	−2.35390
$700$	12738.7	0.687824
$701$	2332.79	0.125689	0.0628447	−	0.998023i	$-0.479983\pi$
$701$	2332.79	0.125689	0.0628447	+	0.998023i	$0.479983\pi$
$702$	−19219.2	−1.03331
$703$	927.364	0.0497527
$704$	−41345.0	−2.21342
$705$	−930.883	−0.0497292
$706$	−17873.8	−0.952815
$707$	2474.15	0.131613
$708$	5814.40	0.308642
$709$	−33435.9	−1.77110	−0.885550	−	0.464544i	$-0.846218\pi$
$709$	−33435.9	−1.77110	−0.885550	+	0.464544i	$0.846218\pi$
$710$	−4007.00	−0.211803
$711$	40017.2	2.11077
$712$	7526.37	0.396155
$713$	−21059.4	−1.10614
$714$	−30869.5	−1.61801
$715$	21560.5	1.12772
$716$	−10548.9	−0.550603
$717$	21362.2	1.11267
$718$	25205.3	1.31010
$719$	21181.7	1.09867	0.549334	−	0.835603i	$-0.314881\pi$
$719$	21181.7	1.09867	0.549334	+	0.835603i	$0.314881\pi$
$720$	5357.82	0.277325
$721$	10926.0	0.564363
$722$	20127.2	1.03748
$723$	11603.8	0.596886
$724$	−3460.98	−0.177661
$725$	10397.5	0.532626
$726$	43498.8	2.22368
$727$	−29543.9	−1.50718	−0.753592	−	0.657343i	$-0.771680\pi$
$727$	−29543.9	−1.50718	−0.753592	+	0.657343i	$0.771680\pi$
$728$	−13102.9	−0.667068
$729$	−28844.5	−1.46545
$730$	−13973.9	−0.708490
$731$	0	0
$732$	−29355.5	−1.48226
$733$	−17766.9	−0.895273	−0.447637	−	0.894216i	$-0.647734\pi$
$733$	−17766.9	−0.895273	−0.447637	+	0.894216i	$0.647734\pi$
$734$	32793.0	1.64906
$735$	−8700.72	−0.436640
$736$	45272.4	2.26734
$737$	−26605.2	−1.32974
$738$	73986.7	3.69036
$739$	−21245.7	−1.05756	−0.528778	−	0.848760i	$-0.677350\pi$
$739$	−21245.7	−1.05756	−0.528778	+	0.848760i	$0.677350\pi$
$740$	1286.78	0.0639229
$741$	−27146.0	−1.34579
$742$	15043.0	0.744268
$743$	−397.687	−0.0196362	−0.00981812	−	0.999952i	$-0.503125\pi$
$743$	−397.687	−0.0196362	−0.00981812	+	0.999952i	$0.503125\pi$
$744$	−12420.5	−0.612042
$745$	−18739.0	−0.921534
$746$	24819.6	1.21811
$747$	27098.6	1.32729
$748$	41561.0	2.03158
$749$	−18538.5	−0.904381
$750$	43591.9	2.12234
$751$	4939.05	0.239985	0.119992	−	0.992775i	$-0.461713\pi$
$751$	4939.05	0.239985	0.119992	+	0.992775i	$0.461713\pi$
$752$	534.470	0.0259177
$753$	26744.7	1.29433
$754$	−36451.3	−1.76058
$755$	−7139.13	−0.344132
$756$	8479.34	0.407924
$757$	−32519.8	−1.56136	−0.780682	−	0.624928i	$-0.785128\pi$
$757$	−32519.8	−1.56136	−0.780682	+	0.624928i	$0.785128\pi$
$758$	13618.9	0.652585
$759$	−77741.7	−3.71785
$760$	−4080.31	−0.194748
$761$	2808.28	0.133771	0.0668856	−	0.997761i	$-0.478694\pi$
$761$	2808.28	0.133771	0.0668856	+	0.997761i	$0.478694\pi$
$762$	7915.22	0.376297
$763$	9434.00	0.447619
$764$	−3430.47	−0.162448
$765$	−14641.2	−0.691965
$766$	20330.6	0.958973
$767$	4732.54	0.222793
$768$	7926.35	0.372419
$769$	−2452.64	−0.115012	−0.0575061	−	0.998345i	$-0.518315\pi$
$769$	−2452.64	−0.115012	−0.0575061	+	0.998345i	$0.518315\pi$
$770$	−16233.7	−0.759769
$771$	18369.0	0.858032
$772$	40685.6	1.89677
$773$	−15873.4	−0.738584	−0.369292	−	0.929313i	$-0.620400\pi$
$773$	−15873.4	−0.738584	−0.369292	+	0.929313i	$0.620400\pi$
$774$	0	0
$775$	9828.49	0.455548
$776$	−13167.2	−0.609118
$777$	−1891.18	−0.0873177
$778$	−58916.3	−2.71498
$779$	23168.1	1.06558
$780$	−37666.9	−1.72909
$781$	−7928.79	−0.363271
$782$	−61643.0	−2.81886
$783$	6920.98	0.315882
$784$	4995.55	0.227567
$785$	11322.1	0.514781
$786$	57664.7	2.61683
$787$	−5695.97	−0.257992	−0.128996	−	0.991645i	$-0.541175\pi$
$787$	−5695.97	−0.257992	−0.128996	+	0.991645i	$0.541175\pi$
$788$	−25539.9	−1.15460
$789$	−20832.1	−0.939977
$790$	29673.5	1.33638
$791$	−16772.2	−0.753919
$792$	−25783.6	−1.15679
$793$	−23893.5	−1.06996
$794$	−39149.6	−1.74983
$795$	12687.8	0.566026
$796$	6037.18	0.268822
$797$	−2203.96	−0.0979528	−0.0489764	−	0.998800i	$-0.515596\pi$
$797$	−2203.96	−0.0979528	−0.0489764	+	0.998800i	$0.515596\pi$
$798$	20439.2	0.906691
$799$	−1460.53	−0.0646683
$800$	−21128.8	−0.933770
$801$	−17881.5	−0.788777
$802$	45.4980	0.00200323
$803$	−27650.6	−1.21515
$804$	46480.1	2.03884
$805$	14108.6	0.617717
$806$	−34456.4	−1.50580
$807$	29468.4	1.28542
$808$	2913.91	0.126870
$809$	−247.927	−0.0107746	−0.00538730	−	0.999985i	$-0.501715\pi$
$809$	−247.927	−0.0107746	−0.00538730	+	0.999985i	$0.501715\pi$
$810$	−11889.4	−0.515743
$811$	16460.2	0.712694	0.356347	−	0.934354i	$-0.384022\pi$
$811$	16460.2	0.712694	0.356347	+	0.934354i	$0.384022\pi$
$812$	16082.0	0.695032
$813$	53678.0	2.31558
$814$	4345.33	0.187105
$815$	6387.74	0.274543
$816$	14948.9	0.641320
$817$	0	0
$818$	−33066.7	−1.41339
$819$	31130.4	1.32818
$820$	32147.3	1.36906
$821$	26642.8	1.13257	0.566286	−	0.824209i	$-0.308380\pi$
$821$	26642.8	1.13257	0.566286	+	0.824209i	$0.308380\pi$
$822$	73211.7	3.10651
$823$	13805.3	0.584716	0.292358	−	0.956309i	$-0.405560\pi$
$823$	13805.3	0.584716	0.292358	+	0.956309i	$0.405560\pi$
$824$	12868.0	0.544026
$825$	36282.3	1.53114
$826$	−3563.30	−0.150101
$827$	−42308.6	−1.77898	−0.889488	−	0.456959i	$-0.848939\pi$
$827$	−42308.6	−1.77898	−0.889488	+	0.456959i	$0.848939\pi$
$828$	76374.7	3.20556
$829$	−1206.36	−0.0505412	−0.0252706	−	0.999681i	$-0.508045\pi$
$829$	−1206.36	−0.0505412	−0.0252706	+	0.999681i	$0.508045\pi$
$830$	20094.1	0.840334
$831$	26144.8	1.09140
$832$	58791.3	2.44978
$833$	−13651.2	−0.567811
$834$	−18875.6	−0.783702
$835$	−13381.0	−0.554571
$836$	−27518.3	−1.13844
$837$	6542.21	0.270170
$838$	−481.139	−0.0198338
$839$	−23105.7	−0.950773	−0.475386	−	0.879777i	$-0.657692\pi$
$839$	−23105.7	−0.950773	−0.475386	+	0.879777i	$0.657692\pi$
$840$	8321.04	0.341789
$841$	−11262.6	−0.461792
$842$	−39213.2	−1.60496
$843$	2144.35	0.0876102
$844$	55913.5	2.28036
$845$	−17801.2	−0.724709
$846$	3088.23	0.125503
$847$	−15620.4	−0.633677
$848$	−7284.77	−0.295000
$849$	−37217.8	−1.50449
$850$	28769.0	1.16090
$851$	−3776.49	−0.152123
$852$	13851.8	0.556990
$853$	−16448.8	−0.660253	−0.330126	−	0.943937i	$-0.607091\pi$
$853$	−16448.8	−0.660253	−0.330126	+	0.943937i	$0.607091\pi$
$854$	17990.3	0.720860
$855$	9694.18	0.387759
$856$	−21833.5	−0.871791
$857$	35801.6	1.42702	0.713512	−	0.700643i	$-0.247103\pi$
$857$	35801.6	1.42702	0.713512	+	0.700643i	$0.247103\pi$
$858$	−127197.	−5.06113
$859$	10727.9	0.426113	0.213057	−	0.977040i	$-0.431658\pi$
$859$	10727.9	0.426113	0.213057	+	0.977040i	$0.431658\pi$
$860$	0	0
$861$	−47247.0	−1.87012
$862$	71561.2	2.82759
$863$	−16939.7	−0.668172	−0.334086	−	0.942543i	$-0.608428\pi$
$863$	−16939.7	−0.668172	−0.334086	+	0.942543i	$0.608428\pi$
$864$	−14064.1	−0.553786
$865$	6854.19	0.269421
$866$	54344.4	2.13244
$867$	−2262.05	−0.0886082
$868$	15201.9	0.594452
$869$	58715.9	2.29206
$870$	23148.5	0.902078
$871$	37831.8	1.47173
$872$	11110.8	0.431489
$873$	31283.2	1.21280
$874$	40814.9	1.57961
$875$	−15653.9	−0.604797
$876$	48306.5	1.86316
$877$	−9358.04	−0.360318	−0.180159	−	0.983638i	$-0.557661\pi$
$877$	−9358.04	−0.360318	−0.180159	+	0.983638i	$0.557661\pi$
$878$	68893.7	2.64812
$879$	−52122.6	−2.00006
$880$	7861.37	0.301144
$881$	11704.6	0.447603	0.223801	−	0.974635i	$-0.428153\pi$
$881$	11704.6	0.447603	0.223801	+	0.974635i	$0.428153\pi$
$882$	28864.8	1.10196
$883$	3294.49	0.125559	0.0627794	−	0.998027i	$-0.480004\pi$
$883$	3294.49	0.125559	0.0627794	+	0.998027i	$0.480004\pi$
$884$	−59098.4	−2.24852
$885$	−3005.42	−0.114154
$886$	−35384.2	−1.34171
$887$	−19593.1	−0.741683	−0.370842	−	0.928696i	$-0.620931\pi$
$887$	−19593.1	−0.741683	−0.370842	+	0.928696i	$0.620931\pi$
$888$	−2227.32	−0.0841712
$889$	−2842.36	−0.107232
$890$	−13259.5	−0.499391
$891$	−23526.0	−0.884568
$892$	15938.9	0.598290
$893$	967.044	0.0362384
$894$	110552.	4.13579
$895$	5452.66	0.203645
$896$	−21174.3	−0.789490
$897$	110546.	4.11486
$898$	33652.0	1.25053
$899$	12408.0	0.460322
$900$	−35644.4	−1.32016
$901$	19906.9	0.736065
$902$	108558.	4.00731
$903$	0	0
$904$	−19753.3	−0.726752
$905$	1788.95	0.0657092
$906$	42117.7	1.54444
$907$	−33443.1	−1.22432	−0.612162	−	0.790733i	$-0.709700\pi$
$907$	−33443.1	−1.22432	−0.612162	+	0.790733i	$0.709700\pi$
$908$	3364.02	0.122950
$909$	−6922.98	−0.252608
$910$	23083.8	0.840901
$911$	31893.5	1.15991	0.579955	−	0.814649i	$-0.303070\pi$
$911$	31893.5	1.15991	0.579955	+	0.814649i	$0.303070\pi$
$912$	−9897.93	−0.359379
$913$	39760.9	1.44129
$914$	−26090.9	−0.944214
$915$	15173.6	0.548224
$916$	43985.3	1.58659
$917$	−20707.4	−0.745713
$918$	19149.7	0.688492
$919$	15843.1	0.568678	0.284339	−	0.958724i	$-0.408226\pi$
$919$	15843.1	0.568678	0.284339	+	0.958724i	$0.408226\pi$
$920$	16616.2	0.595457
$921$	−54698.1	−1.95696
$922$	−64395.6	−2.30017
$923$	11274.5	0.402063
$924$	56118.3	1.99801
$925$	1762.50	0.0626494
$926$	−38348.5	−1.36092
$927$	−30572.3	−1.08320
$928$	−26674.1	−0.943555
$929$	5624.10	0.198623	0.0993114	−	0.995056i	$-0.468336\pi$
$929$	5624.10	0.198623	0.0993114	+	0.995056i	$0.468336\pi$
$930$	21881.7	0.771536
$931$	9038.70	0.318186
$932$	62705.9	2.20386
$933$	12034.4	0.422283
$934$	930.767	0.0326077
$935$	−21482.6	−0.751396
$936$	36663.5	1.28032
$937$	−24982.7	−0.871024	−0.435512	−	0.900183i	$-0.643433\pi$
$937$	−24982.7	−0.871024	−0.435512	+	0.900183i	$0.643433\pi$
$938$	−28484.9	−0.991541
$939$	62610.2	2.17594
$940$	1341.84	0.0465595
$941$	−2409.74	−0.0834806	−0.0417403	−	0.999128i	$-0.513290\pi$
$941$	−2409.74	−0.0834806	−0.0417403	+	0.999128i	$0.513290\pi$
$942$	−66795.4	−2.31031
$943$	−94347.2	−3.25808
$944$	1725.57	0.0594943
$945$	−4382.90	−0.150874
$946$	0	0
$947$	13276.4	0.455569	0.227785	−	0.973712i	$-0.426852\pi$
$947$	13276.4	0.455569	0.227785	+	0.973712i	$0.426852\pi$
$948$	−102579.	−3.51434
$949$	39318.3	1.34492
$950$	−19048.4	−0.650540
$951$	28624.9	0.976051
$952$	13055.5	0.444466
$953$	16222.6	0.551418	0.275709	−	0.961241i	$-0.411087\pi$
$953$	16222.6	0.551418	0.275709	+	0.961241i	$0.411087\pi$
$954$	−42092.2	−1.42849
$955$	1773.18	0.0600825
$956$	−30793.0	−1.04175
$957$	45804.7	1.54718
$958$	−35912.4	−1.21115
$959$	−26290.4	−0.885255
$960$	−37335.6	−1.25521
$961$	−18062.1	−0.606292
$962$	−6178.92	−0.207086
$963$	51872.9	1.73581
$964$	−16726.5	−0.558842
$965$	−21030.1	−0.701535
$966$	−83234.3	−2.77228
$967$	22602.3	0.751647	0.375823	−	0.926691i	$-0.377360\pi$
$967$	22602.3	0.751647	0.375823	+	0.926691i	$0.377360\pi$
$968$	−18396.8	−0.610842
$969$	27047.8	0.896699
$970$	23197.1	0.767851
$971$	8215.32	0.271516	0.135758	−	0.990742i	$-0.456653\pi$
$971$	8215.32	0.271516	0.135758	+	0.990742i	$0.456653\pi$
$972$	59566.7	1.96564
$973$	6778.22	0.223330
$974$	−38008.5	−1.25038
$975$	−51592.3	−1.69464
$976$	−8712.01	−0.285722
$977$	13701.3	0.448662	0.224331	−	0.974513i	$-0.427980\pi$
$977$	13701.3	0.448662	0.224331	+	0.974513i	$0.427980\pi$
$978$	−37684.8	−1.23213
$979$	−26236.9	−0.856522
$980$	12541.8	0.408810
$981$	−26397.5	−0.859129
$982$	−34170.3	−1.11040
$983$	35295.3	1.14521	0.572606	−	0.819830i	$-0.305932\pi$
$983$	35295.3	1.14521	0.572606	+	0.819830i	$0.305932\pi$
$984$	−55644.6	−1.80273
$985$	13201.4	0.427036
$986$	36319.5	1.17307
$987$	−1972.10	−0.0635996
$988$	39130.1	1.26001
$989$	0	0
$990$	45423.8	1.45825
$991$	−10086.0	−0.323302	−0.161651	−	0.986848i	$-0.551682\pi$
$991$	−10086.0	−0.323302	−0.161651	+	0.986848i	$0.551682\pi$
$992$	−25214.3	−0.807011
$993$	41075.0	1.31266
$994$	−8488.96	−0.270879
$995$	−3120.57	−0.0994259
$996$	−69463.5	−2.20987
$997$	−14690.8	−0.466662	−0.233331	−	0.972397i	$-0.574963\pi$
$997$	−14690.8	−0.466662	−0.233331	+	0.972397i	$0.574963\pi$
$998$	−76839.4	−2.43718
$999$	1173.19	0.0371552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.g.1.5		30
43.8	odd	14		43.4.e.a.21.2	✓	60
43.27	odd	14		43.4.e.a.41.2	yes	60
43.42	odd	2		1849.4.a.h.1.26		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.21.2	✓	60	43.8	odd	14
43.4.e.a.41.2	yes	60	43.27	odd	14
1849.4.a.g.1.5		30	1.1	even	1	trivial
1849.4.a.h.1.26		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)

\(f(q)\)	\(=\)	\(q-4.39566 q^{2} -7.85436 q^{3} +11.3218 q^{4} -5.85216 q^{5} +34.5251 q^{6} -12.3980 q^{7} -14.6016 q^{8} +34.6910 q^{9} +O(q^{10})\)	\(q-4.39566 q^{2} -7.85436 q^{3} +11.3218 q^{4} -5.85216 q^{5} +34.5251 q^{6} -12.3980 q^{7} -14.6016 q^{8} +34.6910 q^{9} +25.7241 q^{10} +50.9011 q^{11} -88.9257 q^{12} -72.3797 q^{13} +54.4973 q^{14} +45.9650 q^{15} -26.3910 q^{16} +72.1180 q^{17} -152.490 q^{18} -47.7505 q^{19} -66.2570 q^{20} +97.3782 q^{21} -223.744 q^{22} +194.454 q^{23} +114.686 q^{24} -90.7523 q^{25} +318.156 q^{26} -60.4081 q^{27} -140.368 q^{28} -114.570 q^{29} -202.046 q^{30} -108.300 q^{31} +232.818 q^{32} -399.795 q^{33} -317.006 q^{34} +72.5549 q^{35} +392.765 q^{36} -19.4210 q^{37} +209.895 q^{38} +568.496 q^{39} +85.4507 q^{40} -485.191 q^{41} -428.041 q^{42} +576.293 q^{44} -203.017 q^{45} -854.753 q^{46} -20.2520 q^{47} +207.284 q^{48} -189.290 q^{49} +398.916 q^{50} -566.441 q^{51} -819.469 q^{52} +276.032 q^{53} +265.533 q^{54} -297.881 q^{55} +181.030 q^{56} +375.050 q^{57} +503.612 q^{58} -65.3849 q^{59} +520.407 q^{60} +330.113 q^{61} +476.051 q^{62} -430.098 q^{63} -812.262 q^{64} +423.577 q^{65} +1757.36 q^{66} -522.685 q^{67} +816.506 q^{68} -1527.31 q^{69} -318.927 q^{70} -155.769 q^{71} -506.544 q^{72} -543.223 q^{73} +85.3682 q^{74} +712.801 q^{75} -540.622 q^{76} -631.070 q^{77} -2498.91 q^{78} +1153.53 q^{79} +154.444 q^{80} -462.190 q^{81} +2132.73 q^{82} +781.141 q^{83} +1102.50 q^{84} -422.046 q^{85} +899.877 q^{87} -743.236 q^{88} -515.449 q^{89} +892.395 q^{90} +897.361 q^{91} +2201.57 q^{92} +850.630 q^{93} +89.0210 q^{94} +279.443 q^{95} -1828.64 q^{96} +901.767 q^{97} +832.055 q^{98} +1765.81 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) \) 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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