LMFDB - Embedded newform 1849.4.a.g.1.6

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			1.6
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)

$f(q)$	$=$	$q-4.36589 q^{2} +4.55814 q^{3} +11.0610 q^{4} +9.21441 q^{5} -19.9004 q^{6} +12.2688 q^{7} -13.3641 q^{8} -6.22333 q^{9} +O(q^{10})$	\(q-4.36589 q^{2} +4.55814 q^{3} +11.0610 q^{4} +9.21441 q^{5} -19.9004 q^{6} +12.2688 q^{7} -13.3641 q^{8} -6.22333 q^{9} -40.2291 q^{10} +16.8137 q^{11} +50.4177 q^{12} -74.1834 q^{13} -53.5645 q^{14} +42.0006 q^{15} -30.1420 q^{16} +0.711281 q^{17} +27.1704 q^{18} -31.2912 q^{19} +101.921 q^{20} +55.9232 q^{21} -73.4068 q^{22} +83.8614 q^{23} -60.9154 q^{24} -40.0947 q^{25} +323.877 q^{26} -151.437 q^{27} +135.706 q^{28} +228.700 q^{29} -183.370 q^{30} -243.690 q^{31} +238.509 q^{32} +76.6393 q^{33} -3.10538 q^{34} +113.050 q^{35} -68.8364 q^{36} -82.4344 q^{37} +136.614 q^{38} -338.139 q^{39} -123.142 q^{40} +404.211 q^{41} -244.155 q^{42} +185.977 q^{44} -57.3443 q^{45} -366.130 q^{46} +350.977 q^{47} -137.392 q^{48} -192.475 q^{49} +175.049 q^{50} +3.24212 q^{51} -820.544 q^{52} +106.120 q^{53} +661.156 q^{54} +154.928 q^{55} -163.962 q^{56} -142.630 q^{57} -998.481 q^{58} -684.391 q^{59} +464.569 q^{60} -505.923 q^{61} +1063.93 q^{62} -76.3531 q^{63} -800.171 q^{64} -683.556 q^{65} -334.599 q^{66} +286.489 q^{67} +7.86750 q^{68} +382.252 q^{69} -493.565 q^{70} +131.491 q^{71} +83.1691 q^{72} -728.979 q^{73} +359.900 q^{74} -182.758 q^{75} -346.112 q^{76} +206.285 q^{77} +1476.28 q^{78} +818.448 q^{79} -277.741 q^{80} -522.240 q^{81} -1764.74 q^{82} -866.308 q^{83} +618.567 q^{84} +6.55403 q^{85} +1042.45 q^{87} -224.700 q^{88} -875.385 q^{89} +250.359 q^{90} -910.145 q^{91} +927.593 q^{92} -1110.78 q^{93} -1532.33 q^{94} -288.329 q^{95} +1087.16 q^{96} -931.653 q^{97} +840.327 q^{98} -104.637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.36589	−1.54358	−0.771788	−	0.635880i	$-0.780637\pi$
$2$	−4.36589	−1.54358	−0.771788	+	0.635880i	$0.780637\pi$
$3$	4.55814	0.877215	0.438608	−	0.898679i	$-0.355472\pi$
$3$	4.55814	0.877215	0.438608	+	0.898679i	$0.355472\pi$
$4$	11.0610	1.38263
$5$	9.21441	0.824161	0.412081	−	0.911147i	$-0.364802\pi$
$5$	9.21441	0.824161	0.412081	+	0.911147i	$0.364802\pi$
$6$	−19.9004	−1.35405
$7$	12.2688	0.662455	0.331228	−	0.943551i	$-0.392537\pi$
$7$	12.2688	0.662455	0.331228	+	0.943551i	$0.392537\pi$
$8$	−13.3641	−0.590615
$9$	−6.22333	−0.230494
$10$	−40.2291	−1.27216
$11$	16.8137	0.460866	0.230433	−	0.973088i	$-0.425986\pi$
$11$	16.8137	0.460866	0.230433	+	0.973088i	$0.425986\pi$
$12$	50.4177	1.21286
$13$	−74.1834	−1.58268	−0.791338	−	0.611379i	$-0.790615\pi$
$13$	−74.1834	−1.58268	−0.791338	+	0.611379i	$0.790615\pi$
$14$	−53.5645	−1.02255
$15$	42.0006	0.722967
$16$	−30.1420	−0.470969
$17$	0.711281	0.0101477	0.00507385	−	0.999987i	$-0.498385\pi$
$17$	0.711281	0.0101477	0.00507385	+	0.999987i	$0.498385\pi$
$18$	27.1704	0.355785
$19$	−31.2912	−0.377826	−0.188913	−	0.981994i	$-0.560496\pi$
$19$	−31.2912	−0.377826	−0.188913	+	0.981994i	$0.560496\pi$
$20$	101.921	1.13951
$21$	55.9232	0.581116
$22$	−73.4068	−0.711381
$23$	83.8614	0.760274	0.380137	−	0.924930i	$-0.375877\pi$
$23$	83.8614	0.760274	0.380137	+	0.924930i	$0.375877\pi$
$24$	−60.9154	−0.518096
$25$	−40.0947	−0.320758
$26$	323.877	2.44298
$27$	−151.437	−1.07941
$28$	135.706	0.915929
$29$	228.700	1.46443	0.732217	−	0.681071i	$-0.238486\pi$
$29$	228.700	1.46443	0.732217	+	0.681071i	$0.238486\pi$
$30$	−183.370	−1.11595
$31$	−243.690	−1.41187	−0.705937	−	0.708275i	$-0.749474\pi$
$31$	−243.690	−1.41187	−0.705937	+	0.708275i	$0.749474\pi$
$32$	238.509	1.31759
$33$	76.6393	0.404278
$34$	−3.10538	−0.0156638
$35$	113.050	0.545970
$36$	−68.8364	−0.318687
$37$	−82.4344	−0.366274	−0.183137	−	0.983087i	$-0.558625\pi$
$37$	−82.4344	−0.366274	−0.183137	+	0.983087i	$0.558625\pi$
$38$	136.614	0.583203
$39$	−338.139	−1.38835
$40$	−123.142	−0.486762
$41$	404.211	1.53969	0.769843	−	0.638233i	$-0.220334\pi$
$41$	404.211	1.53969	0.769843	+	0.638233i	$0.220334\pi$
$42$	−244.155	−0.896997
$43$	0	0
$43$	0	0
$44$	185.977	0.637206
$45$	−57.3443	−0.189964
$46$	−366.130	−1.17354
$47$	350.977	1.08926	0.544631	−	0.838676i	$-0.316670\pi$
$47$	350.977	1.08926	0.544631	+	0.838676i	$0.316670\pi$
$48$	−137.392	−0.413141
$49$	−192.475	−0.561153
$50$	175.049	0.495114
$51$	3.24212	0.00890172
$52$	−820.544	−2.18825
$53$	106.120	0.275033	0.137516	−	0.990500i	$-0.456088\pi$
$53$	106.120	0.275033	0.137516	+	0.990500i	$0.456088\pi$
$54$	661.156	1.66615
$55$	154.928	0.379828
$56$	−163.962	−0.391256
$57$	−142.630	−0.331434
$58$	−998.481	−2.26047
$59$	−684.391	−1.51017	−0.755086	−	0.655626i	$-0.772405\pi$
$59$	−684.391	−1.51017	−0.755086	+	0.655626i	$0.772405\pi$
$60$	464.569	0.999594
$61$	−505.923	−1.06191	−0.530957	−	0.847399i	$-0.678167\pi$
$61$	−505.923	−1.06191	−0.530957	+	0.847399i	$0.678167\pi$
$62$	1063.93	2.17933
$63$	−76.3531	−0.152692
$64$	−800.171	−1.56283
$65$	−683.556	−1.30438
$66$	−334.599	−0.624034
$67$	286.489	0.522390	0.261195	−	0.965286i	$-0.415883\pi$
$67$	286.489	0.522390	0.261195	+	0.965286i	$0.415883\pi$
$68$	7.86750	0.0140305
$69$	382.252	0.666924
$70$	−493.565	−0.842747
$71$	131.491	0.219790	0.109895	−	0.993943i	$-0.464949\pi$
$71$	131.491	0.219790	0.109895	+	0.993943i	$0.464949\pi$
$72$	83.1691	0.136133
$73$	−728.979	−1.16877	−0.584387	−	0.811475i	$-0.698665\pi$
$73$	−728.979	−1.16877	−0.584387	+	0.811475i	$0.698665\pi$
$74$	359.900	0.565371
$75$	−182.758	−0.281374
$76$	−346.112	−0.522392
$77$	206.285	0.305303
$78$	1476.28	2.14302
$79$	818.448	1.16560	0.582801	−	0.812615i	$-0.301957\pi$
$79$	818.448	1.16560	0.582801	+	0.812615i	$0.301957\pi$
$80$	−277.741	−0.388154
$81$	−522.240	−0.716379
$82$	−1764.74	−2.37662
$83$	−866.308	−1.14566	−0.572829	−	0.819675i	$-0.694154\pi$
$83$	−866.308	−1.14566	−0.572829	+	0.819675i	$0.694154\pi$
$84$	618.567	0.803467
$85$	6.55403	0.00836335
$86$	0	0
$87$	1042.45	1.28462
$88$	−224.700	−0.272194
$89$	−875.385	−1.04259	−0.521296	−	0.853376i	$-0.674551\pi$
$89$	−875.385	−1.04259	−0.521296	+	0.853376i	$0.674551\pi$
$90$	250.359	0.293224
$91$	−910.145	−1.04845
$92$	927.593	1.05118
$93$	−1110.78	−1.23852
$94$	−1532.33	−1.68136
$95$	−288.329	−0.311389
$96$	1087.16	1.15581
$97$	−931.653	−0.975206	−0.487603	−	0.873065i	$-0.662129\pi$
$97$	−931.653	−0.975206	−0.487603	+	0.873065i	$0.662129\pi$
$98$	840.327	0.866182
$99$	−104.637	−0.106227
$100$	−443.489	−0.443489
$101$	684.651	0.674508	0.337254	−	0.941414i	$-0.390502\pi$
$101$	684.651	0.674508	0.337254	+	0.941414i	$0.390502\pi$
$102$	−14.1548	−0.0137405
$103$	952.202	0.910905	0.455453	−	0.890260i	$-0.349477\pi$
$103$	952.202	0.910905	0.455453	+	0.890260i	$0.349477\pi$
$104$	991.394	0.934751
$105$	515.299	0.478933
$106$	−463.309	−0.424534
$107$	−1668.40	−1.50738	−0.753692	−	0.657228i	$-0.771729\pi$
$107$	−1668.40	−1.50738	−0.753692	+	0.657228i	$0.771729\pi$
$108$	−1675.04	−1.49242
$109$	2171.21	1.90793	0.953966	−	0.299915i	$-0.0969583\pi$
$109$	2171.21	1.90793	0.953966	+	0.299915i	$0.0969583\pi$
$110$	−676.400	−0.586293
$111$	−375.748	−0.321301
$112$	−369.808	−0.311996
$113$	−1661.32	−1.38304	−0.691522	−	0.722356i	$-0.743059\pi$
$113$	−1661.32	−1.38304	−0.691522	+	0.722356i	$0.743059\pi$
$114$	622.706	0.511594
$115$	772.733	0.626589
$116$	2529.66	2.02477
$117$	461.668	0.364797
$118$	2987.98	2.33106
$119$	8.72660	0.00672240
$120$	−561.299	−0.426995
$121$	−1048.30	−0.787603
$122$	2208.80	1.63914
$123$	1842.45	1.35064
$124$	−2695.46	−1.95209
$125$	−1521.25	−1.08852
$126$	333.349	0.235691
$127$	−654.514	−0.457313	−0.228656	−	0.973507i	$-0.573433\pi$
$127$	−654.514	−0.457313	−0.228656	+	0.973507i	$0.573433\pi$
$128$	1585.38	1.09476
$129$	0	0
$130$	2984.33	2.01341
$131$	−2618.77	−1.74659	−0.873295	−	0.487191i	$-0.838022\pi$
$131$	−2618.77	−1.74659	−0.873295	+	0.487191i	$0.838022\pi$
$132$	847.709	0.558966
$133$	−383.907	−0.250293
$134$	−1250.78	−0.806350
$135$	−1395.40	−0.889606
$136$	−9.50562	−0.00599339
$137$	−416.002	−0.259427	−0.129713	−	0.991552i	$-0.541406\pi$
$137$	−416.002	−0.259427	−0.129713	+	0.991552i	$0.541406\pi$
$138$	−1668.87	−1.02945
$139$	−2067.40	−1.26154	−0.630771	−	0.775969i	$-0.717261\pi$
$139$	−2067.40	−1.26154	−0.630771	+	0.775969i	$0.717261\pi$
$140$	1250.45	0.754873
$141$	1599.80	0.955517
$142$	−574.074	−0.339262
$143$	−1247.30	−0.729401
$144$	187.584	0.108555
$145$	2107.34	1.20693
$146$	3182.65	1.80409
$147$	−877.330	−0.492252
$148$	−911.808	−0.506420
$149$	980.358	0.539020	0.269510	−	0.962998i	$-0.413138\pi$
$149$	980.358	0.539020	0.269510	+	0.962998i	$0.413138\pi$
$150$	797.900	0.434322
$151$	−10.8838	−0.00586566	−0.00293283	−	0.999996i	$-0.500934\pi$
$151$	−10.8838	−0.00586566	−0.00293283	+	0.999996i	$0.500934\pi$
$152$	418.178	0.223149
$153$	−4.42654	−0.00233898
$154$	−900.617	−0.471258
$155$	−2245.46	−1.16361
$156$	−3740.16	−1.91957
$157$	1029.44	0.523303	0.261651	−	0.965162i	$-0.415733\pi$
$157$	1029.44	0.523303	0.261651	+	0.965162i	$0.415733\pi$
$158$	−3573.26	−1.79920
$159$	483.711	0.241263
$160$	2197.72	1.08591
$161$	1028.88	0.503648
$162$	2280.05	1.10579
$163$	−939.084	−0.451256	−0.225628	−	0.974214i	$-0.572443\pi$
$163$	−939.084	−0.451256	−0.225628	+	0.974214i	$0.572443\pi$
$164$	4470.99	2.12881
$165$	706.185	0.333191
$166$	3782.21	1.76841
$167$	−1738.17	−0.805409	−0.402705	−	0.915330i	$-0.631930\pi$
$167$	−1738.17	−0.805409	−0.402705	+	0.915330i	$0.631930\pi$
$168$	−747.362	−0.343216
$169$	3306.18	1.50486
$170$	−28.6142	−0.0129095
$171$	194.735	0.0870864
$172$	0	0
$173$	−108.791	−0.0478107	−0.0239053	−	0.999714i	$-0.507610\pi$
$173$	−108.791	−0.0478107	−0.0239053	+	0.999714i	$0.507610\pi$
$174$	−4551.22	−1.98291
$175$	−491.916	−0.212488
$176$	−506.799	−0.217053
$177$	−3119.55	−1.32475
$178$	3821.84	1.60932
$179$	1852.75	0.773637	0.386819	−	0.922156i	$-0.373574\pi$
$179$	1852.75	0.773637	0.386819	+	0.922156i	$0.373574\pi$
$180$	−634.286	−0.262649
$181$	−1238.70	−0.508684	−0.254342	−	0.967114i	$-0.581859\pi$
$181$	−1238.70	−0.508684	−0.254342	+	0.967114i	$0.581859\pi$
$182$	3973.60	1.61837
$183$	−2306.07	−0.931527
$184$	−1120.73	−0.449029
$185$	−759.584	−0.301869
$186$	4849.53	1.91174
$187$	11.9593	0.00467673
$188$	3882.17	1.50604
$189$	−1857.95	−0.715059
$190$	1258.82	0.480653
$191$	2919.13	1.10587	0.552935	−	0.833224i	$-0.313508\pi$
$191$	2919.13	1.10587	0.552935	+	0.833224i	$0.313508\pi$
$192$	−3647.29	−1.37094
$193$	3126.80	1.16618	0.583089	−	0.812408i	$-0.301844\pi$
$193$	3126.80	1.16618	0.583089	+	0.812408i	$0.301844\pi$
$194$	4067.50	1.50530
$195$	−3115.75	−1.14422
$196$	−2128.97	−0.775865
$197$	−577.987	−0.209035	−0.104517	−	0.994523i	$-0.533330\pi$
$197$	−577.987	−0.209035	−0.104517	+	0.994523i	$0.533330\pi$
$198$	456.835	0.163969
$199$	−3122.70	−1.11237	−0.556187	−	0.831057i	$-0.687736\pi$
$199$	−3122.70	−1.11237	−0.556187	+	0.831057i	$0.687736\pi$
$200$	535.829	0.189444
$201$	1305.86	0.458249
$202$	−2989.11	−1.04115
$203$	2805.89	0.970122
$204$	35.8612	0.0123078
$205$	3724.56	1.26895
$206$	−4157.21	−1.40605
$207$	−521.897	−0.175238
$208$	2236.04	0.745391
$209$	−526.120	−0.174127
$210$	−2249.74	−0.739270
$211$	18.2053	0.00593985	0.00296992	−	0.999996i	$-0.499055\pi$
$211$	18.2053	0.00593985	0.00296992	+	0.999996i	$0.499055\pi$
$212$	1173.80	0.380268
$213$	599.353	0.192803
$214$	7284.04	2.32676
$215$	0	0
$216$	2023.81	0.637514
$217$	−2989.80	−0.935303
$218$	−9479.29	−2.94504
$219$	−3322.79	−1.02527
$220$	1713.66	0.525160
$221$	−52.7653	−0.0160605
$222$	1640.47	0.495952
$223$	1922.00	0.577159	0.288580	−	0.957456i	$-0.406817\pi$
$223$	1922.00	0.577159	0.288580	+	0.957456i	$0.406817\pi$
$224$	2926.24	0.872845
$225$	249.523	0.0739327
$226$	7253.15	2.13483
$227$	696.092	0.203530	0.101765	−	0.994808i	$-0.467551\pi$
$227$	696.092	0.203530	0.101765	+	0.994808i	$0.467551\pi$
$228$	−1577.63	−0.458250
$229$	1905.58	0.549888	0.274944	−	0.961460i	$-0.411341\pi$
$229$	1905.58	0.549888	0.274944	+	0.961460i	$0.411341\pi$
$230$	−3373.67	−0.967188
$231$	940.276	0.267816
$232$	−3056.37	−0.864916
$233$	3393.10	0.954032	0.477016	−	0.878895i	$-0.341718\pi$
$233$	3393.10	0.954032	0.477016	+	0.878895i	$0.341718\pi$
$234$	−2015.59	−0.563092
$235$	3234.05	0.897727
$236$	−7570.06	−2.08800
$237$	3730.60	1.02248
$238$	−38.0994	−0.0103765
$239$	4251.40	1.15063	0.575314	−	0.817933i	$-0.304880\pi$
$239$	4251.40	1.15063	0.575314	+	0.817933i	$0.304880\pi$
$240$	−1265.98	−0.340495
$241$	−7017.82	−1.87576	−0.937878	−	0.346964i	$-0.887213\pi$
$241$	−7017.82	−1.87576	−0.937878	+	0.346964i	$0.887213\pi$
$242$	4576.76	1.21572
$243$	1708.34	0.450989
$244$	−5596.02	−1.46823
$245$	−1773.55	−0.462480
$246$	−8043.95	−2.08481
$247$	2321.29	0.597975
$248$	3256.70	0.833873
$249$	−3948.75	−1.00499
$250$	6641.61	1.68021
$251$	2690.62	0.676616	0.338308	−	0.941035i	$-0.390145\pi$
$251$	2690.62	0.676616	0.338308	+	0.941035i	$0.390145\pi$
$252$	−844.543	−0.211116
$253$	1410.02	0.350384
$254$	2857.54	0.705897
$255$	29.8742	0.00733646
$256$	−520.250	−0.127014
$257$	−652.543	−0.158383	−0.0791917	−	0.996859i	$-0.525234\pi$
$257$	−652.543	−0.158383	−0.0791917	+	0.996859i	$0.525234\pi$
$258$	0	0
$259$	−1011.37	−0.242640
$260$	−7560.83	−1.80347
$261$	−1423.28	−0.337543
$262$	11433.3	2.69600
$263$	4954.26	1.16157	0.580785	−	0.814057i	$-0.302746\pi$
$263$	4954.26	1.16157	0.580785	+	0.814057i	$0.302746\pi$
$264$	−1024.21	−0.238773
$265$	977.834	0.226671
$266$	1676.09	0.386346
$267$	−3990.13	−0.914577
$268$	3168.86	0.722271
$269$	−7037.55	−1.59512	−0.797559	−	0.603240i	$-0.793876\pi$
$269$	−7037.55	−1.59512	−0.797559	+	0.603240i	$0.793876\pi$
$270$	6092.16	1.37317
$271$	−85.5726	−0.0191814	−0.00959071	−	0.999954i	$-0.503053\pi$
$271$	−85.5726	−0.0191814	−0.00959071	+	0.999954i	$0.503053\pi$
$272$	−21.4394	−0.00477925
$273$	−4148.57	−0.919718
$274$	1816.22	0.400445
$275$	−674.141	−0.147826
$276$	4228.10	0.922108
$277$	−7482.63	−1.62306	−0.811530	−	0.584311i	$-0.801365\pi$
$277$	−7482.63	−1.62306	−0.811530	+	0.584311i	$0.801365\pi$
$278$	9026.04	1.94729
$279$	1516.57	0.325428
$280$	−1510.81	−0.322458
$281$	−2737.49	−0.581156	−0.290578	−	0.956851i	$-0.593848\pi$
$281$	−2737.49	−0.581156	−0.290578	+	0.956851i	$0.593848\pi$
$282$	−6984.57	−1.47491
$283$	7419.35	1.55843	0.779213	−	0.626759i	$-0.215619\pi$
$283$	7419.35	1.55843	0.779213	+	0.626759i	$0.215619\pi$
$284$	1454.42	0.303887
$285$	−1314.25	−0.273155
$286$	5445.57	1.12589
$287$	4959.20	1.01997
$288$	−1484.32	−0.303696
$289$	−4912.49	−0.999897
$290$	−9200.41	−1.86299
$291$	−4246.61	−0.855466
$292$	−8063.25	−1.61598
$293$	1795.65	0.358031	0.179016	−	0.983846i	$-0.442709\pi$
$293$	1795.65	0.358031	0.179016	+	0.983846i	$0.442709\pi$
$294$	3830.33	0.759828
$295$	−6306.26	−1.24463
$296$	1101.66	0.216327
$297$	−2546.21	−0.497462
$298$	−4280.14	−0.832019
$299$	−6221.13	−1.20327
$300$	−2021.49	−0.389035
$301$	0	0
$302$	47.5177	0.00905409
$303$	3120.74	0.591689
$304$	943.178	0.177944
$305$	−4661.78	−0.875188
$306$	19.3258	0.00361040
$307$	−1176.57	−0.218731	−0.109365	−	0.994002i	$-0.534882\pi$
$307$	−1176.57	−0.218731	−0.109365	+	0.994002i	$0.534882\pi$
$308$	2281.72	0.422120
$309$	4340.27	0.799060
$310$	9803.44	1.79612
$311$	−6297.41	−1.14821	−0.574105	−	0.818781i	$-0.694650\pi$
$311$	−6297.41	−1.14821	−0.574105	+	0.818781i	$0.694650\pi$
$312$	4518.91	0.819978
$313$	−1173.09	−0.211843	−0.105922	−	0.994374i	$-0.533779\pi$
$313$	−1173.09	−0.211843	−0.105922	+	0.994374i	$0.533779\pi$
$314$	−4494.44	−0.807758
$315$	−703.548	−0.125843
$316$	9052.87	1.61159
$317$	−1245.65	−0.220702	−0.110351	−	0.993893i	$-0.535198\pi$
$317$	−1245.65	−0.220702	−0.110351	+	0.993893i	$0.535198\pi$
$318$	−2111.83	−0.372407
$319$	3845.30	0.674907
$320$	−7373.10	−1.28803
$321$	−7604.79	−1.32230
$322$	−4491.99	−0.777419
$323$	−22.2568	−0.00383406
$324$	−5776.51	−0.990485
$325$	2974.37	0.507656
$326$	4099.94	0.696548
$327$	9896.70	1.67367
$328$	−5401.91	−0.909361
$329$	4306.09	0.721587
$330$	−3083.13	−0.514305
$331$	−985.833	−0.163705	−0.0818524	−	0.996644i	$-0.526084\pi$
$331$	−985.833	−0.163705	−0.0818524	+	0.996644i	$0.526084\pi$
$332$	−9582.25	−1.58402
$333$	513.016	0.0844238
$334$	7588.65	1.24321
$335$	2639.82	0.430534
$336$	−1685.64	−0.273687
$337$	−11334.6	−1.83214	−0.916072	−	0.401014i	$-0.868658\pi$
$337$	−11334.6	−1.83214	−0.916072	+	0.401014i	$0.868658\pi$
$338$	−14434.4	−2.32287
$339$	−7572.54	−1.21323
$340$	72.4943	0.0115634
$341$	−4097.34	−0.650684
$342$	−850.193	−0.134425
$343$	−6569.67	−1.03419
$344$	0	0
$345$	3522.23	0.549653
$346$	474.971	0.0737994
$347$	−5204.31	−0.805135	−0.402568	−	0.915390i	$-0.631882\pi$
$347$	−5204.31	−0.805135	−0.402568	+	0.915390i	$0.631882\pi$
$348$	11530.5	1.77616
$349$	−5544.71	−0.850434	−0.425217	−	0.905091i	$-0.639802\pi$
$349$	−5544.71	−0.850434	−0.425217	+	0.905091i	$0.639802\pi$
$350$	2147.65	0.327991
$351$	11234.1	1.70835
$352$	4010.23	0.607232
$353$	2758.98	0.415993	0.207997	−	0.978130i	$-0.433306\pi$
$353$	2758.98	0.415993	0.207997	+	0.978130i	$0.433306\pi$
$354$	13619.6	2.04485
$355$	1211.61	0.181142
$356$	−9682.65	−1.44152
$357$	39.7771	0.00589699
$358$	−8088.91	−1.19417
$359$	−414.845	−0.0609879	−0.0304940	−	0.999535i	$-0.509708\pi$
$359$	−414.845	−0.0609879	−0.0304940	+	0.999535i	$0.509708\pi$
$360$	766.354	0.112196
$361$	−5879.86	−0.857248
$362$	5408.03	0.785192
$363$	−4778.30	−0.690897
$364$	−10067.1	−1.44962
$365$	−6717.11	−0.963259
$366$	10068.0	1.43788
$367$	2138.28	0.304134	0.152067	−	0.988370i	$-0.451407\pi$
$367$	2138.28	0.304134	0.152067	+	0.988370i	$0.451407\pi$
$368$	−2527.75	−0.358066
$369$	−2515.54	−0.354888
$370$	3316.26	0.465957
$371$	1301.97	0.182197
$372$	−12286.3	−1.71241
$373$	−5285.65	−0.733728	−0.366864	−	0.930275i	$-0.619569\pi$
$373$	−5285.65	−0.733728	−0.366864	+	0.930275i	$0.619569\pi$
$374$	−52.2129	−0.00721889
$375$	−6934.07	−0.954864
$376$	−4690.49	−0.643334
$377$	−16965.8	−2.31772
$378$	8111.63	1.10375
$379$	−12413.5	−1.68242	−0.841209	−	0.540711i	$-0.818155\pi$
$379$	−12413.5	−1.68242	−0.841209	+	0.540711i	$0.818155\pi$
$380$	−3189.22	−0.430535
$381$	−2983.37	−0.401162
$382$	−12744.6	−1.70699
$383$	−8332.12	−1.11162	−0.555811	−	0.831309i	$-0.687592\pi$
$383$	−8332.12	−1.11162	−0.555811	+	0.831309i	$0.687592\pi$
$384$	7226.40	0.960341
$385$	1900.79	0.251619
$386$	−13651.3	−1.80008
$387$	0	0
$388$	−10305.0	−1.34835
$389$	7320.42	0.954139	0.477070	−	0.878866i	$-0.341699\pi$
$389$	7320.42	0.954139	0.477070	+	0.878866i	$0.341699\pi$
$390$	13603.0	1.76619
$391$	59.6490	0.00771504
$392$	2572.26	0.331425
$393$	−11936.8	−1.53214
$394$	2523.43	0.322661
$395$	7541.51	0.960645
$396$	−1157.39	−0.146872
$397$	−3845.49	−0.486145	−0.243072	−	0.970008i	$-0.578155\pi$
$397$	−3845.49	−0.486145	−0.243072	+	0.970008i	$0.578155\pi$
$398$	13633.4	1.71703
$399$	−1749.90	−0.219560
$400$	1208.54	0.151067
$401$	5006.78	0.623508	0.311754	−	0.950163i	$-0.399083\pi$
$401$	5006.78	0.623508	0.311754	+	0.950163i	$0.399083\pi$
$402$	−5701.23	−0.707342
$403$	18077.8	2.23454
$404$	7572.94	0.932593
$405$	−4812.13	−0.590412
$406$	−12250.2	−1.49746
$407$	−1386.03	−0.168803
$408$	−43.3280	−0.00525749
$409$	−13425.9	−1.62315	−0.811576	−	0.584247i	$-0.801390\pi$
$409$	−13425.9	−1.62315	−0.811576	+	0.584247i	$0.801390\pi$
$410$	−16261.0	−1.95872
$411$	−1896.20	−0.227573
$412$	10532.3	1.25944
$413$	−8396.69	−1.00042
$414$	2278.55	0.270494
$415$	−7982.51	−0.944207
$416$	−17693.4	−2.08532
$417$	−9423.50	−1.10664
$418$	2296.99	0.268778
$419$	1937.99	0.225959	0.112980	−	0.993597i	$-0.463960\pi$
$419$	1937.99	0.225959	0.112980	+	0.993597i	$0.463960\pi$
$420$	5699.73	0.662186
$421$	13008.2	1.50589	0.752946	−	0.658082i	$-0.228632\pi$
$421$	13008.2	1.50589	0.752946	+	0.658082i	$0.228632\pi$
$422$	−79.4826	−0.00916861
$423$	−2184.25	−0.251068
$424$	−1418.20	−0.162438
$425$	−28.5186	−0.00325496
$426$	−2616.71	−0.297606
$427$	−6207.09	−0.703471
$428$	−18454.2	−2.08415
$429$	−5685.37	−0.639842
$430$	0	0
$431$	445.930	0.0498368	0.0249184	−	0.999689i	$-0.492067\pi$
$431$	445.930	0.0498368	0.0249184	+	0.999689i	$0.492067\pi$
$432$	4564.60	0.508367
$433$	4958.33	0.550306	0.275153	−	0.961401i	$-0.411272\pi$
$433$	4958.33	0.550306	0.275153	+	0.961401i	$0.411272\pi$
$434$	13053.1	1.44371
$435$	9605.55	1.05874
$436$	24015.8	2.63796
$437$	−2624.12	−0.287251
$438$	14507.0	1.58258
$439$	2244.32	0.243999	0.121999	−	0.992530i	$-0.461069\pi$
$439$	2244.32	0.243999	0.121999	+	0.992530i	$0.461069\pi$
$440$	−2070.47	−0.224332
$441$	1197.84	0.129342
$442$	230.368	0.0247907
$443$	1526.48	0.163714	0.0818569	−	0.996644i	$-0.473915\pi$
$443$	1526.48	0.163714	0.0818569	+	0.996644i	$0.473915\pi$
$444$	−4156.15	−0.444239
$445$	−8066.15	−0.859264
$446$	−8391.24	−0.890889
$447$	4468.61	0.472837
$448$	−9817.17	−1.03531
$449$	−8410.88	−0.884040	−0.442020	−	0.897005i	$-0.645738\pi$
$449$	−8410.88	−0.884040	−0.442020	+	0.897005i	$0.645738\pi$
$450$	−1089.39	−0.114121
$451$	6796.28	0.709589
$452$	−18375.9	−1.91223
$453$	−49.6101	−0.00514544
$454$	−3039.06	−0.314164
$455$	−8386.45	−0.864094
$456$	1906.11	0.195750
$457$	15218.4	1.55774	0.778871	−	0.627184i	$-0.215793\pi$
$457$	15218.4	1.55774	0.778871	+	0.627184i	$0.215793\pi$
$458$	−8319.57	−0.848795
$459$	−107.714	−0.0109535
$460$	8547.21	0.866339
$461$	−15195.2	−1.53517	−0.767584	−	0.640948i	$-0.778541\pi$
$461$	−15195.2	−1.53517	−0.767584	+	0.640948i	$0.778541\pi$
$462$	−4105.14	−0.413395
$463$	−18232.8	−1.83013	−0.915064	−	0.403309i	$-0.867860\pi$
$463$	−18232.8	−1.83013	−0.915064	+	0.403309i	$0.867860\pi$
$464$	−6893.49	−0.689703
$465$	−10235.1	−1.02074
$466$	−14813.9	−1.47262
$467$	−358.288	−0.0355024	−0.0177512	−	0.999842i	$-0.505651\pi$
$467$	−358.288	−0.0355024	−0.0177512	+	0.999842i	$0.505651\pi$
$468$	5106.52	0.504378
$469$	3514.89	0.346060
$470$	−14119.5	−1.38571
$471$	4692.35	0.459049
$472$	9146.26	0.891929
$473$	0	0
$474$	−16287.4	−1.57828
$475$	1254.61	0.121191
$476$	96.5251	0.00929458
$477$	−660.421	−0.0633933
$478$	−18561.1	−1.77608
$479$	9899.32	0.944283	0.472141	−	0.881523i	$-0.343481\pi$
$479$	9899.32	0.944283	0.472141	+	0.881523i	$0.343481\pi$
$480$	10017.5	0.952574
$481$	6115.26	0.579692
$482$	30639.0	2.89537
$483$	4689.80	0.441808
$484$	−11595.3	−1.08896
$485$	−8584.63	−0.803727
$486$	−7458.45	−0.696136
$487$	12134.7	1.12911	0.564556	−	0.825395i	$-0.309048\pi$
$487$	12134.7	1.12911	0.564556	+	0.825395i	$0.309048\pi$
$488$	6761.19	0.627182
$489$	−4280.48	−0.395849
$490$	7743.11	0.713874
$491$	15090.3	1.38699	0.693497	−	0.720460i	$-0.256069\pi$
$491$	15090.3	1.38699	0.693497	+	0.720460i	$0.256069\pi$
$492$	20379.4	1.86743
$493$	162.670	0.0148607
$494$	−10134.5	−0.923021
$495$	−964.170	−0.0875479
$496$	7345.31	0.664948
$497$	1613.24	0.145601
$498$	17239.8	1.55128
$499$	−2697.31	−0.241980	−0.120990	−	0.992654i	$-0.538607\pi$
$499$	−2697.31	−0.241980	−0.120990	+	0.992654i	$0.538607\pi$
$500$	−16826.6	−1.50501
$501$	−7922.81	−0.706517
$502$	−11747.0	−1.04441
$503$	1379.96	0.122325	0.0611626	−	0.998128i	$-0.480519\pi$
$503$	1379.96	0.122325	0.0611626	+	0.998128i	$0.480519\pi$
$504$	1020.39	0.0901820
$505$	6308.65	0.555903
$506$	−6156.00	−0.540845
$507$	15070.1	1.32009
$508$	−7239.59	−0.632293
$509$	21509.0	1.87302	0.936512	−	0.350636i	$-0.114035\pi$
$509$	21509.0	1.87302	0.936512	+	0.350636i	$0.114035\pi$
$510$	−130.428	−0.0113244
$511$	−8943.74	−0.774261
$512$	−10411.7	−0.898705
$513$	4738.63	0.407828
$514$	2848.93	0.244477
$515$	8773.97	0.750733
$516$	0	0
$517$	5901.23	0.502003
$518$	4415.55	0.374533
$519$	−495.886	−0.0419402
$520$	9135.10	0.770386
$521$	11509.1	0.967801	0.483901	−	0.875123i	$-0.339220\pi$
$521$	11509.1	0.967801	0.483901	+	0.875123i	$0.339220\pi$
$522$	6213.88	0.521023
$523$	−7328.63	−0.612732	−0.306366	−	0.951914i	$-0.599113\pi$
$523$	−7328.63	−0.612732	−0.306366	+	0.951914i	$0.599113\pi$
$524$	−28966.3	−2.41488
$525$	−2242.22	−0.186398
$526$	−21629.8	−1.79297
$527$	−173.332	−0.0143273
$528$	−2310.06	−0.190402
$529$	−5134.26	−0.421983
$530$	−4269.12	−0.349884
$531$	4259.19	0.348085
$532$	−4246.40	−0.346061
$533$	−29985.8	−2.43682
$534$	17420.5	1.41172
$535$	−15373.3	−1.24233
$536$	−3828.66	−0.308531
$537$	8445.10	0.678646
$538$	30725.2	2.46219
$539$	−3236.22	−0.258616
$540$	−15434.5	−1.22999
$541$	−7202.89	−0.572415	−0.286207	−	0.958168i	$-0.592395\pi$
$541$	−7202.89	−0.572415	−0.286207	+	0.958168i	$0.592395\pi$
$542$	373.601	0.0296080
$543$	−5646.17	−0.446225
$544$	169.647	0.0133705
$545$	20006.4	1.57244
$546$	18112.2	1.41965
$547$	−4157.56	−0.324980	−0.162490	−	0.986710i	$-0.551953\pi$
$547$	−4157.56	−0.324980	−0.162490	+	0.986710i	$0.551953\pi$
$548$	−4601.40	−0.358690
$549$	3148.52	0.244764
$550$	2943.23	0.228181
$551$	−7156.30	−0.553301
$552$	−5108.45	−0.393895
$553$	10041.4	0.772160
$554$	32668.3	2.50532
$555$	−3462.29	−0.264804
$556$	−22867.5	−1.74424
$557$	−22327.8	−1.69849	−0.849244	−	0.528000i	$-0.822942\pi$
$557$	−22327.8	−1.69849	−0.849244	+	0.528000i	$0.822942\pi$
$558$	−6621.16	−0.502323
$559$	0	0
$560$	−3407.56	−0.257135
$561$	54.5121	0.00410250
$562$	11951.6	0.897058
$563$	−13573.2	−1.01606	−0.508030	−	0.861339i	$-0.669626\pi$
$563$	−13573.2	−1.01606	−0.508030	+	0.861339i	$0.669626\pi$
$564$	17695.5	1.32112
$565$	−15308.1	−1.13985
$566$	−32392.1	−2.40555
$567$	−6407.29	−0.474569
$568$	−1757.25	−0.129811
$569$	5624.98	0.414432	0.207216	−	0.978295i	$-0.433560\pi$
$569$	5624.98	0.414432	0.207216	+	0.978295i	$0.433560\pi$
$570$	5737.86	0.421636
$571$	15220.7	1.11553	0.557764	−	0.830000i	$-0.311659\pi$
$571$	15220.7	1.11553	0.557764	+	0.830000i	$0.311659\pi$
$572$	−13796.4	−1.00849
$573$	13305.8	0.970086
$574$	−21651.3	−1.57441
$575$	−3362.40	−0.243864
$576$	4979.72	0.360223
$577$	−681.710	−0.0491854	−0.0245927	−	0.999698i	$-0.507829\pi$
$577$	−681.710	−0.0491854	−0.0245927	+	0.999698i	$0.507829\pi$
$578$	21447.4	1.54342
$579$	14252.4	1.02299
$580$	23309.3	1.66873
$581$	−10628.6	−0.758947
$582$	18540.2	1.32048
$583$	1784.27	0.126753
$584$	9742.14	0.690296
$585$	4254.00	0.300651
$586$	−7839.63	−0.552649
$587$	5340.96	0.375545	0.187772	−	0.982213i	$-0.439873\pi$
$587$	5340.96	0.375545	0.187772	+	0.982213i	$0.439873\pi$
$588$	−9704.17	−0.680601
$589$	7625.35	0.533442
$590$	27532.4	1.92117
$591$	−2634.55	−0.183368
$592$	2484.74	0.172503
$593$	−21506.7	−1.48933	−0.744667	−	0.667436i	$-0.767392\pi$
$593$	−21506.7	−1.48933	−0.744667	+	0.667436i	$0.767392\pi$
$594$	11116.5	0.767870
$595$	80.4104	0.00554035
$596$	10843.8	0.745264
$597$	−14233.7	−0.975791
$598$	27160.8	1.85734
$599$	14146.1	0.964930	0.482465	−	0.875915i	$-0.339742\pi$
$599$	14146.1	0.964930	0.482465	+	0.875915i	$0.339742\pi$
$600$	2442.39	0.166183
$601$	1655.86	0.112386	0.0561930	−	0.998420i	$-0.482104\pi$
$601$	1655.86	0.112386	0.0561930	+	0.998420i	$0.482104\pi$
$602$	0	0
$603$	−1782.91	−0.120408
$604$	−120.386	−0.00811002
$605$	−9659.45	−0.649112
$606$	−13624.8	−0.913316
$607$	−15879.9	−1.06185	−0.530927	−	0.847418i	$-0.678156\pi$
$607$	−15879.9	−1.06185	−0.530927	+	0.847418i	$0.678156\pi$
$608$	−7463.24	−0.497820
$609$	12789.6	0.851006
$610$	20352.8	1.35092
$611$	−26036.7	−1.72395
$612$	−48.9620	−0.00323394
$613$	−16780.0	−1.10561	−0.552805	−	0.833310i	$-0.686443\pi$
$613$	−16780.0	−1.10561	−0.552805	+	0.833310i	$0.686443\pi$
$614$	5136.78	0.337628
$615$	16977.1	1.11314
$616$	−2756.81	−0.180316
$617$	−14010.6	−0.914174	−0.457087	−	0.889422i	$-0.651107\pi$
$617$	−14010.6	−0.914174	−0.457087	+	0.889422i	$0.651107\pi$
$618$	−18949.2	−1.23341
$619$	−816.326	−0.0530063	−0.0265032	−	0.999649i	$-0.508437\pi$
$619$	−816.326	−0.0530063	−0.0265032	+	0.999649i	$0.508437\pi$
$620$	−24837.1	−1.60884
$621$	−12699.7	−0.820646
$622$	27493.8	1.77235
$623$	−10740.0	−0.690670
$624$	10192.2	0.653868
$625$	−9005.57	−0.576356
$626$	5121.58	0.326996
$627$	−2398.13	−0.152747
$628$	11386.7	0.723533
$629$	−58.6340	−0.00371684
$630$	3071.62	0.194248
$631$	11978.4	0.755707	0.377854	−	0.925865i	$-0.376662\pi$
$631$	11978.4	0.755707	0.377854	+	0.925865i	$0.376662\pi$
$632$	−10937.8	−0.688422
$633$	82.9826	0.00521052
$634$	5438.37	0.340671
$635$	−6030.96	−0.376900
$636$	5350.34	0.333577
$637$	14278.5	0.888123
$638$	−16788.2	−1.04177
$639$	−818.310	−0.0506602
$640$	14608.4	0.902260
$641$	14562.7	0.897334	0.448667	−	0.893699i	$-0.351899\pi$
$641$	14562.7	0.897334	0.448667	+	0.893699i	$0.351899\pi$
$642$	33201.7	2.04107
$643$	3387.10	0.207736	0.103868	−	0.994591i	$-0.466878\pi$
$643$	3387.10	0.207736	0.103868	+	0.994591i	$0.466878\pi$
$644$	11380.5	0.696357
$645$	0	0
$646$	97.1709	0.00591817
$647$	16289.3	0.989795	0.494897	−	0.868951i	$-0.335206\pi$
$647$	16289.3	0.989795	0.494897	+	0.868951i	$0.335206\pi$
$648$	6979.26	0.423104
$649$	−11507.1	−0.695986
$650$	−12985.8	−0.783605
$651$	−13627.9	−0.820462
$652$	−10387.2	−0.623919
$653$	−15881.5	−0.951748	−0.475874	−	0.879513i	$-0.657868\pi$
$653$	−15881.5	−0.951748	−0.475874	+	0.879513i	$0.657868\pi$
$654$	−43207.9	−2.58343
$655$	−24130.5	−1.43947
$656$	−12183.7	−0.725144
$657$	4536.68	0.269395
$658$	−18799.9	−1.11382
$659$	28668.4	1.69463	0.847317	−	0.531088i	$-0.178216\pi$
$659$	28668.4	1.69463	0.847317	+	0.531088i	$0.178216\pi$
$660$	7811.13	0.460679
$661$	31453.7	1.85084	0.925421	−	0.378941i	$-0.123712\pi$
$661$	31453.7	1.85084	0.925421	+	0.378941i	$0.123712\pi$
$662$	4304.04	0.252691
$663$	−240.512	−0.0140885
$664$	11577.4	0.676642
$665$	−3537.47	−0.206282
$666$	−2239.77	−0.130315
$667$	19179.1	1.11337
$668$	−19225.9	−1.11358
$669$	8760.74	0.506293
$670$	−11525.2	−0.664562
$671$	−8506.43	−0.489400
$672$	13338.2	0.765673
$673$	12544.9	0.718529	0.359264	−	0.933236i	$-0.383028\pi$
$673$	12544.9	0.718529	0.359264	+	0.933236i	$0.383028\pi$
$674$	49485.4	2.82805
$675$	6071.81	0.346229
$676$	36569.8	2.08066
$677$	14459.9	0.820886	0.410443	−	0.911886i	$-0.365374\pi$
$677$	14459.9	0.820886	0.410443	+	0.911886i	$0.365374\pi$
$678$	33060.9	1.87271
$679$	−11430.3	−0.646031
$680$	−87.5887	−0.00493952
$681$	3172.89	0.178539
$682$	17888.5	1.00438
$683$	20645.9	1.15665	0.578326	−	0.815805i	$-0.303706\pi$
$683$	20645.9	1.15665	0.578326	+	0.815805i	$0.303706\pi$
$684$	2153.97	0.120408
$685$	−3833.21	−0.213809
$686$	28682.5	1.59636
$687$	8685.92	0.482370
$688$	0	0
$689$	−7872.36	−0.435287
$690$	−15377.7	−0.848432
$691$	−28793.3	−1.58517	−0.792583	−	0.609764i	$-0.791264\pi$
$691$	−28793.3	−1.58517	−0.792583	+	0.609764i	$0.791264\pi$
$692$	−1203.34	−0.0661043
$693$	−1283.78	−0.0703704
$694$	22721.4	1.24279
$695$	−19049.8	−1.03971
$696$	−13931.4	−0.758718
$697$	287.508	0.0156243
$698$	24207.6	1.31271
$699$	15466.2	0.836891
$700$	−5441.09	−0.293792
$701$	33535.8	1.80689	0.903446	−	0.428702i	$-0.141029\pi$
$701$	33535.8	1.80689	0.903446	+	0.428702i	$0.141029\pi$
$702$	−49046.9	−2.63697
$703$	2579.47	0.138388
$704$	−13453.8	−0.720256
$705$	14741.2	0.787500
$706$	−12045.4	−0.642117
$707$	8399.88	0.446831
$708$	−34505.4	−1.83163
$709$	33148.9	1.75590	0.877949	−	0.478754i	$-0.158911\pi$
$709$	33148.9	1.75590	0.877949	+	0.478754i	$0.158911\pi$
$710$	−5289.75	−0.279607
$711$	−5093.47	−0.268664
$712$	11698.7	0.615770
$713$	−20436.2	−1.07341
$714$	−173.663	−0.00910246
$715$	−11493.1	−0.601144
$716$	20493.3	1.06965
$717$	19378.5	1.00935
$718$	1811.17	0.0941395
$719$	29532.0	1.53179	0.765897	−	0.642964i	$-0.222295\pi$
$719$	29532.0	1.53179	0.765897	+	0.642964i	$0.222295\pi$
$720$	1728.47	0.0894671
$721$	11682.4	0.603434
$722$	25670.9	1.32323
$723$	−31988.2	−1.64544
$724$	−13701.3	−0.703320
$725$	−9169.68	−0.469729
$726$	20861.5	1.06645
$727$	24493.4	1.24953	0.624767	−	0.780812i	$-0.285194\pi$
$727$	24493.4	1.24953	0.624767	+	0.780812i	$0.285194\pi$
$728$	12163.3	0.619231
$729$	21887.4	1.11199
$730$	29326.2	1.48686
$731$	0	0
$732$	−25507.5	−1.28795
$733$	−8414.17	−0.423990	−0.211995	−	0.977271i	$-0.567996\pi$
$733$	−8414.17	−0.423990	−0.211995	+	0.977271i	$0.567996\pi$
$734$	−9335.49	−0.469454
$735$	−8084.08	−0.405695
$736$	20001.7	1.00173
$737$	4816.94	0.240752
$738$	10982.6	0.547797
$739$	−24915.3	−1.24022	−0.620112	−	0.784513i	$-0.712913\pi$
$739$	−24915.3	−1.24022	−0.620112	+	0.784513i	$0.712913\pi$
$740$	−8401.77	−0.417372
$741$	10580.8	0.524553
$742$	−5684.27	−0.281235
$743$	−4445.87	−0.219520	−0.109760	−	0.993958i	$-0.535008\pi$
$743$	−4445.87	−0.219520	−0.109760	+	0.993958i	$0.535008\pi$
$744$	14844.5	0.731486
$745$	9033.41	0.444240
$746$	23076.6	1.13256
$747$	5391.32	0.264067
$748$	132.282	0.00646618
$749$	−20469.3	−0.998575
$750$	30273.4	1.47391
$751$	−5126.52	−0.249094	−0.124547	−	0.992214i	$-0.539748\pi$
$751$	−5126.52	−0.249094	−0.124547	+	0.992214i	$0.539748\pi$
$752$	−10579.2	−0.513008
$753$	12264.2	0.593538
$754$	74070.8	3.57758
$755$	−100.288	−0.00483425
$756$	−20550.9	−0.988661
$757$	6695.39	0.321464	0.160732	−	0.986998i	$-0.448615\pi$
$757$	6695.39	0.321464	0.160732	+	0.986998i	$0.448615\pi$
$758$	54195.8	2.59694
$759$	6427.08	0.307363
$760$	3853.26	0.183911
$761$	−28439.2	−1.35469	−0.677346	−	0.735665i	$-0.736870\pi$
$761$	−28439.2	−1.35469	−0.677346	+	0.735665i	$0.736870\pi$
$762$	13025.1	0.619224
$763$	26638.3	1.26392
$764$	32288.6	1.52901
$765$	−40.7879	−0.00192770
$766$	36377.1	1.71587
$767$	50770.5	2.39011
$768$	−2371.37	−0.111419
$769$	−33342.3	−1.56353	−0.781765	−	0.623573i	$-0.785680\pi$
$769$	−33342.3	−1.56353	−0.781765	+	0.623573i	$0.785680\pi$
$770$	−8298.65	−0.388393
$771$	−2974.39	−0.138936
$772$	34585.6	1.61239
$773$	−31381.8	−1.46019	−0.730094	−	0.683347i	$-0.760524\pi$
$773$	−31381.8	−1.46019	−0.730094	+	0.683347i	$0.760524\pi$
$774$	0	0
$775$	9770.70	0.452870
$776$	12450.7	0.575971
$777$	−4609.99	−0.212847
$778$	−31960.2	−1.47279
$779$	−12648.2	−0.581733
$780$	−34463.3	−1.58203
$781$	2210.85	0.101294
$782$	−260.421	−0.0119088
$783$	−34633.6	−1.58072
$784$	5801.59	0.264285
$785$	9485.71	0.431286
$786$	52114.6	2.36497
$787$	613.312	0.0277792	0.0138896	−	0.999904i	$-0.495579\pi$
$787$	613.312	0.0277792	0.0138896	+	0.999904i	$0.495579\pi$
$788$	−6393.12	−0.289017
$789$	22582.2	1.01895
$790$	−32925.4	−1.48283
$791$	−20382.5	−0.916205
$792$	1398.38	0.0627390
$793$	37531.1	1.68067
$794$	16789.0	0.750401
$795$	4457.11	0.198839
$796$	−34540.3	−1.53800
$797$	3342.58	0.148557	0.0742786	−	0.997238i	$-0.476335\pi$
$797$	3342.58	0.148557	0.0742786	+	0.997238i	$0.476335\pi$
$798$	7639.88	0.338908
$799$	249.644	0.0110535
$800$	−9562.97	−0.422628
$801$	5447.81	0.240311
$802$	−21859.1	−0.962433
$803$	−12256.8	−0.538648
$804$	14444.1	0.633587
$805$	9480.54	0.415087
$806$	−78925.7	−3.44918
$807$	−32078.2	−1.39926
$808$	−9149.73	−0.398374
$809$	4568.46	0.198539	0.0992697	−	0.995061i	$-0.468349\pi$
$809$	4568.46	0.198539	0.0992697	+	0.995061i	$0.468349\pi$
$810$	21009.3	0.911346
$811$	42027.8	1.81972	0.909861	−	0.414913i	$-0.136188\pi$
$811$	42027.8	1.81972	0.909861	+	0.414913i	$0.136188\pi$
$812$	31036.0	1.34132
$813$	−390.052	−0.0168262
$814$	6051.24	0.260560
$815$	−8653.10	−0.371908
$816$	−97.7240	−0.00419243
$817$	0	0
$818$	58616.1	2.50546
$819$	5664.13	0.241662
$820$	41197.5	1.75449
$821$	−20734.9	−0.881428	−0.440714	−	0.897647i	$-0.645275\pi$
$821$	−20734.9	−0.881428	−0.440714	+	0.897647i	$0.645275\pi$
$822$	8278.59	0.351276
$823$	−25400.2	−1.07582	−0.537908	−	0.843003i	$-0.680785\pi$
$823$	−25400.2	−1.07582	−0.537908	+	0.843003i	$0.680785\pi$
$824$	−12725.3	−0.537994
$825$	−3072.83	−0.129675
$826$	36659.0	1.54423
$827$	1209.68	0.0508643	0.0254321	−	0.999677i	$-0.491904\pi$
$827$	1209.68	0.0508643	0.0254321	+	0.999677i	$0.491904\pi$
$828$	−5772.72	−0.242290
$829$	−14758.5	−0.618318	−0.309159	−	0.951010i	$-0.600048\pi$
$829$	−14758.5	−0.618318	−0.309159	+	0.951010i	$0.600048\pi$
$830$	34850.8	1.45746
$831$	−34106.9	−1.42377
$832$	59359.4	2.47346
$833$	−136.904	−0.00569441
$834$	41142.0	1.70819
$835$	−16016.2	−0.663787
$836$	−5819.43	−0.240753
$837$	36903.7	1.52399
$838$	−8461.06	−0.348786
$839$	−42665.6	−1.75564	−0.877819	−	0.478993i	$-0.841002\pi$
$839$	−42665.6	−1.75564	−0.877819	+	0.478993i	$0.841002\pi$
$840$	−6886.49	−0.282865
$841$	27914.9	1.14457
$842$	−56792.4	−2.32446
$843$	−12477.9	−0.509799
$844$	201.370	0.00821260
$845$	30464.5	1.24025
$846$	9536.19	0.387542
$847$	−12861.4	−0.521752
$848$	−3198.67	−0.129532
$849$	33818.5	1.36708
$850$	124.509	0.00502428
$851$	−6913.06	−0.278468
$852$	6629.46	0.266575
$853$	−5852.96	−0.234937	−0.117469	−	0.993077i	$-0.537478\pi$
$853$	−5852.96	−0.234937	−0.117469	+	0.993077i	$0.537478\pi$
$854$	27099.5	1.08586
$855$	1794.37	0.0717733
$856$	22296.6	0.890283
$857$	−3416.02	−0.136160	−0.0680800	−	0.997680i	$-0.521687\pi$
$857$	−3416.02	−0.136160	−0.0680800	+	0.997680i	$0.521687\pi$
$858$	24821.7	0.987644
$859$	4064.51	0.161443	0.0807213	−	0.996737i	$-0.474278\pi$
$859$	4064.51	0.161443	0.0807213	+	0.996737i	$0.474278\pi$
$860$	0	0
$861$	22604.8	0.894736
$862$	−1946.88	−0.0769270
$863$	24469.0	0.965162	0.482581	−	0.875851i	$-0.339699\pi$
$863$	24469.0	0.965162	0.482581	+	0.875851i	$0.339699\pi$
$864$	−36119.1	−1.42222
$865$	−1002.45	−0.0394037
$866$	−21647.6	−0.849439
$867$	−22391.9	−0.877125
$868$	−33070.2	−1.29318
$869$	13761.1	0.537186
$870$	−41936.8	−1.63424
$871$	−21252.7	−0.826775
$872$	−29016.3	−1.12685
$873$	5797.98	0.224779
$874$	11456.6	0.443394
$875$	−18664.0	−0.721095
$876$	−36753.5	−1.41756
$877$	12803.5	0.492982	0.246491	−	0.969145i	$-0.420722\pi$
$877$	12803.5	0.492982	0.246491	+	0.969145i	$0.420722\pi$
$878$	−9798.46	−0.376631
$879$	8184.85	0.314071
$880$	−4669.85	−0.178887
$881$	−26865.5	−1.02738	−0.513690	−	0.857976i	$-0.671722\pi$
$881$	−26865.5	−1.02738	−0.513690	+	0.857976i	$0.671722\pi$
$882$	−5229.63	−0.199650
$883$	−14093.9	−0.537143	−0.268571	−	0.963260i	$-0.586552\pi$
$883$	−14093.9	−0.537143	−0.268571	+	0.963260i	$0.586552\pi$
$884$	−583.638	−0.0222057
$885$	−28744.8	−1.09180
$886$	−6664.45	−0.252705
$887$	−2558.64	−0.0968554	−0.0484277	−	0.998827i	$-0.515421\pi$
$887$	−2558.64	−0.0968554	−0.0484277	+	0.998827i	$0.515421\pi$
$888$	5021.52	0.189765
$889$	−8030.13	−0.302949
$890$	35216.0	1.32634
$891$	−8780.79	−0.330154
$892$	21259.3	0.797996
$893$	−10982.5	−0.411551
$894$	−19509.5	−0.729860
$895$	17072.0	0.637602
$896$	19450.8	0.725230
$897$	−28356.8	−1.05552
$898$	36721.0	1.36458
$899$	−55732.1	−2.06760
$900$	2759.98	0.102221
$901$	75.4813	0.00279095
$902$	−29671.8	−1.09530
$903$	0	0
$904$	22202.0	0.816846
$905$	−11413.9	−0.419237
$906$	216.592	0.00794238
$907$	22925.3	0.839273	0.419636	−	0.907692i	$-0.362158\pi$
$907$	22925.3	0.839273	0.419636	+	0.907692i	$0.362158\pi$
$908$	7699.48	0.281406
$909$	−4260.81	−0.155470
$910$	36614.3	1.33379
$911$	4883.72	0.177612	0.0888062	−	0.996049i	$-0.471695\pi$
$911$	4883.72	0.177612	0.0888062	+	0.996049i	$0.471695\pi$
$912$	4299.14	0.156095
$913$	−14565.8	−0.527995
$914$	−66442.0	−2.40449
$915$	−21249.0	−0.767729
$916$	21077.7	0.760291
$917$	−32129.3	−1.15704
$918$	470.268	0.0169076
$919$	−16098.7	−0.577855	−0.288927	−	0.957351i	$-0.593299\pi$
$919$	−16098.7	−0.577855	−0.288927	+	0.957351i	$0.593299\pi$
$920$	−10326.9	−0.370073
$921$	−5362.97	−0.191874
$922$	66340.8	2.36965
$923$	−9754.43	−0.347856
$924$	10400.4	0.370290
$925$	3305.18	0.117485
$926$	79602.4	2.82494
$927$	−5925.87	−0.209958
$928$	54547.2	1.92952
$929$	−25419.5	−0.897724	−0.448862	−	0.893601i	$-0.648171\pi$
$929$	−25419.5	−0.897724	−0.448862	+	0.893601i	$0.648171\pi$
$930$	44685.5	1.57559
$931$	6022.78	0.212018
$932$	37531.1	1.31907
$933$	−28704.5	−1.00723
$934$	1564.25	0.0548006
$935$	110.198	0.00385438
$936$	−6169.77	−0.215454
$937$	18786.3	0.654985	0.327493	−	0.944854i	$-0.393796\pi$
$937$	18786.3	0.654985	0.327493	+	0.944854i	$0.393796\pi$
$938$	−15345.6	−0.534171
$939$	−5347.11	−0.185832
$940$	35771.8	1.24122
$941$	−12859.5	−0.445490	−0.222745	−	0.974877i	$-0.571502\pi$
$941$	−12859.5	−0.445490	−0.222745	+	0.974877i	$0.571502\pi$
$942$	−20486.3	−0.708577
$943$	33897.7	1.17058
$944$	20628.9	0.711244
$945$	−17119.9	−0.589324
$946$	0	0
$947$	56380.9	1.93467	0.967336	−	0.253498i	$-0.0815813\pi$
$947$	56380.9	1.93467	0.967336	+	0.253498i	$0.0815813\pi$
$948$	41264.3	1.41371
$949$	54078.2	1.84979
$950$	−5477.50	−0.187067
$951$	−5677.85	−0.193603
$952$	−116.623	−0.00397035
$953$	7899.32	0.268504	0.134252	−	0.990947i	$-0.457137\pi$
$953$	7899.32	0.268504	0.134252	+	0.990947i	$0.457137\pi$
$954$	2883.33	0.0978524
$955$	26898.1	0.911416
$956$	47024.8	1.59089
$957$	17527.4	0.592039
$958$	−43219.4	−1.45757
$959$	−5103.86	−0.171859
$960$	−33607.6	−1.12988
$961$	29594.0	0.993386
$962$	−26698.6	−0.894799
$963$	10383.0	0.347442
$964$	−77624.2	−2.59347
$965$	28811.6	0.961119
$966$	−20475.1	−0.681964
$967$	46059.6	1.53172	0.765862	−	0.643005i	$-0.222313\pi$
$967$	46059.6	1.53172	0.765862	+	0.643005i	$0.222313\pi$
$968$	14009.6	0.465170
$969$	−101.450	−0.00336330
$970$	37479.6	1.24061
$971$	47766.5	1.57868	0.789340	−	0.613956i	$-0.210423\pi$
$971$	47766.5	1.57868	0.789340	+	0.613956i	$0.210423\pi$
$972$	18896.0	0.623550
$973$	−25364.6	−0.835716
$974$	−52978.9	−1.74287
$975$	13557.6	0.445323
$976$	15249.5	0.500128
$977$	−17601.8	−0.576389	−0.288194	−	0.957572i	$-0.593055\pi$
$977$	−17601.8	−0.576389	−0.288194	+	0.957572i	$0.593055\pi$
$978$	18688.1	0.611022
$979$	−14718.5	−0.480495
$980$	−19617.2	−0.639438
$981$	−13512.2	−0.439766
$982$	−65882.5	−2.14093
$983$	−35830.0	−1.16256	−0.581281	−	0.813703i	$-0.697448\pi$
$983$	−35830.0	−1.16256	−0.581281	+	0.813703i	$0.697448\pi$
$984$	−24622.7	−0.797706
$985$	−5325.81	−0.172278
$986$	−710.201	−0.0229385
$987$	19627.8	0.632987
$988$	25675.8	0.826777
$989$	0	0
$990$	4209.46	0.135137
$991$	16423.6	0.526451	0.263226	−	0.964734i	$-0.415214\pi$
$991$	16423.6	0.526451	0.263226	+	0.964734i	$0.415214\pi$
$992$	−58122.4	−1.86027
$993$	−4493.57	−0.143604
$994$	−7043.23	−0.224746
$995$	−28773.8	−0.916776
$996$	−43677.3	−1.38952
$997$	−23560.0	−0.748397	−0.374198	−	0.927349i	$-0.622082\pi$
$997$	−23560.0	−0.748397	−0.374198	+	0.927349i	$0.622082\pi$
$998$	11776.2	0.373515
$999$	12483.6	0.395359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.g.1.6		30
43.2	odd	14		43.4.e.a.4.9	✓	60
43.22	odd	14		43.4.e.a.11.9	yes	60
43.42	odd	2		1849.4.a.h.1.25		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.4.9	✓	60	43.2	odd	14
43.4.e.a.11.9	yes	60	43.22	odd	14
1849.4.a.g.1.6		30	1.1	even	1	trivial
1849.4.a.h.1.25		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)

\(f(q)\)	\(=\)	\(q-4.36589 q^{2} +4.55814 q^{3} +11.0610 q^{4} +9.21441 q^{5} -19.9004 q^{6} +12.2688 q^{7} -13.3641 q^{8} -6.22333 q^{9} +O(q^{10})\)	\(q-4.36589 q^{2} +4.55814 q^{3} +11.0610 q^{4} +9.21441 q^{5} -19.9004 q^{6} +12.2688 q^{7} -13.3641 q^{8} -6.22333 q^{9} -40.2291 q^{10} +16.8137 q^{11} +50.4177 q^{12} -74.1834 q^{13} -53.5645 q^{14} +42.0006 q^{15} -30.1420 q^{16} +0.711281 q^{17} +27.1704 q^{18} -31.2912 q^{19} +101.921 q^{20} +55.9232 q^{21} -73.4068 q^{22} +83.8614 q^{23} -60.9154 q^{24} -40.0947 q^{25} +323.877 q^{26} -151.437 q^{27} +135.706 q^{28} +228.700 q^{29} -183.370 q^{30} -243.690 q^{31} +238.509 q^{32} +76.6393 q^{33} -3.10538 q^{34} +113.050 q^{35} -68.8364 q^{36} -82.4344 q^{37} +136.614 q^{38} -338.139 q^{39} -123.142 q^{40} +404.211 q^{41} -244.155 q^{42} +185.977 q^{44} -57.3443 q^{45} -366.130 q^{46} +350.977 q^{47} -137.392 q^{48} -192.475 q^{49} +175.049 q^{50} +3.24212 q^{51} -820.544 q^{52} +106.120 q^{53} +661.156 q^{54} +154.928 q^{55} -163.962 q^{56} -142.630 q^{57} -998.481 q^{58} -684.391 q^{59} +464.569 q^{60} -505.923 q^{61} +1063.93 q^{62} -76.3531 q^{63} -800.171 q^{64} -683.556 q^{65} -334.599 q^{66} +286.489 q^{67} +7.86750 q^{68} +382.252 q^{69} -493.565 q^{70} +131.491 q^{71} +83.1691 q^{72} -728.979 q^{73} +359.900 q^{74} -182.758 q^{75} -346.112 q^{76} +206.285 q^{77} +1476.28 q^{78} +818.448 q^{79} -277.741 q^{80} -522.240 q^{81} -1764.74 q^{82} -866.308 q^{83} +618.567 q^{84} +6.55403 q^{85} +1042.45 q^{87} -224.700 q^{88} -875.385 q^{89} +250.359 q^{90} -910.145 q^{91} +927.593 q^{92} -1110.78 q^{93} -1532.33 q^{94} -288.329 q^{95} +1087.16 q^{96} -931.653 q^{97} +840.327 q^{98} -104.637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) \) 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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