LMFDB - Embedded newform 1849.4.a.f.1.8

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 59x^{8} + 42x^{7} + 1187x^{6} - 541x^{5} - 9389x^{4} + 2180x^{3} + 22676x^{2} - 320x - 768 $ x^10 - x^9 - 59x^8 + 42x^7 + 1187x^6 - 541x^5 - 9389x^4 + 2180x^3 + 22676x^2 - 320x - 768
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$3.55840$ of defining polynomial
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)

$f(q)$	$=$	$q+3.55840 q^{2} +0.389088 q^{3} +4.66219 q^{4} +1.72780 q^{5} +1.38453 q^{6} +21.1861 q^{7} -11.8773 q^{8} -26.8486 q^{9} +O(q^{10})$	\(q+3.55840 q^{2} +0.389088 q^{3} +4.66219 q^{4} +1.72780 q^{5} +1.38453 q^{6} +21.1861 q^{7} -11.8773 q^{8} -26.8486 q^{9} +6.14819 q^{10} +23.7473 q^{11} +1.81400 q^{12} -30.1835 q^{13} +75.3886 q^{14} +0.672265 q^{15} -79.5615 q^{16} +51.6636 q^{17} -95.5380 q^{18} -29.2445 q^{19} +8.05532 q^{20} +8.24326 q^{21} +84.5025 q^{22} -93.4972 q^{23} -4.62129 q^{24} -122.015 q^{25} -107.405 q^{26} -20.9518 q^{27} +98.7737 q^{28} +59.6234 q^{29} +2.39219 q^{30} +113.579 q^{31} -188.093 q^{32} +9.23980 q^{33} +183.840 q^{34} +36.6053 q^{35} -125.173 q^{36} -68.6936 q^{37} -104.064 q^{38} -11.7440 q^{39} -20.5215 q^{40} +53.9480 q^{41} +29.3328 q^{42} +110.715 q^{44} -46.3890 q^{45} -332.700 q^{46} -455.571 q^{47} -30.9564 q^{48} +105.852 q^{49} -434.177 q^{50} +20.1017 q^{51} -140.721 q^{52} -662.710 q^{53} -74.5550 q^{54} +41.0306 q^{55} -251.633 q^{56} -11.3787 q^{57} +212.164 q^{58} -457.110 q^{59} +3.13423 q^{60} +606.881 q^{61} +404.159 q^{62} -568.818 q^{63} -32.8190 q^{64} -52.1511 q^{65} +32.8789 q^{66} -428.446 q^{67} +240.866 q^{68} -36.3786 q^{69} +130.256 q^{70} +139.913 q^{71} +318.888 q^{72} -481.924 q^{73} -244.439 q^{74} -47.4744 q^{75} -136.344 q^{76} +503.114 q^{77} -41.7900 q^{78} +1104.54 q^{79} -137.466 q^{80} +716.760 q^{81} +191.968 q^{82} -1257.06 q^{83} +38.4317 q^{84} +89.2643 q^{85} +23.1987 q^{87} -282.053 q^{88} -624.540 q^{89} -165.070 q^{90} -639.472 q^{91} -435.902 q^{92} +44.1922 q^{93} -1621.10 q^{94} -50.5287 q^{95} -73.1848 q^{96} +1121.21 q^{97} +376.663 q^{98} -637.583 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9}+O(q^{10}) $ 10 * q + q^2 - 5 * q^3 + 39 * q^4 - 19 * q^5 - 15 * q^6 - 51 * q^7 + 36 * q^8 + 117 * q^9	\( 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9} - 27 q^{10} + 27 q^{11} - 72 q^{12} + 15 q^{13} - 96 q^{14} - 65 q^{15} + 67 q^{16} + 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 9 q^{21} - 190 q^{22} + 61 q^{23} - 202 q^{24} + 151 q^{25} - 21 q^{26} + 97 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} - 253 q^{31} + 399 q^{32} - 424 q^{33} - 231 q^{34} + 355 q^{35} + 1092 q^{36} - 129 q^{37} + 854 q^{38} - 691 q^{39} - 1345 q^{40} + 391 q^{41} - 31 q^{42} + 377 q^{44} - 944 q^{45} - 40 q^{46} - 334 q^{47} - 2401 q^{48} + 115 q^{49} + 424 q^{50} - 795 q^{51} + 564 q^{52} - 773 q^{53} + 182 q^{54} - 1242 q^{55} + 923 q^{56} + 765 q^{57} - 1328 q^{58} - 1483 q^{59} + 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 738 q^{64} + 1063 q^{65} - 1483 q^{66} + 642 q^{67} + 1052 q^{68} - 3503 q^{69} + 85 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} + 2232 q^{74} - 82 q^{75} - 252 q^{76} + 1448 q^{77} + 2822 q^{78} + 1405 q^{79} - 3157 q^{80} - 974 q^{81} - 3304 q^{82} - 543 q^{83} + 3652 q^{84} - 973 q^{85} + 1409 q^{87} + 2686 q^{88} - 2196 q^{89} - 742 q^{90} - 3513 q^{91} - 2629 q^{92} - 983 q^{93} - 4939 q^{94} + 149 q^{95} - 3540 q^{96} - 425 q^{97} - 213 q^{98} + 3181 q^{99}+O(q^{100}) \) 10 * q + q^2 - 5 * q^3 + 39 * q^4 - 19 * q^5 - 15 * q^6 - 51 * q^7 + 36 * q^8 + 117 * q^9 - 27 * q^10 + 27 * q^11 - 72 * q^12 + 15 * q^13 - 96 * q^14 - 65 * q^15 + 67 * q^16 + 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 9 * q^21 - 190 * q^22 + 61 * q^23 - 202 * q^24 + 151 * q^25 - 21 * q^26 + 97 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 - 253 * q^31 + 399 * q^32 - 424 * q^33 - 231 * q^34 + 355 * q^35 + 1092 * q^36 - 129 * q^37 + 854 * q^38 - 691 * q^39 - 1345 * q^40 + 391 * q^41 - 31 * q^42 + 377 * q^44 - 944 * q^45 - 40 * q^46 - 334 * q^47 - 2401 * q^48 + 115 * q^49 + 424 * q^50 - 795 * q^51 + 564 * q^52 - 773 * q^53 + 182 * q^54 - 1242 * q^55 + 923 * q^56 + 765 * q^57 - 1328 * q^58 - 1483 * q^59 + 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 738 * q^64 + 1063 * q^65 - 1483 * q^66 + 642 * q^67 + 1052 * q^68 - 3503 * q^69 + 85 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 + 2232 * q^74 - 82 * q^75 - 252 * q^76 + 1448 * q^77 + 2822 * q^78 + 1405 * q^79 - 3157 * q^80 - 974 * q^81 - 3304 * q^82 - 543 * q^83 + 3652 * q^84 - 973 * q^85 + 1409 * q^87 + 2686 * q^88 - 2196 * q^89 - 742 * q^90 - 3513 * q^91 - 2629 * q^92 - 983 * q^93 - 4939 * q^94 + 149 * q^95 - 3540 * q^96 - 425 * q^97 - 213 * q^98 + 3181 * 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 $

$2$	3.55840	1.25808	0.629042	−	0.777372i	$-0.283447\pi$
$2$	3.55840	1.25808	0.629042	+	0.777372i	$0.283447\pi$
$3$	0.389088	0.0748800	0.0374400	−	0.999299i	$-0.488080\pi$
$3$	0.389088	0.0748800	0.0374400	+	0.999299i	$0.488080\pi$
$4$	4.66219	0.582774
$5$	1.72780	0.154539	0.0772695	−	0.997010i	$-0.475380\pi$
$5$	1.72780	0.154539	0.0772695	+	0.997010i	$0.475380\pi$
$6$	1.38453	0.0942053
$7$	21.1861	1.14394	0.571972	−	0.820273i	$-0.306179\pi$
$7$	21.1861	1.14394	0.571972	+	0.820273i	$0.306179\pi$
$8$	−11.8773	−0.524905
$9$	−26.8486	−0.994393
$10$	6.14819	0.194423
$11$	23.7473	0.650917	0.325459	−	0.945556i	$-0.394481\pi$
$11$	23.7473	0.650917	0.325459	+	0.945556i	$0.394481\pi$
$12$	1.81400	0.0436381
$13$	−30.1835	−0.643954	−0.321977	−	0.946747i	$-0.604347\pi$
$13$	−30.1835	−0.643954	−0.321977	+	0.946747i	$0.604347\pi$
$14$	75.3886	1.43918
$15$	0.672265	0.0115719
$16$	−79.5615	−1.24315
$17$	51.6636	0.737074	0.368537	−	0.929613i	$-0.379859\pi$
$17$	51.6636	0.737074	0.368537	+	0.929613i	$0.379859\pi$
$18$	−95.5380	−1.25103
$19$	−29.2445	−0.353113	−0.176557	−	0.984290i	$-0.556496\pi$
$19$	−29.2445	−0.353113	−0.176557	+	0.984290i	$0.556496\pi$
$20$	8.05532	0.0900613
$21$	8.24326	0.0856584
$22$	84.5025	0.818908
$23$	−93.4972	−0.847631	−0.423815	−	0.905749i	$-0.639309\pi$
$23$	−93.4972	−0.847631	−0.423815	+	0.905749i	$0.639309\pi$
$24$	−4.62129	−0.0393049
$25$	−122.015	−0.976118
$26$	−107.405	−0.810148
$27$	−20.9518	−0.149340
$28$	98.7737	0.666660
$29$	59.6234	0.381786	0.190893	−	0.981611i	$-0.438862\pi$
$29$	59.6234	0.381786	0.190893	+	0.981611i	$0.438862\pi$
$30$	2.39219	0.0145584
$31$	113.579	0.658045	0.329022	−	0.944322i	$-0.393281\pi$
$31$	113.579	0.658045	0.329022	+	0.944322i	$0.393281\pi$
$32$	−188.093	−1.03908
$33$	9.23980	0.0487407
$34$	183.840	0.927301
$35$	36.6053	0.176784
$36$	−125.173	−0.579506
$37$	−68.6936	−0.305220	−0.152610	−	0.988286i	$-0.548768\pi$
$37$	−68.6936	−0.305220	−0.152610	+	0.988286i	$0.548768\pi$
$38$	−104.064	−0.444246
$39$	−11.7440	−0.0482193
$40$	−20.5215	−0.0811183
$41$	53.9480	0.205494	0.102747	−	0.994708i	$-0.467237\pi$
$41$	53.9480	0.205494	0.102747	+	0.994708i	$0.467237\pi$
$42$	29.3328	0.107765
$43$	0	0
$43$	0	0
$44$	110.715	0.379338
$45$	−46.3890	−0.153672
$46$	−332.700	−1.06639
$47$	−455.571	−1.41387	−0.706935	−	0.707279i	$-0.749923\pi$
$47$	−455.571	−1.41387	−0.706935	+	0.707279i	$0.749923\pi$
$48$	−30.9564	−0.0930869
$49$	105.852	0.308606
$50$	−434.177	−1.22804
$51$	20.1017	0.0551921
$52$	−140.721	−0.375280
$53$	−662.710	−1.71755	−0.858776	−	0.512352i	$-0.828774\pi$
$53$	−662.710	−1.71755	−0.858776	+	0.512352i	$0.828774\pi$
$54$	−74.5550	−0.187882
$55$	41.0306	0.100592
$56$	−251.633	−0.600462
$57$	−11.3787	−0.0264411
$58$	212.164	0.480318
$59$	−457.110	−1.00866	−0.504328	−	0.863512i	$-0.668260\pi$
$59$	−457.110	−1.00866	−0.504328	+	0.863512i	$0.668260\pi$
$60$	3.13423	0.00674379
$61$	606.881	1.27382	0.636911	−	0.770937i	$-0.280212\pi$
$61$	606.881	1.27382	0.636911	+	0.770937i	$0.280212\pi$
$62$	404.159	0.827875
$63$	−568.818	−1.13753
$64$	−32.8190	−0.0640996
$65$	−52.1511	−0.0995160
$66$	32.8789	0.0613198
$67$	−428.446	−0.781240	−0.390620	−	0.920552i	$-0.627739\pi$
$67$	−428.446	−0.781240	−0.390620	+	0.920552i	$0.627739\pi$
$68$	240.866	0.429548
$69$	−36.3786	−0.0634706
$70$	130.256	0.222409
$71$	139.913	0.233868	0.116934	−	0.993140i	$-0.462693\pi$
$71$	139.913	0.233868	0.116934	+	0.993140i	$0.462693\pi$
$72$	318.888	0.521962
$73$	−481.924	−0.772671	−0.386336	−	0.922358i	$-0.626259\pi$
$73$	−481.924	−0.772671	−0.386336	+	0.922358i	$0.626259\pi$
$74$	−244.439	−0.383993
$75$	−47.4744	−0.0730917
$76$	−136.344	−0.205785
$77$	503.114	0.744613
$78$	−41.7900	−0.0606639
$79$	1104.54	1.57305	0.786523	−	0.617561i	$-0.211879\pi$
$79$	1104.54	1.57305	0.786523	+	0.617561i	$0.211879\pi$
$80$	−137.466	−0.192115
$81$	716.760	0.983210
$82$	191.968	0.258529
$83$	−1257.06	−1.66241	−0.831205	−	0.555966i	$-0.812349\pi$
$83$	−1257.06	−1.66241	−0.831205	+	0.555966i	$0.812349\pi$
$84$	38.4317	0.0499195
$85$	89.2643	0.113907
$86$	0	0
$87$	23.1987	0.0285881
$88$	−282.053	−0.341670
$89$	−624.540	−0.743833	−0.371916	−	0.928266i	$-0.621299\pi$
$89$	−624.540	−0.743833	−0.371916	+	0.928266i	$0.621299\pi$
$90$	−165.070	−0.193333
$91$	−639.472	−0.736647
$92$	−435.902	−0.493977
$93$	44.1922	0.0492744
$94$	−1621.10	−1.77877
$95$	−50.5287	−0.0545698
$96$	−73.1848	−0.0778062
$97$	1121.21	1.17362	0.586812	−	0.809723i	$-0.300383\pi$
$97$	1121.21	1.17362	0.586812	+	0.809723i	$0.300383\pi$
$98$	376.663	0.388252
$99$	−637.583	−0.647268
$100$	−568.856	−0.568856
$101$	−938.500	−0.924596	−0.462298	−	0.886725i	$-0.652975\pi$
$101$	−938.500	−0.924596	−0.462298	+	0.886725i	$0.652975\pi$
$102$	71.5298	0.0694363
$103$	1093.02	1.04561	0.522807	−	0.852451i	$-0.324885\pi$
$103$	1093.02	1.04561	0.522807	+	0.852451i	$0.324885\pi$
$104$	358.497	0.338015
$105$	14.2427	0.0132376
$106$	−2358.19	−2.16082
$107$	−686.795	−0.620513	−0.310257	−	0.950653i	$-0.600415\pi$
$107$	−686.795	−0.620513	−0.310257	+	0.950653i	$0.600415\pi$
$108$	−97.6814	−0.0870315
$109$	−1514.75	−1.33107	−0.665537	−	0.746365i	$-0.731797\pi$
$109$	−1514.75	−1.33107	−0.665537	+	0.746365i	$0.731797\pi$
$110$	146.003	0.126553
$111$	−26.7278	−0.0228549
$112$	−1685.60	−1.42209
$113$	825.248	0.687016	0.343508	−	0.939150i	$-0.388385\pi$
$113$	825.248	0.687016	0.343508	+	0.939150i	$0.388385\pi$
$114$	−40.4899	−0.0332651
$115$	−161.544	−0.130992
$116$	277.976	0.222495
$117$	810.386	0.640344
$118$	−1626.58	−1.26897
$119$	1094.55	0.843171
$120$	−7.98466	−0.00607414
$121$	−767.064	−0.576307
$122$	2159.52	1.60257
$123$	20.9905	0.0153874
$124$	529.527	0.383491
$125$	−426.792	−0.305387
$126$	−2024.08	−1.43111
$127$	−1637.13	−1.14387	−0.571936	−	0.820298i	$-0.693808\pi$
$127$	−1637.13	−1.14387	−0.571936	+	0.820298i	$0.693808\pi$
$128$	1387.96	0.958436
$129$	0	0
$130$	−185.574	−0.125199
$131$	2493.85	1.66327	0.831636	−	0.555321i	$-0.187404\pi$
$131$	2493.85	1.66327	0.831636	+	0.555321i	$0.187404\pi$
$132$	43.0777	0.0284048
$133$	−619.578	−0.403942
$134$	−1524.58	−0.982865
$135$	−36.2005	−0.0230789
$136$	−613.622	−0.386894
$137$	−2800.85	−1.74666	−0.873331	−	0.487128i	$-0.838045\pi$
$137$	−2800.85	−1.74666	−0.873331	+	0.487128i	$0.838045\pi$
$138$	−129.450	−0.0798513
$139$	−1328.76	−0.810820	−0.405410	−	0.914135i	$-0.632871\pi$
$139$	−1328.76	−0.810820	−0.405410	+	0.914135i	$0.632871\pi$
$140$	170.661	0.103025
$141$	−177.257	−0.105871
$142$	497.865	0.294225
$143$	−716.779	−0.419161
$144$	2136.12	1.23618
$145$	103.017	0.0590008
$146$	−1714.88	−0.972085
$147$	41.1856	0.0231084
$148$	−320.262	−0.177874
$149$	−1747.95	−0.961057	−0.480529	−	0.876979i	$-0.659555\pi$
$149$	−1747.95	−0.961057	−0.480529	+	0.876979i	$0.659555\pi$
$150$	−168.933	−0.0919554
$151$	−2145.54	−1.15630	−0.578151	−	0.815929i	$-0.696226\pi$
$151$	−2145.54	−1.15630	−0.578151	+	0.815929i	$0.696226\pi$
$152$	347.345	0.185351
$153$	−1387.10	−0.732942
$154$	1790.28	0.936785
$155$	196.242	0.101694
$156$	−54.7530	−0.0281009
$157$	3356.46	1.70621	0.853103	−	0.521742i	$-0.174718\pi$
$157$	3356.46	1.70621	0.853103	+	0.521742i	$0.174718\pi$
$158$	3930.40	1.97902
$159$	−257.852	−0.128610
$160$	−324.987	−0.160578
$161$	−1980.84	−0.969641
$162$	2550.52	1.23696
$163$	3418.23	1.64255	0.821277	−	0.570530i	$-0.193262\pi$
$163$	3418.23	1.64255	0.821277	+	0.570530i	$0.193262\pi$
$164$	251.516	0.119757
$165$	15.9645	0.00753234
$166$	−4473.11	−2.09145
$167$	306.031	0.141805	0.0709024	−	0.997483i	$-0.477412\pi$
$167$	306.031	0.141805	0.0709024	+	0.997483i	$0.477412\pi$
$168$	−97.9073	−0.0449626
$169$	−1285.95	−0.585323
$170$	317.638	0.143304
$171$	785.175	0.351134
$172$	0	0
$173$	961.005	0.422334	0.211167	−	0.977450i	$-0.432274\pi$
$173$	961.005	0.422334	0.211167	+	0.977450i	$0.432274\pi$
$174$	82.5503	0.0359662
$175$	−2585.02	−1.11662
$176$	−1889.37	−0.809187
$177$	−177.856	−0.0755281
$178$	−2222.36	−0.935804
$179$	−1863.43	−0.778097	−0.389048	−	0.921217i	$-0.627196\pi$
$179$	−1863.43	−0.778097	−0.389048	+	0.921217i	$0.627196\pi$
$180$	−216.274	−0.0895563
$181$	−1334.46	−0.548010	−0.274005	−	0.961728i	$-0.588348\pi$
$181$	−1334.46	−0.548010	−0.274005	+	0.961728i	$0.588348\pi$
$182$	−2275.50	−0.926763
$183$	236.130	0.0953838
$184$	1110.49	0.444926
$185$	−118.689	−0.0471684
$186$	157.253	0.0619913
$187$	1226.87	0.479775
$188$	−2123.96	−0.823966
$189$	−443.888	−0.170837
$190$	−179.801	−0.0686533
$191$	1383.64	0.524170	0.262085	−	0.965045i	$-0.415590\pi$
$191$	1383.64	0.524170	0.262085	+	0.965045i	$0.415590\pi$
$192$	−12.7695	−0.00479977
$193$	−3458.85	−1.29002	−0.645009	−	0.764175i	$-0.723146\pi$
$193$	−3458.85	−1.29002	−0.645009	+	0.764175i	$0.723146\pi$
$194$	3989.71	1.47652
$195$	−20.2913	−0.00745176
$196$	493.501	0.179847
$197$	3074.24	1.11183	0.555915	−	0.831239i	$-0.312368\pi$
$197$	3074.24	1.11183	0.555915	+	0.831239i	$0.312368\pi$
$198$	−2268.77	−0.814317
$199$	−1601.35	−0.570434	−0.285217	−	0.958463i	$-0.592066\pi$
$199$	−1601.35	−0.570434	−0.285217	+	0.958463i	$0.592066\pi$
$200$	1449.20	0.512369
$201$	−166.703	−0.0584992
$202$	−3339.55	−1.16322
$203$	1263.19	0.436741
$204$	93.7178	0.0321645
$205$	93.2113	0.0317569
$206$	3889.39	1.31547
$207$	2510.27	0.842878
$208$	2401.45	0.800531
$209$	−694.480	−0.229848
$210$	50.6812	0.0166540
$211$	1648.37	0.537811	0.268906	−	0.963167i	$-0.413338\pi$
$211$	1648.37	0.537811	0.268906	+	0.963167i	$0.413338\pi$
$212$	−3089.68	−1.00094
$213$	54.4384	0.0175120
$214$	−2443.89	−0.780658
$215$	0	0
$216$	248.850	0.0783894
$217$	2406.30	0.752766
$218$	−5390.09	−1.67460
$219$	−187.511	−0.0578576
$220$	191.293	0.0586224
$221$	−1559.39	−0.474642
$222$	−95.1082	−0.0287534
$223$	−3002.40	−0.901596	−0.450798	−	0.892626i	$-0.648860\pi$
$223$	−3002.40	−0.901596	−0.450798	+	0.892626i	$0.648860\pi$
$224$	−3984.97	−1.18865
$225$	3275.93	0.970645
$226$	2936.56	0.864324
$227$	3879.92	1.13445	0.567223	−	0.823564i	$-0.308018\pi$
$227$	3879.92	1.13445	0.567223	+	0.823564i	$0.308018\pi$
$228$	−53.0496	−0.0154092
$229$	−2515.37	−0.725854	−0.362927	−	0.931818i	$-0.618223\pi$
$229$	−2515.37	−0.725854	−0.362927	+	0.931818i	$0.618223\pi$
$230$	−574.839	−0.164799
$231$	195.756	0.0557566
$232$	−708.162	−0.200401
$233$	−5299.66	−1.49010	−0.745048	−	0.667011i	$-0.767573\pi$
$233$	−5299.66	−1.49010	−0.745048	+	0.667011i	$0.767573\pi$
$234$	2883.67	0.805606
$235$	−787.135	−0.218498
$236$	−2131.14	−0.587818
$237$	429.763	0.117790
$238$	3894.85	1.06078
$239$	1845.83	0.499569	0.249785	−	0.968301i	$-0.419640\pi$
$239$	1845.83	0.499569	0.249785	+	0.968301i	$0.419640\pi$
$240$	−53.4864	−0.0143856
$241$	−7058.62	−1.88666	−0.943332	−	0.331852i	$-0.892327\pi$
$241$	−7058.62	−1.88666	−0.943332	+	0.331852i	$0.892327\pi$
$242$	−2729.52	−0.725042
$243$	844.582	0.222963
$244$	2829.40	0.742350
$245$	182.891	0.0476916
$246$	74.6926	0.0193586
$247$	882.703	0.227389
$248$	−1349.01	−0.345411
$249$	−489.106	−0.124481
$250$	−1518.69	−0.384203
$251$	28.2073	0.00709334	0.00354667	−	0.999994i	$-0.498871\pi$
$251$	28.2073	0.00709334	0.00354667	+	0.999994i	$0.498871\pi$
$252$	−2651.94	−0.662922
$253$	−2220.31	−0.551738
$254$	−5825.56	−1.43909
$255$	34.7316	0.00852933
$256$	5201.48	1.26989
$257$	8065.79	1.95771	0.978853	−	0.204566i	$-0.0655784\pi$
$257$	8065.79	1.95771	0.978853	+	0.204566i	$0.0655784\pi$
$258$	0	0
$259$	−1455.35	−0.349155
$260$	−243.138	−0.0579953
$261$	−1600.80	−0.379645
$262$	8874.11	2.09254
$263$	−406.722	−0.0953596	−0.0476798	−	0.998863i	$-0.515183\pi$
$263$	−406.722	−0.0953596	−0.0476798	+	0.998863i	$0.515183\pi$
$264$	−109.743	−0.0255842
$265$	−1145.03	−0.265429
$266$	−2204.71	−0.508192
$267$	−243.001	−0.0556982
$268$	−1997.50	−0.455286
$269$	3936.94	0.892339	0.446170	−	0.894948i	$-0.352788\pi$
$269$	3936.94	0.892339	0.446170	+	0.894948i	$0.352788\pi$
$270$	−128.816	−0.0290351
$271$	3626.08	0.812800	0.406400	−	0.913695i	$-0.366784\pi$
$271$	3626.08	0.812800	0.406400	+	0.913695i	$0.366784\pi$
$272$	−4110.43	−0.916293
$273$	−248.811	−0.0551601
$274$	−9966.53	−2.19745
$275$	−2897.52	−0.635372
$276$	−169.604	−0.0369890
$277$	−578.164	−0.125410	−0.0627049	−	0.998032i	$-0.519973\pi$
$277$	−578.164	−0.125410	−0.0627049	+	0.998032i	$0.519973\pi$
$278$	−4728.26	−1.02008
$279$	−3049.44	−0.654355
$280$	−434.771	−0.0927948
$281$	−2953.07	−0.626922	−0.313461	−	0.949601i	$-0.601489\pi$
$281$	−2953.07	−0.626922	−0.313461	+	0.949601i	$0.601489\pi$
$282$	−630.751	−0.133194
$283$	−3505.66	−0.736360	−0.368180	−	0.929754i	$-0.620019\pi$
$283$	−3505.66	−0.736360	−0.368180	+	0.929754i	$0.620019\pi$
$284$	652.300	0.136292
$285$	−19.6601	−0.00408618
$286$	−2550.58	−0.527340
$287$	1142.95	0.235074
$288$	5050.05	1.03325
$289$	−2243.87	−0.456721
$290$	366.576	0.0742279
$291$	436.249	0.0878810
$292$	−2246.82	−0.450292
$293$	1731.50	0.345240	0.172620	−	0.984988i	$-0.444777\pi$
$293$	1731.50	0.345240	0.172620	+	0.984988i	$0.444777\pi$
$294$	146.555	0.0290723
$295$	−789.795	−0.155877
$296$	815.891	0.160212
$297$	−497.550	−0.0972081
$298$	−6219.89	−1.20909
$299$	2822.07	0.545835
$300$	−221.335	−0.0425959
$301$	0	0
$302$	−7634.69	−1.45473
$303$	−365.159	−0.0692337
$304$	2326.74	0.438972
$305$	1048.57	0.196855
$306$	−4935.84	−0.922102
$307$	1628.88	0.302817	0.151409	−	0.988471i	$-0.451619\pi$
$307$	1628.88	0.302817	0.151409	+	0.988471i	$0.451619\pi$
$308$	2345.61	0.433941
$309$	425.280	0.0782955
$310$	698.306	0.127939
$311$	2418.10	0.440894	0.220447	−	0.975399i	$-0.429248\pi$
$311$	2418.10	0.440894	0.220447	+	0.975399i	$0.429248\pi$
$312$	139.487	0.0253106
$313$	−5997.16	−1.08300	−0.541501	−	0.840700i	$-0.682144\pi$
$313$	−5997.16	−1.08300	−0.541501	+	0.840700i	$0.682144\pi$
$314$	11943.6	2.14655
$315$	−982.803	−0.175793
$316$	5149.58	0.916729
$317$	4943.75	0.875927	0.437963	−	0.898993i	$-0.355700\pi$
$317$	4943.75	0.875927	0.437963	+	0.898993i	$0.355700\pi$
$318$	−917.541	−0.161802
$319$	1415.90	0.248511
$320$	−56.7046	−0.00990588
$321$	−267.223	−0.0464640
$322$	−7048.62	−1.21989
$323$	−1510.88	−0.260271
$324$	3341.67	0.572989
$325$	3682.83	0.628575
$326$	12163.4	2.06647
$327$	−589.372	−0.0996707
$328$	−640.754	−0.107865
$329$	−9651.79	−1.61739
$330$	56.8081	0.00947631
$331$	2232.32	0.370693	0.185346	−	0.982673i	$-0.440659\pi$
$331$	2232.32	0.370693	0.185346	+	0.982673i	$0.440659\pi$
$332$	−5860.64	−0.968809
$333$	1844.33	0.303509
$334$	1088.98	0.178402
$335$	−740.269	−0.120732
$336$	−655.846	−0.106486
$337$	−2024.19	−0.327194	−0.163597	−	0.986527i	$-0.552310\pi$
$337$	−2024.19	−0.327194	−0.163597	+	0.986527i	$0.552310\pi$
$338$	−4575.94	−0.736385
$339$	321.094	0.0514438
$340$	416.167	0.0663819
$341$	2697.20	0.428333
$342$	2793.96	0.441755
$343$	−5024.25	−0.790916
$344$	0	0
$345$	−62.8549	−0.00980868
$346$	3419.64	0.531332
$347$	2823.26	0.436774	0.218387	−	0.975862i	$-0.429921\pi$
$347$	2823.26	0.436774	0.218387	+	0.975862i	$0.429921\pi$
$348$	108.157	0.0166604
$349$	−7299.56	−1.11959	−0.559794	−	0.828632i	$-0.689120\pi$
$349$	−7299.56	−1.11959	−0.559794	+	0.828632i	$0.689120\pi$
$350$	−9198.52	−1.40480
$351$	632.400	0.0961682
$352$	−4466.72	−0.676355
$353$	12714.0	1.91699	0.958494	−	0.285113i	$-0.0920313\pi$
$353$	12714.0	1.91699	0.958494	+	0.285113i	$0.0920313\pi$
$354$	−632.882	−0.0950207
$355$	241.741	0.0361417
$356$	−2911.72	−0.433486
$357$	425.877	0.0631366
$358$	−6630.82	−0.978910
$359$	−5811.00	−0.854298	−0.427149	−	0.904181i	$-0.640482\pi$
$359$	−5811.00	−0.854298	−0.427149	+	0.904181i	$0.640482\pi$
$360$	550.974	0.0806635
$361$	−6003.76	−0.875311
$362$	−4748.54	−0.689442
$363$	−298.455	−0.0431538
$364$	−2981.34	−0.429299
$365$	−832.668	−0.119408
$366$	840.244	0.120001
$367$	11929.3	1.69674	0.848370	−	0.529404i	$-0.177584\pi$
$367$	11929.3	1.69674	0.848370	+	0.529404i	$0.177584\pi$
$368$	7438.78	1.05373
$369$	−1448.43	−0.204342
$370$	−422.341	−0.0593418
$371$	−14040.3	−1.96478
$372$	206.032	0.0287158
$373$	373.970	0.0519127	0.0259563	−	0.999663i	$-0.491737\pi$
$373$	373.970	0.0519127	0.0259563	+	0.999663i	$0.491737\pi$
$374$	4365.70	0.603596
$375$	−166.059	−0.0228674
$376$	5410.93	0.742148
$377$	−1799.64	−0.245852
$378$	−1579.53	−0.214927
$379$	14078.0	1.90802	0.954009	−	0.299779i	$-0.0969129\pi$
$379$	14078.0	1.90802	0.954009	+	0.299779i	$0.0969129\pi$
$380$	−235.574	−0.0318018
$381$	−636.988	−0.0856532
$382$	4923.53	0.659449
$383$	−12802.1	−1.70798	−0.853992	−	0.520285i	$-0.825826\pi$
$383$	−12802.1	−1.70798	−0.853992	+	0.520285i	$0.825826\pi$
$384$	540.040	0.0717677
$385$	869.280	0.115072
$386$	−12308.0	−1.62295
$387$	0	0
$388$	5227.29	0.683958
$389$	−9445.56	−1.23113	−0.615564	−	0.788087i	$-0.711072\pi$
$389$	−9445.56	−1.23113	−0.615564	+	0.788087i	$0.711072\pi$
$390$	−72.2046	−0.00937493
$391$	−4830.40	−0.624767
$392$	−1257.23	−0.161989
$393$	970.327	0.124546
$394$	10939.4	1.39877
$395$	1908.42	0.243097
$396$	−2972.53	−0.377211
$397$	11059.8	1.39817	0.699085	−	0.715038i	$-0.253591\pi$
$397$	11059.8	1.39817	0.699085	+	0.715038i	$0.253591\pi$
$398$	−5698.23	−0.717654
$399$	−241.070	−0.0302471
$400$	9707.67	1.21346
$401$	12272.6	1.52834	0.764170	−	0.645014i	$-0.223149\pi$
$401$	12272.6	1.52834	0.764170	+	0.645014i	$0.223149\pi$
$402$	−593.196	−0.0735969
$403$	−3428.22	−0.423751
$404$	−4375.46	−0.538830
$405$	1238.42	0.151944
$406$	4494.93	0.549457
$407$	−1631.29	−0.198673
$408$	−238.753	−0.0289706
$409$	7464.92	0.902486	0.451243	−	0.892401i	$-0.350981\pi$
$409$	7464.92	0.902486	0.451243	+	0.892401i	$0.350981\pi$
$410$	331.683	0.0399528
$411$	−1089.78	−0.130790
$412$	5095.85	0.609356
$413$	−9684.40	−1.15384
$414$	8932.53	1.06041
$415$	−2171.94	−0.256907
$416$	5677.32	0.669119
$417$	−517.005	−0.0607142
$418$	−2471.23	−0.289168
$419$	16392.7	1.91131	0.955653	−	0.294494i	$-0.0951510\pi$
$419$	16392.7	1.91131	0.955653	+	0.294494i	$0.0951510\pi$
$420$	66.4021	0.00771451
$421$	1276.00	0.147716	0.0738580	−	0.997269i	$-0.476469\pi$
$421$	1276.00	0.147716	0.0738580	+	0.997269i	$0.476469\pi$
$422$	5865.54	0.676611
$423$	12231.5	1.40594
$424$	7871.18	0.901552
$425$	−6303.72	−0.719471
$426$	193.713	0.0220316
$427$	12857.5	1.45718
$428$	−3201.97	−0.361619
$429$	−278.890	−0.0313868
$430$	0	0
$431$	−2155.82	−0.240933	−0.120467	−	0.992717i	$-0.538439\pi$
$431$	−2155.82	−0.240933	−0.120467	+	0.992717i	$0.538439\pi$
$432$	1666.96	0.185652
$433$	3525.87	0.391322	0.195661	−	0.980672i	$-0.437315\pi$
$433$	3525.87	0.391322	0.195661	+	0.980672i	$0.437315\pi$
$434$	8562.57	0.947042
$435$	40.0827	0.00441798
$436$	−7062.06	−0.775714
$437$	2734.28	0.299310
$438$	−667.238	−0.0727897
$439$	15251.6	1.65813	0.829065	−	0.559153i	$-0.188873\pi$
$439$	15251.6	1.65813	0.829065	+	0.559153i	$0.188873\pi$
$440$	−487.331	−0.0528013
$441$	−2841.97	−0.306876
$442$	−5548.93	−0.597140
$443$	6397.51	0.686129	0.343064	−	0.939312i	$-0.388535\pi$
$443$	6397.51	0.686129	0.343064	+	0.939312i	$0.388535\pi$
$444$	−124.610	−0.0133192
$445$	−1079.08	−0.114951
$446$	−10683.7	−1.13428
$447$	−680.105	−0.0719639
$448$	−695.307	−0.0733263
$449$	−1781.14	−0.187210	−0.0936048	−	0.995609i	$-0.529839\pi$
$449$	−1781.14	−0.187210	−0.0936048	+	0.995609i	$0.529839\pi$
$450$	11657.0	1.22115
$451$	1281.12	0.133760
$452$	3847.46	0.400375
$453$	−834.804	−0.0865839
$454$	13806.3	1.42723
$455$	−1104.88	−0.113841
$456$	135.148	0.0138791
$457$	−4608.14	−0.471684	−0.235842	−	0.971791i	$-0.575785\pi$
$457$	−4608.14	−0.471684	−0.235842	+	0.971791i	$0.575785\pi$
$458$	−8950.70	−0.913185
$459$	−1082.45	−0.110075
$460$	−753.150	−0.0763387
$461$	2306.59	0.233034	0.116517	−	0.993189i	$-0.462827\pi$
$461$	2306.59	0.233034	0.116517	+	0.993189i	$0.462827\pi$
$462$	696.576	0.0701464
$463$	7772.27	0.780147	0.390073	−	0.920784i	$-0.372450\pi$
$463$	7772.27	0.780147	0.390073	+	0.920784i	$0.372450\pi$
$464$	−4743.73	−0.474616
$465$	76.3552	0.00761481
$466$	−18858.3	−1.87466
$467$	−12345.1	−1.22327	−0.611633	−	0.791142i	$-0.709487\pi$
$467$	−12345.1	−1.22327	−0.611633	+	0.791142i	$0.709487\pi$
$468$	3778.17	0.373175
$469$	−9077.12	−0.893694
$470$	−2800.94	−0.274889
$471$	1305.96	0.127761
$472$	5429.22	0.529449
$473$	0	0
$474$	1529.27	0.148189
$475$	3568.26	0.344680
$476$	5103.01	0.491378
$477$	17792.8	1.70792
$478$	6568.21	0.628500
$479$	14390.6	1.37270	0.686351	−	0.727270i	$-0.259211\pi$
$479$	14390.6	1.37270	0.686351	+	0.727270i	$0.259211\pi$
$480$	−126.449	−0.0120241
$481$	2073.41	0.196548
$482$	−25117.4	−2.37358
$483$	−770.722	−0.0726067
$484$	−3576.20	−0.335856
$485$	1937.22	0.181371
$486$	3005.36	0.280506
$487$	606.724	0.0564544	0.0282272	−	0.999602i	$-0.491014\pi$
$487$	606.724	0.0564544	0.0282272	+	0.999602i	$0.491014\pi$
$488$	−7208.08	−0.668636
$489$	1329.99	0.122994
$490$	650.797	0.0600001
$491$	−7038.63	−0.646943	−0.323471	−	0.946238i	$-0.604850\pi$
$491$	−7038.63	−0.646943	−0.323471	+	0.946238i	$0.604850\pi$
$492$	97.8618	0.00896738
$493$	3080.36	0.281404
$494$	3141.01	0.286074
$495$	−1101.61	−0.100028
$496$	−9036.52	−0.818048
$497$	2964.21	0.267531
$498$	−1740.43	−0.156608
$499$	−3141.95	−0.281870	−0.140935	−	0.990019i	$-0.545011\pi$
$499$	−3141.95	−0.281870	−0.140935	+	0.990019i	$0.545011\pi$
$500$	−1989.78	−0.177972
$501$	119.073	0.0106183
$502$	100.373	0.00892402
$503$	12706.9	1.12639	0.563195	−	0.826324i	$-0.309572\pi$
$503$	12706.9	1.12639	0.563195	+	0.826324i	$0.309572\pi$
$504$	6756.00	0.597095
$505$	−1621.54	−0.142886
$506$	−7900.74	−0.694132
$507$	−500.349	−0.0438290
$508$	−7632.61	−0.666619
$509$	−9077.82	−0.790506	−0.395253	−	0.918572i	$-0.629343\pi$
$509$	−9077.82	−0.790506	−0.395253	+	0.918572i	$0.629343\pi$
$510$	123.589	0.0107306
$511$	−10210.1	−0.883892
$512$	7405.22	0.639194
$513$	612.727	0.0527340
$514$	28701.3	2.46296
$515$	1888.51	0.161588
$516$	0	0
$517$	−10818.6	−0.920312
$518$	−5178.71	−0.439266
$519$	373.915	0.0316244
$520$	619.411	0.0522365
$521$	−8598.76	−0.723068	−0.361534	−	0.932359i	$-0.617747\pi$
$521$	−8598.76	−0.723068	−0.361534	+	0.932359i	$0.617747\pi$
$522$	−5696.30	−0.477625
$523$	−7894.95	−0.660080	−0.330040	−	0.943967i	$-0.607062\pi$
$523$	−7894.95	−0.660080	−0.330040	+	0.943967i	$0.607062\pi$
$524$	11626.8	0.969312
$525$	−1005.80	−0.0836127
$526$	−1447.28	−0.119970
$527$	5867.90	0.485028
$528$	−735.132	−0.0605919
$529$	−3425.28	−0.281522
$530$	−4074.47	−0.333931
$531$	12272.8	1.00300
$532$	−2888.59	−0.235407
$533$	−1628.34	−0.132329
$534$	−864.694	−0.0700730
$535$	−1186.64	−0.0958935
$536$	5088.77	0.410077
$537$	−725.038	−0.0582639
$538$	14009.2	1.12264
$539$	2513.70	0.200877
$540$	−168.774	−0.0134498
$541$	−13540.9	−1.07610	−0.538048	−	0.842914i	$-0.680838\pi$
$541$	−13540.9	−1.07610	−0.538048	+	0.842914i	$0.680838\pi$
$542$	12903.0	1.02257
$543$	−519.223	−0.0410349
$544$	−9717.58	−0.765879
$545$	−2617.19	−0.205703
$546$	−885.367	−0.0693960
$547$	−4395.62	−0.343589	−0.171795	−	0.985133i	$-0.554957\pi$
$547$	−4395.62	−0.343589	−0.171795	+	0.985133i	$0.554957\pi$
$548$	−13058.1	−1.01791
$549$	−16293.9	−1.26668
$550$	−10310.5	−0.799351
$551$	−1743.66	−0.134814
$552$	432.078	0.0333160
$553$	23400.9	1.79947
$554$	−2057.34	−0.157776
$555$	−46.1803	−0.00353197
$556$	−6194.93	−0.472525
$557$	−11923.4	−0.907024	−0.453512	−	0.891250i	$-0.649829\pi$
$557$	−11923.4	−0.907024	−0.453512	+	0.891250i	$0.649829\pi$
$558$	−10851.1	−0.823233
$559$	0	0
$560$	−2912.38	−0.219769
$561$	477.361	0.0359255
$562$	−10508.2	−0.788720
$563$	−12331.1	−0.923080	−0.461540	−	0.887119i	$-0.652703\pi$
$563$	−12331.1	−0.923080	−0.461540	+	0.887119i	$0.652703\pi$
$564$	−826.407	−0.0616986
$565$	1425.86	0.106171
$566$	−12474.5	−0.926403
$567$	15185.4	1.12474
$568$	−1661.78	−0.122758
$569$	13372.1	0.985213	0.492606	−	0.870252i	$-0.336044\pi$
$569$	13372.1	0.985213	0.492606	+	0.870252i	$0.336044\pi$
$570$	−69.9584	−0.00514076
$571$	3289.21	0.241067	0.120533	−	0.992709i	$-0.461539\pi$
$571$	3289.21	0.241067	0.120533	+	0.992709i	$0.461539\pi$
$572$	−3341.76	−0.244276
$573$	538.356	0.0392498
$574$	4067.07	0.295742
$575$	11408.0	0.827387
$576$	881.144	0.0637402
$577$	−4746.04	−0.342426	−0.171213	−	0.985234i	$-0.554769\pi$
$577$	−4746.04	−0.342426	−0.171213	+	0.985234i	$0.554769\pi$
$578$	−7984.59	−0.574593
$579$	−1345.80	−0.0965965
$580$	480.286	0.0343841
$581$	−26632.2	−1.90170
$582$	1552.35	0.110562
$583$	−15737.6	−1.11798
$584$	5723.94	0.405579
$585$	1400.18	0.0989581
$586$	6161.37	0.434341
$587$	20672.2	1.45355	0.726773	−	0.686878i	$-0.241019\pi$
$587$	20672.2	1.45355	0.726773	+	0.686878i	$0.241019\pi$
$588$	192.015	0.0134670
$589$	−3321.56	−0.232365
$590$	−2810.40	−0.196106
$591$	1196.15	0.0832538
$592$	5465.36	0.379434
$593$	655.239	0.0453751	0.0226875	−	0.999743i	$-0.492778\pi$
$593$	655.239	0.0453751	0.0226875	+	0.999743i	$0.492778\pi$
$594$	−1770.48	−0.122296
$595$	1891.16	0.130303
$596$	−8149.27	−0.560079
$597$	−623.064	−0.0427141
$598$	10042.1	0.686706
$599$	17821.2	1.21562	0.607809	−	0.794083i	$-0.292049\pi$
$599$	17821.2	1.21562	0.607809	+	0.794083i	$0.292049\pi$
$600$	563.866	0.0383662
$601$	20715.1	1.40597	0.702984	−	0.711205i	$-0.251850\pi$
$601$	20715.1	1.40597	0.702984	+	0.711205i	$0.251850\pi$
$602$	0	0
$603$	11503.2	0.776859
$604$	−10002.9	−0.673863
$605$	−1325.33	−0.0890618
$606$	−1299.38	−0.0871018
$607$	25430.6	1.70049	0.850244	−	0.526389i	$-0.176454\pi$
$607$	25430.6	1.70049	0.850244	+	0.526389i	$0.176454\pi$
$608$	5500.70	0.366913
$609$	491.491	0.0327032
$610$	3731.22	0.247660
$611$	13750.7	0.910467
$612$	−6466.91	−0.427139
$613$	16857.5	1.11071	0.555357	−	0.831612i	$-0.312582\pi$
$613$	16857.5	1.11071	0.555357	+	0.831612i	$0.312582\pi$
$614$	5796.19	0.380969
$615$	36.2674	0.00237795
$616$	−5975.61	−0.390851
$617$	−9646.72	−0.629437	−0.314718	−	0.949185i	$-0.601910\pi$
$617$	−9646.72	−0.629437	−0.314718	+	0.949185i	$0.601910\pi$
$618$	1513.31	0.0985023
$619$	8241.95	0.535172	0.267586	−	0.963534i	$-0.413774\pi$
$619$	8241.95	0.535172	0.267586	+	0.963534i	$0.413774\pi$
$620$	914.916	0.0592644
$621$	1958.94	0.126585
$622$	8604.57	0.554682
$623$	−13231.6	−0.850902
$624$	934.374	0.0599437
$625$	14514.4	0.928923
$626$	−21340.3	−1.36251
$627$	−270.214	−0.0172110
$628$	15648.4	0.994332
$629$	−3548.96	−0.224970
$630$	−3497.20	−0.221162
$631$	−21434.0	−1.35226	−0.676130	−	0.736783i	$-0.736344\pi$
$631$	−21434.0	−1.35226	−0.676130	+	0.736783i	$0.736344\pi$
$632$	−13118.9	−0.825700
$633$	641.359	0.0402713
$634$	17591.8	1.10199
$635$	−2828.63	−0.176773
$636$	−1202.16	−0.0749507
$637$	−3194.98	−0.198728
$638$	5038.32	0.312647
$639$	−3756.46	−0.232556
$640$	2398.12	0.148116
$641$	4316.55	0.265980	0.132990	−	0.991117i	$-0.457542\pi$
$641$	4316.55	0.265980	0.132990	+	0.991117i	$0.457542\pi$
$642$	−950.887	−0.0584556
$643$	−19770.6	−1.21256	−0.606280	−	0.795251i	$-0.707339\pi$
$643$	−19770.6	−1.21256	−0.606280	+	0.795251i	$0.707339\pi$
$644$	−9235.06	−0.565082
$645$	0	0
$646$	−5376.30	−0.327442
$647$	5551.13	0.337307	0.168653	−	0.985675i	$-0.446058\pi$
$647$	5551.13	0.337307	0.168653	+	0.985675i	$0.446058\pi$
$648$	−8513.14	−0.516092
$649$	−10855.2	−0.656552
$650$	13105.0	0.790800
$651$	936.261	0.0563671
$652$	15936.4	0.957237
$653$	−4038.70	−0.242031	−0.121016	−	0.992651i	$-0.538615\pi$
$653$	−4038.70	−0.242031	−0.121016	+	0.992651i	$0.538615\pi$
$654$	−2097.22	−0.125394
$655$	4308.87	0.257040
$656$	−4292.19	−0.255460
$657$	12939.0	0.768339
$658$	−34344.9	−2.03481
$659$	9730.38	0.575177	0.287589	−	0.957754i	$-0.407146\pi$
$659$	9730.38	0.575177	0.287589	+	0.957754i	$0.407146\pi$
$660$	74.4296	0.00438965
$661$	15692.3	0.923389	0.461695	−	0.887039i	$-0.347242\pi$
$661$	15692.3	0.923389	0.461695	+	0.887039i	$0.347242\pi$
$662$	7943.48	0.466363
$663$	−606.740	−0.0355412
$664$	14930.4	0.872608
$665$	−1070.51	−0.0624247
$666$	6562.85	0.381840
$667$	−5574.62	−0.323613
$668$	1426.77	0.0826401
$669$	−1168.20	−0.0675115
$670$	−2634.17	−0.151891
$671$	14411.8	0.829153
$672$	−1550.50	−0.0890059
$673$	21603.8	1.23739	0.618696	−	0.785630i	$-0.287661\pi$
$673$	21603.8	1.23739	0.618696	+	0.785630i	$0.287661\pi$
$674$	−7202.86	−0.411638
$675$	2556.43	0.145774
$676$	−5995.36	−0.341111
$677$	−24227.5	−1.37539	−0.687694	−	0.726000i	$-0.741377\pi$
$677$	−24227.5	−1.37539	−0.687694	+	0.726000i	$0.741377\pi$
$678$	1142.58	0.0647205
$679$	23754.1	1.34256
$680$	−1060.21	−0.0597903
$681$	1509.63	0.0849473
$682$	9597.71	0.538879
$683$	10388.0	0.581973	0.290986	−	0.956727i	$-0.406017\pi$
$683$	10388.0	0.581973	0.290986	+	0.956727i	$0.406017\pi$
$684$	3660.64	0.204631
$685$	−4839.30	−0.269927
$686$	−17878.3	−0.995038
$687$	−978.701	−0.0543519
$688$	0	0
$689$	20002.9	1.10602
$690$	−223.663	−0.0123401
$691$	7162.33	0.394310	0.197155	−	0.980372i	$-0.436830\pi$
$691$	7162.33	0.394310	0.197155	+	0.980372i	$0.436830\pi$
$692$	4480.39	0.246125
$693$	−13507.9	−0.740437
$694$	10046.3	0.549498
$695$	−2295.83	−0.125303
$696$	−275.537	−0.0150060
$697$	2787.15	0.151465
$698$	−25974.7	−1.40854
$699$	−2062.03	−0.111578
$700$	−12051.8	−0.650739
$701$	−27058.1	−1.45788	−0.728938	−	0.684580i	$-0.759986\pi$
$701$	−27058.1	−1.45788	−0.728938	+	0.684580i	$0.759986\pi$
$702$	2250.33	0.120988
$703$	2008.91	0.107777
$704$	−779.363	−0.0417235
$705$	−306.265	−0.0163611
$706$	45241.4	2.41173
$707$	−19883.2	−1.05769
$708$	−829.199	−0.0440158
$709$	17177.5	0.909895	0.454948	−	0.890518i	$-0.349658\pi$
$709$	17177.5	0.909895	0.454948	+	0.890518i	$0.349658\pi$
$710$	860.211	0.0454692
$711$	−29655.4	−1.56423
$712$	7417.82	0.390442
$713$	−10619.3	−0.557779
$714$	1515.44	0.0794312
$715$	−1238.45	−0.0647767
$716$	−8687.67	−0.453454
$717$	718.191	0.0374077
$718$	−20677.8	−1.07478
$719$	14742.5	0.764677	0.382339	−	0.924022i	$-0.375119\pi$
$719$	14742.5	0.764677	0.382339	+	0.924022i	$0.375119\pi$
$720$	3690.78	0.191038
$721$	23156.8	1.19612
$722$	−21363.8	−1.10121
$723$	−2746.42	−0.141273
$724$	−6221.51	−0.319366
$725$	−7274.93	−0.372668
$726$	−1062.02	−0.0542911
$727$	31249.1	1.59418	0.797088	−	0.603864i	$-0.206373\pi$
$727$	31249.1	1.59418	0.797088	+	0.603864i	$0.206373\pi$
$728$	7595.17	0.386670
$729$	−19023.9	−0.966515
$730$	−2962.96	−0.150225
$731$	0	0
$732$	1100.88	0.0555872
$733$	18663.2	0.940439	0.470220	−	0.882549i	$-0.344175\pi$
$733$	18663.2	0.940439	0.470220	+	0.882549i	$0.344175\pi$
$734$	42449.1	2.13464
$735$	71.1605	0.00357115
$736$	17586.2	0.880755
$737$	−10174.5	−0.508522
$738$	−5154.09	−0.257079
$739$	−15750.2	−0.784008	−0.392004	−	0.919963i	$-0.628218\pi$
$739$	−15750.2	−0.784008	−0.392004	+	0.919963i	$0.628218\pi$
$740$	−553.349	−0.0274885
$741$	343.449	0.0170269
$742$	−49960.8	−2.47186
$743$	16483.1	0.813874	0.406937	−	0.913456i	$-0.366597\pi$
$743$	16483.1	0.813874	0.406937	+	0.913456i	$0.366597\pi$
$744$	−524.882	−0.0258644
$745$	−3020.10	−0.148521
$746$	1330.73	0.0653105
$747$	33750.3	1.65309
$748$	5719.92	0.279600
$749$	−14550.5	−0.709832
$750$	−590.905	−0.0287691
$751$	−22251.6	−1.08119	−0.540594	−	0.841284i	$-0.681800\pi$
$751$	−22251.6	−1.08119	−0.540594	+	0.841284i	$0.681800\pi$
$752$	36245.9	1.75765
$753$	10.9751	0.000531149 0
$754$	−6403.85	−0.309303
$755$	−3707.06	−0.178694
$756$	−2069.49	−0.0995591
$757$	−14562.5	−0.699184	−0.349592	−	0.936902i	$-0.613680\pi$
$757$	−14562.5	−0.699184	−0.349592	+	0.936902i	$0.613680\pi$
$758$	50095.1	2.40044
$759$	−863.895	−0.0413141
$760$	600.142	0.0286440
$761$	−1130.87	−0.0538685	−0.0269342	−	0.999637i	$-0.508574\pi$
$761$	−1130.87	−0.0538685	−0.0269342	+	0.999637i	$0.508574\pi$
$762$	−2266.65	−0.107759
$763$	−32091.7	−1.52267
$764$	6450.78	0.305472
$765$	−2396.62	−0.113268
$766$	−45555.1	−2.14879
$767$	13797.2	0.649528
$768$	2023.83	0.0950895
$769$	−1566.33	−0.0734501	−0.0367251	−	0.999325i	$-0.511693\pi$
$769$	−1566.33	−0.0734501	−0.0367251	+	0.999325i	$0.511693\pi$
$770$	3093.24	0.144770
$771$	3138.30	0.146593
$772$	−16125.8	−0.751789
$773$	29874.3	1.39004	0.695022	−	0.718989i	$-0.255395\pi$
$773$	29874.3	1.39004	0.695022	+	0.718989i	$0.255395\pi$
$774$	0	0
$775$	−13858.3	−0.642329
$776$	−13316.9	−0.616042
$777$	−566.259	−0.0261447
$778$	−33611.0	−1.54886
$779$	−1577.68	−0.0725628
$780$	−94.6021	−0.00434269
$781$	3322.56	0.152228
$782$	−17188.5	−0.786009
$783$	−1249.22	−0.0570159
$784$	−8421.73	−0.383643
$785$	5799.28	0.263675
$786$	3452.81	0.156689
$787$	3714.80	0.168257	0.0841285	−	0.996455i	$-0.473189\pi$
$787$	3714.80	0.168257	0.0841285	+	0.996455i	$0.473189\pi$
$788$	14332.7	0.647945
$789$	−158.251	−0.00714053
$790$	6790.93	0.305836
$791$	17483.8	0.785907
$792$	7572.74	0.339754
$793$	−18317.8	−0.820283
$794$	39355.0	1.75902
$795$	−445.517	−0.0198753
$796$	−7465.78	−0.332434
$797$	−34507.2	−1.53364	−0.766818	−	0.641865i	$-0.778161\pi$
$797$	−34507.2	−1.53364	−0.766818	+	0.641865i	$0.778161\pi$
$798$	−857.824	−0.0380534
$799$	−23536.4	−1.04213
$800$	22950.2	1.01426
$801$	16768.0	0.739662
$802$	43670.8	1.92278
$803$	−11444.4	−0.502945
$804$	−777.202	−0.0340918
$805$	−3422.50	−0.149847
$806$	−12199.0	−0.533114
$807$	1531.81	0.0668183
$808$	11146.8	0.485325
$809$	−3865.29	−0.167981	−0.0839904	−	0.996467i	$-0.526767\pi$
$809$	−3865.29	−0.167981	−0.0839904	+	0.996467i	$0.526767\pi$
$810$	4406.78	0.191159
$811$	31705.3	1.37278	0.686390	−	0.727233i	$-0.259194\pi$
$811$	31705.3	1.37278	0.686390	+	0.727233i	$0.259194\pi$
$812$	5889.22	0.254521
$813$	1410.86	0.0608625
$814$	−5804.78	−0.249948
$815$	5906.01	0.253839
$816$	−1599.32	−0.0686120
$817$	0	0
$818$	26563.2	1.13540
$819$	17168.9	0.732517
$820$	434.569	0.0185071
$821$	−26341.2	−1.11975	−0.559874	−	0.828578i	$-0.689150\pi$
$821$	−26341.2	−1.11975	−0.559874	+	0.828578i	$0.689150\pi$
$822$	−3877.86	−0.164545
$823$	22855.3	0.968027	0.484014	−	0.875060i	$-0.339179\pi$
$823$	22855.3	0.968027	0.484014	+	0.875060i	$0.339179\pi$
$824$	−12982.0	−0.548848
$825$	−1127.39	−0.0475766
$826$	−34460.9	−1.45163
$827$	2106.23	0.0885621	0.0442811	−	0.999019i	$-0.485900\pi$
$827$	2106.23	0.0885621	0.0442811	+	0.999019i	$0.485900\pi$
$828$	11703.4	0.491207
$829$	−47294.6	−1.98144	−0.990718	−	0.135934i	$-0.956597\pi$
$829$	−47294.6	−1.98144	−0.990718	+	0.135934i	$0.956597\pi$
$830$	−7728.64	−0.323211
$831$	−224.957	−0.00939069
$832$	990.593	0.0412772
$833$	5468.69	0.227466
$834$	−1839.71	−0.0763835
$835$	528.760	0.0219144
$836$	−3237.80	−0.133949
$837$	−2379.69	−0.0982725
$838$	58331.9	2.40458
$839$	−18592.7	−0.765068	−0.382534	−	0.923941i	$-0.624948\pi$
$839$	−18592.7	−0.765068	−0.382534	+	0.923941i	$0.624948\pi$
$840$	−169.164	−0.00694847
$841$	−20834.1	−0.854240
$842$	4540.51	0.185839
$843$	−1149.00	−0.0469439
$844$	7684.99	0.313422
$845$	−2221.87	−0.0904552
$846$	43524.4	1.76879
$847$	−16251.1	−0.659262
$848$	52726.2	2.13517
$849$	−1364.01	−0.0551386
$850$	−22431.1	−0.905155
$851$	6422.65	0.258714
$852$	253.802	0.0102055
$853$	−17373.7	−0.697381	−0.348690	−	0.937238i	$-0.613374\pi$
$853$	−17373.7	−0.697381	−0.348690	+	0.937238i	$0.613374\pi$
$854$	45751.9	1.83325
$855$	1356.62	0.0542638
$856$	8157.23	0.325711
$857$	−17612.9	−0.702035	−0.351017	−	0.936369i	$-0.614164\pi$
$857$	−17612.9	−0.702035	−0.351017	+	0.936369i	$0.614164\pi$
$858$	−992.400	−0.0394872
$859$	−29606.2	−1.17596	−0.587980	−	0.808876i	$-0.700077\pi$
$859$	−29606.2	−1.17596	−0.587980	+	0.808876i	$0.700077\pi$
$860$	0	0
$861$	444.708	0.0176023
$862$	−7671.26	−0.303114
$863$	−20822.0	−0.821307	−0.410654	−	0.911791i	$-0.634699\pi$
$863$	−20822.0	−0.821307	−0.410654	+	0.911791i	$0.634699\pi$
$864$	3940.90	0.155176
$865$	1660.42	0.0652671
$866$	12546.5	0.492316
$867$	−873.063	−0.0341993
$868$	11218.6	0.438692
$869$	26229.9	1.02392
$870$	142.630	0.00555818
$871$	12932.0	0.503083
$872$	17991.1	0.698687
$873$	−30102.9	−1.16704
$874$	9729.66	0.376557
$875$	−9042.06	−0.349346
$876$	−874.212	−0.0337179
$877$	40309.5	1.55206	0.776029	−	0.630697i	$-0.217231\pi$
$877$	40309.5	1.55206	0.776029	+	0.630697i	$0.217231\pi$
$878$	54271.2	2.08607
$879$	673.706	0.0258516
$880$	−3264.46	−0.125051
$881$	−9468.84	−0.362104	−0.181052	−	0.983474i	$-0.557950\pi$
$881$	−9468.84	−0.362104	−0.181052	+	0.983474i	$0.557950\pi$
$882$	−10112.9	−0.386075
$883$	−22005.5	−0.838668	−0.419334	−	0.907832i	$-0.637736\pi$
$883$	−22005.5	−0.838668	−0.419334	+	0.907832i	$0.637736\pi$
$884$	−7270.17	−0.276609
$885$	−307.299	−0.0116720
$886$	22764.9	0.863207
$887$	5478.27	0.207376	0.103688	−	0.994610i	$-0.466936\pi$
$887$	5478.27	0.207376	0.103688	+	0.994610i	$0.466936\pi$
$888$	317.453	0.0119967
$889$	−34684.5	−1.30853
$890$	−3839.79	−0.144618
$891$	17021.2	0.639989
$892$	−13997.8	−0.525426
$893$	13323.0	0.499256
$894$	−2420.08	−0.0905366
$895$	−3219.63	−0.120246
$896$	29405.6	1.09640
$897$	1098.03	0.0408721
$898$	−6338.00	−0.235525
$899$	6771.96	0.251232
$900$	15273.0	0.565666
$901$	−34238.0	−1.26596
$902$	4558.74	0.168281
$903$	0	0
$904$	−9801.68	−0.360619
$905$	−2305.68	−0.0846889
$906$	−2970.56	−0.108930
$907$	−45128.8	−1.65213	−0.826063	−	0.563578i	$-0.809424\pi$
$907$	−45128.8	−1.65213	−0.826063	+	0.563578i	$0.809424\pi$
$908$	18088.9	0.661125
$909$	25197.4	0.919412
$910$	−3931.60	−0.143221
$911$	−255.420	−0.00928916	−0.00464458	−	0.999989i	$-0.501478\pi$
$911$	−255.420	−0.00928916	−0.00464458	+	0.999989i	$0.501478\pi$
$912$	905.306	0.0328702
$913$	−29851.8	−1.08209
$914$	−16397.6	−0.593418
$915$	407.985	0.0147405
$916$	−11727.2	−0.423009
$917$	52835.0	1.90269
$918$	−3851.78	−0.138483
$919$	−10556.9	−0.378934	−0.189467	−	0.981887i	$-0.560676\pi$
$919$	−10556.9	−0.378934	−0.189467	+	0.981887i	$0.560676\pi$
$920$	1918.70	0.0687584
$921$	633.776	0.0226749
$922$	8207.76	0.293176
$923$	−4223.06	−0.150600
$924$	912.649	0.0324935
$925$	8381.63	0.297931
$926$	27656.8	0.981489
$927$	−29346.0	−1.03975
$928$	−11214.8	−0.396705
$929$	17013.2	0.600846	0.300423	−	0.953806i	$-0.402872\pi$
$929$	17013.2	0.600846	0.300423	+	0.953806i	$0.402872\pi$
$930$	271.702	0.00958007
$931$	−3095.59	−0.108973
$932$	−24708.0	−0.868389
$933$	940.854	0.0330141
$934$	−43928.9	−1.53897
$935$	2119.79	0.0741439
$936$	−9625.16	−0.336120
$937$	6894.92	0.240392	0.120196	−	0.992750i	$-0.461648\pi$
$937$	6894.92	0.240392	0.120196	+	0.992750i	$0.461648\pi$
$938$	−32300.0	−1.12434
$939$	−2333.42	−0.0810952
$940$	−3669.77	−0.127335
$941$	34775.8	1.20474	0.602370	−	0.798217i	$-0.294223\pi$
$941$	34775.8	1.20474	0.602370	+	0.798217i	$0.294223\pi$
$942$	4647.11	0.160734
$943$	−5043.99	−0.174183
$944$	36368.4	1.25391
$945$	−766.949	−0.0264009
$946$	0	0
$947$	39895.0	1.36897	0.684485	−	0.729027i	$-0.260027\pi$
$947$	39895.0	1.36897	0.684485	+	0.729027i	$0.260027\pi$
$948$	2003.64	0.0686447
$949$	14546.2	0.497565
$950$	12697.3	0.433637
$951$	1923.55	0.0655894
$952$	−13000.3	−0.442585
$953$	−17365.9	−0.590280	−0.295140	−	0.955454i	$-0.595366\pi$
$953$	−17365.9	−0.590280	−0.295140	+	0.955454i	$0.595366\pi$
$954$	63314.0	2.14871
$955$	2390.65	0.0810047
$956$	8605.63	0.291136
$957$	550.908	0.0186085
$958$	51207.6	1.72697
$959$	−59339.1	−1.99808
$960$	−22.0631	−0.000741752 0
$961$	−16890.8	−0.566977
$962$	7378.03	0.247274
$963$	18439.5	0.617034
$964$	−32908.6	−1.09950
$965$	−5976.20	−0.199358
$966$	−2742.53	−0.0913453
$967$	7707.52	0.256315	0.128158	−	0.991754i	$-0.459094\pi$
$967$	7707.52	0.256315	0.128158	+	0.991754i	$0.459094\pi$
$968$	9110.61	0.302506
$969$	−587.864	−0.0194891
$970$	6893.41	0.228180
$971$	−23614.3	−0.780452	−0.390226	−	0.920719i	$-0.627603\pi$
$971$	−23614.3	−0.780452	−0.390226	+	0.920719i	$0.627603\pi$
$972$	3937.60	0.129937
$973$	−28151.3	−0.927532
$974$	2158.97	0.0710244
$975$	1432.95	0.0470677
$976$	−48284.4	−1.58355
$977$	−2369.02	−0.0775760	−0.0387880	−	0.999247i	$-0.512350\pi$
$977$	−2369.02	−0.0775760	−0.0387880	+	0.999247i	$0.512350\pi$
$978$	4732.64	0.154737
$979$	−14831.2	−0.484174
$980$	852.671	0.0277934
$981$	40669.0	1.32361
$982$	−25046.2	−0.813908
$983$	−36764.7	−1.19289	−0.596446	−	0.802653i	$-0.703421\pi$
$983$	−36764.7	−1.19289	−0.596446	+	0.802653i	$0.703421\pi$
$984$	−249.310	−0.00807693
$985$	5311.67	0.171821
$986$	10961.1	0.354030
$987$	−3755.39	−0.121110
$988$	4115.33	0.132516
$989$	0	0
$990$	−3919.98	−0.125844
$991$	−21854.8	−0.700546	−0.350273	−	0.936648i	$-0.613911\pi$
$991$	−21854.8	−0.700546	−0.350273	+	0.936648i	$0.613911\pi$
$992$	−21363.5	−0.683761
$993$	868.568	0.0277575
$994$	10547.8	0.336577
$995$	−2766.80	−0.0881543
$996$	−2280.31	−0.0725444
$997$	32490.3	1.03207	0.516037	−	0.856566i	$-0.327407\pi$
$997$	32490.3	1.03207	0.516037	+	0.856566i	$0.327407\pi$
$998$	−11180.3	−0.354616
$999$	1439.26	0.0455816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.f.1.8		10
43.7	odd	6		43.4.c.a.6.3	✓	20
43.37	odd	6		43.4.c.a.36.3	yes	20
43.42	odd	2		1849.4.a.d.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.3	✓	20	43.7	odd	6
43.4.c.a.36.3	yes	20	43.37	odd	6
1849.4.a.d.1.3		10	43.42	odd	2
1849.4.a.f.1.8		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+3.55840 q^{2} +0.389088 q^{3} +4.66219 q^{4} +1.72780 q^{5} +1.38453 q^{6} +21.1861 q^{7} -11.8773 q^{8} -26.8486 q^{9} +O(q^{10})\)	\(q+3.55840 q^{2} +0.389088 q^{3} +4.66219 q^{4} +1.72780 q^{5} +1.38453 q^{6} +21.1861 q^{7} -11.8773 q^{8} -26.8486 q^{9} +6.14819 q^{10} +23.7473 q^{11} +1.81400 q^{12} -30.1835 q^{13} +75.3886 q^{14} +0.672265 q^{15} -79.5615 q^{16} +51.6636 q^{17} -95.5380 q^{18} -29.2445 q^{19} +8.05532 q^{20} +8.24326 q^{21} +84.5025 q^{22} -93.4972 q^{23} -4.62129 q^{24} -122.015 q^{25} -107.405 q^{26} -20.9518 q^{27} +98.7737 q^{28} +59.6234 q^{29} +2.39219 q^{30} +113.579 q^{31} -188.093 q^{32} +9.23980 q^{33} +183.840 q^{34} +36.6053 q^{35} -125.173 q^{36} -68.6936 q^{37} -104.064 q^{38} -11.7440 q^{39} -20.5215 q^{40} +53.9480 q^{41} +29.3328 q^{42} +110.715 q^{44} -46.3890 q^{45} -332.700 q^{46} -455.571 q^{47} -30.9564 q^{48} +105.852 q^{49} -434.177 q^{50} +20.1017 q^{51} -140.721 q^{52} -662.710 q^{53} -74.5550 q^{54} +41.0306 q^{55} -251.633 q^{56} -11.3787 q^{57} +212.164 q^{58} -457.110 q^{59} +3.13423 q^{60} +606.881 q^{61} +404.159 q^{62} -568.818 q^{63} -32.8190 q^{64} -52.1511 q^{65} +32.8789 q^{66} -428.446 q^{67} +240.866 q^{68} -36.3786 q^{69} +130.256 q^{70} +139.913 q^{71} +318.888 q^{72} -481.924 q^{73} -244.439 q^{74} -47.4744 q^{75} -136.344 q^{76} +503.114 q^{77} -41.7900 q^{78} +1104.54 q^{79} -137.466 q^{80} +716.760 q^{81} +191.968 q^{82} -1257.06 q^{83} +38.4317 q^{84} +89.2643 q^{85} +23.1987 q^{87} -282.053 q^{88} -624.540 q^{89} -165.070 q^{90} -639.472 q^{91} -435.902 q^{92} +44.1922 q^{93} -1621.10 q^{94} -50.5287 q^{95} -73.1848 q^{96} +1121.21 q^{97} +376.663 q^{98} -637.583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9}+O(q^{10}) \) 10 * q + q^2 - 5 * q^3 + 39 * q^4 - 19 * q^5 - 15 * q^6 - 51 * q^7 + 36 * q^8 + 117 * q^9	\( 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9} - 27 q^{10} + 27 q^{11} - 72 q^{12} + 15 q^{13} - 96 q^{14} - 65 q^{15} + 67 q^{16} + 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 9 q^{21} - 190 q^{22} + 61 q^{23} - 202 q^{24} + 151 q^{25} - 21 q^{26} + 97 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} - 253 q^{31} + 399 q^{32} - 424 q^{33} - 231 q^{34} + 355 q^{35} + 1092 q^{36} - 129 q^{37} + 854 q^{38} - 691 q^{39} - 1345 q^{40} + 391 q^{41} - 31 q^{42} + 377 q^{44} - 944 q^{45} - 40 q^{46} - 334 q^{47} - 2401 q^{48} + 115 q^{49} + 424 q^{50} - 795 q^{51} + 564 q^{52} - 773 q^{53} + 182 q^{54} - 1242 q^{55} + 923 q^{56} + 765 q^{57} - 1328 q^{58} - 1483 q^{59} + 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 738 q^{64} + 1063 q^{65} - 1483 q^{66} + 642 q^{67} + 1052 q^{68} - 3503 q^{69} + 85 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} + 2232 q^{74} - 82 q^{75} - 252 q^{76} + 1448 q^{77} + 2822 q^{78} + 1405 q^{79} - 3157 q^{80} - 974 q^{81} - 3304 q^{82} - 543 q^{83} + 3652 q^{84} - 973 q^{85} + 1409 q^{87} + 2686 q^{88} - 2196 q^{89} - 742 q^{90} - 3513 q^{91} - 2629 q^{92} - 983 q^{93} - 4939 q^{94} + 149 q^{95} - 3540 q^{96} - 425 q^{97} - 213 q^{98} + 3181 q^{99}+O(q^{100}) \) 10 * q + q^2 - 5 * q^3 + 39 * q^4 - 19 * q^5 - 15 * q^6 - 51 * q^7 + 36 * q^8 + 117 * q^9 - 27 * q^10 + 27 * q^11 - 72 * q^12 + 15 * q^13 - 96 * q^14 - 65 * q^15 + 67 * q^16 + 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 9 * q^21 - 190 * q^22 + 61 * q^23 - 202 * q^24 + 151 * q^25 - 21 * q^26 + 97 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 - 253 * q^31 + 399 * q^32 - 424 * q^33 - 231 * q^34 + 355 * q^35 + 1092 * q^36 - 129 * q^37 + 854 * q^38 - 691 * q^39 - 1345 * q^40 + 391 * q^41 - 31 * q^42 + 377 * q^44 - 944 * q^45 - 40 * q^46 - 334 * q^47 - 2401 * q^48 + 115 * q^49 + 424 * q^50 - 795 * q^51 + 564 * q^52 - 773 * q^53 + 182 * q^54 - 1242 * q^55 + 923 * q^56 + 765 * q^57 - 1328 * q^58 - 1483 * q^59 + 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 738 * q^64 + 1063 * q^65 - 1483 * q^66 + 642 * q^67 + 1052 * q^68 - 3503 * q^69 + 85 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 + 2232 * q^74 - 82 * q^75 - 252 * q^76 + 1448 * q^77 + 2822 * q^78 + 1405 * q^79 - 3157 * q^80 - 974 * q^81 - 3304 * q^82 - 543 * q^83 + 3652 * q^84 - 973 * q^85 + 1409 * q^87 + 2686 * q^88 - 2196 * q^89 - 742 * q^90 - 3513 * q^91 - 2629 * q^92 - 983 * q^93 - 4939 * q^94 + 149 * q^95 - 3540 * q^96 - 425 * q^97 - 213 * q^98 + 3181 * q^99

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