LMFDB - Embedded newform 6001.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36622 q^{2} -1.16111 q^{3} +3.59897 q^{4} -3.78541 q^{5} +2.74743 q^{6} -1.24944 q^{7} -3.78352 q^{8} -1.65183 q^{9} +O(q^{10})$	\(q-2.36622 q^{2} -1.16111 q^{3} +3.59897 q^{4} -3.78541 q^{5} +2.74743 q^{6} -1.24944 q^{7} -3.78352 q^{8} -1.65183 q^{9} +8.95709 q^{10} +5.90263 q^{11} -4.17879 q^{12} -1.18162 q^{13} +2.95644 q^{14} +4.39526 q^{15} +1.75466 q^{16} +1.00000 q^{17} +3.90859 q^{18} -1.27065 q^{19} -13.6236 q^{20} +1.45073 q^{21} -13.9669 q^{22} -7.24873 q^{23} +4.39306 q^{24} +9.32931 q^{25} +2.79596 q^{26} +5.40127 q^{27} -4.49669 q^{28} -9.12776 q^{29} -10.4001 q^{30} +3.49231 q^{31} +3.41512 q^{32} -6.85358 q^{33} -2.36622 q^{34} +4.72963 q^{35} -5.94491 q^{36} +5.41453 q^{37} +3.00664 q^{38} +1.37198 q^{39} +14.3221 q^{40} -3.88046 q^{41} -3.43274 q^{42} -0.876332 q^{43} +21.2434 q^{44} +6.25286 q^{45} +17.1521 q^{46} -3.03549 q^{47} -2.03735 q^{48} -5.43891 q^{49} -22.0752 q^{50} -1.16111 q^{51} -4.25261 q^{52} +6.64042 q^{53} -12.7806 q^{54} -22.3439 q^{55} +4.72727 q^{56} +1.47536 q^{57} +21.5983 q^{58} +2.21644 q^{59} +15.8184 q^{60} -12.5378 q^{61} -8.26355 q^{62} +2.06386 q^{63} -11.5902 q^{64} +4.47290 q^{65} +16.2170 q^{66} +4.23889 q^{67} +3.59897 q^{68} +8.41654 q^{69} -11.1913 q^{70} -16.2867 q^{71} +6.24974 q^{72} -7.52844 q^{73} -12.8119 q^{74} -10.8323 q^{75} -4.57305 q^{76} -7.37497 q^{77} -3.24640 q^{78} +14.7859 q^{79} -6.64212 q^{80} -1.31594 q^{81} +9.18200 q^{82} +16.6273 q^{83} +5.22113 q^{84} -3.78541 q^{85} +2.07359 q^{86} +10.5983 q^{87} -22.3327 q^{88} +4.50223 q^{89} -14.7956 q^{90} +1.47636 q^{91} -26.0880 q^{92} -4.05494 q^{93} +7.18262 q^{94} +4.80994 q^{95} -3.96531 q^{96} +13.0983 q^{97} +12.8696 q^{98} -9.75016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) $ 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * 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 $

$2$	−2.36622	−1.67317	−0.836583	−	0.547840i	$-0.815450\pi$
$2$	−2.36622	−1.67317	−0.836583	+	0.547840i	$0.815450\pi$
$3$	−1.16111	−0.670365	−0.335182	−	0.942153i	$-0.608798\pi$
$3$	−1.16111	−0.670365	−0.335182	+	0.942153i	$0.608798\pi$
$4$	3.59897	1.79949
$5$	−3.78541	−1.69289	−0.846443	−	0.532480i	$-0.821260\pi$
$5$	−3.78541	−1.69289	−0.846443	+	0.532480i	$0.821260\pi$
$6$	2.74743	1.12163
$7$	−1.24944	−0.472243	−0.236121	−	0.971724i	$-0.575876\pi$
$7$	−1.24944	−0.472243	−0.236121	+	0.971724i	$0.575876\pi$
$8$	−3.78352	−1.33767
$9$	−1.65183	−0.550611
$10$	8.95709	2.83248
$11$	5.90263	1.77971	0.889855	−	0.456244i	$-0.150805\pi$
$11$	5.90263	1.77971	0.889855	+	0.456244i	$0.150805\pi$
$12$	−4.17879	−1.20631
$13$	−1.18162	−0.327722	−0.163861	−	0.986483i	$-0.552395\pi$
$13$	−1.18162	−0.327722	−0.163861	+	0.986483i	$0.552395\pi$
$14$	2.95644	0.790141
$15$	4.39526	1.13485
$16$	1.75466	0.438666
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	3.90859	0.921264
$19$	−1.27065	−0.291508	−0.145754	−	0.989321i	$-0.546561\pi$
$19$	−1.27065	−0.291508	−0.145754	+	0.989321i	$0.546561\pi$
$20$	−13.6236	−3.04633
$21$	1.45073	0.316575
$22$	−13.9669	−2.97775
$23$	−7.24873	−1.51146	−0.755732	−	0.654881i	$-0.772719\pi$
$23$	−7.24873	−1.51146	−0.755732	+	0.654881i	$0.772719\pi$
$24$	4.39306	0.896730
$25$	9.32931	1.86586
$26$	2.79596	0.548333
$27$	5.40127	1.03947
$28$	−4.49669	−0.849795
$29$	−9.12776	−1.69498	−0.847492	−	0.530809i	$-0.821888\pi$
$29$	−9.12776	−1.69498	−0.847492	+	0.530809i	$0.821888\pi$
$30$	−10.4001	−1.89879
$31$	3.49231	0.627237	0.313618	−	0.949549i	$-0.398459\pi$
$31$	3.49231	0.627237	0.313618	+	0.949549i	$0.398459\pi$
$32$	3.41512	0.603713
$33$	−6.85358	−1.19305
$34$	−2.36622	−0.405803
$35$	4.72963	0.799453
$36$	−5.94491	−0.990818
$37$	5.41453	0.890143	0.445071	−	0.895495i	$-0.353178\pi$
$37$	5.41453	0.890143	0.445071	+	0.895495i	$0.353178\pi$
$38$	3.00664	0.487741
$39$	1.37198	0.219693
$40$	14.3221	2.26453
$41$	−3.88046	−0.606026	−0.303013	−	0.952986i	$-0.597993\pi$
$41$	−3.88046	−0.606026	−0.303013	+	0.952986i	$0.597993\pi$
$42$	−3.43274	−0.529683
$43$	−0.876332	−0.133639	−0.0668197	−	0.997765i	$-0.521285\pi$
$43$	−0.876332	−0.133639	−0.0668197	+	0.997765i	$0.521285\pi$
$44$	21.2434	3.20256
$45$	6.25286	0.932122
$46$	17.1521	2.52893
$47$	−3.03549	−0.442771	−0.221386	−	0.975186i	$-0.571058\pi$
$47$	−3.03549	−0.442771	−0.221386	+	0.975186i	$0.571058\pi$
$48$	−2.03735	−0.294066
$49$	−5.43891	−0.776987
$50$	−22.0752	−3.12190
$51$	−1.16111	−0.162587
$52$	−4.25261	−0.589731
$53$	6.64042	0.912132	0.456066	−	0.889946i	$-0.349258\pi$
$53$	6.64042	0.912132	0.456066	+	0.889946i	$0.349258\pi$
$54$	−12.7806	−1.73921
$55$	−22.3439	−3.01285
$56$	4.72727	0.631708
$57$	1.47536	0.195417
$58$	21.5983	2.83599
$59$	2.21644	0.288555	0.144278	−	0.989537i	$-0.453914\pi$
$59$	2.21644	0.288555	0.144278	+	0.989537i	$0.453914\pi$
$60$	15.8184	2.04215
$61$	−12.5378	−1.60530	−0.802651	−	0.596449i	$-0.796578\pi$
$61$	−12.5378	−1.60530	−0.802651	+	0.596449i	$0.796578\pi$
$62$	−8.26355	−1.04947
$63$	2.06386	0.260022
$64$	−11.5902	−1.44878
$65$	4.47290	0.554795
$66$	16.2170	1.99618
$67$	4.23889	0.517863	0.258931	−	0.965896i	$-0.416630\pi$
$67$	4.23889	0.517863	0.258931	+	0.965896i	$0.416630\pi$
$68$	3.59897	0.436440
$69$	8.41654	1.01323
$70$	−11.1913	−1.33762
$71$	−16.2867	−1.93288	−0.966438	−	0.256901i	$-0.917298\pi$
$71$	−16.2867	−1.93288	−0.966438	+	0.256901i	$0.917298\pi$
$72$	6.24974	0.736539
$73$	−7.52844	−0.881137	−0.440568	−	0.897719i	$-0.645223\pi$
$73$	−7.52844	−0.881137	−0.440568	+	0.897719i	$0.645223\pi$
$74$	−12.8119	−1.48936
$75$	−10.8323	−1.25081
$76$	−4.57305	−0.524565
$77$	−7.37497	−0.840455
$78$	−3.24640	−0.367583
$79$	14.7859	1.66354	0.831770	−	0.555120i	$-0.187328\pi$
$79$	14.7859	1.66354	0.831770	+	0.555120i	$0.187328\pi$
$80$	−6.64212	−0.742612
$81$	−1.31594	−0.146216
$82$	9.18200	1.01398
$83$	16.6273	1.82508	0.912540	−	0.408987i	$-0.134118\pi$
$83$	16.6273	1.82508	0.912540	+	0.408987i	$0.134118\pi$
$84$	5.22113	0.569672
$85$	−3.78541	−0.410585
$86$	2.07359	0.223601
$87$	10.5983	1.13626
$88$	−22.3327	−2.38067
$89$	4.50223	0.477235	0.238618	−	0.971114i	$-0.423306\pi$
$89$	4.50223	0.477235	0.238618	+	0.971114i	$0.423306\pi$
$90$	−14.7956	−1.55960
$91$	1.47636	0.154764
$92$	−26.0880	−2.71986
$93$	−4.05494	−0.420477
$94$	7.18262	0.740831
$95$	4.80994	0.493490
$96$	−3.96531	−0.404708
$97$	13.0983	1.32993	0.664964	−	0.746875i	$-0.268447\pi$
$97$	13.0983	1.32993	0.664964	+	0.746875i	$0.268447\pi$
$98$	12.8696	1.30003
$99$	−9.75016	−0.979928
$100$	33.5759	3.35759
$101$	−6.28784	−0.625663	−0.312832	−	0.949809i	$-0.601278\pi$
$101$	−6.28784	−0.625663	−0.312832	+	0.949809i	$0.601278\pi$
$102$	2.74743	0.272036
$103$	16.7732	1.65272	0.826358	−	0.563145i	$-0.190409\pi$
$103$	16.7732	1.65272	0.826358	+	0.563145i	$0.190409\pi$
$104$	4.47067	0.438385
$105$	−5.49160	−0.535925
$106$	−15.7127	−1.52615
$107$	12.8320	1.24052	0.620260	−	0.784396i	$-0.287027\pi$
$107$	12.8320	1.24052	0.620260	+	0.784396i	$0.287027\pi$
$108$	19.4390	1.87052
$109$	6.74933	0.646469	0.323234	−	0.946319i	$-0.395230\pi$
$109$	6.74933	0.646469	0.323234	+	0.946319i	$0.395230\pi$
$110$	52.8704	5.04099
$111$	−6.28684	−0.596720
$112$	−2.19234	−0.207157
$113$	0.908526	0.0854670	0.0427335	−	0.999087i	$-0.486393\pi$
$113$	0.908526	0.0854670	0.0427335	+	0.999087i	$0.486393\pi$
$114$	−3.49103	−0.326965
$115$	27.4394	2.55874
$116$	−32.8506	−3.05010
$117$	1.95183	0.180447
$118$	−5.24457	−0.482801
$119$	−1.24944	−0.114536
$120$	−16.6295	−1.51806
$121$	23.8410	2.16737
$122$	29.6672	2.68594
$123$	4.50562	0.406258
$124$	12.5687	1.12870
$125$	−16.3882	−1.46581
$126$	−4.88354	−0.435061
$127$	11.3232	1.00477	0.502387	−	0.864643i	$-0.332455\pi$
$127$	11.3232	1.00477	0.502387	+	0.864643i	$0.332455\pi$
$128$	20.5947	1.82034
$129$	1.01751	0.0895871
$130$	−10.5838	−0.928265
$131$	−17.2098	−1.50363	−0.751813	−	0.659377i	$-0.770820\pi$
$131$	−17.2098	−1.50363	−0.751813	+	0.659377i	$0.770820\pi$
$132$	−24.6658	−2.14689
$133$	1.58760	0.137663
$134$	−10.0301	−0.866471
$135$	−20.4460	−1.75971
$136$	−3.78352	−0.324434
$137$	6.33094	0.540888	0.270444	−	0.962736i	$-0.412829\pi$
$137$	6.33094	0.540888	0.270444	+	0.962736i	$0.412829\pi$
$138$	−19.9153	−1.69531
$139$	10.2409	0.868620	0.434310	−	0.900764i	$-0.356992\pi$
$139$	10.2409	0.868620	0.434310	+	0.900764i	$0.356992\pi$
$140$	17.0218	1.43861
$141$	3.52452	0.296818
$142$	38.5378	3.23402
$143$	−6.97465	−0.583249
$144$	−2.89841	−0.241535
$145$	34.5523	2.86941
$146$	17.8139	1.47429
$147$	6.31514	0.520864
$148$	19.4867	1.60180
$149$	−3.16199	−0.259041	−0.129520	−	0.991577i	$-0.541344\pi$
$149$	−3.16199	−0.259041	−0.129520	+	0.991577i	$0.541344\pi$
$150$	25.6316	2.09281
$151$	0.431101	0.0350825	0.0175412	−	0.999846i	$-0.494416\pi$
$151$	0.431101	0.0350825	0.0175412	+	0.999846i	$0.494416\pi$
$152$	4.80754	0.389943
$153$	−1.65183	−0.133543
$154$	17.4508	1.40622
$155$	−13.2198	−1.06184
$156$	4.93773	0.395335
$157$	−20.6860	−1.65092	−0.825461	−	0.564459i	$-0.809085\pi$
$157$	−20.6860	−1.65092	−0.825461	+	0.564459i	$0.809085\pi$
$158$	−34.9866	−2.78338
$159$	−7.71023	−0.611461
$160$	−12.9276	−1.02202
$161$	9.05683	0.713779
$162$	3.11381	0.244644
$163$	−5.51060	−0.431624	−0.215812	−	0.976435i	$-0.569240\pi$
$163$	−5.51060	−0.431624	−0.215812	+	0.976435i	$0.569240\pi$
$164$	−13.9657	−1.09054
$165$	25.9436	2.01970
$166$	−39.3437	−3.05366
$167$	11.0854	0.857815	0.428908	−	0.903348i	$-0.358899\pi$
$167$	11.0854	0.857815	0.428908	+	0.903348i	$0.358899\pi$
$168$	−5.48886	−0.423474
$169$	−11.6038	−0.892599
$170$	8.95709	0.686977
$171$	2.09891	0.160508
$172$	−3.15390	−0.240482
$173$	−24.1616	−1.83697	−0.918487	−	0.395452i	$-0.870588\pi$
$173$	−24.1616	−1.83697	−0.918487	+	0.395452i	$0.870588\pi$
$174$	−25.0779	−1.90115
$175$	−11.6564	−0.881140
$176$	10.3571	0.780699
$177$	−2.57352	−0.193437
$178$	−10.6532	−0.798494
$179$	4.36522	0.326272	0.163136	−	0.986604i	$-0.447839\pi$
$179$	4.36522	0.326272	0.163136	+	0.986604i	$0.447839\pi$
$180$	22.5039	1.67734
$181$	5.32928	0.396123	0.198061	−	0.980190i	$-0.436535\pi$
$181$	5.32928	0.396123	0.198061	+	0.980190i	$0.436535\pi$
$182$	−3.49338	−0.258946
$183$	14.5577	1.07614
$184$	27.4257	2.02185
$185$	−20.4962	−1.50691
$186$	9.59485	0.703528
$187$	5.90263	0.431643
$188$	−10.9246	−0.796761
$189$	−6.74855	−0.490885
$190$	−11.3814	−0.825691
$191$	−11.3120	−0.818511	−0.409255	−	0.912420i	$-0.634212\pi$
$191$	−11.3120	−0.818511	−0.409255	+	0.912420i	$0.634212\pi$
$192$	13.4575	0.971210
$193$	25.7145	1.85097	0.925486	−	0.378781i	$-0.123657\pi$
$193$	25.7145	1.85097	0.925486	+	0.378781i	$0.123657\pi$
$194$	−30.9933	−2.22519
$195$	−5.19351	−0.371915
$196$	−19.5745	−1.39818
$197$	−15.6651	−1.11610	−0.558048	−	0.829809i	$-0.688449\pi$
$197$	−15.6651	−1.11610	−0.558048	+	0.829809i	$0.688449\pi$
$198$	23.0710	1.63958
$199$	17.1364	1.21476	0.607382	−	0.794410i	$-0.292220\pi$
$199$	17.1364	1.21476	0.607382	+	0.794410i	$0.292220\pi$
$200$	−35.2976	−2.49592
$201$	−4.92180	−0.347157
$202$	14.8784	1.04684
$203$	11.4046	0.800444
$204$	−4.17879	−0.292574
$205$	14.6891	1.02593
$206$	−39.6891	−2.76527
$207$	11.9737	0.832229
$208$	−2.07334	−0.143760
$209$	−7.50020	−0.518800
$210$	12.9943	0.896692
$211$	3.69561	0.254416	0.127208	−	0.991876i	$-0.459398\pi$
$211$	3.69561	0.254416	0.127208	+	0.991876i	$0.459398\pi$
$212$	23.8987	1.64137
$213$	18.9106	1.29573
$214$	−30.3634	−2.07560
$215$	3.31727	0.226236
$216$	−20.4358	−1.39048
$217$	−4.36342	−0.296208
$218$	−15.9704	−1.08165
$219$	8.74131	0.590683
$220$	−80.4150	−5.42158
$221$	−1.18162	−0.0794841
$222$	14.8760	0.998413
$223$	18.7119	1.25304	0.626520	−	0.779405i	$-0.284478\pi$
$223$	18.7119	1.25304	0.626520	+	0.779405i	$0.284478\pi$
$224$	−4.26698	−0.285099
$225$	−15.4105	−1.02736
$226$	−2.14977	−0.143000
$227$	25.7477	1.70894	0.854468	−	0.519504i	$-0.173883\pi$
$227$	25.7477	1.70894	0.854468	+	0.519504i	$0.173883\pi$
$228$	5.30979	0.351650
$229$	12.3676	0.817271	0.408636	−	0.912698i	$-0.366005\pi$
$229$	12.3676	0.817271	0.408636	+	0.912698i	$0.366005\pi$
$230$	−64.9275	−4.28119
$231$	8.56311	0.563412
$232$	34.5350	2.26734
$233$	20.9886	1.37501	0.687504	−	0.726181i	$-0.258706\pi$
$233$	20.9886	1.37501	0.687504	+	0.726181i	$0.258706\pi$
$234$	−4.61846	−0.301918
$235$	11.4906	0.749561
$236$	7.97690	0.519252
$237$	−17.1680	−1.11518
$238$	2.95644	0.191637
$239$	2.82359	0.182643	0.0913213	−	0.995821i	$-0.470891\pi$
$239$	2.82359	0.182643	0.0913213	+	0.995821i	$0.470891\pi$
$240$	7.71220	0.497821
$241$	5.66147	0.364687	0.182344	−	0.983235i	$-0.441632\pi$
$241$	5.66147	0.364687	0.182344	+	0.983235i	$0.441632\pi$
$242$	−56.4130	−3.62637
$243$	−14.6759	−0.941457
$244$	−45.1232	−2.88872
$245$	20.5885	1.31535
$246$	−10.6613	−0.679738
$247$	1.50143	0.0955334
$248$	−13.2132	−0.839039
$249$	−19.3060	−1.22347
$250$	38.7780	2.45254
$251$	−22.1361	−1.39722	−0.698609	−	0.715503i	$-0.746197\pi$
$251$	−22.1361	−1.39722	−0.698609	+	0.715503i	$0.746197\pi$
$252$	7.42779	0.467907
$253$	−42.7866	−2.68997
$254$	−26.7932	−1.68115
$255$	4.39526	0.275242
$256$	−25.5511	−1.59695
$257$	18.7896	1.17206	0.586032	−	0.810288i	$-0.300689\pi$
$257$	18.7896	1.17206	0.586032	+	0.810288i	$0.300689\pi$
$258$	−2.40766	−0.149894
$259$	−6.76511	−0.420364
$260$	16.0979	0.998347
$261$	15.0775	0.933277
$262$	40.7220	2.51582
$263$	−12.2967	−0.758245	−0.379122	−	0.925347i	$-0.623774\pi$
$263$	−12.2967	−0.758245	−0.379122	+	0.925347i	$0.623774\pi$
$264$	25.9306	1.59592
$265$	−25.1367	−1.54413
$266$	−3.75661	−0.230332
$267$	−5.22756	−0.319922
$268$	15.2557	0.931887
$269$	1.51647	0.0924606	0.0462303	−	0.998931i	$-0.485279\pi$
$269$	1.51647	0.0924606	0.0462303	+	0.998931i	$0.485279\pi$
$270$	48.3797	2.94429
$271$	−7.51629	−0.456582	−0.228291	−	0.973593i	$-0.573314\pi$
$271$	−7.51629	−0.456582	−0.228291	+	0.973593i	$0.573314\pi$
$272$	1.75466	0.106392
$273$	−1.71421	−0.103748
$274$	−14.9804	−0.904996
$275$	55.0675	3.32069
$276$	30.2909	1.82330
$277$	10.8650	0.652815	0.326407	−	0.945229i	$-0.394162\pi$
$277$	10.8650	0.652815	0.326407	+	0.945229i	$0.394162\pi$
$278$	−24.2321	−1.45335
$279$	−5.76871	−0.345364
$280$	−17.8946	−1.06941
$281$	−1.28703	−0.0767777	−0.0383888	−	0.999263i	$-0.512223\pi$
$281$	−1.28703	−0.0767777	−0.0383888	+	0.999263i	$0.512223\pi$
$282$	−8.33978	−0.496627
$283$	−13.7280	−0.816047	−0.408024	−	0.912971i	$-0.633782\pi$
$283$	−13.7280	−0.816047	−0.408024	+	0.912971i	$0.633782\pi$
$284$	−58.6154	−3.47818
$285$	−5.58485	−0.330818
$286$	16.5035	0.975873
$287$	4.84839	0.286192
$288$	−5.64121	−0.332411
$289$	1.00000	0.0588235
$290$	−81.7582	−4.80101
$291$	−15.2085	−0.891537
$292$	−27.0946	−1.58559
$293$	−6.24498	−0.364836	−0.182418	−	0.983221i	$-0.558392\pi$
$293$	−6.24498	−0.364836	−0.182418	+	0.983221i	$0.558392\pi$
$294$	−14.9430	−0.871493
$295$	−8.39012	−0.488491
$296$	−20.4860	−1.19072
$297$	31.8817	1.84996
$298$	7.48196	0.433418
$299$	8.56522	0.495340
$300$	−38.9852	−2.25081
$301$	1.09492	0.0631103
$302$	−1.02008	−0.0586988
$303$	7.30084	0.419422
$304$	−2.22957	−0.127875
$305$	47.4607	2.71759
$306$	3.90859	0.223439
$307$	28.0432	1.60051	0.800255	−	0.599659i	$-0.204697\pi$
$307$	28.0432	1.60051	0.800255	+	0.599659i	$0.204697\pi$
$308$	−26.5423	−1.51239
$309$	−19.4755	−1.10792
$310$	31.2809	1.77663
$311$	−3.33887	−0.189330	−0.0946650	−	0.995509i	$-0.530178\pi$
$311$	−3.33887	−0.189330	−0.0946650	+	0.995509i	$0.530178\pi$
$312$	−5.19092	−0.293878
$313$	8.82936	0.499065	0.249532	−	0.968366i	$-0.419723\pi$
$313$	8.82936	0.499065	0.249532	+	0.968366i	$0.419723\pi$
$314$	48.9475	2.76227
$315$	−7.81256	−0.440188
$316$	53.2140	2.99352
$317$	−26.5871	−1.49328	−0.746641	−	0.665227i	$-0.768335\pi$
$317$	−26.5871	−1.49328	−0.746641	+	0.665227i	$0.768335\pi$
$318$	18.2441	1.02308
$319$	−53.8778	−3.01658
$320$	43.8738	2.45262
$321$	−14.8994	−0.831601
$322$	−21.4304	−1.19427
$323$	−1.27065	−0.0707011
$324$	−4.73605	−0.263114
$325$	−11.0237	−0.611483
$326$	13.0393	0.722178
$327$	−7.83668	−0.433370
$328$	14.6818	0.810666
$329$	3.79265	0.209096
$330$	−61.3881	−3.37930
$331$	2.57328	0.141440	0.0707201	−	0.997496i	$-0.477470\pi$
$331$	2.57328	0.141440	0.0707201	+	0.997496i	$0.477470\pi$
$332$	59.8411	3.28421
$333$	−8.94390	−0.490123
$334$	−26.2305	−1.43527
$335$	−16.0459	−0.876683
$336$	2.54554	0.138871
$337$	−9.06203	−0.493640	−0.246820	−	0.969061i	$-0.579386\pi$
$337$	−9.06203	−0.493640	−0.246820	+	0.969061i	$0.579386\pi$
$338$	27.4570	1.49347
$339$	−1.05489	−0.0572940
$340$	−13.6236	−0.738842
$341$	20.6138	1.11630
$342$	−4.96647	−0.268556
$343$	15.5416	0.839169
$344$	3.31562	0.178766
$345$	−31.8600	−1.71529
$346$	57.1716	3.07356
$347$	−3.29621	−0.176950	−0.0884749	−	0.996078i	$-0.528199\pi$
$347$	−3.29621	−0.176950	−0.0884749	+	0.996078i	$0.528199\pi$
$348$	38.1430	2.04468
$349$	23.0758	1.23522	0.617610	−	0.786485i	$-0.288101\pi$
$349$	23.0758	1.23522	0.617610	+	0.786485i	$0.288101\pi$
$350$	27.5815	1.47429
$351$	−6.38223	−0.340658
$352$	20.1582	1.07443
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	6.08950	0.323653
$355$	61.6518	3.27214
$356$	16.2034	0.858778
$357$	1.45073	0.0767807
$358$	−10.3290	−0.545907
$359$	27.7491	1.46454	0.732271	−	0.681013i	$-0.238460\pi$
$359$	27.7491	1.46454	0.732271	+	0.681013i	$0.238460\pi$
$360$	−23.6578	−1.24688
$361$	−17.3854	−0.915023
$362$	−12.6102	−0.662779
$363$	−27.6820	−1.45293
$364$	5.31337	0.278496
$365$	28.4982	1.49166
$366$	−34.4467	−1.80056
$367$	22.2124	1.15948	0.579739	−	0.814802i	$-0.303155\pi$
$367$	22.2124	1.15948	0.579739	+	0.814802i	$0.303155\pi$
$368$	−12.7191	−0.663028
$369$	6.40988	0.333685
$370$	48.4984	2.52131
$371$	−8.29679	−0.430748
$372$	−14.5936	−0.756643
$373$	−33.1205	−1.71491	−0.857456	−	0.514557i	$-0.827956\pi$
$373$	−33.1205	−1.71491	−0.857456	+	0.514557i	$0.827956\pi$
$374$	−13.9669	−0.722211
$375$	19.0284	0.982624
$376$	11.4848	0.592284
$377$	10.7855	0.555483
$378$	15.9685	0.821332
$379$	31.9877	1.64310	0.821548	−	0.570139i	$-0.193111\pi$
$379$	31.9877	1.64310	0.821548	+	0.570139i	$0.193111\pi$
$380$	17.3109	0.888028
$381$	−13.1475	−0.673565
$382$	26.7667	1.36951
$383$	−16.2592	−0.830806	−0.415403	−	0.909638i	$-0.636359\pi$
$383$	−16.2592	−0.830806	−0.415403	+	0.909638i	$0.636359\pi$
$384$	−23.9127	−1.22029
$385$	27.9173	1.42279
$386$	−60.8461	−3.09699
$387$	1.44756	0.0735834
$388$	47.1404	2.39319
$389$	−16.4340	−0.833237	−0.416618	−	0.909082i	$-0.636785\pi$
$389$	−16.4340	−0.833237	−0.416618	+	0.909082i	$0.636785\pi$
$390$	12.2890	0.622276
$391$	−7.24873	−0.366584
$392$	20.5782	1.03936
$393$	19.9824	1.00798
$394$	37.0671	1.86741
$395$	−55.9706	−2.81618
$396$	−35.0906	−1.76337
$397$	−38.1557	−1.91498	−0.957490	−	0.288467i	$-0.906854\pi$
$397$	−38.1557	−1.91498	−0.957490	+	0.288467i	$0.906854\pi$
$398$	−40.5483	−2.03250
$399$	−1.84337	−0.0922841
$400$	16.3698	0.818491
$401$	−30.7115	−1.53366	−0.766829	−	0.641852i	$-0.778166\pi$
$401$	−30.7115	−1.53366	−0.766829	+	0.641852i	$0.778166\pi$
$402$	11.6460	0.580851
$403$	−4.12657	−0.205559
$404$	−22.6298	−1.12587
$405$	4.98138	0.247527
$406$	−26.9857	−1.33928
$407$	31.9600	1.58420
$408$	4.39306	0.217489
$409$	−39.3172	−1.94411	−0.972056	−	0.234750i	$-0.924573\pi$
$409$	−39.3172	−1.94411	−0.972056	+	0.234750i	$0.924573\pi$
$410$	−34.7576	−1.71656
$411$	−7.35088	−0.362592
$412$	60.3664	2.97404
$413$	−2.76930	−0.136268
$414$	−28.3323	−1.39246
$415$	−62.9410	−3.08965
$416$	−4.03536	−0.197850
$417$	−11.8907	−0.582292
$418$	17.7471	0.868038
$419$	−33.8350	−1.65295	−0.826473	−	0.562977i	$-0.809656\pi$
$419$	−33.8350	−1.65295	−0.826473	+	0.562977i	$0.809656\pi$
$420$	−19.7641	−0.964390
$421$	29.5610	1.44071	0.720357	−	0.693603i	$-0.243978\pi$
$421$	29.5610	1.44071	0.720357	+	0.693603i	$0.243978\pi$
$422$	−8.74461	−0.425681
$423$	5.01412	0.243795
$424$	−25.1241	−1.22014
$425$	9.32931	0.452538
$426$	−44.7465	−2.16797
$427$	15.6652	0.758093
$428$	46.1822	2.23230
$429$	8.09830	0.390990
$430$	−7.84939	−0.378531
$431$	33.4447	1.61097	0.805487	−	0.592613i	$-0.201904\pi$
$431$	33.4447	1.61097	0.805487	+	0.592613i	$0.201904\pi$
$432$	9.47742	0.455983
$433$	−34.8468	−1.67463	−0.837316	−	0.546719i	$-0.815877\pi$
$433$	−34.8468	−1.67463	−0.837316	+	0.546719i	$0.815877\pi$
$434$	10.3248	0.495605
$435$	−40.1189	−1.92355
$436$	24.2907	1.16331
$437$	9.21063	0.440604
$438$	−20.6838	−0.988311
$439$	3.12123	0.148968	0.0744840	−	0.997222i	$-0.476269\pi$
$439$	3.12123	0.148968	0.0744840	+	0.997222i	$0.476269\pi$
$440$	84.5383	4.03021
$441$	8.98417	0.427818
$442$	2.79596	0.132990
$443$	11.4588	0.544424	0.272212	−	0.962237i	$-0.412245\pi$
$443$	11.4588	0.544424	0.272212	+	0.962237i	$0.412245\pi$
$444$	−22.6262	−1.07379
$445$	−17.0428	−0.807904
$446$	−44.2764	−2.09655
$447$	3.67141	0.173652
$448$	14.4813	0.684176
$449$	−1.03249	−0.0487262	−0.0243631	−	0.999703i	$-0.507756\pi$
$449$	−1.03249	−0.0487262	−0.0243631	+	0.999703i	$0.507756\pi$
$450$	36.4645	1.71895
$451$	−22.9049	−1.07855
$452$	3.26976	0.153797
$453$	−0.500553	−0.0235180
$454$	−60.9246	−2.85933
$455$	−5.58861	−0.261998
$456$	−5.58206	−0.261404
$457$	−32.5303	−1.52171	−0.760853	−	0.648925i	$-0.775219\pi$
$457$	−32.5303	−1.52171	−0.760853	+	0.648925i	$0.775219\pi$
$458$	−29.2643	−1.36743
$459$	5.40127	0.252110
$460$	98.7537	4.60441
$461$	−11.1152	−0.517686	−0.258843	−	0.965919i	$-0.583341\pi$
$461$	−11.1152	−0.517686	−0.258843	+	0.965919i	$0.583341\pi$
$462$	−20.2622	−0.942681
$463$	−5.01798	−0.233205	−0.116603	−	0.993179i	$-0.537200\pi$
$463$	−5.01798	−0.233205	−0.116603	+	0.993179i	$0.537200\pi$
$464$	−16.0162	−0.743532
$465$	15.3496	0.711820
$466$	−49.6635	−2.30062
$467$	26.0334	1.20468	0.602341	−	0.798239i	$-0.294235\pi$
$467$	26.0334	1.20468	0.602341	+	0.798239i	$0.294235\pi$
$468$	7.02460	0.324712
$469$	−5.29623	−0.244557
$470$	−27.1891	−1.25414
$471$	24.0186	1.10672
$472$	−8.38592	−0.385993
$473$	−5.17266	−0.237839
$474$	40.6231	1.86588
$475$	−11.8543	−0.543914
$476$	−4.49669	−0.206106
$477$	−10.9689	−0.502230
$478$	−6.68121	−0.305591
$479$	−20.6615	−0.944047	−0.472024	−	0.881586i	$-0.656476\pi$
$479$	−20.6615	−0.944047	−0.472024	+	0.881586i	$0.656476\pi$
$480$	15.0103	0.685124
$481$	−6.39790	−0.291719
$482$	−13.3962	−0.610182
$483$	−10.5159	−0.478492
$484$	85.8033	3.90015
$485$	−49.5823	−2.25142
$486$	34.7262	1.57521
$487$	9.80661	0.444380	0.222190	−	0.975003i	$-0.428680\pi$
$487$	9.80661	0.444380	0.222190	+	0.975003i	$0.428680\pi$
$488$	47.4370	2.14737
$489$	6.39839	0.289345
$490$	−48.7168	−2.20080
$491$	8.56033	0.386322	0.193161	−	0.981167i	$-0.438126\pi$
$491$	8.56033	0.386322	0.193161	+	0.981167i	$0.438126\pi$
$492$	16.2156	0.731057
$493$	−9.12776	−0.411094
$494$	−3.55270	−0.159843
$495$	36.9083	1.65891
$496$	6.12783	0.275147
$497$	20.3492	0.912787
$498$	45.6822	2.04707
$499$	21.0231	0.941125	0.470562	−	0.882367i	$-0.344051\pi$
$499$	21.0231	0.941125	0.470562	+	0.882367i	$0.344051\pi$
$500$	−58.9807	−2.63770
$501$	−12.8713	−0.575049
$502$	52.3788	2.33778
$503$	−27.0043	−1.20406	−0.602031	−	0.798473i	$-0.705642\pi$
$503$	−27.0043	−1.20406	−0.602031	+	0.798473i	$0.705642\pi$
$504$	−7.80866	−0.347825
$505$	23.8020	1.05918
$506$	101.242	4.50077
$507$	13.4732	0.598367
$508$	40.7520	1.80808
$509$	12.8016	0.567421	0.283711	−	0.958910i	$-0.408435\pi$
$509$	12.8016	0.567421	0.283711	+	0.958910i	$0.408435\pi$
$510$	−10.4001	−0.460525
$511$	9.40631	0.416111
$512$	19.2700	0.851621
$513$	−6.86314	−0.303015
$514$	−44.4602	−1.96106
$515$	−63.4935	−2.79786
$516$	3.66201	0.161211
$517$	−17.9174	−0.788005
$518$	16.0077	0.703339
$519$	28.0542	1.23144
$520$	−16.9233	−0.742135
$521$	6.65181	0.291421	0.145711	−	0.989327i	$-0.453453\pi$
$521$	6.65181	0.291421	0.145711	+	0.989327i	$0.453453\pi$
$522$	−35.6767	−1.56153
$523$	35.5738	1.55553	0.777767	−	0.628553i	$-0.216352\pi$
$523$	35.5738	1.55553	0.777767	+	0.628553i	$0.216352\pi$
$524$	−61.9376	−2.70575
$525$	13.5343	0.590685
$526$	29.0966	1.26867
$527$	3.49231	0.152127
$528$	−12.0257	−0.523353
$529$	29.5441	1.28453
$530$	59.4788	2.58359
$531$	−3.66119	−0.158882
$532$	5.71374	0.247722
$533$	4.58522	0.198608
$534$	12.3695	0.535282
$535$	−48.5745	−2.10006
$536$	−16.0379	−0.692732
$537$	−5.06848	−0.218721
$538$	−3.58829	−0.154702
$539$	−32.1038	−1.38281
$540$	−73.5846	−3.16658
$541$	−24.0703	−1.03486	−0.517431	−	0.855725i	$-0.673112\pi$
$541$	−24.0703	−1.03486	−0.517431	+	0.855725i	$0.673112\pi$
$542$	17.7852	0.763938
$543$	−6.18786	−0.265547
$544$	3.41512	0.146422
$545$	−25.5490	−1.09440
$546$	4.05618	0.173588
$547$	−5.23013	−0.223624	−0.111812	−	0.993729i	$-0.535665\pi$
$547$	−5.23013	−0.223624	−0.111812	+	0.993729i	$0.535665\pi$
$548$	22.7849	0.973321
$549$	20.7104	0.883897
$550$	−130.301	−5.55607
$551$	11.5982	0.494101
$552$	−31.8441	−1.35538
$553$	−18.4740	−0.785595
$554$	−25.7089	−1.09227
$555$	23.7982	1.01018
$556$	36.8566	1.56307
$557$	11.8901	0.503798	0.251899	−	0.967754i	$-0.418945\pi$
$557$	11.8901	0.503798	0.251899	+	0.967754i	$0.418945\pi$
$558$	13.6500	0.577851
$559$	1.03549	0.0437965
$560$	8.29891	0.350693
$561$	−6.85358	−0.289358
$562$	3.04539	0.128462
$563$	−27.9357	−1.17735	−0.588676	−	0.808369i	$-0.700350\pi$
$563$	−27.9357	−1.17735	−0.588676	+	0.808369i	$0.700350\pi$
$564$	12.6847	0.534121
$565$	−3.43914	−0.144686
$566$	32.4835	1.36538
$567$	1.64419	0.0690495
$568$	61.6210	2.58556
$569$	17.5423	0.735411	0.367705	−	0.929942i	$-0.380143\pi$
$569$	17.5423	0.735411	0.367705	+	0.929942i	$0.380143\pi$
$570$	13.2150	0.553514
$571$	−21.2859	−0.890786	−0.445393	−	0.895335i	$-0.646936\pi$
$571$	−21.2859	−0.890786	−0.445393	+	0.895335i	$0.646936\pi$
$572$	−25.1016	−1.04955
$573$	13.1345	0.548701
$574$	−11.4723	−0.478846
$575$	−67.6256	−2.82018
$576$	19.1451	0.797714
$577$	−46.1548	−1.92145	−0.960725	−	0.277502i	$-0.910493\pi$
$577$	−46.1548	−1.92145	−0.960725	+	0.277502i	$0.910493\pi$
$578$	−2.36622	−0.0984216
$579$	−29.8573	−1.24083
$580$	124.353	5.16347
$581$	−20.7747	−0.861881
$582$	35.9865	1.49169
$583$	39.1959	1.62333
$584$	28.4840	1.17867
$585$	−7.38849	−0.305476
$586$	14.7770	0.610431
$587$	29.9086	1.23446	0.617230	−	0.786783i	$-0.288255\pi$
$587$	29.9086	1.23446	0.617230	+	0.786783i	$0.288255\pi$
$588$	22.7280	0.937289
$589$	−4.43751	−0.182844
$590$	19.8528	0.817328
$591$	18.1889	0.748191
$592$	9.50068	0.390476
$593$	−13.1448	−0.539792	−0.269896	−	0.962889i	$-0.586989\pi$
$593$	−13.1448	−0.539792	−0.269896	+	0.962889i	$0.586989\pi$
$594$	−75.4390	−3.09530
$595$	4.72963	0.193896
$596$	−11.3799	−0.466140
$597$	−19.8971	−0.814335
$598$	−20.2672	−0.828786
$599$	35.8873	1.46632	0.733158	−	0.680059i	$-0.238046\pi$
$599$	35.8873	1.46632	0.733158	+	0.680059i	$0.238046\pi$
$600$	40.9842	1.67317
$601$	27.8524	1.13612	0.568061	−	0.822986i	$-0.307694\pi$
$601$	27.8524	1.13612	0.568061	+	0.822986i	$0.307694\pi$
$602$	−2.59082	−0.105594
$603$	−7.00194	−0.285141
$604$	1.55152	0.0631304
$605$	−90.2480	−3.66910
$606$	−17.2754	−0.701764
$607$	−11.4409	−0.464373	−0.232187	−	0.972671i	$-0.574588\pi$
$607$	−11.4409	−0.464373	−0.232187	+	0.972671i	$0.574588\pi$
$608$	−4.33943	−0.175987
$609$	−13.2419	−0.536589
$610$	−112.302	−4.54699
$611$	3.58678	0.145106
$612$	−5.94491	−0.240309
$613$	35.9701	1.45282	0.726409	−	0.687263i	$-0.241188\pi$
$613$	35.9701	1.45282	0.726409	+	0.687263i	$0.241188\pi$
$614$	−66.3563	−2.67792
$615$	−17.0556	−0.687749
$616$	27.9033	1.12426
$617$	−44.9639	−1.81018	−0.905088	−	0.425223i	$-0.860196\pi$
$617$	−44.9639	−1.81018	−0.905088	+	0.425223i	$0.860196\pi$
$618$	46.0832	1.85374
$619$	−37.1035	−1.49132	−0.745658	−	0.666328i	$-0.767865\pi$
$619$	−37.1035	−1.49132	−0.745658	+	0.666328i	$0.767865\pi$
$620$	−47.5777	−1.91077
$621$	−39.1524	−1.57113
$622$	7.90048	0.316781
$623$	−5.62525	−0.225371
$624$	2.40737	0.0963719
$625$	15.3895	0.615579
$626$	−20.8922	−0.835019
$627$	8.70852	0.347785
$628$	−74.4483	−2.97081
$629$	5.41453	0.215891
$630$	18.4862	0.736508
$631$	6.84676	0.272565	0.136283	−	0.990670i	$-0.456484\pi$
$631$	6.84676	0.272565	0.136283	+	0.990670i	$0.456484\pi$
$632$	−55.9426	−2.22528
$633$	−4.29099	−0.170552
$634$	62.9109	2.49851
$635$	−42.8630	−1.70097
$636$	−27.7489	−1.10032
$637$	6.42670	0.254635
$638$	127.486	5.04724
$639$	26.9029	1.06426
$640$	−77.9595	−3.08162
$641$	−45.0268	−1.77845	−0.889225	−	0.457470i	$-0.848756\pi$
$641$	−45.0268	−1.77845	−0.889225	+	0.457470i	$0.848756\pi$
$642$	35.2551	1.39141
$643$	−0.311601	−0.0122883	−0.00614416	−	0.999981i	$-0.501956\pi$
$643$	−0.311601	−0.0122883	−0.00614416	+	0.999981i	$0.501956\pi$
$644$	32.5953	1.28444
$645$	−3.85171	−0.151661
$646$	3.00664	0.118295
$647$	−15.0049	−0.589902	−0.294951	−	0.955512i	$-0.595303\pi$
$647$	−15.0049	−0.589902	−0.294951	+	0.955512i	$0.595303\pi$
$648$	4.97889	0.195589
$649$	13.0828	0.513545
$650$	26.0844	1.02311
$651$	5.06639	0.198567
$652$	−19.8325	−0.776701
$653$	30.9778	1.21226	0.606128	−	0.795367i	$-0.292722\pi$
$653$	30.9778	1.21226	0.606128	+	0.795367i	$0.292722\pi$
$654$	18.5433	0.725100
$655$	65.1460	2.54547
$656$	−6.80891	−0.265843
$657$	12.4357	0.485164
$658$	−8.97423	−0.349852
$659$	21.3083	0.830052	0.415026	−	0.909810i	$-0.363772\pi$
$659$	21.3083	0.830052	0.415026	+	0.909810i	$0.363772\pi$
$660$	93.3703	3.63443
$661$	21.6807	0.843280	0.421640	−	0.906763i	$-0.361455\pi$
$661$	21.6807	0.843280	0.421640	+	0.906763i	$0.361455\pi$
$662$	−6.08893	−0.236653
$663$	1.37198	0.0532834
$664$	−62.9095	−2.44136
$665$	−6.00972	−0.233047
$666$	21.1632	0.820057
$667$	66.1647	2.56191
$668$	39.8961	1.54363
$669$	−21.7265	−0.839994
$670$	37.9681	1.46684
$671$	−74.0060	−2.85697
$672$	4.95441	0.191120
$673$	−8.15965	−0.314531	−0.157266	−	0.987556i	$-0.550268\pi$
$673$	−8.15965	−0.314531	−0.157266	+	0.987556i	$0.550268\pi$
$674$	21.4427	0.825943
$675$	50.3901	1.93952
$676$	−41.7617	−1.60622
$677$	−3.62587	−0.139353	−0.0696767	−	0.997570i	$-0.522197\pi$
$677$	−3.62587	−0.139353	−0.0696767	+	0.997570i	$0.522197\pi$
$678$	2.49611	0.0958625
$679$	−16.3655	−0.628049
$680$	14.3221	0.549229
$681$	−29.8958	−1.14561
$682$	−48.7766	−1.86775
$683$	16.0912	0.615714	0.307857	−	0.951433i	$-0.400388\pi$
$683$	16.0912	0.615714	0.307857	+	0.951433i	$0.400388\pi$
$684$	7.55392	0.288831
$685$	−23.9652	−0.915662
$686$	−36.7748	−1.40407
$687$	−14.3600	−0.547870
$688$	−1.53767	−0.0586231
$689$	−7.84643	−0.298925
$690$	75.3877	2.86996
$691$	−43.8445	−1.66792	−0.833961	−	0.551823i	$-0.813932\pi$
$691$	−43.8445	−1.66792	−0.833961	+	0.551823i	$0.813932\pi$
$692$	−86.9570	−3.30561
$693$	12.1822	0.462764
$694$	7.79954	0.296067
$695$	−38.7659	−1.47047
$696$	−40.0988	−1.51994
$697$	−3.88046	−0.146983
$698$	−54.6023	−2.06673
$699$	−24.3700	−0.921756
$700$	−41.9510	−1.58560
$701$	−42.2851	−1.59709	−0.798543	−	0.601938i	$-0.794395\pi$
$701$	−42.2851	−1.59709	−0.798543	+	0.601938i	$0.794395\pi$
$702$	15.1017	0.569978
$703$	−6.87999	−0.259484
$704$	−68.4128	−2.57841
$705$	−13.3418	−0.502480
$706$	−2.36622	−0.0890537
$707$	7.85626	0.295465
$708$	−9.26202	−0.348088
$709$	18.7535	0.704304	0.352152	−	0.935943i	$-0.385450\pi$
$709$	18.7535	0.704304	0.352152	+	0.935943i	$0.385450\pi$
$710$	−145.881	−5.47483
$711$	−24.4238	−0.915964
$712$	−17.0342	−0.638385
$713$	−25.3148	−0.948046
$714$	−3.43274	−0.128467
$715$	26.4019	0.987374
$716$	15.7103	0.587121
$717$	−3.27848	−0.122437
$718$	−65.6604	−2.45042
$719$	−27.1839	−1.01379	−0.506894	−	0.862008i	$-0.669207\pi$
$719$	−27.1839	−1.01379	−0.506894	+	0.862008i	$0.669207\pi$
$720$	10.9717	0.408890
$721$	−20.9571	−0.780484
$722$	41.1377	1.53099
$723$	−6.57356	−0.244473
$724$	19.1800	0.712817
$725$	−85.1557	−3.16260
$726$	65.5015	2.43099
$727$	28.5346	1.05829	0.529144	−	0.848532i	$-0.322513\pi$
$727$	28.5346	1.05829	0.529144	+	0.848532i	$0.322513\pi$
$728$	−5.58582	−0.207024
$729$	20.9881	0.777335
$730$	−67.4329	−2.49580
$731$	−0.876332	−0.0324123
$732$	52.3929	1.93650
$733$	−34.6457	−1.27967	−0.639834	−	0.768513i	$-0.720997\pi$
$733$	−34.6457	−1.27967	−0.639834	+	0.768513i	$0.720997\pi$
$734$	−52.5593	−1.94000
$735$	−23.9054	−0.881764
$736$	−24.7553	−0.912491
$737$	25.0206	0.921646
$738$	−15.1671	−0.558310
$739$	−20.1544	−0.741393	−0.370697	−	0.928754i	$-0.620881\pi$
$739$	−20.1544	−0.741393	−0.370697	+	0.928754i	$0.620881\pi$
$740$	−73.7653	−2.71167
$741$	−1.74331	−0.0640422
$742$	19.6320	0.720713
$743$	−20.9202	−0.767489	−0.383744	−	0.923439i	$-0.625366\pi$
$743$	−20.9202	−0.767489	−0.383744	+	0.923439i	$0.625366\pi$
$744$	15.3419	0.562462
$745$	11.9694	0.438526
$746$	78.3701	2.86933
$747$	−27.4655	−1.00491
$748$	21.2434	0.776736
$749$	−16.0328	−0.585827
$750$	−45.0254	−1.64409
$751$	−43.3456	−1.58170	−0.790852	−	0.612008i	$-0.790362\pi$
$751$	−43.3456	−1.58170	−0.790852	+	0.612008i	$0.790362\pi$
$752$	−5.32626	−0.194229
$753$	25.7024	0.936646
$754$	−25.5209	−0.929415
$755$	−1.63189	−0.0593906
$756$	−24.2879	−0.883341
$757$	14.2253	0.517026	0.258513	−	0.966008i	$-0.416768\pi$
$757$	14.2253	0.517026	0.258513	+	0.966008i	$0.416768\pi$
$758$	−75.6897	−2.74917
$759$	49.6797	1.80326
$760$	−18.1985	−0.660129
$761$	−5.63185	−0.204154	−0.102077	−	0.994776i	$-0.532549\pi$
$761$	−5.63185	−0.204154	−0.102077	+	0.994776i	$0.532549\pi$
$762$	31.1097	1.12699
$763$	−8.43286	−0.305290
$764$	−40.7118	−1.47290
$765$	6.25286	0.226073
$766$	38.4727	1.39008
$767$	−2.61898	−0.0945659
$768$	29.6676	1.07054
$769$	−16.9025	−0.609520	−0.304760	−	0.952429i	$-0.598576\pi$
$769$	−16.9025	−0.609520	−0.304760	+	0.952429i	$0.598576\pi$
$770$	−66.0582	−2.38057
$771$	−21.8167	−0.785710
$772$	92.5459	3.33080
$773$	−37.5928	−1.35212	−0.676059	−	0.736847i	$-0.736314\pi$
$773$	−37.5928	−1.35212	−0.676059	+	0.736847i	$0.736314\pi$
$774$	−3.42523	−0.123117
$775$	32.5808	1.17034
$776$	−49.5575	−1.77901
$777$	7.85501	0.281797
$778$	38.8864	1.39414
$779$	4.93072	0.176661
$780$	−18.6913	−0.669256
$781$	−96.1343	−3.43996
$782$	17.1521	0.613356
$783$	−49.3015	−1.76189
$784$	−9.54346	−0.340838
$785$	78.3049	2.79482
$786$	−47.2826	−1.68651
$787$	−14.9019	−0.531195	−0.265597	−	0.964084i	$-0.585569\pi$
$787$	−14.9019	−0.531195	−0.265597	+	0.964084i	$0.585569\pi$
$788$	−56.3785	−2.00840
$789$	14.2777	0.508301
$790$	132.438	4.71195
$791$	−1.13515	−0.0403612
$792$	36.8899	1.31083
$793$	14.8149	0.526092
$794$	90.2846	3.20408
$795$	29.1864	1.03513
$796$	61.6733	2.18595
$797$	−1.18072	−0.0418233	−0.0209116	−	0.999781i	$-0.506657\pi$
$797$	−1.18072	−0.0418233	−0.0209116	+	0.999781i	$0.506657\pi$
$798$	4.36182	0.154407
$799$	−3.03549	−0.107388
$800$	31.8607	1.12645
$801$	−7.43693	−0.262771
$802$	72.6699	2.56606
$803$	−44.4376	−1.56817
$804$	−17.7134	−0.624704
$805$	−34.2838	−1.20835
$806$	9.76434	0.343934
$807$	−1.76078	−0.0619823
$808$	23.7901	0.836934
$809$	27.0860	0.952292	0.476146	−	0.879366i	$-0.342033\pi$
$809$	27.0860	0.952292	0.476146	+	0.879366i	$0.342033\pi$
$810$	−11.7870	−0.414154
$811$	48.9834	1.72004	0.860021	−	0.510259i	$-0.170451\pi$
$811$	48.9834	1.72004	0.860021	+	0.510259i	$0.170451\pi$
$812$	41.0447	1.44039
$813$	8.72721	0.306077
$814$	−75.6241	−2.65062
$815$	20.8599	0.730690
$816$	−2.03735	−0.0713216
$817$	1.11351	0.0389570
$818$	93.0330	3.25282
$819$	−2.43870	−0.0852149
$820$	52.8658	1.84615
$821$	25.4510	0.888247	0.444123	−	0.895966i	$-0.353515\pi$
$821$	25.4510	0.888247	0.444123	+	0.895966i	$0.353515\pi$
$822$	17.3938	0.606678
$823$	5.62747	0.196161	0.0980806	−	0.995178i	$-0.468730\pi$
$823$	5.62747	0.196161	0.0980806	+	0.995178i	$0.468730\pi$
$824$	−63.4618	−2.21080
$825$	−63.9391	−2.22607
$826$	6.55276	0.228000
$827$	44.1025	1.53359	0.766797	−	0.641890i	$-0.221849\pi$
$827$	44.1025	1.53359	0.766797	+	0.641890i	$0.221849\pi$
$828$	43.0930	1.49759
$829$	28.1710	0.978420	0.489210	−	0.872166i	$-0.337285\pi$
$829$	28.1710	0.978420	0.489210	+	0.872166i	$0.337285\pi$
$830$	148.932	5.16950
$831$	−12.6154	−0.437624
$832$	13.6952	0.474796
$833$	−5.43891	−0.188447
$834$	28.1360	0.974272
$835$	−41.9628	−1.45218
$836$	−26.9930	−0.933573
$837$	18.8629	0.651997
$838$	80.0608	2.76565
$839$	7.19217	0.248301	0.124151	−	0.992263i	$-0.460379\pi$
$839$	7.19217	0.248301	0.124151	+	0.992263i	$0.460379\pi$
$840$	20.7776	0.716894
$841$	54.3161	1.87297
$842$	−69.9477	−2.41056
$843$	1.49438	0.0514690
$844$	13.3004	0.457819
$845$	43.9250	1.51107
$846$	−11.8645	−0.407910
$847$	−29.7879	−1.02352
$848$	11.6517	0.400121
$849$	15.9397	0.547049
$850$	−22.0752	−0.757171
$851$	−39.2485	−1.34542
$852$	68.0587	2.33165
$853$	−41.3150	−1.41460	−0.707299	−	0.706914i	$-0.750087\pi$
$853$	−41.3150	−1.41460	−0.707299	+	0.706914i	$0.750087\pi$
$854$	−37.0673	−1.26842
$855$	−7.94523	−0.271721
$856$	−48.5503	−1.65941
$857$	−43.2074	−1.47594	−0.737968	−	0.674836i	$-0.764214\pi$
$857$	−43.2074	−1.47594	−0.737968	+	0.674836i	$0.764214\pi$
$858$	−19.1623	−0.654191
$859$	−10.9932	−0.375083	−0.187542	−	0.982257i	$-0.560052\pi$
$859$	−10.9932	−0.375083	−0.187542	+	0.982257i	$0.560052\pi$
$860$	11.9388	0.407109
$861$	−5.62949	−0.191853
$862$	−79.1373	−2.69543
$863$	−18.8729	−0.642440	−0.321220	−	0.947005i	$-0.604093\pi$
$863$	−18.8729	−0.642440	−0.321220	+	0.947005i	$0.604093\pi$
$864$	18.4460	0.627545
$865$	91.4616	3.10979
$866$	82.4551	2.80194
$867$	−1.16111	−0.0394332
$868$	−15.7038	−0.533022
$869$	87.2755	2.96062
$870$	94.9299	3.21842
$871$	−5.00874	−0.169715
$872$	−25.5362	−0.864765
$873$	−21.6362	−0.732274
$874$	−21.7943	−0.737204
$875$	20.4760	0.692216
$876$	31.4597	1.06293
$877$	−50.4938	−1.70505	−0.852527	−	0.522683i	$-0.824931\pi$
$877$	−50.4938	−1.70505	−0.852527	+	0.522683i	$0.824931\pi$
$878$	−7.38549	−0.249248
$879$	7.25109	0.244573
$880$	−39.2060	−1.32163
$881$	−13.7891	−0.464566	−0.232283	−	0.972648i	$-0.574620\pi$
$881$	−13.7891	−0.464566	−0.232283	+	0.972648i	$0.574620\pi$
$882$	−21.2585	−0.715810
$883$	−24.6986	−0.831174	−0.415587	−	0.909553i	$-0.636424\pi$
$883$	−24.6986	−0.831174	−0.415587	+	0.909553i	$0.636424\pi$
$884$	−4.25261	−0.143031
$885$	9.74181	0.327467
$886$	−27.1140	−0.910912
$887$	−45.1608	−1.51635	−0.758175	−	0.652051i	$-0.773909\pi$
$887$	−45.1608	−1.51635	−0.758175	+	0.652051i	$0.773909\pi$
$888$	23.7864	0.798218
$889$	−14.1477	−0.474498
$890$	40.3268	1.35176
$891$	−7.76753	−0.260222
$892$	67.3436	2.25483
$893$	3.85705	0.129071
$894$	−8.68735	−0.290548
$895$	−16.5241	−0.552340
$896$	−25.7318	−0.859641
$897$	−9.94513	−0.332058
$898$	2.44309	0.0815270
$899$	−31.8769	−1.06316
$900$	−55.4619	−1.84873
$901$	6.64042	0.221224
$902$	54.1980	1.80459
$903$	−1.27132	−0.0423069
$904$	−3.43742	−0.114327
$905$	−20.1735	−0.670590
$906$	1.18442	0.0393496
$907$	4.55945	0.151394	0.0756970	−	0.997131i	$-0.475882\pi$
$907$	4.55945	0.151394	0.0756970	+	0.997131i	$0.475882\pi$
$908$	92.6653	3.07521
$909$	10.3865	0.344497
$910$	13.2239	0.438366
$911$	17.8484	0.591344	0.295672	−	0.955289i	$-0.404456\pi$
$911$	17.8484	0.591344	0.295672	+	0.955289i	$0.404456\pi$
$912$	2.58877	0.0857227
$913$	98.1446	3.24811
$914$	76.9738	2.54607
$915$	−55.1069	−1.82178
$916$	44.5105	1.47067
$917$	21.5025	0.710077
$918$	−12.7806	−0.421822
$919$	31.0273	1.02349	0.511747	−	0.859136i	$-0.328998\pi$
$919$	31.0273	1.02349	0.511747	+	0.859136i	$0.328998\pi$
$920$	−103.817	−3.42276
$921$	−32.5611	−1.07293
$922$	26.3009	0.866174
$923$	19.2446	0.633445
$924$	30.8184	1.01385
$925$	50.5138	1.66088
$926$	11.8736	0.390192
$927$	−27.7066	−0.910004
$928$	−31.1724	−1.02328
$929$	−3.05093	−0.100098	−0.0500489	−	0.998747i	$-0.515938\pi$
$929$	−3.05093	−0.100098	−0.0500489	+	0.998747i	$0.515938\pi$
$930$	−36.3204	−1.19099
$931$	6.91097	0.226498
$932$	75.5373	2.47431
$933$	3.87678	0.126920
$934$	−61.6006	−2.01563
$935$	−22.3439	−0.730722
$936$	−7.38480	−0.241380
$937$	−13.5621	−0.443056	−0.221528	−	0.975154i	$-0.571104\pi$
$937$	−13.5621	−0.443056	−0.221528	+	0.975154i	$0.571104\pi$
$938$	12.5320	0.409185
$939$	−10.2518	−0.334555
$940$	41.3542	1.34883
$941$	−37.2728	−1.21506	−0.607530	−	0.794297i	$-0.707840\pi$
$941$	−37.2728	−1.21506	−0.607530	+	0.794297i	$0.707840\pi$
$942$	−56.8332	−1.85173
$943$	28.1284	0.915987
$944$	3.88910	0.126580
$945$	25.5460	0.831012
$946$	12.2396	0.397945
$947$	−35.7023	−1.16017	−0.580084	−	0.814556i	$-0.696980\pi$
$947$	−35.7023	−1.16017	−0.580084	+	0.814556i	$0.696980\pi$
$948$	−61.7870	−2.00675
$949$	8.89573	0.288768
$950$	28.0499	0.910058
$951$	30.8705	1.00104
$952$	4.72727	0.153212
$953$	44.2404	1.43309	0.716544	−	0.697542i	$-0.245723\pi$
$953$	44.2404	1.43309	0.716544	+	0.697542i	$0.245723\pi$
$954$	25.9547	0.840314
$955$	42.8207	1.38565
$956$	10.1620	0.328663
$957$	62.5578	2.02221
$958$	48.8895	1.57955
$959$	−7.91011	−0.255431
$960$	−50.9421	−1.64415
$961$	−18.8038	−0.606574
$962$	15.1388	0.488095
$963$	−21.1964	−0.683045
$964$	20.3755	0.656250
$965$	−97.3400	−3.13348
$966$	24.8830	0.800597
$967$	−33.2839	−1.07034	−0.535168	−	0.844745i	$-0.679752\pi$
$967$	−33.2839	−1.07034	−0.535168	+	0.844745i	$0.679752\pi$
$968$	−90.2029	−2.89923
$969$	1.47536	0.0473955
$970$	117.322	3.76700
$971$	−9.43881	−0.302906	−0.151453	−	0.988464i	$-0.548395\pi$
$971$	−9.43881	−0.302906	−0.151453	+	0.988464i	$0.548395\pi$
$972$	−52.8180	−1.69414
$973$	−12.7953	−0.410200
$974$	−23.2045	−0.743521
$975$	12.7996	0.409917
$976$	−21.9997	−0.704192
$977$	−2.48911	−0.0796336	−0.0398168	−	0.999207i	$-0.512677\pi$
$977$	−2.48911	−0.0796336	−0.0398168	+	0.999207i	$0.512677\pi$
$978$	−15.1400	−0.484123
$979$	26.5750	0.849340
$980$	74.0974	2.36695
$981$	−11.1488	−0.355953
$982$	−20.2556	−0.646382
$983$	19.4578	0.620606	0.310303	−	0.950638i	$-0.399569\pi$
$983$	19.4578	0.620606	0.310303	+	0.950638i	$0.399569\pi$
$984$	−17.0471	−0.543442
$985$	59.2990	1.88942
$986$	21.5983	0.687828
$987$	−4.40367	−0.140170
$988$	5.40359	0.171911
$989$	6.35230	0.201991
$990$	−87.3331	−2.77563
$991$	32.0699	1.01873	0.509366	−	0.860550i	$-0.329880\pi$
$991$	32.0699	1.01873	0.509366	+	0.860550i	$0.329880\pi$
$992$	11.9266	0.378671
$993$	−2.98785	−0.0948165
$994$	−48.1506	−1.52724
$995$	−64.8681	−2.05646
$996$	−69.4818	−2.20162
$997$	52.5668	1.66481	0.832404	−	0.554169i	$-0.186964\pi$
$997$	52.5668	1.66481	0.832404	+	0.554169i	$0.186964\pi$
$998$	−49.7453	−1.57466
$999$	29.2453	0.925281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.b.1.12	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.b.1.12	✓	114	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36622 q^{2} -1.16111 q^{3} +3.59897 q^{4} -3.78541 q^{5} +2.74743 q^{6} -1.24944 q^{7} -3.78352 q^{8} -1.65183 q^{9} +O(q^{10})\)	\(q-2.36622 q^{2} -1.16111 q^{3} +3.59897 q^{4} -3.78541 q^{5} +2.74743 q^{6} -1.24944 q^{7} -3.78352 q^{8} -1.65183 q^{9} +8.95709 q^{10} +5.90263 q^{11} -4.17879 q^{12} -1.18162 q^{13} +2.95644 q^{14} +4.39526 q^{15} +1.75466 q^{16} +1.00000 q^{17} +3.90859 q^{18} -1.27065 q^{19} -13.6236 q^{20} +1.45073 q^{21} -13.9669 q^{22} -7.24873 q^{23} +4.39306 q^{24} +9.32931 q^{25} +2.79596 q^{26} +5.40127 q^{27} -4.49669 q^{28} -9.12776 q^{29} -10.4001 q^{30} +3.49231 q^{31} +3.41512 q^{32} -6.85358 q^{33} -2.36622 q^{34} +4.72963 q^{35} -5.94491 q^{36} +5.41453 q^{37} +3.00664 q^{38} +1.37198 q^{39} +14.3221 q^{40} -3.88046 q^{41} -3.43274 q^{42} -0.876332 q^{43} +21.2434 q^{44} +6.25286 q^{45} +17.1521 q^{46} -3.03549 q^{47} -2.03735 q^{48} -5.43891 q^{49} -22.0752 q^{50} -1.16111 q^{51} -4.25261 q^{52} +6.64042 q^{53} -12.7806 q^{54} -22.3439 q^{55} +4.72727 q^{56} +1.47536 q^{57} +21.5983 q^{58} +2.21644 q^{59} +15.8184 q^{60} -12.5378 q^{61} -8.26355 q^{62} +2.06386 q^{63} -11.5902 q^{64} +4.47290 q^{65} +16.2170 q^{66} +4.23889 q^{67} +3.59897 q^{68} +8.41654 q^{69} -11.1913 q^{70} -16.2867 q^{71} +6.24974 q^{72} -7.52844 q^{73} -12.8119 q^{74} -10.8323 q^{75} -4.57305 q^{76} -7.37497 q^{77} -3.24640 q^{78} +14.7859 q^{79} -6.64212 q^{80} -1.31594 q^{81} +9.18200 q^{82} +16.6273 q^{83} +5.22113 q^{84} -3.78541 q^{85} +2.07359 q^{86} +10.5983 q^{87} -22.3327 q^{88} +4.50223 q^{89} -14.7956 q^{90} +1.47636 q^{91} -26.0880 q^{92} -4.05494 q^{93} +7.18262 q^{94} +4.80994 q^{95} -3.96531 q^{96} +13.0983 q^{97} +12.8696 q^{98} -9.75016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * q^99

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