LMFDB - Embedded newform 1003.2.a.g.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, 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("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
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} - 3x^{9} - 10x^{8} + 34x^{7} + 28x^{6} - 129x^{5} - 3x^{4} + 178x^{3} - 56x^{2} - 56x + 15 $ x^10 - 3x^9 - 10x^8 + 34x^7 + 28x^6 - 129x^5 - 3x^4 + 178x^3 - 56x^2 - 56*x + 15
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.13534$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.86166 q^{2} -3.13534 q^{3} +1.46576 q^{4} -1.05085 q^{5} -5.83692 q^{6} +1.46101 q^{7} -0.994564 q^{8} +6.83035 q^{9} +O(q^{10})$	\(q+1.86166 q^{2} -3.13534 q^{3} +1.46576 q^{4} -1.05085 q^{5} -5.83692 q^{6} +1.46101 q^{7} -0.994564 q^{8} +6.83035 q^{9} -1.95633 q^{10} +4.71350 q^{11} -4.59567 q^{12} -2.13191 q^{13} +2.71990 q^{14} +3.29478 q^{15} -4.78306 q^{16} -1.00000 q^{17} +12.7158 q^{18} -7.61942 q^{19} -1.54030 q^{20} -4.58077 q^{21} +8.77492 q^{22} -0.988541 q^{23} +3.11829 q^{24} -3.89571 q^{25} -3.96889 q^{26} -12.0094 q^{27} +2.14150 q^{28} -2.19162 q^{29} +6.13375 q^{30} -4.78338 q^{31} -6.91529 q^{32} -14.7784 q^{33} -1.86166 q^{34} -1.53531 q^{35} +10.0117 q^{36} -0.599545 q^{37} -14.1847 q^{38} +6.68427 q^{39} +1.04514 q^{40} +0.947729 q^{41} -8.52782 q^{42} -6.95171 q^{43} +6.90888 q^{44} -7.17770 q^{45} -1.84032 q^{46} +8.89599 q^{47} +14.9965 q^{48} -4.86544 q^{49} -7.25247 q^{50} +3.13534 q^{51} -3.12488 q^{52} -4.06491 q^{53} -22.3574 q^{54} -4.95320 q^{55} -1.45307 q^{56} +23.8895 q^{57} -4.08005 q^{58} -1.00000 q^{59} +4.82937 q^{60} -2.18787 q^{61} -8.90501 q^{62} +9.97923 q^{63} -3.30777 q^{64} +2.24033 q^{65} -27.5123 q^{66} -1.82976 q^{67} -1.46576 q^{68} +3.09941 q^{69} -2.85822 q^{70} +4.49471 q^{71} -6.79322 q^{72} -8.67288 q^{73} -1.11615 q^{74} +12.2144 q^{75} -11.1683 q^{76} +6.88649 q^{77} +12.4438 q^{78} +13.8052 q^{79} +5.02630 q^{80} +17.1626 q^{81} +1.76435 q^{82} -9.38443 q^{83} -6.71433 q^{84} +1.05085 q^{85} -12.9417 q^{86} +6.87148 q^{87} -4.68788 q^{88} -4.08572 q^{89} -13.3624 q^{90} -3.11475 q^{91} -1.44897 q^{92} +14.9975 q^{93} +16.5613 q^{94} +8.00689 q^{95} +21.6818 q^{96} -4.23736 q^{97} -9.05778 q^{98} +32.1949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) $ 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9 + 4 * q^10 + 12 * q^11 - 24 * q^12 - 11 * q^13 - 12 * q^14 + 9 * q^15 - 3 * q^16 - 10 * q^17 - 22 * q^18 - 5 * q^19 - 36 * q^20 - 10 * q^21 + 6 * q^22 - 7 * q^23 + 35 * q^24 + 2 * q^25 + q^26 - 31 * q^27 - 4 * q^28 + 10 * q^29 - 9 * q^30 + 13 * q^31 - 15 * q^32 - 9 * q^33 + q^34 - 8 * q^35 + 40 * q^36 + 12 * q^37 - 50 * q^38 + 24 * q^39 + 5 * q^40 - 29 * q^41 - 17 * q^42 - 18 * q^43 - 6 * q^44 - 14 * q^45 + 11 * q^46 - 18 * q^47 - 43 * q^48 - 9 * q^49 - 31 * q^50 + 7 * q^51 - 68 * q^52 + 19 * q^54 - 27 * q^55 - 7 * q^56 + 20 * q^57 + 23 * q^58 - 10 * q^59 + 38 * q^60 + 8 * q^61 - 46 * q^62 + 39 * q^63 - 20 * q^64 + 58 * q^65 - 34 * q^66 - 6 * q^67 - 15 * q^68 + 6 * q^69 + 73 * q^70 + 8 * q^71 - 70 * q^72 - 41 * q^73 - 10 * q^74 + 10 * q^75 + 12 * q^76 - 22 * q^77 - 43 * q^78 + 3 * q^79 - 15 * q^80 + 26 * q^81 + 8 * q^82 - 22 * q^84 + 12 * q^85 - 29 * q^86 - 28 * q^87 + 33 * q^88 - 45 * q^89 + 56 * q^90 - 14 * q^91 + 36 * q^92 - 19 * q^93 + 15 * q^94 - 17 * q^95 + 90 * q^96 - 5 * q^97 + 30 * q^98 + 14 * 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 $

$2$	1.86166	1.31639	0.658195	−	0.752848i	$-0.271320\pi$
$2$	1.86166	1.31639	0.658195	+	0.752848i	$0.271320\pi$
$3$	−3.13534	−1.81019	−0.905094	−	0.425211i	$-0.860200\pi$
$3$	−3.13534	−1.81019	−0.905094	+	0.425211i	$0.860200\pi$
$4$	1.46576	0.732882
$5$	−1.05085	−0.469956	−0.234978	−	0.972001i	$-0.575502\pi$
$5$	−1.05085	−0.469956	−0.234978	+	0.972001i	$0.575502\pi$
$6$	−5.83692	−2.38291
$7$	1.46101	0.552211	0.276106	−	0.961127i	$-0.410956\pi$
$7$	1.46101	0.552211	0.276106	+	0.961127i	$0.410956\pi$
$8$	−0.994564	−0.351631
$9$	6.83035	2.27678
$10$	−1.95633	−0.618645
$11$	4.71350	1.42117	0.710587	−	0.703609i	$-0.248429\pi$
$11$	4.71350	1.42117	0.710587	+	0.703609i	$0.248429\pi$
$12$	−4.59567	−1.32665
$13$	−2.13191	−0.591287	−0.295643	−	0.955298i	$-0.595534\pi$
$13$	−2.13191	−0.591287	−0.295643	+	0.955298i	$0.595534\pi$
$14$	2.71990	0.726925
$15$	3.29478	0.850709
$16$	−4.78306	−1.19577
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	12.7158	2.99713
$19$	−7.61942	−1.74801	−0.874007	−	0.485913i	$-0.838487\pi$
$19$	−7.61942	−1.74801	−0.874007	+	0.485913i	$0.838487\pi$
$20$	−1.54030	−0.344422
$21$	−4.58077	−0.999606
$22$	8.77492	1.87082
$23$	−0.988541	−0.206125	−0.103063	−	0.994675i	$-0.532864\pi$
$23$	−0.988541	−0.206125	−0.103063	+	0.994675i	$0.532864\pi$
$24$	3.11829	0.636519
$25$	−3.89571	−0.779141
$26$	−3.96889	−0.778364
$27$	−12.0094	−2.31122
$28$	2.14150	0.404706
$29$	−2.19162	−0.406974	−0.203487	−	0.979078i	$-0.565227\pi$
$29$	−2.19162	−0.406974	−0.203487	+	0.979078i	$0.565227\pi$
$30$	6.13375	1.11986
$31$	−4.78338	−0.859121	−0.429560	−	0.903038i	$-0.641331\pi$
$31$	−4.78338	−0.859121	−0.429560	+	0.903038i	$0.641331\pi$
$32$	−6.91529	−1.22246
$33$	−14.7784	−2.57259
$34$	−1.86166	−0.319271
$35$	−1.53531	−0.259515
$36$	10.0117	1.66861
$37$	−0.599545	−0.0985646	−0.0492823	−	0.998785i	$-0.515693\pi$
$37$	−0.599545	−0.0985646	−0.0492823	+	0.998785i	$0.515693\pi$
$38$	−14.1847	−2.30107
$39$	6.68427	1.07034
$40$	1.04514	0.165251
$41$	0.947729	0.148010	0.0740052	−	0.997258i	$-0.476422\pi$
$41$	0.947729	0.148010	0.0740052	+	0.997258i	$0.476422\pi$
$42$	−8.52782	−1.31587
$43$	−6.95171	−1.06013	−0.530063	−	0.847958i	$-0.677832\pi$
$43$	−6.95171	−1.06013	−0.530063	+	0.847958i	$0.677832\pi$
$44$	6.90888	1.04155
$45$	−7.17770	−1.06999
$46$	−1.84032	−0.271341
$47$	8.89599	1.29761	0.648807	−	0.760953i	$-0.275268\pi$
$47$	8.89599	1.29761	0.648807	+	0.760953i	$0.275268\pi$
$48$	14.9965	2.16456
$49$	−4.86544	−0.695063
$50$	−7.25247	−1.02565
$51$	3.13534	0.439035
$52$	−3.12488	−0.433343
$53$	−4.06491	−0.558358	−0.279179	−	0.960239i	$-0.590062\pi$
$53$	−4.06491	−0.558358	−0.279179	+	0.960239i	$0.590062\pi$
$54$	−22.3574	−3.04246
$55$	−4.95320	−0.667889
$56$	−1.45307	−0.194175
$57$	23.8895	3.16424
$58$	−4.08005	−0.535736
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	4.82937	0.623469
$61$	−2.18787	−0.280128	−0.140064	−	0.990142i	$-0.544731\pi$
$61$	−2.18787	−0.280128	−0.140064	+	0.990142i	$0.544731\pi$
$62$	−8.90501	−1.13094
$63$	9.97923	1.25726
$64$	−3.30777	−0.413471
$65$	2.24033	0.277879
$66$	−27.5123	−3.38654
$67$	−1.82976	−0.223541	−0.111770	−	0.993734i	$-0.535652\pi$
$67$	−1.82976	−0.223541	−0.111770	+	0.993734i	$0.535652\pi$
$68$	−1.46576	−0.177750
$69$	3.09941	0.373125
$70$	−2.85822	−0.341623
$71$	4.49471	0.533424	0.266712	−	0.963776i	$-0.414063\pi$
$71$	4.49471	0.533424	0.266712	+	0.963776i	$0.414063\pi$
$72$	−6.79322	−0.800588
$73$	−8.67288	−1.01508	−0.507542	−	0.861627i	$-0.669446\pi$
$73$	−8.67288	−1.01508	−0.507542	+	0.861627i	$0.669446\pi$
$74$	−1.11615	−0.129749
$75$	12.2144	1.41039
$76$	−11.1683	−1.28109
$77$	6.88649	0.784788
$78$	12.4438	1.40899
$79$	13.8052	1.55321	0.776605	−	0.629987i	$-0.216940\pi$
$79$	13.8052	1.55321	0.776605	+	0.629987i	$0.216940\pi$
$80$	5.02630	0.561957
$81$	17.1626	1.90696
$82$	1.76435	0.194839
$83$	−9.38443	−1.03007	−0.515037	−	0.857168i	$-0.672222\pi$
$83$	−9.38443	−1.03007	−0.515037	+	0.857168i	$0.672222\pi$
$84$	−6.71433	−0.732593
$85$	1.05085	0.113981
$86$	−12.9417	−1.39554
$87$	6.87148	0.736699
$88$	−4.68788	−0.499729
$89$	−4.08572	−0.433085	−0.216543	−	0.976273i	$-0.569478\pi$
$89$	−4.08572	−0.433085	−0.216543	+	0.976273i	$0.569478\pi$
$90$	−13.3624	−1.40852
$91$	−3.11475	−0.326515
$92$	−1.44897	−0.151065
$93$	14.9975	1.55517
$94$	16.5613	1.70816
$95$	8.00689	0.821490
$96$	21.6818	2.21289
$97$	−4.23736	−0.430239	−0.215120	−	0.976588i	$-0.569014\pi$
$97$	−4.23736	−0.430239	−0.215120	+	0.976588i	$0.569014\pi$
$98$	−9.05778	−0.914974
$99$	32.1949	3.23570
$100$	−5.71019	−0.571019
$101$	−4.70259	−0.467925	−0.233963	−	0.972246i	$-0.575169\pi$
$101$	−4.70259	−0.467925	−0.233963	+	0.972246i	$0.575169\pi$
$102$	5.83692	0.577941
$103$	4.99869	0.492535	0.246268	−	0.969202i	$-0.420796\pi$
$103$	4.99869	0.492535	0.246268	+	0.969202i	$0.420796\pi$
$104$	2.12032	0.207915
$105$	4.81372	0.469771
$106$	−7.56746	−0.735017
$107$	6.42787	0.621405	0.310703	−	0.950507i	$-0.399436\pi$
$107$	6.42787	0.621405	0.310703	+	0.950507i	$0.399436\pi$
$108$	−17.6030	−1.69385
$109$	12.8738	1.23308	0.616541	−	0.787323i	$-0.288534\pi$
$109$	12.8738	1.23308	0.616541	+	0.787323i	$0.288534\pi$
$110$	−9.22116	−0.879203
$111$	1.87978	0.178421
$112$	−6.98812	−0.660315
$113$	−4.99370	−0.469768	−0.234884	−	0.972023i	$-0.575471\pi$
$113$	−4.99370	−0.469768	−0.234884	+	0.972023i	$0.575471\pi$
$114$	44.4740	4.16537
$115$	1.03881	0.0968697
$116$	−3.21240	−0.298264
$117$	−14.5617	−1.34623
$118$	−1.86166	−0.171379
$119$	−1.46101	−0.133931
$120$	−3.27687	−0.299136
$121$	11.2171	1.01974
$122$	−4.07307	−0.368758
$123$	−2.97145	−0.267927
$124$	−7.01131	−0.629634
$125$	9.34809	0.836118
$126$	18.5779	1.65505
$127$	13.4599	1.19438	0.597188	−	0.802101i	$-0.296285\pi$
$127$	13.4599	1.19438	0.597188	+	0.802101i	$0.296285\pi$
$128$	7.67265	0.678173
$129$	21.7960	1.91903
$130$	4.17072	0.365797
$131$	−16.9976	−1.48508	−0.742542	−	0.669800i	$-0.766380\pi$
$131$	−16.9976	−1.48508	−0.742542	+	0.669800i	$0.766380\pi$
$132$	−21.6617	−1.88541
$133$	−11.1321	−0.965273
$134$	−3.40639	−0.294267
$135$	12.6202	1.08617
$136$	0.994564	0.0852831
$137$	−16.7022	−1.42697	−0.713485	−	0.700671i	$-0.752884\pi$
$137$	−16.7022	−1.42697	−0.713485	+	0.700671i	$0.752884\pi$
$138$	5.77004	0.491178
$139$	19.7065	1.67148	0.835740	−	0.549125i	$-0.185039\pi$
$139$	19.7065	1.67148	0.835740	+	0.549125i	$0.185039\pi$
$140$	−2.25040	−0.190194
$141$	−27.8919	−2.34892
$142$	8.36761	0.702194
$143$	−10.0488	−0.840321
$144$	−32.6700	−2.72250
$145$	2.30307	0.191260
$146$	−16.1459	−1.33625
$147$	15.2548	1.25820
$148$	−0.878792	−0.0722362
$149$	−17.0162	−1.39402	−0.697011	−	0.717061i	$-0.745487\pi$
$149$	−17.0162	−1.39402	−0.697011	+	0.717061i	$0.745487\pi$
$150$	22.7389	1.85663
$151$	4.67826	0.380712	0.190356	−	0.981715i	$-0.439036\pi$
$151$	4.67826	0.380712	0.190356	+	0.981715i	$0.439036\pi$
$152$	7.57800	0.614657
$153$	−6.83035	−0.552201
$154$	12.8203	1.03309
$155$	5.02663	0.403749
$156$	9.79757	0.784433
$157$	−3.02740	−0.241613	−0.120807	−	0.992676i	$-0.538548\pi$
$157$	−3.02740	−0.241613	−0.120807	+	0.992676i	$0.538548\pi$
$158$	25.7006	2.04463
$159$	12.7449	1.01073
$160$	7.26696	0.574504
$161$	−1.44427	−0.113825
$162$	31.9509	2.51030
$163$	−12.9361	−1.01323	−0.506615	−	0.862172i	$-0.669103\pi$
$163$	−12.9361	−1.01323	−0.506615	+	0.862172i	$0.669103\pi$
$164$	1.38915	0.108474
$165$	15.5300	1.20901
$166$	−17.4706	−1.35598
$167$	−13.3737	−1.03489	−0.517445	−	0.855716i	$-0.673117\pi$
$167$	−13.3737	−1.03489	−0.517445	+	0.855716i	$0.673117\pi$
$168$	4.55587	0.351493
$169$	−8.45494	−0.650380
$170$	1.95633	0.150044
$171$	−52.0433	−3.97985
$172$	−10.1896	−0.776947
$173$	−13.4808	−1.02492	−0.512462	−	0.858710i	$-0.671267\pi$
$173$	−13.4808	−1.02492	−0.512462	+	0.858710i	$0.671267\pi$
$174$	12.7923	0.969784
$175$	−5.69168	−0.430250
$176$	−22.5450	−1.69939
$177$	3.13534	0.235666
$178$	−7.60620	−0.570109
$179$	−14.4245	−1.07814	−0.539068	−	0.842262i	$-0.681224\pi$
$179$	−14.4245	−1.07814	−0.539068	+	0.842262i	$0.681224\pi$
$180$	−10.5208	−0.784175
$181$	12.6774	0.942305	0.471153	−	0.882052i	$-0.343838\pi$
$181$	12.6774	0.942305	0.471153	+	0.882052i	$0.343838\pi$
$182$	−5.79860	−0.429821
$183$	6.85972	0.507085
$184$	0.983167	0.0724800
$185$	0.630034	0.0463210
$186$	27.9202	2.04721
$187$	−4.71350	−0.344685
$188$	13.0394	0.950997
$189$	−17.5459	−1.27628
$190$	14.9061	1.08140
$191$	22.2330	1.60873	0.804363	−	0.594139i	$-0.202507\pi$
$191$	22.2330	1.60873	0.804363	+	0.594139i	$0.202507\pi$
$192$	10.3710	0.748461
$193$	21.8142	1.57022	0.785109	−	0.619357i	$-0.212607\pi$
$193$	21.8142	1.57022	0.785109	+	0.619357i	$0.212607\pi$
$194$	−7.88851	−0.566362
$195$	−7.02419	−0.503013
$196$	−7.13159	−0.509399
$197$	−14.9715	−1.06668	−0.533339	−	0.845902i	$-0.679063\pi$
$197$	−14.9715	−1.06668	−0.533339	+	0.845902i	$0.679063\pi$
$198$	59.9358	4.25945
$199$	1.59309	0.112931	0.0564654	−	0.998405i	$-0.482017\pi$
$199$	1.59309	0.112931	0.0564654	+	0.998405i	$0.482017\pi$
$200$	3.87453	0.273971
$201$	5.73692	0.404651
$202$	−8.75461	−0.615972
$203$	−3.20199	−0.224735
$204$	4.59567	0.321761
$205$	−0.995925	−0.0695584
$206$	9.30583	0.648368
$207$	−6.75208	−0.469302
$208$	10.1971	0.707040
$209$	−35.9141	−2.48423
$210$	8.96149	0.618402
$211$	−2.90202	−0.199783	−0.0998917	−	0.994998i	$-0.531850\pi$
$211$	−2.90202	−0.199783	−0.0998917	+	0.994998i	$0.531850\pi$
$212$	−5.95820	−0.409211
$213$	−14.0925	−0.965599
$214$	11.9665	0.818012
$215$	7.30523	0.498212
$216$	11.9442	0.812697
$217$	−6.98858	−0.474416
$218$	23.9665	1.62322
$219$	27.1924	1.83749
$220$	−7.26022	−0.489484
$221$	2.13191	0.143408
$222$	3.49950	0.234871
$223$	−8.63201	−0.578042	−0.289021	−	0.957323i	$-0.593330\pi$
$223$	−8.63201	−0.578042	−0.289021	+	0.957323i	$0.593330\pi$
$224$	−10.1033	−0.675057
$225$	−26.6090	−1.77394
$226$	−9.29656	−0.618398
$227$	19.1834	1.27325	0.636623	−	0.771175i	$-0.280331\pi$
$227$	19.1834	1.27325	0.636623	+	0.771175i	$0.280331\pi$
$228$	35.0163	2.31901
$229$	25.6590	1.69559	0.847797	−	0.530321i	$-0.177929\pi$
$229$	25.6590	1.69559	0.847797	+	0.530321i	$0.177929\pi$
$230$	1.93391	0.127518
$231$	−21.5915	−1.42061
$232$	2.17971	0.143105
$233$	6.61220	0.433180	0.216590	−	0.976263i	$-0.430507\pi$
$233$	6.61220	0.433180	0.216590	+	0.976263i	$0.430507\pi$
$234$	−27.1089	−1.77217
$235$	−9.34838	−0.609821
$236$	−1.46576	−0.0954131
$237$	−43.2841	−2.81160
$238$	−2.71990	−0.176305
$239$	27.3089	1.76647	0.883234	−	0.468933i	$-0.155361\pi$
$239$	27.3089	1.76647	0.883234	+	0.468933i	$0.155361\pi$
$240$	−15.7592	−1.01725
$241$	5.79161	0.373070	0.186535	−	0.982448i	$-0.440274\pi$
$241$	5.79161	0.373070	0.186535	+	0.982448i	$0.440274\pi$
$242$	20.8824	1.34237
$243$	−17.7823	−1.14073
$244$	−3.20690	−0.205301
$245$	5.11287	0.326649
$246$	−5.53182	−0.352696
$247$	16.2439	1.03358
$248$	4.75738	0.302094
$249$	29.4234	1.86463
$250$	17.4029	1.10066
$251$	8.37951	0.528910	0.264455	−	0.964398i	$-0.414808\pi$
$251$	8.37951	0.528910	0.264455	+	0.964398i	$0.414808\pi$
$252$	14.6272	0.921427
$253$	−4.65949	−0.292940
$254$	25.0578	1.57226
$255$	−3.29478	−0.206327
$256$	20.8994	1.30621
$257$	21.6130	1.34818	0.674091	−	0.738649i	$-0.264536\pi$
$257$	21.6130	1.34818	0.674091	+	0.738649i	$0.264536\pi$
$258$	40.5766	2.52619
$259$	−0.875943	−0.0544285
$260$	3.28380	0.203652
$261$	−14.9695	−0.926591
$262$	−31.6436	−1.95495
$263$	−20.0009	−1.23331	−0.616654	−	0.787235i	$-0.711512\pi$
$263$	−20.0009	−1.23331	−0.616654	+	0.787235i	$0.711512\pi$
$264$	14.6981	0.904605
$265$	4.27162	0.262404
$266$	−20.7241	−1.27068
$267$	12.8101	0.783966
$268$	−2.68200	−0.163829
$269$	28.9907	1.76759	0.883796	−	0.467872i	$-0.154979\pi$
$269$	28.9907	1.76759	0.883796	+	0.467872i	$0.154979\pi$
$270$	23.4944	1.42982
$271$	13.4120	0.814719	0.407360	−	0.913268i	$-0.366450\pi$
$271$	13.4120	0.814719	0.407360	+	0.913268i	$0.366450\pi$
$272$	4.78306	0.290016
$273$	9.76581	0.591054
$274$	−31.0938	−1.87845
$275$	−18.3624	−1.10730
$276$	4.54300	0.273457
$277$	−27.1825	−1.63324	−0.816619	−	0.577177i	$-0.804154\pi$
$277$	−27.1825	−1.63324	−0.816619	+	0.577177i	$0.804154\pi$
$278$	36.6867	2.20032
$279$	−32.6722	−1.95603
$280$	1.52696	0.0912536
$281$	−20.4555	−1.22027	−0.610135	−	0.792297i	$-0.708885\pi$
$281$	−20.4555	−1.22027	−0.610135	+	0.792297i	$0.708885\pi$
$282$	−51.9252	−3.09210
$283$	22.4464	1.33430	0.667149	−	0.744925i	$-0.267515\pi$
$283$	22.4464	1.33430	0.667149	+	0.744925i	$0.267515\pi$
$284$	6.58819	0.390937
$285$	−25.1043	−1.48705
$286$	−18.7074	−1.10619
$287$	1.38464	0.0817330
$288$	−47.2339	−2.78328
$289$	1.00000	0.0588235
$290$	4.28753	0.251772
$291$	13.2856	0.778814
$292$	−12.7124	−0.743937
$293$	−23.3439	−1.36376	−0.681882	−	0.731462i	$-0.738838\pi$
$293$	−23.3439	−1.36376	−0.681882	+	0.731462i	$0.738838\pi$
$294$	28.3992	1.65628
$295$	1.05085	0.0611831
$296$	0.596286	0.0346584
$297$	−56.6065	−3.28464
$298$	−31.6783	−1.83508
$299$	2.10748	0.121879
$300$	17.9034	1.03365
$301$	−10.1565	−0.585413
$302$	8.70932	0.501165
$303$	14.7442	0.847033
$304$	36.4442	2.09022
$305$	2.29913	0.131648
$306$	−12.7158	−0.726912
$307$	−26.9611	−1.53875	−0.769374	−	0.638798i	$-0.779432\pi$
$307$	−26.9611	−1.53875	−0.769374	+	0.638798i	$0.779432\pi$
$308$	10.0940	0.575157
$309$	−15.6726	−0.891582
$310$	9.35787	0.531491
$311$	7.76388	0.440249	0.220125	−	0.975472i	$-0.429354\pi$
$311$	7.76388	0.440249	0.220125	+	0.975472i	$0.429354\pi$
$312$	−6.64794	−0.376365
$313$	−14.6971	−0.830732	−0.415366	−	0.909654i	$-0.636346\pi$
$313$	−14.6971	−0.830732	−0.415366	+	0.909654i	$0.636346\pi$
$314$	−5.63599	−0.318057
$315$	−10.4867	−0.590859
$316$	20.2352	1.13832
$317$	−20.0484	−1.12603	−0.563015	−	0.826447i	$-0.690359\pi$
$317$	−20.0484	−1.12603	−0.563015	+	0.826447i	$0.690359\pi$
$318$	23.7266	1.33052
$319$	−10.3302	−0.578381
$320$	3.47598	0.194313
$321$	−20.1535	−1.12486
$322$	−2.68874	−0.149837
$323$	7.61942	0.423956
$324$	25.1563	1.39757
$325$	8.30531	0.460696
$326$	−24.0825	−1.33381
$327$	−40.3636	−2.23211
$328$	−0.942577	−0.0520451
$329$	12.9972	0.716556
$330$	28.9114	1.59152
$331$	32.5336	1.78821	0.894104	−	0.447860i	$-0.147814\pi$
$331$	32.5336	1.78821	0.894104	+	0.447860i	$0.147814\pi$
$332$	−13.7554	−0.754923
$333$	−4.09510	−0.224410
$334$	−24.8973	−1.36232
$335$	1.92281	0.105054
$336$	21.9101	1.19529
$337$	−6.15161	−0.335099	−0.167550	−	0.985864i	$-0.553585\pi$
$337$	−6.15161	−0.335099	−0.167550	+	0.985864i	$0.553585\pi$
$338$	−15.7402	−0.856154
$339$	15.6569	0.850369
$340$	1.54030	0.0835347
$341$	−22.5465	−1.22096
$342$	−96.8867	−5.23903
$343$	−17.3356	−0.936032
$344$	6.91392	0.372773
$345$	−3.25703	−0.175352
$346$	−25.0966	−1.34920
$347$	14.6831	0.788229	0.394114	−	0.919061i	$-0.371051\pi$
$347$	14.6831	0.788229	0.394114	+	0.919061i	$0.371051\pi$
$348$	10.0720	0.539914
$349$	−9.08372	−0.486240	−0.243120	−	0.969996i	$-0.578171\pi$
$349$	−9.08372	−0.486240	−0.243120	+	0.969996i	$0.578171\pi$
$350$	−10.5959	−0.566377
$351$	25.6031	1.36659
$352$	−32.5952	−1.73733
$353$	−20.2412	−1.07733	−0.538666	−	0.842520i	$-0.681071\pi$
$353$	−20.2412	−1.07733	−0.538666	+	0.842520i	$0.681071\pi$
$354$	5.83692	0.310229
$355$	−4.72329	−0.250686
$356$	−5.98870	−0.317400
$357$	4.58077	0.242440
$358$	−26.8534	−1.41925
$359$	14.1362	0.746078	0.373039	−	0.927816i	$-0.378316\pi$
$359$	14.1362	0.746078	0.373039	+	0.927816i	$0.378316\pi$
$360$	7.13868	0.376241
$361$	39.0555	2.05555
$362$	23.6010	1.24044
$363$	−35.1694	−1.84591
$364$	−4.56550	−0.239297
$365$	9.11393	0.477045
$366$	12.7704	0.667522
$367$	−34.7699	−1.81498	−0.907488	−	0.420078i	$-0.862003\pi$
$367$	−34.7699	−1.81498	−0.907488	+	0.420078i	$0.862003\pi$
$368$	4.72825	0.246477
$369$	6.47332	0.336988
$370$	1.17291	0.0609765
$371$	−5.93888	−0.308332
$372$	21.9828	1.13976
$373$	−13.4427	−0.696035	−0.348018	−	0.937488i	$-0.613145\pi$
$373$	−13.4427	−0.696035	−0.348018	+	0.937488i	$0.613145\pi$
$374$	−8.77492	−0.453740
$375$	−29.3094	−1.51353
$376$	−8.84763	−0.456282
$377$	4.67235	0.240638
$378$	−32.6645	−1.68008
$379$	17.7046	0.909426	0.454713	−	0.890638i	$-0.349742\pi$
$379$	17.7046	0.909426	0.454713	+	0.890638i	$0.349742\pi$
$380$	11.7362	0.602055
$381$	−42.2014	−2.16205
$382$	41.3903	2.11771
$383$	3.93155	0.200893	0.100447	−	0.994942i	$-0.467973\pi$
$383$	3.93155	0.200893	0.100447	+	0.994942i	$0.467973\pi$
$384$	−24.0564	−1.22762
$385$	−7.23669	−0.368816
$386$	40.6105	2.06702
$387$	−47.4826	−2.41368
$388$	−6.21098	−0.315315
$389$	7.40846	0.375624	0.187812	−	0.982205i	$-0.439860\pi$
$389$	7.40846	0.375624	0.187812	+	0.982205i	$0.439860\pi$
$390$	−13.0766	−0.662161
$391$	0.988541	0.0499927
$392$	4.83899	0.244406
$393$	53.2931	2.68828
$394$	−27.8718	−1.40416
$395$	−14.5073	−0.729941
$396$	47.1901	2.37139
$397$	3.08865	0.155015	0.0775075	−	0.996992i	$-0.475304\pi$
$397$	3.08865	0.155015	0.0775075	+	0.996992i	$0.475304\pi$
$398$	2.96578	0.148661
$399$	34.9028	1.74733
$400$	18.6334	0.931671
$401$	−24.0746	−1.20223	−0.601114	−	0.799163i	$-0.705276\pi$
$401$	−24.0746	−1.20223	−0.601114	+	0.799163i	$0.705276\pi$
$402$	10.6802	0.532679
$403$	10.1978	0.507987
$404$	−6.89289	−0.342934
$405$	−18.0354	−0.896186
$406$	−5.96100	−0.295839
$407$	−2.82596	−0.140077
$408$	−3.11829	−0.154379
$409$	33.6886	1.66579	0.832896	−	0.553430i	$-0.186681\pi$
$409$	33.6886	1.66579	0.832896	+	0.553430i	$0.186681\pi$
$410$	−1.85407	−0.0915660
$411$	52.3672	2.58308
$412$	7.32689	0.360970
$413$	−1.46101	−0.0718918
$414$	−12.5700	−0.617784
$415$	9.86166	0.484090
$416$	14.7428	0.722826
$417$	−61.7864	−3.02569
$418$	−66.8598	−3.27022
$419$	27.7467	1.35552	0.677759	−	0.735284i	$-0.262951\pi$
$419$	27.7467	1.35552	0.677759	+	0.735284i	$0.262951\pi$
$420$	7.05578	0.344287
$421$	−12.0457	−0.587073	−0.293537	−	0.955948i	$-0.594832\pi$
$421$	−12.0457	−0.587073	−0.293537	+	0.955948i	$0.594832\pi$
$422$	−5.40257	−0.262993
$423$	60.7627	2.95438
$424$	4.04281	0.196336
$425$	3.89571	0.188970
$426$	−26.2353	−1.27110
$427$	−3.19651	−0.154690
$428$	9.42173	0.455417
$429$	31.5063	1.52114
$430$	13.5998	0.655842
$431$	9.19404	0.442861	0.221431	−	0.975176i	$-0.428927\pi$
$431$	9.19404	0.442861	0.221431	+	0.975176i	$0.428927\pi$
$432$	57.4419	2.76368
$433$	30.5677	1.46899	0.734495	−	0.678614i	$-0.237419\pi$
$433$	30.5677	1.46899	0.734495	+	0.678614i	$0.237419\pi$
$434$	−13.0103	−0.624516
$435$	−7.22091	−0.346216
$436$	18.8699	0.903703
$437$	7.53211	0.360310
$438$	50.6230	2.41886
$439$	−29.9973	−1.43169	−0.715847	−	0.698258i	$-0.753959\pi$
$439$	−29.9973	−1.43169	−0.715847	+	0.698258i	$0.753959\pi$
$440$	4.92627	0.234851
$441$	−33.2327	−1.58251
$442$	3.96889	0.188781
$443$	25.2140	1.19796	0.598978	−	0.800766i	$-0.295574\pi$
$443$	25.2140	1.19796	0.598978	+	0.800766i	$0.295574\pi$
$444$	2.75531	0.130761
$445$	4.29349	0.203531
$446$	−16.0698	−0.760928
$447$	53.3516	2.52344
$448$	−4.83270	−0.228323
$449$	−10.2893	−0.485584	−0.242792	−	0.970078i	$-0.578063\pi$
$449$	−10.2893	−0.485584	−0.242792	+	0.970078i	$0.578063\pi$
$450$	−49.5369	−2.33519
$451$	4.46712	0.210349
$452$	−7.31959	−0.344284
$453$	−14.6679	−0.689160
$454$	35.7129	1.67609
$455$	3.27315	0.153448
$456$	−23.7596	−1.11264
$457$	−7.74574	−0.362330	−0.181165	−	0.983453i	$-0.557987\pi$
$457$	−7.74574	−0.362330	−0.181165	+	0.983453i	$0.557987\pi$
$458$	47.7682	2.23206
$459$	12.0094	0.560553
$460$	1.52265	0.0709941
$461$	−33.0777	−1.54058	−0.770291	−	0.637693i	$-0.779889\pi$
$461$	−33.0777	−1.54058	−0.770291	+	0.637693i	$0.779889\pi$
$462$	−40.1959	−1.87008
$463$	−7.00776	−0.325678	−0.162839	−	0.986653i	$-0.552065\pi$
$463$	−7.00776	−0.325678	−0.162839	+	0.986653i	$0.552065\pi$
$464$	10.4827	0.486646
$465$	−15.7602	−0.730862
$466$	12.3096	0.570233
$467$	−29.5596	−1.36785	−0.683927	−	0.729551i	$-0.739729\pi$
$467$	−29.5596	−1.36785	−0.683927	+	0.729551i	$0.739729\pi$
$468$	−21.3440	−0.986629
$469$	−2.67331	−0.123442
$470$	−17.4035	−0.802762
$471$	9.49194	0.437365
$472$	0.994564	0.0457785
$473$	−32.7669	−1.50662
$474$	−80.5801	−3.70117
$475$	29.6830	1.36195
$476$	−2.14150	−0.0981555
$477$	−27.7647	−1.27126
$478$	50.8398	2.32536
$479$	8.80825	0.402459	0.201230	−	0.979544i	$-0.435506\pi$
$479$	8.80825	0.402459	0.201230	+	0.979544i	$0.435506\pi$
$480$	−22.7844	−1.03996
$481$	1.27818	0.0582799
$482$	10.7820	0.491106
$483$	4.52828	0.206044
$484$	16.4416	0.747346
$485$	4.45285	0.202193
$486$	−33.1045	−1.50165
$487$	20.6650	0.936420	0.468210	−	0.883617i	$-0.344899\pi$
$487$	20.6650	0.936420	0.468210	+	0.883617i	$0.344899\pi$
$488$	2.17598	0.0985019
$489$	40.5589	1.83414
$490$	9.51840	0.429997
$491$	−23.8188	−1.07493	−0.537463	−	0.843287i	$-0.680617\pi$
$491$	−23.8188	−1.07493	−0.537463	+	0.843287i	$0.680617\pi$
$492$	−4.35545	−0.196359
$493$	2.19162	0.0987057
$494$	30.2406	1.36059
$495$	−33.8321	−1.52064
$496$	22.8792	1.02731
$497$	6.56684	0.294563
$498$	54.7762	2.45458
$499$	−43.8573	−1.96332	−0.981661	−	0.190637i	$-0.938945\pi$
$499$	−43.8573	−1.96332	−0.981661	+	0.190637i	$0.938945\pi$
$500$	13.7021	0.612776
$501$	41.9312	1.87335
$502$	15.5998	0.696251
$503$	−23.6629	−1.05508	−0.527539	−	0.849531i	$-0.676885\pi$
$503$	−23.6629	−1.05508	−0.527539	+	0.849531i	$0.676885\pi$
$504$	−9.92498	−0.442094
$505$	4.94174	0.219904
$506$	−8.67437	−0.385623
$507$	26.5091	1.17731
$508$	19.7291	0.875337
$509$	−19.2873	−0.854895	−0.427447	−	0.904040i	$-0.640587\pi$
$509$	−19.2873	−0.854895	−0.427447	+	0.904040i	$0.640587\pi$
$510$	−6.13375	−0.271607
$511$	−12.6712	−0.560541
$512$	23.5622	1.04131
$513$	91.5049	4.04004
$514$	40.2360	1.77473
$515$	−5.25289	−0.231470
$516$	31.9477	1.40642
$517$	41.9313	1.84413
$518$	−1.63071	−0.0716491
$519$	42.2668	1.85531
$520$	−2.22815	−0.0977109
$521$	12.6987	0.556339	0.278169	−	0.960532i	$-0.410272\pi$
$521$	12.6987	0.556339	0.278169	+	0.960532i	$0.410272\pi$
$522$	−27.8681	−1.21975
$523$	3.61701	0.158161	0.0790805	−	0.996868i	$-0.474802\pi$
$523$	3.61701	0.158161	0.0790805	+	0.996868i	$0.474802\pi$
$524$	−24.9144	−1.08839
$525$	17.8453	0.778834
$526$	−37.2348	−1.62351
$527$	4.78338	0.208367
$528$	70.6861	3.07622
$529$	−22.0228	−0.957512
$530$	7.95230	0.345426
$531$	−6.83035	−0.296412
$532$	−16.3170	−0.707431
$533$	−2.02048	−0.0875166
$534$	23.8480	1.03200
$535$	−6.75475	−0.292033
$536$	1.81981	0.0786040
$537$	45.2257	1.95163
$538$	53.9707	2.32684
$539$	−22.9333	−0.987806
$540$	18.4982	0.796035
$541$	−43.5899	−1.87408	−0.937038	−	0.349228i	$-0.886444\pi$
$541$	−43.5899	−1.87408	−0.937038	+	0.349228i	$0.886444\pi$
$542$	24.9685	1.07249
$543$	−39.7480	−1.70575
$544$	6.91529	0.296491
$545$	−13.5284	−0.579494
$546$	18.1806	0.778057
$547$	−14.8572	−0.635247	−0.317624	−	0.948217i	$-0.602885\pi$
$547$	−14.8572	−0.635247	−0.317624	+	0.948217i	$0.602885\pi$
$548$	−24.4816	−1.04580
$549$	−14.9439	−0.637791
$550$	−34.1845	−1.45763
$551$	16.6989	0.711396
$552$	−3.08256	−0.131203
$553$	20.1696	0.857700
$554$	−50.6045	−2.14998
$555$	−1.97537	−0.0838498
$556$	28.8850	1.22500
$557$	38.1052	1.61457	0.807284	−	0.590163i	$-0.200936\pi$
$557$	38.1052	1.61457	0.807284	+	0.590163i	$0.200936\pi$
$558$	−60.8243	−2.57490
$559$	14.8204	0.626838
$560$	7.34349	0.310319
$561$	14.7784	0.623945
$562$	−38.0810	−1.60635
$563$	38.7880	1.63472	0.817359	−	0.576128i	$-0.195437\pi$
$563$	38.7880	1.63472	0.817359	+	0.576128i	$0.195437\pi$
$564$	−40.8830	−1.72148
$565$	5.24765	0.220770
$566$	41.7874	1.75646
$567$	25.0748	1.05304
$568$	−4.47028	−0.187569
$569$	33.6397	1.41025	0.705124	−	0.709084i	$-0.250891\pi$
$569$	33.6397	1.41025	0.705124	+	0.709084i	$0.250891\pi$
$570$	−46.7356	−1.95754
$571$	−12.9672	−0.542660	−0.271330	−	0.962486i	$-0.587463\pi$
$571$	−12.9672	−0.542660	−0.271330	+	0.962486i	$0.587463\pi$
$572$	−14.7291	−0.615856
$573$	−69.7081	−2.91210
$574$	2.57773	0.107592
$575$	3.85106	0.160601
$576$	−22.5932	−0.941384
$577$	24.0110	0.999592	0.499796	−	0.866143i	$-0.333408\pi$
$577$	24.0110	0.999592	0.499796	+	0.866143i	$0.333408\pi$
$578$	1.86166	0.0774347
$579$	−68.3948	−2.84239
$580$	3.37576	0.140171
$581$	−13.7108	−0.568819
$582$	24.7332	1.02522
$583$	−19.1600	−0.793524
$584$	8.62574	0.356936
$585$	15.3022	0.632670
$586$	−43.4583	−1.79524
$587$	−25.4078	−1.04869	−0.524346	−	0.851505i	$-0.675690\pi$
$587$	−25.4078	−1.04869	−0.524346	+	0.851505i	$0.675690\pi$
$588$	22.3599	0.922109
$589$	36.4466	1.50176
$590$	1.95633	0.0805408
$591$	46.9408	1.93089
$592$	2.86766	0.117860
$593$	44.8433	1.84149	0.920746	−	0.390162i	$-0.127581\pi$
$593$	44.8433	1.84149	0.920746	+	0.390162i	$0.127581\pi$
$594$	−105.382	−4.32387
$595$	1.53531	0.0629416
$596$	−24.9417	−1.02165
$597$	−4.99486	−0.204426
$598$	3.92341	0.160440
$599$	−38.8792	−1.58856	−0.794280	−	0.607552i	$-0.792152\pi$
$599$	−38.8792	−1.58856	−0.794280	+	0.607552i	$0.792152\pi$
$600$	−12.1480	−0.495938
$601$	−19.1995	−0.783163	−0.391582	−	0.920143i	$-0.628072\pi$
$601$	−19.1995	−0.783163	−0.391582	+	0.920143i	$0.628072\pi$
$602$	−18.9080	−0.770632
$603$	−12.4979	−0.508954
$604$	6.85723	0.279017
$605$	−11.7875	−0.479231
$606$	27.4487	1.11503
$607$	9.52382	0.386560	0.193280	−	0.981144i	$-0.438087\pi$
$607$	9.52382	0.386560	0.193280	+	0.981144i	$0.438087\pi$
$608$	52.6905	2.13688
$609$	10.0393	0.406814
$610$	4.28020	0.173300
$611$	−18.9655	−0.767261
$612$	−10.0117	−0.404698
$613$	−18.4205	−0.743996	−0.371998	−	0.928233i	$-0.621327\pi$
$613$	−18.4205	−0.743996	−0.371998	+	0.928233i	$0.621327\pi$
$614$	−50.1922	−2.02559
$615$	3.12256	0.125914
$616$	−6.84905	−0.275956
$617$	−22.7535	−0.916023	−0.458011	−	0.888946i	$-0.651438\pi$
$617$	−22.7535	−0.916023	−0.458011	+	0.888946i	$0.651438\pi$
$618$	−29.1769	−1.17367
$619$	18.7386	0.753167	0.376583	−	0.926383i	$-0.377099\pi$
$619$	18.7386	0.753167	0.376583	+	0.926383i	$0.377099\pi$
$620$	7.36786	0.295900
$621$	11.8718	0.476400
$622$	14.4537	0.579540
$623$	−5.96929	−0.239154
$624$	−31.9713	−1.27988
$625$	9.65506	0.386203
$626$	−27.3610	−1.09357
$627$	112.603	4.49693
$628$	−4.43746	−0.177074
$629$	0.599545	0.0239054
$630$	−19.5226	−0.777801
$631$	34.4639	1.37199	0.685993	−	0.727608i	$-0.259368\pi$
$631$	34.4639	1.37199	0.685993	+	0.727608i	$0.259368\pi$
$632$	−13.7302	−0.546158
$633$	9.09882	0.361646
$634$	−37.3232	−1.48229
$635$	−14.1444	−0.561304
$636$	18.6810	0.740748
$637$	10.3727	0.410981
$638$	−19.2313	−0.761374
$639$	30.7005	1.21449
$640$	−8.06284	−0.318712
$641$	5.74692	0.226990	0.113495	−	0.993539i	$-0.463795\pi$
$641$	5.74692	0.226990	0.113495	+	0.993539i	$0.463795\pi$
$642$	−37.5190	−1.48076
$643$	−23.6196	−0.931465	−0.465732	−	0.884926i	$-0.654209\pi$
$643$	−23.6196	−0.931465	−0.465732	+	0.884926i	$0.654209\pi$
$644$	−2.11696	−0.0834199
$645$	−22.9044	−0.901858
$646$	14.1847	0.558091
$647$	14.7551	0.580084	0.290042	−	0.957014i	$-0.406331\pi$
$647$	14.7551	0.580084	0.290042	+	0.957014i	$0.406331\pi$
$648$	−17.0693	−0.670546
$649$	−4.71350	−0.185021
$650$	15.4616	0.606455
$651$	21.9116	0.858782
$652$	−18.9612	−0.742578
$653$	−37.9005	−1.48316	−0.741580	−	0.670865i	$-0.765923\pi$
$653$	−37.9005	−1.48316	−0.741580	+	0.670865i	$0.765923\pi$
$654$	−75.1431	−2.93833
$655$	17.8619	0.697924
$656$	−4.53305	−0.176986
$657$	−59.2388	−2.31113
$658$	24.1962	0.943267
$659$	−48.2938	−1.88126	−0.940630	−	0.339433i	$-0.889765\pi$
$659$	−48.2938	−1.88126	−0.940630	+	0.339433i	$0.889765\pi$
$660$	22.7633	0.886059
$661$	−4.06806	−0.158229	−0.0791146	−	0.996866i	$-0.525209\pi$
$661$	−4.06806	−0.158229	−0.0791146	+	0.996866i	$0.525209\pi$
$662$	60.5664	2.35398
$663$	−6.68427	−0.259596
$664$	9.33341	0.362207
$665$	11.6982	0.453636
$666$	−7.62367	−0.295411
$667$	2.16651	0.0838875
$668$	−19.6027	−0.758453
$669$	27.0643	1.04636
$670$	3.57961	0.138293
$671$	−10.3125	−0.398111
$672$	31.6774	1.22198
$673$	35.4269	1.36561	0.682803	−	0.730602i	$-0.260761\pi$
$673$	35.4269	1.36561	0.682803	+	0.730602i	$0.260761\pi$
$674$	−11.4522	−0.441122
$675$	46.7852	1.80076
$676$	−12.3929	−0.476652
$677$	−9.95542	−0.382618	−0.191309	−	0.981530i	$-0.561273\pi$
$677$	−9.95542	−0.382618	−0.191309	+	0.981530i	$0.561273\pi$
$678$	29.1479	1.11942
$679$	−6.19084	−0.237583
$680$	−1.04514	−0.0400793
$681$	−60.1464	−2.30482
$682$	−41.9738	−1.60726
$683$	36.3048	1.38916	0.694582	−	0.719414i	$-0.255590\pi$
$683$	36.3048	1.38916	0.694582	+	0.719414i	$0.255590\pi$
$684$	−76.2832	−2.91676
$685$	17.5516	0.670613
$686$	−32.2729	−1.23218
$687$	−80.4496	−3.06934
$688$	33.2505	1.26766
$689$	8.66604	0.330150
$690$	−6.06346	−0.230832
$691$	23.4847	0.893400	0.446700	−	0.894684i	$-0.352599\pi$
$691$	23.4847	0.893400	0.446700	+	0.894684i	$0.352599\pi$
$692$	−19.7596	−0.751149
$693$	47.0371	1.78679
$694$	27.3348	1.03762
$695$	−20.7086	−0.785522
$696$	−6.83412	−0.259047
$697$	−0.947729	−0.0358978
$698$	−16.9108	−0.640082
$699$	−20.7315	−0.784137
$700$	−8.34266	−0.315323
$701$	19.1126	0.721872	0.360936	−	0.932591i	$-0.382457\pi$
$701$	19.1126	0.721872	0.360936	+	0.932591i	$0.382457\pi$
$702$	47.6642	1.79897
$703$	4.56819	0.172292
$704$	−15.5912	−0.587615
$705$	29.3103	1.10389
$706$	−37.6822	−1.41819
$707$	−6.87055	−0.258394
$708$	4.59567	0.172716
$709$	−26.9364	−1.01162	−0.505810	−	0.862645i	$-0.668806\pi$
$709$	−26.9364	−1.01162	−0.505810	+	0.862645i	$0.668806\pi$
$710$	−8.79314	−0.330001
$711$	94.2946	3.53632
$712$	4.06351	0.152286
$713$	4.72857	0.177086
$714$	8.52782	0.319146
$715$	10.5598	0.394914
$716$	−21.1429	−0.790147
$717$	−85.6227	−3.19764
$718$	26.3167	0.982130
$719$	−46.4310	−1.73158	−0.865792	−	0.500404i	$-0.833185\pi$
$719$	−46.4310	−1.73158	−0.865792	+	0.500404i	$0.833185\pi$
$720$	34.3314	1.27945
$721$	7.30315	0.271983
$722$	72.7080	2.70591
$723$	−18.1587	−0.675328
$724$	18.5821	0.690599
$725$	8.53791	0.317090
$726$	−65.4733	−2.42994
$727$	7.87108	0.291922	0.145961	−	0.989290i	$-0.453373\pi$
$727$	7.87108	0.291922	0.145961	+	0.989290i	$0.453373\pi$
$728$	3.09782	0.114813
$729$	4.26564	0.157987
$730$	16.9670	0.627977
$731$	6.95171	0.257118
$732$	10.0547	0.371634
$733$	−45.2186	−1.67019	−0.835093	−	0.550108i	$-0.814587\pi$
$733$	−45.2186	−1.67019	−0.835093	+	0.550108i	$0.814587\pi$
$734$	−64.7297	−2.38922
$735$	−16.0306	−0.591296
$736$	6.83605	0.251980
$737$	−8.62458	−0.317691
$738$	12.0511	0.443607
$739$	10.1503	0.373386	0.186693	−	0.982418i	$-0.440223\pi$
$739$	10.1503	0.373386	0.186693	+	0.982418i	$0.440223\pi$
$740$	0.923481	0.0339478
$741$	−50.9303	−1.87097
$742$	−11.0562	−0.405884
$743$	−18.3832	−0.674416	−0.337208	−	0.941430i	$-0.609483\pi$
$743$	−18.3832	−0.674416	−0.337208	+	0.941430i	$0.609483\pi$
$744$	−14.9160	−0.546847
$745$	17.8815	0.655129
$746$	−25.0256	−0.916254
$747$	−64.0989	−2.34526
$748$	−6.90888	−0.252614
$749$	9.39120	0.343147
$750$	−54.5641	−1.99240
$751$	−29.2434	−1.06711	−0.533554	−	0.845766i	$-0.679144\pi$
$751$	−29.2434	−1.06711	−0.533554	+	0.845766i	$0.679144\pi$
$752$	−42.5501	−1.55164
$753$	−26.2726	−0.957427
$754$	8.69831	0.316774
$755$	−4.91617	−0.178918
$756$	−25.7182	−0.935362
$757$	12.3506	0.448890	0.224445	−	0.974487i	$-0.427943\pi$
$757$	12.3506	0.448890	0.224445	+	0.974487i	$0.427943\pi$
$758$	32.9599	1.19716
$759$	14.6091	0.530276
$760$	−7.96337	−0.288862
$761$	−17.5867	−0.637519	−0.318759	−	0.947836i	$-0.603266\pi$
$761$	−17.5867	−0.637519	−0.318759	+	0.947836i	$0.603266\pi$
$762$	−78.5646	−2.84609
$763$	18.8087	0.680921
$764$	32.5884	1.17901
$765$	7.17770	0.259510
$766$	7.31920	0.264454
$767$	2.13191	0.0769790
$768$	−65.5267	−2.36449
$769$	15.9878	0.576534	0.288267	−	0.957550i	$-0.406921\pi$
$769$	15.9878	0.576534	0.288267	+	0.957550i	$0.406921\pi$
$770$	−13.4722	−0.485505
$771$	−67.7640	−2.44046
$772$	31.9744	1.15079
$773$	−31.3297	−1.12685	−0.563426	−	0.826166i	$-0.690517\pi$
$773$	−31.3297	−1.12685	−0.563426	+	0.826166i	$0.690517\pi$
$774$	−88.3962	−3.17734
$775$	18.6347	0.669376
$776$	4.21433	0.151286
$777$	2.74638	0.0985258
$778$	13.7920	0.494467
$779$	−7.22115	−0.258724
$780$	−10.2958	−0.368649
$781$	21.1858	0.758089
$782$	1.84032	0.0658098
$783$	26.3201	0.940605
$784$	23.2717	0.831133
$785$	3.18136	0.113548
$786$	99.2134	3.53882
$787$	11.5340	0.411144	0.205572	−	0.978642i	$-0.434095\pi$
$787$	11.5340	0.411144	0.205572	+	0.978642i	$0.434095\pi$
$788$	−21.9447	−0.781749
$789$	62.7095	2.23252
$790$	−27.0076	−0.960887
$791$	−7.29586	−0.259411
$792$	−32.0198	−1.13778
$793$	4.66436	0.165636
$794$	5.75001	0.204060
$795$	−13.3930	−0.475000
$796$	2.33509	0.0827650
$797$	−10.4376	−0.369719	−0.184859	−	0.982765i	$-0.559183\pi$
$797$	−10.4376	−0.369719	−0.184859	+	0.982765i	$0.559183\pi$
$798$	64.9770	2.30016
$799$	−8.89599	−0.314717
$800$	26.9400	0.952471
$801$	−27.9069	−0.986041
$802$	−44.8186	−1.58260
$803$	−40.8796	−1.44261
$804$	8.40897	0.296562
$805$	1.51772	0.0534925
$806$	18.9847	0.668708
$807$	−90.8956	−3.19968
$808$	4.67703	0.164537
$809$	15.6064	0.548690	0.274345	−	0.961631i	$-0.411539\pi$
$809$	15.6064	0.548690	0.274345	+	0.961631i	$0.411539\pi$
$810$	−33.5757	−1.17973
$811$	−1.21834	−0.0427819	−0.0213909	−	0.999771i	$-0.506809\pi$
$811$	−1.21834	−0.0427819	−0.0213909	+	0.999771i	$0.506809\pi$
$812$	−4.69336	−0.164705
$813$	−42.0511	−1.47480
$814$	−5.26096	−0.184397
$815$	13.5939	0.476174
$816$	−14.9965	−0.524983
$817$	52.9680	1.85311
$818$	62.7165	2.19283
$819$	−21.2749	−0.743404
$820$	−1.45979	−0.0509781
$821$	28.0619	0.979368	0.489684	−	0.871900i	$-0.337112\pi$
$821$	28.0619	0.979368	0.489684	+	0.871900i	$0.337112\pi$
$822$	97.4897	3.40034
$823$	7.76388	0.270632	0.135316	−	0.990803i	$-0.456795\pi$
$823$	7.76388	0.270632	0.135316	+	0.990803i	$0.456795\pi$
$824$	−4.97151	−0.173191
$825$	57.5724	2.00441
$826$	−2.71990	−0.0946376
$827$	33.4556	1.16337	0.581683	−	0.813416i	$-0.302394\pi$
$827$	33.4556	1.16337	0.581683	+	0.813416i	$0.302394\pi$
$828$	−9.89695	−0.343943
$829$	−49.5457	−1.72079	−0.860397	−	0.509625i	$-0.829784\pi$
$829$	−49.5457	−1.72079	−0.860397	+	0.509625i	$0.829784\pi$
$830$	18.3590	0.637251
$831$	85.2263	2.95647
$832$	7.05188	0.244480
$833$	4.86544	0.168578
$834$	−115.025	−3.98299
$835$	14.0538	0.486353
$836$	−52.6417	−1.82065
$837$	57.4457	1.98561
$838$	51.6549	1.78439
$839$	−50.8317	−1.75491	−0.877453	−	0.479663i	$-0.840759\pi$
$839$	−50.8317	−1.75491	−0.877453	+	0.479663i	$0.840759\pi$
$840$	−4.78755	−0.165186
$841$	−24.1968	−0.834372
$842$	−22.4250	−0.772817
$843$	64.1348	2.20892
$844$	−4.25368	−0.146418
$845$	8.88491	0.305650
$846$	113.119	3.88912
$847$	16.3883	0.563109
$848$	19.4427	0.667666
$849$	−70.3769	−2.41533
$850$	7.25247	0.248758
$851$	0.592675	0.0203166
$852$	−20.6562	−0.707670
$853$	33.4238	1.14441	0.572204	−	0.820111i	$-0.306088\pi$
$853$	33.4238	1.14441	0.572204	+	0.820111i	$0.306088\pi$
$854$	−5.95080	−0.203632
$855$	54.6899	1.87035
$856$	−6.39292	−0.218506
$857$	23.6064	0.806379	0.403190	−	0.915116i	$-0.367901\pi$
$857$	23.6064	0.806379	0.403190	+	0.915116i	$0.367901\pi$
$858$	58.6540	2.00241
$859$	−2.75601	−0.0940338	−0.0470169	−	0.998894i	$-0.514971\pi$
$859$	−2.75601	−0.0940338	−0.0470169	+	0.998894i	$0.514971\pi$
$860$	10.7077	0.365131
$861$	−4.34133	−0.147952
$862$	17.1161	0.582978
$863$	−18.3951	−0.626178	−0.313089	−	0.949724i	$-0.601364\pi$
$863$	−18.3951	−0.626178	−0.313089	+	0.949724i	$0.601364\pi$
$864$	83.0488	2.82538
$865$	14.1663	0.481669
$866$	56.9065	1.93376
$867$	−3.13534	−0.106482
$868$	−10.2436	−0.347691
$869$	65.0710	2.20738
$870$	−13.4429	−0.455756
$871$	3.90089	0.132177
$872$	−12.8038	−0.433590
$873$	−28.9427	−0.979561
$874$	14.0222	0.474308
$875$	13.6577	0.461714
$876$	39.8577	1.34667
$877$	37.4582	1.26487	0.632437	−	0.774612i	$-0.282055\pi$
$877$	37.4582	1.26487	0.632437	+	0.774612i	$0.282055\pi$
$878$	−55.8447	−1.88467
$879$	73.1909	2.46867
$880$	23.6915	0.798639
$881$	−3.62861	−0.122251	−0.0611254	−	0.998130i	$-0.519469\pi$
$881$	−3.62861	−0.122251	−0.0611254	+	0.998130i	$0.519469\pi$
$882$	−61.8678	−2.08320
$883$	3.39122	0.114124	0.0570619	−	0.998371i	$-0.481827\pi$
$883$	3.39122	0.114124	0.0570619	+	0.998371i	$0.481827\pi$
$884$	3.12488	0.105101
$885$	−3.29478	−0.110753
$886$	46.9399	1.57698
$887$	27.4896	0.923011	0.461506	−	0.887137i	$-0.347309\pi$
$887$	27.4896	0.923011	0.461506	+	0.887137i	$0.347309\pi$
$888$	−1.86956	−0.0627383
$889$	19.6651	0.659548
$890$	7.99301	0.267926
$891$	80.8960	2.71012
$892$	−12.6525	−0.423636
$893$	−67.7823	−2.26825
$894$	99.3223	3.32183
$895$	15.1580	0.506677
$896$	11.2098	0.374495
$897$	−6.60768	−0.220624
$898$	−19.1552	−0.639218
$899$	10.4834	0.349640
$900$	−39.0026	−1.30009
$901$	4.06491	0.135422
$902$	8.31625	0.276901
$903$	31.8442	1.05971
$904$	4.96656	0.165185
$905$	−13.3221	−0.442842
$906$	−27.3067	−0.907203
$907$	−8.27934	−0.274911	−0.137455	−	0.990508i	$-0.543892\pi$
$907$	−8.27934	−0.274911	−0.137455	+	0.990508i	$0.543892\pi$
$908$	28.1183	0.933140
$909$	−32.1203	−1.06536
$910$	6.09348	0.201997
$911$	19.8604	0.658004	0.329002	−	0.944329i	$-0.393288\pi$
$911$	19.8604	0.658004	0.329002	+	0.944329i	$0.393288\pi$
$912$	−114.265	−3.78369
$913$	−44.2335	−1.46392
$914$	−14.4199	−0.476968
$915$	−7.20856	−0.238308
$916$	37.6100	1.24267
$917$	−24.8336	−0.820079
$918$	22.3574	0.737906
$919$	−27.3839	−0.903312	−0.451656	−	0.892192i	$-0.649167\pi$
$919$	−27.3839	−0.903312	−0.451656	+	0.892192i	$0.649167\pi$
$920$	−1.03316	−0.0340624
$921$	84.5320	2.78542
$922$	−61.5793	−2.02801
$923$	−9.58235	−0.315407
$924$	−31.6480	−1.04114
$925$	2.33565	0.0767958
$926$	−13.0460	−0.428720
$927$	34.1428	1.12140
$928$	15.1557	0.497510
$929$	−4.99697	−0.163945	−0.0819726	−	0.996635i	$-0.526122\pi$
$929$	−4.99697	−0.163945	−0.0819726	+	0.996635i	$0.526122\pi$
$930$	−29.3401	−0.962099
$931$	37.0718	1.21498
$932$	9.69193	0.317470
$933$	−24.3424	−0.796934
$934$	−55.0297	−1.80063
$935$	4.95320	0.161987
$936$	14.4826	0.473377
$937$	−28.9988	−0.947350	−0.473675	−	0.880700i	$-0.657073\pi$
$937$	−28.9988	−0.947350	−0.473675	+	0.880700i	$0.657073\pi$
$938$	−4.97678	−0.162497
$939$	46.0805	1.50378
$940$	−13.7025	−0.446927
$941$	28.2446	0.920748	0.460374	−	0.887725i	$-0.347715\pi$
$941$	28.2446	0.920748	0.460374	+	0.887725i	$0.347715\pi$
$942$	17.6707	0.575743
$943$	−0.936869	−0.0305087
$944$	4.78306	0.155675
$945$	18.4382	0.599795
$946$	−61.0007	−1.98330
$947$	24.3308	0.790644	0.395322	−	0.918543i	$-0.370633\pi$
$947$	24.3308	0.790644	0.395322	+	0.918543i	$0.370633\pi$
$948$	−63.4443	−2.06057
$949$	18.4898	0.600206
$950$	55.2596	1.79286
$951$	62.8585	2.03833
$952$	1.45307	0.0470943
$953$	2.79774	0.0906278	0.0453139	−	0.998973i	$-0.485571\pi$
$953$	2.79774	0.0906278	0.0453139	+	0.998973i	$0.485571\pi$
$954$	−51.6884	−1.67347
$955$	−23.3637	−0.756030
$956$	40.0284	1.29461
$957$	32.3887	1.04698
$958$	16.3979	0.529793
$959$	−24.4022	−0.787988
$960$	−10.8984	−0.351744
$961$	−8.11926	−0.261912
$962$	2.37953	0.0767191
$963$	43.9046	1.41480
$964$	8.48913	0.273417
$965$	−22.9235	−0.737934
$966$	8.43010	0.271234
$967$	2.20344	0.0708578	0.0354289	−	0.999372i	$-0.488720\pi$
$967$	2.20344	0.0708578	0.0354289	+	0.999372i	$0.488720\pi$
$968$	−11.1561	−0.358571
$969$	−23.8895	−0.767440
$970$	8.28967	0.266165
$971$	−9.02502	−0.289627	−0.144813	−	0.989459i	$-0.546258\pi$
$971$	−9.02502	−0.289627	−0.144813	+	0.989459i	$0.546258\pi$
$972$	−26.0646	−0.836023
$973$	28.7914	0.923010
$974$	38.4711	1.23269
$975$	−26.0400	−0.833946
$976$	10.4647	0.334968
$977$	−28.1144	−0.899461	−0.449730	−	0.893164i	$-0.648480\pi$
$977$	−28.1144	−0.899461	−0.449730	+	0.893164i	$0.648480\pi$
$978$	75.5068	2.41444
$979$	−19.2580	−0.615489
$980$	7.49426	0.239395
$981$	87.9322	2.80746
$982$	−44.3424	−1.41502
$983$	17.1272	0.546274	0.273137	−	0.961975i	$-0.411939\pi$
$983$	17.1272	0.546274	0.273137	+	0.961975i	$0.411939\pi$
$984$	2.95530	0.0942115
$985$	15.7329	0.501292
$986$	4.08005	0.129935
$987$	−40.7505	−1.29710
$988$	23.8098	0.757491
$989$	6.87205	0.218518
$990$	−62.9837	−2.00175
$991$	−19.0882	−0.606357	−0.303178	−	0.952934i	$-0.598048\pi$
$991$	−19.0882	−0.606357	−0.303178	+	0.952934i	$0.598048\pi$
$992$	33.0785	1.05024
$993$	−102.004	−3.23699
$994$	12.2252	0.387760
$995$	−1.67410	−0.0530725
$996$	43.1277	1.36655
$997$	28.4245	0.900211	0.450106	−	0.892975i	$-0.351386\pi$
$997$	28.4245	0.900211	0.450106	+	0.892975i	$0.351386\pi$
$998$	−81.6472	−2.58450
$999$	7.20020	0.227804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.g.1.8	✓	10
3.2	odd	2		9027.2.a.j.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.g.1.8	✓	10	1.1	even	1	trivial
9027.2.a.j.1.3		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q+1.86166 q^{2} -3.13534 q^{3} +1.46576 q^{4} -1.05085 q^{5} -5.83692 q^{6} +1.46101 q^{7} -0.994564 q^{8} +6.83035 q^{9} +O(q^{10})\)	\(q+1.86166 q^{2} -3.13534 q^{3} +1.46576 q^{4} -1.05085 q^{5} -5.83692 q^{6} +1.46101 q^{7} -0.994564 q^{8} +6.83035 q^{9} -1.95633 q^{10} +4.71350 q^{11} -4.59567 q^{12} -2.13191 q^{13} +2.71990 q^{14} +3.29478 q^{15} -4.78306 q^{16} -1.00000 q^{17} +12.7158 q^{18} -7.61942 q^{19} -1.54030 q^{20} -4.58077 q^{21} +8.77492 q^{22} -0.988541 q^{23} +3.11829 q^{24} -3.89571 q^{25} -3.96889 q^{26} -12.0094 q^{27} +2.14150 q^{28} -2.19162 q^{29} +6.13375 q^{30} -4.78338 q^{31} -6.91529 q^{32} -14.7784 q^{33} -1.86166 q^{34} -1.53531 q^{35} +10.0117 q^{36} -0.599545 q^{37} -14.1847 q^{38} +6.68427 q^{39} +1.04514 q^{40} +0.947729 q^{41} -8.52782 q^{42} -6.95171 q^{43} +6.90888 q^{44} -7.17770 q^{45} -1.84032 q^{46} +8.89599 q^{47} +14.9965 q^{48} -4.86544 q^{49} -7.25247 q^{50} +3.13534 q^{51} -3.12488 q^{52} -4.06491 q^{53} -22.3574 q^{54} -4.95320 q^{55} -1.45307 q^{56} +23.8895 q^{57} -4.08005 q^{58} -1.00000 q^{59} +4.82937 q^{60} -2.18787 q^{61} -8.90501 q^{62} +9.97923 q^{63} -3.30777 q^{64} +2.24033 q^{65} -27.5123 q^{66} -1.82976 q^{67} -1.46576 q^{68} +3.09941 q^{69} -2.85822 q^{70} +4.49471 q^{71} -6.79322 q^{72} -8.67288 q^{73} -1.11615 q^{74} +12.2144 q^{75} -11.1683 q^{76} +6.88649 q^{77} +12.4438 q^{78} +13.8052 q^{79} +5.02630 q^{80} +17.1626 q^{81} +1.76435 q^{82} -9.38443 q^{83} -6.71433 q^{84} +1.05085 q^{85} -12.9417 q^{86} +6.87148 q^{87} -4.68788 q^{88} -4.08572 q^{89} -13.3624 q^{90} -3.11475 q^{91} -1.44897 q^{92} +14.9975 q^{93} +16.5613 q^{94} +8.00689 q^{95} +21.6818 q^{96} -4.23736 q^{97} -9.05778 q^{98} +32.1949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9 + 4 * q^10 + 12 * q^11 - 24 * q^12 - 11 * q^13 - 12 * q^14 + 9 * q^15 - 3 * q^16 - 10 * q^17 - 22 * q^18 - 5 * q^19 - 36 * q^20 - 10 * q^21 + 6 * q^22 - 7 * q^23 + 35 * q^24 + 2 * q^25 + q^26 - 31 * q^27 - 4 * q^28 + 10 * q^29 - 9 * q^30 + 13 * q^31 - 15 * q^32 - 9 * q^33 + q^34 - 8 * q^35 + 40 * q^36 + 12 * q^37 - 50 * q^38 + 24 * q^39 + 5 * q^40 - 29 * q^41 - 17 * q^42 - 18 * q^43 - 6 * q^44 - 14 * q^45 + 11 * q^46 - 18 * q^47 - 43 * q^48 - 9 * q^49 - 31 * q^50 + 7 * q^51 - 68 * q^52 + 19 * q^54 - 27 * q^55 - 7 * q^56 + 20 * q^57 + 23 * q^58 - 10 * q^59 + 38 * q^60 + 8 * q^61 - 46 * q^62 + 39 * q^63 - 20 * q^64 + 58 * q^65 - 34 * q^66 - 6 * q^67 - 15 * q^68 + 6 * q^69 + 73 * q^70 + 8 * q^71 - 70 * q^72 - 41 * q^73 - 10 * q^74 + 10 * q^75 + 12 * q^76 - 22 * q^77 - 43 * q^78 + 3 * q^79 - 15 * q^80 + 26 * q^81 + 8 * q^82 - 22 * q^84 + 12 * q^85 - 29 * q^86 - 28 * q^87 + 33 * q^88 - 45 * q^89 + 56 * q^90 - 14 * q^91 + 36 * q^92 - 19 * q^93 + 15 * q^94 - 17 * q^95 + 90 * q^96 - 5 * q^97 + 30 * q^98 + 14 * q^99

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