LMFDB - Embedded newform 8003.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, 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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$1$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35186 q^{2} +2.82673 q^{3} +3.53125 q^{4} +2.18646 q^{5} -6.64808 q^{6} +0.649269 q^{7} -3.60130 q^{8} +4.99041 q^{9} +O(q^{10})$	\(q-2.35186 q^{2} +2.82673 q^{3} +3.53125 q^{4} +2.18646 q^{5} -6.64808 q^{6} +0.649269 q^{7} -3.60130 q^{8} +4.99041 q^{9} -5.14224 q^{10} -5.34465 q^{11} +9.98190 q^{12} -0.189937 q^{13} -1.52699 q^{14} +6.18053 q^{15} +1.40724 q^{16} -3.29894 q^{17} -11.7368 q^{18} +1.35877 q^{19} +7.72093 q^{20} +1.83531 q^{21} +12.5699 q^{22} -5.91189 q^{23} -10.1799 q^{24} -0.219405 q^{25} +0.446705 q^{26} +5.62636 q^{27} +2.29273 q^{28} -2.86131 q^{29} -14.5357 q^{30} -0.767405 q^{31} +3.89295 q^{32} -15.1079 q^{33} +7.75866 q^{34} +1.41960 q^{35} +17.6224 q^{36} -7.04121 q^{37} -3.19564 q^{38} -0.536900 q^{39} -7.87408 q^{40} +3.71273 q^{41} -4.31639 q^{42} -0.473048 q^{43} -18.8733 q^{44} +10.9113 q^{45} +13.9040 q^{46} +9.61595 q^{47} +3.97790 q^{48} -6.57845 q^{49} +0.516010 q^{50} -9.32523 q^{51} -0.670715 q^{52} -1.00000 q^{53} -13.2324 q^{54} -11.6859 q^{55} -2.33821 q^{56} +3.84088 q^{57} +6.72941 q^{58} -2.59554 q^{59} +21.8250 q^{60} -3.99537 q^{61} +1.80483 q^{62} +3.24012 q^{63} -11.9702 q^{64} -0.415289 q^{65} +35.5317 q^{66} -3.61822 q^{67} -11.6494 q^{68} -16.7113 q^{69} -3.33870 q^{70} +13.0451 q^{71} -17.9719 q^{72} -9.39429 q^{73} +16.5599 q^{74} -0.620199 q^{75} +4.79817 q^{76} -3.47012 q^{77} +1.26272 q^{78} -2.10091 q^{79} +3.07688 q^{80} +0.932969 q^{81} -8.73183 q^{82} -4.63441 q^{83} +6.48094 q^{84} -7.21300 q^{85} +1.11254 q^{86} -8.08816 q^{87} +19.2477 q^{88} +16.4581 q^{89} -25.6619 q^{90} -0.123320 q^{91} -20.8764 q^{92} -2.16925 q^{93} -22.6154 q^{94} +2.97090 q^{95} +11.0043 q^{96} -10.8351 q^{97} +15.4716 q^{98} -26.6720 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) $ 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * 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 $

$2$	−2.35186	−1.66302	−0.831509	−	0.555512i	$-0.812522\pi$
$2$	−2.35186	−1.66302	−0.831509	+	0.555512i	$0.812522\pi$
$3$	2.82673	1.63201	0.816007	−	0.578042i	$-0.196183\pi$
$3$	2.82673	1.63201	0.816007	+	0.578042i	$0.196183\pi$
$4$	3.53125	1.76563
$5$	2.18646	0.977813	0.488907	−	0.872336i	$-0.337396\pi$
$5$	2.18646	0.977813	0.488907	+	0.872336i	$0.337396\pi$
$6$	−6.64808	−2.71407
$7$	0.649269	0.245401	0.122700	−	0.992444i	$-0.460845\pi$
$7$	0.649269	0.245401	0.122700	+	0.992444i	$0.460845\pi$
$8$	−3.60130	−1.27325
$9$	4.99041	1.66347
$10$	−5.14224	−1.62612
$11$	−5.34465	−1.61147	−0.805736	−	0.592274i	$-0.798230\pi$
$11$	−5.34465	−1.61147	−0.805736	+	0.592274i	$0.798230\pi$
$12$	9.98190	2.88153
$13$	−0.189937	−0.0526790	−0.0263395	−	0.999653i	$-0.508385\pi$
$13$	−0.189937	−0.0526790	−0.0263395	+	0.999653i	$0.508385\pi$
$14$	−1.52699	−0.408105
$15$	6.18053	1.59581
$16$	1.40724	0.351811
$17$	−3.29894	−0.800112	−0.400056	−	0.916491i	$-0.631009\pi$
$17$	−3.29894	−0.800112	−0.400056	+	0.916491i	$0.631009\pi$
$18$	−11.7368	−2.76638
$19$	1.35877	0.311724	0.155862	−	0.987779i	$-0.450185\pi$
$19$	1.35877	0.311724	0.155862	+	0.987779i	$0.450185\pi$
$20$	7.72093	1.72645
$21$	1.83531	0.400497
$22$	12.5699	2.67991
$23$	−5.91189	−1.23271	−0.616357	−	0.787467i	$-0.711392\pi$
$23$	−5.91189	−1.23271	−0.616357	+	0.787467i	$0.711392\pi$
$24$	−10.1799	−2.07796
$25$	−0.219405	−0.0438810
$26$	0.446705	0.0876061
$27$	5.62636	1.08279
$28$	2.29273	0.433286
$29$	−2.86131	−0.531332	−0.265666	−	0.964065i	$-0.585592\pi$
$29$	−2.86131	−0.531332	−0.265666	+	0.964065i	$0.585592\pi$
$30$	−14.5357	−2.65385
$31$	−0.767405	−0.137830	−0.0689150	−	0.997623i	$-0.521954\pi$
$31$	−0.767405	−0.137830	−0.0689150	+	0.997623i	$0.521954\pi$
$32$	3.89295	0.688183
$33$	−15.1079	−2.62995
$34$	7.75866	1.33060
$35$	1.41960	0.239956
$36$	17.6224	2.93707
$37$	−7.04121	−1.15757	−0.578784	−	0.815481i	$-0.696472\pi$
$37$	−7.04121	−1.15757	−0.578784	+	0.815481i	$0.696472\pi$
$38$	−3.19564	−0.518402
$39$	−0.536900	−0.0859729
$40$	−7.87408	−1.24500
$41$	3.71273	0.579831	0.289916	−	0.957052i	$-0.406373\pi$
$41$	3.71273	0.579831	0.289916	+	0.957052i	$0.406373\pi$
$42$	−4.31639	−0.666034
$43$	−0.473048	−0.0721391	−0.0360696	−	0.999349i	$-0.511484\pi$
$43$	−0.473048	−0.0721391	−0.0360696	+	0.999349i	$0.511484\pi$
$44$	−18.8733	−2.84526
$45$	10.9113	1.62656
$46$	13.9040	2.05003
$47$	9.61595	1.40263	0.701315	−	0.712852i	$-0.252597\pi$
$47$	9.61595	1.40263	0.701315	+	0.712852i	$0.252597\pi$
$48$	3.97790	0.574160
$49$	−6.57845	−0.939779
$50$	0.516010	0.0729748
$51$	−9.32523	−1.30579
$52$	−0.670715	−0.0930115
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−13.2324	−1.80070
$55$	−11.6859	−1.57572
$56$	−2.33821	−0.312456
$57$	3.84088	0.508737
$58$	6.72941	0.883614
$59$	−2.59554	−0.337911	−0.168956	−	0.985624i	$-0.554039\pi$
$59$	−2.59554	−0.337911	−0.168956	+	0.985624i	$0.554039\pi$
$60$	21.8250	2.81760
$61$	−3.99537	−0.511555	−0.255778	−	0.966736i	$-0.582332\pi$
$61$	−3.99537	−0.511555	−0.255778	+	0.966736i	$0.582332\pi$
$62$	1.80483	0.229214
$63$	3.24012	0.408217
$64$	−11.9702	−1.49627
$65$	−0.415289	−0.0515102
$66$	35.5317	4.37365
$67$	−3.61822	−0.442036	−0.221018	−	0.975270i	$-0.570938\pi$
$67$	−3.61822	−0.442036	−0.221018	+	0.975270i	$0.570938\pi$
$68$	−11.6494	−1.41270
$69$	−16.7113	−2.01181
$70$	−3.33870	−0.399051
$71$	13.0451	1.54816	0.774082	−	0.633085i	$-0.218212\pi$
$71$	13.0451	1.54816	0.774082	+	0.633085i	$0.218212\pi$
$72$	−17.9719	−2.11801
$73$	−9.39429	−1.09952	−0.549759	−	0.835323i	$-0.685281\pi$
$73$	−9.39429	−1.09952	−0.549759	+	0.835323i	$0.685281\pi$
$74$	16.5599	1.92505
$75$	−0.620199	−0.0716144
$76$	4.79817	0.550387
$77$	−3.47012	−0.395456
$78$	1.26272	0.142974
$79$	−2.10091	−0.236371	−0.118186	−	0.992992i	$-0.537708\pi$
$79$	−2.10091	−0.236371	−0.118186	+	0.992992i	$0.537708\pi$
$80$	3.07688	0.344005
$81$	0.932969	0.103663
$82$	−8.73183	−0.964269
$83$	−4.63441	−0.508692	−0.254346	−	0.967113i	$-0.581860\pi$
$83$	−4.63441	−0.508692	−0.254346	+	0.967113i	$0.581860\pi$
$84$	6.48094	0.707129
$85$	−7.21300	−0.782360
$86$	1.11254	0.119969
$87$	−8.08816	−0.867141
$88$	19.2477	2.05181
$89$	16.4581	1.74456	0.872278	−	0.489010i	$-0.162642\pi$
$89$	16.4581	1.74456	0.872278	+	0.489010i	$0.162642\pi$
$90$	−25.6619	−2.70500
$91$	−0.123320	−0.0129275
$92$	−20.8764	−2.17651
$93$	−2.16925	−0.224941
$94$	−22.6154	−2.33260
$95$	2.97090	0.304807
$96$	11.0043	1.12312
$97$	−10.8351	−1.10014	−0.550069	−	0.835119i	$-0.685399\pi$
$97$	−10.8351	−1.10014	−0.550069	+	0.835119i	$0.685399\pi$
$98$	15.4716	1.56287
$99$	−26.6720	−2.68064
$100$	−0.774774	−0.0774774
$101$	18.9357	1.88417	0.942087	−	0.335369i	$-0.108861\pi$
$101$	18.9357	1.88417	0.942087	+	0.335369i	$0.108861\pi$
$102$	21.9317	2.17156
$103$	−5.41593	−0.533647	−0.266823	−	0.963745i	$-0.585974\pi$
$103$	−5.41593	−0.533647	−0.266823	+	0.963745i	$0.585974\pi$
$104$	0.684019	0.0670736
$105$	4.01283	0.391612
$106$	2.35186	0.228433
$107$	14.2897	1.38144	0.690718	−	0.723124i	$-0.257295\pi$
$107$	14.2897	1.38144	0.690718	+	0.723124i	$0.257295\pi$
$108$	19.8681	1.91181
$109$	6.58682	0.630903	0.315452	−	0.948942i	$-0.397844\pi$
$109$	6.58682	0.630903	0.315452	+	0.948942i	$0.397844\pi$
$110$	27.4835	2.62045
$111$	−19.9036	−1.88917
$112$	0.913679	0.0863346
$113$	−4.67125	−0.439434	−0.219717	−	0.975564i	$-0.570513\pi$
$113$	−4.67125	−0.439434	−0.219717	+	0.975564i	$0.570513\pi$
$114$	−9.03322	−0.846039
$115$	−12.9261	−1.20536
$116$	−10.1040	−0.938134
$117$	−0.947863	−0.0876300
$118$	6.10436	0.561952
$119$	−2.14190	−0.196348
$120$	−22.2579	−2.03186
$121$	17.5653	1.59684
$122$	9.39657	0.850725
$123$	10.4949	0.946293
$124$	−2.70990	−0.243356
$125$	−11.4120	−1.02072
$126$	−7.62031	−0.678871
$127$	−11.4958	−1.02009	−0.510043	−	0.860149i	$-0.670371\pi$
$127$	−11.4958	−1.02009	−0.510043	+	0.860149i	$0.670371\pi$
$128$	20.3663	1.80014
$129$	−1.33718	−0.117732
$130$	0.976702	0.0856624
$131$	−7.13561	−0.623441	−0.311720	−	0.950174i	$-0.600905\pi$
$131$	−7.13561	−0.623441	−0.311720	+	0.950174i	$0.600905\pi$
$132$	−53.3498	−4.64350
$133$	0.882208	0.0764971
$134$	8.50955	0.735113
$135$	12.3018	1.05877
$136$	11.8805	1.01874
$137$	−22.0498	−1.88384	−0.941919	−	0.335841i	$-0.890980\pi$
$137$	−22.0498	−1.88384	−0.941919	+	0.335841i	$0.890980\pi$
$138$	39.3027	3.34567
$139$	−9.02924	−0.765850	−0.382925	−	0.923779i	$-0.625083\pi$
$139$	−9.02924	−0.765850	−0.382925	+	0.923779i	$0.625083\pi$
$140$	5.01296	0.423673
$141$	27.1817	2.28911
$142$	−30.6802	−2.57463
$143$	1.01515	0.0848908
$144$	7.02272	0.585227
$145$	−6.25613	−0.519544
$146$	22.0941	1.82852
$147$	−18.5955	−1.53373
$148$	−24.8643	−2.04383
$149$	−5.37609	−0.440426	−0.220213	−	0.975452i	$-0.570675\pi$
$149$	−5.37609	−0.440426	−0.220213	+	0.975452i	$0.570675\pi$
$150$	1.45862	0.119096
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	−4.89334	−0.396902
$153$	−16.4631	−1.33096
$154$	8.16123	0.657651
$155$	−1.67790	−0.134772
$156$	−1.89593	−0.151796
$157$	17.0154	1.35798	0.678990	−	0.734147i	$-0.262418\pi$
$157$	17.0154	1.35798	0.678990	+	0.734147i	$0.262418\pi$
$158$	4.94106	0.393089
$159$	−2.82673	−0.224174
$160$	8.51177	0.672915
$161$	−3.83841	−0.302509
$162$	−2.19421	−0.172394
$163$	−0.789089	−0.0618062	−0.0309031	−	0.999522i	$-0.509838\pi$
$163$	−0.789089	−0.0618062	−0.0309031	+	0.999522i	$0.509838\pi$
$164$	13.1106	1.02377
$165$	−33.0328	−2.57160
$166$	10.8995	0.845964
$167$	10.1582	0.786063	0.393032	−	0.919525i	$-0.371426\pi$
$167$	10.1582	0.786063	0.393032	+	0.919525i	$0.371426\pi$
$168$	−6.60949	−0.509933
$169$	−12.9639	−0.997225
$170$	16.9640	1.30108
$171$	6.78083	0.518543
$172$	−1.67045	−0.127371
$173$	4.78049	0.363454	0.181727	−	0.983349i	$-0.441831\pi$
$173$	4.78049	0.363454	0.181727	+	0.983349i	$0.441831\pi$
$174$	19.0222	1.44207
$175$	−0.142453	−0.0107684
$176$	−7.52122	−0.566933
$177$	−7.33691	−0.551476
$178$	−38.7072	−2.90123
$179$	−13.6695	−1.02171	−0.510853	−	0.859668i	$-0.670670\pi$
$179$	−13.6695	−1.02171	−0.510853	+	0.859668i	$0.670670\pi$
$180$	38.5306	2.87190
$181$	−1.97701	−0.146950	−0.0734751	−	0.997297i	$-0.523409\pi$
$181$	−1.97701	−0.146950	−0.0734751	+	0.997297i	$0.523409\pi$
$182$	0.290032	0.0214986
$183$	−11.2939	−0.834866
$184$	21.2905	1.56955
$185$	−15.3953	−1.13188
$186$	5.10177	0.374080
$187$	17.6317	1.28936
$188$	33.9563	2.47652
$189$	3.65302	0.265718
$190$	−6.98713	−0.506900
$191$	−13.2396	−0.957984	−0.478992	−	0.877819i	$-0.658998\pi$
$191$	−13.2396	−0.957984	−0.478992	+	0.877819i	$0.658998\pi$
$192$	−33.8365	−2.44194
$193$	−9.58195	−0.689724	−0.344862	−	0.938653i	$-0.612074\pi$
$193$	−9.58195	−0.689724	−0.344862	+	0.938653i	$0.612074\pi$
$194$	25.4827	1.82955
$195$	−1.17391	−0.0840654
$196$	−23.2302	−1.65930
$197$	−8.71250	−0.620740	−0.310370	−	0.950616i	$-0.600453\pi$
$197$	−8.71250	−0.620740	−0.310370	+	0.950616i	$0.600453\pi$
$198$	62.7289	4.45795
$199$	−8.14936	−0.577693	−0.288846	−	0.957375i	$-0.593272\pi$
$199$	−8.14936	−0.577693	−0.288846	+	0.957375i	$0.593272\pi$
$200$	0.790142	0.0558715
$201$	−10.2277	−0.721408
$202$	−44.5342	−3.13341
$203$	−1.85776	−0.130389
$204$	−32.9298	−2.30554
$205$	8.11773	0.566967
$206$	12.7375	0.887464
$207$	−29.5028	−2.05058
$208$	−0.267287	−0.0185330
$209$	−7.26216	−0.502334
$210$	−9.43761	−0.651257
$211$	6.77458	0.466382	0.233191	−	0.972431i	$-0.425083\pi$
$211$	6.77458	0.466382	0.233191	+	0.972431i	$0.425083\pi$
$212$	−3.53125	−0.242527
$213$	36.8749	2.52663
$214$	−33.6074	−2.29735
$215$	−1.03430	−0.0705386
$216$	−20.2622	−1.37867
$217$	−0.498253	−0.0338236
$218$	−15.4913	−1.04920
$219$	−26.5551	−1.79443
$220$	−41.2657	−2.78213
$221$	0.626591	0.0421491
$222$	46.8105	3.14172
$223$	−9.25211	−0.619567	−0.309783	−	0.950807i	$-0.600257\pi$
$223$	−9.25211	−0.619567	−0.309783	+	0.950807i	$0.600257\pi$
$224$	2.52757	0.168881
$225$	−1.09492	−0.0729947
$226$	10.9861	0.730787
$227$	−16.9130	−1.12255	−0.561277	−	0.827628i	$-0.689690\pi$
$227$	−16.9130	−1.12255	−0.561277	+	0.827628i	$0.689690\pi$
$228$	13.5631	0.898240
$229$	−15.9422	−1.05349	−0.526744	−	0.850024i	$-0.676587\pi$
$229$	−15.9422	−1.05349	−0.526744	+	0.850024i	$0.676587\pi$
$230$	30.4004	2.00454
$231$	−9.80909	−0.645391
$232$	10.3044	0.676519
$233$	23.2135	1.52076	0.760382	−	0.649476i	$-0.225012\pi$
$233$	23.2135	1.52076	0.760382	+	0.649476i	$0.225012\pi$
$234$	2.22924	0.145730
$235$	21.0249	1.37151
$236$	−9.16553	−0.596625
$237$	−5.93872	−0.385761
$238$	5.03746	0.326530
$239$	−9.16593	−0.592894	−0.296447	−	0.955049i	$-0.595802\pi$
$239$	−9.16593	−0.592894	−0.296447	+	0.955049i	$0.595802\pi$
$240$	8.69750	0.561421
$241$	−3.09850	−0.199592	−0.0997958	−	0.995008i	$-0.531819\pi$
$241$	−3.09850	−0.199592	−0.0997958	+	0.995008i	$0.531819\pi$
$242$	−41.3111	−2.65558
$243$	−14.2418	−0.913613
$244$	−14.1087	−0.903216
$245$	−14.3835	−0.918928
$246$	−24.6825	−1.57370
$247$	−0.258081	−0.0164213
$248$	2.76365	0.175492
$249$	−13.1002	−0.830193
$250$	26.8395	1.69748
$251$	−19.6078	−1.23764	−0.618818	−	0.785534i	$-0.712388\pi$
$251$	−19.6078	−1.23764	−0.618818	+	0.785534i	$0.712388\pi$
$252$	11.4417	0.720758
$253$	31.5970	1.98649
$254$	27.0365	1.69642
$255$	−20.3892	−1.27682
$256$	−23.9583	−1.49740
$257$	7.29879	0.455286	0.227643	−	0.973745i	$-0.426898\pi$
$257$	7.29879	0.455286	0.227643	+	0.973745i	$0.426898\pi$
$258$	3.14486	0.195790
$259$	−4.57164	−0.284068
$260$	−1.46649	−0.0909478
$261$	−14.2791	−0.883855
$262$	16.7820	1.03679
$263$	4.30882	0.265693	0.132847	−	0.991137i	$-0.457588\pi$
$263$	4.30882	0.265693	0.132847	+	0.991137i	$0.457588\pi$
$264$	54.4080	3.34858
$265$	−2.18646	−0.134313
$266$	−2.07483	−0.127216
$267$	46.5227	2.84714
$268$	−12.7768	−0.780470
$269$	8.30770	0.506530	0.253265	−	0.967397i	$-0.418496\pi$
$269$	8.30770	0.506530	0.253265	+	0.967397i	$0.418496\pi$
$270$	−28.9321	−1.76075
$271$	−16.6422	−1.01094	−0.505472	−	0.862843i	$-0.668682\pi$
$271$	−16.6422	−1.01094	−0.505472	+	0.862843i	$0.668682\pi$
$272$	−4.64242	−0.281488
$273$	−0.348593	−0.0210978
$274$	51.8580	3.13285
$275$	1.17264	0.0707130
$276$	−59.0119	−3.55210
$277$	−0.350159	−0.0210390	−0.0105195	−	0.999945i	$-0.503349\pi$
$277$	−0.350159	−0.0210390	−0.0105195	+	0.999945i	$0.503349\pi$
$278$	21.2355	1.27362
$279$	−3.82967	−0.229276
$280$	−5.11240	−0.305524
$281$	17.1334	1.02209	0.511047	−	0.859553i	$-0.329258\pi$
$281$	17.1334	1.02209	0.511047	+	0.859553i	$0.329258\pi$
$282$	−63.9276	−3.80683
$283$	−6.53218	−0.388298	−0.194149	−	0.980972i	$-0.562194\pi$
$283$	−6.53218	−0.388298	−0.194149	+	0.980972i	$0.562194\pi$
$284$	46.0654	2.73348
$285$	8.39792	0.497450
$286$	−2.38748	−0.141175
$287$	2.41056	0.142291
$288$	19.4274	1.14477
$289$	−6.11696	−0.359821
$290$	14.7136	0.864010
$291$	−30.6279	−1.79544
$292$	−33.1736	−1.94134
$293$	−34.1937	−1.99762	−0.998809	−	0.0488000i	$-0.984460\pi$
$293$	−34.1937	−1.99762	−0.998809	+	0.0488000i	$0.984460\pi$
$294$	43.7341	2.55062
$295$	−5.67505	−0.330414
$296$	25.3575	1.47387
$297$	−30.0709	−1.74489
$298$	12.6438	0.732437
$299$	1.12289	0.0649382
$300$	−2.19008	−0.126444
$301$	−0.307135	−0.0177030
$302$	2.35186	0.135334
$303$	53.5262	3.07500
$304$	1.91212	0.109668
$305$	−8.73572	−0.500206
$306$	38.7189	2.21341
$307$	27.4336	1.56572	0.782859	−	0.622199i	$-0.213760\pi$
$307$	27.4336	1.56572	0.782859	+	0.622199i	$0.213760\pi$
$308$	−12.2539	−0.698228
$309$	−15.3094	−0.870919
$310$	3.94619	0.224128
$311$	−29.2038	−1.65600	−0.827998	−	0.560731i	$-0.810520\pi$
$311$	−29.2038	−1.65600	−0.827998	+	0.560731i	$0.810520\pi$
$312$	1.93354	0.109465
$313$	0.0328369	0.00185605	0.000928026	−	1.00000i	$-0.499705\pi$
$313$	0.0328369	0.00185605	0.000928026		1.00000i	$0.499705\pi$
$314$	−40.0180	−2.25835
$315$	7.08438	0.399160
$316$	−7.41885	−0.417343
$317$	−8.77824	−0.493035	−0.246517	−	0.969138i	$-0.579286\pi$
$317$	−8.77824	−0.493035	−0.246517	+	0.969138i	$0.579286\pi$
$318$	6.64808	0.372806
$319$	15.2927	0.856227
$320$	−26.1723	−1.46307
$321$	40.3931	2.25452
$322$	9.02740	0.503078
$323$	−4.48251	−0.249414
$324$	3.29455	0.183030
$325$	0.0416731	0.00231161
$326$	1.85583	0.102785
$327$	18.6192	1.02964
$328$	−13.3706	−0.738270
$329$	6.24334	0.344206
$330$	77.6885	4.27661
$331$	−32.5836	−1.79096	−0.895479	−	0.445104i	$-0.853167\pi$
$331$	−32.5836	−1.79096	−0.895479	+	0.445104i	$0.853167\pi$
$332$	−16.3653	−0.898161
$333$	−35.1385	−1.92558
$334$	−23.8906	−1.30724
$335$	−7.91108	−0.432228
$336$	2.58273	0.140899
$337$	15.7606	0.858536	0.429268	−	0.903177i	$-0.358772\pi$
$337$	15.7606	0.858536	0.429268	+	0.903177i	$0.358772\pi$
$338$	30.4894	1.65840
$339$	−13.2044	−0.717163
$340$	−25.4709	−1.38136
$341$	4.10151	0.222109
$342$	−15.9476	−0.862346
$343$	−8.81607	−0.476023
$344$	1.70358	0.0918511
$345$	−36.5386	−1.96717
$346$	−11.2431	−0.604431
$347$	−25.3683	−1.36184	−0.680920	−	0.732358i	$-0.738420\pi$
$347$	−25.3683	−1.36184	−0.680920	+	0.732358i	$0.738420\pi$
$348$	−28.5613	−1.53105
$349$	−5.99131	−0.320708	−0.160354	−	0.987060i	$-0.551264\pi$
$349$	−5.99131	−0.320708	−0.160354	+	0.987060i	$0.551264\pi$
$350$	0.335029	0.0179081
$351$	−1.06865	−0.0570405
$352$	−20.8065	−1.10899
$353$	21.1371	1.12502	0.562508	−	0.826792i	$-0.309837\pi$
$353$	21.1371	1.12502	0.562508	+	0.826792i	$0.309837\pi$
$354$	17.2554	0.917114
$355$	28.5225	1.51382
$356$	58.1177	3.08023
$357$	−6.05458	−0.320443
$358$	32.1488	1.69912
$359$	−23.4806	−1.23926	−0.619629	−	0.784895i	$-0.712717\pi$
$359$	−23.4806	−1.23926	−0.619629	+	0.784895i	$0.712717\pi$
$360$	−39.2949	−2.07102
$361$	−17.1537	−0.902828
$362$	4.64966	0.244381
$363$	49.6524	2.60607
$364$	−0.435475	−0.0228251
$365$	−20.5402	−1.07512
$366$	26.5616	1.38840
$367$	−21.7027	−1.13287	−0.566437	−	0.824105i	$-0.691679\pi$
$367$	−21.7027	−1.13287	−0.566437	+	0.824105i	$0.691679\pi$
$368$	−8.31947	−0.433682
$369$	18.5281	0.964532
$370$	36.2076	1.88234
$371$	−0.649269	−0.0337084
$372$	−7.66017	−0.397161
$373$	−7.78919	−0.403309	−0.201655	−	0.979457i	$-0.564632\pi$
$373$	−7.78919	−0.403309	−0.201655	+	0.979457i	$0.564632\pi$
$374$	−41.4673	−2.14422
$375$	−32.2587	−1.66583
$376$	−34.6299	−1.78590
$377$	0.543468	0.0279900
$378$	−8.59140	−0.441894
$379$	3.56636	0.183192	0.0915958	−	0.995796i	$-0.470803\pi$
$379$	3.56636	0.183192	0.0915958	+	0.995796i	$0.470803\pi$
$380$	10.4910	0.538176
$381$	−32.4955	−1.66479
$382$	31.1377	1.59314
$383$	16.5281	0.844547	0.422274	−	0.906468i	$-0.361232\pi$
$383$	16.5281	0.844547	0.422274	+	0.906468i	$0.361232\pi$
$384$	57.5700	2.93786
$385$	−7.58726	−0.386683
$386$	22.5354	1.14702
$387$	−2.36070	−0.120001
$388$	−38.2615	−1.94243
$389$	31.0412	1.57385	0.786925	−	0.617048i	$-0.211672\pi$
$389$	31.0412	1.57385	0.786925	+	0.617048i	$0.211672\pi$
$390$	2.76087	0.139802
$391$	19.5030	0.986309
$392$	23.6909	1.19657
$393$	−20.1704	−1.01746
$394$	20.4906	1.03230
$395$	−4.59356	−0.231127
$396$	−94.1856	−4.73300
$397$	−11.7455	−0.589488	−0.294744	−	0.955576i	$-0.595234\pi$
$397$	−11.7455	−0.589488	−0.294744	+	0.955576i	$0.595234\pi$
$398$	19.1662	0.960713
$399$	2.49377	0.124844
$400$	−0.308756	−0.0154378
$401$	8.07233	0.403113	0.201557	−	0.979477i	$-0.435400\pi$
$401$	8.07233	0.403113	0.201557	+	0.979477i	$0.435400\pi$
$402$	24.0542	1.19971
$403$	0.145759	0.00726075
$404$	66.8668	3.32675
$405$	2.03990	0.101363
$406$	4.36919	0.216839
$407$	37.6328	1.86539
$408$	33.5829	1.66260
$409$	20.7926	1.02813	0.514065	−	0.857752i	$-0.328139\pi$
$409$	20.7926	1.02813	0.514065	+	0.857752i	$0.328139\pi$
$410$	−19.0918	−0.942875
$411$	−62.3287	−3.07445
$412$	−19.1250	−0.942221
$413$	−1.68521	−0.0829236
$414$	69.3864	3.41016
$415$	−10.1329	−0.497406
$416$	−0.739415	−0.0362528
$417$	−25.5232	−1.24988
$418$	17.0796	0.835390
$419$	23.9526	1.17016	0.585081	−	0.810975i	$-0.301063\pi$
$419$	23.9526	1.17016	0.585081	+	0.810975i	$0.301063\pi$
$420$	14.1703	0.691440
$421$	32.4255	1.58032	0.790162	−	0.612898i	$-0.209996\pi$
$421$	32.4255	1.58032	0.790162	+	0.612898i	$0.209996\pi$
$422$	−15.9329	−0.775601
$423$	47.9875	2.33323
$424$	3.60130	0.174894
$425$	0.723804	0.0351097
$426$	−86.7247	−4.20182
$427$	−2.59407	−0.125536
$428$	50.4605	2.43910
$429$	2.86955	0.138543
$430$	2.43253	0.117307
$431$	−1.92059	−0.0925117	−0.0462558	−	0.998930i	$-0.514729\pi$
$431$	−1.92059	−0.0925117	−0.0462558	+	0.998930i	$0.514729\pi$
$432$	7.91765	0.380938
$433$	−15.8278	−0.760635	−0.380317	−	0.924856i	$-0.624185\pi$
$433$	−15.8278	−0.760635	−0.380317	+	0.924856i	$0.624185\pi$
$434$	1.17182	0.0562492
$435$	−17.6844	−0.847902
$436$	23.2597	1.11394
$437$	−8.03291	−0.384266
$438$	62.4540	2.98417
$439$	20.8129	0.993344	0.496672	−	0.867938i	$-0.334555\pi$
$439$	20.8129	0.993344	0.496672	+	0.867938i	$0.334555\pi$
$440$	42.0842	2.00629
$441$	−32.8292	−1.56329
$442$	−1.47366	−0.0700947
$443$	−34.4274	−1.63570	−0.817849	−	0.575433i	$-0.804833\pi$
$443$	−34.4274	−1.63570	−0.817849	+	0.575433i	$0.804833\pi$
$444$	−70.2847	−3.33556
$445$	35.9849	1.70585
$446$	21.7597	1.03035
$447$	−15.1968	−0.718782
$448$	−7.77186	−0.367186
$449$	−16.4141	−0.774629	−0.387314	−	0.921948i	$-0.626597\pi$
$449$	−16.4141	−0.774629	−0.387314	+	0.921948i	$0.626597\pi$
$450$	2.57510	0.121391
$451$	−19.8432	−0.934382
$452$	−16.4954	−0.775877
$453$	−2.82673	−0.132811
$454$	39.7770	1.86683
$455$	−0.269634	−0.0126406
$456$	−13.8322	−0.647750
$457$	17.1914	0.804179	0.402089	−	0.915600i	$-0.368284\pi$
$457$	17.1914	0.804179	0.402089	+	0.915600i	$0.368284\pi$
$458$	37.4938	1.75197
$459$	−18.5610	−0.866355
$460$	−45.6453	−2.12822
$461$	11.6355	0.541918	0.270959	−	0.962591i	$-0.412659\pi$
$461$	11.6355	0.541918	0.270959	+	0.962591i	$0.412659\pi$
$462$	23.0696	1.07330
$463$	17.2073	0.799692	0.399846	−	0.916582i	$-0.369064\pi$
$463$	17.2073	0.799692	0.399846	+	0.916582i	$0.369064\pi$
$464$	−4.02656	−0.186928
$465$	−4.74297	−0.219950
$466$	−54.5949	−2.52906
$467$	2.87758	0.133159	0.0665793	−	0.997781i	$-0.478791\pi$
$467$	2.87758	0.133159	0.0665793	+	0.997781i	$0.478791\pi$
$468$	−3.34714	−0.154722
$469$	−2.34920	−0.108476
$470$	−49.4475	−2.28085
$471$	48.0981	2.21624
$472$	9.34732	0.430245
$473$	2.52828	0.116250
$474$	13.9670	0.641527
$475$	−0.298121	−0.0136787
$476$	−7.56360	−0.346677
$477$	−4.99041	−0.228495
$478$	21.5570	0.985994
$479$	18.2131	0.832176	0.416088	−	0.909324i	$-0.363401\pi$
$479$	18.2131	0.832176	0.416088	+	0.909324i	$0.363401\pi$
$480$	24.0605	1.09821
$481$	1.33738	0.0609795
$482$	7.28723	0.331924
$483$	−10.8501	−0.493699
$484$	62.0275	2.81943
$485$	−23.6905	−1.07573
$486$	33.4948	1.51935
$487$	16.8696	0.764432	0.382216	−	0.924073i	$-0.375161\pi$
$487$	16.8696	0.764432	0.382216	+	0.924073i	$0.375161\pi$
$488$	14.3885	0.651338
$489$	−2.23054	−0.100869
$490$	33.8280	1.52819
$491$	28.5819	1.28988	0.644942	−	0.764232i	$-0.276882\pi$
$491$	28.5819	1.28988	0.644942	+	0.764232i	$0.276882\pi$
$492$	37.0601	1.67080
$493$	9.43930	0.425125
$494$	0.606970	0.0273089
$495$	−58.3172	−2.62116
$496$	−1.07993	−0.0484901
$497$	8.46976	0.379921
$498$	30.8099	1.38063
$499$	30.3202	1.35732	0.678660	−	0.734453i	$-0.262561\pi$
$499$	30.3202	1.35732	0.678660	+	0.734453i	$0.262561\pi$
$500$	−40.2987	−1.80221
$501$	28.7144	1.28287
$502$	46.1149	2.05821
$503$	12.9292	0.576486	0.288243	−	0.957557i	$-0.406929\pi$
$503$	12.9292	0.576486	0.288243	+	0.957557i	$0.406929\pi$
$504$	−11.6686	−0.519762
$505$	41.4021	1.84237
$506$	−74.3118	−3.30356
$507$	−36.6455	−1.62749
$508$	−40.5945	−1.80109
$509$	10.7872	0.478136	0.239068	−	0.971003i	$-0.423158\pi$
$509$	10.7872	0.478136	0.239068	+	0.971003i	$0.423158\pi$
$510$	47.9526	2.12338
$511$	−6.09942	−0.269823
$512$	15.6141	0.690053
$513$	7.64493	0.337532
$514$	−17.1657	−0.757149
$515$	−11.8417	−0.521807
$516$	−4.72192	−0.207871
$517$	−51.3939	−2.26030
$518$	10.7519	0.472410
$519$	13.5132	0.593162
$520$	1.49558	0.0655854
$521$	−27.3887	−1.19992	−0.599961	−	0.800029i	$-0.704817\pi$
$521$	−27.3887	−1.19992	−0.599961	+	0.800029i	$0.704817\pi$
$522$	33.5825	1.46987
$523$	0.115821	0.00506451	0.00253226	−	0.999997i	$-0.499194\pi$
$523$	0.115821	0.00506451	0.00253226	+	0.999997i	$0.499194\pi$
$524$	−25.1976	−1.10076
$525$	−0.402676	−0.0175742
$526$	−10.1337	−0.441852
$527$	2.53163	0.110279
$528$	−21.2605	−0.925243
$529$	11.9505	0.519585
$530$	5.14224	0.223365
$531$	−12.9528	−0.562105
$532$	3.11530	0.135065
$533$	−0.705184	−0.0305449
$534$	−109.415	−4.73484
$535$	31.2438	1.35079
$536$	13.0303	0.562822
$537$	−38.6400	−1.66744
$538$	−19.5386	−0.842368
$539$	35.1595	1.51443
$540$	43.4407	1.86939
$541$	31.6286	1.35982	0.679909	−	0.733296i	$-0.262019\pi$
$541$	31.6286	1.35982	0.679909	+	0.733296i	$0.262019\pi$
$542$	39.1402	1.68122
$543$	−5.58849	−0.239825
$544$	−12.8426	−0.550623
$545$	14.4018	0.616905
$546$	0.819842	0.0350860
$547$	16.7267	0.715180	0.357590	−	0.933879i	$-0.383599\pi$
$547$	16.7267	0.715180	0.357590	+	0.933879i	$0.383599\pi$
$548$	−77.8633	−3.32615
$549$	−19.9386	−0.850957
$550$	−2.75789	−0.117597
$551$	−3.88787	−0.165629
$552$	60.1824	2.56153
$553$	−1.36406	−0.0580056
$554$	0.823526	0.0349883
$555$	−43.5184	−1.84725
$556$	−31.8845	−1.35221
$557$	12.6953	0.537919	0.268960	−	0.963151i	$-0.413320\pi$
$557$	12.6953	0.537919	0.268960	+	0.963151i	$0.413320\pi$
$558$	9.00685	0.381290
$559$	0.0898492	0.00380022
$560$	1.99772	0.0844191
$561$	49.8401	2.10425
$562$	−40.2954	−1.69976
$563$	29.1361	1.22794	0.613971	−	0.789329i	$-0.289571\pi$
$563$	29.1361	1.22794	0.613971	+	0.789329i	$0.289571\pi$
$564$	95.9855	4.04172
$565$	−10.2135	−0.429685
$566$	15.3628	0.645746
$567$	0.605748	0.0254390
$568$	−46.9792	−1.97120
$569$	−24.4091	−1.02328	−0.511642	−	0.859199i	$-0.670963\pi$
$569$	−24.4091	−1.02328	−0.511642	+	0.859199i	$0.670963\pi$
$570$	−19.7508	−0.827268
$571$	22.8812	0.957547	0.478773	−	0.877939i	$-0.341082\pi$
$571$	22.8812	0.957547	0.478773	+	0.877939i	$0.341082\pi$
$572$	3.58474	0.149885
$573$	−37.4248	−1.56344
$574$	−5.66931	−0.236632
$575$	1.29710	0.0540927
$576$	−59.7361	−2.48900
$577$	−25.9784	−1.08150	−0.540748	−	0.841184i	$-0.681859\pi$
$577$	−25.9784	−1.08150	−0.540748	+	0.841184i	$0.681859\pi$
$578$	14.3863	0.598389
$579$	−27.0856	−1.12564
$580$	−22.0920	−0.917320
$581$	−3.00898	−0.124833
$582$	72.0326	2.98585
$583$	5.34465	0.221353
$584$	33.8316	1.39996
$585$	−2.07246	−0.0856858
$586$	80.4188	3.32207
$587$	−15.6146	−0.644485	−0.322243	−	0.946657i	$-0.604437\pi$
$587$	−15.6146	−0.644485	−0.322243	+	0.946657i	$0.604437\pi$
$588$	−65.6655	−2.70800
$589$	−1.04273	−0.0429649
$590$	13.3469	0.549484
$591$	−24.6279	−1.01306
$592$	−9.90869	−0.407245
$593$	14.6430	0.601315	0.300658	−	0.953732i	$-0.402794\pi$
$593$	14.6430	0.601315	0.300658	+	0.953732i	$0.402794\pi$
$594$	70.7226	2.90178
$595$	−4.68318	−0.191992
$596$	−18.9843	−0.777629
$597$	−23.0361	−0.942803
$598$	−2.64087	−0.107993
$599$	41.3504	1.68953	0.844766	−	0.535135i	$-0.179739\pi$
$599$	41.3504	1.68953	0.844766	+	0.535135i	$0.179739\pi$
$600$	2.23352	0.0911830
$601$	−9.15808	−0.373566	−0.186783	−	0.982401i	$-0.559806\pi$
$601$	−9.15808	−0.373566	−0.186783	+	0.982401i	$0.559806\pi$
$602$	0.722340	0.0294404
$603$	−18.0564	−0.735313
$604$	−3.53125	−0.143685
$605$	38.4058	1.56142
$606$	−125.886	−5.11378
$607$	30.0754	1.22072	0.610362	−	0.792122i	$-0.291024\pi$
$607$	30.0754	1.22072	0.610362	+	0.792122i	$0.291024\pi$
$608$	5.28963	0.214523
$609$	−5.25139	−0.212797
$610$	20.5452	0.831851
$611$	−1.82642	−0.0738891
$612$	−58.1353	−2.34998
$613$	4.05911	0.163946	0.0819731	−	0.996635i	$-0.473878\pi$
$613$	4.05911	0.163946	0.0819731	+	0.996635i	$0.473878\pi$
$614$	−64.5201	−2.60382
$615$	22.9466	0.925298
$616$	12.4969	0.503515
$617$	4.68419	0.188578	0.0942892	−	0.995545i	$-0.469942\pi$
$617$	4.68419	0.188578	0.0942892	+	0.995545i	$0.469942\pi$
$618$	36.0055	1.44835
$619$	−13.5790	−0.545786	−0.272893	−	0.962044i	$-0.587981\pi$
$619$	−13.5790	−0.545786	−0.272893	+	0.962044i	$0.587981\pi$
$620$	−5.92509	−0.237957
$621$	−33.2624	−1.33477
$622$	68.6833	2.75395
$623$	10.6857	0.428115
$624$	−0.755549	−0.0302462
$625$	−23.8548	−0.954193
$626$	−0.0772279	−0.00308665
$627$	−20.5282	−0.819816
$628$	60.0859	2.39769
$629$	23.2285	0.926183
$630$	−16.6615	−0.663810
$631$	−24.0659	−0.958048	−0.479024	−	0.877802i	$-0.659009\pi$
$631$	−24.0659	−0.958048	−0.479024	+	0.877802i	$0.659009\pi$
$632$	7.56601	0.300960
$633$	19.1499	0.761141
$634$	20.6452	0.819926
$635$	−25.1350	−0.997454
$636$	−9.98190	−0.395808
$637$	1.24949	0.0495066
$638$	−35.9663	−1.42392
$639$	65.1003	2.57533
$640$	44.5300	1.76020
$641$	25.8986	1.02293	0.511467	−	0.859303i	$-0.329102\pi$
$641$	25.8986	1.02293	0.511467	+	0.859303i	$0.329102\pi$
$642$	−94.9990	−3.74931
$643$	22.7745	0.898137	0.449069	−	0.893497i	$-0.351756\pi$
$643$	22.7745	0.898137	0.449069	+	0.893497i	$0.351756\pi$
$644$	−13.5544	−0.534118
$645$	−2.92368	−0.115120
$646$	10.5422	0.414779
$647$	−15.6913	−0.616890	−0.308445	−	0.951242i	$-0.599809\pi$
$647$	−15.6913	−0.616890	−0.308445	+	0.951242i	$0.599809\pi$
$648$	−3.35990	−0.131989
$649$	13.8723	0.544535
$650$	−0.0980093	−0.00384424
$651$	−1.40843	−0.0552006
$652$	−2.78647	−0.109127
$653$	45.0422	1.76264	0.881319	−	0.472523i	$-0.156657\pi$
$653$	45.0422	1.76264	0.881319	+	0.472523i	$0.156657\pi$
$654$	−43.7897	−1.71231
$655$	−15.6017	−0.609609
$656$	5.22471	0.203991
$657$	−46.8814	−1.82902
$658$	−14.6835	−0.572421
$659$	35.2831	1.37444	0.687218	−	0.726451i	$-0.258832\pi$
$659$	35.2831	1.37444	0.687218	+	0.726451i	$0.258832\pi$
$660$	−116.647	−4.54048
$661$	−1.57733	−0.0613510	−0.0306755	−	0.999529i	$-0.509766\pi$
$661$	−1.57733	−0.0613510	−0.0306755	+	0.999529i	$0.509766\pi$
$662$	76.6322	2.97839
$663$	1.77120	0.0687879
$664$	16.6899	0.647693
$665$	1.92891	0.0747999
$666$	82.6409	3.20227
$667$	16.9158	0.654981
$668$	35.8711	1.38789
$669$	−26.1532	−1.01114
$670$	18.6058	0.718803
$671$	21.3539	0.824358
$672$	7.14477	0.275615
$673$	34.5383	1.33135	0.665677	−	0.746240i	$-0.268143\pi$
$673$	34.5383	1.33135	0.665677	+	0.746240i	$0.268143\pi$
$674$	−37.0668	−1.42776
$675$	−1.23445	−0.0475140
$676$	−45.7789	−1.76073
$677$	4.81359	0.185001	0.0925006	−	0.995713i	$-0.470514\pi$
$677$	4.81359	0.185001	0.0925006	+	0.995713i	$0.470514\pi$
$678$	31.0548	1.19265
$679$	−7.03489	−0.269974
$680$	25.9761	0.996140
$681$	−47.8084	−1.83202
$682$	−9.64619	−0.369372
$683$	32.8625	1.25745	0.628724	−	0.777628i	$-0.283577\pi$
$683$	32.8625	1.25745	0.628724	+	0.777628i	$0.283577\pi$
$684$	23.9448	0.915553
$685$	−48.2108	−1.84204
$686$	20.7342	0.791634
$687$	−45.0642	−1.71931
$688$	−0.665693	−0.0253793
$689$	0.189937	0.00723602
$690$	85.9338	3.27144
$691$	18.4093	0.700323	0.350161	−	0.936689i	$-0.386127\pi$
$691$	18.4093	0.700323	0.350161	+	0.936689i	$0.386127\pi$
$692$	16.8811	0.641724
$693$	−17.3173	−0.657830
$694$	59.6626	2.26476
$695$	−19.7420	−0.748858
$696$	29.1278	1.10409
$697$	−12.2481	−0.463930
$698$	14.0907	0.533342
$699$	65.6182	2.48191
$700$	−0.503037	−0.0190130
$701$	32.5235	1.22840	0.614199	−	0.789151i	$-0.289479\pi$
$701$	32.5235	1.22840	0.614199	+	0.789151i	$0.289479\pi$
$702$	2.51332	0.0948593
$703$	−9.56739	−0.360841
$704$	63.9764	2.41120
$705$	59.4316	2.23832
$706$	−49.7116	−1.87092
$707$	12.2944	0.462377
$708$	−25.9085	−0.973700
$709$	−20.2299	−0.759748	−0.379874	−	0.925038i	$-0.624033\pi$
$709$	−20.2299	−0.759748	−0.379874	+	0.925038i	$0.624033\pi$
$710$	−67.0809	−2.51750
$711$	−10.4844	−0.393196
$712$	−59.2705	−2.22126
$713$	4.53682	0.169905
$714$	14.2395	0.532901
$715$	2.21957	0.0830074
$716$	−48.2705	−1.80395
$717$	−25.9096	−0.967612
$718$	55.2231	2.06091
$719$	5.26701	0.196426	0.0982131	−	0.995165i	$-0.468687\pi$
$719$	5.26701	0.196426	0.0982131	+	0.995165i	$0.468687\pi$
$720$	15.3549	0.572242
$721$	−3.51639	−0.130957
$722$	40.3432	1.50142
$723$	−8.75862	−0.325736
$724$	−6.98134	−0.259459
$725$	0.627785	0.0233154
$726$	−116.776	−4.33395
$727$	32.8962	1.22005	0.610027	−	0.792381i	$-0.291159\pi$
$727$	32.8962	1.22005	0.610027	+	0.792381i	$0.291159\pi$
$728$	0.444112	0.0164599
$729$	−43.0567	−1.59469
$730$	48.3078	1.78795
$731$	1.56056	0.0577193
$732$	−39.8815	−1.47406
$733$	−50.0303	−1.84791	−0.923956	−	0.382498i	$-0.875064\pi$
$733$	−50.0303	−1.84791	−0.923956	+	0.382498i	$0.875064\pi$
$734$	51.0419	1.88399
$735$	−40.6583	−1.49970
$736$	−23.0147	−0.848333
$737$	19.3381	0.712328
$738$	−43.5754	−1.60403
$739$	−3.31631	−0.121993	−0.0609963	−	0.998138i	$-0.519428\pi$
$739$	−3.31631	−0.121993	−0.0609963	+	0.998138i	$0.519428\pi$
$740$	−54.3647	−1.99849
$741$	−0.729525	−0.0267998
$742$	1.52699	0.0560576
$743$	28.8675	1.05905	0.529523	−	0.848296i	$-0.322371\pi$
$743$	28.8675	1.05905	0.529523	+	0.848296i	$0.322371\pi$
$744$	7.81211	0.286406
$745$	−11.7546	−0.430655
$746$	18.3191	0.670710
$747$	−23.1276	−0.846195
$748$	62.2620	2.27653
$749$	9.27785	0.339005
$750$	75.8679	2.77031
$751$	3.02544	0.110400	0.0551999	−	0.998475i	$-0.482420\pi$
$751$	3.02544	0.110400	0.0551999	+	0.998475i	$0.482420\pi$
$752$	13.5320	0.493460
$753$	−55.4261	−2.01984
$754$	−1.27816	−0.0465479
$755$	−2.18646	−0.0795733
$756$	12.8997	0.469159
$757$	0.405510	0.0147385	0.00736926	−	0.999973i	$-0.497654\pi$
$757$	0.405510	0.0147385	0.00736926	+	0.999973i	$0.497654\pi$
$758$	−8.38758	−0.304651
$759$	89.3162	3.24197
$760$	−10.6991	−0.388096
$761$	−46.7594	−1.69503	−0.847513	−	0.530774i	$-0.821901\pi$
$761$	−46.7594	−1.69503	−0.847513	+	0.530774i	$0.821901\pi$
$762$	76.4249	2.76858
$763$	4.27662	0.154824
$764$	−46.7524	−1.69144
$765$	−35.9958	−1.30143
$766$	−38.8718	−1.40450
$767$	0.492990	0.0178008
$768$	−67.7238	−2.44377
$769$	41.0181	1.47915	0.739575	−	0.673075i	$-0.235027\pi$
$769$	41.0181	1.47915	0.739575	+	0.673075i	$0.235027\pi$
$770$	17.8442	0.643060
$771$	20.6317	0.743033
$772$	−33.8363	−1.21779
$773$	−30.9734	−1.11403	−0.557017	−	0.830501i	$-0.688054\pi$
$773$	−30.9734	−1.11403	−0.557017	+	0.830501i	$0.688054\pi$
$774$	5.55205	0.199564
$775$	0.168372	0.00604812
$776$	39.0204	1.40075
$777$	−12.9228	−0.463603
$778$	−73.0046	−2.61734
$779$	5.04475	0.180747
$780$	−4.14537	−0.148428
$781$	−69.7213	−2.49483
$782$	−45.8684	−1.64025
$783$	−16.0988	−0.575323
$784$	−9.25748	−0.330624
$785$	37.2035	1.32785
$786$	47.4381	1.69206
$787$	−9.16751	−0.326787	−0.163393	−	0.986561i	$-0.552244\pi$
$787$	−9.16751	−0.326787	−0.163393	+	0.986561i	$0.552244\pi$
$788$	−30.7660	−1.09599
$789$	12.1799	0.433615
$790$	10.8034	0.384368
$791$	−3.03290	−0.107837
$792$	96.0538	3.41312
$793$	0.758869	0.0269482
$794$	27.6237	0.980329
$795$	−6.18053	−0.219201
$796$	−28.7775	−1.01999
$797$	28.2935	1.00221	0.501103	−	0.865388i	$-0.332928\pi$
$797$	28.2935	1.00221	0.501103	+	0.865388i	$0.332928\pi$
$798$	−5.86499	−0.207618
$799$	−31.7225	−1.12226
$800$	−0.854132	−0.0301981
$801$	82.1327	2.90202
$802$	−18.9850	−0.670384
$803$	50.2092	1.77184
$804$	−36.1167	−1.27374
$805$	−8.39252	−0.295797
$806$	−0.342804	−0.0120748
$807$	23.4837	0.826664
$808$	−68.1931	−2.39902
$809$	−29.1140	−1.02359	−0.511797	−	0.859107i	$-0.671020\pi$
$809$	−29.1140	−1.02359	−0.511797	+	0.859107i	$0.671020\pi$
$810$	−4.79755	−0.168569
$811$	−4.21551	−0.148027	−0.0740133	−	0.997257i	$-0.523581\pi$
$811$	−4.21551	−0.148027	−0.0740133	+	0.997257i	$0.523581\pi$
$812$	−6.56022	−0.230219
$813$	−47.0431	−1.64987
$814$	−88.5071	−3.10217
$815$	−1.72531	−0.0604350
$816$	−13.1229	−0.459392
$817$	−0.642764	−0.0224875
$818$	−48.9014	−1.70980
$819$	−0.615418	−0.0215044
$820$	28.6657	1.00105
$821$	−11.1721	−0.389909	−0.194954	−	0.980812i	$-0.562456\pi$
$821$	−11.1721	−0.389909	−0.194954	+	0.980812i	$0.562456\pi$
$822$	146.589	5.11286
$823$	−7.66442	−0.267165	−0.133582	−	0.991038i	$-0.542648\pi$
$823$	−7.66442	−0.267165	−0.133582	+	0.991038i	$0.542648\pi$
$824$	19.5043	0.679466
$825$	3.31474	0.115405
$826$	3.96337	0.137903
$827$	−37.4183	−1.30116	−0.650581	−	0.759437i	$-0.725475\pi$
$827$	−37.4183	−1.30116	−0.650581	+	0.759437i	$0.725475\pi$
$828$	−104.182	−3.62057
$829$	21.2962	0.739648	0.369824	−	0.929102i	$-0.379418\pi$
$829$	21.2962	0.739648	0.369824	+	0.929102i	$0.379418\pi$
$830$	23.8313	0.827195
$831$	−0.989806	−0.0343360
$832$	2.27358	0.0788221
$833$	21.7019	0.751928
$834$	60.0271	2.07857
$835$	22.2104	0.768623
$836$	−25.6445	−0.886934
$837$	−4.31770	−0.149241
$838$	−56.3333	−1.94600
$839$	39.7046	1.37076	0.685378	−	0.728188i	$-0.259637\pi$
$839$	39.7046	1.37076	0.685378	+	0.728188i	$0.259637\pi$
$840$	−14.4514	−0.498620
$841$	−20.8129	−0.717686
$842$	−76.2604	−2.62811
$843$	48.4316	1.66807
$844$	23.9228	0.823456
$845$	−28.3451	−0.975100
$846$	−112.860	−3.88021
$847$	11.4046	0.391867
$848$	−1.40724	−0.0483249
$849$	−18.4647	−0.633707
$850$	−1.70229	−0.0583880
$851$	41.6268	1.42695
$852$	130.215	4.46108
$853$	39.6051	1.35605	0.678027	−	0.735037i	$-0.262835\pi$
$853$	39.6051	1.35605	0.678027	+	0.735037i	$0.262835\pi$
$854$	6.10090	0.208769
$855$	14.8260	0.507038
$856$	−51.4614	−1.75891
$857$	−31.1748	−1.06491	−0.532455	−	0.846458i	$-0.678730\pi$
$857$	−31.1748	−1.06491	−0.532455	+	0.846458i	$0.678730\pi$
$858$	−6.74877	−0.230399
$859$	−11.6880	−0.398790	−0.199395	−	0.979919i	$-0.563898\pi$
$859$	−11.6880	−0.398790	−0.199395	+	0.979919i	$0.563898\pi$
$860$	−3.65237	−0.124545
$861$	6.81401	0.232221
$862$	4.51697	0.153849
$863$	−49.8343	−1.69638	−0.848189	−	0.529693i	$-0.822307\pi$
$863$	−49.8343	−1.69638	−0.848189	+	0.529693i	$0.822307\pi$
$864$	21.9031	0.745160
$865$	10.4523	0.355390
$866$	37.2248	1.26495
$867$	−17.2910	−0.587234
$868$	−1.75946	−0.0597198
$869$	11.2286	0.380906
$870$	41.5913	1.41008
$871$	0.687233	0.0232860
$872$	−23.7211	−0.803298
$873$	−54.0716	−1.83005
$874$	18.8923	0.639041
$875$	−7.40946	−0.250486
$876$	−93.7729	−3.16829
$877$	−37.3205	−1.26022	−0.630111	−	0.776505i	$-0.716991\pi$
$877$	−37.3205	−1.26022	−0.630111	+	0.776505i	$0.716991\pi$
$878$	−48.9490	−1.65195
$879$	−96.6564	−3.26014
$880$	−16.4448	−0.554355
$881$	25.0086	0.842560	0.421280	−	0.906931i	$-0.361581\pi$
$881$	25.0086	0.842560	0.421280	+	0.906931i	$0.361581\pi$
$882$	77.2097	2.59978
$883$	−37.7411	−1.27009	−0.635045	−	0.772475i	$-0.719019\pi$
$883$	−37.7411	−1.27009	−0.635045	+	0.772475i	$0.719019\pi$
$884$	2.21265	0.0744195
$885$	−16.0418	−0.539240
$886$	80.9686	2.72019
$887$	16.8898	0.567102	0.283551	−	0.958957i	$-0.408487\pi$
$887$	16.8898	0.567102	0.283551	+	0.958957i	$0.408487\pi$
$888$	71.6787	2.40538
$889$	−7.46386	−0.250330
$890$	−84.6316	−2.83686
$891$	−4.98639	−0.167050
$892$	−32.6715	−1.09392
$893$	13.0659	0.437233
$894$	35.7407	1.19535
$895$	−29.8878	−0.999038
$896$	13.2232	0.441756
$897$	3.17410	0.105980
$898$	38.6037	1.28822
$899$	2.19578	0.0732335
$900$	−3.86644	−0.128881
$901$	3.29894	0.109904
$902$	46.6686	1.55389
$903$	−0.868189	−0.0288915
$904$	16.8226	0.559510
$905$	−4.32266	−0.143690
$906$	6.64808	0.220868
$907$	18.6504	0.619278	0.309639	−	0.950854i	$-0.399792\pi$
$907$	18.6504	0.619278	0.309639	+	0.950854i	$0.399792\pi$
$908$	−59.7240	−1.98201
$909$	94.4970	3.13427
$910$	0.634142	0.0210216
$911$	9.09311	0.301268	0.150634	−	0.988590i	$-0.451868\pi$
$911$	9.09311	0.301268	0.150634	+	0.988590i	$0.451868\pi$
$912$	5.40505	0.178979
$913$	24.7693	0.819744
$914$	−40.4318	−1.33736
$915$	−24.6935	−0.816343
$916$	−56.2958	−1.86007
$917$	−4.63293	−0.152993
$918$	43.6530	1.44076
$919$	18.3980	0.606896	0.303448	−	0.952848i	$-0.401862\pi$
$919$	18.3980	0.606896	0.303448	+	0.952848i	$0.401862\pi$
$920$	46.5507	1.53473
$921$	77.5474	2.55528
$922$	−27.3650	−0.901219
$923$	−2.47774	−0.0815558
$924$	−34.6384	−1.13952
$925$	1.54487	0.0507952
$926$	−40.4692	−1.32990
$927$	−27.0277	−0.887706
$928$	−11.1389	−0.365654
$929$	−11.4362	−0.375210	−0.187605	−	0.982245i	$-0.560072\pi$
$929$	−11.4362	−0.375210	−0.187605	+	0.982245i	$0.560072\pi$
$930$	11.1548	0.365781
$931$	−8.93861	−0.292951
$932$	81.9726	2.68510
$933$	−82.5513	−2.70261
$934$	−6.76767	−0.221445
$935$	38.5510	1.26075
$936$	3.41353	0.111575
$937$	−31.2796	−1.02186	−0.510929	−	0.859623i	$-0.670699\pi$
$937$	−31.2796	−1.02186	−0.510929	+	0.859623i	$0.670699\pi$
$938$	5.52498	0.180397
$939$	0.0928212	0.00302910
$940$	74.2441	2.42157
$941$	25.2041	0.821629	0.410814	−	0.911719i	$-0.365244\pi$
$941$	25.2041	0.821629	0.410814	+	0.911719i	$0.365244\pi$
$942$	−113.120	−3.68565
$943$	−21.9493	−0.714766
$944$	−3.65256	−0.118881
$945$	7.98717	0.259823
$946$	−5.94615	−0.193326
$947$	−11.3899	−0.370123	−0.185061	−	0.982727i	$-0.559248\pi$
$947$	−11.3899	−0.370123	−0.185061	+	0.982727i	$0.559248\pi$
$948$	−20.9711	−0.681110
$949$	1.78432	0.0579216
$950$	0.701139	0.0227480
$951$	−24.8137	−0.804640
$952$	7.71362	0.250000
$953$	−7.75782	−0.251300	−0.125650	−	0.992075i	$-0.540102\pi$
$953$	−7.75782	−0.251300	−0.125650	+	0.992075i	$0.540102\pi$
$954$	11.7368	0.379992
$955$	−28.9478	−0.936730
$956$	−32.3672	−1.04683
$957$	43.2284	1.39737
$958$	−42.8346	−1.38392
$959$	−14.3162	−0.462295
$960$	−73.9820	−2.38776
$961$	−30.4111	−0.981003
$962$	−3.14534	−0.101410
$963$	71.3114	2.29798
$964$	−10.9416	−0.352404
$965$	−20.9505	−0.674421
$966$	25.5180	0.821030
$967$	18.8604	0.606510	0.303255	−	0.952909i	$-0.401927\pi$
$967$	18.8604	0.606510	0.303255	+	0.952909i	$0.401927\pi$
$968$	−63.2578	−2.03318
$969$	−12.6709	−0.407047
$970$	55.7167	1.78896
$971$	−3.56158	−0.114296	−0.0571482	−	0.998366i	$-0.518201\pi$
$971$	−3.56158	−0.114296	−0.0571482	+	0.998366i	$0.518201\pi$
$972$	−50.2915	−1.61310
$973$	−5.86240	−0.187940
$974$	−39.6748	−1.27126
$975$	0.117799	0.00377257
$976$	−5.62246	−0.179971
$977$	−10.0827	−0.322573	−0.161287	−	0.986908i	$-0.551564\pi$
$977$	−10.0827	−0.322573	−0.161287	+	0.986908i	$0.551564\pi$
$978$	5.24593	0.167746
$979$	−87.9628	−2.81130
$980$	−50.7918	−1.62248
$981$	32.8709	1.04949
$982$	−67.2207	−2.14510
$983$	15.1214	0.482298	0.241149	−	0.970488i	$-0.422476\pi$
$983$	15.1214	0.482298	0.241149	+	0.970488i	$0.422476\pi$
$984$	−37.7952	−1.20487
$985$	−19.0495	−0.606968
$986$	−22.1999	−0.706990
$987$	17.6482	0.561749
$988$	−0.911348	−0.0289939
$989$	2.79661	0.0889269
$990$	137.154	4.35904
$991$	−40.3158	−1.28067	−0.640337	−	0.768094i	$-0.721205\pi$
$991$	−40.3158	−1.28067	−0.640337	+	0.768094i	$0.721205\pi$
$992$	−2.98747	−0.0948523
$993$	−92.1051	−2.92287
$994$	−19.9197	−0.631815
$995$	−17.8182	−0.564876
$996$	−46.2602	−1.46581
$997$	−45.7915	−1.45023	−0.725116	−	0.688627i	$-0.758214\pi$
$997$	−45.7915	−1.45023	−0.725116	+	0.688627i	$0.758214\pi$
$998$	−71.3090	−2.25725
$999$	−39.6163	−1.25341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.17	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.17	✓	153	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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.35186 q^{2} +2.82673 q^{3} +3.53125 q^{4} +2.18646 q^{5} -6.64808 q^{6} +0.649269 q^{7} -3.60130 q^{8} +4.99041 q^{9} +O(q^{10})\)	\(q-2.35186 q^{2} +2.82673 q^{3} +3.53125 q^{4} +2.18646 q^{5} -6.64808 q^{6} +0.649269 q^{7} -3.60130 q^{8} +4.99041 q^{9} -5.14224 q^{10} -5.34465 q^{11} +9.98190 q^{12} -0.189937 q^{13} -1.52699 q^{14} +6.18053 q^{15} +1.40724 q^{16} -3.29894 q^{17} -11.7368 q^{18} +1.35877 q^{19} +7.72093 q^{20} +1.83531 q^{21} +12.5699 q^{22} -5.91189 q^{23} -10.1799 q^{24} -0.219405 q^{25} +0.446705 q^{26} +5.62636 q^{27} +2.29273 q^{28} -2.86131 q^{29} -14.5357 q^{30} -0.767405 q^{31} +3.89295 q^{32} -15.1079 q^{33} +7.75866 q^{34} +1.41960 q^{35} +17.6224 q^{36} -7.04121 q^{37} -3.19564 q^{38} -0.536900 q^{39} -7.87408 q^{40} +3.71273 q^{41} -4.31639 q^{42} -0.473048 q^{43} -18.8733 q^{44} +10.9113 q^{45} +13.9040 q^{46} +9.61595 q^{47} +3.97790 q^{48} -6.57845 q^{49} +0.516010 q^{50} -9.32523 q^{51} -0.670715 q^{52} -1.00000 q^{53} -13.2324 q^{54} -11.6859 q^{55} -2.33821 q^{56} +3.84088 q^{57} +6.72941 q^{58} -2.59554 q^{59} +21.8250 q^{60} -3.99537 q^{61} +1.80483 q^{62} +3.24012 q^{63} -11.9702 q^{64} -0.415289 q^{65} +35.5317 q^{66} -3.61822 q^{67} -11.6494 q^{68} -16.7113 q^{69} -3.33870 q^{70} +13.0451 q^{71} -17.9719 q^{72} -9.39429 q^{73} +16.5599 q^{74} -0.620199 q^{75} +4.79817 q^{76} -3.47012 q^{77} +1.26272 q^{78} -2.10091 q^{79} +3.07688 q^{80} +0.932969 q^{81} -8.73183 q^{82} -4.63441 q^{83} +6.48094 q^{84} -7.21300 q^{85} +1.11254 q^{86} -8.08816 q^{87} +19.2477 q^{88} +16.4581 q^{89} -25.6619 q^{90} -0.123320 q^{91} -20.8764 q^{92} -2.16925 q^{93} -22.6154 q^{94} +2.97090 q^{95} +11.0043 q^{96} -10.8351 q^{97} +15.4716 q^{98} -26.6720 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * q^99

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