LMFDB - Embedded newform 1003.2.a.g.1.2

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			1.2
Root			$-1.54725$ 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)

$f(q)$	$=$	$q-2.40787 q^{2} -2.54725 q^{3} +3.79784 q^{4} +0.977935 q^{5} +6.13345 q^{6} -2.76854 q^{7} -4.32896 q^{8} +3.48849 q^{9} +O(q^{10})$	\(q-2.40787 q^{2} -2.54725 q^{3} +3.79784 q^{4} +0.977935 q^{5} +6.13345 q^{6} -2.76854 q^{7} -4.32896 q^{8} +3.48849 q^{9} -2.35474 q^{10} +2.66675 q^{11} -9.67405 q^{12} -2.92648 q^{13} +6.66630 q^{14} -2.49105 q^{15} +2.82789 q^{16} -1.00000 q^{17} -8.39983 q^{18} +4.82641 q^{19} +3.71404 q^{20} +7.05218 q^{21} -6.42120 q^{22} -3.45438 q^{23} +11.0269 q^{24} -4.04364 q^{25} +7.04659 q^{26} -1.24431 q^{27} -10.5145 q^{28} -7.70511 q^{29} +5.99812 q^{30} +10.7654 q^{31} +1.84872 q^{32} -6.79289 q^{33} +2.40787 q^{34} -2.70746 q^{35} +13.2487 q^{36} +6.23360 q^{37} -11.6214 q^{38} +7.45449 q^{39} -4.23344 q^{40} +4.84361 q^{41} -16.9807 q^{42} +11.9305 q^{43} +10.1279 q^{44} +3.41152 q^{45} +8.31769 q^{46} +0.561497 q^{47} -7.20336 q^{48} +0.664841 q^{49} +9.73657 q^{50} +2.54725 q^{51} -11.1143 q^{52} +1.76842 q^{53} +2.99614 q^{54} +2.60791 q^{55} +11.9849 q^{56} -12.2941 q^{57} +18.5529 q^{58} -1.00000 q^{59} -9.46059 q^{60} -5.14785 q^{61} -25.9217 q^{62} -9.65804 q^{63} -10.1073 q^{64} -2.86191 q^{65} +16.3564 q^{66} -9.77325 q^{67} -3.79784 q^{68} +8.79917 q^{69} +6.51921 q^{70} -7.55510 q^{71} -15.1015 q^{72} +4.76779 q^{73} -15.0097 q^{74} +10.3002 q^{75} +18.3299 q^{76} -7.38303 q^{77} -17.9494 q^{78} -6.95701 q^{79} +2.76550 q^{80} -7.29590 q^{81} -11.6628 q^{82} -5.65212 q^{83} +26.7830 q^{84} -0.977935 q^{85} -28.7271 q^{86} +19.6269 q^{87} -11.5443 q^{88} -11.1982 q^{89} -8.21449 q^{90} +8.10210 q^{91} -13.1192 q^{92} -27.4222 q^{93} -1.35201 q^{94} +4.71991 q^{95} -4.70914 q^{96} +8.34612 q^{97} -1.60085 q^{98} +9.30295 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40787	−1.70262	−0.851311	−	0.524662i	$-0.824192\pi$
$2$	−2.40787	−1.70262	−0.851311	+	0.524662i	$0.824192\pi$
$3$	−2.54725	−1.47066	−0.735328	−	0.677711i	$-0.762972\pi$
$3$	−2.54725	−1.47066	−0.735328	+	0.677711i	$0.762972\pi$
$4$	3.79784	1.89892
$5$	0.977935	0.437346	0.218673	−	0.975798i	$-0.429827\pi$
$5$	0.977935	0.437346	0.218673	+	0.975798i	$0.429827\pi$
$6$	6.13345	2.50397
$7$	−2.76854	−1.04641	−0.523206	−	0.852206i	$-0.675264\pi$
$7$	−2.76854	−1.04641	−0.523206	+	0.852206i	$0.675264\pi$
$8$	−4.32896	−1.53052
$9$	3.48849	1.16283
$10$	−2.35474	−0.744634
$11$	2.66675	0.804057	0.402028	−	0.915627i	$-0.368305\pi$
$11$	2.66675	0.804057	0.402028	+	0.915627i	$0.368305\pi$
$12$	−9.67405	−2.79266
$13$	−2.92648	−0.811660	−0.405830	−	0.913949i	$-0.633018\pi$
$13$	−2.92648	−0.811660	−0.405830	+	0.913949i	$0.633018\pi$
$14$	6.66630	1.78164
$15$	−2.49105	−0.643186
$16$	2.82789	0.706974
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−8.39983	−1.97986
$19$	4.82641	1.10725	0.553627	−	0.832765i	$-0.313243\pi$
$19$	4.82641	1.10725	0.553627	+	0.832765i	$0.313243\pi$
$20$	3.71404	0.830484
$21$	7.05218	1.53891
$22$	−6.42120	−1.36900
$23$	−3.45438	−0.720288	−0.360144	−	0.932897i	$-0.617272\pi$
$23$	−3.45438	−0.720288	−0.360144	+	0.932897i	$0.617272\pi$
$24$	11.0269	2.25087
$25$	−4.04364	−0.808729
$26$	7.04659	1.38195
$27$	−1.24431	−0.239468
$28$	−10.5145	−1.98705
$29$	−7.70511	−1.43080	−0.715401	−	0.698714i	$-0.753756\pi$
$29$	−7.70511	−1.43080	−0.715401	+	0.698714i	$0.753756\pi$
$30$	5.99812	1.09510
$31$	10.7654	1.93352	0.966761	−	0.255682i	$-0.0823001\pi$
$31$	10.7654	1.93352	0.966761	+	0.255682i	$0.0823001\pi$
$32$	1.84872	0.326810
$33$	−6.79289	−1.18249
$34$	2.40787	0.412946
$35$	−2.70746	−0.457644
$36$	13.2487	2.20812
$37$	6.23360	1.02480	0.512399	−	0.858747i	$-0.328757\pi$
$37$	6.23360	1.02480	0.512399	+	0.858747i	$0.328757\pi$
$38$	−11.6214	−1.88523
$39$	7.45449	1.19367
$40$	−4.23344	−0.669366
$41$	4.84361	0.756444	0.378222	−	0.925715i	$-0.376536\pi$
$41$	4.84361	0.756444	0.378222	+	0.925715i	$0.376536\pi$
$42$	−16.9807	−2.62018
$43$	11.9305	1.81939	0.909694	−	0.415280i	$-0.136316\pi$
$43$	11.9305	1.81939	0.909694	+	0.415280i	$0.136316\pi$
$44$	10.1279	1.52684
$45$	3.41152	0.508559
$46$	8.31769	1.22638
$47$	0.561497	0.0819027	0.0409513	−	0.999161i	$-0.486961\pi$
$47$	0.561497	0.0819027	0.0409513	+	0.999161i	$0.486961\pi$
$48$	−7.20336	−1.03972
$49$	0.664841	0.0949773
$50$	9.73657	1.37696
$51$	2.54725	0.356687
$52$	−11.1143	−1.54128
$53$	1.76842	0.242912	0.121456	−	0.992597i	$-0.461244\pi$
$53$	1.76842	0.242912	0.121456	+	0.992597i	$0.461244\pi$
$54$	2.99614	0.407723
$55$	2.60791	0.351651
$56$	11.9849	1.60155
$57$	−12.2941	−1.62839
$58$	18.5529	2.43612
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−9.46059	−1.22136
$61$	−5.14785	−0.659114	−0.329557	−	0.944136i	$-0.606899\pi$
$61$	−5.14785	−0.659114	−0.329557	+	0.944136i	$0.606899\pi$
$62$	−25.9217	−3.29205
$63$	−9.65804	−1.21680
$64$	−10.1073	−1.26341
$65$	−2.86191	−0.354976
$66$	16.3564	2.01333
$67$	−9.77325	−1.19399	−0.596996	−	0.802244i	$-0.703639\pi$
$67$	−9.77325	−1.19399	−0.596996	+	0.802244i	$0.703639\pi$
$68$	−3.79784	−0.460555
$69$	8.79917	1.05930
$70$	6.51921	0.779194
$71$	−7.55510	−0.896626	−0.448313	−	0.893877i	$-0.647975\pi$
$71$	−7.55510	−0.896626	−0.448313	+	0.893877i	$0.647975\pi$
$72$	−15.1015	−1.77973
$73$	4.76779	0.558027	0.279014	−	0.960287i	$-0.409993\pi$
$73$	4.76779	0.558027	0.279014	+	0.960287i	$0.409993\pi$
$74$	−15.0097	−1.74484
$75$	10.3002	1.18936
$76$	18.3299	2.10259
$77$	−7.38303	−0.841374
$78$	−17.9494	−2.03237
$79$	−6.95701	−0.782724	−0.391362	−	0.920237i	$-0.627996\pi$
$79$	−6.95701	−0.782724	−0.391362	+	0.920237i	$0.627996\pi$
$80$	2.76550	0.309192
$81$	−7.29590	−0.810656
$82$	−11.6628	−1.28794
$83$	−5.65212	−0.620401	−0.310201	−	0.950671i	$-0.600396\pi$
$83$	−5.65212	−0.620401	−0.310201	+	0.950671i	$0.600396\pi$
$84$	26.7830	2.92227
$85$	−0.977935	−0.106072
$86$	−28.7271	−3.09773
$87$	19.6269	2.10422
$88$	−11.5443	−1.23062
$89$	−11.1982	−1.18701	−0.593503	−	0.804832i	$-0.702256\pi$
$89$	−11.1982	−1.18701	−0.593503	+	0.804832i	$0.702256\pi$
$90$	−8.21449	−0.865883
$91$	8.10210	0.849331
$92$	−13.1192	−1.36777
$93$	−27.4222	−2.84355
$94$	−1.35201	−0.139449
$95$	4.71991	0.484253
$96$	−4.70914	−0.480625
$97$	8.34612	0.847420	0.423710	−	0.905798i	$-0.360728\pi$
$97$	8.34612	0.847420	0.423710	+	0.905798i	$0.360728\pi$
$98$	−1.60085	−0.161710
$99$	9.30295	0.934982
$100$	−15.3571	−1.53571
$101$	−12.1932	−1.21327	−0.606634	−	0.794981i	$-0.707481\pi$
$101$	−12.1932	−1.21327	−0.606634	+	0.794981i	$0.707481\pi$
$102$	−6.13345	−0.607302
$103$	−4.60403	−0.453648	−0.226824	−	0.973936i	$-0.572834\pi$
$103$	−4.60403	−0.453648	−0.226824	+	0.973936i	$0.572834\pi$
$104$	12.6686	1.24226
$105$	6.89658	0.673037
$106$	−4.25814	−0.413587
$107$	9.65468	0.933353	0.466676	−	0.884428i	$-0.345451\pi$
$107$	9.65468	0.933353	0.466676	+	0.884428i	$0.345451\pi$
$108$	−4.72569	−0.454729
$109$	5.29872	0.507525	0.253763	−	0.967267i	$-0.418332\pi$
$109$	5.29872	0.507525	0.253763	+	0.967267i	$0.418332\pi$
$110$	−6.27951	−0.598728
$111$	−15.8786	−1.50713
$112$	−7.82915	−0.739785
$113$	−16.7396	−1.57473	−0.787363	−	0.616489i	$-0.788554\pi$
$113$	−16.7396	−1.57473	−0.787363	+	0.616489i	$0.788554\pi$
$114$	29.6025	2.77253
$115$	−3.37816	−0.315015
$116$	−29.2628	−2.71698
$117$	−10.2090	−0.943823
$118$	2.40787	0.221662
$119$	2.76854	0.253792
$120$	10.7836	0.984407
$121$	−3.88842	−0.353493
$122$	12.3953	1.12222
$123$	−12.3379	−1.11247
$124$	40.8852	3.67160
$125$	−8.84410	−0.791040
$126$	23.2553	2.07175
$127$	9.30909	0.826048	0.413024	−	0.910720i	$-0.364473\pi$
$127$	9.30909	0.826048	0.413024	+	0.910720i	$0.364473\pi$
$128$	20.6395	1.82429
$129$	−30.3900	−2.67569
$130$	6.89111	0.604390
$131$	−13.0637	−1.14138	−0.570689	−	0.821167i	$-0.693324\pi$
$131$	−13.0637	−1.14138	−0.570689	+	0.821167i	$0.693324\pi$
$132$	−25.7983	−2.24545
$133$	−13.3621	−1.15864
$134$	23.5327	2.03292
$135$	−1.21685	−0.104730
$136$	4.32896	0.371205
$137$	−19.2443	−1.64415	−0.822075	−	0.569379i	$-0.807184\pi$
$137$	−19.2443	−1.64415	−0.822075	+	0.569379i	$0.807184\pi$
$138$	−21.1873	−1.80358
$139$	1.06758	0.0905513	0.0452756	−	0.998975i	$-0.485583\pi$
$139$	1.06758	0.0905513	0.0452756	+	0.998975i	$0.485583\pi$
$140$	−10.2825	−0.869028
$141$	−1.43027	−0.120451
$142$	18.1917	1.52661
$143$	−7.80421	−0.652621
$144$	9.86508	0.822090
$145$	−7.53510	−0.625756
$146$	−11.4802	−0.950109
$147$	−1.69352	−0.139679
$148$	23.6742	1.94601
$149$	14.9249	1.22269	0.611347	−	0.791362i	$-0.290628\pi$
$149$	14.9249	1.22269	0.611347	+	0.791362i	$0.290628\pi$
$150$	−24.8015	−2.02503
$151$	6.51459	0.530149	0.265075	−	0.964228i	$-0.414603\pi$
$151$	6.51459	0.530149	0.265075	+	0.964228i	$0.414603\pi$
$152$	−20.8933	−1.69467
$153$	−3.48849	−0.282028
$154$	17.7774	1.43254
$155$	10.5279	0.845618
$156$	28.3109	2.26669
$157$	−3.19254	−0.254792	−0.127396	−	0.991852i	$-0.540662\pi$
$157$	−3.19254	−0.254792	−0.127396	+	0.991852i	$0.540662\pi$
$158$	16.7516	1.33268
$159$	−4.50462	−0.357240
$160$	1.80792	0.142929
$161$	9.56360	0.753717
$162$	17.5676	1.38024
$163$	16.6113	1.30109	0.650547	−	0.759466i	$-0.274539\pi$
$163$	16.6113	1.30109	0.650547	+	0.759466i	$0.274539\pi$
$164$	18.3952	1.43643
$165$	−6.64301	−0.517158
$166$	13.6096	1.05631
$167$	3.92325	0.303590	0.151795	−	0.988412i	$-0.451495\pi$
$167$	3.92325	0.303590	0.151795	+	0.988412i	$0.451495\pi$
$168$	−30.5286	−2.35533
$169$	−4.43570	−0.341208
$170$	2.35474	0.180600
$171$	16.8369	1.28755
$172$	45.3102	3.45487
$173$	−14.3121	−1.08813	−0.544065	−	0.839043i	$-0.683116\pi$
$173$	−14.3121	−1.08813	−0.544065	+	0.839043i	$0.683116\pi$
$174$	−47.2589	−3.58269
$175$	11.1950	0.846263
$176$	7.54130	0.568447
$177$	2.54725	0.191463
$178$	26.9638	2.02102
$179$	−23.8514	−1.78274	−0.891369	−	0.453278i	$-0.850255\pi$
$179$	−23.8514	−1.78274	−0.891369	+	0.453278i	$0.850255\pi$
$180$	12.9564	0.965712
$181$	−4.93888	−0.367104	−0.183552	−	0.983010i	$-0.558760\pi$
$181$	−4.93888	−0.367104	−0.183552	+	0.983010i	$0.558760\pi$
$182$	−19.5088	−1.44609
$183$	13.1129	0.969330
$184$	14.9539	1.10241
$185$	6.09606	0.448191
$186$	66.0290	4.84148
$187$	−2.66675	−0.195012
$188$	2.13247	0.155527
$189$	3.44493	0.250582
$190$	−11.3649	−0.824499
$191$	−10.2315	−0.740329	−0.370164	−	0.928966i	$-0.620699\pi$
$191$	−10.2315	−0.740329	−0.370164	+	0.928966i	$0.620699\pi$
$192$	25.7457	1.85804
$193$	−3.33603	−0.240133	−0.120067	−	0.992766i	$-0.538311\pi$
$193$	−3.33603	−0.240133	−0.120067	+	0.992766i	$0.538311\pi$
$194$	−20.0964	−1.44283
$195$	7.29000	0.522048
$196$	2.52496	0.180354
$197$	−9.11146	−0.649165	−0.324582	−	0.945857i	$-0.605224\pi$
$197$	−9.11146	−0.649165	−0.324582	+	0.945857i	$0.605224\pi$
$198$	−22.4003	−1.59192
$199$	−6.44020	−0.456534	−0.228267	−	0.973599i	$-0.573306\pi$
$199$	−6.44020	−0.456534	−0.228267	+	0.973599i	$0.573306\pi$
$200$	17.5048	1.23777
$201$	24.8949	1.75595
$202$	29.3596	2.06574
$203$	21.3319	1.49721
$204$	9.67405	0.677319
$205$	4.73673	0.330828
$206$	11.0859	0.772391
$207$	−12.0506	−0.837572
$208$	−8.27578	−0.573822
$209$	12.8708	0.890295
$210$	−16.6061	−1.14593
$211$	3.20270	0.220483	0.110242	−	0.993905i	$-0.464838\pi$
$211$	3.20270	0.220483	0.110242	+	0.993905i	$0.464838\pi$
$212$	6.71619	0.461270
$213$	19.2448	1.31863
$214$	−23.2472	−1.58915
$215$	11.6673	0.795701
$216$	5.38657	0.366509
$217$	−29.8045	−2.02326
$218$	−12.7586	−0.864123
$219$	−12.1447	−0.820666
$220$	9.90443	0.667756
$221$	2.92648	0.196856
$222$	38.2335	2.56606
$223$	−9.28326	−0.621653	−0.310827	−	0.950467i	$-0.600606\pi$
$223$	−9.28326	−0.621653	−0.310827	+	0.950467i	$0.600606\pi$
$224$	−5.11825	−0.341978
$225$	−14.1062	−0.940414
$226$	40.3067	2.68116
$227$	−4.51500	−0.299671	−0.149836	−	0.988711i	$-0.547874\pi$
$227$	−4.51500	−0.299671	−0.149836	+	0.988711i	$0.547874\pi$
$228$	−46.6909	−3.09218
$229$	−15.7145	−1.03845	−0.519223	−	0.854639i	$-0.673778\pi$
$229$	−15.7145	−1.03845	−0.519223	+	0.854639i	$0.673778\pi$
$230$	8.13416	0.536351
$231$	18.8064	1.23737
$232$	33.3551	2.18987
$233$	18.0439	1.18209	0.591046	−	0.806638i	$-0.298715\pi$
$233$	18.0439	1.18209	0.591046	+	0.806638i	$0.298715\pi$
$234$	24.5820	1.60697
$235$	0.549107	0.0358198
$236$	−3.79784	−0.247218
$237$	17.7212	1.15112
$238$	−6.66630	−0.432112
$239$	12.5552	0.812130	0.406065	−	0.913844i	$-0.366901\pi$
$239$	12.5552	0.812130	0.406065	+	0.913844i	$0.366901\pi$
$240$	−7.04442	−0.454715
$241$	10.1762	0.655507	0.327754	−	0.944763i	$-0.393708\pi$
$241$	10.1762	0.655507	0.327754	+	0.944763i	$0.393708\pi$
$242$	9.36281	0.601864
$243$	22.3174	1.43166
$244$	−19.5507	−1.25160
$245$	0.650172	0.0415379
$246$	29.7080	1.89411
$247$	−14.1244	−0.898714
$248$	−46.6029	−2.95929
$249$	14.3974	0.912397
$250$	21.2954	1.34684
$251$	9.04587	0.570970	0.285485	−	0.958383i	$-0.407845\pi$
$251$	9.04587	0.570970	0.285485	+	0.958383i	$0.407845\pi$
$252$	−36.6797	−2.31060
$253$	−9.21198	−0.579152
$254$	−22.4151	−1.40645
$255$	2.49105	0.155995
$256$	−29.4828	−1.84267
$257$	6.94742	0.433368	0.216684	−	0.976242i	$-0.430476\pi$
$257$	6.94742	0.433368	0.216684	+	0.976242i	$0.430476\pi$
$258$	73.1752	4.55569
$259$	−17.2580	−1.07236
$260$	−10.8691	−0.674071
$261$	−26.8792	−1.66378
$262$	31.4556	1.94333
$263$	−32.1778	−1.98417	−0.992083	−	0.125584i	$-0.959919\pi$
$263$	−32.1778	−1.98417	−0.992083	+	0.125584i	$0.959919\pi$
$264$	29.4062	1.80982
$265$	1.72940	0.106236
$266$	32.1743	1.97273
$267$	28.5246	1.74568
$268$	−37.1172	−2.26729
$269$	0.259667	0.0158322	0.00791610	−	0.999969i	$-0.497480\pi$
$269$	0.259667	0.0158322	0.00791610	+	0.999969i	$0.497480\pi$
$270$	2.93003	0.178316
$271$	−22.0110	−1.33708	−0.668538	−	0.743678i	$-0.733079\pi$
$271$	−22.0110	−1.33708	−0.668538	+	0.743678i	$0.733079\pi$
$272$	−2.82789	−0.171466
$273$	−20.6381	−1.24907
$274$	46.3377	2.79936
$275$	−10.7834	−0.650264
$276$	33.4178	2.01152
$277$	−25.0583	−1.50561	−0.752804	−	0.658244i	$-0.771299\pi$
$277$	−25.0583	−1.50561	−0.752804	+	0.658244i	$0.771299\pi$
$278$	−2.57060	−0.154175
$279$	37.5550	2.24836
$280$	11.7205	0.700432
$281$	18.5910	1.10905	0.554523	−	0.832168i	$-0.312901\pi$
$281$	18.5910	1.10905	0.554523	+	0.832168i	$0.312901\pi$
$282$	3.44391	0.205082
$283$	−29.3260	−1.74325	−0.871624	−	0.490175i	$-0.836933\pi$
$283$	−29.3260	−1.74325	−0.871624	+	0.490175i	$0.836933\pi$
$284$	−28.6931	−1.70262
$285$	−12.0228	−0.712170
$286$	18.7915	1.11117
$287$	−13.4097	−0.791552
$288$	6.44923	0.380024
$289$	1.00000	0.0588235
$290$	18.1435	1.06542
$291$	−21.2597	−1.24626
$292$	18.1073	1.05965
$293$	15.4880	0.904820	0.452410	−	0.891810i	$-0.350564\pi$
$293$	15.4880	0.904820	0.452410	+	0.891810i	$0.350564\pi$
$294$	4.07777	0.237820
$295$	−0.977935	−0.0569376
$296$	−26.9850	−1.56847
$297$	−3.31827	−0.192545
$298$	−35.9372	−2.08179
$299$	10.1092	0.584629
$300$	39.1184	2.25850
$301$	−33.0302	−1.90383
$302$	−15.6863	−0.902644
$303$	31.0591	1.78430
$304$	13.6486	0.782799
$305$	−5.03426	−0.288261
$306$	8.39983	0.480186
$307$	−11.3555	−0.648091	−0.324046	−	0.946041i	$-0.605043\pi$
$307$	−11.3555	−0.648091	−0.324046	+	0.946041i	$0.605043\pi$
$308$	−28.0395	−1.59770
$309$	11.7276	0.667161
$310$	−25.3497	−1.43977
$311$	−16.6833	−0.946024	−0.473012	−	0.881056i	$-0.656833\pi$
$311$	−16.6833	−0.946024	−0.473012	+	0.881056i	$0.656833\pi$
$312$	−32.2702	−1.82694
$313$	−17.4512	−0.986401	−0.493201	−	0.869916i	$-0.664173\pi$
$313$	−17.4512	−0.986401	−0.493201	+	0.869916i	$0.664173\pi$
$314$	7.68721	0.433815
$315$	−9.44494	−0.532162
$316$	−26.4216	−1.48633
$317$	−10.1402	−0.569531	−0.284765	−	0.958597i	$-0.591916\pi$
$317$	−10.1402	−0.569531	−0.284765	+	0.958597i	$0.591916\pi$
$318$	10.8465	0.608244
$319$	−20.5476	−1.15045
$320$	−9.88424	−0.552546
$321$	−24.5929	−1.37264
$322$	−23.0279	−1.28330
$323$	−4.82641	−0.268549
$324$	−27.7087	−1.53937
$325$	11.8336	0.656413
$326$	−39.9978	−2.21527
$327$	−13.4972	−0.746395
$328$	−20.9678	−1.15775
$329$	−1.55453	−0.0857039
$330$	15.9955	0.880524
$331$	27.5888	1.51642	0.758209	−	0.652011i	$-0.226075\pi$
$331$	27.5888	1.51642	0.758209	+	0.652011i	$0.226075\pi$
$332$	−21.4658	−1.17809
$333$	21.7459	1.19167
$334$	−9.44667	−0.516899
$335$	−9.55760	−0.522188
$336$	19.9428	1.08797
$337$	17.1422	0.933794	0.466897	−	0.884312i	$-0.345372\pi$
$337$	17.1422	0.933794	0.466897	+	0.884312i	$0.345372\pi$
$338$	10.6806	0.580948
$339$	42.6399	2.31588
$340$	−3.71404	−0.201422
$341$	28.7087	1.55466
$342$	−40.5410	−2.19221
$343$	17.5392	0.947026
$344$	−51.6467	−2.78460
$345$	8.60502	0.463279
$346$	34.4617	1.85267
$347$	14.7303	0.790765	0.395382	−	0.918517i	$-0.370612\pi$
$347$	14.7303	0.790765	0.395382	+	0.918517i	$0.370612\pi$
$348$	74.5396	3.99574
$349$	−27.1345	−1.45247	−0.726237	−	0.687444i	$-0.758733\pi$
$349$	−27.1345	−1.45247	−0.726237	+	0.687444i	$0.758733\pi$
$350$	−26.9561	−1.44087
$351$	3.64145	0.194366
$352$	4.93007	0.262774
$353$	−14.0796	−0.749379	−0.374689	−	0.927150i	$-0.622251\pi$
$353$	−14.0796	−0.749379	−0.374689	+	0.927150i	$0.622251\pi$
$354$	−6.13345	−0.325989
$355$	−7.38840	−0.392136
$356$	−42.5289	−2.25403
$357$	−7.05218	−0.373241
$358$	57.4311	3.03533
$359$	23.3682	1.23333	0.616663	−	0.787227i	$-0.288484\pi$
$359$	23.3682	1.23333	0.616663	+	0.787227i	$0.288484\pi$
$360$	−14.7683	−0.778359
$361$	4.29422	0.226011
$362$	11.8922	0.625039
$363$	9.90479	0.519867
$364$	30.7704	1.61281
$365$	4.66258	0.244051
$366$	−31.5741	−1.65040
$367$	24.1927	1.26285	0.631423	−	0.775438i	$-0.282471\pi$
$367$	24.1927	1.26285	0.631423	+	0.775438i	$0.282471\pi$
$368$	−9.76862	−0.509224
$369$	16.8969	0.879617
$370$	−14.6785	−0.763100
$371$	−4.89596	−0.254186
$372$	−104.145	−5.39966
$373$	−29.5119	−1.52807	−0.764034	−	0.645176i	$-0.776784\pi$
$373$	−29.5119	−1.52807	−0.764034	+	0.645176i	$0.776784\pi$
$374$	6.42120	0.332032
$375$	22.5281	1.16335
$376$	−2.43070	−0.125354
$377$	22.5489	1.16133
$378$	−8.29494	−0.426646
$379$	20.6590	1.06118	0.530591	−	0.847628i	$-0.321970\pi$
$379$	20.6590	1.06118	0.530591	+	0.847628i	$0.321970\pi$
$380$	17.9255	0.919557
$381$	−23.7126	−1.21483
$382$	24.6362	1.26050
$383$	−16.2503	−0.830350	−0.415175	−	0.909742i	$-0.636280\pi$
$383$	−16.2503	−0.830350	−0.415175	+	0.909742i	$0.636280\pi$
$384$	−52.5741	−2.68291
$385$	−7.22012	−0.367972
$386$	8.03274	0.408856
$387$	41.6195	2.11564
$388$	31.6972	1.60918
$389$	−27.1261	−1.37535	−0.687675	−	0.726019i	$-0.741369\pi$
$389$	−27.1261	−1.37535	−0.687675	+	0.726019i	$0.741369\pi$
$390$	−17.5534	−0.888850
$391$	3.45438	0.174695
$392$	−2.87807	−0.145364
$393$	33.2764	1.67857
$394$	21.9392	1.10528
$395$	−6.80350	−0.342321
$396$	35.3311	1.77545
$397$	18.7280	0.939931	0.469966	−	0.882685i	$-0.344266\pi$
$397$	18.7280	0.939931	0.469966	+	0.882685i	$0.344266\pi$
$398$	15.5072	0.777304
$399$	34.0367	1.70397
$400$	−11.4350	−0.571750
$401$	21.9826	1.09776	0.548879	−	0.835902i	$-0.315055\pi$
$401$	21.9826	1.09776	0.548879	+	0.835902i	$0.315055\pi$
$402$	−59.9437	−2.98972
$403$	−31.5047	−1.56936
$404$	−46.3078	−2.30390
$405$	−7.13492	−0.354537
$406$	−51.3645	−2.54918
$407$	16.6235	0.823996
$408$	−11.0269	−0.545915
$409$	−0.931160	−0.0460429	−0.0230214	−	0.999735i	$-0.507329\pi$
$409$	−0.931160	−0.0460429	−0.0230214	+	0.999735i	$0.507329\pi$
$410$	−11.4054	−0.563274
$411$	49.0200	2.41798
$412$	−17.4854	−0.861442
$413$	2.76854	0.136231
$414$	29.0162	1.42607
$415$	−5.52741	−0.271330
$416$	−5.41023	−0.265258
$417$	−2.71940	−0.133170
$418$	−30.9913	−1.51584
$419$	−11.7376	−0.573417	−0.286709	−	0.958018i	$-0.592561\pi$
$419$	−11.7376	−0.573417	−0.286709	+	0.958018i	$0.592561\pi$
$420$	26.1921	1.27804
$421$	−8.84388	−0.431024	−0.215512	−	0.976501i	$-0.569142\pi$
$421$	−8.84388	−0.431024	−0.215512	+	0.976501i	$0.569142\pi$
$422$	−7.71169	−0.375399
$423$	1.95878	0.0952389
$424$	−7.65544	−0.371781
$425$	4.04364	0.196145
$426$	−46.3389	−2.24512
$427$	14.2520	0.689705
$428$	36.6669	1.77236
$429$	19.8793	0.959781
$430$	−28.0933	−1.35478
$431$	12.1564	0.585554	0.292777	−	0.956181i	$-0.405421\pi$
$431$	12.1564	0.585554	0.292777	+	0.956181i	$0.405421\pi$
$432$	−3.51878	−0.169297
$433$	31.8778	1.53195	0.765975	−	0.642870i	$-0.222257\pi$
$433$	31.8778	1.53195	0.765975	+	0.642870i	$0.222257\pi$
$434$	71.7653	3.44484
$435$	19.1938	0.920272
$436$	20.1237	0.963749
$437$	−16.6722	−0.797541
$438$	29.2430	1.39728
$439$	0.287551	0.0137241	0.00686204	−	0.999976i	$-0.497816\pi$
$439$	0.287551	0.0137241	0.00686204	+	0.999976i	$0.497816\pi$
$440$	−11.2895	−0.538208
$441$	2.31929	0.110442
$442$	−7.04659	−0.335172
$443$	13.3417	0.633884	0.316942	−	0.948445i	$-0.397344\pi$
$443$	13.3417	0.633884	0.316942	+	0.948445i	$0.397344\pi$
$444$	−60.3042	−2.86191
$445$	−10.9511	−0.519132
$446$	22.3529	1.05844
$447$	−38.0175	−1.79816
$448$	27.9824	1.32204
$449$	21.1497	0.998118	0.499059	−	0.866568i	$-0.333679\pi$
$449$	21.1497	0.998118	0.499059	+	0.866568i	$0.333679\pi$
$450$	33.9659	1.60117
$451$	12.9167	0.608224
$452$	−63.5742	−2.99028
$453$	−16.5943	−0.779668
$454$	10.8715	0.510227
$455$	7.92333	0.371451
$456$	53.2206	2.49228
$457$	17.8909	0.836902	0.418451	−	0.908239i	$-0.362573\pi$
$457$	17.8909	0.836902	0.418451	+	0.908239i	$0.362573\pi$
$458$	37.8385	1.76808
$459$	1.24431	0.0580794
$460$	−12.8297	−0.598188
$461$	−1.41428	−0.0658696	−0.0329348	−	0.999458i	$-0.510485\pi$
$461$	−1.41428	−0.0658696	−0.0329348	+	0.999458i	$0.510485\pi$
$462$	−45.2834	−2.10678
$463$	−18.2507	−0.848181	−0.424090	−	0.905620i	$-0.639406\pi$
$463$	−18.2507	−0.848181	−0.424090	+	0.905620i	$0.639406\pi$
$464$	−21.7892	−1.01154
$465$	−26.8171	−1.24361
$466$	−43.4472	−2.01265
$467$	−9.21953	−0.426629	−0.213314	−	0.976984i	$-0.568426\pi$
$467$	−9.21953	−0.426629	−0.213314	+	0.976984i	$0.568426\pi$
$468$	−38.7721	−1.79224
$469$	27.0577	1.24941
$470$	−1.32218	−0.0609876
$471$	8.13220	0.374712
$472$	4.32896	0.199256
$473$	31.8158	1.46289
$474$	−42.6705	−1.95992
$475$	−19.5163	−0.895468
$476$	10.5145	0.481931
$477$	6.16913	0.282465
$478$	−30.2313	−1.38275
$479$	−18.2274	−0.832831	−0.416415	−	0.909174i	$-0.636714\pi$
$479$	−18.2274	−0.832831	−0.416415	+	0.909174i	$0.636714\pi$
$480$	−4.60524	−0.210199
$481$	−18.2425	−0.831788
$482$	−24.5030	−1.11608
$483$	−24.3609	−1.10846
$484$	−14.7676	−0.671254
$485$	8.16196	0.370616
$486$	−53.7375	−2.43758
$487$	−31.6871	−1.43588	−0.717940	−	0.696105i	$-0.754915\pi$
$487$	−31.6871	−1.43588	−0.717940	+	0.696105i	$0.754915\pi$
$488$	22.2848	1.00879
$489$	−42.3131	−1.91346
$490$	−1.56553	−0.0707234
$491$	20.6207	0.930600	0.465300	−	0.885153i	$-0.345946\pi$
$491$	20.6207	0.930600	0.465300	+	0.885153i	$0.345946\pi$
$492$	−46.8573	−2.11249
$493$	7.70511	0.347021
$494$	34.0097	1.53017
$495$	9.09768	0.408910
$496$	30.4434	1.36695
$497$	20.9166	0.938240
$498$	−34.6670	−1.55347
$499$	2.00958	0.0899612	0.0449806	−	0.998988i	$-0.485677\pi$
$499$	2.00958	0.0899612	0.0449806	+	0.998988i	$0.485677\pi$
$500$	−33.5884	−1.50212
$501$	−9.99350	−0.446477
$502$	−21.7813	−0.972146
$503$	−17.4593	−0.778470	−0.389235	−	0.921139i	$-0.627261\pi$
$503$	−17.4593	−0.778470	−0.389235	+	0.921139i	$0.627261\pi$
$504$	41.8093	1.86233
$505$	−11.9242	−0.530618
$506$	22.1812	0.986077
$507$	11.2989	0.501800
$508$	35.3544	1.56860
$509$	−41.2806	−1.82973	−0.914866	−	0.403757i	$-0.867704\pi$
$509$	−41.2806	−1.82973	−0.914866	+	0.403757i	$0.867704\pi$
$510$	−5.99812	−0.265601
$511$	−13.1998	−0.583926
$512$	29.7116	1.31308
$513$	−6.00555	−0.265151
$514$	−16.7285	−0.737862
$515$	−4.50244	−0.198401
$516$	−115.416	−5.08092
$517$	1.49737	0.0658544
$518$	41.5551	1.82582
$519$	36.4566	1.60027
$520$	12.3891	0.543297
$521$	−24.9767	−1.09425	−0.547125	−	0.837051i	$-0.684278\pi$
$521$	−24.9767	−1.09425	−0.547125	+	0.837051i	$0.684278\pi$
$522$	64.7216	2.83279
$523$	−42.0501	−1.83872	−0.919361	−	0.393415i	$-0.871293\pi$
$523$	−42.0501	−1.83872	−0.919361	+	0.393415i	$0.871293\pi$
$524$	−49.6137	−2.16738
$525$	−28.5165	−1.24456
$526$	77.4799	3.37828
$527$	−10.7654	−0.468948
$528$	−19.2096	−0.835990
$529$	−11.0673	−0.481186
$530$	−4.16418	−0.180880
$531$	−3.48849	−0.151388
$532$	−50.7472	−2.20017
$533$	−14.1747	−0.613976
$534$	−68.6836	−2.97223
$535$	9.44165	0.408198
$536$	42.3080	1.82743
$537$	60.7556	2.62180
$538$	−0.625245	−0.0269562
$539$	1.77297	0.0763671
$540$	−4.62142	−0.198874
$541$	17.9925	0.773558	0.386779	−	0.922172i	$-0.373588\pi$
$541$	17.9925	0.773558	0.386779	+	0.922172i	$0.373588\pi$
$542$	52.9997	2.27653
$543$	12.5806	0.539884
$544$	−1.84872	−0.0792630
$545$	5.18181	0.221964
$546$	49.6938	2.12670
$547$	−26.0418	−1.11347	−0.556734	−	0.830691i	$-0.687946\pi$
$547$	−26.0418	−1.11347	−0.556734	+	0.830691i	$0.687946\pi$
$548$	−73.0866	−3.12211
$549$	−17.9582	−0.766438
$550$	25.9650	1.10715
$551$	−37.1880	−1.58426
$552$	−38.0912	−1.62127
$553$	19.2608	0.819052
$554$	60.3372	2.56348
$555$	−15.5282	−0.659135
$556$	4.05451	0.171950
$557$	35.6613	1.51102	0.755510	−	0.655137i	$-0.227389\pi$
$557$	35.6613	1.51102	0.755510	+	0.655137i	$0.227389\pi$
$558$	−90.4275	−3.82810
$559$	−34.9144	−1.47672
$560$	−7.65640	−0.323542
$561$	6.79289	0.286796
$562$	−44.7647	−1.88829
$563$	−12.4478	−0.524614	−0.262307	−	0.964984i	$-0.584483\pi$
$563$	−12.4478	−0.524614	−0.262307	+	0.964984i	$0.584483\pi$
$564$	−5.43194	−0.228726
$565$	−16.3702	−0.688700
$566$	70.6131	2.96809
$567$	20.1990	0.848280
$568$	32.7057	1.37230
$569$	−16.2534	−0.681377	−0.340688	−	0.940176i	$-0.610660\pi$
$569$	−16.2534	−0.681377	−0.340688	+	0.940176i	$0.610660\pi$
$570$	28.9494	1.21256
$571$	23.4754	0.982415	0.491208	−	0.871043i	$-0.336556\pi$
$571$	23.4754	0.982415	0.491208	+	0.871043i	$0.336556\pi$
$572$	−29.6391	−1.23927
$573$	26.0623	1.08877
$574$	32.2889	1.34771
$575$	13.9683	0.582517
$576$	−35.2591	−1.46913
$577$	−36.0434	−1.50050	−0.750252	−	0.661151i	$-0.770068\pi$
$577$	−36.0434	−1.50050	−0.750252	+	0.661151i	$0.770068\pi$
$578$	−2.40787	−0.100154
$579$	8.49772	0.353153
$580$	−28.6171	−1.18826
$581$	15.6482	0.649195
$582$	51.1905	2.12191
$583$	4.71595	0.195315
$584$	−20.6395	−0.854071
$585$	−9.98375	−0.412777
$586$	−37.2931	−1.54057
$587$	−29.2272	−1.20634	−0.603168	−	0.797614i	$-0.706095\pi$
$587$	−29.2272	−1.20634	−0.603168	+	0.797614i	$0.706095\pi$
$588$	−6.43170	−0.265239
$589$	51.9582	2.14090
$590$	2.35474	0.0969431
$591$	23.2092	0.954698
$592$	17.6280	0.724505
$593$	0.717373	0.0294590	0.0147295	−	0.999892i	$-0.495311\pi$
$593$	0.717373	0.0294590	0.0147295	+	0.999892i	$0.495311\pi$
$594$	7.98996	0.327832
$595$	2.70746	0.110995
$596$	56.6823	2.32180
$597$	16.4048	0.671405
$598$	−24.3416	−0.995401
$599$	36.5966	1.49530	0.747649	−	0.664094i	$-0.231183\pi$
$599$	36.5966	1.49530	0.747649	+	0.664094i	$0.231183\pi$
$600$	−44.5890	−1.82034
$601$	38.6194	1.57532	0.787660	−	0.616110i	$-0.211293\pi$
$601$	38.6194	1.57532	0.787660	+	0.616110i	$0.211293\pi$
$602$	79.5324	3.24150
$603$	−34.0939	−1.38841
$604$	24.7413	1.00671
$605$	−3.80262	−0.154599
$606$	−74.7863	−3.03799
$607$	42.5614	1.72752	0.863758	−	0.503908i	$-0.168105\pi$
$607$	42.5614	1.72752	0.863758	+	0.503908i	$0.168105\pi$
$608$	8.92266	0.361861
$609$	−54.3378	−2.20188
$610$	12.1218	0.490799
$611$	−1.64321	−0.0664771
$612$	−13.2487	−0.535548
$613$	−19.4876	−0.787096	−0.393548	−	0.919304i	$-0.628753\pi$
$613$	−19.4876	−0.787096	−0.393548	+	0.919304i	$0.628753\pi$
$614$	27.3425	1.10345
$615$	−12.0657	−0.486534
$616$	31.9608	1.28774
$617$	−8.22744	−0.331224	−0.165612	−	0.986191i	$-0.552960\pi$
$617$	−8.22744	−0.331224	−0.165612	+	0.986191i	$0.552960\pi$
$618$	−28.2386	−1.13592
$619$	−7.44362	−0.299184	−0.149592	−	0.988748i	$-0.547796\pi$
$619$	−7.44362	−0.299184	−0.149592	+	0.988748i	$0.547796\pi$
$620$	39.9831	1.60576
$621$	4.29832	0.172486
$622$	40.1713	1.61072
$623$	31.0027	1.24210
$624$	21.0805	0.843895
$625$	11.5693	0.462770
$626$	42.0203	1.67947
$627$	−32.7853	−1.30932
$628$	−12.1247	−0.483830
$629$	−6.23360	−0.248550
$630$	22.7422	0.906071
$631$	2.77542	0.110488	0.0552438	−	0.998473i	$-0.482406\pi$
$631$	2.77542	0.110488	0.0552438	+	0.998473i	$0.482406\pi$
$632$	30.1166	1.19797
$633$	−8.15809	−0.324255
$634$	24.4163	0.969695
$635$	9.10368	0.361269
$636$	−17.1078	−0.678369
$637$	−1.94565	−0.0770893
$638$	49.4760	1.95877
$639$	−26.3559	−1.04262
$640$	20.1841	0.797847
$641$	−16.8025	−0.663660	−0.331830	−	0.943339i	$-0.607666\pi$
$641$	−16.8025	−0.663660	−0.331830	+	0.943339i	$0.607666\pi$
$642$	59.2165	2.33709
$643$	5.67941	0.223974	0.111987	−	0.993710i	$-0.464279\pi$
$643$	5.67941	0.223974	0.111987	+	0.993710i	$0.464279\pi$
$644$	36.3210	1.43125
$645$	−29.7195	−1.17020
$646$	11.6214	0.457236
$647$	−10.8178	−0.425291	−0.212646	−	0.977129i	$-0.568208\pi$
$647$	−10.8178	−0.425291	−0.212646	+	0.977129i	$0.568208\pi$
$648$	31.5837	1.24072
$649$	−2.66675	−0.104679
$650$	−28.4939	−1.11762
$651$	75.9195	2.97552
$652$	63.0869	2.47067
$653$	24.3695	0.953652	0.476826	−	0.878998i	$-0.341787\pi$
$653$	24.3695	0.953652	0.476826	+	0.878998i	$0.341787\pi$
$654$	32.4994	1.27083
$655$	−12.7754	−0.499177
$656$	13.6972	0.534786
$657$	16.6324	0.648891
$658$	3.74310	0.145921
$659$	12.0945	0.471134	0.235567	−	0.971858i	$-0.424305\pi$
$659$	12.0945	0.471134	0.235567	+	0.971858i	$0.424305\pi$
$660$	−25.2291	−0.982040
$661$	5.09246	0.198074	0.0990369	−	0.995084i	$-0.468424\pi$
$661$	5.09246	0.198074	0.0990369	+	0.995084i	$0.468424\pi$
$662$	−66.4303	−2.58189
$663$	−7.45449	−0.289508
$664$	24.4678	0.949535
$665$	−13.0673	−0.506728
$666$	−52.3612	−2.02896
$667$	26.6164	1.03059
$668$	14.8999	0.576493
$669$	23.6468	0.914238
$670$	23.0135	0.889088
$671$	−13.7280	−0.529965
$672$	13.0375	0.502932
$673$	35.8835	1.38321	0.691604	−	0.722277i	$-0.256905\pi$
$673$	35.8835	1.38321	0.691604	+	0.722277i	$0.256905\pi$
$674$	−41.2761	−1.58990
$675$	5.03154	0.193664
$676$	−16.8461	−0.647926
$677$	−8.68789	−0.333903	−0.166951	−	0.985965i	$-0.553392\pi$
$677$	−8.68789	−0.333903	−0.166951	+	0.985965i	$0.553392\pi$
$678$	−102.671	−3.94307
$679$	−23.1066	−0.886750
$680$	4.23344	0.162345
$681$	11.5009	0.440714
$682$	−69.1267	−2.64700
$683$	−28.2897	−1.08248	−0.541239	−	0.840869i	$-0.682044\pi$
$683$	−28.2897	−1.08248	−0.541239	+	0.840869i	$0.682044\pi$
$684$	63.9437	2.44495
$685$	−18.8197	−0.719062
$686$	−42.2320	−1.61243
$687$	40.0289	1.52720
$688$	33.7382	1.28626
$689$	−5.17526	−0.197162
$690$	−20.7198	−0.788788
$691$	−21.3558	−0.812411	−0.406206	−	0.913782i	$-0.633148\pi$
$691$	−21.3558	−0.812411	−0.406206	+	0.913782i	$0.633148\pi$
$692$	−54.3551	−2.06627
$693$	−25.7556	−0.978376
$694$	−35.4687	−1.34637
$695$	1.04403	0.0396022
$696$	−84.9638	−3.22055
$697$	−4.84361	−0.183465
$698$	65.3363	2.47301
$699$	−45.9622	−1.73845
$700$	42.5168	1.60698
$701$	15.8750	0.599589	0.299795	−	0.954004i	$-0.403082\pi$
$701$	15.8750	0.599589	0.299795	+	0.954004i	$0.403082\pi$
$702$	−8.76814	−0.330932
$703$	30.0859	1.13471
$704$	−26.9536	−1.01585
$705$	−1.39871	−0.0526786
$706$	33.9017	1.27591
$707$	33.7574	1.26958
$708$	9.67405	0.363573
$709$	14.2099	0.533662	0.266831	−	0.963743i	$-0.414023\pi$
$709$	14.2099	0.533662	0.266831	+	0.963743i	$0.414023\pi$
$710$	17.7903	0.667658
$711$	−24.2695	−0.910176
$712$	48.4765	1.81673
$713$	−37.1877	−1.39269
$714$	16.9807	0.635488
$715$	−7.63201	−0.285421
$716$	−90.5838	−3.38528
$717$	−31.9813	−1.19436
$718$	−56.2676	−2.09989
$719$	10.7737	0.401792	0.200896	−	0.979613i	$-0.435615\pi$
$719$	10.7737	0.401792	0.200896	+	0.979613i	$0.435615\pi$
$720$	9.64741	0.359538
$721$	12.7465	0.474703
$722$	−10.3399	−0.384812
$723$	−25.9214	−0.964026
$724$	−18.7571	−0.697101
$725$	31.1567	1.15713
$726$	−23.8494	−0.885136
$727$	12.2910	0.455849	0.227924	−	0.973679i	$-0.426806\pi$
$727$	12.2910	0.455849	0.227924	+	0.973679i	$0.426806\pi$
$728$	−35.0736	−1.29992
$729$	−34.9604	−1.29483
$730$	−11.2269	−0.415526
$731$	−11.9305	−0.441266
$732$	49.8005	1.84068
$733$	−2.79380	−0.103191	−0.0515957	−	0.998668i	$-0.516431\pi$
$733$	−2.79380	−0.103191	−0.0515957	+	0.998668i	$0.516431\pi$
$734$	−58.2528	−2.15015
$735$	−1.65615	−0.0610880
$736$	−6.38616	−0.235397
$737$	−26.0628	−0.960037
$738$	−40.6855	−1.49765
$739$	−27.0017	−0.993274	−0.496637	−	0.867958i	$-0.665432\pi$
$739$	−27.0017	−0.993274	−0.496637	+	0.867958i	$0.665432\pi$
$740$	23.1518	0.851079
$741$	35.9784	1.32170
$742$	11.7888	0.432782
$743$	11.1452	0.408876	0.204438	−	0.978879i	$-0.434463\pi$
$743$	11.1452	0.408876	0.204438	+	0.978879i	$0.434463\pi$
$744$	118.709	4.35210
$745$	14.5956	0.534741
$746$	71.0608	2.60172
$747$	−19.7174	−0.721421
$748$	−10.1279	−0.370313
$749$	−26.7294	−0.976671
$750$	−54.2448	−1.98074
$751$	7.23201	0.263900	0.131950	−	0.991256i	$-0.457876\pi$
$751$	7.23201	0.263900	0.131950	+	0.991256i	$0.457876\pi$
$752$	1.58785	0.0579030
$753$	−23.0421	−0.839701
$754$	−54.2947	−1.97730
$755$	6.37084	0.231859
$756$	13.0833	0.475834
$757$	−31.4025	−1.14134	−0.570671	−	0.821179i	$-0.693317\pi$
$757$	−31.4025	−1.14134	−0.570671	+	0.821179i	$0.693317\pi$
$758$	−49.7442	−1.80679
$759$	23.4652	0.851734
$760$	−20.4323	−0.741158
$761$	43.1599	1.56455	0.782273	−	0.622935i	$-0.214060\pi$
$761$	43.1599	1.56455	0.782273	+	0.622935i	$0.214060\pi$
$762$	57.0968	2.06840
$763$	−14.6697	−0.531080
$764$	−38.8577	−1.40582
$765$	−3.41152	−0.123344
$766$	39.1285	1.41377
$767$	2.92648	0.105669
$768$	75.1001	2.70994
$769$	40.1696	1.44855	0.724277	−	0.689509i	$-0.242174\pi$
$769$	40.1696	1.44855	0.724277	+	0.689509i	$0.242174\pi$
$770$	17.3851	0.626516
$771$	−17.6968	−0.637336
$772$	−12.6697	−0.455993
$773$	−27.7396	−0.997724	−0.498862	−	0.866681i	$-0.666249\pi$
$773$	−27.7396	−0.997724	−0.498862	+	0.866681i	$0.666249\pi$
$774$	−100.214	−3.60213
$775$	−43.5314	−1.56369
$776$	−36.1300	−1.29699
$777$	43.9605	1.57707
$778$	65.3162	2.34170
$779$	23.3772	0.837576
$780$	27.6863	0.991327
$781$	−20.1476	−0.720938
$782$	−8.31769	−0.297440
$783$	9.58754	0.342631
$784$	1.88010	0.0671464
$785$	−3.12209	−0.111432
$786$	−80.1253	−2.85798
$787$	33.5333	1.19533	0.597667	−	0.801744i	$-0.296094\pi$
$787$	33.5333	1.19533	0.597667	+	0.801744i	$0.296094\pi$
$788$	−34.6038	−1.23271
$789$	81.9649	2.91803
$790$	16.3819	0.582844
$791$	46.3443	1.64781
$792$	−40.2721	−1.43101
$793$	15.0651	0.534977
$794$	−45.0946	−1.60035
$795$	−4.40523	−0.156237
$796$	−24.4588	−0.866921
$797$	−14.9418	−0.529264	−0.264632	−	0.964349i	$-0.585251\pi$
$797$	−14.9418	−0.529264	−0.264632	+	0.964349i	$0.585251\pi$
$798$	−81.9560	−2.90121
$799$	−0.561497	−0.0198643
$800$	−7.47554	−0.264300
$801$	−39.0648	−1.38029
$802$	−52.9312	−1.86907
$803$	12.7145	0.448685
$804$	94.5469	3.33441
$805$	9.35258	0.329635
$806$	75.8593	2.67203
$807$	−0.661438	−0.0232837
$808$	52.7838	1.85693
$809$	−20.3279	−0.714690	−0.357345	−	0.933972i	$-0.616318\pi$
$809$	−20.3279	−0.714690	−0.357345	+	0.933972i	$0.616318\pi$
$810$	17.1800	0.603642
$811$	−37.4251	−1.31417	−0.657087	−	0.753815i	$-0.728212\pi$
$811$	−37.4251	−1.31417	−0.657087	+	0.753815i	$0.728212\pi$
$812$	81.0152	2.84308
$813$	56.0676	1.96638
$814$	−40.0272	−1.40295
$815$	16.2447	0.569029
$816$	7.20336	0.252168
$817$	57.5816	2.01452
$818$	2.24211	0.0783936
$819$	28.2641	0.987627
$820$	17.9893	0.628215
$821$	−19.4314	−0.678160	−0.339080	−	0.940758i	$-0.610116\pi$
$821$	−19.4314	−0.678160	−0.339080	+	0.940758i	$0.610116\pi$
$822$	−118.034	−4.11690
$823$	26.3108	0.917138	0.458569	−	0.888659i	$-0.348362\pi$
$823$	26.3108	0.917138	0.458569	+	0.888659i	$0.348362\pi$
$824$	19.9307	0.694317
$825$	27.4680	0.956314
$826$	−6.66630	−0.231950
$827$	18.2811	0.635697	0.317849	−	0.948142i	$-0.397040\pi$
$827$	18.2811	0.635697	0.317849	+	0.948142i	$0.397040\pi$
$828$	−45.7661	−1.59048
$829$	14.0384	0.487575	0.243788	−	0.969829i	$-0.421610\pi$
$829$	14.0384	0.487575	0.243788	+	0.969829i	$0.421610\pi$
$830$	13.3093	0.461972
$831$	63.8299	2.21423
$832$	29.5787	1.02546
$833$	−0.664841	−0.0230354
$834$	6.54797	0.226738
$835$	3.83668	0.132774
$836$	48.8814	1.69060
$837$	−13.3955	−0.463016
$838$	28.2625	0.976312
$839$	44.6921	1.54294	0.771471	−	0.636265i	$-0.219522\pi$
$839$	44.6921	1.54294	0.771471	+	0.636265i	$0.219522\pi$
$840$	−29.8550	−1.03010
$841$	30.3687	1.04720
$842$	21.2949	0.733871
$843$	−47.3560	−1.63103
$844$	12.1633	0.418679
$845$	−4.33783	−0.149226
$846$	−4.71648	−0.162156
$847$	10.7653	0.369899
$848$	5.00092	0.171732
$849$	74.7006	2.56372
$850$	−9.73657	−0.333961
$851$	−21.5332	−0.738149
$852$	73.0884	2.50397
$853$	43.6456	1.49440	0.747199	−	0.664600i	$-0.231398\pi$
$853$	43.6456	1.49440	0.747199	+	0.664600i	$0.231398\pi$
$854$	−34.3171	−1.17431
$855$	16.4654	0.563104
$856$	−41.7947	−1.42851
$857$	−13.3479	−0.455956	−0.227978	−	0.973666i	$-0.573211\pi$
$857$	−13.3479	−0.455956	−0.227978	+	0.973666i	$0.573211\pi$
$858$	−47.8667	−1.63414
$859$	−46.0259	−1.57038	−0.785192	−	0.619253i	$-0.787436\pi$
$859$	−46.0259	−1.57038	−0.785192	+	0.619253i	$0.787436\pi$
$860$	44.3104	1.51097
$861$	34.1580	1.16410
$862$	−29.2711	−0.996977
$863$	−18.1848	−0.619016	−0.309508	−	0.950897i	$-0.600164\pi$
$863$	−18.1848	−0.619016	−0.309508	+	0.950897i	$0.600164\pi$
$864$	−2.30037	−0.0782603
$865$	−13.9963	−0.475889
$866$	−76.7576	−2.60833
$867$	−2.54725	−0.0865092
$868$	−113.193	−3.84201
$869$	−18.5526	−0.629355
$870$	−46.2161	−1.56687
$871$	28.6012	0.969116
$872$	−22.9379	−0.776777
$873$	29.1154	0.985406
$874$	40.1446	1.35791
$875$	24.4853	0.827753
$876$	−46.1238	−1.55838
$877$	41.3885	1.39759	0.698795	−	0.715322i	$-0.253720\pi$
$877$	41.3885	1.39759	0.698795	+	0.715322i	$0.253720\pi$
$878$	−0.692386	−0.0233669
$879$	−39.4519	−1.33068
$880$	7.37490	0.248608
$881$	−6.23337	−0.210007	−0.105004	−	0.994472i	$-0.533485\pi$
$881$	−6.23337	−0.210007	−0.105004	+	0.994472i	$0.533485\pi$
$882$	−5.58455	−0.188042
$883$	−27.9587	−0.940884	−0.470442	−	0.882431i	$-0.655906\pi$
$883$	−27.9587	−0.940884	−0.470442	+	0.882431i	$0.655906\pi$
$884$	11.1143	0.373814
$885$	2.49105	0.0837356
$886$	−32.1251	−1.07926
$887$	−39.5185	−1.32690	−0.663450	−	0.748220i	$-0.730909\pi$
$887$	−39.5185	−1.32690	−0.663450	+	0.748220i	$0.730909\pi$
$888$	68.7376	2.30668
$889$	−25.7726	−0.864386
$890$	26.3688	0.883886
$891$	−19.4564	−0.651813
$892$	−35.2563	−1.18047
$893$	2.71001	0.0906871
$894$	91.5411	3.06159
$895$	−23.3251	−0.779673
$896$	−57.1415	−1.90896
$897$	−25.7506	−0.859788
$898$	−50.9258	−1.69942
$899$	−82.9485	−2.76649
$900$	−53.5731	−1.78577
$901$	−1.76842	−0.0589148
$902$	−31.1018	−1.03558
$903$	84.1362	2.79988
$904$	72.4649	2.41015
$905$	−4.82990	−0.160551
$906$	39.9569	1.32748
$907$	26.5217	0.880639	0.440319	−	0.897841i	$-0.354865\pi$
$907$	26.5217	0.880639	0.440319	+	0.897841i	$0.354865\pi$
$908$	−17.1473	−0.569052
$909$	−42.5358	−1.41082
$910$	−19.0783	−0.632441
$911$	52.6804	1.74538	0.872690	−	0.488274i	$-0.162373\pi$
$911$	52.6804	1.74538	0.872690	+	0.488274i	$0.162373\pi$
$912$	−34.7664	−1.15123
$913$	−15.0728	−0.498838
$914$	−43.0790	−1.42493
$915$	12.8235	0.423933
$916$	−59.6812	−1.97192
$917$	36.1673	1.19435
$918$	−2.99614	−0.0988872
$919$	−48.2137	−1.59042	−0.795212	−	0.606331i	$-0.792641\pi$
$919$	−48.2137	−1.59042	−0.795212	+	0.606331i	$0.792641\pi$
$920$	14.6239	0.482136
$921$	28.9252	0.953119
$922$	3.40541	0.112151
$923$	22.1099	0.727755
$924$	71.4238	2.34967
$925$	−25.2065	−0.828784
$926$	43.9453	1.44413
$927$	−16.0611	−0.527516
$928$	−14.2446	−0.467600
$929$	15.8656	0.520534	0.260267	−	0.965537i	$-0.416189\pi$
$929$	15.8656	0.520534	0.260267	+	0.965537i	$0.416189\pi$
$930$	64.5721	2.11740
$931$	3.20879	0.105164
$932$	68.5276	2.24470
$933$	42.4966	1.39128
$934$	22.1994	0.726387
$935$	−2.60791	−0.0852879
$936$	44.1944	1.44454
$937$	−13.1595	−0.429901	−0.214950	−	0.976625i	$-0.568959\pi$
$937$	−13.1595	−0.429901	−0.214950	+	0.976625i	$0.568959\pi$
$938$	−65.1514	−2.12727
$939$	44.4526	1.45066
$940$	2.08542	0.0680189
$941$	−56.1624	−1.83084	−0.915421	−	0.402497i	$-0.868142\pi$
$941$	−56.1624	−1.83084	−0.915421	+	0.402497i	$0.868142\pi$
$942$	−19.5813	−0.637992
$943$	−16.7317	−0.544858
$944$	−2.82789	−0.0920401
$945$	3.36892	0.109591
$946$	−76.6082	−2.49075
$947$	−16.7139	−0.543130	−0.271565	−	0.962420i	$-0.587541\pi$
$947$	−16.7139	−0.543130	−0.271565	+	0.962420i	$0.587541\pi$
$948$	67.3024	2.18588
$949$	−13.9528	−0.452928
$950$	46.9926	1.52464
$951$	25.8297	0.837584
$952$	−11.9849	−0.388433
$953$	36.9092	1.19561	0.597803	−	0.801643i	$-0.296040\pi$
$953$	36.9092	1.19561	0.597803	+	0.801643i	$0.296040\pi$
$954$	−14.8545	−0.480931
$955$	−10.0058	−0.323780
$956$	47.6827	1.54217
$957$	52.3400	1.69191
$958$	43.8892	1.41800
$959$	53.2787	1.72046
$960$	25.1776	0.812605
$961$	84.8937	2.73851
$962$	43.9256	1.41622
$963$	33.6803	1.08533
$964$	38.6476	1.24476
$965$	−3.26243	−0.105021
$966$	58.6579	1.88729
$967$	−24.8194	−0.798139	−0.399070	−	0.916921i	$-0.630667\pi$
$967$	−24.8194	−0.798139	−0.399070	+	0.916921i	$0.630667\pi$
$968$	16.8328	0.541027
$969$	12.2941	0.394943
$970$	−19.6529	−0.631018
$971$	53.1770	1.70653	0.853265	−	0.521477i	$-0.174619\pi$
$971$	53.1770	1.70653	0.853265	+	0.521477i	$0.174619\pi$
$972$	84.7580	2.71861
$973$	−2.95565	−0.0947539
$974$	76.2984	2.44476
$975$	−30.1433	−0.965358
$976$	−14.5576	−0.465976
$977$	55.5966	1.77869	0.889346	−	0.457234i	$-0.151160\pi$
$977$	55.5966	1.77869	0.889346	+	0.457234i	$0.151160\pi$
$978$	101.884	3.25790
$979$	−29.8628	−0.954420
$980$	2.46925	0.0788772
$981$	18.4845	0.590166
$982$	−49.6520	−1.58446
$983$	−40.3430	−1.28674	−0.643371	−	0.765555i	$-0.722465\pi$
$983$	−40.3430	−1.28674	−0.643371	+	0.765555i	$0.722465\pi$
$984$	53.4102	1.70266
$985$	−8.91042	−0.283909
$986$	−18.5529	−0.590845
$987$	3.95978	0.126041
$988$	−53.6422	−1.70658
$989$	−41.2125	−1.31048
$990$	−21.9060	−0.696219
$991$	45.8264	1.45573	0.727863	−	0.685723i	$-0.240514\pi$
$991$	45.8264	1.45573	0.727863	+	0.685723i	$0.240514\pi$
$992$	19.9021	0.631894
$993$	−70.2757	−2.23013
$994$	−50.3646	−1.59747
$995$	−6.29810	−0.199663
$996$	54.6789	1.73257
$997$	−35.6853	−1.13016	−0.565082	−	0.825035i	$-0.691156\pi$
$997$	−35.6853	−1.13016	−0.565082	+	0.825035i	$0.691156\pi$
$998$	−4.83881	−0.153170
$999$	−7.75654	−0.245406

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.g.1.2	✓	10
3.2	odd	2		9027.2.a.j.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.g.1.2	✓	10	1.1	even	1	trivial
9027.2.a.j.1.9		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)

\(f(q)\)	\(=\)	\(q-2.40787 q^{2} -2.54725 q^{3} +3.79784 q^{4} +0.977935 q^{5} +6.13345 q^{6} -2.76854 q^{7} -4.32896 q^{8} +3.48849 q^{9} +O(q^{10})\)	\(q-2.40787 q^{2} -2.54725 q^{3} +3.79784 q^{4} +0.977935 q^{5} +6.13345 q^{6} -2.76854 q^{7} -4.32896 q^{8} +3.48849 q^{9} -2.35474 q^{10} +2.66675 q^{11} -9.67405 q^{12} -2.92648 q^{13} +6.66630 q^{14} -2.49105 q^{15} +2.82789 q^{16} -1.00000 q^{17} -8.39983 q^{18} +4.82641 q^{19} +3.71404 q^{20} +7.05218 q^{21} -6.42120 q^{22} -3.45438 q^{23} +11.0269 q^{24} -4.04364 q^{25} +7.04659 q^{26} -1.24431 q^{27} -10.5145 q^{28} -7.70511 q^{29} +5.99812 q^{30} +10.7654 q^{31} +1.84872 q^{32} -6.79289 q^{33} +2.40787 q^{34} -2.70746 q^{35} +13.2487 q^{36} +6.23360 q^{37} -11.6214 q^{38} +7.45449 q^{39} -4.23344 q^{40} +4.84361 q^{41} -16.9807 q^{42} +11.9305 q^{43} +10.1279 q^{44} +3.41152 q^{45} +8.31769 q^{46} +0.561497 q^{47} -7.20336 q^{48} +0.664841 q^{49} +9.73657 q^{50} +2.54725 q^{51} -11.1143 q^{52} +1.76842 q^{53} +2.99614 q^{54} +2.60791 q^{55} +11.9849 q^{56} -12.2941 q^{57} +18.5529 q^{58} -1.00000 q^{59} -9.46059 q^{60} -5.14785 q^{61} -25.9217 q^{62} -9.65804 q^{63} -10.1073 q^{64} -2.86191 q^{65} +16.3564 q^{66} -9.77325 q^{67} -3.79784 q^{68} +8.79917 q^{69} +6.51921 q^{70} -7.55510 q^{71} -15.1015 q^{72} +4.76779 q^{73} -15.0097 q^{74} +10.3002 q^{75} +18.3299 q^{76} -7.38303 q^{77} -17.9494 q^{78} -6.95701 q^{79} +2.76550 q^{80} -7.29590 q^{81} -11.6628 q^{82} -5.65212 q^{83} +26.7830 q^{84} -0.977935 q^{85} -28.7271 q^{86} +19.6269 q^{87} -11.5443 q^{88} -11.1982 q^{89} -8.21449 q^{90} +8.10210 q^{91} -13.1192 q^{92} -27.4222 q^{93} -1.35201 q^{94} +4.71991 q^{95} -4.70914 q^{96} +8.34612 q^{97} -1.60085 q^{98} +9.30295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) \) 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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