LMFDB - Embedded newform 1003.2.a.j.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:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-2.28467 q^{2} +0.0353698 q^{3} +3.21973 q^{4} -0.992800 q^{5} -0.0808085 q^{6} -0.288469 q^{7} -2.78667 q^{8} -2.99875 q^{9} +O(q^{10})$	\(q-2.28467 q^{2} +0.0353698 q^{3} +3.21973 q^{4} -0.992800 q^{5} -0.0808085 q^{6} -0.288469 q^{7} -2.78667 q^{8} -2.99875 q^{9} +2.26822 q^{10} +2.40687 q^{11} +0.113881 q^{12} +0.404825 q^{13} +0.659057 q^{14} -0.0351152 q^{15} -0.0728144 q^{16} -1.00000 q^{17} +6.85116 q^{18} -3.02698 q^{19} -3.19655 q^{20} -0.0102031 q^{21} -5.49891 q^{22} +7.26192 q^{23} -0.0985642 q^{24} -4.01435 q^{25} -0.924893 q^{26} -0.212175 q^{27} -0.928791 q^{28} +4.41820 q^{29} +0.0802267 q^{30} +0.846173 q^{31} +5.73971 q^{32} +0.0851305 q^{33} +2.28467 q^{34} +0.286392 q^{35} -9.65515 q^{36} -6.66051 q^{37} +6.91565 q^{38} +0.0143186 q^{39} +2.76661 q^{40} +8.24852 q^{41} +0.0233107 q^{42} +7.83855 q^{43} +7.74946 q^{44} +2.97716 q^{45} -16.5911 q^{46} -5.05604 q^{47} -0.00257543 q^{48} -6.91679 q^{49} +9.17147 q^{50} -0.0353698 q^{51} +1.30343 q^{52} -4.17963 q^{53} +0.484750 q^{54} -2.38954 q^{55} +0.803870 q^{56} -0.107064 q^{57} -10.0941 q^{58} +1.00000 q^{59} -0.113061 q^{60} +8.06798 q^{61} -1.93323 q^{62} +0.865046 q^{63} -12.9677 q^{64} -0.401911 q^{65} -0.194495 q^{66} +1.30243 q^{67} -3.21973 q^{68} +0.256853 q^{69} -0.654312 q^{70} +7.17155 q^{71} +8.35654 q^{72} -1.04739 q^{73} +15.2171 q^{74} -0.141987 q^{75} -9.74603 q^{76} -0.694307 q^{77} -0.0327133 q^{78} -0.314273 q^{79} +0.0722902 q^{80} +8.98874 q^{81} -18.8452 q^{82} +15.2827 q^{83} -0.0328512 q^{84} +0.992800 q^{85} -17.9085 q^{86} +0.156271 q^{87} -6.70716 q^{88} +3.40556 q^{89} -6.80183 q^{90} -0.116780 q^{91} +23.3814 q^{92} +0.0299290 q^{93} +11.5514 q^{94} +3.00518 q^{95} +0.203012 q^{96} +12.7806 q^{97} +15.8026 q^{98} -7.21760 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) $ 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * 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 $

$2$	−2.28467	−1.61551	−0.807754	−	0.589520i	$-0.799317\pi$
$2$	−2.28467	−1.61551	−0.807754	+	0.589520i	$0.799317\pi$
$3$	0.0353698	0.0204208	0.0102104	−	0.999948i	$-0.496750\pi$
$3$	0.0353698	0.0204208	0.0102104	+	0.999948i	$0.496750\pi$
$4$	3.21973	1.60986
$5$	−0.992800	−0.443994	−0.221997	−	0.975047i	$-0.571257\pi$
$5$	−0.992800	−0.443994	−0.221997	+	0.975047i	$0.571257\pi$
$6$	−0.0808085	−0.0329899
$7$	−0.288469	−0.109031	−0.0545155	−	0.998513i	$-0.517361\pi$
$7$	−0.288469	−0.109031	−0.0545155	+	0.998513i	$0.517361\pi$
$8$	−2.78667	−0.985238
$9$	−2.99875	−0.999583
$10$	2.26822	0.717275
$11$	2.40687	0.725698	0.362849	−	0.931848i	$-0.381804\pi$
$11$	2.40687	0.725698	0.362849	+	0.931848i	$0.381804\pi$
$12$	0.113881	0.0328747
$13$	0.404825	0.112278	0.0561392	−	0.998423i	$-0.482121\pi$
$13$	0.404825	0.112278	0.0561392	+	0.998423i	$0.482121\pi$
$14$	0.659057	0.176140
$15$	−0.0351152	−0.00906670
$16$	−0.0728144	−0.0182036
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	6.85116	1.61483
$19$	−3.02698	−0.694436	−0.347218	−	0.937784i	$-0.612874\pi$
$19$	−3.02698	−0.694436	−0.347218	+	0.937784i	$0.612874\pi$
$20$	−3.19655	−0.714769
$21$	−0.0102031	−0.00222650
$22$	−5.49891	−1.17237
$23$	7.26192	1.51421	0.757107	−	0.653290i	$-0.226612\pi$
$23$	7.26192	1.51421	0.757107	+	0.653290i	$0.226612\pi$
$24$	−0.0985642	−0.0201193
$25$	−4.01435	−0.802870
$26$	−0.924893	−0.181386
$27$	−0.212175	−0.0408330
$28$	−0.928791	−0.175525
$29$	4.41820	0.820440	0.410220	−	0.911987i	$-0.365452\pi$
$29$	4.41820	0.820440	0.410220	+	0.911987i	$0.365452\pi$
$30$	0.0802267	0.0146473
$31$	0.846173	0.151977	0.0759885	−	0.997109i	$-0.475789\pi$
$31$	0.846173	0.151977	0.0759885	+	0.997109i	$0.475789\pi$
$32$	5.73971	1.01465
$33$	0.0851305	0.0148193
$34$	2.28467	0.391818
$35$	0.286392	0.0484091
$36$	−9.65515	−1.60919
$37$	−6.66051	−1.09498	−0.547490	−	0.836812i	$-0.684417\pi$
$37$	−6.66051	−1.09498	−0.547490	+	0.836812i	$0.684417\pi$
$38$	6.91565	1.12187
$39$	0.0143186	0.00229281
$40$	2.76661	0.437440
$41$	8.24852	1.28820	0.644101	−	0.764940i	$-0.277232\pi$
$41$	8.24852	1.28820	0.644101	+	0.764940i	$0.277232\pi$
$42$	0.0233107	0.00359693
$43$	7.83855	1.19537	0.597684	−	0.801732i	$-0.296088\pi$
$43$	7.83855	1.19537	0.597684	+	0.801732i	$0.296088\pi$
$44$	7.74946	1.16828
$45$	2.97716	0.443809
$46$	−16.5911	−2.44623
$47$	−5.05604	−0.737499	−0.368749	−	0.929529i	$-0.620214\pi$
$47$	−5.05604	−0.737499	−0.368749	+	0.929529i	$0.620214\pi$
$48$	−0.00257543	−0.000371732 0
$49$	−6.91679	−0.988112
$50$	9.17147	1.29704
$51$	−0.0353698	−0.00495277
$52$	1.30343	0.180753
$53$	−4.17963	−0.574116	−0.287058	−	0.957913i	$-0.592677\pi$
$53$	−4.17963	−0.574116	−0.287058	+	0.957913i	$0.592677\pi$
$54$	0.484750	0.0659661
$55$	−2.38954	−0.322206
$56$	0.803870	0.107422
$57$	−0.107064	−0.0141809
$58$	−10.0941	−1.32543
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−0.113061	−0.0145961
$61$	8.06798	1.03300	0.516500	−	0.856287i	$-0.327235\pi$
$61$	8.06798	1.03300	0.516500	+	0.856287i	$0.327235\pi$
$62$	−1.93323	−0.245520
$63$	0.865046	0.108986
$64$	−12.9677	−1.62096
$65$	−0.401911	−0.0498509
$66$	−0.194495	−0.0239407
$67$	1.30243	0.159117	0.0795587	−	0.996830i	$-0.474649\pi$
$67$	1.30243	0.159117	0.0795587	+	0.996830i	$0.474649\pi$
$68$	−3.21973	−0.390449
$69$	0.256853	0.0309215
$70$	−0.654312	−0.0782053
$71$	7.17155	0.851107	0.425553	−	0.904933i	$-0.360079\pi$
$71$	7.17155	0.851107	0.425553	+	0.904933i	$0.360079\pi$
$72$	8.35654	0.984828
$73$	−1.04739	−0.122588	−0.0612938	−	0.998120i	$-0.519523\pi$
$73$	−1.04739	−0.122588	−0.0612938	+	0.998120i	$0.519523\pi$
$74$	15.2171	1.76895
$75$	−0.141987	−0.0163952
$76$	−9.74603	−1.11795
$77$	−0.694307	−0.0791237
$78$	−0.0327133	−0.00370405
$79$	−0.314273	−0.0353584	−0.0176792	−	0.999844i	$-0.505628\pi$
$79$	−0.314273	−0.0353584	−0.0176792	+	0.999844i	$0.505628\pi$
$80$	0.0722902	0.00808229
$81$	8.98874	0.998749
$82$	−18.8452	−2.08110
$83$	15.2827	1.67749	0.838746	−	0.544523i	$-0.183289\pi$
$83$	15.2827	1.67749	0.838746	+	0.544523i	$0.183289\pi$
$84$	−0.0328512	−0.00358436
$85$	0.992800	0.107684
$86$	−17.9085	−1.93112
$87$	0.156271	0.0167540
$88$	−6.70716	−0.714986
$89$	3.40556	0.360989	0.180495	−	0.983576i	$-0.442230\pi$
$89$	3.40556	0.360989	0.180495	+	0.983576i	$0.442230\pi$
$90$	−6.80183	−0.716976
$91$	−0.116780	−0.0122418
$92$	23.3814	2.43768
$93$	0.0299290	0.00310349
$94$	11.5514	1.19143
$95$	3.00518	0.308325
$96$	0.203012	0.0207199
$97$	12.7806	1.29768	0.648838	−	0.760926i	$-0.275255\pi$
$97$	12.7806	1.29768	0.648838	+	0.760926i	$0.275255\pi$
$98$	15.8026	1.59630
$99$	−7.21760	−0.725396
$100$	−12.9251	−1.29251
$101$	−11.3752	−1.13187	−0.565936	−	0.824449i	$-0.691485\pi$
$101$	−11.3752	−1.13187	−0.565936	+	0.824449i	$0.691485\pi$
$102$	0.0808085	0.00800123
$103$	15.7111	1.54806	0.774032	−	0.633146i	$-0.218237\pi$
$103$	15.7111	1.54806	0.774032	+	0.633146i	$0.218237\pi$
$104$	−1.12812	−0.110621
$105$	0.0101296	0.000988552 0
$106$	9.54908	0.927488
$107$	13.1439	1.27067	0.635336	−	0.772236i	$-0.280862\pi$
$107$	13.1439	1.27067	0.635336	+	0.772236i	$0.280862\pi$
$108$	−0.683145	−0.0657356
$109$	8.42581	0.807047	0.403523	−	0.914969i	$-0.367785\pi$
$109$	8.42581	0.807047	0.403523	+	0.914969i	$0.367785\pi$
$110$	5.45932	0.520525
$111$	−0.235581	−0.0223604
$112$	0.0210047	0.00198476
$113$	18.0544	1.69842	0.849208	−	0.528058i	$-0.177080\pi$
$113$	18.0544	1.69842	0.849208	+	0.528058i	$0.177080\pi$
$114$	0.244605	0.0229094
$115$	−7.20964	−0.672302
$116$	14.2254	1.32080
$117$	−1.21397	−0.112231
$118$	−2.28467	−0.210321
$119$	0.288469	0.0264439
$120$	0.0978546	0.00893286
$121$	−5.20698	−0.473362
$122$	−18.4327	−1.66882
$123$	0.291749	0.0263061
$124$	2.72444	0.244662
$125$	8.94945	0.800463
$126$	−1.97635	−0.176067
$127$	2.65298	0.235414	0.117707	−	0.993048i	$-0.462446\pi$
$127$	2.65298	0.235414	0.117707	+	0.993048i	$0.462446\pi$
$128$	18.1476	1.60403
$129$	0.277248	0.0244103
$130$	0.918234	0.0805344
$131$	−7.11946	−0.622030	−0.311015	−	0.950405i	$-0.600669\pi$
$131$	−7.11946	−0.622030	−0.311015	+	0.950405i	$0.600669\pi$
$132$	0.274097	0.0238571
$133$	0.873189	0.0757151
$134$	−2.97563	−0.257055
$135$	0.210647	0.0181296
$136$	2.78667	0.238955
$137$	22.7982	1.94778	0.973891	−	0.227016i	$-0.0728970\pi$
$137$	22.7982	1.94778	0.973891	+	0.227016i	$0.0728970\pi$
$138$	−0.586825	−0.0499538
$139$	12.3930	1.05116	0.525582	−	0.850743i	$-0.323848\pi$
$139$	12.3930	1.05116	0.525582	+	0.850743i	$0.323848\pi$
$140$	0.922104	0.0779320
$141$	−0.178831	−0.0150603
$142$	−16.3846	−1.37497
$143$	0.974361	0.0814802
$144$	0.218352	0.0181960
$145$	−4.38639	−0.364270
$146$	2.39294	0.198041
$147$	−0.244646	−0.0201780
$148$	−21.4450	−1.76277
$149$	−18.1747	−1.48893	−0.744465	−	0.667662i	$-0.767295\pi$
$149$	−18.1747	−1.48893	−0.744465	+	0.667662i	$0.767295\pi$
$150$	0.324393	0.0264866
$151$	8.76291	0.713115	0.356558	−	0.934273i	$-0.383950\pi$
$151$	8.76291	0.713115	0.356558	+	0.934273i	$0.383950\pi$
$152$	8.43520	0.684185
$153$	2.99875	0.242434
$154$	1.58626	0.127825
$155$	−0.840080	−0.0674769
$156$	0.0461020	0.00369111
$157$	19.8864	1.58711	0.793553	−	0.608502i	$-0.208229\pi$
$157$	19.8864	1.58711	0.793553	+	0.608502i	$0.208229\pi$
$158$	0.718010	0.0571218
$159$	−0.147833	−0.0117239
$160$	−5.69838	−0.450497
$161$	−2.09484	−0.165096
$162$	−20.5363	−1.61349
$163$	−1.94793	−0.152574	−0.0762869	−	0.997086i	$-0.524306\pi$
$163$	−1.94793	−0.152574	−0.0762869	+	0.997086i	$0.524306\pi$
$164$	26.5580	2.07383
$165$	−0.0845176	−0.00657969
$166$	−34.9159	−2.71000
$167$	−2.96944	−0.229782	−0.114891	−	0.993378i	$-0.536652\pi$
$167$	−2.96944	−0.229782	−0.114891	+	0.993378i	$0.536652\pi$
$168$	0.0284327	0.00219363
$169$	−12.8361	−0.987394
$170$	−2.26822	−0.173965
$171$	9.07714	0.694146
$172$	25.2380	1.92438
$173$	−14.1806	−1.07813	−0.539065	−	0.842264i	$-0.681222\pi$
$173$	−14.1806	−1.07813	−0.539065	+	0.842264i	$0.681222\pi$
$174$	−0.357028	−0.0270662
$175$	1.15802	0.0875377
$176$	−0.175255	−0.0132103
$177$	0.0353698	0.00265856
$178$	−7.78060	−0.583180
$179$	−13.6945	−1.02357	−0.511786	−	0.859113i	$-0.671016\pi$
$179$	−13.6945	−1.02357	−0.511786	+	0.859113i	$0.671016\pi$
$180$	9.58564	0.714471
$181$	19.4423	1.44514	0.722569	−	0.691299i	$-0.242961\pi$
$181$	19.4423	1.44514	0.722569	+	0.691299i	$0.242961\pi$
$182$	0.266803	0.0197768
$183$	0.285363	0.0210947
$184$	−20.2366	−1.49186
$185$	6.61255	0.486165
$186$	−0.0683779	−0.00501371
$187$	−2.40687	−0.176008
$188$	−16.2791	−1.18727
$189$	0.0612058	0.00445207
$190$	−6.86586	−0.498102
$191$	−1.90059	−0.137522	−0.0687610	−	0.997633i	$-0.521905\pi$
$191$	−1.90059	−0.137522	−0.0687610	+	0.997633i	$0.521905\pi$
$192$	−0.458666	−0.0331014
$193$	−7.46629	−0.537435	−0.268718	−	0.963219i	$-0.586600\pi$
$193$	−7.46629	−0.537435	−0.268718	+	0.963219i	$0.586600\pi$
$194$	−29.1996	−2.09641
$195$	−0.0142155	−0.00101799
$196$	−22.2702	−1.59073
$197$	11.3101	0.805809	0.402905	−	0.915242i	$-0.368001\pi$
$197$	11.3101	0.805809	0.402905	+	0.915242i	$0.368001\pi$
$198$	16.4898	1.17188
$199$	−2.54626	−0.180499	−0.0902497	−	0.995919i	$-0.528767\pi$
$199$	−2.54626	−0.180499	−0.0902497	+	0.995919i	$0.528767\pi$
$200$	11.1867	0.791018
$201$	0.0460668	0.00324930
$202$	25.9885	1.82855
$203$	−1.27452	−0.0894534
$204$	−0.113881	−0.00797328
$205$	−8.18913	−0.571954
$206$	−35.8948	−2.50091
$207$	−21.7767	−1.51358
$208$	−0.0294771	−0.00204387
$209$	−7.28553	−0.503951
$210$	−0.0231429	−0.00159701
$211$	−19.0377	−1.31061	−0.655306	−	0.755364i	$-0.727460\pi$
$211$	−19.0377	−1.31061	−0.655306	+	0.755364i	$0.727460\pi$
$212$	−13.4573	−0.924248
$213$	0.253657	0.0173803
$214$	−30.0296	−2.05278
$215$	−7.78211	−0.530736
$216$	0.591262	0.0402303
$217$	−0.244095	−0.0165702
$218$	−19.2502	−1.30379
$219$	−0.0370460	−0.00250334
$220$	−7.69367	−0.518707
$221$	−0.404825	−0.0272315
$222$	0.538225	0.0361233
$223$	−4.90878	−0.328716	−0.164358	−	0.986401i	$-0.552555\pi$
$223$	−4.90878	−0.328716	−0.164358	+	0.986401i	$0.552555\pi$
$224$	−1.65573	−0.110628
$225$	12.0380	0.802535
$226$	−41.2484	−2.74380
$227$	12.8538	0.853134	0.426567	−	0.904456i	$-0.359723\pi$
$227$	12.8538	0.853134	0.426567	+	0.904456i	$0.359723\pi$
$228$	−0.344716	−0.0228293
$229$	−18.3267	−1.21106	−0.605530	−	0.795822i	$-0.707039\pi$
$229$	−18.3267	−1.21106	−0.605530	+	0.795822i	$0.707039\pi$
$230$	16.4717	1.08611
$231$	−0.0245575	−0.00161577
$232$	−12.3121	−0.808329
$233$	20.8816	1.36800	0.683998	−	0.729483i	$-0.260240\pi$
$233$	20.8816	1.36800	0.683998	+	0.729483i	$0.260240\pi$
$234$	2.77352	0.181311
$235$	5.01963	0.327445
$236$	3.21973	0.209586
$237$	−0.0111158	−0.000722047 0
$238$	−0.659057	−0.0427203
$239$	−20.7929	−1.34498	−0.672489	−	0.740107i	$-0.734775\pi$
$239$	−20.7929	−1.34498	−0.672489	+	0.740107i	$0.734775\pi$
$240$	0.00255689	0.000165047 0
$241$	−5.76390	−0.371286	−0.185643	−	0.982617i	$-0.559437\pi$
$241$	−5.76390	−0.371286	−0.185643	+	0.982617i	$0.559437\pi$
$242$	11.8962	0.764720
$243$	0.954454	0.0612283
$244$	25.9767	1.66299
$245$	6.86699	0.438716
$246$	−0.666550	−0.0424977
$247$	−1.22540	−0.0779701
$248$	−2.35801	−0.149734
$249$	0.540546	0.0342557
$250$	−20.4466	−1.29315
$251$	26.0623	1.64503	0.822517	−	0.568740i	$-0.192569\pi$
$251$	26.0623	1.64503	0.822517	+	0.568740i	$0.192569\pi$
$252$	2.78521	0.175452
$253$	17.4785	1.09886
$254$	−6.06119	−0.380313
$255$	0.0351152	0.00219900
$256$	−15.5258	−0.970363
$257$	6.50699	0.405895	0.202947	−	0.979190i	$-0.434948\pi$
$257$	6.50699	0.405895	0.202947	+	0.979190i	$0.434948\pi$
$258$	−0.633421	−0.0394351
$259$	1.92135	0.119387
$260$	−1.29404	−0.0802531
$261$	−13.2491	−0.820098
$262$	16.2656	1.00489
$263$	−10.8292	−0.667758	−0.333879	−	0.942616i	$-0.608358\pi$
$263$	−10.8292	−0.667758	−0.333879	+	0.942616i	$0.608358\pi$
$264$	−0.237231	−0.0146006
$265$	4.14954	0.254904
$266$	−1.99495	−0.122318
$267$	0.120454	0.00737168
$268$	4.19347	0.256157
$269$	−27.3800	−1.66939	−0.834694	−	0.550714i	$-0.814355\pi$
$269$	−27.3800	−1.66939	−0.834694	+	0.550714i	$0.814355\pi$
$270$	−0.481260	−0.0292885
$271$	−3.14757	−0.191201	−0.0956006	−	0.995420i	$-0.530477\pi$
$271$	−3.14757	−0.191201	−0.0956006	+	0.995420i	$0.530477\pi$
$272$	0.0728144	0.00441502
$273$	−0.00413047	−0.000249988 0
$274$	−52.0864	−3.14666
$275$	−9.66201	−0.582641
$276$	0.826996	0.0497793
$277$	−1.36143	−0.0818003	−0.0409001	−	0.999163i	$-0.513023\pi$
$277$	−1.36143	−0.0818003	−0.0409001	+	0.999163i	$0.513023\pi$
$278$	−28.3140	−1.69816
$279$	−2.53746	−0.151914
$280$	−0.798082	−0.0476945
$281$	−17.3124	−1.03277	−0.516384	−	0.856357i	$-0.672722\pi$
$281$	−17.3124	−1.03277	−0.516384	+	0.856357i	$0.672722\pi$
$282$	0.408570	0.0243300
$283$	9.95646	0.591850	0.295925	−	0.955211i	$-0.404372\pi$
$283$	9.95646	0.591850	0.295925	+	0.955211i	$0.404372\pi$
$284$	23.0904	1.37017
$285$	0.106293	0.00629624
$286$	−2.22610	−0.131632
$287$	−2.37944	−0.140454
$288$	−17.2119	−1.01422
$289$	1.00000	0.0588235
$290$	10.0215	0.588481
$291$	0.452049	0.0264996
$292$	−3.37231	−0.197349
$293$	28.0377	1.63798	0.818991	−	0.573807i	$-0.194534\pi$
$293$	28.0377	1.63798	0.818991	+	0.573807i	$0.194534\pi$
$294$	0.558935	0.0325977
$295$	−0.992800	−0.0578031
$296$	18.5607	1.07882
$297$	−0.510677	−0.0296325
$298$	41.5232	2.40538
$299$	2.93981	0.170014
$300$	−0.457159	−0.0263941
$301$	−2.26118	−0.130332
$302$	−20.0204	−1.15204
$303$	−0.402338	−0.0231137
$304$	0.220407	0.0126412
$305$	−8.00990	−0.458645
$306$	−6.85116	−0.391655
$307$	−25.8454	−1.47507	−0.737537	−	0.675307i	$-0.764011\pi$
$307$	−25.8454	−1.47507	−0.737537	+	0.675307i	$0.764011\pi$
$308$	−2.23548	−0.127378
$309$	0.555700	0.0316127
$310$	1.91931	0.109009
$311$	−5.59941	−0.317514	−0.158757	−	0.987318i	$-0.550749\pi$
$311$	−5.59941	−0.317514	−0.158757	+	0.987318i	$0.550749\pi$
$312$	−0.0399013	−0.00225897
$313$	−4.54843	−0.257092	−0.128546	−	0.991704i	$-0.541031\pi$
$313$	−4.54843	−0.257092	−0.128546	+	0.991704i	$0.541031\pi$
$314$	−45.4338	−2.56398
$315$	−0.858818	−0.0483889
$316$	−1.01187	−0.0569223
$317$	−8.93083	−0.501606	−0.250803	−	0.968038i	$-0.580695\pi$
$317$	−8.93083	−0.501606	−0.250803	+	0.968038i	$0.580695\pi$
$318$	0.337749	0.0189400
$319$	10.6340	0.595392
$320$	12.8744	0.719698
$321$	0.464898	0.0259481
$322$	4.78602	0.266715
$323$	3.02698	0.168425
$324$	28.9413	1.60785
$325$	−1.62511	−0.0901448
$326$	4.45039	0.246484
$327$	0.298020	0.0164805
$328$	−22.9859	−1.26919
$329$	1.45851	0.0804102
$330$	0.193095	0.0106295
$331$	−4.02845	−0.221424	−0.110712	−	0.993853i	$-0.535313\pi$
$331$	−4.02845	−0.221424	−0.110712	+	0.993853i	$0.535313\pi$
$332$	49.2060	2.70053
$333$	19.9732	1.09452
$334$	6.78419	0.371214
$335$	−1.29305	−0.0706471
$336$	0.000742933 0	4.05303e−5 0
$337$	−15.3754	−0.837550	−0.418775	−	0.908090i	$-0.637540\pi$
$337$	−15.3754	−0.837550	−0.418775	+	0.908090i	$0.637540\pi$
$338$	29.3263	1.59514
$339$	0.638582	0.0346830
$340$	3.19655	0.173357
$341$	2.03663	0.110290
$342$	−20.7383	−1.12140
$343$	4.01456	0.216766
$344$	−21.8435	−1.17772
$345$	−0.255004	−0.0137289
$346$	32.3980	1.74173
$347$	−25.9975	−1.39562	−0.697808	−	0.716284i	$-0.745841\pi$
$347$	−25.9975	−1.39562	−0.697808	+	0.716284i	$0.745841\pi$
$348$	0.503150	0.0269717
$349$	11.8322	0.633361	0.316680	−	0.948532i	$-0.397432\pi$
$349$	11.8322	0.633361	0.316680	+	0.948532i	$0.397432\pi$
$350$	−2.64568	−0.141418
$351$	−0.0858937	−0.00458467
$352$	13.8147	0.736327
$353$	13.9933	0.744790	0.372395	−	0.928074i	$-0.378537\pi$
$353$	13.9933	0.744790	0.372395	+	0.928074i	$0.378537\pi$
$354$	−0.0808085	−0.00429492
$355$	−7.11992	−0.377886
$356$	10.9650	0.581143
$357$	0.0102031	0.000540005 0
$358$	31.2874	1.65359
$359$	26.2148	1.38356	0.691782	−	0.722106i	$-0.256826\pi$
$359$	26.2148	1.38356	0.691782	+	0.722106i	$0.256826\pi$
$360$	−8.29637	−0.437257
$361$	−9.83742	−0.517759
$362$	−44.4194	−2.33463
$363$	−0.184170	−0.00966642
$364$	−0.375998	−0.0197077
$365$	1.03985	0.0544282
$366$	−0.651961	−0.0340786
$367$	−33.6570	−1.75688	−0.878439	−	0.477854i	$-0.841415\pi$
$367$	−33.6570	−1.75688	−0.878439	+	0.477854i	$0.841415\pi$
$368$	−0.528772	−0.0275642
$369$	−24.7352	−1.28767
$370$	−15.1075	−0.785402
$371$	1.20569	0.0625965
$372$	0.0963631	0.00499620
$373$	−11.0803	−0.573718	−0.286859	−	0.957973i	$-0.592611\pi$
$373$	−11.0803	−0.573718	−0.286859	+	0.957973i	$0.592611\pi$
$374$	5.49891	0.284342
$375$	0.316540	0.0163461
$376$	14.0895	0.726612
$377$	1.78860	0.0921176
$378$	−0.139835	−0.00719235
$379$	−25.7772	−1.32409	−0.662043	−	0.749466i	$-0.730310\pi$
$379$	−25.7772	−1.32409	−0.662043	+	0.749466i	$0.730310\pi$
$380$	9.67586	0.496361
$381$	0.0938355	0.00480734
$382$	4.34223	0.222168
$383$	−4.61689	−0.235912	−0.117956	−	0.993019i	$-0.537634\pi$
$383$	−4.61689	−0.235912	−0.117956	+	0.993019i	$0.537634\pi$
$384$	0.641877	0.0327556
$385$	0.689308	0.0351304
$386$	17.0580	0.868230
$387$	−23.5058	−1.19487
$388$	41.1501	2.08908
$389$	36.0849	1.82958	0.914789	−	0.403931i	$-0.132357\pi$
$389$	36.0849	1.82958	0.914789	+	0.403931i	$0.132357\pi$
$390$	0.0324778	0.00164458
$391$	−7.26192	−0.367251
$392$	19.2748	0.973526
$393$	−0.251814	−0.0127023
$394$	−25.8398	−1.30179
$395$	0.312010	0.0156989
$396$	−23.2387	−1.16779
$397$	28.9961	1.45527	0.727636	−	0.685963i	$-0.240619\pi$
$397$	28.9961	1.45527	0.727636	+	0.685963i	$0.240619\pi$
$398$	5.81736	0.291598
$399$	0.0308845	0.00154616
$400$	0.292302	0.0146151
$401$	−6.47712	−0.323452	−0.161726	−	0.986836i	$-0.551706\pi$
$401$	−6.47712	−0.323452	−0.161726	+	0.986836i	$0.551706\pi$
$402$	−0.105247	−0.00524927
$403$	0.342552	0.0170637
$404$	−36.6249	−1.82216
$405$	−8.92403	−0.443438
$406$	2.91185	0.144513
$407$	−16.0310	−0.794626
$408$	0.0985642	0.00487966
$409$	−7.06724	−0.349453	−0.174726	−	0.984617i	$-0.555904\pi$
$409$	−7.06724	−0.349453	−0.174726	+	0.984617i	$0.555904\pi$
$410$	18.7095	0.923996
$411$	0.806369	0.0397752
$412$	50.5856	2.49217
$413$	−0.288469	−0.0141946
$414$	49.7526	2.44520
$415$	−15.1726	−0.744796
$416$	2.32358	0.113923
$417$	0.438340	0.0214656
$418$	16.6451	0.814136
$419$	23.3595	1.14119	0.570593	−	0.821233i	$-0.306713\pi$
$419$	23.3595	1.14119	0.570593	+	0.821233i	$0.306713\pi$
$420$	0.0326147	0.00159143
$421$	27.2417	1.32768	0.663839	−	0.747876i	$-0.268926\pi$
$421$	27.2417	1.32768	0.663839	+	0.747876i	$0.268926\pi$
$422$	43.4950	2.11730
$423$	15.1618	0.737191
$424$	11.6473	0.565641
$425$	4.01435	0.194724
$426$	−0.579522	−0.0280779
$427$	−2.32736	−0.112629
$428$	42.3199	2.04561
$429$	0.0344630	0.00166389
$430$	17.7796	0.857407
$431$	20.8547	1.00454	0.502268	−	0.864712i	$-0.332499\pi$
$431$	20.8547	1.00454	0.502268	+	0.864712i	$0.332499\pi$
$432$	0.0154494	0.000743309 0
$433$	6.99363	0.336092	0.168046	−	0.985779i	$-0.446254\pi$
$433$	6.99363	0.336092	0.168046	+	0.985779i	$0.446254\pi$
$434$	0.557676	0.0267693
$435$	−0.155146	−0.00743868
$436$	27.1288	1.29923
$437$	−21.9817	−1.05153
$438$	0.0846379	0.00404416
$439$	7.52367	0.359085	0.179542	−	0.983750i	$-0.442538\pi$
$439$	7.52367	0.359085	0.179542	+	0.983750i	$0.442538\pi$
$440$	6.65887	0.317449
$441$	20.7417	0.987700
$442$	0.924893	0.0439927
$443$	−30.4588	−1.44714	−0.723570	−	0.690251i	$-0.757500\pi$
$443$	−30.4588	−1.44714	−0.723570	+	0.690251i	$0.757500\pi$
$444$	−0.758506	−0.0359971
$445$	−3.38104	−0.160277
$446$	11.2150	0.531044
$447$	−0.642836	−0.0304051
$448$	3.74079	0.176736
$449$	14.0091	0.661131	0.330565	−	0.943783i	$-0.392761\pi$
$449$	14.0091	0.661131	0.330565	+	0.943783i	$0.392761\pi$
$450$	−27.5029	−1.29650
$451$	19.8531	0.934846
$452$	58.1303	2.73422
$453$	0.309942	0.0145624
$454$	−29.3666	−1.37824
$455$	0.115939	0.00543529
$456$	0.298351	0.0139716
$457$	18.0319	0.843498	0.421749	−	0.906713i	$-0.361416\pi$
$457$	18.0319	0.843498	0.421749	+	0.906713i	$0.361416\pi$
$458$	41.8704	1.95648
$459$	0.212175	0.00990347
$460$	−23.2131	−1.08231
$461$	19.2593	0.896994	0.448497	−	0.893784i	$-0.351960\pi$
$461$	19.2593	0.896994	0.448497	+	0.893784i	$0.351960\pi$
$462$	0.0561059	0.00261028
$463$	20.1960	0.938588	0.469294	−	0.883042i	$-0.344509\pi$
$463$	20.1960	0.938588	0.469294	+	0.883042i	$0.344509\pi$
$464$	−0.321709	−0.0149350
$465$	−0.0297135	−0.00137793
$466$	−47.7075	−2.21001
$467$	−11.8740	−0.549461	−0.274731	−	0.961521i	$-0.588589\pi$
$467$	−11.8740	−0.549461	−0.274731	+	0.961521i	$0.588589\pi$
$468$	−3.90865	−0.180677
$469$	−0.375711	−0.0173487
$470$	−11.4682	−0.528989
$471$	0.703378	0.0324099
$472$	−2.78667	−0.128267
$473$	18.8664	0.867476
$474$	0.0253959	0.00116647
$475$	12.1513	0.557541
$476$	0.928791	0.0425711
$477$	12.5337	0.573877
$478$	47.5049	2.17282
$479$	37.7515	1.72491	0.862456	−	0.506132i	$-0.168925\pi$
$479$	37.7515	1.72491	0.862456	+	0.506132i	$0.168925\pi$
$480$	−0.201551	−0.00919949
$481$	−2.69634	−0.122943
$482$	13.1686	0.599815
$483$	−0.0740941	−0.00337140
$484$	−16.7651	−0.762048
$485$	−12.6886	−0.576160
$486$	−2.18062	−0.0989147
$487$	10.6653	0.483290	0.241645	−	0.970365i	$-0.422313\pi$
$487$	10.6653	0.483290	0.241645	+	0.970365i	$0.422313\pi$
$488$	−22.4828	−1.01775
$489$	−0.0688980	−0.00311568
$490$	−15.6888	−0.708748
$491$	−26.7644	−1.20786	−0.603931	−	0.797037i	$-0.706400\pi$
$491$	−26.7644	−1.20786	−0.603931	+	0.797037i	$0.706400\pi$
$492$	0.939351	0.0423492
$493$	−4.41820	−0.198986
$494$	2.79963	0.125961
$495$	7.16563	0.322071
$496$	−0.0616136	−0.00276653
$497$	−2.06877	−0.0927971
$498$	−1.23497	−0.0553403
$499$	−7.66438	−0.343105	−0.171552	−	0.985175i	$-0.554878\pi$
$499$	−7.66438	−0.343105	−0.171552	+	0.985175i	$0.554878\pi$
$500$	28.8148	1.28864
$501$	−0.105028	−0.00469232
$502$	−59.5437	−2.65757
$503$	−28.2396	−1.25914	−0.629571	−	0.776943i	$-0.716769\pi$
$503$	−28.2396	−1.25914	−0.629571	+	0.776943i	$0.716769\pi$
$504$	−2.41060	−0.107377
$505$	11.2933	0.502544
$506$	−39.9326	−1.77522
$507$	−0.454011	−0.0201633
$508$	8.54187	0.378984
$509$	20.2875	0.899227	0.449613	−	0.893223i	$-0.351562\pi$
$509$	20.2875	0.899227	0.449613	+	0.893223i	$0.351562\pi$
$510$	−0.0802267	−0.00355250
$511$	0.302139	0.0133659
$512$	−0.823754	−0.0364051
$513$	0.642248	0.0283559
$514$	−14.8663	−0.655726
$515$	−15.5980	−0.687331
$516$	0.892663	0.0392973
$517$	−12.1692	−0.535201
$518$	−4.38966	−0.192870
$519$	−0.501565	−0.0220162
$520$	1.11999	0.0491150
$521$	−31.5806	−1.38357	−0.691786	−	0.722103i	$-0.743176\pi$
$521$	−31.5806	−1.38357	−0.691786	+	0.722103i	$0.743176\pi$
$522$	30.2698	1.32487
$523$	45.1437	1.97400	0.986998	−	0.160730i	$-0.0513848\pi$
$523$	45.1437	1.97400	0.986998	+	0.160730i	$0.0513848\pi$
$524$	−22.9227	−1.00138
$525$	0.0409588	0.00178759
$526$	24.7412	1.07877
$527$	−0.846173	−0.0368599
$528$	−0.00619873	−0.000269765 0
$529$	29.7355	1.29285
$530$	−9.48033	−0.411799
$531$	−2.99875	−0.130135
$532$	2.81143	0.121891
$533$	3.33921	0.144637
$534$	−0.275198	−0.0119090
$535$	−13.0493	−0.564170
$536$	−3.62945	−0.156769
$537$	−0.484371	−0.0209022
$538$	62.5543	2.69691
$539$	−16.6478	−0.717071
$540$	0.678226	0.0291862
$541$	−5.93230	−0.255049	−0.127525	−	0.991835i	$-0.540703\pi$
$541$	−5.93230	−0.255049	−0.127525	+	0.991835i	$0.540703\pi$
$542$	7.19117	0.308887
$543$	0.687672	0.0295108
$544$	−5.73971	−0.246088
$545$	−8.36515	−0.358324
$546$	0.00943678	0.000403857 0
$547$	−2.48169	−0.106109	−0.0530547	−	0.998592i	$-0.516896\pi$
$547$	−2.48169	−0.106109	−0.0530547	+	0.998592i	$0.516896\pi$
$548$	73.4040	3.13566
$549$	−24.1939	−1.03257
$550$	22.0745	0.941261
$551$	−13.3738	−0.569743
$552$	−0.715765	−0.0304650
$553$	0.0906580	0.00385517
$554$	3.11042	0.132149
$555$	0.233885	0.00992786
$556$	39.9022	1.69223
$557$	−6.59319	−0.279362	−0.139681	−	0.990197i	$-0.544608\pi$
$557$	−6.59319	−0.279362	−0.139681	+	0.990197i	$0.544608\pi$
$558$	5.79726	0.245418
$559$	3.17324	0.134214
$560$	−0.0208535	−0.000881220 0
$561$	−0.0851305	−0.00359421
$562$	39.5531	1.66845
$563$	−33.0029	−1.39090	−0.695452	−	0.718572i	$-0.744796\pi$
$563$	−33.0029	−1.39090	−0.695452	+	0.718572i	$0.744796\pi$
$564$	−0.575787	−0.0242450
$565$	−17.9244	−0.754087
$566$	−22.7472	−0.956138
$567$	−2.59297	−0.108895
$568$	−19.9848	−0.838543
$569$	14.6909	0.615874	0.307937	−	0.951407i	$-0.400361\pi$
$569$	14.6909	0.615874	0.307937	+	0.951407i	$0.400361\pi$
$570$	−0.242844	−0.0101716
$571$	−33.2605	−1.39191	−0.695955	−	0.718086i	$-0.745019\pi$
$571$	−33.2605	−1.39191	−0.695955	+	0.718086i	$0.745019\pi$
$572$	3.13718	0.131172
$573$	−0.0672236	−0.00280831
$574$	5.43625	0.226905
$575$	−29.1519	−1.21572
$576$	38.8869	1.62029
$577$	6.36795	0.265101	0.132551	−	0.991176i	$-0.457683\pi$
$577$	6.36795	0.265101	0.132551	+	0.991176i	$0.457683\pi$
$578$	−2.28467	−0.0950298
$579$	−0.264081	−0.0109748
$580$	−14.1230	−0.586425
$581$	−4.40858	−0.182899
$582$	−1.03278	−0.0428102
$583$	−10.0598	−0.416635
$584$	2.91873	0.120778
$585$	1.20523	0.0498301
$586$	−64.0570	−2.64617
$587$	−43.0555	−1.77709	−0.888546	−	0.458787i	$-0.848284\pi$
$587$	−43.0555	−1.77709	−0.888546	+	0.458787i	$0.848284\pi$
$588$	−0.787692	−0.0324839
$589$	−2.56134	−0.105538
$590$	2.26822	0.0933813
$591$	0.400035	0.0164553
$592$	0.484981	0.0199326
$593$	4.23783	0.174027	0.0870135	−	0.996207i	$-0.472268\pi$
$593$	4.23783	0.174027	0.0870135	+	0.996207i	$0.472268\pi$
$594$	1.16673	0.0478715
$595$	−0.286392	−0.0117409
$596$	−58.5176	−2.39697
$597$	−0.0900607	−0.00368594
$598$	−6.71650	−0.274658
$599$	5.99120	0.244794	0.122397	−	0.992481i	$-0.460942\pi$
$599$	5.99120	0.244794	0.122397	+	0.992481i	$0.460942\pi$
$600$	0.395671	0.0161532
$601$	−36.7263	−1.49810	−0.749049	−	0.662515i	$-0.769489\pi$
$601$	−36.7263	−1.49810	−0.749049	+	0.662515i	$0.769489\pi$
$602$	5.16605	0.210553
$603$	−3.90567	−0.159051
$604$	28.2142	1.14802
$605$	5.16949	0.210170
$606$	0.919210	0.0373403
$607$	−20.8937	−0.848048	−0.424024	−	0.905651i	$-0.639383\pi$
$607$	−20.8937	−0.848048	−0.424024	+	0.905651i	$0.639383\pi$
$608$	−17.3740	−0.704607
$609$	−0.0450794	−0.00182671
$610$	18.3000	0.740945
$611$	−2.04681	−0.0828051
$612$	9.65515	0.390286
$613$	1.92294	0.0776668	0.0388334	−	0.999246i	$-0.487636\pi$
$613$	1.92294	0.0776668	0.0388334	+	0.999246i	$0.487636\pi$
$614$	59.0482	2.38299
$615$	−0.289648	−0.0116797
$616$	1.93481	0.0779557
$617$	−44.8027	−1.80369	−0.901844	−	0.432061i	$-0.857786\pi$
$617$	−44.8027	−1.80369	−0.901844	+	0.432061i	$0.857786\pi$
$618$	−1.26959	−0.0510705
$619$	5.84917	0.235098	0.117549	−	0.993067i	$-0.462496\pi$
$619$	5.84917	0.235098	0.117549	+	0.993067i	$0.462496\pi$
$620$	−2.70483	−0.108629
$621$	−1.54080	−0.0618300
$622$	12.7928	0.512946
$623$	−0.982400	−0.0393590
$624$	−0.00104260	−4.17374e−5 0
$625$	11.1867	0.447469
$626$	10.3917	0.415335
$627$	−0.257688	−0.0102911
$628$	64.0287	2.55502
$629$	6.66051	0.265572
$630$	1.96212	0.0781727
$631$	−5.11095	−0.203464	−0.101732	−	0.994812i	$-0.532438\pi$
$631$	−5.11095	−0.203464	−0.101732	+	0.994812i	$0.532438\pi$
$632$	0.875776	0.0348365
$633$	−0.673361	−0.0267637
$634$	20.4040	0.810347
$635$	−2.63388	−0.104522
$636$	−0.475981	−0.0188739
$637$	−2.80009	−0.110944
$638$	−24.2953	−0.961860
$639$	−21.5057	−0.850752
$640$	−18.0169	−0.712181
$641$	37.6573	1.48737	0.743687	−	0.668528i	$-0.233075\pi$
$641$	37.6573	1.48737	0.743687	+	0.668528i	$0.233075\pi$
$642$	−1.06214	−0.0419193
$643$	11.4790	0.452687	0.226343	−	0.974048i	$-0.427323\pi$
$643$	11.4790	0.452687	0.226343	+	0.974048i	$0.427323\pi$
$644$	−6.74481	−0.265783
$645$	−0.275252	−0.0108380
$646$	−6.91565	−0.272092
$647$	−0.709398	−0.0278893	−0.0139447	−	0.999903i	$-0.504439\pi$
$647$	−0.709398	−0.0278893	−0.0139447	+	0.999903i	$0.504439\pi$
$648$	−25.0487	−0.984006
$649$	2.40687	0.0944779
$650$	3.71284	0.145630
$651$	−0.00863358	−0.000338377 0
$652$	−6.27181	−0.245623
$653$	43.5017	1.70235	0.851176	−	0.524881i	$-0.175890\pi$
$653$	43.5017	1.70235	0.851176	+	0.524881i	$0.175890\pi$
$654$	−0.680877	−0.0266244
$655$	7.06821	0.276178
$656$	−0.600611	−0.0234499
$657$	3.14086	0.122537
$658$	−3.33222	−0.129903
$659$	−12.7328	−0.495999	−0.248000	−	0.968760i	$-0.579773\pi$
$659$	−12.7328	−0.495999	−0.248000	+	0.968760i	$0.579773\pi$
$660$	−0.272124	−0.0105924
$661$	−6.52571	−0.253821	−0.126910	−	0.991914i	$-0.540506\pi$
$661$	−6.52571	−0.253821	−0.126910	+	0.991914i	$0.540506\pi$
$662$	9.20369	0.357711
$663$	−0.0143186	−0.000556088 0
$664$	−42.5879	−1.65273
$665$	−0.866902	−0.0336170
$666$	−45.6322	−1.76821
$667$	32.0846	1.24232
$668$	−9.56077	−0.369917
$669$	−0.173623	−0.00671264
$670$	2.95421	0.114131
$671$	19.4186	0.749646
$672$	−0.0585628	−0.00225911
$673$	−31.1292	−1.19994	−0.599972	−	0.800021i	$-0.704822\pi$
$673$	−31.1292	−1.19994	−0.599972	+	0.800021i	$0.704822\pi$
$674$	35.1277	1.35307
$675$	0.851743	0.0327836
$676$	−41.3288	−1.58957
$677$	24.4742	0.940621	0.470311	−	0.882501i	$-0.344142\pi$
$677$	24.4742	0.940621	0.470311	+	0.882501i	$0.344142\pi$
$678$	−1.45895	−0.0560306
$679$	−3.68682	−0.141487
$680$	−2.76661	−0.106095
$681$	0.454635	0.0174217
$682$	−4.65302	−0.178174
$683$	−13.3170	−0.509561	−0.254781	−	0.966999i	$-0.582003\pi$
$683$	−13.3170	−0.509561	−0.254781	+	0.966999i	$0.582003\pi$
$684$	29.2259	1.11748
$685$	−22.6341	−0.864803
$686$	−9.17196	−0.350187
$687$	−0.648211	−0.0247308
$688$	−0.570759	−0.0217600
$689$	−1.69202	−0.0644608
$690$	0.582600	0.0221792
$691$	−13.5939	−0.517137	−0.258568	−	0.965993i	$-0.583251\pi$
$691$	−13.5939	−0.517137	−0.258568	+	0.965993i	$0.583251\pi$
$692$	−45.6576	−1.73564
$693$	2.08205	0.0790907
$694$	59.3957	2.25463
$695$	−12.3038	−0.466710
$696$	−0.435477	−0.0165067
$697$	−8.24852	−0.312435
$698$	−27.0326	−1.02320
$699$	0.738577	0.0279356
$700$	3.72849	0.140924
$701$	16.5843	0.626381	0.313191	−	0.949690i	$-0.398602\pi$
$701$	16.5843	0.626381	0.313191	+	0.949690i	$0.398602\pi$
$702$	0.196239	0.00740656
$703$	20.1612	0.760394
$704$	−31.2116	−1.17633
$705$	0.177544	0.00668668
$706$	−31.9702	−1.20321
$707$	3.28138	0.123409
$708$	0.113881	0.00427992
$709$	23.4631	0.881175	0.440587	−	0.897710i	$-0.354770\pi$
$709$	23.4631	0.881175	0.440587	+	0.897710i	$0.354770\pi$
$710$	16.2667	0.610478
$711$	0.942425	0.0353437
$712$	−9.49020	−0.355660
$713$	6.14484	0.230126
$714$	−0.0233107	−0.000872383 0
$715$	−0.967346	−0.0361767
$716$	−44.0925	−1.64781
$717$	−0.735440	−0.0274655
$718$	−59.8922	−2.23516
$719$	−3.96681	−0.147937	−0.0739686	−	0.997261i	$-0.523566\pi$
$719$	−3.96681	−0.147937	−0.0739686	+	0.997261i	$0.523566\pi$
$720$	−0.216780	−0.00807892
$721$	−4.53218	−0.168787
$722$	22.4753	0.836443
$723$	−0.203868	−0.00758194
$724$	62.5990	2.32647
$725$	−17.7362	−0.658706
$726$	0.420768	0.0156162
$727$	6.74839	0.250284	0.125142	−	0.992139i	$-0.460061\pi$
$727$	6.74839	0.250284	0.125142	+	0.992139i	$0.460061\pi$
$728$	0.325427	0.0120611
$729$	−26.9325	−0.997499
$730$	−2.37571	−0.0879291
$731$	−7.83855	−0.289919
$732$	0.918791	0.0339595
$733$	31.8788	1.17747	0.588734	−	0.808326i	$-0.299626\pi$
$733$	31.8788	1.17747	0.588734	+	0.808326i	$0.299626\pi$
$734$	76.8951	2.83825
$735$	0.242884	0.00895892
$736$	41.6813	1.53639
$737$	3.13478	0.115471
$738$	56.5119	2.08023
$739$	−47.6473	−1.75273	−0.876367	−	0.481644i	$-0.840040\pi$
$739$	−47.6473	−1.75273	−0.876367	+	0.481644i	$0.840040\pi$
$740$	21.2906	0.782658
$741$	−0.0433421	−0.00159221
$742$	−2.75461	−0.101125
$743$	21.8911	0.803107	0.401554	−	0.915835i	$-0.368470\pi$
$743$	21.8911	0.803107	0.401554	+	0.915835i	$0.368470\pi$
$744$	−0.0834023	−0.00305768
$745$	18.0438	0.661075
$746$	25.3149	0.926846
$747$	−45.8289	−1.67679
$748$	−7.74946	−0.283348
$749$	−3.79162	−0.138543
$750$	−0.723191	−0.0264072
$751$	36.4704	1.33082	0.665412	−	0.746476i	$-0.268256\pi$
$751$	36.4704	1.33082	0.665412	+	0.746476i	$0.268256\pi$
$752$	0.368152	0.0134251
$753$	0.921817	0.0335929
$754$	−4.08637	−0.148817
$755$	−8.69982	−0.316619
$756$	0.197066	0.00716722
$757$	−4.28485	−0.155736	−0.0778678	−	0.996964i	$-0.524811\pi$
$757$	−4.28485	−0.155736	−0.0778678	+	0.996964i	$0.524811\pi$
$758$	58.8925	2.13907
$759$	0.618211	0.0224396
$760$	−8.37447	−0.303774
$761$	−39.6702	−1.43804	−0.719021	−	0.694988i	$-0.755410\pi$
$761$	−39.6702	−1.43804	−0.719021	+	0.694988i	$0.755410\pi$
$762$	−0.214383	−0.00776629
$763$	−2.43059	−0.0879931
$764$	−6.11939	−0.221392
$765$	−2.97716	−0.107639
$766$	10.5481	0.381118
$767$	0.404825	0.0146174
$768$	−0.549145	−0.0198156
$769$	−28.0318	−1.01085	−0.505426	−	0.862870i	$-0.668665\pi$
$769$	−28.0318	−1.01085	−0.505426	+	0.862870i	$0.668665\pi$
$770$	−1.57484	−0.0567534
$771$	0.230151	0.00828868
$772$	−24.0394	−0.865197
$773$	23.9133	0.860103	0.430052	−	0.902804i	$-0.358495\pi$
$773$	23.9133	0.860103	0.430052	+	0.902804i	$0.358495\pi$
$774$	53.7031	1.93032
$775$	−3.39683	−0.122018
$776$	−35.6155	−1.27852
$777$	0.0679578	0.00243797
$778$	−82.4422	−2.95570
$779$	−24.9681	−0.894574
$780$	−0.0457700	−0.00163883
$781$	17.2610	0.617647
$782$	16.5911	0.593297
$783$	−0.937431	−0.0335011
$784$	0.503642	0.0179872
$785$	−19.7432	−0.704665
$786$	0.575313	0.0205207
$787$	−0.325298	−0.0115956	−0.00579781	−	0.999983i	$-0.501846\pi$
$787$	−0.325298	−0.0115956	−0.00579781	+	0.999983i	$0.501846\pi$
$788$	36.4153	1.29724
$789$	−0.383027	−0.0136361
$790$	−0.712841	−0.0253617
$791$	−5.20814	−0.185180
$792$	20.1131	0.714688
$793$	3.26612	0.115983
$794$	−66.2466	−2.35100
$795$	0.146768	0.00520534
$796$	−8.19825	−0.290579
$797$	−5.24326	−0.185726	−0.0928630	−	0.995679i	$-0.529602\pi$
$797$	−5.24326	−0.185726	−0.0928630	+	0.995679i	$0.529602\pi$
$798$	−0.0705610	−0.00249783
$799$	5.05604	0.178870
$800$	−23.0412	−0.814629
$801$	−10.2124	−0.360838
$802$	14.7981	0.522539
$803$	−2.52093	−0.0889616
$804$	0.148322	0.00523093
$805$	2.07976	0.0733018
$806$	−0.782619	−0.0275666
$807$	−0.968426	−0.0340902
$808$	31.6989	1.11516
$809$	3.17660	0.111683	0.0558417	−	0.998440i	$-0.482216\pi$
$809$	3.17660	0.111683	0.0558417	+	0.998440i	$0.482216\pi$
$810$	20.3885	0.716378
$811$	40.1446	1.40967	0.704833	−	0.709373i	$-0.251022\pi$
$811$	40.1446	1.40967	0.704833	+	0.709373i	$0.251022\pi$
$812$	−4.10359	−0.144008
$813$	−0.111329	−0.00390448
$814$	36.6255	1.28372
$815$	1.93391	0.0677418
$816$	0.00257543	9.01582e−5 0
$817$	−23.7271	−0.830106
$818$	16.1463	0.564543
$819$	0.350193	0.0122367
$820$	−26.3668	−0.920768
$821$	40.4772	1.41266	0.706331	−	0.707882i	$-0.250349\pi$
$821$	40.4772	1.41266	0.706331	+	0.707882i	$0.250349\pi$
$822$	−1.84229	−0.0642572
$823$	24.1142	0.840567	0.420283	−	0.907393i	$-0.361931\pi$
$823$	24.1142	0.840567	0.420283	+	0.907393i	$0.361931\pi$
$824$	−43.7818	−1.52521
$825$	−0.341744	−0.0118980
$826$	0.659057	0.0229315
$827$	14.8383	0.515980	0.257990	−	0.966148i	$-0.416940\pi$
$827$	14.8383	0.515980	0.257990	+	0.966148i	$0.416940\pi$
$828$	−70.1149	−2.43666
$829$	6.37122	0.221281	0.110641	−	0.993860i	$-0.464710\pi$
$829$	6.37122	0.221281	0.110641	+	0.993860i	$0.464710\pi$
$830$	34.6645	1.20322
$831$	−0.0481535	−0.00167043
$832$	−5.24966	−0.181999
$833$	6.91679	0.239652
$834$	−1.00146	−0.0346778
$835$	2.94806	0.102022
$836$	−23.4574	−0.811292
$837$	−0.179536	−0.00620569
$838$	−53.3688	−1.84359
$839$	30.4474	1.05116	0.525581	−	0.850744i	$-0.323848\pi$
$839$	30.4474	1.05116	0.525581	+	0.850744i	$0.323848\pi$
$840$	−0.0282280	−0.000973959 0
$841$	−9.47947	−0.326878
$842$	−62.2383	−2.14487
$843$	−0.612335	−0.0210899
$844$	−61.2963	−2.10991
$845$	12.7437	0.438397
$846$	−34.6397	−1.19094
$847$	1.50205	0.0516112
$848$	0.304337	0.0104510
$849$	0.352158	0.0120860
$850$	−9.17147	−0.314579
$851$	−48.3681	−1.65804
$852$	0.816705	0.0279798
$853$	9.93782	0.340264	0.170132	−	0.985421i	$-0.445581\pi$
$853$	9.93782	0.340264	0.170132	+	0.985421i	$0.445581\pi$
$854$	5.31726	0.181953
$855$	−9.01179	−0.308197
$856$	−36.6279	−1.25191
$857$	17.1104	0.584479	0.292240	−	0.956345i	$-0.405600\pi$
$857$	17.1104	0.584479	0.292240	+	0.956345i	$0.405600\pi$
$858$	−0.0787366	−0.00268802
$859$	16.6034	0.566500	0.283250	−	0.959046i	$-0.408587\pi$
$859$	16.6034	0.566500	0.283250	+	0.959046i	$0.408587\pi$
$860$	−25.0563	−0.854412
$861$	−0.0841605	−0.00286818
$862$	−47.6462	−1.62283
$863$	−22.7732	−0.775209	−0.387604	−	0.921826i	$-0.626697\pi$
$863$	−22.7732	−0.775209	−0.387604	+	0.921826i	$0.626697\pi$
$864$	−1.21782	−0.0414311
$865$	14.0785	0.478683
$866$	−15.9781	−0.542959
$867$	0.0353698	0.00120122
$868$	−0.785918	−0.0266758
$869$	−0.756413	−0.0256596
$870$	0.354458	0.0120172
$871$	0.527257	0.0178654
$872$	−23.4800	−0.795133
$873$	−38.3259	−1.29714
$874$	50.2209	1.69875
$875$	−2.58164	−0.0872753
$876$	−0.119278	−0.00403003
$877$	−53.3352	−1.80100	−0.900500	−	0.434855i	$-0.856799\pi$
$877$	−53.3352	−1.80100	−0.900500	+	0.434855i	$0.856799\pi$
$878$	−17.1891	−0.580104
$879$	0.991689	0.0334489
$880$	0.173993	0.00586530
$881$	4.77928	0.161018	0.0805090	−	0.996754i	$-0.474345\pi$
$881$	4.77928	0.161018	0.0805090	+	0.996754i	$0.474345\pi$
$882$	−47.3880	−1.59564
$883$	7.84743	0.264087	0.132044	−	0.991244i	$-0.457846\pi$
$883$	7.84743	0.264087	0.132044	+	0.991244i	$0.457846\pi$
$884$	−1.30343	−0.0438390
$885$	−0.0351152	−0.00118038
$886$	69.5883	2.33786
$887$	−31.9371	−1.07234	−0.536172	−	0.844109i	$-0.680130\pi$
$887$	−31.9371	−1.07234	−0.536172	+	0.844109i	$0.680130\pi$
$888$	0.656488	0.0220303
$889$	−0.765303	−0.0256674
$890$	7.72458	0.258928
$891$	21.6347	0.724791
$892$	−15.8049	−0.529188
$893$	15.3045	0.512145
$894$	1.46867	0.0491197
$895$	13.5959	0.454460
$896$	−5.23501	−0.174890
$897$	0.103981	0.00347181
$898$	−32.0062	−1.06806
$899$	3.73856	0.124688
$900$	38.7591	1.29197
$901$	4.17963	0.139244
$902$	−45.3578	−1.51025
$903$	−0.0799775	−0.00266148
$904$	−50.3118	−1.67335
$905$	−19.3024	−0.641632
$906$	−0.708117	−0.0235256
$907$	22.4798	0.746429	0.373215	−	0.927745i	$-0.378255\pi$
$907$	22.4798	0.746429	0.373215	+	0.927745i	$0.378255\pi$
$908$	41.3856	1.37343
$909$	34.1113	1.13140
$910$	−0.264882	−0.00878076
$911$	−51.2181	−1.69693	−0.848466	−	0.529250i	$-0.822473\pi$
$911$	−51.2181	−1.69693	−0.848466	+	0.529250i	$0.822473\pi$
$912$	0.00779577	0.000258144 0
$913$	36.7834	1.21735
$914$	−41.1970	−1.36268
$915$	−0.283309	−0.00936589
$916$	−59.0069	−1.94964
$917$	2.05375	0.0678206
$918$	−0.484750	−0.0159991
$919$	−10.5944	−0.349478	−0.174739	−	0.984615i	$-0.555908\pi$
$919$	−10.5944	−0.349478	−0.174739	+	0.984615i	$0.555908\pi$
$920$	20.0909	0.662378
$921$	−0.914146	−0.0301221
$922$	−44.0011	−1.44910
$923$	2.90323	0.0955608
$924$	−0.0790685	−0.00260116
$925$	26.7376	0.879127
$926$	−46.1412	−1.51629
$927$	−47.1138	−1.54742
$928$	25.3592	0.832457
$929$	−45.7872	−1.50223	−0.751115	−	0.660172i	$-0.770484\pi$
$929$	−45.7872	−1.50223	−0.751115	+	0.660172i	$0.770484\pi$
$930$	0.0678856	0.00222606
$931$	20.9369	0.686181
$932$	67.2329	2.20229
$933$	−0.198050	−0.00648388
$934$	27.1281	0.887659
$935$	2.38954	0.0781463
$936$	3.38294	0.110575
$937$	4.33225	0.141528	0.0707642	−	0.997493i	$-0.477456\pi$
$937$	4.33225	0.141528	0.0707642	+	0.997493i	$0.477456\pi$
$938$	0.858377	0.0280270
$939$	−0.160877	−0.00525003
$940$	16.1618	0.527141
$941$	46.8005	1.52565	0.762826	−	0.646604i	$-0.223811\pi$
$941$	46.8005	1.52565	0.762826	+	0.646604i	$0.223811\pi$
$942$	−1.60699	−0.0523585
$943$	59.9001	1.95062
$944$	−0.0728144	−0.00236991
$945$	−0.0607652	−0.00197669
$946$	−43.1034	−1.40141
$947$	54.8967	1.78390	0.891951	−	0.452132i	$-0.149336\pi$
$947$	54.8967	1.78390	0.891951	+	0.452132i	$0.149336\pi$
$948$	−0.0357897	−0.00116240
$949$	−0.424010	−0.0137639
$950$	−27.7618	−0.900712
$951$	−0.315882	−0.0102432
$952$	−0.803870	−0.0260536
$953$	32.4066	1.04975	0.524877	−	0.851178i	$-0.324111\pi$
$953$	32.4066	1.04975	0.524877	+	0.851178i	$0.324111\pi$
$954$	−28.6353	−0.927102
$955$	1.88691	0.0610589
$956$	−66.9473	−2.16523
$957$	0.376124	0.0121584
$958$	−86.2499	−2.78661
$959$	−6.57658	−0.212369
$960$	0.455364	0.0146968
$961$	−30.2840	−0.976903
$962$	6.16026	0.198615
$963$	−39.4153	−1.27014
$964$	−18.5582	−0.597719
$965$	7.41253	0.238618
$966$	0.169281	0.00544652
$967$	−18.0154	−0.579336	−0.289668	−	0.957127i	$-0.593545\pi$
$967$	−18.0154	−0.579336	−0.289668	+	0.957127i	$0.593545\pi$
$968$	14.5102	0.466374
$969$	0.107064	0.00343938
$970$	28.9893	0.930791
$971$	−9.78038	−0.313867	−0.156934	−	0.987609i	$-0.550161\pi$
$971$	−9.78038	−0.313867	−0.156934	+	0.987609i	$0.550161\pi$
$972$	3.07308	0.0985692
$973$	−3.57501	−0.114610
$974$	−24.3667	−0.780759
$975$	−0.0574798	−0.00184083
$976$	−0.587465	−0.0188043
$977$	29.4029	0.940681	0.470341	−	0.882485i	$-0.344131\pi$
$977$	29.4029	0.940681	0.470341	+	0.882485i	$0.344131\pi$
$978$	0.157409	0.00503340
$979$	8.19675	0.261969
$980$	22.1098	0.706272
$981$	−25.2669	−0.806710
$982$	61.1479	1.95131
$983$	38.0528	1.21369	0.606847	−	0.794818i	$-0.292434\pi$
$983$	38.0528	1.21369	0.606847	+	0.794818i	$0.292434\pi$
$984$	−0.813009	−0.0259178
$985$	−11.2286	−0.357774
$986$	10.0941	0.321463
$987$	0.0515872	0.00164204
$988$	−3.94544	−0.125521
$989$	56.9229	1.81004
$990$	−16.3711	−0.520308
$991$	23.0134	0.731045	0.365522	−	0.930803i	$-0.380890\pi$
$991$	23.0134	0.731045	0.365522	+	0.930803i	$0.380890\pi$
$992$	4.85678	0.154203
$993$	−0.142486	−0.00452164
$994$	4.72646	0.149914
$995$	2.52793	0.0801406
$996$	1.74041	0.0551470
$997$	−13.8441	−0.438449	−0.219224	−	0.975674i	$-0.570353\pi$
$997$	−13.8441	−0.438449	−0.219224	+	0.975674i	$0.570353\pi$
$998$	17.5106	0.554288
$999$	1.41319	0.0447114

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.j.1.2	✓	22
3.2	odd	2		9027.2.a.s.1.21		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.j.1.2	✓	22	1.1	even	1	trivial
9027.2.a.s.1.21		22	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)

\(f(q)\)	\(=\)	\(q-2.28467 q^{2} +0.0353698 q^{3} +3.21973 q^{4} -0.992800 q^{5} -0.0808085 q^{6} -0.288469 q^{7} -2.78667 q^{8} -2.99875 q^{9} +O(q^{10})\)	\(q-2.28467 q^{2} +0.0353698 q^{3} +3.21973 q^{4} -0.992800 q^{5} -0.0808085 q^{6} -0.288469 q^{7} -2.78667 q^{8} -2.99875 q^{9} +2.26822 q^{10} +2.40687 q^{11} +0.113881 q^{12} +0.404825 q^{13} +0.659057 q^{14} -0.0351152 q^{15} -0.0728144 q^{16} -1.00000 q^{17} +6.85116 q^{18} -3.02698 q^{19} -3.19655 q^{20} -0.0102031 q^{21} -5.49891 q^{22} +7.26192 q^{23} -0.0985642 q^{24} -4.01435 q^{25} -0.924893 q^{26} -0.212175 q^{27} -0.928791 q^{28} +4.41820 q^{29} +0.0802267 q^{30} +0.846173 q^{31} +5.73971 q^{32} +0.0851305 q^{33} +2.28467 q^{34} +0.286392 q^{35} -9.65515 q^{36} -6.66051 q^{37} +6.91565 q^{38} +0.0143186 q^{39} +2.76661 q^{40} +8.24852 q^{41} +0.0233107 q^{42} +7.83855 q^{43} +7.74946 q^{44} +2.97716 q^{45} -16.5911 q^{46} -5.05604 q^{47} -0.00257543 q^{48} -6.91679 q^{49} +9.17147 q^{50} -0.0353698 q^{51} +1.30343 q^{52} -4.17963 q^{53} +0.484750 q^{54} -2.38954 q^{55} +0.803870 q^{56} -0.107064 q^{57} -10.0941 q^{58} +1.00000 q^{59} -0.113061 q^{60} +8.06798 q^{61} -1.93323 q^{62} +0.865046 q^{63} -12.9677 q^{64} -0.401911 q^{65} -0.194495 q^{66} +1.30243 q^{67} -3.21973 q^{68} +0.256853 q^{69} -0.654312 q^{70} +7.17155 q^{71} +8.35654 q^{72} -1.04739 q^{73} +15.2171 q^{74} -0.141987 q^{75} -9.74603 q^{76} -0.694307 q^{77} -0.0327133 q^{78} -0.314273 q^{79} +0.0722902 q^{80} +8.98874 q^{81} -18.8452 q^{82} +15.2827 q^{83} -0.0328512 q^{84} +0.992800 q^{85} -17.9085 q^{86} +0.156271 q^{87} -6.70716 q^{88} +3.40556 q^{89} -6.80183 q^{90} -0.116780 q^{91} +23.3814 q^{92} +0.0299290 q^{93} +11.5514 q^{94} +3.00518 q^{95} +0.203012 q^{96} +12.7806 q^{97} +15.8026 q^{98} -7.21760 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * q^99

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