LMFDB - Embedded newform 6007.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6007,2,Mod(1,6007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6007.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9661364942$
Analytic rank:	$1$
Dimension:	$237$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52945 q^{2} -1.63373 q^{3} +4.39812 q^{4} +1.74511 q^{5} +4.13244 q^{6} +0.157946 q^{7} -6.06591 q^{8} -0.330925 q^{9} +O(q^{10})$	\(q-2.52945 q^{2} -1.63373 q^{3} +4.39812 q^{4} +1.74511 q^{5} +4.13244 q^{6} +0.157946 q^{7} -6.06591 q^{8} -0.330925 q^{9} -4.41416 q^{10} +1.69435 q^{11} -7.18534 q^{12} +5.97188 q^{13} -0.399516 q^{14} -2.85103 q^{15} +6.54719 q^{16} -0.491258 q^{17} +0.837057 q^{18} -2.79849 q^{19} +7.67518 q^{20} -0.258041 q^{21} -4.28576 q^{22} +2.86095 q^{23} +9.91007 q^{24} -1.95460 q^{25} -15.1056 q^{26} +5.44183 q^{27} +0.694664 q^{28} +0.233944 q^{29} +7.21155 q^{30} -3.55273 q^{31} -4.42896 q^{32} -2.76811 q^{33} +1.24261 q^{34} +0.275632 q^{35} -1.45544 q^{36} -7.79846 q^{37} +7.07863 q^{38} -9.75644 q^{39} -10.5857 q^{40} +4.56773 q^{41} +0.652702 q^{42} +9.56378 q^{43} +7.45193 q^{44} -0.577499 q^{45} -7.23663 q^{46} -11.7813 q^{47} -10.6963 q^{48} -6.97505 q^{49} +4.94407 q^{50} +0.802583 q^{51} +26.2650 q^{52} +0.0221230 q^{53} -13.7648 q^{54} +2.95682 q^{55} -0.958086 q^{56} +4.57197 q^{57} -0.591750 q^{58} -8.07748 q^{59} -12.5392 q^{60} +4.83467 q^{61} +8.98644 q^{62} -0.0522682 q^{63} -1.89154 q^{64} +10.4216 q^{65} +7.00178 q^{66} -0.0716095 q^{67} -2.16061 q^{68} -4.67402 q^{69} -0.697198 q^{70} +6.79101 q^{71} +2.00736 q^{72} -4.63362 q^{73} +19.7258 q^{74} +3.19329 q^{75} -12.3081 q^{76} +0.267615 q^{77} +24.6784 q^{78} +10.4042 q^{79} +11.4255 q^{80} -7.89772 q^{81} -11.5538 q^{82} -3.45695 q^{83} -1.13489 q^{84} -0.857297 q^{85} -24.1911 q^{86} -0.382202 q^{87} -10.2778 q^{88} -12.4994 q^{89} +1.46075 q^{90} +0.943233 q^{91} +12.5828 q^{92} +5.80420 q^{93} +29.8003 q^{94} -4.88366 q^{95} +7.23573 q^{96} -2.96133 q^{97} +17.6430 q^{98} -0.560701 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) $ 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * 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 $

$2$	−2.52945	−1.78859	−0.894296	−	0.447477i	$-0.852323\pi$
$2$	−2.52945	−1.78859	−0.894296	+	0.447477i	$0.852323\pi$
$3$	−1.63373	−0.943235	−0.471617	−	0.881803i	$-0.656330\pi$
$3$	−1.63373	−0.943235	−0.471617	+	0.881803i	$0.656330\pi$
$4$	4.39812	2.19906
$5$	1.74511	0.780436	0.390218	−	0.920723i	$-0.372400\pi$
$5$	1.74511	0.780436	0.390218	+	0.920723i	$0.372400\pi$
$6$	4.13244	1.68706
$7$	0.157946	0.0596979	0.0298490	−	0.999554i	$-0.490497\pi$
$7$	0.157946	0.0596979	0.0298490	+	0.999554i	$0.490497\pi$
$8$	−6.06591	−2.14462
$9$	−0.330925	−0.110308
$10$	−4.41416	−1.39588
$11$	1.69435	0.510865	0.255432	−	0.966827i	$-0.417782\pi$
$11$	1.69435	0.510865	0.255432	+	0.966827i	$0.417782\pi$
$12$	−7.18534	−2.07423
$13$	5.97188	1.65630	0.828150	−	0.560506i	$-0.189393\pi$
$13$	5.97188	1.65630	0.828150	+	0.560506i	$0.189393\pi$
$14$	−0.399516	−0.106775
$15$	−2.85103	−0.736134
$16$	6.54719	1.63680
$17$	−0.491258	−0.119148	−0.0595738	−	0.998224i	$-0.518974\pi$
$17$	−0.491258	−0.119148	−0.0595738	+	0.998224i	$0.518974\pi$
$18$	0.837057	0.197296
$19$	−2.79849	−0.642017	−0.321008	−	0.947076i	$-0.604022\pi$
$19$	−2.79849	−0.642017	−0.321008	+	0.947076i	$0.604022\pi$
$20$	7.67518	1.71622
$21$	−0.258041	−0.0563092
$22$	−4.28576	−0.913728
$23$	2.86095	0.596549	0.298275	−	0.954480i	$-0.403589\pi$
$23$	2.86095	0.596549	0.298275	+	0.954480i	$0.403589\pi$
$24$	9.91007	2.02288
$25$	−1.95460	−0.390920
$26$	−15.1056	−2.96244
$27$	5.44183	1.04728
$28$	0.694664	0.131279
$29$	0.233944	0.0434424	0.0217212	−	0.999764i	$-0.493085\pi$
$29$	0.233944	0.0434424	0.0217212	+	0.999764i	$0.493085\pi$
$30$	7.21155	1.31664
$31$	−3.55273	−0.638088	−0.319044	−	0.947740i	$-0.603362\pi$
$31$	−3.55273	−0.638088	−0.319044	+	0.947740i	$0.603362\pi$
$32$	−4.42896	−0.782937
$33$	−2.76811	−0.481865
$34$	1.24261	0.213106
$35$	0.275632	0.0465904
$36$	−1.45544	−0.242574
$37$	−7.79846	−1.28206	−0.641030	−	0.767516i	$-0.721492\pi$
$37$	−7.79846	−1.28206	−0.641030	+	0.767516i	$0.721492\pi$
$38$	7.07863	1.14831
$39$	−9.75644	−1.56228
$40$	−10.5857	−1.67374
$41$	4.56773	0.713359	0.356680	−	0.934227i	$-0.383909\pi$
$41$	4.56773	0.713359	0.356680	+	0.934227i	$0.383909\pi$
$42$	0.652702	0.100714
$43$	9.56378	1.45846	0.729231	−	0.684267i	$-0.239878\pi$
$43$	9.56378	1.45846	0.729231	+	0.684267i	$0.239878\pi$
$44$	7.45193	1.12342
$45$	−0.577499	−0.0860884
$46$	−7.23663	−1.06698
$47$	−11.7813	−1.71848	−0.859241	−	0.511571i	$-0.829064\pi$
$47$	−11.7813	−1.71848	−0.859241	+	0.511571i	$0.829064\pi$
$48$	−10.6963	−1.54388
$49$	−6.97505	−0.996436
$50$	4.94407	0.699197
$51$	0.802583	0.112384
$52$	26.2650	3.64230
$53$	0.0221230	0.00303883	0.00151942	−	0.999999i	$-0.499516\pi$
$53$	0.0221230	0.00303883	0.00151942	+	0.999999i	$0.499516\pi$
$54$	−13.7648	−1.87316
$55$	2.95682	0.398697
$56$	−0.958086	−0.128030
$57$	4.57197	0.605572
$58$	−0.591750	−0.0777006
$59$	−8.07748	−1.05160	−0.525799	−	0.850609i	$-0.676234\pi$
$59$	−8.07748	−1.05160	−0.525799	+	0.850609i	$0.676234\pi$
$60$	−12.5392	−1.61880
$61$	4.83467	0.619015	0.309508	−	0.950897i	$-0.399836\pi$
$61$	4.83467	0.619015	0.309508	+	0.950897i	$0.399836\pi$
$62$	8.98644	1.14128
$63$	−0.0522682	−0.00658517
$64$	−1.89154	−0.236443
$65$	10.4216	1.29264
$66$	7.00178	0.861860
$67$	−0.0716095	−0.00874850	−0.00437425	−	0.999990i	$-0.501392\pi$
$67$	−0.0716095	−0.00874850	−0.00437425	+	0.999990i	$0.501392\pi$
$68$	−2.16061	−0.262012
$69$	−4.67402	−0.562686
$70$	−0.697198	−0.0833311
$71$	6.79101	0.805945	0.402972	−	0.915212i	$-0.367977\pi$
$71$	6.79101	0.805945	0.402972	+	0.915212i	$0.367977\pi$
$72$	2.00736	0.236570
$73$	−4.63362	−0.542324	−0.271162	−	0.962534i	$-0.587408\pi$
$73$	−4.63362	−0.542324	−0.271162	+	0.962534i	$0.587408\pi$
$74$	19.7258	2.29308
$75$	3.19329	0.368730
$76$	−12.3081	−1.41183
$77$	0.267615	0.0304976
$78$	24.6784	2.79428
$79$	10.4042	1.17056	0.585280	−	0.810831i	$-0.300984\pi$
$79$	10.4042	1.17056	0.585280	+	0.810831i	$0.300984\pi$
$80$	11.4255	1.27742
$81$	−7.89772	−0.877524
$82$	−11.5538	−1.27591
$83$	−3.45695	−0.379449	−0.189725	−	0.981837i	$-0.560760\pi$
$83$	−3.45695	−0.379449	−0.189725	+	0.981837i	$0.560760\pi$
$84$	−1.13489	−0.123827
$85$	−0.857297	−0.0929869
$86$	−24.1911	−2.60859
$87$	−0.382202	−0.0409763
$88$	−10.2778	−1.09561
$89$	−12.4994	−1.32493	−0.662466	−	0.749092i	$-0.730490\pi$
$89$	−12.4994	−1.32493	−0.662466	+	0.749092i	$0.730490\pi$
$90$	1.46075	0.153977
$91$	0.943233	0.0988777
$92$	12.5828	1.31185
$93$	5.80420	0.601867
$94$	29.8003	3.07366
$95$	−4.88366	−0.501053
$96$	7.23573	0.738494
$97$	−2.96133	−0.300677	−0.150339	−	0.988635i	$-0.548036\pi$
$97$	−2.96133	−0.300677	−0.150339	+	0.988635i	$0.548036\pi$
$98$	17.6430	1.78222
$99$	−0.560701	−0.0563526
$100$	−8.59657	−0.859657
$101$	−1.00315	−0.0998168	−0.0499084	−	0.998754i	$-0.515893\pi$
$101$	−1.00315	−0.0998168	−0.0499084	+	0.998754i	$0.515893\pi$
$102$	−2.03009	−0.201009
$103$	−17.1576	−1.69059	−0.845295	−	0.534300i	$-0.820575\pi$
$103$	−17.1576	−1.69059	−0.845295	+	0.534300i	$0.820575\pi$
$104$	−36.2249	−3.55214
$105$	−0.450309	−0.0439457
$106$	−0.0559591	−0.00543523
$107$	−19.1950	−1.85565	−0.927827	−	0.373012i	$-0.878325\pi$
$107$	−19.1950	−1.85565	−0.927827	+	0.373012i	$0.878325\pi$
$108$	23.9338	2.30303
$109$	5.20132	0.498196	0.249098	−	0.968478i	$-0.419866\pi$
$109$	5.20132	0.498196	0.249098	+	0.968478i	$0.419866\pi$
$110$	−7.47912	−0.713106
$111$	12.7406	1.20928
$112$	1.03410	0.0977134
$113$	−14.4984	−1.36390	−0.681950	−	0.731399i	$-0.738868\pi$
$113$	−14.4984	−1.36390	−0.681950	+	0.731399i	$0.738868\pi$
$114$	−11.5646	−1.08312
$115$	4.99266	0.465568
$116$	1.02891	0.0955323
$117$	−1.97624	−0.182704
$118$	20.4316	1.88088
$119$	−0.0775921	−0.00711286
$120$	17.2941	1.57873
$121$	−8.12919	−0.739017
$122$	−12.2290	−1.10717
$123$	−7.46244	−0.672865
$124$	−15.6253	−1.40319
$125$	−12.1365	−1.08552
$126$	0.132210	0.0117782
$127$	4.25155	0.377264	0.188632	−	0.982048i	$-0.439595\pi$
$127$	4.25155	0.377264	0.188632	+	0.982048i	$0.439595\pi$
$128$	13.6425	1.20584
$129$	−15.6246	−1.37567
$130$	−26.3608	−2.31200
$131$	−17.8543	−1.55994	−0.779970	−	0.625817i	$-0.784766\pi$
$131$	−17.8543	−1.55994	−0.779970	+	0.625817i	$0.784766\pi$
$132$	−12.1744	−1.05965
$133$	−0.442009	−0.0383271
$134$	0.181133	0.0156475
$135$	9.49658	0.817335
$136$	2.97993	0.255527
$137$	−1.75320	−0.149786	−0.0748931	−	0.997192i	$-0.523862\pi$
$137$	−1.75320	−0.149786	−0.0748931	+	0.997192i	$0.523862\pi$
$138$	11.8227	1.00642
$139$	21.9602	1.86264	0.931322	−	0.364198i	$-0.118657\pi$
$139$	21.9602	1.86264	0.931322	+	0.364198i	$0.118657\pi$
$140$	1.21226	0.102455
$141$	19.2475	1.62093
$142$	−17.1775	−1.44151
$143$	10.1184	0.846145
$144$	−2.16663	−0.180552
$145$	0.408258	0.0339040
$146$	11.7205	0.969996
$147$	11.3954	0.939873
$148$	−34.2985	−2.81932
$149$	−4.53082	−0.371180	−0.185590	−	0.982627i	$-0.559420\pi$
$149$	−4.53082	−0.371180	−0.185590	+	0.982627i	$0.559420\pi$
$150$	−8.07727	−0.659507
$151$	16.8859	1.37416	0.687079	−	0.726583i	$-0.258893\pi$
$151$	16.8859	1.37416	0.687079	+	0.726583i	$0.258893\pi$
$152$	16.9754	1.37688
$153$	0.162569	0.0131429
$154$	−0.676919	−0.0545477
$155$	−6.19989	−0.497987
$156$	−42.9099	−3.43554
$157$	−19.6448	−1.56782	−0.783912	−	0.620872i	$-0.786779\pi$
$157$	−19.6448	−1.56782	−0.783912	+	0.620872i	$0.786779\pi$
$158$	−26.3168	−2.09365
$159$	−0.0361431	−0.00286633
$160$	−7.72901	−0.611032
$161$	0.451875	0.0356128
$162$	19.9769	1.56953
$163$	12.7660	0.999910	0.499955	−	0.866051i	$-0.333350\pi$
$163$	12.7660	0.999910	0.499955	+	0.866051i	$0.333350\pi$
$164$	20.0894	1.56872
$165$	−4.83064	−0.376065
$166$	8.74417	0.678679
$167$	−13.9819	−1.08195	−0.540974	−	0.841039i	$-0.681944\pi$
$167$	−13.9819	−1.08195	−0.540974	+	0.841039i	$0.681944\pi$
$168$	1.56525	0.120762
$169$	22.6633	1.74333
$170$	2.16849	0.166316
$171$	0.926088	0.0708197
$172$	42.0626	3.20724
$173$	−14.8456	−1.12869	−0.564346	−	0.825538i	$-0.690872\pi$
$173$	−14.8456	−1.12869	−0.564346	+	0.825538i	$0.690872\pi$
$174$	0.966760	0.0732899
$175$	−0.308721	−0.0233371
$176$	11.0932	0.836182
$177$	13.1964	0.991904
$178$	31.6166	2.36976
$179$	−13.5995	−1.01647	−0.508237	−	0.861217i	$-0.669703\pi$
$179$	−13.5995	−1.01647	−0.508237	+	0.861217i	$0.669703\pi$
$180$	−2.53991	−0.189313
$181$	−7.97968	−0.593125	−0.296562	−	0.955013i	$-0.595840\pi$
$181$	−7.97968	−0.593125	−0.296562	+	0.955013i	$0.595840\pi$
$182$	−2.38586	−0.176852
$183$	−7.89854	−0.583877
$184$	−17.3543	−1.27937
$185$	−13.6092	−1.00056
$186$	−14.6814	−1.07649
$187$	−0.832361	−0.0608683
$188$	−51.8156	−3.77904
$189$	0.859515	0.0625205
$190$	12.3530	0.896178
$191$	13.3049	0.962710	0.481355	−	0.876526i	$-0.340145\pi$
$191$	13.3049	0.962710	0.481355	+	0.876526i	$0.340145\pi$
$192$	3.09027	0.223021
$193$	26.7053	1.92229	0.961143	−	0.276050i	$-0.0890254\pi$
$193$	26.7053	1.92229	0.961143	+	0.276050i	$0.0890254\pi$
$194$	7.49052	0.537788
$195$	−17.0260	−1.21926
$196$	−30.6771	−2.19122
$197$	−13.5530	−0.965609	−0.482804	−	0.875728i	$-0.660382\pi$
$197$	−13.5530	−0.965609	−0.482804	+	0.875728i	$0.660382\pi$
$198$	1.41827	0.100792
$199$	15.5124	1.09964	0.549821	−	0.835283i	$-0.314696\pi$
$199$	15.5124	1.09964	0.549821	+	0.835283i	$0.314696\pi$
$200$	11.8564	0.838377
$201$	0.116991	0.00825189
$202$	2.53741	0.178531
$203$	0.0369505	0.00259342
$204$	3.52985	0.247139
$205$	7.97117	0.556731
$206$	43.3993	3.02377
$207$	−0.946759	−0.0658043
$208$	39.0990	2.71103
$209$	−4.74160	−0.327984
$210$	1.13903	0.0786008
$211$	22.8073	1.57012	0.785060	−	0.619419i	$-0.212632\pi$
$211$	22.8073	1.57012	0.785060	+	0.619419i	$0.212632\pi$
$212$	0.0972996	0.00668257
$213$	−11.0947	−0.760195
$214$	48.5528	3.31900
$215$	16.6898	1.13824
$216$	−33.0097	−2.24602
$217$	−0.561138	−0.0380926
$218$	−13.1565	−0.891069
$219$	7.57009	0.511539
$220$	13.0044	0.876758
$221$	−2.93373	−0.197344
$222$	−32.2267	−2.16291
$223$	−27.6865	−1.85403	−0.927013	−	0.375029i	$-0.877633\pi$
$223$	−27.6865	−1.85403	−0.927013	+	0.375029i	$0.877633\pi$
$224$	−0.699537	−0.0467397
$225$	0.646826	0.0431217
$226$	36.6731	2.43946
$227$	−10.3763	−0.688702	−0.344351	−	0.938841i	$-0.611901\pi$
$227$	−10.3763	−0.688702	−0.344351	+	0.938841i	$0.611901\pi$
$228$	20.1081	1.33169
$229$	−12.0593	−0.796900	−0.398450	−	0.917190i	$-0.630452\pi$
$229$	−12.0593	−0.796900	−0.398450	+	0.917190i	$0.630452\pi$
$230$	−12.6287	−0.832711
$231$	−0.437211	−0.0287664
$232$	−1.41909	−0.0931675
$233$	−1.05301	−0.0689852	−0.0344926	−	0.999405i	$-0.510982\pi$
$233$	−1.05301	−0.0689852	−0.0344926	+	0.999405i	$0.510982\pi$
$234$	4.99880	0.326782
$235$	−20.5597	−1.34116
$236$	−35.5257	−2.31253
$237$	−16.9976	−1.10411
$238$	0.196265	0.0127220
$239$	16.0969	1.04122	0.520612	−	0.853793i	$-0.325704\pi$
$239$	16.0969	1.04122	0.520612	+	0.853793i	$0.325704\pi$
$240$	−18.6663	−1.20490
$241$	12.4703	0.803281	0.401641	−	0.915797i	$-0.368440\pi$
$241$	12.4703	0.803281	0.401641	+	0.915797i	$0.368440\pi$
$242$	20.5624	1.32180
$243$	−3.42276	−0.219570
$244$	21.2634	1.36125
$245$	−12.1722	−0.777654
$246$	18.8759	1.20348
$247$	−16.7122	−1.06337
$248$	21.5505	1.36846
$249$	5.64772	0.357910
$250$	30.6987	1.94156
$251$	13.8794	0.876063	0.438032	−	0.898960i	$-0.355676\pi$
$251$	13.8794	0.876063	0.438032	+	0.898960i	$0.355676\pi$
$252$	−0.229882	−0.0144812
$253$	4.84744	0.304756
$254$	−10.7541	−0.674770
$255$	1.40059	0.0877085
$256$	−30.7249	−1.92031
$257$	−5.37759	−0.335445	−0.167722	−	0.985834i	$-0.553641\pi$
$257$	−5.37759	−0.335445	−0.167722	+	0.985834i	$0.553641\pi$
$258$	39.5217	2.46052
$259$	−1.23174	−0.0765363
$260$	45.8352	2.84258
$261$	−0.0774179	−0.00479205
$262$	45.1616	2.79009
$263$	9.81516	0.605229	0.302614	−	0.953113i	$-0.402141\pi$
$263$	9.81516	0.605229	0.302614	+	0.953113i	$0.402141\pi$
$264$	16.7911	1.03342
$265$	0.0386070	0.00237161
$266$	1.11804	0.0685515
$267$	20.4206	1.24972
$268$	−0.314947	−0.0192385
$269$	18.5924	1.13360	0.566800	−	0.823855i	$-0.308181\pi$
$269$	18.5924	1.13360	0.566800	+	0.823855i	$0.308181\pi$
$270$	−24.0211	−1.46188
$271$	12.3799	0.752023	0.376012	−	0.926615i	$-0.377295\pi$
$271$	12.3799	0.752023	0.376012	+	0.926615i	$0.377295\pi$
$272$	−3.21636	−0.195020
$273$	−1.54099	−0.0932649
$274$	4.43464	0.267906
$275$	−3.31177	−0.199707
$276$	−20.5569	−1.23738
$277$	−19.1569	−1.15103	−0.575513	−	0.817792i	$-0.695198\pi$
$277$	−19.1569	−1.15103	−0.575513	+	0.817792i	$0.695198\pi$
$278$	−55.5473	−3.33151
$279$	1.17568	0.0703864
$280$	−1.67196	−0.0999189
$281$	17.8802	1.06664	0.533322	−	0.845912i	$-0.320943\pi$
$281$	17.8802	1.06664	0.533322	+	0.845912i	$0.320943\pi$
$282$	−48.6856	−2.89918
$283$	15.5761	0.925904	0.462952	−	0.886383i	$-0.346790\pi$
$283$	15.5761	0.925904	0.462952	+	0.886383i	$0.346790\pi$
$284$	29.8676	1.77232
$285$	7.97858	0.472610
$286$	−25.5941	−1.51341
$287$	0.721454	0.0425861
$288$	1.46565	0.0863644
$289$	−16.7587	−0.985804
$290$	−1.03267	−0.0606403
$291$	4.83801	0.283609
$292$	−20.3792	−1.19260
$293$	−3.06568	−0.179099	−0.0895494	−	0.995982i	$-0.528543\pi$
$293$	−3.06568	−0.179099	−0.0895494	+	0.995982i	$0.528543\pi$
$294$	−28.8240	−1.68105
$295$	−14.0961	−0.820705
$296$	47.3048	2.74954
$297$	9.22035	0.535019
$298$	11.4605	0.663888
$299$	17.0852	0.988065
$300$	14.0445	0.810858
$301$	1.51056	0.0870672
$302$	−42.7121	−2.45781
$303$	1.63887	0.0941507
$304$	−18.3222	−1.05085
$305$	8.43701	0.483102
$306$	−0.411211	−0.0235074
$307$	−5.16774	−0.294938	−0.147469	−	0.989067i	$-0.547113\pi$
$307$	−5.16774	−0.294938	−0.147469	+	0.989067i	$0.547113\pi$
$308$	1.17700	0.0670659
$309$	28.0309	1.59462
$310$	15.6823	0.890695
$311$	31.6058	1.79220	0.896099	−	0.443854i	$-0.146389\pi$
$311$	31.6058	1.79220	0.896099	+	0.443854i	$0.146389\pi$
$312$	59.1817	3.35050
$313$	12.1724	0.688024	0.344012	−	0.938965i	$-0.388214\pi$
$313$	12.1724	0.688024	0.344012	+	0.938965i	$0.388214\pi$
$314$	49.6905	2.80420
$315$	−0.0912136	−0.00513930
$316$	45.7587	2.57413
$317$	23.8084	1.33721	0.668606	−	0.743616i	$-0.266891\pi$
$317$	23.8084	1.33721	0.668606	+	0.743616i	$0.266891\pi$
$318$	0.0914221	0.00512669
$319$	0.396383	0.0221932
$320$	−3.30094	−0.184528
$321$	31.3595	1.75032
$322$	−1.14300	−0.0636967
$323$	1.37478	0.0764947
$324$	−34.7351	−1.92973
$325$	−11.6726	−0.647482
$326$	−32.2910	−1.78843
$327$	−8.49756	−0.469916
$328$	−27.7074	−1.52989
$329$	−1.86081	−0.102590
$330$	12.2189	0.672626
$331$	−10.2721	−0.564603	−0.282302	−	0.959326i	$-0.591098\pi$
$331$	−10.2721	−0.564603	−0.282302	+	0.959326i	$0.591098\pi$
$332$	−15.2040	−0.834431
$333$	2.58070	0.141422
$334$	35.3664	1.93516
$335$	−0.124966	−0.00682764
$336$	−1.68944	−0.0921667
$337$	12.2079	0.665008	0.332504	−	0.943102i	$-0.392106\pi$
$337$	12.2079	0.665008	0.332504	+	0.943102i	$0.392106\pi$
$338$	−57.3257	−3.11811
$339$	23.6866	1.28648
$340$	−3.77049	−0.204484
$341$	−6.01955	−0.325977
$342$	−2.34249	−0.126667
$343$	−2.20730	−0.119183
$344$	−58.0131	−3.12785
$345$	−8.15667	−0.439140
$346$	37.5513	2.01877
$347$	−31.8895	−1.71192	−0.855958	−	0.517046i	$-0.827032\pi$
$347$	−31.8895	−1.71192	−0.855958	+	0.517046i	$0.827032\pi$
$348$	−1.68097	−0.0901093
$349$	−17.2254	−0.922052	−0.461026	−	0.887387i	$-0.652519\pi$
$349$	−17.2254	−0.922052	−0.461026	+	0.887387i	$0.652519\pi$
$350$	0.780895	0.0417406
$351$	32.4980	1.73461
$352$	−7.50420	−0.399975
$353$	20.2326	1.07687	0.538436	−	0.842666i	$-0.319015\pi$
$353$	20.2326	1.07687	0.538436	+	0.842666i	$0.319015\pi$
$354$	−33.3797	−1.77411
$355$	11.8510	0.628988
$356$	−54.9738	−2.91360
$357$	0.126765	0.00670910
$358$	34.3993	1.81806
$359$	−12.3344	−0.650987	−0.325494	−	0.945544i	$-0.605530\pi$
$359$	−12.3344	−0.650987	−0.325494	+	0.945544i	$0.605530\pi$
$360$	3.50306	0.184627
$361$	−11.1685	−0.587815
$362$	20.1842	1.06086
$363$	13.2809	0.697067
$364$	4.14845	0.217438
$365$	−8.08616	−0.423249
$366$	19.9790	1.04432
$367$	−30.4016	−1.58695	−0.793474	−	0.608604i	$-0.791730\pi$
$367$	−30.4016	−1.58695	−0.793474	+	0.608604i	$0.791730\pi$
$368$	18.7312	0.976430
$369$	−1.51157	−0.0786894
$370$	34.4237	1.78960
$371$	0.00349424	0.000181412 0
$372$	25.5275	1.32354
$373$	14.9670	0.774960	0.387480	−	0.921878i	$-0.373346\pi$
$373$	14.9670	0.774960	0.387480	+	0.921878i	$0.373346\pi$
$374$	2.10542	0.108868
$375$	19.8278	1.02390
$376$	71.4645	3.68550
$377$	1.39709	0.0719536
$378$	−2.17410	−0.111824
$379$	21.2627	1.09219	0.546095	−	0.837723i	$-0.316114\pi$
$379$	21.2627	1.09219	0.546095	+	0.837723i	$0.316114\pi$
$380$	−21.4789	−1.10184
$381$	−6.94588	−0.355848
$382$	−33.6541	−1.72189
$383$	19.0896	0.975431	0.487716	−	0.873003i	$-0.337830\pi$
$383$	19.0896	0.975431	0.487716	+	0.873003i	$0.337830\pi$
$384$	−22.2881	−1.13739
$385$	0.467017	0.0238014
$386$	−67.5496	−3.43818
$387$	−3.16489	−0.160880
$388$	−13.0243	−0.661206
$389$	8.95251	0.453910	0.226955	−	0.973905i	$-0.427123\pi$
$389$	8.95251	0.453910	0.226955	+	0.973905i	$0.427123\pi$
$390$	43.0665	2.18076
$391$	−1.40546	−0.0710774
$392$	42.3101	2.13698
$393$	29.1692	1.47139
$394$	34.2815	1.72708
$395$	18.1564	0.913547
$396$	−2.46603	−0.123923
$397$	−0.565579	−0.0283856	−0.0141928	−	0.999899i	$-0.504518\pi$
$397$	−0.565579	−0.0283856	−0.0141928	+	0.999899i	$0.504518\pi$
$398$	−39.2377	−1.96681
$399$	0.722124	0.0361514
$400$	−12.7972	−0.639858
$401$	−4.21384	−0.210429	−0.105215	−	0.994450i	$-0.533553\pi$
$401$	−4.21384	−0.210429	−0.105215	+	0.994450i	$0.533553\pi$
$402$	−0.295922	−0.0147592
$403$	−21.2164	−1.05687
$404$	−4.41195	−0.219503
$405$	−13.7824	−0.684851
$406$	−0.0934645	−0.00463857
$407$	−13.2133	−0.654959
$408$	−4.86840	−0.241022
$409$	−36.9559	−1.82735	−0.913675	−	0.406446i	$-0.866768\pi$
$409$	−36.9559	−1.82735	−0.913675	+	0.406446i	$0.866768\pi$
$410$	−20.1627	−0.995764
$411$	2.86426	0.141284
$412$	−75.4612	−3.71771
$413$	−1.27581	−0.0627783
$414$	2.39478	0.117697
$415$	−6.03274	−0.296136
$416$	−26.4492	−1.29678
$417$	−35.8771	−1.75691
$418$	11.9937	0.586629
$419$	6.72966	0.328765	0.164383	−	0.986397i	$-0.447437\pi$
$419$	6.72966	0.328765	0.164383	+	0.986397i	$0.447437\pi$
$420$	−1.98051	−0.0966391
$421$	38.4417	1.87354	0.936768	−	0.349952i	$-0.113802\pi$
$421$	38.4417	1.87354	0.936768	+	0.349952i	$0.113802\pi$
$422$	−57.6900	−2.80830
$423$	3.89873	0.189563
$424$	−0.134196	−0.00651715
$425$	0.960213	0.0465772
$426$	28.0634	1.35968
$427$	0.763615	0.0369539
$428$	−84.4219	−4.08069
$429$	−16.5308	−0.798114
$430$	−42.2160	−2.03584
$431$	12.7281	0.613089	0.306545	−	0.951856i	$-0.400827\pi$
$431$	12.7281	0.613089	0.306545	+	0.951856i	$0.400827\pi$
$432$	35.6287	1.71419
$433$	−15.2406	−0.732418	−0.366209	−	0.930533i	$-0.619345\pi$
$433$	−15.2406	−0.732418	−0.366209	+	0.930533i	$0.619345\pi$
$434$	1.41937	0.0681320
$435$	−0.666983	−0.0319794
$436$	22.8760	1.09556
$437$	−8.00633	−0.382995
$438$	−19.1482	−0.914934
$439$	−23.1093	−1.10295	−0.551473	−	0.834193i	$-0.685934\pi$
$439$	−23.1093	−1.10295	−0.551473	+	0.834193i	$0.685934\pi$
$440$	−17.9358	−0.855055
$441$	2.30822	0.109915
$442$	7.42072	0.352968
$443$	−27.7604	−1.31894	−0.659468	−	0.751732i	$-0.729218\pi$
$443$	−27.7604	−1.31894	−0.659468	+	0.751732i	$0.729218\pi$
$444$	56.0346	2.65928
$445$	−21.8128	−1.03402
$446$	70.0316	3.31609
$447$	7.40214	0.350109
$448$	−0.298761	−0.0141151
$449$	−6.78057	−0.319995	−0.159997	−	0.987117i	$-0.551149\pi$
$449$	−6.78057	−0.319995	−0.159997	+	0.987117i	$0.551149\pi$
$450$	−1.63611	−0.0771271
$451$	7.73931	0.364430
$452$	−63.7659	−2.99929
$453$	−27.5871	−1.29615
$454$	26.2464	1.23181
$455$	1.64604	0.0771677
$456$	−27.7332	−1.29873
$457$	33.2600	1.55584	0.777920	−	0.628364i	$-0.216275\pi$
$457$	33.2600	1.55584	0.777920	+	0.628364i	$0.216275\pi$
$458$	30.5033	1.42533
$459$	−2.67334	−0.124781
$460$	21.9583	1.02381
$461$	−15.8806	−0.739632	−0.369816	−	0.929105i	$-0.620579\pi$
$461$	−15.8806	−0.739632	−0.369816	+	0.929105i	$0.620579\pi$
$462$	1.10590	0.0514513
$463$	−20.5717	−0.956048	−0.478024	−	0.878347i	$-0.658647\pi$
$463$	−20.5717	−0.956048	−0.478024	+	0.878347i	$0.658647\pi$
$464$	1.53168	0.0711063
$465$	10.1289	0.469718
$466$	2.66355	0.123386
$467$	−21.7327	−1.00567	−0.502834	−	0.864383i	$-0.667709\pi$
$467$	−21.7327	−1.00567	−0.502834	+	0.864383i	$0.667709\pi$
$468$	−8.69174	−0.401776
$469$	−0.0113104	−0.000522267 0
$470$	52.0046	2.39879
$471$	32.0943	1.47883
$472$	48.9973	2.25528
$473$	16.2044	0.745077
$474$	42.9946	1.97481
$475$	5.46993	0.250977
$476$	−0.341259	−0.0156416
$477$	−0.00732105	−0.000335208 0
$478$	−40.7164	−1.86233
$479$	19.6835	0.899362	0.449681	−	0.893189i	$-0.351538\pi$
$479$	19.6835	0.899362	0.449681	+	0.893189i	$0.351538\pi$
$480$	12.6271	0.576347
$481$	−46.5715	−2.12348
$482$	−31.5429	−1.43674
$483$	−0.738242	−0.0335912
$484$	−35.7531	−1.62514
$485$	−5.16783	−0.234659
$486$	8.65770	0.392721
$487$	−9.28279	−0.420643	−0.210322	−	0.977632i	$-0.567451\pi$
$487$	−9.28279	−0.420643	−0.210322	+	0.977632i	$0.567451\pi$
$488$	−29.3267	−1.32756
$489$	−20.8562	−0.943150
$490$	30.7890	1.39091
$491$	−39.1197	−1.76545	−0.882723	−	0.469894i	$-0.844292\pi$
$491$	−39.1197	−1.76545	−0.882723	+	0.469894i	$0.844292\pi$
$492$	−32.8207	−1.47967
$493$	−0.114927	−0.00517605
$494$	42.2727	1.90194
$495$	−0.978483	−0.0439795
$496$	−23.2604	−1.04442
$497$	1.07261	0.0481132
$498$	−14.2856	−0.640154
$499$	37.3005	1.66980	0.834899	−	0.550403i	$-0.185526\pi$
$499$	37.3005	1.66980	0.834899	+	0.550403i	$0.185526\pi$
$500$	−53.3778	−2.38713
$501$	22.8426	1.02053
$502$	−35.1074	−1.56692
$503$	8.04311	0.358624	0.179312	−	0.983792i	$-0.442613\pi$
$503$	8.04311	0.358624	0.179312	+	0.983792i	$0.442613\pi$
$504$	0.317054	0.0141227
$505$	−1.75060	−0.0779006
$506$	−12.2614	−0.545084
$507$	−37.0257	−1.64437
$508$	18.6988	0.829625
$509$	−31.5199	−1.39709	−0.698547	−	0.715564i	$-0.746170\pi$
$509$	−31.5199	−1.39709	−0.698547	+	0.715564i	$0.746170\pi$
$510$	−3.54273	−0.156875
$511$	−0.731861	−0.0323756
$512$	50.4321	2.22881
$513$	−15.2289	−0.672372
$514$	13.6023	0.599974
$515$	−29.9419	−1.31940
$516$	−68.7190	−3.02518
$517$	−19.9616	−0.877912
$518$	3.11561	0.136892
$519$	24.2538	1.06462
$520$	−63.2163	−2.77222
$521$	−26.0898	−1.14302	−0.571508	−	0.820596i	$-0.693641\pi$
$521$	−26.0898	−1.14302	−0.571508	+	0.820596i	$0.693641\pi$
$522$	0.195825	0.00857101
$523$	36.9072	1.61384	0.806920	−	0.590661i	$-0.201133\pi$
$523$	36.9072	1.61384	0.806920	+	0.590661i	$0.201133\pi$
$524$	−78.5254	−3.43040
$525$	0.504367	0.0220124
$526$	−24.8270	−1.08251
$527$	1.74530	0.0760266
$528$	−18.1233	−0.788716
$529$	−14.8150	−0.644129
$530$	−0.0976546	−0.00424184
$531$	2.67304	0.116000
$532$	−1.94401	−0.0842834
$533$	27.2779	1.18154
$534$	−51.6530	−2.23524
$535$	−33.4974	−1.44822
$536$	0.434377	0.0187622
$537$	22.2179	0.958774
$538$	−47.0286	−2.02755
$539$	−11.8182	−0.509044
$540$	41.7671	1.79737
$541$	−36.7730	−1.58100	−0.790498	−	0.612464i	$-0.790178\pi$
$541$	−36.7730	−1.58100	−0.790498	+	0.612464i	$0.790178\pi$
$542$	−31.3142	−1.34506
$543$	13.0366	0.559456
$544$	2.17576	0.0932851
$545$	9.07686	0.388810
$546$	3.89785	0.166813
$547$	−36.5613	−1.56325	−0.781623	−	0.623751i	$-0.785608\pi$
$547$	−36.5613	−1.56325	−0.781623	+	0.623751i	$0.785608\pi$
$548$	−7.71079	−0.329389
$549$	−1.59991	−0.0682825
$550$	8.37696	0.357195
$551$	−0.654690	−0.0278907
$552$	28.3522	1.20675
$553$	1.64330	0.0698801
$554$	48.4564	2.05872
$555$	22.2337	0.943767
$556$	96.5837	4.09606
$557$	−10.9001	−0.461850	−0.230925	−	0.972972i	$-0.574175\pi$
$557$	−10.9001	−0.461850	−0.230925	+	0.972972i	$0.574175\pi$
$558$	−2.97383	−0.125892
$559$	57.1137	2.41565
$560$	1.80462	0.0762590
$561$	1.35985	0.0574131
$562$	−45.2271	−1.90779
$563$	−25.5474	−1.07670	−0.538348	−	0.842722i	$-0.680951\pi$
$563$	−25.5474	−1.07670	−0.538348	+	0.842722i	$0.680951\pi$
$564$	84.6527	3.56452
$565$	−25.3013	−1.06444
$566$	−39.3990	−1.65606
$567$	−1.24741	−0.0523864
$568$	−41.1937	−1.72845
$569$	5.26754	0.220827	0.110413	−	0.993886i	$-0.464782\pi$
$569$	5.26754	0.220827	0.110413	+	0.993886i	$0.464782\pi$
$570$	−20.1814	−0.845306
$571$	24.3872	1.02057	0.510286	−	0.860005i	$-0.329540\pi$
$571$	24.3872	1.02057	0.510286	+	0.860005i	$0.329540\pi$
$572$	44.5020	1.86072
$573$	−21.7367	−0.908062
$574$	−1.82488	−0.0761691
$575$	−5.59202	−0.233203
$576$	0.625958	0.0260816
$577$	13.0700	0.544110	0.272055	−	0.962282i	$-0.412297\pi$
$577$	13.0700	0.544110	0.272055	+	0.962282i	$0.412297\pi$
$578$	42.3902	1.76320
$579$	−43.6292	−1.81317
$580$	1.79556	0.0745568
$581$	−0.546010	−0.0226523
$582$	−12.2375	−0.507261
$583$	0.0374841	0.00155243
$584$	28.1071	1.16308
$585$	−3.44875	−0.142588
$586$	7.75448	0.320334
$587$	−32.0277	−1.32192	−0.660962	−	0.750419i	$-0.729852\pi$
$587$	−32.0277	−1.32192	−0.660962	+	0.750419i	$0.729852\pi$
$588$	50.1181	2.06684
$589$	9.94225	0.409663
$590$	35.6553	1.46791
$591$	22.1419	0.910796
$592$	−51.0580	−2.09847
$593$	−16.6946	−0.685564	−0.342782	−	0.939415i	$-0.611369\pi$
$593$	−16.6946	−0.685564	−0.342782	+	0.939415i	$0.611369\pi$
$594$	−23.3224	−0.956930
$595$	−0.135407	−0.00555113
$596$	−19.9271	−0.816245
$597$	−25.3430	−1.03722
$598$	−43.2162	−1.76724
$599$	−31.1516	−1.27282	−0.636410	−	0.771351i	$-0.719581\pi$
$599$	−31.1516	−1.27282	−0.636410	+	0.771351i	$0.719581\pi$
$600$	−19.3702	−0.790787
$601$	−43.4059	−1.77056	−0.885282	−	0.465055i	$-0.846035\pi$
$601$	−43.4059	−1.77056	−0.885282	+	0.465055i	$0.846035\pi$
$602$	−3.82088	−0.155728
$603$	0.0236974	0.000965031 0
$604$	74.2663	3.02185
$605$	−14.1863	−0.576755
$606$	−4.14544	−0.168397
$607$	9.36572	0.380143	0.190072	−	0.981770i	$-0.439128\pi$
$607$	9.36572	0.380143	0.190072	+	0.981770i	$0.439128\pi$
$608$	12.3944	0.502659
$609$	−0.0603672	−0.00244620
$610$	−21.3410	−0.864071
$611$	−70.3566	−2.84632
$612$	0.714999	0.0289021
$613$	0.384615	0.0155345	0.00776723	−	0.999970i	$-0.497528\pi$
$613$	0.384615	0.0155345	0.00776723	+	0.999970i	$0.497528\pi$
$614$	13.0715	0.527524
$615$	−13.0227	−0.525128
$616$	−1.62333	−0.0654058
$617$	33.9427	1.36648	0.683240	−	0.730193i	$-0.260570\pi$
$617$	33.9427	1.36648	0.683240	+	0.730193i	$0.260570\pi$
$618$	−70.9028	−2.85213
$619$	−6.94688	−0.279219	−0.139609	−	0.990207i	$-0.544585\pi$
$619$	−6.94688	−0.279219	−0.139609	+	0.990207i	$0.544585\pi$
$620$	−27.2678	−1.09510
$621$	15.5688	0.624755
$622$	−79.9452	−3.20551
$623$	−1.97423	−0.0790957
$624$	−63.8772	−2.55714
$625$	−11.4065	−0.456261
$626$	−30.7895	−1.23059
$627$	7.74650	0.309366
$628$	−86.4000	−3.44774
$629$	3.83106	0.152754
$630$	0.230720	0.00919211
$631$	19.4478	0.774207	0.387103	−	0.922036i	$-0.373476\pi$
$631$	19.4478	0.774207	0.387103	+	0.922036i	$0.373476\pi$
$632$	−63.1108	−2.51041
$633$	−37.2610	−1.48099
$634$	−60.2221	−2.39173
$635$	7.41940	0.294430
$636$	−0.158961	−0.00630323
$637$	−41.6542	−1.65040
$638$	−1.00263	−0.0396945
$639$	−2.24731	−0.0889023
$640$	23.8076	0.941078
$641$	−19.9080	−0.786317	−0.393159	−	0.919471i	$-0.628618\pi$
$641$	−19.9080	−0.786317	−0.393159	+	0.919471i	$0.628618\pi$
$642$	−79.3223	−3.13060
$643$	11.9594	0.471633	0.235816	−	0.971798i	$-0.424224\pi$
$643$	11.9594	0.471633	0.235816	+	0.971798i	$0.424224\pi$
$644$	1.98740	0.0783145
$645$	−27.2667	−1.07362
$646$	−3.47743	−0.136818
$647$	8.21638	0.323019	0.161510	−	0.986871i	$-0.448364\pi$
$647$	8.21638	0.323019	0.161510	+	0.986871i	$0.448364\pi$
$648$	47.9069	1.88196
$649$	−13.6861	−0.537225
$650$	29.5254	1.15808
$651$	0.916749	0.0359302
$652$	56.1463	2.19886
$653$	−43.2844	−1.69385	−0.846924	−	0.531714i	$-0.821548\pi$
$653$	−43.2844	−1.69385	−0.846924	+	0.531714i	$0.821548\pi$
$654$	21.4941	0.840487
$655$	−31.1577	−1.21743
$656$	29.9058	1.16762
$657$	1.53338	0.0598228
$658$	4.70683	0.183491
$659$	−29.3506	−1.14334	−0.571668	−	0.820485i	$-0.693703\pi$
$659$	−29.3506	−1.14334	−0.571668	+	0.820485i	$0.693703\pi$
$660$	−21.2457	−0.826988
$661$	3.08919	0.120156	0.0600778	−	0.998194i	$-0.480865\pi$
$661$	3.08919	0.120156	0.0600778	+	0.998194i	$0.480865\pi$
$662$	25.9826	1.00984
$663$	4.79293	0.186142
$664$	20.9695	0.813776
$665$	−0.771353	−0.0299118
$666$	−6.52776	−0.252946
$667$	0.669303	0.0259155
$668$	−61.4938	−2.37927
$669$	45.2323	1.74878
$670$	0.316096	0.0122119
$671$	8.19160	0.316233
$672$	1.14285	0.0440866
$673$	25.5438	0.984640	0.492320	−	0.870414i	$-0.336149\pi$
$673$	25.5438	0.984640	0.492320	+	0.870414i	$0.336149\pi$
$674$	−30.8793	−1.18943
$675$	−10.6366	−0.409404
$676$	99.6758	3.83369
$677$	35.6805	1.37131	0.685657	−	0.727925i	$-0.259515\pi$
$677$	35.6805	1.37131	0.685657	+	0.727925i	$0.259515\pi$
$678$	−59.9140	−2.30098
$679$	−0.467729	−0.0179498
$680$	5.20029	0.199422
$681$	16.9522	0.649608
$682$	15.2261	0.583039
$683$	−0.637725	−0.0244019	−0.0122009	−	0.999926i	$-0.503884\pi$
$683$	−0.637725	−0.0244019	−0.0122009	+	0.999926i	$0.503884\pi$
$684$	4.07304	0.155737
$685$	−3.05953	−0.116899
$686$	5.58326	0.213170
$687$	19.7016	0.751663
$688$	62.6159	2.38721
$689$	0.132116	0.00503322
$690$	20.6319	0.785442
$691$	−33.7583	−1.28423	−0.642114	−	0.766609i	$-0.721942\pi$
$691$	−33.7583	−1.28423	−0.642114	+	0.766609i	$0.721942\pi$
$692$	−65.2928	−2.48206
$693$	−0.0885604	−0.00336413
$694$	80.6628	3.06192
$695$	38.3230	1.45367
$696$	2.31840	0.0878788
$697$	−2.24393	−0.0849950
$698$	43.5707	1.64917
$699$	1.72034	0.0650693
$700$	−1.35779	−0.0513197
$701$	−13.2193	−0.499287	−0.249644	−	0.968338i	$-0.580313\pi$
$701$	−13.2193	−0.499287	−0.249644	+	0.968338i	$0.580313\pi$
$702$	−82.2019	−3.10251
$703$	21.8239	0.823104
$704$	−3.20493	−0.120790
$705$	33.5889	1.26503
$706$	−51.1773	−1.92608
$707$	−0.158443	−0.00595886
$708$	58.0394	2.18126
$709$	−0.816185	−0.0306525	−0.0153262	−	0.999883i	$-0.504879\pi$
$709$	−0.816185	−0.0306525	−0.0153262	+	0.999883i	$0.504879\pi$
$710$	−29.9766	−1.12500
$711$	−3.44300	−0.129122
$712$	75.8202	2.84148
$713$	−10.1642	−0.380651
$714$	−0.320645	−0.0119998
$715$	17.6577	0.660362
$716$	−59.8122	−2.23529
$717$	−26.2981	−0.982119
$718$	31.1994	1.16435
$719$	21.5535	0.803808	0.401904	−	0.915682i	$-0.368349\pi$
$719$	21.5535	0.803808	0.401904	+	0.915682i	$0.368349\pi$
$720$	−3.78099	−0.140909
$721$	−2.70997	−0.100925
$722$	28.2501	1.05136
$723$	−20.3731	−0.757683
$724$	−35.0956	−1.30432
$725$	−0.457268	−0.0169825
$726$	−33.5934	−1.24677
$727$	47.2239	1.75144	0.875719	−	0.482821i	$-0.160388\pi$
$727$	47.2239	1.75144	0.875719	+	0.482821i	$0.160388\pi$
$728$	−5.72157	−0.212056
$729$	29.2850	1.08463
$730$	20.4535	0.757019
$731$	−4.69828	−0.173772
$732$	−34.7387	−1.28398
$733$	−20.4494	−0.755317	−0.377658	−	0.925945i	$-0.623271\pi$
$733$	−20.4494	−0.755317	−0.377658	+	0.925945i	$0.623271\pi$
$734$	76.8992	2.83840
$735$	19.8861	0.733510
$736$	−12.6710	−0.467061
$737$	−0.121331	−0.00446930
$738$	3.82345	0.140743
$739$	−0.708039	−0.0260456	−0.0130228	−	0.999915i	$-0.504145\pi$
$739$	−0.708039	−0.0260456	−0.0130228	+	0.999915i	$0.504145\pi$
$740$	−59.8546	−2.20030
$741$	27.3032	1.00301
$742$	−0.00883851	−0.000324472 0
$743$	−3.24761	−0.119143	−0.0595716	−	0.998224i	$-0.518973\pi$
$743$	−3.24761	−0.119143	−0.0595716	+	0.998224i	$0.518973\pi$
$744$	−35.2078	−1.29078
$745$	−7.90677	−0.289682
$746$	−37.8582	−1.38609
$747$	1.14399	0.0418564
$748$	−3.66082	−0.133853
$749$	−3.03178	−0.110779
$750$	−50.1534	−1.83134
$751$	23.6716	0.863790	0.431895	−	0.901924i	$-0.357845\pi$
$751$	23.6716	0.863790	0.431895	+	0.901924i	$0.357845\pi$
$752$	−77.1346	−2.81281
$753$	−22.6753	−0.826333
$754$	−3.53386	−0.128696
$755$	29.4678	1.07244
$756$	3.78025	0.137486
$757$	−10.8172	−0.393159	−0.196580	−	0.980488i	$-0.562983\pi$
$757$	−10.8172	−0.393159	−0.196580	+	0.980488i	$0.562983\pi$
$758$	−53.7828	−1.95348
$759$	−7.91941	−0.287456
$760$	29.6238	1.07457
$761$	−48.0037	−1.74013	−0.870066	−	0.492935i	$-0.835924\pi$
$761$	−48.0037	−1.74013	−0.870066	+	0.492935i	$0.835924\pi$
$762$	17.5693	0.636467
$763$	0.821527	0.0297413
$764$	58.5166	2.11706
$765$	0.283701	0.0102572
$766$	−48.2861	−1.74465
$767$	−48.2377	−1.74176
$768$	50.1962	1.81130
$769$	−44.1378	−1.59165	−0.795825	−	0.605526i	$-0.792963\pi$
$769$	−44.1378	−1.59165	−0.795825	+	0.605526i	$0.792963\pi$
$770$	−1.18130	−0.0425709
$771$	8.78553	0.316403
$772$	117.453	4.22722
$773$	−38.5142	−1.38526	−0.692629	−	0.721294i	$-0.743548\pi$
$773$	−38.5142	−1.38526	−0.692629	+	0.721294i	$0.743548\pi$
$774$	8.00543	0.287749
$775$	6.94417	0.249442
$776$	17.9631	0.644839
$777$	2.01232	0.0721917
$778$	−22.6449	−0.811860
$779$	−12.7827	−0.457989
$780$	−74.8824	−2.68122
$781$	11.5063	0.411729
$782$	3.55505	0.127128
$783$	1.27309	0.0454964
$784$	−45.6670	−1.63096
$785$	−34.2822	−1.22359
$786$	−73.7819	−2.63171
$787$	39.2652	1.39965	0.699827	−	0.714313i	$-0.253261\pi$
$787$	39.2652	1.39965	0.699827	+	0.714313i	$0.253261\pi$
$788$	−59.6075	−2.12343
$789$	−16.0353	−0.570873
$790$	−45.9257	−1.63396
$791$	−2.28997	−0.0814220
$792$	3.40116	0.120855
$793$	28.8720	1.02528
$794$	1.43060	0.0507702
$795$	−0.0630735	−0.00223699
$796$	68.2251	2.41818
$797$	22.6274	0.801502	0.400751	−	0.916187i	$-0.368749\pi$
$797$	22.6274	0.801502	0.400751	+	0.916187i	$0.368749\pi$
$798$	−1.82658	−0.0646601
$799$	5.78767	0.204753
$800$	8.65686	0.306066
$801$	4.13636	0.146151
$802$	10.6587	0.376372
$803$	−7.85096	−0.277054
$804$	0.514539	0.0181464
$805$	0.788570	0.0277935
$806$	53.6659	1.89030
$807$	−30.3750	−1.06925
$808$	6.08500	0.214069
$809$	−16.2418	−0.571032	−0.285516	−	0.958374i	$-0.592165\pi$
$809$	−16.2418	−0.571032	−0.285516	+	0.958374i	$0.592165\pi$
$810$	34.8618	1.22492
$811$	40.8289	1.43370	0.716849	−	0.697229i	$-0.245584\pi$
$811$	40.8289	1.43370	0.716849	+	0.697229i	$0.245584\pi$
$812$	0.162513	0.00570308
$813$	−20.2254	−0.709334
$814$	33.4224	1.17145
$815$	22.2780	0.780365
$816$	5.25466	0.183950
$817$	−26.7641	−0.936357
$818$	93.4780	3.26838
$819$	−0.312139	−0.0109070
$820$	35.0581	1.22428
$821$	−44.8055	−1.56372	−0.781861	−	0.623453i	$-0.785729\pi$
$821$	−44.8055	−1.56372	−0.781861	+	0.623453i	$0.785729\pi$
$822$	−7.24501	−0.252699
$823$	−1.53596	−0.0535401	−0.0267701	−	0.999642i	$-0.508522\pi$
$823$	−1.53596	−0.0535401	−0.0267701	+	0.999642i	$0.508522\pi$
$824$	104.077	3.62568
$825$	5.41055	0.188371
$826$	3.22708	0.112285
$827$	−16.2151	−0.563854	−0.281927	−	0.959436i	$-0.590974\pi$
$827$	−16.2151	−0.563854	−0.281927	+	0.959436i	$0.590974\pi$
$828$	−4.16395	−0.144707
$829$	−5.67858	−0.197225	−0.0986126	−	0.995126i	$-0.531440\pi$
$829$	−5.67858	−0.197225	−0.0986126	+	0.995126i	$0.531440\pi$
$830$	15.2595	0.529665
$831$	31.2972	1.08569
$832$	−11.2961	−0.391620
$833$	3.42655	0.118723
$834$	90.7493	3.14239
$835$	−24.3998	−0.844391
$836$	−20.8541	−0.721255
$837$	−19.3333	−0.668258
$838$	−17.0223	−0.588027
$839$	−36.8756	−1.27309	−0.636544	−	0.771241i	$-0.719637\pi$
$839$	−36.8756	−1.27309	−0.636544	+	0.771241i	$0.719637\pi$
$840$	2.73154	0.0942469
$841$	−28.9453	−0.998113
$842$	−97.2364	−3.35099
$843$	−29.2115	−1.00610
$844$	100.309	3.45279
$845$	39.5499	1.36056
$846$	−9.86164	−0.339050
$847$	−1.28397	−0.0441178
$848$	0.144844	0.00497395
$849$	−25.4472	−0.873345
$850$	−2.42881	−0.0833076
$851$	−22.3110	−0.764812
$852$	−48.7957	−1.67171
$853$	26.5873	0.910332	0.455166	−	0.890407i	$-0.349580\pi$
$853$	26.5873	0.910332	0.455166	+	0.890407i	$0.349580\pi$
$854$	−1.93153	−0.0660955
$855$	1.61612	0.0552702
$856$	116.435	3.97968
$857$	−53.4854	−1.82703	−0.913513	−	0.406810i	$-0.866641\pi$
$857$	−53.4854	−1.82703	−0.913513	+	0.406810i	$0.866641\pi$
$858$	41.8138	1.42750
$859$	35.5119	1.21165	0.605825	−	0.795598i	$-0.292843\pi$
$859$	35.5119	1.21165	0.605825	+	0.795598i	$0.292843\pi$
$860$	73.4037	2.50305
$861$	−1.17866	−0.0401687
$862$	−32.1950	−1.09657
$863$	−31.1263	−1.05955	−0.529775	−	0.848138i	$-0.677724\pi$
$863$	−31.1263	−1.05955	−0.529775	+	0.848138i	$0.677724\pi$
$864$	−24.1017	−0.819956
$865$	−25.9072	−0.880872
$866$	38.5504	1.31000
$867$	27.3791	0.929844
$868$	−2.46795	−0.0837677
$869$	17.6283	0.597998
$870$	1.68710	0.0571981
$871$	−0.427643	−0.0144901
$872$	−31.5508	−1.06844
$873$	0.979976	0.0331671
$874$	20.2516	0.685021
$875$	−1.91691	−0.0648035
$876$	33.2941	1.12490
$877$	18.3226	0.618711	0.309356	−	0.950946i	$-0.399887\pi$
$877$	18.3226	0.618711	0.309356	+	0.950946i	$0.399887\pi$
$878$	58.4538	1.97272
$879$	5.00849	0.168932
$880$	19.3588	0.652586
$881$	−11.3059	−0.380905	−0.190452	−	0.981696i	$-0.560995\pi$
$881$	−11.3059	−0.380905	−0.190452	+	0.981696i	$0.560995\pi$
$882$	−5.83852	−0.196593
$883$	−30.1376	−1.01421	−0.507106	−	0.861884i	$-0.669285\pi$
$883$	−30.1376	−1.01421	−0.507106	+	0.861884i	$0.669285\pi$
$884$	−12.9029	−0.433971
$885$	23.0292	0.774117
$886$	70.2185	2.35904
$887$	−16.5064	−0.554230	−0.277115	−	0.960837i	$-0.589378\pi$
$887$	−16.5064	−0.554230	−0.277115	+	0.960837i	$0.589378\pi$
$888$	−77.2833	−2.59346
$889$	0.671514	0.0225219
$890$	55.1743	1.84945
$891$	−13.3815	−0.448296
$892$	−121.768	−4.07711
$893$	32.9699	1.10329
$894$	−18.7234	−0.626203
$895$	−23.7326	−0.793293
$896$	2.15477	0.0719860
$897$	−27.9127	−0.931977
$898$	17.1511	0.572340
$899$	−0.831140	−0.0277201
$900$	2.84482	0.0948272
$901$	−0.0108681	−0.000362069 0
$902$	−19.5762	−0.651816
$903$	−2.46785	−0.0821248
$904$	87.9463	2.92505
$905$	−13.9254	−0.462896
$906$	69.7801	2.31829
$907$	14.9119	0.495143	0.247572	−	0.968870i	$-0.420367\pi$
$907$	14.9119	0.495143	0.247572	+	0.968870i	$0.420367\pi$
$908$	−45.6364	−1.51450
$909$	0.331966	0.0110106
$910$	−4.16358	−0.138021
$911$	40.3519	1.33692	0.668460	−	0.743748i	$-0.266954\pi$
$911$	40.3519	1.33692	0.668460	+	0.743748i	$0.266954\pi$
$912$	29.9336	0.991200
$913$	−5.85726	−0.193847
$914$	−84.1296	−2.78276
$915$	−13.7838	−0.455678
$916$	−53.0381	−1.75243
$917$	−2.82002	−0.0931252
$918$	6.76209	0.223182
$919$	−48.4366	−1.59778	−0.798889	−	0.601479i	$-0.794578\pi$
$919$	−48.4366	−1.59778	−0.798889	+	0.601479i	$0.794578\pi$
$920$	−30.2851	−0.998469
$921$	8.44269	0.278196
$922$	40.1691	1.32290
$923$	40.5551	1.33489
$924$	−1.92290	−0.0632589
$925$	15.2429	0.501183
$926$	52.0351	1.70998
$927$	5.67788	0.186486
$928$	−1.03613	−0.0340126
$929$	26.4943	0.869249	0.434625	−	0.900612i	$-0.356881\pi$
$929$	26.4943	0.869249	0.434625	+	0.900612i	$0.356881\pi$
$930$	−25.6207	−0.840134
$931$	19.5196	0.639729
$932$	−4.63128	−0.151703
$933$	−51.6353	−1.69046
$934$	54.9717	1.79873
$935$	−1.45256	−0.0475038
$936$	11.9877	0.391830
$937$	−29.9807	−0.979426	−0.489713	−	0.871884i	$-0.662899\pi$
$937$	−29.9807	−0.979426	−0.489713	+	0.871884i	$0.662899\pi$
$938$	0.0286092	0.000934122 0
$939$	−19.8864	−0.648969
$940$	−90.4238	−2.94930
$941$	53.7712	1.75289	0.876446	−	0.481501i	$-0.159908\pi$
$941$	53.7712	1.75289	0.876446	+	0.481501i	$0.159908\pi$
$942$	−81.1809	−2.64502
$943$	13.0680	0.425554
$944$	−52.8848	−1.72125
$945$	1.49995	0.0487932
$946$	−40.9881	−1.33264
$947$	41.1104	1.33591	0.667955	−	0.744202i	$-0.267170\pi$
$947$	41.1104	1.33591	0.667955	+	0.744202i	$0.267170\pi$
$948$	−74.7575	−2.42801
$949$	−27.6714	−0.898252
$950$	−13.8359	−0.448896
$951$	−38.8965	−1.26131
$952$	0.470667	0.0152544
$953$	49.6876	1.60954	0.804769	−	0.593588i	$-0.202289\pi$
$953$	49.6876	1.60954	0.804769	+	0.593588i	$0.202289\pi$
$954$	0.0185182	0.000599550 0
$955$	23.2185	0.751333
$956$	70.7962	2.28971
$957$	−0.647582	−0.0209334
$958$	−49.7884	−1.60859
$959$	−0.276911	−0.00894193
$960$	5.39285	0.174053
$961$	−18.3781	−0.592843
$962$	117.800	3.79803
$963$	6.35211	0.204694
$964$	54.8457	1.76646
$965$	46.6035	1.50022
$966$	1.86735	0.0600809
$967$	−43.6905	−1.40499	−0.702496	−	0.711687i	$-0.747931\pi$
$967$	−43.6905	−1.40499	−0.702496	+	0.711687i	$0.747931\pi$
$968$	49.3110	1.58491
$969$	−2.24602	−0.0721524
$970$	13.0718	0.419709
$971$	56.9474	1.82753	0.913765	−	0.406243i	$-0.133161\pi$
$971$	56.9474	1.82753	0.913765	+	0.406243i	$0.133161\pi$
$972$	−15.0537	−0.482848
$973$	3.46853	0.111196
$974$	23.4803	0.752359
$975$	19.0700	0.610727
$976$	31.6535	1.01320
$977$	−11.0546	−0.353667	−0.176833	−	0.984241i	$-0.556585\pi$
$977$	−11.0546	−0.353667	−0.176833	+	0.984241i	$0.556585\pi$
$978$	52.7547	1.68691
$979$	−21.1783	−0.676861
$980$	−53.5348	−1.71011
$981$	−1.72124	−0.0549551
$982$	98.9512	3.15766
$983$	−14.3105	−0.456433	−0.228217	−	0.973610i	$-0.573289\pi$
$983$	−14.3105	−0.456433	−0.228217	+	0.973610i	$0.573289\pi$
$984$	45.2665	1.44304
$985$	−23.6514	−0.753595
$986$	0.290702	0.00925783
$987$	3.04006	0.0967663
$988$	−73.5022	−2.33842
$989$	27.3615	0.870045
$990$	2.47502	0.0786614
$991$	31.4814	1.00004	0.500019	−	0.866014i	$-0.333326\pi$
$991$	31.4814	1.00004	0.500019	+	0.866014i	$0.333326\pi$
$992$	15.7349	0.499583
$993$	16.7818	0.532553
$994$	−2.71312	−0.0860549
$995$	27.0707	0.858200
$996$	24.8393	0.787064
$997$	−12.3564	−0.391331	−0.195666	−	0.980671i	$-0.562687\pi$
$997$	−12.3564	−0.391331	−0.195666	+	0.980671i	$0.562687\pi$
$998$	−94.3496	−2.98659
$999$	−42.4379	−1.34268

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.b.1.19	✓	237

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.b.1.19	✓	237	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52945 q^{2} -1.63373 q^{3} +4.39812 q^{4} +1.74511 q^{5} +4.13244 q^{6} +0.157946 q^{7} -6.06591 q^{8} -0.330925 q^{9} +O(q^{10})\)	\(q-2.52945 q^{2} -1.63373 q^{3} +4.39812 q^{4} +1.74511 q^{5} +4.13244 q^{6} +0.157946 q^{7} -6.06591 q^{8} -0.330925 q^{9} -4.41416 q^{10} +1.69435 q^{11} -7.18534 q^{12} +5.97188 q^{13} -0.399516 q^{14} -2.85103 q^{15} +6.54719 q^{16} -0.491258 q^{17} +0.837057 q^{18} -2.79849 q^{19} +7.67518 q^{20} -0.258041 q^{21} -4.28576 q^{22} +2.86095 q^{23} +9.91007 q^{24} -1.95460 q^{25} -15.1056 q^{26} +5.44183 q^{27} +0.694664 q^{28} +0.233944 q^{29} +7.21155 q^{30} -3.55273 q^{31} -4.42896 q^{32} -2.76811 q^{33} +1.24261 q^{34} +0.275632 q^{35} -1.45544 q^{36} -7.79846 q^{37} +7.07863 q^{38} -9.75644 q^{39} -10.5857 q^{40} +4.56773 q^{41} +0.652702 q^{42} +9.56378 q^{43} +7.45193 q^{44} -0.577499 q^{45} -7.23663 q^{46} -11.7813 q^{47} -10.6963 q^{48} -6.97505 q^{49} +4.94407 q^{50} +0.802583 q^{51} +26.2650 q^{52} +0.0221230 q^{53} -13.7648 q^{54} +2.95682 q^{55} -0.958086 q^{56} +4.57197 q^{57} -0.591750 q^{58} -8.07748 q^{59} -12.5392 q^{60} +4.83467 q^{61} +8.98644 q^{62} -0.0522682 q^{63} -1.89154 q^{64} +10.4216 q^{65} +7.00178 q^{66} -0.0716095 q^{67} -2.16061 q^{68} -4.67402 q^{69} -0.697198 q^{70} +6.79101 q^{71} +2.00736 q^{72} -4.63362 q^{73} +19.7258 q^{74} +3.19329 q^{75} -12.3081 q^{76} +0.267615 q^{77} +24.6784 q^{78} +10.4042 q^{79} +11.4255 q^{80} -7.89772 q^{81} -11.5538 q^{82} -3.45695 q^{83} -1.13489 q^{84} -0.857297 q^{85} -24.1911 q^{86} -0.382202 q^{87} -10.2778 q^{88} -12.4994 q^{89} +1.46075 q^{90} +0.943233 q^{91} +12.5828 q^{92} +5.80420 q^{93} +29.8003 q^{94} -4.88366 q^{95} +7.23573 q^{96} -2.96133 q^{97} +17.6430 q^{98} -0.560701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * q^99

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