LMFDB - Embedded newform 6007.2.a.b.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.72222 q^{2} -1.56731 q^{3} +5.41047 q^{4} -3.83172 q^{5} +4.26655 q^{6} -2.76166 q^{7} -9.28405 q^{8} -0.543552 q^{9} +O(q^{10})$	\(q-2.72222 q^{2} -1.56731 q^{3} +5.41047 q^{4} -3.83172 q^{5} +4.26655 q^{6} -2.76166 q^{7} -9.28405 q^{8} -0.543552 q^{9} +10.4308 q^{10} -1.34677 q^{11} -8.47987 q^{12} +1.84492 q^{13} +7.51783 q^{14} +6.00548 q^{15} +14.4523 q^{16} -7.41934 q^{17} +1.47967 q^{18} -1.13618 q^{19} -20.7314 q^{20} +4.32836 q^{21} +3.66621 q^{22} +2.30042 q^{23} +14.5510 q^{24} +9.68209 q^{25} -5.02228 q^{26} +5.55383 q^{27} -14.9419 q^{28} -5.66994 q^{29} -16.3482 q^{30} -8.79293 q^{31} -20.7741 q^{32} +2.11080 q^{33} +20.1971 q^{34} +10.5819 q^{35} -2.94088 q^{36} -3.36893 q^{37} +3.09294 q^{38} -2.89155 q^{39} +35.5739 q^{40} +2.54517 q^{41} -11.7827 q^{42} -11.6895 q^{43} -7.28667 q^{44} +2.08274 q^{45} -6.26224 q^{46} +2.48741 q^{47} -22.6511 q^{48} +0.626745 q^{49} -26.3568 q^{50} +11.6284 q^{51} +9.98189 q^{52} -12.9910 q^{53} -15.1187 q^{54} +5.16045 q^{55} +25.6394 q^{56} +1.78075 q^{57} +15.4348 q^{58} +2.89279 q^{59} +32.4925 q^{60} +4.64510 q^{61} +23.9363 q^{62} +1.50110 q^{63} +27.6472 q^{64} -7.06922 q^{65} -5.74607 q^{66} +11.1776 q^{67} -40.1421 q^{68} -3.60546 q^{69} -28.8062 q^{70} +0.885310 q^{71} +5.04637 q^{72} +9.11554 q^{73} +9.17097 q^{74} -15.1748 q^{75} -6.14729 q^{76} +3.71932 q^{77} +7.87144 q^{78} +3.54590 q^{79} -55.3771 q^{80} -7.07389 q^{81} -6.92851 q^{82} -9.51140 q^{83} +23.4185 q^{84} +28.4288 q^{85} +31.8214 q^{86} +8.88654 q^{87} +12.5035 q^{88} +11.3894 q^{89} -5.66968 q^{90} -5.09504 q^{91} +12.4463 q^{92} +13.7812 q^{93} -6.77126 q^{94} +4.35354 q^{95} +32.5594 q^{96} +8.92422 q^{97} -1.70614 q^{98} +0.732041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.72222	−1.92490	−0.962450	−	0.271461i	$-0.912493\pi$
$2$	−2.72222	−1.92490	−0.962450	+	0.271461i	$0.912493\pi$
$3$	−1.56731	−0.904884	−0.452442	−	0.891794i	$-0.649447\pi$
$3$	−1.56731	−0.904884	−0.452442	+	0.891794i	$0.649447\pi$
$4$	5.41047	2.70524
$5$	−3.83172	−1.71360	−0.856799	−	0.515651i	$-0.827550\pi$
$5$	−3.83172	−1.71360	−0.856799	+	0.515651i	$0.827550\pi$
$6$	4.26655	1.74181
$7$	−2.76166	−1.04381	−0.521904	−	0.853004i	$-0.674778\pi$
$7$	−2.76166	−1.04381	−0.521904	+	0.853004i	$0.674778\pi$
$8$	−9.28405	−3.28241
$9$	−0.543552	−0.181184
$10$	10.4308	3.29850
$11$	−1.34677	−0.406067	−0.203033	−	0.979172i	$-0.565080\pi$
$11$	−1.34677	−0.406067	−0.203033	+	0.979172i	$0.565080\pi$
$12$	−8.47987	−2.44793
$13$	1.84492	0.511689	0.255844	−	0.966718i	$-0.417647\pi$
$13$	1.84492	0.511689	0.255844	+	0.966718i	$0.417647\pi$
$14$	7.51783	2.00922
$15$	6.00548	1.55061
$16$	14.4523	3.61307
$17$	−7.41934	−1.79945	−0.899727	−	0.436453i	$-0.856234\pi$
$17$	−7.41934	−1.79945	−0.899727	+	0.436453i	$0.856234\pi$
$18$	1.47967	0.348761
$19$	−1.13618	−0.260658	−0.130329	−	0.991471i	$-0.541603\pi$
$19$	−1.13618	−0.260658	−0.130329	+	0.991471i	$0.541603\pi$
$20$	−20.7314	−4.63569
$21$	4.32836	0.944526
$22$	3.66621	0.781638
$23$	2.30042	0.479670	0.239835	−	0.970814i	$-0.422907\pi$
$23$	2.30042	0.479670	0.239835	+	0.970814i	$0.422907\pi$
$24$	14.5510	2.97020
$25$	9.68209	1.93642
$26$	−5.02228	−0.984949
$27$	5.55383	1.06884
$28$	−14.9419	−2.82375
$29$	−5.66994	−1.05288	−0.526441	−	0.850212i	$-0.676474\pi$
$29$	−5.66994	−1.05288	−0.526441	+	0.850212i	$0.676474\pi$
$30$	−16.3482	−2.98476
$31$	−8.79293	−1.57926	−0.789628	−	0.613585i	$-0.789727\pi$
$31$	−8.79293	−1.57926	−0.789628	+	0.613585i	$0.789727\pi$
$32$	−20.7741	−3.67238
$33$	2.11080	0.367444
$34$	20.1971	3.46377
$35$	10.5819	1.78867
$36$	−2.94088	−0.490146
$37$	−3.36893	−0.553849	−0.276925	−	0.960892i	$-0.589315\pi$
$37$	−3.36893	−0.553849	−0.276925	+	0.960892i	$0.589315\pi$
$38$	3.09294	0.501741
$39$	−2.89155	−0.463019
$40$	35.5739	5.62473
$41$	2.54517	0.397489	0.198744	−	0.980051i	$-0.436314\pi$
$41$	2.54517	0.397489	0.198744	+	0.980051i	$0.436314\pi$
$42$	−11.7827	−1.81812
$43$	−11.6895	−1.78263	−0.891317	−	0.453380i	$-0.850218\pi$
$43$	−11.6895	−1.78263	−0.891317	+	0.453380i	$0.850218\pi$
$44$	−7.28667	−1.09851
$45$	2.08274	0.310477
$46$	−6.26224	−0.923317
$47$	2.48741	0.362825	0.181413	−	0.983407i	$-0.441933\pi$
$47$	2.48741	0.362825	0.181413	+	0.983407i	$0.441933\pi$
$48$	−22.6511	−3.26941
$49$	0.626745	0.0895349
$50$	−26.3568	−3.72741
$51$	11.6284	1.62830
$52$	9.98189	1.38424
$53$	−12.9910	−1.78446	−0.892229	−	0.451584i	$-0.850859\pi$
$53$	−12.9910	−1.78446	−0.892229	+	0.451584i	$0.850859\pi$
$54$	−15.1187	−2.05740
$55$	5.16045	0.695836
$56$	25.6394	3.42620
$57$	1.78075	0.235866
$58$	15.4348	2.02669
$59$	2.89279	0.376609	0.188305	−	0.982111i	$-0.439701\pi$
$59$	2.89279	0.376609	0.188305	+	0.982111i	$0.439701\pi$
$60$	32.4925	4.19476
$61$	4.64510	0.594744	0.297372	−	0.954762i	$-0.403890\pi$
$61$	4.64510	0.594744	0.297372	+	0.954762i	$0.403890\pi$
$62$	23.9363	3.03991
$63$	1.50110	0.189121
$64$	27.6472	3.45590
$65$	−7.06922	−0.876829
$66$	−5.74607	−0.707292
$67$	11.1776	1.36556	0.682778	−	0.730626i	$-0.260772\pi$
$67$	11.1776	1.36556	0.682778	+	0.730626i	$0.260772\pi$
$68$	−40.1421	−4.86795
$69$	−3.60546	−0.434046
$70$	−28.8062	−3.44300
$71$	0.885310	0.105067	0.0525335	−	0.998619i	$-0.483270\pi$
$71$	0.885310	0.105067	0.0525335	+	0.998619i	$0.483270\pi$
$72$	5.04637	0.594720
$73$	9.11554	1.06689	0.533446	−	0.845834i	$-0.320897\pi$
$73$	9.11554	1.06689	0.533446	+	0.845834i	$0.320897\pi$
$74$	9.17097	1.06610
$75$	−15.1748	−1.75223
$76$	−6.14729	−0.705143
$77$	3.71932	0.423856
$78$	7.87144	0.891265
$79$	3.54590	0.398945	0.199472	−	0.979903i	$-0.436077\pi$
$79$	3.54590	0.398945	0.199472	+	0.979903i	$0.436077\pi$
$80$	−55.3771	−6.19135
$81$	−7.07389	−0.785988
$82$	−6.92851	−0.765126
$83$	−9.51140	−1.04401	−0.522006	−	0.852942i	$-0.674816\pi$
$83$	−9.51140	−1.04401	−0.522006	+	0.852942i	$0.674816\pi$
$84$	23.4185	2.55517
$85$	28.4288	3.08354
$86$	31.8214	3.43139
$87$	8.88654	0.952737
$88$	12.5035	1.33288
$89$	11.3894	1.20727	0.603635	−	0.797260i	$-0.293718\pi$
$89$	11.3894	1.20727	0.603635	+	0.797260i	$0.293718\pi$
$90$	−5.66968	−0.597636
$91$	−5.09504	−0.534105
$92$	12.4463	1.29762
$93$	13.7812	1.42904
$94$	−6.77126	−0.698402
$95$	4.35354	0.446664
$96$	32.5594	3.32308
$97$	8.92422	0.906118	0.453059	−	0.891481i	$-0.350333\pi$
$97$	8.92422	0.906118	0.453059	+	0.891481i	$0.350333\pi$
$98$	−1.70614	−0.172346
$99$	0.732041	0.0735729
$100$	52.3847	5.23847
$101$	8.65489	0.861194	0.430597	−	0.902544i	$-0.358303\pi$
$101$	8.65489	0.861194	0.430597	+	0.902544i	$0.358303\pi$
$102$	−31.6550	−3.13431
$103$	−15.9954	−1.57607	−0.788035	−	0.615631i	$-0.788901\pi$
$103$	−15.9954	−1.57607	−0.788035	+	0.615631i	$0.788901\pi$
$104$	−17.1283	−1.67957
$105$	−16.5851	−1.61854
$106$	35.3645	3.43490
$107$	−4.07075	−0.393534	−0.196767	−	0.980450i	$-0.563044\pi$
$107$	−4.07075	−0.393534	−0.196767	+	0.980450i	$0.563044\pi$
$108$	30.0489	2.89145
$109$	18.2722	1.75016	0.875078	−	0.483983i	$-0.160810\pi$
$109$	18.2722	1.75016	0.875078	+	0.483983i	$0.160810\pi$
$110$	−14.0479	−1.33941
$111$	5.28015	0.501170
$112$	−39.9122	−3.77135
$113$	−1.49180	−0.140336	−0.0701682	−	0.997535i	$-0.522354\pi$
$113$	−1.49180	−0.140336	−0.0701682	+	0.997535i	$0.522354\pi$
$114$	−4.84758	−0.454018
$115$	−8.81456	−0.821962
$116$	−30.6771	−2.84830
$117$	−1.00281	−0.0927099
$118$	−7.87480	−0.724934
$119$	20.4897	1.87828
$120$	−55.7552	−5.08973
$121$	−9.18621	−0.835110
$122$	−12.6450	−1.14482
$123$	−3.98906	−0.359681
$124$	−47.5739	−4.27226
$125$	−17.9405	−1.60464
$126$	−4.08634	−0.364040
$127$	15.4199	1.36829	0.684147	−	0.729344i	$-0.260175\pi$
$127$	15.4199	1.36829	0.684147	+	0.729344i	$0.260175\pi$
$128$	−33.7134	−2.97988
$129$	18.3211	1.61308
$130$	19.2440	1.68781
$131$	5.45119	0.476272	0.238136	−	0.971232i	$-0.423464\pi$
$131$	5.45119	0.476272	0.238136	+	0.971232i	$0.423464\pi$
$132$	11.4204	0.994022
$133$	3.13775	0.272077
$134$	−30.4278	−2.62856
$135$	−21.2807	−1.83155
$136$	68.8815	5.90654
$137$	−16.2969	−1.39234	−0.696171	−	0.717876i	$-0.745115\pi$
$137$	−16.2969	−1.39234	−0.696171	+	0.717876i	$0.745115\pi$
$138$	9.81484	0.835495
$139$	10.8835	0.923127	0.461563	−	0.887107i	$-0.347289\pi$
$139$	10.8835	0.923127	0.461563	+	0.887107i	$0.347289\pi$
$140$	57.2531	4.83877
$141$	−3.89852	−0.328315
$142$	−2.41001	−0.202243
$143$	−2.48469	−0.207780
$144$	−7.85557	−0.654631
$145$	21.7256	1.80422
$146$	−24.8145	−2.05366
$147$	−0.982300	−0.0810188
$148$	−18.2275	−1.49829
$149$	21.8211	1.78766	0.893828	−	0.448410i	$-0.148009\pi$
$149$	21.8211	1.78766	0.893828	+	0.448410i	$0.148009\pi$
$150$	41.3091	3.37287
$151$	12.7962	1.04134	0.520670	−	0.853758i	$-0.325682\pi$
$151$	12.7962	1.04134	0.520670	+	0.853758i	$0.325682\pi$
$152$	10.5484	0.855587
$153$	4.03280	0.326032
$154$	−10.1248	−0.815880
$155$	33.6921	2.70621
$156$	−15.6447	−1.25258
$157$	5.19762	0.414815	0.207408	−	0.978255i	$-0.433497\pi$
$157$	5.19762	0.414815	0.207408	+	0.978255i	$0.433497\pi$
$158$	−9.65271	−0.767928
$159$	20.3609	1.61473
$160$	79.6007	6.29299
$161$	−6.35296	−0.500684
$162$	19.2567	1.51295
$163$	3.33631	0.261320	0.130660	−	0.991427i	$-0.458290\pi$
$163$	3.33631	0.261320	0.130660	+	0.991427i	$0.458290\pi$
$164$	13.7706	1.07530
$165$	−8.08801	−0.629651
$166$	25.8921	2.00962
$167$	−1.93173	−0.149482	−0.0747408	−	0.997203i	$-0.523813\pi$
$167$	−1.93173	−0.149482	−0.0747408	+	0.997203i	$0.523813\pi$
$168$	−40.1847	−3.10032
$169$	−9.59627	−0.738175
$170$	−77.3895	−5.93550
$171$	0.617575	0.0472272
$172$	−63.2458	−4.82245
$173$	−11.8163	−0.898375	−0.449187	−	0.893438i	$-0.648286\pi$
$173$	−11.8163	−0.898375	−0.449187	+	0.893438i	$0.648286\pi$
$174$	−24.1911	−1.83392
$175$	−26.7386	−2.02125
$176$	−19.4639	−1.46715
$177$	−4.53388	−0.340788
$178$	−31.0044	−2.32387
$179$	7.43352	0.555607	0.277804	−	0.960638i	$-0.410394\pi$
$179$	7.43352	0.555607	0.277804	+	0.960638i	$0.410394\pi$
$180$	11.2686	0.839913
$181$	15.7647	1.17178	0.585890	−	0.810391i	$-0.300745\pi$
$181$	15.7647	1.17178	0.585890	+	0.810391i	$0.300745\pi$
$182$	13.8698	1.02810
$183$	−7.28029	−0.538175
$184$	−21.3572	−1.57447
$185$	12.9088	0.949075
$186$	−37.5155	−2.75077
$187$	9.99216	0.730699
$188$	13.4580	0.981528
$189$	−15.3378	−1.11566
$190$	−11.8513	−0.859783
$191$	−17.6504	−1.27714	−0.638569	−	0.769565i	$-0.720473\pi$
$191$	−17.6504	−1.27714	−0.638569	+	0.769565i	$0.720473\pi$
$192$	−43.3316	−3.12719
$193$	−25.7642	−1.85455	−0.927273	−	0.374386i	$-0.877853\pi$
$193$	−25.7642	−1.85455	−0.927273	+	0.374386i	$0.877853\pi$
$194$	−24.2937	−1.74419
$195$	11.0796	0.793429
$196$	3.39098	0.242213
$197$	21.4851	1.53075	0.765377	−	0.643583i	$-0.222553\pi$
$197$	21.4851	1.53075	0.765377	+	0.643583i	$0.222553\pi$
$198$	−1.99278	−0.141620
$199$	−6.82684	−0.483942	−0.241971	−	0.970284i	$-0.577794\pi$
$199$	−6.82684	−0.483942	−0.241971	+	0.970284i	$0.577794\pi$
$200$	−89.8890	−6.35611
$201$	−17.5187	−1.23567
$202$	−23.5605	−1.65771
$203$	15.6584	1.09901
$204$	62.9150	4.40493
$205$	−9.75238	−0.681136
$206$	43.5429	3.03378
$207$	−1.25040	−0.0869086
$208$	26.6633	1.84877
$209$	1.53018	0.105845
$210$	45.1482	3.11552
$211$	8.05775	0.554719	0.277359	−	0.960766i	$-0.410541\pi$
$211$	8.05775	0.554719	0.277359	+	0.960766i	$0.410541\pi$
$212$	−70.2877	−4.82738
$213$	−1.38755	−0.0950734
$214$	11.0815	0.757514
$215$	44.7910	3.05472
$216$	−51.5621	−3.50835
$217$	24.2830	1.64844
$218$	−49.7408	−3.36887
$219$	−14.2868	−0.965415
$220$	27.9205	1.88240
$221$	−13.6881	−0.920760
$222$	−14.3737	−0.964701
$223$	15.4881	1.03716	0.518581	−	0.855029i	$-0.326461\pi$
$223$	15.4881	1.03716	0.518581	+	0.855029i	$0.326461\pi$
$224$	57.3710	3.83326
$225$	−5.26272	−0.350848
$226$	4.06100	0.270133
$227$	−26.1443	−1.73526	−0.867631	−	0.497209i	$-0.834358\pi$
$227$	−26.1443	−1.73526	−0.867631	+	0.497209i	$0.834358\pi$
$228$	9.63469	0.638073
$229$	−11.8727	−0.784572	−0.392286	−	0.919843i	$-0.628316\pi$
$229$	−11.8727	−0.784572	−0.392286	+	0.919843i	$0.628316\pi$
$230$	23.9952	1.58219
$231$	−5.82931	−0.383541
$232$	52.6401	3.45599
$233$	13.7369	0.899937	0.449969	−	0.893044i	$-0.351435\pi$
$233$	13.7369	0.899937	0.449969	+	0.893044i	$0.351435\pi$
$234$	2.72987	0.178457
$235$	−9.53104	−0.621737
$236$	15.6514	1.01882
$237$	−5.55751	−0.360999
$238$	−55.7773	−3.61551
$239$	−12.0308	−0.778206	−0.389103	−	0.921194i	$-0.627215\pi$
$239$	−12.0308	−0.778206	−0.389103	+	0.921194i	$0.627215\pi$
$240$	86.7928	5.60245
$241$	9.26279	0.596669	0.298334	−	0.954461i	$-0.403569\pi$
$241$	9.26279	0.596669	0.298334	+	0.954461i	$0.403569\pi$
$242$	25.0069	1.60750
$243$	−5.57454	−0.357607
$244$	25.1322	1.60892
$245$	−2.40151	−0.153427
$246$	10.8591	0.692350
$247$	−2.09617	−0.133376
$248$	81.6340	5.18377
$249$	14.9073	0.944710
$250$	48.8378	3.08878
$251$	15.2265	0.961087	0.480544	−	0.876971i	$-0.340439\pi$
$251$	15.2265	0.961087	0.480544	+	0.876971i	$0.340439\pi$
$252$	8.12169	0.511618
$253$	−3.09814	−0.194778
$254$	−41.9763	−2.63383
$255$	−44.5567	−2.79025
$256$	36.4809	2.28006
$257$	11.4207	0.712407	0.356203	−	0.934408i	$-0.384071\pi$
$257$	11.4207	0.712407	0.356203	+	0.934408i	$0.384071\pi$
$258$	−49.8739	−3.10501
$259$	9.30383	0.578112
$260$	−38.2478	−2.37203
$261$	3.08191	0.190766
$262$	−14.8393	−0.916776
$263$	16.0993	0.992728	0.496364	−	0.868114i	$-0.334668\pi$
$263$	16.0993	0.992728	0.496364	+	0.868114i	$0.334668\pi$
$264$	−19.5968	−1.20610
$265$	49.7781	3.05784
$266$	−8.54164	−0.523721
$267$	−17.8506	−1.09244
$268$	60.4759	3.69415
$269$	−12.2087	−0.744378	−0.372189	−	0.928157i	$-0.621393\pi$
$269$	−12.2087	−0.744378	−0.372189	+	0.928157i	$0.621393\pi$
$270$	57.9308	3.52556
$271$	20.0002	1.21493	0.607464	−	0.794347i	$-0.292187\pi$
$271$	20.0002	1.21493	0.607464	+	0.794347i	$0.292187\pi$
$272$	−107.226	−6.50155
$273$	7.98548	0.483303
$274$	44.3639	2.68012
$275$	−13.0396	−0.786315
$276$	−19.5072	−1.17420
$277$	−15.8559	−0.952691	−0.476345	−	0.879258i	$-0.658039\pi$
$277$	−15.8559	−0.952691	−0.476345	+	0.879258i	$0.658039\pi$
$278$	−29.6273	−1.77693
$279$	4.77942	0.286136
$280$	−98.2429	−5.87114
$281$	13.3194	0.794571	0.397285	−	0.917695i	$-0.369952\pi$
$281$	13.3194	0.794571	0.397285	+	0.917695i	$0.369952\pi$
$282$	10.6126	0.631973
$283$	−21.8615	−1.29953	−0.649766	−	0.760135i	$-0.725133\pi$
$283$	−21.8615	−1.29953	−0.649766	+	0.760135i	$0.725133\pi$
$284$	4.78994	0.284231
$285$	−6.82333	−0.404179
$286$	6.76386	0.399955
$287$	−7.02889	−0.414902
$288$	11.2918	0.665378
$289$	38.0466	2.23803
$290$	−59.1419	−3.47293
$291$	−13.9870	−0.819932
$292$	49.3194	2.88620
$293$	−5.18043	−0.302644	−0.151322	−	0.988485i	$-0.548353\pi$
$293$	−5.18043	−0.302644	−0.151322	+	0.988485i	$0.548353\pi$
$294$	2.67404	0.155953
$295$	−11.0844	−0.645356
$296$	31.2774	1.81796
$297$	−7.47974	−0.434019
$298$	−59.4019	−3.44106
$299$	4.24409	0.245442
$300$	−82.1028	−4.74021
$301$	32.2824	1.86073
$302$	−34.8340	−2.00447
$303$	−13.5649	−0.779281
$304$	−16.4204	−0.941777
$305$	−17.7987	−1.01915
$306$	−10.9782	−0.627580
$307$	−24.8220	−1.41667	−0.708334	−	0.705877i	$-0.750553\pi$
$307$	−24.8220	−1.41667	−0.708334	+	0.705877i	$0.750553\pi$
$308$	20.1233	1.14663
$309$	25.0696	1.42616
$310$	−91.7171	−5.20918
$311$	0.921009	0.0522256	0.0261128	−	0.999659i	$-0.491687\pi$
$311$	0.921009	0.0522256	0.0261128	+	0.999659i	$0.491687\pi$
$312$	26.8453	1.51982
$313$	18.7790	1.06145	0.530725	−	0.847544i	$-0.321920\pi$
$313$	18.7790	1.06145	0.530725	+	0.847544i	$0.321920\pi$
$314$	−14.1491	−0.798477
$315$	−5.75182	−0.324078
$316$	19.1850	1.07924
$317$	13.5310	0.759974	0.379987	−	0.924992i	$-0.375928\pi$
$317$	13.5310	0.759974	0.379987	+	0.924992i	$0.375928\pi$
$318$	−55.4269	−3.10819
$319$	7.63612	0.427541
$320$	−105.936	−5.92202
$321$	6.38011	0.356103
$322$	17.2942	0.963765
$323$	8.42973	0.469043
$324$	−38.2731	−2.12628
$325$	17.8627	0.990843
$326$	−9.08217	−0.503015
$327$	−28.6381	−1.58369
$328$	−23.6295	−1.30472
$329$	−6.86936	−0.378720
$330$	22.0173	1.21201
$331$	29.9893	1.64836	0.824181	−	0.566327i	$-0.191636\pi$
$331$	29.9893	1.64836	0.824181	+	0.566327i	$0.191636\pi$
$332$	−51.4612	−2.82430
$333$	1.83119	0.100349
$334$	5.25858	0.287737
$335$	−42.8293	−2.34001
$336$	62.5546	3.41264
$337$	−20.8656	−1.13662	−0.568310	−	0.822815i	$-0.692403\pi$
$337$	−20.8656	−1.13662	−0.568310	+	0.822815i	$0.692403\pi$
$338$	26.1231	1.42091
$339$	2.33810	0.126988
$340$	153.813	8.34171
$341$	11.8421	0.641284
$342$	−1.68118	−0.0909075
$343$	17.6007	0.950351
$344$	108.526	5.85134
$345$	13.8151	0.743781
$346$	32.1665	1.72928
$347$	−7.10567	−0.381452	−0.190726	−	0.981643i	$-0.561084\pi$
$347$	−7.10567	−0.381452	−0.190726	+	0.981643i	$0.561084\pi$
$348$	48.0804	2.57738
$349$	6.37745	0.341377	0.170689	−	0.985325i	$-0.445401\pi$
$349$	6.37745	0.341377	0.170689	+	0.985325i	$0.445401\pi$
$350$	72.7883	3.89070
$351$	10.2464	0.546911
$352$	27.9780	1.49123
$353$	24.0832	1.28182	0.640909	−	0.767617i	$-0.278557\pi$
$353$	24.0832	1.28182	0.640909	+	0.767617i	$0.278557\pi$
$354$	12.3422	0.655982
$355$	−3.39226	−0.180042
$356$	61.6219	3.26595
$357$	−32.1136	−1.69963
$358$	−20.2357	−1.06949
$359$	17.6342	0.930696	0.465348	−	0.885128i	$-0.345929\pi$
$359$	17.6342	0.930696	0.465348	+	0.885128i	$0.345929\pi$
$360$	−19.3363	−1.01911
$361$	−17.7091	−0.932057
$362$	−42.9149	−2.25556
$363$	14.3976	0.755678
$364$	−27.5666	−1.44488
$365$	−34.9282	−1.82823
$366$	19.8185	1.03593
$367$	−3.54969	−0.185292	−0.0926461	−	0.995699i	$-0.529533\pi$
$367$	−3.54969	−0.185292	−0.0926461	+	0.995699i	$0.529533\pi$
$368$	33.2463	1.73308
$369$	−1.38343	−0.0720187
$370$	−35.1406	−1.82687
$371$	35.8768	1.86263
$372$	74.5629	3.86590
$373$	−7.24762	−0.375267	−0.187634	−	0.982239i	$-0.560082\pi$
$373$	−7.24762	−0.375267	−0.187634	+	0.982239i	$0.560082\pi$
$374$	−27.2008	−1.40652
$375$	28.1182	1.45202
$376$	−23.0932	−1.19094
$377$	−10.4606	−0.538748
$378$	41.7528	2.14753
$379$	−0.234710	−0.0120562	−0.00602812	−	0.999982i	$-0.501919\pi$
$379$	−0.234710	−0.0120562	−0.00602812	+	0.999982i	$0.501919\pi$
$380$	23.5547	1.20833
$381$	−24.1677	−1.23815
$382$	48.0482	2.45836
$383$	6.76758	0.345807	0.172904	−	0.984939i	$-0.444685\pi$
$383$	6.76758	0.345807	0.172904	+	0.984939i	$0.444685\pi$
$384$	52.8393	2.69644
$385$	−14.2514	−0.726319
$386$	70.1357	3.56981
$387$	6.35387	0.322985
$388$	48.2843	2.45126
$389$	15.8599	0.804127	0.402063	−	0.915612i	$-0.368293\pi$
$389$	15.8599	0.804127	0.402063	+	0.915612i	$0.368293\pi$
$390$	−30.1612	−1.52727
$391$	−17.0676	−0.863144
$392$	−5.81873	−0.293890
$393$	−8.54368	−0.430971
$394$	−58.4873	−2.94655
$395$	−13.5869	−0.683631
$396$	3.96069	0.199032
$397$	−14.1813	−0.711738	−0.355869	−	0.934536i	$-0.615815\pi$
$397$	−14.1813	−0.711738	−0.355869	+	0.934536i	$0.615815\pi$
$398$	18.5841	0.931539
$399$	−4.91781	−0.246199
$400$	139.928	6.99641
$401$	25.4278	1.26981	0.634903	−	0.772592i	$-0.281040\pi$
$401$	25.4278	1.26981	0.634903	+	0.772592i	$0.281040\pi$
$402$	47.6896	2.37854
$403$	−16.2223	−0.808088
$404$	46.8270	2.32973
$405$	27.1052	1.34687
$406$	−42.6257	−2.11548
$407$	4.53718	0.224900
$408$	−107.958	−5.34474
$409$	8.67213	0.428809	0.214405	−	0.976745i	$-0.431219\pi$
$409$	8.67213	0.428809	0.214405	+	0.976745i	$0.431219\pi$
$410$	26.5481	1.31112
$411$	25.5423	1.25991
$412$	−86.5425	−4.26364
$413$	−7.98889	−0.393107
$414$	3.40386	0.167290
$415$	36.4450	1.78902
$416$	−38.3266	−1.87912
$417$	−17.0578	−0.835323
$418$	−4.16548	−0.203741
$419$	−5.84109	−0.285356	−0.142678	−	0.989769i	$-0.545571\pi$
$419$	−5.84109	−0.285356	−0.142678	+	0.989769i	$0.545571\pi$
$420$	−89.7331	−4.37853
$421$	2.83670	0.138252	0.0691262	−	0.997608i	$-0.477979\pi$
$421$	2.83670	0.138252	0.0691262	+	0.997608i	$0.477979\pi$
$422$	−21.9350	−1.06778
$423$	−1.35204	−0.0657382
$424$	120.610	5.85732
$425$	−71.8347	−3.48449
$426$	3.77722	0.183007
$427$	−12.8282	−0.620799
$428$	−22.0247	−1.06460
$429$	3.89426	0.188017
$430$	−121.931	−5.88003
$431$	−33.9792	−1.63672	−0.818361	−	0.574704i	$-0.805117\pi$
$431$	−33.9792	−1.63672	−0.818361	+	0.574704i	$0.805117\pi$
$432$	80.2655	3.86177
$433$	38.4181	1.84625	0.923127	−	0.384494i	$-0.125624\pi$
$433$	38.4181	1.84625	0.923127	+	0.384494i	$0.125624\pi$
$434$	−66.1038	−3.17308
$435$	−34.0507	−1.63261
$436$	98.8610	4.73458
$437$	−2.61370	−0.125030
$438$	38.8919	1.85833
$439$	−32.8796	−1.56926	−0.784628	−	0.619967i	$-0.787146\pi$
$439$	−32.8796	−1.56926	−0.784628	+	0.619967i	$0.787146\pi$
$440$	−47.9099	−2.28402
$441$	−0.340669	−0.0162223
$442$	37.2620	1.77237
$443$	31.9862	1.51971	0.759856	−	0.650092i	$-0.225270\pi$
$443$	31.9862	1.51971	0.759856	+	0.650092i	$0.225270\pi$
$444$	28.5681	1.35578
$445$	−43.6409	−2.06878
$446$	−42.1621	−1.99643
$447$	−34.2004	−1.61762
$448$	−76.3521	−3.60730
$449$	15.2864	0.721409	0.360704	−	0.932680i	$-0.382536\pi$
$449$	15.2864	0.721409	0.360704	+	0.932680i	$0.382536\pi$
$450$	14.3263	0.675347
$451$	−3.42776	−0.161407
$452$	−8.07132	−0.379643
$453$	−20.0555	−0.942292
$454$	71.1706	3.34020
$455$	19.5228	0.915241
$456$	−16.5326	−0.774208
$457$	−32.4461	−1.51777	−0.758883	−	0.651227i	$-0.774255\pi$
$457$	−32.4461	−1.51777	−0.758883	+	0.651227i	$0.774255\pi$
$458$	32.3201	1.51022
$459$	−41.2057	−1.92332
$460$	−47.6909	−2.22360
$461$	−21.6724	−1.00938	−0.504692	−	0.863299i	$-0.668394\pi$
$461$	−21.6724	−1.00938	−0.504692	+	0.863299i	$0.668394\pi$
$462$	15.8687	0.738277
$463$	31.1615	1.44820	0.724098	−	0.689697i	$-0.242256\pi$
$463$	31.1615	1.44820	0.724098	+	0.689697i	$0.242256\pi$
$464$	−81.9436	−3.80413
$465$	−52.8058	−2.44881
$466$	−37.3950	−1.73229
$467$	14.1665	0.655546	0.327773	−	0.944757i	$-0.393702\pi$
$467$	14.1665	0.655546	0.327773	+	0.944757i	$0.393702\pi$
$468$	−5.42568	−0.250802
$469$	−30.8686	−1.42538
$470$	25.9456	1.19678
$471$	−8.14626	−0.375360
$472$	−26.8568	−1.23618
$473$	15.7431	0.723869
$474$	15.1287	0.694886
$475$	−11.0006	−0.504744
$476$	110.859	5.08120
$477$	7.06131	0.323315
$478$	32.7504	1.49797
$479$	−7.46796	−0.341220	−0.170610	−	0.985339i	$-0.554574\pi$
$479$	−7.46796	−0.341220	−0.170610	+	0.985339i	$0.554574\pi$
$480$	−124.759	−5.69443
$481$	−6.21541	−0.283398
$482$	−25.2153	−1.14853
$483$	9.95704	0.453061
$484$	−49.7017	−2.25917
$485$	−34.1951	−1.55272
$486$	15.1751	0.688357
$487$	−19.2375	−0.871735	−0.435867	−	0.900011i	$-0.643558\pi$
$487$	−19.2375	−0.871735	−0.435867	+	0.900011i	$0.643558\pi$
$488$	−43.1253	−1.95219
$489$	−5.22902	−0.236465
$490$	6.53744	0.295331
$491$	24.1031	1.08776	0.543878	−	0.839164i	$-0.316955\pi$
$491$	24.1031	1.08776	0.543878	+	0.839164i	$0.316955\pi$
$492$	−21.5827	−0.973023
$493$	42.0672	1.89461
$494$	5.70623	0.256735
$495$	−2.80498	−0.126074
$496$	−127.078	−5.70596
$497$	−2.44492	−0.109670
$498$	−40.5809	−1.81847
$499$	28.8810	1.29289	0.646445	−	0.762961i	$-0.276255\pi$
$499$	28.8810	1.29289	0.646445	+	0.762961i	$0.276255\pi$
$500$	−97.0664	−4.34094
$501$	3.02761	0.135264
$502$	−41.4498	−1.85000
$503$	20.9720	0.935093	0.467547	−	0.883968i	$-0.345138\pi$
$503$	20.9720	0.935093	0.467547	+	0.883968i	$0.345138\pi$
$504$	−13.9363	−0.620774
$505$	−33.1631	−1.47574
$506$	8.43381	0.374929
$507$	15.0403	0.667963
$508$	83.4289	3.70156
$509$	−38.9345	−1.72574	−0.862871	−	0.505424i	$-0.831336\pi$
$509$	−38.9345	−1.72574	−0.862871	+	0.505424i	$0.831336\pi$
$510$	121.293	5.37094
$511$	−25.1740	−1.11363
$512$	−31.8822	−1.40901
$513$	−6.31017	−0.278601
$514$	−31.0898	−1.37131
$515$	61.2898	2.70075
$516$	99.1256	4.36376
$517$	−3.34997	−0.147331
$518$	−25.3271	−1.11281
$519$	18.5197	0.812925
$520$	65.6310	2.87811
$521$	−22.1828	−0.971848	−0.485924	−	0.874001i	$-0.661517\pi$
$521$	−22.1828	−0.971848	−0.485924	+	0.874001i	$0.661517\pi$
$522$	−8.38964	−0.367204
$523$	−13.8066	−0.603721	−0.301861	−	0.953352i	$-0.597608\pi$
$523$	−13.8066	−0.603721	−0.301861	+	0.953352i	$0.597608\pi$
$524$	29.4935	1.28843
$525$	41.9076	1.82900
$526$	−43.8259	−1.91090
$527$	65.2377	2.84180
$528$	30.5059	1.32760
$529$	−17.7081	−0.769916
$530$	−135.507	−5.88604
$531$	−1.57238	−0.0682356
$532$	16.9767	0.736033
$533$	4.69564	0.203391
$534$	48.5933	2.10284
$535$	15.5980	0.674360
$536$	−103.773	−4.48231
$537$	−11.6506	−0.502760
$538$	33.2347	1.43285
$539$	−0.844082	−0.0363572
$540$	−115.139	−4.95479
$541$	−36.7679	−1.58078	−0.790388	−	0.612606i	$-0.790121\pi$
$541$	−36.7679	−1.58078	−0.790388	+	0.612606i	$0.790121\pi$
$542$	−54.4450	−2.33861
$543$	−24.7081	−1.06033
$544$	154.130	6.60829
$545$	−70.0138	−2.99906
$546$	−21.7382	−0.930310
$547$	−1.76270	−0.0753678	−0.0376839	−	0.999290i	$-0.511998\pi$
$547$	−1.76270	−0.0753678	−0.0376839	+	0.999290i	$0.511998\pi$
$548$	−88.1742	−3.76662
$549$	−2.52486	−0.107758
$550$	35.4965	1.51358
$551$	6.44210	0.274443
$552$	33.4733	1.42472
$553$	−9.79255	−0.416422
$554$	43.1633	1.83383
$555$	−20.2321	−0.858803
$556$	58.8849	2.49728
$557$	15.8543	0.671767	0.335883	−	0.941904i	$-0.390965\pi$
$557$	15.8543	0.671767	0.335883	+	0.941904i	$0.390965\pi$
$558$	−13.0106	−0.550784
$559$	−21.5662	−0.912154
$560$	152.932	6.46258
$561$	−15.6608	−0.661198
$562$	−36.2584	−1.52947
$563$	−5.69585	−0.240052	−0.120026	−	0.992771i	$-0.538298\pi$
$563$	−5.69585	−0.240052	−0.120026	+	0.992771i	$0.538298\pi$
$564$	−21.0929	−0.888170
$565$	5.71615	0.240480
$566$	59.5118	2.50147
$567$	19.5357	0.820421
$568$	−8.21926	−0.344873
$569$	−33.3296	−1.39725	−0.698625	−	0.715488i	$-0.746205\pi$
$569$	−33.3296	−1.39725	−0.698625	+	0.715488i	$0.746205\pi$
$570$	18.5746	0.778004
$571$	−24.5711	−1.02827	−0.514135	−	0.857709i	$-0.671887\pi$
$571$	−24.5711	−1.02827	−0.514135	+	0.857709i	$0.671887\pi$
$572$	−13.4433	−0.562094
$573$	27.6636	1.15566
$574$	19.1342	0.798644
$575$	22.2728	0.928842
$576$	−15.0277	−0.626154
$577$	−26.3961	−1.09888	−0.549442	−	0.835532i	$-0.685160\pi$
$577$	−26.3961	−1.09888	−0.549442	+	0.835532i	$0.685160\pi$
$578$	−103.571	−4.30799
$579$	40.3803	1.67815
$580$	117.546	4.88083
$581$	26.2672	1.08975
$582$	38.0756	1.57829
$583$	17.4960	0.724609
$584$	−84.6291	−3.50198
$585$	3.84249	0.158867
$586$	14.1023	0.582559
$587$	−20.9383	−0.864216	−0.432108	−	0.901822i	$-0.642230\pi$
$587$	−20.9383	−0.864216	−0.432108	+	0.901822i	$0.642230\pi$
$588$	−5.31471	−0.219175
$589$	9.99038	0.411647
$590$	30.1740	1.24225
$591$	−33.6738	−1.38515
$592$	−48.6887	−2.00110
$593$	−29.7437	−1.22143	−0.610713	−	0.791852i	$-0.709117\pi$
$593$	−29.7437	−1.22143	−0.610713	+	0.791852i	$0.709117\pi$
$594$	20.3615	0.835442
$595$	−78.5107	−3.21862
$596$	118.063	4.83603
$597$	10.6997	0.437911
$598$	−11.5533	−0.472451
$599$	28.7697	1.17550	0.587749	−	0.809043i	$-0.300014\pi$
$599$	28.7697	1.17550	0.587749	+	0.809043i	$0.300014\pi$
$600$	140.884	5.75155
$601$	−18.1855	−0.741803	−0.370901	−	0.928672i	$-0.620951\pi$
$601$	−18.1855	−0.741803	−0.370901	+	0.928672i	$0.620951\pi$
$602$	−87.8798	−3.58171
$603$	−6.07559	−0.247417
$604$	69.2335	2.81707
$605$	35.1990	1.43104
$606$	36.9265	1.50004
$607$	−24.9839	−1.01407	−0.507033	−	0.861927i	$-0.669258\pi$
$607$	−24.9839	−1.01407	−0.507033	+	0.861927i	$0.669258\pi$
$608$	23.6032	0.957238
$609$	−24.5416	−0.994474
$610$	48.4520	1.96176
$611$	4.58906	0.185654
$612$	21.8194	0.881995
$613$	−3.83046	−0.154711	−0.0773554	−	0.997004i	$-0.524648\pi$
$613$	−3.83046	−0.154711	−0.0773554	+	0.997004i	$0.524648\pi$
$614$	67.5710	2.72694
$615$	15.2850	0.616349
$616$	−34.5304	−1.39127
$617$	25.1218	1.01137	0.505683	−	0.862719i	$-0.331240\pi$
$617$	25.1218	1.01137	0.505683	+	0.862719i	$0.331240\pi$
$618$	−68.2450	−2.74522
$619$	−14.3037	−0.574914	−0.287457	−	0.957794i	$-0.592810\pi$
$619$	−14.3037	−0.574914	−0.287457	+	0.957794i	$0.592810\pi$
$620$	182.290	7.32094
$621$	12.7761	0.512688
$622$	−2.50719	−0.100529
$623$	−31.4535	−1.26016
$624$	−41.7895	−1.67292
$625$	20.3324	0.813296
$626$	−51.1205	−2.04319
$627$	−2.39826	−0.0957773
$628$	28.1216	1.12217
$629$	24.9953	0.996626
$630$	15.6577	0.623818
$631$	−43.1655	−1.71839	−0.859196	−	0.511646i	$-0.829036\pi$
$631$	−43.1655	−1.71839	−0.859196	+	0.511646i	$0.829036\pi$
$632$	−32.9203	−1.30950
$633$	−12.6290	−0.501956
$634$	−36.8342	−1.46287
$635$	−59.0847	−2.34471
$636$	110.162	4.36822
$637$	1.15629	0.0458140
$638$	−20.7872	−0.822973
$639$	−0.481212	−0.0190365
$640$	129.181	5.10631
$641$	−26.6399	−1.05221	−0.526106	−	0.850419i	$-0.676348\pi$
$641$	−26.6399	−1.05221	−0.526106	+	0.850419i	$0.676348\pi$
$642$	−17.3681	−0.685463
$643$	−33.4287	−1.31830	−0.659149	−	0.752013i	$-0.729083\pi$
$643$	−33.4287	−1.31830	−0.659149	+	0.752013i	$0.729083\pi$
$644$	−34.3725	−1.35447
$645$	−70.2012	−2.76417
$646$	−22.9476	−0.902860
$647$	25.6152	1.00704	0.503519	−	0.863984i	$-0.332038\pi$
$647$	25.6152	1.00704	0.503519	+	0.863984i	$0.332038\pi$
$648$	65.6744	2.57993
$649$	−3.89593	−0.152928
$650$	−48.6261	−1.90727
$651$	−38.0590	−1.49165
$652$	18.0510	0.706933
$653$	1.48632	0.0581641	0.0290821	−	0.999577i	$-0.490742\pi$
$653$	1.48632	0.0581641	0.0290821	+	0.999577i	$0.490742\pi$
$654$	77.9591	3.04844
$655$	−20.8874	−0.816139
$656$	36.7835	1.43615
$657$	−4.95477	−0.193304
$658$	18.6999	0.728998
$659$	15.6129	0.608191	0.304096	−	0.952642i	$-0.401646\pi$
$659$	15.6129	0.608191	0.304096	+	0.952642i	$0.401646\pi$
$660$	−43.7600	−1.70335
$661$	−13.9619	−0.543055	−0.271528	−	0.962431i	$-0.587529\pi$
$661$	−13.9619	−0.543055	−0.271528	+	0.962431i	$0.587529\pi$
$662$	−81.6374	−3.17293
$663$	21.4534	0.833182
$664$	88.3043	3.42687
$665$	−12.0230	−0.466231
$666$	−4.98490	−0.193161
$667$	−13.0432	−0.505036
$668$	−10.4516	−0.404383
$669$	−24.2746	−0.938511
$670$	116.591	4.50429
$671$	−6.25589	−0.241506
$672$	−89.9180	−3.46866
$673$	−6.10338	−0.235268	−0.117634	−	0.993057i	$-0.537531\pi$
$673$	−6.10338	−0.235268	−0.117634	+	0.993057i	$0.537531\pi$
$674$	56.8006	2.18788
$675$	53.7727	2.06971
$676$	−51.9204	−1.99694
$677$	−36.8242	−1.41527	−0.707635	−	0.706578i	$-0.750238\pi$
$677$	−36.8242	−1.41527	−0.707635	+	0.706578i	$0.750238\pi$
$678$	−6.36482	−0.244440
$679$	−24.6456	−0.945813
$680$	−263.935	−10.1214
$681$	40.9762	1.57021
$682$	−32.2367	−1.23441
$683$	4.13152	0.158088	0.0790441	−	0.996871i	$-0.474813\pi$
$683$	4.13152	0.158088	0.0790441	+	0.996871i	$0.474813\pi$
$684$	3.34138	0.127761
$685$	62.4454	2.38591
$686$	−47.9131	−1.82933
$687$	18.6082	0.709947
$688$	−168.940	−6.44078
$689$	−23.9674	−0.913087
$690$	−37.6077	−1.43170
$691$	−23.0962	−0.878619	−0.439310	−	0.898336i	$-0.644777\pi$
$691$	−23.0962	−0.878619	−0.439310	+	0.898336i	$0.644777\pi$
$692$	−63.9316	−2.43032
$693$	−2.02165	−0.0767960
$694$	19.3432	0.734257
$695$	−41.7026	−1.58187
$696$	−82.5031	−3.12727
$697$	−18.8835	−0.715263
$698$	−17.3608	−0.657116
$699$	−21.5300	−0.814339
$700$	−144.668	−5.46795
$701$	−10.0017	−0.377760	−0.188880	−	0.982000i	$-0.560486\pi$
$701$	−10.0017	−0.377760	−0.188880	+	0.982000i	$0.560486\pi$
$702$	−27.8929	−1.05275
$703$	3.82773	0.144365
$704$	−37.2345	−1.40333
$705$	14.9381	0.562600
$706$	−65.5597	−2.46737
$707$	−23.9018	−0.898921
$708$	−24.5305	−0.921911
$709$	−6.53103	−0.245278	−0.122639	−	0.992451i	$-0.539136\pi$
$709$	−6.53103	−0.245278	−0.122639	+	0.992451i	$0.539136\pi$
$710$	9.23447	0.346564
$711$	−1.92738	−0.0722825
$712$	−105.740	−3.96276
$713$	−20.2274	−0.757523
$714$	87.4201	3.27162
$715$	9.52063	0.356051
$716$	40.2189	1.50305
$717$	18.8559	0.704187
$718$	−48.0041	−1.79150
$719$	11.4017	0.425213	0.212606	−	0.977138i	$-0.431805\pi$
$719$	11.4017	0.425213	0.212606	+	0.977138i	$0.431805\pi$
$720$	30.1004	1.12177
$721$	44.1737	1.64511
$722$	48.2080	1.79412
$723$	−14.5176	−0.539916
$724$	85.2944	3.16994
$725$	−54.8969	−2.03882
$726$	−39.1934	−1.45460
$727$	4.03855	0.149781	0.0748907	−	0.997192i	$-0.476139\pi$
$727$	4.03855	0.149781	0.0748907	+	0.997192i	$0.476139\pi$
$728$	47.3026	1.75315
$729$	29.9587	1.10958
$730$	95.0822	3.51915
$731$	86.7285	3.20777
$732$	−39.3898	−1.45589
$733$	43.7803	1.61706	0.808532	−	0.588453i	$-0.200263\pi$
$733$	43.7803	1.61706	0.808532	+	0.588453i	$0.200263\pi$
$734$	9.66303	0.356669
$735$	3.76390	0.138834
$736$	−47.7892	−1.76153
$737$	−15.0536	−0.554507
$738$	3.76601	0.138629
$739$	19.5976	0.720908	0.360454	−	0.932777i	$-0.382622\pi$
$739$	19.5976	0.720908	0.360454	+	0.932777i	$0.382622\pi$
$740$	69.8428	2.56747
$741$	3.28534	0.120690
$742$	−97.6645	−3.58538
$743$	18.2812	0.670672	0.335336	−	0.942099i	$-0.391150\pi$
$743$	18.2812	0.670672	0.335336	+	0.942099i	$0.391150\pi$
$744$	−127.945	−4.69071
$745$	−83.6125	−3.06332
$746$	19.7296	0.722352
$747$	5.16995	0.189158
$748$	54.0623	1.97671
$749$	11.2420	0.410774
$750$	−76.5438	−2.79499
$751$	−11.8234	−0.431441	−0.215720	−	0.976455i	$-0.569210\pi$
$751$	−11.8234	−0.431441	−0.215720	+	0.976455i	$0.569210\pi$
$752$	35.9487	1.31091
$753$	−23.8646	−0.869673
$754$	28.4760	1.03704
$755$	−49.0314	−1.78444
$756$	−82.9846	−3.01812
$757$	17.9511	0.652442	0.326221	−	0.945294i	$-0.394225\pi$
$757$	17.9511	0.652442	0.326221	+	0.945294i	$0.394225\pi$
$758$	0.638931	0.0232070
$759$	4.85573	0.176252
$760$	−40.4185	−1.46613
$761$	−15.3822	−0.557604	−0.278802	−	0.960349i	$-0.589937\pi$
$761$	−15.3822	−0.557604	−0.278802	+	0.960349i	$0.589937\pi$
$762$	65.7897	2.38331
$763$	−50.4614	−1.82683
$764$	−95.4969	−3.45496
$765$	−15.4526	−0.558689
$766$	−18.4228	−0.665644
$767$	5.33696	0.192707
$768$	−57.1768	−2.06319
$769$	−27.3836	−0.987479	−0.493740	−	0.869610i	$-0.664370\pi$
$769$	−27.3836	−0.987479	−0.493740	+	0.869610i	$0.664370\pi$
$770$	38.7954	1.39809
$771$	−17.8998	−0.644646
$772$	−139.396	−5.01699
$773$	9.35924	0.336628	0.168314	−	0.985733i	$-0.446168\pi$
$773$	9.35924	0.336628	0.168314	+	0.985733i	$0.446168\pi$
$774$	−17.2966	−0.621714
$775$	−85.1339	−3.05810
$776$	−82.8530	−2.97425
$777$	−14.5820	−0.523125
$778$	−43.1740	−1.54786
$779$	−2.89178	−0.103609
$780$	59.9460	2.14641
$781$	−1.19231	−0.0426642
$782$	46.4617	1.66147
$783$	−31.4899	−1.12536
$784$	9.05788	0.323496
$785$	−19.9158	−0.710826
$786$	23.2578	0.829577
$787$	−28.4171	−1.01296	−0.506481	−	0.862251i	$-0.669054\pi$
$787$	−28.4171	−1.01296	−0.506481	+	0.862251i	$0.669054\pi$
$788$	116.245	4.14105
$789$	−25.2326	−0.898304
$790$	36.9865	1.31592
$791$	4.11983	0.146484
$792$	−6.79631	−0.241496
$793$	8.56984	0.304324
$794$	38.6045	1.37002
$795$	−78.0175	−2.76699
$796$	−36.9364	−1.30918
$797$	−4.18532	−0.148252	−0.0741258	−	0.997249i	$-0.523617\pi$
$797$	−4.18532	−0.148252	−0.0741258	+	0.997249i	$0.523617\pi$
$798$	13.3874	0.473907
$799$	−18.4549	−0.652887
$800$	−201.137	−7.11127
$801$	−6.19072	−0.218738
$802$	−69.2201	−2.44425
$803$	−12.2765	−0.433230
$804$	−94.7842	−3.34278
$805$	24.3428	0.857970
$806$	44.1605	1.55549
$807$	19.1348	0.673576
$808$	−80.3524	−2.82679
$809$	−52.4872	−1.84535	−0.922676	−	0.385577i	$-0.874003\pi$
$809$	−52.4872	−1.84535	−0.922676	+	0.385577i	$0.874003\pi$
$810$	−73.7862	−2.59258
$811$	20.7486	0.728582	0.364291	−	0.931285i	$-0.381311\pi$
$811$	20.7486	0.728582	0.364291	+	0.931285i	$0.381311\pi$
$812$	84.7195	2.97307
$813$	−31.3465	−1.09937
$814$	−12.3512	−0.432910
$815$	−12.7838	−0.447798
$816$	168.056	5.88315
$817$	13.2814	0.464659
$818$	−23.6074	−0.825415
$819$	2.76942	0.0967713
$820$	−52.7650	−1.84263
$821$	2.76641	0.0965483	0.0482742	−	0.998834i	$-0.484628\pi$
$821$	2.76641	0.0965483	0.0482742	+	0.998834i	$0.484628\pi$
$822$	−69.5317	−2.42520
$823$	−4.04656	−0.141054	−0.0705271	−	0.997510i	$-0.522468\pi$
$823$	−4.04656	−0.141054	−0.0705271	+	0.997510i	$0.522468\pi$
$824$	148.502	5.17330
$825$	20.4370	0.711524
$826$	21.7475	0.756692
$827$	39.7389	1.38186	0.690928	−	0.722923i	$-0.257202\pi$
$827$	39.7389	1.38186	0.690928	+	0.722923i	$0.257202\pi$
$828$	−6.76524	−0.235108
$829$	31.9495	1.10965	0.554826	−	0.831967i	$-0.312785\pi$
$829$	31.9495	1.10965	0.554826	+	0.831967i	$0.312785\pi$
$830$	−99.2113	−3.44368
$831$	24.8511	0.862075
$832$	51.0069	1.76835
$833$	−4.65003	−0.161114
$834$	46.4350	1.60791
$835$	7.40184	0.256151
$836$	8.27900	0.286335
$837$	−48.8344	−1.68797
$838$	15.9007	0.549281
$839$	−18.0249	−0.622289	−0.311145	−	0.950363i	$-0.600712\pi$
$839$	−18.0249	−0.622289	−0.311145	+	0.950363i	$0.600712\pi$
$840$	153.977	5.31270
$841$	3.14826	0.108561
$842$	−7.72213	−0.266122
$843$	−20.8756	−0.718995
$844$	43.5963	1.50065
$845$	36.7702	1.26493
$846$	3.68054	0.126539
$847$	25.3691	0.871694
$848$	−187.750	−6.44737
$849$	34.2637	1.17593
$850$	195.550	6.70730
$851$	−7.74995	−0.265665
$852$	−7.50731	−0.257196
$853$	23.9776	0.820978	0.410489	−	0.911866i	$-0.365358\pi$
$853$	23.9776	0.820978	0.410489	+	0.911866i	$0.365358\pi$
$854$	34.9211	1.19497
$855$	−2.36638	−0.0809284
$856$	37.7931	1.29174
$857$	5.58134	0.190655	0.0953275	−	0.995446i	$-0.469610\pi$
$857$	5.58134	0.190655	0.0953275	+	0.995446i	$0.469610\pi$
$858$	−10.6010	−0.361913
$859$	−21.4179	−0.730768	−0.365384	−	0.930857i	$-0.619062\pi$
$859$	−21.4179	−0.730768	−0.365384	+	0.930857i	$0.619062\pi$
$860$	242.340	8.26374
$861$	11.0164	0.375438
$862$	92.4989	3.15053
$863$	−31.6797	−1.07839	−0.539195	−	0.842181i	$-0.681271\pi$
$863$	−31.6797	−1.07839	−0.539195	+	0.842181i	$0.681271\pi$
$864$	−115.376	−3.92517
$865$	45.2767	1.53945
$866$	−104.582	−3.55385
$867$	−59.6306	−2.02516
$868$	131.383	4.45942
$869$	−4.77552	−0.161998
$870$	92.6935	3.14260
$871$	20.6217	0.698740
$872$	−169.640	−5.74472
$873$	−4.85078	−0.164174
$874$	7.11505	0.240670
$875$	49.5454	1.67494
$876$	−77.2985	−2.61168
$877$	53.3967	1.80308	0.901540	−	0.432697i	$-0.142438\pi$
$877$	53.3967	1.80308	0.901540	+	0.432697i	$0.142438\pi$
$878$	89.5054	3.02066
$879$	8.11932	0.273858
$880$	74.5803	2.51410
$881$	50.9443	1.71636	0.858179	−	0.513351i	$-0.171596\pi$
$881$	50.9443	1.71636	0.858179	+	0.513351i	$0.171596\pi$
$882$	0.927374	0.0312263
$883$	41.7475	1.40492	0.702458	−	0.711725i	$-0.252086\pi$
$883$	41.7475	1.40492	0.702458	+	0.711725i	$0.252086\pi$
$884$	−74.0590	−2.49087
$885$	17.3726	0.583973
$886$	−87.0735	−2.92529
$887$	−3.12403	−0.104895	−0.0524473	−	0.998624i	$-0.516702\pi$
$887$	−3.12403	−0.104895	−0.0524473	+	0.998624i	$0.516702\pi$
$888$	−49.0212	−1.64504
$889$	−42.5844	−1.42824
$890$	118.800	3.98219
$891$	9.52692	0.319164
$892$	83.7981	2.80577
$893$	−2.82615	−0.0945735
$894$	93.1009	3.11376
$895$	−28.4832	−0.952088
$896$	93.1049	3.11042
$897$	−6.65178	−0.222097
$898$	−41.6129	−1.38864
$899$	49.8554	1.66277
$900$	−28.4738	−0.949127
$901$	96.3850	3.21105
$902$	9.33112	0.310692
$903$	−50.5964	−1.68374
$904$	13.8499	0.460641
$905$	−60.4059	−2.00796
$906$	54.5956	1.81382
$907$	−8.91443	−0.295999	−0.147999	−	0.988987i	$-0.547283\pi$
$907$	−8.91443	−0.295999	−0.147999	+	0.988987i	$0.547283\pi$
$908$	−141.453	−4.69429
$909$	−4.70439	−0.156035
$910$	−53.1452	−1.76175
$911$	17.1485	0.568155	0.284077	−	0.958801i	$-0.408313\pi$
$911$	17.1485	0.568155	0.284077	+	0.958801i	$0.408313\pi$
$912$	25.7358	0.852199
$913$	12.8097	0.423939
$914$	88.3255	2.92155
$915$	27.8960	0.922215
$916$	−64.2371	−2.12245
$917$	−15.0543	−0.497137
$918$	112.171	3.70220
$919$	23.8833	0.787838	0.393919	−	0.919145i	$-0.371119\pi$
$919$	23.8833	0.787838	0.393919	+	0.919145i	$0.371119\pi$
$920$	81.8348	2.69801
$921$	38.9037	1.28192
$922$	58.9970	1.94296
$923$	1.63333	0.0537616
$924$	−31.5393	−1.03757
$925$	−32.6183	−1.07248
$926$	−84.8283	−2.78763
$927$	8.69432	0.285559
$928$	117.788	3.86659
$929$	−14.1385	−0.463870	−0.231935	−	0.972731i	$-0.574506\pi$
$929$	−14.1385	−0.463870	−0.231935	+	0.972731i	$0.574506\pi$
$930$	143.749	4.71371
$931$	−0.712097	−0.0233380
$932$	74.3234	2.43454
$933$	−1.44350	−0.0472582
$934$	−38.5642	−1.26186
$935$	−38.2872	−1.25212
$936$	9.31015	0.304312
$937$	23.6009	0.771008	0.385504	−	0.922706i	$-0.374028\pi$
$937$	23.6009	0.771008	0.385504	+	0.922706i	$0.374028\pi$
$938$	84.0310	2.74371
$939$	−29.4324	−0.960490
$940$	−51.5675	−1.68194
$941$	−3.48456	−0.113593	−0.0567967	−	0.998386i	$-0.518089\pi$
$941$	−3.48456	−0.113593	−0.0567967	+	0.998386i	$0.518089\pi$
$942$	22.1759	0.722530
$943$	5.85495	0.190664
$944$	41.8074	1.36071
$945$	58.7701	1.91179
$946$	−42.8562	−1.39338
$947$	−19.2942	−0.626978	−0.313489	−	0.949592i	$-0.601498\pi$
$947$	−19.2942	−0.626978	−0.313489	+	0.949592i	$0.601498\pi$
$948$	−30.0687	−0.976587
$949$	16.8174	0.545917
$950$	29.9461	0.971580
$951$	−21.2071	−0.687689
$952$	−190.227	−6.16530
$953$	−9.04841	−0.293107	−0.146553	−	0.989203i	$-0.546818\pi$
$953$	−9.04841	−0.293107	−0.146553	+	0.989203i	$0.546818\pi$
$954$	−19.2224	−0.622349
$955$	67.6314	2.18850
$956$	−65.0922	−2.10523
$957$	−11.9681	−0.386875
$958$	20.3294	0.656814
$959$	45.0066	1.45334
$960$	166.035	5.35875
$961$	46.3156	1.49405
$962$	16.9197	0.545513
$963$	2.21267	0.0713022
$964$	50.1161	1.61413
$965$	98.7211	3.17795
$966$	−27.1052	−0.872096
$967$	12.4992	0.401947	0.200973	−	0.979597i	$-0.435590\pi$
$967$	12.4992	0.401947	0.200973	+	0.979597i	$0.435590\pi$
$968$	85.2852	2.74117
$969$	−13.2120	−0.424429
$970$	93.0866	2.98883
$971$	−4.56621	−0.146537	−0.0732683	−	0.997312i	$-0.523343\pi$
$971$	−4.56621	−0.146537	−0.0732683	+	0.997312i	$0.523343\pi$
$972$	−30.1609	−0.967411
$973$	−30.0565	−0.963567
$974$	52.3687	1.67800
$975$	−27.9963	−0.896599
$976$	67.1322	2.14885
$977$	−44.9822	−1.43911	−0.719554	−	0.694437i	$-0.755654\pi$
$977$	−44.9822	−1.43911	−0.719554	+	0.694437i	$0.755654\pi$
$978$	14.2345	0.455171
$979$	−15.3389	−0.490233
$980$	−12.9933	−0.415056
$981$	−9.93188	−0.317100
$982$	−65.6139	−2.09382
$983$	53.0939	1.69343	0.846716	−	0.532045i	$-0.178576\pi$
$983$	53.0939	1.69343	0.846716	+	0.532045i	$0.178576\pi$
$984$	37.0346	1.18062
$985$	−82.3251	−2.62310
$986$	−114.516	−3.64694
$987$	10.7664	0.342698
$988$	−11.3413	−0.360814
$989$	−26.8908	−0.855077
$990$	7.63576	0.242680
$991$	49.9303	1.58609	0.793044	−	0.609165i	$-0.208495\pi$
$991$	49.9303	1.58609	0.793044	+	0.609165i	$0.208495\pi$
$992$	182.666	5.79964
$993$	−47.0024	−1.49158
$994$	6.65561	0.211103
$995$	26.1585	0.829282
$996$	80.6554	2.55566
$997$	−54.2281	−1.71742	−0.858711	−	0.512461i	$-0.828734\pi$
$997$	−54.2281	−1.71742	−0.858711	+	0.512461i	$0.828734\pi$
$998$	−78.6203	−2.48868
$999$	−18.7105	−0.591973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.b.1.7	✓	237

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.b.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.72222 q^{2} -1.56731 q^{3} +5.41047 q^{4} -3.83172 q^{5} +4.26655 q^{6} -2.76166 q^{7} -9.28405 q^{8} -0.543552 q^{9} +O(q^{10})\)	\(q-2.72222 q^{2} -1.56731 q^{3} +5.41047 q^{4} -3.83172 q^{5} +4.26655 q^{6} -2.76166 q^{7} -9.28405 q^{8} -0.543552 q^{9} +10.4308 q^{10} -1.34677 q^{11} -8.47987 q^{12} +1.84492 q^{13} +7.51783 q^{14} +6.00548 q^{15} +14.4523 q^{16} -7.41934 q^{17} +1.47967 q^{18} -1.13618 q^{19} -20.7314 q^{20} +4.32836 q^{21} +3.66621 q^{22} +2.30042 q^{23} +14.5510 q^{24} +9.68209 q^{25} -5.02228 q^{26} +5.55383 q^{27} -14.9419 q^{28} -5.66994 q^{29} -16.3482 q^{30} -8.79293 q^{31} -20.7741 q^{32} +2.11080 q^{33} +20.1971 q^{34} +10.5819 q^{35} -2.94088 q^{36} -3.36893 q^{37} +3.09294 q^{38} -2.89155 q^{39} +35.5739 q^{40} +2.54517 q^{41} -11.7827 q^{42} -11.6895 q^{43} -7.28667 q^{44} +2.08274 q^{45} -6.26224 q^{46} +2.48741 q^{47} -22.6511 q^{48} +0.626745 q^{49} -26.3568 q^{50} +11.6284 q^{51} +9.98189 q^{52} -12.9910 q^{53} -15.1187 q^{54} +5.16045 q^{55} +25.6394 q^{56} +1.78075 q^{57} +15.4348 q^{58} +2.89279 q^{59} +32.4925 q^{60} +4.64510 q^{61} +23.9363 q^{62} +1.50110 q^{63} +27.6472 q^{64} -7.06922 q^{65} -5.74607 q^{66} +11.1776 q^{67} -40.1421 q^{68} -3.60546 q^{69} -28.8062 q^{70} +0.885310 q^{71} +5.04637 q^{72} +9.11554 q^{73} +9.17097 q^{74} -15.1748 q^{75} -6.14729 q^{76} +3.71932 q^{77} +7.87144 q^{78} +3.54590 q^{79} -55.3771 q^{80} -7.07389 q^{81} -6.92851 q^{82} -9.51140 q^{83} +23.4185 q^{84} +28.4288 q^{85} +31.8214 q^{86} +8.88654 q^{87} +12.5035 q^{88} +11.3894 q^{89} -5.66968 q^{90} -5.09504 q^{91} +12.4463 q^{92} +13.7812 q^{93} -6.77126 q^{94} +4.35354 q^{95} +32.5594 q^{96} +8.92422 q^{97} -1.70614 q^{98} +0.732041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) \) 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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